Simple and accurate statistical calculation of jellium-metal surface properties

A simple and analytical statistical calculation of the surface properties of jellium metal is presented in order to demonstrate the applicability of such an approach to problems of greater complexity. In the assumed Kohn-Sham energy functional, the kinetic energy is approximated by its density-gradient series expansion including terms of $O\left({\nabla }^4\right)$ arising from nonlinear response, and exchange and correlation are treated within the local-density approximation. The trial density employed is a one-parameter analytical function originally proposed by Smoluchowski. The surface energies are determined by application of the variational principle for the energy, and the work functions are obtained for these energy-minimized densities by the displaced-profile change-in-self-consistent-field expression. The results thus determined are essentially exact when compared to the fully self-consistent calculations of Lang and Kohn. The inclusion of nonlocal exchange-correlation effects within this formalism together with its extension to real metals is also indicated.