Supporting Information. Role of Lattice Oxygen Participation in Understanding Trends in the Oxygen Evolution Reaction on Perovskites

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1 Supporting Information 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.) jsyoo0927@gmail.com; (A.M.K) kolpak@mit.edu Additional discussion 1. Stability of LOM preferring perovskites (BSCF vs. PBCO) LOM preferring perovskites are generally prone to corrosion and amorphization as has been the case for BSCF (Ba 0.5Sr 0.5Co 0.8Fe 0.2O 3 δ). 6 Although our study shows that the generation and subsequent annihilation of a surface oxygen vacancy is thermodynamically favorable for LOM preferring perovskites, the process may not be performing so reversibly over time, leading to the formation of reduced phases on the perovskite surface. These accumulated oxygen vacancies on the perovskite surface can then diffuse into the bulk, resulting in amorphization. Thus, our study is limited in the sense that we mainly describe the initial catalytic activities of perovskites, i.e., not taking into account the long-term stability. However, recent experiments have shown that double perovskites such as PBCO (Pr 0.5Ba 0.5CoO 3 δ) show not only high OER activities via the lattice-oxygen mediated reaction mechanism but also high catalytic stabilities. 1 One possible explanation for high stabilities of double perovskites is that the diffusion of a surface oxygen vacancy into the bulk is effectively prevented by having two different oxide layers sandwiching the transition-metal oxide layer (see Fig. S11 in SI for the structure of a double perovskite). Let us take PBCO (double perovskite) vs. BaCoO 3 (normal perovskite) as an example. In the case of PBCO, the kinetic barrier for the vacancy diffusion from PrO layer to BaO layer (via the sandwiched CoO 2 layer) is predicted to be high, because the reaction energy is calculated to be extremely uphill (e.g ev) as shown in Fig. S11. On the other hand, in the case of BaCoO 3, the kinetic barrier for the vacancy diffusion from BaO layer to another BaO layer (via the sandwiched CoO 2 layer) is predicted to be low, because the reaction energy is, in principle, thermoneutral when we exclude the thickness effect. In the case of BSCF, the diffusion of a surface oxygen vacancy into the bulk is not effectively prevented as the difference between BaO layer and SrO layer is small due to relatively similar

