Identify the complex and the bonding issue

The complex given is most likely nickel tetracarbonyl, written as $[Ni(CO)_4]$.

We are asked which theory can completely/properly explain the nature of bonding in this complex.

Why this is a special case

In $[Ni(CO)_4]$, the ligand $CO$ is not just a simple donor ligand. It shows:

• $\sigma$-donation from the lone pair on carbon to nickel
• $\pi$-back bonding from filled metal orbitals to empty $\pi^*$ orbitals of $CO$

So the bonding is synergic and involves both ligand-to-metal and metal-to-ligand interactions.

Check each theory

A. Werner's theory

Werner's theory explains:

• primary and secondary valencies
• coordination number
• basic formulation of complexes

But it does not explain orbital overlap, $\sigma$-bonding, or $\pi$-back bonding.

Hence, A is incorrect.

B. Valence Bond Theory (VBT)

VBT can explain:

• hybridisation
• geometry
• whether orbitals are paired/unpaired in a basic way

For $[Ni(CO)_4]$, VBT can describe $sp^3$ hybridisation and tetrahedral geometry.

However, it cannot properly explain the full nature of bonding, especially the important $\pi$-back bonding in metal carbonyls.

Hence, B is incorrect.

C. Crystal Field Theory (CFT)

CFT mainly treats ligands as point charges/point dipoles and explains:

• splitting of $d$-orbitals
• magnetic behaviour
• colour in many complexes

But for metal carbonyls, where covalent interactions and back bonding are crucial, CFT is inadequate.

Hence, C is incorrect.

D. Molecular Orbital Theory (MOT)

MOT explains bonding using orbital interactions between metal and ligands.

In $[Ni(CO)_4]$, MOT can properly account for:

• $\sigma$ donation from $CO$ to $Ni$
• $\pi$ back donation from $Ni$ to $CO$
• the overall covalent nature and stability of the complex

Therefore, MOT completely/properly explains the bonding in $[Ni(CO)_4]$.

Hence, D is correct.

Final answer

The correct option is: $\boxed{D\text{ : Molecular orbital theory}}$

Comparison with stored correct answer

Stored correct answer: D

Our derived answer: D

So they agree.