Metal–nitrogen–carbon sites provide a chemically diverse platform for tuning adsorbate binding, yet the relationships among different C1 adsorption probes remain incompletely resolved. Here, density functional theory and interpretable machine learning are combined across a 35-metal M–N4–C chemical space to examine *COOH, *CO, and *CHO adsorption as complementary probes. The adsorption landscapes are strongly adsorbate dependent, but *COOH and *CHO exhibit a cross-adsorbate scaling relation (R2 = 0.919), consistent with similar metal-dependent stabilization across much of the series. In contrast, relationships involving *CO show larger residual variation. Gradient-boosting models evaluated by nested out-of-fold prediction recover descriptor-based signal for all three targets; *CO is predicted most accurately (R2 = 0.851; MAE = 0.272 eV), whereas *COOH and *CHO show moderate predictability. Permutation importance, direct DFT correlations, and out-of-fold SHAP analysis identify d-electron count as a recurring organizer of *COOH and *CO adsorption and periodic group as a recurring organizer of *CO and *CHO adsorption. Robust regression highlights Os, Ru, and Re as pronounced *COOH–*CO scaling deviations, while Y departs strongly from the tighter *COOH–*CHO relation. Separate Pareto analyses highlight Y, Os, and Ti under different two-objective adsorption trade-offs. The combined analysis distinguishes shared adsorption trends from adsorbate-specific behavior and identifies chemically informative sites for subsequent mechanistic study.
- Open Access
- Article
Cross-Adsorbate Scaling, Interpretable Machine Learning, and Adsorption Trade-Offs across M–N4–C Sites
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Received: 11 September 2026 | Revised: 21 October 2026 | Accepted: 22 October 2026 | Published: 03 November 2026
Abstract
Keywords
interpretable machine learning | single-atom catalysis | intermediate adsorption | adsorption-energy scaling
References
- 1.
Qiao, B.; Wang, A.; Yang, X.; et al. Single-atom catalysis of CO oxidation using Pt1/FeOx. Nat. Chem. 2011, 3, 634–641. https://doi.org/10.1038/nchem.1095.
- 2.
Yang, X.F.; Wang, A.; Qiao, B.; et al. Single-Atom Catalysts: A New Frontier in Heterogeneous Catalysis. Accounts Chem. Res. 2013, 46, 1740–1748. https://doi.org/10.1021/ar300361m.
- 3.
Liu, J. Catalysis by Supported Single Metal Atoms. ACS Catal. 2016, 7, 34–59.
- 4.
Xie, L.; Liu, Y.; Li, S.; et al. Phase and facet engineering for nanoscale catalyst discovery in electrochemical CO2 reduction. Nat. Synth. 2026, 5, 489–505. https://doi.org/10.1038/s44160-026-01025-4.
- 5.
Wang, A.; Li, J.; Zhang, T. Heterogeneous single-atom catalysis. Nat. Rev. Chem. 2018, 2, 65–81.
- 6.
Yang, H.; Lin, Q.; Zhang, C.; et al. Carbon dioxide electroreduction on single-atom nickel decorated carbon membranes with industry compatible current densities. Nat. Commun. 2020, 11, 593.
- 7.
Fauzi, A.; Chen, X.; Zhao, H.; et al. Recent progress of M-N-C single atom electrocatalysts for carbon dioxide reduction reaction. Next Energy 2023, 1, 100045. https://doi.org/10.1016/j.nxener.2023.100045.
- 8.
Back, S.; Lim, J.; Kim, N.Y.; et al. Single-atom catalysts for CO2 electroreduction with significant activity and selectivity improvements. Chem. Sci. 2017, 8, 1090–1096. https://doi.org/10.1039/c6sc03911a.
- 9.
Zhang, J.; Cai, W.; Hu, F.X.; et al. Recent advances in single atom catalysts for the electrochemical carbon dioxide reduction reaction. Chem. Sci. 2021, 12, 6800–6819. https://doi.org/10.1039/d1sc01375k.
- 10.
Wang, G.; Li, S.; Yu, C.; et al. High-Index-Faceted Cu Nanoparticles in Ag–Cu Tandem Catalysts for Selective CO2 Electroreduction. ACS Nanosci. Au 2026, 6, 1029–1036. https://doi.org/10.1021/acsnanoscienceau.6c00129.
