Electron transfer rate free-energy change

FIgurt 12 (a) Potential energy curve for electron transfer from P to Q. (b) Bell-shaped curve of rate constant of electron transfer vs. free energy change (AG) predicted by Marcus theory, (c) Saturation curve of rate constant of bimolecular electron transfer observed in solution. 

M Tachiya. Relation between the electron-transfer rate and the free energy change of reaction. J Phys Chem 93 7050-7052, 1989. 

Our problem now is to determine the functional form of this experimental free energy curve for the intrinsic rate constant ki for electron transfer. In addition to the Marcus eq 4, two other relationships are currently in use to relate the activation free energy to the free energy change in electron transfer reactions (15, JL6). 

The potential energy surfaces on which the electron-transfer process occurs can be represented by simple two-dimensional intersecting parabolic curves (Figure 6.23). These quantitatively relate the rate of electron transfer to the reorganisation energy (A.) and the free-energy changes for the electron-transfer process (AG°) and activation (AG ). 

In semiclassical ET theory, three parameters govern the reaction rates the electronic couphng between the donor and acceptor (%) the free-energy change for the reaction (AG°) and a parameter (X.) related to the extent of inner-shell and solvent nuclear reorganization accompanying the ET reaction [29]. Additionally, when intrinsic ET barriers are small, the dynamics of nuclear motion can limit ET rates through the frequency factor v. These parameters describe the rate of electron transfer between a donor and acceptor held at a fixed distance and orientation (Eq. 1),... 

The rates of electron-transfer reactions can be well predicted provided that the electron transfer is a type of adiabatic outer-sphere reaction and the free-energy change of electron transfer and the reorganization energy (X) associated with the electron transfer are known [1-7]. This means that electron-transfer reactions can be designed quantitatively based on the redox potentials and the reorganization energies of molecules involved in the electron-transfer reactions. 

The free-energy changes (AG) for ET from 90a to DCA, MB and 2,4,6-triphenylpyrylium perchlorate (TPPY+) are —18.4, —10.6 and —32.5 kcalmol-1, respectively, indicative of exothermic electron transfer. The rate of disappearance of 90a was enhanced by addition of Mg(C104)2 (Table 20). 

The electrical contact of redox proteins is one of the most fundamental concepts of bioelectronics. Redox proteins usually lack direct electrical communication with electrodes. This can be explained by the Marcus theory16 that formulates the electron transfer (ET) rate, ket, between a donor-acceptor pair (Eq. 12.1), where d0 and d are the van der Waals and actual distances separating the donor-acceptor pair, respectively, and AG° and X correspond to the free energy change and the reorganization enery accompanying the electron transfer process, respectively. 

Electron transfer reactions between various aromatic molecules in a vitreous MTHF have been investigated in ref. 79 by the same method as in ref. 12. Reactions having free energy changes from AG° = —0.01 to — 2.75 eV have been studied. For each reaction the electron transfer rate constants, k(R), for various distances, R, between the reacting particles have been found from the reaction kinetics assuming random distribution of the... 

Due to the complicated kinetics for both processes no attempt was made in ref. 83 to treat the data quantitatively. It was estimated, however, that the back electron transfer reaction is slower by about 3 orders of magnitude than that of the forward electron transfer. At the same time, the free energy change for the forward reaction (AG° = - 0.4 eV) is smaller than that for the back electron transfer (AG° = — 1.7 eV). This decrease of the reaction rate at large exothermicity was attributed [83] to the decrease of the Franck-Condon factors with increasing J in the situation when J > Er (see Chap. 3, Sect. 5). 

Electron transfer rate constants, kt, free energy changes, - AG°, and stability constants, K1 and Kz, for the reactions of Cr(III)(phen)3 and Ru(II)(bpy)3 with reduced blue copper proteins at 295 K [96]... 

A detailed study of the effect of the medium and temperature on the intramolecular electron transfer rate constant kt in various metal complex systems of the bridge structure has been carried out [25]. The values of kt were found to increase and the activation energy to decrease with increasing polarity of the medium. These effects were accounted for in terms of the modern electron transfer theory (see the case Er > J in Fig. 5 of Chap. 3) by greater changes in the free energy, AG°, due to a higher redox potential of the L/Lr pairs in a more polar medium. 

If a third component (M), which can specifically stabilize one of the products of electron transfer, is introduced into the D -A system, the free energy change of photoinduced electron transfer is shifted to the negative direction, when the activation barrier of electron transfer is reduced to accelerate the rates of electron transfer, as shown in Figure 3, where M forms a complex with A ". It should be emphasized that there is no need to have an interaction of M with A and that the interaction with the reduced state (A ") is sufficient to accelerate the rate of photoinduced electron transfer. This contrasts sharply with the catalysis on conventional ionic or concerted reactions, in which the catalyst interacts with a reactant to accelerate the reactions. The initial interaction between M and A in the complex A-M, where charge is partially transferred from A to M, would also result in acceleration of the photoinduced electron transfer, since the reduction potential of A-M is shifted to the negative direction as compared to that of A. 

It is now well established that the cation radicals of unsaturated and strained hydrocarbons undergo a variety of isomerization (e.g., Scheme 18) and cycloaddition reactions with much faster rates than those of the corresponding neutral molecules [162-165]. A cation radical chain mechanism analogous to Scheme 17 was reported for one-way photoisomerization of cis-stilbene (c-S) to truws-stilbene (f-S) via photoinduced electron transfer, as shown in Scheme 18 [166], Once c-S + is formed, it is known to isomerize to t-S + [167,168]. The free energy change of electron transfer... 

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