The dynamics of vibrational de-excitation of v=1 H-2 on a Cu(100) surface is studied using a six-dimensional quantum wave packet method. The de-excitation probability increases with increasing collision energy and initial molecular rotational quantum number, j. A strong dependence on molecular orientation is found with molecules rotating with helicoptering motion (m(j)=j) exhibiting larger de-excitation probabilities, in general, than those with cartwheeling motion (m(j)=0). The final j-state distribution and quadrupole alignment are computed as functions of collision energy. The competition between vibrational de-excitation and other dynamic processes during the collision is analyzed. The total de-excitation probability is in good agreement with vibrational inelasticities from experiment but the calculations overestimate the population of scattered H-2 in (v=0, j) for large j.