Molecular Symmetry and Group Theory |
The five symmetry elements necessary to specify completely the symmetry of all possible molecules are:
E | — | Identity |
C_{n} | — | Proper Rotation Axis of order n |
σ | — | Mirror Plane |
i | — | Inversion Centre (centre of symmetry) |
S_{n} | — | 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 C_{n} and S_{n} 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.
C_{n} | — | rotate clockwise through 360°/n |
S_{n} | — | rotate clockwise through 360°/n and reflect in the plane perpendicular to the rotation axis |