  A central concern of molecular dynamics simulations are 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 SOAP descriptors currently in
the literature.
