BAND-GAPS IN A GENERALIZED DENSITY-FUNCTIONAL THEORY

As has recently been shown by one of the authors (L.F.), the density-functional scheme of Hohenberg, Kohn, and Sham can consistently be extended to excited states [Physica B 172, 7 (1991)]. Within this generalized density-functional theory it turns out that the energy for electronic excitations across the gap of insulators and semiconductors, can be 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 proves to agree up to first perturbational order with that obtained by Godby et al. [Phys. Rev. B 37, 10 159 (1988)] within the so-called GW approximation.) The present article reports refined calculations on the band gaps of solid rare gases, alkali halides, diamond, and silicon. The results, are to some extent, still affected by the atomic-sphere approximations which we have been employing, but show relatively fair agreement with the experimental data: We also discuss Janak's theorem, the insulator-metal transition under hydrostatic pressure, and the problem of the Fermi surface in metals.