Screened-exchange plus Coulomb-hole correlated Hartree-Fock energy bands for LiF

Green's-function techniques have been used to derive screened-exchange plus Coulomb-hole correlation corrections to Hartree-Fock energy bands. These correlation corrections or energy shifts consist of a statically screened exchange term which is state dependent, and a Coulomb-hole term which is constant in our diagonal approximation for the screening (dielectric) function. These energy shifts raise the occupied bands and lower the conduction bands with a resulting decrease in energy differences. The calculation was done for LiF at general points in the first zone using linear-combination-of-atomic-orbitals Hartree-Fock energy bands and the Penn-model dielectric function. A change in.the band gap at $\Gamma$ of 5.0 eV was obtained compared with the experimental value of 9.3 eV. The calculation was also done using the random-phase-approximation (RPA) dielectric function and it was found that the diagonal part of the RPA gives less than half of the correlation obtained with the Penn model.