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

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. Summation over atom pairs fails to reproduce this behavior. 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 led 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 widely separated bundles of 3 strands have a more negative total vdW energy than 3 widely separated bundles of 2 strands (i.e. an odd-number preference). We also discuss a bundle of 6 strands and explore the relative importance of contributions beyond the sum of two-strand terms.