Calculation Of Reaction Rate Constants Research Articles

Semiclassical instanton approach to calculation of reaction rate constants in multidimensional chemical systems

The semiclassical instanton approximation is revisited in the context of its application to the calculation of chemical reaction rate constants. An analytical expression for the quantum canonical reaction rate constants of multidimensional systems is derived for all temperatures from the deep tunneling to high-temperature regimes. The connection of the derived semiclassical instanton theory with several previously developed reaction rate theories is shown and the numerical procedure for the search of instanton trajectories is provided. The theory is tested on seven different collinear symmetric and asymmetric atom transfer reactions including heavy-light-heavy, light-heavy-light and light-light-heavy systems. The obtained thermal rate constants agree within a factor of 1.5-2 with the exact quantum results in the wide range of temperatures from 200 to 1500 K.

Reactions of C2H with 1- and 2-Butynes: An Ab Initio/RRKM Study of the Reaction Mechanism and Product Branching Ratios

Ab initio CCSD(T)/cc-pVTZ(CBS)//B3LYP/6-311G** calculations of the C(6)H(7) potential energy surface are combined with RRKM calculations of reaction rate constants and product branching ratios to investigate the mechanism and product distribution in the C(2)H + 1-butyne/2-butyne reactions. 2-Ethynyl-1,3-butadiene (C(6)H(6)) + H and ethynylallene (C(5)H(4)) + CH(3) are predicted to be the major products of the C(2)H + 1-butyne reaction. The reaction is initiated by barrierless ethynyl additions to the acetylenic C atoms in 1-butyne and the product branching ratios depend on collision energy and the direction of the initial C(2)H attack. The 2-ethynyl-1,3-butadiene + H products are favored by the central C(2)H addition to 1-butyne, whereas ethynylallene + CH(3) are preferred for the terminal C(2)H addition. A relatively minor product favored at higher collision energies is diacetylene + C(2)H(5). Three other acyclic C(6)H(6) isomers, including 1,3-hexadiene-5-yne, 3,4-hexadiene-1-yne, and 1,3-hexadiyne, can be formed as less important products, but the production of the cyclic C(6)H(6) species, fulvene, and dimethylenecyclobut-1-ene (DMCB), is predicted to be negligible. The qualitative disagreement with the recently measured experimental product distribution of C(6)H(6) isomers is attributed to a possible role of the secondary 2-ethynyl-1,3-butadiene + H reaction, which may generate fulvene as a significant product. Also, the photoionization energy curve assigned to DMCB in experiment may originate from vibrationally excited 2-ethynyl-1,3-butadiene molecules. For the C(2)H + 2-butyne reaction, the calculations predict the C(5)H(4) isomer methyldiacetylene + CH(3) to be the dominant product, whereas very minor products include the C(6)H(6) isomers 1,1-ethynylmethylallene and 2-ethynyl-1,3-butadiene.

고온가속노화시험을 이용한 추진제 KM10의 저장 수명 추정

The propellant KM10, a single propellant manufactured nitrocellulose, is known to cause natural degradation phenomena at long term storage. The self-life was estimated using generally used high temperature acceleration aging tests to analyze the content of stabilizer and using the Arrhenius equation & Berthelot equation to calculate reaction rate constants. According to the result of this study, self-life of propellant KM10 using the Arrhenius equation & Berthelot equation appear significantly different as 43.73, 16.53years and when compared with the paper of E. R. Bixon, self-life of propellant KM10 predicted using the Arrhenius equation was reasonably determined.

Calculation of reaction rate constants using approximate evolution of quantum trajectories in imaginary and real time

Reaction rate constants can be directly obtained from evolution of the flux operator eigenvectors under the Boltzmann and Hamiltonian operators. This is achieved by evolving the quantum trajectory ensemble, representing a wavefunction, in imaginary time seamlessly switching to the real-time dynamics. Quantum–mechanical effects are incorporated through the quantum potential dependent on the trajectory momenta or on the derivatives of the wavefunction amplitude. For practicality the quantum potential and wavefunction nodes are described using linear basis, which is exact for Gaussian wavefunctions. For the Eckart barrier approximate rate constants show significant improvement over the parabolic barrier rate constants.

