Flexible Transition State Theory Research Articles

Theoretical determination of accurate rate constants: Application to the decomposition of a single-molecule precursor

The ring opening is proposed to be the initial step in the unimolecular decomposition of a single-molecule precursor bisazido(dimethylaminopropyl)gallium (BAZIGA) used in a CVD process of gallium nitride. An efficient Monte Carlo importance sampling technique is developed to estimate the canonical partition functions and absolute entropies therefrom by taking the internal rotor hindrance and all coupling arising from the external and internal rotational degrees of freedom into account. This allows the estimation of the free energy difference in the ring opening process of BAZIGA to be made. Canonical flexible transition state theory is applied to the radical Ga–C bond homolysis in the unimolecular decomposition of BAZIGA. The limiting high-pressure rate constant is calculated using a simple model for the potential energy surface based on density functional calculations.

Mechanistic and Kinetic Study of the O + CH2OH Reaction

The mechanism for the O + CH2OH reaction was investigated by various ab initio quantum chemistry methods. For the chemical activation mechanism, that is, the addition/elimination path, the couple-cluster methods including CCSD and CCSD(T) were employed with the cc-pVXZ (X = D, T, Q, 5) basis sets. For the abstraction channels, multireference methods including CASSCF, CASPT2, and MRCISD were used with the cc-pVDZ and cc-pVTZ basis sets. It has been shown that the production of H + HCOOH is the major channel in the chemical activation mechanism. The minor channels include HCO + H2O and OH + CH2O. The hydrogen abstraction by an O atom from the CH2OH radical produces either OH + CH2O or OH + HCOH. Moreover, the two abstraction reactions are essentially barrierless processes. The rate constants for the association of O with CH2OH have been calculated using the flexible transition state theory. A weak negative temperature dependence of the rate constants is found in the range 250-1000 K. Furthermore, it is estimated that the abstraction processes also play an important role in the O + CH2OH reaction. Additionally, the falloff behavior for the OCH2OH --> H + HCOOH reaction has been investigated. The present theoretical results are compared to the experimental measurements to understand the mechanism and kinetic behavior of the O + CH2OH reaction and the unimolecular reaction of the OCH2OH radical.

Flexible transition state theory for a variable reaction coordinate: Derivation of canonical and microcanonical forms with angular momentum conservation

This paper extends work previously presented [J. Chem. Phys. 113, 2648 (2000)] to establish a rigorous expression for the angular momentum resolved microcanonical reactive flux. A kinetic energy expression in terms of the angular momentum, based on the coordinate system described in the above reference, is derived. Analytic integration over momenta conjugate to the coordinates that describe the relative orientation of the fragments is effected at the canonical level. The Laplace transform relation between canonical and microcanonical coefficients is then exploited to yield the angular momentum dependent microcanonical reactive flux. Evaluation of the resulting rate expression involves a numerical integral whose dimension, in most cases, is the same as the integrals in corresponding canonical and standard microcanonical forms.

Flexible Transition State Theory for a Variable Reaction Coordinate: Analytical Expressions and an Application

Completely general canonical and microcanonical (energy-resolved) flexible transition state theory (FTST) rate constant expressions for an arbitrary choice of reaction coordinate have recently been derived [Robertson et al. J. Chem. Phys. 2000, 113, 2648.] by the present authors. The rate expressions apply to any definition of the separation distance between fragments in a barrierless recombination (or dissociation) that is held fixed during hindered rotations at the transition state, and to any combination of fragment structure (atom, linear top, nonlinear top). The minimization of the rate constant with respect to this definition can be regarded as optimizing the reaction coordinate within a canonical or microcanonical framework. The expressions are analytic, with the exception of a configuration integral whose evaluation generally requires numerical integration over an integrand which depends on internal angles (from one to five depending on the fragment structures). The primary component of the integrand is the determinant of the inverse G-matrix associated with the external rotations and the relative internal rotation of the fragments. In this paper, we derive closed-form, analytic expressions for the inverse G-matrix determinant for all combinations of fragment top types for an arbitrary reaction coordinate definition entirely in terms of kinetic energy matrix elements for a centers-of-mass reaction coordinate. For a model potential for CFH2 + H, the effect of optimizing the reaction coordinate definition is displayed, and the optimized coordinate is compared to the traditional center-of-mass definition at the canonical level. The associated rate constant is about a factor of 20% to 45% lower than that obtained using a centers-of-mass reaction coordinate.

