def vertical_recursion(self, r, m, g1, g2, g3, g4, g5, g6):
out1 = out2 = out3 = out4 = out5 = 0
a_1 = g1.exponent
a_2 = g2.exponent
a_3 = g3.exponent
a_4 = g4.exponent
a_5 = a_1 + a_2
a_6 = a_3 + a_4
r_1 = g1.coordinates
r_2 = g2.coordinates
r_5 = gaussian_product_coordinate(a_1, r_1, a_2, r_2)
if r_5[r] != r_1[r]:
out1 = (r_5[r] - r_1[r]) * self.hgp_begin_vertical(
m, g1, g2, g3, g4)
if self.r_7[r] != r_5[r]:
out2 = (self.r_7[r] - r_5[r]) * self.hgp_begin_vertical(
(m + 1), g1, g2, g3, g4)
if g5.integral_exponents[r] >= 0:
out3 = self.os_count(g1.integral_exponents[r]) * (
1 / (2 * a_5)) * self.hgp_begin_vertical(m, g5, g2, g3, g4)
out4 = self.os_count(g1.integral_exponents[r]) * (
self.a_7 / (2 * a_5**2)) * self.hgp_begin_vertical(
(m + 1), g5, g2, g3, g4)
if g6.integral_exponents[r] >= 0:
out5 = self.os_count(g3.integral_exponents[r]) * (
1 / (2 * (a_5 + a_6))) * self.hgp_begin_vertical(
(m + 1), g1, g2, g6, g4)
return out1 + out2 + out3 - out4 + out5
def nuclear_attraction(gaussian_1, gaussian_2, nuclei):
a_1 = gaussian_1.exponent
a_2 = gaussian_2.exponent
l_1 = gaussian_1.integral_exponents
l_2 = gaussian_2.integral_exponents
r_a = gaussian_1.coordinates
r_b = gaussian_2.coordinates
r_c = nuclei.coordinates
r_p = gaussian_product_coordinate(a_1, r_a, a_2, r_b)
r_ab = coordinate_distance(r_a, r_b)
r_pc = coordinate_distance(r_p, r_c)
r_p_a = vector_minus(r_p, r_a)
r_p_b = vector_minus(r_p, r_b)
r_p_c = vector_minus(r_p, r_c)
g = a_1 + a_2
ans = 0
for l in range(l_1[0] + l_2[0] + 1):
for r in range(int(l / 2) + 1):
for i in range(int((l - 2 * r) / 2) + 1):
out1 = a_function(l, r, i, l_1[0], l_2[0], r_p_a[0], r_p_b[0],
r_p_c[0], g)
for m in range(l_1[1] + l_2[1] + 1):
for s in range(int(m / 2) + 1):
for j in range(int((m - 2 * s) / 2) + 1):
out2 = a_function(m, s, j, l_1[1], l_2[1],
r_p_a[1], r_p_b[1], r_p_c[1], g)
for n in range(l_1[2] + l_2[2] + 1):
for t in range(int(n / 2) + 1):
for k in range(int((n - 2 * t) / 2) + 1):
out3 = a_function(
n, t, k, l_1[2], l_2[2], r_p_a[2],
r_p_b[2], r_p_c[2], g)
v = (l + m +
n) - 2 * (r + s + t) - (i + j + k)
out4 = boys_function(v, g * r_pc**2)
out5 = out1 * out2 * out3 * out4
ans += out5
ans *= ((2 * pi) / g) * exp(-(a_1 * a_2 * r_ab**2) / g)
return ans
def orbital_overlap(gaussian_1, gaussian_2):
a_1 = gaussian_1.exponent
a_2 = gaussian_2.exponent
l_1 = gaussian_1.integral_exponents
l_2 = gaussian_2.integral_exponents
r_a = gaussian_1.coordinates
r_b = gaussian_2.coordinates
r_ab = coordinate_distance(r_a, r_b)
r_p = gaussian_product_coordinate(a_1, r_a, a_2, r_b)
r_p_a = vector_minus(r_p, r_a)
r_p_b = vector_minus(r_p, r_b)
g = a_1 + a_2
s_x = s_function(l_1[0], l_2[0], r_p_a[0], r_p_b[0], g)
s_y = s_function(l_1[1], l_2[1], r_p_a[1], r_p_b[1], g)
s_z = s_function(l_1[2], l_2[2], r_p_a[2], r_p_b[2], g)
s_ij = (pi / g)**(3 / 2) * exp(-a_1 * a_2 * r_ab**2 / g) * s_x * s_y * s_z
return s_ij
def os_recursive(self, r, m, g1, g2, g3, g4, g5, g6, g7, g8):
out1 = out2 = out3 = out4 = out5 = out6 = out7 = out8 = 0
a_1 = g1.exponent
a_2 = g2.exponent
a_3 = g3.exponent
a_4 = g4.exponent
