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 : }