Introduction

Electrochemical hydrogen evolution reaction (HER) is an eco-friendly, cost-efficient, and feed-rich technology to manufacture high gravimetric-energy-density and clean hydrogen fuels, which can satisfy rising energy demand while mitigating environmental situations by efficiently converting and storing electricity from intermittent sources (e.g., wind or solar) in their chemical form1,2,3,4,5. Hitherto, Pt-based nanomaterials are the most sophisticated HER electrocatalysts owing to their first-rank bonding strength with hydrogen6,7,8. However, the high cost, suboptimum electrochemical durability, and significantly lower activity in non-acidic electrolytes of Pt bring about tremendous barriers to their large-scale application in electrolyzers and fuel cells9,10,11. This poses a challenge for researchers stemming from the ever-increasing demand for pH-universal HER electrocatalysts with high performance.

High-entropy alloys (HEAs), with five or more elements in near equiatomic ratios and homogeneously mixed solid-solution phase, have excited rapidly growing interest in diverse research areas owing to high configuration entropy, sluggish diffusion, lattice distortion, and cocktail effects12,13. Notably, compared with single or bimetallic catalysts, the multi-component adjustability of HEAs can provide different desired active sites and an almost continuous distribution of binding energy to synchronously stabilize all intermediates during multistep catalytic reactions14. Meanwhile, particular high-entropy mixing states and sluggish diffusion effect can endow the catalyst with remarkable stability by suppressing the galvanic corrosion and preventing the dissolution of atoms into corrosive electrolytes15,16. Similarly, the development of single-atom to high-entropy single-atom catalysts (HESACs) is to impart a variety of different adsorption sites while possessing near 100% utilization efficiency of metal atoms, which is highly beneficial for multistep tandem reactions or reactions requiring multifunctional catalysts (Fig. 1a)17,18,19,20. However, as for HESACs, the lack of synergistic effects between adjacent metal atoms resulting from fully isolated active sites and over-rigid local constructions limit their activities in specific catalytic reactions like low-temperature carbon monoxide oxidation21. Such a tendency will evolve into a definitive scenery of metal elements at the sub-nanometric restriction (nearly 1 nm thickness). Thereinto, sub-nanometric two-dimensional (2D) materials have an extremely large proportion of surface atoms that are accessible to catalytic reactions, which can maximize the utilization efficiency of metal atoms, especially for platinum group metals (PGMs)22,23,24. Meanwhile, high-density active sites show a synergistic effect with neighboring metal atoms, which optimizes their electronic configurations and intermediate adsorption energies, thus boosting their catalytic performance25,26,27. Lamentedly, different metallic elements differ in size, crystal configuration, and electronegativity, resulting in varying degrees of lattice mismatch between them, which is not conducive to HEA formation. Therefore, most of the reported HEAs are still confined to nanoparticles, and the construction of sub-nanometric 2D HEA materials is scarce and challenging28. In addition, the applied potential, reaction temperature, or erosive electrolyte leads to the structural transformation or profound reorganization of electrocatalysts during the actual catalytic process, severely hindering the precise identification of the true catalytically active center and the establishment of structure-activity relationships29. Recently, operando characterization techniques, such as operando X-ray absorption spectroscopy (XAS), Fourier transform infrared (FTIR) spectroscopy, and Raman spectroscopy, provide an effective way to break these barriers, which can track the kinetics of catalysts and monitor the adsorption/desorption behavior of reactive intermediates during catalysis30,31,32,33 (Supplementary Fig. 1). Nevertheless, most of these techniques are applied to the analysis of single-atom and bimetallic catalytic reaction systems due to their clear and well-defined coordination structures34,35,36,37,38. As an equally crucial catalyst system, it remains to be explored to gain atomistic-level insight into active site dynamics and interaction mechanisms for HEAs with tanglesome atomic arrangements and multiple elements of similar electron contrasts under realistic catalytic conditions39.

Fig. 1: Morphology and structure characterizations of sub-nanometric PdRhMoFeMn HEMs.
figure 1

a The structural evolution from monometal catalysts to HEAs and from SACs to HESACs. b–d Low-resolution HAADF-STEM image (b), HRTEM image (c), and aberration-corrected HRSTEM image at the edge of a wrinkle (d) of PdRhMoFeMn HEMs. The inset in d is the AFM image of PdRhMoFeMn HEMs. e, f XRD (e) and SEM-EDS (f) results of PdRhMoFeMn HEMs. g Aberration-corrected HRSTEM and geometric phase analysis (GPA) images of PdRhMoFeMn HEMs and Pd metallenes. h, i aberration-corrected HRSTEM (h) and EDS elemental mapping images (i) of PdRhMoFeMn HEMs.

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This work proposes a general one-pot wet-chemical strategy to fabricate a series of sub-nanometric high-entropy metallenes (HEMs), including but not limited to quinary PdRhMoFeMn, senary PdRhIrCoFeMo, septenary PdRhIrFeMoMnW and octonary PdRhIrMnMoRuFeCo HEMs. The representative quinary PdRhMoFeMn HEMs demonstrate small overpotentials at −10 mA cm–2 (η10), high mass activities, and superior stability over a broad pH range (0–14). Density functional theory (DFT) calculations speculate that the Rh site is the possible active center with the optimal hydrogen adsorption free energy (ΔGH*) (−0.132 eV) in an acidic environment. In neutral and alkaline electrolytes, the Pd site with strong water adsorption energy (−0.34 eV) and small water dissociation energy barrier (0.53 eV) facilitates the dissociation of water to produce protons, followed by the hydrogen spillover from Pd to Rh sites. Additionally, the Mn site shows strong binding energy (−3.05 eV) for hydroxyl groups, which accelerates the water dissociation step. In particular, operando XAS further traces the dynamics of real active sites and visually reveals multi-site synergistic mechanisms for PdRhMoFeMn HEMs in different electrolytes during the electrocatalytic HER, which paves an avenue to rationally design next-generation high-efficiency HEA electrocatalysts with desirable multifunctional active sites for complex multi-electron catalytic processes.

