Oscillation of the Ar2 Molecule using the LAMMPS Molecular Dynamics Simulation Tool

This study investigates the vibrational dynamics of the diatomic argon molecule (Ar2) using molecular dynamics (MD) simulations, with the aim of determining the dispersion relationship between the oscillation frequency f and the system energy E. The interatomic interactions are modeled using the Lennard–Jones potential, a well-established representation of atomic forces, to analyze the molecular behavior over a range of energy states. The simulations are performed with the LAMMPS software package, which enables the calculation of oscillation frequencies corresponding to different energy levels.

The selected energy values span the depth of the Lennard–Jones potential well, ranging from −ε to zero. For each energy level, the equilibrium bond length is determined and the corresponding oscillation frequency is computed. The results demonstrate that the oscillation frequency decreases as the energy increases, highlighting the anharmonic nature of the molecular potential. At higher energies, the oscillation amplitude becomes larger, causing the system to deviate from ideal harmonic motion and resulting in a reduction of the vibrational frequency.

The dispersion curve, which describes the relationship between oscillation frequency and energy, is examined and compared with theoretical predictions. In addition, an analytical approximation based on the theory of small oscillations about the equilibrium bond length is derived to estimate the vibrational frequency at equilibrium energy. The analytical prediction shows good agreement with the numerical results obtained from the molecular dynamics simulations. Overall, the findings provide insight into the anharmonic vibrational behavior of diatomic molecules and contribute to a deeper understanding of molecular interactions and thermodynamic properties in molecular simulation studies.