ORR on Simple Manganese Oxides: Molecular-Level Factors Determining Reaction Mechanisms and Electrocatalytic Activity

Inthisstudywecombineexperimentalrotatingringdiscelectrodedata,theory,molecular-levelmodelingandmicrokineticsimulationsinordertogainadeeperinsightintotheoxygenreductionreaction(ORR)mechanismonsimplemanganeseoxidesinalkalinemedia.Wedemonstratethat“thermodynamic”approachbasedonperiodicaldensityfunctionaltheorycalculationsisunabletoexplaintheexperimentallyobserveddifferencesintheORRkineticsonthemost( α -Mn 2 O 3 ) and the least ( α -MnOOH) active oxide. We perform quantum mechanical cluster calculations and show that faster kinetics of the hydrogen peroxide reduction on the surface of Mn 2 O 3 oxide and the ensuing lower peroxide yield during the ORR are corroborated by the lower barrier for the dissociation of hydrogen peroxide adsorbed on the surface of Mn 2 O 3 arising from adsorbate-adsorbate interactions. We provide the arguments in favor of the outersphere nature of initial O 2 reduction steps and demonstrate that this hypothesis does not contradict the experimental trends observed for ORR and hydrogen peroxide reduction reactions on Mn 2 O 3 and MnOOH.

Electrochemical oxygen reduction reaction (ORR) in alkaline media has recently attracted much attention in connection with the development of liquid and solid alkaline fuel cells and metal-air batteries. Manganese oxides are among the most attractive ORR catalysts, combining activity, stability, environmental friendliness and reasonably low cost. Recently some of us investigated the influence of crystal structure and composition of manganese oxides on their specific (real surface-weighted) electrocatalytic activity in the ORR, and in the reactions of hydrogen peroxide [1][2][3][4][5] which is considered as a likely reaction intermediate. Various oxides have been studied, including A 1-x A x MnO 3 (perovskite-type), 1,2 and simple Mn oxides: [3][4][5] α-Mn 2 O 3 (bixbyite), Mn 3 O 4 (spinel), β-MnO 2 (pyrolusite), and α-MnOOH (manganite). Both the ORR and the hydrogen peroxide reduction reaction (HPRR) were found to be highly dependent on the crystal structure of the oxide, α-Mn 2 O 3 and α-MnOOH, respectively, showing the highest and the lowest activity in both reactions. [3][4][5] A tentative ORR mechanism was proposed, and a kinetic model was developed, 3,4 which allowed us to semi-quantitatively reproduce the experimental observations. It should however be noted that the steps comprised in the proposed ORR mechanism are not necessarily elementary.
In this publication we seek to better understand the nature of elementary steps of the ORR catalyzed by Mn oxides and the origin of the structure sensitivity. In order to do so we use the rotating ring disc electrode (RRDE) to determine the hydrogen peroxide yield during the ORR on four different oxides (α-Mn 2 O 3 , Mn 3 O 4 , β-MnO 2 , and α-MnOOH). Then, we apply a number of complementary computational approaches to get information on the surface composition and structure of the most (α-Mn 2 O 3 ) and the least (α-MnOOH) active Mn oxide, and to provide comparative analysis regarding adsorption and reactivity of O 2 and intermediate dioxygen species on their surfaces. For α-Mn 2 O 3 we consider the (111) crystal plane, which was observed by transmission electron microscopy with atomic resolution. 4 For α-MnOOH, the most stable (110) plane is considered.

J3200
Journal of The Electrochemical Society, 165 (15) J3199-J3208 (2018) with the BET surface area of 25 m 2 · g −1 was obtained by the heattreatment of MnOOH in air at 240 • C. The sample with the BET surface area of 27 m 2 · g −1 was obtained by calcination of an amorphous product of comproportionation of Mn(CH 3 COO) 2 and KMnO 4 in air at 550 • C for 12 h, 11 its electrochemical and electrocatalytic properties were discussed in Ref. 4. The sample with the BET surface area of 8 m 2 · g −1 (see RRDE data in the SI) was obtained by milling of the commercially available Mn 2 O 3 ("Reachim", Russia). 4 MnO 2 (pyrolusite, 48 m 2 /g) was fabricated by the heat-treatment of MnOOH at 600 • C. Mn 3 O 4 (hausmannite, 13 m 2 · g −1 ) was obtained by the heat-treatment of MnOOH in argon atmosphere at 600 • C. According to the XRD data, all samples were pure phases and did not contain crystalline impurities. Carbon of the Sibunit family with the BET and BJH (Barrett-Joyner-Halenda method) surface areas equal to 65 and 52 m 2 · g −1 , respectively, was kindly provided by Dr. P.A. Simonov. It was obtained by hydrocarbon pyrolysis followed by activation as described in Ref. 12.
