Molecular Symmetry and Group Theory
The axis of the highest order rotation is known as the principal axis. By convention the principal axis of a molecule is chosen to be the z-axis (assumed to be vertical). If several axes have the same order, the z-axis is the one passing through the most atoms. Thus for C2H4, the C2 axis passing through both C atoms is the z-axis.
For planar molecules with the z-axis in the plane, the x-axis is perpendicular (^) to the plane.
If the z-axis is perpendicular (^) to the plane, the x-axis passes through the maximum number of atoms.
Mirror planes are related to the principal axis as follows:
Some molecules e.g. XeF4 have two types of dihedral planes: those that bisect the FXeF bonds are labelled σd; those that contain XeF bonds σv.
The H2O molecule has one C2 axis (z-axis) and two mirror planes designated σxz and σyz.