GENERALIZED KOHN-SHAM SCHEMES AND THE BAND-GAP PROBLEM

As an alternative to the standard Kohn-Sham procedure, other exact rea lizations of density-functional theory (generalized Kohn-Sham methods) are presented. The corresponding generalized Kohn-Sham eigenvalue gap s are shown to incorporate part of the discontinuity a,, of the exchan ge-correlation potential of standard Kohn-Sham theory. As an example, a generalized Kohn-Sham procedure splitting the exchange contribution to the total energy into a screened, nonlocal and a local density comp onent is considered. This method leads to band gaps far better than th ose of local-density approximation and to good structural properties f or the materials Si, Ge, GaAs, InP, and InSb.