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Machine Learning of Potential-Energy Surfaces Within a Bond-Order Sampling Scheme

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Computational Science and Its Applications – ICCSA 2019 (ICCSA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11624))

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Abstract

Predicting the values of the potential energy surface (PES) for a given chemical system is essential to running the associated dynamics and modeling its evolution in time. To the purpose of modeling chemical reactions involving few atoms, this task is usually accomplished by fitting or interpolating a set of energies computed at different nuclear geometries through accurate, though computationally demanding, quantum-chemical calculations. Among the several approaches for choosing an appropriate set of geometries and energies, a new scheme has been recently proposed (Rampino S, J Phys Chem A 120:4683–4692, 2016) which is based on a regular sampling in a space-reduced bond-order (SRBO) domain rather than in the more conventional bond-length (BL) domain. In this work we address the performances of four machine-learning (ML) models, as opposed to pure mathematical fitting or interpolation schemes, in predicting the PES of a three-atom system modeling an atom-diatom exchange reaction when coupled to the SRBO sampling scheme. The models (two ensemble-learning, an automated ML, and a deep-learning one), trained on both SRBO and BL datasets, are shown to perform better than popular fitting or interpolation schemes and to give the best results if coupled to SRBO data.

The research leading to these results has received funding from Scuola Normale Superiore through project ‘DIVE: Development of Immersive approaches for the analysis of chemical bonding through Virtual-reality Environments’ (SNS18_B_RAMPINO) and program ‘Finanziamento a supporto della ricerca di base’ (SNS_RB_RAMPINO).

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References

  1. Jaquet, R.: Interpolation and fitting of potential energy surfaces: concepts, recipes and applications. In: Sax, A.F. (ed.) Potential Energy Surfaces. Lecture Notes in Chemistry, vol. 71, pp. 97–175. Springer, Berlin (1999). https://doi.org/10.1007/978-3-642-46879-7_3

    Chapter  Google Scholar 

  2. Behler, J.: Neural network potential-energy surfaces for atomistic simulations. In: Chemical Modelling: Applications and Theory, vol. 7, pp. 1–41. The Royal Society of Chemistry, Cambridge (2010)

    Google Scholar 

  3. Handley, C.M., Popelier, P.L.A.: Potential energy surfaces fitted by artificial neural networks. The J. Phys. Chem. A 114(10), 3371–3383 (2010)

    Article  Google Scholar 

  4. Hughes, Z.E., Thacker, J.C.R., Wilson, A.L., Popelier, P.L.A.: Description of potential energy surfaces of molecules using FFLUX machine learning models. J. Chem. Theor. Comput. 15(1), 116–126 (2019)

    Article  Google Scholar 

  5. Raff, L., Komanduri, R., Hagan, M., Bukkapatnam, S.: Neural Networks in Chemical Reaction Dynamics. Oxford University Press, New York (2012)

    Book  Google Scholar 

  6. Laganà, A., Costantini, A., Gervasi, O., Faginas Lago, N., Manuali, C., Rampino, S.: COMPCHEM: progress towards GEMS a grid empowered molecular simulator and beyond. J. Grid Comput. 8(4), 571–586 (2010)

    Article  Google Scholar 

  7. Rampino, S.: Workflows and data models for atom diatom quantum reactive scattering calculations on the Grid. Ph.D. thesis, Università degli Studi di Perugia (2011)

    Google Scholar 

  8. Manuali, C., Laganà, A., Rampino, S.: GriF: a grid framework for a web service approach to reactive scattering. Comput. Phys. Commun. 181(7), 1179–1185 (2010)

    Article  Google Scholar 

  9. Rampino, S., Faginas Lago, N., Laganà, A., Huarte-Larrañaga, F.: An extension of the grid empowered molecular simulator to quantum reactive scattering. J. Comput. Chem. 33(6), 708–714 (2012)

    Article  Google Scholar 

  10. Rampino, S., Storchi, L., Laganà, A.: Automated simulation of gas-phase reactions on distributed and cloud computing infrastructures. In: Gervasi, O., et al. (eds.) ICCSA 2017. LNCS, vol. 10406, pp. 60–73. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-62398-6_5

    Chapter  Google Scholar 

  11. Rampino, S., Skouteris, D., Laganà, A., Garcia, E.: A comparison of the isotope effect for the N + N\(_2\) reaction calculated on two potential energy surfaces. In: Gervasi, O., Murgante, B., Laganà, A., Taniar, D., Mun, Y., Gavrilova, M.L. (eds.) Computational Science and Its Applications - ICCSA 2008. Lecture Notes in Computer Science, vol. 5072, pp. 1081–1093. Springer, Berlin Heidelberg (2008)

    Chapter  Google Scholar 

  12. Laganà, A., Faginas Lago, N., Rampino, S., Huarte Larrañaga, F., García, E.: Thermal rate coefficients in collinear versus bent transition state reactions: the N+N\(_2\) case study. Physica Scripta 78(5), 058116 (2008)

