Not all cycloaddition reactions take place under thermal conditions.

While the [4 + 2] cycloaddition is thermally allowed, the [2 + 2] cycloaddition requires photochemical activation.

But why?

Recall that a symmetry mismatch between the ground state HOMO and LUMO of ethylene prevents the reaction from occurring in a concerted suprafacial manner under thermal conditions.

Alternatively, photochemical excitation of one of the ethylene molecules promotes an electron from the ground state HOMO to the LUMO.

This leaves the excited state HOMO with the correct symmetry to interact with the ground state LUMO of the other ethylene molecule, resulting in a concerted suprafacial overlap of the two components.

In summary, for photochemical cycloadditions, the key HOMO–LUMO interaction is between the electronic ground state of one component and the excited state of the other. In comparison, thermal cycloadditions occur between the ground state frontier orbitals of both components.