Collision Efficiency of Water in the Unimolecular Reaction CH4 (+H2O) ⇆ CH3 + H (+H2O): One-Dimensional and Two-Dimensional Solutions of the Low-Pressure-Limit Master Equation

Mixed quantum/classical theory (MQCT) approach to the dynamics of molecule-molecule collisions in complex systems

We developed a general theoretical approach and a user-ready computer code that permit study of the dynamics of collisional energy transfer and ro-vibrational energy exchange in complex molecule-molecule collisions. The method is a mixture of classical and quantum mechanics. The internal ro-vibrational motion of collision partners is treated quantum mechanically using a time-dependent Schrödinger equation that captures many quantum phenomena including state quantization and zero-point energy, propensity and selection rules for state-to-state transitions, quantum symmetry and interference phenomena. A significant numerical speed up is obtained by describing the translational motion of collision partners classically, using the Ehrenfest mean-field trajectory approach. Within this framework a family of approximate methods for collision dynamics is developed. Several benchmark studies for diatomic and triatomic molecules, such as H2O and ND3 collided with He, H2 and D2, show that the results of MQCT are in good agreement with full-quantum calculations in a broad range of energies, especially at high collision energies where they become nearly identical to the full quantum results. Numerical efficiency of the method and massive parallelism of the MQCT code permit us to embrace some of the most complicated collisional systems ever studied, such as C6H6 + He, CH3COOH + He and H2O + H2O. Application of MQCT to the collisions of chiral molecules such as CH3CHCH2O + He, and to molecule-surface collisions is also possible and will be pursued in the future.

Mechanism of Thermal Decomposition of Hydroxyacetone: A Flash Pyrolysis Vacuum Ultraviolet Photoionization Time-of-Flight Mass Spectrometry and Density Functional Theory Study

The thermal decomposition mechanism of hydroxyacetone from 850 to 1390 K was examined by using flash pyrolysis vacuum ultraviolet photoionization time-of-flight mass spectrometry combined with density functional theory calculation. The results showed that keto-enol tautomerisms could occur prior to the thermal decomposition of hydroxyacetone. The decomposition pathways of hydroxyacetone and its isomer, 2-hydroxypropanal were characterized. The thermal decomposition reactions started at about 950 K. The homolysis reactions related to the cleavage of the CCO-CCOH bond of hydroxyacetone and 2-hydroxypropanal, as well as CH3 loss of hydroxyacetone, dominated the initial decomposition reactions. The subsequent decompositions of the radical intermediates generated by the initial homolysis decompositions were the major secondary decomposition reactions. The formation pathways of small molecules, such as H2, CH4, H2O, and HCHO, were proposed to proceed via molecular elimination reactions facilitated by the active α-H atoms. These elimination reactions were not negligible at high temperatures above 1230 K.

Thermal Decomposition Mechanism of Tetraethylsilane by Flash Pyrolysis Vacuum Ultraviolet Photoionization Mass Spectrometry and DFT Calculations: The Competition between β-Hydride Elimination and Bond Homolysis

Thermal decomposition of tetraethylsilane was investigated at temperatures up to 1330 K using flash pyrolysis vacuum ultraviolet photoionization mass spectrometry. Density functional theory and transition state theory calculations were performed to corroborate the experimental observations. Both experimental and theoretical evidence showed that the pyrolysis of tetraethylsilane was initiated by Si-C bond fission to the primary reaction products, triethylsilyl (SiEt₃) and ethyl radicals. In the secondary reactions of the triethylsilyl radical, at lower temperatures, the β-hydride elimination pathway (producing HSiEt₂) was found to be more favored than its competing reaction channel, Si-C bond fission (producing :SiEt₂); as the temperature further increased, the Si-C bond fission reaction became significant. Other important secondary reaction products, such as EtHSi═CH₂ (m/z = 72), H₂SiEt (m/z = 59), and SiH₃ (m/z = 31) were identified, and their formation mechanisms were also proposed.

