  We examine the influence of the main approximations employed in
density-functional theory descriptions of the solid phase of molecular hydrogen
near dissociation. We consider the importance of nuclear quantum effects on
equilibrium properties and find that they strongly influence intramolecular
properties, such as bond fluctuations and stability. We demonstrate that the
combination of both thermal and quantum effects make a drastic change to the
predicted optical properties of the molecular solid, suggesting a limited value
to dynamical, e.g., finite-temperature, predictions based on classical ions and
static crystals. We also consider the influence of the chosen
exchange--correlation density functional on the predicted properties of
hydrogen, in particular, the pressure dependence of the band gap and the
zero-point energy. Finally, we use our simulations to make an assessment of the
accuracy of typically employed approximations to the calculation of the Gibbs
free energy of the solid, namely the quasi-harmonic approximation for solids.
We find that, while the approximation is capable of producing free energies
with an accuracy of ~10 meV, this is not enough to make reliable predictions of
the phase diagram of hydrogen from first-principles due to the small free
energy differences seen between several potential structures for the solid;
direct free energy calculations for quantum protons are required in order to
make definite predictions.
