Transition self-exchange reactions

Because of the short timescale for the optical transition, solvent dipole orientations in the initially formed excited state are the same as in the ground state and there is no entropic change. For a self-exchange reaction, the contribution to AG is A0/4 as noted above. 

Using V = 100 cm-1 (0.012 eV) and X = 1 eV, which are reasonable parameters for a moderately rapid self-exchange reaction, t = l/ve = 6x 10 I4s (0.06ps). vet was calculated using the preexponential term in equation (30). This calculation suggests that for reactions at room temperature which are dominated by transitions near the intersection region, re < rn and the assumption that re xn is not justified. 

For the latter reason atom or group transfer may sometimes also take place in outer-sphere processes, and it has even been suggested that atom transfer can be part of an outer-sphere mechanism, if only for the case of hydrogen atom transfer. Such a case is the Fe(II)—Fe(III) self-exchange reaction in water where hydrogen bonding between two ligands in the transition state [2] would... 

It was recently shown (Ratner and Levine, 1980) that the Marcus cross-relation (62) can be derived rigorously for the case that / = 1 by a thermodynamic treatment without postulating any microscopic model of the activation process. The only assumptions made were (1) the activation process for each species is independent of its reaction partner, and (2) the activated states of the participating species (A, [A-], B and [B ]+) are the same for the self-exchange reactions and for the cross reaction. Note that the following assumptions need not be made (3) applicability of the Franck-Condon principle, (4) validity of the transition-state theory, (5) parabolic potential energy curves, (6) solvent as a dielectric continuum and (7) electron transfer is... 

Figure 1. Potential energy as a function of reaction coordinate for a self-exchange reaction. AE, energy barrier for thermal electron transfer (weak coupling) AE2, energy of an intervalence transition which is possible for the system.

Cyano metal complexes undergo a variety of oxidation-reduction reactions. One of the most studied is the fast self-exchange reaction of the [Fe(CN)4] /" anions information from this research was instrumental in establishing the outer-sphere mechanism (see Outer-sphere Reaction) for transition metal oxidation-reduction reactions (see Electrochemistry Applications in Inorganic Chemistry). The nature... 

A high-pressure probe in combination with a NMR instrument was used recently in a study of self-exchange reactions for several cyanometalate complexes, Os(CN)6 -/Os(CN)6 -, Mo(CN)g3-/Mo(CN)8 , and W(CN)8 7W(CN)8 - [57]. The rate constant /cexch was found to be strongly influenced by added cations. Moreover, the values of AV were inconsistent with Marcus theory. It was concluded that partially desolvated cations (Li+, Na+, K+, etc.) bridge the reacting anions in the transition state. 

CH3+ + Y is lowest have the lowest AE0 for the self-exchange reaction. No obvious theoretical reason exists to believe that such a correlation should be found, but the evidence that it exists is unequivocal. The suggestion is strong, then, that at least for these reactions the transition state may have some substantial charge-separated character. The resemblance to the corresponding proton-transfer processes becomes even more intriguing. 

In some of the simplest cases (namely, solvent exchange and self-exchange reactions), the experimental data could be supported by theoretical calculations. Significant developments are expected to occur in this area, such that the theoretical optimization of transition state structures will become standard practice in mechanistic studies. Here again volume of activation data will play a crucial role, since they present an experimental measure of the intrinsic and solvational volume changes in the transition state and form a basis for comparison with theoretical predictions. It will be an ideal situation when volume profiles can be constructed for more complex reaction sequences, for instance for catalytic cycles in enzymatic processes. This will, as in the case of more simple reactions, enhance our understanding of complex chemical processes and improve our ability to tune them. 

For simple outer-sphere self-exchange reactions of transition-metal complexes in both aqueous and polar organic solvents, is dominated by AVj and hence is expected to be negative, regardless of whether electron transfer is fully adiabatic. In cases in which this expectation is not realized, there is usually an identifiable departure from a simple outer-sphere mechanism attributable to inner-sphere pathways, cationic catalysis of anion-anion electron transfer, or structural distortions associated with spin multiplicity changes. Thus, AV can serve as a mechanistic criterion. 

The examples presented in this chapter clearly demonstrate that electron transfer reactions exhibit a characteristic pressure dependence that can be employed to gain further insight into the mechanism of the electron transfer process. The pressure dependence of self-exchange reactions can be used to develop the theoretical interpretation of the observed volumes of activation because the overall reactions involve no net volume change. In the case of nonsymmetrical reactions, the volume profile treatment can reveal information regarding the reorganization involved in going from the reactant to the transition and product... 

An additional contribution to equation 23), Rln gl/gs), arises from any difference in the spatial degeneracy of the ground and transition state for a self-exchange reaction this contributes aboutO.6 J M L Differences in the densities of vibrational states will also contribute in cross electron-transfer reactions. The activation enthalpy is... 

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