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

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 spatial integral. We factorize the integration kernel and use fast Fourier transforms to evaluate the self-consistent potential, total energy, and atomic forces, in O(NlogN) operations. The resulting overhead, for medium and large systems, is a small fraction of the total computational cost, representing a dramatic speedup over the O(N-2) evaluation of the double integral. This opens the realm of first-principles simulations to the large systems of interest in soft matter and biomolecular problems. We apply the method to calculate the binding energies and the barriers for relative translation and rotation in double-wall carbon nanotubes.