Trends in self-energy operators and their corresponding exchange-correlation potentials

Abstract

We examine the trends in the self-energy operators of Si, diamond, GaAs, and AlAs, and in their corresponding exchange-correlation potentials ${V}_{\mathrm{xc}}$ and their discontinuities \ensuremath{\Delta}. The potentials are calculated from the self-energies, thus avoiding use of a local-density approximation (LDA). In each case about 80% of the LDA band-gap error is also present for the true density-functional theory eigenvalue difference derived from ${V}_{\mathrm{xc}}$ and so is caused by \ensuremath{\Delta}. The self-energies themselves, calculated in the Hedin-Lundqvist GW approximation, reproduce the experimental quasiparticle energies accurately, and are also shown to be well modeled by a simple functional form in real space.