Detailed Reaction Kinetics for Hydrocarbon Fuels: The Development and Application of the ReaxFFCHO-S22 Force Field for C/H/O Systems with Enhanced Accuracy

Efficient and accurate reactive force fields (e.g., ReaxFF) are pivotal for large-scale atomistic simulations to comprehend microscopic combustion processes. ReaxFF has been extensively utilized to describe chemical reactions in condensed phases, but most existing ReaxFF models rely on quantum mechanical (QM) data nearly two decades old, particularly in hydrocarbon systems, constraining their accuracy and applicability. Addressing this gap, we introduce a reparametrized ReaxFFCHO-S22 for C/H/O systems, tailored for studying the pyrolysis and combustion of hydrocarbon fuel. Our approach involves high-level QM benchmarks and large database construction for C/H/O systems, global ReaxFF parameter optimization, and molecular dynamics simulations of typical hydrocarbon fuels. Density functional theory (DFT) computations utilized the M06-2X functional at the meta-generalized gradient approximation (meta-GGA) level with a large basis set (6-311++G**). Our new ReaxFFCHO-S22 model exhibits a minimum 10% enhancement in accuracy compared to the previous ReaxFF models for a large variety of hydrocarbon molecules. This advanced ReaxFFCHO-S22 not only enables efficient large-scale studies on the microscopic chemical reactions of more complex hydrocarbon fuel but also can extend to biofuels, energetic materials, polymers, and other pertinent systems, thus serving as a valuable tool for studying chemical reaction dynamics of the large-scale hydrocarbon condensed phase at an atomistic level.

Isomer-resolved unimolecular dynamics of the hydroperoxyalkyl intermediate (•QOOH) in cyclohexane oxidation

The oxidation of cycloalkanes is important in the combustion of transportation fuels and in atmospheric secondary organic aerosol formation. A transient carbon-centered radical intermediate (•QOOH) in the oxidation of cyclohexane is identified through its infrared fingerprint and time- and energy-resolved unimolecular dissociation dynamics to hydroxyl (OH) radical and bicyclic ether products. Although the cyclohexyl ring structure leads to three nearly degenerate •QOOH isomers (β-, γ-, and δ-QOOH), their transition state (TS) barriers to OH products are predicted to differ considerably. Selective characterization of the β-QOOH isomer is achieved at excitation energies associated with the lowest TS barrier, resulting in rapid unimolecular decay to OH products that are detected. A benchmarking approach is employed for the calculation of high-accuracy stationary point energies, in particular TS barriers, for cyclohexane oxidation (C6H11O2), building on higher-level reference calculations for the smaller ethane oxidation (C2H5O2) system. The isomer-specific characterization of β-QOOH is validated by comparison of experimental OH product appearance rates with computed statistical microcanonical rates, including significant heavy-atom tunneling, at energies in the vicinity of the TS barrier. Master-equation modeling is utilized to extend the results to thermal unimolecular decay rate constants at temperatures and pressures relevant to cyclohexane combustion.

Methanediol from cloud-processed formaldehyde is only a minor source of atmospheric formic acid

Atmospheric formic acid is severely underpredicted by models. A recent study proposed that this discrepancy can be resolved by abundant formic acid production from the reaction (1) between hydroxyl radical and methanediol derived from in-cloud formaldehyde processing and provided a chamber-experiment-derived rate constant, k1 = 7.5 × 10-12 cm3 s-1. High-level accuracy coupled cluster calculations in combination with E,J-resolved two-dimensional master equation analyses yield k1 = (2.4 ± 0.5) × 10-12 cm3 s-1 for relevant atmospheric conditions (T = 260-310 K and P = 0-1 atm). We attribute this significant discrepancy to HCOOH formation from other molecules in the chamber experiments. More importantly, we show that reversible aqueous processes result indirectly in the equilibration on a 10 min. time scale of the gas-phase reaction [Formula: see text] (2) with a HOCH2OH to HCHO ratio of only ca. 2%. Although HOCH2OH outgassing upon cloud evaporation typically increases this ratio by a factor of 1.5-5, as determined by numerical simulations, its in-cloud reprocessing is shown using a global model to strongly limit the gas-phase sink and the resulting production of formic acid. Based on the combined findings in this work, we derive a range of 1.2-8.5 Tg/y for the global HCOOH production from cloud-derived HOCH2OH reacting with OH. The best estimate, 3.3 Tg/y, is about 30 times less than recently reported. The theoretical equilibrium constant Keq (2) determined in this work also allows us to estimate the Henry's law constant of methanediol (8.1 × 105 M atm-1 at 280 K).

