Statistical reaction theory

Degenerate rearrangement of bicyclo[3.1.0]hex-2-ene (Chart 2) has a PES, in which four degenerate products are separated through four degenerate TSs with the common energy plateau on the surface.9 Here, four compounds are identical except for the position of deuterium. The rearrangement from 4-exo isomer (6x) is expected to afford 4-endo (6n), 6-exo (7x), and 6-endo (7n) isomers in equal amount if the reaction follows statistical reaction theory (TST). Thus, this reaction provides a situation previously presented by Carpenter to predict nonstatistical product distribution due to dynamics effect.1... 

X—HOCO speed requires that there is less HOCO internal excitation, which results in lower OH internal excitation according to all dictates of statistical reaction theories. 

The average lifetime is defined by Eqs. (13), (15), (20) and (22). According to a general prescription in statistical reaction theory or the phase-space theory due to Light [38], the lifetime of an isomer in a basin a should be given by... 

In the following sections, we will give more detailed explanations of the recent studies mentioned above. The outline of their contents is as follows. In Section II, we will discuss the fundamental assumptions of statistical reaction theory. In particular, we will focus our attention on the dynamical bases of the theory and its limitations. 

In the statistical theory of chemical reactions, the concept of transition states plays a key role. In traditional theory, transition states are considered to be the saddle points in configuration space. As will be discussed later, however, their role in reactions can be more clearly understood when studied in phase space. So far, they are the only phase-space structure that is taken into account in reaction theory. In this section, we will focus attention on their role and the underlying assumptions of the statistical reaction theory. 

Going back to the underlying assumptions of statistical reaction theory, the third one is the most important. This means that the detail of the... 

In Section III, we briefly discussed some of the recent experiments that imply the breakdown of the separation of timescales. These results make us reconsider the underlying assumptions of the statistical reaction theory. Furthermore, they lead us to utilize the recent development in the field of dynamical systems for seeking clues for new ideas. In this section, we will discuss results of such attempts in the study of reaction processes. 

Davis and Gray were the hrst to study IVR from the point of view of nonlinear resonances [2]. They noticed that cantori created by nonlinear resonances constitute bottlenecks for the processes of IVR. As is seen in Figure 3.18, cantori trap orbits for a hnite timescale. Contrary to KAM tori, cantori do not completely keep orbits from passing through them. Nevertheless, their existence results in breakdown of the separation of timescales, thus invalidating the statistical reaction theory. 

Figure 3.24(h) shows the opposite to Figure 3.24(a) in the sense that a web has dense intersections. Moreover, those intersections overlap in phase space creating global chaos. Here, chaotic diffusion takes place in all the directions on the equi-energy surface. Then, the IVR takes place uniformly involving all the degrees of freedom, which is the case where the statistical reaction theory can be applied. 

Figure 3.25(c) exhibits a case where no dynamical correlation exists. Here, the stable and unstable manifolds fall into the potential well, and encounter densely populated resonances. Then, the movement within the web takes so much time that dynamical correlation would be completely lost there, which is the case where the statistical reaction theory is applicable. 

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