Quasiparticle energies in semiconductors: Self-energy correction to the local-density approximation

A model self-energy correction to the local-density approximation is derived from the GW approximation of the self-energy operator. Excitation energies calculated in diamond, Si, Ge, GaAs, and AlAs compare favorably with those obtained with the full GW approximation. Results for GaP are close to experimental data. It is shown that the model consists of a ``scissor'' operator and additional nonrigid corrections.