Frontier-orbital modulation of rhodium single-atom catalysts for enhanced hydrogen evolution

Theoretical design of Rh single-atom catalysts

To gain a comprehensive understanding of metal-support frontier orbital interactions, we construct a model system of Rh single-atom catalysts (SACs), in which the HOMO of the Rh single atoms (Rh_SA) can be effectively modulated by tuning the anion composition in the support (Fig. 1a). First principal density functional theory (DFT) calculations were conducted to investigate the MSIs effects based on the MoS_xSe_2-x and Rh_SA-MoS_xSe_2-x (0 ≤ x ≤ 2) structure models (Supplementary Data 1, Supplementary Figs. 1 and 2). The density of states (DOS) suggests that the incorporation of Rh single-atoms significantly increases the DOS of MoS_xSe_2-x near the Fermi level (Supplementary Fig. 3). Moreover, the band gap of Rh_SA-MoSSe (0.68 eV) is narrower than those of Rh_SA-MoS₂ (0.88 eV), Rh_SA-MoS_1.5Se_0.5 (0.73 eV), Rh_SA-MoS_0.5Se_1.5 (0.70 eV), and Rh_SA-MoSe₂ (0.73 eV), and MoS_xSe_2-x substrates, thereby promoting accelerated electron transfer and optimizing the adsorption and desorption of reaction intermediates. The calculated HOMO position of freestanding Rh atom is predicted to be around -4.50 eV, whereas the LUMO of MoS_xSe_2-x substrates exhibit a volcano-type trend with the S: Se ratio, with MoSSe appearing near the volcano apex (Fig. 1b, Supplementary Fig. 4, and Supplementary Note 1). According to the FMO theory^32,33,34, the elevated LUMO of MoSSe support narrows the energy gap with the highest occupied molecular orbital (HOMO) of Rh atoms, which promotes orbital hybridizations between Rh atoms and support to lead to a high stability.

When electrons are transferred from Rh to MoS_xSe_2-x substrates, the anchored Rh atoms exhibit an unoccupied or partially occupied state (or LUMO) in Rh_SA-MoS_xSe_2-x. Therefore, regulating Rh-MoS_xSe_2-x orbital coupling may facilitate charge transfer and effectively modulate the LUMO position of anchored Rh atoms. As shown in Supplementary Fig. 4c, the projected density of states (PDOS) analysis suggests the LUMO position of Rh atoms exhibits a volcano-type relationship with the S: Se ratio in MoS_xSe_2-x substrates. The higher LUMO of Rh atoms on MoSSe exhibits smaller energy gaps (∆E₁) with the HOMO of OH^– and larger energy gaps (∆E₂) with the HOMO of H₂ molecules (Fig. 1c), which might directly alter the adsorption energies of

key intermediates through systematic tuning of the S: Se ratio in the support. Moreover, the S: Se ratio in Rh_SA-MoS_xSe_2-x series exhibits a volcano-type relationship with both the free energy of hydrogen adsorption (ΔG_H*) and hydroxide adsorption (ΔG_OH*), with Rh_SA-MoSSe located at the volcano apex, displaying optimal adsorption strengths for both species (H and OH) (Fig. 1d and Supplementary Figs. 5 and 6). To further elucidate the impact of MSIs, we evaluated ΔG_H* and ΔG_OH* at all possible and thermodynamically stable adsorption sites on both pristine MoS_xSe_2-x and regions surrounding the Rh atoms in Rh_SA-MoS_xSe_2-x. It is worth noting that the introduction of Rh single-atom appears to substantially promote the adsorption of H and OH at Rh sites, synergistically improving both the thermodynamics and kinetics of HER (Supplementary Fig. 7). Gibbs free energy differences for the alkaline HER process in Rh_SA-MoS_xSe_2-x and MoS_xSe_2-x were calculated in Supplementary Figs. 8–23. H₂O adsorption at Rh sites in Rh_SA-MoS_xSe_2-x is thermodynamically barrier-free and more favorable than at S/Se sites in Rh_SA-MoS_xSe_2-x or MoS_xSe_2-x. The rate-determining step (RDS) for alkaline HER in both systems is H₂O dissociation. Moreover, the water dissociation free energy of Rh_SA-MoS_xSe_2-x exhibits a volcano-type relationship with the S: Se ratio, with the lowest energy barrier observed at an S: Se ratio of 1: 1 (volcano’s apex). Significantly, the incorporation of a Rh single-atom in Rh_SA-MoS_xSe_2-x appears to lower the energy barriers for H₂O dissociation, effectively promoting the water dissociation.

