def integrate(self, g1, g2, g3, g4): self.end_dict = {} g5 = gaussian_product(g1, g2) g6 = gaussian_product(g3, g4) a_1 = g1.exponent a_2 = g2.exponent a_3 = g3.exponent a_4 = g4.exponent a_5 = g5.exponent a_6 = g6.exponent r_1 = g1.coordinates r_2 = g2.coordinates r_3 = g3.coordinates r_4 = g4.coordinates r_5 = g5.coordinates r_6 = g6.coordinates r_12 = coordinate_distance(r_1, r_2) r_34 = coordinate_distance(r_3, r_4) r_56 = coordinate_distance(r_5, r_6) l_1 = g1.integral_exponents l_2 = g2.integral_exponents l_3 = g3.integral_exponents l_4 = g4.integral_exponents l_5 = g5.integral_exponents l_6 = g6.integral_exponents delta = (1/(4*a_5)) + (1/(4*a_6)) ans = 0 for l in range(l_5[0] + 1): for r in range(int(l/2) + 1): for ll in range(l_6[0] + 1): for rr in range(int(ll/2) + 1): for i in range(int((l + ll - 2*r - 2*rr) / 2) + 1): out1 = self.b_function(l, ll, r, rr, i, l_1[0], l_2[0], r_1[0], r_2[0], r_5[0], a_5, l_3[0], l_4[0], r_3[0], r_4[0], r_6[0], a_6) for m in range(l_5[1] + 1): for s in range(int(m/2) + 1): for mm in range(l_6[1] + 1): for ss in range(int(mm/2) + 1): for j in range(int((m + mm - 2*s - 2*ss) / 2) + 1): out2 = self.b_function(m, mm, s, ss, j, l_1[1], l_2[1], r_1[1], r_2[1], r_5[1], a_5, l_3[1], l_4[1], r_3[1], r_4[1], r_6[1], a_6) for n in range(l_5[2] + 1): for t in range(int(n/2) + 1): for nn in range(l_6[2] + 1): for tt in range(int(nn/2) + 1): for k in range(int((n + nn - 2*t - 2*tt) / 2) + 1): out3 = self.b_function(n, nn, t, tt, k, l_1[2], l_2[2], r_1[2], r_2[2], r_5[2], a_5, l_3[2], l_4[2], r_3[2], r_4[2], r_6[2], a_6) v = l + ll + m + mm + n + nn - 2*(r + rr + s + ss + t + tt) - (i + j + k) if v in self.end_dict: out4 = self.end_dict[v] else: out4 = boys_function(v, (r_56**2 / (4 * delta))) self.end_dict[v] = out4 ans += out1 * out2 * out3 * out4 ans *= self.gaussian_product_factor(a_1, a_2, a_3, a_4, a_5, a_6, r_12, r_34) return ans
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 check_basis_functions(self, basis_i, basis_x): i, j, k = basis_i.integral_exponents x, y, z = basis_x.integral_exponents i, j, k = abs(i), abs(j), abs(k) if coordinate_distance(basis_i.coordinates, basis_x.coordinates) <= 1e-3 and i == x and j == y and k == z \ and self.check_primitives(basis_i, basis_x): return True else: return False
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 check_symmetry_operation(self, nuclei_array, symmetry): nuclei_array_copy = [] for nuclei in nuclei_array: coordinates = symmetry.operate(nuclei.coordinates) nuclei_copy = Nuclei(nuclei.element, nuclei.charge, nuclei.mass, coordinates) nuclei_array_copy.append(nuclei_copy) for nuclei_i in nuclei_array: for k, nuclei_k in enumerate(nuclei_array_copy): if coordinate_distance(nuclei_i.coordinates, nuclei_k.coordinates) <= self.error \ and (nuclei_i.charge - nuclei_k.charge) == 0.0: break if k == len(nuclei_array_copy) - 1: return False return True
def coulombs_law(nuc1, nuc2): """Computes the nuclear-nuclear repulsion energy for two nuclei. Parameters ---------- nuc1 : Nuclei nuc2 : Nuclei Returns ------- ans : float """ r_12 = coordinate_distance(nuc1.coordinates, nuc2.coordinates) ans = (nuc1.charge * nuc2.charge) / r_12 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