Theory of dynamical stability for two- and three-dimensional Lennard-Jones crystals

The dynamical stability of three-dimensional (3D) Lennard-Jones (LJ) crystals has been studied for many years. fcc and hcp structures are dynamically stable, while the bcc structure is stable only long-range LJ potentials that characterized by relatively small integer pairs $(m,n)$. Here, we study two-dimensional (2D) crystals, where planar hexagonal, buckled honeycomb, square assumed. We demonstrate property 2D 3D can be classified into four groups depending on instabilities square, investigated within analytical expressions. structure-stability relationship between elemental metals in periodic table also discussed.