Some formal comments on spin projected hartree-fock theory

Abstract

Antisymmetric projection for no spin-orbit coupling is carried out within the one-electron approximation. A basis set is chosen such that one orbital of the minority spin space uniquely “pairs” with one and only one orbital of the majority spin space. The general expression for the expanded wave function given elsewhere [1] are shown to give rise to a relatively condensed, real expression for the system energy. The energy expressions can be separated into parts which one can argue in order: 1 Produce a strong tendency to minimum total spin and maximum overlap (double occupancy). 2 In the case of degenerate or nearly degenerate one-electron states there is a tendency to maximize the total spin value within this manifold (Hunds rule). However, it is expected that this tendency will be smaller than that calculated using restricted Hartree-Fock theory. 3 There is also a tendency opposing and producing some departure from complete overlap. All of these effects depend on terms whose individual elements can be expected to be equal to or larger than the usual exchange integrals.