Reactive islands

Figure 8 displays the escape actions thus obtained for trajectories that react into channel A or B. It confirms, first of all, that all escape actions are positive. Furthermore, they take a maximum in the interior of each reactive island and decrease to zero as the boundaries of the islands are approached. These boundaries therefore coincide with the invariant manifolds that are characterized by 1 = 0. A more detailed study of the island structure [40] reveals in addition that the time-dependent normal form approach is necessary to describe the islands correctly. Neither the harmonic approximation of Section IVB1 nor the earlier autonomous TST described in Section II yield the correct island boundaries. 

Zhao-Rice Approximation Reactive Island Theory... 

Gray-Rice Theory Versus Reactive Island Theory Isomerization in Double-Well Systems Isomerization in a Triple-Well System Isomerization of 3-Phospholene Isomerization of HCN — CNH Isomerization of Cyclobutanone (C4H6O)... 

With this brief overview of classical theories of unimolecular reaction rate, one might wonder why classical mechanics is so useful in treating molecular systems that are microscopic, and one might question when a classical statistical theory should be replaced by a corresponding quantum theory. These general questions bring up the important issue of quantum-classical correspondence in general and the field of quantum chaos [27-29] (i.e., the quantum dynamics of classically chaotic systems) in particular. For example, is it possible to translate the above classical concepts (e.g., phase space separatrix, NHIM, reactive islands) into quantum mechanics, and if yes, how What is the consequence of... 

A beautiful classical theory of unimolecular isomerization called the reactive island theory (RIT) has been developed by DeLeon and Marston [23] and by DeLeon and co-workers [24,25]. In RIT the classical phase-space structures are analyzed in great detail. Indeed, the key observation in RIT is that different cylindrical manifolds in phase space can act as mediators of unimolecular conformational isomerization. Figure 23 illustrates homoclinic tangling of motion near an unstable periodic orbit in a system of two DOFs with a fixed point T, and it applies to a wide class of isomerization reaction with two stable isomer... 

Figure 24. Reactive island structure for a two-well potential isomerization model, generated from the stable and unstable branches of the transition state hxed point, (a) Stable branch structure, (b) Unstable branch structure. [From A. M. O. De Almeida et al., Physica D 46, 265 (1990).]...

The RIs display a number of interesting mathematical and physical properties. To briefly introduce these properties, we define the RIs generated from the same branch (either the stable or the unstable branch) to be of the same family. We also denote by RI +i the reactive island generated from a further iteration of the reactive island RIy. That is, the area of RIy wiU, upon one positive or negative time iteration, map onto RIy+i or RIy-i within the same family. It... 

De Leon and co-workers [34—37] established an elegant reaction theory for a system with two DOFs, the so-called reactive island theory to mediate reactions through cylindrical manifolds apart from the saddles. Their original algorithm depends crucially on the existence of pure unstable periodic orbits in the nonreactive DOFs in the region of the saddles and did not extend to systems with many DOFs. 

Then, how can one capture the global aspects of the phase-space geometry from the geometric structure of the phase space in that local region One can find an essential clue from an insightful classical theory for isomerization reactions composed of two DOFs, so-called reactive island theory (RIT) developed by De Leon, Marston, Mehta, and Ozorio De Almeida [34—37] (see also Ref. 55). 

Figure 9. Schematic picture of the reactive island structure on E+ and the corresponding dynamics in the reaction coordinate q. See text for detail discussions. [Reprinted with permission from A. M. Ozorio de Almeida, N. De Leon, M. A. Mehta, and C. C. Marston, Physica D 46, 265 (1990). Copyright 1990, Elsevier Science Publishers, North-Holland.]...

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