Synthesis and characterizations of Rh_SA-MoS_xSe_2-x catalysts

Inspired by these DFT results, we synthesized Rh single atoms anchored on a series of MoS_xSe_2-x with different S and Se ratios to validate the findings. The synthesis strategy for Rh_SA-MoS_xSe_2-x is illustrated in Supplementary Fig. 24. First, MoS_xSe_2-x with different S and Se contents (denoted as MoS_xSe_2-x, 0 ≤ x ≤ 2) were prepared via a hydrothermal method followed by annealing. Then Rh single-atoms were anchored on the MoS_xSe_2-x substrates (denoted as Rh_SA-MoS_xSe_2-x, 0 ≤ x ≤ 2) using an electrochemical deposition method. The Rh loadings were comparable across the samples (Rh_SA-MoS₂: 0.37 wt.%, Rh_SA-MoS_1.5Se_0.5: 0.42 wt.%, Rh_SA-MoSSe: 0.49 wt.%, Rh_SA-MoS_0.5Se_1.5: 0.44 wt.%, and Rh_SA-MoSe₂: 0.39 wt.%), as determined by inductively coupled plasma optical emission spectrometry (ICP-OES) (Supplementary Fig. 25). Given that all Rh_SA-MoS_xSe_2-x samples were synthesized using the same Rh precursor concentration, number of scanning cycles, and scanning rate, the observed variation in Rh loading is attributed to differences in substrates conductivity and the strong metal-support interactions³⁵. The principle is as follows: According to the hard-soft acid-base (HSAB) principle^36,37,38, the soft acid Rh³⁺ preferentially interacts with the softer base Se over S. Consequently, the higher conductivity of Se than S results in a higher Rh mass loading on MoSe₂ than MoS₂. Owing to the built-in electric field caused by the electron transfer from Se to S^39,40, the MoS_xSe_2-x with both S and Se anions exhibits superior conductivity and stronger metal-support interaction than MoS₂ and MoSe₂. In addition, the adsorption energies of Rh atoms on MoS₂, MoSSe, and MoSe₂ calculated by DFT are -3.66 eV, -3.91 eV, and -3.85 eV, respectively (Supplementary Fig. 26), indicating the stronger metal-support interaction between the Rh atom and MoSSe compared to both MoS₂ and MoSe₂. Therefore, the mass loading of Rh species on MoS_xSe_2-x substrates is in the order of MoSSe > MoS_0.5Se_1.5 ≈ MoS_0.5Se_1.5 > MoSe₂ > MoS₂.

Scanning electron microscope (SEM) (Supplementary Fig. 27) and transmission electron microscopy (TEM) (Supplementary Figs. 28 and 29) characterizations revealed that all Rh_SA-MoS_xSe_2-x exhibit a similar nanoflower morphology, which promotes the exposure of active sites

and enhances mass transfer. Energy-dispersive X-ray (EDX) spectroscopy elemental analysis confirms the uniform distribution of Rh, Mo, and Se in Rh_SA-MoS_xSe_2-x. As shown in Supplementary Figs. 30 and 31, the X-ray diffraction (XRD) patterns and corresponding Raman spectra indicate that all MoS_xSe_2-x samples maintain the same crystal structures as their parent structures of 2H phase MoS₂ (PDF#37-1492) and MoSe₂ (PDF#20-0757) without the impurity phase. Moreover, all main diffraction peaks of MoS_xSe_2-x are shifted toward a small angle with the Se concentration increasing, which is due to the gradual expansion of unit cells upon the substitution of S atoms by larger Se atoms^41,42. Additionally, the synthesized Rh_SA-MoS_xSe_2-x possess the same crystal structure as the 2H phase of MoS_xSe_2-x^43,44, and no distinct Rh-containing phases detected after Rh electrodeposition. In addition, high-resolution transmission electron microscopy (HRTEM) results (Supplementary Figs. 32 and 33) further confirm that the crystal structures of Rh_SA-MoS_xSe_2-x remain well-preserved following Rh decoration.

