We have studied two topics about (i) the structural stabilities and electronic structures of metal-ion containing artificial DNA bases and (ii) conductivity of them. Before proceeding to the main topics, we have shown that a van der Waals corrected density functional method gives the stacking interaction, which agrees well with the reference value obtained by accurate methods in both cases for stacking two bases and two base pairs. We also investigated an origin of structural stability and electronic properties of several metal ion containing artificial DNA bases including chalcogen-substituted compounds. We estimated current-voltage characteristics of stacked natural and metal-containing artificial DNA bases by the scattering theory based on the non-equilibrium Green's function method. We found that the current-voltage characteristics dramatically change by capturing metal ion in the artificial DNA bases.