Marcus approach

Transition state theory is presented with an emphasis on solution reactions and the Marcus approach. Indeed, to allow for this, I have largely eliminated the small amount of material on gas-phase reactions that appeared in the First Edition. Several treatments have been expanded, including linear free-energy relations, NMR line broadening, and pulse radiolytic and flash photolytic methods for picosecond and femtosecond transients. 

It has been shown so far that internal and external factors can be combined in the control of the electron-transfer rate. Although in most cases a simple theoretical treatment, e.g. by the Marcus approach, is prevented by the coincidence of these factors, it is clear that the observed features for the isoenergetic self-exchange differ by the electronic coupling and the free energy of activation. Then it is also difficult to separate the inner- and outer-sphere reorganization energies. 

In conclusion, the free energy change of an ET step is already a good indicator of the feasibility of the reaction. A highly endergonic reaction, with, say, AG° > 20 kcal mol-1, corresponds to a rather slow ET reaction that is not likely to compete with other reactions of polar nature. In the region where AG° lies between 20 and -A kcal mol-1, we need to apply the Marcus approach in order to get an approximate value of the ET rate constant, whereas at AG° < - A kcal mol-1 most intermolecular ET reactions appear to be diffusion controlled. 

The experimental studies reported in the past 10-15 years have attempted to measure the rate of ET at the ITIES, along with its potential dependence. The Marcus approach predicts a potential dependent rate that results from the variation of the rate constant. By contrast, other theories have developed a Frumkin-type approach, where the potential drop between the planes of closest... 

The applicability of Eq. (5.23) to the Ru(hfac)3 electrode reaction may be questioned on the basis that AG, is only slightly less than AG )j. The Sumi-Marcus approach [90], however, does cover cases in which AG[ is not negligible, and we find that replacement of the parameter Q by one derived by differentiation of Eqs (8.6) and (8.7) in reference [90] with respect to pressure, results in no significant change in AVjj(calc), within the experimental uncertainty. There is also the possi-... 

There are three early biokinetic forms of exposure modehng in the literature. These served to bridge the gap between statistical, regression modeling and the current biokinetic models enjoying relatively routine use. These are as follows (1) the Rabinowitz et al. (1976) model (2) the Marcus approach (Marcus, 1985a,b,c) and (3) the Bert model (Bert et al., 1989). 

An obvious extension of the Marcus approach consists of departing from the Gaussian assumption of eqn (18.7) and eqn (18.8), and postulating from the beginning a non-harmonic form for the Landau free energy in the reactant... 

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