Electrochemical measurements were performed in 1 M NaOH electrolyte prepared from Acros Organics 50 wt% aqueous solution in a three-electrode cell at 25 • C using Autolab potentiostat (PG-STAT302N) equipped with an analog scan generator. All parts of the electrochemical cell in contact with the alkaline electrolyte were from Teflon. The RRDE tip comprised a glassy carbon (GC) disc and a Pt ring. Sibunit carbon-oxide compositions with the 1:1 (wt) ratio were deposited on the GC disc as described in Ref. 4 to achieve oxide loadings of 23, 30, and 91 μg per cm 2 of the GC disc. Potentials were measured versus HgO/Hg (IJ Cambria Scientific) in the same solution and recalculated to the reversible hydrogen electrode (RHE) scale (+0.93 V vs. RHE at 25 • C). The area of the Pt counter electrode was ∼6 cm 2 . The electrolyte resistance determined from the high frequency part of the electrochemical impedance spectra (measured in the 1 Hz to 100 kHz range) was equal to ca. 15 . The experimental curves were not corrected for the uncompensated ohmic resistance, as such correction would not result in any noticeable changes of the current-potential curves. The potential at the ring was +1.23 V. Calibration of the RRDE was performed using ferro-ferricyanide redox couple as shown in Figure S1 (Supplementary Information, SI). Experimental collection factor of 0.25 was in good agreement with the theoretical value.
Microkinetic modeling.-For innersphere pathway studied earlier, the modeling is described in Refs. 3,4. The possibility of the O 2 reduction into HO 2 − species through an outer-sphere mechanism was explored with the help of microkinetic modeling considering reaction steps 1, 2 , 3 , 4 and 5 described in Results and discussion section. Since both Mn oxides exhibit significant activity for the reduction of O 2 into HO 2 − , contribution of the carbon particles to the ORR was neglected. The kinetic equations and the parameter values used for the simulations are given in the SI (Calculation of barriers for the outer-sphere scenario (O 2 +e − → ← O 2 − −step 2') section). The model assumes Langmuir adsorption/desorption of HO 2 − on the surface of Mn oxides and Butler-Volmer kinetics for the electron transfer steps. The model considers the escape of O 2 − and HO 2 − from the diffusion layer in order to simulate the RRDE current-potential curves.
Computational details.-Spin-polarized periodical density functional theory (DFT) calculations were performed using the VASP program package 13 with PAW 14 pseudopotentials and the RPBE-GGA functional. 15 The asymmetric four Mn-layer supercells which mimic the MnOOH (110) (8 surface Mn atoms) and Mn 2 O 3 (111) (16 surface Mn atoms) surfaces were constructed from the corresponding bulk structures. An energy cutoff of 600 eV and 2 × 2 × 1 (Mn 2 O 3 ) and 3 × 2 × 1 (MnOOH) k-point meshes were used in all the calculations. The dipole corrections were applied in the direction perpendicular to the surfaces. Only one surface layer together with the adsorbed intermediates was relaxed until the change in total energy of the system was less than 10 −3 eV. The obtained lattice parameters for Mn 2 O 3 are: a = b = c = 9.59205 Å, α = β = γ = 90.0 • . For α-MnOOH: a = 5.44060, b = 5.50974, c = 5.45707 Å; α = 90.0 • , β = 114.7 • , γ = 90.0 • . These parameters are within 10% to the experimental values. 16,17 Active surfaces of Mn 2 O 3 (111) and MnOOH (110) oxides were constructed implying 0.5 monolayer (ML) O ad and 0.5 ML HO ad coverages. Under experimental conditions, these coverages correspond to somewhat different overpotentials (see Results and discussion section). However, this potential shift is not sufficient to cancel out the pronounced difference in the oxides' electrochemical activities toward oxygen reduction. The possible partial coverage of the surfaces with water molecules was addressed neither in the periodical DFT calculation, nor in the microkinetic modeling, as the primary effect is believed to be related largely to the differences of Mn oxides reactive centers configuration and not to the differences in the oxide-water interactions specifics (which is the inevitable assumption on the current stage). In all the calculations a 20 Å vacuum region was introduced to avoid the interaction between the slabs.
The thermodynamics of electrochemical reactions was addressed by means of computational standard hydrogen electrode approach. 18,19 Zero-point energy and entropy corrections were introduced to compute Gibbs free energies for the reactions involving ORR adsorbates.
Cluster calculations were performed at the DFT level using the B3LYP functional as implemented in the Gaussian 09 program suite. 20 The O and H atoms of the adsorbates and oxide clusters were described by the standard 6-311++G(d,p) basis set. The effect of inner electrons of the Mn atoms was included in a relativistic Effective Core Potential LanL2, while a basis of DZ quality was employed to describe Mn valence electrons. The spin-polarized Kohn-Sham formalism was used to treat the open shell systems.
