Activation free energy directed

Figure A3.8.3 Quantum activation free energy curves calculated for the model A-H-A proton transfer reaction described 45. The frill line is for the classical limit of the proton transfer solute in isolation, while the other curves are for different fully quantized cases. The rigid curves were calculated by keeping the A-A distance fixed. An important feature here is the direct effect of the solvent activation process on both the solvated rigid and flexible solute curves. Another feature is the effect of a fluctuating A-A distance which both lowers the activation free energy and reduces the influence of the solvent. The latter feature enliances the rate by a factor of 20 over the rigid case.

The experimental kinetic data obtained with the butyl halides in DMF are shown in Fig. 13 in the form of a plot of the activation free energy, AG, against the standard potential of the aromatic anion radicals, Ep/Q. The electrochemical data are displayed in the same diagrams in the form of values of the free energies of activation at the cyclic voltammetry peak potential, E, for a 0.1 V s scan rate. Additional data have been recently obtained by pulse radiolysis for n-butyl iodide in the same solvent (Grim-shaw et al., 1988) that complete nicely the data obtained by indirect electrochemistry. In the latter case, indeed, the upper limit of obtainable rate constants was 10 m s", beyond which the overlap between the mediator wave and the direct reduction wave of n-BuI is too strong for a meaningful measurement to be carried out. This is about the lower limit of measurable... 

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. 

Moreover, from the data in Table 2 it is possible to estimate the fi ee energy of activation of the reaction studied. In order to do this we must assume, above all, that the optical electron transfer, to which the band correspond, is the same as the themud electron transfer, to which the k values correspond. However, the data in Table 3 cannot be used directly for estimating the activation free energy of the thermal electron transfer reaction. The first obvious reason comes from the fact that the band corresponds to the (Co(NH3)4(pzC02)] -[Ru(CN) ion-pair instead of to the [Co(NH3)4(pzC02)] -[Fe(CN) J "... 

The relation shown here suggests that a measure of the intrinsic rate of a reaction, corrected for its driving force, is given by AF = AF — 0.5 AF°. This amounts to taking the average AF for the reaction in the forward and reverse directions. Under conditions where Marcus relation ki2 = ( 11 12 12/) (42) is applicable, AF = (AF ii-f AF 22 — RT In /). Values for these intrinsic activation free energies are given in Table III. This table shows some patterns of relative reactivity as well as some apparent anomalies. For example, the relative intrinsic... 

The reactivity indices method is based on the assumption of a direct correlation between the activation free energy of a process and some intrinsic parameters, called reactivity indices, related to the electronic properties of the heteroaromatic species involved in the process itself. Some indices, such as charge density, frontier electron density, polarizability, or free valence, pertain to electronic properties of the unperturbed neutral substrate, which is considered in an isolated state. Other indices, such as the localization energy, are related to the stability of the transitional or intermediate state of the substitution process, e.g., the n or a complex in electrophilic substitution reactions (Fig. 1). 

Abraham et al., who add an extra term to Equation 19 to allow for direct dipolar interactions between solvent and solute (17). This term is small for solvents of low dielectric constant but becomes significant for those having b> 10. The theory, thus modified, seems to give fairly satisfactory descriptions of polar effects on conformational equilibria (18), free energies of transfer of ion-pairs (19), and activation free energies of reactions . 

Of more direct interest to kineticists is a reconsideration by Marcus and Sutin of the basis for the well known equation (1) relating activation free energies AG to... 

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