Nature and strength of bonding in a crystal of semiconducting nanotubes: van der Waals density functional calculations and analytical results

The dispersive interaction between nanotubes is investigated through ab initio theory calculations and in an analytical approximation. A van der Waals density functional (vdW-DF) [M. Dion et al., Phys. Rev. Lett. 92, 246401 (2004)] is used to determine and compare the binding of a pair of nanotubes as well as in a nanotube crystal. To analyze the interaction and determine the importance of morphology, we further compare results of our ab initio calculations to a simple analytical result,that we obtain for a pair of well-separated nanotubes. In contrast to traditional density functional theory calculations, the vdW-DF study predicts an intertube vdW bonding with a strength that is consistent with recent observations for the interlayer binding in graphitics. It also produces a nanotube wall-to-wall separation, which is in very good agreement with experiments. Moreover, we find that the vdW-DF result for the nanotube-crystal binding energy can be approximated by a sum of nanotube-pair interactions when these are calculated in vdW-DR This observation suggests a framework for an efficient implementation of quantum-physical modeling of the carbon nanotube bundling in more general nanotube bundles, including nanotube yarn and rope structures.