Breathing mode in Nd-CoO_x for active and stable proton exchange membrane water electrolysis

Domain: physics
Published: 2025-12-09
Editorial outcome: major_revision

Abstract
Proton-exchange membrane water electrolysis in acidic solutions holds great promise for advancing the green-hydrogen economy but limited by using precious-metal catalysts. Here, we develop a low-cost CoOx-based catalyst with oxygen vacancies and Nd-insertion (Nd-CoOx). This catalyst achieves a low overpotential of 317 mV at 10 mA cm−2 for acidic oxygen evolution reaction and remains stable over 800 h. The oxygen vacancies in Nd-CoOx enhance its catalytic activity, while Nd enables the long-term stability through a flexible “breathing mode” during oxygen evolution reaction, as revealed by in-situ methods such as X-ray absorption spectroscopy and Raman spectroscopy. The presence of Nd also improves the catalytic activity with the oxide path mechanism. This favorable strategy can be extended to other lanthanides. When used as the anode, Nd-CoOx delivers good performance in water electrolysis to achieve 200 mA cm−2 at a low cell voltage of 1.69 V with low degradation over 100 h, and can reach 1 and 2 A cm−2 at 1.93 V and 2.12 V, respectively.

Introduction
Water splitting through electrolysis offers a promising route to produce green hydrogen. Various methods have been applied for water splitting, while proton-exchange membrane water electrolysis (PEMWE) in acidic solutions stands out. It provides good hydrogen purity, high current density, and efficient energy conversion1,2. However, the slow oxygen evolution reaction (OER) kinetics remains a major challenge. This reaction includes four proton-coupled electron transfer steps and needs catalysts with both high activity and stability in acidic solutions3,4. Up to now, only rare and expensive Ir- or Ru-based catalysts meet these requirements1,5. Unfortunately, their high cost and limited reserve result in significant barriers to large-scale implementation. Developing low-cost, noble-metal-free catalysts with high efficiency and long-term stability for acidic OER is therefore an urgent priority.

A large amount of 3d transition metal oxides have been developed as efficient OER catalysts6–10. Their multiple chemical states allow them to enhance catalytic activity across a wide pH range. However, most 3d transition metal oxides suffer from severe structural degradation in acidic environments. Recently, Co-based catalysts have shown significant progress for acidic OER11–15. They offer both high activity and improved stability after modification. Theoretical calculations suggest that spinel-type Co3O4 could achieve OER activity comparable to that of Ir- and Ru-based oxides16. Unfortunately, Co3O4 faces challenges in acidic conditions. It undergoes severe dissolution during operation17. Its catalytic performance is further limited by poor conductivity and a lack of sufficient active sites2. To address these problems, various strategies have been developed to modify Co-based catalysts. These include defect engineering, hetero-structure formation, and elemental doping. For instance, introducing oxygen vacancies in Co3O4 was used to improve catalytic activity, while careful control of vacancy content could enhance the stability for acidic OER2. Huang et al. demonstrated that incorporating CeO2 into Co3O4 would modify the local bonding environment, improving stability under acidic conditions11. By incorporating Mn into the spinel lattice of Co3O4, the CoMnOx material was prepared and showed a highly extended lifetime in acid environment18. Recently, La and Mn co-doping in Co3O4 achieved a small overpotential of 353 mV at 10 mA cm−2. This system maintained low degradation for over 360 h in an H-cell, with La stabilizing the surface and Mn improving bulk conductivity13. Beyond La and Mn, W doping also showed notable success12,14. Especially, by introducing W into Co oxide to form a CoWO4 catalyst with vacancies, water-hydroxide networks would fill these vacancies, enabling stable operation for 175 h at 10 mA cm−2 in an H-cell and for 600 h at 1 A cm−2 in PEMWE14. These advancements highlight the potential of modified Co-based materials for acidic OER.

In this work, we reveal the presence of a “breathing mode” in the atomic structure of Nd-modified Co3O4 with oxygen vacancies (Nd-CoOx). This feature enables stable and efficient OER in acidic conditions. The catalyst exhibits a low overpotential of 317 mV at 10 mA cm−2 in an H-cell and remains stable for at least 800 h. The oxygen vacancies in Nd-CoOx enhance its catalytic activity. At the same time, the “breathing mode” around Nd provides structural flexibility, which allows the atomic structure to adapt during OER and prevents structural failure under external potentials. We observed these dynamic structural changes by using in-situ methods such as X-ray absorption spectroscopy (XAS) and Raman spectroscopy. The insertion of Nd also improves the acidic OER activity by creating the oxide path mechanism (OPM). When used as the anode, Nd-CoOx enables PEMWE to obtain a current density of 200 mA cm−2 at a small cell voltage of 1.69 V, with minimal degradation over 100 h. The system also delivers 1 A cm−2 at 1.93 V and 2 A cm−2 at 2.12 V. These performances surpass those of the IrO2 anode, which requires 2.05 V and 2.27 V to reach the same current densities, respectively. These results emphasize the potential of Nd-CoOx as an efficient and cost-effective catalyst for acidic OER in PEMWE systems.

Results
Morphology and structure characterization
The Nd-CoOx catalyst was prepared using a two-step synthesis method combining microwave-assisted heating (MAH) and solution combustion synthesis (SCS) (Fig. 1a). In the first step, carbon cloth (CC) was immersed in a solution containing Co2+ and Nd3+ ions, with microwave heating applied to assist the process. In the second step, the wet CC substrate, loaded with Co2+ and Nd3+ ions, was treated multiple times using the SCS method. This treatment created a rapid oxidation environment, resulting in the formation of the Nd-CoOx catalyst on the CC substrate. The oxidation process produced oxidized Co species, while the rapid treatment resulted in the generation of oxygen and cobalt vacancies. Additionally, the incorporation of Nd ions likely resulted in Nd-insertion within the oxidized Co species. More preparation information can be observed in the Methods section. Scanning electron microscopy (SEM) images (Supplementary Fig. 1) reveal the morphology of Nd-CoOx and control samples (CoOx and NdOx). All samples exhibit porous sheet-like structures on the surface of the CC substrate (ribbons). Synchrotron radiation-based X-ray diffraction (SR-XRD) patterns (Supplementary Fig. 2) show that the primary crystalline phase in both Nd-CoOx and CoOx is Co3O4 (JCPDS No. 42-1467). No distinct peaks for Nd-based materials are observed, suggesting that Nd is likely inserted into the Co3O4 structure. The atomic ratio of Co to Nd in Nd-CoOx is determined to be approximately 15:1 using inductively coupled plasma optical emission spectrometry (ICP-OES, Supplementary Table 1). Transmission electron microscopy (TEM) images of Nd-CoOx (Fig. 1b) confirm its porous sheet morphology. High-resolution TEM (HRTEM) images (Fig. 1c) show the crystal structure for Co3O4, with lattice spacing values of 0.245 nm and 0.467 nm for the (311) and (111) planes of Co3O4, respectively2. A similar Co3O4 structure is observed in the CoOx control sample (Supplementary Fig. 3). Dark-field energy-dispersive X-ray spectroscopy (EDX) elemental mapping images (Fig. 1d) show the homogeneous distributions of Co, Nd, and O elements in Nd-CoOx.

The atomic structure of Nd-CoOx was carefully probed by using aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). In HAADF-STEM, atoms with higher atomic numbers typically produce stronger signal intensities1. As exhibited in Fig. 1e, bright spots corresponding to Nd atoms, which have a higher atomic number than Co, are clearly visible. In contrast, the lighter O atoms are not detectable under the current imaging conditions. These observations strongly suggest that Nd atoms are atomically dispersed within the Co3O4 lattice in Nd-CoOx. Atomic distances around the Nd atoms are analyzed, specifically along Line 1 and Line 2 in Fig. 1e. The Nd-Co distance in Nd-CoOx is measured to be approximately 0.30 nm, while the neighboring Co-Co distance is slightly smaller at about 0.27 nm (shown in Fig. 1f). This difference is likely due to the insertion of larger Nd atoms into the Co3O4 lattice. As illustrated in Fig. 1g, the substitution of Co atoms with larger Nd atoms compresses the local atomic structure, reducing the Co-Co distance in the lattice. Such local structural modifications may play a critical role in maintaining structural stability during the OER3,4.

X-ray photoelectron spectroscopy (XPS) has been used to probe the electronic structures of the catalysts (Supplementary Fig. 4). In the Co 2p spectra of commercial Co3O4 (Com. Co3O4), two distinct peaks are observed at 795.5 eV and 780.5 eV (Supplementary Fig. 4a). These peak positions align well with previously reported values2,5. In comparison, the Co 2p peaks for both CoOx and Nd-CoOx shift to lower binding energy. This shift indicates a lower chemical state of Co in these samples, likely due to the presence of oxygen vacancies (VO) created during the fast oxidation process. The Nd 3d XPS spectra (Supplementary Fig. 4b) reveal a lower chemical state of Nd in Nd-CoOx compared to NdOx. This change is attributed to the influence of CoOx. In the O 1s spectra (Supplementary Fig. 5a), features at 531.3 eV for both CoOx and Nd-CoOx are associated with VO in the metal oxides19,20. The presence of VO introduces excess electrons, which can occupy the metal d-orbitals, leading to a lower oxidation state21. Further evidence of VO is provided by electron paramagnetic resonance (EPR) measurements (Supplementary Fig. 5b). CoOx and Nd-CoOx exhibit much stronger EPR signals at g = 2.003 compared to Co3O4, suggesting the presence of VO. These VO are expected to enhance OER kinetics, thereby improving catalytic activity2,22.

Synchrotron radiation-based XAS has been used to examine the local electronic structure of Nd-CoOx. Fig. 2a displays the normalized Co K-edge X-ray Absorption Near Edge Structure (XANES) spectra for CoOx, Nd-CoOx, CoO, and Co3O4. Both CoOx and Nd-CoOx show different XANES spectra with a comparison to that of standard Co3O4. The white-line peak positions for CoOx and Nd-CoOx are lower than that of Co3O4 but higher than that of CoO. This suggests a reduced Co oxidation state in the Co3O4 structure, likely caused by VO. As displayed in the inset of Fig. 2a, the average valence states of Co in CoOx and Nd-CoOx are calculated from the edge positions, which are approximately 2.2 and 2.3 in CoOx and Nd-CoOx, respectively23. The XANES spectra of CoOx and Nd-CoOx also exhibit a pronounced pre-edge peak A at approximately 7709 eV (quadrupolar transition from 1s to 3d), which might be attributed to the lowered symmetry with oxygen vacancies and defects24,25.

The Fourier-transform (FT) curves of extended X-ray absorption fine structure (EXAFS) spectra are displayed in Fig. 2b. Strong FT peaks at 1.49 Å and 1.63 Å (the actual fitted bond length values are 1.93 and 2.12 Å in Supplementary Table 2) correspond to the Co-O bonds in Co3O4 and CoO, respectively, as expected from their different bond lengths, consistent with previous literature26. Compared to the Co-O FT peak in Co3O4 at 1.49 Å, the CoOx sample shows a longer FT bond length of 1.52 Å (fitted value of 1.95 Å) with reduced peak intensity. This shift is attributed to the presence of VO, which results in fewer Co–O bonds and a lower chemical state for Co. Interestingly, the Co-O FT peak for Nd-CoOx is shorter, appearing at 1.45 Å (fitted value of 1.91 Å). This shift is attributed to Nd-modified electronic and atomic structures. As identified in Fig. 1, when the larger Nd atom replaces a Co atom, the local atomic structure becomes compressed. This compression reduces the Co-Co distance and shortens the surrounding Co-O bond, as observed in Fig. 2b. The detailed R-space (Fourier-transform curves of EXAFS spectra) fitting curves and bond lengths are presented in Supplementary Fig. 6 and Supplementary Table 2. The fitted Co-O bond length for CoOx is 1.95 Å, which is longer than Co3O4 at 1.93 Å. However, in Nd-CoOx, the Co-O bond length is significantly reduced to 1.91 Å. These results align well with the Fourier-transform curves of EXAFS data. The progression of local structural changes—from typical Co3O4 to CoOx with VO (longer Co-O bonds), and finally to Nd-CoOx with both vacancies and Nd-insertion (shorter Co-O bonds due to compression)—is illustrated in Fig. 2f. Wavelet transform (WT) plots of Nd-CoOx, CoOx, and Co3O4 are also shown in Fig. 2c. The WT plots provide two-dimensional information for both k-space and R-space data, facilitating the discrimination of backscattering atoms27. The heavier atom (with a higher atomic number) typically exhibits a better ability to scatter photoelectrons, leading to their oscillations occurring at higher frequencies (high k values)28. In Fig. 2c, Co3O4 shows the Co-O peak at a k value of ~8.0 Å−129, while for Nd-CoOx, this peak shifts to a higher k value (~8.3 Å−1), indicating the Nd-insertion.

