In general, [2 + 2] cycloaddition reactions are thermally not allowed and photochemically allowed. The reaction of ketene with alkene is thermally allowed [2 + 2]cycloaddition. This is because of additional bonding interactions between HOMO of alkene and p-orbital on central carbon of ketene lying perpendicular to the LUMO of ketene.
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Thermal [2+2] cycloaddition reactions
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