Transition State Theory Approach Research Articles

Transition state theory approach to polymer escape from a one dimensional potential well.

The rate of escape of an ideal bead-spring polymer in a symmetric double-well potential is calculated using transition state theory (TST) and the results compared with direct dynamical simulations. The minimum energy path of the transitions becomes flat and the dynamics diffusive for long polymers making the Kramers-Langer estimate poor. However, TST with dynamical corrections based on short time trajectories started at the transition state gives rate constant estimates that agree within a factor of two with the molecular dynamics simulations over a wide range of bead coupling constants and polymer lengths. The computational effort required by the TST approach does not depend on the escape rate and is much smaller than that required by molecular dynamics simulations.

Potential Energy Surfaces and Rates of Spin Transitions

The stability of magnetic states and the mechanism for magnetic transitions can be analyzed in terms of the shape of the energy surface, which gives the energy as a function of the angles determining the orientation of the magnetic moments. Minima on the energy surface correspond to stable or metastable magnetic states and can represent parallel, antiparallel or, more generally, non-collinear arrangements. A rate theory has been developed for systems with arbitrary number, N , of magnetic moments, to estimate the thermal stability of magnetic states and the mechanism for magnetic transitions based on a transition state theory approach. The minimum energy path on the 2 N -dimensional energy surface is determined to identify the transition mechanism and estimate the activation energy barrier. A pre-exponential factor in the rate expression is obtained from the Landau–Lifshitz–Gilbert equation for spin dynamics. The velocity is zero at saddle points so it is particularly important in this context to realize that the transition state is a dividing surface with 2 N − 1 degrees of freedom, not just a saddle point. An application of this rate theory to nanoscale Fe islands on W(110) has revealed how the transition mechanism and rate depend on island shape and size. Qualitative agreement is obtained with experimental measurements both for the activation energy and the pre-exponential factor. In particular, a distinct maximum is observed in the pre-exponential factor for islands where two possible transition mechanisms are competing: Uniform rotation and the formation of a temporary domain wall. The entropy of the transition state is enhanced for those islands making the pre-exponential factor more than an order of magnitude larger than for islands were only the uniform rotation is viable.

Improbability of Void Growth in Aluminum via Dislocation Nucleation under Typical Laboratory Conditions

The rate at which dislocations nucleate from spherical voids subjected to shear loading is predicted from atomistic simulation. By employing the latest version of the finite temperature string method, a variational transition state theory approach can be utilized, enabling atomistic predictions at ordinary laboratory time scales, loads, and temperatures. The simulation results, in conjunction with a continuum model, show that the deformation and growth of voids in Al are not likely to occur via dislocation nucleation under typical loadings regardless of void size.

Statistical Theory for the Kinetics and Dynamics of Roaming Reactions

We present a statistical theory for the effect of roaming pathways on product branching fractions in both unimolecular and bimolecular reactions. The analysis employs a separation into three distinct steps: (i) the formation of weakly interacting fragments in the long-range/van der Waals region of the potential via either partial decomposition (for unimolecular reactants) or partial association (for bimolecular reactants), (ii) the roaming step, which involves the reorientation of the fragments from one region of the long-range potential to another, and (iii) the abstraction, addition, and/or decomposition from the long-range region to yield final products. The branching between the roaming induced channel(s) and other channels is obtained from a steady-state kinetic analysis for the two (or more) intermediates in the long-range region of the potential. This statistical theory for the roaming-induced product branching is illustrated through explicit comparisons with reduced dimension trajectory simulations for the decompositions of H(2)CO, CH(3)CHO, CH(3)OOH, and CH(3)CCH. These calculations employ high-accuracy analytic potentials obtained from fits to wide-ranging CASPT2 ab initio electronic structure calculations. The transition-state fluxes for the statistical theory calculations are obtained from generalizations of the variable reaction coordinate transition state theory approach. In each instance, at low energy the statistical analysis accurately reproduces the branching obtained from the trajectory simulations. At higher energies, e.g., above 1 kcal/mol, increasingly large discrepancies arise, apparently due to a dynamical biasing toward continued decomposition of the incipient molecular fragments (for unimolecular reactions). Overall, the statistical theory based kinetic analysis is found to provide a useful framework for interpreting the factors that determine the significance of roaming pathways in varying chemical environments.

Atomistic predictions of dislocation nucleation with transition state theory

The combined use of atomistic simulations and transition state theory (TST) has enabled significant improvements in the prediction of thermally activated processes in a wide range of applications, e.g., conformation changes in molecules, chemical reactions, kinetic phase transitions, and solid-state diffusion. However, such an approach is still in its infancy with regard to mechanics of materials applications. Focusing here on dislocation nucleation in Al, we examine the utility of five TST-based approaches. Using the finite-temperature string method, we interpret the success and failure of each approach in terms of a full energetic analysis of the nucleation processes. After showing that advanced TST approaches such as variational TST can accurately predict nucleation rates, we employ variational TST to study dislocation nucleation from a free surface under ordinary laboratory conditions. The predictions (1) demonstrate that nucleation will only occur under very high stresses at room temperature, (2) provide an upper bound on the shear strength of Al in dislocation starved contexts, and (3) provide a rate sensitivity signature of the nucleation process.

