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Modeling of molecular atomization energies using machine learning

Atomization energies are an important measure of chemical stability. Machine learning is used to model atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only [1]. Our scheme maps the problem of solving the molecular time-independent Schrödinger equation onto a non-linear statistical regression problem. Kernel ridge regression [2] models are trained on and compared to reference atomization energies computed using density functional theory (PBE0 [3] approximation to Kohn-Sham level of theory [4, 5]). We use a diagonalized matrix representation of molecules based on the inter-nuclear Coulomb repulsion operator in conjunction with a Gaussian kernel. Validation on a set of over 7000 small organic molecules from the GDB database [6] yields mean absolute error of ~10 kcal/mol, while reducing computational effort by several orders of magnitude. Applicability is demonstrated for prediction of binding energy curves using augmentation samples based on physical limits.


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Correspondence to Matthias Rupp.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Rupp, M., Tkatchenko, A., Müller, KR. et al. Modeling of molecular atomization energies using machine learning. J Cheminform 4 (Suppl 1), P33 (2012).

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