Marcus, redox reactions

The last two decades have seen a growing interest in the mechanism of inorganic reactions in solution. Nowhere is this activity more evident than in the topic covered by this review the oxidation-reduction processes of metal complexes. This subject has been reviewed a number of times previously, notably by Taube (1959), Halpern (1961), Sutin (1966), and Sykes (1967). Other articles and books concerned, wholly or partly, with the topic include those by Stranks, Fraser , Strehlow, Reynolds and Lumry , Basolo and Pearson, and Candlin et al ° Important recent articles on the theoretical aspects are those by Marcus and Ruff. Elementary accounts of redox reactions are included in the books by Edwards , Sykes and Benson . The object of the present review is to provide a more detailed survey of the experimental work than has hitherto been available. 

Attempts were made to quantitatively treat the elementary process in electrode reactions since the 1920s by J. A. V. Butler (the transfer of a metal ion from the solution into a metal lattice) and by J. Horiuti and M. Polanyi (the reduction of the oxonium ion with formation of a hydrogen atom adsorbed on the electrode). In its initial form, the theory of the elementary process of electron transfer was presented by R. Gurney, J. B. E. Randles, and H. Gerischer. Fundamental work on electron transfer in polar media, namely, in a homogeneous redox reaction as well as in the elementary step in the electrode reaction was made by R. A. Marcus (Nobel Prize for Chemistry, 1992), R. R. Dogonadze, and V. G. Levich. 

The general relationship for the activation energy including both the electrode reaction and the chemical redox reaction as derived by Marcus in the form... 

It is hardly possible to overestimate the impact that the Marcus-Hush ideas and their experimental exploitation, mainly by Sutin and his coworkers, have made on the study of redox reactions. The treatment here is necessarily brief. Other aspects have been discussed in the references cited. Some important points we have not considered are... 

It has been a characteristic of the discussion that sprang from the Weiss-Marcus views that the comparison of theory with experiments was made largely with redox reactions. It is understandable that theorists have concentrated on these reactions, for they are simpler than the bond-forming reactions which are, however, much more numerous in reality than nonbonding redox reactions. 

Weiss published a paper in 1954 giving a number of modeling ideas concerning the molecular-level mechanism of redox reactions in solution. In 1956 Marcus published (independently) a paper containing similar ideas, but also applied them to electrode reactions. From these works there followed an equation ... 

Magnetic quantum number. 19 Magnetic susceptibility mass. 460-463 molar, 461 volume, 460 Maim. J. O.. 70 Map of twist angles, 490 Marcus theory, 571 Mass spectrometry. 239 Maximum multiplicity, 26-27 Mechanisms inner sphere, 565-567 outer sphere. 558-561 of redox reactions. 557-572 of substitution reactions. 545-547. 551-553 Medicinal chemistry, 954-960 Meissner effect, 285 Melting points, and chemical forces. 307-310... 

Theoretical treatments of charge transfer at electrodes were developed by Gurney, Horiuti, and Eyring and the more recent work of Gerischer, Marcus, Hush, and Levich, among others, permitted the study of simple redox electrode reactions under the same theoretical framework developed for homogeneous redox reactions in solution. 

The Marcus treatment for heterogeneous electron transfer at electrodes is analogous to the homogeneous case of redox reactions in solution discussed in Vol. 2, Chap. 4. The free energy of activation can also be expressed by... 

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. 

The Marcus therory provides an appropriate formalism for calculating the rate constant of an outer-sphere redox reaction from a set of nonkinetic parameters1139"1425. The simplest possible process is a self-exchange reaction, where AG = 0. In an outer-sphere electron self-exchange reaction the electron is transferred within the precursor complex (Eq. 10.4). 

The demise of the famous Hodgkin-Huxley theory of nerve conductance brings to mind other Nobel prizes in electrochemically related areas. In 1959 Heyrovsky was recognized for a new analytical method, and this polarography has been the origin of many modem methods of electroanalysis. The award for Nobel Prize to Mitchell in 1978 (for a chemiosmotic model of membrane function) and metabolism seems to have been based on a lack of awareness of a simpler, clearer (prior) model by Williams for interpreting the same functions. The award to Marcus in 1992 for the theory of redox reactions (1956) seems to have lacked awareness of an earlier publication by Weiss that described similar ideas. 

This problem can also be approached by using the rate theory with thermodynamic analogues as has been done by Randles (10) and Marcus (11). Applying this method on semiconductor redox reactions, Dewald (12) arrived at very similar conclusions as those presented here. The method used here however, shows more directly the influence of the solid itself and it can yield more information for nonequiltbrium conditions. 

The electron transfer reaction from copper to heme within the ternary protein complex was also studied in solution by stopped-flow spectroscopy. Analysis by Marcus theory of the temperature dependence of the limiting first-order rate constant for the redox reaction (Davidson and Jones, 1996) yielded values for the of 1.1 eV and H b of 0.3 cm , and predicted an electron transfer distance between redox centers which was consistent with the distance seen in the crystal structure. Thus, the electron transfer event is rate-limiting for this redox reaction. Experiments are in progress to determine the validity of the predicted pathways for electron transfer shown in Figure 7. 

These complexes are excellent models for theoretical studies. The octacyano complexes of molybdenum and tungsten are stable and inert toward substitution reactions and therefore very suitable for theoretical studies of redox reactions and application of the Marcus theory. The photoreactivity of these systems is also proving to be important. The 0X0- and nitridocyano complexes of Mo(IV), W(IV), Tc(V), Re(V), and Os(VI) are very good candidates for kinetic studies of substitution reactions with both mono- and bidentate ligands and are of interest especially in view of the large variations in the observed reactivity. 

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