= Solution
\b[Both dimers have two <electrons> in a valence sigma-bonding orbital and a formal valence <bond order> of one.] For <hydrogen> the minimal-basis configuration is $(1\sigma_g)^2$, with the $1s$-derived $1\sigma_g$ as <highest occupied molecular orbital> and $1\sigma_u^*$ as <LUMO>. The bonding combination has no internuclear <node>; the antibonding combination does.
For <lithium>, include the filled core pair of levels as well as the valence levels:
$$
\mathrm{Li_2}:\ (1\sigma_g)^2(1\sigma_u)^2(2\sigma_g)^2.
$$
The first two orbitals are predominantly core $1s$ combinations whose bonding and antibonding occupations cancel in a simple bond-order count. The <highest occupied molecular orbital> is predominantly $\sigma_g(2s)$, denoted $2\sigma_g$; the <LUMO> is $2\sigma_u$, predominantly the antibonding $2s$ combination but modified by mixing with compatible $2p$ contributions. The nearby empty $2p$-derived sigma and pi levels must also be shown. Only orbitals of matching symmetry mix, so this does not mean that every $2s$ combination mixes with every $2p$ combination.
On a common qualitative energy reference, <hydrogen> $1s$ is much lower than <lithium>'s valence $2s$, while <lithium>'s core $1s$ levels lie much deeper. The Li valence bonding–antibonding separation is smaller, consistent with its longer and weaker bond. The figure uses a compressed core region and schematic gaps, not measured orbital energies. The role of symmetry-compatible <s–p orbital mixing> in the first-row diatomics is illustrated in institutional molecular-orbital notes.<Diatomic MOs by Timothy Hughbanks>[pp. 1–2: s–p mixing and first-row orbital ordering]{ref}
\Image[/past-exam-of-the-chemistry-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-1-diatomic-orbitals.png]
{title=Original common-reference qualitative orbital diagrams for hydrogen and lithium dimers, including lithium 2p-derived levels and core occupancies}
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