Davis-Gray rate theory unimolecular reaction

The most important element of the Davis-Gray theory of unimolecular reaction rate is the identification of bottlenecks to intramolecular energy flow and the intermolecular separatrix to molecular fragmentation. Davis and Gray s work was motivated by the discovery of bottlenecks in chaotic transport by MacKay, Meiss, and Percival [8,9] and by Bensimon and Kadanoff [10]. 

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. 

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