Flexible transition state theory for a variable reaction coordinate: Derivation of canonical and microcanonical forms

A completely general canonical and microcanonical (energy-resolved) flexible transition state theory (FTST) expression for the rate constant is derived for an arbitrary choice of reaction coordinate. The derivation is thorough and rigorous within the framework of FTST and replaces our previous treatments [Robertson et al., J. Chem. Phys. 103, 2917 (1995); Robertson et al., Faraday Discuss. Chem. Soc. 102, 65 (1995)] which implicitly involved some significant assumptions. The canonical rate expressions obtained here agree with our earlier results. The corresponding microcanonical results are new. The rate expressions apply to any definition of the separation distance between fragments in a barrierless recombination (or dissociation) that is held fixed during hindered rotations at the transition state, and to any combination of fragment structure (atom, linear top, nonlinear top). The minimization of the rate constant with respect to this definition can be regarded as optimizing the reaction coordinate within a canonical or microcanonical framework. The expression is analytic except for a configuration integral whose evaluation generally requires numerical integration over internal angles (from one to five depending on the fragment structures). The form of the integrand in this integral has important conceptual and computational implications. The primary component of the integrand is the determinant of the inverse G-matrix associated with the external rotations and the relative internal motion of the fragments.

A theoretical ab initio and Monte Carlo simulation study of the pyridine+CCl2 reaction kinetics in the gas phase and in carbon tetrachloride solution using canonical flexible transition state theory

The potential energy surface for the pyridine+CCl2 reaction was studied at the abinitio MP4/6-311G(2df,p)//MP2/6-31G(*) level of theory. The MP4/6-311G(2df,p) energies were evaluated by the additivity approximation E[MP4/6-311G(2df,p)]≈E[MP4/6-31G(*)]+E[MP2/6-311G(2df,p)]-E[MP2/6-31G(*)]. The first step proceeds by the addition of CCl2 to pyridine forming a dipolar ylide structure without an activation barrier. Then this species rearranges to a more stable biradical like ylide on a picosecond time scale. The generalized transition state for dipolar ylide formation occurs at a large center of mass distance between the species, and to calculate the reaction rate constant we have used canonical flexible transition state theory. The configurational integral was solved by Monte Carlo simulation and statistical perturbation theory, and the potential of mean force in the gas phase was obtained. This procedure was extended to the liquid phase by including the solvent coordinates in the configurational integral. The activation free energy in the gas phase and in carbon tetrachloride solution was calculated as 1.44 and 2.62 kcal mol-1, respectively. The corresponding rate constants are 5.5×1011 and 7.5×1010 l mol-1 s-1. The last value is in reasonable agreement with the experimental result of 7×109 l mol-1 s-1 determined in isooctane solution.

Application of the Canonical Flexible Transition State Theory to CH3, CF3, and CCl3 Recombination Reactions

Canonical flexible transition state theory is applied to the recombination of CX3 radicals (X = H, F, Cl) using a simple model for the potential-energy surface. The limiting high-pressure rate coefficient, k∞, is calculated, using Monte Carlo integration with stratified sampling for the three reactions in the temperature range from 300 to 2000 K. k∞ exhibits a negative temperature dependence, which becomes more pronounced as the size of X increases. There is a good agreement between the present results and some of the available experimental data. The factors that influence the negative temperature dependence of k∞ and the relative magnitude of k∞ for the three reactions are investigated.

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.

