Recently, machine learning potentials have been advanced as candidates to
combine the high-accuracy of quantum mechanical simulations with the speed of
classical interatomic potentials. A crucial component of a machine learning
potential is the description of local atomic environments by some set of
descriptors. These should ideally be continuous throughout the specified local
atomic environment, twice-differentiable with respect to atomic positions and
complete in the sense of containing all possible information about the
neighborhood. An updated version of the recently proposed Spherical Bessel
descriptors satisfies all three of these properties, and moreover is optimally
complete in the sense of encoding all configurational information with the
smallest possible number of descriptors. The Smooth Overlap of Atomic Position
descriptors that are frequently visited in the literature and the Zernike
descriptors that are built upon a similar basis are included into the
discussion as being the natural counterparts of the Spherical Bessel
descriptors, and shown to be incapable of satisfying the full list of core
requirements for an accurate description. Aside being mathematically and
physically superior, the Spherical Bessel descriptors have also the advantage
of allowing machine learning potentials of comparable accuracy that require
roughly an order of magnitude less computation time per evaluation than the
Smooth Overlap of Atomic Position descriptors, which appear to be the common
choice of descriptors in recent studies.Comment: 15 pages, 5 figures, under review for Journal of Chemical Physic