Transition states near rank-two saddles: Correlated electron dynamics of helium

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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“…[22][23][24][25]. More recently, index two [26][27][28] and higher index 29 saddles have been studied (see also Refs. [30][31][32].…”

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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“…The influence of index two saddle points on reaction dynamics has been studied in Ezra and Wiggins (2009a); Collins et al (2011);Haller et al (2010); Mauguiere et al (2013). The construction of a dividing surface for general index k saddles was given in Collins et al (2011).…”

Section: The Three Degree-of-freedom Saddle-center-center Equilibriummentioning

confidence: 99%

The role of normally hyperbolic invariant manifolds (NHIMS) in the context of the phase space setting for chemical reaction dynamics

Wiggins

2016

Regul. Chaot. Dyn.

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University of Bristol -Explore Bristol Research General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. AbstractIn this paper we give an introduction to the notion of a normally hyperbolic invariant manifold (NHIM) and its role in chemical rection dynamics. We do this by considering simple examples for one, two, and three degree-of-freedom systems where explict calculations can be carried out for all of the relevant geometrical stuctures and their properties can be explicitly understood. We specifically emphasise the notion of a NHIM as a "phase space concept". In particular, we make the observation that the (phase space) NHIM plays the role of "carrying" the (configuration space) properties of a saddle point of the potential energy surface into phase space.We also consider an explicit example of a 2 degree-of-freedom system where a "global" dividing surface can be constructed using two index one saddles and one index two saddle. Such a dividing surface has arisen in several recent applications and, therefore, such a construction may be of wider interest.

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“…Additionally, the current theory for invariant manifolds that may dominate reactions associated with an index 2 saddle and a higher-index saddle are only for the largest repulsive direction [70,71]. However, Minyaev et al [58], for example, showed that aminoborane has internal rotation associated with an index 2 saddle and index 1 saddles and that the weaker repulsive direction around the index 2 saddle, corresponding to the hindered internal rotation, connects the two minima.…”

Section: Introductionmentioning

confidence: 99%

“…To reveal the fundamental mechanism of the passage through a saddle with an index greater than 1, the phase-space structure was recently studied on the basis of normal form (NF) theory [68][69][70][71]. For example, the pioneering studies to extend the dynamical reaction theory into higher-index saddles were reported [68] for concerted reactions.…”

Section: Introductionmentioning

confidence: 99%

“…For example, the pioneering studies to extend the dynamical reaction theory into higher-index saddles were reported [68] for concerted reactions. A dividing surface to separate the reactant and the product was proposed for higher-index saddles [69] and the associated phase-space structure was also discussed [70,71]. Those studies are based on NF theory and therefore rely on two assumptions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reactivity boundaries for chemical reactions associated with higher-index and multiple saddles

Nagahata

Teramoto

et al. 2013

Phys. Rev. E

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Reactivity boundaries that divide the origin and destination of trajectories are of crucial importance to reveal the mechanism of reactions, which was recently found to exist robustly even at high energies for index 1 saddles [Phys. Rev. Lett. 105, 048304 (2010)]. Here we revisit the concept of the reactivity boundary and propose a more general definition that can involve a single reaction associated with a bottleneck composed of higher-index saddles and/or several saddle points with different indices, where the normal form theory, based on expansion around a single stationary point, does not work. We numerically demonstrate the reactivity boundary by using a reduced model system of the H 5 + cation where the proton exchange reaction takes place through a bottleneck composed of two index 2 saddle points and two index 1 saddle points. The cross section of the reactivity boundary in the reactant region of the phase space reveals which initial conditions are effective in making the reaction happen and thus sheds light on the reaction mechanism.

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Transition states near rank-two saddles: Correlated electron dynamics of helium

Cited by 24 publications

References 19 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

The role of normally hyperbolic invariant manifolds (NHIMS) in the context of the phase space setting for chemical reaction dynamics

Reactivity boundaries for chemical reactions associated with higher-index and multiple saddles

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