Marcus-type rate

In molecular doped polymers the variance of the disorder potential that follows from a plot of In p versus T 2 is typically 0.1 eV, comprising contributions from the interaction of a charge carrier with induced as well as with permanent dipoles [64-66]. In molecules that suffer a major structural relaxation after removal or addition of an electron, the polaron contribution to the activation energy has to be taken into account in addition to the (temperature-dependent) disorder effect. In the weak-field limit it gives rise to an extra Boltzmann factor in the expression for p(T). More generally, Marcus-type rates may have to be invoked for the elementary jump process [67]. 

Triplet energy transfer has been examined in a variety of hybrid molecular dyads where unsaturated groups are attached to a central bicyclooctane framework [86]. Some of these systems are illustrated in Fig. 2.9. In each case, there is a reasonably large thermodynamic driving force for triplet energy transfer from the Ru-based donor to the Os-based acceptor such that electron exchange should occur at a rate near the apex of a Marcus-type rate vs. energy gap profile. However, the rates are... 

Experimental values of AG and the pre-exponential factor were obtained from a plot of In k,. vs 1/T under the assumption that the slope is — AG /R, and the hidden assumption that AG is temperature independent (AS is zero). Comparison between the calculated and observed pre-exponential factor was used to infer significant non-adiabaticity, but one may wonder whether inclusion of a nonzero AS would alter this conclusion. From an alternative perspective, reasonable agreement was noted for the values of ke and the homogeneous self-exchange rate constant after a standard Marcus-type correction was made for the differing reaction types. 

Bnrke and Brown examined reactions of [Re(CO)4L], L = PMe3, P(0-t-Pr)3, with Af-methylpyridinium salts. These reactions occur with electron-transfer rate constants in the 10 -10 s range. From Marcus-type (see Marcus... 

Recent theoretical developments have been directed at incorporating the distance dependence of electron-transfer rate constants into the kinetic equations for diffusion-controlled reactions on the micelle surface, rather than assuming that these are collisional processes [82]. Both forward and back electron-electron transfers have been considered, with fitting of experimental data by numerical integration of appropriate differential equations. A standard Marcus-type expression was used to describe the electron-transfer rate constants. In the particular case of electron transfer from a donor to a single acceptor located initially at 0, one has instead of Eq. 10 [82c]... 

In order to illustrate our point about the difficulties associated with phenomenological LFER treatments of reactions in solutions and in enzymes, it is instructive to consider the studies of human carbonic anhydrase III (which will be referred to here as CA III).50 Studies of this system50,51 demonstrated that the rate of PT in mutants of CA III is correlated with the pAa difference between the donor and acceptor. It was found that the observed LFER follows a Marcus type relationship. Although this study provided an excellent benchmark for studies of PT in proteins, it also raised the question about uniqueness of the parameters deduced from phenomenological LFER studies. This issue will be explored below. 

With the model of Equation (19) and with a reasonable estimate of the free energies A(fn and AG°3 we can start to evaluate the apparent activation barrier. Before doing so, we must clarify several points (i) A Marcus type relationship and the corresponding LFERs are only valid for a two-state system (1 —>2), i.e., for a reaction with a single step. However, we have a three-state process that involves a two-step mechanism (1 ->2->3). Fitting such a system to a Marcus type formula can lead to nonphysical parameters (e.g., too small of a value for X). (ii) In order to use the HAW approach in a three-state system (or in a four-state system) we must consider the elementary rate constants and then consider the preequilibrium concentrations. 

NO-complexes. The [Fe(CN)5NO] and [Ru(NH3)5NO] complexes (affording Eno+/no values at 0.10 V) react with very similar addition rate constants, though the [Ru(bpy)(tpm)NO] ion ( no+/no = 0 35 V) showed a much lower value of fead, by 5 orders of magnitude. Figure 7 shows a plot of In fead against Eno+zno fhe three nonheme complexes. A linear trend can be appreciated, with a negative slope of 18.4 0.9 V, in close agreement with a Marcus-type behavior. The plot also includes an estimated value for Mb NO. The mechanistic interpretation for the reaction of Mb NO with O2 is controversial the observed rate constant has been... 

The recombination reaction between the oppositely charged particles is a bimolecular electron transfer reaction, and the back electron transfer rate may be described by the Marcus-type electron transfer rate [69]. 

Both HAT and PCET have been observed to obey Marcus-type kinetics. The rate constant predicted by the Marcus cross relation is dependent on the driving force of the reaction more favorable reactions typically result in more rapid kinetics. Consult [34] and [35] for details... 

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