Kinetics Marcus theory

Electrode kinetics electrode, -> kinetics, Butler-Volmer equation, -> charge transfer kinetics, Marcus theory... 

Samec Z, Weber J (1973) The influence of chemisorbed sulfur on the kinetic parameters of the reduction of Fe " ions on a platinum electrode on the basis of the Marcus theory of electron transfer. J Electroanal Chem Interfacial Electrochem 44 229-238... 

Comparison of equations (2.11) and (2.15) reveals q and r to be kikilk i and A 2//r i, respectively. This enables k to be calculated from qjr. In its simplest forms the structure of the reactive intermediate can be viewed as V(OH)Cr " (when n is 1) or as VOCr (when n is 2). Similar species which have been characterized or implied kinetically are CrOCr (ref. 33), Np02Cr (ref. 37), U02Cr (ref. 31), VOV " (ref. 34), U0Pu02 + (ref. 41), Pu02pe + (ref. 42) and FeOFe + (ref. 38). Predictions on the rate of the V(III)- -Cr(lI) system, based upon Marcus theory", have been made by Dulz and Sutin on the assumption that an outer-sphere process applies. The value arrived at by these authors is 60 times lower than the experimental value. 

On this basis Cr(V), not Cr(IV), is the kinetically important intermediate such that k = 3 k4 and k = k Jk. The hydrogen-ion dependence of the reaction rate has been discussed. Furthermore, comparisons are drawn with the rate of the Cr(VI)+Fe(phen)3 reaction, and Sullivan has speculated on the intimate nature of both mechanisms in the light of Marcus theory... 

In order to account for the foregoing kinetic behavior, we rely on the Marcus theory for outer-sphere electron transfer to provide the quantitative basis for establishing the free energy relationship (8), i.e.,... 

There are three points of significance of this result. One is that it provides strong support for the 10-step mechanism originally proposed for reaction 1. Another is that it facilitates a more robust fitting of the mechanism to the kinetic data obtained for that reaction. Thirdly, it confirms that reaction 2 has a rate constant that is four orders of magnitude greater than predicted by Marcus theory. It is concluded that reaction 2 is poorly modeled as an outer-sphere process and is better described as... 

Apply the Marcus theory to photoinduced electron transfer and show how experimental evidence gives a relationship between the kinetics of the process and the thermodynamic driving force. 

In a series of important papers Marcus and coworkers applied the RRKM (Rice-Ramsberger-Kassel-Marcus) theory of unimolecular reactions to the ozone problem in a successful effort to rationalize the MIF s described above (see Historical Vignette 14.1). The 2002 paper of Gao and Marcus (reading list) considered a kinetic scheme which mildly elaborates that of Equation 14.1... 

Of course, Marcus theory does not stop at this juncture but attempts to provide a quantitative relationship between reaction kinetics and thermodynamics. On the basis of Marcus theory the barrier to a particular reaction AG, may be described as a function of a parameter called the intrinsic barrier, AG, and the free energy of the reaction AG°. The particular relationship is presented in (112). The basic idea here is that the barrier height is composed of two contributions, a kinetic component termed the intrinsic... 

Marcus theory (15) has been applied to the study of the reductions of the jU,2-superoxo complexes [Co2(NH3)8(/u.2-02)(/i2-NH2)]4+ and [Co2(NH3)10(ju.2-O2)]6+ with the well-characterized outer-sphere reagents [Co(bipy)3]2+, [Co(phen)3]2+, and [Co(terpy)2]2+, where bipy = 2,2 -bipyridine, phen = 1,10-phenanthroline, and terpy = 2,2 6, 2"-terpyridine (16a). The kinetics of these reactions could be adequately described using a simple outer-sphere pathway, as predicted by Marcus theory. However, the differences in reactivity between the mono-bridged and di-bridged systems do not appear to be explicable in purely structural terms. Rather, the reactivity differences appear to be caused by charge-dependent effects during the formation of the precursor complex. Some of the values for reduction potentials reported earlier for these species (16a) have been revised and corrected by later work (16b). 

One of the most important new areas of theory of charge transfer reactions is direct molecular simulations, which allows for an unprecedented, molecular level view of solvent motion during reactions in this class. One of the important themes for research of this type is to ascertain the validity at a molecular level of the linear response theory estimates of solvent interactions that are inherent in Marcus theory and related approaches. In addition, the importance of dynamic solvent effects on charge transfer kinetics is being examined. Recent papers on this subject have been published by Warshel [71], Hynes [141] and Bader and Chandler [137, 138],... 

Electron transfer reactions have been characterized with much more rigor in inorganic chemistry than with organic molecules. Marcus has provided the principal description relating the kinetics and thermodynamics of electron transfer between metal complexes (1). The Marcus theory, a computationally simple approach with good predictive power, is an empirical treatment which uses thermodynamic parameters and spectroscopic measurements to calculate kinetic data. It assumes that bimolecular electron transfer reactions occur in three stages as shown in Scheme 1 (1) formation of the precursor complex, (2) electron transfer, and (3) solvation of the redox pair. 

Electron transfer may also dominate the excited state chemistry of open shell radical ions. The fluorescence of the radical anions of anthraquinone and 9,10-dicyanoanthracene and the radical cation of thianthrene are quenched by electron acceptors and donors, respectively, although detailed kinetic analysis of the electron exchange do not correspond exactly either with Weller or Marcus theory (258). The use of excited radical cations as effective electron acceptors represents a... 

It has been reported that rates of proton transfer from carbon acids to water or hydroxide ion can be predicted by application of multi-dimensional Marcus theory to a model whereby diffusion of the base to the carbon acid is followed by simple proton transfer to give a pyramidal anion, planarization of the carbon, and adjustment of the bond lengths to those found in the final anion.124 The intrinsic barriers can be estimated without input of kinetic information. The method has been illustrated by application to a range of carbon acids having considerable variation in apparent intrinsic barrier. 

Inner-sphere electron transfers are characterized by (a) temperature-independent rate constants that are greatly higher and rather poorly correlated by Marcus theory (b) weak dependence on solvent polarity (c) low sensitivity to kinetic salt effects. This type of electron transfer does not produce ion radicals as observable species but deals with the preequilibrium formation of encountered complexes with the charge-transfer (inner-sphere) nature (see also Rosokha Kochi 2001). 

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