Theory of Strongly Correlated Electron Systems. II.Intersite Coulomb Interaction and the Approximation of Renormalized Fermions in Total Energy Calculations

The strong-coupling perturbation theory (SCPT) for correlated electron systems is extended to the case of full Coulomb interaction. The Coulomb mechanism of the orbital polarization is discussed and attention is paid to the importance of spectral weight transfer between the localized and delocalized subsystems of electrons. A one-to-one correspondence between subsets of Feynman graphs of SCPT (which we name the approximation of renormalized Fermions (ARF)) and weak-coupling perturbation theory (WCPT) is established. The comparison of the Galitskii and Migdal expression for the total energy and the Sham equation (which connects the self-energy and the exchange-correlation potential in density functional theory) for WCPT with the ones for the systems with strong electron correlations is used for the formulation of a simple theory for extending the local density approximation to density functional theory (DFT) to include explicitly correlations. The extension requires the inclusion of the many-electron spectral weights in the definition of the charge density and the renormalization of the mixing and hopping matrix elements caused by many body effects.