Symmetry is one way to indicate geometrical aspects of a molecule (or object)

Symmetry elements are geometric operations that leave the appearance of a molecule identical (in all respects) to the starting point:

Types of symmetry elements

1. Inversion

i(x,y,z) → (–x,–y,–z)

2. Rotations

Crotates the molecule by 360°/n; by convention, rotations are clockwise; successive rotations are denoted by superscripts:_{n}

C=_{6}^{2}C_{3}

C= 120° rotation counterclockwise_{3}^{2}0° rotations are denoted by

E.Infinitely small rotations are denoted by

C_{∞}

3. Mirror planes σ reflection through a plane; the plane is often denoted by a subscript

a mirror is a composite symmetry element :

σ=_{xy}C_{2z}imirrors through bonds are usually denoted

σ_{v}mirrors between bonds are usually denoted

σ_{d}mirrors perpendicular to the highest n rotation axis are usually denoted

σ_{h}

4. Improper rotations

Sa rotation followed by a mirror perpendicular to the rotation_{n }

S=_{n}Cthis can exist independent of the rotation or the mirror, e.g._{n}σ_{h}Sin CH_{4}_{4}note:

S=_{2}σC=_{2}i

*Point Group* : the collection of all of the symmetry operations present in a molecule

Point Groups have mathematical significance, but we will take them simply as geometrical descriptions of molecules

To find point groups, we only need to identify certain key symmetry elements