A density functional duster model approach has been applied to the study of the interaction of molecular hydrogen with two different cluster models of the PdCu(111) surface corresponding to a different formal alloy composition both having a single Pd atom in the surface. Despite the similar surface morphology of the two bimetallic clusters, they exhibit a rather different reactivity toward molecular hydrogen. The coordination of the surface Pd atom to other Pd atoms in the second layer appears to be necessary for this atom be able to trap and dissociate molecular hydrogen with a very low energy cost, thus being a potential active site for catalysis. This important result points out that electronic, or ligand, effects do also play an important role in the activity of the PdCu(lll) surface sites toward molecular hydrogen.