A still open issue in many-body theory is the asymptotic behavior of the exchange-correlation energy and potential in the vacuum region of a metal surface. Here we report a numerical study of the position-dependent exchange-correlation energy for jel
lium slabs, as obtained by combining the formally exact adiabatic-connection-fluctuation-dissipation theorem with either time-dependent density-functional theory or an inhomogeneous Singwi-Tosi-Land-Sjolander approach. We find that the inclusion of correlation allows to obtain well-converged semi-infinite-jellium results (independent of the slab thickness) that exhibit an image-like asymptotic behavior close to the classical image potential $V_{im}(z)=-e^2/4z$.
We present a detailed study of the coupling-constant-averaged exchange-correlation hole density at a jellium surface, which we obtain in the random-phase approximation (RPA) of many-body theory. We report contour plots of the exchange-only and exchan
ge-correlation hole densities, the integration of the exchange-correlation hole density over the surface plane, the on-top correlation hole, and the energy density. We find that the on-top correlation hole is accurately described by local and semilocal density-functional approximations. We also find that for electrons that are localized far outside the surface the main part of the corresponding exchange-correlation hole is localized at the image plane.
We propose a simple dynamic exchange-correlation kernel of the uniform electron gas. We model the reduction of the electron-electron interaction due to short-range exchange-correlation effects by introducing a frequency-dependent error-function effec
tive interaction. By imposing the fulfillment of the compresibility and the third-frequency-moment sum rules, as well as the correct asymptotic behavior at large wave vectors, we find an accurate and simple dynamic exchange-correlation kernel that accurately reproduces the wave-vector analysis and the imaginary-frequency analysis of the correlation energy of the uniform electron gas.
