Structure and binding in crystals of cage-like molecules: hexamine and platonic hydrocarbons

In this paper, we show that first-principle calculations using a van der Waals density functional (vdW-DF), [Phys. Rev. Lett. $\mathbf{92}$, 246401 (2004)] permits determination of molecular crystal structure. We study the crystal structures of hexamine and the platonic hydrocarbons (cubane and dodecahedrane). The calculated lattice parameters and cohesion energy agree well with experiments. Further, we examine the asymptotic accounts of the van der Waals forces by comparing full vdW-DF with asymptotic atom-based pair potentials extracted from vdW-DF. The character of the binding differ in the two cases, with vdW-DF giving a significant enhancement at intermediate and relevant binding separations. We analyze consequences of this result for methods such as DFT-D, and question DFT-D's transferability over the full range of separations.