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linear relations are obtained based on the data points for all five lanthanum-based perovskites. On the other hand, Fig. 2b shows that OER via LOM is ...
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Role of Lattice Oxygen Participation in Understanding Trends in the Oxygen Evolution Reaction on Perovskites Jong Suk Yoo, Xi Rong, Yusu Liu, and Alexie M Kolpak ACS Catal., Just Accepted Manuscript • Publication Date (Web): 17 Apr 2018 Downloaded from http://pubs.acs.org on April 17, 2018

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Role of Lattice Oxygen Participation in Understanding Trends in the Oxygen Evolution Reaction on Perovskites Jong Suk Yoo,a,* Xi Rong,a Yusu Liu,b Alexie M. Kolpak a,* a Department

of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States b Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States *Correspondence: (J.S.Y.) [email protected]; (A.M.K) [email protected]

Abstract This study demonstrates the importance of considering lattice oxygen participation in understanding trends in the oxygen evolution reaction (OER) on ABO3 (A = lanthanum or strontium, B = transition metal) perovskites. Using density functional theory, we show that the lattice oxygen mechanism (LOM) can lead to higher OER activity than the conventional adsorbate evolving mechanism (AEM) by minimizing the thermodynamically required overpotential. We also show that the OER activity volcano for AEM is universal for all perovskites, whereas that for LOM depends on the identity of the A cation in ABO3. This explains experimental observations that perovskites such as Pr0.5Ba0.5CoO3–δ and SrCoO3–δ show higher OER activities than the conventionally predicted optimum compounds such as LaNiO3 and SrCoO3. Furthermore, we show that LOM is preferred to AEM in achieving bifunctional catalysts capable of promoting both OER and ORR. Using our overall activity volcano, we finally suggest several candidate materials that are predicted to be highly active for OER via LOM. Keywords: oxygen evolution; perovskite; lattice oxygen; reaction mechanism; activity volcano; density functional theory

Introduction Electrolytic splitting of water into hydrogen and oxygen is a potential approach for the production of hydrogen via renewable energy sources such as wind and solar.1–4 Although the oxygen evolution reaction (OER) occurs as a byproduct of hydrogen production at the anode of water electrolysis, it is a vital technological component because it is a kinetic bottleneck of the overall process.6–8 Beyond renewable energy applications, OER is also essential for life support systems in situations that require the generation of oxygen for air revitalization.9,10 Among various classes of OER electrocatalysts, ABO3 perovskites (A = alkaline earth, B = transition metal) have attracted considerable interest due to their high catalytic activities compared to precious metal based catalysts such as RuO2 and IrO2.11–14 For example, Grimaud et al.,15 and Suntivich et al.16 showed that the intrinsic

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OER activities of Pr0.5Ba0.5CoO3–δ (PBCO) and Ba0.5Sr0.5Co0.8Fe0.2O3–δ (BSCF) are higher than those of IrO2 nanoparticles, and the activity trend on various perovskites is PBCO > BSCF > La0.5Ca0.5CoO3–δ (LCCO) > LaNiO3 > LaCoO3 ≈ La0.5Mn0.5NiO3 > LaMnO3 > LaCrO3.15,16 In addition, Petrie et al.17 showed that LaNiO3 is more active than Pt for OER, and its activity increases with the compressive strain on the material. Previously, theoretical studies employing density functional theory (DFT) have been conducted to explain the OER activity trends on rutiles and perovskites.18–20 Utilizing the scaling relations between adsorption energies of the oxygen-binding species involved in the reaction mechanism shown in Eqns. 1–4, the variation in the theoretical overpotential from one oxide surface to the next was correlated to a single descriptor representing oxygen affinity, i.e., the oxygen adsorption energy (∆GO)19 or relative stability of OH* vs. OOH* (∆GOH – ∆GOOH)20. As a result, a Sabatier’s volcano-shaped relationship was obtained, showing that LaNiO3 and SrCoO3 are near the top of the volcano, with the lowest theoretical overpotentials, due to their optimal trade-off between strong and weak binding of oxygen.20 LaCoO3, LaFeO3, LaMnO3, LaCrO3, and LaVO3 bind oxygen too strongly (left leg of the volcano), whereas LaCuO3binds oxygen too weakly (right leg of the volcano), leading to the following order of OER activity: SrCoO3 ≥ LaNiO3 > LaCoO3 > LaFeO3 > LaMnO3 ≈ LaCuO3 > LaCrO3 > LaVO3.20 This trend agrees remarkably well with that found experimentally, e.g., by Suntivich et al.,16 Bockris et al.,11 and Matsumoto et al.21 * + H2O(l)  OH* + H+ + eOH*  O* + H+ + eO* + H2O(l)  OOH* + H+ + eOOH*  O2(g) + H+ + e-

(1) (2) (3) (4)