2 electronegativities of Ba (0.89 by Pauling scale) and Sr (0.95 by Pauling scale). On the other hand, in the case of PBCO, the diffusion of a surface oxygen vacancy into the bulk is effectively prevented as the difference between the PrO layer and the BaO layer is large due to relatively different electronegativities of Pr (1.13 by Pauling scale) and Ba (0.89 by Pauling scale). Thus, a promising path for developing a novel OER perovskite achieving both high catalytic stability and activity is to conduct screening of perovskites that consist of oxide layers that are very different in terms of the electronegativity of the constituent metal, based on the LOM volcano presented in this study. 2. Effect of the crystalline structures of LaNixOy (001) on OER and ORR We have also taken into consideration the effect of the crystalline structures of LaNi xo y (001) on the theoretical overpotentials for OER and ORR. Fig. S3 and S10 in SI show that all the scaling relations obtained for the cubic structures of lanthanum-based perovskites also hold for the rhombohedral (rhm) and Ruddlesden-Popper (RP) structures of LaNi xo y (001). This suggests that the same volcanoes can be used to compare the activities of LaNi xo y crystals with different structures. Fig. S16 in SI shows that the cubic and RP structures are highly active for both OER via LOM, and ORR via reverse LOM, whereas the rhombohedral structure is only good for ORR via reverse AEM. The predicted order of the OER activity among the LaNi xo y crystals is [La 2NiO 4(RP) La 3Ni 2O 7(RP)-2 LaNiO 3(cubic) La 3Ni 2O 7(RP)-1] LaNiO 3(rhm), whereas that of the ORR activity is [La 2NiO 4(RP) La 3Ni 2O 7(RP)-2 LaNiO 3(rhm) LaNiO 3(cubic) La 3Ni 2O 7(RP)-2]. However, we note here that the activity orders inside the brackets are relatively uncertain as the differences in the calculated overpotentials are extremely small ( η OER < V, and η ORR < V). A more detailed study that includes e.g., the coverage effect, is required to accurately determine the activity orders inside the brackets. Previously, Zhou et al. 2,3 conducted experiments to compare the OER and ORR activities of LaNiO 3.00(cubic), LaNiO 3.00(rhm), La 2NiO 4.27(RP), La 3Ni 2O 7.15(RP). Although it is difficult to directly compare our results to theirs as their catalysts were synthesized as non-stoichiometric nanoparticles with many different facets, 2,3 some agreements can be found. For example, (1) LaNi xo y(cubic or RP) perovskites are good candidates for bifunctional catalysts, (2) LaNiO 3.00(cubic) shows higher bifunctional activity than LaNiO 3.00(rhm), and (3) the OER and ORR potentials measured at 1mA/cm -2 are relatively similar for many LaNi xo y perovskites. Generally, single-facet slab-model calculations match better with experiments when catalytic activities are measured from well-defined epitaxial thin films. 3. Concerted vs. non-concerted charge transfer pathways in OER via LOM Previously, Koper and Shao-Horn et al. 4 claimed that perovskites that are capable of lattice oxygen oxidation exhibit ph-dependent OER activities on the reversible hydrogen electrode scale, indicating non-concerted proton-electron transfers in the OER mechanism. 4 We also believe that the decoupling of proton and electron transfers can take place in any of the four electrochemical steps (perhaps, the rate-limiting one) in LOM. In this study, however, we do not need to assume anything about the mechanism of the proton-electron transfer as we develop our activity volcanoes based on considering only the reaction intermediates. Note that all the reaction intermediates (not transition states) involved in OER are charge-neutral, and therefore, they are the same regardless of whether the proton-electron transfers occur via the concerted or non-concerted pathway. Even in

3 Fig. 4 of the aforementioned reference, 4 we can see that the same reaction intermediates are considered for OER mechanisms with concerted and non-concerted proton-electron transfers. We also do not preclude ph-dependence of the OER on any perovskite surfaces, since we cannot precisely calculate the solvation-dependent energies of the charged transition states formed during non-concerted proton-electron transfers. Such calculations require identifying where the charge localizes in the transition-state species interacting with the water solvent, which cannot be done easily with DFT due to the following reasons: (1) it would be strongly dependent on the functional; (2) it would be inaccurate due to the delocalization error; (3) although the delocalization error can be approximately corrected through some established methods, the impact of the corrections on the electron density is not well known; and (4) higher levels of theory with exact exchange are required, but they are computationally impossible for our heterogeneous systems. In addition, even in the aforementioned reference mentioned, 4 the authors argue that the proton-electron transfer is concerted for LaCoO 3 whereas it is non-concerted for SrCoO 3. However, when calculating and comparing the limiting potential between the two catalysts, they consider the same reaction intermediates for both catalysts (see Fig. 4b, d, and f in the reference), likely due to the difficulties mentioned above in calculating the charged transition states.

4 Additional figures Figure S1. Free energy diagrams for OER via AEM for (a) LaVO 3, (c) LaCoO 3, and via LOM for (b) LaVO 3, (d) LaCoO 3 at ph = 0, T = 298 K, and zero applied potential. All adsorbates with * bind to the transition-metal B site of ABO 3 (001) except H O-site* that binds to the lattice-oxygen 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) and (c) show that G OOH* G OH* is relatively constant with an average value of ~3.1 ev, whereas those in (b) and (d) show that G Vo + OH* G Vo +OO* is relatively constant with an average value of ~1.4 ev (see Table S1 in SI) for all five lanthanum-based perovskites (see Table S1 in SI).