Distributed implementation of the adaptive kinetic Monte Carlo method

The program EON2 is a distributed implementation of the adaptive kinetic Monte Carlo method for long time scale simulations of atomistic systems. The method is based on the transition state theory approach within the harmonic approximation and the key step is the identification of relevant saddle points on the potential energy rim surrounding the energy minimum corresponding to a state of the system. The saddle point searches are carried out in a distributed fashion starting with random initial displacements of the atoms in regions where atoms have less than optimal coordination. The main priorities of this implementation have been to (1) make the code transparent, (2) decouple the master and slaves, and (3) have a well defined interface to the energy and force evaluation. The computationally intensive parts are implemented in C++, whereas the less compute intensive server-side software is written in Python. The platform for distributed computing is BOINC. A simulation of the annealing of a twist and tilt grain boundary in a copper crystal is described as an example application.

Global dynamics and transition state theories: Comparative study of reaction rate constants for gas‐phase chemical reactions

In this review article, we present a systematic comparison of the theoretical rate constants for a range of bimolecular reactions that are calculated by using three different classes of theoretical methods: quantum dynamics (QD), quasi-classical trajectory (QCT), and transition state theory (TST) approaches. The study shows that the difference of rate constants between TST results and those of the global dynamics methods (QD and QCT) are seen to be related to a number of factors including the number of degrees-of-freedom (DOF), the density of states at transition state (TS), etc. For reactions with more DOF and higher density of states at the TS, it is found that the rate constants from TST calculations are systematically higher than those obtained from global dynamics calculations, indicating large recrossing effect for these systems. The physical insight of this phenomenon is elucidated in the present review.

Hydrogen Atom Loss from the Benzene Cation. Why Is the Kinetic Energy Release so Large?

The kinetic energy release distributions (KERDs) associated with the hydrogen loss from the benzene cation and the deuterium loss from the perdeuteriobenzene cation have been remeasured on the metastable time scale and analyzed by the maximum entropy method. The experimental kinetic energy releases are larger than expected statistically, in contradistinction to what has been observed for the C-X fragmentations of the halogenobenzene cations. H(D) loss from C(6)H(6)(+) (C(6)D(6)(+)) occurs via a conical intersection connecting the (2)A(2) and (2)A(1) electronic states. Two models are proposed to account for the experimental data: (i) a modified orbiting transition state theory (OTST) approach incorporating electronic nonadiabaticity; (ii) an electronically nonadiabatic version of the statistical adiabatic channel model (SACM) of Quack and Troe. The latter approach is found to be preferable. It leads to the conclusion that the larger the energy stored in the transitional modes, which partly convert to the relative interfragment motion, the shorter the value of the reaction coordinate at which the adiabatic channels cross, and the larger the probability of undergoing the (2)A(2) --> (2)A(1) transition required for hydrogen loss.

A Two Transition State Model for Radical−Molecule Reactions: A Case Study of the Addition of OH to C2H4

A two transition state model is applied to the study of the addition of hydroxyl radical to ethylene. This reaction serves as a prototypical example of a radical-molecule reaction with a negative activation energy in the high-pressure limit. The model incorporates variational treatments of both inner and outer transition states. The outer transition state is treated with a recently derived long-range transition state theory approach focusing on the longest-ranged term in the potential. High-level quantum chemical estimates are incorporated in a variational transition state theory treatment of the inner transition state. Anharmonic effects in the inner transition state region are explored with direct phase space integration. A two-dimensional master equation is employed in treating the pressure dependence of the addition process. An accurate treatment of the two separate transition state regions at the energy and angular momentum resolved level is essential to the prediction of the temperature dependence of the addition rate. The transition from a dominant outer transition state to a dominant inner transition state is predicted to occur at about 130 K, with significant effects from both transition states over the 10 to 400 K temperature range. Modest adjustment in the ab initio predicted inner saddle point energy yields theoretical predictions which are in quantitative agreement with the available experimental observations. The theoretically predicted capture rate is reproduced to within 10% by the expression [4.93 x 10(-12) (T/298)(-2.488) exp(-107.9/RT) + 3.33 x 10(-12) (T/298)(0.451) exp(117.6/RT); with R = 1.987 and T in K] cm3 molecules(-1) s(-1) over the 10-600 K range.

