Having obtained the putative GM for all of the considered stoichiometries, it is necessary to asses which of the compositions is most stable under different environmental conditions. Taking the formation energies using only the as-calculated absolute DFT energies is insufficient, since the stability of each oxidation state depends on how easy or hard it is to obtain O atoms from the gas-phase environment in contact with these particles. We therefore carry out an ab initio thermodynamics (AITD) analysis, which allows to obtain Gibbs free energies of formation as a function of macroscopic properties of the system from energies obtained by ab initio methods at 0 K. We calculate the Gibbs free energies of each state within the canonical ensemble. This assumes constant volume, temperature, and number of atoms of the system. We further assume the PtyOx particles to be in equilibrium with a gas-phase reservoir of O2 at a given T and pO2. This means that their composition is going to be influenced by the T and pO2. For any structure, the Gibbs free energy (G) is calculated as shown in equation :