= Solution
\b[N$_2$:] <Homo> $\sigma_{2p_z}$; <LUMO> the degenerate $\pi_{2p}^*$ pair.
\b[O$_2$:] the two $\pi_{2p}^*$ orbitals are the highest occupied, singly occupied spatial orbitals. The next completely empty spatial orbital is $\sigma_{2p_z}^*$. An added <electron> can instead occupy the opposite-spin vacancy in a singly occupied pi-star orbital; this distinction matters if “<LUMO>” is being used for an electron-addition <spin> orbital.
\b[Li$_2$:] <Homo> $\sigma_{2s}$; next empty sigma orbital conventionally denoted $\sigma_{2s}^*$ in this elementary diagram. \b[Be$_2$:] <Homo> $\sigma_{2s}^*$; the low empty 2p manifold supplies the <LUMO> candidates, drawn as $\pi_{2p}$ in the stated light-diatomic ordering. Mixing makes these labels descriptions of dominant atomic-orbital character, not strictly unmixed atomic functions.
This distinction is the <open-shell frontier orbital convention>.
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