def os_recursive(self, r, m, g1, g2, g3, g4, g5, g6, g7, g8): 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) out1 = (r_5[r] - r_1[r]) * self.os_begin(m, g1, g2, g3, g4) 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_count(g1.integral_exponents[r]) * (1 / (2 * a_5)) * self.os_begin(m, g5, g2, g3, g4) out4 = self.os_count(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_count(g2.integral_exponents[r]) * (1 / (2 * a_5)) * self.os_begin(m, g1, g6, g3, g4) out6 = self.os_count(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_count(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_count(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, g1, g2, g3, g4): l_1 = g1.integral_exponents l_2 = g2.integral_exponents l_3 = g3.integral_exponents l_4 = g4.integral_exponents l_total = sum(l_1) + sum(l_2) + sum(l_3) + sum(l_4) 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_1 = g1.coordinates r_2 = g2.coordinates r_3 = g3.coordinates r_4 = g4.coordinates 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} while l_total >= 1: boys_out3 = boys_function_recursion(l_total, boys_x, boys_out3) l_total -= 1 self.end_dict[l_total] = boys_out1 * boys_out2 * boys_out3 if sum(l_1) >= sum(l_2) and sum(l_3) >= sum(l_4): return self.hgp_begin_horizontal(g1, g2, g3, g4) elif sum(l_1) >= sum(l_2): return self.hgp_begin_horizontal(g1, g2, g4, g3) elif sum(l_3) >= sum(l_4): return self.hgp_begin_horizontal(g2, g1, g3, g4) else: return self.hgp_begin_horizontal(g2, g1, g4, g3)
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
def vertical_recursion(self, r, m, g1, g2, g3, g4, g5, g6): 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) out1 = (r_5[r] - r_1[r]) * self.hgp_begin_vertical(m, g1, g2, g3, g4) 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