Statistical Rate Theory Research Articles

Products of the Self-Reaction of HCO Radicals: Theoretical Kinetics Studies

The mechanism of the self-reaction of HCO radicals is investigated by using high-level quantum-chemical methods including M05-2X, CCSD, CCSD(T) and CRCC(2,3). Next, the rate coefficients for several product channels as a function of pressure and temperature are computed by employing statistical rate theories. Four important product channels are predicted to be CO + CO + H2, HCOH + OH, cis-(HCO)2 and trans-(CHO)2. It is found that the bimolecular rate coefficients for the formation of cis-(HCO)2 and trans-(CHO)2 are strongly pressure-dependent. The rate coefficients for the product channels CO + CO + H2 and HCOH + OH are predicted to be slightly pressure-dependent. At lower pressures and higher temperatures, the products CO + CO + H2 and HCOH + OH are dominant, while at higher pressures and lower temperatures, cis-(HCO)2 and trans-(CHO)2 formation becomes important.

Theoretical kinetic study of the reaction between dimethyl disulfide and OH radicals

ABSTRACTThe potential energy profile of the reaction between dimethyl disulfide and OH• radicals is explored by utilizing ab initio and hybrid meta density functional theory methods. Having the energies and structural data of the stationary points, statistical rate theories, such as transition state theory and variable reaction coordinate-transition state theory, are employed to compute the overall rate constants, and discuss the mechanism and product channels. On the basis of the calculations, the overall rate coefficient is predicted to be 2.49 × 10−10 cm3 molecule−1 s−1 at 298 K. It is found that in the most favorable pathway, the reaction proceeds via formation of the relatively unstable intermediate CH3S•(OH)SCH3 decomposing rapidly to yield CH3S•+CH3SOH.

A Trajectory-Based Method to Explore Reaction Mechanisms.

The tsscds method, recently developed in our group, discovers chemical reaction mechanisms with minimal human intervention. It employs accelerated molecular dynamics, spectral graph theory, statistical rate theory and stochastic simulations to uncover chemical reaction paths and to solve the kinetics at the experimental conditions. In the present review, its application to solve mechanistic/kinetics problems in different research areas will be presented. Examples will be given of reactions involved in photodissociation dynamics, mass spectrometry, combustion chemistry and organometallic catalysis. Some planned improvements will also be described.

Quantum chemical and theoretical kinetics studies on the reaction of hydroperoxyl radical with chlorine atom

The singlet and triplet potential energy surfaces for the reaction of HO2 radical with Cl atom are explored by using high-level combination W1BD and W1U methods. Statistical rate theories are employed to compute the rate coefficients of the main product channels including HCl + O2( $$ ^{1} \Sigma _{u}^{ - } $$ ), HCl + O2( $$ ^{3} \Sigma _{g}^{ + } $$ ), OH + ClO and HOOCl as a function of pressure and temperature. It is found that the rate coefficients for the product channels OH + ClO and HOOCl are strongly depended on temperature and pressure. At lower pressures and higher temperatures, the product OH + ClO is important, while at higher pressures and lower temperatures, HOOCl is the dominant product. At some moderate temperatures and pressures, the rate coefficients for the formation of OH + ClO and HOOCl could be equal. The product channel HCl + O2( $$ ^{3} \Sigma _{g}^{ + } $$ ) proceeds via formation of a van der Waals complex Cl..HOO and, next, passes through a saddle point structure with a negative energy of − 5.0 kJ mol−1 relative to the reactants. It is shown that a two transition state model suitably describes the kinetics of this product channel.

A new model of meteoric calcium in the mesosphere and lower thermosphere

Abstract. Meteoric ablation produces layers of metal atoms in the mesosphere and lower thermosphere (MLT). It has been known for more than 30 years that the Ca atom layer is depleted by over 2 orders of magnitude compared with Na, despite these elements having nearly the same elemental abundance in chondritic meteorites. In contrast, the Ca+ ion abundance is depleted by less than a factor of 10. To explain these observations, a large database of neutral and ion–molecule reaction kinetics of Ca species, measured over the past decade, was incorporated into the Whole Atmosphere Community Climate Model (WACCM). A new meteoric input function for Ca and Na, derived using a chemical ablation model that has been tested experimentally with a Meteoric Ablation Simulator, shows that Ca ablates almost 1 order of magnitude less efficiently than Na. WACCM-Ca simulates the seasonal Ca layer satisfactorily when compared with lidar observations, but tends to overestimate Ca+ measurements made by rocket mass spectrometry and lidar. A key finding is that CaOH and CaCO3 are very stable reservoir species because they are involved in essentially closed reaction cycles with O2 and O. This has been demonstrated experimentally for CaOH, and in this study for CaCO3 using electronic structure and statistical rate theory. Most of the neutral Ca is therefore locked in these reservoirs, enabling rapid loss through polymerization into meteoric smoke particles, and this explains the extreme depletion of Ca.

