Energies of curved metallic surfaces from the stabilized-jellium model

In the liquid-drop model, the total energy of a system is expanded as a sum of volume, surface, and curvature terms. We derive an expression for the curvature energy of a metal in terms of the electron-density profile for a planar surface, and show that the resulting values agree with the fits of calculated or measured total energies to the liquid-drop expansion. In particular, this expansion accurately describes the formation energies of microscopic voids (including monovacancies) in metals. In our calculations, the curvature energy is determined by the bulk density. It is nearly the same for restricted trial density profiles as for self-consistent Kohn-Sham profiles, for the fourth-order gradient expansion as for the exact kinetic energy, and for jellium as for stabilized jellium. We also report Kohn-Sham results for the surface energy and work function. The stabilized-jellium model, while retaining the simplicity and nonempirical character of jellium, gives a significantly more realistic description of the simple metals, especially those with high bulk densities.