Time‐Dependent Transition State Theory

Bartsch, Thomas; Moix, Jeremy M.; Hernandez, Rigoberto; Kawai, Shinnosuke; Uzer, T.

doi:10.1002/9780470371572.ch4

Cited by 44 publications

(60 citation statements)

References 99 publications

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“…We can thus identify a no-return TS to separate the reactant and the product regions [Eq. (17)], and the stable/unstable invariant manifolds acting as the boundary of reactive and nonreactive trajectories [Eqs. (15) and (16)].…”

Section: Discussionmentioning

confidence: 99%

“…Note that the definition of no-return dividing surface is not unique, that is, not restricted to that given by Eq. (17). For instance, the no-return property holds in the definition of the TS in Eq.…”

Section: B Rigid Rotor and Harmonic Approximationmentioning

confidence: 99%

“…The potential of the theories has been demonstrated not only in chemical reactions with 17,22 and without [23][24][25][26][27] time-dependent external field but also in ionization of a hydrogen atom in crossed electric and magnetic fields, [28][29][30] isomerization of clusters, [31][32][33][34][35][36] and the escape of asteroids from Mars 37,38 [Just recently the theory was also generalized to quantum Hamiltonian systems [39][40][41] and dissipative (generalized) Langevin systems. [42][43][44][45][46][47][48][49][50][51] The dimension of the phase space of an N -particle nonrigid system is (6N − 10) in the upper limit.…”

Section: Introductionmentioning

confidence: 99%

“…Thanks to normal form (NF) theories (a classical analog of quantum Van Vleck perturbation theory), it was revealed in classical Hamiltonian systems with many degrees of freedom, 9,10,17,19,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] that one can robustly extract the NHIM, no-return TS, and the stable/unstable invariant manifolds up to a moderately high energy regime above the saddle point energy, even under the existence of chaos arising from nonlinear couplings. The potential of the theories has been demonstrated not only in chemical reactions with 17,22 and without [23][24][25][26][27] time-dependent external field but also in ionization of a hydrogen atom in crossed electric and magnetic fields, [28][29][30] isomerization of clusters, [31][32][33][34][35][36] and the escape of asteroids from Mars 37,38 [Just recently the theory was also generalized to quantum Hamiltonian systems [39][40][41] and dissipative (generalized) Langevin systems.…”

Section: Introductionmentioning

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: B Rigid Rotor and Harmonic Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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Scaling Perspective on Intramolecular Vibrational Energy Flow: Analogies, Insights, and Challenges

Keshavamurthy¹

2013

Advances in Chemical Physics

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Molecular dynamics out of equilibrium: mechanics and measurables

Hernandez

Popov

2014

WIREs Comput Mol Sci

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Molecular dynamics is fundamentally the integration of the equations of motion over a representation of an atomic and molecular system. The most rigorous choice for performing molecular dynamics entails the use of quantum-mechanical equations of motion and a representation of the molecular system through all of its electrons and atoms. For most molecular problems involving at least hundreds of atoms, but generally many more, this is simply computationally prohibitive. Thus the art of molecular dynamics lies in choosing the representation and the appropriate equations of motion capable of addressing the requisite measurables. When used adroitly, it can provide both equilibrium (averaged) and time-dependent properties of a molecular system. Many computational packages now exist that perform molecular dynamics simulations. They generally include force fields to represent the interactions between atoms and molecules (smoothing out electrons through the Born-Oppenheimer approximation) and integrate the remaining particles classically. Despite these simplifications, all-atom molecular dynamics remains computationally inaccessible if one includes the number of atoms required to simulate mesoscopic solvents. Here we use analytical models to demonstrate how molecular dynamics can be used to limit the solvent size in systems experiencing either equilibrium or nonequilibrium conditions. It is equally important to address the measurables (such as reaction rates) that are to be obtained prior to the generation of the data-intensive trajectories.

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Time‐Dependent Transition State Theory

Cited by 44 publications

References 99 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

Scaling Perspective on Intramolecular Vibrational Energy Flow: Analogies, Insights, and Challenges

Molecular dynamics out of equilibrium: mechanics and measurables

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