Results

Materials synthesis and characterization

Typical sub-nanometric PdRhMoFeMn HEMs were synthesized via a simple one-pot wet-chemical strategy through heating a mixed solution containing palladium(II) acetylacetonate (Pd(acac)2), hexarhodium hexadecacarbonyl (Rh6(CO)16), dodecacarbonyltriiron (Fe3(CO)12), manganese carbonyl (Mn2(CO)10), molybdenum hexacarbonyl (Mo(CO)6), ascorbic acid (AA), and oleylamine (Supplementary Fig. 2). Low-magnification high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and TEM images in Fig. 1b and Supplementary Fig. 3 show that the obtained products are dominated by graphene-like 2D nanosheets with abundant porous nanochannels. High-resolution TEM (HRTEM) image confirms that PdRhMoFeMn HEMs are ultrathin and possess a certain curvature (Fig. 1c). The thickness of PdRhMoFeMn HEMs was determined to be six atomic layers from the edge seen in aberration-corrected HAADF-STEM (Fig. 1d), in good conformity with a thickness of ~1 nm characterized by AFM atomic force microscopy (AFM), affirming the successful formation of sub-nanometric metallenes (Supplementary Fig. 4). The clear lattice fringes in Fig. 1d indicate a lattice spacing of 0.228 nm, slightly higher than the lattice distance of the Pd (111) facet. Additionally, the X-ray diffraction (XRD) pattern in Fig. 1e shows that PdRhMoFeMn HEMs possess a face-centered cubic (fcc) configuration without phase segregation, which is analogous to that of pure Pd. The weakening and broadening of XRD peaks could be attributable to the lattice distortion originating from the interposition of Mn, Fe, Rh, and Mo atoms. The Pd/Rh/Mo/Fe/Mn ratio was determined by the SEM energy dispersive X-ray spectroscopy (SEM-EDS) to be 23.52/20.97/17.42/16.58/21.51 (Fig. 1f). Similar results were obtained from the inductively coupled plasma optical emission spectroscopy (ICP-OES) measurement (Pd/Rh/Mo/Fe/Mn=23.37/19.53/18.07/17.35/21.68) (Supplementary Table 1). The difference between the initial feed ratio and the ratio of elements in the obtained HEMs is due to the difference in the reduction difficulty of various metal precursors40,41. Aberration-corrected HAADF-STEM measurements were employed to further analyze the fine structure of PdRhMoFeMn HEMs. As presented in Fig. 1g, h, many lattice distortions including edge dislocation (ED) and stacking fault (SF) are clearly observed in HEMs, which is a fundamental characteristic of high-entropy structures caused by the disordered distribution of atoms on the equivalent sites but with different size, mass, and electronegativity. The lattice distortion feature was further verified by the (111) lattices from different selected regions in PdRhMoFeMn HEMs, where the average lattice distance varies from 0.221 nm (h4) to 0.229 nm (h1) to 0.232 nm (h2) and to 0.239 nm (h3) (Supplementary Fig. 5). These lattice defects could offer rich low-coordination sites to boost the catalytic activity. Furthermore, aberration-corrected HAADF-STEM-EDS elemental mappings show the homogenous distribution of all elements throughout the HEMs (Fig. 1i). Such a highly stable sub-nanometric HEA nanosheet has been long sought since it can provide various active sites to favor intermediate reaction processes and expose nearly all metal atoms to electrocatalysis, as will be discussed later.

The XAS was performed to deeply probe into the atomic-coordination environment and electronic configuration of sub-nanometric PdRhMoFeMn HEMs. As shown in Fig. 2a, c, the X-ray absorption near-edge structure (XANES) spectra exhibit that the white line intensities of Pd and Rh in PdRhMoFeMn HEMs are closer to Pd and Rh foils and far away from the PdO and Rh2O3 reference samples, indicating that the Pd and Rh species in HEMs mainly sit in the metallic state. Compared to the corresponding metal foils, the post-edges of Pd and Rh in HEMs show slight differences in shape and intensity, confirming the establishment of alloys instead of elemental segregation into pure metals. In addition, the extended X-ray absorption fine structure (EXAFS) spectra of HEMs show an obvious prominent peak at ~2.75 Å for Pd-M (Fig. 2b) and ~2.75 Å for Rh-M (Fig. 2d), respectively. Due to the thinness of the material, lower coordination numbers, and a homogeneous distribution of metal atoms, it is indeed possible to observe Rh-Rh and Pd-Pd neighbors42,43. Moreover, Pd-M and Rh-M are slightly distinct from the Pd-Pd and Rh-Rh bonds in Pd and Rh references. This phenomenon results from small changes in the coordination environment caused by the presence of other smaller atoms (Mo, Fe, and Mn) around the relatively large Pd and Rh atoms. Therefore, M can be Pd, Rh, Mo, Fe, or Mn. The maximum peak intensity of Pd-M and Rh-M at around 8.8 Å can be observed in the wavelength-transformed EXAFS (WT-EXAFS) patterns of Rh and Pd in PdRhMoFeMn HEMs, further verifying a variation in the atomic-coordination environment relative to Pd and Rh foils (Fig. 2g, h). Furthermore, the XANES spectra of Fe, Mo, and Mn show positive energy shifts, suggesting that their chemical states lie between those of the metallic and oxide standard samples, probably due to the exposure of the more easily oxidizable Fe, Mn, and Mo atoms on the catalyst surface (Supplementary Fig. 6). The surface chemical composition of PdRhMoFeMn HEMs was further investigated with X-ray photoelectron spectroscopy (XPS)44,45,46. The XPS survey spectrum identifies that Pd, Rh, Mo, Fe, and Mn elements coexist in HEMs (Supplementary Fig. 7a). The Pd 3d XPS spectrum reveals the presence of main metallic Pd and a small amount of palladium oxide, in which the peaks at 334.83 and 340.14 eV correlate to Pd0 3d5/2 and Pd0 3d3/2, respectively (Fig. 2e)47. The peaks at 336.08 and 341.47eV match Pd2+ 3d5/2 and Pd2+ 3d3/248. Similarly, the majority of Rh exists as a zero-valence substance, with a small proportion as a 1+ or 3+ substance (Fig. 2f). In detail, the high-resolution Rh 3d spectra of PdRhMoFeMn HEMs are composed of six fitting peaks of Rh0 3d5/2 (306.59 eV), Rh0 3d3/2 (311.31 eV), Rh+ 3d5/2 (307.54 eV), Rh+ 3d3/2 (312.58 eV), Rh3+ 3d5/2 (308.13 eV) and Rh3+ 3d3/2 (312.86 eV)49. Furthermore, the Fe 2p, Mn 2p, and Mo 3d spectra indicate that Fe, Mn, and Mo atoms in PdRhMoFeMn HEMs exist in partially oxidized states, consistent with the above-mentioned XANES analysis (Supplementary Fig. 7b–d). Due to the exposure of under-coordinated corner atoms and edge atoms with stronger oxyphilic nature in ultrathin HEMs to air, the trace metal-oxygen species on the catalyst surface are formed, which is a common phenomenon in the reported literature16,26,50. Specifically, the HER activity of RhO2 and PdO is much lower than that of PdRhMoFeMn HEMs (Supplementary Fig. 8), which indicates the effects of these trace amounts of metal-oxygen species on the HER mechanism and performance are minimal, which are generally ignorable in reported literature42,51,52.

