Communication: Non-additivity of van der Waals interactions between nanostructures.

Due to size-dependent non-additivity, the van der Waals interaction (vdW) between nanostructures remains elusive. Here we first develop a model dynamic multipole polarizability for an inhomogeneous system that allows for a cavity. The model recovers the exact zero- and high-frequency limits and respects the paradigms of condensed matter physics (slowly varying density) and quantum chemistry (one- and two-electron densities). We find that the model can generate accurate vdW coefficients for both spherical and non-spherical clusters, with an overall mean absolute relative error of 4%, without any fitting. Based on this model, we study the non-additivity of vdW interactions. We find that there is strong non-additivity of vdW interactions between nanostructures, arising from electron delocalization, inequivalent contributions of atoms, and non-additive many-body interactions. Furthermore, we find that the non-additivity can have increasing size dependence as well as decreasing size dependence with cluster size.