The clusters were constructed using the geometry of Mn 2 O 3 (111) and MnOOH (110) surfaces optimized at the periodical DFT calculations. Each cluster contained 8 Mn atoms, with the two central Mn atoms mimicking the reaction center. The closest Mn atoms on the oxide surfaces were chosen as potential candidates for the reaction centers. The geometry of the active center and the positions of Mn and O atoms in the clusters were frozen during the optimization of adsorbates to keep the initial surface structure. A part of the O atoms was saturated by auxiliary hydrogen atoms to achieve electroneutrality at the model clusters. The ground state multiplicities for the Mn oxide clusters were determined to be 16 and 14 for Mn 2 O 3 and MnOOH clusters and 17 and 15 for the "cluster + OO ad " systems. The spin densities of the Mn atoms correspond to the anti-ferromagnetic state of the model clusters.
The resulting structures were visualized using VESTA program. 21

Results and Discussion
Short summary of the previously published data.-The ORR on Mn oxides has been extensively studied in the past (see Ref. 22 and refs. therein). It appears however that some studies neglected cathodic instability of oxide materials, subjecting them to cycling within wide potential limits exceeding the interval of their stability. Poux et al. and Ryabova et al. [1][2][3][4][5] optimized the preparation of oxide/carbon compositions (carbon addition is required for the improvement of the conductivity of the catalytic layers, its role being discussed in Refs. 5,23) and investigated electrochemical and electrocatalytic properties of Mn oxides with various crystal structures and compositions making sure that the electrode potential was comprised in the interval of the oxide stability. Figure 1 summarizes the key experimental data published in Refs. [1][2][3][4][5]. Panel (a) shows kinetic ORR currents of Mn oxides at 0.9 V vs. RHE normalized to their respective BET surface areas against the formal potential (E f ) of the surface Mn(III)/Mn(IV) redox couple determined from cyclic voltammograms (CVs). 4 One should notice an exponential increase of the electrocatalytic activity with the E f and ca. factor of 50 difference between the kinetic current of the most (Mn 2 O 3 ) and the least (MnOOH) active Mn oxide. To better understand the ORR mechanism, Poux et al. 1  The experimental data for the ORR and hydrogen peroxide reactions on Mn oxides briefly presented above and described in more detail in Refs. 1-5 could be rationalized using microkinetic modeling within a "series" innersphere ORR mechanism assuming that the O 2 molecule adsorbs on the Mn(III) surface centers (presumably associated with OH ad groups) but not on Mn(IV) surface sites (the latter being associated with O ad Kinetic modeling performed within the ORR mechanism comprising steps 1-5, allowed us to reproduce the experimental data for the oxygen and hydrogen peroxide reactions on various Mn oxides taking into account the experimentally determined E f values for step 1 and assuming material-dependent kinetics for steps 2 and/or 3, and 5. 3,4 The different peroxide yields observed using the RRDE and further discussed in Experimental RRDE data section ( Figure 2) as well as the HPRR limiting currents ( Figure 1) are explained by the large difference in the rate constant for step (5) for the studied Mn oxides. The ORR current at 0.9 V vs. RHE is strongly affected by the rate constants of steps 2-3, but also by the formal potential and by the kinetics of step 5, fast reduction of HO 2 − preventing its possible oxidation at 0.9 V. Note that the ratio of rate constants for the step 5 (k 5 ) for Mn 2 O 3 and for MnOOH was estimated from the kinetics of electrochemical reduction and chemical decomposition of HO 2 − as ca. 10 3 . 3 It is worth noting however that steps (1)(2)(3)(4)(5) are tentative and correspond to the combinations of at least two elementary steps. This scheme should be treated as possible but not unique, and in this work we apply molecular modeling in order to either support it or propose an alternative. Figure 2 demonstrates RRDE data for four Mn oxides. At all potentials and loadings, peroxide yields increase in the series Mn 2 O 3 < MnO 2 < Mn 3 O 4 < MnOOH, which agrees well with the decrease of the HPRR limiting currents (see Figures 1b-1d). This observation highlights the fact that the peroxide yield depends on the rate of the HPRR.

Experimental RRDE data.-
For all studied oxides except of the Mn 2 O 3 the peroxide yields depend on the oxide loading, increasing when the loading decreases . Disk currents are normalized to the geometric area of the electrode and corrected to the background currents measured in the N 2 atmosphere. Ring currents are normalized to the geometric area of the disk electrode and to the collection factor.
( Figures 2 and S2). Such a behavior is expectable and has been extensively discussed in previous publications: 1,24,25 the reason is the total number of active cites at the working electrode. As the number of active sites capable of adsorbing hydrogen peroxide intermediate increases, the probability of its re-adsorption increases as well, thus reducing the amount of H 2 O 2 escaping from the catalytic layer and reacting at the ring. It is interesting to note that for Mn 2 O 3 the peroxide yield at the ring does not change as the oxide loading decreases from 91 down to 30 μg · cm −2 , but then slightly increases for the loading of 23 μg · cm −2 (magenta curve in Figure S2). Such a non-linear dependence of the hydrogen peroxide yield on the loading suggests possible contribution of the H 2 O 2 generated at the GC support when the loading is low.
