  The hydrogen phase diagram has a number of unusual features which are
generally well reproduced by density functional calculations. Unfortunately,
these calculations fail to provide good physical insights into why those
features occur. In this paper, we parameterize a model potential for molecular
hydrogen which permits long and large simulations. The model shows excellent
reproduction of the phase diagram, including the broken-symmetry Phase II, an
efficiently-packed phase III and the maximum in the melt curve. It also gives
an excellent reproduction of the vibrational frequencies, including the maximum
in the vibrational frequency $\nu(P)$ and negative thermal expansion. By
detailed study of lengthy molecular dynamics, we give intuitive explanations
for observed and calculated properties. All solid structures approximate to
hexagonal close packed, with symmetry broken by molecular orientation. At high
pressure, Phase I shows significant short-ranged correlations between molecular
orientations. The turnover in Raman frequency is due to increased coupling
between neighboring molecules, rather than weakening of the bond. The liquid is
denser than the close-packed solid because, at molecular separations below
2.3\AA, the favoured relative orientation switches from
quadrupole-energy-minimising to steric-repulsion-minimising. The latter allows
molecules to get closer together, without atoms getting closer but this cannot
be achieved within the constraints of a close-packed layer.
