The bond length of the improved Rosen Morse potential, applying for: Cesium, hydrogen, hydrogen fluoride, hydrogen chloride, lithium, and nitrogen molecules

Abstract

One of the generalized vibrational potentials is the improved Rosen Morse potential (IRMP), which is used in vibrational interactions studies, especially, for the study of the vibrations of the diatomic systems or dimers. The IRMP interaction has three independent fitting parameters which are the bond equilibrium length of the IRMP, the energy well depth of the IRMP, and the range of the well of potential parameter. In this study, the principles of the integral equation theory of the simple fluids are employed with the boundary conditions for deriving a simple formula between the bond equilibrium length of the IRMP and the other two fitting parameters of the IRMP interaction. We investigate the relation between the bond equilibrium length of the IRMP interaction and the absolute temperature. We find that the bond equilibrium length of the IRMP interaction depends on the absolute temperature of the system, and increases slowly with the absolute temperature. Also, we find that the bond equilibrium length of the IRMP interaction depends on the diameter of the particles in the system, and also increases with the diameter of the particles for different temperature values and for different values of the depth of the IRMP well. We find that the bond equilibrium length of the IRMP interaction decreases when the depth of the IRMP well increases for different values of temperature, also we find that this bond length increases when the range of the well of the IRMP parameter increases for different values of temperature and for different values of the depth of the IRMP well. We apply our formula of the bond equilibrium length of the IRMP interaction for six different molecules and dimers, which are the caesium dimer (Cs2), the lithium dimer (Li2), the hydrogen chloride (HCl), the hydrogen fluoride (HF), the nitrogen molecule (N2), and the hydrogen molecule (H2). We find that, in general, the bond equilibrium length of the IRMP interaction for these molecules and dimers is between 0.9 Å and 7Å for a wide range of temperatures, and the largest value is for the caesium dimer and the lowest value is for the hydrogen fluoride molecule. The formula which we derive for the bond equilibrium length of the IRMP interaction can be applied further to a wide range of molecules and dimers.