Benchmarking physics-inspired machine learning models for transition metal complexes with diverse charge and spin states

Physics-inspired machine learning (ML) models can be categorized into two classes: those relying solely on three-dimensional structure and those incorporating electronic information. In this work, we benchmark both classes for predicting quantum-chemical properties of transition metal complexes with diverse charge and spin states, using three complementary datasets. The evaluated methods include molecular representations (SLATM, FCHL, SOAP, and SPAHM family) combined with kernel ridge regression, as well as geometric deep learning models (MACE and 3DMol). We examine how the inclusion of electronic information affects predictive accuracy across datasets and target properties. Models that incorporate electronic information consistently outperform purely structure-based models for properties whose distributions are strongly governed by electronic characters, such as spin-splitting energies and frontier orbital energies. In contrast, structure-only models perform well for predicting the HOMO–LUMO gap and dipole moment magnitude, whose distributions are relatively insensitive to electronic characteristics. Geometric deep learning models with charge and spin embeddings (MACE-QS and 3DMol-QS) show the highest overall accuracy, with 3DMol offering the best computational efficiency among the tested models. These results clarify when geometric information is sufficient and when incorporating electronic information becomes essential, providing practical guidance for selecting effective physics-based ML models for transition metal complexes.