The β-hydride transfer step finishes one catalytic cycle and reforms the Ga-alkyl species. We have also calculated the barrier of β-hydride elimination leading to the Ga-hydride moiety, for which the barrier is significantly higher than the ethylene-assisted barrier (species 1-3 to ‡ b , 2.4 eV), suggesting that the Ga-hydride is unlikely to form. Overall, based on the free energy analysis, we predict that Ga-alkyl favors the formation of short oligomers, since the termination step (β-hydride transfer) will be faster than the propagation step (migratory insertion) due to a much lower activation barrier. This behavior has been observed in the experiments, where butenes are the primary products detected. On the other hand, the C-A mechanism will not be dominated by the Ga-hydride spices, given a high barrier of β-hydride elimination step.