Effect of temperature and substitution on Cope rearrangement: a symmetry perspective

Many reactions feature symmetry variation along the reaction path on the potential energy surface. The interconversion of the point group symmetry of the stationary points can be characteristic of these processes. Increasing the temperature, however, leads to the loss of symmetry in its traditional yes-no language. We find that in such cases the instantaneous distance of the molecular structure from its symmetric counterpart is a suitable collective variable that can describe the reaction process. We show that this quantity, the continuous symmetry measure (CSM), has a positive linear relationship with temperature, implying that even highly symmetric molecules should be considered as asymmetric above 0 K. Using ab initio molecular dynamics, we simulate the temperature-induced Cope rearrangements of several fluxional molecules and employ different CSMs to follow the reaction progress. We use this methodology to demonstrate the validity of important concepts governing these reactions: Woodward-Hoffmann rules and TS aromaticity. Statistical analysis of the CSM distributions reveals that ligands connected to the carbon frame have profound effect on the reaction course. In particular, our results show that lower temperatures tend to enhance the differences between the TS-stabilizing effect of the substituents.