Outer-sphere

Electron transfer reactions are conceptually simple. The coupled stmctural changes may be modest, as in tire case of outer-sphere electron transport processes. Otlier electron transfer processes result in bond fonnation or... 

Here X is tire reorganization energy associated witli the curvature of tire reactant and product free energy wells and tlieir displacement witli respect to one another. Assuming a stmctureless polarizable medium, Marcus computed the solvent or outer-sphere component of tire reorganization energy to be... 

Rate fonrrulations that treat tire iinrer-sphere nrode(s) quairtum nrechairically aird tire outer sphere modes classically are used ratlrer widely. The rate expression for a single hanrronic quairtum mode is... 

A powerful application of outer-sphere electron transfer theory relates the ET rate between D and A to the rates of self exchange for the individual species. Self-exchange rates correspond to electron transfer in D/D (/cjj) and A/A (/c22)- These rates are related through the cross-relation to the D/A electron transfer reaction by the expression... 

C3.2.2.12 COMPETITION BETWEEN INNER SPHERE AND OUTER SPHERE NUCLEAR POLARIZATION DYNAMICS... 

Iron(II) ediylenediaminetetraacetic acid [15651 -72-6] Fe(EDTA) or A/,Ar-l,2-ethaiiediylbis[A[-(carboxymethyl)glyciQato]ferrate(2—), is a colorless, air-sensitive anion. It is a good reducing agent, having E° = —0.1171, and has been used as a probe of outer sphere electron-transfer mechanisms. It can be prepared by addition of an equivalent amount of the disodium salt, Na2H2EDTA, to a solution of iron(II) in hydrochloric acid. Diammonium [56174-59-5] and disodium [14729-89-6] salts of Fe(EDTA) 2— are known. 

Oxidation—Reduction. Redox or oxidation—reduction reactions are often governed by the hard—soft base rule. For example, a metal in a low oxidation state (relatively soft) can be oxidized more easily if surrounded by hard ligands or a hard solvent. Metals tend toward hard-acid behavior on oxidation. Redox rates are often limited by substitution rates of the reactant so that direct electron transfer can occur (16). If substitution is very slow, an outer sphere or tunneling reaction may occur. One-electron transfers are normally favored over multielectron processes, especially when three or more species must aggregate prior to reaction. However, oxidative addition... 

Outer sphere electron transfer (e.g., [11-19,107,160-162]), ion transfer [10,109,163,164] and proton transfer [165] are among the reactions near electrodes and the hquid/liquid interface which have been studied by computer simulation. Much of this work has been reviewed recently [64,111,125,126] and will not be repeated here. All studies involve the calculation of a free energy profile as a function of a spatial or a collective solvent coordinate. 

Outer-sphere. Here, electron transfer from one reactant to the other is effected without changing the coordination sphere of either. This is likely to be the ea.se if both reactants are coordinatively. saturated and can safely be assumed to be so if the rate of the redox process is faster than the rates observed for substitution (ligand tran.sfer) reactions of the species in question. A good example is the reaction. 

The superb elegance of this demonstration lies in the choice of reactants which permits no alternative mechani.sm. Cr" (d ) and Co" (d ) species are known to be substitutionally labile whereas Cr" (d ) and Co " (low-spin d ) are substitutionally inert, Only if electron transfer is preceded by the formation of a bridged internrediate can the inert cobalt reactant be persuaded to release a Cl ligand and so allow the quantitative formation of the (then inert) chromium product. Corroboration that electron transfer does not occur by an outer-sphere mechanism followed by los.s of CP from the chromium is provided by the fact that, if Cl is added to the solution, none of it finds its way into the chromium product. 

The observed rate law for inner-sphere, as for outer-sphere, reactions is commonly first order in each reactant but this does not indicate which step is ratc-dcteriiiining. Again, details should be obtained from more extensive accounts." ... 

It was found in pilot calculations that it is necessary to enclose the molecule by an outer sphere that includes the entire molecule. I have denoted the region from the outer sphere radius to infinity as region III. The wavefunction is assumed to be of an atonnic type in region III. 

The first step is to choose a molecular geometry, the atomic sphere radii and the exchange parameters for each atom and the outer sphere region. I have summarized these in Table 12.1. 

The sphere radii were deduced from Slater s (1965) table based on crystal data. The basic molecular HF-Xa equations were originally derived on the basis that the spheres did not overlap (Schwarz and Connolly, 1971). But the equations remain valid when the spheres are allowed to overlap, provided that each sphere does not contain more than one nucleus and that none of the nuclei lie outside the outer sphere. A 10% overlap seems to be normal practice, and our results are given in Table 12.2. 

For the silica gel (Figure 3A), the solution was removed slightly less effectively, and more Cs was left (ca. 0.0020 atoms/A2). The spectral behavior is quite similar to that of boehmite, except that there is a peak due to surface Cs coordinated by only water molecules and not in contact with the surface oxygens (so-called outer sphere complexes)at 30% RH. Complete dynamical averaging among sites at frequencies greater than ca. 10 kHz occurs at 70% RH and greater. 

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. 

For illite and kaolinite with decreasing solution concentration (Figure 5) there are two important changes. The relative intensity for inner sphere complexes increases, and the chemical shifts become substantially less positive or more negative due to the reduced Cs/water ratio, especially for the outer sphere complexes. Washing with DI water removes most of the Cs in outer sphere complexes and causes spectral changes parallel to those caused by decreasing solution concentration (data not shown). 

