Overlap integral spectral

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... 

Takakusa H, Kikuchi K, Urano Y, Kojima H, Nagano T (2003) A novel design method of ratiometric fluorescent probes based on fluorescence resonance energy transfer switching by spectral overlap integral. Chemistry 9 1479-1485... 

The integral is the spectral overlap integral of the donor emission f (v) with the acceptor absorption profile f (v) for resonance condition. F(R) summarizes the essential mechanisms, like the Dexter (1953) exchange or the Forster (1951) multipole mechanism with their specific R distance dependences. 

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 experimental estimation of the coupling for the A6N compound has been obtained applying Fermi s Golden Rule to the experimental rate and using an experimentally determined spectral overlap integral (see ref. [37]). 

Figure 2.12 Resonance condition for energy transfer from D to A. The thick horizontal bars in the left hand diagram represent electronic and the thin bars vibrational states. The dark area on the right represents the spectral overlap integral J...

By applying Fermi s golden rule, Forster derived a very important relation between the critical transfer distance R0 and experimentally accessible spectral quantities (Equation 2.35),° 67,68 namely the luminescence quantum yield of the donor in the absence of acceptor A, orientation factor, k, the average refractive index of the medium in the region of spectral overlap, n, and the spectral overlap integral, J. The quantities J and k will be defined below. Equation 2.35 yields remarkably consistent values for the distance between donor and acceptor chromophores D and A, when this distance is known. FRET is, therefore, widely applied to determine the distance between markers D and A that are attached to biopolymers, for example, whose tertiary structure is not known and thus... 

The spectral overlap integral J can be expressed in terms of either wavenumbers or wavelengths (Equation 2.36). The area covered by the emission spectrum of D is normalized by definition and the quantities / and lx are the normalized spectral radiant intensities of the donor D expressed in wavenumbers and wavelengths, respectively. Note that the spectral overlap integrals J defined here differ from those relevant for radiative energy transfer (Equation 2.33). Only the spectral distributions of the emission by D /,P and, are normalized, whereas the transition moment for excitation of A enters explicitly by way of the molar absorption coefficient sA. The integrals J" and Jx are equal, because the emission spectrum of D is normalized to unit area and the absorption coefficients sA are equal on both scales. 

Equation 2.36 Spectral overlap integral for nonradiative energy transfer... 

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