Introduction

Transition metal-activated peroxymonosulfate (PMS) processes offer exceptional reactivity and adaptability for water decontamination1,2,3,4, yet their broad application is critically limited by sluggish reaction kinetics5. The core challenge lies in designing catalysts that efficiently activate PMS to generate reactive oxygen species (ROS)6. Conventional transition metal catalysts suffer from inadequate active-site exposure7 and poor reversibility of redox metal pairs (Mn+1/Mn+), leading to rapid performance decay. While advanced architectures like single-atom catalysts (SACs) maximize atomic utilization8, their single-site mechanism struggles to orchestrate multistep processes—adsorption, activation, and desorption—essential for complex PMS reactions9.

Dual-atom catalysts (DACs) emerge as a transformative solution, leveraging synergistic intermetallic sites and planar asymmetry to modulate charge distribution, enhance metal loading, and accelerate reaction dynamics10,11. However, the activity origin of DACs remains obscured by an incomplete mechanistic understanding of how electronic and geometric factors jointly govern PMS activation12. Prior studies reveal a volcano-shaped relationship between adsorption strength and catalytic activity of SACs, i.e., weak adsorption permits *PMS diffusion away from active sites, while excessive binding impedes *PMS/SO42− desorption, inducing catalyst passivation13. Although defect engineering14 and spin manipulation11 highlight roles of antibonding occupancy and charge transfer from metal to PMS, they fail to decode the synergy between orbital hybridization and geometric constraints unique to DACs.

Fundamentally, the adsorption strength of PMS is governed by the coupling between the transition metal 3 d orbital and oxygen 2p orbital of PMS15,16,17. Specifically, the t2g orbitals (dxz, dyz and dzy), constituting σ-bonding states, and the eg orbitals (\({d}_{{z}^{2}}\) and \({d}_{{x}^{2}}-{d}_{{y}^{2}}\)) (Supplementary Fig. 1), forming σ*-antibonding states, collectively determine the d-band center position and orbital occupation levels16. According to the classic d-band theory, upward shifts in the d-band center of metal catalysts reduce σ*-antibonding state occupancy, thereby strengthening adsorbate-catalyst interactions18,19. While this theory effectively rationalizes adsorption trends in SACs, it critically fails to capture the intermetallic orbital hybridization inherent to DACs, where dual-site coupling generates distinct bonding/antibonding states20,21,22. Equally critical are geometric parameters (e.g., interatomic distance, rcatalyst) which govern PMS adsorption configurations, O-H elongation in adsorbed PMS (rO-H) for 1O2 generation, and charge transfer efficiency23. Nevertheless, the geometric roles in DACs remain underexplored24, primarily due to the complexity of dual-site coordination environments during PMS activation. Suboptimal M1-M2 (> 5.0 Å) hinder electron delocalization and compromise orbital overlap essential for synergistic effects25, whereas overly short distances induce steric clashes and suppress ROS generation26. Current descriptors, however, address electronic or geometric effects in isolation, leaving their cooperative interplay unresolved27. Thus, a universal descriptor unifying electronic and geometric determinants is imperative to elucidate DACs structure-activity relationships in PMS-mediated water decontamination (Fig. 1a).

Fig. 1: Electronic-geometric descriptor framework of FeM DACs.
Fig. 1: Electronic-geometric descriptor framework of FeM DACs.The alternative text for this image may have been generated using AI.
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a Literature survey on the application SACs and DACs for PMS activation (2020–2025). b The structural model of FeM DACs. c Advancements in DACs for PMS activation (red circle: Fe-based DACs, yellow rhombus: non-Fe-based DACs; corresponding references: [1 ~ 23] in Supporting Information). d A schematic illustration depicting the d-band center and orbital hybridization in DACs. e PDOS plots of 3 d orbitals for transition metals (Ti, Cr, Mn, Fe, Co, Ni, V and Cu) (arranged left to right) in FeM DACs. f The relationship between IOES and Eads of diverse FeM DACs towards PMS. g Evolution of stable O-H bond lengths in PMS activated by FeM DACs. h Structural parameters governing descriptor design: O-H bond length in PMS (rO-H) and interatomic Fe-M distance (rcatalyst) in FeM DACs. i The correlation between the and IOGS of various FeM DACs. j The balance between adsorption and activation in catalytic degradation. k The binary descriptor (BD) of IOES and IOGS deciphered by machine learning. Source data are provided as a Source Data file.

