Franck-Condon type approximation

Whereas absorption spectra can be obtained at a given temperature via Monte-Carlo t q)e simulations, the reach of equilibrium in an excited state of an isolated cluster is less obvious, and even less is the definition of a relevant temperature. In any case, the final state may be strongly dependent on the excitation process. Here we will ignore the vibrations of the Na(3p)Arn cluster. We assume a Franck-Condon type approximation and that emission takes place from relaxed equilibrium geometry structures on the Na(3p)Arn excited PES. The Einstein coefficients of the lines of emission towards the ground state at energy AE are given by... 

Adiabatic and Condon." Since the Condon approximation separates the electronic and the vibrational parts of the problem (see Section 10c), most of the papers using this approximation emphasize the latter aspect. Specifically, they analyze the so-called Franck-Condon overlap integrals [the (Xm X ) of Eq. (42)] and the occupancy factors of these vibrational levels. Such analyses include (1) the influence of mode type and/or number as well as... 

Using the harmonic and the Franck-Condon approximations, it is possible to advance in calculating the sums of the (18) type using the method of generating functions developed by Kubo and Toyozawa [8, 9] for the calculation of the probabilities of optical and non-radiative transitions in the impurity centres in crystals. According to this method we can rewrite eqn. (18) as... 

The time-dependent perturbation theory of the rates of radiative ET is based on the Born-Oppenheimer approximation [59] and the Franck Condon principle (i.e. on the separation of electronic and nuclear motions). The theory predicts that the ET rate constant, k i, is given by a golden rule -type equation, i.e., it is proportional to the product of the square of the donor-acceptor electronic coupling (V) and a Franck Condon weighted density of states FC) ... 

The rates of outer-sphere self-exchange reactions vary considerably as illustrated in Table 26.9. Qearly, the reactants must approach closely for the electron to migrate from reductant to oxidant. This reductant-oxidant pair is called the encounter or precursor complex. When electron transfer occurs, there is an important restriction imposed upon it by the Franck Condon approximation (see Section 20.7). Consider a self-exchange reaction of the type ... 

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