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Calculation of vibrational-rotational bound states and metastable states of a diatomic beryllium molecule important for laser spectroscopy [1] are presented. The solution to the problem is performed using the potential curve given in [2,3] and the authors' software package that implement the iteration Newton method and the high-accuracy finite element method [4]. The efficiency of the proposed approach is demonstrated by calculated for the vibrational-rotational bound states and the first time sharp metastable states with complex eigenenergies (with negative imaginary parts of order $10^{-20}\div10^{-3}$ cm$^{-1}$) in a diatomic beryllium molecule.
[1] Merritt,J.M., Bondybey, V.E., Heaven, M.C. Science 324 (5934), 1548-1551 (2009)
[2] Mitin, A.V., Chem. Phys. Lett. 682, 30-33 (2017)
[3] Gusev, A., Chuluunbaatar, O., Vinitsky, S., et al. Proceedings of SPIE, 11066, 1106619 (2019)
[4] Gusev A.A., Hai L.L., Chuluunbaatar O., et al. Lect. Notes in Computer Sci. 9301, 182-197 (2015).