Density Functional Theory versus the Hartree Fock Method: Comparative Assessment

TL;DR

This paper compares the Hartree-Fock and Density Functional Theory methods for many-electron systems, highlighting their differences, limitations, and the role of correlation energy in accurately describing electronic properties.

Contribution

It provides a detailed comparison of HF and DFT, discusses the realization of HF within DFT, and clarifies the nature of correlation energy and excitation spectra.

Findings

Correlation energy is essential for HF within DFT.

Single-particle spectra differ between KS and HF methods.

Total correlation energy cannot be derived from uniform electron systems.

Abstract

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.