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

Abstract

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) [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 furthermore compare results of our ab initio calculations with 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 produce 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-DF. This observation suggests a framework for an efficient implementation of quantum-physical modeling of the CNT bundling in more general nanotube bundles, including nanotube yarn and rope structures.

Rings sliding on a honeycomb network: Adsorption contours, interactions, and assembly of benzene on Cu(111)

“…21,28 In many respect the present vdW-DF calculations are similar to those presented in Refs. [30][31][32][33]43, and 44. The physisorption system requires us to resolve very-small energy differences ͑e.g., the variation in adsorption energy with site͒ and to ensure accurate and well-converged evaluations of changes in the nonlocal correlation E c nl ͓n͔.…”

“…42 This term retains information about, for example, the kinetic-energy repulsion that adds to the surface corrugation. 43 Finally, we determine the total vdW-DF energy as the sum…”

“…͑1͒ involves a real-space integral, the evaluation of E c nl ͓n͔ depends slightly on the grid sampling because of the rapid variation in the kernel at small ⌶. 19,43 We employ a number of additional calculational steps to enhance accuracy and test the convergence in the evaluation of Eq. ͑1͒:…”

Role of van der Waals bonding in the layered oxideV2O5: First-principles density-functional calculations

“…Then n is used for evaluating the long-range correlation contribution arising from the vdW interactions, E c nl . Following the systematic procedure described in more detail in several other publications, 22,25,26 and summarized below, we combine the sc-GGA and nonlocal results to obtain E vdW-DF .…”

“…Unlike DFT-D, vdW-DF provides a framework which is well suited to include effects of image planes. 22 The DFT-D omission of image planes can result in inconsistencies of the description across a range of distances. 23 This effect could be important in materials such as V 2 O 5 where the corrugation is large, and where as a result both relatively small and larger distances contribute to the vdW interaction simultaneously.…”