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Fourier series of atomic radial distribution functions: A molecular fingerprint for machine learning models of quantum chemical properties

von Lilienfeld, O. Anatole and Ramakrishnan, Raghunathan and Rupp, Matthias and Knoll, Aaron. (2015) Fourier series of atomic radial distribution functions: A molecular fingerprint for machine learning models of quantum chemical properties. International Journal of Quantum Chemistry, 115 (16). pp. 1084-1093.

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Official URL: http://edoc.unibas.ch/53267/

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Abstract

We introduce a fingerprint representation of molecules based on a Fourier series of atomic radial distribution functions. This fingerprint is unique (except for chirality), continuous, and differentiable with respect to atomic coordinates and nuclear charges. It is invariant with respect to translation, rotation, and nuclear permutation, and requires no preconceived knowledge about chemical bonding, topology, or electronic orbitals. As such, it meets many important criteria for a good molecular representation, suggesting its usefulness for machine learning models of molecular properties trained across chemical compound space. To assess the performance of this new descriptor, we have trained machine learning models of molecular enthalpies of atomization for training sets with up to 10 k organic molecules, drawn at random from a published set of 134 k organic molecules with an average atomization enthalpy of over 1770 kcal/mol. We validate the descriptor on all remaining molecules of the 134 k set. For a training set of 10 k molecules, the fingerprint descriptor achieves a mean absolute error of 8.0 kcal/mol. This is slightly worse than the performance attained using the Coulomb matrix, another popular alternative, reaching 6.2 kcal/mol for the same training and test sets.
Faculties and Departments:05 Faculty of Science > Departement Chemie > Chemie > Physikalische Chemie (Lilienfeld)
UniBasel Contributors:von Lilienfeld, Anatole
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Wiley
ISSN:0020-7608
e-ISSN:1097-461X
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:25 Jan 2017 14:25
Deposited On:25 Jan 2017 14:25

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