Inner-sphere model

The equilibrium and inner-sphere modeling results discussed above are consistent with the following overall equilibrium... 

Since a very recent luminescence study again clearly favors the inner-sphere model (Tanaka and Yamashita, 1984), it seems reasonable to assume that the inner-sphere contribution cannot be neglected. Judging from the solid state structures, moreover, this would be the preferred model. There is an obvious need for an X-ray diffraction, neutron diffraction or EXAFS study in solution to settle this question. 

Fig. 5. A model for S042- substitution on [Be(H20)4]2+ proceeding from the outer-sphere complex on the left through the transition state at center to the inner-sphere complex at the right of the figure (16, 66).

N. Sutin, Brookhaven National Laboratory Strictly speaking, the outer-sphere and inner-sphere designations refer to limiting cases. In practice, reactions can have intermediate outer-sphere or inner-sphere character this occurs, for example, when there is extensive interpenetration of the inner-coordination shells of the two reactants. Treating this intermediate situation requires modification of the usual expressions for outer-sphere reactions — particularly those expressions that are based upon a hard-sphere model for the reactants. 

The model presented here is simplified in several ways (harmonic approximation, purely classical treatment of inner-sphere reorganization), and it says little about the pre-exponential factor A. But it does... 

B. Structural Models of dcr/Acr Inner-Sphere Electron-Transfer Transition States... 

Iron(III)-catalyzed autoxidation of ascorbic acid has received considerably less attention than the comparable reactions with copper species. Anaerobic studies confirmed that Fe(III) can easily oxidize ascorbic acid to dehydroascorbic acid. Xu and Jordan reported two-stage kinetics for this system in the presence of an excess of the metal ion, and suggested the fast formation of iron(III) ascorbate complexes which undergo reversible electron transfer steps (21). However, Bansch and coworkers did not find spectral evidence for the formation of ascorbate complexes in excess ascorbic acid (22). On the basis of a combined pH, temperature and pressure dependence study these authors confirmed that the oxidation by Fe(H20)g+ proceeds via an outer-sphere mechanism, while the reaction with Fe(H20)50H2+ is substitution-controlled and follows an inner-sphere electron transfer path. To some extent, these results may contradict with the model proposed by Taqui Khan and Martell (6), because the oxidation by the metal ion may take place before the ternary oxygen complex is actually formed in Eq. (17). 

A SET process has been postulated between Rh(III) oxidative adducts and an NAD(P)H model compound (cf. Section 18.2.4) [91]. Oxidative adducts formed by Sn2, SNAr, or inner-sphere SET pathways may produce radicals by homolytic M-C bond cleavage [130, 155, 176, 199]. 

Surface complexation models attempt to represent on a molecular level realistic surface complexes e.g., models attempt to distinguish between inner- or outer-sphere surface complexes, i.e., those that lose portions of or retain their primary hydration sheath, respectively, in forming surface complexes. The type of bonding is also used to characterize different types of surface complexes e.g., a distinction between coordinative (sharing of electrons) or ionic bonding is often made. While surface coordination complexes are always inner-sphere, ion-pair complexes can be either inner- or outer-sphere. Representing model analogues to surface complexes has two parts stoichiometry and closeness of approach of metal ion to... 

According to a recent model (13) nuclear tunneling factors for the inner-sphere modes can be defined by... 

The value of log rn for the Fe(H20) 2+ - Fe(H20)6 + exchange (which features a relatively large inner-sphere barrier) is plotted as a function of 1/T in Figure 5. The nuclear tunneling factors are close to unity at room temperature but become very large at low temperatures. As a consequence of nuclear tunneling, the electron transfer rates at low temperatures will be much faster than those calculated from the classical model. 

To summarize, in this article we have discussed some aspects of a semiclassical electron-transfer model (13) in which quantum-mechanical effects associated with the inner-sphere are allowed for through a nuclear tunneling factor, and electronic factors are incorporated through an electronic transmission coefficient or adiabaticity factor. We focussed on the various time scales that characterize the electron transfer process and we presented one example to indicate how considerations of the time scales can be used in understanding nonequilibrium phenomena. 

In order to make things a bit more concrete at this point we display in Figure 1 a sterically favorable configuration for a reactive ion pair (Tl). Only the 3d atomic orbitals most directly involved in the electron exchange are shown. The theoretical model developed here is based on a so-called "outer-sphere" mechanism, in which the inner-sphere reactants preserve their integrity in the course of the exchange reaction (aside from bond distortions associated with the activation step). The... 

---