Entropies and Free Energies of Protonation and Proton-Transfer Reactions

Abstract

Entropies, enthalpies, and free energies for gas-phase protonation and proton-transfer reactions have been calculated and compared with state-of-the-art experimental values. Statistical entropies have been determined by using ab initio molecular parameters and several previously defined models (E1, E2, and E3). The accuracy of the ab initio proton-transfer entropies (ΔS) obtained with the E3 procedure (1 J mol-1 K-1) is significantly better than that normally attainable for ΔS values derived from van't Hoff plots of experimental equilibrium data for proton-transfer reactions (5−10 J mol-1 K-1). In fact, even the simplest E1 procedure produces proton-transfer entropies that are accurate to about 1−2 J mol-1 K-1. The commonly used isoelectronic approach to estimating entropies of gas-phase ions has been tested. Errors associated with this approximation are generally about 1−3 J mol-1 K-1, but can increase to 5−10 J mol-1 K-1 for systems that have low energy torsional or other floppy modes. G2 enthalpies and E3 entropies have been used to obtain free energies (ΔG) for 25 experimentally observed proton-transfer reactions. The ab initio free energies are in very good agreement with experimental values, the mean absolute deviation being 2.2 kJ mol-1 and maximum deviation 4.9 kJ mol-1. There is also very good agreement between theory and experiment for the enthalpies of these proton-transfer reactions with a mean absolute deviation and maximum deviation of 2.7 and 8.5 kJ mol-1, respectively. Theoretical proton affinity (ΔH) and gas-phase basicity (ΔG) scales have been constructed on the basis of G2 energies for 39 molecules and corresponding protonated species. There is generally good agreement between theory and experiment. The small deviations that do exist between theoretical and experimental values appear to correlate with the proton affinity magnitude.