Figure 2d presents the Nd L3-edge XANES spectra for Nd-CoOx, NdOx, and Nd2O3. Nd-CoOx shows the lowest white-line intensity, indicating a relatively lower valence state for Nd. The corresponding Fourier-transform curves of EXAFS curves are shown in Fig. 2e. For NdOx, the Nd-O FT peak appears at 2.01 Å, similar to that of standard Nd2O3. This indicates an oxidized Nd structure in NdOx. In contrast, the Nd-O FT peak for Nd-CoOx sample occurs at 1.94 Å, standing for a shorter Nd-O bond. This reduction in bond length is attributed to the insertion of Nd into the smaller Co3O4 lattice (primarily on the surface Co vacancy sites). The limited space at the Co sites in the Co3O4 lattice forces the Nd-O bond to shorten. The longer Nd-O bonds also exert compressive forces on the surrounding Co-O bonds, as illustrated in Fig. 2f. This local electronic and structural modulation may play an important role in improving the OER performance.

Evaluation of OER performance
The electrocatalytic OER activities of Nd-CoOx and reference samples were evaluated in a standard three-electrode cell using 0.1 M HClO4 electrolyte. Commercial Co3O4 and IrO2 were used as reference catalysts. The Nd concentration in Nd-CoOx was optimized, as exhibited in Supplementary Fig. 7. As illustrated in Fig. 3a, NdOx is almost inactive for OER. Commercial Co3O4 displays an overpotential of 509 mV to obtain a current density of 10 mA cm−2. Introducing oxygen vacancies (VO) in CoOx significantly enhances its performance, reducing the overpotential to 418 mV at 10 mA cm−2. This improvement highlights the critical role of VO in boosting OER activity. However, both catalysts show lower activity compared to the benchmark IrO2 catalyst, which requires 335 mV at 10 mA cm−2. Remarkably, the introduction of Nd into CoOx to form Nd-CoOx further improves the OER performance. Nd-CoOx exhibits an overpotential of just 317 mV at 10 mA cm−2, even lower than that of commercial IrO2 (335 mV). The LSV curves without iR correction and the corresponding performance errors are summarized in Supplementary Fig. 8. Since pure NdOx shows negligible OER activity, the good performance of Nd-CoOx is primarily assigned to the synergistic effect of Nd and CoOx.

Tafel slopes of the catalysts are shown in Supplementary Fig. 9. Nd-CoOx exhibits a smaller Tafel slope of 82 mV dec−1 compared to CoOx (89 mV dec−1), IrO2 (97 mV dec−1), and Co3O4 (96 mV dec−1). This indicates more favorable OER kinetics for the Nd-CoOx30. Electrochemical impedance spectroscopy (EIS) curves (see Supplementary Fig. 10 and Supplementary Table 3) reveal that Nd-CoOx has the smallest charge transfer resistance (Rct) of 8.9 Ω, indicating quick charge transfer properties. Double-layer capacitance (Cdl) measurements are applied to estimate the electrochemically active surface area (ECSA) of the catalysts. Nd-CoOx shows a significantly higher Cdl value when compared to CoOx and NdOx (Supplementary Fig. 11), indicating the presence of more active sites due to Nd-incorporation. The combination of a smaller Tafel slope, lower charge transfer resistance, and higher active site density confirms that Nd-CoOx is a competitive catalyst for the acidic OER.

Except for the high activity, the Nd-CoOx catalyst demonstrates robust stability for acidic OER. As displayed in Fig. 3b, Nd-CoOx maintains its activity at the current density of 10 mA cm−2 for at least 800 h. The overpotential increases by only 76 mV after 800 h, corresponding to a degradation rate of just 95 μV h−1. This result strongly confirms the good stability of Nd-CoOx under acidic conditions1,12. In comparison, commercial Co3O4 and CoOx (without Nd) exhibit much shorter stabilities, lasting only 30 h—more than one order of magnitude shorter than Nd-CoOx. Furthermore, Nd-CoOx shows minimal degradation during cycling. After 5000 cyclic voltammetry (CV) cycles, the overpotential increases by just 15 mV at 10 mA cm−2 (Fig. 3c). The stability of Nd-CoOx also extends to large current densities. At 100 and 200 mA cm−2, the catalyst operates stably for over 100 h without significant performance loss (Supplementary Fig. 12). In contrast, CoOx without Nd shows rapid decay at 100 mA cm−2, failing within 20 h (Supplementary Fig. 13b). The beneficial effect of Nd in CoOx for acidic OER is also observed with other lanthanides, such as La and Pr. As shown in Supplementary Fig. 13a, Pr-CoOx and La-CoOx exhibit similar OER activities. Both catalysts maintain stability at 100 mA cm−2 (Supplementary Fig. 13b) and operate for over 200 h at 10 mA cm−2 (Supplementary Fig. 14). The results highlight the versatility of lanthanide incorporation in enhancing OER performance and stability.

To assess the practical application of Nd-CoOx for electrochemical water electrolysis, a proton-exchange membrane electrolyzer was used (Supplementary Fig. 15a). The setup used Nd-CoOx as the anode (for OER) and commercial Pt/C as the cathode (for HER). A Nafion 117 membrane was employed as the proton-exchange membrane. The current-voltage polarization curves (with iR correction) are shown in Fig. 3d. The Nd-CoOx ║Pt/C cell demonstrates higher catalytic activity when compared to the reference IrO2 ║Pt/C cell. Notably, the Nd-CoOx ║Pt/C electrolyzer needs only 1.93 V to obtain a large current density of 1 A cm−2 at 80 °C, and 2.12 V for 2 A cm−2. Both values surpass those of the IrO2 ║Pt/C electrolyzer, which requires 2.05 V at 1 A cm−2 and 2.27 V at 2 A cm−2. The current-voltage polarization curves (no iR correction) are also presented in Supplementary Fig. 15b. The stability of the PEM electrolyzer with Nd-CoOx was measured under constant current conditions (Fig. 3e). At the high current density of 200 mA cm−2, the electrolyzer exhibited a stable operating voltage of approximately 1.69 V for over 100 h. Nd-CoOx exhibits high efficiency and robust stability, making it competitive among noble-metal-free catalysts for OER in acidic environment, as summarized in Supplementary Table 4. These results highlight the potential of Nd-CoOx as a good anode catalyst for practical water electrolysis systems.

In-situ investigations
It is well established that VO can enhance the catalytic activity of Co3O4 for acidic OER, as observed with the CoOx sample2,11,13. However, the specific role of Nd in CoOx, which significantly improves both OER activity and stability, remains unclear. This is particularly intriguing because a high concentration of vacancies often leads to structural failure during operation, resulting in poor catalyst durability2. However, the Nd-CoOx catalyst in this study demonstrates good OER stability, maintaining performance for at least 800 h. This robust stability likely arises from the critical role of Nd in stabilizing the CoOx crystal structure. To investigate the working mechanism of Nd-CoOx for stable and active acidic OER, in-situ XAS experiments have been conducted at both the Co K-edge and Nd L-edge during the OER process (Supplementary Fig. 16a). Figure 4a, b show the in-situ Co K-edge XANES and Fourier-transform curves of EXAFS spectra of CoOx, respectively. The XANES spectra for CoOx remain largely unchanged during OER. However, the corresponding Fourier-transform curves of EXAFS data reveal changes in bonding under applied potentials (Fig. 4b). Specifically, the Co-O bond length in CoOx gradually shortens as the applied potential increases from the open-circuit potential (OCP) to 1.65 V vs. RHE. This shortening indicates a decrease in the Co-O distance and suggests a higher Co oxidation state under the applied potential. Similar behavior has also been observed for Co3O4 in the literature11,13. Interestingly, as shown in the magnified view in Fig. 4b, the shortened Co-O bond does not fully recover to its original length after OER (during the OCP again measurement). This indicates some irreversible structural changes that likely contribute to the poor structural stability of CoOx during acidic OER, as previously reported in the literature11.

The in-situ Co K-edge XANES and Fourier-transform curves of EXAFS spectra of Nd-CoOx have been presented in Fig. 4d, e, respectively. The XANES spectra reveal a positive energy shift with increasing applied potential. This shift indicates a higher chemical state of Co under applied potential, which enhances OER activity14,30. Notably, the energy shift fully recovers after the OER process, as shown in Fig. 4d. Further insights can be drawn from the Fourier-transform curves of EXAFS data in Fig. 4e. The Co-O bond length in Nd-CoOx changes progressively with increasing potential. Interestingly, the Co-O bond shows an increase in length, opposite to the behavior observed for CoOx (see the magnified region from 1.45 to 1.51 Å). Typically, as the chemical state of Co increases with higher potential, the Co-O bond shortens, as seen in CoOx. However, the presence of Nd alters this behavior by modifying the local atomic structure to maintain structural stability. As discussed in Figs. 1 and 2, Nd-insertion significantly compresses the Co-O bond to a shorter initial length than that in normal Co3O4. During applied potentials, the Nd-O bond also undergoes changes, influencing the surrounding Co-O bonds. As shown in Supplementary Fig. 16d, the initial Nd-O FT peak at 1.94 Å shifts to a shorter FT length of 1.89 Å under applied potential. This reduced N-O distance implies a higher chemical state of Nd. The shortened Nd-O bond consequently exerts a stretching effect on the surrounding Co-O bonds, resulting in the observed elongation of the Co-O bond in Fig. 4e. Remarkably, both the elongated Co-O bond and shortened Nd-O bond fully recover to their initial states after the OER process (Fig. 4e and Supplementary Fig. 16d). This recovery highlights the good ability of Nd-CoOx to maintain structural stability during OER, presenting a significant advantage for long-term operation.

To clearly illustrate the bond length changes during OER, structural models of Nd-CoOx with and without applied potential are presented in Fig. 4g. These models highlight the “breathing mode” behavior, where Co-O and Nd-O bonds undergo squeezing and stretching processes to balance atomic-level structural stress during OER. The bond length changes in Nd-CoOx and CoOx are compared in Fig. 4h. For CoOx, only the Co-O bond changes, decreasing in length with increasing potential. Importantly, this bond does not fully recover after OER, indicating irreversible structural changes. In contrast, for Nd-CoOx, the Nd-O bond plays an important role. Changes in the Nd-O bond significantly influence the Co-O bond length, which increases along with applied potential but fully recovers after the reaction. This difference likely explains the disparity in OER stability between Nd-CoOx and CoOx. In CoOx, gradual structural changes during acidic OER result in structural stress and eventual collapse under long-term operation. In Nd-CoOx, the Nd-insertion introduces a controllable and reversible structure change, allowing it to maintain good stability. R-space fitting curves and results for Nd-CoOx during OER, presented in Supplementary Fig. 17 and Supplementary Table 5, further confirm these bond length changes. This dynamic structural adaptability underscores the robust stability of Nd-CoOx in challenging acidic environments.

In-situ Raman spectroscopy was performed to further investigate the “breathing mode” described above (Supplementary Fig. 16b). The Raman spectra for both CoOx and Nd-CoOx, shown in Fig. 4c, f, exhibit characteristic peaks corresponding to the typical Eg, F2g, and A1g features of Co3O4, as reported in the literature30,31. With increasing potential from the open-circuit potential (OCP) to 1.65 V vs. RHE, the main A1g peak shifts significantly. For CoOx, the A1g peak shifts from 694.1 cm−1 to 694.8 cm−1, indicating lattice contraction due to shortened Co-O bonds under applied potential11,30. However, after the OER process, this blue shift does not recover to its initial value (Fig. 4c). This irreversible shift suggests continuous structural stress in the harsh acidic environment, leading to structural failure and limited stability. This behavior aligns with observations reported in previous studies11. For Nd-CoOx, a similar blue shift of the A1g peak is observed, from 692.6 cm−1 to 694.7 cm−1, corresponding to lattice contraction. However, unlike CoOx, the peak fully recovers once the applied potential is removed, as shown in Fig. 4f. This recovery is attributed to the controllable and reversible structural changes enabled by Nd-insertion, which contributes to the catalyst’s long-term stability. The A1g peak shifts with applied potential for both CoOx and Nd-CoOx are compared in Fig. 4h. In CoOx, the peak shows irreversible changes, while in Nd-CoOx, it exhibits flexible and fully recoverable shifts across a relatively larger range. The initial lower A1g value for Nd-CoOx (692.6 cm−1) is likely due to lattice expansion caused by the incorporation of larger Nd atoms into the structure. The in-situ Raman results are consistent with the in-situ XAS findings, further confirming the “breathing mode” in Nd-CoOx. This dynamic mode allows for structural flexibility and stability under harsh OER conditions. Atomic-level structural changes during long-term operation for both Nd-CoOx and CoOx are illustrated in Supplementary Fig. 18a, b, respectively. These results highlight the critical role of Nd-insertion in enhancing structural adaptability and stability.

The XAS results for Nd-CoOx, recorded before and after 800 h operation at 10 mA cm−2, are presented in Supplementary Fig. 19. Measurements at both the Co K-edge and Nd L3-edge reveal that Co and Nd exhibit more oxidized states after the long-term stability test. Despite this oxidation, the catalyst maintains its overall electronic structure, consistent with its robust stability. Additional structural analyses, including XRD, SEM, and TEM results for Nd-CoOx after 800 h of operation, are shown in Supplementary Fig. 20. These analyses reveal that the morphology and crystalline structure of Nd-CoOx remain largely unchanged compared to its initial state before OER. This strongly supports the critical role of the flexible “breathing mode” enabled by Nd-insertion in maintaining structural integrity and stability during extended OER operation.

