METAL-SURFACE CORRELATION ENERGY FROM THE LIQUID DROP MODEL: A BACK-OF-THE-ENVELOPE ESTIMATE

The liquid drop model applied to the one-electron problem provides an elementary estimate of the correlation contribution to the surface and curvature energies of jellium, in terms of bulk electron density and bulk correlation energy. Within the random phase approximation (RPA), this estimate correctly predicts the size of the surface correlation energy, its strong dependence upon bulk density, and its weak dependence upon surface density profile. The local density approximation (LDA) to RPA predicts surface correlation energies that are far too small, as a consequence of the LDA self-interaction error. Possible implications beyond RPA are discussed. The power and limitations of the liquid drop expansion are illustrated by the example of one-electron jellium spheroids.