  A cluster consisting of many atoms or molecules may be considered, in some
circustances, to be a single large molecule with a well defined polarizability.
Once the polarizability of such a cluster is known, one can evaluate certain
properties, e.g. the cluster's van der Waals interactions, using expressions
derived for molecules. In the present work, we evaluate the static
polarizability of a cluster using a microscopic method that is exact within the
linear and dipolar approximations. Numerical examples are presented for various
shapes and sizes of clusters composed of identical atoms, where the term "atom"
actually refers to a generic constituent, which could be any polarizable
entity. The results for the cluster's polarizabilities are compared with those
obtained by assuming simple additivity of the constituents' atomic
polarizabilities; in many cases, the difference is large, demonstrating the
inadequacy of the additivity approximation. Comparison is made (for symmetrical
geometries) with results obtained from continuum models of the polarizability.
Also, the surface effects due to the nonuniform local field near a surface or
edge are shown to be significant.
