  Identifying the atomic structure and properties of solid hydrogen under high
pressures is a long-standing problem of high-pressure physics with far-reaching
significance in planetary and materials science. Determining the
pressure-temperature phase diagram of hydrogen is challenging for experiment
and theory due to the extreme conditions and the required accuracy in the
quantum mechanical treatment of the constituent electrons and nuclei,
respectively. Here, we demonstrate explicitly that coupled cluster theory can
serve as a computationally efficient theoretical tool to predict solid hydrogen
phases with high accuracy. We present a first principles study of solid
hydrogen phases at pressures ranging from 100 to 450 GPa. The computed static
lattice enthalpies are compared to state-of-the-art diffusion Monte Carlo
results and density functional theory calculations. Our coupled cluster theory
results for the most stable phases including C2/c-24 and P21/c-24 are in good
agreement with those obtained using diffusion Monte Carlo, with the exception
of Cmca-4, which is predicted to be significantly less stable. We discuss the
scope of the employed methods and how they can contribute as efficient and
complementary theoretical tools to solve the long-standing puzzle of
understanding solid hydrogen phases at high pressures.
