Nonuniversality of the dispersion interaction: analytic benchmarks for van der Waals energy functionals

TL;DR

This paper demonstrates that the asymptotic behavior of dispersion forces varies with material properties, challenging the universal D^{-4} decay and providing analytical benchmarks for van der Waals energy functionals.

Contribution

It analytically evaluates the cross-correlation energy between layered materials, revealing non-universal decay behaviors and offering benchmarks for van der Waals functionals.

Findings

Graphene sheets exhibit a D^{-3} decay in dispersion energy.

Current approximations predict a D^{-4} decay, which is often inadequate.

The results apply broadly to nanotubes, nanowires, and layered metals.

Abstract

We highlight the non-universality of the asymptotic behavior of dispersion forces, such that a sum of inverse sixth power contributions is often inadequate. We analytically evaluate the cross-correlation energy Ec between two pi-conjugated layers separated by a large distance D within the electromagnetically non-retarded Random Phase Approximation, via a tight-binding model. For two perfect semimetallic graphene sheets at T=0K we find Ec = C D^{-3}, in contrast to the "insulating" D^{-4} dependence predicted by currently accepted approximations. We also treat the case where one graphene layer is replaced by a thin metal, a model relevant to the exfoliation of graphite. Our general considerations also apply to nanotubes, nanowires and layered metals.