Transforming disorder in the design of advanced high-entropy oxide electrocatalysts for zinc-air batteries

Domain: chemistry
Published: 2026-02-23
Editorial outcome: major_revision

Abstract
Research on high-entropy oxides generally is limited to elemental and structural interpretations applied to the performance of cathodes. However, there are only limited data on the principles of increasing disorder in terms of structural, electronic, and atomic mechanisms as materials convert from ordered to disordered. Zn-air battery cathodes are limited by slow kinetics, imbalanced oxygen evolution reaction charging, imbalanced oxygen reduction reaction discharging, and scalability (through the necessity of benchmark noble metals). The present work pioneers the engineering of multilevel disorder in high-entropy oxides, thereby transforming an intrinsically inactive matrix into a highly active cathode. Systematic modification of the disorder through increasing number of cations lead to the abrupt development of structural (2D defects), electronic (semimetallic conductivity), and atomic (low-coordination Ce) disorder. This multilevel disorder engineering of high-entropy oxides results in MnNiCoFe-CeO2 catalysts with stable active sites, rapid and balanced bifunctional (oxygen evolution/reduction reaction) performance, thereby promising Zn-air battery efficiencies and electrochemical durabilities greater than those of the benchmark materials).

Introduction
High-entropy oxides (HEOs) are an emerging class of chemically- complex, single-phase, solid solutions containing at least five different cations1,2. They have high configurational entropies arising from their disordered multicomponent oxide systems. These establish an infinite number of tuneable permutations of elemental combinations through structural, electronic, and atomic hybridizations, allowing multifunctional materials design for catalytic and other energy-storage applications3–5.

The distinctive features of HEOs enable the development of bifunctional catalysts that are well suited for alkaline conditions owing to their corrosion resistance from hydroxides, where metals and non-oxides are subject to such corrosion6. These attributes establish HEOs as promising candidates for cathodes in zinc-air batteries (ZABs), where the oxygen evolution reaction (OER) governs charging, and the oxygen reduction reaction (ORR) drives discharging. The benchmark cathodes still are dominated by noble-metal catalysts (Pt/C+IrO2) owing to its corrosion resistance and well-suited catalytic activity with balanced OER/ORR kinetics7. Most design strategies for high-performance cathodes are based on composites, combining OER-favorable (e.g., NiFe-based) with ORR-favorable (e.g., noble metal/carbon-based) materials8–10. While this composite approach seeks to capitalize on the strengths of each component, it frequently suffers from significant kinetic or performance imbalances between OER and ORR7. This limitation is likely due to the focus on optimization of one aspect of catalytic performance while overlooking the critical need for balanced kinetics and activity between the two reactions. Therefore, this necessitates the development of advanced electrocatalysts capable of bifunctionality, effectively accelerating both OER and ORR by optimizing their reaction mechanisms.

OER mechanisms are well-documented, involving active sites in the form of redox-capable cations and lattice oxygen11. The ORR mechanism remains uncertain, particularly for oxide-based catalysts12. It has been shown recently that the ORR mechanism for pure metal catalysts may involve oxygen gas adsorption on metal surfaces and that this is facilitated by the existence of unpaired electrons of the metal ions, where each oxygen molecule requires two unpaired electrons from the metal site for bond formation13. CeO2 is a promising material well-suited for OER owing to Ce4f0 to Ce4f1 redox electron transfer, intrinsic point defect formation (Ce3+), and charge-compensating oxygen vacancies14. However, CeO2 is a wide-band-gap semiconductor, resulting in poor charge transfer between CeO2 and active sites for OER/ORR in ZABs. Transition metal (TM) doping can alter the d band center to improving the charge transfer, which can activate reactive species adsorption15. Further, CeO2 exhibits a large solid solubility range, making it an potential candidate for the development of HEOs16.

There are four recognized key effects in HEOs: high-entropy effect, lattice distortion effect, sluggish-diffusion effect, and cocktail effect17. Of these, lattice distortion has attracted the most attention owing to its strong influence on the overall material properties. This effect originates from the coexistence of multiple cations of varying ionic radii, valence states, electronegativities, and coordination within the same sublattice. These coexistences cause atomic mismatches, which can lower the symmetry of the unit cell; introduce lattice distortion and strain; and generate 0D, 1D, 2D, and 3D defects, which may require charge compensation18. Further, the distances between neighboring ions occur over a distribution rather than at fixed values, thus placing the structure in a thermodynamically nonequilibrium state17. This deviation can lower the energy barriers for molecular adsorption, activation, and OER/ORR conversion in electrocatalytic reactions19. Despite the significance of lattice distortion, the current understanding of such disorder in HEOs remains limited20,21. Most studies focus primarily on identifying high concentrations of defects (e.g., oxygen or metal vacancies) and the absence of long-range order21,22. However, a comprehensive analysis of disorder from a structural, electronic, and atomic perspective remains lacking. In particular, there is a need for a systematic correlation of this multilevel disorder with the corresponding electrocatalytic performance, especially for bifunctional OER/ORR catalysts for ZABs. The present work explores this correlation through the performance of ZABs, with the aim of elucidating the mechanisms of the roles of disorder in HEO in governing catalytic activity.

To the preceding aim, the present work introduces a different non-noble-metal MnNiCoFe-CeO2-based HEO and a conceptual mechanistic framework that facilitates simultaneous improvement in multilevel disorder through structural-, electronic-, and atomic-level disorders, leading to improvement in the OER/ORR activities as well as promising performance and stability in ZABs. This analysis provides a platform for the application of disorder engineering in the design of systematic ranges of progressively more complex systems, from individual oxides to HEOs.

Results
Structural disorder
The fabrication strategy involves a simple approach to HEO self-assembly at room temperature (Fig. 1a). A Ce-based coordination polymer Ce(TCA)(OH)·2H2O(Ce-CP) and different 3d-TM salts were dissolved in a polar aqueous ethanol solution to yield nanospheres of the nominal composition Mn0.035Ni0.035Co0.035Fe0.035Ce0.860O2, as confirmed by Supplementary Table 1. The Cl– ions on the Ce-CP surface facilitate electrostatic interactions with TMX+ ions23. The resultant atomic-scale mixing and strong attraction enable metastable solid solubilities that are retained during room-temperature oxidation and dechlorination in aqueous alkaline solution, leading to the formation of complex HEOs.

With stepwise building and structural development of HEOs can be examined by X-ray diffraction (XRD) (Fig. 1b). Mn addition to CeO2 (Mn-CeO2) results in the formation of Mn3O4 precipitates, which suggests the exceeding of the solubility limit of Mn in CeO2. However, the subsequent addition of Ni2+, Co2+ (MnNiCo-CeO2), and Fe3+ (MnNiCoFe-CeO2) caused a reversion to homogeneous, single-phase, cubic, solid solutions. This implies that the homogeneity regions of the more complex solid solutions are larger than that for single-element-doped (Mn) alone. Rietveld-peak refinement data (Fig. 1c, Supplementary Tables 2-3, and Supplementary Fig. 1) reveal in-depth structural information. In structural analysis, peak shifts in diffraction patterns reflect changes in lattice dimensions while peak broadening is indicative of alterations in crystallinity, often linked to crystallite size. However, other factors, such as dislocation density and strain, which can be used to represent the extent of lattice distortion and so reflect structural disorder, generally are overlooked. These factors provide significant clues in the understanding of defect density and consequent structural disorder. Comprehensive analysis of all of this lattice information suggests that, as the number of TMs increases, the crystallite size decreases while lattice distortion (quantified through dislocation density and microstrain) increases. In order to decouple the effects of crystallite size and lattice distortion, high-resolution transmission electron microscopy (HRTEM) images (Supplementary Fig. 2) are used to illustrate that there is little variation between the observed crystallite sizes of CeO2 and high-entropy MnNiCoFe-CeO2 and that the crystallite size remains essentially constant from the bulk to the surface. These data thus confirm that the lattice distortion associated with the structural disorder in MnNiCoFe-CeO2 derives from increased dislocation density and microstrain rather than a decrease in crystallite size. Therefore, it is possible to isolate the lattice distortion and structural disorder in HEOs, as shown in Fig. 1c. The introduction of the single cation Mn results in the formation of a secondary phase, with minimal structural alteration to the primary matrix. This indicates limited interaction between the host lattice and the added Mn ions, thus maintaining the overall lattice stability. In contrast, the formation of a solid solution, with the addition of three cations (Mn, Ni, and Co), is accompanied by moderate changes in lattice parameters. This alteration likely represents the onset of matrix structural disorder, as the varying ionic radii and bonding characteristics of the cations introduce localized strain and lattice distortion. These changes suggest the beginning of a more complex multielement interaction, setting the stage for enhanced structural heterogeneity and the characteristic lattice distortion observed in HEOs. After the addition of the fifth element (Fe), there was an exponential change in the lattice parameter, indicative of a high degree of lattice distortion and structural disorder.

Further, these highly distorted and disordered structures can be observed clearly in the selected area electron diffraction (SAED) pattern (Fig. 1g), as revealed by the additional dots (representing disordered states) in the proximity of single-phase concentric rings. Several unusual types of 2D planar defects (Fig. 1d, e) appear, supporting the conclusion of a high extent of structural disorder and correspondingly improved reactivity. The morphology of MnNiCoFe-CeO2, showing spherically shaped particles (Fig. 1f, Supplementary Fig. 3), with a homogeneous distribution of all elements (Fig. 1h), combined with XRD and SAED results, indicate the formation of a homogeneous solid solution. MnNiCoFe-CeO2 exhibits the highest defect density in laser Raman microspectroscopy (Supplementary Fig. 4), as evidenced by the maximal defect concentration of 51.7%. This observation, combined with the absence of TM-O bonding features in the Raman spectra, confirms the presence of significant structural disorder and the maintenance of a single-phase structure of the Ce-O framework in the HEO state. The high defect concentration is indicative of a high frequency of oxygen vacancies, as evidenced by the 605 cm−1 Raman peak intensity. This high concentration of oxygen vacancies is likely to cause clustering in order to lower the total elastic energy of the system24. Such clustered vacancies are likely to be responsible for the formation of extended 2D structural defects, including the observed stacking faults, twin boundaries, and dislocations, which disrupt the oxygen sublattice25,26. These findings also provide a possible explanation for the apparent mismatch between surface-sensitive techniques, such as XPS, and bulk-sensitive techniques, such as Raman. While XPS may underestimate the extent of defect formation due to its shallow probe depth, the 2D defects identified by HADDF for the material surface offer direct evidence of surface-localized oxygen sublattice distortion, thereby aligning with the XPS- and Raman-based observations.

For a deeper understanding of defects contributing to structural disorder in HEOs, it is essential to explore the alteration in the nature of the chemical bonding. Surface-chemical analysis by X-ray photoelectron spectroscopy (XPS) is used to determine not only surface valence changes of elements but also the chemical bonding alteration27. The oxygen environment serves as a reliable indicator of the behavior of different cations as oxygen acts as the direct bridge between them. The deconvoluted O 1s spectra (Fig. 2a) reveals constant oxygen defect concentration in CeO2 (19%) and Mn-CeO2 (~20%) based on the relative areal proportions of the O-lattice (529 eV), and O-defective (531 eV) peaks28, suggesting unchanged metal-oxygen bonding and the high stability of the oxygen-sublattice. With increasing solid solution complexity (MnNiCo-CeO2), there is a small increase in O-defective/O-lattice ratio (22%) (Supplementary Fig. 5), suggesting that the addition of Ni and Co facilitates the formation of a small amount of oxygen vacancies, which are classified as point defects29. These individual oxygen vacancies may introduce localized disruptions in the lattice, but they are limited to a minor effect. However, a significant enhancement in the O-defective/O-lattice ratio (up to 85%) is observed in MnNiCoFe-CeO2. This reveal that the defects in the HEO are not limited to point effect (individual oxygen vacancies) but suggest that the oxygen vacancies are clustered, which would correspond to significant destabilization of the oxygen-sublattice in forming the 2D defect illustrated in Fig. 1d, e. This dramatic increase highlight that the addition of the fifth element fundamentally alters the defect dynamics in the HEOs. This phenomenon induces a significant transformation in the oxygen environment, resulting in the destabilization of the oxygen sublattice. This destabilization is likely driven by multivalence charge transfer (MVCT)30,31 which amplifies the effects of multiple metal ions simultaneously interacting with oxygen ions. This collective interaction reduces the intrinsic metal-oxygen bonding affinity, destabilizing the oxygen sublattice and forming 2D defects, thus causing the structural disorder.

Electronic disorder
The phenomenon of MVCT31 in HEOs equates to the presence of electronic disorder. Therefore, the distinctive effect of each cation on the charge transfer can be elucidated through analysis of their chemical bonding alteration, as revealed through the deconvolution and comparison of the 3d, 2p, and 3p XPS spectra for CeO2, Mn-CeO2, MnNiCo-CeO2, and MnNiCoFe-CeO2 (Supplementary Fig. 5). The Ce3d spectrum of CeO2 show two different Ce chemical environments, with the presence of Ce4+ (882.2 eV, 888.7 eV, and 898.2 eV) and Ce3+ (880.3 eV and 884.1 eV)28. In Mn-CeO2, the Ce3+ and Ce4+ binding energies are unchanged, suggesting retention of the original Ce chemical environments after the addition of Mn (Fig. 2b). However, in MnNiCo-CeO2, the binding energies of Ce3+ and Ce4+ are increased, indicating that the addition of Ni and Co cause electronic interactions within the Ce environment. These interactions result in alterations to the Ce-O bond, which can be attributed to the formation of a solid solution. The addition of Ni and Co also promotes the Ce-O bond to a state of enhanced ionicity, reflecting a significant modification in the bonding nature. These changes are likely driven by the smaller crystal radii and higher electronegativities of Ni and Co compared to those of Ce4+ and Ce3+, thereby encouraging electron transfer toward the Ni and Co sites (Supplementary Fig. 6, 7 and Table 4). The addition of Fe in MnNiCoFe-CeO2 induces a further increase in the binding energy of Ce3+ but no noticeable effect on Ce4+. This shift for Ce3+ is likely due to the higher electronegativity of Fe3+ (1.556, Supplementary Table 4) compared to that of Ce3+ (1.348). Since both of these closely associated ions share the same valence state, this suggests a reason for the fixed valence state of Fe. However, the electronegativity of Ce4+ (Ce4+ = 1.608) is very close to that of Fe3+, confirming that little shift in binding energy for Ce4+ would be expected. In MnNiCoFe-CeO2, the binding energies of Mn, Ni, and Co exhibit lower binding energies, indicating distortions in the TM-O bonds. Therefore, the overall lattice distortion in MnNiCoFe-CeO2 is likely to reflect the cumulative result of distortions occurring in both the Ce-O and TM-O bonds. These shifts also suggest an increase in TM-O bond covalency, underscoring the alteration of the structural order in the HEO relative to that of the less complex solid solutions. The importance of the alteration of the chemical environment and the resultant improvement in charge-transfer phenomena is supported by the multiple charge-transfer permutations between the four TMs and Ce of the HEO, although the Fe shows only one stable valence as confirmed by Supplementary Table 5 and Fig. 8.

The observed improvement in charge-transfer phenomena suggests a corresponding alteration in the electronic structure of HEOs. To gain deeper insights into these changes, quantitative electron paramagnetic resonance (EPR) spectroscopy was employed to investigate the distribution and behavior of unpaired electrons. Variations in signal intensity, lineshapes, and g-factors provide valuable insights into the redistribution of electron density and the nature of electronic interactions within the HEO lattice32,33. The three less-complex solid solutions display multiple low-intensity hyperfine (Supplementary Fig. 9), indicating a limited number of unpaired electrons in the lattice, likely trapped at point defect sites such as oxygen vacancies34. However, MnNiCoFe-CeO2 exhibits a prominent, isolated peak, indicating a significantly higher proportion of unpaired electrons within the HEO in Fig. 2c. Notably, the contributions of the three-dimensional g-factors (gx, gy, gz) become nearly equal32, reflecting a transition to anisotropic and electron-rich environment in the HEO, suggesting a high degree of electronic disorder. The differentiation of the g-factors allows the identification of lattice-localized electrons (g-factor < 2.003) and surface delocalized electrons (g-factor > 2.003)32. The highest peak intensity (g-factor = 2.120) indicates that substantial proportions of the unpaired electrons are surface-delocalized. This delocalization is likely to be a key factor in providing high electronic conductivity, enabling efficient charge transport. The asymmetric EPR signal is indicative of a Dysonian nature, which arises owing to a skin effect and microwave penetration in materials with appreciable electrical conductivity, such as metallic or semimetallic systems35,36. This asymmetry serves as strong evidence that the material has undergone a transition from semiconducting to more conductive behavior associated with a high extent of electronic disorder, which is facilitated by partial reduction, a high concentration of oxygen vacancies, and mixed-valence states. In such systems, unpaired electron spins can become delocalized or interact with conduction electrons, further contributing to the Dysonian response and enhanced signal intensity. The high concentration of delocalized electrons present in the HEO can enable them to interact with reactive species, thereby enhancing the material’s ability to adsorb and desorb oxygen species efficiently. The presence of a high concentration of delocalized electrons is supported further by photoluminescence spectra for MnNiCoFe-CeO2 (Supplementary Fig. 9), which show low recombination extents, which are consistent with high electron mobility and transport, thus representing the delocalized state. The direct evidence for a transformation into an electron-rich environment with high electronic conductivity in the HEO is demonstrated by the 100-fold increase in tunneling current density (from −30 pA in CeO2 to −3 nA at the bias voltage at −1 V), as shown in Fig. 2d. Such high current tunneling in MnNiCoFe-CeO2 indicates highly conductivity and efficient charge transport37. This effectively metallic conductivity, which is attributed to a greatly increased electron mean free path and electronic disorder, also represents optimized electron transfer in the HEO, which provides a crucial advantage for catalytic and electrochemical reactions.

The detailed electronic structure was analyzed further in order to understand the electronic transfer behavior shown in Fig. 2e and Supplementary Figs 10–12. CeO2 shows general semiconducting features, with a band gap of 2.4 eV and work function (WF) of 5.5 eV. Mn-CeO2 shows a band gap slightly reduced to 2.1 eV, without any change to the WF. MnNiCo-CeO2 exhibits a further decrease in the band gap to 1.5 eV, but the WF changes to lower value, accompanied by a downward shift in the position of the d-band center. The position of the d-band center, determined through VB-UPS, is indicative of the material’s tendency to adsorb molecules on transition metal sites during catalytic and electrochemical reactions38. These shifts in both the WF and d-band center suggest slight electronic disorder and rearrangement of the d-band position above the Fermi level, leading to potential benefits in the catalytic processes and air battery performance as they facilitate the respective adsorption and desorption of reactants and products, thus improving overall reaction kinetics. In MnNiCoFe-CeO2, the WF and the d-band center return to their original positions as observed in CeO2. However, an intriguing change is observed in the band gap, which decreases significantly to ~0.75 eV. This reduction indicates a high extent of electronic disorder and a transition towards semimetallic properties39, which directly correlates with the enhanced electronic conductivity. The distinction in band structures for MnNiCo-CeO2 and MnNiCoFe-CeO2 suggests that these materials facilitate different electronic disorder and electrocatalytic reaction mechanisms. In MnNiCo-CeO2, the electronic structure is slightly altered with low d-band position, which can reduce the activation energy for the adsorption of reactive species; in MnNiCoFe-CeO2, the electronic structure is highly disordered by transformation from the original semiconducting to semimetallic properties with enhanced electronic conductivity from the narrow band gap, leading to the promotion of more rapid charge transfer processes.

