"""
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 = 4
lauxmax = 6
write = False
out_dir = devel_ints
keys = ['~2c2e', '~3c2e_sph']
sph = False
opt_basic = True
normalize = cgto
"""
import numpy
[docs]
def cart_gto3d_0(ax, da, A, R):
"""3D Cartesian s-Gaussian shell.
Exponent ax, contraction coeff. da, centered at A, evaluated at R.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((1,), dtype=float)
# 1 item(s)
result[0] = numpy.sum(
da
* numpy.exp(-ax * ((A[0] - R[0]) ** 2 + (A[1] - R[1]) ** 2 + (A[2] - R[2]) ** 2))
)
return result
[docs]
def cart_gto3d_1(ax, da, A, R):
"""3D Cartesian p-Gaussian shell.
Exponent ax, contraction coeff. da, centered at A, evaluated at R.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((3,), dtype=float)
x0 = A[0] - R[0]
x1 = A[1] - R[1]
x2 = A[2] - R[2]
x3 = da * numpy.exp(-ax * (x0**2 + x1**2 + x2**2))
# 3 item(s)
result[0] = numpy.sum(-x0 * x3)
result[1] = numpy.sum(-x1 * x3)
result[2] = numpy.sum(-x2 * x3)
return result
[docs]
def cart_gto3d_2(ax, da, A, R):
"""3D Cartesian d-Gaussian shell.
Exponent ax, contraction coeff. da, centered at A, evaluated at R.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((6,), dtype=float)
x0 = A[0] - R[0]
x1 = x0**2
x2 = A[1] - R[1]
x3 = x2**2
x4 = A[2] - R[2]
x5 = x4**2
x6 = da * numpy.exp(-ax * (x1 + x3 + x5))
x7 = 0.5773502691896258 * x6
x8 = x0 * x6
# 6 item(s)
result[0] = numpy.sum(x1 * x7)
result[1] = numpy.sum(x2 * x8)
result[2] = numpy.sum(x4 * x8)
result[3] = numpy.sum(x3 * x7)
result[4] = numpy.sum(x2 * x4 * x6)
result[5] = numpy.sum(x5 * x7)
return result
[docs]
def cart_gto3d_3(ax, da, A, R):
"""3D Cartesian f-Gaussian shell.
Exponent ax, contraction coeff. da, centered at A, evaluated at R.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((10,), dtype=float)
x0 = A[0] - R[0]
x1 = x0**2
x2 = A[1] - R[1]
x3 = x2**2
x4 = A[2] - R[2]
x5 = x4**2
x6 = da * numpy.exp(-ax * (x1 + x3 + x5))
x7 = 0.2581988897471611 * x6
x8 = x2 * x6
x9 = 0.5773502691896258
x10 = x1 * x9
x11 = x4 * x6
x12 = x3 * x9
x13 = x0 * x6
x14 = x5 * x9
# 10 item(s)
result[0] = numpy.sum(-(x0**3) * x7)
result[1] = numpy.sum(-x10 * x8)
result[2] = numpy.sum(-x10 * x11)
result[3] = numpy.sum(-x12 * x13)
result[4] = numpy.sum(-x0 * x4 * x8)
result[5] = numpy.sum(-x13 * x14)
result[6] = numpy.sum(-(x2**3) * x7)
result[7] = numpy.sum(-x11 * x12)
result[8] = numpy.sum(-x14 * x8)
result[9] = numpy.sum(-(x4**3) * x7)
return result
[docs]
def cart_gto3d_4(ax, da, A, R):
"""3D Cartesian g-Gaussian shell.
Exponent ax, contraction coeff. da, centered at A, evaluated at R.
Generated code; DO NOT modify by hand!"""
result = numpy.zeros((15,), dtype=float)
x0 = -A[0] + R[0]
x1 = x0**2
x2 = -A[1] + R[1]
x3 = x2**2
x4 = -A[2] + R[2]
x5 = x4**2
x6 = da * numpy.exp(-ax * (x1 + x3 + x5))
x7 = 0.09759000729485332 * x6
x8 = 0.2581988897471611 * x6
x9 = x0**3 * x8
x10 = 0.3333333333333333 * x6
x11 = x1 * x10
x12 = 1.732050807568877
x13 = x12 * x4
x14 = x2**3
x15 = x0 * x8
x16 = x10 * x3
x17 = x4**3
# 15 item(s)
result[0] = numpy.sum(x0**4 * x7)
result[1] = numpy.sum(x2 * x9)
result[2] = numpy.sum(x4 * x9)
result[3] = numpy.sum(x11 * x3)
result[4] = numpy.sum(x11 * x13 * x2)
result[5] = numpy.sum(x11 * x5)
result[6] = numpy.sum(x14 * x15)
result[7] = numpy.sum(x0 * x13 * x16)
result[8] = numpy.sum(x0 * x10 * x12 * x2 * x5)
result[9] = numpy.sum(x15 * x17)
result[10] = numpy.sum(x2**4 * x7)
result[11] = numpy.sum(x14 * x4 * x8)
result[12] = numpy.sum(x16 * x5)
result[13] = numpy.sum(x17 * x2 * x8)
result[14] = numpy.sum(x4**4 * x7)
return result
cart_gto3d = {
(0,): cart_gto3d_0,
(1,): cart_gto3d_1,
(2,): cart_gto3d_2,
(3,): cart_gto3d_3,
(4,): cart_gto3d_4,
}