Theory of Metal Surfaces: Charge Density and Surface Energy

TLDR

The paper first examines the jellium model of a metal surface and then calculates two corrections to the surface energy that arise when the positive background is replaced by a pseudopotential model of the ions. Using the theory of the inhomogeneous electron gas with local exchange and correlation energies, the authors obtain self‑consistent electron density distributions and compute two corrections—cleavage energy of a neutralized lattice and interaction energy between pseudopotentials and electrons. The results show a negative surface energy for rs ≤ 2.5, that the two corrections become essential for rs ≤ 4, and that the corrected surface energy agrees semiquantitatively with surface‑tension measurements for eight simple metals (≈25 % error) but disagrees for Pb.

Abstract

The first part of this paper deals with the jellium model of a metal surface. The theory of the inhomogeneous electron gas, with local exchange and correlation energies, is used. Self-consistent electron density distributions are obtained. The surface energy is found to be negative for high densities (${\mathcal{r}}_{s}\ensuremath{\le}2.5$). In the second part, two corrections to the surface energy are calculated which arise when the positive background model is replaced by a pseudopotential model of the ions. One correction is a cleavage energy of a classical neutralized lattice, the other an interaction energy of the pseudopotentials with the electrons. Both of these corrections are essential at higher densities (${\mathcal{r}}_{s}\ensuremath{\le}4$). The resulting surface energy is in semiquantitative agreement with surface-tension measurements for eight simple metals (Li, Na, K, Rb, Cs, Mg, Zn, Al), typical errors being about 25%. For Pb there is a serious disagreement.