Statistical Theories and the Information-Theoretic Approach

Rate constants for the opposing processes of unimolecular dissociation and bimolecular association are related by equations similar to those derived in Section 1.3.1. For 

K v T) (2( t ) where Qtr is the partition function associated with relative translational motion of A 4- BC, and Q[nt and e are the internal partition function and the zero-point energy of ABC. 

Nowadays, phase-space theory is mainly used to generate least-biased state distributions in an information-theoretic analysis of experimental data/ ° This approach was first formulated by Bernstein and Levine and has been extended and widely applied over the past few years. A central feature of the method is its proposal of a quantitative measure of the surprisal of a particular outcome, for example, the observation that in the reaction H + CI2 - HCl -I- Cl, 42% of the HCl molecules are formed in i = 3. To do this, it is necessary to define one s prior expectation. If the observed result coincides with this, it causes no surprise. The prior is usually provided by the least biased choice obtained via phase-space theory.  

The surprisal associated with the formation of CO in a particular v level in thermal studies of the exoergic reaction is defined in terms of the observed probability, P v ) and that expected on prior grounds, P v )  

A plot of I(v T) againstthe energy of the r level expressed as a fraction of the average total energy available is linear. It provides a sound basis for obtaining information about the values of P v ) below v = 6, which have been difficult to determine directly.  

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