How important is bishomoaromatic stabilization in determining the relative barrier heights for the degenerate Cope rearrangements of semibullvalene, barbaralane, bullvalene, and dihydrobullvalene?

[structure: see text] B3LYP/6-31G* calculations have been used to investigate the origins of the relative barrier heights for the degenerate Cope rearrangements of semibullvalene (1), barbaralane (2), bullvalene (3), and dihydrobullvalene (4). We conclude from our calculations that, of the four transition structures (TSs), that for rearrangement of 1 has the smallest amount of interallylic bonding. Nevertheless, relief of strain in the reactant confers on 1 the lowest barrier to Cope rearrangement. Conjugation between the cyclopropane ring and the pi bond of the etheno bridge in 3 makes the barrier for its Cope rearrangement higher than that for 4 and also contributes to making the barrier for 3 higher than that for 2. However, the relatively low barrier to the Cope rearrangement of 2 is largely due to the TS for this reaction having the largest amount of interallylic bonding of all four TSs.