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.

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 that of the SB descriptors.

Thermal transport in a water–Cu nanocolloid system was investigated using equilibrium molecular dynamics. A systematic analysis of the Green–Kubo calculations is presented to clarify the effect of simulation parameters. Several sources of error were identified and quantified for the thermal conductivity estimations, and the effect of the base fluid potential was investigated. Simulations were carried out with a single copper particle for different diameters and water potentials, and thermal enhancements exceeding both theoretical and experimental results were observed in parallel with some other studies in the literature. The anomalous Green–Kubo thermal enhancement results could be explained by the interfacial dynamics and the neglect of calibrating the interaction potential to satisfy the physically-observed energy flow at the interface.