Hole localization in ${\mathbf{Fe}}_2{\mathbf{O}}_3$ from density functional theory and wave-function-based methods

Hematite ($\alpha -{\mathrm{Fe}}_2{\mathrm{O}}_3$) is a promising photocatalyst material for water splitting, where photoinduced holes lead to the oxidation of water and the release of molecular oxygen. In this work, we investigate the properties of holes in hematite using density functional theory (DFT) calculations with hybrid functionals. We find that holes form small polarons and, depending on the fraction of exact exchange included in the PBE0 functional, the site where the holes localize changes from Fe to O. We find this result to be independent of the size and structure of the system: small ${\mathrm{Fe}}_2{\mathrm{O}}_3$ clusters with tetrahedral coordination, larger clusters with octahedral coordination, ${\mathrm{Fe}}_2{\mathrm{O}}_3$(001) surfaces in contact with water, and bulk ${\mathrm{Fe}}_2{\mathrm{O}}_3$ display a very similar behavior in terms of hole localization as a function of the fraction of exact exchange. We then use wave-function-based methods such as coupled cluster with single and double excitations and Møller-Plesset second-order perturbation theory applied on a cluster model of ${\mathrm{Fe}}_2{\mathrm{O}}_3$ to shed light on which of the two solutions is correct. We find that these high-level quantum chemistry methods suggest holes in hematite are localized on oxygen atoms. We also explore the use of the $\mathrm{DFT}+U$ approach as a computationally convenient way to overcome the known limitations of generalized gradient approximation functionals and recover a gap in line with experiments and hole localization on oxygen in agreement with quantum chemistry methods.

Figure 1

PDOS for bulk ${\mathrm{Fe}}_2{\mathrm{O}}_3$ obtained using PBE0 with $X=10$% (left) and $X=50$% (right). Positive values represent the spin-up channel, negative values the spin-down channel.

Figure 2

PDOS for bulk ${\mathrm{Fe}}_2{\mathrm{O}}_3$ with one hole obtained using PBE0 with 10% (left) and 50% (right) fractions of exact exchange. Positive values represent the spin-up channel, negative values the spin-down channel.

Figure 3

Isosurfaces displaying the hole in bulk ${\mathrm{Fe}}_2{\mathrm{O}}_3$ with obtained using PBE0 with 10% (left) and 50% (right) fractions of exact exchange. The isosurfaces display the difference in charge density between a system with a hole and a neutral one, with the same ionic positions, corresponding to the ones obtained relaxing the system in the presence of a hole. The yellow and blue areas indicate charge accumulation and depletion, respectively.

Figure 4

Geometry of the neutral (a) ${\mathrm{Fe}}_2{\mathrm{O}}_6{\mathrm{H}}_6$, (b) ${\mathrm{Fe}}_4{\mathrm{O}}_{12}{\mathrm{H}}_{12}$, and (c) ${\mathrm{Fe}}_6{\mathrm{O}}_{18}{\mathrm{H}}_{18}$ clusters.

Figure 5

PDOS for (a) dimer (${\mathrm{Fe}}_2{\mathrm{O}}_6{\mathrm{H}}_6$), (b) tetramer (${\mathrm{Fe}}_4{\mathrm{O}}_{12}{\mathrm{H}}_{12}$), and (c) hexamer (${\mathrm{Fe}}_6{\mathrm{O}}_{18}{\mathrm{H}}_{18}$) clusters with one hole obtained using all-electron HF method, respectively. Positive values represent the spin-up channel, negative values the spin-down channel. (d)–(f) Display isosurface of the charge density difference between charged and neutral clusters in ${\mathrm{Fe}}_2{\mathrm{O}}_6{\mathrm{H}}_6, {\mathrm{Fe}}_4{\mathrm{O}}_{12}{\mathrm{H}}_{12}$, and ${\mathrm{Fe}}_6{\mathrm{O}}_{18}{\mathrm{H}}_{18}$ clusters with obtained using all-electron HF method, respectively.

Figure 6

Model of the $\alpha -{\mathrm{Fe}}_2{\mathrm{O}}_3\left(001\right)$ slab in water.

Figure 7

PDOS on snapshots extracted from the MD simulations of the ${\mathrm{Fe}}_2{\mathrm{O}}_3$(001) surface in water, obtained using PBE0 with 10% (left) and 50% (right) fractions of exact exchange.