Herein, we introduce a machine learning-assisted binary descriptor (BD) that unifies orbital electronic structure (IOES) and orbital geometric structure (IOGS) indices to decipher the structure-activity relationships of DACs in PMS activation (Supplementary Fig. 2). The electronic component (IOES = \(\frac{{{{{\rm{e}}}}}_{{{{\rm{g}}}}}}{{{{{\rm{t}}}}}_{2{{{\rm{g}}}}}}\)) quantifies d-p hybridization strength, where optimal eg (\({d}_{{z}^{2}}\) and \({d}_{{x}^{2}}-{d}_{{y}^{2}}\)) and t2g (dxz, dyz and dzy) occupancy balances σ* antibonding depletion and adsorption energy. Concurrently, the geometric term (IOGS = \(\frac{{{{{\rm{r}}}}}_{{{{\rm{O}}}}-{{{\rm{H}}}}}}{{{{{\rm{r}}}}}_{{{\mathrm{catalyst}}}}}\)) encodes the geometric coupling through rcatalyst and rO-H, correlating varying coordination environments with ROS generation barriers. Using Fe-based DACs (FeM; M = Ti, V, Cr, Mn, Fe, Co, Ni, Cu) as model systems (Fig. 1c and Supplementary Table 1), we identify FeMn DACs with minimum BD values as top performers, achieving a high PMS activation rate (kobs = 1.2 min–1) and operational stability. This BD framework transcends classical d-band theory, bridging electronic-geometric synergies from orbital-level insights to practical catalyst design, and establishes a universal strategy for environmental catalysis optimization.

Results

Orbital hybridization-guided development of unified electronic-geometric descriptors

DACs offer a spectrum of intermetallic active sites that enable synergistic regulation of PMS adsorption and activation processes28,29,30. Here, we utilized Fe-based SACs, recognized for their high activity and tunable coordination environments, as structural scaffolds to construct a systematic series of FeM DACs (M = Ti, V, Cr, Mn, Fe, Co, Ni, Cu)31,32. The optimized atomic models of these DACs were obtained via density functional theory (DFT) and are presented in Fig. 1b and Supplementary Fig. 3.

Prior studies have demonstrated that PMS adsorption strength is governed by 3d orbital hybridization of active metal centers33. Introduction of a secondary metal, such as cobalt (Co), into Fe SACs has been shown to reconstruct spin states and modulate the d-orbital configuration of FeCo DACs, thereby altering PMS binding affinity11. Spin state thus emerges as a pivotal electronic factor influencing the adsorption energetics of PMS11. In FeM DACs, the incorporation of hetero-transition metals induces reorganization of the 3 d electronic structure of Fe via metal-metal interactions, significantly influencing d-band center position and orbital occupancy (Fig. 1d). Density of states (DOS) analysis revealed a progressive downward shift in the eg/t2g ratio across FeM DACs (FeTi > FeCr > FeMn > FeCo > FeNi > FeFe > FeV > FeCu; Supplementary Table 2), corresponding to a gradual reduction in the number of accessible active sites (Fig. 1e).

This orbital reconfiguration, driven by Fe–M coupling, generates σ* antibonding states, with their filling degree directly determining PMS adsorption strength. Moreover, the occupancy of eg (σ*) and t2g (σ) orbitals influences the adsorption and activation of intermediates during PMS conversion16. To systematically capture this effect, we defined an orbital electronic structure index (IOES), representing the σ/σ* ratio, to quantify the effective availability of active sites for PMS adsorption16. A higher IOES indicated a higher availability of active sites for PMS binding. DFT-calculated adsorption energies (Eads) of PMS on FeM DACs exhibited a strong positive correlation with IOES values (Fig. 1f, Supplementary Fig. 4 and Supplementary Table 2), affirming the predictive capacity of the descriptor.

Beyond electronic effects, geometrical parameters—specifically the interatomic Fe–M distance (rcatalyst) and O-H bond length in PMS (rO-H) were found to significantly influence PMS activation thermodynamics (Fig. 1g, h). To integrate these structural factors, we established an orbital geometric structure index (IOGS), incorporating both rcatalyst and rO–H to reflect the geometric modulation of Gibbs free energy (ΔG). Volcano-shaped correlations between IOGS and ΔG across the FeM DACs (Fig. 1i and Supplementary Table 3) indicated that intermediate IOGS values favor optimal PMS activation.

To evaluate the generalizability of IOES and IOGS, we expanded our analysis beyond symmetric FeM–N6 coordination to asymmetric heteronuclear configurations, exemplified by FeMnN5C. Remarkably, linear correlations between IOES and Eads, as well as between IOGS and ΔG, were preserved regardless of local coordination asymmetry (Supplementary Figs. 7, 8). This robustness arises from the orbital-level sensitivity of IOES to d–p hybridization and the geometric adaptability encoded by IOGS through Fe–M distance and O–H elongation. By accurately capturing dual-site synergy across diverse DAC environments, this BD (Fig.1j, k) provided a unified, dynamically tunable metric for rational DAC design, bridging electronic and geometric domains to enable high-efficiency PMS activation.

