Marcus theory prediction

Figure 6.24 Marcus theory predictions of the dependence of the electron-transfer rate on the thermodynamic driving force...

For this simple case, Marcus theory predicts the rate constant for electron transfer to be... 

The use of the energy-gap reaction coordinate allows us to calculate solvent reorganization energies in a way analogous to that in the Marcus theory for electron transfer reactions.19 The major difference here is that the diabatic states for electron transfer reactions are well-defined, whereas for chemical reactions, the definition of the effective diabatic states is not straightforward. The Marcus theory predicts that... 

Thus, classical Marcus theory predicts an electron transfer rate that has a Gaussian dependence on the free energy of the reaction (Marcus, 1956 Marcus and Sutin, 1985). 

FIGURE 3. Marcus theory predicts a Gaussian dependence of the electron transfer rate ket on free energy AG, which appears as a parabolic dependence on a log plot. The maximum rate is found when the driving force matches the reorganization energy, AG = fiX. 

The Marcus theory predicts that the k, values should increase up to a maximum and then decrease with increasing the oxidation potentials of D, or with decreasing the reduction potentials of A [19], The region where k, decreases with increasing the AG values is called the Marcus inverted region . The bell-shaped curve a in Fig. 2 illustrates this theory. 

The activation free energy AG is dehned by two terms. One term is the reaction free energy [AG ], which is derived from the redox potential difference of the donor and acceptor. The second term is the medium reorganization energy (k), which is the energy stored in the solvent inertial degrees of freedom when the electron is shifted suddenly from donor to acceptor (1-5). Marcus theory predicts the activation free energy ... 

The theoretical ket values were nearly two orders smaller than those experimentally obtained. This may be attributed to disregarding the internal vibration and/or the nuclear tunneling effect. An estimation of the former effect by Sumi-Marcus theory predicts one-two orders increase in the rate with conserving the relative difference in the rates in different solvents. 

At equilibrium, that is, the Marcus theory predicts that the activation... 

Since photoinitiation occurs in specific monomeric mixtures, as Marcus theory predicts, the properties of the to-be-photopolymerized mixture (polarity, viscosity, electron-donating or electron-accepting properties) may play an important role in the overall efficiency of the process. Considering this, the monomer can participate in the photoinduced electron transfer process, either as a light-absorbing chromophore, as a hydrogen atom source, or as an electron donor/electron acceptor. 

Marcus theory predicts that the nuclear factor in the electron transfer rate expression will be maximal when - AG° = X. Under these conditions, the electron transfer process will be temperature independent. The first two electron transfer steps in the RC approximately exhibit this behavior. The rate of the D 4>a step actually increases slightly (by a factor of 2-4) as the temperature decreases from 300 to 8 K (180). Consequently, X may be estimated to be in the range 0.3 to 0.5 V (—7-10 kcal/mol) from the A ° values for these two steps (Table IV). These values are approximately 4 times smaller than those observed for ruthenated proteins discussed previously. Sequestration of the redox groups in a membrane-bound protein complex, away from aqueous solution, may serve to decrease the value of X by minimizing the reorganization energy of a highly polar solvent. 

Modem electron transfer theory has its conceptual origins in activated complex theory, and in theories of nonradiative decay. The analysis by Marcus in the 1950s provided quantitative connections between the solvent characteristics and the key parameters controlling the rate of ET. The Marcus theory predicts an adiabatic bimolecular ET rate as... 

Roberts et al. (1982) concluded that the multistep mechanism involving an electron transfer process can be excluded, considering of the a-value of a Br nsted plot (a=0.5) observed over a wide range of cationic substrates, which agrees with the Marcus theory for atom transfer. The Br nsted a for an atom or group transfer depends on the position of a substituent and the tightness of the transition state (t) as well as on the resemblence of the transition state to reactants and/or products. The Marcus theory predicts that t can be related to the rates of symmetrical reactions. Rates and equilibrium constants were measured for the reactions of 10-methylacridane with a series of 1-benzyl-3-cyanopyridinium ions substituted in the... 

Kolasinski KW, Gogola JW, Barclay WB (2012) A test of Marcus theory predictions for electroless etching of silicon. J Phys Chem C 116 21472-21481 Lehmann V (2002) Electrochemistry of silicon instrumentation, science, materials and applications. Wiley-VCH, Weinheim... 

Me2-4,4 -bipy ) have been used to evaluate the rate constant for inter-molecular reaction transfer within the ion pair. Use of a thermochemical cycle has provided a value for the rate of the overall reaction [Fe(CN)6] + PQ " (k2 0.2 X 10" M s ), which compares well with Marcus theory predictions. It is suggested that data on electron transfer processes may be derived from analysis of charge transfer absorption band characteristics. 

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