Density-functional theory of the band gap

There is a correction to the energy band gap obtained from the eigenvalues of the exact one-electron density-functional equation due to the discontinuity in the exchange-correlation potential in an insulator. This correction is expressed in terms of the electron self-energy. If the local-density approximation is used for the exchange-correlation potential, then an additional correction to the gap is needed. Both terms are evaluated for a two-plane-wave model with exchange only. Empirical evidence is also given for the discontinuity.