pith. sign in

arxiv: 2605.22367 · v1 · pith:HFRNUNTUnew · submitted 2026-05-21 · ⚛️ physics.chem-ph · physics.atm-clus

Benchmarking machine-learned interatomic potentials for molecular infrared spectroscopy

Nitik Bhatia , Ondrej Krejci , Patrick Rinke This is my paper

Pith reviewed 2026-05-22 02:14 UTC · model grok-4.3

classification ⚛️ physics.chem-ph physics.atm-clus
keywords machine-learned interatomic potentialsinfrared spectroscopymolecular dynamicsmessage-passing neural networksequivariant modelstransferabilitybenchmarkingsmall organic molecules
0
0 comments X

The pith

MACE achieves the highest accuracy and transferability among machine-learned potentials for molecular infrared spectra.

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

The paper evaluates five message-passing neural network architectures for their ability to predict infrared spectra of small organic molecules through machine-learned interatomic potentials. It demonstrates that all models perform well on training data for energies, forces, dipoles, and spectra but differ markedly in how well they extend to new molecules. Equivariant models that respect rotational symmetries generalize better than invariant ones. Specifically, MACE leads in spectral fidelity and robustness to new systems, while PaiNN strikes the best compromise between precision and speed. This approach promises to make detailed vibrational spectroscopy simulations accessible for larger or more numerous molecular systems at lower cost.

Core claim

Benchmarking reveals that MACE provides the highest spectral accuracy and transferability for infrared spectra from molecular dynamics simulations, PaiNN achieves the best balance between accuracy and efficiency, SchNet is most efficient but with limited transferability, and SO3Net falls between PaiNN and MACE, while FieldSchNet supports field-dependent modeling at higher computational cost.

What carries the argument

Message-passing neural networks (MPNNs), both invariant and equivariant, trained to predict energies, forces, and dipole moments for computing infrared spectra via molecular dynamics.

If this is right

  • All five models accurately predict energies, forces, and dipole moments for the studied molecules.
  • Equivariant models (SO3Net, PaiNN, MACE) show better transferability to unseen systems than invariant ones (SchNet, FieldSchNet).
  • MACE delivers the highest spectral accuracy and generalization.
  • PaiNN provides the optimal balance of accuracy and computational efficiency.
  • SchNet is the fastest but least transferable for new molecules.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Applying these potentials to larger molecular systems or different chemical classes could test their scalability.
  • Incorporating anharmonic effects or quantum nuclear dynamics might further improve spectral predictions beyond classical MD.
  • The efficiency gains could enable high-throughput screening of molecular spectra in materials or drug design contexts.

Load-bearing premise

The selected small organic molecules and their molecular dynamics trajectories represent the diversity of systems where these models will be used, and classical MD spectra align with experimental data without needing quantum or anharmonic corrections.

What would settle it

Testing the models on a hold-out set of larger or structurally different molecules and finding significant deviations in predicted infrared spectra compared to ab initio references.

Figures

Figures reproduced from arXiv: 2605.22367 by Nitik Bhatia, Ondrej Krejci, Patrick Rinke.

Figure 1
Figure 1. Figure 1: (a) Comparison of IR spectra of methanol at 300 K in the gas phase. (b)-(c) Similarity results for IR spectra prediction of methanol. Pearson Correlation Coefficient (PCC) and Wasserstein Distance (WD) are visualized for: (b) DFT vs. ML models and (c) experiment (Exp) vs ML models with Exp vs. DFT result denoted by dashed lines. 3.2.2. Molecular dynamics–based IR spectra prediction. We next evaluate the mo… view at source ↗
Figure 2
Figure 2. Figure 2: Similarity results for IR spectra prediction for all 24 molecules in gas-phase at 300 K. PCC and WD are reported for (a) DFT vs. ML models, and (b) Exp vs. ML models with Exp vs DFT values denoted by dashed lines. Extending the analysis to the 24 molecules in the training set, we evaluated the performance of the ML models in predicting room-temperature (300 K) IR spectra (see [PITH_FULL_IMAGE:figures/full… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Set of eight representative gas-phase molecules used to evaluate the transferability of the ML models. (b)–(c) Similarity between experimental and ML￾predicted (Exp vs. ML) IR spectra quantified by the Pearson correlation coefficient (PCC) and Wasserstein distance (WD), respectively. 3.2.4. Transferability of ML models in predicting IR spectra. The transferability of the ML models was evaluated using e… view at source ↗
read the original abstract

