Van der Waals density functionals applied to solids

The van der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)] is a promising approach for including dispersion in approximate density functional theory exchange-correlation functionals. Indeed, an improved description of systems held by dispersion forces has been demonstrated in the literature. However, despite many applications, standard general tests on a broad range of materials are lacking. Here we calculate the lattice constants, bulk moduli, and atomization energies for a range of solids using the original vdW-DF and several of its offspring. We find that the original vdW-DF overestimates lattice constants in a similar manner to how it overestimates binding distances for gas phase dimers. However, some of the modified vdW functionals lead to average errors which are similar to those of PBE or better. Likewise, atomization energies that are slightly better than from PBE are obtained from the modified vdW-DFs. Although the tests reported here are for "hard" solids, not normally materials for which dispersion forces are thought to be important, we find a systematic improvement in cohesive properties for the alkali metals and alkali halides when non-local correlations are accounted for.