Optimized effective potential for the extended Hubbard model

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 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 Hatree-Fock eigenvalues are interconnected by a scaling transformation (iii) The band-gap problem is attributed to the derivative discontinuity of the basic variable as a 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 KS eigenvalues. [S0163-1829(99)16535-4].