Bond-Breaking Electron Transfer

The free-energy surfaces of the initial and final states, Uf ,r) and Uf(P,r), then involve two contributions the parabolic free energy as a function of the slow polarization, (7/(P) and (7/(P), and nonparabolic molecular potential f/ (r) and 

The activation free energy may therefore be represented as a sum of two contributions  

The optimum values of AF and AF must be chosen such as to minimize the total activation free energy in Eq. (34.38) with the constraint 

FIGURE 34.8 Free-energy surfaces for the dissociative electron transfer reaction (a) for the solvent polarization (b) along the coordinate r of the molecnlar chemical bond. corresponds to stable molecule in oxidized form. U is the decay potential for the rednced foim. AFj and AF are the partial free energies of the transition determining mntnal arrangement of the two sets of the free-energy surfaces. 

In the model where the potentials are described by Morse/expo- 

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KoperMTM, Voth GA. 1998. A theory for adiabatic bond breaking electron transfer reactions at metal electrodes. Chem Phys Lett 282 100-106. 

Santos E, Schmickler W. 2007a. Catalyzed bond-breaking electron transfer Effect of the separation of the reactant from the electrode. J Electroanal Chem 607 101-106. 

Santos E, Koper MTM, Schmickler W. 2008. Bond-breaking electron transfer of diatomic reactants at metal electrodes. Chem Phys 344 195-201. 

Bilirubin oxidase, 603-606, 621-626 Biomimetic catalysts, 679-686 Bond-breaking electron transfer reactions, 43-44... 

We have applied this formalism to the simplest type of bond-breaking electron-transfer reaction at a metal electrode [71,74]. The type of reaction we have in mind is the reductive cleavage of an R-X molecule ... 

Assuming a simple Marcus-type model for the interaction with the solvent, one can derive an analytical expression for the potential (free) energy surface of the bond-breaking electron-transfer reaction as a function of the collective solvent coordinate q and the distance r between the fragments R and X [71,75]. The activation energy of the reaction can also be calculated explicitly ... 

In order to test the (in)correctness of the Marcus solvent model, we have carried out extensive MD simulations of a bond-breaking electron-transfer reaction in water at a platinum electrode. Figure 10a shows the computer simulated potential energy surface obtained by a two dimensional umbrella sampling technique. Analysis of the results in Figure 10a brings to light two important effects of the solvent the Marcus model does not account for. 

The double adiabatic approach provides a convenient starting point for a detpt theory (2i). The principle modification is the treatment of the FC factors for the overlap of the proton initial and final eigenstates, when the final proton state is characterized by a repulsive surface. The sum over final proton states becomes an integration over a continuum of states, and bound-unbound FC factors need to be evaluated. An approach can be formulated with methods that have been used to discuss bond-breaking electron-transfer reactions (22). If the motion along the repulsive surface for the dissociation can treated classically. 

In very recent work, Lieder (165) calculated standard potentials of the dithiocarbamate-thiuram disulfide redox system via thermochemical cycles and computational electrochemistry. A pathway proceeding via a single electron detachment is predicted to be the most favorable mechanism for dithiocarbamate oxidation, while thiuram disulfide reduction can proceed via two pathways. In the gas phase, reduction followed by sulfur-sulfur bond cleavage is energetically preferred, while in solution a concerted bond-breaking electron-transfer mechanism is predicted to be equally probable. 

The reactions between the ions are generally very rapid. In ionic reactions, where two ions simply combine, the rate of reaction is governed by the diffusion of ions towards each other and activation energy for the combination is very small. However, there are many reactions between ions which may be as slow as reactions between neutral molecules. Thus, reactions involve the making and breaking of covalent bonds or electron transfer. 

To briefly recap what has already been covered in Section 2, redox-active metals break the 0-0 bond by electron transfer, hence LOOH decomposes heteroly tic ally to generate radicals and ions. Reducing metals such as Fe and Cu generate alkoxyl radicals (LO ) and hydroxide ions (0H ), whereas oxidizing metals such... 

