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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 $ν(P)$ 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 2.3Å, 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.