[5,5] sigmatropic rearrangement. DFT prediction of a diradical mechanism for a Woodward-Hoffmann "allowed" thermal pericyclic reaction

The mechanisms of the degenerate [5,5] sigmatropic rearrangements of 5,5a,10,10a-tetrahydroheptalene and (Z,Z)-1,3,7,9-decatetraene were explored with restricted and unrestricted Becke3LYP/6-31G* hybrid HF-DFT calculations. The restricted DFT wavefunctions for the synchronous, concerted transition structures for these formally Woodward-Hoffmann allowed 10-electron rearrangements are unstable with respect to unrestricted wavefunctions. A stepwise diradical mechanism is predicted for both reactions. The 9 kcal/mol preference for the [5s,5s] mechanism over the [5a,5a] pathway in the rearrangement of decatetraene results primarily from the geometric distortions that the system must adopt in the [5a,5a] transition structure. The geometric and electronic characteristics of the [5,5] and [3,3] (Cope) rearrangements are compared.