Data-guided design of double-atom catalysts for enhanced electrocatalytic performance†

Chenyang Wei^a, Wenbo Mu*^b, Hongyuan Zhang^a, Zhenghui Liu*^c and Tiancheng Mu*^ad
aSchool of Chemistry and Life Resources, Renmin University of China, Beijing 100872, P.R. China. E-mail: tcmu@ruc.edu.cn
^bDepartment of Computer Science and Engineering, University of California San Diego, La Jolla, CA 92093-0404, USA. E-mail: wmu@uscd.edu
^cSchool of Pharmaceutical and Chemical Engineering, Taizhou University, Taizhou 318000, Zhejiang, China. E-mail: liuzhenghui@iccas.ac.cn
^dKey Laboratory of Green Chemical Media and Reactions, Ministry of Education, School of Chemistry and Chemical Engineering, Henan Normal University, Xinxiang, Henan 453007, P. R. China

First published on 10th July 2025

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Introduction

The increasing concentration of atmospheric CO₂, coupled with the demand for sustainable growth, has driven significant interest in electrocatalysis as a promising solution.^1–3 Electrocatalysis offers advantages such as high energy efficiency, excellent atom economy, and a reduced environmental footprint. However, the current catalyst design methodologies face challenges, particularly in achieving optimal reaction selectivity and mitigating material degradation under electrochemical conditions. These challenges necessitate the development of advanced catalysts that combine high activity with specificity to enhance electrocatalysis for widespread adoption.

Atomic catalysts (ACs), particularly double-atom catalysts (DACs), have garnered attention due to their exceptional metal atom utilization and enhanced catalytic activity.^4–9 By dispersing metal atoms across two-dimensional (2D) substrates, ACs offer a high density of active sites. DACs, which introduce a second metal atom, further enhance catalytic versatility and promote complex inter-metallic interactions, modifying the electronic and geometric properties of active sites. These changes allow for targeted optimization of catalytic performance, highlighting DACs as a promising platform for advancing catalytic processes. However, DACs face a significant challenge: the vast chemical space of possible combinations (Fig. 1), especially when considering diverse 2D substrates. Within this vast chemical landscape, some DAC configurations may suffer from thermodynamic or electrochemical instability, while others may fail to meet desired catalytic criteria. This brings us to a key question: How can we effectively predict the properties of DACs within such an expansive chemical space? Traditional density functional theory (DFT) calculations, while accurate, are computationally expensive, and relying solely on chemists' intuition often lacks the precision when predicting the effects of complex substrate–metal interactions.

The rapid advancement of machine learning (ML) has positioned it as a transformative tool in material discovery, synthesis, and characterization.^10–17 ML efficiently detects patterns and relationships within large datasets, enabling rapid predictions and accelerating research. By uncovering complex relationships that are often beyond traditional models, ML has the potential to revolutionize scientific research. For instance, Google DeepMind's Graph Networks for Materials Exploration (GNoME) has enabled the creation of an extensive database of stable crystals, predicting approximately 220 million structures.¹⁸ Likewise, Amir Kotobi's team used graph neural networks (GNNs) to predict X-ray absorption spectra (XAS) of organic molecules, enhancing interpretability through class activation maps (CAM).¹⁹ Another example includes Tongtong Yang and collaborators, who proposed a ML approach leveraging spectroscopic descriptors to predict catalytic properties and achieve structural inversion.²⁰ These advancements highlight ML's potential to replace traditional labor-intensive methods and deliver substantial time efficiencies. Specifically, some instances indicate that ML has the promise in the design of ACs.^4,5,21 However, most studies have focused on transition-metal-based ACs on specific substrates or employed conservative doping strategies that minimally alter the substrate's structural framework (Fig. S1†). This trend is even more pronounced in DACs research, where simplified approaches facilitate the analysis of metal–metal interactions and the development of straightforward predictive frameworks. While these methods are effective in idealized scenarios, they diverge from real-world complexities. In practical applications, optimal ACs require exploring diverse substrate–metal combinations, as substrates can significantly alter the electron density and structure of metals, imparting unique properties to the catalysts.^22,23 These complexities pose significant challenges for ML, which must account for the dynamic interactions between substrates and metals to accurately reflect real-world conditions.

