Spin-state energetics of metallocenes: How do best wave function and density functional theory results compare with the experimental data?

We benchmark the accuracy of quantum-chemical methods, including wave function theory methods [coupled cluster theory at the CCSD(T) level, multiconfigurational perturbation-theory (CASPT2, NEVPT2) and internally contracted multireference configuration interaction (MRCI)] and 30 density functional theory (DFT) approximations, in reproducing the spin-state splittings of metallocenes. The reference values of the electronic energy differences are derived from the experimental spin-crossover enthalpy for manganocene and the spectral data of singlet-triplet transitions for ruthenocene, ferrocene, and cobaltocenium. For ferrocene and cobaltocenium we revise the previous experimental interpretations regarding the lowest triplet energy; our argument is based on the comparison with the lowest singlet excitation energy and herein reported, carefully determined absorption spectrum of ferrocene. When deriving vertical energies from the experimental band maxima, we go beyond the routine vertical energy approximation by introducing vibronic corrections based on simulated vibrational envelopes. The benchmarking result confirms the high accuracy of the CCSD(T) method (in particular, for UCCSD(T) based on Hartree-Fock orbitals we find for our dataset: maximum error 0.12 eV, weighted mean absolute error 0.07 eV, weighted mean signed error 0.01 eV). The high accuracy of the single-reference method is corroborated by the analysis of a multiconfigurational character of the complete active space wave function for the triplet state of ferrocene. On the DFT side, our results confirm the non-universality problem with approximate functionals. The present study is an important step toward establishing an extensive and representative benchmark set of experiment-derived spin-state energetics for transition metal complexes.