Metal surface properties in the linear potential approximation

Jellium metal surface properties including the dipole barrier, work function, and surface energy are obtained in the linear-potential approximation to the effective potential at the surface. The metal surface position and field strength are determined, respectively, by the requirement of overall charge neutrality and the constraint set on the electrostatic potential by the Budd-Vannimenus theorem. The surface energies are obtained both within the local density approximation and by application of a sum rule due to Vannimenus and Budd, and the two methods compared. The calculations are primarily analytic and all properties, with the exception of the exchange-correlation energy, are given in terms of universal functions of the field strength. The effects of correlation on the various properties are studied by employing three different approximations for the correlation energy per particle. The results obtained employing the Wigner expression for the correlation energy closely approximate those of Lang and Kohn. The use of different correlation functions, however, leads to only small differences in the results for the dipole barrier, work function, and the exchange-correlation contribution to the energy, but the results for the total surface energy are significantly different.