Retarded and nonretarded van der Waals interactions between a cluster and a second cluster or a conducting surface

TL;DR

This paper derives van der Waals interactions between clusters and surfaces in both retarded and nonretarded regimes, highlighting the importance of many-body effects and providing formulas for different separation distances.

Contribution

It presents a unified derivation of van der Waals interactions for clusters in both regimes, including many-body screening effects and corrections to pairwise additivity.

Findings

Interaction magnitude depends on static polarizability at large separations

Expressions for interaction coefficients are derived using a resonant frequency model

Many-body screening effects can significantly alter interaction strengths

Abstract

In some respects, a cluster consisting of many atoms may be regarded as a single large atom. Knowing the dielectric properties of such a cluster permits one to evaluate the form of the van der Waals (dispersion) interactions between two clusters or between one cluster and a surface. In this paper, we derive these interactions in two extreme opposite regimes of separation: fully retarded and nonretarded. In the fully retarded regime (very large separation), the magnitude of the interaction is determined by just the static polarizability of the cluster(s). In the nonretarded regime (small separation), we employ a single resonant frequency model of thecluster polarizability to derive expressions for the interactions' coefficients. Numerical examples are presented to demonstrate that many-body screening of these interactions can be significant. The results represent the corrections to the commonly used approximation of pairwise additivity of interatomic interactions.