Transition path sampling: rearrangement of cage water hexamer

Abstract The hydrogen bond exchange reaction of cage water hexamer has been investigated. With an aid of transition path sampling method, a transition state for this reaction has been found. The transition state ensemble has been investigated as a function of energy, and the distribution of the structures of sampled transition states is consistent with that obtained by other method. From the ab initio calculations, it has been confirmed to be a transition state with one imaginary frequency along the reaction coordinate. The most important structural parameters for the transition are retardation (increase of r a and O⋯O distance) and C 2 rotation of a water molecule. I obtained rate constants at temperatures ranging from 0 to 300 K considering quantum mechanical tunneling effect. At temperatures below 100 K, the tunneling effect is very important, while at high temperatures, the classical transition state theory approach gives reasonable data. Transition path sampling method is very useful to find transition states for many complicated chemical reactions in which we do not know about transition states or it is hard to find a transition state by quantum mechanical approaches.

The substitution reactions RH + O 2 → RO 2 + H: transition state theory calculations based on the ab initio and DFT potential energy surface

The new class of substitution reactions with oxygen molecule as an agent has been studied by combination of quantum chemistry calculation and transition state theory (TST). The ‘inversion substitution’ processes RH + O 2 → RO 2 + H (R=CH 3 and SiH 3) have been investigated. The energy for the stationary points (reagents, products and transition states) on the reaction coordinate has been calculated by G2M(CC,MP2) method and rate constants have been calculated within TST approach. The results show that in methane case the reaction considered (CH 4 + O 2 → CH 3O 2 + H) does not compete with generally accepted mechanism (CH 4 + O 2 → CH 3 + HO 2), but it does at elevated temperature in silane case.

Collisionless fragmentation of non-rotating Nin(n = 4–14)clusters: a molecular dynamics study

Collisionless fragmentation of non-rotating Nin(n = 4–14)clusters is studied using micro-canonical molecular dynamics (MD) computersimulations. The clusters are modelled by an embedded-atom potential energysurface. The distributions of the channel-specific fragmentation probabilities, andthe global and channel-specific fragmentation rate constants are computed andanalysed as functions of the internal energy and size of the clusters. The trendsderived from the dynamical calculations are compared to the fragmentationenergy patterns, those of the Rice–Ramsperger–Kassel (RRK) and statisticalapproaches. The rate constants are an order of magnitude smaller for the RRKmodel than with both the MD and transition-state theory approaches. The resultsare also compared with the other multi-channel fragmentation works.

Pyrolytic kinetics of sludge from a petrochemical factory wastewater treatment plant--a transition state theory approach.

The pyrolysis of hydrocarbon-rich sludge in an oxygen-free environment can provide useful liquefaction products and residues. When applied to sewage sludge, energy and time costs are the major factors that affect the operation. Therefore, it is important to understand how the process is affected by temperature. The pyrolysis kinetics of sludge from a petrochemical factory wastewater treatment plant was studied to reveal the effects of temperature on the reaction rate and the magnitude of deltaH and deltaS of the reaction barrier. Oven-dried sludge samples were pyrolyzed in an isothermal reactor under six different temperatures. The residues were weighed at frequent intervals within a total 30-min experiment period. Data analysis indicated that a first order reaction model could describe the pyrolysis kinetics, across all experimental temperature ranges. When transition state theory was applied, the results indicated that the major reaction barrier came from the entropy term of the activation free energy. Therefore, increasing the pyrolysis temperature to overcome the reaction barrier yielded no apparent improvement, but strategies that reduced the entropy should significantly improve the reaction.

A General Reaction Path Dual-Level Direct Dynamics Calculation of the Reaction of Hydroxyl Radical with Dimethyl Sulfide

Three approaches are used to calculate the gas-phase rate constant for the abstraction of hydrogen by the hydroxyl radical from dimethyl sulfide (i.e., DMS + OH· → DMS· + H2O): the variational transition state theory approach, a dual-level direct transition state method based on a reaction path determined at the MBPT(2)/6-31+G(d,p) level, with energetics obtained using the MBPT(2), CCSD, and CCSD(T) methods, and 6-31+G(d,p), 6-311++G(d,p), and 6-311++G(2df,2pd) basis sets. All computed reaction rates include corrections for light atom tunneling. The potential for the dual-level direct dynamics method is supplied by a semiempirical approach in which the PM3 NDDO Hamiltonian has been optimized for this specific class of reactions. The computed thermal rate constants are in good agreement with those determined experimentally, typically within a factor of 2 for our best result. A vibrational-mode correlation analysis is presented. A statistical diabatic model is used to predict changes in the reaction rate due to excitation of a specific vibrational mode in the reactants. A significant enhancement in the rate is predicted for the excitation of the C−H stretching mode.

