  A recent paper [J. Chem. Phys. 132, 134705 (2010)] illustrated the potential
of the van der Waals density functional (vdW-DF) method [Phys. Rev. Lett. 92,
246401 (2004)] for efficient first-principle accounts of structure and cohesion
in molecular crystals. Since then, modifications of the original vdW-DF version
(identified as vdW-DF1) has been proposed, and there is also a new version
called vdW-DF2 [ArXiv 1003.5255], within the vdW-DF framework. Here we
investigate the performance and nature of the modifications and the new version
for the binding of a set of simple molecular crystals: hexamine, dodecahedrane,
C60, and graphite. These extended systems provide benchmarks for computational
methods dealing with sparse matter. We show that a previously documented
enhancement of non-local correlations of vdW-DF1 over an asymptotic atom-based
account close to and a few A, beyond binding separation persists in vdW-DF2.
The calculation and analysis of the binding in molecular crystals requires
appropriate computational tools. In this paper, we also present details on our
real-space parallel implementation of the vdW-DF correlation and on the method
used to generate asymptotic atom-based pair potentials based on vdW-DF.
