# Continuous and Optimally Complete Description of Chemical Environments Using Spherical Bessel Descriptors

## TL;DR

This paper introduces an improved Spherical Bessel descriptor for atomic environments that is continuous, twice-differentiable, complete, and computationally efficient, advancing machine learning potentials in quantum chemistry.

## Contribution

The paper presents an updated Spherical Bessel descriptor that is mathematically complete, physically accurate, and computationally faster than existing descriptors like SOAP.

## Key findings

- Spherical Bessel descriptors are optimally complete and continuous.
- They outperform SOAP in computational efficiency by roughly an order of magnitude.
- They enable machine learning potentials with comparable accuracy at reduced computational cost.

## Abstract

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.