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Is there a Norrish reaction for beta, gamma-unsaturated ketones? I know that Norrish reaction is used for saturated ketones, but in my homework I found this question. I have looked a lot in books and websites but I haven't found anything

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Beta, gamma-unsaturated ketones can undergo Norrish photoreactions from the excited singlet state. For example, in the case (1) below $\ce{R'}$ would be an allyl radical if we had started with a beta, gamma-unsaturated ketone.

Ketone Norrish photoreaction scheme

From this solvent caged biradical several things can happen. The acyl radical can decarbonylate (lose carbon monoxide) and then recombine with either end of the allyl radical to produce hydrocarbons. Also the radical pair could simply recombine. This would regenerate the starting material, or if the allyl radical has different substituents on each end, then it could recombine at the other end of the allyl radical to produce an isomeric beta, gamma unsaturated ketone.

However, the really interesting photochemistry observed with beta, gamma-unsaturated ketones occurs from the triplet state and is known as the oxa-di-pi-methane rearrangement. The following figure (2) provides an example showing the "characteristic" 3-membered ring in the final product.

example of above reaction with formation of 3 membered ring

It is just the "oxo" analogue of the all-carbon photo di-pi-methane rearrangement.

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