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REVIEW 3 major objections 6 minor 55 references

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

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A 137-parameter neural network predicts termolecular recombination rates with about 10% error across eight decades of collision energy.

desk verdict Interpolation evidence is solid and the application is new, but the headline extrapolation claim is unquantified and the 'learning physics' language overreaches. read the letter →

arxiv 2507.01793 v1 pith:5OQRJYA2 submitted 2025-07-02 physics.chem-ph physics.atom-ph

Daniel Julian , Jesús Pérez-Ríos This is my paper
classification physics.chem-phphysics.atom-ph
keywords machinelearningtermolecularreactionsatomrecombinationopacityfunctionsneuralnetworksurrogatethree-bodyreactionrates
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that a small feed-forward neural network can learn the opacity function—the reaction probability as a function of collision energy and impact parameter—for an ion-atom-atom recombination reaction, and can do so well enough to yield termolecular rate coefficients with relative error at or below about 10% over eight decades of energy. The authors train two networks, one for SrCs+ formation and one for Cs2 formation, on classical trajectory data, and show that the networks not only interpolate across the whole training range but also extrapolate to energies beyond it. If this holds, machine learning offers a fast surrogate for costly trajectory calculations of termolecular reactions, a class of reactions previously untouched by machine learning. The broader motivation is a step toward a universal chemical predictor that maps reactants and physical conditions to products and branching ratios.

What carries the argument

The load-bearing object is the opacity function Pr(Ec, b), the probability that a collision at energy Ec and impact parameter b leads to a given product; the reaction cross section is obtained by integrating $b^{4}$ Pr(Ec,b) up to bmax(Ec), and the rate k3 follows from the cross section. The machine-learning machinery is a feed-forward network that learns $\sqrt$(Pr) from these two features, with a sigmoid output to keep probabilities in [0,1], trained on classical trajectories generated in hyperspherical coordinates with pairwise Lennard-Jones potentials. The same architecture is used for both product channels, showing that the method transfers across channels of the same reaction.

What would settle it

Measure the energy-dependent three-body recombination rate k3(Ec) for Sr+ + Cs + Cs in a trap or merged-beam experiment across at least part of the $10^{-4}$ to $10^{4}$ K range and compare with the neural-network curve; a disagreement larger than the claimed about 10% that also shows up in the classical-trajectory benchmark would mean the training data, not the network, is the limiting step.

Watch

Extended reading notes

Core claim

The central claim is that a compact, fully connected neural network with 137 tunable parameters, using log10(Ec) and impact parameter b as inputs and the square root of the opacity as target, can reproduce the classical-trajectory opacity functions for Sr+ + Cs + Cs → SrCs+ + Cs and Sr+ + Cs + Cs → Cs2 + Sr+ throughout $10^{-4}$ to $10^{4}$ K with relative RMSE below about 6% for the ion channel and about 10% for the neutral channel. From these predicted opacities the authors compute energy-dependent recombination rates k3(Ec) that agree with the classical trajectory rates, including in an extrapolation regime at collision energies above any used in training. The authors interpret this as the network learning the underlying physics—in particular the crossover from long-range-dominated to short-range-dominated recombination around the molecular ion dissociation energy, and the location of the maximum impact parameter bmax at each energy.

Load-bearing premise

The neural networks are trained only on classical-trajectory simulations that use pairwise interaction potentials, so the predictions inherit whatever errors those simulations have compared with the real Sr+ + Cs + Cs reaction.

