Dielectric scaling of the self-energy scissor operator in semiconductors and insulators

The self-energy correction to local-density-functional theory energy gaps of insulators can be approximated as a large, constant energy shift (the scissor operator) of unoccupied bands relative to occupied bands, modulated by smaller wave-vector- and energy-dependent components. A rule for estimating the scissor correction is reported that allows for an approximate yet reasonably accurate correction to density-functional gaps. The validity of the proposed correction is demonstated for a large set of insulators.