Does the bromine atom in 64 spontaneously fly away from the carbon No This is a silly question because 64 is a quite stable molecule. It is, however, possible for the bromine to be pulled off, but what can exert a pull on the bromine The only difference between the reaction that converted 64 to 65 and the reaction of Nal in ether that gives no reaction is the presence of water. What is special or different about water Refer to Table 11.2 to see that water is polar and protic. As seen in Section 11.2.3 (Figure 11.6), the 6+ hydrogen of water can coordinate with the 6- Br atom of 64, allowing water to pull on bromine. If water is pulling on bromine, eventually the C-Br bond breaks, with transfer of both electrons in that bond to form the bromide ion. This process will generate a carbocation intermediate with a formal charge of +1 on the reactive carbon. 

For a more detailed look at this reaction, iodomethane reacts with lithium metal, which is assumed to exist as a simple dimer (Li-Li). The products are lithium iodide and CHgLi (methyllithium, 33). When the lithium dimer comes close to the C-I bond of iodomethane, the polarized C-I bond induces a polarized Li-Li structure (an induced dipole) and the transition state of the reaction is taken to be 31. Rather than transferring two electrons, the Li-Li bond breaks with transfer of only one electron (homolytic cleavage remember that Li is in group 1), which leads to formation of a methyl radical ( 0113) and a lithium radical ( Li), as well as a lithium cation and an iodine anion (see 32). Transition state 31 represents the transfer of single electrons to generate radicals. When the methyl radical and the lithium radical combine, each donates... 

Most interest focuses on very fast reactions. This includes systems whose mean reaction times range from roughly 1 minute to 10 14 second. Reactions that involve bond making or breaking are not likely to occur in less than 10 13 second, since this is the scale of molecular vibrations. Some unimolecular electron transfer events may, however, occur more rapidly. 

A proton transfer reaction involves breaking a covalent bond. For an acid, an H — X bond breaks as the acid transfers a proton to the base, and the bonding electrons are converted to a lone pair on X. Breaking the H — X bond becomes easier to accomplish as the bond energy becomes weaker and as the bonding electrons become more polarized toward X. Bond strengths and bond polarities help explain trends in acidity among neutral molecules. 

As other examples one may quote the symmetry-breaking of the CASSCF (4e in 4MO) calculation of the inn twisted excited state of ethylene (G. Trinquier and Malrieu, in "The structirre of Double Bond". Patai ed., John Wiley (1990) p 1, or the symmetry-breaking in electron transfer problems (A. Faradzed, M. Dupuis, E. dementi and A. Aviram, J. Amer. Chem. Soc. 112, 4206 (1992). 

The reduced sites donate electrons to the reactant oxygen molecule and to intermediates formed, this electron transfer being coupled with bond breaking and making involved in the ORR process. 

In this chapter, we wiU review electrochemical electron transfer theory on metal electrodes, starting from the theories of Marcus [1956] and Hush [1958] and ending with the catalysis of bond-breaking reactions. On this route, we will explore the relation to ion transfer reactions, and also cover the earlier models for noncatalytic bond breaking. Obviously, this will be a tour de force, and many interesting side-issues win be left unexplored. However, we hope that the unifying view that we present, based on a framework of model Hamiltonians, will clarify the various aspects of this most important class of electrochemical reactions. 

Figure 2.1 (Plate 2.1) shows a classification of the processes that we consider they aU involve interaction of the reactants both with the solvent and with the metal electrode. In simple outer sphere electron transfer, the reactant is separated from the electrode by at least one layer of solvent hence, the interaction with the metal is comparatively weak. This is the realm of the classical theories of Marcus [1956], Hush [1958], Levich [1970], and German and Dogonadze [1974]. Outer sphere transfer can also involve the breaking of a bond (Fig. 2. lb), although the reactant is not in direct contact with the metal. In inner sphere processes (Fig. 2. Ic, d) the reactant is in contact with the electrode depending on the electronic structure of the system, the electronic interaction can be weak or strong. Naturally, catalysis involves a strong...

As demonstrated in Section 2.2, the energy of activation of simple electron transfer reactions is determined by the energy of reorganization of the solvent, which is typically about 0.5-1 eV. Thus, these reactions are typically much faster than bondbreaking reactions, and do not require catalysis by a J-band. However, before considering the catalysis of bond breaking in detail, it is instructive to apply the ideas of the preceding section to simple electron transfer, and see what effects the abandomnent of the wide band approximation has. 

Saveant JM. 1993. Electron transfer, bond breaking, and bond formation. Acc Chem Res 26 455 461. 

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