Inner sphere SET

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]. 

Much controversy has thus existed around the alternative between a normal but polar Sn2 reaction and a SET process before it was realized that the inner sphere SET variety is in effect very close to the polar S 2 mechanism [5,22,23]. In principle, only the outer sphere SET reaction leading to well separated el tron exchange products can be treated simply in terms of individual free radical species with their specific reactivity [5,12]. The freedom of radicals in this context refers to their existence within a chemical meaningful period of time and to the full set of motional degrees of freedom. 

Single Electron Transfer A single electron transfer (SET) mechanism is often difficult to distinguish from an SN2 reaction because the principal product of these two pathways is the same, apart from the stereochemistry at carbon (race-mization instead of inversion). The radicals formed can recombine rapidly in a solvent cage (inner-sphere ET) [2, 193, 194]. The [HFe(CO)5] -catalyzed deiodina-tion of iodobenzene may serve as an example [179] (Eq. (13)). 

We can simplify by considering that k.- k.w, and by setting k k-i = Kos. Kos is the equilibrium constant of the outer sphere complex. For the rate of the formation of MeLJ2 n)+ inner-sphere complex (now written without water), we have... 

The Marcus classical free energy of activation is AG , the adiabatic preexponential factor A may be taken from Eyring s Transition State Theory as (kg T /h), and Kel is a dimensionless transmission coefficient (0 < k l < 1) which includes the entire efiFect of electronic interactions between the donor and acceptor, and which becomes crucial at long range. With Kel set to unity the rate expression has only nuclear factors and in particular the inner sphere and outer sphere reorganization energies mentioned in the introduction are dominant parameters controlling AG and hence the rate. It is assumed here that the rate constant may be taken as a unimolecular rate constant, and if needed the associated bimolecular rate constant may be constructed by incorporation of diffusional processes as ... 

Romanian scientists compared one-electron transfer reactions from triphenylmethyl or 2-methyl benzoyl chloride to nitrobenzene in thermal (210°C) conditions and on ultrasonic stimulation at 50°C (lancu et al. 1992, Vinatoru et al. 1994, Chivu et al. 2006). In the first step, the chloride cation-radical and the nitrobenzene anion-radicals are formed. In the thermal and acoustic variants, the reactions lead to the same set of products with one important exception The thermal reaction results in the formation of HCl, whereas ultrasonic stimulation results in CI2 evolution. At present, it is difficult to elucidate the mechanisms behind these two reactions. As an important conclusion, the sonochemical process goes through the inner-sphere electron transfer. The outer-sphere electron transfer mechanism is operative in the thermally induced process. 

As in Eq. (64), the electron spin spectral densities could be evaluated by expanding the electron spin tensor operators in a Liouville space basis set of the static Hamiltonian. The outer-sphere electron spin spectral densities are more complicated to evaluate than their inner-sphere counterparts, since they involve integration over the variable u, in analogy with Eqs. (68) and (69). The main simplifying assumption employed for the electron spin system is that the electron spin relaxation processes can be described by the Redfield theory in the same manner as for the inner-sphere counterpart (95). A comparison between the predictions of the analytical approach presented above, and other models of the outer-sphere relaxation, the Hwang and Freed model (HF) (138), its modification including electron spin... 

Fig. 3. Simulation curves of the inner sphere relaxivity as function of Xji/ for a mono-aquo Gd(III) complex at 25°C and 20 MHz for increasing values of the rotational correlation time. The other relaxation parameters were set as follows = 5.0 x 10 s ...

In terms of the development of an understanding of the reactivity patterns of inorganic complexes, the two metals which have been pivotal are platinum and cobalt. This importance is to a large part a consequence of each metal having available one or more oxidation states which are kinetically inert. Platinum is a particularly useful element of this pair because it has two kinetically inert sets of complexes (divalent and tetravalent) in addition to the complexes of platinum(O), which is a kinetically labile center. The complexes of divalent and tetravalent platinum show significant differences. Divalent platinum forms four-coordinate planar complexes which have a coordinately unsaturated 16-electron d8 platinum center, whereas tetravalent platinum is an 18-electron d6 center which is coordinately saturated in its usual hexacoordination. In terms of mechanistic interpretation one must therefore consider both associative and dissociative substitution pathways, in addition to mechanisms involving electron transfer or inner-sphere atom transfer redox processes. A number of books and articles have been written about replacement reactions in platinum complexes, and a number of these are summarized in Table 13. 

Some comments need to be made concerning the data in Table 1. For some couples an extensive set of additional data are available in a variety of media, e.g. Fe3+/2+. For others, data are available for a series of structurally related analogs, e.g. Fe(C5H5)2+/0. For couples like Cr(bipy)3+/° (5, Table 1) the electron transfer process is ligand n (bipy) rather than metal based and in clusters like those in couples 19 and 26 (Table 1) the redox levels are almost surely delocalized over the cluster unit. The inclusion of some of the entries listed as inner-sphere cases is not based on product studies but, rather, mechanistic details have been inferred from rate comparisons, as illustrated in a later section of the chapter. 

A large number of radical reactions proceed by redox mechanisms. These all require electron transfer (ET), often termed single electron transfer (SET), between two species and electrochemical methods are very useful to determine details of the reactions (see Chapter 6). We shall consider two examples here - reduction with samarium di-iodide (Sml2) and SRN1 (substitution, radical-nucleophilic, unimolecular) reactions. The SET steps can proceed by inner-sphere or outer-sphere mechanisms as defined in Marcus theory [19,20]. 

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. 

Inner-sphere electron transfer always involves nucleophilic addition or substitution with an electrophile via a single-electron-transfer (SET) step 42... 

The inner sphere of relatively small ions is generally accepted to have 4 or 6 dipoles in symmetrical tetrahedral or octahedral coordination, depending on the ion size and charge. In principle, these might respectively accommodate 4 and 8 other oriented intercalated dipoles as a second shell. In the tetrahedral case, the second dipole group would be at (180 - ( >)0 from the first, where < > is the tetrahedral angle, i.e., at 70.53°. In the octahedral arrangement, the second set are... 

Figure 7.2 Quasi-chemical contributions of the hydration free energy of Be (aq). Cluster geometries were optimized using the B3LYP hybrid density functional (Becke, 1993) and the 6-31- -G(d, p) basis set. Frequency calculations confirmed a true minimum, and the zero point energies were computed at the same level of theory. Single-point energies were calculated using the 6-311- -G(2d, p) basis set. A purely inner-shell n = 5 cluster was not found the optimization gave structures with four (4) inner-sphere water molecules and one (1) outer-sphere water molecule. For n = 6 both a purely inner-shell configuration, and a structure with four (4) inner-shell and two (2) outer-shell water molecules were obtained. The quasi-chemical theory here utilizes only the inner-shell structure. O - rin [/ff -f (left ordinate) vs. n. A ...

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