For an in-depth understanding of the electronic disorder at the atomic scale, the X-ray absorption near-edge structure (XANES) spectra of the Ce L3-edge were examined. The four observed white-line peaks associated with the electronic structure of Ce in CeO2 (5720–5760 eV)40–42 were subjected to Gaussian mode fitting (Fig. 2f, Supplementary Fig. 13, and Supplementary Table 6). Pre-edge peak A is associated with the final states of the Ce 5d orbitals at the bottom of the conduction band. Peak B arises from a dipole-induced transition of Ce 2p electrons to the Ce 4f15d final state, which involves an extra electron in the Ce 4f orbital (associated with Ce3+). Peak C represents charge transfer from the Ce 4f15d final state of Ce to the O 2p orbital of the ligand. Peak D is attributed to a different final state configuration (associated with Ce4+), which is the 4f05d state. The deconvolutions reveal that CeO2 and MnNiCo-CeO2 are similar in that they exhibit the typical local structure of CeO2, as evidenced by the consistency of the integrated peak areas for all four peaks and the greater intensities of peaks C and D relative to those of A and B (Supplementary Table 3). In contrast, the shifts from CeO2 and MnNiCo-CeO2 to MnNiCoFe-CeO2 demonstrate an increase in the integrated B peak area and a decrease in that for peak C. These results for MnNiCoFe-CeO2 are consistent with increasing electron delocalization in the Ce 4f orbital (associated with Ce3+) and decreasing delocalization of the electrons in the O 2p orbital of the ligand. Thus, the increase in the net disorder of the HEO is apparent. On the other hand, Peak D is consistent in its lower intensity for MnNiCoFe-CeO2 relative to those of CeO2 and MnNiCo-CeO2. Since this decrease is consistent with a decrease in [Ce4+] and a complementary increase in [Ce3+] (as shown by with the observed increased B peak area), then the addition of a fifth metal indicates a further increase in electron disorder deriving from the additional charge transfer between Ce and this metal. The inset of Fig. 2f reveals a minor leftward shift in the absorption edge for MnNiCo-CeO2 compared to that of CeO2, indicating that the incorporation of Mn, Ni, and Co induces only a relatively small change in the electron transfer between these metals and Ce and thus the Ce4+ ↔ Ce3+ redox. In contrast, the shift for MnNiCoFe-CeO2 is significantly greater, which again is consistent with increased electron disorder deriving from the additional charge transfer between Ce and the fifth metal.

The observation for the Ce site in XANES contradicts that for the Ce site in the XPS spectra of the HEO. While the peak shifts in XPS suggest electron transfer from Ce toward the TM sites, both the XANES and XPS data indicate an increase in the relative concentration of Ce3+. This seemingly contradictory result can be explained by considering the electronic nature of Ce43. Owing to the delocalized Ce free electrons (as shown by the band structure analysis and CAFM), Ce can donate electrons from the Ce conduction band to both the neighboring transition metals (as shown by XPS data) and the Ce3+ state associated with the 4f electron orbital (as shown by XANES data). Thus, both the electron transfer and increase in [Ce3+] can occur simultaneously. In addition, the large formation of oxygen vacancies provides the necessary charge compensation at the Ce sites, as confirmed by Raman, EPR, and XPS data, further stabilizing the reduced Ce3+ state despite the electron transfer from Ce toward the TMs.

Atomic disorder
Extended X-ray absorption fine structure (EXAFS) results show the local Ce-O bond environment, which can reveal changes at the atomic scale. The phase-uncorrected Fourier transform EXAFS (FT-EXAFS) data for CeO2 (Fig. 2g, Supplementary Fig. 14, and Supplementary Table 7) show that CeO2 exhibits bond lengths of 2.34 Å (Ce-O) and 4.27 Å (Ce-O-Ce), which match those of the cubic structure (2.37 Å and 4.30 Å, respectively), with a coordination number (CN) of 842,44. MnNiCo-CeO2 (Fig. 2g) shows a slight decrease in the respective bond lengths (2.30 Å and 4.21 Å) and a reduction in the CN to 7.47, indicating minor bond and lattice distortion. These changes are likely to be consistent with the formation of individual oxygen vacancies. In contrast, MnNiCoFe-CeO2 (Fig. 2h) six different Ce-O bond lengths (2.19 and 2.24 Å [contracted] and 2.44, 2.53, 2.61, and 2.87 Å [expanded]) and a low CN of 6.10. These significant alterations in the Ce lattice demonstrate the conversion of eight equidistant bonds to six irregularly disordered bonds and a correspondingly significant decrease in the crystal symmetry, which are indicative of significant atomic disorders. The formation of low-CN disordered Ce centers render the Ce sites unsaturated, which can provide empty coordination positions capable of binding reactive molecules such as OH− and O2. This can result because unsaturated sites have an innate tendency to achieve maximal coordination. This phenomenon suggests that low-CN disordered Ce centers can serve as pivotal active sites in electrocatalytic processes, including electrocatalytic OER/ORR reactions in air battery systems. Further, the marked reduction in Ce–O–Ce bond intensity signifies a disruption in the long-range order44,45, suggesting that Ce atoms are randomly dispersed throughout the crystal lattice (as evidenced by element occupancy analysis (Supplementary Table 3 and HR-HAADF atomic-line profiles in Supplementary Fig. 15). This randomness suggests that a high extent of atomic disorder and the resultant active sites are not only in close proximity, but they also are distributed randomly within the lattice, thus having the potential to enhance the overall catalytic performance by providing abundant and readily accessible sites for electrochemical reactions.

The atomic disorder and lattice distortion in Fig. 3a, which reflect structural asymmetry, are indicated by the highly irregular interionic angles. The inter-plane angle along [111] and [100] zone axes in MnNiCoFe-CeO2 are fully disordered, shifting to 52° to 112° from the ideal respective angles of 60° and 90° (Fig. 3b–d)46. This lattice distortion probably derives largely from the mixed substitutional-interstitial solid solubility of all of the transition metal ions in the matrix phase, as revealed by the XRD refinement (Supplementary Table 3 and Fig. 1), ADF-STEM images (Supplementary Fig. 15), and related defect equilibria, the latter of which support the charge-compensation basis for the formation of oxygen vacancies and free electrons (Supplementary Table 8).

In order to assess the impact of the electronic environment induced by the TMs on the atomic disorder and performance of the HEO, linear scans of the electron energy loss spectroscopy (EELS) spectra were done on the TMs within an HEO crystal. Detailed analyses of the atomic surface effects also were done since catalytic reactions occur predominantly at the surface (Fig. 3e–i and Supplementary Fig. 16). The matrix Ce M4,5-edges indicate electron transitions from the Ce 3d3/2 (Ce M4) and Ce 3d5/2 (Ce M5) core levels to the Ce 4f unoccupied electronic states47. From the bulk to the surface, the disappearance of the M5 satellite peaks and the increased M5:M4 intensity ratio indicate a reduction for Ce4+ to Ce3+, implying a high density of surface f-electrons and subsequent surface reactivity47. Further, the positive shift in the M5 peak energy from bulk to surface suggests an altered surface Ce electronic environment. The respective 3d TM (Mn, Ni, Co, and Fe) states exhibit an L3-edge (2p to unoccupied 3d) and an L2-edge (2p to unoccupied 3d), the differences between which were analyzed through the L2,3-edge energy loss difference (ΔE) (Supplementary Tables 9–12)48. Surface-specific ΔE and L2,3-edge shift changes were observed for Mn, Ni, and Fe, indicating enhanced charge-transfer dynamics and modification of the electronic environment (influenced by changes in oxidation state, coordination number, bond length, and associated defect generation)49. In contrast, Co exhibited minimal ΔE variation or L2,3-edge shift changes, suggesting a more passive electronic role, likely contributing to structural and electronic stability within the HEO matrix. The O K-edge (Fig. 3j) reveals distinct peaks (A, B, C) that correspond to electronic hybridization between O 2p states and the unoccupied 3d or 4f states of metals orbitals, while peak D represents the cubic structural framework50. The broadened and partial degeneration of all peaks is consistent with variable extents of atomic disorder from bulk-to-surface.

An in-depth understanding of the electronic structure can be gained by analysis of the projected density of states (PDOS), as shown in Fig. 3k, l. The pristine CeO2 shows generic semiconductor features such that the Ce 4f domain is located on the conduction band; this feature also is identified as the upper Hubbard band (UHB); both of these correspond to the Ce 4f0 to Ce 4f1 electronic transition51. The O 2p domain is located at the valence band with slight Ce 4f-O 2p hybridization, suggesting the strong ionic and weak covalent bonding nature of CeO252. The lower Hubbard band (LHB) is a critical feature used to determine the lowest ionization potential of metal ions. In the case of CeO2, the LHB is observed at a relatively high energy level of approximately −16 eV, indicating a deeply localized electronic state. This positioning suggests that the Ce4+ ions in CeO2 exhibit a strong affinity to retain their electrons, making it energetically unfavorable to adsorb oxygen effectively during catalytic reactions. The MnNiCoFe-CeO2 (Supplementary data 1) exhibits a significantly different electronic behavior compared to pristine CeO2, characterized by the absence of a band gap. This indicates a transition to a semimetallic state, as seen in Fig. 3l. The semimetallic nature of MnNiCoFe-CeO2 is illustrated further by the approximately equal DOS of the TMs near the Fermi energy level (Fig. 3i and Supplementary Fig. 17). This balanced contribution from the TMs near the Fermi level suggests a high density of free electrons, which underpins increased electronic conductivity.

The electron localization function (ELF) and charge density difference plots (Fig. 3m, n and Supplementary Fig. 18) imply the electron densities of atoms. As shown in Fig. 3n, m and Supplementary Figs. 18 and 19, the interactions between the Ce-O bonds and Co, Ni, Fe, and Mn exhibit relatively high electron densities, indicating a clear redistribution of electronic charge from Ce to the TMs. Further, the oxygen ions that bridge the high-CN Ce and TMs show lower electron densities relative to those arising from those that bridge low-CN Ce and TMs. These data again propose the role of the greater amount of charge transfer and resultant increased electronic disorder associated with the low-CN Ce relative to that of the high-CN Ce. It is counter-intuitive for there to be a higher electron density of the low-CN Ce, which would be expected to be lower owing to the under coordination. This apparent contradiction is heightened in light of the differential electronegativities of Ce, where the higher value for a higher Ce4+/Ce3+ ratio of high-CN Ce would be expected to exhibit a higher electron density compared to that for the lower Ce4+/Ce3+ ratio of low-CN Ce. The low-CN Ce would result in highly catalytically reactive sites that would facilitate the adsorption and the subsequent reduction of O2 molecules. The asymmetry of the densities of states of Ce 4f shown in Fig. 3o further supports the critical importance of the alteration of charge transfer and electronic disorder associated with the HEO.

OER/ORR performance and kinetics
A fundamental understanding of the operational mechanism of HEOs in OER (charging) and ORR (discharging) is essential to the design of high-performance and efficient cathodes in ZABs. Figure 4 and Supplementary Fig. 21 show electrocatalysis data for OER and ORR performances, each measured in triplicate to ensure reproducibility, with corresponding error bars included to indicate experimental variability. As shown in Fig. 4a–c and Supplementary Table 13, the OER activity was evaluated using three key metrics: (1) overpotential at 10 mA cm−2 (representing onset OER performance), (2) overpotential at 50 mA cm−2 (reflecting high-rate performance), and (3) Tafel slope (indicating reaction kinetics). Stoichiometric single-phase CeO2 exhibited poor performance, demonstrating inferior onset OER performance, high-rate capability, and sluggish kinetics. In contrast, Mn-CeO2, which forms a dual-phase mineralogy, showed similarly poor onset OER performance but moderately improved high-rate capability and OER kinetics. These data suggest that, while the intrinsic activity is limited, the formation of heterojunctions could enhance charge transport, albeit at the risk of blocking active sites. Further improvement was observed in the homogeneous solid solution catalysts MnNiFe-CeO2 and MnNiCo-CeO2. These systems displayed small onset performance and average high-rate capability and OER kinetics, which are attributed to the introduction of slight structural disorder in the form of point defects and individual charge-compensating oxygen vacancies (which act as additional adsorption sites at low oxygen vacancy concentrations ([V::O])). Additionally, slight electronic disorder (d-band relocation and enhanced charge transfer) was found to optimize the binding energy of the reaction intermediates53, further improving intrinsic activity and reaction kinetics. Importantly, the similar OER preformation between MnNiFe-CeO2 and MnNiCo-CeO2 reveals that the improved OER performance is not due to the presence of only Fe, a known active-site element54, but rather the overall increase in material complexity and disorder. Of all of the catalysts examined, the high-entropy oxide MnNiCoFe-CeO2 demonstrated the most significant enhancement, outperforming even the commercial benchmark IrO2 in onset OER performance, high-rate capability, and OER kinetics. As shown in Supplementary Fig. 20, despite the Ni (common active site in OER as well) in the MnNiCoFe-CeO2 HEO, no distinct Ni oxidation peak was observed during CV or LSV measurements55. This absence indicates that Ni does not serve as an active redox center in the OER process. Instead, it is likely to play a synergistic assisting role, contributing to the modulation of the local electronic environment through MVCT, thereby enhancing overall conductivity and structural stability. This conclusion is supported further by the subsequently presented XANES data and DFT simulations, both of which confirm that Ni does not participate directly in discrete redox transitions under OER conditions but rather supports the activity of the active metal centers.

A similar trend is observed in the ORR performance. Three metrics were used to evaluate the activity: (1) half-wave potential, which reflects the intrinsic ORR activity; (2) diffusion-limited current density, which reflects the mass transport capability; and (3) Tafel slope, which indicates the ORR kinetics from Fig. 4d–f and Supplementary Fig. 22. Pristine CeO2 exhibits inferior ORR activity, with average mass transport and kinetics, consistent with its known limitations as a stoichiometric single-phase material. Mn-CeO2 shows a moderate improvement in ORR activity, although both mass transport and ORR kinetics are reduced. These data suggest that the biphasic system behaves differently in ORR compared to that in OER. The improvement in activity may stem from the presence of Mn3O4 as a secondary phase, which is known to be catalytically active for ORR56,57. Conversely, the declines in mass transport and ORR kinetics likely result from partial blocking of O2 gas access due to surface occlusion. MnNiFe-CeO2 and MnNiCo-CeO2 catalysts display similar average ORR performances, mass transports, and ORR kinetics. These results suggest that these specific dopant combinations produce only incremental effects on the activity. Nevertheless, the presence of slight structural and electronic disorder appears to influence positively the ORR performance, consistent with the benefits observed in the OER process. Notably, the high-entropy oxide MnNiCoFe-CeO2 demonstrates great ORR activity, mass transport, and ORR kinetics. Although it does not match the benchmark performance of commercial Pt/C catalysts in terms of half-wave potential, it achieves comparable mass transport capability and even better ORR kinetics. This further confirms that the great activity and efficiency of MnNiCoFe-CeO2 is not attributable to the simple additive effects of individual metal dopants, as shown in the electron transfer numbers of MnNiCoFe-CeO2 > MnNiCo-CeO2 ≈ MnNiFe-CeO2 > Mn-CeO2 > CeO2 in Supplementary Fig. 23. Instead, it arises from the multilevel disorder, structural, electronic, and atomic, which collectively gives rise to highly active, catalytic sites and improved electronic transport properties.

This enhanced activity in OER and ORR is explained by comparison between the two types of solid solutions. For the example MnNiCo-CeO2, the existence of 0D point defect formation, low dislocation density, and low microstrain equate to a relatively low extent of lattice distortion (structural disorder). MnNiCo-CeO2 exhibited limited-valence-state charge transfer (four permutations – Mn2/3+, Ni2+, Co2+, Ce3/4+), semiconducting behavior (electronic disorder), low [Ce3+], and eightfold Ce coordination (atomic disorder). In contrast, for MnNiCoFe-CeO2, there were 2D defect formation (additional adsorption sites in the form of stacking faults, twin boundaries, and dislocations, which result from the formation of what are likely to be associated oriented oxygen vacancy clusters (high [V::O]) associated with the high [Ce3+]), high dislocation density, and high microstrain. This exhibited enhanced multiple-valence-state charge transfer (sixteen permutations – Mn2/3+, Ni2/3+, Co2/3+, Fe3+ Ce3/4+), semimetallic behavior (thus enhancing electron transport), high [Ce3+], and ~sixfold Ce coordination (which acts as active site).

For further investigation of the electrochemical behavior of MnNiCoFe-CeO2, the Koutecky-Levich curves (Fig. 4g and Supplementary Figs. 24, 25) denote that this HEO system favors a four-electron reduction pathway (the same as Pt/C), with no by-product formation, demonstrating that the HEO has highly efficient electron transfer and adequate binding energies for oxygen atoms. The low electrochemical surface area of MnNiCoFe-CeO2 (Fig. 4h and Supplementary Fig. 26) highlight the necessity of maximal disordering of the structure through alteration of the bond nature to maximize the intrinsic electrocatalytic activity in HEOs. The Nyquist plot (Fig. 4i) reveals low electrical and ionic resistances in MnNiCoFe-CeO2, confirming the catalytic benefits of its semimetallic electrical conductivity and highly disordered lattice. Moreover, the HEO shows stable long-term performance in both OER and ORR. The OER stabilities of CeO2, MnNiCo-CeO2, and MnNiCoFe-CeO2 were evaluated under both low (10 mA cm−2) and high (50 mA cm−2) current densities (Fig. 4j). The CeO2 rapidly lost activity, decreasing by ~40% within ~10 h at 10 mA cm−2, completely losing activity within only ~3 h at 50 mA cm−2, revealing its poor durability under intense operating conditions. MnNiCo-CeO2 exhibited great stability, maintaining ~50% activity for ~24 h at 10 mA cm−2, although it also failed within ~6 h at 50 mA cm−2. In contrast, the MnNiCoFe-CeO2 demonstrated great long-term stability, retaining ~98% of its initial activity for ~50 h at both 10 mA cm−2 and 50 mA cm−2. This high stability is attributed to electronic disorder in the multiple charge-transfer permutations between the Ce and four TMs of the HEO, which have the potential to homogenize the bulk charge transfer and hence electrical conductivity.

More to the point, this homogenization would reduce the differential field and valence effects imposed during the extended mean free path of electron transfer, as suggested in Fig. 2d. More generally, the increased configurational entropy would result in decreased Gibbs free energy and hence chemical stability. These considerations apply to the preceding OER data but also to ORR data, where again the homogeneous nanostructure of HEO outperformed the composite microstructure of benchmark Pt/C (Fig. 4k and Supplementary Fig. 27). This optimized charge transfer and low Gibbs free energy state explain the great long-term stability of the HEO catalyst compared to commercial Pt/C. Although the HEO exhibits a slightly lower electron transfer number than the composite Pt/C, this difference can be attributed to the intrinsic nature of the materials. The Pt/C composite generally possesses higher Gibbs free energy from mixed phases and charge trapping at heterogeneous interfaces, which can compromise long-term electrochemical stability. In contrast, the HEO, as a well-mixed single-phase solid solution, minimizes interfacial charge trapping and provides a more stable energy landscape. The Pt/C composite system shows a higher apparent electron transfer number, likely due to its greater selectivity toward the four-electron ORR pathway.

Active site characteristics
Examination of the stability of the multilevel disorder at different time scales is essential to understand the operational and degradation mechanisms of HEOs during catalytic reactions, as shown in Fig. 5a. The structural stability of the HEO in terms of OER and ORR after activation and extended testing was analyzed by Raman. As shown in Fig. 5b, no additional peaks appeared after activation, indicating that the Ce-O framework remains the dominant active phase. Even after long-term cycling, the Raman spectra remain unchanged, further confirming the high structural stability of the HEO and the absence of TM-containing secondary phase, which are observed commonly to result from TM diffusion, hydroxylation, and/or oxidation58,59. This stabilization is facilitated by the large extent of lattice distortion as a form of stress relief. Further, the relatively small changes in the oxygen defect concentrations in the HEO of <13% (shifting from the initial 51.7 to 45.8–58.2%; Fig. 5) confirm this stability. The electronic stability was assessed by EPR spectroscopy, as shown in Supplementary Fig. 28, where the decreases in the g-values immediately after OER and ORR activation indicate temporary electron localization, probably associated with OH− or O2 adsorption at active sites. However, after long-term cycling, the g-values returned to their original states and no signal splitting was observed, confirming reversible and stable electronic disorder behavior. The atomic stability of the HEO was evaluated by EDS mapping of pristine and post-reaction HEOs (Supplementary Fig. 29). These data confirm the maintenance of elemental homogeneity in the absence of volumetric segregation, thus supporting compositional consistency under operating conditions.

