EXACT AND APPROXIMATE HARTREE-FOCK CALCULATIONS FOR EXTENDED METALLIC SYSTEMS

Starting out with the electron gas, we make a survey of the reasons for the singularity in the derivative of the orbital energy with respect to the wave number at the Fermi level for a realistic extended metallic system. Some properties of the occupation function are reviewed and it is pointed out that the direct reason for the singularity resides in a divergent lattice sum originating in the exchange part of the orbital energy. Numerical aspects are discussed, in particular with reference to the difficulty in detecting this singularity in actual computations.