5 Figure S2. Free energy diagrams for OER via AEM for (a) SrVO 3, (c) SrCoO 3, (e) SrNiO 3, (g) SrCuO 3, and via LOM for (b) SrVO 3, (d) SrCoO 3 (f) SrNiO 3, (h) SrCuO 3, at ph = 0, T = 298 K, and zero applied potential. All adsorbates with * bind to the transition-metal B site of ABO 3 (001) except H O-site* that 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), (c), (e), and (g) show that G OOH* G OH* is relatively constant with an average value of ~3.0 ev, whereas those in (b), (d), (f), and (h) show that G Vo + OH* G Vo +OO* is relatively constant with an average value of ~1.6 ev (see Table S1 in SI) for all four or five strontium-based perovskites (see Table S1 in SI).

6 Figure S3. The scaling relations of adsorption energies when the calculated adsorption energies of (a) OH*, and (b) OOH* are scaled to the calculated adsorption energy of atomic oxygen ( E O), and when the energies of (c) V o + OO*, (d) V o + OH*, (e) H O-site* + OH*, and (f) V o are scaled to E O. All adsorption energies are relative to gas-phase H 2O and H 2. In each plot, circles, squares, and triangles indicate lanthanum-, strontium-, and barium-based perovskites, respectively. The black, red, and green solid lines show the linear scaling relations separately obtained for lanthanum-, strontium-, and barium-based perovskites, respectively. On the other hand, the blue solid lines show those obtained for both lanthanum- and strontium-based perovskites. Note that OH* on SrMnO 3, OOH* on SrCrO 3, and V O + OH* on SrCrO 3 are not shown as the surface reconstructs significantly upon the adsorption of the adsorbate. V O + OO* on BaCuO 3 is also not shown as OO* desorbs. Finally, RMSE s in (e) and (f) are slightly large compared to others. This is because, (1) H O-site* itself does not scale well with O*, and (2) coordination geometries are different between O* and V O. However, by considering H O-site* and OH* together in the same supercell, the energy can be empirically scaled to E O. This is because, the variation in E HO-site is much lower than that in E OH* across different perovskites. We had to consider H O- site* and OH* together in the same supercell in order to describe all reaction free energies as functions of E O, such that we can directly compare the LOM volcano with AEM volcano in the same descriptor space.

7 Figure S4. Negative reaction free energies of the four charge transfer steps in OER via LOM for lanthanumbased perovskites, which are plotted as functions of G O. The shaded region shows the theoretical activity volcano for OER via LOM, and the dashed line indicates the equilibrium potential for OER (1.23 V). Thus, the difference between the dashed line and the line that forms the volcano represents the theoretical overpotential for OER via LOM.

8 Figure S5. O 2(g) formation energies calculated with either the RPBE (red) or HSE06 hybrid (blue) functional at different O O bond distances in O 2(g). The black square represents the experimental measurement. Note that the RPBE functional predicts the O O distance to be ~1.24 Å whereas the HSE06 hybrid functional predicts it to be much closer to the experimental value of ~1.21 Å. As a result, RPBE over-stabilizes O 2(g) by 0.4~0.5 ev in the range of O O distances that we find in OO* on different perovskites (see Fig. S6 in SI). Figure S6. OO* formation energies calculated with the RPBE functional at different O O bond distances in OO* on different surfaces. Here, we note that we were unable to obtain these values with the HSE06 hybrid functional due to computational expense.

