We have calculated a two-dimensional (2D) potential energy surface (PES) for H-2 interacting with a Pd(111) surface. The geometry considered is for H-2 approaching a bridge site and dissociating into neighboring hollow sites and the subsurface sites directly below these. Density functional calculations were performed using both the local density approximation (LDA) and the generalized gradient approximation (GGA). The LDA PES gives the usual overbinding and shows no barrier (relative to the bottom of the H-2 potential) to subsurface absorption, while the GGA PES agrees with the experimental adsorption energies and has a large barrier. We have performed quantum mechanical wave packet calculations on the GGA PES to obtain the direct subsurface absorption probability. We have also calculated the barrier height’s dependence on a coordinate that can be associated with a local surface vibrational mode and the results suggest that this degree of freedom should be taken into account in the dynamical calculations.