Results are reported of a four-dimensional dynamics study on the dissociation of H-2 on Cu(100), The potential-energy surface was taken from density functional calculations, which employed the generalized gradient approximation and a slab representation for the surface. Reaction occurs preferentially in impacts near the bridge and hollow sites. Collisions near top sites promote vibrational excitation. The conclusion that vibrationally inelastic scattering and reaction occur preferentially on different sites can be generalized to other low index Cu surfaces. Resonances affect the reaction in the 4D model through a mechanism in which the molecule, trapped by excitation of the molecular bond which is weakened at the surface near top sites, is allowed more time to tunnel through the barrier to reaction. The calculated dependence of the diffraction probabilities on incidence energy suggests that a measurement of low-order diffraction would be able to determine whether the minimum barrier to reaction occurs for impacts on the bridge sites (as theory predicts) or on the hollow or top sites, The calculated reaction probabilities are in good agreement with experiment, further improvement being expected from including the rotational degrees of freedom in the model.