= Solution
In the <electronic state correlation diagram>, the singly occupied reactant orbitals for triplet <oxygen> have <symmetries> $B_1$ and $A_2$, so their spatial product is $B_2$. The reactant state is therefore a triplet ${}^3B_2$, whereas the closed-shell product is ${}^1A_1$. \b[A strictly spin-conserving path cannot correlate triplet reactants directly to the ground-state product.] It correlates to an excited triplet product configuration or requires <intersystem crossing>; the symmetric direct reaction consequently has a substantial electronic obstacle.
Simply changing the <oxygen> spin does not repair the occupied carbon-orbital correlation. The lowest <oxygen> singlet manifold has spatial components of $A_1$ and $B_2$ <symmetry> in this subgroup. The $A_1$ singlet can have an avoided crossing with another $A_1$ configuration and reach the product singlet; the $B_2$ singlet cannot mix directly with the product ${}^1A_1$ while $C_{2v}$ is maintained. Following either closed-shell <oxygen> singlet component in the orbital diagram still leaves the carbon-pi <electron> pair in the rising $\sigma_+^*$ orbital. Its redistribution into the final occupied orbitals requires configuration mixing at an avoided crossing. \b[A barrier is therefore expected even for the symmetry-constrained concerted singlet addition; singlet does not imply barrierless.] The state curves in the original diagram are schematic, illustrating this avoided-crossing argument rather than computed energies.<Selection rules for singlet-oxygen reactions. Concerted addition reactions by David R. Kearns>[1969, orbital and state correlation for concerted olefin additions]{ref}
The real singlet reaction can lower this obstacle through asymmetric or stepwise pathways that are absent from the stipulated direct approach. A primary multireference study explicitly distinguishes singlet and triplet addition through biradical intermediates, supporting that limitation of a one-coordinate <symmetry> argument.<Singlet and triplet potential surfaces for the O2+C2H4 reaction by Kyoyeon Park and others>[2010, abstract and calculated addition/isomerization surfaces]{ref} Neither correlation alone nor a spin label supplies a numerical <activation energy>.
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