= Solution
The symmetric approach preserves the <C2v molecular point group> with its twofold axis z and mirror planes xz and yz. The molecular ring lies in xz. Classify orbitals by <reflection> signs $(\sigma_{xz},\sigma_{yz})$: $A_1=(+,+)$, $B_1=(+,-)$, $B_2=(-,+)$, $A_2=(-,-)$. With globally defined p-orbital phases the <molecular orbital correlation diagram> gives
$$
\boxed{\begin{array}{c|c|c}
\text{reactant orbital}&C_{2v}&\text{product orbital}\\ \hline
\pi_{O,z}&A_1&\sigma_+\\
\pi_C&A_1&\sigma_+^*\\
\pi_{O,z}^*&B_1&\sigma_-\\
\pi_C^*&B_1&\sigma_-^*\\
\pi_{O,y}&B_2&n_+\\
\pi_{O,y}^*&A_2&n_-
\end{array}}
$$
Within either two-orbital <symmetry> block the lower member remains correlated with the lower product member; the <non-crossing rule> prevents swapping their order through an ordinary same-symmetry crossing. Crossings between different <irreducible representations> are allowed. The crucial consequence is that the occupied <carbon> pi orbital correlates to a C–O-antibonding combination, rather than both initially occupied $A_1$ orbitals becoming the two product bonding orbitals.
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2a-correlation.png]
{title=Original six-orbital correlation and schematic state correlation for the symmetric oxygen addition}
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