Theoretical Study of the Pyrolysis of Methyltrichlorosilane in the Gas Phase. 3. Reaction Rate Constant Calculations

The rate constants for the gas-phase reactions in the silicon carbide chemical vapor deposition of methyltrichlorosilane (Ge, Y. B.; Gordon, M. S.; Battaglia, F.; Fox, R. O. J. Phys. Chem. A 2007, 111, 1462.) were calculated. Transition state theory was applied to the reactions with a well-defined transition state; canonical variational transition state theory was applied to the barrierless reactions by finding the generalized transition state with the maximum Gibbs free energy along the reaction path. Geometry optimizations were carried out with second-order perturbation theory (MP2) and the cc-pVDZ basis set. The partition functions were calculated within the harmonic oscillator and rigid rotor approximations. The final potential energy surfaces were obtained using the left-eigenstate coupled-cluster theory, CR-CC(2,3) with the cc-pVTZ basis set. The high-pressure approximation was applied to the unimolecular reactions. The predicted rate constants for more than 50 reactions were compared with the experimental ones at various temperatures and pressures; the deviations are generally less than 1 order of magnitude. Theory is found to be in reasonable agreement with the experiments.

An ab initio/RRKM study of the reaction mechanism and product branching ratios of the reactions of ethynyl radical with allene and methylacetylene

Ab initio CCSD(T)/cc-pVTZ//B3LYP/6-311G** calculations of the C(5)H(5) potential energy surface have been performed to investigate the reaction mechanism of ethynyl radical (C(2)H) with C(3)H(4) isomers, allene and methylacetylene. They were followed by RRKM calculations of reaction rate constants and product branching ratios under single-collision conditions. The results show that the C(2)H + CH(2)CCH(2) reaction in a case of statistical behavior is expected to produce 1,4-pentadiyne (56-63%), ethynylallene (22-24%), and pentatetraene (10-15%), with the most favorable pathways including H losses from the initial HCCCH(2)CCH(2) adduct leading to either 1,4-pentadiyne or ethynylallene, and a multistep route HCCC(CH(2))(2) --> four-member ring --> CH(2)CCCHCH(2) --> CH(2)CCCCH(2) + H featuring a formal insertion of C(2)H into a double bond of allene followed by H elimination giving rise to pentatetraene. On the contrary, the C(2)H + CH(3)CCH reaction produces diacetylene + methyl (21-61%) by CH(3) loss from the HCCC(CH)CH(3) initial adduct as well as methyldiacetylene + H (27-56%) and ethynylallene + H (11-22%) by H eliminations from CHCCHCCH(3). The calculated product branching ratios are in general agreement with the available experimental data, although some quantitative deviations from experiment and possible reasons for them are also discussed. The present calculations confirm that the C(2)H + C(3)H(4) reactions proceed without entrance barriers and lead, via intermediates and transition states residing lower in energy than the initial reactants, to the C(5)H(4) + H and C(4)H(2) + CH(3) products exothermic by 20-36 kcal mol(-1), with strong dependence of the product distribution on the reacting C(3)H(4) isomer, making these reactions fast under low-temperature conditions of Titan's atmosphere where they can serve as a source of more complex unsaturated hydrocarbons.

Quantum rate dynamics for proton transfer reactions in condensed phase: The exact hierarchical equations of motion approach

We apply the recently developed Liouville space hierarchical equations of motion (HEOM) method to calculate the quantum rate dynamics for a model system of proton transfer reaction in condensed phase, which consist of a double well coupled to a harmonic bath with the Debye spectral density. The HEOM method provides a new way to directly calculate nonequilibrium reduced system dynamics, and the calculated reaction rate constants compare well with previous numerical exact results. The HEOM method also allows us to perform long time simulations, which enables systematic studies of the reaction dynamics at low frictions. The applicability of perturbative quantum master equations at various orders is also investigated by comparing with numerical exact HEOM results.

