Theoretical kinetic study of thermal unimolecular decomposition of cyclic alkyl radicals.

Whereas many studies have been reported on the reactions of aliphatic hydrocarbons, the chemistry of cyclic hydrocarbons has not been explored extensively. In the present work, a theoretical study of the gas-phase unimolecular decomposition of cyclic alkyl radicals was performed by means of quantum chemical calculations at the CBS-QB3 level of theory. Energy barriers and high-pressure-limit rate constants were calculated systematically. Thermochemical data were obtained from isodesmic reactions, and the contribution of hindered rotors was taken into account. Classical transition state theory was used to calculate rate constants. The effect of tunneling was taken into account in the case of CH bond breaking. Three-parameter Arrhenius expressions were derived in the temperature range of 500-2000 K at atmospheric pressure, and the CC and CH bond breaking reactions were studied for cyclic alkyl radicals with a ring size ranging from three to seven carbon atoms, with and without a lateral alkyl chain. For the ring-opening reactions, the results clearly show an increase of the activation energy as the pi bond is being formed in the ring (endo ring opening) in contrast to the cases in which the pi bond is formed on the side chain (exo ring opening). These results are supported by analyses of the electronic charge density that were performed with Atoms in Molecules (AIM) theory. For all cycloalkyl radicals considered, CH bond breaking exhibits larger activation energies than CC bond breaking, except for cyclopentyl for which the ring-opening and H-loss reactions are competitive over the range of temperatures studied. The theoretical results compare rather well with the experimental data available in the literature. Evans-Polanyi correlations for CC and CH beta-scissions in alkyl and cycloalkyl free radicals were derived. The results highlight two different types of behavior depending on the strain energy in the reactant.