Correlated-basis-functions theory of metal surfaces

A new method for treating metal surfaces is presented which will complement the conventional density-functional theory. It makes use of the correlated-basis-functions approach, which has proven useful for treating liquid and solid helium, nuclear matter, and homogeneous and mildly inhomogeneous Coulomb systems. It is a variational theory that deals directly with the wave function—one that contains in a balanced way both single-particle elements and explicit many-particle correlation factors. The surface-energy expression does not require a density-gradient expansion. It does not draw information from independent work on the homogeneous electron liquid and is thus totally self-contained. Discrete ion-lattice effects are accounted for without the need to invoke a low-order perturbation theory. Systematic improvements are possible, either through the introduction of higher-order irreducible correlation factors or through a diagrammatic perturbation theory in the correlated representation. Most importantly, approximate many-particle wave functions for describing the ground-state and low-lying excitations are made available. They can be used for determining adsorption properties such as the substrate-mediated interaction between adatoms. In this paper we describe the theory in detail and report on numerical results obtained for the entire range of metals, $2\lesssim r_s\lesssim 6$. Our surface energies show slight improvement over those obtained with density-functional methods. Our work functions are not quite as good at small $r_s$; there the electron-density profiles display slightly higher peaks and longer tails. We discovered no new startling results and had not expected to do so. The main accomplishment is the establishment of a self-contained theory and a basis for future calculations considered impossible or difficult in the density-functional formalism. Discussions are carried out in that spirit.