Towards a more accurate van der Waals density functional

The van der Waals density functional (vdW-DF) of Dion {\it et al}. [1] has attracted considerable attention, because the functional is able to describe intra- and intermolecular bondings with different natures, e.g., covalent and van der Waals bondings in a seamless fashion within the framework of density functional theory. However, the accuracy of the functional is yet to be improved for the applications to various systems. Here I propose an exchange functional for the second version of vdW-DF [2], which improves the accuracy of vdW-DF. The keys in the improved exchange are the matching to the gradient expansion approximation in the slowly varying limit and the large density gradient behavior set in Becke's exchange (B86b)[3]. Systematic study on gas phase molecules, solids, and molecular adsorption demonstrates the applicability of the proposed functional to a wide variety of materials. [1] M.~Dion {\it et al}., Phys. Rev Lett. {\bf 92}, 246401 (2004). [2] K.~Lee {\it et al}., Phys. Rev. B {\bf 82}, 081101 (R) (2010). [3] A.~D.~Becke, J. Chem. Phys. {\bf 85}, 7184 (1986).