The molecular geometries, energy properties, H-bonding patterns, and electrostatic potential characters of the thymine (T) and uracil (U) tetrads and the role of the potassium cation in the formation of the T tetrad and U tetrad have. been studied at the B3LYP/6-311G(d,p) and the HF/6-311G(dp) levels of theory. Both the T and the U tetrads are found to be stable in the isolated form. The stabilization energy of the U tetrad is about 6.8 kcal/mol, more than that of the T tetrad. The lower stabilization energy of the T tetrad suggests the repulsion between the methyl group of the bases and the O2 atoms of their neighbors. While the nonplanar U tetrad has a bowl-like shape, the nonplanar T tetrad exhibits a propeller structure. The presence of a cation is critical for the formation of T or U tetrads in the G tetrad-containing tetraplexes. The cation-tetrad interaction energy has been evaluated to be about 65 kcal/mol for both tetrads. The similarity between both the cation-tetrad interaction energies and the K+-04 distances predicted for the both tetrads suggests that the electrostatic interaction between the K+ ion and the O4 atoms dominates the cation-tetrad interactions. It has been found that the K+-T tetrad and the K+-U tetrad complexes alone could not be stable in aqueous solutions because of the high hydration energy of K+. However, the stacking of the T tetrad or the U tetrad on the adjacent G tetrad will be greatly enhanced in the presence of potassium cations in the tetraplexes.