However, previous theoretical studies cannot explain recent experimental findings that there are perovskites such as PBCO,15 BSCF,16 LCCO,16 SrCoO3–δ23 and compressively strained LaNiO3,17 that are more active than the conventionally predicted optimum compounds such as pristine LaNiO3 and SrCoO3. One explanation for this discrepancy could be that these catalysts do not actually follow the reaction mechanism shown above. Recently, Mefford et al.22 found that the high catalytic activities of a range of La1–xSrxCoO3–δ compounds can be rationalized by the participation of lattice oxygen in the OER mechanism as revealed through DFT calculations. Grimaud et al.23 also found direct experimental evidence, using in situ 18O isotope labelling mass spectrometry, that the oxygen gas generated during OER comes from lattice oxygen on La1–xSrxCoO3–δ, PBCO, and SrCoO3–δ, whereas it comes from the water solvent on LaCoO3. In addition, a recent DFT study showed that a new OER mechanism (see Eqns. 5–8) in which lattice oxygen participates via the reversible formation of a surface oxygen vacancy (Vo) is energetically preferred to the previously proposed mechanism for LaNiO3.24 The authors also showed that it is highly favorable for the surface lattice oxygen to shift out of the surface plane to interact with OH* to form Vo and OO* on LaNiO3 and other less stable perovskites.24 OH*  (Vo + OO*)† + H+ + e– (Vo + OO*)† + H2O(l)  O2(g) + (Vo + OH*)† + H+ + e–

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(5) (6)

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(Vo + OH*)† + H2O(l)  (HO-site* + OH*)† + H+ + e– (7) † + – (HO-site* + OH*)  OH* + H + e (8) † Parenthesis is used to indicate that adsorbates are calculated in the same supercell. Thus, it seems that two different OER mechanisms, i.e., the adsorbate evolution mechanism (AEM) shown in Eqns. 1–4,19,20 and the lattice-oxygen participation mechanism (LOM) shown in Eqns. 5– 8,24 can compete on some highly active perovskites (see Scheme 1). This accentuates the need to understand which reaction mechanism is more favorable for which perovskites, and how the competition between the two different reaction mechanisms changes the previously obtained OER activity volcano. In this study, DFT calculations and the computational hydrogen electrode model (H+ + e– ⇌ 0.5 H2 at U = 0 V vs. RHE)25 are used to calculate the reaction energetics and theoretical overpotentials for OER via both AEM and LOM for LaVO3, LaCrO3, LaCoO3, LaNiO3, and LaCuO3. We also show that, due to smaller thermodynamic limitations, LOM can be preferred to AEM for maximizing the OER activities of certain perovskites. Finally, we present an overall OER activity volcano that takes into account both AEM and LOM, and use the plot to approximately identify other potentially promising perovskites for OER via LOM.

Scheme 1. Illustration of the competition between the adsorbate evolution mechanism (AEM) and latticeoxygen participation mechanism (LOM).

Results and discussion Fig. 1 shows the calculated free energy changes along the reaction coordinate of OER via both AEM and LOM for LaCrO3, LaNiO3, and LaCuO3 (see Fig. S1 of Supporting Information (SI) for LaVO3 and LaCoO3). It can be seen that AEM is much preferred to LOM for strongly binding surfaces like LaVO3 (∆GO = –0.82 eV) and LaCrO3 (∆GO = 0.38 eV) as the formation of VO is very uphill in free energy (see Fig. S3f in SI). On the other hand, LOM is much preferred to AEM for weakly binding surfaces like LaCuO3 (∆GO = 4.38 eV), as the formation of VO is energetically plausible (see Fig. S3f in SI), and the adsorbates that bind to the transition metal site neighboring VO are much more stable than those that bind to the site without neighboring VO. For moderately binding surfaces like LaNiO3 (∆GO =

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3.21 eV), both mechanisms are highly favorable, but LOM is slightly preferred to AEM as the theoretical overpotential (= limiting potential – equilibrium potential) for the former mechanism for LaNiO3 (1.44 eV – 1.23 eV = 0.21 eV) is slightly lower than that for the latter (1.67 eV – 1.23 eV = 0.44 eV). However, more detailed studies that include coverage effect, solvent effect, and kinetic barriers are required to accurately determine the most probable reaction mechanism for LaNiO3. In general, LOM is expected to govern the top and weakly binding leg of the OER activity volcano for lanthanum-based perovskites, emphasizing the importance of considering the lattice oxygen participation in analyzing catalytic trends and predicting highly active perovskites.

Figure 1. Free energy diagrams for OER via AEM for (a) LaCrO3, (b) LaNiO3, (c) LaCuO3, and via LOM for (d) LaCrO3, (e) LaNiO3, (f) LaCuO3 at pH = 0, T = 298 K, and zero applied potential (U = 0 V vs. RHE). All adsorbates with * bind to the transition metal site of ABO3 (001) except HO-site*, which binds to the latticeoxygen site. In each plot, the value of the reaction free energy for the potential-determining step (namely, the limiting potential) is shown in blue. The red arrows in (a), (b), and (c) show that ∆GOOH – ∆GOH is relatively constant for AEM, with an average value of ~3.1 eV, whereas those in (d), (e), and (f) show that ∆GVo +OH – ∆GVo +OO is relatively constant for LOM, with an average value of ~1.4 eV for all five lanthanum-based perovskites (see Table S1 in SI).

