Structural stabilities of small sulfur clusters

We acquired 68 small sulfar clusters from S-3 to S-13 with molecular graphics and then carried out the optimizations and vibrational frequencies by density functional calculations. The non-minimum structures with negative vibrational frequencies were excluded. When designing these isomers, the sulfur atoms could be in one-fold, two-fold and three-fold. The sulfur clusters with three-fold atom are higher in energies. It is rare to form a cage structure with multi-fold atom(s). By comparing the total energies of the different isomers, the energies of ring structures are higher than those of chain ones from S-5. The large neutral sulfur clusters are mostly ring structures.