New density functional and atoms in molecules method of computing relative pKa values in solution

A theoretical structure-property relation between pK(a) and Bader's atoms in molecules (AIM) energy of the dissociating proton was obtained by an approximation of the standard gas-phase expression for the equilibrium constant expressed in terms of molecular partition functions. This relation was then tested by solvated density functional computations on a series of aliphatic carboxylic acids, substituted benzoic acids, phenols, anilinium ions, and pyridinium ions using the COSMO solvation model. Comparison with accurate experimental, values indicates that average unsigned errors of generally less than 0.2 pK(a) units can be achieved in the calculation of relative pK(a) values. The inclusion of specifically hydrogen-bonded water molecules in the vicinity of the dissociating proton was found to improve the agreement between theory and experiment greatly. Computed pK(a) values for some diprotic acids were also investigated.