Predicting third-body collision efficiencies for water and other polyatomic baths

Low-pressure-limit microcanonical (collisional activation) and thermal rate constants are predicted using a combination of automated ab initio potential energy surface construction, classical trajectories, transition state theory, and a detailed kinetic...

Permutationally Invariant Polynomial Expansions with Unrestricted Complexity

A general strategy is presented for constructing and validating permutationally invariant polynomial (PIP) expansions for chemical systems of any stoichiometry. Demonstrations are made for three categories of gas-phase dynamics and kinetics: collisional energy-transfer trajectories for predicting pressure-dependent kinetics, three-body collisions for describing transient van der Waals adducts relevant to atmospheric chemistry, and nonthermal reactivity via quasiclassical trajectories. In total, 30 systems are considered with up to 15 atoms and 39 degrees of freedom. Permutational invariance is enforced in PIP expansions with as many as 13 million terms and 13 permutationally distinct atom types by taking advantage of petascale computational resources. The quality of the PIP expansions is demonstrated through the systematic convergence of in-sample and out-of-sample errors with respect to both the number of training data and the order of the expansion, and these errors are shown to predict errors in the dynamics for both reactive and nonreactive applications. The parallelized code distributed as part of this work enables the automation of PIP generation for complex systems with multiple channels and flexible user-defined symmetry constraints and for automatically removing unphysical unconnected terms from the basis set expansions, all of which are required for simulating complex reactive systems.

Energy Dependence of Ensemble-Averaged Energy Transfer Moments and Its Effect on Competing Decomposition Reactions

We carried out a direct dynamics study on the internal-energy dependence of the ensemble-averaged energy transfer moments of the isobutyl radical in collisions with N₂ bath gas. We find a linear dependence of the downward moment ⟨ΔE_d⟩ and the root-mean-square moment ⟨ΔE2⟩ on the initial internal energy, but the upward moment ⟨ΔE_u⟩ is found to be independent of the molecule's internal energy. We improved the exponential-down relaxation model by including a linear dependence of ⟨ΔE_d⟩ on the initial energy, and we used the improved treatment in the 1D master equation for isobutyl radical decomposition reactions and for a model of competitive reactions with a larger difference in barrier heights. We calculated phenomenological rate constants and branching ratios from chemically significant eigenmodes of the master equation and showed that the energy dependence of ⟨ΔE_d⟩ has a greater influence on channels with higher barriers in competitive reactions. Rate constants and branching ratios from master equation calculations indicate that for a given temperature and pressure, there is a constant ⟨ΔE_d⟩ that can reproduce results obtained with an E-dependent ⟨ΔE_d⟩. But a constant ⟨ΔE_d⟩ cannot do this for all temperatures and pressures, with larger differences when the barriers for the competing channels differ more. We conclude that when the branching ratio of competitive reactions is sensitive to pressure, including the energy dependence of ⟨ΔE_d⟩ in master equation simulations can make a significant difference in the results.

On the Rate Constant for NH2+HO2 and Third-Body Collision Efficiencies for NH2+H(+M) and NH2+NH2(+M)

In low-temperature flash photolysis of NH₃/O₂/N₂ mixtures, the NH₂ consumption rate and the product distribution is controlled by the reactions NH₂ + HO₂ → products (R1), NH₂ + H (+M) → NH₃ (+M) (R2), and NH₂ + NH₂ (+M) → N₂H₄ (+M) (R3). In the present work, published flash photolysis experiments by, among others, Cheskis and co-workers, are re-interpreted using recent direct measurements of NH₂ + H (+N₂) and NH₂ + NH₂ (+N₂) from Altinay and Macdonald. To facilitate analysis of the FP data, relative third-body collision efficiencies compared to N₂ for R2 and R3 were calculated for O₂ and NH₃ as well as for other selected molecules. Results were in good agreement with the limited experimental data. Based on reported NH₂ decay rates in flash photolysis of NH₃/O₂/N₂, a rate constant for NH₂ + HO₂ → NH₃ + O₂ (R1a) of k_1a = 1.5(±0.5) × 10¹⁴ cm³ mol^-1 s^-1 at 295 K was derived. This value is higher than earlier determinations based on the FP results but in good agreement with recent theoretical work. Kinetic modeling of reported N₂O yields indicates that NH₂ + HO₂ → H₂NO + O (R1c) is competing with R1a, but perturbation experiments with addition of CH₄ indicate that it is not a dominating channel. Measured HNO profiles indicate that this component is formed directly by NH₂ + HO₂ → HNO + H₂O (R1b), but theoretical work indicates that R1b is only a minor channel. Based on this analysis, we estimate k_1c = 2.5 × 10¹³ cm³ mol^-1 s^-1 and k_1b = 2.5 × 10¹² cm³ mol^-1 s^-1 at 295 K, with significant uncertainty margins.

