The energy exchange between a D-2 molecule and the phonon states of a copper surface has been modelled using quantum wavepackets. For processes where the molecule gains internal energy, we predict a gain in molecular energy near the excitation threshold. This gain decreased with increasing translational energy, and was insensitive to the final state of the molecule. For non-activated processes, with a decrease in molecular internal energy, a net loss of energy to the substrate was found. This loss increased as the change in internal energy of the molecule increased. These results are in good agreement with experimental observation. (C) 2002 Published by Elsevier Science B.V.