Investigating the Association Reactions of HOCH2CO and HOCHCHO with O2: A Quantum Computational and Master Equation Study

Glycolaldehyde, HOCH₂CHO, is an important multifunctional atmospheric trace gas formed in the oxidation of ethylene and isoprene and emitted directly from burning biomass. The initial step in the atmospheric photooxidation of HOCH₂CHO yields HOCH₂CO and HOCHCHO radicals; both of these radicals react rapidly with O₂ in the troposphere. This study presents a comprehensive theoretical investigation of the HOCH₂CO + O₂ and HOCHCHO + O₂ reactions using high-level quantum chemical calculations and energy-grained master equation simulations. The HOCH₂CO + O₂ reaction results in the formation of a HOCH₂C(O)O₂ radical, while the HOCHCHO + O₂ reaction yields (HCO)₂ + HO₂. Density functional theory calculations have identified two open unimolecular pathways associated with the HOCH₂C(O)O₂ radical that yield HCOCOOH + OH or HCHO + CO₂ + OH products; the former novel bimolecular product pathway has not been previously reported in the literature. Master equation simulations based on the potential energy surface calculated here for the HOCH₂CO + O₂ recombination reaction support experimental product yield data from the literature and indicate that, even at total pressures of 1 atm, the HOCH₂CO + O₂ reaction yields ∼11% OH at 298 K.

Investigation of Methylcyclopentadiene Reactivity: Abstraction Reactions and Methylcyclopentadienyl Radical Unimolecular Decomposition

Understanding the reactivities of methylcyclopentadiene and the methylcyclopentadienyl radical is important in order to improve our comprehension of the chemical kinetics leading to the formation, decomposition, and growth of the first aromatic ring, as it has been shown that five-membered-ring species are important intermediates in the reaction kinetics of aromatic species. In this work, the rate constants of some key H-abstraction reactions from methylcyclopentadiene to produce the methylcyclopentadienyl radical and the formation of fulvene and benzene from the latter are theoretically determined. Rate constants are evaluated using the ab initio transition state theory-based master equation approach, determining structures and Hessians of all stationary points at the ωB97X-D/aug-cc-pVTZ level, energies at the CCSD(T) level extrapolated to the complete basis set limit, RRKM rate constants using conventional and variational transition state theory, and phenomenological rate constants through the solution of the one-dimensional master equation. Variational corrections are determined in both internal and Cartesian coordinates, and it is found that the choice of the coordinate system can impact the accuracy of the calculated rate constants by up to a factor of 4 for H-abstraction reactions and 2 for the unimolecular decomposition of the methylcyclopentadienyl radical. The calculated rate constants are in good agreement with the available literature data. Prompt dissociation of methylcyclopentadienyl radicals accessed following H-abstraction from methylcyclopentadiene was also investigated, and the corresponding rate constants were determined; the results show that prompt dissociation plays a key role under combustion conditions. Finally, lumping of theoretically derived rate constants to account for methylcyclopentadiene ⇄ methylcyclopentadienyl tautomerism allowed the derivation of a simplified set of rate constants suitable to be inserted into kinetic mechanisms.

