Forster spectral overlap

The manifestation of the dipole-dipole approximation can be seen explicitly in Equation (3.134) as the R 6 dependence of the energy transfer rate. In Equation (3.134) the electronic and nuclear factors are entangled because the dipole-dipole electronic coupling is partitioned between k24>d/(td R6) and the Forster spectral overlap integral, which contains the acceptor dipole strength. Therefore, for the purposes of examining the theory it is useful to write the Fermi Golden Rule expression explicitly,... 

The Forster spectral overlap is an incredibly useful quantity for understanding EET in donor-acceptor pairs, but unfortunately it turns out to be useless for describing molecular aggregates and disordered systems. However, in the... 

Self-assembly of functionalized carboxylate-core dendrons around Er +, Tb +, or Eu + ions leads to the formation of dendrimers [19]. Experiments carried out in toluene solution showed that UV excitation of the chromophoric groups contained in the branches caused the sensitized emission of the lanthanide ion, presumably by an energy transfer Forster mechanism. The much lower sensitization effect found for Eu + compared with Tb + was ascribed to a weaker spectral overlap, but it could be related to the fact that Eu + can quench the donor excited state by electron transfer [20]. 

It is possible to estimate the rate of vertical singlet energy transfer (9.31) and (9.33) (when Forster-type energy transfer is negligible, spectral overlap integral is very small) from the relation... 

This is the famous Forster relation that expresses the singlet-singlet transition rate constant in terms of the spectral overlap of the emission spectra of D and absorption spectra of A. 

For the design of complexing bifluorophores, much attention should be paid to the Forster critical radius of the donor-acceptor pair as compared to the interchromophoric distance (Figure 2.13). This critical radius depends on the donor quantum yield and on the spectral overlap between donor emission and acceptor emission. Complex-... 

The energy transfer efficiency is directly proportional to the spectral overlap, and this also directly affects the Forster distance of a particular D-A pair. Figure 10.5 shows the D and A excitation and emission spectra in an ideal energy transfer system, wherein D and A have very distinct excitation spectra (so that A can only be excited by energy transfer and not by direct photon absorption at the wavelengths used to excite D)—the D emission and A excitation spectra overlap strongly—and the D and A emission maxima are well separated, so that the quenching of D fluorescence and the enhancement of A fluorescence can be individually measured.98 99... 

The rate of EET between a pair of weakly coupled donor (D) and acceptor (A) molecules, according to Forster theory, [76] depends on the interchromophoric distance R, expressed in units of cm, their relative orientation (through the orientation factor k), and the spectral overlap I between donor emission and acceptor absorption spectra. The rate expression is ... 

As introduced in Section 3.1, Forster theory assumes that there is no inhomogeneous line broadening, i.e. static disorder, in the spectra of donor emission and acceptor absorption. However, if one considers an ensemble of inhomoge-neously broadened spectra, the spectral overlap is given by ... 

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