The oxygen evolution reaction (OER) is a crucial process in (photo)electrochemical water splitting, a technology vital for sustainable fuel production. This four-electron process (2H₂O → O₂ + 4H⁺ + 4e⁻) is the rate-limiting step, and understanding its mechanism is key to improving efficiency. Natural photosynthesis employs the oxygen-evolving complex (OEC) in photosystem II, a Mn₄CaO₅ cluster, to catalyze the OER. The OEC stores four oxidizing equivalents before the O-O bond formation, mitigating the energy cost of water oxidation. While the precise O-O bond formation mechanism remains debated (nucleophilic attack or direct coupling of oxo groups), significant advancements in understanding the OEC's structure and function have been achieved. In contrast, understanding synthetic OER catalysts is challenging due to difficulties in characterizing the electrode/electrolyte interface during operation. DFT simulations have provided insights, often modelling a sequential one-electron proton-coupled electron transfer (PCET) steps, leading to intermediates before O₂ release. The O-O bond formation is usually described by nucleophilic attack. This model has successfully explained trends in various catalysts, identifying the interaction strength between water oxidation intermediates and surface metal sites as a key activity descriptor. Recent research, however, indicates alternative mechanisms. Some oxides utilize lattice oxygen oxidation, while others favour direct oxo ligand coupling. A significant departure is the discovery of multihole OER characteristics in several semiconducting oxides, including haematite (α-Fe₂O₃). Studies using transient absorption spectroscopy (TAS) reveal a power law dependence of the OER rate on surface hole density (ph = kOER[h]α), indicating multihole involvement. This suggests an analogy between semiconducting oxide photoelectrochemical OER and the OEC in plants, with hole accumulation preceding the slow O-O bond formation. However, achieving accurate characterization of the heterogeneous OER active site and identifying reaction intermediates remains a hurdle. Studies using in operando techniques have shown some promise, notably the detection of Fe(IV)-oxo in α-Fe₂O₃. Previous work on IrO₂ showed that the OER proceeds through nucleophilic water attack on a surface oxyl, with an activation energy decreasing linearly with surface hole concentration, demonstrating an exponential dependence rather than a power law. This study aims to bridge this gap by combining experimental and theoretical approaches to elucidate the multihole OER mechanism on α-Fe₂O₃.

The literature extensively explores the oxygen evolution reaction (OER), particularly focusing on the mechanistic differences between biological systems (photosystem II) and synthetic catalysts. Studies on the oxygen-evolving complex (OEC) in photosystem II have provided an atomic-level understanding of the sequential four-electron oxidation steps, with the O-O bond formation being the rate-limiting step. Two main models exist for O-O bond formation: nucleophilic attack of water or hydroxide on a metal-oxo entity and direct coupling of two oxo or oxyl groups. Ab initio simulations and recent experiments tend to favour the latter. In the context of heterogeneous catalysts, Density Functional Theory (DFT) simulations have provided crucial insights into the OER mechanism on metal oxide surfaces. These simulations often depict a sequence of one-electron proton-coupled electron transfer (PCET) steps, where water is progressively oxidized to various intermediates before O₂ is released. A common model emphasizes the importance of the interaction between water oxidation intermediates and the surface metal sites as a key determinant of catalytic activity. However, growing evidence points to deviations from this conventional PCET model. Some studies highlight the involvement of lattice oxygen in the OER of certain oxides. Other studies describe a mechanism in which direct coupling of two oxo groups occurs rather than peroxo intermediate formation via nucleophilic attack. The observation of a power-law dependence of the OER rate on surface hole concentration in several semiconducting metal oxides is of considerable interest and prompted further research into multihole mechanisms.

