Marcus-Br0nsted plot

Figure 2. Marcus-Br0nsted plot AE vs. AE° for the reaction of substituted benzyl anions with methyl bromide.

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. 

Another approach used to interpret curvature of Br0nsted plots has been given by Murdoch (1972). This model, which incorporates Marcus theory, shows that the diffusive steps (10a, c) of the three-stage Eigen mechanism can also influence curvature. It is shown mathematically that increased difficulty of diffusion has the same... 

The Marcus equation is also examined in Chapter 9. As discussed previously regarding the Lewis chapter, the quadratic term of the Marcus equation leads to a dependency of rate on the square of pKa, so that Brpnsted plots would be expected to be curved. Bordwell and co-workers observe curvature in some of their Br0nsted plots but conclude that the curvature is too large to be a Marcus effect and actually results from a solvation effect for some heteroatom substituents. These workers suggest that the curvature observed for Brpnsted plots in water results from differential solvation. 

This expression is analogous to the one predicted by Marcus theory for the slope of the Br0nsted plot for a proton-transfer reaction see Section 8.2.5, Equation (8.36).) When is close to zero, the plot will be expected to be approximately linear with a slope of 0.5. This is in fact generally confirmed by experiment, with some exceptions that can be rationalised. Some values are shown in Table 9.3 [14]. (There are as yet far fewer examples of such linear free-energy relations for electron transfer than for proton transfer.) Figure 9.8 shows a plot for some redox reactions of Fe(III), with a slope of 0.50 as expected [15]. 

Note that the slopes of the Br0nsted and Tafel plots, need not necesarily be constant over a large free energy range and, in fact, the Marcus—Levich theoretical treatment predicts a quadratic dependence [32c]. 

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