Marcus equation application

The first attempt to describe the dynamics of dissociative electron transfer started with the derivation from existing thermochemical data of the standard potential for the dissociative electron transfer reaction, rx r.+x-,12 14 with application of the Butler-Volmer law for electrochemical reactions12 and of the Marcus quadratic equation for a series of homogeneous reactions.1314 Application of the Marcus-Hush model to dissociative electron transfers had little basis in electron transfer theory (the same is true for applications to proton transfer or SN2 reactions). Thus, there was no real justification for the application of the Marcus equation and the contribution of bond breaking to the intrinsic barrier was not established. 

Arnett and coworkers later examined the reaction of lithium pinacolone enoiate with substituted benzaldehydes in THE at 25 °C. The determination of the heat of reaction indicated that the Hammett p value for the process is 331. Although the aldol reaction was instantaneous in THF at 25 °C, the reaction with o- or p-methylbenzaldehyde could be followed using a rapid injection NMR method in methylcyclohexane solvent at —80 °C. Application of Eberson s criterion based on the Marcus equation, which relates the free energy of ET determined electrochemically and the free energy of activation determined by kinetics, revealed that the barriers for the ET mechanism should be unacceptably high. They concluded that the reaction proceeds via the polar mechanism . Consistent with the polar mechanism, cyclizable probe experiments were negative . The mechanistic discrepancy between the reactions of benzaldehyde and benzophenone was later solved by carbon kinetic isotope effect study vide infraf. ... 

The applicability of the Marcus equation (Eq. 14) to MCET reactions was examined using a ferrocene-naphthoquinone dyad (Fc—NQ) as discussed below (Scheme 19)(121,122). No ET from the Fc to NQ moiety occurs in Fc—NQ with a... 

Application of the Marcus equation for electron transfer affords the electron exchange rate of the molybdenum radical/anion couple. The value is fcge = 3 X 10 L mol s. The high value argues that very little nuclear reorganization is needed to add an electron to the SOMO of the 17e radical. 

Magnetic moment, 153, 155, 160 Magnetic quantum number, 153 Magnetization, 160 Magnetogyric ratio, 153, 160 Main reaction, 237 Marcus equation, 227, 238, 314 Marcus plot, slope of, 227, 354 Marcus theory, applicability of, 358 reactivity-selectivity principle and, 375 Mass, reduced, 189, 294 Mass action law, 11, 60, 125, 428 Mass balance relationships, 19, 21, 34, 60, 64, 67, 89, 103, 140, 147 Maximum velocity, enzyme-catalyzed, 103 Mean, harmonic, 370 Mechanism classification of. 8 definition of, 3 study of, 6, 115 Medium effects, 385, 418, 420 physical theories of, 405 Meisenheimer eomplex, 129 Menschutkin reaction, 404, 407, 422 Mesomerism, 323 Method of residuals, 73 Michaelis constant, 103 Michaelis—Menten equation, 103 Microscopic reversibility, 125... 

The data summarized in Table 2 indicate that the series of cyanine borates with the n-butyltriphenylborate counterion possess a negative AGei value, i.e., they fulfill the basic Rehm Weller requirements for effective photoinduced electron transfer processes. Extending this to a practical application of the Marcus equation (see... 

Many reactions exhibit effects of thermodynamics on reaction rates. Embodied in the Bell-Evans-Polanyi principle and extended and modified by many critical chemists in a variety of interesting ways, the idea can be expressed quantitatively in its simplest form as the Marcus theory (15-18). Murdoch (19) showed some time ago how the Marcus equation can be derived from simple concepts based on the Hammond-Leffler postulate (20-22). Further, in this context, the equation is expected to be applicable to a wide range of reactions rather than only the electron-transfer processes for which it was originally developed and is generally used. Other more elaborate theories may be more correct (for instance, in terms of the physical aspects of the assumptions involving continuity). For the present, our discussion is in terms of Marcus theory, in part because of its simplicity and clear presentation of concepts and in part because our data are not sufficiently reliable to choose anything else. We do have sufficient data to show that Marcus theory cannot explain all of the results, but we view these deviations as fairly minor. 

The first application of the Marcus equation (3e) to methyl transfers was the study by Albery and Kreevoy (4, 5) based on data in solutions. In this study, the thermodynamic data of Abraham and McLennan (6) were used, and the identity barriers were more or less treated as adjustable parameters. The treatment was qualitatively plausible, but the quantitative identity barriers were not completely convincing. An important study (7) showed the application of the Marcus equation to methyl transfer in the gas phase. 

