Source code for pysisyphus.wavefunction.ints.int3c2e3d_sph

"""
Molecular integrals over Gaussian basis functions generated by sympleints.
See https://github.com/eljost/sympleints for more information.

sympleints version: 0.1.dev79+g63f1ef8.d20230515
symppy version: 1.10.1

sympleints was executed with the following arguments:
	lmax = 3
	lauxmax = 4
	write = False
	out_dir = devel_ints
	keys = ['2c2e', '3c2e_sph']
	sph = False
	opt_basic = True
	normalize = cgto
"""

import numpy
from pysisyphus.wavefunction.ints.boys import boys


[docs] def int3c2e3d_sph_000(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ss|s) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 1, 1), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = cx + x0 # 1 item(s) result[0, 0, 0] = numpy.sum( 34.98683665524972 * da * db * dc * x1 * x2 ** (-0.5) * boys( 0, cx * x0 * ( (-x1 * (ax * A[0] + bx * B[0]) + C[0]) ** 2 + (-x1 * (ax * A[1] + bx * B[1]) + C[1]) ** 2 + (-x1 * (ax * A[2] + bx * B[2]) + C[2]) ** 2 ) / x2, ) * numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) / cx ) return result
[docs] def int3c2e3d_sph_001(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ss|p) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 1, 3), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) + C[0] x3 = cx + x0 x4 = -x1 * (ax * A[1] + bx * B[1]) + C[1] x5 = -x1 * (ax * A[2] + bx * B[2]) + C[2] x6 = ( 34.98683665524972 * da * db * dc * x3 ** (-1.5) * boys(1, cx * x0 * (x2**2 + x4**2 + x5**2) / x3) * numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) / cx ) # 3 item(s) result[0, 0, 0] = numpy.sum(-x2 * x6) result[0, 0, 1] = numpy.sum(-x4 * x6) result[0, 0, 2] = numpy.sum(-x5 * x6) return result
[docs] def int3c2e3d_sph_002(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ss|d) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 1, 6), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) + C[0] x3 = x2**2 x4 = cx + x0 x5 = -x1 * (ax * A[1] + bx * B[1]) + C[1] x6 = x5**2 x7 = -x1 * (ax * A[2] + bx * B[2]) + C[2] x8 = x7**2 x9 = ( 17.49341832762486 * da * db * dc * x0 * x4 ** (-2.5) * boys(2, cx * x0 * (x3 + x6 + x8) / x4) * numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) / cx ) x10 = 1.154700538379252 * x9 x11 = 2.0 * x2 * x9 # 6 item(s) result[0, 0, 0] = numpy.sum(x10 * x3) result[0, 0, 1] = numpy.sum(x11 * x5) result[0, 0, 2] = numpy.sum(x11 * x7) result[0, 0, 3] = numpy.sum(x10 * x6) result[0, 0, 4] = numpy.sum(2.0 * x5 * x7 * x9) result[0, 0, 5] = numpy.sum(x10 * x8) return result
[docs] def int3c2e3d_sph_003(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ss|f) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 1, 10), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = x1 * (ax * A[0] + bx * B[0]) - C[0] x3 = cx + x0 x4 = x2**2 x5 = x1 * (ax * A[1] + bx * B[1]) - C[1] x6 = x5**2 x7 = x1 * (ax * A[2] + bx * B[2]) - C[2] x8 = x7**2 x9 = ( 17.49341832762486 * da * db * dc * x0**2 * x3 ** (-3.5) * boys(3, cx * x0 * (x4 + x6 + x8) / x3) * numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) / cx ) x10 = 0.5163977794943223 * x9 x11 = x5 * x9 x12 = 1.154700538379252 x13 = x12 * x4 x14 = x7 * x9 x15 = x12 * x6 x16 = x2 * x9 x17 = x12 * x8 # 10 item(s) result[0, 0, 0] = numpy.sum(x10 * x2**3) result[0, 0, 1] = numpy.sum(x11 * x13) result[0, 0, 2] = numpy.sum(x13 * x14) result[0, 0, 3] = numpy.sum(x15 * x16) result[0, 0, 4] = numpy.sum(2.0 * x11 * x2 * x7) result[0, 0, 5] = numpy.sum(x16 * x17) result[0, 0, 6] = numpy.sum(x10 * x5**3) result[0, 0, 7] = numpy.sum(x14 * x15) result[0, 0, 8] = numpy.sum(x11 * x17) result[0, 0, 9] = numpy.sum(x10 * x7**3) return result
[docs] def int3c2e3d_sph_004(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ss|g) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 1, 15), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = x1 * (ax * A[0] + bx * B[0]) - C[0] x3 = cx + x0 x4 = x2**2 x5 = x1 * (ax * A[1] + bx * B[1]) - C[1] x6 = x5**2 x7 = x1 * (ax * A[2] + bx * B[2]) - C[2] x8 = x7**2 x9 = ( 17.49341832762486 * da * db * dc * x0**3 * x3 ** (-4.5) * boys(4, cx * x0 * (x4 + x6 + x8) / x3) * numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) / cx ) x10 = 0.1951800145897066 * x9 x11 = 0.5163977794943223 * x9 x12 = x11 * x2**3 x13 = 0.6666666666666667 * x9 x14 = x13 * x4 x15 = 1.732050807568877 x16 = x15 * x7 x17 = x5**3 x18 = x11 * x2 x19 = x13 * x6 x20 = x7**3 # 15 item(s) result[0, 0, 0] = numpy.sum(x10 * x2**4) result[0, 0, 1] = numpy.sum(x12 * x5) result[0, 0, 2] = numpy.sum(x12 * x7) result[0, 0, 3] = numpy.sum(x14 * x6) result[0, 0, 4] = numpy.sum(x14 * x16 * x5) result[0, 0, 5] = numpy.sum(x14 * x8) result[0, 0, 6] = numpy.sum(x17 * x18) result[0, 0, 7] = numpy.sum(x16 * x19 * x2) result[0, 0, 8] = numpy.sum(x13 * x15 * x2 * x5 * x8) result[0, 0, 9] = numpy.sum(x18 * x20) result[0, 0, 10] = numpy.sum(x10 * x5**4) result[0, 0, 11] = numpy.sum(x11 * x17 * x7) result[0, 0, 12] = numpy.sum(x19 * x8) result[0, 0, 13] = numpy.sum(x11 * x20 * x5) result[0, 0, 14] = numpy.sum(x10 * x7**4) return result
[docs] def int3c2e3d_sph_010(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sp|s) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 3, 1), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = cx + x1 x3 = x2 ** (-1.0) x4 = x1 ** (-1.0) x5 = -x4 * (ax * A[0] + bx * B[0]) x6 = x5 + C[0] x7 = -x4 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x4 * (ax * A[2] + bx * B[2]) x10 = x9 + C[2] x11 = cx * x1 * x3 * (x10**2 + x6**2 + x8**2) x12 = boys(0, x11) / cx x13 = x3 * boys(1, x11) x14 = A[1] - B[1] x15 = A[2] - B[2] x16 = ( 34.98683665524972 * da * db * dc * x2 ** (-0.5) * x4 * numpy.exp(-ax * bx * x4 * (x0**2 + x14**2 + x15**2)) ) # 3 item(s) result[0, 0, 0] = numpy.sum(x16 * (x0 * x12 - x12 * (x5 + A[0]) + x13 * x6)) result[0, 1, 0] = numpy.sum(x16 * (x12 * x14 - x12 * (x7 + A[1]) + x13 * x8)) result[0, 2, 0] = numpy.sum(x16 * (x10 * x13 + x12 * x15 - x12 * (x9 + A[2]))) return result
[docs] def int3c2e3d_sph_011(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sp|p) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 3, 3), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = x2 + C[0] x4 = cx + x0 x5 = x4 ** (-1.0) x6 = -x1 * (ax * A[1] + bx * B[1]) x7 = x6 + C[1] x8 = -x1 * (ax * A[2] + bx * B[2]) x9 = x8 + C[2] x10 = cx * x0 * x5 * (x3**2 + x7**2 + x9**2) x11 = x5 * boys(2, x10) x12 = cx ** (-1.0) x13 = boys(1, x10) x14 = x11 * x3 - x12 * x13 * (x2 + A[0]) x15 = 2.0 * x3 x16 = x12 * x13 x17 = x1 * x16 x18 = A[0] - B[0] x19 = x16 * x18 x20 = A[1] - B[1] x21 = A[2] - B[2] x22 = ( 17.49341832762486 * da * db * dc * x4 ** (-1.5) * numpy.exp(-ax * bx * x1 * (x18**2 + x20**2 + x21**2)) ) x23 = 2.0 * x7 x24 = -x22 * (x14 + x19) x25 = 2.0 * x9 x26 = x16 * x20 x27 = x11 * x7 - x12 * x13 * (x6 + A[1]) x28 = -x22 * (x26 + x27) x29 = x16 * x21 x30 = x11 * x9 - x12 * x13 * (x8 + A[2]) x31 = -x22 * (x29 + x30) # 9 item(s) result[0, 0, 0] = numpy.sum(x22 * (-x14 * x15 - x15 * x19 + x17)) result[0, 0, 1] = numpy.sum(x23 * x24) result[0, 0, 2] = numpy.sum(x24 * x25) result[0, 1, 0] = numpy.sum(x15 * x28) result[0, 1, 1] = numpy.sum(x22 * (x17 - x23 * x26 - x23 * x27)) result[0, 1, 2] = numpy.sum(x25 * x28) result[0, 2, 0] = numpy.sum(x15 * x31) result[0, 2, 1] = numpy.sum(x23 * x31) result[0, 2, 2] = numpy.sum(x22 * (x17 - x25 * x29 - x25 * x30)) return result
[docs] def int3c2e3d_sph_012(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sp|d) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 3, 6), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = x2 + C[0] x4 = -x3 x5 = cx + x0 x6 = x5 ** (-1.0) x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x8 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = x10 + C[2] x12 = -x11 x13 = cx * x0 * x6 x14 = x13 * (x12**2 + x4**2 + x9**2) x15 = boys(3, x14) x16 = x15 * x6 x17 = cx ** (-1.0) x18 = x17 * boys(2, x14) x19 = -x18 * (x2 + A[0]) x20 = x3 * (x16 * x4 - x19) x21 = x3**2 x22 = x8**2 x23 = x11**2 x24 = boys(2, x13 * (x21 + x22 + x23)) x25 = x17 * x24 x26 = x1 * x25 x27 = A[0] - B[0] x28 = A[1] - B[1] x29 = A[2] - B[2] x30 = ( 17.49341832762486 * da * db * dc * x0 * x5 ** (-2.5) * numpy.exp(-ax * bx * x1 * (x27**2 + x28**2 + x29**2)) ) x31 = x3 * x30 x32 = 1.154700538379252 x33 = x30 * (2.0 * x17 * x24 * x27 * x3 - 2.0 * x20 - x26) x34 = x15 * x4 * x6 - x19 - x25 * x27 x35 = x30 * x32 x36 = x34 * x35 x37 = x11 * x30 x38 = 2.0 * x8 x39 = x25 * x28 x40 = -x18 * (x7 + A[1]) x41 = x15 * x6 * x9 - x39 - x40 x42 = x35 * x41 x43 = x8 * (x16 * x9 - x40) x44 = x26 - 2.0 * x39 * x8 + 2.0 * x43 x45 = x30 * x8 x46 = x25 * x29 x47 = -x18 * (x10 + A[2]) x48 = x12 * x15 * x6 - x46 - x47 x49 = x35 * x48 x50 = x11 * (x12 * x16 - x47) x51 = -2.0 * x11 * x46 + x26 + 2.0 * x50 # 18 item(s) result[0, 0, 0] = numpy.sum(x31 * x32 * (x17 * x24 * x27 * x3 - x20 - x26)) result[0, 0, 1] = numpy.sum(x33 * x8) result[0, 0, 2] = numpy.sum(x11 * x33) result[0, 0, 3] = numpy.sum(-x22 * x36) result[0, 0, 4] = numpy.sum(-x34 * x37 * x38) result[0, 0, 5] = numpy.sum(-x23 * x36) result[0, 1, 0] = numpy.sum(-x21 * x42) result[0, 1, 1] = numpy.sum(-x31 * x44) result[0, 1, 2] = numpy.sum(-2.0 * x11 * x31 * x41) result[0, 1, 3] = numpy.sum(x32 * x45 * (x17 * x24 * x28 * x8 - x26 - x43)) result[0, 1, 4] = numpy.sum(-x37 * x44) result[0, 1, 5] = numpy.sum(-x23 * x42) result[0, 2, 0] = numpy.sum(-x21 * x49) result[0, 2, 1] = numpy.sum(-x31 * x38 * x48) result[0, 2, 2] = numpy.sum(-x31 * x51) result[0, 2, 3] = numpy.sum(-x22 * x49) result[0, 2, 4] = numpy.sum(-x45 * x51) result[0, 2, 5] = numpy.sum(x32 * x37 * (x11 * x17 * x24 * x29 - x26 - x50)) return result
[docs] def int3c2e3d_sph_013(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sp|f) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 3, 10), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - C[0] x4 = cx + x0 x5 = x4 ** (-1.5) x6 = x3 * x5 x7 = x3**2 x8 = -x1 * (ax * A[1] + bx * B[1]) x9 = -x8 - C[1] x10 = x9**2 x11 = -x1 * (ax * A[2] + bx * B[2]) x12 = -x11 - C[2] x13 = x12**2 x14 = x0 / x4 x15 = cx * x14 * (x10 + x13 + x7) x16 = 17.49341832762486 x17 = A[0] - B[0] x18 = A[1] - B[1] x19 = A[2] - B[2] x20 = numpy.exp(-ax * bx * x1 * (x17**2 + x18**2 + x19**2)) x21 = 2.0 * x16 * x20 x22 = x1 * x21 x23 = x22 * boys(4, x15) x24 = cx ** (-1.0) x25 = x4 ** (-0.5) x26 = boys(3, x15) x27 = -2.0 * x1 * x16 * x20 * x24 * x25 * x26 * (x2 + A[0]) - x23 * x6 x28 = x27 * x3 x29 = 0.5 / (ax + bx) x30 = x24 * x26 x31 = x22 * x25 * x29 * x30 x32 = x14 * x3 x33 = x21 * x30 x34 = x29 * x33 x35 = x0 * x34 * x4 ** (-2.5) x36 = x3**3 x37 = x0**2 x38 = x33 * x37 * x4 ** (-3.5) x39 = x17 * x38 x40 = da * db * dc x41 = 0.2581988897471611 * x40 x42 = x14 * x9 x43 = x34 * x5 x44 = x43 * x9 x45 = x3 * x9 x46 = x7 * x9 x47 = 0.5773502691896258 * x40 x48 = x12 * x14 x49 = x12 * x43 x50 = x12 * x35 x51 = x12 * x7 x52 = x37 / x4**2 x53 = x28 * x52 x54 = x10 * x35 x55 = x10 * x3 x56 = x52 * x9 x57 = x50 * x9 x58 = x12 * x45 x59 = x13 * x35 x60 = x13 * x3 x61 = x9**3 x62 = x0**3 / x4**3 x63 = x27 * x62 x64 = x10 * x12 x65 = x13 * x9 x66 = x12**3 x67 = x23 * x5 x68 = -2.0 * x1 * x16 * x20 * x24 * x25 * x26 * (x8 + A[1]) - x67 * x9 x69 = x62 * x68 x70 = x18 * x38 x71 = x68 * x9 x72 = x31 + x71 x73 = x62 * x7 x74 = x42 * x72 + x44 x75 = x3 * x52 x76 = x48 * x71 + x49 x77 = -2.0 * x1 * x16 * x20 * x24 * x25 * x26 * (x11 + A[2]) - x12 * x67 x78 = x62 * x77 x79 = x19 * x38 x80 = x12 * x77 + x31 x81 = x62 * x80 x82 = x48 * x80 + x49 # 30 item(s) result[0, 0, 0] = numpy.sum( x41 * (x14 * (x32 * (x32 * (x28 + x31) + x34 * x6) + x35 * x7) + x36 * x39) ) result[0, 0, 1] = numpy.sum( x47 * (x14 * (x32 * (x28 * x42 + x44) + x35 * x45) + x39 * x46) ) result[0, 0, 2] = numpy.sum( x47 * (x14 * (x3 * x50 + x32 * (x28 * x48 + x49)) + x39 * x51) ) result[0, 0, 3] = numpy.sum(x47 * (x14 * (x10 * x53 + x54) + x39 * x55)) result[0, 0, 4] = numpy.sum(x40 * (x14 * (x12 * x28 * x56 + x57) + x39 * x58)) result[0, 0, 5] = numpy.sum(x47 * (x14 * (x13 * x53 + x59) + x39 * x60)) result[0, 0, 6] = numpy.sum(x41 * x61 * (x39 + x63)) result[0, 0, 7] = numpy.sum(x47 * x64 * (x39 + x63)) result[0, 0, 8] = numpy.sum(x47 * x65 * (x39 + x63)) result[0, 0, 9] = numpy.sum(x41 * x66 * (x39 + x63)) result[0, 1, 0] = numpy.sum(x36 * x41 * (x69 + x70)) result[0, 1, 1] = numpy.sum(x47 * (x46 * x70 + x72 * x73)) result[0, 1, 2] = numpy.sum(x47 * x51 * (x69 + x70)) result[0, 1, 3] = numpy.sum(x47 * (x55 * x70 + x74 * x75)) result[0, 1, 4] = numpy.sum(x40 * (x58 * x70 + x75 * x76)) result[0, 1, 5] = numpy.sum(x47 * x60 * (x69 + x70)) result[0, 1, 6] = numpy.sum(x41 * (x14 * (x42 * x74 + x54) + x61 * x70)) result[0, 1, 7] = numpy.sum(x47 * (x14 * (x42 * x76 + x57) + x64 * x70)) result[0, 1, 8] = numpy.sum(x47 * (x14 * (x13 * x52 * x71 + x59) + x65 * x70)) result[0, 1, 9] = numpy.sum(x41 * x66 * (x69 + x70)) result[0, 2, 0] = numpy.sum(x36 * x41 * (x78 + x79)) result[0, 2, 1] = numpy.sum(x47 * (x46 * x79 + x73 * x77 * x9)) result[0, 2, 2] = numpy.sum(x47 * (x51 * x79 + x73 * x80)) result[0, 2, 3] = numpy.sum(x47 * x55 * (x78 + x79)) result[0, 2, 4] = numpy.sum(x40 * (x45 * x81 + x58 * x79)) result[0, 2, 5] = numpy.sum(x47 * (x60 * x79 + x75 * x82)) result[0, 2, 6] = numpy.sum(x41 * x61 * (x78 + x79)) result[0, 2, 7] = numpy.sum(x47 * (x10 * x81 + x64 * x79)) result[0, 2, 8] = numpy.sum(x47 * (x56 * x82 + x65 * x79)) result[0, 2, 9] = numpy.sum(x41 * (x14 * (x48 * x82 + x59) + x66 * x79)) return result
[docs] def int3c2e3d_sph_014(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sp|g) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 3, 15), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - C[0] x4 = cx + x0 x5 = x4 ** (-1.5) x6 = x3 * x5 x7 = x3**2 x8 = -x1 * (ax * A[1] + bx * B[1]) x9 = -x8 - C[1] x10 = x9**2 x11 = -x1 * (ax * A[2] + bx * B[2]) x12 = -x11 - C[2] x13 = x12**2 x14 = x0 / x4 x15 = cx * x14 * (x10 + x13 + x7) x16 = 17.49341832762486 x17 = A[0] - B[0] x18 = A[1] - B[1] x19 = A[2] - B[2] x20 = numpy.exp(-ax * bx * x1 * (x17**2 + x18**2 + x19**2)) x21 = 2.0 * x16 * x20 x22 = x1 * x21 x23 = x22 * boys(5, x15) x24 = cx ** (-1.0) x25 = x4 ** (-0.5) x26 = boys(4, x15) x27 = -2.0 * x1 * x16 * x20 * x24 * x25 * x26 * (x2 + A[0]) - x23 * x6 x28 = x27 * x3 x29 = 0.5 / (ax + bx) x30 = x24 * x26 x31 = x22 * x25 * x29 * x30 x32 = x14 * x3 x33 = x21 * x30 x34 = x29 * x33 x35 = x34 * x7 x36 = x0 * x4 ** (-2.5) x37 = x3**3 x38 = x0**2 x39 = x38 * x4 ** (-3.5) x40 = x34 * x39 x41 = x3**4 x42 = x0**3 x43 = x33 * x4 ** (-4.5) * x42 x44 = x17 * x43 x45 = da * db * dc x46 = 0.09759000729485332 * x45 x47 = x14 * x9 x48 = x34 * x5 x49 = x48 * x9 x50 = x3 * x9 x51 = x34 * x36 x52 = x7 * x9 x53 = x37 * x9 x54 = 0.2581988897471611 * x45 x55 = x12 * x14 x56 = x12 * x48 x57 = x12 * x51 x58 = x12 * x37 x59 = x38 / x4**2 x60 = x28 * x59 x61 = x10 * x51 x62 = x10 * x3 x63 = x10 * x7 x64 = 0.3333333333333333 * x45 x65 = x59 * x9 x66 = x57 * x9 x67 = x12 * x44 x68 = 1.732050807568877 * x64 x69 = x13 * x51 x70 = x13 * x7 x71 = x9**3 x72 = x42 / x4**3 x73 = x28 * x72 x74 = x40 * x71 x75 = x3 * x71 x76 = x10 * x12 x77 = x40 * x76 x78 = x13 * x9 x79 = x40 * x78 x80 = x13 * x50 x81 = x12**3 x82 = x40 * x81 x83 = x3 * x81 x84 = x9**4 x85 = x0**4 / x4**4 x86 = x27 * x85 x87 = x12 * x71 x88 = x10 * x13 x89 = x81 * x9 x90 = x12**4 x91 = x23 * x5 x92 = -2.0 * x1 * x16 * x20 * x24 * x25 * x26 * (x8 + A[1]) - x9 * x91 x93 = x85 * x92 x94 = x18 * x43 x95 = x9 * x92 x96 = x31 + x95 x97 = x37 * x85 x98 = x47 * x96 + x49 x99 = x7 * x72 x100 = x55 * x95 + x56 x101 = x12 * x94 x102 = x47 * x98 + x61 x103 = x3 * x59 x104 = x100 * x47 + x66 x105 = x13 * x59 * x95 + x69 x106 = -2.0 * x1 * x16 * x20 * x24 * x25 * x26 * (x11 + A[2]) - x12 * x91 x107 = x106 * x85 x108 = x19 * x43 x109 = x106 * x12 + x31 x110 = x109 * x85 x111 = x108 * x12 x112 = x109 * x55 + x56 x113 = x112 * x72 x114 = x112 * x55 + x69 # 45 item(s) result[0, 0, 0] = numpy.sum( x46 * ( x14 * (x32 * (x32 * (x32 * (x28 + x31) + x34 * x6) + x35 * x36) + x37 * x40) + x41 * x44 ) ) result[0, 0, 1] = numpy.sum( x54 * (x14 * (x32 * (x32 * (x28 * x47 + x49) + x50 * x51) + x40 * x52) + x44 * x53) ) result[0, 0, 2] = numpy.sum( x54 * ( x14 * (x12 * x35 * x39 + x32 * (x3 * x57 + x32 * (x28 * x55 + x56))) + x44 * x58 ) ) result[0, 0, 3] = numpy.sum( x64 * (x14 * (x32 * (x10 * x60 + x61) + x40 * x62) + x44 * x63) ) result[0, 0, 4] = numpy.sum( x68 * (x14 * (x12 * x40 * x50 + x32 * (x12 * x28 * x65 + x66)) + x52 * x67) ) result[0, 0, 5] = numpy.sum( x64 * (x14 * (x13 * x3 * x40 + x32 * (x13 * x60 + x69)) + x44 * x70) ) result[0, 0, 6] = numpy.sum(x54 * (x14 * (x71 * x73 + x74) + x44 * x75)) result[0, 0, 7] = numpy.sum(x68 * (x14 * (x73 * x76 + x77) + x62 * x67)) result[0, 0, 8] = numpy.sum(x68 * (x14 * (x73 * x78 + x79) + x44 * x80)) result[0, 0, 9] = numpy.sum(x54 * (x14 * (x73 * x81 + x82) + x44 * x83)) result[0, 0, 10] = numpy.sum(x46 * x84 * (x44 + x86)) result[0, 0, 11] = numpy.sum(x54 * x87 * (x44 + x86)) result[0, 0, 12] = numpy.sum(x64 * x88 * (x44 + x86)) result[0, 0, 13] = numpy.sum(x54 * x89 * (x44 + x86)) result[0, 0, 14] = numpy.sum(x46 * x90 * (x44 + x86)) result[0, 1, 0] = numpy.sum(x41 * x46 * (x93 + x94)) result[0, 1, 1] = numpy.sum(x54 * (x53 * x94 + x96 * x97)) result[0, 1, 2] = numpy.sum(x54 * x58 * (x93 + x94)) result[0, 1, 3] = numpy.sum(x64 * (x63 * x94 + x98 * x99)) result[0, 1, 4] = numpy.sum(x68 * (x100 * x99 + x101 * x52)) result[0, 1, 5] = numpy.sum(x64 * x70 * (x93 + x94)) result[0, 1, 6] = numpy.sum(x54 * (x102 * x103 + x75 * x94)) result[0, 1, 7] = numpy.sum(x68 * (x101 * x62 + x103 * x104)) result[0, 1, 8] = numpy.sum(x68 * (x103 * x105 + x80 * x94)) result[0, 1, 9] = numpy.sum(x54 * x83 * (x93 + x94)) result[0, 1, 10] = numpy.sum(x46 * (x14 * (x102 * x47 + x74) + x84 * x94)) result[0, 1, 11] = numpy.sum(x54 * (x14 * (x104 * x47 + x77) + x87 * x94)) result[0, 1, 12] = numpy.sum(x64 * (x14 * (x105 * x47 + x79) + x88 * x94)) result[0, 1, 13] = numpy.sum(x54 * (x14 * (x72 * x81 * x95 + x82) + x89 * x94)) result[0, 1, 14] = numpy.sum(x46 * x90 * (x93 + x94)) result[0, 2, 0] = numpy.sum(x41 * x46 * (x107 + x108)) result[0, 2, 1] = numpy.sum(x54 * (x106 * x9 * x97 + x108 * x53)) result[0, 2, 2] = numpy.sum(x54 * (x108 * x58 + x109 * x97)) result[0, 2, 3] = numpy.sum(x63 * x64 * (x107 + x108)) result[0, 2, 4] = numpy.sum(x52 * x68 * (x110 + x111)) result[0, 2, 5] = numpy.sum(x64 * (x108 * x70 + x112 * x99)) result[0, 2, 6] = numpy.sum(x54 * x75 * (x107 + x108)) result[0, 2, 7] = numpy.sum(x62 * x68 * (x110 + x111)) result[0, 2, 8] = numpy.sum(x68 * (x108 * x80 + x113 * x50)) result[0, 2, 9] = numpy.sum(x54 * (x103 * x114 + x108 * x83)) result[0, 2, 10] = numpy.sum(x46 * x84 * (x107 + x108)) result[0, 2, 11] = numpy.sum(x54 * (x108 * x87 + x110 * x71)) result[0, 2, 12] = numpy.sum(x64 * (x10 * x113 + x108 * x88)) result[0, 2, 13] = numpy.sum(x54 * (x108 * x89 + x114 * x65)) result[0, 2, 14] = numpy.sum(x46 * (x108 * x90 + x14 * (x114 * x55 + x82))) return result
[docs] def int3c2e3d_sph_020(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sd|s) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 6, 1), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = cx + x0 x3 = x2 ** (-1.0) x4 = -x1 * (ax * A[0] + bx * B[0]) x5 = x4 + C[0] x6 = -x5 x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x8 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = x10 + C[2] x12 = -x11 x13 = cx * x3 x14 = x0 * x13 x15 = x14 * (x12**2 + x6**2 + x9**2) x16 = boys(1, x15) x17 = x16 * x3 x18 = cx ** (-1.0) x19 = x18 * boys(0, x15) x20 = x1 * (x17 - x19) x21 = A[0] - B[0] x22 = x14 * (x11**2 + x5**2 + x8**2) x23 = x18 * boys(0, x22) x24 = x3 * boys(1, x22) x25 = x4 + A[0] x26 = 2.0 * x21 x27 = -x25 x28 = x17 * x6 - x19 * x27 x29 = x3 * boys(2, x15) x30 = x16 * x18 x31 = x13 * x5 x32 = A[1] - B[1] x33 = A[2] - B[2] x34 = ( 17.49341832762486 * da * db * dc * x1 * x2 ** (-0.5) * numpy.exp(-ax * bx * x1 * (x21**2 + x32**2 + x33**2)) ) x35 = 0.5773502691896258 * x34 x36 = x7 + A[1] x37 = x23 * x32 - x23 * x36 + x24 * x8 x38 = -x36 x39 = x17 * x9 - x19 * x38 x40 = x29 * x9 - x30 * x38 x41 = 2.0 * x34 x42 = x10 + A[2] x43 = x11 * x24 + x23 * x33 - x23 * x42 x44 = -x42 x45 = x12 * x17 - x19 * x44 x46 = x12 * x29 - x30 * x44 x47 = 2.0 * x32 x48 = x13 * x8 x49 = 2.0 * x33 # 6 item(s) result[0, 0, 0] = numpy.sum( x35 * ( -x20 + 2.0 * x25 * x28 - x26 * x28 + x26 * (x21 * x23 - x23 * x25 + x24 * x5) + 2.0 * x31 * (x27 * x30 - x29 * x6) ) ) result[0, 1, 0] = numpy.sum(x41 * (x21 * x37 + x25 * x39 - x28 * x32 - x31 * x40)) result[0, 2, 0] = numpy.sum(x41 * (x21 * x43 + x25 * x45 - x28 * x33 - x31 * x46)) result[0, 3, 0] = numpy.sum( x35 * (-x20 + 2.0 * x36 * x39 + x37 * x47 - x39 * x47 - 2.0 * x40 * x48) ) result[0, 4, 0] = numpy.sum(x41 * (x32 * x43 - x33 * x39 + x36 * x45 - x46 * x48)) result[0, 5, 0] = numpy.sum( x35 * (-2.0 * x11 * x13 * x46 - x20 + 2.0 * x42 * x45 + x43 * x49 - x45 * x49) ) return result
[docs] def int3c2e3d_sph_021(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sd|p) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 6, 3), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = x3 + C[0] x5 = cx + x1 x6 = x5 ** (-1.0) x7 = -x2 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x2 * (ax * A[2] + bx * B[2]) x10 = x9 + C[2] x11 = cx * x6 x12 = x1 * x11 x13 = x12 * (x10**2 + x4**2 + x8**2) x14 = x6 * boys(2, x13) x15 = cx ** (-1.0) x16 = x3 + A[0] x17 = boys(1, x13) x18 = x14 * x4 - x15 * x16 * x17 x19 = -x18 x20 = 2.0 * x19 x21 = x15 * x17 x22 = x2 * x21 x23 = x20 * x4 + x22 x24 = x0 * x21 x25 = 2.0 * x4 x26 = -x4 x27 = -x8 x28 = -x10 x29 = x12 * (x26**2 + x27**2 + x28**2) x30 = boys(2, x29) x31 = x30 * x6 x32 = x15 * boys(1, x29) x33 = x2 * (x31 - x32) x34 = -x16 x35 = 2.0 * x26 * x31 - 2.0 * x32 * x34 x36 = x6 * boys(3, x29) x37 = x15 * x30 x38 = x11 * x4 x39 = -x16 * x35 + x33 + 2.0 * x38 * (x26 * x36 - x34 * x37) x40 = A[1] - B[1] x41 = A[2] - B[2] x42 = ( 17.49341832762486 * da * db * dc * x5 ** (-1.5) * numpy.exp(-ax * bx * x2 * (x0**2 + x40**2 + x41**2)) ) x43 = 0.5773502691896258 * x42 x44 = x43 * (x0 * x20 - 2.0 * x0 * (x18 + x24) + x39) x45 = x7 + A[1] x46 = x14 * x8 - x15 * x17 * x45 x47 = -x46 x48 = -x2 * x47 x49 = -x45 x50 = x27 * x31 - x32 * x49 x51 = x27 * x36 - x37 * x49 x52 = -x16 * x50 + x38 * x51 x53 = 2.0 * x52 x54 = x21 * x40 x55 = -x46 - x54 x56 = x0 * x55 x57 = 2.0 * x8 x58 = 2.0 * x47 x59 = x22 + x58 * x8 x60 = -x54 * x57 + x59 x61 = -x19 * x2 x62 = x19 * x40 x63 = 2.0 * x10 x64 = x9 + A[2] x65 = x10 * x14 - x15 * x17 * x64 x66 = -x65 x67 = -x2 * x66 x68 = -x64 x69 = x28 * x31 - x32 * x68 x70 = x28 * x36 - x37 * x68 x71 = -x16 * x69 + x38 * x70 x72 = 2.0 * x71 x73 = x21 * x41 x74 = -x65 - x73 x75 = x0 * x74 x76 = x19 * x41 x77 = x22 + x63 * x66 x78 = -x63 * x73 + x77 x79 = 2.0 * x50 x80 = x11 * x51 * x57 + x33 - x45 * x79 x81 = x43 * (2.0 * x40 * x55 + x40 * x58 + x80) x82 = x40 * x74 x83 = x41 * x47 x84 = x11 * x70 x85 = -x45 * x69 + x8 * x84 x86 = 2.0 * x41 x87 = 2.0 * x69 x88 = x33 + x63 * x84 - x64 * x87 x89 = x43 * (x66 * x86 + x74 * x86 + x88) # 18 item(s) result[0, 0, 0] = numpy.sum( x43 * (x0 * x23 + x0 * (x23 - x24 * x25) - x2 * x35 + x39 * x4) ) result[0, 0, 1] = numpy.sum(x44 * x8) result[0, 0, 2] = numpy.sum(x10 * x44) result[0, 1, 0] = numpy.sum(x42 * (x23 * x40 + x25 * x56 + x4 * x53 + x48)) result[0, 1, 1] = numpy.sum(x42 * (x0 * x60 + x53 * x8 + x57 * x62 + x61)) result[0, 1, 2] = numpy.sum(x42 * x63 * (x52 + x56 + x62)) result[0, 2, 0] = numpy.sum(x42 * (x23 * x41 + x25 * x75 + x4 * x72 + x67)) result[0, 2, 1] = numpy.sum(x42 * x57 * (x71 + x75 + x76)) result[0, 2, 2] = numpy.sum(x42 * (x0 * x78 + x10 * x72 + x61 + x63 * x76)) result[0, 3, 0] = numpy.sum(x4 * x81) result[0, 3, 1] = numpy.sum(x43 * (-x2 * x79 + x40 * x59 + x40 * x60 + x8 * x80)) result[0, 3, 2] = numpy.sum(x10 * x81) result[0, 4, 0] = numpy.sum(x25 * x42 * (x82 + x83 + x85)) result[0, 4, 1] = numpy.sum(x42 * (x41 * x59 + x57 * x82 + x57 * x85 + x67)) result[0, 4, 2] = numpy.sum(x42 * (x40 * x78 + x48 + x63 * x83 + x63 * x85)) result[0, 5, 0] = numpy.sum(x4 * x89) result[0, 5, 1] = numpy.sum(x8 * x89) result[0, 5, 2] = numpy.sum(x43 * (x10 * x88 - x2 * x87 + x41 * x77 + x41 * x78)) return result
[docs] def int3c2e3d_sph_022(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sd|d) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 6, 6), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = x2 + C[0] x4 = -x3 x5 = cx + x0 x6 = x5 ** (-1.0) x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x8 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = x10 + C[2] x12 = -x11 x13 = cx * x6 x14 = x0 * x13 x15 = x14 * (x12**2 + x4**2 + x9**2) x16 = boys(3, x15) x17 = x16 * x6 x18 = x2 + A[0] x19 = -x18 x20 = cx ** (-1.0) x21 = x20 * boys(2, x15) x22 = x19 * x21 x23 = x17 * x4 - x22 x24 = x23 * x3 x25 = x3**2 x26 = x8**2 x27 = x11**2 x28 = x14 * (x25 + x26 + x27) x29 = boys(2, x28) x30 = x20 * x29 x31 = x1 * x30 x32 = 2.0 * x24 + x31 x33 = x1 * (x17 - x21) x34 = x6 * boys(4, x15) x35 = -2.0 * x13 * x3 * (x16 * x19 * x20 - x34 * x4) - 2.0 * x18 * x23 + x33 x36 = x1 * x23 x37 = x24 + x31 x38 = A[0] - B[0] x39 = 2.0 * x38 x40 = x3 * x39 x41 = A[1] - B[1] x42 = A[2] - B[2] x43 = ( 17.49341832762486 * da * db * dc * x0 * x5 ** (-2.5) * numpy.exp(-ax * bx * x1 * (x38**2 + x41**2 + x42**2)) ) x44 = 0.3333333333333333 * x43 x45 = x6 * boys(3, x28) x46 = x18 * x20 * x29 - x3 * x45 x47 = 1.732050807568877 x48 = x44 * x47 x49 = x48 * ( 2.0 * x1 * x46 - x3 * x35 - x32 * x38 + x38 * (2.0 * x20 * x29 * x3 * x38 - x32) ) x50 = 2.0 * x46 x51 = x44 * (x35 + x38 * x50 - x39 * (-x16 * x4 * x6 + x22 + x30 * x38)) x52 = x11 * x47 x53 = x17 * x9 x54 = x7 + A[1] x55 = -x54 x56 = x21 * x55 x57 = x53 - x56 x58 = -x16 * x20 * x55 + x34 * x9 x59 = x13 * x4 x60 = x19 * x57 - x58 * x59 x61 = x3 * x60 x62 = x1 * x57 x63 = -x62 x64 = x30 * x41 x65 = -x53 + x56 + x64 x66 = -x65 x67 = x3 * x38 x68 = x3 * x43 x69 = 0.6666666666666667 * x47 x70 = x68 * x69 x71 = -x36 x72 = x60 * x8 x73 = 2.0 * x72 x74 = x57 * x8 x75 = x31 + 2.0 * x74 x76 = x1 * x75 x77 = -2.0 * x64 * x8 + x75 x78 = x32 * x41 x79 = x11 * x43 x80 = x31 + x74 x81 = x20 * x29 * x41 * x8 - x80 x82 = x41 * x8 x83 = x43 * x8 x84 = x69 * x83 x85 = -x77 x86 = x43 * x69 x87 = x12 * x17 x88 = x10 + A[2] x89 = -x88 x90 = x21 * x89 x91 = x87 - x90 x92 = -x91 x93 = x12 * x34 - x16 * x20 * x89 x94 = -x93 x95 = -x19 * x92 + x59 * x94 x96 = x3 * x95 x97 = x1 * x91 x98 = -x97 x99 = x30 * x42 x100 = -x87 + x90 + x99 x101 = -x100 x102 = x32 * x42 x103 = x11 * x95 x104 = x11 * x91 x105 = 2.0 * x104 + x31 x106 = x1 * x105 x107 = -0.5 * x106 x108 = 2.0 * x11 x109 = x105 - x108 * x99 x110 = -x109 x111 = x104 + x31 x112 = x11 * x20 * x29 * x42 - x111 x113 = x11 * x42 x114 = x69 * x79 x115 = x20 * x29 * x54 - x45 * x8 x116 = 2.0 * x41 x117 = 2.0 * x8 x118 = x117 * x13 * x58 + x33 - 2.0 * x54 * x57 x119 = x44 * (x115 * x116 + x116 * x66 + x118) x120 = x41 * x85 x121 = x41 * x75 x122 = -x118 * x8 + 2.0 * x62 x123 = x3 * x48 x124 = 2.0 * x82 x125 = x100 * x41 x126 = x13 * x9 * x94 - x55 * x92 x127 = x11 * x126 x128 = 2.0 * x42 x129 = x108 * x13 * x93 + x33 - 2.0 * x88 * x91 x130 = x44 * (x101 * x128 - x128 * (x11 * x45 - x20 * x29 * x88) + x129) x131 = -x11 * x129 + 2.0 * x97 x132 = x105 * x42 - x110 * x42 - x131 x133 = 2.0 * x113 # 36 item(s) result[0, 0, 0] = numpy.sum( x44 * ( x1 * x32 - x3 * (x3 * x35 - 2.0 * x36) - x37 * x40 + x40 * (x20 * x29 * x3 * x38 - x37) ) ) result[0, 0, 1] = numpy.sum(x49 * x8) result[0, 0, 2] = numpy.sum(x11 * x49) result[0, 0, 3] = numpy.sum(-x26 * x51) result[0, 0, 4] = numpy.sum(-x51 * x52 * x8) result[0, 0, 5] = numpy.sum(-x27 * x51) result[0, 1, 0] = numpy.sum(-x70 * (x37 * x41 + x61 + x63 + x66 * x67)) result[0, 1, 1] = numpy.sum( -0.5 * x43 * (2.0 * x3 * (x71 + x73) + 2.0 * x67 * x77 - x76 + 2.0 * x78 * x8) ) result[0, 1, 2] = numpy.sum(-x79 * (x40 * x66 + 2.0 * x61 + x63 + x78)) result[0, 1, 3] = numpy.sum(x84 * (x36 + x38 * x81 - x46 * x82 - x72)) result[0, 1, 4] = numpy.sum(x79 * (x36 + x38 * x85 - x50 * x82 - x73)) result[0, 1, 5] = numpy.sum(x27 * x86 * (-x23 * x41 + x38 * x65 - x60)) result[0, 2, 0] = numpy.sum(-x70 * (x101 * x67 + x37 * x42 + x96 + x98)) result[0, 2, 1] = numpy.sum(-x83 * (x101 * x40 + x102 + 2.0 * x96 + x98)) result[0, 2, 2] = numpy.sum( -x43 * (x102 * x11 + x107 + x109 * x67 + x3 * (2.0 * x103 + x71)) ) result[0, 2, 3] = numpy.sum(x26 * x86 * (x100 * x38 - x23 * x42 - x95)) result[0, 2, 4] = numpy.sum( x83 * (-2.0 * x11 * x23 * x42 - 2.0 * x11 * x95 + x110 * x38 + x36) ) result[0, 2, 5] = numpy.sum(x114 * (-x103 + x112 * x38 - x113 * x46 + x36)) result[0, 3, 0] = numpy.sum(-x119 * x25) result[0, 3, 1] = numpy.sum(x123 * (x120 - x121 + x122)) result[0, 3, 2] = numpy.sum(-x119 * x3 * x52) result[0, 3, 3] = numpy.sum(x44 * (x122 * x8 - x124 * x80 + x124 * x81 + x76)) result[0, 3, 4] = numpy.sum(x11 * x48 * (2.0 * x1 * x115 - x118 * x8 + x120 - x121)) result[0, 3, 5] = numpy.sum(-x119 * x27) result[0, 4, 0] = numpy.sum(x25 * x86 * (x125 - x126 - x42 * x57)) result[0, 4, 1] = numpy.sum(x68 * (x117 * x125 - 2.0 * x126 * x8 - x42 * x75 + x97)) result[0, 4, 2] = numpy.sum( x68 * (-2.0 * x11 * x126 - 2.0 * x11 * x42 * x57 + x110 * x41 + x62) ) result[0, 4, 3] = numpy.sum(-x84 * (x101 * x82 + x126 * x8 + x42 * x80 + x98)) result[0, 4, 4] = numpy.sum( -x43 * (x107 + x109 * x82 + x11 * x42 * x75 + x8 * (2.0 * x127 + x63)) ) result[0, 4, 5] = numpy.sum(x114 * (x112 * x41 - x113 * x115 - x127 + x62)) result[0, 5, 0] = numpy.sum(-x130 * x25) result[0, 5, 1] = numpy.sum(-x130 * x3 * x47 * x8) result[0, 5, 2] = numpy.sum(-x123 * x132) result[0, 5, 3] = numpy.sum(-x130 * x26) result[0, 5, 4] = numpy.sum(-x132 * x48 * x8) result[0, 5, 5] = numpy.sum(x44 * (x106 + x11 * x131 - x111 * x133 + x112 * x133)) return result
[docs] def int3c2e3d_sph_023(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sd|f) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 6, 10), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - C[0] x5 = x4**2 x6 = -x2 * (ax * A[1] + bx * B[1]) x7 = -x6 - C[1] x8 = x7**2 x9 = -x2 * (ax * A[2] + bx * B[2]) x10 = -x9 - C[2] x11 = x10**2 x12 = cx + x1 x13 = x12 ** (-1.0) x14 = x1 * x13 x15 = cx * x14 * (x11 + x5 + x8) x16 = boys(4, x15) x17 = x12 ** (-1.5) x18 = 17.49341832762486 x19 = A[1] - B[1] x20 = A[2] - B[2] x21 = numpy.exp(-ax * bx * x2 * (x0**2 + x19**2 + x20**2)) x22 = 2.0 * x18 * x21 x23 = x2 * x22 x24 = x17 * x23 x25 = x16 * x24 x26 = cx ** (-1.0) x27 = x12 ** (-0.5) x28 = -x3 - A[0] x29 = boys(3, x15) x30 = 2.0 * x18 * x2 * x21 * x26 * x27 * x28 * x29 - x25 * x4 x31 = x30 * x4 x32 = 0.5 / (ax + bx) x33 = x26 * x29 x34 = x23 * x27 * x32 * x33 x35 = x31 + x34 x36 = x14 * x4 x37 = x22 * x33 x38 = x32 * x37 x39 = x17 * x38 x40 = x35 * x36 + x39 * x4 x41 = x1 * x12 ** (-2.5) * x38 x42 = x14 * (x36 * x40 + x41 * x5) x43 = x4**3 x44 = x1**2 x45 = x12 ** (-3.5) * x37 * x44 x46 = x0 * x45 x47 = x32 * (2.0 * x18 * x2 * x21 * x26 * x27 * x29 - x25) x48 = x24 * boys(5, x15) x49 = cx * x13 x50 = x4 * x49 x51 = ( x28 * x30 + x47 - x50 * (2.0 * x16 * x18 * x2 * x21 * x26 * x27 * x28 - x4 * x48) ) x52 = x4 * x51 x53 = x30 * x32 x54 = 2.0 * x53 x55 = x14 * x32 x56 = 2.0 * x55 x57 = da * db * dc x58 = 0.06666666666666667 * x57 x59 = 2.23606797749979 * x58 x60 = x14 * x7 x61 = x39 * x7 x62 = x31 * x60 + x61 x63 = x4 * x7 x64 = x14 * (x36 * x62 + x41 * x63) x65 = x46 * x5 x66 = 0.3333333333333333 * x57 x67 = x10 * x14 x68 = x10 * x39 x69 = x31 * x67 + x68 x70 = x10 * x41 x71 = x14 * (x36 * x69 + x4 * x70) x72 = x44 / x12**2 x73 = x72 * x8 x74 = x41 * x8 x75 = x14 * (x31 * x73 + x74) x76 = x4 * x46 x77 = x7 * x72 x78 = x10 * x77 x79 = x7 * x70 x80 = x14 * (x31 * x78 + x79) x81 = x10 * x63 x82 = 1.732050807568877 * x66 x83 = x11 * x72 x84 = x11 * x41 x85 = x14 * (x31 * x83 + x84) x86 = x7**3 x87 = x1**3 / x12**3 x88 = x86 * x87 x89 = x30 * x88 x90 = x8 * x87 x91 = x10 * x90 x92 = x30 * x91 x93 = x10 * x8 x94 = x11 * x87 x95 = x7 * x94 x96 = x30 * x95 x97 = x11 * x7 x98 = x10**3 x99 = x87 * x98 x100 = x30 * x99 x101 = -x6 - A[1] x102 = 2.0 * x101 * x18 * x2 * x21 * x26 * x27 * x29 - x25 * x7 x103 = x43 * x87 x104 = x102 * x103 x105 = x19 * x45 x106 = x104 + x105 * x43 x107 = x102 * x32 x108 = 2.0 * x101 * x16 * x18 * x2 * x21 * x26 * x27 - x48 * x7 x109 = x102 * x28 - x108 * x50 x110 = x109 * x4 x111 = x5 * x72 x112 = 3.872983346207417 * x58 x113 = x102 * x7 x114 = x113 + x34 x115 = x5 * x87 x116 = x114 * x115 x117 = x105 * x5 x118 = x116 + x117 * x7 x119 = x114 * x14 x120 = x119 * x32 x121 = x109 * x7 x122 = x121 + x53 x123 = x4 * x72 x124 = x123 * x32 x125 = x10 * x115 x126 = x102 * x125 x127 = x10 * x117 + x126 x128 = x107 * x67 x129 = x119 * x7 + x61 x130 = x123 * x129 x131 = x105 * x4 x132 = x130 + x131 * x8 x133 = x129 * x55 x134 = x60 * (x122 + x53) x135 = x113 * x67 + x68 x136 = x123 * x135 x137 = x105 * x81 + x136 x138 = x135 * x55 x139 = x53 * x67 x140 = x121 * x67 + x139 x141 = x4 * x94 x142 = x102 * x141 x143 = x11 * x131 + x142 x144 = x107 * x83 x145 = x14 * (x129 * x60 + x74) x146 = x105 * x86 + x145 x147 = x14 * (x135 * x60 + x79) x148 = x105 * x93 + x147 x149 = x14 * (x113 * x83 + x84) x150 = x105 * x97 + x149 x151 = x53 * x83 x152 = x102 * x99 x153 = x105 * x98 + x152 x154 = -x9 - A[2] x155 = -x10 * x25 + 2.0 * x154 * x18 * x2 * x21 * x26 * x27 * x29 x156 = x103 * x155 x157 = x20 * x45 x158 = x156 + x157 * x43 x159 = x155 * x32 x160 = -x10 * x48 + 2.0 * x154 * x16 * x18 * x2 * x21 * x26 * x27 x161 = x155 * x28 - x160 * x50 x162 = x161 * x4 x163 = x115 * x7 x164 = x155 * x163 x165 = x157 * x5 x166 = x164 + x165 * x7 x167 = x159 * x60 x168 = x123 * x7 x169 = x10 * x155 + x34 x170 = x115 * x169 x171 = x10 * x165 + x170 x172 = x169 * x55 x173 = x10 * x161 + x53 x174 = x4 * x90 x175 = x155 * x174 x176 = x157 * x4 x177 = x175 + x176 * x8 x178 = x159 * x73 x179 = x63 * x87 x180 = x169 * x179 x181 = x157 * x81 + x180 x182 = x169 * x32 * x77 x183 = x169 * x67 + x68 x184 = x123 * x183 x185 = x11 * x176 + x184 x186 = x183 * x55 x187 = x139 + x173 * x67 x188 = x155 * x88 x189 = x157 * x86 + x188 x190 = x169 * x90 x191 = x157 * x93 + x190 x192 = x183 * x77 x193 = x157 * x97 + x192 x194 = x14 * (x183 * x67 + x84) x195 = x157 * x98 + x194 x196 = x49 * x7 x197 = x101 * x102 - x108 * x196 + x47 x198 = x197 * x7 x199 = 2.0 * x107 x200 = x198 + x199 x201 = 2.0 * x120 + x200 * x60 x202 = x67 * (x198 + x199) x203 = x101 * x155 - x160 * x196 x204 = x159 + x203 * x7 x205 = x10 * x203 + x107 x206 = x167 + x204 * x60 x207 = x172 + x205 * x60 x208 = x128 + x205 * x67 x209 = -x10 * x160 * x49 + x154 * x155 + x47 x210 = x10 * x209 + 2.0 * x159 x211 = 2.0 * x172 + x210 * x67 # 60 item(s) result[0, 0, 0] = numpy.sum( x59 * ( x0 * x42 + x0 * (x42 + x43 * x46) + x14 * (x36 * (x35 * x56 + x36 * (x52 + x54)) + x40 * x56) ) ) result[0, 0, 1] = numpy.sum( x66 * (x0 * x64 + x0 * (x64 + x65 * x7) + x14 * (x36 * x60 * (x52 + x54) + x56 * x62)) ) result[0, 0, 2] = numpy.sum( x66 * ( x0 * x71 + x0 * (x10 * x65 + x71) + x14 * (x36 * x67 * (x52 + x54) + x56 * x69) ) ) result[0, 0, 3] = numpy.sum( x66 * (x0 * x75 + x0 * (x75 + x76 * x8) + x14 * x73 * (x52 + x54)) ) result[0, 0, 4] = numpy.sum( x82 * (x0 * x80 + x0 * (x46 * x81 + x80) + x14 * x78 * (x52 + x54)) ) result[0, 0, 5] = numpy.sum( x66 * (x0 * x85 + x0 * (x11 * x76 + x85) + x14 * x83 * (x52 + x54)) ) result[0, 0, 6] = numpy.sum(x59 * (x0 * x89 + x0 * (x46 * x86 + x89) + x51 * x88)) result[0, 0, 7] = numpy.sum(x66 * (x0 * x92 + x0 * (x46 * x93 + x92) + x51 * x91)) result[0, 0, 8] = numpy.sum(x66 * (x0 * x96 + x0 * (x46 * x97 + x96) + x51 * x95)) result[0, 0, 9] = numpy.sum(x59 * (x0 * x100 + x0 * (x100 + x46 * x98) + x51 * x99)) result[0, 1, 0] = numpy.sum( x112 * (x0 * x106 + x14 * (x107 * x111 + x36**2 * (2.0 * x107 + x110)) + x19 * x42) ) result[0, 1, 1] = numpy.sum( x82 * (x0 * x118 + x14 * (x114 * x124 + x36 * (x120 + x122 * x36)) + x19 * x64) ) result[0, 1, 2] = numpy.sum( x82 * (x0 * x127 + x14 * (x10 * x107 * x123 + x36 * (x110 * x67 + x128)) + x19 * x71) ) result[0, 1, 3] = numpy.sum(x82 * (x0 * x132 + x14 * (x133 + x134 * x36) + x19 * x75)) result[0, 1, 4] = numpy.sum(x57 * (x0 * x137 + x14 * (x138 + x140 * x36) + x19 * x80)) result[0, 1, 5] = numpy.sum(x82 * (x0 * x143 + x14 * (x110 * x83 + x144) + x19 * x85)) result[0, 1, 6] = numpy.sum( x112 * (x0 * x146 + x14 * (x134 * x60 + x53 * x73) + x19 * x89) ) result[0, 1, 7] = numpy.sum( x82 * (x0 * x148 + x14 * (x140 * x60 + x53 * x78) + x19 * x92) ) result[0, 1, 8] = numpy.sum(x82 * (x0 * x150 + x14 * (x121 * x83 + x151) + x19 * x96)) result[0, 1, 9] = numpy.sum(x112 * (x0 * x153 + x100 * x19 + x109 * x99)) result[0, 2, 0] = numpy.sum( x112 * (x0 * x158 + x14 * (x111 * x159 + x36**2 * (2.0 * x159 + x162)) + x20 * x42) ) result[0, 2, 1] = numpy.sum( x82 * (x0 * x166 + x14 * (x159 * x168 + x36 * (x162 * x60 + x167)) + x20 * x64) ) result[0, 2, 2] = numpy.sum( x82 * (x0 * x171 + x14 * (x124 * x169 + x36 * (x172 + x173 * x36)) + x20 * x71) ) result[0, 2, 3] = numpy.sum(x82 * (x0 * x177 + x14 * (x162 * x73 + x178) + x20 * x75)) result[0, 2, 4] = numpy.sum( x57 * (x0 * x181 + x14 * (x168 * x173 + x182) + x20 * x80) ) result[0, 2, 5] = numpy.sum(x82 * (x0 * x185 + x14 * (x186 + x187 * x36) + x20 * x85)) result[0, 2, 6] = numpy.sum(x112 * (x0 * x189 + x161 * x88 + x20 * x89)) result[0, 2, 7] = numpy.sum(x82 * (x0 * x191 + x173 * x90 + x20 * x92)) result[0, 2, 8] = numpy.sum(x82 * (x0 * x193 + x187 * x77 + x20 * x96)) result[0, 2, 9] = numpy.sum( x112 * (x0 * x195 + x100 * x20 + x14 * (x151 + x187 * x67)) ) result[0, 3, 0] = numpy.sum(x59 * (x103 * x197 + x104 * x19 + x106 * x19)) result[0, 3, 1] = numpy.sum(x66 * (x115 * x200 + x116 * x19 + x118 * x19)) result[0, 3, 2] = numpy.sum(x66 * (x125 * x197 + x126 * x19 + x127 * x19)) result[0, 3, 3] = numpy.sum(x66 * (x123 * x201 + x130 * x19 + x132 * x19)) result[0, 3, 4] = numpy.sum(x82 * (x123 * x202 + x136 * x19 + x137 * x19)) result[0, 3, 5] = numpy.sum(x66 * (x141 * x197 + x142 * x19 + x143 * x19)) result[0, 3, 6] = numpy.sum( x59 * (x14 * (2.0 * x133 + x201 * x60) + x145 * x19 + x146 * x19) ) result[0, 3, 7] = numpy.sum( x66 * (x14 * (2.0 * x138 + x202 * x60) + x147 * x19 + x148 * x19) ) result[0, 3, 8] = numpy.sum( x66 * (x14 * x83 * (x198 + x199) + x149 * x19 + x150 * x19) ) result[0, 3, 9] = numpy.sum(x59 * (x152 * x19 + x153 * x19 + x197 * x99)) result[0, 4, 0] = numpy.sum(x112 * (x103 * x203 + x104 * x20 + x158 * x19)) result[0, 4, 1] = numpy.sum(x82 * (x115 * x204 + x116 * x20 + x166 * x19)) result[0, 4, 2] = numpy.sum(x82 * (x115 * x205 + x126 * x20 + x171 * x19)) result[0, 4, 3] = numpy.sum(x82 * (x123 * x206 + x130 * x20 + x177 * x19)) result[0, 4, 4] = numpy.sum(x57 * (x123 * x207 + x136 * x20 + x181 * x19)) result[0, 4, 5] = numpy.sum(x82 * (x123 * x208 + x142 * x20 + x185 * x19)) result[0, 4, 6] = numpy.sum( x112 * (x14 * (x178 + x206 * x60) + x145 * x20 + x189 * x19) ) result[0, 4, 7] = numpy.sum( x82 * (x14 * (x182 + x207 * x60) + x147 * x20 + x19 * x191) ) result[0, 4, 8] = numpy.sum( x82 * (x14 * (x186 + x208 * x60) + x149 * x20 + x19 * x193) ) result[0, 4, 9] = numpy.sum( x112 * (x14 * (x144 + x208 * x67) + x152 * x20 + x19 * x195) ) result[0, 5, 0] = numpy.sum(x59 * (x103 * x209 + x156 * x20 + x158 * x20)) result[0, 5, 1] = numpy.sum(x66 * (x163 * x209 + x164 * x20 + x166 * x20)) result[0, 5, 2] = numpy.sum(x66 * (x115 * x210 + x170 * x20 + x171 * x20)) result[0, 5, 3] = numpy.sum(x66 * (x174 * x209 + x175 * x20 + x177 * x20)) result[0, 5, 4] = numpy.sum(x82 * (x179 * x210 + x180 * x20 + x181 * x20)) result[0, 5, 5] = numpy.sum(x66 * (x123 * x211 + x184 * x20 + x185 * x20)) result[0, 5, 6] = numpy.sum(x59 * (x188 * x20 + x189 * x20 + x209 * x88)) result[0, 5, 7] = numpy.sum(x66 * (x190 * x20 + x191 * x20 + x210 * x90)) result[0, 5, 8] = numpy.sum(x66 * (x192 * x20 + x193 * x20 + x211 * x77)) result[0, 5, 9] = numpy.sum( x59 * (x14 * (2.0 * x186 + x211 * x67) + x194 * x20 + x195 * x20) ) return result
[docs] def int3c2e3d_sph_024(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sd|g) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 6, 15), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - C[0] x5 = x4**2 x6 = -x2 * (ax * A[1] + bx * B[1]) x7 = -x6 - C[1] x8 = x7**2 x9 = -x2 * (ax * A[2] + bx * B[2]) x10 = -x9 - C[2] x11 = x10**2 x12 = cx + x1 x13 = x12 ** (-1.0) x14 = x1 * x13 x15 = cx * x14 * (x11 + x5 + x8) x16 = boys(5, x15) x17 = x12 ** (-1.5) x18 = 17.49341832762486 x19 = A[1] - B[1] x20 = A[2] - B[2] x21 = numpy.exp(-ax * bx * x2 * (x0**2 + x19**2 + x20**2)) x22 = 2.0 * x18 * x21 x23 = x2 * x22 x24 = x17 * x23 x25 = x16 * x24 x26 = cx ** (-1.0) x27 = x12 ** (-0.5) x28 = -x3 - A[0] x29 = boys(4, x15) x30 = 2.0 * x18 * x2 * x21 * x26 * x27 * x28 * x29 - x25 * x4 x31 = x30 * x4 x32 = 0.5 / (ax + bx) x33 = x26 * x29 x34 = x23 * x27 * x32 * x33 x35 = x31 + x34 x36 = x14 * x4 x37 = x22 * x33 x38 = x32 * x37 x39 = x17 * x38 x40 = x35 * x36 + x39 * x4 x41 = x38 * x5 x42 = x1 * x12 ** (-2.5) x43 = x36 * x40 + x41 * x42 x44 = x4**3 x45 = x1**2 x46 = x12 ** (-3.5) * x45 x47 = x38 * x46 x48 = x14 * (x36 * x43 + x44 * x47) x49 = x4**4 x50 = x1**3 x51 = x12 ** (-4.5) * x37 * x50 x52 = x0 * x51 x53 = x32 * (2.0 * x18 * x2 * x21 * x26 * x27 * x29 - x25) x54 = x24 * boys(6, x15) x55 = cx * x13 x56 = x4 * x55 x57 = ( x28 * x30 + x53 - x56 * (2.0 * x16 * x18 * x2 * x21 * x26 * x27 * x28 - x4 * x54) ) x58 = x4 * x57 x59 = x30 * x32 x60 = 2.0 * x59 x61 = x14 * x32 x62 = 2.0 * x61 x63 = da * db * dc x64 = 0.009523809523809524 * x63 x65 = 5.916079783099616 * x64 x66 = x14 * x7 x67 = x39 * x7 x68 = x31 * x66 + x67 x69 = x38 * x42 x70 = x4 * x69 x71 = x36 * x68 + x7 * x70 x72 = x41 * x46 x73 = x14 * (x36 * x71 + x7 * x72) x74 = x44 * x52 x75 = 0.06666666666666667 * x63 x76 = 2.23606797749979 * x75 x77 = x10 * x14 x78 = x10 * x39 x79 = x31 * x77 + x78 x80 = x10 * x70 + x36 * x79 x81 = x14 * (x10 * x72 + x36 * x80) x82 = x45 / x12**2 x83 = x8 * x82 x84 = x69 * x8 x85 = x31 * x83 + x84 x86 = x4 * x8 x87 = x14 * (x36 * x85 + x47 * x86) x88 = x5 * x8 x89 = 1.732050807568877 x90 = 0.1111111111111111 * x63 * x89 x91 = x7 * x82 x92 = x10 * x91 x93 = x10 * x7 x94 = x69 * x93 x95 = x31 * x92 + x94 x96 = x14 * (x36 * x95 + x4 * x47 * x93) x97 = x5 * x93 x98 = 0.3333333333333333 * x63 x99 = x11 * x82 x100 = x11 * x69 x101 = x100 + x31 * x99 x102 = x11 * x4 x103 = x14 * (x101 * x36 + x102 * x47) x104 = x11 * x5 x105 = x7**3 x106 = x50 / x12**3 x107 = x105 * x106 x108 = x105 * x47 x109 = x14 * (x107 * x31 + x108) x110 = x105 * x52 x111 = x106 * x8 x112 = x10 * x111 x113 = x10 * x47 * x8 x114 = x14 * (x112 * x31 + x113) x115 = x10 * x86 x116 = x106 * x7 x117 = x11 * x116 x118 = x11 * x47 * x7 x119 = x14 * (x117 * x31 + x118) x120 = x102 * x7 x121 = x10**3 x122 = x106 * x121 x123 = x121 * x47 x124 = x14 * (x122 * x31 + x123) x125 = x121 * x4 x126 = x7**4 x127 = x1**4 / x12**4 x128 = x126 * x127 x129 = x128 * x30 x130 = x105 * x127 x131 = x10 * x130 x132 = x131 * x30 x133 = x127 * x30 x134 = x11 * x8 x135 = x133 * x134 x136 = x127 * x57 x137 = x121 * x7 x138 = x133 * x137 x139 = x10**4 x140 = x127 * x139 x141 = x140 * x30 x142 = -x6 - A[1] x143 = 2.0 * x142 * x18 * x2 * x21 * x26 * x27 * x29 - x25 * x7 x144 = x127 * x49 x145 = x143 * x144 x146 = x19 * x51 x147 = x145 + x146 * x49 x148 = x143 * x32 x149 = 2.0 * x142 * x16 * x18 * x2 * x21 * x26 * x27 - x54 * x7 x150 = x143 * x28 - x149 * x56 x151 = x150 * x4 x152 = x5 * x82 x153 = x106 * x44 x154 = 10.2469507659596 * x64 x155 = x143 * x7 x156 = x155 + x34 x157 = x127 * x44 x158 = x156 * x157 x159 = x146 * x44 x160 = x158 + x159 * x7 x161 = x14 * x156 x162 = x161 * x32 x163 = x150 * x7 x164 = x163 + x59 x165 = x4 * x82 x166 = x156 * x32 x167 = x106 * x5 x168 = 3.872983346207417 * x75 x169 = x10 * x157 x170 = x143 * x169 x171 = x10 * x159 + x170 x172 = x148 * x77 x173 = x10 * x148 x174 = x161 * x7 + x67 x175 = x167 * x174 x176 = x146 * x88 + x175 x177 = x174 * x61 x178 = x66 * (x164 + x59) x179 = x165 * x32 x180 = x155 * x77 + x78 x181 = x167 * x180 x182 = x146 * x97 + x181 x183 = x180 * x61 x184 = x59 * x77 x185 = x163 * x77 + x184 x186 = x89 * x98 x187 = x127 * x143 x188 = x104 * x187 x189 = x104 * x146 + x188 x190 = x148 * x99 x191 = x174 * x66 + x84 x192 = x165 * x191 x193 = x105 * x146 x194 = x192 + x193 * x4 x195 = x191 * x61 x196 = x178 * x66 + x59 * x83 x197 = x180 * x66 + x94 x198 = x165 * x197 x199 = x115 * x146 + x198 x200 = x197 * x61 x201 = x185 * x66 + x59 * x92 x202 = x100 + x155 * x99 x203 = x165 * x202 x204 = x120 * x146 + x203 x205 = x202 * x61 x206 = x59 * x99 x207 = x163 * x99 + x206 x208 = x125 * x187 x209 = x125 * x146 + x208 x210 = x122 * x148 x211 = x14 * (x108 + x191 * x66) x212 = x126 * x146 + x211 x213 = x14 * (x113 + x197 * x66) x214 = x10 * x193 + x213 x215 = x14 * (x118 + x202 * x66) x216 = x134 * x146 + x215 x217 = x14 * (x122 * x155 + x123) x218 = x137 * x146 + x217 x219 = x122 * x59 x220 = x140 * x143 x221 = x139 * x146 + x220 x222 = -x9 - A[2] x223 = -x10 * x25 + 2.0 * x18 * x2 * x21 * x222 * x26 * x27 * x29 x224 = x144 * x223 x225 = x20 * x51 x226 = x224 + x225 * x49 x227 = x223 * x32 x228 = -x10 * x54 + 2.0 * x16 * x18 * x2 * x21 * x222 * x26 * x27 x229 = x223 * x28 - x228 * x56 x230 = x229 * x4 x231 = x157 * x7 x232 = x223 * x231 x233 = x225 * x44 x234 = x232 + x233 * x7 x235 = x227 * x66 x236 = x165 * x7 x237 = x10 * x223 + x34 x238 = x157 * x237 x239 = x10 * x233 + x238 x240 = x237 * x61 x241 = x10 * x229 + x59 x242 = x237 * x32 x243 = x127 * x5 x244 = x243 * x8 x245 = x223 * x244 x246 = x225 * x88 + x245 x247 = x227 * x83 x248 = x111 * x4 x249 = x243 * x7 x250 = x237 * x249 x251 = x225 * x97 + x250 x252 = x242 * x91 x253 = x116 * x4 x254 = x237 * x77 + x78 x255 = x167 * x254 x256 = x104 * x225 + x255 x257 = x254 * x61 x258 = x184 + x241 * x77 x259 = x130 * x4 x260 = x223 * x259 x261 = x105 * x225 x262 = x260 + x261 * x4 x263 = x107 * x227 x264 = x127 * x86 x265 = x237 * x264 x266 = x115 * x225 + x265 x267 = x111 * x242 x268 = x253 * x254 x269 = x120 * x225 + x268 x270 = x254 * x32 * x91 x271 = x100 + x254 * x77 x272 = x165 * x271 x273 = x125 * x225 + x272 x274 = x271 * x61 x275 = x206 + x258 * x77 x276 = x128 * x223 x277 = x126 * x225 + x276 x278 = x130 * x237 x279 = x10 * x261 + x278 x280 = x111 * x254 x281 = x134 * x225 + x280 x282 = x271 * x91 x283 = x137 * x225 + x282 x284 = x14 * (x123 + x271 * x77) x285 = x139 * x225 + x284 x286 = x55 * x7 x287 = x142 * x143 - x149 * x286 + x53 x288 = x287 * x7 x289 = 2.0 * x148 x290 = x288 + x289 x291 = 2.0 * x162 + x290 * x66 x292 = x77 * (x288 + x289) x293 = x127 * x287 x294 = 2.0 * x177 + x291 * x66 x295 = 2.0 * x183 + x292 * x66 x296 = x99 * (x288 + x289) x297 = x142 * x223 - x228 * x286 x298 = x227 + x297 * x7 x299 = x10 * x297 + x148 x300 = x235 + x298 * x66 x301 = x240 + x299 * x66 x302 = x172 + x299 * x77 x303 = x247 + x300 * x66 x304 = x252 + x301 * x66 x305 = x257 + x302 * x66 x306 = x190 + x302 * x77 x307 = -x10 * x228 * x55 + x222 * x223 + x53 x308 = x10 * x307 + 2.0 * x227 x309 = 2.0 * x240 + x308 * x77 x310 = 2.0 * x257 + x309 * x77 # 90 item(s) result[0, 0, 0] = numpy.sum( x65 * ( x0 * x48 + x0 * (x48 + x49 * x52) + x14 * (x36 * (x36 * (x35 * x62 + x36 * (x58 + x60)) + x40 * x62) + x43 * x62) ) ) result[0, 0, 1] = numpy.sum( x76 * ( x0 * x73 + x0 * (x7 * x74 + x73) + x14 * (x36 * (x36 * x66 * (x58 + x60) + x62 * x68) + x62 * x71) ) ) result[0, 0, 2] = numpy.sum( x76 * ( x0 * x81 + x0 * (x10 * x74 + x81) + x14 * (x36 * (x36 * x77 * (x58 + x60) + x62 * x79) + x62 * x80) ) ) result[0, 0, 3] = numpy.sum( x90 * ( x0 * x87 + x0 * (x52 * x88 + x87) + x14 * (x36 * x83 * (x58 + x60) + x62 * x85) ) ) result[0, 0, 4] = numpy.sum( x98 * ( x0 * x96 + x0 * (x52 * x97 + x96) + x14 * (x36 * x92 * (x58 + x60) + x62 * x95) ) ) result[0, 0, 5] = numpy.sum( x90 * ( x0 * x103 + x0 * (x103 + x104 * x52) + x14 * (x101 * x62 + x36 * x99 * (x58 + x60)) ) ) result[0, 0, 6] = numpy.sum( x76 * (x0 * x109 + x0 * (x109 + x110 * x4) + x107 * x14 * (x58 + x60)) ) result[0, 0, 7] = numpy.sum( x98 * (x0 * x114 + x0 * (x114 + x115 * x52) + x112 * x14 * (x58 + x60)) ) result[0, 0, 8] = numpy.sum( x98 * (x0 * x119 + x0 * (x119 + x120 * x52) + x117 * x14 * (x58 + x60)) ) result[0, 0, 9] = numpy.sum( x76 * (x0 * x124 + x0 * (x124 + x125 * x52) + x122 * x14 * (x58 + x60)) ) result[0, 0, 10] = numpy.sum( x65 * (x0 * x129 + x0 * (x126 * x52 + x129) + x128 * x57) ) result[0, 0, 11] = numpy.sum( x76 * (x0 * x132 + x0 * (x10 * x110 + x132) + x131 * x57) ) result[0, 0, 12] = numpy.sum( x90 * (x0 * x135 + x0 * (x134 * x52 + x135) + x134 * x136) ) result[0, 0, 13] = numpy.sum( x76 * (x0 * x138 + x0 * (x137 * x52 + x138) + x136 * x137) ) result[0, 0, 14] = numpy.sum( x65 * (x0 * x141 + x0 * (x139 * x52 + x141) + x140 * x57) ) result[0, 1, 0] = numpy.sum( x154 * ( x0 * x147 + x14 * (x148 * x153 + x36 * (x148 * x152 + x36**2 * (2.0 * x148 + x151))) + x19 * x48 ) ) result[0, 1, 1] = numpy.sum( x168 * ( x0 * x160 + x14 * (x166 * x167 + x36 * (x165 * x166 + x36 * (x162 + x164 * x36))) + x19 * x73 ) ) result[0, 1, 2] = numpy.sum( x168 * ( x0 * x171 + x14 * (x167 * x173 + x36 * (x165 * x173 + x36 * (x151 * x77 + x172))) + x19 * x81 ) ) result[0, 1, 3] = numpy.sum( x98 * (x0 * x176 + x14 * (x174 * x179 + x36 * (x177 + x178 * x36)) + x19 * x87) ) result[0, 1, 4] = numpy.sum( x186 * (x0 * x182 + x14 * (x179 * x180 + x36 * (x183 + x185 * x36)) + x19 * x96) ) result[0, 1, 5] = numpy.sum( x98 * ( x0 * x189 + x103 * x19 + x14 * (x102 * x106 * x148 + x36 * (x151 * x99 + x190)) ) ) result[0, 1, 6] = numpy.sum( x168 * (x0 * x194 + x109 * x19 + x14 * (x195 + x196 * x36)) ) result[0, 1, 7] = numpy.sum( x186 * (x0 * x199 + x114 * x19 + x14 * (x200 + x201 * x36)) ) result[0, 1, 8] = numpy.sum( x186 * (x0 * x204 + x119 * x19 + x14 * (x205 + x207 * x36)) ) result[0, 1, 9] = numpy.sum( x168 * (x0 * x209 + x124 * x19 + x14 * (x122 * x151 + x210)) ) result[0, 1, 10] = numpy.sum( x154 * (x0 * x212 + x129 * x19 + x14 * (x107 * x59 + x196 * x66)) ) result[0, 1, 11] = numpy.sum( x168 * (x0 * x214 + x132 * x19 + x14 * (x112 * x59 + x201 * x66)) ) result[0, 1, 12] = numpy.sum( x98 * (x0 * x216 + x135 * x19 + x14 * (x117 * x59 + x207 * x66)) ) result[0, 1, 13] = numpy.sum( x168 * (x0 * x218 + x138 * x19 + x14 * (x122 * x163 + x219)) ) result[0, 1, 14] = numpy.sum(x154 * (x0 * x221 + x140 * x150 + x141 * x19)) result[0, 2, 0] = numpy.sum( x154 * ( x0 * x226 + x14 * (x153 * x227 + x36 * (x152 * x227 + x36**2 * (2.0 * x227 + x230))) + x20 * x48 ) ) result[0, 2, 1] = numpy.sum( x168 * ( x0 * x234 + x14 * (x167 * x227 * x7 + x36 * (x227 * x236 + x36 * (x230 * x66 + x235))) + x20 * x73 ) ) result[0, 2, 2] = numpy.sum( x168 * ( x0 * x239 + x14 * (x167 * x242 + x36 * (x179 * x237 + x36 * (x240 + x241 * x36))) + x20 * x81 ) ) result[0, 2, 3] = numpy.sum( x98 * (x0 * x246 + x14 * (x227 * x248 + x36 * (x230 * x83 + x247)) + x20 * x87) ) result[0, 2, 4] = numpy.sum( x186 * (x0 * x251 + x14 * (x242 * x253 + x36 * (x236 * x241 + x252)) + x20 * x96) ) result[0, 2, 5] = numpy.sum( x98 * (x0 * x256 + x103 * x20 + x14 * (x179 * x254 + x36 * (x257 + x258 * x36))) ) result[0, 2, 6] = numpy.sum( x168 * (x0 * x262 + x109 * x20 + x14 * (x107 * x230 + x263)) ) result[0, 2, 7] = numpy.sum( x186 * (x0 * x266 + x114 * x20 + x14 * (x241 * x248 + x267)) ) result[0, 2, 8] = numpy.sum( x186 * (x0 * x269 + x119 * x20 + x14 * (x236 * x258 + x270)) ) result[0, 2, 9] = numpy.sum( x168 * (x0 * x273 + x124 * x20 + x14 * (x274 + x275 * x36)) ) result[0, 2, 10] = numpy.sum(x154 * (x0 * x277 + x128 * x229 + x129 * x20)) result[0, 2, 11] = numpy.sum(x168 * (x0 * x279 + x130 * x241 + x132 * x20)) result[0, 2, 12] = numpy.sum(x98 * (x0 * x281 + x111 * x258 + x135 * x20)) result[0, 2, 13] = numpy.sum(x168 * (x0 * x283 + x138 * x20 + x275 * x91)) result[0, 2, 14] = numpy.sum( x154 * (x0 * x285 + x14 * (x219 + x275 * x77) + x141 * x20) ) result[0, 3, 0] = numpy.sum(x65 * (x144 * x287 + x145 * x19 + x147 * x19)) result[0, 3, 1] = numpy.sum(x76 * (x157 * x290 + x158 * x19 + x160 * x19)) result[0, 3, 2] = numpy.sum(x76 * (x169 * x287 + x170 * x19 + x171 * x19)) result[0, 3, 3] = numpy.sum(x90 * (x167 * x291 + x175 * x19 + x176 * x19)) result[0, 3, 4] = numpy.sum(x98 * (x167 * x292 + x181 * x19 + x182 * x19)) result[0, 3, 5] = numpy.sum(x90 * (x104 * x293 + x188 * x19 + x189 * x19)) result[0, 3, 6] = numpy.sum(x76 * (x165 * x294 + x19 * x192 + x19 * x194)) result[0, 3, 7] = numpy.sum(x98 * (x165 * x295 + x19 * x198 + x19 * x199)) result[0, 3, 8] = numpy.sum(x98 * (x165 * x296 + x19 * x203 + x19 * x204)) result[0, 3, 9] = numpy.sum(x76 * (x125 * x293 + x19 * x208 + x19 * x209)) result[0, 3, 10] = numpy.sum( x65 * (x14 * (2.0 * x195 + x294 * x66) + x19 * x211 + x19 * x212) ) result[0, 3, 11] = numpy.sum( x76 * (x14 * (2.0 * x200 + x295 * x66) + x19 * x213 + x19 * x214) ) result[0, 3, 12] = numpy.sum( x90 * (x14 * (2.0 * x205 + x296 * x66) + x19 * x215 + x19 * x216) ) result[0, 3, 13] = numpy.sum( x76 * (x122 * x14 * (x288 + x289) + x19 * x217 + x19 * x218) ) result[0, 3, 14] = numpy.sum(x65 * (x140 * x287 + x19 * x220 + x19 * x221)) result[0, 4, 0] = numpy.sum(x154 * (x144 * x297 + x145 * x20 + x19 * x226)) result[0, 4, 1] = numpy.sum(x168 * (x157 * x298 + x158 * x20 + x19 * x234)) result[0, 4, 2] = numpy.sum(x168 * (x157 * x299 + x170 * x20 + x19 * x239)) result[0, 4, 3] = numpy.sum(x98 * (x167 * x300 + x175 * x20 + x19 * x246)) result[0, 4, 4] = numpy.sum(x186 * (x167 * x301 + x181 * x20 + x19 * x251)) result[0, 4, 5] = numpy.sum(x98 * (x167 * x302 + x188 * x20 + x19 * x256)) result[0, 4, 6] = numpy.sum(x168 * (x165 * x303 + x19 * x262 + x192 * x20)) result[0, 4, 7] = numpy.sum(x186 * (x165 * x304 + x19 * x266 + x198 * x20)) result[0, 4, 8] = numpy.sum(x186 * (x165 * x305 + x19 * x269 + x20 * x203)) result[0, 4, 9] = numpy.sum(x168 * (x165 * x306 + x19 * x273 + x20 * x208)) result[0, 4, 10] = numpy.sum( x154 * (x14 * (x263 + x303 * x66) + x19 * x277 + x20 * x211) ) result[0, 4, 11] = numpy.sum( x168 * (x14 * (x267 + x304 * x66) + x19 * x279 + x20 * x213) ) result[0, 4, 12] = numpy.sum( x98 * (x14 * (x270 + x305 * x66) + x19 * x281 + x20 * x215) ) result[0, 4, 13] = numpy.sum( x168 * (x14 * (x274 + x306 * x66) + x19 * x283 + x20 * x217) ) result[0, 4, 14] = numpy.sum( x154 * (x14 * (x210 + x306 * x77) + x19 * x285 + x20 * x220) ) result[0, 5, 0] = numpy.sum(x65 * (x144 * x307 + x20 * x224 + x20 * x226)) result[0, 5, 1] = numpy.sum(x76 * (x20 * x232 + x20 * x234 + x231 * x307)) result[0, 5, 2] = numpy.sum(x76 * (x157 * x308 + x20 * x238 + x20 * x239)) result[0, 5, 3] = numpy.sum(x90 * (x20 * x245 + x20 * x246 + x244 * x307)) result[0, 5, 4] = numpy.sum(x98 * (x20 * x250 + x20 * x251 + x249 * x308)) result[0, 5, 5] = numpy.sum(x90 * (x167 * x309 + x20 * x255 + x20 * x256)) result[0, 5, 6] = numpy.sum(x76 * (x20 * x260 + x20 * x262 + x259 * x307)) result[0, 5, 7] = numpy.sum(x98 * (x20 * x265 + x20 * x266 + x264 * x308)) result[0, 5, 8] = numpy.sum(x98 * (x20 * x268 + x20 * x269 + x253 * x309)) result[0, 5, 9] = numpy.sum(x76 * (x165 * x310 + x20 * x272 + x20 * x273)) result[0, 5, 10] = numpy.sum(x65 * (x128 * x307 + x20 * x276 + x20 * x277)) result[0, 5, 11] = numpy.sum(x76 * (x130 * x308 + x20 * x278 + x20 * x279)) result[0, 5, 12] = numpy.sum(x90 * (x111 * x309 + x20 * x280 + x20 * x281)) result[0, 5, 13] = numpy.sum(x76 * (x20 * x282 + x20 * x283 + x310 * x91)) result[0, 5, 14] = numpy.sum( x65 * (x14 * (2.0 * x274 + x310 * x77) + x20 * x284 + x20 * x285) ) return result
[docs] def int3c2e3d_sph_030(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sf|s) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 10, 1), dtype=float) x0 = A[0] - B[0] x1 = 0.5 / (ax + bx) x2 = ax + bx x3 = x2 ** (-1.0) x4 = -x3 * (ax * A[0] + bx * B[0]) x5 = -x4 - C[0] x6 = -x3 * (ax * A[1] + bx * B[1]) x7 = -x6 - C[1] x8 = -x3 * (ax * A[2] + bx * B[2]) x9 = -x8 - C[2] x10 = cx + x2 x11 = cx / x10 x12 = x11 * x2 * (x5**2 + x7**2 + x9**2) x13 = boys(1, x12) x14 = 17.49341832762486 x15 = A[1] - B[1] x16 = A[2] - B[2] x17 = numpy.exp(-ax * bx * x3 * (x0**2 + x15**2 + x16**2)) x18 = 2.0 * x14 * x17 * x3 x19 = x10 ** (-1.5) * x18 x20 = x13 * x19 x21 = cx ** (-1.0) x22 = x10 ** (-0.5) x23 = boys(0, x12) x24 = x1 * (2.0 * x14 * x17 * x21 * x22 * x23 * x3 - x20) x25 = -x4 - A[0] x26 = x20 * x5 x27 = -2.0 * x14 * x17 * x21 * x22 * x23 * x25 * x3 + x26 x28 = -x27 x29 = boys(2, x12) x30 = x19 * x29 x31 = 2.0 * x13 * x14 * x17 * x21 * x22 * x25 * x3 - x30 * x5 x32 = x11 * x31 x33 = x24 + x25 * x28 - x32 * x5 x34 = x0 * x28 + x33 x35 = x18 * x21 * x22 * x23 x36 = x1 * (2.0 * x13 * x14 * x17 * x21 * x22 * x3 - x30) x37 = x19 * boys(3, x12) x38 = x11 * x5 x39 = da * db * dc x40 = 0.2581988897471611 * x39 x41 = -x6 - A[1] x42 = 2.0 * x13 * x14 * x17 * x21 * x22 * x3 * x41 - x30 * x7 x43 = x11 * x42 x44 = x20 * x7 x45 = -2.0 * x14 * x17 * x21 * x22 * x23 * x3 * x41 + x44 x46 = -x1 * (x43 + x45) x47 = -x45 x48 = x43 * x5 x49 = x15 * x28 + x25 * x47 - x48 x50 = x15 * x35 + x35 * x41 - x44 x51 = x25 * x47 - x48 x52 = 2.0 * x14 * x17 * x21 * x22 * x29 * x3 * x41 - x37 * x7 x53 = 0.5773502691896258 * x39 x54 = -x8 - A[2] x55 = 2.0 * x13 * x14 * x17 * x21 * x22 * x3 * x54 - x30 * x9 x56 = x11 * x55 x57 = x20 * x9 x58 = -2.0 * x14 * x17 * x21 * x22 * x23 * x3 * x54 + x57 x59 = -x1 * (x56 + x58) x60 = -x58 x61 = x5 * x56 x62 = x16 * x28 + x25 * x60 - x61 x63 = x16 * x35 + x35 * x54 - x57 x64 = x25 * x60 - x61 x65 = 2.0 * x14 * x17 * x21 * x22 * x29 * x3 * x54 - x37 * x9 x66 = x24 + x41 * x47 - x43 * x7 x67 = x15 * x47 + x66 x68 = x15 * x50 + x67 x69 = x11 * x7 x70 = x36 + x41 * x42 - x52 * x69 x71 = x56 * x7 x72 = x16 * x47 + x41 * x60 - x71 x73 = x15 * x63 + x72 x74 = x41 * x60 - x71 x75 = x41 * x55 - x65 * x69 x76 = x24 + x54 * x60 - x56 * x9 x77 = x16 * x60 + x76 x78 = x16 * x63 + x77 x79 = x11 * x9 x80 = x36 + x54 * x55 - x65 * x79 # 10 item(s) result[0, 0, 0] = numpy.sum( x40 * ( x0 * x33 + x0 * x34 + x0 * (x0 * (x0 * x35 + x25 * x35 - x26) + x34) - 2.0 * x1 * (x27 + x32) + x25 * x33 - x38 * ( x25 * x31 + x36 - x38 * (2.0 * x14 * x17 * x21 * x22 * x25 * x29 * x3 - x37 * x5) ) ) ) result[0, 1, 0] = numpy.sum( x53 * ( x0 * x49 + x0 * (x0 * x50 + x49) + x15 * x33 + x25 * x51 - x38 * (x25 * x42 - x38 * x52) + x46 ) ) result[0, 2, 0] = numpy.sum( x53 * ( x0 * x62 + x0 * (x0 * x63 + x62) + x16 * x33 + x25 * x64 - x38 * (x25 * x55 - x38 * x65) + x59 ) ) result[0, 3, 0] = numpy.sum( x53 * (x0 * x68 + x15 * x49 + x15 * x51 + x25 * x66 - x38 * x70) ) result[0, 4, 0] = numpy.sum( x39 * (x0 * x73 + x15 * x62 + x16 * x51 + x25 * x74 - x38 * x75) ) result[0, 5, 0] = numpy.sum( x53 * (x0 * x78 + x16 * x62 + x16 * x64 + x25 * x76 - x38 * x80) ) result[0, 6, 0] = numpy.sum( x40 * (x15 * x66 + x15 * x67 + x15 * x68 + x41 * x66 + 2.0 * x46 - x69 * x70) ) result[0, 7, 0] = numpy.sum( x53 * (x15 * x72 + x15 * x73 + x16 * x66 + x41 * x74 + x59 - x69 * x75) ) result[0, 8, 0] = numpy.sum( x53 * (x15 * x78 + x16 * x72 + x16 * x74 + x41 * x76 - x69 * x80) ) result[0, 9, 0] = numpy.sum( x40 * (x16 * x76 + x16 * x77 + x16 * x78 + x54 * x76 + 2.0 * x59 - x79 * x80) ) return result
[docs] def int3c2e3d_sph_031(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sf|p) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 10, 3), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - C[0] x5 = 0.5 / (ax + bx) x6 = -x2 * (ax * A[1] + bx * B[1]) x7 = -x6 - C[1] x8 = -x2 * (ax * A[2] + bx * B[2]) x9 = -x8 - C[2] x10 = cx + x1 x11 = x10 ** (-1.0) x12 = x1 * x11 x13 = cx * x12 * (x4**2 + x7**2 + x9**2) x14 = boys(2, x13) x15 = x10 ** (-1.5) x16 = 17.49341832762486 x17 = A[1] - B[1] x18 = A[2] - B[2] x19 = numpy.exp(-ax * bx * x2 * (x0**2 + x17**2 + x18**2)) x20 = x16 * x19 * x2 x21 = 2.0 * x15 * x20 x22 = x14 * x21 x23 = cx ** (-1.0) x24 = x10 ** (-0.5) x25 = boys(1, x13) x26 = x5 * (2.0 * x16 * x19 * x2 * x23 * x24 * x25 - x22) x27 = -x3 - A[0] x28 = -2.0 * x16 * x19 * x2 * x23 * x24 * x25 * x27 + x22 * x4 x29 = -x28 x30 = boys(3, x13) x31 = x21 * x30 x32 = 2.0 * x14 * x16 * x19 * x2 * x23 * x24 * x27 - x31 * x4 x33 = cx * x11 x34 = x32 * x33 x35 = x26 + x27 * x29 - x34 * x4 x36 = x29 * x5 x37 = x12 * (x35 * x4 + 2.0 * x36) x38 = 2.0 * x5 x39 = x23 * x25 x40 = x20 * x24 * x38 * x39 x41 = x12 * (x29 * x4 + x40) x42 = x0 * x41 + x37 x43 = 2.0 * x15 * x16 * x19 * x39 x44 = x0 * x43 x45 = x5 * (2.0 * x14 * x16 * x19 * x2 * x23 * x24 - x31) x46 = x21 * boys(4, x13) x47 = x33 * x4 x48 = ( x27 * x35 - x38 * (x28 + x34) - x47 * ( x27 * x32 + x45 - x47 * (2.0 * x16 * x19 * x2 * x23 * x24 * x27 * x30 - x4 * x46) ) ) x49 = x35 * x5 x50 = da * db * dc x51 = 0.2581988897471611 * x50 x52 = x12 * x7 x53 = x35 * x52 x54 = x29 * x52 x55 = x0 * x54 + x53 x56 = x12 * x9 x57 = x35 * x56 x58 = x29 * x56 x59 = x0 * x58 + x57 x60 = -x6 - A[1] x61 = -2.0 * x16 * x19 * x2 * x23 * x24 * x25 * x60 + x22 * x7 x62 = -x61 x63 = x5 * x62 x64 = 2.0 * x14 * x16 * x19 * x2 * x23 * x24 * x60 - x31 * x7 x65 = x33 * x64 x66 = x27 * x62 - x4 * x65 x67 = x12 * (x4 * x66 + x63) x68 = x17 * x41 + x67 x69 = x12 * x4 x70 = x62 * x69 x71 = x17 * x43 x72 = x4 * x71 + x70 x73 = -x5 * (x61 + x65) x74 = 2.0 * x16 * x19 * x2 * x23 * x24 * x30 * x60 - x46 * x7 x75 = x27 * x66 - x47 * (x27 * x64 - x47 * x74) + x73 x76 = x5 * x66 x77 = 2.0 * x76 x78 = 0.5773502691896258 * x50 x79 = x12 * (x36 + x66 * x7) x80 = x17 * x54 + x79 x81 = x12 * (x40 + x62 * x7) x82 = x7 * x71 + x81 x83 = x56 * x66 x84 = x17 * x58 + x83 x85 = x56 * x62 x86 = x71 * x9 + x85 x87 = -x8 - A[2] x88 = -2.0 * x16 * x19 * x2 * x23 * x24 * x25 * x87 + x22 * x9 x89 = -x88 x90 = x5 * x89 x91 = 2.0 * x14 * x16 * x19 * x2 * x23 * x24 * x87 - x31 * x9 x92 = x33 * x91 x93 = x27 * x89 - x4 * x92 x94 = x12 * (x4 * x93 + x90) x95 = x18 * x41 + x94 x96 = x69 * x89 x97 = x18 * x43 x98 = x4 * x97 + x96 x99 = -x5 * (x88 + x92) x100 = 2.0 * x16 * x19 * x2 * x23 * x24 * x30 * x87 - x46 * x9 x101 = x27 * x93 + x47 * (x100 * x47 - x27 * x91) + x99 x102 = x5 * x93 x103 = 2.0 * x102 x104 = x52 * x93 x105 = x104 + x18 * x54 x106 = x52 * x89 x107 = x106 + x7 * x97 x108 = x12 * (x36 + x9 * x93) x109 = x108 + x18 * x58 x110 = x12 * (x40 + x89 * x9) x111 = x110 + x9 * x97 x112 = x26 + x60 * x62 - x65 * x7 x113 = x112 * x69 x114 = x113 + x17 * x70 x115 = x114 + x17 * x72 x116 = x112 * x5 x117 = x33 * x7 x118 = -x117 * x74 + x45 + x60 * x64 x119 = x112 * x27 - x118 * x47 x120 = x12 * (x112 * x7 + 2.0 * x63) x121 = x120 + x17 * x81 x122 = x121 + x17 * x82 x123 = x112 * x56 x124 = x123 + x17 * x85 x125 = x124 + x17 * x86 x126 = x60 * x89 - x7 * x92 x127 = x126 * x69 x128 = x127 + x18 * x70 x129 = x128 + x17 * x98 x130 = x126 * x5 x131 = -x100 * x117 + x60 * x91 x132 = x126 * x27 - x131 * x47 x133 = x12 * (x126 * x7 + x90) x134 = x133 + x18 * x81 x135 = x107 * x17 + x134 x136 = x12 * (x126 * x9 + x63) x137 = x136 + x18 * x85 x138 = x111 * x17 + x137 x139 = x26 + x87 * x89 - x9 * x92 x140 = x139 * x69 x141 = x140 + x18 * x96 x142 = x141 + x18 * x98 x143 = x139 * x5 x144 = x33 * x9 x145 = -x100 * x144 + x45 + x87 * x91 x146 = x139 * x27 - x145 * x47 x147 = x139 * x52 x148 = x106 * x18 + x147 x149 = x107 * x18 + x148 x150 = x12 * (x139 * x9 + 2.0 * x90) x151 = x110 * x18 + x150 x152 = x111 * x18 + x151 x153 = x112 * x60 - x117 * x118 + 2.0 * x73 x154 = -x117 * x131 + x126 * x60 + x99 x155 = 2.0 * x130 x156 = -x117 * x145 + x139 * x60 x157 = x139 * x87 - x144 * x145 + 2.0 * x99 # 30 item(s) result[0, 0, 0] = numpy.sum( x51 * ( x0 * x37 + x0 * x42 + x0 * (x0 * (x4 * x44 + x41) + x42) + x12 * (x4 * x48 + 3.0 * x49) ) ) result[0, 0, 1] = numpy.sum( x51 * (x0 * x53 + x0 * x55 + x0 * (x0 * (x44 * x7 + x54) + x55) + x48 * x52) ) result[0, 0, 2] = numpy.sum( x51 * (x0 * x57 + x0 * x59 + x0 * (x0 * (x44 * x9 + x58) + x59) + x48 * x56) ) result[0, 1, 0] = numpy.sum( x78 * (x0 * x68 + x0 * (x0 * x72 + x68) + x12 * (x4 * x75 + x77) + x17 * x37) ) result[0, 1, 1] = numpy.sum( x78 * (x0 * x80 + x0 * (x0 * x82 + x80) + x12 * (x49 + x7 * x75) + x17 * x53) ) result[0, 1, 2] = numpy.sum( x78 * (x0 * x84 + x0 * (x0 * x86 + x84) + x17 * x57 + x56 * x75) ) result[0, 2, 0] = numpy.sum( x78 * (x0 * x95 + x0 * (x0 * x98 + x95) + x12 * (x101 * x4 + x103) + x18 * x37) ) result[0, 2, 1] = numpy.sum( x78 * (x0 * x105 + x0 * (x0 * x107 + x105) + x101 * x52 + x18 * x53) ) result[0, 2, 2] = numpy.sum( x78 * (x0 * x109 + x0 * (x0 * x111 + x109) + x12 * (x101 * x9 + x49) + x18 * x57) ) result[0, 3, 0] = numpy.sum( x78 * (x0 * x115 + x12 * (x116 + x119 * x4) + x17 * x67 + x17 * x68) ) result[0, 3, 1] = numpy.sum( x78 * (x0 * x122 + x12 * (x119 * x7 + x77) + x17 * x79 + x17 * x80) ) result[0, 3, 2] = numpy.sum(x78 * (x0 * x125 + x119 * x56 + x17 * x83 + x17 * x84)) result[0, 4, 0] = numpy.sum( x50 * (x0 * x129 + x12 * (x130 + x132 * x4) + x17 * x95 + x18 * x67) ) result[0, 4, 1] = numpy.sum( x50 * (x0 * x135 + x105 * x17 + x12 * (x102 + x132 * x7) + x18 * x79) ) result[0, 4, 2] = numpy.sum( x50 * (x0 * x138 + x109 * x17 + x12 * (x132 * x9 + x76) + x18 * x83) ) result[0, 5, 0] = numpy.sum( x78 * (x0 * x142 + x12 * (x143 + x146 * x4) + x18 * x94 + x18 * x95) ) result[0, 5, 1] = numpy.sum(x78 * (x0 * x149 + x104 * x18 + x105 * x18 + x146 * x52)) result[0, 5, 2] = numpy.sum( x78 * (x0 * x152 + x108 * x18 + x109 * x18 + x12 * (x103 + x146 * x9)) ) result[0, 6, 0] = numpy.sum(x51 * (x113 * x17 + x114 * x17 + x115 * x17 + x153 * x69)) result[0, 6, 1] = numpy.sum( x51 * (x12 * (3.0 * x116 + x153 * x7) + x120 * x17 + x121 * x17 + x122 * x17) ) result[0, 6, 2] = numpy.sum(x51 * (x123 * x17 + x124 * x17 + x125 * x17 + x153 * x56)) result[0, 7, 0] = numpy.sum(x78 * (x113 * x18 + x128 * x17 + x129 * x17 + x154 * x69)) result[0, 7, 1] = numpy.sum( x78 * (x12 * (x154 * x7 + x155) + x120 * x18 + x134 * x17 + x135 * x17) ) result[0, 7, 2] = numpy.sum( x78 * (x12 * (x116 + x154 * x9) + x123 * x18 + x137 * x17 + x138 * x17) ) result[0, 8, 0] = numpy.sum(x78 * (x127 * x18 + x128 * x18 + x142 * x17 + x156 * x69)) result[0, 8, 1] = numpy.sum( x78 * (x12 * (x143 + x156 * x7) + x133 * x18 + x134 * x18 + x149 * x17) ) result[0, 8, 2] = numpy.sum( x78 * (x12 * (x155 + x156 * x9) + x136 * x18 + x137 * x18 + x152 * x17) ) result[0, 9, 0] = numpy.sum(x51 * (x140 * x18 + x141 * x18 + x142 * x18 + x157 * x69)) result[0, 9, 1] = numpy.sum(x51 * (x147 * x18 + x148 * x18 + x149 * x18 + x157 * x52)) result[0, 9, 2] = numpy.sum( x51 * (x12 * (3.0 * x143 + x157 * x9) + x150 * x18 + x151 * x18 + x152 * x18) ) return result
