Wave-vector decomposition of the exchange and correlation contributions to a metallic surface energy

We decompose the lowest-order nonlocal corrections to the local-density approximation to the exchange and correlation component of the metallic surface energy in terms of its wave-vector components. Comparison with the full exchange shows significant improvement over the local-density form. An interpolation between the surface-plasmon-dominated small-wave-vector contributions and the nonlocal correction for large $q$ is suggested, and some of the difficulties inherent in this method are discussed.