Modeling Collisional Transitions in Thermal Unimolecular Reactions: Successive Trajectories and Two-Dimensional Master Equation for Trifluoromethane Decomposition in an Argon Bath

Collisional transition processes in thermal unimolecular reactions are modeled by collision frequency, Z, and probability distribution function, P(E, J; E', J'), which describes the probabilities of collisional transitions from the initial state specified by the total energy and angular momentum, (E', J'), to the final states, (E, J). The validity of the collisional transition model, consisting of Z and P(E, J; E', J'), is assessed here for the title reaction. The present model and its parameters are derived from the moments of transition probabilities calculated by classical trajectory simulations. The model explicitly accounts for coupling between the energy and angular momentum transfer and the dependence of transition probability on the initial state. The performance of the model is evaluated by comparing the rate constants calculated by solving the two-dimensional master equation with those obtained from the classical trajectory calculations of the sequence of successive collisions. The rate constants are also compared with available experimental data. The present collisional transition model is found to perform fairly well for predicting the pressure-dependent rate constants. The uncertainty in the prediction and sensitivities of the rate constants to the model parameters are discussed. A simplified version of the model is proposed, which performs as well as the full model. The simplifications and robust procedures for calculating the model parameters are described.

Collision Efficiency Parameter Influence on Pressure-Dependent Rate Constant Calculations Using the SS-QRRK Theory

The system-specific quantum Rice-Ramsperger-Kassel (SS-QRRK) theory (J. Am. Chem. Soc. 2016, 138, 2690) is suitable to determine rate constants below the high-pressure limit. Its current implementation allows incorporating variational effects, multidimensional tunneling, and multistructural torsional anharmonicity in rate constant calculations. Master equation solvers offer a more rigorous approach to compute pressure-dependent rate constants, but several implementations available in the literature do not incorporate the aforementioned effects. However, the SS-QRRK theory coupled with a formulation of the modified strong collision model underestimates the value of unimolecular pressure-dependent rate constants in the high-temperature regime for reactions involving large molecules. This underestimation is a consequence of the definition for collision efficiency, which is part of the energy transfer model. Selection of the energy transfer model and its parameters constitutes a common issue in pressure-dependent calculations. To overcome this underestimation problem, we evaluated and implemented in a bespoke Python code two alternative definitions for the collision efficiency using the SS-QRRK theory and tested their performance by comparing the pressure-dependent rate constants with the Rice-Ramsperger-Kassel-Marcus/Master Equation (RRKM/ME) results. The modeled systems were the tautomerization of propen-2-ol and the decomposition of 1-propyl, 1-butyl, and 1-pentyl radicals. One of the tested definitions, which Dean et al. explicitly derived (Z. Phys. Chem. 2000, 214, 1533), corrected the underestimation of the pressure-dependent rate constants and, in addition, qualitatively reproduced the trend of RRKM/ME data. Therefore, the used SS-QRRK theory with accurate definitions for the collision efficiency can yield results that are in agreement with those from more sophisticated methodologies such as RRKM/ME.

