Electron transfer adiabatic

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. 

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Figure 2.2 Adiabatic and non-adiabatic electron transfer (schematic). The splitting at the intersection has been exaggerated.

Schmickler W. 1986. A theory of adiabatic electron transfer reactions. J Electroanal Chem 204 31-43. 

Ab initio thermodynamics, 129-155 Acetaldehyde oxidation, 196-197, 624 Acetic acid, 192-198, 394-395 Active sites in electrocatalysis, 93-124, 159-198, 237,250,253 Adiabatic and non-adiabatic electron transfer, 34... 

FIGURE 6.6 Potential energy diagram for the theory of electron transfer reactions. The activated complex is at S. For reasonably fast reactions, the reactant adheres to the lower curve and slithers into the product curve through the activated complex—that is, an adiabatic electron transfer occurs. 

Thus, from equation (63), the magnitude of the electronic coupling matrix element may finally be estimated, leading to values of 21 and 24 meV for EDA and perylene, respectively. That these values are quite reasonable derives from the observation that they correspond to moderately non-adiabatic electron transfer at the ground state (with electronic factors of 2 /(1 + P) - 0.5 and 0.6 with EDA and perylene, respectively). 

As such, the thermal process in equation (60) proceeds via the same reactive intermediates (arising from an adiabatic electron transfer) as that observed in the photochemical processes in equations (57) and (58). The proposed electron-transfer activation for the thermal retropinacol reaction is further confirmed by the efficient cleavage of benzpinacol with tris-phenanthroline iron(III), which is a prototypical outer-sphere one-electron oxidant195 (equation 61). 

The extension of the same mechanistic reasoning to the corresponding thermal process (carried out in the dark) is not generally rigorous. Most commonly, the adiabatic electron-transfer step (kET) is significantly slower than the fast back electron transfer and follow-up reactions (fcf) described in Section 7, and the pseudo-steady-state concentration is too low for the ion-radical pair to be directly observed (equation 99). 

The charge transfer Scheme V is akin to the adiabatic electron transfer cycle in Scheme IV. In this case the work term Wp required to bring the products D+ and A together to the mean separation rp in the CT excited state is given by ... 

When a reaction is adiabatic, the electron is transferred every time the system crosses the reaction hypersurface. In this case the preexponential factor is determined solely by the dynamics of the inner-and outer-sphere reorganization. Consequently the reaction rate is independent of the strength of the electronic interaction between the reactant and the metal. In particular, the reaction rate should be independent of the nature of the metal, which acts simply as an electron donor and acceptor. Almost by definition adiabatic electron-transfer reactions are expected to be fast. 

V,/V-dimethylaniline, especially when those strong donors are paired with the relatively electron-poor MES derivative of the bis(arene)iron(ll) acceptor. As such, the dark reactions arise via essentially the same multistep mechanism as that for charge-transfer de-ligation, the difference arising from an adiabatic electron transfer (10) as the initial step that is thermally allowed when the driving force -AGET is sufficient to surmount... 

The increased importance of charge transfer in proceeding up the series of NO+ complexes with the enhanced donor strength of arenes that vary from benzene with IP = 9.23 eV to the electron-rich hexamethylbenzene (IP - 7.85 eV) has its chemical consequences with respect to thermal (adiabatic) electron transfer. Thus the benzene complex with Z = 0.52 is persistent in acetonitrile solution for long periods, provided the solution is protected from adventitious moisture and light. By contrast, the hexamethylbenzene complex with Z = 0.97 slowly liberates nitric oxide under... 

Finally, we ask, if the reactive triads in Schemes 1 and 19 are common to both electrophilic and charge-transfer nitration, why is the nucleophilic pathway (k 2) apparently not pertinent to the electrophilic activation of toluene and anisole One obvious answer is that the electrophilic nitration of these less reactive [class (ii)] arenes proceeds via a different mechanism, in which N02 is directly transferred from V-nitropyridinium ion in a single step, without the intermediacy of the reactive triad, since such an activation process relates to the more conventional view of electrophilic aromatic substitution. However, the concerted mechanism for toluene, anisole, mesitylene, t-butylbenzene, etc., does not readily accommodate the three unique facets that relate charge-transfer directly to electrophilic nitration, viz., the lutidine syndrome, the added N02 effect, and the TFA neutralization (of Py). Accordingly, let us return to Schemes 10 and 19, and inquire into the nature of thermal (adiabatic) electron transfer in (87) vis-a-vis the (vertical) charge-transfer in (62). 