To address these challenges, this study employs four prototypical 2D graphitic carbon nitride (C_xN_y) substrates, which, to our knowledge, have not been extensively used in DACs. These substrates introduce significant modifications to the substrate structure and coordination environment surrounding the metal atoms, bringing the study closer to realistic material design processes. Using high-throughput DFT calculations, we initially investigate DAC-driven CO₂ reduction reaction (CO₂RR) activity across 46 distinct DACs, revealing that conventional descriptor-the Gibbs free energy change for CO adsorbates (ΔG_CO*) does not adequately capture CO₂RR performance. Consequently, we leverage ML to predict the limiting potential (U_L) of CO₂RR and estimate key stability metrics-binding energy (ΔE_bind), dissolution potential (U_diss), and the Gibbs free energy for H adsorbates (ΔG_H*)-which serve as proxies for thermal, electrochemical stability and competing hydrogen evolution reaction (HER) activity. In subsequent analyses, ML further dissects the adsorption behavior of intermediates, revealing that the d-electron count within bimetallic systems-via alterations in the d-band center and electron transfer-is crucial for modulating adsorption, while DAC stability is influenced by both substrate and intrinsic metal properties. Building on preceding insights, we identify the N vacancy in graphitic carbon nitride (N-C₃N₄) as a promising substrate for stabilizing bimetallic atoms and explore the oxygen evolution reaction (OER) activity, noting that traditional descriptors like OH adsorption Gibbs free energy (ΔG_OH*) fall short, thus prompting ML-based prediction of the theoretical overpotential (η^OER). Finally, we present an innovative framework that integrates high-throughput DFT with advanced ML techniques to predict DAC performance in key catalytic reactions. By employing symbolic regression via the PySR library, we enhance the interpretability of adsorption predictions for key intermediates-thereby laying the groundwork for future descriptor development-while reducing computation time by approximately 3750 times. Ultimately, our approach streamlines the DAC discovery process and offers an efficient pathway for identifying high-performance catalysts for sustainable energy applications.

Experimental

DFT calculations

In this study, spin-polarized DFT calculations were performed using version 6.3.0 of the Vienna Ab initio Simulation Package (VASP),²⁴ utilizing the projector augmented wave (PAW) method. All calculations were conducted with a set cutoff energy for plane waves of 500 eV. Electronic interactions were described utilizing the generalized gradient approximation (GGA) in conjunction with the Perdew–Burke–Ernzerhof (PBE) functional.²⁵ DFT+U corrections were not applied, consistent with common practice in high-throughput catalyst screening involving diverse transition metals. This decision ensures methodological consistency and computational efficiency across 3d, 4d, and 5d systems. This approach has been commonly adopted in recent high-throughput studies, where GGA-PBE functionals have been used without Hubbard U corrections to efficiently evaluate catalyst performance trends across a broad chemical space.^26–30 The Grimme's semiempirical DFT-D3 method was employed for dispersion correction to address long-range van der Waals (vdW) interactions.³¹ To preclude interactions between neighboring layers, a vacuum buffer of 15 Å was maintained along the z-axis. The Brillouin zone was sampled using a 2 × 2 × 1 Monkhorst–Pack k-point grid for geometric optimization, while a finer 4 × 4 × 1 k-point grid was selected for electronic structure calculations requiring higher precision. The convergence criterion for energy was established at 10⁻⁵ eV, and for forces, it was set at 0.02 eV Å⁻¹. The free energy change for each reaction step was computed utilizing the computational hydrogen electrode (CHE) model,³² as described in the ESI.† Solvent effects were not explicitly modelled in our DFT calculations, which were conducted under vacuum conditions within the CHE framework. This approximation is widely adopted in high-throughput electrocatalysis studies to enable efficient screening of large catalyst libraries, and has been shown to preserve meaningful energetic trends across diverse catalyst systems.^33–38 The thermodynamic stability of superior DACs was carried out by ab initio molecular dynamics (AIMD) simulation within the NVT ensemble at 400 K up to 10 ps with a time step of 2 fs.

