Van der Waals coefficients for alkali metal clusters and their size dependence

In this paper we employ the hydrodynamic formulation of time-dependent density functional theory to obtain the van der Waals coefficients C-6 and C-8 of alkali metal clusters of various sizes including very large clusters. Such calculations become computation ally very demanding in the orbital-based Kohn-Sham formalism, but are quite simple in the hydrodynamic approach. We show that for interactions between the clusters of the same sizes, C-6 and C-8 scale as the sixth and the eighth power of the cluster radius, respectively, and approach their classically predicted values for the large size clusters.