Outer transition state solvation

In particular, the reactant may penetrate the inner layer and contact directly the metal surface even in the absence of bona fide chemical interactions as a result of stabilizing image or Van der Waals interactions. This is most likely to occur with relatively weakly solvated species. Reactions occurring via such transition states can, in a sense, be considered to be inner- rather than outer-sphere processes. In terms of the above reaction classification, they nevertheless may be of the weak-overlap type if the... 

These results mean that the solvent environment of a discharging ion on the inner side of the outer Helmholtz plane can be quite substantially modified toward a state of orientational saturation depending on qM and T. The entropy of activation of a process involving change of charge number is closely associated with changing state of solvation in formation of the transition state. Hence it can be seen, at least qualitatively, how an influence of potential on solvent dipole orientation in the inner layer could be transmitted as a potential or field effect on the entropy of activation. This... 

The acid-catalyzed decomposition of /i-superoxo complexes of the type [Co(III)2(/>t02)(en)4(NH3)2] involves intramolecular electron transfer with AV around 20cm moP. Reductions by [Fe(CN)e] of [Co(edta)] and [Co(NH3)5py] are outer sphere but, in the latter case, detection of an outer-sphere precursor allows evaluation of A V for electron transfer of 23.9cm moP comparable with other values/ Attempts to rationalize this suggest almost complete electron transfer in the transition state. Similar activation volumes for electron transfer are found in reduction of [(NH3)5CoOH2] by [FeCCN) ], but there is a marked discrepancy in reaction volumes for precursor formation with those of other cobalt(III) oxidants. Such differences may be due in part to solvation effects which vary with ionic strength and the necessity of studying ionic strength dependencies of activation volumes for electron transfer reactions between complex ions has been pointed out. ... 

But if we examine the localized near the donor or the acceptor crystal vibrations or intra-molecular vibrations, the electron transition may induce much larger changes in such modes. It may be the substantial shifts of the equilibrium positions, the frequencies, or at last, the change of the set of normal modes due to violation of the space structure of the centers. The local vibrations at electron transitions between the atomic centers in the polar medium are the oscillations of the rigid solvation spheres near the centers. Such vibrations are denoted by the inner-sphere vibrations in contrast to the outer-sphere vibrations of the medium. The expressions for the rate constant cited above are based on the smallness of the shift of the equilibrium position or the frequency in each mode (see Eqs. (11) and (13)). They may be useless for the case of local vibrations that are, as a rule, high-frequency ones. The general formal approach to the description of the electron transitions in such systems based on the method of density function was developed by Kubo and Toyozawa [7] within the bounds of the conception of the harmonic vibrations in the initial and final states. 

Thirdly, it will be important to gain more direct information on the stability of outer-sphere precursor states, especially with regard to the limitations of simple electrostatic models (Sect. 4.2). One possible approach is to evaluate Kp for stable reactants by means of differential capacitance and/or surface tension measurements. Little double-layer compositional data have been obtained so far for species, such as multicharged transition-metal complexes, organometallics, and simple aromatic molecules that act as outer-sphere reactants. The development of theoretical double-layer models that account for solvation differences in the bulk and interfacial environments would also be of importance in this regard. 

Additional alterations in the work terms with the electrode material for outer-sphere reactions may arise from discreteness-of-charge effects or from differences in the nature of the reactant-solvent interactions in the bulk solution and at the reaction plane. Thus metals that strongly chemisorb inner-layer solvent (e.g., HjO at Pt) also may alter the solvent structure in the vicinity of the outer plane, thereby influencing k bs variations in the stability of the outer-sphere precursor (and successor) states. Such an effect has been invoked to explain the substantial decreases (up to ca. 10 -fold) in the rate constants for some transition-metal aquo couples seen when changing the electrode materiaf from Hg to more hydrophilic metals such as Pt. Much milder substrate effects are observed for the electroreduction of more weakly solvated ammine complexes . 

A spectroscopic study of Eu -Br showed that the increase in the Br concentration causes a larger enhancement in the intensity and band area of the -> transitions than for the Fj -> transitions. These modifications in the spectra were attributed to changes in the structure and nature of the inner solvation sphere of Eu in the excited state as compared to that of the ground state (Marcantonatos et al. 1984). The differences in intensity between absorption and emission bands would, therefore, reflect formation of inner-sphere complexes by Br in the excited state while outer-sphere complexation would dominate the ground state. It was proposed (Marcantonatos et al. 1981, 1982) that excitation of Eu " ion to the state would result in an expansion of the 4f and a shrinkage of the 5p orbitals with an overall decrease in the metal ion radius. The consequent contraction of the iimer shell would be expected to produce more compact and less easily disrupted outer hydration spheres for both ( Dj) Eu(H20)g and ( Di)Eu(H20)g with a possible increase in kobs-... 

We present a derivation of the broadening due to the solvent according to a system/ bath quantum approach, originally worked out in the field of solid-state physics to treat the effect of electron/phonon couplings in the electronic transitions of electron traps in crystals [67, 68]. This approach has the advantage to treat all the nuclear degrees of freedom of the system solute/medium on the same foot, namely as coupled oscillators. The same type of approach has been adopted by Jortner and co-workers [69] to derive a quantum theory of thermal electron transfer in polar solvents. In that case, the solvent outside the first solvation shell was treated as a dielectric continuum and, in the frame of the polaron theory, the vibrational modes of the outer medium, that is, the polar modes, play the same role as the lattice optical modes of the crystal investigated elsewhere [67,68]. The total Hamiltonian of the solute (5) and the medium (m) can be formally written as... 

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