ML models

Feature engineering

In this study, we integrated both elemental and structural descriptors in our ML models to capture the characteristics of DACs. All models incorporate elemental information-including atomic mass, atomic number, and valence electronic configurations-to represent the intrinsic chemical properties of each atom (see Tables S1 and S2†). Formal oxidation states were not included as descriptors, as they are often ill-defined under DFT and strongly dependent on the local bonding environment, particularly in supported bimetallic systems. Instead, tabulated elemental properties such as d-electron count serve as robust and physically meaningful proxies for redox behavior, consistent with established practices in ML-based catalyst discovery.^26,43 To further probe oxidation-related effects, we conducted additional DFT analyses using Bader charge and projected density of states (PDOS), which provided insight into charge transfer and local electronic structure for selected DAC configurations. For structural descriptors, two distinct sets were employed for different purposes. For our analysis models, we used bond lengths around the bimetallic centers (i.e., distances between the two metals, between metals and surrounding atoms, and to adsorbates) to characterize the local bonding environment (Table S1†). In contrast, for predicting the catalytic properties of DACs, we employed two global descriptors: Coulomb Matrix (CM) and Smooth Overlap of Atomic Positions (SOAP).

Due to the high dimensionality of CM and SOAP, we applied dimensionality reduction techniques (PCA or t-SNE) to retain essential information while reducing the computational burden.

Model interpretation and analysis

Results and discussion

Setting the stage for DACs selection in CO₂RR applications

Before rapidly screening DACs for CO₂RR activity, it is essential to define the selection prerequisites. A common strategy is to employ descriptors that can quickly differentiate catalysts with high CO₂RR activity from those with significant hydrogen evolution reaction (HER) activity. For HER, ΔG_H* is widely recognized as a robust descriptor due to HER's relatively simple mechanism involving only H adsorption and desorption.⁴⁷ In contrast, CO₂RR proceeds via multiple steps involving intermediates such as COOH* and CO*, complicating the choice of a descriptor, a subject of ongoing debate.^48,49 To assess whether the widely accepted ΔG_CO* can reliably predict CO₂RR performance in our case, we analyzed its correlation with U_L, which directly quantify CO₂RR activity, on DACs across the selected four distinct substrates (Fig. 2). The analysis revealed an approximate volcano relationship between ΔG_CO* and U_L. However, beyond the volcano's peak (approximately −0.105 eV), the correlation weakens, likely due to variations in CO binding strength. This divergence originates from the fact that ΔG_CO*, as a single-intermediate descriptor, only reflects the thermodynamics of one step in the overall pathway. It fails to capture the energy landscape of other critical elementary steps-particularly COOH formation and protonation-which often act as the potential-determining steps (PDS) depending on the local binding environment. For DACs with strong CO adsorption (i.e., more negative ΔG_CO*), CO desorption becomes more energetically demanding, shifting the PDS to step 3 of CO₂RR-namely, CO release (CO* + H₂O → Slab + CO(g) + H₂O). In this regime, ΔG_CO* remains a relevant descriptor for U_L. Conversely, when CO binds weakly to the DAC surface, the PDS shifts to either step 1-protonation of CO₂ (Slab + CO₂(g) + 2H⁺ + e⁻ → COOH* + H⁺)-or step 2-protonation of COOH (COOH* + H⁺ + e⁻ → CO* + H₂O). In these cases, ΔG_CO* no longer governs the kinetics, leading to a diminished correlation with U_L and limiting its predictive utility.

In contrast, the limiting potential U_L inherently captures the thermodynamic span of all elementary steps and explicitly identifies the highest-energy barrier across the entire reaction pathway. This makes it a more comprehensive and physically meaningful descriptor for multi-step reactions like CO₂RR, where the PDS can shift dynamically depending on catalyst composition or coordination environment, making it a more robust descriptor for CO₂RR. To improve high-throughput prediction in this context, we further leveraged ML to construct composite descriptors that integrate electronic and geometric, features-beyond single-adsorbate energetics-to more accurately represent the complex multi-step nature of CO₂RR on diverse DAC surfaces.

To support this framework, we constructed a comprehensive dataset encompassing both stability and reactivity metrics. In addition to U_L, we computed the ΔE_bind and U_diss of DACs to evaluate their stability. A more negative ΔE_bind indicates enhanced thermal stability and a higher likelihood of experimental validation, while a positive U_diss suggests metal resistance to dissolution during electrochemical processes. An illustrative heatmap (Fig. S2†) compares these stability metrics across various DACs. Additionally, we computed ΔG_H* for approximately 120 DACs to quantify their HER activity, thereby providing further data for subsequent ML modeling.

