Alternative structure of ${\mathrm{TiO}}_2$ with higher energy valence band edge

We propose an alternative structure of ${\mathrm{TiO}}_2$ anatase that has a higher energy oxygen $p$-like valence band maximum than pristine ${\mathrm{TiO}}_2$ anatase and thus has a much better alignment with the water splitting levels. This alternative structure is unique when considering a large subspace of possible structural distortions of ${\mathrm{TiO}}_2$ anatase. We propose two routes towards this state and argue that one of them might have been realized in the recently discovered so-called black ${\mathrm{TiO}}_2$.

Figure 1

Two kinds of Ti-O octahedra in bulk ${\mathrm{TiO}}_2$ anatase.

Figure 2

Crystal structure of pristine bulk ${\mathrm{TiO}}_2$ anatase.

Figure 3

Structural distortion ${\xi }_i$ that reduces value of $F\left({\xi }_i\right)$.

Figure 4

Conduction band minimum $\left({\epsilon }_{\mathrm{c}}\right)$, valence band maximum $\left({\epsilon }_{\mathrm{v}}\right)$, the total energy $\left(E_{\mathrm{tot}}\right)$, and decomposition into irreducible modes $\left({\xi }_i\right)$ along a path that minimizes $F$.

Figure 5

Band structure along a path in $k$-space in pristine ${\mathrm{TiO}}_2$ anatase (left), with applied $A_{1\mathrm{g}}$ distortion (middle), and with both $A_{1\mathrm{g}}$ and $B_{2\mathrm{u}}$ distortions (right). The titanium core levels are aligned among three panels. The red dashed lines are guides to the eye.

Figure 6

Contour plot of total energy $E_{\mathrm{tot}}$ per one atom as a function of distortions $A_{1\mathrm{g}}$ and $B_{2\mathrm{u}}$. The red arrow shows the approximate direction in which $F$ is minimized.

Figure 7

Stable structure with $\uparrow$ $\uparrow$ configuration in bulk. This distortion is also stable on the surface.

Figure 8

Band structure without (left) and with (right) $\uparrow$ $\uparrow$ on the surface. The band structure is aligned relative to the vacuum level above each surface. The red dashed lines are guides to the eye.

Figure 9

Surface with $\uparrow \uparrow$ termination stabilized using a simplified approach based on pseudohydrogen atoms (see text for details).