# Elements of Symmetry

Session Objectives

By the end of this session, students will be able to:

• What are elements of symmetry?

• Types of symmetry

## Symmetry and Stereochemistry

• There are three elements of symmetry that a molecule may possess

1. Rotation

2. Reflection

3. Inversion

## Symmetry Operations: Reflection

Symmetry operations are spatial transformations (rotations, reflections, inversions).

• A molecule is said to possess a symmetry element if the molecule is unchanged in appearance after applying the symmetry operation corresponding to the symmetry element.

• The blue plane is a plane of symmetry of A.

• The operation of reflection (М) involves projection of each atom onto the plane, followed by movement through the plane to a distance equal to the projection distance.

• Reflection through the plane is a symmetry operation on A.

• Although the red and magenta H’s have changed places, the molecule looks the same.

• We say that A possesses reflection symmetry.

Animations of the reflection process

Elements of symmetry

## Symmetry Operations: Rotation

• A molecule is said to possess a symmetry element if the molecule is unchanged in appearance after applying the symmetry operation corresponding to the symmetry element.

• The red axis is an axis of symmetry of A.

• The operation of rotation (Cn) involves rotation of the molecule 360/n degrees about an axis.

• The axis shown is a “C2” axis.

• Rotation about the axis is a symmetry operation on A.

• Although the red and magenta H’s have changed places, the molecule looks the same.

• We say that A possesses 2-fold rotational symmetry.

Elements of symmetry

## Symmetry Operations: Inversion

• A molecule is said to possess a symmetry element if the molecule is unchanged in appearance after applying the symmetry operation corresponding to the symmetry element.

• The blue point is an inversion center of G.

• The operation of inversion (i) involves the projection of each atom onto a point at the center of the molecule, followed by movement through the point to a distance equal to the projection distance.

• Inversion through the point is a symmetry operation on G.

• Although inversion exchanges all three groups attached to the central carbon, the molecule looks the same. We say that G possesses inversion symmetry.

## Alternating axis of symmetry (Sn) or Rotation reflection axis of Symmetry or improper axis of Symmetry

• A molecular has an alternating axis of symmetry of order (n) if rotation about the axis by 360/n degree following by reflaction in a plane perpendicular to this axis produces an equivalent structure.

Summary

• Chirality is only the criteria for optical isomerism

• The molecule should lack these elements of symmetry to possess optical isomerism

• Different types of symmetry

Plane of symmetry - reflection

Axis of symmetry - rotation

Centre of symmetry – inversion centre

Alternating axis of symmetry