- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Machine learning prediction of a chemical reaction over 8 decades of energy

Daniel Julian and Jesús Pérez-Ríos*

  • *Contact author: jesus.perezrios@stonybrook.edu
PDF

Phys. Rev. Research 7, L042034 – Published 12 November, 2025

DOI: https://doi.org/10.1103/gkwq-ls2k

Abstract

Recent progress in machine learning has sparked increased interest in utilizing this technology to predict the outcomes of chemical reactions. The ultimate aim of such endeavors is to develop a universal model that can predict products for any chemical reaction given reactants and physical conditions. In pursuit of ever more universal chemical predictors, machine learning models for atom-diatom and diatom-diatom reactions have been developed, yet no such models exist for termolecular reactions. Accordingly, we introduce neural networks trained to predict opacity functions of atom recombination reactions. Our models predict the recombination of Sr++Cs+Cs→SrCs++ Cs and Sr++Cs+Cs→Cs2+Sr+ over multiple orders of magnitude of energy, yielding overall results with a relative error ≲10%. Even far beyond the range of energies seen during training, our models predict the atom recombination reaction rate accurately. As a result, the machine is capable of learning the physics behind the atom recombination reaction dynamics.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (56)

  1. Z. Tu, T. Stuyver, and C. W. Coley, Predictive chemistry: Machine learning for reaction deployment, reaction development, and reaction discovery, Chem. Sci. 14, 226 (2023).
  2. J. A. Keith, V. Vassilev-Galindo, B. Cheng, S. Chmiela, M. Gastegger, K.-R. Müller, and A. Tkatchenko, Combining machine learning and computational chemistry for predictive insights into chemical systems, Chem. Rev. 121, 9816 (2021).
  3. M. Meuwly, Machine learning for chemical reactions, Chem. Rev. 121, 10218 (2021).
  4. P. Friederich, G. dos Passos Gomes, R. De Bin, A. Aspuru-Guzik, and D. Balcells, Machine learning dihydrogen activation in the chemical space surrounding Vaska's complex, Chem. Sci. 11, 4584 (2020).
  5. J. Yu, S. Ruan, H. Song, L. Zhang, and M. Yang, Machine learning rate constants of hydrogen abstraction reactions between ester and H atom, Combust. Flame 255, 112901 (2023).
  6. Y. Shi, J. Wang, Q. Wang, Q. Jia, F. Yan, Z.-H. Luo, and Y.-N. Zhou, Supervised machine learning algorithms for predicting rate constants of ozone reaction with micropollutants, Ind. Eng. Chem. Res. 61, 8359 (2022).
  7. S. Käser, L. I. Vazquez-Salazar, M. Meuwly, and K. Töpfer, Neural network potentials for chemistry: Concepts, applications and prospects, Digital Discovery 2, 28 (2023).
  8. A. M. Miksch, T. Morawietz, J. Kästner, A. Urban, and N. Artrith, Strategies for the construction of machine-learning potentials for accurate and efficient atomic-scale simulations, Mach. Learn.: Sci. Technol. 2, 031001 (2021).
  9. D. S. Rasheeda, A. M. Santa Daría, B. Schröder, E. Mátyus, and J. Behler, High-dimensional neural network potentials for accurate vibrational frequencies: The formic acid dimer benchmark, Phys. Chem. Chem. Phys. 24, 29381 (2022).
  10. J. Behler and M. Parrinello, Generalized neural-network representation of high-dimensional potential-energy surfaces, Phys. Rev. Lett. 98, 146401 (2007).
  11. J. Cui and R. V. Krems, Efficient non-parametric fitting of potential energy surfaces for polyatomic molecules with Gaussian processes, J. Phys. B: At. Mol. Opt. Phys. 49, 224001 (2016).
  12. C. Qu Jr., Q. Yu, B. L. Van Hoozen Jr, J. M. Bowman, and R. A. Vargas-Hernández, Assessing Gaussian process regression and permutationally invariant polynomial approaches to represent high-dimensional potential energy surfaces, J. Chem. Theory Comput. 14, 3381 (2018).
  13. X. Liu, W. Wang, and J. Pérez-Ríos, Molecular dynamics-driven global potential energy surfaces: Application to the AlF dimer, J. Chem. Phys. 159, 144103 (2023).
