Intramolecular dynamics bottlenecks

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

In two-mode [17] and three-mode [20] systems it was shown that dynamical bottlenecks exist to intramolecular energy transfer that is, cantori are buried in the reactant basin, which form partial barriers between irregular regions of phase space. This brought about multiply... 

The behavior of molecules within the intermolecular bottleneck, that is to say intramolecular dynamics, is also of interest. For example, trajeaories can be trapped for signficant periods of time within resonance zones inside the intermolecular bottleneck. A classical resonance is a region of phase space where, locally, the condition... 

Figure 14. An Hel2 surface of section for an unstable trajectory which forms a collision complex. The total energy is —2661.6 cm . Also shown are the reaction separatrix and the intramolecular bottleneck, (a) Graph showing the full dynamics of the trajectory. (b)-(f) Graphs illustrating the trajectory over five consecutive time ranges. These graphs are arranged to demonstrate the manner in which the trajectory moves with respect to the bottleneck and the separatrix. [From M. J. Davis and S. K. Gray, J. Chem. Phys. 84, 5389 (1986).]...

With only the most effective intramolecular energy transfer bottleneck accounted for, a simple kinetics model describing the dynamics of He-la predissociation can be defined ... 

It is worth mentioning that Davis and Gray also found that at low energy, for example, when I2 is initially in a vibrational state with v < 5, no classical dissociation occurs. Furthermore, if I2 is initially in a vibrational state with 20 > V > 5, the dynamics appears to be so complicated that including only one intramolecular bottleneck does not suffice. Indeed, in the case of v = 10 Davis and Gray used two intramolecular bottlenecks to model the Hel2 fragmentation reaction. The two bottlenecks on a PSS are illustrated in Fig. 17. It is seen that... 

The Davis-Gray theory teaches us that by retaining the most important elements of the nonhnear reaction dynamics it is possible to accurately locate the intramolecular bottlenecks and to have an exact phase space separatrix as the transition state. Unfortunately, even for systems with only two DOFs, there may be considerable technical difficulties associated with locating the exact bottlenecks and the separatrix. Exact calculations of the fluxes across these phase space structures present more problems. For these reasons, further development of unimolecular reaction rate theory requires useful approximations. 

The fact that classical unstable periodic trajectories can manifest themselves in the Wigner function implies that nonstatistical behavior in the quanmm dynamics can be intimately related to the phase-space structure of the classical molecular dynamics. Consider, for example, the bottlenecks to intramolecular energy flow. Since the intramolecular bottlenecks are caused by remnants of the most robust tori, they are presumably related to the least unstable periodic trajectories. Hence quantum scars, being most significant in the case of the least unstable periodic trajectories, are expected to be more or less connected with intramolecular bottlenecks. Indeed, this observation motivated a recent proposal [75] to semiclassically locate quantum intramolecular bottlenecks. Specifically, the most robust intramolecular bottlenecks are associated with the least unstable periodic trajectories for which Eq. (332) holds, that is,... 

The effective Hamiltonian approach clearly shows the important role of intramolecular energy flow in the quantum dynamics of unimolecular dissociation. It suggests that unless intramolecular energy flow is dominantly rapid, there exist two drastically different time scales in the reaction dynamics. This is consistent with the classical concept that nonstatistical behavior in intramolecular energy flow, such as bottleneck effects, can dramatically alter the kinetics of unimolecular reaction. 

This hnding concerning quantum transport in classically chaotic systems sheds new light on quantum effects in unimolecular reaction dynamics. For example, one expects that intramolecular bottlenecks associated with canton, if treated quantum mechanically, would be more effective than in a classical statistical theory even when nh is smaller than the reaction flux crossing the intramolecular dividing surface. Clearly, it would be interesting to examine realistic molecular systems in a similar fashion. 

If the unimolecular dissociation is not random and not in accord with Eq. (2.2) it is thought that classical bottlenecks restricting intramolecular vibrational-energy redistribution (IVR) may be manifested in the quantum dynamics [16]. Thus, there is considerable interest in identifying the nature of the unimolecular dynamics of excited molecules. In this section Monte... 

Chemical kinetics is all about bottlenecks. They determine the reaction mechanism on different timescales. We have seen that ET can be hmited by nonadiabatic transitions, solvent dynamics, intramolecular vibrational relaxation, translational diffusion, and conformational fluctuations either of the reactants themselves or of the embedding medium. The interplay between different mechanisms as well as nonequilibrium initial condition may result in rich kinetic behaviors, with strong nonexponentiality and coherence effects observed in recent experiments. 

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