Stability of sulfur molecules and insights into sulfur allotropy

Using ab initio evolutionary algorithm USPEX, we predict structures of sulfur molecules S (n = 2 - 21). It is shown that for n ≥ 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 (Δ²E), fragmentation energy (E_frag) and HOMO-LUMO gaps. The S₈ molecule has the highest value of Δ²E 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 S₁₂ and S₆ also have strongly positive Δ²E. Another well-known molecule, S₇, has negative Δ²E, but at temperatures above 900 K has positive second-order free energy difference Δ²G. Generally, Δ²E (or Δ²G 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, etc.