- Benzene - C6H6:
Benzene has a center of symmetry, i
It also has a rotational axis passing through the center and perpendicular to the molecular plane. This axis in fact combines a C6, a C3, and a C2 axis.
The molecule has two sets of C2 axes in the molecular plane:
(a) 3C2' axes passing through the center and containing two C-H bonds.
(b) 3C2" axes passing through the center and through the center of pairs of bonds on opposite sides of the hexagon.
Benzene has a plane corresponding to the molecular plane which is perpendicular to the C6 principal axis of rotation i.e. a sh plane.
It also has 3sv planes associated with the three C2' axes and containing the principal axis (C6) and the center (i).
In addition there are 3sd planes associated with the three C2" and containing the principal axis (C6) and the center (i).
Finally, because there is a C6, C3, and a C2 axis perpendicular to the molecular plane, there also exists an S6, S3, and an S2 axis but the latter is redundant since it is equivalent to the already defined center of inversion, I.
Benzene's Symmetry Elements are:
One i, Center of inversion
One C6 rotation axis perpendicular to the molecular plane
One C3 rotation axis perpendicular to the molecular plane.
One C2 rotation axis perpendicular to the molecular plane.
Three C2' rotation axes in the molecular plane.
Three C2" rotation axes in the molecular plane.
One sh reflection plane corresponding to the molecular plane.
Three sv reflection planes containing the principal axis (C6).
Three sd reflection planes containing the principal axis (C6)
One S6 improper axis coincident with the C6 axis.
One S3 improper axis coincident with the C3 axis.