Fig. 2: Electronic structure investigations.
figure 2

a, b The Pd K-edge XANES spectra and FT-EXAFS spectra of PdRhMoFeMn HEMs, PdO, and Pd foil with phase correction. c, d The Rh K-edge XANES spectra and FT-EXAFS spectra of PdRhMoFeMn HEMs, Rh2O3, and Rh foil with phase correction. e, f Pd 3 d and Rh 3 d XPS spectra of PdRhMoFeMn HEMs. g 2D WT-EXAFS spectra of PdRhMoFeMn HEMs, PdO, and Pd foil. h 2D WT-EXAFS spectra of PdRhMoFeMn HEMs, Rh2O3, and Rh foil.

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To understand the growth mechanism of PdRhMoFeMn HEMs, time-dependent TEM-EDS experiments were carried out. As demonstrated in Supplementary Fig. 9, Pd(acac)2 is first reduced to form small Pd metallene seeds due to only the appearance of the Pd peak at the first 1 min reaction, then Rh atoms from the decomposition of Rh6(CO)16 begin to integrate into the initial Pd metallene. Finally, Mo, Fe, and Mn atoms decomposed from Fe3(CO)12, Mn2(CO)10, and Mo(CO)6 are alloyed into this nanosheet to form HEMs with a distinctively curved geometry. CO molecules decomposed from carbonyl metal compounds act as a capping agent, confining the Pd (111)-facet growth and leading to the 2D construction, analogous to reported PdMo bimetallene26. Using the same preparation scheme but altering the type and concentration of metal precursors and reaction temperature, senary PdRhIrCoFeMo HEMs, septenary PdRhIrFeMoMnW HEMs, and octonary PdRhIrMnMoRuFeCo HEMs were successfully fabricated. TEM and AFM analyses confirm the metallene morphology and ultrathin structure of less than 1.5 nm (Supplementary Figs. 10 and 11). HRTEM images show that there was no formation of nanoparticles or clusters on the surfaces of senary, octonary, and septenary HEMs, proving that all metal atoms are well mixed within the metallenes. They also display clear lattice fringes with lattice distances of 0.227, 0.230, and 0.229 nm, corresponding to the {111} facets of senary, octonary, and septenary HEMs, respectively. From the STEM-EDS element mappings (Supplementary Fig. 10), SEM-EDS (Supplementary Fig. 12), and ICP-OES results (Supplementary Table 1), each element content of HEMs is in the range of 5–35% and distributed homogeneously around the HEMs without component segregation. In addition, the XRD pattern shows that all HEMs have an fcc alloy structure without phase separation. The broadening and weakening of their peaks and the shift of peak positions relative to pure Pd are due to the introduction of other metal elements, proving the successful formation of single-phase HEMs (Supplementary Fig. 13). Therefore, our synthetic strategy possesses general suitability for the manufacture of HEMs.

Electrocatalytic performance toward HER

To assess the potential electrocatalytic capabilities of as-prepared HEMs, the HER activity of sub-nanometric PdRhMoFeMn HEMs was first measured utilizing a standard three-electrode configuration in a 0.5 M H2SO4 aqueous solution. For comparison, the HER performance of PdMoFeMn (Supplementary Fig. 14), RhMoFeMn (Supplementary Fig. 15), and PdRh metallenes (Supplementary Fig. 16) synthesized by the same preparation method as PdRhMoFeMn HEMs, and Pt/C catalysts were also investigated as reference substances under the same electrochemical test conditions. All the polarization curves were calibrated against reversible hydrogen electrode (RHE) as shown in Supplementary Figs. 17 and 18. Figure 3a shows that PdRhMoFeMn HEMs have a near-zero onset potential (−0.16 mV) and only require a η10 of 6 mV, lower than those of RhMoFeMn metallenes (20 mV), PdRh metallenes (16 mV), and Pt/C (13 mV). However, the η10 of PdMoFeMn metallenes increases sharply to 57 mV, 51 mV higher than that of PdRhMoFeMn HEMs, indicating that Rh is the potential active site under acidic conditions. Impressively, PdRhMoFeMn HEMs produce an industrial-level current density (500 mA cm−2) at a small overpotential of 46 mV, which is much better than reference samples (Supplementary Fig. 19). Moreover, the resulting Tafel slope of PdRhMoFeMn HEMs is 16 mV dec−1, smaller than those of RhMoFeMn metallenes (30 mV dec−1), PdMoFeMn metallenes (64 mV dec−1), PdRh metallenes (32 mV dec−1), and Pt/C (17 mV dec−1) (Fig. 3b). This result reflects that the Rh introduction optimizes the electrochemical hydrogen adsorption/desorption and the HER pathway changes from the Volmer-Heyrovsky mechanism for PdMoFeMn metallenes to the Volmer-Tafel mechanism for PdRhMoFeMn HEMs53,54. Through extrapolating the Tafel plots, the exchange current density (j0) of PdRhMoFeMn HEMs was determined (4.9 mA cm−2). It is remarkably greater than that of RhMoFeMn metallenes (2.2 mA cm−2), PdMoFeMn metallenes (1.2 mA cm−2), PdRh metallenes (2.2 mA cm−2), and Pt/C (1.8 mA cm−2), suggesting the fastest kinetic essence towards hydrogen evolution (Supplementary Fig. 20). To fairly evaluate their potential for practical applications, the calculated mass activity of each sample was normalized with the loading of PGMs. Figure 3c shows that PdRhMoFeMn HEMs achieve the highest mass activity of 35.7 A per milligram PGMs at an overpotential of 50 mV, which is 16.2, 178.4, 37.5, and 9.1 times higher than those of RhMoFeMn metallenes, PdMoFeMn metallenes, PdRh metallenes, and Pt/C, respectively. As a key evaluation parameter for advanced electrocatalysts, the electrochemical durability of PdRhMoFeMn HEMs was further assessed in a 0.5 M H2SO4 electrolyte. As illustrated in Fig. 3d, the polarization curves of PdRhMoFeMn HEMs before and after 10,000 cyclic voltammetry (CV) cycles remain virtually unchanged, and the η100 of PdRhMoFeMn HEMs increases only 1 mV after 10,000 cycles. In striking contrast, the polarization curves of RhMoFeMn metallenes, PdMoFeMn metallenes, PdRh metallenes, and Pt/C have displayed visible deterioration after 10,000 cycles (Supplementary Fig. 21). Moreover, the chronopotentiometry curve in Fig. 3d shows that PdRhMoFeMn HEMs have only 3 mV degradation after 20 h, further proving its superior long-term stability. Besides, the TEM images show that PdRhMoFeMn HEMs maintain the nanosheet shape, and the distribution of the nanosheet is still uniform without aggregation (Supplementary Fig. 22a, b). XRD results in Supplementary Fig. 22c suggest that (111) facet-dominated fcc structure could be well retained after 10,000 cycles. Moreover, the ICP-OES characterizations before and after 10,000 cycles indicate that there was no obvious change in the composition of PdRhMoFeMn HEMs (Supplementary Fig. 22d). Supplementary Fig. 23 also shows that after 10,000 cycles, there are no significant changes observed in the XANES spectra of each element. However, some metallic Pd sites may appear (Supplementary Fig. 23a), with a relatively small impact on the performance of PdRhMoFeMn HEMs, which is proved by almost unchanged HER activity after 10,000 cycles (Fig. 3d).

