Inner activation barrier

The change in the inner-sphere structure of the reacting partners usually leads to a decrease in the transition probability. If the intramolecular degrees of freedom behave classically, their reorganization results in an increase in the activation barrier. In the simplest case where the intramolecular vibrations are described as harmonic oscillators with unchanged frequencies, this leads to an increase in the reorganization energy ... 

In the context of the Marcus formulation, the lowering of the activation barrier in an inner-sphere process could arise from the reduction of the work term wp as a result of the strong interaction in the ionic products, e.g., [RitSn+ IrCU3 ] and [RitSn+TCNE ]. The electrostatic potential in such an ion pair is attractive and may cause the tetraalkyltin to achieve a quasi five-coordinate configuration in the precursor complex, reminiscent of a variety of trigonal bipyramidal structures already well-known for tin(IV) derivatives, i.e.,... 

J.K. Kochi I agree. The quantitative treatment of inner-sphere mechanisms is difficult from a purely theoretical point of view. The phenomemological approach describes the activation barrier for inner-sphere process quantitatively, but provides no theoretical basis, unfortunately. 

If ligands are involved in the formation of discrete intermediates or if metal ions become ligand-bridged, the process is designated as inner-sphere (IS) electron transfer [52]. In these cases, the electronic interaction between the redox centers is increased substantially, and leads to a lowering of the activation barrier (and hence to increased rates) for the ET reaction [13, 15, 53],... 

The crucial point is that the difference of potential available to effect electrode reactions and surmount activation barriers is not simply the difference between the Galvani potential (i.e. the Fermi energy) and the potential in solution. On the side of the solid it is the Volta potential and on the side of the solution it is the potential at the inner Helmholtz plane, where species have to reach to in order for electron transfer to be possible. Corrections to rate constants for the latter are commonly carried out using the Gouy-Chapman model of the electrolyte double layer and will be described in Section 6.9. 

Experimental estimates of <5r/c , are relatively difficult to obtain. While they can, in principle, be extracted from temperature-dependence studies, this approach is complicated by uncertainties in the entropic term (Sect. 4.3). An alternative method has recently been described for some Cr(III) reductions which involves comparing the work-corrected rate constants, kco , with unimolecular rate constants, ket, for structurally related reactants that reduce via ligand-bridged pathways [30]. Provided that the corresponding outer- and inner-sphere pathways involve the same activation barrier (Sect. 4.6) and the latter also follow adiabatic pathways, we can write [30]... 

Kakiuchi [130] integrated the Nernst-Planck equation by assuming a constant gradient of the electrochemical potential in the inner layer at the ITIES. This layer was not supposed to be necessarily the same entity as the ion-free inner layer at the interface (Sec. 2.3.2). In the absence of an activation barrier at the interface, the... 

Fig. 1 Conceptual energy landscapes for bound states c confined by sharp activation barriers. Oriented at an angle 9 to the molecular coordinate x, external force / adds a mechanical potential — (/cos 6)x that tilts the landscape and lowers the barrier. For sharp barriers, the energy contours local to barriers—transition states s —are highly curved and change little in shape or location under force, (a) A single barrier under force, (b) A cascade of barriers under force. The inner barrier emerges to dominate kinetics when the outer barrier is driven below it by k T.

The inner and outer sphere reorganization energies for this reaction are 50.7 and 27.7kJmol , respectively. This gives a value of equal to 314kJmol . The lowering of the activation barrier due to interaction of the energy profiles... 

The reactants first have to be brought to reaction distance, as shown in Figure I7.I0 this requires a work term associated with the lost translational and rotational free ener gy involved in bringing the two reactants together. It also involves a change in the electrostatics as the distance between the two species moves from infinity to the reaction distance. This first term is given the abbreviation AG ( in Equation (17.43). Once the two coordination compounds are at reaction distance, there is still an activation barrier associated with the formation of the precursor complex, as shown in Figure I7.I0. This barrier involves both inner-sphere (AG ) and outer-sphere (AG-g) components. 

Kragten et al.I carried out DFT calculations to determine the reaction energies and the activation barriers for a sequence of elementary steps that make up both the inner- and outer-sphere mechanisms. The effects of solution are included via the explicit introduction of one or two acetic acid molecules along with an overall reaction field. The solute is modeled by a cluster in which the charge is balanced by the coordination of protons to... 

Figure 6.20. Energy diagram of the inner- and outer-sphere mechanisms, including solvent effects. Activation barriers are indicated by the small arcs a barrier as low as the reaction energy is designated by no act. The structure number refers to models shown in Pig.

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