a_5 = a_1 + a_2
a_6 = a_3 + a_4
r_1 = g1.coordinates
r_2 = g2.coordinates
r_5 = gaussian_product_coordinate(a_1, r_1, a_2, r_2)
if r_5[r] != r_1[r]:
out1 = (r_5[r] - r_1[r]) * self.os_begin(m, g1, g2, g3, g4)
if self.r_7[r] != r_5[r]:
out2 = (self.r_7[r] - r_5[r]) * self.os_begin(
m + 1, g1, g2, g3, g4)
if g5.integral_exponents[r] >= 0:
out3 = self.os_int(g1.integral_exponents[r]) * (
1 / (2 * a_5)) * self.os_begin(m, g5, g2, g3, g4)
out4 = self.os_int(g1.integral_exponents[r]) * (
self.a_7 /
(2 * a_5**2)) * self.os_begin(m + 1, g5, g2, g3, g4)
if g6.integral_exponents[r] >= 0:
out5 = self.os_int(g2.integral_exponents[r]) * (
1 / (2 * a_5)) * self.os_begin(m, g1, g6, g3, g4)
out6 = self.os_int(g2.integral_exponents[r]) * (
self.a_7 /
(2 * a_5**2)) * self.os_begin(m + 1, g1, g6, g3, g4)
if g7.integral_exponents[r] >= 0:
out7 = self.os_int(g3.integral_exponents[r]) * (
1 / (2 * (a_5 + a_6))) * self.os_begin(m + 1, g1, g2, g7, g4)
if g8.integral_exponents[r] >= 0:
out8 = self.os_int(g4.integral_exponents[r]) * (
1 / (2 * (a_5 + a_6))) * self.os_begin(m + 1, g1, g2, g3, g8)
return out1 + out2 + out3 - out4 + out5 - out6 + out7 + out8
def integrate(self, basis_i, basis_j, basis_k, basis_l):
l_1 = basis_i.integral_exponents
l_2 = basis_j.integral_exponents
l_3 = basis_k.integral_exponents
l_4 = basis_l.integral_exponents
l_total = sum(l_1) + sum(l_2) + sum(l_3) + sum(l_4)
r_1 = basis_i.coordinates
r_2 = basis_j.coordinates
r_3 = basis_k.coordinates
r_4 = basis_l.coordinates
primitives_i = basis_i.primitive_gaussian_array
primitives_j = basis_j.primitive_gaussian_array
primitives_k = basis_k.primitive_gaussian_array
primitives_l = basis_l.primitive_gaussian_array
n_i = basis_i.normalisation
n_j = basis_j.normalisation
n_k = basis_k.normalisation
n_l = basis_l.normalisation
n = n_i * n_j * n_k * n_l
ans = 0.0
for g1, g2, g3, g4 in itertools.product(primitives_i, primitives_j,
primitives_k, primitives_l):
c_1 = g1.contraction
c_2 = g2.contraction
c_3 = g3.contraction
c_4 = g4.contraction
n_1 = g1.normalisation
n_2 = g2.normalisation
n_3 = g3.normalisation
n_4 = g4.normalisation
contraction = c_1 * c_2 * c_3 * c_4 * n_1 * n_2 * n_3 * n_4 * n
a_1 = g1.exponent
a_2 = g2.exponent
a_3 = g3.exponent
a_4 = g4.exponent
a_5 = a_1 + a_2
a_6 = a_3 + a_4
self.a_7 = (a_5 * a_6) / (a_5 + a_6)
r_5 = gaussian_product_coordinate(a_1, r_1, a_2, r_2)
r_6 = gaussian_product_coordinate(a_3, r_3, a_4, r_4)
self.r_7 = gaussian_product_coordinate(a_5, r_5, a_6, r_6)
r_12 = coordinate_distance(r_1, r_2)
r_34 = coordinate_distance(r_3, r_4)
r_56 = coordinate_distance(r_5, r_6)
boys_x = (a_5 * a_6 * r_56**2) / (a_5 + a_6)
boys_out1 = (2 * pi**(5 / 2)) / (a_5 * a_6 * sqrt(a_5 + a_6))
boys_out2 = exp(((-a_1 * a_2 * r_12**2) / a_5) -
((a_3 * a_4 * r_34**2) / a_6))
boys_out3 = boys_function(l_total, boys_x)
self.end_dict = {l_total: boys_out1 * boys_out2 * boys_out3}
m = l_total
while m >= 1:
boys_out3 = boys_function_recursion(m, boys_x, boys_out3)
m -= 1
self.end_dict[m] = boys_out1 * boys_out2 * boys_out3
ans += contraction * self.os_begin(0, g1, g2, g3, g4)
return ans