DFT calculations
Density functional theory (DFT) calculations have been performed to explore the OER working mechanism of Nd-CoOx. According to the aberration-corrected HAADF-STEM result in Fig. 1e and XRD patterns in Supplementary Fig. 2, Co3O4 (311) is the dominant facet, which has thus been used for the calculations. The CoOx catalyst was mimicked by a Co3O4 (311) surface (standard spinel structure), which incorporated oxygen vacancy sites. The computational model of Nd-CoOx was constructed by replacing surface Co atoms with Nd atoms. The configuration of Nd-CoOx is displayed in Supplementary Fig. 21, and the optimized atomic structures around Co and Nd are shown in Fig. 5a. The Co-O bond length in CoOx is approximately 1.915 Å, consistent with values reported in the literature2,32,33. In Nd-CoOx, the incorporation of Nd shortens the Co-O bond to 1.878 Å and extends the Nd-O bond to approximately 2.366 Å. The shortened Co-O bond results from structural distortions induced by Nd, which has a larger atomic radius. These changes in Co-O bond length align closely with the XAS results in Fig. 2. We further perform the calculation to simulate the status with applied potential based on the constant electrode potential model (with structural relaxation and self-consistent field calculations). When an external potential correction of 1.55 V (vs. vacuum energy level) is simulated using the constant electrode potential model, the Co-O bond in Nd-CoOx stretches slightly to 1.885 Å, while the Nd-O bond shortens to 2.325 Å (Fig. 5a). These computational findings strongly support the presence of a flexible “breathing mode” in Nd-CoOx, as revealed by in-situ XAS and Raman spectroscopy.

Differential electrochemical mass spectrometry (DEMS) was used to experimentally identify the OER reaction pathway (Supplementary Fig. 22a). The detailed analysis procedures are illustrated in the Supplementary Information. As shown in Fig. 5b, the Nd-CoOx catalyst, after five cycles of cyclic voltammetry in an acidic solution containing H218O, produces three gaseous products: 32O2, 34O2, and 36O2. According to the literature34,35. The adsorbate evolution mechanism (AEM) typically generates only 34O2 and 36O2, without producing 32O2. The detection of 32O2 in this study indicates a reaction pathway different from AEM, including direct coupling between surface-adsorbed 16O atoms on Co sites and lattice 16O, or 16O atoms on adjacent metal (such as Nd) sites. This behavior is characteristic of the lattice-oxygen-mediated mechanism (LOM) or the oxide path mechanism (OPM)1,36. Further evidence comes from tetramethylammonium (TMA+) experiments, shown in Supplementary Fig. 22b. The results show minimal changes in the reaction when TMA+ is added, effectively ruling out the LOM pathway37,38. Considering all experimental results, the evidence suggests that the OER process on the Nd-CoOx catalyst follows the OPM pathway. This mechanism has been illustrated in Fig. 5d.

DFT calculations have been further used to probe the reaction mechanism of OER on Nd-CoOx. Gibbs free energy (ΔG) diagrams of the AEM and OPM pathways are presented in Fig. 5c and Supplementary Data 1. In the AEM pathway, the reaction proceeds via a sequence of intermediates: OH*, O*, OOH*, and finally O2 formation on the active sites. The potential-determining step (PDS) in this pathway should be the conversion of OH* to O*, which requires a significant free energy uphill of 2.166 eV. In contrast, the OPM pathway follows a different sequence: OH* → OH*-OH* → O*-OH* → O2. The PDS in this case is the transition from O*-OH* to O2 (see Fig. 5c), which involves a substantially lower ΔG of 1.879 eV. These findings suggest that, thermodynamically, the OPM pathway is much more favorable than the AEM pathway. The impact of applied bias voltages on the OER free energy profiles was also studied using constant electrode potential models. At a higher bias voltage of U = 1.55 V, all steps in the OPM pathway become thermodynamically downhill, while the AEM pathway still requires an energy uphill of 0.301 eV. By comparing the energy profiles of the two pathways, it is clear that the sluggish kinetics of the AEM pathway arise from the slow formation process of O* intermediate with high-energy. Meanwhile, the OPM pathway prevents such high-energy intermediates entirely, resulting in more efficient kinetics. For comparison, the Gibbs free energy diagrams for CoOx through AEM and OPM pathways are also provided in Fig. 5c and Supplementary data 1. Schematic illustrations of the adsorbed intermediates on optimized CoOx structure through the AEM and OPM pathways can be found in Supplementary Fig. S23 and S24, respectively. The AEM pathway is more favorable for CoOx according to the calculations. However, the PDS energies for CoOx following the AEM pathway are 2.205 eV (0.00 V) and 0.266 eV (1.55 V), which are much higher than those for Nd-CoOx following the OPM pathway (1.879 eV (0.00 V) and −0.013 eV (1.55 V)). These results demonstrate that Nd incorporation modifies the fundamental OER mechanism from AEM to OPM and then significantly enhances the catalytic performance by lowering the reaction energy barriers. This conclusion is well-aligned with the enhanced catalytic activity of Nd-CoOx, as demonstrated in Fig. 3a.

The charge transfer analysis can be observed in Supplementary Fig. 25, in which O* adsorption on CoOx results in a large electron transfer (0.71 e-) from the catalyst, with an adsorption free energy of 1.366 eV (far from the ideal value of 2.46 eV). In contrast, O* adsorption on Nd-CoOx exhibits a weaker interaction, with only 0.53 e- transferred, leading to a much higher adsorption free energy of 2.754 eV (close to the ideal value of 2.46 eV). The electronegativity difference between Nd and Co induces the surface charge redistribution, thereby affecting the adsorption energy of intermediates and triggering the OPM pathway. A comparison between Nd-CoOx (with oxygen vacancies) and Nd-Co3O4 (without oxygen vacancies) is also shown in Supplementary Fig. 25c and 25d, demonstrating that oxygen vacancies further reduce the adsorption of the O*-OH* intermediate (reduced electron transfer and longer Co-O bonds). The calculated energy values on CoOx and Nd-CoOx are provided in Supplementary Table 6.

The working mechanism of Nd-CoOx is illustrated in Fig. 5e. For the CoOx catalyst, OER activity is enhanced by the presence of vacancies. However, under acidic conditions and high applied potentials, the active Co sites become further oxidized. This oxidation shortens the Co-O bond length, leading to continuous lattice contraction. Over time, unevenly distributed structural stress, especially around the vacancies, causes structural failure (Fig. 5e). As a result, CoOx displays limited OER stability. In contrast, the insertion of Nd into CoOx introduces a flexible “breathing mode” in the atomic structure. This flexibility helps resist structural failure under applied potential, ensuring sustained durability during acidic OER. Additionally, the presence of Nd near Co enhances the OER activity by enabling the reaction to proceed via the OPM pathway. This results in a catalyst that is both stable and highly active, making it suitable for PEMWE. The beneficial role of Nd in enhancing the performance of CoOx offers a universal strategy that could be extended to other lanthanides, such as La or Pr, as discussed in Fig. 3f. This approach highlights the potential of lanthanide incorporation for improving catalytic performance in acidic OER.

Methods
Chemicals and reagents
Commercial Co3O4 (99.9%), Co(NO3)2·6H2O (99%), Nd(NO3)3·6H2O (99.9%), La(NO3)3·6H2O (99.9%) and Pr(NO3)3·6H2O (99.9%) have been obtained from Shanghai Aladdin Industrial Co., Ltd. Ethylene glycol (EG, 99%), Ethanol (EA), Isopropyl alcohol (IPA, 99.5%) and IrO2 (99.9%) have been obtained from Shanghai Macklin Biochemical Industrial Co., Ltd. HClO4 (70-72%) has been obtained from Yonghua Chemical CO., LTD. Carbon cloth (CC) has been obtained from Suzhou Keshenghe Metal Materials Co., Ltd. Nafion (5 wt%) has been obtained from Sigma-Aldrich (Shanghai) Trading Co., Ltd. Platinum carbon loaded on carbon paper (20 wt% Pt/C) and cation exchange membrane (Nafion 117) have been obtained from Suzhou Sinero Technology Co., Ltd. Deionized water (resistivity ≥18.2 MΩ) was produced using an ultrapure water purification system. All reagents were of analytical grade and used directly without additional purification.

Preparation of CoOx and M-CoOx porous nanosheets on carbon cloth
The CoOx catalysts were prepared through microwave heating and the solution combustion method. Carbon cloth (CC) (2 cm × 4 cm) was carefully cleaned under ultrasonication treatment to remove the surface oxides. Then 3.6 mM Co(NO3)2·6H2O and 5 mL Ethylene glycol (EG) were mixed to form a homogeneous solution. The cleaned CC was put in the above solution for 20 s with microwave heating. Subsequently, the CC was taken out and ignited directly with an alcohol lamp, and the final catalyst was obtained after repeating the ignition several times. M-CoOx was synthesized by using the same steps, except for the addition of 0.4 mM M(NO3)3·xH2O (M = La, Pr, Nd). The optimal loading of Nd-CoOx catalysts was around 7.5 mg cm−2 on CC. Nd-CoOx electrocatalyst prepared on CC was used as a working electrode in a three-electrode system. Nd-CoOx electrocatalyst powder was scraped from the CC and used as an anode catalyst in PEMWE.

Preparation of IrO2 electrodes
7.5 mg IrO2, 20 μL Nafion (5 wt%), 250 μL ethanol, and 230 μL deionized water were mixed and then ultrasonicated for 30 min to form a homogeneous ink. 50 μL ink was dropped on carbon cloth and then dried at 60 °C in vacuum for 12 h to form the IrO2 electrode (0.25 cm−2). It was around 3 mg cm−2 IrO2 on carbon cloth.

Proton-exchange membrane (PEM) cell test
Nd-CoOx (or IrO2) has been used as the anode with Pt/C on carbon paper (Pt/C-CP) as the cathode in a PEM cell. 5 mg Nd-CoOx was added into a mixture of isopropanol (500 μL), deionized water (450 μL) and Nafion solution (50 μL, 5 wt%). After sonication in a water bath for 60 min, a homogeneous anode ink was obtained. To construct the membrane electrode assembly (MEA), the Nafion 117 membrane was sprayed with anodic ink under vacuum adsorption to prevent swelling, with the anodic loading about 5 mg cm−2. Subsequently, the Pt/C-CP, 0.4 mm Ti plate and the Nafion 117 membrane (loaded with anodic ink) were hot pressed at 363 K for 30 s, obtaining the membrane electrode assembly (MEA). The PEM cell was measured in pure water for 60 min at 80 °C (effective area around 1.0 cm−2).

Materials characterization
SEM (ZEISS G500), HRTEM (TALOS 200X), ICP-OES (Avio 200), XPS (Thermo Fischer ESCALAB 250X), and XRD (Empyrean powder diffractometer) have been employed for structural characterizations. XAS measurements were performed at the Shanghai Synchrotron Radiation Facility (https://cstr.cn/31124.02.SSRF.BL11B) and National Synchrotron Radiation Laboratory (https://cstr.cn/31131.02.HLS.XMCD.a and https://cstr.cn/31131.02.HLS.XMCD.b). The XAS data were analyzed by using the ATHENA and ARTEMIS software39. The XANES spectra were firstly normalized by subtracting pre-edge and post-edge background, and then treated by calibrating the energy shift based on E0 of the reference samples. The EXAFS results were analyzed by using the Fourier transform of k-space data in a window (Hanning window with dk = 1) of 2.0−11.0 Å−1 for Co K-edge, and k-weighting was set to three without phase shift. The selected k ranges (2.0−11.0 Å−1 for Co K-edge) were also used for wavelet transform analysis (Morlet function, kappa Morlet = 15, sigma Morlet = 1). The first shell peaks of the FT spectra were fitted by using shell structural models based on the crystal structures of Co3O4.

Electrochemical measurements
A standard three-electrode system (CHI 760E) was used at room temperature (~25 °C). 0.1 M HClO4 solution was used in all tests with Pt wire, Ag/AgCl, and the synthesized samples (0.5 × 0.5 cm) as counter, reference, and working electrodes, respectively. Backward scan (from positive to negative potentials, 5 mV s−1) was utilized to avoid the oxidative peaks. A scan rate of 100 mV s−1 was applied during the long-term cyclic voltammetry (CV) measurements. The potential was converted to the value versus the reversible hydrogen electrode (RHE) according to Eq. (1)

ERHE = EAg/AgCl + E0Ag/AgCl + 0.059 × pH (1)

where E0Ag/AgCl is the difference value between standard hydrogen electrode and Ag/AgCl electrode. The pH value of the electrolyte was measured multiple times, and the average value obtained was approximately 1.08 ± 0.02. E0Ag/AgCl was determined by referencing to a Pt/C working electrode in a H2-saturated solution, and the corrected potential was about 0.2 V. The electrochemical impedance spectroscopy measurement (EIS) measurements were conducted at a current density of 10 mA cm−2, with an additional alternating voltage of 5 mV applied over the frequency range of 0.1 Hz to 100 kHz.