Elucidating DAC parameters: a symbiosis of ML and DFT insights

ML transcends basic prediction; when interpreted properly, it provides profound insights into data. By employing SHAP, we can identify the features most influential in our ML models. Although our previous analysis indicates that ΔG_CO* is not a flawless descriptor for CO₂RR activity, it remains crucial for two reasons: first, ΔG_CO* reflects CO binding strength and thus helps pinpoint the PDS in CO₂RR; second, when ΔG_CO* falls below approximately −0.105 eV, it correlates reliably with CO₂RR performance. This underscores the importance of examining CO adsorption properties, so we focus our ML models on this intermediate with SHAP analysis guiding our interpretation.

SHAP analysis (Fig. 3b) highlights that descriptors related to the coordination environment-such as the ratio of nitrogen atoms near the bimetallic center (denoted ‘number of N’)-are highly influential. The high SHAP value associated with the nitrogen ratio indicates that nitrogen atoms are essential for modulating the electronic configuration of the bimetallic centers, which directly influences their ability to adsorb intermediates like CO. Previous studies have demonstrated how nitrogen atoms in the substrate can interact with the metal's d-electrons, enhancing or reducing CO adsorption strength.^50–52 Furthermore, the contribution of transition metal d-electrons to predicting ΔG_CO* suggests that both the nitrogen environment and the d-electron configuration of the metals are crucial for optimizing catalytic performance. By selecting appropriate substrates and metal pairs based on these features, we can design more efficient catalysts for reactions like CO₂ reduction.

To substantiate the impact of d-electrons on CO adsorption, we applied the Pearson correlation coefficient (p) to evaluate the relationships between the number of outermost electrons (N_e), s-electrons (θ_s), d-electrons (θ_d), and the C–O bond length (l_C–O) (Fig. 3a). Our findings reveal a strong correlation between the number of d-electrons in transition metals and l_C–O-a trend not observed for s-electrons-suggesting that d-electrons uniquely promote CO activation by elongating the C–O bond. Bader charge analysis (Table S4†) further confirms that transition metal d-electrons predominantly donate charge to CO, enhancing its activation. Moreover, correlating Bader charge transfer (|e|) with l_C–O shows that greater d-electron transfer corresponds to longer C–O bonds, signaling amplified CO activation (Fig. S3†). A heatmap (Fig. 3c) further illustrates a critical balance in the electronic configuration of bimetallic systems: neither an excess nor a deficiency of d-electrons favors optimal CO activation, as fully occupied d-orbitals impede activation while too few d-electrons lead to insufficient electron donation, and consequently, is detrimental to CO₂RR efficiency.

Subsequently, to elucidate how bimetallic atoms influence adsorption behavior and electronic structure, we computed the PDOS (Fig. S4† and 3d). These PDOS plots reveal the interaction between the two metals-evident from overlapping regions-and demonstrate how bimetallic structures modulate the d-band center (ε_d), as summarized in Table S5.† For example, in Pt–Pt and Pt–Ni combinations on a C₂N substrate (Fig. 3di and ii), replacing one Pt atom with Ni shifts the remaining Pt's ε_d closer to the Fermi level (E_F), resulting in the overall ε_d being adjusted toward E_F, thereby altering ΔG_CO*. A similar trend is observed in other metal pairings (e.g., NiSc and NiW on g-C₃N₄ substrates), underscoring the mutual influence of the metal partners. Such ε_d shifts, by modulating the adsorption strength of CO, directly influence CO₂RR activity through changes in intermediate stabilization and desorption energetics. Similar effects on OH adsorption are expected in OER, as discussed later.

To gain a more integrated understanding of the factors influencing ΔG_CO*, we examined the correlations among ΔG_CO*, ε_d, and |e| (Fig. S5†, 3e and f). Fig. S5† presents a synthesized view of these parameters, revealing a volcano relationship between ΔG_CO* and ε_d. Notably, ε_d has a more substantial impact on ΔG_CO* than |e|, in line with the majority of related works that position ε_d as an informative descriptor for adsorption energetics for transition metals; although higher ε_d generally corresponds to increased |e|, the relationship is not strictly linear. Fig. 3e further illustrates a volcano-shaped dependence, where a smaller gap between ε_d and E_F facilitates electron migration from the metal site to the adsorbate, thereby enhancing CO adsorption. This observation is supported by Fig. 3f, which shows that DACs with ε_d near E_F exhibit significant charge transfer |e|, emphasizing the role of electron displacement in CO activation.

