Intrinsic barriers to the formation and reaction of carbocations

The Marcus equation relates the activation barriers (Delta G(double dagger)) for organic reactions to the overall thermodynamic driving force (Delta G degrees) and the intrinsic barrier Lambda, which is the value of Delta G(double dagger) when Delta G degrees = 0. Most treatments of substituent effects on the rate and equilibrium constants for the reactions of structurally homologous organic substrates make the assumption that the intrinsic barrier Lambda remains constant with changes in Delta G degrees. However, there is good evidence for the nucleophilic addition of solvent to carbocations XArCH(R)(+) that changes in the aromatic ring substituent X and the benzyl substituent R result in large changes in the intrinsic barrier. Evidence is presented that: (1) There is no significant work required for formation of the reactive complex for proton transfer from carboxylic acids to a homologous series of alpha-methoxystyrenes XArC(OMe)=CH2. (2) There is a difference in the curvature of the energy surfaces for the reactant and product states that results in their intersection at a transition state in which proton transfer has proceeded ca. two-thirds of the way from RCO2H to XArC(OMe)=CH2.