Bond lengths unimolecular reaction rates

Elements of classical dynamics of unimolecular reactions in particular, the Slater theory for indirect reactions, where the molecule is modeled as a set of uncoupled harmonic oscillators. Reaction is defined to occur when a particular bond length attains a critical value, and the rate constant is given as the frequency with which this occurs. 

Slater [13] has criticized the RRKM theory, mainly on the grounds that the proposed model assumes that the intramolecular transfer of energy between vibrational degrees of freedom is very rapid compared to the rate of reaction. In fact, all theories of unimolecular reactions, aside from Slater s, involve this particular assumption. Slater assumes that the rate of intramolecular vibrational-energy transfer is very slow. He then performs a normal-mode analysis of the reacting molecule, assuming that reaction occurs when the bond to be broken reaches a certain critical length. A formally correct expression for is obtained, namely. 

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