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A simple procedure to perform Hartree-Fock calculations in solids using extended basis functions is proposed. The method also applies when correlation is added with the self-consistent Coulomb-hole-plus-screened-exchange (COHSEX) scheme. Application to silicon in the pseudopotential approach yields excitation energies which agree with recent results by Hybertsen and Louie. We find that the simple diagonal COHSEX approximation does not provide satisfactory indirect excitation energies in silicon but is quite accurate for the direct ones.
Gygi et al. (Mon,) studied this question.