Density Functional Theory versus the Hartree Fock Method: Comparative Assessment

Details Density Functional Theory versus the Hartree Fock Method: Comparative Assessment Density Functional Theory versus the Hartree Fock Method: Comparative Assessment

2002-04-04

arxiv.org/abs/cond-mat/0204104v2

Physica Scripta T68, C133 (2003)

Physics

Condensed Matter

Materials Science

16 pages, Revtex, no figures

Scientific paper

10.1238/Physica.Regular.068aC013

We compare two different approaches to investigations of many-electron systems. The first is the Hartree-Fock (HF) method and the second is the Density Functional Theory (DFT). Overview of the main features and peculiar properties of the HF method are presented. A way to realize the HF method within the Kohn-Sham (KS) approach of the DFT is discussed. We show that this is impossible without including a specific correlation energy, which is defined by the difference between the sum of the kinetic and exchange energies of a system considered within KS and HF, respectively. It is the nonlocal exchange potential entering the HF equations that generates this correlation energy. We show that the total correlation energy of a finite electron system, which has to include this correlation energy, cannot be obtained from considerations of uniform electron systems. The single-particle excitation spectrum of many-electron systems is related to the eigenvalues of the corresponding KS equations. We demonstrate that this spectrum does not coincide in general with the eigenvalues of KS or HF equations.

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