Davis-Gray rate theory

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. 

When the effect of intramolecular energy transfer is taken into account, more accurate rate constants can be obtained. We first compare the rate constants associated with the intramolecular bottleneck from the MRRKM theory with those from the Davis-Gray turnstile approach. As seen in Table III, they are in reasonable agreement. Hence, the Davis-Gray theory and the MRRKM theory predict similar overall reaction rates. This is demonstrated in Table IV. Table IV also shows that the predissociation rate constants would have been overestimated by a factor more than 100 if the RRKM theory were to be directly applied. 

With this simplification, Gray, Rice, and Davis obtained reasonably accurate values for the predissociation rate constant as a function of initial vibrational excitation. The rate constant thus obtained is larger than that from exact trajectory calculations by about a factor of two. By contrast, the RRKM theory would give a rate constant that is about three orders of magnitude larger than is observed. 

Gray, Rice and Davis and Gray and Rice have further developed the theory sketched above, with emphasis on analytical approximations that reduce the complexity of calculations and that permit the interpretation of variation of fragmentation rate with parameters such as vibrational frequency difference, van der Waals well depth, etc. The theory has been applied to the study of isomerization, where it successfully resolves the problem of "surface recrossing. An estimate of the effect of... 

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