9 Figure S7. The shaded region indicates the theoretical activity volcano for OER via LOM for lanthanum-based perovskites (a) without or (b) with the 0.4 ev correction to OO* adsorption energies on different perovskites. Note that the red line shifts up whereas the black line shifts down slightly when we apply the correction. As a result, the top of the activity volcano decreases slightly and shifts to the right by ~0.25 ev. This can be seen more clearly in Fig. S8 in SI. Figure S8. The shaded region indicates the overall OER activity volcano that takes into account both AEM (black) and LOM (red) for lanthanum-based perovskites (a) without or (b) with the 0.4 ev correction to OO* adsorption energies on different perovskites. Note that even with the maximum correction of 0.4 ev, the top of the activity volcano for OER via LOM is still slightly higher than that for OER via AEM. As a consequence, any conclusions made in this study are not significantly affected by the actual value of the correction if it is less than 0.4 ev. Note that applying the maximum correction to OO* puts LaNiO 3 on the AEM volcano instead of the LOM volcano. This indicates that a much more detailed study that takes into account the coverage effect, solvent effect, and kinetic barriers must be considered to accurately determine the more favorable reaction mechanism for LaNiO 3.

10 Figure S9. The calculated free adsorption energies (ev) of atomic oxygen on strained LaNiO 3 (see Table S2 in SI for their values). The strain ranges from tensile (+) to compressive ( ) relative to the lattice parameters of pristine LaNiO 3. All adsorption energies are relative to gas-phase H 2O and H 2. Figure S10. The calculated energies of (a) V o formation, (b) V o + OO*, and (c) V o + OH* plotted against E O for CoO 2 terminated Pr 0.5Ba 0.5CoO 3 δ (001) with double-perovskite structures, 1 and NiO x terminated LaNi xo y (001) with different crystal structures (RP: Ruddlesden-Popper, rhm: rhombohedral). 2,3 All energies are relative to gas-phase H 2O and H 2. The black, red, and green solid lines represent the linear scaling relations separately obtained for lanthanum-, strontium-, and barium-based perovskites, respectively, which are from Fig. S3 in SI. PBCO indicates Pr 0.5Ba 0.5CoO 3 with PrO as the second oxide layer (and BaO as the fourth oxide layer), and BPCO indicates the same compound with BaO as the second oxide layer (and PrO as the fourth oxide layer). Clean means the perovskite is stoichiometric (vacancy-free). O vac 2nd or O vac 4th means there is one oxygen vacancy in the second or fourth outermost oxide layer, respectively. LSMO in (a) indicates MnO 2 terminated La 0.5Sr 0.5MnO 3 (001) with LaO as the second oxide layer (and SrO as the fourth oxide layer). See Fig. S11 in SI for more details about the PBCO and BPCO slabs, and Fig. S17 in SI for more details about the LaNi xo y slabs. Note that V o + OO* and V o + OH* are not shown for LSMO and LaNiO 3(rhm) as AEM is preferred to LOM on these surfaces.

11 Figure S11. (Left) The side view of the (2 2 10) slab models used to obtain the data points in Fig. S10 in SI. The light green, dark green, pink, and red atoms indicate praseodymium, barium, cobalt, and oxygen atoms, respectively. Crossed atoms indicate that they were fixed during structural relaxation. PBCO indicates CoO 2 terminated Pr 0.5Ba 0.5CoO 3 (001) with PrO as the second oxide layer, and BPCO indicates the same compound with BrO as the second oxide layer. (Right) The relative energies when one lattice oxygen vacancy is created in a different oxide layer. Note that the vacancy is preferred to be in the outermost PrO layer for both PBCO and BPCO. Thus, PBCO without any oxygen vacancies (PBCO_clean), PBCO with one oxygen vacancy in the second oxide layer (PBCO_O vac 2nd ), BPCO without any oxygen vacancies (BPCO_clean), and BPCO with one oxygen vacancy in the fourth oxide layer (BPCO_O vac 4th ) are used to approximately model the OER activities of the previously synthesized Pr 0.5Ba 0.5CoO 3 δ catalysts 1 with unknown amounts of oxygen vacancies (see Fig. S13 in SI). Figure S12. Negative reaction free energies of the four charge transfer steps in OER via LOM for strontiumbased perovskites, which are plotted as functions of G O. The shaded region shows the theoretical activity volcano for OER via LOM, and the dashed line indicates the equilibrium potential for OER (1.23 V). Thus, the difference between the dashed line and the line that forms the volcano represents the theoretical overpotential for OER via LOM. Note that the red and green lines are the same as those shown in Fig. S4 in SI. However, the black and blue lines are different as they are obtained based on only strontium-based perovskites. We also note here that, unlike the case of Fig. 2b of the manuscript, it is absolutely clear here that the red line flattens the top of the activity volcano as it goes lower than the top of the volcano by 0.4 ~ 0.5 ev, and the expected DFT error in calculating adsorption energies on solid surfaces is about 0.2 ev.