Controlled synthesis and atomic-scale validation of FeM DACs

To validate the theoretical framework and BD proposed herein, a series of FeM dual-atom catalysts (DACs; M = Ti, V, Cr, Mn, Fe, Co, Ni, Cu) was rationally synthesized using an innovative dual-template pyrolysis strategy (Fig. 2a). This approach was specifically developed to address the pervasive nitrogen loss and poor metal dispersion associated with conventional pyrolysis. The method strategically integrates ZIF-8 as a sacrificial microporous template with PEO-PPO-PEO (P123) as a mesopore-directing agent, which also functions as a nitrogen-stabilizing buffer. During pyrolysis, zinc volatilization from ZIF-8 generated atomic-scale vacancies and simultaneously released nitrogen ligands, promoting the formation of well-defined Fe-N4/M-N4 coordination motifs (Fig. 2h–k). Concurrently, P123 dynamically stabilized the evolving carbon matrix by assuming two essential roles by (i) directing the formation of hierarchical mesoporosity to prevent structural collapse, and (ii) buffering volatile nitrogen species to preserve sufficient N content for stable metal–N4 coordination.

Fig. 2: Synthesis and properties of FeM DACs.
Fig. 2: Synthesis and properties of FeM DACs.The alternative text for this image may have been generated using AI.
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a Schematic diagram of FeM DACs preparation procedures (FePc: iron phthalocyanine; 2-MeIM: dimethylimidazole; P123: polyethylene oxide–polypropylene oxide–polyethylene oxide). HAADF-HRTEM images of b FeMn DACs, c FeFe DACs, d FeCo DACs, e FeNi DACs, f FeV DACs and g FeCu DACs. h–m 3D atomic resolution map of the Fe-M sites. Analysis of the intensity profile of two adjacent atoms of n FeMn DACs, o FeFe DACs, p FeCo DACs, q FeNi DACs, r FeV DACs, and s FeCu DACs (blue rectangle: DACs, yellow circles: SACs). Source data are provided as a Source Data file.

Confined pyrolysis within this dual-templated architecture enabled precise control over Fe-M interatomic distances (2.20–2.50 Å), achieving uniform dispersion of dual-metal sites with high metal loadings (Fe: 1.24-1.42 wt%; M: 1.02-1.24 wt%, ICP-MS; Supplementary Table 4) and a catalyst yield exceeding 50%—a notable advance in DAC synthesis scalability. Aberration-Corrected High-Angle Annular Dark-Field Scanning Transmission Electron Microscopy (AC-HAADF-STEM, Fig. 2b–g and Supplementary Fig. 6) unambiguously revealed abundant and spatially isolated Fe-M pairs with site prevalence exceeding 73-86%. X-ray spectroscopy (EDS) line scans (Fig. 2n–s and Supplementary Fig. 10) confirmed alternating Fe/M signals at precisely controlled 2.27-2.47 Å spacings (Fig. 2n–s and Supplementary Fig. 11), aligning well with theoretical dual-site configurations. Collectively, this methodology establishes a robust and generalizable platform for synthesizing N4-coordinated DACs with tailored porosity and exceptional nitrogen retention.

Comprehensive material characterization further validated the atomic dispersion and uniformity of the FeM DACs. X-ray diffraction (XRD) patterns (Supplementary Fig. 12) exhibited only broad peaks at 26° and 44°, corresponding to the C (002) and C (101) planes, with no detectable metal crystallites—indicative of atomically dispersed metal centers. X-ray photoelectron spectroscopy (XPS) analysis confirmed the expected elemental compositions (Supplementary Fig. 13). Critically, high-resolution N 1 s spectra (Supplementary Fig. 14) deconvoluted into four distinct peaks i.e., pyridinic N (398.21 eV), metal-coordinated N (399.02 eV), pyrrolic N (400.62 eV), and graphitic N (401.72 eV), with the metal-N signature providing direct spectroscopic evidence of successful Fe/M–N4 coordination. Consistent metal 2p spectra across all FeM DACs (Supplementary Fig. 15) further corroborated uniform metal–N bonding. In addition, N2 adsorption–desorption isotherms (Supplementary Fig. 16 and Supplementary Table 7) and hydrophilicity profiles (Supplementary Fig. 17) confirmed comparable surface area, porosity, and wettability, eliminating material heterogeneity as a confounding variable in catalytic assessments.

