Within the generalized gradient approximation (GGA) of density functional theory (DFT) we have calculated a three-dimensional (3D) potential energy surface (PES) including an angular degree of freedom for a H-2 molecule interacting with a Pd(lll) surface. There is an entrance channel barrier (approximate to 0.09 eV) to both dissociative chemisorption and direct subsurface absorption, but after this barrier is crossed direct subsurface absorption can proceed almost without a barrier. 3D quantum mechanical wave packet calculations incorporating the rotation of H-2 in a plane perpendicular to the surface show a large part of the hydrogen going directly subsurface even at low incident kinetic energies. The wave packet calculations also show that in the low energy regime rotation inhibits direct subsurface absorption at low j(0) and promotes it at high j(0).