BAND-GAPS IN A GENERALIZED DENSITY-FUNCTIONAL THEORY

As has recently been shown by one of the authors (L.F.), the density-f unctional scheme of Hohenberg, Kohn, and Sham can consistently be exte nded to excited states [Physica B 172, 7 (1991)]. Within this generali zed density-functional theory it turns out that the energy for electro nic excitations across the gap of insulators and semiconductors, can b e expressed as the sum of the so-called Kohn-Sham gap and a correction that is usually of the same order of magnitude. (This correction prov es to agree up to first perturbational order with that obtained by God by et al. [Phys. Rev. B 37, 10 159 (1988)] within the so-called GW app roximation.) The present article reports refined calculations on the b and gaps of solid rare gases, alkali halides, diamond, and silicon. Th e results, are to some extent, still affected by the atomic-sphere app roximations which we have been employing, but show relatively fair agr eement with the experimental data: We also discuss Janak's theorem, th e insulator-metal transition under hydrostatic pressure, and the probl em of the Fermi surface in metals.