Marcus equation, nucleophilic reactions

Bunting and Kanter have developed a modified form of the Marcus equation to treat the changes in intrinsic barrier A observed for deprotonation of /J-keto esters and amides.81 It would be useful to consider similar modifications of the Marcus equation to model the variable intrinsic barriers observed for carboca-tion-nucleophile addition reactions. 

For thermoneutral identity reactions, there is no thermochemical driving force. In the case of non-identity nucleophilic substitution reactions - when the nucleophile and nucleofuge are different - reaction exothermicity may be taken quantitatively into account. This can be quite elegantly considered by applying the simple Marcus equation [104-109]. For cationic reactions, where interactions with the neutral nucleophile and nucleofuge are quite weak,... 

The Marcus equation was first formulated to model the dependence of rate constants for electron transfer on the reaction driving force [47-49]. Marcus assumed in his treatment that the energy of the transition state for electron transfer can be calculated from the position of the intersection of parabolas that describe the reactant and product states (Fig. 1.2A). This equation may be generalized to proton transfer (Fig. 1.2A) [46, 50, 51], carbocation-nucleophile addition [52], bimolecular nucleophilic substitution [53, 54] and other reactions [55-57] by assuming that their reaction coordinate profiles may also be constructed from the intersection of... 

The purpose of this chapter is to give an introduction to the subject of nucleophilicity. The chapters of the present volume are collected into five groups (1) Marcus theory, methyl transfers, and gas-phase reactions (2) Br0nsted equation, hard-scft acid-base theory, and factors determining nucleophilicity (3) linear free-energy relationships for solvent nucleophilicity (4) complex nucleophilic reactions and (5) enhancement of nucleophilicity. The present chapter is divided in the same way, giving an introduction to each of the five topics followed by a description of key points in each chapter as they relate to current studies of nucleophilicity and the other chapters of the book. 

The rate constants of the reaction CH3Y + X- CH X + Y in sulfolane solution are described by the Marcus equation the quadratic term contributes very little. The Marcus equation then reduces to the expression log kyx = My + Nx, where My is a property of CH3Y only and Nx is a property of CG X only. Each term includes only the identity rates and the equilibria for methylation of a reference nucleophile. The two terms are determined independently of unsymmetric rate measurements, in contrast to the Swain-Scott equation. Short tables of both terms are presented. Extension to other solvents and to other reactions including group transfers is discussed. With other alkyl groups, the simple expression may cover the continuum from elimination-addition to addition-elimination and may also cover other group transfers. 

Curved Brpnsted plots or other structure-reactivity correlations are often taken as evidence for changes in transition-state structure with changing properties of the reactant that might be described by the Marcus equation (24) or other equations. However, it is important to evaluate other possible explanations for such curvature, including solvation effects that could decrease the reactivity of basic nucleophiles without any change in the structure of the transition state for nucleophilic attack. For example, solvation effects could provide a relatively simple explanation for the curvature of structure-reactivity correlations for reactions of basic oxygen anion nucleophiles with acyl compounds and carbon acids. 

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. ... 

The extent to which the effect of changing substituents on the values of ks and kp is the result of a change in the thermodynamic driving force for the reaction (AG°), a change in the relative intrinsic activation barriers A for ks and kp, or whether changes in both of these quantities contribute to the overall substituent effect. This requires at least a crude Marcus analysis of the substituent effect on the rate and equilibrium constants for the nucleophile addition and proton transfer reactions (equation 2).71-72... 

We now explore whether the pattern of reactivity predicted by the Marcus theory is found for methyl transfer reactions in water. We use equation (29) to calculate values of G from the experimental data where, from (27), G = j(JGlx + AG Y). The values of G should then be made up of a contribution from the symmetrical reaction for the nucleophile X and for the leaving group Y. We then examine whether the values of G 29) calculated for the cross reactions from (29) agree with the values of G(27) calculated from (27) using a set of values for the symmetrical reactions. The problem is similar to the proof of Kohlrausch s law of limiting ionic conductances. 

For reactions involving the halide ions there are again enough data to see if the Marcus pattern predicted by these equations is found. Values of m X Y from plots such as those shown in Fig. 14 are collected in Table 13. The value for mBr, Br can be calculated using (58)-(60) and either the data for the Cl-or for the I- nucleophile. Assuming that a we obtain (61) using the data for I-, and (62) for Cl-. Very reasonable agreement is found. 

Most systematic studies on gas-phase SN2 reactions have been carried out with methyl halides, substrates which are free of complications due to competing elimination. Application of the Marcus rate-equilibrium formalism to the double-minimum potential energy surface led to the development of a model for intrinsic nucleophilicity in S 2 reactions233. The key quantities in this model are the central energy barriers, Eq, to degenerate reactions, like the one of equation 22, which are free of a thermodynamic driving force. 

As Bunnett has noted (4), the kinetic barrier to nucleophilic attack is affected by the thermodynamics of the reaction. If this thermodynamic contribution could be removed, then intrinsic nucleophilicities for substitution reactions could be obtained that would be independent of the leaving group. Pioneering work by Albery and Kreevoy (7), Pellerite and Brauman (8), and Lewis et al. (9) has shown that Marcus theory can be applied to methyl-transfer reactions to separate thermodynamic and kinetic contributions and provide intrinsic barriers to nucleophilic attack. One expression of Marcus theory is given in equation 1, where AE is the activation energy, AE° is the heat of reaction, and AE0 is the intrinsic activation energy or the barrier to reaction in the absence of any thermodynamic driving force. 

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