The electronic structures of the three oxidation states of the "noninnocent" ligand 3,6-di-tert-butylorthoquinone (3,6-DTBQ) have been studied by nonlocal gradient-corrected density functional theory. Optimized structures obtained at the B3LYP/6-31G* and BLYP/6-31G* levels show that neutral 3,6-DTBQ has two equivalent C-O double bonds and a nonaromatic six-membered carbon ring. Upon one- and two-electron reduction to its semiquinone (3,6-DTBSQ) and catechol (3,6-DTBCat) oxidation states, respectively, the single bonds of the ligand become shorter whereas its double bonds elongate. The carbon ring of catechol acquires nearly aromatic character perturbed by a long C1-C2 bond. The calculations confirm that 3,6-DTBQ and 3,6-DTBCat have closed-shell configurations and singlet ground states whereas the 3,6-DTBSQ has an open-shell configuration and a doublet ground state. Analogous calculations have also been carried out on the 3,5-di-tert-butylsemiquinone (3,5-DTBSQ) isomer. Single point calculations at the U-B3LYP/6-311G** level show that both semiquinone isomers have smaller negative charge densities at the carbons bonded to their tert-butyl groups relative to other carbons of their six-membered rings. The spin densities of both semiquinone isomers are mainly localized at their oxygens with somewhat different delocalization patterns throughout the six-membered ring. Detailed descriptions of the composition of frontier molecular orbitals are given that reveal subtle differences between charge distributions and molecular orbital energies across the orthoquinone/semiquinone/catechol redox series. Finally, optimized geometric parameters for the closely related molecule 1,2-benzoquinone have been obtained and compared with its X-ray structure to assess possible discrepancies between experimental and theoretical methods.