Atomic-scale structural validation was achieved via synchrotron-based X-ray absorption spectroscopy. The Fe K-edge X-ray absorption near-edge structure (XANES) spectra of FeMn DACs placed the Fe absorption edge between that of FeO and Fe₂O₃, indicating a valence state between +2 and +3 (Fig. 3a). Fourier transform (FT) extended X-ray absorption fine structure (EXAFS) spectra revealed Fe-Mn coordination at R = 2.0 Å (coordination number, CN = 0.99), along with Fe-N (CN = 3.9, R = 1.7 Å) and Mn-N (CN = 4.0, R = 1.9 Å) (Fig. 3b, e). Absence of Fe–Fe scattering signals at ~ 2.2 Å confirmed atomic dispersion of Fe species. Best-fit EXAFS analysis indicated a predominant FeN4 coordination environment (Fig. 3c and Supplementary Fig. 18). Similar analysis at the Mn K-edge revealed a Mn valence state between 0 and + 2 (Fig. 3d), with Mn–N coordination at ~ 1.5 Å (Fig. 3e) and CN = 4, supporting the presence of MnN4 motifs (Fig. 3f).

Fig. 3: Fine structure of FeM DACs.
Fig. 3: Fine structure of FeM DACs.The alternative text for this image may have been generated using AI.
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a Normalized Fe K-edge XANES spectra, b Fourier-transformed k3-weighted Fe K-edge EXAFS spectra of Fe foil, FeO, Fe2O3 and FeMn DACs, c Fe K-edge EXAFS fitting of FeMn DACs, d Normalized Mn K-edge XANES spectra, e Fourier-transformed k3-weighted Mn K-edge EXAFS spectra of Mn foil, MnO, Mn2O3 and FeMn DACs, f Mn K-edge EXAFS fitting of FeMn DACs, g WT analysis of Fe and Mn K-edge EXAFS spectra for Fe foil, FeMn DACs (Fe), Mn foil and FeMn DACs (Mn). Source data are provided as a Source Data file.

Wavelet transforms (WT) contour plots further substantiated dual-site coordination. The Fe species exhibited WT intensity at 6.4 Å−1 (Fe-N), while Mn-N coordination was marked by a distinct peak at 4.5 Å−1 (Fig. 3g). Quantitative fitting yielded consistent Fe-Mn CN values (0.99) and Fe-N/Mn-N CNs (3.9/4.0), confirming the formation of a FeMnN6 coordination architecture anchored within the carbon matrix (Fig. 3g, Supplementary Fig. 19 and Supplementary Table 8). Collectively, these findings provided compelling atomic-scale evidence for the successful synthesis of well-defined FeM DACs, laying a solid foundation for subsequent catalytic evaluations.

IOES Quantifies orbital-controlled PMS adsorption thermodynamics

In PMS-based advanced oxidation processes, pollutant degradation began with the critical step of PMS adsorption, followed by its activation34. The binding affinity of PMS to catalytic sites was primarily governed by the degree of d-p orbital hybridization and d-d orbital coupling, which jointly influenced adsorption energy and surface charge redistribution35,36,37. In the synthesized FeM DACs, the interatomic distances between adjacent metal atoms (2.20–2.50 Å; Fig. 2n–s) promoted strong electronic interactions, leading to pronounced reorganization of d-p hybridization states, which directly modulated PMS adsorption capacity.

To elucidate this adsorption mechanism, we quantified the Eads of PMS across the FeM DAC series (Fig. 4a). To establish the predictive relationship between IOES descriptor and PMS adsorption, we systematically correlated IOES values with adsorption capacities quantified via UV-vis absorption spectroscopy, where PMS aqueous solution (spiked with methyl orange, MO) concentration decay directly reflected catalyst affinity (Fig. 4b), with the detailed methods in Supplementary Note 11. FeMn DACs exhibited the strongest Eads (− 2.52 eV), followed by FeFe (− 2.36 eV), FeCo (− 2.31 eV), FeNi (− 2.25 eV), FeV (− 2.24 eV), and FeCu (− 2.22 eV) (Fig. 4a), consistent with experimental PMS uptake kinetics (FeMn > FeFe > FeCo > FeNi > FeV > FeCu, Fig. 4b). Within 60 s, FeMn DACs achieved the most rapid PMS adsorption, as visualized by solution decolorization (Fig. 4b inset). The coordination environment-dependent variations can optimize d-d orbital coupling, thereby enhancing d-p orbital hybridization, thereby increasing PMS binding. However, excessively strong adsorption can hinder the desorption of reaction intermediates and deactivate the catalyst surface. Consequently, the moderate IOES value of FeMn translated to the suitable orbital hybridization for optimized PMS adsorption-desorption, mechanistically explaining its superior performance.

