  The self consistent version of the density functional theory is presented,
which allows to calculate the ground state and dynamic properties of finite
multi-electron systems. An exact functional equation for the effective
interaction, from which one can construct the action functional, density
functional, the response functions, and excitation spectra of the considered
systems, is outlined. In the context of the density functional theory we
consider the single particle excitation spectra of electron systems and relate
the single particle spectrum to the eigenvalues of the corresponding Kohn-Sham
equations. We find that the single particle spectrum coincides neither with the
eigenvalues of the Kohn-Sham equations nor with those of the Hartree-Fock
equations.