Potential Nonstatistical Effects on the Unimolecular Decomposition of H2O2

An attempt is made to evaluate the nonstatistical effects in the thermal decomposition of hydrogen peroxide (H₂O₂). Previous experimental studies on this reaction reported an unusual pressure dependence of the rate constant indicating broader falloff behavior than expected from conventional theory. In this work, the possibility that the rate constant is affected by nonstatistical effects is investigated based on classical trajectory calculations on the global potential energy surfaces of H₂O₂ and H₂O₂ + Ar. The emphasis is on the intramolecular energy redistribution from the K-rotor, that is, the external rotor for rotation around the principal axis of least moment of inertia. The calculations for the H₂O₂ molecules excited above the dissociation threshold suggest that the energy redistribution from the torsion and K-rotor to vibrations can be competitive with dissociation. In particular, the slow redistribution of the energy associated with the K-rotor significantly affects the dissociation rate. The successive trajectory calculations for collisions of H₂O₂ with Ar show that the energy associated with the K-rotor can be collisionally transferred more efficiently than the vibrational energy. On the basis of these results and several assumptions, a simple model is proposed to account for the nonstatistical effects on the pressure-dependent thermal rate constants. The model predicts significant broadening of the falloff curve of the rate constants but still cannot fully explain the experimental data.

Wave Packet Approach to Adiabatic and Nonadiabatic Dynamics of Cold Inelastic Scatterings

Due to the extremely large de Broglie wavelength of cold molecules, cold inelastic scattering is always characterized by the time-independent close-coupling (TICC) method. However, the TICC method is difficult to apply to collisions of large molecular systems. Here, we present a new strategy for characterizing cold inelastic scattering using wave packet (WP) method. In order to deal with the long de Broglie wavelength of cold molecules, the total wave function is divided into interaction, asymptotic and long-range regions (IALR). The three regions use different numbers of ro-vibrational basis functions, especially the long-range region, which uses only one function corresponding to the initial ro-vibrational state. Thus, a very large grid range can be used to characterize long de Broglie wavelengths in scattering coordinates. Due to its better numerical scaling law, the IALR-WP method has great potential in studying the inelastic scatterings of larger collision systems at cold and ultracold regimes.

Reaction of Methylidyne with Ethane: The C-C Insertion Is Unimportant

High-accuracy coupled-cluster calculations in combination with the E,J-resolved master-equation analysis are used to study the reaction mechanism and kinetics of methylidyne with ethane. This reaction plays an important role in the combustion of hydrocarbon fuels and in interstellar chemistry. Two distinct mechanisms, the C-C and the C-H insertions of CH in C₂H₆, are characterized. The C-C insertion pathway is identified to have a large barrier of 34.5 kcal mol^-1 and hence plays no significant role in kinetics. The C-H insertion pathway is found to have no barrier, leading to a highly vibrationally excited n-C₃H₇ radical, which rapidly dissociates (within 50 ps) to yield CH₃ + C₂H₄ and H + C₃H₆ in a roughly 7:3 ratio. These findings are in good agreement with an experimental result that indicates that about 20% of the reaction goes to H + C₃H₆. The reaction of the electronically excited quartet state of the CH radical with C₂H₆ is examined for the first time and found to proceed as a direct H-abstraction via a small barrier of 0.4 kcal mol^-1 to yield triplet CH₂ and C₂H₅. The reaction on the quartet state surface is negligibly slow at low temperatures characteristic of interstellar environments but becomes important at high combustion temperatures.

Mechanism, Thermochemistry, and Kinetics of the Reversible Reactions: C2H3 + H2 ⇌ C2H4 + H ⇌ C2H5

High-level coupled cluster theory, in conjunction with Active Thermochemical Tables (ATcT) and E,J-resolved master equation calculations were used in a study of the title reactions, which play an important role...

Concluding Remarks on Faraday Discussion on Unimolecular Reactions

This Faraday Discussion, marking the centenary of Lindemann’s explanation of the pressure-dependence of unimolecular reactions, presented recent advances in measuring and computing collisional energy transfer efficiencies, microcanonical rate coefficients, pressure-dependent...