Interestingly, certain DACs enriched with pre-transition metals (e.g., Zr, Ti, Sc) display a positive ε_d due to their incompletely occupied d-orbitals, resulting in empty d-bands above E_F. In DACs such as NbZr_g-C₃N₄, VZr_CN, and FeSc_CN, these unpaired d-electrons are more available, leading to higher Bader charge transfer values (Fig. 3f) and affect ΔG_CO* and CO₂RR activity. Aside from these anomalies, the overall volcanic trend between ε_d and ΔG_CO* is evident. Moreover, we hypothesize that these exceptions may partly arise from alternative CO adsorption modes: while most DACs adopt an end-on conformation (with C as the adsorption site), the anomalous DACs favor side-on adsorption (Fig. S6†).

Finally, we evaluated ΔG_H* for a subset of 12 DACs along with their ε_d and |e| values (Fig. S7†). These results indicate that a ε_d closer to E_F enhances hydrogen adsorption and that d-electron migration modulates ΔG_H* in a manner similar to CO adsorption. The high SHAP values associated with d-electrons further reinforce these findings.

For analyzing ΔE_bind, our ML model (Fig. 4b) indicates that both the spatial distance between transition metals and substrate atoms, and the distance between the two metal atoms themselves, are crucial. This is intuitively plausible: if the metal atoms are too close or if they possess excessively large atomic radii, strong repulsive forces may arise, compromising DAC stability. Concurrently, substrate-related features are also highly influential, underscoring the critical role of substrate type and structure. To clearly present these findings and reinforce our ML analysis, we detail ΔE_bind in Fig. 4a. Both the substrate and the transition metals type significantly affect ΔE_bind, consistent with our ML insights. Among the substrates, N-C₃N₄ exhibits a notably lower ΔE_bind compared to others, suggesting a stronger potential for securely anchoring dual metal atoms.⁵³ We postulate that this enhanced binding is attributed not only to the large pore structures and surface area of N-C₃N₄, but also critically to the presence of nitrogen vacancies, which introduce undercoordinated carbon atoms and locally distorted triazine units that provide flexible, asymmetric binding pockets for dual-metal anchoring. These defect-induced coordination environments enable diverse metal–support interactions and facilitate charge transfer from the substrate to the metal centers, thereby stabilizing the metal pair and modulating their oxidation states.^54,55 This dual effect-structural adaptability and electronic enrichment-underlies the superior anchoring capability of N-C₃N₄ observed in our ΔE_bind analysis.

Furthermore, our analysis reveals that the atomic radii of the di-metal pairs impact ΔE_bind. Metal pairs with similar radii tend to have comparable ΔE_bind values, while those with significant radii differences show pronounced disparities. For instance, on the CN substrate, metal pairs such as NiFe, NiCo, CoFe, and FeFe-having similar atomic radii-exhibit similar ΔE_bind values. A similar pattern is observed for NiCo and NiFe on N-C₃N₄ and for CoPt, CrPt, and CuPt on C₂N. Conversely, metal pairs with large radii differences (e.g., ZrV and ZrNb on N-C₃N₄, or NbSc, NiSc, VFe, and VW on g-C₃N₄) display substantial variations in ΔE_bind.

Finally, the d-electron configuration of transition metals also influences DAC thermal stability. Transition metals such as Zn, Cd, Ag, and Au typically have a stable configuration with 10 d-electrons, which limits their ability to bond with surrounding atoms and hinders DAC formation, often resulting in altered ΔE_bind values and distorted configurations.

Probing the OER facilitated by DACs

The oxygen evolution reaction (OER) is critical for sustainable energy, and DACs with both strong OER and HER activity are particularly promising for overall water splitting.^56–58 Based on previous analyses, we identified DACs with N-C₃N₄ substrates as exceptionally stable; hence, our focus here is on these systems.

