Molecular size dependent falloff rate constants for the recombination reactions of alkyl radicals with O2 and implications for simplified kinetics of alkylperoxy radicals

The recombination reactions of prototypical alkyl radicals (R) with O2, R + O2 → RO2, have been investigated theoretically by using the variational transition state theory and Rice–Ramsperger–Kassel–Marcus theory/master equation calculations based on the CASPT2(7,5)/aug‐cc‐pVDZ//B3LYP/6‐311G(d,p) potential energy curves and B3LYP/6‐311G(d,p) geometries and vibrational frequencies. The calculated high‐pressure limiting rate constants well reproduced the experimental room temperature rate constants for ethyl, i‐propyl, n‐butyl, s‐butyl, and t‐butyl radicals and were nearly the same for the same class of alkyl radicals, namely for primary (ethyl and n‐butyl) and for secondary (i‐propyl and s‐butyl) radicals. Hypothetical falloff calculations ignoring the subsequent dissociation/isomerization reactions of RO2 indicated that the low‐pressure limiting (LPL) rate constants increase monotonically and systematically with the size of the molecule and are almost identical for the same‐sized C4 alkyl radicals, n‐butyl, s‐butyl, and t‐butyl. With the extended calculations for 1‐hexyl (C6H13) and 2,4,4‐trimethylpentyl (C8H17)+ O2 based on the B3LYP/6‐311G(d,p) calculations and estimated potential energy curves, class‐specific molecular size dependent falloff rate expression was proposed. The analysis of the unexpected behavior of the LPL rate constants for large alkyl radicals at high temperatures suggested the collapse of the assumption of the steady‐state dissociation or the Lindemann–Hinshelwood type of the mechanism. The analysis of the dissociation/recombination steady state suggested near‐Boltzmann distribution of RO2 in partial equilibrium with R + O2, which implies the possible simplification of the kinetic modeling by using the high‐pressure limiting rate constants for the subsequent reactions of RO2. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 44: 59–74, 2012