Performance of quantum chemistry methods for a benchmark set of spin-state energetics derived from experimental data of 17 transition metal complexes (SSE17)

Reliable prediction of spin-state energetics for transition metal (TM) complexes is recognized as a challenging and compelling problem in quantum chemistry, with implications for modeling catalytic reaction mechanisms and computational discovery of materials. The computed spin–state energetics are highly variable with the choice of method and credible reference data are scarce, making it difficult to conduct conclusive computational studies of open-shell TM systems. Here, we present a novel benchmark set of first-row TM spin–state energetics, which is derived from curated experimental data of 17 representative complexes containing Fe(II), Fe(III), Co(II), Co(III), Mn(II), and Ni(II) with chemically diverse ligands. The reference values of adiabatic or vertical energy differences are derived from spin-crossover enthalpies (9 complexes) or energies of spin-forbidden absorption bands in reflectance spectra (8 complexes). These are carefully back-corrected for relevant vibrational and environmental effects (due to solvation or crystal lattice) in order to provide the reference values directly comparable with computed electronic energy differences. The new benchmark set makes it possible to assess the accuracy of spin–state energetics from approximate density functional theory (DFT) and wave function methods with a level of statistical reliability not attained in earlier studies. The lowest mean absolute error (MAE) of 1.5 kcal/mol and maximum error of −3.5 kcal/mol are found for the coupled-cluster CCSD(T) method, which outperforms all tested multireference methods: CASPT2, MRCI+Q, CASPT2/CC and CASPT2+δMRCI. Contrary to earlier claims in the literature, the use of Kohn–Sham instead of Hartree–Fock orbitals in the reference determinant is not found to consistently improve the accuracy of the CCSD(T) spin–state energetics. The best performing DFT methods are double-hybrids (PWPB95-D3(BJ), B2PLYP-D3(BJ)) with the MAEs below 3 kcal/mol and maximum errors within 6 kcal/mol, whereas DFT methods traditionally recommended for spin states (e.g., B3LYP*-D3(BJ) and TPSSh-D3(BJ)) are found to perform much worse with the MAEs of 5–7 kcal/mol and maximum errors beyond 10 kcal/mol. The results of this work are relevant for the proper choice of methods to characterize TM systems in computational catalysis and (bio)inorganic chemistry, and may also stimulate new developments in quantum-chemical or machine learning approaches.