In order to model one of the key steps in hydrosulfurization (HDS), density functional calculations of the dissociation of H-2 on the edges of a Co promoted MoS2 (Co-Mo-S) slab have been performed. The results show that the heterolytic dissociation of hydrogen is not favored, but there appears to exist different homolytic pathways with similar activation barriers. It is shown that the dissociation process couples strongly to flexible sulfur atoms such that dynamic surface reconstructions occur during the adsorption process. By calculating the minimum energy reaction path we find that S atoms at the edge of the MoS2 slabs can move up to extract one of the Il atoms of the dissociating H-2 molecule and transport it to the other side of the slab where it diffuses on. Transition metal sulfides constitute an important class of heterogeneous catalysts and the active part of many enzymes, and we suggest that the catalytic activity of these systems may be closely coupled to the flexibility of the sulfur ligands.