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Several transition metal promoted sigmatropic shifts were examined using modern quantum chemical methods. For each reaction, it was determined whether direct transition state complexation or, instead, transition metal intervention was the source of rate acceleration and stereoselection.

First, a combination of physical organic experiments and quantum chemical calculations was used to construct a detailed mechanistic model for the Ni(0)-N-heterocyclic carbene-catalyzed vinylcyclopropane-cyclopentene rearrangement that involves a mutistep oxidative addition/haptotropic shift/reductive elimination pathway. No evidence for the intermediacy of radicals or zwitterions was found. The roles of substituents on the vinylcyclopropane substrate and variations in the ligands on Ni were evaluated. It was postulated that bulky carbene ligands facilitate formation of the active catalyst species.

This study was also extended to vinylcyclobutane systems.  Density functional theory calculations were used to evaluate the feasibility of Ni(0)-N-heterocyclic carbene-promoted [1,3] sigmatropic rearrangements of bicyclo[3.2.0]hept-2-enes to bicyclo[2.2.1]hept-2-enes. It was predicted that transition metal intervention lowers the barrier and changes the stereoselectivity for such reactions. Moreover, the addition of electron-withdrawing groups to the migrating carbon was found to lower the barrier for oxidative addition, while incorporation of sterically hindered groups was found to increase the driving force for the reaction.

Rh-catalyzed [1,3] sigmatropic shifts of hydrogen were also examined. Recently, a Rh(I)-catalyzed rearrangement of N-allylaziridines to (Z)-N-alkenylaziridines was reported to proceed with high stereoselectivities. We used quantum chemical calculations to compare and contrast two mechanisms for the rearrangement, including one that proceeds through an aza-metallacyclopentene intermediate as well as a hydrometalation/beta-hydride elimination mechanism. It was found that the latter mechanism corresponds to the lower energy pathway, which, counterintuitively, exhibits a kinetic preference for the formation of products with Z double bonds.

Finally, Pd(0)-promoted [3,5] sigmatropic shifts were examined in detail using density functional theory calculations and a particular catalyst/substrate combination predicted to show rate acceleration and altered stereoselectivity resulting from transition state complexation was designed. These predictions are being put to the test experimentally.