Free energy of reorganization

Similar to homogeneous electron-transfer processes, one can consider the observed electrochemical rate constant, k, , to be related to the electrochemical free energy of reorganization for the elementary electron-transfer step, AG, by... 

The estimates given above lead to the true value of real activation energy A = E - FiF - EnCoul kcal for n. In accordance with (7.9a), the corresponding value of standard free energy of reorganization AG is 18 kcal. 

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... 

Because the rates of chemical reactions are controlled by the free energy of the transition state, information about the stmcture of transition states is crucial to understanding reaction mechanism. However, because transition states have only transitory existence, it is not possible to make experimental measurements that provide direct information about their structure.. Hammond has discussed the circumstances under which it is valid to relate transition-state stmcture to the stmcture of reactants, intermediates, and products. His statements concerning transition-state stmcture are known as Hammond s postulate. Discussing individual steps in a reaction mechanism, Hammond s postulate states if two states, as, for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have neariy the same energy content, their interconversion will involve only a small reorganization of molecular stmcture. ... 

From a comparison of Eqs. (9) and (22) we see that H = F(0 ). To elucidate the physical meaning of the exponent in Eq. (22), we consider first the case when 0 = 1 (barrierless reaction). In this case Eq. (20) determines the change of the free energy of the system F(l) when it is polarized by the electric field AEU = E -E (only the free energy related to the inertial polarization is considered). It may be easily seen that the absolute value of F(l) is equal to the energy of the reorganization of the medium Es (>0). 

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... 

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. 

Since it has been shown that nonideal mixing occurs in the 2.5-15.0 dyn cm 1 range, the excess free energies of interaction were calculated for compressions of each pure component and their mixtures to each of these surface pressures. In addition, these surface pressures are below the ESPs and/or monolayer stability limits so that dynamic processes arising from reorganization, relaxation, or film loss do not contribute significantly to the work of compression. 

The forward and backward activation free energies and the corresponding rate constants thus depend on an extrinsic factor, the standard free energy of the reaction, AG° = E — E°, and an intrinsic factor, the standard activation free energy, that reflects the solvent and internal reorganization energy, Aq and A [equation (1.31)]. 

So far, only the nuclear reorganization energy attending electron transfer has been discussed, yielding the expressions above of the free energy of activation in the framework of classical transition state theory. A second series of important factors are those that govern the preexponential factor, k, raising in particular the question of the adiabaticity or nonadiabaticity of electron transfer between a molecule and the electronic states in the electrode. 

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. 

The Marcus classical free energy of activation is AG , the adiabatic preexponential factor A may be taken from Eyring s Transition State Theory as (kg T /h), and Kel is a dimensionless transmission coefficient (0 < k l < 1) which includes the entire efiFect of electronic interactions between the donor and acceptor, and which becomes crucial at long range. With Kel set to unity the rate expression has only nuclear factors and in particular the inner sphere and outer sphere reorganization energies mentioned in the introduction are dominant parameters controlling AG and hence the rate. It is assumed here that the rate constant may be taken as a unimolecular rate constant, and if needed the associated bimolecular rate constant may be constructed by incorporation of diffusional processes as ... 

Reorganization Energy 2, (Continuum) and the Free Energy of Activation... 

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