Pressure-Dependent Kinetics of the Reaction between CH3OO and OH Focusing on the Product Yield of Methyltrioxide (CH3OOOH)

The reaction kinetics of methyl peroxy radical (CH₃OO) and hydroxyl radical (OH) has attracted an increasing level of interest in the past decade, while the branching yields of various product channels are still under debate. In this work, a comprehensive theoretical effort was made to investigate the branching yield of the stabilized methyltrioxide (CH₃OOOH, TRIOX) adduct, which has recently been a research focus. Our computed branching ratio of TRIOX at 298 K and 760 Torr is ∼0.04, in agreement with the result of multiplexed photoionization mass spectrometry. We show that the large branching yield obtained in an early theoretical study mainly originated from the collision-induced strong stabilization presented in their simulation. Our findings clarify the controversial product yield results for this important species in recent studies. The computed rate constants over wide temperature and pressure ranges allow better integration of this reaction into global atmospheric models and low-temperature combustion kinetic models.

Nonthermal rate constants for CH4 * + X → CH3 + HX, X = H, O, OH, and O2

Quasiclassical trajectories are used to compute nonthermal rate constants, k^*, for abstraction reactions involving highly-excited methane CH₄ ^* and the radicals H, O, OH, and O₂. Several temperatures and internal energies of methane, E_vib, are considered, and significant nonthermal rate enhancements for large E_vib are found. Specifically, when CH₄ ^* is internally excited close to its dissociation threshold (E_vib ≈ D₀ = 104 kcal/mol), its reactivity with H, O, and OH is shown to be collision-rate-limited and to approach that of comparably-sized radicals, such as CH₃, with k^* > 10^-10 cm³ molecule^-1 s^-1. Rate constants this large are more typically associated with barrierless reactions, and at 1000 K, this represents a nonthermal rate enhancement, k^*/k, of more than two orders of magnitude relative to thermal rate constants k. We show that large nonthermal rate constants persist even after significant internal cooling, with k^*/k > 10 down to E_vib ≈ D₀/4. The competition between collisional cooling and nonthermal reactivity is studied using a simple model, and nonthermal reactions are shown to account for up to 35%-50% of the fate of the products of H + CH₃ = CH₄ ^* under conditions of practical relevance to combustion. Finally, the accuracy of an effective temperature model for estimating k^* from k is quantified.

Collision Frequency for Energy Transfer in Unimolecular Reactions

Pressure dependence of unimolecular reaction rates is governed by the energy transfer in collisions of reactants with bath gas molecules. Pressure-dependent rate constants can be theoretically determined by solving master equations for unimolecular reactions. In general, master equation formulations describe energy transfer processes using a collision frequency and a probability distribution model of the energy transferred per collision. The present study proposes a novel method for determining the collision frequency from the results of classical trajectory calculations. Classical trajectories for collisions of several polyatomic molecules (ethane, methane, tetrafluoromethane, and cyclohexane) with monatomic colliders (Ar, Kr, and Xe) were calculated on potential energy surfaces described by the third-order density-functional tight-binding method in combination with simple pairwise interaction potentials. Low-order (including non-integer-order) moments of the energy transferred in deactivating collisions were extracted from the trajectories and compared with those derived using some probability distribution models. The comparison demonstrates the inadequacy of the conventional Lennard-Jones collision model for representing the collision frequency and suggests a robust method for evaluating the collision frequency that is consistent with a given probability distribution model, such as the exponential-down model. The resulting collision frequencies for the exponential-down model are substantially higher than the Lennard-Jones collision frequencies and are close to the (hypothetical) capture rate constants for dispersion interactions. The practical adequacy of the exponential-down model is also briefly discussed.

Predicting pressure-dependent unimolecular rate constants using variational transition state theory with multidimensional tunneling combined with system-specific quantum RRK theory: a definitive test for fluoroform dissociation

Understanding the falloff in rate constants of gas-phase unimolecular reaction rate constants as the pressure is lowered is a fundamental problem in chemical kinetics, with practical importance for combustion, atmospheric chemistry, and essentially all gas-phase reaction mechanisms. In the present work, we use our recently developed system-specific quantum RRK theory, calibrated by canonical variational transition state theory with small-curvature tunneling, combined with the Lindemann-Hinshelwood mechanism, to model the dissociation reaction of fluoroform (CHF3), which provides a definitive test for falloff modeling. Our predicted pressure-dependent thermal rate constants are in excellent agreement with experimental values over a wide range of pressures and temperatures. The present validation of our methodology, which is able to include variational transition state effects, multidimensional tunneling based on the directly calculated potential energy surface along the tunneling path, and torsional and other vibrational anharmonicity, together with state-of-the-art reaction-path-based direct dynamics calculations, is important because the method is less empirical than models routinely used for generating full mechanisms, while also being simpler in key respects than full master equation treatments and the full reduced falloff curve and modified strong collision methods of Troe.

