On the intraatomic Coulomb and exchange energies in degenerate narrow bands

Abstract
In degenerate narrow bands studied in the tight binding limit, Wannier functions of partial bands cannot be used for computing intraatomic Coulomb interactions, because each of them involves several atomic states, on different sites. In the (Hartree-Fock) approximation using one determinant made of Bloch functions, the change in intraatomic Coulomb energy from free atoms to paramagnetic metal thus varies parabolically with the numbers of occupied atomic states, and not with the number of occupied states in each partial band. This justifies earlier treatments of the problem and corrects a recent work by Thalmeier and Falicov. The change in intraatomic exchange energy is also explicitly given