The advantages of the general Hartree–Fock method for future computer simulation of materials

Abstract

The general Hartree–Fock (GHF) method is a quantum mechanical method for electronic structure calculations that uses a single determinantal wave function with no restrictions on the one-electron orbitals other than orthonormality and the use of a specific basis set. The more familiar restricted Hartree–Fock (RHF) and unrestricted Hartree–Fock (UHF) methods can be regarded as special cases of the GHF method in which additional restrictions are imposed on the occupied orbitals. We propose that the GHF method is very suitable as an electronic structure method to be incorporated into computer simulations that combine the calculation of the Born–Oppenheimer ground state surface with the simulation of the motion of the nuclei on that surface. In particular, for many problems of interest there is only a single GHF minimum of the energy, and the GHF wave function is a continuous function of nuclear positions. The RHF and UHF methods, in comparison, typically have a multiplicity of local minima with curve crossings that generate a discontinuous behavior of the ground electronic state wave function as a function of nuclear positions. In this paper, we use energy minimization techniques to identify and characterize the UHF and GHF electronic minima at fixed nuclear positions for three model systems. The results verify the above assertions and suggest that the GHF method would be more suitable than the RHF or UHF methods for computer simulations.