Origin of the size-dependence of the equilibrium van der Waals binding between nanostructures

TL;DR

This paper investigates how the van der Waals binding energy between nanostructures depends on their size, revealing surprising size-independence in certain spherical nanoclusters and strong size dependence in low-dimensional systems.

Contribution

It provides a detailed analysis of the size dependence of vdW interactions treating nanostructures as whole objects, not collections of atoms, and considers the interplay of vdW coefficients and distances.

Findings

vdW energy can be size-independent for quasi-spherical nanoclusters

Low-dimensional systems show strong size dependence in vdW interactions

Size dependence varies significantly between different nanostructure geometries

Abstract

Nanostructures can be bound together at equilibrium by the van der Waals (vdW) effect, a small but ubiquitous many-body attraction that presents challenges to density functional theory. How does the binding energy depend upon the size or number of atoms in one of a pair of identical nanostructures? To answer this question, we treat each nanostructure properly as a whole object, not as a collection of atoms. Our calculations start from an accurate static dipole polarizability for each considered nanostructure, and an accurate equilibrium center-to-center distance for the pair (the latter from experiment, or from the vdW-DF-cx functional). We consider the competition in each term $-C_{2k}/d^{2k}$ ($k=3, 4, 5$) of the long-range vdW series for the interaction energy, between the size dependence of the vdW coefficient $C_{2k}$ and that of the $2k$-th power of the center-to-center distance $d$. The damping of these vdW terms can be negligible, but in any case it does not affect the size dependence for a given term in the absence of non-vdW binding. To our surprise, the vdW energy can be size-independent for quasi-spherical nanoclusters bound to one another by vdW interaction, even with strong nonadditivity of the vdW coefficient, as demonstrated for fullerenes. We also show that, for low-dimensional systems, the vdW interaction yields the strongest size-dependence, in stark contrast to that of fullerenes. We illustrate this with parallel planar polycyclic aromatic hydrocarbons. Other cases are between, as shown by sodium clusters.