One-electron reduction of the dioxygen molecule by the reduced form of mitochondrial ubiquinones (Q) of the NADH dehydrogenase (complex I) and mitochondrial cytochrome bc1 (complex III) is believed to be the main source of the superoxide anion radical O2*- and the hydroperoxide radical OOH*. In this work, we modeled the energetics of four possible reactions of the triplet ((3)Sigma(g)) dioxygen-molecule reduction by fully reduced and protonated ubiquinone (QH2; reaction 1), its deprotonated form (QH-; reaction 2), the semiquinone radical (QH*; reaction 3), and the semiquinone anion radical (Q*-; reaction 4), by means of ab initio calculations with the 6-31G(d) and 6-31+G(d) basis set in the restricted open-shell Hartree-Fock (ROHF), unrestricted Hartree-Fock (UHF), and complete active space self-consistent field (CASSCF) with dynamic correlation [at the second-order Møller-Plesset (MP2) or multiple reference Møller-Plesset (MRMP), respectively] schemes and the basis set superposition error (BSSE) correction included, as well as semiempirical AM1 and PM3 calculations in the UHF and ROHF schemes. 2-Butene-1,4-dione and p-benzoquinone were selected as model compounds. For the reduced forms of both compounds, reaction 1 turned out to be energetically unfavorable at all levels of theory, this agreeing with the experimentally observed diminished reductive properties of hydroquinone derivatives at low pH. For 2-butene-1,4-dione treated at the most advanced MRMP/CASSCF/6-31+G(d) level, the energies of reactions 1-4 are 4.7, -34.3, -15.0, and -4.1 kcal/mol, respectively. This finding suggests that reactions 2 and 3 are the most likely mechanisms of electron transfer to molecular oxygen in aprotic environments and that proton transfer is involved in this process. Nearly the same energies of reactions 2 and 3 were calculated at the MRMP/CASSCF/6-31+G(d) level for reduced forms of p-benzoquinone. Inclusion of diffuse functions in the basis set and dynamic correlation at the CASSCF level appears essential. Because deprotonated ubiquinol is unlikely to exist in physiological environments, reaction 3 appears to be the most likely mechanism of one-electron reduction of oxygen; however, if oxygen can penetrate cytochrome bc1 as far as the Q(o) center where ubiquinol can be deprotonated, reaction 2 can also come into play. The energies of reactions 2 and 3 calculated at the MRMP/CASSCF/6-31+G(d) level are most closely reproduced in the ab initio and semiempirical UHF PM3 calculations. Additional semiempirical calculations on more realistic models of ubiquinone, 2,3-dimethoxy-6-methyl-p-benzoquinone and 2,3-dimethoxy-5-isoprenyl-6-methyl-p-benzoquinone, gave qualitatively the same relations between the energies of reactions 2 and 3 as those carried out for p-benzoquinone species, thereby suggesting that this method could be used in studying electron-transfer reactions from reduced quinone derivatives to molecular oxygen in more complex systems, such as a model of the Q(o) site of cytochrome bc1, where applying ab initio methods is unfeasible.