We address here the chemical character and the mobility of hole polarons in BiVO 4 (BVO). Two distinct structures for hole polarons in BVO have been reported in the literature to date. "Standard" hybrid density functional theory (DFT) calculations have predicted hole polarons to be (BiO 8 ) dodecahedroncentered polarons, while Hubbard U-DFT (DFT + U) calculations have predicted single oxygen atom-centered polarons. Resolving these contrasting findings is critical to validate theory in materials research. We investigated the structure of hole polarons in BVO using hybrid DFT with varying fractions (α) of the exact exchange interaction that enters hybrid functionals. For values of the fraction α, from α = 0.25 to α = 0.45, we obtained both structures, the h + (BiO 8 ) hole structure and the h + (O) hole structure. For the smaller values of α, the h + (BiO 8 ) structure is lower in energy, while for the larger values of α, the h + (O) structure is more stable. The piece-wise linearity of DFT energies E(q) with respect to a point defect charge q is maintained satisfactorily in all cases, although the deviation is the smallest for hybrid DFT with a small exact exchange fraction. For α = 0.25, we determined the diffusivity of h + (BiO 8 ) holes from the Marcus/Holstein two-state model. The activation barrier for Bi-to-Bi hops (ΔG # ∼ 76 meV) and mobility (μ ∼ 0.029 cm 2 V −1 s −1 ) are found to be in close agreement with the published THz experimental data (ΔG # ∼ 90 meV and μ exp ∼ 0.02 cm 2 V −1 s −1 , respectively). In h + (BiO 8 ) structures, nearly 25% of the hole charge and unpaired spin reside on the Bi atom and the rest is divided among the eight O atoms. The hole is best described as a Bi-centered hole, rather than a Bi 6s hole. In contrast, in h + (O) structures, about 75% of the unpaired spin population resides on the O atom. These findings suggest that if one wishes to resolve this theoretical dichotomy, there remains a need for further experimental characterization of hole polarons in BVO with techniques that could identify the oxidation state of Bi and O atoms in operando conditions and help validate theoretical results of structure and transport.

SrTiO3 (STO) is a widely used photocatalyst for water splitting, which has no photoactivity without a cocatalyst. The reason for this unclear. Here, we performed an oxygen evolution reaction (OER) on clean and oxygen deficient (100), (110), and (111) surfaces on STO by density functional theory. Combining our results with experimental results in the literature, we demonstrated that the overpotential is small enough for OER to occur on (100) surfaces. There is no photoactivity due to the photogenerated holes that cannot migrate to the (100) surfaces. On the (110) and (111) surfaces, the overpotential is very high, which prevents the OER from taking place on these two surfaces. Our work gives a guidance principle to understand the water splitting from the overpotential of OER and migrating photogenerated carriers. It may be helpful to design high efficiency photocatalysts based on STO.

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TaON and Ta 3 N 5 are considered promising materials for photocatalytic and photoelectrochemical water splitting. In contrast, their counterpart Ta 2 O 5 does not exhibit good photocatalytic performance. This may be explained with the different charge carrier transport mechanisms in these materials, which are not well understood yet. Herein, we investigate the charge transport properties in Ta 2 O 5 , TaON, and Ta 3 N 5 by polaron hopping and bandlike models. First, the polaron binding energies were calculated to evaluate whether the small polaron occurs in these materials. Then we performed calculations to localize the excess carriers as small polarons using a hybrid density func-tional. We find that the small polaron hopping is the charge transfer mechanism in Ta 2 O 5, whereas our calculations indicate that this mechanism may not occur in TaON and Ta 3 N 5 . We also investigated the bandlike model mechanism by calculating the charge carrier mobility of these materials using the effective mass approximation, but the calculated mobility is not consistent with experimental results. This study is a first step towards understanding charge transport in oxynitrides and nitrides and furthermore establishes a simple rule to determine whether a small polaron occurs in a material.

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