Implications of the M-OO∙∙OO-M recombination mechanism on materials screening and the oxygen evolution reaction

Identification of active electrocatalysts for the oxygen evolution reaction (OER), corresponding to the bottleneck in electrolyzers to produce gaseous hydrogen as energy vector, by electronic structure calculations relies on the assumption of the mononuclear mechanism, comprising the *OH, *O, and *OOH intermediates. This mechanistic description is thermodynamically hampered by a scaling relation between the *OH and *OOH adsorbates, which may serve as an explanation why OER catalysts commonly require large overpotentials to reach sufficient current densities. Recently, an alternate OER pathway was proposed that, in contrast to the mononuclear description, consists of the formation of two adjacent *OO adsorbates, and gaseous oxygen is produced by chemical recombination of the neighboring *OO intermediates. In the present manuscript, a data-driven model based on a dedicated assessment of the elementary reaction steps is deduced, which enables evaluating the mononuclear and *OO pathways by the same set of parameters. Potential-dependent volcano plots are constructed to comprehend the energetics of the competing mechanisms. It is demonstrated that the alternate OER pathway consisting of the *OO∙∙*OO recombination step may excel the mononuclear description at overpotentials corresponding to typical OER conditions. Consequently, it is suggested that future studies, aiming at the identification of OER materials, may not omit the *OO∙∙*OO recombination mechanism when using concepts of materials screening in a heuristic fashion or multiscale modeling.


Introduction
Oxygen evolution reaction (OER) is the limiting process in electrolyzers for the conversion of electrical energy into gaseous hydrogen as energy carrier [1][2][3]. Four proton-electron pairs need to be transferred for the formation of a single oxygen molecule in the reaction mechanism (cf equation (1)), thus causing a sluggish reaction kinetics: 2 H 2 O → O 2 + 4H + + 4e − , U 0 = 1.23 V vs. RHE/ reversible hydrogen electrode . (1) About 10 years ago, Koper related the poor kinetics of the OER to a scaling relation of the intermediate states in the OER mechanism [4], which is assumed to follow the so-called mononuclear description [5]. In this pathway, successive stabilization of the * OH, * O, and * OOH adsorbates on an electrode surface is required, summarized in equations (2) Please note that M denotes the catalytically active surface site (e.g. an undercoordinated metal atom), and the ∆G j (j = 1, 2, 3, 4) values refer to the free-energy changes of the respective proton-electron transfer step in the OER. Since the equilibrium potential of the OER amounts to 1.23 V on the RHE scale (cf equation (1)), the ∆G j values sum up to 4 × 1.23 eV = 4.92 eV at U = 0 V vs. RHE.
The scaling relation between the * OH and * OOH intermediates couples the free-energy changes ∆G 2 and ∆G 3 in that their sum amounts to (3.20 ± 0.20) eV at U = 0 V vs. RHE, thus exceeding the predicted theoretical optimum of 2e × 1.23 V = 2.46 eV [6,7]. Please note that the theoretical optimum of 2.46 eV as scaling-relation intercept (SRI) has been challenged recently, pointing out that overpotential and kinetic effects may shift the ideal SRI to about 2.76 eV [8,9].
Despite the ambiguity of the optimum SRI in the literature, theoretical studies aiming at the identification of new catalytic materials for the OER by materials screening have largely focused on the mononuclear mechanism (cf equations (2)-(5)), using the concept of volcano plots to identify promising electrocatalysts [10][11][12][13][14][15][16][17][18][19][20]. Since almost a decade, the notion of breaking scaling relation to reduce the SRI of 3.2 eV has been put forth as a design criterion to obtain improved OER catalysts because a smaller SRI may be accompanied with higher electrocatalytic activity [21,22]. Yet, this approach is also discussed controversially in the literature given that there is evidence that breaking scaling relation can cause optimization of electrocatalysts in the wrong direction to lower activity [23][24][25].