Since OER activity is closely linked to the adsorption behavior of intermediates (OH*, O*, and OOH*) within the associative mechanism⁵⁹ and ΔG_OH* is a common descriptor for OER,^60,61 we first investigated ΔG_OH* in DACs with N-C₃N₄. Given that the OH adsorption strength also depends on the d electron count in transition metals,^14,61 we performed DFT calculations across diverse DACs to correlate ΔG_OH* with the number of d electrons. However, the presence of dual metal sites in DACs makes it challenging to determine the exact d electron count, unlike in single-atom catalysts' system. To address this, we developed a preliminary method to identify the dominant metal for OH adsorption by measuring the distances between the adsorbed OH and each metal atom. For example, in a MoFe DAC, the proximity of OH to Fe allowed us to assign a d electron count of 6 based on Fe's configuration (Fig. S10†). Cases with ambiguous adsorption preference were excluded from the initial analysis. The resulting violin plot in Fig. 5a shows that OH adsorption strength generally decreases as the d electron count increases, although potential biases from data exclusion warrant cautious consideration about this conclusion.

To more comprehensively probe the relationship between ΔG_OH* and d electron count, we refined our method by introducing a weighted descriptor ϕ. In this approach, weights are assigned to the d electron count of each metal based on its proximity to the adsorbed O atom, since OH typically adsorbs with the O atom closest to the metal. Detailed methodology is provided in the ESI note accompanying Fig. S10.† This refined approach allowed us to include DACs where preferential OH adsorption was previously ambiguous. As illustrated in Fig. 5b, the data now more clearly reveal that a higher average d electron count correlates with weaker OH adsorption. Complementary SHAP analysis (Fig. S11†) further supports the critical role of d electron count and the spatial relationship between the adsorbed OH and the metal sites in determining ΔG_OH*.

To gain a refined understanding of adsorption in DACs, we selected six representative systems for detailed analysis to re-establish the relationship between ΔG_OH*, ε_d, and |e| (Fig. 5c and g). Our findings are twofold: (1) a ε_d closer to E_F correlates with stronger OH adsorption; and (2) increased d-electron transfer-as indicated by a higher |e|-correlates with a lower ΔG_OH*. However, these parameters do not exhibit a strict linear correlation, suggesting that additional factors (e.g., varied adsorption modes and steric hindrances in different DAC structures) also influence OH adsorption. An R² of approximately 0.6 (Fig. 5b) further indicates that, while the d-electron count is a key determinant, it alone cannot fully capture OH adsorption strength. Ultimately, to validate ϕ's rationality for essential adsorption characteristics, we examined its correlations with ε_d and |e| (Fig. S12†). We found that a higher ϕ corresponds to a more negative ε_d (i.e., shifted further from E_F), which attenuates OH adsorption-a trend consistent with previous findings linking increased d-electron presence to larger ΔG_OH*. Moreover, a higher ϕ is associated with reduced charge transfer, reflecting diminished electron donation as ε_d moves away from E_F. Thus, ϕ not only reflects the overall adsorption energy but also encapsulates intrinsic factors governing adsorption, validating it as generally adept and rational parameter for assessing OER activity in DACs with single substrate.

Following our examination of the correlation between ΔG_OH* and d electrons, we extended our investigation to the remaining OER intermediates-namely, O* and OOH* and their relationship with OH*. Accordingly, we computed the energy barriers along the OER pathway for approximately 30 DACs (Fig. S13†). Concurrently, we calculated the Gibbs free energy changes for O* and OOH* (ΔG_O* and ΔG_OOH*, respectively) and visualized their relationships with ΔG_OH* in Fig. 5d and e. The results indicate a linear relationship between ΔG_OH* and both ΔG_O* and ΔG_OOH*, although the correlation for ΔG_O* is notably weaker than that for ΔG_OOH*. Traditionally, on transition metal surfaces, the robust linear relationships of both yield a characteristic volcano plot correlating ΔG_OH* with η^OER, thereby establishing ΔG_OH* as a reliable descriptor of OER activity.²² However, in the DACs studied here, these relationships are obscured; when examining the correlation between η^OER and ΔG_OH* (Fig. 5f), the expected volcano trend is not clearly observed. This obscured trend underscores the complexity of intermediate adsorption in DACs, where adsorbates may bind to one or both metal atoms or even to the substrate, deviating from conventional transition metal surface models.

