Transfer learning methodology for predictionData extraction and cation encodingThe proposed transfer learning loop, as depicted in Fig. 1, comprises seven steps: data extraction, cation encoding, feature embedding, clustering, local prediction, global ensembling, and experimental validation with active learning closed loop. Due to the limited availability of perovskite oxide data for OER, we additionally collected data for non-OER perovskite oxides (see Supplementary Data 1 for a comprehensive list of data collected and predicted in this work). This approach expanded the dataset by 48.9% from 94 to 140 entries (Fig. 2a). The enriched dataset encompasses a diverse range of features, including material compositions, oxygen vacancy concentration, and chemical valence state distributions.Fig. 1: Transfer learning workflow to discover perovskite electrocatalysts for the oxygen evolution reaction.The OER-specific data subset is more extensive than the non-OER subset, incorporating various parameters for the characterization of the OER catalysts, including mass loading (in mg cm–2), electrolyte concentration (in mol L–1), substrate type (rotating disk electrode, glassy carbon or glassy carbon electrode), and the overpotential required to achieve a current density of 10 mA cm–2 (in mV). All catalysts were synthesized using the sol-gel method. While previous studies reported negligible variations in individual features when employing chemical valence state distributions for feature encoding62,63, our findings indicate that a specific material composition can be linked to a broad range of cation-encoded data points. For example, a perovskite composition (Co/Fe in B-site) with 10 distinct chemical valence distributions, could generate 419,281 data points (Fig. 2b). Such substantial cumulative discrepancies would significantly reduce the accuracy of the data. Therefore, we computed 20 intrinsic features for each perovskite composition based on cation encoding (see Supplementary Note 1 for computational details).Fig. 2: Evaluation and prediction of transfer learning models.a Distribution of OER data, associated OER activities (overpotential), juxtaposed with non-OER data across 2-D embeddings. b Visualization of cation encoding for a specific material formula, encompassing multiple hypothesized valence states, represented by 419,281 data points (sampling ratio of 1:1000 in the figure). c Comparative analysis of various embedding parameter settings. The gradation of bar colors from lighter to darker corresponds to the test set outcomes for 3, 5, 7, 10, and 15 folds cross-validation, respectively. The line graph delineates the ensemble outcomes of a 10-fold cross-validation conducted on the entire dataset. d The reconstruction RMSE of the AESC. Red and blue bars denote AESC trained on OER data only and on both OER and non-OER data, respectively. The x-axis catalogs the datasets employed for computing the reconstruction RMSE. e Evaluation of K-Means clustering performance. f A comparative assessment of the prediction accuracy for OER activities. g First round of OER activities prediction. The error bar represents the standard deviation of the prediction. h Enhanced prediction accuracy attained through active learning processes for both PSCF and PSCFM. The error bar represents the standard deviation of the prediction. i Second-round of OER activities prediction. The error bar represents the standard deviation of the prediction.Feature embeddingWe employed a pre-training process that utilizes an auto-encoder with shortcut connections (AESC)22 to project cation encoding into embeddings with reduced dimensionality while preserving informational integrity, thereby enhancing the data density. We used an n-fold cross-validation methodology to identify the most effective AESC architecture, evaluating a range of configurations from simplistic to intricate. Subsequently, we synthesized these sub-models using an ensemble strategy by computing the arithmetic mean of all predictions. The performance evaluation matrix (Supplementary Note 2) employed the correlation of determination (R2) to access the correlation between the encoder inputs and the decoder outputs (reconstruction). A two-dimensional embedding was selected to maintain a balance between model performance and visualization requirements. Screened from 400 different models, the ensemble model constructed through 10-fold cross-validation, demonstrated an impressive R2 of 0.77 and 0.96 on the test and the entire dataset, respectively (See Fig. 2c and Supplementary Fig. 1 for the full results). Furthermore, to evaluate the efficacy of transfer learning, the ability of an AESC to capture different classes of material information was measured using the reconstruction root mean square error (RMSE). As illustrated in Fig. 2d, the proposed AESC demonstrates superior reconstruction fidelity on non-OER datasets, achieving a significant reduction in RMSE from 3.25 to 1.05. This compelling result suggests that material embeddings extracted through transfer learning approaches are effective in capturing the characteristics of unreported OER candidates. Notwithstanding, the findings in Fig. 2d alone are insufficient to conclusively establish the efficacy of transfer learning; its robustness must be further rigorously evaluated through comprehensive experimentation.Clustering and location predictionWe subsequently employed the embeddings of OER materials, along with their corresponding reaction conditions, as input variables for the model. 