A novel approach to describe chemical environments in high-dimensional neural network potentials

A central concern of molecular dynamics simulations is the potential energy surfaces that govern atomic interactions. These hypersurfaces define the potential energy of the system and have generally been calculated using either predefined analytical formulas (classical) or quantum mechanical simulations (ab initio). The former can accurately reproduce only a selection of material properties, whereas the latter is restricted to short simulation times and small systems. Machine learning potentials have recently emerged as a third approach to model atomic interactions, and are purported to offer the accuracy of ab initio simulations with the speed of classical potentials. However, the performance of machine learning potentials depends crucially on the description of a local atomic environment. A set of invariant, orthogonal, and differentiable descriptors for an atomic environment is proposed, implemented in a neural network potential for solid-state silicon, and tested in molecular dynamics simulations. Neural networks using the proposed descriptors are found to outperform ones using the Behler-Parinello and smooth overlap of atomic position descriptors in the literature.