Editorial extensions

If this is right

  • If the claimed accuracy holds, energy-dependent termolecular recombination rates can be obtained from neural-network opacities at a tiny fraction of the cost of running new classical trajectory ensembles.
  • The demonstrated extrapolation beyond the training-energy window suggests the models capture the functional form of the recombination dynamics, not just a memorized interpolation.
  • The same architecture trained separately on each product channel predicts both the molecular-ion and neutral-molecule channels of an ion-atom-atom reaction, indicating channel-level transferability.
  • Accurate bmax prediction from the network means the integration domain for cross sections and rates is recovered without additional trajectory calculations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • One could test whether the same two-feature, 137-parameter architecture transfers to other ion-atom-atom systems by retraining only on that system's trajectory data; the authors' universality argument suggests it should, but this paper only demonstrates Sr+ + Cs + Cs.
  • The paper's rate accuracy comes mostly from large impact parameters; an inference is that the network's errors at small b would matter more for differential or state-resolved observables, so applications beyond total rates should validate small-b behavior explicitly.
  • A natural extension is to use the network as a surrogate inside kinetic models or plasma simulations where k3(Ec) is needed repeatedly, reducing the bottleneck of on-the-fly trajectory calculations.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript reports two fully connected feed-forward neural networks that predict the opacity function Pr(Ec,b) for the two product channels of the termolecular recombination Sr+ + Cs + Cs, namely SrCs+ + Cs (NN-ion) and Cs2 + Sr+ (NN-mol). The networks are trained on opacity data generated with the Py3BR classical trajectory code using pairwise Lennard-Jones (and polarization) potentials. For collision energies inside the training range, the paper reports relative RMSEs below 6% for NN-ion (Fig. 2) and around 10% for NN-mol (Fig. 3), and the interpolation tests also show that the networks capture bmax and the large-b behavior. The authors then use Eq. (3) to compute energy-dependent recombination rates and, on the basis of Fig. 4, claim that the models predict rates accurately even for energies beyond the training range (orange-shaded region). The paper's central claim is that a compact 137-parameter surrogate can reproduce classical-trajectory recombination opacities and rates over eight decades of collision energy and extrapolate beyond the training range.

Significance. If the extrapolation claim were quantitatively established, this would be a novel and useful proof-of-concept: it is, to my knowledge, the first machine-learning surrogate for termolecular recombination opacities; the architecture is very small (137 parameters per model); and the interpolation results convincingly show that the networks learn bmax and the long-range part of the opacity function across a wide energy range. The work is honest in that the target is the authors' own classical-trajectory simulation, not independent experimental data; the phrase 'accurate' must be read as 'accurate relative to Py3BR'. The manuscript would be strengthened by releasing the trained models and the train/test datasets. The main unresolved point is the extrapolation regime, which is the most novel claim and currently lacks quantitative support.

major comments (3)
  1. [Extrapolation claim, Fig. 4 and Eq. (3)] The abstract states that 'even far beyond the range of energies seen during training, our models predict the atom recombination reaction rate accurately,' but the manuscript provides no quantitative error for any extrapolated energy. The test energies in the orange-shaded region of Fig. 4 are never listed, and no relative errors are given for either k3 or the opacity functions in that regime. This is especially consequential because Eq. (3) integrates Pr(Ec,b)b^4 db, so a correct bmax and large-b behavior can produce an accurate rate even when the small-b opacity is wrong; visual agreement in Fig. 4 cannot establish that the extrapolated opacity is learned. Please list the extrapolation energies, report per-point errors for k3 and for Pr(Ec,b), and include opacity comparisons in the orange-shaded region.
  2. [Eqs. (4)-(5) and Fig. 4] The classical-trajectory reference rates in Fig. 4 are shown without error bars or any propagation of the binomial uncertainties defined in Eq. (4). Without this, 'excellent agreement' is only a qualitative judgment, and the claimed less-than-10% relative error cannot be statistically evaluated. The authors should propagate the uncertainties through Eqs. (3) and (5) and display them, or at least state the magnitude of the statistical Monte Carlo error on the reference rates.
  3. [Test dataset definition] The training energies are specified for both models, but the test energies are not. Figs. 2 and 3 show a few test energies in the panels, but for Fig. 4 no test energy values are given, and the caption does not identify which points lie in the extrapolation region. This prevents reproduction and makes it impossible for a reader to judge how far beyond the training range the extrapolation actually goes. Please provide the complete list of test collision energies and explicitly mark which are outside the training range for each model.
minor comments (6)
  1. [Introduction] The text states that the models predict probabilities 'with a less-than-or-equal-to 5% relative error,' yet the reported RMSEs for NN-mol are around 10% (Fig. 3); please reconcile this number or specify that it applies only to NN-ion.
  2. [Potential parameters] The manuscript refers to the potentials as 'Lennard-Jones' but for Cs-Sr+ the parameters are C4 and C8, implying a polarization-type potential; please state the explicit functional forms used for V(r) for both pairs.
  3. [Fig. 4 caption] The phrase 'the models predicts' in the Fig. 4 caption should be 'the models predict.'
  4. [Extrapolation paragraph] The phrase 'very different from the ones the machine has been exposed too' contains a typo ('too' should be 'to').
  5. [Notation] The acronym AR (atom recombination) used for the classical trajectory results may be confused with 'auto-regressive'; consider using 'CT' or 'simulation' to label the reference data.
  6. [Reproducibility] The paper does not state the train/test split or whether the test opacities were generated at energies not used during training; adding a sentence on this would help reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the neural network is trained on opacity data at some collision energies and tested at held-out energies; the predicted rates are deterministic integrals of the predicted opacities, so no prediction reduces to its input by construction.

