2.3 Computational Methods
Density functional theory (DFT) calculations were carried out by the Vienna ab initio simulation package (VASP). The projector augmented wave (PAW) pseudo-potential was adopted to describe the ion-electron interactions, and the PW91 gradient-corrected functional was employed in the calculation of the exchange correlation energy. An energy cutoff of 400 eV was used for the plane-wave basis set. Numerical convergence thresholds of 10-6 eV in energy and 10-2 eV/Å in force were achieved on structural optimization. The Brillouin zone was sampled on the basis of the Monkhorst-Pack scheme with a 5×5×1 k-point mesh [27]. A five-layer slab was used in the calculations. The atoms in the top two layers were fully relaxed while the rest of the atoms were fixed in their equilibrium positions.
Formation energy (E f) of oxygen vacancy is defined as shown in the formula (4):
E f = E v -E i - 1/2E O2 (4)
E v and E i are total energy of the structure with and without an oxygen vacancy.E O2 is the total energy of an oxygen molecule.
The oxygen adsorption energy E O was defined relative to the isolated substrate and the O2 in the gas phase, as shown in the formula (5):
E O = E [surf+O] -E [surf] - 1/2E O2 (5)
where E [surf + O] andE [surf] are the total energies of the surface with and without the O adsorbate, respectively.E O2 is the total energy of an oxygen molecule.