  The newly developed "strongly constrained and appropriately normed" (SCAN)
meta-generalized-gradient approximation (meta-GGA) can generally improve over
the non-empirical Perdew-Burke-Ernzerhof (PBE) GGA not only for strong chemical
bonding, but also for the intermediate-range van der Waals (vdW) interaction.
However, the long-range vdW interaction is still missing. To remedy this, we
propose here pairing SCAN with the non-local correlation part from the rVV10
vdW density functional, with only two empirical parameters. The resulting
SCAN+rVV10 yields excellent geometric and energetic results not only for
molecular systems, but also for solids and layered-structure materials, as well
as the adsorption of benzene on coinage metal surfaces. Especially, SCAN+rVV10
outperforms all current methods with comparable computational efficiencies,
accurately reproducing the three most fundamental parameters---the inter-layer
binding energies, inter-, and intra-layer lattice constants---for 28
layered-structure materials. Hence, we have achieved with SCAN+rVV10 a
promising vdW density functional for general geometries, with minimal
empiricism.
