Reduced parabolic model for radical addition reactions

The transition state of addition of free radicals and atoms to multiple bonds is considered as a result of intersecting of two parabolic potential curves. One of them characterizes the stretching vibration of the attacked multiple bond, and another curve characterizes the stretching vibration of the bond formed in the transition state. The force constant of the latter is calculated by an empirical equation that correlates the force constant with the bond dissociation energy. In the framework of this model, the thermally neutral activation energy (Ee0) and the elongation of the attacked and formed bonds (re) in the transition state were calculated from the experimental data (activation energy (Ee) and enthalpy of reaction (ΔHe)) for the addition of an H atom and methyl, alkoxyl, aminyl, triethylsilyl, and peroxyl radicals to the C=C bond and the addition of H• and •CH3 to the C=O and C≡C bonds. Analysis of the data obtained showed that Ee0 depends linearly on the |ΔHe| + Ee sum, i.e., Ee0/kJ mol−1 = 14.2 + 0.61 · (Ee − ΔHe), and the bond elongation in the transition state for addition of the most part of radicals to ethylene and acetylene vary within (0.65–0.87)·10−10 m. The factors affecting the activation energy of the radical addition reactions are discussed.