Atomic orbits in molecules and materials for improving machine learning force fields

Abstract The accurate representation of atoms within their environment forms the backbone of any reliable machine learning force field (MLFF). While modern MLFFs treat atoms of the same type as indistinguishable, their identities can be further resolved by accounting for the composition of their chemical environment. This can improve the parameterization of the MLFF model in chemically diverse systems. In this work, we introduce a novel, data-driven approach designed to find permutation symmetries in isolated and periodic systems, delivering key insights that enable the identification of atomic ‘orbits’, atoms that share consistent chemical and structural environments throughout the dataset. We demonstrate the effectiveness of the orbit representation by incorporating it into the kernel-based symmetric gradient-domain ML (sGDML) model and the equivariant message-passing neural network, MACE. For sGDML, trained on ethanol, 1,8-naphthyridine, D-alanine, and D-histidine adsorbed on graphene, we establish a strong correlation between force prediction accuracy and chemical diversity, quantified by orbit count. The results for the Ac-Phe-Ala5-Lys molecule further underscore the critical role of orbits in force reconstruction across various MLFF architectures. Incorporating orbits into MACE enables us to reduce the model size by an order of magnitude while preserving predictive accuracy, as demonstrated for the CsPbI 3 perovskite slab and graphene with a pyridinic-N defect. Overall, our approach provides a scalable and efficient solution for modeling complex chemical systems with state-of-the-art MLFFs.