Reaction Dynamics Through Kinetic Transition States

Çiftçi, Ünver; Waalkens, Holger

doi:10.1103/physrevlett.110.233201

Cited by 21 publications

(20 citation statements)

References 15 publications

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“…[15][16][17][18][19][20][21][22][23] In time-dependent systems-that is, those that are exposed to an external field or thermal noise,-the theory has been generalized over the last decade around a timedependent DS in phase space that is associated with the so-called transition state (TS) trajectory [24][25][26][27][28][29][30] and has been shown to provide a recrossing-free DS by which formally exact reaction rates can be calculated. In time-independent systems, such a DS can locally be constructed via a normally hyperbolic invariant manifold.…”

Section: Introductionmentioning

confidence: 99%

Lagrangian descriptors in dissipative systems

Junginger

Hernandez

2016

Phys. Chem. Chem. Phys.

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The reaction dynamics of time-dependent systems can be resolved through a recrossing-free dividing surface associated with the transition state trajectory-that is, the unique trajectory which is bound to the barrier region for all time in response to a given time-dependent potential. A general procedure based on the minimization of Lagrangian descriptors has recently been developed by Craven and Hernandez [Phys. Rev. Lett., 2015, 115, 148301] to construct this particular trajectory without requiring perturbative expansions relative to the naive transition state point at the top of the barrier. The extension of the method to account for dissipation in the equations of motion requires additional considerations established in this paper because the calculation of the Lagrangian descriptor involves the integration of trajectories in forward and backward time. The two contributions are in general very different because the friction term can act as a source (in backward time) or sink (in forward time) of energy, leading to the possibility that information about the phase space structure may be lost due to the dominance of only one of the terms. To compensate for this effect, we introduce a weighting scheme within the Lagrangian descriptor and demonstrate that for thermal Langevin dynamics it preserves the essential phase space structures, while they are lost in the nonweighted case.

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Section: Introductionmentioning

confidence: 99%

Lagrangian descriptors in dissipative systems

Junginger

Hernandez

2016

Phys. Chem. Chem. Phys.

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“…These pathways persist even in reactions whose state-to-state transitions are not dictated by purely configurational changes. 26 In systems subjected to time-varying external forcing, the characterization of the NHIM as a hypersphere of constant energy breaks down. For example, field-matter interactions constitute processes in which energy is exchanged with a reacting system.…”

Section: Introductionmentioning

confidence: 99%

Chemical reactions induced by oscillating external fields in weak thermal environments

Craven

Bartsch

Hernandez

2015

The Journal of Chemical Physics

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Chemical reaction rates must increasingly be determined in systems that evolve under the control of external stimuli. In these systems, when a reactant population is induced to cross an energy barrier through forcing from a temporally varying external field, the transition state that the reaction must pass through during the transformation from reactant to product is no longer a fixed geometric structure, but is instead timedependent. For a periodically forced model reaction, we develop a recrossing-free dividing surface that is attached to a transition state trajectory [T. Bartsch, R. Hernandez, and T. Uzer, Phys. Rev. Lett. 95, 058301 (2005)]. We have previously shown that for single-mode sinusoidal driving, the stability of the timevarying transition state directly determines the reaction rate [G. T. Craven, T. Bartsch, and R. Hernandez, J. Chem. Phys. 141, 041106 (2014)]. Here, we extend our previous work to the case of multi-mode driving waveforms. Excellent agreement is observed between the rates predicted by stability analysis and rates obtained through numerical calculation of the reactive flux. We also show that the optimal dividing surface and the resulting reaction rate for a reactive system driven by weak thermal noise can be approximated well using the transition state geometry of the underlying deterministic system. This agreement persists as long as the thermal driving strength is less than the order of that of the periodic driving. The power of this result is its simplicity. The surprising accuracy of the time-dependent noise-free geometry for obtaining transition state theory rates in chemical reactions driven by periodic fields reveals the dynamics without requiring the cost of brute-force calculations.

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“…It can be constructed using a normal form expan-sion. 13,24,32,[36][37][38][39][40][41][42] For a multidimensional timedependent system that is driven by an external field or subject to thermal noise, the question arises whether the NHIM can be generalized in such a way that it can still be used to construct a recrossing-free DS. Recent successful constructions [43][44][45] of such a DS suggests that it is indeed possible to do so.…”

Section: Introductionmentioning

confidence: 99%

Invariant Manifolds and Rate Constants in Driven Chemical Reactions

et al. 2019

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Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition state trajectory.Here, we extend our recent methods by constructing points on the NHIM accurately even for multidimensional cases. We also advance the implementation of machine learning approaches to construct smooth versions of the NHIM from a known high-accuracy set of its points. That is, we expand on our earlier use of neural nets, and introduce the use of Gaussian process regression for the determination of the NHIM. Finally, we compare and contrast all of these methods for a challenging twodimensional model barrier case so as to illustrate their accuracy and general applicability.

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Reaction Dynamics Through Kinetic Transition States

Cited by 21 publications

References 15 publications

Lagrangian descriptors in dissipative systems

Lagrangian descriptors in dissipative systems

Chemical reactions induced by oscillating external fields in weak thermal environments

Invariant Manifolds and Rate Constants in Driven Chemical Reactions

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