Theoretical perspectives on the Cope rearrangement in bullvalene systems

Using the semi-empirical AM1 SCF-MO method, transition states have been located for Cope rearrangements in various bullvalene systems, including degenerate unsubstituted and difluoro substituted cases as well as non-degenerate monofluoro substituted cases. Transition states have been located for non-degenerate cases using the routine SADDLE keyword of the MOPAC package. By assuming transition state symmetry about the reaction coordinate for degenerate cases, computational time is substantially saved with no loss of essential accuracy. All these transition states incorporate a boat-shaped cyclic six-membered moiety. Activation energy barriers range between 24.0 and 32.5 kcal/mol, rather high compared with experimental values reported, and thus systematically corrected. The non-degenerate cases have transition states whose positions along the reaction coordinate (as gauged by appropriate geometry markers) agree well with their slightly "late" character predicted from reaction endothermicity by the Hammond postulate. The effects of fluorine substitution on activation energy and transition state geometry as predicted by these calculations accord well with chemical intuition based on the inductive effect. The application of a systematic correction to the activation barriers leads to more reasonable values. For the non-degenerate monofluoro substituted cases, these corrected activation barriers are used to construct an energy profile diagram to represent all the interconversions, which lead us to infer a minimal energy requirement of 19.22 kcal/mol for complete scrambling of the carbons during Cope rearrangement of these systems.