CV test was performed within a small potential window (0.86–0.96 V vs Ag/AgCl) at scan rates from 20 to 100 mV s−1 (20 mV s⁻¹ intervals) to determine the double-layer capacitance (Cdl), from which the electrochemically active surface area was estimated. A 90% iR compensation was applied to the polarization curves obtained at high current densities. Chronopotentiometry (CP) measurements were performed to assess the long-term stability under various current densities.

Preparation of 0.1 M HClO4 solution: Measuring approximately 8.6 mL of concentrated HClO4 (70%–72%) and slowly adding it, under stirring, to deionized water (500 mL) in a beaker. Following cooling, the solution was quantitatively transferred to a 1000 mL amber volumetric flask, diluted to the mark with deionized water, and homogenized. Finally, the electrolyte was stored in a dark, cool environment at ambient temperature.

DFT calculations
All the DFT calculations were conducted by using Vienna ab initio Simulation Package (VASP 5.4.4)40,41. The electron-ion interactions were described in terms of the projector augmented-wave (PAW) potentials42. The exchange and correlation interactions between electrons were described by the revised Perdew-Burke-Ernzerhof (PBE) within the generalized gradient approximation (GGA-RPBE)43. The Co-Nd system was constructed as a model for theoretical calculations. The plane wave cutoff for these systems was 500 eV. The criterion of convergence of energy was set to 1 × 10−4 eV. The internal coordinates of each system were fully optimized until the residual Hellmann-Feynman forces were less than 0.02 eV/Å per atom. The lattice parameters in the direction perpendicular to the surface were set as 30 Å, which could thus avoid interactions between periodic slabs. The Brillouin zones were sampled by 1×2×1 k-point meshes generated according to the Monkhorst-Pack scheme. The Hubbard U (DFT+U) corrections for 3d and 4f species were made. Based on the previous works, the Ueff of Co was set as 3, and the Ueff value of Nd (4f-transition metal) was set as 544,45. The reaction Gibbs free energies (ΔG) could be obtained using Eq. (2):

ΔG = ΔE + ΔEZPE − TΔS (2)

In which E was the energy that could be directly obtained from the DFT calculations. EZPE was zero-point energy. T was 298.15 K in this work, and S was the entropy. Constant potential calculations were employed to unravel the properties of electrochemical processes as a function of the electrode potential. Therefore, the reaction free energies for Nd-CoOx were calculated under constant electrode potentials. The electrode potential (U) referenced to that of SHE was given by Eq. (3)46:

U = −μ(e−) − ΦSHE / e (3)

In which -μ(e−) and ΦSHE represented the chemical potential of electrons and work function of the SHE, respectively. We used 4.4 eV for ΦSHE47. The information energy (Ef) was calculated by Eq. (4):

Ef = Etotal − Esubstrate − ECo (4)

Where Etotal, Esubstrate, and ECo were the energies of the whole catalyst, the system without Co atom, and an isolated Co atom in vacuum, respectively. The dissolution potentials of cobalt (Udiss) was obtained by Eq. (5):

Udiss = U0diss − Ef / Ne (5)