Constructing an integrative ML paradigm for DAC blueprinting

In our previous analysis, we examined the CO₂RR, HER, stability, and OER activities of DACs on various substrates. Our results indicated that relying solely on simple descriptors-such as adsorption energies of key intermediates or elemental properties only-fails to predict catalyst performance accurately. Consequently, integrating ML became essential. However, representing the complex structural information of DACs poses a challenge: manually inputting data for numerous atoms is impractical, while focusing only on atoms near the central bimetallic sites sacrifices critical structural detail. Our initial, basic analysis ML models could not capture such complexity, limiting their regression performance. To overcome this, we developed an advanced ML framework that incorporates DFT-derived data, enabling fast and accurate predictions for DAC material design while reducing reliance on labor-intensive DFT calculations across chemical space.

In summary, our workflow (Fig. 6a) consists of several modules built on the XGBoost algorithm, which performs well on small to medium-sized datasets and avoids overfitting common with neural networks. XGBoost's numerous hyperparameters allow extensive optimization for superior performance. We extract optimized atomic coordinates and unit cell information in batches and convert these data into either CM or SOAP-two widely used feature construction methods in DFT. Our comparison reveals that SOAP outperforms CM (Fig. 6b) because it accounts for crystal structure repeatability and complex van der Waals interactions, thereby better simulating the true atomic environment for crystal materials. t-SNE visualization of SOAP features (Fig. 6c) shows that the four clusters correspond to the four substrate types in our dataset, with both g-C₃N₄ and N-C₃N₄ grouped distinctly on the right, and CN and C₂N on the left, indicating that SOAP effectively retains the key structural information of these materials. We also tested the impact of hyperparameter tuning on model performance, investigating whether CM could outperform SOAP. However, even after additional hyperparameter tuning (using Optuna for optimization, Table S6†), the XGBoost model with SOAP consistently outperforms the one using CM. This confirms that capturing structural repeatability is crucial for materials feature engineering. Nonetheless, SOAP has limitations due to its high storage requirements and longer computational times, highlighting the need for future advancements in feature engineering methods.

In our framework, we employed an active learning strategy that iteratively selects the most uncertain examples (uncertainty sampling) for each learning loop. This approach, effective even when data are generated via generative diffusion models (Fig. S15†), continuously refines model predictions by focusing on uncertain cases. To ensure the reliability of the generated data, we performed a comprehensive analysis of the samples produced by the diffusion mode (Table S7 and Fig. S15†). The analysis involved three key metrics: Maximum Mean Discrepancy (MMD), Average Cosine Similarity (ACS), and Nearest-Neighbor Consistency (NNC), along with t-SNE visualization of generated data. These results confirm that the generated data align closely with the real data, thereby ensuring their suitability for model training and validation. In large-scale DFT predictions, active learning significantly reduces computational costs and broadens the model's applicability. Despite its reliance on uncertainty estimation, its iterative nature provides a strong theoretical and practical foundation for automated materials exploration. Using this strategy, we achieved high-precision predictions for DAC properties (Fig. 6d, e and Table S8†) sequentially: first assessing DAC stability (ΔE_bind and U_diss) using multi-objective predictions, then evaluating HER activity (ΔG_H*) and the CO₂RR limiting potential (U_L) with single-objective predictions to rapidly screen promising CO₂RR electrocatalytic DACs. Furthermore, by integrating these predictions with ranking recommendations (Table S9†), we quickly identified the most stable catalysts, particularly those with potential dual functionality for overall water splitting (the purple dots located in the blue shadow in Fig. 6d). Additionally, we selected five DACs with the N-C₃N₄ substrate, which were proved to be stable with AIMD analysis (Fig. S16†), and compared DFT-calculated and ML-predicted values (Fig. 6f). The results show minimal discrepancies between the calculated and predicted values. Notably, CuNi emerges as the most promising bifunctional water splitting catalyst, while CuPd and PtZn metal pairs excel only in OER performance. Among them, PtZn demonstrates an η^OER close to 0.15 eV, significantly outperforming other materials in OER. Both PtMn and VTi exhibit reasonable U_L values, but VTi stands out with strong CO₂RR activity and HER resistance, with its CO₂RR limiting potential approaching −0.15 V, nearly the peak of the theoretical volcano plot, while PtMn significantly underperforms in CO₂RR for its low HER resistance.

