Some Studies of the General Hartree-Fock Method

Abstract

Publisher Summary This chapter discusses the original Hartree–Fock method—referred as the GHF-scheme— for some simple atomic and molecular systems by using general spin-orbitals of a complex character, and there exist GHF solutions of TSDW type which give lower energies than the Restricted Hartree–Fock (RHF), and unrestricted Hartree–Fock (UHF)-schemes, but also that quite a few SCF solutions of different type may exist simultaneously. The purpose of the chapter is to find the “absolute minimum” for the energy on the hypersurface associated with the Self- Consistent-Field (SCF) procedure. At the same time it is observed that, whenever such an absolute minimum is found, the associated Slater determinant D is usually a mixture of different symmetry types. Projected Hartree–Fock (PHF) scheme preserves many of the fundamental features of the independent-particle-model. It has been shown that, even for two-electron systems, the PHF scheme gives a lower energy when one is using general spin-orbitals (GSOs) and that the same is true also for the lithium atom. it has not been easy to carry out an extension of the PHF-scheme using complex GSO's to many-electron systems. In such a case, it is certainly important to learn the ways to handle determinants built up from complex general spin orbitals, and it is hoped that the study in this chapter will be of value not only as an expose of the GHF method but also as a first step toward an extension of the PHF-sceme.