91 out of a total of 94 points were included, and the rest 3 points were excluded due to their uncertainty in the reaction conditions. The model was then trained to predict the overpotential at a current density of 10 mA cm−2. A novel ensemble model of Gradient Boosting Regressor (GBR)23 was implemented, with hyperparameter optimization conducted through a grid search of a consistent set of hyperparameters (48,600 different combinations for each model, see Supplementary Note 3 for the full list). However, visualization revealed an uneven distribution of data in the 2D embedding space. A model indiscriminately trained on the entire dataset exhibited low accuracy, with an RMSE of 42.79 mV, highlighting the inconsistency in OER performance attributable to the inherent complexity of our material system. To address this issue, we employed a data segmentation strategy. The data was divided into clusters characterized by greater internal consistency, allowing for individualized model training for each cluster. An unsupervised learning method, K-Means clustering in Lloyd style24 was utilized to classify the data into multiple clusters based on Euclidean distances (See Supplementary Figs. 2–4 for data visualization). This approach promotes homogeneity within clusters and facilitates effective GBR training for each cluster. Additionally, as an alternative to spatial-location based clustering, a sorting principle informed by domain knowledge (phase-sorting) was also considered. This method divided the data into seven categories: unknown, cubic, hexagonal, monoclinic, orthorhombic, rhombohedral, and tetragonal. To determine the optimal cluster number for K-Means clustering, we evaluated a range of cluster sizes from 1 to 19. Six different metrics were employed to guide this selection process (Fig. 2e). Examining the sum of squared distance of each data point to its nearest cluster center revealed a leveling off in the data once the cluster count reached 5 or 6, suggesting potential options for the number of clusters25. Additionally, we adopted phase-sorting as a benchmark for K-Means clustering. Based on a composite of metrics from various measurements, including Adjusted Rand Index26, V-Measure, Completeness, Homogeneity27 and Silhouette28 scores (see Supplementary Note 4 for computational details), we selected cluster sizes of 5, 6, 13, 15, and 18 as they represent inflection points. Notably, none of these configurations achieved particularly high scores across all evaluation metrics. This unsatisfactory result may be attributed to the fact that a significant portion of the dataset (24 out of 94 entries) falls into the ‘unknown’ category in phase-sorting clustering. Therefore, relying solely on clustering analyses to determine the most effective clustering methodology is insufficient. This highlights the importance to employ predictive models trained on a variety of clustering approaches to achieve a more robust assessment.We employed a 3-fold cross-validation approach to tune the hyperparameters of the GBR models for each cluster to predict OER activities. Subsequently, the optimized models were refitted to the corresponding dataset within each cluster without concerns about overfitting, based on the assumption of high intra-cluster consistency. For cluster comprising fewer than 3 data points, the arithmetic mean of the overpotential values was used as the predicted outcome. We opted for a 3-fold cross-validation strategy primarily because a higher number of folds could preclude smaller clusters from undergoing effective cross-validation. In instances where clusters comprise fewer than three data points, the arithmetic mean of the overpotentials inherent to the cluster was employed as a fixed output. Each model trained in this fashion was predicated on data exclusive to individual, independent clusters, a methodology we refer to as ‘local prediction’. The most effective model was constructed based on 13 clusters for K-Means, achieving a relatively lower overall RMSE of 29.8 mV, while the model based on phase-sorting yields a RMSE of 33.45 mV (Fig. 2f). This slight improvement primarily arises from an inability of a singular clustering methodology to categorize all data points comprehensively, coupled with the fact that local prediction models do not accommodate intersecting clustering schemes.Global ensemblingIn the realm of local prediction, individual cluster-based models operate autonomously, devoid of inter-cluster information exchange, leading to the underutilization of substantial datasets. To address this inefficiency, transfer learning is used to synergize models trained across disparate clusters. Rinehart et al. proposed a methodology capable of evaluating the effectiveness of transfer learning by quantifying the