Transition State in a Noisy Environment

Bartsch, Thomas; Hernandez, Rigoberto; Uzer, T.

doi:10.1103/physrevlett.95.058301

Cited by 85 publications

(132 citation statements)

References 31 publications

(30 reference statements)

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“…16 The shift (19) and (20) to the TS trajectory as a time-dependent origin is described by the generating function…”

Section: F (T) → 0 As T → ±∞ It Is Clear From (28) That S [µ F ](T)mentioning

confidence: 99%

“…Recent work by Bartsch et al [19][20][21] on TST for time-dependent problems has addressed the inclusion of stochastic time-dependent forces (due to solvents in liquid phase reactions, for example). Starting from the Langevin equation of motion, they showed the existence of a "transition state trajectory," which stays in the vicinity of the barrier for all time.…”

Section: Introductionmentioning

confidence: 99%

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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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“…16 The shift (19) and (20) to the TS trajectory as a time-dependent origin is described by the generating function…”

Section: F (T) → 0 As T → ±∞ It Is Clear From (28) That S [µ F ](T)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transition state theory for laser-driven reactions

Kawai

Bandrauk

Jaffé

et al. 2007

The Journal of Chemical Physics

Self Cite

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“…[24][25][26][27] Unstable POs are of importance in the field of classical reaction dynamics in classical systems where they form recrossingfree dividing surfaces. 2,3, 11,[28][29][30] They are important for understanding tunneling dynamics through a barrier in quantum mechanical reactions wherein the PO on the inverted potential, −V , is the instanton trajectory providing the leading contribution to the path integral. 31 In common between all of these cases, is the invariance of POs as they provide a scaffold from which to obtain other geometric structures, and thus remain objects of current interest such as in, e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

Variational principle for the determination of unstable periodic orbits and instanton trajectories at saddle points

2017

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The complexity of arbitray dynamical systems and chemical reactions, in particular, can often be resolved if only the appropriate periodic orbit-in the form of a limit cycle, dividing surface, instanton trajectories or some other related structure-can be uncovered. Determining such a periodic orbit, no matter how beguilingly simple it appears, is often very challenging. We present a method for the direct construction of unstable periodic orbits and instanton trajectories at saddle points by means of Lagrangian descriptors. Such structures result from the minimization of a scalarvalued phase space function without need for any additional constraints or knowledge. We illustrate the approach for two-degree of freedom systems at a rank-1 saddle point of the underlying potential energy surface by constructing both periodic orbits at energies above the saddle point as well as instanton trajectories below the saddle point energy.

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“…For example, in the context of chemical reaction dynamics, LCPT has been applied to seeking (locally-)no-return transition state and the associated reaction coordinate buried in the phase space for many-degrees of freedom Hamiltonian systems such as intramolecular proton transfer in malonaldehyde [37,38], argon cluster isomerization [30][31][32][33][34][35][36], O( 1 D) + N 2 O → NO + NO [39], a hydrogen atom in crossed electric and magnetic fields [29,40], HCN isomerization [41,42,1,2], and so forth. LCPT was generalized to dissipative systems such as multidimensional (generalized) Langevin formulation to describe reactions under thermal fluctuation, in which no-return transition state can be obtained by incorporating nonlinearity of the system and interactions with heat bath [43][44][45][46][47][48][49][50]. The pioneering studies on semiclassical analog of LCPT was also carried out in late 1980s for multidimensional resonant, nonresonant, and nearly resonant systems [51][52][53]: They presented a method for deriving corrections in powers of Planck's constant by the reflection of the underlying (near) divergence properties of classical chaos, which was found to be effective even at low order corrections in improving the accuracy of the energy eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

A new method to improve validity range of Lie canonical perturbation theory: with a central focus on a concept of non-blow-up region

2014

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Validity ranges of Lie Canonical Perturbation Theory (LCPT) are investigated in terms of non blow-up regions. We investigate how the validity ranges depend on the perturbation order in two systems, one of which is a simple Hamiltonian system with one degree of freedom and the other is a HCN molecule. Our analysis of the former system indicates that non blow-up regions become reduced in size as the perturbation order increases. In case of LCPT by Dragt and Finn and that by Deprit, the non blow-up regions enclose the region inside the separatrix of the Hamiltonian but it may not be the case for LCPT by Hori. We also analyze how well the actions constructed by these LCPTs approximate the true action of the Hamiltonian in the non blow-up regions and find that the conventional truncated LCPT does not work over the whole region inside the separatrix whereas LCPT by Dragt and Finn without truncation does. Our analysis of the latter system indicates that non blow-up regions do not necessarily cover the whole regions inside the HCN well.We propose a new perturbation method to improve non blow-up regions and validity ranges inside them. Our method is free from blowing up and retains the same normal form as the conventional LCPT. We demonstrate our method in the two systems and show that the actions constructed by our method have larger validity ranges than those by the conventional and our previous methods proposed in [1,2].

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Transition State in a Noisy Environment

Cited by 85 publications

References 31 publications

Transition state theory for laser-driven reactions

Transition state theory for laser-driven reactions

Variational principle for the determination of unstable periodic orbits and instanton trajectories at saddle points

A new method to improve validity range of Lie canonical perturbation theory: with a central focus on a concept of non-blow-up region

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