MVO-10: A Gas-Phase Oxide Benchmark for Localization/Delocalization in Mixed-Valence Systems.

Ten simple gas-phase, main-group as well as transition-metal, mixed-valence (MV) oxo complexes are suggested for the screening of electronic-structure methods for the computational study of localization vs delocalization of charge and spin density in MV systems, without the usual added complication of environmental effects. Benchmark coupled-cluster energies up to CCSDT(Q)/CBS (for Al2O4-, Si2O4+, Si2O4-, ScO2, TiO2+) and CCSD(T)/CBS (for Ti2O4-, Ti2O4-, V2O4+, Cr2O6-) quality are provided as a basis for screening a variety of density-functional methods, ranging from a generalized gradient approximation via global and range-separated to local hybrid functionals. Additionally, experimental evidence for a delocalized D2d structure of the somewhat larger V4O10- is used. None of the functionals is fully satisfactory when tasked with describing simultaneously the most extreme cases, the localized Al2O4- and the delocalized V4O10-. While relatively large exact-exchange admixtures are required for the former, and for related localized cases, lower ones are preferable for the latter, as well for other delocalized d1d0 systems. The overall best combined performance is provided by a Lh-SVWN (g(r) = 0.670 τW/τ) local hybrid, the MN15 global hybrid, and the ωB97X-D range-separated hybrid. We also provide vibrational data for comparison with experiment.