Self exchange reactions activation volumes

The Marcus-Hush theory was adapted to calculation of the volumes of activation for self-exchange [Co(en)3] + 2+, [Co(sep)]3+/2+, [Co(diAMsar)]3+/2+ [Co(diAMHsar)]5+/4+ [CoD3(BR)2]3+ 2+ and [Co([9]aneS3)2] + + reactions [301, 333, 342, 355]. A plot of the calculated and observed mean volumes of activation for these reactions in aqueous solution is shown in Fig. 57. The Marcus-Hush theory is quantitatively successful in the description of aqueous systems for a variety of self-exchange reactions including the... 

In some of the simplest cases (namely, solvent exchange and self-exchange reactions), the experimental data could be supported by theoretical calculations. Significant developments are expected to occur in this area, such that the theoretical optimization of transition state structures will become standard practice in mechanistic studies. Here again volume of activation data will play a crucial role, since they present an experimental measure of the intrinsic and solvational volume changes in the transition state and form a basis for comparison with theoretical predictions. It will be an ideal situation when volume profiles can be constructed for more complex reaction sequences, for instance for catalytic cycles in enzymatic processes. This will, as in the case of more simple reactions, enhance our understanding of complex chemical processes and improve our ability to tune them. 

Much of our earlier work on pressure effects on the kinetics of electron transfer reactions focused upon the rate constants kex and corresponding volume of activation for self-exchange reactions... 

Both involve high-pressure electrochemistry. One is the measurement of the pressure dependence of the rate constant for electron transfer in a given couple at an electrode, but it is not immediately clear how feg] and the corresponding volume of activation relate to feex and AV, respectively, for the self-exchange reaction of the same couple. This is a major theme of this chapter, and is pursued in detail below. The other method involves invocation of the cross relation of Marcus [5], which expresses the rate constant ku for the oxidation of, say, A by B+ in terms of its equilibrium constant and the rate constants kn and fe22 for the respective A+/A and B+/B self-exchange reactions ... 

The examples presented in this chapter clearly demonstrate that electron transfer reactions exhibit a characteristic pressure dependence that can be employed to gain further insight into the mechanism of the electron transfer process. The pressure dependence of self-exchange reactions can be used to develop the theoretical interpretation of the observed volumes of activation because the overall reactions involve no net volume change. In the case of nonsymmetrical reactions, the volume profile treatment can reveal information regarding the reorganization involved in going from the reactant to the transition and product... 

An advantage of dynamic techniques such as cyclic voltammetry is that potentials of unstable states can be more readily evaluated. They are most applicable to proteins whose function is to transfer electrons (cytochromes, ferredoxins, etc.) rather than catalyze redox reactions. Flavo-proteins and dinuclear iron proteins are in this category they have the equivalent of very low self-exchange rates, meaning that they cannot readily transfer electrons to each other, and they also do not interact well with electrodes. This is because their active sites are only accessible to small molecules. Accessibility to active sites of enzymes is also a topic that has been addressed by Willner in Chapter 17 in this volume. In our flavoprotein and dinuclear iron cluster work, we will consider only those proteins that have the dual function of transferring electrons and selectively catalyzing reactions. 

Figure 9.6 Pressure-effect on rates of some self-exchange electron-transfer reactions between metal ions comparison of observed volumes of activation with values calculated from classical Marcus theory for adiabatic reactions. The plot shows calculated and observed AP values (cm mol ) at mid-range of pressure (100 MPa, except 70 MPa for Fe(H20)g ) for adiabatic (filled symbols) and nonadiabatic (open circles) self-exchange in couples with rigid ligands. Solvents (o, ) water ( ) CD3CN (A) (CD3)2CO (V) CD3OD. Key (A,B) (C,D) Cu(dmp)2 (E-G) Ru(hfac)j (H) Fe(C5H5)2 (I-K) Mn(CN-t-Bu)g ...

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