Density functional theory with nonlocal corrections is used together with cluster models to examine various pathways for H-2 desorption from the Si(100)2X1 surface. The barrier calculated for direct desorption of H-2 from the doubly-occupied dimer is appreciably larger than the experimentally observed activation energy at submonolayer coverages. We propose a mechanism in which surface defects are converted into dihydride (SiH2) species from which H-2 desorption occurs. The barrier calculated for this process (57 kcal/mol) is in excellent agreement with the measured activation energy. The barrier for defect migration is predicted to be only 14 kcal/mol, so that a single defect can account for the desorption of H, from a large number of monohydride sites. Single-point calculations for several of the optimized structures are carried out using the quadratic configuration interaction (QCI) method. The reaction energies and barrier heights calculated with the QCI and density functional theory (DFT) methods are in excellent agreement.