degree of similarity among datasets, a measure dependent on the discernment of domain-specific knowledge29. Rao et al. estimated prediction uncertainty through similarity, measured by the distance between estimated-training data points30, proposing that prediction accuracy diminishes as the distance between the prediction point and cluster center increases. In contrast to these approaches, we developed a global ensemble method that incorporates both domain knowledge and data distance metrics to assess data similarity. The similarity metric involves calculating the Euclidean distance between a predicted point and each cluster’s centroid. Importantly, the relationship between similarity and prediction accuracy is not predetermined; instead, it is elucidated through the inductive capabilities of a ML model, termed global ensembling (Supplementary Note 5).Global ensembling facilitates the transfer learning of data across various clusters, enabling a broader integration of cluster-specific information. Notably, when employing 13 clusters as the optimal configuration for local prediction, the RMSE substantially decreases from 29.8 mV to a global value of 9.80 mV (Fig. 2f). Furthermore, unlike in local prediction models where clusters operate independently, the global ensemble approach enables the integration of diverse clustering methodologies, as information could be transferred between spatial information and domain knowledge. This comprehensive incorporation of clustering data considerably enriches the informational substrate available for model learning, thereby enhancing the model’s capacity for accurate fitting. The model combining phase-sorting cluster, no clustering (1 cluster), K-Means 5, 6, 13, 15, and 18 clusters outperform the remaining local and global models with an RMSE of 8.90 mV and is selected as the final model to initialize the first-round prediction of novel materials. It is important to note that there are nuanced distinctions in the computation of the RMSE among direct refit, local prediction, and global ensemble strategies. The ultimate efficacy of the predictive model requires experimental validation.Experimental verification and active learningWe used this well-calibrated global ensemble model to conduct experimental validation of material candidates. Due to the inherent complexities associated with predicting the properties of perovskite oxide materials with higher structural entropy, our initial prediction was restricted to quaternary and quinary compositions (specifically, the overall cation type is 3 or 4: AA’BO or AA’BB’O, with the A site fixed to 6 different combinations, including Ba + Sr, La + Ca, La + Sr, Pr + Ba, Pr + Ca and Pr + Sr. The B site was selected from Co, Fe, Mn, Nb, Zr, Ni, Cu, Sn, Ir and Ru. A total of 7050 different formulas were generated in a combinatorial manner). Any particular A/B stoichiometry could correspond to multiple valence states, resulting in a range of predicted overpotential values. (See Supplementary Note 6 for speculative rules concerning valence state distribution). Thirty chemical formulas were selected from over 5 million prediction points for experimental validation (Supplementary Fig. 5). Importantly, the material with the composition PSCF was predicted to be a high-performance material (Fig. 2g) with the lowest overpotential of 340.81 mV (364.80 ± 18.55 mV). All samples were synthesized using the sol-gel method followed by annealing at 850 °C in air. Our X-ray diffraction (XRD) results confirmed the formation of 10 phase-pure perovskites (Supplementary Fig. 6a), while the remaining samples exhibited perovskite structures with significant impurities or intermediate phases (Supplementary Fig. 6b, c). Preliminarily the linear sweep voltammetry (LSV) evaluation confirmed an overpotential of 327 mV for PSCF. Subsequent X-ray photoelectron spectroscopy (XPS) characterization revealed the oxidative valence states of each cation in PSCF (detailed results are presented later in the paper). Thereafter, the data for PSCF were processed through cation encoding, feature embedding, and re-incorporated into our training sets for both local and global regressors in the second-round training iteration (Fig. 2h). This represents a typical active learning practice that involves augmenting the most recent experimental findings while continuously refining the model30. See Supplementary Figs. 7 and 8 for the second-round training results.In the second round, a total of 9000 hexanary (AA’BB’B”O) formulas were generated, with the A sites being fixed with Pr + Sr, and the B sites incorporating three elements selected from the same list in the first-round prediction. This resulted in the shortlisting of 6 hexahydroxy formulas from an extensive dataset of over 20 million predicted data points (Supplementary Fig. 9). The PSCFM with Mn partially substituting Fe in PSCF was optimized from the second-cycle prediction, achieving a minimum predicted overpotential of 302.92 mV (322.75 mV ± 14.09 mV) (Fig. 2i). Subsequently, all these selected materials were fabricated, screened by XRD and evaluated by LSV measurement (Supplementary Fig. 6d). Consistent