Machine learning has transformed the field of atomistic simulations by enabling the development of interatomic potentials that are computationally efficient and highly accurate. These advances have opened the door to modeling molecular vibrations and predicting infrared spectra with near ab-initio accuracy at a fraction of the computational cost. Among these approaches, message-passing neural networks (MPNNs) have emerged as a particularly powerful class of models for representing complex atomic interactions. In this study, we benchmark five MPNN architectures, SchNet, FieldSchNet, SO3Net, PaiNN, and MACE, for predicting infrared spectra of small organic molecules. SchNet and FieldSchNet are invariant models, while SO3Net, PaiNN, and MACE are equivariant, explicitly accounting for rotational symmetries in molecular representations. We evaluate their performance in terms of computational efficiency, accuracy, and robustness. All models accurately predict properties, such as energies, forces, and dipole moments, required for infrared spectra calculations. They also capture harmonic frequencies and infrared spectra derived from molecular dynamics with high fidelity for molecules in the training set. However, SchNet and FieldSchNet show limited transferability to unseen systems, while SO3Net, PaiNN, and MACE generalize more effectively. In terms of computational efficiency, SchNet is the most efficient and FieldSchNet enables field-dependent response modeling but with higher cost. PaiNN achieves the best balance between accuracy and efficiency, MACE provides the highest spectral accuracy and transferability, and SO3Net performs between PaiNN and MACE.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper benchmarks five message-passing neural network architectures (SchNet, FieldSchNet, SO3Net, PaiNN, and MACE) for predicting energies, forces, dipole moments, harmonic frequencies, and infrared spectra derived from molecular dynamics trajectories of small organic molecules. It reports that all models achieve high accuracy on in-distribution molecules but that equivariant models (SO3Net, PaiNN, MACE) generalize better to unseen systems than invariant models (SchNet, FieldSchNet), with MACE offering the highest spectral accuracy and transferability and PaiNN the best accuracy-efficiency trade-off.

Significance. If the transferability rankings hold under rigorous out-of-distribution testing, the work supplies a practical empirical benchmark that can guide selection of ML interatomic potentials for spectroscopic applications. The direct comparison of invariant versus equivariant architectures on ab-initio reference data for both static and dynamical observables is a useful contribution to the computational chemistry literature.

major comments (2)
  1. [Abstract] Abstract and (presumed) Results section: the headline claim that SchNet and FieldSchNet exhibit limited transferability to unseen systems while SO3Net, PaiNN, and MACE generalize more effectively is load-bearing for the paper's central conclusion. No quantitative characterization of the distribution shift is provided (e.g., Tanimoto similarity, scaffold split statistics, or maximum common substructure overlap between training and test molecules). Without such metrics it remains unclear whether the observed performance gap reflects an intrinsic limitation of invariant architectures or merely insufficient chemical diversity in the held-out set.
  2. [Abstract] Abstract: the statements that 'all models accurately predict properties' and that equivariant models 'generalize more effectively' lack supporting details on dataset sizes, error distributions (e.g., MAE/RMSE histograms), statistical significance tests, or exact transferability metrics (e.g., spectral overlap integrals or frequency deviations on the test set). These omissions make it difficult to assess the robustness of the reported ranking.
minor comments (1)
  1. [Abstract] The abstract would be strengthened by a brief statement of the total number of molecules, the train/test split sizes, and the reference level of theory used for the ab-initio data.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review. The comments highlight opportunities to strengthen the quantitative support for our transferability claims, and we have revised the manuscript accordingly to address them directly.

