Role of Entropy in Hydrogen Abstraction by tert-Butoxy Radicals: A Quantum Chemistry and Continuum Solvation Study

tert-butoxy is a prototype radical in radical chemistry that underlies oxidation reactions in many biological and chemical systems. The literature contains a large number of experimental measurements of the rate coefficients of reactions of tert-butoxy radical with different substrates and in different solvents. In an article published in 2004, Finn et al. [J. Am. Chem. Soc. 2004, 126, 7578] experimentally concluded that the H-abstractions involving the tert-butoxy radical were controlled by entropy. In this work, we used theoretical chemistry tools to examine this conclusion. First, a methodology to compute accurate kinetic data was defined, based on quantum chemistry and continuum solvation models: the gas phase rate coefficient was calculated using quantum chemistry calculations and partition functions corrected for internal rotors. Corrections of the gas-phase kinetic data for solvent environment were then computed using the implicit solvent models and diffusion. Since rate coefficients of H-atom abstraction from cyclohexane by tert-butoxy were measured in the gas and liquid phases, they were used as a validation reference for each step of our methodology. The comparison with the gas phase rate coefficients demonstrates that a costly calculation (up to QCISD(T)/cc-pVTZ on 12 heavy atoms) is necessary to accurately calculate kinetic data. Solvation corrections were computed with the SMD model and two levels of COSMO-RS calculations (TZVP and TZVPD-FINE). Our results show that the highest level, TZVPD-FINE, must be used to correctly describe the solvation corrections, especially for radicals and transition state structures. The computed rate coefficients for H-abstractions by tert-butoxy from cyclohexane, cyclopentane, toluene, tetrahydrofuran, dioxolane, and N-methylpyrrole were compared with experiments, and the good agreement observed (within a factor of ≈2) validates the theoretical approach and even revealed an incorrect experimental interpretation of the reaction with N-methylpyrrole. The theoretical calculations support that tert-butoxy H-abstractions are entropy-controlled under the experimental conditions of the target data.