Numerical solution of the Hartree-Fock equation in molecular geometries

Solutions of the restricted Hartree-Fock equations are obtained for small molecules using a combination of variationally optimized atomic orbitals centered on the nuclei and corrections computed on a Cartesian mesh. The problem of finding the corrections is reduced to the problem of solving the Hartree-Fock equations with inhomogeneous terms. An iterative method is developed in which the equation is treated as an inhomogeneous Helmholtz equation with the potential terms transferred to the inhomogeneous term. Terms in the equation that arise from rapid variation of the orbitals in the neighborhoods of the nuclei are treated analytically. The Helmholtz equation can then be solved using a fast Fourier transform method. Results for a number of small molecules that are accurate at the millihartree level are presented. The method for solving the inhomogeneous Hartree-Fock equation should be applicable to other problems of quantum chemistry.