Metal surface energies in the infinite and step-potential approximations

Jellium-metal surface energies for the infinite and finite step-potential barrier models have been obtained both by application of the Vannimenus-Budd theorem and by the determination of the individual components of the energy within the local exchange-correlation approximation. These two different methods for obtaining surface energies are then compared in light of their dependence on different physical properties. The barrier height in the step model is determined in each case either by the requirement of self-consistency of the surface dipole barrier or by application of the Budd-Vannimenus theorem, the metal surface position being fixed by the charge neutrality condition. An analytic expression for the derivative of the surface energy with respect to the Wigner-Seitz radius is also derived for the infinite-barrier model by use of the Vannimenus-Budd theorem. Finally a variational calculation of the surface energy within the local-density approximation is performed for the step model, the results closely approximating those of Lang and Kohn for medium and low densities.