By performing constant pressure ab initio molecular dynamics simulations we analyse the high pressure phases of molecular solid hydrogen. We use a gradient corrected LDA, and a freshly implemented efficient technique for Brillouin zone sampling. An extremely good k-point sampling turns out to be crucial for obtaining the correct ground state. Our constant pressure approach allows us to optimize simultaneously the ori-entational degrees of freedom, the lattice constants, and the space group. This can be done either by a local optimization tehcnique, or by running molecular dynamics (MD) trajectories. The MD allows for the system to undergo structural transformations spontaneously. In the lower pressure, namely for the broken symmetry phase (BSP or phase II), we find a quadrupolar orthorhombic structure, of Pca21 symmetry. By means of an MD investigation, we find, at higher pressures, a slightly distorted orthorhombic structure of Cmc21 symmetry. This structure cannot be straightforwardly identified with the H-A phase (or phase III) because: 1) it is metallic, and 2) the Raman vibron discontinuity would be far too large compared to experiment. In fact, we argue that this phase is the first metallic molecular phase of hydrogen. Metallization would happen then, not via a band-overlap mechanism, but due to a structural transformation. By comparing total enthalpies, we also give suggestions for the structure of phase III.