with the predictions, the PSCFM demonstrated a reduced overpotential of 315 mV at 10 mA cm−2, validating the reliability of our model. Notably, without the implementation of active learning methodologies, the initially predicted mean performance of PSCFM in the first round was 353.82 mV (Fig. 2h), highlighting the crucial role of active learning in identifying such promising materials. Further validation of our active learning strategy involved incorporating precisely encoded valence state distributions of PSCFM into the training set for a third predictive cycle. See Supplementary Figs. 10 and 11 for the third-round training results.The mean predictive error (MPE), defined as the discrepancy between the predicted average and the experimental values, demonstrated significant improvements across all three rounds of analysis for PSCF. MPE for PSCF decreased from an initial value of 37.91 mV in the first-round to 13.82 mV in the second round, ultimately reaching an impressively low 3.40 mV by the third round (Fig. 2h and Supplementary Fig. 12). For the PSCFM, the initial MPE of 39.07 mV was reduced to 9.91 mV in the third round, accompanied by a concurrent decrease in standard deviation by 3.38 mV (Fig. 2h). These findings suggest that despite the inherent complexity of hexanary systems, the application of active learning strategies facilitates a degree of convergence in predictive values, leading to enhanced predictive accuracy.Characterizations of predicted materialsThe quantitively Rietveld refinement of the XRD patterns demonstrates that both PSCF and PSCFM primarily crystallize in a cubic phase with a Pm-3m space group (Fig. 3a). The scanning electron microscopy (SEM) images reveal the similar macroscopical morphology between PSCF and PSCFM (Supplementary Fig. 13). The transmission electron microscopy (TEM) image confirms the average particle size of ~100 nm. The atomic-scale high-angle annular dark field (HAADF)-scanning transmission electron microscopy (STEM) and elemental maps (Fig. 3b) confirm the uniform dispersion of all elements without observable phase segregation. The Pr and Mn atoms are located at the positions of Sr and Co/Fe, respectively, indicating that Pr and Mn occupy the A and B sites of PSCFM.Fig. 3: Experimental validation and performance of predicted perovskite electrocatalysts.a Rietveld refinement of the XRD patterns for PSCF and PSCFM. b Representative TEM image, HAADF-STEM image and atomic-scale elemental mapping for Pr, Sr, Co, Fe, and Mn in PSCFM. c LSV curves of various electrocatalysts in 1 M KOH electrolyte. The potentials are iR corrected. The measured R for IrO2, PSCF and PSCFM was 5.98 ± 0.07, 6.0 ± 0.04 and 6.0 ± 0.06 Ω, respectively. The curves without iR-correction are shown in Supplementary Fig. 42. d Electrochemical double-layer capacitance (Cdl) plot. e Tafel slope plots. The potentials are iR corrected. The measured R for IrO2, PSCF and PSCFM was 5.98 ± 0.07, 6.0 ± 0.04 and 6.0 ± 0.06 Ω, respectively. f Charge transfer resistance (Rct) vs. applied voltage without iR-correction. g Galvanostatic test of PSCF and PSCFM in a three-electrode configuration at 20 mA cm−2 without iR-correction. h Galvanostatic test of PSCF and PSCFM in a two-electrode configuration at 10 mA cm−2 without iR-correction. 20% Pt/C was used as the cathodic electrode. i LSV curve for the electrolyzer in 6 M KOH solution without iR-correction. j Stability test of the electrolyzer at current densities of 30 mA cm−2 and 50 mA cm−2 without iR-correction.As shown in Fig. 3c, the LSV curves clearly demonstrate that PSCFM and PSCF requires overpotential of only 315 mV and 327 mV, respectively, to achieve a current density of 10 mA cm–2, outperforming commercial IrO2 (375 mV). To compare the intrinsic activity of various electrocatalysts, the electrochemical double-layer capacitance (Cdl) and electrochemical active surface area (ECSA) were both measured and calculated (Fig. 3d, Supplementary Fig. 14 and Supplementary Table 7). The specific activity (defined as current density normalized on ECSA) of all catalysts is then calculated (Supplementary Fig. 15), which follows the order of PSCFM > PSCF > IrO2 at a representative potential of 1.6 V. However, the ECSA values of all electrocatalysts are similar, suggesting that the significant difference in OER performance arises from the distinct reactivity of individual catalytic site. Consistent with this observation, the turnover frequency (TOF) curves also demonstrate the superior activity of PSCFM over PSCF and IrO2 (Supplementary Fig. 16). Figure 3e demonstrates that PSCFM exhibits the smallest Tafel slope of 54.5 mV dec−1, followed by PSCF (57.1 mV dec−1), and commercial IrO2 (75.4 mV dec−1), indicating that the predicted electrocatalysts achieve favorable kinetics and accelerated electron transfer for OER.Furthermore, in situ electrochemical impedance spectroscopy (EIS) was conducted at different potentials to elucidate the potential dependent charge-transfer kinetics during the OER (Fig. 3f, Supplementary Fig. 17 and Supplementary Table 8). The equivalent electric circuit consisted of electrolyte resistance (Rs) in series with two