molecules. Photochemical [1,3] shifts Photochemical [1,3] shifts should proceed through suprafacial shifts; however, most are non-concerted because they proceed through a triplet state (i.e., have a diradical mechanism, to which the Woodward-Hoffmann rules do not apply). [1,5] shifts A [1,5] shift involves the shift of 1 substituent (hydride, alkyl, or aryl) down 5 atoms of a π system. Hydrogen has been shown to shift in both cyclic and open-chain compounds at temperatures at or above 200 ˚C. These reactions are predicted to proceed suprafacially, via a Hückel-topology transition state. Photoirradiation would require an antarafacial shift of hydrogen. Although rare, there are examples where antarafacial shifts are favored: In contrast to hydrogen [1,5] shifts, there have never been any observed [1,5] alkyl shifts in an open-chain compound. Several studies have, however, been done to determine rate preferences for [1,5] alkyl shifts in cyclic systems: carbonyl and carboxyl> hydride> phenyl and vinyl>> alkyl. Alkyl groups undergo [1,5] shifts very poorly, usually requiring high temperatures, however, for cyclohexadiene, the temperature for alkyl shifts isn't much higher than that for carbonyls, the best migratory group. A study showed that this is because alkyl shifts on cyclohexadienes proceed through a different mechanism. First the ring opens, followed by a [1,7] shift, and then the ring reforms electrocyclically: This same mechanistic process is seen below, without the final electrocyclic ring-closing reaction, in the interconversion of lumisterol to vitamin D2. [1,7] shifts [1,7] sigmatropic shifts are predicted by the Woodward–Hoffmann rules to proceed in an antarafacial fashion, via a Mobius topology transition state. An antarafacial [1,7] shift is observed in the conversion of lumisterol to vitamin D2, where following an electrocyclic ring opening to previtamin D2, a methyl hydrogen shifts. Bicyclic nonatrienes also undergo [1,7] shifts in a so-called walk rearrangement, which is the shift of divalent group, as part of a three-membered ring, in a bicyclic molecule. [3,3] shifts [3,3] sigmatropic shifts are well studied sigmatropic rearrangements. The Woodward–Hoffman rules predict that these six-electron reactions would proceed suprafacially, via a Hückel topology transition state. Claisen rearrangement Discovered in 1912 by Rainer Ludwig Claisen, the Claisen rearrangement is the first recorded example of a [3,3]-sigmatropic rearrangement. This rearrangement is a useful carbon-carbon bond-forming reaction. An example of Claisen rearrangement is the [3,3] rearrangement of an allyl vinyl ether, which upon heating yields a γ,δ-unsaturated carbonyl. The formation of a carbonyl group makes this reaction, unlike other sigmatropic