Abstract: This paper presents the normal-mode analytical approach of Fumi-Tosi ionic liquid based on molecular dynamics simulation. We replace the Lennard-Jones potential with the Fumi-Tosi potential (including the long-range potential) and handle the long-range Coulomb interaction using the equivalent Coulomb potential. The computation methods of the elements of Hessian matrix and the eigenvalues of Hessian matrix are discussed. It is shown that the Hessian matrix and the density of states can be obtained reasonably using the equivalent Coulomb potential in the form of the complementary error function.The numerical results of the configuration-averaged densities of states in liquid RbCl show that they have similar characteristics to those in Lennard-Jones liquids.

Key words: Hessian matrix, Eigenvalues of matrix, Density of states