Addition complex formation vs. direct abstraction in the OH+C2H4 reaction

The potential energy surface of the C2H5O system was studied by high level ab initio methods. Unimolecular rate constants have been computed using a simple transition state theory approach. The good agreement between predicted and experimental high pressure limiting rate constants supported the reliability of the proposed procedure. The direct bimolecular H-atom abstraction from ethylene by OH is unimportant and the reaction proceeds ia the intermediate adduct. We predict high pressure bimolecular rate constants above 600 K for the following reactions under the condition that the pre-equilibrium is established:

Extension of path integral quantum transition state theory to the case of nonadiabatic activated dynamics

In this paper, a methodology is introduced by which one may compute rates of nonadiabatic processes for arbitrary potential forms. This method augments the extant path-integral transition state theory approach in which information about the inherently dynamical rate process is obtained from a static analysis of a free energy surface. The present resulting formula reduces to previous single adiabatic surface results when the adiabatic surface are well separated. Numerical examples show that the method well approximates the exact results in the nonadiabatic limit and over a large range of temperatures for quadratic and for nonquadratic potentials. Corroborating these results, analysis of the rate formula for a single-oscillator spin-boson Hamiltonian in the nonadiabatic classical-limit reveals close agreement with the known exact result.

Quantum mechanical transition state theory and tunneling corrections

An efficient implementation of the quantum mechanical transition state theory recently proposed by Hansen and Andersen [J. Chem. Phys. 101, 6032 (1994); J. Phys. Chem. 100, 1137 (1996)] is presented. Their method approximates the flux–flux autocorrelation function by using short-time information to fit an assumed functional form (with physically correct properties). The approach described here exploits the low rank of the half-Boltzmannized flux operator, thereby facilitating application to reactions involving many degrees of freedom. In addition, we show how the quantum transition state theory can be used to obtain tunneling corrections within the framework of more traditional transition state theory approaches, i.e., those making an assumption of separability. Directions for possible improvements of the theory are discussed.

Molecular Modeling of Methane Diffusion in Glassy Atactic Polypropylene via Multidimensional Transition State Theory

A multidimensional transition state theory (TST) approach is formulated for the study of elementary jumps involved in the diffusion of a gaseous penetrant in a glassy polymer, taking explicitly into account the coupling between polymer and penetrant degrees of freedom along each jump. In this approach, an initial picture of states (local minima of the potential energy of the polymer + penetrant system) and “macrostates” (i.e., collections of states communicating over barriers small relative to kBT) is obtained through geometric analysis of accessible volume in representative glassy polymer configurations. Saddle points of the potential energy are computed using the “necks” between accessible volume clusters as initial guesses and progressively augmenting the set of degrees of freedom with respect to which the saddle point is calculated. Starting from the saddle points, states and reaction paths are then mapped out in the multidimensional space of penetrant and polymer degrees of freedom, using Fukui's int...

Large Curvature Tunneling Effects Reveal Concerted Hydrogen Exchange Rates in Cyclic Hydrogen Fluoride Clusters Comparable to Carboxylic Acid Dimers

Reaction rate constants for the concerted proton transfer in cyclic hydrogen fluoride clusters obtained by using a variational transition state theory approach with high-level data at three stationary points and with interpolated corrections based on semiempirical Hamiltonians specially parametrized for these systemsMP2/6-311++G(3df,3pd)///PM3-SRPare reported. For the first time multidimensional tunneling is included in the large curvature limit. The corresponding small curvature limit is benchmarked against higher level calculations. The ridge of the reaction swath is defined in a general way and serves together with an estimate of the barrier width as a validation of the potential energy hypersurfaces. Recent experimental and theoretical results concerning carboxylic acids, whose hypersurfaces are found to be very similar to those of the HF clusters, underline the relevancy of the investigated concerted proton exchange motion. A reaction rate constant k(300 K) = 2.86 × 109 s-1 is found for (HF)5, which is similar to carboxylic acid dimers, whose experimental k(300 K) lie near 1010 s-1.

Radiative Association of NO+ with 3-Pentanone: Rate, Binding Energy, and Temperature Dependence

Measurements were made of the radiative association kinetics of NO+ with 3-pentanone as a function of temperature from 300 to 400 K, using the Fourier-transform ion cyclotron resonance ion-trapping mass spectrometer. Both the absolute association rate and the temperature dependence were compared with the predictions of two levels of theory, a simple RRKM-based approach previously applied to several systems, and a new, detailed variational transition state theory (VTST) approach incorporating ab initio calculations of vibrational frequencies and IR emission intensities. The analysis by the VTST approach was considered reliable and successful enough to justify averaging with a previous thermochemical determination to give a revised binding energy for the complex of 41.6 ± 2 kcal mol-1 (1.80 ± 0.1 eV). The VTST approach also gave excellent agreement with the observed temperature dependence. The RRKM estimate of the rate was in satisfactory agreement with observation, but the slope of the temperature dependen...