Thermal [2 + 2] cycloadditions

Despite what we have told you about allowed cycloadditions, there are some thermal [2 + 2] cycloadditions giving four-membered rings. These feature a simple alkene reacting with an electrophilic alkene of a peculiar type. It must have two double bonds to the same carbon atom. The most important examples are ketenes and isocyanates. The structures have two π bonds at right angles. Here are typical reactions of dimethyl ketene to give a cyclobutanone and chlorosulfonyl isocyanate to give a β-lactam.

To understand why these reactions work, we need to consider a new and potentially fruitful way for two alkenes to approach each other. thermal cycloadditions between two alkenes do not work because the HOMO/LUMO combination is antibonding at one end. If one alkene turns at 90° to the other, there is a way in which the HOMO of one might bond at both ends to the LUMO of the other. First, we turn the HOMO of one alkene so that we are looking down on the p orbitals. Then we add the LUMO of the other alkene on top of this HOMO and at 90° to it so that there is the possibility of bonding overlap at both ends. This arrangement looks quite promising until we notice that there is antibonding at the other two corners! Overall there is no net bonding. We can tilt the balance in favour of bond ing by adding a p orbital to one end of the LUMO and at a right angle to it so that both orbitals of the HOMO can bond to this extra p orbital. There are now four bonding interactions but only two antibonding. The balance is in favour of a reaction. This is also quite difficult to draw! Ketenes have a central sp carbon atom with an extra π bond (the C=O) at right angles to the first alkene—perfect for thermal [2 + 2] cycloadditions. They are also electrophilic and so have suitable low-energy LUMOs.

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