The free energy was calculated by ASE thermochemistry . For reference molecules and stable species, we use Idea-gas limit. For the adsorbates, we use Harmonic limit. The vibration frequency was calculated by VASP (IBRION=5) which as an input to ASE thermochemistry. For the adsorbate frequency, we just calculated the frequency of adsorbate atoms and fixed the surface because the contribution of phonon inside metal/metal oxides are neglectable compared to the vibration of adsorbates. The free energy of slab+ads is: