Simplified Hartree-Fock Method for Calculating Ground-State Properties and Energy-Band Structures

Abstract

The derivation of an exact equivalent to the canonical restricted Hartree-Fock method is discussed. This method yields a solution to the energy-band problem and for the calculation of ground-state energies and ground-state charge densities in a form similar to the familiar linear combination of atomic orbitals (LCAO). The present form achieves a substantial degree of simplification when compared with the traditional LCAO method in that using the present techniques all four-center integrals are rigorously absent. Also presented is a rigorous extension of these techniques, useful for calculating the virtual orbitals of the system. These techniques should be useful for solid-state and molecular studies. The technique is illustrated for the case of solid fcc helium as a function of the lattice constant. It is argued that by employing the present techniques, solutions to the Hartree-Fock problem for a solid may be obtained more efficiently than for competing Hartree-Fock techniques. The inclusion of many-body effects is discussed.