High-quality quantum chemical data for spin state determination in transition-metal complexes

Abstract

Machine learning (ML) models have achieved remarkable success in organic chemistry, where reliable reference data, most commonly from density functional theory (DFT), enable accurate predictions. In contrast, ML approaches remain far less reliable for transition metal complexes, particularly for spin-state energetics (SSE), due to the erratic and system-dependent behavior of DFT. To begin addressing this fundamental data limitation, we present a benchmark dataset of 50 first-row mononuclear octahedral complexes spanning d⁴–d⁶, with spin energy gaps computed at the high-level CASPT2/CC multireference level. Using this high-accuracy dataset, we systematically benchmark a broad range of DFT methods and demonstrate that the optimal fraction of Hartree–Fock exchange is intrinsically dependent on the specific spin-state transition. Furthermore, we introduce an electronic-structure-based descriptor, Des-δ, and employ a Δ-machine-learning (Δ-ML) framework to extrapolate CASPT2/CC-level accuracy to an expanded library of 500 complexes.