Master Equation Analysis of Pressure-Dependent Atmospheric Reactions

Understanding the kinetics and atmospheric degradation mechanism of chlorotrifluoroethylene (CF2CFCl) initiated by OH radicals

The atmospheric degradation of chlorotrifluoroethylene (CTFE) by OH˙ was investigated using density functional theory (DFT). The potential energy surfaces were also defined in terms of single-point energies derived from the linked cluster CCSD(T) theory. With an energy barrier of -2.62 to -0.99 kcal mol^-1 using the M06-2x method, the negative temperature dependence was determined. The OH˙ attack on C_α and C_β atoms (labeled pathways R1 and R2, respectively) shows that reaction R2 is 4.22 and 4.42 kcal mol^-1, respectively, more exothermic and exergonic than reaction R1. The main pathway should be the addition of OH˙ to the β-carbon, resulting in ˙CClF-CF₂OH species. At 298 K, the calculated rate constant was 9.87 × 10^-13 cm³ molecule^-1 s^-1. The TST and RRKM calculations of rate constants and branching ratios were performed at P = 1 bar and in the fall-off pressure regime over the temperature range of 250-400 K. The formation of HF and ˙CClF-CFO species via the 1,2-HF loss process is the most predominant pathway both kinetically and thermodynamically. With increasing temperature and decreasing pressure, the regioselectivity of unimolecular processes of energized adducts [CTFE-OH]˙ gradually decreases. Pressures greater than 10^-4 bar are often adequate for assuring saturation of the estimated unimolecular rates when compared to the RRKM rates (in high-pressure limit). Subsequent reactions involve the addition of O₂ to the [CTFE-OH]˙ adducts at the α-position of the OH group. The [CTFE-OH-O₂]˙ peroxy radical primarily reacts with NO and then directly decomposes into NO₂ and oxy radicals. "Carbonic chloride fluoride", "carbonyl fluoride", and "2,2-difluoro-2-hydroxyacetyl fluoride" are predicted to be stable products in an oxidative atmosphere.

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.

ABC+D: A time-independent coupled-channel quantum dynamics program for elastic and ro-vibrational inelastic scattering between atoms and triatomic molecules in full dimensionality

We discuss the details of a time-independent quantum mechanical method and its implementation for full-dimensional non-reactive scattering between a closed-shell triatomic molecule and a closed-shell atom. By solving the time-independent Schrödinger equation within the coupled-channel framework using a log-derivative method, the state-to-state scattering matrix (S-matrix) can be determined for inelastic scattering involving both the rotational and vibrational modes of the molecule. Various approximations are also implemented. The ABC+D code provides an important platform for understanding an array of physical phenomena involving collisions between atoms and molecules.

Recent advances in quantum theory on ro-vibrationally inelastic scattering

Molecular collisions are of fundamental importance in understanding intermolecular interaction and dynamics. Its importance is accentuated in cold and ultra-cold collisions because of the dominant quantum mechanical nature of the scattering. We review recent advances in the time-independent approach to quantum mechanical characterization of non-reactive scattering in tetratomic systems, which is ideally suited for large collisional de Broglie wavelengths characteristic in cold and ultracold conditions. We discuss quantum scattering algorithms between two diatoms and between a triatom and an atom and their implementation, as well as various approximate schemes. They not only enable the characterization of collision dynamics in realistic systems but also serve as benchmarks for developing more approximate methods.

Full-Dimensional Quantum Dynamics Studies of Ro-vibrationally Inelastic Scattering of H2O with Ar: A Benchmark Test of the Rigid-Rotor Approximation

While the rigid-rotor (RR) approximation is usually considered to be accurate for describing pure rotationally inelastic scattering involving diatoms in their ground or low-lying vibrational states, its validity in scattering involving polyatomic molecules has not been fully examined. The existence of soft/anharmonic vibrational modes in polyatomic molecules could make rotational-vibrational energy transfer rather efficient, thus undermining the premise of the RR approximation. In this work, we conduct a benchmark test of the RR approximation in the rotationally inelastic scattering of the H₂O(v₂ = 0, 1) + Ar system by comparing with full-dimensional quantum scattering calculations. We demonstrate that the error in the RR rate coefficient for v₂ = 0 is less than 5%, while it can reach up to 20% for some initial states within the v₂ = 1 manifold. These results indicate that the RR approximation gradually deteriorates with increasing quantum number v₂. Vibrational relaxation dynamics of this system was also studied, and it is found that transitions from initial states with a large rotational quantum number of projection on the a principal axis are more efficient. These results shed valuable light on ro-vibrationally inelastic scattering involving polyatomic molecules.

