Nonstatistical behavior

Throughout the chapter, we have presented the methodology of VMP and discussed some specific examples, where controlling the photodissociation products ensuing from an electronically excited state is achievable via preexcitation of specific vibrational states in the initial electronic state. This mode selectivity worked so far, with only two exceptions, for molecules not larger than tetratomic. The main reason for this limit is believed to be IVR however, additional work has to be carried out in larger molecules in attempt to find out what are the limits of size and conditions where nonstatistical behavior is still feasible. 

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. 

Another common symptom of reactions that display nonstatistical behavior is a bimodal distribution of trajectory lifetimes. The nonstatistical trajectories have much shorter lifetimes than predicted by TST or RRKM. Trajectories will then cluster in two (or more) groups, the very short lifetime group and those with a much longer lifetime, consistent with statistical dynamics. Both direct trajectories that seemingly avoid local minima and bimodal lifetime distributions will be seen in many of the examples to follow. 

Unlike the other pericycUc reactions discussed previously in this chapter, the diradical species here resides in a relatively deep well, greater than 12 kcal mol , and so the PES about the diradical cannot be described as a caldera. Nonetheless, this reaction exhibits nonstatistical behavior. 

To try to distinguish whether 102 is intervening, Carpenter carried out the photolysis of a different labeled version of 98 (namely, 98 ). The resulting product distribution is shown in Scheme 8.13. It appears that the reaction predominantly passes through 102, but the ratio of products that come from 100 nonetheless shows nonstatistical behavior. 

In the first edition of this book, I stressed that more trajectory studies were needed to determine how broad the scope of nonstatistical behavior in organic reactions really is. In the meantime, many new examples of nonstatistical dynamics have been reported. Dynamic effects are real, critical to understanding experimental results, and probably more pervasive than once thought. 

Singleton feels that nonstatistical dynamics are not important in most reactions, but that they are important in a great many Maybe 1 out of 5 cases will have something interesting, he speculates. If you go through our cases, what we find is mostly by accident. But it s not complete random chance that a reaction has nonstatistical behavior. Now we are designing systems to force dynamic effect on it. ... 

Before concluding this section to proceed to the next topic about a geometry that can bring the statistical nature into the system, we slightly touch upon the nonexponential behavior, which is a key to consider the nonstatistical behavior of chemical reaction. This is interesting from the viewpoint of the onset of statistical mechanics and also from the study of the role of chaos in mechanics. 

Nonstatistical Behavior in the Low Energy. Comparing loglVa (f) in Fig. 6 with Fig. 5, we immediately notice (see Figs. 6b to 6d) that the behaviors of COCT, 1ST, and SKEW are not very strange in that (i) the curves are mostly linear, (ii) they are parallel to each other within the same structure, except in the... 

In an interesting study, Chang et al. (146), have proposed the use of power spectra (Fourier transforms of r(t)) as a diagnostic tool for nonstatistical behavior in unimolecular decomposition. 

Most of the experimental tests of RRKM theory have supported its assumptions. At the same time, few of the claims of nonstatistical behavior have withstood the test of time. Experimental artifacts have been the major sources of the apparent nonRRKM behavior. In fact, it appears that as experiments have become more controlled and refined, the more dramatic has been the validation of the statistical assumptions. The theory has been tested from long times (msec) to short times (psec), from large molecules to the very smallest molecules. 

The most dramatic evidence for nonstatistical behavior has been reported in the dissociation of loosely bound van der Waals dimers (see chapter 10) where the coupling between the high-frequency modes of the monomers and the low-frequency inter-molecular modes is weak. In a dimer such as H—F---H—F, infrared radiation can be... 

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