Symmetries, vibrational instabilities, and routes to stable structures of clusters of Al, Sn, and As

We investigate the stability of small clusters using density functional theory to compute the total energy, forces, and vibrational frequencies using linear response. We exhibit an efficient and computationally low-cost route to finding stable structures, by starting with high-symmetry structures and distorting them according to their unstable modes. We illustrate this by application to 4-, 6-, and 13-atom clusters of Al, Sn, and As. This technique also naturally elucidates the origins of stability of the lower symmetry structures, which is variously due to the linear or pseudo Jahn-Teller effect, combined with a lowering of various contributions to the total energy. We show that the situation is more complex than has generally been appreciated.