van der Waals energy of a cluster near a metal surface

The van der Waals energy of a cluster formed by the atoms of a metallic solid is derived for clusters in the presence of a semi-infinite metal surface. The derivation is based on surface-plasmon model and independent potential model for the metal and cluster electrons, respectively. The calculations provide an expression for the interaction energy which is valid for all separations between the cluster and the metal surface. A significant feature of the derivation is that it includes the effect of dispersion of the surface plasmons. The inclusion allows us to examine the interaction energy when the cluster is sufficiently close to the metal surface and to show explicitly that at the surface the energy saturates to a finite value.