  We derive the exchange-correlation potential corresponding to the nonlocal
van der Waals density functional [M. Dion, H. Rydberg, E. Schroder, D. C.
Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)]. We use this
potential for a self-consistent calculation of the ground state properties of a
number of van der Waals complexes as well as crystalline silicon. For the
latter, where little or no van der Waals interaction is expected, we find that
the results are mostly determined by semilocal exchange and correlation as in
standard generalized gradient approximations (GGA), with the fully nonlocal
term giving little effect. On the other hand, our results for the van der Waals
complexes show that the self-consistency has little effect at equilibrium
separations. This finding validates previous calculations with the same
functional that treated the fully nonlocal term as a post GGA perturbation. A
comparison of our results with wave-function calculations demonstrates the
usefulness of our approach. The exchange-correlation potential also allows us
to calculate Hellmann-Feynman forces, hence providing the means for efficient
geometry relaxations as well as unleashing the potential use of other standard
techniques that depend on the self-consistent charge distribution. The nature
of the van der Waals bond is discussed in terms of the self-consistent bonding
charge.
