  Establishing the phase diagram of hydrogen is a major challenge for
experimental and theoretical physics. Experiment alone cannot establish the
atomic structure of solid hydrogen at high pressure, because hydrogen scatters
X-rays only weakly. Instead our understanding of the atomic structure is
largely based on density functional theory (DFT). By comparing Raman spectra
for low-energy structures found in DFT searches with experimental spectra,
candidate atomic structures have been identified for each experimentally
observed phase. Unfortunately, DFT predicts a metallic structure to be
energetically favoured at a broad range of pressures up to 400 GPa, where it is
known experimentally that hydrogen is nonmetallic. Here we show that more
advanced theoretical methods (diffusion quantum Monte Carlo calculations) find
the metallic structure to be uncompetitive, and predict a phase diagram in
reasonable agreement with experiment. This greatly strengthens the claim that
the candidate atomic structures accurately model the experimentally observed
phases.