The identification, evolution, and stability of the active sites were examined by ex situ XANES and EXAFS analyses of Mn, Ni, Co, Fe, and Ce at different time stages (initial, post-activation, post-testing, and long-term)60. These data elucidate the oxidation state changes, coordination environment evolution, and role of multication interactions in sustaining catalytic activity and stability. In order to evaluate the behavior of the TMs during catalysis, the Mn, Ni, Co, and Fe K-edges were examined. Both the XANES and EXAFS spectra show only minor variations in Fig. 5c and Supplementary Fig. 30, confirming that the TMs undergo minimal changes under operating conditions. The charge-transfer dynamics revealed by the XANES data allow differentiation of the contributions of the individual TMs to the OER and ORR in Fig. 5c61. Ni and Fe show more positive edge shifts during OER, indicating their greater participation in oxygen evolution. In contrast, Mn and Co exhibit more negative edge shifts during ORR, suggesting their greater involvement in oxygen reduction. These minor yet distinct contributions suggest that Mn and Co act as auxiliary facilitators during ORR, whereas Ni and Fe assist during OER, while Ce is the dominant active center. The EXAFS analysis of the TMs also confirms only subtle modifications in the local coordination environments, indicating that they are not active sites. Detailed inspection of the EXAFS data (Supplementary Fig. 30) reveals that all four TMs experienced small increases in M-O coordination after activation (upward trajectory), consistent with limited oxygen adsorption58,59. Over extended cycling, the first coordination sphere exhibits a slight decrease (downward trajectory, though still above pre-testing levels), which probably reflects the role of individual point defects. In contrast, the second coordination sphere exhibits a slight increase (upward trajectory), which is consistent with modest M-O-M ordering of the lattice after long-term testing58,59.

In the case of Ce, more pronounced spectral shifts in XANES were observed during OER and ORR processes, indicating electron-transfer processes associated with Ce sites, as shown in Fig. 5d. The distinct shift in the Ce L3-edge after OER, compared to that after ORR, suggests that Ce plays fundamentally different roles in the two reactions. The oxidation of Ce active sites is attributed to their direct participation in OER by the Ce3+ → Ce4+ transition, highlighting that OER has a stronger impact on the Ce oxidation state. Such redox transitions likely facilitate Ce-OH bond formation. Both post-testing and long-term stability measurements reveal further oxidation of the Ce sites, indicating that Ce oxidation plays an important role in OER activation. In contrast, the absence of a significant shift after ORR suggests a more passive role, where Ce sites act primarily as adsorption centers for O2 molecules, without notable changes in oxidation state. The data for XANES over long-term cycling confirm that Ce largely retains its original electronic configuration, thus reflecting its high atomic stability.

The local atomic coordination of Ce, which was characterized by EXAFS, further illustrates the distinct behavior of the Ce-O bonds during OER (Fig. 5e) and ORR (Fig. 5f). After OER activation, the disordered Ce-O bond structure is preserved although the overall intensity increases suggest higher Ce coordination while maintaining the bonding types (both ordered Ce-O and disordered Ce-O) of the initial HEO. Increasing the coordination of the Ce is indicative of OH⁻ bonding at the Ce center, confirming the role of Ce as the active site. After 10 h, the Ce-O bonds display a positive shift, which confirms structural alteration and bond elongation, consistent with the upward trajectory observed during stability testing. After long-term OER cycling, the Ce-O bonds return to their initial state, thus retaining the bonding characteristics of the initial HEO and confirming that local structural degradation is not significant under OER conditions. In contrast, Ce active sites behaved differently in ORR. After activation, the ordered Ce-O bonds remain largely unchanged while the intensity of the disordered Ce-O bonds increases, where the latter suggests weak Ce-O₂ interactions that promote O₂ adsorption and reduction, confirming that Ce is the active site for ORR. However, after extended ORR testing and long-term operation, the amount of disordered Ce-O bonds diminishes, thereby increasing the proportion of ordered Ce-O bonds. This effectively decreases the dynamic flexibility of the Ce-O bonds, thus leading to electron localization at the Ce sites and reducing the availability of delocalized electrons required for efficient O₂ adsorption and dissociation during ORR. Together, these findings demonstrate that Ce defect sites act as crucial active centers, playing distinct roles in OER and ORR: in OER, they participate directly through redox cycling and bond reconstruction while, in ORR, they function mainly as adsorption centers.

In order to identify which of the metal constituents are the active sites in the high-entropy oxide, both OER and ORR pathways, each involving four electron transfer steps, were analyzed using first-principles DFT simulations, as shown in Fig. 5g. Optimized surface models were constructed for each metal ion site (Mn, Ni, Co, Fe, Ce), with adsorption energies calculated for all key oxygenic intermediates (*OH, *O, *OOH) along the reaction pathways. Of all the sites, Ce ions exhibited the lowest energy barriers across the reaction steps, suggesting that these are the primary active sites. For Ce, the rate-determining step is the formation of *OOH, with the largest free energy barrier (ΔG) of 1.63 eV. Similar trends were observed for other metal sites but with higher energy barriers for *OOH formation. The calculated overpotentials of Mn, Ni, Co, Fe, and Ce are used to represent the overall OER/ORR activity of these metal ions in Fig. 5h, aligning the dominance of Ce (only 0.4 eV) with the experimental activity trend. These findings suggest the pivotal role of low-CN Ce sites in facilitating both OER and ORR processes, while the other transition metals primarily play supportive roles, as also confirmed by the EXAFS data.

TMs commonly are identified as active sites in OER and ORR reactions62,63. However, in the present work, they have been shown not to serve as the primary active centers. This difference is explained in terms of multilevel disorder engineering in high-entropy oxides. (1) Structural disorder: A large number of oxygen vacancies are formed, and these preferentially localize and cluster around Ce owing to its flexible Ce3+/Ce4+ redox couple and the low energy barrier for vacancy formation. This reduces the likelihood of TM participation in reactions with active oxygen intermediates. (2) Electronic disorder: The semimetallic nature of the HEO, combined with the presence of multiple cations, induces strong electronic disorder (d-band broadening and shifting). This bridging effect suppresses the distinct localized redox activity of individual TMs, thereby reducing any catalytic contribution and, instead, acting primarily as charge-transfer mediators rather than distinct active sites. (3) Atomic disorder: EXAFS analysis shows that, in HEOs, TMs typically are locked into high-CN frameworks with limited distortion. This structural rigidity further reduces their ability to participate directly in catalytic reactions. Together, these factors explain why, unlike in conventional catalysts, the TMs in this HEO system do not act as dominant active sites, with Ce defect centers’ instead playing the primary catalytic role.

Promising Zn-air battery performance
The rechargeable ZAB was assembled by coupling the MnNiCoFe-CeO2 as cathode with a pure Zn plate as an anode (Fig. 6a). The discharge stage of the ZAB was powered by the ORR on the catalyst surface and stripping Zn2+ from the anode, while the cell was charged through the OER coupling with the Zn2+ plating. The battery with MnNiCoFe-CeO2 shows an open circuit voltage of 1.461 V while the one with benchmark Pt/C+IrO2 displays a lower voltage of 1.424 V, as shown in Fig. 6b. The MnNiCoFe-CeO2 ZAB yields a high specific capacity of 739.6 mAh g−1Zn, with a stable discharge plateau of 1.19 V at a current density of 5 mA cm−2 (Fig. 6c). This capacity was calculated according to the consumption of the Zn anode, which was ~90% of the theoretical capacity of Zn (824 mAh g−1), thus verifying the promising performance of the assembled ZAB. The MnNiCoFe-CeO2 ZAB delivers promising peak power density of 162.7 mW cm−2, which is much higher than that of the benchmark IrO2+Pt/C (127.5 mW cm−2), as shown in Fig. 6d. Further, the MnNiCoFe-CeO2 catalyst also displays stable rate capacity, maintaining higher discharge voltages at current densities from 2 mA cm−2 to 40 mA cm−2 and good voltage retention compared to the Pt/C+IrO2 benchmark electrode (Fig. 6e). The resultant chemical stability and catalytic activity of MnNiCoFe-CeO2 supports its cycling stability of the ZABs, exhibiting stable operation over 450 h at a current density of 5 mA cm−2, while the benchmark Pt/C+IrO2 lasts only for <100 h (Fig. 6f). The ZAB also exhibits reduced overpotentials (0.7 vs 1.0 V), with constantly higher discharge plateaux and lower charge voltages (inset of Fig. 6f), demonstrating the promising catalytic performance of MnNiCoFe-CeO2. More importantly, the spike at the end of the stability testing suggests an unknown associated effect on the anode, confirmed by the Zn anode’s being fully corroded after the long-term test, as shown in Supplementary Fig. 31. Thus, a more stable zinc anode could be expected to result in the prolongation of the cycling stability of this type of ZAB. Further examination of the impact of degradation of the cathode was done using XANES and EXAFS analyses, as shown in Supplementary Fig. 32. These data reveal that the electronic configuration and low CN of Ce are stable, so deterioration of the cathode is not the principal cause battery failure. This overall combination of notable performance and long-term stability reveals MnNiCoFe-CeO2 to be the top promising cathode for ZABs, as confirmed in Supplementary Table 15.

These findings of promising performance of MnNiCoFe-CeO2 in ZABs highlight the critical importance of multilevel disorder engineering in HEOs, as shown in Fig. 6g. In the single-phase oxide of minimal disorder, the electrochemical performance is poor. In the dual-phase heterojunction, the electrochemical performance is just slightly enhanced by this effect. In the lower-complexity solid solutions, the degree of structural disorder is limited, where there are (1) isolated point defects and individual charge-compensating oxygen vacancies that provide only a small number of active adsorption sites. The modest lattice distortion helps to maintain a coherent lattice framework with minimal internal strain. Electronic disorder still retains the semiconducting properties, but with d-band relocation’s modifying the binding energy of the reaction intermediates, while the mixed-valence states of the metals enhance charge transfer to a commensurately limited extent. However, the largely unchanged atomic disorder contributes little to catalytic improvement.

In contrast, the highly disordered HEO leverages the board synergy between structural, electronic, and atomic disorders, thereby significantly enhancing the electrocatalytic activity. The structural disorder is manifested as 2D defects; including stacking faults, twin boundaries, and dislocations; which are associated with oxygen vacancy clusters. These defects offer additional adsorption sites while preventing long-range ordering or phase segregation, thereby enhancing single-phase stability during cycling. The electronic disorder is evidenced by semimetallic behavior, which promotes high electronic conductivity and facilitates multivalence charge transfer across sixteen redox permutations (e.g., Mn2+/4+, Ni2+/3+, Co2+/3+, Fe3+, Ce3+/4+), allowing the potential for all cations to contribute cooperatively, as evidenced by the XANES data in Fig. 5c, d. Finally, the atomic disorder introduces a higher fraction of Ce3+ and low-coordination Ce, that latter of which is the active site that enhances the OER/ORR performance further, as shown in Supplementary Table 13, and leads to the promising ZAB performance and stability, as shown in Supplementary Table 15. Further, this multilevel disorder engineering suggests a fundamental roadmap for the design of materials, paving the way for sustainable energy solutions.

Methods
Chemicals and materials
All metal salts [Ce(NO3)3·6H2O (99.00%) and MnCl2, NiCl2, CoCl2, and FeCl3 (99.95%)] as well as NaOH and ethanol (≥99.00%) were from Sigma-Aldrich (Sydney, Australia). Trichloroacetic acid (TCA, Cl3CCOOH, ≥99.00%) was sourced from Chem-Supply Pty Ltd. (Sydney, Australia). Experiments employed a standard three-electrode arrangement: FTO-coated glass served as the working electrode (Wuhan Geao Scientific Education Instrument, Wuhan, China; sheet resistance ~21 Ω square–1), a Pt plate (4 cm2) was used as the counter electrode, and an Ag/AgCl electrode (BASi Inc., Evansville, IN, USA) provided the reference. Before measurements, the FTO electrode was sequentially sonicated in acetone, ethanol, and DI water for 5 min per step.

Synthesis of Ce-CPd precursors
Chronopotentiometric deposition was performed using an electrochemical workstation (EzstatPro; 300 μV potential resolution and 3 nA current resolution in the ±100 μA range) together with the three-electrode configuration described above. Fresh electrolyte was prepared immediately before each experiment by dissolving trichloroacetic acid (0.05 м) and Ce(NO3)3·6H2O (0.05 м) in deionized water and making up the volume to 150 mL. The solution pH was then brought to 6.2±0.1 by titration with 1 M NaOH (pH 14.0±0.1). The electrolyte was transferred to glass bottles and kept at ambient conditions until use. Deposition was conducted galvanostatically at 30 mA over an FTO working area of 15 cm2, which provided uniform films while maintaining a high growth rate.

Synthesis of Ce-CP derived CeO2
To synthesize the CeO2, Ce-CP (300 mg) precursor was dispersed in 300 mL bipolar medium (DI water: ethanol volume ratio: 1:1 v/v) and mixed for 20 min at 400 rpm. The resultant solution was dried at 80 °C in air for 12 h. The NaOH aqueous solution (0.15 м) was added for oxidation and mixed for 5 h. The resultant suspensions were centrifuged at 2800 × g for 10 min, followed by resuspension in DI water and centrifuging additional three times. The samples then were reduction annealed at 400 °C for 4 h in forming gas (5% H2 + 95% Ar; heating rate 3 °C/min). The resultant CeO2 powders were stored in sealed containers prior to characterization and testing.

Synthesis of TMO high-entropy oxide
The TMO-based high entropy oxide was synthesized using an identical procedure to that for CeO2 powders except that the TM salts (8 mol% per each element, metal basis) were added to the solution containing the Ce-CP when the bipolar medium was formed.

Characterization
Powder XRD patterns were recorded using a Philips X Pert multipurpose diffractometer with Cu Kα radiation (45 kV, 40 mA), using a step size of 100.00° in 2θ and a scan rate of 0.2° min−1 (2θ). Diffraction peaks were processed in XPert HighScore Plus. High-resolution TEM (HRTEM), selected-area electron diffraction (SAED), and EDS measurements were carried out on a JEOL JEM-F200 S/TEM operated at 200 kV. Surface morphology and compositional mapping by SEM/EDS were performed using an FEI Nova NanoSEM in both primary and secondary electron imaging modes, with an accelerating voltage of 10–15 kV. ADF-STEM imaging and EELS analyses were conducted on a JEOL JEM-GrandARM 300F2 double aberration-corrected STEM (AC-STEM) operated at 300 kV. ADF-STEM data were recorded using a 200 mm camera length, corresponding to inner and outer collection angles of 32 and 175 mrad, respectively. EELS spectra were acquired using a Gatan GIF Continuum spectrometer equipped with a K3 single electron detector. For EELS acquisition, a 2 cm camera length and a 32 mrad convergence angle were applied, together with an EELS entrance aperture of 108 mrad. The energy resolution was determined from the FWHM of the zero-loss peak (ΔE ZLP = 0.54 eV), and spectra were collected with a dispersion of 0.18 eV per channel. The EELS energy axis was corrected to compensate for ZLP drift and background subtraction was performed using power-law fitting. Raman microspectroscopy was performed on a Renishaw inVia confocal Raman microscope equipped with a helium–neon green laser and a 1800 grooves mm−1 grating. Spectra were collected from 100 to 1500 cm−1 with 1 cm−1 resolution (laser power 35 mW; spot diameter ~2 μm). Data handling used Renishaw WiRE 4.4, and spectral positions were calibrated using the Si band near 520 cm−1. XPS and UPS were acquired on a Thermo Fisher Scientific ESCALAB 250Xi system using a monochromated Al Kα source (1486.6 eV) and a hemispherical analyzer. During measurements, the analysis chamber pressure was maintained below 0.8–1.0 kPa. Binding energies were referenced to the C 1s peak set to 285 eV. Peak fitting employed mixed Gaussian–Lorentzian lineshapes, and spectra were normalized to minimize contributions from adventitious carbon (C 1s at 285–286 eV). Conductive AFM (CAFM) was performed with a Bruker AFM platform. Local current–voltage (I–V) responses were measured using a PtIr-coated conductive probe to assess nanoscale electrical conductivity. X-ray absorption fine structure (XAFS) measurements were collected at the XAFCA beamline (Australian Synchrotron, Melbourne) at the Mn, Ni, Co, and Fe K-edges and the Ce LIII-edge. Post-cycled samples of the Ce LIII-edge XAFS data was carried out using easyXAFS. Spectra were processed in Athena, including linear-combination fitting (LCF), and EXAFS modeling was completed in Artemis (Demeter XAS suite). EXAFS signals were obtained following background removal and normalization, k3-weighting, and fast Fourier transformation (FFT) of the XAS data. mm Photoluminescence (PL) spectra were obtained at room temperature using a Shimadzu RF-5301PC spectrofluorophotometer with 325 nm excitation. EPR measurements were performed on a Bruker EMX X-band ESR spectrometer operating at 9.8 GHz; spectra were recorded with a center field of 3200 mT modulation amplitude of 4 G, and microwave power of 0.6325 mW, and were processed in Bruker Xenon. Diffuse reflectance UV–Vis–NIR spectra were measured using a PerkinElmer Lambda 1050 double-beam spectrophotometer equipped with a triple-detector configuration, across 200–1500 nm. The indirect optical band gap was estimated using the Kubelka–Munk transformation.

Electrochemical oxygen evolution reaction characterization
Catalyst inks were formulated by dispersing 5 mg of the catalyst in 0.5 mL of a 1:1 (v/v) ethanol/DI-water mixture, then adding 25 μL of Nafion solution (Sigma-Aldrich, 99.99%) as a binder. The dispersion was ultrasonicated until fully uniform. The resulting ink was drop-cast onto Teflon-treated carbon-fiber paper (1×1 cm2) to prepare the working electrode, giving a mass loading of 0.5 mg cm−2. A 1.0 м KOH electrolyte (pH 14.0±0.1) was prepared by dissolving 28.06 g KOH in deionized water and diluting to 0.50 L in a volumetric flask; the solution was stored in a PTFE bottle at 25 °C. Electrochemical measurements were carried out in this electrolyte using a three-electrode configuration comprised of the catalyst-coated carbon paper working electrode, a graphite rod counter electrode, and a Hg/HgO reference electrode. The Hg/HgO reference was calibrated against a reversible hydrogen electrode (RHE) in 1.0 м KOH using a Pt wire working electrode under hydrogen-saturated conditions (high-purity H2). All experiments were conducted at 25 °C and ambient pressure with a CHI 760E electrochemical workstation. Measured potentials were corrected for ohmic losses using 85% IR compensation and are reported versus RHE, calculated according to: E RHE (V) = E Hg/HgO (V) + 0.098 + 0.059 × pH. Cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) were performed in the same 1.0 M KOH solution. EIS spectra were recorded at 1.3 V vs RHE from 100 kHz to 0.1 Hz using a 10 mV a.c. amplitude, and the solution resistance was obtained from impedance analysis. The electrochemically active surface area (ECSA) was estimated from the double-layer capacitance (C dl) by collecting CVs in a non-Faradaic potential window (0.98–1.08 V vs RHE) at several scan rates; C dl was taken from the slope of capacitive current versus scan rate. ECSA was then calculated using. ECSA = C dl / C s, with a specific capacitance C s = 60 μF cm−2. Durability toward OER was assessed galvanostatically in 1.0 м KOH for 50 h at two current densities (10 and 50 mA cm−2).

