2 00 2 Density functional theory versus the Hartree Fock method : comparative assessment

We compare two different approaches to investigations of many-electron systems. The first one is the Hartree-Fock (HF) method and the second one is the Density Functional Theory (DFT). Overview of the main features and peculiar properties of HF method is presented. We discuss a way to realize the HF method within the Kohn-Sham (KS) theory and show that it is impossible without including a specific correlation energy which is defined by the difference between the sum of the kinetic and exchange energy of a system embedded into a nonlocal external potential and the sum of the ones embedded into a local one. We demonstrate that this impossibility is not related to any intrinsic difficulties of the density functional theory. The single-particle excitation spectra of many-electron systems are related to the eigenvalues of the corresponding KS equations. We show that the single-particle spectra do not generally coincide with the eigenvalues of both the KS and HF equations.