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Tunneling in Hydrogen-Transfer Isomerization of n-Alkyl Radicals

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journal contribution
posted on 12.01.2012 by Baptiste Sirjean, Enoch Dames, Hai Wang, Wing Tsang
The role of quantum tunneling in hydrogen shift in linear heptyl radicals is explored using multidimensional, small-curvature tunneling method for the transmission coefficients and a potential energy surface computed at the CBS-QB3 level of theory. Several one-dimensional approximations (Wigner, Skodje and Truhlar, and Eckart methods) were compared to the multidimensional results. The Eckart method was found to be sufficiently accurate in comparison to the small-curvature tunneling results for a wide range of temperature, but this agreement is in fact fortuitous and caused by error cancellations. High-pressure limit rate constants were calculated using the transition state theory with treatment of hindered rotations and Eckart transmission coefficients for all hydrogen-transfer isomerizations in n-pentyl to n-octyl radicals. Rate constants are found in good agreement with experimental kinetic data available for n-pentyl and n-hexyl radicals. In the case of n-heptyl and n-octyl, our calculated rates agree well with limited experimentally derived data. Several conclusions made in the experimental studies of Tsang et al. (Tsang, W.; McGivern, W. S.; Manion, J. A. Proc. Combust. Inst. 2009, 32, 131–138) are confirmed theoretically: older low-temperature experimental data, characterized by small pre-exponential factors and activation energies, can be reconciled with high-temperature data by taking into account tunneling; at low temperatures, transmission coefficients are substantially larger for H-atom transfers through a five-membered ring transition state than those with six-membered rings; channels with transition ring structures involving greater than 8 atoms can be neglected because of entropic effects that inhibit such transitions. The set of computational kinetic rates were used to derive a general rate rule that explicitly accounts for tunneling. The rate rule is shown to reproduce closely the theoretical rate constants.