electrochemical resistors Rct (larger diameter of the low-frequency region) and R1 (smaller diameter of the high-frequency region). The adsorption behavior of the reactants (OH-) on the catalyst surface was described by Rct and CPEct. Evidently, the Rct with the adsorbed OH- intermediate species during OER predominately governs the variations in total charge transfer resistance. The PSCFM with a lower Rct at all potentials exhibits faster kinetics in the adsorption of OH- during OER. This is further corroborated by the Bode plot (Supplementary Fig. 18). The PSCFM delivers the highest frequency of 9.8 Hz (compared to IrO2 at 4.8 Hz and PSCF at 8.6 Hz), confirming its fastest kinetics. Finally, the durability of the samples was evaluated by conducting galvanostatic tests in both three and two electrode modes.The results reveal remarkable stability of PSCFM in both three-electrode and two-electrode electrolyzer configurations. In a three-electrode setup, the overpotential of PSCF and PSCFM exhibits only a ~3 mV fluctuation at a current density of 20 mA cm−2 over a 20 h test (Fig. 3g). Furthermore, a two-electrode electrolyzer employing 20 wt% Pt/C supported carbon cloth as the cathode and PSCFM supported carbon cloth as the anode demonstrates stable electrolysis at 10 mA cm−2 for ~50 h (Fig. 3h). Notably, the voltage increases with PSCFM (1.3%) is significantly lower compared to that with PSCF (2.3%), highlighting the superior durability of PSCFM in practical applications. The Faraday efficiency of PSCFM and PSCF anode catalysts was determined by measuring the concentration of gaseous products using gas chromatography based on an efficient four-electron reaction process. As shown in Supplementary Fig. 19 and Supplementary Table 10, the high Faraday efficiency over 96% could be achieved for all measured points, suggesting the good OER selectivity of both electrocatalysts. The durability of PSCFM was also evaluated in an alkaline water electrolyzer (membrane electrode assembly (MEA) mode) (Fig. 3i, j). Clearly, the electrolyzer equipped with a PSCFM anode and a Pt/C cathode exhibited only slight voltage vibration during continuous galvanostatic measurement at 30 mA cm−2 and 50 mA cm−2 for at least 80 h, implying its promising stability for practical applications.Dissection of structure and electronic configurationTo elucidate the intrinsic factors underlying their exceptional performance, the electronic configurations of both electrocatalysts were analyzed using XPS and X-ray absorption spectroscopy (XAS). The XPS analysis revealed (Supplementary Figs. 20 and 21) an estimated chemical valence of Co is 2.46 and 2.49 for PSCFM and PSCF, respectively. This near-identical chemical valence is confirmed by the Co L-edge XAS (Supplementary Fig. 22), which include reference materials of CoO (Co2+) and Co3O4 (Co2+/Co3+) with distinct Co valences. The overlapping Co L3-edge peak positions of PSCF and PSCFM further indicate their similar Co valence states. Consistently, the deconvolution of XPS data indicates that the chemical valence of Fe is 2.38 in PSCF and 2.37 in PSCFM following the incorporation of Mn (valence of 3.39), also conforming with the results of Fe L3-edge XAS data.Figure 4a compares the O 1s XPS spectra of different samples to distinguish the different surface oxygen species. Deconvolution reveals four well-fitted peaks: lattice oxygen at 528.1 eV (P1), O- at 529.5 eV (P2), OH-/CO32- at 531.5 eV (P3), and adsorbed water (H2O) at 533.1 eV (P4). Notably, PSCFM exhibited a higher percentage of P2 and P3 (79.6%) compared to PSCF (73.6%), suggesting PSCFM has a higher content of oxygen vacancy-related surface absorbed oxygen species31,32,33. Vacant oxygen sites facilitate nucleophilic attack of OH− and promote O-O bonding. Previous studies have demonstrated that oxygen vacancies in transition metal oxides induce the formation of new electronic states through hybridization of O 2p and metal 3d orbitals within the bandgap. These states directly contribute to the enhanced adsorption of intermediates on oxygen vacancies and the improved electronic conductivity34. In addition, the calculated bandgap for PSCF and PSCFM is 0.61 and 0.41 eV, respectively, consistent with the resistivity measurements (981 kΩ for PSCF and 387 kΩ for PSCFM at 25 oC). To corroborate the hypothesis of enhanced reactant adsorption, methanol was used as a probe to assess the adsorption capacity of OER intermediates. As OH− is an electrophilic OER intermediate, it readily reacts with nucleophilic methanol. Consequently, the increase in current density between the methanol oxidation reaction (MOR) and OER polarization curves correlates with the surface coverage of OH−. Prior to analysis, the Cdl values for both PSCF and PSCFM catalysts were determined in MOR (Supplementary Fig. 23). The Cdl for PSCF (2.15 mF cm−2) and PSCFM (2.66 mF cm−2) in MOR are similar to those achieved in OER. This indicates that the influence of ECSA on the current increase in MOR is negligible. As shown in Supplementary Fig. 24 and Fig. 4b, the significantly higher MOR current density of PSCFM (2.5 times that of PSCF) clearly demonstrates a stronger affinity