A generalized q-deformed Eckart model for the spectroscopic and thermodynamic properties of diatomic molecules

A generalized q-deformed Eckart potential is parameterized for diatomic molecules using dissociation, equilibrium, curvature and spectroscopic constraints. The radial Schrödinger equation is solved with a Pekeris approximation of the centrifugal term. Potential-energy curves and vibrational energies are assessed for Br 2 , Cl 2 , ICl and RbCs against spectroscopically reconstructed reference data. The potential-energy percentage average absolute deviations are 1.2266%, 0.6461%, 0.2457% and 2.5430%, respectively; the corresponding vibrational-energy deviations are 1.4933%, 1.0259%, 0.5743% and 1.6687%. Thermodynamic calculations for ICl, BrCl and SO cover 300–6000 K. A temperature-independent partition-function offset is calibrated for each molecule against NIST-JANAF Gibbs-energy data. After calibration, the mean entropy and Gibbs-energy-function deviations are 0.0998% and 0.1443% for BrCl, and 0.3368% and 0.2518% for SO. The SO enthalpy increment differs from the reference value by − 9.027 kJ mol − 1 at 6000 K. Mean percentage deviations in \({log ₁₀}{K_p}\) are 8.5061%, 6.1582% and 7.7610% for ICl, BrCl and SO, with substantial low-temperature discrepancies. The results connect spectroscopic parameterization with molecular thermodynamic calculations and identify limitations in the centrifugal approximation and equilibrium predictions.