Marcus relationship

Indeed, the oxidation of Fe(CN)g by O2 (as well as by H2O2 and BrOj) proceeds via the rds of dissociation of the hexa- to the penta-cyano complex. The value of k in (8.90) is 5.6 X lO M s at pH > 3.8. Traces of Fe from decomposition of the cyano complex promote catalytic oxidation (Prob. 19). A large number of complexes of the type Fe(CN)5X" for both Fe(II) and Fe(III) have been studied and cross-reaction redox kinetics abound. Care has to be exercised in the use of FeiCN) . Daylight can induce changes in the complex even within an hour and catalytic effects (traces of Cu Sec. 3.1.4) have to be considered. In addition, the sensitivity of the values of and rate constants to medium effects lessen the value of the iron-cyano complexes as reactant partners for the demonstration of Marcus relationships. Nevertheless, they, with other inorganic complexes, have been extensively employed to probe the peripheral characteristics of metallopro-teins. 

In summary, then, it appears that the Marcus relationship and the CM model are closely related. The former provides a quantitative framework for tackling reactivity problems while the latter is qualitative in nature. The CM model however makes up for this deficiency by providing added insight into the factors governing reactivity through a physical description of the reaction barriers in any given case. In this sense the CM model is more chemical in its format than the functional form of the Marcus equation. 

The observed behavior qualitatively follows the Marcus relationship for atom transfer, which predicts that the ratio of rate constants for hydrogen transfer from a common donor to two different acceptors will depend only on the relative energies of the bonds being formed, as described below. 

Notwithstanding the possibility of variation of an intrinsic barrier within a reaction series, for comparisons between different reactions it is often convenient to assume that an unmodified Marcus expression applies. This approximation is justified partly by the high intrinsic barriers and small amounts of curvature characteristic of most reactions at carbon, including reactions of carbocations. The Marcus relationship then provides a common framework for comparisons between reactions based on the measurement of even a single combination of rate and equilibrium constants. Thus, calculation... 

The acidity constants of protonated ketones, pA %, are needed to determine the free energy of reaction associated with the rate constants ArG° = 2.3RT(pKe + pK ). Most ketones are very weak bases, pAT < 0, so that the acidity constant K b cannot be determined from the pi I rate profile in the range 1 < PH <13 (see Equation (11) and Fig. 3). The acidity constants of a few simple ketones were determined in highly concentrated acid solutions.19 Also, carbon protonation of the enols of carboxylates listed in Table 1 (entries cyclopentadienyl 1-carboxylate to phenylcyanoacetate) give the neutral carboxylic acids, the carbon acidities of which are known and are listed in the column headed pA . As can be seen from Fig. 10, the observed rate constants k, k for carbon protonation of these enols (8 data points marked by the symbol in Fig. 10) accurately follow the overall relationship that is defined mostly by the data points for k, and k f. We can thus reverse the process by assuming that the Marcus relationship determined above holds for the protonation of enols and use the experimental rate constants to estimate the acidity constants A e of ketones via the fitted Marcus relation, Equation (19). This procedure indicates, for example, that protonated 2,4-cyclohexadienone is less acidic than simple oxygen-protonated ketones, pA = —1.3. 

Fig. 2. Plot of the fluorescence quenching rate constants k, vs the free energy changes AG for the electron transfer process (a) Marcus relationship, (b) Rehm-Weller relationship...

A, direct measurement of the exchange reaction B, estimate of the self-exchange rate by application of the Marcus relationship to cross reactions. 

The parabolic shape of the curve, going from a slope of d log kid log K of 0 for very exergonic redox reactions to for reactions close to AG = 0 and to -1 for rather endergonic reactions, is typical for the Marcus relationship (equation 46). 

The relationship and trend between AG (or log k) and AG (or log K) of the Marcus relationship can be appreciated by looking at the simplified scheme of Figure 11.17d. Figure 11.17d illustrates that a small activation energy (AG ... 

Figure 2 shows this for oxidation of various substituted phenanthroline Fe(II) complexes by Ce(IV). An average rate constant of 2 x 103 M 1 s -1 was found for the phenanthroline-Fe(II)-FE(III) exchanges by this approach (Dulz and Sutin, 1963) this compares with a value of 4 M i s-1 for the free ions. Many studies have verified the Marcus relationship for metal ion redox reactions, and large deviations are assumed to indicate that the reaction occurs by an inner-sphere mechanism. (Note An outer-sphere mechanism can be inferred if the redox reaction is faster than the rates of ligand exchange for the metal ions.)... 

Equation 5.7 Classical Marcus relationship for the activation free energy of electron transfer... 

The kinetic behavior of the reductions of several Cu(II)N2S2 complexes, containing thioether/pyridyl chelate ligands, by ferrocene and l,r-dimethyl-ferrocene in acetonitrile points to the formation of a precursor complex prior to electron transfer.The rate constant for the oxidation of (hydroxyethyl)-ferrocene by [2-pyridyl(methylbis(2-ethyl)thioethyl)amine]copper(II) yields a [Cu(pmas)] self-exchange rate constant of 47 M s from the Marcus theory relation.The addition of NJ increases the rate of oxidation (F" and I" have no effect) by shifting the reduction potential upon the formation of [Cu(pmas)N3] and Cu(pmas)(N3)2 (NJ displacement of a thioether sulfur occurs in the latter species). The application of the Marcus relationship to the reductions of the [l,8-bis(2-pyridyl)-3,6-dithiaoctane]copper(II) complex by a series of Ru(II) ammine and bipyridyl complexes in 50% aqueous CH3OH yields a self-exchange rate constant of 0.63 s for the [Cu(pdto)] couple. " From the rate... 

