The popular local-density approximation neglects long-range correlations which, in the presence of the rapid rate of change of the electron density at the surface, lead to observable effects. We evaluate the exchange-correlation potential ${\mathit{V}}_{\mathrm{xc}}$ for the electron gas-vacuum interface from the knowledge of the electron self-energy ${\mathrm{\Sigma }}_{\mathrm{xc}}$ in the GW approximation. The electron-electron correlations built into ${\mathrm{\Sigma }}_{\mathrm{xc}}$ automatically produce an imagelike surface barrier. Our result for ${\mathit{V}}_{\mathrm{xc}}$ is the basis of a nonlocal density-functional calculation of the electronic structure of Al(100) which yields a Rydberg series of image states from first principles.

• Received 1 October 1991

DOI:https://doi.org/10.1103/PhysRevLett.68.1359