Size And Density Dependences Of The Screening Effect In Metal Clusters

We employ a jellium sphere as a model for a metal cluster and calculate the change in the electronic states when an extra positive point charge is introduced at its center, by solving the Kohn–Sham equation in the local-density approximation and in the local-spin-density approximation with the self-interaction correction, and by solving the Hartree–Fock equation. The screening charge density around the extra charge is estimated by subtracting the charge induced near the cluster surface from the total induced charge density. It is found that, even for small clusters with the number of atomsN=20, 40, and 58, the screening effect is similar to that in the bulk jellium and that the screening charge distributions for larger clusters withN=92almost coincide with that in the bulk. The density dependence of the screening charge is also investigated by calculating the screening charge forrs=3.0, 4.0, and 5.0. It is shown that the period of oscillation of these screening charge distributions can almost be scaled byrsand it is close to that of the Friedel oscillation. The results obtained by three methods are compared with special attention to the effect of the self-interaction.