Activated Rate Processes in Condensed Phases: the Kramers Theory Revisited

Nitzan, Abraham

doi:10.1002/9780470122693.ch11

Cited by 75 publications

(7 citation statements)

References 110 publications

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“…Usually, the boundary between these regions contains an energetic saddle point in phase space to which an appropriate dividing surface (DS) can be attached. Transition state theory (TST) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] then provides a powerful basis for the qualitative and quantitative description of the reaction. The rate is obtained from the flux through the DS and it is exact if and only if the DS is free of recrossings.…”

Section: Introductionmentioning

confidence: 99%

Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors

Feldmaier

Junginger

Main

et al. 2017

Chemical Physics Letters

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Dynamics between reactants and products are often mediated by a rate-determining barrier and an associated dividing surface leading to the transition state theory rate. This framework is challenged when the barrier is time-dependent because its motion can give rise to recrossings across the fixed dividing surface. A non-recrossing time-dependent dividing surface can neverthless be attached to the TS trajectory resulting in recrossing-free dynamics. We extend the formalism -contstructed using Lagrangian Descriptors-to systems with additional bath degrees of freedom. The propagation of reactant ensembles provides a numerical demonstration that our dividing surface is recrossing-free and leads to exact TST rates.

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Section: Introductionmentioning

confidence: 99%

Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors

Feldmaier

Junginger

Main

et al. 2017

Chemical Physics Letters

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“…Even simple scattering type experiments when carried out in solutions require ultra-short time resolution if information on the energy distributions is to be obtained. The understanding of reaction dynamics in solutions has been greatly advanced by theoretical studies [4][5][6][7][8][9][10] and recent experimental work [11][12][13][14][15][16][17][18][19][20][21][22][23][24] on small molecules. The experiments generally involve ultrafast laser studies of photodissociation, photoisomerization, geminate (or cage) reactions and the vibrational relaxation of molecules.…”

Section: Introductionmentioning

confidence: 99%

“…Presumably this is also appropriate for surfaces that are not too anharmonic. Equation (7) is the same result that pertains for a classical Brownian particle in a harmonic force field [43] where T 2 is identified with the dynamical friction [44].…”

Section: Introductionmentioning

confidence: 99%

Energy and phase relaxation accompanying impulsive reactions in liquids

Gnanakaran

Lim

Pugliano

et al. 1996

J. Phys.: Condens. Matter

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Experiments made possible by new laser methods explore ultrafast features of solution phase reaction dynamics. The results from two examples are given. Photodissociation of small molecules such as and in solution yields highly excited vibrational state distributions and narrow bond length distributions. The dynamics in the transition state region and the ensuing dynamics can be followed by femtosecond laser experiments that probe the phase and energy loss processes. The mercuric iodide experiments show that the phase relaxation is dominated by coherence transfer processes which have a strong analogy to classical motions. The population relaxation dynamics gives results similar to those from classical molecular dynamics simulations which suggest, notwithstanding the significant polarity of the molecules and solvents, that the relaxations are dominated by Lennard - Jones repulsion at sufficiently low frequencies.

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“…determining rate constants. TST rates are given by the particle flux through that surface [16][17][18][19][20][21][22][23][24][25][26][27]. It has been applied in various fields of physics and chemistry, including, e. g., atomic physics [28], solid state physics [29], cluster formation [30,31], diffusion dynamics [32,33], and cosmology [34], to name a few.…”

Section: Introductionmentioning

confidence: 99%

On the stability of satellites at unstable libration points of sun-planet-moon systems

Reiff,

Zatsch,

Main

et al. 2021

Preprint

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The five libration points of a sun-planet system are stable or unstable fixed positions at which satellites or asteroids can remain fixed relative to the two orbiting bodies. A moon orbiting around the planet causes a time-dependent perturbation on the system. Here, we address the sense in which invariant structure remains. We employ a transition state theory developed previously for periodically driven systems with a rank-1 saddle in the context of chemical reactions. We find that a satellite can be parked on a so-called time-periodic transition state trajectory-which is an orbit restricted to the vicinity of the libration point L2 for infinitely long time-and investigate the stability properties of that orbit.

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Activated Rate Processes in Condensed Phases: the Kramers Theory Revisited

Cited by 75 publications

References 110 publications

Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors

Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors

Energy and phase relaxation accompanying impulsive reactions in liquids

On the stability of satellites at unstable libration points of sun-planet-moon systems

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