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We introduce a fingerprint representation of molecules based on a Fourierseries of atomic radial distribution functions. This fingerprint is unique(except for chirality), continuous, and differentiable with respect to atomiccoordinates and nuclear charges. It is invariant with respect to translation,rotation, and nuclear permutation, and requires no pre-conceived knowledgeabout chemical bonding, topology, or electronic orbitals. As such it meets manyimportant criteria for a good molecular representation, suggesting itsusefulness for machine learning models of molecular properties trained acrosschemical compound space. To assess the performance of this new descriptor wehave trained machine learning models of molecular enthalpies of atomization fortraining sets with up to 10k organic molecules, drawn at random from apublished set of 134k organic molecules. We validate the descriptor on allremaining molecules of the 134k set. For a training set of 5k molecules thefingerprint descriptor achieves a mean absolute error of 8.0 kcal/mol,respectively. This is slightly worse than the performance attained using theCoulomb matrix, another popular alternative, reaching 6.2 kcal/mol for the sametraining and test sets.

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