Proton transfer Marcus theory

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. ... 

Rates of addition to carbonyls (or expulsion to regenerate a carbonyl) can be estimated by appropriate forms of Marcus Theory. " These reactions are often subject to general acid/base catalysis, so that it is commonly necessary to use Multidimensional Marcus Theory (MMT) - to allow for the variable importance of different proton transfer modes. This approach treats a concerted reaction as the result of several orthogonal processes, each of which has its own reaction coordinate and its own intrinsic barrier independent of the other coordinates. If an intrinsic barrier for the simple addition process is available then this is a satisfactory procedure. Intrinsic barriers are generally insensitive to the reactivity of the species, although for very reactive carbonyl compounds one finds that the intrinsic barrier becomes variable. ... 

Marcus, R. A., Similarities and differences between electron and proton transfers at electrodes and in solution, Theory of hydrogen evolution reaction, Proc. Electrochem. Soc., 80-3, 1 (1979). 

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. 

This enzyme [EC 4.2.1.1], also referred to as carbonate dehydratase, is a zinc-dependent enzyme that catalyzes the reaction of carbon dioxide with water to form carbonic acid (or, of bicarbonate and a proton). See also Proton Transfer in Aqueous Solution Manometric Assay Methods Marcus Rate Theory... 

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. 

The 1977 review of Martynov et al. [12] discusses existing mechanisms of ESPT, excited-state intramolecular proton transfer (ESIPT) and excited-state double-proton transfer (ESDPT). Various models that have been proposed to account for the kinetics of proton-transfer reactions in general. They include that of association-proton-transfer-dissociation model of Eigen [13], Marcus adaptation of electron-transfer theory [14], and the intersecting state model by Varandas and Formosinho [15,16], Gutman and Nachliel s [17] review in 1990 offers a framework of general conclusions about the mechanism and dynamics of proton-transfer processes. 

Electrochemical and photochemical processes are the most convenient inputs and outputs for interfacial supramolecular assemblies in terms of flexibility, speed and ease of detection. This chapter provides the theoretical background for understanding electrochemical and optically driven processes, both within supramolecular assemblies and at the ISA interface. The most important theories of electron and energy transfer, including the Marcus, Forster and Dexter models, are described. Moreover, the distance dependence of electron and energy transfer are considered and proton transfer, as well as photoisomerization, are discussed. 

Marcus theory (Marcus, 1968, 1969), originally developed to interpret the rates of electron transfer reactions, has been successfully applied to proton transfer reactions as well. The theory relates... 

Considerable work has been invested in the experimental verification of Marcus theory. Kreevoy and Konasewich (1971) have studied the hydrolysis of the diazoacetate ion catalysed by a series of phenols and carboxylic acids (20). Proton transfer takes place in the... 

Apart from these studies of curved Br nsted plots which have been utilized to verify Marcus theory, many additional examples of curved plots are known together they provide considerable evidence in support of an inverse relationship between reactivity and selectivity in proton transfer reactions. 

Eigen (1964) found that a plot of ApR against the rate constant for proton transfer between acetylacetone and a series of bases gave a curved plot. It should be noted, however, that Eigen s explanation for curvature is quite different from the one based on Marcus theory and the reactivity-selectivity principle. The curvature discussed by Eigen is attributed to a change from a rate-determining proton transfer to a diffusion controlled reaction which is independent of the catalyst p. 

Support for this contention of solvent involvement in the proton transfer comes from Marcus s theory (1968). The relationship (11)... 

The Br0nsted plots (Fig. 3) give information on this point. The higher curvature of the plot for DMSO compared to methanol is indicative of a lower intrinsic barrier to proton transfer for the dipolar aprotic solvent. Since in the extended Marcus theory the solvent effect has already been taken into account, one would expect the intrinsic barrier for proton transfer to be identical in the two systems. This is not the case. Therefore it appears that separation of the mechanism into reagent positioning with concomitant solvent reorganization is not warranted. 

Modern theoretical developments in the theory of proton-transfer reactions suggest that such linear Bronsted plots are only a first approximation when the range of the P-KHA-values is narrow. When a wider range of bases is used, the curve obtained should be such that the Gibbs free energy of activation AG fits the Marcus eqn (6). This equation was derived (Cohen and Marcus, 1968 ... 

Application of Marcus rate theory to proton transfer in enzyme-catalyzed reactions was discussed by Kresge and Silverman, 1999. Relationships of log KIE and kinetics of the enzyme catalysis (kcat) and parameters of the reaction driving force were found to be in agreement with the Marcus model. 

Kresge, AJ. and Silverman, D.N. (1999) Application of Marcus rate theory to proton transfer in enzymy atalyzed reactions, in Schramm, V. L. and Purich, D. L. (eds.), Methods in Enzymology 308, Enzyme kinetics and Mechanism, Part E, Academic Press, San Diego, pp. 276- 297. 

BEBO-based Marcus equation or the hyperbolic relation which is not based on theory but is easier to use and gives about the same answer. The reduction in isotope effect predicted by the Westheimer transition state symmetry arguments is harder to correlate, yet the wide range of isotope effects virtually requires this explanation, in contrast to the case in proton transfers. 

In fact, transient assembly of H-bonded water files is probably common in enzyme function. In carbonic anhydrase, for example, the rate-limiting step is proton transfer from the active-site Zn2+-OH2 complex to the surface, via a transient, H-bonded water network that conducts H+. Analysis of the relationship between rates and free energies (p K differences) by standard Marcus theory shows that the major contribution to the observed activation barrier is in the work term for assembling the water chain (Ren et al., 1995). 

Bronsted plots for other carbon acids may be curves but this is not detected because of the limited range of reactivity over which the reactions can be studied and the Bronsted relation is therefore a sufficiently good approximation. The demonstration of a sharply curved Bronsted plot for diazoacetate ion came shortly after a new rate-equilibrium equation for proton transfer reactions had been proposed by Marcus. This will be discussed fully in Sect. 5.2 but it should be noted here that with this new theory, Bronsted plot curvature is easily accounted for. 

Recently a new method has been developed for analysing rate-equilibrium data for proton transfer reactions (Marcus Theory) [200], Although the theory has not been tested extensively, it seems to have received fairly wide acceptance. This new treatment leads to various parameters which are useful in understanding results for carbon acids and offers an explanation for some anomalies in Bronsted plots such as curvature and Bronsted exponents outside the range 0 < a or j3 < 1. 

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