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

The wave-vector analysis γ(K), whose integral gives the nonuniform part of the exchange-correlation energy, is studied for a planar metallic surface. It is shown (1) that for "exchange only" γ(K)→-0.009662/r_s³ a.u. as K→0 for the infinite barrier surface; (2) that this limit is universal—for all planar surfaces in an exchange-only approximation, γ approaches this same universal number; (3) how the limit above reverts to that previously derived by the authors [γ(K)∝|K| as K→0] when electron correlation is included. The method of wave-vector interpolation, which relies on the latter limit for the Coulomb-correlated surface, thus withstands recent questioning based on the "exchange-only" approximation. Finally, the probable small-K behavior of γ(K) for a system of neutral fermions is discussed.