Quantum Effects in Unimolecular Reactions

One difficulty with the Slater and RRK theories as we have employed them lies in the use of a classical mechanical model of a molecule. The first formulation of the problem of a chemical reaction in quantum-mechanical terms was made by London, who used a very crude approximation to resolve the problem mathematically. A study by Golden et al.  

If such a molecule has s oscillators (s degrees of freedom) and there are j quanta distributed among them, the total number of ways of distributing the j quanta among the s oscillators is q(sj) 

SO that the probability Pm(sj ), of finding m or more quanta in the reactive oscillator when the molecule has a total of j quanta (j m) 

If now we assume that the rate at which the quanta become redistributed is equal to some constant v, we can write for the mean rate of decomposition k(Ej)  

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This hnding concerning quantum transport in classically chaotic systems sheds new light on quantum effects in unimolecular reaction dynamics. For example, one expects that intramolecular bottlenecks associated with canton, if treated quantum mechanically, would be more effective than in a classical statistical theory even when nh is smaller than the reaction flux crossing the intramolecular dividing surface. Clearly, it would be interesting to examine realistic molecular systems in a similar fashion. 

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