On the Solution of the Hartree-Fock Equation in Terms of Localized Orbitals

Abstract

The Hartree-Fock method is discussed with emphasis placed on the transformation properties of the Hartree-Fock equation. It is emphasized that the Hartree-Fock equation may be solved in terms of non-orthogonal one-electron functions, and that in some cases it may be more convenient to choose such solutions. Equations are developed which define the localized one-electron functions and it is shown how these equations may be solved. For a system of closed shell atoms or ions, it is suggested that the localized orbitals of each atom or ion can be expanded in terms of functions centered on its nucleus. This suggestion is based on the success of the ionic theory of crystals. Due to the symmetry of a crystal, it is suggested that use of the localized orbitals could lead to expressions for the first order, Hartree-Fock density matrix and the Hartree-Fock energy of a crystal, i.e., one could obtain the solution of the Hartree-Fock equation for a crystal.