Leveraging high-spin DFT features for prediction of spin state gaps in 3d transition metal complexes

Abstract

Determining spin state energy gaps (SSE) of 3d transition metal complexes (TMCs) is a major challenge in theoretical chemistry, as high-level quantum methods, though reliable, are computationally impractical 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 and low-spin structures. Our descriptors aim to incorporate the knowledge of crystal field theory into the ML model. They include atomic energy levels of bare metal ions, natural charges of ligating atoms, d-orbital molecular orbital eigenvalues derived from an high spin calculation, HOMO–LUMO gaps of free ligands, and simple identity-based features. We train ML models on 1434 SSE values spanning 934 complexes and demonstrate their transferability to more challenging complexes having bidentate π-bonding ligands despite being trained on simpler Werner-type monodentate complexes. We achieved a minimum MAE of 4.0 kcal mol⁻¹ on the monodentate test set, and maintained a comparable MAE of 6.6 kcal mol⁻¹ in the transferability assessment. This approach bypasses the need for multi-reference low-spin 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 additional electronic structure-based descriptors for SSE predictions.