Theoretical Investigations for Kinetics of the Chemical Reactions: H + SiClx (x = 1, 2, 3)

Hydrogen atoms and SiCl_x (x = 1, 2, 3) radicals coexist during the hydrogenation of silicon tetrachloride (STC, SiCl₄), an important process in the fabrication of industrial polysilicon. In this work, the mechanisms and kinetics of the reactions between H and SiCl_x (x = 1, 2, 3) were studied by theory. The structures and vibrational frequencies of reactants, products, intermediates, and transition states (TSs) were determined at the B2PLYP/may-cc-pVTZ level. The single-point energies of minima and saddle points were refined using the coupled-cluster single-double with triple perturbative (CCSD(T)) with the complete basis set extrapolation method. Some special treatments were designed to obtain reliable wave functions for unimolecular reactions without tight TSs by the density functional theory. Subsequently, Lennard-Jones (L-J) parameters between each intermediate (SiHCl_x) and bath gas (He) were obtained at the MP2/jul-cc-pVTZ level to derive reliable temperature- and pressure-dependent rate coefficients for unimolecular reactions according to the variational Rice-Ramsperger-Kassel-Marcus theory. For bimolecular reactions, rate coefficients were determined by the variational transition-state theory. The rate coefficients of barrierless reactions were derived based on the loose TSs with the maximum free energy. Finally, the master equation analysis was used to investigate the variation of the rate coefficients with pressure and temperature in the activated paths.

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...

Chemistry of Functionalized Reactive Organic Intermediates in the Earth's Atmosphere: Impact, Challenges, and Progress

The gas-phase oxidation of organic compounds is an important chemical process in the Earth's atmosphere. It governs oxidant levels and controls the production of key secondary pollutants, and hence has major implications for air quality and climate. Organic oxidation is largely controlled by the chemistry of a few reactive intermediates, namely, alkyl (R) radicals, alkoxy (RO) radicals, peroxy (RO₂) radicals, and carbonyl oxides (R₁R₂COO), which may undergo a number of unimolecular and bimolecular reactions. Our understanding of these intermediates, and the reaction pathways available to them, is based largely on studies of unfunctionalized intermediates, formed in the first steps of hydrocarbon oxidation. However, it has become increasingly clear that intermediates with functional groups, which are generally formed later in the oxidation process, can exhibit fundamentally different reactivity than unfunctionalized ones. In this Perspective, we explore the unique chemistry available to functionalized organic intermediates in the Earth's atmosphere. After a brief review of the canonical chemistry available to unfunctionalized intermediates, we discuss how the addition of functional groups can introduce new reactions, either by changing the energetics or kinetics of a given reaction or by opening up new chemical pathways. We then provide examples of atmospheric reaction classes that are available only to functionalized intermediates. Some of these, such as unimolecular H-shift reactions of RO₂ radicals, have been elucidated only relatively recently, and can have important impacts on atmospheric chemistry (e.g., on radical cycling or organic aerosol formation); it seems likely that other, as-yet undiscovered reactions of (multi)functional intermediates may also exist. We discuss the challenges associated with the study of the chemistry of such intermediates and review novel experimental and theoretical approaches that have recently provided (or hold promise for providing) new insights into their atmospheric chemistry. The continued use and development of such techniques and the close collaboration between experimentalists and theoreticians are necessary for a complete, detailed understanding of the chemistry of functionalized intermediates and their impact on major atmospheric chemical processes.

Simplified Protocol for the Calculation of Multiconformer Transition State Theory Rate Constants Applied to Tropospheric OH-Initiated Oxidation Reactions

Chemical kinetics plays a fundamental role in the understanding and modeling of tropospheric chemical processes, one of the most important being the atmospheric degradation of volatile organic compounds. These potentially harmful molecules are emitted into the troposphere by natural and anthropogenic sources and are chemically removed by undergoing oxidation processes, most frequently initiated by reaction with OH radicals, the atmosphere's "detergent". Obtaining the respective rate constants is therefore of critical importance, with calculations based on transition state theory (TST) often being the preferred choice. However, for molecules with rich conformational variety, a single-conformer method such as lowest-conformer TST is unsuitable while state-of-the-art TST-based methodologies easily become unmanageable. In this Feature Article, the author reviews his own cost-effective protocol for the calculation of bimolecular rate constants of OH-initiated reactions in the high-pressure limit based on multiconformer transition state theory. The protocol, which is easily extendable to other oxidation reactions involving saturated organic molecules, is based on a variety of freeware and open-source software and tested against a series of oxidation reactions of hydrofluoropolyethers, computationally very challenging molecules with potential environmental relevance. The main features, advantages and disadvantages of the protocol are presented, along with an assessment of its predictive utility based on a comparison with experimental rate constants.