Where U0diss was the standard dissolution potential of Co atom, and N was the transferred electron number during the dissolution48.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this manuscript, the authors developed a low-cost Co3O4-based catalyst with oxygen vacancies and Nd-insertion, which demonstrates a low overpotential of 317 mV at 10 mA cm-2 for the acidic oxygen evolution reaction and maintains stability for at least 800 hours. The authors propose that the Nd doping induces a flexible \"breathing mode\" mechanism, significantly enhancing long-term stability. While the study is scientifically rigorous, there are still some points that require clarification.\nThe specific comments are as follows:\n1、 The authors demonstrate through EPR testing that, compared to Co3O4, CoOx has more oxygen vacancies, and Nb-CoOₓ has the most oxygen vacancies. However, based on the structural diagram in Fig. 2f, it is evident that Nd occupies the oxygen vacancies in CoOₓ and enters the CoOx lattice. According to this structure, shouldn’t the oxygen vacancies in Nd-CoOx be lower than those in CoOx?\n2、 To demonstrate the impact of Nd on the catalytic activity enhancement, it is recommended that the authors compare the catalytic activity of Nd-Co3O4.\n3、 The authors referenced the work published in Science 384, 1373-1380 (2024), which achieved 600 hours of stability at a current density of 1 A cm-2. The authors also mentioned that current densities of 1 A cm-2 and 2 A cm-2 can be achieved at 1.93 V and 2.12 V, respectively. It is recommended that the authors provide stability data for the catalyst at 1 A cm-2 or 2 A cm-2.\n4、 The authors suggest through in situ XAS that at certain potentials, the Co-O bond length increases, and after stopping the reaction, the Co-O bond length undergoes reversible recovery due to the presence of Nd-O. However, during the prolonged stability testing, the Co-O bond length continuously increases under the certain potential. How does the catalyst maintain efficient stability under these conditions?\n5、 In the abstract, the authors mention that the enhanced performance and stability is due to the combined effect of Nd and oxygen vacancies. However, throughout the manuscript, the authors use in situ characterization and DFT calculations to show that Nd-O interactions are the primary factor enhancing catalyst stability. What role do the vacancies play in the stability?", "reviewer_2": "In this manuscript, Feng et al. investigated the catalytic activity and reaction mechanism of Nd-CoOx for OER. The authors did systematic experiments and DFT calculations. However, the theoretical part should be supplemented, and many points are not clear to be published in this journal.\n(1) Authors did not provide details about the simulation models. For example, (1) what is the crystal structure of Co3O4? (2) Why was the (110) facet used for this DFT, even though the (311) facet was observed at HRTEM? XRD also shows that (311) was the dominant facet? (3) How many layers were fixed or relaxed? (4) How many oxygen vacancies were formed to describe CoOx? (5) How to define the most stable site of Nd at the surface of CoOx or bulk CoOx?\n(2) All of the considered configurations are required to check the reliability of simulation results. (2-1) How to define the possible adsorption sites for reaction intermediates\n(2-2) adsorption energy corresponding to each adsorption site\n(2-1) DFT-calculated values for ∆E, ∆ZPE, and ∆S\n(3) For oxide materials, DFT+U is more appropriate for describing their electronic structure. Why did the authors not consider the DFT+U?\n(4) In my knowledge, the external potential is the correction term to correct Gibbs free energy, not the option for structure relaxation. However, the authors addressed that “When an external potential correction 340 of 1.55 V (vs. vacuum energy level) is applied using the constant electrode potential model, the Co-O bond in Nd-CoOx stretches slightly to 1.881 Å, while the Nd-O bond shortens to 2.258 Å” I cannot understand.\n(5) In order to explore the effect of Nd doping on the catalytic activity of CoOx for OER, the Gibbs free energy diagram should be compared with that of pure CoOx.\n(6) The merit of DFT is that it provides a fundamental understanding of material properties. In this sense, it might be better to add electronic structure or charge transfer analysis to explain the role of Nd or oxygen vacancy in the catalytic activity of CoOx for OER.", "reviewer_3": "In \" Breathing mode in Nd-CoOx for active and stable proton exchange membrane water electrolysis\", Feng et al. have developed a low-cost catalyst based on Co3O4 with oxygen vacancies and Nd-insertion (Nd-CoOx) as a stable and active material for acidic oxygen evolution reaction (OER). The paper is compelling and may lead to advancements in the field of electrochemistry and the authors are clearly well-versed in multi-technique characterization protocols. However, the manuscript presents many issues, and the results are not properly justified by the experimental results. I therefore believe that the manuscript in its current state is not suitable for publication in Nature Communications.\nIn particular, I would like to highlight the following points:\n- When looking at Figure 2a the sentence “The spectra of both CoOx and Nd-CoOx closely resemble that of standard Co3O4, indicating similar chemical states” seems to be wrong. The spectrum of the reference Co3O4 is very different from the others and therefore the local structure around the Co atom is supposed to be different. This is also proved by the existence of a pre-edge peak in the XANES spectra of CoOx and Nd-CoOx that is not present in the reference compound. This peak is due to the existence of quadrupolar transitions and is indicative of a distortion in the coordination sphere of the photoabsorber. The appearance of this peak and its meaning should be discussed in the paper.\n- At line 144 the authors discuss the position of the FT first peak, and they state that “they correspond to the Co-O bonds in Co3O4 and CoO, respectively”. This is not correct as the FT shown are not phase-shift corrected and therefore the position of the FT peaks falls at lower distances as compared to the bond lengths. This is also clear from Table S2 where the Co-O distances are much longer. Moreover, the position of the FT’s strongly depends on how they have been calculated, and the results of the fits should be considered rather than the position of the experimental FT spectra.\n- At line 152 the authors state “The detailed EXAFS fitting curves and bond lengths are presented in Supplementary Fig. 6 and Supplementary Table 2.” Regrettably, Figure S6 shows the FT and not the EXAFS spectra. Moreover, no details are provided on the fitting procedures and the errors on the distances, DW factors and coordination numbers should be reported to allow one to compare the results.\n- More details on the Wavelet transform (WT) plots shown in Fig. 2c should be provided.\n- At line 168 the sentences “Nd-CoOx shows the lowest white-line intensity, indicating a relatively lower valence state for Nd.” Is not clear. What do they mean with “lower valence state”? If it is the oxidation state this relates to the position of the rising edge and not to the intensity of the white line. Moreover, Fig. 2e shows the Fourier Transforms and NOT the EXAFS curves.\n- The major flaw of this investigation is the analysis of the XAS data that has been carried out to demonstrate the \"breathing mode\" behavior. Throughout the manuscript the authors mention the EXFAS spectra while no EXAFS data are reported. The differences in the position of the FT first peak are very small and a proper quantitative analysis of the XAS data should be carried out in the k space to really demonstrate the existence of a contraction and expansion of the distances. Showing only the experimental FT’s is not a proper procedure.\n-The lack of fundamental details in the XAFS methodology makes this part unsuitable for publication. There is no description on how the fitting of the experimental data has been carried out: which program has been used? Has the fitting procedure carried out only on the first shell of the FT spectra? Moreover, figures showing the extracted χ(k)k^2 EXAFS signals should be included to really highlight the differences among the samples."}, "author_response": "Response to the Comments\nReviewer #1:\nIn this manuscript, the authors developed a low-cost Co O -based catalyst with oxygen vacancies and Nd-\n3 4\ninsertion, which demonstrates a low overpotential of 317 mV at 10 mA cm-2 for the acidic oxygen evolution\nreaction and maintains stability for at least 800 hours. The authors propose that the Nd doping induces a flexible\n\"breathing mode\" mechanism, significantly enhancing long-term stability. While the study is scientifically\nrigorous, there are still some points that require clarification.\nThe specific comments are as follows:\nResponse: Thank you for the positive and valuable comments to improve our work. According to your\ncomments, we have provided more data and carefully revised the manuscript.\n1. The authors demonstrate through EPR testing that, compared to Co O , CoO has more oxygen vacancies,\n3 4 x\nand Nd-CoO has the most oxygen vacancies. However, based on the structural diagram in Fig. 2f, it is evident\nx\nthat Nd occupies the oxygen vacancies in CoO and enters the CoO lattice. According to this structure,\nx x\nshouldn’t the oxygen vacancies in Nd-CoO be lower than those in CoO ?\nx x\nResponse: Thank you for the valuable comments. As illustrated in Fig. 2f, the CoO sample contains both\nx\noxygen vacancies (denoted as O ) and Co vacancies (denoted as Co ) due to the presence of defects. For the\nv v\nNd-CoO sample, the larger Nd atoms actually occupy the Co vacancy sites instead of the oxygen vacancy sites,\nx\nas evidenced by the presence of Nd-O bond in Fig. 2e instead of Nd-Co bond (if Nd occupies the oxygen\nvacancy site, there will be Nd-Co bond). Thus the Nd-insertion will reduce the Co vacancy content but will not\n1\ndecrease the amount of oxygen vacancies. The EPR signal is a well-known method for the detection of oxygen\nvacancies, providing similar oxygen contents for both Nd-CoO and CoO . We have carefully explained this\nx x\nissue in the revised manuscript (schematic diagram in Fig. 2f).\n2. To demonstrate the impact of Nd on the catalytic activity enhancement, it is recommended that the authors\ncompare the catalytic activity of Nd-Co O .\n3 4\nResponse: Thank you for the valuable comments. According to your suggestion, the catalytic activity of Nd-\nCo O sample with very limited oxygen vacancies has been compared. The CoO sample was further annealed\n3 4 x\nat 450 °C for 5 hours to obtain the pure Co O sample with limited oxygen vacancies (better crystal structure).\n3 4\nSubsequently, neodymium (Nd) was loaded onto pure Co O via the similar solution combustion synthesis,\n3 4\nresulting in the formation of Nd-modified Co O (Nd-Co O ) with limited oxygen vacancies. As shown in Fig.\n3 4 3 4\nR1, the XRD results indicate that the Nd-Co O sample exhibits the Co O phase, in which the sharper peak\n3 4 3 4\nshape stands for better crystal structure with less vacancies. The HRTEM images of Nd-Co O in Fig. R2 display\n3 4\ntypical lattice fringes for Co O , and the elemental mapping confirms that Nd is evenly distributed in the sample.\n3 4\nElectrochemical measurements in Fig. R3 show that Nd-Co O exhibits an OER overpotential of 381 mV at the\n3 4\ncurrent density of 10 mA cm−2, which is much lower than that of pure Co O (452 mV). These results strongly\n3 4\nconfirm the impact of Nd on the catalytic activity enhancement for acidic OER. However, the overpotential of\nNd-Co O (381 mV) is much higher than that of Nd-CoO (317 mV) with both Nd and oxygen vacancies,\n3 4 x\nsuggesting the synergistic effect of Nd and oxygen vacancies to improve the OER activity.\nx 3 4\nFig. R2. (a) TEM, (b) HRTEM, and (c) dark-field elemental mapping images of Nd-Co O : O (green), Co (red)\n3 4\nand Nd (Cyan), respectively.\nFig. R3. Electrochemical OER performances of pure Co O (p-Co O ), Nd-Co O and Nd-CoO .\n3 4 3 4 3 4 x\n3\n3. The authors referenced the work published in Science 384, 1373-1380 (2024), which achieved 600 hours of\nstability at a current density of 1 A cm-2. The authors also mentioned that current densities of 1 A cm-2 and 2 A\ncm-2 can be achieved at 1.93 V and 2.12 V, respectively. It is recommended that the authors provide stability\ndata for the catalyst at 1 A cm−2 or 2 A cm−2.\nResponse: Thank you for the valuable comments. We fully acknowledge the critical technical challenge you\npoint out regarding the stability of non-noble metal catalysts in acidic OER systems under high current densities\n(Science 2024, 384, 1373-1380; Nat. Catal. 2022, 5, 109-118; Energy Environ. Sci. 2024, 17, 4196-4204).\nAccording to your valuable suggestion, we conducted a 10-hour stability test at an industrial-level current\ndensity of 1 A cm−2, as shown in the following Supplementary Fig. 15c. The results demonstrate that the Nd-\nCoO catalyst exhibits a good short-term stability at 1 A cm−2. However, we clearly recognize that achieving a\nx\nlong-term stability under such harsh conditions remains a great challenge. Recently, a breakthrough study\npublished in Science (Science 2024, 384, 1373-1380) has demonstrated the stable operation for 600 hours at 1\nA cm-2, which is indeed a remarkable achievement. However, in comparison, the vast majority of previously\nreported Co-based materials (Science 2023, 380, 609-616; Nat. Synth. 2025, 4, 327-335; Nat.Catal. 2022, 5,\n109-118) still showed low stability under such harsh conditions, indicating that the fundamental challenges of\nmaterial corrosion and dissolution in acidic environments at high current densities had yet to be fully resolved.\nIn our future research, we will focus on exploring interfacial engineering and structural regulation strategies to\nimprove the long-term stability of catalysts under high current densities. We would like to thank you again for\nyour constructive suggestions, which have provided valuable guidance to improve our work.\ncurves (without iR correction) of the PEM cell by using IrO ║Pt/C and Nd-CoO ║Pt/C. (c)\n2 x\nChronopotentiometry curve of Nd-CoO at 1 A cm−2 in the PEMWE.\nx\n5\n4. The authors suggest through in situ XAS that at certain potentials, the Co-O bond length increases, and after\nstopping the reaction, the Co-O bond length undergoes reversible recovery due to the presence of Nd-O.\nHowever, during the prolonged stability testing, the Co-O bond length continuously increases under the certain\npotential. How does the catalyst maintain efficient stability under these conditions?\nResponse: Thank you for the valuable comments. We agree with you that the Co-O bond length in Nd-CoO\nx\nincreases at certain potentials and undergoes reversible recovery due to the presence of Nd-O. The Co-O bond\nlength in Nd-CoO will keep the elongated state during the stability testing. However, the elongated Co-O bond\nx\nlength only increases with the increased potential, which will not continuously increase with the prolonged\nreaction time. The elongated Co-O bond length in Nd-CoO is also in a reasonable range even at a high potential\nx\nof 1.65 V vs. RHE (FT peak position around 1.51 Å in Fig. 4e), which is similar to the normal state of Co-O\nbond length in CoO (FT peak position around 1.52 Å in Fig. 4e). This is also part of the favorable effects of\nx\n\"breathing mode\" with Nd-insertion in Nd-CoO . The limited Co-O bond length elongation will not significantly\nx\nchange the structure during the reaction (for example, keeping 1.51 Å at 1.65 V vs. RHE) and then the catalyst\ncan maintain efficient stability under the working conditions. Furthermore, as shown in Supplementary Fig. 19,\nboth Co-O and Nd-O bond can keep a stable state even after 800 h operation, confirming the excellent structural\nstability. We have clarified this issue in the revised manuscript.