Frequency dependence vibration coupling

The fonn of the classical (equation C3.2.11) or semiclassical (equation C3.2.11) rate equations are energy gap laws . That is, the equations reflect a free energy dependent rate. In contrast with many physical organic reactivity indices, these rates are predicted to increase as -AG grows, and then to drop when -AG exceeds a critical value. In the classical limit, log(/cg.j.) has a parabolic dependence on -AG. Wlren high-frequency chemical bond vibrations couple to the ET process, the dependence on -AG becomes asymmetrical, as mentioned above. 

At present the body of data on reactions in clusters is insufficient to test the above two microcanonical approaches. For electron transfers in solution it seems clear that the vibrational assistance approach, stemming from Eq. (1.2), with its extensions mentioned earlier, is the one that has been the most successful [27-30]. For slow isomerizations Sumi and Asano have pointed out that an analysis based on Eq. (1.2) was again needed [40]. An approach based on Eq. (1.1) or on its extension to include a frequency-dependent friction, they noted, led to unphysical correlation times [40]. In investigations of fast isomerizations the most commonly studied system has been the photoex-cited trans-stilbene [5, 41-43,46]. Difficulties encountered by a one-coordinate treatment for that system have been reported [4, 8]. Indeed, coherence results for photoexcited cw-stilbene have shown a coupling of a phenyl torsional mode to the torsional mode about the C=C bond [42, 47]. 

Finally, note that the relaxation equation [Eq. (76)] is usually written in terms of the hydrodynamic modes. In many problems of chemical interest, nonhydrodynamic modes such as intramolecular vibration, play an important role [50]. Presence of such coupling creates an extra channel for dissipation. Thus, the memory kernel, T, gets renormalized and acquires an additional frequency-dependent term [16, 43]. 

Figure 2.4. The energy-gap dependence of the nuclear Franck-Condon factor, which incorporates the role of the high-frequency intramolecular modes. Sc = A/2 is the dimensionless electron-vibration coupling, given in terms which reduce replacement (A) between the minimum of the nuclear potential surfaces of the initial and final electronic states. (Bixon and Jortner, 1999) Reproduced with permission.

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