= Solution
Six inward-directed donor orbitals form <symmetry-adapted linear combinations> of $a_{1g}+e_g+t_{1u}$ symmetry. They mix respectively with <metal> $4s$, $(3d_{z^2},3d_{x^2-y^2})$ and $4p$ orbitals. Thus the sigma framework contains six occupied <bonding molecular orbitals> and six corresponding <antibonding molecular orbitals>. The <metal> $(d_{xy},d_{xz},d_{yz})$ orbitals have no sigma-compatible partner and remain nonbonding $t_{2g}$ orbitals in this model. The important metal-dominated <octahedral splitting> is
$$
\boxed{\Delta_o=\varepsilon(e_g^*)-\varepsilon(t_{2g}).}
$$
The $e_g^*$ orbitals point directly toward the donors; the $t_{2g}$ orbitals point between them. The original diagram shows the entire sigma framework, rather than treating the five <metal> d levels as the whole molecular-orbital diagram.
\Image[/past-exam-of-the-chemistry-b-course-of-the-university-of-cambridge/2022/paper-2-orbitals.png]
{title=Sigma-only octahedral orbitals and the donation/backbonding channels of end-on dinitrogen}
For the same donor set and approximately the same geometry, \b[$\Delta_o(\mathrm{Co^{III}})>\Delta_o(\mathrm{Co^{II}})$]. The higher <metal> charge usually shortens the <metal>–donor distances and strengthens the interaction that raises $e_g^*$. This comparison holds other chemical variables fixed: changing the ligand at the same time could reverse a comparison between two unrelated complexes.
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