\n6\n5. In the abstract, the authors mention that the enhanced performance and stability is due to the combined effect\nof Nd and oxygen vacancies. However, throughout the manuscript, the authors use in situ characterization and\nDFT calculations to show that Nd-O interactions are the primary factor enhancing catalyst stability. What role\ndo the vacancies play in the stability?\nResponse: Thank you for the valuable comments. The excellent catalytic stability should be mainly attributed\nto the insertion of Nd with a flexible \"breathing mode\", while the oxygen vacancies can only enhance its\ncatalytic activity. The presence of Nd also improves the acidic OER activity by enabling the catalyst to follow\nthe oxide path mechanism. The oxygen vacancies have almost no contribution to the stability. We have carefully\nmodified the abstract in the revised manuscript to clarify the roles of Nd and oxygen vacancies: \"The oxygen\nvacancies in Nd-CoO enhance its catalytic activity, while Nd plays a key role in maintaining long-term stability,\nx\nwhich allows the atomic structure to adapt during OER through a flexible \"breathing mode\" \".\nIn this manuscript, Feng et al. investigated the catalytic activity and reaction mechanism of Nd-CoO for OER.\nx\nThe authors did systematic experiments and DFT calculations. However, the theoretical part should be\nsupplemented, and many points are not clear to be published in this journal.\nResponse: Thank you for the positive and valuable comments to improve our work. According to your\ncomments, we have provided more data and carefully revised the manuscript.\n1. Authors did not provide details about the simulation models.\n(1) what is the crystal structure of Co O ?\n3 4\nResponse: Thank you for the valuable comments. According to the data in XRD (Supplementary Fig. 2) and\nHRTEM (Fig. 1c and 1e), the primary crystalline phase in both Nd-CoO and CoO should be Co O (JCPDS\nx x 3 4\nNo. 42-1467). For calculation, the crystal structure of Co O is a standard spinel structure belonging to the cubic\n3 4\ncrystal system with the space group of Fd-3m.\n(2) Why was the (110) facet used for this DFT, even though the (311) facet was observed at HRTEM? XRD also\nshows that (311) was the dominant facet?\nResponse: Thank you for the valuable comments. We have observed the (220) facet in Nd-CoO from the TEM\nx\nimages (Fig. 1c and 1e in the revised manuscript) and the XRD spectrum (Supplementary Fig. 2), thus we have\nused the (110) facet for the DFT calculation. However, we agree with you that the (311) facet is the dominant\nfacet. According to your comments, we have then calculated the system based on the (311) facet in the revised\nmanuscript. As shown in the revised manuscript (see revised Fig. 5), the results calculated based on the new\n(311) model are also similar that previously calculated based on the (110) model, in good agreement with our\n8\nconclusion.\n(3) How many layers were fixed or relaxed?\nResponse: Thank you for the valuable comments. The present calculation model was based on the (311) facet,\nwhich had a terrace-step-kink structure with a large supercell surface area. To balance the accuracy and the\nefficiency, a three-layer atomic model was thus used according to the literatures (ACS Catal. 2024, 14, 16353;\nAdv. Mater. 2025, 37, 2501381). Convergence tests confirmed the low surface energy errors at this thickness.\nOnly the topmost layer was relaxed while the underlying two layers remained fixed, with adsorption model tests\nconfirming negligible effects of fixed layers on key surface states through selective relaxation of sub-surface\natoms.\n(4) How many oxygen vacancies were formed to describe CoO ?\nx\nResponse: Thank you for the valuable comments. For calculation, the Co O (311) surface served as the base\n3 4\nstructure, where a single oxygen vacancy was introduced per 1×1 surface unit cell of the Co O (311) surface.\n3 4\nThis configuration simultaneously ensured the structural integrity (geometry optimization converged at the\nmaximum force on each atom < 0.02 eV/Å without lattice collapse) and maintained the charge neutrality under\nDFT+U formalism (U = 3 eV for Co).\neff\n(5) How to define the most stable site of Nd at the surface of CoO or bulk CoO ?\nx x\nResponse: Thank you for the valuable comments. To determine the most stable Nd doping configuration on the\nCoO (311) surface, we performed a systematic computational screening by substituting Nd at all distinct cobalt\nx\nsites spanning heterogeneous chemical environments (including sites with various coordination numbers). After\nfull structural relaxation using DFT+U (U = 3.0 eV for Co 3d orbitals), we identified the thermodynamically\neff\npreferred Nd incorporation site through the comparative total energy analysis (as shown in Fig. R4).\n3 4\n2. All of the considered configurations are required to check the reliability of simulation results.\n(2-1) How to define the possible adsorption sites for reaction intermediates?\nResponse: Thank you for the valuable comments. We sincerely thank the reviewer for raising this critical point\nregarding the adsorption site verification, which significantly enhances the rigor of our study. To ensure the\nreliability of calculation, we implemented a stringent two-stage protocol during the adsorption configuration\nscreening. Initially, systematic scanning of all possible high-symmetry sites on the Nd-CoO (311) surface was\nx\nperformed using DFT+U calculations with a plane-wave energy cutoff of 500 eV, comprehensively covering\npotential adsorption configurations. Subsequently, full structural optimizations were conducted under rigorous\nconvergence criteria (the maximum force on each atom < 0.02 eV/Å without lattice collapse), identifying the\nmost stable adsorption sites for key intermediates (OH*, O*, OOH*, OH*-OH*, and O*-OH*)\ninvolved in\nads\nR8 and R9). This methodology adhered to the established protocols for simulating adsorbed intermediates on\ncatalyst surfaces.\n(2-2) adsorption energy corresponding to each adsorption site?\nResponse: Thank you for the valuable comments. The adsorption energies corresponding to each adsorption site\nare now provided in the following Fig. R5, R6, R7, R8 and R9.\nFig. R5. Optimized adsorption configurations of OH* on Nd-CoO and their adsorption energies.\nx\nx\nFig. R7. Optimized adsorption configurations of OOH* on Nd-CoO and their adsorption energies.\nx\nx\nFig. R9. Optimized adsorption configurations of O*-OH* on Nd-CoO and their adsorption energies.\nx\n(2-3) DFT-calculated values for ∆E, ∆ZPE, and ∆S?\nResponse: Thank you for the valuable comments. The calculated ∆E, ∆E and T∆S of each intermediate on\nZPE\nCoO and Nd-CoO are now listed in Supplementary Table 6.\nx x\nZPE x x\nΔE/eV (U = 0.00\nSystems Intermediates ΔE/eV (U = 1.55 V) ΔE /eV T∆S/eV\nZPE\nV)\nOH* -0.372 -0.133 0.354 0.088\nO* 0.852 1.354 0.069 0.048\nCoO OH*-OH* 0.052 0.444 0.712 0.177\nx\nO*-OH* 1.408 2.028 0.418 0.146\nOOH* 2.883 2.918 0.446 0.138\nOH* 0.329 0.753 0.336 0.073\nO* 2.661 2.770 0.060 0.067\nNd-CoO OH*-OH* 0.956 1.675 0.702 0.144\nx\nO*-OH* 2.896 3.400 0.416 0.149\nOOH* 3.178 3.383 0.423 0.120\n3. For oxide materials, DFT+U is more appropriate for describing their electronic structure. Why did the authors\nnot consider the DFT+U?\nResponse: Thank you for the valuable comments. We agree with you that the DFT + U effects are essential for\nanalyzing the electronic structure of oxide materials. We have then used DFT + U method in the revised\nmanuscript to describe the electronic structures of CoO and Nd-CoO . Based on the literatures (Adv. Mater.\nx x\n2024, 36, 2310106; Adv. Energy Mater. 2023, 13, 2203244), we assigned U values of 3 for Co and 5 for Nd in\nDFT + U calculations. We have added the detailed information of DFT+U calculations in the revised\nconclusions, as discussed in the revised manuscript.\n4. In my knowledge, the external potential is the correction term to correct Gibbs free energy, not the option for\nstructure relaxation. However, the authors addressed that “When an external potential correction 340 of 1.55 V\n(vs. vacuum energy level) is applied using the constant electrode potential model, the Co-O bond in Nd-CoO\nx\nstretches slightly to 1.881 Å, while the Nd-O bond shortens to 2.258 Å” I cannot understand.\nResponse: Thank you for the valuable comments. We agree with you that the conventional constant-potential\nmethods only need the self-consistent field (SCF) calculations, in which the voltage-induced structural changes\nare negligible. Technically, the constant-potential model should be applied at the geometry relaxation stage (Adv.\nFunct. Mater, 2023, 33, 2208736; J. Am. Chem. Soc, 2024, 146, 32539-32549). However, our experimental\nresults reveal that the bond length changes at applied external potentials are critical, as denoted as a flexible\n\"breathing mode\". To further understand this phenomenon, here we perform the additional calculations by\nconsidering the potential effect. Fortunately, some previous studies (Adv. Funct. Mater, 2023, 33, 2208736; J.\nAm. Chem. Soc, 2024, 146, 32539-32549) also reported that variations in applied potential during\nelectrochemical reactions significantly modulated the structural dynamics of catalysts and the adsorption\nbehavior of intermediates. According to the literatures, we thus performed the theoretical calculations which\ncould account for the regulatory effects of potential on the configuration of catalyst active sites and intermediate\nadsorption behavior. From an electrochemical perspective, the applied external potential not only influences the\nreaction free energies by modulating the system's Fermi level, but also alters the surface charge distribution of\ncatalysts, thereby inducing significant changes in key bond lengths of intermediate states. Our calculations\n15\nfinally reveal that with the effect of the applied potential from 0.00 V to 1.55 V, the Co-O bond length of Nd-\nCoO elongates from 1.878 Å to 1.885 Å, while the Nd-O bond of Nd-CoO contracts from 2.366 Å to 2.325 Å\nx x\n(shown in Fig. 5). Our data compellingly demonstrated the substantial potential-dependent modulation of\nintermediate bond lengths in this specific system. We have clarified this issue in the revised manuscript.\nFig. 5: DFT calculations and the working mechanism. a, Optimized computational models of CoO and Nd-CoO\nx x\nwithout applied potential, along with the model of Nd-CoO with potential correction (1.55 V with reference to the\nx\nvacuum energy level). b, The DEMS signals of 32O , 34O and 36O tested for Nd-CoO in H 18O acidic solution. c,\n2 2 2 x 2\nGibbs free energy diagrams for Nd-CoO through AEM and OPM pathways at 0 V and 1.55 V (with constant\nx\nelectrode potential corrections). d, Illustration of the OPM pathway on Nd-CoO . e, Schematic diagrams of the\nx\nstructural variations of CoO and Nd-CoO before and after OER.\nx x\n16\n5. In order to explore the effect of Nd doping on the catalytic activity of CoO for OER, the Gibbs free energy\nx\ndiagram should be compared with that of pure CoO .\nx\nResponse: Thank you for the valuable comments. We have now provided the Gibbs free energy diagrams for\nthe OER on pure CoO at 0.00 V and 1.55 V in the revised manuscript. The AEM and OPM pathways on pure\nx\nCoO are illustrated in Supplementary Fig. S23 and S24, respectively. Since the calculated OPM pathway on\nx\npure CoO requires very high PDS energies of 3.362 eV (0.00 V) and 1.192 eV (1.55 V), pure CoO should\nx x\nfollow the AEM pathway. The calculated PDS energies for pure CoO following the AEM pathway are 2.205\nx\neV (0.00 V) and 0.266 eV (1.55 V), which are much higher than those for Nd-CoO following the OPM pathway\nx\n(1.879 eV (0.00 V) and -0.013 eV (1.55 V)). These findings demonstrate that Nd incorporation changes the\nfundamental OER mechanism from AEM to OPM and then significantly enhances the catalytic performance by\nlowering the reaction energy barriers. This conclusion is well-aligned with the enhanced catalytic activity of\nNd-CoO in Fig. 3a. We have added the corresponding discussion in the revised manuscript.\nx\nx\nvia AEM. (b) Gibbs free energy diagrams for CoO through AEM pathway at 0.00 V and 1.55 V (with constant\nx\nelectrode potential corrections). Co, O, and H atoms are represented in blue, pink/red, and white, respectively.\nx\nvia OPM. (b) Gibbs free energy diagrams for CoO through OPM pathway at 0.00 V and 1.55 V (with constant\nx\nelectrode potential corrections). Co, O, and H atoms are represented in blue, pink/red, and white, respectively.\n6. The merit of DFT is that it provides a fundamental understanding of material properties. In this sense, it might\n1\nbe better to add electronic structure or charge transfer analysis to explain the role of Nd or oxygen vacancy in\nthe catalytic activity of CoO for OER.\nx\nResponse: Thank you for the valuable comments. According to your comments, we have added the charge\ntransfer analysis to explain the role of Nd in the catalytic activity of Nd-CoO for OER. Additional calculations,\nx\nincluding differential charge densities and Bader charge analysis of O* on CoO and O* on Nd-CoO , have now\nx x\nbeen provided Supplementary Fig. 25. Free energy profiles (Supplementary Fig. 23 and Supplementary Fig. 24)\nreveal that pristine CoO follows the AEM pathway, but suffers from the strong adsorption of oxygen\nx\nintermediates (e.g., O*), limiting the OER performance. For example, O* adsorption on CoO shows a large\nx\nelectron transfer of 0.71 e- from the catalyst and the corresponding adsorption free energy (1.366 eV)\nsignificantly deviates from the ideal value (2.46 eV) (Supplementary Fig. 25a). In comparison, adsorption of\nO* on Nd-CoO exhibits a weaker interaction, with only 0.53 e- transferred leading to a higher adsorption free\nx\nenergy of 2.754 eV, consequently approaching the ideal value of 2.46 eV (Supplementary Fig. 25b). Thus, we\nconsider that the electronegativity difference between Nd and Co (J. Am. Chem. Soc, 2019, 141, 342-351; Adv.\nEnergy Mater, 2023, 13, 2203244) induces the surface charge redistribution, thereby affects the adsorption\nenergy of intermediates and then triggers the OPM pathway to enhance the performance. The effect of oxygen\nvacancy is also analyzed by the calculations. For both Nd-CoO and Nd-Co O , OER proceeds via OPM with\nx 3 4\nthe third proton-electron transfer step (OH*-OH* → O*-OH*) as the potential-determining step (PDS). A\ncomparison between Nd-CoO (with oxygen vacancies) and Nd-Co O (without oxygen vacancies)\nx 3 4\ndemonstrates that oxygen vacancies further reduce the adsorption of the O*-OH* intermediate, supported by\nthe charge analysis (reduced electron transfer 0.89 e- compared to 0.90 e-) and longer Co-O bonds (e.g., 1.681\nÅ, 1.823 Å vs. 1.680 Å, 1.821 Å) (Supplementary Fig. 25c and 25d). Thus, Nd doping drives the mechanistic\nshift from AEM to OPM, while oxygen vacancies tune the intermediate adsorption by modulating the electronic\nstructure of Co sites adjacent to Nd. This synergistic effect significantly enhances the overall OER activity. We\nhave clarified this issue in the revised manuscript.\nx\n(b) O* adsorbed on Nd-CoO , (c) O*-OH* adsorbed on Nd-CoO , and (d) O*-OH* adsorbed on Nd-Co O . The\nx x 3 4\nelectron accumulation and depletion are represented with yellow and blue contours, with iso-surfaces being\n0.02 |e|/Å3.