Interestingly, Fig. 1 also shows that LOM is preferred to AEM for maximizing the OER activities of lanthanum-based perovskites. The most ideal OER catalyst with zero overpotential needs to facilitate the reaction at the equilibrium potential of 1.23 V. This requires every charge transfer step to have a reaction free energy of 1.23 eV, evenly splitting the constant free energy difference of 4.92 eV between 2H2O and O2 + 2H2 (2H2 is equivalent to 4H+ + 4e– at zero potential based on the computational hydrogen electrode model)25 among the four electrochemical steps. However, this is extremely difficult to achieve in reality due to the existence of strong linear correlations between adsorption energies of similarly bound adsorbates.26–28

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In the case of AEM, for example, OH* and OOH* bind to the same surface site via oxygen bound to another atom in the adsorbate. As indicated by the red arrows in Fig. 1a-c (Fig. S1a, b in SI), this similarity in adsorption chemistry results in a relatively constant free energy difference of ~3.1 eV between ∆GOH and ∆GOOH for all five lanthanum-based perovskites. Note that a similar value of ~3.2 eV was previously reported for various classes of materials including transition metals,29,30 rutiles,19 and perovskites.20 This free energy difference defines the fundamental limitation of OER via AEM, i.e., ∆G for OH*  OOH* = 3.1 eV is 0.64 eV away from the ideal value of 2.46 eV (= 1.23 eV/step × 2 steps); thus, thermodynamically, the smallest overpotential possible for AEM is 0.32 V (= 0.64 eV/2e). On the other hand, in the case of LOM, OH* and OO* are the similarly bound adsorbates, with a relatively constant ∆G for Vo + OO*  Vo +OH* of ~1.4 eV for all five lanthanum-based perovskites, as shown by the red arrows in Fig. 1d-f (Fig. S1c, d in SI). Thus, OER via LOM for lanthanum-based perovskites is fundamentally limited by the fact that ∆G for Vo + OO*  Vo +OH* = 1.4 eV is 0.17 eV away from the ideal value of 1.23 eV, leading to the thermodynamically required overpotential of 0.17 V. In summary, a lanthanum-based perovskite is likely to be closer to the ideal catalyst with zero overpotential if LOM is thermodynamically more favorable than AEM, and a promising path for optimizing activity is to modify the catalyst surface to selectively change the relative stability of OO* and OH* to yield ∆G for Vo + OO*  Vo +OH* = 1.23 eV. Since all reaction species involved in AEM or LOM, except HO-site*, bind to the surface transitionmetal B site of ABO3 via oxygen, their adsorption energies (or more precisely speaking, the initial and final state energies of all elementary reactions shown in Eqns. 1 - 8 relative to gas-phase H2 and H2O) can be linearly scaled to ∆EO (see Fig. S3 in SI).26–28 In addition, by considering HO-site* and OH* in the same supercell, the calculated energy (∆E(HO-site + OH)), and the formation energy of VO (∆EVo ) can be empirically scaled to –∆EO (see Fig. S3e and f in SI). Thus, the variations in the reaction free energies of AEM and LOM for different perovskites can be described as functions of only one descriptor, ∆GO, which produces the activity volcanoes for OER via AEM and LOM as shown by the shaded regions in Fig. 2a and b, respectively. Fig. 2a shows that OER via AEM is limited by O*  OOH* (Eqn. 3, blue line in Fig. 2a) for strongly binding lanthanum-based perovskites, whereas it is limited by OH*  O* (Eqn. 2, red line in Fig. 2a) or *  OH* (Eqn. 1, black line in Fig. 2a) for weakly binding ones. It also shows that the optimum value of ∆GO for OER via AEM is ~3.1 eV (the optimum value of another commonly used descriptor, ∆GO – ∆GOH is ~1.5 eV, see Fig. S20 in SI for the OER volcano relative to ∆GO – ∆GOH), which matches well with the previously found optimum values of ∆GO = ~2.5 eV on rutiles17 and ∆GO – ∆GOH = ~1.6 eV on perovskites18. LaNiO3 is very close to the top, but is slightly on the right leg of the volcano, indicating that an ideal catalyst needs to bind oxygen slightly more strongly than LaNiO3. However, we show below that many of the recently discovered state-of-the-art catalysts such as compressively strained LaNiO3,17 SrCoO3–δ,23 and PBCO,15 show oxygen adsorption energies that are different from the predicted optimum value of ~3.1 eV.

