Charge particle collisions If a lithium $\mathrm{Li^+}$ cation falls toward a fluorine $\mathrm{F^-}$ anion slowly in vacuum, can they find a stable 'orbital'?
If not an 'orbital' will they form some kind of stable two-body linear oscillator? 
 A: It seems that lithium fluoride exists, so the answer is yes, if the energy of scattering falls within a bound energy level:

Lithium fluoride is an inorganic compound with the chemical formula LiF. It is a colorless solid, that transitions to white with decreasing crystal size. 

Molecules are characterized by orbitals  electron orbitals, . I suppose that in principle one could define a lithium orbital and a fluoride orbital, just a change of the quantum mechanical functions, because the electron orbitals   simulate atoms, since the nucleus is in a very small volume of the atom. The models have to be more complicated than simple oscillators.


Complete acetylene (H–C≡C–H) molecular orbital set. The left column shows MO's which are occupied in the ground state, with the lowest-energy orbital at the top. The white and grey line visible in some MO's is the molecular axis passing through the nuclei. The orbital wave functions are positive in the red regions and negative in the blue. The right column shows virtual MO's which are empty in the ground state, but may be occupied in excited states.

So models do exist for atoms bound in molecules.
