The exclusion principle for interacting electrons: Kohn - Sham versus Thomas - Fermi

Abstract

Many anomalies and paradoxes in density-functional theory arise from the assumption that an exact mean-field theory of electrons requires only local potential functions. It is shown here that this assumption arises from a logical hiatus in deriving orbital-based Kohn-Sham theory, which incorporates the exclusion principle for electrons, from density-based Hohenberg-Kohn theory, which does not. The inconsistencies are removed by building the exclusion principle into density-based theory from the outset. This logic replaces any implication regarding exact local potential functions by explicit specification of nonlocal potentials determined by exact N-electron theory. These general results are examined here in the unrestricted Hartree-Fock variational model, using a two-electron atom in its lowest triplet state Is2s 3S as a test case to illustrate the implied inconsistencies and their resolution. It is shown that implications of the unrestricted Hartree - Fock model are not modified if overlap products are included in its variational functional. © 2004 Wiley Periodicals, Inc.