Density-functional approach to second-harmonic generation at metal surfaces

Abstract

Using density-functional theory we have determined the longitudinal second-harmonic response of various simple-metal surfaces in the limit of small frequencies. The metal is described by the semi-infinite jellium model and the electron distributions in the absence and in the presence of the external field are calculated self-consistently using the local-density approximation. Previous theoretical estimates of the normal component of the surface current density were based on the free-electron or the hydrodynamic model which do not adequately describe the detailed behavior of the electronic density in the vicinity of the surface. We find that, at low frequencies, the longitudinal surface current is proportional to the static second-order polarization whose integrated weight is given by the first moment of the second-order induced density. The centroid of the second-order polarization lies about 0.5 Bohr radii farther away from the positive background edge than the static image plane. Its integrated weight is 1–2 orders of magnitude larger than in the hydrodynamic model. Correspondingly, the a parameter, which had been introduced by Rudnick and Stern as a measure of the longitudinal second-harmonic response, is also significantly larger than its hydrodynamic value.