Theoretical Study on the Kinetics of the Reaction of C2H with C2H2

In this theoretical research, the mechanism of the C2H + C2H2 reaction is studied by high-level quantum-chemical methods and kinetics of the reaction is investigated by statistical rate theories. High-level electronic structure calculation methods including M06-2X, CCSD(T), CBS-Q and G4 methods are employed to explore the doublet potential energy surface of the reaction and compute the molecular properties necessary for carrying out the statistical rate theory calculations. After locating stationary points of the reaction, steady-state approximation to the chemically-activated intermediates along with some statistical manipulations are applied to derive some practical integral equations for the rate constants of formation of all possible products of the reaction. Unimolecular rate constants are computed by RRKM theory. VRC-TST is used to compute the sum of quantum states for internal degrees of freedom of loose transition states. The present calculations reveal that the product HCCCCH + H (P8) is the dominant product over whole pressure and temperature range considered in the present study. Nonetheless, at low temperatures and high pressures, other intermediate products especially HCC(H)CCH and H2CCCCH, become significant. The overall computed rate constants are nearly constant over the temperature range 100-500 K and slightly increase at higher temperatures.

Ab initio studies on the photodissociation dynamics of the 1,1-difluoroethyl radical.

Born-Oppenheimer molecular dynamics trajectory calculations at the HCTH147/6-31G** level of theory simulate the dissociation dynamics of photolytically excited 1,1-difluoroethyl radicals. EOMCCSD/AUG-cc-pVDZ calculations show that an excitation energy of 94.82 kcal/mol is necessary to initiate photodissociation reactions. In contrast to photodissociation dynamics of ethyl radicals where a large discrepancy between actual dissociation rates and rates that are predicted by statistical rate theories, we find reaction rates of 5.1 × 1011 s-1 for the dissociation of an H atom, which is in perfect accord with what is predicted by Rice-Ramsperger-Kassel-Marcus (RRKM) calculations and there is no indication of any nonstatistical effects. However, our trajectory calculations show a much larger fraction of C-C bond breakage reaction of 56% occurring than that expected by RRKM (only 16%).

Quantum Chemical and Statistical Rate Theory Studies of the Vinyl Hydroperoxides Formed in trans-2-Butene and 2,3-Dimethyl-2-butene Ozonolysis.

The vinyl hydroperoxide (VHP), the major isomerization product of the syn-alkyl Criegee intermediate (CI) formed in alkene ozonolysis, is a direct precursor of hydroxyl radical (OH), the most important oxidant in the troposphere. While simulations of CI reactivity have usually assumed the VHP to be a prompt and quantitative source of OH, recent quantum chemical studies have revealed subtleties in VHP reactivity such as a barrier to peroxy bond homolysis and a possible rearrangement to a hydroxycarbonyl. In this work, we use M06-L, Weizmann-1 Brueckner Doubles, and equation-of-motion spin-flip coupled-cluster theories to calculate a comprehensive reaction mechanism for the syn and anti conformers of the parent VHP formed in trans-2-butene ozonolysis and the 1-methyl VHP formed in 2,3-dimethyl-2-butene ozonolysis. We predict that for the parent VHP the anti homolysis transition structure (TS) is 3 kcal mol-1 lower in energy than the syn TS, but for the 1-methyl system, the syn TS is 2 kcal mol-1 lower in energy. Statistical rate theory simulations based on the quantum chemical data predict that the parent VHP preferentially decomposes to vinoxy and OH radicals under all tropospheric conditions, while the 1-methyl VHP preferentially decomposes to 1-methylvinoxy and OH radicals only close to 298 K; at 200 K, the 1-methyl VHP preferentially rearranges to hydroxyacetone. Lower temperatures and higher pressures favor the temporary accumulation of both the parent and the 1-methyl VHP.

Comparison study on the calculation formula of evaporation mass flux through the plane vapour-liquid interface

In order to understand the influence of various factors on the evaporation rate on the vapor-liquid interface, the evaporation process of water in pure steam environment was calculated based on the statistical rate theory (SRT), and the results were compared with those from the traditional Hertz-Knudsen equation. It is found that the evaporation rate on the vapor-liquid interface increases with the increase of evaporation temperature and evaporation temperature difference and the decrease of vapor pressure. When the steam is in a superheated state, even if the temperature of the liquid phase is lower than that of the vapor phase, the evaporation may also occur on the vapor-liquid interface; at this time, the absolute value of the critical temperature difference for occurring evaporation decreases with the increase of vapor pressure. When the evaporation temperature difference is smaller, the theoretical calculation results based on the SRT are basically the same as the predicated results from the Hertz-Knudsen equation; but the deviation between them increases with the increase of temperature difference.

Failure and Redemption of Statistical and Nonstatistical Rate Theories in the Hydroboration of Alkenes.

Our previous work found that canonical forms of transition state theory incorrectly predict the regioselectivity of the hydroboration of propene with BH3 in solution. In response, it has been suggested that alternative statistical and nonstatistical rate theories can adequately account for the selectivity. This paper uses a combination of experimental and theoretical studies to critically evaluate the ability of these rate theories, as well as dynamic trajectories and newly developed localized statistical models, to predict quantitative selectivities and qualitative trends in hydroborations on a broader scale. The hydroboration of a series of terminally substituted alkenes with BH3 was examined experimentally, and a classically unexpected trend is that the selectivity increases as the alkyl chain is lengthened far from the reactive centers. Conventional and variational transition state theories can predict neither the selectivities nor the trends. The canonical competitive nonstatistical model makes somewhat better predictions for some alkenes but fails to predict trends, and it performs poorly with an alkene chosen to test a specific prediction of the model. Added nonstatistical corrections to this model make the predictions worse. Parametrized Rice-Ramsperger-Kassel-Marcus (RRKM)-master equation calculations correctly predict the direction of the trend in selectivity versus alkene size but overpredict its magnitude, and the selectivity with large alkenes remains unpredictable with any parametrization. Trajectory studies in explicit solvent can predict selectivities without parametrization but are impractical for predicting small changes in selectivity. From a lifetime and energy analysis of the trajectories, "localized RRKM-ME" and "competitive localized noncanonical" rate models are suggested as steps toward a general model. These provide the best predictions of the experimental observations and insight into the selectivities.

Analytical solution of Langmuir behavior of Statistical Rate Theory: Adsorption at solid/solution interface

In this study, the first complete analytical solution for Langmuir behavior of the Statistical Rate Theory at solid/solution interface is provided. The rate equations for dependence of the amount adsorbed on time were derived at the different condition. The kinetics data were created by numerical solution of rate equation developed from the fundamental SRT approach to adsorption at solid/solution interface based on Langmuir model. The created data were used to examine the accuracy of the new equations. Some empirical data were chosen to check the applicability of the new linear rate equations. The perfect agreement between the results of the obtained rate equations and the created and empirical data prove the accuracy of the analytical solution of Langmuir behavior of SRT rate equation at solid/solution interface.

Effect of the Thermocouple on Measuring the Temperature Discontinuity at a Liquid-Vapor Interface.

The coupled heat and mass transfer that occurs in evaporation is of interest in a large number of fields such as evaporative cooling, distillation, drying, coating, printing, crystallization, welding, atmospheric processes, and pool fires. The temperature jump that occurs at an evaporating interface is of central importance to understanding this complex process. Over the past three decades, thermocouples have been widely used to measure the interfacial temperature jumps at a liquid-vapor interface during evaporation. However, the reliability of these measurements has not been investigated so far. In this study, a numerical simulation of a thermocouple when it measures the interfacial temperatures at a liquid-vapor interface is conducted to understand the possible effects of the thermocouple on the measured temperature and features in the temperature profile. The differential equations of heat transfer in the solid and fluids as well as the momentum transfer in the fluids are coupled together and solved numerically subject to appropriate boundary conditions between the solid and fluids. The results of the numerical simulation showed that while thermocouples can measure the interfacial temperatures in the liquid correctly, they fail to read the actual interfacial temperatures in the vapor. As the results of our numerical study suggest, the temperature jumps at a liquid-vapor interface measured experimentally by using a thermocouple are larger than what really exists at the interface. For a typical experimental study of evaporation of water at low pressure, it was found that the temperature jumps measured by a thermocouple are overestimated by almost 50%. However, the revised temperature jumps are still in agreement with the statistical rate theory of interfacial transport. As well as addressing the specific application of the liquid-vapor temperature jump, this paper provides significant insight into the role that heat transfer plays in the operation of thermocouples in general.