The structural models of the Rh_SA-MoS₂, Rh_SA-MoSSe, and Rh_SA-MoSe₂ catalysts are presented in Fig. 2a–c, respectively. The aberration-corrected high-angle annular dark-field scanning TEM (HAADF-STEM) detects the atomically dispersed Rh atoms (bright spots) on the MoS_xSe_2-x nanosheets (Fig. 2d–f). Furthermore, the different intensity profiles along the dashed yellow rectangles in the HAADF-STEM images confirm the single-atom dispersion of Rh atoms. The Fourier transformed extended X-ray absorption fine spectroscopy (FT-EXAFS) spectra of Rh K-edge in Rh_SA-MoS₂, Rh_SA-MoSSe, and Rh_SA-MoSe₂ all display a main characteristic peak below 3 Å (Fig. 2g), matching to the Rh-S/Se coordination^22,33. In contrast to the Rh foil reference, the absence of a metallic Rh-Rh scattering signal rules out the presence of Rh nanoparticles or clusters, confirming the atomic dispersion of Rh species in Rh_SA-MoS₂, Rh_SA-MoSSe, and Rh_SA-MoSe₂. The Rh K-edge EXAFS data fitting curves in Supplementary Fig. 34 and corresponding fitting data in Supplementary Table 1 unveiled the mean Ru-S/Se coordination number of the three catalysts was about 3.5, which was consistent with theoretical calculation models. Given the higher ionic radius and relative atomic mass of Se^2- compared to S^{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,45}, the bond distance of Rh-S (2.3 Å) is shorter than Rh-Se (2.5 Å). Furthermore, Wavelet transformed EXAFS (WT-EXAFS) contour plots reveal single intensity maxima for Rh in Rh_SA-MoS₂, Rh_SA-MoSSe, and Rh_SA-MoSe₂ at approximately 6.7, 8.0, and 9.4 Å^-1 (Fig. 2h), corresponding to the Rh-S, Rh-S/Se, and Rh-Se coordination paths³⁴, respectively. Notably, both the coordination path lengths and k-space positions of Rh-S/Se exhibit a linear correlation with the S: Se ratio in Rh_SA-MoS_xSe_2-x (Fig. 2i), providing further evidence that Rh single-atoms are covalently bonded to S/Se and that their coordination environment can be precisely tuned by adjusting the Se: S ratio in MoS_xSe_2-x substrates.

As shown in Fig. 3a, the synergistic electronic interactions among Rh, S, and Se in Rh_SA-MoS_xSe_2-x are characterized through Rh-S, S-Rh-Se, and Rh-Se coordination units. Owing to the higher polarizability volume and larger covalent radii of Se than S^41,42,45, the closer size match between S 3p and Rh 4 d orbitals and the shorter Rh-S bond facilitates more effective orbital overlap, resulting in strong σ-bonding and weak π-back bonding in Rh-S bond. Moreover, the higher polarizability and more diffuse 4p orbitals of Se enhance its π-acceptor capacity, leading to stronger π-back bonding and weak σ-bonding in Rh-Se bond. The bonding characteristics and strength of the Rh-S and Rh-Se bonds in Rh_SA-MoS_xSe_2-x were investigated using crystal orbital Hamilton population (COHP) and integrated COHP (ICOHP) analysis (Fig. 3b). The COHP curves of All three systems show dominant bonding states below the Fermi level, confirming stable Rh-S and Rh-Se bonds^46,47, with ICOHP values of -1.16 (Rh_SA-MoS₂), -1.21 (Rh_SA-MoSSe), and -1.17 (Rh_SA-MoSe₂). Notably, the more negative ICOHP value of Rh-MoSSe indicates a stronger covalent interaction due to the asymmetric structure that polarizes the electron density and enhances orbital overlap. However, the three systems exhibit slightly different anti-bonding characteristics near the Fermi level. Rh_SA-MoS₂ displays more pronounced anti-bonding features suggestive of partial occupation of destabilizing states than Rh_SA-MoSe₂, while Rh_SA-MoSSe exhibits an intermediate level that reflects its asymmetric chalcogen environment. Charge density difference (CDD) analyses reveal charge redistribution between Rh single-atoms and coordinated S/Se atoms^48,49, resulting in a marked reduction of electron density around Rh atoms (Supplementary Fig. 35a). Bader charge analysis quantifies such electron transfer, affording positive values of 0.22 |e| (Rh-MoS₂), 0.14 |e| (Rh-MoSSe), and 0.01 |e| (Rh-MoSe₂), which further confirm the electron donation from Rh to the substrates. The substantial transfer in Rh-MoS₂ (0.22 |e | ) signifies strong ionic character, while the negligible transfer in Rh-MoSe₂ (0.01 |e | ) confirms a nearly non-ionic interaction. Thus, the decreasing Bader charges quantitatively capture the transition from polar ionic-covalent bonding in Rh-MoS₂ to weak covalent bonding in Rh-MoSe₂, fully consistent with the CDD observations.

