Toward Elimination of Discrepancies between Theory and Experiment: Double Proton Transfer in Dimers of Carboxylic Acids

Abstract

We present for the first time a fully ab initio dual-level reaction path dynamics calculation of the synchronous proton exchange in carboxylic acid dimers that is consistent with a wide variety of experimental findings, such as reaction rates k, tunneling splittings Δ0, apparent activation energy curves Ea (T), crossover temperatures Tc and kinetic isotope effects. For the dimer of formic acid, we find k = 2.5 × 109 s-1 (300 K), with an associated ground-state splitting Δ0 = 0.09 cm-1. Similar to experiments with crystals of benzoic acid dimers, we obtain Tc = 100 K as the border between the high- and low-temperature regions of the rate constant. More than half of the hydrogenic motion occurs by quantum tunneling. The total hydrogenic motion of about 0.7 Å coincides perfectly with neutron scattering results. In contrast to all previous studies, the experimental activation energy curves can be reproduced reasonably by inclusion of tunneling from the vibrational ground state for three different isotopic species. Remaining small discrepancies from experiments with benzoic acid dimers in the coherent limit (k ≈ 1010 s-1 (300 K), Δ0 = 0.32 cm-1) are explained mainly by vibrational excitation of normal modes coupled to the reaction path and the higher reaction barrier in the formic acid dimer, i.e., a difference of 1.0 kcal/mol at the B3LYP/6-31+G(d) level of theory. Closer inspection of the normal modes involved reveals that the excitation of the interdimer stretch and the OH stretch could enhance the rates and enlarge the splittings considerably by shortening the O−O distance. The reaction path with a total of 103 Hessian calculations has been obtained at the B3LYP/6-31+G(d) level of theory and corrected to a G2* reaction barrier and MP2/6-31G(d,p) frequencies at the stationary points stemming from a recent excellent benchmark study by Kim [Kim, Y. J. Am. Chem. Soc. 1996, 118, 1522−1528].