Origin of the different photoactivity of $\mathrm{N}$-doped anatase and rutile ${\mathrm{TiO}}_2$

We have investigated the origin of the experimentally observed change in photoactivity of anatase and rutile ${\mathrm{TiO}}_2$ induced by substitutional $\mathrm{N}$-doping using state-of-the-art density functional theory calculations. Our results show that in both polymorphs $\mathrm{N}2p$ localized states just above the top of the $\mathrm{O}2p$ valence are present. In anatase these states cause a redshift of the absorption band edge towards the visible region. In rutile, instead, this effect is offset by the concomitant $\mathrm{N}$-induced contraction of the $\mathrm{O}2p$ band, resulting in an overall increase of the optical transition energy. Experimental trends are well described by these results.

Figure 1

$\mathrm{N}$-doped ${\mathrm{TiO}}_2$ (a) anatase $\left(96\text{−}\text{atom}\right)$ and (b) rutile $\left(72\text{−}\text{atom}\right)$ supercells. Bond lengths in $\mathrm{\AA }$ (computed at $\Gamma$; values in italic refer to $K_{\mathrm{LS}}$). For comparison, the $\mathrm{Ti}\text{−}\mathrm{O}$ bondlengths of undoped anatase (rutile) are 1.942 (1.956) and $2.002\left(1.999\right)\mathrm{\AA }$.

Figure 2

Electron density corresponding to the highest singly occupied state in $\mathrm{N}$-doped ${\mathrm{TiO}}_2$. (a) Anatase, (b) rutile.

Figure 3

Schematic representation of the band structure of pure and $\mathrm{N}$-doped anatase and rutile. Energies are not in scale.