The density matrix, density, and Fermi hole in Hartree–Fock theory

Abstract

In density matrix and density functional theory, one is concerned with methods that bypass explicit calculation of antisymmetric wave functions but nevertheless take full account of the Fermionic nature of the problem. The purpose of this paper is to examine two quite different approaches which achieve this aim. The first of these involves general many‐electron theory and subsequent closure yielding an integrodifferential equation for the density matrix. Despite the interesting nature of this equation, analytical progress is hampered by its nonlinearity. Hence we have considered an alternative more practical variational procedure which, for some simpler systems, has the additional merit of yielding closed differential equations for the density.