  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.
