Symmetry Operations

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

Example Molecules

• Water
• Benzene
• Ethane (staggered)
• Methane

Going Further

• Point groups
• Applications

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Proper Rotation (C_n)

The rotation operations (both proper and improper) occur with respect to line called an axis of rotation. A proper rotation is performed by rotating the molecule 360°/n, where n is the order of the axis. If the resulting configuation is indistinguishable from the original, we say there exists an n-fold proper rotation axis (or C_n axis) in the molecule.

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

• The water molecule contains a C₂ axis
• Ethane contains both C₂ and C₃ axes

Proper rotation axes: