Intrinsic free energy activation

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 ,... 

Intrinsic free energy of activation for homogeneous self-exchange, obtained from values of corr giVen in Table 1 using AGih = "RT ln(kcorr/Zh) where 2 x 1()11, -1 ... 

An intrinsic free energy of activation, which would exist if the reactants... 

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... 

To further substautiate these insights for the ORR mechanism, Wang and co-workers analyzed the four-electron ORR in acidic media using an intrinsic kinetic equation with the free energies of activation and adsorption as the kinetic parameters [Wang JX et al., 2007]. The kinetic model consisted of four essential elementary reactions ... 

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. ... 

Figure 14-4. Intrinsic reaction coordinate for the transesterification of the dinucleotide model with B3LYP and M06-2X functionals. Relative free energies of reaction and activation are provided in kcal/mol...

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). 

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-... 

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

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. 

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 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)]. 

Twice the intrinsic electrochemical free energy of activation, obtained from value of ks... 

Valuable information on mechanisms has been obtained from data on solvent exchange (4.4).The rate law, one of the most used mechanistic tools, is not useful in this instance, unfortunately, since the concentration of one of the reactants, the solvent, is invariant. Sometimes the exchange can be examined in a neutral solvent, although this is difficult to find. The reactants and products are however identical in (4.4), there is no free energy of reaction to overcome, and the activation parameters have been used exclusively, with great effect, to assign mechanism. This applies particularly to volumes of activation, since solvation differences are approximately zero and the observed volume of activation can be equated with the intrinsic one (Sec. 2.3.3). 

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