Mapping the metastability of Lennard-Jones clusters by the maximum vibrational frequency

We study the structure-stability relationship of the Lennard-Jones (LJ) clusters from a point of view of vibrations. By assuming the size up to $N=1610$, we demonstrate that the $N$-dependence of the maximum vibrational frequency reflects the geometry of the core (the interior of cluster) that will determine the overall geometry of the cluster. This allows us to identify the formation of non-icosahedral structures for $N\le 150$, the vacancy formation at the core for $N\ge 752$, and the transition from icosahedral to decahedral structures at $N = 1034$. We apply the maximum frequency analysis to classify metastable clusters for $19\le N \le 39$, where transformation pathways between different structures are visualized, and the energy barrier height is estimated simultaneously.