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 D_2d 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 τ_W/τ) local hybrid, the MN15 global hybrid, and the ωB97X-D range-separated hybrid. We also provide vibrational data for comparison with experiment.