[Al2O4](-), a Benchmark Gas-Phase Class II Mixed-Valence Radical Anion for the Evaluation of Quantum-Chemical Methods

The radical anion [Al2O4](-) has been identified as a rare example of a small gas-phase mixed-valence system with partially localized, weakly coupled class II character in the Robin/Day classification. It exhibits a low-lying C2v minimum with one terminal oxyl radical ligand and a high-lying D2h minimum at about 70 kJ/mol relative energy with predominantly bridge-localized-hole character. Two identical C2v minima and the D2h minimum are connected by two C2v-symmetrical transition states, which are only ca. 6-10 kJ/mol above the D2h local minimum. The small size of the system and the absence of environmental effects has for the first time enabled the computation of accurate ab initio benchmark energies, at the CCSDT(Q)/CBS level using W3-F12 theory, for a class-II mixed-valence system. These energies have been used to evaluate wave function-based methods [CCSD(T), CCSD, SCS-MP2, MP2, UHF] and density functionals ranging from semilocal (e.g., BLYP, PBE, M06L, M11L, N12) via global hybrids (B3LYP, PBE0, BLYP35, BMK, M06, M062X, M06HF, PW6B95) and range-separated hybrids (CAM-B3LYP, ωB97, ωB97X-D, LC-BLYP, LC-ωPBE, M11, N12SX), the B2PLYP double hybrid, and some local hybrid functionals. Global hybrids with about 35-43% exact-exchange (EXX) admixture (e.g., BLYP35, BMK), several range hybrids (CAM-B3LYP, ωB97X-D, ω-B97), and a local hybrid provide good to excellent agreement with benchmark energetics. In contrast, too low EXX admixture leads to an incorrect delocalized class III picture, while too large EXX overlocalizes and gives too large energy differences. These results provide support for previous method choices for mixed-valence systems in solution and for the treatment of oxyl defect sites in alumosilicates and SiO2. Vibrational gas-phase spectra at various computational levels have been compared directly to experiment and to CCSD(T)/aug-cc-pV(T+d)Z data.