where G slab is the free energy of the surface supercell, A is the area of the exposed surface, , respectively. The chemical potential of oxygen is set by assuming equilibrium with O 2 gas at ambient conditions. To correct the well known oxygen overbinding error, the same approach as in Ref. 13 was employed, obtaining a correction of 740 meV and 630 meV using GGA and HSE(α=0.48), respectively.