Nonmonotonic Temperature Dependence of the Pressure-Dependent Reaction Rate Constant and Kinetic Isotope Effect of Hydrogen Radical Reaction with Benzene Calculated by Variational Transition-State Theory

The reaction between H and benzene is a prototype for reactions of radicals with aromatic hydrocarbons. Here we report calculations of the reaction rate constants and the branching ratios of the two channels of the reaction (H addition and H abstraction) over a wide temperature and pressure range. Our calculations, obtained with an accurate potential energy surface, are based on variational transition-state theory for the high-pressure limit of the addition reaction and for the abstraction reaction and on system-specific quantum Rice-Ramsperger-Kassel theory calibrated by variational transition-state theory for pressure effects on the addition reaction. The latter is a very convenient way to include variational effects, corner-cutting tunneling, and anharmonicity in falloff calculations. Our results are in very good agreement with the limited experimental data and show the importance of including pressure effects in the temperature interval where the mechanism changes from addition to abstraction. We found a negative temperature effect of the total reaction rate constants at 1 atm pressure in the temperature region where experimental data are missing and accurate theoretical data were previously missing as well. We also calculated the H + C₆H₆/C₆D₆ and D + C₆H₆/C₆D₆ kinetic isotope effects, and we compared our H + C₆H₆ results to previous theoretical data for H + toluene. We report a very novel nonmonotonic dependence of the kinetic isotope effect on temperature. A particularly striking effect is the prediction of a negative temperature dependence of the total rate constant over 300-500 K wide temperature ranges, depending on the pressure but generally in the range from 600 to 1700 K, which includes the temperature range of ignition in gasoline engines, which is important because aromatics are important components of common fuels.

Variational transition state theory: theoretical framework and recent developments

This article reviews the fundamentals of variational transition state theory (VTST), its recent theoretical development, and some modern applications.

Kinetics of Hydrogen Radical Reactions with Toluene Including Chemical Activation Theory Employing System-Specific Quantum RRK Theory Calibrated by Variational Transition State Theory

Pressure-dependent reactions are ubiquitous in combustion and atmospheric chemistry. We employ a new calibration procedure for quantum Rice-Ramsperger-Kassel (QRRK) unimolecular rate theory within a chemical activation mechanism to calculate the pressure-falloff effect of a radical association with an aromatic ring. The new theoretical framework is applied to the reaction of H with toluene, which is a prototypical reaction in the combustion chemistry of aromatic hydrocarbons present in most fuels. Both the hydrogen abstraction reactions and the hydrogen addition reactions are calculated. Our system-specific (SS) QRRK approach is adjusted with SS parameters to agree with multistructural canonical variational transition state theory with multidimensional tunneling (MS-CVT/SCT) at the high-pressure limit. The new method avoids the need for the usual empirical estimations of the QRRK parameters, and it eliminates the need for variational transition state theory calculations as a function of energy, although in this first application we do validate the falloff curves by comparing SS-QRRK results without tunneling to multistructural microcanonical variational transition state theory (MS-μVT) rate constants without tunneling. At low temperatures, the two approaches agree well with each other, but at high temperatures, SS-QRRK tends to overestimate falloff slightly. We also show that the variational effect is important in computing the energy-resolved rate constants. Multiple-structure anharmonicity, torsional-potential anharmonicity, and high-frequency-mode vibrational anharmonicity are all included in the rate computations, and torsional anharmonicity effects on the density of states are investigated. Branching fractions, which are both temperature- and pressure-dependent (and for which only limited data is available from experiment), are predicted as a function of pressure.