Reduction of the two-dimensional master equation to a Smoluchowsky type differential equation with application to CH4→CH3+H

A master equation (ME) approximation describing the effect of vibrational/rotational (V/R) relaxation on unimolecular reactions in the gas phase is presented. It is demonstrated that some forms of ME can be transformed exactly to an effective two-dimensional Smoluchowsky type differential equation (SE) in the V/R energy variables, V and R. The SE allows interpretation in a unified way of both weak and strong collision limits. Analytical expressions for the unimolecular reaction rate coefficient ku(T) are derived for simple models of the energy dependence of the microscopic reaction rate k(V,R) and V/R density of states. For realistic k(V,R) (obtained from flexible transition state theory for the reaction CH4→ArCH3+H) the SE is solved numerically. Both numerical and analytical calculations show that the collisional rotational energy transfer can, in principle, affect the rate coefficient ku(T). However, for the particular reaction considered, ku is found to be less sensitive to changes in the average rotational energy transfer than to changes in the average vibrational energy transfer. Furthermore, the strong collision limit is achieved only for unrealistically large values of the average rotational energy transfer. This means that it is a good approximation in this case one can treat V/R energy transfer and dissociation by a one-dimensional master equation in total energy.

Angular momentum dependence of variational transition states for selected association reactions

The total angular momentum dependence of variational transition states for several reactions without a potential energy barrier on the minimum energy path is illustrated. High-pressure thermal rate constants for Li ++(CH 3) 2O→Li +(CH 3) 2O and Li ++H 2O→Li +(H 2O) from 200 to 1000 K are obtained from flexible transition-state theory (FTST), with potential functions of Coriongiu, Clementi, Pretsch and Simon and of Clementi and Popkie, respectively. For Li +(H 2O) the canonically determined rate constants are 20–50% higher than the microcanonically determined ones, and for Li +(CH 3) 2O ≈ 55% higher. These differences are attributed to the strong dependence of the transition states on total angular momentum.

Multiple transition states in chemical reactions: Variational transition state theory studies of the HO2 and HeH+2 systems

The results of a microcanonical variational transition state theory study of the HO2 and HeH+2 systems are reported. The calculations were carried out using a modification of the Wardlaw–Marcus flexible transition state theory method in which the sum of states N(E,R) is calculated directly. For the HO2 system, the results obtained using the Melius–Blint potential surface are in excellent agreement with previously reported variational transition state theory calculations of Rai and Truhlar on this system. In particular, two transition states were found for the HO2→OH+O half-reaction. However, calculations using the Lemon–Hase surface produced only one transition state. From calculations carried out on surfaces constructed by combining the two original surfaces and calculations carried out using an orbiting transition state variational model (i.e., ignoring the angular part of the potential), it is shown conclusively that the two transition states found for the Melius–Blint surface arise from the peculiar shape of the minimum reaction path for this surface. Also, the orbiting transition state calculations suggest that phase space theory can describe this half-reaction on the Lemon–Hase surface over a large energy range provided that the potential along the minimum reaction path is used in the phase space theory calculations. Other calculations, in which the parameters of the Lemon–Hase surface were adjusted, were also carried out in order to determine the conditions necessary to support multiple transition states. The results of these calculations suggest that multiple transition states are more likely to occur when a strong bottleneck is present in the angular part of the potential, especially when the intermediate complex exists in a shallow well. These predictions were confirmed by the results obtained for the HeH+2 system using the McLaughlin–Thompson–Joseph–Sathyamurthy surface. Two transition states were found for the HeH+2→HeH++H half-reaction and calculations using the orbiting model showed that the origin of the multiple transition states is not the minimum reaction path as in the case of the Melius–Blint surface. Furthermore, the energy at which ‘‘transition state switching’’ occurs is in reasonable accord with the energy at which phase space theory calculations begin to diverge from the experimental data on the cross section for this system. Lifetime calculations for the pseudocomplex lying between the two transition states suggest that the observation of multiple transition states may be possible using femtosecond transition state spectroscopy. Finally, calculations on the HeH+2→He+H+2 half-reaction showed that one transition state exists for this half-reaction at low energy, while at higher energy there are no transition states.