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### Abstract

Photoelectrochemical water splitting is a promising source of clean, renewable fuel in the form of hydrogen. Despite extensive research endeavors, the widespread adoption of this technology is impeded due to suboptimal catalysts for the oxygen evolution reaction (OER) taking place on the anode. Studies have shown that linear scaling relationships exist between the binding energies of the OER intermediates. These relationships are responsible for the emergence of an overpotential which limits the catalytic efficiency of electrochemical cells. This work is devoted to the study of the OER, the emergence of linear scaling relationships, and possible avenues for overcoming them. We employ a selection of ab-initio computational free energy methods based on density functional theory in order to investigate the OER at atomistic model semiconductor interfaces. An approach based on thermodynamic integration and \textit{ab-initio} molecular dynamics simulations is used to isolate the effect of the solvent on the OER free energy steps. The observed effect is twofold. First, the presence of explicit water affects the equilibrium configurations of the reaction intermediates. Second, explicit water modifies the OER free energy steps by up to 0.5 eV. This effect is rationalized in terms of electrostatic interactions at the interface. Next, we verify the existence of the linear scaling relationships across a set of semiconductor and metal interfaces. We establish the robustness of the scaling relationships with respect to the adopted energy functional. Two potential approaches of breaking the linear scaling are considered. First, a bifunctional mechanism that involves two close but functionally different active sites is investigated. The performance of the proposed mechanism is studied on a set of model interfaces, and the results indicate that specific combinations of catalysts may overcome the limitations imposed by the linear scaling relationship. We were able to establish general trends governing the efficiency of the bifunctional mechanism. In particular, a correlation between the valence band maximum and the hydrogen binding energy may be used as a descriptor in future searches for suitable hydrogen acceptors within the bifunctional scheme. Next, a detailed study of NiOOH/FeOOH catalysts identifies features most favorable to the bifunctional mechanism. Overpotentials as low as 0.13 eV are found for specific configurations. These results support the bifunctional mechanism as a means to break the linear scaling relationships. Second, hole polarons at the TiO$_2$ surface induced by electronegative adsorbates in the OER intermediates are studied. The computational hydrogen electrode method in conjunction with a hybrid density functional is employed to quantify the effect of the surface polarons on the OER free energy steps. We find that the hole bipolarons reduce the overpotential of the reaction-determining step leading to good agreement with experiment. The stability of the polarons is further confirmed at the hydrated surface through a free energy study involving the explicit treatment of the solvent. Finally, the polaron energy level is aligned with respect to the redox levels in water to better understand the role of the polarons in the OER. Since the occurrence of surface hole polarons is unrelated to the scaling relationships, it offers an additional handle in the search for improved catalysts.