Triad formation in Scheme 10 is a two-step process (88) involving the metastable A-nitropyridinyl radical, whereas the adiabatic electron transfer in Scheme 19 is likely to occur irreversibly with the simultaneous cleavage of the N-N02 bond, as in (89). As a result, the nascent pair (Py and N02) in (88) can suffer greater diffusive separation from ArH+- compared with that in (89). If so, the complexation of the aromatic cation radical by pyridine (90), as recently delineated by Reitstoen and Parker (1991) is (kinetically)... 

The counterpart to the photo-induced electron transfer is the corresponding thermal transformation of the electron donor-acceptor complex the barrier to such an adiabatic electron transfer is included in Fig. 18 as T, with the implicit understanding that solvation is an intrinsic part of the activation process (Fukuzumi and Kochi, 1983). When the rate of back electron transfer is diminished (e.g. by a reduced driving force), the dynamics for the contact ion pair must also include diffusive separation to solvent-separated ion pairs and to free D+- and A-- (Masnovi and Kochi, 1985a,b Yabe et al., 1991). 

Although their conceptual basis is now firmly established, non-adiabatic electron transfer processes are still the subject of intensive theoretical studies. Nevertheless, the framework provided by the standard formalism presented in this section seems sufficiently general to be used for the interpretation of kinetic data obtained in biological systems. Owing to the great number of parameters involved in the theoretical expressions, attainment of useful information requires obtaining numerous data by elaborate experiments. The next section is devoted to a review of the different approaches that have been developed over the last few years. 

It was shown in Sect. 2 that the standard formalism appropriate for non-adiabatic electron transfer processes leads to the definition of an electronic and a nuclear factor in the rate expression. This separation into factors of quite different physical origin is conceptually very useful. As a matter of fact, it is systematically emphasized throughout this presentation to clarify the nature of the different parameters involved in biological electron transfers. It happens also to be very useful when the relation between the kinetics and the biochemical function of these processes is considered. This is illustrated below by a few examples. 

Calhoun and Voth also utilized molecular dynamic simulations using the Anderson-Newns Hamiltonian to determine the free energy profile for an adiabatic electron transfer involving an Fe /Fe redox couple at an electrolyte/Pt(lll) metal interface. This treatment expands upon their earlier simulation by including, in particular, the influence of the motion of the redox ions and the counterions at the interface. 

The calculation of the transmission coefficient for adiabatic electron transfer modeled by the classical Hamiltonian Hajis based on a similar procedure developed for simulations of general chemical reactions in solution. The basic idea is to start the dynamic trajectory from an equilibrium ensemble constrained to the transition state. By following each trajectory until its fate is determined (reactive or nonreactive), it is possible to determine k. A large number of trajectories are needed to sample the ensemble and to provide an accurate value of k. More details... 

Pig. 2-37. Redox reaction cycle FeJ5 - Fejj + ei iD, - FeJ in aqueous solution solid arrow=adiabatic electron transfer, dotted arrow = hydrate structure reorganization X = reorganization energy ered.d = most probable donor level eox.a = most probable acceptor level. 

The dependence of et for electron transfer in the encounter complex in Scheme 7 on AGet has been well established by Marcus as given by Eq. (1), where the pre-exponential factor should be replaced by h/ksT for adiabatic electron transfer [1-4]. 

Marcus stressed that only harmonic modes U = were involved in the ion-solvent interactions and went further than Weiss in formulating a simple equation for the rate of adiabatic electron transfer, taking the case of an isotopic reaction so that the AG° term was eliminated. Under this condition and using Eq. (9.32), the current density (or electrochemical reaction rate) at a given overpotential t], in the cathodic direction (T] is negative) is... 

The essentials of quantum kinetics were in place by 1954, Weiss having added to the Gurney theory a comprehensive theory of redox reactions. By this date, tunneling, adiabatic and non-adiabatic electron transfer, the simplicity introduced by considering redox reactions between isotopes, the separate contribution from outer sphere and inner sphere, and in particular the equation for the reorganization energy involving and stat had all been published. 

The Marcus treatment uses a classical statistical mechanical approach to calculate the activation energy required to surmount the barrier. It assumes a weakly adiabatic electron transfer process and non-equilibrium dielectric polarization of the solvent (continuum) as the source of activation. This model also considers the vibrational contributions of the inner solvation sphere. The Hush treatment considers ion-dipole and ligand field concepts in the treatment of inner coordination sphere contributions to the energy of activation [55, 56]. 

The Marcus theory of adiabatic electron-transfer processes. 95... 

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