X-ray photoelectron spectroscopy (XPS) and X-ray absorption near-edge structure (XANES) analyses were performed to elucidate the electronic structures and chemical compositions of Rh_SA-MoS_xSe_2-x catalysts. Rh K-edge XANES spectra (Fig. 3c) reveal a positive shift in edge absorption energies of Rh single-atoms with increasing Se content, confirming effective modulation of the Rh electronic structure through variation of the Se: S ratio. Quantitative analysis of the XANES data indicates oxidation states of Rh single-atom in Rh_SA-MoS₂, Rh_SA-MoSSe, and Rh_SA-MoSe₂ are +1.67, +1.36, and +0.74, respectively (Fig. 3d). Relative to Rh⁰ foil (4d⁸5s¹) and Rh^Ⅲ₂O₃ (4d⁵5s¹) standards, the d-band hole count for Rh_SA-MoSSe is estimated to be 3.36, lower than that of Rh_SA-MoS₂ (3.67) but higher than Rh_SA-MoSe₂ (2.74), reflecting moderate d-orbital vacancy induced by d–p orbital hybridization in Rh_SA-MoS_xSe_2-x⁵⁰. High-resolution Rh 3 d XPS spectra (Fig. 3e) show a negative shift in binding energies with increasing Se contents, consistent with XANES results. Both the Rh oxidation state and Rh 3d_5/2 binding energy exhibit a linear correlation with the S: Se ratio in Rh_SA-MoS_xSe_2-x (Fig. 3f). High-resolution Mo 3 d, S 2p, and Se 3 d spectra further confirm

the successful synthesis of Rh_SA-MoS_xSe_2-x variants with distinct S:Se ratios^43,50 (Supplementary Fig. 35b–d). Collectively, these electronic structure characterizations demonstrate that the d-band structure of Rh single-atoms can be precisely tuned by modulating the S: Se ratio of MoS_xSe_2-x supports via MSIs. The electronic properties of Rh_SA-MoS_xSe_2-x and MoS_xSe_2-x were further probed through work function (W_f) measurements using ultraviolet photoelectron spectroscopy (UPS). As shown in Supplementary Fig. 36, W_f displays a volcano-type dependence on the S: Se ratio for both Rh_SA-MoS_xSe_2-x and MoS_xSe_2-x, with Rh_SA-MoSSe exhibiting a significantly lower W_f (3.54 eV) compared to Rh_SA-MoS₂ (3.75 eV), Rh_SA-MoSe₂ (4.04 eV), and pristine MoS_xSe_2-x substrates (5.51 ~ 5.71 eV). The incorporation of Rh single atoms and the precise tuning of the S: Se ratio in MoSxSe2-x markedly enhance electron transfer capabilities, thereby facilitating the adsorption and activation of reactants.

