Question

(a) What is the maximum possible degree of degeneracy of the orbitals in benzene? (b) What is the maximum possible degree of degeneracy of the orbitals in 1,4-dichlorobenzene?

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$\textbf{(a): Benzene}$

To calculate the degeneracy, first we have to find the point group of benzene molecule. Once we know the point group of the benzene molecule, then with the help of character table of that point group, degeneracy of the orbitals can be calculated.

Benzene (C$_6$H$_6$) is a flat molecule with 6 carbon atom and 6 hydrogen atom. To calculate the point group of benzene we find the symmetry elements present in the molecule by applying the symmetry operations.

As, we know that if a molecule have a principal axis C$_n$, subsidiary axis perpendicular to the principal axis, and horizontal (molecular plane), then the point group of the molecule will be D$_{nh}$ type.

The symmetry elements which are required to identify the point group of are shown in figure. Rest of the symmetry elements will be shown in the character table.

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