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

An analytical representation for the potential energy curve for the ground state $X^1\Sigma^+$ of the hydrogen fluoride molecule (HF) is presented in the frame of the Born-Oppenheimer approximation. The analytical expression for the potential energy curve is based in a two point Pad\'e approximant which correctly reproduces the asymptotic behaviors at small $R\rightarrow 0$ and large $R\rightarrow\infty$ internuclear distances, obtaining not less than 4-5 s.d. when compared with experimental results. The rovibrational spectra of the diatomic molecule HF is calculated by solving the Schr\"odinger equation for nuclear motion. The ground state $X^1\Sigma^+$ contains 21 vibrational states ($\nu,0$) and 722 rovibrational states ($\nu,L$). A slight modification in the differential equation for nuclear motion allows us to obtain the rovibrational spectrum of the ground state of the deuterium fluoride (DF) and tritium fluoride (TF) molecules. Full spectra is presented for this two isotopologues species of HF.