The results of a quantum-mechanical study of vibrational relaxation of hydrogen adsorbed on a Si(100) surface with the multi-configurational time-dependent Hartree (MCTDH) method are presented. A two-dimensional subsystem is coupled non-linearly to a bath of harmonic oscillators (phonons of the Si bulk), and the relaxation of subsystem vibrations proceeds primarily via a two-phonon process. Characteristic times of the system evolution agree well with our previous perturbation theory study. The vibrational population decay is non-exponential, exhibiting pronounced recurrences due to finite bath size. The dependence of the lifetimes of the vibrational levels on the bath size and on the coupling details is investigated. (c) 2006 Elsevier B.V. All rights reserved.