full rationale

The derivation chain is: classical-trajectory opacities from Py3BR -> neural network features (Ec, b) and target sqrt(Pr) -> predicted opacities -> rates via Eq. (3) and Eq. (5). Training and test energies are distinct, so the network must generalize to unseen points; this is a standard surrogate-modeling benchmark, not a circular reduction. The rate is a fixed integral of the predicted opacity, and no fitted parameter is later renamed as a prediction. The abstract's extrapolation claim is not numerically supported in the text, and the accuracy of the Lennard-Jones/Py3BR ground truth rests on prior work by the same group, but these are verification and provenance concerns, not equivalences between the model output and its training data. No equation or self-citation defines the predicted quantities in terms of themselves.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

No new entities are introduced. The central claim depends on the trustworthiness of the classical trajectory surrogate and on the neural network weights fitted to it.

free parameters (1)
  • Neural network weights and biases (137 per model, 2 models) = Not disclosed
    The only numbers fitted to data in this work. They are optimized with Adam to minimize MSE on the classical trajectory opacity data and are central to the prediction claim.
assumptions (4)
  • domain assumption Classical trajectory calculations in hyperspherical coordinates give accurate opacities for Sr+ + Cs + Cs recombination.
    Training and test targets are generated by Py3BR using this method; the paper does not validate against experiment. Invoked in the dataset section.
  • domain assumption Pairwise Lennard-Jones potentials with parameters C6, C12, C4, C8 represent the real interatomic interactions.
    Cites refs 47-50; if these potentials deviate from reality, the ML model inherits the deviation.
  • domain assumption All ion-atom-atom reactions share the same physics, so one reaction is enough to assess the ML approach.
    Stated in the text citing ref 45; underlies the generality claim beyond Sr+ + Cs + Cs.
  • ad hoc to paper The opacity function is a smooth function of log10(Ec) and b, so extrapolation is meaningful.
    Implicit in the extrapolation experiment; no theoretical guarantee is given.

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Cite this review

Pith. "Pith review of Machine learning prediction of a chemical reaction over 8 decades of energy." pith.science (2026). https://pith.science/paper/5OQRJYA2

@misc{pith2026250701793,
  author       = {Pith},
  title        = {Pith review of: Machine learning prediction of a chemical reaction over 8 decades of energy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5OQRJYA2}},
  note         = {Machine review of arXiv:2507.01793}
}
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 $\rightarrow$ SrCs$^+$ + Cs and Sr$^+$ + Cs + Cs $\rightarrow$ Cs$_2$ + Sr$^+$ over multiple orders of magnitude of energy, yielding overall results with a relative error $\lesssim 10\%$. 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.

Figures

Figures reproduced from arXiv: 2507.01793 by the authors.