Silane-initiated nucleation in chemically active plasmas: validation of density functionals, mechanisms, and pressure-dependent variational transition state calculations

Pressure-dependent rate constants for nucleation in nanodusty plasmas are calculated by variational transition state theory with system-specific quantum RRK theory.

Kinetics of Propargyl Radical Dissociation

Due to the prominent role of the propargyl radical for hydrocarbon growth within combustion environments, it is important to understand the kinetics of its formation and loss. The ab initio transition state theory-based master equation method is used to obtain theoretical kinetic predictions for the temperature and pressure dependence of the thermal decomposition of propargyl, which may be its primary loss channel under some conditions. The potential energy surface for the decomposition of propargyl is first mapped at a high level of theory with a combination of coupled cluster and multireference perturbation calculations. Variational transition state theory is then used to predict the microcanonical rate coefficients, which are subsequently implemented within the multiple-well multiple-channel master equation. A variety of energy transfer parameters are considered, and the sensitivity of the thermal rate predictions to these parameters is explored. The predictions for the thermal decomposition rate coefficient are found to be in good agreement with the limited experimental data. Modified Arrhenius representations of the rate constants are reported for utility in combustion modeling.

“Plug and play” full-dimensional ab initio potential energy and dipole moment surfaces and anharmonic vibrational analysis for CH4–H2O

The first full-dimensional potential energy surface of CH₄–H₂O dimer is presented, and vibrational analysis of this dimer is performed.

Predictive a priori pressure-dependent kinetics

The ability to predict the pressure dependence of chemical reaction rates would be a great boon to kinetic modeling of processes such as combustion and atmospheric chemistry. This pressure dependence is intimately related to the rate of collision-induced transitions in energy E and angular momentum J. We present a scheme for predicting this pressure dependence based on coupling trajectory-based determinations of moments of the E,J-resolved collisional transfer rates with the two-dimensional master equation. This completely a priori procedure provides a means for proceeding beyond the empiricism of prior work. The requisite microcanonical dissociation rates are obtained from ab initio transition state theory. Predictions for the CH4 = CH3 + H and C2H3 = C2H2 + H reaction systems are in excellent agreement with experiment.

The pyrolysis of 2-methylfuran: a quantum chemical, statistical rate theory and kinetic modelling study

Due to the rapidly growing interest in the use of biomass derived furanic compounds as potential platform chemicals and fossil fuel replacements, there is a simultaneous need to understand the pyrolysis and combustion properties of such molecules. To this end, the potential energy surfaces for the pyrolysis relevant reactions of the biofuel candidate 2-methylfuran have been characterized using quantum chemical methods (CBS-QB3, CBS-APNO and G3). Canonical transition state theory is employed to determine the high-pressure limiting kinetics, k(T), of elementary reactions. Rice-Ramsperger-Kassel-Marcus theory with an energy grained master equation is used to compute pressure-dependent rate constants, k(T,p), and product branching fractions for the multiple-well, multiple-channel reaction pathways which typify the pyrolysis reactions of the title species. The unimolecular decomposition of 2-methylfuran is shown to proceed via hydrogen atom transfer reactions through singlet carbene intermediates which readily undergo ring opening to form collisionally stabilised acyclic C5H6O isomers before further decomposition to C1-C4 species. Rate constants for abstraction by the hydrogen atom and methyl radical are reported, with abstraction from the alkyl side chain calculated to dominate. The fate of the primary abstraction product, 2-furanylmethyl radical, is shown to be thermal decomposition to the n-butadienyl radical and carbon monoxide through a series of ring opening and hydrogen atom transfer reactions. The dominant bimolecular products of hydrogen atom addition reactions are found to be furan and methyl radical, 1-butene-1-yl radical and carbon monoxide and vinyl ketene and methyl radical. A kinetic mechanism is assembled with computer simulations in good agreement with shock tube speciation profiles taken from the literature. The kinetic mechanism developed herein can be used in future chemical kinetic modelling studies on the pyrolysis and oxidation of 2-methylfuran, or the larger molecular structures for which it is a known pyrolysis/combustion intermediate (e.g. cellulose, coals, 2,5-dimethylfuran).