Fig. 4: Key factors for PMS adsorption.
Fig. 4: Key factors for PMS adsorption.The alternative text for this image may have been generated using AI.
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a Difference charge density of PMS on FeMn DACs, FeFe DACs, FeCo DACs, FeNi DACs, FeV DACs and FeCu DACs, and the corresponding PMS Eads. b UV-vis absorption spectra, inset: visualized photograph of PMS adsorption. c Linear regression fitting between the adsorption intensity and IOES. d PDOS of Fe/M 3d-orbitals and O 2p-orbitals in FeM DACs-PMS. e Comparison of the in-situ Raman spectra for the FeMn DACs and FeV DACs toward PMS depending on different reaction time. f Contour maps of the relating in situ Raman spectra. Data in b and c are presented as mean ± s.d. (n  ≥  3). Source data are provided as a Source Data file.

The secondary metal variants-dependent universality was mechanistically explained through PDOS analysis. FeMn-PMS complexes exhibited enhanced splitting between bonding (π, σ) and antibonding (π*, σ*) states (Fig. 4d and Supplementary Figs. 20–26), attributed to Mn (dxz, dyz and \({d}_{{x}^{2}}-{d}_{{y}^{2}}\)), which enhanced orbital overlap with O 2p orbitals from PMS38. This splitting reflected stronger PMS binding due to Mn-induced electronic perturbation. In contrast, FeV DACs displayed reduced orbital splitting and higher orbital occupancy, corresponding to weaker PMS affinity.

Operando Raman spectroscopy provided real-time insights into PMS adsorption dynamics. Upon PMS addition, FeMn DACs exhibited rapid disappearance of HSO3−/HSO5− species and the emergence of metastable *PMS formation (1047/1084 cm−1), followed by the appearance of SO42− (981 cm−1) (Fig. 4e)39. Compared to FeV DACs, the FeMn DACs demonstrated a more prolonged and intense response of *PMS and SO42−, inferring enhanced PMS adsorption and activation efficiency. Contour plots revealed a clear decrease in the HSO5− peak (1062 cm−1) over time and a corresponding increase in SO42− (981 cm−1), supporting the conversion of PMS via a partial conversion of HSO5− to SO42− and 1O2 (SO5•− + SO5•− → 1O2 + 2 SO42−) (Fig. 4f). Thus-observed generation pathway of 1O2 will be further confirmed by the subsequent validation.

IOGS Dictates geometric-dependent PMS activation kinetics

While the IOES descriptor effectively captured PMS adsorption thermodynamics via orbital hybridization, the subsequent activation of PMS for particularly the generation of reactive oxygen species (ROS), was fundamentally governed by geometric factors encoded in the IOGS descriptor. Introduction of dual-metal centers induces significant electronic perturbations that reshape ROS generation pathways40. This activation involves complex ROS conversion, generating metastable intermediates (e.g., 1O241, SO4•−42, ·OH43 and O2•−44), characterized by unoccupied π∗orbitals. DFT calculations revealed that 1O2 formation via 2SO5•− → 1O2 + 2SO42⁻ was kinetically favored over radical pathways. This preference stems from preferential O-H bond cleavage compared to O-O bond cleavage during PMS activation (Supplementary Figs. 27, 28), yielding SO5•− as a critical intermediate. This mechanism predicts SO5•− as a crucial metastable intermediate, corroborated by experimental detection of *PMS and SO42⁻ species (Fig. 4e).

To identify the dominant ROS, a series of targeted quenching experiments was conducted. Using 1,3-diphenylisobenzofuran (DPBF) as a selective 1O2 probe, FeMn DACs exhibited the highest 1O2 yield—exceeding those of other FeM DACs (FeFe, FeCo, FeNi, FeV, FeCu) by 0.03–0.59% (Supplementary Fig. 29). This was further validated by electron paramagnetic resonance (EPR) spectroscopy, which confirmed a 1O2 signal intensity of 574 arb. u. for FeMn DACs, outperforming other DACs (256–416 arb. u.; Fig. 5b and Supplementary Fig. 30). Correspondingly, 1O2 was responsible for 95.82–98.21% of the SDZ degradation (Supplementary Fig. 31), and virtually no O2•− were detected (Supplementary Fig. 32). Methanol quenching induced negligible inhibition (< 15%), effectively ruling out SO4•− participation (Fig. 5a). In addition, the absence of high-valent metal–oxo species (Supplementary Fig. 33) and analysis of electron transfer pathways (Supplementary Fig. 34) confirmed a nonradical-dominated oxidation mechanism. Together, these results unambiguously established 1O2 as the primary ROS, resolving prior ambiguities in ROS attribution and highlighting the critical role of dual-site synergy in driving efficient nonradical PMS activation.