Fig. 3: Electrocatalytic HER performance evaluation of sub-nanometric PdRhMoFeMn HEMs.
figure 3

The non-iR corrected polarization curves were provided in the Supplementary Information. a, b Polarization curves with iR-compensation (a), corresponding Tafel plots (b) of PdRhMoFeMn HEMs, RhMoFeMn metallenes, PdMoFeMn metallenes, PdRh metallenes, and Pt/C in 0.5 M H2SO4 electrolyte. c η10 (left) and mass activities (right) at an overpotential of 50 mV of these nanocatalysts in 0.5 M H2SO4 electrolyte. d Polarization curves of PdRhMoFeMn HEMs with iR-compensation before and after 10,000 CV cycles in 0.5 M H2SO4 electrolyte. The insert is the chronopotentiometry curve of PdRhMoFeMn HEMs without iR-compensation operated at 10 mA cm–2 in 0.5 M H2SO4 electrolyte. e, f Polarization curves with iR-compensation (e), corresponding Tafel plots (f) of PdRhMoFeMn HEMs and Pt/C in 1.0 M PBS and 1.0 M KOH electrolytes, respectively. The testing conditions include GCE surface area: 0.07 cm2, catalyst loading: 0.286 mg cm‒2, nobel metal loading: 0.028 mg cm‒2 (PdRhMoFeMn HEMs), 0.027 mg cm‒2 (RhMoFeMn metallenes), 0.039 mg cm‒2 (RhMoFeMn metallenes), and 0.057 mg cm‒2 (PdRh metallenes and Pt/C), electrolyte pH: 0.37 ± 0.05 (0.5 M H2SO4), 6.96 ± 0.03 (1 M PBS), and 13.81 ± 0.14 (1 M KOH), electrolyte resistance: 6.4 ± 0.3 Ω (0.5 M H2SO4), 21.6 ± 0.6 Ω (1 M PBS), and 5.5 ± 0.4 Ω (1 M KOH).

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Since proton or hydroxide concentration will always affect the performance of electrocatalysts during electrolysis, a hopeful electrocatalyst should function effectively at all pH. Therefore, the HER activities of PdRhMoFeMn HEMs were also examined under neutral and alkaline conditions. As shown in Fig. 3e and Supplementary Fig. 24, PdRhMoFeMn HEMs require the smallest η10 of 23 and 26 mV and the highest mass activities of 1.97 and 2.93 A per milligram PGMs at an overpotential of 100 mV in 1.0 M PBS and 1.0 M KOH, respectively, outperforming all control samples. Furthermore, the Tafel analysis was applied to insight into the HER kinetics of various catalysts in neutral and alkaline electrolytes (Fig. 3f). Under the neutral condition, the Tafel slopes of RhMoFeMn and PdMoFeMn metallenes are 75 and 96 mV dec−1, respectively, whereas PdRh metallene shows a Tafel slope of 56 mV dec−1 (Supplementary Fig. 24b), indicating that the RDS for RhMoFeMn and PdMoFeMn metallenes is the Volmer step (* + H2O + e– → H* + OH–), whereas the RDS for PdRh metallenes is the Heyrovsky step (H* + H2O + e– → H2 + OH–)30. It suggests that the coexistence of Pd and Rh is beneficial for the water dissociation reaction. The Tafel slope of PdRhMoFeMn HEMs further decreases to 33 mV dec−1, demonstrating that the intervention of Mo, Fe, and Mn can alter the HER pathway from the Heyrovsky mechanism with electrochemical desorption as the RDS for PdRh metallenes to the Volmer-Tafel mechanism for PdRhMoFeMn HEMs with chemical desorption of hydrogen as the RDS55. In alkaline electrolytes, the Tafel slope of RhMoFeMn, PdMoFeMn, and PdRh metallenes are 85, 168, and 101 mV dec−1, respectively, while PdRhMoFeMn HEMs demonstrate a Tafel slope of 41 mV dec−1, indicating that the reaction HER pathways of all sample are the Volmer-Heyrovsky mechanism but only the RDS for PdRhMoFeMn HEMs is the Heyrovsky step (Supplementary Fig. 24e)56. It can be inferred that the Mo, Fe, and Mn atoms may have a strong adsorption capacity for hydroxide ions, thus accelerating the water dissociation step on the catalyst surface, similar to previous literature reports57. Meanwhile, PdRhMoFeMn HEMs show the greatest j0 of 2.0 mA cm−2 in the neutral medium and 2.3 mA cm−2 in the alkaline medium, further proving its superior HER kinetics (Supplementary Fig. 25). As shown in Supplementary Figs. 26 and 27, the polarization curves of PdRhMoFeMn HEMs have a negligible negative shift after 10,000 cycles relative to those of RhMoFeMn metallenes, PdMoFeMn metallenes, PdRh metallenes, and Pt/C in 1.0 M PBS and 1.0 M KOH media, suggesting the excellent stability and durability under both neutral and alkaline conditions.

