Adiabatic electron-transfer regime

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. 

In this section, we switch gears slightly to address another contemporary topic, solvation dynamics coupled into the ESPT reaction. One relevant, important issue of current interest is the ESPT coupled excited-state charge transfer (ESCT) reaction. Seminal theoretical approaches applied by Hynes and coworkers revealed the key features, with descriptions of dynamics and electronic structures of non-adiabatic [119, 120] and adiabatic [121-123] proton transfer reactions. The most recent theoretical advancement has incorporated both solvent reorganization and proton tunneling and made the framework similar to electron transfer reaction, [119-126] such that the proton transfer rate kpt can be categorized into two regimes (a) For nonadiabatic limit [120] ... 

The general framework of the quantum mechanical rate expression for long-range electron transfer processes in the very weak or non-adiabatic regime will be presented in Sect. 2 with an emphasis on the inclusion of superexchange interactions. The relation between the simplest case of direct donor-acceptor interactions, on the one hand, and long-range electronic interactions important in proteins, on the other, is considered in terms of the elements of electron transfer theory. 

The experiments of Vos and eo-workers raise the question of whether the coherent nuclear motion associated with the P state that persists on the time-scale of eleetron transfer is coupled to the primary electron transfer reaction. In particular, do any of the nuclear vibrations coupled to the P state facilitate the transfer of electrons from P to Ba The observation of coherent nuclear motion that persists on the time-scale of primary electron transfer raises the possibility that this nuclear motion may be an important parameter that governs the characteristics of this reaction, which would place this process in a near-adiabatic regime. Of obvious importance is the question of whether it is possible to observe coherence in the formation of a produet state such as P Ba". A number of recent studies have addressed this difficult problem with conflicting conclusions (Sp"rlein et al., 1998 Streltsov et al., 1998 Vos et al., 1998 Streltsov et al., 1996) and, as discussed in reeent review (Vos and Martin, 1999) at present this question remains to be answered. 

Finally, an intriguing point that come from this work is that these relatively long-distance electron transfer reactions compete with femtosecond time-scale energy transfer between and P, and thus must also take place on sub-picosecond time-scale. Therefore, it is most likely that these electron transfer reactions occur in the adiabatic regime, and are driven by a vibrationally-unrelaxedBa state. 

The thermal-induced intramolecular electron transfer rates of mixed-valence biferrocene monocation (Fe(II),Fe(III)) were determined in seven solvents and at various temperatures by the proton paramagnetic relaxation measurements. The rate constants of pico-second order were obtained at 298 K and the frequency factors showed a solvent dependence. The effect of solvent friction on the barrier crossing in the reaction trajectory was examined in the strong adiabatic regime. 

Applications are then presented in Section IV. These examples should served as a guide as to what kinds of problems can be studied with these techniques and the limitations and possibilities for these methods. We present three examples (1) a dynamical test of the centroid quantum transition-state theory for electron transfer (ET) reactions in the crossover regime between adiabatic and nonadiabatic electron transfer, (2) the primary electron transfer reaction in bacterial photosynthesis, and (3) the diffusion kinetics of a Brownian particle in a periodic potential. Finally, Section V offers an outlook and a perspective of the current status of the field from our vantage point. 

This is similar to the adiabatic limit of the Marcus theory which is applicable for reaction operating in the adiabatic regime. This limit regime is illustrated in Figure 5.4 in the case of an electron transfer reaction between an electron donor and an acceptor molecule separated by a distance J da- To draw these curves we have assumed that the potential coupling decayed exponentially with the... 

Figure 5.4 Transition from the adiabatic to non-adiabatic regime for an electron transfer between a donor and an acceptor as a function of the separating distance and the characteristic decoherence time.

Feldberg, S. W., and N. Sutin, Distance dependence of heterogeneous electron transfer through the nonadiabatic and adiabatic regimes, Chem. Phys., Vol. 324, 2006 pp. 216-225. 

Under the latter condition, feet is proportional to (// ). The value of / depends on the overlap between the electronic wavefunctions of the donor and acceptor groups, which decreases exponentially with donor-acceptor distance. It should be noticed that the amount of electronic interaction required to promote photoinduced electron transfer is very small in a common chemical sense. In fact, by substituting reasonable numbers for the parameters in (2.26), it can be easily verified that, for an activationless reaction, / values of a few wavenumbers are sufficient to give rates in the sub-nanosecond time scale, while a few hundred wavenumbers may be sufficient to reach the limiting adiabatic regime (2.25). 

---