  We investigate the van der Waals interactions in solid molecular hydrogen
structures. We calculate enthalpy and the Gibbs free energy to obtain zero and
finite temperature phase diagrams, respectively. We employ density functional
theory (DFT) to calculate the electronic structure and Density functional
perturbation theory (DFPT) with van der Waals (vdW) functionals to obtain
phonon spectra. We focus on the solid molecular $C2/c$, $Cmca$-12, $P6_3/m$,
$Cmca$, and $Pbcn$ structures within the pressure range of 200 $<$ P $<$ 450
GPa. We propose two structures of the $C2/c$ and $Pbcn$ for phase III which are
stabilized within different pressure range above 200 GPa. We find that vdW
functionals have a big effect on vibrations and finite-temperature phase
stability, however, different vdW functionals have different effects. We
conclude that, in addition to the vdW interaction, a correct treatment of the
high charge gradient limit is essential. We show that the dependence of
molecular bond-lengths on exchange-correlation also has a considerable
influence on the calculated metallization pressure, introducing errors of up to
100GPa.