To investigate the reasons for the enhanced HER performance of PdRhMoFeMn HEMs, we analyzed the electrochemical double-layer capacitance (Cdl) by performing CV tests with different scan rates. Whereby, PdRhMoFeMn HEMs exhibit the Cdl values of 14.8, 14.6 and 19.0 mF cm−2, superior to RhMoFeMn metallenes (12.6, 3.9, and 15.8 mF cm−2), PdMoFeMn metallenes (4.4, 7.1 and 8.1 mF cm−2), and PdRh metallenes (2.8, 6.4, and 6.2 mF cm−2) in 0.5 M H2SO4, 1.0 M PBS, and 1.0 M KOH electrolytes, respectively, suggesting that PdRhMoFeMn HEMs possess more exposed electroactive sites for enhanced HER activity (Supplementary Fig. 28–30). Thereafter, the turnover frequency (TOF) was determined to quantify the electrocatalytic efficiency of each active site. As shown in Supplementary Fig. 31, PdRhMoFeMn HEMs have higher TOF values than other benchmarked electrocatalysts in the entire investigated potential range at all pH levels, indicating a prominent catalytic capacity for hydrogen production. Distinctly, PdRhMoFeMn HEMs deliver high TOF values of 19.40 H2 s−1, which is about 16.58, 176.36, 27.32, and 4.92 times higher than those of RhMoFeMn metallenes (1.17 H2 s−1), PdMoFeMn metallenes (0.11 H2 s−1), PdRh metallenes (0.71 H2 s−1) and Pt/C (3.94 H2 s−1) at an overpotential of 50 mV in acidic media, respectively (Supplementary Fig. 31b). Moreover, PdRhMoFeMn HEMs also show considerably greater TOF values of 1.08 and 1.59 H2 s−1 than all control catalysts at an overpotential of 100 mV in 1.0 M PBS and 1.0 M KOH, respectively (Supplementary Fig. 31d–f). Additionally, the HER performance of quinary PdRhMoFeMn HEMs was also compared with that of senary PdRhIrCoFeMo, septenary PdRhIrFeMoMnW, and octonary PdRhIrMnMoRuFeCo HEMs. As shown in Supplementary Fig. 32, PdRhMoFeMn HEMs exhibit smaller overpotential than senary, septenary, and octonary HEMs at the same current density under acidic, neutral, and alkaline environments. PdRhMoFeMn HEMs have larger Cdl values than senary, septenary, and octonary HEMs over a wide pH range, proving the higher atomic utilization efficiency of PdRhMoFeMn HEMs (Supplementary Figs. 33–35). Particularly, all these HEMs exhibit small negative shifts after 10,000 CV cycles, indicating their excellent electrochemical stability (Supplementary Fig. 36). The remarkable HER performance of PdRhMoFeMn HEMs outperforms other modern noble metal-based electrocatalysts over a broad pH range (Supplementary Fig. 37, Supplementary Table 2–4).

Theoretical simulations

To understand the synergistic mechanisms of multiple active sites on PdRhMoFeMn HEMs for the enhanced HER performance in the pH 0 to pH 14 range, the theoretical study was conducted for PdRh, PdMoFeMn, RhMoFeMn, and PdRhMoFeMn (Fig. 4a, Supplementary Figs. 38 and 39). As shown in Fig. 4b and Supplementary data 1, molecular dynamics simulations were first implemented to evaluate the thermal stability of PdRhMoFeMn HEMs under different temperatures (300 K, 400 K, and 500 K). The free energy of PdRhMoFeMn HEMs fluctuates in a narrow range with time evolution in all cases at 300, 400, and 500 K. This result indicates that the structure of PdRhMoFeMn HEMs is thermally stable, which is verified by the long-term electrochemical stability tests for HER. Supplementary Fig. 40 and Supplementary data 2 show that electrons are transferred from Fe, Mo, and Mn to Pd and Rh in HEMs due to the lower electronegativity of Fe, Mo, and Mn.

Fig. 4: DFT calculations results.
figure 4

a The computational modeling of PdRhMoFeMn HEMs. b Molecular dynamics simulations of PdRhMoFeMn HEMs at 300, 400, and 500 K. c The ΔGH* profiles on various catalytic sites of PdRhMoFeMn HEMs. d The COHP calculations of RhMoFeMn metallenes, PdRh metallenes, and PdRhMoFeMn HEMs. e The Rh-H binding strength of RhMoFeMn metallenes, PdRh metallenes, and PdRhMoFeMn HEMs. f The ΔGH* of RhMoFeMn metallenes, PdRh metallenes, and PdRhMoFeMn HEMs at different pH values. g The adsorption energy of water and hydroxide at different sites for PdRhMoFeMn HEMs. h The reaction energy profile for water dissociation on various catalytic sites of PdRhMoFeMn HEMs.

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The Gibbs free energy of hydrogen adsorption (ΔGH*) is a common indicator to evaluate electrocatalysts’ HER performance. Supplementary Fig. 41 shows the atomic configurations of different sites in PdRhMoFeMn HEMs during the H* adsorption process and the detailed calculation of ΔGH* for the above-mentioned sites was listed in Supplementary Table 5. Figure 4c reveals that the Rh top site has the lowest ΔGH* (−0.132 eV) relative to other comparison sites, indicating that the Rh site has the best binding strength to hydrogen and serves as the main active ingredient to contribute to the excellent acidic HER performance. Subsequently, the ΔGH* of Rh sites in PdRh, PdMoFeMn, RhMoFeMn, and PdRhMoFeMn were also calculated (Supplementary Fig. 42). As displayed in Supplementary Fig. 43 and Supplementary Table 6, the ΔGH* of PdRhMoFeMn is −0.132 eV, which is significantly higher than that of PdRh (−0.528 eV) and RhMoFeMn (−0.465 eV). This indicates that the H* adsorption and desorption of PdRhMoFeMn are facilitated after the formation of high-entropy due to the weakened metal (Pd, Mo, Fe, Mn)-Hads (M-Hads) bonds. Such weakened M-Hads bond can be further verified by the projected density of state (PDOS) and the crystal orbital Hamilton population (COHP) calculations. It can be found that the d-band center of Rh in PdRhMoFeMn (-1.95 eV) moves away from the Fermi level compared with those of Rh in PdRh (−1.43 eV) and RhMoFeMn (−1.68 eV) (Supplementary Fig. 44), revealing a weaker H* adsorption on the catalyst surface. Meanwhile, the integrated COHP (ICOHP) value for Rh in PdRhMoFeMn with H2 (−0.89 eV) is higher than that of Rh in RhMoFeMn (−1.17 eV), and Rh in PdRh (−1.34 eV), suggesting the increased antibonding-orbital occupancy in the PdRhMoFeMn than those in PdRh and RhMoFeMn and the increased difficulty for the H2 adsorption at Rh sites in PdRhMoFeMn (Fig. 4d). The increased antibonding-orbital occupancy can destabilize the H 1s-d antibonding, which leads to the further intensified desorption of Rh sites for hydrogen gas. Therefore, Rh in the PdRhMoFeMn electrocatalyst exhibits weaker M-Hads bonds (with a longer bond length of 1.61 Å) than the PdRh catalyst (1.31 Å) and thus displays fast H2 evolution (Fig. 4e). Specially, the Rh site in PdRhMoFeMn shows a ΔGH* that is closer to the optimal value (0 eV) compared with other sites and all control catalysts throughout the entire pH range, which agrees with the electrochemical measurement results (Fig. 4f and Supplementary Fig. 45).