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Figure 2. Negative reaction free energies of the four charge transfer steps in OER via (a) AEM and (b) LOM for lanthanum-based perovskites, which are plotted as functions of ∆GO. In each figure, the shaded region shows the theoretical activity volcano for OER, and the dashed horizontal line indicates the equilibrium potential for OER (1.23 V). Thus, the difference between the dashed horizontal line and the line that forms the activity volcano represents the theoretical overpotential for OER. Since LOM requires the catalyst surface to be initially covered with oxygen species, the dotted vertical lines in (b) show the boundaries where OH* and O* are stable under the OER operating potential of 1.8 V (see Fig. S21 in SI for details). Note that the data points for LaCrO3 and LaVO3 are not shown for some linear relations in (b) due to the scale of the axes although all linear relations are obtained based on the data points for all five lanthanum-based perovskites.

On the other hand, Fig. 2b shows that OER via LOM is limited by OH*  VO + OO* (Eqn. 5, black line in Fig. 2b) for strongly binding lanthanum-based perovskites, by VO + OO*  VO + O2(g) + OH* (Eqn. 6, red line in Fig. 2b) for a small portion of moderately binding ones, and by HO-site* + OH*  OH* (Eqn. 8, green line in Fig. 2b) for weakly binding ones. However, it is important to note here that there is uncertainty in whether or not the red line actually flattens the top of the activity volcano. This is because, the red line goes lower than the top of the activity volcano by only 0.1 eV, and the DFT error expected in calculating adsorption energies on solid surfaces is about 0.2 eV. Herein, we choose to exclude the red line in determining the shape of the activity volcano based on the finding that doing so results in better agreement with the experimental study on how epitaxial strain influences the OER activity of LaNiO3.17 This will be discussed in more detail below where we discuss the results shown in Fig. 3b. In addition, we need to address the well-known over-binding of O2(g) within the RPBE functional,31 which leads to over-stabilization of O2(g) relative to 2O(g) by ~0.4 eV compared to experiments (see Fig. S5 in SI). Although we mitigate this problem by referencing the calculated electronic energies of all adsorbates and O2(g) relative to H2O(g) and H2(g), the problem may still exist in calculating the electronic energies of OO* in LOM. Since OO* interacts weakly with the surface, the problem is likely to be less severe in OO* than O2(g). To quantitatively examine the over-binding error in OO*, HSE0633 calculations are essential, but they are computationally too expensive for our systems (see Fig. S6 in SI). Therefore, we just note here the possibility that both the red and black lines in Fig. 2b shift up and down, respectively, by less than 0.4 eV, if we corrected the calculated adsorption energies of OO* by less than 0.4 eV (see Fig. S7 in SI for a comparison of the volcano with and

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without the maximum correction value of 0.4 eV). Since it is extremely difficult to quantify the exact over-binding error in OO* on different perovskites, we consistently show all our results without the error considered, and then qualitatively discuss what happens when we apply some correction to the calculated adsorption energies of OO*. However, it is extremely important to note here that any qualitative conclusions made in this study are not significantly affected by the choice of the correction value for OO* if it is in between 0.0 eV and 0.4 eV (see Fig. S8 in SI). Fig. 2b also shows that the optimum value of ∆GO for OER via LOM for lanthanum-based perovskites is ~3.3 eV, which is about 0.2 eV weaker binding than that for OER via AEM. Interestingly, the top of the activity volcano not only shifts to the right by ~0.2 eV but also rises up by ~0.15 eV as the reaction mechanism switches from AEM to LOM, indicating that LOM is indeed more favorable than AEM for maximizing the OER activities of lanthanum-based perovskites. A comparison between Fig. 2a and b reveals that the left leg of the volcano for LOM is generally lower than that for AEM, whereas the right leg of the volcano for LOM is generally higher than that for AEM. This can be seen more clearly in Fig. 3a, in which we present the overall OER activity volcano that considers both AEM and LOM for lanthanum-based perovskites. Fig. 3a indeed shows that the top and right leg of the OER activity volcano are governed by LOM, whereas the left leg is governed by AEM, indicating the importance of considering lattice oxygen participation in understanding and finding the most active lanthanum-based perovskites. Finally, Fig. 3b shows that the lowest overpotential that can be reached via LOM is ~0.1 V, whereas it is ~0.25 V for AEM.

Figure 3. The shaded region in (a) shows the overall OER activity volcano that takes into account both AEM (black) and LOM (red). It is obtained by combining Fig. 2a and b. The dashed horizontal line in (a) indicates the equilibrium potential for OER (1.23 V). Since LOM requires the catalyst surface to be initially covered with oxygen species, the dotted vertical lines in (a) show the boundaries where OH* and O* are stable under the OER operating potential of 1.8 V (see Fig. S21 in SI for details). (b) Theoretical overpotential (= equilibrium potential – limiting potential) vs. ∆GO for the region shown as the black box in (a). The dashed red line in (b) shows the red line in Fig. 2b, which has been excluded in determining the shape of the LOM volcano. Filled markers in (a) indicate the data points used to construct the volcano based on calculations of the reaction energetics. Empty markers in (b) also indicate those added to the constructed volcano by calculating ∆GO per surface. They are LaNiO3 surfaces with either tensile (+) or compressive (–) strain relative to the lattice parameters of pristine LaNiO3.

