Marcus reorganization energy

Length of the bridge containing adenine-cytosine base pairs only Lowest unoccupied molecular orbital Marcus reorganization energy Mass of the tunneling particle... 

Moreover, the plot of the corresponding a(E) variations in Fig. 16b shows that a depends linearly on the potential with a slope (0.249 V ), in close agreement with that predicted (0.210 V ) from the Marcus reorganization energy (29kcal/mol) determined from Eq. (107). 

Andres, G. O., Martinez Junza, V., Crovetto, L., Braslavsky, S. E., Photoinduced Electron Transfer from Tetrasulfonated Porphyrin to Benzoquinone Revisited. The Structural Volume normalized Entropy Change Correlates with Marcus Reorganization Energy, J. Phys. Chem. A 2006, 110, 10185 10190. 

Here X is tire reorganization energy associated witli the curvature of tire reactant and product free energy wells and tlieir displacement witli respect to one another. Assuming a stmctureless polarizable medium, Marcus computed the solvent or outer-sphere component of tire reorganization energy to be... 

Fig. 12. Marcus model of two harmonic terms in the limit of strong coupling. Reorganization energy E, is shown.

Marcus theory. Consider that the reorganization energy for the ET reaction, AAb, can be approximated as the mean of the reorganization energies for the EE reactions Aab = (Aaa + ABb)/2. Show that substitution of this expression into Eq. (10-63) gives the usual form of the Marcus cross relation. 

In subsequent works, Marcus developed his theory further in a series of papers providing expressions for the work terms, the reorganization energy and the macroscopic ET rate constants [3 6]. Assuming a sharp liquid-liquid boundary, the solution of the mean molar volume of reactants yields an expression for of the form... 

The flat interface model employed by Marcus does not seem to be in agreement with the rough picture obtained from molecular dynamics simulations [19,21,64-66]. Benjamin examined the main assumptions of work terms [Eq. (19)] and the reorganization energy [Eq. (18)] by MD simulations of the water-DCE junction [8,19]. It was found that the electric field induced by both liquids underestimates the effect of water molecules and overestimates the effect of DCE molecules in the case of the continuum approach. However, the total field as a function of the charge of the reactants is consistent in both analyses. In conclusion, the continuum model remains as a good approximation despite the crude description of the liquid-liquid boundary. 

According to the Marcus theory [9], the electron transfer rate depends upon the reaction enthalpy (AG), the electronic coupling (V) and the reorganization energy (A). By changing the electron donor and the bridge we measured the influence of these parameters on the charge transfer rate. The re-... 

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. 

The value of E° was hence determined by the reaction of R4M with Fe3+ complexes as outer-sphere SET oxidizers. Using five complexes with a range of different E° values, from 1.15 to 1.42 V, the rate constants were determined193. This was followed up by Eberson who, by application of the Marcus theory, was able to determine from the E° values (shown in Table 18) standard potentials and reorganization energies. Most compounds... 

Electron mediators successfully used with oxidases include 2,6-dichlorophenolindophol, hexacyanoferrate-(III), tetrathiafulvalene, tetracyano-p-quinodimethane, various quinones and ferrocene derivatices. From Marcus theory it is evident that for long-range electron transfer the reorganization energies of the redox compound have to be low. Additionally, the redox potential of the mediator should be about 0 to 100 mV vs. standard calomel electrode (SCE) for a flavoprotein (formal potential of glucose oxidase is about -450 mV vs SCE) in order to attain rapid vectrial electron transfer from the active site of the enzyme to the oxidized form of the redox species. 

In most cases, when the driving force is lower than the reorganization energy, the electron transfer rate increases when the driving force AG0 is increased. There is, however, the so-called Marcus inversion region (—AG0>A), such that the larger the driving force, the lower the electron transfer rate. 

The reorganization energy of a self-exchange reaction is denoted A(0) (from the fact that AG° = 0) and is an important quantity in the Marcus theory, where it can be shown that the activation free energy of a self-exchange reaction, AG(0), is equal to X.(0)/4. It is also possible to measure rate constants of self-exchange processes experimentally and thus get access to (0) via this relationship. 

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