    Article  Google Scholar 

  13. Rampino, S., Pirani, F., Garcia, E., Laganà, A.: A study of the impact of long range interactions on the reactivity of N + N\(_2\) using the Grid Empowered Molecular Simulator GEMS. Int. J. Web Grid Serv. 6(2), 196–212 (2010)

    Article  Google Scholar 

  14. Laganà, A., Rampino, S.: A grid empowered virtual versus real experiment for the barrierless Li + FH \(\rightarrow \) LiF + H reaction. In: Murgante, B., et al. (eds.) ICCSA 2014. LNCS, vol. 8579, pp. 571–584. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09144-0_39

    Chapter  Google Scholar 

  15. Rossi, E., et al.: Code interoperability and standard data formats in quantum chemistry and quantum dynamics: the Q5/D5Cost data model. J. Comput. Chem. 35(8), 611–621 (2014)

    Article  Google Scholar 

  16. Rampino, S., Monari, A., Rossi, E., Evangelisti, S., Laganà, A.: A priori modeling of chemical reactions on computational grid platforms: workflows and data models. Chem. Phys. 398, 192–198 (2012)

    Article  Google Scholar 

  17. EGI: The European grid infrastructure. http://www.egi.eu/. Accessed 27 Feb 2019

  18. Rampino, S., Skouteris, D., Laganà, A., García, E., Saracibar, A.: A comparison of the quantum state-specific efficiency of N + N\(_2\) reaction computed on different potential energy surfaces. Phys. Chem. Chem. Phys. 11, 1752–1757 (2009)

    Article  Google Scholar 

  19. Rampino, S., Garcia, E., Pirani, F., Laganà, A.: Accurate quantum dynamics on grid platforms: some effects of long range interactions on the reactivity of N + N\(_2\). In: Taniar, D., Gervasi, O., Murgante, B., Pardede, E., Apduhan, B.O. (eds.) Computational Science and Its Applications - ICCSA 2010. Lecture Notes in Computer Science, vol. 6019, pp. 1–12. Springer, Berlin Heidelberg (2010). https://doi.org/10.1007/978-3-642-12189-0_1

    Chapter  Google Scholar 

  20. Rampino, S., Skouteris, D., Laganà, A.: The O + O\(_2\) reaction: quantum detailed probabilities and thermal rate coefficients. Theor. Chem. Acc.: Theor. Comput. Model. 123(3/4), 249–256 (2009)

    Article  Google Scholar 

  21. Rampino, S., Skouteris, D., Laganà, A.: Microscopic branching processes: the O + O\(_2\) reaction and its relaxed potential representations. Int. J. Quantum Chem. 110(2), 358–367 (2010)

    Article  Google Scholar 

  22. Rampino, S., Pastore, M., Garcia, E., Pacifici, L., Laganà, A.: On the temperature dependence of the rate coefficient of formation of C\(_2^+\) from C + CH\(^+\). Monthly Not. Roy. Astron. Soc. 460(3), 2368–2375 (2016)

    Article  Google Scholar 

  23. Pacifici, L., Pastore, M., Garcia, E., Laganà, A., Rampino, S.: A dynamics investigation of the C + CH\(^+\)\(\rightarrow \) C\(_2^+\) + H reaction on an ab initio bond-order like potential. J. Phys. Chem. A 120(27), 5125–5135 (2016)

    Article  Google Scholar 

  24. Rampino, S., Suleimanov, Y.V.: Thermal rate coefficients for the astrochemical process C + CH\(^+\)\(\rightarrow \) C\(_2^+\) + H by ring polymer molecular dynamics. J. Phys. Chem. A 120(50), 9887–9893 (2016)

    Article  Google Scholar 

  25. Rampino, S.: Configuration-space sampling in potential energy surface fitting: a space-reduced bond-order grid approach. J. Phys. Chem. A 120(27), 4683–4692 (2016)

    Article  Google Scholar 

  26. Pauling, L.: Atomic radii and interatomic distances in metals. J. Am. Chem. Soc. 69(3), 542–553 (1947)

    Article  Google Scholar 

  27. Garcia, E., Laganà, A.: Diatomic potential functions for triatomic scattering. Mol. Phys. 56(3), 621–627 (1985)

    Article  Google Scholar 

  28. Garcia, E., Laganà, A.: A new bond-order functional form for triatomic molecules. Mol. Phys. 56(3), 629–639 (1985)

    Article  Google Scholar 

  29. Laganà, A.: A rotating bond order formulation of the atom diatom potential energy surface. J. Chem. Phys. 95(3), 2216–2217 (1991)

    Article  Google Scholar 

  30. Laganà, A., Ochoa de Aspuru, G., Garcia, E.: The largest angle generalization of the rotating bond order potential: three different atom reactions. J. Chem. Phys. 108(10), 3886–3896 (1998)

    Google Scholar 

  31. Laganà, A., Crocchianti, S., Faginas Lago, N., Pacifici, L., Ferraro, G.: A nonorthogonal coordinate approach to atom-diatom parallel reactive scattering calculations. Collect. Czechoslovak Chem. Commun. 68(2), 307–330 (2003)