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As mentioned above, Petrie et al.17 recently found that compressive strains as small as –1.2 % can improve the OER activity of LaNiO3, while tensile strains of up to +2.7 % have the opposite effect.17 To explain the experimental results with our theoretical study, we have obtained the values of ∆GO on various strained LaNiO3 surfaces. The predicted overpotentials are shown by the overall OER activity volcano plot in Fig. 3b. Interestingly, we find that compressive strain gradually weakens ∆GO on LaNiO3, whereas tensile strain significantly strengthens it (see Fig. S9 in SI). Therefore, LaNiO3 with a compressive strain of –4.0 % has the lowest overpotential of ~0.1 V, which is ~0.1 V lower than that of strain-free LaNiO3. Thus, our overall volcano successfully corroborates the experimental trend toward enhanced OER activity with compressive strain on LaNiO3. On the other hand, if we considered only the AEM volcano shown as black lines in Fig. 3b, we cannot explain the strain-induced effect observed on LaNiO3, as the AEM volcano gives the opposite trend, with tensile strain of +1.0 % improving the OER activity of LaNiO3 and any compressive strain worsening it. However, we clearly state here that our theoretical explanation of the experimentally observed strain effect on LaNiO3 is based on the assumption that the top of the LOM volcano for lanthanum based perovskites is not flattened by the red line shown in Fig. 2b. For example, if we assume that the top of the LOM volcano for lanthanum based perovskites is flat, as indicated by the red dashed line in Fig. 3b, our study would show that compressive strain on LaNiO3 slightly decreases the OER activity, which contradicts previous experiments. Insofar that the uncertainty about the top of the LOM volcano for lanthanum based perovskites may render this part of our study more speculative than desired, we note here that all the other parts of our study are valid regardless of such concerns. This is because, all the other activity volcanoes shown in this study (e.g. the LOM volcano for strontium based perovskites as shown in Fig. S12 in SI) are much less ambiguous about a certain scaling relation such as the red line contributing to shaping of the volcano. In addition to improving OER activity, Petrie et al.17 also found that compressive strain improves the oxygen reduction reaction (ORR) activity of LaNiO3, promoting bifunctionality of the catalyst. Thus, we constructed the ORR activity volcanoes via reverse AEM and reverse LOM based on Fig. 2a and b, respectively, as shown in Fig. S14 in SI. The slight weakening of ∆GO on LaNiO3 via compressive strain leads to a higher overpotential for ORR via reverse AEM (see Fig. S14a in SI) whereas it leads to a lower overpotential for ORR via reverse LOM (see Fig. S14b in SI), indicating that lattice oxygen participation can explain the enhanced OER and ORR activities of compressively strained LaNiO3. Since the optimum value of ∆GO for OER via LOM (∆GO = ~3.3 eV, see Fig. 2b) is close to that for ORR via reverse LOM (∆GO = ~3.6 eV, see Fig. S14b in SI), we can claim that bifunctionality can be achieved more easily on materials that contain surface lattice oxygen (i.e., metal oxides) compared to oxygen-free materials such as pure metals for which LOM cannot occur. Furthermore, our overall ORR activity volcano predicts that the ORR trend on different perovskites is LaNiO3 > LaMnO3 > LaCoO3 (see Fig. S14c in SI), which is in fair agreement with the experimental finding of LaNiO3 > LaMnO3 ≈ LaCoO3.35 On the other hand, if we considered only reverse AEM, an incorrect ORR trend of LaMnO3 > LaCoO3 > LaNiO3 is predicted, as shown in Fig. S14a in SI. However, we note here the possibility that reverse LOM is kinetically hindered compared to reverse

