The interaction of a point charge with a metal surface: theory and calculations for (111), (100) and (110) aluminium surfaces

The asymptotic form of the image interaction is derived for a classical external point charge at a distance z 1 outside a periodic metallic surface, generalizing to real metals the analytical result of Lang and Kohn (1973) for jellium. The centre of gravity z c of the induced charge coincides with the position of the image plane z 0 in the limit of linear response. However, whereas z c is shown to depend through non-linear response on the magnitude of the external charge q, z 0 is independent of q. We show that surface periodicity does not modulate z 0 , but adds to the image interaction a periodic component decaying exponentially with z. In addition, the long-ranged effect of non-linearity on the interaction energy is a term attractive to a positive external charge and proportional to q 3 /(z 1 -z 0 ) 4 . We report first-principles pseudopotential calculations of the interaction energy with three aluminium surfaces: (111), (100) and (110). A supercell geometry is used. A discrete classical model without adjustable parameters reproduces the effect of the surface periodicity on the image interaction at each of the three surfaces.