Symmetry Operations

• Introduction
• Identity
• Reflection
• Inversion
• Proper Rotation
• Improper Rotation

Example Molecules

• Water
• Benzene
• Ethane (staggered)
• Methane

Going Further

• Point groups
• Applications

This project supported by
NSF-DUE #0536710

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Improper Rotation (S_n)

An improper rotation is performed by rotating the molecule 360°/n followed by reflection through the plane perpendicular to the rotation axis. If the resulting configuation is indistinguishable from the original, we say there exists an n-fold improper rotation axis (or S_n axis) in the molecule.

Each of the following molecules contains one or more improper axes:

• Staggered ethane contains an S₆ axis
• Methane contains three S₄ axes

Improper rotation axes: