Rare Event Kinetics and Free Energies in Path Space

6 Rare Event Kinetics and Free Energies in Path Space 

On a phenomenological level, transitions between long-lived stable states can be described in terms of reaction rate constants. Consider, for instance a solution of two well-defined chemical species s3 and 38 that can interconvert through the unimolecular reaction 

The solution is assumed to be sufficiently dilute that the solute molecules do not interact with each other (at the same time we assume that there still is a macroscopic number of solute molecules in the solution). Due to the reaction the concentrations Cst and c /( of molecules of type / / and 38, respectively, can change in time. The concentration of c decreases when molecules of type s8 transform into molecules of type 38 and increases due to the inverse reaction. Since, according to the assumptions, the solute molecules are statistically independent from each other, the time evolution of c t) is well described by the phenomenological [33] 

The calculation of reaction rate constants with the transition path sampling methods does not require understanding of the reaction mechanism, for instance in the form of an appropriate reaction coordinate. If such information is available other methods such as the reactive flux formalism are likely to yield reaction rate constants at a lower computational cost than transition path sampling. 

An analogous loss-gain equation holds for the concentration cag(t) 

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