[docs] def int3c2e3d_sph_032(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sf|d) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 10, 6), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - C[0] x5 = 0.5 / (ax + bx) x6 = x4**2 x7 = -x2 * (ax * A[1] + bx * B[1]) x8 = -x7 - C[1] x9 = x8**2 x10 = -x2 * (ax * A[2] + bx * B[2]) x11 = -x10 - C[2] x12 = x11**2 x13 = cx + x1 x14 = x13 ** (-1.0) x15 = x1 * x14 x16 = cx * x15 * (x12 + x6 + x9) x17 = boys(3, x16) x18 = x13 ** (-1.5) x19 = 17.49341832762486 x20 = A[1] - B[1] x21 = A[2] - B[2] x22 = numpy.exp(-ax * bx * x2 * (x0**2 + x20**2 + x21**2)) x23 = x19 * x2 * x22 x24 = 2.0 * x18 * x23 x25 = x17 * x24 x26 = cx ** (-1.0) x27 = x13 ** (-0.5) x28 = boys(2, x16) x29 = x5 * (2.0 * x19 * x2 * x22 * x26 * x27 * x28 - x25) x30 = -x3 - A[0] x31 = -2.0 * x19 * x2 * x22 * x26 * x27 * x28 * x30 + x25 * x4 x32 = -x31 x33 = boys(4, x16) x34 = x24 * x33 x35 = 2.0 * x17 * x19 * x2 * x22 * x26 * x27 * x30 - x34 * x4 x36 = cx * x14 x37 = x35 * x36 x38 = x29 + x30 * x32 - x37 * x4 x39 = x38 * x4 x40 = x32 * x5 x41 = 2.0 * x40 x42 = x39 + x41 x43 = x15 * x4 x44 = x32 * x4 x45 = 2.0 * x5 x46 = x26 * x28 x47 = x45 * x46 x48 = x23 * x27 * x47 x49 = x44 + x48 x50 = x15 * x45 x51 = x15 * (x42 * x43 + x49 * x50) x52 = x19 * x22 x53 = x4 * x52 x54 = x18 * x47 x55 = x15 * (x43 * x49 + x53 * x54) x56 = x0 * x55 + x51 x57 = 2.0 * x1 * x13 ** (-2.5) * x46 x58 = x52 * x57 x59 = x0 * x58 x60 = x5 * (2.0 * x17 * x19 * x2 * x22 * x26 * x27 - x34) x61 = x24 * boys(5, x16) x62 = x36 * x4 x63 = ( x30 * x38 - x45 * (x31 + x37) - x62 * ( x30 * x35 + x60 - x62 * (2.0 * x19 * x2 * x22 * x26 * x27 * x30 * x33 - x4 * x61) ) ) x64 = x4 * x63 x65 = x38 * x5 x66 = 3.0 * x65 x67 = x15 * x5 x68 = da * db * dc x69 = 0.06666666666666667 * x68 x70 = 2.23606797749979 * x69 x71 = x15 * x8 x72 = x15 * x71 * (x39 + x41) x73 = x52 * x54 x74 = x73 * x8 x75 = x15 * (x44 * x71 + x74) x76 = x0 * x75 + x72 x77 = x53 * x57 x78 = x0 * x77 x79 = 3.872983346207417 * x69 x80 = x11 * x15 x81 = x15 * x80 * (x39 + x41) x82 = x11 * x73 x83 = x15 * (x44 * x80 + x82) x84 = x0 * x83 + x81 x85 = x1**2 / x13**2 x86 = x85 * x9 x87 = x38 * x86 x88 = x32 * x86 x89 = x0 * x88 + x87 x90 = x8 * x85 x91 = x11 * x90 x92 = x38 * x91 x93 = x32 * x91 x94 = x0 * x93 + x92 x95 = x11 * x8 x96 = x12 * x85 x97 = x38 * x96 x98 = x32 * x96 x99 = x0 * x98 + x97 x100 = -x7 - A[1] x101 = -2.0 * x100 * x19 * x2 * x22 * x26 * x27 * x28 + x25 * x8 x102 = -x101 x103 = x102 * x5 x104 = 2.0 * x100 * x17 * x19 * x2 * x22 * x26 * x27 - x34 * x8 x105 = x104 * x36 x106 = x102 * x30 - x105 * x4 x107 = x106 * x4 x108 = x103 + x107 x109 = x15 * x43 * (x103 + x108) x110 = x109 + x20 * x55 x111 = x6 * x85 x112 = x102 * x111 x113 = x20 * x58 x114 = x112 + x113 * x6 x115 = -x5 * (x101 + x105) x116 = 2.0 * x100 * x19 * x2 * x22 * x26 * x27 * x33 - x61 * x8 x117 = x106 * x30 + x115 - x62 * (x104 * x30 - x116 * x62) x118 = x117 * x4 x119 = x106 * x5 x120 = 2.0 * x119 x121 = 0.3333333333333333 * x68 x122 = x102 * x8 x123 = x122 + x48 x124 = x123 * x15 x125 = x106 * x8 x126 = x125 + x40 x127 = x15 * (x124 * x5 + x126 * x43) x128 = x127 + x20 * x75 x129 = x4 * x85 x130 = x123 * x129 x131 = x20 * x77 x132 = x130 + x131 * x8 x133 = x117 * x8 x134 = x133 + x65 x135 = x126 * x50 x136 = 1.732050807568877 * x121 x137 = x103 * x80 x138 = x15 * (x107 * x80 + x137) x139 = x138 + x20 * x83 x140 = x11 * x129 x141 = x102 * x140 x142 = x11 * x131 + x141 x143 = x120 * x80 x144 = x15 * x71 * (x126 + x40) x145 = x144 + x20 * x88 x146 = x15 * (x124 * x8 + x74) x147 = x113 * x9 + x146 x148 = x40 * x80 x149 = x15 * (x125 * x80 + x148) x150 = x149 + x20 * x93 x151 = x15 * (x122 * x80 + x82) x152 = x113 * x95 + x151 x153 = x65 * x80 x154 = x106 * x96 x155 = x154 + x20 * x98 x156 = x102 * x96 x157 = x113 * x12 + x156 x158 = -x10 - A[2] x159 = x11 * x25 - 2.0 * x158 * x19 * x2 * x22 * x26 * x27 * x28 x160 = -x159 x161 = x160 * x5 x162 = -x11 * x34 + 2.0 * x158 * x17 * x19 * x2 * x22 * x26 * x27 x163 = x162 * x36 x164 = x160 * x30 - x163 * x4 x165 = x164 * x4 x166 = x161 + x165 x167 = x15 * x43 * (x161 + x166) x168 = x167 + x21 * x55 x169 = x111 * x160 x170 = x21 * x58 x171 = x169 + x170 * x6 x172 = -x5 * (x159 + x163) x173 = -x11 * x61 + 2.0 * x158 * x19 * x2 * x22 * x26 * x27 * x33 x174 = x164 * x30 + x172 - x62 * (x162 * x30 - x173 * x62) x175 = x174 * x4 x176 = x164 * x5 x177 = 2.0 * x176 x178 = x161 * x71 x179 = x15 * (x165 * x71 + x178) x180 = x179 + x21 * x75 x181 = x129 * x8 x182 = x160 * x181 x183 = x21 * x77 x184 = x182 + x183 * x8 x185 = x11 * x160 + x48 x186 = x15 * x185 x187 = x186 * x5 x188 = x11 * x164 + x40 x189 = x15 * (x187 + x188 * x43) x190 = x189 + x21 * x83 x191 = x129 * x185 x192 = x11 * x183 + x191 x193 = x11 * x174 + x65 x194 = x188 * x50 x195 = x164 * x86 x196 = x195 + x21 * x88 x197 = x160 * x86 x198 = x170 * x9 + x197 x199 = x188 * x90 x200 = x199 + x21 * x93 x201 = x185 * x90 x202 = x170 * x95 + x201 x203 = x15 * (x148 + x188 * x80) x204 = x203 + x21 * x98 x205 = x15 * (x11 * x186 + x82) x206 = x12 * x170 + x205 x207 = x100 * x102 - x105 * x8 + x29 x208 = x111 * x207 x209 = x112 * x20 + x208 x210 = x114 * x20 + x209 x211 = x207 * x5 x212 = x36 * x8 x213 = x100 * x104 - x116 * x212 + x60 x214 = x207 * x30 - x213 * x62 x215 = x214 * x4 x216 = x207 * x8 x217 = 2.0 * x103 x218 = x216 + x217 x219 = x129 * x218 x220 = x130 * x20 + x219 x221 = x132 * x20 + x220 x222 = x218 * x67 x223 = x214 * x8 x224 = x120 + x223 x225 = x140 * x207 x226 = x141 * x20 + x225 x227 = x142 * x20 + x226 x228 = x211 * x80 x229 = x15 * (x124 * x45 + x218 * x71) x230 = x146 * x20 + x229 x231 = x147 * x20 + x230 x232 = x15 * x80 * (x216 + x217) x233 = x151 * x20 + x232 x234 = x152 * x20 + x233 x235 = x207 * x96 x236 = x156 * x20 + x235 x237 = x157 * x20 + x236 x238 = x100 * x160 - x163 * x8 x239 = x111 * x238 x240 = x112 * x21 + x239 x241 = x171 * x20 + x240 x242 = x238 * x5 x243 = x100 * x162 - x173 * x212 x244 = x238 * x30 - x243 * x62 x245 = x161 + x238 * x8 x246 = x129 * x245 x247 = x130 * x21 + x246 x248 = x184 * x20 + x247 x249 = x176 + x244 * x8 x250 = x103 + x11 * x238 x251 = x129 * x250 x252 = x141 * x21 + x251 x253 = x192 * x20 + x252 x254 = x11 * x244 + x119 x255 = x15 * (x178 + x245 * x71) x256 = x146 * x21 + x255 x257 = x198 * x20 + x256 x258 = x15 * (x187 + x250 * x71) x259 = x151 * x21 + x258 x260 = x20 * x202 + x259 x261 = x15 * (x137 + x250 * x80) x262 = x156 * x21 + x261 x263 = x20 * x206 + x262 x264 = -x11 * x163 + x158 * x160 + x29 x265 = x111 * x264 x266 = x169 * x21 + x265 x267 = x171 * x21 + x266 x268 = x264 * x5 x269 = x11 * x36 x270 = x158 * x162 - x173 * x269 + x60 x271 = x264 * x30 - x270 * x62 x272 = x271 * x4 x273 = x181 * x264 x274 = x182 * x21 + x273 x275 = x184 * x21 + x274 x276 = x268 * x71 x277 = x11 * x264 + 2.0 * x161 x278 = x129 * x277 x279 = x191 * x21 + x278 x280 = x192 * x21 + x279 x281 = x277 * x67 x282 = x11 * x271 + x177 x283 = x264 * x86 x284 = x197 * x21 + x283 x285 = x198 * x21 + x284 x286 = x277 * x90 x287 = x201 * x21 + x286 x288 = x202 * x21 + x287 x289 = x15 * (x186 * x45 + x277 * x80) x290 = x205 * x21 + x289 x291 = x206 * x21 + x290 x292 = x100 * x207 + 2.0 * x115 - x212 * x213 x293 = x292 * x8 x294 = 3.0 * x211 x295 = x293 + x294 x296 = x100 * x238 + x172 - x212 * x243 x297 = 2.0 * x242 x298 = x296 * x8 + x297 x299 = x11 * x296 + x211 x300 = x250 * x50 x301 = x100 * x264 - x212 * x270 x302 = x268 + x301 * x8 x303 = x11 * x301 + x297 x304 = x158 * x264 + 2.0 * x172 - x269 * x270 x305 = x11 * x304 + 3.0 * x268 # 60 item(s) result[0, 0, 0] = numpy.sum( x70 * ( x0 * x51 + x0 * x56 + x0 * (x0 * (x55 + x59 * x6) + x56) + x15 * (3.0 * x42 * x67 + x43 * (x64 + x66)) ) ) result[0, 0, 1] = numpy.sum( x79 * ( x0 * x72 + x0 * x76 + x0 * (x0 * (x75 + x78 * x8) + x76) + x15 * x71 * (x64 + x66) ) ) result[0, 0, 2] = numpy.sum( x79 * ( x0 * x81 + x0 * x84 + x0 * (x0 * (x11 * x78 + x83) + x84) + x15 * x80 * (x64 + x66) ) ) result[0, 0, 3] = numpy.sum( x70 * (x0 * x87 + x0 * x89 + x0 * (x0 * (x59 * x9 + x88) + x89) + x63 * x86) ) result[0, 0, 4] = numpy.sum( x79 * (x0 * x92 + x0 * x94 + x0 * (x0 * (x59 * x95 + x93) + x94) + x63 * x91) ) result[0, 0, 5] = numpy.sum( x70 * (x0 * x97 + x0 * x99 + x0 * (x0 * (x12 * x59 + x98) + x99) + x63 * x96) ) result[0, 1, 0] = numpy.sum( x121 * ( x0 * x110 + x0 * (x0 * x114 + x110) + x15 * (x108 * x50 + x43 * (x118 + x120)) + x20 * x51 ) ) result[0, 1, 1] = numpy.sum( x136 * (x0 * x128 + x0 * (x0 * x132 + x128) + x15 * (x134 * x43 + x135) + x20 * x72) ) result[0, 1, 2] = numpy.sum( x136 * (x0 * x139 + x0 * (x0 * x142 + x139) + x15 * (x118 * x80 + x143) + x20 * x81) ) result[0, 1, 3] = numpy.sum( x121 * (x0 * x145 + x0 * (x0 * x147 + x145) + x15 * x71 * (x134 + x65) + x20 * x87) ) result[0, 1, 4] = numpy.sum( x136 * (x0 * x150 + x0 * (x0 * x152 + x150) + x15 * (x133 * x80 + x153) + x20 * x92) ) result[0, 1, 5] = numpy.sum( x121 * (x0 * x155 + x0 * (x0 * x157 + x155) + x117 * x96 + x20 * x97) ) result[0, 2, 0] = numpy.sum( x121 * ( x0 * x168 + x0 * (x0 * x171 + x168) + x15 * (x166 * x50 + x43 * (x175 + x177)) + x21 * x51 ) ) result[0, 2, 1] = numpy.sum( x136 * (x0 * x180 + x0 * (x0 * x184 + x180) + x15 * x71 * (x175 + x177) + x21 * x72) ) result[0, 2, 2] = numpy.sum( x136 * (x0 * x190 + x0 * (x0 * x192 + x190) + x15 * (x193 * x43 + x194) + x21 * x81) ) result[0, 2, 3] = numpy.sum( x121 * (x0 * x196 + x0 * (x0 * x198 + x196) + x174 * x86 + x21 * x87) ) result[0, 2, 4] = numpy.sum( x136 * (x0 * x200 + x0 * (x0 * x202 + x200) + x193 * x90 + x21 * x92) ) result[0, 2, 5] = numpy.sum( x121 * (x0 * x204 + x0 * (x0 * x206 + x204) + x15 * (x153 + x193 * x80) + x21 * x97) ) result[0, 3, 0] = numpy.sum( x121 * (x0 * x210 + x109 * x20 + x110 * x20 + x15 * x43 * (2.0 * x211 + x215)) ) result[0, 3, 1] = numpy.sum( x136 * (x0 * x221 + x127 * x20 + x128 * x20 + x15 * (x222 + x224 * x43)) ) result[0, 3, 2] = numpy.sum( x136 * (x0 * x227 + x138 * x20 + x139 * x20 + x15 * (x215 * x80 + x228)) ) result[0, 3, 3] = numpy.sum( x121 * (x0 * x231 + x144 * x20 + x145 * x20 + x15 * (x135 + x224 * x71)) ) result[0, 3, 4] = numpy.sum( x136 * (x0 * x234 + x149 * x20 + x15 * (x143 + x223 * x80) + x150 * x20) ) result[0, 3, 5] = numpy.sum(x121 * (x0 * x237 + x154 * x20 + x155 * x20 + x214 * x96)) result[0, 4, 0] = numpy.sum( x136 * (x0 * x241 + x109 * x21 + x15 * x43 * (2.0 * x242 + x244 * x4) + x168 * x20) ) result[0, 4, 1] = numpy.sum( x68 * (x0 * x248 + x127 * x21 + x15 * (x245 * x67 + x249 * x43) + x180 * x20) ) result[0, 4, 2] = numpy.sum( x68 * (x0 * x253 + x138 * x21 + x15 * (x250 * x67 + x254 * x43) + x190 * x20) ) result[0, 4, 3] = numpy.sum( x136 * (x0 * x257 + x144 * x21 + x15 * x71 * (x176 + x249) + x196 * x20) ) result[0, 4, 4] = numpy.sum( x68 * (x0 * x260 + x149 * x21 + x15 * (x188 * x67 + x254 * x71) + x20 * x200) ) result[0, 4, 5] = numpy.sum( x136 * (x0 * x263 + x15 * x80 * (x119 + x254) + x154 * x21 + x20 * x204) ) result[0, 5, 0] = numpy.sum( x121 * (x0 * x267 + x15 * x43 * (2.0 * x268 + x272) + x167 * x21 + x168 * x21) ) result[0, 5, 1] = numpy.sum( x136 * (x0 * x275 + x15 * (x272 * x71 + x276) + x179 * x21 + x180 * x21) ) result[0, 5, 2] = numpy.sum( x136 * (x0 * x280 + x15 * (x281 + x282 * x43) + x189 * x21 + x190 * x21) ) result[0, 5, 3] = numpy.sum(x121 * (x0 * x285 + x195 * x21 + x196 * x21 + x271 * x86)) result[0, 5, 4] = numpy.sum(x136 * (x0 * x288 + x199 * x21 + x200 * x21 + x282 * x90)) result[0, 5, 5] = numpy.sum( x121 * (x0 * x291 + x15 * (x194 + x282 * x80) + x203 * x21 + x204 * x21) ) result[0, 6, 0] = numpy.sum( x70 * (x111 * x292 + x20 * x208 + x20 * x209 + x20 * x210) ) result[0, 6, 1] = numpy.sum( x79 * (x129 * x295 + x20 * x219 + x20 * x220 + x20 * x221) ) result[0, 6, 2] = numpy.sum( x79 * (x140 * x292 + x20 * x225 + x20 * x226 + x20 * x227) ) result[0, 6, 3] = numpy.sum( x70 * (x15 * (3.0 * x222 + x295 * x71) + x20 * x229 + x20 * x230 + x20 * x231) ) result[0, 6, 4] = numpy.sum( x79 * (x15 * x80 * (x293 + x294) + x20 * x232 + x20 * x233 + x20 * x234) ) result[0, 6, 5] = numpy.sum(x70 * (x20 * x235 + x20 * x236 + x20 * x237 + x292 * x96)) result[0, 7, 0] = numpy.sum( x121 * (x111 * x296 + x20 * x240 + x20 * x241 + x208 * x21) ) result[0, 7, 1] = numpy.sum( x136 * (x129 * x298 + x20 * x247 + x20 * x248 + x21 * x219) ) result[0, 7, 2] = numpy.sum( x136 * (x129 * x299 + x20 * x252 + x20 * x253 + x21 * x225) ) result[0, 7, 3] = numpy.sum( x121 * (x15 * (x245 * x50 + x298 * x71) + x20 * x256 + x20 * x257 + x21 * x229) ) result[0, 7, 4] = numpy.sum( x136 * (x15 * (x299 * x71 + x300) + x20 * x259 + x20 * x260 + x21 * x232) ) result[0, 7, 5] = numpy.sum( x121 * (x15 * (x228 + x299 * x80) + x20 * x262 + x20 * x263 + x21 * x235) ) result[0, 8, 0] = numpy.sum( x121 * (x111 * x301 + x20 * x267 + x21 * x239 + x21 * x240) ) result[0, 8, 1] = numpy.sum( x136 * (x129 * x302 + x20 * x275 + x21 * x246 + x21 * x247) ) result[0, 8, 2] = numpy.sum( x136 * (x129 * x303 + x20 * x280 + x21 * x251 + x21 * x252) ) result[0, 8, 3] = numpy.sum( x121 * (x15 * (x276 + x302 * x71) + x20 * x285 + x21 * x255 + x21 * x256) ) result[0, 8, 4] = numpy.sum( x136 * (x15 * (x281 + x303 * x71) + x20 * x288 + x21 * x258 + x21 * x259) ) result[0, 8, 5] = numpy.sum( x121 * (x15 * (x300 + x303 * x80) + x20 * x291 + x21 * x261 + x21 * x262) ) result[0, 9, 0] = numpy.sum( x70 * (x111 * x304 + x21 * x265 + x21 * x266 + x21 * x267) ) result[0, 9, 1] = numpy.sum( x79 * (x181 * x304 + x21 * x273 + x21 * x274 + x21 * x275) ) result[0, 9, 2] = numpy.sum( x79 * (x129 * x305 + x21 * x278 + x21 * x279 + x21 * x280) ) result[0, 9, 3] = numpy.sum(x70 * (x21 * x283 + x21 * x284 + x21 * x285 + x304 * x86)) result[0, 9, 4] = numpy.sum(x79 * (x21 * x286 + x21 * x287 + x21 * x288 + x305 * x90)) result[0, 9, 5] = numpy.sum( x70 * (x15 * (3.0 * x281 + x305 * x80) + x21 * x289 + x21 * x290 + x21 * x291) ) return result
[docs] def int3c2e3d_sph_033(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sf|f) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 10, 10), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - C[0] x5 = 0.5 / (ax + bx) x6 = x4**2 x7 = -x2 * (ax * A[1] + bx * B[1]) x8 = -x7 - C[1] x9 = x8**2 x10 = -x2 * (ax * A[2] + bx * B[2]) x11 = -x10 - C[2] x12 = x11**2 x13 = cx + x1 x14 = x13 ** (-1.0) x15 = x1 * x14 x16 = cx * x15 * (x12 + x6 + x9) x17 = boys(4, x16) x18 = x13 ** (-1.5) x19 = 17.49341832762486 x20 = A[1] - B[1] x21 = A[2] - B[2] x22 = numpy.exp(-ax * bx * x2 * (x0**2 + x20**2 + x21**2)) x23 = x19 * x22 x24 = x2 * x23 x25 = 2.0 * x18 * x24 x26 = x17 * x25 x27 = cx ** (-1.0) x28 = x13 ** (-0.5) x29 = boys(3, x16) x30 = x5 * (2.0 * x19 * x2 * x22 * x27 * x28 * x29 - x26) x31 = -x3 - A[0] x32 = -2.0 * x19 * x2 * x22 * x27 * x28 * x29 * x31 + x26 * x4 x33 = -x32 x34 = boys(5, x16) x35 = x25 * x34 x36 = 2.0 * x17 * x19 * x2 * x22 * x27 * x28 * x31 - x35 * x4 x37 = cx * x14 x38 = x36 * x37 x39 = x30 + x31 * x33 - x38 * x4 x40 = x39 * x4 x41 = x33 * x5 x42 = 2.0 * x41 x43 = x40 + x42 x44 = x15 * x4 x45 = x33 * x4 x46 = 2.0 * x5 x47 = x27 * x29 x48 = x46 * x47 x49 = x24 * x28 * x48 x50 = x45 + x49 x51 = x15 * x46 x52 = x43 * x44 + x50 * x51 x53 = x23 * x48 x54 = x18 * x53 x55 = x4 * x54 + x44 * x50 x56 = x15 * (x44 * x52 + x51 * x55) x57 = x1 * x13 ** (-2.5) * x53 x58 = x15 * (x44 * x55 + x57 * x6) x59 = x0 * x58 + x56 x60 = x4**3 x61 = x1**2 x62 = 2.0 * x13 ** (-3.5) * x23 * x47 * x61 x63 = x0 * x62 x64 = x5 * (2.0 * x17 * x19 * x2 * x22 * x27 * x28 - x35) x65 = x25 * boys(6, x16) x66 = x37 * x4 x67 = ( x31 * x39 - x46 * (x32 + x38) - x66 * ( x31 * x36 + x64 - x66 * (2.0 * x19 * x2 * x22 * x27 * x28 * x31 * x34 - x4 * x65) ) ) x68 = x4 * x67 x69 = x39 * x5 x70 = 3.0 * x69 x71 = x15 * x5 x72 = 3.0 * x71 x73 = da * db * dc x74 = 0.06666666666666667 * x73 x75 = x15 * x8 x76 = x75 * (x40 + x42) x77 = x54 * x8 x78 = x45 * x75 + x77 x79 = x15 * (x44 * x76 + x51 * x78) x80 = x4 * x8 x81 = x15 * (x44 * x78 + x57 * x80) x82 = x0 * x81 + x79 x83 = x6 * x63 x84 = 2.23606797749979 * x74 x85 = x11 * x15 x86 = x85 * (x40 + x42) x87 = x11 * x54 x88 = x45 * x85 + x87 x89 = x15 * (x44 * x86 + x51 * x88) x90 = x11 * x57 x91 = x15 * (x4 * x90 + x44 * x88) x92 = x0 * x91 + x89 x93 = x61 / x13**2 x94 = x9 * x93 x95 = x15 * x94 * (x40 + x42) x96 = x57 * x9 x97 = x15 * (x45 * x94 + x96) x98 = x0 * x97 + x95 x99 = x4 * x63 x100 = x8 * x93 x101 = x100 * x11 x102 = x101 * x15 * (x40 + x42) x103 = x8 * x90 x104 = x15 * (x101 * x45 + x103) x105 = x0 * x104 + x102 x106 = x11 * x80 x107 = 3.872983346207417 * x74 x108 = x12 * x93 x109 = x108 * x15 * (x40 + x42) x110 = x12 * x57 x111 = x15 * (x108 * x45 + x110) x112 = x0 * x111 + x109 x113 = x8**3 x114 = x1**3 / x13**3 x115 = x113 * x114 x116 = x115 * x39 x117 = x115 * x33 x118 = x0 * x117 + x116 x119 = x114 * x9 x120 = x11 * x119 x121 = x120 * x39 x122 = x120 * x33 x123 = x0 * x122 + x121 x124 = x11 * x9 x125 = x114 * x12 x126 = x125 * x8 x127 = x126 * x39 x128 = x126 * x33 x129 = x0 * x128 + x127 x130 = x12 * x8 x131 = x11**3 x132 = x114 * x131 x133 = x132 * x39 x134 = x132 * x33 x135 = x0 * x134 + x133 x136 = -x7 - A[1] x137 = -2.0 * x136 * x19 * x2 * x22 * x27 * x28 * x29 + x26 * x8 x138 = -x137 x139 = x138 * x5 x140 = 2.0 * x136 * x17 * x19 * x2 * x22 * x27 * x28 - x35 * x8 x141 = x140 * x37 x142 = x138 * x31 - x141 * x4 x143 = x142 * x4 x144 = x139 + x143 x145 = x44 * (x139 + x144) x146 = x6 * x93 x147 = x15 * (x139 * x146 + x145 * x44) x148 = x147 + x20 * x58 x149 = x114 * x60 x150 = x138 * x149 x151 = x20 * x62 x152 = x150 + x151 * x60 x153 = -x5 * (x137 + x141) x154 = 2.0 * x136 * x19 * x2 * x22 * x27 * x28 * x34 - x65 * x8 x155 = x142 * x31 + x153 - x66 * (x140 * x31 - x154 * x66) x156 = x155 * x4 x157 = x142 * x5 x158 = 2.0 * x157 x159 = x138 * x8 x160 = x159 + x49 x161 = x15 * x160 x162 = x142 * x8 x163 = x162 + x41 x164 = x161 * x5 + x163 * x44 x165 = x4 * x93 x166 = x165 * x5 x167 = x15 * (x160 * x166 + x164 * x44) x168 = x167 + x20 * x81 x169 = x114 * x6 x170 = x160 * x169 x171 = x151 * x6 x172 = x170 + x171 * x8 x173 = x155 * x8 x174 = x173 + x69 x175 = x163 * x51 x176 = 0.3333333333333333 * x73 x177 = x139 * x85 x178 = x143 * x85 + x177 x179 = x11 * x165 x180 = x15 * (x139 * x179 + x178 * x44) x181 = x180 + x20 * x91 x182 = x11 * x169 x183 = x138 * x182 x184 = x11 * x171 + x183 x185 = x158 * x85 x186 = x161 * x8 + x77 x187 = x75 * (x163 + x41) x188 = x15 * (x186 * x71 + x187 * x44) x189 = x188 + x20 * x97 x190 = x165 * x186 x191 = x151 * x4 x192 = x190 + x191 * x9 x193 = x75 * (x174 + x69) x194 = x187 * x51 x195 = x159 * x85 + x87 x196 = x41 * x85 x197 = x162 * x85 + x196 x198 = x15 * (x195 * x71 + x197 * x44) x199 = x104 * x20 + x198 x200 = x165 * x195 x201 = x106 * x151 + x200 x202 = x69 * x85 x203 = x173 * x85 + x202 x204 = x197 * x51 x205 = 1.732050807568877 * x176 x206 = x108 * x139 x207 = x15 * (x108 * x143 + x206) x208 = x111 * x20 + x207 x209 = x125 * x4 x210 = x138 * x209 x211 = x12 * x191 + x210 x212 = x108 * x158 x213 = x15 * (x187 * x75 + x41 * x94) x214 = x117 * x20 + x213 x215 = x15 * (x186 * x75 + x96) x216 = x113 * x151 + x215 x217 = x15 * (x101 * x41 + x197 * x75) x218 = x122 * x20 + x217 x219 = x15 * (x103 + x195 * x75) x220 = x124 * x151 + x219 x221 = x108 * x41 x222 = x15 * (x108 * x162 + x221) x223 = x128 * x20 + x222 x224 = x15 * (x108 * x159 + x110) x225 = x130 * x151 + x224 x226 = x108 * x69 x227 = x132 * x142 x228 = x134 * x20 + x227 x229 = x132 * x138 x230 = x131 * x151 + x229 x231 = -x10 - A[2] x232 = x11 * x26 - 2.0 * x19 * x2 * x22 * x231 * x27 * x28 * x29 x233 = -x232 x234 = x233 * x5 x235 = -x11 * x35 + 2.0 * x17 * x19 * x2 * x22 * x231 * x27 * x28 x236 = x235 * x37 x237 = x233 * x31 - x236 * x4 x238 = x237 * x4 x239 = x234 + x238 x240 = x44 * (x234 + x239) x241 = x15 * (x146 * x234 + x240 * x44) x242 = x21 * x58 + x241 x243 = x149 * x233 x244 = x21 * x62 x245 = x243 + x244 * x60 x246 = -x5 * (x232 + x236) x247 = -x11 * x65 + 2.0 * x19 * x2 * x22 * x231 * x27 * x28 * x34 x248 = x237 * x31 + x246 - x66 * (x235 * x31 - x247 * x66) x249 = x248 * x4 x250 = x237 * x5 x251 = 2.0 * x250 x252 = x234 * x75 x253 = x238 * x75 + x252 x254 = x165 * x8 x255 = x15 * (x234 * x254 + x253 * x44) x256 = x21 * x81 + x255 x257 = x169 * x8 x258 = x233 * x257 x259 = x244 * x6 x260 = x258 + x259 * x8 x261 = x11 * x233 + x49 x262 = x261 * x71 x263 = x11 * x237 + x41 x264 = x262 + x263 * x44 x265 = x15 * (x166 * x261 + x264 * x44) x266 = x21 * x91 + x265 x267 = x169 * x261 x268 = x11 * x259 + x267 x269 = x11 * x248 + x69 x270 = x263 * x51 x271 = x234 * x94 x272 = x15 * (x238 * x94 + x271) x273 = x21 * x97 + x272 x274 = x119 * x4 x275 = x233 * x274 x276 = x244 * x4 x277 = x275 + x276 * x9 x278 = x100 * x5 x279 = x261 * x278 x280 = x15 * (x254 * x263 + x279) x281 = x104 * x21 + x280 x282 = x114 * x80 x283 = x261 * x282 x284 = x106 * x244 + x283 x285 = x261 * x85 + x87 x286 = x285 * x71 x287 = x196 + x263 * x85 x288 = x15 * (x286 + x287 * x44) x289 = x111 * x21 + x288 x290 = x165 * x285 x291 = x12 * x276 + x290 x292 = x202 + x269 * x85 x293 = x287 * x51 x294 = x115 * x237 x295 = x117 * x21 + x294 x296 = x115 * x233 x297 = x113 * x244 + x296 x298 = x119 * x263 x299 = x122 * x21 + x298 x300 = x119 * x261 x301 = x124 * x244 + x300 x302 = x100 * x287 x303 = x128 * x21 + x302 x304 = x100 * x285 x305 = x130 * x244 + x304 x306 = x15 * (x221 + x287 * x85) x307 = x134 * x21 + x306 x308 = x15 * (x110 + x285 * x85) x309 = x131 * x244 + x308 x310 = x136 * x138 - x141 * x8 + x30 x311 = x149 * x310 x312 = x150 * x20 + x311 x313 = x152 * x20 + x312 x314 = x310 * x5 x315 = x37 * x8 x316 = x136 * x140 - x154 * x315 + x64 x317 = x31 * x310 - x316 * x66 x318 = x317 * x4 x319 = x310 * x8 x320 = 2.0 * x139 x321 = x319 + x320 x322 = x169 * x321 x323 = x170 * x20 + x322 x324 = x172 * x20 + x323 x325 = x321 * x71 x326 = x317 * x8 x327 = x158 + x326 x328 = x182 * x310 x329 = x183 * x20 + x328 x330 = x184 * x20 + x329 x331 = x314 * x85 x332 = x161 * x46 + x321 * x75 x333 = x165 * x332 x334 = x190 * x20 + x333 x335 = x192 * x20 + x334 x336 = x332 * x71 x337 = x175 + x327 * x75 x338 = x85 * (x319 + x320) x339 = x165 * x338 x340 = x20 * x200 + x339 x341 = x20 * x201 + x340 x342 = x338 * x71 x343 = x185 + x326 * x85 x344 = x209 * x310 x345 = x20 * x210 + x344 x346 = x20 * x211 + x345 x347 = x108 * x314 x348 = x15 * (x186 * x51 + x332 * x75) x349 = x20 * x215 + x348 x350 = x20 * x216 + x349 x351 = x15 * (x195 * x51 + x338 * x75) x352 = x20 * x219 + x351 x353 = x20 * x220 + x352 x354 = x108 * x15 * (x319 + x320) x355 = x20 * x224 + x354 x356 = x20 * x225 + x355 x357 = x132 * x310 x358 = x20 * x229 + x357 x359 = x20 * x230 + x358 x360 = x136 * x233 - x236 * x8 x361 = x149 * x360 x362 = x150 * x21 + x361 x363 = x20 * x245 + x362 x364 = x360 * x5 x365 = x136 * x235 - x247 * x315 x366 = x31 * x360 - x365 * x66 x367 = x234 + x360 * x8 x368 = x169 * x367 x369 = x170 * x21 + x368 x370 = x20 * x260 + x369 x371 = x250 + x366 * x8 x372 = x11 * x360 + x139 x373 = x169 * x372 x374 = x183 * x21 + x373 x375 = x20 * x268 + x374 x376 = x11 * x366 + x157 x377 = x252 + x367 * x75 x378 = x165 * x377 x379 = x190 * x21 + x378 x380 = x20 * x277 + x379 x381 = x75 * (x250 + x371) x382 = x262 + x372 * x75 x383 = x165 * x382 x384 = x200 * x21 + x383 x385 = x20 * x284 + x384 x386 = x263 * x71 + x376 * x75 x387 = x177 + x372 * x85 x388 = x165 * x387 x389 = x21 * x210 + x388 x390 = x20 * x291 + x389 x391 = x85 * (x157 + x376) x392 = x15 * (x271 + x377 * x75) x393 = x21 * x215 + x392 x394 = x20 * x297 + x393 x395 = x15 * (x279 + x382 * x75) x396 = x21 * x219 + x395 x397 = x20 * x301 + x396 x398 = x15 * (x286 + x387 * x75) x399 = x21 * x224 + x398 x400 = x20 * x305 + x399 x401 = x15 * (x206 + x387 * x85) x402 = x21 * x229 + x401 x403 = x20 * x309 + x402 x404 = -x11 * x236 + x231 * x233 + x30 x405 = x149 * x404 x406 = x21 * x243 + x405 x407 = x21 * x245 + x406 x408 = x404 * x5 x409 = x11 * x37 x410 = x231 * x235 - x247 * x409 + x64 x411 = x31 * x404 - x410 * x66 x412 = x4 * x411 x413 = x257 * x404 x414 = x21 * x258 + x413 x415 = x21 * x260 + x414 x416 = x408 * x75 x417 = x11 * x404 + 2.0 * x234 x418 = x169 * x417 x419 = x21 * x267 + x418 x420 = x21 * x268 + x419 x421 = x417 * x71 x422 = x11 * x411 + x251 x423 = x274 * x404 x424 = x21 * x275 + x423 x425 = x21 * x277 + x424 x426 = x408 * x94 x427 = x282 * x417 x428 = x21 * x283 + x427 x429 = x21 * x284 + x428 x430 = x278 * x417 x431 = x261 * x51 + x417 * x85 x432 = x165 * x431 x433 = x21 * x290 + x432 x434 = x21 * x291 + x433 x435 = x431 * x71 x436 = x270 + x422 * x85 x437 = x115 * x404 x438 = x21 * x296 + x437 x439 = x21 * x297 + x438 x440 = x119 * x417 x441 = x21 * x300 + x440 x442 = x21 * x301 + x441 x443 = x100 * x431 x444 = x21 * x304 + x443 x445 = x21 * x305 + x444 x446 = x15 * (x285 * x51 + x431 * x85) x447 = x21 * x308 + x446 x448 = x21 * x309 + x447 x449 = x136 * x310 + 2.0 * x153 - x315 * x316 x450 = x449 * x8 x451 = 3.0 * x314 x452 = x450 + x451 x453 = 3.0 * x325 + x452 * x75 x454 = x85 * (x450 + x451) x455 = x136 * x360 + x246 - x315 * x365 x456 = 2.0 * x364 x457 = x455 * x8 + x456 x458 = x11 * x455 + x314 x459 = x367 * x51 + x457 * x75 x460 = x372 * x51 x461 = x458 * x75 + x460 x462 = x331 + x458 * x85 x463 = x387 * x51 x464 = x136 * x404 - x315 * x410 x465 = x408 + x464 * x8 x466 = x11 * x464 + x456 x467 = x416 + x465 * x75 x468 = x421 + x466 * x75 x469 = x460 + x466 * x85 x470 = x231 * x404 + 2.0 * x246 - x409 * x410 x471 = x11 * x470 + 3.0 * x408 x472 = 3.0 * x421 + x471 * x85 # 100 item(s) result[0, 0, 0] = numpy.sum( x74 * ( x0 * x56 + x0 * x59 + x0 * (x0 * (x58 + x60 * x63) + x59) + x15 * (x44 * (x43 * x72 + x44 * (x68 + x70)) + x52 * x72) ) ) result[0, 0, 1] = numpy.sum( x84 * ( x0 * x79 + x0 * x82 + x0 * (x0 * (x8 * x83 + x81) + x82) + x15 * (x44 * x75 * (x68 + x70) + x72 * x76) ) ) result[0, 0, 2] = numpy.sum( x84 * ( x0 * x89 + x0 * x92 + x0 * (x0 * (x11 * x83 + x91) + x92) + x15 * (x44 * x85 * (x68 + x70) + x72 * x86) ) ) result[0, 0, 3] = numpy.sum( x84 * ( x0 * x95 + x0 * x98 + x0 * (x0 * (x9 * x99 + x97) + x98) + x15 * x94 * (x68 + x70) ) ) result[0, 0, 4] = numpy.sum( x107 * ( x0 * x102 + x0 * x105 + x0 * (x0 * (x104 + x106 * x63) + x105) + x101 * x15 * (x68 + x70) ) ) result[0, 0, 5] = numpy.sum( x84 * ( x0 * x109 + x0 * x112 + x0 * (x0 * (x111 + x12 * x99) + x112) + x108 * x15 * (x68 + x70) ) ) result[0, 0, 6] = numpy.sum( x74 * (x0 * x116 + x0 * x118 + x0 * (x0 * (x113 * x63 + x117) + x118) + x115 * x67) ) result[0, 0, 7] = numpy.sum( x84 * (x0 * x121 + x0 * x123 + x0 * (x0 * (x122 + x124 * x63) + x123) + x120 * x67) ) result[0, 0, 8] = numpy.sum( x84 * (x0 * x127 + x0 * x129 + x0 * (x0 * (x128 + x130 * x63) + x129) + x126 * x67) ) result[0, 0, 9] = numpy.sum( x74 * (x0 * x133 + x0 * x135 + x0 * (x0 * (x131 * x63 + x134) + x135) + x132 * x67) ) result[0, 1, 0] = numpy.sum( x84 * ( x0 * x148 + x0 * (x0 * x152 + x148) + x15 * (x145 * x51 + x44 * (x144 * x51 + x44 * (x156 + x158))) + x20 * x56 ) ) result[0, 1, 1] = numpy.sum( x176 * ( x0 * x168 + x0 * (x0 * x172 + x168) + x15 * (x164 * x51 + x44 * (x174 * x44 + x175)) + x20 * x79 ) ) result[0, 1, 2] = numpy.sum( x176 * ( x0 * x181 + x0 * (x0 * x184 + x181) + x15 * (x178 * x51 + x44 * (x156 * x85 + x185)) + x20 * x89 ) ) result[0, 1, 3] = numpy.sum( x176 * (x0 * x189 + x0 * (x0 * x192 + x189) + x15 * (x193 * x44 + x194) + x20 * x95) ) result[0, 1, 4] = numpy.sum( x205 * (x0 * x199 + x0 * (x0 * x201 + x199) + x102 * x20 + x15 * (x203 * x44 + x204)) ) result[0, 1, 5] = numpy.sum( x176 * (x0 * x208 + x0 * (x0 * x211 + x208) + x109 * x20 + x15 * (x108 * x156 + x212)) ) result[0, 1, 6] = numpy.sum( x84 * ( x0 * x214 + x0 * (x0 * x216 + x214) + x116 * x20 + x15 * (x193 * x75 + x69 * x94) ) ) result[0, 1, 7] = numpy.sum( x176 * ( x0 * x218 + x0 * (x0 * x220 + x218) + x121 * x20 + x15 * (x101 * x69 + x203 * x75) ) ) result[0, 1, 8] = numpy.sum( x176 * (x0 * x223 + x0 * (x0 * x225 + x223) + x127 * x20 + x15 * (x108 * x173 + x226)) ) result[0, 1, 9] = numpy.sum( x84 * (x0 * x228 + x0 * (x0 * x230 + x228) + x132 * x155 + x133 * x20) ) result[0, 2, 0] = numpy.sum( x84 * ( x0 * x242 + x0 * (x0 * x245 + x242) + x15 * (x240 * x51 + x44 * (x239 * x51 + x44 * (x249 + x251))) + x21 * x56 ) ) result[0, 2, 1] = numpy.sum( x176 * ( x0 * x256 + x0 * (x0 * x260 + x256) + x15 * (x253 * x51 + x44 * x75 * (x249 + x251)) + x21 * x79 ) ) result[0, 2, 2] = numpy.sum( x176 * ( x0 * x266 + x0 * (x0 * x268 + x266) + x15 * (x264 * x51 + x44 * (x269 * x44 + x270)) + x21 * x89 ) ) result[0, 2, 3] = numpy.sum( x176 * (x0 * x273 + x0 * (x0 * x277 + x273) + x15 * x94 * (x249 + x251) + x21 * x95) ) result[0, 2, 4] = numpy.sum( x205 * ( x0 * x281 + x0 * (x0 * x284 + x281) + x102 * x21 + x15 * (x100 * x263 * x46 + x254 * x269) ) ) result[0, 2, 5] = numpy.sum( x176 * (x0 * x289 + x0 * (x0 * x291 + x289) + x109 * x21 + x15 * (x292 * x44 + x293)) ) result[0, 2, 6] = numpy.sum( x84 * (x0 * x295 + x0 * (x0 * x297 + x295) + x115 * x248 + x116 * x21) ) result[0, 2, 7] = numpy.sum( x176 * (x0 * x299 + x0 * (x0 * x301 + x299) + x119 * x269 + x121 * x21) ) result[0, 2, 8] = numpy.sum( x176 * (x0 * x303 + x0 * (x0 * x305 + x303) + x100 * x292 + x127 * x21) ) result[0, 2, 9] = numpy.sum( x84 * (x0 * x307 + x0 * (x0 * x309 + x307) + x133 * x21 + x15 * (x226 + x292 * x85)) ) result[0, 3, 0] = numpy.sum( x84 * ( x0 * x313 + x147 * x20 + x148 * x20 + x15 * (x146 * x314 + x44**2 * (2.0 * x314 + x318)) ) ) result[0, 3, 1] = numpy.sum( x176 * ( x0 * x324 + x15 * (x166 * x321 + x44 * (x325 + x327 * x44)) + x167 * x20 + x168 * x20 ) ) result[0, 3, 2] = numpy.sum( x176 * ( x0 * x330 + x15 * (x179 * x314 + x44 * (x318 * x85 + x331)) + x180 * x20 + x181 * x20 ) ) result[0, 3, 3] = numpy.sum( x176 * (x0 * x335 + x15 * (x336 + x337 * x44) + x188 * x20 + x189 * x20) ) result[0, 3, 4] = numpy.sum( x205 * (x0 * x341 + x15 * (x342 + x343 * x44) + x198 * x20 + x199 * x20) ) result[0, 3, 5] = numpy.sum( x176 * (x0 * x346 + x15 * (x108 * x318 + x347) + x20 * x207 + x20 * x208) ) result[0, 3, 6] = numpy.sum( x84 * (x0 * x350 + x15 * (x194 + x337 * x75) + x20 * x213 + x20 * x214) ) result[0, 3, 7] = numpy.sum( x176 * (x0 * x353 + x15 * (x204 + x343 * x75) + x20 * x217 + x20 * x218) ) result[0, 3, 8] = numpy.sum( x176 * (x0 * x356 + x15 * (x108 * x326 + x212) + x20 * x222 + x20 * x223) ) result[0, 3, 9] = numpy.sum(x84 * (x0 * x359 + x132 * x317 + x20 * x227 + x20 * x228)) result[0, 4, 0] = numpy.sum( x107 * ( x0 * x363 + x147 * x21 + x15 * (x146 * x364 + x44**2 * (2.0 * x364 + x366 * x4)) + x20 * x242 ) ) result[0, 4, 1] = numpy.sum( x205 * ( x0 * x370 + x15 * (x166 * x367 + x44 * (x367 * x71 + x371 * x44)) + x167 * x21 + x20 * x256 ) ) result[0, 4, 2] = numpy.sum( x205 * ( x0 * x375 + x15 * (x166 * x372 + x44 * (x372 * x71 + x376 * x44)) + x180 * x21 + x20 * x266 ) ) result[0, 4, 3] = numpy.sum( x205 * (x0 * x380 + x15 * (x377 * x71 + x381 * x44) + x188 * x21 + x20 * x273) ) result[0, 4, 4] = numpy.sum( x73 * (x0 * x385 + x15 * (x382 * x71 + x386 * x44) + x198 * x21 + x20 * x281) ) result[0, 4, 5] = numpy.sum( x205 * (x0 * x390 + x15 * (x387 * x71 + x391 * x44) + x20 * x289 + x207 * x21) ) result[0, 4, 6] = numpy.sum( x107 * (x0 * x394 + x15 * (x250 * x94 + x381 * x75) + x20 * x295 + x21 * x213) ) result[0, 4, 7] = numpy.sum( x205 * (x0 * x397 + x15 * (x263 * x278 + x386 * x75) + x20 * x299 + x21 * x217) ) result[0, 4, 8] = numpy.sum( x205 * (x0 * x400 + x15 * (x287 * x71 + x391 * x75) + x20 * x303 + x21 * x222) ) result[0, 4, 9] = numpy.sum( x107 * (x0 * x403 + x15 * (x108 * x157 + x391 * x85) + x20 * x307 + x21 * x227) ) result[0, 5, 0] = numpy.sum( x84 * ( x0 * x407 + x15 * (x146 * x408 + x44**2 * (2.0 * x408 + x412)) + x21 * x241 + x21 * x242 ) ) result[0, 5, 1] = numpy.sum( x176 * ( x0 * x415 + x15 * (x254 * x408 + x44 * (x412 * x75 + x416)) + x21 * x255 + x21 * x256 ) ) result[0, 5, 2] = numpy.sum( x176 * ( x0 * x420 + x15 * (x166 * x417 + x44 * (x421 + x422 * x44)) + x21 * x265 + x21 * x266 ) ) result[0, 5, 3] = numpy.sum( x176 * (x0 * x425 + x15 * (x412 * x94 + x426) + x21 * x272 + x21 * x273) ) result[0, 5, 4] = numpy.sum( x205 * (x0 * x429 + x15 * (x254 * x422 + x430) + x21 * x280 + x21 * x281) ) result[0, 5, 5] = numpy.sum( x176 * (x0 * x434 + x15 * (x435 + x436 * x44) + x21 * x288 + x21 * x289) ) result[0, 5, 6] = numpy.sum(x84 * (x0 * x439 + x115 * x411 + x21 * x294 + x21 * x295)) result[0, 5, 7] = numpy.sum( x176 * (x0 * x442 + x119 * x422 + x21 * x298 + x21 * x299) ) result[0, 5, 8] = numpy.sum( x176 * (x0 * x445 + x100 * x436 + x21 * x302 + x21 * x303) ) result[0, 5, 9] = numpy.sum( x84 * (x0 * x448 + x15 * (x293 + x436 * x85) + x21 * x306 + x21 * x307) ) result[0, 6, 0] = numpy.sum( x74 * (x149 * x449 + x20 * x311 + x20 * x312 + x20 * x313) ) result[0, 6, 1] = numpy.sum( x84 * (x169 * x452 + x20 * x322 + x20 * x323 + x20 * x324) ) result[0, 6, 2] = numpy.sum( x84 * (x182 * x449 + x20 * x328 + x20 * x329 + x20 * x330) ) result[0, 6, 3] = numpy.sum( x84 * (x165 * x453 + x20 * x333 + x20 * x334 + x20 * x335) ) result[0, 6, 4] = numpy.sum( x107 * (x165 * x454 + x20 * x339 + x20 * x340 + x20 * x341) ) result[0, 6, 5] = numpy.sum( x84 * (x20 * x344 + x20 * x345 + x20 * x346 + x209 * x449) ) result[0, 6, 6] = numpy.sum( x74 * (x15 * (3.0 * x336 + x453 * x75) + x20 * x348 + x20 * x349 + x20 * x350) ) result[0, 6, 7] = numpy.sum( x84 * (x15 * (3.0 * x342 + x454 * x75) + x20 * x351 + x20 * x352 + x20 * x353) ) result[0, 6, 8] = numpy.sum( x84 * (x108 * x15 * (x450 + x451) + x20 * x354 + x20 * x355 + x20 * x356) ) result[0, 6, 9] = numpy.sum( x74 * (x132 * x449 + x20 * x357 + x20 * x358 + x20 * x359) ) result[0, 7, 0] = numpy.sum( x84 * (x149 * x455 + x20 * x362 + x20 * x363 + x21 * x311) ) result[0, 7, 1] = numpy.sum( x176 * (x169 * x457 + x20 * x369 + x20 * x370 + x21 * x322) ) result[0, 7, 2] = numpy.sum( x176 * (x169 * x458 + x20 * x374 + x20 * x375 + x21 * x328) ) result[0, 7, 3] = numpy.sum( x176 * (x165 * x459 + x20 * x379 + x20 * x380 + x21 * x333) ) result[0, 7, 4] = numpy.sum( x205 * (x165 * x461 + x20 * x384 + x20 * x385 + x21 * x339) ) result[0, 7, 5] = numpy.sum( x176 * (x165 * x462 + x20 * x389 + x20 * x390 + x21 * x344) ) result[0, 7, 6] = numpy.sum( x84 * (x15 * (x377 * x51 + x459 * x75) + x20 * x393 + x20 * x394 + x21 * x348) ) result[0, 7, 7] = numpy.sum( x176 * (x15 * (x382 * x51 + x461 * x75) + x20 * x396 + x20 * x397 + x21 * x351) ) result[0, 7, 8] = numpy.sum( x176 * (x15 * (x462 * x75 + x463) + x20 * x399 + x20 * x400 + x21 * x354) ) result[0, 7, 9] = numpy.sum( x84 * (x15 * (x347 + x462 * x85) + x20 * x402 + x20 * x403 + x21 * x357) ) result[0, 8, 0] = numpy.sum( x84 * (x149 * x464 + x20 * x407 + x21 * x361 + x21 * x362) ) result[0, 8, 1] = numpy.sum( x176 * (x169 * x465 + x20 * x415 + x21 * x368 + x21 * x369) ) result[0, 8, 2] = numpy.sum( x176 * (x169 * x466 + x20 * x420 + x21 * x373 + x21 * x374) ) result[0, 8, 3] = numpy.sum( x176 * (x165 * x467 + x20 * x425 + x21 * x378 + x21 * x379) ) result[0, 8, 4] = numpy.sum( x205 * (x165 * x468 + x20 * x429 + x21 * x383 + x21 * x384) ) result[0, 8, 5] = numpy.sum( x176 * (x165 * x469 + x20 * x434 + x21 * x388 + x21 * x389) ) result[0, 8, 6] = numpy.sum( x84 * (x15 * (x426 + x467 * x75) + x20 * x439 + x21 * x392 + x21 * x393) ) result[0, 8, 7] = numpy.sum( x176 * (x15 * (x430 + x468 * x75) + x20 * x442 + x21 * x395 + x21 * x396) ) result[0, 8, 8] = numpy.sum( x176 * (x15 * (x435 + x469 * x75) + x20 * x445 + x21 * x398 + x21 * x399) ) result[0, 8, 9] = numpy.sum( x84 * (x15 * (x463 + x469 * x85) + x20 * x448 + x21 * x401 + x21 * x402) ) result[0, 9, 0] = numpy.sum( x74 * (x149 * x470 + x21 * x405 + x21 * x406 + x21 * x407) ) result[0, 9, 1] = numpy.sum( x84 * (x21 * x413 + x21 * x414 + x21 * x415 + x257 * x470) ) result[0, 9, 2] = numpy.sum( x84 * (x169 * x471 + x21 * x418 + x21 * x419 + x21 * x420) ) result[0, 9, 3] = numpy.sum( x84 * (x21 * x423 + x21 * x424 + x21 * x425 + x274 * x470) ) result[0, 9, 4] = numpy.sum( x107 * (x21 * x427 + x21 * x428 + x21 * x429 + x282 * x471) ) result[0, 9, 5] = numpy.sum( x84 * (x165 * x472 + x21 * x432 + x21 * x433 + x21 * x434) ) result[0, 9, 6] = numpy.sum( x74 * (x115 * x470 + x21 * x437 + x21 * x438 + x21 * x439) ) result[0, 9, 7] = numpy.sum( x84 * (x119 * x471 + x21 * x440 + x21 * x441 + x21 * x442) ) result[0, 9, 8] = numpy.sum( x84 * (x100 * x472 + x21 * x443 + x21 * x444 + x21 * x445) ) result[0, 9, 9] = numpy.sum( x74 * (x15 * (3.0 * x435 + x472 * x85) + x21 * x446 + x21 * x447 + x21 * x448) ) return result
[docs] def int3c2e3d_sph_034(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (sf|g) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((1, 10, 15), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - C[0] x5 = 0.5 / (ax + bx) x6 = x4**2 x7 = -x2 * (ax * A[1] + bx * B[1]) x8 = -x7 - C[1] x9 = x8**2 x10 = -x2 * (ax * A[2] + bx * B[2]) x11 = -x10 - C[2] x12 = x11**2 x13 = cx + x1 x14 = x13 ** (-1.0) x15 = x1 * x14 x16 = cx * x15 * (x12 + x6 + x9) x17 = boys(5, x16) x18 = x13 ** (-1.5) x19 = 17.49341832762486 x20 = A[1] - B[1] x21 = A[2] - B[2] x22 = numpy.exp(-ax * bx * x2 * (x0**2 + x20**2 + x21**2)) x23 = x19 * x22 x24 = x2 * x23 x25 = 2.0 * x18 * x24 x26 = x17 * x25 x27 = cx ** (-1.0) x28 = x13 ** (-0.5) x29 = boys(4, x16) x30 = x5 * (2.0 * x19 * x2 * x22 * x27 * x28 * x29 - x26) x31 = -x3 - A[0] x32 = -2.0 * x19 * x2 * x22 * x27 * x28 * x29 * x31 + x26 * x4 x33 = -x32 x34 = boys(6, x16) x35 = x25 * x34 x36 = 2.0 * x17 * x19 * x2 * x22 * x27 * x28 * x31 - x35 * x4 x37 = cx * x14 x38 = x36 * x37 x39 = x30 + x31 * x33 - x38 * x4 x40 = x39 * x4 x41 = x33 * x5 x42 = 2.0 * x41 x43 = x40 + x42 x44 = x15 * x4 x45 = x33 * x4 x46 = 2.0 * x5 x47 = x27 * x29 x48 = x46 * x47 x49 = x24 * x28 * x48 x50 = x45 + x49 x51 = x15 * x46 x52 = x43 * x44 + x50 * x51 x53 = x23 * x48 x54 = x18 * x53 x55 = x4 * x54 + x44 * x50 x56 = x44 * x52 + x51 * x55 x57 = x53 * x6 x58 = x1 * x13 ** (-2.5) x59 = x44 * x55 + x57 * x58 x60 = x15 * (x44 * x56 + x51 * x59) x61 = x4**3 x62 = x1**2 x63 = x13 ** (-3.5) * x62 x64 = x53 * x63 x65 = x15 * (x44 * x59 + x61 * x64) x66 = x0 * x65 + x60 x67 = x4**4 x68 = x1**3 x69 = 2.0 * x13 ** (-4.5) * x23 * x47 * x68 x70 = x0 * x69 x71 = x5 * (2.0 * x17 * x19 * x2 * x22 * x27 * x28 - x35) x72 = x25 * boys(7, x16) x73 = x37 * x4 x74 = ( x31 * x39 - x46 * (x32 + x38) - x73 * ( x31 * x36 + x71 - x73 * (2.0 * x19 * x2 * x22 * x27 * x28 * x31 * x34 - x4 * x72) ) ) x75 = x4 * x74 x76 = x39 * x5 x77 = 3.0 * x76 x78 = x15 * x5 x79 = 3.0 * x78 x80 = da * db * dc x81 = 0.009523809523809524 * x80 x82 = 2.645751311064591 * x81 x83 = x15 * x8 x84 = x83 * (x40 + x42) x85 = x54 * x8 x86 = x45 * x83 + x85 x87 = x44 * x84 + x51 * x86 x88 = x53 * x58 x89 = x4 * x88 x90 = x44 * x86 + x8 * x89 x91 = x15 * (x44 * x87 + x51 * x90) x92 = x57 * x63 x93 = x15 * (x44 * x90 + x8 * x92) x94 = x0 * x93 + x91 x95 = x61 * x70 x96 = 0.06666666666666667 * x80 x97 = x11 * x15 x98 = x97 * (x40 + x42) x99 = x11 * x54 x100 = x45 * x97 + x99 x101 = x100 * x51 + x44 * x98 x102 = x100 * x44 + x11 * x89 x103 = x15 * (x101 * x44 + x102 * x51) x104 = x15 * (x102 * x44 + x11 * x92) x105 = x0 * x104 + x103 x106 = x62 / x13**2 x107 = x106 * x9 x108 = x107 * (x40 + x42) x109 = x88 * x9 x110 = x107 * x45 + x109 x111 = x15 * (x108 * x44 + x110 * x51) x112 = x4 * x9 x113 = x15 * (x110 * x44 + x112 * x64) x114 = x0 * x113 + x111 x115 = x6 * x9 x116 = 3.872983346207417 x117 = 0.02222222222222222 * x116 * x80 x118 = x106 * x8 x119 = x11 * x118 x120 = x119 * (x40 + x42) x121 = x11 * x8 x122 = x121 * x88 x123 = x119 * x45 + x122 x124 = x15 * (x120 * x44 + x123 * x51) x125 = x15 * (x121 * x4 * x64 + x123 * x44) x126 = x0 * x125 + x124 x127 = x121 * x6 x128 = 2.23606797749979 * x96 x129 = x106 * x12 x130 = x129 * (x40 + x42) x131 = x12 * x88 x132 = x129 * x45 + x131 x133 = x15 * (x130 * x44 + x132 * x51) x134 = x12 * x4 x135 = x15 * (x132 * x44 + x134 * x64) x136 = x0 * x135 + x133 x137 = x12 * x6 x138 = x8**3 x139 = x68 / x13**3 x140 = x138 * x139 x141 = x140 * x15 * (x40 + x42) x142 = x138 * x64 x143 = x15 * (x140 * x45 + x142) x144 = x0 * x143 + x141 x145 = x138 * x70 x146 = x139 * x9 x147 = x11 * x146 x148 = x147 * x15 * (x40 + x42) x149 = x11 * x64 * x9 x150 = x15 * (x147 * x45 + x149) x151 = x0 * x150 + x148 x152 = x11 * x112 x153 = x139 * x8 x154 = x12 * x153 x155 = x15 * x154 * (x40 + x42) x156 = x12 * x64 * x8 x157 = x15 * (x154 * x45 + x156) x158 = x0 * x157 + x155 x159 = x134 * x8 x160 = x11**3 x161 = x139 * x160 x162 = x15 * x161 * (x40 + x42) x163 = x160 * x64 x164 = x15 * (x161 * x45 + x163) x165 = x0 * x164 + x162 x166 = x160 * x4 x167 = x8**4 x168 = x1**4 / x13**4 x169 = x167 * x168 x170 = x169 * x39 x171 = x169 * x33 x172 = x0 * x171 + x170 x173 = x138 * x168 x174 = x11 * x173 x175 = x174 * x39 x176 = x174 * x33 x177 = x0 * x176 + x175 x178 = x168 * x39 x179 = x12 * x9 x180 = x178 * x179 x181 = x168 * x179 x182 = x181 * x33 x183 = x0 * x182 + x180 x184 = x160 * x8 x185 = x178 * x184 x186 = x168 * x184 x187 = x186 * x33 x188 = x0 * x187 + x185 x189 = x11**4 x190 = x168 * x189 x191 = x190 * x39 x192 = x190 * x33 x193 = x0 * x192 + x191 x194 = -x7 - A[1] x195 = -2.0 * x19 * x194 * x2 * x22 * x27 * x28 * x29 + x26 * x8 x196 = -x195 x197 = x196 * x5 x198 = 2.0 * x17 * x19 * x194 * x2 * x22 * x27 * x28 - x35 * x8 x199 = x198 * x37 x200 = x196 * x31 - x199 * x4 x201 = x200 * x4 x202 = x197 + x201 x203 = x44 * (x197 + x202) x204 = x106 * x6 x205 = x197 * x204 + x203 * x44 x206 = x139 * x61 x207 = x15 * (x197 * x206 + x205 * x44) x208 = x20 * x65 + x207 x209 = x168 * x67 x210 = x196 * x209 x211 = x20 * x69 x212 = x210 + x211 * x67 x213 = -x5 * (x195 + x199) x214 = 2.0 * x19 * x194 * x2 * x22 * x27 * x28 * x34 - x72 * x8 x215 = x200 * x31 + x213 - x73 * (x198 * x31 - x214 * x73) x216 = x215 * x4 x217 = x200 * x5 x218 = 2.0 * x217 x219 = 5.916079783099616 * x81 x220 = x196 * x8 x221 = x220 + x49 x222 = x15 * x221 x223 = x200 * x8 x224 = x223 + x41 x225 = x222 * x5 + x224 * x44 x226 = x106 * x4 x227 = x221 * x5 x228 = x225 * x44 + x226 * x227 x229 = x139 * x6 x230 = x15 * (x227 * x229 + x228 * x44) x231 = x20 * x93 + x230 x232 = x168 * x61 x233 = x221 * x232 x234 = x211 * x61 x235 = x233 + x234 * x8 x236 = x215 * x8 x237 = x236 + x76 x238 = x224 * x51 x239 = x197 * x97 x240 = x201 * x97 + x239 x241 = x11 * x197 x242 = x226 * x241 + x240 * x44 x243 = x15 * (x229 * x241 + x242 * x44) x244 = x104 * x20 + x243 x245 = x11 * x232 x246 = x196 * x245 x247 = x11 * x234 + x246 x248 = x218 * x97 x249 = x222 * x8 + x85 x250 = x83 * (x224 + x41) x251 = x249 * x78 + x250 * x44 x252 = x226 * x5 x253 = x15 * (x249 * x252 + x251 * x44) x254 = x113 * x20 + x253 x255 = x229 * x249 x256 = x115 * x211 + x255 x257 = x83 * (x237 + x76) x258 = x250 * x51 x259 = 1.732050807568877 x260 = 0.1111111111111111 * x259 * x80 x261 = x220 * x97 + x99 x262 = x41 * x97 x263 = x223 * x97 + x262 x264 = x261 * x78 + x263 * x44 x265 = x15 * (x252 * x261 + x264 * x44) x266 = x125 * x20 + x265 x267 = x229 * x261 x268 = x127 * x211 + x267 x269 = x76 * x97 x270 = x236 * x97 + x269 x271 = x263 * x51 x272 = 0.3333333333333333 * x80 x273 = x129 * x197 x274 = x129 * x201 + x273 x275 = x134 * x139 x276 = x15 * (x197 * x275 + x274 * x44) x277 = x135 * x20 + x276 x278 = x168 * x196 x279 = x137 * x278 x280 = x137 * x211 + x279 x281 = x129 * x218 x282 = x109 + x249 * x83 x283 = x107 * x41 + x250 * x83 x284 = x15 * (x282 * x78 + x283 * x44) x285 = x143 * x20 + x284 x286 = x226 * x282 x287 = x138 * x211 x288 = x286 + x287 * x4 x289 = x107 * x76 + x257 * x83 x290 = x283 * x51 x291 = x122 + x261 * x83 x292 = x119 * x41 + x263 * x83 x293 = x15 * (x291 * x78 + x292 * x44) x294 = x150 * x20 + x293 x295 = x226 * x291 x296 = x152 * x211 + x295 x297 = x119 * x76 + x270 * x83 x298 = x292 * x51 x299 = x129 * x220 + x131 x300 = x129 * x41 x301 = x129 * x223 + x300 x302 = x15 * (x299 * x78 + x301 * x44) x303 = x157 * x20 + x302 x304 = x226 * x299 x305 = x159 * x211 + x304 x306 = x129 * x76 x307 = x129 * x236 + x306 x308 = x301 * x51 x309 = x161 * x197 x310 = x15 * (x161 * x201 + x309) x311 = x164 * x20 + x310 x312 = x166 * x278 x313 = x166 * x211 + x312 x314 = x161 * x218 x315 = x15 * (x140 * x41 + x283 * x83) x316 = x171 * x20 + x315 x317 = x15 * (x142 + x282 * x83) x318 = x167 * x211 + x317 x319 = x15 * (x147 * x41 + x292 * x83) x320 = x176 * x20 + x319 x321 = x15 * (x149 + x291 * x83) x322 = x11 * x287 + x321 x323 = x15 * (x154 * x41 + x301 * x83) x324 = x182 * x20 + x323 x325 = x15 * (x156 + x299 * x83) x326 = x179 * x211 + x325 x327 = x161 * x41 x328 = x15 * (x161 * x223 + x327) x329 = x187 * x20 + x328 x330 = x15 * (x161 * x220 + x163) x331 = x184 * x211 + x330 x332 = x161 * x76 x333 = x190 * x200 x334 = x192 * x20 + x333 x335 = x190 * x196 x336 = x189 * x211 + x335 x337 = -x10 - A[2] x338 = x11 * x26 - 2.0 * x19 * x2 * x22 * x27 * x28 * x29 * x337 x339 = -x338 x340 = x339 * x5 x341 = -x11 * x35 + 2.0 * x17 * x19 * x2 * x22 * x27 * x28 * x337 x342 = x341 * x37 x343 = x31 * x339 - x342 * x4 x344 = x343 * x4 x345 = x340 + x344 x346 = x44 * (x340 + x345) x347 = x204 * x340 + x346 * x44 x348 = x15 * (x206 * x340 + x347 * x44) x349 = x21 * x65 + x348 x350 = x209 * x339 x351 = x21 * x69 x352 = x350 + x351 * x67 x353 = -x5 * (x338 + x342) x354 = -x11 * x72 + 2.0 * x19 * x2 * x22 * x27 * x28 * x337 * x34 x355 = x31 * x343 + x353 - x73 * (x31 * x341 - x354 * x73) x356 = x355 * x4 x357 = x343 * x5 x358 = 2.0 * x357 x359 = x340 * x83 x360 = x344 * x83 + x359 x361 = x226 * x8 x362 = x340 * x361 + x360 * x44 x363 = x229 * x8 x364 = x15 * (x340 * x363 + x362 * x44) x365 = x21 * x93 + x364 x366 = x232 * x8 x367 = x339 * x366 x368 = x351 * x61 x369 = x367 + x368 * x8 x370 = x11 * x339 + x49 x371 = x370 * x78 x372 = x11 * x343 + x41 x373 = x371 + x372 * x44 x374 = x252 * x370 + x373 * x44 x375 = x370 * x5 x376 = x15 * (x229 * x375 + x374 * x44) x377 = x104 * x21 + x376 x378 = x232 * x370 x379 = x11 * x368 + x378 x380 = x11 * x355 + x76 x381 = x372 * x51 x382 = x107 * x340 x383 = x107 * x344 + x382 x384 = x146 * x4 x385 = x15 * (x340 * x384 + x383 * x44) x386 = x113 * x21 + x385 x387 = x168 * x6 x388 = x387 * x9 x389 = x339 * x388 x390 = x115 * x351 + x389 x391 = x118 * x375 x392 = x361 * x372 + x391 x393 = x153 * x4 x394 = x15 * (x375 * x393 + x392 * x44) x395 = x125 * x21 + x394 x396 = x387 * x8 x397 = x370 * x396 x398 = x127 * x351 + x397 x399 = x372 * x46 x400 = x370 * x97 + x99 x401 = x400 * x78 x402 = x262 + x372 * x97 x403 = x401 + x402 * x44 x404 = x15 * (x252 * x400 + x403 * x44) x405 = x135 * x21 + x404 x406 = x229 * x400 x407 = x137 * x351 + x406 x408 = x269 + x380 * x97 x409 = x402 * x51 x410 = x140 * x340 x411 = x15 * (x140 * x344 + x410) x412 = x143 * x21 + x411 x413 = x173 * x4 x414 = x339 * x413 x415 = x138 * x351 x416 = x4 * x415 + x414 x417 = x146 * x375 x418 = x15 * (x372 * x384 + x417) x419 = x150 * x21 + x418 x420 = x112 * x168 x421 = x370 * x420 x422 = x152 * x351 + x421 x423 = x118 * x5 x424 = x400 * x423 x425 = x15 * (x361 * x402 + x424) x426 = x157 * x21 + x425 x427 = x393 * x400 x428 = x159 * x351 + x427 x429 = x131 + x400 * x97 x430 = x429 * x78 x431 = x300 + x402 * x97 x432 = x15 * (x430 + x431 * x44) x433 = x164 * x21 + x432 x434 = x226 * x429 x435 = x166 * x351 + x434 x436 = x306 + x408 * x97 x437 = x431 * x51 x438 = x169 * x343 x439 = x171 * x21 + x438 x440 = x169 * x339 x441 = x167 * x351 + x440 x442 = x173 * x372 x443 = x176 * x21 + x442 x444 = x173 * x370 x445 = x11 * x415 + x444 x446 = x146 * x402 x447 = x182 * x21 + x446 x448 = x146 * x400 x449 = x179 * x351 + x448 x450 = x118 * x431 x451 = x187 * x21 + x450 x452 = x118 * x429 x453 = x184 * x351 + x452 x454 = x15 * (x327 + x431 * x97) x455 = x192 * x21 + x454 x456 = x15 * (x163 + x429 * x97) x457 = x189 * x351 + x456 x458 = x194 * x196 - x199 * x8 + x30 x459 = x209 * x458 x460 = x20 * x210 + x459 x461 = x20 * x212 + x460 x462 = x458 * x5 x463 = x37 * x8 x464 = x194 * x198 - x214 * x463 + x71 x465 = x31 * x458 - x464 * x73 x466 = x4 * x465 x467 = x458 * x8 x468 = 2.0 * x197 x469 = x467 + x468 x470 = x232 * x469 x471 = x20 * x233 + x470 x472 = x20 * x235 + x471 x473 = x469 * x78 x474 = x465 * x8 x475 = x218 + x474 x476 = x229 * x5 x477 = x245 * x458 x478 = x20 * x246 + x477 x479 = x20 * x247 + x478 x480 = x462 * x97 x481 = x11 * x462 x482 = x222 * x46 + x469 * x83 x483 = x229 * x482 x484 = x20 * x255 + x483 x485 = x20 * x256 + x484 x486 = x482 * x78 x487 = x238 + x475 * x83 x488 = x97 * (x467 + x468) x489 = x229 * x488 x490 = x20 * x267 + x489 x491 = x20 * x268 + x490 x492 = x488 * x78 x493 = x248 + x474 * x97 x494 = x168 * x458 x495 = x137 * x494 x496 = x20 * x279 + x495 x497 = x20 * x280 + x496 x498 = x129 * x462 x499 = x249 * x51 + x482 * x83 x500 = x226 * x499 x501 = x20 * x286 + x500 x502 = x20 * x288 + x501 x503 = x499 * x78 x504 = x258 + x487 * x83 x505 = x261 * x51 + x488 * x83 x506 = x226 * x505 x507 = x20 * x295 + x506 x508 = x20 * x296 + x507 x509 = x505 * x78 x510 = x271 + x493 * x83 x511 = x129 * (x467 + x468) x512 = x226 * x511 x513 = x20 * x304 + x512 x514 = x20 * x305 + x513 x515 = x511 * x78 x516 = x129 * x474 + x281 x517 = x166 * x494 x518 = x20 * x312 + x517 x519 = x20 * x313 + x518 x520 = x161 * x462 x521 = x15 * (x282 * x51 + x499 * x83) x522 = x20 * x317 + x521 x523 = x20 * x318 + x522 x524 = x15 * (x291 * x51 + x505 * x83) x525 = x20 * x321 + x524 x526 = x20 * x322 + x525 x527 = x15 * (x299 * x51 + x511 * x83) x528 = x20 * x325 + x527 x529 = x20 * x326 + x528 x530 = x15 * x161 * (x467 + x468) x531 = x20 * x330 + x530 x532 = x20 * x331 + x531 x533 = x190 * x458 x534 = x20 * x335 + x533 x535 = x20 * x336 + x534 x536 = x194 * x339 - x342 * x8 x537 = x209 * x536 x538 = x21 * x210 + x537 x539 = x20 * x352 + x538 x540 = x5 * x536 x541 = x194 * x341 - x354 * x463 x542 = x31 * x536 - x541 * x73 x543 = 10.2469507659596 * x81 x544 = x340 + x536 * x8 x545 = x232 * x544 x546 = x21 * x233 + x545 x547 = x20 * x369 + x546 x548 = x357 + x542 * x8 x549 = x116 * x96 x550 = x11 * x536 + x197 x551 = x232 * x550 x552 = x21 * x246 + x551 x553 = x20 * x379 + x552 x554 = x11 * x542 + x217 x555 = x359 + x544 * x83 x556 = x229 * x555 x557 = x21 * x255 + x556 x558 = x20 * x390 + x557 x559 = x83 * (x357 + x548) x560 = x371 + x550 * x83 x561 = x229 * x560 x562 = x21 * x267 + x561 x563 = x20 * x398 + x562 x564 = x372 * x78 + x554 * x83 x565 = x259 * x272 x566 = x239 + x550 * x97 x567 = x229 * x566 x568 = x21 * x279 + x567 x569 = x20 * x407 + x568 x570 = x97 * (x217 + x554) x571 = x382 + x555 * x83 x572 = x226 * x571 x573 = x21 * x286 + x572 x574 = x20 * x416 + x573 x575 = x107 * x357 + x559 * x83 x576 = x391 + x560 * x83 x577 = x226 * x576 x578 = x21 * x295 + x577 x579 = x20 * x422 + x578 x580 = x372 * x423 + x564 * x83 x581 = x401 + x566 * x83 x582 = x226 * x581 x583 = x21 * x304 + x582 x584 = x20 * x428 + x583 x585 = x402 * x78 + x570 * x83 x586 = x273 + x566 * x97 x587 = x226 * x586 x588 = x21 * x312 + x587 x589 = x20 * x435 + x588 x590 = x129 * x217 + x570 * x97 x591 = x15 * (x410 + x571 * x83) x592 = x21 * x317 + x591 x593 = x20 * x441 + x592 x594 = x15 * (x417 + x576 * x83) x595 = x21 * x321 + x594 x596 = x20 * x445 + x595 x597 = x146 * x5 x598 = x15 * (x424 + x581 * x83) x599 = x21 * x325 + x598 x600 = x20 * x449 + x599 x601 = x15 * (x430 + x586 * x83) x602 = x21 * x330 + x601 x603 = x20 * x453 + x602 x604 = x15 * (x309 + x586 * x97) x605 = x21 * x335 + x604 x606 = x20 * x457 + x605 x607 = -x11 * x342 + x30 + x337 * x339 x608 = x209 * x607 x609 = x21 * x350 + x608 x610 = x21 * x352 + x609 x611 = x5 * x607 x612 = x11 * x37 x613 = x337 * x341 - x354 * x612 + x71 x614 = x31 * x607 - x613 * x73 x615 = x4 * x614 x616 = x366 * x607 x617 = x21 * x367 + x616 x618 = x21 * x369 + x617 x619 = x611 * x83 x620 = x11 * x607 + 2.0 * x340 x621 = x232 * x620 x622 = x21 * x378 + x621 x623 = x21 * x379 + x622 x624 = x620 * x78 x625 = x11 * x614 + x358 x626 = x388 * x607 x627 = x21 * x389 + x626 x628 = x21 * x390 + x627 x629 = x107 * x611 x630 = x396 * x620 x631 = x21 * x397 + x630 x632 = x21 * x398 + x631 x633 = x423 * x620 x634 = x370 * x51 + x620 * x97 x635 = x229 * x634 x636 = x21 * x406 + x635 x637 = x21 * x407 + x636 x638 = x634 * x78 x639 = x381 + x625 * x97 x640 = x413 * x607 x641 = x21 * x414 + x640 x642 = x21 * x416 + x641 x643 = x140 * x611 x644 = x420 * x620 x645 = x21 * x421 + x644 x646 = x21 * x422 + x645 x647 = x597 * x620 x648 = x393 * x634 x649 = x21 * x427 + x648 x650 = x21 * x428 + x649 x651 = x423 * x634 x652 = x400 * x51 + x634 * x97 x653 = x226 * x652 x654 = x21 * x434 + x653 x655 = x21 * x435 + x654 x656 = x652 * x78 x657 = x409 + x639 * x97 x658 = x169 * x607 x659 = x21 * x440 + x658 x660 = x21 * x441 + x659 x661 = x173 * x620 x662 = x21 * x444 + x661 x663 = x21 * x445 + x662 x664 = x146 * x634 x665 = x21 * x448 + x664 x666 = x21 * x449 + x665 x667 = x118 * x652 x668 = x21 * x452 + x667 x669 = x21 * x453 + x668 x670 = x15 * (x429 * x51 + x652 * x97) x671 = x21 * x456 + x670 x672 = x21 * x457 + x671 x673 = x194 * x458 + 2.0 * x213 - x463 * x464 x674 = x673 * x8 x675 = 3.0 * x462 x676 = x674 + x675 x677 = 3.0 * x473 + x676 * x83 x678 = x97 * (x674 + x675) x679 = x168 * x673 x680 = 3.0 * x486 + x677 * x83 x681 = 3.0 * x492 + x678 * x83 x682 = x129 * (x674 + x675) x683 = x194 * x536 + x353 - x463 * x541 x684 = 2.0 * x540 x685 = x683 * x8 + x684 x686 = x11 * x683 + x462 x687 = x51 * x544 + x685 * x83 x688 = x51 * x550 x689 = x686 * x83 + x688 x690 = x480 + x686 * x97 x691 = x51 * x555 + x687 * x83 x692 = x51 * x560 + x689 * x83 x693 = x51 * x566 x694 = x690 * x83 + x693 x695 = x498 + x690 * x97 x696 = x51 * x586 x697 = x194 * x607 - x463 * x613 x698 = x611 + x697 * x8 x699 = x11 * x697 + x684 x700 = x619 + x698 * x83 x701 = x624 + x699 * x83 x702 = x688 + x699 * x97 x703 = x629 + x700 * x83 x704 = x633 + x701 * x83 x705 = x638 + x702 * x83 x706 = x693 + x702 * x97 x707 = x337 * x607 + 2.0 * x353 - x612 * x613 x708 = x11 * x707 + 3.0 * x611 x709 = 3.0 * x624 + x708 * x97 x710 = 3.0 * x638 + x709 * x97 # 150 item(s) result[0, 0, 0] = numpy.sum( x82 * ( x0 * x60 + x0 * x66 + x0 * (x0 * (x65 + x67 * x70) + x66) + x15 * (x44 * (x44 * (x43 * x79 + x44 * (x75 + x77)) + x52 * x79) + x56 * x79) ) ) result[0, 0, 1] = numpy.sum( x96 * ( x0 * x91 + x0 * x94 + x0 * (x0 * (x8 * x95 + x93) + x94) + x15 * (x44 * (x44 * x83 * (x75 + x77) + x79 * x84) + x79 * x87) ) ) result[0, 0, 2] = numpy.sum( x96 * ( x0 * x103 + x0 * x105 + x0 * (x0 * (x104 + x11 * x95) + x105) + x15 * (x101 * x79 + x44 * (x44 * x97 * (x75 + x77) + x79 * x98)) ) ) result[0, 0, 3] = numpy.sum( x117 * ( x0 * x111 + x0 * x114 + x0 * (x0 * (x113 + x115 * x70) + x114) + x15 * (x107 * x44 * (x75 + x77) + x108 * x79) ) ) result[0, 0, 4] = numpy.sum( x128 * ( x0 * x124 + x0 * x126 + x0 * (x0 * (x125 + x127 * x70) + x126) + x15 * (x119 * x44 * (x75 + x77) + x120 * x79) ) ) result[0, 0, 5] = numpy.sum( x117 * ( x0 * x133 + x0 * x136 + x0 * (x0 * (x135 + x137 * x70) + x136) + x15 * (x129 * x44 * (x75 + x77) + x130 * x79) ) ) result[0, 0, 6] = numpy.sum( x96 * ( x0 * x141 + x0 * x144 + x0 * (x0 * (x143 + x145 * x4) + x144) + x140 * x15 * (x75 + x77) ) ) result[0, 0, 7] = numpy.sum( x128 * ( x0 * x148 + x0 * x151 + x0 * (x0 * (x150 + x152 * x70) + x151) + x147 * x15 * (x75 + x77) ) ) result[0, 0, 8] = numpy.sum( x128 * ( x0 * x155 + x0 * x158 + x0 * (x0 * (x157 + x159 * x70) + x158) + x15 * x154 * (x75 + x77) ) ) result[0, 0, 9] = numpy.sum( x96 * ( x0 * x162 + x0 * x165 + x0 * (x0 * (x164 + x166 * x70) + x165) + x15 * x161 * (x75 + x77) ) ) result[0, 0, 10] = numpy.sum( x82 * (x0 * x170 + x0 * x172 + x0 * (x0 * (x167 * x70 + x171) + x172) + x169 * x74) ) result[0, 0, 11] = numpy.sum( x96 * (x0 * x175 + x0 * x177 + x0 * (x0 * (x11 * x145 + x176) + x177) + x174 * x74) ) result[0, 0, 12] = numpy.sum( x117 * (x0 * x180 + x0 * x183 + x0 * (x0 * (x179 * x70 + x182) + x183) + x181 * x74) ) result[0, 0, 13] = numpy.sum( x96 * (x0 * x185 + x0 * x188 + x0 * (x0 * (x184 * x70 + x187) + x188) + x186 * x74) ) result[0, 0, 14] = numpy.sum( x82 * (x0 * x191 + x0 * x193 + x0 * (x0 * (x189 * x70 + x192) + x193) + x190 * x74) ) result[0, 1, 0] = numpy.sum( x219 * ( x0 * x208 + x0 * (x0 * x212 + x208) + x15 * (x205 * x51 + x44 * (x203 * x51 + x44 * (x202 * x51 + x44 * (x216 + x218)))) + x20 * x60 ) ) result[0, 1, 1] = numpy.sum( x128 * ( x0 * x231 + x0 * (x0 * x235 + x231) + x15 * (x228 * x51 + x44 * (x225 * x51 + x44 * (x237 * x44 + x238))) + x20 * x91 ) ) result[0, 1, 2] = numpy.sum( x128 * ( x0 * x244 + x0 * (x0 * x247 + x244) + x103 * x20 + x15 * (x242 * x51 + x44 * (x240 * x51 + x44 * (x216 * x97 + x248))) ) ) result[0, 1, 3] = numpy.sum( x260 * ( x0 * x254 + x0 * (x0 * x256 + x254) + x111 * x20 + x15 * (x251 * x51 + x44 * (x257 * x44 + x258)) ) ) result[0, 1, 4] = numpy.sum( x272 * ( x0 * x266 + x0 * (x0 * x268 + x266) + x124 * x20 + x15 * (x264 * x51 + x44 * (x270 * x44 + x271)) ) ) result[0, 1, 5] = numpy.sum( x260 * ( x0 * x277 + x0 * (x0 * x280 + x277) + x133 * x20 + x15 * (x274 * x51 + x44 * (x129 * x216 + x281)) ) ) result[0, 1, 6] = numpy.sum( x128 * (x0 * x285 + x0 * (x0 * x288 + x285) + x141 * x20 + x15 * (x289 * x44 + x290)) ) result[0, 1, 7] = numpy.sum( x272 * (x0 * x294 + x0 * (x0 * x296 + x294) + x148 * x20 + x15 * (x297 * x44 + x298)) ) result[0, 1, 8] = numpy.sum( x272 * (x0 * x303 + x0 * (x0 * x305 + x303) + x15 * (x307 * x44 + x308) + x155 * x20) ) result[0, 1, 9] = numpy.sum( x128 * (x0 * x311 + x0 * (x0 * x313 + x311) + x15 * (x161 * x216 + x314) + x162 * x20) ) result[0, 1, 10] = numpy.sum( x219 * ( x0 * x316 + x0 * (x0 * x318 + x316) + x15 * (x140 * x76 + x289 * x83) + x170 * x20 ) ) result[0, 1, 11] = numpy.sum( x128 * ( x0 * x320 + x0 * (x0 * x322 + x320) + x15 * (x147 * x76 + x297 * x83) + x175 * x20 ) ) result[0, 1, 12] = numpy.sum( x260 * ( x0 * x324 + x0 * (x0 * x326 + x324) + x15 * (x154 * x76 + x307 * x83) + x180 * x20 ) ) result[0, 1, 13] = numpy.sum( x128 * (x0 * x329 + x0 * (x0 * x331 + x329) + x15 * (x161 * x236 + x332) + x185 * x20) ) result[0, 1, 14] = numpy.sum( x219 * (x0 * x334 + x0 * (x0 * x336 + x334) + x190 * x215 + x191 * x20) ) result[0, 2, 0] = numpy.sum( x219 * ( x0 * x349 + x0 * (x0 * x352 + x349) + x15 * (x347 * x51 + x44 * (x346 * x51 + x44 * (x345 * x51 + x44 * (x356 + x358)))) + x21 * x60 ) ) result[0, 2, 1] = numpy.sum( x128 * ( x0 * x365 + x0 * (x0 * x369 + x365) + x15 * (x362 * x51 + x44 * (x360 * x51 + x44 * x83 * (x356 + x358))) + x21 * x91 ) ) result[0, 2, 2] = numpy.sum( x128 * ( x0 * x377 + x0 * (x0 * x379 + x377) + x103 * x21 + x15 * (x374 * x51 + x44 * (x373 * x51 + x44 * (x380 * x44 + x381))) ) ) result[0, 2, 3] = numpy.sum( x260 * ( x0 * x386 + x0 * (x0 * x390 + x386) + x111 * x21 + x15 * (x107 * x44 * (x356 + x358) + x383 * x51) ) ) result[0, 2, 4] = numpy.sum( x272 * ( x0 * x395 + x0 * (x0 * x398 + x395) + x124 * x21 + x15 * (x392 * x51 + x44 * (x118 * x399 + x361 * x380)) ) ) result[0, 2, 5] = numpy.sum( x260 * ( x0 * x405 + x0 * (x0 * x407 + x405) + x133 * x21 + x15 * (x403 * x51 + x44 * (x408 * x44 + x409)) ) ) result[0, 2, 6] = numpy.sum( x128 * (x0 * x412 + x0 * (x0 * x416 + x412) + x140 * x15 * (x356 + x358) + x141 * x21) ) result[0, 2, 7] = numpy.sum( x272 * ( x0 * x419 + x0 * (x0 * x422 + x419) + x148 * x21 + x15 * (x146 * x399 + x380 * x384) ) ) result[0, 2, 8] = numpy.sum( x272 * ( x0 * x426 + x0 * (x0 * x428 + x426) + x15 * (x118 * x402 * x46 + x361 * x408) + x155 * x21 ) ) result[0, 2, 9] = numpy.sum( x128 * (x0 * x433 + x0 * (x0 * x435 + x433) + x15 * (x436 * x44 + x437) + x162 * x21) ) result[0, 2, 10] = numpy.sum( x219 * (x0 * x439 + x0 * (x0 * x441 + x439) + x169 * x355 + x170 * x21) ) result[0, 2, 11] = numpy.sum( x128 * (x0 * x443 + x0 * (x0 * x445 + x443) + x173 * x380 + x175 * x21) ) result[0, 2, 12] = numpy.sum( x260 * (x0 * x447 + x0 * (x0 * x449 + x447) + x146 * x408 + x180 * x21) ) result[0, 2, 13] = numpy.sum( x128 * (x0 * x451 + x0 * (x0 * x453 + x451) + x118 * x436 + x185 * x21) ) result[0, 2, 14] = numpy.sum( x219 * (x0 * x455 + x0 * (x0 * x457 + x455) + x15 * (x332 + x436 * x97) + x191 * x21) ) result[0, 3, 0] = numpy.sum( x219 * ( x0 * x461 + x15 * (x206 * x462 + x44 * (x204 * x462 + x44**2 * (2.0 * x462 + x466))) + x20 * x207 + x20 * x208 ) ) result[0, 3, 1] = numpy.sum( x128 * ( x0 * x472 + x15 * (x44 * (x252 * x469 + x44 * (x44 * x475 + x473)) + x469 * x476) + x20 * x230 + x20 * x231 ) ) result[0, 3, 2] = numpy.sum( x128 * ( x0 * x479 + x15 * (x229 * x481 + x44 * (x226 * x481 + x44 * (x466 * x97 + x480))) + x20 * x243 + x20 * x244 ) ) result[0, 3, 3] = numpy.sum( x260 * ( x0 * x485 + x15 * (x252 * x482 + x44 * (x44 * x487 + x486)) + x20 * x253 + x20 * x254 ) ) result[0, 3, 4] = numpy.sum( x272 * ( x0 * x491 + x15 * (x252 * x488 + x44 * (x44 * x493 + x492)) + x20 * x265 + x20 * x266 ) ) result[0, 3, 5] = numpy.sum( x260 * ( x0 * x497 + x15 * (x275 * x462 + x44 * (x129 * x466 + x498)) + x20 * x276 + x20 * x277 ) ) result[0, 3, 6] = numpy.sum( x128 * (x0 * x502 + x15 * (x44 * x504 + x503) + x20 * x284 + x20 * x285) ) result[0, 3, 7] = numpy.sum( x272 * (x0 * x508 + x15 * (x44 * x510 + x509) + x20 * x293 + x20 * x294) ) result[0, 3, 8] = numpy.sum( x272 * (x0 * x514 + x15 * (x44 * x516 + x515) + x20 * x302 + x20 * x303) ) result[0, 3, 9] = numpy.sum( x128 * (x0 * x519 + x15 * (x161 * x466 + x520) + x20 * x310 + x20 * x311) ) result[0, 3, 10] = numpy.sum( x219 * (x0 * x523 + x15 * (x290 + x504 * x83) + x20 * x315 + x20 * x316) ) result[0, 3, 11] = numpy.sum( x128 * (x0 * x526 + x15 * (x298 + x510 * x83) + x20 * x319 + x20 * x320) ) result[0, 3, 12] = numpy.sum( x260 * (x0 * x529 + x15 * (x308 + x516 * x83) + x20 * x323 + x20 * x324) ) result[0, 3, 13] = numpy.sum( x128 * (x0 * x532 + x15 * (x161 * x474 + x314) + x20 * x328 + x20 * x329) ) result[0, 3, 14] = numpy.sum( x219 * (x0 * x535 + x190 * x465 + x20 * x333 + x20 * x334) ) result[0, 4, 0] = numpy.sum( x543 * ( x0 * x539 + x15 * (x206 * x540 + x44 * (x204 * x540 + x44**2 * (x4 * x542 + 2.0 * x540))) + x20 * x349 + x207 * x21 ) ) result[0, 4, 1] = numpy.sum( x549 * ( x0 * x547 + x15 * (x44 * (x252 * x544 + x44 * (x44 * x548 + x544 * x78)) + x476 * x544) + x20 * x365 + x21 * x230 ) ) result[0, 4, 2] = numpy.sum( x549 * ( x0 * x553 + x15 * (x44 * (x252 * x550 + x44 * (x44 * x554 + x550 * x78)) + x476 * x550) + x20 * x377 + x21 * x243 ) ) result[0, 4, 3] = numpy.sum( x272 * ( x0 * x558 + x15 * (x252 * x555 + x44 * (x44 * x559 + x555 * x78)) + x20 * x386 + x21 * x253 ) ) result[0, 4, 4] = numpy.sum( x565 * ( x0 * x563 + x15 * (x252 * x560 + x44 * (x44 * x564 + x560 * x78)) + x20 * x395 + x21 * x265 ) ) result[0, 4, 5] = numpy.sum( x272 * ( x0 * x569 + x15 * (x252 * x566 + x44 * (x44 * x570 + x566 * x78)) + x20 * x405 + x21 * x276 ) ) result[0, 4, 6] = numpy.sum( x549 * (x0 * x574 + x15 * (x44 * x575 + x571 * x78) + x20 * x412 + x21 * x284) ) result[0, 4, 7] = numpy.sum( x565 * (x0 * x579 + x15 * (x44 * x580 + x576 * x78) + x20 * x419 + x21 * x293) ) result[0, 4, 8] = numpy.sum( x565 * (x0 * x584 + x15 * (x44 * x585 + x581 * x78) + x20 * x426 + x21 * x302) ) result[0, 4, 9] = numpy.sum( x549 * (x0 * x589 + x15 * (x44 * x590 + x586 * x78) + x20 * x433 + x21 * x310) ) result[0, 4, 10] = numpy.sum( x543 * (x0 * x593 + x15 * (x140 * x357 + x575 * x83) + x20 * x439 + x21 * x315) ) result[0, 4, 11] = numpy.sum( x549 * (x0 * x596 + x15 * (x372 * x597 + x580 * x83) + x20 * x443 + x21 * x319) ) result[0, 4, 12] = numpy.sum( x272 * (x0 * x600 + x15 * (x402 * x423 + x585 * x83) + x20 * x447 + x21 * x323) ) result[0, 4, 13] = numpy.sum( x549 * (x0 * x603 + x15 * (x431 * x78 + x590 * x83) + x20 * x451 + x21 * x328) ) result[0, 4, 14] = numpy.sum( x543 * (x0 * x606 + x15 * (x161 * x217 + x590 * x97) + x20 * x455 + x21 * x333) ) result[0, 5, 0] = numpy.sum( x219 * ( x0 * x610 + x15 * (x206 * x611 + x44 * (x204 * x611 + x44**2 * (2.0 * x611 + x615))) + x21 * x348 + x21 * x349 ) ) result[0, 5, 1] = numpy.sum( x128 * ( x0 * x618 + x15 * (x363 * x611 + x44 * (x361 * x611 + x44 * (x615 * x83 + x619))) + x21 * x364 + x21 * x365 ) ) result[0, 5, 2] = numpy.sum( x128 * ( x0 * x623 + x15 * (x44 * (x252 * x620 + x44 * (x44 * x625 + x624)) + x476 * x620) + x21 * x376 + x21 * x377 ) ) result[0, 5, 3] = numpy.sum( x260 * ( x0 * x628 + x15 * (x384 * x611 + x44 * (x107 * x615 + x629)) + x21 * x385 + x21 * x386 ) ) result[0, 5, 4] = numpy.sum( x272 * ( x0 * x632 + x15 * (x393 * x5 * x620 + x44 * (x361 * x625 + x633)) + x21 * x394 + x21 * x395 ) ) result[0, 5, 5] = numpy.sum( x260 * ( x0 * x637 + x15 * (x252 * x634 + x44 * (x44 * x639 + x638)) + x21 * x404 + x21 * x405 ) ) result[0, 5, 6] = numpy.sum( x128 * (x0 * x642 + x15 * (x140 * x615 + x643) + x21 * x411 + x21 * x412) ) result[0, 5, 7] = numpy.sum( x272 * (x0 * x646 + x15 * (x384 * x625 + x647) + x21 * x418 + x21 * x419) ) result[0, 5, 8] = numpy.sum( x272 * (x0 * x650 + x15 * (x361 * x639 + x651) + x21 * x425 + x21 * x426) ) result[0, 5, 9] = numpy.sum( x128 * (x0 * x655 + x15 * (x44 * x657 + x656) + x21 * x432 + x21 * x433) ) result[0, 5, 10] = numpy.sum( x219 * (x0 * x660 + x169 * x614 + x21 * x438 + x21 * x439) ) result[0, 5, 11] = numpy.sum( x128 * (x0 * x663 + x173 * x625 + x21 * x442 + x21 * x443) ) result[0, 5, 12] = numpy.sum( x260 * (x0 * x666 + x146 * x639 + x21 * x446 + x21 * x447) ) result[0, 5, 13] = numpy.sum( x128 * (x0 * x669 + x118 * x657 + x21 * x450 + x21 * x451) ) result[0, 5, 14] = numpy.sum( x219 * (x0 * x672 + x15 * (x437 + x657 * x97) + x21 * x454 + x21 * x455) ) result[0, 6, 0] = numpy.sum( x82 * (x20 * x459 + x20 * x460 + x20 * x461 + x209 * x673) ) result[0, 6, 1] = numpy.sum( x96 * (x20 * x470 + x20 * x471 + x20 * x472 + x232 * x676) ) result[0, 6, 2] = numpy.sum( x96 * (x20 * x477 + x20 * x478 + x20 * x479 + x245 * x673) ) result[0, 6, 3] = numpy.sum( x117 * (x20 * x483 + x20 * x484 + x20 * x485 + x229 * x677) ) result[0, 6, 4] = numpy.sum( x128 * (x20 * x489 + x20 * x490 + x20 * x491 + x229 * x678) ) result[0, 6, 5] = numpy.sum( x117 * (x137 * x679 + x20 * x495 + x20 * x496 + x20 * x497) ) result[0, 6, 6] = numpy.sum( x96 * (x20 * x500 + x20 * x501 + x20 * x502 + x226 * x680) ) result[0, 6, 7] = numpy.sum( x128 * (x20 * x506 + x20 * x507 + x20 * x508 + x226 * x681) ) result[0, 6, 8] = numpy.sum( x128 * (x20 * x512 + x20 * x513 + x20 * x514 + x226 * x682) ) result[0, 6, 9] = numpy.sum( x96 * (x166 * x679 + x20 * x517 + x20 * x518 + x20 * x519) ) result[0, 6, 10] = numpy.sum( x82 * (x15 * (3.0 * x503 + x680 * x83) + x20 * x521 + x20 * x522 + x20 * x523) ) result[0, 6, 11] = numpy.sum( x96 * (x15 * (3.0 * x509 + x681 * x83) + x20 * x524 + x20 * x525 + x20 * x526) ) result[0, 6, 12] = numpy.sum( x117 * (x15 * (3.0 * x515 + x682 * x83) + x20 * x527 + x20 * x528 + x20 * x529) ) result[0, 6, 13] = numpy.sum( x96 * (x15 * x161 * (x674 + x675) + x20 * x530 + x20 * x531 + x20 * x532) ) result[0, 6, 14] = numpy.sum( x82 * (x190 * x673 + x20 * x533 + x20 * x534 + x20 * x535) ) result[0, 7, 0] = numpy.sum( x219 * (x20 * x538 + x20 * x539 + x209 * x683 + x21 * x459) ) result[0, 7, 1] = numpy.sum( x128 * (x20 * x546 + x20 * x547 + x21 * x470 + x232 * x685) ) result[0, 7, 2] = numpy.sum( x128 * (x20 * x552 + x20 * x553 + x21 * x477 + x232 * x686) ) result[0, 7, 3] = numpy.sum( x260 * (x20 * x557 + x20 * x558 + x21 * x483 + x229 * x687) ) result[0, 7, 4] = numpy.sum( x272 * (x20 * x562 + x20 * x563 + x21 * x489 + x229 * x689) ) result[0, 7, 5] = numpy.sum( x260 * (x20 * x568 + x20 * x569 + x21 * x495 + x229 * x690) ) result[0, 7, 6] = numpy.sum( x128 * (x20 * x573 + x20 * x574 + x21 * x500 + x226 * x691) ) result[0, 7, 7] = numpy.sum( x272 * (x20 * x578 + x20 * x579 + x21 * x506 + x226 * x692) ) result[0, 7, 8] = numpy.sum( x272 * (x20 * x583 + x20 * x584 + x21 * x512 + x226 * x694) ) result[0, 7, 9] = numpy.sum( x128 * (x20 * x588 + x20 * x589 + x21 * x517 + x226 * x695) ) result[0, 7, 10] = numpy.sum( x219 * (x15 * (x51 * x571 + x691 * x83) + x20 * x592 + x20 * x593 + x21 * x521) ) result[0, 7, 11] = numpy.sum( x128 * (x15 * (x51 * x576 + x692 * x83) + x20 * x595 + x20 * x596 + x21 * x524) ) result[0, 7, 12] = numpy.sum( x260 * (x15 * (x51 * x581 + x694 * x83) + x20 * x599 + x20 * x600 + x21 * x527) ) result[0, 7, 13] = numpy.sum( x128 * (x15 * (x695 * x83 + x696) + x20 * x602 + x20 * x603 + x21 * x530) ) result[0, 7, 14] = numpy.sum( x219 * (x15 * (x520 + x695 * x97) + x20 * x605 + x20 * x606 + x21 * x533) ) result[0, 8, 0] = numpy.sum( x219 * (x20 * x610 + x209 * x697 + x21 * x537 + x21 * x538) ) result[0, 8, 1] = numpy.sum( x128 * (x20 * x618 + x21 * x545 + x21 * x546 + x232 * x698) ) result[0, 8, 2] = numpy.sum( x128 * (x20 * x623 + x21 * x551 + x21 * x552 + x232 * x699) ) result[0, 8, 3] = numpy.sum( x260 * (x20 * x628 + x21 * x556 + x21 * x557 + x229 * x700) ) result[0, 8, 4] = numpy.sum( x272 * (x20 * x632 + x21 * x561 + x21 * x562 + x229 * x701) ) result[0, 8, 5] = numpy.sum( x260 * (x20 * x637 + x21 * x567 + x21 * x568 + x229 * x702) ) result[0, 8, 6] = numpy.sum( x128 * (x20 * x642 + x21 * x572 + x21 * x573 + x226 * x703) ) result[0, 8, 7] = numpy.sum( x272 * (x20 * x646 + x21 * x577 + x21 * x578 + x226 * x704) ) result[0, 8, 8] = numpy.sum( x272 * (x20 * x650 + x21 * x582 + x21 * x583 + x226 * x705) ) result[0, 8, 9] = numpy.sum( x128 * (x20 * x655 + x21 * x587 + x21 * x588 + x226 * x706) ) result[0, 8, 10] = numpy.sum( x219 * (x15 * (x643 + x703 * x83) + x20 * x660 + x21 * x591 + x21 * x592) ) result[0, 8, 11] = numpy.sum( x128 * (x15 * (x647 + x704 * x83) + x20 * x663 + x21 * x594 + x21 * x595) ) result[0, 8, 12] = numpy.sum( x260 * (x15 * (x651 + x705 * x83) + x20 * x666 + x21 * x598 + x21 * x599) ) result[0, 8, 13] = numpy.sum( x128 * (x15 * (x656 + x706 * x83) + x20 * x669 + x21 * x601 + x21 * x602) ) result[0, 8, 14] = numpy.sum( x219 * (x15 * (x696 + x706 * x97) + x20 * x672 + x21 * x604 + x21 * x605) ) result[0, 9, 0] = numpy.sum( x82 * (x209 * x707 + x21 * x608 + x21 * x609 + x21 * x610) ) result[0, 9, 1] = numpy.sum( x96 * (x21 * x616 + x21 * x617 + x21 * x618 + x366 * x707) ) result[0, 9, 2] = numpy.sum( x96 * (x21 * x621 + x21 * x622 + x21 * x623 + x232 * x708) ) result[0, 9, 3] = numpy.sum( x117 * (x21 * x626 + x21 * x627 + x21 * x628 + x388 * x707) ) result[0, 9, 4] = numpy.sum( x128 * (x21 * x630 + x21 * x631 + x21 * x632 + x396 * x708) ) result[0, 9, 5] = numpy.sum( x117 * (x21 * x635 + x21 * x636 + x21 * x637 + x229 * x709) ) result[0, 9, 6] = numpy.sum( x96 * (x21 * x640 + x21 * x641 + x21 * x642 + x413 * x707) ) result[0, 9, 7] = numpy.sum( x128 * (x21 * x644 + x21 * x645 + x21 * x646 + x420 * x708) ) result[0, 9, 8] = numpy.sum( x128 * (x21 * x648 + x21 * x649 + x21 * x650 + x393 * x709) ) result[0, 9, 9] = numpy.sum( x96 * (x21 * x653 + x21 * x654 + x21 * x655 + x226 * x710) ) result[0, 9, 10] = numpy.sum( x82 * (x169 * x707 + x21 * x658 + x21 * x659 + x21 * x660) ) result[0, 9, 11] = numpy.sum( x96 * (x173 * x708 + x21 * x661 + x21 * x662 + x21 * x663) ) result[0, 9, 12] = numpy.sum( x117 * (x146 * x709 + x21 * x664 + x21 * x665 + x21 * x666) ) result[0, 9, 13] = numpy.sum( x96 * (x118 * x710 + x21 * x667 + x21 * x668 + x21 * x669) ) result[0, 9, 14] = numpy.sum( x82 * (x15 * (3.0 * x656 + x710 * x97) + x21 * x670 + x21 * x671 + x21 * x672) ) return result
[docs] def int3c2e3d_sph_100(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ps|s) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 1, 1), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = x2 + C[0] x4 = cx + x0 x5 = x4 ** (-1.0) x6 = -x1 * (ax * A[1] + bx * B[1]) x7 = x6 + C[1] x8 = -x1 * (ax * A[2] + bx * B[2]) x9 = x8 + C[2] x10 = cx * x0 * x5 * (x3**2 + x7**2 + x9**2) x11 = x5 * boys(1, x10) x12 = cx ** (-1.0) x13 = boys(0, x10) x14 = ( 34.98683665524972 * da * db * dc * x1 * x4 ** (-0.5) * numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) ) # 3 item(s) result[0, 0, 0] = numpy.sum(x14 * (x11 * x3 - x12 * x13 * (x2 + A[0]))) result[1, 0, 0] = numpy.sum(x14 * (x11 * x7 - x12 * x13 * (x6 + A[1]))) result[2, 0, 0] = numpy.sum(x14 * (x11 * x9 - x12 * x13 * (x8 + A[2]))) return result
[docs] def int3c2e3d_sph_101(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ps|p) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 1, 3), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = x2 + C[0] x4 = cx + x0 x5 = x4 ** (-1.0) x6 = -x1 * (ax * A[1] + bx * B[1]) x7 = x6 + C[1] x8 = -x1 * (ax * A[2] + bx * B[2]) x9 = x8 + C[2] x10 = cx * x0 * x5 * (x3**2 + x7**2 + x9**2) x11 = x5 * boys(2, x10) x12 = cx ** (-1.0) x13 = boys(1, x10) x14 = -2.0 * x11 * x3 + 2.0 * x12 * x13 * (x2 + A[0]) x15 = x1 * x12 * x13 x16 = ( 17.49341832762486 * da * db * dc * x4 ** (-1.5) * numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) ) x17 = x14 * x16 x18 = -2.0 * x11 * x7 + 2.0 * x12 * x13 * (x6 + A[1]) x19 = x16 * x18 x20 = -2.0 * x11 * x9 + 2.0 * x12 * x13 * (x8 + A[2]) x21 = x16 * x20 # 9 item(s) result[0, 0, 0] = numpy.sum(x16 * (x14 * x3 + x15)) result[0, 0, 1] = numpy.sum(x17 * x7) result[0, 0, 2] = numpy.sum(x17 * x9) result[1, 0, 0] = numpy.sum(x19 * x3) result[1, 0, 1] = numpy.sum(x16 * (x15 + x18 * x7)) result[1, 0, 2] = numpy.sum(x19 * x9) result[2, 0, 0] = numpy.sum(x21 * x3) result[2, 0, 1] = numpy.sum(x21 * x7) result[2, 0, 2] = numpy.sum(x16 * (x15 + x20 * x9)) return result
[docs] def int3c2e3d_sph_102(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ps|d) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 1, 6), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = x2 + C[0] x4 = -x3 x5 = cx + x0 x6 = x5 ** (-1.0) x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x8 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = x10 + C[2] x12 = -x11 x13 = cx * x0 * x6 x14 = x13 * (x12**2 + x4**2 + x9**2) x15 = x6 * boys(3, x14) x16 = x2 + A[0] x17 = cx ** (-1.0) x18 = x17 * boys(2, x14) x19 = 2.0 * x3 x20 = x19 * (x15 * x4 + x16 * x18) x21 = x3**2 x22 = x8**2 x23 = x11**2 x24 = x13 * (x21 + x22 + x23) x25 = boys(2, x24) x26 = x1 * x17 * x25 x27 = 2.0 * x26 x28 = ( 17.49341832762486 * da * db * dc * x0 * x5 ** (-2.5) * numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) ) x29 = x28 * x3 x30 = 1.732050807568877 x31 = 0.3333333333333333 * x30 x32 = x28 * (x20 + x26) x33 = x6 * boys(3, x24) x34 = x16 * x17 * x25 - x3 * x33 x35 = 0.6666666666666667 * x28 * x30 x36 = x34 * x35 x37 = 2.0 * x8 x38 = x11 * x28 x39 = x7 + A[1] x40 = x17 * x25 * x39 - x33 * x8 x41 = x35 * x40 x42 = x37 * (x15 * x9 + x18 * x39) x43 = x28 * x8 x44 = x10 + A[2] x45 = -x11 * x33 + x17 * x25 * x44 x46 = x35 * x45 x47 = 2.0 * x11 x48 = x26 + x45 * x47 # 18 item(s) result[0, 0, 0] = numpy.sum(-x29 * x31 * (x20 + x27)) result[0, 0, 1] = numpy.sum(-x32 * x8) result[0, 0, 2] = numpy.sum(-x11 * x32) result[0, 0, 3] = numpy.sum(-x22 * x36) result[0, 0, 4] = numpy.sum(-x34 * x37 * x38) result[0, 0, 5] = numpy.sum(-x23 * x36) result[1, 0, 0] = numpy.sum(-x21 * x41) result[1, 0, 1] = numpy.sum(-x29 * (x26 + x37 * x40)) result[1, 0, 2] = numpy.sum(-x19 * x38 * x40) result[1, 0, 3] = numpy.sum(-x31 * x43 * (x27 + x42)) result[1, 0, 4] = numpy.sum(-x38 * (x26 + x42)) result[1, 0, 5] = numpy.sum(-x23 * x41) result[2, 0, 0] = numpy.sum(-x21 * x46) result[2, 0, 1] = numpy.sum(-x19 * x43 * x45) result[2, 0, 2] = numpy.sum(-x29 * x48) result[2, 0, 3] = numpy.sum(-x22 * x46) result[2, 0, 4] = numpy.sum(-x43 * x48) result[2, 0, 5] = numpy.sum(-x31 * x38 * (x27 + x47 * (x12 * x15 + x18 * x44))) return result
