The Zusman Equation

Here, the solvent frequency scale is approximated to be cojl in the Ohmie spectral density. In the nonadiabatic limit (g l) the Zusman equation (eqn (12.41)) prediets the classical FGR ... 

The Zusman equation (ZE)/ due mainly to its physically insightful picture on solvation dynamics, is (at least used to be) one of the most commonly used approaches in the study of quantum transfer processes. In this approach, the electronic system degrees of freedom are coupled to a collective bath coordinate that is assumed to be diffusive. The only approximation involved is the classical high temperature treatment of bath. To account for the dynamic Stokes shift, the standard ZE includes also the imaginary part of bath correlation function. This part does not depend on temperature and is therefore exact in the diffusion regime. 

We have presented a comprehensive account of the theoretical background of the Zusman equation and its recently development. We have discussed in detail, both the physical picture and mathematical derivation, of how the Zusman... 

The idea is to substitute this D(t) into the rate equations (9.52). This approach may be useful for the description of the short-time behavior [84, 103-107]. However, it can be shown that it predicts the stationary value for the rate constant totally determined by the long-time value of D(t), which is /t. In other words, it simply reproduces Zusman s result in this limit, which is certainly not the case (see Fig. 9.14, e.g.). 

Equation (9.78) can be used to define the Zusman parameter C as a ratio of kj and k 2, similar to Eq. (9.61). However, in contrast to Eq. (9.61), since ki 2 now depends only on the reorganization energy of the slow mode while /cm is a function of the total reorganization energy, C will contain a certain activation factor. For example, for symmetric reactions (AG = 0) we obtain. 

In the adiabatie limit and strongly eondensed phases, however, it is known that Zusman equation should give way to Calef and Wolynes s Kramers adiabatie theory ... 

Modified Zusman Equation versus HEOM 13.3.1 The HEOM Formalism... 

Modified Zusman Equation for Quantum Solvation Dynamics and Rate Processes 327 The associated annihilation and creation operators that satisfy [dn, djj] = 1 are ... 

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