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

We examine the trends in the self-energy operators of Si, diamond, GaAs, and AlAs, and in their corresponding exchange-correlation potentials V_xc and their discontinuities Δ. 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_xc and so is caused by Δ. 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.