Electronic configuration of $\mathrm{Cu^{2+}}$ in an octahedral field

Copper(II) is $3d^9$.

In an octahedral crystal field: $t_{2g}^6 e_g^3$

Since the $e_g$ set is unevenly occupied, octahedral $\mathrm{Cu^{2+}}$ complexes show Jahn–Teller distortion.

Nature of Jahn–Teller distortion in $d^9$ systems

For $d^9$ octahedral complexes, distortion is usually tetragonal elongation or sometimes compression, in order to remove degeneracy.

The distortion becomes more pronounced when:

• the octahedral environment is more flexible,
• all six ligands are identical and can rearrange freely,
• there is no rigid chelate constraint.

Examine each option

Option A: $\left[\mathrm{Cu(H_2O)_6}\right]\mathrm{SO_4}$

• Complex cation is $\left[\mathrm{Cu(H_2O)_6}\right]^{2+}$.
• It is a regular octahedral aqua complex with six identical monodentate ligands.
• Water is a relatively weak ligand and offers little structural rigidity.
• Therefore, Jahn–Teller distortion can occur most freely and strongly.

Option B: $\left[\mathrm{Cu(en)(H_2O)_4}\right]\mathrm{SO_4}$

• One bidentate ligand $\mathrm{en}$ introduces chelation.
• Chelation makes the structure more rigid than the pure aqua complex.
• Hence distortion is present, but less than in option A.

Option C: cis-$\left[\mathrm{Cu(en)_2Cl_2}\right]$

• Two bidentate $\mathrm{en}$ ligands strongly constrain the geometry.
• The cis arrangement further fixes ligand positions.
• Structural flexibility is less, so Jahn–Teller distortion is reduced compared with A.

Option D: trans-$\left[\mathrm{Cu(en)_2Cl_2}\right]$

• Again, two chelating $\mathrm{en}$ ligands make the complex rigid.
• Though trans geometry may allow axial elongation along the $\mathrm{Cl}$ axis, the chelate rings still reduce overall distortion compared with the fully aquated complex.

Conclusion

The complex showing the maximum Jahn–Teller distortion will be the one with the least rigidity and most freely distortable octahedral environment: $\boxed{\left[\mathrm{Cu(H_2O)_6}\right]\mathrm{SO_4}}$

Comparison with stored correct answer

Stored correct answer: $A$

Derived answer: $A$

Hence, the derived answer agrees with the stored answer.