A Marcus treatment of rate constants for protonation of ring-substituted alpha-methoxystyrenes: intrinsic reaction barriers and the shape of the reaction coordinate.

Rate and equilibrium constants were determined for protonation of ring-substituted -methoxystyrenes by hydronium ion and by carboxylic acids to form the corresponding ring-substituted alpha-methyl alpha-methoxybenzyl carbocations at 25 degrees 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 alpha for protonation by carboxylic acids increases from 0.67 to 0.77 over this range of phenyl ring substituents, and the Brønsted coefficient beta 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, (inverted theta)alpha/ (inverted theta) deltaG(av) degrees=(inverted theta)beta/(inverted theta)delta G(av) degrees= 1/8lambda = 0.011, is used to calculate a Marcus intrinsic reaction barrier of lambda= 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 alpha= 0.66 for thermoneutral proton transfer is greater than alpha= 0.50 required by a reaction that follows the Marcus equation. This elevated value of beta 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.