The fact that certain metal complexes will bind hydrogen in molecular form has provided an opportunity to examine in the solid state the simplest hindered molecular rotation problem, namely, that of a dumbbell molecule in a double-minimum potential with one rotational degree of freedom. The barrier to rotation of this novel ligand is derived from inelastic neutron scattering measurements of its rotational transitions and interpreted in terms of the various types of interactions that give rise to it. These include the direct electronic interaction between dihydrogen and the metal, electronic effects (via the metal) of the other ligands on the metal, and steric effects. The remarkable result of these studies is that the barrier to rotation of dihydrogen serves as a very sensitive probe of some of the electronic interactions between the metal and its ligands. It also serves as the principal quantiative benchmark for electronic calculations aimed at arriving at an understanding of dihydrogen metal binding. In this paper we combine several new barrier height results with those from our previous work to discuss systematics of the variation of barrier height with the type of metal center, the nature of the coligands and counterions as well as their implications for metal-dihydrogen binding, and H-H bond activation.