Continuous and optimally complete description of chemical environments using Spherical Bessel descriptors

Abstract

Recently, machine learning potentials have been advanced as candidates to combine the high-accuracy of electronic structure methods 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 invariant to the symmetries of the physical system, twice-differentiable with respect to atomic positions (including when an atom leaves the environment), and complete to allow the atomic environment to be reconstructed up to symmetry. The stronger condition of optimal completeness requires that the condition for completeness be satisfied with the minimum possible number of descriptors. Evidence is provided that an updated version of the recently proposed Spherical Bessel (SB) descriptors satisfies the first two properties and a necessary condition for optimal completeness. The Smooth Overlap of Atomic Position (SOAP) descriptors and the Zernike descriptors are natural counterparts of the SB descriptors and are included for comparison. The standard construction of the SOAP descriptors is shown to not satisfy the condition for optimal completeness and, moreover, is found to be an order of magnitude slower to compute than that of the SB descriptors.