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A still open issue in many-body theory is the asymptotic behavior of theexchange-correlation energy and potential in the vacuum region of a metalsurface. Here we report a numerical study of the position-dependentexchange-correlation energy for jellium slabs, as obtained by combining theformally exact adiabatic-connection-fluctuation-dissipation theorem with eithertime-dependent density-functional theory or an inhomogeneousSingwi-Tosi-Land-Sj\"olander approach. We find that the inclusion ofcorrelation allows to obtain well-converged semi-infinite-jellium results(independent of the slab thickness) that exhibit an image-like asymptoticbehavior close to the classical image potential $V_{im}(z)=-e^2/4z$.

physical review. b, condensed matter and materials physics

Adiabatic-Connection-Fluctuation-Dissipation approach to the long-range  behavior of the exchange-correlation energy at metal surfaces: A numerical  study for jellium slabs