The metal-mediated hydroxypyridone base pairs containing Ni2+, Cu2+, Zn2+, Pd2+, Cd2+, Pt2+, and Hg(2+)ions were designed theoretically using by density functional theory (DFT) method in Gaussian 09 program. The calculations which were performed in the gas phase, methanol, water, and formamide were done at B3LYP functional with LANL2DZ and 6-311++G (d, p) basis sets which were used metals and rest atoms, respectively. The Gibbs free energies of the complexes were calculated and their relative stabilities were determined in the mentioned fields. Furthermore, geometric parameters, HOMO, LUMO, energy gap energies of the compounds were computed in all media and effect on these parameters of solvents were determined. Based on these parameters, the relative conductivities of the investigated molecules were predicted. On the other hand, using Atomistix ToolKit (ATK-VNL) 2016 program, nonequilibrium Green's function (NEGF) calculations based on the combination DFT of the mentioned complexes were carried out. The transport properties of the molecules were found in detailed via NEGF-DFT method.