SpringerLink
Log in

Artificial neural networks and their utility in fitting potential energy curves and surfaces and related problems

  • Perspective Article
  • Published:
Journal of Chemical Sciences Aims and scope Submit manuscript

Abstract

Artificial intelligence (AI) and machine learning (ML) methods have touched practically all aspects of our life. Their utility ranges from separating different quality agricultural produce to facial recognition to guiding us through most steps in our day-to-day life. In this perspective article, we demonstrate the utility of artificial neural network (ANN) method in fitting potential energy curves and surfaces and point out the potential applications to predicting and analyzing dynamical observables. Although the regression methods seem to be successful in fitting potential energy surfaces using limited ab initio data, the ANN method yields accurate fits of surfaces when enough number of ab initio points on the potential energy surface become available. The possibility of utilizing the ANN method for fitting excitation function data is pointed out and the implications are discussed.

Graphical abstract

This perspective article illustrates how the artificial neural network can be used to interpolate accurately potential energy curves and surfaces for molecular systems and how the method can be extended to systems with avoided crossing of potential energy curves and to multidimensional excitation function data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13

Similar content being viewed by others

References

  1. Khemani D 2020 Artificial intelligence: The age-old quest for thinking machines Resonance 25 33

    Article  Google Scholar 

  2. Sharma D 2020 Deep learning without tears Resonance 25 15

    Article  Google Scholar 

  3. Raff L, Komanduri R, Hagan M and Bukkapatnam S 2012 Neural networks in chemical reaction dynamics (OUP: USA)

  4. Sarkar K and Bhattacharyya S P 2017 Soft-computing in Physical and Chemical Sciences: A shift in computing paradigm (Boca Raton: CRC Press)

    Book  Google Scholar 

  5. Behler J 2015 Constructing high-dimensional neural network potentials: a tutorial review Int. J. Quantum Chem. 115 1032

    Article  CAS  Google Scholar 

  6. Behler J 2016 Perspective: Machine learning potentials for atomistic simulations J. Chem. Phys. 145 170901

    Article  PubMed  ADS  Google Scholar 

  7. Jiang B, Li J and Guo H 2016 Potential energy surfaces from high fidelity fitting of ab initio points: the permutation invariant polynomial-neural network approach Int. Rev. Phys. Chem. 35 479

    Article  CAS  Google Scholar 

  8. Krems R 2019 Bayesian machine learning for quantum molecular dynamics Phys. Chem. Phys. Chem. 21 13392

    Article  CAS  Google Scholar 

  9. Unke O T, Koner D, Patra S, Käser S and Meuwly M 2020 High-dimensional potential energy surfaces for molecular simulations: from empiricism to machine learning Mach. Learn.: Sci. Technol. 1 013001

  10. Manzhos S and Carrington Jr. T 2020 Neural network potential energy surfaces for small molecules and reactions Chem. Rev. 121 10187

    Article  PubMed  Google Scholar 

  11. Mitra A, Jana G, Pal R, Gaikwad P, Sural S and Chattaraj P K 2021 Determination of stable structure of a cluster using convolutional neural network and particle swarm optimization Theor. Chem. Acc. 140 30

    Article  CAS  Google Scholar 

  12. Biswas R, Rashmi R and Lourderaj U 2020 Machine learning in chemical dynamics Resonance 25 59

    Article  Google Scholar 

  13. Kushwaha A and Dhilip Kumar T J 2022 Benchmarking pes-learn’s machine learning models predicting accurate potential energy surface for quantum scattering Int. J. Quantum Chem. e27007

  14. Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, Robb M A, Cheeseman J R, Scalmani G, Barone V, Petersson G A, Nakatsuji H, Li X, Caricato M, Marenich A V, Bloino J, Janesko B G, Gomperts R, Mennucci B, Hratchian H P, Ortiz J V, Izmaylov A F, Sonnenberg J L, Williams-Young D, Ding F, Lipparini F, Egidi F, Goings J, Peng B, Petrone A, Henderson T, Ranasinghe D, Zakrzewski V G, Gao J, Rega N, Zheng G, Liang W, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Throssell K, Montgomery J A Jr, Peralta J E, Ogliaro F, Bearpark M J, Heyd J J, Brothers E N, Kudin K N, Staroverov V N, Keith T A, Kobayashi R, Normand J, Raghavachari K, Rendell A P, Burant J C, Iyengar S S, Tomasi J, Cossi M, Millam J M, Klene M, Adamo C, Cammi R, Ochterski J W, Martin R L, Morokuma K, Farkas O, Foresman J B and Fox D J 2016. Gaussian 16 Revision C.01 Gaussian Inc. Wallingford CT