Calculation of Transport Parameters Using ab initio and AMOEBA Polarizable Force Field Methods

The transport properties of chemical species such as coefficients of diffusion, thermal conductivity, and viscosity have been widely used in combustion modeling. Lennard-Jones parameters fitted from the accurate intermolecular potential energy surfaces are crucial to obtain such information. Hence, a fast and accurate energy function is always desired for this purpose. In this study, the quality of a widely used polarizable force field AMOEBA was examined for the interaction between noble gases and n-alkanes. First, the intermolecular energy was compared between AMOEBA, MP2/CBS, MP2/aug'-cc-pVDZ, and QCISD(T)/CBS. The root mean squared error of the original AMOEBA was 10.31 cm^-1 against QCISD(T)/CBS for all conformations. This was comparable with the errors of 10.84 and 7.75 cm^-1 for MP2/aug'-cc-pVDZ and MP2/CBS, respectively. Further optimizing the van der Waals parameters of noble gases, the error of the force field against QCISD(T)/CBS was reduced to 6.24 cm^-1, even better than the MP2/CBS results. Based on the optimized force field parameters, the intermolecular Lennard-Jones parameters were derived using the spherically averaged method and one-dimensional minimization method for a set of (n-alkanes, noble gases) pairs. The discrepancy of the one-dimensional minimization predicted Lennard-Jones collision rates from the tabulated values was typically within 10%, while it could be as large as 20-30% for the spherically averaged method. Additionally, the binary diffusion coefficients were calculated using the present Lennard-Jones parameters. In this case, the parameters derived from the spherically averaged method perform better. The mean unsigned error of the diffusion coefficients is usually within 5%, which is in good agreement with the experimental results. The results demonstrate that the AMOEBA force field can be used to generate the transport parameters systematically.

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.

A perspective on the development of gas-phase chemical mechanisms for Eulerian air quality models

An essential component of a three-dimensional air quality model is its gas-phase mechanism. We present an overview of the necessary atmospheric chemistry and a discussion of the types of mechanisms with some specific examples such as the Master Chemical Mechanism, the Carbon Bond, SAPRC and the Regional Atmospheric Chemistry Mechanism (RACM). The first versions of the Carbon Bond and SAPRC mechanisms were developed through a hierarchy of chemical species approach that relied heavily on chemical environmental chamber data. Now a new approach has been proposed where the first step is to develop a highly detailed explicit mechanism such as the Master Chemical Mechanism and the second step is to test the detailed explicit mechanism against laboratory and field data. Finally, the detailed mechanism is condensed for use in a three-dimensional air quality model. Here it is argued that the development of highly detailed explicit mechanisms is very valuable for research, but we suggest that combining the hierarchy of chemical species and the detailed explicit mechanism approaches would be better than either alone.Implication: Many gas-phase mechanisms are available for urban, regional and global air quality modeling. A "hierarchy of chemical species approach," relying heavily on smog-chamber data was used for the development of the early series of mechanisms. Now the development of large, explicit master mechanisms that may be condensed is a significant, trend. However, a continuing problem with air quality mechanism development is due to the high complexity of atmospheric chemistry and the current availability of laboratory measurements. This problem requires a balance between completeness and speculation so that models maintain their utility for policymakers.

