High-dimensional, wave packet calculations have been carried out to model the surface temperature dependence of rovibrationally inelastic scattering and dissociation of hydrogen molecules from the Cu(111) surface. Both the molecule and the vibrating surface are treated fully quantum-mechanically. It is found, in agreement with experimental data, that the surface temperature dependence of a variety of dynamical processes has an Arrhenius form with an activation energy dependent on molecular translational energy and on the initial and final molecular states. The activation energy increases linearly with decreasing translational energy below the threshold energy. Above threshold the behavior is more complex. A quasianalytical model is proposed that faithfully reproduces the Arrhenius law and the translational energy dependence of the activation energy. In this model, it is essential to include quantized energy transfer between the surface and the molecule. It further predicts that for any process characterized by a large energy barrier and multiphonon excitation, the linear change in activation energy up to threshold has slope-1. This explains successfully the universal nature of the unit slope found experimentally for H-2 and D-2 dissociation on Cu. (C) 2004 American Institute of Physics.