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

By O. von Lilienfeld, R. Ramakrishnan, Matthias Rupp , A. Knoll. 2013

211 citations recorded by the source corpus.

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. © 2015 Wiley Periodicals, Inc.

Subfields: Computational Theory and Mathematics, Materials Chemistry, Physical and Theoretical Chemistry

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Citations in the corpus

Wavelet Scattering Regression of Quantum Chemical Energies (2016, methodology): “More recently machine learning algorithms have been developed to interpolate molecular energies across “chemical compound space,” fitting the potential energy surface across a range of molecules with different compositions [41, 46, 16].”
SpookyNet: Learning force fields with electronic degrees of freedom and nonlocal effects (2021, background): “learned descriptors SchNet(14) O(n) (3) (3) (3) (3) (3) PhysNet(5) O(n) (3) (3) (3) (3) (3) DimeNet(6) O(n(2)) 3 3 (3) 3 (3) NequIP(8) O(n) 3 (3) (3) (3) (3) PaiNN(7) O(n) 3 (3) (3) (3) (3) SpookyNet O(n) 3 3 (3) (3) (3)”
Prediction Errors of Molecular Machine Learning Models Lower than Hybrid DFT Error. (2017, background): “…have also been benchmarked on QM9 (or QM7 which is a smaller but similar data set), such as Fourier series of radial distance distributions, 16 motifs, 17 the smooth overlap of atomic positions (SOAP) 18 in combination with regularized entropy match, 19 constant size descriptors based on…”
Neural Networks for the Prediction of Organic Chemistry Reactions (2016, unknown): “29 This last example is particularly interesting as Go is a complex board game with a search space of 10 170 , which is on the order of chemical space for medium sized molecules.”