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AEM. For example, the charge transfer barrier for OH* + H+ + e–  OH* + HO-site* (Eqn. 8 for reverse LOM) can be higher than that for OH* + H+ + e–  * + H2O (Eqn. 1 for reverse AEM) under ORR conditions. Detailed theoretical studies combined with experiments are needed to validate the possibility of promoting ORR via reverse LOM. We have also extended the study to investigate AEM vs. LOM for strontium-based perovskites. The calculated free energy diagrams for SrVO3, SrCoO3, SrNiO3, and SrCuO3 are shown in Fig. S2 in SI. Here again, strongly binding surfaces like SrVO3 (∆GO = 0.05 eV) prefer AEM whereas weakly binding surfaces like SrNiO3 (∆GO = 3.56 eV) and SrCuO3 (∆GO = 4.18 eV) prefer LOM. For moderately binding surfaces like SrCoO3 (∆GO = 3.03 eV), both mechanisms are highly favorable, but AEM is slightly preferred to LOM, as the limiting potential for the former mechanism is lower than that for the latter by ~0.05 eV. However, more detailed studies that consider oxygen vacancies in the bulk, adsorbate coverage, solvent, and kinetic barriers are required to accurately determine the most probable reaction mechanism for SrCoO3. Fig. S2 in SI also shows that LOM is fundamentally preferred to AEM for maximizing the OER activities of strontium-based perovskites, as the average ∆G for OH*  OOH* for all four strontium-based perovskites (~3.0 eV, see Table S1 in SI) is 0.54 eV away from the ideal value of 2.46 eV, whereas the average ∆G for Vo + OO*  Vo +OH* for all five strontium-based perovskites (~1.6 eV, see Table S1 in SI) is 0.41 eV away from the ideal value of 1.23 eV. Interestingly, we find that the linear scaling relations of ∆EOH, ∆EOOH, and ∆EHO-site + OH vs. ∆EO (see Fig. S3a, b, e in SI) are nearly the same for both lanthanum- and strontium-based perovskites, whereas those of ∆EVo + OO, and ∆EVo + OH vs. ∆EO (see Fig. S3c, d in SI) are different by approximately a constant value of ~1 eV in the y-intercept. This difference arises from the fact that the formation energy of the surface oxygen vacancy (∆EVo) depends on the identity of the underlying oxide layer, i.e., the composition of the AO plane of ABO3. For example, Fig. S3f in SI shows that ∆EVo is lower for strontium-based perovskites than lanthanum-based ones because strontium (electronegativity of 1.0) has two valence electrons whereas lanthanum (electronegativity of 1.1) has three. ∆EVo is also generally lower for barium-based perovskites than strontium-based ones, as barium and strontium have two valence electrons, but the atomic radius of barium (electronegativity of 0.9) is larger than that of strontium (electronegativity of 1.0). Thus, LOM is likely to be more favorable than AEM when the A-site element of ABO3 is more tolerant to VO formation in the AO layer (or less electronegative). In addition, we can see that the AEM volcano shown in Fig. 2a can be used to describe OER activities of all perovskites, whereas the black and blue lines of the LOM volcano shown in Fig. 2b can shift up and down, respectively, depending on the identity of A in ABO3. Fig. 4a shows the LOM volcano for strontium-based perovskites compared to the AEM volcano for all perovskites, and the LOM volcano for lanthanum-based perovskites. As discussed above, the top of the LOM volcano for strontium-based perovskites is ~0.1 eV higher than that of the AEM volcano for all perovskites, indicating the importance of considering lattice oxygen participation in understanding and finding the most active strontium-based perovskites. The top of the LOM volcano for strontium-based perovskites is much broader (2.2 eV ≤ ∆GO ≤ 3.4 eV) than that of the LOM volcano for lanthanum-based perovskites, suggesting that more strontium-based materials

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that are moderately binding are prone to LOM. Since experimentally synthesized SrCoO3–δ often contains oxygen vacancies,23 we have added SrCoO2.88 and SrCoO2.75 to the overall OER volcano by calculating ∆GO per surface, as shown in Fig. 4b. We can see that ∆GO depends quite significantly on the oxygen vacancy concentration, and all SrCoOx (x = 3.00, 2.88, and 2.75) compounds prefer LOM to AEM. This agrees with experiments by Grimaud et al.23 that the oxygen gas generated during OER comes from lattice oxygen on SrCoO3–δ, whereas it comes from the water solvent on LaCoO3. Although Fig. 4b shows that LaNiO3 is slightly better than SrCoO2.75, the opposite will show if we apply a correction to OO* adsorption energies as discussed above. Thus, more detailed studies are required to accurately compare the OER activity between LaNiO3 and SrCoOx.

Figure 4. The shaded region in (a) shows the overall OER activity volcano that takes into account AEM for all perovskites (black), LOM for lanthanum-based perovskites (red), and LOM for strontium-based perovskites (blue). The black and red volcanoes are from Fig. 2a and b, respectively, whereas the blue volcano is from Fig. S12 in SI. The dashed horizontal line in (a) indicates the equilibrium potential for OER (1.23 V). Since LOM requires the catalyst surface to be initially covered with oxygen species, the dotted vertical lines in (a) show the boundaries where OH* and O* are stable under the OER operating potential of 1.8 V (see Fig. S21 in SI for details). (b) Theoretical overpotential (= equilibrium potential – limiting potential) vs. ∆GO for the region shown as the black box in (a). Filled markers in (a) indicate the data points used to construct the volcano based on calculations of the reaction energetics. Empty makers in (b) indicate those added to the constructed volcano by calculating ∆GO per surface. SrCoO2.88 (or SrCoO2.75) surface is obtained by removing one (or two) lattice oxygen atom in the second oxide layer (i.e., the SrO layer) of the CoO2 terminated stoichiometric Sr8Co8O24 (001) slab. Black diamonds in (b) indicate various lanthanum- or strontium-based perovskite surfaces with cubic structures that are predicted to be highly active for OER via LOM. Their identities as well as x and y values are provided in Table S3 in SI. The dashed arrows in (b) show how the volcanoes will change if we apply a correction to OO*.

