Ab initio band structure calculations within a density functional formalism were performed to compute the binding energy curves for atomic hydrogen interacting with high-symmetry adsorption sites of the (111) surface of copper. For a two-layer slab of Cu atoms and H coverage equal to 0.25, the binding energies are 2.23, 3.12 and 3.24 eV, for on top, bridge and threefold sites, so the chemisorption of H2 on Cu(111) is exothermic for threefold and bridge sites, but endothermic for on top sites. Starting from the ab initio results for the H-Cu(111) system, a LEPS potential for the interaction of H2 with the Cu(111) surface was built. In this model potential, the most favoured approaches correspond to a H2 molecule parallel to the Cu surface, and have activation barriers of 0.6 eV, located at the corner between entrance and exit reaction channels. The LEPS potential was used in quasiclassical trajectory calculations to simulate the adsorption of a beam of H2 molecules on Cu(111). The dynamical results show that (a) when H2 is in its ground vibrational state, the dissociative adsorption probability, Palpha , increases from 0 to 0.90 along a roughly sigmoidal curve when increasing the collision kinetic energy from 0.4 to 1.3 eV; (b) the vibrational energy of H2 can be as effective as the translational one in promoting chemisorption; (c) dissociation of H2 is inhibited by rotational motion at low j values, but enhanced by high values of j;(d) Pa scales with normal component of collision energy; (e) no azimuthal corrugation of the surface is observed.