A novel formula of equilibrium bond distance of the quantum oscillator with temperature dependence in diatomic molecules

Morse potential, a basic interaction potential used in the study of the non-harmonic oscillations between atoms and molecules, can be used for studying diatomic molecules. The full description of Morse interaction can be done using three parameters, and one important parameter of Morse potential is the bond distance of the equilibrium state of the potential. This parameter describes the equilibrium situation of the interaction itself. In this communication, we aim to derive a novel formula for the previous equilibrium distance. We derive the formula depending on the basic principle of the integral equation theory of the distribution functions. Depending on the derived formula, we find that the bond distance of the equilibrium state is a function of the temperature of the system via a nonlinear relationship. Also, we find that the bond distance of the equilibrium state is a function of the other two parameters of the Morse potential. Based on the derived formula, we found that the bond distance of the equilibrium state increases slowly with the absolute temperature of the system. Also, we calculate this bond distance for two diatomic molecules: the first one is the hydrogen chloride molecule, and the other is the hydrogen fluoride molecule. The bond distance of the equilibrium state, which are calculated in this work, are reliable and comparable to the experimental results of this distance.