Since the key quantity is the number of active surface sites, the peroxide yield should not only depend on the catalyst loading but also on the specific surface area of the catalyst. Figure S3 shows RRDE data for three Mn 2 O 3 samples with S BET surface areas of 8, 25 and 27 m 2 · g −1 . One may notice that even for the low surface area sample the yield of the peroxide detected at the ring at low electrode potentials does not exceed 2.5%.
The low peroxide yields observed for Mn 2 O 3 could be rationalized either by assuming a "direct" ORR pathway (proceeding via the O-O bond breaking in a O 2 molecule), or a "series" ORR pathway occurring via intermediate formation of H 2 O 2 provided that its catalytic decomposition (e.g. in step 5) is faster than its desorption in step 4. These different scenarios will be explored below with the help of quantum chemical calculations.
Periodical DFT calculations.-Periodical DFT calculations were used for estimating adsorption energies of the reaction intermediates: OO ad , HOO ad , HO ad , and O ad assumed within a "series" mechanism. As it was previously mentioned, four-layer slabs were constructed to mimic MnOOH (110) and Mn 2 O 3 (111) surfaces. These calculations allowed us to assess surface restructuring of the two oxides, at least at a qualitative level. Given the large size of the Mn 2 O 3 (111) cell (190 atoms in the asymmetric cell) and the difficulties associated with accurate ab initio calculations for large systems, in our calculations only one surface layer was optimized, which induces some degree of inaccuracy in the obtained geometries of the surfaces. The results should thus be treated as an initial guess of the surface reconstruction trends. Figure 3 shows the geometries of the optimized first layers of Mn oxide surfaces. The active centers, which are assigned to the closest Mn atoms, are marked in the Figure Table S2 shows the geometries of the adsorbates and lists the corresponding bond lengths and angles in the structure. It can be seen that molecular oxygen is relatively weakly adsorbed at the model surfaces, with the Mn-Oo distance being 1.96-2.05 Å. The HOO ad intermediate adopts  In the framework of thermodynamic approaches, the free energy difference for the surfaces with various adsorbed intermediates is used to assess the kinetics of multistep processes without computing reaction activation energies. 18,19,26,27 This simplification assumes a straightforward relationship between the activation energy and the reaction free energy, which is not obvious, especially for the innersphere steps. For the ORR, free energy diagrams are usually constructed for the reaction pathway involving successive interconversion of the adsorbed OO ad , HOO ad , OH ad and O ad intermediates. Despite the thermodynamic approach remains a convenient and valid method for comparing adsorption energies of the intermediates and for the initial screening of potential catalysts, sometimes it fails to describe the experimental trends and to give correct predictions on the nature of the reaction limiting step. [28][29][30] In this work, we followed a simplified procedure to evaluate the interaction energies of the ORR intermediates with the Mn oxide surfaces, which did not involve an extensive search for the minimum energy surface at a given potential with the account for the fractional occupation of the surface by water molecules. Instead, we used MnOOH (110) and Mn 2 O 3 (111) surfaces at 0.5 ML OH ad and 0.5 ML O ad coverages and computed the free energy diagrams for the potentials, which correspond to these coverages based on the available experimental information (formal potentials of the two oxides). Under these conditions, the 0.5 O ad coverage corresponds to the potential of ca. 0.98 V for Mn 2 O 3 and 0.9 V for MnOOH. 4 The free energy diagrams for the two oxides, calculated for these potentials, are shown in Figure 4.
The free energy diagram suggests that for MnOOH the potential determining step (PDS) involves HOO ad formation from OO ad , while for Mn 2 O 3 the PDS could be attributed to the OH ad desorption step. While supporting the higher activity of Mn 2 O 3 , the thermodynamic approach fails to explain the most notable difference between the Mn 2 O 3 and the MnOOH oxide: kinetic limitation of the bond-breaking in HOO ad for MnOOH but not for Mn 2 O 3 evidenced by Figures 1b,  1d. This calls for a more detailed computational investigation of the hydrogen peroxide decomposition reaction, which involves the bond breaking in the hydrogen peroxide intermediate and thus is likely to be associated with a high energy barrier at least at the MnOOH (110) surface. In the next section we address the successive steps in the ORR mechanism, discuss possible elementary steps and estimate their activation barriers. [31][32][33] the ORR on Pt and Au electrodes in alkaline media was discussed in the framework of an outer-sphere mechanism. Given the low adsorption energies of O 2 at MnOOH and Mn 2 O 3 oxide surfaces (−0.03 and +0.07 eV, respectively), the outer-sphere scenario cannot be excluded. Within an outer-sphere mechanism, the first steps of the ORR can be expressed as follows:

Quantum chemical modeling of activation barriers for the elementary steps.-In a number of publications
HO 2 − species can then adsorb at the oxide surface: In what follows we consider feasibility of different ORR pathways based on relevant calculations. − species was considered within cluster approach, which involves some uncertainties related to the finite cluster size and boundary effects, but allows modeling charged species.