Adsorption kinetics at the solid/solution interface: Statistical Rate Theory (SRT) at close to equilibrium

In this study, derivation of the modified pseudo first order kinetics model (MPFO) from Statistical Rate Theory (SRT) has been investigated. I have shown that derivation of MPFO model from SRT cannot be true. I have proved that the assumptions that applied for derivation of MPFO from SRT in the previous research are false. These assumption cause that K1s` (adsorption/desorption rate at equilibrium) and KL(Langmuir constant) will become zero simultaneously. In this research work I have shown that K1s` and KL cannot be zero simultaneously. Finally, I have concluded that derivation of MPFO from SRT approach is false.

A Chemical Kinetic Investigation on Butyl Formate Oxidation: Ab Initio Calculations and Experiments in a Jet-Stirred Reactor

Biofuels are expected to play a significant role in the quest for greener energy generation. In this perspective, esters produced from biomass are promising candidates. This work presents the first computational kinetic study on n-butyl formate (BF) oxidation under combustion conditions coupled to an experimental study in a jet-stirred reactor. Absolute rate constants for hydrogen abstraction reactions by the OH radical were calculated using the G3//MP2/aug-cc-pVDZ model chemistry, in conjunction with statistical rate theory (TST). Subsequently, the fate of the butyl formate radicals was also investigated by calculating absolute rate constants for combustion relevant decomposition channels such as β-scission and hydrogen transfer reactions. The derived rate expressions were used in the presently developed detailed kinetic mechanism, which was validated over experimental data obtained in a jet-stirred reactor at 10 atm and for three different mixtures (φ = 0.45, 0.9, and 1.8). Rate of production analyses w...

Furfural: The Unimolecular Dissociative Photoionization Mechanism of the Simplest Furanic Aldehyde.

The unimolecular dissociation reactions of energy-selected furfural cations have been studied by imaging photoelectron photoion coincidence spectroscopy at the vacuum-ultraviolet (VUV) beamline of the Swiss Light Source. In the photon energy range of 10.9-14.5 eV, furfural ions decay by numerous fragmentation channels. Modeling the breakdown diagram yielded the 0 K appearance energies of 10.95 ± 0.10, 11.16, and 12.03 eV for the c-C4H3O-CO+ (m/z = 95), c-C4H4O+ (m/z = 68), and c-C3H3+ (m/z = 39) fragment ions, respectively, formed by parallel dissociation channels. An internal conversion from the A″ to the A' electronic state via a conical intersection takes place along the reaction coordinate in the case of the H-loss channel (c-C4H3O-CO+ formation). Quantum chemical calculations and experimental results confirmed a fast conversion to the A' state and that the rate-determining step is a tight transition state on the potential energy surface. Appearance energies were also derived for the sequential dissociation products from the furan cation, c-C4H4O+, for the formation of CH2CO+ (m/z = 42), C3H4+ (m/z = 40), and CHO+ (m/z = 29) at 12.81, 12.80, and 13.34 eV, respectively. Statistical rate theory modeling of the breakdown diagram can also be used to predict the fractional ion abundances and thermal shifts in mass spectrometric pyrolysis studies to help assigning the m/z channels either to ionization of the neutrals or to dissociative ionization processes, with potential use for combustion diagnostics. The cationic geometry optimizations yielded functional-dependent spurious DFT minima and a deviating planar MP2 optimized geometry, which are briefly discussed.

