The energetics of three primary cycles are compared, as shown in Figure . A proton transfer cycle can occur on the empty Ga 3+ site starting from ethylene activation by Ga 3+ , followed by insertion of another ethylene unit (species 1 to 4, Fig. ). The Ga-butenyl species can then desorb via a proton transfer step, forming n-butene, completing the oligomerization cycle via proton transfer and reforming of the empty Ga 3+ site (region a, Fig. ). Alternatively, the Ga-butenyl species may activate pathway transfer processes (region b, Fig. ). β-hydride elimination can activate another oligomerization cycle, where butadiene and Ga-hydride are formed, proceeding to a C-A mechanism (species 4-6b, Fig. ). Further, as mentioned above, β-hydride elimination can be assisted by an incoming alkene molecule, which accepts a hydrogen atom and becomes an alkyl intermediate, which may be another key intermediate in the C-A cycle (species 4-7c, Fig. ).