Similarly, our study also suggests that the lattice oxygen participation mechanism needs to be considered to explain the experimentally observed high OER activities of PBCO,15 BSCF,16 and LCCO.16 We will take PBCO15 as an example, as it has been reported to show both high activity and stability, whereas BSCF16 corrodes into amorphous structures that are hard to model with periodic DFT (see the additional discussion section in SI for our discussion on the stability of LOM preferring

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perovskites including PBCO and BSCF). Since the shape of the LOM volcano depends strongly on the alkaline earth element A of ABO3, we first computed ∆EVo, ∆EVo + OO, and ∆EVo + OH on four different PBCO (001) surfaces containing oxygen vacancies in different oxide layers, and found that they approximately follow the linear scaling relations obtained for strontium-based perovskites (see Fig. S10 in SI). We then computed ∆GO on the four different PBCO surfaces. Plotting them on the overall OER activity volcano obtained for strontium-based perovskites (Fig. S13 in SI), we find that (1) all four PBCO surfaces prefer LOM to AEM, and (2) the OER activities of these surfaces are either comparable to or slightly higher than those of SrCoO3–δ, which are in agreement with experiments.15,23 Note that none of the four PBCO surfaces would be predicted to show the highest OER activity based on only the AEM volcano. We have also taken into consideration the effect of the crystalline structures of LaNixOy (001) on OER and ORR, and found that the cubic and Ruddlesden-Popper structures are better candidates for bifunctional catalysts than the rhombohedral structure, in line with experiments (see the additional discussion section in SI for details).40,41 Previously, Koper and Shao-Horn et al.23 suggested a new reaction mechanism (namely, the Oads – Olatt mechanism or OOM) similar to LOM. One main difference between LOM and OOM is that LOM assumes the active site of a perovskite to be the transition-metal (TM) site,24 whereas OOM assumes it to be the lattice-oxygen site.23 In LOM, a surface lattice oxygen shifts out of the surface plane to react with OH* on the TM site to form Vo and OO* (the barriers are ~0.2 eV and ~0.1 eV on LaNiO3 and LaCuO3, respectively), whereas in OOM, O* on the oxygen site desorbs as O2 (Oads – Olatt) to form Vo. Table S4 in SI compares the calculated adsorption energies of O* and OH* on the TM vs. oxygen site for different perovskites. We can see that OH* is more stable on the oxygen site for LaCuO3 and SrNiO3. This indicates that LOM may not be so feasible for weakly binding surfaces, since it requires OH* to be on the TM site to produce O2, and the diffusion barrier of OH* on the oxygen site to the TM site (slightly uphill reaction, see Table S4 in SI) can be high. On the other hand, O* and OH* are significantly more stable on the TM site for LaCrO3 and LaCoO3, and OH* is the same for LaNiO3 and SrCoO3 too. This indicates that OOM may not be so feasible for strongly and moderately binding surfaces, since it requires O* and OH* to be on the oxygen site to produce O2, and the diffusion barrier of these two species on the TM site to the oxygen site (a very uphill reaction, see Table S4 in SI) is probably very high. Thus, Fig. S18 in SI compares the calculated free energy diagrams for OER via LOM vs. OOM for different perovskites considering only the single site case where no diffusion of oxygen adsorbates between the two different sites is required to produce O2. We can see that the LOM is generally preferred to OOM, with lower limiting potentials for all perovskites. We also note here the possibility of non-concerted charge transfers taking place in any elementary steps of LOM as suggested by Koper and Shao-Horn et al.23 to explain the pH-dependent OER activities of perovskites that are capable of OOM (see the additional discussion section in SI for details). Finally, we have screened 275 different lanthanum- and strontium-based perovskites (B0.5B’0.5O2terminated A1.0B0.5B’0.5O3 perovskites, where A = La or Sr, and B, B’ = transition metal) by calculating ∆GO per surface. The results are plotted on the overall OER activity volcano in Fig. 4b. We note that neither oxygen nor metal vacancies were considered in screening these perovskites, although

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significant amounts may be present in some highly active perovskites36 like PBCO,15 BSCF,16 and LCCO.16 As shown by the black diamonds in Fig. 4b, only 44 out of the 275 surfaces considered are predicted to be close to the top of the overall OER activity volcano with a theoretical overpotential similar to or lower than that of LaNiO3. Among the 44 surfaces, we identify 18 (shown in Table S3 in SI) that do not contain precious metals such as Pd, Rh, Ru, and Ag, and therefore have potential as inexpensive but highly active OER catalysts. In addition, we predict that lanthanum-based perovskites with 3.3 eV < ∆GO < 3.6 eV, and strontium-based perovskites with ∆GO = ~2.5 eV, which are close to both peaks of the OER and ORR activity volcanoes (compare Fig. 3 with Fig. S14c in SI, and Fig. 4 with Fig S15c in SI), are good candidates for bifunctional catalysts that promote OER via LOM, and ORR via reverse LOM, with relatively low overpotentials for both reactions. However, we note here that many of the identified materials may not be thermodynamically stable, as we made the assumption in the screening that they all form undistorted cubic structures with no oxygen or metal vacancies, which may not be true, particularly for perovskites that bind oxygen relatively weakly.24,36 Thus, future studies are required to include the effects of the lattice distortions and vacancies on ∆GO on these perovskites.