Electrochemical oxygen reduction reaction characterization
The electrolyte 0.1 м KOH (pH = 13.0±0.1) was prepared by dissolving 5.61 g KOH pellets in deionized water, diluting to 1 L in a volumetric flask, thoroughly mixing, transferring to a PTFE bottle, and storing at 25 °C. Test electrodes were prepared by drop-casting 10 μL of an ink made by ultrasonically blending 2.5 mg catalyst, 2.5 mg Ketjen Black 300J, 50 μL 5 wt% Nafion, and 950 μL isopropanol, giving 25 μg catalyst per electrode (loading = 0.2 mg cm⁻²) on a polished glassy carbon rotating disk electrode (RDE, Pine Research Instrumentation) or a rotating ring-disk electrode (RRDE, Pine Research Instrumentation) followed by drying in air (geometric area, A = 0.125 cm2). Electrochemical measurements were performed, collected, and analyzed in a standard three-compartment cell (0.1 M KOH in all compartments) on a CHI 760E workstation using a glassy carbon working electrode, a graphite rod counter electrode, and a Hg/HgO reference electrode; data were acquired with the CHI software and processed offline. The Hg/HgO reference was calibrated vs RHE in H₂-saturated 0.1 м KOH at 25 °C using a Pt wire, and all potentials were IR-compensated at 85% and converted to the RHE scale using E RHE (V) = E Hg/HgO (V) + 0.098 + 0.059 × pH. The solution resistance was determined through EIS analysis. CV tests were conducted in nitrogen- and oxygen-saturated 0.1 м KOH electrolyte at room temperature, which assessed the catalytic properties of the materials. The tests employed a scan rate of 50 mV/s within a voltage range of 0.05 to 1.1 V. Linear sweep voltammetry (LSV) curves were obtained in an oxygen-saturated 0.1 м KOH solution, which was tested at a sweep rate of 5 mV/s and various rotation speeds in the range 400-2500 rpm. In order to ensure that the electrolyte was fully saturated with oxygen, pure oxygen (99.999%) was bubbled into the solutions for 20 minutes before each measurement, with the flow’s continuing during testing. The hydrogen peroxide yield (HO2%) was calculated as follows: H2O2% = 200 Ir / N |Id| + Ir, where N is the current collection efficiency of the Pt ring (37%), Ir is the ring current, and Id is the disk current of the rotating-ring disk electrode (RRDE). The electron transfer number, n, was calculated as follows: n = 4 |Id| / (|Id| + (Ir/N)). Chronoamperometry (CA) was applied in order to assess the durability of the different catalysts toward ORR in 0.1 м KOH O2-saturated electrolyte at the potential of 0.7 V.

Zn-air battery assembly
All ZAB measurements were performed using a custom-made flow-type Zn–air cell, in which the catholyte was continuously circulated through the battery chamber (cell structure illustrated in Fig. 6a). The zinc anode consisted of commercial zinc foil with a thickness of 50 μm. The foil was cut into circular disks with a diameter of 15 mm, followed by ultrasonic cleaning in a mixed ethanol/acetone solution for 20 min. After cleaning, the zinc foil was wiped with a dust-free cloth and air-dried prior to use. The Zn-air batteries were assembled in the form of a flow-type cell with a Zn foil (1 cm2) as the anode, active-material-loaded carbon paper as the cathode, and a mixture of 0.2 M Zn(Ac)2 (zinc acetate) and 6 м KOH as the electrolyte. Glass fiber separators (Whatman) were employed and cut into circular disks with a diameter of 18 mm before assembly. The cathode was prepared by spraying the active material dispersion using a spray gun onto the hydrophobic carbon paper (12 mm diameter). The dispersion was prepared by mixing 5 mg HEO and 5 mg carbon black with 100 μL Nafion (5%) in 2 mL methanol. The comparison electrode was prepared through the same process using commercial Pt/C+IrO2 as the active material. The dispersion was prepared by mixing 5 mg HEO and 5 mg carbon black with 100 μL Nafion (5%) in 2 mL methanol. The comparison electrode was prepared through the same process using commercial IrO2+Pt/C as the active material. The airflow was controlled by a mass flow controller (MFC). The flow rate was kept at 20 sccm. The catholyte was pumped through a peristaltic pump with a flow rate of ~30 ml/min. Compressed air was directly supplied to the cathode and regulated through the connection of the MFC. During the tests, the electrolyte was pumped continuously into the cell to ensure the smooth flow of the electrolytes in the compartments. The cathode compartment has an opening (1 cm2) connected to an oxygen tank to allow the oxygen to flow to the cathode. All ZAB tests were conducted at room temperature (~23 °C) under ambient laboratory conditions, with a relative humidity of ~40%.

