Recent Developments in Transition State Theory

Pechukas, Philip

doi:10.1002/bbpc.19820860509

Cited by 44 publications

(8 citation statements)

References 76 publications

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“…A phase space approach is essential to obtain a rigorous dynamical definition of the transition state (TS) in multimode systems, this being the Normally Hyperbolic Invariant Manifold (NHIM) [66]. The NHIM generalizes the concept of the periodic orbit (PO) dividing surface [116][117][118] to N ≥ 3 mode systems. The Poincaré-Birkoff normalization theory has been implemented as an efficient computational tool for realizing such phase space structures as the NHIM and the TS dividing surface.…”

Section: Ch 7)mentioning

confidence: 99%

Nonstatistical dynamics on the caldera

Collins

Kramer

Carpenter

et al. 2014

The Journal of Chemical Physics

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We explore both classical and quantum dynamics of a model potential exhibiting a caldera: that is, a shallow potential well with two pairs of symmetry related index one saddles associated with entrance/exit channels. Classical trajectory simulations at several different energies confirm the existence of the "dynamical matching" phenomenon originally proposed by Carpenter, where the momentum direction associated with an incoming trajectory initiated at a high energy saddle point determines to a considerable extent the outcome of the reaction (passage through the diametrically opposing exit channel). By studying a "stretched" version of the caldera model, we have uncovered a generalized dynamical matching: bundles of trajectories can reflect off a hard potential wall so as to end up exiting predominantly through the transition state opposite the reflection point. We also investigate the effects of dissipation on the classical dynamics. In addition to classical trajectory studies, we examine the dynamics of quantum wave packets on the caldera potential (stretched and unstretched). These computations reveal a quantum mechanical analogue of the "dynamical matching" phenomenon, where the initial expectation value of the momentum direction for the wave packet determines the exit channel through which most of the probability density passes to product.

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Section: Ch 7)mentioning

confidence: 99%

Nonstatistical dynamics on the caldera

Collins

Kramer

Carpenter

et al. 2014

The Journal of Chemical Physics

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“…A phase space approach is essential to obtain a rigorous dynamical definition of the TS in multimode systems, this being the Normally Hyperbolic Invariant Manifold (NHIM) 83 . The NHIM generalizes the concept of the periodic orbit dividing surface (PODS) [111][112][113] to N ≥ 3 mode systems. A recent reappraisal of the gap time formalism for unimolecular rates 98 has led to novel diagnostics for nonstatistical behavior ('nonexponential decay') in isomerization processes, leading to a necessary condition for ergodicity.…”

Section: Introductionmentioning

confidence: 99%

Nonstatistical dynamics on potentials exhibiting reaction path bifurcations and valley-ridge inflection points

Collins

Carpenter

Ezra

et al. 2013

The Journal of Chemical Physics

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We study reaction dynamics on a model potential energy surface exhibiting post-transition state bifurcation in the vicinity of a valley ridge inflection (VRI) point. We compute fractional yields of products reached after the VRI region is traversed, both with and without dissipation. It is found that apparently minor variations in the potential lead to significant changes in the reaction dynamics. Moreover, when dissipative effects are incorporated, the product ratio depends in a complicated and highly non-monotonic fashion on the dissipation parameter. Dynamics in the vicinity of the VRI point itself play essentially no role in determining the product ratio, except in the highly dissipative regime.

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“…Transition state theory (TST) 1–6 is a popular and widely employed approach for calculating the rate coefficients of chemical reactions. Figure 1 illustrates the basic idea.…”

Section: Introductionmentioning

confidence: 99%

Ensemble‐averaged variational transition state theory with optimized multidimensional tunneling for enzyme kinetics and other condensed‐phase reactions

Truhlar

Gao

Garcia‐Viloca

et al. 2004

Int J of Quantum Chemistry

125

207

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ABSTRACT:This paper provides an overview of a new method developed to include quantum mechanical effects and free energy sampling in calculations of reaction rates in enzymes. The paper includes an overview of variational transition state theory with optimized multidimensional tunneling for simple gas-phase reactions and then shows how this is extended to incorporate free energy effects and to include protein motions in the reaction coordinate by ensemble averaging. Finally we summarize recent comparisons to experiment for primary and secondary kinetic isotope effects for proton and hydride transfer reactions catalyzed by enzymes.

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Recent Developments in Transition State Theory

Abstract: ReakrionskinetikA number of recent developments in classical and quantum transition state rate theory are briefly discussed.

Cited by 44 publications

References 76 publications

Nonstatistical dynamics on the caldera

Nonstatistical dynamics on the caldera

Nonstatistical dynamics on potentials exhibiting reaction path bifurcations and valley-ridge inflection points

Ensemble‐averaged variational transition state theory with optimized multidimensional tunneling for enzyme kinetics and other condensed‐phase reactions

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