Analytical Solution for Nonlinear Vibration of Diatomic Molecules

Within the past decade, the emphasis of scientific research has shifted to the study of the behavior of materials at the atomic scale of matter. The most common elements occur as diatomic molecules, such as oxygen, hydrogen, and nitrogen. Therefore, many researchers have a tendency to this type of molecules. In this paper, the Morse potential is applied in the Lagrange equation to calculate the oscillation of the nuclei. The vibration equation of diatomic molecules in nonlinear form is established. The method of Lindstedt-Poincaré (L-P) in different orders of approximation is implemented to solve the nonlinear equation of motion. As a prototype, the displacement response and frequencies in different initial conditions are obtained for diatomic molecule Al2. It has been shown that the frequency of molecules varies with changing initial conditions. The validity of the analytical solution is discussed by comparing it with numerical solution. The results show good agreement between the analytical and the numerical solutions. Finally, the frequencies of diatomic molecule Al2 is obtained from Gaussian software (Gaussian 09) and is compared with those obtained from the analytical solutions.