Potential effects on instantaneous normal modes of liquids

We calculated the instantaneous-normal-mode (INM) densities of states for liquid Na, Lennard-Jones (LJ) liquid and truncated LJ liquid with the same reduced density and temperature by both molecular-dynamics simulation and the vector-random-walk approach under two-body approximation. By comparing the calculated results for these three liquids, we give some physical insights in the relationship between the INM density of state and the two-particle interaction potential. The effects of the short-range repulsive core, the long-range tail in the potential and the presence of attractive well are elucidated.