Skirting the transition state, a new paradigm in reaction rate theory

Bowman, Joel M.

doi:10.1073/pnas.0607810103

Cited by 39 publications

(31 citation statements)

References 15 publications

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“…In fact, a body of work has called into question the utility of concepts such as the reaction path and/or transition state (TS). [40][41][42][43][44][45][46][47][48][49] Of particular interest for the present work is the recognition that there are important classes of chemical reaction, such as ion-molecule reactions and association reactions in barrierless systems, for which the transition state is not necessarily directly associated with the presence of a saddle point on the potential energy surface; such transition states might be generated dynamically, and so are associated with critical points of the amended or effective potential, which includes centrifugal contributions to the energy. [50][51][52] The phenomenon of transition state switching in ion-molecule reactions [53][54][55] provides a good example of the dynamical complexity possible in such systems, as does the widely studied phenomenon of roaming.…”

Section: Introductionmentioning

confidence: 99%

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

Mauguière

Collins

Kramer

et al. 2016

The Journal of Chemical Physics

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We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori, it is possible to define phase space dividing surfaces that are analogous to the dividing surfaces governing transition from reactants to products near a critical point of the potential energy surface. We investigate the problem of capture of an atom by a diatomic molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom distances, away from any critical points on the potential. This normally hyperbolic invariant manifold is the anchor for the construction of a dividing surface in phase space, which defines the outer or loose transition state governing capture dynamics. We present an algorithm for sampling an approximate capture dividing surface, and apply our methods to the recombination of the ozone molecule. We treat both 2 and 3 degrees of freedom models with zero total angular momentum. We have located the normally hyperbolic invariant manifold from which the orbiting (outer) transition state is constructed. This forms the basis for our analysis of trajectories for ozone in general, but with particular emphasis on the roaming trajectories. C 2016 AIP Publishing LLC.[http://dx

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Section: Introductionmentioning

confidence: 99%

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

Mauguière

Collins

Kramer

et al. 2016

The Journal of Chemical Physics

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“…We consider two examples: first, the dynamical definition of stepwise (sequential) versus concerted isomerization mechanisms on a multiwell potential surface; second, the classification of reactive trajectories in a system in which there are two distinct transition states. In the latter case our analysis of dynamics in the vicinity of the index two saddle suggests a rigorous identification of so-called "non-MEP" [57,58,59,60,61,62] or "roaming" trajectories [63,64,65,66,67,68] based on phase space structures.…”

Section: Index Two Saddles and Isomerization Dynamicsmentioning

confidence: 99%

“…All isomerizing trajectories except those of class (+−; −−) can therefore be labelled "non-MEP" trajectories [57,58,59,60,61,62]. All such non-MEP trajectories can be regarded as "roaming" trajectories [63,64,65,66,67,68].…”

Section: B Competing Transition States and Non-mep Mechanismsmentioning

confidence: 99%

“…The general relation between configuration space topology (distribution of saddles) and phase transitions is also of great current interest [56]. Several examples of non-MEP or non-IRC reactions [45,57,58,59,60,61,62] and "roaming" mechanisms [63,64,65,66,67,68] have been identified in recent years; the dynamics of these reactions is not mediated by a single conventional transition state associated with an index one saddle.…”

Section: Introductionmentioning

confidence: 99%

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Phase-space geometry and reaction dynamics near index 2 saddles

Ezra¹,

Wiggins²

2009

J. Phys. A: Math. Theor.

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We study the phase space geometry associated with index 2 saddles of a potential energy surface and its influence on reaction dynamics for n degree-of-freedom (DoF) Hamiltonian systems. In recent years similar studies have been carried out for index 1 saddles of potential energy surfaces, and the phase space geometry associated with classical transition state theory has been elucidated.In this case the existence of a normally hyperbolic invariant manifold (NHIM) of saddle stability type has been shown, where the NHIM serves as the "anchor" for the construction of dividing surfaces having the no-recrossing property and minimal flux. For the index 1 saddle case the stable and unstable manifolds of the NHIM are co-dimension one in the energy surface and have the structure of spherical cylinders, and thus act as the conduits for reacting trajectories in phase space.The situation for index 2 saddles is quite different, and their relevance for reaction dynamics has not previously been fully recognized. We show that NHIMs with their stable and unstable manifolds still exist, but that these manifolds by themselves lack sufficient dimension to act as barriers in the energy surface in order to constrain reactions. Rather, in the index 2 case there are different types of invariant manifolds, containing the NHIM and its stable and unstable manifolds, that act as codimension one barriers in the energy surface. These barriers divide the energy surface in the vicinity of the index 2 saddle into regions of qualitatively different trajectories exhibiting a wider variety of dynamical behavior than for the case of index 1 saddles. In particular, we can identify a class of trajectories, which we refer to as "roaming trajectories", which are not associated with reaction along the classical minimum energy path (MEP). We illustrate the significance of our analysis of the index 2 saddle for reaction dynamics with two examples. The first involves isomerization on a potential energy surface with multiple (four) symmetry equivalent minima; the dynamics in the vicinity of the saddle enables a rigorous distinction to be made between stepwise (sequential) and concerted ("hilltop crossing") isomerization pathways. The second example involves two potential minima connected by two distinct transition states associated with conventional index one saddles, and an index two saddle that sits between the two index one saddles. For the case of non-equivalent index one saddles, our analysis suggests a rigorous dynamical definition of "non-MEP" or "roaming" reactive events.

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“…1,2 Such a reaction pathway is initiated by the frustrated dissociation to form radical products, followed by the meandering of the incipient radicals around varied conguration spaces of the moieties in at regions of the potential energy surface (PES) and ultimately reaching an attractive portion of the PES that leads to intramolecular abstraction and to the molecular products. Since then, the roaming mechanism has attracted much attention, and evidence of roaming has been observed in many other unimolecular dissociation systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and also some bimolecular reactions. [17][18][19][20] In this work, we report the rst full-dimensional reaction dynamics simulations of the important combustion reaction of hydrogen with ethylene, using a new, high-level ab initio PES.…”

Section: Introductionmentioning

confidence: 99%

Collision-induced and complex-mediated roaming dynamics in the H + C₂H₄ → H₂ + C₂H₃ reaction

Han

et al. 2020

Chem. Sci.

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Skirting the transition state, a new paradigm in reaction rate theory

Cited by 39 publications

References 15 publications

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

Phase-space geometry and reaction dynamics near index 2 saddles

Collision-induced and complex-mediated roaming dynamics in the H + C₂H₄ → H₂ + C₂H₃ reaction

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Skirting the transition state, a new paradigm in reaction rate theory

Cited by 39 publications

References 15 publications

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

Phase-space geometry and reaction dynamics near index 2 saddles

Collision-induced and complex-mediated roaming dynamics in the H + C2H4 → H2 + C2H3 reaction

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Collision-induced and complex-mediated roaming dynamics in the H + C₂H₄ → H₂ + C₂H₃ reaction