The semiclassical Marcus equation can be applied to electron transfer between spatially fixed and oriented redox centers (26). Values obtained by employing this theoretical framework are in good agreement for both wild type and single-site mutants of Pae azurin (15), thus supporting the applicability of this analysis of the LRET process. The mechanism of intramolecular electron transfer through matrices of biological macromolecules, mainly proteins, has attracted considerable current interest (25). Moreover, the question of whether... 

The reactions of the photochemically prepared [U02] ion with a series of chromium, ruthenium, and cobalt complexes have been studied/ An application of the Marcus equation to the cross-reaction data yields a [U02] self-exchange rate constant in the range of 1-15 s The reactions with the chromium and... 

Reactions of cobalt complexes of macrocyclic tetramine ligands with various couples (including the highly oxidizing MnCl /, hitherto little studied) have been reported. Inner-sphere and outer-sphere reactions involving, for example, [Ru(NH3)6py] +/ + have been characterized. A free-energy correlation for reactions between [Co(N4)(OH2)2] with inner-sphere oxidants shows the expected slope 9AG /3AG 0.5 down to a limit of AG a 7 kcal mol, which is believed to represent diffusion control. Application of the Marcus equations (1) and (3) to reactions of both types leads to an assessment of the factors con-... 

The requirements for application of the Marcus equation to reactions other than electron transfer are expressed in precise and succinct form hy J. Jortner, Faraday Discuss. Chem. Soc. 74 (1982) 306, 307. See also the contributions to that Discussion by R.A. Marcus, p. 306 and J.R. Murdoch, pp. 297 seq. 

KAB 98] Kabatc J., Pietrzak M., Paczkowski J., Cyanine borates revisited. Application of the Marcus equation for the description of the kinetics of photoinitiated free radical polymerization . Macromolecules, vol. 31, pp. 4651-4654, 1998. 

Several useful reviews have appeared this year. Synthesis-related reviews include the synthetic applications of selenium-stabilized carbenium ions/ the use of C-acylnitrilium ions to initiate cyclization in the synthesis of heterocycles/ and the involvement of carbocation intermediates in the cyclization of olefins with mercuric triflate. Solvolysis and rearrangement in unsaturated carbon cage compounds is reviewed/ backside r-bond assistance is suggested as being always involved." The Marcus equation is shown to be very useful in the determination of intrinsic barriers to the formation and reactions of carbocations. ... 

S. Scheiner and X. Duan, Applicability of the Marcus equation to proton transfer in symmetric and unsymmetric systems, J. Mol. Struct. (Theochem), 285 (1993) 27. 

If A > — 1, AG = w,. Qualitatively, w, is related to the maximum rate for a reaction strongly favoured by AG , and 2 is the parameter which governs the curvature of the Bronsted plot. The Marcus equation thus relates AG to AG°, as does the Bronsted equation, but is more explicit about the various factors affecting the rate. The need for reactant and solvent reorganization is recognized by the inclusion of the term w,. The equation, as originally applied to electron-transfer reactions, was derived for weak-overlap interactions, and its application to atom- and proton-transfer reactions, which involve strong-overlap interactions, requires justification by successful application. 

Murdoch [53] derives an equation similar to the Marcus equation, equation 11, by the application of Hammond s postulate to the Eigen mechanism... 

Marcus equation was later found to be also applicable to proton transfer and group transfer reactions. 

Equation (5-69) is an important result. It was first obtained by Marcus " in the context of electron-transfer reactions. Marcus derivation is completely different from the one given here. In electron transfer from one molecule (or ion) to another, no bonds are broken or formed, so the transition state theory does not seem to be applicable. Marcus assumed negligible orbital overlap in the electron-transfer transition state, but he later obtained the same equation for group transfer reactions requiring significant overlap. Many applications have been made to proton transfers and nucleophilic displacements. ... 

In many cases, the values of A n and k2i may be directly or indirectly determined. We shall say no more about this relationship here, other than to indicate that it proves to be generally applicable, and is sufficiently accepted that the Marcus-Hush equation is now used to establish when an outer-sphere pathway is operative. In the context of this chapter, the involvement of the Kn term is interesting for it relates to the relative stabilization of various oxidation states by particular ligand sets. The factors which stabilize or destabilize particular oxidation states continue to play their roles in determining the value of Kn, and hence the rate of the electron transfer reaction. 

How applicable is the Marcus rate equation to organic chemistry ... 

The reversibility of the [Os(bpy)3]3+/2+ couple makes it useful for the determination of the electron self-exchange rates of other couples by application of the Marcus cross-reaction equation. Recently, this has been applied to the oxidation of S032- to S042- (622). The new rate constant for this reaction of 1.63 x 107 M-1 sec-1 is consistent with the... 

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