The interaction of a point charge with an aluminium (111) surface

Abstract

The self-consistent response of an Al(111) surface to the external potential of a negative point charge of 1e − is calculated, as a function of the position of the external charge. The metal atoms are represented by norm-conserving Pseudopotentials on a periodically repeated slab of three atomic planes separated by five atomic layers of vacuum, with twelve atoms per unit cell. Comparison of the energy is made with two classical models: (a) the classical continuum model (CCM) of a metal, in which a surface is characterised by the position of the image plane, and (b) a discrete classical model (DCM), in which the atoms are treated as polarisable point charges. The CCM gives an accurate description of the interaction energy when the charge is more than about 2.5 Å from the surface atomic layer. At closer approach a strong corrugation appears in the interaction energy, which becomes lower over atom sites than hollow sites. The image plane position with the CCM, fitted to the self-consistent calculations, is situated 0.15 Å outside the geometrical surface (jellium edge). Separate calculations with an external charge of 1 2 e show the significance of non-linear response; with this weaker external charge, the effective image plane is 0.29 Å outside the geometrical surface and the non-linear effect on the energy is relatively small. The interaction energy even at small distances is well described by the DCM, which correctly predicts the site dependence of the image interaction.