Can singlet oxygen facilitate a (2+2) cycloaddition reaction, for example between two alkenes, by reacting first with the pi-electrons in one alkene and then lowering the energy barrier for the second alkene to attack (given the instability of 1,2-dioxetane)? Are there any examples of this sort of thing?
I'm not aware of any such examples. In the reactions of singlet oxygen with olefins only products from cycloaddition to form a dioxetane and \ or products from the ene reaction are observed. There are no reports of olefin dimerization.