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2+2 cycloaddition to give fused 4 and 5 membered rings

Does anyone know how I get a fused 4 and 5 membered ring from an open chain system?
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Photo excitations of ethene give 4 membered rings.

Think about FMO theory.
This gives a 4 membered rings. If one of the alkenes was a 5 membered cycle (e.g. cyclopentene), you would get a 5 and a 4 ring fused together.



If you want to form the 5 members cycle, you can use a 1,3-dipolar cycloaddition, [3+2]:

http://en.wikipedia.org/wiki/1,3-Dipolar_cycloaddition

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