Forster calculation

It should be pointed out that the Forster calculations are based on the point dipole assumption which may be inaccurate when the separation distance is similar to the molecular size, as is the case for LHCII. In this situation the transition monopole approximation should also be considered. For chla Chang [172] has estimated that this leads to a Forster correction factor of 0.6-2.0 depending on orientation. 

The metal-NADH distance determined by fluorescence studies on the cobalt-substituted enzyme, using binary NADH, thio-NADH, and Rose Bengal/enzyme complexes, differs from the above.242 The minimum metal-NADH distance determined by Forster calculations based on the energy transfer from bound ligand to cobalt(n) is reported as 19 A. It is thought possible that the discrepancy between this value and that determined by X-ray diffraction may be due to conformational changes in solution. 

As more detailed studies of excited state p/ -values accumulate and our understanding of acidic and basic solutions deepens, it should become possible to discover local effects which will explain consistently both the trends in the appropriate acidity scales and the spectral effects (absorption-fluorescence spacings) related to departures from the simple Forster calculation of the pAT shift upon excitation. 

The true acidity of a photoacid is a difficult-to-obtain quantity. Formally, since pKj = -log(kp,/k.p,), where kp, and k p, are overall rates for forward and back proton transfer, respectively, the pfQ obtained from the Forster calculation must be considered approximate. 

Forster calculated that the rate of energy transfer kt should be proportional to the rate of fluorescence kf, to an orientation factor K , to the spectral overlap interval /, to the inverse fourth power of the refractive index n, and to the inverse sixth power of the distance r separating the two chromophores. 

Sandstrom et al. (65) evaluated the Kj value for 4,5-dimethyl-A-4-thiazoline-2-thione (46) in water (Scheme 19) K-j= 10. A-4-Thiazoline-2-thiones are less basic in the first excited state (61) than in the ground state, so application of Forster s cycle suggests that the thione form is even more favored in the first excited state. Huckel molecular orbital (HMO) calculations suggest that electronic effects due to substitution in... 

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. 

Here, rDA is the distance between donor and acceptor and R0 is the Forster radius for the donor-acceptor pair. The Forster radius is the key quality measure for a VFP-FRET pair. R0 is defined as the distance at which 50% FRET occurs and can be calculated from the following equation [105, 106] ... 

Developed into a power series in R 1, where R is the intermolecular separation, H exhibits the dipole-dipole, dipole-quadrupole terms in increasing order. When nonvanishing, the dipole-dipole term is the most important, leading to the Forster process. When the dipole transition is forbidden, higher-order transitions come into play (Dexter, 1953). For the Forster process, H is well known, but 0. and 0, are still not known accurately enough to make an a priori calculation with Eq. (4.2). Instead, Forster (1947) makes a simplification based on the relative slowness of the transfer process. Under this condition, energy is transferred between molecules that are thermally equilibriated. The transfer rate then contains the same combination of Franck-Condon factors and vibrational distribution as are involved in the vibrionic transitions for the emission of the donor and the adsorptions of the acceptor. Forster (1947) thus obtains... 

Forster (1968) points out that R0 is independent of donor radiative lifetime it only depends on the quantum efficiency of its emission. Thus, transfer from the donor triplet state is not forbidden. The slow rate of transfer is partially offset by its long lifetime. The importance of Eq. (4.4) is that it allows calculation in terms of experimentally measured quantities. For a large class of donor-acceptor pairs in inert solvents, Forster reports Rg values in the range 50-100 A. On the other hand, for scintillators such as PPO (diphenyl-2,5-oxazole), pT (p-terphenyl), and DPH (diphenyl hexatriene) in the solvents benzene, toluene, and p-xylene, Voltz et al. (1966) have reported Rg values in the range 15-20 A. Whatever the value of R0 is, it is clear that a moderate red shift of the acceptor spectrum with respect to that of the donor is favorable for resonant energy transfer. 

Figure 14 Fluorescence intensity ratio of acceptors at 417 nm and donors at 360 nm plotted against the molar fraction of MP-CUA in mixed LB films with (O) PA and ( ) AA The dotted line shows the calculated dependence by Forster energy transfer. 

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. 

T. Forster, W. Von Rybinski, H. Tesmann, and A. Wadle Calculation of Optimum Emulsifier Mixtures for Phase Inversion Emulsification. Int. J. Cosmet. Sci. 16, 84... 

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