The reactions of radicals with O2 play the important role in the biological, medicinal, and industrial processes. The mechanism of this reaction is studied previously for the alkane, alkene, alkyne, phenols, and close-related radicals. According to these studies, the formation of intermediates in these reactions is predicted only for the aromatic radicals. Thus, the Van der Waals complexes of O2 with phenyl or benzyl radicals are predicted, as well as the π-π cluster for benzene. However, the possibility of the formation of such intermediate π-π clusters in the case of bisphenol radicals and the thermochemistry of its formation is not studied. Bisphenols are one of the main components of bio-oil, produced during pyrolysis of lignin-contained biomass. Synthetic bisphenols are used in polycarbonate plastics, epoxy resins, and thermal papers. Their mechanism of oxidation is important for the determination of fire safety of these materials, the possibility of using them as additives for fuels for the decreasing and the description of the ignition delays, as well as for the determination of its health risk assessment in medicine. The five DFT (M06-2X (i = 1), B3LYP (i = 2), wB97XD (i = 3), M08HX (i = 4), MN15 (i = 5)) approaches with 6-311 + + G(d,p) basis set are used for the determination of standard enthalpies of atomization (ΔraHo(Yi)) of considered compounds (molecules, radicals, and transition states). These values of ΔraHo(Yi) are corrected using the empirical linear calibration dependencies, reported previously. The different calibration dependencies are used for the hydrocarbons (including the aromatics and simple oxygenated derivatives) and for the peroxides. The corrected values of ΔraHo(Yi, CORR) are used according to Hess's law for the determination of ΔfHo(Yi, CORR). The most consistent values of ΔfHo(Y, MEAN) are derived from the coordination of the values of ΔfHo(Yi, CORR) using the intersection of their values of standard deviations (3SDi). These values of ΔfHo(Y, MEAN), as well as the B3LYP values of So(Y), which are accounting the frequency correction and internal rotations, as well as their temperature dependencies, are used for the determination of thermochemistry of considered reactions and of the calculation, within transition state theory (TST), of the values of high-pressure limits of the rate constant. The values of Ho(Yi), So(Yi), and Go(Yi) are calculated using the Gaussian 16w program. The temperature dependencies of thermochemical properties and the values of rate constants are determined using the ChemRate program (v.1.5). The optimized structures are visualized using the Chemcraft.