Forster energy transfer rate

Triplet decay in the [Mg, Fe " (H20)] and [Zn, Fe (H20)] hybrids monitored at 415 nm, the Fe " / P isosbestic point, or at 475 nm, where contributions from the charge-separated intermediate are minimal, remains exponential, but the decay rate is increased to kp = 55(5) s for M = Mg and kp = 138(7) s for M = Zn. Two quenching processes in addition to the intrinsic decay process (k ) can contribute to deactivation of MP when the iron containing-chain of the hybrid is oxidized to the Fe P state electron transfer quenching as in Eq. (1) (rate constant kj, and Forster energy transfer (rate constant kj. The triplet decay in oxidized hybrids thus is characterized by kp, the net rate of triplet disappearance (kp = k -I- ki -I- kj. The difference in triplet decay rate constants for the oxidized and reduced hybrids gives the quenching rate constant, k = kp — kj, = k, -I- k , which is thus an upper bound to k(. 

As just discussed, uncertainties in R and k are currently the rule for all pigment pairs in C-phycocyanin. Because these quantities enter, respectively as / and k . the formula for the pairwise Forster energy transfer rates (see. e.g.. Ref. 1), those rates are also still highly uncertain despite the structural information. It is therefore premature to attempt to analyse the kinetic properties of energy transfer in C-phycocyanin on the basis of the Forster formula. In the meantime, the structural data provide a useful guide for the analysis of experimental results relevant to energy transfer in C-phycocyanin [69]. 

These data can be analyzed by comparing the calculated Forster energy transfer rate to the experimental energy transfer rate A et- From this comparison, the contribution of Coulombic interactions to this process can be estimated. When discrepancies are observed, involvement of an electronic coupling contribution is claimed, and the larger the difference between A p and A et, the stronger the electronic coupling. 

Another major energy transfer process, the so-called Forster transfer mechanism is based on a dipole-dipole interaction between the host excited state and the guest ground state (Figure 4.2) [24], It does not include the transfer of electrons and may occur over significantly larger distances. The rate constant of the Forster energy transfer is inversely proportional to the sixth power of the distance R between the molecules ... 

As will be shown in detail in Section IV, the large-barrier case leads to well-behaved time-independent reaction rates k = const, but for the no-barrier case, time-dependent reaction rates k = k t) are predicted. These can also appear in other processes, for example, in Forster energy transfer, where k t) is proportional to t112.59... 

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 energy transfer processes can occur by two mechanisms the Forster-type mechanism (through-space) [55], based on coulombic interactions, and the Dexter-type mechanism (through-bond) [56], based on exchange interactions. The energy transfer rate constants according to the Forster and Dexter treatments can be evaluated by Eqs. (4) [55] and (5) [56], respectively ... 

Analysis of the data showed the presence of a fast intramolecular photoinduced energy transfer process from pyrene -perylene to pyrene-perylene (ken 6.2 x 109 s 1) with a high yield (>90%), followed by efficient intramolecular electron transfer from pyrene-perylene to pyrene +-perylene (70%, ket 6.6 x 109s 1). Both processes occur from the pyrene unit to the perylene moiety. The Forster distance was calculated to be 3.4 nm and the corresponding donor-acceptor distance was calculated from the energy transfer rate as 0.9 nm. No indications for energy hopping between different pyrene moieties were observed. 

The self-assembled diad Zn P-PH2P consisting of a zinc porphyrin donor and a free base porphyrin acceptor (Scheme 7.4) was studied by time-resolved fluorescence [21]. The driving force of the assembly is the site selective binding of an imidazole connected to a free base porphyrin. Evidence for Forster back transfer was obtained from the analysis of the fluorescence decay (Fig. 7.8) and the relevant rate was quantitatively evaluated for the first time. The transfer efficiency [13] is 0.98, and the rate constants for direct and back transfer were found to be 24.4 x 10 s and 0.6 X 10 s respectively. These values are consistent with the Forster energy transfer mechanism. 

Early studies—for example, the work of Arnold and co-workers [153, 154] and Duysens [155]—exposed the role of energy transfer in the capture of light by chlorophyll pigments and subsequent transfer to a trap. Such studies were considerably aided by Forster theory, which provided a means to predict energy transfer rates based on simple experimental observables. 

Furthermore the fluorescence lifetime of the donor molecules is significantly reduced as a consequence of efficient energy transfer to the lower energy trap. Since Forster energy transfer is mediated by dipole-dipole interaction without the need of direct overlap of orbitals, it can overcome distances up to 10 nm. It allows only singlet-singlet transition at low acceptor concentration and at a much faster rate of <10 s. 

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