Point symmetry groups and equilibrium structure parameters of the following complexes of gold, silver, copper, mercury, cadmium, zinc, and barium with xenon and krypton have been determined using (U)PBE0/SDD and (U)MP2/SDD quantum chemical methods: MtNg (2) (+) (D (ah) , C (2v) ); AuNg (3) (2+) , AgNg (3) (2+) , and CuNg (3) (2+) (C (2v) ); HgNg (3) (2+) , CdNg (3) (2+) , ZnNg (3) (2+) , and BaNg (3) (2+) (D (3h) ); AuNg (4) (2+) and AgNg (4) (2+) (D (4h) ); CuNg (4) (2+) (D (2d) , flattened out tetrahedron); HgNg (4) (2+) , CdNg (4) (2+) , ZnNg (4) (2+) , BaNg (4) (2+) , and MtNg (4) (2+) (T (d) ). The computed free energies of decomposition into the single-charged MtNg (2) (+) and Ng (2) (+) cations show metastability of the twice-charged complexes of Au(II), Ag(II), Cu(II), Hg(II), Cd(II), and Zn(II) with four atoms of xenon or krypton.