A Direct Transition State Theory Based Study of Methyl Radical Recombination Kinetics

Toward an Accurate Black-Box Tool for the Kinetics of Gas-Phase Reactions Involving Barrier-less Elementary Steps

An enhanced computational protocol has been devised for the accurate characterization of gas-phase barrier-less reactions in the framework of the reaction-path (RP) and variable reaction coordinate variational transition-state theory. In particular, the synergistic combination of density functional theory and Monte Carlo sampling to optimize reactive fluxes led to a reliable yet effective computational workflow. A black-box strategy has been developed for selecting the most suited density functional with reference to a high-level one-dimensional reference potential. At the same time, different descriptions of hindered rotations are automatically selected, depending on the corresponding harmonic frequencies along the RP. The performance of the new tool is investigated by means of two prototypical reactions involving different degrees of static and dynamic correlation, namely, H2S + Cl and CH3 + CH3. The remarkable agreement of the computed kinetic parameters with the available experimental data confirms the accuracy and robustness of the proposed approach. Together with their intrinsic interest, these results also pave the way toward systematic investigations of gas-phase reactions involving barrier-less elementary steps by a reliable, user-friendly tool, which can be confidently used also by nonspecialists.

HO2 + NO2: Kinetics, Thermochemistry, and Evidence for a Bimolecular Product Channel

A master equation (ME) analysis of available experimental data has been carried out on the reaction HO₂ + NO₂ + M ⇋ HO₂NO₂ + M (1a)/(-1a). The analysis, based on the ME code MESMER, uses both the association and dissociation kinetic data from the literature, and provides improved thermochemistry on reaction 1a. Our preferred model assigns two low-frequency vibrations of HO₂NO₂ as hindered rotors and couples these to the external rotations. This model gives Δ_rH°₀(1a) = -93.9 ± 1.0 kJ mol^-1, which implies that Δ_fH°₀ HO₂NO₂ = -42.0 ± 1.0 kJ mol^-1 (uncertainties are 2σ). A significant contributor to the uncertainty derives from modeling the interaction between the internal and external rotors. Using this improved kinetics for reaction 1a/-1a, data at elevated temperatures, 353-423 K, which show no evidence of the expected equilibration, have been reanalyzed, indicating that an additional reaction is occurring that masks the equilibration. Based on a published ab initio study, this additional channel is assigned to the bimolecular reaction HO₂ + NO₂ → H-NO₂ + O₂ (1b); H-NO₂ is nitryl hydride and has not previously been directly observed in experiments. The output of the master equation analysis has been parametrized and Troe expressions are provided for an improved description of k_1a(p,T) and k_-1a(p,T).

Reaction Profiles and Kinetics for Radical-Radical Hydrogen Abstraction via Multireference Coupled Cluster Theory

Radical-radical abstractions in hydrocarbon oxidation chemistry are disproportionation reactions that are generally exothermic with little or no barrier yet are underappreciated and poorly studied. Such challenging multireference electronic structure problems are tackled here using the recently developed state-specific multireference coupled cluster methods Mk-MRCCSD and Mk-MRCCSD(T), as well as the companion perturbation theory Mk-MRPT2 and the established MRCISD, MRCISD+Q, and CASPT2 approaches. Reaction paths are investigated for five prototypes involving radical-radical hydrogen abstraction: H + BeH → H₂+ Be, H + NH₂ → H₂ + NH, CH₃ + C₂H₅ → CH₄ + C₂H₄, H + C₂H₅ → H₂ + C₂H₄, and H + HCO → H₂ + CO. Full configuration interaction (FCI) benchmark computations for the H + BeH, H + NH₂, and H + HCO reactions prove that Mk-MRCCSD(T) provides superior accuracy for the interaction energies in the entrance channel, with mean absolute errors less than 0.3 kcal mol^-1 and percentage deviations less than 10% over the fragment separations of relevance to kinetics. To facilitate combustion studies, energetics for the CH₃ + C₂H₅, H + C₂H₅, and H + HCO reactions were computed at each level of theory with correlation-consistent basis sets (cc-pVXZ, X = T, Q, 5) and extrapolated to the complete basis set (CBS) limit. These CBS energies were coupled with CASPT2 projected vibrational frequencies along a minimum energy path to obtain rate constants for these three reactions. The rigorous Mk-MRCCSD(T)/CBS results demonstrate unequivocally that these three reactions proceed with no barrier in the entrance channel, contrary to some earlier predictions. Mk-MRCCSD(T) also reveals that the economical CASPT2 method performs well for large interfragment separations but may deteriorate substantially at shorter distances.

