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.