Electron-transfer reaction activation energy

Static dielectric constant Electron transfer Reaction free energy Activation free energy Activation enthalpy Electronic coupling matrix element... 

Within this framework, by considering the physical situation of the electrode double layer, the free energy of activation of an electron transfer reaction can be identified with the reorganization energy of the solvation sheath around the ion. This idea will be carried through in detail for the simple case of the strongly solvated... 

In our simple model, the expression in A2.4.135 corresponds to the activation energy for a redox process in which only the interaction between the central ion and the ligands in the primary solvation shell is considered, and this only in the fonn of the totally synnnetrical vibration. In reality, the rate of the electron transfer reaction is also infiuenced by the motion of molecules in the outer solvation shell, as well as by other... 

This section contains a brief review of the molecular version of Marcus theory, as developed by Warshel [81]. The free energy surface for an electron transfer reaction is shown schematically in Eigure 1, where R represents the reactants and A, P represents the products D and A , and the reaction coordinate X is the degree of polarization of the solvent. The subscript o for R and P denotes the equilibrium values of R and P, while P is the Eranck-Condon state on the P-surface. The activation free energy, AG, can be calculated from Marcus theory by Eq. (4). This relation is based on the assumption that the free energy is a parabolic function of the polarization coordinate. Eor self-exchange transfer reactions, we need only X to calculate AG, because AG° = 0. Moreover, we can write... 

Use die activated complex theory for explaining clearly how the applied potential affects the rate constant of an electron-transfer reaction. Draw free energy curves and use proper equations for your explanation. 

As demonstrated in Section 2.2, the energy of activation of simple electron transfer reactions is determined by the energy of reorganization of the solvent, which is typically about 0.5-1 eV. Thus, these reactions are typically much faster than bondbreaking reactions, and do not require catalysis by a J-band. However, before considering the catalysis of bond breaking in detail, it is instructive to apply the ideas of the preceding section to simple electron transfer, and see what effects the abandomnent of the wide band approximation has. 

The expression in Eq. (10) for the exponent in Eq. (9) is quite similar to that for the activation free energy in electron transfer reactions derived by Marcus using the methods of nonequilibrium classical thermodynamics8 ... 

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. 

FIGURE 6.6 Potential energy diagram for the theory of electron transfer reactions. The activated complex is at S. For reasonably fast reactions, the reactant adheres to the lower curve and slithers into the product curve through the activated complex—that is, an adiabatic electron transfer occurs. 

As with the Marcus-Hush model of outer-sphere electron transfers, the activation free energy, AG, is a quadratic function of the free energy of the reaction, AG°, as depicted by equation (7), where the intrinsic barrier free energy (equation 8) is the sum of two contributions. One involves the solvent reorganization free energy, 2q, as in the Marcus-Hush model of outer-sphere electron transfer. The other, which represents the contribution of bond breaking, is one-fourth of the bond dissociation energy (BDE). This approach is... 

Our problem now is to determine the functional form of this experimental free energy curve for the intrinsic rate constant ki for electron transfer. In addition to the Marcus eq 4, two other relationships are currently in use to relate the activation free energy to the free energy change in electron transfer reactions (15, JL6). 

Cyclic chain termination with aromatic amines also occurs in the oxidation of tertiary aliphatic amines (see Table 16.1). To explain this fact, a mechanism of the conversion of the aminyl radical into AmH involving the (3-C—H bonds was suggested [30]. However, its realization is hampered because this reaction due to high triplet repulsion should have high activation energy and low rate constant. Since tertiary amines have low ionization potentials and readily participate in electron transfer reactions, the cyclic mechanism in systems of this type is realized apparently as a sequence of such reactions, similar to that occurring in the systems containing transition metal complexes (see below). 

The molecular models of electron transfer reactions are in general much more complicated and do not generate the simple relations of the free energy of activation as in the continuum theory. However, it is important to focus on alternative molecular models at this time because of the fundamental flaws of continuum theory and its inconsistencies with experiments, as pointed out earlier. 

---