We examine the existence of stable bound states of some diatomic molecular ions where the neutral molecule itself is either unbound or barely bound. Two bound states have been found for the ${\mathrm{HeH}}^{\ensuremath{-}}$ ion even though HeH is known to be unbound. We have found no bound states for ${\mathrm{He}}_{2}^{\ensuremath{-}}$ even though
4He2 is known to have one bound state. The predicted binding energies for ${\mathrm{HeH}}^{\ensuremath{-}}$ are of the order of 1 K and depend sensitively on the isotope combinations. Other weakly bound negative ions such as ${\mathrm{NeH}}^{\ensuremath{-}}$ and ${\mathrm{ArH}}^{\ensuremath{-}}$ have also been investigated. These weakly bound molecular ions are good candidates for cold collision experiments.
The relativistic correlation-potential method was used to calculate binding energies and fine-structure intervals for Pd, Ba, and Yb negative ions and to investigate low-energy electron scattering by Yb, Hg, and Ra atoms. The results for the binding energies are the following: 540 meV for the 5s state of ${\mathrm{Pd}}^{\mathrm{\ensuremath{-}}}$, 190 and 133 meV for the 6
p1/2 and 6
p3/2 states of ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, and 36 meV for the 6
p1/2 state of the ${\mathrm{Yb}}^{\mathrm{\ensuremath{-}}}$. A number of prominent p and d resonances are revealed in the scattering phase-shift calculations. These p or d resonances lead to a phenomenon of 100% polarization of the scattered electron beam at appropriate electron energy and scattering angle. A criterion is proposed to measure the strength of the nonlocal correlation potential and to evaluate its ability to create a bound state: FG(r',r)\ensuremath{\Sigma}(r,r')dr dr'>1 is the necessary condition for the formation of a bound state. Here \ensuremath{\Sigma} is the correlation potential and G is the electron Green's function at zero energy.