Influence of the size of the formed cycle on the reactivity of free radicals in cyclization reactions

Numerous experimental data for the cyclization of free radicals C·H₂(CH₂)_nCH=CH₂ cyclo-[(CH₂)_n+1CH(C·H₂)], and C·H₂(CH₂)_nCH=CHR cyclo-[(CH₂)_n+1C·HCHR] were analyzed in the framework of the parabolic model. The activation energy of thermoneutral (H_e = 0) cyclization E_e0 decreases linearly with an increase in the energy of cycle strain E_rsc: E_e0(n) (kJ mol–1) = 85.5 – 0.44E_rsc(n) (n is the number of atoms in the cycle). The activation entropy of cyclization S^# also depends on the cycle size: the larger the cycle, the lower S^#. A linear dependence of S^# on the difference between the entropies of formation S° of cyclic hydrocarbon and the corresponding paraffin was found: S^# = 1.00[S°(cycle) – S°(C_nH_2n+2)]. The E_e0 values coincide for cyclization reactions with the formation of the six-membered cycle and the bimolecular addition of alkyl radicals to olefins.