Fig. 1. Side view of (a) the three-layer unrelaxed anatase (1 0 1) slab with surface area of , which is labeled 1×1–3 cell. The first layer of Ti₂O₄ is in the dashed line; (b) the three-layer relaxed slab with surface area of , which is used in surface properties calculations and labeled 2×2–3 cell (Ti₂₄O₄₈); and (c) the first layer of the relaxed undoped surface having a VO_2C (Ti₂₄O₄₇), (b) the first layer of the relaxed N-doped surface having a VO_2C (Ti₂₄O₄₆N). Relevant surface species are indicated in (a) and (b). Ti and O atoms are represented by small and big light gray spheres, N atoms are black spheres, respectively. The directions of atomic relaxations are labeled by arrows in (c) and (d).

Fig. 2. Density of the states (DOS) and band structures of: (a) the pure surface Ti₂₄O₄₈; (b) the surface having a VO_2C, Ti₂₄O₄₇; (c) the N-doped surface Ti₂₄O₄₇N; (d) the N-doped surface having a VO_2C, Ti₂₄O₄₆N; and (e) the N-doped charge neutral surface Ti₂₄O₄₅N₂.

Fig. 3. Partial density of states (PDOS) of some selected atoms, O1, O2, Ti1 and Ti2: (a) in the charge neutral N-doped surface Ti₂₄O₄₅N₂; and (b) in the pure surface Ti₂₄O₄₈. O1 and Ti1 locate in the bottom of the slab, while O2 and Ti2 are on the surface, which are the nearest neighbors of the surface N dopant in Ti₂₄O₄₅N₂.

Bridging oxygen vacancy formation energies (E_vf) performed for different size and slab thickness of surface cells, and ionic displacements in the surfaces having bridging oxygen vacancies

The displacement differences are calculated in [1 0 1] direction respect to the equivalent positions in the relaxed defect-free surfaces. Only two surface Ti atoms (Ti_5C and Ti_6C) locating next to the bridging oxygen vacancy are selected. Negative values indicate that atoms move inwards.