\nIn \" Breathing mode in Nd-CoO for active and stable proton exchange membrane water electrolysis\", Feng et\nx\nal. have developed a low-cost catalyst based on Co O with oxygen vacancies and Nd-insertion (Nd-CoO ) as\n3 4 x\na stable and active material for acidic oxygen evolution reaction (OER). The paper is compelling and may lead\nto advancements in the field of electrochemistry and the authors are clearly well-versed in multi-technique\ncharacterization protocols. However, the manuscript presents many issues, and the results are not properly\njustified by the experimental results. I therefore believe that the manuscript in its current state is not suitable for\npublication in Nature Communications.\nResponse: Thank you for the positive and valuable comments to improve our work. According to your\ncomments, we have provided more data and carefully revised the manuscript.\n1. When looking at Figure 2a the sentence “The spectra of both CoO and Nd-CoO closely resemble that of\nx x\nstandard Co O , indicating similar chemical states” seems to be wrong. The spectrum of the reference Co O is\n3 4 3 4\nvery different from the others and therefore the local structure around the Co atom is supposed to be different.\nThis is also proved by the existence of a pre-edge peak in the XANES spectra of CoO and Nd-CoO that is not\nx x\npresent in the reference compound. This peak is due to the existence of quadrupolar transitions and is indicative\nof a distortion in the coordination sphere of the photoabsorber. The appearance of this peak and its meaning\nshould be discussed in the paper.\nResponse: Thank you for the valuable comments. We agree with you that the spectrum of the reference Co O\n3 4\nis different from the others and the local structure around the Co atom is different. The chemical states of Co in\nboth CoO and Nd-CoO are much lower than that in Co O , along with the different local structures. We have\nx x 3 4\nmodified this statement in the revised manuscript as “Both CoO and Nd-CoO show different XANES spectra\nx x\nwhen compared to that of standard Co O ”. The pre-edge peak is also discussed in the revised manuscript. This\n3 4\npre-edge peak primarily arises from the quadrupolar transition of 1s electron to unoccupied 3d orbitals, in which\nthe coordination environment (symmetry) can affect the intensity (X-Ray Spectrom. 2008, 37, 572–584). In the\nXANES spectrum of CoO (octahedral coordination), the very weak pre-edge peak can be attributed to the weak\n1\n1s–3d electric quadrupole transition in the standard octahedral environment, as shown in the magnified Fig.\nenvironments), the hybridization of 3d and p orbitals can enhance the pre-edge peak intensity due to the electric\ndipole transitions. Co O contains both tetrahedral and octahedral coordination environments, resulting in a\n3 4\nhigher intensity of the pre-edge peak when compared to CoO (see Fig. R10b). Moreover, with large amounts of\noxygen vacancies and defects, both the CoO and Nd-CoO samples show lowered symmetry with a higher\nx x\nconcentration of tetrahedral Co2+ coordination, leading to the pronounced pre-edge peak intensity (X-Ray\nSpectrom. 2008, 37, 572–584; J. Phys. Chem. B 2007, 111, 5101-5110). We have modified the related statements\nand added the corresponding discussion in the revised manuscript.\nFig. R10. (a) Co K-edge XANES spectra of CoO, Co O , CoO and Nd-CoO . (b) The magnified area of pre-edge\n3 4 x x\npeak.\n2. At line 144 the authors discuss the position of the FT first peak, and they state that “they correspond to the\nCo-O bonds in Co O and CoO, respectively”. This is not correct as the FT shown are not phase-shift corrected\n3 4\nand therefore the position of the FT peaks falls at lower distances as compared to the bond lengths. This is also\nclear from Table S2 where the Co-O distances are much longer. Moreover, the position of the FT’s strongly\ndepends on how they have been calculated, and the results of the fits should be considered rather than the\nposition of the experimental FT spectra.\nResponse: Thank you for the valuable comments. We agree with you that the FT peak positions are not the real\nbond length values. We have modified the related statements and noted that they are FT peak positions in the\nrevised manuscript. The fitting results have also been provided along with the FT peak positions to\n5\nsimultaneously describe the bond length changes in the revised manuscript. We have provided the detailed XAS\ndata processing methodology and fitting procedure in the Methods section (Supplementary Information).\n3. At line 152 the authors state “The detailed EXAFS fitting curves and bond lengths are presented in\nSupplementary Fig. 6 and Supplementary Table 2.” Regrettably, Figure S6 shows the FT and not the EXAFS\nspectra. Moreover, no details are provided on the fitting procedures and the errors on the distances, DW factors\nand coordination numbers should be reported to allow one to compare the results.\nResponse: Thank you for the valuable comments. We appreciate your comment on this mistake. We have\nreplaced “EXAFS fitting” with “R-space fitting (Fourier-transform curves of EXAFS spectra)” in the revised\nmanuscript. The corresponding EXAFS spectra of various samples are also shown in the following Fig. R11.\nAccording to the comments, we have provided the detailed information on the R-space fitting procedure in the\nMethods section (Supplementary Information). The fitting parameter errors on the distances, DW factors and\ncoordination numbers are now provided in Supplementary Table 2 and Table 5.\nCo K−edge\n)\nu.\na. EXAFS\n(\ny\nt\nsi\nn\ne\nt\nn\nd\ni\ne\nz\nali CoO\nm CoO\n3 4\nr\no CoO\nN X\nNd−CoO\nX\n7700 7800 7900 8000 8100 8200\nFig. R11. Co K-edge XAS spectra of CoO, Co O , CoO and Nd-CoO .\n3 4 x x\nSupplementary Table 2. Structure parameters obtained from the R-space fitting curves at the Co K-edge.\nSample Path S 2 CN R (Å) ΔE (eV) σ2 (Å2)\n0 0\n0.008(±\nCoO Co-O 1.0 3.9 (± 0.3) 2.12 (± 0.02) 3.4\n0.001)\n6\n0.003(±\nCo O Co-O 1.0 3.9 (± 0.2) 1.93 (± 0.01) 1.3\n3 4\n0.0008)\n0.003(±\nCoO Co-O 1.0 3.8 (± 0.1) 1.95 (± 0.01) 4.3\nx\n0.0005)\n0.003(±\nNd-CoO Co-O 1.0 3.1 (± 0.2) 1.91 (± 0.01) -0.4\nx\n0.0006)\nNote: CN is the coordination number; R is the interatomic distance; ΔE is the edge-energy shift; σ2 is the Debye-\n4. More details on the Wavelet transform (WT) plots shown in Fig. 2c should be provided.\nResponse: Thank you for the valuable comments. The details for plotting the Wavelet transform (WT) plots in\nFig. 2c are now provided in the revised Methods section (Supplementary Information) as bellow: “The EXAFS\nresults were analyzed by using Fourier transform of k-space data in a window (Hanning window with dk =1) of\n2.0−11.0 Å−1 for Co K-edge, and k-weighting was set to be 3 for all spectra without correction for phase shift.\nThe same k ranges (2.0−11.0 Å−1 for Co K-edge) were used for wavelet transform analysis (Morlet function,\nkappaMorlet= 15, sigmaMorlet = 1).”\nIn addition, we have also carefully analyzed the WT data in the revised manuscript. “The WT plots provide both\nk-space and R-space data in two dimensions, facilitating the discrimination of backscattering atoms. The heavier\natom (with higher atomic number) typically exhibits a stronger ability to scatter photoelectrons, resulting in\ntheir oscillations appearing at higher frequencies (high k values). In Fig. 2c, Co O shows the Co-O peak at a k\n3 4\nvalue of ~8.0 Å−1, while for Nd-CoO , this peak shifts to a higher k value (~8.3 Å−1) indicating the Nd-insertion.”\nx\n5. At line 168 the sentences “Nd-CoOx shows the lowest white-line intensity, indicating a relatively lower\nvalence state for Nd.” Is not clear. What do they mean with “lower valence state”? If it is the oxidation state this\nrelates to the position of the rising edge and not to the intensity of the white line. Moreover, Fig. 2e shows the\nFourier Transforms and NOT the EXAFS curves.\nResponse: Thank you for the valuable comments. We have revised the statement on EXAFS curves in Fig. 2e\n7\nby using “the corresponding Fourier-transform curves of EXAFS spectra” in the revised manuscript.\nWe confirm that at line 168 the sentences for lower valence state mean the oxidation state. We agree with you\nthat typically the oxidation state of metal elements can be related to the position of the rising edge (white line\npeak position), especially for the 3d metal elements such as Co, Ni, and Fe. However, for the high atomic\nnumber elements (4d, 5d transition metals or rare earth elements) such as Ag, Pt, Au, and Nd, the white line\npeak intensity is also a good measure of the oxidation state regarding the unoccupied hole populations. The\nwhite line peak intensity typically reflects the density of unoccupied state. When getting electrons from other\nelements, the additional electrons can fill the unoccupied orbits to reduce its density and then the white line\npeak intensity will decrease. Then the decreased white line peak intensity typically stands for a lower chemical\nstate, especially for the high atomic number elements such as Nd. This phenomenon has been clearly\ndemonstrated in the literatures. For example, T.K. Sham et al. showed that the XANES white line peak intensity\nof Pd and Ag could be directly used to probe the oxidation state and charge transfer of metals (Phys. Rev. Lett.\n1996, 77, 4824-4827). The sixth period elements such as Pt, Ir, Au, W also showed a strong relationship between\nthe oxidation state and the white line peak intensity, while the energy position of rising edge exhibited very\nslight changes, as demonstrated in the literatures (Nat. Commun. 2023, 14, 5365; Nat. Commun. 2024, 15, 6650;\nJ. Appl. Phys. 1996, 79, 7134; Phys. Rev. 1994, 49, 1647; Nanoscale Horiz. 2023, 8, 1273). The following Fig.\nR12 shows some examples in the literatures to demonstrate the influence of oxidation state on the white line\npeak intensity. Thus in this work the lowest white-line intensity of Nd-CoOx can be used to reveal a relatively\nlower oxidation state of Nd.\n[FIGURE REDACTED]\nFig. R12. (a) Ir L -edge and (b) Pt L -edge XANES spectra to show the relationship between oxidation state\n3 3\n8\nand white line peak intensity (from Nat. Commun. 2023, 14, 5365 and Nat. Commun. 2024, 15, 6650,\nrespectively).\n6. The major flaw of this investigation is the analysis of the XAS data that has been carried out to demonstrate\nthe \"breathing mode\" behavior. Throughout the manuscript the authors mention the EXFAS spectra while no\nEXAFS data are reported. The differences in the position of the FT first peak are very small and a proper\nquantitative analysis of the XAS data should be carried out in the k space to really demonstrate the existence of\na contraction and expansion of the distances. Showing only the experimental FT’s is not a proper procedure.\nResponse: Thank you for the valuable comments. Firstly, we have carefully revised the whole manuscript by\nreplacing the “EXAFS spectra” as “Fourier transform curves of the EXAFS spectra”. The EXAFS spectra are\nalso provided in the following Fig. R11.\nWe also agree with you that the k-space data are important for the analysis and appreciate your valuable\nsuggestion. We have provided the k-space data in the following Fig. R13 and Fig. R14. However, the k-space\ncurves contain all the contributions from multiple atomic shells (for example, Co-O and Co-O-Co) and they are\nnot easy to be used to directly understand the structural change of a single Co-O shell. The multiple shell overlap\nin k-space can also be observed from the wavelet transform (WT) plots in Fig. 2c, which provide both k-space\nand R-space data in two dimensions (Phys. Rev. B 2005, 71, 094110). The Co-O and Co-O-Co peak overlap in\nk-space can be widely observed in the literatures (Nat. Commun. 2022, 13, 2900; Adv. Mater. 2025, 2408906;\nNat. Commun. 2022, 13, 7754). Thus we have analyzed the experimental FT curves to demonstrate the changes\nof Co-O, which is actually a commonly used analysis method for exploring this goal as widely reported in the\nliteratures (Nat. Commun. 2021, 12, 3036; Science 2023, 380, 609-616; Nat. Commun. 2025, 16, 3502).\nWe also agree with you that the differences in the position of the FT first peak are small. However, the\ndifferences are clear and show a gradually changing trend along with the increased potential. Especially, the\ndifferences between the OCP curve position (1.45 Å) and the 1.65 V curve position (1.51 Å) can be an obvious\nvalue of 0.06 Å, which should stand for the real structural change and can never be considered as the\nexperimental error. To further confirm this change, we have also carefully measured the sample after reaction\n(OCP again), which can well recover to support our conclusion.\nfrequently used to probe the local electronic and atomic changes as reported in the literatures (Nat. Commun.\n2021, 12, 3036; Nat. Commun. 2025, 16, 3502; Adv. Mater. 2023, 35, 2305939; Angew. Chem. Int. Ed. 2025,\n64, e202507144; Science 2025, 388, 430-436; Science 2023, 380, 609-616). For example, Liu et al. observed a\nclear negative shift of 0.06 Å for the peak assigned to the Co-O bond, indicating a shortening of the Co-O bond\nlength (Science 2023, 380, 609-616). Interestingly, the corresponding k-space spectra showed very small\nchanges (see following Fig. R15). Peng et al. also reported a slight positive shift of Ru-O peak and a slight\nnegative shift of Co-O peak in the R-space curve of RuO /LiCoO catalyst, standing for the strong evidence for\n2 2\nthe elongation of Ru-O bond and the shortening of Co-O bond (Nat. Commun. 2025, 16, 3502).\nAlthough the R-space peaks show clear shift, the k-space curves may have very small changes due to the\nmultiple atomic shell contributions. Jin et al. detected obvious changes in the Co-O bond length, while the\nrelated k-space spectra were virtually unaltered (see following Fig. R16; Nat. Commun. 2021, 12, 3036). Similar\nphenomenon with clear R-space difference but very small changes in k-space curves can also be observed for\nvarious metal elements as reported in the literatures (see following Fig. R17; Adv. Mater. 2023, 35, 2305939).\nThus in this work we mainly use the experimental FT curves to demonstrate the \"breathing mode\" behavior.\nIn order to further reveal the dynamic evolution of Co-O bond during OER process, we have also carefully fitted\nthe Fourier-transform curves of in-situ EXAFS data for Nd-CoO . As shown in Supplementary Fig. 17 and\nx\nSupplementary Table 5, the Co-O bond length positively increases with the increased potentials and\nsubsequently recovers to its initial value after the reaction (OCP again), confirming the presence of \"breathing\nmode\" behavior in Nd-CoO during the OER process.\nx\n)\nu.\na. EXAFS\n(\ny\nt\nsi\nn\ne\nt\nn\nd\ni\ne\nz\nali CoO\nm CoO\n3 4\nr\no CoO\nN X\nNd−CoO\nX\n7700 7800 7900 8000 8100 8200\nFig. R11. Co K-edge XAS spectra of CoO, Co O , CoO and Nd-CoO .\n3 4 x x\nFig. R13. Co K-edge k3-weighted EXAFS functions of various samples.\nNd−CoO:\nx\nOCP\n1.45 V\n1.55 V\n1.65 V\n) OCP again\n3\n−\nÅ\n(\n)\nk\n(\nc\n3\nk\n2 4 6 8 10\nk (Å−1)\nFig. R14. Co K-edge k3-weighted EXAFS functions of Nd-CoO at different applied potentials.\nx\n11\n[FIGURE REDACTED]\nFig. R15. The R-space and k-space curves of LMCF catalyst during OER at the Co K-edge (Science 2023, 380,\n609-616).\n[FIGURE REDACTED]\nFig. R16. The R-space and k-space curves of various catalysts at the Co K-edge (Nat. Commun. 2021, 12, 3036).\n12\n[FIGURE REDACTED]\nFig. R17. The R-space and k-space curves of MOF@POM catalyst during OER at the Co K-edge (Adv. Mater.\n2023, 35, 2305939).\nSupplementary Figure 17. R-space fitting curves at the Co K-edge for Nd-CoO at (a) OCP, (b) 1.45 V vs.\nx\nRHE, (c) 1.55 V vs. RHE, (d) 1.65 V vs. RHE and (e) OCP again, respectively.\nSupplementary Table 5. Structure parameters obtained from the R-space fitting curves at the Co K-edge for\nthe Nd-CoO sample during OER.