Outer Sphere Concepts

In 1954 Weiss32 used Bernal and Fowler s simplified solvation model,16 with an Inner Sphere of ionic coordination, i.e., a small spherical double layer around the ion of charge ze, followed by a sharp discontinuity at radius q, the edge of the Outer Sphere or Dielectric Continuum. He used a simple electrostatic argument to determine the energy to remove an electron at optical frequency from the Inner Sphere  

Weiss considered that the total energy on removing an electron from the central ion (of initial charge z + 1) at optical frequency to infinity should be on the order of  

The Outer Sphere part of this expression is similar to the functions used by Landau34 and Mott and Gurney35 for the polarization 

---

Chemical and electrochemical reactions in condensed phases are generally quite complex processes only outer-sphere electron-transfer reactions are sufficiently simple that we have reached a fair understanding of them in terms of microscopic concepts. In this chapter we give a simple derivation of a semiclassical theory of outer-sphere electron-transfer reactions, which was first systematically developed by Marcus [1] and Hush [2] in a series of papers. A more advanced treatment will be presented in Chapter 19. 

This conception of an 8, 2 reaction as an electron-shift process is obviously equivalent to its conception as an inner sphere electron transfer, i.e. a single electron transfer concerted with the breaking of the R—X bond and the formation of the R—Nu bond. Faced with an experimental system, however, the first question—ET or 8 2 —still remains, whatever intimate description of the 8, 2 reaction one may consider most appropriate. If this is thought of in terms of inner sphere electron transfer, the question thus raised is part of the more general problem of distinguishing outer sphere from inner sphere electron-transfer processes (Lexa et ai, 1981), an actively investigated question in other areas of chemistry, particularly that of coordination complex chemistry (Taube, 1970 Espenson, 1986). 

Bridge mediation mechanisms in heterogeneous outer sphere electrochemical reactions has also been theoretically treated using the pull—push and push-pull mechanistic concepts [84]. Schmidt [85] has considered theoretically homogeneous inner sphere bridge electron transfer reactions without atom or ion transfer. Bridge mediation in electron transfer reactions may also involve simultaneous atom or ion transfer. Heyrovsky [86] invoked mediation of electron transfer by formation of bridges to explain the enhancement of the rate of electroreduction of indium (III) ions in the presence of specifically adsorbed halide ions on mercury. 

The theoretical results obtained for outer-sphere electron transfer based on self-exchange reactions provide the essential background for discussing the interplay between theory and experiment in a variety of electron transfer processes. The next topic considered is outer-sphere electron transfer for net reactions where AG O and application of the Marcus cross reaction equation for correlating experimental data. A consideration of reactions for which AG is highly favorable leads to some peculiar features and the concept of electron transfer in the inverted region and, also, excited state decay. 

As mentioned in the introduction, the debate concerning the observation or the absence of the M.LR. has shifted in recent years to various models of the role of the solvent in e.t. reactions. In this section we shall consider the concept of the outer sphere reorganization in the Marcus-Hush theory, its implications and experimental predictions the more recent concepts of the dynamics of solvent relaxation as a controlling factor in e.t. will then be discussed. 

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. 

Now, the non-adiabatic electron transitions is examined only when electron matrix element Fif is small (see the criterion (10) and (10a)). It is the criterion of applicability of the perturbation theory on F f, but it is not the criterion of applicability of the concept of non-adiabatic transition between two crossing diabatic terms. As it is known (see, for example, ref. [5]) the true image of terms is changed on taking into account the interaction V. Denote two terms without inter-term interaction as E[(R) and E (R), where R is the generalized nuclear coordinate. If the crystal phonons (or the outer-sphere variables in a polar medium) only participate in the transition, then E[(R) and E (R) are the parabolic terms independent of the value of shift of... 

The concept of second- or outer-sphere coordination, originally introduced by Werner3, has played a major role in the subsequent development of the theory of bonding in metal complexes and has recently re-emerged as a means of describing higher-order... 

I. The IUPAC nomenclature used in this chapter is described by K. J. Laidler, ( hcmical Kinetics, Harper Row, New York, 1987, Chap. 1. See also I. Mills, T. ( viias, K. Homann, N. Kallay, and K. Kuchitsu, Quantities, Units, and Symbols in Physical Chemistry, Blackwell, Oxford, 1988. For an introduction to the concepts of lirmical species, including outer-sphere and inner-sphere complexes, see, for example,... 

These three types of surface species—inner-sphere complex, outer-sphere complex, and diffuse-layer—represent three modes of adsorption of small aqueous ions that contribute to the formation of the electrochemical double layer on clay mineral surfaces. No inference of special planes containing adsorbed ions is required by these surface chemical speciation concepts, nor is detailed molecular structure implied, other than the general notions of surface complexes and vicinal dissociated ions. It is sometimes convenient, although not necessary, to group the two types of surface complex into a Stern layer to distinguish them from diffuse-layer ions [18]. This geometric partitioning of surface species, however, should not be taken to mean that diffuse-layer ions necessarily approach a particle surface less closely than do Stern-layer ions. 

These speciation concepts are illustrated in Fig. 3 for the idealized basal-plane surface of a smectite, such as montmorillonite. Also shown are the characteristic residence-time scales for a water molecule diffusing in the bulk liquid (L) for an ion in the diffuse swarm (DI) for an outer-sphere surface complex (OSQ and for an inner-sphere surface complex (ISC). These time scales, ranging from picosecond to nanosecond [20,21], can be compared with the molecular time scales that are probed by conventional optical, magnetic resonance, and neutron scattering spectroscopies (Fig. 3). For example, all three surface species remain immobile while being probed by optical spectroscopy, whereas only the surface complexes may remain immobile while being probed by electron spin resonance (ESR) spectroscopy [21-23]. 

Before we proceed to translate the outer-/inner-sphere concepts to a terminology more suitable for organic molecules and while we still have the... 

---