[docs] def int3c2e3d_sph_103(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ps|f) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 1, 10), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - C[0] x4 = cx + x0 x5 = x4 ** (-1.5) x6 = x3 * x5 x7 = x3**2 x8 = -x1 * (ax * A[1] + bx * B[1]) x9 = -x8 - C[1] x10 = x9**2 x11 = -x1 * (ax * A[2] + bx * B[2]) x12 = -x11 - C[2] x13 = x12**2 x14 = x0 / x4 x15 = cx * x14 * (x10 + x13 + x7) x16 = 17.49341832762486 x17 = numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) x18 = 2.0 * x16 * x17 x19 = x1 * x18 x20 = x19 * boys(4, x15) x21 = cx ** (-1.0) x22 = x4 ** (-0.5) x23 = boys(3, x15) x24 = -2.0 * x1 * x16 * x17 * x21 * x22 * x23 * (x2 + A[0]) - x20 * x6 x25 = x24 * x3 x26 = 0.5 / (ax + bx) x27 = x21 * x23 x28 = x19 * x22 * x26 * x27 x29 = x14 * x3 x30 = x18 * x26 * x27 x31 = x0 * x30 * x4 ** (-2.5) x32 = da * db * dc x33 = x14 * x32 x34 = 0.2581988897471611 x35 = x33 * x34 x36 = x14 * x9 x37 = x30 * x5 x38 = x37 * x9 x39 = x3 * x31 x40 = 0.5773502691896258 x41 = x33 * x40 x42 = x12 * x14 x43 = x12 * x37 x44 = x0**2 / x4**2 x45 = x25 * x44 x46 = x10 * x31 x47 = x12 * x9 x48 = x31 * x47 x49 = x13 * x31 x50 = x9**3 x51 = x0**3 / x4**3 x52 = x32 * x51 x53 = x34 * x52 x54 = x24 * x53 x55 = x10 * x40 x56 = x24 * x52 x57 = x40 * x9 x58 = x12**3 x59 = x3**3 x60 = x20 * x5 x61 = -2.0 * x1 * x16 * x17 * x21 * x22 * x23 * (x8 + A[1]) - x60 * x9 x62 = x53 * x61 x63 = x61 * x9 x64 = x28 + x63 x65 = x40 * x7 x66 = x52 * x65 x67 = x36 * x64 + x38 x68 = x3 * x32 x69 = x44 * x68 x70 = x40 * x69 x71 = x42 * x63 + x43 x72 = x51 * x68 x73 = -2.0 * x1 * x16 * x17 * x21 * x22 * x23 * (x11 + A[2]) - x12 * x60 x74 = x53 * x73 x75 = x12 * x73 + x28 x76 = x51 * x75 x77 = x32 * x76 x78 = x42 * x75 + x43 # 30 item(s) result[0, 0, 0] = numpy.sum(x35 * (x29 * (x29 * (x25 + x28) + x30 * x6) + x31 * x7)) result[0, 0, 1] = numpy.sum(x41 * (x29 * (x25 * x36 + x38) + x39 * x9)) result[0, 0, 2] = numpy.sum(x41 * (x12 * x39 + x29 * (x25 * x42 + x43))) result[0, 0, 3] = numpy.sum(x41 * (x10 * x45 + x46)) result[0, 0, 4] = numpy.sum(x33 * (x45 * x47 + x48)) result[0, 0, 5] = numpy.sum(x41 * (x13 * x45 + x49)) result[0, 0, 6] = numpy.sum(x50 * x54) result[0, 0, 7] = numpy.sum(x12 * x55 * x56) result[0, 0, 8] = numpy.sum(x13 * x56 * x57) result[0, 0, 9] = numpy.sum(x54 * x58) result[1, 0, 0] = numpy.sum(x59 * x62) result[1, 0, 1] = numpy.sum(x64 * x66) result[1, 0, 2] = numpy.sum(x12 * x61 * x66) result[1, 0, 3] = numpy.sum(x67 * x70) result[1, 0, 4] = numpy.sum(x69 * x71) result[1, 0, 5] = numpy.sum(x13 * x40 * x61 * x72) result[1, 0, 6] = numpy.sum(x35 * (x36 * x67 + x46)) result[1, 0, 7] = numpy.sum(x41 * (x36 * x71 + x48)) result[1, 0, 8] = numpy.sum(x41 * (x13 * x44 * x63 + x49)) result[1, 0, 9] = numpy.sum(x58 * x62) result[2, 0, 0] = numpy.sum(x59 * x74) result[2, 0, 1] = numpy.sum(x66 * x73 * x9) result[2, 0, 2] = numpy.sum(x65 * x77) result[2, 0, 3] = numpy.sum(x55 * x72 * x73) result[2, 0, 4] = numpy.sum(x68 * x76 * x9) result[2, 0, 5] = numpy.sum(x70 * x78) result[2, 0, 6] = numpy.sum(x50 * x74) result[2, 0, 7] = numpy.sum(x55 * x77) result[2, 0, 8] = numpy.sum(x32 * x44 * x57 * x78) result[2, 0, 9] = numpy.sum(x35 * (x42 * x78 + x49)) return result
[docs] def int3c2e3d_sph_104(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ps|g) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 1, 15), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - C[0] x4 = cx + x0 x5 = x4 ** (-1.5) x6 = x3 * x5 x7 = x3**2 x8 = -x1 * (ax * A[1] + bx * B[1]) x9 = -x8 - C[1] x10 = x9**2 x11 = -x1 * (ax * A[2] + bx * B[2]) x12 = -x11 - C[2] x13 = x12**2 x14 = x0 / x4 x15 = cx * x14 * (x10 + x13 + x7) x16 = 17.49341832762486 x17 = numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) x18 = 2.0 * x16 * x17 x19 = x1 * x18 x20 = x19 * boys(5, x15) x21 = cx ** (-1.0) x22 = x4 ** (-0.5) x23 = boys(4, x15) x24 = -2.0 * x1 * x16 * x17 * x21 * x22 * x23 * (x2 + A[0]) - x20 * x6 x25 = x24 * x3 x26 = 0.5 / (ax + bx) x27 = x21 * x23 x28 = x19 * x22 * x26 * x27 x29 = x14 * x3 x30 = x18 * x26 * x27 x31 = x30 * x7 x32 = x0 * x4 ** (-2.5) x33 = x3**3 x34 = x0**2 x35 = x34 * x4 ** (-3.5) x36 = x30 * x35 x37 = da * db * dc x38 = x14 * x37 x39 = 0.09759000729485332 x40 = x38 * x39 x41 = x14 * x9 x42 = x30 * x5 x43 = x42 * x9 x44 = x30 * x32 x45 = x3 * x44 x46 = x31 * x35 x47 = 0.2581988897471611 x48 = x38 * x47 x49 = x12 * x14 x50 = x12 * x42 x51 = x34 / x4**2 x52 = x10 * x25 x53 = x10 * x44 x54 = x3 * x36 x55 = 0.3333333333333333 * x38 x56 = x51 * x9 x57 = x12 * x9 x58 = x44 * x57 x59 = 1.732050807568877 x60 = x55 * x59 x61 = x13 * x51 x62 = x13 * x44 x63 = x9**3 x64 = x0**3 / x4**3 x65 = x25 * x64 x66 = x36 * x63 x67 = x10 * x12 * x36 x68 = x13 * x9 x69 = x36 * x68 x70 = x12**3 x71 = x36 * x70 x72 = x9**4 x73 = x0**4 / x4**4 x74 = x24 * x73 x75 = x37 * x39 x76 = x74 * x75 x77 = x37 * x47 x78 = x74 * x77 x79 = 0.3333333333333333 * x37 x80 = x13 * x79 x81 = x12**4 x82 = x3**4 x83 = x20 * x5 x84 = -2.0 * x1 * x16 * x17 * x21 * x22 * x23 * (x8 + A[1]) - x83 * x9 x85 = x73 * x84 x86 = x75 * x85 x87 = x84 * x9 x88 = x28 + x87 x89 = x73 * x77 x90 = x33 * x89 x91 = x77 * x85 x92 = x41 * x88 + x43 x93 = x64 * x79 x94 = x7 * x93 x95 = x49 * x87 + x50 x96 = x41 * x92 + x53 x97 = x3 * x51 x98 = x77 * x97 x99 = x41 * x95 + x58 x100 = x59 * x79 x101 = x100 * x97 x102 = x61 * x87 + x62 x103 = -2.0 * x1 * x16 * x17 * x21 * x22 * x23 * (x11 + A[2]) - x12 * x83 x104 = x103 * x73 x105 = x104 * x75 x106 = x103 * x12 + x28 x107 = x100 * x106 * x73 x108 = x106 * x49 + x50 x109 = x63 * x89 x110 = x108 * x93 x111 = x108 * x49 + x62 # 45 item(s) result[0, 0, 0] = numpy.sum( x40 * (x29 * (x29 * (x29 * (x25 + x28) + x30 * x6) + x31 * x32) + x33 * x36) ) result[0, 0, 1] = numpy.sum( x48 * (x29 * (x29 * (x25 * x41 + x43) + x45 * x9) + x46 * x9) ) result[0, 0, 2] = numpy.sum( x48 * (x12 * x46 + x29 * (x12 * x45 + x29 * (x25 * x49 + x50))) ) result[0, 0, 3] = numpy.sum(x55 * (x10 * x54 + x29 * (x51 * x52 + x53))) result[0, 0, 4] = numpy.sum(x60 * (x29 * (x12 * x25 * x56 + x58) + x54 * x57)) result[0, 0, 5] = numpy.sum(x55 * (x13 * x54 + x29 * (x25 * x61 + x62))) result[0, 0, 6] = numpy.sum(x48 * (x63 * x65 + x66)) result[0, 0, 7] = numpy.sum(x60 * (x12 * x52 * x64 + x67)) result[0, 0, 8] = numpy.sum(x60 * (x65 * x68 + x69)) result[0, 0, 9] = numpy.sum(x48 * (x65 * x70 + x71)) result[0, 0, 10] = numpy.sum(x72 * x76) result[0, 0, 11] = numpy.sum(x12 * x63 * x78) result[0, 0, 12] = numpy.sum(x10 * x74 * x80) result[0, 0, 13] = numpy.sum(x70 * x78 * x9) result[0, 0, 14] = numpy.sum(x76 * x81) result[1, 0, 0] = numpy.sum(x82 * x86) result[1, 0, 1] = numpy.sum(x88 * x90) result[1, 0, 2] = numpy.sum(x12 * x33 * x91) result[1, 0, 3] = numpy.sum(x92 * x94) result[1, 0, 4] = numpy.sum(x59 * x94 * x95) result[1, 0, 5] = numpy.sum(x7 * x80 * x85) result[1, 0, 6] = numpy.sum(x96 * x98) result[1, 0, 7] = numpy.sum(x101 * x99) result[1, 0, 8] = numpy.sum(x101 * x102) result[1, 0, 9] = numpy.sum(x3 * x70 * x91) result[1, 0, 10] = numpy.sum(x40 * (x41 * x96 + x66)) result[1, 0, 11] = numpy.sum(x48 * (x41 * x99 + x67)) result[1, 0, 12] = numpy.sum(x55 * (x102 * x41 + x69)) result[1, 0, 13] = numpy.sum(x48 * (x64 * x70 * x87 + x71)) result[1, 0, 14] = numpy.sum(x81 * x86) result[2, 0, 0] = numpy.sum(x105 * x82) result[2, 0, 1] = numpy.sum(x103 * x9 * x90) result[2, 0, 2] = numpy.sum(x106 * x90) result[2, 0, 3] = numpy.sum(x10 * x104 * x7 * x79) result[2, 0, 4] = numpy.sum(x107 * x7 * x9) result[2, 0, 5] = numpy.sum(x108 * x94) result[2, 0, 6] = numpy.sum(x103 * x109 * x3) result[2, 0, 7] = numpy.sum(x10 * x107 * x3) result[2, 0, 8] = numpy.sum(x110 * x3 * x59 * x9) result[2, 0, 9] = numpy.sum(x111 * x98) result[2, 0, 10] = numpy.sum(x105 * x72) result[2, 0, 11] = numpy.sum(x106 * x109) result[2, 0, 12] = numpy.sum(x10 * x110) result[2, 0, 13] = numpy.sum(x111 * x56 * x77) result[2, 0, 14] = numpy.sum(x40 * (x111 * x49 + x71)) return result
[docs] def int3c2e3d_sph_110(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pp|s) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 3, 1), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = cx + x0 x3 = x2 ** (-1.0) x4 = -x1 * (ax * A[0] + bx * B[0]) x5 = x4 + C[0] x6 = -x5 x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x8 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = x10 + C[2] x12 = -x11 x13 = cx * x3 x14 = x0 * x13 * (x12**2 + x6**2 + x9**2) x15 = boys(1, x14) x16 = x15 * x3 x17 = cx ** (-1.0) x18 = x17 * boys(0, x14) x19 = x1 * (x16 - x18) x20 = x4 + A[0] x21 = -x20 x22 = x16 * x6 - x18 * x21 x23 = 2.0 * x22 x24 = A[0] - B[0] x25 = x3 * boys(2, x14) x26 = x15 * x17 x27 = x13 * x5 x28 = A[1] - B[1] x29 = A[2] - B[2] x30 = ( 17.49341832762486 * da * db * dc * x1 * x2 ** (-0.5) * numpy.exp(-ax * bx * x1 * (x24**2 + x28**2 + x29**2)) ) x31 = x7 + A[1] x32 = -x31 x33 = x16 * x9 - x18 * x32 x34 = x25 * x9 - x26 * x32 x35 = -x20 * x33 + x27 * x34 x36 = 2.0 * x30 x37 = x10 + A[2] x38 = -x37 x39 = x12 * x16 - x18 * x38 x40 = x12 * x25 - x26 * x38 x41 = -x20 * x39 + x27 * x40 x42 = 2.0 * x33 x43 = x13 * x8 x44 = -x31 * x39 + x40 * x43 x45 = 2.0 * x39 # 9 item(s) result[0, 0, 0] = numpy.sum( -x30 * (x19 - x20 * x23 + x23 * x24 - 2.0 * x27 * (x21 * x26 - x25 * x6)) ) result[0, 1, 0] = numpy.sum(-x36 * (x22 * x28 + x35)) result[0, 2, 0] = numpy.sum(-x36 * (x22 * x29 + x41)) result[1, 0, 0] = numpy.sum(-x36 * (x24 * x33 + x35)) result[1, 1, 0] = numpy.sum(x30 * (-x19 - x28 * x42 + x31 * x42 - 2.0 * x34 * x43)) result[1, 2, 0] = numpy.sum(-x36 * (x29 * x33 + x44)) result[2, 0, 0] = numpy.sum(-x36 * (x24 * x39 + x41)) result[2, 1, 0] = numpy.sum(-x36 * (x28 * x39 + x44)) result[2, 2, 0] = numpy.sum( x30 * (-2.0 * x11 * x13 * x40 - x19 - x29 * x45 + x37 * x45) ) return result
[docs] def int3c2e3d_sph_111(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pp|p) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 3, 3), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = x2 + C[0] x4 = cx + x0 x5 = x4 ** (-1.0) x6 = -x3 x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x8 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = x10 + C[2] x12 = -x11 x13 = cx * x5 x14 = x0 * x13 x15 = x14 * (x12**2 + x6**2 + x9**2) x16 = boys(2, x15) x17 = x16 * x5 x18 = cx ** (-1.0) x19 = x18 * boys(1, x15) x20 = x1 * (x17 - x19) x21 = x2 + A[0] x22 = -x21 x23 = 2.0 * x17 * x6 - 2.0 * x19 * x22 x24 = x5 * boys(3, x15) x25 = x16 * x18 x26 = x13 * x3 x27 = x20 - x21 * x23 - 2.0 * x26 * (x22 * x25 - x24 * x6) x28 = A[0] - B[0] x29 = x14 * (x11**2 + x3**2 + x8**2) x30 = x5 * boys(2, x29) x31 = boys(1, x29) x32 = x18 * x21 * x31 - x3 * x30 x33 = 2.0 * x32 x34 = x1 * x18 * x31 x35 = x3 * x33 + x34 x36 = A[1] - B[1] x37 = A[2] - B[2] x38 = ( 17.49341832762486 * da * db * dc * x4 ** (-1.5) * numpy.exp(-ax * bx * x1 * (x28**2 + x36**2 + x37**2)) ) x39 = x38 * (x27 + x28 * x33) x40 = x7 + A[1] x41 = x18 * x31 * x40 - x30 * x8 x42 = -x1 * x41 x43 = -x40 x44 = x17 * x9 - x19 * x43 x45 = x24 * x9 - x25 * x43 x46 = -x21 * x44 + x26 * x45 x47 = 2.0 * x46 x48 = x3 * x47 + x42 x49 = x32 * x36 x50 = 2.0 * x8 x51 = -x1 * x32 x52 = x47 * x8 + x51 x53 = 2.0 * x11 x54 = x38 * x53 x55 = x10 + A[2] x56 = -x11 * x30 + x18 * x31 * x55 x57 = -x1 * x56 x58 = -x55 x59 = x12 * x17 - x19 * x58 x60 = x12 * x24 - x25 * x58 x61 = -x21 * x59 + x26 * x60 x62 = 2.0 * x61 x63 = x3 * x62 + x57 x64 = x32 * x37 x65 = x38 * x50 x66 = x11 * x62 + x51 x67 = x28 * x41 x68 = 2.0 * x3 x69 = 2.0 * x41 x70 = x34 + x69 * x8 x71 = 2.0 * x44 x72 = x13 * x45 * x50 + x20 - x40 * x71 x73 = x38 * (x36 * x69 + x72) x74 = x37 * x41 x75 = x13 * x60 x76 = -x40 * x59 + x75 * x8 x77 = x38 * x68 x78 = 2.0 * x76 x79 = x57 + x78 * x8 x80 = x11 * x78 + x42 x81 = x28 * x56 x82 = 2.0 * x56 x83 = x11 * x82 + x34 x84 = x36 * x56 x85 = 2.0 * x59 x86 = x20 + x53 * x75 - x55 * x85 x87 = x38 * (x37 * x82 + x86) # 27 item(s) result[0, 0, 0] = numpy.sum(x38 * (-x1 * x23 + x27 * x3 + x28 * x35)) result[0, 0, 1] = numpy.sum(x39 * x8) result[0, 0, 2] = numpy.sum(x11 * x39) result[0, 1, 0] = numpy.sum(x38 * (x35 * x36 + x48)) result[0, 1, 1] = numpy.sum(x38 * (x49 * x50 + x52)) result[0, 1, 2] = numpy.sum(x54 * (x46 + x49)) result[0, 2, 0] = numpy.sum(x38 * (x35 * x37 + x63)) result[0, 2, 1] = numpy.sum(x65 * (x61 + x64)) result[0, 2, 2] = numpy.sum(x38 * (x53 * x64 + x66)) result[1, 0, 0] = numpy.sum(x38 * (x48 + x67 * x68)) result[1, 0, 1] = numpy.sum(x38 * (x28 * x70 + x52)) result[1, 0, 2] = numpy.sum(x54 * (x46 + x67)) result[1, 1, 0] = numpy.sum(x3 * x73) result[1, 1, 1] = numpy.sum(x38 * (-x1 * x71 + x36 * x70 + x72 * x8)) result[1, 1, 2] = numpy.sum(x11 * x73) result[1, 2, 0] = numpy.sum(x77 * (x74 + x76)) result[1, 2, 1] = numpy.sum(x38 * (x37 * x70 + x79)) result[1, 2, 2] = numpy.sum(x38 * (x53 * x74 + x80)) result[2, 0, 0] = numpy.sum(x38 * (x63 + x68 * x81)) result[2, 0, 1] = numpy.sum(x65 * (x61 + x81)) result[2, 0, 2] = numpy.sum(x38 * (x28 * x83 + x66)) result[2, 1, 0] = numpy.sum(x77 * (x76 + x84)) result[2, 1, 1] = numpy.sum(x38 * (x50 * x84 + x79)) result[2, 1, 2] = numpy.sum(x38 * (x36 * x83 + x80)) result[2, 2, 0] = numpy.sum(x3 * x87) result[2, 2, 1] = numpy.sum(x8 * x87) result[2, 2, 2] = numpy.sum(x38 * (-x1 * x85 + x11 * x86 + x37 * x83)) return result
[docs] def int3c2e3d_sph_112(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pp|d) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 3, 6), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = x2 + C[0] x4 = -x3 x5 = cx + x0 x6 = x5 ** (-1.0) x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x8 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = x10 + C[2] x12 = -x11 x13 = cx * x6 x14 = x0 * x13 x15 = x14 * (x12**2 + x4**2 + x9**2) x16 = boys(3, x15) x17 = x16 * x6 x18 = x2 + A[0] x19 = -x18 x20 = cx ** (-1.0) x21 = boys(2, x15) x22 = x20 * x21 x23 = x17 * x4 - x19 * x22 x24 = x23 * x3 x25 = x3**2 x26 = x8**2 x27 = x11**2 x28 = x14 * (x25 + x26 + x27) x29 = boys(2, x28) x30 = x1 * x20 * x29 x31 = 2.0 * x24 + x30 x32 = x1 * (x17 - x22) x33 = 2.0 * x23 x34 = x6 * boys(4, x15) x35 = 2.0 * x3 x36 = -x13 * x35 * (x16 * x19 * x20 - x34 * x4) - x18 * x33 + x32 x37 = x1 * x23 x38 = A[0] - B[0] x39 = x24 + x30 x40 = 1.732050807568877 x41 = A[1] - B[1] x42 = A[2] - B[2] x43 = ( 17.49341832762486 * da * db * dc * x0 * x5 ** (-2.5) * numpy.exp(-ax * bx * x1 * (x38**2 + x41**2 + x42**2)) ) x44 = x40 * x43 x45 = 0.3333333333333333 * x44 x46 = x6 * boys(3, x28) x47 = -x43 * (-2.0 * x1 * (x18 * x20 * x29 - x3 * x46) + x3 * x36 + x31 * x38) x48 = x33 * x38 + x36 x49 = x45 * x48 x50 = x11 * x43 x51 = x7 + A[1] x52 = -x51 x53 = x17 * x9 - x20 * x21 * x52 x54 = x1 * x53 x55 = -x54 x56 = -x16 * x20 * x52 + x34 * x9 x57 = x13 * x4 x58 = x19 * x53 - x56 * x57 x59 = x3 * x58 x60 = x55 + x59 x61 = x3 * x43 x62 = 0.6666666666666667 * x40 x63 = x61 * x62 x64 = x31 * x41 x65 = -x37 x66 = x58 * x8 x67 = x65 + 2.0 * x66 x68 = x53 * x8 x69 = x30 + 2.0 * x68 x70 = x1 * x69 x71 = x3 * x67 - 0.5 * x70 x72 = x55 + 2.0 * x59 x73 = x23 * x41 x74 = x73 * x8 x75 = x65 + x66 x76 = x43 * x8 x77 = x62 * x76 x78 = 0.6666666666666667 * x44 x79 = x27 * x78 x80 = x10 + A[2] x81 = -x80 x82 = x12 * x17 - x20 * x21 * x81 x83 = -x82 x84 = x12 * x34 - x16 * x20 * x81 x85 = -x84 x86 = -x19 * x83 + x57 * x85 x87 = x3 * x86 x88 = x1 * x82 x89 = -x88 x90 = x87 + x89 x91 = x31 * x42 x92 = 2.0 * x87 + x89 x93 = x11 * x86 x94 = x65 + 2.0 * x93 x95 = x11 * x82 x96 = x30 + 2.0 * x95 x97 = x1 * x96 x98 = -0.5 * x97 x99 = x3 * x94 + x98 x100 = x23 * x42 x101 = x26 * x78 x102 = x100 * x11 x103 = x65 + x93 x104 = x50 * x62 x105 = x38 * x53 x106 = x105 * x3 x107 = x38 * x69 x108 = x30 + x68 x109 = 2.0 * x53 x110 = 2.0 * x8 x111 = -x109 * x51 + x110 * x13 * x56 + x32 x112 = x109 * x41 + x111 x113 = x112 * x45 x114 = x41 * x69 x115 = -x111 * x8 + 2.0 * x54 x116 = x42 * x53 x117 = x13 * x85 * x9 - x52 * x83 x118 = x25 * x78 x119 = x42 * x69 x120 = x117 * x8 x121 = 2.0 * x120 + x89 x122 = x11 * x116 x123 = x11 * x117 x124 = 2.0 * x123 + x55 x125 = x120 + x89 x126 = x124 * x8 + x98 x127 = x123 + x55 x128 = x38 * x82 x129 = x128 * x3 x130 = x38 * x96 x131 = x30 + x95 x132 = x41 * x82 x133 = x132 * x8 x134 = x41 * x96 x135 = 2.0 * x82 x136 = 2.0 * x11 x137 = x13 * x136 * x84 - x135 * x80 + x32 x138 = x135 * x42 + x137 x139 = x138 * x45 x140 = -x11 * x137 + 2.0 * x88 x141 = -x140 + x42 * x96 # 54 item(s) result[0, 0, 0] = numpy.sum( -x45 * (-x1 * x31 + x3 * (x3 * x36 - 2.0 * x37) + x35 * x38 * x39) ) result[0, 0, 1] = numpy.sum(x47 * x8) result[0, 0, 2] = numpy.sum(x11 * x47) result[0, 0, 3] = numpy.sum(-x26 * x49) result[0, 0, 4] = numpy.sum(-x48 * x50 * x8) result[0, 0, 5] = numpy.sum(-x27 * x49) result[0, 1, 0] = numpy.sum(-x63 * (x39 * x41 + x60)) result[0, 1, 1] = numpy.sum(-x43 * (x64 * x8 + x71)) result[0, 1, 2] = numpy.sum(-x50 * (x64 + x72)) result[0, 1, 3] = numpy.sum(-x77 * (x74 + x75)) result[0, 1, 4] = numpy.sum(-x50 * (x67 + 2.0 * x74)) result[0, 1, 5] = numpy.sum(-x79 * (x58 + x73)) result[0, 2, 0] = numpy.sum(-x63 * (x39 * x42 + x90)) result[0, 2, 1] = numpy.sum(-x76 * (x91 + x92)) result[0, 2, 2] = numpy.sum(-x43 * (x11 * x91 + x99)) result[0, 2, 3] = numpy.sum(-x101 * (x100 + x86)) result[0, 2, 4] = numpy.sum(-x76 * (2.0 * x102 + x94)) result[0, 2, 5] = numpy.sum(-x104 * (x102 + x103)) result[1, 0, 0] = numpy.sum(-x63 * (x106 + x60)) result[1, 0, 1] = numpy.sum(-x43 * (x107 * x3 + x71)) result[1, 0, 2] = numpy.sum(-x50 * (2.0 * x106 + x72)) result[1, 0, 3] = numpy.sum(-x77 * (x108 * x38 + x75)) result[1, 0, 4] = numpy.sum(-x50 * (x107 + x67)) result[1, 0, 5] = numpy.sum(-x79 * (x105 + x58)) result[1, 1, 0] = numpy.sum(-x113 * x25) result[1, 1, 1] = numpy.sum(x61 * (-x114 + x115)) result[1, 1, 2] = numpy.sum(-x112 * x3 * x50) result[1, 1, 3] = numpy.sum(x45 * (-x108 * x110 * x41 + x115 * x8 + x70)) result[1, 1, 4] = numpy.sum( -x50 * (-2.0 * x1 * (x20 * x29 * x51 - x46 * x8) + x111 * x8 + x114) ) result[1, 1, 5] = numpy.sum(-x113 * x27) result[1, 2, 0] = numpy.sum(-x118 * (x116 + x117)) result[1, 2, 1] = numpy.sum(-x61 * (x119 + x121)) result[1, 2, 2] = numpy.sum(-x61 * (2.0 * x122 + x124)) result[1, 2, 3] = numpy.sum(-x77 * (x108 * x42 + x125)) result[1, 2, 4] = numpy.sum(-x43 * (x11 * x119 + x126)) result[1, 2, 5] = numpy.sum(-x104 * (x122 + x127)) result[2, 0, 0] = numpy.sum(-x63 * (x129 + x90)) result[2, 0, 1] = numpy.sum(-x76 * (2.0 * x129 + x92)) result[2, 0, 2] = numpy.sum(-x43 * (x130 * x3 + x99)) result[2, 0, 3] = numpy.sum(-x101 * (x128 + x86)) result[2, 0, 4] = numpy.sum(-x76 * (x130 + x94)) result[2, 0, 5] = numpy.sum(-x104 * (x103 + x131 * x38)) result[2, 1, 0] = numpy.sum(-x118 * (x117 + x132)) result[2, 1, 1] = numpy.sum(-x61 * (x121 + 2.0 * x133)) result[2, 1, 2] = numpy.sum(-x61 * (x124 + x134)) result[2, 1, 3] = numpy.sum(-x77 * (x125 + x133)) result[2, 1, 4] = numpy.sum(-x43 * (x126 + x134 * x8)) result[2, 1, 5] = numpy.sum(-x104 * (x127 + x131 * x41)) result[2, 2, 0] = numpy.sum(-x139 * x25) result[2, 2, 1] = numpy.sum(-x138 * x3 * x76) result[2, 2, 2] = numpy.sum(-x141 * x61) result[2, 2, 3] = numpy.sum(-x139 * x26) result[2, 2, 4] = numpy.sum(-x141 * x76) result[2, 2, 5] = numpy.sum(x45 * (x11 * x140 - x131 * x136 * x42 + x97)) return result
[docs] def int3c2e3d_sph_113(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pp|f) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 3, 10), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - C[0] x4 = 0.5 / (ax + bx) x5 = x3**2 x6 = -x1 * (ax * A[1] + bx * B[1]) x7 = -x6 - C[1] x8 = x7**2 x9 = -x1 * (ax * A[2] + bx * B[2]) x10 = -x9 - C[2] x11 = x10**2 x12 = cx + x0 x13 = x12 ** (-1.0) x14 = x0 * x13 x15 = cx * x14 * (x11 + x5 + x8) x16 = boys(4, x15) x17 = x12 ** (-1.5) x18 = 17.49341832762486 x19 = A[0] - B[0] x20 = A[1] - B[1] x21 = A[2] - B[2] x22 = numpy.exp(-ax * bx * x1 * (x19**2 + x20**2 + x21**2)) x23 = 2.0 * x18 * x22 x24 = x1 * x23 x25 = x17 * x24 x26 = x16 * x25 x27 = cx ** (-1.0) x28 = x12 ** (-0.5) x29 = boys(3, x15) x30 = x4 * (2.0 * x1 * x18 * x22 * x27 * x28 * x29 - x26) x31 = -x2 - A[0] x32 = 2.0 * x1 * x18 * x22 * x27 * x28 * x29 * x31 - x26 * x3 x33 = x25 * boys(5, x15) x34 = cx * x13 x35 = x3 * x34 x36 = ( x30 + x31 * x32 - x35 * (2.0 * x1 * x16 * x18 * x22 * x27 * x28 * x31 - x3 * x33) ) x37 = x3 * x36 x38 = x32 * x4 x39 = 2.0 * x38 x40 = x14 * x3 x41 = x3 * x32 x42 = x27 * x29 x43 = x24 * x28 * x4 * x42 x44 = x41 + x43 x45 = x14 * x4 x46 = 2.0 * x45 x47 = x23 * x4 * x42 x48 = x17 * x47 x49 = x3 * x48 + x40 * x44 x50 = x0 * x12 ** (-2.5) * x47 x51 = x40 * x49 + x5 * x50 x52 = x14 * x19 x53 = da * db * dc x54 = 0.2581988897471611 * x53 x55 = x14 * x7 x56 = x48 * x7 x57 = x41 * x55 + x56 x58 = x3 * x50 x59 = x40 * x57 + x58 * x7 x60 = 0.5773502691896258 * x53 x61 = x10 * x14 x62 = x10 * x48 x63 = x41 * x61 + x62 x64 = x10 * x58 + x40 * x63 x65 = x0**2 / x12**2 x66 = x65 * x8 x67 = x50 * x8 x68 = x41 * x66 + x67 x69 = x65 * x7 x70 = x10 * x69 x71 = x10 * x50 * x7 x72 = x41 * x70 + x71 x73 = x11 * x65 x74 = x11 * x50 x75 = x41 * x73 + x74 x76 = x7**3 x77 = x0**3 / x12**3 x78 = x36 * x77 x79 = x76 * x77 x80 = x19 * x32 x81 = x77 * x8 x82 = x10 * x81 x83 = x11 * x7 x84 = x77 * x83 x85 = x10**3 x86 = x77 * x85 x87 = -x6 - A[1] x88 = 2.0 * x1 * x18 * x22 * x27 * x28 * x29 * x87 - x26 * x7 x89 = x4 * x88 x90 = 2.0 * x1 * x16 * x18 * x22 * x27 * x28 * x87 - x33 * x7 x91 = x31 * x88 - x35 * x90 x92 = x3 * x91 x93 = x5 * x65 x94 = x14 * (x40**2 * (2.0 * x89 + x92) + x89 * x93) x95 = x14 * x20 x96 = x7 * x88 x97 = x43 + x96 x98 = x14 * x97 x99 = x4 * x98 x100 = x7 * x91 x101 = x100 + x38 x102 = x3 * x65 x103 = x102 * x4 x104 = x14 * (x103 * x97 + x40 * (x101 * x40 + x99)) x105 = x61 * x89 x106 = x14 * (x10 * x102 * x89 + x40 * (x105 + x61 * x92)) x107 = x56 + x7 * x98 x108 = x107 * x45 x109 = x55 * (x101 + x38) x110 = x14 * (x108 + x109 * x40) x111 = x61 * x96 + x62 x112 = x111 * x45 x113 = x38 * x61 x114 = x100 * x61 + x113 x115 = x14 * (x112 + x114 * x40) x116 = x73 * x89 x117 = x14 * (x116 + x73 * x92) x118 = x14 * (x109 * x55 + x38 * x66) x119 = x20 * x32 x120 = x14 * (x114 * x55 + x38 * x70) x121 = x38 * x73 x122 = x14 * (x100 * x73 + x121) x123 = x86 * x91 x124 = -x9 - A[2] x125 = 2.0 * x1 * x124 * x18 * x22 * x27 * x28 * x29 - x10 * x26 x126 = x125 * x4 x127 = 2.0 * x1 * x124 * x16 * x18 * x22 * x27 * x28 - x10 * x33 x128 = x125 * x31 - x127 * x35 x129 = x128 * x3 x130 = x14 * (x126 * x93 + x40**2 * (2.0 * x126 + x129)) x131 = x14 * x21 x132 = x126 * x55 x133 = x3 * x69 x134 = x14 * (x126 * x133 + x40 * (x129 * x55 + x132)) x135 = x10 * x125 + x43 x136 = x135 * x45 x137 = x10 * x128 + x38 x138 = x14 * (x103 * x135 + x40 * (x136 + x137 * x40)) x139 = x126 * x66 x140 = x14 * (x129 * x66 + x139) x141 = x135 * x4 * x69 x142 = x14 * (x133 * x137 + x141) x143 = x135 * x61 + x62 x144 = x143 * x45 x145 = x113 + x137 * x61 x146 = x14 * (x144 + x145 * x40) x147 = x128 * x79 x148 = x21 * x32 x149 = x137 * x81 x150 = x145 * x69 x151 = x14 * (x121 + x145 * x61) x152 = x3**3 * x77 x153 = x19 * x88 x154 = x5 * x77 x155 = x154 * x97 x156 = x10 * x154 x157 = x102 * x19 x158 = x3 * x77 x159 = x11 * x158 x160 = x107 * x55 + x67 x161 = x111 * x55 + x71 x162 = x73 * x96 + x74 x163 = x34 * x7 x164 = -x163 * x90 + x30 + x87 * x88 x165 = x20 * x88 x166 = x164 * x7 x167 = 2.0 * x89 x168 = x166 + x167 x169 = x168 * x55 + 2.0 * x99 x170 = x102 * x20 x171 = x61 * (x166 + x167) x172 = x125 * x87 - x127 * x163 x173 = x152 * x172 x174 = x21 * x88 x175 = x126 + x172 * x7 x176 = x154 * x175 x177 = x10 * x172 + x89 x178 = x154 * x177 x179 = x132 + x175 * x55 x180 = x102 * x179 x181 = x102 * x21 x182 = x136 + x177 * x55 x183 = x102 * x182 x184 = x105 + x177 * x61 x185 = x102 * x184 x186 = x14 * (x139 + x179 * x55) x187 = x14 * (x141 + x182 * x55) x188 = x14 * (x144 + x184 * x55) x189 = x14 * (x116 + x184 * x61) x190 = x125 * x19 x191 = x154 * x7 x192 = x135 * x19 x193 = x3 * x81 x194 = x158 * x7 x195 = x143 * x69 x196 = x143 * x61 + x74 x197 = x125 * x20 x198 = x135 * x20 x199 = -x10 * x127 * x34 + x124 * x125 + x30 x200 = x125 * x21 x201 = x10 * x199 + 2.0 * x126 x202 = x135 * x21 x203 = 2.0 * x136 + x201 * x61 # 90 item(s) result[0, 0, 0] = numpy.sum( x54 * (x14 * (x40 * (x40 * (x37 + x39) + x44 * x46) + x46 * x49) + x51 * x52) ) result[0, 0, 1] = numpy.sum( x60 * (x14 * (x40 * x55 * (x37 + x39) + x46 * x57) + x52 * x59) ) result[0, 0, 2] = numpy.sum( x60 * (x14 * (x40 * x61 * (x37 + x39) + x46 * x63) + x52 * x64) ) result[0, 0, 3] = numpy.sum(x60 * (x14 * x66 * (x37 + x39) + x52 * x68)) result[0, 0, 4] = numpy.sum(x53 * (x14 * x70 * (x37 + x39) + x52 * x72)) result[0, 0, 5] = numpy.sum(x60 * (x14 * x73 * (x37 + x39) + x52 * x75)) result[0, 0, 6] = numpy.sum(x54 * (x76 * x78 + x79 * x80)) result[0, 0, 7] = numpy.sum(x60 * (x10 * x78 * x8 + x80 * x82)) result[0, 0, 8] = numpy.sum(x60 * (x78 * x83 + x80 * x84)) result[0, 0, 9] = numpy.sum(x54 * (x78 * x85 + x80 * x86)) result[0, 1, 0] = numpy.sum(x54 * (x51 * x95 + x94)) result[0, 1, 1] = numpy.sum(x60 * (x104 + x59 * x95)) result[0, 1, 2] = numpy.sum(x60 * (x106 + x64 * x95)) result[0, 1, 3] = numpy.sum(x60 * (x110 + x68 * x95)) result[0, 1, 4] = numpy.sum(x53 * (x115 + x72 * x95)) result[0, 1, 5] = numpy.sum(x60 * (x117 + x75 * x95)) result[0, 1, 6] = numpy.sum(x54 * (x118 + x119 * x79)) result[0, 1, 7] = numpy.sum(x60 * (x119 * x82 + x120)) result[0, 1, 8] = numpy.sum(x60 * (x119 * x84 + x122)) result[0, 1, 9] = numpy.sum(x54 * (x119 * x86 + x123)) result[0, 2, 0] = numpy.sum(x54 * (x130 + x131 * x51)) result[0, 2, 1] = numpy.sum(x60 * (x131 * x59 + x134)) result[0, 2, 2] = numpy.sum(x60 * (x131 * x64 + x138)) result[0, 2, 3] = numpy.sum(x60 * (x131 * x68 + x140)) result[0, 2, 4] = numpy.sum(x53 * (x131 * x72 + x142)) result[0, 2, 5] = numpy.sum(x60 * (x131 * x75 + x146)) result[0, 2, 6] = numpy.sum(x54 * (x147 + x148 * x79)) result[0, 2, 7] = numpy.sum(x60 * (x148 * x82 + x149)) result[0, 2, 8] = numpy.sum(x60 * (x148 * x84 + x150)) result[0, 2, 9] = numpy.sum(x54 * (x148 * x86 + x151)) result[1, 0, 0] = numpy.sum(x54 * (x152 * x153 + x94)) result[1, 0, 1] = numpy.sum(x60 * (x104 + x155 * x19)) result[1, 0, 2] = numpy.sum(x60 * (x106 + x153 * x156)) result[1, 0, 3] = numpy.sum(x60 * (x107 * x157 + x110)) result[1, 0, 4] = numpy.sum(x53 * (x111 * x157 + x115)) result[1, 0, 5] = numpy.sum(x60 * (x117 + x153 * x159)) result[1, 0, 6] = numpy.sum(x54 * (x118 + x160 * x52)) result[1, 0, 7] = numpy.sum(x60 * (x120 + x161 * x52)) result[1, 0, 8] = numpy.sum(x60 * (x122 + x162 * x52)) result[1, 0, 9] = numpy.sum(x54 * (x123 + x153 * x86)) result[1, 1, 0] = numpy.sum(x152 * x54 * (x164 + x165)) result[1, 1, 1] = numpy.sum(x60 * (x154 * x168 + x155 * x20)) result[1, 1, 2] = numpy.sum(x156 * x60 * (x164 + x165)) result[1, 1, 3] = numpy.sum(x60 * (x102 * x169 + x107 * x170)) result[1, 1, 4] = numpy.sum(x53 * (x102 * x171 + x111 * x170)) result[1, 1, 5] = numpy.sum(x159 * x60 * (x164 + x165)) result[1, 1, 6] = numpy.sum(x54 * (x14 * (2.0 * x108 + x169 * x55) + x160 * x95)) result[1, 1, 7] = numpy.sum(x60 * (x14 * (2.0 * x112 + x171 * x55) + x161 * x95)) result[1, 1, 8] = numpy.sum(x60 * (x14 * x73 * (x166 + x167) + x162 * x95)) result[1, 1, 9] = numpy.sum(x54 * x86 * (x164 + x165)) result[1, 2, 0] = numpy.sum(x54 * (x152 * x174 + x173)) result[1, 2, 1] = numpy.sum(x60 * (x155 * x21 + x176)) result[1, 2, 2] = numpy.sum(x60 * (x156 * x174 + x178)) result[1, 2, 3] = numpy.sum(x60 * (x107 * x181 + x180)) result[1, 2, 4] = numpy.sum(x53 * (x111 * x181 + x183)) result[1, 2, 5] = numpy.sum(x60 * (x159 * x174 + x185)) result[1, 2, 6] = numpy.sum(x54 * (x131 * x160 + x186)) result[1, 2, 7] = numpy.sum(x60 * (x131 * x161 + x187)) result[1, 2, 8] = numpy.sum(x60 * (x131 * x162 + x188)) result[1, 2, 9] = numpy.sum(x54 * (x174 * x86 + x189)) result[2, 0, 0] = numpy.sum(x54 * (x130 + x152 * x190)) result[2, 0, 1] = numpy.sum(x60 * (x134 + x190 * x191)) result[2, 0, 2] = numpy.sum(x60 * (x138 + x154 * x192)) result[2, 0, 3] = numpy.sum(x60 * (x140 + x190 * x193)) result[2, 0, 4] = numpy.sum(x53 * (x142 + x192 * x194)) result[2, 0, 5] = numpy.sum(x60 * (x143 * x157 + x146)) result[2, 0, 6] = numpy.sum(x54 * (x147 + x190 * x79)) result[2, 0, 7] = numpy.sum(x60 * (x149 + x192 * x81)) result[2, 0, 8] = numpy.sum(x60 * (x150 + x19 * x195)) result[2, 0, 9] = numpy.sum(x54 * (x151 + x196 * x52)) result[2, 1, 0] = numpy.sum(x54 * (x152 * x197 + x173)) result[2, 1, 1] = numpy.sum(x60 * (x176 + x191 * x197)) result[2, 1, 2] = numpy.sum(x60 * (x154 * x198 + x178)) result[2, 1, 3] = numpy.sum(x60 * (x180 + x193 * x197)) result[2, 1, 4] = numpy.sum(x53 * (x183 + x194 * x198)) result[2, 1, 5] = numpy.sum(x60 * (x143 * x170 + x185)) result[2, 1, 6] = numpy.sum(x54 * (x186 + x197 * x79)) result[2, 1, 7] = numpy.sum(x60 * (x187 + x198 * x81)) result[2, 1, 8] = numpy.sum(x60 * (x188 + x195 * x20)) result[2, 1, 9] = numpy.sum(x54 * (x189 + x196 * x95)) result[2, 2, 0] = numpy.sum(x152 * x54 * (x199 + x200)) result[2, 2, 1] = numpy.sum(x191 * x60 * (x199 + x200)) result[2, 2, 2] = numpy.sum(x154 * x60 * (x201 + x202)) result[2, 2, 3] = numpy.sum(x193 * x60 * (x199 + x200)) result[2, 2, 4] = numpy.sum(x194 * x53 * (x201 + x202)) result[2, 2, 5] = numpy.sum(x60 * (x102 * x203 + x143 * x181)) result[2, 2, 6] = numpy.sum(x54 * x79 * (x199 + x200)) result[2, 2, 7] = numpy.sum(x60 * x81 * (x201 + x202)) result[2, 2, 8] = numpy.sum(x60 * (x195 * x21 + x203 * x69)) result[2, 2, 9] = numpy.sum(x54 * (x131 * x196 + x14 * (2.0 * x144 + x203 * x61))) return result
[docs] def int3c2e3d_sph_114(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pp|g) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 3, 15), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - C[0] x4 = 0.5 / (ax + bx) x5 = x3**2 x6 = -x1 * (ax * A[1] + bx * B[1]) x7 = -x6 - C[1] x8 = x7**2 x9 = -x1 * (ax * A[2] + bx * B[2]) x10 = -x9 - C[2] x11 = x10**2 x12 = cx + x0 x13 = x12 ** (-1.0) x14 = x0 * x13 x15 = cx * x14 * (x11 + x5 + x8) x16 = boys(5, x15) x17 = x12 ** (-1.5) x18 = 17.49341832762486 x19 = A[0] - B[0] x20 = A[1] - B[1] x21 = A[2] - B[2] x22 = numpy.exp(-ax * bx * x1 * (x19**2 + x20**2 + x21**2)) x23 = 2.0 * x18 * x22 x24 = x1 * x23 x25 = x17 * x24 x26 = x16 * x25 x27 = cx ** (-1.0) x28 = x12 ** (-0.5) x29 = boys(4, x15) x30 = x4 * (2.0 * x1 * x18 * x22 * x27 * x28 * x29 - x26) x31 = -x2 - A[0] x32 = 2.0 * x1 * x18 * x22 * x27 * x28 * x29 * x31 - x26 * x3 x33 = x25 * boys(6, x15) x34 = cx * x13 x35 = x3 * x34 x36 = ( x30 + x31 * x32 - x35 * (2.0 * x1 * x16 * x18 * x22 * x27 * x28 * x31 - x3 * x33) ) x37 = x3 * x36 x38 = x32 * x4 x39 = 2.0 * x38 x40 = x14 * x3 x41 = x3 * x32 x42 = x27 * x29 x43 = x24 * x28 * x4 * x42 x44 = x41 + x43 x45 = x14 * x4 x46 = 2.0 * x45 x47 = x23 * x4 * x42 x48 = x17 * x47 x49 = x3 * x48 + x40 * x44 x50 = x47 * x5 x51 = x0 * x12 ** (-2.5) x52 = x40 * x49 + x50 * x51 x53 = x3**3 x54 = x0**2 x55 = x12 ** (-3.5) * x54 x56 = x47 * x55 x57 = x40 * x52 + x53 * x56 x58 = x14 * x19 x59 = da * db * dc x60 = 0.09759000729485332 * x59 x61 = x14 * x7 x62 = x48 * x7 x63 = x41 * x61 + x62 x64 = x47 * x51 x65 = x3 * x64 x66 = x40 * x63 + x65 * x7 x67 = x50 * x55 x68 = x40 * x66 + x67 * x7 x69 = 0.2581988897471611 * x59 x70 = x10 * x14 x71 = x10 * x48 x72 = x41 * x70 + x71 x73 = x10 * x65 + x40 * x72 x74 = x10 * x67 + x40 * x73 x75 = x54 / x12**2 x76 = x75 * x8 x77 = x64 * x8 x78 = x41 * x76 + x77 x79 = x3 * x8 x80 = x40 * x78 + x56 * x79 x81 = 0.3333333333333333 * x59 x82 = x7 * x75 x83 = x10 * x82 x84 = x10 * x7 x85 = x64 * x84 x86 = x41 * x83 + x85 x87 = x3 * x56 * x84 + x40 * x86 x88 = 1.732050807568877 * x81 x89 = x11 * x75 x90 = x11 * x64 x91 = x41 * x89 + x90 x92 = x11 * x3 x93 = x40 * x91 + x56 * x92 x94 = x7**3 x95 = x0**3 / x12**3 x96 = x94 * x95 x97 = x56 * x94 x98 = x41 * x96 + x97 x99 = x8 * x95 x100 = x10 * x99 x101 = x10 * x56 * x8 x102 = x100 * x41 + x101 x103 = x7 * x95 x104 = x103 * x11 x105 = x11 * x56 * x7 x106 = x104 * x41 + x105 x107 = x10**3 x108 = x107 * x95 x109 = x107 * x56 x110 = x108 * x41 + x109 x111 = x7**4 x112 = x0**4 / x12**4 x113 = x112 * x36 x114 = x111 * x112 x115 = x19 * x32 x116 = x112 * x94 x117 = x10 * x116 x118 = x11 * x8 x119 = x112 * x115 x120 = x107 * x7 x121 = x10**4 x122 = x112 * x121 x123 = -x6 - A[1] x124 = 2.0 * x1 * x123 * x18 * x22 * x27 * x28 * x29 - x26 * x7 x125 = x124 * x4 x126 = 2.0 * x1 * x123 * x16 * x18 * x22 * x27 * x28 - x33 * x7 x127 = x124 * x31 - x126 * x35 x128 = x127 * x3 x129 = x5 * x75 x130 = x53 * x95 x131 = x14 * (x125 * x130 + x40 * (x125 * x129 + x40**2 * (2.0 * x125 + x128))) x132 = x14 * x20 x133 = x124 * x7 x134 = x133 + x43 x135 = x134 * x14 x136 = x135 * x4 x137 = x127 * x7 x138 = x137 + x38 x139 = x3 * x75 x140 = x134 * x4 x141 = x5 * x95 x142 = x14 * (x140 * x141 + x40 * (x139 * x140 + x40 * (x136 + x138 * x40))) x143 = x125 * x70 x144 = x10 * x125 x145 = x14 * (x141 * x144 + x40 * (x139 * x144 + x40 * (x128 * x70 + x143))) x146 = x135 * x7 + x62 x147 = x146 * x45 x148 = x61 * (x138 + x38) x149 = x139 * x4 x150 = x14 * (x146 * x149 + x40 * (x147 + x148 * x40)) x151 = x133 * x70 + x71 x152 = x151 * x45 x153 = x38 * x70 x154 = x137 * x70 + x153 x155 = x14 * (x149 * x151 + x40 * (x152 + x154 * x40)) x156 = x125 * x89 x157 = x14 * (x125 * x92 * x95 + x40 * (x128 * x89 + x156)) x158 = x146 * x61 + x77 x159 = x158 * x45 x160 = x148 * x61 + x38 * x76 x161 = x14 * (x159 + x160 * x40) x162 = x151 * x61 + x85 x163 = x162 * x45 x164 = x154 * x61 + x38 * x83 x165 = x14 * (x163 + x164 * x40) x166 = x133 * x89 + x90 x167 = x166 * x45 x168 = x38 * x89 x169 = x137 * x89 + x168 x170 = x14 * (x167 + x169 * x40) x171 = x108 * x125 x172 = x14 * (x108 * x128 + x171) x173 = x14 * (x160 * x61 + x38 * x96) x174 = x20 * x32 x175 = x14 * (x100 * x38 + x164 * x61) x176 = x14 * (x104 * x38 + x169 * x61) x177 = x112 * x174 x178 = x108 * x38 x179 = x14 * (x108 * x137 + x178) x180 = x122 * x127 x181 = -x9 - A[2] x182 = 2.0 * x1 * x18 * x181 * x22 * x27 * x28 * x29 - x10 * x26 x183 = x182 * x4 x184 = 2.0 * x1 * x16 * x18 * x181 * x22 * x27 * x28 - x10 * x33 x185 = x182 * x31 - x184 * x35 x186 = x185 * x3 x187 = x14 * (x130 * x183 + x40 * (x129 * x183 + x40**2 * (2.0 * x183 + x186))) x188 = x14 * x21 x189 = x183 * x61 x190 = x3 * x82 x191 = x14 * (x141 * x183 * x7 + x40 * (x183 * x190 + x40 * (x186 * x61 + x189))) x192 = x10 * x182 + x43 x193 = x192 * x45 x194 = x10 * x185 + x38 x195 = x192 * x4 x196 = x14 * (x141 * x195 + x40 * (x149 * x192 + x40 * (x193 + x194 * x40))) x197 = x183 * x76 x198 = x14 * (x183 * x3 * x99 + x40 * (x186 * x76 + x197)) x199 = x195 * x82 x200 = x194 * x3 x201 = x103 * x3 x202 = x14 * (x195 * x201 + x40 * (x199 + x200 * x82)) x203 = x192 * x70 + x71 x204 = x203 * x45 x205 = x153 + x194 * x70 x206 = x14 * (x149 * x203 + x40 * (x204 + x205 * x40)) x207 = x183 * x96 x208 = x14 * (x186 * x96 + x207) x209 = x195 * x99 x210 = x14 * (x200 * x99 + x209) x211 = x203 * x4 * x82 x212 = x14 * (x190 * x205 + x211) x213 = x203 * x70 + x90 x214 = x213 * x45 x215 = x168 + x205 * x70 x216 = x14 * (x214 + x215 * x40) x217 = x114 * x185 x218 = x21 * x32 x219 = x116 * x194 x220 = x205 * x99 x221 = x112 * x218 x222 = x215 * x82 x223 = x14 * (x178 + x215 * x70) x224 = x112 * x3**4 x225 = x124 * x19 x226 = x112 * x53 x227 = x134 * x226 x228 = x10 * x226 x229 = x141 * x19 x230 = x11 * x5 x231 = x112 * x225 x232 = x139 * x19 x233 = x107 * x3 x234 = x158 * x61 + x97 x235 = x101 + x162 * x61 x236 = x105 + x166 * x61 x237 = x108 * x133 + x109 x238 = x34 * x7 x239 = x123 * x124 - x126 * x238 + x30 x240 = x124 * x20 x241 = x239 * x7 x242 = 2.0 * x125 x243 = x241 + x242 x244 = 2.0 * x136 + x243 * x61 x245 = x141 * x20 x246 = x70 * (x241 + x242) x247 = x112 * x239 x248 = x112 * x240 x249 = 2.0 * x147 + x244 * x61 x250 = x139 * x20 x251 = 2.0 * x152 + x246 * x61 x252 = x89 * (x241 + x242) x253 = x123 * x182 - x184 * x238 x254 = x224 * x253 x255 = x124 * x21 x256 = x183 + x253 * x7 x257 = x226 * x256 x258 = x10 * x253 + x125 x259 = x226 * x258 x260 = x189 + x256 * x61 x261 = x141 * x260 x262 = x141 * x21 x263 = x193 + x258 * x61 x264 = x141 * x263 x265 = x143 + x258 * x70 x266 = x141 * x265 x267 = x112 * x255 x268 = x197 + x260 * x61 x269 = x139 * x268 x270 = x139 * x21 x271 = x199 + x263 * x61 x272 = x139 * x271 x273 = x204 + x265 * x61 x274 = x139 * x273 x275 = x156 + x265 * x70 x276 = x139 * x275 x277 = x14 * (x207 + x268 * x61) x278 = x14 * (x209 + x271 * x61) x279 = x14 * (x211 + x273 * x61) x280 = x14 * (x214 + x275 * x61) x281 = x14 * (x171 + x275 * x70) x282 = x182 * x19 x283 = x226 * x7 x284 = x19 * x192 x285 = x112 * x5 x286 = x285 * x8 x287 = x285 * x7 x288 = x116 * x3 x289 = x112 * x79 x290 = x201 * x203 x291 = x203 * x99 x292 = x213 * x82 x293 = x109 + x213 * x70 x294 = x182 * x20 x295 = x192 * x20 x296 = -x10 * x184 * x34 + x181 * x182 + x30 x297 = x182 * x21 x298 = x10 * x296 + 2.0 * x183 x299 = x192 * x21 x300 = 2.0 * x193 + x298 * x70 x301 = 2.0 * x204 + x300 * x70 # 135 item(s) result[0, 0, 0] = numpy.sum( x60 * ( x14 * (x40 * (x40 * (x40 * (x37 + x39) + x44 * x46) + x46 * x49) + x46 * x52) + x57 * x58 ) ) result[0, 0, 1] = numpy.sum( x69 * (x14 * (x40 * (x40 * x61 * (x37 + x39) + x46 * x63) + x46 * x66) + x58 * x68) ) result[0, 0, 2] = numpy.sum( x69 * (x14 * (x40 * (x40 * x70 * (x37 + x39) + x46 * x72) + x46 * x73) + x58 * x74) ) result[0, 0, 3] = numpy.sum( x81 * (x14 * (x40 * x76 * (x37 + x39) + x46 * x78) + x58 * x80) ) result[0, 0, 4] = numpy.sum( x88 * (x14 * (x40 * x83 * (x37 + x39) + x46 * x86) + x58 * x87) ) result[0, 0, 5] = numpy.sum( x81 * (x14 * (x40 * x89 * (x37 + x39) + x46 * x91) + x58 * x93) ) result[0, 0, 6] = numpy.sum(x69 * (x14 * x96 * (x37 + x39) + x58 * x98)) result[0, 0, 7] = numpy.sum(x88 * (x100 * x14 * (x37 + x39) + x102 * x58)) result[0, 0, 8] = numpy.sum(x88 * (x104 * x14 * (x37 + x39) + x106 * x58)) result[0, 0, 9] = numpy.sum(x69 * (x108 * x14 * (x37 + x39) + x110 * x58)) result[0, 0, 10] = numpy.sum(x60 * (x111 * x113 + x114 * x115)) result[0, 0, 11] = numpy.sum(x69 * (x10 * x113 * x94 + x115 * x117)) result[0, 0, 12] = numpy.sum(x118 * x81 * (x113 + x119)) result[0, 0, 13] = numpy.sum(x120 * x69 * (x113 + x119)) result[0, 0, 14] = numpy.sum(x60 * (x113 * x121 + x115 * x122)) result[0, 1, 0] = numpy.sum(x60 * (x131 + x132 * x57)) result[0, 1, 1] = numpy.sum(x69 * (x132 * x68 + x142)) result[0, 1, 2] = numpy.sum(x69 * (x132 * x74 + x145)) result[0, 1, 3] = numpy.sum(x81 * (x132 * x80 + x150)) result[0, 1, 4] = numpy.sum(x88 * (x132 * x87 + x155)) result[0, 1, 5] = numpy.sum(x81 * (x132 * x93 + x157)) result[0, 1, 6] = numpy.sum(x69 * (x132 * x98 + x161)) result[0, 1, 7] = numpy.sum(x88 * (x102 * x132 + x165)) result[0, 1, 8] = numpy.sum(x88 * (x106 * x132 + x170)) result[0, 1, 9] = numpy.sum(x69 * (x110 * x132 + x172)) result[0, 1, 10] = numpy.sum(x60 * (x114 * x174 + x173)) result[0, 1, 11] = numpy.sum(x69 * (x117 * x174 + x175)) result[0, 1, 12] = numpy.sum(x81 * (x118 * x177 + x176)) result[0, 1, 13] = numpy.sum(x69 * (x120 * x177 + x179)) result[0, 1, 14] = numpy.sum(x60 * (x122 * x174 + x180)) result[0, 2, 0] = numpy.sum(x60 * (x187 + x188 * x57)) result[0, 2, 1] = numpy.sum(x69 * (x188 * x68 + x191)) result[0, 2, 2] = numpy.sum(x69 * (x188 * x74 + x196)) result[0, 2, 3] = numpy.sum(x81 * (x188 * x80 + x198)) result[0, 2, 4] = numpy.sum(x88 * (x188 * x87 + x202)) result[0, 2, 5] = numpy.sum(x81 * (x188 * x93 + x206)) result[0, 2, 6] = numpy.sum(x69 * (x188 * x98 + x208)) result[0, 2, 7] = numpy.sum(x88 * (x102 * x188 + x210)) result[0, 2, 8] = numpy.sum(x88 * (x106 * x188 + x212)) result[0, 2, 9] = numpy.sum(x69 * (x110 * x188 + x216)) result[0, 2, 10] = numpy.sum(x60 * (x114 * x218 + x217)) result[0, 2, 11] = numpy.sum(x69 * (x117 * x218 + x219)) result[0, 2, 12] = numpy.sum(x81 * (x118 * x221 + x220)) result[0, 2, 13] = numpy.sum(x69 * (x120 * x221 + x222)) result[0, 2, 14] = numpy.sum(x60 * (x122 * x218 + x223)) result[1, 0, 0] = numpy.sum(x60 * (x131 + x224 * x225)) result[1, 0, 1] = numpy.sum(x69 * (x142 + x19 * x227)) result[1, 0, 2] = numpy.sum(x69 * (x145 + x225 * x228)) result[1, 0, 3] = numpy.sum(x81 * (x146 * x229 + x150)) result[1, 0, 4] = numpy.sum(x88 * (x151 * x229 + x155)) result[1, 0, 5] = numpy.sum(x81 * (x157 + x230 * x231)) result[1, 0, 6] = numpy.sum(x69 * (x158 * x232 + x161)) result[1, 0, 7] = numpy.sum(x88 * (x162 * x232 + x165)) result[1, 0, 8] = numpy.sum(x88 * (x166 * x232 + x170)) result[1, 0, 9] = numpy.sum(x69 * (x172 + x231 * x233)) result[1, 0, 10] = numpy.sum(x60 * (x173 + x234 * x58)) result[1, 0, 11] = numpy.sum(x69 * (x175 + x235 * x58)) result[1, 0, 12] = numpy.sum(x81 * (x176 + x236 * x58)) result[1, 0, 13] = numpy.sum(x69 * (x179 + x237 * x58)) result[1, 0, 14] = numpy.sum(x60 * (x122 * x225 + x180)) result[1, 1, 0] = numpy.sum(x224 * x60 * (x239 + x240)) result[1, 1, 1] = numpy.sum(x69 * (x20 * x227 + x226 * x243)) result[1, 1, 2] = numpy.sum(x228 * x69 * (x239 + x240)) result[1, 1, 3] = numpy.sum(x81 * (x141 * x244 + x146 * x245)) result[1, 1, 4] = numpy.sum(x88 * (x141 * x246 + x151 * x245)) result[1, 1, 5] = numpy.sum(x230 * x81 * (x247 + x248)) result[1, 1, 6] = numpy.sum(x69 * (x139 * x249 + x158 * x250)) result[1, 1, 7] = numpy.sum(x88 * (x139 * x251 + x162 * x250)) result[1, 1, 8] = numpy.sum(x88 * (x139 * x252 + x166 * x250)) result[1, 1, 9] = numpy.sum(x233 * x69 * (x247 + x248)) result[1, 1, 10] = numpy.sum(x60 * (x132 * x234 + x14 * (2.0 * x159 + x249 * x61))) result[1, 1, 11] = numpy.sum(x69 * (x132 * x235 + x14 * (2.0 * x163 + x251 * x61))) result[1, 1, 12] = numpy.sum(x81 * (x132 * x236 + x14 * (2.0 * x167 + x252 * x61))) result[1, 1, 13] = numpy.sum(x69 * (x108 * x14 * (x241 + x242) + x132 * x237)) result[1, 1, 14] = numpy.sum(x122 * x60 * (x239 + x240)) result[1, 2, 0] = numpy.sum(x60 * (x224 * x255 + x254)) result[1, 2, 1] = numpy.sum(x69 * (x21 * x227 + x257)) result[1, 2, 2] = numpy.sum(x69 * (x228 * x255 + x259)) result[1, 2, 3] = numpy.sum(x81 * (x146 * x262 + x261)) result[1, 2, 4] = numpy.sum(x88 * (x151 * x262 + x264)) result[1, 2, 5] = numpy.sum(x81 * (x230 * x267 + x266)) result[1, 2, 6] = numpy.sum(x69 * (x158 * x270 + x269)) result[1, 2, 7] = numpy.sum(x88 * (x162 * x270 + x272)) result[1, 2, 8] = numpy.sum(x88 * (x166 * x270 + x274)) result[1, 2, 9] = numpy.sum(x69 * (x233 * x267 + x276)) result[1, 2, 10] = numpy.sum(x60 * (x188 * x234 + x277)) result[1, 2, 11] = numpy.sum(x69 * (x188 * x235 + x278)) result[1, 2, 12] = numpy.sum(x81 * (x188 * x236 + x279)) result[1, 2, 13] = numpy.sum(x69 * (x188 * x237 + x280)) result[1, 2, 14] = numpy.sum(x60 * (x122 * x255 + x281)) result[2, 0, 0] = numpy.sum(x60 * (x187 + x224 * x282)) result[2, 0, 1] = numpy.sum(x69 * (x191 + x282 * x283)) result[2, 0, 2] = numpy.sum(x69 * (x196 + x226 * x284)) result[2, 0, 3] = numpy.sum(x81 * (x198 + x282 * x286)) result[2, 0, 4] = numpy.sum(x88 * (x202 + x284 * x287)) result[2, 0, 5] = numpy.sum(x81 * (x203 * x229 + x206)) result[2, 0, 6] = numpy.sum(x69 * (x208 + x282 * x288)) result[2, 0, 7] = numpy.sum(x88 * (x210 + x284 * x289)) result[2, 0, 8] = numpy.sum(x88 * (x19 * x290 + x212)) result[2, 0, 9] = numpy.sum(x69 * (x213 * x232 + x216)) result[2, 0, 10] = numpy.sum(x60 * (x114 * x282 + x217)) result[2, 0, 11] = numpy.sum(x69 * (x116 * x284 + x219)) result[2, 0, 12] = numpy.sum(x81 * (x19 * x291 + x220)) result[2, 0, 13] = numpy.sum(x69 * (x19 * x292 + x222)) result[2, 0, 14] = numpy.sum(x60 * (x223 + x293 * x58)) result[2, 1, 0] = numpy.sum(x60 * (x224 * x294 + x254)) result[2, 1, 1] = numpy.sum(x69 * (x257 + x283 * x294)) result[2, 1, 2] = numpy.sum(x69 * (x226 * x295 + x259)) result[2, 1, 3] = numpy.sum(x81 * (x261 + x286 * x294)) result[2, 1, 4] = numpy.sum(x88 * (x264 + x287 * x295)) result[2, 1, 5] = numpy.sum(x81 * (x203 * x245 + x266)) result[2, 1, 6] = numpy.sum(x69 * (x269 + x288 * x294)) result[2, 1, 7] = numpy.sum(x88 * (x272 + x289 * x295)) result[2, 1, 8] = numpy.sum(x88 * (x20 * x290 + x274)) result[2, 1, 9] = numpy.sum(x69 * (x213 * x250 + x276)) result[2, 1, 10] = numpy.sum(x60 * (x114 * x294 + x277)) result[2, 1, 11] = numpy.sum(x69 * (x116 * x295 + x278)) result[2, 1, 12] = numpy.sum(x81 * (x20 * x291 + x279)) result[2, 1, 13] = numpy.sum(x69 * (x20 * x292 + x280)) result[2, 1, 14] = numpy.sum(x60 * (x132 * x293 + x281)) result[2, 2, 0] = numpy.sum(x224 * x60 * (x296 + x297)) result[2, 2, 1] = numpy.sum(x283 * x69 * (x296 + x297)) result[2, 2, 2] = numpy.sum(x226 * x69 * (x298 + x299)) result[2, 2, 3] = numpy.sum(x286 * x81 * (x296 + x297)) result[2, 2, 4] = numpy.sum(x287 * x88 * (x298 + x299)) result[2, 2, 5] = numpy.sum(x81 * (x141 * x300 + x203 * x262)) result[2, 2, 6] = numpy.sum(x288 * x69 * (x296 + x297)) result[2, 2, 7] = numpy.sum(x289 * x88 * (x298 + x299)) result[2, 2, 8] = numpy.sum(x88 * (x201 * x300 + x21 * x290)) result[2, 2, 9] = numpy.sum(x69 * (x139 * x301 + x213 * x270)) result[2, 2, 10] = numpy.sum(x114 * x60 * (x296 + x297)) result[2, 2, 11] = numpy.sum(x116 * x69 * (x298 + x299)) result[2, 2, 12] = numpy.sum(x81 * (x21 * x291 + x300 * x99)) result[2, 2, 13] = numpy.sum(x69 * (x21 * x292 + x301 * x82)) result[2, 2, 14] = numpy.sum(x60 * (x14 * (2.0 * x214 + x301 * x70) + x188 * x293)) return result
[docs] def int3c2e3d_sph_120(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pd|s) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 6, 1), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = cx + x1 x4 = x3 ** (-1.0) x5 = -x2 * (ax * A[0] + bx * B[0]) x6 = x5 + C[0] x7 = -x6 x8 = -x2 * (ax * A[1] + bx * B[1]) x9 = x8 + C[1] x10 = -x9 x11 = -x2 * (ax * A[2] + bx * B[2]) x12 = x11 + C[2] x13 = -x12 x14 = cx * x4 x15 = x1 * x14 x16 = x15 * (x10**2 + x13**2 + x7**2) x17 = boys(1, x16) x18 = x17 * x4 x19 = cx ** (-1.0) x20 = x19 * boys(0, x16) x21 = x2 * (x18 - x20) x22 = x5 + A[0] x23 = -x22 x24 = x18 * x7 - x20 * x23 x25 = 2.0 * x24 x26 = boys(2, x16) x27 = x26 * x4 x28 = x17 * x19 x29 = -x23 * x28 + x27 * x7 x30 = x14 * x29 x31 = x21 - x22 * x25 + 2.0 * x30 * x6 x32 = x15 * (x12**2 + x6**2 + x9**2) x33 = x4 * boys(1, x32) x34 = boys(0, x32) x35 = 2.0 * x2 x36 = x2 * (x27 - x28) x37 = 2.0 * x22 x38 = x4 * boys(3, x16) x39 = x19 * x26 x40 = x14 * x6 x41 = 2.0 * x40 x42 = A[1] - B[1] x43 = A[2] - B[2] x44 = ( 17.49341832762486 * da * db * dc * x3 ** (-0.5) * numpy.exp(-ax * bx * x2 * (x0**2 + x42**2 + x43**2)) ) x45 = x2 * x44 x46 = 0.5773502691896258 * x45 x47 = x8 + A[1] x48 = -x47 x49 = x10 * x27 - x28 * x48 x50 = x14 * x49 x51 = x2 * (x19 * x34 * x47 - x33 * x9 - x50) x52 = x10 * x18 - x20 * x48 x53 = -x22 * x52 + x50 * x6 x54 = x24 * x42 + x53 x55 = 2.0 * x0 x56 = x10 * x38 - x39 * x48 x57 = x11 + A[2] x58 = -x57 x59 = x13 * x27 - x28 * x58 x60 = x14 * x59 x61 = x2 * (-x12 * x33 + x19 * x34 * x57 - x60) x62 = x13 * x18 - x20 * x58 x63 = -x22 * x62 + x6 * x60 x64 = x24 * x43 + x63 x65 = x13 * x38 - x39 * x58 x66 = 2.0 * x42 x67 = 2.0 * x47 x68 = x21 + 2.0 * x50 * x9 - x52 * x67 x69 = x14 * x9 x70 = 2.0 * x69 x71 = x36 - x49 * x67 + x56 * x70 x72 = -x22 * x68 + x40 * x71 + x53 * x66 x73 = -x49 x74 = x14 * x73 x75 = x23 * x52 + x7 * x74 x76 = -x62 x77 = -x59 x78 = x14 * x77 x79 = x10 * x78 - x48 * x76 x80 = -x14 * x65 x81 = x10 * x80 - x48 * x77 x82 = -x22 * x79 + x40 * x81 x83 = x43 * x75 + x82 x84 = x35 * x44 x85 = 2.0 * x43 x86 = 2.0 * x57 x87 = 2.0 * x12 * x60 + x21 - x62 * x86 x88 = x12 * x14 x89 = x36 - x59 * x86 + 2.0 * x65 * x88 x90 = -x22 * x87 + x40 * x89 + x63 * x85 x91 = x52 * x66 + x68 x92 = -x47 * x62 + x60 * x9 x93 = x43 * x52 + x92 x94 = -x47 * x87 + x69 * x89 + x85 * x92 x95 = x2 * (x62 + x78) x96 = -x23 * x76 + x7 * x78 x97 = -x42 * x62 - x92 x98 = x62 * x85 + x87 # 18 item(s) result[0, 0, 0] = numpy.sum( x46 * ( -x0 * x31 - x0 * (x0 * x25 + x31) + x22 * x31 + x35 * (-x19 * x22 * x34 + x30 + x33 * x6) + x40 * (x29 * x37 - x36 + x41 * (x23 * x39 - x38 * x7)) ) ) result[0, 1, 0] = numpy.sum( -x45 * (-2.0 * x22 * x53 + x31 * x42 - x41 * (x22 * x49 - x40 * x56) + x51 + x54 * x55) ) result[0, 2, 0] = numpy.sum( -x45 * (-2.0 * x22 * x63 + x31 * x43 - x41 * (x22 * x59 - x40 * x65) + x55 * x64 + x61) ) result[0, 3, 0] = numpy.sum(-x46 * (x54 * x66 + x72)) result[0, 4, 0] = numpy.sum(-x84 * (x42 * x64 + x83)) result[0, 5, 0] = numpy.sum(-x46 * (x64 * x85 + x90)) result[1, 0, 0] = numpy.sum( -x46 * ( x2 * (x52 + x74) - x37 * x75 - x41 * (x14 * x56 * x7 + x23 * x73) + x55 * x75 + x55 * (x0 * x52 + x53) ) ) result[1, 1, 0] = numpy.sum(-x45 * (x0 * x91 + x72)) result[1, 2, 0] = numpy.sum(-x84 * (x0 * x93 + x83)) result[1, 3, 0] = numpy.sum( x46 * (-x42 * x68 - x42 * x91 + x47 * x68 - 2.0 * x51 - x69 * x71) ) result[1, 4, 0] = numpy.sum( -x45 * (x43 * x68 - 2.0 * x47 * x92 + x61 + x66 * x93 - x70 * (x47 * x59 - x65 * x69)) ) result[1, 5, 0] = numpy.sum(-x46 * (x85 * x93 + x94)) result[2, 0, 0] = numpy.sum( -x46 * ( -x37 * x96 - x41 * (x23 * x77 - x7 * x80) + x55 * x96 + x55 * (x0 * x62 + x63) + x95 ) ) result[2, 1, 0] = numpy.sum(x84 * (x0 * x97 - x42 * x96 - x82)) result[2, 2, 0] = numpy.sum(-x45 * (x0 * x98 + x90)) result[2, 3, 0] = numpy.sum( x46 * (-x66 * x79 + x66 * x97 + x67 * x79 - x70 * x81 - x95) ) result[2, 4, 0] = numpy.sum(-x45 * (x42 * x98 + x94)) result[2, 5, 0] = numpy.sum( x46 * (-x43 * x87 - x43 * x98 + x57 * x87 - 2.0 * x61 - x88 * x89) ) return result
[docs] def int3c2e3d_sph_121(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pd|p) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 6, 3), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = x3 + C[0] x5 = cx + x1 x6 = x5 ** (-1.0) x7 = -x4 x8 = -x2 * (ax * A[1] + bx * B[1]) x9 = x8 + C[1] x10 = -x9 x11 = -x2 * (ax * A[2] + bx * B[2]) x12 = x11 + C[2] x13 = -x12 x14 = cx * x6 x15 = x1 * x14 x16 = x15 * (x10**2 + x13**2 + x7**2) x17 = boys(2, x16) x18 = x17 * x6 x19 = cx ** (-1.0) x20 = x19 * boys(1, x16) x21 = x2 * (x18 - x20) x22 = x3 + A[0] x23 = -x22 x24 = x18 * x7 - x20 * x23 x25 = 2.0 * x24 x26 = boys(3, x16) x27 = x26 * x6 x28 = x17 * x19 x29 = -x23 * x28 + x27 * x7 x30 = 2.0 * x4 x31 = x14 * x30 x32 = x21 - x22 * x25 + x29 * x31 x33 = -x32 x34 = x2 * x25 + x33 * x4 x35 = 2.0 * x2 x36 = x2 * (x27 - x28) x37 = x6 * boys(4, x16) x38 = ( -cx * x4 * x6 * (2.0 * x22 * x29 + x31 * (x19 * x23 * x26 - x37 * x7) - x36) + x22 * x33 - x35 * (x14 * x29 - x24) ) x39 = x15 * (x12**2 + x4**2 + x9**2) x40 = x6 * boys(2, x39) x41 = boys(1, x39) x42 = x19 * x22 * x41 - x4 * x40 x43 = x19 * x2 * x41 x44 = x30 * x42 + x43 x45 = A[1] - B[1] x46 = A[2] - B[2] x47 = ( 17.49341832762486 * da * db * dc * x5 ** (-1.5) * numpy.exp(-ax * bx * x2 * (x0**2 + x45**2 + x46**2)) ) x48 = 0.5773502691896258 x49 = x47 * x48 x50 = x47 * x9 x51 = -x48 * (-x0 * x33 + x0 * (x0 * x25 + x32) + x38) x52 = x12 * x47 x53 = x8 + A[1] x54 = -x53 x55 = x10 * x27 - x28 * x54 x56 = -x55 x57 = x14 * x56 x58 = x10 * x18 - x20 * x54 x59 = x2 * (x57 + x58) x60 = x23 * x58 + x57 * x7 x61 = 2.0 * x22 x62 = x10 * x37 - x19 * x26 * x54 x63 = x14 * x7 x64 = -x31 * (x23 * x56 + x62 * x63) + x59 - x60 * x61 x65 = -x64 x66 = x4 * x65 x67 = x19 * x41 * x53 - x40 * x9 x68 = -x2 * x67 x69 = x14 * x4 x70 = -x22 * x58 + x55 * x69 x71 = x30 * x70 + x68 x72 = x44 * x45 + x71 x73 = x35 * x60 x74 = x42 * x45 x75 = 2.0 * x9 x76 = -x2 * x42 x77 = 2.0 * x70 x78 = x76 + x77 * x9 x79 = x74 * x75 + x78 x80 = x45 * x9 x81 = 0.5 * x2 * x33 x82 = -x65 * x9 + x81 x83 = 2.0 * x0 x84 = x11 + A[2] x85 = -x84 x86 = x13 * x27 - x28 * x85 x87 = -x86 x88 = x14 * x87 x89 = x13 * x18 - x20 * x85 x90 = x2 * (x88 + x89) x91 = -x89 x92 = -x23 * x91 + x7 * x88 x93 = x13 * x37 - x19 * x26 * x85 x94 = -x93 x95 = -x31 * (x23 * x87 - x63 * x94) - x61 * x92 + x90 x96 = -x95 x97 = x4 * x96 x98 = -x12 * x40 + x19 * x41 * x84 x99 = -x2 * x98 x100 = -x22 * x89 + x69 * x86 x101 = x100 * x30 + x99 x102 = x101 + x44 * x46 x103 = x35 * x92 x104 = x42 * x46 x105 = 2.0 * x12 x106 = x100 * x105 + x76 x107 = x104 * x105 + x106 x108 = x12 * x46 x109 = -x12 * x96 + x81 x110 = 2.0 * x53 x111 = x14 * x75 x112 = -x110 * x58 + x111 * x55 + x21 x113 = -x112 x114 = -x111 * x62 - x36 + 2.0 * x53 * x55 x115 = x114 * x69 x116 = x113 * x22 - x115 x117 = 0.5 * x2 x118 = -x112 * x117 + x116 * x4 + x45 * x71 x119 = x2 * x70 x120 = x116 * x9 - 2.0 * x119 + x45 * x78 x121 = 2.0 * x45 x122 = x113 * x22 - x115 + x45 * x77 x123 = x48 * x52 x124 = x14 * x9 x125 = x124 * x86 - x53 * x89 x126 = x125 * x2 x127 = x10 * x88 - x54 * x91 x128 = x10 * x14 * x94 - x54 * x87 x129 = -x127 * x22 + x128 * x69 x130 = -x126 + x129 * x30 x131 = x130 + x46 * x71 x132 = x100 + x104 x133 = 2.0 * x80 x134 = x100 * x2 x135 = x129 * x75 - x134 x136 = x135 + x46 * x78 x137 = x105 * x129 - x119 x138 = x108 * x77 + x137 x139 = x105 * x14 x140 = x139 * x86 + x21 - 2.0 * x84 * x89 x141 = -x140 x142 = -x139 * x93 - x36 + 2.0 * x84 * x86 x143 = x142 * x69 x144 = x141 * x22 - x143 x145 = -x117 * x140 x146 = x101 * x46 + x144 * x4 + x145 x147 = 2.0 * x46 x148 = x100 * x147 + x141 * x22 - x143 x149 = x48 * x50 x150 = x106 * x46 + x12 * x144 - 2.0 * x134 x151 = x0 * x67 x152 = x43 + x67 * x75 x153 = x0 * (x112 + x121 * x67) x154 = x113 * x9 + x35 * x58 x155 = x152 * x45 - x154 x156 = x46 * x67 x157 = x125 + x156 x158 = x0 * x30 x159 = x125 * x75 + x99 x160 = x152 * x46 + x159 x161 = x105 * x125 + x68 x162 = x105 * x156 + x161 x163 = -cx * x114 * x6 * x9 + x113 * x53 + 2.0 * x59 x164 = x113 * x45 - x163 - x45 * (x112 + x121 * x58) x165 = x4 * x47 x166 = x165 * x48 x167 = -x110 * x127 + x111 * x128 + x90 x168 = -x167 x169 = x168 * x9 x170 = x127 * x35 x171 = x113 * x117 - x12 * x168 x172 = x124 * x142 x173 = x125 * x147 + x141 * x53 - x172 x174 = x141 * x53 - x172 x175 = x145 + x159 * x46 + x174 * x9 x176 = x12 * x174 - 2.0 * x126 + x161 * x46 x177 = x0 * x98 x178 = x105 * x98 + x43 x179 = x45 * x98 x180 = x125 + x179 x181 = x159 + x179 * x75 x182 = x161 + x178 * x45 x183 = x140 + x147 * x98 x184 = x0 * x183 x185 = x12 * x141 + x35 * x89 x186 = x178 * x46 - x185 x187 = x183 * x45 x188 = -cx * x12 * x142 * x6 + x141 * x84 + 2.0 * x90 x189 = x141 * x46 - x188 - x46 * (x140 + x147 * x89) # 54 item(s) result[0, 0, 0] = numpy.sum( 0.5 * x49 * (2.0 * x0**2 * x44 - 4.0 * x0 * x34 + 3.0 * x2 * x33 + 2.0 * x38 * x4) ) result[0, 0, 1] = numpy.sum(-x50 * x51) result[0, 0, 2] = numpy.sum(-x51 * x52) result[0, 1, 0] = numpy.sum(x47 * (x0 * x72 - x34 * x45 - x66 - x73)) result[0, 1, 1] = numpy.sum(x47 * (x0 * x79 + x32 * x80 + x82)) result[0, 1, 2] = numpy.sum(x52 * (-x33 * x45 + x64 + x83 * (x24 * x45 + x60))) result[0, 2, 0] = numpy.sum(x47 * (x0 * x102 - x103 - x34 * x46 - x97)) result[0, 2, 1] = numpy.sum(x50 * (-x33 * x46 + x83 * (x24 * x46 + x92) + x95)) result[0, 2, 2] = numpy.sum(x47 * (x0 * x107 + x108 * x32 + x109)) result[0, 3, 0] = numpy.sum(x49 * (x118 + x45 * x72)) result[0, 3, 1] = numpy.sum(x49 * (x120 + x45 * x79)) result[0, 3, 2] = numpy.sum(x123 * (x121 * (x70 + x74) + x122)) result[0, 4, 0] = numpy.sum(x47 * (x102 * x45 + x131)) result[0, 4, 1] = numpy.sum(x47 * (x132 * x133 + x136)) result[0, 4, 2] = numpy.sum(x47 * (x107 * x45 + x138)) result[0, 5, 0] = numpy.sum(x49 * (x102 * x46 + x146)) result[0, 5, 1] = numpy.sum(x149 * (x132 * x147 + x148)) result[0, 5, 2] = numpy.sum(x49 * (x107 * x46 + x150)) result[1, 0, 0] = numpy.sum(x49 * (x0 * x71 + x0 * (x151 * x30 + x71) - x66 - x73)) result[1, 0, 1] = numpy.sum(x49 * (x0 * x78 + x0 * (x0 * x152 + x78) + x82)) result[1, 0, 2] = numpy.sum(x123 * (x0 * x77 + x64 + x83 * (x151 + x70))) result[1, 1, 0] = numpy.sum(x47 * (x118 + x153 * x4)) result[1, 1, 1] = numpy.sum(x47 * (x0 * x155 + x120)) result[1, 1, 2] = numpy.sum(x52 * (x122 + x153)) result[1, 2, 0] = numpy.sum(x47 * (x131 + x157 * x158)) result[1, 2, 1] = numpy.sum(x47 * (x0 * x160 + x136)) result[1, 2, 2] = numpy.sum(x47 * (x0 * x162 + x138)) result[1, 3, 0] = numpy.sum(-x164 * x166) result[1, 3, 1] = numpy.sum( 0.5 * x49 * (3.0 * x113 * x2 - 2.0 * x154 * x45 + 2.0 * x155 * x45 + 2.0 * x163 * x9) ) result[1, 3, 2] = numpy.sum(-x123 * x164) result[1, 4, 0] = numpy.sum(x165 * (-x113 * x46 + x121 * (x127 + x46 * x58) + x167)) result[1, 4, 1] = numpy.sum(x47 * (-x154 * x46 + x160 * x45 - x169 - x170)) result[1, 4, 2] = numpy.sum(x47 * (x108 * x112 + x162 * x45 + x171)) result[1, 5, 0] = numpy.sum(x166 * (x147 * x157 + x173)) result[1, 5, 1] = numpy.sum(x49 * (x160 * x46 + x175)) result[1, 5, 2] = numpy.sum(x49 * (x162 * x46 + x176)) result[2, 0, 0] = numpy.sum(x49 * (x0 * x101 + x0 * (x101 + x177 * x30) - x103 - x97)) result[2, 0, 1] = numpy.sum(x149 * (x100 * x83 + x83 * (x100 + x177) + x95)) result[2, 0, 2] = numpy.sum(x49 * (x0 * x106 + x0 * (x0 * x178 + x106) + x109)) result[2, 1, 0] = numpy.sum(x47 * (x101 * x45 + x130 + x158 * x180)) result[2, 1, 1] = numpy.sum(x47 * (x0 * x181 + x100 * x133 + x135)) result[2, 1, 2] = numpy.sum(x47 * (x0 * x182 + x106 * x45 + x137)) result[2, 2, 0] = numpy.sum(x47 * (x146 + x184 * x4)) result[2, 2, 1] = numpy.sum(x50 * (x148 + x184)) result[2, 2, 2] = numpy.sum(x47 * (x0 * x186 + x150)) result[2, 3, 0] = numpy.sum(x166 * (x121 * x125 + x121 * x180 + x167)) result[2, 3, 1] = numpy.sum(x49 * (x159 * x45 - x169 - x170 + x181 * x45)) result[2, 3, 2] = numpy.sum(x49 * (x161 * x45 + x171 + x182 * x45)) result[2, 4, 0] = numpy.sum(x165 * (x173 + x187)) result[2, 4, 1] = numpy.sum(x47 * (x175 + x187 * x9)) result[2, 4, 2] = numpy.sum(x47 * (x176 + x186 * x45)) result[2, 5, 0] = numpy.sum(-x166 * x189) result[2, 5, 1] = numpy.sum(-x149 * x189) result[2, 5, 2] = numpy.sum( 0.5 * x49 * (2.0 * x12 * x188 + 3.0 * x141 * x2 - 2.0 * x185 * x46 + 2.0 * x186 * x46) ) return result
[docs] def int3c2e3d_sph_122(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pd|d) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 6, 6), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = x3 + C[0] x5 = -x4 x6 = cx + x1 x7 = x6 ** (-1.0) x8 = -x2 * (ax * A[1] + bx * B[1]) x9 = x8 + C[1] x10 = -x9 x11 = -x2 * (ax * A[2] + bx * B[2]) x12 = x11 + C[2] x13 = -x12 x14 = cx * x7 x15 = x1 * x14 x16 = x15 * (x10**2 + x13**2 + x5**2) x17 = boys(3, x16) x18 = x17 * x7 x19 = x3 + A[0] x20 = -x19 x21 = cx ** (-1.0) x22 = x21 * boys(2, x16) x23 = x18 * x5 - x20 * x22 x24 = x23 * x4 x25 = x4**2 x26 = x9**2 x27 = x12**2 x28 = x15 * (x25 + x26 + x27) x29 = boys(2, x28) x30 = x2 * x21 * x29 x31 = 2.0 * x24 + x30 x32 = x18 - x22 x33 = x2 * x32 x34 = 2.0 * x19 x35 = boys(4, x16) x36 = x35 * x7 x37 = x17 * x21 x38 = -x20 * x37 + x36 * x5 x39 = 2.0 * x4 x40 = x14 * x39 x41 = -x23 * x34 + x33 + x38 * x40 x42 = -x41 x43 = x2 * x23 x44 = x4 * x42 + 2.0 * x43 x45 = x2 * x31 + x4 * x44 x46 = x24 + x30 x47 = x0 * x39 x48 = 1.5 * x2 x49 = x36 - x37 x50 = x2 * x49 x51 = x7 * boys(5, x16) x52 = x14 * x4 x53 = ( x19 * x42 - 2.0 * x2 * (x14 * x38 - x23) - x52 * (2.0 * x19 * x38 + x40 * (x20 * x21 * x35 - x5 * x51) - x50) ) x54 = 0.5 * x4 x55 = A[1] - B[1] x56 = A[2] - B[2] x57 = ( 17.49341832762486 * da * db * dc * x1 * x6 ** (-2.5) * numpy.exp(-ax * bx * x2 * (x0**2 + x55**2 + x56**2)) ) x58 = 0.3333333333333333 * x57 x59 = x7 * boys(3, x28) x60 = x19 * x21 * x29 - x4 * x59 x61 = -2.0 * x2 * x60 + x4 * x41 x62 = -x61 x63 = 1.732050807568877 x64 = x58 * x63 x65 = x64 * (x0 * x62 - x0 * (x0 * x31 + x61) - x4 * x53 + x41 * x48) x66 = 2.0 * x0 x67 = x58 * (x0 * x41 + x0 * (x23 * x66 + x41) + x53) x68 = x8 + A[1] x69 = -x68 x70 = x10 * x18 - x22 * x69 x71 = x2 * x70 x72 = -x71 x73 = -x70 x74 = x10 * x36 - x17 * x21 * x69 x75 = -x74 x76 = x14 * x75 x77 = -x20 * x73 + x5 * x76 x78 = x4 * x77 x79 = x72 + 2.0 * x78 x80 = x2 * (x70 + x76) x81 = x10 * x51 - x21 * x35 * x69 x82 = -x81 x83 = x14 * x5 x84 = -x34 * x77 - x40 * (x20 * x75 - x82 * x83) + x80 x85 = -x84 x86 = x2 * x77 x87 = 2.0 * x86 x88 = x4 * x85 + x87 x89 = x72 + x78 x90 = x46 * x55 + x89 x91 = x31 * x55 x92 = 2.0 * x9 x93 = x70 * x9 x94 = x30 + 2.0 * x93 x95 = x2 * x94 x96 = -x43 x97 = x77 * x9 x98 = x96 + 2.0 * x97 x99 = x39 * x98 - x95 x100 = x91 * x92 + x99 x101 = 0.5 * x0 x102 = -x2 * x42 x103 = x85 * x9 x104 = x2 * x98 x105 = -x104 x106 = x105 - x54 * (x102 + 2.0 * x103) x107 = x79 + x91 x108 = -x19 * x70 + x52 * x74 x109 = -2.0 * x108 * x2 + x4 * x84 x110 = x12 * x57 x111 = x23 * x55 x112 = x111 * x9 x113 = x96 + x97 x114 = x112 + x113 x115 = x41 * x55 x116 = x115 * x9 x117 = x2 * x42 x118 = -x103 + x117 x119 = x64 * x9 x120 = 2.0 * x112 + x98 x121 = -0.5 * x2 * x41 + x84 * x9 x122 = x111 + x77 x123 = x27 * x64 x124 = x11 + A[2] x125 = -x124 x126 = -x125 * x22 + x13 * x18 x127 = x126 * x2 x128 = -x127 x129 = -x126 x130 = -x125 * x17 * x21 + x13 * x36 x131 = -x130 x132 = x131 * x14 x133 = -x129 * x20 + x132 * x5 x134 = x133 * x4 x135 = x128 + 2.0 * x134 x136 = x2 * (x126 + x132) x137 = -x125 * x21 * x35 + x13 * x51 x138 = -x137 x139 = -x133 * x34 + x136 - x40 * (x131 * x20 - x138 * x83) x140 = -x139 x141 = x133 * x2 x142 = 2.0 * x141 x143 = x140 * x4 + x142 x144 = x128 + x134 x145 = x144 + x46 * x56 x146 = x31 * x56 x147 = x135 + x146 x148 = -x126 * x19 + x130 * x52 x149 = x139 * x4 - 2.0 * x148 * x2 x150 = x57 * x9 x151 = 2.0 * x12 x152 = x12 * x126 x153 = 2.0 * x152 + x30 x154 = x153 * x2 x155 = -x154 x156 = x12 * x133 x157 = 2.0 * x156 + x96 x158 = x155 + x157 * x39 x159 = x146 * x151 + x158 x160 = x12 * x140 x161 = x157 * x2 x162 = -x161 x163 = x162 - x54 * (x102 + 2.0 * x160) x164 = x41 * x56 x165 = x23 * x56 x166 = x133 + x165 x167 = x26 * x64 x168 = x12 * x165 x169 = x157 + 2.0 * x168 x170 = 0.5 * x117 x171 = -x160 x172 = x12 * x164 + x171 x173 = x156 + x96 x174 = x168 + x173 x175 = x12 * x64 x176 = 2.0 * x55 x177 = 2.0 * x70 x178 = x14 * x92 x179 = -x177 * x68 + x178 * x74 + x33 x180 = -x179 x181 = x180 * x2 x182 = -x2 * x32 x183 = 2.0 * x69 x184 = -x2 * x49 x185 = x10 * x14 x186 = -x20 * (-2.0 * x10 * x76 + x182 + x183 * x73) + x83 * ( x183 * x75 + x184 - 2.0 * x185 * x82 ) x187 = x186 * x4 x188 = x176 * x89 + x181 + x187 x189 = x4 * x58 x190 = 0.5 * x55 x191 = x186 * x9 x192 = x191 - x87 x193 = x180 * x9 + 2.0 * x71 x194 = 0.5 * x2 x195 = x190 * x99 + x192 * x4 + x193 * x194 x196 = 0.5 * x181 x197 = x187 + x196 + x55 * x79 x198 = x192 * x9 x199 = x176 * x9 x200 = x113 * x199 x201 = x55 * x98 x202 = x176 * x77 + x186 x203 = x27 * x58 x204 = x10 * x132 - x129 * x69 x205 = -x131 * x69 + x138 * x185 x206 = x20 * x204 - x205 * x83 x207 = x2 * x204 x208 = x206 * x4 - x207 x209 = x208 + x56 * x89 x210 = x4 * x57 x211 = 0.6666666666666667 * x63 x212 = x210 * x211 x213 = x55 * x9 x214 = 0.5 * x56 x215 = -x141 x216 = x206 * x9 x217 = x204 * x9 x218 = x128 + 2.0 * x217 x219 = x2 * x218 x220 = -0.5 * x219 + x4 * (x215 + 2.0 * x216) x221 = x214 * x99 + x220 x222 = x12 * x56 x223 = -x86 x224 = x12 * x206 x225 = x223 + 2.0 * x224 x226 = x12 * x204 x227 = 2.0 * x226 + x72 x228 = x2 * x227 x229 = x225 * x4 - 0.5 * x228 x230 = x222 * x79 + x229 x231 = x215 + x216 x232 = x113 * x56 + x231 x233 = x150 * x211 x234 = -0.5 * x161 + x225 * x9 x235 = x222 * x98 + x234 x236 = x223 + x224 x237 = x108 * x222 + x236 x238 = x110 * x211 x239 = 2.0 * x56 x240 = 2.0 * x126 x241 = x14 * x151 x242 = -x124 * x240 + x130 * x241 + x33 x243 = -x242 x244 = x2 * x243 x245 = 2.0 * x125 x246 = 2.0 * x13 x247 = x129 * x245 - x132 * x246 + x182 x248 = x131 * x245 - x138 * x14 * x246 + x184 x249 = -x20 * x247 + x248 * x83 x250 = x249 * x4 x251 = x144 * x239 + x244 + x250 x252 = 0.5 * x244 x253 = x135 * x56 + x250 + x252 x254 = x12 * x249 - x142 x255 = x12 * x243 + 2.0 * x127 x256 = x194 * x255 x257 = x158 * x214 + x254 * x4 + x256 x258 = x133 * x239 + x249 x259 = x26 * x58 x260 = x12 * x254 x261 = 2.0 * x222 x262 = x173 * x261 x263 = x0 * x70 x264 = x0 * x94 x265 = x30 + x93 x266 = x58 * x9 x267 = x177 * x55 + x179 x268 = x0 * x4 x269 = x267 * x268 x270 = x4 * x64 x271 = x55 * x94 x272 = x193 - x271 x273 = x193 * x9 + x95 x274 = -x199 * x265 + x273 x275 = x179 * x9 - 2.0 * x2 * (x21 * x29 * x68 - x59 * x9) x276 = -x271 - x275 x277 = x56 * x70 x278 = x204 + x277 x279 = x56 * x94 x280 = x218 + x279 x281 = x12 * x277 x282 = x227 + 2.0 * x281 x283 = x128 + x217 x284 = x265 * x56 + x283 x285 = x155 + x227 * x92 x286 = x151 * x279 + x285 x287 = x226 + x72 x288 = x281 + x287 x289 = x14 * x9 x290 = x180 * x68 + x289 * (x178 * x81 + x50 - 2.0 * x68 * x74) + 2.0 * x80 x291 = x179 * x55 + x267 * x55 + x290 x292 = x25 * x58 x293 = -x290 * x9 x294 = 0.5 * x9 x295 = -x275 x296 = x179 * x56 x297 = x136 + x178 * x205 - 2.0 * x204 * x68 x298 = x25 * x64 x299 = -x297 x300 = x299 * x9 x301 = 2.0 * x207 x302 = x300 + x301 x303 = x12 * x299 x304 = -x303 x305 = x12 * x296 + x304 x306 = -x228 x307 = x294 * (x180 * x2 - 2.0 * x303) + x306 x308 = x185 * x248 - x247 * x69 x309 = x204 * x239 + x308 x310 = x308 * x9 x311 = x218 * x56 + x252 + x310 x312 = -x301 x313 = x12 * x308 + x312 x314 = x239 * x283 + x244 + x310 x315 = x214 * x285 + x256 + x313 * x9 x316 = x12 * x313 x317 = x261 * x287 x318 = x0 * x126 x319 = x0 * x153 x320 = x152 + x30 x321 = x12 * x58 x322 = x126 * x55 x323 = x204 + x322 x324 = x218 + x322 * x92 x325 = x153 * x55 x326 = x227 + x325 x327 = x283 + x322 * x9 x328 = x285 + x325 * x92 x329 = x287 + x320 * x55 x330 = x240 * x56 + x242 x331 = x268 * x330 x332 = -x153 * x56 + x255 x333 = -x332 x334 = -x330 x335 = x12 * x255 + x154 x336 = -x261 * x320 + x335 x337 = x334 * x55 x338 = x12 * x14 * (-2.0 * x124 * x130 + x137 * x241 + x50) + x124 * x243 + 2.0 * x136 x339 = x242 * x56 + x330 * x56 + x338 x340 = -x12 * x338 x341 = 1.5 * x2 * x243 - x255 * x56 - x332 * x56 - x340 # 108 item(s) result[0, 0, 0] = numpy.sum( x58 * ( x0 * x45 + x0 * (x45 - x46 * x47) - x44 * x48 - x54 * (3.0 * x2 * x42 + x39 * x53) ) ) result[0, 0, 1] = numpy.sum(x65 * x9) result[0, 0, 2] = numpy.sum(x12 * x65) result[0, 0, 3] = numpy.sum(-x26 * x67) result[0, 0, 4] = numpy.sum(-x12 * x63 * x67 * x9) result[0, 0, 5] = numpy.sum(-x27 * x67) result[0, 1, 0] = numpy.sum(x64 * (x2 * x79 + x4 * x88 + x45 * x55 - x47 * x90)) result[0, 1, 1] = numpy.sum(x57 * (-x100 * x101 - x106 + x55 * x62 * x9)) result[0, 1, 2] = numpy.sum(x110 * (-x0 * x107 - x109 + x55 * x62)) result[0, 1, 3] = numpy.sum(-x119 * (x114 * x66 + x116 + x118)) result[0, 1, 4] = numpy.sum(-x110 * (x0 * x120 + x116 + x121)) result[0, 1, 5] = numpy.sum(-x123 * (x115 + x122 * x66 + x84)) result[0, 2, 0] = numpy.sum(x64 * (x135 * x2 + x143 * x4 - x145 * x47 + x45 * x56)) result[0, 2, 1] = numpy.sum(x150 * (-x0 * x147 - x149 + x56 * x62)) result[0, 2, 2] = numpy.sum(x57 * (-x101 * x159 + x12 * x56 * x62 - x163)) result[0, 2, 3] = numpy.sum(-x167 * (x139 + x164 + x166 * x66)) result[0, 2, 4] = numpy.sum(-x150 * (x0 * x169 + x170 + x172)) result[0, 2, 5] = numpy.sum(-x175 * (x117 + x172 + x174 * x66)) result[0, 3, 0] = numpy.sum(-x189 * (x176 * x90 + x188)) result[0, 3, 1] = numpy.sum(-x64 * (x100 * x190 + x195)) result[0, 3, 2] = numpy.sum(-x175 * (x107 * x55 + x197)) result[0, 3, 3] = numpy.sum(-x58 * (x105 + x114 * x199 + x198 + x200)) result[0, 3, 4] = numpy.sum(-x175 * (x120 * x55 + x192 + x201)) result[0, 3, 5] = numpy.sum(-x203 * (x122 * x176 + x202)) result[0, 4, 0] = numpy.sum(-x212 * (x145 * x55 + x209)) result[0, 4, 1] = numpy.sum(-x57 * (x147 * x213 + x221)) result[0, 4, 2] = numpy.sum(-x57 * (x159 * x190 + x230)) result[0, 4, 3] = numpy.sum(-x233 * (x166 * x213 + x232)) result[0, 4, 4] = numpy.sum(-x57 * (x169 * x213 + x235)) result[0, 4, 5] = numpy.sum(-x238 * (x174 * x55 + x237)) result[0, 5, 0] = numpy.sum(-x189 * (x145 * x239 + x251)) result[0, 5, 1] = numpy.sum(-x119 * (x147 * x56 + x253)) result[0, 5, 2] = numpy.sum(-x64 * (x159 * x214 + x257)) result[0, 5, 3] = numpy.sum(-x259 * (x166 * x239 + x258)) result[0, 5, 4] = numpy.sum(-x119 * (x157 * x56 + x169 * x56 + x254)) result[0, 5, 5] = numpy.sum(-x58 * (x162 + x174 * x261 + x260 + x262)) result[1, 0, 0] = numpy.sum( x58 * (x2 * x79 + x4 * x88 - x47 * x89 - x47 * (x263 * x4 + x89)) ) result[1, 0, 1] = numpy.sum(-x64 * (x101 * x99 + x101 * (x264 * x39 + x99) + x106)) result[1, 0, 2] = numpy.sum(-x175 * (x0 * x79 + x0 * (x263 * x39 + x79) + x109)) result[1, 0, 3] = numpy.sum(-x266 * (x113 * x66 + x118 + x66 * (x0 * x265 + x113))) result[1, 0, 4] = numpy.sum(-x175 * (x0 * x98 + x0 * (x264 + x98) + x121)) result[1, 0, 5] = numpy.sum(-x203 * (x108 * x66 + x66 * (x263 + x77) + x84)) result[1, 1, 0] = numpy.sum(-x270 * (x188 + x269)) result[1, 1, 1] = numpy.sum(x57 * (-x195 + x268 * x272)) result[1, 1, 2] = numpy.sum(-x110 * (x197 + x269)) result[1, 1, 3] = numpy.sum(x64 * (x0 * x274 + x104 - x198 - x200)) result[1, 1, 4] = numpy.sum(x110 * (x0 * x276 - x191 - x201 + x87)) result[1, 1, 5] = numpy.sum(-x123 * (x0 * x267 + x202)) result[1, 2, 0] = numpy.sum(-x212 * (x209 + x268 * x278)) result[1, 2, 1] = numpy.sum(-x57 * (x221 + x268 * x280)) result[1, 2, 2] = numpy.sum(-x57 * (x230 + x268 * x282)) result[1, 2, 3] = numpy.sum(-x233 * (x0 * x284 + x232)) result[1, 2, 4] = numpy.sum(-x57 * (x101 * x286 + x235)) result[1, 2, 5] = numpy.sum(-x238 * (x0 * x288 + x237)) result[1, 3, 0] = numpy.sum(-x291 * x292) result[1, 3, 1] = numpy.sum( 0.5 * x270 * (-3.0 * x180 * x2 + 2.0 * x193 * x55 + 2.0 * x272 * x55 + 2.0 * x293) ) result[1, 3, 2] = numpy.sum(-x175 * x291 * x4) result[1, 3, 3] = numpy.sum( -x58 * (x193 * x48 - x273 * x55 - x274 * x55 + x294 * (3.0 * x180 * x2 - 2.0 * x293)) ) result[1, 3, 4] = numpy.sum(x175 * (x179 * x48 + x276 * x55 - x290 * x9 + x295 * x55)) result[1, 3, 5] = numpy.sum(-x203 * x291) result[1, 4, 0] = numpy.sum(-x298 * (x176 * x278 + x296 + x297)) result[1, 4, 1] = numpy.sum(x210 * (x193 * x56 - x280 * x55 + x302)) result[1, 4, 2] = numpy.sum(-x210 * (x196 + x282 * x55 + x305)) result[1, 4, 3] = numpy.sum(x64 * (-x199 * x284 + x219 + x273 * x56 + x302 * x9)) result[1, 4, 4] = numpy.sum(x57 * (x12 * x295 * x56 - x190 * x286 - x307)) result[1, 4, 5] = numpy.sum(-x175 * (x176 * x288 + x181 + x305)) result[1, 5, 0] = numpy.sum(-x292 * (x239 * x278 + x309)) result[1, 5, 1] = numpy.sum(-x270 * (x280 * x56 + x311)) result[1, 5, 2] = numpy.sum(-x270 * (x227 * x56 + x282 * x56 + x313)) result[1, 5, 3] = numpy.sum(-x266 * (x239 * x284 + x314)) result[1, 5, 4] = numpy.sum(-x64 * (x214 * x286 + x315)) result[1, 5, 5] = numpy.sum(-x58 * (x261 * x288 + x306 + x316 + x317)) result[2, 0, 0] = numpy.sum( x58 * (x135 * x2 + x143 * x4 - x144 * x47 - x47 * (x144 + x318 * x4)) ) result[2, 0, 1] = numpy.sum(-x119 * (x0 * x135 + x0 * (x135 + x318 * x39) + x149)) result[2, 0, 2] = numpy.sum(-x64 * (x101 * x158 + x101 * (x158 + x319 * x39) + x163)) result[2, 0, 3] = numpy.sum(-x259 * (x139 + x148 * x66 + x66 * (x133 + x318))) result[2, 0, 4] = numpy.sum(-x119 * (x0 * x157 + x0 * (x157 + x319) + x170 + x171)) result[2, 0, 5] = numpy.sum( -x321 * (x117 + x171 + x173 * x66 + x66 * (x0 * x320 + x173)) ) result[2, 1, 0] = numpy.sum(-x212 * (x144 * x55 + x208 + x268 * x323)) result[2, 1, 1] = numpy.sum(-x57 * (x135 * x213 + x220 + x268 * x324)) result[2, 1, 2] = numpy.sum(-x57 * (x158 * x190 + x229 + x268 * x326)) result[2, 1, 3] = numpy.sum(-x233 * (x0 * x327 + x148 * x213 + x231)) result[2, 1, 4] = numpy.sum( -x57 * (x101 * x328 + x213 * (x148 * x151 - x2 * x60) + x234) ) result[2, 1, 5] = numpy.sum(-x238 * (x0 * x329 + x173 * x55 + x236)) result[2, 2, 0] = numpy.sum(-x270 * (x251 + x331)) result[2, 2, 1] = numpy.sum(-x150 * (x253 + x331)) result[2, 2, 2] = numpy.sum(-x57 * (x257 + x268 * x333)) result[2, 2, 3] = numpy.sum(x167 * (x0 * x334 - x258)) result[2, 2, 4] = numpy.sum(x150 * (x0 * x332 - x12 * x249 + x142 - x157 * x56)) result[2, 2, 5] = numpy.sum(x64 * (x0 * x336 + x161 - x260 - x262)) result[2, 3, 0] = numpy.sum( -x292 * (x176 * x323 - x176 * (x126 * x68 - x130 * x289) + x297) ) result[2, 3, 1] = numpy.sum(x270 * (-x218 * x55 + x300 - x312 - x324 * x55)) result[2, 3, 2] = numpy.sum(-x270 * (x196 + x227 * x55 + x304 + x326 * x55)) result[2, 3, 3] = numpy.sum( x58 * (-x199 * x283 - x199 * x327 + x2 * x218 + x302 * x9) ) result[2, 3, 4] = numpy.sum(-x64 * (x190 * x285 + x190 * x328 + x307)) result[2, 3, 5] = numpy.sum(-x321 * (x176 * x287 + x176 * x329 + x181 + x304)) result[2, 4, 0] = numpy.sum(x298 * (-x309 + x337)) result[2, 4, 1] = numpy.sum(x210 * (-x311 + x337 * x9)) result[2, 4, 2] = numpy.sum(x210 * (-x12 * x308 - x227 * x56 + x301 + x332 * x55)) result[2, 4, 3] = numpy.sum(-x119 * (x213 * x330 + x314)) result[2, 4, 4] = numpy.sum(-x57 * (x213 * x333 + x315)) result[2, 4, 5] = numpy.sum(x64 * (x228 - x316 - x317 + x336 * x55)) result[2, 5, 0] = numpy.sum(-x292 * x339) result[2, 5, 1] = numpy.sum(-x119 * x339 * x4) result[2, 5, 2] = numpy.sum(-x270 * x341) result[2, 5, 3] = numpy.sum(-x259 * x339) result[2, 5, 4] = numpy.sum(-x119 * x341) result[2, 5, 5] = numpy.sum( -0.5 * x58 * ( x12 * (3.0 * x2 * x243 - 2.0 * x340) + 2.0 * x255 * x48 - 2.0 * x335 * x56 - 2.0 * x336 * x56 ) ) return result
