  The high-pressure II-III phase transition in solid hydrogen is investigated
using the random phase approximation and diffusion Monte Carlo. Good agreement
between the methods is found confirming that an accurate treatment of exchange
and correlation increases the transition pressure by more than 100 GPa with
respect to semilocal density functional approximations. Using an optimized
hybrid functional, we then reveal a low-symmetry structure for phase II
generated by an out-of-plane librational instability of the C2/c phase III
structure. This instability weakens the in-plane polarization of C2/c leading
to the well-known experimental signatures of the II-III phase transition such
as a sharp shift in vibron frequency, infrared activity and $c/a$ lattice
parameter ratio. Finally, we discuss the zero-point vibrational energy that
plays an important role in stabilizing phase III at lower pressures.