Dissociation-Induced Depletion of High-Energy Reactant Molecules as a Mechanism for Pressure-Dependent Rate Constants for Bimolecular Reactions

In 1922, Lindemann proposed the now-well-known mechanism for pressure-dependent rate constants for unimolecular reactions: reactant molecules with sufficiently high energies dissociate more quickly than collisions can reestablish the Boltzmann distribution...

High-accuracy first-principles-based rate coefficients for the reaction of OH and CH3OOH

The ˙OH-initiated oxidation of methyl hydroperoxide was theoretically characterized using high-accuracy composite amHEAT-345(Q) coupled-cluster calculations followed by a two-dimensional E,J resolved master equation analysis.

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...

Energy-resolved and time-dependent unimolecular dissociation of hydroperoxyalkyl radicals (•QOOH)

Hydroperoxyalkyl radicals (•QOOH) are transient intermediates in the atmospheric oxidation of volatile organic compounds and combustion of hydrocarbon fuels in low temperature (< 1000 K) environments. The carbon-centered •QOOH radicals...

Spiers Memorial Lecture: theory of unimolecular reactions

One hundred years ago, at an earlier Faraday Discussion meeting, Lindemann presented a mechanism that provides the foundation for contemplating the pressure dependence of unimolecular reactions. Since that time, our...

Solving the chemical master equation for monomolecular reaction systems and beyond: a Doi-Peliti path integral view

The chemical master equation (CME) is a fundamental description of interacting molecules commonly used to model chemical kinetics and noisy gene regulatory networks. Exact time-dependent solutions of the CME-which typically consists of infinitely many coupled differential equations-are rare, and are valuable for numerical benchmarking and getting intuition for the behavior of more complicated systems. Jahnke and Huisinga's landmark calculation of the exact time-dependent solution of the CME for monomolecular reaction systems is one of the most general analytic results known; however, it is hard to generalize, because it relies crucially on special properties of monomolecular reactions. In this paper, we rederive Jahnke and Huisinga's result on the time-dependent probability distribution and moments of monomolecular reaction systems using the Doi-Peliti path integral approach, which reduces solving the CME to evaluating many integrals. While the Doi-Peliti approach is less intuitive, it is also more mechanical, and hence easier to generalize. To illustrate how the Doi-Peliti approach can go beyond the method of Jahnke and Huisinga, we also find an explicit and exact time-dependent solution to a problem involving an autocatalytic reaction that Jahnke and Huisinga identified as not solvable using their method. Most interestingly, we are able to find a formal exact time-dependent solution for any CME whose list of reactions involves only zero and first order reactions, which may be the most general result currently known. This formal solution also yields a useful algorithm for efficiently computing numerical solutions to CMEs of this type.

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.

Watching a hydroperoxyalkyl radical (•QOOH) dissociate

A prototypical hydroperoxyalkyl radical (•QOOH) intermediate, transiently formed in the oxidation of volatile organic compounds, was directly observed through its infrared fingerprint and energy-dependent unimolecular decay to hydroxyl radical and cyclic ether products. Direct time-domain measurements of •QOOH unimolecular dissociation rates over a wide range of energies were found to be in accord with those predicted theoretically using state-of-the-art electronic structure characterizations of the transition state barrier region. Unimolecular decay was enhanced by substantial heavy-atom tunneling involving O-O elongation and C-C-O angle contraction along the reaction pathway. Master equation modeling yielded a fully a priori prediction of the pressure-dependent thermal unimolecular dissociation rates for the •QOOH intermediate-again increased by heavy-atom tunneling-which are required for global models of atmospheric and combustion chemistry.

