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…