Spin-polarized density functional theory
First-principles calculations based on density functional theory (DFT)64 were carried out using the PBEsol exchange-correlation energy functional65 as this is implemented in the VASP software66. The projector-augmented wave (PAW) method67 was employed to represent the ionic cores by considering the following electronic states as valence: Ce 5p, 6s, 5d, 4f; Co 4s, 3d; Fe 4s, 3d; Mn 4s, 3d; Ni 4s, 3d; O 2s, 2p. An energy cutoff of 650 eV and dense Monkhorst-Pack k-point grids, equivalent to 12×12×12 for the cubic fluorite unit cell containing 12 atoms, were used for integrations within the Brillouin zone, leading to total energies converged to within less than 1 meV per atom. Atomic relaxations were concluded when the forces in all of the atoms were below 0.005 eV/Å. The supercells employed for the simulation of CeO2 and MnNiCoFe-CeO2 surfaces included a large vacuum region of 25 Å height and a similar region of materials layers. In particular, the (111), (110), (400), (221), and (331) surface supercells contained respective totals of 243, 192, 216, 156, and 120 atoms. The Hubbard-U scheme, from to Dudarev et al.68–70 was employed in the PBEsol calculations for treatment of the Ni, Fe, Co, and Mn d electrons and of the Ce f electrons, adopting respective U values of 4, 4, 4, 4, and 3 eV68–70. The chemically disordered systems were simulated by generating up to ten different configurations and performing averages over them. The surface formation energy, E surf, was estimated using the formula: E surf = (E DFT − N*E bulk) / 2*S, where E DFT is the energy of the slab supercell directly obtained from the DFT calculations, E bulk is the energy per formula unit of the corresponding bulk system, N is the number of formula units in the surface supercell, and S is the area of the surface supercell perpendicular to the vacuum direction.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors present Ce-based High Entropy Oxides (HEOs) as bifunctional electrocatalysts for rechargeable Zn-air batteries. They elucidate the role of transition metals and the underlying reaction mechanisms of HEOs. The HEOs exhibit outstanding OER/ORR performance and excellent stability, thereby enabling the development of long-cycle, high-voltage, and high-power Zn-air batteries. However, we recommend publishing this manuscript after the following issues are adequately addressed.\n1.Data confirming that the catalyst has the composition Mn₀.₀₆Ni₀.₀₆Co₀.₀₆Fe₀.₀₆Ce₀.₇₆O₂ should be provided.\n2.What is the effect of altering the sequence of transition metal (TM) incorporation? Does the order of TM addition influence the catalytic properties?\n3.In Supplementary Fig. 4, what are the reasons that the binding energy of Ce⁴⁺ does not decrease after the incorporation of Fe in the XPS data?\n4.In Fig. 2f, evidence is required to support the origin of the observed peaks.\n5.In Fig. 2f, is peak B a shifted version of peak C? It is difficult to identify peaks C and D in the red line, and peak E is significantly decreased. Does the introduction of Fe suppress electron and charge transfer with Ce⁴⁺?\n6.Typo : Lines 339-348 (Fig.5 à Fig.3)\n7.In Fig. 3m and Supplementary Fig. 15a, it is difficult to understand the interactions and bonding among the elements.\n8.How does the OER stability of the catalyst compare to that of other catalysts? (Fig. 4j)\n9.Despite showing a lower electron transfer number, why does MnNiCoFe-CeO₂ exhibit higher stability compared to the commercial 20 wt% Pt/C catalyst? (Fig. 4g, k, Supplementary Fig. 17c, d)\n10.In Fig. 4k, is the retention value of Pt/C (58.7%) accurately represented?\n11.Typo : Supplementary Fig.19 (a), (b)\n12.In the OER/ORR tests, the catalytic mechanism is explained based on the interaction between Ce and O. How do the reactions and bonding behaviors of the other transition metals proceed during the OER/ORR tests? (Fig. 5 b, c, d)", "reviewer_2": "In this work, the author's team pioneered the engineering in multi-level disorder and formation of a new type of HEO, transforming essentially inactive matrices into highly active cathodes, generating bifunctional (OER/ORR) and stable metal active sites. The research content of this work is relatively novel. The work of designing structural/electronic disorder in HEO is conducive to establishing a new transformation path for catalysts in battery design. However, major revisions are still needed before the manuscript is published, as follows:\n1. The synthesis and research of high-entropy catalysts and their applications in batteries have been extensive. What is the most significant innovation of this work compared to others? To enhance readers' cognition and reading, the abstract part should focus on highlighting the high-entropy oxides of this work rather than introducing them briefly.\n2. What is the most serious challenge that high-entropy oxides are currently facing in the field of catalysis? What key problems have been successfully solved by the synthesized MnNiCoFe-CeO2 catalyst? The summary of the content in the introduction part is not in-depth and comprehensive enough and needs to be adjusted.\n3. What is the proportion of metal atoms in the high-entropy oxide MnNiCoFe-CeO2 and can it be precisely regulated? What is the combination mode of the five metal elements and what roles do they each play in ORR/OER?\n4. What is the chemical state of the metal in MnNiCoFe-CeO2? Metal, chloride, or oxide? Why do Mn, Ni and Co all have multiple valence states in the catalyst, while Fe has only one valence state? Do different valence states have an impact on the catalytic effect?\n5. The catalytic mechanism of high-entropy oxides is the highlight and attractive part of this article. It is suggested that the author elaborate on the mechanism part separately. By conducting in-depth studies on the conversion disorder characteristics of the MnNiCoFe-CeO2 catalyst and the reasons for achieving excellent performance in ORR/OER, the catalytic mechanism is further revealed.\n6. It is suggested that the structure and performance of the MnNiCoFe-CeO2 catalyst after operation be characterized to prove its stability.\n7. Battery performance as a proof of concept is best listed separately rather than mixed with catalytic performance comparison and reaction mechanisms. Such thinking logic is not conducive to readers' understanding.\n8. There are many errors in format, description and language in the manuscript. For example, the format of the upper and lower annotations, the font, the interval, the type of concatenator, etc. Also, in lines 339, 341 and 348, it should be Figure 3 instead of Figure 5, and in line 527, it should be Pt instead of Pr. There are many similar problems in the manuscript, as well as language issues. The author needs to correct and revise the entire manuscript.", "reviewer_3": "In this work, Zhang et al. reported a bifunctional catalyst of MnNiCoFe-CeO2 for ORR and OER. They added the Fe atoms to adjust the electronic properties of Ce atoms and the Ni, Co and Mn atoms to induce the lattice distortion and point defect. As a result, the charge and discharge process in ZAB with HEO as the catalysts were optimized. Multiple characterizations were employed to elucidate the detailed structure of catalyst. However, in my opinion, there are numerous issues need to be addressed in the manuscript, particularly the presence of many vague expressions and conclusions lacking the convincing evidences. Furthermore, the OER/ORR performance is also unsatisfactory. Below are my specific comments:\n1. Based on the characterizations in Fig. S1b, many small-sized high-entropy nanocrystals (~4 nm) exist on the surface of the nanosphere. However, no clear lattice can be observed on the core of the nanosphere, can the authors give some evidences to claim the species of the core? In addition, the authors should explain the detailed method for calculating the dislocation density and microstrain from XRD patterns. Moreover, the Raman peak at nearly 605 cm-1 is attributed to O vacancy rather than lattice distortion in Fig. S3 (J. Phys. Chem. C, 2012, 116, 10009-10016), and this value (51.7%) is inconsistent with the O vacancy ratio (85%) detected by XPS in Fig. 2a.\n2. The authors proposed that lattice distortion in HEOs originates from \"substitution-interstitial solid solution with uniform mixing of transition metal ions\", but relies solely on ADF-STEM images (Fig.S12) and Table 3, lacking quantitative analysis (such as lattice parameter refinement and element occupancy analysis). It is suggested to perform the XRD refinement to verify the lattice distortion and the specific O vacancy content.\n3. According to the authors' description and XPS results, the electrons on Ce sites are transferred to Ni and Co sites, thus the valence states of Ce in MnNiCoFe-CeO2 should be higher than CeO2. However, as shown in Fig.2f, the white line peak position of MnNiCoFe-CeO2 is lower than that of CeO2, indicating the decreased valence state of the former. These two conclusions are contradictory. In addition, the EPR signal of O vacancy in Fig.2c is weird, as it should be a symmetric pattern (Nat. Commun. 2023, 14, 1412). Moreover, the detailed EXAFS fitting parameters in Fig.2g and 2h should be provided.\n4. The conclusion derived from the EELS in Fig.3a-3j is not convincing. It is not reasonable to directly judge the bond length change using the ΔE because that ΔE is also influenced by other factors including valence state and coordination number. The authors can use the DFT to simulate the theoretic EELS spectrum and compare it with the experimental result to validate it (Phys. Rev. B, 2020, 101, 165112; ACS Catal., 2019, 9, 10031).\n5. I would suggest the authors to repeat the OER and ORR activity tests for 3 times and add the error bars on the corresponding LSVs. In addition, since the MnNiCoFe-CeO2 catalyst consists of the Ni species, a Ni oxidation peak should be observed on the LSV, while it is not presented in Fig.4a. The curves of limiting diffusion currents for MnNiCo-CeO2, Mn-CeO2 in Fig.4d are abnormal. In addition, why the OER stability curve in Fig.3j shows an upward tendency at nearly 13h? is this a signal that the catalyst will undergo the reconstruction during the OER? Therefore, I think the authors should conduct the CV to activate the MnNiCoFe-CeO2 before testing its performance, and this also can explain the disappearance of Ni oxidation peak in Fig.4a. In addition, both the OER/ORR activity and stability of this catalyst are unsatisfactory compared with the reported values in the literature.\n6. The authors concluded that Ce atoms are the true active sites for both OER and ORR, while Ni, Fe, Co and Mn act as the co-catalysts. I have some concerns on this conclusion. On the one hand, Ni and Co are widely recognized as reaction sites for OER, and Mn is also an active site for ORR. It is unlikely that they can only modify the electronic structure of Ce during the reaction. On the other hand, since the authors only conducted XAS on Ce before and after the reaction, the provided evidence is insufficient. I would suggest that the authors supplement with in-situ XAS experiments for all elements including Ni, Mn, Fe, and Co, and perform DFT calculations to determine the reaction free energy of each site, thereby accurately identifying the true active sites.\n7. Some mistakes should be noticed. For example, the scale bar should be added to Fig.1h, the atomic orbitals in the manuscript such as 3d, 2p should be italicized, many punctuations are forgotten or misused. The authors should carefully review and check the manuscript again."}, "author_response": "Manuscript ID: NCOMMS-24-49259A-Z\nTransforming Disorder in the Design of Advanced High-Entropy Oxide Electrocatalysts for Zinc-Air\nBatteries\nXiaoran Zheng et al.\nThank the reviewers for the comments made in response to the abovenamed manuscript. We attach our\npoint-by-point responses to the comments; additional characterisation and application tests have been\ndone accordingly. All textual modifications are given in the responses, and they are highlighted in this\ndocument and the revised text. The paper format, including references, has been adapted to the journal\nstyle.\nGeneral: The authors present Ce-based High Entropy Oxides (HEOs) as bifunctional\nelectrocatalysts for rechargeable Zn-air batteries. They elucidate the role of transition\nmetals and the underlying reaction mechanisms of HEOs. The HEOs exhibit outstanding\nOER/ORR performance and excellent stability, thereby enabling the development of\nlong-cycle, high-voltage, and high-power Zn-air batteries. However, we recommend\npublishing this manuscript after the following issues are adequately addressed.\nResponse: The authors thank the reviewer for the positive comments.\nComment 1: Data confirming that the catalyst has the composition Mn₀.₀₆Ni₀.₀₆Co₀.₀₆Fe₀.₀₆Ce₀.₇₆O₂\nshould be provided.\nResponse: We have performed quantitative STEM-EDS analysis on the as-synthesized sample. A\ncorresponding paragraph detailing the observed deviation from the nominal composition,\nhas been added to the revised manuscript. The additional texts (Manuscript Page 3 and\nSupplementary Information Page 7) and table (Supplementary Information Page 7) have\nbeen added.\nManuscript Page 3:\nA Ce-based coordination polymer Ce(TCA) (OH) ·2H O (Ce-CP) and different 3d-TM salts were\n2 2 2\ndissolved in a polar aqueous ethanol solution to yield nanospheres of the nominal composition\nMn Ni Co Fe Ce O , as confirmed by Supplementary Table 1.\n0.035 0.035 0.035 0.035 0.860 2\nSupplementary Information Page 7:\nSupplementary Table 1 Quantitative STEM-EDS data for high-entropy oxide\nCe Mn Ni Co Fe\nEDS Spot 1 86.23 3.46 3.41 3.40 3.50\nEDS Spot 2 85.75 3.62 3.54 3.41 3.68\nEDS Spot 3 86.14 3.40 3.47 3.46 3.53\n86.04 3.49 3.47 3.46 3.54\nAveragea\n(±0.26) (±0.11) (±0.07) (±0.06) (±0.04)\nTheoretical\n0.7600 0.0600 0.0600 0.0600 0.0600\nRatio\nExperimental\n0.8600 0.0350 0.0350 0.0350 0.0350\nRatio\na (Standard deviation)\nThe discrepancy between the theoretical and experimental ratio is likely to originate in (1) incomplete\nsolubilization, (2) differential precipitation, and/or (3) preferential leaching during washing.\nComment 2: What is the effect of altering the sequence of transition metal (TM) incorporation? Does\nthe order of TM addition influence the catalytic properties?\nResponse: In order to evaluate any effects of the sequence of addition of transition metal (TM)\nincorporation, MnNiFe-CeO was synthesized and tested for its OER and ORR\n2\nperformance. The corresponding results and discussion have been added in the revised\nmanuscript. Two sections of additional text have been added. (1) The first section gives\nthe rationale for the selection of the different compositional permutations, The additional\ntext (Supplementary Information Page 6) has been added. (2) The second section\ndiscusses the effects of these permutations on the properties. The additional text\n2\n(Manuscript Pages 14-17) has been added. The additional table (Supplementary\nInformation Page 34) and image (Supplementary Information Page 37) have been added:\nSupplementary Information Page 6:\nExperimental design\nConcerning the rationale for the selection of the different permutations of compositions, it is clear that,\nwith four TMs and Ce, there are four compositions for metal + Ce, sixteen compositions for 2 TMs +\nCe, 3 compositions for 3 TMs + Ce, and 1 composition for 4 TMs + Ce. This gives a total number of\n24 possible compositions. This large number was reduced in light of the following:\n• 4 Permutations of TM + Ce: There are many publications for all four metals8 (Mn9-11, Ni12-14,\nCo15-17, Fe18-20) but only biphasic Mn-CeO exhibits promising ORR performance, so only this\n2\ncomposition was examined.\n• 16 Permutations of 2 TMs + Ce: There are many publications for these largely biphasic\ncompositions8,21-26, but none exhibits outstanding OER/ORR performance, so none of these\ncompositions was examined.\n• 3 Permutations of 3 TMs + Ce: There is a limited number of publications for these homogenous\nsolid-solution compositions, but NiCoFe-CeO is reported to focus on water splitting 27,28, so\n2\nonly MnNiFe-CeO and MnNiCo-CeO were examined.\n2 2\n• 1 Permutation of 4 TMs + Ce: This homogeneous MnNiCoFe-CeO solid solution composition\n2\nis the focal point of the present work.\n2 3 4 2\n(2021).\n2 2 2\nCathode Catalyst for Passive Direct Methanol Fuel Cells. Appl. Catal. A General, 627, 118378\n(2021).\nElectrocatalytic Oxygen Evolution Activity. Sci. Adv., 9, eadh1320 (2023).\n2\nthe Electrocatalytic Oxygen Evolution Reaction: Embedded or Surface-Loaded. Adv. Funct.\nMater., 28, 1706056 (2018).\n2\nthe O-H Bond Length of Adsorbed Water at the Electrolyte/Electrode Interface.\nChemSusChem, 16, e202300348 (2023).\nCo) on CeO -rGO for Boosting Electrocatalytic Oxygen Evolution Reaction. Chemosphere,\n2\n341, 140012 (2023).\nInterfaces, 13, 46998-47009 (2021).\n3 4 2\nOxygen Evolution Catalysis in Acid. Nat. Comm., 12, 3036 (2021).\n2 2\nReduction over Fe-Doped CeO . ACS Sustain. Chem. Eng., 11, 15609-15619 (2023).\n2\n3\n2 3 2\nComposite as Novel Heterogeneous Electro-Fenton Catalyst. Che. Engineer. J., 428, 131403\n(2022)\nCeria for Efficient Electrocatalyst Based Water Splitting. Nanoscale Adv., 6, 4672-4682 (2024).\n2-x\nHigh-Valence Ni for Efficient Water Oxidation. Adv. Energy Mater., 11, 2002731 (2021).\nDoped CeO (111). Catalysis Today, 293-294, 82-88 (2017).\n2\nOmega, 8, 30802-30823 (2023).\nInterfacial Oxygen Vacancies for Enhanced Overall Water Splitting. Inter. J. Hydrogen Energy,\n82, 311-319 (2024).\nOxysulfide/Cerium Oxide with Strong Electronic Communication to Boost Water/Simulated\nSeawater Splitting. Science of The Total Environment 976, 179330 (2025).\nManuscript Pages 14-16:\nAs shown in Fig. 4a-c and Supplementary Table 13, the OER activity was evaluated using three key\nmetrics: (1) overpotential at 10 mA cm-2 (representing onset OER performance), (2) overpotential at\n50 mA cm-2 (reflecting high-rate performance), and (3) Tafel slope (indicating reaction kinetics).\nStoichiometric single-phase CeO exhibited poor performance, demonstrating inferior onset OER\n2\nperformance, high-rate capability, and sluggish kinetics. In contrast, Mn-CeO , which forms a dual-\n2\nphase mineralogy, showed similarly poor onset OER performance but moderately improved high-rate\ncapability and OER kinetics. These data suggest that, while the intrinsic activity is limited, the\nformation of heterojunctions could enhance charge transport, albeit at the risk of blocking active sites.\nFurther improvement was observed in the homogeneous solid solution catalysts MnNiFe-CeO and\n2\nand OER kinetics, which are attributed to the introduction of slight structural disorder in the form of\npoint defects and individual charge-compensating oxygen vacancies (which act as additional adsorption\nsites at low oxygen vacancy concentrations ([V••]). Additionally, slight electronic disorder (d-band\nO\nrelocation and enhanced charge transfer) was found to optimize the binding energy of the reaction\nintermediates54, further improving intrinsic activity and reaction kinetics. Importantly, the similar OER\npreformation between MnNiFe-CeO and MnNiCo-CeO reveals that the improved OER performance\n2 2\nis not due to the presence of only Fe, a known active-site element55, but rather the overall increase in\nmaterial complexity and disorder. Of all of the catalysts examined, the high-entropy oxide MnNiCoFe-\nCeO demonstrated the most significant enhancement, outperforming even the commercial benchmark\ndoes not serve as an active redox center in the OER process. Instead, it is likely to play a synergistic\nassisting role, contributing to the modulation of the local electronic environment through MVCT,\nthereby enhancing overall conductivity and structural stability. This conclusion is supported further by\nthe subsequently presented XANES data and DFT simulations, both of which confirm that Ni does not\nparticipate directly in discrete redox transitions under OER conditions but rather supports the activity\nof the active metal centers.\nA similar trend is observed in the ORR performance. Three metrics were used to evaluate the\nactivity: (1) half-wave potential, which reflects the intrinsic ORR activity; (2) diffusion-limited current\ndensity, which reflects the mass transport capability; and (3) Tafel slope, which indicates the ORR\n4\nkinetics from Figs. 4d-f and Supplementary Fig. 21. Pristine CeO exhibits inferior ORR activity, with\n2\naverage mass transport and kinetics, consistent with its known limitations as a stoichiometric single-\nphase material. Mn-CeO shows a moderate improvement in ORR activity, although both mass\n2\ntransport and ORR kinetics are reduced. These data suggest that the biphasic system behaves differently\nin ORR compared to that in OER. The improvement in activity may stem from the presence of Mn O\n3 4\nas a secondary phase, which is known to be catalytically active for ORR 57,58. Conversely, the declines\nin mass transport and ORR kinetics likely result from partial blocking of O gas access due to surface\n2\nocclusion. MnNiFe-CeO and MnNiCo-CeO catalysts display similar average ORR performances,\n2 2\nmass transports, and ORR kinetics. These results suggest that these specific dopant combinations\nproduce only incremental effects on the activity. Nevertheless, the presence of slight structural and\nelectronic disorder appears to influence positively the ORR performance, consistent with the benefits\nobserved in the OER process. Notably, the high-entropy oxide MnNiCoFe-CeO demonstrates superior\nperformance of commercial Pt/C catalysts in terms of half-wave potential, it achieves comparable mass\ntransport capability and even better ORR kinetics. This further confirms that the superior activity and\nefficiency of MnNiCoFe-CeO is not attributable to the simple additive effects of individual metal\n2\ndopants, as shown in the electron transfer numbers of MnNiCoFe-CeO > MnNiCo-CeO ≈ MnNiFe-\n2 2\nCeO > Mn-CeO > CeO in Supplementary Fig. 22. Instead, it arises from the multilevel disorder,\n2 2 2\nstructural, electronic, and atomic, which collectively gives rise to new, highly active, catalytic sites and\nimproved electronic transport properties.\nThis superior activity in OER and ORR is explained by comparison between the two types of solid\nsolutions. For the example MnNiCo-CeO , the existence of 0D point defect formation, low dislocation\n2\ndensity, and low microstrain equate to a relatively low extent of lattice distortion (structural disorder).\nMnNiCo-CeO exhibited limited-valence-state charge transfer (four permutations – Mn2/3+, Ni2+, Co2+,\n(atomic disorder). In contrast, for MnNiCoFe-CeO , there were 2D defect formation (additional\n2\nadsorption sites in the form of stacking faults, twin boundaries, and dislocations, which result from the\nformation of what are likely to be associated oriented oxygen vacancy clusters (high [V••]) associated\nO\nwith the high [Ce3+]), high dislocation density, and high microstrain. This exhibited enhanced multiple-\nvalence-state charge transfer (sixteen permutations – Mn2/3+, Ni2/3+, Co2/3+, Fe3+ Ce3/4+), semimetallic\nbehaviour (thus enhancing electron transport), high [Ce3+], and ~sixfold Ce coordination (which acts as\na new type of active site).\nOER Activity of Ni and Co Based Catalysts. Nano Energy, 80, 105514 (2021).