  15. Barca G M J, Bertoni C, Carrington L, Datta D, De Silva N, Deustua J E, Fedorov D G, Gour J R, Gunina A O, Guidez E, Harville T, Irle S, Ivanic J, Kowalski K, Leang S S, Li H, Li W, Lutz J J, Magoulas I, Mato J, Mironov V, Nakata H, Pham B Q, Piecuch P, Poole D, Pruitt S R, Rendell A P, Roskop L B, Ruedenberg K, Sattasathuchana T, Schmidt M W, Shen J, Slipchenko L, Sosonkina M, Sundriyal V, Tiwari A, Galvez Vallejo J L, Westheimer B, Wloch M, Xu P, Zahariev F and Gordon M S 2020 Recent developments in the general atomic and molecular electronic structure system J. Chem. Phys. 152 154102

    Article  CAS  PubMed  ADS  Google Scholar 

  16. Werner H J, Knowles P J, Knizia G, Manby F R, Schütz M et al. Molpro version 2022.2, a package of ab initio programs, see https://www.molpro.net.

  17. Shao Y, Gan Z, Epifanovsky E, Gilbert A T, Wormit M, Kussmann J, Lange A W, Behn A, Deng J, Feng X, Ghosh D, Goldey M, Horn P R, Jacobson L D, Kaliman I, Khaliullin R Z, Kuś T, Landau A, Liu J, Proynov E I, Rhee Y M, Richard R M, Rohrdanz M A, Steele R P, Sundstrom E J, III H L W, Zimmerman P M, Zuev D, Albrecht B, Alguire E, Austin B, Beran G J O, Bernard Y A, Berquist E, Brandhorst K, Bravaya K B, Brown S T, Casanova D, Chang C M, Chen Y, Chien S H, Closser K D, Crittenden D L, Diedenhofen M, Jr. R A D, Do H, Dutoi A D, Edgar R G, Fatehi S, Fusti-Molnar L, Ghysels A, Golubeva-Zadorozhnaya A, Gomes J, Hanson-Heine M W, Harbach P H, Hauser A W, Hohenstein E G, Holden Z C, Jagau T C, Ji H, Kaduk B, Khistyaev K, Kim J, Kim J, King R A, Klunzinger P, Kosenkov D, Kowalczyk T, Krauter C M, Lao K U, Laurent A D, Lawler K V, Levchenko S V, Lin C Y, Liu F, Livshits E, Lochan R C, Luenser A, Manohar P, Manzer S F, Mao S P, Mardirossian N, Marenich A V, Maurer S A, Mayhall N J, Neuscamman E, Oana C M, Olivares-Amaya R, O’Neill D P, Parkhill J A, Perrine T M, Peverati R, Prociuk A, Rehn D R, Rosta E, Russ N J, Sharada S M, Sharma S, Small D W, Sodt A, Stein T, Stück D, Su Y C, Thom A J, Tsuchimochi T, Vanovschi V, Vogt L, Vydrov O, Wang T, Watson M A, Wenzel J, White A, Williams C F, Yang J, Yeganeh S, Yost S R, You Z Q, Zhang I Y, Zhang X, Zhao Y, Brooks B R, Chan G K, Chipman D M, Cramer C J, III W A G, Gordon M S, Hehre W J, Klamt A, III H F S, Schmidt M W, Sherrill C D, Truhlar D G, Warshel A, Xu X, Aspuru-Guzik A, Baer R, Bell A T, Besley N A, Chai J D, Dreuw A, Dunietz B D, Furlani T R, Gwaltney S R, Hsu C P, Jung Y, Kong J, Lambrecht D S, Liang W, Ochsenfeld C, Rassolov V A, Slipchenko L V, Subotnik J E, Voorhis T V, Herbert J M, Krylov A I, Gill P M and Head-Gordon M 2015 Advances in molecular quantum chemistry contained in the Q-Chem 4 program package Mol. Phys. 113 184

  18. Murrell J N, Carter S, Farantos S, Huxley P and Varandas A J C 1984 Molecular potential energy functions (Chichester: Wiley)

    Google Scholar 

  19. Sathyamurthy N 1985 Computational fitting of ab initio potential energy surfaces Comput. Phys. Rep. 3 1

    Article  CAS  ADS  Google Scholar 

  20. Schatz G C 1989 The analytical representation of electronic potential-energy surfaces Rev. Mod. Phys. 61 669

    Article  CAS  ADS  Google Scholar 

  21. Kwon H Y, Morrow Z, Kelley C and Jakubikova E 2021 Interpolation methods for molecular potential energy surface construction J. Phys. Chem. A 125 9725

