Stability of sulfur molecules and insights into sulfur allotropy

Using ab initio evolutionary algorithm USPEX, we predict structures of sulfur molecules S-n (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 (Delta E-2), fragmentation energy (E-frag) and HOMO-LUMO gaps. The S-8 molecule has the highest value of Delta E-2 and forms the most common allotropic form of sulfur (orthorhombic alpha-S), into which all other modifications convert over time at room temperature. Commonly found molecules S-12 and S-6 also have strongly positive Delta E-2. Another well-known molecule, S-7, has negative Delta E-2, but at temperatures above 900 K has positive second-order free energy difference Delta(2)G. Generally, Delta E-2 (or Delta(2)G 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.