The Contribution of Medium Modes

Equation 4.118 can be expressed in terms of separate contributions of the intramolecular high-frequency mode and intermolecular low-frequency modes. Using the expansion 

4) To pursue this matter a little further, we remark that we may define a model Hamiltonian for vibrational relaxation of the molecule in a dense medium in the form Hm = Cq l e q f — j 

Equation 4.126 describes the nonradiative decay of a small molecule strongly coupled to the medium in terms of a superposition of an intramolecular (Poisson) distribution and Gaussian. The summation over the occupation numbers n of the intramolecular accepting mode in the final electronic state is implied in Equation 6.126. The contribution of the medium modes in terms of the parameters Em and Dm is contained in the Gaussian distribution. For Aj /2 1, it may happen 

The methods we have described for studying electronic relaxation and decay of electronic states may be applied to a variety of problems. These include, for example, the study of vibrational relaxations (VR) which will be illustrated with a simple application to the decay of an initially prepared harmonic molecular oscillator state t = l,ria of a macroscopic system to the final state f = 0,n a The system is supposed to contain a guest, represented by a harmonic molecular oscillator of frequency co, coupled to a very large number of medium (phonon) states n of considerable lower frequencies Then, for the VR rate w , we have [130] 

We might calculate w directly. It is simpler, however, to evaluate it using the generating function technique of Chapter 3. By following the same steps that led to representation (4.99) one can represent the generating function of eq. (4.127) in the form 

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