Unified Analytical Treatment of Molecular Energy Spectra and Thermodynamic Properties with the q-Deformed Tietz Model

A precise characterization of molecular vibrations and thermodynamic properties is essential for applications in spectroscopy, computational modeling, and chemical process design. In this study, the q-deformed Tietz (qDT) oscillator is applied to examine vibrational energy spectra of diatomic molecules and thermodynamic properties of nonlinear symmetric triatomic molecules. Vibrational energy eigenvalues were obtained analytically using the improved Nikiforov-Uvarov method. The symmetric vibrational mode was described with the qDT oscillator, while asymmetric and bending modes were modeled using the rigid rotor harmonic oscillator (RRHO); translational and rotational contributions were incorporated from standard models. For diatomic molecules (BrF, CO+, CrO, ICl, KRb, NaBr), mean absolute percentage errors (MAPE) ranged from 0.53% to 1.73% for vibrational energy eigenvalues and 0.34% to 1.08% for potential fits. Extending the analysis to triatomic molecules, thermodynamic properties of AlCl2, BF2, Cl2O, OF2, O3, and SO2 were calculated with the qDT model, yielding low MAPE benchmarked against NIST-JANAF reference data: entropy 0.203% to 0.614%, enthalpy 1.792% to 5.861%, Gibbs free energy 0.419% to 1.270%, and constant-pressure heat capacity 1.475% to 4.978%. These results demonstrate the versatility and accuracy of the qDT oscillator as an analytical framework connecting molecular potentials, vibrational energies, and thermodynamic functions, providing a practical and tractable approach for modeling both diatomic and symmetric triatomic systems.