Marcus intrinsic

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)°... 

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... 

In Ch. 19 Williams describes theoretical simulations of free-energy-relation-ships in proton transfer processes. Both linear and non-linear relations are observed, usually described in terms of Bronsted coefficients or Marcus intrinsic barriers. Derived from empirical data, the phenomenological parameters of themselves do not lead to satisfying explanations at a fundamental molecular level. Theoretical simulations can fill in this gap. 

Ft, Tr, Bu) [45a]) or failure to obtain any sort of sensible FER at all (e.g. nucleophilic addition to a carbonyl group concerted with PT [47], cf. HYW [38]) probably indicates that the TSs involve structural features not present in either the reactants or products [48]. This type of behavior sometimes manifests itself in terms of large variations in Marcus intrinsic barriers [6c]. 

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...

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],... 

Marcus Intrinsic Barriers for Proton Transfer at Carbon... 

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. 

The Marcus intrinsic barriers for deprotonation of carbon acids to form enolates that are stabilized by resonance delocalization of negative charge from carbon to oxygen are larger than for deprotonation of carbon acids to form carbanions where the charge is localized mainly at carbon. 

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

Intramolecular aldol reaction of (14) to give (16), promoted by lyate ion, has been found to proceed by rate-determining deprotonative formation of enolate intermediate (15) the intramolecular addition (/cc) occurs more rapidly than reprotonation of (15) by H2O or D2O ( hoh or A dod), c/ hoh = 35. However, when the reaction is catalysed by high concentrations of 3-substituted quinuclidine buffers, the enolate addition is rate determining and competitive with reprotonation of (15) k-Q /k (lmol ) increases from 7 to 450 as the acidity of the buffer acid increases from p/(bh = 11-5 to 7.5. The unexpectedly small Marcus intrinsic value for addition of (15) to the carbonyl group has been attributed to favourable interactions between the soft-soft acid-base pair. 

The susceptibility of the aldehyde function of (41) to hydrate in 70% H2O-30% Me2SO explains the extremely low Marcus intrinsic reactivity found for this aldehydic carbon acid. Evidence suggests that the rate-limiting step of the overall ionization process is the attainment of equilibrium between (40) and (41). The intrinsic reactivity is six log units greater for keto analogs, Ph3P+CH2COR. 

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