Complex [Cp*Ir(dmpm)H-2](2+) (dmpm = bis(dimethylphosphino) methane) has been reported to display temperature-dependent spin-spin coupling constant ((1)J(HD)) and isotope effect on the H-1 NMR chemical shift (Delta delta). A combined electronic structure density functional theory + quantum nuclear dynamics study is used to determine from first-principles the unusual temperature dependence of the spin-spin coupling constant. It is found that the potential energy surface describing the motion of the Ir-H-2 unit has a deeper minimum in the dihydride region and is characterized by important anharmonicities. These anomalies affect the nature of the vibrational states of the unit and are the main reason for the unusual temperature dependence of (1)J(HD) and Delta delta. These results suggest experimental tests to identify compressed dihydride transition metal complexes.