So far, there is only little progress relating to the identification of alternate OER pathways [26]. Recently, Binninger and Doublet performed electronic structure calculations in the density functional theory (DFT) approximation to re-investigate the OER over IrO 2 (110) [27]. The authors reported a novel OER pathway where the catalytic cycle commences from a fully * O-covered surface and contains the formation of gaseous oxygen via the recombination of two adjacent * OO * OO groups (cf equations (6)-(10)): The meaningfulness of this pathway is substantiated by the fact that the proposed mechanism is consistent with recently reported experimental results of the OER over IrO 2 from operando x-ray spectroscopy or cyclic voltammetry [28][29][30]. Additionally, the * OO intermediate (cf equations (6)-(10)) has been spectroscopically identified and computationally predicted by Rao, Kolb, and others for the case of RuO 2 [31,32], thus further corroborating this intermediate species as a precursor for oxygen formation over solid-state electrodes.
Given that Binninger reported that the * OO·· * OO recombination mechanism is thermodynamically and kinetically favored over the mononuclear description for IrO 2 (110) [27], it appears important to generally assess the validity of this mechanism for any OER material. In the present work, a data-driven methodology in conjunction with a descriptor-based approach is used to compare the energetics of the mononuclear and * OO·· * OO recombination mechanisms by volcano-based analyses. It is demonstrated that the * OO·· * OO recombination pathway may excel the mononuclear mechanism for typical OER overpotentials, thus opening new doors within the search of OER catalysts by heuristic materials screening.

Method
We make use of an in-house data-science approach that connects the adsorption free energies of the OER intermediates, ∆G j , to electrocatalytic activity by the descriptor G max (η), in the following denoted as G max (U) where U indicates the applied electrode potential on the RHE scale [33]. The peculiarity of this descriptor refers to the fact that G max (U) analyzes the largest free-energy span between the intermediates with smallest and highest free energy in the free-energy landscape as a function of the applied electrode potential [34]. The free-energy span governing G max (U) correlates with electrocatalytic activity since a Brønsted-Evans-Polanyi (BEP) relation between this descriptor and the reaction kinetics with a sensitivity of 0.2 eV has been reported [33]. Additionally, knowledge of G max (U) enables discussing rate-determining states, which are often referred to as the rate-determining steps, of a mechanistic description [35].
We start the discussion with the mononuclear mechanism (cf equations (2)-(5)). The free energies of the reaction intermediates in dependence of the ∆G j values are indicated by equations (11)- (15): The scaling relation between the * OH and * OOH intermediates reads (cf equation (16)): Besides, another scaling relation between the * OH and * O intermediates has been reported in theoretical studies [6,10]: It should be noted that the scaling relation of equation (17) is not as robust as the scaling relation between the * OH and * OOH intermediates. Yet, application of this scaling relation allows simplifying the mononuclear mechanism to a set of three parameters (U, SRI, and ∆G 1 ), and, at a later stage of the manuscript, the approximation of equation (17) is validated by comparing the observed rate-determining states in the framework of G max (U) with a microkinetic study.
Taking equations (16) and (17) into account, equations (11)-(15) translate to: Determination of G max (U) comprises the assessment of all possible free-energy spans between the intermediate states in the mononuclear mechanism, summarized in equation (23): The largest free-energy span of equation (23) defines the descriptor G max (U), as indicated by equation (24): In the same fashion as for the mononuclear mechanism, the energetics of the * OO·· * OO recombination pathway (cf equations (6)-(10)) is analyzed. The free energies of the reaction intermediates in dependence of the ∆G j values are given by equations (25)-(30): In the following, the free-energy changes of equations (25)- (30) are correlated to the free-energy change ∆G 1 and the SRI. We conclude: Please note that the formation of the * OO adsorbate from the * OOH intermediate is approximated by the same scaling relation as present between the * O and * OH intermediates (cf equation (17)). This simplification is justified since both processes contain the removal of one proton-electron pair from surface oxygen.
Taking the subtleties of equations (31)-(34) into account, equations (25)-(30) translate to: In analogy to the mononuclear mechanism, G max (U) can be derived by application of equation (24), assessing all possible free-energy spans between the intermediate states of equations (35)- (40).