for OH− and thus higher OH− coverage on the PSCFM surface. Furthermore, to investigate the absorption of reactants on the PSCF and PSCFM during OER, Laviron analysis was conducted for both materials. As shown in Supplementary Fig. 25, the steady-state redox currents associated with OH− transfer show a linear correlation with the square root of potential scan rates in the cyclic voltammetry (CV, 1 to 35 mV s−1) curves. Notably, PSCFM shows a larger redox constant (Ks = 0.17 s–1) compared to PSCF (Ks = 0.16 s–1), suggesting a stronger binding strength between *OH intermediates and the surface35,36. These results agree with the in situ EIS analysis (Fig. 3f), which suggest enhanced OH− absorption on the catalyst37.Fig. 4: Mechanistic insights into OER for the optimized electrocatalysts.a Deconvolution of O 1s XPS spectra for PSCF and PSCFM electrodes. The inset figure shows the relative percentage of each fitted peak. b LSV curves of PSCF and PSCFM in 1.0 M KOH with and without methanol (0.602 mol L−1) without iR-correction. The inset figure compares the integrated area of the current increase region. c Comparison of oxygen diffusion coefficients for different electrodes. d Current densities of various electrocatalysts at 1.5 V vs RHE under different pH conditions. e Polarization curves of different electrocatalysts in 1 M KOH and 1 M TMAOH electrolytes. The potentials are iR corrected and the measured R for PSCF and PSCFM was 6.0 ± 0.04 and 6.0 ± 0.06 Ω in 1 M KOH, respectively. The potentials are iR corrected and the measured R for PSCF and PSCFM was 3.94 ± 0.16 and 4.01 ± 0.14 Ω in 1 M TMAOH, respectively. f DEMS signals for 16O18O (I34) and 18O18O (I36) from the reaction products of 18O-labeled electrocatalysts in 1 M KOH with H216O.To further corroborate the high oxygen vacancy concentration in our materials, electrochemical oxygen intercalation in PSCF and PSCFM was examined using CV experiments conducted in an Ar saturated 6 M KOH solution. The observed redox peaks arise from the insertion and extraction of oxygen ions into and from the oxygen-vacant sites. The PSCFM exhibits a larger current density in the intercalation regime, indicating its abundance of sites for oxygen intercalation38. Additionally, the oxygen ion diffusion coefficients (Do) of various catalysts were determined using chronoamperometry (Supplementary Fig. 26c, d). Subsequently, we used a bounded three-dimensional (3D) diffusion model, based on Brunauer–Emmett–Teller (BET) surface area (Supplementary Fig. 27), to estimate the Do of the materials. As shown in Fig. 4c, the Do of commercial IrO2 is estimated to be 1.34 × 10−12 cm2 s−1. PSCF and PSCFM exhibit an order of magnitude higher diffusion coefficient Do of 3.15 × 10−11 cm2 s−1 and 3.95 × 10−11 cm2 s−1, respectively, highlighting their fast oxygen exchange capability, as predicted for the electrocatalysts.Hybrid reaction mechanismPreliminary characterizations have collectively confirmed the high concentration of oxygen vacancies in PSCFM and PSCF. These oxygen vacancies could further facilitate the kinetically favorable well-known LOM pathway to bypass the overpotential cap of 370 mV through the adsorbate evolution mechanism (AEM). In the LOM pathway, the deprotonation of hydroxyl groups has become non-concerted and decoupled from subsequent electron transfer39. To investigate the feasibility of the LOM pathway, we evaluated the electrocatalysts in a series of KOH electrolytes with varying pH values of 12.5–14 (Supplementary Fig. 28). The pH dependence of OER activity on the reversible hydrogen electrode (RHE) scale indicates the presence of non-concerted proton–electron transfer steps during the OER40. It is notable that the increased current density of PSCFM and PSCF at 1.5 V (vs RHE) significantly exceeds that of IrO2 (Fig. 4d), revealing that PSCFM and PSCF exhibit remarkable pH-dependent OER activity and pronounced lattice-oxygen involvement. Moreover, the slopes (ρ) of the OER activity plots on the RHE scale provide insights into reaction orders. The slopes of PSCFM (0.63) and PSCF (0.51) are considerably larger than that of IrO2 (0.33), further confirming the favorable LOM pathway for PSCFM and PSCF during the OER. Furthermore, we compared the OER activities of PSCF and PSCFM electrodes in 1 M KOH and TMAOH solutions. Peroxo-like (O22−) negative species are generally recognized as key intermediates in the LOM pathway, which can be captured by tetramethylammonium cation (TMA+), leading to retarded OER kinetics for electrocatalysts via the LOM pathway41. As depicted in Fig. 4e, the OER activity of PSCFM and PSCF in TMAOH-containing electrolyte is significantly diminished, with overpotential increases of 37 mV and 29 mV, respectively, at a current density of 5 mA cm−2. This reduction in activity is attributed to the inhibition of the LOM pathway due to the strong binding of TMA+ to peroxo-like (O22−) negative species, which are key intermediates in the LOM mechanism. Moreover, we performed 18O isotope labeling differential electrochemical mass spectrometry (DEMS) to provide direct evidence of lattice oxygen participation during the OER (Fig. 4f). The