Leveraging High-Spin DFT Features for Prediction of Spin State Gaps in 3d Transition Metal Complexes

Determining spin state gap energetics (SSE) in 3d transition metal complexes (TMCs) is a major challenge in theoretical chemistry, as high-level quantum methods, though reliable, are time-intensive for large-scale studies. This work explores a machine learning (ML)-based approach to predict DFT adiabatic SSE gaps using descriptors derived from a single high-spin DFT calculation. This approach is adopted to eliminate the differential treatment of electronic correlation between high spin (HS) and low spin (LS) structures. Our descriptors try to inculcate the knowledge of crystal field theory into the ML model. It includes atomic energy levels of bare metal ions, natural charges and d-orbital molecular orbital eigenvalues derived from an HS calculation, ligand HOMO-LUMO gaps, and simple identity-based features. We train ML models on 1434 SSE values spanning 934 complexes and demonstrate their transferability to more complex bidentate π-bonding ligands despite being trained on simpler Werner-type monodentate complexes. This approach bypasses the need for multi-reference low-spin (LS) optimizations while retaining predictive accuracy, offering a cost-effective strategy for SSE estimation in transition metal chemistry. We hope the insights covered in this study will contribute to the development of further electronic structure-based descriptors for SSE predictions.