HCl, DCl and TCl diatomic molecules in their ground state: predicting Born-Oppenheimer rovibrational spectra

The analytic Born-Oppenheimer (B-O) potential curve for the ground state $X^1{\mathrm{\Sigma }}^{+}$ of the molecule (H,D,T)Cl is constructed for the whole range of internuclear distances $R\in [0,\mathrm{\infty })$ with an accuracy of 3-5 figures in comparison with the RKR-style potential curve derived from available experimental data on vibrational energies. With an accuracy of 3-4 significant figures in the energies, it is predicted for HCl (DCl, TCl) the 836 (1625, 2366) B-O rovibrational bound states with maximal vibrational number ${\nu }_{max}=20(29,35)$ and maximal angular momentum $L_{max}=64(90,109)$ including 24 (46, 63) weakly-bound states (close to the dissociation limit) with energies $\lesssim {10}^{-4}$ Hartree. Insufficiency of existing experimental data is indicated and a prediction of the bulk of missing rovibrational states is made for all HCl, DCl, TCl molecules.