A New Look at the Transition State: Wigner's Dynamical Perspective Revisited

Jaffé, Charles; Kawai, Shinnosuke; Palacián, Jesús F.; Yanguas, Patricia; Uzer, T.

doi:10.1002/0471712531.ch3

Cited by 46 publications

(44 citation statements)

References 9 publications

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“…(17)], and the stable/unstable invariant manifolds acting as the boundary of reactive and nonreactive trajectories [Eqs. (15) and (16)]. The nonlinear coordinate transformation with spatial rotation requires manipulation of rational functions, in contrast to that without spatial rotation in which only the manipulation of polynomials, easier in the implementation, was needed.…”

Section: Discussionmentioning

confidence: 99%

“…Recent theoretical developments on nonlinear dynamics through the saddle have revealed the robust existence of no-return transition state (TS) and the reaction pathway along which all reactive trajectories necessarily follow not in the configuration space but in the phase space. In addition to what chemists have long envisioned as TS, [1][2][3][4][5][6][7][8] it was revealed that there exist another important "building blocks" in the phase space for the understanding of the origin of the reactions: that is, normally hyperbolic invariant manifold (NHIM) and the stable/unstable invariant manifolds [9][10][11][12][13][14][15][16][17] (and their remnants 16,[18][19][20][21] ). An invariant manifold is a set of points in the phase space such that, once the system is in that manifold, the system will stay in it perpetually.…”

Section: Introductionmentioning

confidence: 99%

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Phase space geometry of dynamics passing through saddle coupled with spatial rotation

Kawai

Komatsuzaki

2011

The Journal of Chemical Physics

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Nonlinear reaction dynamics through a rank-one saddle is investigated for many-particle system with spatial rotation. Based on the recently developed theories of the phase space geometry in the saddle region, we present a theoretical framework to incorporate the spatial rotation which is dynamically coupled with the internal vibrational motions through centrifugal and Coriolis interactions. As an illustrative simple example, we apply it to isomerization reaction of HCN with some nonzero total angular momenta. It is found that no-return transition state (TS) and a set of impenetrable reaction boundaries to separate the "past" and "future" of trajectories can be identified analytically under rovibrational couplings. The three components of the angular momentum are found to have distinct effects on the migration of the "anchor" of the TS and the reaction boundaries through rovibrational couplings and anharmonicities in vibrational degrees of freedom. This method provides new insights in understanding the origin of a wide class of reactions with nonzero angular momentum.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Phase space geometry of dynamics passing through saddle coupled with spatial rotation

Kawai

Komatsuzaki

2011

The Journal of Chemical Physics

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“…[1][2][3] In the calculation of the coefficients in Eq. (60), once again one has to pay attention to convergence.…”

Section: Time-dependent Normal Form Theorymentioning

confidence: 99%

“…In this paper, we combine the concept of the TS trajectory with the method of normal form (NF) expansions based on Lie transformations 22 which has been shown to be an effective tool to calculate invariant manifolds in autonomous systems [1][2][3][4][5][6][7][8][9] (see also Refs. 23,24 for a quantum version of Lie transformations).…”

Section: Introductionmentioning

confidence: 99%

Transition state theory for laser-driven reactions

Kawai

Bandrauk

Jaffé

et al. 2007

The Journal of Chemical Physics

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Recent developments in Transition State Theory brought about by dynamical systems theory are extended to time-dependent systems such as laser-driven reactions. Using time-dependent normal form theory, we construct a reaction coordinate with regular dynamics inside the transition region. The conservation of the associated action enables one to extract time-dependent invariant manifolds that act as separatrices between reactive and non-reactive trajectories and thus make it possible to predict the ultimate fate of a trajectory. We illustrate the power of our approach on a driven Hénon-Heiles system, which serves as a simple example of a reactive system with several open channels. The present generalization of Transition State Theory to driven systems will allow one to study processes such as the control of chemical reactions through laser pulses.

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“…For example, the Restricted Three-Body problem (RTBP) (made up of Sun-Jupiter-Asteroid), is closely related to Rydberg atom ionization in microwave fields [1][2][3]. The basic theory of chemical reactions, Transition State Theory [4][5][6], has turned out to be relevant for asteroid capture [7][8][9] and may one day be useful for the design of spacecraft missions [10]. More recently, the celestial-atomic analogy has been extended to the ionization properties of atoms subjected to strong and short circularly polarized (CP) laser fields [11].…”

Section: Introductionmentioning

confidence: 99%

Microcanonical initial distribution strategy for classical simulations in strong field physics

Mauger

Kamor

Chandre

et al. 2013

UVX 2012 - 11e Colloque Sur Les Sources Cohérentes Et Incohérentes UV, VUV Et X ; Applications Et Développements Récents

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Abstract. Classical models in strong field physics typically require a careful selection of initial conditions which correspond accurately to the state selection. We compare two such procedures, the (many) pilot atom technique and the microcanonical strategy. We show that for some range of parameters, the pilot atom strategy may lead to artifacts due to the correlations between the different initial conditions. On the other hand, the microcanonical strategy is, by design, free of such artifacts for all admissible parameters.

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A New Look at the Transition State: Wigner's Dynamical Perspective Revisited

Cited by 46 publications

References 9 publications

Phase space geometry of dynamics passing through saddle coupled with spatial rotation

Phase space geometry of dynamics passing through saddle coupled with spatial rotation

Transition state theory for laser-driven reactions

Microcanonical initial distribution strategy for classical simulations in strong field physics

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