Correlation between molecular acidity (pKa) and vibrational spectroscopy

Molecular acidity is an important physicochemical property, which is often represented by the pKa value as the measure of acidity strength. However, the accurate calculation and prediction of pKa values is still an unsolved problem for computational chemistry. In this work, we present for the first time a direct correlation between pKa values and local vibrational frequencies for 15 different groups of compounds with various substituents. This correlation was derived from a quadratic function of two selected local vibrational frequencies as independent variables used to characterize electronic structure features influencing the molecular acidity. In total, 180 molecules were investigated with this correlation model. For each group of molecules, we found a strong correlation with root mean squared errors and mean absolute errors of less than 0.11 and 0.09 pKa units, respectively. The correlation between pKa and local vibrational modes, established in this work, can be generally applied to all compounds whose pKa values are dominated by electronic substituent effects. In this regard, the new correlation model constitutes a powerful link between the well-known Hammett equation and vibrational spectroscopy. Furthermore, it allows a quick prediction of the pKa values for new group members with different substituents.