An application of the Marcus relationship to the rate constants for the oxidations of [VO(TCDA)] (TGDA = l,4,7-triazacyclononane-N,Ar -diacetate) and [VO(DOCDA)] (DOCDA = l-oxa-4,7-diazacyclononane-A/,N -diacetate) by [Ni([9]aneN3)2] yields self-exchange rate constants of 0.75 and 0.54 s" for... 

The electron self-exchange rate constant for the [Cr(CNdipp)6] couple (CNdipp = 2,6-diisopropylphenyl isocyanide) in CD2CI2 has been measured between -89 and +22 °C using H NMR line-broadening techniques, with an extrapolated value of 1.8 x 10 M s determined for 25 The kinetics of the outer-sphere oxidations of tris(polypyridine)chromium(II) complexes by a series of tris(chelate)cobalt(III) species have been studied in aqueous solution. " The cross-reaction rate constants obey the Marcus relationship, with the exception of [Co(bpy)3] " and [Co(phen)3] ", for which mild nonadiabaticity (/[Pg.18]

The rate constants and activation parameters (including AV ) for electron self-exchange in the [Mn(CNC(CH)3)6]-"/ -" and [Mn(CNC6Hu)6] couples have been determined by Mn NMR line broadening in several pure and binary organic solvent systems. The values of A V cover a range of about 12 cm moP (-9 to -21 cm mol ) with no simple correlation with solvent parameters observed. A self-exchange rate constant of 0.7 0.4 M" s" has been calculated for the [Mn(edta)(H20)] and [Mn(cdta)(H20)] couples from the application of the Marcus relationship to outer-sphere cross-reactions with a variety of metal complexes in aqueous solution. Deviations from the correlation were observed for the nonadiabatic reactions with osmium tris(polypyridine) complexes. 

The electron self-exchange rate constants for several Fe(II)/Fe(III) porphyrin couples have been measured by H NMR line-broadening techniques in 5 1 acetone/water at -20 The relative rate constants for the [Fe(P)(l-MeIm)2] couples, P = octaethylporphyrin chlorin < isobacteriochlorin, have been attributed to differences in outer-sphere reorganization, related to the steric bulk. The rate-determining step in the metallopophyrin-catalyzed reductions of dioxygen by substituted ferrocenes is the electron transfer between the ferrocene and the metalloporphyrin (M = Fe, Co, and The Marcus relationship provides a... 

The kinetic data for a series of outer-sphere electron transfer reactions between the [Rh2(02CCH3)4(CH3CN)2] couple and nickel tetraaza macrocycles and iron and ruthenium tris(polypyridine) complexes in acetonitrile have been correlated in terms of the Marcus relationship, yielding a [Rh2] electron exchange rate constant of 3.0 1.7 x 10 M A somewhat smaller value of 5.3 1.3 x... 

One of the most fundamental achievements of the seminal Marcus theory on electron-transfer reactions is the nowadays widely used quadratic driving force-activation free energy Marcus relationship... 

In a subsequent investigation, Deshayes and Piotrowiak provided clear support for the parabolic Marcus relationship and explained earlier data in a quantitative manner by... 

C.F. Bemasconi and J.X. Ni, Proton transfer from carbon acids to carbanions. 1. Reactions of various carbon acids with the anions of substituted benzylmalononitriles in 90% Me2SO-10% water. Determination of intrinsic barriers of identity reactions fifom the Marcus relationship, J. Am. Chem. Soc., 115 (1993) 5060. 

Rodriguez-Lopez, J., Minguzzi, A., Bard, A.J. The reaction of various reductants with oxide films on Pt electrodes as studied by the surface interrogation mode of scanning electrochemical microscopy (Sl-SECM). Possible validity of a Marcus relationship. 7. Phys. Chem. C 2010, 114, 18645-18655. 

The value of 6 is somewhat smaller than that predicted from the simplified Marcus relationship (0.5). From the log kc thus... 

The kinetics of several electron transfer reactions of the molybdenum cuboidal system [Mo4S4(edta)2]" ( = 2, 3, 4) with cross-reactants such as [Co(edta)]-, [Fe(edta)]-, [Co(dipic)2] , [Fe(H20)e], and [Pta ] -, have been investigated. The electron self-exchange rate constants determined for the [Mo4S4(edta)2] and [Mo4S4(edta)2] couples, by an application of the Marcus relationship, are 1.5 x 10 and 7.7 x 10 M s , respectively. The rate constants for the outer-sphere oxidation of two dimeric complexes, [MoW 0)2(p-edta-AT,lV )]2- and [W2(0)2(p-0)(p-S)(p-edta-Ar,iV )] -, by [IrCl ] in addic aqueous solution have been measured. While the oxidation of the former complex shows a simple second-order rate law, the kinetics of the oxidation of the latter complex exhibited a rate retardation in the presence of the [IrCl6] complex. 

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