Electrocatalytic HER performance of Rh_SA-MoS_xSe_2-x

Electrochemical measurements were performed to elucidate the impact of the d-band structure of Rh single atoms on alkaline HER performance. As shown in the 95% iR-compensated linear sweep voltammetry (LSV) curves (Fig. 4a and Supplementary Fig. 37c and d), Rh_SA– MoSSe exhibits HER activity, achieving a low overpotential of 46 mV at a current density of 10 mA cm^-2, outperforming Rh_SA-MoS₂ (122.5 mV), Rh_SA-MoS_1.5Se_0.5 (65.5 mV), Rh_SA-MoS_0.5Se_1.5 (70.5 mV), Rh_SA-MoSe₂ (91 mV), pristine MoS_xSe_2-x substrates, and commercial Pt/C catalysts. Moreover, the LSV curves of all samples without iR calibration were provide in Supplementary Fig. 37a and b. Specifically, Rh_SA-MoSSe demonstrates a high mass activity of 3.48 A mg^-1 (normalized to Rh loading) at an overpotential of 100 mV, approximately 50-fold higher than that of commercial Pt/C (0.07 A mg^-1). Tafel plots were analyzed to probe HER kinetics⁵¹ (Supplementary Fig. 37c and d), revealing that Rh_SA-MoSSe possesses a significantly lower Tafel slope (56 mV dec^-1) compared to Rh_SA-MoS₂ (111 mV dec^-1), Rh_SA-MoS_1.5Se_0.5 (94 mV dec^-1), Rh_SA-MoS_0.5Se_1.5 (84 mV dec^-1), Rh_SA-MoSe₂ (99 mV dec^-1), Pt/C (40-121 mV dec^-1), and MoS_xSe_2-x substrates, indicating accelerated Volmer reaction kinetics. Moreover, we have added the relationship between the computed ∆G(H₂O) and experimental overpotential required to achieve a current density of 10 mA cm^-2 (ŋ₁₀) based on the Brønsted-Evans-Polanyi (BEP) relationship⁷. As shown in Supplementary Fig. 40c, a lower ∆G(H₂O) corresponds to a smaller overpotential and thus significantly enhanced alkaline HER activity, suggesting the critical role of water dissociation kinetics in determining the overall alkaline HER performance. In this work, the water dissociation barrier of Rh_SA-MoS_xSe_2-x is limited to 0.74 eV due to the modulation scope of EMSI in TMD-based supports. Therefore, future high-performance alkaline HER electrocatalysts should be rationally designed by constructing active sites with intrinsically low water-dissociation energy and by optimizing electronic structures to further reduce ΔG(H₂O), thereby promoting water-dissociation kinetics and enhancing alkaline HER activity.

The catalyst’s mass activity is fundamentally determined by the product of the electrochemically active surface area (ECSA, normalized by mass) and the specific activity (SA, catalytic current normalized by ECSA)^52,53,54. In contrast to the geometrical surface area, the ECSA represents the actual surface area accessible to the electrolyte. The ECSA were estimated via double-layer capacitances (C_dl) measurements derived from cyclic voltammogram (CV) (Supplementary Figs. 38 and 39). Owing to the built-in electric field and in-plane dipole moment caused by the electron transfer from Se to S^39,40, the MoS_xSe_2-x with both S and Se anions exhibits superior conductivity and hydrophilic than MoS₂ and MoSe₂. Moreover, the introduction of Rh increases the number of active sites and enhances charge transfer efficiency. Therefore, Rh_SA-MoSSe exhibits the highest C_dl (92.6 mF cm^-2) compared to Rh_SA-MoS₂ (52.4 mF cm^-2), Rh_SA-MoS_1.5Se_0.5 (65.5 mF cm^-2), Rh_SA-MoS_0.5Se_1.5 (74.4 mF cm^-2), Rh_SA-MoSe₂ (52.5 mF cm^-2), and pristine MoS_xSe_2-x substrates, suggesting a greater abundance of exposed active sites. Normalizing activity by ECSA thus offers a more accurate and meaningful metric for evaluating the catalytic properties of diverse electrocatalysts, accounting for variations in size, shape, morphology, topography, and porosity^55,56. Therefore, polarization curves of Rh_SA-MoS_xSe_2-x and MoS_xSe_2-x samples, normalized to ECSA, confirm the superior intrinsic activities of Rh_SA-MoSSe (Supplementary Fig. 40).