Fig. 5: Key factors for PMS activation.
Fig. 5: Key factors for PMS activation.The alternative text for this image may have been generated using AI.
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a Effect of reactive oxygen species quenchers on SDZ, SM2, SP, SMM, SMZ and SMD degradation in the FeMn DACs-PMS system. b The TEMP-1O2 signals in different FeM DACs-PMS systems. c Energy profiles of 1O2 generation for the FeM-PMS system. d EIS spectra at various temperatures for different FeM DACs. e Linear relationship between the inverse of absolute temperature (T) and the logarithm of the reciprocal of the charge-transfer resistance. f Activation energy of SO5•−-to-1O2 conversion for the FeM DACs. g Linear regression fitting between the activation energy and IOGS of varied catalysts. Data in a, e, f and g are presented as mean ± s.d. (n  ≥  3). Source data are provided as a Source Data file.

Energy profiles revealed FeMn afforded the lowest energy barrier for 1O2 formation, followed by FeFe < FeCo < FeNi < FeV, with FeCu the highest (Fig. 5c). Thermodynamic assessment of ΔG between reactants and products24 revealed a strong positive correlation with catalytic activity (Supplementary Fig. 35). Electrochemical impedance spectroscopy (EIS) across a temperature range established a linear relationship between the inverse of absolute temperature (1/T) and the logarithm of reciprocal charge-transfer resistance (1/Rct), with the slope corresponding to activation energy (Fig. 5d–e). The fitted activation energies followed FeMn < FeFe < FeCo < FeNi < FeV < FeCu, aligning precisely with the energy profile sequence (Fig. 5f). Strikingly, a robust linear correlation (R2 = 0.93) between activation energy and IOGS across all these FeM DACs confirmed the intrinsic linkage between geometric-electronic synergy and PMS efficiency (Fig. 5g). The superior catalytic performance of FeMn DACs over FeSACs and other FeM DACs counterparts was further validated through pollutant degradation experiments (Supplementary Fig. 36).

Industrial translation: flow-through reactor validates BD-guided design

The orbital electronic structure index (IOES) and orbital geometric structure index (IOGS) served as descriptors governing adsorption and activation processes, respectively. Enhanced IOES values strengthened PMS adsorption at dual-atom sites, yet excessively high values may induce catalyst passivation by hindering intermediate desorption. Similarly, decreased IOGS lowered the activation barrier for O-H bond cleavage in adsorbed PMS, facilitating the generation of 1O2. Within PMS-based advanced oxidation systems, catalytic cycles involved sequential substrate adsorption, ROS generation and organic oxidation at DACs interfaces. Thus, holistic activity assessment required simultaneous evaluation of IOES and IOGS, as conceptualized in Fig. 1. DACs with high IOES but suboptimal IOGS (e.g., FeCr DACs) exhibited strong PMS binding energies yet depressed kinetics due to high activation energies. Materials with moderate IOES and intermediate IOGS (e.g., FeCo DACs) achieved partial activity and suffered from limited nonradical generation. Optimal systems balanced suboptimal IOES with optimal IOGS (e.g., FeMn DACs), enabling efficient PMS activation and rapid interfacial turnover (Fig. 6a). Thus, the established BD framework provided a critical link between theoretical catalyst design and practical PMS activation by unifying adsorption-conversion dynamics. This BD integrated orbital electronic structure (IOES) and orbital geometric structure (IOGS) indices to quantify dual-site synergy through the following equation derived by least-squares-based machine learning (Supplementary Note 1):

$${{{\rm{B}}}}{{{\rm{D}}}}={1.37}{ * }{{{{\rm{I}}}}}_{{{{\rm{OES}}}}}+{14}{ * }{{{{\rm{I}}}}}_{{{{\rm{OGS}}}}}-4.75$$
(1)
Fig. 6: Binary descriptor validation in PMS activation and stability evaluation.
Fig. 6: Binary descriptor validation in PMS activation and stability evaluation.The alternative text for this image may have been generated using AI.
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a Schematic of the secondary metal (Mn, Co and Cu) on the catalytic performance. b The lnKobs values in the FeM-PMS system, inset: the molecular structural formula of the six contaminants. c Linearity between the lnKobs values and the binary descriptor. d Comparison of lnKobs for SDZ between this work and the currently reported literature (Corresponding references: [9 ~ 20] in Supporting Information). e Degradation performance of SDZ under different pH, co-existence of HA and anions in the FeMn-PMS system. Data in b are presented as mean ± s.d. (n  ≥  3). Source data are provided as a Source Data file.

