Dynamical correlation effects in the surface energy of metals

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Abstract
Starting from an exact expression for the total energy of an inhomogeneous system, we study the effect of correlations in the surface energy of a bounded electron gas. In contrast to previous work, the correlation problem is treated for two interacting half-solids as a function of separation, and the surface energy is obtained from the work required to increase the separation from zero to infinity. The analysis is based on a hydrodynamic description for electron gases of constant mean densities confined to half-spaces. It is shown that the correlation part in the surface energy reduces exactly to a previous expression in terms of zero-point energy shifts of dispersed-surface-plasmon modes. It is also shown that a similar treatment for an isolated metal half-space leads to a contribution which differs qualitatively from the surface energy for our model. By means of a separate argument it is demonstrated that the surface energy is relatively more sensitive to the presence of an electron screening length than to the details of surface-plasmon dispersion models.