Potential Energy Surface for Large Barrierless Reaction Systems: Application to the Kinetic Calculations of the Dissociation of Alkanes and the Reverse Recombination Reactions

The isodesmic reaction method is applied to calculate the potential energy surface (PES) along the reaction coordinates and the rate constants of the barrierless reactions for unimolecular dissociation reactions of alkanes to form two alkyl radicals and their reverse recombination reactions. The reaction class is divided into 10 subclasses depending upon the type of carbon atoms in the reaction centers. A correction scheme based on isodesmic reaction theory is proposed to correct the PESs at UB3LYP/6-31+G(d,p) level. To validate the accuracy of this scheme, a comparison of the PESs at B3LYP level and the corrected PESs with the PESs at CASPT2/aug-cc-pVTZ level is performed for 13 representative reactions, and it is found that the deviations of the PESs at B3LYP level are up to 35.18 kcal/mol and are reduced to within 2 kcal/mol after correction, indicating that the PESs for barrierless reactions in a subclass can be calculated meaningfully accurately at a low level of ab initio method using our correction scheme. High-pressure limit rate constants and pressure dependent rate constants of these reactions are calculated based on their corrected PESs and the results show the pressure dependence of the rate constants cannot be ignored, especially at high temperatures. Furthermore, the impact of molecular size on the pressure-dependent rate constants of decomposition reactions of alkanes and their reverse reactions has been studied. The present work provides an effective method to generate meaningfully accurate PESs for large molecular system.

Theoretical Analysis of the Effect of C═C Double Bonds on the Low-Temperature Reactivity of Alkenylperoxy Radicals

Biodiesel contains a large proportion of unsaturated fatty acid methyl esters. Its combustion characteristics, especially its ignition behavior at low temperatures, have been greatly affected by these C═C double bonds. In this work, we performed a theoretical analysis of the effect of C═C double bonds on the low-temperature reactivity of alkenylperoxy radicals, the key intermediates from the low-temperature combustion of biodiesel. To understand how double bonds affect the fate of peroxy radicals, we selected three representative peroxy radicals from heptane, heptene, and heptadiene having zero, one, and two double C═C bonds, respectively, for study. The potential energy surfaces were explored at the CBS-QB3 level, and the reaction rate constants were computed using canonical/variational transition state theories. We have found that the double bond is responsible for the very different bond dissociation energies of the various types of C-H bonds, which in turn affect significantly the reaction kinetics of alkenylperoxy radicals.

Experimental and theoretical investigation of the self-reaction of phenyl radicals

A combination of experiment and theory is applied to the self-reaction kinetics of phenyl radicals. The dissociation of phenyl iodide is observed with both time-of-flight mass spectrometry, TOF-MS, and laser schlieren, LS, diagnostics coupled to a diaphragmless shock tube for temperatures ranging from 1276 to 1853 K. The LS experiments were performed at pressures of 22 +/- 2, 54 +/- 7, and 122 +/- 6 Torr, and the TOF-MS experiments were performed at pressures in the range 500-700 Torr. These observations are sensitive to both the dissociation of phenyl iodide and to the subsequent self-reaction of the phenyl radicals. The experimental observations indicate that both these reactions are more complicated than previously assumed. The phenyl iodide dissociation yields approximately 6% C(6)H(4) + HI in addition to the major and commonly assumed C(6)H(5) + I channel. The self-reaction of phenyl radicals does not proceed solely by recombination, but also through disproportionation to benzene + o-/m-/p-benzynes, with comparable rate coefficients for both. The various channels in the self-reaction of phenyl radicals are studied with ab initio transition state theory based master equation calculations. These calculations elucidate the complex nature of the C(6)H(5) self-reaction and are consistent with the experimental observations. The theoretical predictions are used as a guide in the development of a model for the phenyl iodide pyrolysis that accurately reproduces the observed laser schlieren profiles over the full range of the observations.

