Phase space classical unimolecular reaction rate

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 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. 

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