The model clusters were constructed from the "periodical" oxide surfaces optimized as described above. Each cluster contained an active center (Mn(1)-Mn(2) atoms), which was supported by six additional Mn octahedra ( Figure 5). The Mn-O H bond length values for the adsorbed OH computed within the cluster and periodical DFT However, the energy barrier along this path appears to be too high for the predominance of this "direct" pathway: ca. 2.5 eV, which is calculated as the difference in the energy values for the equilibrium bond length in the adsorbed O 2 (1.27 Å) and the transition state (energy of the cluster with the O-O bond length 1.7 Å). Similar tendencies in the adsorption geometries were also observed for the O 2 − ion. Based on these considerations we conclude that the "direct" pathway, which should involve dissociative adsorption of O 2 at two neighboring Mn atoms at the Mn 2 O 3 surface, is not feasible due to a very high activation barrier. The origin of the enhanced activity of Mn 2 O 3 and the low H 2 O 2 yield are thus likely to be related to other steps in the ORR mechanism, such as fast bond breaking in H 2 O 2 . This computational result provides a basis for considering the 'series' pathway as more probable. Furthermore, rather long Mn-O O bond lengths (ca. 2.0 Å) and the associated low adsorption energy values imply feasibility of the outer-sphere scenario for the first ET to the O 2 molecule, which is considered in the next sub-section. For outersphere reactions, the key factors which should be addressed are electrode/reactant electronic overlap, solvent reorganization responsible for the barrier height (in addition to molecular reorganization), and works of approach.  to the edge of the valence band, 37,38 hence we can consider the oxides as conductors when calculating the ET free energy surface. For the case of a different position of the Fermi level within the energy gap, another version of the Anderson model (suitable for semiconductors) should be employed. 39 Three orientations were considered for the O 2 approach to the active center of the model clusters: planar orientation with the O-O bond parallel to the active center plane, and two vertical orientations ( (1) and (2)) with the O-O bond being normal to the active center plane (Figure 7). The potential energy scans along the normal to the cluster "surface" (Figure 8) allowed to specify the distances, which correspond to the minimum energy values for the cluster + O 2 systems. In Figure 8, the differences between the system energies and the energy of the cluster + O 2 at a significantly high separation (7 Å) are shown. For both oxides, Figure 8  Possible presence of "OH vacancies" was modeled by eliminating surface OH groups from Mn(1) and Mn(2) atoms of the active center ("dehydroxylated" cluster, Figure S4b). In this case, the adsorption minima in the approach terms were shifted to shorter distances: 4.1, 3.0 and 2.9 Å for planar and two vertical orientations (1) and (2), respectively ( Figure S4b). The presence of OH vacancies and the associated decrease in the closest approach distance might contribute to the lowering of the effective outer-sphere ET barrier.
The ET barriers were estimated for the three selected orientations of the O 2 molecule at O 2 -cluster separations corresponding to the energy minimum values. For the "hydroxylated" surfaces of both oxides the ET barriers, E a , were estimated as ca. 0.30 eV (in accordance with the Marcus theory, E a = λ/4 if zero overvoltage is assumed). In our calculations we do not consider the case of "vacancy" formation on the active center, as in alkaline media the Mn atoms are likely to be occupied either by water molecules or by adsorbed OH species, which should form a rather stable hydrogen-bonded layer. The transfer of the O 2 molecule through this layer toward the adsorption site on the Mn atom needs surmounting an additional barrier (work terms), which should be considered as well. 31,32 Hydroxylated surfaces correspond, on the other hand, to a more realistic environment for the first ET step, especially given rather high O 2 -cluster separations (4-5 Å). Our estimates indicate that for these surfaces the ET barrier in the outersphere case does not exceed 0.3 eV, which allows us to consider the outer-sphere scenario as highly probable.
Electronic transmission coefficients, κ (see pertinent details of model calculations in Ref. 36) were estimated for the three orientations of O 2 in the vicinity of the hydroxylated cluster surfaces ( Figure S5). For the Mn 2 O 3 oxide, the κ values for the distance corresponding to the interaction minima span from 10 −2 (planar and vertical (1)) to 10 −1 (vertical (2)), while for MnOOH lower transmission coefficient values are observed (ca. 10 −2 for all the orientations). For larger O 2 -cluster separations the κ values show an exponential decrease. Note that the adiabatic limit (κ ∼ 1) is not reached for the hydroxylated surfaces, which implies non-adiabatic regime (weak orbital coupling) with the ET rate being dependent on the oxide nature. As for all orientations κ values for Mn 2 O 3 surface are 2-15 times higher than those for MnOOH and the ET barrier values are very close, we can anticipate the former oxide to be more active in the first outersphere ET step. Additional calculations are required, however, for a more accurate prediction of the transmission coefficients, since the cluster model cannot reproduce differences in the electronic structure of the two oxides quantitatively.
