Lecture No. 07

Elements of symmetry

Session Objectives

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

➢What are elements of symmetry

➢Types of symmetry

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Symmetry and Stereochemistry

There are three elements of symmetry

that a molecule may possess…

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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.

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

A O

H H

C The operation of reflection (М) involves

C projection of each atom onto the plane, followed

by movement through the plane to a distance

H H equal to the projection distance.

H H H H

O М O

H H H H

C C

C C

H H H H

Reflection through the plane is a symmetry

operation on A. Although the red and magenta

М H’s have changed places, the molecule looks

H O H H O H the same. We say that A possesses reflection

H H H H symmetry.

C C

C C

H H H H Animations of the reflection process

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Symmetry Operations: Rotation

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.

Animations of the rotation process The red axis is an axis of symmetry of A.

O The operation of rotation (Cn) involves rotation of

A H H the molecule 360/n degrees about an axis.

The axis shown is a “C2” axis.

H H H H

Rotation about the axis is a symmetry

O O operation on A. Although the red and magenta

H’s have changed places, the molecule looks

H H H H the same. We say that A possesses 2-fold

rotational symmetry.

H H H H H H H H

180°

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Elements of symmetry

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Symmetry Operations: Inversion

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.

H3C H The blue point is an inversion center of G.

Br The operation of inversion (i) involves the

G projection of each atom onto a point at the center

of the molecule, followed by movement through the

Br point to a distance equal to the projection distance.

H CH3

H3C H H3CH Inversion through the point is a symmetry

Br Br operation on G. Although inversion exchanges all

three groups attached to the central carbon, the

Br Br molecule looks the same. We say that G

H CH3 H CH3 possesses inversion symmetry.

Animations of the inversion process

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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

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Thank You

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