The nonlocal exchange (Hartree-Fock approximation), as a crucial quantity in the correct description of the many-body problem, is gaining increasing attention in the field of electronic structures of solids. Because of the nonlocality, the numerical solution of the Hartree-Fock equation is very cumbersome and ab initio Hartree-Fock methods for solids are just now being developed. We suggest an efficient approximation scheme which yields the Fock matrix and the total energy as well as the band structure. Numerical results for diamond and silicon are presented.
von der Linden, W., Fulde, P., & Bohnen, K-P. (1986). Efficient approach to the ab initio Hartree-Fock problem of solids, with application to diamond and silicon. Physical review / E, 34(2), 1063. https://doi.org/10.1103/PhysRevB.34.1063