Marcus theory, applications

Magnesium, arylation 273 Marcus theory, application to dediazonia-tion 197... 

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... 

E. Laborda, M. C. Henstridge, and R. G. Compton. Asymmetric Marcus theory Application to electrode kinetics, J. Electroanal. Chem. 667, 48-53 (2012). 

This is the reverse of the first step in the SnI mechanism. As written here, this reaction is called cation-anion recombination, or an electrophile-nucleophile reaction. This type of reaction lacks the symmetry of a group transfer reaction, and we should therefore not expect Marcus theory to be applicable, as Ritchie et al. have emphasized. Nevertheless, the electrophile-nucleophile reaction possesses the simplifying feature that bond formation occurs in the absence of bond cleavage. 

Applications of the Marcus theory are by no means limited to electron transfer. The generality of this approach has been cited.38... 

Recently, Hurwitz and Kustin have reinvestigated this exchange reaction using the same isotopic procedure and the 2-butanone separation method, in conjunction with a stopped flow apparatus. A rate coefficient of 2.3 x 10 l.mole . sec was obtained for the conditions, temperature 25 °C and ionic strength 0.1 M. Application of the Marcus theory to results obtained for the reaction... 

The value of E° was hence determined by the reaction of R4M with Fe3+ complexes as outer-sphere SET oxidizers. Using five complexes with a range of different E° values, from 1.15 to 1.42 V, the rate constants were determined193. This was followed up by Eberson who, by application of the Marcus theory, was able to determine from the E° values (shown in Table 18) standard potentials and reorganization energies. Most compounds... 

Marcus theory, first developed for electron transfer reactions, then extended to atom transfer, is now being applied to catalytic systems. Successful applications to catalysis by labile metal ions include such reactions as decarboxylation of oxaloacetate, ketonization of enolpyru-vate, and pyruvate dimerization (444). 

Before we can enter a discussion of the redox processes involved in the two mechanisms defined above, we need a simple theoretical background which provides relevant insights into the phenomenon of ET. The Marcus theory of outer-sphere ET provides such a framework for the delineation of mechanistic domains, thanks to its origin in a simple model and its classical nature (Marcus, 1964 Marcus and Sutin, 1985 for applications in organic chemistry, see Eberson, 1982b, 1987). 

Spin trapping is an often-used technique in the study of possible radical production in biological systems (for reviews see Kalyanaraman, 1982 Mason, 1984 Mottley and Mason, 1989), particularly by the detection and monitoring of spin adducts of the hydroxyl and hydroperoxyl ( OOH) radicals in view of their relation to possible damage mechanisms. This is a large area of research which it is not possible to cover in a limited review, and the treatment will therefore be restricted to a discussion of the electron transfer properties of biochemical systems (for a review on the application of the Marcus theory to reactions between xenobiotics and redox proteins, see Eberson, 1985) and... 

Our approach to these problems has been to study S 2 reactions in the gas phase. Ion-molecule studies have proven very effective in understanding equilibrium behavior of ions in solution (4), and we think there is great potential in the dynamic areas. As it happens, we find that Marcus theory may be especially applicable, in that the process of interest is a unimolecular one and obviates dealing with encounters, work terms, etc. Thus, we can readily extract solvent free quantities of interest. 

It should be noted that application of the Marcus theory to these reactions is much more straightforward than application to reactions in solution. Since we are dealing with a single unimolecular step, namely, rearrangement of the reactant complex to the product complex, we need not be concerned with the work terms (2) which must be included in treatments of solution-phase reactions. These terms represent the work required to bring reactants or products to their mean separations in the activated complex, and include Coulombic and desolvation effects. 

One difficulty that arises within the Marcus formulation is that the intrinsic barrier term is ideally treated as a constant. Earlier applications of Marcus theory were based on this assumption (Cohen and Marcus, 1968 Kreevoy and Konasewich, 1970 Kreevoy and Oh, 1973 Albery et al., 1972). However, as regards methyl transfer, this assumption is clearly invalid. 

Hammond behaviour may be observed if the intersecting parabolae are of different curvature. The physical interpretation of this difference in curvature is that bond-making and bond-breaking processes are not necessarily synchronous as is assumed in conventional Marcus theory. While such a modification in the theory may overcome the inherent problem of treating anti-Hammond effects it does make application of the Marcus theory more difficult by the introduction of additional unknowns into the free energy relationship of (112). 

Take a mean value of 80 (i.e., 0.83 eV). Numerical calculations show that T] < 0.2 V is the condition up to which 9.38 yields the experimental version of Tafel s law (of course, the value depends on the Fs chosen and the allowed T, for the applicability of 9.38 will be roughly halved at the lower limit and doubled at the higher one. In any case, this harmonic approximation, which is involved in the Weiss—Marcus theory, cannot be applied to the experimental current-potential data, which in reality extend over 0.2 V and even 1.0 V (for hydrogen and oxygen evolution). 

For applications of Marcus theory to proion transfers, sec Marcus /. Phys. Chem. 1968, 72. 891 Krccvuv Konascwich Adv. Chem. Phys. 1971, 21. 243 Krcsgc Chem. Soc. Rev. 1973, 2. 475-503. 

Applications of the Marcus theory to reactions of nickel(III) species with Fe2+ and V02+ aquo ions 158) lead to values of 10 3-10-2 M l sec-1 for Fe3+/2+ and 10-103 M-1 sec-1 for VO(OH)2+/+. These rate constants are larger than for the corresponding data derived using poly (pyridine) derivatives where there may be a contribution from the n -n interaction of the ligand orbitals. 

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. 

However, even for the simple methyl transfer reactions, there is considerable confusion and some disagreement about the details of the mechanism. Some authors (Sneen, 1973) have suggested that ionization of RX always precedes attack by the nucleophile, while others have maintained that the nucleophile attacks the covalent substrate. Extensive references to both points of view are given by McLennan (1976). In the present review the application of the Marcus theory of atom transfer (Marcus, 1968a) allows us to deduce values of the parameter a which describes the symmetry of the transition state. We shall compare this information about the transition state with that from changing the solvent, from isotope effects, and from Hammett relations. We shall then attempt to deduce a model for the transition state which is consistent for all the different types of data. 

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