Marcus rate theory, electron transfer

Clearly, the intrinsic rate of electron transfer is dominated by /. and modern theories have shown that X can be expressed as the sum of two terms Xh the contribution from vibrational modes within the charged ionic unit, and XQy the contribution from the solvent dipole re-orientation effects. Expressions for both of these terms have been given by Marcus ... 

A key point that must be made is diat quantum mechanical tunneling through the Marcus-theory barrier when it is non-zero can increase the rate for electron transfer just as is true for any other activated process. Because the electron is so light a particle, tunneling can be a major contributor to die overall rate. Models for electron tunneling will not, however, be presented here. 

The various factors that affect the rate of electron transfer were incorporated by Marcus into a quantitative theory. Electron transfer is often discussed in... 

Electron-transfer pathways In spite of the success of the Marcus theory, rates of electron-transfer from the iron of cytochrome c have been found to vary for different pathways.150 153 155 For example, transfer of an electron from Fe(II) in reduced cytochrome c to an Ru(III) complex on His 33 was fast ( 440 s-1)157 but... 

Radicals can be either reduced (to anions or organometallics) or oxidized to cations by formal single electron transfer (Scheme 11).50 Such redox reactions can be conducted either chemically or electro-chemically51 and the rates of electron transfer are usually analyzed by the Marcus theory and related treatments.50 These rates depend (in part) on the difference in reduction potential between the radical and the reductant (or oxidant). Thus a species such as an a-amino radical with high-lying singly occupied molecular orbital (SOMO) is more readily oxidized, while a species such as the malonyl radical with a low-lying SOMO is more readily reduced. The inherent difference in reduction potential of substituted radicals is an important control element in several kinds of reactions. 

In addition photoexcitation can also result in the transfer of an excited state electron to a distant acceptor group resulting in charge separation. This process can be understood within the framework of Marcus theory and subsequent more sophisticated theoretical treatments.2,5 The rate of electron transfer (ke]) drops with distance according to an attenuation factor / el ke °c exp(—/ el /yB) where /Xb is the distance between donor and acceptor components A and B. When the donor and acceptor components are separated by a vacuum J3el is estimated to be ca. 2-5 A-1. However when some kind of material substance is involved such as a bridge L the electron transfer process can be... 

The Marcus Inverted Region (MIR) is that part of the function of rate constant versus free energy where a chemical reaction becomes slower as it becomes more exothermic. It has been observed in many thermal electron transfer processes such as neutralization of ion pairs, but not for photoinduced charge separation between neutral molecules. The reasons for this discrepancy have been the object of much controversy in recent years, and the present article gives a critical summary of the theoretical basis of the MIR as well as of the explanations proposed for its absence in photoinduced electron transfer. The role of the solvent receives special attention, notably in view of the possible effects of dielectric saturation in the field of ions. The relationship between the MIR and the theories of radiationless transitions is a topic of current development, although in the Marcus-Hush Model electron transfer is treated as a thermally activated process. 

The plateau in Fig. 13.9 corresponds to the diffusion-limited region where the rate of electron transfer is faster than the rate of diffusion. According to the Marcus theory of electron transfer, the observed rate constant of an intermolecular electron transfer is given by [23]... 

Some notions of the mechanism of electron transfer were given in Section 4.2. Any theory must be realistic and take into account the reorientation of the ionic atmosphere in mathematical terms. There have been many contributions in this area, especially by Marcus, Hush, Levich, Dog-nadze, and others5-9. The theories have been of a classical or quantum-mechanical nature, the latter being more difficult to develop but more correct. It is fundamental that the theories permit quantitative comparison between rates of electron transfer in electrodes and in homogeneous solution. 

Marcus theory (Marcus, 1968, 1969), originally developed to interpret the rates of electron transfer reactions, has been successfully applied to proton transfer reactions as well. The theory relates... 

The above equations predict the absolute rates of electron-transfer reactions, but by far the most popular and useful aspect of the Marcus theory is comparison of rates of different, related reactions. 

One particular example of the use of pulse radiolysis to general chemistry was the work of Miller and co-workers on the rates of electron-transfer reactions. These studies, which were begun using reactants captured in glasses, were able to show the distance dependence of the reaction of the electron with electron acceptors. Further work, where molecular frameworks were able to fix the distance between electron donors and acceptors, showed the dependence of electron-transfer rate on the energetics of the reaction. These studies were the first experimental confirmation of the electron transfer theory of Marcus. 

Marcus theory of electron transfer (Eq. 4) [91] to the rate of electron transfer from ferrocyanide to HRP compound I (8 x 10 M s ) [105], An even larger reorganization energy (2 = 78.0 kcal mol ) [104] was derived from the electron self-exchange rate between HRP compound II and ferric HRP (4.9 x 10 m s ) [104], The extremely large 2 value (78.0 kcal mol ) for the metal-centered electron-exchange between HRP compound II (Fe ) and ferric HRP (Fe ) is consistent with the large... 

According to the semiclassical Marcus theory [6], the rate of electron transfer depends on the reduction potential (AGq), the electronic coupling matrix element Hda), and the reorganisation energy (A) ... 

The Marcus Theory can also be applied for heterogeneous electron transfer reaction at electrode surfaces [24 and references therein]. The electronic coupling between the protein and the electrode can be varied using different self-assembled monolayers controlling the orientation of the redox active protein on the surface and the distance between the redox active site of the protein and the electrode. The driving force is related to the appHed potential and the redox potential of the protein. In many cases the rate of electron transfer across the protein-electrode interface is limited by conformational reorganization. This has focussed the efforts of many groups on tailored interaction between proteins and enzymes and electrode surfaces. 

---