Marcus treatment

The quantities of anA and 3 uc are sensitivity eoeffieients elosely analogous to the quantity a that we eneountered in the Marcus treatment, and their interpretation is... 

The BEP/Hammond/Marcus treatment only considers changes due to energy differences between the reactant and product, i.e. changes in the TS position along the reaction coordinate. It is often useful also to include changes that may occur in a direction perpendicular to the reaction coordinate. Such two-dimensional diagrams are associated with the names of More O Ferrall and Jenks (MOJ diagrams). 

The Marcus treatment applies to both inorganic and organic reactions, and has been particularly useful for ET reactions between metal complexes that adopt the outer-sphere mechanism. Because the coordination spheres of both participants remain intact in the transition state and products, the assumptions of the model are most often satisfied. To illustrate the treatment we shall consider a family of reactions involving partners with known EE rate constants. 

The Brpnsted equations relate a rate eonstant k to an equilibrium constant K. In Chapter 6, we saw that the Marcus equation also relates a rate term (in that case AG ) to an equilibrium term AG°. When the Marcus treatment is applied to proton... 

In conforming to an expected linear free energy relationship, the Ce(lV) oxidation of various 1,10-phenanthroline and bipyridyl complexes of Ru(II) in 0.5 M sulphuric acid are consistent with the requirements of the Marcus treatment . The results for the oxidation of the 3- and 5-sulphonic-substituted ferroin complexes by Ce(IV) suggest that the ligand does not function as an electron mediator, and that the mechanism is outer-sphere in type. Second-order rate coefficients for the oxidation of Ru(phen)j, Ru(bipy)3, and Ru(terpy)3 are 5.8x10, 8,8 X 10, and 7.0 x 10 l.mole . sec, respectively, in 0.5 M H2SO4 at 25 °C a rapid-mixing device was employed. 

Section 3, are commonly classified as inner-sphere (contact) ion pairs (Kochi, 1988). Accordingly, in organic and organometallic processes a strong distinction must be made in their behaviour from that of other less common outer-sphere ion pairs that are pertinent to the Marcus treatment of electron-transfer dynamics (Eberson, 1987 Lee et al., 1991). 

The competition between the OsvCl6 reaction with a neutral compound (A) and a negatively charged one (A-), respectively, which is the experimental situation in some of the spin trapping reactions mentioned above, was analysed by the Marcus treatment for some model cases in dichloromethane or acetonitrile. These data are shown in Table 7, giving the details of the calculations in order to illustrate the use of equations (20) and (21) and the importance of the electrostatic factors, particularly in dichloromethane. The assumptions behind the calculations are given in the table heading and footnotes. 

How does this happen The answer is easily envisioned if the assumption in Marcus treatments, that the relevant potential surfaces cross only and always in the harmonic parabolic region, is dropped. When the crossing of potential surfaces for reactant and product occurs in the highly anharmonic region near the... 

From this brief description it is quite apparent that the qualitative elements of the Marcus treatment for an electron transfer process are identical to the CM model. In CM terms the reaction involves the avoided crossing of reactant (Fe2+ + Fe3+) with product (Fe3+ + Fe2+) configurations, with the reaction co-ordinate just being the distortion-relaxation motion of the solvation sphere. Thus in CM terms any electron transfer reaction involves the avoided crossing of the DA (donor-acceptor) and D+A" configurations, and for such reactions at least, based on the equivalence with Marcus theory, the CM model has a solid foundation. 

The Marcus treatment uses a classical statistical mechanical approach to calculate the activation energy required to surmount the barrier. It assumes a weakly adiabatic electron transfer process and non-equilibrium dielectric polarization of the solvent (continuum) as the source of activation. This model also considers the vibrational contributions of the inner solvation sphere. The Hush treatment considers ion-dipole and ligand field concepts in the treatment of inner coordination sphere contributions to the energy of activation [55, 56]. 

The Marcus treatment for heterogeneous electron transfer at electrodes is analogous to the homogeneous case of redox reactions in solution discussed in Vol. 2, Chap. 4. The free energy of activation can also be expressed by... 

Marcus treatment does not exclude a radical pathway in lithium dialkyl-amide reduction of benzophenone. It does, however, seem to be excluded (Newcomb and Burchill 1984a,b) by observations on the reductions of benzophenone by N-lithio-N-butyl-5-methyl-l-hex-4-enamine in THF containing HMPA. Benzophenone is reduced to diphenylmethanol in good yield, and the amine yields a mixture of the acyclic imines no cyclic amines, expected from radical cyclization of a putative aminyl radical, were detected. An alternative scheme (17) shown for the lithium diethylamide reduction, accounts for rapid formation of diphenylmethoxide, and for formation of benzophenone ketyl under these conditions. Its key features are retention of the fast hydride transfer, presumably via the six-centre cyclic array, for the formation of diphenylmethoxide (Kowaski et al., 1978) and the slow deprotonation of lithium benzhydrolate to a dianion which disproportion-ates rapidly with benzophenone yielding the ketyl. The mechanism demands that rates for ketyl formation are twice that for deprotonation of the lithium diphenylmethoxide, and, within experimental uncertainty, this is the case. 

When NMA+ reacts with phenyl-substituted N-phenyldihydronicotin-amides, X-PhNAH, also in anhydrous acetonitrile (Powell and Bruice, 1983b), rate and equilibrium data yield a Bronsted plot with a slope of 0.51, consistent with a centrally located transition state. The primary k.i.e. s h2/ d2, increase from 3.98 for X = />-methoxy to 4.77 for X = m-trifluoro-methyl at 50° and may indicate a trend to a more symmetrical transition state. Marcus treatment of the substituent dependence of the k.i.e. s yields an intrinsic barrier AG = 22.2 kJ mol - L. The temperature dependence of the k.i.e. for reduction by X-PhNAH with X = / -methyl gives [A ] = 7.68 kJ mol-1, but AJA = 4.3 is unusually large. A tunnelling correction of ca. 2 was estimated so that the semi-classical k.i.e. was in the range 2 to 3. 

Electron transfer reactions may be correlated by the Marcus treatment and some peculiarities of the use of this model, in the case of oxyanions, are pinpointed. 

The rate of proton transfer has been measured for a number of metal hydride/organic amine combinations. The rates appear to follow Marcus behavior see Marcus Treatment), in which the rate goes up with driving force (equation 21, where ab is the rate of proton transfer between AH and B , and Kxr is the equilibrium constant for the proton transfer). Proton transfer appears to be the slow step in the process, rather than slow electron transfer followed by fast H atom transfer, because the rates show an isotope effect. For example, in the self-exchange of [CpM(H,D)(CO)3]/[CpM(CO)3] , kn/ko is 3.6, 3.7, and 3.7 for Cr, Mo, and W. There seems to be a good relation between thermodynamic acidity and kinetic... 

The BEP/Hammond/Marcus treatment only considers changes due to energy differences ... 

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