State of the art for ab initio vs empirical potentials for HeH$^+$ (2e$^-$), BeH$^+$ (4e$^-$), BeH (5e$^-$), Li$_2$ (6e$^-$) and BH (6e$^-$)

For large internuclear distances, the potential energy between two atoms is known analytically, based on constants that are calculated from atomic \textit{ab initio} rather than molecular \textit{ab initio}. This analytic form can be built into models for molecular potentials that are fitted to spectroscopic data. Such empirical potentials constitute the most accurate molecular potentials known. For HeH$^+$, and BeH$^+$, the long-range form of the potential is based only on the polarizabilities for He and H respectively, for which we have included up to 4th order QED corrections. For BeH, the best \texit{ab initio} potential matches all but one observed vibrational spacing to < 1 cm${^-}$ accuracy, and for Li$_2$ the discrepancy in the spacings is < 0.08 cm$^{-1}$ for all vibrational levels. But experimental methods such as photoassociation require the absolute energies, not spacings, and these are still several in several cm$^{-1}$ disagreement. So empirical potentials are still the only reliable way to predict energies for few-electron systems. We also give predictions for various unobserved "halo nucleonic molecules" containing the "halo" isotopes: $^{6,8}$He, $^{11}$Li, $^{11,14}$Be and $^{8,17,19}$B.