To validate the BD-PMS activation relationship, Kobs for six sulfonamide antibiotics were analyzed (Fig. 6b). All contaminants exhibited consistent degradation trends across FeM DACs, ranked as FeMn > FeFe > FeCo > FeNi > FeV > FeCu, aligning with the strong linear correlations (R2 = 0.85–0.94) between BD and lnKobs, underscoring geometric-electronic synergy in catalytic efficiency (Fig. 6c). In terms of the contaminant degradation kinetics, our FeMn DACs catalyst represented a substantial advance and thus achieved higher lnKobs values compared with state-of-the-art Fenton-like systems (Fig. 6d and Supplementary Table 9). Benefitting from these favorable merits, the FeMn/PMS system demonstrated broad pH adaptability (pH 3–11, Fig. 6e and Supplementary Fig. 42), high matrix tolerance (e.g., humic acid and anions, Fig. 6e and Supplementary Fig. 43), and 34.5% mineralization efficiency (Supplementary Fig. 44). Note that the degradation efficiency and mineralization rate of our FeM-PMS system could be substantially improved by optimizing operational parameters, including catalyst dosage, SDZ antibiotic concentrations, and solution pH44. Further improvement in catalytic performance could be achieved by reactor configuration innovations and advanced oxidant activation pathway engineering to enhance practical applicability.

To translate the exceptional catalytic performance of FeMn DACs into tangible water remediation solutions, we engineered a scalable flow-through reactor centered on a porous copper foam substrate (25 × 25 mm). This substrate served a dual function: acting as a robust conductive scaffold and an integral catalytic platform. FeMn DACs were uniformly immobilized onto the copper foam via spray-coating followed by chemical cross-linking, forming a highly active and stable catalytic layer (Fig. 7a and Supplementary Fig. 45). Critically, the underlying mechanism of PMS activation hinged on a synergistic interplay between the copper substrate and the anchored FeMn DACs. Copper initiated the catalytic cycle by facilitating crucial electron transfer for primary PMS activation, generating initial reactive species (e.g., SO4•− or ·OH). Simultaneously, the adjacent FeMn DACs sites acted as highly efficient co-catalysts, profoundly enhancing PMS decomposition kinetics and steering the reaction dominantly towards the nonradical pathway (e.g., via synergistic Cu(I)/Cu(II), Mn(II/III/IV), and Fe(II)/Fe(III) redox cycles). This dual-site synergy enabled exceptional 1O2 generation and unparalleled pollutant degradation kinetics. Importantly, the copper substrate played a sustained and active role beyond initiation, directly participating in the continuous catalyst regeneration cycle alongside the Fe-Mn pair.

Fig. 7: Practical application of PMS activation on environmental remediation.
Fig. 7: Practical application of PMS activation on environmental remediation.The alternative text for this image may have been generated using AI.
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a Schematic illustration of the poisoning resistance mechanism in the FeMn DACs. b The mechanism schematic of PMS activation by the copper foam membrane-based system hinges on the synergistic interplay between the copper substrate and the anchored FeMn DACs. c Photo of the continuous-flow reactor for the treatment of 5 L micropollutant-containing wastewater. d The C/C0 values of SDZ depending on time in five consecutive cycles. e Comparison of the three-dimensional fluorescence of practical river water before and after treatment. f 30-day SDZ filtration by the continuous-flow reactor, with a stable removal efficiency > 90%. Experimental conditions: [SDZ]0 = 1 mg L–1, [PMS]0 = 0.1 mg L–1 and flow rate = 1 mL min–1. g Water flux of CuM and FeMn DACs-CuM, inset: visualized photograph and contact angle of CuM and FeMn DACs-CuM. h Different scenarios for PMS activation applications produced from these DACs catalysts. Source data are provided as a Source Data file.

Capitalizing on this synergistic and dual-functional design, we constructed a continuous-flow electrochemical reactor. Cross-sectional SEM confirmed the uniform distribution of FeMn DACs within the Cu matrix (Supplementary Fig. 46), maximizing active site accessibility and utilization. The immobilization process significantly enhanced surface hydrophilicity, evidenced by a dramatic reduction in contact angle from 128.12° (bare Cu foam) to 77.11° (functionalized electrode) (Fig. 7g), crucially promoting interfacial mass transfer of pollutants and PMS to the catalytic sites. Operating under continuous dead-end filtration mode (Fig. 7b), the reactor achieved near-complete oxidation of SDZ (Fig. 7c, d), validated by comprehensive 3D fluorescence analysis showing substantial elimination of characteristic organic peaks (Fig. 7e). Most significantly, the reactor sustained an industrially relevant high flux of 122.3 L m⁻2 h⁻1 while maintaining > 90% SDZ removal efficiency continuously over 30 days (Fig. 7f). This exceptional long-term operational stability and inherent fouling resistance were paramount for practical, large-scale implementation, overcoming a major hurdle in advanced oxidation processes (AOPs) for water treatment.

