  Antiferromagnetic and charge ordered Hartree-Fock solutions of the one-band
Hubbard model with on-site and nearest-neighbor Coulomb repulsions are exactly
mapped onto an auxiliary local Kohn-Sham (KS) problem within a
density-functional theory. The mapping provides a new insight into the
interpretation of the KS equations. (i) With an appropriate choice of the basic
variable, there is a universal form of the KS potential, which is applicable
both for the antiferromagnetic and the charge ordered solutions. (ii) The
Kohn-Sham and Hartree-Fock eigenvalues are interconnected by a scaling
transformation. (iii) The band-gap problem is attributed to the derivative
discontinuity of the basic variable as the function of the electron number,
rather than a finite discontinuity of the KS potential. (iv) It is argued that
the conductivity gap and the energies of spin-wave excitations can be entirely
defined by the parameters of the ground state and the KS eigenvalues.
