Atom-centered symmetry functions for constructing high-dimensional neural network potentials

Abstract

Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces. Once constructed, neural network potentials can provide the energies and forces many orders of magnitude faster than electronic structure calculations, and thus enable molecular dynamics simulations of large systems. However, Cartesian coordinates are not a good choice to represent the atomic positions, and a transformation to symmetry functions is required. Using simple benchmark systems, the properties of several types of symmetry functions suitable for the construction of high-dimensional neural network potential-energy surfaces are discussed in detail. The symmetry functions are general and can be applied to all types of systems such as molecules, crystalline and amorphous solids, and liquids.

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

“…As discussed in Ref. [137], these are all crucial criteria for representing atomistic systems within statistical models.…”

A fingerprint based metric for measuring similarities of crystalline structures

“…In addition, we also show the configurational distances arising from the Oganov and Valle and BCM 13,33 fingerprints as well as from a fingerprint based on the amplitudes of symmetry functions. 36 All our data sets contain both the global minimum (geometric ground state) as well as local minima (metastable) structures, obtained from minima hopping runs. 9 Energies and forces were calculated with the Density Functional based Tight binding method (DFTB+) 44 method for SiC and the molecular crystals, and the Lenosky tight-binding scheme was used for Si.…”

“…For molecular crystals, Chisholm et al 35 used intermolecular contact distances and a matching algorithm to characterize and compare structures. Atomic and molecular environment descriptors are also needed in the context of machine learning schemes for force fields, [36][37][38] bonding pattern recognition, 39 or to compare vacancy, interstitial, and intercalation sites. 40 These descriptors could also be used to measure similarities between structures.…”

Learning scheme to predict atomic forces and accelerate materials simulations

“…Such a fingerprint should differentiate dissimilar configurations with adequate accuracy, and be invariant to transformations of the environment such as translation, rotation and permutation of like elements. While several such prescriptions have been proposed in the past [12][13][14][15][16][17][18] , the present objective, namely, mapping the vectorial force experienced by an atom to its configurational environment, places stringent constraints on the nature of the fingerprint. We argue that the following fingerprint function, V k i (η), may be used to accurately represent the k th component of the force on atom i 12 :…”