  We study the electronic excitation spectra in solid molecular hydrogen (phase
I) at ambient temperature and 5-90 GPa pressures using Quantum Monte Carlo
methods and Many-Body Perturbation Theory. In this range, the system changes
from a wide gap molecular insulator to a semiconductor, altering the nature of
the excitations from localized to delocalized. Computed gaps and spectra agree
with experiments, proving the ability to predict accurately band gaps of
many-body systems in presence of nuclear quantum and thermal effects.
