The reaction of H-2 on Cu(100) is studied using a wave-packet method to solve a four-dimensional quantum mechanical model for impact on the high-symmetry hollow and top sites. The potential energy surface (PES) is a fit to the results of density functional calculations treating a periodic overlayer of Hz on a Cu slab. The dynamics calculations include motion in the azimuthal coordinate although the PES does not depend on phi for impact on the top and hollow sites. Large dissociation probabilities (similar to 0.9) are found for impact at the hollow site but those for impact at the top site are lower (similar to 0.3). Dissociation probabilities for molecules incident with "helicoptering" motion (m(j) =j) are larger than those for molecules with "cartwheeling" motion (m(j) = 0). This differs from the results of previous calculations for impact at the azimuthally corrugated bridge site which predicted comparable probabilities for the two orientations of incident molecules. The dissociation probabilities from fixed-site calculations at the different impact sites are combined to yield an averaged probability which is compared with experiment and the results of six-dimensional quantum calculations. Vibrationally inelastic scattering is predicted to occur primarily for impact at the top site.