At this stage of the manuscript, it is important to leave a note on the mechanism and energetics of the * OO·· * OO recombination pathway. The mechanistic description used in this analysis (cf equations (6)-(10)) differs slightly to the one reported by Binninger and Doublet in a recent work in that the authors also postulated the occurrence of * OH intermediates that may stabilize adjacent * OO groups [27]. First, it should be noted that all chemical steps in the formulation by Binninger were combined with the subsequent electrochemical step, except for the * OO·· * OO coupling step. This reduction is substantiated because other chemical steps than the * OO·· * OO coupling step do not govern the reaction rate [27]. Besides, the sequence of the elementary steps in Binninger's mechanisms are slightly rearranged. This simplification of the * OO·· * OO recombination pathway is, however, needed to correlate the energetics to the same set of parameters (U, SRI, and ∆G 1 ) as obtained for the mononuclear mechanism (vide supra). It needs to be stressed that the essence of the * OO·· * OO recombination pathway (cf equations (6)-(10)) remains identical to the one reported by Binninger and Doublet in that adjacent * OO groups are successively formed on the electrode surface, and they recombine under the formation of gaseous oxygen.
Given that the concept of G max (U) allows deriving potential-dependent activity trends, volcano plots are constructed for applied electrode potentials of U = 1.40 V, 1.50 V, and 1.60 V vs. RHE. In contrast to the common practice of calculating the ∆G j values for a certain material class, we make use of a data-driven methodology by defining a basis set [36] for the free-energy change ∆G 1 , which serves as the descriptor in the analysis. Following the perspective by Rossmeisl and coworkers on a decade of atomic-scale simulations in the OER [10], a typical value range for ∆G 1 corresponds to [−0.50, 2.50] eV. Therefore, all possible ∆G 1 values in this range with a step size of 0.01 eV are tracked, and the descriptor G max (U) is calculated for the respective electrode potentials to approximate electrocatalytic activity. From the resulting volcano curve, the data range with lowest G max (U) at the volcano apex, corresponding to highest catalytic activity, is extracted. This procedure is carried out for both the mononuclear and * OO·· * OO recombination mechanisms to identify which mechanistic pathway is kinetically preferred in the approximation of G max (U). Please note that this analysis cannot be conducted by the popular concept of the thermodynamic overpotential, η TD , as activity descriptor [37] since the energetics of a chemical reaction step (cf equation (10)) needs to be evaluated for a thorough assessment of activity which is beyond the scope of η TD [33].
For the derivation of the potential-dependent volcano plots of both mechanistic pathways, a code has been programmed in Wolfram Mathematica, which is included in section 2 of the supplemental. All results can be reproduced based on the attached file.

Mononuclear mechanism
Following the methodology in the previous section, a volcano plot for the mononuclear mechanism at U = 1.40 V vs. RHE is constructed, using SRI of 3.2 eV. The resulting volcano curve is depicted in figure 1(a). It becomes evident that different reaction steps refer to the largest free-energy span governing G max (U): while for ∆G 1 < 0.32 eV, the sequence * O → * OOH → * +O 2 limits activity, the G max (U) determining free-energy span switches to * O → * OOH (0.32 eV < ∆G 1 < 0.70 eV), * OH → * O → * OOH (0.70 eV < ∆G 1 < 0.90 eV), * OH → * O (0.90 eV < ∆G 1 < 1.40 eV), and * → * OH → * O (∆G 1 > 1.40 eV) for larger values of ∆G 1 . At the volcano apex, the formation of * OOH out of * OH is reconciled with the bottleneck, and G max (U) amounts to 0.40 eV.
Based on the free-energy spans governing G max (U), the rate-determining states are discussed for a Tafel slope of b = 40 mV dec −1 in figure 1(b). Please note that b = 40 mV dec −1 indicates that the second elementary electrochemical step reveals the highest transition-state free energy whereas the first step is pre-equilibrated [38,39]. This assumption is related to the fact that highly active OER catalyst reach a Tafel slope larger than 60 mV dec −1 , indicating that the first elementary electrochemical step governs the rate, at OER overpotentials exceeding 400 mV (U > 1.63 V vs. RHE) [40]. Therefore, it can be concluded that most likely b = 40 mV dec −1 may be met in the potential regime of 1.40 V < U vs. RHE < 1.63 V vs. RHE.
