Marcus intrinsic reaction barrier

Table 3 compares the thermodynamic driving force AG°, calculated from the equilibrium constant Aadd (Scheme 50), and the derived Marcus intrinsic reaction barriers for reversible addition of nucleophiles Y to 48 and the tri-phenylmethyl carbocation (Ph3C+).4 There are nearly constant differences between the values for the thermodynamic driving force for addition of nucleophiles to 48 and Ph3C+ ((A(j°(48) AG0(PhC+) = 8.4 kcal/mol) and those for... 

Table 1.1. Rate constants, equilibrium constants, and Marcus intrinsic reaction barriers for deprotonation of a-carbonyl carbon by hydroxide ion in wateK l.

Many laboratories, including our own, have used the Marcus equation empirically as a relatively simple and convenient framework for describing the differences in the intrinsic difficulty for related reactions, after correction for differences in the reaction thermodynamic driving force. This has led to the determination of the Marcus intrinsic barriers for a variety of proton transfer reactions by experiment and through calculations [58-65], This compilation of intrinsic reaction barriers represents an attempt to compress an essential feature of these kinetic barriers to a single experimental parameter. An examination of the substituent effects on these intrinsic barriers has provided useful insight into the transition state for organic reactions [66],... 

The parameter A reflects the intrinsic reaction barrier . It coincides with the free activation energy for degenerate conversions (A = AG at AG° = 0). If the quadratic term in the Marcus equation is neglected it takes the form... 

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... 

Our analysis of literature data will focus on two closely related questions about the influence of changes in the relative thermodynamic driving force and Marcus intrinsic barrier for the reaction of simple carbocations with Bronsted bases (alkene formation) and Lewis bases (nucleophile addition) on the values of ks/kp determined by experiment. 

To what extent are the variations in the rate constant ratio /cs//cpobserved for changing structure of aliphatic and benzylic carbocations the result of changes in the Marcus intrinsic barriers Ap and As for the deprotonation and solvent addition reactions It is not generally known whether there are significant differences in the intrinsic barriers for the nucleophile addition and proton transfer reactions of carbocations. 

The more favorable partitioning of [1+ ] to form [l]-OH than to form [2] must be due, at least in part, to the 4.0 kcal mol-1 larger thermodynamic driving force for the former reaction (Kadd = 900 for conversion of [2] to [l]-OH, Table 1). However, thermodynamics alone cannot account for the relative values of ks and kp for reactions of [1+] that are limited by the rate of chemical bond formation, which may be as large as 600. A ratio of kjkp = 600 would correspond to a 3.8 kcal mol-1 difference in the activation barriers for ks and kp, which is almost as large as the 4.0 kcal mol 1 difference in the stability of [1]-OH and [2]. However, only a small fraction of this difference should be expressed at the relatively early transition states for the reactions of [1+], because these reactions are strongly favored thermodynamically. These results are consistent with the conclusion that nucleophile addition to [1+] is an inherently easier reaction than deprotonation of this carbocation, and therefore that nucleophile addition has a smaller Marcus intrinsic barrier. However, they do not allow for a rigorous estimate of the relative intrinsic barriers As — Ap for these reactions. 

Table 2 Rate constants, equilibrium constants, and estimated Marcus intrinsic barriers for the formation and reaction of ring-substituted l-phenylethyl carbocations X-[6+] (Scheme 8)°... 

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... 

The above model has been further explored to account for reaction efficiencies in terms of a scheme where nucleophilicities and leaving group abilities can be rationalized by a structure-reactivity pattern. Pellerite and Brau-man (1980, 1983) have proposed that the central energy barrier for an exothermic reaction (see Fig. 3) can be analysed in terms of a thermodynamic driving force, due to the exothermicity of the reaction, and an intrinsic energy barrier. The separation between these two components has been carried out by extending to SN2 reactions the theory developed by Marcus for electron transfer reactions in solutions (Marcus, 1964). While the validity of the Marcus theory to atom and group transfer is open to criticism, the basic assumption of the proposed model is that the intrinsic barrier of reaction (38)... 

