Nonlocal Hartree-Fock Exchange in Narrow-Band Materials

Abstract

One computational problem of CO calculations in the mean-field approximation is connected with the convergence properties of the nonlocal HF exchange which gives rise to a cos(kj) dependence in matrix elements of the Fock operator. The asymptotic behavior of exchange interactions and relevant physical consequences of real-space truncation criteria have been analyzed in simple model solids [III.40–III.45]. Ukrainski investigated exchange phenomena in a one-orbital one-electron system and found a (−1)^jj⁻² decay of the exchange summation. Furthermore he pointed out that divergent energy gradients, see eq. (III.59), occur at the Fermi surface leading to vanishing density of states (DOS) distributions, N(E).