Where the internal energy (U) can be approximated as the total energy obtained in the DFT calculations of the system. F vib and F conf correspond to the vibrational and configurational contributions to the free energies, respectively. The Gibbs free energy of formation for the oxides is, thus, obtained by the difference of the Gibbs free energy of the oxide with the Gibbs free energy of the fully reduced cluster and the chemical potential of oxygen, related to temperature and pressure, as shown in equation 2.