12 Figure S13. 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 in the manuscript, respectively, whereas the blue volcano is from Fig. S12 in SI. The four purple crosses on the blue volcano represent PBCO_clean, BPCO_O vac 4th, BPCO_clean, and PBCO_O vac 2nd in order from left to right (see Fig. S11 in SI for more details about these surfaces). The dashed arrows show how the volcanoes will change if we apply a correction to OO*.

13 Figure S14. Negative reaction free energies of the four charge transfer steps in ORR via reverse (a) AEM or (b) LOM for lanthanum-based perovskites, which are plotted as functions of G O. (c) is obtained by combining (a) and (b). In each figure, the shaded region shows the upside-down theoretical activity volcano for ORR, and the dashed line indicates the equilibrium potential for ORR (1.23 V). Thus, the difference between the dashed line and the line that forms the upside-down volcano represents the theoretical overpotential for ORR. Filled markers indicate the data points used to construct the volcano based on calculations of the reaction energetics, and empty makers indicate those added to the constructed volcano by calculating G O per surface. Note that the data points for some perovskites are not within the plotted area for some linear relations in (b) and (c), but all linear relations are obtained based on the data points for all five lanthanum-based perovskites.

14 Figure S15. Negative reaction free energies of the four charge transfer steps in ORR via reverse (a) AEM or (b) LOM for strontium-based perovskites, which are plotted as functions of G O. (c) is obtained by combining (a) and (b). In each figure, the shaded region shows the upside-down theoretical activity volcano for ORR, and the dashed line indicates the equilibrium potential for ORR (1.23 V). Thus, the difference between the dashed line and the line that forms the upside-down volcano represents the theoretical overpotential for ORR. Filled markers indicate the data points used to construct the volcano based on calculations of the reaction energetics, and empty makers indicate those added to the constructed volcano by calculating G O per surface. Note that (a) is the same as Fig. S14a in SI as the activity volcano for ORR via reverse AEM is universal for all perovskites. However, (b) is different from Fig. S14b in SI as the black and blue lines are obtained based on only strontium-based perovskites.

15 Figure S16. NiO x terminated LaNi xo y (001) in either cubic, rhombohedral (rhm), or Ruddlesden-Popper (RP) structures 2,3 added to the overall (a) OER and (b) ORR activity volcano for lanthanum-based perovskites. For more details about these surfaces, see Fig. S17 in SI. Figure S17. The top and side views of the (2 2 a) slab models used to obtain LaNi xo y data points in Fig. S10 and S16 in SI. The light blue, green, and red atoms indicate lanthanum, nickel, and oxygen atoms, respectively. Crossed atoms indicate that they were fixed during structural relaxation.

16 Figure S18. Free energy diagrams for OER via LOM for (a) LaCoO 3, (c) LaNiO 3, (e) SrCoO 3, (g) LaCuO 3, and those via the O ads O latt mechanism suggested by Koper and Shao-Horn et al. 4 for (b) LaCoO 3, (d) LaNiO 3 (f) SrCoO 3, (h) LaCuO 3, at ph = 0, T = 298 K, and zero applied potential. In the case of LOM, all adsorbates with * bind to the transition-metal (TM) site of ABO 3 (001) except H O-site* that binds to the lattice-oxygen (O) site. In the case of O ads O latt, all adsorbates with * bind to the O site. In each plot, the value of the reaction free energy for the potential-determining step (namely, the limiting potential) is shown in blue. Note that the limiting potential of 2.69 V in (b), and 1.85 V in (f) match with those (2.27 V and 1.84 V, respectively) previously reported by Koper and Shao-Horn et al. 4 The reason why our values are slightly higher is that RPBE is used in this study whereas PW91 is used in their studies. 4

