Symmetry and Stereochemistry

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

C C

O H

H

HH

H

H

C C

O H

H

HH

H

Hσ

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 (σ) involves projection of each atom onto the plane, followed by movement through the plane to a distance equal to the projection distance.

A C C

O H

H

HH

H

H

Animations of the reflection process

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. C C

O H

H

HH

H

H

C C

O H

H

HH

H

Hσ

Symmetry Operations: Rotation

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.

Animations of the rotation process

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.

O

H H

H H H H

180°

O

H H

H H H H

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.

A O

H H

H H H H

H

H

CH3

Br

H3C

Br

Symmetry Operations: Inversion

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.

G

Animations of the inversion process

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.

H

H

CH3

Br

H3C

Br

H

H

CH3

Br

H3C

Br

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.