Theoretical Kinetic Study of Thermal Decomposition of Cyclohexane

In the present work, the reaction mechanisms for thermal decomposition of cyclohexane in the gas phase have been investigated using quantum chemical calculations and transition-state theory. Three series of reaction schemes containing 38 elementary reactions are proposed. The geometry optimization and vibrational frequencies of reactants, transition states, and products are determined at the BH&HLYP/cc-pVDZ level, while energies are calculated at the CCSD­(T)/cc-pVDZ level. The rate constants for the reactions without transition states, including the initial steps of cyclohexane decomposition (C–C bond scission or C–H bond scission), are obtained by the canonical variational transition-state theory (CVT), while the rate constants for the other reactions with saddle-point transition states are obtained by the conventional transition-state theory (TST) in the temperature range of 300–3000 K. The rate constants are in good agreement with data available from the literature. The kinetic parameters in the modified Arrhenius equation form for all of the reactions studied are given and can be used in chemical kinetic modeling studies

Flux Projection Tree Method for Mechanism Reduction

Merits and demerits of the directed relation graph (DRG) method are analyzed. On the basis of these analyses, a flux projection tree (FPT) method for mechanism reduction is proposed. A tree-type structure is constructed in FPT based on the contribution of each species to the global flux; that is, the importance of each species is quantified by normalized projection of its participation flux vector upon the total species flux vector. Because a tree-type structure is simpler than a graph-type structure, FPT tends to be more efficient than DRG and path flux analysis (PFA) in computation. Additionally, the significance of each species in a mechanism is estimated on the basis of its contribution to the global species flux, instead of its contribution to the flux of a single species in a pre-chosen important species set, as in DRG and PFA. Thus, a reduced model obtained by FPT is more accurate in most cases. Detailed mechanisms for oxidation of ethylene, <i>n</i>-heptane, and PRF50 were reduced with FPT, and the reliability of the resulting skeletal mechanisms is comparable or even better than that of the skeletal mechanisms obtained by DRG or PFA with similar size. Because of its high efficiency, FPT can be used as the first-step reduction method or on-the-fly mechanism reduction approach in numerical simulations of reaction flow

Theoretical Prediction of Rate Constants for Hydrogen Abstraction by OH, H, O, CH₃, and HO₂ Radicals from Toluene

Hydrogen abstraction from toluene by OH, H, O, CH₃, and HO₂ radicals are important reactions in oxidation process of toluene. Geometries and corresponding harmonic frequencies of the reactants, transition states as well as products involved in these reactions are determined at the B3LYP/6-31G­(2df,p) level. To achieve highly accurate thermochemical data for these stationary points on the potential energy surfaces, the Gaussian-4­(G4) composite method was employed. Torsional motions are treated either as free rotors or hindered rotors in calculating partion functions to determine thermodynamic properties. The obtained standard enthalpies of formation for reactants and some prodcuts are shown to be in excellent agreement with experimental data with the largest error of 0.5 kcal mol^–1. The conventional transition state theory (TST) with tunneling effects was adopted to determine rate constants of these hydrogen abstraction reactions based on results from quantum chemistry calculations. To faciliate its application in kinetic modeling, the obtained rate constants are given in Arrhenius expression: <i>k</i>(<i>T</i>) = <i>AT</i>ⁿ exp­(−<i>E</i>_a<i>R</i>/<i>T</i>). The obtained reaction rate constants also agree reasonably well with available expermiental data and previous theoretical values. Branching ratios of these reactions have been determined. The present reaction rates for these reactions have been used in a toluene combustion mechanism, and their effects on some combustion properties are demonstrated

Forest plot showing the effect of Tai Chi on balance in individuals with Parkinson's disease compared with no intervention.

<p>Forest plot showing the effect of Tai Chi on balance in individuals with Parkinson's disease compared with no intervention.</p

Study selection process.

<p>RCTs: randomized controlled trials, Non-RCTs: non-randomized controlled trials.</p

Flux Projection Tree Method for Mechanism Reduction

Merits and demerits of the directed relation graph (DRG) method are analyzed. On the basis of these analyses, a flux projection tree (FPT) method for mechanism reduction is proposed. A tree-type structure is constructed in FPT based on the contribution of each species to the global flux; that is, the importance of each species is quantified by normalized projection of its participation flux vector upon the total species flux vector. Because a tree-type structure is simpler than a graph-type structure, FPT tends to be more efficient than DRG and path flux analysis (PFA) in computation. Additionally, the significance of each species in a mechanism is estimated on the basis of its contribution to the global species flux, instead of its contribution to the flux of a single species in a pre-chosen important species set, as in DRG and PFA. Thus, a reduced model obtained by FPT is more accurate in most cases. Detailed mechanisms for oxidation of ethylene, <i>n</i>-heptane, and PRF50 were reduced with FPT, and the reliability of the resulting skeletal mechanisms is comparable or even better than that of the skeletal mechanisms obtained by DRG or PFA with similar size. Because of its high efficiency, FPT can be used as the first-step reduction method or on-the-fly mechanism reduction approach in numerical simulations of reaction flow

Interpretation and Application of Reaction Class Transition State Theory for Accurate Calculation of Thermokinetic Parameters Using Isodesmic Reaction Method

We present a further interpretation of reaction class transition state theory (RC-TST) proposed by Truong et al. for the accurate calculation of rate coefficients for reactions in a class. It is found that the RC-TST can be interpreted through the isodesmic reaction method, which is usually used to calculate reaction enthalpy or enthalpy of formation for a species, and the theory can also be used for the calculation of the reaction barriers and reaction enthalpies for reactions in a class. A correction scheme based on this theory is proposed for the calculation of the reaction barriers and reaction enthalpies for reactions in a class. To validate the scheme, 16 combinations of various ab initio levels with various basis sets are used as the approximate methods and CCSD­(T)/CBS method is used as the benchmarking method in this study to calculate the reaction energies and energy barriers for a representative set of five reactions from the reaction class: R_cCH­(R_b)­CR_aCH₂ + OH^• → R_cC^•(R_b)­CR_aCH₂ + H₂O (R_a, R_b, and R_c in the reaction formula represent the alkyl or hydrogen). Then the results of the approximate methods are corrected by the theory. The maximum values of the average deviations of the energy barrier and the reaction enthalpy are 99.97 kJ/mol and 70.35 kJ/mol, respectively, before correction and are reduced to 4.02 kJ/mol and 8.19 kJ/mol, respectively, after correction, indicating that after correction the results are not sensitive to the level of the ab initio method and the size of the basis set, as they are in the case before correction. Therefore, reaction energies and energy barriers for reactions in a class can be calculated accurately at a relatively low level of ab initio method using our scheme. It is also shown that the rate coefficients for the five representative reactions calculated at the BHandHLYP/6-31G­(d,p) level of theory via our scheme are very close to the values calculated at CCSD­(T)/CBS level. Finally, reaction barriers and reaction enthalpies and rate coefficients of all the target reactions calculated at the BHandHLYP/6-31G­(d,p) level of theory via the same scheme are provided

Forest plot showing the effect of Tai Chi on balance, gait velocity, step length in individuals with Parkinson's disease compared with other active therapies.

<p>Forest plot showing the effect of Tai Chi on balance, gait velocity, step length in individuals with Parkinson's disease compared with other active therapies.</p

Risk of bias.

<p>Red (-): high risk of bias; Yellow (?): unclear risk of bias; Green (+): low risk of bias.</p