Stability of sulfur molecules and insights into sulfur allotropy.

Abstract

Using ab initio evolutionary algorithm USPEX, we predict structures of sulfur molecules Sn (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 (Efrag) 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.