State Theory Based Master Equation Research Articles

On the decomposition mechanism of propanal: rate constants evaluation and kinetic simulations

The reactivity of aldehydes has been the subject of considerable interest in chemical kinetics, with propanal often chosen as the representative species. Despite its relevance, the reactivity of propanal is currently estimated from analogy and fitting of experimental data measured in limited temperature and pressure ranges, while the few literature theoretical studies have focused more on the exploration the potential energy surface (PES) than on the estimation of rate constants. The purpose of this work is to reinvestigate the propanal decomposition kinetics using the ab initio transition state theory based master equation approach with the intent of: (1) Determining accurate rate constants of key reaction channels; (2) Updating and validating an existing kinetic model by simulating available experimental data on propanal pyrolysis. It is found that propanal decomposition at the initial stages of pyrolysis occurs through four unimolecular barrierless reactions to form CHO + C2H5, CH2CHO + CH3, CH3CHCHO + H, and CH3CH2CO + H, and a termolecular pathway leading to the formation of C2H4 + CO + H2. High pressure rate constants were determined for each barrierless reaction channel using Variable Reaction Coordinate Transition State Theory and used to estimate phenomenological temperature and pressure dependent channel specific rate constants integrating the 1 dimensional master equation over the whole PES. The decomposition rate constants so determined are in agreement with the few available experimental data and significantly faster than previous literature estimates. The estimated kinetic parameters were finally implemented into the CRECK kinetic mechanism, leading to an improved agreement with shock tube pyrolysis data from the literature.

Advancing chemical kinetic modeling

Chemical Engineering Quantitative prediction of the time evolution of chemical mixtures is the central problem of reactive chemical engineering. This is a challenging task because of the thousands of elementary chemical reactions that must be considered in chemical kinetic modeling. Usually, such models are developed and refined gradually over many years. Using broadband rotational spectroscopy, combined with automated ab initio transition state theory–based master equation calculations and high-level thermochemical parametrization, Zaleski et al. reveal an important role of a variety of radical substitution reactions in the flash pyrolysis of acetone that was previously omitted in the corresponding combustion mechanisms. Their unified combination of modeling, experiment, and theory is a promising approach in the development of comprehensive chemical kinetic models. J. Am. Chem. Soc. 143 , 3124 (2021).

Theory and modeling of relevance to prompt-NO formation at high pressure

An improved understanding of NOx formation at high pressures would be of considerable utility to efforts to develop advanced combustion devices. A combination of theoretical and modeling studies are implemented in an effort to improve the accuracy of models for the prompt NO process, which is the dominant source of NO under many conditions, and to improve our understanding of the role of this process at high pressures. The theoretical effort implements state-of-the-art treatments of NCN thermochemistry, the interrelated CH + N2 and NCN + H kinetics, and the kinetics of the NCN + OH reaction. For both reaction systems, we implement high level ab initio transition state theory based master equation simulations paying particular attention to the role of stabilization processes. For the NCN + H kinetics we include a treatment of inter-system crossing. The modeling effort focuses on exploring the role of pressure and prompt NO for premixed laminar flames at pressures ranging from 1 to 15 atm, via a comparison with the available experimental data. Additional simulations at higher pressures further explore the mechanistic changes at the pressures of relevance to applied combustion devices (e.g., 100 atm).

Theoretical kinetics of O + C2H4

The reaction of atomic oxygen with ethylene is a fundamental oxidation step in combustion and is prototypical of reactions in which oxygen adds to double bonds. For 3O+C2H4 and for this class of reactions generally, decomposition of the initial adduct via spin-allowed reaction channels on the triplet surface competes with intersystem crossing (ISC) and a set of spin-forbidden reaction channels on the ground-state singlet surface. The two surfaces share some bimolecular products but feature different intermediates, pathways, and transition states. The overall product branching is therefore a sensitive function of the ISC rate. The 3O+C2H4 reaction has been extensively studied, but previous experimental work has not provided detailed branching information at elevated temperatures, while previous theoretical studies have employed empirical treatments of ISC. Here we predict the kinetics of 3O+C2H4 using an ab initio transition state theory based master equation (AITSTME) approach that includes an a priori description of ISC. Specifically, the ISC rate is calculated using Landau–Zener statistical theory, consideration of the four lowest-energy electronic states, and a direct classical trajectory study of the product branching immediately after ISC. The present theoretical results are largely in good agreement with existing low-temperature experimental kinetics and molecular beam studies. Good agreement is also found with past theoretical work, with the notable exception of the predicted product branching at elevated temperatures. Above ∼1000K, we predict CH2CHO+H and CH2+CH2O as the major products, which differs from the room temperature preference for CH3+HCO (which is assumed to remain at higher temperatures in some models) and from the prediction of a previous detailed master equation study.

