Chapter 14, Problem 14.76E

Interpretation Introduction

(a)

Interpretation:

The individual symmetry element for the $C_{\text{3v}}$ group as either proper rotations or improper rotations is to be stated.

Concept introduction:

Proper rotation is when rotation occurs through the axis of rotation. It is done by rotating the molecule through $360°/n$, where $n$ is the order of the axis.

Improper rotation is when rotation occurs through the axis of rotation as well as reflection in a plane which is perpendicular to the axis of rotation.

Proper rotations are $E$ and $C_n$, and improper rotations are $\sigma$, $i$, and $S_n$.

Interpretation Introduction

(b)

Interpretation:

The individual symmetry element for the $T_{\text{d}}$ group as either proper rotations or improper rotations is to be stated.

Concept introduction:

Proper rotation is when rotation occurs through the axis of rotation. It is done by rotating the molecule through $360°/n$ where $n$ is the order of the axis.

Improper rotation is when rotation occurs through the axis of rotation as well as reflection in a plane which is perpendicular to the axis of rotation.

Proper rotations are $E$ and $C_n$, and improper rotations are $\sigma$, $i$ and $S_n$.

Interpretation Introduction

(c)

Interpretation:

The individual symmetry element for the $D_{\text{6h}}$ group as either proper rotations or improper rotations is to be stated.

Concept introduction:

Proper rotation is when rotation occurs through the axis of rotation. It is done by rotating the molecule through $360°/n$ where $n$ is the order of the axis.

Improper rotation is when rotation occurs through the axis of rotation as well as reflection in a plane which is perpendicular to the axis of rotation.

Proper rotations are $E$ and $C_n$, and improper rotations are $\sigma$, $i$ and $S_n$.

Interpretation Introduction

(d)

Interpretation:

The individual symmetry element for the $S_4$ group as either proper rotations or improper rotations is to be stated.

Concept introduction:

Proper rotation is when rotation occurs through the axis of rotation. It is done by rotating the molecule through $360°/n$ where $n$ is the order of the axis.

Improper rotation is when rotation occurs through the axis of rotation as well as reflection in a plane which is perpendicular to the axis of rotation.

Proper rotations are $E$ and $C_n$, and improper rotations are $\sigma$, $i$ and $S_n$.

Interpretation Introduction

(e)

Interpretation:

The individual symmetry element for the $D_{\infty \text{h}}$ group as either proper rotations or improper rotations is to be stated.

Concept introduction:

Proper rotation is when rotation occurs through the axis of rotation. It is done by rotating the molecule through $360°/n$ where $n$ is the order of the axis.

Improper rotation is when rotation occurs through the axis of rotation as well as reflection in a plane which is perpendicular to the axis of rotation.

Proper rotations are $E$ and $C_n$, and improper rotations are $\sigma$, $i$ and $S_n$.

Interpretation Introduction

(f)

Interpretation:

The individual symmetry element for the $O$ group as either proper rotations or improper rotations is to be stated.

Concept introduction:

Proper rotation is when rotation occurs through the axis of rotation. It is done by rotating the molecule through $360°/n$ where $n$ is the order of the axis.

Improper rotation is when rotation occurs through the axis of rotation as well as reflection in a plane which is perpendicular to the axis of rotation.

Proper rotations are $E$ and $C_n$, and improper rotations are $\sigma$, $i$, and $S_n$.