We have extended Sham's work to derive the density-functional-theory

The conventional quantum-mechanical definition of the correlation energy of an interacting inhomogeneous electron gas differs from the Kohn-Sham density-functional-theory definition, the latter being a mathematical artifact. In this paper, we estimate the correlation energy for the inhomogeneous electron gas at jellium metal surfaces within the rubric of density-functional theory. The accuracy of these estimates is founded on the use of physically realistic densities, the application of the variational principle for the energy, and the assumption that the exchange-correlation-energy functional of the density is approximated accurately by the wave-vector-analysis method. These are the first realistic estimates of this property, with the kinetic, electrostatic, and nonlocal exchange-energy contributions being determined exactly. In contrast to the previously accepted conclusion that for surfaces correlation effects are as significant as exchange, our results indicate the ratio of these energies to lie between 34'Fo and 97% over the metallic density range, the smaller ratios corresponding to the higher density metals as one might intuitively expect to be the case. We also demonstrate for these realistic metal surface densities the usually assumed cancellation of errors in the local-density approximation for exchange and correlation taken separately. Furthermore we show that the density profiles at surfaces would have to be unphysically slowly varying for the correlation-energy gradient-expansion approximation to converge. This latter fact is substantiated by consideration of convergence conditions which are shown not to be satisfied. Finally, we also examine a modified gradient-expansion approximation due to Langreth and Mehl and show it to be very accurate. Consequently, these results have enabled us to study the "exact" surface correlation-energy density as a function of the density profile, and helped in understanding better the failure of both the localdensity and gradient-expansion approximations for this property.

No abstract