The ΔGH* descriptor is not enough to fully reveal the HER performance of the catalyst under neutral and alkaline conditions due to the involvement of water adsorption and dissociation steps. Therefore, we systematically calculated the water adsorption and dissociation processes to uncover the origin of the superior performance of PdRhMoFeMn HEMs in neutral and alkaline electrolytes (Supplementary Fig. 46–49). Figure 4g shows that the Pd atom exhibits greater water adsorption energy than the rest of the four metal sites in PdRhMoFeMn HEMs. Likewise, the energy barrier required to break the H-OH bond is lowest on the Pd site as 0.53 eV relative to the Rh (0.57 eV), Mo (0.82 eV), Fe (0.67 eV), and Mn sites (0.78 eV) (Fig. 4h). The above analyses indicate that the H2O adsorption and dissociation steps preferentially occur on the Pd site. Moreover, Fig. 4g and Supplementary Figs. 50 shows that the Mn atom has the highest binding energy to hydroxyl groups among the atoms in PdRhMoFeMn HEMs and the favorable OH desorption energy of PdRhMoFeMn at Mn sites is −0.85 eV, which can accelerate water dissociation into H and OH intermediates, followed by the reaction on the Rh site to produce H257,58. In addition, the Pd site in PdRhMoFeMn HEMs possesses the strongest adsorption capacity for water and requires the lowest water dissociation energy than PdRh, PdMoFeMn, and RhMoFeMn, highlighting the important role of high-entropy effects (Supplementary Figs. 51 and 52). Moreover, Fe and Mo have similar atomic radius to Pd, Rh, and Mn, which is more favorable for the formation of highly stable HEMs. Consequently, the high-entropy effects and the collaborative action of multiple active sites contribute to the improved water adsorption, the reduced water dissociation energy barrier, and the optimized formation and release behavior of H2, which synergistically promote the HER performance of PdRhMoFeMn HEMs over a wide pH range.

Operando XAS study

To deeply shed light on the role of each active site and the corresponding catalytic reaction mechanism, the operando XAS measurements were performed on the PdRhMoFeMn HEM catalyst using a tailor-made cell in the three electrolytes representing universal pH (Supplementary Fig. 53). Supplementary Figs. 54–56 demonstrate the consistency of data processing and well-normalization across a wide range of XANES spectra. Under acidic conditions, the operando XANES spectrum of Pd sites in Fig. 5a shows the unchanged electron structure. In contrast, the decreasing white line intensity of Rh sites indicates high electronic density (Fig. 5b). These phenomena suggest that the electronic structure change of Rh sites can facilitate the interaction with the proton, thus promoting the kinetics during HER. The XANES spectra in Fig. 5c, d demonstrate a reduction in the white line intensity of both Pd and Rh, indicating an enhanced electron density on both Pd and Rh atoms upon the application of a reduction potential. This observation suggests that there is a charge transfer from other metal sites, which enhances the reactivity of the intermediate H* on the catalyst surface. Additionally, the operando XANES spectra of Mn show a decrease in electronic density, indicating a consistent result of charge transfer towards the Rh and Pd sites (Supplementary Figs. 57). In the neutral media, the Pd and Rh also exhibit the same catalytic behaviors compared with alkaline conditions, the increasing electronic density could facilitate the adsorption and desorption of intermediates (Fig. 5e, f). Figure 5g provides a detailed insight into the electronic structure of the HEM catalyst in different electrolytes under the catalytic process. Notably, the Pd site maintains the same electronic structure under acidic media. The increasing electron density of Pd sites in alkaline and neutral conditions accelerates the water dissociation process known as the Volmer step. Furthermore, Mn sites exhibit a decreased electronic density in each electrolyte, suggesting the charge redistribution in the HEM catalyst, which benefits the charge transfer towards other multi-metal sites (Supplementary Figs. 57). Noting that the high electron density of Rh under each electrolyte indicates that more charge transfer occurs at Rh sites, which are considered the primary reaction sites.

Fig. 5: Operando XANES measurements of HER behaviors in various electrolytes.
figure 5

a, b Operando XANES spectra of Pd and Rh at various potentials in 0.5 M H2SO4. c, d Operando XANES spectra of Pd and Rh at studied potentials in 1.0 M KOH. e, f Operando XANES spectra of Pd and Rh at applied potentials in 1.0 M PBS. g Schematic illustration of the binding sites for H* and OH* in various electrolytes.

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Operando EXAFS measurements were used to observe local geometry changes. As depicted in Fig. 6 and Supplementary Fig. 58, the Mn, Pd, and Rh sites exhibit distinct geometric structures, providing a clear insight into the detailed reaction mechanisms during the HER process. Specifically, for the Mn site, Mn-O remains nearly unchanged in acidic solutions (Supplementary Fig. 58a and Supplementary Table 7). An increase in Mn-O is observed only under alkaline and neutral conditions, suggesting the generation of more oxygen-related groups at the Mn sites (Supplementary Fig. 58b,c and Supplementary Tables 8 and 9). The EXAFS fitting of Mn also clearly demonstrates the changes under different conditions (Supplementary Fig. 59). Figure 6a, b, and Supplementary Figs. 60a and 61a show that both Pd and Rh sites exhibit an unchanged geometric structure, suggesting a self-adaptive behavior in bonding with protons during the acidic HER. Supplementary Tables 10 and 11 further demonstrate the almost unchanged coordination environment of Pd and Rh. Notably, only Rh sites show a high electron density in XANES results, implying again that the Rh site serves as the main active center that interacts with protons in acidic media. In Fig. 6c, a slight increase in the Pd-O peak intensity is observed under alkaline conditions. EXAFS fitting further shows a clear trend of increased coordination numbers (Supplementary Fig. 60b and Supplementary Table 12), indicating some chemisorbed O on Pd sites. At the same time, the gradual increase in the coordination numbers of Pd-M implies the occurred structural reconstruction. Rh EXAFS results show that no obvious change in the coordination number of Rh-M was observed, suggesting that protons could easily react on electron-rich Rh sites in alkaline media (Fig. 6d, Supplementary Fig. 61b and Supplementary Table 13). In neutral electrolyte, similar phenomena as those under alkaline conditions were observed. The coordination numbers of Pd-O and Pd-M increase (Fig. 6e, Supplementary Fig. 60c and Supplementary Table 14) and the coordination environment of Rh-M is almost unchanged (Fig. 6f, Supplementary Fig. 61c and Supplementary Table 15). Furthermore, Fig. 6g clearly reflects the stable coordination environment of Rh-M. The increased coordination number of Pd-M in alkaline and neutral electrolytes implies local atomic rearrangement, which is beneficial for the activation of the catalyst and improves its HER kinetics. Simultaneously, based on Supplementary Fig. 62 k-space spectra, where a slight contribution from Pd-O is observed between 3–6 Å−1, indicating the trend of chemisorbed oxygen species on Pd sites, and Pd-O fitting was also conducted to further understand the HER mechanisms. This result, combined with the above theoretical calculations and Tafel slope analysis, suggests a possible water dissociation process on Pd sites. Therefore, chemisorbed oxygen-related species were observed in Pd, Rh, and Mn, but only Mn formed obvious oxides in the end. Importantly, the above-mentioned relevant characterizations after stability tests indicate that the formation of trace amounts of Mn-related oxides has little effect on the morphology, crystal structure, and electronic structure of HEMs. DFT calculations also show that the ΔGH*, OH* adsorption energy, and OH* desorption energy of Mn-O/PdRhMoFeMn HEMs is −0.13, −3.18, and −0.84 eV, respectively, which is close to that of PdRhMoFeMn HEMs (−0.132, −3.05, and −0.85 eV) (Supplementary Figs. 63–67). These results indicate that the formation of trace oxide clusters during the reaction has minimal impact on its HER performance, which is consistent with its excellent HER stability.

