Kinetics of the benzyl + HO2 and benzoxyl + OH barrierless association reactions: fate of the benzyl hydroperoxide adduct under combustion and atmospheric conditions

Abstract

Radical–radical association reactions are challenging to address theoretically due to difficulties finding the bottleneck that variationally minimizes the reactive flux. For this purpose, the variable reaction coordinate (VRC) formulation of the variational transition state theory (VTST) represents an appropriate tool. In this work, we revisited the kinetics of two radical–radical association reactions of importance in combustion modelling and poly-aromatic hydrocarbon (PAH) chemistry by performing VRC calculations: benzyl + HO₂ and benzoxyl + OH, both forming the adduct benzyl hydroperoxide. Our calculated rate constants are significantly lower than those previously reported based on VTST calculations, which results from a more efficient minimization of the reactive flux through the bottleneck achieved by the VRC formulation. Both reactions show different trends in the variation of their rate constants with temperature. We observed that if the pair of single occupied molecular orbitals (SOMOs) of the associating radicals show a similar nature, i.e. similar character, and thereby a small energy gap, a highly stabilized transition state structure is formed as the result of a very efficient SOMO–SOMO overlap, which may cancel out the free energy bottleneck for the formation of the adduct and result in large rate constants with a negative temperature dependence. This is the case of the benzoxyl and OH radical pair, whose SOMOs show O_2p nature with an energy gap of 20.2 kcal mol⁻¹. On the other hand, the benzyl and HO₂ radical pair shows lower rate constants with a positive temperature dependence due to the larger difference between both SOMOs (a 28.9 kcal mol⁻¹ energy gap) as a consequence of the contribution of the multiple resonance structures of the benzyl radical. The reverse dissociation rate constants were also calculated using multi-structural torsional anharmonicity partition functions, which were not included in previous work, and the results show a much slower dissociation of benzyl hydroperoxide. Our work may help to improve kinetic models of interest in combustion and PAH formation, as well as to gain further understanding of radical–radical association reactions, which are ubiquitous in different environments.