And the Marcus equation

The latter is, except for a couple of terms related to solvent reorganization, the Marcus equation. The central idea is that the activation energy can be decomposed into a component characteristic of the reaction type, the intrinsic activation energy, and a correction due to the reaction energy being different from zero. Similar reactions should have similar intrinsic activation energies, and the Marcus equation obeys both the BEP... 

If AG° Marcus equation can be approximated by a linear free energy relationship (LEER) (Equation 1.14). 

The Bell-Evans-Polanyi relationship, Hammond s postulate, and the Marcus equation are all approaches to analyzing, understanding, and predicting relationships between the thermodynamics and kinetics of a series of closely related reactions. This is an important issue in organic chemistry, where series of reactions differing only in peripheral substituents are common. Each of these approaches provides a sound basis for the intuitive expectation that substituents that favor a reaction in a thermodynamic... 

This discussion of sources of curvature in Br insted-type plots should suggest caution in the interpretation of observed curvature. There is a related matter, concerning particularly item 5 in this list, namely, the effect of a change in transition state structure. Br nsted-type plots are sometimes linear over quite remarkable ranges, of the order 10 pK units, and this linearity has evoked interest because it seems to be incompatible with Marcus theory, which we reviewed in Section 5.3. The Marcus equation (Eq. 5-69) for the plot of log k against log K of the same reaction series requires curvature, the slope of the plot being the coefficient a. given by Eq. (5-67). A Brjinsted plot, however, is not a Marcus plot, because it correlates rates and equilibria of different reactions. The slope p of a Br nsted plot is defined p = d log kobs/d pK, which we can expand as... 

Actually the assumptions can be made even more general. The energy as a function of the reaction coordinate can always be decomposed into an intrinsic term, which is symmetric with respect to jc = 1 /2, and a thermodynamic contribution, which is antisymmetric. Denoting these two energy functions h2 and /zi, it can be shown that the Marcus equation can be derived from the square condition, /z2 = h. The intrinsic and thermodynamic parts do not have to be parabolas and linear functions, as in Figure 15.28 they can be any type of function. As long as the intrinsic part is the square of the thermodynamic part, the Marcus equation is recovered. The idea can be taken one step further. The /i2 function can always be expanded in a power series of even powers of hi, i.e. /z2 = C2h + C4/z. The exact values of the c-coefficients only influence the... 

Equation (3.34) without the H X ) and the H 2la terms is identical to the Marcus equation for methyl transfer reactions (Ref. 13). This equation predicts, at the range ( AG0 < a), a linear relationship between AAG0 and AAg by... 

When R is CH3 the process is called methyl transfer. For such reactions, the work terms and are assumed to be very small compared to AG° and can be neglected, so that the Marcus equation simplifies to... 

Bunting and Kanter have developed a modified form of the Marcus equation to treat the changes in intrinsic barrier A observed for deprotonation of /J-keto esters and amides.81 It would be useful to consider similar modifications of the Marcus equation to model the variable intrinsic barriers observed for carboca-tion-nucleophile addition reactions. 

The first attempt to describe the dynamics of dissociative electron transfer started with the derivation from existing thermochemical data of the standard potential for the dissociative electron transfer reaction, rx r.+x-,12 14 with application of the Butler-Volmer law for electrochemical reactions12 and of the Marcus quadratic equation for a series of homogeneous reactions.1314 Application of the Marcus-Hush model to dissociative electron transfers had little basis in electron transfer theory (the same is true for applications to proton transfer or SN2 reactions). Thus, there was no real justification for the application of the Marcus equation and the contribution of bond breaking to the intrinsic barrier was not established. 

Figure 5, Relationship of the activation free energy for electron transfer with the electrode potentials of various FeL33 according to Equation 6 (left), and the driving force according to the Marcus Equation 4 (right).

Figure 3. Relationship between the Marcus equation quantities AE, AE and...

As a result of this behavior we can substitute back into the Marcus equation and find this relationship now in terms of... 

These results suggest that the Marcus equations can be applied quite successfully to gas phase displacement reactions, as suggested by Professor Brauman. We are currently generating more cross reactions and intend to test other rate-equilibrium relationships using our data. 

Figure 7 Dependence of log A bet on AG°bet in MeCN (solid line) and benzene (broken line). The lines are drawn schematically based on the Marcus equation [Eq. (1)]. The AG°bet value at which bet is maximum corresponds to -X [Eq. (1)].

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