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Symmetry Tutorial - Introduction
Welcome to the world of symmetry! Symmetry plays an central role in the analysis of the structure, bonding, and spectroscopy of molecules. In this tutorial, we will explore the basic symmetry elements and operations and their use in determining the symmetry classification (point group) of different molecules.
The symmetry properties of objects (and molecules) may be described in terms of the presence of certain symmetry elements and their associated symmetry operations. The various symmetry elements and operations are described in the table below.
Symmetry Elements and Operations
|
element
|
operation
|
symbol
|
| symmetry plane |
reflection through plane |
|
| inversion center |
inversion: every point x,y,z translated to -x,-y,-z |
i
|
| proper axis |
rotation about axis by 360/n degrees |
Cn
|
| improper axis |
1. rotation by 360/n degrees
2. reflection through plane perpendicular to rotation axis |
Sn
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