Question

Why in the tetrahedral splitting, terms e and \[{t_2}\] are used, whereas, in octahedral splitting, terms as \[{e_g}\] and \[{t_{2g}}\] are used?
(A) Due to the approach of the ligands from the axis
(B) Due to the approach of the ligands in between the axis
(C) Due to the symmetry present in the octahedral system
(D) Due to the symmetry present in the tetrahedral system

Answer 1

Hint: If any system is symmetric or has centre of inversion symmetry, it is called gerade orbital, symbolised by g. while if no such symmetry exists, the g term is removed. Octahedral is a symmetric system while tetrahedral is not symmetric.

Complete step-by-step answer:
In an octahedral complex, six ligands are attached to the central transition metal. The d-orbital splits into two different levels. The bottom three energy levels are named as \[{d_{xy}}, {d_{yz}},{d_{xz}}\] and collectively referred to as \[{t_{2g}}\]. The two upper energy levels are named as \[{d_{{z^2}}}, {d_{{x^2} - {y^2}}}\], and collectively referred to as \[{e_g}\].
In a tetrahedral complex, four ligands are attached to the central metal. The d orbitals too split into two different energy levels. The top three consist of the \[{d_{xy}}, {d_{yz}}, {d_{xz}}\] orbitals and collectively referred as \[{t_2}\]. The bottom two consist of the \[{d_{{z^2}}}, {d_{{x^2} - {y^2}}}\] orbitals and are collectively referred to as e. The reason for this is due to poor orbital overlap between the metal and the ligand orbitals. The orbitals are directed on the axes, while the ligands are not as per the tetrahedral structure.
This difference in ‘g’ terms in both the structure is due to their symmetry. The word g stands for gerade which means symmetry, it is a German word. If the sign of the lobes remains the same, we call it a gerade orbital and if the signs are changed, the orbital is ungerade. In gerade, the centre of inversion symmetry is present.

Tetrahedral complexes have no centre of symmetry and thus its orbital do not have g term in it. While in an octahedral system, g term is included because it is symmetric. Therefore, in the tetrahedral splitting, terms e and \[{t_2}\] are used, whereas, in octahedral splitting, terms as \[{e_g}\] and \[{t_{2g}}\] are used.

Hence, the correct option is (C).

Note: This can also be understood by Laporte selection rule which states that for a coordination complex that contains a centre of symmetry, only transitions which involve a change in parity of lobes are allowed. That is why octahedral is symmetric, hence allowed and vice versa for tetrahedral.