Molecular orbital calculations at the ab initio level are used to study polytopal rearrangements in H2Ru(PH3)4 and H2Fe(CO)4 as models of 18-electron, octahedral metal dihydrides. It is found that, in both cases, the transition state for these rearrangements is a dihydrogen species. For H2Fe(CO)4, this is a square pyramidal complex where the H2 ligand occupies an apical position and is rotated by 45 degrees from its original orientation. This is precisely analogous to the transition state for Fe-olefin rotation in (olefin)Fe(CO)4 complexes and has a very similar electronic origin. Another transition state very close in energy is found wherein the basic coordination geometry is a trigonal bipyramid and the H2 ligand is coordinated in the axial position. For H2Ru(PH3)4, the former stationary point lies at a much higher energy and the latter clearly serves as the transition state for hydride exchange. The reason for this difference is discussed along with the roles of electron correlation in the two compounds.