\nStructures, Performance, and In Situ Characterization Methods. DeCarbon, 7, 100097 (2025).\nby Coupling MnO/Mn O Composite Materials with N-Doped Carbon. ACS Sustain. Chem. &\n3 4\nEngineer., 12, 8425-8435 (2024).\n3 4\nGraphene Electrocatalyst for Efficient Oxygen Reduction Reaction in Alkaline Media. J.\nMater. Chem. A, 2, 14493-14501 (2014).\nSupplementary Table 13 Comparisons of OER and ORR activities\nOverpotential Overpotential\nComparative Comparative Tafel slope Comparative\nDescription OER Samples at 10 mA cm-2 at 50 mA cm-2\nvalue value (mV·dec-2) value\n(mV) (mV)\nStandard Commercial IrO 360 Superior 559 Average 135 Inferior\nSolid-solution 2\nMnNiCo-CeO 365 Superior 421 Average 76 Average\nHalfwave Comparative Comparative Tafel slope Comparative\nDescription ORR Samples density (mA\npotential (V) value value (mV·dec-2) value\ncm-2)\nStandard Commercial Pt/C 0.81 Superior -4.70 Superior 208 Inferior\nSingle-phase CeO 0.65 Inferior -2.98 Average 90 Average\nSolid-solution 2\nMnNiCo-CeO 0.69 Average -3.30 Average 96 Average\n2\nSupplementary Fig. 22 Electron transfer plots\nComment 3: In Supplementary Fig. 4, what are the reasons that the binding energy of Ce⁴⁺ does not\ndecrease after the incorporation of Fe in the XPS data?\nResponse: Concerning the effect of Fe, the additional text (Manuscript Page 7) has been added.\nManuscript Page 7:\nThe addition of Fe in MnNiCoFe-CeO induces a further increase in the binding energy of Ce3+ but no\n2\nnoticeable effect on Ce4+. This shift for Ce3+ is likely due to the higher electronegativity of Fe3+ (1.556,\nSupplementary Table 4) compared to that of Ce3+ (1.348). Since both of these closely associated ions\nshare the same valence state, this suggests a reason for the fixed valence state of Fe. However, the\nelectronegativity of Ce4+ (Ce4+ = 1.608) is very close to that of Fe3+, confirming that little shift in binding\nenergy for Ce4+ would be expected.\nComment 4: In Fig. 2f, evidence is required to support the origin of the observed peaks.\nComment 5: In Fig. 2f, is peak B a shifted version of peak C? It is difficult to identify peaks C and D\nin the red line, and peak E is significantly decreased. Does the introduction of Fe suppress\nelectron and charge transfer with Ce⁴⁺?\nResponse: In response to Comments 4 and 5, (1) the XANES data now have been analyzed using\npeak fitting based on a Gaussian model, as implemented in the Athena software. has been\nadded. This deconvolution has resulted in re-assessment of the XANES peaks, which are\nenlarged for clarity. The additional text (Manuscript Page 9), image and (Supplementary\nInformation Page 24) and table (Supplementary Information Page 24) have been added.\n(2) For addressing the effect of introduction of fifth metal (Fe), the additional text\n(Manuscript Page 10) has been added.\n(7)\nManuscript Pages 9-10:\nThe four observed white-line peaks associated with the electronic structure of Ce in CeO (5720-5760\n2\neV) 41-43 were subjected to Gaussian mode fitting (Fig. 2f, Supplementary Fig. 13, and Supplementary\nTable 6). Pre-edge peak A is associated with the final states of the Ce 5d orbitals at the bottom of the\nconduction band. Peak B arises from a dipole-induced transition of Ce 2p electrons to the Ce 4f 15d\nfinal state, which involves an extra electron in the Ce 4f orbital (associated with Ce3+). Peak C\nrepresents charge transfer from the Ce 4f 15d final state of Ce to the O 2p orbital of the ligand. Peak D\nis attributed to a different final state configuration (associated with Ce4+), which is the 4f 05d state. The\ndeconvolutions reveal that CeO and MnNiCo-CeO are similar in that they exhibit the typical local\n2 2\nstructure of CeO , as evidenced by the consistency of the integrated peak areas for all four peaks and\n2\nthe greater intensities of peaks C and D relative to those of A and B (Supplementary Table 3). In contrast,\nthe shifts from CeO and MnNiCo-CeO to MnNiCoFe-CeO demonstrate an increase in the integrated\n2 2 2\nB peak area and a decrease in that for peak C. These results for MnNiCoFe-CeO are consistent with\n2\nincreasing electron delocalization in the Ce 4f orbital (associated with Ce3+) and decreasing\ndelocalization of the electrons in the O 2p orbital of the ligand. Thus, the increase in the net disorder\nof the HEO is apparent. On the other hand, Peak D is consistent in its lower intensity for MnNiCoFe-\nCeO relative to those of CeO and MnNiCo-CeO . Since this decrease is consistent with a decrease in\n2 2 2\n[Ce4+] and a complementary increase in [Ce3+] (as shown by with the observed increased B peak area),\nthen the addition of a fifth metal indicates a further increase in electron disorder deriving from the\nadditional charge transfer between Ce and this metal. The inset of Fig. 2f reveals a minor leftward shift\nin the absorption edge for MnNiCo-CeO compared to that of CeO , indicating that the incorporation\n2 2\nof Mn, Ni, and Co induces only a relatively small change in the electron transfer between these metals\nand Ce and thus the Ce4+ ↔ Ce3+ redox. In contrast, the shift for MnNiCoFe-CeO is significantly\n2\ngreater, which again is consistent with increased electron disorder deriving from the additional charge\ntransfer between Ce and the fifth metal.\nRev. B, 99, 180403 (2019).\nAbsorption Spectroscopy using IFEFFIT. J. Synchrotron Radi., 12, 537-541 (2005).\n(8)\nSupplementary Information Page 24:\nSupplementary Fig.13 Deconvolution of Ce-L edge XANES spectra with Gaussian mode fitting.\nXANES Peak\nSample A B C D\n2p→5d 2p→4f 15d 2p→4f 15dL 2p→4f 05d\nCeO 3.04% 10.95% 30.57% 55.45%\nResponse: These have been corrected.\nComment 7: In Fig. 3m and Supplementary Fig. 15a, it is difficult to understand the interactions and\nbonding among the elements.\nResponse: To facilitate clearer visualization and understanding of the elemental interactions,\nfurther\nanalysis of charge-density differences. The additional text (Manuscript Pages 13-14) and\nimage (Supplementary Information Page 33) have been added:\nManuscript Pages 13-14:\nThe electron localization function (ELF) and charge density difference plots (Figs 3m,n and\nSupplementary Fig. 18) reveal the electron densities of atoms. As shown in Figs 3n,m and\nSupplementary Figs. 18 and 19, the interactions between the Ce-O bonds and Co, Ni, Fe, and Mn exhibit\n(9)\nrelatively high electron densities, indicating a clear redistribution of electronic charge from Ce to the\nTMs. Further, the oxygen ions that bridge the high-CN Ce and TMs show lower electron densities\nrelative to those arising from those that bridge low-CN Ce and TMs. These data again confirm the role\nof the greater amount of charge transfer and resultant increased electron disorder associated with the\nlow-CN Ce relative to that of the high-CN Ce. It is counterintuitive for there to be a higher electron\ndensity of the low-CN Ce, which would be expected to be lower owing to the undercoordination. This\napparent contradiction is heightened in light of the differential electronegativities of Ce, where the\nhigher value for a higher Ce4+/Ce3+ ratio of high-CN Ce would be expected to exhibit a higher electron\ndensity compared to that for the lower Ce4+/Ce3+ ratio of low-CN Ce. The low-CN Ce would result in\nhighly catalytically reactive sites that would facilitate the adsorption and the subsequent reduction of\nO molecules. The asymmetry of the densities of states of Ce 4f shown in Fig. 3o further supports the\n2\ncritical importance of the alteration of charge transfer and electron disorder associated with the\nHEO.\nSupplementary Information Page 33:\nSupplementary Fig. 19 Electronic structure analyses: (a) representative atomic arrangement within\nthe HEO crystal structure, (b) representative electronic charge transfer (yellow perimeter = electron\ndensity) for different atom environments\nComment 8: How does the OER stability of the catalyst compare to that of other catalysts? (Fig. 4j)\nComment 9: Despite showing a lower electron transfer number, why does MnNiCoFe-CeO exhibit\n2\nhigher stability compared to the commercial 20 wt% Pt/C catalyst? (Fig. 4g, k,\nSupplementary Fig.17c, d)\nResponse: (1) Long-term OER stability tests of both pristine CeO₂ and MnNiCo-CeO₂ catalysts\nhave been conducted. The additional text (Manuscript Pages 17-18) and image\n(Manuscript Page 16) have been added. (2) For further discussion comparing the\nstability of the 20 wt% Pt/C and HEO catalysts, the additional text (Manuscript Pages\n17-18) have e been added\n(10)\nManuscript Pages 17:\nThe OER stabilities of CeO , MnNiCo-CeO , and MnNiCoFe-CeO were evaluated under both low (10\n2 2 2\nmA cm-2) and high (50 mA cm-2) current densities (Fig. 4j). The CeO rapidly lost activity, decreasing\n2\nby ~40% within ~10 h at 10 mA cm-2, completely losing activity within only ~3 h at 50 mA cm-2,\nrevealing its poor durability under extreme operating conditions. MnNiCo-CeO exhibited superior\n2\nstability, maintaining ~50% activity for ~24 h at 10 mA cm-2, although it also failed within ~6 h at\n50 mA cm-2. In contrast, the MnNiCoFe-CeO demonstrated remarkable long-term stability, retaining\n2\n~98% of its initial activity for ~50 h at both 10 mA cm-2 and 50 mA cm-2. This exceptional stability is\nattributed to electronic disorder in the multiple charge-transfer permutations between the Ce and four\nTMs of the HEO, which have the potential to homogenize the bulk charge transfer and hence electrical\nconductivity.\nMore to the point, this homogenization would reduce the differential field and valence effects imposed\nduring the extended mean free path of electron transfer, as suggested in Fig. 2d. More generally, the\nincreased configurational entropy would result in decreased Gibbs free energy and hence chemical\nstability. These considerations apply to the preceding OER data but also to ORR data, where again the\nhomogeneous nanostructure of HEO outperformed the composite microstructure of benchmark Pt/C\n(Fig. 4k and Supplementary Fig. 26). This optimized charge transfer and low Gibbs free energy state\nexplain the superior long-term stability of the HEO catalyst compared to commercial Pt/C. Although\nthe HEO exhibits a slightly lower electron transfer number than the composite Pt/C, this difference can\nbe attributed to the intrinsic nature of the materials. The Pt/C composite generally possesses higher\nGibbs free energy from mixed phases and charge trapping at heterogeneous interfaces, which can\ncompromise long-term electrochemical stability. In contrast, the HEO, as a well-mixed single-phase\nsolid solution, minimizes interfacial charge trapping and provides a more stable energy landscape. The\nPt/C composite system shows a higher apparent electron transfer number, likely due to its greater\nselectivity toward the four-electron ORR pathway.\nManuscript Page 16:\nFig. 4(j) OER stability testing\nComment 10: In Fig. 4k, is the retention value of Pt/C (58.7%) accurately represented?\nResponse: The image (Manuscript Page 16) has been revised:\nManuscript Page 15:\nFig. 4 (k) ORR stability testing\n(11)\nComment 11: Typo : Supplementary Fig.19 (a), (b)\nResponse: The typos (Supplementary Information Page 41) have been corrected.\nSupplementary Information Page 41:\nSupplementary Fig. 26 Normalized current response comparison in ORR stability test of: CeO ,\n2 2\nComment 12: In the OER/ORR tests, the catalytic mechanism is explained based on the interaction\nbetween Ce and O. How do the reactions and bonding behaviors of the other transition\nmetals proceed during the OER/ORR tests? (Fig. 5 b, c, d)\nResponse: In order to investigate the behavior of the transition metals during OER and ORR, ex-\nsitu XAS measurements were conducted at the Mn K-edge, Ni K-edge, Fe K-edge, Co\nK-edge, and Ce L₃-edge for HEO subjected to different long-term electrochemical\nconditions. The additional text (Manuscript Pages 18-19) and image (Supplementary\nInformation Page 46) have been added.\nManuscript Pages 18:\nThe identification, evolution, and stability of the active sites were examined by ex situ XANES and\nEXAFS analyses of Mn, Ni, Co, Fe, and Ce at different time stages (initial, post-activation, post-testing,\nand long-term) 61. These data elucidate the oxidation state changes, coordination environment evolution,\nand role of multi cation interactions in sustaining catalytic activity and stability. In order to evaluate\nthe behavior of the TMs during catalysis, the Mn, Ni, Co, and Fe K-edges were examined. Both the\nXANES and EXAFS spectra show only minor variations in Fig. 5c and Supplementary Fig. 29,\nconfirming that the TMs undergo minimal changes under operating conditions. The charge-transfer\ndynamics revealed by the XANES data allow differentiation of the contributions of the individual TMs\nto the OER and ORR in Fig. 5c62. Ni and Fe show more positive edge shifts during OER, indicating\ntheir greater participation in oxygen evolution. In contrast, Mn and Co exhibit more negative edge\nshifts during ORR, suggesting their greater involvement in oxygen reduction. These minor yet distinct\n(12)\ncontributions suggest that Mn and Co act as auxiliary facilitators during ORR, whereas Ni and Fe assist\nduring OER, while Ce is the dominant active centre. The EXAFS analysis of the TMs also confirms\nonly subtle modifications in the local coordination environments, indicating that they are not active\nsites. Detailed inspection of the EXAFS data (Supplementary Fig. 29) reveals that all four TMs\nexperienced small increases in M-O coordination after activation (upward trajectory), consistent with\nlimited oxygen adsorption59,60. Over extended cycling, the first coordination sphere exhibits a slight\ndecrease (downward trajectory, though still above pre-testing levels), which probably reflects the role\nof individual point defects. In contrast, the second coordination sphere exhibits a slight increase\n(upward trajectory), which is consistent with modest M-O-M ordering of the lattice after long-term\ntesting 59,60.\nReaction Mechanisms to Rational Design. Chem. Rev., 123, 6257-6358 (2023).\nEntropy Alloy Electrocatalysts. Nat. Comm., 13, 2662 (2022).\nAcidic Water Oxidation of Trigonal Iridium Oxide. Angew. Chem. Int. Ed., 64. e202423353\n(2025).\nSupplementary Information Page 46:\nSupplementary Fig. 29 Fourier-transforms of K2-weighted Mn-K, Co-K, Ni-K, and Fe-K edge\nEXAFS forMnNiCoFe-CeO\n2\n(13)\nReviewer 2\nGeneral: In this work, the author's team pioneered the engineering in multi-level disorder and\nformation of a new type of HEO, transforming essentially inactive matrices into highly\nactive cathodes, generating bifunctional (OER/ORR) and stable metal active sites. The\nresearch content of this work is relatively novel. The work of designing\nstructural/electronic disorder in HEO is conducive to establishing a new transformation\npath for catalysts in battery design. However, major revisions are still needed before the\nmanuscript is published, as follows:\nResponse: The authors thank the reviewer for the positive comments.\nComment 1: The synthesis and research of high-entropy catalysts and their applications in batteries\nhave been extensive. What is the most significant innovation of this work compared to\nothers? To enhance readers' cognition and reading, the abstract part should focus on\nhighlighting the high-entropy oxides of this work rather than introducing them briefly.\nResponse: To emphasis the discovery in this high-entropy oxide, the additional text (Manuscript\nPage 1) has been added:\nManuscript Page 1:\nResearch on high-entropy oxides generally is limited to elemental and structural interpretations applied\nto the performance of cathodes. However, there are only limited data on the principles of increasing\ndisorder in terms of structural, electronic, and atomic mechanisms as materials convert from ordered to\ndisordered. Zn-air battery (ZAB) cathodes are limited by slow kinetics, imbalanced OER charging and\nORR discharging, and scalability through the necessity of benchmark noble metals. The present work\npioneers the engineering of multilevel disorder in a new HEO, thereby transforming an intrinsically\ninactive matrix into a highly active cathode. Systematic modification of the disorder through increasing\nnumber of cations leads to the abrupt development of structural (2D defects), electronic (semimetallic\nconductivity), and atomic (low-coordination Ce) disorder. This multilevel disorder engineering of\nHEOs results in MnNiCoFe-CeO catalysts with stable active sites, rapid and balanced bifunctional\n2\n(OER/ORR) performance, outstanding ZAB efficiency superior to benchmark materials, and\nelectrochemical durability.\nComment 2: What is the most serious challenge that high-entropy oxides are currently facing in the\nfield of catalysis? What key problems have been successfully solved by the synthesized\nMnNiCoFe-CeO catalyst? The summary of the content in the introduction part is not in-\n2\ndepth and comprehensive enough and needs to be adjusted.\nResponse: To provide this context, the additional text (Manuscript Pages 2-3) has been added.\nManuscript Pages 2-3:\nThere are four recognized key effects in HEOs: high-entropy effect, lattice distortion effect, sluggish-\ndiffusion effect, and cocktail effect18. Of these, lattice distortion has attracted the most attention owing\nto its strong influence on the overall material properties. This effect originates from the coexistence of\nmultiple cations of varying ionic radii, valence states, electronegativities, and coordination within the\nsame sublattice. These coexistences cause atomic mismatches, which can lower the symmetry of the\nunit cell; introduce lattice distortion and strain; and generate 0D, 1D, 2D, and 3D defects, which may\nrequire charge compensation19. Further, the distances between neighboring ions occur over a\ndistribution rather than at fixed values, thus placing the structure in a thermodynamically\nnonequilibrium state18. This deviation can lower the energy barriers for molecular adsorption, activation,\nand OER/ORR conversion in electrocatalytic reactions 20. Despite the significance of lattice distortion,\nthe current understanding of such disorder in HEOs remains limited 21,22. Most studies focus primarily\n(14)\non identifying high concentrations of defects (e.g., oxygen or metal vacancies) and the absence of long-\nrange order 22,23. However, a comprehensive analysis of disorder from a structural, electronic, and\natomic perspective remains lacking. In particular, there is a need for a systematic correlation of this\nmultilevel disorder with the corresponding electrocatalytic performance, especially for bifunctional\nOER/ORR catalysts for ZABs. The present work explores this correlation through the performance of\nZABs, with the aim of elucidating the mechanisms of the roles of disorder in HEO in governing catalytic\nactivity.\nTo the preceding aim, the present work introduces a novel nonnoble-metal MnNiCoFe-CeO -based\ndisorder through structural-, electronic-, and atomic-level disorders, leading to improvement in the\nOER/ORR activities as well as outstanding performance and stability in ZABs. This analysis provides\na platform for the application of disorder engineering in the design of systematic ranges of progressively\nmore complex systems, from individual oxides to HEOs.\n8, 471-485 (2024).\nAlloy. Nat. Comm., 15, 1402 (2024).\nChem. Soc. Rev., 52, 8319-8373 (2023).\n138659 (2023).\nStrain. Adv. Mater,, 37, 2501209 (2025).\nDefects of Hierarchical Metal Oxides@Graphene Fibers toward High-Performance Wearable\nSupercapacitors. Adv. Mater., 36, 2406483 (2024).\nComment 3: What is the proportion of metal atoms in the high-entropy oxide MnNiCoFe-CeO and\n2\ncan it be precisely regulated? What is the combination mode of the five metal elements\nand what roles do they each play in ORR/OER?\nResponse: These questions are answered in Comments 1 and 5 in response to the issues raised by\nReviewer 1.\nComment 4: What is the chemical state of the metal in MnNiCoFe-CeO ? Metal, chloride, or oxide?\none valence state? Do different valence states have an impact on the catalytic effect?\nResponse: (1)As solutes in a solid solution of CeO , the transition metals are ionic solutes, albeit\n2\nthey are in close association with the adjacent oxygen ions, the additional text\n(Manuscript Pages 6-7) has been added. (2)Concerning the effects of oxidation states in\ndifferent oxide elements, particular attention is given to how these states evolve\nprogressively during the formation of the HEO, the additional text (Manuscript Pages 6-\n7 and Supplementary Information Page 18-19), table (Supplementary Information Page\n18) and image (Supplementary Information Page 19) have been added.\nManuscript Pages 6-7:\nIn Mn-CeO , the Ce3+ and Ce4+ XPS binding energies are unchanged, suggesting retention of the original\n2\nenergies of Ce3+ and Ce4+ are increased, indicating that the addition of Ni and Co cause new electronic\ninteractions within the Ce environment. These interactions result in alterations to the Ce-O bond, which\ncan be attributed to the formation of a solid solution. The addition of Ni and Co also promotes the Ce-\nO bond to a state of enhanced ionicity, reflecting a significant modification in the bonding nature. These\n(15)\nchanges are likely driven by the smaller crystal radii and higher electronegativities of Ni and Co\ncompared to those of Ce4+ and Ce3+, thereby encouraging electron transfer toward the Ni and Co sites\n(Supplementary Fig. 6,7 and Table 4). The addition of Fe in MnNiCoFe-CeO induces a further increase\n2\nin the binding energy of Ce3+ but no noticeable effect on Ce4+. This shift for Ce3+ is likely due to the\nhigher electronegativity of Fe3+ (1.556, Supplementary Table 4) compared to that of Ce3+ (1.348). Since\nboth of these closely associated ions share the same valence state, this suggests a reason for the fixed\nvalence state of Fe. However, the electronegativity of Ce4+ (Ce4+ = 1.608) is very close to that of Fe3+,\nconfirming that little shift in binding energy for Ce4+ would be expected. In MnNiCoFe-CeO , the\n2\nbinding energies of Mn, Ni, and Co exhibit lower binding energies, indicating distortions in the TM-O\nbonds. Therefore, the overall lattice distortion in MnNiCoFe-CeO is likely to reflect the cumulative\n2\nresult of distortions occurring in both the Ce-O and TM-O bonds. These shifts also suggest an increase\nin TM-O bond covalency, underscoring the alteration of the structural order in the HEO relative to that\nof the less complex solid solutions. The importance of the alteration of the chemical environment and\nthe resultant improvement in charge-transfer phenomena is supported by the multiple charge-transfer\npermutations between the four TMs and Ce of the HEO, although the Fe shows only one stable valence\nas confirmed by Supplementary Table 5 and Fig. 8.\nSupplementary Information Page 18\nSupplementary Table 5 Redox potentials for relevant ions\nElement Redox pair Reduction potential (V vs SHE)\nMn3+/Mn2+ 1.51\nMn\nMn3+/Mn4+ 0.95\nNi Ni2+/Ni3+ 1.60\nCo Co2+/Co3+ 1.82\nFe Fe2+/Fe3+ 0.77\nCe Ce4+/Ce3+ 1.61\nThe oxidation state variability is characterised by the following observed changes in the oxidation states:\nMn: Mn3+ → Mn2+/Mn4+ Reduction + Oxidation\nNi: Ni2+ → Ni2+/Ni3+ Oxidation\nCo: Co3+ → Co2+/Co3+ Reduction\nFe: Fe3+ → Fe3+ No Change\nCe: Ce4+ → Ce3+/Ce4+ Reduction\nThese permutations can be clarified by calculation of the reduction potentials using the HSC 6\nsoftware package; these data are given in Supplementary Table 5. Comparing these data with the XPS\ndata, it is clear that the most favored oxidation state is Fe3+, which supports its detection as the only\nvalence state of Fe. Similarly, oxidation of Mn3+ to Mn4+ would be expected to be favored.