Dynamical Reaction Theory based on Geometric Structures in Phase Space

Kawai, Shinnosuke; Teramoto, Hiroshi; Li, Chun‐Biu; Komatsuzaki, Tamiki; Toda, Mikito

doi:10.1002/9781118087817.ch4

Cited by 15 publications

(31 citation statements)

References 101 publications

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“…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%

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: 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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“…While H 0 can take any kind of functional form, recent studies [7][8][9][22][23][24][25][26][27] have found that it is possible to introduce a coordinate transformation ðx; $; q 2 ; . .…”

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confidence: 99%

“…The set f x ¼ 0g divides the future of the reaction due to its invariance (no trajectory can cross it). Here the transformation and the final form of the Hamiltonian are calculated by canonical perturbation theory [28,29] as in the previous works [7][8][9][22][23][24][25][26][27]. The difference is the choice of terms to be held in the final Hamiltonian.…”

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confidence: 99%

“…Studies of the dynamics in the vicinity of the saddle have made great contributions to the calculation of reaction rates, as well as to physical insights into not only reaction dynamics [1][2][3][4][5][6] but also, for example, ionization of a hydrogen atom in crossed electric and magnetic fields [7,8], isomerization of clusters [9], the escape of asteroids from Mars [10], the diffusion of impurities in crystalline materials [11], and the folding or unfolding of proteins [12,13]. Among the central concepts in the study of dynamics in the saddle region are the ''transition state'' (TS) [14][15][16][17][18][19][20][21] and several invariant manifolds [22,23]. The TS is originally defined as a surface dividing the phase space into two distinct regions, i.e., reactant and product, through which the system passes once and only once when undergoing the reaction from one region before being ''captured'' in the other region.…”

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confidence: 99%

“…(4) is called ''partial normal form'' (PNF) in the sense that only the action of the reactive mode is transformed as an invariant, which survives robustly even at a moderately high energy regime (because resonance does not meet between the reactive and nonreactive modes [7][8][9][22][23][24][25][26][27]). It is also possible to construct a ''full normal form'' that makes all the actions transform as invariants of motion [7][8][9][10][22][23][24][25].…”

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Robust Existence of a Reaction Boundary to Separate the Fate of a Chemical Reaction

Kawai

Komatsuzaki

2010

Phys. Rev. Lett.

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Nonlinear dynamics around a rank-one saddle is investigated in a high energy regime above the reaction threshold. The transition state (TS) is considered as a surface of a ''point of no return'' through which all reactive trajectories pass only once in the process of climbing over the saddle before being captured in the product state. A no-return TS ceases to exist above a certain high energy regime. However, even at high energies where the no-return TS can no longer exist, it is shown that ''an impenetrable barrier'' in the phase space robustly persists, which acts as a boundary between reactive and nonreactive trajectories. This implies that we can yet predict the fate of reactions even when the no-return TS may not exist. As an example, we show the analysis of dynamical systems theory for a hydrogen atom in crossed electric and magnetic fields.

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Non‐statistical dynamics for the allene oxide to cyclopropanone conversion

Rush

Gallo

Stumetz

et al. 2022

J of Physical Organic Chem

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Whether one is interested in mode selective chemistry or non‐statistical reaction dynamics, understanding which vibrational modes contribute to a reaction is important. We investigated the ring‐opening of 2‐methylideneoxirane (a.k.a., allene oxide) to the oxyallyl diradical and subsequent ring‐closure to cyclopropanone using hybrid density functional theory (DFT) and atom centered density matrix propagation (ADMP) molecular dynamics in Gaussian. DFT calculations for this ring‐opening and subsequent ring‐closure show that the energetics allow for the possibility of non‐statistical events, as suggested by the similarities between the imaginary vibrational modes and a twisting motion. ADMP simulations starting near the ring‐opening transition state lead to faster ring‐closure than for simulations starting from the intermediate diradical with the same energy. Analysis of the simulation data identified the presence of a vibrational state near 200 cm−1, corresponding to a disrotatory twisting motion. Selectively exciting this mode leads to a fast reaction time of 50 fs. This work predicts non‐statistical dynamics in the conversion of allene oxide to cyclopropanone.

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Dynamical Reaction Theory based on Geometric Structures in Phase Space

Cited by 15 publications

References 101 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

Robust Existence of a Reaction Boundary to Separate the Fate of a Chemical Reaction

Non‐statistical dynamics for the allene oxide to cyclopropanone conversion

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