Chemistry - Coordination Chemistry Question with Solution | TestHub

John-Teller distortion occurs in octahedral complexes when the $e_g$ or $t_{2g}$ orbitals are asymmetrically filled. This leads to a degeneracy in the orbitals, which is relieved by a distortion of the complex geometry.

For option B, ${\left[\mathrm{Co}(\mathrm{SFL}{)}_6\right]}^{\text{II }}$, Co(II) has a $d^7$ configuration. In a strong field, the electron configuration is $t_{2g}^6{e}_g^1$. The singly occupied $e_g$ orbital causes a significant John-Teller distortion.

Let's analyze the other options:

A. ${\left[\mathrm{Cr}(\mathrm{SFL}{)}_6\right]}^{\text{III }}$: Cr(III) is $d^3$. In an octahedral field, it is $t_{2g}^3{e}_g^0$. This is a symmetric filling, so no John-Teller distortion.

C. ${\left[\mathrm{Ni}(\mathrm{WFL}{)}_6\right]}^{\text{II }}$: Ni(II) is $d^8$. In an octahedral field, it is $t_{2g}^6{e}_g^2$. This is a symmetric filling, so no John-Teller distortion.

D. ${\left[\mathrm{Fe}(\mathrm{SFL}{)}_6\right]}^{\text{II }}$: Fe(II) is $d^6$. In a strong field, it is $t_{2g}^6{e}_g^0$. This is a symmetric filling, so no John-Teller distortion.

The final answer is $\boxed{B}$.