This study combined experimental and computational techniques to investigate the OER mechanism in haematite photoanodes. Experimentally, an α-Fe₂O₃ photoanode was prepared via electrodeposition on an F:SnO₂ substrate followed by thermal annealing. The film had a thickness of ~200 nm with particle sizes of 50–100 nm. Raman and X-ray diffraction analysis confirmed the successful synthesis of haematite. Transient photocurrent measurements under chopped illumination (450 nm laser) were employed to determine the dependence of the OER rate on hole concentration. The integrated cathodic current transients directly measured the total charge, including surface and bulk holes, providing a direct measure of the hole number. Additionally, the double-layer charge was extracted from the fitted current transients representing surface holes and excluding diffusion-limited processes. Computationally, Density Functional Theory (DFT) calculations were performed using the QUANTUM ESPRESSO code with the rVV10 exchange-correlation functional. The (0001) facet of haematite was modeled due to its prevalence in crystalline haematite. The calculations focused on the hydroxylated surface in contact with water, considering PCET steps leading to the dehydrogenation of surface hydroxy groups. First-principles molecular dynamics (FPMD) simulations, incorporating solvation effects, were used to assess the free energy changes associated with PCET steps. The position of the valence band maximum (VBM) was estimated using a three-step approach. Time-dependent density functional theory (TDDFT) calculations were performed to compute the optical absorption spectra of the haematite/water interface, allowing comparison with experimental TAS data. To investigate the OER mechanism, several elementary steps were considered, including the conventional PCET mechanism, and pathways involving direct water or hydroxide dissociation. Nudged elastic band (NEB) calculations, performed in explicit solvent, determined the activation energies for O-O bond formation. The dependence of activation energies on surface hole coverage was analyzed. Finally, a steady-state microkinetic model, built within the framework of transition-state theory, was used to integrate the elementary steps and investigate the overall OER rate's dependence on surface hole concentration and temperature. This model incorporated the concentration of photogenerated valence band holes in the space charge layer (SCL) and the surface coverage of oxyl intermediates. The model also considered the effects of pH on reaction energies and rates.

The experimental measurements revealed a near third-order dependence of the OER rate on the surface hole density at all applied potentials. Analysis of the transient photocurrent measurements, using both the integrated charge and the extracted double-layer charge (surface holes), consistently supported this third-order behavior. This contradicts previous findings reporting first-order dependence at low hole densities. DFT calculations showed that photogenerated holes driven to the solid/liquid interface promote the dehydrogenation of surface hydroxy groups via PCET steps, leading to the formation of Fe-oxo/oxyl intermediates. TDDFT simulations successfully reproduced the experimentally observed broad absorption band around 650 nm, associated with these surface holes. Analysis of several O-O bond formation mechanisms, through DFT calculations, revealed three pathways: standard PCET leading to a hydroperoxo intermediate, and water molecule dissociation producing either hydroperoxo or superoxo intermediates. Kinetic analysis, using NEB calculations, showed that the most favorable pathway involved dissociative adsorption of a hydroxide ion on three nearby Fe-oxo/oxyl groups (three surface holes), resulting in a superoxo intermediate. This reaction has a weakly dependent activation energy on the number of surface holes. The microkinetic model, integrating these elementary steps, successfully reproduced several experimental features: the third-order power-law dependence of the OER rate on the surface hole concentration, the low apparent activation energy (0.18 eV), the linear increase in the OER rate with light intensity, and the increase in rate with increasing pH. The model indicated that the O-O bond formation predominantly occurs via the three-site mechanism (step 9), involving a hydroxide ion, while pathways involving water molecules play a minor role. At high SCL hole concentration, the hole diffusion (step 1) becomes the rate limiting step, while at low SCL hole concentration, step 9 becomes the rate limiting step.

The findings demonstrate a multisite mechanism for the OER in haematite, contrasting with the commonly assumed single-site PCET mechanism. The observed third-order dependence on surface hole density arises from the requirement of three nearby oxyl sites for the dissociative adsorption of a hydroxide ion, leading to superoxo intermediate formation. This is analogous to the OEC in photosystem II, where hole accumulation at multiple sites precedes O-O bond formation. The weak dependence of the activation energy on surface hole coverage in haematite distinguishes it from metallic oxides like IrO₂, where a strong linear dependence leads to an exponential rate dependence. The observed near-independence of the free-energy cost of the initial PCET step on surface hole concentration mirrors the redox potential "levelling" seen in the OEC. The microkinetic model's success in reproducing experimental findings validates the proposed mechanism, emphasizing the importance of multisite interactions and the role of hydroxide ions in the OER on haematite. The model also supports a linear relationship between photocurrent and pH, consistent with some experimental observations but not all, highlighting the complexity of factors influencing the OER process.

This study provides a comprehensive understanding of the multihole OER mechanism in haematite photoanodes. The third-order dependence of the OER rate on surface hole concentration stems from a three-site mechanism involving hydroxide ion dissociation, supported by both experimental and theoretical findings. The analogy with the biological OEC highlights the importance of multisite interactions for efficient water oxidation. Future work could focus on refining the microkinetic model to include more detailed surface chemistry, exploring the influence of different crystal facets, and examining the role of surface states in controlling the OER kinetics at varying pH conditions.

While the microkinetic model successfully reproduces key experimental observations, certain simplifications were made. The model does not explicitly consider the detailed generation, recombination, and diffusion of holes within the space charge layer (SCL), nor the spatial distribution of holes within the SCL. The model also simplified surface chemistry, neglecting the acid-base equilibrium of surface sites. Finally, the DFT calculations relied on a static approach for calculating activation energies, although thermodynamic integration validated this approach for the key step.