When hybridisation involving -orbitals are considered then all the five -orbitals are not degenerate, rather and form two different sets of orbitals and orbitals of appropriate set is involved in the hybridisation. Which of the following orbitals can not undergo hybridisation amongst themselves.

Question

Accepted Answer

When considering hybridisation involving d-orbitals, the d-orbitals split into two sets in the presence of ligands or a specific molecular geometry. These sets are $d_{x^{2} - y^{2}}, d_{z^{2}}$ (e_g set) and $d_{x y}, d_{y z}, d_{z x}$ (t_2g set).

For hybridisation to occur, the orbitals involved must have comparable energies and appropriate symmetry. The given options represent different sets of orbitals:

I. $d_{x^{2} - y^{2}}, s, p_{x}, p_{y}$ : These orbitals can hybridise to form $d s p^{2}$ hybrid orbitals, which are involved in square planar geometry.
II. $d_{z^{2}}, s, p_{x}, p_{y}$ : The $d_{z^{2}}$ orbital has a different symmetry and orientation compared to $p_{x}$ and $p_{y}$ orbitals, making it difficult for them to effectively overlap and hybridise to form a common set of hybrid orbitals in a simple manner. While $d_{z^{2}}$ can be involved in hybridisation (e.g., $s p^{3} d$ or $s p^{3} d^{2}$ ), it typically combines with $p_{z}$ and other orbitals, not just $p_{x}$ and $p_{y}$ in this specific combination for a planar geometry.
III. $d_{x y}, s, p_{x}, p_{y}$ : These orbitals can hybridise to form $d s p^{2}$ hybrid orbitals, which are involved in square planar geometry.
IV. $d_{x^{2} - y^{2}}, p_{x}, p_{y}, p_{z}$ : The $d_{x^{2} - y^{2}}$ orbital lies in the xy-plane, while $p_{z}$ is along the z-axis. These orbitals have different orientations and symmetries, making their direct hybridisation together in this specific combination difficult. Hybridisation typically involves orbitals that can effectively overlap to form equivalent hybrid orbitals. For example, $d_{x^{2} - y^{2}}$ combines with $s, p_{x}, p_{y}$ for $d s p^{2}$ , or with $s, p_{x}, p_{y}, p_{z}, d_{z^{2}}$ for $s p^{3} d^{2}$ .

Therefore, the combinations in options II and IV are generally not considered to undergo hybridisation amongst themselves due to incompatible symmetries and orientations for effective overlap.

Option Analysis:

A) only II: Incorrect, as IV also cannot undergo hybridisation in the given combination.
B) II & III: Incorrect, as III can undergo hybridisation.
C) I, II & IV: Incorrect, as I can undergo hybridisation.
D) II & IV: Correct, as both these combinations of orbitals are not suitable for effective hybridisation due to symmetry and orientation mismatches.

Correct Answer: (D)

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