Inner-sphere PRE

Theoretical models for outer-sphere nuclear spin relaxation in paramagnetic systems, including an improved description of the electron spin relaxation, have been developed intensively for the last couple of years. They can be treated as counterparts of the models of inner-sphere PRE, described in the Section V.B and V.C. 

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... 

An analytical theory of the outer-sphere PRE for slowly rotating systems with an arbitrary electron spin quantum number S, appropriate at the limit of low field, has been proposed by Kruk et al. (144). The theory deals with the case of axial as well as rhombic static ZFS. In analogy to the inner sphere case (95), the PRE for the low field limit could be expressed in terms of the electron spin spectral densities s ... 

Models for the outer-sphere PRE, allowing for faster rotational motion, have been developed, in analogy with the inner sphere approaches discussed in the Section V.C. The outer-sphere counterpart of the work by Kruk et al. 123) was discussed in the same paper. In the limit of very low magnetic field, the expressions for the outer-sphere PRE for slowly rotating systems 96,144) were found to remain valid for an arbitrary rotational correlation time Tr. New, closed-form expressions were developed for outer-sphere relaxation in the high-field limit. The Redfield description of the electron spin relaxation in terms of spectral densities incorporated into that approach, was valid as long as the conditions A t j 1 and 1 were fulfilled. The validity... 

Ru Ru step and a self-exchange rate of 2xlO" M s for the c -[Ru 0)2(L)] " /cw [Ru (0)2(L)]+ couple has been estimated a mechanism involving a pre-equilibrium protonation of ci5-[Ru (0)2(L)]+ followed by outer-sphere electron transfer is proposed for the Ru Ru step. For reduction by [Fe(H20)6] +, an outer-sphere mechanism is proposed for the first step and an inner-sphere mechanism is proposed for the second step. ... 

The Levich—Dogonadze—Kuznetsov (LDK) treatment [65] considers that the only source of activation is the polarization electrostatic fluctuations (harmonic oscillations) of the solvent around the reacting ion and uses essentially the same model as the Marcus—Hush approach. However, unlike the latter, it provides a quantum mechanical calculation of both the pre-exponential factor and the activation energy but neglects intramolecular (inner sphere) vibrations (1013—1014 s 1). 

Although preponderant attention has been devoted to theoretical descriptions of the barrier height, also of importance is the development of models for the dynamics of surmounting the electron-transfer barrier. As noted above, the pre-equilibrium treatment embodied in eqns. (10) and (12) is normally expected to be applicable to outer-, as well as inner-, sphere processes. We shall now consider theoretical models for each of the preexponential factors in the expression for ket [eqn. (12)] vn, xel, and Tn, in turn. 

This contribution to the PRE is called inner-sphere relaxation. The ligand or solvent molecules can also experience PRE without ever entering the inner coordination sphere of the paramagnetic species. This second mechanism, referred to as outer-sphere (OS) relaxation, is usually less important and more... 

Fig. 2 shows calculated Tim and Xm values for the 1 and 2 flash experiments assuming the PRE results from one exchangeable H2O. xm is in the range 10-20 ps this is the expected range for protolysis reactions of water coordinated to (+3) or (+4) ions. Measured Tim values in S2 range from <10 ps when T<17°C to near 50 ps at 30°C, with an extremely rapid temperature dependence in this region, which is believed to result from very small electron exchange couplings within the OEC (3). Measured Tim values have been used to calculate electron spin relaxation times xsi of the Mn ion that acts as the H relaxation trap (Fig. 3). Calculations assume an inner sphere dipolar interaction to a single H2O. Four situations were considered (1) that the trap consists of a Mn(lll) monomer (S=2, pe=4.9 BM), (2) a manganese(IV) monomer (S=3/2, pe=3.9 BM), and...

Ag(HI06)2] oxidation of A-methylethylamine to HCHO and C2H5NH2 in alkaline medium was first order in Ag(lll) and the substrate. Rates increased with HO , but decreased with increasing periodate ion concentration. The proposed reaction mechanism involved the formation of an intermediate [Ag(HIOg)(OH)(MeNHEt)] in a pre-equilibrium followed by rate-determining inner-sphere electron transfer from the... 

In MAO-activated catalyst systems, alkyl zirconocenium cations are likewise thought to be present, presumably in weakly botmd inner-sphere ion pairs with anions of the type MeMAO [26, 29]. These anions - still only vaguely characterized as large agglomerates [32] - are assumed to be formed from MAO by uptake of a methyl anion from the alkyl zirconocene precursor. In equilibrium with these inner-sphere ion pairs A, outer-sphere ion pairs B (Fig. 3) are observed in MAO-activated pre-catalyst systems [29, 32-34] that contain a heterobinuclear cationic AlMes adduct [35], presumably together with MeMAO as counter-anion. 

As metal ions in aqueous solutions form hydrated aqua complexes, complex-formation processes should be considered as reactions involving replacement of water molecules by ligand particles. Kinetic data for the formation of metal complexes obtained by various methods showed [27] that the formation of ML complexes proceeds via a rapid pre-equilibrium, resulting in the formation of an outer sphere complex M(H20)L. Then, this intermediate loses water in the rate-determining step of inner sphere complex (ML) formation. 

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. 

Steric Control of the Inner/Outer-Sphere Electron Transfer 461 Thermal and Photochemical ET in Strongly Coupled CT Complexes 463 Electron-Transfer Paradigm for Arene Transformation via CT Complexes 465 Electron-Transfer Activation of Electrophilic Aromatic Substitution 469 Structural Pre-organization of the Reactants in CT Complexes 470 CT Complexes in Aromatic Nitration and Nitrosation 472 Concluding Summary 475 References 475... 

---