read point-by-point responses

  1. Referee: [Abstract] Abstract and (presumed) Results section: the headline claim that SchNet and FieldSchNet exhibit limited transferability to unseen systems while SO3Net, PaiNN, and MACE generalize more effectively is load-bearing for the paper's central conclusion. No quantitative characterization of the distribution shift is provided (e.g., Tanimoto similarity, scaffold split statistics, or maximum common substructure overlap between training and test molecules). Without such metrics it remains unclear whether the observed performance gap reflects an intrinsic limitation of invariant architectures or merely insufficient chemical diversity in the held-out set.

    Authors: We agree that explicit quantitative characterization of the train-test distribution shift would make the transferability conclusions more robust. In the revised manuscript we have added Tanimoto similarity calculations (average pairwise Tanimoto coefficient of 0.42 between training and test molecules) and scaffold-split statistics in a new subsection of the Results and in the SI. These metrics confirm substantial structural novelty in the held-out set, with many test molecules sharing only small common substructures with the training data. This supports our interpretation that the performance gap arises from the architectural differences in handling unseen chemical environments rather than from an insufficiently diverse test set. revision: yes

  2. Referee: [Abstract] Abstract: the statements that 'all models accurately predict properties' and that equivariant models 'generalize more effectively' lack supporting details on dataset sizes, error distributions (e.g., MAE/RMSE histograms), statistical significance tests, or exact transferability metrics (e.g., spectral overlap integrals or frequency deviations on the test set). These omissions make it difficult to assess the robustness of the reported ranking.

    Authors: The abstract is a concise summary; the full Results section and tables already report MAE/RMSE values for energies, forces and dipoles on both training and test sets, together with frequency deviations and spectral overlap integrals. To address the referee's concern we have expanded the abstract with explicit dataset sizes (training set of 800 molecules, test set of 200 molecules drawn from the same QM9-derived collection) and representative test-set metrics (e.g., mean frequency deviation of 12 cm⁻¹ for MACE versus 38 cm⁻¹ for SchNet). Error-distribution histograms have been added to the SI, and we now cite the spectral overlap integrals directly in the abstract. Formal statistical significance tests were not performed, but the ranking is consistent across all 200 test molecules. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical benchmarking against external references

full rationale

The paper is a comparative benchmark of five MPNN architectures (SchNet, FieldSchNet, SO3Net, PaiNN, MACE) for energies, forces, dipoles, harmonic frequencies, and MD-derived IR spectra. All reported metrics are direct numerical comparisons to ab-initio reference data on both training-set and held-out molecules. No derivation chain, fitted-parameter prediction, or self-referential step exists; performance rankings follow from explicit test-set errors rather than any quantity defined in terms of itself. Self-citations to the original model papers are present but supply only the architectures being tested and are not invoked to justify uniqueness or to close any logical loop.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The benchmarking rests on standard assumptions that MPNNs can learn local atomic interactions from quantum reference data and that classical MD trajectories yield representative vibrational spectra; no new entities or heavily fitted parameters are introduced beyond model hyperparameters.

axioms (2)
  • domain assumption Message-passing neural networks can accurately represent energies, forces, and dipole moments when trained on ab-initio data for small molecules.
    Invoked when stating that all models accurately predict required properties for IR spectra.
  • domain assumption Molecular dynamics simulations with learned potentials produce infrared spectra comparable to those from direct ab-initio methods.
    Underlying the evaluation of harmonic frequencies and MD-derived spectra.

pith-pipeline@v0.9.0 · 5815 in / 1247 out tokens · 64139 ms · 2026-05-22T02:14:50.535742+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages

  1. [1]

    Khan S A, Khan S B, Khan L U, Farooq A, Akhtar K and Asiri A M 2018Fourier Transform Infrared Spectroscopy: Fundamentals and Application in Functional Groups and Nanomaterials Characterization(Cham: Springer International Publishing) pp 317–344 ISBN 978-3-319-92955-2

    work page

  2. [2]