Conclusions In summary, based on periodic DFT calculations, we have shown that the lattice oxygen on the surface layer of some highly active perovskites participate in formation of reaction intermediates via the reversible formation of VO, enabling OER to occur via LOM. We have also shown that this mechanism can be more favorable than AEM for maximizing the OER activity due to a relatively constant value of ∆G = 1.4~1.6 eV for Vo + OO*  Vo +OH*, which leads to a minimum OER overpotential of 0.17~0.41 eV for LOM. In contrast, the minimum overpotential for OER via AEM is 0.32~0.54 eV due to a relatively constant value of ∆G = 3.0~3.1 eV for OH*  OOH*. Employing the linear scaling relations between reaction steps, we have constructed the OER activity volcanoes separately for AEM and LOM, and found that the AEM volcano is universal for all perovskites, whereas the LOM volcano, whose peak is slightly higher than that of the AEM volcano, strongly depends on the identity of A in ABO3. Our overall OER activity volcano that considers both AEM and LOM successfully explains the recent experimental findings that state-of-the-art catalysts such as compressively strained LaNiO3,17 SrCoO3–δ,23 and PBCO,15 show oxygen adsorption energies that are different from the conventionally predicted optimum value of ~3.1 eV. Furthermore, we have discussed the thermodynamic feasibility of ORR via reverse LOM based on the overall ORR activity volcano that corroborates not only the experimental trend in ORR on different perovskites,35 but also the bifunctionality of pristine LaNiO3(cubic),40 compressively strained LaNiO3(cubic),17 and Ruddlesden-Popper (RP) structures of LaNixOy.41 We have also compared our LOM to another recently suggested mechanism, namely, OOM, and found that LOM is generally preferred to OOM because OH* is more stable on the TM site than the oxygen site for most perovskites. Finally, we have screened 275 different lanthanum- and strontium-based perovskites, identifying a variety of new perovskite compositions with potential for higher OER activity than that of LaNiO3. This work has demonstrated the importance of considering lattice oxygen participation in understanding

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trends in OER and ORR on highly active perovskites, and provided a guiding principle for the development of new and more efficient catalysts for oxygen-based catalysis.

Methods Spin polarized calculations were performed using VASP37 with PAW38 pseudopotentials and the RPBE-GGA31 functional. The fast algorithm, accurate precision, and 4×4×1 Monkhorst-Pack39 kpoint mesh were used for all calculations with an energy cutoff of 520 eV and Gaussian smearing of 0.1 eV. The LMAXMIX parameter was set to 6 to account for the f-electrons in rare earth elements. The slab models were based on (2×2×4) supercells, which were separated by > 17 AW of vacuum space perpendicular to the slab surface. Top two oxide layers of the slab models as well as adsorbates were relaxed until the forces on each atom were less than 10-3 eV/AW . All adsorption energies were referenced to gas-phase H2O and H2, and calculated in the low coverage limit of 0.25 ML. All free energies included zero-point-energy and entropic corrections to the calculated electronic energies. The corrections, taken from previous studies19,20,24,25, are +0.05 eV, +0.35 eV, +0.40 eV, –0.03 eV, +0.27 eV, and +0.28 eV for O*, OH*, OOH*, OO*, Vo + OH*, and HO-site*, respectively, independent of the perovskite composition. All A1.0B0.5B’0.5O3 perovskites (A, A’ = La, Ba, Sr, and B, B’ = transition metal) considered in this study were (001) facet, terminated with ideal B0.5B’0.5O2 surfaces, and modeled as cubic structures without any oxygen or metal vacancies in in the bulk, unless noted otherwise. For calculations involving SrCoO3–δ, (2×2×4) supercells were used with the top three oxide layers relaxed since oxygen vacancies were in the second outermost oxide layer. For calculations involving Pr0.5Ba0.5CoO3–δ, (2×2×10) supercells were used, with the top seven oxide layers relaxed since oxygen vacancies were in the first to sixth outermost oxide layer (see Fig. S11 in SI). For calculations involving LaNiO3(rhm), La2NiO4(RP), and La3Ni2O7(RP), (2×2×9), (2×2×4), and (2×2×5) supercells were used, respectively, with more than top two oxide layers relaxed (see Fig. S17 in SI). Finally, we ran RPBE+U calculations, and found that they are less accurate in describing the experimentally obtained OER trend on perovskites (see Fig. S19 in SI) probably because Ueff values were chosen based on bulk properties,32 which has been done in some previous studies.15,23,34

Associated content The Supporting Information is available free of charge on the ACS Publications website. It includes additional discussion, figures, and tables.

Author Information Corresponding Authors * E-mail: (J.S.Y.) [email protected]; (A.M.K) [email protected]. Notes The authors declare no competing financial interest.

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Acknowledgements J.S.Y., X.R., and A.M.K. acknowledge support from the Skoltech-MIT Center for Electrochemical Energy Storage. Computations were performed using computational resources from XSEDE and NERSC.

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