[docs] def int3c2e3d_sph_123(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pd|f) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 6, 10), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - C[0] x5 = 0.5 / (ax + bx) x6 = x4**2 x7 = -x2 * (ax * A[1] + bx * B[1]) x8 = -x7 - C[1] x9 = x8**2 x10 = -x2 * (ax * A[2] + bx * B[2]) x11 = -x10 - C[2] x12 = x11**2 x13 = cx + x1 x14 = x13 ** (-1.0) x15 = x1 * x14 x16 = cx * x15 * (x12 + x6 + x9) x17 = boys(4, x16) x18 = x13 ** (-1.5) x19 = 17.49341832762486 x20 = A[1] - B[1] x21 = A[2] - B[2] x22 = numpy.exp(-ax * bx * x2 * (x0**2 + x20**2 + x21**2)) x23 = x19 * x22 x24 = x2 * x23 x25 = 2.0 * x18 * x24 x26 = x17 * x25 x27 = cx ** (-1.0) x28 = x13 ** (-0.5) x29 = boys(3, x16) x30 = x5 * (2.0 * x19 * x2 * x22 * x27 * x28 * x29 - x26) x31 = -x3 - A[0] x32 = -2.0 * x19 * x2 * x22 * x27 * x28 * x29 * x31 + x26 * x4 x33 = -x32 x34 = boys(5, x16) x35 = x25 * x34 x36 = 2.0 * x17 * x19 * x2 * x22 * x27 * x28 * x31 - x35 * x4 x37 = cx * x14 x38 = x36 * x37 x39 = x30 + x31 * x33 - x38 * x4 x40 = x39 * x4 x41 = x33 * x5 x42 = 2.0 * x41 x43 = x40 + x42 x44 = x15 * x4 x45 = x33 * x4 x46 = 2.0 * x5 x47 = x27 * x29 * x46 x48 = x24 * x28 * x47 x49 = x45 + x48 x50 = x15 * x46 x51 = x43 * x44 + x49 * x50 x52 = x23 * x47 x53 = x18 * x52 x54 = x4 * x53 + x44 * x49 x55 = x15 * (x44 * x51 + x50 * x54) x56 = x1 * x13 ** (-2.5) * x52 x57 = x44 * x54 + x56 * x6 x58 = x0 * x15 x59 = x5 * (2.0 * x17 * x19 * x2 * x22 * x27 * x28 - x35) x60 = x25 * boys(6, x16) x61 = x37 * x4 x62 = ( x31 * x39 - x46 * (x32 + x38) - x61 * ( x31 * x36 + x59 - x61 * (2.0 * x19 * x2 * x22 * x27 * x28 * x31 * x34 - x4 * x60) ) ) x63 = x4 * x62 x64 = x39 * x5 x65 = 3.0 * x64 x66 = x15 * x5 x67 = 3.0 * x66 x68 = da * db * dc x69 = 0.06666666666666667 * x68 x70 = 2.23606797749979 * x69 x71 = x15 * x8 x72 = x71 * (x40 + x42) x73 = x53 * x8 x74 = x45 * x71 + x73 x75 = x15 * (x44 * x72 + x50 * x74) x76 = x4 * x8 x77 = x44 * x74 + x56 * x76 x78 = 0.3333333333333333 * x68 x79 = x11 * x15 x80 = x79 * (x40 + x42) x81 = x11 * x53 x82 = x45 * x79 + x81 x83 = x15 * (x44 * x80 + x50 * x82) x84 = x11 * x56 x85 = x4 * x84 + x44 * x82 x86 = x1**2 / x13**2 x87 = x86 * x9 x88 = x15 * x87 * (x40 + x42) x89 = x56 * x9 x90 = x45 * x87 + x89 x91 = x8 * x86 x92 = x11 * x91 x93 = x15 * x92 * (x40 + x42) x94 = x8 * x84 x95 = x45 * x92 + x94 x96 = 1.732050807568877 * x78 x97 = x12 * x86 x98 = x15 * x97 * (x40 + x42) x99 = x12 * x56 x100 = x45 * x97 + x99 x101 = x1**3 / x13**3 x102 = x101 * x8**3 x103 = x102 * x39 x104 = x0 * x33 x105 = x101 * x9 x106 = x105 * x11 x107 = x106 * x39 x108 = x101 * x12 x109 = x108 * x8 x110 = x109 * x39 x111 = x101 * x11**3 x112 = x111 * x39 x113 = -x7 - A[1] x114 = -2.0 * x113 * x19 * x2 * x22 * x27 * x28 * x29 + x26 * x8 x115 = -x114 x116 = x115 * x5 x117 = 2.0 * x113 * x17 * x19 * x2 * x22 * x27 * x28 - x35 * x8 x118 = x117 * x37 x119 = x115 * x31 - x118 * x4 x120 = x119 * x4 x121 = x116 + x120 x122 = x44 * (x116 + x121) x123 = x6 * x86 x124 = x15 * (x116 * x123 + x122 * x44) x125 = x15 * x20 x126 = x124 + x125 * x57 x127 = -x5 * (x114 + x118) x128 = 2.0 * x113 * x19 * x2 * x22 * x27 * x28 * x34 - x60 * x8 x129 = x119 * x31 + x127 - x61 * (x117 * x31 - x128 * x61) x130 = x129 * x4 x131 = x119 * x5 x132 = 2.0 * x131 x133 = x15 * (x122 * x50 + x44 * (x121 * x50 + x44 * (x130 + x132))) x134 = 3.872983346207417 * x69 x135 = x115 * x8 x136 = x135 + x48 x137 = x136 * x15 x138 = x119 * x8 x139 = x138 + x41 x140 = x137 * x5 + x139 * x44 x141 = x4 * x86 x142 = x141 * x5 x143 = x15 * (x136 * x142 + x140 * x44) x144 = x125 * x77 + x143 x145 = x129 * x8 x146 = x145 + x64 x147 = x139 * x50 x148 = x15 * (x140 * x50 + x44 * (x146 * x44 + x147)) x149 = x116 * x79 x150 = x120 * x79 + x149 x151 = x11 * x141 x152 = x15 * (x116 * x151 + x150 * x44) x153 = x125 * x85 + x152 x154 = x132 * x79 x155 = x15 * (x150 * x50 + x44 * (x130 * x79 + x154)) x156 = x137 * x8 + x73 x157 = x71 * (x139 + x41) x158 = x15 * (x156 * x66 + x157 * x44) x159 = x125 * x90 + x158 x160 = x71 * (x146 + x64) x161 = x157 * x50 x162 = x15 * (x160 * x44 + x161) x163 = x135 * x79 + x81 x164 = x41 * x79 x165 = x138 * x79 + x164 x166 = x15 * (x163 * x66 + x165 * x44) x167 = x125 * x95 + x166 x168 = x64 * x79 x169 = x145 * x79 + x168 x170 = x165 * x50 x171 = x15 * (x169 * x44 + x170) x172 = x116 * x97 x173 = x15 * (x120 * x97 + x172) x174 = x100 * x125 + x173 x175 = x132 * x97 x176 = x15 * (x130 * x97 + x175) x177 = x15 * (x157 * x71 + x41 * x87) x178 = x20 * x33 x179 = x102 * x178 + x177 x180 = x15 * (x160 * x71 + x64 * x87) x181 = x15 * (x165 * x71 + x41 * x92) x182 = x106 * x178 + x181 x183 = x15 * (x169 * x71 + x64 * x92) x184 = x41 * x97 x185 = x15 * (x138 * x97 + x184) x186 = x109 * x178 + x185 x187 = x64 * x97 x188 = x15 * (x145 * x97 + x187) x189 = x111 * x119 x190 = x111 * x178 + x189 x191 = x111 * x129 x192 = -x10 - A[2] x193 = x11 * x26 - 2.0 * x19 * x192 * x2 * x22 * x27 * x28 * x29 x194 = -x193 x195 = x194 * x5 x196 = -x11 * x35 + 2.0 * x17 * x19 * x192 * x2 * x22 * x27 * x28 x197 = x196 * x37 x198 = x194 * x31 - x197 * x4 x199 = x198 * x4 x200 = x195 + x199 x201 = x44 * (x195 + x200) x202 = x15 * (x123 * x195 + x201 * x44) x203 = x15 * x21 x204 = x202 + x203 * x57 x205 = -x5 * (x193 + x197) x206 = -x11 * x60 + 2.0 * x19 * x192 * x2 * x22 * x27 * x28 * x34 x207 = x198 * x31 + x205 - x61 * (x196 * x31 - x206 * x61) x208 = x207 * x4 x209 = x198 * x5 x210 = 2.0 * x209 x211 = x15 * (x201 * x50 + x44 * (x200 * x50 + x44 * (x208 + x210))) x212 = x195 * x71 x213 = x199 * x71 + x212 x214 = x4 * x91 x215 = x15 * (x195 * x214 + x213 * x44) x216 = x203 * x77 + x215 x217 = x15 * (x213 * x50 + x44 * x71 * (x208 + x210)) x218 = x11 * x194 + x48 x219 = x218 * x66 x220 = x11 * x198 + x41 x221 = x219 + x220 * x44 x222 = x15 * (x142 * x218 + x221 * x44) x223 = x203 * x85 + x222 x224 = x11 * x207 + x64 x225 = x220 * x50 x226 = x15 * (x221 * x50 + x44 * (x224 * x44 + x225)) x227 = x195 * x87 x228 = x15 * (x199 * x87 + x227) x229 = x203 * x90 + x228 x230 = x15 * x87 * (x208 + x210) x231 = x5 * x91 x232 = x218 * x231 x233 = x15 * (x214 * x220 + x232) x234 = x203 * x95 + x233 x235 = x15 * (x214 * x224 + x220 * x46 * x91) x236 = x218 * x79 + x81 x237 = x236 * x66 x238 = x164 + x220 * x79 x239 = x15 * (x237 + x238 * x44) x240 = x100 * x203 + x239 x241 = x168 + x224 * x79 x242 = x238 * x50 x243 = x15 * (x241 * x44 + x242) x244 = x102 * x198 x245 = x21 * x33 x246 = x102 * x245 + x244 x247 = x102 * x207 x248 = x105 * x220 x249 = x106 * x245 + x248 x250 = x105 * x224 x251 = x238 * x91 x252 = x109 * x245 + x251 x253 = x241 * x91 x254 = x15 * (x184 + x238 * x79) x255 = x111 * x245 + x254 x256 = x15 * (x187 + x241 * x79) x257 = x113 * x115 - x118 * x8 + x30 x258 = x257 * x5 x259 = x37 * x8 x260 = x113 * x117 - x128 * x259 + x59 x261 = x257 * x31 - x260 * x61 x262 = x261 * x4 x263 = x124 * x20 + x15 * (x123 * x258 + x44**2 * (2.0 * x258 + x262)) x264 = x257 * x8 x265 = 2.0 * x116 x266 = x264 + x265 x267 = x266 * x66 x268 = x261 * x8 x269 = x132 + x268 x270 = x143 * x20 + x15 * (x142 * x266 + x44 * (x267 + x269 * x44)) x271 = x258 * x79 x272 = x15 * (x151 * x258 + x44 * (x262 * x79 + x271)) + x152 * x20 x273 = x137 * x46 + x266 * x71 x274 = x273 * x66 x275 = x147 + x269 * x71 x276 = x15 * (x274 + x275 * x44) + x158 * x20 x277 = x79 * (x264 + x265) x278 = x277 * x66 x279 = x154 + x268 * x79 x280 = x15 * (x278 + x279 * x44) + x166 * x20 x281 = x258 * x97 x282 = x15 * (x262 * x97 + x281) + x173 * x20 x283 = x15 * (x161 + x275 * x71) + x177 * x20 x284 = x15 * (x170 + x279 * x71) + x181 * x20 x285 = x15 * (x175 + x268 * x97) + x185 * x20 x286 = x111 * x261 + x189 * x20 x287 = x113 * x194 - x197 * x8 x288 = x287 * x5 x289 = x113 * x196 - x206 * x259 x290 = x287 * x31 - x289 * x61 x291 = x15 * (x123 * x288 + x44**2 * (2.0 * x288 + x290 * x4)) x292 = x124 * x21 + x291 x293 = x195 + x287 * x8 x294 = x209 + x290 * x8 x295 = x15 * (x142 * x293 + x44 * (x293 * x66 + x294 * x44)) x296 = x143 * x21 + x295 x297 = x11 * x287 + x116 x298 = x11 * x290 + x131 x299 = x15 * (x142 * x297 + x44 * (x297 * x66 + x298 * x44)) x300 = x152 * x21 + x299 x301 = x212 + x293 * x71 x302 = x71 * (x209 + x294) x303 = x15 * (x301 * x66 + x302 * x44) x304 = x158 * x21 + x303 x305 = x219 + x297 * x71 x306 = x220 * x66 + x298 * x71 x307 = x15 * (x305 * x66 + x306 * x44) x308 = x166 * x21 + x307 x309 = x149 + x297 * x79 x310 = x79 * (x131 + x298) x311 = x15 * (x309 * x66 + x310 * x44) x312 = x173 * x21 + x311 x313 = x15 * (x209 * x87 + x302 * x71) x314 = x177 * x21 + x313 x315 = x15 * (x220 * x231 + x306 * x71) x316 = x181 * x21 + x315 x317 = x15 * (x238 * x66 + x310 * x71) x318 = x185 * x21 + x317 x319 = x15 * (x131 * x97 + x310 * x79) x320 = x189 * x21 + x319 x321 = -x11 * x197 + x192 * x194 + x30 x322 = x321 * x5 x323 = x11 * x37 x324 = x192 * x196 - x206 * x323 + x59 x325 = x31 * x321 - x324 * x61 x326 = x325 * x4 x327 = x15 * (x123 * x322 + x44**2 * (2.0 * x322 + x326)) + x202 * x21 x328 = x322 * x71 x329 = x15 * (x214 * x322 + x44 * (x326 * x71 + x328)) + x21 * x215 x330 = x11 * x321 + 2.0 * x195 x331 = x330 * x66 x332 = x11 * x325 + x210 x333 = x15 * (x142 * x330 + x44 * (x331 + x332 * x44)) + x21 * x222 x334 = x322 * x87 x335 = x15 * (x326 * x87 + x334) + x21 * x228 x336 = x231 * x330 x337 = x15 * (x214 * x332 + x336) + x21 * x233 x338 = x218 * x50 + x330 * x79 x339 = x338 * x66 x340 = x225 + x332 * x79 x341 = x15 * (x339 + x340 * x44) + x21 * x239 x342 = x102 * x325 + x21 * x244 x343 = x105 * x332 + x21 * x248 x344 = x21 * x251 + x340 * x91 x345 = x15 * (x242 + x340 * x79) + x21 * x254 x346 = x101 * x4**3 x347 = x0 * x115 x348 = x101 * x6 x349 = x136 * x348 x350 = x11 * x348 x351 = x0 * x141 x352 = x108 * x4 x353 = x156 * x71 + x89 x354 = x163 * x71 + x94 x355 = x135 * x97 + x99 x356 = x257 * x346 x357 = x115 * x20 x358 = x346 * x357 + x356 x359 = x266 * x348 x360 = x20 * x349 + x359 x361 = x257 * x350 x362 = x350 * x357 + x361 x363 = x141 * x273 x364 = x141 * x20 x365 = x156 * x364 + x363 x366 = x141 * x277 x367 = x163 * x364 + x366 x368 = x257 * x352 x369 = x352 * x357 + x368 x370 = x15 * (x156 * x50 + x273 * x71) x371 = x125 * x353 + x370 x372 = x15 * (x163 * x50 + x277 * x71) x373 = x125 * x354 + x372 x374 = x15 * x97 * (x264 + x265) x375 = x125 * x355 + x374 x376 = x111 * x257 x377 = x111 * x357 + x376 x378 = x287 * x346 x379 = x115 * x21 x380 = x346 * x379 + x378 x381 = x293 * x348 x382 = x21 * x349 + x381 x383 = x297 * x348 x384 = x350 * x379 + x383 x385 = x141 * x301 x386 = x141 * x21 x387 = x156 * x386 + x385 x388 = x141 * x305 x389 = x163 * x386 + x388 x390 = x141 * x309 x391 = x352 * x379 + x390 x392 = x15 * (x227 + x301 * x71) x393 = x203 * x353 + x392 x394 = x15 * (x232 + x305 * x71) x395 = x203 * x354 + x394 x396 = x15 * (x237 + x309 * x71) x397 = x203 * x355 + x396 x398 = x15 * (x172 + x309 * x79) x399 = x111 * x379 + x398 x400 = x113 * x257 + 2.0 * x127 - x259 * x260 x401 = x400 * x8 x402 = 3.0 * x258 x403 = x401 + x402 x404 = 3.0 * x267 + x403 * x71 x405 = x79 * (x401 + x402) x406 = x113 * x287 + x205 - x259 * x289 x407 = x346 * x406 x408 = 2.0 * x288 x409 = x406 * x8 + x408 x410 = x348 * x409 x411 = x11 * x406 + x258 x412 = x348 * x411 x413 = x293 * x50 + x409 * x71 x414 = x141 * x413 x415 = x297 * x50 x416 = x411 * x71 + x415 x417 = x141 * x416 x418 = x271 + x411 * x79 x419 = x141 * x418 x420 = x15 * (x301 * x50 + x413 * x71) x421 = x15 * (x305 * x50 + x416 * x71) x422 = x309 * x50 x423 = x15 * (x418 * x71 + x422) x424 = x15 * (x281 + x418 * x79) x425 = x113 * x321 - x259 * x324 x426 = x21 * x378 + x346 * x425 x427 = x322 + x425 * x8 x428 = x21 * x381 + x348 * x427 x429 = x11 * x425 + x408 x430 = x21 * x383 + x348 * x429 x431 = x328 + x427 * x71 x432 = x141 * x431 + x21 * x385 x433 = x331 + x429 * x71 x434 = x141 * x433 + x21 * x388 x435 = x415 + x429 * x79 x436 = x141 * x435 + x21 * x390 x437 = x15 * (x334 + x431 * x71) + x21 * x392 x438 = x15 * (x336 + x433 * x71) + x21 * x394 x439 = x15 * (x339 + x435 * x71) + x21 * x396 x440 = x15 * (x422 + x435 * x79) + x21 * x398 x441 = x0 * x194 x442 = x348 * x8 x443 = x0 * x218 x444 = x105 * x4 x445 = x101 * x76 x446 = x236 * x91 x447 = x236 * x79 + x99 x448 = x194 * x20 x449 = x346 * x448 + x378 x450 = x381 + x442 * x448 x451 = x20 * x218 x452 = x348 * x451 + x383 x453 = x385 + x444 * x448 x454 = x388 + x445 * x451 x455 = x236 * x364 + x390 x456 = x102 * x448 + x392 x457 = x105 * x451 + x394 x458 = x20 * x446 + x396 x459 = x125 * x447 + x398 x460 = x321 * x346 x461 = x194 * x21 x462 = x346 * x461 + x460 x463 = x321 * x442 x464 = x442 * x461 + x463 x465 = x330 * x348 x466 = x21 * x218 x467 = x348 * x466 + x465 x468 = x321 * x444 x469 = x444 * x461 + x468 x470 = x330 * x445 x471 = x445 * x466 + x470 x472 = x141 * x338 x473 = x236 * x386 + x472 x474 = x102 * x321 x475 = x102 * x461 + x474 x476 = x105 * x330 x477 = x105 * x466 + x476 x478 = x338 * x91 x479 = x21 * x446 + x478 x480 = x15 * (x236 * x50 + x338 * x79) x481 = x203 * x447 + x480 x482 = x192 * x321 + 2.0 * x205 - x323 * x324 x483 = x11 * x482 + 3.0 * x322 x484 = 3.0 * x331 + x483 * x79 # 180 item(s) result[0, 0, 0] = numpy.sum( x70 * ( x0 * x55 + x0 * (x55 + x57 * x58) + x15 * (x44 * (x43 * x67 + x44 * (x63 + x65)) + x51 * x67) ) ) result[0, 0, 1] = numpy.sum( x78 * ( x0 * x75 + x0 * (x58 * x77 + x75) + x15 * (x44 * x71 * (x63 + x65) + x67 * x72) ) ) result[0, 0, 2] = numpy.sum( x78 * ( x0 * x83 + x0 * (x58 * x85 + x83) + x15 * (x44 * x79 * (x63 + x65) + x67 * x80) ) ) result[0, 0, 3] = numpy.sum( x78 * (x0 * x88 + x0 * (x58 * x90 + x88) + x15 * x87 * (x63 + x65)) ) result[0, 0, 4] = numpy.sum( x96 * (x0 * x93 + x0 * (x58 * x95 + x93) + x15 * x92 * (x63 + x65)) ) result[0, 0, 5] = numpy.sum( x78 * (x0 * x98 + x0 * (x100 * x58 + x98) + x15 * x97 * (x63 + x65)) ) result[0, 0, 6] = numpy.sum( x70 * (x0 * x103 + x0 * (x102 * x104 + x103) + x102 * x62) ) result[0, 0, 7] = numpy.sum( x78 * (x0 * x107 + x0 * (x104 * x106 + x107) + x106 * x62) ) result[0, 0, 8] = numpy.sum( x78 * (x0 * x110 + x0 * (x104 * x109 + x110) + x109 * x62) ) result[0, 0, 9] = numpy.sum( x70 * (x0 * x112 + x0 * (x104 * x111 + x112) + x111 * x62) ) result[0, 1, 0] = numpy.sum(x134 * (x0 * x126 + x133 + x20 * x55)) result[0, 1, 1] = numpy.sum(x96 * (x0 * x144 + x148 + x20 * x75)) result[0, 1, 2] = numpy.sum(x96 * (x0 * x153 + x155 + x20 * x83)) result[0, 1, 3] = numpy.sum(x96 * (x0 * x159 + x162 + x20 * x88)) result[0, 1, 4] = numpy.sum(x68 * (x0 * x167 + x171 + x20 * x93)) result[0, 1, 5] = numpy.sum(x96 * (x0 * x174 + x176 + x20 * x98)) result[0, 1, 6] = numpy.sum(x134 * (x0 * x179 + x103 * x20 + x180)) result[0, 1, 7] = numpy.sum(x96 * (x0 * x182 + x107 * x20 + x183)) result[0, 1, 8] = numpy.sum(x96 * (x0 * x186 + x110 * x20 + x188)) result[0, 1, 9] = numpy.sum(x134 * (x0 * x190 + x112 * x20 + x191)) result[0, 2, 0] = numpy.sum(x134 * (x0 * x204 + x21 * x55 + x211)) result[0, 2, 1] = numpy.sum(x96 * (x0 * x216 + x21 * x75 + x217)) result[0, 2, 2] = numpy.sum(x96 * (x0 * x223 + x21 * x83 + x226)) result[0, 2, 3] = numpy.sum(x96 * (x0 * x229 + x21 * x88 + x230)) result[0, 2, 4] = numpy.sum(x68 * (x0 * x234 + x21 * x93 + x235)) result[0, 2, 5] = numpy.sum(x96 * (x0 * x240 + x21 * x98 + x243)) result[0, 2, 6] = numpy.sum(x134 * (x0 * x246 + x103 * x21 + x247)) result[0, 2, 7] = numpy.sum(x96 * (x0 * x249 + x107 * x21 + x250)) result[0, 2, 8] = numpy.sum(x96 * (x0 * x252 + x110 * x21 + x253)) result[0, 2, 9] = numpy.sum(x134 * (x0 * x255 + x112 * x21 + x256)) result[0, 3, 0] = numpy.sum(x70 * (x126 * x20 + x263)) result[0, 3, 1] = numpy.sum(x78 * (x144 * x20 + x270)) result[0, 3, 2] = numpy.sum(x78 * (x153 * x20 + x272)) result[0, 3, 3] = numpy.sum(x78 * (x159 * x20 + x276)) result[0, 3, 4] = numpy.sum(x96 * (x167 * x20 + x280)) result[0, 3, 5] = numpy.sum(x78 * (x174 * x20 + x282)) result[0, 3, 6] = numpy.sum(x70 * (x179 * x20 + x283)) result[0, 3, 7] = numpy.sum(x78 * (x182 * x20 + x284)) result[0, 3, 8] = numpy.sum(x78 * (x186 * x20 + x285)) result[0, 3, 9] = numpy.sum(x70 * (x190 * x20 + x286)) result[0, 4, 0] = numpy.sum(x134 * (x20 * x204 + x292)) result[0, 4, 1] = numpy.sum(x96 * (x20 * x216 + x296)) result[0, 4, 2] = numpy.sum(x96 * (x20 * x223 + x300)) result[0, 4, 3] = numpy.sum(x96 * (x20 * x229 + x304)) result[0, 4, 4] = numpy.sum(x68 * (x20 * x234 + x308)) result[0, 4, 5] = numpy.sum(x96 * (x20 * x240 + x312)) result[0, 4, 6] = numpy.sum(x134 * (x20 * x246 + x314)) result[0, 4, 7] = numpy.sum(x96 * (x20 * x249 + x316)) result[0, 4, 8] = numpy.sum(x96 * (x20 * x252 + x318)) result[0, 4, 9] = numpy.sum(x134 * (x20 * x255 + x320)) result[0, 5, 0] = numpy.sum(x70 * (x204 * x21 + x327)) result[0, 5, 1] = numpy.sum(x78 * (x21 * x216 + x329)) result[0, 5, 2] = numpy.sum(x78 * (x21 * x223 + x333)) result[0, 5, 3] = numpy.sum(x78 * (x21 * x229 + x335)) result[0, 5, 4] = numpy.sum(x96 * (x21 * x234 + x337)) result[0, 5, 5] = numpy.sum(x78 * (x21 * x240 + x341)) result[0, 5, 6] = numpy.sum(x70 * (x21 * x246 + x342)) result[0, 5, 7] = numpy.sum(x78 * (x21 * x249 + x343)) result[0, 5, 8] = numpy.sum(x78 * (x21 * x252 + x344)) result[0, 5, 9] = numpy.sum(x70 * (x21 * x255 + x345)) result[1, 0, 0] = numpy.sum(x70 * (x0 * x124 + x0 * (x124 + x346 * x347) + x133)) result[1, 0, 1] = numpy.sum(x78 * (x0 * x143 + x0 * (x0 * x349 + x143) + x148)) result[1, 0, 2] = numpy.sum(x78 * (x0 * x152 + x0 * (x152 + x347 * x350) + x155)) result[1, 0, 3] = numpy.sum(x78 * (x0 * x158 + x0 * (x156 * x351 + x158) + x162)) result[1, 0, 4] = numpy.sum(x96 * (x0 * x166 + x0 * (x163 * x351 + x166) + x171)) result[1, 0, 5] = numpy.sum(x78 * (x0 * x173 + x0 * (x173 + x347 * x352) + x176)) result[1, 0, 6] = numpy.sum(x70 * (x0 * x177 + x0 * (x177 + x353 * x58) + x180)) result[1, 0, 7] = numpy.sum(x78 * (x0 * x181 + x0 * (x181 + x354 * x58) + x183)) result[1, 0, 8] = numpy.sum(x78 * (x0 * x185 + x0 * (x185 + x355 * x58) + x188)) result[1, 0, 9] = numpy.sum(x70 * (x0 * x189 + x0 * (x111 * x347 + x189) + x191)) result[1, 1, 0] = numpy.sum(x134 * (x0 * x358 + x263)) result[1, 1, 1] = numpy.sum(x96 * (x0 * x360 + x270)) result[1, 1, 2] = numpy.sum(x96 * (x0 * x362 + x272)) result[1, 1, 3] = numpy.sum(x96 * (x0 * x365 + x276)) result[1, 1, 4] = numpy.sum(x68 * (x0 * x367 + x280)) result[1, 1, 5] = numpy.sum(x96 * (x0 * x369 + x282)) result[1, 1, 6] = numpy.sum(x134 * (x0 * x371 + x283)) result[1, 1, 7] = numpy.sum(x96 * (x0 * x373 + x284)) result[1, 1, 8] = numpy.sum(x96 * (x0 * x375 + x285)) result[1, 1, 9] = numpy.sum(x134 * (x0 * x377 + x286)) result[1, 2, 0] = numpy.sum(x134 * (x0 * x380 + x292)) result[1, 2, 1] = numpy.sum(x96 * (x0 * x382 + x296)) result[1, 2, 2] = numpy.sum(x96 * (x0 * x384 + x300)) result[1, 2, 3] = numpy.sum(x96 * (x0 * x387 + x304)) result[1, 2, 4] = numpy.sum(x68 * (x0 * x389 + x308)) result[1, 2, 5] = numpy.sum(x96 * (x0 * x391 + x312)) result[1, 2, 6] = numpy.sum(x134 * (x0 * x393 + x314)) result[1, 2, 7] = numpy.sum(x96 * (x0 * x395 + x316)) result[1, 2, 8] = numpy.sum(x96 * (x0 * x397 + x318)) result[1, 2, 9] = numpy.sum(x134 * (x0 * x399 + x320)) result[1, 3, 0] = numpy.sum(x70 * (x20 * x356 + x20 * x358 + x346 * x400)) result[1, 3, 1] = numpy.sum(x78 * (x20 * x359 + x20 * x360 + x348 * x403)) result[1, 3, 2] = numpy.sum(x78 * (x20 * x361 + x20 * x362 + x350 * x400)) result[1, 3, 3] = numpy.sum(x78 * (x141 * x404 + x20 * x363 + x20 * x365)) result[1, 3, 4] = numpy.sum(x96 * (x141 * x405 + x20 * x366 + x20 * x367)) result[1, 3, 5] = numpy.sum(x78 * (x20 * x368 + x20 * x369 + x352 * x400)) result[1, 3, 6] = numpy.sum( x70 * (x15 * (3.0 * x274 + x404 * x71) + x20 * x370 + x20 * x371) ) result[1, 3, 7] = numpy.sum( x78 * (x15 * (3.0 * x278 + x405 * x71) + x20 * x372 + x20 * x373) ) result[1, 3, 8] = numpy.sum( x78 * (x15 * x97 * (x401 + x402) + x20 * x374 + x20 * x375) ) result[1, 3, 9] = numpy.sum(x70 * (x111 * x400 + x20 * x376 + x20 * x377)) result[1, 4, 0] = numpy.sum(x134 * (x20 * x380 + x21 * x356 + x407)) result[1, 4, 1] = numpy.sum(x96 * (x20 * x382 + x21 * x359 + x410)) result[1, 4, 2] = numpy.sum(x96 * (x20 * x384 + x21 * x361 + x412)) result[1, 4, 3] = numpy.sum(x96 * (x20 * x387 + x21 * x363 + x414)) result[1, 4, 4] = numpy.sum(x68 * (x20 * x389 + x21 * x366 + x417)) result[1, 4, 5] = numpy.sum(x96 * (x20 * x391 + x21 * x368 + x419)) result[1, 4, 6] = numpy.sum(x134 * (x20 * x393 + x21 * x370 + x420)) result[1, 4, 7] = numpy.sum(x96 * (x20 * x395 + x21 * x372 + x421)) result[1, 4, 8] = numpy.sum(x96 * (x20 * x397 + x21 * x374 + x423)) result[1, 4, 9] = numpy.sum(x134 * (x20 * x399 + x21 * x376 + x424)) result[1, 5, 0] = numpy.sum(x70 * (x21 * x380 + x426)) result[1, 5, 1] = numpy.sum(x78 * (x21 * x382 + x428)) result[1, 5, 2] = numpy.sum(x78 * (x21 * x384 + x430)) result[1, 5, 3] = numpy.sum(x78 * (x21 * x387 + x432)) result[1, 5, 4] = numpy.sum(x96 * (x21 * x389 + x434)) result[1, 5, 5] = numpy.sum(x78 * (x21 * x391 + x436)) result[1, 5, 6] = numpy.sum(x70 * (x21 * x393 + x437)) result[1, 5, 7] = numpy.sum(x78 * (x21 * x395 + x438)) result[1, 5, 8] = numpy.sum(x78 * (x21 * x397 + x439)) result[1, 5, 9] = numpy.sum(x70 * (x21 * x399 + x440)) result[2, 0, 0] = numpy.sum(x70 * (x0 * x202 + x0 * (x202 + x346 * x441) + x211)) result[2, 0, 1] = numpy.sum(x78 * (x0 * x215 + x0 * (x215 + x441 * x442) + x217)) result[2, 0, 2] = numpy.sum(x78 * (x0 * x222 + x0 * (x222 + x348 * x443) + x226)) result[2, 0, 3] = numpy.sum(x78 * (x0 * x228 + x0 * (x228 + x441 * x444) + x230)) result[2, 0, 4] = numpy.sum(x96 * (x0 * x233 + x0 * (x233 + x443 * x445) + x235)) result[2, 0, 5] = numpy.sum(x78 * (x0 * x239 + x0 * (x236 * x351 + x239) + x243)) result[2, 0, 6] = numpy.sum(x70 * (x0 * x244 + x0 * (x102 * x441 + x244) + x247)) result[2, 0, 7] = numpy.sum(x78 * (x0 * x248 + x0 * (x105 * x443 + x248) + x250)) result[2, 0, 8] = numpy.sum(x78 * (x0 * x251 + x0 * (x0 * x446 + x251) + x253)) result[2, 0, 9] = numpy.sum(x70 * (x0 * x254 + x0 * (x254 + x447 * x58) + x256)) result[2, 1, 0] = numpy.sum(x134 * (x0 * x449 + x20 * x202 + x291)) result[2, 1, 1] = numpy.sum(x96 * (x0 * x450 + x20 * x215 + x295)) result[2, 1, 2] = numpy.sum(x96 * (x0 * x452 + x20 * x222 + x299)) result[2, 1, 3] = numpy.sum(x96 * (x0 * x453 + x20 * x228 + x303)) result[2, 1, 4] = numpy.sum(x68 * (x0 * x454 + x20 * x233 + x307)) result[2, 1, 5] = numpy.sum(x96 * (x0 * x455 + x20 * x239 + x311)) result[2, 1, 6] = numpy.sum(x134 * (x0 * x456 + x20 * x244 + x313)) result[2, 1, 7] = numpy.sum(x96 * (x0 * x457 + x20 * x248 + x315)) result[2, 1, 8] = numpy.sum(x96 * (x0 * x458 + x20 * x251 + x317)) result[2, 1, 9] = numpy.sum(x134 * (x0 * x459 + x20 * x254 + x319)) result[2, 2, 0] = numpy.sum(x134 * (x0 * x462 + x327)) result[2, 2, 1] = numpy.sum(x96 * (x0 * x464 + x329)) result[2, 2, 2] = numpy.sum(x96 * (x0 * x467 + x333)) result[2, 2, 3] = numpy.sum(x96 * (x0 * x469 + x335)) result[2, 2, 4] = numpy.sum(x68 * (x0 * x471 + x337)) result[2, 2, 5] = numpy.sum(x96 * (x0 * x473 + x341)) result[2, 2, 6] = numpy.sum(x134 * (x0 * x475 + x342)) result[2, 2, 7] = numpy.sum(x96 * (x0 * x477 + x343)) result[2, 2, 8] = numpy.sum(x96 * (x0 * x479 + x344)) result[2, 2, 9] = numpy.sum(x134 * (x0 * x481 + x345)) result[2, 3, 0] = numpy.sum(x70 * (x20 * x378 + x20 * x449 + x407)) result[2, 3, 1] = numpy.sum(x78 * (x20 * x381 + x20 * x450 + x410)) result[2, 3, 2] = numpy.sum(x78 * (x20 * x383 + x20 * x452 + x412)) result[2, 3, 3] = numpy.sum(x78 * (x20 * x385 + x20 * x453 + x414)) result[2, 3, 4] = numpy.sum(x96 * (x20 * x388 + x20 * x454 + x417)) result[2, 3, 5] = numpy.sum(x78 * (x20 * x390 + x20 * x455 + x419)) result[2, 3, 6] = numpy.sum(x70 * (x20 * x392 + x20 * x456 + x420)) result[2, 3, 7] = numpy.sum(x78 * (x20 * x394 + x20 * x457 + x421)) result[2, 3, 8] = numpy.sum(x78 * (x20 * x396 + x20 * x458 + x423)) result[2, 3, 9] = numpy.sum(x70 * (x20 * x398 + x20 * x459 + x424)) result[2, 4, 0] = numpy.sum(x134 * (x20 * x462 + x426)) result[2, 4, 1] = numpy.sum(x96 * (x20 * x464 + x428)) result[2, 4, 2] = numpy.sum(x96 * (x20 * x467 + x430)) result[2, 4, 3] = numpy.sum(x96 * (x20 * x469 + x432)) result[2, 4, 4] = numpy.sum(x68 * (x20 * x471 + x434)) result[2, 4, 5] = numpy.sum(x96 * (x20 * x473 + x436)) result[2, 4, 6] = numpy.sum(x134 * (x20 * x475 + x437)) result[2, 4, 7] = numpy.sum(x96 * (x20 * x477 + x438)) result[2, 4, 8] = numpy.sum(x96 * (x20 * x479 + x439)) result[2, 4, 9] = numpy.sum(x134 * (x20 * x481 + x440)) result[2, 5, 0] = numpy.sum(x70 * (x21 * x460 + x21 * x462 + x346 * x482)) result[2, 5, 1] = numpy.sum(x78 * (x21 * x463 + x21 * x464 + x442 * x482)) result[2, 5, 2] = numpy.sum(x78 * (x21 * x465 + x21 * x467 + x348 * x483)) result[2, 5, 3] = numpy.sum(x78 * (x21 * x468 + x21 * x469 + x444 * x482)) result[2, 5, 4] = numpy.sum(x96 * (x21 * x470 + x21 * x471 + x445 * x483)) result[2, 5, 5] = numpy.sum(x78 * (x141 * x484 + x21 * x472 + x21 * x473)) result[2, 5, 6] = numpy.sum(x70 * (x102 * x482 + x21 * x474 + x21 * x475)) result[2, 5, 7] = numpy.sum(x78 * (x105 * x483 + x21 * x476 + x21 * x477)) result[2, 5, 8] = numpy.sum(x78 * (x21 * x478 + x21 * x479 + x484 * x91)) result[2, 5, 9] = numpy.sum( x70 * (x15 * (3.0 * x339 + x484 * x79) + x21 * x480 + x21 * x481) ) return result
[docs] def int3c2e3d_sph_124(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pd|g) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 6, 15), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - C[0] x5 = 0.5 / (ax + bx) x6 = x4**2 x7 = -x2 * (ax * A[1] + bx * B[1]) x8 = -x7 - C[1] x9 = x8**2 x10 = -x2 * (ax * A[2] + bx * B[2]) x11 = -x10 - C[2] x12 = x11**2 x13 = cx + x1 x14 = x13 ** (-1.0) x15 = x1 * x14 x16 = cx * x15 * (x12 + x6 + x9) x17 = boys(5, x16) x18 = x13 ** (-1.5) x19 = 17.49341832762486 x20 = A[1] - B[1] x21 = A[2] - B[2] x22 = numpy.exp(-ax * bx * x2 * (x0**2 + x20**2 + x21**2)) x23 = x19 * x22 x24 = x2 * x23 x25 = 2.0 * x18 * x24 x26 = x17 * x25 x27 = cx ** (-1.0) x28 = x13 ** (-0.5) x29 = boys(4, x16) x30 = x5 * (2.0 * x19 * x2 * x22 * x27 * x28 * x29 - x26) x31 = -x3 - A[0] x32 = -2.0 * x19 * x2 * x22 * x27 * x28 * x29 * x31 + x26 * x4 x33 = -x32 x34 = boys(6, x16) x35 = x25 * x34 x36 = 2.0 * x17 * x19 * x2 * x22 * x27 * x28 * x31 - x35 * x4 x37 = cx * x14 x38 = x36 * x37 x39 = x30 + x31 * x33 - x38 * x4 x40 = x39 * x4 x41 = x33 * x5 x42 = 2.0 * x41 x43 = x40 + x42 x44 = x15 * x4 x45 = x33 * x4 x46 = 2.0 * x5 x47 = x27 * x29 * x46 x48 = x24 * x28 * x47 x49 = x45 + x48 x50 = x15 * x46 x51 = x43 * x44 + x49 * x50 x52 = x23 * x47 x53 = x18 * x52 x54 = x4 * x53 + x44 * x49 x55 = x44 * x51 + x50 * x54 x56 = x52 * x6 x57 = x1 * x13 ** (-2.5) x58 = x44 * x54 + x56 * x57 x59 = x15 * (x44 * x55 + x50 * x58) x60 = x4**3 x61 = x1**2 x62 = x13 ** (-3.5) * x61 x63 = x52 * x62 x64 = x44 * x58 + x60 * x63 x65 = x0 * x15 x66 = x5 * (2.0 * x17 * x19 * x2 * x22 * x27 * x28 - x35) x67 = x25 * boys(7, x16) x68 = x37 * x4 x69 = ( x31 * x39 - x46 * (x32 + x38) - x68 * ( x31 * x36 + x66 - x68 * (2.0 * x19 * x2 * x22 * x27 * x28 * x31 * x34 - x4 * x67) ) ) x70 = x4 * x69 x71 = x39 * x5 x72 = 3.0 * x71 x73 = x15 * x5 x74 = 3.0 * x73 x75 = da * db * dc x76 = 0.009523809523809524 * x75 x77 = 5.916079783099616 * x76 x78 = x15 * x8 x79 = x78 * (x40 + x42) x80 = x53 * x8 x81 = x45 * x78 + x80 x82 = x44 * x79 + x50 * x81 x83 = x52 * x57 x84 = x4 * x83 x85 = x44 * x81 + x8 * x84 x86 = x15 * (x44 * x82 + x50 * x85) x87 = x56 * x62 x88 = x44 * x85 + x8 * x87 x89 = 0.06666666666666667 * x75 x90 = 2.23606797749979 * x89 x91 = x11 * x15 x92 = x91 * (x40 + x42) x93 = x11 * x53 x94 = x45 * x91 + x93 x95 = x44 * x92 + x50 * x94 x96 = x11 * x84 + x44 * x94 x97 = x15 * (x44 * x95 + x50 * x96) x98 = x11 * x87 + x44 * x96 x99 = x61 / x13**2 x100 = x9 * x99 x101 = x100 * (x40 + x42) x102 = x83 * x9 x103 = x100 * x45 + x102 x104 = x15 * (x101 * x44 + x103 * x50) x105 = x63 * x9 x106 = x103 * x44 + x105 * x4 x107 = 1.732050807568877 x108 = 0.1111111111111111 * x107 * x75 x109 = x8 * x99 x110 = x109 * x11 x111 = x110 * (x40 + x42) x112 = x11 * x8 x113 = x112 * x83 x114 = x110 * x45 + x113 x115 = x15 * (x111 * x44 + x114 * x50) x116 = x112 * x4 * x63 + x114 * x44 x117 = 0.3333333333333333 * x75 x118 = x12 * x99 x119 = x118 * (x40 + x42) x120 = x12 * x83 x121 = x118 * x45 + x120 x122 = x15 * (x119 * x44 + x121 * x50) x123 = x12 * x4 x124 = x121 * x44 + x123 * x63 x125 = x8**3 x126 = x1**3 / x13**3 x127 = x125 * x126 x128 = x127 * x15 * (x40 + x42) x129 = x125 * x63 x130 = x127 * x45 + x129 x131 = x126 * x9 x132 = x11 * x131 x133 = x132 * x15 * (x40 + x42) x134 = x105 * x11 x135 = x132 * x45 + x134 x136 = x126 * x8 x137 = x12 * x136 x138 = x137 * x15 * (x40 + x42) x139 = x12 * x63 * x8 x140 = x137 * x45 + x139 x141 = x11**3 x142 = x126 * x141 x143 = x142 * x15 * (x40 + x42) x144 = x141 * x63 x145 = x142 * x45 + x144 x146 = x1**4 / x13**4 x147 = x146 * x8**4 x148 = x147 * x39 x149 = x0 * x33 x150 = x125 * x146 x151 = x11 * x150 x152 = x151 * x39 x153 = x146 * x39 x154 = x12 * x9 x155 = x153 * x154 x156 = x146 * x149 x157 = x146 * x69 x158 = x141 * x8 x159 = x153 * x158 x160 = x11**4 * x146 x161 = x160 * x39 x162 = -x7 - A[1] x163 = -2.0 * x162 * x19 * x2 * x22 * x27 * x28 * x29 + x26 * x8 x164 = -x163 x165 = x164 * x5 x166 = 2.0 * x162 * x17 * x19 * x2 * x22 * x27 * x28 - x35 * x8 x167 = x166 * x37 x168 = x164 * x31 - x167 * x4 x169 = x168 * x4 x170 = x165 + x169 x171 = x44 * (x165 + x170) x172 = x6 * x99 x173 = x165 * x172 + x171 * x44 x174 = x126 * x60 x175 = x15 * (x165 * x174 + x173 * x44) x176 = x15 * x20 x177 = x175 + x176 * x64 x178 = -x5 * (x163 + x167) x179 = 2.0 * x162 * x19 * x2 * x22 * x27 * x28 * x34 - x67 * x8 x180 = x168 * x31 + x178 - x68 * (x166 * x31 - x179 * x68) x181 = x180 * x4 x182 = x168 * x5 x183 = 2.0 * x182 x184 = x15 * ( x173 * x50 + x44 * (x171 * x50 + x44 * (x170 * x50 + x44 * (x181 + x183))) ) x185 = 10.2469507659596 * x76 x186 = x164 * x8 x187 = x186 + x48 x188 = x15 * x187 x189 = x168 * x8 x190 = x189 + x41 x191 = x188 * x5 + x190 * x44 x192 = x4 * x99 x193 = x187 * x5 x194 = x191 * x44 + x192 * x193 x195 = x126 * x6 x196 = x15 * (x193 * x195 + x194 * x44) x197 = x176 * x88 + x196 x198 = x180 * x8 x199 = x198 + x71 x200 = x190 * x50 x201 = x15 * (x194 * x50 + x44 * (x191 * x50 + x44 * (x199 * x44 + x200))) x202 = 3.872983346207417 * x89 x203 = x165 * x91 x204 = x169 * x91 + x203 x205 = x11 * x165 x206 = x192 * x205 + x204 * x44 x207 = x15 * (x195 * x205 + x206 * x44) x208 = x176 * x98 + x207 x209 = x183 * x91 x210 = x15 * (x206 * x50 + x44 * (x204 * x50 + x44 * (x181 * x91 + x209))) x211 = x188 * x8 + x80 x212 = x78 * (x190 + x41) x213 = x211 * x73 + x212 * x44 x214 = x192 * x5 x215 = x15 * (x211 * x214 + x213 * x44) x216 = x106 * x176 + x215 x217 = x78 * (x199 + x71) x218 = x212 * x50 x219 = x15 * (x213 * x50 + x44 * (x217 * x44 + x218)) x220 = x186 * x91 + x93 x221 = x41 * x91 x222 = x189 * x91 + x221 x223 = x220 * x73 + x222 * x44 x224 = x15 * (x214 * x220 + x223 * x44) x225 = x116 * x176 + x224 x226 = x71 * x91 x227 = x198 * x91 + x226 x228 = x222 * x50 x229 = x15 * (x223 * x50 + x44 * (x227 * x44 + x228)) x230 = x107 * x117 x231 = x118 * x165 x232 = x118 * x169 + x231 x233 = x123 * x126 x234 = x15 * (x165 * x233 + x232 * x44) x235 = x124 * x176 + x234 x236 = x118 * x183 x237 = x15 * (x232 * x50 + x44 * (x118 * x181 + x236)) x238 = x102 + x211 * x78 x239 = x100 * x41 + x212 * x78 x240 = x15 * (x238 * x73 + x239 * x44) x241 = x130 * x176 + x240 x242 = x100 * x71 + x217 * x78 x243 = x239 * x50 x244 = x15 * (x242 * x44 + x243) x245 = x113 + x220 * x78 x246 = x110 * x41 + x222 * x78 x247 = x15 * (x245 * x73 + x246 * x44) x248 = x135 * x176 + x247 x249 = x110 * x71 + x227 * x78 x250 = x246 * x50 x251 = x15 * (x249 * x44 + x250) x252 = x118 * x186 + x120 x253 = x118 * x41 x254 = x118 * x189 + x253 x255 = x15 * (x252 * x73 + x254 * x44) x256 = x140 * x176 + x255 x257 = x118 * x71 x258 = x118 * x198 + x257 x259 = x254 * x50 x260 = x15 * (x258 * x44 + x259) x261 = x142 * x165 x262 = x15 * (x142 * x169 + x261) x263 = x145 * x176 + x262 x264 = x142 * x183 x265 = x15 * (x142 * x181 + x264) x266 = x15 * (x127 * x41 + x239 * x78) x267 = x20 * x33 x268 = x147 * x267 + x266 x269 = x15 * (x127 * x71 + x242 * x78) x270 = x15 * (x132 * x41 + x246 * x78) x271 = x151 * x267 + x270 x272 = x15 * (x132 * x71 + x249 * x78) x273 = x15 * (x137 * x41 + x254 * x78) x274 = x146 * x267 x275 = x154 * x274 + x273 x276 = x15 * (x137 * x71 + x258 * x78) x277 = x142 * x41 x278 = x15 * (x142 * x189 + x277) x279 = x158 * x274 + x278 x280 = x142 * x71 x281 = x15 * (x142 * x198 + x280) x282 = x160 * x168 x283 = x160 * x267 + x282 x284 = x160 * x180 x285 = -x10 - A[2] x286 = x11 * x26 - 2.0 * x19 * x2 * x22 * x27 * x28 * x285 * x29 x287 = -x286 x288 = x287 * x5 x289 = -x11 * x35 + 2.0 * x17 * x19 * x2 * x22 * x27 * x28 * x285 x290 = x289 * x37 x291 = x287 * x31 - x290 * x4 x292 = x291 * x4 x293 = x288 + x292 x294 = x44 * (x288 + x293) x295 = x172 * x288 + x294 * x44 x296 = x15 * (x174 * x288 + x295 * x44) x297 = x15 * x21 x298 = x296 + x297 * x64 x299 = -x5 * (x286 + x290) x300 = -x11 * x67 + 2.0 * x19 * x2 * x22 * x27 * x28 * x285 * x34 x301 = x291 * x31 + x299 - x68 * (x289 * x31 - x300 * x68) x302 = x301 * x4 x303 = x291 * x5 x304 = 2.0 * x303 x305 = x15 * ( x295 * x50 + x44 * (x294 * x50 + x44 * (x293 * x50 + x44 * (x302 + x304))) ) x306 = x288 * x78 x307 = x292 * x78 + x306 x308 = x109 * x4 x309 = x288 * x308 + x307 * x44 x310 = x195 * x8 x311 = x15 * (x288 * x310 + x309 * x44) x312 = x297 * x88 + x311 x313 = x15 * (x309 * x50 + x44 * (x307 * x50 + x44 * x78 * (x302 + x304))) x314 = x11 * x287 + x48 x315 = x314 * x73 x316 = x11 * x291 + x41 x317 = x315 + x316 * x44 x318 = x214 * x314 + x317 * x44 x319 = x314 * x5 x320 = x15 * (x195 * x319 + x318 * x44) x321 = x297 * x98 + x320 x322 = x11 * x301 + x71 x323 = x316 * x50 x324 = x15 * (x318 * x50 + x44 * (x317 * x50 + x44 * (x322 * x44 + x323))) x325 = x100 * x288 x326 = x100 * x292 + x325 x327 = x131 * x4 x328 = x15 * (x288 * x327 + x326 * x44) x329 = x106 * x297 + x328 x330 = x15 * (x100 * x44 * (x302 + x304) + x326 * x50) x331 = x109 * x319 x332 = x308 * x316 + x331 x333 = x136 * x4 x334 = x15 * (x319 * x333 + x332 * x44) x335 = x116 * x297 + x334 x336 = x316 * x46 x337 = x15 * (x332 * x50 + x44 * (x109 * x336 + x308 * x322)) x338 = x314 * x91 + x93 x339 = x338 * x73 x340 = x221 + x316 * x91 x341 = x339 + x340 * x44 x342 = x15 * (x214 * x338 + x341 * x44) x343 = x124 * x297 + x342 x344 = x226 + x322 * x91 x345 = x340 * x50 x346 = x15 * (x341 * x50 + x44 * (x344 * x44 + x345)) x347 = x127 * x288 x348 = x15 * (x127 * x292 + x347) x349 = x130 * x297 + x348 x350 = x127 * x15 * (x302 + x304) x351 = x131 * x319 x352 = x15 * (x316 * x327 + x351) x353 = x135 * x297 + x352 x354 = x15 * (x131 * x336 + x322 * x327) x355 = x109 * x5 x356 = x338 * x355 x357 = x15 * (x308 * x340 + x356) x358 = x140 * x297 + x357 x359 = x15 * (x109 * x340 * x46 + x308 * x344) x360 = x120 + x338 * x91 x361 = x360 * x73 x362 = x253 + x340 * x91 x363 = x15 * (x361 + x362 * x44) x364 = x145 * x297 + x363 x365 = x257 + x344 * x91 x366 = x362 * x50 x367 = x15 * (x365 * x44 + x366) x368 = x147 * x291 x369 = x21 * x33 x370 = x147 * x369 + x368 x371 = x147 * x301 x372 = x150 * x316 x373 = x151 * x369 + x372 x374 = x150 * x322 x375 = x131 * x340 x376 = x146 * x369 x377 = x154 * x376 + x375 x378 = x131 * x344 x379 = x109 * x362 x380 = x158 * x376 + x379 x381 = x109 * x365 x382 = x15 * (x277 + x362 * x91) x383 = x160 * x369 + x382 x384 = x15 * (x280 + x365 * x91) x385 = x162 * x164 - x167 * x8 + x30 x386 = x385 * x5 x387 = x37 * x8 x388 = x162 * x166 - x179 * x387 + x66 x389 = x31 * x385 - x388 * x68 x390 = x389 * x4 x391 = ( x15 * (x174 * x386 + x44 * (x172 * x386 + x44**2 * (2.0 * x386 + x390))) + x175 * x20 ) x392 = x385 * x8 x393 = 2.0 * x165 x394 = x392 + x393 x395 = x394 * x73 x396 = x389 * x8 x397 = x183 + x396 x398 = x195 * x5 x399 = ( x15 * (x394 * x398 + x44 * (x214 * x394 + x44 * (x395 + x397 * x44))) + x196 * x20 ) x400 = x386 * x91 x401 = x11 * x386 x402 = ( x15 * (x195 * x401 + x44 * (x192 * x401 + x44 * (x390 * x91 + x400))) + x20 * x207 ) x403 = x188 * x46 + x394 * x78 x404 = x403 * x73 x405 = x200 + x397 * x78 x406 = x15 * (x214 * x403 + x44 * (x404 + x405 * x44)) + x20 * x215 x407 = x91 * (x392 + x393) x408 = x407 * x73 x409 = x209 + x396 * x91 x410 = x15 * (x214 * x407 + x44 * (x408 + x409 * x44)) + x20 * x224 x411 = x118 * x386 x412 = x15 * (x233 * x386 + x44 * (x118 * x390 + x411)) + x20 * x234 x413 = x211 * x50 + x403 * x78 x414 = x413 * x73 x415 = x218 + x405 * x78 x416 = x15 * (x414 + x415 * x44) + x20 * x240 x417 = x220 * x50 + x407 * x78 x418 = x417 * x73 x419 = x228 + x409 * x78 x420 = x15 * (x418 + x419 * x44) + x20 * x247 x421 = x118 * (x392 + x393) x422 = x421 * x73 x423 = x118 * x396 + x236 x424 = x15 * (x422 + x423 * x44) + x20 * x255 x425 = x142 * x386 x426 = x15 * (x142 * x390 + x425) + x20 * x262 x427 = x15 * (x243 + x415 * x78) + x20 * x266 x428 = x15 * (x250 + x419 * x78) + x20 * x270 x429 = x15 * (x259 + x423 * x78) + x20 * x273 x430 = x15 * (x142 * x396 + x264) + x20 * x278 x431 = x160 * x389 + x20 * x282 x432 = x162 * x287 - x290 * x8 x433 = x432 * x5 x434 = x162 * x289 - x300 * x387 x435 = x31 * x432 - x434 * x68 x436 = x15 * (x174 * x433 + x44 * (x172 * x433 + x44**2 * (x4 * x435 + 2.0 * x433))) x437 = x175 * x21 + x436 x438 = x288 + x432 * x8 x439 = x303 + x435 * x8 x440 = x15 * (x398 * x438 + x44 * (x214 * x438 + x44 * (x438 * x73 + x439 * x44))) x441 = x196 * x21 + x440 x442 = x11 * x432 + x165 x443 = x11 * x435 + x182 x444 = x15 * (x398 * x442 + x44 * (x214 * x442 + x44 * (x44 * x443 + x442 * x73))) x445 = x207 * x21 + x444 x446 = x306 + x438 * x78 x447 = x78 * (x303 + x439) x448 = x15 * (x214 * x446 + x44 * (x44 * x447 + x446 * x73)) x449 = x21 * x215 + x448 x450 = x315 + x442 * x78 x451 = x316 * x73 + x443 * x78 x452 = x15 * (x214 * x450 + x44 * (x44 * x451 + x450 * x73)) x453 = x21 * x224 + x452 x454 = x203 + x442 * x91 x455 = x91 * (x182 + x443) x456 = x15 * (x214 * x454 + x44 * (x44 * x455 + x454 * x73)) x457 = x21 * x234 + x456 x458 = x325 + x446 * x78 x459 = x100 * x303 + x447 * x78 x460 = x15 * (x44 * x459 + x458 * x73) x461 = x21 * x240 + x460 x462 = x331 + x450 * x78 x463 = x316 * x355 + x451 * x78 x464 = x15 * (x44 * x463 + x462 * x73) x465 = x21 * x247 + x464 x466 = x339 + x454 * x78 x467 = x340 * x73 + x455 * x78 x468 = x15 * (x44 * x467 + x466 * x73) x469 = x21 * x255 + x468 x470 = x231 + x454 * x91 x471 = x118 * x182 + x455 * x91 x472 = x15 * (x44 * x471 + x470 * x73) x473 = x21 * x262 + x472 x474 = x15 * (x127 * x303 + x459 * x78) x475 = x21 * x266 + x474 x476 = x131 * x5 x477 = x15 * (x316 * x476 + x463 * x78) x478 = x21 * x270 + x477 x479 = x15 * (x340 * x355 + x467 * x78) x480 = x21 * x273 + x479 x481 = x15 * (x362 * x73 + x471 * x78) x482 = x21 * x278 + x481 x483 = x15 * (x142 * x182 + x471 * x91) x484 = x21 * x282 + x483 x485 = -x11 * x290 + x285 * x287 + x30 x486 = x485 * x5 x487 = x11 * x37 x488 = x285 * x289 - x300 * x487 + x66 x489 = x31 * x485 - x488 * x68 x490 = x4 * x489 x491 = ( x15 * (x174 * x486 + x44 * (x172 * x486 + x44**2 * (2.0 * x486 + x490))) + x21 * x296 ) x492 = x486 * x78 x493 = ( x15 * (x310 * x486 + x44 * (x308 * x486 + x44 * (x490 * x78 + x492))) + x21 * x311 ) x494 = x11 * x485 + 2.0 * x288 x495 = x494 * x73 x496 = x11 * x489 + x304 x497 = ( x15 * (x398 * x494 + x44 * (x214 * x494 + x44 * (x44 * x496 + x495))) + x21 * x320 ) x498 = x100 * x486 x499 = x15 * (x327 * x486 + x44 * (x100 * x490 + x498)) + x21 * x328 x500 = x355 * x494 x501 = x4 * x494 x502 = x15 * (x136 * x5 * x501 + x44 * (x308 * x496 + x500)) + x21 * x334 x503 = x314 * x50 + x494 * x91 x504 = x503 * x73 x505 = x323 + x496 * x91 x506 = x15 * (x214 * x503 + x44 * (x44 * x505 + x504)) + x21 * x342 x507 = x127 * x486 x508 = x15 * (x127 * x490 + x507) + x21 * x348 x509 = x476 * x494 x510 = x15 * (x327 * x496 + x509) + x21 * x352 x511 = x355 * x503 x512 = x15 * (x308 * x505 + x511) + x21 * x357 x513 = x338 * x50 + x503 * x91 x514 = x513 * x73 x515 = x345 + x505 * x91 x516 = x15 * (x44 * x515 + x514) + x21 * x363 x517 = x147 * x489 + x21 * x368 x518 = x150 * x496 + x21 * x372 x519 = x131 * x505 + x21 * x375 x520 = x109 * x515 + x21 * x379 x521 = x15 * (x366 + x515 * x91) + x21 * x382 x522 = x146 * x4**4 x523 = x0 * x164 x524 = x146 * x60 x525 = x187 * x524 x526 = x11 * x524 x527 = x0 * x195 x528 = x12 * x6 x529 = x146 * x523 x530 = x0 * x192 x531 = x141 * x4 x532 = x129 + x238 * x78 x533 = x134 + x245 * x78 x534 = x139 + x252 * x78 x535 = x142 * x186 + x144 x536 = x385 * x522 x537 = x164 * x20 x538 = x522 * x537 + x536 x539 = x394 * x524 x540 = x20 * x525 + x539 x541 = x385 * x526 x542 = x526 * x537 + x541 x543 = x195 * x403 x544 = x195 * x20 x545 = x211 * x544 + x543 x546 = x195 * x407 x547 = x220 * x544 + x546 x548 = x146 * x385 x549 = x528 * x548 x550 = x146 * x537 x551 = x528 * x550 + x549 x552 = x192 * x413 x553 = x192 * x20 x554 = x238 * x553 + x552 x555 = x192 * x417 x556 = x245 * x553 + x555 x557 = x192 * x421 x558 = x252 * x553 + x557 x559 = x531 * x548 x560 = x531 * x550 + x559 x561 = x15 * (x238 * x50 + x413 * x78) x562 = x176 * x532 + x561 x563 = x15 * (x245 * x50 + x417 * x78) x564 = x176 * x533 + x563 x565 = x15 * (x252 * x50 + x421 * x78) x566 = x176 * x534 + x565 x567 = x142 * x15 * (x392 + x393) x568 = x176 * x535 + x567 x569 = x160 * x385 x570 = x160 * x537 + x569 x571 = x432 * x522 x572 = x164 * x21 x573 = x522 * x572 + x571 x574 = x438 * x524 x575 = x21 * x525 + x574 x576 = x442 * x524 x577 = x526 * x572 + x576 x578 = x195 * x446 x579 = x195 * x21 x580 = x211 * x579 + x578 x581 = x195 * x450 x582 = x220 * x579 + x581 x583 = x195 * x454 x584 = x146 * x572 x585 = x528 * x584 + x583 x586 = x192 * x458 x587 = x192 * x21 x588 = x238 * x587 + x586 x589 = x192 * x462 x590 = x245 * x587 + x589 x591 = x192 * x466 x592 = x252 * x587 + x591 x593 = x192 * x470 x594 = x531 * x584 + x593 x595 = x15 * (x347 + x458 * x78) x596 = x297 * x532 + x595 x597 = x15 * (x351 + x462 * x78) x598 = x297 * x533 + x597 x599 = x15 * (x356 + x466 * x78) x600 = x297 * x534 + x599 x601 = x15 * (x361 + x470 * x78) x602 = x297 * x535 + x601 x603 = x15 * (x261 + x470 * x91) x604 = x160 * x572 + x603 x605 = x162 * x385 + 2.0 * x178 - x387 * x388 x606 = x605 * x8 x607 = 3.0 * x386 x608 = x606 + x607 x609 = 3.0 * x395 + x608 * x78 x610 = x91 * (x606 + x607) x611 = x146 * x605 x612 = 3.0 * x404 + x609 * x78 x613 = 3.0 * x408 + x610 * x78 x614 = x118 * (x606 + x607) x615 = x162 * x432 + x299 - x387 * x434 x616 = x522 * x615 x617 = 2.0 * x433 x618 = x615 * x8 + x617 x619 = x524 * x618 x620 = x11 * x615 + x386 x621 = x524 * x620 x622 = x438 * x50 + x618 * x78 x623 = x195 * x622 x624 = x442 * x50 x625 = x620 * x78 + x624 x626 = x195 * x625 x627 = x400 + x620 * x91 x628 = x195 * x627 x629 = x446 * x50 + x622 * x78 x630 = x192 * x629 x631 = x450 * x50 + x625 * x78 x632 = x192 * x631 x633 = x454 * x50 x634 = x627 * x78 + x633 x635 = x192 * x634 x636 = x411 + x627 * x91 x637 = x192 * x636 x638 = x15 * (x458 * x50 + x629 * x78) x639 = x15 * (x462 * x50 + x631 * x78) x640 = x15 * (x466 * x50 + x634 * x78) x641 = x470 * x50 x642 = x15 * (x636 * x78 + x641) x643 = x15 * (x425 + x636 * x91) x644 = x162 * x485 - x387 * x488 x645 = x21 * x571 + x522 * x644 x646 = x486 + x644 * x8 x647 = x21 * x574 + x524 * x646 x648 = x11 * x644 + x617 x649 = x21 * x576 + x524 * x648 x650 = x492 + x646 * x78 x651 = x195 * x650 + x21 * x578 x652 = x495 + x648 * x78 x653 = x195 * x652 + x21 * x581 x654 = x624 + x648 * x91 x655 = x195 * x654 + x21 * x583 x656 = x498 + x650 * x78 x657 = x192 * x656 + x21 * x586 x658 = x500 + x652 * x78 x659 = x192 * x658 + x21 * x589 x660 = x504 + x654 * x78 x661 = x192 * x660 + x21 * x591 x662 = x633 + x654 * x91 x663 = x192 * x662 + x21 * x593 x664 = x15 * (x507 + x656 * x78) + x21 * x595 x665 = x15 * (x509 + x658 * x78) + x21 * x597 x666 = x15 * (x511 + x660 * x78) + x21 * x599 x667 = x15 * (x514 + x662 * x78) + x21 * x601 x668 = x15 * (x641 + x662 * x91) + x21 * x603 x669 = x0 * x287 x670 = x524 * x8 x671 = x0 * x314 x672 = x146 * x6 x673 = x672 * x9 x674 = x672 * x8 x675 = x150 * x4 x676 = x146 * x9 x677 = x4 * x676 x678 = x333 * x338 x679 = x131 * x338 x680 = x109 * x360 x681 = x144 + x360 * x91 x682 = x20 * x287 x683 = x522 * x682 + x571 x684 = x574 + x670 * x682 x685 = x20 * x314 x686 = x524 * x685 + x576 x687 = x578 + x673 * x682 x688 = x581 + x674 * x685 x689 = x338 * x544 + x583 x690 = x586 + x675 * x682 x691 = x589 + x677 * x685 x692 = x20 * x678 + x591 x693 = x360 * x553 + x593 x694 = x147 * x682 + x595 x695 = x150 * x685 + x597 x696 = x20 * x679 + x599 x697 = x20 * x680 + x601 x698 = x176 * x681 + x603 x699 = x485 * x522 x700 = x21 * x287 x701 = x522 * x700 + x699 x702 = x485 * x670 x703 = x670 * x700 + x702 x704 = x494 * x524 x705 = x21 * x314 x706 = x524 * x705 + x704 x707 = x485 * x673 x708 = x673 * x700 + x707 x709 = x494 * x674 x710 = x674 * x705 + x709 x711 = x195 * x503 x712 = x338 * x579 + x711 x713 = x485 * x675 x714 = x675 * x700 + x713 x715 = x501 * x676 x716 = x677 * x705 + x715 x717 = x333 * x503 x718 = x21 * x678 + x717 x719 = x192 * x513 x720 = x360 * x587 + x719 x721 = x147 * x485 x722 = x147 * x700 + x721 x723 = x150 * x494 x724 = x150 * x705 + x723 x725 = x131 * x503 x726 = x21 * x679 + x725 x727 = x109 * x513 x728 = x21 * x680 + x727 x729 = x15 * (x360 * x50 + x513 * x91) x730 = x297 * x681 + x729 x731 = x285 * x485 + 2.0 * x299 - x487 * x488 x732 = x11 * x731 + 3.0 * x486 x733 = 3.0 * x495 + x732 * x91 x734 = 3.0 * x504 + x733 * x91 # 270 item(s) result[0, 0, 0] = numpy.sum( x77 * ( x0 * x59 + x0 * (x59 + x64 * x65) + x15 * (x44 * (x44 * (x43 * x74 + x44 * (x70 + x72)) + x51 * x74) + x55 * x74) ) ) result[0, 0, 1] = numpy.sum( x90 * ( x0 * x86 + x0 * (x65 * x88 + x86) + x15 * (x44 * (x44 * x78 * (x70 + x72) + x74 * x79) + x74 * x82) ) ) result[0, 0, 2] = numpy.sum( x90 * ( x0 * x97 + x0 * (x65 * x98 + x97) + x15 * (x44 * (x44 * x91 * (x70 + x72) + x74 * x92) + x74 * x95) ) ) result[0, 0, 3] = numpy.sum( x108 * ( x0 * x104 + x0 * (x104 + x106 * x65) + x15 * (x100 * x44 * (x70 + x72) + x101 * x74) ) ) result[0, 0, 4] = numpy.sum( x117 * ( x0 * x115 + x0 * (x115 + x116 * x65) + x15 * (x110 * x44 * (x70 + x72) + x111 * x74) ) ) result[0, 0, 5] = numpy.sum( x108 * ( x0 * x122 + x0 * (x122 + x124 * x65) + x15 * (x118 * x44 * (x70 + x72) + x119 * x74) ) ) result[0, 0, 6] = numpy.sum( x90 * (x0 * x128 + x0 * (x128 + x130 * x65) + x127 * x15 * (x70 + x72)) ) result[0, 0, 7] = numpy.sum( x117 * (x0 * x133 + x0 * (x133 + x135 * x65) + x132 * x15 * (x70 + x72)) ) result[0, 0, 8] = numpy.sum( x117 * (x0 * x138 + x0 * (x138 + x140 * x65) + x137 * x15 * (x70 + x72)) ) result[0, 0, 9] = numpy.sum( x90 * (x0 * x143 + x0 * (x143 + x145 * x65) + x142 * x15 * (x70 + x72)) ) result[0, 0, 10] = numpy.sum( x77 * (x0 * x148 + x0 * (x147 * x149 + x148) + x147 * x69) ) result[0, 0, 11] = numpy.sum( x90 * (x0 * x152 + x0 * (x149 * x151 + x152) + x151 * x69) ) result[0, 0, 12] = numpy.sum( x108 * (x0 * x155 + x0 * (x154 * x156 + x155) + x154 * x157) ) result[0, 0, 13] = numpy.sum( x90 * (x0 * x159 + x0 * (x156 * x158 + x159) + x157 * x158) ) result[0, 0, 14] = numpy.sum( x77 * (x0 * x161 + x0 * (x149 * x160 + x161) + x160 * x69) ) result[0, 1, 0] = numpy.sum(x185 * (x0 * x177 + x184 + x20 * x59)) result[0, 1, 1] = numpy.sum(x202 * (x0 * x197 + x20 * x86 + x201)) result[0, 1, 2] = numpy.sum(x202 * (x0 * x208 + x20 * x97 + x210)) result[0, 1, 3] = numpy.sum(x117 * (x0 * x216 + x104 * x20 + x219)) result[0, 1, 4] = numpy.sum(x230 * (x0 * x225 + x115 * x20 + x229)) result[0, 1, 5] = numpy.sum(x117 * (x0 * x235 + x122 * x20 + x237)) result[0, 1, 6] = numpy.sum(x202 * (x0 * x241 + x128 * x20 + x244)) result[0, 1, 7] = numpy.sum(x230 * (x0 * x248 + x133 * x20 + x251)) result[0, 1, 8] = numpy.sum(x230 * (x0 * x256 + x138 * x20 + x260)) result[0, 1, 9] = numpy.sum(x202 * (x0 * x263 + x143 * x20 + x265)) result[0, 1, 10] = numpy.sum(x185 * (x0 * x268 + x148 * x20 + x269)) result[0, 1, 11] = numpy.sum(x202 * (x0 * x271 + x152 * x20 + x272)) result[0, 1, 12] = numpy.sum(x117 * (x0 * x275 + x155 * x20 + x276)) result[0, 1, 13] = numpy.sum(x202 * (x0 * x279 + x159 * x20 + x281)) result[0, 1, 14] = numpy.sum(x185 * (x0 * x283 + x161 * x20 + x284)) result[0, 2, 0] = numpy.sum(x185 * (x0 * x298 + x21 * x59 + x305)) result[0, 2, 1] = numpy.sum(x202 * (x0 * x312 + x21 * x86 + x313)) result[0, 2, 2] = numpy.sum(x202 * (x0 * x321 + x21 * x97 + x324)) result[0, 2, 3] = numpy.sum(x117 * (x0 * x329 + x104 * x21 + x330)) result[0, 2, 4] = numpy.sum(x230 * (x0 * x335 + x115 * x21 + x337)) result[0, 2, 5] = numpy.sum(x117 * (x0 * x343 + x122 * x21 + x346)) result[0, 2, 6] = numpy.sum(x202 * (x0 * x349 + x128 * x21 + x350)) result[0, 2, 7] = numpy.sum(x230 * (x0 * x353 + x133 * x21 + x354)) result[0, 2, 8] = numpy.sum(x230 * (x0 * x358 + x138 * x21 + x359)) result[0, 2, 9] = numpy.sum(x202 * (x0 * x364 + x143 * x21 + x367)) result[0, 2, 10] = numpy.sum(x185 * (x0 * x370 + x148 * x21 + x371)) result[0, 2, 11] = numpy.sum(x202 * (x0 * x373 + x152 * x21 + x374)) result[0, 2, 12] = numpy.sum(x117 * (x0 * x377 + x155 * x21 + x378)) result[0, 2, 13] = numpy.sum(x202 * (x0 * x380 + x159 * x21 + x381)) result[0, 2, 14] = numpy.sum(x185 * (x0 * x383 + x161 * x21 + x384)) result[0, 3, 0] = numpy.sum(x77 * (x177 * x20 + x391)) result[0, 3, 1] = numpy.sum(x90 * (x197 * x20 + x399)) result[0, 3, 2] = numpy.sum(x90 * (x20 * x208 + x402)) result[0, 3, 3] = numpy.sum(x108 * (x20 * x216 + x406)) result[0, 3, 4] = numpy.sum(x117 * (x20 * x225 + x410)) result[0, 3, 5] = numpy.sum(x108 * (x20 * x235 + x412)) result[0, 3, 6] = numpy.sum(x90 * (x20 * x241 + x416)) result[0, 3, 7] = numpy.sum(x117 * (x20 * x248 + x420)) result[0, 3, 8] = numpy.sum(x117 * (x20 * x256 + x424)) result[0, 3, 9] = numpy.sum(x90 * (x20 * x263 + x426)) result[0, 3, 10] = numpy.sum(x77 * (x20 * x268 + x427)) result[0, 3, 11] = numpy.sum(x90 * (x20 * x271 + x428)) result[0, 3, 12] = numpy.sum(x108 * (x20 * x275 + x429)) result[0, 3, 13] = numpy.sum(x90 * (x20 * x279 + x430)) result[0, 3, 14] = numpy.sum(x77 * (x20 * x283 + x431)) result[0, 4, 0] = numpy.sum(x185 * (x20 * x298 + x437)) result[0, 4, 1] = numpy.sum(x202 * (x20 * x312 + x441)) result[0, 4, 2] = numpy.sum(x202 * (x20 * x321 + x445)) result[0, 4, 3] = numpy.sum(x117 * (x20 * x329 + x449)) result[0, 4, 4] = numpy.sum(x230 * (x20 * x335 + x453)) result[0, 4, 5] = numpy.sum(x117 * (x20 * x343 + x457)) result[0, 4, 6] = numpy.sum(x202 * (x20 * x349 + x461)) result[0, 4, 7] = numpy.sum(x230 * (x20 * x353 + x465)) result[0, 4, 8] = numpy.sum(x230 * (x20 * x358 + x469)) result[0, 4, 9] = numpy.sum(x202 * (x20 * x364 + x473)) result[0, 4, 10] = numpy.sum(x185 * (x20 * x370 + x475)) result[0, 4, 11] = numpy.sum(x202 * (x20 * x373 + x478)) result[0, 4, 12] = numpy.sum(x117 * (x20 * x377 + x480)) result[0, 4, 13] = numpy.sum(x202 * (x20 * x380 + x482)) result[0, 4, 14] = numpy.sum(x185 * (x20 * x383 + x484)) result[0, 5, 0] = numpy.sum(x77 * (x21 * x298 + x491)) result[0, 5, 1] = numpy.sum(x90 * (x21 * x312 + x493)) result[0, 5, 2] = numpy.sum(x90 * (x21 * x321 + x497)) result[0, 5, 3] = numpy.sum(x108 * (x21 * x329 + x499)) result[0, 5, 4] = numpy.sum(x117 * (x21 * x335 + x502)) result[0, 5, 5] = numpy.sum(x108 * (x21 * x343 + x506)) result[0, 5, 6] = numpy.sum(x90 * (x21 * x349 + x508)) result[0, 5, 7] = numpy.sum(x117 * (x21 * x353 + x510)) result[0, 5, 8] = numpy.sum(x117 * (x21 * x358 + x512)) result[0, 5, 9] = numpy.sum(x90 * (x21 * x364 + x516)) result[0, 5, 10] = numpy.sum(x77 * (x21 * x370 + x517)) result[0, 5, 11] = numpy.sum(x90 * (x21 * x373 + x518)) result[0, 5, 12] = numpy.sum(x108 * (x21 * x377 + x519)) result[0, 5, 13] = numpy.sum(x90 * (x21 * x380 + x520)) result[0, 5, 14] = numpy.sum(x77 * (x21 * x383 + x521)) result[1, 0, 0] = numpy.sum(x77 * (x0 * x175 + x0 * (x175 + x522 * x523) + x184)) result[1, 0, 1] = numpy.sum(x90 * (x0 * x196 + x0 * (x0 * x525 + x196) + x201)) result[1, 0, 2] = numpy.sum(x90 * (x0 * x207 + x0 * (x207 + x523 * x526) + x210)) result[1, 0, 3] = numpy.sum(x108 * (x0 * x215 + x0 * (x211 * x527 + x215) + x219)) result[1, 0, 4] = numpy.sum(x117 * (x0 * x224 + x0 * (x220 * x527 + x224) + x229)) result[1, 0, 5] = numpy.sum(x108 * (x0 * x234 + x0 * (x234 + x528 * x529) + x237)) result[1, 0, 6] = numpy.sum(x90 * (x0 * x240 + x0 * (x238 * x530 + x240) + x244)) result[1, 0, 7] = numpy.sum(x117 * (x0 * x247 + x0 * (x245 * x530 + x247) + x251)) result[1, 0, 8] = numpy.sum(x117 * (x0 * x255 + x0 * (x252 * x530 + x255) + x260)) result[1, 0, 9] = numpy.sum(x90 * (x0 * x262 + x0 * (x262 + x529 * x531) + x265)) result[1, 0, 10] = numpy.sum(x77 * (x0 * x266 + x0 * (x266 + x532 * x65) + x269)) result[1, 0, 11] = numpy.sum(x90 * (x0 * x270 + x0 * (x270 + x533 * x65) + x272)) result[1, 0, 12] = numpy.sum(x108 * (x0 * x273 + x0 * (x273 + x534 * x65) + x276)) result[1, 0, 13] = numpy.sum(x90 * (x0 * x278 + x0 * (x278 + x535 * x65) + x281)) result[1, 0, 14] = numpy.sum(x77 * (x0 * x282 + x0 * (x160 * x523 + x282) + x284)) result[1, 1, 0] = numpy.sum(x185 * (x0 * x538 + x391)) result[1, 1, 1] = numpy.sum(x202 * (x0 * x540 + x399)) result[1, 1, 2] = numpy.sum(x202 * (x0 * x542 + x402)) result[1, 1, 3] = numpy.sum(x117 * (x0 * x545 + x406)) result[1, 1, 4] = numpy.sum(x230 * (x0 * x547 + x410)) result[1, 1, 5] = numpy.sum(x117 * (x0 * x551 + x412)) result[1, 1, 6] = numpy.sum(x202 * (x0 * x554 + x416)) result[1, 1, 7] = numpy.sum(x230 * (x0 * x556 + x420)) result[1, 1, 8] = numpy.sum(x230 * (x0 * x558 + x424)) result[1, 1, 9] = numpy.sum(x202 * (x0 * x560 + x426)) result[1, 1, 10] = numpy.sum(x185 * (x0 * x562 + x427)) result[1, 1, 11] = numpy.sum(x202 * (x0 * x564 + x428)) result[1, 1, 12] = numpy.sum(x117 * (x0 * x566 + x429)) result[1, 1, 13] = numpy.sum(x202 * (x0 * x568 + x430)) result[1, 1, 14] = numpy.sum(x185 * (x0 * x570 + x431)) result[1, 2, 0] = numpy.sum(x185 * (x0 * x573 + x437)) result[1, 2, 1] = numpy.sum(x202 * (x0 * x575 + x441)) result[1, 2, 2] = numpy.sum(x202 * (x0 * x577 + x445)) result[1, 2, 3] = numpy.sum(x117 * (x0 * x580 + x449)) result[1, 2, 4] = numpy.sum(x230 * (x0 * x582 + x453)) result[1, 2, 5] = numpy.sum(x117 * (x0 * x585 + x457)) result[1, 2, 6] = numpy.sum(x202 * (x0 * x588 + x461)) result[1, 2, 7] = numpy.sum(x230 * (x0 * x590 + x465)) result[1, 2, 8] = numpy.sum(x230 * (x0 * x592 + x469)) result[1, 2, 9] = numpy.sum(x202 * (x0 * x594 + x473)) result[1, 2, 10] = numpy.sum(x185 * (x0 * x596 + x475)) result[1, 2, 11] = numpy.sum(x202 * (x0 * x598 + x478)) result[1, 2, 12] = numpy.sum(x117 * (x0 * x600 + x480)) result[1, 2, 13] = numpy.sum(x202 * (x0 * x602 + x482)) result[1, 2, 14] = numpy.sum(x185 * (x0 * x604 + x484)) result[1, 3, 0] = numpy.sum(x77 * (x20 * x536 + x20 * x538 + x522 * x605)) result[1, 3, 1] = numpy.sum(x90 * (x20 * x539 + x20 * x540 + x524 * x608)) result[1, 3, 2] = numpy.sum(x90 * (x20 * x541 + x20 * x542 + x526 * x605)) result[1, 3, 3] = numpy.sum(x108 * (x195 * x609 + x20 * x543 + x20 * x545)) result[1, 3, 4] = numpy.sum(x117 * (x195 * x610 + x20 * x546 + x20 * x547)) result[1, 3, 5] = numpy.sum(x108 * (x20 * x549 + x20 * x551 + x528 * x611)) result[1, 3, 6] = numpy.sum(x90 * (x192 * x612 + x20 * x552 + x20 * x554)) result[1, 3, 7] = numpy.sum(x117 * (x192 * x613 + x20 * x555 + x20 * x556)) result[1, 3, 8] = numpy.sum(x117 * (x192 * x614 + x20 * x557 + x20 * x558)) result[1, 3, 9] = numpy.sum(x90 * (x20 * x559 + x20 * x560 + x531 * x611)) result[1, 3, 10] = numpy.sum( x77 * (x15 * (3.0 * x414 + x612 * x78) + x20 * x561 + x20 * x562) ) result[1, 3, 11] = numpy.sum( x90 * (x15 * (3.0 * x418 + x613 * x78) + x20 * x563 + x20 * x564) ) result[1, 3, 12] = numpy.sum( x108 * (x15 * (3.0 * x422 + x614 * x78) + x20 * x565 + x20 * x566) ) result[1, 3, 13] = numpy.sum( x90 * (x142 * x15 * (x606 + x607) + x20 * x567 + x20 * x568) ) result[1, 3, 14] = numpy.sum(x77 * (x160 * x605 + x20 * x569 + x20 * x570)) result[1, 4, 0] = numpy.sum(x185 * (x20 * x573 + x21 * x536 + x616)) result[1, 4, 1] = numpy.sum(x202 * (x20 * x575 + x21 * x539 + x619)) result[1, 4, 2] = numpy.sum(x202 * (x20 * x577 + x21 * x541 + x621)) result[1, 4, 3] = numpy.sum(x117 * (x20 * x580 + x21 * x543 + x623)) result[1, 4, 4] = numpy.sum(x230 * (x20 * x582 + x21 * x546 + x626)) result[1, 4, 5] = numpy.sum(x117 * (x20 * x585 + x21 * x549 + x628)) result[1, 4, 6] = numpy.sum(x202 * (x20 * x588 + x21 * x552 + x630)) result[1, 4, 7] = numpy.sum(x230 * (x20 * x590 + x21 * x555 + x632)) result[1, 4, 8] = numpy.sum(x230 * (x20 * x592 + x21 * x557 + x635)) result[1, 4, 9] = numpy.sum(x202 * (x20 * x594 + x21 * x559 + x637)) result[1, 4, 10] = numpy.sum(x185 * (x20 * x596 + x21 * x561 + x638)) result[1, 4, 11] = numpy.sum(x202 * (x20 * x598 + x21 * x563 + x639)) result[1, 4, 12] = numpy.sum(x117 * (x20 * x600 + x21 * x565 + x640)) result[1, 4, 13] = numpy.sum(x202 * (x20 * x602 + x21 * x567 + x642)) result[1, 4, 14] = numpy.sum(x185 * (x20 * x604 + x21 * x569 + x643)) result[1, 5, 0] = numpy.sum(x77 * (x21 * x573 + x645)) result[1, 5, 1] = numpy.sum(x90 * (x21 * x575 + x647)) result[1, 5, 2] = numpy.sum(x90 * (x21 * x577 + x649)) result[1, 5, 3] = numpy.sum(x108 * (x21 * x580 + x651)) result[1, 5, 4] = numpy.sum(x117 * (x21 * x582 + x653)) result[1, 5, 5] = numpy.sum(x108 * (x21 * x585 + x655)) result[1, 5, 6] = numpy.sum(x90 * (x21 * x588 + x657)) result[1, 5, 7] = numpy.sum(x117 * (x21 * x590 + x659)) result[1, 5, 8] = numpy.sum(x117 * (x21 * x592 + x661)) result[1, 5, 9] = numpy.sum(x90 * (x21 * x594 + x663)) result[1, 5, 10] = numpy.sum(x77 * (x21 * x596 + x664)) result[1, 5, 11] = numpy.sum(x90 * (x21 * x598 + x665)) result[1, 5, 12] = numpy.sum(x108 * (x21 * x600 + x666)) result[1, 5, 13] = numpy.sum(x90 * (x21 * x602 + x667)) result[1, 5, 14] = numpy.sum(x77 * (x21 * x604 + x668)) result[2, 0, 0] = numpy.sum(x77 * (x0 * x296 + x0 * (x296 + x522 * x669) + x305)) result[2, 0, 1] = numpy.sum(x90 * (x0 * x311 + x0 * (x311 + x669 * x670) + x313)) result[2, 0, 2] = numpy.sum(x90 * (x0 * x320 + x0 * (x320 + x524 * x671) + x324)) result[2, 0, 3] = numpy.sum(x108 * (x0 * x328 + x0 * (x328 + x669 * x673) + x330)) result[2, 0, 4] = numpy.sum(x117 * (x0 * x334 + x0 * (x334 + x671 * x674) + x337)) result[2, 0, 5] = numpy.sum(x108 * (x0 * x342 + x0 * (x338 * x527 + x342) + x346)) result[2, 0, 6] = numpy.sum(x90 * (x0 * x348 + x0 * (x348 + x669 * x675) + x350)) result[2, 0, 7] = numpy.sum(x117 * (x0 * x352 + x0 * (x352 + x671 * x677) + x354)) result[2, 0, 8] = numpy.sum(x117 * (x0 * x357 + x0 * (x0 * x678 + x357) + x359)) result[2, 0, 9] = numpy.sum(x90 * (x0 * x363 + x0 * (x360 * x530 + x363) + x367)) result[2, 0, 10] = numpy.sum(x77 * (x0 * x368 + x0 * (x147 * x669 + x368) + x371)) result[2, 0, 11] = numpy.sum(x90 * (x0 * x372 + x0 * (x150 * x671 + x372) + x374)) result[2, 0, 12] = numpy.sum(x108 * (x0 * x375 + x0 * (x0 * x679 + x375) + x378)) result[2, 0, 13] = numpy.sum(x90 * (x0 * x379 + x0 * (x0 * x680 + x379) + x381)) result[2, 0, 14] = numpy.sum(x77 * (x0 * x382 + x0 * (x382 + x65 * x681) + x384)) result[2, 1, 0] = numpy.sum(x185 * (x0 * x683 + x20 * x296 + x436)) result[2, 1, 1] = numpy.sum(x202 * (x0 * x684 + x20 * x311 + x440)) result[2, 1, 2] = numpy.sum(x202 * (x0 * x686 + x20 * x320 + x444)) result[2, 1, 3] = numpy.sum(x117 * (x0 * x687 + x20 * x328 + x448)) result[2, 1, 4] = numpy.sum(x230 * (x0 * x688 + x20 * x334 + x452)) result[2, 1, 5] = numpy.sum(x117 * (x0 * x689 + x20 * x342 + x456)) result[2, 1, 6] = numpy.sum(x202 * (x0 * x690 + x20 * x348 + x460)) result[2, 1, 7] = numpy.sum(x230 * (x0 * x691 + x20 * x352 + x464)) result[2, 1, 8] = numpy.sum(x230 * (x0 * x692 + x20 * x357 + x468)) result[2, 1, 9] = numpy.sum(x202 * (x0 * x693 + x20 * x363 + x472)) result[2, 1, 10] = numpy.sum(x185 * (x0 * x694 + x20 * x368 + x474)) result[2, 1, 11] = numpy.sum(x202 * (x0 * x695 + x20 * x372 + x477)) result[2, 1, 12] = numpy.sum(x117 * (x0 * x696 + x20 * x375 + x479)) result[2, 1, 13] = numpy.sum(x202 * (x0 * x697 + x20 * x379 + x481)) result[2, 1, 14] = numpy.sum(x185 * (x0 * x698 + x20 * x382 + x483)) result[2, 2, 0] = numpy.sum(x185 * (x0 * x701 + x491)) result[2, 2, 1] = numpy.sum(x202 * (x0 * x703 + x493)) result[2, 2, 2] = numpy.sum(x202 * (x0 * x706 + x497)) result[2, 2, 3] = numpy.sum(x117 * (x0 * x708 + x499)) result[2, 2, 4] = numpy.sum(x230 * (x0 * x710 + x502)) result[2, 2, 5] = numpy.sum(x117 * (x0 * x712 + x506)) result[2, 2, 6] = numpy.sum(x202 * (x0 * x714 + x508)) result[2, 2, 7] = numpy.sum(x230 * (x0 * x716 + x510)) result[2, 2, 8] = numpy.sum(x230 * (x0 * x718 + x512)) result[2, 2, 9] = numpy.sum(x202 * (x0 * x720 + x516)) result[2, 2, 10] = numpy.sum(x185 * (x0 * x722 + x517)) result[2, 2, 11] = numpy.sum(x202 * (x0 * x724 + x518)) result[2, 2, 12] = numpy.sum(x117 * (x0 * x726 + x519)) result[2, 2, 13] = numpy.sum(x202 * (x0 * x728 + x520)) result[2, 2, 14] = numpy.sum(x185 * (x0 * x730 + x521)) result[2, 3, 0] = numpy.sum(x77 * (x20 * x571 + x20 * x683 + x616)) result[2, 3, 1] = numpy.sum(x90 * (x20 * x574 + x20 * x684 + x619)) result[2, 3, 2] = numpy.sum(x90 * (x20 * x576 + x20 * x686 + x621)) result[2, 3, 3] = numpy.sum(x108 * (x20 * x578 + x20 * x687 + x623)) result[2, 3, 4] = numpy.sum(x117 * (x20 * x581 + x20 * x688 + x626)) result[2, 3, 5] = numpy.sum(x108 * (x20 * x583 + x20 * x689 + x628)) result[2, 3, 6] = numpy.sum(x90 * (x20 * x586 + x20 * x690 + x630)) result[2, 3, 7] = numpy.sum(x117 * (x20 * x589 + x20 * x691 + x632)) result[2, 3, 8] = numpy.sum(x117 * (x20 * x591 + x20 * x692 + x635)) result[2, 3, 9] = numpy.sum(x90 * (x20 * x593 + x20 * x693 + x637)) result[2, 3, 10] = numpy.sum(x77 * (x20 * x595 + x20 * x694 + x638)) result[2, 3, 11] = numpy.sum(x90 * (x20 * x597 + x20 * x695 + x639)) result[2, 3, 12] = numpy.sum(x108 * (x20 * x599 + x20 * x696 + x640)) result[2, 3, 13] = numpy.sum(x90 * (x20 * x601 + x20 * x697 + x642)) result[2, 3, 14] = numpy.sum(x77 * (x20 * x603 + x20 * x698 + x643)) result[2, 4, 0] = numpy.sum(x185 * (x20 * x701 + x645)) result[2, 4, 1] = numpy.sum(x202 * (x20 * x703 + x647)) result[2, 4, 2] = numpy.sum(x202 * (x20 * x706 + x649)) result[2, 4, 3] = numpy.sum(x117 * (x20 * x708 + x651)) result[2, 4, 4] = numpy.sum(x230 * (x20 * x710 + x653)) result[2, 4, 5] = numpy.sum(x117 * (x20 * x712 + x655)) result[2, 4, 6] = numpy.sum(x202 * (x20 * x714 + x657)) result[2, 4, 7] = numpy.sum(x230 * (x20 * x716 + x659)) result[2, 4, 8] = numpy.sum(x230 * (x20 * x718 + x661)) result[2, 4, 9] = numpy.sum(x202 * (x20 * x720 + x663)) result[2, 4, 10] = numpy.sum(x185 * (x20 * x722 + x664)) result[2, 4, 11] = numpy.sum(x202 * (x20 * x724 + x665)) result[2, 4, 12] = numpy.sum(x117 * (x20 * x726 + x666)) result[2, 4, 13] = numpy.sum(x202 * (x20 * x728 + x667)) result[2, 4, 14] = numpy.sum(x185 * (x20 * x730 + x668)) result[2, 5, 0] = numpy.sum(x77 * (x21 * x699 + x21 * x701 + x522 * x731)) result[2, 5, 1] = numpy.sum(x90 * (x21 * x702 + x21 * x703 + x670 * x731)) result[2, 5, 2] = numpy.sum(x90 * (x21 * x704 + x21 * x706 + x524 * x732)) result[2, 5, 3] = numpy.sum(x108 * (x21 * x707 + x21 * x708 + x673 * x731)) result[2, 5, 4] = numpy.sum(x117 * (x21 * x709 + x21 * x710 + x674 * x732)) result[2, 5, 5] = numpy.sum(x108 * (x195 * x733 + x21 * x711 + x21 * x712)) result[2, 5, 6] = numpy.sum(x90 * (x21 * x713 + x21 * x714 + x675 * x731)) result[2, 5, 7] = numpy.sum(x117 * (x21 * x715 + x21 * x716 + x677 * x732)) result[2, 5, 8] = numpy.sum(x117 * (x21 * x717 + x21 * x718 + x333 * x733)) result[2, 5, 9] = numpy.sum(x90 * (x192 * x734 + x21 * x719 + x21 * x720)) result[2, 5, 10] = numpy.sum(x77 * (x147 * x731 + x21 * x721 + x21 * x722)) result[2, 5, 11] = numpy.sum(x90 * (x150 * x732 + x21 * x723 + x21 * x724)) result[2, 5, 12] = numpy.sum(x108 * (x131 * x733 + x21 * x725 + x21 * x726)) result[2, 5, 13] = numpy.sum(x90 * (x109 * x734 + x21 * x727 + x21 * x728)) result[2, 5, 14] = numpy.sum( x77 * (x15 * (3.0 * x514 + x734 * x91) + x21 * x729 + x21 * x730) ) return result
[docs] def int3c2e3d_sph_130(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pf|s) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 10, 1), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - A[0] x5 = 0.5 / (ax + bx) x6 = -x3 - C[0] x7 = -x2 * (ax * A[1] + bx * B[1]) x8 = -x7 - C[1] x9 = -x2 * (ax * A[2] + bx * B[2]) x10 = -x9 - C[2] x11 = cx + x1 x12 = cx / x11 x13 = x1 * x12 * (x10**2 + x6**2 + x8**2) x14 = boys(1, x13) x15 = 17.49341832762486 x16 = A[1] - B[1] x17 = A[2] - B[2] x18 = numpy.exp(-ax * bx * x2 * (x0**2 + x16**2 + x17**2)) x19 = 2.0 * x11 ** (-1.5) * x15 * x18 * x2 x20 = x14 * x19 x21 = cx ** (-1.0) x22 = x11 ** (-0.5) x23 = boys(0, x13) x24 = 2.0 * x15 * x18 * x2 * x21 * x22 * x23 - x20 x25 = x24 * x5 x26 = -2.0 * x15 * x18 * x2 * x21 * x22 * x23 * x4 + x20 * x6 x27 = -x26 x28 = boys(2, x13) x29 = x19 * x28 x30 = -2.0 * x14 * x15 * x18 * x2 * x21 * x22 * x4 + x29 * x6 x31 = -x30 x32 = x12 * x31 x33 = x32 * x6 x34 = x25 + x27 * x4 - x33 x35 = 2.0 * x5 x36 = x5 * (2.0 * x14 * x15 * x18 * x2 * x21 * x22 - x29) x37 = boys(3, x13) x38 = x19 * x37 x39 = 2.0 * x15 * x18 * x2 * x21 * x22 * x28 * x4 - x38 * x6 x40 = x12 * x39 x41 = x31 * x4 + x36 - x40 * x6 x42 = x12 * x41 x43 = x34 * x4 - x35 * (x26 + x32) - x42 * x6 x44 = x0 * x34 + x43 x45 = -x24 * x5 x46 = x5 * (2.0 * x15 * x18 * x2 * x21 * x22 * x28 - x38) x47 = x19 * boys(4, x13) x48 = x12 * x6 x49 = da * db * dc x50 = 0.2581988897471611 * x49 x51 = -x7 - A[1] x52 = -2.0 * x14 * x15 * x18 * x2 * x21 * x22 * x51 + x29 * x8 x53 = -x52 x54 = x12 * x53 x55 = -2.0 * x15 * x18 * x2 * x21 * x22 * x23 * x51 + x20 * x8 x56 = -x5 * (x54 + x55) x57 = -x55 x58 = x54 * x6 x59 = -x4 * x57 + x58 x60 = -x59 x61 = 2.0 * x15 * x18 * x2 * x21 * x22 * x28 * x51 - x38 * x8 x62 = x12 * x61 x63 = x4 * x53 - x6 * x62 x64 = x12 * x63 x65 = x4 * x60 + x56 - x6 * x64 x66 = x16 * x34 + x65 x67 = x4 * x57 - x58 x68 = x16 * x27 + x67 x69 = -x5 * (x52 + x62) x70 = 2.0 * x15 * x18 * x2 * x21 * x22 * x37 * x51 - x47 * x8 x71 = ( -x35 * (x59 + x64) + x4 * x65 - x48 * (x4 * x63 - x48 * (x4 * x61 - x48 * x70) + x69) ) x72 = 0.5773502691896258 * x49 x73 = -x9 - A[2] x74 = x10 * x29 - 2.0 * x14 * x15 * x18 * x2 * x21 * x22 * x73 x75 = -x74 x76 = x12 * x75 x77 = x10 * x20 - 2.0 * x15 * x18 * x2 * x21 * x22 * x23 * x73 x78 = -x5 * (x76 + x77) x79 = -x77 x80 = x6 * x76 x81 = -x4 * x79 + x80 x82 = -x81 x83 = -x10 * x38 + 2.0 * x15 * x18 * x2 * x21 * x22 * x28 * x73 x84 = x12 * x83 x85 = x4 * x75 - x6 * x84 x86 = x12 * x85 x87 = x4 * x82 - x6 * x86 + x78 x88 = x17 * x34 + x87 x89 = x4 * x79 - x80 x90 = x17 * x27 + x89 x91 = -x5 * (x74 + x84) x92 = -x10 * x47 + 2.0 * x15 * x18 * x2 * x21 * x22 * x37 * x73 x93 = ( -x35 * (x81 + x86) + x4 * x87 - x48 * (x4 * x85 - x48 * (x4 * x83 - x48 * x92) + x91) ) x94 = x54 * x8 x95 = x25 + x51 * x57 - x94 x96 = x36 + x51 * x53 - x62 * x8 x97 = x12 * x96 x98 = x6 * x97 x99 = x16 * x60 + x4 * x95 - x98 x100 = x16 * x68 + x99 x101 = x5 * (-x45 + x51 * x57 - x94 - x97) x102 = x4 * x95 - x98 x103 = x12 * x8 x104 = -x103 * x70 + x46 + x51 * x61 x105 = x101 + x102 * x4 + x16 * x65 + x48 * (x104 * x48 - x4 * x96) x106 = x76 * x8 x107 = x106 - x51 * x79 x108 = -x107 x109 = x51 * x75 - x8 * x84 x110 = x109 * x12 x111 = x110 * x6 x112 = x108 * x4 - x111 x113 = x112 + x17 * x60 x114 = x113 + x16 * x90 x115 = -x5 * (x107 + x110) x116 = x108 * x4 - x111 x117 = -x103 * x92 + x51 * x83 x118 = x115 + x116 * x4 - x48 * (x109 * x4 - x117 * x48) x119 = x118 + x17 * x65 x120 = x10 * x76 x121 = -x120 + x25 + x73 * x79 x122 = -x10 * x84 + x36 + x73 * x75 x123 = x12 * x122 x124 = x123 * x6 x125 = x121 * x4 - x124 + x17 * x82 x126 = x125 + x17 * x90 x127 = x5 * (-x120 - x123 - x45 + x73 * x79) x128 = x121 * x4 - x124 x129 = x10 * x12 x130 = -x129 * x92 + x46 + x73 * x83 x131 = x127 + x128 * x4 + x17 * x87 - x48 * (x122 * x4 - x130 * x48) x132 = x51 * x95 + 2.0 * x56 - x8 * x97 x133 = -x103 * x104 + x51 * x96 + 2.0 * x69 x134 = x102 * x16 + x132 * x4 - x133 * x48 + x16 * x99 x135 = x108 * x51 - x110 * x8 + x78 x136 = -x103 * x117 + x109 * x51 + x91 x137 = x135 * x4 - x136 * x48 x138 = x102 * x17 + x113 * x16 + x137 x139 = x123 * x8 x140 = x121 * x51 - x139 x141 = -x103 * x130 + x122 * x51 x142 = x116 * x17 + x140 * x4 - x141 * x48 x143 = x113 * x17 + x142 x144 = -x10 * x123 + x121 * x73 + 2.0 * x78 x145 = x122 * x73 - x129 * x130 + 2.0 * x91 x146 = x125 * x17 + x128 * x17 + x144 * x4 - x145 * x48 x147 = x0 * x60 + x65 x148 = x16 * x57 + x95 x149 = -x106 + x51 * x79 x150 = x149 + x17 * x57 x151 = x132 + x16 * x95 x152 = x148 * x16 + x151 x153 = x135 + x17 * x95 x154 = x150 * x16 + x153 x155 = x108 * x17 + x121 * x51 - x139 x156 = x150 * x17 + x155 x157 = -x103 * x136 + 2.0 * x115 + x135 * x51 x158 = -x103 * x141 + x127 + x135 * x17 + x140 * x51 x159 = -x103 * x145 + x140 * x17 + x144 * x51 + x155 * x17 x160 = x0 * x82 + x87 x161 = x112 + x16 * x82 x162 = x149 + x16 * x79 x163 = x121 + x17 * x79 x164 = x108 * x16 + x135 x165 = x16 * x162 + x164 x166 = x155 + x16 * x163 x167 = x121 * x17 + x144 x168 = x163 * x17 + x167 # 30 item(s) result[0, 0, 0] = numpy.sum( x50 * ( x0 * x43 + x0 * x44 + x0 * (x0 * (x0 * x27 + x34) + x44) + x4 * x43 + x48 * ( x35 * (x30 + x40) - x4 * x41 + x48 * ( x39 * x4 + x46 - x48 * (2.0 * x15 * x18 * x2 * x21 * x22 * x37 * x4 - x47 * x6) ) ) - 3.0 * x5 * (-x27 * x4 + x33 + x42 + x45) ) ) result[0, 1, 0] = numpy.sum( x72 * (x0 * x66 + x0 * (x0 * x68 + x66) + x16 * x43 + x71) ) result[0, 2, 0] = numpy.sum( x72 * (x0 * x88 + x0 * (x0 * x90 + x88) + x17 * x43 + x93) ) result[0, 3, 0] = numpy.sum(x72 * (x0 * x100 + x105 + x16 * x66)) result[0, 4, 0] = numpy.sum(x49 * (x0 * x114 + x119 + x16 * x88)) result[0, 5, 0] = numpy.sum(x72 * (x0 * x126 + x131 + x17 * x88)) result[0, 6, 0] = numpy.sum(x50 * (x100 * x16 + x134)) result[0, 7, 0] = numpy.sum(x72 * (x114 * x16 + x138)) result[0, 8, 0] = numpy.sum(x72 * (x126 * x16 + x143)) result[0, 9, 0] = numpy.sum(x50 * (x126 * x17 + x146)) result[1, 0, 0] = numpy.sum( x50 * (x0 * x147 + x0 * x65 + x0 * (x0 * (x0 * x57 + x67) + x147) + x71) ) result[1, 1, 0] = numpy.sum(x72 * (x0 * x99 + x0 * (x0 * x148 + x99) + x105)) result[1, 2, 0] = numpy.sum(x72 * (x0 * x113 + x0 * (x0 * x150 + x113) + x119)) result[1, 3, 0] = numpy.sum(x72 * (x0 * x152 + x134)) result[1, 4, 0] = numpy.sum(x49 * (x0 * x154 + x138)) result[1, 5, 0] = numpy.sum(x72 * (x0 * x156 + x143)) result[1, 6, 0] = numpy.sum( x50 * (3.0 * x101 - x103 * x133 + x132 * x16 + x132 * x51 + x151 * x16 + x152 * x16) ) result[1, 7, 0] = numpy.sum(x72 * (x132 * x17 + x153 * x16 + x154 * x16 + x157)) result[1, 8, 0] = numpy.sum(x72 * (x153 * x17 + x156 * x16 + x158)) result[1, 9, 0] = numpy.sum(x50 * (x156 * x17 + x159)) result[2, 0, 0] = numpy.sum( x50 * (x0 * x160 + x0 * x87 + x0 * (x0 * (x0 * x79 + x89) + x160) + x93) ) result[2, 1, 0] = numpy.sum( x72 * (x0 * x161 + x0 * (x0 * x162 + x161) + x118 + x16 * x87) ) result[2, 2, 0] = numpy.sum(x72 * (x0 * x125 + x0 * (x0 * x163 + x125) + x131)) result[2, 3, 0] = numpy.sum(x72 * (x0 * x165 + x116 * x16 + x137 + x16 * x161)) result[2, 4, 0] = numpy.sum(x49 * (x0 * x166 + x125 * x16 + x142)) result[2, 5, 0] = numpy.sum(x72 * (x0 * x168 + x146)) result[2, 6, 0] = numpy.sum(x50 * (x135 * x16 + x157 + x16 * x164 + x16 * x165)) result[2, 7, 0] = numpy.sum(x72 * (x155 * x16 + x158 + x16 * x166)) result[2, 8, 0] = numpy.sum(x72 * (x159 + x16 * x168)) result[2, 9, 0] = numpy.sum( x50 * (3.0 * x127 - x129 * x145 + x144 * x17 + x144 * x73 + x167 * x17 + x168 * x17) ) return result
