Mössbauer spectroscopy, experimental thermodynamic measurements, and computational studies were performed to investigate the properties of molecular hydrogen binding to the organometallic fragments [MHdppe2]+ (M = Fe, Ru, Os; dppe =1,2-bis(diphenylphosphino)ethane) to form the dihydrogen complex fragments [MH(η2-H2)dppe2]+. Mössbauer spectroscopy showed that the dehydrogenated complex [FeHdppe2]+ adopts a geometry consistent with the triplet spin state, transitioning to a singlet state complex upon addition of the dihydrogen molecule in a manner similar to the previously studied dinitrogen complexes. From simulations, this spin transition behavior was found to be responsible for the strong binding behavior experimentally observed in the iron complex. Spin-singlet to spin-singlet transitions were found to exhibit thermodynamics consistent with the 5d > 3d > 4d binding trend observed for other transition metal dihydrogen complexes. Finally, the method for distinguishing between dihydrogen and dihydride complexes based on partial quadrupole splittings observed in Mössbauer spectra was confirmed, providing a tool for further characterization of these unique species for Mössbauer active compounds.