  TiO2 is a technologically important material. In particular, its anatase
polymorph plays a major role in photocatalysis, which can also accommodate
charged and neutral vacancies. There is, however, scant theoretical work on the
vacancy charge and associated diffusion from surface to subsurface and bulk in
the literature. Here, we aim to understand +2 charge and neutral vacancy
diffusion on anatase (101) surface using 72 and 216 atoms surface slabs
employing a semi-local density functional and the Hubbard model. The
activation-relaxation technique nouveau (ARTn) coupled with Quantum Espresso is
used to investigate the activated mechanisms responsible for the diffusion of
oxygen vacancies. The small slab model over-stabilizes the +2 charged topmost
surface vacancy, which is attributed to the strong Coulomb repulsion between
vacancy and neighboring Ti+4 ions. The larger slab allows atoms to relax
parallel to the surface, decreasing the +2 charged topmost surface vacancy
stability. The calculated surface-to-subsurface barriers for the +2 charged
vacancy and diffusion of the neutral vacancy on a slab of 216 atoms are 0.82 eV
and 0.52 eV, respectively. Furthermore, the bulk vacancy prefers to migrate
toward the subsurface with relatively low activation barriers 0.19 eV and 0.27
eV and the reverse process has to overcome 0.38 eV and 0.40 eV barriers for the
+2 charged and the neutral vacancies. This explains the experimentally observed
high concentration of vacancies at the subsurface sites rather than in the
bulk, and the dynamic diffusion of vacancies from the bulk to the subsurface
and from the subsurface to the bulk is highly likely on the surface of anatase
(101). Finally, we provide a plausible explanation for the origin of recently
observed subsurface-to-surface diffusion of oxygen vacancy from the calculated
results.