A technical note on the derivation of the rate-determining states is needed. For the sequence * O → * OOH → * +O 2 , the step * O → * OOH is pre-equilibrated whereas the step * OOH → * +O 2 reveals the highest transition-state free energy, and thus may be reconciled with the rate-determining step (RDS). It should be noted that * OOH decomposition as the RDS was suggested by Shao-Horn and coworkers for the OER over RuO 2 , hence confirming the importance of this elementary step on the OER rate [28,29]. For the sequence * O → * OOH (0.32 eV < ∆G 1 < 0.70 eV), the same conclusion is drawn for a Tafel slope of b = 40 mV dec −1 . While the formation of * OOH from * O is thermodynamically restrained, the transition state for O 2 formation has the highest transition-state free energy. Therefore, the areas ∆G 1 < 0.32 eV and In a previous microkinetic study, it was reported that * O formation, * OOH formation, and * OOH decomposition are three possible RDS for the OER over any solid-state electrode [41]. Figure 1(B) confirms this picture by using the approximation of G max (U), and this finding may validate the usage of the scaling relation between the * OH and * O intermediates (cf equation (17)) as well as the * OOH and * OO intermediates (cf equations (33) and (34)) in the present analysis.
In the next step, volcano plots for the mononuclear mechanism are constructed for U = 1.50 V and 1.60 vs. RHE, which are depicted in figure 2. A discussion on the RDS for these potential values can be found in section 1 of the supplemental (cf figure S1).
Upon increasing electrode potential, the free-energy span governing G max (U) is not altered qualitatively, however, the respective ∆G 1 ranges are affected in that the free-energy regimes for * O → * OOH and * OH → * O as limiting steps become broader. These elementary steps correspond to the potential-determining steps in the thermodynamic picture of the descriptor η TD [42,43]. As expected, electrocatalytic activity for the mononuclear mechanism is increased with increasing electrode potential due to smaller values of the descriptor G max (U). At the volcano apex, G max (U) = 0.20 eV or 0 eV for U = 1.50 V and 1.60 vs. RHE, respectively is observed. Therefore, we conclude for the mononuclear mechanism:

* OO·· * OO recombination mechanism
In the same fashion as for the mononuclear mechanism in the previous subsection, volcano plots for the * OO·· * OO recombination pathway are derived at different electrode potentials. The results are compiled in figure 3. Figure 3(a) reveals that different sequences limit OER activity at U = 1.40 V vs. RHE, namely Similar to the mononuclear mechanism, the free-energy span governing G max (U) does not change with increasing electrode potential, but the ∆G 1 regimes for * O → * OOH and * OOH → * OO become broader so that the sequence * O → * OO vanishes as limiting reaction sequence for U = 1.60 V vs. RHE.
Please note that discussion of the RDS for the * OO·· * OO recombination path is not straightforward because, in contrast to the mononuclear description, this mechanism takes place on two adjacent active sites. Therefore, further information on the RDS for this pathway is not provided in the present work, which mainly focuses on electrocatalytic activity of the competing mononuclear and * OO·· * OO recombination mechanisms by means of a data-driven framework.
Upon increasing overpotential, electrocatalytic activity for the * OO·· * OO recombination mechanism is increased due to smaller values of the descriptor G max (U). At the volcano apex, G max (U) = 0.80 eV, 0.40 eV, and 0 eV for U = 1.40 V, 1.50 V, and 1.60 vs. RHE, respectively is observed. Therefore, we conclude for the * OO·· * OO recombination mechanism: (

Implications of the * OO·· * OO recombination pathway for materials screening
Comparing electrocatalytic activity for the mononuclear and * OO·· * OO recombination mechanisms, it is evident that the mononuclear mechanism prevails for U = 1.40 V and 1.50 V vs. RHE due to smaller values of the descriptor G max (U). However, due to the larger ( ∂Gmax(U) ∂U ) SRI slope, the * OO·· * OO recombination pathway excels the mononuclear mechanism for U > 1.60 V vs. RHE at the volcano apex. This finding is of importance, indicating that the * OO·· * OO recombination pathway may be even more widespread among different materials. So far, the analysis of the mononuclear and * OO·· * OO recombination mechanisms relies on SRI = 3.2 eV. While this is the most often reported SRI in the literature, recent studies indicate that the SRI is not universal among all materials but rather depends on the respective material class, the exchange correlation functional employed in the DFT calculations, and the consideration or neglection of solvation [44,45]. Given that SRI values as low as 2.8 eV have been reported for the material class of transition-metal oxides [46,47], the analysis of the mononuclear and * OO·· * OO recombination mechanisms is extended to SRI values of 2.8 eV, 2.9 eV, 3.0 eV, and 3.1 eV. The corresponding procedure can be reproduced by changing the SRI value in the attached code of section 2 of the supplemental.
