  Accurate mass-interpolation and mass-asymptotic formulas are derived for one-
and two-center three-body ions with unit charges. The derived formulas are
applied to predict accurate numerical values of the total energies of the
ground (bound) $1^{1}S(L = 0)-$states in one-center atomic ions $X^{+} e^{-}
e^{-}$ and analogous ground (bound) $1 s \sigma-$states in the two-center,
quasi-adiabatic (or quasi-molecular) $X^{+} X^{+} e^{-}$ ions. We also discuss
a few problems which currently remain unsolved for the $Q^{-1}$ expansions
constructed for the ground (bound) states in few-electron atoms and ions.