Figure 1
Figure 1. FIG. 1. Displayed above is the overall scheme of this work. The collision energy [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. FNN-prediction of opacity functions for the formation [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Energy-dependent atom recombination reaction rates [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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Works this paper leans on

55 extracted references · 51 canonical work pages

  1. [1]

    Z. Tu, T. Stuyver, and C. W. Coley, Predictive chem- istry: machine learning for reaction deployment, reaction development, and reaction discovery, Chem. Sci. 14, 226 (2023)

    work page 2023

  2. [2]

    J. A. Keith, V. Vassilev-Galindo, B. Cheng, S. Chmiela, M. Gastegger, K.-R. M¨ uller, and A. Tkatchenko, Com- bining machine learning and computational chemistry for predictive insights into chemical systems, Chemical Re- views 121, 9816 (2021)

    work page 2021

  3. [3]

    Meuwly, Machine learning for chemical reactions, Chemical Reviews 121, 10218 (2021)

    M. Meuwly, Machine learning for chemical reactions, Chemical Reviews 121, 10218 (2021)

    work page 2021

  4. [4]

    Friederich, G

    P. Friederich, G. dos Passos Gomes, R. De Bin, A. Aspuru-Guzik, and D. Balcells, Machine learning di- hydrogen activation in the chemical space surrounding vaska’s complex, Chem. Sci. 11, 4584 (2020)

    work page 2020

  5. [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, Combustion and Flame 255, 112901 (2023)

    work page 2023

  6. [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 microp- ollutants, Industrial & Engineering Chemistry Research 61, 8359 (2022)

    work page 2022

  7. [7]

    K¨ aser, L

    S. K¨ aser, L. I. Vazquez-Salazar, M. Meuwly, and K. T¨ opfer, Neural network potentials for chemistry: con- cepts, applications and prospects, Digital Discovery 2, 28 (2023)

    work page 2023

  8. [8]

    A. M. Miksch, T. Morawietz, J. K¨ astner, A. Urban, and N. Artrith, Strategies for the construction of machine- learning potentials for accurate and efficient atomic-scale simulations, Machine Learning: Science and Technology 2, 031001 (2021)

    work page 2021

Show all 55 references
  1. [9]

    D. S. Rasheeda, A. M. Santa Dar ´ ıa, B. Schr¨ oder, E. M´ atyus, and J. Behler, High-dimensional neural net- work potentials for accurate vibrational frequencies: the formic acid dimer benchmark, Physical Chemistry Chem- ical Physics 24, 29381 (2022)

    2022

  2. [10]

    Behler and M

    J. Behler and M. Parrinello, Generalized neural-network representation of high-dimensional potential-energy sur- faces, Physical Review Letters 98, 146401 (2007)

    2007

  3. [11]

    Cui and R

    J. Cui and R. V. Krems, Efficient non-parametric fit- ting of potential energy surfaces for polyatomic molecules with gaussian processes, Journal of Physics B: Atomic, Molecular and Optical Physics 49, 224001 (2016)

    2016

  4. [12]

    C. Qu, Q. Yu, B. L. Van Hoozen Jr, J. M. Bowman, and R. A. Vargas-Hern´ andez, Assessing gaussian process regression and permutationally invariant polynomial ap- proaches to represent high-dimensional potential energy surfaces, Journal of Chemical Theory and Computation 14, 33...

    2018

  5. [13]

    X. Liu, W. Wang, and J. P´ erez-R ´ ıos, Molecular dynamics-driven global potential energy surfaces: Appli- cation to the alf dimer, The Journal of Chemical Physics 159, 144103 (2023)

    2023

  6. [14]

    Garc ´ ıa-Andrade, P

    X. Garc ´ ıa-Andrade, P. Garc ´ ıa Tahoces, J. P´ erez-R ´ ıos, and E. Mart ´ ınez N´ u˜ nez, Barrier height prediction by ma- chine learning correction of semiempirical calculations, The Journal of Physical Chemistry A 127, 2274 (2023)

    2023

  7. [15]

    Jorner, T

    K. Jorner, T. Brinck, P.-O. Norrby, and D. Buttar, Ma- chine learning meets mechanistic modelling for accurate prediction of experimental activation energies, Chem. Sci. 12, 1163 (2021)

    2021

  8. [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)

    2023

  9. [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, Chemistry – A European Journal 24, 12354 (2018)

    2018

  10. [18]

