Question

The symmetry element that does NOT belong to the \( C_{4v} \) point group is:

• A. \( C_4 \)
• B. \( C_2 \)
• C. \( i \)
• D. \( \sigma_v \)

Hint:

The point group \( C_{4v} \) contains rotational and vertical reflection symmetry elements, but it lacks an inversion center. Always check if a group is centrosymmetric before assuming \( i \) is present.

Answer 1

The Correct Option is C

The \( C_{4v} \) point group contains the following symmetry elements:

• A principal axis of four-fold rotational symmetry: \( C_4 \)
• One \( C_2 \) axis (as \( C_4^2 = C_2 \))
• Four vertical mirror planes: \( \sigma_v \) and \( \sigma_d \)
• The identity element \( E \)

However, the inversion center \( i \) is not present in \( C_{4v} \). The presence of an inversion center is characteristic of certain other point groups such as \( C_i, D_{nh}, O_h \), etc., but not \( C_{4v} \), which is a non-centrosymmetric point group.

\[ \boxed{\text{The inversion center } (i) \text{ is not part of the } C_{4v} \text{ point group.}} \]