= Solution
The active set contains four <oxygen> pi orbitals and two <carbon> pi orbitals, with \b[eight <electrons> in six orbitals]. The noninteracting levels, using the parameters inferred below, are
$$
\begin{array}{c|c|c}
\text{fragment orbitals}&E\ /\mathrm{eV}&\text{occupation}\\ \hline
\pi_{O,z},\ \pi_{O,y}&-16.1&2,2\\
\pi_{O,z}^*,\ \pi_{O,y}^*&-12.1&1,1\quad(\text{parallel spins})\\
\pi_C&-10.5&2\\
\pi_C^*&-5.5&0
\end{array}
$$
Each bonding <oxygen> orbital has equal-phase coefficients on its two O atoms; its antibonding partner reverses one coefficient. The two pi directions are z in the prospective ring plane and y perpendicular to it. <carbon> pi and pi-star use z-directed <p orbitals> with equal and opposite coefficient signs. In this separated-fragment comparison the occupations are those of neutral triplet O$_2$ plus neutral <ethene>. \b[Do not refill the combined list solely by energy], which would move an <electron> between infinitely separated fragments and describe a charge-transfer state instead.
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2a-active-orbitals.png]
{title=Original signed-orbital sketches for the six reactant and six product active orbitals}
Back to article page
