Importance of the embedding environment on the strain within small rings in siliceous materials

The effect of the local environment on the energetic strain within small (SiO)(N) rings (with N=2,3) in silica materials is investigated via periodic model systems employing density functional calculations. Through comparison of the energies of various nonterminated systems containing small rings in strained and relatively unstrained environments, with alpha quartz, we demonstrate how small ring strain is affected by the nature of the embedding environment. We compare our findings with numerous previously reported calculations, often predicting significantly different small-ring strain energies, leading to a critical assessment of methods of calculating accurate localized ring energies. The results have relevance for estimates of the strain-induced response (e.g., chemical, photo, and radio) of small silica rings, and the propensity for them to form in bulk glasses, thin films, and nanoclusters.