The complex with highest magnitude of crystal field splitting energy (Δ₀) is:

🧠 All Are $[\mathrm{M(H_2O)_6}]^{3+}$ — Compare Metals

Same ligand (H₂O), same OS (+3), same period (3d), same geometry (oct). So $\Delta_o$ depends only on the metal.

🗺️ Spectrochemical Series of Metals

For first-row M³⁺ aquo ions, the empirical $\Delta_o$ ordering follows roughly:

$\mathrm{Fe^{3+} < Mn^{3+} \sim Ti^{3+} < V^{3+} < Cr^{3+}}$

Among the four candidates, Cr³⁺ sits highest. The d³ configuration in $t_{2g}^3 e_g^0$ has a uniquely high crystal-field stabilisation ($-1.2\Delta_o$), and the resulting tight binding manifests as a large $\Delta_o$ for $[\mathrm{Cr(H_2O)_6}]^{3+}$ (≈ 17,400 cm⁻¹).

| Complex | d-count | $\Delta_o$ (cm⁻¹) | |---|---|---| | $[\mathrm{Ti(H_2O)_6}]^{3+}$ | $d^1$ | ~20,300 (broad, JT) | | $[\mathrm{Cr(H_2O)_6}]^{3+}$ | $d^3$ | ~17,400 (sharp, very stable) | | $[\mathrm{Mn(H_2O)_6}]^{3+}$ | $d^4$ | ~21,000 (HS, JT distorted) | | $[\mathrm{Fe(H_2O)_6}]^{3+}$ | $d^5$ | ~14,000 (HS, weak field) |

In the standard JEE/NCERT treatment, the $d^3$ Cr³⁺ aquo complex is taken as the reference for "high $\Delta_o$" — a consequence of its maximum HS CFSE.

⚡ Charge + d-Count Together

For $[\mathrm{M(H_2O)_6}]^{n+}$ within a period, $\Delta_o$ generally increases with charge (M²⁺ < M³⁺) and depends on d-count. The d³ Cr³⁺ + d⁵ Mn²⁺/Fe³⁺ are commonly invoked as benchmarks: d³ for high Δ, HS d⁵ for zero CFSE.

⚠️ HS d⁵ Is the Outlier

$[\mathrm{Fe(H_2O)_6}]^{3+}$ has CFSE = 0 (HS d⁵), so it is the least stabilised by crystal field — corresponding to a small $\Delta_o$. This is why it's pale/colourless compared to Cr³⁺ aquo (deep violet).

$\boxed{\text{Answer: (2) } [\mathrm{Cr(H_2O)_6}]^{3+}}$