Figure 1

(a) Ball and stick model of the defective ${\mathrm{TiO}}_2(110)$ surface. Red (dark gray) and blue (light gray) spheres are O and Ti atoms, respectively. Panels (b), (c), and (d) depict the spin density (at $0.005e/{\AA }^3$) of three configurations from Table  with different charge localization topologies.Reuse & Permissions

Figure 2

(a) Dynamics of the fractional occupation of particular Ti $d$ orbitals during a time fragment of the $\mathrm{PBE}+U$ simulation carried out at 1000 K; at $t=0$ the charge is localized in the second subsurface layer at Ti(24) and Ti(31); populations of about 1 and 0 correspond to ${\mathrm{Ti}}^{3+}$ and ${\mathrm{Ti}}^{4+}$ charge states, respectively. (b) Same as (a) but the charge is initially localized in the first layer at Ti(11) and subsurface at Ti(29) at 700 K. (c) Distribution function of the average population of all available Ti sites by the two excess electrons obtained from the full simulation underlying (a); inset provides layer-averaged populations. (d) Electronic density of states ($\alpha (\beta )$ spins: red (black) lines) of the three structures from Fig. 1; peaks in the band gap correspond to reduced Ti sites; the top of the valence band is set to 0 eV, and the red area filling the gap states (scaled by 10 to enhance visibility) stems from ${\mathrm{Ti}}^{3+}$ sites as labeled.Reuse & Permissions