The CH(X2Π) + H2O reaction: two transition state kinetics

The reaction of ground state methylidyne (CH) with water vapor (H2O) is theoretically re-investigated using high-level coupled cluster computations in combination with semi-classical transition state theory (SCTST) and two-dimensional master equation simulations. Insertion of CH into a H-O bond of H2O over a submerged barrier via a well-skipping mechanism yielding solely H and CH2O is characterized. The reaction kinetics is effectively determined by the formation of a pre-reaction van der Waals complex (PRC, HC-OH2) and its subsequent isomerization to activated CH2OH in competition with PRC re-dissociation. The tunneling effects are found to be minor, while variational effects in the PRC → CH2OH step are negligible. The calculated rate coefficient k(T) is nearly pressure-independent, but strongly depends on temperature with pronounced down-up behavior: a high value of 2 × 10-10 cm3 s-1 at 50 K, followed by a fairly steep decrease down to 8 × 10-12 cm3 s-1 at 900 K, but increasing again to 5 × 10-11 cm3 s-1 at 3500 K. Over the T-range of this work, k(T) can be expressed as: k(T, P = 0) = 2.31 × 10-11 (T/300 K)-1.615 exp(-38.45/T) cm3 s-1 for T = 50-400 K k(T, P = 0) = 1.15 × 10-12 (T/300 K)0.8637 exp(892.6/T) cm3 s-1 for T = 400-1000 K k(T, P = 0) = 4.57 × 10-15 (T/300 K)3.375 exp(3477.4/T) cm3 s-1 for T = 1000-3500 K.

Parametric Sensitivity in a Generalized Model for Atmospheric Pressure Chemical Ionization Reactions

Gas phase reactions between hydrated protons H⁺(H₂O)_n and a substance M, as seen in atmospheric pressure chemical ionization (APCI) with mass spectrometry (MS) and ion mobility spectrometry (IMS), were modeled computationally using initial amounts of [M] and [H⁺(H₂O)_n], rate constants k₁ to form protonated monomer (MH⁺(H₂O)_x) and k₂ to form proton bound dimer (M₂H⁺(H₂O)_z), and diffusion constants. At 1 × 10¹⁰ cm^-3 (0.4 ppb) for [H⁺(H₂O)_n] and vapor concentrations for M from 10 ppb to 10 ppm, a maximum signal was reached at 4.5 μs to 4.6 ms for MH⁺(H₂O)_x and 7.8 μs to 46 ms for M₂H⁺(H₂O)_z. Maximum yield for protonated monomer for a reaction time of 1 ms was ∼40% for k₁ from 10^-11 to 10^-8 cm³·s^-1, for k₂/k₁ = 0.8, and specific values of [M]. This model demonstrates that ion distributions could be shifted from [M₂H⁺(H₂O)_z] to [MH⁺(H₂O)_x] using excessive levels of [H⁺(H₂O)_n], even for [M] > 10 ppb, as commonly found in APCI MS and IMS measurements. Ion losses by collisions on surfaces were insignificant with losses of <0.5% for protonated monomer and <0.1% for proton bound dimer of dimethyl methylphosphonate (DMMP) at 5 ms. In this model, ion production in an APCI environment is treated over ranges of parameters important in mass spectrometric measurements. The models establish a foundation for detailed computations on response with mixtures of neutral substances.

Thermal Decomposition of CH3O: A Curious Case of Pressure-Dependent Tunneling Effects

The thermal unimolecular decomposition of a methoxy radical (CH₃O), a key intermediate in the combustion of methane, methanol, and other hydrocarbons, was studied using high-level coupled-cluster calculations, followed by E,J-resolved master equation analyses. The experimental results available for a wide range of temperature and pressure are in striking agreement with the calculations. In line with a previous theoretical study that used a one-dimensional master equation, the tunneling correction is found to exhibit a marked pressure dependence, being the largest at low pressure. This curious effect on the tunneling enhancement also affects the calculated kinetic isotope effect, which falls initially with pressure but is predicted to rise again at high pressures. These findings serve to reconcile a set of conflicting results regarding the importance of tunneling in this prototype unimolecular reaction and also motivate further experimental investigation. This study also exemplifies how changes in the energy redistribution due to collisions manifest in the tunneling rates.

