An extensive methodological theoretical study of the kinetics of the benzylperoxy radical isomerization

Theoretical calculations are carried out on benzylperoxy radical four-center isomerization reaction. Geometry optimizations and vibrational frequency calculations are performed using three methods (B3LYP, MPW1K, and MP2) and seven basis sets (6-31G(d,p), 6-31+G(d,p), 6-31++G(d,p), 6-311G(d,p), cc-pVDZ, aug-cc-pVDZ, and cc-pVTZ). Single-point energy calculations are performed with the highly-correlated ab initio coupled cluster method in the space of single, double, and triple (perturbatively) electron excitations (CCSD(T)) using the 6-311G(d,p), 6-311+G(d,p), 6-311++G(d,p), 6-311+G(3df,2p), and cc-pVTZ basis sets, and with the CASPT2/ANO-L-VDZP level of theory. Canonical transition state theory with a Wigner tunneling correction is used to calculate the high-pressure limit rate constant. The rate constants at 773 K calculated with the CASPT2/ANO-L-VDZP//B3LYP/cc-pVDZ and CASPT2/ANO-L-VDZP//B3LYP/aug-cc-pVDZ levels of theory are in very good agreement with the literature value from Ellis et al. These levels of theory are then used to compute the temperature dependence of rate constant and leads to the following three-parameter Arrhenius expressions over the range 600–2000 K: k (s−1) = 1.34 × 1010 T0.79 exp(−133.1 kJ mol−1/RT) and k (s−1) = 1.85 × 1010 T0.78 exp(−133.9 kJ mol−1/RT) at the CASPT2/ANO-L-VDZP//B3LYP/cc-pVDZ and CASPT2/ANO-L-VDZP//B3LYP/aug-cc-pVDZ levels of theory, respectively. These relations can be used in oxidation thermokinetic models involving toluene and alkylbenzenes.