Activation free energy intrinsic barrier

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... 

Figure 14. Dependence of the Rehm-Weller free energy relationship on the intrinsic barrier AG. Key left, activation free energy change and right, transfer...

AGq is the standard activation free energy, also termed the intrinsic barrier, which may be defined as the common value of the forward and backward activation free energies when the driving force is zero (i.e., when the electrode potential equals the standard potential of the A/B couple). Expression of the forward and backward rate constants ensues ... 

The E° difference is a necessary but not a sufficient condition. The rate constant for either ET (in general, / et) may be described in a simple way by equation (4). The activation free energy AG is usually expressed as a quadratic function of AG°, no matter whether we deal with an outer-sphere ET or a dissociative ET. However, even if the condition (AG")c < (AG°)sj holds (hereafter, subscripts C and ST will be used to denote the parameters for the concerted and stepwise ETs, respectively), the kinetic requirements (intrinsic barriers and pre-exponential factors) of the two ETs have to be taken into account. While AGq depends only slightly on the ET mechanism, is dependent on it to a large extent. For a concerted dissociative ET, the Saveant model leads to AG j % BDE/4. Thus, (AGy )c is significantly larger than (AG )sj no matter how significant AGy, is in (AG( )gj (see, in particular. Section 4). In fact, within typical dissociative-type systems such as... 

Equation (7) expresses an important distinction between the activation free energy for the overall electrochemical reaction in the absence of a net driving force, AG 0, and the intrinsic barrier for the electron-transfer step, AG, t. The former is most directly related to the experimental standard rate constant, whereas the latter is of more fundamental significance from a theoretical standpoint (vide infra). It is therefore desirable to provide reasonable estimates of wp and ws so that the experimental kinetics can be related directly to the energetics of the electron-transfer step. 

One application of PI-QTST to PT has been to study a model A-H-A PT solute in a polar solvent [77]. This computational study provided a detailed examination of the specific features of PT, including the competition between proton tunneling and solvent activation, the influence from intramolecular vibrational modulation of the PT barrier, and the role of electronic polarizability of both the solute and the solvent. Changes in the total quantum activation free energy, and hence the reaction probability, due to these different effects were calculated (cf. Fig. 18). By virtue of these studies, it was found that to fully understand the rate of a given PT reaction, one must deal with a number of complex, nonlinear interactions. Examples of such interactions include the nonlinear dependence of the solute dipole on the position of the proton, the coupling of the solute dipole to both the proton coordinate and to other vibrational modes, and the intrinsically nonlinear interactions arising from both solute and solvent polarizability effects. Perhaps the most important conclusion... 

Hemicarceplexes are stabilized by intrinsic and constrictive binding energy. The latter, a physical barrier, is the activation free energy required for a guest to enter the inner cavity and typically amounts to 25-30kcalmol In carceplexes, this barrier is so high that guest escape is impossible without host destraction. Isolated from the bulk phase, the... 

For the identity reactions, the intrinsic barriers are their free energies of activation, which can be determined by tracer studies or less directly by rate-equilibrium correlations. ... 

In Eq. (7-21), AGo is the intrinsic barrier, the free energy of activation of the (hypothetical) member of the reaction series having AG" = 0. It is evident that the Marcus equation predicts a nonlinear free energy relationship, although if a limited... 

An intrinsic free energy of activation, which would exist if the reactants and products had the same AG° This is a kinetic part, called the intrinsic barrier AG ,... 

Alternatively one can make use of No Barrier Theory (NBT), which allows calculation of the free energy of activation for such reactions with no need for an empirical intrinsic barrier. This approach treats a real chemical reaction as a result of several simple processes for each of which the energy would be a quadratic function of a suitable reaction coordinate. This allows interpolation of the reaction hypersurface a search for the lowest saddle point gives the free energy of activation. This method has been applied to enolate formation, ketene hydration, carbonyl hydration, decarboxylation, and the addition of water to carbocations. ... 

Each of these free energy relationships employs the intrinsic barrier AGo+ as the disposable parameter. [The intrinsic barrier represents the activation energy for electron transfer when the driving force is zero, i.e., AG = AGo at AG = 0 or the equili-... 

Overall, steric and electronic factors, which are seen to be small, are found to work in opposite directions and, to some degree, cancel each other out. Consequently, the intrinsic free activation barriers and reaction free energies (AG nt, AG nt), respectively, span a small range for catalysts I-IV and differ by less than l.Okcalmol-1. Thus, oxidative coupling represents the one process (beside allylic isomerization, cf. Section 5.3) among all the critical elementary steps of the C8-cyclodimer channel, that is least influenced by electronic and steric factors. 

Using the values of E°roor/rovro- determined from thermochemical cycles or convolution analysis, the log fchom can be plotted as a function of the reaction free energy shown in Figs 8 and 9. The data convincingly illustrate the parabolic nature of the expected quadratic-activation driving force relationship and thus equation (7). Because of the low BDE(O-O), and thus low intrinsic barrier, the parabolic nature is much more apparent in these systems than in others that undergo dissociative ET. 

---