In the Ga site activation analysis on 3CN sites, the formation of a Ga-alkyl moiety through β-hydride transfer is the most energetically favorable pathway. Following the site activation, the coordination of an ethylene molecule to the alkyl group occurs, which initiates the C-A oligomerization cycle. Our analysis starts from the Ga-alkyl species, and Figure shows the free energy diagram of C-A mechanism on a 3CN site. However, we analyze two types of C-A mechanisms (Figure ) starting from either Ga-hydride or Ga-alkyl These configurations may, in principle, interconvert. We further analyze the related possibility that 3CN and 4CN sites may catalyze the C-A mechanism beginning with the Ga-hydride species, which can be produced with a hydrogen gas treatment. The ethylene physisorption on Ga-ethyl species is exothermic, with a free energy change of -0.3 eV (species 1-1 to 1-2). The migratory insertion of the second ethylene molecule, which approaches Ga and binds to the ethyl group, has an activation barrier of 1.7 eV (species 1-2 to 1-3). Following the physisorption of an additional ethylene molecule, the activation barrier of the βhydride transfer (species 1-4 to 1-5, 1.0 eV) is much lower than that of the ethylene insertion step.