This work successfully bridged the gap between atomically precise nanoscale catalysis (FeMn DACs) and macro-engineering (flow-through reactor). The seamless integration demonstrated how a fundamental understanding of dual-atom synergy can be translated into a robust, scalable, and cost-effective technology. The demonstrated performance, stability, and adaptability established this copper foam-supported FeMn DACs system as a highly viable and promising solution for on-demand water decontamination across diverse scenarios, including remote communities, disaster relief, aging infrastructure systems, and industrial wastewater streams (Fig. 7h).

Discussion

This study transcends classical d-band theory by establishing a universal binary descriptor (BD) that unifies orbital electronic structure (IOES) and geometric parameters (IOGS) to mechanistically decode peroxymonosulfate (PMS) activation in dual-atom catalysts. The IOES index quantitatively correlates d-p hybridization strength with PMS adsorption thermodynamics, while IOGS encodes interatomic distance-dependent geometric constraints that dictate O-H bond activation barriers—a critical determinant for 1O2-dominant nonradical pathways. Rigorous validation across heteronuclear pairs (Fe-M) and asymmetric coordination environments (FeMnN5C) confirms BD robustness (R2 = 0.80-0.90), with machine learning-derived BD enabling precise catalyst screening. Optimized FeMn DACs achieve unprecedented performance: fast kinetics (kobs = 1.2 min–1, 94.2% 1O2 selectivity, and > 90% sulfadiazine removal for 30 days at industrial flux (122.3 L m−2 h−1) in a flow-through reactor. By bridging orbital-level insights to scalable water remediation, this framework provides a general strategy for designing electronic-geometric synergistic catalysts in advanced oxidation processes.

Methods

Detailed information on chemicals and materials, characterization, analytical methods, and Density Functional Theory (DFT) calculations were available in Supporting Information (Supplementary Notes 3–6).

Preparation of FeM-DACs

A dual-template strategy combining host-guest chemistry and soft-templating, augmented by controlled thermal pyrolysis, was employed to embed iron phthalocyanine (FePc) within a bimetallic ZnM–ZIF framework (where M = Mn, Fe, Co, Ni, V, or Cu). This yielded the ZnM–ZIF@FePc precursor, which was subsequently pyrolyzed at 910 °C (5 °C min−1) under N2 atmosphere for 2 h to afford FeM DACs supported on N-doped carbon. Specifically, 0.3 g of P123, 2 g of 2-methylimidazole, and 0.1 mM FePc were dissolved into 40 mL methanol under vigorous stirring for 30 min. Simultaneously, 0.4 mM transition metal chloride (MnCl2·4H2O/FeCl3·6H2O/CoCl2·6H2O/NiPc/VCl3/CuCl2·2H2O) and 1.8 g Zn (NO3)2·6H2O were dissolved into 40 mL methanol. The latter solution was added dropwise into the former solution, followed by stirring for ≥ 4 h. The ZnM–ZIF@FePc precursor was then collected by centrifugation, dried, and pyrolyzed to yield FeM DACs as black powders. This methodology leverages ZIF-8 as a self-sacrificing microporous template, while introducing P123 soft template to direct mesopore formation, establishing a synergistically regulated hierarchical porous architecture. During pyrolysis, P123 dynamically stabilizes the pore structure, mitigating framework collapse in ZIF-derived carbons and enabling high surface area with abundant mesoporosity. Thus-acquired hierarchically porous structure enables it reserve sufficient N content for controllable formation of MN4 coordination and afford high-loading DACs (Variants FeMn (2.0 Å) to FeMn (4.5 Å) DACs were synthesized analogously using 0.1, 0.075, and 0.05 mM FePc, respectively).

Catalytic tests and analytical methods

The degradation of antibiotics was conducted in a 100 mL beaker with magnetic stirring at room temperature (25.0 ± 2.0 °C). Initially, 5.0 mg of FeM DACs were added into 50.0 mL of the antibiotic-containing solution (10 mg L−1), followed by 5 min of magnetic stirring to achieve adsorption-desorption equilibrium. Subsequently, 0.1 mM PMS was introduced to initiate the reaction. The supernatant samples were collected at pre-determined intervals throughout the process. All experiments were performed in triplicate to ensure reproducibility.

The filtration experiments were conducted using a custom-made continuous-flow reactor. Cu foam with a pore size of 50 μm and dimensions of 25 × 25 mm was obtained from commercial sources. Subsequently, 2.5 g of copper powder was evenly mixed with the prepared Cu foam under a pressure of 25 MPa and subjected to calcination to create the Cu foam membrane. The feed solution was prepared by adding the SDZ stock solution to 5 L river water to achieve a concentration similar to that used in batch experiments. The water flux of the Cu foam filtration system was recorded throughout the process.