First-principles study of low-index surfaces of lead

We report a density-functional theory study for Pb(111), Pb(100), and Pb(110) surfaces using ab initio pseudopotentials and a plane-wave basis set. Creating the pseudopotential with the 6s, 6p, and 6d states in the valence shell is found to yield good results for the bulk lattice constant, bulk modulus, and cohesive energy. Convergence of the surface energies with plane-wave cutoff, k-mesh, vacuum and slab thickness was carefully checked, as was the effect of the nonlinearity of the core-valence exchange-correlation interaction. Employing the local-density approximation of the exchange-correlation functional we obtain excellent agreement of the calculated surface energies and surface-energy anisotropies with recent experimental results. However, with the generalized gradient approximation the calculated surface energies are about 30% too low. For all three studied surfaces, the calculations give interlayer relaxations that are in reasonable agreement with low-energy electron diffraction analysis. The relaxations exhibit a damped oscillatory behavior away from the surface, which is typical for a metal surface.