    Article  CAS  PubMed  Google Scholar 

  22. McKay M D, Beckman R J and Conover W J 1979 A comparison of three methods for selecting values of input variables in the analysis of output from a computer Code Technometrics 21 239

    MathSciNet  Google Scholar 

  23. Perepu P K, Mishra B K and Panda A N 2023 Prediction of interaction energy for rare gas dimers using machine learning approaches J. Chem. Sci. (in press)

  24. Giri K, González-Sánchez L, Biswas R, Yurtsever E, Gianturco F, Sathyamurthy N, Lourderaj U and Wester R 2022 HeH\(^+\) collisions with H\(_2\): Rotationally inelastic cross sections and rate coefficients from quantum dynamics at interstellar temperatures J. Phys. Chem. A 126 2244

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. MATLAB 2018 version 9.5.0 (R2018b) (Natick, Massachusetts: The MathWorks Inc.)

    Google Scholar 

  26. Hutson J M and Le Sueur C R 2019 MOLSCAT: A program for non-reactive quantum scattering calculations on atomic and molecular collisions Comput. Phys. Commun. 241 9

    Article  CAS  ADS  Google Scholar 

  27. Hutson J M and Le Sueur C R MOLSCAT: A program for non-reactive quantum scattering calculations on atomic and molecular collisions Version 2020.0 https://github.com/molscat/molscat.

  28. Wang J, Blake A, McCoy D and Torop L 1990 Analytical potential curves for the X\(^1\Sigma ^+\) and \(0^+\) states of NaI Chem. Phys. Lett. 175 225

    Article  CAS  ADS  Google Scholar 

  29. F Kazuumi and Sun R 2022 Interpolating Moving Ridge Regression (IMRR): A Machine Learning Algorithm to Predict Energy Gradients for ab initio Molecular Dynamics Chem. Phys. 557 111482

    Article  Google Scholar 

  30. Nandi A, Qu C, Houston P L, Conte R and Bowman J M 2021 \(\Delta \)-machine learning for potential energy surfaces: A PIP approach to bring a DFT-based PES to CCSD(T) level of theory J. Chem. Phys. 154 051102

    Article  CAS  PubMed  ADS  Google Scholar 

  31. Huang Z, Zweig G, Levit M, Dumoulin B, Oguz B and Chang S 2014 Accelerating recurrent neural network training via two stage classes and parallelization in 2013 IEEE Workshop on Automatic Speech Recognition and Understanding p. 326 (IEEE)

  32. Chen X, Eversole A, Li G, Yu D and Seide F 2012 Pipelined back-propagation for context-dependent deep neural networks Proc. Interspeech 2012 26

  33. Eyring H 1935 The activated complex in chemical reactions J. Chem. Phys. 3 107

    Article  CAS  ADS  Google Scholar 

  34. Eyring H and Polanyi M 1931 Uber einfache gasreaktionen Z. Phys. Chem. 12 279

    CAS  Google Scholar 

  35. Eyring H and Polanyi M 2013 On simple gas reactions Z. Phys. Chem. 227 1221

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank Dr. Brijesh Mishra of Krea university for providing us the potential energy values for H\(_2\). RB and UL thank NISER Bhubaneswar for computational facilities and Dr. Kousik Giri for discussions.

Author information

Authors and Affiliations

  1. School of Chemical Sciences, National Institute of Science Education and Research (NISER) Bhubaneswar, An OCC of Homi Bhabha National Institute, Khurda, 752050, Odisha, India

    Rupayan Biswas & Upakarasamy Lourderaj

  2. School of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, SAS Nagar, Manauli, 140306, India

    Narayanasami Sathyamurthy

Authors
  1. Rupayan Biswas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Upakarasamy Lourderaj
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Narayanasami Sathyamurthy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Upakarasamy Lourderaj or Narayanasami Sathyamurthy.

Additional information

Dedicated to Prof. S.P. Bhattacharyya on the occasion of his 75th birthday.

Special Issue on Interplay of Structure and Dynamics in Reaction Pathways, Chemical Reactivity and Biological Systems.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Biswas, R., Lourderaj, U. & Sathyamurthy, N. Artificial neural networks and their utility in fitting potential energy curves and surfaces and related problems. J Chem Sci 135, 22 (2023). https://doi.org/10.1007/s12039-023-02136-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12039-023-02136-7

Keywords

Search

Navigation