Theoretical analysis of kinetic isotope effects on proton transfer reactions between substituted α-methoxystyrenes and substituted acetic acids

Primary kinetic isotope effects (KIEs) on a series of carboxylic acid-catalyzed protonation reactions of aryl-substituted α-methoxystyrenes (X-1) to form oxocarbenium ions have been computed using the second-order Kleinert variational perturbation theory (KP2) in the framework of Feynman path integrals (PI) along with the potential energy surface obtained at the B3LYP/6-31+G(d,p) level. Good agreement with the experimental data was obtained, demonstrating that this novel computational approach for computing KIEs of organic reactions is a viable alternative to the traditional method employing Bigeleisen equation and harmonic vibrational frequencies. Although tunneling makes relatively small contributions to the lowering of the free energy barriers for the carboxylic acid catalyzed protonation reaction, it is necessary to include tunneling contributions to obtain quantitative estimates of the KIEs. Consideration of anharmonicity can further improve the calculated KIEs for the protonation of substituted α-methoxystyrenes by chloroacetic acid, but for the reactions of the parent and 4-NO₂ substituted α-methoxystyrene with substituted carboxylic acids, the correction of anharmonicity overestimates the computed KIEs for strong acid catalysts. In agreement with experimental findings, the largest KIEs are found in nearly ergoneutral reactions, ΔG° ≈ 0, where the transition structures are nearly symmetric and the reaction barriers are relatively low. Furthermore, the optimized transition structures are strongly dependent on the free energy for the formation of the carbocation intermediate, that is, the driving force ΔG°, along with a good correlation of Hammond shift in the transition state structure.