Surface energy of a bounded electron gas: Analysis of the accuracy of the local-density approximation via ab initio self-consistent-field calculations

We report an ab initio evaluation of the surface energy of a simple metal, performed via a coupling-constant integration over the dynamical density-response function. The rapid rate of change of the electron density at the surface is treated exactly. Long-range correlations are treated self-consistently in the random-phase approximation; short-range correlations are included in time-dependent local-density-functional theory. Our results provide a numerical measure of the error introduced by the usual local-density approximation; this error is found to be small.