Kinetics Marcus model

This equation, based on the Marcus model, therefore gives us a relationship between the kinetics (kEr) and the thermodynamic driving force (AG°) of the electron-transfer process. Analysis of the equation predicts that one of three distinct kinetic regions will exist, as shown in Figure 6.24, depending on the driving force of the process. 

Figure 17.6 Free energy curves for reactant and product states of an electron transfer process in the kinetic regimes of the Marcus model.

There are two major concepts involved in the physico-chemical description of a chemical reaction the energetics, which determines the feasibility of the reaction, and the kinetics which determines its rate. In general these two concepts are independent and the rate of a chemical reaction can be varied according to the mechanism (e.g. catalysis) but within certain assumptions there is a mathematical relationship between the rate constant and the reaction free energy difference. These relationships are either linear (linear free energy relationship, LFE) or quadratic (QFE), the latter being often referred to as the Marcus model — a description which should not hide the important contributions of other workers in this field [1],... 

Computer simulations have provided further insight into the model of random fluctuations as a prerequisite for e.t. in polar solvents [60], It has been shown that spontaneous local polarity fluctuations of the magnitude envisaged by the Marcus model are so improbable as to be statistically insignificant and it was necessary to assume that the solvent could adjust continuously in order to follow the position of the electron in the course of e.t., as if e.t. would be slow enough to be the rate-determining kinetic step. To what extent such a modification of the model... 

Application of Marcus rate theory to proton transfer in enzyme-catalyzed reactions was discussed by Kresge and Silverman, 1999. Relationships of log KIE and kinetics of the enzyme catalysis (kcat) and parameters of the reaction driving force were found to be in agreement with the Marcus model. 

This equation based on Marcus model gives the relation between the kinetics (ATet) and thermodynamic driving force (AG ) of PET process. Analysis of this equation gives three distinct kinetic regions, as shown in Fig. 6.20, depending on AG°. 

One of the leading preoccupations of this book is that the development of ultrafast techniques in reaction kinetics, and of the Marcus model for elementary-reaction mechanisms, coupled with computerised molecular dynamics, have the capacity to transform our view of what can be expected in our understanding of what goes on in chemical reactions. These are landmark achievements, and their success depends on studies of fast reactions. Their claims to a special place in mechanistic chemistry may be outlined as follows. 

Temperature dependence data were analyzed using a form of the Marcus model [68, 74, 75] that simultaneously takes into account the temperature dependence of the Gibbs free energy of the reaction, AG°. This modified form of the model allowed determination of accurate values for the reorganization energies for ET and CPET, Aet and Acpet, respectively. When the traditional adiabatic Marcus model was used, values of 29.7 and 48.2 kcal moP were calculated for Aet and Acpet, respectively, which implied that CPET is far less kinetically accessible. When the temperature dependence of AG° was accounted for, however, values of 41.5 and 52.4 kcal moP were obtained for Aet and Acpet, respectively, which corresponds to less dramatic difference in reorganization energies for the two pathways. 

Marcus AH. 1985a. Multicompartment kinetic models for lead I. Bone diffusion models for long-term retention. Environ Res 36 442-458. 

Marcus AH. 1985b. Multicompartment kinetic models for lead II. Linear kinetics and variable absorption in humans without excessive lead exposure. Environ Res 36 459-472. 

Marcus AH. 1985c. Multicompartment kinetic models for lead III. Lead in blood plasma and erythrocytes. Environ Res 36 473-489. 

There are three points of significance of this result. One is that it provides strong support for the 10-step mechanism originally proposed for reaction 1. Another is that it facilitates a more robust fitting of the mechanism to the kinetic data obtained for that reaction. Thirdly, it confirms that reaction 2 has a rate constant that is four orders of magnitude greater than predicted by Marcus theory. It is concluded that reaction 2 is poorly modeled as an outer-sphere process and is better described as... 

When electron transfer is forced to take place at a large distance from the electrode by means of an appropriate spacer, the reaction quickly falls within the nonadiabatic limit. H is then a strongly decreasing function of distance. Several models predict an exponential decrease of H with distance with a coefficient on the order of 1 A-1.39 The version of the Marcus-Hush model presented so far is simplified in the sense that it assumed that only the electronic states of the electrode of energy close or equal to the Fermi level are involved in the reaction.31 What are the changes in the model predictions brought about by taking into account that all electrode electronic states are actually involved is the question that is examined now. The kinetics... 

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