Probing cations recognized by a crown ether with the 3D-RISM theory

Three-dimensional distributions of water as well as cations (Li+, K+, Mg2+, Ca2+) inside and outside a crown ether (12-crown-4) in aqueous solutions of electrolytes are calculated by means of the 3D-RISM theory. The results show a conspicuous peak inside the host cavity in the cases of Li+ and Mg2+ indicating that the cations are recognized by the host molecule. On the other hand, no such peaks are observed inside the cavity for K+ and Ca2+. The theoretical observations are in complete agreement with experimental findings except for Mg2+, for which no experimental results are reported to our best knowledge. The results are interpreted in terms of the free energy gain due to the electrostatic interaction between the guest and host molecules, and of the dehydration penalty.