The rates of electron transfer processes

Electron transfer is of crucial importance in many biological reactions, and we need to see how to use the strategies we have developed to discuss them quantitatively. 

Consider electron transfer from a donor species D to an acceptor species A in solution. The net reaction, the observed rate law, and the equilibrium constant are 

In the first step of the mechanism, D and A must diffuse through the solution and encounter to form a complex DA, in which the donor and acceptor are separated by a distance comparable to r, the distance between the edges of each species. Next, electron transfer occurs within the DA complex to yield D+A. The D A complex has two possible fates. One is the regeneration of DA. The other is to break apart and for the ions to diffuse through the solution. We show in the following Justification that fcobs in eqn 8.24 is given by 

Justification 8.4 The rate constant for electron transfer in solution 

We begin by equating the rate of the net reaction (eqn 8.24) to the rate of formation of separated ions, the reaction products  

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In essence, these empirical findings allow control of the rate of electron-transfer processes by creating the appropriate structural conditions. It is, of course, straightforward to extend such a correlation of structure and electron-transfer kinetics to higher homologues. 

The transfer of a single electron between two chemical entities is the simplest of oxidation-reduction processes, but it is of central importance in vast areas of chemistry. Electron transfer processes constitute the fundamental steps in biological utilization of oxygen, in electrical conductivity, in oxidation reduction reactions of organic and inorganic substrates, in many catalytic processes, in the transduction of the sun s energy by plants and by synthetic solar cells, and so on. The breadth and complexity of the subject is evident from the five volume handbook Electron Transfer in Chemistry (V. Balzani, Ed.), published in 2001. The most fimdamental principles that govern the efficiencies, the yields or the rates of electron-transfer processes are independent of the nature of the substrates. The properties of the substrates do dictate the conditions for apphcability of those fimdamental... 

Mass amplification is another strategy to increase the mass sensitivity of a standard QCM device and crystal. Such approaches commonly involve enzymatic catalysis to greatly increase either the rates of electron transfer processes in EQCM applications or to increase rates of insoluble mass deposition as the product of an enzymatic reaction [157-159]. However, mass amplification can also involve the use of larger mass objects binding to the QCM crystal, such as gold particles. We expect that future studies will continue to adapt these general mass amplification strategies to specific systems. 

The rates of electron-transfer processes in the oxidation of polycyclic aromatic hydrocarbons have been considered by Peover and White, who estimated from cyclic voltammograms the apparent standard rate constant for 9,10-diphenylanthracene radical cation formation to be of the order 1 cm... 

Another concept of general interest that has been revised is the use of the Rehm-Weller equation for predicting the rate of electron transfer processes involving excited states. A recent investigation found significant discrepancies in both AG and kg values obtained in this way. Rather, the revised data were in good accord with the Sandros-Boltzmann equation... 

Equation 9.11 implies that the rates of electron transfer processes should decrease exponentially with distance between the electron donor and acceptor. This prediction is supported by the experimental evidence that we discussed in Section 8.11, where we showed that, when the temperature and Gibbs energy of activation are held constant, the rate constant of electron transfer is proportional to e where r is the edge-to-edge distance between electron donor and acceptor and /i is a constant with a value that depends on the medium through which the electron must travel from donor to acceptor. It follows that tunneling is an essential mechanistic feature of the electron transfer processes between proteins, such as those associated with oxidative phosphorylation. 

An electronically excited state of a molecule can be considered as a new species whose chemical properties might differ considerably from those of the same molecule taken in its ground state. Although some of the properties of the excited state are now well understood, mainly those involving thermodynamic aspects, it is extremely difficult to predict other parameters such as the lifetime of the excited state and the rate of electron transfer processes [3—5]. 

However, metal ions in higher oxidation states are generally smaller than the same metal ion in lower oxidation states. In the above example, the Co(ii)-N bonds are longer than Co(iii)-N bonds. Consider what happens as the two reactants come together in their ground states and an outer-sphere electron transfer occurs. We expect the rate of electron transfer from one center to another to be very much faster than the rate of any nuclear motion. In other words, electron transfer is very much faster than any molecular vibrations, and the nuclei are essentially static during the electron transfer process (Fig. 9-6). 

Cobalt(II) complexes of three water-soluble porphyrins are catalysts for the controlled potential electrolytic reduction of H O to Hi in aqueous acid solution. The porphyrin complexes were either directly adsorbed on glassy carbon, or were deposited as films using a variety of methods. Reduction to [Co(Por) was followed by a nucleophilic reaction with water to give the hydride intermediate. Hydrogen production then occurs either by attack of H on Co(Por)H, or by a disproportionation reaction requiring two Co(Por)H units. Although the overall I easibility of this process was demonstrated, practical problems including the rate of electron transfer still need to be overcome. " " ... 

Homogeneous Processes with Tris-phenanthroline Metal(III) Oxidants. The rates of electron transfer for the oxidation of these organometal and alkyl radical donors (hereafter designated generically as RM and R, respectively, for convenience) by a series of tris-phenanthroline complexes ML33+ of iron(III), ruthe-nium(III), and osmium(III) will be considered initially, since they have been previously established by Sutin and others as outer-sphere oxidants (5). 

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 ). 

Electron-poor olefins with higher oxidation potentials may decrease the rate of electron transfer and other processes competing for deactivation of the iminium salt excited states may increase. Alternate reaction pathways involving olefin-arene 2 + 2 cycloaddition may take place in the photochemistry of 133 with electron-poor olefins (equation 62)120,121. 

In Chapter 7 general kinetics of electrode reactions is presented with kinetic parameters such as stoichiometric number, reaction order, and activation energy. In most cases the affinity of reactions is distributed in multiple steps rather than in a single particular rate step. Chapter 8 discusses the kinetics of electron transfer reactions across the electrode interfaces. Electron transfer proceeds through a quantum mechanical tunneling from an occupied electron level to a vacant electron level. Complexation and adsorption of redox particles influence the rate of electron transfer by shifting the electron level of redox particles. Chapter 9 discusses the kinetics of ion transfer reactions which are based upon activation processes of Boltzmann particles. 

The importance of this is that it is not simply the changes in NADH and ADP concentrations that regulate the rate of electron transfer and ATP generation, but also the concentration ratios NADH/NAD and ATP/ADP that is, the falls in the concentrations of ATP and NAD pulF the process to the right whereas the increases in the... 

Temperature Dependence of the Kinetics. In an earlier article (22) we gave a detailed analysis of the temperature dependence of the rate of electron transfer from 1 (BPh ) to Q (Figure 4). Here we summarize some of the important considerations and discuss further the possible insights that the temperature and detection-wavelength dependence of the kinetics may give into the molecular mechanism of electron transfer and the overall charge separation process. 

Finally, it may be useful to note that the Fermi golden rule and time correlation function expressions often used (see ref. 12, for example) to express the rates of electron transfer have been shown [13], for other classes of dynamical processes, to be equivalent to LZ estimates of these same rates. So, it should not be surprising that our approach, in which we focus on events with no reorganization energy requirement and we use LZ theory to evaluate the intrinsic rates, is closely related to the more common approach used to treat electron transfer in condensed media where the reorganization energy plays a central role in determining the rates but the z factor plays a second central role. 

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