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Construction of Machine Learned Force Fields with Quantum Chemical Accuracy: Applications and Chemical Insights

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Machine Learning Meets Quantum Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 968))

Abstract

Highly accurate force fields are a mandatory requirement to generate predictive simulations. Here we present the path for the construction of machine learned molecular force fields by discussing the hierarchical pathway from generating the dataset of reference calculations to the construction of the machine learning model, and the validation of the physics generated by the model. We will use the symmetrized gradient-domain machine learning (sGDML) framework due to its ability to reconstruct complex high-dimensional potential energy surfaces (PES) with high precision even when using just a few hundreds of molecular conformations for training. The data efficiency of the sGDML model allows using reference atomic forces computed with high-level wave-function-based approaches, such as the gold standard coupled-cluster method with single, double, and perturbative triple excitations (CCSD(T)). We demonstrate that the flexible nature of the sGDML framework captures local and non-local electronic interactions (e.g., H-bonding, lone pairs, steric repulsion, changes in hybridization states (e.g., \(sp^2 \rightleftharpoons sp^3\)), n → π ∗ interactions, and proton transfer) without imposing any restriction on the nature of interatomic potentials. The analysis of sGDML models trained for different molecular structures at different levels of theory (e.g., density functional theory and CCSD(T)) provides empirical evidence that a higher level of theory generates a smoother PES. Additionally, a careful analysis of molecular dynamics simulations yields new qualitative insights into dynamics and vibrational spectroscopy of small molecules close to spectroscopic accuracy.

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Notes

  1. 1.

    It is important to notice that while the scaling of the performance in ML-FFs depends only on the number of atoms, while in the case of ab initio quantum chemical calculations their performance depends on the level of theory and on the size of the basis used to approximate the wave-function and the number of electrons.

  2. 2.

    To the best knowledge of the authors up to this day these are the only two ways have been used in the PES reconstruction problem.

  3. 3.

    The symbol \(\hat {f}\) will be reserved to represent the predictor function of the machine learning model.

  4. 4.

    The components of the force vector are orthogonal in \(\mathbb {R}^{3N}\), space where the function is defined.

  5. 5.

    The reason of such difference between NNs and kernel models is that, while kernels rely on feature engineering (i.e., handcrafted descriptors), NNs represent an end-to-end formalism to describe the data. This means that NNs require more data to infer the representation that optimally describes the system.

  6. 6.

    Even though this is a fundamental property of quantum systems, the invariance of the energy to permutations of atoms of the same species is preserved even in classical mechanics. As will be the case in all the examples discussed in this chapter.

  7. 7.

    Even though the MAE is in the same order as the required accuracy, we have to mention that this error is computed in the whole dataset. This means that the error in the highly sampled regions (e.g., local minima) will be lower than the reported MAE.

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Acknowledgements

S.C., A.T., and K.-R.M. thank the Deutsche Forschungsgemeinschaft, Germany (projects MU 987/20-1 and EXC 2046/1 [ID: 390685689]) for funding this work. A.T. is funded by the European Research Council with ERC-CoG grant BeStMo. This work was supported by the German Ministry for Education and Research as Berlin Big Data Centre (01IS14013A) and Berlin Center for Machine Learning (01IS18037I). This work was also supported by the Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (No. 2017-0-00451). This publication only reflects the authors views. Funding agencies are not liable for any use that may be made of the information contained herein. Part of this research was performed while the authors were visiting the Institute for Pure and Applied Mathematics, which is supported by the National Science Foundation, United States.

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Authors and Affiliations

  1. Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany

    Huziel E. Sauceda

  2. Machine Learning Group, Technische Universität Berlin, Berlin, Germany

    Stefan Chmiela

  3. Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg, Luxembourg

    Igor Poltavsky & Alexandre Tkatchenko

  4. Machine Learning Group, Technische Universität Berlin, Berlin, Germany

    Klaus-Robert Müller

  5. Max Planck Institute for Informatics, Stuhlsatzenhausweg, Saarbrücken, Germany

    Klaus-Robert Müller

  6. Department of Brain and Cognitive Engineering, Korea University, Anam-dong, Seongbuk-gu, Seoul, Korea

    Klaus-Robert Müller

Authors
  1. Huziel E. Sauceda
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  2. Stefan Chmiela
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  3. Igor Poltavsky
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  5. Alexandre Tkatchenko
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Correspondence to Huziel E. Sauceda .

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Editors and Affiliations

  1. Machine Learning, Technical University of Berlin, Berlin, Germany

    Kristof T. Schütt

  2. Machine Learning Group, Technical University of Berlin, Berlin, Germany

    Stefan Chmiela

  3. Institute of Physical Chemistry and MARVEL, University of Basel, Basel, Switzerland

    O. Anatole von Lilienfeld

  4. Department of Physics and Materials Science, University of Luxembourg, Luxembourg, Luxembourg

    Alexandre Tkatchenko

  5. Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Japan

    Koji Tsuda

  6. Computer Science, Technical University of Berlin, Berlin, Germany

    Klaus-Robert Müller

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Sauceda, H.E., Chmiela, S., Poltavsky, I., Müller, KR., Tkatchenko, A. (2020). Construction of Machine Learned Force Fields with Quantum Chemical Accuracy: Applications and Chemical Insights. In: Schütt, K., Chmiela, S., von Lilienfeld, O., Tkatchenko, A., Tsuda, K., Müller, KR. (eds) Machine Learning Meets Quantum Physics. Lecture Notes in Physics, vol 968. Springer, Cham. https://doi.org/10.1007/978-3-030-40245-7_14

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