\nSimultaneously, the detection of the mixed valence states of the other ions contrasted with the reduction\npotentials in the range 1.51-1.82 demonstrates that these values also are commensurate with the\nformation of mixed valences. Such combinations of variable valences are consistent with the\nphenomenon of multivalence charge transfer32, which basically is intervalence charge transfer between\nmore than two ions. Again, this is indicative of the role of multiple-valence-state charge transfer.\n(16)\nSupplementary Information Page 19\nSupplementary Fig. 8 Thermodynamic stability diagrams calculated for 400ºC\nThe oxidation states were explored further by calculation of the thermodynamics stability diagrams at\nthe reduction annealing temperature of 400ºC, as shown in Supplementary Fig. 8. The solid red line\nshows the oxygen concentration at atmospheric pressure, although forming gas in a polycrystalline\nalumina tube and purging (viz., without evacuation and backfilling) were used. More broadly, the use\nof forming gas can achieve reducing atmospheres with oxygen partial pressures of ~10–15 atm33, as\nshown by the dashed red line. Using this generality as a benchmark, these data suggest that the oxidation\nstates would be likely to be:\nMn: Mn3+ → Mn2+/Mn3+ Reduction\nNi: Ni2+ → Ni2+ No Change\nCo: Co3+ → Co2+ Reduction\nFe: Fe3+ → Fe3+ No Change\nCe: Ce4+ → Ce4+ No Change\nIf these data reflect the achievement of equilibrium, then they also suggest the role of multivalence\ncharge transfer in generating non-equilibrium valence states.\n2 2 3 2 5\nMetals 12, 768 (2022).\n(17)\nComment 5: The catalytic mechanism of high-entropy oxides is the highlight and attractive part of\nthis article. It is suggested that the author elaborate on the mechanism part separately. By\nconducting in-depth studies on the conversion disorder characteristics of the MnNiCoFe-\nCeO catalyst and the reasons for achieving excellent performance in ORR/OER,\n2\nthe catalytic mechanism is further revealed.\nResponse: The catalysis aspects are segregated, the additional image (Manuscript Page 19) and text\n(Manuscript Page 20-21) have been added.\nManuscript Page 19:\nFig. 5 Active-site characterization for HEO in ex situ OER and ORR at different times scales: (a)\nSchematic of effect of multilevel disorder engineering; (b) Laser Raman microspectra; (c) Normalized\nMn-K, Ni-K, Co-K and Fe-K edge XANES spectra; (d) Normalized Ce-L edge XANES spectra; (e)\nManuscript Pages 20-21:\nIn order to identify which of the metal constituents are the active sites in the high-entropy oxide,\nboth\nOER and ORR pathways, each involving four electron transfer steps, were analyzed using first-\nprinciples DFT simulations, as shown in Fig. 5g. Optimized surface models were constructed for each\nmetal ion site (Mn, Ni, Co, Fe, Ce), with adsorption energies calculated for all key oxygenic\nintermediates (*OH, *O, *OOH) along the reaction pathways. Of all the sites, Ce ions exhibited the\nlowest energy barriers across the reaction steps, again indicating that these are the primary active sites.\nFor Ce, the rate-determining step is the formation of *OOH, with the largest free energy barrier (ΔG)\n(18)\nof 1.63 eV. Similar trends were observed for other metal sites but with higher energy barriers for *OOH\nformation. The calculated overpotentials of Mn, Ni, Co, Fe, and Ce are used to represent the overall\nOER/ORR activity of these metal ions in Fig. 5h, confirming the dominance of Ce (only 0.4 eV) in the\nexperimental activity trend. These findings highlight the pivotal role of low-CN Ce sites in facilitating\nboth OER and ORR processes, while the other transition metals primarily play supportive roles, as also\nsuggested by the EXAFS data.\nComment 6: It is suggested that the structure and performance of the MnNiCoFe-CeO catalyst after\n2\noperation be characterized to prove its stability.\nResponse: This comment has been addressed in the response to Reviewer 1, Comments 12 and\nReviewer 2, Comments 5.\nComment 7: Battery performance as a proof of concept is best listed separately rather than mixed with\ncatalytic performance comparison and reaction mechanisms. Such thinking logic is not\nconducive to readers' understanding.\nResponse: (1) The response to Comment 5 segregates the catalytic performance. (2) Fig. 6 has been\nrevised in order to segregate the battery performance. The additional image (Manuscript\nPage 23 and text (Manuscript Pages 23-24) and have been added.\nManuscript Page 22:\nFig. 6 Rechargeable ZAB performance of HEO and Pt/C+IrO : (a) schematic illustration of\n2\nconstruction of ZAB; (b) OCP curves; (c) specific capacity test curve for HEO; (d) power density curves;\n(e) rate capabilities at different rates from 2 to 40 mA cm-2 and back to 2 mA cm-2; (f) long-term cycling\n(19)\nperformances at charging/discharging rate of 5 mA cm-2 (5 min charge and 5 min discharge); (g)\ncomparison of ZAB power densities and stabilities; (h) Schematic of multilevel disorder in HEO for\nhigh performance ZABs\nManuscript Pages 23-24:\nThese findings of outstanding performance of MnNiCoFe-CeO in ZABs highlight the critical\n2\nimportance of multilevel disorder engineering in HEOs, as shown in Fig. 6h. In the single-phase oxide\nof minimal disorder, the electrochemical performance is poor. In the dual-phase heterojunction, the\nelectrochemical performance is just slightly enhanced by this effect. In the lower-complexity solid\nsolutions, the degree of structural disorder is limited, where there are isolated point defects and\nindividual charge-compensating oxygen vacancies that provide only a small number of active\nadsorption sites. The modest lattice distortion helps to maintain a coherent lattice framework with\nminimal internal strain. Electronic disorder still retains the semiconducting properties, but with d-band\nrelocation’s modifying the binding energy of the reaction intermediates, while the mixed-valence states\nof the metals enhance charge transfer to a commensurately limited extent. However, the largely\nunchanged atomic disorder contributes little to catalytic improvement.\nIn contrast, the highly disordered HEO leverages the extensive synergy between structural,\nelectronic, and atomic disorders, thereby significantly enhancing the electrocatalytic activity. The\nstructural disorder is manifested as 2D defects; including stacking faults, twin boundaries, and\ndislocations; which are associated with oxygen vacancy clusters. These defects offer additional\nadsorption sites while preventing long-range ordering or phase segregation, thereby enhancing single-\nphase stability during cycling. The electronic disorder is evidenced by semimetallic behavior, which\npromotes high electronic conductivity and facilitates multivalence charge transfer across sixteen redox\npermutations (e.g., Mn2+/4+, Ni2+/3+, Co2+/3+, Fe3+, Ce3+/4+), allowing the potential for all cations to\ncontribute cooperatively, as evidenced by the XANES data in Figs 5c,d. Finally, the atomic disorder\nintroduces a higher fraction of Ce3+ and low-coordination Ce, that latter of which is a new type of active\nsite that enhances the OER/ORR performance further, as shown in Supplementary Table 13, and leads\nto the outstanding ZAB performance and stability, as shown in Fig. 6g. Further, this multilevel disorder\nengineering suggests a fundamental roadmap for the design of new types of materials, paving the way\nfor innovative and sustainable energy solutions.\nComment 8: There are many errors in format, description and language in the manuscript. For\nexample, the format of the upper and lower annotations, the font, the interval, the type of\nconcatenator, etc. Also, in lines 339, 341 and 348, it should be Figure 3 instead of Figure\n5, and in line 527, it should be Pt instead of Pr. There are many similar problems in the\nmanuscript, as well as language issues. The author needs to correct and revise the entire\nmanuscript.\nResponse: The text has been revised completely, with attention.\n(20)\nReviewer 3\nGeneral: In this work, Zhang et al. reported a bifunctional catalyst of MnNiCoFe-CeO2 for ORR\nand OER. They added the Fe atoms to adjust the electronic properties of Ce atoms and\nthe Ni, Co and Mn atoms to induce the lattice distortion and point defect. As a result, the\ncharge and discharge process in ZAB with HEO as the catalysts were optimized. Multiple\ncharacterizations were employed to elucidate the detailed structure of catalyst. However,\nin my opinion, there are numerous issues need to be addressed in the manuscript,\nparticularly the presence of many vague expressions and conclusions lacking the\nconvincing evidences. Furthermore, the OER/ORR performance is also unsatisfactory.\nBelow are my specific comments:\nResponse: The authors thank the reviewer for the critical comments.\nComment 1: Based on the characterizations in Fig. S1b, many small-sized high-entropy nanocrystals\n(~4 nm) exist on the surface of the nanosphere. However, no clear lattice can be observed\non the core of the nanosphere, can the authors give some evidences to claim the species\nof the core? In addition, the authors should explain the detailed method for calculating\nthe dislocation density and microstrain from XRD patterns. Moreover, the Raman peak\nat nearly 605 cm-1 is attributed to O vacancy rather than lattice distortion in Fig. S3 (J.\nPhys. Chem. C, 2012, 116, 10009-10016), and this value (51.7%) is inconsistent with the\nO vacancy ratio (85%) detected by XPS in Fig. 2a\nResponse: (1) A TEM image replacing the original image has been added, thereby confirming the\nsize of the nanosphere. This image now includes a TEM image for the HEO; both show\nthat the nanocrystals in the bulk are equivalent to those on the surface, thus confirming\nthat the crystallite size remains constant from bulk to surface. The additional text\n(Manuscript Page 4) and image (Supplementary Information Page 12) have been added.\n(2) The methods (Supplementary Information Page 8) for the calculation of the\ndislocation density and microstain have been added; (3) The text has been edited for the\nattribution of the Raman peak at 605 cm-1. The difference in the numbers 51.7% and\n85% also has been addressed in the text. The additional text (Manuscript Pages 4-5) has\nbeen added.\nManuscript Page 4:\nIn order to decouple the effects of crystallite size and lattice distortion, high-resolution transmission\nelectron microscopy (HRTEM) images (Supplementary Fig. 2) are used to illustrate that there is little\nvariation between the observed crystallite sizes of CeO and high-entropy MnNiCoFe-CeO and that\n2 2\nthe crystallite size remains essentially constant from the bulk to the surface.\nSupplementary Information Page 12:\nSupplementary Fig. 2 HRTEM images of: (a) CeO , (b) MnNiCoFe-CeO\n2 2\n(21)\nSupplementary Information Page 8 :\nThe dislocation density of the samples was estimated from powder XRD data using CuKα radiation (λ\n= 1.5406 Å). The full width at half maximum (FWHM, β) of the five major peaks was obtained by\nprofile refinement. The average crystallite size (D) was obtained using the Scherrer equation, D =\nkλ/(βcosθ), using the standard shape factor of 𝑘 = 0.9. The dislocation density (ρ) was calculated using\nthe Williamson-Smallman equation, ρ = 1/D2. The microstrain was calculated using the Williamson-\nHall equation, βcosθ = (kλ/D) + 4𝜀sinθ, where 𝜀 is the microstrain.\nManuscript Pages 4-5:\nMnNiCoFe-CeO exhibits the highest defect density in laser Raman microspectroscopy (Supplementary\nthe absence of TM-O bonding features in the Raman spectra, confirms the presence of significant\nstructural disorder and the maintenance of a single-phase structure of the Ce-O framework in the HEO\nstate. The high defect concentration is indicative of a high frequency of oxygen vacancies, as evidenced\nby the 605 cm-1 Raman peak intensity. This high concentration of oxygen vacancies is likely to cause\nclustering in order to lower the total elastic energy of the system 25. Such clustered vacancies are likely\nto be responsible for the formation of extended 2D structural defects, including the observed stacking\nfaults, twin boundaries, and dislocations, which disrupt the oxygen sublattice26,27. These findings also\nprovide a possible explanation for the apparent mismatch between surface-sensitive techniques, such as\nXPS, and bulk-sensitive techniques, such as Raman. While XPS may underestimate the extent of defect\nformation due to its shallow probe depth, the 2D defects identified by HADDF for the material surface\noffer direct evidence of surface-localized oxygen sublattice distortion, thereby aligning with the XPS-\nand Raman-based observations.\n309, 752-755 (2005).\n8, 3500-3505 (2017).\nIntercalation Pseudocapacitance in Mo Single-Ion-Implanted CeO Nanoflakes. ACS Applied\n2-x\nMater. & Inter., 13, 59820-59833 (2021).\nComment 2: The authors proposed that lattice distortion in HEOs originates from \"substitution-\ninterstitial solid solution with uniform mixing of transition metal ions” but relies solely\non ADF-STEM images (Fig.S12) and Table 3, lacking quantitative analysis (such as\nlattice parameter refinement and element occupancy analysis). It is suggested to perform\nthe XRD refinement to verify the lattice distortion and the specific O vacancy content.\nResponse: The XRD lattice parameter refinement and element occupancy analysis data and\nadditional text (Supplementary Information Pages 9-11) have been added:\nSupplementary Information Pages 9-10 :\nSupplementary Table 3 Structural refinement data of MnNiCoFe-CeO\na b c α β γ GOF\n9.83477 9.68179 10.16791 91.185 90.233 87.97 4.01\nElement occupancy analysis\nAtom x y z Fraction Calculated Ratio Uiso\n(22)\n(Experimental Ratio)\nNi1 0.03149 0.49467 0.44112 0.054 0.033\nNi2 0.74669 0.24277 0.55661 0.054 0.033\nNi3 0.73723 0.75906 0.01092 0.054 0.0348 0.033\nNi4 0.27666 0.98199 0.77961 0.054 (0.0350) 0.033\nNi5 0.97809 0.26130 0.22356 0.054 0.033\nNi6 0.96098 0.25609 0.74027 0.054 0.033\nFe1 0.01351 1.00686 0.58733 0.054 0.037\nFe2 0.49259 0.50203 0.53905 0.054 0.037\nFe3 0.25301 0.80040 0.55392 0.054 0.0348 0.037\nFe4 0.74055 0.22332 0.92087 0.054 (0.0350) 0.037\nFe5 0.82474 0.49550 0.20395 0.054 0.037\nFe6 0.75763 0.48994 0.77624 0.054 0.037\nCo1 0.93312 0.01121 0.05432 0.054 0.029\nCo2 0.05131 0.50238 0.95288 0.054 0.029\nCo3 0.20886 0.23172 0.96689 0.054 0.0348 0.029\nCo4 0.24994 0.29297 0.44981 0.054 (0.0350) 0.029\nCo5 0.18868 0.48859 0.70229 0.054 0.029\nCo6 0.77331 -0.01683 0.76427 0.054 0.029\nMn1 0.26416 0.72954 0.98401 0.054 0.036\nMn2 0.24525 0.50008 0.18628 0.054 0.036\nMn3 0.74603 0.00079 0.27369 0.054 0.0348 0.036\nMn4 0.98695 0.74628 0.22425 0.054 (0.0350) 0.036\nMn5 0.02759 0.70135 0.72085 0.054 0.036\nMn6 0.41143 0.25052 0.71657 0.054 0.036\nCe1 0.51668 0.00707 0.00970 1.000 0.042\nCe2 0.49487 0.02144 0.49719 1.000 0.042\nCe3 0.50315 0.46366 0.98646 1.000 0.042\nCe4 0.77833 0.74049 0.49439 1.000 0.8600 0.042\nCe5 0.22589 0.02125 0.23451 1.000 (0.8600) 0.042\nCe6 0.57441 0.29478 0.28530 1.000 0.042\nCe7 0.47406 0.71438 0.28233 1.000 0.042\nCe8 0.52919 0.74023 0.75180 1.000 0.042\nO1 0.08108 0.15749 0.09258 0.233 0.018\nO2 0.08231 0.15131 0.65556 0.233 0.018\nO3 0.10624 0.63886 0.10110 0.233 0.018\nO4 0.17943 0.65071 0.61245 0.233 0.018\nO5 0.57891 0.06175 0.21666 0.233 0.018\nO6 0.56017 0.21425 0.64315 0.233 0.018\nO7 0.64703 0.49571 0.17999 0.233 0.018\nO8 0.74221 0.65387 0.68413 0.233 0.018\nO9 0.18552 0.40794 0.04580 0.233 0.018\nO10 0.13711 0.39805 0.55204 0.233 1.6040 0.018\nO11 0.03730 0.91445 0.17103 0.233 (2.0000 Theoretical) 0.018\nO12 0.13879 0.87316 0.70103 0.233 0.018\nO13 0.63184 0.24289 0.05160 0.233 0.018\nO14 0.57951 0.51128 0.69112 0.233 0.018\nO15 0.57213 0.78517 0.08305 0.233 0.018\nO16 0.65072 0.91061 0.62992 0.233 0.018\nO17 0.33204 0.13299 0.06844 0.233 0.018\nO18 0.31065 0.19071 0.58881 0.233 0.018\nO19 0.36122 0.61060 0.10119 0.233 0.018\nO20 0.41449 0.67527 0.55020 0.233 0.018\n(23)\nO21 0.85310 0.12498 0.18156 0.233 0.018\nO22 0.84955 0.11809 0.66056 0.233 0.018\nO23 0.84498 0.66927 0.12415 0.233 0.018\nO24 0.95837 0.61068 0.56915 0.233 0.018\nO25 0.39697 0.38253 0.18211 0.233 0.018\nO26 0.36596 0.43287 0.67395 0.233 0.018\nO27 0.34217 0.85650 0.13316 0.233 0.018\nO28 0.37419 0.90226 0.64441 0.233 0.018\nO29 0.93085 0.40183 0.10164 0.233 0.018\nO30 0.84146 0.37503 0.64394 0.233 0.018\nO31 0.77308 0.92649 0.08875 0.233 0.018\nO32 0.90651 0.86550 0.65467 0.233 0.018\nO33 0.04560 0.15261 0.36576 0.233 0.018\nO34 0.17009 0.08957 0.86836 0.233 0.018\nO35 0.09015 0.73807 0.34460 0.233 0.018\nO36 0.15608 0.61073 0.85016 0.233 0.018\nO37 0.68616 0.12018 0.42249 0.233 0.018\nO38 0.65142 0.10500 0.83090 0.233 0.018\nO39 0.60876 0.60135 0.42743 0.233 0.018\nO40 0.67296 0.60309 0.92048 0.233 0.018\nO41 0.12063 0.38369 0.30722 0.233 0.018\nO42 0.09524 0.36146 0.81967 0.233 0.018\nO43 0.13052 0.92646 0.48273 0.233 0.018\nO44 0.13535 0.87323 0.95954 0.233 0.018\nO45 0.63529 0.36721 0.48118 0.233 0.018\nO46 0.63889 0.35781 0.83886 0.233 0.018\nO47 0.61898 0.86494 0.36512 0.233 0.018\nO48 0.67671 0.86312 0.87242 0.233 0.018\nO49 0.36139 0.15716 0.35521 0.233 0.018\nO50 0.41722 0.08676 0.8039 0.233 0.018\nO51 0.26690 0.58671 0.32463 0.233 0.018\nO52 0.39357 0.62293 0.87530 0.233 0.018\nO53 0.94273 0.10402 0.44055 0.233 0.018\nO54 0.87242 0.08400 0.90027 0.233 0.018\nO55 0.91125 0.58425 0.32694 0.233 0.018\nO56 0.92374 0.59206 0.83235 0.233 0.018\nO57 0.39720 0.39942 0.43000 0.233 0.018\nO58 0.35013 0.31361 0.87593 0.233 0.018\nO59 0.34659 0.87203 0.39584 0.233 0.018\nO60 0.36895 0.86282 0.89119 0.233 0.018\nO61 0.83357 0.34289 0.30967 0.233 0.018\nO62 0.85832 0.34624 0.87008 0.233 0.018\nO63 0.85906 0.86435 0.32046 0.233 0.018\nO64 1.00188 0.86334 0.94162 0.233 0.018\n(24)\nSupplementary Information Page 11 :\nSupplementary Fig. 1 Simulated crystal structure of MnNiCoFe-CeO based on data in Supplementary\nSupplementary Table 3 gives the lattice parameter refinement of the HEO as well as the element\noccupancy analysis data. Fig. X visualizes these data in a structure schematic. This image confirms\nthe d sixfold and eightfold coordination of all of the transition metals, thereby supporting the conclusion\nthat the solid solubility mechanism is mixed substitutional-interstitial. These data also contrast the\nstoichiometries of the included species, showing that the transition metals and Ce are close to the\nexperimental values (Supplementary Table 1). With an oxygen stoichiometry of ~1.6 and a minimal\noxygen stoichiometry of CeO (where all Ce is Ce3+), then the oxygen vacancy concentration is 80%\n1.5\n((2.0-1.6)/0.5) of the maximum. This can be contrasted with the equivalent data from XANES\n(Supplementary Table 6), which are [Ce3+] = 67.34 (46.40) and [Ce4+] = 32.66 (22.50), giving an oxygen\nstoichiometry of ~1.66 and hence an oxygen vacancy concentration of ~68% ((2.00 – 1.66)/0.50). This\nalso can be contrasted with the data for XPS (Supplementary Fig. 5), which reveal an oxygen vacancies\nconcentration of ~85%, thus explaining the preceding differential. These high oxygen vacancy\nconcentrations are consistent with the conclusion of oxygen vacancy clustering and 2D defects\nformation.\nManuscript Page 11:\nThis lattice distortion probably derives largely from the mixed substitutional-interstitial solid solubility\nof all of the transition metal ions in the matrix phase, as revealed by the XRD refinement\n(Supplementary Table 3 and Fig. 1), ADF-STEM images (Supplementary Fig.15), and related defect\nequilibria, the latter of which support the charge-compensation basis for the formation of oxygen\nvacancies and free electrons (Supplementary Table 8).\nComment 3: According to the authors' description and XPS results, the electrons on Ce sites are\ntransferred to Ni and Co sites, thus the valence states of Ce in MnNiCoFe-CeO should\n2\nbe higher than CeO . However, as shown in Fig.2f, the white line peak position of\n2 2\nthe former. These two conclusions are contradictory. In addition, the EPR signal of O\nvacancy in Fig.2c is weird, as it should be a symmetric pattern (Nat. Commun. 2023, 14,\n1412). Moreover, the detailed EXAFS fitting parameters in Fig.2g and 2h should be\nprovided.\nResponse: (1) A more detailed explanation addressing the apparent contradiction in the Ce valence\nstates and their role in charge transfer has been incorporated into the main text\n(25)\n(Manuscript Page 10). (2) In addition, the section discussing EPR has been expanded\n(Manuscript Pages 7-8) to further explain for understanding oxygen vacancies. (3) The\nset of EXAFS fitting parameters are added (Supplementary Information Page 26).\nManuscript Page 10:\nThe observation for the Ce site in XANES contradicts that for the Ce site in the XPS spectra of the\nHEO. While the peak shifts in XPS suggest electron transfer from Ce toward the TM sites, both the\nXANES and XPS data indicate an increase in the relative concentration of Ce3+. This seemingly\ncontradictory result can be explained by considering the electronic nature of Ce44. Owing to the\ndelocalized Ce free electrons (as shown by the band structure analysis and CAFM), Ce can donate\nelectrons from the Ce conduction band to both the neighboring transition metals (as shown by XPS\ndata) and the Ce3+ state associated with the 4f electron orbital (as shown by XANES data). Thus, both\nthe electron transfer and increase in [Ce3+] can occur simultaneously. In addition, the extensive\nformation of oxygen vacancies provides the necessary charge compensation at the Ce sites, as confirmed\nby Raman, EPR, and XPS data, further stabilizing the reduced Ce3+ state despite the electron transfer\nfrom Ce toward the TMs.\nCe Films. Nat. Comm., 12, 2520 (2021).\nManuscript Pages 7-8:\nThe asymmetric EPR signal is indicative of a Dysonian nature, which arises owing to a skin effect and\nmicrowave penetration in materials with appreciable electrical conductivity, such as metallic or\nsemimetallic systems 36,37. This asymmetry serves as strong evidence that the material has undergone\na transition from semiconducting to more conductive behavior associated with a high extent of\nelectronic disorder, which is facilitated by partial reduction, a high concentration of oxygen vacancies,\nand mixed-valence states. In such systems, unpaired electron spins can become delocalized or interact\nwith conduction electrons, further contributing to the Dysonian response and enhanced signal intensity.\nPhysica Status Solidi B, 248, 2950-2956 (2011).\nStorage Mechanism of Hard Carbon. Nat. Comm., 15, 3013 (2024).\nSupplementary Information Page 26:\nSupplementary Table 7. EXAFS fitting parameters\nSamples Shell N R(Å) σ2 (x 10-3 Å2) ΔE0 (eV) R-factor\nCe-O 8.00 2.34 4.46 5.62 0.020\nCeO\nCe-O 7.47 2.30 4.90 5.71 0.010\nMnNiCo-CeO\n2.19 4.31 5.12 0.003\n2.24 4.31 5.12 0.003\n2.44 4.31 5.12 0.003\nMnNiCoFe-CeO Ce-O 6.10\n2 2.53 4.31 5.12 0.003\n2.61 4.31 5.12 0.003\n2.87 4.31 5.12 0.003\nComment 4: The conclusion derived from the EELS in Fig.3a-3j is not convincing. It is not reasonable\nto directly judge the bond length change using the ΔE because that ΔE is also influenced\nby other factors including valence state and coordination number. The authors can use\n(26)\nthe DFT to simulate the theoretic EELS spectrum and compare it with the experimental\nresult to validate it (Phys. Rev. B, 2020, 101, 165112; ACS Catal., 2019, 9, 10031).