用多体展开提升模型对配位异构体的区分能力，加速过渡金属配合物筛选

Graph-based machine learning models for materials properties show great potential to accelerate virtual high-throughput screening of large chemical spaces. However, in their simplest forms, graph-based models do not include any 3D information and are unable to distinguish stereoisomers such as those arising from different orderings of ligands around a metal center in coordination complexes. In this work we present a modification to revised autocorrelation descriptors, our molecular graph featurization method for machine learning various spin state dependent properties of octahedral transition metal complexes (TMCs). Inspired by analytical semi-empirical models for TMCs, the new modeling strategy is based on the many-body expansion (MBE) and allows one to tune the captured stereoisomer information by changing the truncation order of the MBE. We present the necessary modifications to include this approach in two commonly used machine learning methods, kernel ridge regression and feed-forward neural networks. On a test set composed of all possible isomers of binary transition metal complexes, the best MBE models achieve mean absolute errors of 2.75 kcal/mol on spin-splitting energies and 0.26 eV on frontier orbital energy gaps, a 30-40% reduction in error compared to models based on our previous approach. We also observe improved generalization to previously unseen ligands where the best-performing models exhibit mean absolute errors of 4.00 kcal/mol (i.e., a 0.73 kcal/mol reduction) on the spin-splitting energies and 0.53 eV (i.e., a 0.10 eV reduction) on the frontier orbital energy gaps. Because the new approach incorporates insights from electronic structure theory, such as ligand additivity relationships, these models exhibit systematic generalization from homoleptic to heteroleptic complexes, allowing for efficient screening of TMC search spaces.