Surface energy and stress of lead (111) and (110) surfaces

First-principles calculations of the surface energy and stress tensor of the Pb (111) and (110) surfaces are presented. The (111) and (110) surface energies are found to be almost the same, in contrast to the results of other calculations, which do not include the three-dimensional character of the charge density in a self-consistent manner. A very large inward relaxation of the outermost atomic layer of the (110) surface is predicted, in agreement with recent experimental results. The origin of the surface energy and stress is understood in terms of the spillout of electronic charge at the surface. The jellium model is found to provide a rather poor description of the Pb surfaces, but a simple modification of the jellium model improves the agreement significantly.