Ab initio methods for reactive potential surfaces

Case studies of ten reactions using a variety of standard electronic structure methods are presented. These case studies are used to illustrate the usefulness and shortcomings of these standard methods for various classes of reactions. Limited comparisons with experiment are made. The reactions studied include four radical-radical combinations, H + CH(3)--> CH(4), CH(3) + CH(3)--> C(2)H(6), H + HCO --> H(2)CO and CH(3) + HCO --> CH(3)CHO, three abstraction reactions, H + HO(2)--> H(2) + O(2), H + HCO --> H(2) + CO and CH(3) + HCO --> CH(4) + CO, a radical-molecule addition, H + HCCH --> C(2)H(3), and two molecular decompositions, H(2)CO --> H(2) + CO and CH(3)CHO --> CH(4) + CO. The electronic structure methods used are DFT, MP2, CCSD(T), QCISD(T), CASSCF, CASPT2, and CAS+1+2+QC.

Theoretical study on the methyl radical with chlorinated methyl radicals CH(3-n)Cln (n = 1, 2, 3) and CCl2

Radical-radical reactions involving chlorinated methyl radicals are particularly important in the mechanism of combustion of chlorinated hydrocarbons. Yet, they are usually difficult to study experimentally. In this paper, four chloride-related radical-radical reactions, i.e., CH3+CH(3-n)Cln (n = 1, 2, 3) and CH3+CCl2, are theoretically studied for the first time by means of the Gaussian-3//B3LYP potential energy surface survey combined with the master equation study over a wide range of temperatures and pressures. Our calculated results show that the three CH3+CH(3-n)Cln reactions can barrierlessly generate the former two kinetically allowed products P1 H(2)C=C(H)(3-n)Cl(n-1)+HCl and P2 CH3CH(3-n)Cl(n-1)+Cl with the very high predominance of P1 over P2. For the CH3 reaction with the biradical CCl2, which inevitably takes place during the CH3+CCl3 reaction and yet has never been studied experimentally or theoretically, H(2)C=CCl2+H and H(2)C=C(H)Cl+Cl are predicted to be the respective major and minor products. The results are compared with the recent laser photolysis/photoionization mass spectroscopy study on the CH3+CH(3-n)Cln (n = 1, 2, 3) reactions. The predicted rate constants and product branching ratios of the CH3+CCl2 reaction await future experimental verification.

Effects of Chain Length on the Rates of C−C Bond Dissociation in Linear Alkanes and Polyethylene

Molecular dynamics modeling of C-C bond dissociation is performed for a series of linear alkanes and polyethylene macromolecules with the chain lengths ranging from one to a thousand constituent ethylene monomers (PE-1-PE-1000). The rate constants obtained in molecular dynamics calculations are compared with those determined using variational transition state theory with the same potential energy surface. The results of simulations demonstrate a significant accelerating effect of chain length on the rates of C-C bond scission. Per-bond rate constant values increase with the increasing chain length, up to an order of magnitude, in the sequence of linear alkanes from PE-1 (ethane) to PE-5 (decane); this dependence becomes saturated for longer chain lengths. Stiffening the potentials of bending and especially the torsional degrees of freedom diminishes the accelerating effect of chain length, while constraining the bond distances for all C-C bonds except the one undergoing dissociation has no effect. The results of the calculations are compared with existing experimental data on the dependences of the rates of thermal decomposition of linear alkanes on the alkane chain length.

