Energy transfer Dexter theory

Here we present a brief review of the physical principles underlying fluorescence energy transfer. The theory was developed primarily by Fdrster and extended by Dexter.Forster did some early experimental studies, and Stryer and Haugland convincingly showed that fluorescence energy transfer could be used as a molecular ruler to measure distances. Emphasis is on developing an intuitive feel for the important relevant parameters. Both a classical and a quantum mechanical approach are given. 

In the original Forster-Dexter theory [79-81] the superexchange terms in 7), have been ignored, that is, 7, - = //) . We shall present the derivation of their theory in our framework. Consider the energy transfer... 

According to the Dexter theory of energy transfer, the distance dependence of energy transfer by the exchange mechanism falls off rapidly and is given by ... 

In the Collins-Kimball theory, the rate constant for the reaction was assumed to be distance-independent. Further refinement proposed by Wilemski and Fix-manc) consists of considering that the reaction rate constant has an exponential dependence on distance, which is indeed predicted for electron transfer reactions and energy transfer via electron exchange (see Dexter s formula in Section 4.6.3). The rate constant can thus be written in the following form ... 

The Forster [62,63] and Dexter [64] theory in photo-induced energy transfer is discussed. For the singlet-singlet energy transfer [65,66]... 

Electrochemical and photochemical processes are the most convenient inputs and outputs for interfacial supramolecular assemblies in terms of flexibility, speed and ease of detection. This chapter provides the theoretical background for understanding electrochemical and optically driven processes, both within supramolecular assemblies and at the ISA interface. The most important theories of electron and energy transfer, including the Marcus, Forster and Dexter models, are described. Moreover, the distance dependence of electron and energy transfer are considered and proton transfer, as well as photoisomerization, are discussed. 

Luminescence of rare earth ions can be understood, based on transitions between (almost) atomic eigenstates of the system [5.220, 5.221]. Forster and Dexter first described energy transfer between localized centers in luminescent material [5.222-5.224]. Besides orbital theory, semiconductor theory has also contributed to the understanding of radiative transitions Both band-to-band transitions and transitions involving localized donor and/or acceptor states fit within this framework. Nevertheless, there are also still open questions concerning the theoretical aspects. 

Strome and Klier 107,108) applied the Forster-Dexter theory of resonance energy transfer to explain these experimental observations, i,e., the energy transfer from the excited state of the Cu species to the coexistent... 

Details on the mechanisms and theories of excitation energy transfer via dipole-dipole interaction (FRET Forster resonance energy transfer) and via exchange interaction (Dexter s mechanism) can be found in B. Valeur, Molecular Fluorescence. Principles and Applications, Wiley-VCH, Weinheim, 2002, chap. 4 and 9. 

DL Dexter (1953) A theory of sensitized luminescence in solids. J Chem Phys 21 836-860 T Gillbro and RJ Cogdell (1989) Carotenoid fluorescence. Chem Phys Lett 158 312-316 T Katoh, U Nagashima and M Mimuro (1991) Fluorescence properties of the allenic carotenoid fucoxanthin Implication for energy transfer in photosynthetic pigment systems. Photosynthesis Res 27 221-226 AP Shreve, JK Trautman, TG Owens and AC Albrecht (1991) A femtosecond study of electronic state dynamics of fucoxanthin and implication for photosynthetic carotenoid-to-chlorophyll energy transfer mechanisms. Chem Phys 154 171-178... 

The theoretical dipole-dipole transition probabilities calculated from Dexter s formula are 0.6 sec-i for 3% Gd and 3% Tb. Comparing this result with the experimentally determined energy transfer probability (817 sec i) given in Table 13 we see that the experimental results do not agree with the theory of the resonant energy transfer process. 

According to the theory of Miyakawa and Dexter (77) on phonon-assisted energy transfer in soMds, the probability of this process depends on the energy gap, AE, between the levels of the donor and the acceptor in the form ... 

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