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The DFT/vdW-WF method, recently developed to include the Van der Waals interactions in Density Functional Theory (DFT) using the maximally localized Wannier functions, is applied to the study of the adsorption of rare-gas atoms (Ne, Ar, Kr, and Xe) on the Cu(111) and Pb(111) surfaces at three high-symmetry sites. We evaluate the equilibrium binding energies and distances and the induced work-function changes and dipole moments. We find that for Ne, Ar, and Kr on the Cu(111) surface the different adsorption configurations are characterized by very similar binding energies while the favored adsorption site for Xe on Cu(111) is on top of a Cu atom, in agreement with previous theoretical calculations and experimental findings and in common with other close-packed metal surfaces. Instead, the favored site is always the hollow one on the Pb(111) surface, which therefore represents an interesting system where …