The complex that has highest crystal field splitting energy $$(\Delta)$$, is:

The magnitude of the crystal field splitting energy ($$\Delta$$) depends heavily on the nature of the coordinating ligands, the oxidation state of the central metal ion, and the geometry of the complex:

• Ligand Field Strength (Spectrochemical Series): According to the spectrochemical series, ligands split the $d$-orbitals to different extents: $$\text{Cl}^\ominus < \text{H}_2\text{O} < \text{NH}_3 < \text{CN}^\ominus$$ Cyanide ($$\text{CN}^\ominus$$) is a powerful $$\pi$$-acceptor strong-field ligand, causing the maximum splitting compared to weak or moderate donors like $$\text{NH}_3$$, $$\text{H}_2\text{O}$$, or $$\text{Cl}^\ominus$$.
• Geometry Effect ($$\Delta_o$$ vs $$\Delta_t$$): Octahedral complexes produce significantly larger splitting than tetrahedral complexes ($$\Delta_t \approx \frac{4}{9}\Delta_o$$). Therefore, the tetrahedral complex $$K_2[\text{CoCl}_4]$$ will have a very low $$\Delta$$ value.

Conclusion:

Because cyanide sits at the highest end of the spectrochemical series and forms a stable octahedral coordination sphere, its complex experiences the greatest orbital splitting.

Answer: Option A — $$K_3[\text{Co}(\text{CN})_6]$$