A marcus treatment of rate constants for protonation of ring-substituted α-methoxystyrenes: Intrinsic reaction barriers and the shape of the reaction coordinate

Rate and equilibrium constants were determined for protonation of ring-substituted α-methoxystyrenes by hydronium ion and by carboxylic acids to form the corresponding ring-substituted α-methyl α-methoxybenzyl carbocations at 25°C and I = 1.0 (KCl). The thermodynamic barrier to carbocation formation increases by 14.5 kcal/mol as the phenyl ring substituent(s) is changed from 4-MeO- to 3,5-di-NO₂-, and as the carboxylic acid is changed from dichloroacetic to acetic acid. The Brønsted coefficient a for protonation by carboxylic acids increases from 0.67 to 0.77 over this range of phenyl ring substituents, and the Brønsted coefficient β for proton transfer increases from 0.63 to 0.69 as the carboxylic acid is changed from dichloroacetic to acetic acid. The change in these Brønsted coefficients with changing reaction driving force, ∂α/∂ΔG°_av = ∂β/ ∂ΔG°_av = 1/8Λ = 0.011, is used to calculate a Marcus intrinsic reaction barrier of Λ = 11 kcal/mol which is close to the barrier of 13 kcal/mol for thermoneutral proton transfer between this series of acids and bases. The value of α = 0.66 for thermoneutral proton transfer is greater than α = 0.50 required by a reaction that follows the Marcus equation. This elevated value of β may be due to an asymmetry in the reaction coordinate that arises from the difference in the intrinsic barriers for proton transfer at the oxygen acid reactant and resonance-stabilized carbon acid product.