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Beryllium monohydride (BeH): Where we are now, after 86 years of spectroscopy

BeH is one of the most important benchmark systems for ab initio methods and for studying Born-Oppenheimer breakdown. However the best empirical potential and best ab initio potential for the ground electronic state to date give drastically different predictions in the long-range region beyond which measurements have been made, which is about \sim1000 cm^{-1} for ^{9} BeH, \sim3000 cm^{-1} for ^{9} BeD, and \sim13000 cm^{-1} for ^{9} BeT. Improved empirical potentials and Born-Oppenheimer breakdown corrections have now been built for the ground electronic states X(1^{2}Σ^{+}) of all three isotopologues. The predicted dissociation energy for ^{9} BeH from the new empirical potential is now closer to the current best ab initio prediction by more than 66% of the discrepancy between the latter and the previous best empirical potential. The previous best empirical potential predicted the existence of unobserved vibrational levels for all three isotopologues, and the current best ab initio study also predicted the existence of all of these levels, and four more. The present empirical potential agrees with the ab initio prediction of all of these extra levels not predicted by the earlier empirical potential. With one exception, all energy spacings between vibrational energy levels for which measurements have been made, are predicted with an agreement of better than 1 cm^{-1} between the new empirical potential and the current best ab initio potential, but some predictions for unobserved levels are still in great disagreement, and the equilibrium bond lengths are different by orders of magnitude.