Crown ether is one of well-known host molecules and able to selectively sequester metal cation. We employed M06-2X density functional theory with IEFPCM and SMD continuum solvation models to study selectivity of dibenzo-18-crown-6-ether (DB18C6) for alkaline earth dications, $Ba^{2+}$, $Sr^{2+}$, $Ca^{2+}$, and $Mg^{2+}$ in the gas phase and in aqueous solution. $Mg^{2+}$ showed predominantly strong binding affinity in the gas phase because of strong polarization of CO bonds by cation. In aqueous solution, binding free energy differences became smaller among these dications. However, $Mg^{2+}$ had the best binding, being incompatible with experimental observations in aqueous solution. The enthalpies of the dication exchange reaction between DB18C6 and water cluster molecules were computed as another estimation of selectivity in aqueous solution. These results also demonstrated that $Mg^{2+}$ bound to DB18C6 better than $Ba^{2+}$. We speculated that the species determining selectivity in water could be 2:1 complexes of two DB18C6s and one dication.