  14. X. García-Andrade, P. García Tahoces, J. Pérez-Ríos, and E. Martínez Núñez, Barrier height prediction by machine learning correction of semiempirical calculations, J. Phys. Chem. A 127, 2274 (2023).
  15. K. Jorner, T. Brinck, P.-O. Norrby, and D. Buttar, Machine learning meets mechanistic modelling for accurate prediction of experimental activation energies, Chem. Sci. 12, 1163 (2021).
  16. S. G. Espley, E. H. E. Farrar, D. Buttar, S. Tomasi, and M. N. Grayson, Machine learning reaction barriers in low data regimes: A horizontal and diagonal transfer learning approach, Digital Discovery 2, 941 (2023).
  17. S. Choi, Y. Kim, J. W. Kim, Z. Kim, and W. Y. Kim, Feasibility of activation energy prediction of gas-phase reactions by machine learning, Chem. Eur. J. 24, 12354 (2018).
  18. H. Ji, A. Rágyanszki, and R. A. Fournier, Machine learning estimation of reaction energy barriers, Comput. Theor. Chem. 1229, 114332 (2023).
  19. S. Vargas, M. R. Hennefarth, Z. Liu, and A. N. Alexandrova, Machine learning to predict Diels–Alder reaction barriers from the reactant state electron density, J. Chem. Theory Comput. 17, 6203 (2021).
  20. C. A. Grambow, L. Pattanaik, and W. H. Green, Deep learning of activation energies, J. Phys. Chem. Lett. 11, 2992 (2020).
  21. J. S. Smith, B. Nebgen, N. Lubbers, O. Isayev, and A. E. Roitberg, Less is more: Sampling chemical space with active learning, J. Chem. Phys. 148, 241733 (2018).
  22. J. Vandermause, S. B. Torrisi, S. Batzner, Y. Xie, L. Sun, A. M. Kolpak, and B. Kozinsky, On-the-fly active learning of interpretable Bayesian force fields for atomistic rare events, npj Comput. Mater. 6, 20 (2020).
  23. S. Stocker, G. Csányi, K. Reuter, and J. T. Margraf, Machine learning in chemical reaction space, Nat. Commun. 11, 5505 (2020).
  24. J. Zeng, L. Cao, C.-H. Chin, H. Ren, J. Z. H. Zhang, and T. Zhu, ReacNetGenerator: An automatic reaction network generator for reactive molecular dynamics simulations, Phys. Chem. Chem. Phys. 22, 683 (2020).
  25. E. Heid and W. H. Green, Machine learning of reaction properties via learned representations of the condensed graph of reaction, J. Chem. Inf. Model. 62, 2101 (2022).
  26. D. Koner, O. T. Unke, K. Boe, R. J. Bemish, and M. Meuwly, Exhaustive state-to-state cross sections for reactive molecular collisions from importance sampling simulation and a neural network representation, J. Chem. Phys. 150, 211101 (2019).
  27. X. Huang, K.-M. Gu, C.-M. Guo, and X.-L. Cheng, Dissociation cross sections and rates in O2 + N collisions: Molecular dynamics simulations combined with machine learning, Phys. Chem. Chem. Phys. 25, 29475 (2023).
  28. M. S. Priyadarshini, S. Venturi, I. Zanardi, and M. Panesi, Efficient quasi-classical trajectory calculations by means of neural operator architectures, Phys. Chem. Chem. Phys. 25, 13902 (2023).
  29. K.-M. Gu, H. Zhang, and X.-L. Cheng, Exhaustive state-specific dissociation study of the N2(1Σg+)+N(4S) system using QCT combined with a neural network method, J. Chem. Phys. 158, 244302 (2023).
  30. J. Arnold, J. C. San Vicente Veliz, D. Koner, N. Singh, R. J. Bemish, and M. Meuwly, Machine learning product state distributions from initial reactant states for a reactive atom–diatom collision system, J. Chem. Phys. 156, 034301 (2022).
  31. X. Huang and X. Cheng, State-to-state dynamics and machine learning predictions of inelastic and reactive O(3P)+CO(1Σ+) collisions relevant to hypersonic flows, J. Chem. Phys. 160, 174310 (2024).
  32. A. Jasinski, J. Montaner, R. C. Forrey, B. H. Yang, P. C. Stancil, N. Balakrishnan, J. Dai, R. A. Vargas-Hernández, and R. V. Krems, Machine learning corrected quantum dynamics calculations, Phys. Rev. Res. 2, 032051 (2020).
  33. D. E. Mihalik, R. Wang, B. H. Yang, P. C. Stancil, T. J. Price, R. C. Forrey, N. Balakrishnan, and R. V. Krems, Accurate machine learning of rate coefficients for state-to-state transitions in molecular collisions, J. Chem. Phys. 162, 024116 (2025).
