The Robin Day class II/III mixed-valence character is established quantum-chemically for a series of mixed-valence diquinone radical anions. Particular emphasis is placed on the radical anion of tetrathiafulvalenedibenzoquinone, O-TTF-Q, which has recently been used to evaluate constrained density functional approaches (CDFT) and new range hybrid functionals. Using a computational protocol based on hybrid functionals with 35-42% exact-exchange admixture and inclusion of solvent models during the structure optimization, it is demonstrated that a) Q-TTF-Q(center dot-), 1, and the related diquinone radical anions 2-4 are all delocalized class III species in the gas phase and in nonpolar solvents, in contrast to previous assumptions; b) 1,4,5,8-anthracenetetraone radical anion, 2, remains class III in polar aprotic solvents, c) systems 1, 3 and 4 become class II, providing excellent agreement between computed and experimental intervalence charge-transfer excitations, thermal electron-transfer (ET) barriers and ESR hyperfine couplings. The direct conductor-like screening model for real solvents (D-COSMO-RS) allows the inclusion of specific hydrogen-bonding effects without the computational effort of molecular dynamics simulations and provides increased ET barriers, as well as a predicted incipient symmetry breaking for 2, due to hydrogen bonding in alcohol solvents. For the first time D-COSMO-RS optimizations in solvent mixtures have been evaluated. As previous computational studies of Q-TTF-Q(center dot-) neglected solvent effects during structure optimizations and obtained charge localization in gas-phase optimizations by CDFT or by exaggerated exact-exchange admixtures, they provided at best the right answer for the wrong reason.