Nonlocal Hartree-Fock Exchange in Narrow-Band Materials
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).
KeywordsFermi Correlation Exchange Matrix Element Relevant Physical Consequence Exchange Summation Intercell Interaction
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