Van der waals dispersion forces between dielectric nanoclusters

Various methods are evaluated for their ability to calculate accurate van der Waals (VDW) dispersion forces between nanoclusters. We compare results for spheres using several methods: the simple Hamaker two-body method, the Lifshitz (DLP) theory with the Derjaguin approximation, the Langbein result for spheres, and our "coupled dipole method" (CDM). The assumptions and shortcomings of each method are discussed. The CDM accounts for all n-body forces, does not assume a continuous and homogeneous dielectric function in each material, accounts for the discreteness of atoms in the particles, can be used for particles of arbitrary shape, and can exactly include the effects of various media. At present, the CDM does not account for retardation. It is shown that even for spheres, methods other than the CDM often give errors of 20% or more for VDW dispersion forces between typical dielectric materials. A related calculation for metals reveals an error in the Hamaker two-body result of nearly a factor of 2.