Surface relaxation and surface stress of 4d transition metals

Using the density functional theory formulated within the framework of the exact muffin-tin orbitals method, we present a systematic study of the top layer relaxation and surface stress of 4d transition metals. Our calculations predict layer contractions for most surfaces. We also find that the relaxations of the close packed surfaces decrease with increasing atomic number through the 4d series. We propose that the relaxation is mainly due to the reduction of the number of sp electrons in the surface layer relative to bulk. The surface stress is found to be very sensitive to the relaxation and, therefore, an accurate determination of the layer relaxation is necessary for obtaining reliable values for the surface stress. Comparing the top layer relaxations for the close packed surfaces, we see essential deviations between data derived in different ab initio calculations. At the same time, the overall trend for the present surface stress of 4d metals is in reasonable agreement with recent full-potential data.