In the present studies, modified Pöschl-Teller potential (MPTP) is constructed from second Pöschl-Teller potential through conditions to be satisfied by a diatomic molecule potential. Expressions for bound state energy eigenvalues and molar entropy are derived for the MPTP. The equations obtained are applied to seven diatomic molecules: 7Li2 (a 3Σu+), Na2 (c 1Πu), CO (X 1Σ+), MgO (X 1Σ+), SO (X 3Σ-), SiO (X 2Σ+), and TiO (X 2Σ+). Numerical data are analyzed using average absolute deviation (AAD) from the dissociation energy and mean absolute deviation (MAD) from the Rydberg-Klein-Rees (RKR) data. The AAD and MAD results show that MPTP is superior over the improved Pöschl-Teller potential, and it is approximately equivalent to the improved Tietz potential for most of the diatomic molecules investigated. Expression of analytical molar entropy of the MPTP accurately predicts molar entropy of gaseous CO molecule with a MAD of 0.1993% from experimental data obtained from the literature.

In this study, the improved Tietz potential was used to describe the internal vibration of a diatomic molecule. With the help of the expression for bound state energy levels, a more generalized equation for the upper bound vibrational quantum number and canonical partition function were obtained for the diatomic system. The obtained partition function was used to derive analytical equation for the prediction of constant pressure (isobaric) molar heat capacity of diatomic molecules. The analytical model was used to predict the constant pressure molar heat capacity data of the ground state CO, BBr, HBr, HI, P2, KBr, Br2, PBr, SiO and Cl2 molecules. The upper bound vibrational quantum number obtained for the molecules are 85, 100, 21, 21, 115, 301, 89, 157, 110 and 67. The computed average absolute deviation are 2.3462%, 1.1342%, 2.3350%, 1.9078%, 0.7268%, 2.4041%, 1.7849%, 1.8989%, 2.5209% and 2.1523%. The present results are in good agreement with available literature data on gaseous molecules.