Validity Comparison Between Asymptotic Dispersion Energy Formalisms for Nanomaterials

The asymptotic dispersion attraction between anisotropic nanostructures has recently been shown, as a general proposition, to be anomalous in metallic and near-metallic cases. In particular it is not valid to use the common procedure of adding 1/R-6 energy contributions from multiple elements separated by distance R, in cases such as graphene, two-dimensional metals, and metallic nano-tubes. The most commonly used version of Lifshitz theory is also unsuitable because it is adapted only to thick-slab geometry. There is a considerable choice of analytic and semi-analytic formalisms that avoid this pitfall. Examples include (i) microscopic correlation energy calculations within the Random Phase Approximation (RPA) and related methods, (ii) several types of perturbation theory, and (iii) a summation of the zero-point or thermal energies of coupled plasmons. After a brief summary of the field, the present work provides a comparative study of the validity and utility of these methods.