High-order rotational invariants for structural representations: Application to linearized machine learning interatomic potential

Machine-learning interatomic potential (MLIP) has been of growing interest as a useful method to describe the energetics of systems of interest. Firstly, we examine the accuracy of linearized pairwise MLIPs and angular-dependent MLIPs for 31 elemental metals [1]. They correspond to generalizations of the embedded atom method (EAM) and modified EAM potentials, respectively. Building the optimal MLIPs for the 31 elemental metals, we show the robustness of the linearized frameworks, the general trend of the predictive power of MLIPs and the limitation of pairwise MLIPs. We also introduce higher-order rotational invariants for improving the accuracy of linearized MLIPs.In this study, a set of rotational invariants up to six-order is derived by the general process of reducing Kronecker products of irreducible representations for SO(3) group. The use of high-order invariants significantly improves the prediction error for a wide range of structures generated from many structure types.
[1] A. Takahashi, A. Seko and I. Tanaka, Phys. Rev. Mater. 1, 063801 (2017). A. Takahashi, A. Seko, and I. Tanaka, J. Chem. Phys. 148, 234106 (2018).