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 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
