Free energies are evaluated at 523 K and are calculated using the equation G = EDFT + EZPE -TS, where EDFT is the ground-state potential energy from DFT. The zero-point energy corrections (EZPE) are calculated from the harmonic vibrational states. For vibrational modes with wave numbers above 150 cm -1 , harmonic partition functions are employed to estimate entropies, while for modes with lower frequencies, particle-in-a-box (PIB) and free rotor schemes, depending on the geometric characteristics of the vibrations, are used (see Supporting Information for an example). The adsorption energies (Gads) are referenced to empty sites (GGa) and appropriate amounts of gaseous ethylene molecules at 1 atm (Gethylene). However, the free energy of Ga-hydride or Ga-alkyl moieties is used for the GGa term in the C-A cycles.