High-resolution infrared spectroscopy of jet cooled trans-deuteroxycarbonyl (trans-DOCO) radical

The rovibrational spectrum of jet cooled trans-deuteroxycarbonyl (trans-DOCO) radical has been explored at suppressed-Doppler resolution via direct infrared absorption spectroscopy. The trans-DOCO is produced in a supersonic slit discharge of rare-gas/CO mixture doped with D₂O, whereby the OD forms an energized adduct with CO, cooling in the supersonic expansion and stabilizing DOCO in the trans well. Active laser-frequency stabilization and collisional quenching of Doppler broadening along the slit axis yield <10 MHz frequency precision, with the absorbance noise approaching the quantum shot-noise limit. The current high-resolution spectral results are in excellent agreement with recent studies of the trans-DOCO radical by infrared frequency comb spectroscopy under room temperature conditions [Bui et al., Mol. Phys. 116, 3710 (2018)]. Combined with previous microwave/millimeter wave rotational studies, the suppressed-Doppler infrared data permit characterization of the vibrational ground state, improved structural parameters for the OD stretch vibrational level, and trans-DOCO spin-rotation information in both ground and excited vibrational states. Additionally, the infrared data reveal a-type and much weaker b-type contributions to the spectrum, analysis of which yields orientation of the OD stretch transition dipole moment in the body fixed frame. Of dynamical interest is whether the nascent trans-DOCO complex formed in the entrance channel has sufficient time to convert into the cis-DOCO isomer, or whether this is quenched by rapid stabilization into the trans-DOCO well. Ab initio and Rice-Ramsperger-Kassel-Marcus analysis of the intrinsic reaction coordinate for trans-DOCO to cis-DOCO interconversion rates supports the latter scenario, which helps explain the failure of previous high resolution infrared efforts to detect cis-hydroxycarbonyl.

Pressure-dependent kinetics of methyl formate reactions with OH at combustion, atmospheric and interstellar temperatures

Pressure dependence occurs in bimolecular hydrogen abstraction reactions at combustion, atmospheric and interstellar temperatures.

Reaction kinetics of OH + HNO3 under conditions relevant to the upper troposphere/lower stratosphere

Key upper atmosphere reaction of HNO₃ + OH studied over extended pressure and temperature range using new alternative detection method.

Direct measurements of DOCO isomers in the kinetics of OD + CO

Quantitative and mechanistically detailed kinetics of the reaction of hydroxyl radical (OH) with carbon monoxide (CO) have been a longstanding goal of contemporary chemical kinetics. This fundamental prototype reaction plays an important role in atmospheric and combustion chemistry, motivating studies for accurate determination of the reaction rate coefficient and its pressure and temperature dependence at thermal reaction conditions. This intricate dependence can be traced directly to details of the underlying dynamics (formation, isomerization, and dissociation) involving the reactive intermediates cis- and trans-HOCO, which can only be observed transiently. Using time-resolved frequency comb spectroscopy, comprehensive mechanistic elucidation of the kinetics of the isotopic analog deuteroxyl radical (OD) with CO has been realized. By monitoring the concentrations of reactants, intermediates, and products in real time, the branching and isomerization kinetics and absolute yields of all species in the OD + CO reaction are quantified as a function of pressure and collision partner.

Theoretical and kinetic study of the reaction of C2H3 + HO2 on the C2H3O2H potential energy surface

We systematically investigate the C₂H₃ + HO₂ reaction combined with conventional transition state theory, variable reaction coordinate transition state theory and Rice–Ramsberger–Kassel–Marcus/master-equation theory.

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.

CH3CO + O2 + M (M = He, N2) Reaction Rate Coefficient Measurements and Implications for the OH Radical Product Yield

The gas-phase CH3CO + O2 reaction is known to proceed via a chemical activation mechanism leading to the formation of OH and CH3C(O)OO radicals via bimolecular and termolecular reactive channels, respectively. In this work, rate coefficients, k, for the CH3CO + O2 reaction were measured over a range of temperature (241-373 K) and pressure (0.009-600 Torr) with He and N2 as the bath gas and used to characterize the bi- and ter-molecular reaction channels. Three independent experimental methods (pulsed laser photolysis-laser-induced fluorescence (PLP-LIF), pulsed laser photolysis-cavity ring-down spectroscopy (PLP-CRDS), and a very low-pressure reactor (VLPR)) were used to characterize k(T,M). PLP-LIF was the primary method used to measure k(T,M) in the high-pressure regime under pseudo-first-order conditions. CH3CO was produced by PLP, and LIF was used to monitor the OH radical bimolecular channel reaction product. CRDS, a complementary high-pressure method, measured k(295 K,M) over the pressure range 25-600 Torr (He) by monitoring the temporal CH3CO radical absorption following its production via PLP in the presence of excess O2. The VLPR technique was used in a relative rate mode to measure k(296 K,M) in the low-pressure regime (9-32 mTorr) with CH3CO + Cl2 used as the reference reaction. A kinetic mechanism analysis of the combined kinetic data set yielded a zero pressure limit rate coefficient, kint(T), of (6.4 ± 4) × 10(-14) exp((820 ± 150)/T) cm(3) molecule(-1) s(-1) (with kint(296 K) measured to be (9.94 ± 1.3) × 10(-13) cm(3) molecule(-1) s(-1)), k0(T) = (7.39 ± 0.3) × 10(-30) (T/300)(-2.2±0.3) cm(6) molecule(-2) s(-1), and k∞(T) = (4.88 ± 0.05) × 10(-12) (T/300)(-0.85±0.07) cm(3) molecule(-1) s(-1) with Fc = 0.8 and M = N2. A He/N2 collision efficiency ratio of 0.60 ± 0.05 was determined. The phenomenological kinetic results were used to define the pressure and temperature dependence of the OH radical yield in the CH3CO + O2 reaction. The present results are compared with results from previous studies and the discrepancies are discussed.

