Molecular Symmetry and Group Theory
The five symmetry elements necessary to specify completely the symmetry of all possible molecules are:
|Cn||||Proper Rotation Axis of order n|
|i||||Inversion Centre (centre of symmetry)|
|Sn||||Improper Rotation (rotation-reflection) axis of order n|
A molecule is said to possess a symmetry element if the application of a symmetry operation generated by the element leaves the molecule indistinguishable from its starting position.
The elements E, σ and i each generate one operation:
|E||||the operation of doing nothing (all molecules possess the identity element!)|
|σ||||reflect in the plane|
|i||||invert through the centre of the molecule|
The elements Cn and Sn can each generate a number of operations. This is because the effect of applying the basic operation more than once often counts as a separate operation.
|Cn||||rotate clockwise through 360°/n|
|Sn||||rotate clockwise through 360°/n and reflect in the plane perpendicular to the rotation axis|