- 11.
Cui, X.; An, W.; Liu, X.; et al. C2N-graphene supported single-atom catalysts for CO2 electrochemical reduction reaction: Mechanistic insight and catalyst screening. Nanoscale 2018, 10, 15262–15272. https://doi.org/10.1039/c8nr04961k.
- 12.
Yang, Y.T.; Li, J.; Zhang, C.; et al. Theoretical Insights into Nitrogen-Doped Graphene-Supported Fe, Co, and Ni as Single-Atom Catalysts for CO2 Reduction Reaction. J. Phys. Chem. C 2022, 126, 4338–4346. https://doi.org/10.1021/acs.jpcc.1c09740.
- 13.
Qin, C.; Li, T.; Masakorala, G.; et al. Boosting CO2-to-C2H4 electrocatalysis on Cu2O with waste-derived porous carbon from coconut shells. Chem. Commun. 2026, 62, 10482–10486. https://doi.org/10.1039/d6cc01782g.
- 14.
Wang, Q.; Liu, K.; Hu, K.; et al. Attenuating metal-substrate conjugation in atomically dispersed nickel catalysts for electroreduction of CO2 to CO. Nat. Commun. 2022, 13, 6082. https://doi.org/10.1038/s41467-022-33692-0.
- 15.
Wang, J.; Huang, Y.C.; Wang, Y.; et al. Atomically Dispersed Metal–Nitrogen–Carbon Catalysts with d‑Orbital Electronic Configuration-Dependent Selectivity for Electrochemical CO2‑to-CO Reduction. ACS Catal. 2023, 13, 2374–2385.
- 16.
Butler, K.T.; Davies, D.W.; Cartwright, H.; et al. Machine learning for molecular and materials science. Nature 2018, 559, 547–555. https://doi.org/10.1038/s41586-018-0337-2.
- 17.
Palkovits, S. A Primer about Machine Learning in Catalysis—A Tutorial with Code. ChemCatChem 2020, 12, 3995–4008.
- 18.
Shi, Y.; Liang, Z. Machine learning accelerates the screening of single-atom catalysts towards CO2 electroreduction. Appl. Catal. A Gen. 2024, 676, 119674. https://doi.org/10.1016/j.apcata.2024.119674.
- 19.
Tran, K.; Ulissi, Z.W. Active learning across intermetallics to guide discovery of electrocatalysts for CO2 reduction and H2 evolution. Nat. Catal. 2018, 1, 696–703. https://doi.org/10.1038/s41929-018-0142-1.
- 20.
Esterhuizen, J.A.; Goldsmith, B.R.; Linic, S. Interpretable machine learning for knowledge generation in heterogeneous catalysis. Nat. Catal. 2022, 5, 175–184. https://doi.org/10.1038/s41929-022-00744-z.
- 21.
Zhong, M.; Tran, K.; Min, Y.; et al. Accelerated discovery of CO2 electrocatalysts using active machine learning. Nature 2020, 581, 178–183. https://doi.org/10.1038/s41586-020-2242-8.
- 22.
Varma, S.; Simon, R.M. Bias in error estimation when using cross-validation for model selection. BMC Bioinform. 2006, 7, 91. https://doi.org/10.1186/1471-2105-7-91.
- 23.
Nguyen, T.N.; Salehi, M.; Le, Q.V.; et al. Fundamentals of Electrochemical CO2 Reduction on Single-Metal-Atom Catalysts. ACS Catal. 2020, 10, 10068–10095. https://doi.org/10.1021/acscatal.0c02643.
- 24.
Yao, L.; Ye, S.; Li, Z.; et al. Electrochemical nitrate-to-ammonia conversion over a broad concentration range via a hollow Co3O4/CuO catalyst. Green Chem. 2026, 28, 7827–7835. https://doi.org/10.1039/d6gc00484a.
- 25.
Wang, L.; Shen, B.; He, Z.D.; et al. Universal framework for efficient estimation of stability in multi-principal element alloys. Nat. Commun. 2026, 17, 3093. https://doi.org/10.1038/s41467-026-69585-9.