Theory, measurements, and modeling of OH and HO2 formation in the reaction of cyclohexyl radicals with O2

The production of OH and HO(2) in Cl-initiated oxidation of cyclohexane has been measured using pulsed-laser photolytic initiation and continuous-laser absorption detection. The experimental data are modeled by master equation calculations that employ new G2(MP2)-like ab initio characterizations of important stationary points on the cyclo-C(6)H(11)O(2) surface. These ab initio calculations are a substantial expansion on previously published characterizations, including explicit consideration of conformational changes (chair-boat, axial-equatorial) and torsional potentials. The rate constants for the decomposition and ring-opening of cyclohexyl radical are also computed with ab initio based transition state theory calculations. Comparison of kinetic simulations based on the master equation results with the present experimental data and with literature determinations of branching fractions suggests adjustment of several transition state energies below their ab initio values. Simulations with the adjusted values agree well with the body of experimental data. The results once again emphasize the importance of both direct and indirect components of the kinetics for the production of both HO(2) and OH in radical + O(2) reactions.

Long-range transition state theory

The implementation of variational transition state theory (VTST) for long-range asymptotic potential forms is considered, with particular emphasis on the energy and total angular momentum resolved (microJ-VTST) implementation. A long-range transition state approximation yields a remarkably simple and universal description of the kinetics of reactions governed by long-range interactions. The resulting (microJ-VTST) implementation is shown to yield capture-rate coefficients that compare favorably with those from trajectory simulations (deviating by less than 10%) for a wide variety of neutral and ionic long-range potential forms. Simple analytic results are derived for many of these cases. A brief comparison with a variety of low-temperature experimental studies illustrates the power of this approach as an analysis tool. The present VTST approach allows for a simple analysis of the applicability conditions for some related theoretical approaches. It also provides an estimate of the temperature or energy at which the "long-range transition state" moves to such short separations that short-range effects, such as chemical bonding, steric repulsion, and electronic state selectivity, must be considered.

On Modeling the Pressure-dependent Photoisomerization of trans-Stilbene by Including Slow Intramolecular Vibrational Energy Redistribution

Experimental data for the photoisomerization of trans-stilbene (S(1)) in thermal bath gases at pressures up to 20 bar obtained previously by Meyer, Schroeder, and Troe (J. Phys. Chem. A 1999, 103, 10528-10539) are modeled by using a full collisional-reaction master equation that includes non-RRKM (Rice-Ramsperger-Kassel-Marcus) effects due to slow intramolecular vibrational energy redistribution (IVR). The slow IVR effects are modeled by incorporating the theoretical results obtained recently by Leitner et al. (J. Phys. Chem. A 2003, 107, 10706-10716), who used the local random matrix theory. The present results show that the experimental rate constants of Meyer et al. are described to within about a factor of 2 over much of the experimental pressure range. However, a number of assumptions and areas of disagreement will require further investigation. These include a discrepancy between the calculated and experimental thermal rate constants near zero pressure, a leveling off of the experimental rate constants that is not predicted by theory and which depends on the identity of the collider gas, the need to use rate constants for collision-induced IVR that are larger than the estimated total collision rate constants, and the choice of barrier-crossing frequency. Despite these unsettled issues, the theory of Leitner et al. shows great promise for accounting for possible non-RRKM effects in an important class of reactions.

