Do 1-dimensional metals prefer to form even-numbered van der Waals clusters ?

TL;DR

This paper investigates whether one-dimensional metallic strands prefer even-numbered clusters due to van der Waals interactions, using non-perturbative analysis to challenge previous conjectures about odd-numbered bundle stability.

Contribution

The study provides a non-perturbative analysis showing that odd-numbered strand bundles can be energetically favored, countering earlier perturbative predictions of even-numbered preferences.

Findings

6-strand analysis shows 3+3 bundles are more stable than 2+2+2 bundles

Non-perturbative results contradict earlier perturbative predictions

Discussion of multi-strand contributions beyond pairwise interactions

Abstract

Parallel quasi-one-dimensional metals are known to experience strong dispersion (van der Waals, vdW) interactions that fall off unusually slowly with separation between the metals. Examples include nanotube brushes, nano-wire arrays, and also common biological structures. In a many-stranded bundle, there are potentially strong multi-strand vdW interactions that go beyond a simple sum of negative (attractive) pairwise inter-strand energies. Perturbative analysis showed that these contributions alternate in sign, with the odd (triplet, quintuplet, ...) terms being positive (repulsive). The triplet case leds to the intriguing speculation that these strands may prefer to coalesce into even-numbered bundles, which could have implications for the formation kinetics of DNA, for example. Here we use a non-perturbative vdW energy analysis to show that this conjecture is not true in general. As our counter-example we consider 6 strands and show that 2 well-separated bundles of 3 strands have a more negative total vdW energy than 3 well-separated bundles of 2 strands ( i.e. an odd-number preference). We also discuss a bundle of 6 strands and explore the relative contributions beyond pairwise interactions.