    H. Ji, A. R´ agyanszki, and R. A. Fournier, Machine learn- ing estimation of reaction energy barriers, Computational and Theoretical Chemistry 1229, 114332 (2023)

    2023

  11. [19]

    Vargas, M

    S. Vargas, M. R. Hennefarth, Z. Liu, and A. N. Alexan- drova, Machine learning to predict diels–alder reaction barriers from the reactant state electron density, Journal of Chemical Theory and Computation 17, 6203 (2021)

    2021

  12. [20]

    C. A. Grambow, L. Pattanaik, and W. H. Green, Deep learning of activation energies, The Journal of Physical Chemistry Letters 11, 2992 (2020)

    2020

  13. [21]

    J. S. Smith, B. Nebgen, N. Lubbers, O. Isayev, and A. E. Roitberg, Less is more: Sampling chemical space with active learning, The Journal of chemical physics 148 (2018)

    2018

  14. [22]

    Vandermause, S

    J. Vandermause, S. B. Torrisi, S. Batzner, Y. Xie, L. Sun, A. M. Kolpak, and B. Kozinsky, On-the-fly active learn- ing of interpretable bayesian force fields for atomistic rare events, npj Computational Materials 6, 20 (2020)

    2020

  15. [23]

    Stocker, G

    S. Stocker, G. Cs´ anyi, K. Reuter, and J. T. Margraf, Ma- chine learning in chemical reaction space, Nature Com- munications 11, 5505 (2020)

    2020

  16. [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 sim- ulations, Phys. Chem. Chem. Phys. 22, 683 (2020)

    2020

  17. [25]

    Heid and W

    E. Heid and W. H. Green, Machine learning of reaction properties via learned representations of the condensed graph of reaction, Journal of Chemical Information and Modeling 62, 2101 (2022)

    2022

  18. [26]

    Koner, O

    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, The Journal of Chemical Physics 150, 211101 (2019)

    2019

  19. [27]

    Huang, K.-M

    X. Huang, K.-M. Gu, C.-M. Guo, and X.-L. Cheng, Dis- sociation cross sections and rates in o2 + n collisions: molecular dynamics simulations combined with machine learning, Phys. Chem. Chem. Phys. 25, 29475 (2023)

    2023

  20. [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)

    2023

  21. [29]

    K.-M. Gu, H. Zhang, and X.-L. Cheng, Exhaustive state- specific dissociation study of the N2(Σg+1)+N(S4) sys- tem using QCT combined with a neural network method, 6 The Journal of Chemical Physics 158, 244302 (2023)

    2023

  22. [30]

    Arnold, J

    J. Arnold, J. C. San Vicente Veliz, D. Koner, N. Singh, R. J. Bemish, and M. Meuwly, Machine learning prod- uct state distributions from initial reactant states for a reactive atom–diatom collision system, The Journal of Chemical Physics 156, 034301 (2022)

    2022

  23. [31]

    Huang and X

    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, The Journal of Chemical Physics 160, 174310 (2024)

    2024

  24. [32]

    Jasinski, J

    A. Jasinski, J. Montaner, R. C. Forrey, B. H. Yang, P. C. Stancil, N. Balakrishnan, J. Dai, R. A. Vargas- Hern´ andez, and R. V. Krems, Machine learning cor- rected quantum dynamics calculations, Phys. Rev. Res. 2, 032051 (2020)

    2020

  25. [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, The Journal of Chemical Physics 162, 024116 (2025)

    2025

  26. [34]

    Julian, R

    D. Julian, R. Koots, and J. P´ erez-R ´ ıos, Machine-learning models for atom-diatom reactions across isotopologues, Phys. Rev. A 110, 032811 (2024)

    2024

  27. [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 experi- ment, Symposium (International) on Combustion 13, 21 (1971), thirteenth symposium (International) on Com- bustion

    1971

  28. [36]

    D. R. Flower, Three-body recombination of hydrogen in the early universe, Monthly Notices of the Royal Astro- nomical Society: Letters 523, L1 (2023)

    2023

  29. [37]

    Mirahmadi and J

    M. Mirahmadi and J. P.-R. and, Three-body recombina- tion in physical chemistry, International Reviews in Phys- ical Chemistry 41, 233 (2022)

