The oxidation of hydrocarbons of different structures under the same conditions is an important stage in the study of the chemical properties of both the hydrocarbons themselves and the oxidation catalysts. In a 50% H2O2/Cu2Cl4·2DMG/CH3CN system, where DMG is dimethylglyoxime (Butane-2,3-dione dioxime), at 50 °C under the same or similar conditions, we oxidized eleven RH hydrocarbons of different structures: mono-, bi- and tri-cyclic, framework and aromatic. To compare the composition of the oxidation products of these hydrocarbons, we introduced a new quantitative characteristic, “distributive oxidation depth D(O), %” and showed the effectiveness of its application. The adiabatic ionization potentials (AIP) and the vertical ionization potentials (VIP) of the molecules of eleven oxidized and related hydrocarbons were calculated using the DFT method in the B3LYP/TZVPP level of theory for comparison with experimental values and correlation with D(O). The same calculations of AIP were made for the molecules of the oxidant, solvent, DMG, related compounds and products. It is shown that component X, which determines the mechanism of oxidation of hydrocarbons RH with AIP(Exp) ≥ AIP(X) = 8.55 ± 0.03 eV, is a trans-DMG molecule. Firstly theoretically estimated experimental values of AIP(trans-DMG) = 8.53 eV and AIP(cis-DMG) = 8.27 eV.