A formula of Tietz potential parameters and applying for scandium iodine, nitrogen iodine, rubidium hydride, nitrogen, and carbon monoxide molecules

Abstract

Tietz potential has several applications in the study of diatomic molecules in the discussion of vibrational states, especially in the quantum mechanics studies of the oscillations. Tietz potential has multiple forms; one of the Tietz potential forms has four parameters of the spectroscopic fitting. The spectroscopic fitting parameters of the Tietz potential are the Tietz potential equilibrium bond length, the Tietz potential depth, the width of the potential, and the parameter that controls the values as ratio of the depth of the well. This work focuses on finding a formula between the four parameters of the spectroscopic fitting employing some of principles of the statistical mechanics. Based on the derived formula, we discuss the relationship of the equilibrium bond length of Tietz potential interaction as a function to the absolute temperature. Based on this discussion, the equilibrium bond length of Tietz potential interaction varies slowly with absolute temperature. Besides, equilibrium bond length of Tietz potential varies linearly with the radius of the particles of the system. Also, the equilibrium bond length of Tietz potential varies with the Tietz potential depth, the width parameter of Tietz potential, and the fourth parameter of the Tietz potential. The formula of the Tietz interaction is applied to five different dimers or molecules. The five considered molecules are nitrogen dimer, scandium iodine dimer, nitrogen iodine dimer, rubidium hydride dimer, and carbon monoxide molecule. Generally, it is found that the equilibrium bond length of Tietz potential interaction values varies from 1 to 5 Å for different absolute temperature intervals. Besides, it is found that the scandium iodine dimer has the largest value of the equilibrium bond length of Tietz potential interaction, while carbon monoxide dimer has the lowest value of the equilibrium bond length of Tietz potential interaction. Generally, the derived formula of the four parameters of the spectroscopic fitting of Tietz potential can be applied for multiple molecules and dimers.