Chemical equilibrium constants of diatomic molecules from a q-deformed hyperbolic interaction potential

Abstract Context: Chemical equilibrium constants depend on the molecular energy levels that determine the partition functions and Gibbs free energies of the reacting species. This study employs a q-deformed hyperbolic interaction potential (qHIP) to calculate the chemical equilibrium constants for the formation of BrF, ClF, IF, and SO from their homonuclear reactants. The qHIP parameters are related to the equilibrium bond length, dissociation energy, and vibrational wavenumber. The calculated chemical equilibrium constants are compared with NIST-JANAF values over 300–6000 K. The average relative absolute deviations are 0.345% for BrF over 300–6000 K, 0.751% for ClF over 300–4600 K, 0.871% for IF over 400–6000 K, and 0.905% for SO over 900–6000 K. ClF exhibits increasing deviations above 4600 K, whereas the largest discrepancies for SO occur below 900 K. These results specify the temperature intervals over which the qHIP-derived equilibrium constants agree closely with NIST-JANAF data. Methods The radial Schrödinger equation containing the qHIP was solved using the parametric Nikiforov-Uvarov method to obtain the vibrational energy eigenvalues. The qHIP parameters were determined from the equilibrium bond length, dissociation energy, and vibrational wavenumber by imposing equilibrium, dissociation, and curvature conditions on the potential. The vibrational energy eigenvalues were used to construct the vibrational partition function, with a molecule-dependent correction parameter determined from Gibbs free-energy data. The vibrational contribution was combined with the rotational and translational partition functions to calculate the molecular Gibbs free energies. Gibbs free-energy changes for the formation of BrF, ClF, IF, and SO were then used to determine their chemical equilibrium constants. The calculated values were assessed against NIST-JANAF data using the relative absolute deviation and average relative absolute deviation.