  34. D. Julian, R. Koots, and J. Pérez-Ríos, Machine-learning models for atom-diatom reactions across isotopologues, Phys. Rev. A 110, 032811 (2024).
  35. V. H. Shui, J. P. Appleton, and J. C. Keck, The three-body recombination and dissociation of diatomic molecules: A comparison between theory and experiment, in Proceedings of the 13th International Symposium  on Combustion (Elsevier, Amsterdam, Netherlands, 1971), Vol. 13, p. 21.
  36. D. R. Flower, Three-body recombination of hydrogen in the early universe, Mon. Not. R. Astron. Soc.: Lett. 523, L1 (2023).
  37. M. Mirahmadi and J. Pérez-Ríos, Three-body recombination in physical chemistry, Int. Rev. Phys. Chem. 41, 233 (2022).
  38. G. Porter and J. A. SMITH, Mechanism of atom recombination, Nature (London) 184, 446 (1959).
  39. J. Troe, Atom and radical recombination reactions, Annu. Rev. Phys. Chem. 29, 223 (1978).
  40. G. Porter, Atom recombination, Chemistry in Microtime (World Scientific Publishing, Singapore, 1997), pp. 129–159.
  41. F. A. Lindemann, S. Arrhenius, I. Langmuir, N. R. Dhar, J. Perrin, and W. C. McC. Lewis, Discussion on “the radiation theory of chemical action”, Trans. Faraday Soc. 17, 598 (1922).
  42. C. N. Hinshelwood and N. V. Sidgwick, On the theory of unimolecular reactions, Proc. R. Soc. London Ser. A 113, 230 (1926).
  43. A. Krükow, A. Mohammadi, A. Härter, J. H. Denschlag, J. Pérez-Ríos, and C. H. Greene, Energy scaling of cold atom-atom-ion three-body recombination, Phys. Rev. Lett. 116, 193201 (2016).
  44. J. Pérez-Ríos and C. H. Greene, Universal temperature dependence of the ion-neutral-neutral three-body recombination rate, Phys. Rev. A 98, 062707 (2018).
  45. R. Koots, G. Ding, and J. Pérez-Ríos, Direct three-body atom recombination: Halogen atoms, J. Chem. Phys. 163, 024307 (2025).
  46. M. Mirahmadi, J. Pérez-Ríos, O. Egorov, V. Tyuterev, and V. Kokoouline, Ozone formation in ternary collisions: Theory and experiment reconciled, Phys. Rev. Lett. 128, 108501 (2022).
  47. M. Mirahmadi and J. Pérez-Ríos, Ion-atom-atom three-body recombination: From the cold to the thermal regime, J. Chem. Phys. 158, 024103 (2023).
  48. Y. Wang, M. Mirahmadi, and J. Pérez-Ríos, On the role of non-additive interactions in three-body recombination, Phys. Chem. Chem. Phys. 26, 7264 (2024).
  49. M. Aymar, R. Guérout, and O. Dulieu, Structure of the alkali-metal-atom + strontium molecular ions: Towards photoassociation and formation of cold molecular ions, J. Chem. Phys. 135, 064305 (2011).
  50. W. Weickenmeier, U. Diemer, M. Wahl, M. Raab, W. Demtröder, and W. Müller, Accurate ground state potential of Cs2 up to the dissociation limit, J. Chem. Phys. 82, 5354 (1985).
  51. P. Schwerdtfeger and J. K. Nagle, 2018 Table of static dipole polarizabilities of the neutral elements in the periodic table, Mol. Phys. 117, 1200 (2019).
  52. R. Koots, Y. Wang, M. Mirahmadi, and J. Pérez-Ríos, Py3BR: A software for computing atomic three-body recombination rates, J. Comput. Chem. 45, 1505 (2024).
  53. D. Kingma and J. Ba, Adam: A method for stochastic optimization, in International Conference on Learning Representations (2014).
  54. X. Glorot and Y. Bengio, Understanding the difficulty of training deep feedforward neural networks, in Proceedings of the 13th International Conference on Artificial Intelligence and Statistics, edited by Y. W. Teh and M. Titterington (PMLR, Chia Laguna Resort, Sardinia, Italy, 2010), Vol. 9, pp. 249–256.
  55. M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin et al., , 2015, tensorflow.org.
  56. D. Julian, NN_AR, https://github.com/dbjulian/NN_AR (2025).

Outline

Information

Phys. Rev. Research 7, L042034– Published 12 November, 2025
  • Received 25 June 2025
  • Accepted 25 October 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation