Thermal Rate Constants For Reactions Research Articles

Prediction of Absolute Rate Constants for the Reactions of NH2 with Alkanes from ab Initio G2M/TST Calculations

Systematic ab initio calculations of potential energy surfaces for the reactions of NH{sub 2} with various alkanes (CH{sub 4}, C{sub 2}H{sub 6}, C{sub 3}H{sub 8}, and i-C{sub 4}H{sub 10}) which involve abstraction of a hydrogen atom from primary, secondary, and tertiary C-H bonds have been performed using the G2M method. The calculated activation barrier for the NH{sub 2} + CH{sub 4} reaction, 15.2 kcal/mol, is higher than those for the H-abstraction from a primary C-H bond in C{sub 2}H{sub 6}, C{sub 3}H{sub 8}, and i-C{sub 4}H{sub 10}, 11--12 kcal/mol. The barrier height decreases to 8.4 and 8.3 kcal/mol for the abstraction from a secondary C-H bond in C{sub 3}H{sub 8} and a tertiary C-H bond in i-C{sub 4}H{sub 10}, respectively, in line with the weakening strength of the C-H bond and the increase of the reaction exothermicity. The G2M energies and the molecular and transition-state parameters are used to compute thermal reaction rate constants within the transition-state theory formalism with tunneling corrections. A good agreement of the theoretical rate constants with the experimental is found if the computed barriers are adjusted by 0.5--2 kcal/mol, which is within the accuracy of the G2M method. The H-abstraction from the tertiary C-H bondmore » is shown to be faster than the other considered reactions at T {le} 2000 K, while the secondary H-abstraction is the second fastest reaction at T {le} 1600 K. The rate of the primary H-abstraction decreases with the increase of the alkane size, from ethane to propane and to isobutane. The calculated rate constants for the H-abstraction by NH{sub 2} from primary, secondary, and tertiary C-H bonds can serve as models for the reactions of the amino radical with various saturated hydrocarbons.« less

Semiclassical approximations for the calculation of thermal rate constants for chemical reactions in complex molecular systems

Two different semiclassical approaches are presented for extending flux correlation function methodology for computing thermal reaction rate constants, which has been extremely successful for the “direct” calculation of rate constants in small molecule (∼3–4 atoms) reactions, to complex molecular systems, i.e., those with many degrees of freedom. First is the popular mixed quantum-classical approach that has been widely used by many persons, and second is an approximate version of the semiclassical initial value representation that has recently undergone a rebirth of interest as a way for including quantum effects in molecular dynamics simulations. Both of these are applied to the widely studied system-bath model, a one-dimensional double well potential linearly coupled to an infinite bath of harmonic oscillators. The former approximation is found to be rather poor while the latter is quite good.

The quantum transition state wavepacket method

The accurate calculation of thermal rate constants for reactions in the gas phase often requires both accurate potential energy surfaces (PESs) and the use of quantum mechanics, particularly in the case of light atom (H) transfers in reactions with activation energy barriers between reactants and products. The thermal rate constant k(T) can be calculated directly or as a thermal average over the cumulative reaction probability N(E). Both k(T) and N(E) can be calculated exactly and directly in terms of flux formulations first presented by Miller etal. In this paper we review the recent reformulation of the calculation of N(E) in terms of the time evolution of transition state wavepackets (TSWPs), which then provides a very effective method for reactions with activation energy barriers. This method requires a single time propagation for each TSWP contributing to the desired thermal rate constant from which the required contributions to N(E) for all E can be obtained. We then apply this to the calculation of N(E) and k(T) for the interesting four atom reaction H2(D2)+CN→HCN(DCN)+H(D). The system has a metastable well in the PES at the linear CNHH configuration. The results and a discussion of the influence of this secondary TS well are presented.

Quantum Mechanical Pressure-Dependent Reaction and Recombination Rates for O + OH → H + O2, HO2

We extend recent flux−flux autocorrelation function methods for the direct computation of thermal reaction rate constants and unimolecular recombination rates to the case where both reaction and recombination are possible. Rather than a single transition state dividing surface, dividing surfaces are placed on both the reactant (r) and product (p) sides of the intermediate collision complex region. The thermal recombination rate expression then involves a flux cross-correlation function Crp(t) in addition to the usual autocorrelation function Crr(t), both of which are computed during a single quantum time propagation. This method is applied to the three-dimensional O + OH ⇌ H + O2 (J = 0) reactions, employing parallel computation because of the necessary large basis (218 grid points) and long propagation times (2−3 ps). Thermal rate constants (in the absence of recombination effects) are presented for T = 500−2000 K, using the J-shifting approximation to account for nonzero total angular momentum; good agr...

Reaction-Path Dynamics of Hydroxyl Radical Reactions with Ethane and Haloethanes

A detailed analysis of reaction-path dynamics of hydrogen abstraction from ethane, fluoroethane, and chloroethane by hydroxyl radical has been performed by the variational transition-state theory augmented with multidimensional semiclassical tunneling approximations. The minimum energy path and its first and second derivatives were calculated at the MP2(full)/6-31G(d,p) level of theory. The calculated barrier heights were further improved by Gaussian-2(MP2) methodology. This dual-level dynamic approach has been used to calculate the reaction rate constants for temperatures from 200 to 1000 K. The contribution from tunneling effect was evaluated using the semiclassical zero-curvature and small-curvature tunneling approximations. The calculated thermal reaction rate constants agree well with the experimental results. The variational effects on the location of central dynamical bottleneck are significant for all three reactions. The competition between potential and vibrational energies in determining the lo...

The influence of hindered rotations on recombination/dissociation kinetics

AbstractThe variational canonical flexible transition state theory expressions for the thermal reaction rate constant are reviewed and then applied to the barrier‐less recombination reactions H + CCH, H + CF3, and CH + H2. The rate constant expressions can classically accommodate any description of the hindering potential governing relative orientation changes between the reactants at a given distance. The distance held fixed during the relative orientation changes can be fully optimized. The three applications display comparable and large variations between the harmonic oscillator and free rotor limits of the hindering potential. The actual hindering potentials are all derived from similar ab initio electronic structure calculations. With these potentials, the rate constant for H + CF3 is somewhat free‐rotor like, the rate constant for CH + H2 is mostly harmonic‐oscillator like, and the rate constant for H+CCH is largely in between these two limits.

Canonical flexible transition state theory revisited

A simple formula for the canonical flexible transition state theory expression for the thermal reaction rate constant is derived that is exact in the limit of the reaction path being well approximated by the distance between the centers of mass of the reactants. This formula evaluates classically the contribution to the rate constant from transitional degrees of freedom (those that evolve from free rotations in the limit of infinite separation of the reactants). As a result of this treatment, the formula contains the product of two factors: one that exclusively depends on the collision kinematics and one that exclusively depends on the potential energy surface that controls the transitional degrees of freedom. This second factor smoothly varies, in the classical limit, from harmonic oscillator to hindered rotor to free rotor partition functions as the potential energy surface varies from quadratic to sinusoidal to a constant in its dependence on the relative orientation angles of the fragments. An application to the recombination of CH3+H essentially demonstrates exact agreement with a previous flexible transition state theory study in which all integrals are carried out numerically. The simple formulas presented in this paper allow the classical inclusion of large amplitude motion of arbitrary complexity in the determination of the canonical rate constant for reactions whose reaction path is dominated by the distance between the centers of mass of the reactants.

Trajectory studies of the reaction F−+HCl→HF+Cl−. I. Reaction rate constant

Ab initio calculations at the MP4/6–31G** level in conjunction with experimental data were used to derive an analytical potential energy function for the reaction F−+HCl→HF+Cl−. A Monte Carlo-classical trajectory method was used to estimate the thermal energy reaction rate constants at various temperatures. The results showed that the reaction efficiency decreases sharply as temperature increases. At room temperature, the calculated reaction rate constant is in excellent agreement with the experimental result. Reaction rate constants were also calculated as a function of relative translational energy at internal (vibrational and rotational) temperatures of 50, 300, and 3000 K. It was observed that the rate constant exhibits a similar relative translational energy dependence as the temperature dependence. Calculated results show no internal temperature dependence of the reaction rate constant.

Flux–flux correlation function study of resonance effects in reactive collision

Thermal rate constants for a one-dimensional model of a reactive collision involving a transient resonance are calculated by using autocorrelation functions of the flux operator in a finite basis set representation [Miller, Schwartz, and Tromp (MST), J. Chem. Phys. 79, 4889 (1983)] and performing either integration over time (MST) or Pade extrapolation to zero of an energy parameter [Lefebvre, Ryaboy, and Moiseyev, J. Chem. Phys. 98, 8601 (1993)]. The two procedures prove to be equally successful. We observe that in the time dependent approach, the correlation function of the reactive flux operator shows, as expected, damped oscillations with a period which slightly depends on the temperature. However, these oscillations are decaying on a time scale that is significantly shorter than the resonance lifetime. This finding shows that the flux–flux correlation function approach is applicable to calculations of thermal rate constants for reactions which proceed via formation of intermediate complexes as well as to studies of short time direct reactive processes.

Reactions of trans-hydroxycarbonyl radical studied by infrared spectroscopy

trans-HOCO was produced by 193-nm photolysis of acrylic acid C 2 H 3 CO 2 H, and its reactions were studied using the rotational-vibrational transitions of the ν 1 O-H stretch. The thermal reaction rate constants for the reactions with O 2 and NO show no isotope dependence (±10% uncertainty) and have the following values: 1.9 (±0.2)×10 -12 cm 3 molecule -1 s -1 for O 2 and 2.45 (±0.2)×10 -12 cm 3 molecule -1 s -1 for NO at 293±2 K. The lack of an H/D isotope dependence is interpreted in terms of complex formation and dissociation, a mechanism in which hydrogen transfer is not the rate-limiting process

Dynamical trajectory study of the reaction O(3P)+ Cl2? OCl + Cl

The dynamics of the reaction O(3P)+ Cl2→ OCl + Cl have been studied using the quasiclassical trajectory method. The calculations are carried out on three empirical LEPS-type potential-energy surfaces, all possessing approximately the same classical barrier height but differing significantly in dynamical characteristics. The adjustable parameters of all surfaces are tested against the experimental data and the thermal reaction rate constant. The dynamical behaviour of the reaction as deduced from comparison with molecular beam data is most closely described by a potential-energy surface that possesses a minimum classical barrier in the collinear configuration located early in the entrance valley of the reaction.

A personal history of the early development of the flowing afterglow technique for ion-molecule reaction studies

A personal perspective of the historical development of the flowing afterglow (FA) technique for measuring thermal energy ion-molecule reaction rate constants is presented. The technique was developed in the period starting in late 1962 in what was then the National Bureau of Standards in Boulder, Colorado. The motivation was primarily to obtain a quantitative understanding of the ion chemistry of the terrestrial ionosphere, a program that was substantially achieved. The thermal energy measurements were extended in temperature from 300 K to a range of 80 K–900 K and subsequently to a center-of-mass kinetic energy range up to ∼ 2 eV with the introduction of a drift tube into the FA. The chemical versatility, in regard to both the ion and the neutral reactants measured, remains unequaled and FA systems are currently in widespread use around the world for a variety of chemical research programs.

Quantum thermal rate constants for the exchange reactions of hydrogen isotopes: D+H2

Accurate thermal rate constants for the D+H2 reactions are determined for the Liu–Siegbahn–Truhlar–Horowitz potential energy surface over the temperature range 300–1500 K. We evaluate the rate constants via the quantum flux–flux autocorrelation function formulation of Miller [J. Chem. Phys. 61, 1823 (1974)] using the adiabatically adjusted principal axis hyperspherical coordinates of Pack [Chem. Phys. Lett. 108, 333 (1984)] and a symmetry adapted discrete variable representation used earlier for the H+H2 reaction [T. J. Park and J. C. Light, J. Chem. Phys. 91, 974 (1989)]. The initial L2 basis of ∼15 000 functions is sequentially diagonalized and truncated, with a final reduction to ∼420 accurate eigenvectors of the symmetry adapted (C2v) Hamiltonians for J=0. Direct products of these functions with symmetry adapted rotation functions are then used as the basis for the J>0 Hamiltonians. Nuclear spin symmetries are also included. For J>0, the individual J, KJ blocks of the Hamiltonian are diagonalized, the Coriolis coupling is neglected, and the KJ±2 coupling is included by perturbation theory. The thermal rate constants are evaluated for each total angular momentum from the flux–flux autocorrelation function. Angular momenta up to J=25 are required to converge the rate constants at 1500 K to ∼5%. Thermal rate constants as functions of T (and J) are presented for the D+H2 reaction and compared with experiment and other calculations. Agreement with experiment for D+H2 is excellent up to about 1000 K and remains within a factor of 2 of the experimental rate constant up to 1500 K. Thus agreement of the rates over more than four orders of magnitude is quite reasonable.

The analysis of muonium hyperfine interaction measurements of thermal rate constants for addition reactions

A new model is developed for the analysis of muon spin relaxation (μSR) measurements of muonium (Mu) reaction rates with other chemical species. The kinetics component of the model is specifically developed for addition reactions but can be extended to direct reactions. The polarization component of the model assumes that the adduct formed possesses a single, effective spin precession frequency. The complete model is solved to obtain an analytic expression for the μSR signal as a function of time. Both a time-ordered sequence method and a Boltzmann spin equation method give equivalent solutions. These solutions are analyzed under various kinetic conditions. It is concluded that the coefficient controlling the decay of the μSR signal is closely related to the adduct formation rate constant, i.e., the high pressure limit of the apparent bimolecular addition rate constant. In the most favorable case, the decay constant gives the adduct formation rate constant directly at all pressures of buffer gas.

Mu+H2 and Mu+D2 reaction kinetics from 480 To 675 K

This paper reports preliminary new measurements of the thermal reaction rate constants of muonium (Mu) with hydrogen and deuterium gases in the range 480–675 K. From Arrhenius plots of the measured reaction rate constants new values of the pre-exponential factors log10 (A) and activation energies Ea have been determined for these reactions, representing a significant improvement over earlier results.

Reaction probabilities for the reactions of hydrogen atoms at selected initial energies in hydrogen iodide–iodine mixtures

The reactions of photochemically generated H atoms formed at selected initial energies in HI-I2 mixtures have been investigated. A kinetic analysis of reaction rates in systems with and without added I2 allowed the measurement of integrated reaction probabilities for the reaction H + HI → H2+ I. At initial H atom energies of 49 and 106 kJ mol–1 the respective reaction probabilities were 0.11 ± 0.02 and 0.35 ± 0.02. At 178 kJ mol–1, after allowance for partial photolytic yield of electronically excited I atoms, a reaction probability close to unity is indicated. In each set of experiments the analysis also yielded the ratio of thermal rate constants for reactions of H atoms with I2(k6) and HI(k3) as 11.6 ± 0.4. The reaction probabilities are discussed with particular reference to the very high values found in earlier work for other H atom + hydrogen halide reactions.

Laser studies of methyl radical reactions with Cl2 and Br2: Absolute rate constants, product vibrational excitation, and hot radical reactions

Reactions of methyl radicals with Cl2 and Br2 are studied by pulsed laser dissociation of CH3I followed by time-resolved detection of infrared vibrational fluorescence from the C–H stretch modes of the methyl halide product. This method provides a determination of the absolute rate constants for the methyl radical reactions. The rate constants for thermal reactions of CH3 with Cl2 and Br2 are 1.5(±0.1)×10−12 and 2.0(±0.4)×10−11 cm3 molecule−1 s−1, respectively. From the fluorescence intensity of the methyl halide product, an estimate can be made of the fraction of energy available upon reaction that goes into product vibration. For both reactions this is determined to be about 0.5. In addition, the reaction rates are observed to be considerably enhanced for hot methyl radicals produced in the dissociation of CH3I. The enhancement is shown to be due predominantly to the translational excitation, as opposed to the vibrational excitation, imparted in the photofragmentation.

The average cos δ approach to the theoretical calculation of thermal energy ion-dipolar molecule reaction rate constant

A simplified method is presented to compute the average interaction potential of an ion reacting with a dipolar molecule at thermal collision energies. Using this potential and applying the Langevin criteria for capture collisions, an expression for the reaction rate constant is derived. The theoretical rate constant is compared with many experimental data, the results of recent trajectory calculations and the predictions of other theories. It is shown to be in good agreement with experiment and it is found close to other models based on statistical or variational methods. It is also found in good agreement with detailed trajectory calculations Presentation d'une methode simplifiee pour le calcul du potentiel d'interaction moyen entre un ion et une molecule polaire, qui reagissent, avec energies thermiques. Calcul de la constante de vitesse de reaction a l'aide de ce potentiel et des criteres de Langevin pour les collisions avec capture. Bon accord avec des donnees experimentales et theoriques anterieures

Reaction probabilities, resonances, and thermal rate constants for the collinear reactions H + FH and D + FD on a low-barrier surface. Close-coupling and tunneling calculations, variational transition-state theory, and the unified statistical model

Reaction probabilities, resonances, and thermal rate constants for the collinear reactions H + FH and D + FD on a low-barrier surface. Close-coupling and tunneling calculations, variational transition-state theory, and the unified statistical model

Detailed balance in quasiclassical trajectory calculations of thermal rate constants for chemical reactions

Thermal rate constants for chemical reactions from quasiclassical trajectory calculations are discussed. For H2 + I ? H + HI trajectories for reverse reaction have been calculated giving a complete standard QCT rate constant for it. (AIP)