[docs] def int3c2e3d_sph_131(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pf|p) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 10, 3), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - C[0] x5 = -x3 - A[0] x6 = 0.5 / (ax + bx) x7 = -x2 * (ax * A[1] + bx * B[1]) x8 = -x7 - C[1] x9 = -x2 * (ax * A[2] + bx * B[2]) x10 = -x9 - C[2] x11 = cx + x1 x12 = x11 ** (-1.0) x13 = cx * x12 x14 = x1 * x13 * (x10**2 + x4**2 + x8**2) x15 = boys(2, x14) x16 = 17.49341832762486 x17 = A[1] - B[1] x18 = A[2] - B[2] x19 = numpy.exp(-ax * bx * x2 * (x0**2 + x17**2 + x18**2)) x20 = x16 * x19 * x2 x21 = 2.0 * x11 ** (-1.5) * x20 x22 = x15 * x21 x23 = cx ** (-1.0) x24 = x11 ** (-0.5) x25 = boys(1, x14) x26 = 2.0 * x16 * x19 * x2 * x23 * x24 * x25 - x22 x27 = x26 * x6 x28 = -2.0 * x16 * x19 * x2 * x23 * x24 * x25 * x5 + x22 * x4 x29 = -x28 x30 = boys(3, x14) x31 = x21 * x30 x32 = -2.0 * x15 * x16 * x19 * x2 * x23 * x24 * x5 + x31 * x4 x33 = -x32 x34 = x13 * x33 x35 = x34 * x4 x36 = x27 + x29 * x5 - x35 x37 = 2.0 * x6 x38 = x6 * (2.0 * x15 * x16 * x19 * x2 * x23 * x24 - x31) x39 = boys(4, x14) x40 = x21 * x39 x41 = 2.0 * x16 * x19 * x2 * x23 * x24 * x30 * x5 - x4 * x40 x42 = x13 * x41 x43 = x33 * x5 + x38 - x4 * x42 x44 = x13 * x43 x45 = x36 * x5 - x37 * (x28 + x34) - x4 * x44 x46 = x36 * x6 x47 = x1 * x12 x48 = x47 * (x4 * x45 + 3.0 * x46) x49 = x29 * x6 x50 = x47 * (x36 * x4 + 2.0 * x49) x51 = x0 * x50 + x48 x52 = x20 * x23 * x24 * x25 * x37 x53 = x47 * (x29 * x4 + x52) x54 = -x26 * x6 x55 = x6 * (2.0 * x16 * x19 * x2 * x23 * x24 * x30 - x40) x56 = x21 * boys(5, x14) x57 = x13 * x4 x58 = ( x45 * x5 + x57 * ( x37 * (x32 + x42) - x43 * x5 + x57 * ( x41 * x5 + x55 - x57 * (2.0 * x16 * x19 * x2 * x23 * x24 * x39 * x5 - x4 * x56) ) ) - 3.0 * x6 * (-x29 * x5 + x35 + x44 + x54) ) x59 = x45 * x6 x60 = da * db * dc x61 = 0.2581988897471611 * x60 x62 = x47 * x8 x63 = x45 * x62 x64 = x36 * x62 x65 = x0 * x64 + x63 x66 = x0 * x29 x67 = x10 * x47 x68 = x45 * x67 x69 = x36 * x67 x70 = x0 * x69 + x68 x71 = -x7 - A[1] x72 = -2.0 * x15 * x16 * x19 * x2 * x23 * x24 * x71 + x31 * x8 x73 = -x72 x74 = x13 * x73 x75 = -2.0 * x16 * x19 * x2 * x23 * x24 * x25 * x71 + x22 * x8 x76 = -x6 * (x74 + x75) x77 = -x75 x78 = x4 * x74 - x5 * x77 x79 = -x78 x80 = 2.0 * x16 * x19 * x2 * x23 * x24 * x30 * x71 - x40 * x8 x81 = x13 * x80 x82 = -x4 * x81 + x5 * x73 x83 = x13 * x82 x84 = -x4 * x83 + x5 * x79 + x76 x85 = x6 * x79 x86 = 2.0 * x85 x87 = x47 * (x4 * x84 + x86) x88 = x17 * x50 + x87 x89 = x6 * x77 x90 = x47 * (x4 * x79 + x89) x91 = x17 * x53 + x90 x92 = -x6 * (x72 + x81) x93 = 2.0 * x16 * x19 * x2 * x23 * x24 * x39 * x71 - x56 * x8 x94 = ( -x37 * (x78 + x83) + x5 * x84 - x57 * (x5 * x82 - x57 * (x5 * x80 - x57 * x93) + x92) ) x95 = x6 * x84 x96 = x47 * (x4 * x94 + 3.0 * x95) x97 = 0.5773502691896258 * x60 x98 = x47 * (x46 + x8 * x84) x99 = x17 * x64 + x98 x100 = x47 * (x49 + x79 * x8) x101 = x17 * x29 x102 = x100 + x101 * x62 x103 = x47 * (x59 + x8 * x94) x104 = x67 * x84 x105 = x104 + x17 * x69 x106 = x67 * x79 x107 = x101 * x67 + x106 x108 = x67 * x94 x109 = -x9 - A[2] x110 = x10 * x31 - 2.0 * x109 * x15 * x16 * x19 * x2 * x23 * x24 x111 = -x110 x112 = x111 * x13 x113 = x10 * x22 - 2.0 * x109 * x16 * x19 * x2 * x23 * x24 * x25 x114 = -x6 * (x112 + x113) x115 = -x113 x116 = x112 * x4 - x115 * x5 x117 = -x116 x118 = -x10 * x40 + 2.0 * x109 * x16 * x19 * x2 * x23 * x24 * x30 x119 = x118 * x13 x120 = x111 * x5 - x119 * x4 x121 = x120 * x13 x122 = x114 + x117 * x5 - x121 * x4 x123 = x117 * x6 x124 = 2.0 * x123 x125 = x47 * (x122 * x4 + x124) x126 = x125 + x18 * x50 x127 = x115 * x6 x128 = x47 * (x117 * x4 + x127) x129 = x128 + x18 * x53 x130 = -x6 * (x110 + x119) x131 = -x10 * x56 + 2.0 * x109 * x16 * x19 * x2 * x23 * x24 * x39 x132 = ( x122 * x5 - x37 * (x116 + x121) - x57 * (x120 * x5 + x130 - x57 * (x118 * x5 - x131 * x57)) ) x133 = x122 * x6 x134 = x47 * (x132 * x4 + 3.0 * x133) x135 = x122 * x62 x136 = x135 + x18 * x64 x137 = x117 * x62 x138 = x18 * x29 x139 = x137 + x138 * x62 x140 = x132 * x62 x141 = x47 * (x10 * x122 + x46) x142 = x141 + x18 * x69 x143 = x47 * (x10 * x117 + x49) x144 = x138 * x67 + x143 x145 = x47 * (x10 * x132 + x59) x146 = x74 * x8 x147 = -x146 + x27 + x71 * x77 x148 = x147 * x6 x149 = x38 + x71 * x73 - x8 * x81 x150 = x13 * x149 x151 = x147 * x5 - x150 * x4 x152 = x47 * (x148 + x151 * x4) x153 = x152 + x17 * x90 x154 = x153 + x17 * x91 x155 = x6 * (-x146 - x150 - x54 + x71 * x77) x156 = x13 * x8 x157 = -x156 * x93 + x55 + x71 * x80 x158 = x151 * x5 + x155 - x57 * (x149 * x5 - x157 * x57) x159 = x151 * x6 x160 = x17 * x87 + x47 * (x158 * x4 + 2.0 * x159) x161 = x47 * (x151 * x8 + x86) x162 = x100 * x17 + x161 x163 = x102 * x17 + x162 x164 = x17 * x98 + x47 * (x158 * x8 + 2.0 * x95) x165 = x151 * x67 x166 = x106 * x17 + x165 x167 = x107 * x17 + x166 x168 = x104 * x17 + x158 * x67 x169 = x112 * x8 - x115 * x71 x170 = -x169 x171 = x170 * x6 x172 = x111 * x71 - x119 * x8 x173 = x13 * x172 x174 = x170 * x5 - x173 * x4 x175 = x47 * (x171 + x174 * x4) x176 = x175 + x18 * x90 x177 = x129 * x17 + x176 x178 = -x6 * (x169 + x173) x179 = x118 * x71 - x131 * x156 x180 = x174 * x5 + x178 - x57 * (x172 * x5 - x179 * x57) x181 = x174 * x37 x182 = x47 * (x180 * x4 + x181) x183 = x18 * x87 + x182 x184 = x47 * (x123 + x174 * x8) x185 = x100 * x18 + x184 x186 = x139 * x17 + x185 x187 = x47 * (x133 + x180 * x8) x188 = x18 * x98 + x187 x189 = x47 * (x10 * x174 + x85) x190 = x106 * x18 + x189 x191 = x144 * x17 + x190 x192 = x47 * (x10 * x180 + x95) x193 = x104 * x18 + x192 x194 = x10 * x112 x195 = x109 * x115 - x194 + x27 x196 = x195 * x6 x197 = -x10 * x119 + x109 * x111 + x38 x198 = x13 * x197 x199 = x195 * x5 - x198 * x4 x200 = x47 * (x196 + x199 * x4) x201 = x128 * x18 + x200 x202 = x129 * x18 + x201 x203 = x6 * (x109 * x115 - x194 - x198 - x54) x204 = x10 * x13 x205 = x109 * x118 - x131 * x204 + x55 x206 = x199 * x5 + x203 - x57 * (x197 * x5 - x205 * x57) x207 = x199 * x6 x208 = x125 * x18 + x47 * (x206 * x4 + 2.0 * x207) x209 = x199 * x62 x210 = x137 * x18 + x209 x211 = x139 * x18 + x210 x212 = x135 * x18 + x206 * x62 x213 = x47 * (x10 * x199 + x124) x214 = x143 * x18 + x213 x215 = x144 * x18 + x214 x216 = x141 * x18 + x47 * (x10 * x206 + 2.0 * x133) x217 = x147 * x71 - x150 * x8 + 2.0 * x76 x218 = x217 * x6 x219 = x149 * x71 - x156 * x157 + 2.0 * x92 x220 = x217 * x5 - x219 * x57 x221 = x152 * x17 + x153 * x17 + x47 * (x218 + x220 * x4) x222 = x161 * x17 + x162 * x17 + x47 * (3.0 * x159 + x220 * x8) x223 = x165 * x17 + x166 * x17 + x220 * x67 x224 = x114 + x170 * x71 - x173 * x8 x225 = x224 * x6 x226 = x130 - x156 * x179 + x172 * x71 x227 = x224 * x5 - x226 * x57 x228 = x47 * (x225 + x227 * x4) x229 = x152 * x18 + x17 * x176 + x228 x230 = x47 * (x181 + x227 * x8) x231 = x161 * x18 + x17 * x185 + x230 x232 = x47 * (x10 * x227 + x159) x233 = x165 * x18 + x17 * x190 + x232 x234 = x195 * x71 - x198 * x8 x235 = x234 * x6 x236 = -x156 * x205 + x197 * x71 x237 = x234 * x5 - x236 * x57 x238 = x175 * x18 + x47 * (x235 + x237 * x4) x239 = x176 * x18 + x238 x240 = x18 * x184 + x47 * (x207 + x237 * x8) x241 = x18 * x185 + x240 x242 = x18 * x189 + x47 * (x10 * x237 + x181) x243 = x18 * x190 + x242 x244 = -x10 * x198 + x109 * x195 + 2.0 * x114 x245 = x244 * x6 x246 = x109 * x197 + 2.0 * x130 - x204 * x205 x247 = x244 * x5 - x246 * x57 x248 = x18 * x200 + x18 * x201 + x47 * (x245 + x247 * x4) x249 = x18 * x209 + x18 * x210 + x247 * x62 x250 = x18 * x213 + x18 * x214 + x47 * (x10 * x247 + 3.0 * x207) x251 = x0 * x90 + x87 x252 = x4 * x47 x253 = x0 * x77 x254 = x0 * x100 + x98 x255 = x47 * (x52 + x77 * x8) x256 = x0 * x106 + x104 x257 = x147 * x252 x258 = x17 * x77 x259 = x252 * x258 + x257 x260 = x47 * (x147 * x8 + 2.0 * x89) x261 = x17 * x255 + x260 x262 = x147 * x67 x263 = x258 * x67 + x262 x264 = x170 * x252 x265 = x18 * x77 x266 = x252 * x265 + x264 x267 = x47 * (x127 + x170 * x8) x268 = x18 * x255 + x267 x269 = x47 * (x10 * x170 + x89) x270 = x265 * x67 + x269 x271 = x217 * x252 x272 = x17 * x257 + x271 x273 = x17 * x259 + x272 x274 = x47 * (3.0 * x148 + x217 * x8) x275 = x17 * x260 + x274 x276 = x17 * x261 + x275 x277 = x217 * x67 x278 = x17 * x262 + x277 x279 = x17 * x263 + x278 x280 = x224 * x252 x281 = x18 * x257 + x280 x282 = x17 * x266 + x281 x283 = 2.0 * x171 x284 = x47 * (x224 * x8 + x283) x285 = x18 * x260 + x284 x286 = x17 * x268 + x285 x287 = x47 * (x10 * x224 + x148) x288 = x18 * x262 + x287 x289 = x17 * x270 + x288 x290 = x234 * x252 x291 = x18 * x264 + x290 x292 = x18 * x266 + x291 x293 = x47 * (x196 + x234 * x8) x294 = x18 * x267 + x293 x295 = x18 * x268 + x294 x296 = x47 * (x10 * x234 + x283) x297 = x18 * x269 + x296 x298 = x18 * x270 + x297 x299 = 3.0 * x155 - x156 * x219 + x217 * x71 x300 = -x156 * x226 + 2.0 * x178 + x224 * x71 x301 = x252 * x300 x302 = x47 * (3.0 * x225 + x300 * x8) x303 = x47 * (x10 * x300 + x218) x304 = -x156 * x236 + x203 + x234 * x71 x305 = x18 * x280 + x252 * x304 x306 = x18 * x284 + x47 * (2.0 * x235 + x304 * x8) x307 = x18 * x287 + x47 * (x10 * x304 + 2.0 * x225) x308 = -x156 * x246 + x244 * x71 x309 = x18 * x290 + x18 * x291 + x252 * x308 x310 = x18 * x293 + x18 * x294 + x47 * (x245 + x308 * x8) x311 = x18 * x296 + x18 * x297 + x47 * (x10 * x308 + 3.0 * x235) x312 = x0 * x128 + x125 x313 = x0 * x115 x314 = x0 * x137 + x135 x315 = x0 * x143 + x141 x316 = x47 * (x10 * x115 + x52) x317 = x128 * x17 + x175 x318 = x115 * x17 x319 = x252 * x318 + x264 x320 = x137 * x17 + x184 x321 = x267 + x318 * x62 x322 = x143 * x17 + x189 x323 = x17 * x316 + x269 x324 = x195 * x252 x325 = x115 * x18 x326 = x252 * x325 + x324 x327 = x195 * x62 x328 = x325 * x62 + x327 x329 = x47 * (x10 * x195 + 2.0 * x127) x330 = x18 * x316 + x329 x331 = x17 * x264 + x280 x332 = x17 * x319 + x331 x333 = x17 * x267 + x284 x334 = x17 * x321 + x333 x335 = x17 * x269 + x287 x336 = x17 * x323 + x335 x337 = x17 * x326 + x291 x338 = x17 * x328 + x294 x339 = x17 * x330 + x297 x340 = x244 * x252 x341 = x18 * x324 + x340 x342 = x18 * x326 + x341 x343 = x244 * x62 x344 = x18 * x327 + x343 x345 = x18 * x328 + x344 x346 = x47 * (x10 * x244 + 3.0 * x196) x347 = x18 * x329 + x346 x348 = x18 * x330 + x347 x349 = x109 * x244 + 3.0 * x203 - x204 * x246 # 90 item(s) result[0, 0, 0] = numpy.sum( x61 * ( x0 * x48 + x0 * x51 + x0 * (x0 * (x0 * x53 + x50) + x51) + x47 * (x4 * x58 + 4.0 * x59) ) ) result[0, 0, 1] = numpy.sum( x61 * (x0 * x63 + x0 * x65 + x0 * (x0 * (x62 * x66 + x64) + x65) + x58 * x62) ) result[0, 0, 2] = numpy.sum( x61 * (x0 * x68 + x0 * x70 + x0 * (x0 * (x66 * x67 + x69) + x70) + x58 * x67) ) result[0, 1, 0] = numpy.sum( x97 * (x0 * x88 + x0 * (x0 * x91 + x88) + x17 * x48 + x96) ) result[0, 1, 1] = numpy.sum( x97 * (x0 * x99 + x0 * (x0 * x102 + x99) + x103 + x17 * x63) ) result[0, 1, 2] = numpy.sum( x97 * (x0 * x105 + x0 * (x0 * x107 + x105) + x108 + x17 * x68) ) result[0, 2, 0] = numpy.sum( x97 * (x0 * x126 + x0 * (x0 * x129 + x126) + x134 + x18 * x48) ) result[0, 2, 1] = numpy.sum( x97 * (x0 * x136 + x0 * (x0 * x139 + x136) + x140 + x18 * x63) ) result[0, 2, 2] = numpy.sum( x97 * (x0 * x142 + x0 * (x0 * x144 + x142) + x145 + x18 * x68) ) result[0, 3, 0] = numpy.sum(x97 * (x0 * x154 + x160 + x17 * x88)) result[0, 3, 1] = numpy.sum(x97 * (x0 * x163 + x164 + x17 * x99)) result[0, 3, 2] = numpy.sum(x97 * (x0 * x167 + x105 * x17 + x168)) result[0, 4, 0] = numpy.sum(x60 * (x0 * x177 + x126 * x17 + x183)) result[0, 4, 1] = numpy.sum(x60 * (x0 * x186 + x136 * x17 + x188)) result[0, 4, 2] = numpy.sum(x60 * (x0 * x191 + x142 * x17 + x193)) result[0, 5, 0] = numpy.sum(x97 * (x0 * x202 + x126 * x18 + x208)) result[0, 5, 1] = numpy.sum(x97 * (x0 * x211 + x136 * x18 + x212)) result[0, 5, 2] = numpy.sum(x97 * (x0 * x215 + x142 * x18 + x216)) result[0, 6, 0] = numpy.sum(x61 * (x154 * x17 + x221)) result[0, 6, 1] = numpy.sum(x61 * (x163 * x17 + x222)) result[0, 6, 2] = numpy.sum(x61 * (x167 * x17 + x223)) result[0, 7, 0] = numpy.sum(x97 * (x17 * x177 + x229)) result[0, 7, 1] = numpy.sum(x97 * (x17 * x186 + x231)) result[0, 7, 2] = numpy.sum(x97 * (x17 * x191 + x233)) result[0, 8, 0] = numpy.sum(x97 * (x17 * x202 + x239)) result[0, 8, 1] = numpy.sum(x97 * (x17 * x211 + x241)) result[0, 8, 2] = numpy.sum(x97 * (x17 * x215 + x243)) result[0, 9, 0] = numpy.sum(x61 * (x18 * x202 + x248)) result[0, 9, 1] = numpy.sum(x61 * (x18 * x211 + x249)) result[0, 9, 2] = numpy.sum(x61 * (x18 * x215 + x250)) result[1, 0, 0] = numpy.sum( x61 * (x0 * x251 + x0 * x87 + x0 * (x0 * (x252 * x253 + x90) + x251) + x96) ) result[1, 0, 1] = numpy.sum( x61 * (x0 * x254 + x0 * x98 + x0 * (x0 * (x0 * x255 + x100) + x254) + x103) ) result[1, 0, 2] = numpy.sum( x61 * (x0 * x104 + x0 * x256 + x0 * (x0 * (x106 + x253 * x67) + x256) + x108) ) result[1, 1, 0] = numpy.sum(x97 * (x0 * x153 + x0 * (x0 * x259 + x153) + x160)) result[1, 1, 1] = numpy.sum(x97 * (x0 * x162 + x0 * (x0 * x261 + x162) + x164)) result[1, 1, 2] = numpy.sum(x97 * (x0 * x166 + x0 * (x0 * x263 + x166) + x168)) result[1, 2, 0] = numpy.sum(x97 * (x0 * x176 + x0 * (x0 * x266 + x176) + x183)) result[1, 2, 1] = numpy.sum(x97 * (x0 * x185 + x0 * (x0 * x268 + x185) + x188)) result[1, 2, 2] = numpy.sum(x97 * (x0 * x190 + x0 * (x0 * x270 + x190) + x193)) result[1, 3, 0] = numpy.sum(x97 * (x0 * x273 + x221)) result[1, 3, 1] = numpy.sum(x97 * (x0 * x276 + x222)) result[1, 3, 2] = numpy.sum(x97 * (x0 * x279 + x223)) result[1, 4, 0] = numpy.sum(x60 * (x0 * x282 + x229)) result[1, 4, 1] = numpy.sum(x60 * (x0 * x286 + x231)) result[1, 4, 2] = numpy.sum(x60 * (x0 * x289 + x233)) result[1, 5, 0] = numpy.sum(x97 * (x0 * x292 + x239)) result[1, 5, 1] = numpy.sum(x97 * (x0 * x295 + x241)) result[1, 5, 2] = numpy.sum(x97 * (x0 * x298 + x243)) result[1, 6, 0] = numpy.sum( x61 * (x17 * x271 + x17 * x272 + x17 * x273 + x252 * x299) ) result[1, 6, 1] = numpy.sum( x61 * (x17 * x274 + x17 * x275 + x17 * x276 + x47 * (4.0 * x218 + x299 * x8)) ) result[1, 6, 2] = numpy.sum(x61 * (x17 * x277 + x17 * x278 + x17 * x279 + x299 * x67)) result[1, 7, 0] = numpy.sum(x97 * (x17 * x281 + x17 * x282 + x18 * x271 + x301)) result[1, 7, 1] = numpy.sum(x97 * (x17 * x285 + x17 * x286 + x18 * x274 + x302)) result[1, 7, 2] = numpy.sum(x97 * (x17 * x288 + x17 * x289 + x18 * x277 + x303)) result[1, 8, 0] = numpy.sum(x97 * (x17 * x292 + x18 * x281 + x305)) result[1, 8, 1] = numpy.sum(x97 * (x17 * x295 + x18 * x285 + x306)) result[1, 8, 2] = numpy.sum(x97 * (x17 * x298 + x18 * x288 + x307)) result[1, 9, 0] = numpy.sum(x61 * (x18 * x292 + x309)) result[1, 9, 1] = numpy.sum(x61 * (x18 * x295 + x310)) result[1, 9, 2] = numpy.sum(x61 * (x18 * x298 + x311)) result[2, 0, 0] = numpy.sum( x61 * (x0 * x125 + x0 * x312 + x0 * (x0 * (x128 + x252 * x313) + x312) + x134) ) result[2, 0, 1] = numpy.sum( x61 * (x0 * x135 + x0 * x314 + x0 * (x0 * (x137 + x313 * x62) + x314) + x140) ) result[2, 0, 2] = numpy.sum( x61 * (x0 * x141 + x0 * x315 + x0 * (x0 * (x0 * x316 + x143) + x315) + x145) ) result[2, 1, 0] = numpy.sum( x97 * (x0 * x317 + x0 * (x0 * x319 + x317) + x125 * x17 + x182) ) result[2, 1, 1] = numpy.sum( x97 * (x0 * x320 + x0 * (x0 * x321 + x320) + x135 * x17 + x187) ) result[2, 1, 2] = numpy.sum( x97 * (x0 * x322 + x0 * (x0 * x323 + x322) + x141 * x17 + x192) ) result[2, 2, 0] = numpy.sum(x97 * (x0 * x201 + x0 * (x0 * x326 + x201) + x208)) result[2, 2, 1] = numpy.sum(x97 * (x0 * x210 + x0 * (x0 * x328 + x210) + x212)) result[2, 2, 2] = numpy.sum(x97 * (x0 * x214 + x0 * (x0 * x330 + x214) + x216)) result[2, 3, 0] = numpy.sum(x97 * (x0 * x332 + x17 * x175 + x17 * x317 + x228)) result[2, 3, 1] = numpy.sum(x97 * (x0 * x334 + x17 * x184 + x17 * x320 + x230)) result[2, 3, 2] = numpy.sum(x97 * (x0 * x336 + x17 * x189 + x17 * x322 + x232)) result[2, 4, 0] = numpy.sum(x60 * (x0 * x337 + x17 * x201 + x238)) result[2, 4, 1] = numpy.sum(x60 * (x0 * x338 + x17 * x210 + x240)) result[2, 4, 2] = numpy.sum(x60 * (x0 * x339 + x17 * x214 + x242)) result[2, 5, 0] = numpy.sum(x97 * (x0 * x342 + x248)) result[2, 5, 1] = numpy.sum(x97 * (x0 * x345 + x249)) result[2, 5, 2] = numpy.sum(x97 * (x0 * x348 + x250)) result[2, 6, 0] = numpy.sum(x61 * (x17 * x280 + x17 * x331 + x17 * x332 + x301)) result[2, 6, 1] = numpy.sum(x61 * (x17 * x284 + x17 * x333 + x17 * x334 + x302)) result[2, 6, 2] = numpy.sum(x61 * (x17 * x287 + x17 * x335 + x17 * x336 + x303)) result[2, 7, 0] = numpy.sum(x97 * (x17 * x291 + x17 * x337 + x305)) result[2, 7, 1] = numpy.sum(x97 * (x17 * x294 + x17 * x338 + x306)) result[2, 7, 2] = numpy.sum(x97 * (x17 * x297 + x17 * x339 + x307)) result[2, 8, 0] = numpy.sum(x97 * (x17 * x342 + x309)) result[2, 8, 1] = numpy.sum(x97 * (x17 * x345 + x310)) result[2, 8, 2] = numpy.sum(x97 * (x17 * x348 + x311)) result[2, 9, 0] = numpy.sum( x61 * (x18 * x340 + x18 * x341 + x18 * x342 + x252 * x349) ) result[2, 9, 1] = numpy.sum(x61 * (x18 * x343 + x18 * x344 + x18 * x345 + x349 * x62)) result[2, 9, 2] = numpy.sum( x61 * (x18 * x346 + x18 * x347 + x18 * x348 + x47 * (x10 * x349 + 4.0 * x245)) ) return result
[docs] def int3c2e3d_sph_132(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pf|d) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 10, 6), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - C[0] x5 = -x3 - A[0] x6 = 0.5 / (ax + bx) x7 = x4**2 x8 = -x2 * (ax * A[1] + bx * B[1]) x9 = -x8 - C[1] x10 = x9**2 x11 = -x2 * (ax * A[2] + bx * B[2]) x12 = -x11 - C[2] x13 = x12**2 x14 = cx + x1 x15 = x14 ** (-1.0) x16 = cx * x15 x17 = x1 * x16 * (x10 + x13 + x7) x18 = boys(3, x17) x19 = x14 ** (-1.5) x20 = 17.49341832762486 x21 = A[1] - B[1] x22 = A[2] - B[2] x23 = numpy.exp(-ax * bx * x2 * (x0**2 + x21**2 + x22**2)) x24 = x2 * x20 * x23 x25 = 2.0 * x19 * x24 x26 = x18 * x25 x27 = cx ** (-1.0) x28 = x14 ** (-0.5) x29 = boys(2, x17) x30 = 2.0 * x2 * x20 * x23 * x27 * x28 * x29 - x26 x31 = x30 * x6 x32 = -2.0 * x2 * x20 * x23 * x27 * x28 * x29 * x5 + x26 * x4 x33 = -x32 x34 = boys(4, x17) x35 = x25 * x34 x36 = -2.0 * x18 * x2 * x20 * x23 * x27 * x28 * x5 + x35 * x4 x37 = -x36 x38 = x16 * x37 x39 = x38 * x4 x40 = x31 + x33 * x5 - x39 x41 = 2.0 * x6 x42 = x6 * (2.0 * x18 * x2 * x20 * x23 * x27 * x28 - x35) x43 = boys(5, x17) x44 = x25 * x43 x45 = 2.0 * x2 * x20 * x23 * x27 * x28 * x34 * x5 - x4 * x44 x46 = x16 * x45 x47 = x37 * x5 - x4 * x46 + x42 x48 = x16 * x47 x49 = -x4 * x48 + x40 * x5 - x41 * (x32 + x38) x50 = x4 * x49 x51 = x40 * x6 x52 = 3.0 * x51 x53 = x50 + x52 x54 = x1 * x15 x55 = x4 * x54 x56 = x4 * x40 x57 = x33 * x6 x58 = 2.0 * x57 x59 = x56 + x58 x60 = 3.0 * x6 x61 = x54 * x60 x62 = x54 * (x53 * x55 + x59 * x61) x63 = x33 * x4 x64 = x27 * x29 * x41 x65 = x24 * x28 * x64 x66 = x63 + x65 x67 = x41 * x54 x68 = x54 * (x55 * x59 + x66 * x67) x69 = x0 * x68 + x62 x70 = x19 * x20 * x23 * x64 x71 = x4 * x70 + x55 * x66 x72 = x0 * x54 x73 = -x30 * x6 x74 = x6 * (2.0 * x2 * x20 * x23 * x27 * x28 * x34 - x44) x75 = x25 * boys(6, x17) x76 = x16 * x4 x77 = ( x49 * x5 - x60 * (-x33 * x5 + x39 + x48 + x73) + x76 * ( x41 * (x36 + x46) - x47 * x5 + x76 * ( x45 * x5 + x74 - x76 * (2.0 * x2 * x20 * x23 * x27 * x28 * x43 * x5 - x4 * x75) ) ) ) x78 = x4 * x77 x79 = x49 * x6 x80 = 4.0 * x79 x81 = x54 * x6 x82 = da * db * dc x83 = 0.06666666666666667 * x82 x84 = 2.23606797749979 * x83 x85 = x54 * x9 x86 = x54 * x85 * (x50 + x52) x87 = x54 * x85 * (x56 + x58) x88 = x0 * x87 + x86 x89 = x70 * x9 x90 = x63 * x85 + x89 x91 = 3.872983346207417 * x83 x92 = x12 * x54 x93 = x54 * x92 * (x50 + x52) x94 = x54 * x92 * (x56 + x58) x95 = x0 * x94 + x93 x96 = x12 * x70 x97 = x63 * x92 + x96 x98 = x1**2 / x14**2 x99 = x10 * x98 x100 = x49 * x99 x101 = x40 * x99 x102 = x0 * x101 + x100 x103 = x0 * x33 x104 = x9 * x98 x105 = x104 * x12 x106 = x105 * x49 x107 = x105 * x40 x108 = x0 * x107 + x106 x109 = x13 * x98 x110 = x109 * x49 x111 = x109 * x40 x112 = x0 * x111 + x110 x113 = -x8 - A[1] x114 = -2.0 * x113 * x18 * x2 * x20 * x23 * x27 * x28 + x35 * x9 x115 = -x114 x116 = x115 * x16 x117 = -2.0 * x113 * x2 * x20 * x23 * x27 * x28 * x29 + x26 * x9 x118 = -x6 * (x116 + x117) x119 = -x117 x120 = x116 * x4 - x119 * x5 x121 = -x120 x122 = 2.0 * x113 * x2 * x20 * x23 * x27 * x28 * x34 - x44 * x9 x123 = x122 * x16 x124 = x115 * x5 - x123 * x4 x125 = x124 * x16 x126 = x118 + x121 * x5 - x125 * x4 x127 = x126 * x4 x128 = x121 * x6 x129 = 2.0 * x128 x130 = x127 + x129 x131 = x119 * x6 x132 = x121 * x4 x133 = x131 + x132 x134 = x54 * (x130 * x55 + x133 * x67) x135 = x134 + x21 * x68 x136 = x54 * x55 * (x131 + x133) x137 = x21 * x54 x138 = x136 + x137 * x71 x139 = -x6 * (x114 + x123) x140 = 2.0 * x113 * x2 * x20 * x23 * x27 * x28 * x43 - x75 * x9 x141 = ( x126 * x5 - x41 * (x120 + x125) - x76 * (x124 * x5 + x139 - x76 * (x122 * x5 - x140 * x76)) ) x142 = x141 * x4 x143 = x126 * x6 x144 = 3.0 * x143 x145 = x54 * (x130 * x61 + x55 * (x142 + x144)) x146 = 0.3333333333333333 * x82 x147 = x126 * x9 x148 = x147 + x51 x149 = x121 * x9 x150 = x149 + x57 x151 = x150 * x67 x152 = x54 * (x148 * x55 + x151) x153 = x152 + x21 * x87 x154 = x119 * x9 x155 = x154 + x65 x156 = x54 * (x150 * x55 + x155 * x81) x157 = x137 * x90 + x156 x158 = x141 * x9 x159 = x158 + x79 x160 = x54 * (x148 * x61 + x159 * x55) x161 = 1.732050807568877 * x146 x162 = x129 * x92 x163 = x54 * (x127 * x92 + x162) x164 = x163 + x21 * x94 x165 = x131 * x92 x166 = x54 * (x132 * x92 + x165) x167 = x137 * x97 + x166 x168 = x54 * x92 * (x142 + x144) x169 = x54 * x85 * (x148 + x51) x170 = x101 * x21 + x169 x171 = x54 * x85 * (x150 + x57) x172 = x21 * x33 x173 = x171 + x172 * x99 x174 = x54 * x85 * (x159 + x79) x175 = x51 * x92 x176 = x54 * (x147 * x92 + x175) x177 = x107 * x21 + x176 x178 = x57 * x92 x179 = x54 * (x149 * x92 + x178) x180 = x105 * x172 + x179 x181 = x79 * x92 x182 = x54 * (x158 * x92 + x181) x183 = x109 * x126 x184 = x111 * x21 + x183 x185 = x109 * x121 x186 = x109 * x172 + x185 x187 = x109 * x141 x188 = -x11 - A[2] x189 = x12 * x35 - 2.0 * x18 * x188 * x2 * x20 * x23 * x27 * x28 x190 = -x189 x191 = x16 * x190 x192 = x12 * x26 - 2.0 * x188 * x2 * x20 * x23 * x27 * x28 * x29 x193 = -x6 * (x191 + x192) x194 = -x192 x195 = x191 * x4 - x194 * x5 x196 = -x195 x197 = -x12 * x44 + 2.0 * x188 * x2 * x20 * x23 * x27 * x28 * x34 x198 = x16 * x197 x199 = x190 * x5 - x198 * x4 x200 = x16 * x199 x201 = x193 + x196 * x5 - x200 * x4 x202 = x201 * x4 x203 = x196 * x6 x204 = 2.0 * x203 x205 = x202 + x204 x206 = x194 * x6 x207 = x196 * x4 x208 = x206 + x207 x209 = x54 * (x205 * x55 + x208 * x67) x210 = x209 + x22 * x68 x211 = x54 * x55 * (x206 + x208) x212 = x22 * x54 x213 = x211 + x212 * x71 x214 = -x6 * (x189 + x198) x215 = -x12 * x75 + 2.0 * x188 * x2 * x20 * x23 * x27 * x28 * x43 x216 = ( x201 * x5 - x41 * (x195 + x200) - x76 * (x199 * x5 + x214 - x76 * (x197 * x5 - x215 * x76)) ) x217 = x216 * x4 x218 = x201 * x6 x219 = 3.0 * x218 x220 = x54 * (x205 * x61 + x55 * (x217 + x219)) x221 = x54 * x85 * (x202 + x204) x222 = x22 * x87 + x221 x223 = x206 * x85 x224 = x54 * (x207 * x85 + x223) x225 = x212 * x90 + x224 x226 = x54 * x85 * (x217 + x219) x227 = x12 * x201 + x51 x228 = x12 * x196 + x57 x229 = x228 * x67 x230 = x54 * (x227 * x55 + x229) x231 = x22 * x94 + x230 x232 = x12 * x194 + x65 x233 = x232 * x81 x234 = x54 * (x228 * x55 + x233) x235 = x212 * x97 + x234 x236 = x12 * x216 + x79 x237 = x54 * (x227 * x61 + x236 * x55) x238 = x201 * x99 x239 = x101 * x22 + x238 x240 = x196 * x99 x241 = x22 * x33 x242 = x240 + x241 * x99 x243 = x216 * x99 x244 = x104 * x227 x245 = x107 * x22 + x244 x246 = x104 * x228 x247 = x105 * x241 + x246 x248 = x104 * x236 x249 = x54 * (x175 + x227 * x92) x250 = x111 * x22 + x249 x251 = x54 * (x178 + x228 * x92) x252 = x109 * x241 + x251 x253 = x54 * (x181 + x236 * x92) x254 = x116 * x9 x255 = x113 * x119 - x254 + x31 x256 = x255 * x6 x257 = x113 * x115 - x123 * x9 + x42 x258 = x16 * x257 x259 = x255 * x5 - x258 * x4 x260 = x259 * x4 x261 = x256 + x260 x262 = x54 * x55 * (x256 + x261) x263 = x136 * x21 + x262 x264 = x138 * x21 + x263 x265 = x6 * (x113 * x119 - x254 - x258 - x73) x266 = x16 * x9 x267 = x113 * x122 - x140 * x266 + x74 x268 = x259 * x5 + x265 - x76 * (x257 * x5 - x267 * x76) x269 = x268 * x4 x270 = x259 * x6 x271 = 2.0 * x270 x272 = x134 * x21 + x54 * (x261 * x67 + x55 * (x269 + x271)) x273 = x255 * x9 x274 = 2.0 * x131 x275 = x273 + x274 x276 = x259 * x9 x277 = x129 + x276 x278 = x54 * (x275 * x81 + x277 * x55) x279 = x156 * x21 + x278 x280 = x157 * x21 + x279 x281 = x268 * x9 x282 = 2.0 * x143 x283 = x281 + x282 x284 = x152 * x21 + x54 * (x277 * x67 + x283 * x55) x285 = x256 * x92 x286 = x54 * (x260 * x92 + x285) x287 = x166 * x21 + x286 x288 = x167 * x21 + x287 x289 = x163 * x21 + x54 * x92 * (x269 + x271) x290 = x54 * (x151 + x277 * x85) x291 = x171 * x21 + x290 x292 = x173 * x21 + x291 x293 = x169 * x21 + x54 * (x148 * x67 + x283 * x85) x294 = x54 * (x162 + x276 * x92) x295 = x179 * x21 + x294 x296 = x180 * x21 + x295 x297 = x176 * x21 + x54 * x92 * (x281 + x282) x298 = x109 * x259 x299 = x185 * x21 + x298 x300 = x186 * x21 + x299 x301 = x109 * x268 + x183 * x21 x302 = -x113 * x194 + x191 * x9 x303 = -x302 x304 = x303 * x6 x305 = x113 * x190 - x198 * x9 x306 = x16 * x305 x307 = x303 * x5 - x306 * x4 x308 = x304 + x307 * x4 x309 = x54 * x55 * (x304 + x308) x310 = x136 * x22 + x309 x311 = x21 * x213 + x310 x312 = -x6 * (x302 + x306) x313 = x113 * x197 - x215 * x266 x314 = x307 * x5 + x312 - x76 * (x305 * x5 - x313 * x76) x315 = x307 * x41 x316 = x54 * (x308 * x67 + x55 * (x314 * x4 + x315)) x317 = x134 * x22 + x316 x318 = x206 + x303 * x9 x319 = x203 + x307 * x9 x320 = x54 * (x318 * x81 + x319 * x55) x321 = x156 * x22 + x320 x322 = x21 * x225 + x321 x323 = x218 + x314 * x9 x324 = x319 * x67 x325 = x54 * (x323 * x55 + x324) x326 = x152 * x22 + x325 x327 = x12 * x303 + x131 x328 = x12 * x307 + x128 x329 = x54 * (x327 * x81 + x328 * x55) x330 = x166 * x22 + x329 x331 = x21 * x235 + x330 x332 = x12 * x314 + x143 x333 = x328 * x67 x334 = x54 * (x332 * x55 + x333) x335 = x163 * x22 + x334 x336 = x54 * x85 * (x203 + x319) x337 = x171 * x22 + x336 x338 = x21 * x242 + x337 x339 = x54 * x85 * (x218 + x323) x340 = x169 * x22 + x339 x341 = x54 * (x228 * x81 + x328 * x85) x342 = x179 * x22 + x341 x343 = x21 * x247 + x342 x344 = x54 * (x227 * x81 + x332 * x85) x345 = x176 * x22 + x344 x346 = x54 * x92 * (x128 + x328) x347 = x185 * x22 + x346 x348 = x21 * x252 + x347 x349 = x54 * x92 * (x143 + x332) x350 = x183 * x22 + x349 x351 = x12 * x191 x352 = x188 * x194 + x31 - x351 x353 = x352 * x6 x354 = -x12 * x198 + x188 * x190 + x42 x355 = x16 * x354 x356 = x352 * x5 - x355 * x4 x357 = x356 * x4 x358 = x353 + x357 x359 = x54 * x55 * (x353 + x358) x360 = x211 * x22 + x359 x361 = x213 * x22 + x360 x362 = x6 * (x188 * x194 - x351 - x355 - x73) x363 = x12 * x16 x364 = x188 * x197 - x215 * x363 + x74 x365 = x356 * x5 + x362 - x76 * (x354 * x5 - x364 * x76) x366 = x365 * x4 x367 = x356 * x6 x368 = 2.0 * x367 x369 = x209 * x22 + x54 * (x358 * x67 + x55 * (x366 + x368)) x370 = x353 * x85 x371 = x54 * (x357 * x85 + x370) x372 = x22 * x224 + x371 x373 = x22 * x225 + x372 x374 = x22 * x221 + x54 * x85 * (x366 + x368) x375 = x12 * x352 + 2.0 * x206 x376 = x375 * x81 x377 = x12 * x356 + x204 x378 = x54 * (x376 + x377 * x55) x379 = x22 * x234 + x378 x380 = x22 * x235 + x379 x381 = x12 * x365 + 2.0 * x218 x382 = x22 * x230 + x54 * (x377 * x67 + x381 * x55) x383 = x356 * x99 x384 = x22 * x240 + x383 x385 = x22 * x242 + x384 x386 = x22 * x238 + x365 * x99 x387 = x104 * x377 x388 = x22 * x246 + x387 x389 = x22 * x247 + x388 x390 = x104 * x381 + x22 * x244 x391 = x54 * (x229 + x377 * x92) x392 = x22 * x251 + x391 x393 = x22 * x252 + x392 x394 = x22 * x249 + x54 * (x227 * x67 + x381 * x92) x395 = x113 * x255 + 2.0 * x118 - x258 * x9 x396 = x395 * x6 x397 = x113 * x257 + 2.0 * x139 - x266 * x267 x398 = x395 * x5 - x397 * x76 x399 = x398 * x4 x400 = x21 * x262 + x21 * x263 + x54 * x55 * (2.0 * x396 + x399) x401 = x395 * x9 x402 = 3.0 * x256 x403 = x401 + x402 x404 = x403 * x81 x405 = x398 * x9 x406 = 3.0 * x270 x407 = x405 + x406 x408 = x21 * x278 + x21 * x279 + x54 * (x404 + x407 * x55) x409 = x396 * x92 x410 = x21 * x286 + x21 * x287 + x54 * (x399 * x92 + x409) x411 = x21 * x290 + x21 * x291 + x54 * (x277 * x61 + x407 * x85) x412 = x21 * x294 + x21 * x295 + x54 * x92 * (x405 + x406) x413 = x109 * x398 + x21 * x298 + x21 * x299 x414 = x113 * x303 + x193 - x306 * x9 x415 = x414 * x6 x416 = x113 * x305 + x214 - x266 * x313 x417 = x414 * x5 - x416 * x76 x418 = x54 * x55 * (x4 * x417 + 2.0 * x415) x419 = x21 * x310 + x22 * x262 + x418 x420 = 2.0 * x304 x421 = x414 * x9 + x420 x422 = x315 + x417 * x9 x423 = x54 * (x421 * x81 + x422 * x55) x424 = x21 * x321 + x22 * x278 + x423 x425 = x12 * x414 + x256 x426 = x12 * x417 + x270 x427 = x54 * (x425 * x81 + x426 * x55) x428 = x21 * x330 + x22 * x286 + x427 x429 = x54 * (x324 + x422 * x85) x430 = x21 * x337 + x22 * x290 + x429 x431 = x54 * (x333 + x426 * x85) x432 = x21 * x342 + x22 * x294 + x431 x433 = x54 * x92 * (x270 + x426) x434 = x21 * x347 + x22 * x298 + x433 x435 = x113 * x352 - x355 * x9 x436 = x435 * x6 x437 = x113 * x354 - x266 * x364 x438 = x435 * x5 - x437 * x76 x439 = x22 * x309 + x54 * x55 * (x4 * x438 + 2.0 * x436) x440 = x22 * x310 + x439 x441 = x353 + x435 * x9 x442 = x367 + x438 * x9 x443 = x22 * x320 + x54 * (x441 * x81 + x442 * x55) x444 = x22 * x321 + x443 x445 = x12 * x435 + x420 x446 = x12 * x438 + x315 x447 = x22 * x329 + x54 * (x445 * x81 + x446 * x55) x448 = x22 * x330 + x447 x449 = x22 * x336 + x54 * x85 * (x367 + x442) x450 = x22 * x337 + x449 x451 = x22 * x341 + x54 * (x377 * x81 + x446 * x85) x452 = x22 * x342 + x451 x453 = x22 * x346 + x54 * (x333 + x446 * x92) x454 = x22 * x347 + x453 x455 = -x12 * x355 + x188 * x352 + 2.0 * x193 x456 = x455 * x6 x457 = x188 * x354 + 2.0 * x214 - x363 * x364 x458 = x455 * x5 - x457 * x76 x459 = x4 * x458 x460 = x22 * x359 + x22 * x360 + x54 * x55 * (2.0 * x456 + x459) x461 = x456 * x85 x462 = x22 * x371 + x22 * x372 + x54 * (x459 * x85 + x461) x463 = x12 * x455 + 3.0 * x353 x464 = x463 * x81 x465 = x12 * x458 + 3.0 * x367 x466 = x22 * x378 + x22 * x379 + x54 * (x464 + x465 * x55) x467 = x22 * x383 + x22 * x384 + x458 * x99 x468 = x104 * x465 + x22 * x387 + x22 * x388 x469 = x22 * x391 + x22 * x392 + x54 * (x377 * x61 + x465 * x92) x470 = x0 * x136 + x134 x471 = x7 * x98 x472 = x0 * x119 x473 = x0 * x156 + x152 x474 = x4 * x98 x475 = x155 * x474 x476 = x0 * x166 + x163 x477 = x12 * x474 x478 = x0 * x171 + x169 x479 = x155 * x85 + x89 x480 = x0 * x179 + x176 x481 = x154 * x92 + x96 x482 = x0 * x185 + x183 x483 = x255 * x471 x484 = x119 * x21 x485 = x471 * x484 + x483 x486 = x275 * x474 x487 = x21 * x475 + x486 x488 = x255 * x477 x489 = x477 * x484 + x488 x490 = x54 * (x155 * x67 + x275 * x85) x491 = x137 * x479 + x490 x492 = x54 * x92 * (x273 + x274) x493 = x137 * x481 + x492 x494 = x109 * x255 x495 = x109 * x484 + x494 x496 = x303 * x471 x497 = x119 * x22 x498 = x471 * x497 + x496 x499 = x318 * x474 x500 = x22 * x475 + x499 x501 = x327 * x474 x502 = x477 * x497 + x501 x503 = x54 * (x223 + x318 * x85) x504 = x212 * x479 + x503 x505 = x54 * (x233 + x327 * x85) x506 = x212 * x481 + x505 x507 = x54 * (x165 + x327 * x92) x508 = x109 * x497 + x507 x509 = x395 * x471 x510 = x21 * x483 + x509 x511 = x21 * x485 + x510 x512 = x403 * x474 x513 = x21 * x486 + x512 x514 = x21 * x487 + x513 x515 = x395 * x477 x516 = x21 * x488 + x515 x517 = x21 * x489 + x516 x518 = x54 * (x275 * x61 + x403 * x85) x519 = x21 * x490 + x518 x520 = x21 * x491 + x519 x521 = x54 * x92 * (x401 + x402) x522 = x21 * x492 + x521 x523 = x21 * x493 + x522 x524 = x109 * x395 x525 = x21 * x494 + x524 x526 = x21 * x495 + x525 x527 = x414 * x471 x528 = x22 * x483 + x527 x529 = x21 * x498 + x528 x530 = x421 * x474 x531 = x22 * x486 + x530 x532 = x21 * x500 + x531 x533 = x425 * x474 x534 = x22 * x488 + x533 x535 = x21 * x502 + x534 x536 = x54 * (x318 * x67 + x421 * x85) x537 = x22 * x490 + x536 x538 = x21 * x504 + x537 x539 = x327 * x67 x540 = x54 * (x425 * x85 + x539) x541 = x22 * x492 + x540 x542 = x21 * x506 + x541 x543 = x54 * (x285 + x425 * x92) x544 = x22 * x494 + x543 x545 = x21 * x508 + x544 x546 = x435 * x471 x547 = x22 * x496 + x546 x548 = x22 * x498 + x547 x549 = x441 * x474 x550 = x22 * x499 + x549 x551 = x22 * x500 + x550 x552 = x445 * x474 x553 = x22 * x501 + x552 x554 = x22 * x502 + x553 x555 = x54 * (x370 + x441 * x85) x556 = x22 * x503 + x555 x557 = x22 * x504 + x556 x558 = x54 * (x376 + x445 * x85) x559 = x22 * x505 + x558 x560 = x22 * x506 + x559 x561 = x54 * (x445 * x92 + x539) x562 = x22 * x507 + x561 x563 = x22 * x508 + x562 x564 = x113 * x395 + 3.0 * x265 - x266 * x397 x565 = x564 * x9 x566 = 4.0 * x396 x567 = x565 + x566 x568 = x113 * x414 - x266 * x416 + 2.0 * x312 x569 = x471 * x568 x570 = 3.0 * x415 + x568 * x9 x571 = x474 * x570 x572 = x12 * x568 + x396 x573 = x474 * x572 x574 = x54 * (x421 * x61 + x570 * x85) x575 = x54 * (x425 * x61 + x572 * x85) x576 = x54 * (x409 + x572 * x92) x577 = x113 * x435 - x266 * x437 + x362 x578 = x22 * x527 + x471 * x577 x579 = 2.0 * x436 + x577 * x9 x580 = x22 * x530 + x474 * x579 x581 = x12 * x577 + 2.0 * x415 x582 = x22 * x533 + x474 * x581 x583 = x22 * x536 + x54 * (x441 * x67 + x579 * x85) x584 = x22 * x540 + x54 * (x445 * x67 + x581 * x85) x585 = x22 * x543 + x54 * (x425 * x67 + x581 * x92) x586 = x113 * x455 - x266 * x457 x587 = x22 * x546 + x22 * x547 + x471 * x586 x588 = x456 + x586 * x9 x589 = x22 * x549 + x22 * x550 + x474 * x588 x590 = x12 * x586 + 3.0 * x436 x591 = x22 * x552 + x22 * x553 + x474 * x590 x592 = x22 * x555 + x22 * x556 + x54 * (x461 + x588 * x85) x593 = x22 * x558 + x22 * x559 + x54 * (x464 + x590 * x85) x594 = x22 * x561 + x22 * x562 + x54 * (x445 * x61 + x590 * x92) x595 = x0 * x211 + x209 x596 = x0 * x194 x597 = x0 * x224 + x221 x598 = x104 * x4 x599 = x0 * x234 + x230 x600 = x0 * x232 x601 = x0 * x240 + x238 x602 = x0 * x246 + x244 x603 = x0 * x251 + x249 x604 = x232 * x92 + x96 x605 = x21 * x211 + x309 x606 = x194 * x21 x607 = x471 * x606 + x496 x608 = x21 * x224 + x320 x609 = x499 + x598 * x606 x610 = x21 * x234 + x329 x611 = x21 * x232 x612 = x474 * x611 + x501 x613 = x21 * x240 + x336 x614 = x503 + x606 * x99 x615 = x21 * x246 + x341 x616 = x104 * x611 + x505 x617 = x21 * x251 + x346 x618 = x137 * x604 + x507 x619 = x352 * x471 x620 = x194 * x22 x621 = x471 * x620 + x619 x622 = x352 * x598 x623 = x598 * x620 + x622 x624 = x375 * x474 x625 = x22 * x232 x626 = x474 * x625 + x624 x627 = x352 * x99 x628 = x620 * x99 + x627 x629 = x104 * x375 x630 = x104 * x625 + x629 x631 = x54 * (x232 * x67 + x375 * x92) x632 = x212 * x604 + x631 x633 = x21 * x496 + x527 x634 = x21 * x607 + x633 x635 = x21 * x499 + x530 x636 = x21 * x609 + x635 x637 = x21 * x501 + x533 x638 = x21 * x612 + x637 x639 = x21 * x503 + x536 x640 = x21 * x614 + x639 x641 = x21 * x505 + x540 x642 = x21 * x616 + x641 x643 = x21 * x507 + x543 x644 = x21 * x618 + x643 x645 = x21 * x621 + x547 x646 = x21 * x623 + x550 x647 = x21 * x626 + x553 x648 = x21 * x628 + x556 x649 = x21 * x630 + x559 x650 = x21 * x632 + x562 x651 = x455 * x471 x652 = x22 * x619 + x651 x653 = x22 * x621 + x652 x654 = x455 * x598 x655 = x22 * x622 + x654 x656 = x22 * x623 + x655 x657 = x463 * x474 x658 = x22 * x624 + x657 x659 = x22 * x626 + x658 x660 = x455 * x99 x661 = x22 * x627 + x660 x662 = x22 * x628 + x661 x663 = x104 * x463 x664 = x22 * x629 + x663 x665 = x22 * x630 + x664 x666 = x54 * (x375 * x61 + x463 * x92) x667 = x22 * x631 + x666 x668 = x22 * x632 + x667 x669 = x188 * x455 + 3.0 * x362 - x363 * x457 x670 = x12 * x669 + 4.0 * x456 # 180 item(s) result[0, 0, 0] = numpy.sum( x84 * ( x0 * x62 + x0 * x69 + x0 * (x0 * (x68 + x71 * x72) + x69) + x54 * (4.0 * x53 * x81 + x55 * (x78 + x80)) ) ) result[0, 0, 1] = numpy.sum( x91 * ( x0 * x86 + x0 * x88 + x0 * (x0 * (x72 * x90 + x87) + x88) + x54 * x85 * (x78 + x80) ) ) result[0, 0, 2] = numpy.sum( x91 * ( x0 * x93 + x0 * x95 + x0 * (x0 * (x72 * x97 + x94) + x95) + x54 * x92 * (x78 + x80) ) ) result[0, 0, 3] = numpy.sum( x84 * (x0 * x100 + x0 * x102 + x0 * (x0 * (x101 + x103 * x99) + x102) + x77 * x99) ) result[0, 0, 4] = numpy.sum( x91 * (x0 * x106 + x0 * x108 + x0 * (x0 * (x103 * x105 + x107) + x108) + x105 * x77) ) result[0, 0, 5] = numpy.sum( x84 * (x0 * x110 + x0 * x112 + x0 * (x0 * (x103 * x109 + x111) + x112) + x109 * x77) ) result[0, 1, 0] = numpy.sum( x146 * (x0 * x135 + x0 * (x0 * x138 + x135) + x145 + x21 * x62) ) result[0, 1, 1] = numpy.sum( x161 * (x0 * x153 + x0 * (x0 * x157 + x153) + x160 + x21 * x86) ) result[0, 1, 2] = numpy.sum( x161 * (x0 * x164 + x0 * (x0 * x167 + x164) + x168 + x21 * x93) ) result[0, 1, 3] = numpy.sum( x146 * (x0 * x170 + x0 * (x0 * x173 + x170) + x100 * x21 + x174) ) result[0, 1, 4] = numpy.sum( x161 * (x0 * x177 + x0 * (x0 * x180 + x177) + x106 * x21 + x182) ) result[0, 1, 5] = numpy.sum( x146 * (x0 * x184 + x0 * (x0 * x186 + x184) + x110 * x21 + x187) ) result[0, 2, 0] = numpy.sum( x146 * (x0 * x210 + x0 * (x0 * x213 + x210) + x22 * x62 + x220) ) result[0, 2, 1] = numpy.sum( x161 * (x0 * x222 + x0 * (x0 * x225 + x222) + x22 * x86 + x226) ) result[0, 2, 2] = numpy.sum( x161 * (x0 * x231 + x0 * (x0 * x235 + x231) + x22 * x93 + x237) ) result[0, 2, 3] = numpy.sum( x146 * (x0 * x239 + x0 * (x0 * x242 + x239) + x100 * x22 + x243) ) result[0, 2, 4] = numpy.sum( x161 * (x0 * x245 + x0 * (x0 * x247 + x245) + x106 * x22 + x248) ) result[0, 2, 5] = numpy.sum( x146 * (x0 * x250 + x0 * (x0 * x252 + x250) + x110 * x22 + x253) ) result[0, 3, 0] = numpy.sum(x146 * (x0 * x264 + x135 * x21 + x272)) result[0, 3, 1] = numpy.sum(x161 * (x0 * x280 + x153 * x21 + x284)) result[0, 3, 2] = numpy.sum(x161 * (x0 * x288 + x164 * x21 + x289)) result[0, 3, 3] = numpy.sum(x146 * (x0 * x292 + x170 * x21 + x293)) result[0, 3, 4] = numpy.sum(x161 * (x0 * x296 + x177 * x21 + x297)) result[0, 3, 5] = numpy.sum(x146 * (x0 * x300 + x184 * x21 + x301)) result[0, 4, 0] = numpy.sum(x161 * (x0 * x311 + x21 * x210 + x317)) result[0, 4, 1] = numpy.sum(x82 * (x0 * x322 + x21 * x222 + x326)) result[0, 4, 2] = numpy.sum(x82 * (x0 * x331 + x21 * x231 + x335)) result[0, 4, 3] = numpy.sum(x161 * (x0 * x338 + x21 * x239 + x340)) result[0, 4, 4] = numpy.sum(x82 * (x0 * x343 + x21 * x245 + x345)) result[0, 4, 5] = numpy.sum(x161 * (x0 * x348 + x21 * x250 + x350)) result[0, 5, 0] = numpy.sum(x146 * (x0 * x361 + x210 * x22 + x369)) result[0, 5, 1] = numpy.sum(x161 * (x0 * x373 + x22 * x222 + x374)) result[0, 5, 2] = numpy.sum(x161 * (x0 * x380 + x22 * x231 + x382)) result[0, 5, 3] = numpy.sum(x146 * (x0 * x385 + x22 * x239 + x386)) result[0, 5, 4] = numpy.sum(x161 * (x0 * x389 + x22 * x245 + x390)) result[0, 5, 5] = numpy.sum(x146 * (x0 * x393 + x22 * x250 + x394)) result[0, 6, 0] = numpy.sum(x84 * (x21 * x264 + x400)) result[0, 6, 1] = numpy.sum(x91 * (x21 * x280 + x408)) result[0, 6, 2] = numpy.sum(x91 * (x21 * x288 + x410)) result[0, 6, 3] = numpy.sum(x84 * (x21 * x292 + x411)) result[0, 6, 4] = numpy.sum(x91 * (x21 * x296 + x412)) result[0, 6, 5] = numpy.sum(x84 * (x21 * x300 + x413)) result[0, 7, 0] = numpy.sum(x146 * (x21 * x311 + x419)) result[0, 7, 1] = numpy.sum(x161 * (x21 * x322 + x424)) result[0, 7, 2] = numpy.sum(x161 * (x21 * x331 + x428)) result[0, 7, 3] = numpy.sum(x146 * (x21 * x338 + x430)) result[0, 7, 4] = numpy.sum(x161 * (x21 * x343 + x432)) result[0, 7, 5] = numpy.sum(x146 * (x21 * x348 + x434)) result[0, 8, 0] = numpy.sum(x146 * (x21 * x361 + x440)) result[0, 8, 1] = numpy.sum(x161 * (x21 * x373 + x444)) result[0, 8, 2] = numpy.sum(x161 * (x21 * x380 + x448)) result[0, 8, 3] = numpy.sum(x146 * (x21 * x385 + x450)) result[0, 8, 4] = numpy.sum(x161 * (x21 * x389 + x452)) result[0, 8, 5] = numpy.sum(x146 * (x21 * x393 + x454)) result[0, 9, 0] = numpy.sum(x84 * (x22 * x361 + x460)) result[0, 9, 1] = numpy.sum(x91 * (x22 * x373 + x462)) result[0, 9, 2] = numpy.sum(x91 * (x22 * x380 + x466)) result[0, 9, 3] = numpy.sum(x84 * (x22 * x385 + x467)) result[0, 9, 4] = numpy.sum(x91 * (x22 * x389 + x468)) result[0, 9, 5] = numpy.sum(x84 * (x22 * x393 + x469)) result[1, 0, 0] = numpy.sum( x84 * (x0 * x134 + x0 * x470 + x0 * (x0 * (x136 + x471 * x472) + x470) + x145) ) result[1, 0, 1] = numpy.sum( x91 * (x0 * x152 + x0 * x473 + x0 * (x0 * (x0 * x475 + x156) + x473) + x160) ) result[1, 0, 2] = numpy.sum( x91 * (x0 * x163 + x0 * x476 + x0 * (x0 * (x166 + x472 * x477) + x476) + x168) ) result[1, 0, 3] = numpy.sum( x84 * (x0 * x169 + x0 * x478 + x0 * (x0 * (x171 + x479 * x72) + x478) + x174) ) result[1, 0, 4] = numpy.sum( x91 * (x0 * x176 + x0 * x480 + x0 * (x0 * (x179 + x481 * x72) + x480) + x182) ) result[1, 0, 5] = numpy.sum( x84 * (x0 * x183 + x0 * x482 + x0 * (x0 * (x109 * x472 + x185) + x482) + x187) ) result[1, 1, 0] = numpy.sum(x146 * (x0 * x263 + x0 * (x0 * x485 + x263) + x272)) result[1, 1, 1] = numpy.sum(x161 * (x0 * x279 + x0 * (x0 * x487 + x279) + x284)) result[1, 1, 2] = numpy.sum(x161 * (x0 * x287 + x0 * (x0 * x489 + x287) + x289)) result[1, 1, 3] = numpy.sum(x146 * (x0 * x291 + x0 * (x0 * x491 + x291) + x293)) result[1, 1, 4] = numpy.sum(x161 * (x0 * x295 + x0 * (x0 * x493 + x295) + x297)) result[1, 1, 5] = numpy.sum(x146 * (x0 * x299 + x0 * (x0 * x495 + x299) + x301)) result[1, 2, 0] = numpy.sum(x146 * (x0 * x310 + x0 * (x0 * x498 + x310) + x317)) result[1, 2, 1] = numpy.sum(x161 * (x0 * x321 + x0 * (x0 * x500 + x321) + x326)) result[1, 2, 2] = numpy.sum(x161 * (x0 * x330 + x0 * (x0 * x502 + x330) + x335)) result[1, 2, 3] = numpy.sum(x146 * (x0 * x337 + x0 * (x0 * x504 + x337) + x340)) result[1, 2, 4] = numpy.sum(x161 * (x0 * x342 + x0 * (x0 * x506 + x342) + x345)) result[1, 2, 5] = numpy.sum(x146 * (x0 * x347 + x0 * (x0 * x508 + x347) + x350)) result[1, 3, 0] = numpy.sum(x146 * (x0 * x511 + x400)) result[1, 3, 1] = numpy.sum(x161 * (x0 * x514 + x408)) result[1, 3, 2] = numpy.sum(x161 * (x0 * x517 + x410)) result[1, 3, 3] = numpy.sum(x146 * (x0 * x520 + x411)) result[1, 3, 4] = numpy.sum(x161 * (x0 * x523 + x412)) result[1, 3, 5] = numpy.sum(x146 * (x0 * x526 + x413)) result[1, 4, 0] = numpy.sum(x161 * (x0 * x529 + x419)) result[1, 4, 1] = numpy.sum(x82 * (x0 * x532 + x424)) result[1, 4, 2] = numpy.sum(x82 * (x0 * x535 + x428)) result[1, 4, 3] = numpy.sum(x161 * (x0 * x538 + x430)) result[1, 4, 4] = numpy.sum(x82 * (x0 * x542 + x432)) result[1, 4, 5] = numpy.sum(x161 * (x0 * x545 + x434)) result[1, 5, 0] = numpy.sum(x146 * (x0 * x548 + x440)) result[1, 5, 1] = numpy.sum(x161 * (x0 * x551 + x444)) result[1, 5, 2] = numpy.sum(x161 * (x0 * x554 + x448)) result[1, 5, 3] = numpy.sum(x146 * (x0 * x557 + x450)) result[1, 5, 4] = numpy.sum(x161 * (x0 * x560 + x452)) result[1, 5, 5] = numpy.sum(x146 * (x0 * x563 + x454)) result[1, 6, 0] = numpy.sum( x84 * (x21 * x509 + x21 * x510 + x21 * x511 + x471 * x564) ) result[1, 6, 1] = numpy.sum( x91 * (x21 * x512 + x21 * x513 + x21 * x514 + x474 * x567) ) result[1, 6, 2] = numpy.sum( x91 * (x21 * x515 + x21 * x516 + x21 * x517 + x477 * x564) ) result[1, 6, 3] = numpy.sum( x84 * (x21 * x518 + x21 * x519 + x21 * x520 + x54 * (4.0 * x404 + x567 * x85)) ) result[1, 6, 4] = numpy.sum( x91 * (x21 * x521 + x21 * x522 + x21 * x523 + x54 * x92 * (x565 + x566)) ) result[1, 6, 5] = numpy.sum( x84 * (x109 * x564 + x21 * x524 + x21 * x525 + x21 * x526) ) result[1, 7, 0] = numpy.sum(x146 * (x21 * x528 + x21 * x529 + x22 * x509 + x569)) result[1, 7, 1] = numpy.sum(x161 * (x21 * x531 + x21 * x532 + x22 * x512 + x571)) result[1, 7, 2] = numpy.sum(x161 * (x21 * x534 + x21 * x535 + x22 * x515 + x573)) result[1, 7, 3] = numpy.sum(x146 * (x21 * x537 + x21 * x538 + x22 * x518 + x574)) result[1, 7, 4] = numpy.sum(x161 * (x21 * x541 + x21 * x542 + x22 * x521 + x575)) result[1, 7, 5] = numpy.sum(x146 * (x21 * x544 + x21 * x545 + x22 * x524 + x576)) result[1, 8, 0] = numpy.sum(x146 * (x21 * x548 + x22 * x528 + x578)) result[1, 8, 1] = numpy.sum(x161 * (x21 * x551 + x22 * x531 + x580)) result[1, 8, 2] = numpy.sum(x161 * (x21 * x554 + x22 * x534 + x582)) result[1, 8, 3] = numpy.sum(x146 * (x21 * x557 + x22 * x537 + x583)) result[1, 8, 4] = numpy.sum(x161 * (x21 * x560 + x22 * x541 + x584)) result[1, 8, 5] = numpy.sum(x146 * (x21 * x563 + x22 * x544 + x585)) result[1, 9, 0] = numpy.sum(x84 * (x22 * x548 + x587)) result[1, 9, 1] = numpy.sum(x91 * (x22 * x551 + x589)) result[1, 9, 2] = numpy.sum(x91 * (x22 * x554 + x591)) result[1, 9, 3] = numpy.sum(x84 * (x22 * x557 + x592)) result[1, 9, 4] = numpy.sum(x91 * (x22 * x560 + x593)) result[1, 9, 5] = numpy.sum(x84 * (x22 * x563 + x594)) result[2, 0, 0] = numpy.sum( x84 * (x0 * x209 + x0 * x595 + x0 * (x0 * (x211 + x471 * x596) + x595) + x220) ) result[2, 0, 1] = numpy.sum( x91 * (x0 * x221 + x0 * x597 + x0 * (x0 * (x224 + x596 * x598) + x597) + x226) ) result[2, 0, 2] = numpy.sum( x91 * (x0 * x230 + x0 * x599 + x0 * (x0 * (x234 + x474 * x600) + x599) + x237) ) result[2, 0, 3] = numpy.sum( x84 * (x0 * x238 + x0 * x601 + x0 * (x0 * (x240 + x596 * x99) + x601) + x243) ) result[2, 0, 4] = numpy.sum( x91 * (x0 * x244 + x0 * x602 + x0 * (x0 * (x104 * x600 + x246) + x602) + x248) ) result[2, 0, 5] = numpy.sum( x84 * (x0 * x249 + x0 * x603 + x0 * (x0 * (x251 + x604 * x72) + x603) + x253) ) result[2, 1, 0] = numpy.sum( x146 * (x0 * x605 + x0 * (x0 * x607 + x605) + x209 * x21 + x316) ) result[2, 1, 1] = numpy.sum( x161 * (x0 * x608 + x0 * (x0 * x609 + x608) + x21 * x221 + x325) ) result[2, 1, 2] = numpy.sum( x161 * (x0 * x610 + x0 * (x0 * x612 + x610) + x21 * x230 + x334) ) result[2, 1, 3] = numpy.sum( x146 * (x0 * x613 + x0 * (x0 * x614 + x613) + x21 * x238 + x339) ) result[2, 1, 4] = numpy.sum( x161 * (x0 * x615 + x0 * (x0 * x616 + x615) + x21 * x244 + x344) ) result[2, 1, 5] = numpy.sum( x146 * (x0 * x617 + x0 * (x0 * x618 + x617) + x21 * x249 + x349) ) result[2, 2, 0] = numpy.sum(x146 * (x0 * x360 + x0 * (x0 * x621 + x360) + x369)) result[2, 2, 1] = numpy.sum(x161 * (x0 * x372 + x0 * (x0 * x623 + x372) + x374)) result[2, 2, 2] = numpy.sum(x161 * (x0 * x379 + x0 * (x0 * x626 + x379) + x382)) result[2, 2, 3] = numpy.sum(x146 * (x0 * x384 + x0 * (x0 * x628 + x384) + x386)) result[2, 2, 4] = numpy.sum(x161 * (x0 * x388 + x0 * (x0 * x630 + x388) + x390)) result[2, 2, 5] = numpy.sum(x146 * (x0 * x392 + x0 * (x0 * x632 + x392) + x394)) result[2, 3, 0] = numpy.sum(x146 * (x0 * x634 + x21 * x309 + x21 * x605 + x418)) result[2, 3, 1] = numpy.sum(x161 * (x0 * x636 + x21 * x320 + x21 * x608 + x423)) result[2, 3, 2] = numpy.sum(x161 * (x0 * x638 + x21 * x329 + x21 * x610 + x427)) result[2, 3, 3] = numpy.sum(x146 * (x0 * x640 + x21 * x336 + x21 * x613 + x429)) result[2, 3, 4] = numpy.sum(x161 * (x0 * x642 + x21 * x341 + x21 * x615 + x431)) result[2, 3, 5] = numpy.sum(x146 * (x0 * x644 + x21 * x346 + x21 * x617 + x433)) result[2, 4, 0] = numpy.sum(x161 * (x0 * x645 + x21 * x360 + x439)) result[2, 4, 1] = numpy.sum(x82 * (x0 * x646 + x21 * x372 + x443)) result[2, 4, 2] = numpy.sum(x82 * (x0 * x647 + x21 * x379 + x447)) result[2, 4, 3] = numpy.sum(x161 * (x0 * x648 + x21 * x384 + x449)) result[2, 4, 4] = numpy.sum(x82 * (x0 * x649 + x21 * x388 + x451)) result[2, 4, 5] = numpy.sum(x161 * (x0 * x650 + x21 * x392 + x453)) result[2, 5, 0] = numpy.sum(x146 * (x0 * x653 + x460)) result[2, 5, 1] = numpy.sum(x161 * (x0 * x656 + x462)) result[2, 5, 2] = numpy.sum(x161 * (x0 * x659 + x466)) result[2, 5, 3] = numpy.sum(x146 * (x0 * x662 + x467)) result[2, 5, 4] = numpy.sum(x161 * (x0 * x665 + x468)) result[2, 5, 5] = numpy.sum(x146 * (x0 * x668 + x469)) result[2, 6, 0] = numpy.sum(x84 * (x21 * x527 + x21 * x633 + x21 * x634 + x569)) result[2, 6, 1] = numpy.sum(x91 * (x21 * x530 + x21 * x635 + x21 * x636 + x571)) result[2, 6, 2] = numpy.sum(x91 * (x21 * x533 + x21 * x637 + x21 * x638 + x573)) result[2, 6, 3] = numpy.sum(x84 * (x21 * x536 + x21 * x639 + x21 * x640 + x574)) result[2, 6, 4] = numpy.sum(x91 * (x21 * x540 + x21 * x641 + x21 * x642 + x575)) result[2, 6, 5] = numpy.sum(x84 * (x21 * x543 + x21 * x643 + x21 * x644 + x576)) result[2, 7, 0] = numpy.sum(x146 * (x21 * x547 + x21 * x645 + x578)) result[2, 7, 1] = numpy.sum(x161 * (x21 * x550 + x21 * x646 + x580)) result[2, 7, 2] = numpy.sum(x161 * (x21 * x553 + x21 * x647 + x582)) result[2, 7, 3] = numpy.sum(x146 * (x21 * x556 + x21 * x648 + x583)) result[2, 7, 4] = numpy.sum(x161 * (x21 * x559 + x21 * x649 + x584)) result[2, 7, 5] = numpy.sum(x146 * (x21 * x562 + x21 * x650 + x585)) result[2, 8, 0] = numpy.sum(x146 * (x21 * x653 + x587)) result[2, 8, 1] = numpy.sum(x161 * (x21 * x656 + x589)) result[2, 8, 2] = numpy.sum(x161 * (x21 * x659 + x591)) result[2, 8, 3] = numpy.sum(x146 * (x21 * x662 + x592)) result[2, 8, 4] = numpy.sum(x161 * (x21 * x665 + x593)) result[2, 8, 5] = numpy.sum(x146 * (x21 * x668 + x594)) result[2, 9, 0] = numpy.sum( x84 * (x22 * x651 + x22 * x652 + x22 * x653 + x471 * x669) ) result[2, 9, 1] = numpy.sum( x91 * (x22 * x654 + x22 * x655 + x22 * x656 + x598 * x669) ) result[2, 9, 2] = numpy.sum( x91 * (x22 * x657 + x22 * x658 + x22 * x659 + x474 * x670) ) result[2, 9, 3] = numpy.sum(x84 * (x22 * x660 + x22 * x661 + x22 * x662 + x669 * x99)) result[2, 9, 4] = numpy.sum( x91 * (x104 * x670 + x22 * x663 + x22 * x664 + x22 * x665) ) result[2, 9, 5] = numpy.sum( x84 * (x22 * x666 + x22 * x667 + x22 * x668 + x54 * (4.0 * x464 + x670 * x92)) ) return result
[docs] def int3c2e3d_sph_133(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pf|f) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 10, 10), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - C[0] x5 = -x3 - A[0] x6 = 0.5 / (ax + bx) x7 = x4**2 x8 = -x2 * (ax * A[1] + bx * B[1]) x9 = -x8 - C[1] x10 = x9**2 x11 = -x2 * (ax * A[2] + bx * B[2]) x12 = -x11 - C[2] x13 = x12**2 x14 = cx + x1 x15 = x14 ** (-1.0) x16 = cx * x15 x17 = x1 * x16 * (x10 + x13 + x7) x18 = boys(4, x17) x19 = x14 ** (-1.5) x20 = 17.49341832762486 x21 = A[1] - B[1] x22 = A[2] - B[2] x23 = numpy.exp(-ax * bx * x2 * (x0**2 + x21**2 + x22**2)) x24 = x20 * x23 x25 = x2 * x24 x26 = 2.0 * x19 * x25 x27 = x18 * x26 x28 = cx ** (-1.0) x29 = x14 ** (-0.5) x30 = boys(3, x17) x31 = 2.0 * x2 * x20 * x23 * x28 * x29 * x30 - x27 x32 = x31 * x6 x33 = -2.0 * x2 * x20 * x23 * x28 * x29 * x30 * x5 + x27 * x4 x34 = -x33 x35 = boys(5, x17) x36 = x26 * x35 x37 = -2.0 * x18 * x2 * x20 * x23 * x28 * x29 * x5 + x36 * x4 x38 = -x37 x39 = x16 * x38 x40 = x39 * x4 x41 = x32 + x34 * x5 - x40 x42 = 2.0 * x6 x43 = x6 * (2.0 * x18 * x2 * x20 * x23 * x28 * x29 - x36) x44 = boys(6, x17) x45 = x26 * x44 x46 = 2.0 * x2 * x20 * x23 * x28 * x29 * x35 * x5 - x4 * x45 x47 = x16 * x46 x48 = x38 * x5 - x4 * x47 + x43 x49 = x16 * x48 x50 = -x4 * x49 + x41 * x5 - x42 * (x33 + x39) x51 = x4 * x50 x52 = x41 * x6 x53 = 3.0 * x52 x54 = x51 + x53 x55 = x1 * x15 x56 = x4 * x55 x57 = x4 * x41 x58 = x34 * x6 x59 = 2.0 * x58 x60 = x57 + x59 x61 = 3.0 * x6 x62 = x55 * x61 x63 = x54 * x56 + x60 * x62 x64 = x34 * x4 x65 = x28 * x30 * x42 x66 = x25 * x29 * x65 x67 = x64 + x66 x68 = x42 * x55 x69 = x56 * x60 + x67 * x68 x70 = x55 * (x56 * x63 + x62 * x69) x71 = x24 * x65 x72 = x19 * x71 x73 = x4 * x72 + x56 * x67 x74 = x55 * (x56 * x69 + x68 * x73) x75 = x0 * x74 + x70 x76 = x1 * x14 ** (-2.5) * x71 x77 = x56 * x73 + x7 * x76 x78 = x0 * x55 x79 = -x31 * x6 x80 = x6 * (2.0 * x2 * x20 * x23 * x28 * x29 * x35 - x45) x81 = x26 * boys(7, x17) x82 = x16 * x4 x83 = ( x5 * x50 - x61 * (-x34 * x5 + x40 + x49 + x79) + x82 * ( x42 * (x37 + x47) - x48 * x5 + x82 * ( x46 * x5 + x80 - x82 * (2.0 * x2 * x20 * x23 * x28 * x29 * x44 * x5 - x4 * x81) ) ) ) x84 = x4 * x83 x85 = x50 * x6 x86 = 4.0 * x85 x87 = x55 * x6 x88 = 4.0 * x87 x89 = da * db * dc x90 = 0.06666666666666667 * x89 x91 = x55 * x9 x92 = x91 * (x51 + x53) x93 = x91 * (x57 + x59) x94 = x55 * (x56 * x92 + x62 * x93) x95 = x72 * x9 x96 = x64 * x91 + x95 x97 = x55 * (x56 * x93 + x68 * x96) x98 = x0 * x97 + x94 x99 = x4 * x9 x100 = x56 * x96 + x76 * x99 x101 = 2.23606797749979 * x90 x102 = x12 * x55 x103 = x102 * (x51 + x53) x104 = x102 * (x57 + x59) x105 = x55 * (x103 * x56 + x104 * x62) x106 = x12 * x72 x107 = x102 * x64 + x106 x108 = x55 * (x104 * x56 + x107 * x68) x109 = x0 * x108 + x105 x110 = x12 * x76 x111 = x107 * x56 + x110 * x4 x112 = x1**2 / x14**2 x113 = x10 * x112 x114 = x113 * x55 * (x51 + x53) x115 = x113 * x55 * (x57 + x59) x116 = x0 * x115 + x114 x117 = x10 * x76 x118 = x113 * x64 + x117 x119 = x112 * x9 x120 = x119 * x12 x121 = x120 * x55 * (x51 + x53) x122 = x120 * x55 * (x57 + x59) x123 = x0 * x122 + x121 x124 = x110 * x9 x125 = x120 * x64 + x124 x126 = 3.872983346207417 * x90 x127 = x112 * x13 x128 = x127 * x55 * (x51 + x53) x129 = x127 * x55 * (x57 + x59) x130 = x0 * x129 + x128 x131 = x13 * x76 x132 = x127 * x64 + x131 x133 = x1**3 / x14**3 x134 = x133 * x9**3 x135 = x134 * x50 x136 = x134 * x41 x137 = x0 * x136 + x135 x138 = x0 * x34 x139 = x10 * x133 x140 = x12 * x139 x141 = x140 * x50 x142 = x140 * x41 x143 = x0 * x142 + x141 x144 = x13 * x133 x145 = x144 * x9 x146 = x145 * x50 x147 = x145 * x41 x148 = x0 * x147 + x146 x149 = x12**3 * x133 x150 = x149 * x50 x151 = x149 * x41 x152 = x0 * x151 + x150 x153 = -x8 - A[1] x154 = -2.0 * x153 * x18 * x2 * x20 * x23 * x28 * x29 + x36 * x9 x155 = -x154 x156 = x155 * x16 x157 = -2.0 * x153 * x2 * x20 * x23 * x28 * x29 * x30 + x27 * x9 x158 = -x6 * (x156 + x157) x159 = -x157 x160 = x156 * x4 - x159 * x5 x161 = -x160 x162 = 2.0 * x153 * x2 * x20 * x23 * x28 * x29 * x35 - x45 * x9 x163 = x16 * x162 x164 = x155 * x5 - x163 * x4 x165 = x16 * x164 x166 = x158 + x161 * x5 - x165 * x4 x167 = x166 * x4 x168 = x161 * x6 x169 = 2.0 * x168 x170 = x167 + x169 x171 = x159 * x6 x172 = x161 * x4 x173 = x171 + x172 x174 = x170 * x56 + x173 * x68 x175 = x56 * (x171 + x173) x176 = x55 * (x174 * x56 + x175 * x68) x177 = x176 + x21 * x74 x178 = x112 * x7 x179 = x55 * (x171 * x178 + x175 * x56) x180 = x21 * x55 x181 = x179 + x180 * x77 x182 = -x6 * (x154 + x163) x183 = 2.0 * x153 * x2 * x20 * x23 * x28 * x29 * x44 - x81 * x9 x184 = ( x166 * x5 - x42 * (x160 + x165) - x82 * (x164 * x5 + x182 - x82 * (x162 * x5 - x183 * x82)) ) x185 = x184 * x4 x186 = x166 * x6 x187 = 3.0 * x186 x188 = x55 * (x174 * x62 + x56 * (x170 * x62 + x56 * (x185 + x187))) x189 = x166 * x9 x190 = x189 + x52 x191 = x161 * x9 x192 = x191 + x58 x193 = x192 * x68 x194 = x190 * x56 + x193 x195 = x159 * x9 x196 = x195 + x66 x197 = x196 * x55 x198 = x192 * x56 + x197 * x6 x199 = x55 * (x194 * x56 + x198 * x68) x200 = x199 + x21 * x97 x201 = x112 * x4 x202 = x201 * x6 x203 = x55 * (x196 * x202 + x198 * x56) x204 = x100 * x180 + x203 x205 = x184 * x9 x206 = x205 + x85 x207 = x55 * (x194 * x62 + x56 * (x190 * x62 + x206 * x56)) x208 = 0.3333333333333333 * x89 x209 = x102 * x169 x210 = x102 * x167 + x209 x211 = x102 * x171 x212 = x102 * x172 + x211 x213 = x55 * (x210 * x56 + x212 * x68) x214 = x108 * x21 + x213 x215 = x12 * x201 x216 = x55 * (x171 * x215 + x212 * x56) x217 = x111 * x180 + x216 x218 = x55 * (x102 * x56 * (x185 + x187) + x210 * x62) x219 = x91 * (x190 + x52) x220 = x91 * (x192 + x58) x221 = x220 * x68 x222 = x55 * (x219 * x56 + x221) x223 = x115 * x21 + x222 x224 = x197 * x9 + x95 x225 = x55 * (x220 * x56 + x224 * x87) x226 = x118 * x180 + x225 x227 = x91 * (x206 + x85) x228 = x55 * (x219 * x62 + x227 * x56) x229 = x102 * x52 x230 = x102 * x189 + x229 x231 = x102 * x58 x232 = x102 * x191 + x231 x233 = x232 * x68 x234 = x55 * (x230 * x56 + x233) x235 = x122 * x21 + x234 x236 = x102 * x195 + x106 x237 = x55 * (x232 * x56 + x236 * x87) x238 = x125 * x180 + x237 x239 = x102 * x85 x240 = x102 * x205 + x239 x241 = x55 * (x230 * x62 + x240 * x56) x242 = 1.732050807568877 * x208 x243 = x127 * x169 x244 = x55 * (x127 * x167 + x243) x245 = x129 * x21 + x244 x246 = x127 * x171 x247 = x55 * (x127 * x172 + x246) x248 = x132 * x180 + x247 x249 = x127 * x55 * (x185 + x187) x250 = x55 * (x113 * x52 + x219 * x91) x251 = x136 * x21 + x250 x252 = x55 * (x113 * x58 + x220 * x91) x253 = x21 * x34 x254 = x134 * x253 + x252 x255 = x55 * (x113 * x85 + x227 * x91) x256 = x55 * (x120 * x52 + x230 * x91) x257 = x142 * x21 + x256 x258 = x55 * (x120 * x58 + x232 * x91) x259 = x140 * x253 + x258 x260 = x55 * (x120 * x85 + x240 * x91) x261 = x127 * x52 x262 = x55 * (x127 * x189 + x261) x263 = x147 * x21 + x262 x264 = x127 * x58 x265 = x55 * (x127 * x191 + x264) x266 = x145 * x253 + x265 x267 = x127 * x85 x268 = x55 * (x127 * x205 + x267) x269 = x149 * x166 x270 = x151 * x21 + x269 x271 = x149 * x161 x272 = x149 * x253 + x271 x273 = x149 * x184 x274 = -x11 - A[2] x275 = x12 * x36 - 2.0 * x18 * x2 * x20 * x23 * x274 * x28 * x29 x276 = -x275 x277 = x16 * x276 x278 = x12 * x27 - 2.0 * x2 * x20 * x23 * x274 * x28 * x29 * x30 x279 = -x6 * (x277 + x278) x280 = -x278 x281 = x277 * x4 - x280 * x5 x282 = -x281 x283 = -x12 * x45 + 2.0 * x2 * x20 * x23 * x274 * x28 * x29 * x35 x284 = x16 * x283 x285 = x276 * x5 - x284 * x4 x286 = x16 * x285 x287 = x279 + x282 * x5 - x286 * x4 x288 = x287 * x4 x289 = x282 * x6 x290 = 2.0 * x289 x291 = x288 + x290 x292 = x280 * x6 x293 = x282 * x4 x294 = x292 + x293 x295 = x291 * x56 + x294 * x68 x296 = x56 * (x292 + x294) x297 = x55 * (x295 * x56 + x296 * x68) x298 = x22 * x74 + x297 x299 = x55 * (x178 * x292 + x296 * x56) x300 = x22 * x55 x301 = x299 + x300 * x77 x302 = -x6 * (x275 + x284) x303 = -x12 * x81 + 2.0 * x2 * x20 * x23 * x274 * x28 * x29 * x44 x304 = ( x287 * x5 - x42 * (x281 + x286) - x82 * (x285 * x5 + x302 - x82 * (x283 * x5 - x303 * x82)) ) x305 = x304 * x4 x306 = x287 * x6 x307 = 3.0 * x306 x308 = x55 * (x295 * x62 + x56 * (x291 * x62 + x56 * (x305 + x307))) x309 = x91 * (x288 + x290) x310 = x292 * x91 x311 = x293 * x91 + x310 x312 = x55 * (x309 * x56 + x311 * x68) x313 = x22 * x97 + x312 x314 = x119 * x4 x315 = x55 * (x292 * x314 + x311 * x56) x316 = x100 * x300 + x315 x317 = x55 * (x309 * x62 + x56 * x91 * (x305 + x307)) x318 = x12 * x287 + x52 x319 = x12 * x282 + x58 x320 = x319 * x68 x321 = x318 * x56 + x320 x322 = x12 * x280 + x66 x323 = x322 * x87 x324 = x319 * x56 + x323 x325 = x55 * (x321 * x56 + x324 * x68) x326 = x108 * x22 + x325 x327 = x55 * (x202 * x322 + x324 * x56) x328 = x111 * x300 + x327 x329 = x12 * x304 + x85 x330 = x55 * (x321 * x62 + x56 * (x318 * x62 + x329 * x56)) x331 = x113 * x55 * (x288 + x290) x332 = x115 * x22 + x331 x333 = x113 * x292 x334 = x55 * (x113 * x293 + x333) x335 = x118 * x300 + x334 x336 = x113 * x55 * (x305 + x307) x337 = x119 * x42 x338 = x55 * (x314 * x318 + x319 * x337) x339 = x122 * x22 + x338 x340 = x119 * x6 x341 = x322 * x340 x342 = x55 * (x314 * x319 + x341) x343 = x125 * x300 + x342 x344 = x55 * (x119 * x318 * x61 + x314 * x329) x345 = x102 * x318 + x229 x346 = x102 * x319 + x231 x347 = x346 * x68 x348 = x55 * (x345 * x56 + x347) x349 = x129 * x22 + x348 x350 = x102 * x322 + x106 x351 = x350 * x87 x352 = x55 * (x346 * x56 + x351) x353 = x132 * x300 + x352 x354 = x102 * x329 + x239 x355 = x55 * (x345 * x62 + x354 * x56) x356 = x134 * x287 x357 = x136 * x22 + x356 x358 = x134 * x282 x359 = x22 * x34 x360 = x134 * x359 + x358 x361 = x134 * x304 x362 = x139 * x318 x363 = x142 * x22 + x362 x364 = x139 * x319 x365 = x140 * x359 + x364 x366 = x139 * x329 x367 = x119 * x345 x368 = x147 * x22 + x367 x369 = x119 * x346 x370 = x145 * x359 + x369 x371 = x119 * x354 x372 = x55 * (x102 * x345 + x261) x373 = x151 * x22 + x372 x374 = x55 * (x102 * x346 + x264) x375 = x149 * x359 + x374 x376 = x55 * (x102 * x354 + x267) x377 = x156 * x9 x378 = x153 * x159 + x32 - x377 x379 = x378 * x6 x380 = x153 * x155 - x163 * x9 + x43 x381 = x16 * x380 x382 = x378 * x5 - x381 * x4 x383 = x382 * x4 x384 = x379 + x383 x385 = x56 * (x379 + x384) x386 = x55 * (x178 * x379 + x385 * x56) x387 = x179 * x21 + x386 x388 = x181 * x21 + x387 x389 = x6 * (x153 * x159 - x377 - x381 - x79) x390 = x16 * x9 x391 = x153 * x162 - x183 * x390 + x80 x392 = x382 * x5 + x389 - x82 * (x380 * x5 - x391 * x82) x393 = x392 * x4 x394 = x382 * x6 x395 = 2.0 * x394 x396 = x176 * x21 + x55 * (x385 * x68 + x56 * (x384 * x68 + x56 * (x393 + x395))) x397 = x378 * x9 x398 = 2.0 * x171 x399 = x397 + x398 x400 = x382 * x9 x401 = x169 + x400 x402 = x399 * x87 + x401 * x56 x403 = x55 * (x202 * x399 + x402 * x56) x404 = x203 * x21 + x403 x405 = x204 * x21 + x404 x406 = x392 * x9 x407 = 2.0 * x186 x408 = x406 + x407 x409 = x199 * x21 + x55 * (x402 * x68 + x56 * (x401 * x68 + x408 * x56)) x410 = x102 * x379 x411 = x102 * x383 + x410 x412 = x55 * (x215 * x379 + x411 * x56) x413 = x21 * x216 + x412 x414 = x21 * x217 + x413 x415 = x21 * x213 + x55 * (x102 * x56 * (x393 + x395) + x411 * x68) x416 = x197 * x42 + x399 * x91 x417 = x193 + x401 * x91 x418 = x55 * (x416 * x87 + x417 * x56) x419 = x21 * x225 + x418 x420 = x21 * x226 + x419 x421 = x190 * x68 + x408 * x91 x422 = x21 * x222 + x55 * (x417 * x68 + x421 * x56) x423 = x102 * (x397 + x398) x424 = x102 * x400 + x209 x425 = x55 * (x423 * x87 + x424 * x56) x426 = x21 * x237 + x425 x427 = x21 * x238 + x426 x428 = x102 * (x406 + x407) x429 = x21 * x234 + x55 * (x424 * x68 + x428 * x56) x430 = x127 * x379 x431 = x55 * (x127 * x383 + x430) x432 = x21 * x247 + x431 x433 = x21 * x248 + x432 x434 = x127 * x55 * (x393 + x395) + x21 * x244 x435 = x55 * (x221 + x417 * x91) x436 = x21 * x252 + x435 x437 = x21 * x254 + x436 x438 = x21 * x250 + x55 * (x219 * x68 + x421 * x91) x439 = x55 * (x233 + x424 * x91) x440 = x21 * x258 + x439 x441 = x21 * x259 + x440 x442 = x21 * x256 + x55 * (x230 * x68 + x428 * x91) x443 = x55 * (x127 * x400 + x243) x444 = x21 * x265 + x443 x445 = x21 * x266 + x444 x446 = x127 * x55 * (x406 + x407) + x21 * x262 x447 = x149 * x382 x448 = x21 * x271 + x447 x449 = x21 * x272 + x448 x450 = x149 * x392 + x21 * x269 x451 = -x153 * x280 + x277 * x9 x452 = -x451 x453 = x452 * x6 x454 = x153 * x276 - x284 * x9 x455 = x16 * x454 x456 = -x4 * x455 + x452 * x5 x457 = x4 * x456 + x453 x458 = x56 * (x453 + x457) x459 = x55 * (x178 * x453 + x458 * x56) x460 = x179 * x22 + x459 x461 = x21 * x301 + x460 x462 = -x6 * (x451 + x455) x463 = x153 * x283 - x303 * x390 x464 = x456 * x5 + x462 - x82 * (x454 * x5 - x463 * x82) x465 = x42 * x456 x466 = x55 * (x458 * x68 + x56 * (x457 * x68 + x56 * (x4 * x464 + x465))) x467 = x176 * x22 + x466 x468 = x292 + x452 * x9 x469 = x289 + x456 * x9 x470 = x468 * x87 + x469 * x56 x471 = x55 * (x202 * x468 + x470 * x56) x472 = x203 * x22 + x471 x473 = x21 * x316 + x472 x474 = x306 + x464 * x9 x475 = x469 * x68 x476 = x55 * (x470 * x68 + x56 * (x474 * x56 + x475)) x477 = x199 * x22 + x476 x478 = x12 * x452 + x171 x479 = x12 * x456 + x168 x480 = x478 * x87 + x479 * x56 x481 = x55 * (x202 * x478 + x480 * x56) x482 = x216 * x22 + x481 x483 = x21 * x328 + x482 x484 = x12 * x464 + x186 x485 = x479 * x68 x486 = x55 * (x480 * x68 + x56 * (x484 * x56 + x485)) x487 = x213 * x22 + x486 x488 = x310 + x468 * x91 x489 = x91 * (x289 + x469) x490 = x55 * (x488 * x87 + x489 * x56) x491 = x22 * x225 + x490 x492 = x21 * x335 + x491 x493 = x91 * (x306 + x474) x494 = x489 * x68 x495 = x55 * (x493 * x56 + x494) x496 = x22 * x222 + x495 x497 = x323 + x478 * x91 x498 = x319 * x87 + x479 * x91 x499 = x55 * (x497 * x87 + x498 * x56) x500 = x22 * x237 + x499 x501 = x21 * x343 + x500 x502 = x318 * x87 + x484 * x91 x503 = x498 * x68 x504 = x55 * (x502 * x56 + x503) x505 = x22 * x234 + x504 x506 = x102 * x478 + x211 x507 = x102 * (x168 + x479) x508 = x55 * (x506 * x87 + x507 * x56) x509 = x22 * x247 + x508 x510 = x21 * x353 + x509 x511 = x102 * (x186 + x484) x512 = x507 * x68 x513 = x55 * (x511 * x56 + x512) x514 = x22 * x244 + x513 x515 = x55 * (x113 * x289 + x489 * x91) x516 = x22 * x252 + x515 x517 = x21 * x360 + x516 x518 = x55 * (x113 * x306 + x493 * x91) x519 = x22 * x250 + x518 x520 = x55 * (x319 * x340 + x498 * x91) x521 = x22 * x258 + x520 x522 = x21 * x365 + x521 x523 = x55 * (x318 * x340 + x502 * x91) x524 = x22 * x256 + x523 x525 = x55 * (x346 * x87 + x507 * x91) x526 = x22 * x265 + x525 x527 = x21 * x370 + x526 x528 = x55 * (x345 * x87 + x511 * x91) x529 = x22 * x262 + x528 x530 = x55 * (x102 * x507 + x127 * x168) x531 = x22 * x271 + x530 x532 = x21 * x375 + x531 x533 = x55 * (x102 * x511 + x127 * x186) x534 = x22 * x269 + x533 x535 = x12 * x277 x536 = x274 * x280 + x32 - x535 x537 = x536 * x6 x538 = -x12 * x284 + x274 * x276 + x43 x539 = x16 * x538 x540 = -x4 * x539 + x5 * x536 x541 = x4 * x540 x542 = x537 + x541 x543 = x56 * (x537 + x542) x544 = x55 * (x178 * x537 + x543 * x56) x545 = x22 * x299 + x544 x546 = x22 * x301 + x545 x547 = x6 * (x274 * x280 - x535 - x539 - x79) x548 = x12 * x16 x549 = x274 * x283 - x303 * x548 + x80 x550 = x5 * x540 + x547 - x82 * (x5 * x538 - x549 * x82) x551 = x4 * x550 x552 = x540 * x6 x553 = 2.0 * x552 x554 = x22 * x297 + x55 * (x543 * x68 + x56 * (x542 * x68 + x56 * (x551 + x553))) x555 = x537 * x91 x556 = x541 * x91 + x555 x557 = x55 * (x314 * x537 + x556 * x56) x558 = x22 * x315 + x557 x559 = x22 * x316 + x558 x560 = x22 * x312 + x55 * (x556 * x68 + x56 * x91 * (x551 + x553)) x561 = x12 * x536 + 2.0 * x292 x562 = x561 * x87 x563 = x12 * x540 + x290 x564 = x56 * x563 + x562 x565 = x55 * (x202 * x561 + x56 * x564) x566 = x22 * x327 + x565 x567 = x22 * x328 + x566 x568 = x12 * x550 + 2.0 * x306 x569 = x22 * x325 + x55 * (x56 * (x56 * x568 + x563 * x68) + x564 * x68) x570 = x113 * x537 x571 = x55 * (x113 * x541 + x570) x572 = x22 * x334 + x571 x573 = x22 * x335 + x572 x574 = x113 * x55 * (x551 + x553) + x22 * x331 x575 = x340 * x561 x576 = x55 * (x314 * x563 + x575) x577 = x22 * x342 + x576 x578 = x22 * x343 + x577 x579 = x22 * x338 + x55 * (x314 * x568 + x337 * x563) x580 = x102 * x561 + x322 * x68 x581 = x580 * x87 x582 = x102 * x563 + x320 x583 = x55 * (x56 * x582 + x581) x584 = x22 * x352 + x583 x585 = x22 * x353 + x584 x586 = x102 * x568 + x318 * x68 x587 = x22 * x348 + x55 * (x56 * x586 + x582 * x68) x588 = x134 * x540 x589 = x22 * x358 + x588 x590 = x22 * x360 + x589 x591 = x134 * x550 + x22 * x356 x592 = x139 * x563 x593 = x22 * x364 + x592 x594 = x22 * x365 + x593 x595 = x139 * x568 + x22 * x362 x596 = x119 * x582 x597 = x22 * x369 + x596 x598 = x22 * x370 + x597 x599 = x119 * x586 + x22 * x367 x600 = x55 * (x102 * x582 + x347) x601 = x22 * x374 + x600 x602 = x22 * x375 + x601 x603 = x22 * x372 + x55 * (x102 * x586 + x345 * x68) x604 = x153 * x378 + 2.0 * x158 - x381 * x9 x605 = x6 * x604 x606 = x153 * x380 + 2.0 * x182 - x390 * x391 x607 = x5 * x604 - x606 * x82 x608 = x4 * x607 x609 = x21 * x386 + x21 * x387 + x55 * (x178 * x605 + x56**2 * (2.0 * x605 + x608)) x610 = x604 * x9 x611 = 3.0 * x379 x612 = x610 + x611 x613 = x612 * x87 x614 = x607 * x9 x615 = 3.0 * x394 x616 = x614 + x615 x617 = x21 * x403 + x21 * x404 + x55 * (x202 * x612 + x56 * (x56 * x616 + x613)) x618 = x102 * x605 x619 = x21 * x412 + x21 * x413 + x55 * (x215 * x605 + x56 * (x102 * x608 + x618)) x620 = x399 * x62 + x612 * x91 x621 = x620 * x87 x622 = x401 * x62 + x616 * x91 x623 = x21 * x418 + x21 * x419 + x55 * (x56 * x622 + x621) x624 = x102 * (x610 + x611) x625 = x624 * x87 x626 = x102 * (x614 + x615) x627 = x21 * x425 + x21 * x426 + x55 * (x56 * x626 + x625) x628 = x127 * x605 x629 = x21 * x431 + x21 * x432 + x55 * (x127 * x608 + x628) x630 = x21 * x435 + x21 * x436 + x55 * (x417 * x62 + x622 * x91) x631 = x21 * x439 + x21 * x440 + x55 * (x424 * x62 + x626 * x91) x632 = x127 * x55 * (x614 + x615) + x21 * x443 + x21 * x444 x633 = x149 * x607 + x21 * x447 + x21 * x448 x634 = x153 * x452 + x279 - x455 * x9 x635 = x6 * x634 x636 = x153 * x454 + x302 - x390 * x463 x637 = x5 * x634 - x636 * x82 x638 = x55 * (x178 * x635 + x56**2 * (x4 * x637 + 2.0 * x635)) x639 = x21 * x460 + x22 * x386 + x638 x640 = 2.0 * x453 x641 = x634 * x9 + x640 x642 = x465 + x637 * x9 x643 = x55 * (x202 * x641 + x56 * (x56 * x642 + x641 * x87)) x644 = x21 * x472 + x22 * x403 + x643 x645 = x12 * x634 + x379 x646 = x12 * x637 + x394 x647 = x55 * (x202 * x645 + x56 * (x56 * x646 + x645 * x87)) x648 = x21 * x482 + x22 * x412 + x647 x649 = x468 * x68 + x641 * x91 x650 = x475 + x642 * x91 x651 = x55 * (x56 * x650 + x649 * x87) x652 = x21 * x491 + x22 * x418 + x651 x653 = x478 * x68 x654 = x645 * x91 + x653 x655 = x485 + x646 * x91 x656 = x55 * (x56 * x655 + x654 * x87) x657 = x21 * x500 + x22 * x425 + x656 x658 = x102 * x645 + x410 x659 = x102 * (x394 + x646) x660 = x55 * (x56 * x659 + x658 * x87) x661 = x21 * x509 + x22 * x431 + x660 x662 = x55 * (x494 + x650 * x91) x663 = x21 * x516 + x22 * x435 + x662 x664 = x55 * (x503 + x655 * x91) x665 = x21 * x521 + x22 * x439 + x664 x666 = x55 * (x512 + x659 * x91) x667 = x21 * x526 + x22 * x443 + x666 x668 = x55 * (x102 * x659 + x127 * x394) x669 = x21 * x531 + x22 * x447 + x668 x670 = x153 * x536 - x539 * x9 x671 = x6 * x670 x672 = x153 * x538 - x390 * x549 x673 = x5 * x670 - x672 * x82 x674 = x22 * x459 + x55 * (x178 * x671 + x56**2 * (x4 * x673 + 2.0 * x671)) x675 = x22 * x460 + x674 x676 = x537 + x670 * x9 x677 = x552 + x673 * x9 x678 = x22 * x471 + x55 * (x202 * x676 + x56 * (x56 * x677 + x676 * x87)) x679 = x22 * x472 + x678 x680 = x12 * x670 + x640 x681 = x12 * x673 + x465 x682 = x22 * x481 + x55 * (x202 * x680 + x56 * (x56 * x681 + x680 * x87)) x683 = x22 * x482 + x682 x684 = x555 + x676 * x91 x685 = x91 * (x552 + x677) x686 = x22 * x490 + x55 * (x56 * x685 + x684 * x87) x687 = x22 * x491 + x686 x688 = x562 + x680 * x91 x689 = x563 * x87 + x681 * x91 x690 = x22 * x499 + x55 * (x56 * x689 + x688 * x87) x691 = x22 * x500 + x690 x692 = x102 * x680 + x653 x693 = x102 * x681 + x485 x694 = x22 * x508 + x55 * (x56 * x693 + x692 * x87) x695 = x22 * x509 + x694 x696 = x22 * x515 + x55 * (x113 * x552 + x685 * x91) x697 = x22 * x516 + x696 x698 = x22 * x520 + x55 * (x340 * x563 + x689 * x91) x699 = x22 * x521 + x698 x700 = x22 * x525 + x55 * (x582 * x87 + x693 * x91) x701 = x22 * x526 + x700 x702 = x22 * x530 + x55 * (x102 * x693 + x512) x703 = x22 * x531 + x702 x704 = -x12 * x539 + x274 * x536 + 2.0 * x279 x705 = x6 * x704 x706 = x274 * x538 + 2.0 * x302 - x548 * x549 x707 = x5 * x704 - x706 * x82 x708 = x4 * x707 x709 = x22 * x544 + x22 * x545 + x55 * (x178 * x705 + x56**2 * (2.0 * x705 + x708)) x710 = x705 * x91 x711 = x22 * x557 + x22 * x558 + x55 * (x314 * x705 + x56 * (x708 * x91 + x710)) x712 = x12 * x704 + 3.0 * x537 x713 = x712 * x87 x714 = x12 * x707 + 3.0 * x552 x715 = x22 * x565 + x22 * x566 + x55 * (x202 * x712 + x56 * (x56 * x714 + x713)) x716 = x113 * x705 x717 = x22 * x571 + x22 * x572 + x55 * (x113 * x708 + x716) x718 = x340 * x712 x719 = x22 * x576 + x22 * x577 + x55 * (x314 * x714 + x718) x720 = x102 * x712 + x561 * x62 x721 = x720 * x87 x722 = x102 * x714 + x563 * x62 x723 = x22 * x583 + x22 * x584 + x55 * (x56 * x722 + x721) x724 = x134 * x707 + x22 * x588 + x22 * x589 x725 = x139 * x714 + x22 * x592 + x22 * x593 x726 = x119 * x722 + x22 * x596 + x22 * x597 x727 = x22 * x600 + x22 * x601 + x55 * (x102 * x722 + x582 * x62) x728 = x0 * x179 + x176 x729 = x133 * x4**3 x730 = x0 * x159 x731 = x0 * x203 + x199 x732 = x133 * x7 x733 = x196 * x732 x734 = x0 * x216 + x213 x735 = x12 * x732 x736 = x0 * x225 + x222 x737 = x0 * x201 x738 = x0 * x237 + x234 x739 = x0 * x247 + x244 x740 = x144 * x4 x741 = x0 * x252 + x250 x742 = x117 + x224 * x91 x743 = x0 * x258 + x256 x744 = x124 + x236 * x91 x745 = x0 * x265 + x262 x746 = x127 * x195 + x131 x747 = x0 * x271 + x269 x748 = x378 * x729 x749 = x159 * x21 x750 = x729 * x749 + x748 x751 = x399 * x732 x752 = x21 * x733 + x751 x753 = x378 * x735 x754 = x735 * x749 + x753 x755 = x201 * x416 x756 = x201 * x21 x757 = x224 * x756 + x755 x758 = x201 * x423 x759 = x236 * x756 + x758 x760 = x378 * x740 x761 = x740 * x749 + x760 x762 = x55 * (x224 * x68 + x416 * x91) x763 = x180 * x742 + x762 x764 = x55 * (x236 * x68 + x423 * x91) x765 = x180 * x744 + x764 x766 = x127 * x55 * (x397 + x398) x767 = x180 * x746 + x766 x768 = x149 * x378 x769 = x149 * x749 + x768 x770 = x452 * x729 x771 = x159 * x22 x772 = x729 * x771 + x770 x773 = x468 * x732 x774 = x22 * x733 + x773 x775 = x478 * x732 x776 = x735 * x771 + x775 x777 = x201 * x488 x778 = x201 * x22 x779 = x224 * x778 + x777 x780 = x201 * x497 x781 = x236 * x778 + x780 x782 = x201 * x506 x783 = x740 * x771 + x782 x784 = x55 * (x333 + x488 * x91) x785 = x300 * x742 + x784 x786 = x55 * (x341 + x497 * x91) x787 = x300 * x744 + x786 x788 = x55 * (x351 + x506 * x91) x789 = x300 * x746 + x788 x790 = x55 * (x102 * x506 + x246) x791 = x149 * x771 + x790 x792 = x604 * x729 x793 = x21 * x748 + x792 x794 = x21 * x750 + x793 x795 = x612 * x732 x796 = x21 * x751 + x795 x797 = x21 * x752 + x796 x798 = x604 * x735 x799 = x21 * x753 + x798 x800 = x21 * x754 + x799 x801 = x201 * x620 x802 = x21 * x755 + x801 x803 = x21 * x757 + x802 x804 = x201 * x624 x805 = x21 * x758 + x804 x806 = x21 * x759 + x805 x807 = x604 * x740 x808 = x21 * x760 + x807 x809 = x21 * x761 + x808 x810 = x55 * (x416 * x62 + x620 * x91) x811 = x21 * x762 + x810 x812 = x21 * x763 + x811 x813 = x55 * (x423 * x62 + x624 * x91) x814 = x21 * x764 + x813 x815 = x21 * x765 + x814 x816 = x127 * x55 * (x610 + x611) x817 = x21 * x766 + x816 x818 = x21 * x767 + x817 x819 = x149 * x604 x820 = x21 * x768 + x819 x821 = x21 * x769 + x820 x822 = x634 * x729 x823 = x22 * x748 + x822 x824 = x21 * x772 + x823 x825 = x641 * x732 x826 = x22 * x751 + x825 x827 = x21 * x774 + x826 x828 = x645 * x732 x829 = x22 * x753 + x828 x830 = x21 * x776 + x829 x831 = x201 * x649 x832 = x22 * x755 + x831 x833 = x21 * x779 + x832 x834 = x201 * x654 x835 = x22 * x758 + x834 x836 = x21 * x781 + x835 x837 = x201 * x658 x838 = x22 * x760 + x837 x839 = x21 * x783 + x838 x840 = x55 * (x488 * x68 + x649 * x91) x841 = x22 * x762 + x840 x842 = x21 * x785 + x841 x843 = x55 * (x497 * x68 + x654 * x91) x844 = x22 * x764 + x843 x845 = x21 * x787 + x844 x846 = x506 * x68 x847 = x55 * (x658 * x91 + x846) x848 = x22 * x766 + x847 x849 = x21 * x789 + x848 x850 = x55 * (x102 * x658 + x430) x851 = x22 * x768 + x850 x852 = x21 * x791 + x851 x853 = x670 * x729 x854 = x22 * x770 + x853 x855 = x22 * x772 + x854 x856 = x676 * x732 x857 = x22 * x773 + x856 x858 = x22 * x774 + x857 x859 = x680 * x732 x860 = x22 * x775 + x859 x861 = x22 * x776 + x860 x862 = x201 * x684 x863 = x22 * x777 + x862 x864 = x22 * x779 + x863 x865 = x201 * x688 x866 = x22 * x780 + x865 x867 = x22 * x781 + x866 x868 = x201 * x692 x869 = x22 * x782 + x868 x870 = x22 * x783 + x869 x871 = x55 * (x570 + x684 * x91) x872 = x22 * x784 + x871 x873 = x22 * x785 + x872 x874 = x55 * (x575 + x688 * x91) x875 = x22 * x786 + x874 x876 = x22 * x787 + x875 x877 = x55 * (x581 + x692 * x91) x878 = x22 * x788 + x877 x879 = x22 * x789 + x878 x880 = x55 * (x102 * x692 + x846) x881 = x22 * x790 + x880 x882 = x22 * x791 + x881 x883 = x153 * x604 + 3.0 * x389 - x390 * x606 x884 = x883 * x9 x885 = 4.0 * x605 x886 = x884 + x885 x887 = 4.0 * x613 + x886 * x91 x888 = x102 * (x884 + x885) x889 = x153 * x634 - x390 * x636 + 2.0 * x462 x890 = x729 * x889 x891 = 3.0 * x635 + x889 * x9 x892 = x732 * x891 x893 = x12 * x889 + x605 x894 = x732 * x893 x895 = x62 * x641 + x891 * x91 x896 = x201 * x895 x897 = x62 * x645 + x893 * x91 x898 = x201 * x897 x899 = x102 * x893 + x618 x900 = x201 * x899 x901 = x55 * (x62 * x649 + x895 * x91) x902 = x55 * (x62 * x654 + x897 * x91) x903 = x55 * (x62 * x658 + x899 * x91) x904 = x55 * (x102 * x899 + x628) x905 = x153 * x670 - x390 * x672 + x547 x906 = x22 * x822 + x729 * x905 x907 = 2.0 * x671 + x9 * x905 x908 = x22 * x825 + x732 * x907 x909 = x12 * x905 + 2.0 * x635 x910 = x22 * x828 + x732 * x909 x911 = x676 * x68 + x907 * x91 x912 = x201 * x911 + x22 * x831 x913 = x68 * x680 + x909 * x91 x914 = x201 * x913 + x22 * x834 x915 = x102 * x909 + x645 * x68 x916 = x201 * x915 + x22 * x837 x917 = x22 * x840 + x55 * (x68 * x684 + x91 * x911) x918 = x22 * x843 + x55 * (x68 * x688 + x91 * x913) x919 = x22 * x847 + x55 * (x68 * x692 + x91 * x915) x920 = x22 * x850 + x55 * (x102 * x915 + x658 * x68) x921 = x153 * x704 - x390 * x706 x922 = x22 * x853 + x22 * x854 + x729 * x921 x923 = x705 + x9 * x921 x924 = x22 * x856 + x22 * x857 + x732 * x923 x925 = x12 * x921 + 3.0 * x671 x926 = x22 * x859 + x22 * x860 + x732 * x925 x927 = x710 + x91 * x923 x928 = x201 * x927 + x22 * x862 + x22 * x863 x929 = x713 + x91 * x925 x930 = x201 * x929 + x22 * x865 + x22 * x866 x931 = x102 * x925 + x62 * x680 x932 = x201 * x931 + x22 * x868 + x22 * x869 x933 = x22 * x871 + x22 * x872 + x55 * (x716 + x91 * x927) x934 = x22 * x874 + x22 * x875 + x55 * (x718 + x91 * x929) x935 = x22 * x877 + x22 * x878 + x55 * (x721 + x91 * x931) x936 = x22 * x880 + x22 * x881 + x55 * (x102 * x931 + x62 * x692) x937 = x0 * x299 + x297 x938 = x0 * x280 x939 = x0 * x315 + x312 x940 = x732 * x9 x941 = x0 * x327 + x325 x942 = x0 * x322 x943 = x0 * x334 + x331 x944 = x139 * x4 x945 = x0 * x342 + x338 x946 = x133 * x99 x947 = x0 * x352 + x348 x948 = x0 * x358 + x356 x949 = x0 * x364 + x362 x950 = x0 * x369 + x367 x951 = x119 * x350 x952 = x0 * x374 + x372 x953 = x102 * x350 + x131 x954 = x21 * x299 + x459 x955 = x21 * x280 x956 = x729 * x955 + x770 x957 = x21 * x315 + x471 x958 = x773 + x940 * x955 x959 = x21 * x327 + x481 x960 = x21 * x322 x961 = x732 * x960 + x775 x962 = x21 * x334 + x490 x963 = x777 + x944 * x955 x964 = x21 * x342 + x499 x965 = x780 + x946 * x960 x966 = x21 * x352 + x508 x967 = x350 * x756 + x782 x968 = x21 * x358 + x515 x969 = x134 * x955 + x784 x970 = x21 * x364 + x520 x971 = x139 * x960 + x786 x972 = x21 * x369 + x525 x973 = x21 * x951 + x788 x974 = x21 * x374 + x530 x975 = x180 * x953 + x790 x976 = x536 * x729 x977 = x22 * x280 x978 = x729 * x977 + x976 x979 = x536 * x940 x980 = x940 * x977 + x979 x981 = x561 * x732 x982 = x22 * x322 x983 = x732 * x982 + x981 x984 = x536 * x944 x985 = x944 * x977 + x984 x986 = x561 * x946 x987 = x946 * x982 + x986 x988 = x201 * x580 x989 = x350 * x778 + x988 x990 = x134 * x536 x991 = x134 * x977 + x990 x992 = x139 * x561 x993 = x139 * x982 + x992 x994 = x119 * x580 x995 = x22 * x951 + x994 x996 = x55 * (x102 * x580 + x350 * x68) x997 = x300 * x953 + x996 x998 = x21 * x770 + x822 x999 = x21 * x956 + x998 x1000 = x21 * x773 + x825 x1001 = x1000 + x21 * x958 x1002 = x21 * x775 + x828 x1003 = x1002 + x21 * x961 x1004 = x21 * x777 + x831 x1005 = x1004 + x21 * x963 x1006 = x21 * x780 + x834 x1007 = x1006 + x21 * x965 x1008 = x21 * x782 + x837 x1009 = x1008 + x21 * x967 x1010 = x21 * x784 + x840 x1011 = x1010 + x21 * x969 x1012 = x21 * x786 + x843 x1013 = x1012 + x21 * x971 x1014 = x21 * x788 + x847 x1015 = x1014 + x21 * x973 x1016 = x21 * x790 + x850 x1017 = x1016 + x21 * x975 x1018 = x21 * x978 + x854 x1019 = x21 * x980 + x857 x1020 = x21 * x983 + x860 x1021 = x21 * x985 + x863 x1022 = x21 * x987 + x866 x1023 = x21 * x989 + x869 x1024 = x21 * x991 + x872 x1025 = x21 * x993 + x875 x1026 = x21 * x995 + x878 x1027 = x21 * x997 + x881 x1028 = x704 * x729 x1029 = x1028 + x22 * x976 x1030 = x1029 + x22 * x978 x1031 = x704 * x940 x1032 = x1031 + x22 * x979 x1033 = x1032 + x22 * x980 x1034 = x712 * x732 x1035 = x1034 + x22 * x981 x1036 = x1035 + x22 * x983 x1037 = x704 * x944 x1038 = x1037 + x22 * x984 x1039 = x1038 + x22 * x985 x1040 = x712 * x946 x1041 = x1040 + x22 * x986 x1042 = x1041 + x22 * x987 x1043 = x201 * x720 x1044 = x1043 + x22 * x988 x1045 = x1044 + x22 * x989 x1046 = x134 * x704 x1047 = x1046 + x22 * x990 x1048 = x1047 + x22 * x991 x1049 = x139 * x712 x1050 = x1049 + x22 * x992 x1051 = x1050 + x22 * x993 x1052 = x119 * x720 x1053 = x1052 + x22 * x994 x1054 = x1053 + x22 * x995 x1055 = x55 * (x102 * x720 + x580 * x62) x1056 = x1055 + x22 * x996 x1057 = x1056 + x22 * x997 x1058 = x274 * x704 + 3.0 * x547 - x548 * x706 x1059 = x1058 * x12 + 4.0 * x705 x1060 = x102 * x1059 + 4.0 * x713 # 300 item(s) result[0, 0, 0] = numpy.sum( x90 * ( x0 * x70 + x0 * x75 + x0 * (x0 * (x74 + x77 * x78) + x75) + x55 * (x56 * (x54 * x88 + x56 * (x84 + x86)) + x63 * x88) ) ) result[0, 0, 1] = numpy.sum( x101 * ( x0 * x94 + x0 * x98 + x0 * (x0 * (x100 * x78 + x97) + x98) + x55 * (x56 * x91 * (x84 + x86) + x88 * x92) ) ) result[0, 0, 2] = numpy.sum( x101 * ( x0 * x105 + x0 * x109 + x0 * (x0 * (x108 + x111 * x78) + x109) + x55 * (x102 * x56 * (x84 + x86) + x103 * x88) ) ) result[0, 0, 3] = numpy.sum( x101 * ( x0 * x114 + x0 * x116 + x0 * (x0 * (x115 + x118 * x78) + x116) + x113 * x55 * (x84 + x86) ) ) result[0, 0, 4] = numpy.sum( x126 * ( x0 * x121 + x0 * x123 + x0 * (x0 * (x122 + x125 * x78) + x123) + x120 * x55 * (x84 + x86) ) ) result[0, 0, 5] = numpy.sum( x101 * ( x0 * x128 + x0 * x130 + x0 * (x0 * (x129 + x132 * x78) + x130) + x127 * x55 * (x84 + x86) ) ) result[0, 0, 6] = numpy.sum( x90 * (x0 * x135 + x0 * x137 + x0 * (x0 * (x134 * x138 + x136) + x137) + x134 * x83) ) result[0, 0, 7] = numpy.sum( x101 * (x0 * x141 + x0 * x143 + x0 * (x0 * (x138 * x140 + x142) + x143) + x140 * x83) ) result[0, 0, 8] = numpy.sum( x101 * (x0 * x146 + x0 * x148 + x0 * (x0 * (x138 * x145 + x147) + x148) + x145 * x83) ) result[0, 0, 9] = numpy.sum( x90 * (x0 * x150 + x0 * x152 + x0 * (x0 * (x138 * x149 + x151) + x152) + x149 * x83) ) result[0, 1, 0] = numpy.sum( x101 * (x0 * x177 + x0 * (x0 * x181 + x177) + x188 + x21 * x70) ) result[0, 1, 1] = numpy.sum( x208 * (x0 * x200 + x0 * (x0 * x204 + x200) + x207 + x21 * x94) ) result[0, 1, 2] = numpy.sum( x208 * (x0 * x214 + x0 * (x0 * x217 + x214) + x105 * x21 + x218) ) result[0, 1, 3] = numpy.sum( x208 * (x0 * x223 + x0 * (x0 * x226 + x223) + x114 * x21 + x228) ) result[0, 1, 4] = numpy.sum( x242 * (x0 * x235 + x0 * (x0 * x238 + x235) + x121 * x21 + x241) ) result[0, 1, 5] = numpy.sum( x208 * (x0 * x245 + x0 * (x0 * x248 + x245) + x128 * x21 + x249) ) result[0, 1, 6] = numpy.sum( x101 * (x0 * x251 + x0 * (x0 * x254 + x251) + x135 * x21 + x255) ) result[0, 1, 7] = numpy.sum( x208 * (x0 * x257 + x0 * (x0 * x259 + x257) + x141 * x21 + x260) ) result[0, 1, 8] = numpy.sum( x208 * (x0 * x263 + x0 * (x0 * x266 + x263) + x146 * x21 + x268) ) result[0, 1, 9] = numpy.sum( x101 * (x0 * x270 + x0 * (x0 * x272 + x270) + x150 * x21 + x273) ) result[0, 2, 0] = numpy.sum( x101 * (x0 * x298 + x0 * (x0 * x301 + x298) + x22 * x70 + x308) ) result[0, 2, 1] = numpy.sum( x208 * (x0 * x313 + x0 * (x0 * x316 + x313) + x22 * x94 + x317) ) result[0, 2, 2] = numpy.sum( x208 * (x0 * x326 + x0 * (x0 * x328 + x326) + x105 * x22 + x330) ) result[0, 2, 3] = numpy.sum( x208 * (x0 * x332 + x0 * (x0 * x335 + x332) + x114 * x22 + x336) ) result[0, 2, 4] = numpy.sum( x242 * (x0 * x339 + x0 * (x0 * x343 + x339) + x121 * x22 + x344) ) result[0, 2, 5] = numpy.sum( x208 * (x0 * x349 + x0 * (x0 * x353 + x349) + x128 * x22 + x355) ) result[0, 2, 6] = numpy.sum( x101 * (x0 * x357 + x0 * (x0 * x360 + x357) + x135 * x22 + x361) ) result[0, 2, 7] = numpy.sum( x208 * (x0 * x363 + x0 * (x0 * x365 + x363) + x141 * x22 + x366) ) result[0, 2, 8] = numpy.sum( x208 * (x0 * x368 + x0 * (x0 * x370 + x368) + x146 * x22 + x371) ) result[0, 2, 9] = numpy.sum( x101 * (x0 * x373 + x0 * (x0 * x375 + x373) + x150 * x22 + x376) ) result[0, 3, 0] = numpy.sum(x101 * (x0 * x388 + x177 * x21 + x396)) result[0, 3, 1] = numpy.sum(x208 * (x0 * x405 + x200 * x21 + x409)) result[0, 3, 2] = numpy.sum(x208 * (x0 * x414 + x21 * x214 + x415)) result[0, 3, 3] = numpy.sum(x208 * (x0 * x420 + x21 * x223 + x422)) result[0, 3, 4] = numpy.sum(x242 * (x0 * x427 + x21 * x235 + x429)) result[0, 3, 5] = numpy.sum(x208 * (x0 * x433 + x21 * x245 + x434)) result[0, 3, 6] = numpy.sum(x101 * (x0 * x437 + x21 * x251 + x438)) result[0, 3, 7] = numpy.sum(x208 * (x0 * x441 + x21 * x257 + x442)) result[0, 3, 8] = numpy.sum(x208 * (x0 * x445 + x21 * x263 + x446)) result[0, 3, 9] = numpy.sum(x101 * (x0 * x449 + x21 * x270 + x450)) result[0, 4, 0] = numpy.sum(x126 * (x0 * x461 + x21 * x298 + x467)) result[0, 4, 1] = numpy.sum(x242 * (x0 * x473 + x21 * x313 + x477)) result[0, 4, 2] = numpy.sum(x242 * (x0 * x483 + x21 * x326 + x487)) result[0, 4, 3] = numpy.sum(x242 * (x0 * x492 + x21 * x332 + x496)) result[0, 4, 4] = numpy.sum(x89 * (x0 * x501 + x21 * x339 + x505)) result[0, 4, 5] = numpy.sum(x242 * (x0 * x510 + x21 * x349 + x514)) result[0, 4, 6] = numpy.sum(x126 * (x0 * x517 + x21 * x357 + x519)) result[0, 4, 7] = numpy.sum(x242 * (x0 * x522 + x21 * x363 + x524)) result[0, 4, 8] = numpy.sum(x242 * (x0 * x527 + x21 * x368 + x529)) result[0, 4, 9] = numpy.sum(x126 * (x0 * x532 + x21 * x373 + x534)) result[0, 5, 0] = numpy.sum(x101 * (x0 * x546 + x22 * x298 + x554)) result[0, 5, 1] = numpy.sum(x208 * (x0 * x559 + x22 * x313 + x560)) result[0, 5, 2] = numpy.sum(x208 * (x0 * x567 + x22 * x326 + x569)) result[0, 5, 3] = numpy.sum(x208 * (x0 * x573 + x22 * x332 + x574)) result[0, 5, 4] = numpy.sum(x242 * (x0 * x578 + x22 * x339 + x579)) result[0, 5, 5] = numpy.sum(x208 * (x0 * x585 + x22 * x349 + x587)) result[0, 5, 6] = numpy.sum(x101 * (x0 * x590 + x22 * x357 + x591)) result[0, 5, 7] = numpy.sum(x208 * (x0 * x594 + x22 * x363 + x595)) result[0, 5, 8] = numpy.sum(x208 * (x0 * x598 + x22 * x368 + x599)) result[0, 5, 9] = numpy.sum(x101 * (x0 * x602 + x22 * x373 + x603)) result[0, 6, 0] = numpy.sum(x90 * (x21 * x388 + x609)) result[0, 6, 1] = numpy.sum(x101 * (x21 * x405 + x617)) result[0, 6, 2] = numpy.sum(x101 * (x21 * x414 + x619)) result[0, 6, 3] = numpy.sum(x101 * (x21 * x420 + x623)) result[0, 6, 4] = numpy.sum(x126 * (x21 * x427 + x627)) result[0, 6, 5] = numpy.sum(x101 * (x21 * x433 + x629)) result[0, 6, 6] = numpy.sum(x90 * (x21 * x437 + x630)) result[0, 6, 7] = numpy.sum(x101 * (x21 * x441 + x631)) result[0, 6, 8] = numpy.sum(x101 * (x21 * x445 + x632)) result[0, 6, 9] = numpy.sum(x90 * (x21 * x449 + x633)) result[0, 7, 0] = numpy.sum(x101 * (x21 * x461 + x639)) result[0, 7, 1] = numpy.sum(x208 * (x21 * x473 + x644)) result[0, 7, 2] = numpy.sum(x208 * (x21 * x483 + x648)) result[0, 7, 3] = numpy.sum(x208 * (x21 * x492 + x652)) result[0, 7, 4] = numpy.sum(x242 * (x21 * x501 + x657)) result[0, 7, 5] = numpy.sum(x208 * (x21 * x510 + x661)) result[0, 7, 6] = numpy.sum(x101 * (x21 * x517 + x663)) result[0, 7, 7] = numpy.sum(x208 * (x21 * x522 + x665)) result[0, 7, 8] = numpy.sum(x208 * (x21 * x527 + x667)) result[0, 7, 9] = numpy.sum(x101 * (x21 * x532 + x669)) result[0, 8, 0] = numpy.sum(x101 * (x21 * x546 + x675)) result[0, 8, 1] = numpy.sum(x208 * (x21 * x559 + x679)) result[0, 8, 2] = numpy.sum(x208 * (x21 * x567 + x683)) result[0, 8, 3] = numpy.sum(x208 * (x21 * x573 + x687)) result[0, 8, 4] = numpy.sum(x242 * (x21 * x578 + x691)) result[0, 8, 5] = numpy.sum(x208 * (x21 * x585 + x695)) result[0, 8, 6] = numpy.sum(x101 * (x21 * x590 + x697)) result[0, 8, 7] = numpy.sum(x208 * (x21 * x594 + x699)) result[0, 8, 8] = numpy.sum(x208 * (x21 * x598 + x701)) result[0, 8, 9] = numpy.sum(x101 * (x21 * x602 + x703)) result[0, 9, 0] = numpy.sum(x90 * (x22 * x546 + x709)) result[0, 9, 1] = numpy.sum(x101 * (x22 * x559 + x711)) result[0, 9, 2] = numpy.sum(x101 * (x22 * x567 + x715)) result[0, 9, 3] = numpy.sum(x101 * (x22 * x573 + x717)) result[0, 9, 4] = numpy.sum(x126 * (x22 * x578 + x719)) result[0, 9, 5] = numpy.sum(x101 * (x22 * x585 + x723)) result[0, 9, 6] = numpy.sum(x90 * (x22 * x590 + x724)) result[0, 9, 7] = numpy.sum(x101 * (x22 * x594 + x725)) result[0, 9, 8] = numpy.sum(x101 * (x22 * x598 + x726)) result[0, 9, 9] = numpy.sum(x90 * (x22 * x602 + x727)) result[1, 0, 0] = numpy.sum( x90 * (x0 * x176 + x0 * x728 + x0 * (x0 * (x179 + x729 * x730) + x728) + x188) ) result[1, 0, 1] = numpy.sum( x101 * (x0 * x199 + x0 * x731 + x0 * (x0 * (x0 * x733 + x203) + x731) + x207) ) result[1, 0, 2] = numpy.sum( x101 * (x0 * x213 + x0 * x734 + x0 * (x0 * (x216 + x730 * x735) + x734) + x218) ) result[1, 0, 3] = numpy.sum( x101 * (x0 * x222 + x0 * x736 + x0 * (x0 * (x224 * x737 + x225) + x736) + x228) ) result[1, 0, 4] = numpy.sum( x126 * (x0 * x234 + x0 * x738 + x0 * (x0 * (x236 * x737 + x237) + x738) + x241) ) result[1, 0, 5] = numpy.sum( x101 * (x0 * x244 + x0 * x739 + x0 * (x0 * (x247 + x730 * x740) + x739) + x249) ) result[1, 0, 6] = numpy.sum( x90 * (x0 * x250 + x0 * x741 + x0 * (x0 * (x252 + x742 * x78) + x741) + x255) ) result[1, 0, 7] = numpy.sum( x101 * (x0 * x256 + x0 * x743 + x0 * (x0 * (x258 + x744 * x78) + x743) + x260) ) result[1, 0, 8] = numpy.sum( x101 * (x0 * x262 + x0 * x745 + x0 * (x0 * (x265 + x746 * x78) + x745) + x268) ) result[1, 0, 9] = numpy.sum( x90 * (x0 * x269 + x0 * x747 + x0 * (x0 * (x149 * x730 + x271) + x747) + x273) ) result[1, 1, 0] = numpy.sum(x101 * (x0 * x387 + x0 * (x0 * x750 + x387) + x396)) result[1, 1, 1] = numpy.sum(x208 * (x0 * x404 + x0 * (x0 * x752 + x404) + x409)) result[1, 1, 2] = numpy.sum(x208 * (x0 * x413 + x0 * (x0 * x754 + x413) + x415)) result[1, 1, 3] = numpy.sum(x208 * (x0 * x419 + x0 * (x0 * x757 + x419) + x422)) result[1, 1, 4] = numpy.sum(x242 * (x0 * x426 + x0 * (x0 * x759 + x426) + x429)) result[1, 1, 5] = numpy.sum(x208 * (x0 * x432 + x0 * (x0 * x761 + x432) + x434)) result[1, 1, 6] = numpy.sum(x101 * (x0 * x436 + x0 * (x0 * x763 + x436) + x438)) result[1, 1, 7] = numpy.sum(x208 * (x0 * x440 + x0 * (x0 * x765 + x440) + x442)) result[1, 1, 8] = numpy.sum(x208 * (x0 * x444 + x0 * (x0 * x767 + x444) + x446)) result[1, 1, 9] = numpy.sum(x101 * (x0 * x448 + x0 * (x0 * x769 + x448) + x450)) result[1, 2, 0] = numpy.sum(x101 * (x0 * x460 + x0 * (x0 * x772 + x460) + x467)) result[1, 2, 1] = numpy.sum(x208 * (x0 * x472 + x0 * (x0 * x774 + x472) + x477)) result[1, 2, 2] = numpy.sum(x208 * (x0 * x482 + x0 * (x0 * x776 + x482) + x487)) result[1, 2, 3] = numpy.sum(x208 * (x0 * x491 + x0 * (x0 * x779 + x491) + x496)) result[1, 2, 4] = numpy.sum(x242 * (x0 * x500 + x0 * (x0 * x781 + x500) + x505)) result[1, 2, 5] = numpy.sum(x208 * (x0 * x509 + x0 * (x0 * x783 + x509) + x514)) result[1, 2, 6] = numpy.sum(x101 * (x0 * x516 + x0 * (x0 * x785 + x516) + x519)) result[1, 2, 7] = numpy.sum(x208 * (x0 * x521 + x0 * (x0 * x787 + x521) + x524)) result[1, 2, 8] = numpy.sum(x208 * (x0 * x526 + x0 * (x0 * x789 + x526) + x529)) result[1, 2, 9] = numpy.sum(x101 * (x0 * x531 + x0 * (x0 * x791 + x531) + x534)) result[1, 3, 0] = numpy.sum(x101 * (x0 * x794 + x609)) result[1, 3, 1] = numpy.sum(x208 * (x0 * x797 + x617)) result[1, 3, 2] = numpy.sum(x208 * (x0 * x800 + x619)) result[1, 3, 3] = numpy.sum(x208 * (x0 * x803 + x623)) result[1, 3, 4] = numpy.sum(x242 * (x0 * x806 + x627)) result[1, 3, 5] = numpy.sum(x208 * (x0 * x809 + x629)) result[1, 3, 6] = numpy.sum(x101 * (x0 * x812 + x630)) result[1, 3, 7] = numpy.sum(x208 * (x0 * x815 + x631)) result[1, 3, 8] = numpy.sum(x208 * (x0 * x818 + x632)) result[1, 3, 9] = numpy.sum(x101 * (x0 * x821 + x633)) result[1, 4, 0] = numpy.sum(x126 * (x0 * x824 + x639)) result[1, 4, 1] = numpy.sum(x242 * (x0 * x827 + x644)) result[1, 4, 2] = numpy.sum(x242 * (x0 * x830 + x648)) result[1, 4, 3] = numpy.sum(x242 * (x0 * x833 + x652)) result[1, 4, 4] = numpy.sum(x89 * (x0 * x836 + x657)) result[1, 4, 5] = numpy.sum(x242 * (x0 * x839 + x661)) result[1, 4, 6] = numpy.sum(x126 * (x0 * x842 + x663)) result[1, 4, 7] = numpy.sum(x242 * (x0 * x845 + x665)) result[1, 4, 8] = numpy.sum(x242 * (x0 * x849 + x667)) result[1, 4, 9] = numpy.sum(x126 * (x0 * x852 + x669)) result[1, 5, 0] = numpy.sum(x101 * (x0 * x855 + x675)) result[1, 5, 1] = numpy.sum(x208 * (x0 * x858 + x679)) result[1, 5, 2] = numpy.sum(x208 * (x0 * x861 + x683)) result[1, 5, 3] = numpy.sum(x208 * (x0 * x864 + x687)) result[1, 5, 4] = numpy.sum(x242 * (x0 * x867 + x691)) result[1, 5, 5] = numpy.sum(x208 * (x0 * x870 + x695)) result[1, 5, 6] = numpy.sum(x101 * (x0 * x873 + x697)) result[1, 5, 7] = numpy.sum(x208 * (x0 * x876 + x699)) result[1, 5, 8] = numpy.sum(x208 * (x0 * x879 + x701)) result[1, 5, 9] = numpy.sum(x101 * (x0 * x882 + x703)) result[1, 6, 0] = numpy.sum( x90 * (x21 * x792 + x21 * x793 + x21 * x794 + x729 * x883) ) result[1, 6, 1] = numpy.sum( x101 * (x21 * x795 + x21 * x796 + x21 * x797 + x732 * x886) ) result[1, 6, 2] = numpy.sum( x101 * (x21 * x798 + x21 * x799 + x21 * x800 + x735 * x883) ) result[1, 6, 3] = numpy.sum( x101 * (x201 * x887 + x21 * x801 + x21 * x802 + x21 * x803) ) result[1, 6, 4] = numpy.sum( x126 * (x201 * x888 + x21 * x804 + x21 * x805 + x21 * x806) ) result[1, 6, 5] = numpy.sum( x101 * (x21 * x807 + x21 * x808 + x21 * x809 + x740 * x883) ) result[1, 6, 6] = numpy.sum( x90 * (x21 * x810 + x21 * x811 + x21 * x812 + x55 * (4.0 * x621 + x887 * x91)) ) result[1, 6, 7] = numpy.sum( x101 * (x21 * x813 + x21 * x814 + x21 * x815 + x55 * (4.0 * x625 + x888 * x91)) ) result[1, 6, 8] = numpy.sum( x101 * (x127 * x55 * (x884 + x885) + x21 * x816 + x21 * x817 + x21 * x818) ) result[1, 6, 9] = numpy.sum( x90 * (x149 * x883 + x21 * x819 + x21 * x820 + x21 * x821) ) result[1, 7, 0] = numpy.sum(x101 * (x21 * x823 + x21 * x824 + x22 * x792 + x890)) result[1, 7, 1] = numpy.sum(x208 * (x21 * x826 + x21 * x827 + x22 * x795 + x892)) result[1, 7, 2] = numpy.sum(x208 * (x21 * x829 + x21 * x830 + x22 * x798 + x894)) result[1, 7, 3] = numpy.sum(x208 * (x21 * x832 + x21 * x833 + x22 * x801 + x896)) result[1, 7, 4] = numpy.sum(x242 * (x21 * x835 + x21 * x836 + x22 * x804 + x898)) result[1, 7, 5] = numpy.sum(x208 * (x21 * x838 + x21 * x839 + x22 * x807 + x900)) result[1, 7, 6] = numpy.sum(x101 * (x21 * x841 + x21 * x842 + x22 * x810 + x901)) result[1, 7, 7] = numpy.sum(x208 * (x21 * x844 + x21 * x845 + x22 * x813 + x902)) result[1, 7, 8] = numpy.sum(x208 * (x21 * x848 + x21 * x849 + x22 * x816 + x903)) result[1, 7, 9] = numpy.sum(x101 * (x21 * x851 + x21 * x852 + x22 * x819 + x904)) result[1, 8, 0] = numpy.sum(x101 * (x21 * x855 + x22 * x823 + x906)) result[1, 8, 1] = numpy.sum(x208 * (x21 * x858 + x22 * x826 + x908)) result[1, 8, 2] = numpy.sum(x208 * (x21 * x861 + x22 * x829 + x910)) result[1, 8, 3] = numpy.sum(x208 * (x21 * x864 + x22 * x832 + x912)) result[1, 8, 4] = numpy.sum(x242 * (x21 * x867 + x22 * x835 + x914)) result[1, 8, 5] = numpy.sum(x208 * (x21 * x870 + x22 * x838 + x916)) result[1, 8, 6] = numpy.sum(x101 * (x21 * x873 + x22 * x841 + x917)) result[1, 8, 7] = numpy.sum(x208 * (x21 * x876 + x22 * x844 + x918)) result[1, 8, 8] = numpy.sum(x208 * (x21 * x879 + x22 * x848 + x919)) result[1, 8, 9] = numpy.sum(x101 * (x21 * x882 + x22 * x851 + x920)) result[1, 9, 0] = numpy.sum(x90 * (x22 * x855 + x922)) result[1, 9, 1] = numpy.sum(x101 * (x22 * x858 + x924)) result[1, 9, 2] = numpy.sum(x101 * (x22 * x861 + x926)) result[1, 9, 3] = numpy.sum(x101 * (x22 * x864 + x928)) result[1, 9, 4] = numpy.sum(x126 * (x22 * x867 + x930)) result[1, 9, 5] = numpy.sum(x101 * (x22 * x870 + x932)) result[1, 9, 6] = numpy.sum(x90 * (x22 * x873 + x933)) result[1, 9, 7] = numpy.sum(x101 * (x22 * x876 + x934)) result[1, 9, 8] = numpy.sum(x101 * (x22 * x879 + x935)) result[1, 9, 9] = numpy.sum(x90 * (x22 * x882 + x936)) result[2, 0, 0] = numpy.sum( x90 * (x0 * x297 + x0 * x937 + x0 * (x0 * (x299 + x729 * x938) + x937) + x308) ) result[2, 0, 1] = numpy.sum( x101 * (x0 * x312 + x0 * x939 + x0 * (x0 * (x315 + x938 * x940) + x939) + x317) ) result[2, 0, 2] = numpy.sum( x101 * (x0 * x325 + x0 * x941 + x0 * (x0 * (x327 + x732 * x942) + x941) + x330) ) result[2, 0, 3] = numpy.sum( x101 * (x0 * x331 + x0 * x943 + x0 * (x0 * (x334 + x938 * x944) + x943) + x336) ) result[2, 0, 4] = numpy.sum( x126 * (x0 * x338 + x0 * x945 + x0 * (x0 * (x342 + x942 * x946) + x945) + x344) ) result[2, 0, 5] = numpy.sum( x101 * (x0 * x348 + x0 * x947 + x0 * (x0 * (x350 * x737 + x352) + x947) + x355) ) result[2, 0, 6] = numpy.sum( x90 * (x0 * x356 + x0 * x948 + x0 * (x0 * (x134 * x938 + x358) + x948) + x361) ) result[2, 0, 7] = numpy.sum( x101 * (x0 * x362 + x0 * x949 + x0 * (x0 * (x139 * x942 + x364) + x949) + x366) ) result[2, 0, 8] = numpy.sum( x101 * (x0 * x367 + x0 * x950 + x0 * (x0 * (x0 * x951 + x369) + x950) + x371) ) result[2, 0, 9] = numpy.sum( x90 * (x0 * x372 + x0 * x952 + x0 * (x0 * (x374 + x78 * x953) + x952) + x376) ) result[2, 1, 0] = numpy.sum( x101 * (x0 * x954 + x0 * (x0 * x956 + x954) + x21 * x297 + x466) ) result[2, 1, 1] = numpy.sum( x208 * (x0 * x957 + x0 * (x0 * x958 + x957) + x21 * x312 + x476) ) result[2, 1, 2] = numpy.sum( x208 * (x0 * x959 + x0 * (x0 * x961 + x959) + x21 * x325 + x486) ) result[2, 1, 3] = numpy.sum( x208 * (x0 * x962 + x0 * (x0 * x963 + x962) + x21 * x331 + x495) ) result[2, 1, 4] = numpy.sum( x242 * (x0 * x964 + x0 * (x0 * x965 + x964) + x21 * x338 + x504) ) result[2, 1, 5] = numpy.sum( x208 * (x0 * x966 + x0 * (x0 * x967 + x966) + x21 * x348 + x513) ) result[2, 1, 6] = numpy.sum( x101 * (x0 * x968 + x0 * (x0 * x969 + x968) + x21 * x356 + x518) ) result[2, 1, 7] = numpy.sum( x208 * (x0 * x970 + x0 * (x0 * x971 + x970) + x21 * x362 + x523) ) result[2, 1, 8] = numpy.sum( x208 * (x0 * x972 + x0 * (x0 * x973 + x972) + x21 * x367 + x528) ) result[2, 1, 9] = numpy.sum( x101 * (x0 * x974 + x0 * (x0 * x975 + x974) + x21 * x372 + x533) ) result[2, 2, 0] = numpy.sum(x101 * (x0 * x545 + x0 * (x0 * x978 + x545) + x554)) result[2, 2, 1] = numpy.sum(x208 * (x0 * x558 + x0 * (x0 * x980 + x558) + x560)) result[2, 2, 2] = numpy.sum(x208 * (x0 * x566 + x0 * (x0 * x983 + x566) + x569)) result[2, 2, 3] = numpy.sum(x208 * (x0 * x572 + x0 * (x0 * x985 + x572) + x574)) result[2, 2, 4] = numpy.sum(x242 * (x0 * x577 + x0 * (x0 * x987 + x577) + x579)) result[2, 2, 5] = numpy.sum(x208 * (x0 * x584 + x0 * (x0 * x989 + x584) + x587)) result[2, 2, 6] = numpy.sum(x101 * (x0 * x589 + x0 * (x0 * x991 + x589) + x591)) result[2, 2, 7] = numpy.sum(x208 * (x0 * x593 + x0 * (x0 * x993 + x593) + x595)) result[2, 2, 8] = numpy.sum(x208 * (x0 * x597 + x0 * (x0 * x995 + x597) + x599)) result[2, 2, 9] = numpy.sum(x101 * (x0 * x601 + x0 * (x0 * x997 + x601) + x603)) result[2, 3, 0] = numpy.sum(x101 * (x0 * x999 + x21 * x459 + x21 * x954 + x638)) result[2, 3, 1] = numpy.sum(x208 * (x0 * x1001 + x21 * x471 + x21 * x957 + x643)) result[2, 3, 2] = numpy.sum(x208 * (x0 * x1003 + x21 * x481 + x21 * x959 + x647)) result[2, 3, 3] = numpy.sum(x208 * (x0 * x1005 + x21 * x490 + x21 * x962 + x651)) result[2, 3, 4] = numpy.sum(x242 * (x0 * x1007 + x21 * x499 + x21 * x964 + x656)) result[2, 3, 5] = numpy.sum(x208 * (x0 * x1009 + x21 * x508 + x21 * x966 + x660)) result[2, 3, 6] = numpy.sum(x101 * (x0 * x1011 + x21 * x515 + x21 * x968 + x662)) result[2, 3, 7] = numpy.sum(x208 * (x0 * x1013 + x21 * x520 + x21 * x970 + x664)) result[2, 3, 8] = numpy.sum(x208 * (x0 * x1015 + x21 * x525 + x21 * x972 + x666)) result[2, 3, 9] = numpy.sum(x101 * (x0 * x1017 + x21 * x530 + x21 * x974 + x668)) result[2, 4, 0] = numpy.sum(x126 * (x0 * x1018 + x21 * x545 + x674)) result[2, 4, 1] = numpy.sum(x242 * (x0 * x1019 + x21 * x558 + x678)) result[2, 4, 2] = numpy.sum(x242 * (x0 * x1020 + x21 * x566 + x682)) result[2, 4, 3] = numpy.sum(x242 * (x0 * x1021 + x21 * x572 + x686)) result[2, 4, 4] = numpy.sum(x89 * (x0 * x1022 + x21 * x577 + x690)) result[2, 4, 5] = numpy.sum(x242 * (x0 * x1023 + x21 * x584 + x694)) result[2, 4, 6] = numpy.sum(x126 * (x0 * x1024 + x21 * x589 + x696)) result[2, 4, 7] = numpy.sum(x242 * (x0 * x1025 + x21 * x593 + x698)) result[2, 4, 8] = numpy.sum(x242 * (x0 * x1026 + x21 * x597 + x700)) result[2, 4, 9] = numpy.sum(x126 * (x0 * x1027 + x21 * x601 + x702)) result[2, 5, 0] = numpy.sum(x101 * (x0 * x1030 + x709)) result[2, 5, 1] = numpy.sum(x208 * (x0 * x1033 + x711)) result[2, 5, 2] = numpy.sum(x208 * (x0 * x1036 + x715)) result[2, 5, 3] = numpy.sum(x208 * (x0 * x1039 + x717)) result[2, 5, 4] = numpy.sum(x242 * (x0 * x1042 + x719)) result[2, 5, 5] = numpy.sum(x208 * (x0 * x1045 + x723)) result[2, 5, 6] = numpy.sum(x101 * (x0 * x1048 + x724)) result[2, 5, 7] = numpy.sum(x208 * (x0 * x1051 + x725)) result[2, 5, 8] = numpy.sum(x208 * (x0 * x1054 + x726)) result[2, 5, 9] = numpy.sum(x101 * (x0 * x1057 + x727)) result[2, 6, 0] = numpy.sum(x90 * (x21 * x822 + x21 * x998 + x21 * x999 + x890)) result[2, 6, 1] = numpy.sum(x101 * (x1000 * x21 + x1001 * x21 + x21 * x825 + x892)) result[2, 6, 2] = numpy.sum(x101 * (x1002 * x21 + x1003 * x21 + x21 * x828 + x894)) result[2, 6, 3] = numpy.sum(x101 * (x1004 * x21 + x1005 * x21 + x21 * x831 + x896)) result[2, 6, 4] = numpy.sum(x126 * (x1006 * x21 + x1007 * x21 + x21 * x834 + x898)) result[2, 6, 5] = numpy.sum(x101 * (x1008 * x21 + x1009 * x21 + x21 * x837 + x900)) result[2, 6, 6] = numpy.sum(x90 * (x1010 * x21 + x1011 * x21 + x21 * x840 + x901)) result[2, 6, 7] = numpy.sum(x101 * (x1012 * x21 + x1013 * x21 + x21 * x843 + x902)) result[2, 6, 8] = numpy.sum(x101 * (x1014 * x21 + x1015 * x21 + x21 * x847 + x903)) result[2, 6, 9] = numpy.sum(x90 * (x1016 * x21 + x1017 * x21 + x21 * x850 + x904)) result[2, 7, 0] = numpy.sum(x101 * (x1018 * x21 + x21 * x854 + x906)) result[2, 7, 1] = numpy.sum(x208 * (x1019 * x21 + x21 * x857 + x908)) result[2, 7, 2] = numpy.sum(x208 * (x1020 * x21 + x21 * x860 + x910)) result[2, 7, 3] = numpy.sum(x208 * (x1021 * x21 + x21 * x863 + x912)) result[2, 7, 4] = numpy.sum(x242 * (x1022 * x21 + x21 * x866 + x914)) result[2, 7, 5] = numpy.sum(x208 * (x1023 * x21 + x21 * x869 + x916)) result[2, 7, 6] = numpy.sum(x101 * (x1024 * x21 + x21 * x872 + x917)) result[2, 7, 7] = numpy.sum(x208 * (x1025 * x21 + x21 * x875 + x918)) result[2, 7, 8] = numpy.sum(x208 * (x1026 * x21 + x21 * x878 + x919)) result[2, 7, 9] = numpy.sum(x101 * (x1027 * x21 + x21 * x881 + x920)) result[2, 8, 0] = numpy.sum(x101 * (x1030 * x21 + x922)) result[2, 8, 1] = numpy.sum(x208 * (x1033 * x21 + x924)) result[2, 8, 2] = numpy.sum(x208 * (x1036 * x21 + x926)) result[2, 8, 3] = numpy.sum(x208 * (x1039 * x21 + x928)) result[2, 8, 4] = numpy.sum(x242 * (x1042 * x21 + x930)) result[2, 8, 5] = numpy.sum(x208 * (x1045 * x21 + x932)) result[2, 8, 6] = numpy.sum(x101 * (x1048 * x21 + x933)) result[2, 8, 7] = numpy.sum(x208 * (x1051 * x21 + x934)) result[2, 8, 8] = numpy.sum(x208 * (x1054 * x21 + x935)) result[2, 8, 9] = numpy.sum(x101 * (x1057 * x21 + x936)) result[2, 9, 0] = numpy.sum( x90 * (x1028 * x22 + x1029 * x22 + x1030 * x22 + x1058 * x729) ) result[2, 9, 1] = numpy.sum( x101 * (x1031 * x22 + x1032 * x22 + x1033 * x22 + x1058 * x940) ) result[2, 9, 2] = numpy.sum( x101 * (x1034 * x22 + x1035 * x22 + x1036 * x22 + x1059 * x732) ) result[2, 9, 3] = numpy.sum( x101 * (x1037 * x22 + x1038 * x22 + x1039 * x22 + x1058 * x944) ) result[2, 9, 4] = numpy.sum( x126 * (x1040 * x22 + x1041 * x22 + x1042 * x22 + x1059 * x946) ) result[2, 9, 5] = numpy.sum( x101 * (x1043 * x22 + x1044 * x22 + x1045 * x22 + x1060 * x201) ) result[2, 9, 6] = numpy.sum( x90 * (x1046 * x22 + x1047 * x22 + x1048 * x22 + x1058 * x134) ) result[2, 9, 7] = numpy.sum( x101 * (x1049 * x22 + x1050 * x22 + x1051 * x22 + x1059 * x139) ) result[2, 9, 8] = numpy.sum( x101 * (x1052 * x22 + x1053 * x22 + x1054 * x22 + x1060 * x119) ) result[2, 9, 9] = numpy.sum( x90 * (x1055 * x22 + x1056 * x22 + x1057 * x22 + x55 * (x102 * x1060 + 4.0 * x721)) ) return result
[docs] def int3c2e3d_sph_134(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (pf|g) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((3, 10, 15), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = -x3 - C[0] x5 = -x3 - A[0] x6 = 0.5 / (ax + bx) x7 = x4**2 x8 = -x2 * (ax * A[1] + bx * B[1]) x9 = -x8 - C[1] x10 = x9**2 x11 = -x2 * (ax * A[2] + bx * B[2]) x12 = -x11 - C[2] x13 = x12**2 x14 = cx + x1 x15 = x14 ** (-1.0) x16 = cx * x15 x17 = x1 * x16 * (x10 + x13 + x7) x18 = boys(5, x17) x19 = x14 ** (-1.5) x20 = 17.49341832762486 x21 = A[1] - B[1] x22 = A[2] - B[2] x23 = numpy.exp(-ax * bx * x2 * (x0**2 + x21**2 + x22**2)) x24 = x20 * x23 x25 = x2 * x24 x26 = 2.0 * x19 * x25 x27 = x18 * x26 x28 = cx ** (-1.0) x29 = x14 ** (-0.5) x30 = boys(4, x17) x31 = 2.0 * x2 * x20 * x23 * x28 * x29 * x30 - x27 x32 = x31 * x6 x33 = -2.0 * x2 * x20 * x23 * x28 * x29 * x30 * x5 + x27 * x4 x34 = -x33 x35 = boys(6, x17) x36 = x26 * x35 x37 = -2.0 * x18 * x2 * x20 * x23 * x28 * x29 * x5 + x36 * x4 x38 = -x37 x39 = x16 * x38 x40 = x39 * x4 x41 = x32 + x34 * x5 - x40 x42 = 2.0 * x6 x43 = x6 * (2.0 * x18 * x2 * x20 * x23 * x28 * x29 - x36) x44 = boys(7, x17) x45 = x26 * x44 x46 = 2.0 * x2 * x20 * x23 * x28 * x29 * x35 * x5 - x4 * x45 x47 = x16 * x46 x48 = x38 * x5 - x4 * x47 + x43 x49 = x16 * x48 x50 = -x4 * x49 + x41 * x5 - x42 * (x33 + x39) x51 = x4 * x50 x52 = x41 * x6 x53 = 3.0 * x52 x54 = x51 + x53 x55 = x1 * x15 x56 = x4 * x55 x57 = x4 * x41 x58 = x34 * x6 x59 = 2.0 * x58 x60 = x57 + x59 x61 = 3.0 * x6 x62 = x55 * x61 x63 = x54 * x56 + x60 * x62 x64 = x34 * x4 x65 = x28 * x30 * x42 x66 = x25 * x29 * x65 x67 = x64 + x66 x68 = x42 * x55 x69 = x56 * x60 + x67 * x68 x70 = x56 * x63 + x62 * x69 x71 = x24 * x65 x72 = x19 * x71 x73 = x4 * x72 + x56 * x67 x74 = x56 * x69 + x68 * x73 x75 = x55 * (x56 * x70 + x62 * x74) x76 = x7 * x71 x77 = x1 * x14 ** (-2.5) x78 = x56 * x73 + x76 * x77 x79 = x55 * (x56 * x74 + x68 * x78) x80 = x0 * x79 + x75 x81 = x4**3 x82 = x1**2 x83 = x14 ** (-3.5) * x82 x84 = x71 * x83 x85 = x56 * x78 + x81 * x84 x86 = x0 * x55 x87 = -x31 * x6 x88 = x6 * (2.0 * x2 * x20 * x23 * x28 * x29 * x35 - x45) x89 = x26 * boys(8, x17) x90 = x16 * x4 x91 = ( x5 * x50 - x61 * (-x34 * x5 + x40 + x49 + x87) + x90 * ( x42 * (x37 + x47) - x48 * x5 + x90 * ( x46 * x5 + x88 - x90 * (2.0 * x2 * x20 * x23 * x28 * x29 * x44 * x5 - x4 * x89) ) ) ) x92 = x4 * x91 x93 = x50 * x6 x94 = 4.0 * x93 x95 = x55 * x6 x96 = 4.0 * x95 x97 = da * db * dc x98 = 0.009523809523809524 * x97 x99 = 2.645751311064591 * x98 x100 = x55 * x9 x101 = x100 * (x51 + x53) x102 = x100 * (x57 + x59) x103 = x101 * x56 + x102 * x62 x104 = x72 * x9 x105 = x100 * x64 + x104 x106 = x102 * x56 + x105 * x68 x107 = x55 * (x103 * x56 + x106 * x62) x108 = x71 * x77 x109 = x108 * x4 x110 = x105 * x56 + x109 * x9 x111 = x55 * (x106 * x56 + x110 * x68) x112 = x0 * x111 + x107 x113 = x76 * x83 x114 = x110 * x56 + x113 * x9 x115 = 0.06666666666666667 * x97 x116 = x12 * x55 x117 = x116 * (x51 + x53) x118 = x116 * (x57 + x59) x119 = x117 * x56 + x118 * x62 x120 = x12 * x72 x121 = x116 * x64 + x120 x122 = x118 * x56 + x121 * x68 x123 = x55 * (x119 * x56 + x122 * x62) x124 = x109 * x12 + x121 * x56 x125 = x55 * (x122 * x56 + x124 * x68) x126 = x0 * x125 + x123 x127 = x113 * x12 + x124 * x56 x128 = x82 / x14**2 x129 = x10 * x128 x130 = x129 * (x51 + x53) x131 = x129 * (x57 + x59) x132 = x55 * (x130 * x56 + x131 * x62) x133 = x10 * x108 x134 = x129 * x64 + x133 x135 = x55 * (x131 * x56 + x134 * x68) x136 = x0 * x135 + x132 x137 = x10 * x84 x138 = x134 * x56 + x137 * x4 x139 = 3.872983346207417 x140 = 0.02222222222222222 * x139 * x97 x141 = x128 * x9 x142 = x12 * x141 x143 = x142 * (x51 + x53) x144 = x142 * (x57 + x59) x145 = x55 * (x143 * x56 + x144 * x62) x146 = x12 * x9 x147 = x108 * x146 x148 = x142 * x64 + x147 x149 = x55 * (x144 * x56 + x148 * x68) x150 = x0 * x149 + x145 x151 = x146 * x4 * x84 + x148 * x56 x152 = 2.23606797749979 * x115 x153 = x128 * x13 x154 = x153 * (x51 + x53) x155 = x153 * (x57 + x59) x156 = x55 * (x154 * x56 + x155 * x62) x157 = x108 * x13 x158 = x153 * x64 + x157 x159 = x55 * (x155 * x56 + x158 * x68) x160 = x0 * x159 + x156 x161 = x13 * x4 x162 = x158 * x56 + x161 * x84 x163 = x9**3 x164 = x1**3 / x14**3 x165 = x163 * x164 x166 = x165 * x55 * (x51 + x53) x167 = x165 * x55 * (x57 + x59) x168 = x0 * x167 + x166 x169 = x163 * x84 x170 = x165 * x64 + x169 x171 = x10 * x164 x172 = x12 * x171 x173 = x172 * x55 * (x51 + x53) x174 = x172 * x55 * (x57 + x59) x175 = x0 * x174 + x173 x176 = x12 * x137 x177 = x172 * x64 + x176 x178 = x164 * x9 x179 = x13 * x178 x180 = x179 * x55 * (x51 + x53) x181 = x179 * x55 * (x57 + x59) x182 = x0 * x181 + x180 x183 = x13 * x84 * x9 x184 = x179 * x64 + x183 x185 = x12**3 x186 = x164 * x185 x187 = x186 * x55 * (x51 + x53) x188 = x186 * x55 * (x57 + x59) x189 = x0 * x188 + x187 x190 = x185 * x84 x191 = x186 * x64 + x190 x192 = x1**4 / x14**4 x193 = x192 * x9**4 x194 = x193 * x50 x195 = x193 * x41 x196 = x0 * x195 + x194 x197 = x0 * x34 x198 = x163 * x192 x199 = x12 * x198 x200 = x199 * x50 x201 = x199 * x41 x202 = x0 * x201 + x200 x203 = x192 * x50 x204 = x10 * x13 x205 = x203 * x204 x206 = x192 * x204 x207 = x206 * x41 x208 = x0 * x207 + x205 x209 = x185 * x9 x210 = x203 * x209 x211 = x192 * x209 x212 = x211 * x41 x213 = x0 * x212 + x210 x214 = x12**4 * x192 x215 = x214 * x50 x216 = x214 * x41 x217 = x0 * x216 + x215 x218 = -x8 - A[1] x219 = -2.0 * x18 * x2 * x20 * x218 * x23 * x28 * x29 + x36 * x9 x220 = -x219 x221 = x16 * x220 x222 = -2.0 * x2 * x20 * x218 * x23 * x28 * x29 * x30 + x27 * x9 x223 = -x6 * (x221 + x222) x224 = -x222 x225 = x221 * x4 - x224 * x5 x226 = -x225 x227 = 2.0 * x2 * x20 * x218 * x23 * x28 * x29 * x35 - x45 * x9 x228 = x16 * x227 x229 = x220 * x5 - x228 * x4 x230 = x16 * x229 x231 = x223 + x226 * x5 - x230 * x4 x232 = x231 * x4 x233 = x226 * x6 x234 = 2.0 * x233 x235 = x232 + x234 x236 = x224 * x6 x237 = x226 * x4 x238 = x236 + x237 x239 = x235 * x56 + x238 * x68 x240 = x56 * (x236 + x238) x241 = x239 * x56 + x240 * x68 x242 = x128 * x7 x243 = x236 * x242 + x240 * x56 x244 = x55 * (x241 * x56 + x243 * x68) x245 = x21 * x79 + x244 x246 = x164 * x81 x247 = x55 * (x236 * x246 + x243 * x56) x248 = x21 * x55 x249 = x247 + x248 * x85 x250 = -x6 * (x219 + x228) x251 = 2.0 * x2 * x20 * x218 * x23 * x28 * x29 * x44 - x89 * x9 x252 = ( x231 * x5 - x42 * (x225 + x230) - x90 * (x229 * x5 + x250 - x90 * (x227 * x5 - x251 * x90)) ) x253 = x252 * x4 x254 = x231 * x6 x255 = 3.0 * x254 x256 = x55 * ( x241 * x62 + x56 * (x239 * x62 + x56 * (x235 * x62 + x56 * (x253 + x255))) ) x257 = 5.916079783099616 * x98 x258 = x231 * x9 x259 = x258 + x52 x260 = x226 * x9 x261 = x260 + x58 x262 = x261 * x68 x263 = x259 * x56 + x262 x264 = x224 * x9 x265 = x264 + x66 x266 = x265 * x55 x267 = x261 * x56 + x266 * x6 x268 = x263 * x56 + x267 * x68 x269 = x128 * x4 x270 = x265 * x6 x271 = x267 * x56 + x269 * x270 x272 = x55 * (x268 * x56 + x271 * x68) x273 = x111 * x21 + x272 x274 = x164 * x7 x275 = x55 * (x270 * x274 + x271 * x56) x276 = x114 * x248 + x275 x277 = x252 * x9 x278 = x277 + x93 x279 = x55 * (x268 * x62 + x56 * (x263 * x62 + x56 * (x259 * x62 + x278 * x56))) x280 = x116 * x234 x281 = x116 * x232 + x280 x282 = x116 * x236 x283 = x116 * x237 + x282 x284 = x281 * x56 + x283 * x68 x285 = x12 * x236 x286 = x269 * x285 + x283 * x56 x287 = x55 * (x284 * x56 + x286 * x68) x288 = x125 * x21 + x287 x289 = x55 * (x274 * x285 + x286 * x56) x290 = x127 * x248 + x289 x291 = x55 * (x284 * x62 + x56 * (x116 * x56 * (x253 + x255) + x281 * x62)) x292 = x100 * (x259 + x52) x293 = x100 * (x261 + x58) x294 = x293 * x68 x295 = x292 * x56 + x294 x296 = x104 + x266 * x9 x297 = x293 * x56 + x296 * x95 x298 = x55 * (x295 * x56 + x297 * x68) x299 = x135 * x21 + x298 x300 = x269 * x6 x301 = x55 * (x296 * x300 + x297 * x56) x302 = x138 * x248 + x301 x303 = x100 * (x278 + x93) x304 = x55 * (x295 * x62 + x56 * (x292 * x62 + x303 * x56)) x305 = 1.732050807568877 x306 = 0.1111111111111111 * x305 * x97 x307 = x116 * x52 x308 = x116 * x258 + x307 x309 = x116 * x58 x310 = x116 * x260 + x309 x311 = x310 * x68 x312 = x308 * x56 + x311 x313 = x116 * x264 + x120 x314 = x310 * x56 + x313 * x95 x315 = x55 * (x312 * x56 + x314 * x68) x316 = x149 * x21 + x315 x317 = x55 * (x300 * x313 + x314 * x56) x318 = x151 * x248 + x317 x319 = x116 * x93 x320 = x116 * x277 + x319 x321 = x55 * (x312 * x62 + x56 * (x308 * x62 + x320 * x56)) x322 = 0.3333333333333333 * x97 x323 = x153 * x234 x324 = x153 * x232 + x323 x325 = x153 * x236 x326 = x153 * x237 + x325 x327 = x55 * (x324 * x56 + x326 * x68) x328 = x159 * x21 + x327 x329 = x161 * x164 x330 = x55 * (x236 * x329 + x326 * x56) x331 = x162 * x248 + x330 x332 = x55 * (x153 * x56 * (x253 + x255) + x324 * x62) x333 = x100 * x292 + x129 * x52 x334 = x100 * x293 + x129 * x58 x335 = x334 * x68 x336 = x55 * (x333 * x56 + x335) x337 = x167 * x21 + x336 x338 = x100 * x296 + x133 x339 = x55 * (x334 * x56 + x338 * x95) x340 = x170 * x248 + x339 x341 = x100 * x303 + x129 * x93 x342 = x55 * (x333 * x62 + x341 * x56) x343 = x100 * x308 + x142 * x52 x344 = x100 * x310 + x142 * x58 x345 = x344 * x68 x346 = x55 * (x343 * x56 + x345) x347 = x174 * x21 + x346 x348 = x100 * x313 + x147 x349 = x55 * (x344 * x56 + x348 * x95) x350 = x177 * x248 + x349 x351 = x100 * x320 + x142 * x93 x352 = x55 * (x343 * x62 + x351 * x56) x353 = x153 * x52 x354 = x153 * x258 + x353 x355 = x153 * x58 x356 = x153 * x260 + x355 x357 = x356 * x68 x358 = x55 * (x354 * x56 + x357) x359 = x181 * x21 + x358 x360 = x153 * x264 + x157 x361 = x55 * (x356 * x56 + x360 * x95) x362 = x184 * x248 + x361 x363 = x153 * x93 x364 = x153 * x277 + x363 x365 = x55 * (x354 * x62 + x364 * x56) x366 = x186 * x234 x367 = x55 * (x186 * x232 + x366) x368 = x188 * x21 + x367 x369 = x186 * x236 x370 = x55 * (x186 * x237 + x369) x371 = x191 * x248 + x370 x372 = x186 * x55 * (x253 + x255) x373 = x55 * (x100 * x333 + x165 * x52) x374 = x195 * x21 + x373 x375 = x55 * (x100 * x334 + x165 * x58) x376 = x21 * x34 x377 = x193 * x376 + x375 x378 = x55 * (x100 * x341 + x165 * x93) x379 = x55 * (x100 * x343 + x172 * x52) x380 = x201 * x21 + x379 x381 = x55 * (x100 * x344 + x172 * x58) x382 = x199 * x376 + x381 x383 = x55 * (x100 * x351 + x172 * x93) x384 = x55 * (x100 * x354 + x179 * x52) x385 = x207 * x21 + x384 x386 = x55 * (x100 * x356 + x179 * x58) x387 = x206 * x376 + x386 x388 = x55 * (x100 * x364 + x179 * x93) x389 = x186 * x52 x390 = x55 * (x186 * x258 + x389) x391 = x21 * x212 + x390 x392 = x186 * x58 x393 = x55 * (x186 * x260 + x392) x394 = x211 * x376 + x393 x395 = x186 * x93 x396 = x55 * (x186 * x277 + x395) x397 = x214 * x231 x398 = x21 * x216 + x397 x399 = x214 * x226 x400 = x214 * x376 + x399 x401 = x214 * x252 x402 = -x11 - A[2] x403 = x12 * x36 - 2.0 * x18 * x2 * x20 * x23 * x28 * x29 * x402 x404 = -x403 x405 = x16 * x404 x406 = x12 * x27 - 2.0 * x2 * x20 * x23 * x28 * x29 * x30 * x402 x407 = -x6 * (x405 + x406) x408 = -x406 x409 = x4 * x405 - x408 * x5 x410 = -x409 x411 = -x12 * x45 + 2.0 * x2 * x20 * x23 * x28 * x29 * x35 * x402 x412 = x16 * x411 x413 = -x4 * x412 + x404 * x5 x414 = x16 * x413 x415 = -x4 * x414 + x407 + x410 * x5 x416 = x4 * x415 x417 = x410 * x6 x418 = 2.0 * x417 x419 = x416 + x418 x420 = x408 * x6 x421 = x4 * x410 x422 = x420 + x421 x423 = x419 * x56 + x422 * x68 x424 = x56 * (x420 + x422) x425 = x423 * x56 + x424 * x68 x426 = x242 * x420 + x424 * x56 x427 = x55 * (x425 * x56 + x426 * x68) x428 = x22 * x79 + x427 x429 = x55 * (x246 * x420 + x426 * x56) x430 = x22 * x55 x431 = x429 + x430 * x85 x432 = -x6 * (x403 + x412) x433 = -x12 * x89 + 2.0 * x2 * x20 * x23 * x28 * x29 * x402 * x44 x434 = ( x415 * x5 - x42 * (x409 + x414) - x90 * (x413 * x5 + x432 - x90 * (x411 * x5 - x433 * x90)) ) x435 = x4 * x434 x436 = x415 * x6 x437 = 3.0 * x436 x438 = x55 * ( x425 * x62 + x56 * (x423 * x62 + x56 * (x419 * x62 + x56 * (x435 + x437))) ) x439 = x100 * (x416 + x418) x440 = x100 * x420 x441 = x100 * x421 + x440 x442 = x439 * x56 + x441 * x68 x443 = x141 * x4 x444 = x420 * x443 + x441 * x56 x445 = x55 * (x442 * x56 + x444 * x68) x446 = x111 * x22 + x445 x447 = x274 * x9 x448 = x55 * (x420 * x447 + x444 * x56) x449 = x114 * x430 + x448 x450 = x55 * (x442 * x62 + x56 * (x100 * x56 * (x435 + x437) + x439 * x62)) x451 = x12 * x415 + x52 x452 = x12 * x410 + x58 x453 = x452 * x68 x454 = x451 * x56 + x453 x455 = x12 * x408 + x66 x456 = x455 * x95 x457 = x452 * x56 + x456 x458 = x454 * x56 + x457 * x68 x459 = x300 * x455 + x457 * x56 x460 = x55 * (x458 * x56 + x459 * x68) x461 = x125 * x22 + x460 x462 = x455 * x6 x463 = x55 * (x274 * x462 + x459 * x56) x464 = x127 * x430 + x463 x465 = x12 * x434 + x93 x466 = x55 * (x458 * x62 + x56 * (x454 * x62 + x56 * (x451 * x62 + x465 * x56))) x467 = x129 * (x416 + x418) x468 = x129 * x420 x469 = x129 * x421 + x468 x470 = x55 * (x467 * x56 + x469 * x68) x471 = x135 * x22 + x470 x472 = x171 * x4 x473 = x55 * (x420 * x472 + x469 * x56) x474 = x138 * x430 + x473 x475 = x55 * (x129 * x56 * (x435 + x437) + x467 * x62) x476 = x42 * x452 x477 = x141 * x476 + x443 * x451 x478 = x141 * x462 x479 = x443 * x452 + x478 x480 = x55 * (x477 * x56 + x479 * x68) x481 = x149 * x22 + x480 x482 = x178 * x4 x483 = x55 * (x462 * x482 + x479 * x56) x484 = x151 * x430 + x483 x485 = x451 * x61 x486 = x55 * (x477 * x62 + x56 * (x141 * x485 + x443 * x465)) x487 = x116 * x451 + x307 x488 = x116 * x452 + x309 x489 = x488 * x68 x490 = x487 * x56 + x489 x491 = x116 * x455 + x120 x492 = x491 * x95 x493 = x488 * x56 + x492 x494 = x55 * (x490 * x56 + x493 * x68) x495 = x159 * x22 + x494 x496 = x55 * (x300 * x491 + x493 * x56) x497 = x162 * x430 + x496 x498 = x116 * x465 + x319 x499 = x55 * (x490 * x62 + x56 * (x487 * x62 + x498 * x56)) x500 = x165 * x55 * (x416 + x418) x501 = x167 * x22 + x500 x502 = x165 * x420 x503 = x55 * (x165 * x421 + x502) x504 = x170 * x430 + x503 x505 = x165 * x55 * (x435 + x437) x506 = x55 * (x171 * x476 + x451 * x472) x507 = x174 * x22 + x506 x508 = x171 * x462 x509 = x55 * (x452 * x472 + x508) x510 = x177 * x430 + x509 x511 = x55 * (x171 * x485 + x465 * x472) x512 = x141 * x42 x513 = x55 * (x443 * x487 + x488 * x512) x514 = x181 * x22 + x513 x515 = x141 * x6 x516 = x491 * x515 x517 = x55 * (x443 * x488 + x516) x518 = x184 * x430 + x517 x519 = x55 * (x141 * x487 * x61 + x443 * x498) x520 = x116 * x487 + x353 x521 = x116 * x488 + x355 x522 = x521 * x68 x523 = x55 * (x520 * x56 + x522) x524 = x188 * x22 + x523 x525 = x116 * x491 + x157 x526 = x525 * x95 x527 = x55 * (x521 * x56 + x526) x528 = x191 * x430 + x527 x529 = x116 * x498 + x363 x530 = x55 * (x520 * x62 + x529 * x56) x531 = x193 * x415 x532 = x195 * x22 + x531 x533 = x193 * x410 x534 = x22 * x34 x535 = x193 * x534 + x533 x536 = x193 * x434 x537 = x198 * x451 x538 = x201 * x22 + x537 x539 = x198 * x452 x540 = x199 * x534 + x539 x541 = x198 * x465 x542 = x171 * x487 x543 = x207 * x22 + x542 x544 = x171 * x488 x545 = x206 * x534 + x544 x546 = x171 * x498 x547 = x141 * x520 x548 = x212 * x22 + x547 x549 = x141 * x521 x550 = x211 * x534 + x549 x551 = x141 * x529 x552 = x55 * (x116 * x520 + x389) x553 = x216 * x22 + x552 x554 = x55 * (x116 * x521 + x392) x555 = x214 * x534 + x554 x556 = x55 * (x116 * x529 + x395) x557 = x221 * x9 x558 = x218 * x224 + x32 - x557 x559 = x558 * x6 x560 = x218 * x220 - x228 * x9 + x43 x561 = x16 * x560 x562 = -x4 * x561 + x5 * x558 x563 = x4 * x562 x564 = x559 + x563 x565 = x56 * (x559 + x564) x566 = x242 * x559 + x56 * x565 x567 = x55 * (x246 * x559 + x56 * x566) x568 = x21 * x247 + x567 x569 = x21 * x249 + x568 x570 = x6 * (x218 * x224 - x557 - x561 - x87) x571 = x16 * x9 x572 = x218 * x227 - x251 * x571 + x88 x573 = x5 * x562 + x570 - x90 * (x5 * x560 - x572 * x90) x574 = x4 * x573 x575 = x562 * x6 x576 = 2.0 * x575 x577 = x21 * x244 + x55 * ( x56 * (x56 * (x56 * (x574 + x576) + x564 * x68) + x565 * x68) + x566 * x68 ) x578 = x558 * x9 x579 = 2.0 * x236 x580 = x578 + x579 x581 = x562 * x9 x582 = x234 + x581 x583 = x56 * x582 + x580 * x95 x584 = x300 * x580 + x56 * x583 x585 = x274 * x6 x586 = x55 * (x56 * x584 + x580 * x585) x587 = x21 * x275 + x586 x588 = x21 * x276 + x587 x589 = x573 * x9 x590 = 2.0 * x254 x591 = x589 + x590 x592 = x21 * x272 + x55 * ( x56 * (x56 * (x56 * x591 + x582 * x68) + x583 * x68) + x584 * x68 ) x593 = x116 * x559 x594 = x116 * x563 + x593 x595 = x12 * x559 x596 = x269 * x595 + x56 * x594 x597 = x55 * (x274 * x595 + x56 * x596) x598 = x21 * x289 + x597 x599 = x21 * x290 + x598 x600 = x21 * x287 + x55 * ( x56 * (x116 * x56 * (x574 + x576) + x594 * x68) + x596 * x68 ) x601 = x100 * x580 + x266 * x42 x602 = x100 * x582 + x262 x603 = x56 * x602 + x601 * x95 x604 = x55 * (x300 * x601 + x56 * x603) x605 = x21 * x301 + x604 x606 = x21 * x302 + x605 x607 = x100 * x591 + x259 * x68 x608 = x21 * x298 + x55 * (x56 * (x56 * x607 + x602 * x68) + x603 * x68) x609 = x116 * (x578 + x579) x610 = x116 * x581 + x280 x611 = x56 * x610 + x609 * x95 x612 = x55 * (x300 * x609 + x56 * x611) x613 = x21 * x317 + x612 x614 = x21 * x318 + x613 x615 = x116 * (x589 + x590) x616 = x21 * x315 + x55 * (x56 * (x56 * x615 + x610 * x68) + x611 * x68) x617 = x153 * x559 x618 = x153 * x563 + x617 x619 = x55 * (x329 * x559 + x56 * x618) x620 = x21 * x330 + x619 x621 = x21 * x331 + x620 x622 = x21 * x327 + x55 * (x153 * x56 * (x574 + x576) + x618 * x68) x623 = x100 * x601 + x296 * x68 x624 = x100 * x602 + x294 x625 = x55 * (x56 * x624 + x623 * x95) x626 = x21 * x339 + x625 x627 = x21 * x340 + x626 x628 = x100 * x607 + x292 * x68 x629 = x21 * x336 + x55 * (x56 * x628 + x624 * x68) x630 = x100 * x609 + x313 * x68 x631 = x100 * x610 + x311 x632 = x55 * (x56 * x631 + x630 * x95) x633 = x21 * x349 + x632 x634 = x21 * x350 + x633 x635 = x100 * x615 + x308 * x68 x636 = x21 * x346 + x55 * (x56 * x635 + x631 * x68) x637 = x153 * (x578 + x579) x638 = x153 * x581 + x323 x639 = x55 * (x56 * x638 + x637 * x95) x640 = x21 * x361 + x639 x641 = x21 * x362 + x640 x642 = x153 * (x589 + x590) x643 = x21 * x358 + x55 * (x56 * x642 + x638 * x68) x644 = x186 * x559 x645 = x55 * (x186 * x563 + x644) x646 = x21 * x370 + x645 x647 = x21 * x371 + x646 x648 = x186 * x55 * (x574 + x576) + x21 * x367 x649 = x55 * (x100 * x624 + x335) x650 = x21 * x375 + x649 x651 = x21 * x377 + x650 x652 = x21 * x373 + x55 * (x100 * x628 + x333 * x68) x653 = x55 * (x100 * x631 + x345) x654 = x21 * x381 + x653 x655 = x21 * x382 + x654 x656 = x21 * x379 + x55 * (x100 * x635 + x343 * x68) x657 = x55 * (x100 * x638 + x357) x658 = x21 * x386 + x657 x659 = x21 * x387 + x658 x660 = x21 * x384 + x55 * (x100 * x642 + x354 * x68) x661 = x55 * (x186 * x581 + x366) x662 = x21 * x393 + x661 x663 = x21 * x394 + x662 x664 = x186 * x55 * (x589 + x590) + x21 * x390 x665 = x214 * x562 x666 = x21 * x399 + x665 x667 = x21 * x400 + x666 x668 = x21 * x397 + x214 * x573 x669 = -x218 * x408 + x405 * x9 x670 = -x669 x671 = x6 * x670 x672 = x218 * x404 - x412 * x9 x673 = x16 * x672 x674 = -x4 * x673 + x5 * x670 x675 = x4 * x674 + x671 x676 = x56 * (x671 + x675) x677 = x242 * x671 + x56 * x676 x678 = x55 * (x246 * x671 + x56 * x677) x679 = x22 * x247 + x678 x680 = x21 * x431 + x679 x681 = -x6 * (x669 + x673) x682 = x218 * x411 - x433 * x571 x683 = x5 * x674 + x681 - x90 * (x5 * x672 - x682 * x90) x684 = x42 * x674 x685 = x55 * ( x56 * (x56 * (x56 * (x4 * x683 + x684) + x675 * x68) + x676 * x68) + x677 * x68 ) x686 = x22 * x244 + x685 x687 = 10.2469507659596 * x98 x688 = x420 + x670 * x9 x689 = x417 + x674 * x9 x690 = x56 * x689 + x688 * x95 x691 = x300 * x688 + x56 * x690 x692 = x55 * (x56 * x691 + x585 * x688) x693 = x22 * x275 + x692 x694 = x21 * x449 + x693 x695 = x436 + x683 * x9 x696 = x68 * x689 x697 = x55 * (x56 * (x56 * (x56 * x695 + x696) + x68 * x690) + x68 * x691) x698 = x22 * x272 + x697 x699 = x115 * x139 x700 = x12 * x670 + x236 x701 = x12 * x674 + x233 x702 = x56 * x701 + x700 * x95 x703 = x300 * x700 + x56 * x702 x704 = x55 * (x56 * x703 + x585 * x700) x705 = x22 * x289 + x704 x706 = x21 * x464 + x705 x707 = x12 * x683 + x254 x708 = x68 * x701 x709 = x55 * (x56 * (x56 * (x56 * x707 + x708) + x68 * x702) + x68 * x703) x710 = x22 * x287 + x709 x711 = x100 * x688 + x440 x712 = x100 * (x417 + x689) x713 = x56 * x712 + x711 * x95 x714 = x55 * (x300 * x711 + x56 * x713) x715 = x22 * x301 + x714 x716 = x21 * x474 + x715 x717 = x100 * (x436 + x695) x718 = x68 * x712 x719 = x55 * (x56 * (x56 * x717 + x718) + x68 * x713) x720 = x22 * x298 + x719 x721 = x100 * x700 + x456 x722 = x100 * x701 + x452 * x95 x723 = x56 * x722 + x721 * x95 x724 = x55 * (x300 * x721 + x56 * x723) x725 = x22 * x317 + x724 x726 = x21 * x484 + x725 x727 = x100 * x707 + x451 * x95 x728 = x68 * x722 x729 = x55 * (x56 * (x56 * x727 + x728) + x68 * x723) x730 = x22 * x315 + x729 x731 = x305 * x322 x732 = x116 * x700 + x282 x733 = x116 * (x233 + x701) x734 = x56 * x733 + x732 * x95 x735 = x55 * (x300 * x732 + x56 * x734) x736 = x22 * x330 + x735 x737 = x21 * x497 + x736 x738 = x116 * (x254 + x707) x739 = x68 * x733 x740 = x55 * (x56 * (x56 * x738 + x739) + x68 * x734) x741 = x22 * x327 + x740 x742 = x100 * x711 + x468 x743 = x100 * x712 + x129 * x417 x744 = x55 * (x56 * x743 + x742 * x95) x745 = x22 * x339 + x744 x746 = x21 * x504 + x745 x747 = x100 * x717 + x129 * x436 x748 = x68 * x743 x749 = x55 * (x56 * x747 + x748) x750 = x22 * x336 + x749 x751 = x100 * x721 + x478 x752 = x100 * x722 + x452 * x515 x753 = x55 * (x56 * x752 + x751 * x95) x754 = x22 * x349 + x753 x755 = x21 * x510 + x754 x756 = x100 * x727 + x451 * x515 x757 = x68 * x752 x758 = x55 * (x56 * x756 + x757) x759 = x22 * x346 + x758 x760 = x100 * x732 + x492 x761 = x100 * x733 + x488 * x95 x762 = x55 * (x56 * x761 + x760 * x95) x763 = x22 * x361 + x762 x764 = x21 * x518 + x763 x765 = x100 * x738 + x487 * x95 x766 = x68 * x761 x767 = x55 * (x56 * x765 + x766) x768 = x22 * x358 + x767 x769 = x116 * x732 + x325 x770 = x116 * x733 + x153 * x233 x771 = x55 * (x56 * x770 + x769 * x95) x772 = x22 * x370 + x771 x773 = x21 * x528 + x772 x774 = x116 * x738 + x153 * x254 x775 = x68 * x770 x776 = x55 * (x56 * x774 + x775) x777 = x22 * x367 + x776 x778 = x55 * (x100 * x743 + x165 * x417) x779 = x22 * x375 + x778 x780 = x21 * x535 + x779 x781 = x55 * (x100 * x747 + x165 * x436) x782 = x22 * x373 + x781 x783 = x171 * x6 x784 = x55 * (x100 * x752 + x452 * x783) x785 = x22 * x381 + x784 x786 = x21 * x540 + x785 x787 = x55 * (x100 * x756 + x451 * x783) x788 = x22 * x379 + x787 x789 = x55 * (x100 * x761 + x488 * x515) x790 = x22 * x386 + x789 x791 = x21 * x545 + x790 x792 = x55 * (x100 * x765 + x487 * x515) x793 = x22 * x384 + x792 x794 = x55 * (x100 * x770 + x521 * x95) x795 = x22 * x393 + x794 x796 = x21 * x550 + x795 x797 = x55 * (x100 * x774 + x520 * x95) x798 = x22 * x390 + x797 x799 = x55 * (x116 * x770 + x186 * x233) x800 = x22 * x399 + x799 x801 = x21 * x555 + x800 x802 = x55 * (x116 * x774 + x186 * x254) x803 = x22 * x397 + x802 x804 = x12 * x405 x805 = x32 + x402 * x408 - x804 x806 = x6 * x805 x807 = -x12 * x412 + x402 * x404 + x43 x808 = x16 * x807 x809 = -x4 * x808 + x5 * x805 x810 = x4 * x809 x811 = x806 + x810 x812 = x56 * (x806 + x811) x813 = x242 * x806 + x56 * x812 x814 = x55 * (x246 * x806 + x56 * x813) x815 = x22 * x429 + x814 x816 = x22 * x431 + x815 x817 = x6 * (x402 * x408 - x804 - x808 - x87) x818 = x12 * x16 x819 = x402 * x411 - x433 * x818 + x88 x820 = x5 * x809 + x817 - x90 * (x5 * x807 - x819 * x90) x821 = x4 * x820 x822 = x6 * x809 x823 = 2.0 * x822 x824 = x22 * x427 + x55 * ( x56 * (x56 * (x56 * (x821 + x823) + x68 * x811) + x68 * x812) + x68 * x813 ) x825 = x100 * x806 x826 = x100 * x810 + x825 x827 = x443 * x806 + x56 * x826 x828 = x55 * (x447 * x806 + x56 * x827) x829 = x22 * x448 + x828 x830 = x22 * x449 + x829 x831 = x22 * x445 + x55 * ( x56 * (x100 * x56 * (x821 + x823) + x68 * x826) + x68 * x827 ) x832 = x12 * x805 + 2.0 * x420 x833 = x832 * x95 x834 = x12 * x809 + x418 x835 = x56 * x834 + x833 x836 = x300 * x832 + x56 * x835 x837 = x55 * (x56 * x836 + x585 * x832) x838 = x22 * x463 + x837 x839 = x22 * x464 + x838 x840 = x12 * x820 + 2.0 * x436 x841 = x22 * x460 + x55 * ( x56 * (x56 * (x56 * x840 + x68 * x834) + x68 * x835) + x68 * x836 ) x842 = x129 * x806 x843 = x129 * x810 + x842 x844 = x55 * (x472 * x806 + x56 * x843) x845 = x22 * x473 + x844 x846 = x22 * x474 + x845 x847 = x22 * x470 + x55 * (x129 * x56 * (x821 + x823) + x68 * x843) x848 = x515 * x832 x849 = x443 * x834 + x848 x850 = x4 * x832 x851 = x55 * (x178 * x6 * x850 + x56 * x849) x852 = x22 * x483 + x851 x853 = x22 * x484 + x852 x854 = x22 * x480 + x55 * (x56 * (x443 * x840 + x512 * x834) + x68 * x849) x855 = x116 * x832 + x455 * x68 x856 = x855 * x95 x857 = x116 * x834 + x453 x858 = x56 * x857 + x856 x859 = x55 * (x300 * x855 + x56 * x858) x860 = x22 * x496 + x859 x861 = x22 * x497 + x860 x862 = x116 * x840 + x451 * x68 x863 = x22 * x494 + x55 * (x56 * (x56 * x862 + x68 * x857) + x68 * x858) x864 = x165 * x806 x865 = x55 * (x165 * x810 + x864) x866 = x22 * x503 + x865 x867 = x22 * x504 + x866 x868 = x165 * x55 * (x821 + x823) + x22 * x500 x869 = x783 * x832 x870 = x55 * (x472 * x834 + x869) x871 = x22 * x509 + x870 x872 = x22 * x510 + x871 x873 = x22 * x506 + x55 * (x171 * x42 * x834 + x472 * x840) x874 = x515 * x855 x875 = x55 * (x443 * x857 + x874) x876 = x22 * x517 + x875 x877 = x22 * x518 + x876 x878 = x22 * x513 + x55 * (x443 * x862 + x512 * x857) x879 = x116 * x855 + x491 * x68 x880 = x879 * x95 x881 = x116 * x857 + x489 x882 = x55 * (x56 * x881 + x880) x883 = x22 * x527 + x882 x884 = x22 * x528 + x883 x885 = x116 * x862 + x487 * x68 x886 = x22 * x523 + x55 * (x56 * x885 + x68 * x881) x887 = x193 * x809 x888 = x22 * x533 + x887 x889 = x22 * x535 + x888 x890 = x193 * x820 + x22 * x531 x891 = x198 * x834 x892 = x22 * x539 + x891 x893 = x22 * x540 + x892 x894 = x198 * x840 + x22 * x537 x895 = x171 * x857 x896 = x22 * x544 + x895 x897 = x22 * x545 + x896 x898 = x171 * x862 + x22 * x542 x899 = x141 * x881 x900 = x22 * x549 + x899 x901 = x22 * x550 + x900 x902 = x141 * x885 + x22 * x547 x903 = x55 * (x116 * x881 + x522) x904 = x22 * x554 + x903 x905 = x22 * x555 + x904 x906 = x22 * x552 + x55 * (x116 * x885 + x520 * x68) x907 = x218 * x558 + 2.0 * x223 - x561 * x9 x908 = x6 * x907 x909 = x218 * x560 + 2.0 * x250 - x571 * x572 x910 = x5 * x907 - x90 * x909 x911 = x4 * x910 x912 = ( x21 * x567 + x21 * x568 + x55 * (x246 * x908 + x56 * (x242 * x908 + x56**2 * (2.0 * x908 + x911))) ) x913 = x9 * x907 x914 = 3.0 * x559 x915 = x913 + x914 x916 = x915 * x95 x917 = x9 * x910 x918 = 3.0 * x575 x919 = x917 + x918 x920 = ( x21 * x586 + x21 * x587 + x55 * (x56 * (x300 * x915 + x56 * (x56 * x919 + x916)) + x585 * x915) ) x921 = x116 * x908 x922 = x12 * x908 x923 = ( x21 * x597 + x21 * x598 + x55 * (x274 * x922 + x56 * (x269 * x922 + x56 * (x116 * x911 + x921))) ) x924 = x100 * x915 + x580 * x62 x925 = x924 * x95 x926 = x100 * x919 + x582 * x62 x927 = x21 * x604 + x21 * x605 + x55 * (x300 * x924 + x56 * (x56 * x926 + x925)) x928 = x116 * (x913 + x914) x929 = x928 * x95 x930 = x116 * (x917 + x918) x931 = x21 * x612 + x21 * x613 + x55 * (x300 * x928 + x56 * (x56 * x930 + x929)) x932 = x153 * x908 x933 = x21 * x619 + x21 * x620 + x55 * (x329 * x908 + x56 * (x153 * x911 + x932)) x934 = x100 * x924 + x601 * x62 x935 = x934 * x95 x936 = x100 * x926 + x602 * x62 x937 = x21 * x625 + x21 * x626 + x55 * (x56 * x936 + x935) x938 = x100 * x928 + x609 * x62 x939 = x938 * x95 x940 = x100 * x930 + x610 * x62 x941 = x21 * x632 + x21 * x633 + x55 * (x56 * x940 + x939) x942 = x153 * (x913 + x914) x943 = x942 * x95 x944 = x153 * (x917 + x918) x945 = x21 * x639 + x21 * x640 + x55 * (x56 * x944 + x943) x946 = x186 * x908 x947 = x21 * x645 + x21 * x646 + x55 * (x186 * x911 + x946) x948 = x21 * x649 + x21 * x650 + x55 * (x100 * x936 + x62 * x624) x949 = x21 * x653 + x21 * x654 + x55 * (x100 * x940 + x62 * x631) x950 = x21 * x657 + x21 * x658 + x55 * (x100 * x944 + x62 * x638) x951 = x186 * x55 * (x917 + x918) + x21 * x661 + x21 * x662 x952 = x21 * x665 + x21 * x666 + x214 * x910 x953 = x218 * x670 + x407 - x673 * x9 x954 = x6 * x953 x955 = x218 * x672 + x432 - x571 * x682 x956 = x5 * x953 - x90 * x955 x957 = x55 * (x246 * x954 + x56 * (x242 * x954 + x56**2 * (x4 * x956 + 2.0 * x954))) x958 = x21 * x679 + x22 * x567 + x957 x959 = 2.0 * x671 x960 = x9 * x953 + x959 x961 = x684 + x9 * x956 x962 = x55 * (x56 * (x300 * x960 + x56 * (x56 * x961 + x95 * x960)) + x585 * x960) x963 = x21 * x693 + x22 * x586 + x962 x964 = x12 * x953 + x559 x965 = x12 * x956 + x575 x966 = x55 * (x56 * (x300 * x964 + x56 * (x56 * x965 + x95 * x964)) + x585 * x964) x967 = x21 * x705 + x22 * x597 + x966 x968 = x100 * x960 + x68 * x688 x969 = x100 * x961 + x696 x970 = x55 * (x300 * x968 + x56 * (x56 * x969 + x95 * x968)) x971 = x21 * x715 + x22 * x604 + x970 x972 = x68 * x700 x973 = x100 * x964 + x972 x974 = x100 * x965 + x708 x975 = x55 * (x300 * x973 + x56 * (x56 * x974 + x95 * x973)) x976 = x21 * x725 + x22 * x612 + x975 x977 = x116 * x964 + x593 x978 = x116 * (x575 + x965) x979 = x55 * (x300 * x977 + x56 * (x56 * x978 + x95 * x977)) x980 = x21 * x736 + x22 * x619 + x979 x981 = x100 * x968 + x68 * x711 x982 = x100 * x969 + x718 x983 = x55 * (x56 * x982 + x95 * x981) x984 = x21 * x745 + x22 * x625 + x983 x985 = x100 * x973 + x68 * x721 x986 = x100 * x974 + x728 x987 = x55 * (x56 * x986 + x95 * x985) x988 = x21 * x754 + x22 * x632 + x987 x989 = x68 * x732 x990 = x100 * x977 + x989 x991 = x100 * x978 + x739 x992 = x55 * (x56 * x991 + x95 * x990) x993 = x21 * x763 + x22 * x639 + x992 x994 = x116 * x977 + x617 x995 = x116 * x978 + x153 * x575 x996 = x55 * (x56 * x995 + x95 * x994) x997 = x21 * x772 + x22 * x645 + x996 x998 = x55 * (x100 * x982 + x748) x999 = x21 * x779 + x22 * x649 + x998 x1000 = x55 * (x100 * x986 + x757) x1001 = x1000 + x21 * x785 + x22 * x653 x1002 = x55 * (x100 * x991 + x766) x1003 = x1002 + x21 * x790 + x22 * x657 x1004 = x55 * (x100 * x995 + x775) x1005 = x1004 + x21 * x795 + x22 * x661 x1006 = x55 * (x116 * x995 + x186 * x575) x1007 = x1006 + x21 * x800 + x22 * x665 x1008 = x218 * x805 - x808 * x9 x1009 = x1008 * x6 x1010 = x218 * x807 - x571 * x819 x1011 = x1008 * x5 - x1010 * x90 x1012 = x22 * x678 + x55 * ( x1009 * x246 + x56 * (x1009 * x242 + x56**2 * (2.0 * x1009 + x1011 * x4)) ) x1013 = x1012 + x22 * x679 x1014 = x1008 * x9 + x806 x1015 = x1011 * x9 + x822 x1016 = x22 * x692 + x55 * ( x1014 * x585 + x56 * (x1014 * x300 + x56 * (x1014 * x95 + x1015 * x56)) ) x1017 = x1016 + x22 * x693 x1018 = x1008 * x12 + x959 x1019 = x1011 * x12 + x684 x1020 = x22 * x704 + x55 * ( x1018 * x585 + x56 * (x1018 * x300 + x56 * (x1018 * x95 + x1019 * x56)) ) x1021 = x1020 + x22 * x705 x1022 = x100 * x1014 + x825 x1023 = x100 * (x1015 + x822) x1024 = x22 * x714 + x55 * (x1022 * x300 + x56 * (x1022 * x95 + x1023 * x56)) x1025 = x1024 + x22 * x715 x1026 = x100 * x1018 + x833 x1027 = x100 * x1019 + x834 * x95 x1028 = x22 * x724 + x55 * (x1026 * x300 + x56 * (x1026 * x95 + x1027 * x56)) x1029 = x1028 + x22 * x725 x1030 = x1018 * x116 + x972 x1031 = x1019 * x116 + x708 x1032 = x22 * x735 + x55 * (x1030 * x300 + x56 * (x1030 * x95 + x1031 * x56)) x1033 = x1032 + x22 * x736 x1034 = x100 * x1022 + x842 x1035 = x100 * x1023 + x129 * x822 x1036 = x22 * x744 + x55 * (x1034 * x95 + x1035 * x56) x1037 = x1036 + x22 * x745 x1038 = x100 * x1026 + x848 x1039 = x100 * x1027 + x515 * x834 x1040 = x22 * x753 + x55 * (x1038 * x95 + x1039 * x56) x1041 = x1040 + x22 * x754 x1042 = x100 * x1030 + x856 x1043 = x100 * x1031 + x857 * x95 x1044 = x22 * x762 + x55 * (x1042 * x95 + x1043 * x56) x1045 = x1044 + x22 * x763 x1046 = x1030 * x116 + x989 x1047 = x1031 * x116 + x739 x1048 = x22 * x771 + x55 * (x1046 * x95 + x1047 * x56) x1049 = x1048 + x22 * x772 x1050 = x22 * x778 + x55 * (x100 * x1035 + x165 * x822) x1051 = x1050 + x22 * x779 x1052 = x22 * x784 + x55 * (x100 * x1039 + x783 * x834) x1053 = x1052 + x22 * x785 x1054 = x22 * x789 + x55 * (x100 * x1043 + x515 * x857) x1055 = x1054 + x22 * x790 x1056 = x22 * x794 + x55 * (x100 * x1047 + x881 * x95) x1057 = x1056 + x22 * x795 x1058 = x22 * x799 + x55 * (x1047 * x116 + x775) x1059 = x1058 + x22 * x800 x1060 = -x12 * x808 + x402 * x805 + 2.0 * x407 x1061 = x1060 * x6 x1062 = x402 * x807 + 2.0 * x432 - x818 * x819 x1063 = x1060 * x5 - x1062 * x90 x1064 = x1063 * x4 x1065 = ( x22 * x814 + x22 * x815 + x55 * (x1061 * x246 + x56 * (x1061 * x242 + x56**2 * (2.0 * x1061 + x1064))) ) x1066 = x100 * x1061 x1067 = ( x22 * x828 + x22 * x829 + x55 * (x1061 * x447 + x56 * (x1061 * x443 + x56 * (x100 * x1064 + x1066))) ) x1068 = x1060 * x12 + 3.0 * x806 x1069 = x1068 * x95 x1070 = x1063 * x12 + 3.0 * x822 x1071 = ( x22 * x837 + x22 * x838 + x55 * (x1068 * x585 + x56 * (x1068 * x300 + x56 * (x1069 + x1070 * x56))) ) x1072 = x1061 * x129 x1073 = x22 * x844 + x22 * x845 + x55 * (x1061 * x472 + x56 * (x1064 * x129 + x1072)) x1074 = x1068 * x515 x1075 = ( x22 * x851 + x22 * x852 + x55 * (x1068 * x482 * x6 + x56 * (x1070 * x443 + x1074)) ) x1076 = x1068 * x116 + x62 * x832 x1077 = x1076 * x95 x1078 = x1070 * x116 + x62 * x834 x1079 = x22 * x859 + x22 * x860 + x55 * (x1076 * x300 + x56 * (x1077 + x1078 * x56)) x1080 = x1061 * x165 x1081 = x22 * x865 + x22 * x866 + x55 * (x1064 * x165 + x1080) x1082 = x1068 * x783 x1083 = x22 * x870 + x22 * x871 + x55 * (x1070 * x472 + x1082) x1084 = x1076 * x515 x1085 = x22 * x875 + x22 * x876 + x55 * (x1078 * x443 + x1084) x1086 = x1076 * x116 + x62 * x855 x1087 = x1086 * x95 x1088 = x1078 * x116 + x62 * x857 x1089 = x22 * x882 + x22 * x883 + x55 * (x1087 + x1088 * x56) x1090 = x1063 * x193 + x22 * x887 + x22 * x888 x1091 = x1070 * x198 + x22 * x891 + x22 * x892 x1092 = x1078 * x171 + x22 * x895 + x22 * x896 x1093 = x1088 * x141 + x22 * x899 + x22 * x900 x1094 = x22 * x903 + x22 * x904 + x55 * (x1088 * x116 + x62 * x881) x1095 = x0 * x247 + x244 x1096 = x192 * x4**4 x1097 = x0 * x224 x1098 = x0 * x275 + x272 x1099 = x192 * x81 x1100 = x1099 * x265 x1101 = x0 * x289 + x287 x1102 = x1099 * x12 x1103 = x0 * x301 + x298 x1104 = x0 * x274 x1105 = x0 * x317 + x315 x1106 = x0 * x330 + x327 x1107 = x13 * x7 x1108 = x1097 * x192 x1109 = x0 * x339 + x336 x1110 = x0 * x269 x1111 = x0 * x349 + x346 x1112 = x0 * x361 + x358 x1113 = x0 * x370 + x367 x1114 = x185 * x4 x1115 = x0 * x375 + x373 x1116 = x100 * x338 + x169 x1117 = x0 * x381 + x379 x1118 = x100 * x348 + x176 x1119 = x0 * x386 + x384 x1120 = x100 * x360 + x183 x1121 = x0 * x393 + x390 x1122 = x186 * x264 + x190 x1123 = x0 * x399 + x397 x1124 = x1096 * x558 x1125 = x21 * x224 x1126 = x1096 * x1125 + x1124 x1127 = x1099 * x580 x1128 = x1100 * x21 + x1127 x1129 = x1102 * x558 x1130 = x1102 * x1125 + x1129 x1131 = x274 * x601 x1132 = x21 * x274 x1133 = x1131 + x1132 * x296 x1134 = x274 * x609 x1135 = x1132 * x313 + x1134 x1136 = x192 * x558 x1137 = x1107 * x1136 x1138 = x1125 * x192 x1139 = x1107 * x1138 + x1137 x1140 = x269 * x623 x1141 = x21 * x269 x1142 = x1140 + x1141 * x338 x1143 = x269 * x630 x1144 = x1141 * x348 + x1143 x1145 = x269 * x637 x1146 = x1141 * x360 + x1145 x1147 = x1114 * x1136 x1148 = x1114 * x1138 + x1147 x1149 = x55 * (x100 * x623 + x338 * x68) x1150 = x1116 * x248 + x1149 x1151 = x55 * (x100 * x630 + x348 * x68) x1152 = x1118 * x248 + x1151 x1153 = x55 * (x100 * x637 + x360 * x68) x1154 = x1120 * x248 + x1153 x1155 = x186 * x55 * (x578 + x579) x1156 = x1122 * x248 + x1155 x1157 = x214 * x558 x1158 = x1125 * x214 + x1157 x1159 = x1096 * x670 x1160 = x22 * x224 x1161 = x1096 * x1160 + x1159 x1162 = x1099 * x688 x1163 = x1100 * x22 + x1162 x1164 = x1099 * x700 x1165 = x1102 * x1160 + x1164 x1166 = x274 * x711 x1167 = x22 * x274 x1168 = x1166 + x1167 * x296 x1169 = x274 * x721 x1170 = x1167 * x313 + x1169 x1171 = x274 * x732 x1172 = x1160 * x192 x1173 = x1107 * x1172 + x1171 x1174 = x269 * x742 x1175 = x22 * x269 x1176 = x1174 + x1175 * x338 x1177 = x269 * x751 x1178 = x1175 * x348 + x1177 x1179 = x269 * x760 x1180 = x1175 * x360 + x1179 x1181 = x269 * x769 x1182 = x1114 * x1172 + x1181 x1183 = x55 * (x100 * x742 + x502) x1184 = x1116 * x430 + x1183 x1185 = x55 * (x100 * x751 + x508) x1186 = x1118 * x430 + x1185 x1187 = x55 * (x100 * x760 + x516) x1188 = x1120 * x430 + x1187 x1189 = x55 * (x100 * x769 + x526) x1190 = x1122 * x430 + x1189 x1191 = x55 * (x116 * x769 + x369) x1192 = x1160 * x214 + x1191 x1193 = x1096 * x907 x1194 = x1124 * x21 + x1193 x1195 = x1126 * x21 + x1194 x1196 = x1099 * x915 x1197 = x1127 * x21 + x1196 x1198 = x1128 * x21 + x1197 x1199 = x1102 * x907 x1200 = x1129 * x21 + x1199 x1201 = x1130 * x21 + x1200 x1202 = x274 * x924 x1203 = x1131 * x21 + x1202 x1204 = x1133 * x21 + x1203 x1205 = x274 * x928 x1206 = x1134 * x21 + x1205 x1207 = x1135 * x21 + x1206 x1208 = x192 * x907 x1209 = x1107 * x1208 x1210 = x1137 * x21 + x1209 x1211 = x1139 * x21 + x1210 x1212 = x269 * x934 x1213 = x1140 * x21 + x1212 x1214 = x1142 * x21 + x1213 x1215 = x269 * x938 x1216 = x1143 * x21 + x1215 x1217 = x1144 * x21 + x1216 x1218 = x269 * x942 x1219 = x1145 * x21 + x1218 x1220 = x1146 * x21 + x1219 x1221 = x1114 * x1208 x1222 = x1147 * x21 + x1221 x1223 = x1148 * x21 + x1222 x1224 = x55 * (x100 * x934 + x62 * x623) x1225 = x1149 * x21 + x1224 x1226 = x1150 * x21 + x1225 x1227 = x55 * (x100 * x938 + x62 * x630) x1228 = x1151 * x21 + x1227 x1229 = x1152 * x21 + x1228 x1230 = x55 * (x100 * x942 + x62 * x637) x1231 = x1153 * x21 + x1230 x1232 = x1154 * x21 + x1231 x1233 = x186 * x55 * (x913 + x914) x1234 = x1155 * x21 + x1233 x1235 = x1156 * x21 + x1234 x1236 = x214 * x907 x1237 = x1157 * x21 + x1236 x1238 = x1158 * x21 + x1237 x1239 = x1096 * x953 x1240 = x1124 * x22 + x1239 x1241 = x1161 * x21 + x1240 x1242 = x1099 * x960 x1243 = x1127 * x22 + x1242 x1244 = x1163 * x21 + x1243 x1245 = x1099 * x964 x1246 = x1129 * x22 + x1245 x1247 = x1165 * x21 + x1246 x1248 = x274 * x968 x1249 = x1131 * x22 + x1248 x1250 = x1168 * x21 + x1249 x1251 = x274 * x973 x1252 = x1134 * x22 + x1251 x1253 = x1170 * x21 + x1252 x1254 = x274 * x977 x1255 = x1137 * x22 + x1254 x1256 = x1173 * x21 + x1255 x1257 = x269 * x981 x1258 = x1140 * x22 + x1257 x1259 = x1176 * x21 + x1258 x1260 = x269 * x985 x1261 = x1143 * x22 + x1260 x1262 = x1178 * x21 + x1261 x1263 = x269 * x990 x1264 = x1145 * x22 + x1263 x1265 = x1180 * x21 + x1264 x1266 = x269 * x994 x1267 = x1147 * x22 + x1266 x1268 = x1182 * x21 + x1267 x1269 = x55 * (x100 * x981 + x68 * x742) x1270 = x1149 * x22 + x1269 x1271 = x1184 * x21 + x1270 x1272 = x55 * (x100 * x985 + x68 * x751) x1273 = x1151 * x22 + x1272 x1274 = x1186 * x21 + x1273 x1275 = x55 * (x100 * x990 + x68 * x760) x1276 = x1153 * x22 + x1275 x1277 = x1188 * x21 + x1276 x1278 = x68 * x769 x1279 = x55 * (x100 * x994 + x1278) x1280 = x1155 * x22 + x1279 x1281 = x1190 * x21 + x1280 x1282 = x55 * (x116 * x994 + x644) x1283 = x1157 * x22 + x1282 x1284 = x1192 * x21 + x1283 x1285 = x1008 * x1096 x1286 = x1159 * x22 + x1285 x1287 = x1161 * x22 + x1286 x1288 = x1014 * x1099 x1289 = x1162 * x22 + x1288 x1290 = x1163 * x22 + x1289 x1291 = x1018 * x1099 x1292 = x1164 * x22 + x1291 x1293 = x1165 * x22 + x1292 x1294 = x1022 * x274 x1295 = x1166 * x22 + x1294 x1296 = x1168 * x22 + x1295 x1297 = x1026 * x274 x1298 = x1169 * x22 + x1297 x1299 = x1170 * x22 + x1298 x1300 = x1030 * x274 x1301 = x1171 * x22 + x1300 x1302 = x1173 * x22 + x1301 x1303 = x1034 * x269 x1304 = x1174 * x22 + x1303 x1305 = x1176 * x22 + x1304 x1306 = x1038 * x269 x1307 = x1177 * x22 + x1306 x1308 = x1178 * x22 + x1307 x1309 = x1042 * x269 x1310 = x1179 * x22 + x1309 x1311 = x1180 * x22 + x1310 x1312 = x1046 * x269 x1313 = x1181 * x22 + x1312 x1314 = x1182 * x22 + x1313 x1315 = x55 * (x100 * x1034 + x864) x1316 = x1183 * x22 + x1315 x1317 = x1184 * x22 + x1316 x1318 = x55 * (x100 * x1038 + x869) x1319 = x1185 * x22 + x1318 x1320 = x1186 * x22 + x1319 x1321 = x55 * (x100 * x1042 + x874) x1322 = x1187 * x22 + x1321 x1323 = x1188 * x22 + x1322 x1324 = x55 * (x100 * x1046 + x880) x1325 = x1189 * x22 + x1324 x1326 = x1190 * x22 + x1325 x1327 = x55 * (x1046 * x116 + x1278) x1328 = x1191 * x22 + x1327 x1329 = x1192 * x22 + x1328 x1330 = x218 * x907 + 3.0 * x570 - x571 * x909 x1331 = x1330 * x9 x1332 = 4.0 * x908 x1333 = x1331 + x1332 x1334 = x100 * x1333 + 4.0 * x916 x1335 = x116 * (x1331 + x1332) x1336 = x1330 * x192 x1337 = x100 * x1334 + 4.0 * x925 x1338 = x100 * x1335 + 4.0 * x929 x1339 = x153 * (x1331 + x1332) x1340 = x218 * x953 - x571 * x955 + 2.0 * x681 x1341 = x1096 * x1340 x1342 = x1340 * x9 + 3.0 * x954 x1343 = x1099 * x1342 x1344 = x12 * x1340 + x908 x1345 = x1099 * x1344 x1346 = x100 * x1342 + x62 * x960 x1347 = x1346 * x274 x1348 = x100 * x1344 + x62 * x964 x1349 = x1348 * x274 x1350 = x116 * x1344 + x921 x1351 = x1350 * x274 x1352 = x100 * x1346 + x62 * x968 x1353 = x1352 * x269 x1354 = x100 * x1348 + x62 * x973 x1355 = x1354 * x269 x1356 = x100 * x1350 + x62 * x977 x1357 = x1356 * x269 x1358 = x116 * x1350 + x932 x1359 = x1358 * x269 x1360 = x55 * (x100 * x1352 + x62 * x981) x1361 = x55 * (x100 * x1354 + x62 * x985) x1362 = x55 * (x100 * x1356 + x62 * x990) x1363 = x55 * (x100 * x1358 + x62 * x994) x1364 = x55 * (x116 * x1358 + x946) x1365 = x1008 * x218 - x1010 * x571 + x817 x1366 = x1096 * x1365 + x1239 * x22 x1367 = 2.0 * x1009 + x1365 * x9 x1368 = x1099 * x1367 + x1242 * x22 x1369 = x12 * x1365 + 2.0 * x954 x1370 = x1099 * x1369 + x1245 * x22 x1371 = x100 * x1367 + x1014 * x68 x1372 = x1248 * x22 + x1371 * x274 x1373 = x100 * x1369 + x1018 * x68 x1374 = x1251 * x22 + x1373 * x274 x1375 = x116 * x1369 + x68 * x964 x1376 = x1254 * x22 + x1375 * x274 x1377 = x100 * x1371 + x1022 * x68 x1378 = x1257 * x22 + x1377 * x269 x1379 = x100 * x1373 + x1026 * x68 x1380 = x1260 * x22 + x1379 * x269 x1381 = x100 * x1375 + x1030 * x68 x1382 = x1263 * x22 + x1381 * x269 x1383 = x116 * x1375 + x68 * x977 x1384 = x1266 * x22 + x1383 * x269 x1385 = x1269 * x22 + x55 * (x100 * x1377 + x1034 * x68) x1386 = x1272 * x22 + x55 * (x100 * x1379 + x1038 * x68) x1387 = x1275 * x22 + x55 * (x100 * x1381 + x1042 * x68) x1388 = x1279 * x22 + x55 * (x100 * x1383 + x1046 * x68) x1389 = x1282 * x22 + x55 * (x116 * x1383 + x68 * x994) x1390 = x1060 * x218 - x1062 * x571 x1391 = x1096 * x1390 + x1285 * x22 + x1286 * x22 x1392 = x1061 + x1390 * x9 x1393 = x1099 * x1392 + x1288 * x22 + x1289 * x22 x1394 = 3.0 * x1009 + x12 * x1390 x1395 = x1099 * x1394 + x1291 * x22 + x1292 * x22 x1396 = x100 * x1392 + x1066 x1397 = x1294 * x22 + x1295 * x22 + x1396 * x274 x1398 = x100 * x1394 + x1069 x1399 = x1297 * x22 + x1298 * x22 + x1398 * x274 x1400 = x1018 * x62 + x116 * x1394 x1401 = x1300 * x22 + x1301 * x22 + x1400 * x274 x1402 = x100 * x1396 + x1072 x1403 = x1303 * x22 + x1304 * x22 + x1402 * x269 x1404 = x100 * x1398 + x1074 x1405 = x1306 * x22 + x1307 * x22 + x1404 * x269 x1406 = x100 * x1400 + x1077 x1407 = x1309 * x22 + x1310 * x22 + x1406 * x269 x1408 = x1030 * x62 + x116 * x1400 x1409 = x1312 * x22 + x1313 * x22 + x1408 * x269 x1410 = x1315 * x22 + x1316 * x22 + x55 * (x100 * x1402 + x1080) x1411 = x1318 * x22 + x1319 * x22 + x55 * (x100 * x1404 + x1082) x1412 = x1321 * x22 + x1322 * x22 + x55 * (x100 * x1406 + x1084) x1413 = x1324 * x22 + x1325 * x22 + x55 * (x100 * x1408 + x1087) x1414 = x1327 * x22 + x1328 * x22 + x55 * (x1046 * x62 + x116 * x1408) x1415 = x0 * x429 + x427 x1416 = x0 * x408 x1417 = x0 * x448 + x445 x1418 = x1099 * x9 x1419 = x0 * x463 + x460 x1420 = x0 * x455 x1421 = x0 * x473 + x470 x1422 = x192 * x7 x1423 = x10 * x1422 x1424 = x0 * x483 + x480 x1425 = x1422 * x9 x1426 = x0 * x496 + x494 x1427 = x0 * x503 + x500 x1428 = x198 * x4 x1429 = x0 * x509 + x506 x1430 = x10 * x192 x1431 = x1430 * x4 x1432 = x0 * x517 + x513 x1433 = x482 * x491 x1434 = x0 * x527 + x523 x1435 = x0 * x533 + x531 x1436 = x0 * x539 + x537 x1437 = x0 * x544 + x542 x1438 = x171 * x491 x1439 = x0 * x549 + x547 x1440 = x141 * x525 x1441 = x0 * x554 + x552 x1442 = x116 * x525 + x190 x1443 = x21 * x429 + x678 x1444 = x21 * x408 x1445 = x1096 * x1444 + x1159 x1446 = x21 * x448 + x692 x1447 = x1162 + x1418 * x1444 x1448 = x21 * x463 + x704 x1449 = x21 * x455 x1450 = x1099 * x1449 + x1164 x1451 = x21 * x473 + x714 x1452 = x1166 + x1423 * x1444 x1453 = x21 * x483 + x724 x1454 = x1169 + x1425 * x1449 x1455 = x21 * x496 + x735 x1456 = x1132 * x491 + x1171 x1457 = x21 * x503 + x744 x1458 = x1174 + x1428 * x1444 x1459 = x21 * x509 + x753 x1460 = x1177 + x1431 * x1449 x1461 = x21 * x517 + x762 x1462 = x1179 + x1433 * x21 x1463 = x21 * x527 + x771 x1464 = x1141 * x525 + x1181 x1465 = x21 * x533 + x778 x1466 = x1183 + x1444 * x193 x1467 = x21 * x539 + x784 x1468 = x1185 + x1449 * x198 x1469 = x21 * x544 + x789 x1470 = x1187 + x1438 * x21 x1471 = x21 * x549 + x794 x1472 = x1189 + x1440 * x21 x1473 = x21 * x554 + x799 x1474 = x1191 + x1442 * x248 x1475 = x1096 * x805 x1476 = x22 * x408 x1477 = x1096 * x1476 + x1475 x1478 = x1418 * x805 x1479 = x1418 * x1476 + x1478 x1480 = x1099 * x832 x1481 = x22 * x455 x1482 = x1099 * x1481 + x1480 x1483 = x1423 * x805 x1484 = x1423 * x1476 + x1483 x1485 = x1425 * x832 x1486 = x1425 * x1481 + x1485 x1487 = x274 * x855 x1488 = x1167 * x491 + x1487 x1489 = x1428 * x805 x1490 = x1428 * x1476 + x1489 x1491 = x1430 * x850 x1492 = x1431 * x1481 + x1491 x1493 = x482 * x855 x1494 = x1433 * x22 + x1493 x1495 = x269 * x879 x1496 = x1175 * x525 + x1495 x1497 = x193 * x805 x1498 = x1476 * x193 + x1497 x1499 = x198 * x832 x1500 = x1481 * x198 + x1499 x1501 = x171 * x855 x1502 = x1438 * x22 + x1501 x1503 = x141 * x879 x1504 = x1440 * x22 + x1503 x1505 = x55 * (x116 * x879 + x525 * x68) x1506 = x1442 * x430 + x1505 x1507 = x1159 * x21 + x1239 x1508 = x1445 * x21 + x1507 x1509 = x1162 * x21 + x1242 x1510 = x1447 * x21 + x1509 x1511 = x1164 * x21 + x1245 x1512 = x1450 * x21 + x1511 x1513 = x1166 * x21 + x1248 x1514 = x1452 * x21 + x1513 x1515 = x1169 * x21 + x1251 x1516 = x1454 * x21 + x1515 x1517 = x1171 * x21 + x1254 x1518 = x1456 * x21 + x1517 x1519 = x1174 * x21 + x1257 x1520 = x1458 * x21 + x1519 x1521 = x1177 * x21 + x1260 x1522 = x1460 * x21 + x1521 x1523 = x1179 * x21 + x1263 x1524 = x1462 * x21 + x1523 x1525 = x1181 * x21 + x1266 x1526 = x1464 * x21 + x1525 x1527 = x1183 * x21 + x1269 x1528 = x1466 * x21 + x1527 x1529 = x1185 * x21 + x1272 x1530 = x1468 * x21 + x1529 x1531 = x1187 * x21 + x1275 x1532 = x1470 * x21 + x1531 x1533 = x1189 * x21 + x1279 x1534 = x1472 * x21 + x1533 x1535 = x1191 * x21 + x1282 x1536 = x1474 * x21 + x1535 x1537 = x1286 + x1477 * x21 x1538 = x1289 + x1479 * x21 x1539 = x1292 + x1482 * x21 x1540 = x1295 + x1484 * x21 x1541 = x1298 + x1486 * x21 x1542 = x1301 + x1488 * x21 x1543 = x1304 + x1490 * x21 x1544 = x1307 + x1492 * x21 x1545 = x1310 + x1494 * x21 x1546 = x1313 + x1496 * x21 x1547 = x1316 + x1498 * x21 x1548 = x1319 + x1500 * x21 x1549 = x1322 + x1502 * x21 x1550 = x1325 + x1504 * x21 x1551 = x1328 + x1506 * x21 x1552 = x1060 * x1096 x1553 = x1475 * x22 + x1552 x1554 = x1477 * x22 + x1553 x1555 = x1060 * x1418 x1556 = x1478 * x22 + x1555 x1557 = x1479 * x22 + x1556 x1558 = x1068 * x1099 x1559 = x1480 * x22 + x1558 x1560 = x1482 * x22 + x1559 x1561 = x1060 * x1423 x1562 = x1483 * x22 + x1561 x1563 = x1484 * x22 + x1562 x1564 = x1068 * x1425 x1565 = x1485 * x22 + x1564 x1566 = x1486 * x22 + x1565 x1567 = x1076 * x274 x1568 = x1487 * x22 + x1567 x1569 = x1488 * x22 + x1568 x1570 = x1060 * x1428 x1571 = x1489 * x22 + x1570 x1572 = x1490 * x22 + x1571 x1573 = x1068 * x1431 x1574 = x1491 * x22 + x1573 x1575 = x1492 * x22 + x1574 x1576 = x1076 * x482 x1577 = x1493 * x22 + x1576 x1578 = x1494 * x22 + x1577 x1579 = x1086 * x269 x1580 = x1495 * x22 + x1579 x1581 = x1496 * x22 + x1580 x1582 = x1060 * x193 x1583 = x1497 * x22 + x1582 x1584 = x1498 * x22 + x1583 x1585 = x1068 * x198 x1586 = x1499 * x22 + x1585 x1587 = x1500 * x22 + x1586 x1588 = x1076 * x171 x1589 = x1501 * x22 + x1588 x1590 = x1502 * x22 + x1589 x1591 = x1086 * x141 x1592 = x1503 * x22 + x1591 x1593 = x1504 * x22 + x1592 x1594 = x55 * (x1086 * x116 + x62 * x879) x1595 = x1505 * x22 + x1594 x1596 = x1506 * x22 + x1595 x1597 = x1060 * x402 - x1062 * x818 + 3.0 * x817 x1598 = 4.0 * x1061 + x12 * x1597 x1599 = 4.0 * x1069 + x116 * x1598 x1600 = 4.0 * x1077 + x116 * x1599 # 450 item(s) result[0, 0, 0] = numpy.sum( x99 * ( x0 * x75 + x0 * x80 + x0 * (x0 * (x79 + x85 * x86) + x80) + x55 * (x56 * (x56 * (x54 * x96 + x56 * (x92 + x94)) + x63 * x96) + x70 * x96) ) ) result[0, 0, 1] = numpy.sum( x115 * ( x0 * x107 + x0 * x112 + x0 * (x0 * (x111 + x114 * x86) + x112) + x55 * (x103 * x96 + x56 * (x100 * x56 * (x92 + x94) + x101 * x96)) ) ) result[0, 0, 2] = numpy.sum( x115 * ( x0 * x123 + x0 * x126 + x0 * (x0 * (x125 + x127 * x86) + x126) + x55 * (x119 * x96 + x56 * (x116 * x56 * (x92 + x94) + x117 * x96)) ) ) result[0, 0, 3] = numpy.sum( x140 * ( x0 * x132 + x0 * x136 + x0 * (x0 * (x135 + x138 * x86) + x136) + x55 * (x129 * x56 * (x92 + x94) + x130 * x96) ) ) result[0, 0, 4] = numpy.sum( x152 * ( x0 * x145 + x0 * x150 + x0 * (x0 * (x149 + x151 * x86) + x150) + x55 * (x142 * x56 * (x92 + x94) + x143 * x96) ) ) result[0, 0, 5] = numpy.sum( x140 * ( x0 * x156 + x0 * x160 + x0 * (x0 * (x159 + x162 * x86) + x160) + x55 * (x153 * x56 * (x92 + x94) + x154 * x96) ) ) result[0, 0, 6] = numpy.sum( x115 * ( x0 * x166 + x0 * x168 + x0 * (x0 * (x167 + x170 * x86) + x168) + x165 * x55 * (x92 + x94) ) ) result[0, 0, 7] = numpy.sum( x152 * ( x0 * x173 + x0 * x175 + x0 * (x0 * (x174 + x177 * x86) + x175) + x172 * x55 * (x92 + x94) ) ) result[0, 0, 8] = numpy.sum( x152 * ( x0 * x180 + x0 * x182 + x0 * (x0 * (x181 + x184 * x86) + x182) + x179 * x55 * (x92 + x94) ) ) result[0, 0, 9] = numpy.sum( x115 * ( x0 * x187 + x0 * x189 + x0 * (x0 * (x188 + x191 * x86) + x189) + x186 * x55 * (x92 + x94) ) ) result[0, 0, 10] = numpy.sum( x99 * (x0 * x194 + x0 * x196 + x0 * (x0 * (x193 * x197 + x195) + x196) + x193 * x91) ) result[0, 0, 11] = numpy.sum( x115 * (x0 * x200 + x0 * x202 + x0 * (x0 * (x197 * x199 + x201) + x202) + x199 * x91) ) result[0, 0, 12] = numpy.sum( x140 * (x0 * x205 + x0 * x208 + x0 * (x0 * (x197 * x206 + x207) + x208) + x206 * x91) ) result[0, 0, 13] = numpy.sum( x115 * (x0 * x210 + x0 * x213 + x0 * (x0 * (x197 * x211 + x212) + x213) + x211 * x91) ) result[0, 0, 14] = numpy.sum( x99 * (x0 * x215 + x0 * x217 + x0 * (x0 * (x197 * x214 + x216) + x217) + x214 * x91) ) result[0, 1, 0] = numpy.sum( x257 * (x0 * x245 + x0 * (x0 * x249 + x245) + x21 * x75 + x256) ) result[0, 1, 1] = numpy.sum( x152 * (x0 * x273 + x0 * (x0 * x276 + x273) + x107 * x21 + x279) ) result[0, 1, 2] = numpy.sum( x152 * (x0 * x288 + x0 * (x0 * x290 + x288) + x123 * x21 + x291) ) result[0, 1, 3] = numpy.sum( x306 * (x0 * x299 + x0 * (x0 * x302 + x299) + x132 * x21 + x304) ) result[0, 1, 4] = numpy.sum( x322 * (x0 * x316 + x0 * (x0 * x318 + x316) + x145 * x21 + x321) ) result[0, 1, 5] = numpy.sum( x306 * (x0 * x328 + x0 * (x0 * x331 + x328) + x156 * x21 + x332) ) result[0, 1, 6] = numpy.sum( x152 * (x0 * x337 + x0 * (x0 * x340 + x337) + x166 * x21 + x342) ) result[0, 1, 7] = numpy.sum( x322 * (x0 * x347 + x0 * (x0 * x350 + x347) + x173 * x21 + x352) ) result[0, 1, 8] = numpy.sum( x322 * (x0 * x359 + x0 * (x0 * x362 + x359) + x180 * x21 + x365) ) result[0, 1, 9] = numpy.sum( x152 * (x0 * x368 + x0 * (x0 * x371 + x368) + x187 * x21 + x372) ) result[0, 1, 10] = numpy.sum( x257 * (x0 * x374 + x0 * (x0 * x377 + x374) + x194 * x21 + x378) ) result[0, 1, 11] = numpy.sum( x152 * (x0 * x380 + x0 * (x0 * x382 + x380) + x200 * x21 + x383) ) result[0, 1, 12] = numpy.sum( x306 * (x0 * x385 + x0 * (x0 * x387 + x385) + x205 * x21 + x388) ) result[0, 1, 13] = numpy.sum( x152 * (x0 * x391 + x0 * (x0 * x394 + x391) + x21 * x210 + x396) ) result[0, 1, 14] = numpy.sum( x257 * (x0 * x398 + x0 * (x0 * x400 + x398) + x21 * x215 + x401) ) result[0, 2, 0] = numpy.sum( x257 * (x0 * x428 + x0 * (x0 * x431 + x428) + x22 * x75 + x438) ) result[0, 2, 1] = numpy.sum( x152 * (x0 * x446 + x0 * (x0 * x449 + x446) + x107 * x22 + x450) ) result[0, 2, 2] = numpy.sum( x152 * (x0 * x461 + x0 * (x0 * x464 + x461) + x123 * x22 + x466) ) result[0, 2, 3] = numpy.sum( x306 * (x0 * x471 + x0 * (x0 * x474 + x471) + x132 * x22 + x475) ) result[0, 2, 4] = numpy.sum( x322 * (x0 * x481 + x0 * (x0 * x484 + x481) + x145 * x22 + x486) ) result[0, 2, 5] = numpy.sum( x306 * (x0 * x495 + x0 * (x0 * x497 + x495) + x156 * x22 + x499) ) result[0, 2, 6] = numpy.sum( x152 * (x0 * x501 + x0 * (x0 * x504 + x501) + x166 * x22 + x505) ) result[0, 2, 7] = numpy.sum( x322 * (x0 * x507 + x0 * (x0 * x510 + x507) + x173 * x22 + x511) ) result[0, 2, 8] = numpy.sum( x322 * (x0 * x514 + x0 * (x0 * x518 + x514) + x180 * x22 + x519) ) result[0, 2, 9] = numpy.sum( x152 * (x0 * x524 + x0 * (x0 * x528 + x524) + x187 * x22 + x530) ) result[0, 2, 10] = numpy.sum( x257 * (x0 * x532 + x0 * (x0 * x535 + x532) + x194 * x22 + x536) ) result[0, 2, 11] = numpy.sum( x152 * (x0 * x538 + x0 * (x0 * x540 + x538) + x200 * x22 + x541) ) result[0, 2, 12] = numpy.sum( x306 * (x0 * x543 + x0 * (x0 * x545 + x543) + x205 * x22 + x546) ) result[0, 2, 13] = numpy.sum( x152 * (x0 * x548 + x0 * (x0 * x550 + x548) + x210 * x22 + x551) ) result[0, 2, 14] = numpy.sum( x257 * (x0 * x553 + x0 * (x0 * x555 + x553) + x215 * x22 + x556) ) result[0, 3, 0] = numpy.sum(x257 * (x0 * x569 + x21 * x245 + x577)) result[0, 3, 1] = numpy.sum(x152 * (x0 * x588 + x21 * x273 + x592)) result[0, 3, 2] = numpy.sum(x152 * (x0 * x599 + x21 * x288 + x600)) result[0, 3, 3] = numpy.sum(x306 * (x0 * x606 + x21 * x299 + x608)) result[0, 3, 4] = numpy.sum(x322 * (x0 * x614 + x21 * x316 + x616)) result[0, 3, 5] = numpy.sum(x306 * (x0 * x621 + x21 * x328 + x622)) result[0, 3, 6] = numpy.sum(x152 * (x0 * x627 + x21 * x337 + x629)) result[0, 3, 7] = numpy.sum(x322 * (x0 * x634 + x21 * x347 + x636)) result[0, 3, 8] = numpy.sum(x322 * (x0 * x641 + x21 * x359 + x643)) result[0, 3, 9] = numpy.sum(x152 * (x0 * x647 + x21 * x368 + x648)) result[0, 3, 10] = numpy.sum(x257 * (x0 * x651 + x21 * x374 + x652)) result[0, 3, 11] = numpy.sum(x152 * (x0 * x655 + x21 * x380 + x656)) result[0, 3, 12] = numpy.sum(x306 * (x0 * x659 + x21 * x385 + x660)) result[0, 3, 13] = numpy.sum(x152 * (x0 * x663 + x21 * x391 + x664)) result[0, 3, 14] = numpy.sum(x257 * (x0 * x667 + x21 * x398 + x668)) result[0, 4, 0] = numpy.sum(x687 * (x0 * x680 + x21 * x428 + x686)) result[0, 4, 1] = numpy.sum(x699 * (x0 * x694 + x21 * x446 + x698)) result[0, 4, 2] = numpy.sum(x699 * (x0 * x706 + x21 * x461 + x710)) result[0, 4, 3] = numpy.sum(x322 * (x0 * x716 + x21 * x471 + x720)) result[0, 4, 4] = numpy.sum(x731 * (x0 * x726 + x21 * x481 + x730)) result[0, 4, 5] = numpy.sum(x322 * (x0 * x737 + x21 * x495 + x741)) result[0, 4, 6] = numpy.sum(x699 * (x0 * x746 + x21 * x501 + x750)) result[0, 4, 7] = numpy.sum(x731 * (x0 * x755 + x21 * x507 + x759)) result[0, 4, 8] = numpy.sum(x731 * (x0 * x764 + x21 * x514 + x768)) result[0, 4, 9] = numpy.sum(x699 * (x0 * x773 + x21 * x524 + x777)) result[0, 4, 10] = numpy.sum(x687 * (x0 * x780 + x21 * x532 + x782)) result[0, 4, 11] = numpy.sum(x699 * (x0 * x786 + x21 * x538 + x788)) result[0, 4, 12] = numpy.sum(x322 * (x0 * x791 + x21 * x543 + x793)) result[0, 4, 13] = numpy.sum(x699 * (x0 * x796 + x21 * x548 + x798)) result[0, 4, 14] = numpy.sum(x687 * (x0 * x801 + x21 * x553 + x803)) result[0, 5, 0] = numpy.sum(x257 * (x0 * x816 + x22 * x428 + x824)) result[0, 5, 1] = numpy.sum(x152 * (x0 * x830 + x22 * x446 + x831)) result[0, 5, 2] = numpy.sum(x152 * (x0 * x839 + x22 * x461 + x841)) result[0, 5, 3] = numpy.sum(x306 * (x0 * x846 + x22 * x471 + x847)) result[0, 5, 4] = numpy.sum(x322 * (x0 * x853 + x22 * x481 + x854)) result[0, 5, 5] = numpy.sum(x306 * (x0 * x861 + x22 * x495 + x863)) result[0, 5, 6] = numpy.sum(x152 * (x0 * x867 + x22 * x501 + x868)) result[0, 5, 7] = numpy.sum(x322 * (x0 * x872 + x22 * x507 + x873)) result[0, 5, 8] = numpy.sum(x322 * (x0 * x877 + x22 * x514 + x878)) result[0, 5, 9] = numpy.sum(x152 * (x0 * x884 + x22 * x524 + x886)) result[0, 5, 10] = numpy.sum(x257 * (x0 * x889 + x22 * x532 + x890)) result[0, 5, 11] = numpy.sum(x152 * (x0 * x893 + x22 * x538 + x894)) result[0, 5, 12] = numpy.sum(x306 * (x0 * x897 + x22 * x543 + x898)) result[0, 5, 13] = numpy.sum(x152 * (x0 * x901 + x22 * x548 + x902)) result[0, 5, 14] = numpy.sum(x257 * (x0 * x905 + x22 * x553 + x906)) result[0, 6, 0] = numpy.sum(x99 * (x21 * x569 + x912)) result[0, 6, 1] = numpy.sum(x115 * (x21 * x588 + x920)) result[0, 6, 2] = numpy.sum(x115 * (x21 * x599 + x923)) result[0, 6, 3] = numpy.sum(x140 * (x21 * x606 + x927)) result[0, 6, 4] = numpy.sum(x152 * (x21 * x614 + x931)) result[0, 6, 5] = numpy.sum(x140 * (x21 * x621 + x933)) result[0, 6, 6] = numpy.sum(x115 * (x21 * x627 + x937)) result[0, 6, 7] = numpy.sum(x152 * (x21 * x634 + x941)) result[0, 6, 8] = numpy.sum(x152 * (x21 * x641 + x945)) result[0, 6, 9] = numpy.sum(x115 * (x21 * x647 + x947)) result[0, 6, 10] = numpy.sum(x99 * (x21 * x651 + x948)) result[0, 6, 11] = numpy.sum(x115 * (x21 * x655 + x949)) result[0, 6, 12] = numpy.sum(x140 * (x21 * x659 + x950)) result[0, 6, 13] = numpy.sum(x115 * (x21 * x663 + x951)) result[0, 6, 14] = numpy.sum(x99 * (x21 * x667 + x952)) result[0, 7, 0] = numpy.sum(x257 * (x21 * x680 + x958)) result[0, 7, 1] = numpy.sum(x152 * (x21 * x694 + x963)) result[0, 7, 2] = numpy.sum(x152 * (x21 * x706 + x967)) result[0, 7, 3] = numpy.sum(x306 * (x21 * x716 + x971)) result[0, 7, 4] = numpy.sum(x322 * (x21 * x726 + x976)) result[0, 7, 5] = numpy.sum(x306 * (x21 * x737 + x980)) result[0, 7, 6] = numpy.sum(x152 * (x21 * x746 + x984)) result[0, 7, 7] = numpy.sum(x322 * (x21 * x755 + x988)) result[0, 7, 8] = numpy.sum(x322 * (x21 * x764 + x993)) result[0, 7, 9] = numpy.sum(x152 * (x21 * x773 + x997)) result[0, 7, 10] = numpy.sum(x257 * (x21 * x780 + x999)) result[0, 7, 11] = numpy.sum(x152 * (x1001 + x21 * x786)) result[0, 7, 12] = numpy.sum(x306 * (x1003 + x21 * x791)) result[0, 7, 13] = numpy.sum(x152 * (x1005 + x21 * x796)) result[0, 7, 14] = numpy.sum(x257 * (x1007 + x21 * x801)) result[0, 8, 0] = numpy.sum(x257 * (x1013 + x21 * x816)) result[0, 8, 1] = numpy.sum(x152 * (x1017 + x21 * x830)) result[0, 8, 2] = numpy.sum(x152 * (x1021 + x21 * x839)) result[0, 8, 3] = numpy.sum(x306 * (x1025 + x21 * x846)) result[0, 8, 4] = numpy.sum(x322 * (x1029 + x21 * x853)) result[0, 8, 5] = numpy.sum(x306 * (x1033 + x21 * x861)) result[0, 8, 6] = numpy.sum(x152 * (x1037 + x21 * x867)) result[0, 8, 7] = numpy.sum(x322 * (x1041 + x21 * x872)) result[0, 8, 8] = numpy.sum(x322 * (x1045 + x21 * x877)) result[0, 8, 9] = numpy.sum(x152 * (x1049 + x21 * x884)) result[0, 8, 10] = numpy.sum(x257 * (x1051 + x21 * x889)) result[0, 8, 11] = numpy.sum(x152 * (x1053 + x21 * x893)) result[0, 8, 12] = numpy.sum(x306 * (x1055 + x21 * x897)) result[0, 8, 13] = numpy.sum(x152 * (x1057 + x21 * x901)) result[0, 8, 14] = numpy.sum(x257 * (x1059 + x21 * x905)) result[0, 9, 0] = numpy.sum(x99 * (x1065 + x22 * x816)) result[0, 9, 1] = numpy.sum(x115 * (x1067 + x22 * x830)) result[0, 9, 2] = numpy.sum(x115 * (x1071 + x22 * x839)) result[0, 9, 3] = numpy.sum(x140 * (x1073 + x22 * x846)) result[0, 9, 4] = numpy.sum(x152 * (x1075 + x22 * x853)) result[0, 9, 5] = numpy.sum(x140 * (x1079 + x22 * x861)) result[0, 9, 6] = numpy.sum(x115 * (x1081 + x22 * x867)) result[0, 9, 7] = numpy.sum(x152 * (x1083 + x22 * x872)) result[0, 9, 8] = numpy.sum(x152 * (x1085 + x22 * x877)) result[0, 9, 9] = numpy.sum(x115 * (x1089 + x22 * x884)) result[0, 9, 10] = numpy.sum(x99 * (x1090 + x22 * x889)) result[0, 9, 11] = numpy.sum(x115 * (x1091 + x22 * x893)) result[0, 9, 12] = numpy.sum(x140 * (x1092 + x22 * x897)) result[0, 9, 13] = numpy.sum(x115 * (x1093 + x22 * x901)) result[0, 9, 14] = numpy.sum(x99 * (x1094 + x22 * x905)) result[1, 0, 0] = numpy.sum( x99 * (x0 * x1095 + x0 * x244 + x0 * (x0 * (x1096 * x1097 + x247) + x1095) + x256) ) result[1, 0, 1] = numpy.sum( x115 * (x0 * x1098 + x0 * x272 + x0 * (x0 * (x0 * x1100 + x275) + x1098) + x279) ) result[1, 0, 2] = numpy.sum( x115 * (x0 * x1101 + x0 * x287 + x0 * (x0 * (x1097 * x1102 + x289) + x1101) + x291) ) result[1, 0, 3] = numpy.sum( x140 * (x0 * x1103 + x0 * x298 + x0 * (x0 * (x1104 * x296 + x301) + x1103) + x304) ) result[1, 0, 4] = numpy.sum( x152 * (x0 * x1105 + x0 * x315 + x0 * (x0 * (x1104 * x313 + x317) + x1105) + x321) ) result[1, 0, 5] = numpy.sum( x140 * (x0 * x1106 + x0 * x327 + x0 * (x0 * (x1107 * x1108 + x330) + x1106) + x332) ) result[1, 0, 6] = numpy.sum( x115 * (x0 * x1109 + x0 * x336 + x0 * (x0 * (x1110 * x338 + x339) + x1109) + x342) ) result[1, 0, 7] = numpy.sum( x152 * (x0 * x1111 + x0 * x346 + x0 * (x0 * (x1110 * x348 + x349) + x1111) + x352) ) result[1, 0, 8] = numpy.sum( x152 * (x0 * x1112 + x0 * x358 + x0 * (x0 * (x1110 * x360 + x361) + x1112) + x365) ) result[1, 0, 9] = numpy.sum( x115 * (x0 * x1113 + x0 * x367 + x0 * (x0 * (x1108 * x1114 + x370) + x1113) + x372) ) result[1, 0, 10] = numpy.sum( x99 * (x0 * x1115 + x0 * x373 + x0 * (x0 * (x1116 * x86 + x375) + x1115) + x378) ) result[1, 0, 11] = numpy.sum( x115 * (x0 * x1117 + x0 * x379 + x0 * (x0 * (x1118 * x86 + x381) + x1117) + x383) ) result[1, 0, 12] = numpy.sum( x140 * (x0 * x1119 + x0 * x384 + x0 * (x0 * (x1120 * x86 + x386) + x1119) + x388) ) result[1, 0, 13] = numpy.sum( x115 * (x0 * x1121 + x0 * x390 + x0 * (x0 * (x1122 * x86 + x393) + x1121) + x396) ) result[1, 0, 14] = numpy.sum( x99 * (x0 * x1123 + x0 * x397 + x0 * (x0 * (x1097 * x214 + x399) + x1123) + x401) ) result[1, 1, 0] = numpy.sum(x257 * (x0 * x568 + x0 * (x0 * x1126 + x568) + x577)) result[1, 1, 1] = numpy.sum(x152 * (x0 * x587 + x0 * (x0 * x1128 + x587) + x592)) result[1, 1, 2] = numpy.sum(x152 * (x0 * x598 + x0 * (x0 * x1130 + x598) + x600)) result[1, 1, 3] = numpy.sum(x306 * (x0 * x605 + x0 * (x0 * x1133 + x605) + x608)) result[1, 1, 4] = numpy.sum(x322 * (x0 * x613 + x0 * (x0 * x1135 + x613) + x616)) result[1, 1, 5] = numpy.sum(x306 * (x0 * x620 + x0 * (x0 * x1139 + x620) + x622)) result[1, 1, 6] = numpy.sum(x152 * (x0 * x626 + x0 * (x0 * x1142 + x626) + x629)) result[1, 1, 7] = numpy.sum(x322 * (x0 * x633 + x0 * (x0 * x1144 + x633) + x636)) result[1, 1, 8] = numpy.sum(x322 * (x0 * x640 + x0 * (x0 * x1146 + x640) + x643)) result[1, 1, 9] = numpy.sum(x152 * (x0 * x646 + x0 * (x0 * x1148 + x646) + x648)) result[1, 1, 10] = numpy.sum(x257 * (x0 * x650 + x0 * (x0 * x1150 + x650) + x652)) result[1, 1, 11] = numpy.sum(x152 * (x0 * x654 + x0 * (x0 * x1152 + x654) + x656)) result[1, 1, 12] = numpy.sum(x306 * (x0 * x658 + x0 * (x0 * x1154 + x658) + x660)) result[1, 1, 13] = numpy.sum(x152 * (x0 * x662 + x0 * (x0 * x1156 + x662) + x664)) result[1, 1, 14] = numpy.sum(x257 * (x0 * x666 + x0 * (x0 * x1158 + x666) + x668)) result[1, 2, 0] = numpy.sum(x257 * (x0 * x679 + x0 * (x0 * x1161 + x679) + x686)) result[1, 2, 1] = numpy.sum(x152 * (x0 * x693 + x0 * (x0 * x1163 + x693) + x698)) result[1, 2, 2] = numpy.sum(x152 * (x0 * x705 + x0 * (x0 * x1165 + x705) + x710)) result[1, 2, 3] = numpy.sum(x306 * (x0 * x715 + x0 * (x0 * x1168 + x715) + x720)) result[1, 2, 4] = numpy.sum(x322 * (x0 * x725 + x0 * (x0 * x1170 + x725) + x730)) result[1, 2, 5] = numpy.sum(x306 * (x0 * x736 + x0 * (x0 * x1173 + x736) + x741)) result[1, 2, 6] = numpy.sum(x152 * (x0 * x745 + x0 * (x0 * x1176 + x745) + x750)) result[1, 2, 7] = numpy.sum(x322 * (x0 * x754 + x0 * (x0 * x1178 + x754) + x759)) result[1, 2, 8] = numpy.sum(x322 * (x0 * x763 + x0 * (x0 * x1180 + x763) + x768)) result[1, 2, 9] = numpy.sum(x152 * (x0 * x772 + x0 * (x0 * x1182 + x772) + x777)) result[1, 2, 10] = numpy.sum(x257 * (x0 * x779 + x0 * (x0 * x1184 + x779) + x782)) result[1, 2, 11] = numpy.sum(x152 * (x0 * x785 + x0 * (x0 * x1186 + x785) + x788)) result[1, 2, 12] = numpy.sum(x306 * (x0 * x790 + x0 * (x0 * x1188 + x790) + x793)) result[1, 2, 13] = numpy.sum(x152 * (x0 * x795 + x0 * (x0 * x1190 + x795) + x798)) result[1, 2, 14] = numpy.sum(x257 * (x0 * x800 + x0 * (x0 * x1192 + x800) + x803)) result[1, 3, 0] = numpy.sum(x257 * (x0 * x1195 + x912)) result[1, 3, 1] = numpy.sum(x152 * (x0 * x1198 + x920)) result[1, 3, 2] = numpy.sum(x152 * (x0 * x1201 + x923)) result[1, 3, 3] = numpy.sum(x306 * (x0 * x1204 + x927)) result[1, 3, 4] = numpy.sum(x322 * (x0 * x1207 + x931)) result[1, 3, 5] = numpy.sum(x306 * (x0 * x1211 + x933)) result[1, 3, 6] = numpy.sum(x152 * (x0 * x1214 + x937)) result[1, 3, 7] = numpy.sum(x322 * (x0 * x1217 + x941)) result[1, 3, 8] = numpy.sum(x322 * (x0 * x1220 + x945)) result[1, 3, 9] = numpy.sum(x152 * (x0 * x1223 + x947)) result[1, 3, 10] = numpy.sum(x257 * (x0 * x1226 + x948)) result[1, 3, 11] = numpy.sum(x152 * (x0 * x1229 + x949)) result[1, 3, 12] = numpy.sum(x306 * (x0 * x1232 + x950)) result[1, 3, 13] = numpy.sum(x152 * (x0 * x1235 + x951)) result[1, 3, 14] = numpy.sum(x257 * (x0 * x1238 + x952)) result[1, 4, 0] = numpy.sum(x687 * (x0 * x1241 + x958)) result[1, 4, 1] = numpy.sum(x699 * (x0 * x1244 + x963)) result[1, 4, 2] = numpy.sum(x699 * (x0 * x1247 + x967)) result[1, 4, 3] = numpy.sum(x322 * (x0 * x1250 + x971)) result[1, 4, 4] = numpy.sum(x731 * (x0 * x1253 + x976)) result[1, 4, 5] = numpy.sum(x322 * (x0 * x1256 + x980)) result[1, 4, 6] = numpy.sum(x699 * (x0 * x1259 + x984)) result[1, 4, 7] = numpy.sum(x731 * (x0 * x1262 + x988)) result[1, 4, 8] = numpy.sum(x731 * (x0 * x1265 + x993)) result[1, 4, 9] = numpy.sum(x699 * (x0 * x1268 + x997)) result[1, 4, 10] = numpy.sum(x687 * (x0 * x1271 + x999)) result[1, 4, 11] = numpy.sum(x699 * (x0 * x1274 + x1001)) result[1, 4, 12] = numpy.sum(x322 * (x0 * x1277 + x1003)) result[1, 4, 13] = numpy.sum(x699 * (x0 * x1281 + x1005)) result[1, 4, 14] = numpy.sum(x687 * (x0 * x1284 + x1007)) result[1, 5, 0] = numpy.sum(x257 * (x0 * x1287 + x1013)) result[1, 5, 1] = numpy.sum(x152 * (x0 * x1290 + x1017)) result[1, 5, 2] = numpy.sum(x152 * (x0 * x1293 + x1021)) result[1, 5, 3] = numpy.sum(x306 * (x0 * x1296 + x1025)) result[1, 5, 4] = numpy.sum(x322 * (x0 * x1299 + x1029)) result[1, 5, 5] = numpy.sum(x306 * (x0 * x1302 + x1033)) result[1, 5, 6] = numpy.sum(x152 * (x0 * x1305 + x1037)) result[1, 5, 7] = numpy.sum(x322 * (x0 * x1308 + x1041)) result[1, 5, 8] = numpy.sum(x322 * (x0 * x1311 + x1045)) result[1, 5, 9] = numpy.sum(x152 * (x0 * x1314 + x1049)) result[1, 5, 10] = numpy.sum(x257 * (x0 * x1317 + x1051)) result[1, 5, 11] = numpy.sum(x152 * (x0 * x1320 + x1053)) result[1, 5, 12] = numpy.sum(x306 * (x0 * x1323 + x1055)) result[1, 5, 13] = numpy.sum(x152 * (x0 * x1326 + x1057)) result[1, 5, 14] = numpy.sum(x257 * (x0 * x1329 + x1059)) result[1, 6, 0] = numpy.sum( x99 * (x1096 * x1330 + x1193 * x21 + x1194 * x21 + x1195 * x21) ) result[1, 6, 1] = numpy.sum( x115 * (x1099 * x1333 + x1196 * x21 + x1197 * x21 + x1198 * x21) ) result[1, 6, 2] = numpy.sum( x115 * (x1102 * x1330 + x1199 * x21 + x1200 * x21 + x1201 * x21) ) result[1, 6, 3] = numpy.sum( x140 * (x1202 * x21 + x1203 * x21 + x1204 * x21 + x1334 * x274) ) result[1, 6, 4] = numpy.sum( x152 * (x1205 * x21 + x1206 * x21 + x1207 * x21 + x1335 * x274) ) result[1, 6, 5] = numpy.sum( x140 * (x1107 * x1336 + x1209 * x21 + x1210 * x21 + x1211 * x21) ) result[1, 6, 6] = numpy.sum( x115 * (x1212 * x21 + x1213 * x21 + x1214 * x21 + x1337 * x269) ) result[1, 6, 7] = numpy.sum( x152 * (x1215 * x21 + x1216 * x21 + x1217 * x21 + x1338 * x269) ) result[1, 6, 8] = numpy.sum( x152 * (x1218 * x21 + x1219 * x21 + x1220 * x21 + x1339 * x269) ) result[1, 6, 9] = numpy.sum( x115 * (x1114 * x1336 + x1221 * x21 + x1222 * x21 + x1223 * x21) ) result[1, 6, 10] = numpy.sum( x99 * (x1224 * x21 + x1225 * x21 + x1226 * x21 + x55 * (x100 * x1337 + 4.0 * x935)) ) result[1, 6, 11] = numpy.sum( x115 * (x1227 * x21 + x1228 * x21 + x1229 * x21 + x55 * (x100 * x1338 + 4.0 * x939)) ) result[1, 6, 12] = numpy.sum( x140 * (x1230 * x21 + x1231 * x21 + x1232 * x21 + x55 * (x100 * x1339 + 4.0 * x943)) ) result[1, 6, 13] = numpy.sum( x115 * (x1233 * x21 + x1234 * x21 + x1235 * x21 + x186 * x55 * (x1331 + x1332)) ) result[1, 6, 14] = numpy.sum( x99 * (x1236 * x21 + x1237 * x21 + x1238 * x21 + x1330 * x214) ) result[1, 7, 0] = numpy.sum(x257 * (x1193 * x22 + x1240 * x21 + x1241 * x21 + x1341)) result[1, 7, 1] = numpy.sum(x152 * (x1196 * x22 + x1243 * x21 + x1244 * x21 + x1343)) result[1, 7, 2] = numpy.sum(x152 * (x1199 * x22 + x1246 * x21 + x1247 * x21 + x1345)) result[1, 7, 3] = numpy.sum(x306 * (x1202 * x22 + x1249 * x21 + x1250 * x21 + x1347)) result[1, 7, 4] = numpy.sum(x322 * (x1205 * x22 + x1252 * x21 + x1253 * x21 + x1349)) result[1, 7, 5] = numpy.sum(x306 * (x1209 * x22 + x1255 * x21 + x1256 * x21 + x1351)) result[1, 7, 6] = numpy.sum(x152 * (x1212 * x22 + x1258 * x21 + x1259 * x21 + x1353)) result[1, 7, 7] = numpy.sum(x322 * (x1215 * x22 + x1261 * x21 + x1262 * x21 + x1355)) result[1, 7, 8] = numpy.sum(x322 * (x1218 * x22 + x1264 * x21 + x1265 * x21 + x1357)) result[1, 7, 9] = numpy.sum(x152 * (x1221 * x22 + x1267 * x21 + x1268 * x21 + x1359)) result[1, 7, 10] = numpy.sum(x257 * (x1224 * x22 + x1270 * x21 + x1271 * x21 + x1360)) result[1, 7, 11] = numpy.sum(x152 * (x1227 * x22 + x1273 * x21 + x1274 * x21 + x1361)) result[1, 7, 12] = numpy.sum(x306 * (x1230 * x22 + x1276 * x21 + x1277 * x21 + x1362)) result[1, 7, 13] = numpy.sum(x152 * (x1233 * x22 + x1280 * x21 + x1281 * x21 + x1363)) result[1, 7, 14] = numpy.sum(x257 * (x1236 * x22 + x1283 * x21 + x1284 * x21 + x1364)) result[1, 8, 0] = numpy.sum(x257 * (x1240 * x22 + x1287 * x21 + x1366)) result[1, 8, 1] = numpy.sum(x152 * (x1243 * x22 + x1290 * x21 + x1368)) result[1, 8, 2] = numpy.sum(x152 * (x1246 * x22 + x1293 * x21 + x1370)) result[1, 8, 3] = numpy.sum(x306 * (x1249 * x22 + x1296 * x21 + x1372)) result[1, 8, 4] = numpy.sum(x322 * (x1252 * x22 + x1299 * x21 + x1374)) result[1, 8, 5] = numpy.sum(x306 * (x1255 * x22 + x1302 * x21 + x1376)) result[1, 8, 6] = numpy.sum(x152 * (x1258 * x22 + x1305 * x21 + x1378)) result[1, 8, 7] = numpy.sum(x322 * (x1261 * x22 + x1308 * x21 + x1380)) result[1, 8, 8] = numpy.sum(x322 * (x1264 * x22 + x1311 * x21 + x1382)) result[1, 8, 9] = numpy.sum(x152 * (x1267 * x22 + x1314 * x21 + x1384)) result[1, 8, 10] = numpy.sum(x257 * (x1270 * x22 + x1317 * x21 + x1385)) result[1, 8, 11] = numpy.sum(x152 * (x1273 * x22 + x1320 * x21 + x1386)) result[1, 8, 12] = numpy.sum(x306 * (x1276 * x22 + x1323 * x21 + x1387)) result[1, 8, 13] = numpy.sum(x152 * (x1280 * x22 + x1326 * x21 + x1388)) result[1, 8, 14] = numpy.sum(x257 * (x1283 * x22 + x1329 * x21 + x1389)) result[1, 9, 0] = numpy.sum(x99 * (x1287 * x22 + x1391)) result[1, 9, 1] = numpy.sum(x115 * (x1290 * x22 + x1393)) result[1, 9, 2] = numpy.sum(x115 * (x1293 * x22 + x1395)) result[1, 9, 3] = numpy.sum(x140 * (x1296 * x22 + x1397)) result[1, 9, 4] = numpy.sum(x152 * (x1299 * x22 + x1399)) result[1, 9, 5] = numpy.sum(x140 * (x1302 * x22 + x1401)) result[1, 9, 6] = numpy.sum(x115 * (x1305 * x22 + x1403)) result[1, 9, 7] = numpy.sum(x152 * (x1308 * x22 + x1405)) result[1, 9, 8] = numpy.sum(x152 * (x1311 * x22 + x1407)) result[1, 9, 9] = numpy.sum(x115 * (x1314 * x22 + x1409)) result[1, 9, 10] = numpy.sum(x99 * (x1317 * x22 + x1410)) result[1, 9, 11] = numpy.sum(x115 * (x1320 * x22 + x1411)) result[1, 9, 12] = numpy.sum(x140 * (x1323 * x22 + x1412)) result[1, 9, 13] = numpy.sum(x115 * (x1326 * x22 + x1413)) result[1, 9, 14] = numpy.sum(x99 * (x1329 * x22 + x1414)) result[2, 0, 0] = numpy.sum( x99 * (x0 * x1415 + x0 * x427 + x0 * (x0 * (x1096 * x1416 + x429) + x1415) + x438) ) result[2, 0, 1] = numpy.sum( x115 * (x0 * x1417 + x0 * x445 + x0 * (x0 * (x1416 * x1418 + x448) + x1417) + x450) ) result[2, 0, 2] = numpy.sum( x115 * (x0 * x1419 + x0 * x460 + x0 * (x0 * (x1099 * x1420 + x463) + x1419) + x466) ) result[2, 0, 3] = numpy.sum( x140 * (x0 * x1421 + x0 * x470 + x0 * (x0 * (x1416 * x1423 + x473) + x1421) + x475) ) result[2, 0, 4] = numpy.sum( x152 * (x0 * x1424 + x0 * x480 + x0 * (x0 * (x1420 * x1425 + x483) + x1424) + x486) ) result[2, 0, 5] = numpy.sum( x140 * (x0 * x1426 + x0 * x494 + x0 * (x0 * (x1104 * x491 + x496) + x1426) + x499) ) result[2, 0, 6] = numpy.sum( x115 * (x0 * x1427 + x0 * x500 + x0 * (x0 * (x1416 * x1428 + x503) + x1427) + x505) ) result[2, 0, 7] = numpy.sum( x152 * (x0 * x1429 + x0 * x506 + x0 * (x0 * (x1420 * x1431 + x509) + x1429) + x511) ) result[2, 0, 8] = numpy.sum( x152 * (x0 * x1432 + x0 * x513 + x0 * (x0 * (x0 * x1433 + x517) + x1432) + x519) ) result[2, 0, 9] = numpy.sum( x115 * (x0 * x1434 + x0 * x523 + x0 * (x0 * (x1110 * x525 + x527) + x1434) + x530) ) result[2, 0, 10] = numpy.sum( x99 * (x0 * x1435 + x0 * x531 + x0 * (x0 * (x1416 * x193 + x533) + x1435) + x536) ) result[2, 0, 11] = numpy.sum( x115 * (x0 * x1436 + x0 * x537 + x0 * (x0 * (x1420 * x198 + x539) + x1436) + x541) ) result[2, 0, 12] = numpy.sum( x140 * (x0 * x1437 + x0 * x542 + x0 * (x0 * (x0 * x1438 + x544) + x1437) + x546) ) result[2, 0, 13] = numpy.sum( x115 * (x0 * x1439 + x0 * x547 + x0 * (x0 * (x0 * x1440 + x549) + x1439) + x551) ) result[2, 0, 14] = numpy.sum( x99 * (x0 * x1441 + x0 * x552 + x0 * (x0 * (x1442 * x86 + x554) + x1441) + x556) ) result[2, 1, 0] = numpy.sum( x257 * (x0 * x1443 + x0 * (x0 * x1445 + x1443) + x21 * x427 + x685) ) result[2, 1, 1] = numpy.sum( x152 * (x0 * x1446 + x0 * (x0 * x1447 + x1446) + x21 * x445 + x697) ) result[2, 1, 2] = numpy.sum( x152 * (x0 * x1448 + x0 * (x0 * x1450 + x1448) + x21 * x460 + x709) ) result[2, 1, 3] = numpy.sum( x306 * (x0 * x1451 + x0 * (x0 * x1452 + x1451) + x21 * x470 + x719) ) result[2, 1, 4] = numpy.sum( x322 * (x0 * x1453 + x0 * (x0 * x1454 + x1453) + x21 * x480 + x729) ) result[2, 1, 5] = numpy.sum( x306 * (x0 * x1455 + x0 * (x0 * x1456 + x1455) + x21 * x494 + x740) ) result[2, 1, 6] = numpy.sum( x152 * (x0 * x1457 + x0 * (x0 * x1458 + x1457) + x21 * x500 + x749) ) result[2, 1, 7] = numpy.sum( x322 * (x0 * x1459 + x0 * (x0 * x1460 + x1459) + x21 * x506 + x758) ) result[2, 1, 8] = numpy.sum( x322 * (x0 * x1461 + x0 * (x0 * x1462 + x1461) + x21 * x513 + x767) ) result[2, 1, 9] = numpy.sum( x152 * (x0 * x1463 + x0 * (x0 * x1464 + x1463) + x21 * x523 + x776) ) result[2, 1, 10] = numpy.sum( x257 * (x0 * x1465 + x0 * (x0 * x1466 + x1465) + x21 * x531 + x781) ) result[2, 1, 11] = numpy.sum( x152 * (x0 * x1467 + x0 * (x0 * x1468 + x1467) + x21 * x537 + x787) ) result[2, 1, 12] = numpy.sum( x306 * (x0 * x1469 + x0 * (x0 * x1470 + x1469) + x21 * x542 + x792) ) result[2, 1, 13] = numpy.sum( x152 * (x0 * x1471 + x0 * (x0 * x1472 + x1471) + x21 * x547 + x797) ) result[2, 1, 14] = numpy.sum( x257 * (x0 * x1473 + x0 * (x0 * x1474 + x1473) + x21 * x552 + x802) ) result[2, 2, 0] = numpy.sum(x257 * (x0 * x815 + x0 * (x0 * x1477 + x815) + x824)) result[2, 2, 1] = numpy.sum(x152 * (x0 * x829 + x0 * (x0 * x1479 + x829) + x831)) result[2, 2, 2] = numpy.sum(x152 * (x0 * x838 + x0 * (x0 * x1482 + x838) + x841)) result[2, 2, 3] = numpy.sum(x306 * (x0 * x845 + x0 * (x0 * x1484 + x845) + x847)) result[2, 2, 4] = numpy.sum(x322 * (x0 * x852 + x0 * (x0 * x1486 + x852) + x854)) result[2, 2, 5] = numpy.sum(x306 * (x0 * x860 + x0 * (x0 * x1488 + x860) + x863)) result[2, 2, 6] = numpy.sum(x152 * (x0 * x866 + x0 * (x0 * x1490 + x866) + x868)) result[2, 2, 7] = numpy.sum(x322 * (x0 * x871 + x0 * (x0 * x1492 + x871) + x873)) result[2, 2, 8] = numpy.sum(x322 * (x0 * x876 + x0 * (x0 * x1494 + x876) + x878)) result[2, 2, 9] = numpy.sum(x152 * (x0 * x883 + x0 * (x0 * x1496 + x883) + x886)) result[2, 2, 10] = numpy.sum(x257 * (x0 * x888 + x0 * (x0 * x1498 + x888) + x890)) result[2, 2, 11] = numpy.sum(x152 * (x0 * x892 + x0 * (x0 * x1500 + x892) + x894)) result[2, 2, 12] = numpy.sum(x306 * (x0 * x896 + x0 * (x0 * x1502 + x896) + x898)) result[2, 2, 13] = numpy.sum(x152 * (x0 * x900 + x0 * (x0 * x1504 + x900) + x902)) result[2, 2, 14] = numpy.sum(x257 * (x0 * x904 + x0 * (x0 * x1506 + x904) + x906)) result[2, 3, 0] = numpy.sum(x257 * (x0 * x1508 + x1443 * x21 + x21 * x678 + x957)) result[2, 3, 1] = numpy.sum(x152 * (x0 * x1510 + x1446 * x21 + x21 * x692 + x962)) result[2, 3, 2] = numpy.sum(x152 * (x0 * x1512 + x1448 * x21 + x21 * x704 + x966)) result[2, 3, 3] = numpy.sum(x306 * (x0 * x1514 + x1451 * x21 + x21 * x714 + x970)) result[2, 3, 4] = numpy.sum(x322 * (x0 * x1516 + x1453 * x21 + x21 * x724 + x975)) result[2, 3, 5] = numpy.sum(x306 * (x0 * x1518 + x1455 * x21 + x21 * x735 + x979)) result[2, 3, 6] = numpy.sum(x152 * (x0 * x1520 + x1457 * x21 + x21 * x744 + x983)) result[2, 3, 7] = numpy.sum(x322 * (x0 * x1522 + x1459 * x21 + x21 * x753 + x987)) result[2, 3, 8] = numpy.sum(x322 * (x0 * x1524 + x1461 * x21 + x21 * x762 + x992)) result[2, 3, 9] = numpy.sum(x152 * (x0 * x1526 + x1463 * x21 + x21 * x771 + x996)) result[2, 3, 10] = numpy.sum(x257 * (x0 * x1528 + x1465 * x21 + x21 * x778 + x998)) result[2, 3, 11] = numpy.sum(x152 * (x0 * x1530 + x1000 + x1467 * x21 + x21 * x784)) result[2, 3, 12] = numpy.sum(x306 * (x0 * x1532 + x1002 + x1469 * x21 + x21 * x789)) result[2, 3, 13] = numpy.sum(x152 * (x0 * x1534 + x1004 + x1471 * x21 + x21 * x794)) result[2, 3, 14] = numpy.sum(x257 * (x0 * x1536 + x1006 + x1473 * x21 + x21 * x799)) result[2, 4, 0] = numpy.sum(x687 * (x0 * x1537 + x1012 + x21 * x815)) result[2, 4, 1] = numpy.sum(x699 * (x0 * x1538 + x1016 + x21 * x829)) result[2, 4, 2] = numpy.sum(x699 * (x0 * x1539 + x1020 + x21 * x838)) result[2, 4, 3] = numpy.sum(x322 * (x0 * x1540 + x1024 + x21 * x845)) result[2, 4, 4] = numpy.sum(x731 * (x0 * x1541 + x1028 + x21 * x852)) result[2, 4, 5] = numpy.sum(x322 * (x0 * x1542 + x1032 + x21 * x860)) result[2, 4, 6] = numpy.sum(x699 * (x0 * x1543 + x1036 + x21 * x866)) result[2, 4, 7] = numpy.sum(x731 * (x0 * x1544 + x1040 + x21 * x871)) result[2, 4, 8] = numpy.sum(x731 * (x0 * x1545 + x1044 + x21 * x876)) result[2, 4, 9] = numpy.sum(x699 * (x0 * x1546 + x1048 + x21 * x883)) result[2, 4, 10] = numpy.sum(x687 * (x0 * x1547 + x1050 + x21 * x888)) result[2, 4, 11] = numpy.sum(x699 * (x0 * x1548 + x1052 + x21 * x892)) result[2, 4, 12] = numpy.sum(x322 * (x0 * x1549 + x1054 + x21 * x896)) result[2, 4, 13] = numpy.sum(x699 * (x0 * x1550 + x1056 + x21 * x900)) result[2, 4, 14] = numpy.sum(x687 * (x0 * x1551 + x1058 + x21 * x904)) result[2, 5, 0] = numpy.sum(x257 * (x0 * x1554 + x1065)) result[2, 5, 1] = numpy.sum(x152 * (x0 * x1557 + x1067)) result[2, 5, 2] = numpy.sum(x152 * (x0 * x1560 + x1071)) result[2, 5, 3] = numpy.sum(x306 * (x0 * x1563 + x1073)) result[2, 5, 4] = numpy.sum(x322 * (x0 * x1566 + x1075)) result[2, 5, 5] = numpy.sum(x306 * (x0 * x1569 + x1079)) result[2, 5, 6] = numpy.sum(x152 * (x0 * x1572 + x1081)) result[2, 5, 7] = numpy.sum(x322 * (x0 * x1575 + x1083)) result[2, 5, 8] = numpy.sum(x322 * (x0 * x1578 + x1085)) result[2, 5, 9] = numpy.sum(x152 * (x0 * x1581 + x1089)) result[2, 5, 10] = numpy.sum(x257 * (x0 * x1584 + x1090)) result[2, 5, 11] = numpy.sum(x152 * (x0 * x1587 + x1091)) result[2, 5, 12] = numpy.sum(x306 * (x0 * x1590 + x1092)) result[2, 5, 13] = numpy.sum(x152 * (x0 * x1593 + x1093)) result[2, 5, 14] = numpy.sum(x257 * (x0 * x1596 + x1094)) result[2, 6, 0] = numpy.sum(x99 * (x1239 * x21 + x1341 + x1507 * x21 + x1508 * x21)) result[2, 6, 1] = numpy.sum(x115 * (x1242 * x21 + x1343 + x1509 * x21 + x1510 * x21)) result[2, 6, 2] = numpy.sum(x115 * (x1245 * x21 + x1345 + x1511 * x21 + x1512 * x21)) result[2, 6, 3] = numpy.sum(x140 * (x1248 * x21 + x1347 + x1513 * x21 + x1514 * x21)) result[2, 6, 4] = numpy.sum(x152 * (x1251 * x21 + x1349 + x1515 * x21 + x1516 * x21)) result[2, 6, 5] = numpy.sum(x140 * (x1254 * x21 + x1351 + x1517 * x21 + x1518 * x21)) result[2, 6, 6] = numpy.sum(x115 * (x1257 * x21 + x1353 + x1519 * x21 + x1520 * x21)) result[2, 6, 7] = numpy.sum(x152 * (x1260 * x21 + x1355 + x1521 * x21 + x1522 * x21)) result[2, 6, 8] = numpy.sum(x152 * (x1263 * x21 + x1357 + x1523 * x21 + x1524 * x21)) result[2, 6, 9] = numpy.sum(x115 * (x1266 * x21 + x1359 + x1525 * x21 + x1526 * x21)) result[2, 6, 10] = numpy.sum(x99 * (x1269 * x21 + x1360 + x1527 * x21 + x1528 * x21)) result[2, 6, 11] = numpy.sum(x115 * (x1272 * x21 + x1361 + x1529 * x21 + x1530 * x21)) result[2, 6, 12] = numpy.sum(x140 * (x1275 * x21 + x1362 + x1531 * x21 + x1532 * x21)) result[2, 6, 13] = numpy.sum(x115 * (x1279 * x21 + x1363 + x1533 * x21 + x1534 * x21)) result[2, 6, 14] = numpy.sum(x99 * (x1282 * x21 + x1364 + x1535 * x21 + x1536 * x21)) result[2, 7, 0] = numpy.sum(x257 * (x1286 * x21 + x1366 + x1537 * x21)) result[2, 7, 1] = numpy.sum(x152 * (x1289 * x21 + x1368 + x1538 * x21)) result[2, 7, 2] = numpy.sum(x152 * (x1292 * x21 + x1370 + x1539 * x21)) result[2, 7, 3] = numpy.sum(x306 * (x1295 * x21 + x1372 + x1540 * x21)) result[2, 7, 4] = numpy.sum(x322 * (x1298 * x21 + x1374 + x1541 * x21)) result[2, 7, 5] = numpy.sum(x306 * (x1301 * x21 + x1376 + x1542 * x21)) result[2, 7, 6] = numpy.sum(x152 * (x1304 * x21 + x1378 + x1543 * x21)) result[2, 7, 7] = numpy.sum(x322 * (x1307 * x21 + x1380 + x1544 * x21)) result[2, 7, 8] = numpy.sum(x322 * (x1310 * x21 + x1382 + x1545 * x21)) result[2, 7, 9] = numpy.sum(x152 * (x1313 * x21 + x1384 + x1546 * x21)) result[2, 7, 10] = numpy.sum(x257 * (x1316 * x21 + x1385 + x1547 * x21)) result[2, 7, 11] = numpy.sum(x152 * (x1319 * x21 + x1386 + x1548 * x21)) result[2, 7, 12] = numpy.sum(x306 * (x1322 * x21 + x1387 + x1549 * x21)) result[2, 7, 13] = numpy.sum(x152 * (x1325 * x21 + x1388 + x1550 * x21)) result[2, 7, 14] = numpy.sum(x257 * (x1328 * x21 + x1389 + x1551 * x21)) result[2, 8, 0] = numpy.sum(x257 * (x1391 + x1554 * x21)) result[2, 8, 1] = numpy.sum(x152 * (x1393 + x1557 * x21)) result[2, 8, 2] = numpy.sum(x152 * (x1395 + x1560 * x21)) result[2, 8, 3] = numpy.sum(x306 * (x1397 + x1563 * x21)) result[2, 8, 4] = numpy.sum(x322 * (x1399 + x1566 * x21)) result[2, 8, 5] = numpy.sum(x306 * (x1401 + x1569 * x21)) result[2, 8, 6] = numpy.sum(x152 * (x1403 + x1572 * x21)) result[2, 8, 7] = numpy.sum(x322 * (x1405 + x1575 * x21)) result[2, 8, 8] = numpy.sum(x322 * (x1407 + x1578 * x21)) result[2, 8, 9] = numpy.sum(x152 * (x1409 + x1581 * x21)) result[2, 8, 10] = numpy.sum(x257 * (x1410 + x1584 * x21)) result[2, 8, 11] = numpy.sum(x152 * (x1411 + x1587 * x21)) result[2, 8, 12] = numpy.sum(x306 * (x1412 + x1590 * x21)) result[2, 8, 13] = numpy.sum(x152 * (x1413 + x1593 * x21)) result[2, 8, 14] = numpy.sum(x257 * (x1414 + x1596 * x21)) result[2, 9, 0] = numpy.sum( x99 * (x1096 * x1597 + x1552 * x22 + x1553 * x22 + x1554 * x22) ) result[2, 9, 1] = numpy.sum( x115 * (x1418 * x1597 + x1555 * x22 + x1556 * x22 + x1557 * x22) ) result[2, 9, 2] = numpy.sum( x115 * (x1099 * x1598 + x1558 * x22 + x1559 * x22 + x1560 * x22) ) result[2, 9, 3] = numpy.sum( x140 * (x1423 * x1597 + x1561 * x22 + x1562 * x22 + x1563 * x22) ) result[2, 9, 4] = numpy.sum( x152 * (x1425 * x1598 + x1564 * x22 + x1565 * x22 + x1566 * x22) ) result[2, 9, 5] = numpy.sum( x140 * (x1567 * x22 + x1568 * x22 + x1569 * x22 + x1599 * x274) ) result[2, 9, 6] = numpy.sum( x115 * (x1428 * x1597 + x1570 * x22 + x1571 * x22 + x1572 * x22) ) result[2, 9, 7] = numpy.sum( x152 * (x1431 * x1598 + x1573 * x22 + x1574 * x22 + x1575 * x22) ) result[2, 9, 8] = numpy.sum( x152 * (x1576 * x22 + x1577 * x22 + x1578 * x22 + x1599 * x482) ) result[2, 9, 9] = numpy.sum( x115 * (x1579 * x22 + x1580 * x22 + x1581 * x22 + x1600 * x269) ) result[2, 9, 10] = numpy.sum( x99 * (x1582 * x22 + x1583 * x22 + x1584 * x22 + x1597 * x193) ) result[2, 9, 11] = numpy.sum( x115 * (x1585 * x22 + x1586 * x22 + x1587 * x22 + x1598 * x198) ) result[2, 9, 12] = numpy.sum( x140 * (x1588 * x22 + x1589 * x22 + x1590 * x22 + x1599 * x171) ) result[2, 9, 13] = numpy.sum( x115 * (x141 * x1600 + x1591 * x22 + x1592 * x22 + x1593 * x22) ) result[2, 9, 14] = numpy.sum( x99 * (x1594 * x22 + x1595 * x22 + x1596 * x22 + x55 * (4.0 * x1087 + x116 * x1600)) ) return result
[docs] def int3c2e3d_sph_200(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ds|s) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((6, 1, 1), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = cx + x0 x3 = x2 ** (-1.0) x4 = -x1 * (ax * A[0] + bx * B[0]) x5 = x4 + C[0] x6 = -x5 x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x8 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = x10 + C[2] x12 = -x11 x13 = cx * x3 x14 = x0 * x13 * (x12**2 + x6**2 + x9**2) x15 = boys(1, x14) x16 = x15 * x3 x17 = cx ** (-1.0) x18 = x17 * boys(0, x14) x19 = x1 * (x16 - x18) x20 = x4 + A[0] x21 = -x20 x22 = x3 * boys(2, x14) x23 = x15 * x17 x24 = x13 * x5 x25 = ( 17.49341832762486 * da * db * dc * x1 * x2 ** (-0.5) * numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) ) x26 = 0.5773502691896258 * x25 x27 = x7 + A[1] x28 = -x27 x29 = x16 * x9 - x18 * x28 x30 = x22 * x9 - x23 * x28 x31 = 2.0 * x25 x32 = x10 + A[2] x33 = -x32 x34 = x12 * x16 - x18 * x33 x35 = x12 * x22 - x23 * x33 x36 = x13 * x8 # 6 item(s) result[0, 0, 0] = numpy.sum( x26 * (-x19 + 2.0 * x20 * (x16 * x6 - x18 * x21) + 2.0 * x24 * (x21 * x23 - x22 * x6)) ) result[1, 0, 0] = numpy.sum(x31 * (x20 * x29 - x24 * x30)) result[2, 0, 0] = numpy.sum(x31 * (x20 * x34 - x24 * x35)) result[3, 0, 0] = numpy.sum(x26 * (-x19 + 2.0 * x27 * x29 - 2.0 * x30 * x36)) result[4, 0, 0] = numpy.sum(x31 * (x27 * x34 - x35 * x36)) result[5, 0, 0] = numpy.sum(x26 * (-2.0 * x11 * x13 * x35 - x19 + 2.0 * x32 * x34)) return result
[docs] def int3c2e3d_sph_201(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ds|p) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((6, 1, 3), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = x2 + C[0] x4 = cx + x0 x5 = x4 ** (-1.0) x6 = -x3 x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x8 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = x10 + C[2] x12 = -x11 x13 = cx * x5 x14 = x0 * x13 x15 = x14 * (x12**2 + x6**2 + x9**2) x16 = boys(2, x15) x17 = x16 * x5 x18 = cx ** (-1.0) x19 = x18 * boys(1, x15) x20 = x1 * (x17 - x19) x21 = x2 + A[0] x22 = -x21 x23 = x17 * x6 - x19 * x22 x24 = x5 * boys(3, x15) x25 = x16 * x18 x26 = x13 * x3 x27 = x20 - 2.0 * x21 * x23 - 2.0 * x26 * (x22 * x25 - x24 * x6) x28 = ( 17.49341832762486 * da * db * dc * x4 ** (-1.5) * numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) ) x29 = 0.5773502691896258 * x28 x30 = x27 * x29 x31 = x14 * (x11**2 + x3**2 + x8**2) x32 = x5 * boys(2, x31) x33 = x7 + A[1] x34 = boys(1, x31) x35 = x1 * (-x18 * x33 * x34 + x32 * x8) x36 = -x33 x37 = x17 * x9 - x19 * x36 x38 = x24 * x9 - x25 * x36 x39 = -2.0 * x21 * x37 + 2.0 * x26 * x38 x40 = x1 * (-x18 * x21 * x34 + x3 * x32) x41 = x10 + A[2] x42 = x1 * (x11 * x32 - x18 * x34 * x41) x43 = -x41 x44 = x12 * x17 - x19 * x43 x45 = x12 * x24 - x25 * x43 x46 = -2.0 * x21 * x44 + 2.0 * x26 * x45 x47 = 2.0 * x37 x48 = x13 * x8 x49 = x20 - x33 * x47 + 2.0 * x38 * x48 x50 = x29 * x49 x51 = -2.0 * x33 * x44 + 2.0 * x45 * x48 x52 = 2.0 * x44 x53 = 2.0 * x11 * x13 * x45 + x20 - x41 * x52 x54 = x29 * x53 # 18 item(s) result[0, 0, 0] = numpy.sum(x29 * (-2.0 * x1 * x23 + x27 * x3)) result[0, 0, 1] = numpy.sum(x30 * x8) result[0, 0, 2] = numpy.sum(x11 * x30) result[1, 0, 0] = numpy.sum(x28 * (x3 * x39 + x35)) result[1, 0, 1] = numpy.sum(x28 * (x39 * x8 + x40)) result[1, 0, 2] = numpy.sum(x11 * x28 * x39) result[2, 0, 0] = numpy.sum(x28 * (x3 * x46 + x42)) result[2, 0, 1] = numpy.sum(x28 * x46 * x8) result[2, 0, 2] = numpy.sum(x28 * (x11 * x46 + x40)) result[3, 0, 0] = numpy.sum(x3 * x50) result[3, 0, 1] = numpy.sum(x29 * (-x1 * x47 + x49 * x8)) result[3, 0, 2] = numpy.sum(x11 * x50) result[4, 0, 0] = numpy.sum(x28 * x3 * x51) result[4, 0, 1] = numpy.sum(x28 * (x42 + x51 * x8)) result[4, 0, 2] = numpy.sum(x28 * (x11 * x51 + x35)) result[5, 0, 0] = numpy.sum(x3 * x54) result[5, 0, 1] = numpy.sum(x54 * x8) result[5, 0, 2] = numpy.sum(x29 * (-x1 * x52 + x11 * x53)) return result
[docs] def int3c2e3d_sph_202(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ds|d) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((6, 1, 6), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = x2 + C[0] x4 = -x3 x5 = cx + x0 x6 = x5 ** (-1.0) x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x8 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = x10 + C[2] x12 = -x11 x13 = cx * x6 x14 = x0 * x13 x15 = x14 * (x12**2 + x4**2 + x9**2) x16 = boys(3, x15) x17 = x16 * x6 x18 = x2 + A[0] x19 = -x18 x20 = cx ** (-1.0) x21 = x20 * boys(2, x15) x22 = x17 * x4 - x19 * x21 x23 = x3**2 x24 = x8**2 x25 = x11**2 x26 = x14 * (x23 + x24 + x25) x27 = boys(2, x26) x28 = x1 * x20 * x27 x29 = x1 * (x17 - x21) x30 = x6 * boys(4, x15) x31 = x13 * x3 x32 = -2.0 * x18 * x22 + x29 - 2.0 * x31 * (x16 * x19 * x20 - x30 * x4) x33 = x1 * x22 x34 = 2.0 * x33 x35 = ( 17.49341832762486 * da * db * dc * x0 * x5 ** (-2.5) * numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) ) x36 = 0.3333333333333333 * x35 x37 = x6 * boys(3, x26) x38 = x18 * x20 * x27 - x3 * x37 x39 = 1.732050807568877 x40 = x36 * x39 x41 = x40 * (2.0 * x1 * x38 - x3 * x32) x42 = x32 * x36 x43 = x11 * x39 x44 = x7 + A[1] x45 = -x44 x46 = x17 * x9 - x21 * x45 x47 = x1 * x46 x48 = 2.0 * x47 x49 = -x48 x50 = -x16 * x20 * x45 + x30 * x9 x51 = x13 * x4 x52 = 2.0 * x19 * x46 - 2.0 * x50 * x51 x53 = x3 * x52 x54 = x3 * x40 x55 = -x33 x56 = x52 * x8 x57 = x55 + x56 x58 = 2.0 * x46 x59 = x1 * (x28 + x58 * x8) x60 = -x47 x61 = x11 * x35 x62 = -x34 x63 = x40 * x8 x64 = 0.6666666666666667 * x35 * x39 x65 = x10 + A[2] x66 = -x65 x67 = x12 * x17 - x21 * x66 x68 = x1 * x67 x69 = 2.0 * x68 x70 = -x69 x71 = -x67 x72 = x12 * x30 - x16 * x20 * x66 x73 = -x72 x74 = -2.0 * x19 * x71 + 2.0 * x51 * x73 x75 = x3 * x74 x76 = x35 * x8 x77 = x11 * x74 x78 = 2.0 * x11 x79 = x1 * (x28 + x67 * x78) x80 = -0.5 * x79 x81 = -x18 * x67 + x31 * x72 x82 = x11 * x40 x83 = 2.0 * x8 x84 = x13 * x50 * x83 + x29 - x44 * x58 x85 = x36 * x84 x86 = x48 - x8 * x84 x87 = x20 * x27 * x44 - x37 * x8 x88 = x13 * x72 x89 = -x44 * x67 + x8 * x88 x90 = x3 * x35 x91 = x13 * x73 * x9 - x45 * x71 x92 = x78 * x91 x93 = x29 - 2.0 * x65 * x67 + x78 * x88 x94 = x36 * x93 x95 = -x11 * x93 + x69 # 36 item(s) result[0, 0, 0] = numpy.sum( x36 * (x1 * (2.0 * x22 * x3 + x28) - x3 * (x3 * x32 - x34)) ) result[0, 0, 1] = numpy.sum(x41 * x8) result[0, 0, 2] = numpy.sum(x11 * x41) result[0, 0, 3] = numpy.sum(-x24 * x42) result[0, 0, 4] = numpy.sum(-x42 * x43 * x8) result[0, 0, 5] = numpy.sum(-x25 * x42) result[1, 0, 0] = numpy.sum(-x54 * (x49 + x53)) result[1, 0, 1] = numpy.sum(0.5 * x35 * (-2.0 * x3 * x57 + x59)) result[1, 0, 2] = numpy.sum(-x61 * (x53 + x60)) result[1, 0, 3] = numpy.sum(-x63 * (x56 + x62)) result[1, 0, 4] = numpy.sum(-x57 * x61) result[1, 0, 5] = numpy.sum(x25 * x64 * (x18 * x46 - x31 * x50)) result[2, 0, 0] = numpy.sum(-x54 * (x70 + x75)) result[2, 0, 1] = numpy.sum(x76 * (x68 - x75)) result[2, 0, 2] = numpy.sum(-x35 * (x3 * (x55 + x77) + x80)) result[2, 0, 3] = numpy.sum(-x24 * x64 * x81) result[2, 0, 4] = numpy.sum(x76 * (x1 * x38 - x78 * x81)) result[2, 0, 5] = numpy.sum(-x82 * (x62 + x77)) result[3, 0, 0] = numpy.sum(-x23 * x85) result[3, 0, 1] = numpy.sum(x54 * x86) result[3, 0, 2] = numpy.sum(-x3 * x43 * x85) result[3, 0, 3] = numpy.sum(x36 * (x59 + x8 * x86)) result[3, 0, 4] = numpy.sum(x82 * (2.0 * x1 * x87 - x8 * x84)) result[3, 0, 5] = numpy.sum(-x25 * x85) result[4, 0, 0] = numpy.sum(-x23 * x64 * x89) result[4, 0, 1] = numpy.sum(x90 * (-x1 * (x11 * x37 - x20 * x27 * x65) - x83 * x89)) result[4, 0, 2] = numpy.sum(x90 * (x1 * x87 - x78 * x89)) result[4, 0, 3] = numpy.sum(-x63 * (x70 + x83 * x91)) result[4, 0, 4] = numpy.sum(-x35 * (x8 * (x60 + x92) + x80)) result[4, 0, 5] = numpy.sum(-x82 * (x49 + x92)) result[5, 0, 0] = numpy.sum(-x23 * x94) result[5, 0, 1] = numpy.sum(-x3 * x39 * x8 * x94) result[5, 0, 2] = numpy.sum(x54 * x95) result[5, 0, 3] = numpy.sum(-x24 * x94) result[5, 0, 4] = numpy.sum(x63 * x95) result[5, 0, 5] = numpy.sum(x36 * (x11 * x95 + x79)) return result
[docs] def int3c2e3d_sph_203(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ds|f) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((6, 1, 10), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - C[0] x4 = 0.5 / (ax + bx) x5 = x3**2 x6 = -x1 * (ax * A[1] + bx * B[1]) x7 = -x6 - C[1] x8 = x7**2 x9 = -x1 * (ax * A[2] + bx * B[2]) x10 = -x9 - C[2] x11 = x10**2 x12 = cx + x0 x13 = x12 ** (-1.0) x14 = cx * x13 x15 = x0 * x14 * (x11 + x5 + x8) x16 = boys(4, x15) x17 = x12 ** (-1.5) x18 = 17.49341832762486 x19 = numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) x20 = 2.0 * x1 * x18 * x19 x21 = x17 * x20 x22 = x16 * x21 x23 = cx ** (-1.0) x24 = x12 ** (-0.5) x25 = boys(3, x15) x26 = x4 * (2.0 * x1 * x18 * x19 * x23 * x24 * x25 - x22) x27 = -x2 - A[0] x28 = 2.0 * x1 * x18 * x19 * x23 * x24 * x25 * x27 - x22 * x3 x29 = x21 * boys(5, x15) x30 = x14 * x3 x31 = ( x26 + x27 * x28 - x30 * (2.0 * x1 * x16 * x18 * x19 * x23 * x24 * x27 - x29 * x3) ) x32 = x3 * x31 x33 = x28 * x4 x34 = 2.0 * x33 x35 = x0 * x13 x36 = x3 * x35 x37 = x28 * x3 x38 = x23 * x25 x39 = x20 * x24 * x38 * x4 x40 = x37 + x39 x41 = x35 * x4 x42 = 2.0 * x41 x43 = 2.0 * x17 * x18 * x19 * x38 * x4 x44 = 2.23606797749979 x45 = da * db * dc x46 = x35 * x45 x47 = 0.06666666666666667 * x46 x48 = x44 * x47 x49 = x35 * x7 x50 = x43 * x7 x51 = 0.3333333333333333 * x46 x52 = x10 * x35 x53 = x10 * x43 x54 = x0**2 / x12**2 x55 = x32 * x54 x56 = x54 * x8 x57 = x54 * x7 x58 = x10 * x57 x59 = 1.732050807568877 x60 = x51 * x59 x61 = x11 * x54 x62 = x0**3 / x12**3 x63 = 0.06666666666666667 * x45 * x62 x64 = x63 * x7**3 x65 = x31 * x44 x66 = 0.3333333333333333 * x45 x67 = x62 * x66 x68 = x67 * x8 x69 = x10**3 * x63 x70 = -x6 - A[1] x71 = 2.0 * x1 * x18 * x19 * x23 * x24 * x25 * x70 - x22 * x7 x72 = x4 * x71 x73 = 2.0 * x1 * x16 * x18 * x19 * x23 * x24 * x70 - x29 * x7 x74 = x27 * x71 - x30 * x73 x75 = x3 * x74 x76 = x54 * x72 x77 = 3.872983346207417 x78 = x47 * x77 x79 = x7 * x71 x80 = x39 + x79 x81 = x35 * x80 x82 = x4 * x81 x83 = x7 * x74 x84 = x33 + x83 x85 = x4 * x54 x86 = x3 * x85 x87 = x52 * x72 x88 = x41 * (x50 + x7 * x81) x89 = x49 * (x33 + x84) x90 = x41 * (x52 * x79 + x53) x91 = x33 * x52 x92 = x52 * x83 + x91 x93 = x11 * x76 x94 = x33 * x61 x95 = -x9 - A[2] x96 = 2.0 * x1 * x18 * x19 * x23 * x24 * x25 * x95 - x10 * x22 x97 = x4 * x96 x98 = 2.0 * x1 * x16 * x18 * x19 * x23 * x24 * x95 - x10 * x29 x99 = x27 * x96 - x30 * x98 x100 = x3 * x99 x101 = x54 * x97 x102 = x49 * x97 x103 = x3 * x7 x104 = x10 * x96 + x39 x105 = x104 * x41 x106 = x10 * x99 + x33 x107 = x56 * x97 x108 = x104 * x7 * x85 x109 = x41 * (x104 * x52 + x53) x110 = x106 * x52 + x91 x111 = x57 * x66 x112 = x14 * x7 x113 = -x112 * x73 + x26 + x70 * x71 x114 = x113 * x44 x115 = x3**3 * x63 x116 = x113 * x7 x117 = 2.0 * x72 x118 = x116 + x117 x119 = x5 * x67 x120 = x118 * x49 + 2.0 * x82 x121 = x3 * x45 x122 = x121 * x54 x123 = 0.3333333333333333 * x122 x124 = x52 * (x116 + x117) x125 = x123 * x59 x126 = 0.3333333333333333 * x121 * x62 x127 = -x112 * x98 + x70 * x96 x128 = x127 * x7 + x97 x129 = x119 * x59 x130 = x10 * x127 + x72 x131 = x102 + x128 * x49 x132 = x105 + x130 * x49 x133 = x130 * x52 + x87 x134 = -x10 * x14 * x98 + x26 + x95 * x96 x135 = x134 * x44 x136 = x10 * x134 + 2.0 * x97 x137 = 2.0 * x105 + x136 * x52 # 60 item(s) result[0, 0, 0] = numpy.sum( x48 * (x36 * (x36 * (x32 + x34) + x40 * x42) + x42 * (x3 * x43 + x36 * x40)) ) result[0, 0, 1] = numpy.sum(x51 * (x36 * x49 * (x32 + x34) + x42 * (x37 * x49 + x50))) result[0, 0, 2] = numpy.sum(x51 * (x36 * x52 * (x32 + x34) + x42 * (x37 * x52 + x53))) result[0, 0, 3] = numpy.sum(x51 * (x34 * x56 + x55 * x8)) result[0, 0, 4] = numpy.sum(x60 * (x10 * x55 * x7 + x34 * x58)) result[0, 0, 5] = numpy.sum(x51 * (x11 * x55 + x34 * x61)) result[0, 0, 6] = numpy.sum(x64 * x65) result[0, 0, 7] = numpy.sum(x10 * x31 * x68) result[0, 0, 8] = numpy.sum(x11 * x31 * x67 * x7) result[0, 0, 9] = numpy.sum(x65 * x69) result[1, 0, 0] = numpy.sum(x78 * (x36**2 * (2.0 * x72 + x75) + x5 * x76)) result[1, 0, 1] = numpy.sum(x60 * (x36 * (x36 * x84 + x82) + x80 * x86)) result[1, 0, 2] = numpy.sum(x60 * (x10 * x3 * x76 + x36 * (x52 * x75 + x87))) result[1, 0, 3] = numpy.sum(x60 * (x36 * x89 + x88)) result[1, 0, 4] = numpy.sum(x46 * (x36 * x92 + x90)) result[1, 0, 5] = numpy.sum(x60 * (x61 * x75 + x93)) result[1, 0, 6] = numpy.sum(x78 * (x33 * x56 + x49 * x89)) result[1, 0, 7] = numpy.sum(x60 * (x33 * x58 + x49 * x92)) result[1, 0, 8] = numpy.sum(x60 * (x61 * x83 + x94)) result[1, 0, 9] = numpy.sum(x69 * x74 * x77) result[2, 0, 0] = numpy.sum(x78 * (x101 * x5 + x36**2 * (x100 + 2.0 * x97))) result[2, 0, 1] = numpy.sum(x60 * (x101 * x103 + x36 * (x100 * x49 + x102))) result[2, 0, 2] = numpy.sum(x60 * (x104 * x86 + x36 * (x105 + x106 * x36))) result[2, 0, 3] = numpy.sum(x60 * (x100 * x56 + x107)) result[2, 0, 4] = numpy.sum(x46 * (x106 * x3 * x57 + x108)) result[2, 0, 5] = numpy.sum(x60 * (x109 + x110 * x36)) result[2, 0, 6] = numpy.sum(x64 * x77 * x99) result[2, 0, 7] = numpy.sum(x106 * x59 * x68) result[2, 0, 8] = numpy.sum(x110 * x111 * x59) result[2, 0, 9] = numpy.sum(x78 * (x110 * x52 + x94)) result[3, 0, 0] = numpy.sum(x114 * x115) result[3, 0, 1] = numpy.sum(x118 * x119) result[3, 0, 2] = numpy.sum(x10 * x113 * x119) result[3, 0, 3] = numpy.sum(x120 * x123) result[3, 0, 4] = numpy.sum(x124 * x125) result[3, 0, 5] = numpy.sum(x11 * x113 * x126) result[3, 0, 6] = numpy.sum(x48 * (x120 * x49 + 2.0 * x88)) result[3, 0, 7] = numpy.sum(x51 * (x124 * x49 + 2.0 * x90)) result[3, 0, 8] = numpy.sum(x51 * x61 * (x116 + x117)) result[3, 0, 9] = numpy.sum(x114 * x69) result[4, 0, 0] = numpy.sum(x115 * x127 * x77) result[4, 0, 1] = numpy.sum(x128 * x129) result[4, 0, 2] = numpy.sum(x129 * x130) result[4, 0, 3] = numpy.sum(x125 * x131) result[4, 0, 4] = numpy.sum(x122 * x132) result[4, 0, 5] = numpy.sum(x125 * x133) result[4, 0, 6] = numpy.sum(x78 * (x107 + x131 * x49)) result[4, 0, 7] = numpy.sum(x60 * (x108 + x132 * x49)) result[4, 0, 8] = numpy.sum(x60 * (x109 + x133 * x49)) result[4, 0, 9] = numpy.sum(x78 * (x133 * x52 + x93)) result[5, 0, 0] = numpy.sum(x115 * x135) result[5, 0, 1] = numpy.sum(x119 * x134 * x7) result[5, 0, 2] = numpy.sum(x119 * x136) result[5, 0, 3] = numpy.sum(x126 * x134 * x8) result[5, 0, 4] = numpy.sum(x103 * x136 * x59 * x67) result[5, 0, 5] = numpy.sum(x123 * x137) result[5, 0, 6] = numpy.sum(x135 * x64) result[5, 0, 7] = numpy.sum(x136 * x68) result[5, 0, 8] = numpy.sum(x111 * x137) result[5, 0, 9] = numpy.sum(x48 * (2.0 * x109 + x137 * x52)) return result
[docs] def int3c2e3d_sph_204(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (ds|g) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((6, 1, 15), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - C[0] x4 = 0.5 / (ax + bx) x5 = x3**2 x6 = -x1 * (ax * A[1] + bx * B[1]) x7 = -x6 - C[1] x8 = x7**2 x9 = -x1 * (ax * A[2] + bx * B[2]) x10 = -x9 - C[2] x11 = x10**2 x12 = cx + x0 x13 = x12 ** (-1.0) x14 = cx * x13 x15 = x0 * x14 * (x11 + x5 + x8) x16 = boys(5, x15) x17 = x12 ** (-1.5) x18 = 17.49341832762486 x19 = numpy.exp( -ax * bx * x1 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2) ) x20 = 2.0 * x18 * x19 x21 = x1 * x20 x22 = x17 * x21 x23 = x16 * x22 x24 = cx ** (-1.0) x25 = x12 ** (-0.5) x26 = boys(4, x15) x27 = x4 * (2.0 * x1 * x18 * x19 * x24 * x25 * x26 - x23) x28 = -x2 - A[0] x29 = 2.0 * x1 * x18 * x19 * x24 * x25 * x26 * x28 - x23 * x3 x30 = x22 * boys(6, x15) x31 = x14 * x3 x32 = ( x27 + x28 * x29 - x31 * (2.0 * x1 * x16 * x18 * x19 * x24 * x25 * x28 - x3 * x30) ) x33 = x3 * x32 x34 = x29 * x4 x35 = 2.0 * x34 x36 = x0 * x13 x37 = x3 * x36 x38 = x29 * x3 x39 = x24 * x26 x40 = x21 * x25 * x39 * x4 x41 = x38 + x40 x42 = x36 * x4 x43 = 2.0 * x42 x44 = x20 * x39 * x4 x45 = x17 * x44 x46 = x3 * x45 + x37 * x41 x47 = x0 * x12 ** (-2.5) * x44 x48 = 5.916079783099616 x49 = da * db * dc x50 = x36 * x49 x51 = 0.009523809523809524 * x50 x52 = x48 * x51 x53 = x36 * x7 x54 = x45 * x7 x55 = x38 * x53 + x54 x56 = x3 * x7 x57 = 2.23606797749979 x58 = 0.06666666666666667 * x50 x59 = x57 * x58 x60 = x10 * x36 x61 = x10 * x45 x62 = x38 * x60 + x61 x63 = x0**2 / x12**2 x64 = x33 * x8 x65 = x63 * x8 x66 = x38 * x63 x67 = x47 * x8 x68 = 1.732050807568877 x69 = 0.1111111111111111 * x68 x70 = x50 * x69 x71 = x63 * x7 x72 = x10 * x71 x73 = x10 * x7 x74 = x47 * x73 x75 = 0.3333333333333333 * x50 x76 = x11 * x63 x77 = x11 * x47 x78 = x7**3 x79 = x0**3 / x12**3 x80 = x33 * x79 x81 = x78 * x79 x82 = x79 * x8 x83 = x10 * x82 x84 = x11 * x7 x85 = x79 * x84 x86 = x10**3 x87 = x79 * x86 x88 = x0**4 / x12**4 x89 = x49 * x88 x90 = 0.009523809523809524 * x89 x91 = x7**4 * x90 x92 = x32 * x48 x93 = 0.06666666666666667 * x57 x94 = x89 * x93 x95 = x78 * x94 x96 = x11 * x69 * x89 x97 = x86 * x94 x98 = x10**4 * x90 x99 = -x6 - A[1] x100 = 2.0 * x1 * x18 * x19 * x24 * x25 * x26 * x99 - x23 * x7 x101 = x100 * x4 x102 = 2.0 * x1 * x16 * x18 * x19 * x24 * x25 * x99 - x30 * x7 x103 = x100 * x28 - x102 * x31 x104 = x103 * x3 x105 = x5 * x63 x106 = x3**3 x107 = x101 * x79 x108 = 10.2469507659596 x109 = x108 * x51 x110 = x100 * x7 x111 = x110 + x40 x112 = x111 * x36 x113 = x112 * x4 x114 = x103 * x7 x115 = x114 + x34 x116 = x111 * x4 x117 = x3 * x63 x118 = x5 * x79 x119 = 3.872983346207417 x120 = x119 * x58 x121 = x101 * x60 x122 = x112 * x7 + x54 x123 = x122 * x42 x124 = x53 * (x115 + x34) x125 = x117 * x4 x126 = x110 * x60 + x61 x127 = x126 * x42 x128 = x34 * x60 x129 = x114 * x60 + x128 x130 = x68 * x75 x131 = x101 * x76 x132 = x42 * (x122 * x53 + x67) x133 = x124 * x53 + x34 * x65 x134 = x42 * (x126 * x53 + x74) x135 = x129 * x53 + x34 * x72 x136 = x42 * (x110 * x76 + x77) x137 = x34 * x76 x138 = x114 * x76 + x137 x139 = x107 * x86 x140 = x34 * x87 x141 = -x9 - A[2] x142 = 2.0 * x1 * x141 * x18 * x19 * x24 * x25 * x26 - x10 * x23 x143 = x142 * x4 x144 = 2.0 * x1 * x141 * x16 * x18 * x19 * x24 * x25 - x10 * x30 x145 = x142 * x28 - x144 * x31 x146 = x145 * x3 x147 = x143 * x79 x148 = x143 * x53 x149 = x117 * x7 x150 = x10 * x142 + x40 x151 = x150 * x42 x152 = x10 * x145 + x34 x153 = x150 * x4 x154 = x143 * x65 x155 = x3 * x8 x156 = x153 * x71 x157 = x56 * x79 x158 = x150 * x60 + x61 x159 = x158 * x42 x160 = x128 + x152 * x60 x161 = x143 * x81 x162 = x153 * x82 x163 = x158 * x4 * x71 x164 = x42 * (x158 * x60 + x77) x165 = x137 + x160 * x60 x166 = 0.06666666666666667 * x119 x167 = x166 * x89 x168 = 0.3333333333333333 * x49 x169 = x166 * x49 x170 = x14 * x7 x171 = x100 * x99 - x102 * x170 + x27 x172 = x171 * x48 x173 = x3**4 * x90 x174 = x171 * x7 x175 = 2.0 * x101 x176 = x174 + x175 x177 = x106 * x94 x178 = 2.0 * x113 + x176 * x53 x179 = x49 * x69 x180 = x118 * x179 x181 = x60 * (x174 + x175) x182 = x118 * x168 x183 = 2.0 * x123 + x178 * x53 x184 = x49 * x93 x185 = x117 * x184 x186 = 2.0 * x127 + x181 * x53 x187 = x117 * x168 x188 = x76 * (x174 + x175) x189 = x142 * x99 - x144 * x170 x190 = x143 + x189 * x7 x191 = x106 * x167 x192 = x10 * x189 + x101 x193 = x148 + x190 * x53 x194 = x151 + x192 * x53 x195 = x121 + x192 * x60 x196 = x154 + x193 * x53 x197 = x117 * x169 x198 = x156 + x194 * x53 x199 = x187 * x68 x200 = x159 + x195 * x53 x201 = x131 + x195 * x60 x202 = -x10 * x14 * x144 + x141 * x142 + x27 x203 = x202 * x48 x204 = x10 * x202 + 2.0 * x143 x205 = x168 * x204 * x88 x206 = 2.0 * x151 + x204 * x60 x207 = 2.0 * x159 + x206 * x60 # 90 item(s) result[0, 0, 0] = numpy.sum( x52 * ( x37 * (x37 * (x37 * (x33 + x35) + x41 * x43) + x43 * x46) + x43 * (x37 * x46 + x47 * x5) ) ) result[0, 0, 1] = numpy.sum( x59 * (x37 * (x37 * x53 * (x33 + x35) + x43 * x55) + x43 * (x37 * x55 + x47 * x56)) ) result[0, 0, 2] = numpy.sum( x59 * ( x37 * (x37 * x60 * (x33 + x35) + x43 * x62) + x43 * (x10 * x3 * x47 + x37 * x62) ) ) result[0, 0, 3] = numpy.sum( x70 * (x37 * (x35 * x65 + x63 * x64) + x43 * (x66 * x8 + x67)) ) result[0, 0, 4] = numpy.sum(x75 * (x37 * x72 * (x33 + x35) + x43 * (x66 * x73 + x74))) result[0, 0, 5] = numpy.sum(x70 * (x37 * x76 * (x33 + x35) + x43 * (x11 * x66 + x77))) result[0, 0, 6] = numpy.sum(x59 * (x35 * x81 + x78 * x80)) result[0, 0, 7] = numpy.sum(x75 * (x10 * x64 * x79 + x35 * x83)) result[0, 0, 8] = numpy.sum(x75 * (x35 * x85 + x80 * x84)) result[0, 0, 9] = numpy.sum(x59 * (x35 * x87 + x80 * x86)) result[0, 0, 10] = numpy.sum(x91 * x92) result[0, 0, 11] = numpy.sum(x10 * x32 * x95) result[0, 0, 12] = numpy.sum(x32 * x8 * x96) result[0, 0, 13] = numpy.sum(x32 * x7 * x97) result[0, 0, 14] = numpy.sum(x92 * x98) result[1, 0, 0] = numpy.sum( x109 * (x106 * x107 + x37 * (x101 * x105 + x37**2 * (2.0 * x101 + x104))) ) result[1, 0, 1] = numpy.sum( x120 * (x116 * x118 + x37 * (x116 * x117 + x37 * (x113 + x115 * x37))) ) result[1, 0, 2] = numpy.sum( x120 * (x10 * x107 * x5 + x37 * (x10 * x101 * x117 + x37 * (x104 * x60 + x121))) ) result[1, 0, 3] = numpy.sum(x75 * (x122 * x125 + x37 * (x123 + x124 * x37))) result[1, 0, 4] = numpy.sum(x130 * (x125 * x126 + x37 * (x127 + x129 * x37))) result[1, 0, 5] = numpy.sum(x75 * (x107 * x11 * x3 + x37 * (x104 * x76 + x131))) result[1, 0, 6] = numpy.sum(x120 * (x132 + x133 * x37)) result[1, 0, 7] = numpy.sum(x130 * (x134 + x135 * x37)) result[1, 0, 8] = numpy.sum(x130 * (x136 + x138 * x37)) result[1, 0, 9] = numpy.sum(x120 * (x104 * x87 + x139)) result[1, 0, 10] = numpy.sum(x109 * (x133 * x53 + x34 * x81)) result[1, 0, 11] = numpy.sum(x120 * (x135 * x53 + x34 * x83)) result[1, 0, 12] = numpy.sum(x75 * (x138 * x53 + x34 * x85)) result[1, 0, 13] = numpy.sum(x120 * (x114 * x87 + x140)) result[1, 0, 14] = numpy.sum(x103 * x108 * x98) result[2, 0, 0] = numpy.sum( x109 * (x106 * x147 + x37 * (x105 * x143 + x37**2 * (2.0 * x143 + x146))) ) result[2, 0, 1] = numpy.sum( x120 * (x118 * x143 * x7 + x37 * (x143 * x149 + x37 * (x146 * x53 + x148))) ) result[2, 0, 2] = numpy.sum( x120 * (x118 * x153 + x37 * (x125 * x150 + x37 * (x151 + x152 * x37))) ) result[2, 0, 3] = numpy.sum(x75 * (x147 * x155 + x37 * (x146 * x65 + x154))) result[2, 0, 4] = numpy.sum(x130 * (x153 * x157 + x37 * (x149 * x152 + x156))) result[2, 0, 5] = numpy.sum(x75 * (x125 * x158 + x37 * (x159 + x160 * x37))) result[2, 0, 6] = numpy.sum(x120 * (x146 * x81 + x161)) result[2, 0, 7] = numpy.sum(x130 * (x152 * x3 * x82 + x162)) result[2, 0, 8] = numpy.sum(x130 * (x149 * x160 + x163)) result[2, 0, 9] = numpy.sum(x120 * (x164 + x165 * x37)) result[2, 0, 10] = numpy.sum(x108 * x145 * x91) result[2, 0, 11] = numpy.sum(x152 * x167 * x78) result[2, 0, 12] = numpy.sum(x160 * x168 * x82) result[2, 0, 13] = numpy.sum(x165 * x169 * x71) result[2, 0, 14] = numpy.sum(x109 * (x140 + x165 * x60)) result[3, 0, 0] = numpy.sum(x172 * x173) result[3, 0, 1] = numpy.sum(x176 * x177) result[3, 0, 2] = numpy.sum(x10 * x171 * x177) result[3, 0, 3] = numpy.sum(x178 * x180) result[3, 0, 4] = numpy.sum(x181 * x182) result[3, 0, 5] = numpy.sum(x171 * x5 * x96) result[3, 0, 6] = numpy.sum(x183 * x185) result[3, 0, 7] = numpy.sum(x186 * x187) result[3, 0, 8] = numpy.sum(x187 * x188) result[3, 0, 9] = numpy.sum(x171 * x3 * x97) result[3, 0, 10] = numpy.sum(x52 * (2.0 * x132 + x183 * x53)) result[3, 0, 11] = numpy.sum(x59 * (2.0 * x134 + x186 * x53)) result[3, 0, 12] = numpy.sum(x70 * (2.0 * x136 + x188 * x53)) result[3, 0, 13] = numpy.sum(x59 * x87 * (x174 + x175)) result[3, 0, 14] = numpy.sum(x172 * x98) result[4, 0, 0] = numpy.sum(x108 * x173 * x189) result[4, 0, 1] = numpy.sum(x190 * x191) result[4, 0, 2] = numpy.sum(x191 * x192) result[4, 0, 3] = numpy.sum(x182 * x193) result[4, 0, 4] = numpy.sum(x182 * x194 * x68) result[4, 0, 5] = numpy.sum(x182 * x195) result[4, 0, 6] = numpy.sum(x196 * x197) result[4, 0, 7] = numpy.sum(x198 * x199) result[4, 0, 8] = numpy.sum(x199 * x200) result[4, 0, 9] = numpy.sum(x197 * x201) result[4, 0, 10] = numpy.sum(x109 * (x161 + x196 * x53)) result[4, 0, 11] = numpy.sum(x120 * (x162 + x198 * x53)) result[4, 0, 12] = numpy.sum(x75 * (x163 + x200 * x53)) result[4, 0, 13] = numpy.sum(x120 * (x164 + x201 * x53)) result[4, 0, 14] = numpy.sum(x109 * (x139 + x201 * x60)) result[5, 0, 0] = numpy.sum(x173 * x203) result[5, 0, 1] = numpy.sum(x177 * x202 * x7) result[5, 0, 2] = numpy.sum(x177 * x204) result[5, 0, 3] = numpy.sum(x202 * x5 * x69 * x8 * x89) result[5, 0, 4] = numpy.sum(x205 * x5 * x7) result[5, 0, 5] = numpy.sum(x180 * x206) result[5, 0, 6] = numpy.sum(x202 * x3 * x95) result[5, 0, 7] = numpy.sum(x155 * x205) result[5, 0, 8] = numpy.sum(x157 * x168 * x206) result[5, 0, 9] = numpy.sum(x185 * x207) result[5, 0, 10] = numpy.sum(x203 * x91) result[5, 0, 11] = numpy.sum(x204 * x95) result[5, 0, 12] = numpy.sum(x179 * x206 * x82) result[5, 0, 13] = numpy.sum(x184 * x207 * x71) result[5, 0, 14] = numpy.sum(x52 * (2.0 * x164 + x207 * x60)) return result