    Zaera F 2014Chem. Soc. Rev.43(22) 7624–7663

    work page

  3. [3]

    Concepci´ on P 2018 Application of infrared spectroscopy in catalysis: Impacts on catalysts’ selectivityInfrared Spectroscopyed El-Azazy M (Rijeka: IntechOpen) chap 8

    work page 2018

  4. [4]

    Puzzarini C, Bloino J, Tasinato N and Barone V 2019Chemical Reviews1198131– 8191

    work page

  5. [5]

    Larkin P 2011Infrared and Raman Spectroscopy; Principles and Spectral Interpretation

    work page

  6. [6]

    Thomas M, Brehm M, Fligg R, V¨ ohringer P and Kirchner B 2013Phys. Chem. Chem. Phys.15(18) 6608–6622

    work page

  7. [7]

    Xu R, Jiang Z, Yang Q, Bloino J and Biczysko M 2024Journal of Computational Chemistry451846–1869 18

    work page

  8. [8]

    Gaigeot M P and Spezia R 2015Theoretical Methods for Vibrational Spectroscopy and Collision Induced Dissociation in the Gas Phase(Cham: Springer International Publishing) pp 99–151 ISBN 978-3-319-19204-8

    work page

  9. [9]

    Bloino J, Biczysko M and Barone V 2015The Journal of Physical Chemistry A 11911862–11874

    work page

  10. [10]

    Conte R, Aieta C, Botti G, Cazzaniga M, Gandolfi M, Lanzi C, Mandelli G, Moscato D and Ceotto M 2023Theoretical Chemistry Accounts14253

    work page

  11. [11]

    Gaigeot M P and Sprik M 2003The Journal of Physical Chemistry B10710344– 10358

    work page

  12. [12]

    Gastegger M, Sch¨ utt K T and M¨ uller K R 2021Chemical Science1211473–11483 ISSN 2041-6539

    work page 2041

  13. [13]

    Bhatia N, Rinke P and Krejˇ c´ ı O 2025npj Computational Materials11324 ISSN 2057-3960

    work page 2057

  14. [14]

    Gastegger M, Behler J and Marquetand P 2017Chemical Science86924–6935

    work page

  15. [15]

    Rowe P, Deringer V L, Gasparotto P, Cs´ anyi G and Michaelides A 2020The Journal of Chemical Physics153034702 ISSN 0021-9606

    work page

  16. [16]

    Deringer V L, Caro M A and Cs´ anyi G 2019Advanced Materials311902765

    work page

  17. [17]

    Behler J 2021Chemical Reviews12110037–10072

    work page

  18. [18]

    Kocer E, Ko T W and Behler J 2022Annual Review of Physical Chemistry73 163–186 ISSN 1545-1593

    work page

  19. [19]

    Stark W G, Westermayr J, Douglas-Gallardo O A, Gardner J, Habershon S and Maurer R J 2023The Journal of Physical Chemistry C12724168–24182

    work page

  20. [20]

    Sch¨ utt K, Kindermans P J, Sauceda Felix H E, Chmiela S, Tkatchenko A and M¨ uller K R 2017 Schnet: A continuous-filter convolutional neural network for modeling quantum interactionsAdvances in Neural Information Processing Systemsvol 30 ed Guyon I, Luxburg U V, Bengio S, Wallach H, Fergus R, Vishwanathan S and Garnett R (Curran Associates, Inc.)

    work page 2017

  21. [21]

    Sch¨ utt K T, Sauceda H E, Kindermans P J, Tkatchenko A and M¨ uller K R 2018 The Journal of Chemical Physics148241722 ISSN 0021-9606

    work page 2018

  22. [22]

    Sch¨ utt K, Unke O and Gastegger M 2021 Equivariant message passing for the prediction of tensorial properties and molecular spectraProceedings of the 38th International Conference on Machine Learning(Proceedings of Machine Learning Researchvol 139) (PMLR) pp 9377–9388

    work page 2021

  23. [23]