Low Temperature Kinetics of the First Steps of Water Cluster Formation.

We present a combined experimental and theoretical low temperature kinetic study of water cluster formation. Water cluster growth takes place in low temperature (23-69K) supersonic flows. The observed kinetics of formation of water clusters are reproduced with a kinetic model based on theoretical predictions for the first steps of clusterization. The temperature- and pressure-dependent association and dissociation rate coefficients are predicted with an abinitio transition state theory based master equation approach over a wide range of temperatures (20-100K) and pressures (10^{-6}-10 bar).

Uncertainty propagation in the derivation of phenomenological rate coefficients from theory: A case study of n-propyl radical oxidation

Global uncertainty and sensitivity analysis is used to study the propagation of uncertainties in fundamental theoretical parameters through to uncertainties in the predicted temperature and pressure dependent phenomenological rate coefficients. Predictions are obtained from ab initio transition state theory based master equation calculations. The fundamental parameters for these rate predictions include barrier heights, well depths, vibrational frequencies, collision frequency, and energy transfer parameters. A random sampling high-dimensional model representation (HDMR) approach is used to perform the global sensitivity analysis. This approach determines the predicted distributions of the phenomenological rate coefficients based on a quasi-random sample of the fundamental parameters within their uncertainty range. Sensitivity analysis then identifies the main parameters which contribute to variance in the predicted distributions. Here the approach is applied to a study of the oxidation of the propyl radical, employing the parameters derived in our recent theoretical study. We find rates at 3σ variances that typically differ from the most frequent values by factors of 4–6, with the uncertainties decreasing with increasing temperature. For the well skipping reactions there are more parameters that contribute significantly to the variance, the second-order sensitivities are greater, and the uncertainties increased with increasing pressure. For the other reactions, the uncertainties tend to decrease with increasing pressure.

Shock Tube Explorations of Roaming Radical Mechanisms: The Decompositions of Isobutane and Neopentane

The thermal decompositions of isobutane and neopentane have been studied using both shock tube experiments and ab initio transition state theory based master equation calculations. Dissociation rate constants for these molecules have been measured at high temperatures (1260-1566 K) behind reflected shock waves using high-sensitivity H-ARAS detection. The two major dissociation channels at high temperature are iso-C(4)H(10) → CH(3) + i-C(3)H(7) (1a) and neo-C(5)H(12) → CH(3) + t-C(4)H(9) (2a). Ultrahigh-sensitivity ARAS detection of H-atoms produced from the rapid decomposition of the product radicals, i-C(3)H(7) in (1a) and t-C(4)H(9) in (2a), through i-C(3)H(7) + M → H + C(3)H(6) + M (3a) and t-C(4)H(9) + M → H + i-C(4)H(8) + M (4a) allowed measurements of both the total decomposition rate constants, k(total), and the branching to radical products, which were observed to be equivalent in both systems, k(1a)/k(total) and k(2a)/k(total) = 0.79 ± 0.05. Theoretical analyses indicate that in isobutane, the non-H-atom fraction has two contributions, the dominant fraction being due to the roaming radical mechanism leading to molecular products through iso-C(4)H(10) → CH(4) + C(3)H(6) (1b) with k(1b)/k(total) = 0.16, and a minor fraction that involves the isomerization of i-C(3)H(7) to n-C(3)H(7) that then subsequently forms methyl radicals, i-C(3)H(7) + M → n-C(3)H(7) + M → CH(3) + C(2)H(4) + M (3b). In contrast to isobutane, in neopentane, the contribution to the non-H-atom fraction is exclusively through the roaming radical mechanism that leads to neo-C(5)H(12) → CH(4) + i-C(4)H(8) (2b) with k(2b)/k(total) = 0.21. These quantitative measurements of larger contributions from the roaming mechanism for larger molecules are in agreement with the qualitative theoretical arguments that suggest long-range dispersion interactions (which become increasingly important for larger molecules) may enhance roaming.