\nResponse: This issue has been considered in some detail. The principle considerations that are the\noutcomes of these considerations are: (1) The publications cited only lightly touch on\nthe EELS data and their interpretation concerning the oxidation state and structural\ndisorder, effectively being somewhat speculative. (2) EELS simulations are extremely\nrare in the literature because simulating core-level EELS using DFT is highly\nchallenging, particularly for complex systems in HEOs, because accurately modelling of\nthe localized core excitations requires constructing large supercells in order to avoid\nartificial periodic interactions with the core hole. This significantly increases the\ncomputational cost and complexity. (3) We have altered the text so that the claims are\nmore modest and broader while removing the comment about the bond length change.\nInstead, the EELS discussion focuses on experimentally observed surface-specific\nfeatures that confirm the high surface reactivity. The additional text (Manuscript Pages\n12-13) has been added.\nManuscript Pages 12-13:\nIn order to assess the impact of the electronic environment induced by the TMs on the atomic disorder\nand performance of the HEO, linear scans of the electron energy loss spectroscopy (EELS) spectra were\ndone on the TMs within an HEO crystal. Detailed analyses of the atomic surface effects also were done\nsince catalytic reactions occur predominantly at the surface (Fig. 3e-i and Supplementary Fig. 16). The\nmatrix Ce M -edges indicate electron transitions from the Ce3d (Ce M ) and Ce3d (Ce M ) core\n4,5 3/2 4 5/2 5\nlevels to the Ce4f unoccupied electronic states48. From the bulk to the surface, the disappearance of the\nM satellite peaks and the increased M :M intensity ratio indicate a reduction for Ce4+ to Ce3+, implying\n5 5 4\na high density of surface f-electrons and subsequent surface reactivity48. Further, the positive shift in\nthe M peak energy from bulk to surface suggests an altered surface Ce electronic environment. The\n5\nrespective 3d TM (Mn, Ni, Co, and Fe) states exhibit an L -edge (2p to unoccupied 3d) and an L -\n2 1/2 3\nedge (2p to unoccupied 3d), the differences between which were analyzed through the L -edge\n3/2 2,3\nenergy loss difference (ΔE) (Supplementary Table 9-12) 49. Surface-specific ΔE and L -edge shift\n2\nchanges were observed for Mn, Ni, and Fe, indicating enhanced charge-transfer dynamics and\nmodification of the electronic environment (influenced by changes in oxidation state, coordination\nnumber, bond length, and associated defect generation) 50. In contrast, Co exhibited minimal ΔE\nvariation or L -edge shift changes, suggesting a more passive electronic role, likely contributing to\n2\nstructural and electronic stability within the HEO matrix.\nComment 5: I would suggest the authors to repeat the OER and ORR activity tests for 3 times and add\nthe error bars on the corresponding LSVs. In addition, since the MnNiCoFe-CeO\n2\ncatalyst consists of the Ni species, a Ni oxidation peak should be observed on the LSV,\nwhile it is not presented in Fig.4a. The curves of limiting diffusion currents for MnNiCo-\nCeO , Mn-CeO in Fig.4d are abnormal. In addition, why the OER stability curve in\n2 2\nFig.3j shows an upward tendency at nearly 13h? is this a signal that the catalyst will\nundergo the reconstruction during the OER? Therefore, I think the authors should\nconduct the CV to activate the MnNiCoFe-CeO2 before testing its performance, and this\nalso can explain the disappearance of Ni oxidation peak in Fig.4a. In addition, both the\nOER/ORR activity and stability of this catalyst are unsatisfactory compared with the\nreported values in the literature.\nResponse: (1) The OER and ORR measurements were done in triplicate in order to confirm data\nreproducibility. The error bars have been added to the corresponding LSV curves, albeit\nas shaded borders, and the revised figures have been added to the manuscript.\nIntroductory text has been added. (2) CV activation tests were conducted in order to\ninvestigate the Ni redox behavior. Discussion to address the absence of the Ni oxidation\npeak in the LSV curves has been added so as to clarify this point. (3) The upward shift\n(27)\nobserved in the OER stability curve nearly 10 hours (upward tendency) has been\nanalyzed in detail. This behavior is attributed to possible dynamic restructuring of the\nCe active sites, the discussion of which has been added to the manuscript. (4) A new\ncomparative figure has been added in order to highlight the excellent electrochemical\nperformance (OER and ORR) of the MnNiCoFe-CeO HEO catalyst against other\n2\nbifunctional materials. This comparative analysis is now included in the revised\nmanuscript.\nManuscript Pages 14:\nFig. 4 shows electrocatalysis data for OER and ORR performances, each measured in triplicate to ensure\nreproducibility, with corresponding error bars included to indicate experimental variability.\nManuscript Pages 15:\nFig. 4 OER performance: (a) LSV curves (shaded regions indicative of error bars for triplicate\nmeasurement), (b) overpotentials, (c) Tafel plots; ORR performance: (d) LSV curves (shaded regions\nindicative of error bars for triplicate measurement), (e) half-wave potentials and limited current density,\n(f) Tafel plots\nManuscript Pages 14:\nAs shown in Supplementary Fig. 20, despite the Ni (common active site in OER as well) in the\nMnNiCoFe-CeO HEO, no distinct Ni oxidation peak was observed during CV or LSV measurements56.\nis likely to play a synergistic assisting role, contributing to the modulation of the local electronic\nenvironment through MVCT, thereby enhancing overall conductivity and structural stability. This\nconclusion is supported further by the subsequently presented XANES data and DFT simulations, both\nof which confirm that Ni does not participate directly in discrete redox transitions under OER conditions\nbut rather supports the activity of the active metal centers.\n(28)\nSupplementary Information Page 35 :\nSupplementary Fig. 20 CV activation curves\nAs shown in Supplementary Fig. 20, the CV activation curves show a slight increase in OER\nperformance followed by stabilization. This enhancement can be attributed to several factors, including\nsurface restructuring of the catalyst, improved electrolyte-catalyst interfacial contact, and/or enhanced\nionic transport pathways within the electrode matrix. Importantly, based on ex situ XANES and Raman\nanalyses, the bulk structure of the catalyst remains stable, suggesting that the observed activation is due\nprimarily to electrode/electrolyte interface-level alteration rather than bulk materials change.\nManuscript Pages 17-20:\nExamination of the stability of the multilevel disorder at different time scales is essential to understand\nthe operational and degradation mechanisms of HEOs during catalytic reactions, as shown in Fig. 5a.\nThe structural stability of the HEO in terms of OER and ORR after activation and extended testing was\nanalyzed by Raman. As shown in Fig. 5b, no additional peaks appeared after activation, indicating that\nthe Ce-O framework remains the dominant active phase. Even after long-term cycling, the Raman\nspectra remain unchanged, further confirming the high structural stability of the HEO and the absence\nof TM-containing secondary phase, which are observed commonly to result from TM diffusion,\nhydroxylation, and/or oxidation 59,60. This stabilization is facilitated by the large extent of lattice\ndistortion as a form of stress relief. Further, the relatively small changes in the oxygen defect\nconcentrations in the HEO of <13% (shifting from the initial 51.7% to 45.8-58.2%; Fig. 5) confirm this\nstability. The electronic stability was assessed by EPR spectroscopy, as shown in Supplementary Fig.\n27, where the decreases in the g-values immediately after OER and ORR activation indicate temporary\nelectron localization, probably associated with OH– or O adsorption at active sites. However, after\n2\nlong-term cycling, the g-values returned to their original states and no signal splitting was observed,\nconfirming reversible and stable electronic disorder behavior. The atomic stability of the HEO was\nevaluated by EDS mapping of pristine and post-reaction HEOs (Supplementary Fig. 28). These data\nconfirm the maintenance of elemental homogeneity in the absence of volumetric segregation, thus\nsupporting compositional consistency under operating conditions.\nThe identification, evolution, and stability of the active sites were examined by ex situ XANES and\nEXAFS analyses of Mn, Ni, Co, Fe, and Ce at different time stages (initial, post-activation, post-testing,\nand long-term) 61. These data elucidate the oxidation state changes, coordination environment evolution,\nand role of multi cation interactions in sustaining catalytic activity and stability. In order to evaluate\n(29)\nthe behavior of the TMs during catalysis, the Mn, Ni, Co, and Fe K-edges were examined. Both the\nXANES and EXAFS spectra show only minor variations in Fig. 5c and Supplementary Fig. 29,\nconfirming that the TMs undergo minimal changes under operating conditions. The charge-transfer\ndynamics revealed by the XANES data allow differentiation of the contributions of the individual TMs\nto the OER and ORR in Fig. 5c62. Ni and Fe show more positive edge shifts during OER, indicating\ntheir greater participation in oxygen evolution. In contrast, Mn and Co exhibit more negative edge\nshifts during ORR, suggesting their greater involvement in oxygen reduction. These minor yet distinct\ncontributions suggest that Mn and Co act as auxiliary facilitators during ORR, whereas Ni and Fe assist\nduring OER, while Ce is the dominant active centre. The EXAFS analysis of the TMs also confirms\nonly subtle modifications in the local coordination environments, indicating that they are not active\nsites. Detailed inspection of the EXAFS data (Supplementary Fig. 29) reveals that all four TMs\nexperienced small increases in M-O coordination after activation (upward trajectory), consistent with\nlimited oxygen adsorption59,60. Over extended cycling, the first coordination sphere exhibits a slight\ndecrease (downward trajectory, though still above pre-testing levels), which probably reflects the role\nof individual point defects. In contrast, the second coordination sphere exhibits a slight increase\n(upward trajectory), which is consistent with modest M-O-M ordering of the lattice after long-term\ntesting 59,60.\nIn the case of Ce, more pronounced spectral shifts in XANES were observed during OER and ORR\nprocesses, indicating electron-transfer processes associated with Ce sites, as shown in Fig. 5d. The\ndistinct shift in the Ce L -edge after OER, compared to that after ORR, suggests that Ce plays\n3\nfundamentally different roles in the two reactions. The oxidation of Ce active sites is attributed to their\ndirect participation in OER by the Ce3+ → Ce4+ transition, highlighting that OER has a stronger impact\non the Ce oxidation state. Such redox transitions likely facilitate Ce-OH bond formation. Both post-\ntesting and long-term stability measurements reveal further oxidation of the Ce sites, indicating that Ce\noxidation plays an important role in OER activation. In contrast, the absence of a significant shift after\nORR suggests a more passive role, where Ce sites act primarily as adsorption centers for O molecules,\n2\nwithout notable changes in oxidation state. The data for XANES over long-term cycling confirm that\nCe largely retains its original electronic configuration, thus reflecting its high atomic stability.\nThe local atomic coordination of Ce, which was characterized by EXAFS, further illustrates the\ndistinct behavior of the Ce-O bonds during OER (Fig. 5e) and ORR (Fig. 5f). After OER activation,\nthe disordered Ce-O bond structure is preserved although the overall intensity increases suggest higher\nCe coordination while maintaining the bonding types (both ordered Ce-O and disordered Ce-O) of the\ninitial HEO. Increasing the coordination of the Ce is indicative of OH⁻ bonding at the Ce center,\nconfirming the role of Ce as the active site. After 10 h, the Ce-O bonds display a positive shift, which\nconfirms structural alteration and bond elongation, consistent with the upward trajectory observed\nduring stability testing. After long-term OER cycling, the Ce-O bonds return to their initial state, thus\nretaining the bonding characteristics of the initial HEO and confirming that local structural degradation\nis not significant under OER conditions. In contrast, Ce active sites behave differently in ORR. After\nactivation, the ordered Ce-O bonds remain largely unchanged while the intensity of the disordered Ce-\nO bonds increases, where the latter suggests weak Ce-O₂ interactions that promote O₂ adsorption and\nreduction, confirming that Ce is the active site for ORR. However, after extended ORR testing and\nlong-term operation, the amount of disordered Ce-O bonds diminishes, thereby increasing the\nproportion of ordered Ce-O bonds. This effectively decreases the dynamic flexibility of the Ce-O bonds,\nthus leading to electron localization at the Ce sites and reducing the availability of delocalized electrons\nrequired for efficient O₂ adsorption and dissociation during ORR. Together, these findings demonstrate\nthat Ce defect sites act as crucial active centers, playing distinct roles in OER and ORR: in OER, they\nparticipate directly through redox cycling and bond reconstruction while, in ORR, they function mainly\nas adsorption centers.\nIn order to identify which of the metal constituents are the active sites in the high-entropy oxide,\nboth OER and ORR pathways, each involving four electron transfer steps, were analyzed using first-\nprinciples DFT simulations, as shown in Fig. 5g. Optimized surface models were constructed for each\nmetal ion site (Mn, Ni, Co, Fe, Ce), with adsorption energies calculated for all key oxygenic\nintermediates (*OH, *O, *OOH) along the reaction pathways. Of all the sites, Ce ions exhibited the\nlowest energy barriers across the reaction steps, again indicating that these are the primary active sites.\nFor Ce, the rate-determining step is the formation of *OOH, with the largest free energy barrier (ΔG)\n(30)\nof 1.63 eV. Similar trends were observed for other metal sites but with higher energy barriers for *OOH\nformation. The calculated overpotentials of Mn, Ni, Co, Fe, and Ce are used to represent the overall\nOER/ORR activity of these metal ions in Fig. 5h, confirming the dominance of Ce (only 0.4 eV) in the\nexperimental activity trend. These findings highlight the pivotal role of low-CN Ce sites in facilitating\nboth OER and ORR processes, while the other transition metals primarily play supportive roles, as also\nsuggested by the EXAFS data.\nSupplementary Information Page 49:\nThe data for catalysts in Supplementary Table 14 show that the HEO exhibits superior OER/ORR\nperformance than MnNiCo-CeO . These data also show that, in comparison to metal-carbon catalysts,\n2\nthe activities (left column) for both OER and ORR are average, the kinetics (middle column) for both\nOER and ORR are superior, and the OER stability (right column) is superior but the ORR stability (right\ncolumn) is average. In comparison to oxide catalysts, the activities for OER are superior but for ORR\nare average, the kinetics for both OER and ORR are superior, and OER stability is superior but the ORR\nstability is average. However, theses data on their own are independent and unable to foreshadow\nentirely a material’s performance in batteries.\nHence, the power density and stability data for ZABs are given in Fig. 6g. These data reveal, for\nboth of these parameters, the HEO exhibits outstanding performance. These data are attributed to three\npossible features: (1) a balanced bifunctional performance, as required for battery charge/discharge\nphenomena. (2) The HEO is chemically compatible with the zinc anode, as evidenced by the high OCP\n(Fig. 6b). (3) The multilevel disorder, multiplicity of ions, and MVCT contribute to improved and\nuniform charge transfer, which allows good charge-carrier-utilization efficiency.\nManuscript Pages 22:\nFig. 6 (g) Comparison of ZAB power densities and stabilities\n(31)\nSupplementary Information Page 42:\nSupplementary Table 14 Comparison of OER/ORR performances and kinetics with those of other state-of-the-art catalysts\nOER ORR\nMaterial Overpotential Tafel slope Half-wave Tafel slope Ref.\nStability (h) Stability (h)\n(V@10mA cm-2) (mV dec-1) potential (V) (mV dec-1)\nPresent Work\nMnNiCo-CeO 1.60 63 10 0.69 96 3\nMnNiCoFe-CeO 1.53 57 50 0.73 53 7\nSingle-atom Fe-N -C 1.83 243 -- 0.91 69 15 36\nx\nHNG-900 1.69 154 -- 0.78 72 -- 37\nNCN-1000 1.55 142 3 0.82 86 3 38\nLDH-POF 1.48 99 -- 0.80 46 -- 39\nFeCoNiMnIr/NCNT 1.53 82 1000 cycles 0.83 68 1000 cycles 40\nPt/C+Ir/C 1.62 81 -- 0.85 83 -- 36\nCMP@PNC 1.54 74 32 0.78 62 7000 cycles 41\nFeNi @NC 1.52 73 10 0.78 78 10 42\nP/Fe–N–C 1.53 65 7 0.90 -- -- 44\nCo@NPC-H 1.58 57 -- 0.77 33 35 45\nOxide Catalysts\nLa CoMnO >1.8V 130 -- 0.75 104 -- 46\n2 6\nMnO -TiC 1.56 110 -- 0.80 72 3.33 47\nx\nCe-Co O 1.67 105 28 0.69 64 -- 48\n3 4\nCoFeNiMnCuZnO -PMA 1.45 98 -- 0.78 81 -- 49\nx\nCo O 1.57 85 -- 0.71 115 -- 48\n3 4\nCoP /CeO /C 1.57 80 30 0.75 58 ~5 50\n3 2\nLa Sr CoO 1.62 77 -- 0.62 153 -- 51\n0.7 0.3 3−δ\nAmorphous-CoO 1.59 69 12 0.85 73 12 52\nLaCo Ru O δ 1.69 43 -- 0.63 -- -- 53\n1−x x 3−\nMnCo O -A ~1.65 -- -- 0.78 45 -- 54\n2 4\n(32)\nIncorporation. J. Am. Chem. Soc., 145, 3647-3655 (2023).\nBifunctional Electrocatalysts for Oxygen Evolution and Reduction. Carbon, 144, 492-499\n(2019).\nThe Correlation between Electrocatalytic Activity and Complex Spin Configuration. ACS Appl.\nMater. Interfaces, 10, 19746-19754 (2018).\nx\nElectrocatalyst for Corrosion Resistant Oxygen Electrode of Zn-Air Batteries. Nano Energy,\n67, 104208 (2020).\n3 4\nRechargeable Aqueous Zn-Air Battery. Adv. Funct. Mater., 33, 2212021 (2023).\nPhotoelectrocatalysts for Zn-Air Batteries. J. Am. Chem. Soc., 146, 10735-10744 (2024).\n3 2\nOxygen Electrocatalysts for Rechargeable Zn-Air Batteries. Appl. Catal. B Environ., 321,\n122029 (2023).\nCatalyze Bifunctional Oxygen Activation for a Rechargeable Zn-Air Battery. ACS Appl. Mater.\nInterfaces, 12, 40355-40363 (2020).\nfor High Performance and Robust Rechargeable Zn-Air Batteries. Adv. Funct. Mater., 31,\n2101239 (2021).\n20612-20620 (2020).\nGeometrical-Site Occupation Modification Driven by the Oxygen Evolution Reaction. Adv.\nMater., 34, 2202874 (2022).\nComment 6: The authors concluded that Ce atoms are the true active sites for both OER and ORR,\nwhile Ni, Fe, Co and Mn act as the co-catalysts. I have some concerns on this conclusion.\nOn the one hand, Ni and Co are widely recognized as reaction sites for OER, and Mn is\nalso an active site for ORR. It is unlikely that they can only modify the electronic\nstructure of Ce during the reaction. On the other hand, since the authors only conducted\nXAS on Ce before and after the reaction, the provided evidence is insufficient. I would\nsuggest that the authors supplement with in-situ XAS experiments for all elements\nincluding Ni, Mn, Fe, and Co, and perform DFT calculations to determine the reaction\nfree energy of each site, thereby accurately identifying the true active sites.\nResponse: (1) Since in situ XAS is not available to us, we have undertaken ex situ XAS for all of\nthe metals (Mn, Ni, Co, Fe, Ce) after OER and ORR testing at different stages for both\nOER and ORR. These results are given in detail in the response to Reviewer 1, Comment\n12. (2) DFT simulations were carried out in order to support the interpretation of the\nexperimental findings. These calculations reveal a strong correlation with the\nexperimental results, thus supporting the conclusion that only Ce is the active site. Thus,\nthe ex situ XAS data provide the same role had we been able to do in situ XAS. The\ntheoretical analysis and its correlation with the experiment data are discussed in the\nresponse to Reviewer 2, Comment 5.\nManuscript Page 20-21:\nTMs commonly are identified as active sites in OER and ORR reactions63,64. However, in the present\nwork, they have been shown not to serve as the primary active centers. This difference is explained in\n(33)\nterms of multilevel disorder engineering in high-entropy oxides. (1) Structural disorder: A large\nnumber of oxygen vacancies are formed and these preferentially localize and cluster around Ce owing\nto its flexible Ce3+/Ce4+ redox couple and the low energy barrier for vacancy formation. This reduces\nthe likelihood of TM participation in reactions with active oxygen intermediates. (2) Electronic\ndisorder: The semimetallic nature of the HEO, combined with the presence of multiple cations, induces\nstrong electronic disorder (d-band broadening and shifting). This bridging effect suppresses the distinct\nlocalized redox activity of individual TMs, thereby reducing any catalytic contribution and, instead,\nacting primarily as charge-transfer mediators rather than distinct active sites. (3) Atomic disorder:\nEXAFS analysis shows that, in HEOs, TMs typically are locked into high-CN frameworks with limited\ndistortion. This structural rigidity further reduces their ability to participate directly in catalytic\nreactions. Together, these factors explain why, unlike in conventional catalysts, the TMs in this HEO\nsystem do not act as dominant active sites, with Ce defect centers’ instead playing the primary catalytic\nrole.\nElectrocatalytic Systems for Oxygen Reduction and Evolution Reactions. ChemElectroChem,\n8, 3433-3456 (2021).\n(2020).\nComment 7: Some mistakes should be noticed. For example, the scale bar should be added to Fig.1h,\nthe atomic orbitals in the manuscript such as 3d, 2p should be italicized, many\npunctuations are forgotten or misused. The authors should carefully review and check\nthe manuscript again.\nResponse: The text has been reviewed carefully.\n(34)"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have thoroughly and convincingly addressed all reviewer comments. The revisions have strengthened the scientific rigor and clarity of the manuscript, and the presented results hold substantial significance to the field. I therefore recommend this manuscript for publication in Nature Communications.", "reviewer_2": "The authors have addressed my comments.", "reviewer_3": "The authors have addressed my previous concerns thoroughly, and the scientific validity of the manuscript have been improved. Although in situ XAS was not available to the authors, they provided ex-situ XAS data for all elements (Mn, Ni, Co, Fe, Ce) at different reaction stages (initial, after activation, after testing, after long-term cycling). These data reveal that only the electronic structure and coordination environment of Ce underwent significant changes, while the other transition metals showed minimal variation, robustly confirming Ce is the primary active site. Furthermore, the authors supplemented their findings with DFT calculations, which theoretically corroborated that Ce serves as the main active site. Therefore, I would suggest the acceptance of the revised manuscript."}, "author_response": ""}]

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