The reaction processes of an incident H atom with the H- or D-terminated Si(001)-(2 x 1) surface are theoretically investigated by using first-principles molecular dynamics simulations. Because the atomic hydrogen reaction process producing an H-2 (HD) molecule is exothermic, this reaction is considered to be observed in many cases. It is found that an H-2 (HD) molecule is produced in all of the cases treated in this study. The final kinetic energy of the resultant H-2 (HD) molecule is found to be mostly distributed to the vibrational energy, whereas the translational energy of the resultant molecule is estimated to be relatively low. In this reaction process, a resultant H-2 (HD) molecule is weakly trapped into a bound state site between two Si dimer rows on the surface followed by the desorption from the surface. This type of reaction processes corresponds to the direct abstraction of Eley-Rideal mechanism, which is in good agreement with the previous experimental results. (c) 2004 Elsevier B.V. All rights reserved.