Temperature dependence electron transfer theory

EPR studies on electron transfer systems where neighboring centers are coupled by spin-spin interactions can yield useful data for analyzing the electron transfer kinetics. In the framework of the Condon approximation, the electron transfer rate constant predicted by electron transfer theories can be expressed as the product of an electronic factor Tab by a nuclear factor that depends explicitly on temperature (258). On the one hand, since iron-sulfur clusters are spatially extended redox centers, the electronic factor strongly depends on how the various sites of the cluster are affected by the variation in the electronic structure between the oxidized and reduced forms. Theoret-... 

Coming back to aromatic anion radicals, a more accurate comparison between the experimental reaction kinetics and the predictions of the dissociative electron transfer theory revealed that the agreement is good when steric hindrance is maximal (tertiary carbon acceptors) and that the reaction is faster and faster than predicted as steric hindrance decreases, as discussed in detail in Section 3.2.2 (see, particularly, Figure 3.1). These results were interpreted as indicating an increase in the ET character of the reaction as steric hindrance increases. Similar conclusions were drawn from the temperature dependence of the kinetics, showing that the entropy of activation increases with steric hindrance, paralleling the increase in the ET character of the reaction. 

A Failure of Continuum Theory Temperature Dependence of the Solvent Reorganization Energy of Electron Transfer in Highly Polar Solvents. 

The lifetime of the MLCT excited state of [Ru(bipy)3] has been measured in several solvents and at different temperatures. Among the- conclusions drawn are that k, is only slightly solvent-dependent, that k , agrees quantitatively with predictions of energy gap law for radiationless transitions, and that the solvent dependence of kinetic parameters for MLCT —> d, dctransitions can be considered in the context of electron-transfer theory. These results may have implications for the use of [Ru(bipy)3] as sensitizer. The solvent dependence of the MLCT transitions of [Ru(bipy)3], [Os(bipy)3], [Os(bipy)2(py)2p, and [Os(bipy)2 l,2-(Ph2P)2CsH4 f has been interpreted in... 

Contrary to outer sphere electron transfer reactions, the validity of the Butler-Volmer law for ion transfer reactions is doubtful. Conway and coworkers [225] have collected data for a number of proton and ion transfer reactions and find a pronounced dependence of the transfer coefficient on temperature in all cases. These findings were supported by experiments conducted in liquid and frozen aqueous electrolytes over a large temperature range [226, 227]. On the other hand, Tsionskii et al. [228] have claimed that any apparent dependence of the transfer coefficient on temperature is caused by double layer effects, a statement which is difficult to validate because double layer corrections, in particular their temperature dependence, depend on an exact knowledge of the distribution of the electrostatic potential at the interface, which is not available experimentally. Here, computer simulations may be helpful in the future. Theoretical treatments of ion transfer reactions are few they are generally based on variants of electron transfer theory, which is surprising in view of the different nature of the elementary act [229]. 

Instead of the quantity given by Eq. (15), the quantity given by Eq. (10) was treated as the activation energy of the process in the earlier papers on the quantum mechanical theory of electron transfer reactions. This difference between the results of the quantum mechanical theory of radiationless transitions and those obtained by the methods of nonequilibrium thermodynamics has also been noted in Ref. 9. The results of the quantum mechanical theory were obtained in the harmonic oscillator model, and Eqs. (9) and (10) are valid only if the vibrations of the oscillators are classical and their frequencies are unchanged in the course of the electron transition (i.e., (o k = w[). It might seem that, in this case, the energy of the transition and the free energy of the transition are equal to each other. However, we have to remember that for the solvent, the oscillators are the effective ones and the parameters of the system Hamiltonian related to the dielectric properties of the medium depend on the temperature. Therefore, the problem of the relationship between the results obtained by the two methods mentioned above deserves to be discussed. 

In summary, to apply the Marcus theory of electron transfer, it is necessary to see if the temperature dependence of the electron transfer rate constant can be described by a function of the Arrhenius form. When this is valid, one can then determine the activation energy AEa only under this condition can we use AEa to determine if the parabolic dependence on AG/ is valid and if the reaction coordinate is defined. 

Electron transfer from the excited states of Fe(II) to the H30 f cation in aqueous solutions of H2S04 which results in the formation of Fe(III) and of H atoms has been studied by Korolev and Bazhin [36, 37]. The quantum yield of the formation of Fe(III) in 5.5 M H2S04 at 77 K has been found to be only two times smaller than at room temperature. Photo-oxidation of Fe(II) is also observed at 4.2 K. The actual very weak dependence of the efficiency of Fe(II) photo-oxidation on temperature points to the tunneling mechanism of this process [36, 37]. Bazhin and Korolev [38], have made a detailed theoretical analysis in terms of the theory of radiationless transitions of the mechanism of electron transfer from the excited ions Fe(II) to H30 1 in solutions. In this work a simple way is suggested for an a priori estimation of the maximum possible distance, RmSiX, of tunneling between a donor and an acceptor in solid matrices. This method is based on taking into account the dependence... 

A further example of the use of this technique to introduce a ferrocene redox centre to a platinum surface is given in equation (32). A comparative survey was made of the rates of heterogeneous charge transfer between the platinum electrode and ferrocene both in solution and immobilized on the surface. Both processes show an Arrhenius temperature dependence but AGact(soIii) / A( ACT(surface bound). Absolute rate theory was unsatisfactory for the surface reaction and the need to involve electron tunnelling and a specific model for the conformation of the surface was indicated.66... 

Two questions are inseparable how to optimize ion radical reactions, and how to facilitate electron transfer. As noted in the preceding chapters, electron transfers between donors and acceptors can proceed as outer-sphere or inner-sphere processes. In this connection, the routes to distinguish and regulate one and another process should be mentioned. The brief statement by Hubig, Rathore, and Kochi (1999) seems to be appropriate Outer-sphere electron transfers are characterized by (a) bimolecular rate constants that are temperature dependent and well correlated by Markus theory (b) no evidence for the formation of (discrete) encounter complexes (c) high dependence on solvent polarity (d) enhanced sensitivity to kinetic salt effects. 

Inner-sphere electron transfers are characterized by (a) temperature-independent rate constants that are greatly higher and rather poorly correlated by Marcus theory (b) weak dependence on solvent polarity (c) low sensitivity to kinetic salt effects. This type of electron transfer does not produce ion radicals as observable species but deals with the preequilibrium formation of encountered complexes with the charge-transfer (inner-sphere) nature (see also Rosokha Kochi 2001). 

Figure 5.2 Tafel plots of In k versus overpotential for a mixed self-assembled monolayer containing HS(CH2)i600C-ferrocene and HS(CH2)isCH3 in 1.0 M HCIO4 at three different temperatures V, 1 °C O/ 25 °C , 47°C. The solid lines are the predictions of the Marcus theory for a standard heterogeneous electron transfer rate constant of 1.25 s-1 at 25 °C, and a reorganization energy of 0.85 eV (= 54.8 kj moh1). Reprinted with permission from C. E. D Chidsey, Free energy and temperature dependence of electron transfer at the metal-electrolyte interface, Science, 251, 919-922 (1991). Copyright (1991) American Association for the Advancement of Science...

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