    2022

  30. [38]

    PORTER and J

    G. PORTER and J. A. SMITH, Mechanism of atom re- combination, Nature 184, 446 (1959)

    1959

  31. [39]

    Troe, Atom and radical recombination reactions, An- nual Review of Physical Chemistry 29, 223 (1978)

    J. Troe, Atom and radical recombination reactions, An- nual Review of Physical Chemistry 29, 223 (1978)

    1978

  32. [40]

    W. S. P. C. Inc, ed., Atom recombination, in Chemistry in Microtime (1997) pp. 129–159

    1997

  33. [41]

    the radiation theory of chemical action

    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)

    1922

  34. [42]

    C. N. Hinshelwood and N. V. Sidgwick, On the theory of unimolecular reactions, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathemat- ical and Physical Character 113, 230 (1926)

    1926

  35. [43]

    Kr¨ ukow, A

    A. Kr¨ ukow, A. Mohammadi, A. H¨ arter, J. H. Den- schlag, J. P´ erez-R ´ ıos, and C. H. Greene, Energy scaling of cold atom-atom-ion three-body recombination, Phys. Rev. Lett. 116, 193201 (2016)

    2016

  36. [44]

    P´ erez-R ´ ıos and C

    J. P´ erez-R ´ ıos and C. H. Greene, Universal temperature dependence of the ion-neutral-neutral three-body recom- bination rate, Phys. Rev. A 98, 062707 (2018)

    2018

  37. [45]

    Mirahmadi and J

    M. Mirahmadi and J. P´ erez-R ´ ıos, Ion-atom-atom three- body recombination: From the cold to the thermal regime, The Journal of Chemical Physics 158, 024103 (2023)

    2023

  38. [46]

    The target of the models is the opacity function Pr(Ec, b)

    Specifically, the features were log10(Ec) with Ec in K and b in units of the Bohr radius a0. The target of the models is the opacity function Pr(Ec, b)

  39. [47]

    Y. Wang, M. Mirahmadi, and J. P´ erez-R ´ ıos, On the role of non-additive interactions in three-body recombination, Phys. Chem. Chem. Phys. 26, 7264 (2024)

    2024

  40. [48]

    Aymar, R

    M. Aymar, R. Gu´ erout, and O. Dulieu, Structure of the alkali-metal-atom + strontium molecular ions: Towards photoassociation and formation of cold molecular ions, The Journal of Chemical Physics 135, 064305 (2011)

    2011

  41. [49]

    Weickenmeier, U

    W. Weickenmeier, U. Diemer, M. Wahl, M. Raab, W. Demtr¨ oder, and W. M¨ uller, Accurate ground state potential of cs2 up to the dissociation limit, The Journal of Chemical Physics 82, 5354 (1985)

    1985

  42. [50]

    Schwerdtfeger and J

    P. Schwerdtfeger and J. K. N. and, 2018 table of static dipole polarizabilities of the neutral elements in the pe- riodic table*, Molecular Physics 117, 1200 (2019)

    2019

  43. [51]

    Koots, Y

    R. Koots, Y. Wang, M. Mirahmadi, and J. P´ erez-R ´ ıos, Py3br: A software for computing atomic three-body re- combination rates, Journal of Computational Chemistry 45, 1505 (2024)

    2024

  44. [52]

    Furthermore, trajectories for additional impact parame- ters were run as needed to either reach bmax or to more finely sample impact parameters, which were uniformly sampled for b ∈ [0, bmax]

  45. [53]

    D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv preprint arXiv:1412.6980 (2014)

    2014 arXiv

  46. [54]

    Glorot and Y

    X. Glorot and Y. Bengio, Understanding the difficulty of training deep feedforward neural networks, in Pro- ceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics , Proceedings of Ma- chine Learning Research, Vol. 9, edited by Y. W. Teh a...

    2010

  47. [55]

    Abadi, A

    M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Is- ard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Lev- enberg, D. Man´ e, R. Monga, S. Moore, D. Murray, C. Olah...

    2015

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