Catalyst size matters: Tuning the molecular mechanism of the water–gas shift reaction on titanium carbide based compounds

The molecular mechanism of the water–gas shift reaction catalyzed by titanium carbide compounds was studied using a density functional approach. Three different catalyst models have been considered: the extended TiC(001) surface, the Ti8C12 MetCar, and a Ti14C13 nanoparticle. Adsorption of reactants, intermediates, and products occurs on different sites, demonstrating the chemical versatility of the TiC substrates. Thus, adsorption energies depend not only on the existence of low-coordinated sites, but also on the nature of atoms involved in the adsorption site. The two most likely molecular mechanisms, redox and associative, were considered. The first of these mechanisms involves complete water dissociation, whereas the second involves formation of the carboxyl (OCOH) intermediate. The catalytic activity was found to be highest for the TiC(001) surface, due to the overly strong adsorption of reactants and products on either Ti14C13 or Ti8C12. This has important consequences for the underlying chemistry, as evidenced by the corresponding reaction energy profiles, which show that the redox mechanism is the preferred route for the reaction occurring on the nanoparticles, whereas the carboxyl formation route is preferred for the reaction occurring above the TiC(001) surface. However, the calculated reaction rate constants indicate that the reaction will hardly occur on the former, whereas it is quite feasible on the latter. The present study suggests that TiC and similar transition metal carbides can be good catalysts for the water–gas shift reaction and can be potential substitutes for current low-temperature catalysts. In addition, the results point to a possible tuning to control the particle size or rate of steps.

Calculating reaction rate constants and estimating the efficacy of selective enzyme inhibitors

The dynamic steady state of a pair of forward and backward enzymatic reactions is dependent on the balance between the enzymes catalyzing the reactions. By selectively inhibiting one or more of the enzymes involved, this balance is shifted into a new steady state, making it possible to calculate the reaction rate constants after measurement of the reactants. Ideally, the inhibitors should completely eliminate either reaction, but this is often not the case. Here we present and discuss a method for calculating the reaction rate constants and, thus, for evaluating the efficacy of one or more inhibitors when introduced to a forward–backward pair of enzymatic reactions.

A novel software tool for high throughput measurements of interconversion barriers: DCXplorer

The software program DCXplorer is introduced to directly access interconversion rate constants in dynamic chromatography and electrophoresis. The program utilizes the unified equation of chromatography which can evaluate reaction rate constants of all kinds of first order reactions of processes taking place during a separation process. Evaluations with DCXplorer are facilitated by a graphical user interface which allows zooming into the area of interest of an interconversion profile and calculating reaction rate constants without a time consuming simulation process. DCXplorer was applied to determine the enantiomerization barrier of the diuretic drug chlorthalidone by pressure supported dynamic capillary electrokinetic chromatography (DEKC) under acidic conditions at pH 5.00 and pH 3.75. Activation parameters Δ H ╪ and Δ S ╪ were obtained from temperature dependent measurements between 15.0 and 35.0 °C in 5 K steps at pH 3.75 and between 30.0 and 50.0 °C in 10 K steps at pH 5.00.

Computational Study of the Oxidation and Decomposition of Dibenzofuran under Atmospheric Conditions

The atmospheric degradation of dibenzofuran (DF) initiated by OH addition has been studied by using density functional theory (B3LYP method). Site C1 in DF is predicted to be the favored site for OH addition, with a branching ratio of 0.61 to produce a DF-OH(1) adduct. The calculated reaction rate constant for OH addition to DF has been used to predict the atmospheric lifetime of DF to be 0.45 day. Three different modes of attack of O2 ((3)Sigma(g)) on DF-OH(1) have been examined. Abstraction of hydrogen gem to OH in DF-OH(1) by O2 ((3)Sigma(g)) (producing 1-dibenzofuranol I) and dioxygen addition in the three radical sites in cis and trans orientation (relative to the ispo-added OH) of the pi-delocalized electron system of DF-OH(1) are feasible under atmospheric conditions. The free energy of activation (at 298.15 K) for the formation of 1-dibenzofuranol is 15.1 kcal/mol with a free energy change of -36.3 kcal/mol, while the formation of DF-OH(1)-O2 adducts are endergonic by 9.2-21.8 kcal/mol with a 16.3-23.6 kcal/mol free energy of activation. On the basis of the calculated reaction rate constants, the formation of 1-dibenzofuranol is more important than the formation of DF-OH-O2 adducts. The results presented here are a first attempt to gain a better understanding of the atmospheric oxidation of dioxin-like compounds on a precise molecular basis.