Pressure effects on the relaxation of an excited nitromethane molecule in an argon bath

Classical molecular dynamics simulations were performed to study the relaxation of nitromethane in an Ar bath (of 1000 atoms) at 300 K and pressures 10, 50, 75, 100, 125, 150, 300, and 400 atm. The molecule was instantaneously excited by statistically distributing 50 kcal/mol among the internal degrees of freedom. At each pressure, 1000 trajectories were integrated for 1000 ps, except for 10 atm, for which the integration time was 5000 ps. The computed ensemble-averaged rotational energy decay is ∼100 times faster than the vibrational energy decay. Both rotational and vibrational decay curves can be satisfactorily fit with the Lendvay-Schatz function, which involves two parameters: one for the initial rate and one for the curvature of the decay curve. The decay curves for all pressures exhibit positive curvature implying the rate slows as the molecule loses energy. The initial rotational relaxation rate is directly proportional to density over the interval of simulated densities, but the initial vibrational relaxation rate decreases with increasing density relative to the extrapolation of the limiting low-pressure proportionality to density. The initial vibrational relaxation rate and curvature are fit as functions of density. For the initial vibrational relaxation rate, the functional form of the fit arises from a combinatorial model for the frequency of nitromethane "simultaneously" colliding with multiple Ar atoms. Roll-off of the initial rate from its low-density extrapolation occurs because the cross section for collision events with L Ar atoms increases with L more slowly than L times the cross section for collision events with one Ar atom. The resulting density-dependent functions of the initial rate and curvature represent, reasonably well, all the vibrational decay curves except at the lowest density for which the functions overestimate the rate of decay. The decay over all gas phase densities is predicted by extrapolating the fits to condensed-phase densities.

Ring Polymer Molecular Dynamics Calculations of Thermal Rate Constants for the O((3)P) + CH4 → OH + CH3 Reaction: Contributions of Quantum Effects

The thermal rate constant of the O((3)P) + CH4 → OH + CH3 reaction is investigated with ring polymer molecular dynamics on a full-dimensional potential energy surface. Good agreement with experimental and full-dimensional quantum multiconfiguration time-dependent Hartree results between 300 and 1500 K was obtained. It is shown that quantum effects, for example, tunneling and zero-point energy, can be effectively and efficiently included in this path-integral based approach implemented with classical trajectories. Convergence with respect to the number of beads is rapid, suggesting wide applicability for other reactions involving polyatomic molecules.

Interception of excited vibrational quantum states by O2 in atmospheric association reactions

Bimolecular reactions in Earth's atmosphere are generally assumed to proceed between reactants whose internal quantum states are fully thermally relaxed. Here, we highlight a dramatic role for vibrationally excited bimolecular reactants in the oxidation of acetylene. The reaction proceeds by preliminary adduct formation between the alkyne and OH radical, with subsequent O(2) addition. Using a detailed theoretical model, we show that the product-branching ratio is determined by the excited vibrational quantum-state distribution of the adduct at the moment it reacts with O(2). Experimentally, we found that under the simulated atmospheric conditions O(2) intercepts ~25% of the excited adducts before their vibrational quantum states have fully relaxed. Analogous interception of excited-state radicals by O(2) is likely common to a range of atmospheric reactions that proceed through peroxy complexes.