17 Figure S19. Negative reaction free energies of the four charge transfer steps in OER via AEM for lanthanumbased perovskites, which are plotted as functions of G O. (a) is obtained with RPBE, whereas (b) is obtained with RPBE+U eff (U eff = 3.1, 3.5, 3.3, 6.4, and 4.0 for vanadium, chromium, cobalt, nickel, and copper, respectively, which are taken from previous studies 5 on bulk properties such as oxidation energies of transition metal oxides). The shaded region shows the theoretical activity volcano for OER via AEM, and the dashed line indicates the equilibrium potential for OER (1.23 V). Thus, the difference between the dashed line and the line that forms the volcano represents the theoretical overpotential for OER via AEM. We can see that data points are much less scattered in (a) than (b) in forming linear relations, and (a) describes the experimentally obtained OER trend 6 of LaNiO 3 > LaCoO 3 > LaMnO 3 > LaCrO 3 better than (b). This shows that using RPBE+U with U eff values obtained based on bulk properties does not necessarily improve the accuracy of calculating surface properties such as adsorption energies. Figure S20. Negative reaction free energies of the four charge transfer steps in OER via AEM for lanthanumbased perovskites, which are plotted as functions of G O G OH. The shaded region shows the theoretical activity volcano for OER via AEM, and the dashed line indicates the equilibrium potential for OER (1.23 V). Thus, the difference between the dashed line and the line that forms the volcano represents the theoretical overpotential for OER via AEM.

18 Figure S21. Surface coverages as functions of applied potential (U vs. RHE). Although the equilibrium potential for OER is 1.23 V, experiments are often conducted at higher potentials (U = catalyst s theoretical overpotential + α) to generate sufficiently high current densities. For example, ~1000 ma/cm 2 is required for industrial application. 8 Since many laboratory-discovered catalysts are not fully geometrically optimized (e.g. number of active sites per surface area), and assuming that there can be ~10-fold increase in current density via geometric optimization of laboratory-discovered catalysts, we would like to define the lab-scale operating potential as the potential under which laboratory-discovered catalysts generate ~100 ma/cm 2. We find that 1.8 V (shown as the dashed horizontal line) is the lab-scale operating potential for many state-of-the-art catalysts such as PBCO and BSCF. 1,6 Thus, this figure shows that perovskite surfaces with 2.9 ev < G O < 3.5 ev are mainly covered with OH* under the lab-scale operating potential, enabling LOM. Furthermore, we note here that OER on perovskites is often conducted under basic conditions (high ph). This means that OH* formation can be even more favorable that that shown here, since we have assumed ph = 0 in calculating H 2O OH* + H + + e and OH* O* + H + + e employing the computational hydrogen electrode model. 7 Applying more basic conditions (e.g. alkaline electrolytes such as KOH solutions) will lead to more weakly binding catalysts to be covered with OH*, enabling LOM. This is because, OH - OH* + e (no bond breaking involved) is predicted to be both thermodynamically and kinetically more favorable than H 2O OH* + H + + e (bond breaking involved) under basic conditions. However, the reaction free energy of the former reaction is difficult to calculate as we cannot easily obtain the energy of OH anion surrounded by certain number of water molecules. In addition, we would like to note here that O* is not a spectator species preventing LOM. Although Scheme 1 in the main text indicates that O* is not directly involved in LOM (this is because we have considered only the electrochemical steps that consist of LOM), our recent study 9 has found that step #5 in Scheme 1 (OH* (V o + OO*) + H + + e ) actually occurs via two-step process: OH* O* + H + + e (electrochemical) followed by O* + O lattice OO* + V O (non-electrochemical) in which O* is directly involved. This two-step process has been shown to be both thermodynamically and kinetically favorable for LOM preferring perovskites such as LaNiO 3 and LaCuO 3. 9 Thus, LOM is still feasible on O* covered surfaces via (1) O* + O lattice OO* + V O (non-electrochemical); (2) step # 6 in Scheme 1; (3) step #7 in Scheme 1; (4) step #8 in Scheme 1; (5) OH* O* + H + + e, although our activity volcanoes indicate that AEM is generally preferred to LOM on O* covered (strongly binding) surfaces.

