The theory that can completely/properly explain the nature of bonding in [Ni(CO)4] is:

🧠 CO Bonding Has Two Components

The metal-to-CO bond in $[\mathrm{Ni(CO)_4}]$ has two simultaneous components:

1. σ-donation from CO's lone pair on carbon into a metal hybrid orbital.
2. π-back-donation from filled metal d-orbitals into CO's empty $\pi^*$ antibonding orbitals.

This synergic (mutually reinforcing) bonding cannot be properly described by any single one of Werner's, CFT, or VBT — it requires the molecular orbital framework, which can handle delocalised π-orbital interactions.

🗺️ Why Each Theory Fails (or Succeeds)

• Werner's theory describes primary/secondary valencies — purely electrostatic, no π-bonding picture. Fails.
• CFT treats ligands as point charges — has no mechanism for back-donation. Fails for CO.
• VBT assigns hybridisation but doesn't include π-acceptor behaviour. Predicts geometry correctly but misses bonding details.
• MOT builds molecular orbitals from metal d/s/p and ligand π/σ orbitals — naturally captures synergic bonding. Succeeds.

⚡ The "Synergic Trigger"

Whenever a question says "explain the bonding in $\mathrm{[Ni(CO)_4]}$", "$[\mathrm{Fe(CO)_5}]$", "$[\mathrm{Cr(CO)_6}]$", or any metal carbonyl — and offers MOT as an option — pick MOT. CFT and VBT both miss the back-bonding entirely.

⚠️ VBT Looks Tempting

Many students recall that VBT correctly predicts $\mathrm{sp^3}$ tetrahedral geometry for $[\mathrm{Ni(CO)_4}]$ and assume that means "VBT explains the bonding". VBT explains the geometry, not the synergic π-back-donation that actually stabilises the M–CO bond. Geometry ≠ full bonding picture.

$\boxed{\text{Answer: (2) Molecular orbital theory}}$