The turnover frequency (TOF) of Rh_SA-MoSSe at -100 mV vs. RHE (19.34 s^-1) surpasses that of Rh_SA-MoS₂ (2.15 s^-1), Rh_SA-MoS_1.5Se_0.5 (6.05 s^-1), Rh_SA-MoS_0.5Se_1.5 (9.89 s^-1), Rh_SA-MoSe₂ (6.97 s^-1), and is competitive with most reported noble metal-based and transition metal dichalcogenide (TMD) catalysts^{12,13,17,50,57,58,59,60,61,62} (Supplementary Fig. 41d and Supplementary Table 2). Moreover, the faradaic efficiency of Rh_SA-MoSSe surpasses that of Rh_SA-MoS₂ (2.15 s^-1), Rh_SA-MoS_1.5Se_0.5 (6.05 s^-1), Rh_SA-MoS_0.5Se_1.5 (9.89 s^-1), Rh_SA-MoSe₂ (6.97 s^-1), MoS_xSe_2-x substrates, and Pt/C (Supplementary Fig. 41e). Notably, the S: Se ratio in Rh_SA-MoS_xSe_2-x exhibits a volcano-type relationship with HER activity, Tafel slope, C_dl, intrinsic activity, and TOF, with Rh_SA-MoSSe at the volcano’s apex displaying optimal overall HER performance (Supplementary Fig. 41a–c). This underscores the effectiveness of precisely tuning the d-band structure of Rh single-atoms to enhance HER activity and kinetics. To further quantify the impact of MSIs modulation via the S:Se ratio variation in MoS_xSe_2-x supports, the enhancement rates of Rh_SA-MoS_xSe_2-x relative to pristine MoS_xSe_2-x substrates were evaluated for activity, Tafel slope, ECSA, and intrinsic activity, based on the following equation:

The enhancement rate (δ_{Enhance rate}) is defined as the ratio of the performance metrics (activity, Tafel slope, ECSA, and intrinsic activity) for Rh_SA-MoS_xSe_2-x (N_{RhSA-MoSxSe2-x}) relative to those for pristine MoS_xSe_2-x (N_MoSxSe2-x). Notably, the enhancement rates for activity, Tafel slope, ECSA, and intrinsic activity exhibit a volcano-type dependence on the S: Se ratio, with the highest enhancement rate observed at an S: Se ratio of 1: 1 (volcano’s apex) (Fig. 4d). Moreover, the Pt and Ru single atoms anchored on MoS_xSe_2-x were also successfully synthesized to demonstrate the generality of the design strategy. The XRD of Ru_SA-MoSSe and Pt_SA-MoS_xSe_2-x was shown in Supplementary Fig. 42, confirming that no diffraction peaks of Ru or Pt nanoparticles were observed. Additionally, the SEM and corresponding elemental mapping results reveals the uniform distribution of every element (Supplementary Figs. 43 and 44). Notably, the S: Se ratio in both Ru_SA-MoS_xSe_2-x and Pt_SA-MoS_xSe_2-x exhibits a volcano-type relationship with HER activity and Tafel slope, with Ru_SA-MoSSe and Pt_SA-MoSSe at the volcano’s apex displaying optimal overall HER performance (Supplementary Figs. 45 and 46).

