  We present quantum Monte Carlo calculations for various reaction pathways of
H$_2$ with Si(001), using large model clusters of the surface. We obtain
reaction energies and energy barriers noticeably higher than those from
approximate exchange-correlation functionals. In improvement over previous
studies, our adsorption barriers closely agree with experimental data. For
desorption, the calculations give barriers for conventional pathways in excess
of the presently accepted experimental value, and pinpoint the role of coverage
effects and desorption from steps.