19 Additional tables Table S1. The calculated reaction free energies (ev) on different perovskites. Note that G for OH* OOH* for SrMnO 3 is not available (N/A) as the surface reconstructs significantly upon the adsorption of OH*. Note that the average values may change slightly depending on the selection of perovskites. However, our average value of 3.09 or 3.04 ev obtained for OH* OOH* (AEM) is in good agreement with 3.2 ev obtained in the previous study 10 by considering larger number of perovskites. This indicates that our selection of perovskites (1 strongly binding, 3 moderately binding, and 1 weakly binding) is a good representation of a large number of perovskites. OH* OOH* V o + OO* V o +OH* LaVO LaCrO LaCoO LaNiO LaCuO Average SrVO SrMnO 3 N/A 1.59 SrCoO SrNiO SrCuO Average Combined Average Table S2. The calculated free adsorption energies (ev) of atomic oxygen on strained LaNiO 3. The strain ranges from tensile (+) to compressive ( ) relative to the lattice parameters of pristine LaNiO 3. Strain on LaNiO 3 (%) G O (ev)

20 Table S3. The calculated adsorption energies (ev) of atomic oxygen and the predicted limiting potentials (V) for various perovskites (vacancy-free A 1.0B 0.5B 0.5O 3 (001) where A = lanthanum or strontium, B, B = transition metal, and B, B are homogeneously mixed) with cubic structures. All adsorption energies are relative to gas-phase H 2O and H 2. Blue indicates perovskites that do not consist of precious metals such as Pd, Rh, Ru, and Ag. One can obtain theoretical overpotentials by subtracting the limiting potentials from the equilibrium potential for OER ( 1.23 V). Surface G O (ev) Limiting pot. (V) Surface G O (ev) Limiting pot. (V) LaFe 0.5Ni 0.5O SrMo 0.5Ag 0.5O LaCu 0.5Pd 0.5O SrMn 0.5Pd 0.5O LaCo 0.5Pd 0.5O SrCu 0.5Mo 0.5O LaPd 0.5Ag 0.5O SrMo 0.5Rh 0.5O LaRu 0.5Pd 0.5O SrRh 0.5Pd 0.5O LaMn 0.5Pd 0.5O SrCr 0.5Fe 0.5O LaCr 0.5Pd 0.5O SrCr 0.5Ni 0.5O LaNi 0.5Cu 0.5O SrRh 0.5Ag 0.5O LaNi 0.5Pd 0.5O SrMn 0.5Rh 0.5O LaCu 0.5Tc 0.5O SrMn 0.5Tc 0.5O LaCr 0.5Cu 0.5O SrCo 0.5Mo 0.5O LaPdO SrMn 0.5Rh 0.5O LaNiO SrMn 0.5Ni 0.5O LaMo 0.5Pd 0.5O SrMn 0.5Ru 0.5O LaNi 0.5Ag 0.5O SrCr 0.5Ag 0.5O LaCu 0.5Ru 0.5O SrCr 0.5Cu 0.5O SrCu 0.5Rh 0.5O SrCo 0.5Rh 0.5O SrCr 0.5Co 0.5O SrRhO SrMnO SrNi 0.5Rh 0.5O SrMn 0.5Co 0.5O SrCo 0.5Ru 0.5O SrNi 0.5Tc 0.5O SrCo 0.5Rh 0.5O SrCoO SrCo 0.5Tc 0.5O

