1. 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”

5. 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

11. 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,

15. 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.

16. 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