Forster equation

Energy transfer measurements were used, together with fluorescence and absorption spectral data of the donor and acceptor moieties, to calculate the donor-acceptor separation via the Forster equation. The average values of R obtained assuming random donor-acceptor orientations were 21.3 1.6 for (1) and 16.7 + 1.4 for (2). The average separation obtained from molecular models is 21.8 + 2.0 for (1) and 21.5 2.0 for (2). The somewhat low calculated separation between the groups of (2) may be due to nonrandom donor-acceptor orientations. 

The range of distance that allows reliable determination is derived from the Forster equation (Eq. 6.1) as R0 R[Pg.258]

Intensive effort has been devoted to the optimization of CCP structures for improved fluorescence output of CCP-based FRET assays. The inherent optoelectronic properties of CCPs make PET one of the most detrimental processes for FRET. Before considering the parameters in the Forster equation, it is of primary concern to reduce the probability of PET. As the competition between FRET and PET is mainly determined by the energy level alignment between donor and acceptor, it can be minimized by careful choice of CCP and C. A series of cationic poly(fluorene-co-phenylene) (PFP) derivatives (IBr, 9, 10 and 11, chemical structures in Scheme 8) was synthesized to fine-tune the donor/acceptor energy levels for improved FRET [70]. FI or Tex Red (TR) labeled ssDNAg (5 -ATC TTG ACT ATG TGG GTG CT-3 ) were chosen as the energy acceptor. The emission spectra of IBr, 9, 10 and 11 are similar in shape with emission maxima at 415, 410, 414 and 410 nm, respectively. The overlap between the emission of these polymers and the absorption of FI or TR is thus similar. Their electrochemical properties were determined by cyclic voltammetry experiments. The calculated HOMO and LUMO... 

Finally, as described in Box 4.1 of Chapter 4, an exact numerical solution of the diffusion equation (based on Fick s second law with an added sink term that falls off as r-6) was calculated by Butler and Pilling (1979). These authors showed that, even for high values of Ro ( 60 A), large errors are made when using the Forster equation for diffusion coefficients > 10 s cm2 s 1. Equation (9.34) proposed by Gosele et al. provides an excellent approximation. 

Using the Forster equation the distance between the two calcium-binding sites in parvalbumin (Fig. 6-7) has been estimated by energy transfer from Eu(III) in one site to Tb(III) in the other165 to within 10-15% of the distance of 1.18 nm based on X-ray crystallography. 

The first term, Vs, accounts for the Coulomb-exchange direct interaction between D and A (see Eq.10), and the second, Vexpucit, describes a solvent-mediated chromophore-chromophore contribution between the transition densities. In addition to this explicit medium effect (VexpuCit), we note that another implicit effect of the environment is included in the Vs term, due to changes on the transition densities upon solvation. It is useful to define a screening factor s, conceptually equivalent to the 1/n2 term in the Forster equation, so that V = sVs ... 

In these graphs a Bohr radius value (L) of 4.8 A (the value for porphyrin) is used in the Dexter equation 33.18 Also, the solid lines correspond to hypothetical situations in which only the Forster mechanism operates the dotted lines are hypothetical situations for when the Dexter mechanism is the only process.18 The curved lines are simulated lines obtained with equation 32 (Forster) or 33 (Dexter) but transposed onto the other graph (i.e., Forster equation plotted against Dexter formulation and vice versa). 

The dynamics of the EET process is expressed in terms of a rate constant, k, which depends on several factors spectral properties of the D/A molecules, electron coupling between them, and the account of the screening effect of the solvent as a dielectric medium. In the so called weak coupling regime, the rate constant is predicted by the following Forster equation ... 

The Forster equation for the first-order rate constant, ke, for energy transfer by the inductive-resonance mechanism can be written in simplified form... 

To apply the Forster equation, the emission and absorption line shapes must be identical for all donors and acceptors, respectively. However, in many types of condensed-phase media (e.g., glasses, crystals, proteins, surfaces), each of the donors and acceptors lie in a different local environment, which leads to a distribution of static offsets of the excitation energies relative to the average, which persists longer than the time scale for EET. When such inhomogeneous contributions to the line broadening become significant, Forster theory cannot be used in an unmodified form [16, 63]. 

Thus, in rigid solutions, the critical transfer distance R0 can be determined experimentally either from the observed relative quantum yields of D or A at various concentrations of A (Equation 2.44) or from time-resolved measurement of the fluorescence decay of D (Equation 2.42). The results are in good agreement with those calculated from the Forster Equation 2.37. 

The shape of the decay profile of an excited donor is determined, amongst other parameters, by the distribution profile of the surrounding acceptors. Thus, the classical three dimensional Forster equation for non-collisional, one step electronic energy transfer (ET), had to be modified for the case of a two dimensional arrangement of donors and acceptors (35). This has been generalized recently, to include not only two and three dimensional acceptor distributions, but also D-dimensional distributions (36) ... 

As can be seen from the Forster equation, the dimensions of the system under study are the most important factor to be considered when choosing a D and A system. The choice of the donor/acceptor molecule is dictated by several factors ... 

The approximate expression for lonit) can be used to predict the donor intensity at any time, and thus it can be used for analyas of FD and ID data. Figure 15.4 shows FD data for the indole-dansylamide D-A pairs in methanol, which is less viscous than propylene glycol and allows significant difiiision during the donor s exched-state lifetime. In this case, the FOrster equation (Eq. [IS.l]) does not fit the data (dashed curve in Figure 15.4) because... 

K. A tentative explanation for this unusual behavior is the inhibition of molecular motions at 77 K, which may be responsible for a favorable orientation of transition moment dipoles at room temperature. Indeed, a too well organized structure may impose lower values of that usually intervenes in the Forster equation as a statistical value that stems from a random chromophore orientation. 

According to the Forster equation, the donor-acceptor distance is obtained from ... 

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