Forsters Model

The asymptotic value of s, so = 0.54, falls in between the predictions of Forster model, sa = 1/n2 = 0.5, which assumes infinitely thin point dipoles, and the Onsager value, sa = 3/( hr1 + 1) = 0.6, which considers point dipoles contained in spherical cavities. It is reasonable to think that real molecules fall in between these two limits. The solvent screening factors obtained for the data set, along with the fitted screening function, Eq. 14, and the Forster and Onsager values are plotted in Fig. 8. 

Based on the classical Dexter-Forster model of inter-ionic interaction induced energy transfer, the excitation probability of ion i can be expressed as (Dexter, 1953 Forster, 1948 ... 

Rieger P. T., Palese S. P. and Miller R. J. D. (1997), On the Forster model computational and ultrafast studies of electronic energy transport , Chem. Phys. 221, 85-102. 

Figure 14. Downhill exciton relaxation rates as a function of energy gap between two monomers, predicted by the Forster model (open triangles), the traditional Redheld model (open circles), and the modihed Redheld model (hlled circles). In (a) the electronic couphng, Ju = lOOcm and in b) Ju =20cm . The reorganization energy, if = lOOcm and the spectral density is represented by a Gaussian correlation function with Zg = 100 fs [163],...

Second, an averaging can be implemented with respect to the coupling within the donor or acceptor supermolecules (panel c of Fig. 18). In this case we would couple and p directly. Such an averaging is invoked in analyses of RC energy transfer when, for example, either the P or P+ special pair states are taken to be the energy acceptor in the Forster model, where donors and acceptors are treated as point dipoles associated with each spectroscopic band (i.e., P+ and P ). This approach fails to account for the true interactions within a multichromophoric assembly, as we have already described. 

There are two main approaches for the deduction of the stretched exponential law. The first is based on the fractal properties of the characteristic relaxation times spectrum. In order to give a short mathematical description of these variants the so-called forsteric model of direct transfer [5] can be applied. The above-mentioned model was the result of investigations on excitation transfer from donor to statistical defects in condensed media. A law of excitation decrease of the selected donor, which is located in the origin of coordinates, at the expense of direct energy transfer to a defect located in the junction Rj of a lattice with the defined structure is considered. The relaxation function V llO the... 

Besides the obvious discrepancy between the measured distributions of EET rates and those calculated according to Forster theory (illustrated in Fig. 21a), the validity of the Forster model was further checked by plotting the experimentally determined EET rates against the spectral overlaps of individual molecules of 1, which according to the standard Forster expression of the EET rate should yield a linear dependence (see Eq. (1), [12]). The dashed line in Fig. 21b represents a linear fit to the data. Although the slope of this line showed good agreement with... 

It is important to note that the Dexter and Forster models involve a number of simplifications, in particular in treating the systems as involving point dipoles. More recent theoretical studies have concentrated on overcoming these limitations [65, 66]. 

Hence a plot of log( — 1) against log R should be linear with a slope of 6. The experimental plot, shown in Figure 6.19(b), is a good straight line with a slope of 5.9 0.3, in excellent agreement. This observed inverse sixth-power dependence of et on the distance R strongly supports the Forster model. 

Hennebicq E et al (2005) Exciton migration in rigid-rod conjugated polymers an improved Forster model. J Am Chem Soc 127 47 - 762... 

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