If tricyclic analogs are formed by bridging the C1 and C8 carbons of bicyclo[5.1.0]octa-2,7-diene, similar degenerate rearrangements are observed. Examples will be displayed above by clicking on the diagram again. For three of these compounds the activation energy is even lower due to a combination of increased ground state strain and transition state stabilization by interallylic bonding. The remarkable C10H10 hydrocarbon bullvalene is exceptional in two respects. First, its ground state is stabilized relative to the dihydro analog by π-conjugation with the three-membered ring. Second, its three-fold symmetry permits numerous self-replicating Cope rearrangements leading to over a million (10!/3=1,209,600) identical valence tautomers. All the carbons and hydrogens in bullvalene appear to be equivalent on the nmr time scale at 100 ºC, and cannot be discriminated until cooled to -15 ºC. Molecules of this kind are termed fluxional. It is important to recognize that valence tautomerization of this kind is not resonance (the relative positions of the atoms undergo small changes).
In the following model carbon is dark grey and hydrogen is cyan. The Show Rearrangement button activates a three stage demonstration. First, the original valence tautomer is drawn with carbon 1 colored light green and labeled. Next an approximation of the Cope transition state is shown with dotted lines representing the shifting electrons. Finally the valence tautomeric product of that [3,3] sigmatropic rearrangement is drawn, with the designated carbon still colored.
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