  BaH (and its isotopomers) is an attractive molecular candidate for laser
cooling to ultracold temperatures and a potential precursor for the production
of ultracold gases of hydrogen and deuterium. The theoretical challenge is to
simulate the laser cooling cycle as reliably as possible and this paper
addresses the generation of a highly accurate ab initio $^{2}\Sigma^+$
potential for such studies. The performance of various basis sets within the
multi-reference configuration-interaction (MRCI) approximation with the
Davidson correction (MRCI+Q) is tested and taken to the complete basis set
limit. It is shown that the calculated molecular constants using a 46 electron
Effective Core-Potential (ECP), the augmented polarized core-valence quintuplet
basis set (aug-pCV5Z-PP) but only including three active electrons in the MRCI
calculation are in close agreement with the available experimental values. The
predicted dissociation energy D$_e$ for the X$^2\Sigma^+$ state (extrapolated
to the complete basis set (CBS) limit) is 16895.12 cm$^{-1}$ (2.094 eV), which
agrees within 0.1$\%$ of a revised experimental value of $<$16910.6 cm$^{-1}$,
while the calculated r$_e$ is within 0.03 pm of the experimental result.
