The potassium cation affinities (PCAs) of 136 ligands (20 classes) in the gas phase were established by hybrid density functional theory calculations (B3-LYP with the 6-311+G(3df,2p) basis set). For these 136 ligands, 70 experimental values are available for comparison. Except for five specific PCA values-those of phenylalanine, cytosine, guanine, adenine (kinetic-method measurement), and Me(2)SO (by high-pressure mass spectrometric equilibrium measurement)-our theoretical estimates and the experimental affinities are in excellent agreement (mean absolute deviation (MAD) of 4.5 kJ mol(-1)). Comparisons with previously reported theoretical PCAs are also made. The effect of substituents on the modes of binding and the PCAs of unsubstituted parent ligands are discussed. Linear relations between Li+/Na+ and K+ affinities suggest that for the wide range of ligands studied here, the nature of binding between the cations and a given ligand is similar, and this allows the estimation of PCAs from known Li+ and/or Na+ affinities. Furthermore, empirical equations relating the PCAs of ligands with their dipole moments, polarizabilities (or molecular weights), and the number of binding sites were established. Such equations offer a simple method for estimating the PCAs of ligands not included in the present study.