The authors calculated the single occupied molecular orbital energies of the substrate radical and the phthalimide catalyst radical by the Hartree-Fock quantum chemical method (PM7). According to the research, low numerical values of ∆Esomo characterise N-hydroxyphthalimide derivatives containing electron-donating substituents in their structure and possess high catalytic activity. Application of such compounds allows ones to intensify essentially the process of alkylaromatic hydrocarbons aerobic liquid-phase oxidation with preservation of feedstock conversion high parameters and selectivity of its hydroperoxide formation. The calculated data are in good agreement with the experimentally obtained data. Hence, the proposed method can be used to evaluate the catalytic activity of phthalimide compounds with respect to a wide range of aromatic hydrocarbons.