Linear-scaling self-consistent implementation of the van der Waals density functional

An efficient linear-scaling approach to the van der Waals density functional in electronic-structure calculations is demonstrated. The nonlocal correlation potential needed in self-consistent calculations is derived in a practical form. This enables also an efficient determination of the Hellmann-Feynman forces on atoms. The numerical implementation employs adaptive quadrature grids in real space resulting in a fast and an accurate evaluation of the functional and the potential. The approach is incorporated in the atomic orbital code <emph type="5">SIESTA. The application of the method to the S22 set of noncovalently bonded molecules and comparison with the quantum chemistry data reveal an overall agreement but show that different exchange functionals should be used for different types of bonds.