Theoretical Study of Radical–Molecule Reactions with Negative Activation Energies in Combustion: Hydroxyl Radical Addition to Alkenes

Many of the radical–molecule reactions are nonelementary reactions with negative activation energies, which usually proceed through two steps. They exist extensively in the atmospheric chemistry and hydrocarbon fuel combustion, so they are extensively studied both theoretically and experimentally. At the same time, various models, such as a two transition state model, a steady-state model, an equilibrium-state model, and a direct elementary dynamics model are proposed to get the kinetic parameters for the overall reaction. In this paper, a conversion temperature TC1 is defined as the temperature at which the standard molar Gibbs free energy change of the formation of the reaction complex is equal to zero, and it is found that when T ≫ TC1, the direct elementary dynamics model with an inclusion of the tunneling correction of the second step reaction is applicable to calculate the overall reaction rate constants for this kind of reaction system. The reaction class of hydroxyl radical addition to alkenes is chosen as the objects of this study, five reactions are chosen as the representative for the reaction class, and their single-point energies are calculated using the method of CCSD(T)/CBS, and it is shown that the highest conversion temperature for the five reactions is 139.89 K, far below the usual initial low-temperature (550 K) oxidation chemistry of hydrocarbon fuels; therefore, the steady-state approximation method is applicable. All geometry optimizations are performed at the BH&HLYP/6-311+G(d,p) level, and the result shows that the geometric parameters in the reaction centers are conserved; hence, the isodesmic reaction method is applicable to this reaction class. To validate the accuracy of this scheme, a comparison of electronic energy difference at the BH&HLYP/6-311+G(d,p) level and the corrected electronic energy difference with the electronic energy difference at the CCSD(T)/CBS level is performed for the five representative reactions, and it is shown that the maximum absolute deviation of electronic energy difference can be reduced from 2.54 kcal·mol–1 before correction to 0.58 kcal·mol–1 after correction, indicating that the isodesmic reaction method is applicable for the accurate calculation of the kinetic parameters for large-size molecular systems with a negative activation energy reaction. The overall rate constants for 44 reactions of the reaction class of hydroxyl radical addition to alkenes are calculated using the transition-state theory in combination with the isodesmic correction scheme, and high-pressure limit rate rules for the reaction class are developed. In addition, the thermodynamic parameter is calculated and the results indicate that our dynamics model is applicable for our studied reaction class. A chemical kinetic modeling and sensitivity analysis using the calculated kinetic data is performed for the combustion of ethene, and the results indicate the studied reaction is important for the low-to-medium temperature combustion modeling of ethene.