Theoretical Study of the Mechanism and Kinetics of the Oxidation of Cyclopenta[a]Naphthalenyl Radical C13H9 with Molecular Oxygen

Electronic structure/Rice-Ramsperger-Kassel-Marcus Master equation calculations were applied to unravel the oxidation mechanism and kinetics of the cyclopenta[a]naphthalenyl radical with molecular oxygen. The reaction has been shown to proceed through the addition of O₂ in the ortho-position in the five-membered ring of C₁₃H₉. At low temperatures, the reaction yields a collisionally stabilized C₁₃H₉O₂ complex, which rapidly decomposes back to the reactants. In the high-temperature regime, above 800, 900, 1125, and 1375 K at pressures of 0.03, 1, 10, and 100 atm, respectively, the reaction forms bimolecular products including 3H-/1H-cyclopenta[a]naphthalen-3-one + OH as the prevailing product together with 1-ethanol-substituted 2-naphthyl radical + CO and 3H-benzo[f]chromen-3-one + H as minor ones, with the branching ratio of the OH elimination channel growing with temperature and the rate constants for the individual bimolecular channels being independent of pressure. The calculated rate constants and product branching for cyclopenta[a]naphthalenyl + O₂ closely agree with those reported earlier for the indenyl + O₂ reaction and are recommended for the combustion kinetic models for the oxidation reactions of five-membered rings on free edges of larger polycyclic aromatic hydrocarbon molecules. The results also confirm that the oxidation of a π radical located on a five-membered ring with molecular oxygen is very slow.

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.

Theoretical Study of the Phenoxy Radical Recombination with the O(3P) Atom, Phenyl plus Molecular Oxygen Revisited

Quantum chemical calculations of the C₆H₅O₂ potential energy surface (PES) were carried out to study the mechanism of the phenoxy + O(³P) and phenyl + O₂ reactions. CASPT2(15e,13o)/CBS//CASSCF(15e,13o)/DZP multireference calculations were utilized to map out the minimum energy path for the entrance channels of the phenoxy + O(³P) reaction. Stationary points on the C₆H₅O₂ PES were explored at the CCSD(T)-F12/cc-pVTZ-f12//B3LYP/6-311++G** level for the species with a single-reference character of the wave function and at the CASPT2(15e,13o)/CBS//B3LYP/6-311++G** level of theory for the species with a multireference character of the wave function. Conventional, variational, and variable reaction coordinate transition-state theories were employed in Rice-Ramsperger-Kassel-Marcus master equation calculations to assess temperature- and pressure-dependent phenomenological rate constants and product branching ratios. The main bimolecular product channels of the phenoxy + O(³P) reaction are concluded to be para/ortho-benzoquinone + H, 2,4-cyclopentadienone + HCO and, at high temperatures, also phenyl + O₂. The main bimolecular product channels of the phenyl + O₂ reaction include 2,4-cyclopentadienone + HCO at lower temperatures and phenoxy + O(³P) at higher temperatures. For both the phenoxy + O(³P) and phenyl + O₂ reactions, the collisional stabilization of peroxybenzene at low temperatures and high pressures competes with the bimolecular product channels.

Two-Dimensional Master Equation Modeling of Some Multichannel Unimolecular Reactions

Multichannel thermal decomposition reactions of n-propyl radicals, 1-pentyl radicals, and toluene are investigated by solving a two-dimensional master equation formulated as a function of total energy (E) and angular momentum (J). The primary aim of this study is to elucidate the role of angular momentum in the kinetics of multichannel unimolecular reactions. The collisional transition processes of the reactants colliding with argon are characterized based on the classical trajectory calculations and implemented in the master equation. The rate constants calculated by using the two-dimensional master equation are compared with those of one-dimensional master equations. The consequence of the explicit treatment of angular momentum depends on the J dependence of the microscopic rate constants and is particularly emphasized in the thermal decomposition of toluene, for which the C-H and C-C bond fission channels are considered. The centrifugal effect is insignificant in the energetically favored C-H bond fission but is substantial in the energetically higher C-C bond fission, which causes rotational channel switching of the microscopic rate constants. The proper treatment of the J-dependent channel coupling effect, weak collisional transfer of J, and initial-J-dependent collisional energy transfer are found to be essential for predicting the branching fractions at low pressures.