Rather low values of the transmission coefficient call for considering competition between the non-adiabatic outer-sphere and an inner-sphere ET involving adsorbed O 2 . As it was already mentioned, adsorption of O 2 molecule from solution is likely to be accompanied by surmounting an additional energy barrier upon approaching the surface, occupied by OH ad and H 2 O molecules (which is illustrated on a qualitative level by the repulsive approach terms for the hydroxylated surface). Data on the O 2 approach toward Mn oxide surfaces is currently unavailable in the literature. To make a qualitative estimate one may use the reported potential of the mean force (PMF) profiles, calculated for the approach of O 2 toward the Ag(100) surface. 30,31 For Ag(100) the PMF is ca. 0.8 eV for O 2 and ca. 0.5 eV for O 2 − at 2-3 Å distances, which corresponds to the adsorbed state of the molecule/anion. As the expression for the ET rate constant should include the exponential term exp(-W i /k B T), where W i has the order of 0.5-0.8 eV, the rate constant should decrease at least by 10 orders of magnitude both for O 2 and for O 2 − . Thus, the additional barrier of 0.5-0.8 eV cannot be compensated by a ca. 10 2 increase in the electronic transmission coefficient, which should take place when switching from an outer-sphere to an inner-sphere mechanism. In our calculations a very weak O 2 adsorption energy was computed without the account for the solvating media, but these results point to the absence of strong oxide/adsorbate interactions. Thus, we have no experimental or theoretical implications to consider oxygen species adsorption to be much stronger on Mn oxides than on gold or silver facets. To conclude, we predict the difference in O 2 outersphere reduction rates on Mn 2 O 3 and MnOOH up to one order of magnitude due to the difference in the orbital overlap. We also demonstrate that the rate of this outersphere transfer of the first electron can be higher than that for the alternative innersphere step. − . It is difficult to distinguish between these two scenarios given the current level of understanding of the reaction mechanism. It is however worth noting that the superoxide ion (O 2 − ) is stronger adsorbed on oxide surfaces than the O 2 molecule. 40,41 The barrier for the outer-sphere proton coupled ET to O 2 − is very low -ca. 0.05 eV, 32 making it an unlikely candidate for the reaction limiting step, whose rate could account for the observed difference in the activities of the MnOOH and Mn 2 O 3 oxides.
Since the adsorption energy (from periodical DFT calculations) of HO 2 species at MnOOH is by ca. 0.15 eV lower as compared to that of Mn 2 O 3 , the higher yields of the HO 2 − at the ring may be partially due to the easier desorption of HO 2 − from the MnOOH surface. The chemical bond-breaking step can be represented by step 5 , which involves participation of two neighbor Mn atoms. This process was modeled as a stepwise elongation of the O-O bond of HOO ad adsorbed at the active center, which allowed constructing of a potential energy surface. For the potential energy scan the O-O bond in HO 2 − was constrained to remain perpendicular to the active center plane, following the approach described in Refs. 31,32. Figures 9a, 9b show the corresponding barriers for the bond breaking in HO 2 − adsorbed at Mn 2 O 3 and MnOOH oxide surfaces, which were estimated as ca. 0.5 eV and 0.8 eV correspondingly. The geometries of transition states (TS, lower panels of Figure 9) suggest that smaller distances between neighboring Mn atoms in Mn 2 O 3 allow for the existence of stabilizing interactions between O ad and OH ad , which facilitate the OH − detachment and decrease the activation barrier. For MnOOH such kind of interactions is unlikely, as the distance between the adjacent Mn centers is too large.
Thus we conclude that adsorbate-adsorbate interactions may allow for a significant reduction of the bond breaking barrier height, which could determine higher activity of Mn 2 O 3 with respect to the reduction of hydrogen peroxide species explaining the experimentally observed kinetically limited HPRR for MnOOH but not for Mn 2 O 3 . Note however, that the exact barrier heights should be taken with caution given the vast number of approximations and simplifications in our cluster calculations.