The strong interaction between OH* species and catalysts surfaces is well-established for accelerating water dissociation in the HER^4,7. To probe the OH adsorption capacity at CO adsorption sites⁹, CO-stripping voltammetry was employed to assess the water dissociation capabilities of the Rh_SA-MoS_xSe_2-x catalysts (Supplementary Fig. 47a). Among them, Rh_SA-MoSSe exhibited the lowest onset potential for CO oxidation (0.28 V), compared to Rh_SA-MoS₂ (0.31 V), Rh_SA-MoS_1.5Se_0.5 (0.30 V), Rh_SA-MoS_0.5Se_1.5 (0.30 V), and Rh_SA-MoSe₂ (0.32 V), indicating a stronger Rh-OH interaction and enhanced water dissociation kinetics. The H adsorption ability of Rh_SA-MoS_xSe_2-x catalysts was evaluated through the desorption of underpotential-deposited hydrogen (H_upd)^9,10,63. As shown in Supplementary Fig. 47b, Rh_SA-MoSSe displayed a notably low H_upd potential (0.12 V), compared to Rh_SA-MoS₂ (0.26 V), Rh_SA-MoS_1.5Se_0.5 (0.15 V), Rh_SA-MoS_0.5Se_1.5 (0.15 V), and Rh_SA-MoSe₂ (0.16 V), facilitating H recombination during HER. Furthermore, the S: Se ratio in Rh_SA-MoS_xSe_2-x catalysts exhibited a volcano-type correlation with both OH and H adsorption strengths, with Rh_SA-MoSSe at the volcano’s apex demonstrating optimal adsorption capabilities for both H and OH (Fig. 4c), consistent with theoretical predictions. The catalyst’s stability across varying current densities was evaluated through multi-step current experiments, where the potential rapidly stabilized at each step, indicating efficient mass transport at the electrode surface during the HER (Fig. 4e). Long-term durability of Rh_SA-MoSSe was assessed via chronopotentiometry, demonstrating negligible potential decay over 450 h at a high current density of 1 A cm^-2, outperforming the commercial Pt/C, MoSSe, Rh_SA-MoS₂, and Rh_SA-MoSe₂ (Supplementary Fig. 48). The experimental findings are fully consistent with the trends predicted by the above DFT calculations. Moreover, the stability time of Rh_SA-MoSSe at 1 A cm^-2 is competitive with most reported noble metal-based and transition metal dichalcogenide (TMD) catalysts (Fig. 4f and Supplementary Table 3)^{13,17,51,57,58,59,64,65,66,67,68,69,70,71,72,73,74,75,76}. These findings underscore the catalyst’s robust electrochemical stability and potential for industrial applications. Structural integrity of Rh_SA-MoSSe post long-term HER testing was investigated using XRD, SEM, HAADF-STEM, and XPS. XRD analysis (Supplementary Fig. 49) confirmed that the crystal structure of Rh_SA-MoSSe remained intact after extended HER operation. SEM (Supplementary Fig. 50) and HAADF-STEM (Supplementary Fig. 51) images verified that Rh_SA-MoSSe retained its original morphology and atomic dispersion of Rh after 500 h testing. XPS analysis (Supplementary Fig. 52) further revealed that the oxidation states of Rh, Mo, S, and Se in Rh_SA– MoSSe remained stable and unaltered post testing. Collectively, these structural characterizations demonstrate that Rh_SA-MoSSe exhibits HER activity and stability, attributed to the precise tuning of the Rh single-atoms d-band structure, which optimizes intermediate adsorption energies and significantly enhances alkaline HER performance.

The anion exchange membrane water electrolyzer (AEMWE) tests were employed to further evaluate the application potential of Rh_SA-MoSSe catalyst for industrial water splitting. The homemade NiFe LDH@NF as an anode electrocatalyst (Supplementary Fig. 53) was assembled with Rh_SA-MoSSe and operated in 1.0 M KOH electrolyte at 80 °C. The polarization curves showed the Rh_SA-MoSSe | |NiFe LDH@NF exhibit a cell voltage of 1.58 V and 1.70 V at current densities of 0.5 A cm^-2 and 1.0 A cm^-2 for AEMWE, respectively, which is superior to commercial Pt/C | |NiFe LDH@NF and MoSSe | |NiFe LDH@NF systems (Fig. 4g). Furthermore, the AEMWE of Rh_SA-MoSSe | |NiFe LDH@NF was continuously operated for over 500 h at a current density of 1 A cm^-2 (Fig. 4h). The overpotential at 1.0 A cm^-2 and stability time of were comparable to those of recently reported catalysts for AEMWE (Supplementary Table 4)^{9,59,66,67,68,69,70,73,76,77}. The above results confirm the advanced and reliable potential of the Rh_SA-MoSSe catalyst for industrial water-splitting applications.

