A theoretical study of the kinetics of the benzylperoxy radical isomerization.

The rate constant of the benzylperoxy isomerization reaction has been computed using 54 different levels of theory and has been compared to the experimental value reported at 773 K. The aim of this methodology work is to demonstrate that standard theoretical methods are not adequate to obtain quantitative rate constants for the reaction under study. The use of the elaborated CASPT2 method is essential to estimate a quantitative rate constant. Geometry optimizations and vibrational frequency calculations are performed using three different methods (B3LYP, MPW1K, and MP2) and six different basis sets (6-31G(d,p), 6-31+G(d,p), 6-31++G(d,p), 6-311G(d,p), 6-311+G(d,p), and cc-pVDZ). Single-point energy calculations are performed with the highly correlated ab initio coupled cluster method in the space of single, double, and triple (pertubatively) electron excitations CCSD(T) using the 6-31G(d,p) basis set, and with the CASPT2 level of theory with the ANO-L-VDZP basis set. Canonical transition-state theory with a simple Wigner tunneling correction is used to predict the high-pressure limit rate constants as a function of temperature. We recommend the use of the CASPT2/ANO-L-VDZP//B3LYP/cc-pVDZ level of theory to compute the temperature dependence of the rate constant of the four-center isomerization of the benzylperoxy radical. It is given by the following relation: k(600-2000 K) (in s (-1)) = (1.29 x 10 (10)) T (0.79) exp[(-133.1 in kJ mol (-1))/ RT]. These parameters can be used in the thermokinetic models involving aromatic compounds at high pressure. This computational procedure can be extended to predict rate constants for other similar reactions where no available experimental data exist.