In a similar fashion to the potential-dependent analysis, we determine the slope of the mononuclear and * OO·· * OO recombination mechanisms at the volcano apex for the variation of G max (U) with SRI at constant electrode potential. We obtain for the mononuclear mechanism (cf equation (43)) and the * OO·· * OO recombination pathway (cf equation (44)): ( Similar to the potential dependence, the * OO·· * OO recombination pathway is stronger affected by a decrease in the SRI than the mononuclear mechanism, which can be related to the steeper slope of the volcano curve. Consequently, the * OO·· * OO recombination pathway surpasses the mononuclear mechanism even at lower electrode potentials if the SRI is smaller than 3.2 eV. This finding is summarized in figure 4, providing a U-SRI map that indicates the preferred reaction mechanism using the concept of G max (U) to approximate electrocatalytic activity. Figure 4 is the main result of this study, illustrating that the * OO·· * OO recombination pathway can be the energetically preferred pathway at electrode potentials as low as 1.40 V vs. RHE. This finding demonstrates that the * OO·· * OO recombination mechanism is of relevance for the heuristic discovery of OER materials, and thus, should not be neglected in future screening studies that make use of the concept of volcano plots.
Yet, I would like to point out to be careful about the interpretation of the preferred reaction mechanism using the framework of G max (U). This descriptor relies on a BEP relation between the potential-dependent intermediate energetics and the potential-dependent kinetics with an uncertainty of 0.2 eV [33]. Therefore, only if one of the two mechanisms reveals G max (U) value smaller than 0.2 eV than the other, it can be concluded in an impartial fashion that the other mechanism can be neglected. However, this finding directly underpins the main conclusion of this study in that the * OO·· * OO recombination mechanism competes with the mononuclear pathway for typical OER conditions. Although, which of these two mechanisms is the operating one for a given electrode material requires further analyses using the DFT approach. Finally, let me outline a few caveats of the conducted trend study using a data-science approach. It should be noted that the presented model relies on the tacit assumption that structural reorganizations do not impact activity. It is well-known that OER materials are prone to decompose under experimental operando conditions [48,49], but these effects cannot be captured by the activity analysis of the competing mononuclear and * OO·· * OO recombination mechanisms. Besides, the impact of the electrochemical interface on the catalytic processes is simplified in that only the energetics of the intermediate states is accounted for. Double layer and surface charging effects or the presence of ions [50][51][52][53] are omitted in the analysis because they go beyond the scope of this work. Finally, computational assessment of the scaling relation between the * OO and * OOH intermediates assumed in this work (cf equations (33) and (34)) is desirable because so far, there is no trend study available that allows quantifying the energetics of the * OO and * OOH adsorbates in a class of materials.

Conclusions
The present manuscript reports a data-driven methodology to compare the energetics of the mononuclear and * OO·· * OO recombination mechanisms in the OER. Using a dedicated analysis of the free-energy changes of the mechanistic descriptions in combination with scaling relations for oxygen-containing intermediates, both mechanisms are referred to a set of three parameters, namely the applied electrode potential, U, the SRI, and the free-energy change for the formation of the * OH adsorbate, ∆G 1 . Electrocatalytic activity is evaluated by the descriptor G max (U), which relies on a potential-dependent assessment of the intermediate states' energetics, but equally factors kinetic effects in the analysis via BEP relation. For both mechanistic descriptions, volcano plots are constructed for varying conditions of U and SRI.
The volcano plots allow gaining insight into limiting reaction steps and enable determining the slopes ( slopes. This can be seen as the main reason why the * OO·· * OO recombination mechanism can be preferred over the mononuclear description in a typical OER potential regime of U = (1.40 V-1.60 V) vs. RHE.
I would like to emphasize that the focus of the present contribution is not on the calculation of new data for the OER or the investigation of a new materials class, but rather aims at an unbiased comparison of the mononuclear and * OO·· * OO recombination mechanisms by a rigorous thermodynamic analysis. Given that the * OO·· * OO recombination mechanism is competitive to the mononuclear description under typical OER conditions, the * OO·· * OO pathway cannot be neglected in future screening studies that aim at heuristic materials discovery by the analysis of the reaction intermediates' free energies.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).