Marcus theory extended

Marcus theory, first developed for electron transfer reactions, then extended to atom transfer, is now being applied to catalytic systems. Successful applications to catalysis by labile metal ions include such reactions as decarboxylation of oxaloacetate, ketonization of enolpyru-vate, and pyruvate dimerization (444). 

The above model has been further explored to account for reaction efficiencies in terms of a scheme where nucleophilicities and leaving group abilities can be rationalized by a structure-reactivity pattern. Pellerite and Brau-man (1980, 1983) have proposed that the central energy barrier for an exothermic reaction (see Fig. 3) can be analysed in terms of a thermodynamic driving force, due to the exothermicity of the reaction, and an intrinsic energy barrier. The separation between these two components has been carried out by extending to SN2 reactions the theory developed by Marcus for electron transfer reactions in solutions (Marcus, 1964). While the validity of the Marcus theory to atom and group transfer is open to criticism, the basic assumption of the proposed model is that the intrinsic barrier of reaction (38)... 

Take a mean value of 80 (i.e., 0.83 eV). Numerical calculations show that T] < 0.2 V is the condition up to which 9.38 yields the experimental version of Tafel s law (of course, the value depends on the Fs chosen and the allowed T, for the applicability of 9.38 will be roughly halved at the lower limit and doubled at the higher one. In any case, this harmonic approximation, which is involved in the Weiss—Marcus theory, cannot be applied to the experimental current-potential data, which in reality extend over 0.2 V and even 1.0 V (for hydrogen and oxygen evolution). 

The Br0nsted plots (Fig. 3) give information on this point. The higher curvature of the plot for DMSO compared to methanol is indicative of a lower intrinsic barrier to proton transfer for the dipolar aprotic solvent. Since in the extended Marcus theory the solvent effect has already been taken into account, one would expect the intrinsic barrier for proton transfer to be identical in the two systems. This is not the case. Therefore it appears that separation of the mechanism into reagent positioning with concomitant solvent reorganization is not warranted. 

Inner-sphere (electron transfer) — is, historically, an - electron transfer between two metal centers sharing a ligand or atom in their respective coordination shells. The term was then extended to any case in which the interaction energy between the donor and acceptor centers in the -> transition state is significant (>20 kj mol-1). See also -> Marcus theory. 

It is well known from Marcus theory that for diabatic free energies that are harmonic with respect to the reaction coordinate, (7 is a quadratic function of AC° (Eq. 27) [8, 9]. This result may be extended to H and S and is represented as follows [36, 93] ... 

The most accepted modern activation theory for the outer electron transfer is that of Rudolph A. Marcus (Nobel Prize in Chemistry in 1992) [14], which is different from the transition state theory. His studies on unimolecular reactions and the transition and collision theories committed him to elaborate on the Rice-Ramsperger-Kassel-Marcus (RRKM) theory in 1952. This theory is an extension of the previous RRK theory proposed by Rice, Ramsperger, and Kassel between 1927 and 1928. Moreover, Hush and Marcus further extended the electron transfer theory of Marcus for inner electron transfers [15-17]. 

Many reactions exhibit effects of thermodynamics on reaction rates. Embodied in the Bell-Evans-Polanyi principle and extended and modified by many critical chemists in a variety of interesting ways, the idea can be expressed quantitatively in its simplest form as the Marcus theory (15-18). Murdoch (19) showed some time ago how the Marcus equation can be derived from simple concepts based on the Hammond-Leffler postulate (20-22). Further, in this context, the equation is expected to be applicable to a wide range of reactions rather than only the electron-transfer processes for which it was originally developed and is generally used. Other more elaborate theories may be more correct (for instance, in terms of the physical aspects of the assumptions involving continuity). For the present, our discussion is in terms of Marcus theory, in part because of its simplicity and clear presentation of concepts and in part because our data are not sufficiently reliable to choose anything else. We do have sufficient data to show that Marcus theory cannot explain all of the results, but we view these deviations as fairly minor. 

Moreover, Marcus demonstrated that it is possible for AG values for some electron-transfer reactions to increase as AG° values become more negative (Figure 6.38), giving rise to what is known as the inverted region in a plot of In k versus -AG°. ° Marcus theory has been extended to proton-, hydrogen-and group-transfer reactions as well. ° For these processes, however, it is... 

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