[docs] def int3c2e3d_sph_210(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (dp|s) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((6, 3, 1), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = cx + x1 x4 = x3 ** (-1.0) x5 = -x2 * (ax * A[0] + bx * B[0]) x6 = x5 + C[0] x7 = -x6 x8 = -x2 * (ax * A[1] + bx * B[1]) x9 = x8 + C[1] x10 = -x9 x11 = -x2 * (ax * A[2] + bx * B[2]) x12 = x11 + C[2] x13 = -x12 x14 = cx * x4 x15 = x1 * x14 x16 = x15 * (x10**2 + x13**2 + x7**2) x17 = boys(1, x16) x18 = x17 * x4 x19 = cx ** (-1.0) x20 = x19 * boys(0, x16) x21 = x2 * (x18 - x20) x22 = x5 + A[0] x23 = -x22 x24 = 2.0 * x22 x25 = boys(2, x16) x26 = x25 * x4 x27 = x17 * x19 x28 = -x23 * x27 + x26 * x7 x29 = x14 * x28 x30 = x21 - x24 * (x18 * x7 - x20 * x23) + 2.0 * x29 * x6 x31 = x15 * (x12**2 + x6**2 + x9**2) x32 = x4 * boys(1, x31) x33 = boys(0, x31) x34 = 2.0 * x2 x35 = x2 * (x26 - x27) x36 = x4 * boys(3, x16) x37 = x14 * x6 x38 = 2.0 * x37 x39 = A[1] - B[1] x40 = A[2] - B[2] x41 = ( 17.49341832762486 * da * db * dc * x3 ** (-0.5) * numpy.exp(-ax * bx * x2 * (x0**2 + x39**2 + x40**2)) ) x42 = x2 * x41 x43 = 0.5773502691896258 * x42 x44 = -x30 x45 = x8 + A[1] x46 = -x45 x47 = x10 * x26 - x17 * x19 * x46 x48 = -x47 x49 = x14 * x48 x50 = x10 * x18 - x20 * x46 x51 = x23 * x50 + x49 * x7 x52 = x10 * x36 - x19 * x25 * x46 x53 = x14 * x7 x54 = x2 * (x49 + x50) - x24 * x51 - x38 * (x23 * x48 + x52 * x53) x55 = x11 + A[2] x56 = -x55 x57 = x13 * x26 - x17 * x19 * x56 x58 = -x57 x59 = x14 * x58 x60 = x13 * x18 - x20 * x56 x61 = x2 * (x59 + x60) x62 = -x60 x63 = -x23 * x62 + x59 * x7 x64 = x13 * x36 - x19 * x25 * x56 x65 = -x64 x66 = -x24 * x63 - x38 * (x23 * x58 - x53 * x65) + x61 x67 = 2.0 * x51 x68 = x14 * x47 x69 = x21 - 2.0 * x45 * x50 + 2.0 * x68 * x9 x70 = -x69 x71 = x14 * x9 x72 = 2.0 * x71 x73 = x35 - 2.0 * x45 * x47 + x52 * x72 x74 = x10 * x59 - x46 * x62 x75 = x10 * x14 * x65 - x46 * x58 x76 = -x22 * x74 + x37 * x75 x77 = x34 * x41 x78 = 2.0 * x63 x79 = x14 * x57 x80 = 2.0 * x12 * x79 + x21 - 2.0 * x55 * x60 x81 = -x80 x82 = x12 * x14 x83 = x35 - 2.0 * x55 * x57 + 2.0 * x64 * x82 x84 = -x83 x85 = -2.0 * x45 * x74 + x61 + x72 * x75 x86 = 2.0 * x74 # 18 item(s) result[0, 0, 0] = numpy.sum( x43 * ( -x0 * x30 + x22 * x30 + x34 * (-x19 * x22 * x33 + x29 + x32 * x6) + x37 * (x24 * x28 - x35 + x38 * (x19 * x23 * x25 - x36 * x7)) ) ) result[0, 1, 0] = numpy.sum(x43 * (x39 * x44 - x54)) result[0, 2, 0] = numpy.sum(x43 * (x40 * x44 - x66)) result[1, 0, 0] = numpy.sum(-x42 * (x0 * x67 + x54)) result[1, 1, 0] = numpy.sum(-x42 * (x22 * x70 + x37 * x73 + x39 * x67)) result[1, 2, 0] = numpy.sum(-x77 * (x40 * x51 + x76)) result[2, 0, 0] = numpy.sum(-x42 * (x0 * x78 + x66)) result[2, 1, 0] = numpy.sum(-x77 * (x39 * x63 + x76)) result[2, 2, 0] = numpy.sum(x42 * (-x22 * x81 + x37 * x84 - x40 * x78)) result[3, 0, 0] = numpy.sum(x43 * (-x0 * x69 + x22 * x69 - x37 * x73)) result[3, 1, 0] = numpy.sum( x43 * (x34 * (-x19 * x33 * x45 + x32 * x9 + x68) - x39 * x69 + x45 * x69 - x71 * x73) ) result[3, 2, 0] = numpy.sum(x43 * (x40 * x70 - x85)) result[4, 0, 0] = numpy.sum(-x77 * (x0 * x74 + x76)) result[4, 1, 0] = numpy.sum(-x42 * (x39 * x86 + x85)) result[4, 2, 0] = numpy.sum(x42 * (-x40 * x86 - x45 * x81 + x71 * x84)) result[5, 0, 0] = numpy.sum(x43 * (-x0 * x80 + x22 * x80 - x37 * x83)) result[5, 1, 0] = numpy.sum(x43 * (-x39 * x80 + x45 * x80 - x71 * x83)) result[5, 2, 0] = numpy.sum( x43 * (x34 * (x12 * x32 - x19 * x33 * x55 + x79) - x40 * x80 + x55 * x80 - x82 * x83) ) return result
[docs] def int3c2e3d_sph_211(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (dp|p) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((6, 3, 3), dtype=float) x0 = A[0] - B[0] x1 = ax + bx x2 = x1 ** (-1.0) x3 = -x2 * (ax * A[0] + bx * B[0]) x4 = x3 + C[0] x5 = cx + x1 x6 = x5 ** (-1.0) x7 = -x4 x8 = -x2 * (ax * A[1] + bx * B[1]) x9 = x8 + C[1] x10 = -x9 x11 = -x2 * (ax * A[2] + bx * B[2]) x12 = x11 + C[2] x13 = -x12 x14 = cx * x6 x15 = x1 * x14 x16 = x15 * (x10**2 + x13**2 + x7**2) x17 = boys(2, x16) x18 = x17 * x6 x19 = cx ** (-1.0) x20 = x19 * boys(1, x16) x21 = x18 - x20 x22 = x2 * x21 x23 = x3 + A[0] x24 = -x23 x25 = x18 * x7 - x20 * x24 x26 = boys(3, x16) x27 = x26 * x6 x28 = x17 * x19 x29 = -x24 * x28 + x27 * x7 x30 = x14 * x4 x31 = 2.0 * x30 x32 = -x22 + 2.0 * x23 * x25 - x29 * x31 x33 = 2.0 * x2 * x25 + x32 * x4 x34 = x23 * x32 x35 = 2.0 * x2 x36 = x35 * (-x14 * x29 + x25) x37 = x27 - x28 x38 = x2 * x37 x39 = x6 * boys(4, x16) x40 = 2.0 * x23 * x29 + x31 * (x19 * x24 * x26 - x39 * x7) - x38 x41 = x2 * x32 x42 = A[1] - B[1] x43 = A[2] - B[2] x44 = ( 17.49341832762486 * da * db * dc * x5 ** (-1.5) * numpy.exp(-ax * bx * x2 * (x0**2 + x42**2 + x43**2)) ) x45 = 0.5773502691896258 x46 = x44 * x45 x47 = x44 * x9 x48 = x45 * (x0 * x32 + x30 * x40 - x34 - x36) x49 = x12 * x44 x50 = x8 + A[1] x51 = -x50 x52 = x10 * x27 - x17 * x19 * x51 x53 = -x52 x54 = x14 * x53 x55 = x10 * x18 - x20 * x51 x56 = x2 * (x54 + x55) x57 = -x55 x58 = -x24 * x57 + x54 * x7 x59 = 2.0 * x23 x60 = x10 * x39 - x19 * x26 * x51 x61 = -x60 x62 = x14 * x7 x63 = -x31 * (x24 * x53 - x61 * x62) + x56 - x58 * x59 x64 = -x63 x65 = x35 * x58 + x4 * x64 x66 = x64 * x9 x67 = 0.5 * x41 x68 = -x67 x69 = x45 * x49 x70 = x11 + A[2] x71 = -x70 x72 = x13 * x27 - x17 * x19 * x71 x73 = -x72 x74 = x14 * x73 x75 = x13 * x18 - x20 * x71 x76 = x2 * (x74 + x75) x77 = -x75 x78 = -x24 * x77 + x7 * x74 x79 = x13 * x39 - x19 * x26 * x71 x80 = -x79 x81 = -x31 * (x24 * x73 - x62 * x80) - x59 * x78 + x76 x82 = -x81 x83 = x35 * x78 + x4 * x82 x84 = x45 * x47 x85 = x12 * x82 x86 = x15 * (x12**2 + x4**2 + x9**2) x87 = x6 * boys(2, x86) x88 = boys(1, x86) x89 = x2 * (-x19 * x50 * x88 + x87 * x9) x90 = -x23 * x55 + x30 * x52 x91 = 2.0 * x90 x92 = x4 * x91 + x89 x93 = x2 * (-x19 * x23 * x88 + x4 * x87) x94 = x9 * x91 + x93 x95 = x14 * x9 x96 = 2.0 * x95 x97 = x22 - 2.0 * x50 * x55 + x52 * x96 x98 = -x97 x99 = -x38 + 2.0 * x50 * x52 - x60 * x96 x100 = x30 * x99 x101 = -x100 + x23 * x98 x102 = 0.5 * x2 x103 = x2 * x90 x104 = 2.0 * x103 x105 = -x50 * x75 + x72 * x95 x106 = x105 * x2 x107 = x10 * x74 - x51 * x77 x108 = x10 * x14 x109 = x108 * x80 - x51 * x73 x110 = -2.0 * x107 * x23 + 2.0 * x109 * x30 x111 = -x106 + x110 * x4 x112 = -x23 * x75 + x30 * x72 x113 = x112 * x2 x114 = x110 * x9 - x113 x115 = -x103 + x110 * x12 x116 = x2 * (x12 * x87 - x19 * x70 * x88) x117 = 2.0 * x112 x118 = x116 + x117 * x4 x119 = x117 * x12 + x93 x120 = x12 * x14 x121 = 2.0 * x120 x122 = x121 * x72 + x22 - 2.0 * x70 * x75 x123 = -x122 x124 = -x121 * x79 - x38 + 2.0 * x70 * x72 x125 = x124 * x30 x126 = x123 * x23 - x125 x127 = -x102 * x122 x128 = 2.0 * x113 x129 = -x2 * x21 x130 = 2.0 * x51 x131 = x24 * (-2.0 * x10 * x54 + x129 + x130 * x57) x132 = -x2 * x37 x133 = x62 * (-2.0 * x108 * x61 + x130 * x53 + x132) x134 = x102 * x98 x135 = x35 * x55 + x9 * x98 x136 = x50 * x98 x137 = 2.0 * x56 x138 = -x136 - x137 + x42 * x98 + x95 * x99 x139 = x4 * x44 x140 = x139 * x45 x141 = 1.5 * x2 x142 = -2.0 * x107 * x50 + x109 * x96 + x76 x143 = -x142 x144 = x107 * x35 + x143 * x9 x145 = x12 * x143 x146 = 2.0 * x105 x147 = x116 + x146 * x9 x148 = x12 * x146 + x89 x149 = x124 * x95 x150 = x123 * x50 - x149 x151 = 2.0 * x106 x152 = 2.0 * x71 x153 = 2.0 * x13 x154 = x129 + x152 * x77 - x153 * x74 x155 = x154 * x24 x156 = x132 - x14 * x153 * x80 + x152 * x73 x157 = x156 * x62 x158 = x102 * x123 x159 = x12 * x123 + x35 * x75 x160 = x154 * x51 x161 = x108 * x156 x162 = x123 * x70 x163 = 2.0 * x76 x164 = x120 * x124 + x123 * x43 - x162 - x163 # 54 item(s) result[0, 0, 0] = numpy.sum( 0.5 * x46 * (-2.0 * x0 * x33 + 2.0 * x4 * (-cx * x4 * x40 * x6 + x34 + x36) + 3.0 * x41) ) result[0, 0, 1] = numpy.sum(-x47 * x48) result[0, 0, 2] = numpy.sum(-x48 * x49) result[0, 1, 0] = numpy.sum(-x46 * (x33 * x42 + x65)) result[0, 1, 1] = numpy.sum(-x46 * (x32 * x42 * x9 + x66 + x68)) result[0, 1, 2] = numpy.sum(x69 * (-x32 * x42 + x63)) result[0, 2, 0] = numpy.sum(-x46 * (x33 * x43 + x83)) result[0, 2, 1] = numpy.sum(x84 * (-x32 * x43 + x81)) result[0, 2, 2] = numpy.sum(-x46 * (x12 * x32 * x43 + x68 + x85)) result[1, 0, 0] = numpy.sum(x44 * (x0 * x92 - x65)) result[1, 0, 1] = numpy.sum(x44 * (x0 * x94 - x66 + x67)) result[1, 0, 2] = numpy.sum(x49 * (x0 * x91 + x63)) result[1, 1, 0] = numpy.sum(x44 * (x101 * x4 - x102 * x97 + x42 * x92)) result[1, 1, 1] = numpy.sum(x44 * (x101 * x9 - x104 + x42 * x94)) result[1, 1, 2] = numpy.sum(x49 * (-x100 + x23 * x98 + x42 * x91)) result[1, 2, 0] = numpy.sum(x44 * (x111 + x43 * x92)) result[1, 2, 1] = numpy.sum(x44 * (x114 + x43 * x94)) result[1, 2, 2] = numpy.sum(x44 * (x115 + x12 * x43 * x91)) result[2, 0, 0] = numpy.sum(x44 * (x0 * x118 - x83)) result[2, 0, 1] = numpy.sum(x47 * (x0 * x117 + x81)) result[2, 0, 2] = numpy.sum(x44 * (x0 * x119 + x67 - x85)) result[2, 1, 0] = numpy.sum(x44 * (x111 + x118 * x42)) result[2, 1, 1] = numpy.sum(x44 * (x114 + x117 * x42 * x9)) result[2, 1, 2] = numpy.sum(x44 * (x115 + x119 * x42)) result[2, 2, 0] = numpy.sum(x44 * (x118 * x43 + x126 * x4 + x127)) result[2, 2, 1] = numpy.sum(x47 * (x117 * x43 + x123 * x23 - x125)) result[2, 2, 2] = numpy.sum(x44 * (x119 * x43 + x12 * x126 - x128)) result[3, 0, 0] = numpy.sum(x46 * (-x0 * x4 * x98 + x134 - x4 * (x131 - x133))) result[3, 0, 1] = numpy.sum(x46 * (-x0 * x135 + x101 * x9 - x104)) result[3, 0, 2] = numpy.sum(x69 * (-x0 * x98 - x131 + x133)) result[3, 1, 0] = numpy.sum(-x138 * x140) result[3, 1, 1] = numpy.sum( x46 * (-x135 * x42 + x141 * x98 + x9 * (-cx * x6 * x9 * x99 + x136 + x137)) ) result[3, 1, 2] = numpy.sum(-x138 * x69) result[3, 2, 0] = numpy.sum(x140 * (x142 - x43 * x98)) result[3, 2, 1] = numpy.sum(-x46 * (x135 * x43 + x144)) result[3, 2, 2] = numpy.sum(x46 * (-x12 * x43 * x98 + x134 - x145)) result[4, 0, 0] = numpy.sum(x44 * (x0 * x146 * x4 + x111)) result[4, 0, 1] = numpy.sum(x44 * (x0 * x147 + x114)) result[4, 0, 2] = numpy.sum(x44 * (x0 * x148 + x115)) result[4, 1, 0] = numpy.sum(x139 * (x142 + x146 * x42)) result[4, 1, 1] = numpy.sum(x44 * (-x144 + x147 * x42)) result[4, 1, 2] = numpy.sum(x44 * (x134 - x145 + x148 * x42)) result[4, 2, 0] = numpy.sum(x139 * (x123 * x50 + x146 * x43 - x149)) result[4, 2, 1] = numpy.sum(x44 * (x127 + x147 * x43 + x150 * x9)) result[4, 2, 2] = numpy.sum(x44 * (x12 * x150 + x148 * x43 - x151)) result[5, 0, 0] = numpy.sum(x46 * (-x0 * x123 * x4 + x158 - x4 * (x155 - x157))) result[5, 0, 1] = numpy.sum(x84 * (-x0 * x123 - x155 + x157)) result[5, 0, 2] = numpy.sum(x46 * (-x0 * x159 + x12 * x126 - x128)) result[5, 1, 0] = numpy.sum(x140 * (-x123 * x42 - x160 + x161)) result[5, 1, 1] = numpy.sum(x46 * (-x123 * x42 * x9 + x158 - x9 * (x160 - x161))) result[5, 1, 2] = numpy.sum(x46 * (x12 * x150 - x151 - x159 * x42)) result[5, 2, 0] = numpy.sum(-x140 * x164) result[5, 2, 1] = numpy.sum(-x164 * x84) result[5, 2, 2] = numpy.sum( x46 * (x12 * (-cx * x12 * x124 * x6 + x162 + x163) + x123 * x141 - x159 * x43) ) return result
[docs] def int3c2e3d_sph_212(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (dp|d) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((6, 3, 6), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = cx + x0 x3 = x2 ** (-1.0) x4 = -x1 * (ax * A[0] + bx * B[0]) x5 = x4 + C[0] x6 = -x5 x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = x7 + C[1] x9 = -x8 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = x10 + C[2] x12 = -x11 x13 = cx * x3 x14 = x0 * x13 x15 = x14 * (x12**2 + x6**2 + x9**2) x16 = boys(3, x15) x17 = x16 * x3 x18 = cx ** (-1.0) x19 = x18 * boys(2, x15) x20 = x17 - x19 x21 = x1 * x20 x22 = x4 + A[0] x23 = -x22 x24 = x17 * x6 - x19 * x23 x25 = boys(4, x15) x26 = x25 * x3 x27 = x16 * x18 x28 = -x23 * x27 + x26 * x6 x29 = 2.0 * x5 x30 = x13 * x29 x31 = x21 - 2.0 * x22 * x24 + x28 * x30 x32 = -x31 x33 = 2.0 * x1 x34 = x26 - x27 x35 = x1 * x34 x36 = x3 * boys(5, x15) x37 = x13 * x5 x38 = ( x22 * x32 - x33 * (x13 * x28 - x24) - x37 * (2.0 * x22 * x28 + x30 * (x18 * x23 * x25 - x36 * x6) - x35) ) x39 = 0.5 * x5 x40 = A[0] - B[0] x41 = x5**2 x42 = x8**2 x43 = x11**2 x44 = x14 * (x41 + x42 + x43) x45 = boys(2, x44) x46 = x1 * x18 * x45 x47 = x1 * x24 x48 = x32 * x5 + 2.0 * x47 x49 = x1 * (2.0 * x24 * x5 + x46) + x48 * x5 x50 = 1.5 * x1 x51 = A[1] - B[1] x52 = A[2] - B[2] x53 = ( 17.49341832762486 * da * db * dc * x0 * x2 ** (-2.5) * numpy.exp(-ax * bx * x1 * (x40**2 + x51**2 + x52**2)) ) x54 = 0.3333333333333333 * x53 x55 = x3 * boys(3, x44) x56 = 2.0 * x1 * (x18 * x22 * x45 - x5 * x55) - x31 * x5 x57 = 1.732050807568877 x58 = x54 * x57 x59 = x58 * (x31 * x50 - x38 * x5 + x40 * x56) x60 = x54 * (x31 * x40 + x38) x61 = x7 + A[1] x62 = -x61 x63 = x17 * x9 - x19 * x62 x64 = x1 * x63 x65 = -x64 x66 = -x63 x67 = -x16 * x18 * x62 + x26 * x9 x68 = -x67 x69 = x13 * x68 x70 = -x23 * x66 + x6 * x69 x71 = x5 * x70 x72 = x65 + 2.0 * x71 x73 = x1 * (x63 + x69) x74 = 2.0 * x22 x75 = -x18 * x25 * x62 + x36 * x9 x76 = -x75 x77 = x13 * x6 x78 = -x30 * (x23 * x68 - x76 * x77) - x70 * x74 + x73 x79 = -x78 x80 = x1 * x70 x81 = 2.0 * x80 x82 = x1 * x72 + x5 * (x5 * x79 + x81) x83 = -x47 x84 = x70 * x8 x85 = x83 + 2.0 * x84 x86 = x1 * x85 x87 = -x1 * x32 x88 = x79 * x8 x89 = -x39 * (x87 + 2.0 * x88) x90 = x51 * x56 x91 = x5 * x78 x92 = -x22 * x63 + x37 * x67 x93 = x11 * x58 x94 = x31 * x51 x95 = x8 * x94 x96 = x1 * x32 x97 = -x88 + x96 x98 = x54 * x8 x99 = -0.5 * x1 * x31 + x78 * x8 x100 = x43 * x54 x101 = x10 + A[2] x102 = -x101 x103 = -x102 * x19 + x12 * x17 x104 = x1 * x103 x105 = -x104 x106 = -x103 x107 = -x102 * x16 * x18 + x12 * x26 x108 = -x107 x109 = x108 * x13 x110 = -x106 * x23 + x109 * x6 x111 = x110 * x5 x112 = x105 + 2.0 * x111 x113 = x1 * (x103 + x109) x114 = -x102 * x18 * x25 + x12 * x36 x115 = -x114 x116 = -x110 * x74 + x113 - x30 * (x108 * x23 - x115 * x77) x117 = -x116 x118 = x1 * x110 x119 = 2.0 * x118 x120 = x1 * x112 + x5 * (x117 * x5 + x119) x121 = x52 * x56 x122 = x116 * x5 x123 = -x103 * x22 + x107 * x37 x124 = x58 * x8 x125 = x11 * x110 x126 = 2.0 * x125 + x83 x127 = x1 * x126 x128 = x11 * x117 x129 = -x39 * (2.0 * x128 + x87) x130 = x31 * x52 x131 = x42 * x54 x132 = 0.5 * x96 x133 = -x128 x134 = x11 * x130 + x133 x135 = x11 * x54 x136 = x65 + x71 x137 = x29 * x40 x138 = x1 * (x46 + 2.0 * x63 * x8) x139 = -0.5 * x138 + 0.5 * x29 * x85 x140 = -x86 x141 = x11 * x53 x142 = x83 + x84 x143 = 2.0 * x40 x144 = x43 * x58 x145 = 2.0 * x51 x146 = 2.0 * x8 x147 = x13 * x146 x148 = x147 * x67 + x21 - 2.0 * x61 * x63 x149 = -x148 x150 = x1 * x149 x151 = -x1 * x20 x152 = 2.0 * x62 x153 = -x1 * x34 x154 = x13 * x9 x155 = -x23 * (x151 + x152 * x66 - 2.0 * x69 * x9) + x77 * ( x152 * x68 + x153 - 2.0 * x154 * x76 ) x156 = x155 * x5 x157 = x150 + x156 x158 = x5 * x58 x159 = x155 * x8 x160 = x159 - x81 x161 = x149 * x8 + 2.0 * x64 x162 = 0.5 * x1 x163 = x160 * x5 + x161 * x162 x164 = 0.5 * x150 x165 = x156 + x164 x166 = x160 * x8 x167 = x145 * x8 x168 = -x106 * x62 + x109 * x9 x169 = -x108 * x62 + x115 * x154 x170 = x168 * x23 - x169 * x77 x171 = x1 * x168 x172 = x170 * x5 - x171 x173 = x5 * x53 x174 = 0.6666666666666667 * x57 x175 = x173 * x174 x176 = -x118 x177 = x170 * x8 x178 = x168 * x8 x179 = x105 + 2.0 * x178 x180 = x1 * x179 x181 = -0.5 * x180 + x5 * (x176 + 2.0 * x177) x182 = x11 * x52 x183 = -x80 x184 = x11 * x170 x185 = x183 + 2.0 * x184 x186 = x11 * x168 x187 = 2.0 * x186 + x65 x188 = x1 * x187 x189 = x185 * x5 - 0.5 * x188 x190 = x176 + x177 x191 = x53 * x8 x192 = x174 * x191 x193 = -0.5 * x127 + x185 * x8 x194 = x183 + x184 x195 = x141 * x174 x196 = x105 + x111 x197 = x1 * (2.0 * x103 * x11 + x46) x198 = -x197 x199 = 0.5 * x126 * x29 + 0.5 * x198 x200 = -x127 x201 = x42 * x58 x202 = x125 + x83 x203 = x51 * x8 x204 = 2.0 * x52 x205 = x11 * x13 x206 = -2.0 * x101 * x103 + 2.0 * x107 * x205 + x21 x207 = -x206 x208 = x1 * x207 x209 = 2.0 * x102 x210 = 2.0 * x12 x211 = x106 * x209 - x109 * x210 + x151 x212 = x108 * x209 - x115 * x13 * x210 + x153 x213 = -x211 * x23 + x212 * x77 x214 = x213 * x5 x215 = x208 + x214 x216 = 0.5 * x208 x217 = x214 + x216 x218 = x11 * x213 - x119 x219 = 2.0 * x104 + x11 * x207 x220 = x162 * x219 x221 = x218 * x5 + x220 x222 = x11 * x218 x223 = 2.0 * x182 x224 = x148 * x40 x225 = x224 * x5 x226 = x5 * x54 x227 = x40 * x5 x228 = x138 + x161 * x8 x229 = 2.0 * x1 * (x18 * x45 * x61 - x55 * x8) - x148 * x8 x230 = -x147 * x75 - x35 + 2.0 * x61 * x67 x231 = x13 * x8 x232 = x149 * x61 - x230 * x231 + 2.0 * x73 x233 = x148 * x51 + x232 x234 = x41 * x54 x235 = -x232 * x8 x236 = 0.5 * x8 x237 = x148 * x52 x238 = x113 + x147 * x169 - 2.0 * x168 * x61 x239 = -x238 x240 = 2.0 * x171 x241 = x239 * x8 + x240 x242 = x11 * x239 x243 = -x242 x244 = x11 * x237 + x243 x245 = x180 + x241 * x8 x246 = x236 * (x1 * x149 - 2.0 * x242) x247 = x105 + x178 x248 = 0.5 * x146 * x187 + 0.5 * x198 x249 = x186 + x65 x250 = x41 * x58 x251 = -x188 x252 = x154 * x212 - x211 * x62 x253 = x252 * x8 x254 = x11 * x252 - x240 x255 = x208 + x253 x256 = x220 + x254 * x8 x257 = x11 * x254 x258 = x206 * x40 x259 = x258 * x5 x260 = x219 * x40 x261 = 2.0 * x101 * x107 - 2.0 * x114 * x205 - x35 x262 = x11 * x219 + x197 x263 = x206 * x51 x264 = x231 * x261 x265 = x263 * x8 x266 = x219 * x51 x267 = x101 * x207 + 2.0 * x113 - x205 * x261 x268 = x206 * x52 + x267 x269 = -x11 * x267 x270 = 1.5 * x1 * x207 - x219 * x52 - x269 # 108 item(s) result[0, 0, 0] = numpy.sum( -x54 * (x39 * (3.0 * x1 * x32 + x29 * x38) - x40 * x49 + x48 * x50) ) result[0, 0, 1] = numpy.sum(x59 * x8) result[0, 0, 2] = numpy.sum(x11 * x59) result[0, 0, 3] = numpy.sum(-x42 * x60) result[0, 0, 4] = numpy.sum(-x11 * x57 * x60 * x8) result[0, 0, 5] = numpy.sum(-x43 * x60) result[0, 1, 0] = numpy.sum(x54 * (x49 * x51 + x82)) result[0, 1, 1] = numpy.sum(x58 * (x8 * x90 + x86 - x89)) result[0, 1, 2] = numpy.sum(x93 * (x33 * x92 + x90 - x91)) result[0, 1, 3] = numpy.sum(-x98 * (x95 + x97)) result[0, 1, 4] = numpy.sum(-x93 * (x95 + x99)) result[0, 1, 5] = numpy.sum(-x100 * (x78 + x94)) result[0, 2, 0] = numpy.sum(x54 * (x120 + x49 * x52)) result[0, 2, 1] = numpy.sum(x124 * (x121 - x122 + x123 * x33)) result[0, 2, 2] = numpy.sum(x58 * (x11 * x121 + x127 - x129)) result[0, 2, 3] = numpy.sum(-x131 * (x116 + x130)) result[0, 2, 4] = numpy.sum(-x124 * (x132 + x134)) result[0, 2, 5] = numpy.sum(-x135 * (x134 + x96)) result[1, 0, 0] = numpy.sum(x58 * (-x136 * x137 + x82)) result[1, 0, 1] = numpy.sum(-x53 * (x139 * x40 + x140 + x89)) result[1, 0, 2] = numpy.sum(x141 * (2.0 * x1 * x92 - x40 * x72 - x91)) result[1, 0, 3] = numpy.sum(-x124 * (x142 * x143 + x97)) result[1, 0, 4] = numpy.sum(-x141 * (x40 * x85 + x99)) result[1, 0, 5] = numpy.sum(-x144 * (x143 * x70 + x78)) result[1, 1, 0] = numpy.sum(-x158 * (x136 * x145 + x157)) result[1, 1, 1] = numpy.sum(-x53 * (x139 * x51 + x163)) result[1, 1, 2] = numpy.sum(-x141 * (x165 + x51 * x72)) result[1, 1, 3] = numpy.sum(-x58 * (x140 + x142 * x167 + x166)) result[1, 1, 4] = numpy.sum(-x141 * (x160 + x51 * x85)) result[1, 1, 5] = numpy.sum(-x144 * (x145 * x70 + x155)) result[1, 2, 0] = numpy.sum(-x175 * (x136 * x52 + x172)) result[1, 2, 1] = numpy.sum(-x53 * (x139 * x52 + x181)) result[1, 2, 2] = numpy.sum(-x53 * (x182 * x72 + x189)) result[1, 2, 3] = numpy.sum(-x192 * (x142 * x52 + x190)) result[1, 2, 4] = numpy.sum(-x53 * (x182 * x85 + x193)) result[1, 2, 5] = numpy.sum(-x195 * (x182 * x70 + x194)) result[2, 0, 0] = numpy.sum(x58 * (x120 - x137 * x196)) result[2, 0, 1] = numpy.sum(x191 * (2.0 * x1 * x123 - x112 * x40 - x122)) result[2, 0, 2] = numpy.sum(-x53 * (x129 + x199 * x40 + x200)) result[2, 0, 3] = numpy.sum(-x201 * (x110 * x143 + x116)) result[2, 0, 4] = numpy.sum(-x191 * (x126 * x40 + x132 + x133)) result[2, 0, 5] = numpy.sum(-x93 * (x133 + x143 * x202 + x96)) result[2, 1, 0] = numpy.sum(-x175 * (x172 + x196 * x51)) result[2, 1, 1] = numpy.sum(-x53 * (x112 * x203 + x181)) result[2, 1, 2] = numpy.sum(-x53 * (x189 + x199 * x51)) result[2, 1, 3] = numpy.sum(-x192 * (x110 * x203 + x190)) result[2, 1, 4] = numpy.sum(-x53 * (x126 * x203 + x193)) result[2, 1, 5] = numpy.sum(-x195 * (x194 + x202 * x51)) result[2, 2, 0] = numpy.sum(-x158 * (x196 * x204 + x215)) result[2, 2, 1] = numpy.sum(-x191 * (x112 * x52 + x217)) result[2, 2, 2] = numpy.sum(-x53 * (x199 * x52 + x221)) result[2, 2, 3] = numpy.sum(-x201 * (x110 * x204 + x213)) result[2, 2, 4] = numpy.sum(-x191 * (x126 * x52 + x218)) result[2, 2, 5] = numpy.sum(-x58 * (x200 + x202 * x223 + x222)) result[3, 0, 0] = numpy.sum(-x226 * (x157 + x225)) result[3, 0, 1] = numpy.sum(x58 * (x161 * x227 - x163)) result[3, 0, 2] = numpy.sum(-x93 * (x165 + x225)) result[3, 0, 3] = numpy.sum(x54 * (-x166 + x228 * x40 + x86)) result[3, 0, 4] = numpy.sum(x93 * (-x159 + x229 * x40 + x81)) result[3, 0, 5] = numpy.sum(x100 * (-x149 * x22 - x224 + x230 * x37)) result[3, 1, 0] = numpy.sum(-x233 * x234) result[3, 1, 1] = numpy.sum( 0.5 * x158 * (-3.0 * x1 * x149 + 2.0 * x161 * x51 + 2.0 * x235) ) result[3, 1, 2] = numpy.sum(-x233 * x5 * x93) result[3, 1, 3] = numpy.sum( -x54 * (x161 * x50 - x228 * x51 + x236 * (3.0 * x1 * x149 - 2.0 * x235)) ) result[3, 1, 4] = numpy.sum(x93 * (x148 * x50 + x229 * x51 - x232 * x8)) result[3, 1, 5] = numpy.sum(-x100 * x233) result[3, 2, 0] = numpy.sum(-x234 * (x237 + x238)) result[3, 2, 1] = numpy.sum(x158 * (x161 * x52 + x241)) result[3, 2, 2] = numpy.sum(-x158 * (x164 + x244)) result[3, 2, 3] = numpy.sum(x54 * (x228 * x52 + x245)) result[3, 2, 4] = numpy.sum(x58 * (x182 * x229 + x188 - x246)) result[3, 2, 5] = numpy.sum(-x135 * (x150 + x244)) result[4, 0, 0] = numpy.sum(-x175 * (x168 * x227 + x172)) result[4, 0, 1] = numpy.sum(-x53 * (x179 * x227 + x181)) result[4, 0, 2] = numpy.sum(-x53 * (x187 * x227 + x189)) result[4, 0, 3] = numpy.sum(-x192 * (x190 + x247 * x40)) result[4, 0, 4] = numpy.sum(-x53 * (x193 + x248 * x40)) result[4, 0, 5] = numpy.sum(-x195 * (x194 + x249 * x40)) result[4, 1, 0] = numpy.sum(-x250 * (x145 * x168 + x238)) result[4, 1, 1] = numpy.sum(x173 * (-x179 * x51 + x241)) result[4, 1, 2] = numpy.sum(-x173 * (x164 + x187 * x51 + x243)) result[4, 1, 3] = numpy.sum(x58 * (-x167 * x247 + x245)) result[4, 1, 4] = numpy.sum(-x53 * (x246 + x248 * x51 + x251)) result[4, 1, 5] = numpy.sum(-x93 * (x145 * x249 + x150 + x243)) result[4, 2, 0] = numpy.sum(-x250 * (x168 * x204 + x252)) result[4, 2, 1] = numpy.sum(-x173 * (x179 * x52 + x216 + x253)) result[4, 2, 2] = numpy.sum(-x173 * (x187 * x52 + x254)) result[4, 2, 3] = numpy.sum(-x124 * (x204 * x247 + x255)) result[4, 2, 4] = numpy.sum(-x53 * (x248 * x52 + x256)) result[4, 2, 5] = numpy.sum(-x58 * (x223 * x249 + x251 + x257)) result[5, 0, 0] = numpy.sum(-x226 * (x215 + x259)) result[5, 0, 1] = numpy.sum(-x124 * (x217 + x259)) result[5, 0, 2] = numpy.sum(x58 * (-x221 + x260 * x5)) result[5, 0, 3] = numpy.sum(x131 * (-x207 * x22 - x258 + x261 * x37)) result[5, 0, 4] = numpy.sum(x124 * (-x11 * x213 + x119 + x260)) result[5, 0, 5] = numpy.sum(x54 * (x127 - x222 + x262 * x40)) result[5, 1, 0] = numpy.sum(x234 * (-x207 * x61 - x263 + x264)) result[5, 1, 1] = numpy.sum(-x158 * (-x162 * x206 + x265 + x8 * (x207 * x61 - x264))) result[5, 1, 2] = numpy.sum(x158 * (-x11 * x252 + x240 + x266)) result[5, 1, 3] = numpy.sum(-x98 * (x255 + x265)) result[5, 1, 4] = numpy.sum(x58 * (-x256 + x266 * x8)) result[5, 1, 5] = numpy.sum(x54 * (x188 - x257 + x262 * x51)) result[5, 2, 0] = numpy.sum(-x234 * x268) result[5, 2, 1] = numpy.sum(-x124 * x268 * x5) result[5, 2, 2] = numpy.sum(-x158 * x270) result[5, 2, 3] = numpy.sum(-x131 * x268) result[5, 2, 4] = numpy.sum(-x124 * x270) result[5, 2, 5] = numpy.sum( -0.5 * x54 * (x11 * (3.0 * x1 * x207 - 2.0 * x269) + 2.0 * x219 * x50 - 2.0 * x262 * x52) ) return result
[docs] def int3c2e3d_sph_213(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (dp|f) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((6, 3, 10), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - C[0] x4 = -x2 - A[0] x5 = 0.5 / (ax + bx) x6 = x3**2 x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = -x7 - C[1] x9 = x8**2 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = -x10 - C[2] x12 = x11**2 x13 = cx + x0 x14 = x13 ** (-1.0) x15 = cx * x14 x16 = x0 * x15 * (x12 + x6 + x9) x17 = boys(4, x16) x18 = x13 ** (-1.5) x19 = 17.49341832762486 x20 = A[0] - B[0] x21 = A[1] - B[1] x22 = A[2] - B[2] x23 = numpy.exp(-ax * bx * x1 * (x20**2 + x21**2 + x22**2)) x24 = x1 * x19 * x23 x25 = 2.0 * x18 * x24 x26 = x17 * x25 x27 = cx ** (-1.0) x28 = x13 ** (-0.5) x29 = boys(3, x16) x30 = x5 * (2.0 * x1 * x19 * x23 * x27 * x28 * x29 - x26) x31 = -2.0 * x1 * x19 * x23 * x27 * x28 * x29 * x4 + x26 * x3 x32 = -x31 x33 = boys(5, x16) x34 = x25 * x33 x35 = 2.0 * x1 * x17 * x19 * x23 * x27 * x28 * x4 - x3 * x34 x36 = x15 * x35 x37 = -x3 * x36 + x30 + x32 * x4 x38 = 2.0 * x5 x39 = x5 * (2.0 * x1 * x17 * x19 * x23 * x27 * x28 - x34) x40 = x25 * boys(6, x16) x41 = x15 * x3 x42 = ( x37 * x4 - x38 * (x31 + x36) - x41 * ( x35 * x4 + x39 - x41 * (2.0 * x1 * x19 * x23 * x27 * x28 * x33 * x4 - x3 * x40) ) ) x43 = x3 * x42 x44 = x37 * x5 x45 = 3.0 * x44 x46 = x0 * x14 x47 = x3 * x46 x48 = x3 * x37 x49 = x32 * x5 x50 = 2.0 * x49 x51 = x48 + x50 x52 = x46 * x5 x53 = 3.0 * x52 x54 = x3 * x32 x55 = x27 * x29 * x38 x56 = x24 * x28 * x55 x57 = x54 + x56 x58 = x38 * x46 x59 = x47 * x51 + x57 * x58 x60 = x18 * x19 * x23 * x55 x61 = x47 * x59 + x58 * (x3 * x60 + x47 * x57) x62 = x20 * x46 x63 = da * db * dc x64 = 0.06666666666666667 * x63 x65 = 2.23606797749979 * x64 x66 = x46 * x8 x67 = x66 * (x48 + x50) x68 = x60 * x8 x69 = x47 * x67 + x58 * (x54 * x66 + x68) x70 = 0.3333333333333333 * x63 x71 = x11 * x46 x72 = x71 * (x48 + x50) x73 = x11 * x60 x74 = x47 * x72 + x58 * (x54 * x71 + x73) x75 = x0**2 / x13**2 x76 = x75 * x9 x77 = x76 * (x48 + x50) x78 = x75 * x8 x79 = x11 * x78 x80 = x79 * (x48 + x50) x81 = 1.732050807568877 * x70 x82 = x12 * x75 x83 = x82 * (x48 + x50) x84 = x8**3 x85 = x0**3 / x13**3 x86 = x42 * x85 x87 = x84 * x85 x88 = x20 * x37 x89 = x85 * x9 x90 = x11 * x89 x91 = x12 * x8 x92 = x85 * x91 x93 = x11**3 x94 = x85 * x93 x95 = -x7 - A[1] x96 = 2.0 * x1 * x17 * x19 * x23 * x27 * x28 * x95 - x34 * x8 x97 = x15 * x96 x98 = -2.0 * x1 * x19 * x23 * x27 * x28 * x29 * x95 + x26 * x8 x99 = -x5 * (x97 + x98) x100 = -x98 x101 = x100 * x4 - x3 * x97 x102 = 2.0 * x1 * x19 * x23 * x27 * x28 * x33 * x95 - x40 * x8 x103 = x101 * x4 + x41 * (x102 * x41 - x4 * x96) + x99 x104 = x103 * x3 x105 = x101 * x5 x106 = 2.0 * x105 x107 = x100 * x5 x108 = x101 * x3 x109 = x107 + x108 x110 = x47 * (x107 + x109) x111 = x46 * (x110 * x58 + x47 * (x109 * x58 + x47 * (x104 + x106))) x112 = x21 * x46 x113 = x103 * x8 x114 = x113 + x44 x115 = x101 * x8 x116 = x115 + x49 x117 = x116 * x58 x118 = x100 * x8 x119 = x118 + x56 x120 = x116 * x47 + x119 * x52 x121 = x46 * (x120 * x58 + x47 * (x114 * x47 + x117)) x122 = x106 * x71 x123 = x107 * x71 x124 = x108 * x71 + x123 x125 = x46 * (x124 * x58 + x47 * (x104 * x71 + x122)) x126 = x66 * (x114 + x44) x127 = x66 * (x116 + x49) x128 = x127 * x58 x129 = x46 * (x126 * x47 + x128) x130 = x44 * x71 x131 = x113 * x71 + x130 x132 = x49 * x71 x133 = x115 * x71 + x132 x134 = x133 * x58 x135 = x46 * (x131 * x47 + x134) x136 = x106 * x82 x137 = x46 * (x104 * x82 + x136) x138 = x46 * (x126 * x66 + x44 * x76) x139 = x21 * x37 x140 = x46 * (x131 * x66 + x44 * x79) x141 = x44 * x82 x142 = x46 * (x113 * x82 + x141) x143 = x103 * x94 x144 = -x10 - A[2] x145 = 2.0 * x1 * x144 * x17 * x19 * x23 * x27 * x28 - x11 * x34 x146 = x145 * x15 x147 = -2.0 * x1 * x144 * x19 * x23 * x27 * x28 * x29 + x11 * x26 x148 = -x5 * (x146 + x147) x149 = -x147 x150 = -x146 * x3 + x149 * x4 x151 = 2.0 * x1 * x144 * x19 * x23 * x27 * x28 * x33 - x11 * x40 x152 = x148 + x150 * x4 - x41 * (x145 * x4 - x151 * x41) x153 = x152 * x3 x154 = x150 * x5 x155 = 2.0 * x154 x156 = x149 * x5 x157 = x150 * x3 x158 = x156 + x157 x159 = x47 * (x156 + x158) x160 = x46 * (x159 * x58 + x47 * (x158 * x58 + x47 * (x153 + x155))) x161 = x22 * x46 x162 = x156 * x66 x163 = x157 * x66 + x162 x164 = x46 * (x163 * x58 + x47 * x66 * (x153 + x155)) x165 = x11 * x152 + x44 x166 = x11 * x150 + x49 x167 = x166 * x58 x168 = x11 * x149 + x56 x169 = x168 * x52 x170 = x166 * x47 + x169 x171 = x46 * (x170 * x58 + x47 * (x165 * x47 + x167)) x172 = x46 * x76 * (x153 + x155) x173 = x3 * x78 x174 = x46 * (x165 * x173 + x166 * x38 * x78) x175 = x130 + x165 * x71 x176 = x132 + x166 * x71 x177 = x176 * x58 x178 = x46 * (x175 * x47 + x177) x179 = x152 * x87 x180 = x22 * x37 x181 = x165 * x89 x182 = x175 * x78 x183 = x46 * (x141 + x175 * x71) x184 = x6 * x75 x185 = x107 * x184 + x110 * x47 x186 = 3.872983346207417 * x64 x187 = x3 * x75 x188 = x187 * x5 x189 = x119 * x188 + x120 * x47 x190 = x11 * x187 x191 = x107 * x190 + x124 * x47 x192 = x119 * x66 + x68 x193 = x127 * x47 + x192 * x52 x194 = x118 * x71 + x73 x195 = x133 * x47 + x194 * x52 x196 = x107 * x82 x197 = x108 * x82 + x196 x198 = x127 * x66 + x49 * x76 x199 = x133 * x66 + x49 * x79 x200 = x49 * x82 x201 = x115 * x82 + x200 x202 = x101 * x94 x203 = x100 * x95 + x30 - x8 * x97 x204 = x203 * x5 x205 = x15 * x8 x206 = -x102 * x205 + x39 + x95 * x96 x207 = x203 * x4 - x206 * x41 x208 = x207 * x3 x209 = x46 * (x184 * x204 + x47**2 * (2.0 * x204 + x208)) x210 = x203 * x8 x211 = 2.0 * x107 x212 = x210 + x211 x213 = x212 * x52 x214 = x207 * x8 x215 = x106 + x214 x216 = x46 * (x188 * x212 + x47 * (x213 + x215 * x47)) x217 = x204 * x71 x218 = x46 * (x190 * x204 + x47 * (x208 * x71 + x217)) x219 = x119 * x58 + x212 * x66 x220 = x219 * x52 x221 = x117 + x215 * x66 x222 = x46 * (x220 + x221 * x47) x223 = x71 * (x210 + x211) x224 = x223 * x52 x225 = x122 + x214 * x71 x226 = x46 * (x224 + x225 * x47) x227 = x204 * x82 x228 = x46 * (x208 * x82 + x227) x229 = x46 * (x128 + x221 * x66) x230 = x46 * (x134 + x225 * x66) x231 = x46 * (x136 + x214 * x82) x232 = x207 * x94 x233 = -x146 * x8 + x149 * x95 x234 = x233 * x5 x235 = x145 * x95 - x151 * x205 x236 = x233 * x4 - x235 * x41 x237 = x46 * (x184 * x234 + x47**2 * (2.0 * x234 + x236 * x3)) x238 = x156 + x233 * x8 x239 = x154 + x236 * x8 x240 = x46 * (x188 * x238 + x47 * (x238 * x52 + x239 * x47)) x241 = x107 + x11 * x233 x242 = x105 + x11 * x236 x243 = x46 * (x188 * x241 + x47 * (x241 * x52 + x242 * x47)) x244 = x162 + x238 * x66 x245 = x66 * (x154 + x239) x246 = x46 * (x244 * x52 + x245 * x47) x247 = x169 + x241 * x66 x248 = x166 * x52 + x242 * x66 x249 = x46 * (x247 * x52 + x248 * x47) x250 = x123 + x241 * x71 x251 = x71 * (x105 + x242) x252 = x46 * (x250 * x52 + x251 * x47) x253 = x46 * (x154 * x76 + x245 * x66) x254 = x5 * x78 x255 = x46 * (x166 * x254 + x248 * x66) x256 = x46 * (x176 * x52 + x251 * x66) x257 = x46 * (x105 * x82 + x251 * x71) x258 = x156 * x184 + x159 * x47 x259 = x156 * x173 + x163 * x47 x260 = x168 * x188 + x170 * x47 x261 = x156 * x76 x262 = x157 * x76 + x261 x263 = x168 * x254 x264 = x166 * x173 + x263 x265 = x168 * x71 + x73 x266 = x265 * x52 x267 = x176 * x47 + x266 x268 = x150 * x87 x269 = x166 * x89 x270 = x176 * x78 x271 = x176 * x71 + x200 x272 = -x11 * x146 + x144 * x149 + x30 x273 = x272 * x5 x274 = x11 * x15 x275 = x144 * x145 - x151 * x274 + x39 x276 = x272 * x4 - x275 * x41 x277 = x276 * x3 x278 = x46 * (x184 * x273 + x47**2 * (2.0 * x273 + x277)) x279 = x273 * x66 x280 = x46 * (x173 * x273 + x47 * (x277 * x66 + x279)) x281 = x11 * x272 + 2.0 * x156 x282 = x281 * x52 x283 = x11 * x276 + x155 x284 = x46 * (x188 * x281 + x47 * (x282 + x283 * x47)) x285 = x273 * x76 x286 = x46 * (x277 * x76 + x285) x287 = x254 * x281 x288 = x46 * (x173 * x283 + x287) x289 = x168 * x58 + x281 * x71 x290 = x289 * x52 x291 = x167 + x283 * x71 x292 = x46 * (x290 + x291 * x47) x293 = x276 * x87 x294 = x283 * x89 x295 = x291 * x78 x296 = x46 * (x177 + x291 * x71) x297 = x3**3 * x85 x298 = x20 * x203 x299 = x6 * x85 x300 = x212 * x299 x301 = x11 * x299 x302 = x187 * x20 x303 = x3 * x85 x304 = x12 * x303 x305 = x192 * x58 + x219 * x66 x306 = x194 * x58 + x223 * x66 x307 = x82 * (x210 + x211) x308 = x203 * x95 - x205 * x206 + 2.0 * x99 x309 = x203 * x21 x310 = x308 * x8 x311 = 3.0 * x204 x312 = x310 + x311 x313 = 3.0 * x213 + x312 * x66 x314 = x187 * x21 x315 = x71 * (x310 + x311) x316 = x148 - x205 * x235 + x233 * x95 x317 = x297 * x316 x318 = x203 * x22 x319 = 2.0 * x234 x320 = x316 * x8 + x319 x321 = x299 * x320 x322 = x11 * x316 + x204 x323 = x299 * x322 x324 = x238 * x58 + x320 * x66 x325 = x187 * x324 x326 = x187 * x22 x327 = x241 * x58 x328 = x322 * x66 + x327 x329 = x187 * x328 x330 = x217 + x322 * x71 x331 = x187 * x330 x332 = x46 * (x244 * x58 + x324 * x66) x333 = x46 * (x247 * x58 + x328 * x66) x334 = x250 * x58 x335 = x46 * (x330 * x66 + x334) x336 = x46 * (x227 + x330 * x71) x337 = x233 * x297 x338 = x20 * x299 x339 = x244 * x66 + x261 x340 = x247 * x66 + x263 x341 = x250 * x66 + x266 x342 = x196 + x250 * x71 x343 = x21 * x299 x344 = -x205 * x275 + x272 * x95 x345 = x297 * x344 x346 = x273 + x344 * x8 x347 = x299 * x346 x348 = x22 * x299 x349 = x11 * x344 + x319 x350 = x299 * x349 x351 = x279 + x346 * x66 x352 = x187 * x351 x353 = x282 + x349 * x66 x354 = x187 * x353 x355 = x327 + x349 * x71 x356 = x187 * x355 x357 = x46 * (x285 + x351 * x66) x358 = x46 * (x287 + x353 * x66) x359 = x46 * (x290 + x355 * x66) x360 = x46 * (x334 + x355 * x71) x361 = x20 * x272 x362 = x272 * x8 x363 = x3 * x89 x364 = x303 * x8 x365 = x281 * x364 x366 = x281 * x89 x367 = x289 * x78 x368 = x265 * x58 + x289 * x71 x369 = x21 * x272 x370 = x144 * x272 + 2.0 * x148 - x274 * x275 x371 = x22 * x272 x372 = x11 * x370 + 3.0 * x273 x373 = 3.0 * x282 + x372 * x71 # 180 item(s) result[0, 0, 0] = numpy.sum( x65 * (x46 * (x47 * (x47 * (x43 + x45) + x51 * x53) + x53 * x59) + x61 * x62) ) result[0, 0, 1] = numpy.sum( x70 * (x46 * (x47 * x66 * (x43 + x45) + x53 * x67) + x62 * x69) ) result[0, 0, 2] = numpy.sum( x70 * (x46 * (x47 * x71 * (x43 + x45) + x53 * x72) + x62 * x74) ) result[0, 0, 3] = numpy.sum(x70 * (x46 * x76 * (x43 + x45) + x62 * x77)) result[0, 0, 4] = numpy.sum(x81 * (x46 * x79 * (x43 + x45) + x62 * x80)) result[0, 0, 5] = numpy.sum(x70 * (x46 * x82 * (x43 + x45) + x62 * x83)) result[0, 0, 6] = numpy.sum(x65 * (x84 * x86 + x87 * x88)) result[0, 0, 7] = numpy.sum(x70 * (x11 * x86 * x9 + x88 * x90)) result[0, 0, 8] = numpy.sum(x70 * (x86 * x91 + x88 * x92)) result[0, 0, 9] = numpy.sum(x65 * (x86 * x93 + x88 * x94)) result[0, 1, 0] = numpy.sum(x65 * (x111 + x112 * x61)) result[0, 1, 1] = numpy.sum(x70 * (x112 * x69 + x121)) result[0, 1, 2] = numpy.sum(x70 * (x112 * x74 + x125)) result[0, 1, 3] = numpy.sum(x70 * (x112 * x77 + x129)) result[0, 1, 4] = numpy.sum(x81 * (x112 * x80 + x135)) result[0, 1, 5] = numpy.sum(x70 * (x112 * x83 + x137)) result[0, 1, 6] = numpy.sum(x65 * (x138 + x139 * x87)) result[0, 1, 7] = numpy.sum(x70 * (x139 * x90 + x140)) result[0, 1, 8] = numpy.sum(x70 * (x139 * x92 + x142)) result[0, 1, 9] = numpy.sum(x65 * (x139 * x94 + x143)) result[0, 2, 0] = numpy.sum(x65 * (x160 + x161 * x61)) result[0, 2, 1] = numpy.sum(x70 * (x161 * x69 + x164)) result[0, 2, 2] = numpy.sum(x70 * (x161 * x74 + x171)) result[0, 2, 3] = numpy.sum(x70 * (x161 * x77 + x172)) result[0, 2, 4] = numpy.sum(x81 * (x161 * x80 + x174)) result[0, 2, 5] = numpy.sum(x70 * (x161 * x83 + x178)) result[0, 2, 6] = numpy.sum(x65 * (x179 + x180 * x87)) result[0, 2, 7] = numpy.sum(x70 * (x180 * x90 + x181)) result[0, 2, 8] = numpy.sum(x70 * (x180 * x92 + x182)) result[0, 2, 9] = numpy.sum(x65 * (x180 * x94 + x183)) result[1, 0, 0] = numpy.sum(x186 * (x111 + x185 * x62)) result[1, 0, 1] = numpy.sum(x81 * (x121 + x189 * x62)) result[1, 0, 2] = numpy.sum(x81 * (x125 + x191 * x62)) result[1, 0, 3] = numpy.sum(x81 * (x129 + x193 * x62)) result[1, 0, 4] = numpy.sum(x63 * (x135 + x195 * x62)) result[1, 0, 5] = numpy.sum(x81 * (x137 + x197 * x62)) result[1, 0, 6] = numpy.sum(x186 * (x138 + x198 * x62)) result[1, 0, 7] = numpy.sum(x81 * (x140 + x199 * x62)) result[1, 0, 8] = numpy.sum(x81 * (x142 + x201 * x62)) result[1, 0, 9] = numpy.sum(x186 * (x143 + x20 * x202)) result[1, 1, 0] = numpy.sum(x186 * (x112 * x185 + x209)) result[1, 1, 1] = numpy.sum(x81 * (x112 * x189 + x216)) result[1, 1, 2] = numpy.sum(x81 * (x112 * x191 + x218)) result[1, 1, 3] = numpy.sum(x81 * (x112 * x193 + x222)) result[1, 1, 4] = numpy.sum(x63 * (x112 * x195 + x226)) result[1, 1, 5] = numpy.sum(x81 * (x112 * x197 + x228)) result[1, 1, 6] = numpy.sum(x186 * (x112 * x198 + x229)) result[1, 1, 7] = numpy.sum(x81 * (x112 * x199 + x230)) result[1, 1, 8] = numpy.sum(x81 * (x112 * x201 + x231)) result[1, 1, 9] = numpy.sum(x186 * (x202 * x21 + x232)) result[1, 2, 0] = numpy.sum(x186 * (x161 * x185 + x237)) result[1, 2, 1] = numpy.sum(x81 * (x161 * x189 + x240)) result[1, 2, 2] = numpy.sum(x81 * (x161 * x191 + x243)) result[1, 2, 3] = numpy.sum(x81 * (x161 * x193 + x246)) result[1, 2, 4] = numpy.sum(x63 * (x161 * x195 + x249)) result[1, 2, 5] = numpy.sum(x81 * (x161 * x197 + x252)) result[1, 2, 6] = numpy.sum(x186 * (x161 * x198 + x253)) result[1, 2, 7] = numpy.sum(x81 * (x161 * x199 + x255)) result[1, 2, 8] = numpy.sum(x81 * (x161 * x201 + x256)) result[1, 2, 9] = numpy.sum(x186 * (x202 * x22 + x257)) result[2, 0, 0] = numpy.sum(x186 * (x160 + x258 * x62)) result[2, 0, 1] = numpy.sum(x81 * (x164 + x259 * x62)) result[2, 0, 2] = numpy.sum(x81 * (x171 + x260 * x62)) result[2, 0, 3] = numpy.sum(x81 * (x172 + x262 * x62)) result[2, 0, 4] = numpy.sum(x63 * (x174 + x264 * x62)) result[2, 0, 5] = numpy.sum(x81 * (x178 + x267 * x62)) result[2, 0, 6] = numpy.sum(x186 * (x179 + x20 * x268)) result[2, 0, 7] = numpy.sum(x81 * (x181 + x20 * x269)) result[2, 0, 8] = numpy.sum(x81 * (x182 + x20 * x270)) result[2, 0, 9] = numpy.sum(x186 * (x183 + x271 * x62)) result[2, 1, 0] = numpy.sum(x186 * (x112 * x258 + x237)) result[2, 1, 1] = numpy.sum(x81 * (x112 * x259 + x240)) result[2, 1, 2] = numpy.sum(x81 * (x112 * x260 + x243)) result[2, 1, 3] = numpy.sum(x81 * (x112 * x262 + x246)) result[2, 1, 4] = numpy.sum(x63 * (x112 * x264 + x249)) result[2, 1, 5] = numpy.sum(x81 * (x112 * x267 + x252)) result[2, 1, 6] = numpy.sum(x186 * (x21 * x268 + x253)) result[2, 1, 7] = numpy.sum(x81 * (x21 * x269 + x255)) result[2, 1, 8] = numpy.sum(x81 * (x21 * x270 + x256)) result[2, 1, 9] = numpy.sum(x186 * (x112 * x271 + x257)) result[2, 2, 0] = numpy.sum(x186 * (x161 * x258 + x278)) result[2, 2, 1] = numpy.sum(x81 * (x161 * x259 + x280)) result[2, 2, 2] = numpy.sum(x81 * (x161 * x260 + x284)) result[2, 2, 3] = numpy.sum(x81 * (x161 * x262 + x286)) result[2, 2, 4] = numpy.sum(x63 * (x161 * x264 + x288)) result[2, 2, 5] = numpy.sum(x81 * (x161 * x267 + x292)) result[2, 2, 6] = numpy.sum(x186 * (x22 * x268 + x293)) result[2, 2, 7] = numpy.sum(x81 * (x22 * x269 + x294)) result[2, 2, 8] = numpy.sum(x81 * (x22 * x270 + x295)) result[2, 2, 9] = numpy.sum(x186 * (x161 * x271 + x296)) result[3, 0, 0] = numpy.sum(x65 * (x209 + x297 * x298)) result[3, 0, 1] = numpy.sum(x70 * (x20 * x300 + x216)) result[3, 0, 2] = numpy.sum(x70 * (x218 + x298 * x301)) result[3, 0, 3] = numpy.sum(x70 * (x219 * x302 + x222)) result[3, 0, 4] = numpy.sum(x81 * (x223 * x302 + x226)) result[3, 0, 5] = numpy.sum(x70 * (x228 + x298 * x304)) result[3, 0, 6] = numpy.sum(x65 * (x229 + x305 * x62)) result[3, 0, 7] = numpy.sum(x70 * (x230 + x306 * x62)) result[3, 0, 8] = numpy.sum(x70 * (x231 + x307 * x62)) result[3, 0, 9] = numpy.sum(x65 * (x232 + x298 * x94)) result[3, 1, 0] = numpy.sum(x297 * x65 * (x308 + x309)) result[3, 1, 1] = numpy.sum(x70 * (x21 * x300 + x299 * x312)) result[3, 1, 2] = numpy.sum(x301 * x70 * (x308 + x309)) result[3, 1, 3] = numpy.sum(x70 * (x187 * x313 + x219 * x314)) result[3, 1, 4] = numpy.sum(x81 * (x187 * x315 + x223 * x314)) result[3, 1, 5] = numpy.sum(x304 * x70 * (x308 + x309)) result[3, 1, 6] = numpy.sum(x65 * (x112 * x305 + x46 * (3.0 * x220 + x313 * x66))) result[3, 1, 7] = numpy.sum(x70 * (x112 * x306 + x46 * (3.0 * x224 + x315 * x66))) result[3, 1, 8] = numpy.sum(x70 * (x112 * x307 + x46 * x82 * (x310 + x311))) result[3, 1, 9] = numpy.sum(x65 * x94 * (x308 + x309)) result[3, 2, 0] = numpy.sum(x65 * (x297 * x318 + x317)) result[3, 2, 1] = numpy.sum(x70 * (x22 * x300 + x321)) result[3, 2, 2] = numpy.sum(x70 * (x301 * x318 + x323)) result[3, 2, 3] = numpy.sum(x70 * (x219 * x326 + x325)) result[3, 2, 4] = numpy.sum(x81 * (x223 * x326 + x329)) result[3, 2, 5] = numpy.sum(x70 * (x304 * x318 + x331)) result[3, 2, 6] = numpy.sum(x65 * (x161 * x305 + x332)) result[3, 2, 7] = numpy.sum(x70 * (x161 * x306 + x333)) result[3, 2, 8] = numpy.sum(x70 * (x161 * x307 + x335)) result[3, 2, 9] = numpy.sum(x65 * (x318 * x94 + x336)) result[4, 0, 0] = numpy.sum(x186 * (x20 * x337 + x237)) result[4, 0, 1] = numpy.sum(x81 * (x238 * x338 + x240)) result[4, 0, 2] = numpy.sum(x81 * (x241 * x338 + x243)) result[4, 0, 3] = numpy.sum(x81 * (x244 * x302 + x246)) result[4, 0, 4] = numpy.sum(x63 * (x247 * x302 + x249)) result[4, 0, 5] = numpy.sum(x81 * (x250 * x302 + x252)) result[4, 0, 6] = numpy.sum(x186 * (x253 + x339 * x62)) result[4, 0, 7] = numpy.sum(x81 * (x255 + x340 * x62)) result[4, 0, 8] = numpy.sum(x81 * (x256 + x341 * x62)) result[4, 0, 9] = numpy.sum(x186 * (x257 + x342 * x62)) result[4, 1, 0] = numpy.sum(x186 * (x21 * x337 + x317)) result[4, 1, 1] = numpy.sum(x81 * (x238 * x343 + x321)) result[4, 1, 2] = numpy.sum(x81 * (x241 * x343 + x323)) result[4, 1, 3] = numpy.sum(x81 * (x244 * x314 + x325)) result[4, 1, 4] = numpy.sum(x63 * (x247 * x314 + x329)) result[4, 1, 5] = numpy.sum(x81 * (x250 * x314 + x331)) result[4, 1, 6] = numpy.sum(x186 * (x112 * x339 + x332)) result[4, 1, 7] = numpy.sum(x81 * (x112 * x340 + x333)) result[4, 1, 8] = numpy.sum(x81 * (x112 * x341 + x335)) result[4, 1, 9] = numpy.sum(x186 * (x112 * x342 + x336)) result[4, 2, 0] = numpy.sum(x186 * (x22 * x337 + x345)) result[4, 2, 1] = numpy.sum(x81 * (x238 * x348 + x347)) result[4, 2, 2] = numpy.sum(x81 * (x241 * x348 + x350)) result[4, 2, 3] = numpy.sum(x81 * (x244 * x326 + x352)) result[4, 2, 4] = numpy.sum(x63 * (x247 * x326 + x354)) result[4, 2, 5] = numpy.sum(x81 * (x250 * x326 + x356)) result[4, 2, 6] = numpy.sum(x186 * (x161 * x339 + x357)) result[4, 2, 7] = numpy.sum(x81 * (x161 * x340 + x358)) result[4, 2, 8] = numpy.sum(x81 * (x161 * x341 + x359)) result[4, 2, 9] = numpy.sum(x186 * (x161 * x342 + x360)) result[5, 0, 0] = numpy.sum(x65 * (x278 + x297 * x361)) result[5, 0, 1] = numpy.sum(x70 * (x280 + x338 * x362)) result[5, 0, 2] = numpy.sum(x70 * (x281 * x338 + x284)) result[5, 0, 3] = numpy.sum(x70 * (x286 + x361 * x363)) result[5, 0, 4] = numpy.sum(x81 * (x20 * x365 + x288)) result[5, 0, 5] = numpy.sum(x70 * (x289 * x302 + x292)) result[5, 0, 6] = numpy.sum(x65 * (x293 + x361 * x87)) result[5, 0, 7] = numpy.sum(x70 * (x20 * x366 + x294)) result[5, 0, 8] = numpy.sum(x70 * (x20 * x367 + x295)) result[5, 0, 9] = numpy.sum(x65 * (x296 + x368 * x62)) result[5, 1, 0] = numpy.sum(x65 * (x297 * x369 + x345)) result[5, 1, 1] = numpy.sum(x70 * (x343 * x362 + x347)) result[5, 1, 2] = numpy.sum(x70 * (x281 * x343 + x350)) result[5, 1, 3] = numpy.sum(x70 * (x352 + x363 * x369)) result[5, 1, 4] = numpy.sum(x81 * (x21 * x365 + x354)) result[5, 1, 5] = numpy.sum(x70 * (x289 * x314 + x356)) result[5, 1, 6] = numpy.sum(x65 * (x357 + x369 * x87)) result[5, 1, 7] = numpy.sum(x70 * (x21 * x366 + x358)) result[5, 1, 8] = numpy.sum(x70 * (x21 * x367 + x359)) result[5, 1, 9] = numpy.sum(x65 * (x112 * x368 + x360)) result[5, 2, 0] = numpy.sum(x297 * x65 * (x370 + x371)) result[5, 2, 1] = numpy.sum(x70 * (x299 * x370 * x8 + x348 * x362)) result[5, 2, 2] = numpy.sum(x70 * (x281 * x348 + x299 * x372)) result[5, 2, 3] = numpy.sum(x363 * x70 * (x370 + x371)) result[5, 2, 4] = numpy.sum(x81 * (x22 * x365 + x364 * x372)) result[5, 2, 5] = numpy.sum(x70 * (x187 * x373 + x289 * x326)) result[5, 2, 6] = numpy.sum(x65 * x87 * (x370 + x371)) result[5, 2, 7] = numpy.sum(x70 * (x22 * x366 + x372 * x89)) result[5, 2, 8] = numpy.sum(x70 * (x22 * x367 + x373 * x78)) result[5, 2, 9] = numpy.sum(x65 * (x161 * x368 + x46 * (3.0 * x290 + x373 * x71))) return result
[docs] def int3c2e3d_sph_214(ax, da, A, bx, db, B, cx, dc, C): """Cartesian (dp|g) three-center two-electron repulsion integral. These integrals MUST BE converted to spherical harmonics! Integral generation utilized Ahlrichs (truncated) vertical recursion relation. There, some terms are omitted, that would cancel anyway, after Cartesian->Spherical transformation. Generated code; DO NOT modify by hand!""" result = numpy.zeros((6, 3, 15), dtype=float) x0 = ax + bx x1 = x0 ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - C[0] x4 = -x2 - A[0] x5 = 0.5 / (ax + bx) x6 = x3**2 x7 = -x1 * (ax * A[1] + bx * B[1]) x8 = -x7 - C[1] x9 = x8**2 x10 = -x1 * (ax * A[2] + bx * B[2]) x11 = -x10 - C[2] x12 = x11**2 x13 = cx + x0 x14 = x13 ** (-1.0) x15 = cx * x14 x16 = x0 * x15 * (x12 + x6 + x9) x17 = boys(5, x16) x18 = x13 ** (-1.5) x19 = 17.49341832762486 x20 = A[0] - B[0] x21 = A[1] - B[1] x22 = A[2] - B[2] x23 = numpy.exp(-ax * bx * x1 * (x20**2 + x21**2 + x22**2)) x24 = x19 * x23 x25 = x1 * x24 x26 = 2.0 * x18 * x25 x27 = x17 * x26 x28 = cx ** (-1.0) x29 = x13 ** (-0.5) x30 = boys(4, x16) x31 = x5 * (2.0 * x1 * x19 * x23 * x28 * x29 * x30 - x27) x32 = -2.0 * x1 * x19 * x23 * x28 * x29 * x30 * x4 + x27 * x3 x33 = -x32 x34 = boys(6, x16) x35 = x26 * x34 x36 = 2.0 * x1 * x17 * x19 * x23 * x28 * x29 * x4 - x3 * x35 x37 = x15 * x36 x38 = -x3 * x37 + x31 + x33 * x4 x39 = 2.0 * x5 x40 = x5 * (2.0 * x1 * x17 * x19 * x23 * x28 * x29 - x35) x41 = x26 * boys(7, x16) x42 = x15 * x3 x43 = ( x38 * x4 - x39 * (x32 + x37) - x42 * ( x36 * x4 + x40 - x42 * (2.0 * x1 * x19 * x23 * x28 * x29 * x34 * x4 - x3 * x41) ) ) x44 = x3 * x43 x45 = x38 * x5 x46 = 3.0 * x45 x47 = x0 * x14 x48 = x3 * x47 x49 = x3 * x38 x50 = x33 * x5 x51 = 2.0 * x50 x52 = x49 + x51 x53 = x47 * x5 x54 = 3.0 * x53 x55 = x3 * x33 x56 = x28 * x30 * x39 x57 = x25 * x29 * x56 x58 = x55 + x57 x59 = x39 * x47 x60 = x48 * x52 + x58 * x59 x61 = x24 * x56 x62 = x18 * x61 x63 = x3 * x62 + x48 * x58 x64 = x48 * x60 + x59 * x63 x65 = x0 * x13 ** (-2.5) * x61 x66 = x48 * x64 + x59 * (x48 * x63 + x6 * x65) x67 = x20 * x47 x68 = da * db * dc x69 = 0.009523809523809524 * x68 x70 = 5.916079783099616 * x69 x71 = x47 * x8 x72 = x71 * (x49 + x51) x73 = x62 * x8 x74 = x55 * x71 + x73 x75 = x48 * x72 + x59 * x74 x76 = x3 * x65 x77 = x48 * x75 + x59 * (x48 * x74 + x76 * x8) x78 = 0.06666666666666667 * x68 x79 = 2.23606797749979 * x78 x80 = x11 * x47 x81 = x80 * (x49 + x51) x82 = x11 * x62 x83 = x55 * x80 + x82 x84 = x48 * x81 + x59 * x83 x85 = x48 * x84 + x59 * (x11 * x76 + x48 * x83) x86 = x0**2 / x13**2 x87 = x86 * x9 x88 = x87 * (x49 + x51) x89 = x65 * x9 x90 = x48 * x88 + x59 * (x55 * x87 + x89) x91 = 1.732050807568877 x92 = 0.1111111111111111 * x68 * x91 x93 = x8 * x86 x94 = x11 * x93 x95 = x94 * (x49 + x51) x96 = x11 * x65 * x8 x97 = x48 * x95 + x59 * (x55 * x94 + x96) x98 = 0.3333333333333333 * x68 x99 = x12 * x86 x100 = x99 * (x49 + x51) x101 = x12 * x65 x102 = x100 * x48 + x59 * (x101 + x55 * x99) x103 = x8**3 x104 = x0**3 / x13**3 x105 = x103 * x104 x106 = x105 * (x49 + x51) x107 = x104 * x9 x108 = x107 * x11 x109 = x108 * (x49 + x51) x110 = x104 * x8 x111 = x110 * x12 x112 = x111 * (x49 + x51) x113 = x11**3 x114 = x104 * x113 x115 = x114 * (x49 + x51) x116 = x8**4 x117 = x0**4 / x13**4 x118 = x117 * x43 x119 = x116 * x117 x120 = x20 * x38 x121 = x103 * x117 x122 = x11 * x121 x123 = x12 * x9 x124 = x117 * x120 x125 = x113 * x8 x126 = x11**4 x127 = x117 * x126 x128 = -x7 - A[1] x129 = 2.0 * x1 * x128 * x17 * x19 * x23 * x28 * x29 - x35 * x8 x130 = x129 * x15 x131 = -2.0 * x1 * x128 * x19 * x23 * x28 * x29 * x30 + x27 * x8 x132 = -x5 * (x130 + x131) x133 = -x131 x134 = -x130 * x3 + x133 * x4 x135 = 2.0 * x1 * x128 * x19 * x23 * x28 * x29 * x34 - x41 * x8 x136 = x132 + x134 * x4 - x42 * (x129 * x4 - x135 * x42) x137 = x136 * x3 x138 = x134 * x5 x139 = 2.0 * x138 x140 = x133 * x5 x141 = x134 * x3 x142 = x140 + x141 x143 = x48 * (x140 + x142) x144 = x6 * x86 x145 = x140 * x144 + x143 * x48 x146 = x47 * ( x145 * x59 + x48 * (x143 * x59 + x48 * (x142 * x59 + x48 * (x137 + x139))) ) x147 = x21 * x47 x148 = x136 * x8 x149 = x148 + x45 x150 = x134 * x8 x151 = x150 + x50 x152 = x151 * x59 x153 = x133 * x8 x154 = x153 + x57 x155 = x154 * x47 x156 = x151 * x48 + x155 * x5 x157 = x3 * x86 x158 = x157 * x5 x159 = x154 * x158 + x156 * x48 x160 = x47 * (x159 * x59 + x48 * (x156 * x59 + x48 * (x149 * x48 + x152))) x161 = x139 * x80 x162 = x140 * x80 x163 = x141 * x80 + x162 x164 = x11 * x140 x165 = x157 * x164 + x163 * x48 x166 = x47 * (x165 * x59 + x48 * (x163 * x59 + x48 * (x137 * x80 + x161))) x167 = x71 * (x149 + x45) x168 = x71 * (x151 + x50) x169 = x168 * x59 x170 = x155 * x8 + x73 x171 = x168 * x48 + x170 * x53 x172 = x47 * (x171 * x59 + x48 * (x167 * x48 + x169)) x173 = x45 * x80 x174 = x148 * x80 + x173 x175 = x50 * x80 x176 = x150 * x80 + x175 x177 = x176 * x59 x178 = x153 * x80 + x82 x179 = x176 * x48 + x178 * x53 x180 = x47 * (x179 * x59 + x48 * (x174 * x48 + x177)) x181 = x139 * x99 x182 = x140 * x99 x183 = x141 * x99 + x182 x184 = x47 * (x183 * x59 + x48 * (x137 * x99 + x181)) x185 = x167 * x71 + x45 * x87 x186 = x168 * x71 + x50 * x87 x187 = x186 * x59 x188 = x47 * (x185 * x48 + x187) x189 = x174 * x71 + x45 * x94 x190 = x176 * x71 + x50 * x94 x191 = x190 * x59 x192 = x47 * (x189 * x48 + x191) x193 = x45 * x99 x194 = x148 * x99 + x193 x195 = x50 * x99 x196 = x150 * x99 + x195 x197 = x196 * x59 x198 = x47 * (x194 * x48 + x197) x199 = x114 * x139 x200 = x47 * (x114 * x137 + x199) x201 = x47 * (x105 * x45 + x185 * x71) x202 = x21 * x38 x203 = x47 * (x108 * x45 + x189 * x71) x204 = x47 * (x111 * x45 + x194 * x71) x205 = x117 * x202 x206 = x114 * x45 x207 = x47 * (x114 * x148 + x206) x208 = x127 * x136 x209 = -x10 - A[2] x210 = 2.0 * x1 * x17 * x19 * x209 * x23 * x28 * x29 - x11 * x35 x211 = x15 * x210 x212 = -2.0 * x1 * x19 * x209 * x23 * x28 * x29 * x30 + x11 * x27 x213 = -x5 * (x211 + x212) x214 = -x212 x215 = -x211 * x3 + x214 * x4 x216 = 2.0 * x1 * x19 * x209 * x23 * x28 * x29 * x34 - x11 * x41 x217 = x213 + x215 * x4 - x42 * (x210 * x4 - x216 * x42) x218 = x217 * x3 x219 = x215 * x5 x220 = 2.0 * x219 x221 = x214 * x5 x222 = x215 * x3 x223 = x221 + x222 x224 = x48 * (x221 + x223) x225 = x144 * x221 + x224 * x48 x226 = x47 * ( x225 * x59 + x48 * (x224 * x59 + x48 * (x223 * x59 + x48 * (x218 + x220))) ) x227 = x22 * x47 x228 = x221 * x71 x229 = x222 * x71 + x228 x230 = x3 * x93 x231 = x221 * x230 + x229 * x48 x232 = x47 * (x231 * x59 + x48 * (x229 * x59 + x48 * x71 * (x218 + x220))) x233 = x11 * x217 + x45 x234 = x11 * x215 + x50 x235 = x234 * x59 x236 = x11 * x214 + x57 x237 = x236 * x53 x238 = x234 * x48 + x237 x239 = x158 * x236 + x238 * x48 x240 = x47 * (x239 * x59 + x48 * (x238 * x59 + x48 * (x233 * x48 + x235))) x241 = x221 * x87 x242 = x222 * x87 + x241 x243 = x47 * (x242 * x59 + x48 * x87 * (x218 + x220)) x244 = x234 * x39 x245 = x5 * x93 x246 = x236 * x245 x247 = x230 * x234 + x246 x248 = x47 * (x247 * x59 + x48 * (x230 * x233 + x244 * x93)) x249 = x173 + x233 * x80 x250 = x175 + x234 * x80 x251 = x250 * x59 x252 = x236 * x80 + x82 x253 = x252 * x53 x254 = x250 * x48 + x253 x255 = x47 * (x254 * x59 + x48 * (x249 * x48 + x251)) x256 = x105 * x47 * (x218 + x220) x257 = x107 * x3 x258 = x47 * (x107 * x244 + x233 * x257) x259 = x47 * (x230 * x249 + x250 * x39 * x93) x260 = x193 + x249 * x80 x261 = x195 + x250 * x80 x262 = x261 * x59 x263 = x47 * (x260 * x48 + x262) x264 = x119 * x217 x265 = x22 * x38 x266 = x121 * x233 x267 = x107 * x249 x268 = x117 * x265 x269 = x260 * x93 x270 = x47 * (x206 + x260 * x80) x271 = x3**3 x272 = x104 * x271 x273 = x140 * x272 + x145 * x48 x274 = 10.2469507659596 * x69 x275 = x104 * x6 x276 = x275 * x5 x277 = x154 * x276 + x159 * x48 x278 = 3.872983346207417 * x78 x279 = x164 * x275 + x165 * x48 x280 = x158 * x170 + x171 * x48 x281 = x158 * x178 + x179 * x48 x282 = x91 * x98 x283 = x104 * x12 * x3 x284 = x140 * x283 + x183 * x48 x285 = x170 * x71 + x89 x286 = x186 * x48 + x285 * x53 x287 = x178 * x71 + x96 x288 = x190 * x48 + x287 * x53 x289 = x101 + x153 * x99 x290 = x196 * x48 + x289 * x53 x291 = x114 * x140 x292 = x114 * x141 + x291 x293 = x105 * x50 + x186 * x71 x294 = x108 * x50 + x190 * x71 x295 = x111 * x50 + x196 * x71 x296 = x114 * x50 x297 = x114 * x150 + x296 x298 = x127 * x134 x299 = x128 * x133 - x130 * x8 + x31 x300 = x299 * x5 x301 = x15 * x8 x302 = x128 * x129 - x135 * x301 + x40 x303 = x299 * x4 - x302 * x42 x304 = x3 * x303 x305 = x47 * (x272 * x300 + x48 * (x144 * x300 + x48**2 * (2.0 * x300 + x304))) x306 = x299 * x8 x307 = 2.0 * x140 x308 = x306 + x307 x309 = x308 * x53 x310 = x303 * x8 x311 = x139 + x310 x312 = x47 * (x276 * x308 + x48 * (x158 * x308 + x48 * (x309 + x311 * x48))) x313 = x300 * x80 x314 = x11 * x300 x315 = x47 * (x275 * x314 + x48 * (x157 * x314 + x48 * (x304 * x80 + x313))) x316 = x155 * x39 + x308 * x71 x317 = x316 * x53 x318 = x152 + x311 * x71 x319 = x47 * (x158 * x316 + x48 * (x317 + x318 * x48)) x320 = x80 * (x306 + x307) x321 = x320 * x53 x322 = x161 + x310 * x80 x323 = x47 * (x158 * x320 + x48 * (x321 + x322 * x48)) x324 = x300 * x99 x325 = x47 * (x283 * x300 + x48 * (x304 * x99 + x324)) x326 = x170 * x59 + x316 * x71 x327 = x326 * x53 x328 = x169 + x318 * x71 x329 = x47 * (x327 + x328 * x48) x330 = x178 * x59 + x320 * x71 x331 = x330 * x53 x332 = x177 + x322 * x71 x333 = x47 * (x331 + x332 * x48) x334 = x99 * (x306 + x307) x335 = x334 * x53 x336 = x181 + x310 * x99 x337 = x47 * (x335 + x336 * x48) x338 = x114 * x300 x339 = x47 * (x114 * x304 + x338) x340 = x47 * (x187 + x328 * x71) x341 = x47 * (x191 + x332 * x71) x342 = x47 * (x197 + x336 * x71) x343 = x47 * (x114 * x310 + x199) x344 = x127 * x303 x345 = x128 * x214 - x211 * x8 x346 = x345 * x5 x347 = x128 * x210 - x216 * x301 x348 = x345 * x4 - x347 * x42 x349 = x47 * (x272 * x346 + x48 * (x144 * x346 + x48**2 * (x3 * x348 + 2.0 * x346))) x350 = x221 + x345 * x8 x351 = x219 + x348 * x8 x352 = x47 * (x276 * x350 + x48 * (x158 * x350 + x48 * (x350 * x53 + x351 * x48))) x353 = x11 * x345 + x140 x354 = x11 * x348 + x138 x355 = x47 * (x276 * x353 + x48 * (x158 * x353 + x48 * (x353 * x53 + x354 * x48))) x356 = x228 + x350 * x71 x357 = x71 * (x219 + x351) x358 = x47 * (x158 * x356 + x48 * (x356 * x53 + x357 * x48)) x359 = x237 + x353 * x71 x360 = x234 * x53 + x354 * x71 x361 = x47 * (x158 * x359 + x48 * (x359 * x53 + x360 * x48)) x362 = x162 + x353 * x80 x363 = x80 * (x138 + x354) x364 = x47 * (x158 * x362 + x48 * (x362 * x53 + x363 * x48)) x365 = x241 + x356 * x71 x366 = x219 * x87 + x357 * x71 x367 = x47 * (x365 * x53 + x366 * x48) x368 = x246 + x359 * x71 x369 = x234 * x245 + x360 * x71 x370 = x47 * (x368 * x53 + x369 * x48) x371 = x253 + x362 * x71 x372 = x250 * x53 + x363 * x71 x373 = x47 * (x371 * x53 + x372 * x48) x374 = x182 + x362 * x80 x375 = x138 * x99 + x363 * x80 x376 = x47 * (x374 * x53 + x375 * x48) x377 = x47 * (x105 * x219 + x366 * x71) x378 = x107 * x5 x379 = x47 * (x234 * x378 + x369 * x71) x380 = x47 * (x245 * x250 + x372 * x71) x381 = x47 * (x261 * x53 + x375 * x71) x382 = x47 * (x114 * x138 + x375 * x80) x383 = x221 * x272 + x225 * x48 x384 = x275 * x8 x385 = x221 * x384 + x231 * x48 x386 = x236 * x276 + x239 * x48 x387 = x221 * x257 + x242 * x48 x388 = x110 * x3 x389 = x388 * x5 x390 = x236 * x389 + x247 * x48 x391 = x158 * x252 + x254 * x48 x392 = x105 * x221 x393 = x105 * x222 + x392 x394 = x236 * x378 x395 = x234 * x257 + x394 x396 = x245 * x252 x397 = x230 * x250 + x396 x398 = x101 + x252 * x80 x399 = x398 * x53 x400 = x261 * x48 + x399 x401 = x119 * x215 x402 = x121 * x234 x403 = x107 * x250 x404 = x261 * x93 x405 = x261 * x80 + x296 x406 = -x11 * x211 + x209 * x214 + x31 x407 = x406 * x5 x408 = x11 * x15 x409 = x209 * x210 - x216 * x408 + x40 x410 = x4 * x406 - x409 * x42 x411 = x3 * x410 x412 = x47 * (x272 * x407 + x48 * (x144 * x407 + x48**2 * (2.0 * x407 + x411))) x413 = x407 * x71 x414 = x47 * (x384 * x407 + x48 * (x230 * x407 + x48 * (x411 * x71 + x413))) x415 = x11 * x406 + 2.0 * x221 x416 = x415 * x53 x417 = x11 * x410 + x220 x418 = x47 * (x276 * x415 + x48 * (x158 * x415 + x48 * (x416 + x417 * x48))) x419 = x407 * x87 x420 = x47 * (x257 * x407 + x48 * (x411 * x87 + x419)) x421 = x245 * x415 x422 = x47 * (x389 * x415 + x48 * (x230 * x417 + x421)) x423 = x236 * x59 + x415 * x80 x424 = x423 * x53 x425 = x235 + x417 * x80 x426 = x47 * (x158 * x423 + x48 * (x424 + x425 * x48)) x427 = x105 * x407 x428 = x47 * (x105 * x411 + x427) x429 = x378 * x415 x430 = x47 * (x257 * x417 + x429) x431 = x245 * x423 x432 = x47 * (x230 * x425 + x431) x433 = x252 * x59 + x423 * x80 x434 = x433 * x53 x435 = x251 + x425 * x80 x436 = x47 * (x434 + x435 * x48) x437 = x119 * x410 x438 = x121 * x417 x439 = x107 * x425 x440 = x435 * x93 x441 = x47 * (x262 + x435 * x80) x442 = x117 * x3**4 x443 = x20 * x299 x444 = x117 * x271 x445 = x308 * x444 x446 = x11 * x444 x447 = x20 * x275 x448 = x12 * x6 x449 = x117 * x443 x450 = x157 * x20 x451 = x113 * x3 x452 = x285 * x59 + x326 * x71 x453 = x287 * x59 + x330 * x71 x454 = x289 * x59 + x334 * x71 x455 = x114 * (x306 + x307) x456 = x128 * x299 + 2.0 * x132 - x301 * x302 x457 = x21 * x299 x458 = x456 * x8 x459 = 3.0 * x300 x460 = x458 + x459 x461 = 3.0 * x309 + x460 * x71 x462 = x21 * x275 x463 = x80 * (x458 + x459) x464 = x117 * x456 x465 = x117 * x457 x466 = 3.0 * x317 + x461 * x71 x467 = x157 * x21 x468 = 3.0 * x321 + x463 * x71 x469 = x99 * (x458 + x459) x470 = x128 * x345 + x213 - x301 * x347 x471 = x442 * x470 x472 = x22 * x299 x473 = 2.0 * x346 x474 = x470 * x8 + x473 x475 = x444 * x474 x476 = x11 * x470 + x300 x477 = x444 * x476 x478 = x350 * x59 + x474 * x71 x479 = x275 * x478 x480 = x22 * x275 x481 = x353 * x59 x482 = x476 * x71 + x481 x483 = x275 * x482 x484 = x313 + x476 * x80 x485 = x275 * x484 x486 = x117 * x472 x487 = x356 * x59 + x478 * x71 x488 = x157 * x487 x489 = x157 * x22 x490 = x359 * x59 + x482 * x71 x491 = x157 * x490 x492 = x362 * x59 x493 = x484 * x71 + x492 x494 = x157 * x493 x495 = x324 + x484 * x80 x496 = x157 * x495 x497 = x47 * (x365 * x59 + x487 * x71) x498 = x47 * (x368 * x59 + x490 * x71) x499 = x47 * (x371 * x59 + x493 * x71) x500 = x374 * x59 x501 = x47 * (x495 * x71 + x500) x502 = x47 * (x338 + x495 * x80) x503 = x345 * x442 x504 = x20 * x444 x505 = x365 * x71 + x392 x506 = x368 * x71 + x394 x507 = x371 * x71 + x396 x508 = x374 * x71 + x399 x509 = x291 + x374 * x80 x510 = x21 * x444 x511 = x128 * x406 - x301 * x409 x512 = x442 * x511 x513 = x407 + x511 * x8 x514 = x444 * x513 x515 = x22 * x444 x516 = x11 * x511 + x473 x517 = x444 * x516 x518 = x413 + x513 * x71 x519 = x275 * x518 x520 = x416 + x516 * x71 x521 = x275 * x520 x522 = x481 + x516 * x80 x523 = x275 * x522 x524 = x419 + x518 * x71 x525 = x157 * x524 x526 = x421 + x520 * x71 x527 = x157 * x526 x528 = x424 + x522 * x71 x529 = x157 * x528 x530 = x492 + x522 * x80 x531 = x157 * x530 x532 = x47 * (x427 + x524 * x71) x533 = x47 * (x429 + x526 * x71) x534 = x47 * (x431 + x528 * x71) x535 = x47 * (x434 + x530 * x71) x536 = x47 * (x500 + x530 * x80) x537 = x20 * x406 x538 = x406 * x8 x539 = x117 * x6 x540 = x539 * x9 x541 = x539 * x8 x542 = x20 * x415 x543 = x121 * x3 x544 = x117 * x3 * x9 x545 = x388 * x423 x546 = x121 * x415 x547 = x107 * x423 x548 = x433 * x93 x549 = x398 * x59 + x433 * x80 x550 = x21 * x406 x551 = x21 * x415 x552 = x209 * x406 + 2.0 * x213 - x408 * x409 x553 = x22 * x406 x554 = x11 * x552 + 3.0 * x407 x555 = x22 * x415 x556 = 3.0 * x416 + x554 * x80 x557 = 3.0 * x424 + x556 * x80 # 270 item(s) result[0, 0, 0] = numpy.sum( x70 * ( x47 * (x48 * (x48 * (x48 * (x44 + x46) + x52 * x54) + x54 * x60) + x54 * x64) + x66 * x67 ) ) result[0, 0, 1] = numpy.sum( x79 * (x47 * (x48 * (x48 * x71 * (x44 + x46) + x54 * x72) + x54 * x75) + x67 * x77) ) result[0, 0, 2] = numpy.sum( x79 * (x47 * (x48 * (x48 * x80 * (x44 + x46) + x54 * x81) + x54 * x84) + x67 * x85) ) result[0, 0, 3] = numpy.sum( x92 * (x47 * (x48 * x87 * (x44 + x46) + x54 * x88) + x67 * x90) ) result[0, 0, 4] = numpy.sum( x98 * (x47 * (x48 * x94 * (x44 + x46) + x54 * x95) + x67 * x97) ) result[0, 0, 5] = numpy.sum( x92 * (x102 * x67 + x47 * (x100 * x54 + x48 * x99 * (x44 + x46))) ) result[0, 0, 6] = numpy.sum(x79 * (x105 * x47 * (x44 + x46) + x106 * x67)) result[0, 0, 7] = numpy.sum(x98 * (x108 * x47 * (x44 + x46) + x109 * x67)) result[0, 0, 8] = numpy.sum(x98 * (x111 * x47 * (x44 + x46) + x112 * x67)) result[0, 0, 9] = numpy.sum(x79 * (x114 * x47 * (x44 + x46) + x115 * x67)) result[0, 0, 10] = numpy.sum(x70 * (x116 * x118 + x119 * x120)) result[0, 0, 11] = numpy.sum(x79 * (x103 * x11 * x118 + x120 * x122)) result[0, 0, 12] = numpy.sum(x123 * x92 * (x118 + x124)) result[0, 0, 13] = numpy.sum(x125 * x79 * (x118 + x124)) result[0, 0, 14] = numpy.sum(x70 * (x118 * x126 + x120 * x127)) result[0, 1, 0] = numpy.sum(x70 * (x146 + x147 * x66)) result[0, 1, 1] = numpy.sum(x79 * (x147 * x77 + x160)) result[0, 1, 2] = numpy.sum(x79 * (x147 * x85 + x166)) result[0, 1, 3] = numpy.sum(x92 * (x147 * x90 + x172)) result[0, 1, 4] = numpy.sum(x98 * (x147 * x97 + x180)) result[0, 1, 5] = numpy.sum(x92 * (x102 * x147 + x184)) result[0, 1, 6] = numpy.sum(x79 * (x106 * x147 + x188)) result[0, 1, 7] = numpy.sum(x98 * (x109 * x147 + x192)) result[0, 1, 8] = numpy.sum(x98 * (x112 * x147 + x198)) result[0, 1, 9] = numpy.sum(x79 * (x115 * x147 + x200)) result[0, 1, 10] = numpy.sum(x70 * (x119 * x202 + x201)) result[0, 1, 11] = numpy.sum(x79 * (x122 * x202 + x203)) result[0, 1, 12] = numpy.sum(x92 * (x123 * x205 + x204)) result[0, 1, 13] = numpy.sum(x79 * (x125 * x205 + x207)) result[0, 1, 14] = numpy.sum(x70 * (x127 * x202 + x208)) result[0, 2, 0] = numpy.sum(x70 * (x226 + x227 * x66)) result[0, 2, 1] = numpy.sum(x79 * (x227 * x77 + x232)) result[0, 2, 2] = numpy.sum(x79 * (x227 * x85 + x240)) result[0, 2, 3] = numpy.sum(x92 * (x227 * x90 + x243)) result[0, 2, 4] = numpy.sum(x98 * (x227 * x97 + x248)) result[0, 2, 5] = numpy.sum(x92 * (x102 * x227 + x255)) result[0, 2, 6] = numpy.sum(x79 * (x106 * x227 + x256)) result[0, 2, 7] = numpy.sum(x98 * (x109 * x227 + x258)) result[0, 2, 8] = numpy.sum(x98 * (x112 * x227 + x259)) result[0, 2, 9] = numpy.sum(x79 * (x115 * x227 + x263)) result[0, 2, 10] = numpy.sum(x70 * (x119 * x265 + x264)) result[0, 2, 11] = numpy.sum(x79 * (x122 * x265 + x266)) result[0, 2, 12] = numpy.sum(x92 * (x123 * x268 + x267)) result[0, 2, 13] = numpy.sum(x79 * (x125 * x268 + x269)) result[0, 2, 14] = numpy.sum(x70 * (x127 * x265 + x270)) result[1, 0, 0] = numpy.sum(x274 * (x146 + x273 * x67)) result[1, 0, 1] = numpy.sum(x278 * (x160 + x277 * x67)) result[1, 0, 2] = numpy.sum(x278 * (x166 + x279 * x67)) result[1, 0, 3] = numpy.sum(x98 * (x172 + x280 * x67)) result[1, 0, 4] = numpy.sum(x282 * (x180 + x281 * x67)) result[1, 0, 5] = numpy.sum(x98 * (x184 + x284 * x67)) result[1, 0, 6] = numpy.sum(x278 * (x188 + x286 * x67)) result[1, 0, 7] = numpy.sum(x282 * (x192 + x288 * x67)) result[1, 0, 8] = numpy.sum(x282 * (x198 + x290 * x67)) result[1, 0, 9] = numpy.sum(x278 * (x200 + x292 * x67)) result[1, 0, 10] = numpy.sum(x274 * (x201 + x293 * x67)) result[1, 0, 11] = numpy.sum(x278 * (x203 + x294 * x67)) result[1, 0, 12] = numpy.sum(x98 * (x204 + x295 * x67)) result[1, 0, 13] = numpy.sum(x278 * (x207 + x297 * x67)) result[1, 0, 14] = numpy.sum(x274 * (x20 * x298 + x208)) result[1, 1, 0] = numpy.sum(x274 * (x147 * x273 + x305)) result[1, 1, 1] = numpy.sum(x278 * (x147 * x277 + x312)) result[1, 1, 2] = numpy.sum(x278 * (x147 * x279 + x315)) result[1, 1, 3] = numpy.sum(x98 * (x147 * x280 + x319)) result[1, 1, 4] = numpy.sum(x282 * (x147 * x281 + x323)) result[1, 1, 5] = numpy.sum(x98 * (x147 * x284 + x325)) result[1, 1, 6] = numpy.sum(x278 * (x147 * x286 + x329)) result[1, 1, 7] = numpy.sum(x282 * (x147 * x288 + x333)) result[1, 1, 8] = numpy.sum(x282 * (x147 * x290 + x337)) result[1, 1, 9] = numpy.sum(x278 * (x147 * x292 + x339)) result[1, 1, 10] = numpy.sum(x274 * (x147 * x293 + x340)) result[1, 1, 11] = numpy.sum(x278 * (x147 * x294 + x341)) result[1, 1, 12] = numpy.sum(x98 * (x147 * x295 + x342)) result[1, 1, 13] = numpy.sum(x278 * (x147 * x297 + x343)) result[1, 1, 14] = numpy.sum(x274 * (x21 * x298 + x344)) result[1, 2, 0] = numpy.sum(x274 * (x227 * x273 + x349)) result[1, 2, 1] = numpy.sum(x278 * (x227 * x277 + x352)) result[1, 2, 2] = numpy.sum(x278 * (x227 * x279 + x355)) result[1, 2, 3] = numpy.sum(x98 * (x227 * x280 + x358)) result[1, 2, 4] = numpy.sum(x282 * (x227 * x281 + x361)) result[1, 2, 5] = numpy.sum(x98 * (x227 * x284 + x364)) result[1, 2, 6] = numpy.sum(x278 * (x227 * x286 + x367)) result[1, 2, 7] = numpy.sum(x282 * (x227 * x288 + x370)) result[1, 2, 8] = numpy.sum(x282 * (x227 * x290 + x373)) result[1, 2, 9] = numpy.sum(x278 * (x227 * x292 + x376)) result[1, 2, 10] = numpy.sum(x274 * (x227 * x293 + x377)) result[1, 2, 11] = numpy.sum(x278 * (x227 * x294 + x379)) result[1, 2, 12] = numpy.sum(x98 * (x227 * x295 + x380)) result[1, 2, 13] = numpy.sum(x278 * (x227 * x297 + x381)) result[1, 2, 14] = numpy.sum(x274 * (x22 * x298 + x382)) result[2, 0, 0] = numpy.sum(x274 * (x226 + x383 * x67)) result[2, 0, 1] = numpy.sum(x278 * (x232 + x385 * x67)) result[2, 0, 2] = numpy.sum(x278 * (x240 + x386 * x67)) result[2, 0, 3] = numpy.sum(x98 * (x243 + x387 * x67)) result[2, 0, 4] = numpy.sum(x282 * (x248 + x390 * x67)) result[2, 0, 5] = numpy.sum(x98 * (x255 + x391 * x67)) result[2, 0, 6] = numpy.sum(x278 * (x256 + x393 * x67)) result[2, 0, 7] = numpy.sum(x282 * (x258 + x395 * x67)) result[2, 0, 8] = numpy.sum(x282 * (x259 + x397 * x67)) result[2, 0, 9] = numpy.sum(x278 * (x263 + x400 * x67)) result[2, 0, 10] = numpy.sum(x274 * (x20 * x401 + x264)) result[2, 0, 11] = numpy.sum(x278 * (x20 * x402 + x266)) result[2, 0, 12] = numpy.sum(x98 * (x20 * x403 + x267)) result[2, 0, 13] = numpy.sum(x278 * (x20 * x404 + x269)) result[2, 0, 14] = numpy.sum(x274 * (x270 + x405 * x67)) result[2, 1, 0] = numpy.sum(x274 * (x147 * x383 + x349)) result[2, 1, 1] = numpy.sum(x278 * (x147 * x385 + x352)) result[2, 1, 2] = numpy.sum(x278 * (x147 * x386 + x355)) result[2, 1, 3] = numpy.sum(x98 * (x147 * x387 + x358)) result[2, 1, 4] = numpy.sum(x282 * (x147 * x390 + x361)) result[2, 1, 5] = numpy.sum(x98 * (x147 * x391 + x364)) result[2, 1, 6] = numpy.sum(x278 * (x147 * x393 + x367)) result[2, 1, 7] = numpy.sum(x282 * (x147 * x395 + x370)) result[2, 1, 8] = numpy.sum(x282 * (x147 * x397 + x373)) result[2, 1, 9] = numpy.sum(x278 * (x147 * x400 + x376)) result[2, 1, 10] = numpy.sum(x274 * (x21 * x401 + x377)) result[2, 1, 11] = numpy.sum(x278 * (x21 * x402 + x379)) result[2, 1, 12] = numpy.sum(x98 * (x21 * x403 + x380)) result[2, 1, 13] = numpy.sum(x278 * (x21 * x404 + x381)) result[2, 1, 14] = numpy.sum(x274 * (x147 * x405 + x382)) result[2, 2, 0] = numpy.sum(x274 * (x227 * x383 + x412)) result[2, 2, 1] = numpy.sum(x278 * (x227 * x385 + x414)) result[2, 2, 2] = numpy.sum(x278 * (x227 * x386 + x418)) result[2, 2, 3] = numpy.sum(x98 * (x227 * x387 + x420)) result[2, 2, 4] = numpy.sum(x282 * (x227 * x390 + x422)) result[2, 2, 5] = numpy.sum(x98 * (x227 * x391 + x426)) result[2, 2, 6] = numpy.sum(x278 * (x227 * x393 + x428)) result[2, 2, 7] = numpy.sum(x282 * (x227 * x395 + x430)) result[2, 2, 8] = numpy.sum(x282 * (x227 * x397 + x432)) result[2, 2, 9] = numpy.sum(x278 * (x227 * x400 + x436)) result[2, 2, 10] = numpy.sum(x274 * (x22 * x401 + x437)) result[2, 2, 11] = numpy.sum(x278 * (x22 * x402 + x438)) result[2, 2, 12] = numpy.sum(x98 * (x22 * x403 + x439)) result[2, 2, 13] = numpy.sum(x278 * (x22 * x404 + x440)) result[2, 2, 14] = numpy.sum(x274 * (x227 * x405 + x441)) result[3, 0, 0] = numpy.sum(x70 * (x305 + x442 * x443)) result[3, 0, 1] = numpy.sum(x79 * (x20 * x445 + x312)) result[3, 0, 2] = numpy.sum(x79 * (x315 + x443 * x446)) result[3, 0, 3] = numpy.sum(x92 * (x316 * x447 + x319)) result[3, 0, 4] = numpy.sum(x98 * (x320 * x447 + x323)) result[3, 0, 5] = numpy.sum(x92 * (x325 + x448 * x449)) result[3, 0, 6] = numpy.sum(x79 * (x326 * x450 + x329)) result[3, 0, 7] = numpy.sum(x98 * (x330 * x450 + x333)) result[3, 0, 8] = numpy.sum(x98 * (x334 * x450 + x337)) result[3, 0, 9] = numpy.sum(x79 * (x339 + x449 * x451)) result[3, 0, 10] = numpy.sum(x70 * (x340 + x452 * x67)) result[3, 0, 11] = numpy.sum(x79 * (x341 + x453 * x67)) result[3, 0, 12] = numpy.sum(x92 * (x342 + x454 * x67)) result[3, 0, 13] = numpy.sum(x79 * (x343 + x455 * x67)) result[3, 0, 14] = numpy.sum(x70 * (x127 * x443 + x344)) result[3, 1, 0] = numpy.sum(x442 * x70 * (x456 + x457)) result[3, 1, 1] = numpy.sum(x79 * (x21 * x445 + x444 * x460)) result[3, 1, 2] = numpy.sum(x446 * x79 * (x456 + x457)) result[3, 1, 3] = numpy.sum(x92 * (x275 * x461 + x316 * x462)) result[3, 1, 4] = numpy.sum(x98 * (x275 * x463 + x320 * x462)) result[3, 1, 5] = numpy.sum(x448 * x92 * (x464 + x465)) result[3, 1, 6] = numpy.sum(x79 * (x157 * x466 + x326 * x467)) result[3, 1, 7] = numpy.sum(x98 * (x157 * x468 + x330 * x467)) result[3, 1, 8] = numpy.sum(x98 * (x157 * x469 + x334 * x467)) result[3, 1, 9] = numpy.sum(x451 * x79 * (x464 + x465)) result[3, 1, 10] = numpy.sum(x70 * (x147 * x452 + x47 * (3.0 * x327 + x466 * x71))) result[3, 1, 11] = numpy.sum(x79 * (x147 * x453 + x47 * (3.0 * x331 + x468 * x71))) result[3, 1, 12] = numpy.sum(x92 * (x147 * x454 + x47 * (3.0 * x335 + x469 * x71))) result[3, 1, 13] = numpy.sum(x79 * (x114 * x47 * (x458 + x459) + x147 * x455)) result[3, 1, 14] = numpy.sum(x127 * x70 * (x456 + x457)) result[3, 2, 0] = numpy.sum(x70 * (x442 * x472 + x471)) result[3, 2, 1] = numpy.sum(x79 * (x22 * x445 + x475)) result[3, 2, 2] = numpy.sum(x79 * (x446 * x472 + x477)) result[3, 2, 3] = numpy.sum(x92 * (x316 * x480 + x479)) result[3, 2, 4] = numpy.sum(x98 * (x320 * x480 + x483)) result[3, 2, 5] = numpy.sum(x92 * (x448 * x486 + x485)) result[3, 2, 6] = numpy.sum(x79 * (x326 * x489 + x488)) result[3, 2, 7] = numpy.sum(x98 * (x330 * x489 + x491)) result[3, 2, 8] = numpy.sum(x98 * (x334 * x489 + x494)) result[3, 2, 9] = numpy.sum(x79 * (x451 * x486 + x496)) result[3, 2, 10] = numpy.sum(x70 * (x227 * x452 + x497)) result[3, 2, 11] = numpy.sum(x79 * (x227 * x453 + x498)) result[3,