Appraising spin-state energetics in transition metal complexes using double-hybrid models: accountability of SOS0-PBESCAN0-2(a) as a promising paradigm

Double-hybrid (DH) approximations have entered into the limelight of density functional theory (DFT) computations of different properties; however, little is known regarding their accountability for spin-state energetics in transition metal complexes. In this work, taking high-level all-electron fixed-node diffusion Monte Carlo data as a reference, we present a survey of the applicability of parameterized and parameter-free DHs as well as their dispersion and non-local corrected versions for predicting the spin splitting energies of transition metal complexes collected from the literature and from our own proposals herein. Our proposed parameter-free DH based on the spin-opposite-scaled (SOS) scheme incorporating the Perdew-Burke-Ernzerhof (PBE) exchange and strongly constrained and appropriately normed (SCAN) correlation as well as high balanced fractions of nonlocal exchange and correlation without any additional correction, SOS0-PBESCAN0-2(a), is found to be superior for overall performance. This model not only surpasses other DFT approximations from various rungs of the "Jacob's Ladder" classification and recently reported DHs for the present purpose but also outperforms wave function-based approaches in most cases. Dissecting the roles played by the non-local exchange and correlation contributions as well as their interplay, it is shown that this good performance arises mainly from an appropriate compromise between energy- and density-driven errors. Furthermore, by employing the proposed model and a variety of modified versions thereof, we scrutinize the roles of various factors, such as the ligand field strength and oxidation state of the metal ions, in both qualitative and quantitative descriptions of spin-state energetics in other complexes with different metals and ligands. Through a comprehensive survey, reliable double-hybrid models have been validated and proposed for spin-state energetics in transition metal complexes.