Wave-vector- and frequency-dependent dielectric functions in the hartree-fock-slater approximation

The time-dependent Hartree-Fock-Slater equation was used to derive an expression for the wave-vector- and frequency-dependent dielectric function ϵ(q, ω). The effect of including the Xα exchange in the derivation is to subtract a term from the Coulomb contribution to the dielectric function in the random phase approximation. Self-consistent LCAO Hartree-Fock-Slater energy bands were used to compute (q, ω) at several points q along the [100], [110], and [111] axes in the first Brillouin zone. The real and imaginary parts of the dielectric function were computed independently. It was found that for wave vectors in the first Brillouin zone, there is little difference between the random phase and Hartree-Fock-Slater dielectric functions.