State specific rate constants Porter-Thomas distribution

If all the resonance states which fomi a microcanonical ensemble have random i, and are thus intrinsically unassignable, a situation arises which is caWtA. statistical state-specific behaviour [95]. Since the wavefunction coefficients of the i / are Gaussian random variables when projected onto (]). basis fiinctions for any zero-order representation [96], the distribution of the state-specific rate constants will be as statistical as possible. If these within the energy interval E E+ AE fomi a conthuious distribution, Levine [97] has argued that the probability of a particular k is given by the Porter-Thomas [98] distribution... 

Figure 8.4 Porter-Thomas distribution of state specific rate constants, Eq. (8.15), for v 1, 2,4, 8, and In these plots x = k and (x) = k (Polik et al, 1990b).

The connection between the Porter-Thomas nonexponential N(r, E) distribution and RRKM theory is made through the parameters k and v. The average of the statistical state-specific rate constants k is expected to be similar to the RRKM rate constant k(E). This can be illustrated (Waite and Miller, 1980) by considering a separable (uncoupled) two-dimensional Hamilton H = + Hy whose decomposition path is... 

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