The purpose of our work is to characterize and present a theoretical comparative study of a variety of compounds based on DNA base pairs linked with some transition metal ions in gas phase: C-M-G (Cytosine-metal-Guanine) where M = Ag(I), Zn(II), Cd(II) and A-M-T (Adenine-metal-Thyminate) where M = Co(II), Ru(I), Ni(I), Y(II), Zn(I), Cd(I), Cu(II). Geometry optimization and frequency calculations were carried out at DFT/ZORA/BLYP-D/TZ2P level. M-N and M-O bonds were investigated with the quantum chemical topology (QCT): Quantum theory of atoms in molecules (QTAIM) and electron localization functions (ELF). The hydrogen bonds: N10-H center dot center dot center dot O7 for A-M-T complexes and N7-H center dot center dot center dot O10 for C-M-T ones were visualized and discussed, QTAIM and ELF prove the existence of O7-H center dot center dot center dot N10 hydrogen bond for some A-M-T systems, since the bond critical point (BCP) of N7-H having del(2) rho(r) < 0, so it has a covalent character confirming the existence of a tautomer process of these complexes. Bonding energy E-(bond), Pauli repulsion E-(Pauli), electrostatic E-(elect), and orbital E-(orb) interactions were represented and compared together. Hirschfeld's charges showed the existence of charge transfer process in the bridge moieties. It seems that, in contrast to natural base pairs that are stabilized by hydrogen bonding, Hoogsteen-type base pairs are held together by coordinative bond with metal ions.