Relaxed atomic geometries and chemisorption energies have been calculated for the dissociative adsorption of molecular hydrogen on vicinal Si(001) surfaces. We employ density-functional theory, together with a pseudopotential for Si, and apply the generalized gradient approximation by Perdew and Wang to the exchange-correlation functional. We find the double-atomic-height rebonded DB step, which is known to be stable on the clean surface, to remain stable on partially hydrogencovered surfaces. The H atoms preferentially bind to the Si atoms at the rebonded step edge, with a chemisorption energy difference with respect to the terrace sites of > ∼ 0.1 eV. A surface with rebonded single atomic height SA and SB steps gives very similar results. The interaction between H-Si-Si-H mono-hydride units is shown to be unimportant for the calculation of the step-edge hydrogen-occupation. Our results confirm the interpretation and results of the recent H2 adsorption experiments on vicinal Si surfaces by Raschke and Höfer described in the preceding paper.