Predictive theory for the combination kinetics of two alkyl radicals

An ab initio transition state theory based procedure for accurately predicting the combination kinetics of two alkyl radicals is described. This procedure employs direct evaluations of the orientation dependent interaction energies at the CASPT2/cc-pvdz level within variable reaction coordinate transition state theory (VRC-TST). One-dimensional corrections to these energies are obtained from CAS+1+2/aug-cc-pvtz calculations for CH3 + CH3 along its combination reaction path. Direct CAS+1+2/aug-cc-pvtz calculations demonstrate that, at least for the purpose of predicting the kinetics, the corrected CASPT2/cc-pvdz potential energy surface is an accurate approximation to the CAS+1+2/aug-cc-pvtz surface. Furthermore, direct trajectory simulations, performed at the B3LYP/6-31G* level, indicate that there is little local recrossing of the optimal VRC transition state dividing surface. The corrected CASPT2/cc-pvdz potential is employed in obtaining direct VRC-TST kinetic predictions for the self and cross combinations of methyl, ethyl, iso-propyl, and tert-butyl radicals. Comparisons with experiment suggest that the present dynamically corrected VRC-TST approach provides quantitatively accurate predictions for the capture rate. Each additional methyl substituent adjacent to a radical site is found to reduce the rate coefficient by about a factor of two. In each instance, the rate coefficients are predicted to decrease quite substantially with increasing temperature, with the more sterically hindered reactants having a more rapid decrease. The simple geometric mean rule, relating the capture rate for the cross reaction to those for the self-reactions, is in remarkably good agreement with the more detailed predictions. With suitable generalizations the present approach should be applicable to a wide array of radical-radical combination reactions.

Determination of the Rate Constant for the Radical−Radical Reaction NCO(X2Π) + CH3(X2A2‘ ‘) at 293 K and an Estimate of Possible Product Channels

The rate constant for the reaction of the cyanato radical, NCO(X2Pi), with the methyl radical, CH3(X2A2' '), has been measured to be (2.1 +/- 1.3(-0.80)) x 10(-10) cm3 molecule(-1) s(-1), where the uncertainty includes both random and systematic errors at the 68% confidence level. The measurements were conducted over a pressure range of 2.8-4.3 Torr of CH4 and at a temperature of 293 +/- 2 K. The radicals were generated by the 248-nm photolysis of ClNCO in a large excess of CH4. The subsequent rapid reaction, Cl + CH4, generated the CH3 radical. The rate constant for the Cl + CH4 reaction was measured to be (9.2 +/- 0.2) x 10(-14) cm3 molecule(-1) s(-1), where the uncertainty is the scatter of one standard deviation in the data. The progress of the reaction was followed by time-resolved infrared absorption spectroscopy on single rovibrational transitions from the ground vibrational level. Multiple species were detected in these experiments, including NCO, CH3, HCl, C2H6, HCN, HNC, NH, and HNCO. Temporal concentration profiles of the observed species were simulated using a kinetic model, and rate constants were determined by minimizing the sum of the squares of the residuals between experimental observations and model calculations. Both HCN and HNC seem to be minor products (<0.3% each) of the NCO + CH3 reaction. The peak concentrations of NH and HNCO were small, accounting for <1% of the initial NCO concentration; however, their temporal profiles could not be fit by the model kinetics. The observed C2H6 temporal profile always peaked at significantly higher concentrations than the model predictions, and several reaction models were constructed to help explain these observations. The most likely product channel seems to be the recombination channels, producing CH3NCO and CH3OCN.

Product Study of the Reaction of CH3 with OH Radicals at Low Pressures and Temperatures of 300 and 612 K†

The product distribution for the title reaction was studied using our time-of-flight mass spectrometer (TOFMS) connected to a tubular flow reactor. The methyl and hydroxyl radicals were produced by an excimer laser pulse (lambda = 193 nm) photolyzing acetone and nitrous oxide in the presence of excess water or hydrogen. Helium was used as the bath gas; the total density was held constant at 1.2 x 10(17) cm(-3). At 300 K the observations were consistent with singlet methylene ((1)CH(2)) and water as the main product channel with a small contribution of methanol. In contrast, at about 610 K three channels-formaldehyde isomers and methanol in addition to (1)CH(2) + H(2)O-are formed with similar yields. When acetone-d(6) was used, the production of both CHDO and CD(2)O was observed, indicating that two different formaldehyde-producing channels are operating simultaneously. These experimental results are compared with RRKM and master equation calculations on the basis of the properties of the methanol potential energy surface from a recent ab initio study.