Mechanism insights into catalytic activity

Operando electrochemical impedance spectroscopy (EIS) was conducted to probe charge-transfer kinetics and elucidate HER⁷⁸. The equivalent circuit for both Rh_SA-MoS_xSe_2-x and pristine MoS_xSe_2-x comprises four components: electron transfer resistance (R) from the cathode to the interface (R₁, part 1), accumulation of reaction intermediate (Volmer step, R₂, part 2), charge transfer during the interfacial reaction (Heyrovsky step, R₃, part 3), and electrolyte resistance (R_s, part 4) (Fig. 5a). The low-frequency region is primarily associated with the Volmer step, while the high-frequency region reflects electron transfer from the catalyst’s inner layer to surface-active sites, driven by distinct relaxation time. Bode plots at overpotential of 100 mV (Fig. 5b) reveal significantly reduced phase angles at low frequencies for Rh_SA-MoS_xSe_2-x compared to MoS_xSe_2-x supports, indicating that Rh single-atoms enhance the Volmer step kinetics. Analysis of Nyquist plots and optimized fitting parameters (Fig. 5c–f) shows that Rh_SA-MoS_xSe_2-x catalysts exhibit substantially lower charge transfer resistances than their pristine MoS_xSe_2-x counterparts. Notably, R₁, R₂, and R₃ display a volcano-type dependence on the S: Se ratio in both Rh_SA-MoS_xSe_2-x and MoS_xSe_2-x, with Rh_SA-MoSSe at the volcano’s top exhibiting the lowest R₁, R₂, and R₃ values, signifying accelerated HER charge transfer kinetics and a rapid Faradaic reaction at the catalyst-electrolyte interface. Operando EIS measurements at varying applied biases further clarify the charge transfer dynamics and HER mechanism of Rh_SA-MoS_xSe_2-x. Bode plot (Fig. 5g) for Rh_SA-MoS₂, Rh_SA-MoSSe, and Rh_SA-MoSe₂ reveal a single phase-angle peak spanning low-frequency (Volmer step) and mid-frequency (Heyrovsky step) regions as the applied bias decreases, suggesting that Rh_SA-MoS_xSe_2-x follows a mixed Heyrovsky-Volmer and Tafel-Volmer mechanism rather than a singular Heyrovsky-Volmer pathway. Notably, Rh_SA-MoSSe exhibits a smaller phase angle and a faster phase-angle decrease rate (0.05 to -0.05 V) compared to Rh_SA-MoS₂ and Rh_SA-MoSe₂ (Fig. 5h), further confirming its superior HER kinetics.

To elucidate the enhanced alkaline HER activity of Rh_SA-MoSSe, operando infrared absorption (IR) spectroscopy and in situ Raman spectroscopy were employed to investigate adsorption site and binding energy dynamics of reaction intermediates under HER operating conditions (Supplementary Figs. 54 and 55). As shown in Fig. 6a, with decreasing bias potential, distinct absorption peaks emerged at approximately 1030, 1621, and 3200 ~ 3600 cm^-1. The peak at ~1030 cm^-1 is attributed to S/Se-OH formation, while the broad peak at 3200 ~ 3600 cm^-1 and the peak located at ~1621 cm^-1 for Rh_SA-MoS₂, Rh_SA-MoSSe, and Rh_SA-MoSe₂ correspond to the O-H stretching and δ(H-O-H) bending modes of interfacial water molecules, respectively^63,79. Moreover, water-related peaks for Rh_SA-MoSSe appeared at a more positive potential (0.15 V) compared to Rh_SA-MoS₂ (0.1 V) and Rh_SA-MoSe₂ (0.1 V), indicating that Rh_SA-MoSSe facilitates water dissociation more effectively. The vibrational Stark effect, which describes potential-dependent shifts in adsorbate vibrational frequencies³, reveals that S/Se-OH in Rh_SA-MoSSe is more responsive to the local electric field than in Rh_SA-MoS₂ and Rh_SA-MoSe₂, as evidenced by steeper Stark slopes (Fig. 6b). In-situ Raman spectroscopy further probed the catalytic processes in Rh_SA-MoS_xSe_2-x during alkaline HER. As presented in Fig. 6c, Raman peaks at ~1522 and ~1395 cm^-1 for Rh_SA-MoSSe emerged at 0.15 V, corresponding to adsorbed OH species generated during the HER⁵⁸. In contrast, OH-related Raman peaks for Rh_SA-MoS₂ and Rh_SA-MoSe₂ appeared at 0.1 V, underscoring the stronger OH binding and accelerated water dissociation kinetics of Rh_SA-MoSSe. Additionally, the Stark slopes for ^*OH in Rh_SA-MoSSe indicate greater sensitivity to the local electric field compared to Rh_SA-MoS₂ and Rh_SA-MoSe₂ (Fig. 6d). These findings suggest that precise modulation of the S: Se ratio optimizes OH adsorption at Rh single atom sites, thereby enhancing H₂O adsorption and dissociation (Fig. 6e).