Exchange-correlation energy of a metallic surface: Wave-vector analysis

The exchange-correlation energy of a jellium metal surface is analyzed in terms of the wavelength of the fluctuations that contribute to it, using a three-dimensional scheme different from that used by other authors. It is shown that with this scheme there exists an exact limiting form at long wavelengths which includes all many-body correlations and which is independent of the surface density profile. The local-density approximation is formulated as a function of wavelength, and it is shown to be exact at short wavelength. The interpolation scheme between these limits, which was discussed previously, is formulated and checked more completely and used to calculate surface energies.