Quality of honeys influenced by thermal treatment

Honey producers have been heating honeys at mild temperatures below 100 °C chiefly in order to prevent post-bottling crystallization. In this study, we aimed to determine the effects of thermal treatment on the HMF content of honeydew and floral honey during the isothermal heating process at mild temperatures. Water content, formol number, total acidity, pH value and minerals were also determined in both honey types as their characteristics differ with composition, which is able to affect the rate of HMF formation. Potassium content and pH value were found as the distinguishing properties and both were greater in honeydew honey than in floral honey ( p<0.01). Honeydew and floral honey samples were heated at 75, 90 and 100 °C for 15–90 min and analysed for HMF content by HPLC-RP. The Arrhenius model was used to calculate reaction rate constants and activation energies which were found to be different for each of the honey types. Heating at 90 °C for up to 90 min in floral honeys and up to 75 min in honeydew honeys did not cause a significant increase of HMF and not exceed the threshold level of 40 mg kg −1. Our results show that the excessive HMF content might be related to primitive storage conditions rather than overheating.

The Reaction of Tricarbon with Acetylene: An Ab Initio/RRKM Study of the Potential Energy Surface and Product Branching Ratios

Ab initio calculations of the potential energy surface for the C3(1Sigmag+)+C2H2(1Sigmag+) reaction have been performed at the RCCSD(T)/cc-pVQZ//B3LYP/6-311G(d,p) + ZPE[B3LYP/6-311G(d,p)] level with extrapolation to the complete basis set limit for key intermediates and products. These calculations have been followed by statistical calculations of reaction rate constants and product branching ratios. The results show the reaction to begin with the formation of the 3-(didehydrovinylidene)cyclopropene intermediate i1 or five-member ring isomer i7 with the entrance barriers of 7.6 and 13.8 kcal/mol, respectively. i1 rearranges to the other C5H2 isomers, including ethynylpropadienylidene i2, singlet pentadiynylidene i3, pentatetraenylidene i4, ethynylcyclopropenylidene i5, and four- and five-member ring structures i6, i7, and i8 by ring-closure and ring-opening processes and hydrogen migrations. i2, i3, and i4 lose a hydrogen atom to produce the most stable linear isomer of C5H with the overall reaction endothermicity of approximately 24 kcal/mol. H elimination from i5 leads to the formation of the cyclic C5H isomer, HC2C3, +H, 27 kcal/ mol above C3+C2H2. 1,1-H2 loss from i4 results in the linear pentacarbon C5+H2 products endothermic by 4 kcal/mol. The H elimination pathways occur without exit barriers, whereas the H2 loss from i4 proceeds via a tight transition state 26.4 kcal/mol above the reactants. The characteristic energy threshold for the reaction under single collision conditions is predicted be in the range of approximately 24 kcal/mol. Product branching ratios obtained by solving kinetic equations with individual rate constants calculated using RRKM and VTST theories for collision energies between 25 and 35 kcal/mol show that l-C5H+H are the dominant reaction products, whereas HC2C3+H and l-C5+H2 are minor products with branching ratios not exceeding 2.5% and 0.7%, respectively. The ethynylcyclopropenylidene isomer i5 is calculated to be the most stable C5H2 species, more favorable than triplet pentadiynylidene i3t by approximately 2 kcal/mol.

Optimizing the Performance of the Multiconfiguration Molecular Mechanics Method

Multiconfiguration molecular mechanics (MCMM) is a general algorithm for constructing potential energy surfaces for reactive systems (Kim, Y.; Corchado, J. C.; Villà, J.; Xing, J.; Truhlar, D. G. J. Chem. Phys. 2000, 112, 2718). This paper illustrates how the performance of the MCMM method can be improved by adopting improved molecular mechanics parameters. We carry out calculations of reaction rate constants using variational transition state theory with optimized multidimensional tunneling on the MCMM PESs for three hydrogen transfer reactions, and we compare the results to direct dynamics. We find that the MCMM method with as little as one electronic structure Hessian can describe the dynamically important regions of the ground-electronic state PES, including the corner-cutting-tunneling region of the reaction swath, with practical accuracy.