I use kinetic barrier to mean the free energy of activation and thermodynamic barrier to refer to the equilibrium free energy change for the reaction (barrier when this is positive driving force when it is negative). The intrinsic barrier is calculated as a function of A(7 and AG° by Marcus theory. 

Rate constants for electron transfer may be related to the free energy AG° of the reaction through the classical Marcus equation Eq. (5), where AGq is the intrinsic activation barrier of the reaction process [90, 91]. 

Figure 1.2. A, Reaction coordinate profiles for proton transfer at carbon constructed from the intersection of parabolas for the reactant and product states. B, The reaction coordinate profile for a reaction where AC° = 0 and ACt is equal to the Marcus intrinsic barrier A...

There is only a small barrier for thermoneutral proton transfer between electronegative oxygen or nitrogen acids and bases [31]. These reactions proceed by encounter-controlled formation of a hydrogen-bonded complex between the acid and base (ka, Scheme 1.6), proton transfer across this complex (kp, Scheme 1.6), followed by diffusional separation to products (k a, Scheme 1.6) [31]. Much larger Marcus intrinsic barriers are observed for proton transfer to and from carbon [67]. There are at least two causes for this difference in intrinsic barriers for proton transfer between electronegative atoms and proton transfer at carbon. 

Coriolis coupling (p. 906 and 912) critical points (p. 888) cross section (p. 901) curvature coupling (p. 906 and 914) cycloaddition reaction (p. 944) democratic coordinates (p. 898) diabatic and adiabatic states (p. 949) donating mode (p. 914) early and late reaction barriers (p. 895) electrophilic attack (p. 938) entrance and exit channels (p. 895) exo- and endothermic reactions (p. 909) femtosecond spectroscopy (p. 889) Franck-Condon factors (p. 962) intrinsic reaction coordinate (IRC) (p. 902) inverse Marcus region (p. 954) mass-weighted coordinates (p. 903)... 

Marcus showed that if within a log k — log X relationship variations in the rate constant solely reflect changes in the equilibrium constant, then log k, or in Marcus s formulation the free energy of activation AG may be expressed in terms of a free energy of the proton-transfer step of the reaction AGr, and an intrinsic energy barrier to proton-transfer for reaction of a substrate and. acid for which AGg = 0 ... 

If the intrinsic barrier AGq could be independently estimated, the Marcus equation (5-69) provides a route to the calculation of rate constants. An additivity property has frequently been invoked for this purpose.For the cross-reaction... 

In Eq. (7-21), AGo is the intrinsic barrier, the free energy of activation of the (hypothetical) member of the reaction series having AG" = 0. It is evident that the Marcus equation predicts a nonlinear free energy relationship, although if a limited... 

Other measures of nucleophilicity have been proposed. Brauman et al. studied Sn2 reactions in the gas phase and applied Marcus theory to obtain the intrinsic barriers of identity reactions. These quantities were interpreted as intrinsic nucleo-philicities. Streitwieser has shown that the reactivity of anionic nucleophiles toward methyl iodide in dimethylformamide (DMF) is correlated with the overall heat of reaction in the gas phase he concludes that bond strength and electron affinity are the important factors controlling nucleophilicity. The dominant role of the solvent in controlling nucleophilicity was shown by Parker, who found solvent effects on nucleophilic reactivity of many orders of magnitude. For example, most anions are more nucleophilic in DMF than in methanol by factors as large as 10, because they are less effectively shielded by solvation in the aprotic solvent. Liotta et al. have measured rates of substitution by anionic nucleophiles in acetonitrile solution containing a crown ether, which forms an inclusion complex with the cation (K ) of the nucleophile. These rates correlate with gas phase rates of the same nucleophiles, which, in this crown ether-acetonitrile system, are considered to be naked anions. The solvation of anionic nucleophiles is treated in Section 8.3. 

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. ... 

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