Marcus theory for electron transfer reactions

To fully understand the relaxation pathways for photoinduced charge-transfer reactions in solutions we need to take solvent effects into account. For that reason it is necessary to recall some basic principles of the classical Marcus Theory for electron-transfer reactions in solution. 

The use of the energy-gap reaction coordinate allows us to calculate solvent reorganization energies in a way analogous to that in the Marcus theory for electron transfer reactions.19 The major difference here is that the diabatic states for electron transfer reactions are well-defined, whereas for chemical reactions, the definition of the effective diabatic states is not straightforward. The Marcus theory predicts that... 

The approach used to obtain the EVB free energy functionals (the Ag of Eq. (8.12)) was originally developed in Ref [1] in order to provide the microscopic equivalent of Marcus theory for electron transfer reactions [29]. This approach allows one to explore the validity of the Marcus formula on a microscopic molecular level [62]. While this point is now widely accepted by the ET community [44], the validity of the EVB as perhaps the most general tool in microscopic LFER studies of PT reactions is less appreciated. This issue will be addressed below. 

Fig. 30. Free energy curves in the Marcus theory for electron transfer reactions.

Marcus has developed his primarily classical theory for electron transfer reactions in homogeneous solutions. In the simplest type of reaction a single electron is transferred without breaking or forming bonds. A bimolecular exchange reaction is given by... 

Because of the large dielectric constant of water, electron transfer reactions in this liquid are strongly coupled to solvent polarization modes. The equilibrium solvent effects are well accounted for within the celebrated Marcus theory of electron transfer reactions [19]. The dynamic effects of electron transfer reactions have been the subject of many interesting discussions in the scientific literature and revealed some nice aspects of chemical kinetics in general, as articulated below. Study of the dynamics of electron transfer uses the results obtained in SD. 

Marcus RA (1965) On the theory of electron-transfer reactions. VI. Unified treatment for homogeneous and electrode reactions. J Chem Phys 43 679... 

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)... 

MARCUS , RUDOLPH A. 11923-1. Prolessor Marcus from the California Institute of Technology. Pasadena. California, won the Nobel prize lor chemistry in 1992 for his contributions in the theory of electron transfer reactions in chemical systems. 

Fig. 9 Test of the Marcus theory of electron transfer where fcca,c for the cross-reaction O, + R - R, + On is calculated from the thermodynamic free energies and the free energies of activation of the symmetrical reactions. The symbols are as follows O, Ce(IV), x IrCl -, + Mo(CN)j-, Fe(CN) ", R O, Fe(CN)J , A Mo(CN)f, W(CN)<-...

The theory of the multi-vibrational electron transitions based on the adiabatic representation for the wave functions of the initial and final states is the subject of this chapter. Then, the matrix element for radiationless multi-vibrational electron transition is the product of the electron matrix element and the nuclear element. The presented theory is devoted to the calculation of the nuclear component of the transition probability. The different calculation methods developed in the pioneer works of S.I. Pekar, Huang Kun and A. Rhys, M. Lax, R. Kubo and Y. Toyozawa will be described including the operator method, the method of the moments, and density matrix method. In the description of the high-temperature limit of the general formula for the rate constant, specifically Marcus s formula, the concept of reorganization energy is introduced. The application of the theory to electron transfer reactions in polar media is described. Finally, the adiabatic transitions are discussed. 

The forty-year-old Marcus cross-rate theory for calculating the rate constant for electron-transfer reactions between different species ky of Eq. 1) was derived classically and ignores separation of Ay and As, tunneling, and variations in both the preexponential factor and Ke [21]. 

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