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



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 1s2s 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. Int J Quantum Chem, 2004