Inner and Outer sphere

For kaolinite the sample permeability was very low and the solution was poorly removed. The spectra (Figure 3C) are consequently complex, containing peaks for inner and outer sphere complexes, CsCl precipitate from resMual solution (near 200 ppm) and a complex spinning sideband pattern. Spectral resolution is poorer, but at 70% RH for instance, inner sphere complexes resonate near 16 ppm and outer sphere complexes near 31 ppm. Dynamical averaging of the inner and outer sphere complexes occurs at 70% RH, and at 100% RH even the CsCl precipitate is dissolved in the water film and averaged. 

Differentiation between inner- and outer-sphere complexes may be possible on the basis of determination of activation volumes of dediazoniations catalyzed by various metal complexes, similar to the differentiation between heterolytic and homolytic dediazoniations in DMSO made by Kuokkanen, 1989 (see Sec. 8.7). If outer-sphere complexes are involved in a dediazoniation, larger (positive) volumes of activation are expected than those for the comparable reactions with inner-sphere complexes. Such investigations have not been made, however, so far as we are aware. 

Particular use was made of conductivity measurements of cobalt(iii) and platinum(ii) complexes which allowed a facile determination of the number and type of ions present in solution. For example, the compounds Co(NH3) Cl3 would give a monocation and an monoanion (n=4), a dication and two monoanions (n = 5) and a trication and three monoanions (n=6) respectively. In some cases, it was also possible to distinguish chemically between inner and outer sphere chloride by precipitation of the outer sphere species as AgCl. 

Reductions of various Co(ni) complexes by Fe(II) have been studied under high pressures . The motivation for performing such experiments resides in the possibility that the volume of activation (AF ), like the entropy of activation, might be a criterion for distinguishing between inner- and outer-sphere reactions. For reactions of the type... 

The complex has been separated by ion exchange and characterised by direct analysis . The complex has a distinctive absorption spectrum (Fig. 11), quite unlike that of Np(V) and Cr(III). The rate coefficient for the first-order decomposition of the complex is 2.32 x 10 sec at 25 °C in 1.0 M HCIO. Sullivan has obtained a value for the equilibrium constant of the complex, K = [Np(V) Cr(III)]/[Np(V)][Cr(III)], of 2.62 + 0.48 at 25 °C by spectrophotometric experiments. The associated thermodynamic functions are AH = —3.3 kcal. mole" and AS = —9.0 cal.deg . mole . The rates of decay and aquation of the complex, measured at 992 m/t, were investigated in detail. The same complex is formed when Np(VI) is reduced by Cr(II), and it is concluded that the latter reaction proceeds through both inner- and outer-sphere paths. It is noteworthy that the substitution-inert Rh(lII), like Cr(III), forms a complex with Np(V) °. This bright-yellow Np(V) Rh(III) dimer has been separated by ion-exchange... 

It has been shown so far that internal and external factors can be combined in the control of the electron-transfer rate. Although in most cases a simple theoretical treatment, e.g. by the Marcus approach, is prevented by the coincidence of these factors, it is clear that the observed features for the isoenergetic self-exchange differ by the electronic coupling and the free energy of activation. Then it is also difficult to separate the inner- and outer-sphere reorganization energies. 

A natural question is In which temporal order do the reorganization processes and the proper electron transfer take place The answer is given by the Frank-Condon principle, which in this context states First the heavy particles of the inner and outer sphere must assume a suitable intermediate configuration, then the electron is exchanged isoenergetically, and finally the system relaxes to its new equilibrium... 

Figure 6.1 Reorganization of inner and outer sphere during an electron-transfer reaction.

To develop these ideas into a quantitative theory, we require models for the inner and outer sphere and their reorganization. The problem is similar to that encountered in infrared and Raman spectroscopy, where... 

A is a measure for the energy required to reorganize the inner and outer sphere during the reaction. The energy of activation for the oxidation is the saddle point energy minus the initial energy ered, which gives ... 

The exact form of the pre-exponential factor A (see Chapter 5) is still being debated from the preceding considerations it is apparent that we must distinguish two cases If the reaction is adiabatic, the pre-exponential factor will be determined solely by the dynamics of the inner and outer sphere if it is nonadiabatic, it will depend on the electronic overlap between the initial and final state, which determines the probability with which the reaction proceeds once the system is on the reaction hypersurface. 

Innumerable experiments have been performed on both inner- and outer-sphere electron-transfer reactions. We do not review them here, but present a few results that are directly relevant to the theoretical issues raised in the preceding chapters. 

When a reaction is adiabatic, the electron is transferred every time the system crosses the reaction hypersurface. In this case the preexponential factor is determined solely by the dynamics of the inner-and outer-sphere reorganization. Consequently the reaction rate is independent of the strength of the electronic interaction between the reactant and the metal. In particular, the reaction rate should be independent of the nature of the metal, which acts simply as an electron donor and acceptor. Almost by definition adiabatic electron-transfer reactions are expected to be fast. 

Figure 10.1 Comparison of inner- and outer-sphere modes of activation, where S is the substrate. (From Cowan, 2002. With kind permission of Springer Science and Business Media.)...

Complexation reactions are assumed to proceed by a mechanism that involves initial formation of a species in which the cation and the ligand (anion) are separated by one or more intervening molecules of water. The expulsion of this water leads to the formation of the inner sphere complex, in which the anion and cation are in direct contact. Some ligands cannot displace the water and complexation terminates with the formation of the outer sphere species, in which the cation and anion are separated by a molecule of water. Metal cations have been found to form stable inner and outer sphere complexes and for some ligands both forms of complexes may be present simultaneously. 

The action of one-electron redox systems is readily understandable in the context of inner- and outer-sphere mechanisms, whereas two-electron redox systems require additional considerations. First, if a double one-electron transfer is possible from an organic substrate to the same metal ion, does it mean that the same molecule of an organic donor provides these two electrons, or do two molecules of the substrate act as one-electron donors ... 

In this case, the inner and outer sphere contributions... 

Fig. 5. Temperature dependence of the proton relaxivity (20 MHz) for Na[GdD0TA(H20)] (top) and [GdD0TAM(H20)]tfl3 (bottom) and individual contributions of the inner and outer sphere mechanisms.

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