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.

Combustion in the future: The importance of chemistry

Combustion involves chemical reactions that are often highly exothermic. Combustion systems utilize the energy of chemical compounds released during this reactive process for transportation, to generate electric power, or to provide heat for various applications. Chemistry and combustion are interlinked in several ways. The outcome of a combustion process in terms of its energy and material balance, regarding the delivery of useful work as well as the generation of harmful emissions, depends sensitively on the molecular nature of the respective fuel. The design of efficient, low-emission combustion processes in compliance with air quality and climate goals suggests a closer inspection of the molecular properties and reactions of conventional, bio-derived, and synthetic fuels. Information about flammability, reaction intensity, and potentially hazardous combustion by-products is important also for safety considerations. Moreover, some of the compounds that serve as fuels can assume important roles in chemical energy storage and conversion. Combustion processes can furthermore be used to synthesize materials with attractive properties. A systematic understanding of the combustion behavior thus demands chemical knowledge. Desirable information includes properties of the thermodynamic states before and after the combustion reactions and relevant details about the dynamic processes that occur during the reactive transformations from the fuel and oxidizer to the products under the given boundary conditions. Combustion systems can be described, tailored, and improved by taking chemical knowledge into account. Combining theory, experiment, model development, simulation, and a systematic analysis of uncertainties enables qualitative or even quantitative predictions for many combustion situations of practical relevance. This article can highlight only a few of the numerous investigations on chemical processes for combustion and combustion-related science and applications, with a main focus on gas-phase reaction systems. It attempts to provide a snapshot of recent progress and a guide to exciting opportunities that drive such research beyond fossil combustion.

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 Rate Constant Caused by Tunneling Effects: OH + HNO3 as an Example

Tunneling effects on chemical reactions are well-known and have been unambiguously demonstrated by processes that involve the motion of hydrogen atoms at low temperature. However, the process by which tunneling effects cause a falloff curve (i.e., how reaction rate constants depend on pressure) has apparently not been previously documented. This work points out that falloff curves can indeed be caused by tunneling and explains the effect in simple terms. This is an interesting feature of quantum tunneling, which can appear in low temperature chemistry (such as in atmospheric or interstellar environments). In this Letter, we use high-level coupled-cluster calculations in combination with master-equation methods on the well-studied reaction of OH with HNO₃, which plays an important role in the upper troposphere and lower stratosphere. Our results in combination with available experimental data clearly demonstrate that the tunneling correction depends on not just temperature, but also pressure.

Theoretical study of the reaction mechanism and kinetics of the phenyl + propargyl association

Potential energy surface for the phenyl + propargyl radical recombination reaction has been studied at the CCSD(T)-F12/cc-pVTZ-f12//B3LYP/6-311G** level of theory for the closed-shell singlet species and at the triplet-singlet gap CASPT2/cc-pVTZ-CCSD(T)-F12/cc-pVTZ-f12//CASSCF/cc-pVTZ level of theory for the diradical species. High-pressure limit rate constants for the barrierless channels were evaluated with variable reaction coordinate transition state theory (VRC-TST). Rice-Ramsperger-Kassel-Marcus Master Equation (RRKM-ME) calculations have been performed to assess temperature- and pressure-dependent phenomenological rate constants and product branching ratios. The entrance channels of the radical association reaction produce 3-phenyl-1-propyne and phenylallene which can further dissociate/isomerize into a variety of unimolecular and bimolecular products. Theoretical evidence is presented that, at combustion relevant conditions, the phenyl + propargyl recombination provides a feasible mechanism for the addition of a second five-member ring to the first six-member aromatic ring producing the prototype two-ring species indene and indenyl. Rate expressions for all important reaction channels in a broad range of temperatures and pressures have been generated for kinetic modeling.

Rotationally inelastic scattering of O3–Ar: state-to-state rates with the multiconfigurational time dependent Hartree method

The rates of state-changing collisions are compared for different isotopologues of ozone from quantum scattering calculations with the MCTDH method.

