Symmetry operations: Transformations mapping the nuclear frame of a molecule onto an indistinguishable version of itself  symmetry elements: symmetry axes, planes, points.   1. Symmetry axes or proper rotation axes Cn: If a rotation by  = 2/n around an axis is a symmetry operation, the axis is called an “n-fold symmetry axis” Cn axis with the highest n is called “principal symmetry axis”, defines z-axis, or “vertical” direction. additional symmetry axes (not collinear with principal axis): Cn’, Cn”

2. Symmetry planes : If a reflection on a plane is a symmetry operation, the plane is called a “symmetry plane” .   If a symmetry plane ... … contains the principal symmetry axis  “vertical symmetry plane” v (xz plane) and v’, v” (others) or the planes are labeled vA, vB, vC, etc. … is perpendicular to the principal symmetry axis  “horizontal symmetry plane” h. … is vertical and bisects the angle between two symmetry axes  “dihedral symmetry plane” d

3. Inversion center i If a reflection on a point is a symmetry operation, the point is called “inversion center” i Examples: all homonuc. diatomic molecules,

4. Improper Rotations or Rotary-Reflection Axes Sn If a rotation by  = 2/n, followed by a reflection at a plane perpendicular to the rotation axis is a symmetry operation, the axis is called “n-fold improper rotation axis” or “n-fold rotary-reflection axis” Sn.

S6 4. Improper Rotations or Rotary-Reflection Axes Sn If a rotation by  = 2/n, followed by a reflection at a plane perpendicular to the rotation axis is a symmetry operation, the axis is called “n-fold improper rotation axis” or “n-fold rotary-reflection axis” Sn. S6