Gas-phase Boudouard disproportionation reaction between highly vibrationally excited CO molecules

The gas-phase Boudouard disproportionation reaction between two highly vibrationally excited CO molecules in the ground electronic state has been studied in optically pumped CO. The gas temperature and the CO vibrational level populations in the reaction region, as well as the CO 2 concentration in the reaction products have been measured using FTIR emission and absorption spectroscopy. The results demonstrate that CO 2 formation in the optically pumped reactor is controlled by the high CO vibrational level populations, rather than by CO partial pressure or by flow temperature. The disproportionation reaction rate constant has been determined from the measured CO 2 and CO concentrations using the perfectly stirred reactor (PSR) approximation. The reaction activation energy, 11.6 ± 0.3 eV (close to the CO dissociation energy of 11.09 eV), was evaluated using the statistical transition state theory, by comparing the dependence of the measured CO 2 concentration and of the calculated reaction rate constant on helium partial pressure. The disproportionation reaction rate constant measured at the present conditions is k f = (9 ± 4) × 10 −18 cm 3/s. The reaction rate constants obtained from the experimental measurements and from the transition state theory are in good agreement.

Hybrid Density Functional Theory with Specific Reaction Parameter: Hydrogen Abstraction Reaction of Fluoromethane by the Hydroxyl Radical

Three potential energy surfaces with specific reaction parameters are developed and tested for the OH + CH(3)F --> H(2)O + CH(2)F reaction. The goal of this work is to determine surfaces that provide calculated reaction rate constants that are comparable to the experimental data. The potential energy surfaces are constructed using hybrid and hybrid meta density functional theory methods, and the levels of electronic structure theory used in this study are mPW1PW91, B1B95, and mPW1B95 in conjunction with the 6-31+G(d,p) basis set. The reaction rate constants are calculated over the range 200-1,500 K using variational transition state theory with multidimensional tunneling contributions. New specific-reaction-parameter Hartree-Fock contributions are determined, and the hybrid density functional theory methods with these new contributions (35.5 +/- 1.2% for mPW1PW91, 36.6 +/- 1.2% for B1B95, and 40.7 +/- 1.2% for mPW1B95, respectively) reproduce accurate rate constants over an extended temperature range. On these potential energy surfaces, the classical barrier height for the hydrogen abstraction reaction is determined to be 3.4-3.8 kcal/mol, with a best estimate value of 3.6 kcal/mol.

Computational Studies of Chemical Reactions: The HNC–HCN and CH3NC–CH3CN Isomerizations

A series of computational chemistry projects is described that focuses on the isomerization reactions, HNC–HCN and CH3NC–CH3CN. These projects guide students through several applications involving transition state location and optimization, intrinsic reaction coordinate potential energy surface construction, and the calculation of reaction rate constants. The calculations are at a high enough level of theory to allow them to obtain good results, while not demanding unrealistic computing resources or computational sophistication.

Potential Energy Surface and Product Branching Ratios for the Reaction of Dicarbon, C2(XΣg+), with Methylacetylene, CH3CCH(X1A1): An Ab Initio/RRKM Study

Ab initio calculations of the potential energy surface for the C(2)(X(1)Sigma(g)(+)) + CH(3)CCH(X(1)A(1)) reaction have been carried at the G2M level of theory. The calculations show that the dicarbon molecule in the ground singlet electronic state can add to methylacetylene without a barrier producing a three-member or a four-member ring intermediate, which can rapidly rearrange to the most stable H(3)CCCCCH isomer on the C(5)H(4) singlet surface. This isomer can then lose a hydrogen atom (H) or molecular hydrogen (H(2)) from the CH(3) group with the formation of H(2)CCCCCH and HCCCCCH, respectively. Alternatively, H atom migrations and three-member-ring closure/opening rearrangements followed by H and H(2) losses can lead to other isomers of the C(5)H(3) and C(5)H(2) species. According to the calculated energetics, the C(2)(X(1)Sigma(g)(+)) + CH(3)CCH reaction is likely to be a major source of the C(5)H(3) radicals (in particular, the most stable H(2)CCCCCH and HCCCHCCH isomers, which are relevant to the formation of benzene through the reactions with CH(3)). Among heavy-fragment product channels, only C(3)H(3) + C(2)H and c-C(3)H(2) + C(2)H(2) might compete with C(5)H(3) + H and C(5)H(2) + H(2). RRKM calculations of reaction rate constants and product branching ratios depending on the reactive collision energy showed that the major reaction products are expected to be H(2)CCCCCH + H (64-66%) and HCCCHCCH + H (34-30%), with minor contributions from HCCCCCH + H(2) (1-2%), HCCCHCC + H(2) (up to 1%), C(3)H(3) + C(2)H (up to 1%), and c-C(3)H(2) + C(2)H(2) (up to 0.1%) if the energy randomization is complete. The calculations also indicate that the C(2)(X(1)Sigma(g)(+)) + CH(3)CCH(X(1)A(1)) reaction can proceed by direct H-abstraction of a methyl hydrogen to form C(3)H(3) + C(2)H almost without a barrier.

