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An improved Hulburt‐Hirschfelder (IHH) quantum mechanical anharmonic oscillator model which describes the exact analytical potential energy curves (PECs) of diatomic molecules is presented. The IHH analytical potential function that involves a variable parameter, four empirically determined low‐order molecular vibrational and rotational spectral constants and the dissociation energy was applied to the ground electronic states of HF and HCl, yielding a good agreement between the Rydberg‐Klein‐Rees (RKR) potential energy points and the calculations. Correspondingly, with the determined IHH PECs, the partition functions at temperatures 300–6000 Kelvin (K) and rovibrational line intensities are evaluated, and coincide well with those quoted in the HITRAN2020 database compilation. The methodology could be valuable for the detection of molecules in interstellar clouds using infrared spectroscopy, as well as thermochemical reactions. [ABSTRACT FROM AUTHOR]