Breakdown of energy transfer gap laws revealed by full-dimensional quantum scattering between HF molecules

Inelastic collisions involving molecular species are key to energy transfer in gaseous environments. They are commonly governed by an energy gap law, which dictates that transitions are dominated by those between initial and final states with roughly the same ro-vibrational energy. Transitions involving rotational inelasticity are often further constrained by the rotational angular momentum. Here, we demonstrate using full-dimensional quantum scattering on an ab initio based global potential energy surface (PES) that HF-HF inelastic collisions do not obey the energy and angular momentum gap laws. Detailed analyses attribute the failure of gap laws to the exceedingly strong intermolecular interaction. On the other hand, vibrational state-resolved rate coefficients are in good agreement with existing experimental results, validating the accuracy of the PES. These new and surprising results are expected to extend our understanding of energy transfer and provide a quantitative basis for numerical simulations of hydrogen fluoride chemical lasers.

Chemical Kinetics Approves the Occurrence of C (3Pj) Reaction with H2O

Although both atomic carbon and water are omnipresent in human life, there is a debate about the possibility of carbon reaction with water. Some low-temperature spectroscopic investigations have rejected the reaction, whereas some room-temperature experiments and theoretical studies have accepted the possibility of the reaction by reporting rate coefficients ranging from 10⁵ to 10⁹ L mol^-1 s^-1. This study provides new lines of evidence about the reaction through exploration of the reaction mechanism using the CCSD(T) method and solving the corresponding master equation by following two main approaches. According to the results, the rate coefficient of the reaction is significantly influenced by the tunneling and hindered rotation effects, in addition to the selected total angular momentum (J). Furthermore, the total rate coefficient of the reaction increases dramatically (from 10⁷ to 10¹¹ L mol^-1 s^-1) with the rise of temperature from 100 to 4000 K, while the total rate coefficient is insensitive to pressure (0.1-10 atm). Despite some differences between the results of the two approaches, the rate coefficients of both methods are consistent with the previously reported rate coefficients. Also, in agreement with the previous studies, the major products are ²HOC + ²H and ²HCO + ²H. In general, the findings approve the occurrence of the title reaction and indicate that the mentioned conflict is due to the sensitivity of the reaction to the investigated temperature and J level. The sensitivity does not permit low-temperature spectroscopic studies to detect any products and varies the measured and calculated rate coefficients.

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.

Pressure effects on the vibrational and rotational relaxation of vibrationally excited OH (ν, J) in an argon bath

Quasi-classical molecular dynamics simulations were used to study the energy relaxation of an initially non-rotating, vibrationally excited (ν = 4) hydroxyl radical (OH) in an Ar bath at 300 K and at high pressures from 50 atm to 400 atm. A Morse oscillator potential represented the OH, and two sets of interaction potentials were used based on whether the Ar-H potential was a Buckingham (Exp6) or a Lennard-Jones (LJ) potential. The vibrational and rotational energies were monitored for 25 000-90 000 ps for Exp6 trajectories and 5000 ps for LJ trajectories. Comparisons to measured vibrational relaxation rates show that Exp6 rates are superior. Simulated initial vibrational relaxation rates are linearly proportional to pressure, implying no effect of high-pressure breakdown in the isolated binary collision approximation. The vibrational decay curves upward from single-exponential decay. A model based on transition rates that exponentially depend on the anharmonic energy gap between vibrational levels fits the vibrational decay well at all pressures, suggesting that anharmonicity is a major cause of the curvature. Due to the competition of vibration-to-rotation energy transfer and bath gas relaxation, the rotational energy overshoots and then relaxes to its thermal value. Approximate models with adjustable rates for this competition successfully reproduced the rotational results. These models show that a large fraction of the vibrational energy loss is initially converted to rotational energy but that fraction decreases rapidly as the vibrational energy content of OH decreases. While simulated rates change dramatically between Exp6 and LJ potentials, the mechanisms remain the same.