Fig. 6: Operando EXAFS measurements of HER behaviors in various electrolytes.
figure 6

a, b Operando EXAFS spectra of Pd and Rh at different potentials in 0.5 M H2SO4 without phase correction. c, d Operando EXAFS spectra of Pd and Rh at varied potentials in 1.0 M KOH without phase correction. e, f Operando EXAFS spectra of Pd and Rh at applied potentials in 1.0 M PBS without phase correction. g The structural change of Pd-M and Rh-M in FT magnitude relative to the OCP state in various electrolytes. h Schematic illustration of multi-site synergistic mechanisms for HER in various electrolytes.

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These results illustrate the HER mechanisms of PdRhMoFeMn HEMs under different conditions (Fig. 6h). In acidic electrolytes, two H* absorbed on the Rh sites with the high electron density as the primary active species combine to generate H2 and release through the Vomer-Tafel mechanism. Under alkaline conditions, the HER on the HEM surface follows the Volmer-Heyrovsky mechanism. The adsorbed water molecule dissociates on the Pd site to generate intermediate H* and OH, and then the generated H* moves to the Rh site to combine with a proton in another water molecule in the electrolyte to form H2. Simultaneously, the formed OH intermediates are absorbed onto the Mn sites, which can destabilize bonds in the water molecule and release more Pd sites to accelerate the water dissociation process57. Subsequently, the OH adsorbed on the Mn sites is desorbed into the electrolyte. The difference between the reaction mechanism in neutral electrolyte and alkaline is that two protons produced by the dissociation of water on the Pd site are respectively absorbed on the Rh site and coupled to form H2 through the Vomer-Tafel path.

Discussion

In summary, highly curved and sub-nanometer-thick HEMs composed of up to eight metallic elements were synthesized by a general one-pot wet-chemical method. Theoretic calculations reveal that Rh sites with optimal ΔGH* in PdRhMoFeMn HEMs serve as the potential active center for the stepped-up coupling of H* to H2, contributing to excellent acidic HER performance. Moreover, strong hydroxyl group adsorption at Mn sites is conducive to water dissociation at Pd sites during the critical Volmer step, thus changing the rate-determining steps and achieving rapid H2 generation in neutral and alkaline solutions. More importantly, operando XAS verified the ability of HEMs to stabilize multiple intermediates at different active centers, and atomically observed the active sites of Pd, Rh, and Mn and the mechanisms of multi-site synergy in various electrolytes during the electrocatalytic HER processes. Benefiting from the characteristic high-entropy effect, ultra-high atomic utilization efficiency, and multi-site cooperative behavior, the PdRhMoFeMn HEMs show low η10 and small Tafel slopes (6 mV and 16 mV dec−1 in 0.5 M H2SO4 solution; 23 mV and 33 mV dec−1 in 1.0 M PBS solution; 26 mV and 41 mV dec−1 in 1.0 M KOH solution), outperforming most reported noble metal-based HER catalysts. This work sheds light on the relevance between specific active sites and reaction intermediates in-depth, guiding the rational design of a new generation of 2D HEA electrocatalysts with editable active sites beyond other energy conversion technologies.

Methods

Chemicals

Palladium(ii) acetylacetonate (Pd(acac)2, 99%), hexarhodium hexadecacarbonyl (Rh6(CO)16, Rh 57–60%), dodecacarbonyltriiron (Fe3(CO)12, 96%), Manganese carbonyl (Mn2(CO)10, 98.0%), molybdenum hexacarbonyl (Mo(CO)6, 98.0%), dodecacarbonyltetrairidium (Ir4(CO)12, 98%), octacarbonyldicobalt (Co2(CO)8, 98%), tungsten hexacarbonyl (W(CO)6, 97%), triruthenium dodecacarbonyl (Ru3(CO)12, 99%), ascorbic acid (AA, 99%), cyclohexane (99.7%), oleylamine (OAm, 70%) and acetone (≥99.5%) were purchased from Sigma-Aldrich without further processing.

Fabrication of HEMs

In the synthesis of the representative sub-nanometric PdRhMoFeMn HEMs, 9.5 mg Pd(acac)2, 5.5 mg Rh6(CO)16, 5.5 mg Fe3(CO)12, 5.0 mg Mn2(CO)10, 35 mg Mo(CO)6 and 25 mg AA was ultrasonically dispersed in 6.0 mL OAm to form the precursor solution. Afterwards, an oil bath at 150 °C was used to heat the mixture for eight hours. The HEM product was collected after centrifugation and four washes with a mixed solution of cyclohexane, acetone, and ethanol. For the synthesis of RhMoFeMn, PdMoFeMn, and PdRh metallenes, all the conditions were the same as those of PdRhMoFeMn HEMs except for varying the kinds of metallic precursors.

The preparations of senary PdRhIrCoFeMo HEMs, septenary PdRhIrFeMoMnW HEMs, and octonary PdRhIrMnMoRuFeCo HEMs were similar to that of quinary PdRhMoFeMn HEMs, except that the reaction temperature was 160 °C and the content of each metal salt was different in the precursor solutions, which were summarized in the Supplementary Table 16.

