HF, DF, TF: approximating potential curves, calculating rovibrational states

A simple analytical expression for the potential energy curve for the ground state X (1)sigma(+) of the hydrogen fluoride molecule HF obtained in the framework of the Born-Oppenheimer approximation is proposed. This analytical expression for the potential energy curve is based in the two point Pade approximation, which correctly reproduces the asymptotic behavior at small R -> 0 and large R -> infinity internuclear distances, and position and depth of potential well, leading to the accuracy of 4-5 decimal digits when compared with experimental data. The rovibrational spectra of the diatomic molecule HF is calculated by solving the Schrodinger equation for nuclear motion using the Lagrange-mesh method. The ground state X (1)sigma(+) contains 21 vibrational states (nu, 0) and 724 rovibrational states (nu, L) with maximal angular momentum equal to 55. The change of reduced mass in the Schrodinger equation for nuclear motion allows us to obtain the rovibrational spectrum of the ground state potential curve of the deuterium fluoride DF (contains 29 vibrational states (nu, 0) and 1377 rovibrational states (nu, L)) and tritium fluoride TF (contains 35 vibrational states (nu, 0) and 1967 rovibrational states (nu, L)) with maximal angular momenta 76 and 92, respectively. Entire rovibrational spectra is presented for the HF molecule and its two isotopologues DF and TF.