We have applied the open-system treatment, recently developed by the authors, to a simple adsorbate-metal surface model potential. The open-system treatment is found to give a quasi-diabatic representation where the adsorbate electronic states cross the metal ones in the manifold consisting of the Born-Oppenheimer potential energy curves of the whole system. On the obtained quasi-diabatic curves, one can effectively follow time propagation of a nuclear wave packet. The computed propagation has revealed that the formation of a metastable adsorbate leads to the coherent vibrational motion of the neutral adsorbate as well as the desorption induced by electronic transitions. (C) 2008 Elsevier B. V. All rights reserved.