= Solution
Each <cyanide> contributes charge $-1$, so the formal nickel <oxidation state> is $+2$ and the metal has \b[$d^8$]. The requested diagram retains only the five principally metal-$3d$ <molecular orbitals>; the mainly ligand <bonding molecular orbitals> lie below them and are omitted.
In the square, $d_{x^2-y^2}$ points directly towards all four ligand donors and gives the highest, strongly <antibonding molecular orbital>, $B_{1g}$. The $d_{z^2}$ function also has an allowed $A_{1g}$ interaction, but its in-plane overlap is smaller. Including the allowed nickel $4s$ mixing gives a principally $d$ $A_{1g}$ level with relatively weak antibonding character. The $B_{2g}$ and $E_g$ metal functions have no ligand partner in the <sigma bond> donor basis and are nonbonding in this minimal model. The useful qualitative ordering is therefore
$$
\boxed{D_{4h}:\quad (B_{2g},E_g)_{\rm nb}<A_{1g}<B_{1g}.}
$$
The three nonbonding functions are shown together because the sigma-only model does not determine their finer splitting. Additional electrostatic and <pi backbonding> interactions can change the ordering of the lower $d$ levels; <molecular symmetry> alone does not fix these <energy> gaps.<Bonding in Molecules by John E. McGrady>[2022 lecture notes, square-planar sigma-only molecular-orbital discussion, printed pp. 60–61]{ref}
In the tetrahedron, the ligand $T_2$ combinations interact with the metal $T_2$ functions, producing higher $d$-derived <antibonding molecular orbitals>. The metal $E$ pair has no sigma donor partner and remains nonbonding:
$$
\boxed{T_d:\quad E_{\rm nb}<T_{2,\rm antibonding}.}
$$
The diagram fills both arrangements with eight metal <electrons>; the square is shown in its fully paired state.
\Image[/past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2023/paper-1-nickel-d-levels.png]
{title=Original qualitative d-derived orbital diagrams for square-planar and tetrahedral nickel(II), with eight electrons and schematic energy gaps}
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