Nucleic acid tetraplexes and lipophilic self-assembling G-quadruplexes contain stacked base tetrads with intercalated metal ions as basic building blocks. Thus far, quantum-chemical studies have been used to explore the geometric and energetic properties of base tetrads with and without metal ions. Recently, for the first time, work on a sandwiched G-tetrad complex has been studied. We report here results of a systematic B3LYP density functional study on sandwiched G-, C-, U-, and T-tetrads with Na+ and K+ at different symmetries that substantially extend the recent work. The results include detailed information on total energies as well as on metal ion tetrad and base-base interaction energies. The geometrical parameters of the sandwiched metal ion complexes are compared to both experimental structures and to calculated geometries of complexes of single tetrads with metal ions. A microsolvation model explains the ion selectivity preference of K+ over Na+ in a qualitative sense.