Roaming radicals in the thermal decomposition of dimethyl ether: Experiment and theory

The thermal dissociation of dimethyl ether has been studied with a combination of reflected shock tube experiments and ab initio dynamics simulations coupled with transition state theory based master equation calculations. The experiments use the extraordinary sensitivity provided by H-atom ARAS detection with an unreversed light source to measure both the total decomposition rate and the branching to radical products versus molecular products, with the molecular products arising predominantly through roaming according to the theoretical analysis. The experimental observations also provide a measure of the rate coefficient for H + CH 3OCH 3. An evaluation of the available experimental results for H + CH 3OCH 3 can be expressed by a three parameter Arrhenius expression as, k = 6.54 × 10 - 24 T 4.13 exp ( - 896 / T ) cm 3 molecule - 1 s - 1 ( 273 - 1465 K ) The potential energy surface is explored with high level ab initio electronic structure theory. The dynamics of roaming versus radical formation is studied with a reduced dimensional trajectory approach. The requisite potential energy surface is obtained from an interpolative moving least squares fit to wide-ranging ab initio data for the long-range interactions between methyl and methoxy. The predicted roaming and radical micro-canonical fluxes are incorporated in a master equation treatment of the temperature and pressure dependence of the dissociation process. The tight (i.e., non-roaming) transition states leading to a variety of additional molecular fragments are also included in the master equation analysis, but are predicted to have a negligible contribution to product formation. The final theoretical results reliably reproduce the measured dissociation rate to radical products reported here and are well reproduced over the 500–2000 K temperature range and the 0.01–300 bar pressure range by the following modified Arrhenius parameters for the Troe falloff format: k 1 , ∞ ( T ) = 2.33 × 10 19 T - 0.661 exp ( - 42345 / T ) s - 1 k 1 , 0 ( T ) = 2.86 × 10 35 T - 11.4 exp ( - 46953 / T ) cm 3 molecule - 1 s - 1 F cent ( T ) = exp ( - T / 880 ) The experimentally observed branching ratio of 0.19 ± 0.07 provides a direct measure of the contribution from the roaming radical mechanism. The theoretical analysis predicts a much smaller roaming contribution of 0.02.

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.

An experimental and theoretical high temperature kinetic study of the thermal unimolecular dissociation of fluoroethane

The thermal dissociation of fluoroethane has been studied using shock tube (ST)/time-of-flight mass spectrometry (TOF-MS) at 500 and 1200 Torr over the temperature range 1200-1550 K. The ST/TOF-MS experiments confirm that elimination of HF is the only reaction channel and rate coefficients for this reaction were extracted from concentration/time profiles derived from the mass spectra. Results from a novel diaphragmless shock tube coupled to the TOF-MS are also presented and demonstrate the unique ability of this apparatus to generate sufficiently reproducible shock waves that signal averaging can be performed over multiple experiments; something that is not possible with a conventional shock tube. The dissociation is also studied with ab initio transition state theory based master equation simulations. A modest increase in the calculated barrier height (i.e., by 1 kcal mol(-1)) yields predicted high pressure rate coefficients that are in good agreement with the existing literature data. The present pressure dependent observations are accurately reproduced for a downwards energy transfer for neon at 1200 to 1500 K of approximately 270 cm(-1), which is somewhat smaller than that found in previous studies on fluorinated ethanes with the same bath gases.

Resolving the mystery of prompt CO 2: The HCCO+O 2 reaction

The potential energy surface for the reaction of the ketenyl radical (HCCO) with O 2 is characterized with a combination of density functional. Moller Plesset perturbation and coupled cluster theories. Trajectory simulations, employing directly determined density functional force fields are used to explore the mechanism further. Variational transition state theory based master equation simulations, implementing the quantum, chemically determined molecular properties, provide estimated product state distributions and rate constants. For all temperatures considered here (300–2500 K), the dominant products are CO 2 +CO+H independent of pressure up to 100 atm, thereby explaining the coincident formation of CO 2 and CO in the oxidation of acetylene. These products arise primarily from the decomposition of the initial OOCHCO adduct via the formation of a four-membered OCCO ring, followed by, in succession, the splitting of the OO, the CC, and the CH bonds. At low temperatures, the modest barrier in the entrance channel, which arises from the need to break the, resonances in the reactants prior to bond formation, provides the rate-limiting transition state. A variational treatment of this transition state reduces the calculated rate coefficient relative to conventional transition state theory by ≈35%. At higher tempratures, the formation of the four-membered ring becomes a rate-limiting step, even though this process is essentially barrierless. An OCHCO+O channel becomes increasingly important with increasing temeprature, but still contributes only about 10% at 2500 K. The direct dynamics simulations indicate that various H transfers may occur during the final dissociation, steps, primarily to yield CO+CO+OH with an overall branching ratio of about 9%. A downward adjustment by 3.2 kcal/mol of the HCCO+O 2 entrance barrier results in total rate coefficients that are in good agreement with experiment. The predicted channel-specific rate coefficients are then 7.94×10 −12 T −0.142 exp(−1150/ RT )(CO 2 +CO+H), 3.62×10 −22 T 269 exp(−3541/ RT )(OCHCO+O) and 3.17×10 −13 T −0.020 exp(−1023/ RT )(CO+CO+OH) cm 3 molecule −1 s −1 , where R =1.987 cal mol −1 K −1 .