The dissociative chemisorption of N2 on the (0001) rhenium crystal surface is studied theoretically at high impact energies. The dynamics of the molecule is accordingly treated classically excluding tunneling processes. This study extends previous low energy studies in three important ways: (1) all six degrees of freedom of the N2 molecule are considered; (2) lateral variations (corrugation) are included in the molecule-crystal interaction potential; (3) energy exchange between the molecule and the surface is allowed for by treating the dynamics of the crystal atoms within a linear phonon forcing model. It is found that the energy transfer from the molecule to the phonons of the crystal is very significant. The smaller than unity dissociative sticking probability found experimentally even at the highest impact energies well above the barrier energy can be accounted for by the Landau-Zener probability of a transition from the dissociative potential energy surface (PES) to a non-dissociative PES.