Hush theory

Here we mention as an example that in the coordination-chemistry field optical MMCT transitions between weakly coupled species are usually evaluated using the Hush theory [10,11]. The energy of the MMCT transition is given by = AE + x- Here AE is the difference between the potentials of both redox couples involved in the CT process. The reorganizational energy x is the sum of inner-sphere and outer-sphere contributions. The former depends on structural changes after the MMCT excitation transition, the latter depends on solvent polarity and the distance between the redox centres. However, similar approaches are also known in the solid state field since long [12]. 

In the isoelectronic zirconates this absorption band is not observed [17]. The spectral position of these MMCT bands has been interpreted in terms of the relevant ionization potentials [17], an approach which runs parallel with the Hush theory [10]. The fact that the MMCT transition is at higher energy in the Cr(III)-Ti(IV) pair than in the Fe(II)-Ti(IV) pair is due to the more than 10 eV higher ionization potentials of the trivalent transition-metal ions compared to the divalent transition-metal ions. The fact that the MMCT absorption band is not observed in the zirconates in contradiction to the titanates is due to the higher ionization potential of the Ti(III) species ... 

The first term is just the electronic energy of the reactant, including the interaction with the solvent the second is the energy of the solvent. The sum of these two terms is the adiabatic part of the potential energy in the original Marcus and Hush theory. The last part is the correction due to the finite width of the density of states the denominator in the logarithmic term is often left out, because it just adds a constant. 

Azo-bridged ferrocene oligomers also show a marked dependence on the redox potentials and IT-band characteristics of the solvent, as is usual for class II mixed valence complexes 21,22). As for the conjugated ferrocene dimers, 2 and 241 the effects of solvents on the electron-exchange rates were analyzed on the basis of the Marcus-Hush theory, in which the t/max of the IT band depends on (l/Dop — 1 /Ds), where Dop and Ds are the solvent s optical and static dielectric constants, respectively (155-157). However, a detailed analysis of the solvent effect on z/max of the IT band of the azo-bridged ferrocene oligomers, 252,64+, and 642+, indicates that the i/max shift is dependent not only on the parameters in the Marcus-Hush theory but also on the nature of the solvent as donor or acceptor (92). 

Marcus equation, 19 112 Marcus-Hush theory, 13 430 Marflex, 7 636... 

In the case of stepwise electron-transfer bond-breaking processes, the kinetics of the electron transfer can be analysed according to the Marcus-Hush theory of outer sphere electron transfer. This is a first reason why we will start by recalling the bases and main outcomes of this theory. It will also serve as a starting point for attempting to analyse inner sphere processes. Alkyl and aryl halides will serve as the main experimental examples because they are common reactants in substitution reactions and because, at the same time, a large body of rate data, both electrochemical and chemical, are available. A few additional experimental examples will also be discussed. 

The activation parameters for the cation-independent pathway ( o) can be accounted for by a modified semiclassical Marcus-Hush theory. Lower enthalpies, and more positive volumes of activation are noted for the M +-catalyzed pathway. - ... 

The forbidden retro-[ls -I- 2s]-cycloaddition can now be treated using a simple curve-crossing model analagous to the Marcus-Hush theory of electron-transfer [11]. The ground state at the quadricyclane-like geometry is the... 

The energy curves in Figure 22 are closely related to the Marcus-Hush theory for electron transfer. The formalism we employ emphasizes a dipole model for the solute solvent interaction, i.e., an Onsager cavity model. However, a Born charge model based on ion solvation as something in between [135] would be essentially equivalent because we do not attempt to calculate Bop and Bor but rather determine them empirically. 

This has important implications with respect to the shape of the voltammetric response predicted by the different models. Thus, the MHC model has been proven, theoretically and experimentally, to be unable to fit the voltammetric response of redox systems that show BV transfer coefficients significantly different from 0.5 [30]. In such cases, as well as in the analysis of surface-confined redox systems, the use of the asymmetric Marcus-Hush theory has been recommended [35] which considers that the force constants for the redox species can be different leading to Gibbs energy curves of different curvatures. 

For x 1, the process is nonadiabatic and is expected to follow the Marcus-Hush theory with the rate constant of e.t. given as... 

As mentioned in the introduction, the debate concerning the observation or the absence of the M.LR. has shifted in recent years to various models of the role of the solvent in e.t. reactions. In this section we shall consider the concept of the outer sphere reorganization in the Marcus-Hush theory, its implications and experimental predictions the more recent concepts of the dynamics of solvent relaxation as a controlling factor in e.t. will then be discussed. 

The classical (or semiclassical) equation for the rate constant of e.t. in the Marcus-Hush theory is fundamentally an Arrhenius-Eyring transition state equation, which leads to two quite different temperature effects. The preexponential factor implies only the usual square-root dependence related to the activation entropy so that the major temperature effect resides in the exponential term. The quadratic relationship of the activation energy and the reaction free energy then leads to the prediction that the influence of the temperature on the rate constant should go through a minimum when AG is zero, and then should increase as AG° becomes either more negative, or more positive (Fig. 12). In a quantitative formulation, the derivative dk/dT is expected to follow a bell-shaped function [83]. 

We begin by reviewing the elements of the classical theory of ET, developed independently by Marcus and Hush.4,5 While more sophisticated theoretical treatments of ET exist,6,7 Marcus-Hush theory will largely serve the purposes of... 

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