Double Hydrogen-Atom Exchange Reactions of HX (X = F, Cl, Br, I) with HO₂

A novel double hydrogen atom exchange process, HX + H′O₂ → H′X + HO₂ for the halogen series X = F, Cl, Br, and I, is identified using theoretical methods. These concerted reactions are mediated through a stabilized five-membered planar ring transition state structure. The transition state barrier for the double exchange process is found to be significantly lower than that for the abstraction reaction of a single hydrogen atom. Density functional theory employing the M11 exchange functional is used to compute parameters of the potential energy surface and the rate coefficients are obtained using transition state theory with small curvature tunneling. For low temperatures, the exchange reaction proceeds at a rate several orders of magnitude faster than the abstraction channel, which is also calculated. The exchange process may be observed using isotope scrambling reactions; such reactions may contribute to observed isotope abundances in the atmosphere. The rate coefficients for the isotopically labeled reactions are computed. It is found that the trends in reactivity within the series of halogen reactions can be quantitatively understood using the degree of electron delocalization at the transition state. The barriers are found to fall as the electronegativity of the halogen atom decreases

Sum over Histories Representation for Kinetic Sensitivity Analysis: How Chemical Pathways Change When Reaction Rate Coefficients Are Varied

The sensitivity of kinetic observables is analyzed using a newly developed sum over histories representation of chemical kinetics. In the sum over histories representation, the concentrations of the chemical species are decomposed into the sum of probabilities for chemical pathways that follow molecules from reactants to products or intermediates. Unlike static flux methods for reaction path analysis, the sum over histories approach includes the explicit time dependence of the pathway probabilities. Using the sum over histories representation, the sensitivity of an observable with respect to a kinetic parameter such as a rate coefficient is then analyzed in terms of how that parameter affects the chemical pathway probabilities. The method is illustrated for species concentration target functions in H₂ combustion where the rate coefficients are allowed to vary over their associated uncertainty ranges. It is found that large sensitivities are often associated with rate limiting steps along important chemical pathways or by reactions that control the branching of reactive flux

Sum over Histories Representation for Chemical Kinetics

A new representation for chemical kinetics is introduced that is based on a sum over histories formulation that employs chemical pathways defined at a molecular level. The time evolution of a chemically reactive system is described by enumerating the most important pathways followed by a chemical moiety. An explicit formula for the pathway probabilities is derived and takes the form of an integral over a time-ordered product. When evaluating long pathways, the time-ordered product has a simple Monte Carlo representation that is computationally efficient. A small numerical stochastic simulation was used to identify the most important paths to include in the representation. The method was applied to a realistic H₂/O₂ combustion problem and is shown to yield accurate results

Following Molecules through Reactive Networks: Surface Catalyzed Decomposition of Methanol on Pd(111), Pt(111), and Ni(111)

We present a model of the surface kinetics of the dehydrogenation reaction of methanol on the Pd(111), Pt(111), and Ni(111) metal surfaces. The mechanism consists of 10 reversible dehydrogenation reactions that lead to the final products of CO and H₂. The rate coefficients for each step are calculated using <i>ab initio</i> transition state theory that employs a new approach to obtain the symmetry factors. The potential energies and frequencies of the reagents and transition states are computed using plane wave DFT with the PW91 exchange correlation functional. The mechanism is investigated for low coverages using a global sensitivity analysis that monitors the response of a target function of the kinetics to the value of the rate coefficients. On Pd(111) and Ni(111), the reaction COH → CO + H is found to be rate limiting, and overall rates are highly dependent upon the decomposition time of the COH intermediate. Reactions at branches in the reaction network are also particularly important in the kinetics. A stochastic atom-following approach to pathway analysis is used to elucidate both the pathway probabilities in the kinetics and the dependence of the pathways on the values of the key rate coefficients of the mechanisms. On Pd(111) and Ni(111) there exists significant competition between the pathway containing the slow step and faster pathways that bypass the slow step. A discussion is given of the dependence of the model target’s probability density function on the chemical pathways

Theoretical Determination of the Rate Coefficient for the HO₂+ HO₂ → H₂O₂<i>+</i>O₂ Reaction: Adiabatic Treatment of Anharmonic Torsional Effects

The HO₂ + HO₂ → H₂O₂ + O₂ chemical reaction is studied using statistical rate theory in conjunction with high level ab initio electronic structure calculations. A new theoretical rate coefficient is generated that is appropriate for both high and low temperature regimes. The transition state region for the ground triplet potential energy surface is characterized using the CASPT2/CBS/aug-cc-pVTZ method with 14 active electrons and 10 active orbitals. The reaction is found to proceed through an intermediate complex bound by approximately 9.79 kcal/mol. There is no potential barrier in the entrance channel, although the free energy barrier was determined using a large Monte Carlo sampling of the HO₂ orientations. The inner (tight) transition state lies below the entrance threshold. It is found that this inner transition state exhibits two saddle points corresponding to torsional conformations of the complex. A unified treatment based on vibrational adiabatic theory is presented that permits the reaction to occur on an equal footing for any value of the torsional angle. The quantum tunneling is also reformulated based on this new approach. The rate coefficient obtained is in good agreement with low temperature experimental results but is significantly lower than the results of shock tube experiments for high temperatures

Quantum Tunneling Affects Engine Performance

We study the role of individual reaction rates on engine performance, with an emphasis on the contribution of quantum tunneling. It is demonstrated that the effect of quantum tunneling corrections for the reaction HO₂ + HO₂ = H₂O₂ + O₂ can have a noticeable impact on the performance of a high-fidelity model of a compression-ignition (e.g., diesel) engine, and that an accurate prediction of ignition delay time for the engine model requires an accurate estimation of the tunneling correction for this reaction. The three-dimensional model includes detailed descriptions of the chemistry of a surrogate for a biodiesel fuel, as well as all the features of the engine, such as the liquid fuel spray and turbulence. This study is part of a larger investigation of how the features of the dynamics and potential energy surfaces of key reactions, as well as their reaction rate uncertainties, affect engine performance, and results in these directions are also presented here