  We study the structural and electronic properties of phase III of solid
hydrogen using accurate many-electron theories and compare to state-of-the-art
experimental findings. The atomic structures of phase III modelled by C2/c-24
crystals are fully optimized on the level of second-order perturbation theory,
demonstrating that previously employed structures optimized on the level of
approximate density functionals exhibit errors in the H$_2$ bond lengths that
cause significant discrepancies in the computed quasi particle band gaps and
vibrational frequencies compared to experiment. Using the newly optimized
atomic structures, we study the band gap closure and change in vibrational
frequencies as a function of pressure. Our findings are in good agreement with
recent experimental observations and may prove useful in resolving
long-standing discrepancies between experimental estimates of metallization
pressures possibly caused by disagreeing pressure calibrations.
