Line data Source code
1 : /*----------------------------------------------------------------------------*/
2 : /* CP2K: A general program to perform molecular dynamics simulations */
3 : /* Copyright 2000-2025 CP2K developers group <https://cp2k.org> */
4 : /* */
5 : /* SPDX-License-Identifier: MIT */
6 : /*----------------------------------------------------------------------------*/
7 :
8 : /*
9 : * libgrpp - a library for the evaluation of integrals over
10 : * generalized relativistic pseudopotentials.
11 : *
12 : * Copyright (C) 2021-2023 Alexander Oleynichenko
13 : */
14 :
15 : /**
16 : * Calculation of overlap integrals.
17 : *
18 : * The recursive Obara-Saika scheme is used to calculate 1- and 2-center overlap
19 : * integrals. For details, see: T. Helgaker, P. Jorgensen, J. Olsen, Molecular
20 : * Electronic-Structure Theory, John Wiley & Sons Ltd, 2000. Chapter 9.3.1,
21 : * "Overlap integrals"
22 : */
23 :
24 : #include <math.h>
25 : #include <stdlib.h>
26 : #include <string.h>
27 : #ifndef M_PI
28 : #define M_PI 3.14159265358979323846
29 : #endif
30 :
31 : #include "grpp_norm_gaussian.h"
32 : #include "grpp_overlap.h"
33 : #include "libgrpp.h"
34 :
35 : #include "grpp_utils.h"
36 :
37 : static void overlap_integrals_shell_pair_obara_saika(libgrpp_shell_t *shell_A,
38 : libgrpp_shell_t *shell_B,
39 : double alpha_A,
40 : double alpha_B,
41 : double *overlap_matrix);
42 :
43 : /**
44 : * Calculates overlap integral between two shells represented by contracted
45 : * Gaussian functions.
46 : */
47 0 : void libgrpp_overlap_integrals(libgrpp_shell_t *shell_A,
48 : libgrpp_shell_t *shell_B,
49 : double *overlap_matrix) {
50 0 : int size_A = libgrpp_get_shell_size(shell_A);
51 0 : int size_B = libgrpp_get_shell_size(shell_B);
52 :
53 0 : double *buf = calloc(size_A * size_B, sizeof(double));
54 :
55 0 : memset(overlap_matrix, 0, size_A * size_B * sizeof(double));
56 :
57 : // loop over primitives in contractions
58 0 : for (int i = 0; i < shell_A->num_primitives; i++) {
59 0 : for (int j = 0; j < shell_B->num_primitives; j++) {
60 0 : double alpha_i = shell_A->alpha[i];
61 0 : double alpha_j = shell_B->alpha[j];
62 0 : double coef_A_i = shell_A->coeffs[i];
63 0 : double coef_B_j = shell_B->coeffs[j];
64 :
65 0 : overlap_integrals_shell_pair_obara_saika(shell_A, shell_B, alpha_i,
66 : alpha_j, buf);
67 :
68 0 : libgrpp_daxpy(size_A * size_B, coef_A_i * coef_B_j, buf, overlap_matrix);
69 : }
70 : }
71 :
72 0 : free(buf);
73 0 : }
74 :
75 0 : static void overlap_integrals_shell_pair_obara_saika(libgrpp_shell_t *shell_A,
76 : libgrpp_shell_t *shell_B,
77 : double alpha_A,
78 : double alpha_B,
79 : double *overlap_matrix) {
80 0 : int size_A = libgrpp_get_shell_size(shell_A);
81 0 : int size_B = libgrpp_get_shell_size(shell_B);
82 0 : int L_A = shell_A->L;
83 0 : int L_B = shell_B->L;
84 0 : double N_A = libgrpp_gaussian_norm_factor(L_A, 0, 0, alpha_A);
85 0 : double N_B = libgrpp_gaussian_norm_factor(L_B, 0, 0, alpha_B);
86 :
87 0 : double p = alpha_A + alpha_B;
88 0 : double mu = alpha_A * alpha_B / (alpha_A + alpha_B);
89 0 : double *A = shell_A->origin;
90 0 : double *B = shell_B->origin;
91 :
92 0 : double S[3][LIBGRPP_MAX_BASIS_L][LIBGRPP_MAX_BASIS_L];
93 :
94 0 : for (int coord = 0; coord < 3; coord++) {
95 0 : double P = (alpha_A * A[coord] + alpha_B * B[coord]) / p;
96 :
97 0 : double X_AB = A[coord] - B[coord];
98 0 : double X_PA = P - A[coord];
99 0 : double X_PB = P - B[coord];
100 0 : double pfac = 1.0 / (2.0 * p);
101 :
102 0 : for (int i = 0; i <= L_A; i++) {
103 0 : for (int j = 0; j <= L_B; j++) {
104 0 : double S_ij = 0.0;
105 :
106 0 : if (i + j == 0) {
107 0 : S[coord][0][0] = sqrt(M_PI / p) * exp(-mu * X_AB * X_AB);
108 0 : continue;
109 : }
110 :
111 0 : if (i == 0) { // upward by j
112 0 : S_ij += X_PB * S[coord][i][j - 1];
113 0 : if (j - 1 > 0) {
114 0 : S_ij += (j - 1) * pfac * S[coord][i][j - 2];
115 : }
116 : } else { // upward by i
117 0 : S_ij += X_PA * S[coord][i - 1][j];
118 0 : if (i - 1 > 0) {
119 0 : S_ij += (i - 1) * pfac * S[coord][i - 2][j];
120 : }
121 0 : if (j > 0) {
122 0 : S_ij += j * pfac * S[coord][i - 1][j - 1];
123 : }
124 : }
125 :
126 0 : S[coord][i][j] = S_ij;
127 : }
128 : }
129 : }
130 :
131 : // loop over cartesian functions inside the shells
132 0 : for (int m = 0; m < size_A; m++) {
133 0 : for (int n = 0; n < size_B; n++) {
134 0 : int n_A = shell_A->cart_list[3 * m + 0];
135 0 : int l_A = shell_A->cart_list[3 * m + 1];
136 0 : int m_A = shell_A->cart_list[3 * m + 2];
137 0 : int n_B = shell_B->cart_list[3 * n + 0];
138 0 : int l_B = shell_B->cart_list[3 * n + 1];
139 0 : int m_B = shell_B->cart_list[3 * n + 2];
140 :
141 0 : overlap_matrix[m * size_B + n] =
142 0 : N_A * N_B * S[0][n_A][n_B] * S[1][l_A][l_B] * S[2][m_A][m_B];
143 : }
144 : }
145 0 : }
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