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 the SB descriptors.

Choosing the right molecular machine learning potential

“…43,48 The list of developed LDs for molecules is extensive. It includes, among others, BP-ACSFs (Behler-Parrinello's atom-centered symmetry functions) 70 and its ANI-AEV (atomic environment vectors) 46 and wACSF (weighted ACSF) modifications, 71 SOAP (smooth overlap of atomic positions), 43 aSLATM (atomic Spectrum of London and Axilrod-Teller-Muto), 45 FCHL (Faber-Christensen-Huang-Lilienfeld), 44 Gaussian moments, 72 spherical Bessel functions, 73,74 and descriptors used in DPMD (deep potential molecular dynamics) 47 and DeepPot-SE (DPMD-smooth edition). 75 Local descriptors can be fixed before training an MLP.…”

Choosing the right molecular machine learning potential

“…43,48 The list of developed LDs for molecules is extensive. It includes, among others, BP-ACSFs (Behler-Parrinello's atom-centered symmetry functions) 70 and its ANI-AEV (atomic environment vectors) 46 and wACSF (weighted ACSF) modifications, 71 SOAP (smooth overlap of atomic positions), 43 aSLATM (atomic Spectrum of London and Axilrod-Teller-Muto), 45 FCHL (Faber-Christensen-Huang-Lilienfeld), 44 Gaussian moments, 72 spherical Bessel functions, 73,74 and descriptors used in DPMD (deep potential molecular dynamics) 47 and DeepPot-SE (DPMD-smooth edition). 75 Local descriptors can be fixed before training an MLP.…”

Incompleteness of Atomic Structure Representations

“…, incorporates information on higher-order correlations, and there is a widespread belief in the community [7,23,24], supported by numerical evidence [13], that the 3-body correlations likely provide an over-complete description of an atomic environment. The completeness (injectivity) of the structure-representation map would guarantee that any atom-centered property can be described byF, which extends to any atomcentered decomposition of extensive properties, such as the total energy [7].…”