We present results of six-dimensional (6D) quantum wave-packet calculations for the dissociative adsorption of (v = 0,j = 4,m(j)) H-2 on Cu(100). The potential-energy surface is a fit to points calculated using density-functional theory (DFT), with the generalized gradient approximation (GGA), and a slab representation for the surface. New aspects of the methodology we use to adapt the wave function to the symmetry of the surface, which relate to calculations for initial rotational states with odd m(j) (the magnetic quantum number), are explained. Invoking detailed balance, we calculate the quadrupole alignment for H-2 as it would be measured in an associative desorption experiment. The reaction of the helicopter (v = O,j = 4,m(j) = 4) state is preferred over that of the ( v = 0,j = 4,m(j) = 0) cartwheel state for all but the lowest collision energies considered here. The energy dependence of the quadrupole alignment that we predict for (v = 0,j =4) H-2 desorbing from Cu(100) is in good qualitative agreement with velocity-resolved associative desorption experiments for D-2 + Cu(111). The vibrational excitation probability P(v = 0,j --> v = 1) is much larger for j = 4 than for j = 0, and the m(j)-dependence of P(v = 0,j = 4,m(j) --> v = 1) is markedly different from that of the initial-state-resolved reaction probability. For all but the highest collision energies, vibrational excitation from the (v = 0,j = 4) state is accompanied by loss of rotational energy, in agreement with results of molecular beam experiments on scattering of H-2 and D-2 from Cu(111).