The formation of molecular hydrogen from the reaction of an ideal Si(001) (2x1) monohydride surface with gas-phase atomic hydrogen is simulated using classical trajectory calculations on an empirical potential energy surface. Apart from a direct Eley-Rideal reaction, reactions mediated by a "hot precursor" and induced desorption of homonuclear molecules are observed. For a reaction between light hydrogen and deuterium, the reactive cross section is large, similar to 25 Angstrom(2), and the reaction product is mainly HD, with a few percent admixture of homonuclear hydrogen molecules. About 0.8 eV of the exothermicity of the reaction end up as kinetic energy of the molecules, while 0.6 eV and 0.3 eV are found in vibration and rotation, respectively, Exchanging the isotope offered in the gas-phase and in the adsorbate has a small effect on the cross section and internal energy distribution. Details of the energy distribution could help to distinguish between the different reaction mechanisms. On the basis of the calculations, several dynamical features are predicted that could be tested experimentally.