The interaction of PdN clusters (N = 2, 3, 4, 7, and 13) with multiple H-2 adsorbate molecules is investigated using density functional theory with the hybrid PBE0 functional. The optimal structure for each PdNH2(L) complex is determined systematically via a sequential addition of H-2 units. The adsorption energy for each successive H-2 addition is computed to determine the maximum number of molecules that can be stably added to a PdN at T = 0 K. The Gibbs free energy is then used to determine the saturation coverage at finite temperature. For N = 2, 3, and 4, a single H-2 is found to dissociate, and up to two additional molecular H-2 units per Pd atom can bind stably to the clusters at 0 K. At 300 K, one H-2 unit dissociates, and only one additional H-2 molecular unit per Pd atom is stably bound. For N = 7 and T = 0 K, two H-2 units dissociate, and 11 additional H-2 units bind molecularly. At 300 K, two units dissociate, and eight are bound molecularly. For N = 3, 4, and 7, we find that an additional H-2 unit may dissociate if the underlying cluster structure rearranges. Eight H-2 units dissociate on Pd-13 at 0 K. At least one additional H-2 binds molecularly at 0 K, but none bind at 300 K. This suggests that only dissociated H-2 units will stably bind to larger Pd particles at room temperature. The influence of molecularly adsorbed H-2 units on the migration of dissociated H atoms is investigated in a preliminary way. Both barrier heights and the relative stability of local minima of Pd4H2(L) are found to be affected by the degree of molecular H-2 coverage.