Characterization

The TEM, HRTEM, HAADF-STEM, and EDS elemental mapping images of these as-prepared samples were obtained using an FEI Tecnai F20 transmission electron microscope with a 200 kV acceleration voltage. The HRSTEM images were acquired with JEOL JEM-ARM200F aberration-corrected transmission electron microscope. The Thermo Scientific K-Alpha spectrometer was used for XPS analyses. XRD patterns were studied using an X’Pert PRO MPD (D8) instrument. The composition of these synthesized samples was determined using ICP-OES (PerkinElmer ICP 2100). ATHENA was used to process the acquired EXAFS data. EXAFS fitting was performed using the ARTEMIS module of the Demeter software packages based on the reported literature59, and the details are presented in the Supplementary Information.

Electrochemical measurements

All catalyst samples were synthesized by dispersing as-prepared nanoparticles onto Ketjen carbon. All catalysts had a metal load of 20%. In the case of preparing the carbon-supported PdRhMoFeMn HEA catalyst, 4 mg PdRhMoFeMn HEAs dissolved in 4 ml cyclohexane were mixed with 16 mg Ketjen carbon dissolved in 16 ml cyclohexane, followed by sonicating for 2 hours. After magnetically stirring overnight, the loaded sample obtained by centrifugation was redispersed in 20 mL acetic acid and heated at 70 °C for 120 min to clean the organic residues on the surface of PdRhMoFeMn HEAs. Then, the catalyst was obtained via centrifugation, followed by three washes with ethanol, and dried in a vacuum at 50 °C. The homogeneous catalyst ink was created by ultrasonically dispersing 4 mg of the above-obtained catalyst in 1 ml solution consisting of 290 μL ethanol, 690 μL water, and 20 mL 5 wt% Nafion under an ice-water bath. Subsequently, the working electrode was prepared by drop-casting 5 μL electrocatalyst suspension onto a glassy carbon electrode (GCE) (diameter: 3 mm, area: 0.07 cm2) and subsequent air drying. Therefore, the loading of the catalyst is 0.286 mg cm‒2.

CHI 760E electrochemical workstation with a standard three-electrode system was applied to carry out all electrochemical tests. A GCE (diameter: 3 mm, area: 0.07 cm2) with a surface-modified catalyst and a carbon rod (diameter: 6 mm) were the working and counter electrodes, respectively. An Ag/AgCl electrode (3 M KCl) was used as the reference electrode in 1.0 M PBS (100 mL), whereas that in 0.5 M H2SO4 (100 mL) and 1.0 M KOH (100 mL) was a Hg/HgO electrode. The determined practical electrolyte pH values are 0.37 ± 0.05 for a 0.5 M H2SO4 solution, 6.96 ± 0.03 for a 1 M PBS solution, and 13.81 ± 0.14 for a 1 M KOH solution. All electrolytes is freshly prepared and used. The calibration of reference electrodes was included in Supplementary Information (Supplementary Fig. 17). To assess the HER performance of these samples, linear sweep voltammetry (LSV) was conducted with 100% iR-compensation at a sweep rate of 10 mV s−1 in N2-saturated 0.5 M H2SO4, 1 M PBS, and 1 M KOH electrolyte, respectively (i was the real working current and R is the measured series resistance). LSV curve was recorded until three repeated curves were obtained to ensure the accuracy of the electrochemical tests. Meanwhile, the resistance for the iR-compensation was obtained at the open circuit potential of electrochemical cell. For stability measurements, a chronoamperometry method was performed in the 0.5 M H2SO4 electrolyte at 10 mA cm−2 for 20 h. CV curves were recorded with gradually increased scan rates from 20 to 100 mV s−1 to estimate the Cdl of the aforementioned samples. The TOF of various electrocatalysts was calculated following the equation53,60.

$${{\rm{TOF}}}({{{\rm{s}}}}^{-1})=\frac{j\times S}{n\times F\times N}({{{\rm{s}}}}^{-1})$$

In the above formula, the following symbols are used: j, S, n, F, and N. The first three of these refer to the current density (A cm‒2), the geometric area of a GCE (0.07 cm2), and the number of electrons that participated in the electrocatalytic reaction (2 for HER), respectively. The latter two symbols represent Faraday’s constant (96485.3 C mol‒1) and the upper limit number of active sites on a GCE, respectively. In calculating the N value, all noble metal atoms present in each sample loaded on a GCE were denoted to be active ingredients. Consequently, the resulting TOF represents the lower limit value.

Operando quick-scanning X-ray absorption measurements

Operando quick-scanning XAS tests were performed in transmission mode at TPS BL-44A in the National Synchrotron Radiation Research Center (NSRRC). These measurements relied on an electron storage ring operating at 3.0 GeV and a current of 360 mA. The collection time for each spectrum was 3 minutes, during which a continuous potential was applied, decreasing from 0 to −0.1 V (relative to RHE) (i–t). In transmission mode, both the sample spectrum and the reference spectrum (metal foil corresponding to each element) were collected simultaneously to ensure energy calibration. This experiment utilized a three-electrode setup with a self-assembled cell, featuring a large 3 ×3 cm2 window sealed with Kapton tape (Supplementary Fig. 53). A small stick with a circular hole (0.5 cm2) was also sealed with Kapton tape to shorten the distance between the electrode and the window, allowing X-rays to pass through the window and the electrode/electrolyte interface. Platinum was chosen as the counter electrode, while an Ag/AgCl electrode served as the reference electrode, with electrolytes of 0.5 M H2SO4, 1.0 M PBS, and 1.0 M KOH. The measurement methods were consistent across different electrolytes. Regarding the working electrode preparation, the catalyst powder used was a PdRhMoFeMn HEMs. 10 mg of catalyst powder were dissolved in ethanol containing 50 μL of a 5% Nafion solution (Sigma-Aldrich). The dispersion was further improved through sonication for 20 minutes. Subsequently, the mixed solution was uniformly drop-coated onto a 1 × 0.5 cm2 carbon cloth and allowed to dry to obtain the working electrode.

Computational details

All calculations were done using the VASP model based on the MedeA platform61. The generalized gradient approximation and Perdew-Burke-Ernzerhof method on the basis of DFT were employed to depict the electron wave functions with an energy cutoff of 450 eV. Gamma point geometry optimization was conducted till the maximum force on each atom was 0.01 eV Å−1 and the delta energy between self-consistent field cycles was lower than 10−5 eV. The details of PdRhMoFeMn HEM building are included in Supplementary Information62. To precisely reflect the calculations, the DFT + U corrections for transition metal (Rh:2.0 eV, Pd: 2.0 eV, Fe: 2.5 eV, Mo: 3.5 eV, and Mn: 4.0 eV) were employed63.