Fractional behavior in nonergodic reaction processes of isomerization

Shojiguchi, Akira; Li, Chun‐Biu; Komatsuzaki, Tamiki; Toda, Mikito

doi:10.1103/physreve.75.035204

Cited by 14 publications

(12 citation statements)

References 33 publications

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“…5͑a͔͒. Such power law decay has been seen in other models for isomerization, 142,143 and is in general associated with fractional kinetics. 141 ͑Nonexponential lifetime distributions have also been fitted using sums of exponentials.…”

Section: ͑33b͒mentioning

confidence: 85%

“…129,130 Local random matrix theories have served as the foundation for quantum theoretical treatments of isomerization reactions in large molecules, [131][132][133][134][135] while attention has also been given to related scaling approaches [136][137][138][139][140] and to fractional kinetics. [141][142][143] An important advance was the realization that normally hyperbolic invariant manifolds 144,145 ͑NHIMs͒ provide a natural and theoretically well-founded generalization of PODS to the N Ն 3 DoF case ͑cf. Ref.…”

Section: Introductionmentioning

confidence: 99%

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Microcanonical rates, gap times, and phase space dividing surfaces

Ezra

Waalkens

Wiggins

2009

The Journal of Chemical Physics

112

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The general approach to classical unimolecular reaction rates due to Thiele is revisited in light of recent advances in the phase space formulation of transition state theory for multidimensional systems. Key concepts, such as the phase space dividing surface separating reactants from products, the average gap time, and the volume of phase space associated with reactive trajectories, are both rigorously defined and readily computed within the phase space approach. We analyze in detail the gap time distribution and associated reactant lifetime distribution for the isomerization reaction HCN CNH, previously studied using the methods of phase space transition state theory. Both algebraic ͑power law͒ and exponential decay regimes have been identified. Statistical estimates of the isomerization rate are compared with the numerically determined decay rate. Correcting the RRKM estimate to account for the measure of the reactant phase space region occupied by trapped trajectories results in a drastic overestimate of the isomerization rate. Compensating but as yet not fully understood trapping mechanisms in the reactant region serve to slow the escape rate sufficiently that the uncorrected RRKM estimate turns out to be reasonably accurate, at least at the particular energy studied. Examination of the decay properties of subensembles of trajectories that exit the HCN well through either of two available symmetry related product channels shows that the complete trajectory ensemble effectively attains the full symmetry of the system phase space on a short time scale t Շ 0.5 ps, after which the product branching ratio is 1:1, the "statistical" value. At intermediate times, this statistical product ratio is accompanied by nonexponential ͑nonstatistical͒ decay. We point out close parallels between the dynamical behavior inferred from the gap time distribution for HCN and nonstatistical behavior recently identified in reactions of some organic molecules.

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Section: ͑33b͒mentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Microcanonical rates, gap times, and phase space dividing surfaces

Ezra

Waalkens

Wiggins

2009

The Journal of Chemical Physics

112

View full text Add to dashboard Cite

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“…Moreover, the power-law decay of the survival probability has been observed experimentally [11]. Recently, we have also obtained numerical results of classical mechanics showing that isomerization processes in HCN exhibit the power-law decay of the survival probability [31]. These results lead us to the following question; To what extent can we define the rate constant?…”

Section: Introductionmentioning

confidence: 90%

Dynamical foundation and limitations of statistical reaction theory

Shojiguchi

Komatsuzaki

et al. 2008

Communications in Nonlinear Science and Numerical Simulation

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“…Following the initial studies, which were perhaps ahead of their time, far fewer efforts were made for almost a decade but there has been a renewal of interest in the problem over the last few years with the NHIMs playing a crucial role. Armed with the understanding that the notion of partial barriers, chaos, and resonances are very different in N ≥ 3 fresh insights on transition state and RRKM theories, and hence IVR, are beginning to emerge [58,59,60,61,62,63,64,65,66,67,68,69].…”

Section: Introductionmentioning

confidence: 99%

Dynamical tunnelling in molecules: quantum routes to energy flow

Keshavamurthy¹

2007

International Reviews in Physical Chemistry

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Dynamical tunneling, introduced in the molecular context, is more than two decades old and refers to phenomena that are classically forbidden but allowed by quantum mechanics. The barriers for dynamical tunneling, however, can arise in the momentum or more generally in the full phase space of the system. On the other hand the phenomenon of intramolecular vibrational energy redistribution (IVR) has occupied a central place in the field of chemical physics for a much longer period of time. Despite significant progress in understanding IVR a priori prediction of the pathways and rates is still a difficult task. Although the two phenomena seem to be unrelated several studies indicate that dynamical tunneling, in terms of its mechanism and timescales, can have important implications for IVR. It is natural to associate dynamical tunneling with a purely quantum mechanism of IVR. Examples include the observation of local mode doublets, clustering of rotational energy levels, and extremely narrow vibrational features in high resolution molecular spectra. Many researchers have demonstrated the usefulness of a phase space perspective towards understanding the mechanism of IVR. Interestingly dynamical tunneling is also strongly influenced by the nature of the underlying classical phase space. Recent studies show that chaos and nonlinear resonances in the phase space can enhance or suppress dynamical tunneling by many orders of magnitude. Is it then possible that both the classical and quantum mechanisms of IVR, and the potential competition between them, can be understood within the phase space perspective? This review focuses on addressing the question by providing the current state of understanding of dynamical tunneling from the phase space perspective and the consequences for intramolecular vibrational energy flow in polyatomic molecules.

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Fractional behavior in nonergodic reaction processes of isomerization

Cited by 14 publications

References 33 publications

Microcanonical rates, gap times, and phase space dividing surfaces

Microcanonical rates, gap times, and phase space dividing surfaces

Dynamical foundation and limitations of statistical reaction theory

Dynamical tunnelling in molecules: quantum routes to energy flow

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