Kohn-Sham exchange potential exact to first order in ρ(K→)/ρ0

Abstract

The Kohn-Sham exchange potential may be written, exact to first order in ρ(K→)/${\rho }_0$, $V_x^{\mathrm{KS}}$=-(3/2) (3/π${)}^{1/3}$ ${\rho }_0^{\mathrm{-}2/3}$ ${\mathcal{J}}_{\mathrm{K}\to }^{\mathcal{’}}$ρ(K→)F(K)$e^{i\mathrm{k}\to \cdot \mathrm{r}\to }$. We here evaluate the universal function F(K/$k_F$) for all K/$k_F$ and find large corrections to the local-density approximation which should result in much improved values for semiconductor energy gaps.