Thermodynamic properties of diatomic molecules from the Frost–Musulin potential

In this work, we examine the Frost–Musulin potential as a compact bound-region spectral model for H $$_2$$ and LiH and quantify how its discrete spectrum propagates into standard-state thermodynamic functions. The radial Schrödinger equation is treated within a near-equilibrium Pekeris representation, and the resulting finite bound-state ladder is combined with ideal-gas translational and rigid-rotor rotational factors. To clarify the model specificity, we include a direct comparison with the Morse potential matched to the same spectroscopic constants. The comparison shows that the relative performance of the Frost–Musulin and Morse spectra is molecule dependent: Morse gives a more accurate common-range s-state ladder for H $$_2$$ , whereas this potential performs better for LiH. This potential thermodynamic benchmark reproduces the Gibbs free-energy deviation at sub-percent level over the studied temperature windows, while derivative-sensitive quantities such as $$C_p$$ and $$H^\circ (T)-H^\circ _{298.15}$$ show increasing high-temperature deviations. These deviations are associated with the finite bound-state ladder, the local nature of the Pekeris approximation, the factorized vibrational-plus-rigid-rotor treatment, and the absence of near-dissociative and continuum contributions. The work therefore provides a comparative benchmark and a quantitative domain of validity for FM-based bound-state thermodynamics rather than a new solution method.