In this manuscript, we investigate two plausible pathways for addition of H2 across the bond Ta=C in η5-(C5H 5)2Ta(H)=CH2. One of the investigated reaction pathways involves a single concerted step with a four-membered transition state keeping the oxidation state of tantalum unaltered, where as the other pathway deals with a two step reaction with α-insertion of H2 to produce a 16e- Ta(III)-methyl species and a subsequent oxidative addition. We must emphasize that an experimental study by Bregel et al. [J Am Chem Soc 2002, 124:13827-13832] on a derivative of the investigated chemical system in the present study showed that the two step strategy of α-insertion followed by subsequent oxidative addition is the preferred one. Our numerical investigations using DFT and AIM calculations lead to a similar conclusion. To establish our conclusion, we employ various basis sets to obtain the free energy of activation of the reaction. The AIM technique especially helps us to characterize the bond critical points at the optimized geometries of the reactants, products, transition states, and intermediates for the two step mechanism. © 2014 Springer-Verlag.