\nx\nSample Path S 2 CN R (Å) ΔE (eV) σ2 (Å2)\n0 0\n13\n0.003 (±\nOCP Co-O 1.0 3.1 (± 0.2) 1.91 (± 0.01) -0.4\n0.0006)\n0.005 (±\n1.45 V vs. RHE Co-O 1.0 3.4 (± 0.2) 1.92 (± 0.01) 2.6\n0.001)\n0.004 (±\n1.55 V vs. RHE Co-O 1.0 3.6 (± 0.3) 1.93 (± 0.01) 2.4\n0.0012)\n0.004 (±\n1.65 V vs. RHE Co-O 1.0 3.8 (± 0.1) 1.94 (± 0.01) 2.2\n0.0008)\n0.003 (±\nOCP again Co-O 1.0 3.3 (± 0.1) 1.91 (± 0.01) 1.6\n0.0005)\nNote: CN is the coordination number; R is the interatomic distance; ΔE is the edge-energy shift; σ2 is the Debye-\n7. The lack of fundamental details in the XAFS methodology makes this part unsuitable for publication. There\nis no description on how the fitting of the experimental data has been carried out: which program has been used?\nHas the fitting procedure carried out only on the first shell of the FT spectra? Moreover, figures showing the\nextracted χ(k)k^2 EXAFS signals should be included to really highlight the differences among the samples.\nResponse: Thank you for the valuable comments. We have provided the detailed information regarding the\nprocessing of XAS data in the revised Supplementary Information. For example, the XAS data were analyzed\nby using the ATHENA and ARTEMIS software. Since we focus on the changes of Co-O bond, we have only\ncarried out the fitting procedure on the first shell of the FT spectra. The extracted χ(k)k^3 EXAFS signals (k-\nspace data) for various samples and the in-situ data of Nd-CoO at the Co K-edge are provided in the following\nx\nFig. R13 and Fig. R14, respectively. Differences can be clearly observed among the curves, similar to those Co-\nbased materials reported in the literatures (Nat. Commun. 2021, 12, 3036; Nat. Commun. 2025, 16, 3502;\nScience 2025, 388, 430-436; Science 2023, 380, 609-616). However, the k-space curves are not easy to be used\nto directly understand the structural information due to the influence of multiple atomic shells, thus we mainly\nuse the R-space curves (FT spectra) to demonstrate the changes of Co-O for \"breathing mode\" in Nd-CoO\nx\nduring OER.\nNd−CoO:\nx\nOCP\n1.45 V\n1.55 V\n1.65 V\n) OCP again\n3\n−\nÅ\n(\n)\nk\n(\nc\n3\nk\n2 4 6 8 10\nk (Å−1)\nFig. R14. Co K-edge k3-weighted EXAFS functions of Nd-CoO at different applied potentials.\nx\n15"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have provided comprehensive and persuasive responses to all my comments. The revisions and additions made to the manuscript have significantly improved its clarity and scientific rigor. I recommend acceptance.", "reviewer_2": "The authors have addressed my comments well, and the quality of the manuscript has been improved. However, several points are still unclear to be published in this journal.\n(1) For comments 1-3, authors should show the results for the convergence tests of surface energy in response letter.\n(2) For comments 1-4, oxygen vacancy formation energy with possible sites is also required to confirm the most stable site for oxygen vacancy formation.\n(3) For comments 1-5, why did the aurhots only consider the top layer as the doping site of Nd?\n(4) For comment 2-1, why did the aurhots not consider the Nd site as an adsorption site?\n(5) For comment 4, how did the authors consider the applied potential effect on DFT calculations? Which option was used for the DFT calculations? What is the software name (VASP, QE, and so on)?\n(6) For comment 5, it might be better to add the results for the comparison of catalytic activity between pure CoOx and Nd-dopec CoOx in the main manuscript (Fig. 5c).", "reviewer_3": "The authors have satisfactorily addressed all my main concerns, and I consider the manuscript suitable for publication in its present form."}, "author_response": "Response to the Comments\nReviewer #2:\nThe authors have addressed my comments well, and the quality of the manuscript has been improved. However,\nseveral points are still unclear to be published in this journal.\nResponse: Thank you for the positive and valuable comments to improve our work. According to your\ncomments, we have provided more data and carefully revised the manuscript.\n(1) For comments 1-3, authors should show the results for the convergence tests of surface energy in response\nletter.\nResponse: Thank you for the valuable comments. We are sorry for the unclear response in our previous version.\nAs shown in Fig. R1, the surface energy has been evaluated for Co O (311) surfaces with slab thicknesses\n3 4\nranging from 1 to 4 layers according to the literatures (Nanoscale, 2017, 9, 13089-13094; Nano Res. 2023, 16,\n439-448; Nat. Commun., 2023, 14, 2720; Sci. Adv. 2022, 8, eabq5751; Adv. Funct. Mater. 2024, 34, 2316654).\nThe results demonstrate that the surface energy converges with the increased number of layers, and the value\nfor the 4-layer model is essentially identical to that of the 3-layer structure. This suggests that the surface energy\nhas reached convergence at 3 layers. Therefore, all the models for CoO and Nd-CoO in this study have been\nx x\nconstructed with three layers to ensure accurate and computationally efficient representation of the surface\nproperties.\nThe surface energy has been evaluated via the following expression (Nanoscale, 2017, 9, 13089-13094;\nNano Res. 2023, 16, 439-448; Nat. Commun., 2023, 14, 2720; Sci. Adv. 2022, 8, eabq5751; Adv. Funct. Mater.\n2024, 34, 2316654):\n1 1\nE = [𝐸𝑢𝑛𝑟𝑒𝑙𝑎𝑥 −𝑛𝐸 ]+ [𝐸𝑟𝑒𝑙𝑎𝑥 −𝐸𝑢𝑛𝑟𝑒𝑙𝑎𝑥]\n2𝐴 𝑠𝑙𝑎𝑏 𝑏𝑢𝑙𝑘 𝐴 𝑠𝑙𝑎𝑏 𝑠𝑙𝑎𝑏\nWhere A is the surface area of the Co O (311) slab, 𝐸𝑢𝑛𝑟𝑒𝑙𝑎𝑥 is the energy of the as-cleaved Co O (311)\n3 4 𝑠𝑙𝑎𝑏 3 4\nsurface before relaxation, 𝐸 is the energy of the optimized bulk Co O , and 𝐸𝑟𝑒𝑙𝑎𝑥 is the energy of the\n𝑏𝑢𝑙𝑘 3 4 𝑠𝑙𝑎𝑏\nslab after structural relaxation with only the top layer allowed to relax.\n3 4\n(2) For comments 1-4, oxygen vacancy formation energy with possible sites is also required to confirm the most\nstable site for oxygen vacancy formation.\nResponse: Thank you for the valuable comments. To determine the most stable site for oxygen vacancy\nformation on the Nd-Co O (311) surface, we performed a systematic computational screening by selectively\n3 4\nremoving one oxygen atom at all distinct oxygen sites spanning heterogeneous chemical environments. After\nfull structural relaxation using DFT+U (Ueff = 3.0 eV for Co 3d orbitals), we identified the thermodynamically\nmost favorable vacancy site through the comparative total energy analysis (as shown in Fig. R2).\nx\nvacancy sites).\n(3) For comments 1-5, why did the authors only consider the top layer as the doping site of Nd?\nResponse: Thank you for the valuable comments. The calculation model with top layer doping is based on both\nexperimental and computational perspectives: (1) According to the TEM results, Nd-CoO shows a porous\nx\nnanosheet morphology (thin layer), with a lot of atoms exposed on the surface. Moreover, according to the\naberration-corrected HAADF-STEM image in Fig. 1e, the Nd atoms can be clearly observed on the surface\nlayer of Nd-CoO . Thus the top layer doping model has been supported by the experimental observation. (2)\nx\nFirst, since the oxygen evolution reaction (OER) is a surface process, dopants must be near the surface to directly\nmodulate the electronic structure of Co/O active sites; bulk doping has a relatively weak effect. Second, the\nionic radius of Nd3+ is significantly larger than that of Co ions. Doping in the bulk will introduce considerable\nlattice strain, whereas the surface allows effective strain relaxation, making surface doping thermodynamically\nmore favorable. Furthermore, modeling bulk doping will require thicker slab models and sampling multiple\ndoping sites, leading to prohibitively high computational costs. Focusing on surface doping will enable more\naccurate and tractable simulations. This approach is also consistent with commonly adopted practices in\ncomputational catalysis studies (Angew. Chem. Int. Ed. 2025, 64, e202415306; Angew. Chem. Int. Ed. 2025,\n64, e202425569). Thus, the decision to place Nd at the surface has been based on a combination of experimental\nobservation, relevance to the reaction, thermodynamic stability, computational efficiency, and established\nconventions in the field, which ensures an effective and efficient investigation into the mechanistic role of Nd\ndoping.\n(4) For comment 2-1, why did the authors not consider the Nd site as an adsorption site?\nResponse: Thank you for the valuable comments. We fully acknowledge that all potential adsorption sites should,\nin principle, be considered. However, in this study, Nd sites have not been regarded as the active centers,\nbased on the following rationales: (1) The highly localized 4f orbitals of Nd3+ ions preclude effective electronic\nexchange with key OER intermediates (e.g., *OOH, *O, *OH), thereby inhibiting the formation of stable\nchemical adsorption (we have tried the models with intermediates adsorbed on Nd but they are not stable); (2)\nThe doping concentration of Nd in the experimentally synthesized materials is low, and both theoretical and\nexperimental studies confirm that undoped CoO itself exhibits intrinsic OER catalytic activity. Therefore, we\nx\npropose that rare-earth doping enhances catalytic activity primarily through indirect effects, such as modulating\nthe electronic structure of native metal sites and enhancing metal-oxygen covalency—rather than by serving as\ndirect reaction centers. This perspective is also supported by multiple studies, including those on Nd-doped\nCo O systems (Applied Catalysis B: Environment and Energy 2024, 352, 123990; Angew. Chem. Int. Ed. 2025,\n3 4\n64, e202510478; Small 2024, 20, 2401964). In conclusion, the role of Nd is primarily to modulate the local\n4\nchemical environment of Co/O sites, rather than creating new active sites.\n(5) For comment 4, how did the authors consider the applied potential effect on DFT calculations? Which option\nwas used for the DFT calculations? What is the software name (VASP, QE, and so on)?\nResponse: Thank you for the valuable comments. In our work, the effect of external potential has been\nincorporated by using a grand canonical formulation, which aligns with conventional constant-potential DFT\nmethodologies. Specifically, the applied potential has been controlled by adjusting the total number of electrons\nin the system. A distinctive aspect of our approach is that the potential has been applied not only during the self-\nconsistent field (SCF) electronic steps but also consistently throughout the geometry relaxation process (Adv.\nFunct. Mater, 2023, 33, 2208736; J. Am. Chem. Soc, 2024, 146, 32539-32549). This ensures that the atomic\nstructures are optimized under the explicit influence of the external potential, thereby allowing us to\nmeaningfully capture voltage-induced structural changes, such as the evolution of Nd–O and Co–O bond lengths,\nand directly correlate them with the flexible \"breathing mode\" observed experimentally. All DFT calculations\nin this study were performed using the Vienna Ab initio Simulation Package (VASP). We have clarified this\nissue in the revised manuscript.\n(6) For comment 5, it might be better to add the results for the comparison of catalytic activity between pure\nCoO and Nd-doped CoO in the main manuscript (Fig. 5c).\nx x\nResponse: Thank you for the valuable comments. We have added the results for the comparison of catalytic\nactivity between pure CoO and Nd-doped CoO in the revised manuscript (Fig. 5c, both AEM and OPM pathways\nx x\nat 0 V and 1.55 V).\nx\nCoO without applied potential, along with the model of Nd-CoO with potential correction (1.55 V with\nx x\nreference to the vacuum energy level). b, The DEMS signals of 32O , 34O and 36O tested for Nd-CoO in H 18O\n2 2 2 x 2\nacidic solution. c, Gibbs free energy diagrams for Nd-CoO and CoO through AEM and OPM pathways at 0 V\nx x\nand 1.55 V (with constant electrode potential corrections). d, Illustration of the OPM pathway on Nd-CoO .\nx\ne,\nSchematic diagrams of the structural variations of CoO and Nd-CoO before and after OER.\nx x\n6"}, {"round": 3, "reviewer_comments": {"reviewer_2": "The authors have addressed my comments well, and the quality of the manuscript has been further improved. In response to my comment 5, \"the applied potential has been controlled by adjusting the total number of electrons in the system\". I think that applied potential cannot be described by the number of electrons. It is more likely to be the current, not the potential. It is my last comment."}, "author_response": "Response to the Comments\nReviewer #2 (Remarks to the Author):\nThe authors have addressed my comments well, and the quality of the manuscript has been further improved.\nIn response to my comment 5, \"the applied potential has been controlled by adjusting the total number of\nelectrons in the system\". I think that applied potential cannot be described by the number of electrons. It is more\nlikely to be the current, not the potential. It is my last comment.\nResponse: Thank you for the valuable comments. We agree with you that in an experimental context, directly\ncontrolling the electron number corresponds to a charging/discharging current rather than applying the electrode\npotential. However, in this work we have used the specific states with different electron numbers to simulate\nthe catalyst state under external potential, instead of directly applying the potential. We are not simulating the\ndynamic current flow of an experiment, but rather the stable, equilibrated state of the interface at a specific\npotential with different electron numbers. We would like to modify the response statement as “the state with\napplied potential has been simulated by tuning the total number of electrons in the system”. We have revised\nthe manuscript according to the comments. We have also carefully explained the methodological rationale\nprevalent in computational electrochemistry in the following contents.\nIn the framework of standard periodic density functional theory (DFT) calculations, the modeled system\nconstitutes an electrically isolated, charge-neutral supercell. This configuration inherently lacks an internal\nreference potential—such as the reference electrode employed in experimental setups—thereby precluding\ndirect control of the \"electrode potential\" as an explicit variable (Phys. Rev. B, 2006, 73, 115407). This\nfundamental limitation represents a long-standing challenge in the field of computational electrochemistry. For\ninstance, the early development of the computational hydrogen electrode (CHE) model was motivated precisely\nby the need to circumvent the challenges associated with explicitly modeling charged interfaces, offering instead\na robust thermodynamic approximation (J. Phys. Chem. B, 2004, 108, 17886–17892). More recently, to achieve\na more physically realistic representation of electrochemical interfaces, researchers have developed explicit\nconstant-potential methods, the core of which involves incorporating a compensating charge background to\nmaintain overall charge neutrality while effectively fixing the electrode potential (J. Am. Chem. Soc. 2023, 145,\n46, 25264–25273; Adv. Funct. Mater. 2023, 33, 2208736; ACS Catal. 2025, 15, 10, 7993–8004). The\n1\nfundamental principle is that adding/removing electrons systematically shifts the system's Fermi level. This is\nthen mapped to an experimental potential scale (e.g., vs. the Standard Hydrogen Electrode) using the well-\nestablished CHE framework.\nTherefore, while the computational electron numbers have been tuned, the physical state we are modeling\nis a series of equilibrium systems, each at a different, constant electrode potential for simulation. We are not\nsimulating the dynamic current flow of an experiment, but rather the stable, equilibrated state of the interface\nat a specific potential. This method has now been widely accepted for calculating the potential-dependent\nreaction energetics.\n2"}]

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