On the bound state spectrum in one-electron diatomic ions

The total energies of a large number of diatomic (or two-center) one-electron $A^{+} B^{+} e^{-}$ ions with unit electrical charges are determined numerically to high accuracy. Based on these results we derive some accurate mass-interpolation formulas for the total energies of such three-body systems (ions). These formulas can be applied to the both symmetric $A^{+} A^{+} e^{-}$ and non-symmetric $A^{+} B^{+} e^{-}$ diatomic ions. Based on the results obtained in this study we also consider a few actual and currently unsolved problems, which are known for the two-center (or diatomic) one-electron ions.