Microkinetic modeling: confronting computational data to experimental results.-To check whether the experimental data are compatible with the ORR mechanism comprising outer-sphere ET step(s) emerging from quantum chemical modeling, microkinetic modeling was performed. The model considers outersphere ET steps 2 and 3 followed by HO 2 − adsorption on the oxide surface (step 4), inner-sphere reduction of HO 2 − into water (step 5) and conversion of the generated O ad into OH ad (step 1). Microkinetic modeling is used to simulate the ORR RRDE and HPRR/HPOR (hydrogen peroxide oxidation) current-potential curves, which are then compared to the experimental ones. The kinetic equations and the values of the rate constants used in the simulations of the ORR RRDE current potential curves are given in the SI (Calculation of barriers for the outer-sphere  42 Since E • 2 is lower than E • 3 the onset and the half-wave potentials of the ORR current potential curves depend on the rate constant of step (2 ), k 2 , while the hydrogen peroxide oxidation reaction kinetics is strongly influenced by the rate constant of step (3 ), k 3 . As discussed in Short summary of the previously published data section, the HO 2 − reduction kinetics is much faster on the Mn 2 O 3 oxide than on the MnOOH counterpart (cf. Figure 1). On Mn 2 O 3 , the reduction current below 0.85 V vs. RHE is limited by the HO 2 − diffusion while on MnOOH, the HO 2 − reduction limiting current is much inferior of the diffusion limit. As a consequence, a larger HO 2 − escape is observed during the ORR on MnOOH compared to that of Mn 2 O 3 . Differences in the HO 2 − reduction kinetics can be attributed to the faster HO-O bond breaking (step 5 or 5 ) on Mn 2 O 3 compared to MnOOH predicted by quantum chemical calculations. Experimentally, a constant limiting current is observed on MnOOH over a wide range of potentials (Figures 1b, 1d) evidencing that the HO-O ad bond breaking (step 5 or 5 ) is a chemical step, i.e. not activated by the electrode potential (cf. Short summary of the previously published data and Bond breaking in the hydrogen peroxide intermediate sections).
The simulation results are collected in Figures 10a, 10b, 10c. Panel 10c shows simulated ORR RRDE (full curves) and HPRR/HPOR (dashed curves) current-potential curves. It should be mentioned that in the outer-sphere model, not only the HO 2 − , but also the O 2 − species generated at the disc electrode may escape from the diffusion layer and be oxidized at the ring. Thus, the current due to the O 2 − oxidation is added up to the oxidation of HO 2 − at the ring. This is shown in Figure 10b, where the full lines correspond to the simulated HO 2 − escape currents, while dashed curves are used to plot the O 2 − escape currents. Note that the yields plotted in panel 10a account for the sum of the HO 2 − and the O 2 − escape currents. Three simulated current-potential curves are compared in Figure  10 for different combinations of the rate constant values. In the first case (purple curves), rather fast kinetics is considered for steps (2 ) (k 2 = 10 6 cm 3 · mol −1 · s −1 ) and (3 ) (k 3 = 10 8 cm 3 · mol −1 · s −1 ) as well as for the inner-sphere HO 2 − reduction kinetics. The experimentally observed diffusion-limited HPRR currents on Mn 2 O 3 below 0.85 V, and the amount of HO 2 − escaping the catalyst layer (cf. Figures 1 and 2) can be semi-quantitatively reproduced assuming k 5 = 40 s −1 . However, above 0.85 V, the HO 2 − reduction current depends on the kinetics of step 1, which is linked to the formal potential of the Mn(IV)/Mn(III) redox transition. In agreement with the experiment, the Mn(IV)/Mn(III) redox potential of 0.98 V is assumed for Mn 2 O 3 . 4 This set of parameters allows one to reproduce the main experimental observations for the Mn 2 O 3 oxide including the half-wave potential of the ORR current-potential curve as well as the HPRR/HPOR mixed potential.
To sum up, the kinetic modeling shows that the experimental ORR and HPRR/HPOR data cannot be reproduced with materialsindependent fast transfer of the first and the second electron and at least one of these steps has to be "slow" in order to simulate the behavior of MnOOH. It was possible to reproduce the experimentally observed differences in the ORR and HPRR/HPOR kinetics by assuming ca. 10 fold smaller k 2 for MnOOH compared to Mn 2 O 3 . It is interesting to notice that a factor 10 between Mn 2 O 3 and MnOOH was also found within the inner-sphere reduction of O 2 into HO 2 − (steps 2 and 3, see Ref. 3). The observed tenfold difference in the k 2 values (required to reproduce experimental current-potential curves) could be explained by the difference in the electronic transmission coefficients assuming the non-adiabatic reaction rate control (Calculation of barriers for the outer-sphere scenario (O 2 + e − → ← O 2 − − step 2') section).