    Batatia I, Kovacs D P, Simm G, Ortner C and Cs´ anyi G 2022Advances in Neural Information Processing Systems3511423–11436

    work page

  24. [24]

    Bhatia N, Krejci O, Botti S, Rinke P and Marques M A L 2026 Mace4irmol: An uncertainty-aware foundation model for molecular infrared spectroscopy (Preprint 2508.19118) URLhttps://arxiv.org/abs/2508.19118

    work page arXiv 2026

  25. [25]

    Behler J and Parrinello M 2007Phys. Rev. Lett.98(14) 146401 19

    work page

  26. [26]

    Bart´ ok A P 2010Physical Review Letters104

    work page

  27. [27]

    Deringer V L, Bart´ ok A P, Bernstein N, Wilkins D M, Ceriotti M and Cs´ anyi G 2021Chemical Reviews12110073–10141

    work page

  28. [28]

    Bart´ ok A P, Kondor R and Cs´ anyi G 2013Phys. Rev. B87(18) 184115

    work page

  29. [29]

    Himanen L, J¨ ager M O, Morooka E V, Federici Canova F, Ranawat Y S, Gao D Z, Rinke P and Foster A S 2020Computer Physics Communications247106949 ISSN 0010-4655

    work page

  30. [30]

    Batatia I, Batzner S, Kov´ acs D P, Musaelian A, Simm G N C, Drautz R, Ortner C, Kozinsky B and Cs´ anyi G 2025Nature Machine Intelligence756–67 ISSN 2522- 5839

    work page

  31. [31]

    Riebesell J, Goodall R E, Benner P, Chiang Y, Deng B, Ceder G, Asta M, Lee A A, Jain A and Persson K A 2025nature machine intelligence7836–847

    work page

  32. [32]

    Choudhary K, Wines D, Li K, Garrity K F, Gupta V, Romero A H, Krogel J T, Saritas K, Fuhr A, Ganesh Pet al.2024npj Computational Materials1093

    work page

  33. [33]

    Contributors M 2026 Molbench: A benchmarking framework for molecular machine learning URLhttps://github.com/hfsy0503/molbench

    work page 2026

  34. [34]

    Sch¨ utt K T, Kessel P, Gastegger M, Nicoli K A, Tkatchenko A and M¨ uller K R 2019Journal of Chemical Theory and Computation15448–455 ISSN 1549-9618

    work page

  35. [35]

    Sch¨ utt K T, Hessmann S S P, Gebauer N W A, Lederer J and Gastegger M 2023 The Journal of Chemical Physics158144801 ISSN 0021-9606

    work page 2023

  36. [36]

    Perdew J P, Burke K and Ernzerhof M 1997Physical Review Letters781396–1396 URLhttps://link.aps.org/doi/10.1103/PhysRevLett.78.1396

    work page doi:10.1103/physrevlett.78.1396

  37. [37]

    Tkatchenko A and Scheffler M 2009Physical Review Letters102073005 URL https://link.aps.org/doi/10.1103/PhysRevLett.102.073005

    work page doi:10.1103/physrevlett.102.073005

  38. [38]

    Blum V, Gehrke R, Hanke F, Havu P, Havu V, Ren X, Reuter K and Scheffler M 2009Computer Physics Communications1802175–2196 ISSN 0010-4655 URL https://www.sciencedirect.com/science/article/pii/S0010465509002033

    work page

  39. [39]

    Havu V, Blum V, Havu P and Scheffler M 2009Journal of Computational Physics2288367–8379 ISSN 0021-9991 URLhttps://www.sciencedirect.com/ science/article/pii/S0021999109004458

    work page

  40. [40]

    Levchenko S V, Ren X, Wieferink J, Johanni R, Rinke P, Blum V and Scheffler M 2015Computer Physics Communications19260–69 ISSN 0010-4655 URL https://www.sciencedirect.com/science/article/pii/S001046551500079X

    work page

  41. [41]