- 26.
Su, X.; Yang, X.; Huang, Y.; et al. Single-Atom Catalysis toward Efficient CO2 Conversion to CO and Formate Products. Accounts Chem. Res. 2018, 52, 656–664. https://doi.org/10.1021/acs.accounts.8b00478.
- 27.
Hansen, H.A.; Varley, J.B.; Peterson, A.A.; et al. Understanding Trends in the Electrocatalytic Activity of Metals and Enzymes for CO2 Reduction to CO. J Phys. Chem. Lett. 2013, 4, 388–392.
- 28.
Huang, Y.; Wang, J.; Hu, H.; et al. Heteroatom-doped M-N4-C Single-atom catalysts towards electrochemical reactions of CO2: A machine learning-assisted DFT study. Mol. Catal. 2025, 572, 114793. https://doi.org/10.1016/j.mcat.2024.114793.
- 29.
Zhang, S.; Fan, Q.; Xia, R.; et al. CO2 Reduction: From Homogeneous to Heterogeneous Electrocatalysis. Accounts Chem. Res. 2020, 53, 255–264. https://doi.org/10.1021/acs.accounts.9b00496.
- 30.
Kolb, M.J.; Loffreda, D.; Sautet, P.; et al. Structure-sensitive scaling relations among carbon-containing species and their possible impact on CO2 electroreduction. J. Catal. 2021, 395, 136–142. https://doi.org/10.1016/j.jcat.2020.12.026.
- 31.
Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169–11186. https://doi.org/10.1103/physrevb.54.11169.
- 32.
Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758–1775. https://doi.org/10.1103/physrevb.59.1758.
- 33.
Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. https://doi.org/10.1103/physrevlett.77.3865.
- 34.
Ji, Z.; Chen, A.; Sun, J.; et al. Elucidating the fundamental governing principles of CO2 reduction on single-atom catalysts through interpretable machine learning. J. Mater. Chem. A 2026, 14, 14612–14622. https://doi.org/10.1039/d5ta10584f.
- 35.
Lundberg, S.M.; Erion, G.; Chen, H.; et al. From local explanations to global understanding with explainable AI for trees. Nat. Mach. Intell. 2020, 2, 56–67. https://doi.org/10.1038/s42256-019-0138-9.
- 36.
Montemore, M.M.; Medlin, J.W. Scaling relations between adsorption energies for computational screening and design of catalysts. Catal. Sci. Technol. 2014, 4, 3748–3761. https://doi.org/10.1039/c4cy00335g.
- 37.
Govindarajan, N.; García-Lastra, J.M.; Meijer, E.J.; et al. Does the breaking of adsorption-energy scaling relations guarantee enhanced electrocatalysis? Curr. Opin. Electrochem. 2018, 8, 110–117.
- 38.
Calle-Vallejo, F.; Loffreda, D.; Koper, M.T.M.; et al. Introducing structural sensitivity into adsorption–energy scaling relations by means of coordination numbers. Nat. Chem. 2015, 7, 403–410. https://doi.org/10.1038/nchem.2226.
- 39.
Abild-Pedersen, F.; Greeley, J.; Studt, F.; et al. Scaling Properties of Adsorption Energies for Hydrogen-Containing Molecules on Transition-Metal Surfaces. Phys. Rev. Lett. 2007, 99, 016105. https://doi.org/10.1103/physrevlett.99.016105.
- 40.
Greeley, J. Theoretical Heterogeneous Catalysis: Scaling Relationships and Computational Catalyst Design. Annu. Rev. Chem. Biomol. Eng. 2016, 7, 605–635. https://doi.org/10.1146/annurev-chembioeng-080615-034413.
- 41.
Bennett, J.A.; Orouji, N.; Khan, M.; et al. Autonomous reaction Pareto-front mapping with a self-driving catalysis laboratory. Nat. Chem. Eng. 2024, 1, 240–250. https://doi.org/10.1038/s44286-024-00033-5.
- 42.
Zhang, Z.; Xing, Z.; Gou, X.; et al. Operando electrochemiluminescence imaging of intermediate evolution and kinetics in electrocatalytic nitrate reduction. Nat. Commun. 2026, 17, 10552.
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