Trends of the surface relaxations, surface energies, and work functions of the 4<i>d</i>transition metals

Density-functional-theory calculations of the surface energies, surface relaxations, and work functions for a number of low-index surfaces of the 4d transition metals from Y to Ag are presented. The calculations were done for seven-layer slabs using the full-potential linear-muffin-tin-orbital method. Agreement with experimentally obtained results is very good for the cases where experimental data are available. Roughly parabolic behavior is found for the top-layer relaxation and the surface energy across the series. The study of trends makes it possible to extract the relevance of different models and to interpret the results within a simple physical picture. The trend in top-layer relaxation can be understood in a model that combines the effects of the inward electrostatic force due to Smoluchowski smoothing with the directed forces due to the localized d bonds. The calculated surface energies can be explained by a bond-cutting model, but only if the change of the bond strength with coordination number is taken into account. We find that popular models that relate the surface energy to quantities such as the cohesive energy are flawed because their estimate of the surface energy erroneously includes contributions of the free-atom spin polarization and orbital structure. Several predictions of the surface dependence of work functions, surface energies, and surface relaxations are given.