Strong coupling limit, electron-transfer

In this model there is a quantitative difference between RLT and electron transfer stemming from the aforementioned difference in phonon spectra. RLT is the weak-coupling case S < 1, while for electron transfer in polar media the strong-coupling limit is reached, when S > 1. In particular, in the above example of ST conversion in aromatic hydrocarbon molecules S = 0.5-1.0. 

In the strong-coupling limit at high temperatures the electron transfer rate constant is given by the Marcus formula [Marcus 1964]... 

One may wonder whether a purely harmonic model is always realistic in biological systems, since strongly unharmonic motions are expected at room temperature in proteins [30,31,32] and in the solvent. Marcus has demonstrated that it is possible to go beyond the harmonic approximation for the nuclear motions if the temperature is high enough so that they can be treated classically. More specifically, he has examined the situation in which the motions coupled to the electron transfer process include quantum modes, as well as classical modes which describe the reorientations of the medium dipoles. Marcus has shown that the rate expression is then identical to that obtained when these reorientations are represented by harmonic oscillators in the high temperature limit, provided that AU° is replaced by the free energy variation AG [33]. In practice, tractable expressions can be derived only in special cases, and we will summarize below the formulae that are more commonly used in the applications. 

In Equation 6.88, K0 is the equilibrium constant for the formation of the collision complex, (V) 2 is the electronic coupling, and F is the Franck-Condon factor. In contrast to the radiationless relaxation, the energy transfer process cannot be rationalized only in the limit of the strong and weak coupling limits shown in Figure 6.16. 

The relevance of adiabatic electron transfer to the primary charge separation reaction has been the subject of considerable discussion, mainly due to the observation of undamped low-frequency nuclear motions associated with the P state (see Section 5.5). More recently, sub-picosecond time-scale electron transfer has been observed at cryogenic temperatures, driven either by the P state in certain mutant reaction centres (see Section 5.6) or by the monomeric BChls in both wild-type and mutant reaction centres (see Section 5.7). These observations have led to the proposal that such ultra-fast electron transfer reactions require strong electronic coupling between the co-factors and occur on a time-scale in which vibrational relaxation is not complete, which would place these reactions in the adiabatic regime. Finally, as discussed in Section 2.2, evidence has been obtained that electron transfer from QpJ to Qg is limited by nuclear rearrangement, rather than by the driving force for the reaction. 

When the donor and acceptor are sufficiently close, as in an ion pair or in covalently linked complexes, electron transfer can be promoted by the absorption of light. An absorption band corresponding to the light induced electron transfer is usnally called a charge transfer (CT) absorption band . The molecnlar parameters that determine the CT absorptivity, bandwidth, and band shape are the same molecular parameters that determine the magnitude of the electron-transfer rate constant.In the weak-coupling limit, the absorptivity of the CT absorption band is small (much less than 10 cm ) in the strong-... 

There are many studies of the transfer of electrons from enzymes to substrates, across biological membranes, to (or from) electrodes from (or to) substrates, between adsorbed molecular dyes and semiconductor particles, within synthetic films and nano-scale arrays, within molecular wires , and so on. Only a few, general comments will be offered on these topics here. The basic physics of molecular electron transfer does not change with the scale of the system, as long as identifiable molecular moieties are present with at least partly localized electronic configurations. The nature of the properties observed, the experimental probes available, and the level of theoretical treatment that is useful may be very different. Different approaches, different limiting models are used for extended arrays (or lattices) of very strongly coupled moieties. 

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