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In this study, the reparametrised Pöschl–Teller (RPT) oscillator is constructed for applications to diatomic molecules. Equations for bound state eigen energies and molar entropy are derived for the oscillator. With the aid of the proposed model, seven diatomic molecules are analysed including  7 Li 2  ( a3 Σ u+ ), Na 2  ( c1 Π u ), HCl (X  1 Σ + ), MgO (X  1 Σ + ), SO (X  3 Σ - ), SiO (X  2 Σ + ), and TiO (X  2 Σ + ). The average absolute deviation (AAD) and mean absolute percentage deviation (MAPD) are employed as the goodness of fit indicators. Computed AAD and MAPD reveal that the RPT oscillator is an excellent model for the diatomic molecules, the potential is approximately equivalent to the improved Tietz and improved Scarf potentials in the literature. An MAPD of 0.3609% from observed data of gaseous HCl molecule is obtained using the equation of molar entropy proposed in this work. This is an indication that the RPT oscillator is a good model for representing the internal vibration of the HCl molecule.

Reparametrised Pöschl–Teller oscillator and analytical molar entropy equation for diatomic molecules