    Article  Google Scholar 

  32. Rampino, S., Laganà, A.: Bond order uniform grids for quantum reactive scattering. Int. J. Quantum Chem. 112(7), 1818–1828 (2012)

    Article  Google Scholar 

  33. Pedregosa, F., et al.: Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)

    MathSciNet  MATH  Google Scholar 

  34. Feurer, M., Klein, A., Eggensperger, K., Springenberg, J., Blum, M., Hutter, F.: Efficient and robust automated machine learning. In: Cortes, C., Lawrence, N.D., Lee, D.D., Sugiyama, M., Garnett, R. (eds.) Advances in Neural Information Processing Systems, vol. 28, pp. 2962–2970. Curran Associates, Inc. (2015)

    Google Scholar 

  35. Chollet, F.: Keras (2015). https://github.com/fchollet/keras. Accessed 27 Feb 2019

  36. Aguado, A., Paniagua, M.: A new functional form to obtain analytical potentials of triatomic molecules. J. Chem. Phys. 96(2), 1265–1275 (1992)

    Article  Google Scholar 

  37. Aguado, A., Tablero, C., Paniagua, M.: Global fit of ab initio potential energy surfaces I. Triatomic systems. Comput. Phys. Commun. 108(2–3), 259–266 (1998)

    Article  Google Scholar 

  38. Shepard, D.: A two-dimensional interpolation function for irregularly-spaced data. In: Proceedings of the 1968 23rd ACM National Conference, ACM 1968, pp. 517–524. ACM, New York (1968)

    Google Scholar 

  39. Surowiecki, J.: The Wisdom of Crowds: Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, Societies, and Nations. Doubleday & Co, New York (2004)

    Google Scholar 

  40. Breiman, L.: Random forests. Mach. Learn. 45(1), 5–32 (2001)

    Article  Google Scholar 

  41. Quinlan, J.R.: Induction of decision trees. Mach. Learn. 1(1), 81–106 (1986)

    Google Scholar 

  42. Chen, T., Guestrin, C.: XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2016, pp. 785–794. ACM, New York (2016)

    Google Scholar 

  43. Snoek, J., Larochelle, H., Adams, R.P.: Practical Bayesian optimization of machine learning algorithms. In: Proceedings of the 25th International Conference on Neural Information Processing Systems, NIPS 2012, vol. 2, pp. 2951–2959. Curran Associates Inc., USA (2012)

    Google Scholar 

  44. Brochu, E., Cora, V.M., de Freitas, N.: A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. eprint arXiv:1012.2599, arXiv.org, December 2010

  45. Feurer, M., Eggensperger, K., Falkner, S., Lindauer, M., Hutter, F.: Practical automated machine learning for the AutoML challenge 2018. In: ICML 2018 AutoML Workshop (2018)

    Google Scholar 

  46. Esteva, A., et al.: A guide to deep learning in healthcare. Nat. Med. 25(1), 24–29 (2019)

    Article  Google Scholar 

  47. Zou, J., Huss, M., Abid, A., Mohammadi, P., Torkamani, A., Telenti, A.: A primer on deep learning in genomics. Nat. Genet. 51(1), 12–18 (2019)

    Article  Google Scholar 

  48. Nash, W., Drummond, T., Birbilis, N.: A review of deep learning in the study of materials degradation. npj Mater. Degrad. 2(1), 37 (2018)

    Article  Google Scholar 

  49. LeCun, Y., Bengio, Y., Hinton, G.: Deep learning. Nature 521(7553), 436–444 (2015)

    Article  Google Scholar 

  50. Salvadori, A., Fusè, M., Mancini, G., Rampino, S., Barone, V.: Diving into chemical bonding: an immersive analysis of the electron charge rearrangement through virtual reality. J. Comput. Chem. 39(31), 2607–2617 (2018)

    Article  Google Scholar 

  51. Salvadori, A., et al.: A walk through chemistry: exploring potential-energy surfaces with virtual reality (2019, in preparation)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Scuola Normale Superiore, Piazza dei Cavalireri 7, 56126, Pisa, Italy

    Daniele Licari, Sergio Rampino & Vincenzo Barone

Authors
  1. Daniele Licari
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  2. Sergio Rampino
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  3. Vincenzo Barone
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Corresponding author

Correspondence to Sergio Rampino .

Editor information

Editors and Affiliations

  1. Covenant University, Ota, Nigeria

    Sanjay Misra

  2. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  3. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  4. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  5. Saint Petersburg State University, Saint Petersburg, Russia

    Vladimir Korkhov

  6. Polytechnic University of Bari, Bari, Italy

    Carmelo Torre

  7. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  8. Monash University, Clayton, VIC, Australia

    David Taniar

  9. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  10. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

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Licari, D., Rampino, S., Barone, V. (2019). Machine Learning of Potential-Energy Surfaces Within a Bond-Order Sampling Scheme. In: Misra, S., et al. Computational Science and Its Applications – ICCSA 2019. ICCSA 2019. Lecture Notes in Computer Science(), vol 11624. Springer, Cham. https://doi.org/10.1007/978-3-030-24311-1_28

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  • DOI: https://doi.org/10.1007/978-3-030-24311-1_28

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