  We study metallization of molecular hydrogen under pressure using exact
exchange (EXX) Kohn-Sham density-functional theory in order to avoid well-known
underestimates of band gaps associated with standard local-density or
generalized-gradient approximations. Compared with the standard methods, the
EXX approach leads to considerably (1 - 2 eV) higher gaps and significant
changes in the relative energies of different structures. Metallization is
predicted to occur at a density of >= 0.6 mol/cm^3 (corresponding to a pressure
of >= 400 GPa), consistent with all previous measurements.
