Efficient Implementation of a van der Waals Density Functional: Application to Double-Wall Carbon Nanotubes

TLDR

The van der Waals density functional of Dion et al expresses the nonlocal correlation energy as a double spatial integral. The authors present an efficient implementation of this functional. The implementation factorizes the integration kernel and uses fast Fourier transforms to evaluate the self‑consistent potential, total energy, and atomic forces in N.

Abstract

We present an efficient implementation of the van der Waals density functional of Dion et al [Phys. Rev. Lett. 92, 246401 (2004)], which expresses the nonlocal correlation energy as a double spacial integral. We factorize the integration kernel and use fast Fourier transforms to evaluate the selfconsistent potential, total energy, and atomic forces, in N log(N) operations. The resulting overhead in total computational cost, over semilocal functionals, is very moderate for medium and large systems. We apply the method to calculate the binding energies and the barriers for relative translation and rotation in double-wall carbon nanotubes.