Stability of sulfur molecules and insights into sulfur allotropy.

Using evolutionary algorithm USPEX, we predict structures of sulfur molecules S ( = 2 - 21). It is shown that for ≥ 5 stable structures of sulfur molecules are closed helical rings, which is in agreement with the experimental data and previous calculations. We investigate the stability of molecules using the following criteria: second-order energy difference (Δ), fragmentation energy () and HOMO-LUMO gaps. The S molecule has the highest value of Δ and forms the most common allotropic form of sulfur (orthorhombic α-S), into which all other modifications convert over time at room temperature. Commonly found molecules S and S also have strongly positive Δ. Another well-known molecule, S, has negative Δ, but at temperatures above 900 K has positive second-order free energy difference Δ. Generally, Δ (or Δ at finite temperatures) is a quantitative measure of the stability allowing one to predict the ease of formation of molecules and corresponding molecular crystals. Temperature dependence of the above-mentioned measures of stability explains a wide range of facts about sulfur crystalline allotropes, molecules in the gas phase,