Hydrogen Abstraction Acetylene Addition and Diels-Alder Mechanisms of PAH Formation: A Detailed Study Using First Principles Calculations.

Extensive ab initio Gaussian-3-type calculations of potential energy surfaces (PES), which are expected to be accurate within 1-2 kcal/mol, combined with statistical theory calculations of reaction rate constants have been applied to study various possible pathways in the hydrogen abstraction acetylene addition (HACA) mechanism of naphthalene and acenaphthalene formation as well as Diels-Alder pathways to acenaphthalene, phenanthrene, and pyrene. The barrier heights; reaction energies; and molecular parameters of the reactants, products, intermediates, and transition states have been generated for all types of reactions involved in the HACA and Diels-Alder mechanisms, including H abstraction from various aromatic intermediates, acetylene addition to radical sites, ring closures leading to the formation of additional aromatic rings, elimination of hydrogen atoms, H disproportionation, C2H2 cycloaddition, and H2 loss. The reactions participating in various HACA sequences (e.g., Frenklach's, alternative Frenklach's, and Bittner and Howard's routes) are demonstrated to have relatively low barriers and high rate constants under combustion conditions. A comparison of the significance of different HACA mechanisms in PAH growth can be made in the future using PES and molecular parameters obtained in the present work. The results show that the Diels-Alder mechanism cannot compete with the HACA pathways even at high combustion temperatures, because of high barriers and consequently low reaction rate constants. The calculated energetic parameters and rate constants have been compared with experimental and theoretical data available in the literature.

The Reaction of Phenyl Radical with Molecular Oxygen: A G2M Study of the Potential Energy Surface

Ab initio G2M calculations have been performed to investigate the potential energy surface for the reaction of C6H5 with O2. The reaction is shown to start with an exothermic barrierless addition of O2 to the radical site of C6H5 to produce phenylperoxy (1) and, possibly, 1,2-dioxaspiro[2.5]octadienyl (dioxiranyl, 8) radicals. Next, 1 loses the terminal oxygen atom to yield the phenoxy + O products (3) or rearranges to 8. The dioxiranyl can further isomerize to a seven-member ring 2-oxepinyloxy radical (10), which can give rise to various products including C5H5 + CO2, pyranyl + CO, o-benzoquinone + H, and 2-oxo-2,3-dihydrofuran-4-yl + C2H2. Once 10 is produced, it is unlikely to go back to 8 and 1, because the barriers separating 10 from the products are much lower than the reverse barrier from 10 to 8. Thus, the branching ratio of C6H5O + O against the other products is mostly controlled by the critical transition states between 1 and 3, 1 and 8, and 8 and 10. According to the calculated barriers, the most favorable product channel for the decomposition of 10 is C5H5 + CO2, followed by pyranyl + CO and o-benzoquinone + H. Since C6H5O + O and C5H5 + CO2 are expected to be the major primary products of the C6H5 + O2 reaction and thermal decomposition of C6H5O leads to C5H5 + CO, cyclopentadienyl radicals are likely to be the major product of phenyl radical oxidation, and so it results in degradation of the six-member aromatic ring to the five-member cyclopentadienyl ring. Future multichannel RRKM calculations of reaction rate constants are required to support these conclusions and to quantify the product branching ratios at various combustion conditions.