Relative Rates of Hydrogen Shift Isomerizations Depend Strongly on Multiple-Structure Anharmonicity

Abstract

Hydroperoxyalkylperoxy species (OOQOOH) are important intermediates that are generated during the autoignition of transport fuels. A key reaction of hydroperoxyalkylperoxy radicals is a [1,5] hydrogen shift, for which kinetics data are experimentally unavailable. Here we study two typical OOQOOH reactions and compare their kinetics to one another and to a previous study to learn the effect of structural variations of the alkyl group on the competition between alternative [1,5] hydrogen shifts of hydroperoxyalkylperoxy species. We use electronic structure calculations to determine previously missing thermochemical data, and we use variational transition state theory (VTST) with multidimensional tunneling (MT), multiple structures, torsional potential anharmonicity, and high-frequency anharmonicity to obtain more accurate rate constants than the ones that can computed by conventional single-structure harmonic transition state theory (TST) and than the empirically estimated rate constants that are currently used in combustion modeling. The calculated temperature range is 298−1500 K. The roles of various factors in determining the rates are elucidated, and we find an especially strong effect of multiple structure anharmonicity due to torsions. Thus, even though there is some cancellation between the anharmonicity of the reactant and the anharmonicity of the transition state, and even though the reactants are very similar in structure, differing only by a methyl group, the effect of multiple structure anharmonicity has a large effect on the relative rates-as large as a factor of 17 at room temperature and as large as a factor of 7 at 1500 K. This has broad implications for the estimation of reaction rates in many subfields of chemistry, including combustion chemistry and atmospheric chemistry, where rates of reaction of complex molecules are usually estimated without explicit consideration of this fundamental entropic effect. In addition, the pressure-dependence of the rate constants is modeled by system-specific quantum Rice-Ramsperger-Kassel (SS-QRRK) theory for a reversible isomerization.

The Importance of Peroxy Radical Hydrogen-Shift Reactions in Atmospheric Isoprene Oxidation

“…Reaction rate coefficients are calculated using multiconformer transition state theory (MC-TST). ,− The inclusion of multiple conformers is important as it can have a large effect on the calculated rate coefficient as shown, e.g., in Møller et al and in a very recent study employing multistructural variational transition state theory (MS-VTST). , The expression for the reaction rate coefficient, k , in MC-TST is ,− where κ is the tunneling coefficient, k B is the Boltzmann constant, T is the temperature, h is Planck’s constant, E is the energy ( E e +ZPVE), and Q is the partition function (harmonic oscillator and rigid rotor). The sums over all transition state and reactant conformers sum their partition functions (evaluated at the lowest vibrational energy level) weighted by their Boltzmann factor calculated relative to the corresponding lowest-energy conformer.…”

“…18,46−48 The inclusion of multiple conformers is important as it can have a large effect on the calculated rate coefficient as shown, e.g., in Møller et al and in a very recent study employing multistructural variational transition state theory (MS-VTST). 18,49 The expression for the reaction rate coefficient, k, in MC-TST is 18,46−48…”

Multistructural Anharmonicity Controls the Radical Generation Process in Biofuel Combustion

“…Most textbooks explain transition state theory in terms of the properties of a single reactant structure and single saddle point. However, chain molecules and transition states of reactions involving chain molecules have multiple conformers, and these can have a large effect on reaction rates and branching fractions. − …”

Master equation study of hydrogen abstraction from HCHO by OH via a chemically activated intermediate

“…Similarly, when we ignore the tunneling contribution in the low-pressure limit of CUS theory, 66 we obtainwhere the superscript ‘QC’ denotes “quasiclassical” which means tunneling is excluded in this flux coefficient (whereas when we do not mark a flux coefficient with superscript QC, it does include tunneling). As in previous articles 38,70–74 we label the result without tunneling as quasiclassical rather than classical because we still include quantum effects in the partition functions. Eqn (41) and (42) are consistent except that the former is derived from microcanonical ensemble, and the latter is from the canonical ensemble.…”