However, we still encountered a challenge: while high-dimensional descriptors such as SOAP and CM enhance accuracy by retaining more information, they also compromise interpretability for their high dimension. To address this, we incorporated High-Performance Symbolic Regression (PySR) into our framework. By integrating prior knowledge from SHAP analysis and chemical logic, we provided PySR with key descriptors most likely to influence key intermediate adsorption, achieving high-precision fits (Table S10† and Fig. 6g). The interpretability offered by PySR yields valuable insights into adsorption patterns; furthermore, focusing on atomic features in the immediate vicinity of the adsorbate suggests that the adsorption strength in DACs is primarily determined by the local bimetallic environment. This makes the selection of such features a more efficient approach for ML model construction, with minimal loss in predictive accuracy. In particular, we emphasize that the “simple” versions of the PySR models rely solely on elemental properties such as electronegativity, electron affinity, and the number of valence d-electrons-features that can be directly obtained from publicly available databases (e.g., the NIST database) without requiring prior DFT calculations. This enables rapid, interpretable estimation of catalytic behavior without incurring the computational cost of quantum mechanical simulations. Consequently, these compact symbolic expressions can serve as efficient surrogates for predicting adsorption energetics of key intermediates, allowing researchers to pre-screen candidate DACs at negligible cost. This balance between transparency and computational simplicity makes the simple models particularly suitable for early-stage catalyst discovery.

Importantly, our ML framework significantly expedites the identification of potential CO₂RR and water-splitting DACs. As shown in Fig. S17,† our strategy approximately outperforms complex DFT calculations by a factor of 3750, underscoring its efficiency. Note that the DFT computational time referenced pertains only to the DACs in our dataset; expanding DFT analysis to cover the entire chemical space would lead to an exponential increase in computational time and cost, rendering it impractical for real-world applications. We therefore anticipate that ML will increasingly supplant less efficient DFT methods and become increasingly prevalent in the discovery and development of novel materials systems.

Conclusions

In summary, our study provides pivotal insights into the design and optimization of DACs for various electrocatalytic processes. By integrating high-throughput DFT calculations with advanced ML algorithms for analysis, we studied numerous metal/substrate combinations and identified key parameters that govern catalytic efficiency. Regarding DACs for CO₂RR, our research challenges the traditional reliance on ΔG_CO* as the sole determinant of catalytic activity, highlighting the inherent complexity of these processes. We found that the number of d-electrons in transition metals critically influences CO adsorption by modulating ε_d, as evidenced by variations in Bader charge analyses. These variations lead to distinct C–O bond lengths and diverse CO binding strengths, which in turn profoundly impact CO₂RR activity-a trend that parallels observations in DAC-mediated HER processes. Furthermore, our ML approaches reveal that DAC stability is largely governed by the nature of the supporting substrate and the metal's atomic radius, primarily due to atomic repulsion. Notably, configurations with a fully occupied outer d-shell (10 d-electrons) exhibit diminished bonding strength. In the context of OER, our study demonstrates that ΔG_OH*, despite being influenced by the transition metals' d-electrons, is insufficient as a standalone metric for OER activity because complex adsorption modes introduce discrepancies that weaken the expected volcano relationship.

Moreover, in the latter part of our study, we established a ML framework not only delivers precise catalytic predictions consistent with theoretical results but also substantially reduces computational costs, underscoring ML's transformative potential in catalyst development. Ultimately, the methodologies and insights from this study chart a definitive course for using ML to advance the design of atomic catalysts for energy conversion and storage, a key step toward a sustainable energy paradigm.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Author contributions

Chenyang Wei: writing – original draft, validation, methodology, investigation, visualization, data curation. Wenbo Mu: conceptualization, methodology, formal analysis, investigation. Hongyuan Zhang: formal analysis, visualization, data curation. Zhenghui Liu: supervision, resources, conceptualization. Tiancheng Mu: writing – review & editing, supervision, resources, project administration, funding acquisition.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors thank the National Natural Science Foundation of China (22238011) and Open Research Fund of School of Chemistry and Chemical Engineering, Henan Normal University for financial support.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta03021h

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