intense peak corresponding to 16O16O (m/z = 32) observed for both PSCF and PSCFM (Supplementary Fig. 29) indicates the presence of oxygen evolution via the AEM, involving the sequential formation of *OH, *O, and OOH intermediates. As shown in Supplementary Fig. 30, in situ attenuated total reflection Fourier transform infrared (ATR-FTIR) spectra of both PSCF and PSCFM catalysts exhibit an absorption band at approximately 1230 cm−1, which is characteristic of surface-adsorbed superoxide (*OOH) during the OER42. This finding further supports the AEM pathway for both catalysts43. Nevertheless, pronounced periodical signals of 16O18O (m/z = 34) were detected in both PSCFM and PSCF during the DEMS experiment (Fig. 4f), indicating that the oxygen atoms in metal-oxygen bonds can also be activated to form O-O bond with neighboring OH or lattice oxygen to release gaseous O244. The calculated contents of 18O16O (m/z = 34) for PSCF and PSCFM were around 0.60% and 0.65%, respectively, both higher than the natural isotopic abundance of 18O ( ~0.2%) in the electrolyte45. Notably, the intensity of the 18O18O (m/z = 36) signal for both materials was extremely low, confirming that the released oxygen does not originate from adjacent oxygen atoms in the metal-oxygen bonds. Therefore, the hybrid mechanism of AEM and LOM is confirmed for both electrocatalysts.To gain further insights into the physical nature of the predicted electrocatalysts for the OER, the oxygen K-edge XAS spectra in total electron yield (TEY) mode were measured for PSCF and PSCFM (Fig. 5a). The spectra collected in TEY mode are surface sensitive (~couple nanometers) due to the limited penetration depth of electrons. The pre-edge peaks below ~530 eV correspond to the oxygen hole states at the conduction band minimum (CBM) induced by the high valent metal32. Peaks A and B reflect the degree of hybridization between the oxygen 2p state and the transition metal 3d state46, while peak C represents the interaction between the oxygen 2p state and the Sr 4d state, and peak D corresponds to the mixed state of the transition metal 4sp orbitals. The normalized intensity and energy position of peaks A and B can be used to characterize the covalent degree of the metal-oxygen bonding, which is a crucial factor influencing oxygen adsorption and redox processes. Clearly, the PSCFM exhibits a pre-edge peak of O K-edge at lower energy compared to PSCF, reducing the energy difference between the redox potentials of OH/O2 and CBM, thereby facilitating electron transfer associated with OER47. Moreover, the higher A + B peak intensity of PSCFM compared to PSCF clearly demonstrates the enhanced metal 3d-O 2p hybridization. These experimental findings are supported by theoretical simulation which analyzed the density of state for PSCF and PSCFM to investigate the band gap and rational regulation of transition metal 3d and O 2p orbitals. The overlap of metal 3d and O 2p orbital is further quantified and evaluated by calculating the metal-oxygen covalency, defined as the difference in band center between the metal d-band orbital and oxygen p-band orbitals. As further shown in Supplementary Figs. 31, 32, the metal 3d and O 2p band centers are located at −1.381 eV and −2.871 eV vs. the Fermi level in PSCF. However, their locations shift to −1.318 eV and −2.602 eV after the incorporation of Mn, indicating the increased covalency of metal-O bonds in PSCFM compared to PSCF, thus lowering the energy penalty required for lattice oxygen oxidation.Fig. 5: Impact of Mn doping on perovskite oxides for OER.a O K-edge XAS analysis of PSCF and PSCFM. b Free energy diagrams for OER via the AEM and LOM pathways for PSCF and PSCFM. c HRTEM image and HAADF-STEM EDX elementary mapping of PSCFM after stability testing. d Comparison of Co content in the electrolyte after stability testing, measured by ICP-MS. e Oxidation states of PSCF and PSCFM based on Bader charge calculations (electron transfer differences). Blue, red and purple spheres represent Co, O and Mn element, respectively. f Pathway and free energy for Vo refilling by absorbed *OH on PSCF and PSCFM. Brown, blue, red, pink, green, purple and yellow spheres represent Fe, Co, O, H, Sr, Mn and Pr element, respectively.We next explore the energetic pathway of alkaline OER on both PSCF and PSCFM to rationalize the correlation between high performance and engaged LOM. The evolution of all absorption intermediates via AEM and LOM are presented in Supplementary Figs. 33–36. As shown in Supplementary Fig. 37, the absorption energy of OH- on Co and Fe cationic sites in PSCF is calculated to be −1.836 eV and −0.471 eV, respectively, indicating that Co sites are the preferable absorption sites. Similarly, Co is also the most energetic favorable absorption site for PSCFM (−2.391 eV on Co, −1.093 eV on Fe and −1.583 eV on Mn). Specifically, in the traditional AEM pathway, the potential determining step (PDS) is the deprotonation of *OOH to form *OO (Intermediate state 3, IS3), which results in a calculated overpotential of 0.71 V on PSCF. We then investigated the energy variation based on LOM. The black curve illustrates the reaction