The kinetics and mechanisms of the self-reaction of allyl radicals and the cross-reaction between allyl and propargyl radicals were studied both experimentally and theoretically. The experiments were carried out over the temperature range 295-800 K and the pressure range 20-200 Torr (maintained by He or N(2)). The allyl and propargyl radicals were generated by the pulsed laser photolysis of respective precursors, 1,5-hexadiene and propargyl chloride, and were probed by using a cavity ring-down spectroscopy technique. The temperature-dependent absorption cross sections of the radicals were measured relative to that of the HCO radical. The rate constants have been determined to be k(C(3)H(5) + C(3)H(5)) = 1.40 × 10(-8)T(-0.933) exp(-225/T) cm(3) molecule(-1) s(-1) (Δ log(10)k = ± 0.088) and k(C(3)H(5) + C(3)H(3)) = 1.71 × 10(-7)T(-1.182) exp(-255/T) cm(3) molecule(-1) s(-1) (Δ log(10)k = ± 0.069) with 2σ uncertainty limits. The potential energy surfaces for both reactions were calculated with the CBS-QB3 and CASPT2 quantum chemical methods, and the product channels have been investigated by the steady-state master equation analyses based on the Rice-Ramsperger-Kassel-Marcus theory. The results indicated that the reaction between allyl and propargyl radicals produces five-membered ring compounds in combustion conditions, while the formations of the cyclic species are unlikely in the self-reaction of allyl radicals. The temperature- and pressure-dependent rate constant expressions for the important reaction pathways are presented for kinetic modeling.

Pressure dependence of unimolecular reaction rates is governed by the energy transfer in collisions of reactants with bath gas molecules. Pressure-dependent rate constants can be theoretically determined by solving master equations for unimolecular reactions. In general, master equation formulations describe energy transfer processes using a collision frequency and a probability distribution model of the energy transferred per collision. The present study proposes a novel method for determining the collision frequency from the results of classical trajectory calculations. Classical trajectories for collisions of several polyatomic molecules (ethane, methane, tetrafluoromethane, and cyclohexane) with monatomic colliders (Ar, Kr, and Xe) were calculated on potential energy surfaces described by the third-order density-functional tight-binding method in combination with simple pairwise interaction potentials. Low-order (including non-integer-order) moments of the energy transferred in deactivating collisions were extracted from the trajectories and compared with those derived using some probability distribution models. The comparison demonstrates the inadequacy of the conventional Lennard-Jones collision model for representing the collision frequency and suggests a robust method for evaluating the collision frequency that is consistent with a given probability distribution model, such as the exponential-down model. The resulting collision frequencies for the exponential-down model are substantially higher than the Lennard-Jones collision frequencies and are close to the (hypothetical) capture rate constants for dispersion interactions. The practical adequacy of the exponential-down model is also briefly discussed.

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The kinetics and mechanisms of the recombination reaction between benzyl and propargyl radicals have been computationally investigated by using the B3LYP, CBS-QB3, and CASPT2 quantum chemical methods, and the steady-state unimolecular master equation analysis based on the Rice-Ramsperger-Kassel-Marcus theory. Six distinct recombination channels arising from the radicals' nonequivalent resonance structures (three for benzyl and two for propargyl) were investigated at the CASPT2/cc-pVTZ//B3LYP/6-311G(d,p) level, and the respective rate constants were calculated with the variational transition state theory. It was found that the reaction dominantly proceeds by the addition of the propargyl radical to the alpha(CH 2 ) site of the benzyl radical and the additions to the ortho-and the para-sites are unfavorable due to the loss of the aromaticity. The isomerization reaction pathways of the initially formed adducts to methylenecyclopenta-fused compounds through diradical intermediates were identified. Methylene-indanyl radicals were also identified as products, which are produced by direct H-atom elimination reactions from the diradical and methylenated indanes. The results of the master equation analyses indicated that the 1-methylene-2-indanyl radical is dominantly produced at high temperature (>1500 K), but the overall rate constant is significantly smaller than the high-pressure limit within the pressure range studied (0.001-100 atm). The reactions of the triplet biradicals via the intersystem crossing were also suggested to be important and are discussed qualitatively. Investigations on the subsequent reactions of 1-methylene-2-indanyl radicals revealed that the radicals rapidly decompose to 1-methyleneindene or naphthalene + H. The temperature-and pressure-dependent rate expressions are proposed for kinetic modeling.

The kinetics and mechanisms of the reactions of o-benzyne with propargyl and benzyl radicals have been investigated computationally. The possible reaction pathways have been explored by quantum chemical calculations at the M06-2X/6-311+G(3df,2p)//B3LYP/6-311G(d,p) level and the mechanisms have been investigated by the Rice-Ramsperger-Kassel-Marcus theory/master-equation calculations. It was found that the o-benzyne associates with the propargyl and benzyl radicals without pronounced barriers and the activated adducts easily isomerize to five-membered ring species. Indenyl radical and fluorene + H were predicted to be dominantly produced by the reactions of o-benzyne with propargyl and benzyl radicals, respectively, with the rate constants close to the high-pressure limits at temperatures below 2000 K. The related reactions on the two potential energy surfaces, namely, the reaction between fulvenallenyl radical and acetylene and the decomposition reactions of indenyl and α-phenylbenzyl radicals were also investigated. The high reactivity of o-benzyne toward the resonance stabilized radicals suggested a potential role of o-benzyne as a precursor of polycyclic aromatic hydrocarbons in combustion.