A new analysis of image charge theory

Abstract

Ab initio cluster model wavefunctions for Al and Pt surfaces have been used to investigate the response of metal surfaces to the presence of point charges above the surface. The dipole moment curves, μ( z), as a function of the distance of the point charge above the surface have been used to characterize the metallic response. There are three regions where the behavior of μ( z) is different. In the region where z>∼15–20 bohr, the asymptotic behavior given by image charge theory holds. In the region where z<∼4 bohr, the well known failure of the asymptotic formula is found; this reflects the fact that the point charge penetrates the metal charge density. In an intermediate region, ∼4< z<∼15–20 bohr, a new and unexpected behavior has been found. The magnitude of the slope of the dipole moment curve is significantly larger than the value of the point charge! In this region the metallic response is strongly dependent on the distance of the point charge from the metal surface. Further, the magnitude of the slope is quite different for positive and negative point charges indicating that the metallic response has important contributions from non-linear terms.