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

Understand

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 pre-conceived 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.