paths for LOM with the release of 34O2 (denoted as LOM-34O2). In comparison, in the LOM-34O2 pathway, the PDS is the absorption of OH on Ov (IS3) after O2 release, giving a calculated overpotential of 0.46 V. This DFT calculation strongly suggests that oxygen evolution favors LOM over traditional AEM. After partially substituting Fe with Mn, the calculation of PSCFM further illustrates that the rate determining step (RDS). (IS3) via AEM has a lower calculated overpotential of 0.63 eV. While for LOM, the energy barrier of RDS (IS3) also decreases by 0.12 eV to 0.34 eV. This result is consistent with the experimentally confirmed conclusion of facilitated *OH absorption in PSCFM (Fig. 4b). Our theoretical calculation results confirm that the partial substitution of Co with Mn simultaneously reduces the kinetic barrier of AEM and LOM.Anti-degradation via Mn-O-Co motifThe PSCFM not only exhibited enhanced electrochemical activity but also demonstrated superior resistance to catalyst decay compared to PSCF, as shown in Fig. 3. To elucidate the origin of this improved stability, the morphology, structure, electronic state, and dissolution rate of the post-OER (after 10 h stability test in two electrode configuration) electrodes were comprehensively characterized to gain insights into the dynamic material evolution during OER. While XRD and SEM data revealed that the overall crystal structures and morphologies of PSCF and PSCFM remained intact after the OER stability test (Supplementary Fig. 38), the high-resolution transmission electron microscopy (HRTEM) image of PSCFM after OER measurement showed an amorphous surface region with a depth of ~2 nm, adjacent to the bulk with a highly ordered atomic arrangement (Fig. 5c). Atomic scale scanning transmission electron microscopy energy dispersive X-ray mapping further confirmed the B site-rich/A site-deficient nature of the delocalized surface shell. As previously demonstrated, surface amorphization resulting from A-site leaching and B-site redeposition occurs in perovskites with an O 2p-band center closer to EF48, a characteristic of LOM31. Conversely, perovskites with an O 2p band positioned far from the EF may experience amorphization due to B-site leaching at high potentials. In our study, time-dependent inductively coupled plasma mass spectrometry (ICP-MS) measurements for both samples (Fig. 5d) revealed orders of magnitude higher dissolution rate of Sr than Co in both materials, confirming that A-site leaching is responsible for the reconstruction. Regardless of the underlying mechanism driving the reconstruction, suppressing the dissolution of the crucial B-site element is critical for achieving satisfactory long-term operation.The ICP-MS measurement highlights the higher loss of Co in PSCF (7.59 ppb) compared to PSCFM (4.01 ppb), implying that the formation of Mn-O-Co conjugate is critical for the enhanced stability. To elucidate the mechanism behind its stability, the electron density distribution was investigated. As shown in Fig. 5e, the Bader charges of Co and Mn are positive, indicating their roles as electron donors. The higher electron density on the oxygen bridge Obridge (from 1.03− to 1.08−) is also evident. Notably, the substation of Co with Mn to form Co-Obridge-Mn leads to electron redistribution and electron colocalization around Co, accompanied by a decrease in the Co Bader charge from 0.7+ to 0.63+. This finding aligns with the XPS results. The reduced Bader charge reveals an orderly decrease in the degree of ionization, which can significantly enhance resistance to cation leaching49.In addition to the beneficial confinement of Co, the dynamic reversibility of Olattice/VO is another critical factor influencing surface stability. To complete a reversible LOM cycle, the VO generated by lattice oxygen migration to form *OOH on M (step 2 in LOM, M is the cation center) should be replenished by further absorption of *OH (step 4 in LOM). However, many electrocatalytic platforms fail to exhibit satisfactory stability due to rapid surface oxygen exchange kinetics50, resulting in continuous depletion of lattice oxygen. The O 1s XPS data reveal that the percentage of (P2 + P3) peak in PSCF increased by 15.1%, more than twice that of PSCFM (Supplementary Figs. 39 and 40), confirming that lattice oxygen in PSCF is less reversible. These results are further supported by the O K-edge XAS analysis of post-OER electrocatalysts (Supplementary Fig. 41), where a completely diminished O-projected density of unoccupied states was observed in PSCF. Consistent with these experimental findings, the DFT calculations (Fig. 5f) also confirm that the absorption of *OH is thermodynamically more favorable on VO in the Co-VO-Mn motif (−2.63 eV) than in the Co-VO-Co counterpart (−2.46 eV), facilitating the refilling of Olattice and generation of BO6. Additionally, the Co element exhibits a significant valence increase from 2.49 to 2.59 in PSCF, likely due to substantial surface dissolution and reconstruction (Supplementary Table 9). In contrast, the valence of Co in PSCFM only shows pretty subtle variation (0.01), indicating a more dynamically stable site.
