Computational elucidation of the reaction mechanisms of elemental sulfur and polysulfides with cyanide and phosphines

The reactions of elemental sulfur (S8) and polysulfides with nucleophiles are relevant to organic synthesis, materials science and biochemistry, but the mechanisms by which they operate are still unknown. Depending on the nature of the nucleophile, a broad variety of products can be obtained, but reaction pathways are difficult to probe experimentally due to the inherent thermodynamic and kinetic instability of polysulfide intermediates. Using Density Functional Theory (DFT) calculations at the ωB97X-D/aug-cc-pV(T+d)Z/SMD(MeCN) // ωB97X-D/ aug-cc-pVDZ/SMD(MeCN) level of theory, this study provides the first comprehensive picture of the mechanisms behind the reaction of elemental sulfur and polysulfides with cyanide and phosphines, which quantitatively generate the monosulfide products thiocyanate and phosphine sulfides, respectively. These reactions are prototypical of the reactions of sulfur with other strong nucleophiles including carbon-based systems, and are important for the titration and detection of elemental sulfur in complex media. We first demonstrate that from the two mechanisms proposed more than 60 years ago, the Foss-Bartlett hypothesis is the most likely nucleophilic decomposition pathway for polysulfide intermediates containing good leaving groups. Importantly, we find that unimolecular decomposition pathways, either cyclizative or not, have the lowest activation barriers for most polysulfide intermediates. This indicates that such intermediates are fleeting in solution as they rapidly decompose even without an external nucleophile. Other bimolecular decomposition pathways were also located, including scrambling reactions and attack on thiosulfoxides, which are less likely to intervene as they require larger concentrations of highly-reactive intermediates. Overall, our results indicate that for long polysulfides intramolecular cyclization is the most favorable decomposition pathway. For short polysulfides, a mixture of unimolecular decomposition and nucleophilic attack can be expected, in addition to scrambling pathways if the concentration of nucleophile is low. Overall, this work highlighted the various pathways available for polysulfide decomposition, allowing the study of polysulfide reactivity in more complex settings such as organic transformations or biochemical pathways.