Calculation of van der Walls coefficients of alkali metal clusters by hydrodynamic approach to time-dependent density-functional theory

In this paper we employ the hydrodynamic formulation of time-dependent density functional theory to obtain the van der Waal coefficients $C_{6}$ and $C_{8}$ of alkali-metal clusters of various sizes including very large clusters. Such calculation becomes computationally very demanding in the orbital-based Kohn-Sham formalism, but quite simple in the hydrodynamic approach. We show that for interactions between the clusters of same sizes, $C_{6}$ and $C_{8}$ sale as the sixth and the eighth power of the cluster radius rsepectively, and approach the respective classically predicted values for the large size clusters.