21 Table S4. The calculated adsorption energies (ev) of O* and OH* on the transition-metal (TM) vs. latticeoxygen (O latt) site for various ABO 3 (001) perovskites in cubic structures. All adsorption energies are relative to gas-phase H 2O and H 2. Blue indicates the more stable adsorption between the two sites. In the manuscript, we group LaVO 3, LaCrO 3 and LaCoO 3 as relatively strongly binding, SrCoO 3 and LaNiO 3 as relatively moderately binding, and SrNiO 3 and LaCuO 3 as relatively weakly binding, based on the calculated adsorption energy of O* on the TM site. O* OH* Surface TM site O latt site TM site O latt site LaVO Unstable LaCrO Unstable LaCoO SrCoO LaNiO SrNiO LaCuO References 1. Grimaud, A.; May, K. J.; Carlton, C. E.; Lee, Y.-L.; Risch, M.; Hong, W. T.; Zhou, J.; Shao-Horn, Y. Double Perovskites as a Family of Highly Active Catalysts for Oxygen Evolution in Alkaline Solution. Nat. Commun. 2013, 4, Zhou, W.; Sunarso, J. Enhancing Bi-functional Electrocatalytic Activity of Perovskite by Temperature Shock: A Case Study of LaNiO 3 δ. J. Phys. Chem. Lett. 2013, 4, Yu, J.; Sunarso. J.; Zhu, Y.; Xu, X.; Ran, R.; Zhou, W.; Shao, Z. Activity and Stability of Ruddlesden Popper-Type La n+1ni no 3n+1 (n=1, 2, 3, and ) Electrocatalysts for Oxygen Reduction and Evolution Reactions in Alkaline Media. Chem. Eur. J. 2016, 22, Grimaud, A.; Diaz-Morales, O.; Han, B.; Hong, W. T.; Lee, Y. -L.; Giordano, L.; Stoerzinger, K. A.; Koper, M. T. M.; Shao-Horn, Y. Activating Lattice Oxygen Redox Reactions in Metal Oxides to Catalyse Oxygen Evolution. Nat. Chem. 2017, 9, Wang, L.; Maxisch, T.; Ceder, G. Oxidation Energies of Transition Metal Oxides Within the GGA+U Framework. Phys. Rev. B 2006, 73, Suntivich, J.; May, K. J.; Gasteiger, H. A.; Goodenough, J. B.; Shao-Horn, Y. A Perovskite Oxide Optimized for Oxygen Evolution Catalysis from Molecular Orbital Principles. Science 2011, 334, Nørskov, J. K.; Rossmeisl, J.; Logadottir, A.; Lindqvist, L.; Kitchin, J. R.; Bligaard, T.; Jónsson, H. Origin of the Overpotential for Oxygen Reduction at a Fuel-Cell Cathode. J. Phys. Chem. B 2004, 108,

22 8. Lu, X.; Zhao, C. Electrodeposition of Hierarchically Structured Three-dimensional Nickel iron Electrodes for Efficient Oxygen Evolution at High Current Densities. Nat. Commun. 2015, 6, Yoo, J. S.; Liu, Y.; Rong, X.; Kolpak, A.M. Electronic Origin and Kinetic Feasibility of the Lattice Oxygen Participation During the Oxygen Evolution Reaction on Perovskites, J. Phys. Chem. Lett. 2018, 9, Man, I. C.; Su, H. -Y.; Calle-Vallejo, F.; Hansen, H. A.; Martínez, J. I.; Inoglu, N. G.; Kitchin, J.; Jaramillo, T. F.; Nørskov, J. K.; Rossmeisl, J. Universality in Oxygen Evolution Electrocatalysis on Oxide Surfaces. ChemCatChem 2011, 3,