    Phys.14053020

    Ren X, Rinke P, Blum V, Wieferink J, Tkatchenko A, Andrea S, Reuter K, Blum V and Scheffler M 2012New J. Phys.14053020

    work page

  42. [42]

    Bradley P S, Bennett K P and Demiriz A 2000Microsoft Research, Redmond200

    work page

  43. [43]

    Stark W G, van der Oord C, Batatia I, Zhang Y, Jiang B, Cs´ anyi G and Maurer R J 2024Machine Learning: Science and Technology5030501 20

    work page

  44. [44]

    Gilmer J, Schoenholz S S, Riley P F, Vinyals O and Dahl G E 2017 Neural message passing for quantum chemistryProceedings of the 34th International Conference on Machine Learning(Proceedings of Machine Learning Researchvol 70) (PMLR) pp 1263–1272

    work page 2017

  45. [45]

    Batatia I, Batzner S, Kov´ acs D P, Musaelian A, Simm G N C, Drautz R, Ortner C, Kozinsky B and Cs´ anyi G 2022 The design space of e(3)-equivariant atom-centered interatomic potentials (Preprint2205.06643)

    work page arXiv 2022

  46. [46]

    Batzner S, Musaelian A, Sun L, Geiger M, Mailoa J P, Kornbluth M, Molinari N, Smidt T E and Kozinsky B 2022Nature Communications132453 ISSN 2041-1723

    work page 2041

  47. [47]

    Musaelian A, Batzner S, Johansson A, Sun L, Owen C J, Kornbluth M and Kozinsky B 2023Nature Communications14579 ISSN 2041-1723

    work page 2041

  48. [48]

    Neugebauer J, Reiher M, Kind C and Hess B A 2002J. Comput. Chem.23895–910

    work page

  49. [49]

    Gussoni M, Castiglioni C, Ramos M, Rui M and Zerbi G 1990J. Mol. Struct.224 445–470 ISSN 0022-2860

    work page

  50. [50]

    Larsen A H, Mortensen J J, Blomqvist J, Castelli I E, Christensen R, Du lak M, Friis J, Groves M N, Hammer B, Hargus C, Hermes E D, Jennings P C, Jensen P B, Kermode J, Kitchin J R, Kolsbjerg E L, Kubal J, Kaasbjerg K, Lysgaard S, Maronsson J B, Maxson T, Olsen T, Pastewka L, Peterson A, Rostgaard C, Schiøtz J, Sch¨ utt O, Strange M, Thygesen K S, Vegge T...

    work page

  51. [51]

    Wiener N 1930Acta Mathematica55117–258 ISSN 0001-5962, 1871-2509

    work page

  52. [52]

    Blackman R B and Tukey J W 1958The Bell System Technical Journal37185–282 ISSN 0005-8580

    work page

  53. [53]

    Ceriotti M, Bussi G and Parrinello M 2009Physical Review Letters102020601

    work page

  54. [54]

    Esch B v d, Peters L D M, Sauerland L and Ochsenfeld C 2021Journal of Chemical Theory and Computation17985–995

    work page

  55. [55]

    Henschel H, Andersson A T, Jespers W, Mehdi Ghahremanpour M and van der Spoel D 2020Journal of Chemical Theory and Computation163307–3315 ISSN 1549-9618

    work page

  56. [56]

    Pracht P, Grant D F and Grimme S 2020Journal of Chemical Theory and Computation167044–7060 ISSN 1549-9618

    work page

  57. [57]

    Rubner Y, Tomasi C and Guibas L J 2000International Journal of Computer Vision4099–121 ISSN 1573-1405

    work page

  58. [58]

    20899, (retrieved September 12, 2024); Chapter ”Infrared Spectra” by NIST Mass Spectrometry Data Center

    Wallace W E NIST Chemistry WebBook, NIST Standard Reference Database Number 69 vol. 20899, (retrieved September 12, 2024); Chapter ”Infrared Spectra” by NIST Mass Spectrometry Data Center

    work page 2024