  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 D_B
step, which is known to be stable on the clean surface, to remain stable on
partially hydrogen-covered 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 >sim 0.1 eV. A surface with rebonded single
atomic height S_A and S_B 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 H_2 adsorption experiments on vicinal
Si surfaces by Raschke and Hoefer described in the preceding paper.