Nighttime atmospheric chemistry of iodine

Abstract. Little attention has so far been paid to the nighttime atmospheric chemistry of iodine species. Current atmospheric models predict a buildup of HOI and I2 during the night that leads to a spike of IO at sunrise, which is not observed by measurements. In this work, electronic structure calculations are used to survey possible reactions that HOI and I2 could undergo at night in the lower troposphere, and hence reduce their nighttime accumulation. The new reaction NO3+ HOI → IO + HNO3 is proposed, with a rate coefficient calculated from statistical rate theory over the temperature range 260–300 K and at a pressure of 1000 hPa to be k(T) = 2.7 × 10−12 (300 K/T)2.66 cm3 molecule−1 s−1. This reaction is included in two atmospheric models, along with the known reaction between I2 and NO3, to explore a new nocturnal iodine radical activation mechanism. The results show that this iodine scheme leads to a considerable reduction of nighttime HOI and I2, which results in the enhancement of more than 25 % of nighttime ocean emissions of HOI + I2 and the removal of the anomalous spike of IO at sunrise. We suggest that active nighttime iodine can also have a considerable, so far unrecognized, impact on the reduction of the NO3 radical levels in the marine boundary layer (MBL) and hence upon the nocturnal oxidizing capacity of the marine atmosphere. The effect of this is exemplified by the indirect effect on dimethyl sulfide (DMS) oxidation.

Controlling Selectivity by Controlling Energy Partitioning in a Thermal Reaction in Solution

The comparison of experimental and predicted kinetic isotope effects in the α-cleavage of alkoxy radicals is used here to judge the applicability of statistical rate theories. It is found that the governing rate theory and the statistical versus nonstatistical nature of the cleavage depend on the cleavage barrier and how much energy is imparted to the radical. The latter can then be controlled by changing the size of substituents in the system. With a large alkyl group substituent, the vibrational energy of the alkoxy radical is increased, but this energy is not statistically distributed, leading to a lower isotope effect than predicted by statistical theories. The observed isotope effect can be approximately rationalized using a semistatistical localized RRKM model.

Rich Athermal Ground‐State Chemistry Triggered by Dynamics through a Conical Intersection

AbstractA fundamental tenet of statistical rate theories (such as transition state theory and RRKM) is the rapidity of vibrational relaxation. Excited‐state reactions happen quite quickly (sub‐picosecond) and thus can exhibit nonstatistical behavior. However, it is often thought that any diversity of photoproducts results from different conical intersections connecting the excited and ground electronic states. It is also conceivable that the large energy of the photon, which is converted to vibrational energy after electronic transitions could lead to athermal hot ground state reactions and that these might be responsible for the diversity of photoproducts. Here we show that this is the case for sulfines, where a single conical intersection is implicated in the electronic transition but the excited state reaction leads to nine different products within less than a picosecond.

Rich Athermal Ground-State Chemistry Triggered by Dynamics through a Conical Intersection.

A fundamental tenet of statistical rate theories (such as transition state theory and RRKM) is the rapidity of vibrational relaxation. Excited-state reactions happen quite quickly (sub-picosecond) and thus can exhibit nonstatistical behavior. However, it is often thought that any diversity of photoproducts results from different conical intersections connecting the excited and ground electronic states. It is also conceivable that the large energy of the photon, which is converted to vibrational energy after electronic transitions could lead to athermal hot ground state reactions and that these might be responsible for the diversity of photoproducts. Here we show that this is the case for sulfines, where a single conical intersection is implicated in the electronic transition but the excited state reaction leads to nine different products within less than a picosecond.

The reaction of methyl peroxy and hydroxyl radicals as a major source of atmospheric methanol.

Methyl peroxy, a key radical in tropospheric chemistry, was recently shown to react with the hydroxyl radical at an unexpectedly high rate. Here, the molecular reaction mechanisms are elucidated using high-level quantum chemical methodologies and statistical rate theory. Formation of activated methylhydrotrioxide, followed by dissociation into methoxy and hydroperoxy radicals, is found to be the main reaction pathway, whereas methylhydrotrioxide stabilization and methanol formation (from activated and stabilized methylhydrotrioxide) are viable minor channels. Criegee intermediate formation is found to be negligible. Given the theoretical uncertainties, useful constraints on the yields are provided by atmospheric methanol measurements. Using a global chemistry-transport model, we show that the only explanation for the high observed methanol abundances over remote oceans is the title reaction with an overall methanol yield of ∼30%, consistent with the theoretical estimates given their uncertainties. This makes the title reaction a major methanol source (115 Tg per year), comparable to global terrestrial emissions.