A density functional theory study of the cyclization and ring opening reactions of selected 2,2-diphenyl-cyclopropyl radicals

Cyclization and ring opening reactions of selected 2,2-diphenyl-cyclopropyl radicals were studied using density functional theory (DFT) calculations at the UB3LYP/6-31G∗ level of theory. The free energy barrier of the cyclization reactions A, B, C, and D (see Scheme 1) were computed to be 7.3, 6.4, 9.3, and 7.6 kcal/mol, respectively. While for the cyclization reaction E (see Scheme 1), the energy barrier was reduced dramatically to 1.4 kcal/mol. For the ring opening reactions, the free energy barriers were computed to be 2.9, 3.0, 2.8, 2.7 and 1.0 kcal/mol, respectively. The free energy barriers of the cyclization were correlated well with both the corresponding spin densities changes and the structural changes between the corresponding radical reactants and transition states. The rate constants calculated were in reasonably good agreement with experimental data where available.