The reaction of H-2 on Cu(100) is investigated using a four-dimensional (4D) quantum dynamical fixed-site model to assess the influence of molecular rotation on dissociation over the most reactive (the bridge) site. The potential energy surface (PES) is a fit to the results of density functional calculations performed using a generalized gradient approximation treating a Cu slab with a periodic overlayer of H-2. Dissociation probabilities for molecules with "helicoptering" (m(j)=j) and "cartwheeling" (m(j)=0) rotational motions are here found to be comparable because of the strong corrugation in the azimuthal coordinate. The calculations indicate that reaction is accompanied by significant rotationally inelastic scattering, Surprisingly, vibrational excitation is also found to be an efficient process in collisions with the reactive bridge site. Ln these collisions, the molecular axis is tilted away from the orientation parallel from the surface. Considering the approximate nature of the 4D model used, the calculated reaction probabilities are in good agreement with experiment, indicating that the PES that was used is accurate.