The main hyperparameters to be considered for SOAP are the cutoff radius r cut within which the neighborhood is expanded and the broadness of the Gaussians used to smear out the atomic positions (σ atom ). The choice of these lengthscales governs the range in which the environment of an atom affects its electronegativity and how sensitive it is to changes of the atomic positions. In the following, we keep the ratio between these parameters constant (σ atom = rcut 8 ) so that for larger cutoffs, the atomic positions are smeared out more strongly. The idea of keeping this ratio fixed is based on the fact that the expressiveness of a given atom-centered basis set is limited by the number of basis functions, meaning that it can either provide a high-resolution picture that is short-ranged or a lower-resolution picture that is longer-ranged. Alternatively, one could increase the number of basis functions for larger cutoff radii instead, but this would lead to a significantly increased computational cost. The particular constant of proportionality we use was found to work well empirically.