Concluding Remarks
In this manuscript we presented experimental RRDE data for the ORR on various Mn oxides supplemented with the previously published results of RDE measurements for the HPRR/HPOR. Then, we applied a number of complementary quantum chemical approaches in order to rationalize the experimentally observed differences between the most (Mn 2 O 3 ) and the least active (MnOOH) oxides. We aimed to refrain from defining the activity descriptors, but rather focused on molecular-level factors, which determine the reaction mechanisms. We found that periodical DFT calculations within conventional thermodynamic approach cannot account for the differences between Mn 2 O 3 and MnOOH, in particular with regard to the slow bond breaking in the hydrogen peroxide intermediate corroborated by the experimentally observed kinetically limited HPRR and high hydrogen peroxide yield during the ORR on MnOOH. Activation barriers of likely elementary steps were considered using cluster calculations. The latter helped us in rationalizing much faster bond breaking of the hydrogen peroxide intermediate adsorbed on the surface of Mn 2 O 3 compared to that on MnOOH. Faster dissociation of the hydrogen peroxide adsorbed on the surface of Mn 2 O 3 oxide is explained by adsorbate-adsorbate interactions, which decrease the activation barrier for bond-breaking in the HO 2 − ad intermediate. The cluster calculations also suggest that a "direct" ORR mechanism occurring through bond breaking in the O 2 molecule is unlikely, and that the ORR in alkaline media may involve outer-sphere ET steps for the transfer of the first and the second electrons.
According to microkinetic modeling, the experimental differences between Mn 2 O 3 and MnOOH cannot be reproduced considering material-independent kinetics for the transfer of the first and the second electrons. While fast outer-sphere ET steps are compatible with the ORR on Mn 2 O 3 , they cannot account for the ORR on MnOOH, where at least one of the ET steps must be ca. 10 times slower than on Mn 2 O 3 to reproduce the experimental data. As follows from the quantum chemical calculations, the difference of the oxides' activity in the first ET steps might originate from the nonadiabatic regime of ET, with the stronger orbital overlap determining higher activity of the hydroxylated surface of Mn 2 O 3 oxide. Indeed, we found that transmission coefficient values for Mn 2 O 3 are 2-15 times higher than those for MnOOH, which would explain the differences in oxides' activity in the first ET steps. Another possibility is a competing scenario involving inner-sphere steps with somewhat higher (compared to the outer-sphere ET steps) activation barriers but occurring in adiabatic limit (κ ≈1).
The computational results reported in this study undoubtedly involve a large number of approximations, which should be taken into account critically when comparing the calculated and experimental trends. First, the solvent-solute and the solvent-electrode interactions are taken into account neither in periodical DFT, nor in cluster calculations, as these would increase the system size to a hardly treatable value, although examples of both implicit and explicit solvent modeling, compatible with periodical DFT methods, are starting to appear. 43,44 The focus of the computational study is thus placed exclusively at the electrode/reactant interactions. Second major approximation is related to the application of the cluster approach to describe the orbital overlap effect on the ET rate for the two oxides, as this approach does not allow to reproduce the difference in the oxides' electronic structures quantitatively. In this case, as well as in the case of the bond-breaking step, we can outline mainly geometrical factors, which affect the differences in the MnOOH and Mn 2 O 3 activities.
In the periodical DFT calculations we did not follow the DFT+U approach, which in some cases allows for a more accurate account of the oxides' electronic structure and its effect on the geometry of adsorbates and the energetics of adsorption. However, the DFT+U approach is not universal, and has some shortcomings that may cause inaccuracy in computed energies and geometrical parameters (see discussion in Refs. 45,46). Indeed, for Mn 2 O 3 oxide PBE+U tends to overestimate the equilibrium volumes and also it favors a half-metallic state, rather than an insulating character as derived from the hybrid functional approaches. 47 Another approximation consists in the simplification of the bondbreaking mechanism, which could involve much more complex rearrangements in the reaction layer with the participation of H 2 O and OH − species. However, within the framework of the adopted approach for the potential energy surface construction, introducing a large number of degrees of freedom from solution species would make the problem unsolvable. Last, the reaction steps in the formal kinetic modeling do not directly correspond to the elementary steps, which are addressed in the computational study. This does not allow us to directly compare the values of the rate constants resulting from formal kinetic modeling and from quantum chemical calculations, but rather rely on the outlined general trends in the differences of oxides' activity.
Common electrocatalytic reaction schemes are primarily associated with adsorbed reactants and intermediates. In this work, we follow a different strategy and show that important mechanistic aspects of the electrocatalytic reaction kinetics can be determined by factors, which do not necessarily imply the ET to the reactant in the adsorbed state. In such cases, kinetic modeling is unlikely to distinguish between outer-and innersphere scenarios due to the large number of experimentally inaccessible parameters involved in simulations. However, our analysis points to the higher probability of the outersphere scenario in the first ORR step(s) on Mn oxides based on the currently available information on the reaction layer structure.
The computational approaches used in this work were previously applied to model simpler ET reactions on metals. Here we extended this treatment to describe the kinetics of a complex multistep reaction on oxides and estimate the key parameters of the quantum mechanical ET theory (of course, within the accuracy imposed by the approximations used). Further development in the predictive analysis of electrocatalytic reaction rates on oxides should involve a more detailed specification of the reaction layer structure (classical or ab initio MD simulations) as well as more accurate estimates of ET "microscopic" parameters (reorganization energy, orbital overlap, frequency factors). Further experimental studies should include pH effects and kinetics of probe outer-sphere electrochemical reactions and their dependence on the type of oxide.