Molecular Pöschl-Teller oscillator-based modeling of ozone thermal properties

A hybrid vibrational model is developed to study the thermal properties of ozone (O₃), using the molecular Pöschl-Teller (MPT) oscillator to describe the symmetric stretch mode, while treating the remaining vibrational modes with harmonic oscillators. Analytical expressions derived from the total partition function are used to compute key thermodynamic quantities: Gibbs free energy (ΔG), entropy (S), enthalpy (ΔH), and heat capacity at constant pressure (C_p). Model predictions are evaluated over a wide temperature range (300-6000 K) and compared against NASA Glenn polynomial estimates and NIST-JANAF reference data using the relative error in absolute percentage (REAP). The MPT model achieves mean REAP values of 0.107% for ΔG, 0.130% for S, 1.386% for ΔH, and 3.205% for C_p, demonstrating improved accuracy, especially at elevated temperatures. These results highlight the model's enhanced ability to capture anharmonic vibrational effects in ozone, with relevance to atmospheric chemistry, combustion processes, and high-temperature aerospace applications.

The symmetric stretching vibration of O₃ is modeled using the molecular Pöschl-Teller (MPT) oscillator, while the bending and antisymmetric stretch modes are treated as harmonic oscillators. Rotational and translational motions are modeled using classical statistical mechanics. Closed-form expressions for the partition function and derived thermodynamic quantities are obtained analytically and evaluated across the 300-6000 K temperature range. Model performance is assessed using the relative error in absolute percentage (REAP) by comparing predictions with those from the NASA Glenn polynomial method and NIST-JANAF tabulations. All numerical evaluations and visualizations are performed using custom MATLAB scripts.