The theory that can completely/properly explain the nature of bonding in [Ni(CO)$$_4$$] is:

We begin with the species in question, $$[ \text{Ni(CO)}_4 ]$$, which is a typical metal carbonyl. The atomic number of nickel is $$28$$, so an isolated $$\text{Ni}$$ atom has the ground-state electronic configuration $$[ \text{Ar} ]\,3d^{8}\,4s^{2}$$. In the complex the nickel is in the zero oxidation state, so it still possesses a total of $$10$$ valence electrons $$\bigl(3d^{8}4s^{2}\bigr)$$.

The 18-electron rule (which is only an electron-counting guideline) states that a stable transition-metal complex often achieves a valence electron count of $$18$$. Applying the rule, we write

$$\text{Electron count of the complex}= \text{Metal valence electrons} + \text{Electrons donated by ligands}.$$

Each neutral carbonyl ligand $$\text{CO}$$ donates a pair of electrons ($$\sigma$$ donation), so four $$\text{CO}$$ ligands supply $$4 \times 2 = 8$$ electrons. Adding these to the metal’s $$10$$ electrons,

$$10 + 8 = 18,$$

so the complex satisfies the 18-electron rule. While this arithmetic explains why $$[ \text{Ni(CO)}_4 ]$$ is stable, it gives no insight into the actual nature of the bonding.

Now we recall that the $$\text{CO}$$ ligand is a strong $$\sigma$$ donor and a strong $$\pi$$ acceptor. Thus two simultaneous interactions operate:

$$\text{CO}\;:\; \sigma\text{-donor}\; (\,\text{lone pair on C}\,\rightarrow\,\text{empty orbital on Ni}\,)$$

$$\text{CO}\;:\; \pi\text{-acceptor}\; (\,\text{filled Ni }3d\,\rightarrow\,\pi^* \text{ of CO}\,)$$

This synergic $$\sigma$$ donation and $$\pi$$ back-donation cannot be described adequately by simple electrostatic models. Let us examine each candidate theory:

Werner’s theory treats coordination merely in terms of primary and secondary valencies; it does not discuss $$\sigma$$ and $$\pi$$ orbital overlap, so it fails.

Crystal Field Theory (CFT) improves on Werner by introducing the splitting of metal $$d$$-orbitals in an electrostatic field of point charges. However, CFT still treats the metal-ligand bond as purely ionic; it cannot account for covalent $$\pi$$ back-bonding into the ligand’s $$\pi^*$$ orbitals, so it is insufficient.

Valence Bond Theory (VBT) does allow for hybridisation (here one could write an $$sp^3$$ set on Ni to obtain a tetrahedral shape), but VBT is essentially a localized, two-centre-two-electron picture and likewise has no place for the delocalised $$\pi$$ back-donation that is essential in metal carbonyl chemistry.

Molecular Orbital Theory (MOT), on the other hand, constructs delocalised orbitals that extend over both metal and ligands. In the MO diagram of $$[ \text{Ni(CO)}_4 ]$$ we explicitly include:

• a set of ligand-based $$\sigma$$ orbitals combining with metal $$s$$, $$p$$ and $$d_{sp^3}$$ hybrids to form bonding and antibonding $$\sigma$$ MOs, and

• a set of metal $$d_{\pi}$$ orbitals overlapping with the ligand $$\pi^*$$ orbitals to form bonding $$\pi$$ MOs (back-bonding) that stabilize the complex and lower the C-O stretching frequency observed experimentally.

Because MOT simultaneously handles $$\sigma$$ donation, $$\pi$$ back-donation, the 18-electron count, and spectroscopic consequences, it is the only theory in the list that can completely and properly explain the bonding in $$[ \text{Ni(CO)}_4 ]$$.

Hence, the correct answer is Option 2.