The surface behavior of Na is similar to that of Cs, except that inner sphere complexes are not observed. Although Na has the same charge as Cs, it has a smaller ionic radius and thus a larger hydration energy. Conseguently, Na retains its shell of hydration waters. For illite (Figure 6), outer sphere complexes resonate between -7.7 and -1.1 ppm and NaCl... 

The formulated principals correlating crystal structure features with the X Nb(Ta) ratio do not take into account the impact of the second cation. Nevertheless, substitution of a second cation in compounds of similar types can change the character of the bonds within complex ions. Specifically, the decrease in the ionic radius of the second (outer-sphere) cation leads not only to a decrease in its coordination number but also to a decrease in the ionic bond component of the complex [277]. 

NbFs Four-folded rings ofNbF6 octahedrons No outer-sphere cation, rings are linked via Van der Waals forces only, low melting point, low stability. 

This dissociation is in effect an extension of the diameter d2 of the second coordination sphere and the subsequent decrease in the intrinsic interaction potential of the outer sphere. Therewith, the inter-spherical interaction potential between the central atom and the first coordination sphere increases, leading to shortening of the distance di, which in turn leads to an increase in the frequency of the Ta-F bond vibration. 

The equilibrium between the complexes formed according to Equation (80) depends both on the concentration of fluorine ions and on the potential of interionic interactions, namely the nature of the outer-sphere cations [358]. The influence of the concentration of fluorine ions and of the nature of the outer-sphere cations on the equilibrium in Equation (80) can be demonstrated by the spectral transformations observed at 850°C for M2TaF7 - MF systems, where M = alkali metal [358]. 

Table 55 presents the results discussed above. Fluoride melts containing tantalum contain two types of complex ions, namely TaF6 and TaF72 . The equilibrium between the complexes depends on the concentration of fluoride ions in the system, but mostly upon the nature of the outer-sphere cations. The complex ionic structure of the melts can be adjusted by adding cations with a certain polarization potential. For instance, the presence of low polarization potential cations, such as cesium, leads primarily to the formation of TaF72 complexes, while the addition of cations with relatively high polarization potentials, such as lithium or sodium, shifts the equilibrium towards the formation of TaF6 ions. 

The nature of outer-sphere alkali metal cations can actually define the ionic equilibrium and also has an affect on complex anions. Fig. 77 illustrates the influence of the cationic surrounding on the wave numbers. 

A slight but systematic decrease in the wave number of the complexes bond vibrations, observed when moving from sodium to cesium, corresponds to the increase in the covalency of the inner-sphere bonds. Taking into account that the ionic radii of rubidium and cesium are greater than that of fluorine, it can be assumed that the covalent bond share results not only from the polarization of the complex ion but from that of the outer-sphere cation as well. This mechanism could explain the main differences between fluoride ions and oxides. For instance, melts of alkali metal nitrates display a similar influence of the alkali metal on the vibration frequency, but covalent interactions are affected mostly by the polarization of nitrate ions in the field of the outer-sphere alkali metal cations [359]. 

Higher melt temperatures lead to an increase in band intensity and merging thereof, as shown in Fig. 84. The merging of bands that occurs at increased temperatures can be explained by the augmentation of ion diffusion that causes an averaging of the potential of inter-ionic interactions between the NbF6 ions and the outer-sphere cations. 

The equilibrium in Equation (85) depends on three conditions the concentration of the components, the nature of the X ions, and the nature of the outer-sphere cations. 

The third factor that strongly affects the equilibrium between hexa- and heptacoordinated complexes (85) is the nature of the second, outer-sphere cations. Increasing the ionic radii of the cations causes the equilibrium in Equation (85) to shift to the left, forming mostly hexacoordinated complexes MeF6 The mechanism of interionic equilibrium in fluoride melts can be presented schematically as follows ... 

The anions MeF6 and X approach each other closely to form the heptacoordinated complex MeF6X(n+1)", or separate from one another, according to the polarization potential of the outer-sphere cation (alkali metal cation -M+). This process is unique in that the mode frequencies of the complexes remain practically unchanged despite varying conditions. This particular stability of the complexes is due to the high charge density of Ta5+ and Nbs+. 

It is obvious that calculated values are systematically lower than the experimental data. Comparison of the experimental and calculated values of coefficient p shows that along with the changes in occupancy levels that appear at elevated temperatures, inter-particular interactions also make a significant contribution. Band intensity is generally defined as the derivative of the dipole moment with respect to the normal coordinate. It is, therefore, logical to assume that thermal extension and outer-sphere cation replacement have a similar influence on the potential of inter-ionic interactions, which, in turn, lead to the intensity changes. 

Sergienko et al. [375, 376] showed that the band intensity of fluoride complexes increases systematically when outer-sphere cations undergo sequential transition from lithium to cesium. 

Thus, increasing the temperature exerts an influence on the fluoride complexes that is similar to the influence of outer-sphere cations and is expressed by an increase of the covalent contribution to the bonds between fluoride complexes and outer-sphere cations. 

Increasing the temperature generally promotes an increase in the covalent contribution to the bond between complex anions and outer-sphere cations ... 

According to the Marcus theory [64] for outer-sphere reactions, there is good correlation between the heterogeneous (electrode) and homogeneous (solution) rate constants. This is the theoretical basis for the proposed use of hydrated-electron rate constants (ke) as a criterion for the reactivity of an electrolyte component towards lithium or any electrode at lithium potential. Table 1 shows rate-constant values for selected materials that are relevant to SE1 formation and to lithium batteries. Although many important materials are missing (such as PC, EC, diethyl carbonate (DEC), LiPF6, etc.), much can be learned from a careful study of this table (and its sources). 

---