Energy Dexter

The occurrence of energy transfer requires electronic interactions and therefore its rate decreases with increasing distance. Depending on the interaction mechanism, the distance dependence may follow a 1/r (resonance (Forster) mechanism) or e (exchange (Dexter) mechanisms) [ 1 ]. In both cases, energy transfer is favored by overlap between the emission spectrum of the donor and the absorption spectrum of the acceptor. 

If the charge distributions of the D and A overlap than a new class of interactions has to be considered, namely the exchange interaction between the electrons on D and on A. This type of energy transfer is called Dexter transfer [80, 96,98], Here we briefly outline the physical principles involved. 

In contrast to the dipole-dipole interaction, the electron-exchange interaction is short ranged its rate decreases exponentially with the donor-acceptor distance (Dexter, 1953). This is expected since, for the electron exchange between D and A, respective orbital overlap would be needed. If the energy transfer is envisaged via an intermediate collision complex or an exciplex, D + A—(D-------A)- D + A, then Wigner s rule applies there must be a spin com-... 

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... 

The rate of energy transfer at a very short donor-acceptor separation R by the exchange mechanism has been given by Dexter (1953) as follows ... 

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... 

Figure 23. Two principal mechanisms of excitation energy transfer (EET). (a) The Forster dipole-dipole mechanism, in which the active electrons, one and two, remain, respectively, on D and A throughout the process, (b) In the (Dexter) exchange mechanism, electrons one and two exchange locations.

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 ... 

Murphy CB, Zhang Y, Troxler T, Ferry V, Martin JJ, Jones WE Jr (2004) Probing Forster and Dexter energy-transfer mechanisms in fluorescent conjugated polymer chemosensors. J Phys Chem B 108 1537-1543... 

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 ... 

By substituting Eq. (B4.4.5) into Eq. (B4.4.7), we obtain the Forster rate constant kjl (Eq. 4.78 in the text) for energy transfer in the case of long-range dipole-dipole interaction, and substitution of Eq. (B4.4.6) into Eq. (B4.4.7) leads to the Dexter rate constant k fl (Eq. 4.85 in the text) for the short-range exchange interaction. 

Dexter s formulation of exchange energy transfer (very weak coupling) In contrast to the inverse sixth power dependence on distance for the dipole-dipole mechanism, an exponential dependence is to be expected from the exchange mechanism. The rate constant for transfer can be written as... 

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