MO diagram construction for K₄[Co(CN)Cl₅]

[edvard_inorganic]

I am working on a problem where I need to construct the molecular orbital diagram for K₄[Co(CN)Cl₅].

From the character table of C₄v, the symmetry-adapted combinations are as follows:

Metal orbitals: a₁, b₁, b₂, e

Ligand σ orbitals: 3a₁ and e

Cyanide π orbitals: e (π acceptors)

I already know these assignments, but I am unsure how to systematically combine them into the final MO diagram. Specifically, how should the π* orbitals of CN (irrep e) be incorporated along with the σ framework of both CN⁻ and Cl⁻ in order to represent π backbonding properly?

Is there a standard step-by-step approach for building this diagram under C₄v symmetry, or any references/examples of similar mixed-ligand complexes that could help clarify the process?

[ChenBeier]

Chloride is a halogen and cyanide is a Pseudohalogen. Both are single negative charged. The molecule should looks like the iron compound K₄[Fe(CN)₆] Cobalt has two electron more as iron
Pictures can find

[geometrylitegame]

In practice the tricky bit is that the CN π* (irrep e) and the ligand σ e SALCs live in the same irreducible representation, so the metal e orbitals (dxz, dyz together with px, py) will simultaneously handle σ bonding and π backbonding and the two kinds of interaction will mix.