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Question #44589

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The Question

Consider the diamagnetic coordination complex $\ce{trans-[Co(en)_2Cl_2]^+}$ at 298 K. The central metal satisfies the Effective Atomic Number (EAN) rule, yet the complex exhibits a pronounced tetragonal distortion ( $D_{4h}$ symmetry) due to its heteroleptic coordination sphere. Ethylenediamine ( $\ce{en}$ ) acts exclusively as a strong $\sigma$ -donor, whereas the chloride ligand ( $\ce{Cl^-}$ ) acts as both a weak $\sigma$ -donor and a $\pi$ -donor. Based on Ligand Field Theory (LFT), which of the following correctly represents the energy sequence of the metal $3d$ -orbitals and identifies the Highest Occupied Molecular Orbital (HOMO)?

Options

A.
$E(d_{xy}) < E(d_{xz}) = E(d_{yz}) < E(d_{z^2}) < E(d_{x^2-y^2})$ ; HOMO: $d_{xz}, d_{yz}$
B.
$E(d_{xz}) = E(d_{yz}) < E(d_{xy}) < E(d_{z^2}) < E(d_{x^2-y^2})$ ; HOMO: $d_{xy}$
C.
$E(d_{xy}) < E(d_{xz}) = E(d_{yz}) < E(d_{x^2-y^2}) < E(d_{z^2})$ ; HOMO: $d_{xz}, d_{yz}$
D.
$E(d_{xz}) = E(d_{yz}) < E(d_{xy}) < E(d_{x^2-y^2}) < E(d_{z^2})$ ; HOMO: $d_{xy}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

Crystal Field Splitting (Octahedral)|Geometric Isomerism Requirements|EAN Rule (Sidgwick's Rule)

Why This Question Is Tricky

Common Mistakes

This problem tests the critical distinction between simple Crystal Field Theory (CFT) and Ligand Field Theory (LFT).

Students often apply a simplified CFT model where weaker axial ligands strictly mean less electrostatic repulsion, leading them to incorrectly assume $d_{xz}$ and $d_{yz}$ drop in energy below $d_{xy}$ (Option B).

The 'Hidden Variable' is the $\pi$ -donor nature of the $\ce{Cl^-}$ ligand.

While $\ce{Cl^-}$ is a weak $\sigma$ -donor (lowering $d_{z^2}$ ), its $\pi$ -donation creates an antibonding interaction that raises the energy of the $d_{xz}$ and $d_{yz}$ orbitals above the $\pi$ -nonbonding $d_{xy}$ orbital, fundamentally altering the HOMO of the complex despite it satisfying the standard 18-electron rule.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Coordination Compounds - Class 12
Concept	Crystal Field Splitting (Octahedral)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free