Electron transfer reactions Non-adiabatic

Mutation of Amieyanin Alters the Hab for Electron Transfer from MADH 

Reduction of Amicyanin by Different Redox Forms of MADH  

Rate-limiting Step Electron Transfer Electron Transfer Proton Transfer Electron Transfer 

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Although the two-fold symmetry displayed by the reaction centre is striking, it is only a pseudo-symmetry, because differences in the amino aeid sequences of the L and M subunits result in small differences in the positions and relative orientations of equivalent cofactors on the two branehes, and in differences of the protein environment of equivalent cofactors. The root cause of the functional asymmetry that is observed when electron transfer is monitored is therefore asymmetry in the detailed structure of the cofactor protein system on the two branches. Assuming that the transmembrane electron transfer process can basically be described as a non-adiabatic electron transfer reaction according to the Marcus equation, this... 

The dynamical theory also provides a framework for the study of the diabatic free energy profiles as functions of the reaction coordinate required in the theory of non-adiabatic electron transfer reactions. We illustrate this new application by calculating the free energy profiles in solvents covering a wide range of polarity. 

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 distance between the electron donor and acceptor affects the rates and mechanisms of PCET reactions in two different ways. First, an increase in this distance results in a decrease in the coupling between ET states (la/2a, aj2b, bj2a, bj2b). In the limit of electronically non-adiabatic electron transfer, a decrease in this coupling results in a decrease in the rate. Moreover, as the distance between the electron donor and acceptor increases, the interaction between the proton and the electron decreases. Thus, for a symmetric PT system with an initial state of la, EPT is favorable for short electron donor-acceptor distances and ET becomes equally favorable as this distance increases. 

The relative rates of the reactions leading to formation of either ground-state or excited-state products can be evaluated in terms of formalisms developed by Marcus [26], Hopfield [27], Jortner [28], and others [29]. The development of the semiclassical and quantum-mechanical expressions for electron transfer are discussed in Chapters. 3-5 (Volume I, Part 1). A general expression for the rate constant of a non-adiabatic electron-transfer process is given below. 

The adiabatic redox reactions at electrodes were first considered by MARCUS /40a,145/ in a classical (semiclassical) framework. lEVICH, DOGONADZE and KUSNETSOV /146,147/, SGHMICKLER and VIELSTICH /169/ a.o. have developed a quantum theory for non-adiabatic electron transfer electrode reactions based on the oscillator-model. The complete quantum-mechanical treatment of the same model by CHRISTOV /37d,e/ comprises adiabatic and non-adiabatic redox reactions at electrodes. 

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] ... 

Fig. 5 Potential energy hypersurfaces as a function of the reaction coordinate for adiabatic (A, single-minimum potential B, double-minimum potential) and non-adiabatic (C) electron-transfer reactions.

Fe3+X6...Fe2+X6, which is the reactant of the outer-sphere electron transfer reaction mentioned above when X = Y. Clearly the ground state involves a symmetric linear combination of a state with the electron on the right (as written) and one with the electron on the left. Thus we could create the localized states by using the SCRF method to calculate the symmetric and antisymmetric stationary states and taking plus and minus linear combinations. This is reasonable but does not take account of the fact that the orbitals for non-transferred electrons should be optimized for the case where the transferred electron is localized (in contrast to which, the SCRF orbitals are all optimized for the delocalized adiabatic structure). The role of solvent-induced charge localization has also been studied for ionic dissociation reactions [109],... 

Returning to equation (38), in the limit that ve vn, Ke = 1 and vet = vn. Electron transfer reactions that fall into this domain where the probability of electron transfer is unity in the intersection region have been called adiabatic by Marcus. Reactions for which Kei < 1, have been called non-adiabatic . In the limit that ve 2vn and e = vjvn, the pre-exponential term for electron transfer is given by vet = ve. This was the limit assumed in the quantum mechanical treatment using time dependent perturbation theory. 

The use of the terms adiabatic and non-adiabatic in this way leads to a source of confusion. Normally, in describing surface-crossing processes, a process which remains on the same potential curve is called adiabatic and in that sense every net electron transfer reaction is an adiabatic process. Processes which involve a transition between different states as between the two different potential curves in Figure lb are usually called non-adiabatic. Such processes have some special features and will be returned to in a later section dealing with the inverted region and excited state decay. 

Normally, it is not possible to explore this domain experimentally using bimolecular electron transfer reactions. In the absence of an activational requirement, electron transfer becomes sufficiently facile that the reactions are partly or wholly diffusion-limited and kabs ta kD. The exception is for reactions which have a large non-adiabatic contribution so that ket = vcKA and if ve is sufficiently small, kobs = vcAa.73... 

The theory of electron transfer in chemical and biological systems has been discussed by Marcus and many other workers 74 84). Recently, Larson 8l) has discussed the theory of electron transfer in protein and polymer-metal complex structures on the basis of a model first proposed by Marcus. In biological systems, electrons are mediated between redox centers over large distances (1.5 to 3.0 nm). Under non-adiabatic conditions, as the two energy surfaces have little interaction (Fig. 5), the electron transfer reaction does not occur. If there is weak interaction between the two surfaces, a, and a2, the system tends to split into two continuous energy surfaces, A3 and A2, with a small gap A which corresponds to the electronic coupling matrix element. Under such conditions, electron transfer from reductant to oxidant may occur, with the probability (x) given by Eq. (10),... 

In Ref. [317] the temperature independence of the intramolecular electron transfer reaction in a cofacial Zinc porphyrin-quinone cage molecule was observed in the range 80-300 K and interpreted in terms of non-adiabatic electron tunneling. 

In a coupled electron transfer reaction, the preceding adiabatic reaction step influences the experimentally-determined rate constant even though the electron transfer step is the slowest for the overall redox reaction. This occurs when the relatively fast reaction step which precedes electron transfer is very unfavorable (i.e. Kx (kx/kfix) l)- In Hii case, ks will be influenced by the equilibrium constant for that non-electron transfer process such that ks = kgT Kx (Harris et ah, 1994 Davidson, 1996). It follows that the experimentally-derived X ( lobs) may contain contributions from both the electron transfer event and the preceding reaction step (i.e. obs [ ET. x])- For example, lo sfor interprotein electron transfer reactions may reflect contributions from an intracomplex rearrangement of proteins after binding to achieve an optimum orientation for electron transfer. As with a true electron transfer reaction, k3 will vary with AG° since ks is proportional to ksT, although H b may also be affected by the coupling. 

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