Point Groups

A point group is a collection of Symmetry Elements.

  • C_1={E}
  • C_s={E, \sigma_h}
  • C_i={E, i}
  • C_{nv} = {E, rotation of \dfrac{360}{n} deg, n vertical reflection planes}
  • C_{nh} ={E, rotation of \dfrac{360}{n} deg, horizontal reflection plane}

Hydrogen

You might be curious about the hydrogen molecule, since it is one of the first molecules we consider. This one is a little more trick than the others we cover today. One axis of rotation lets you rotate the molecule 180 degrees, but another has an infinite number of rotations. The point group is D_{ \infty h}.

Water

The point group is C_{2v}. The molecule has a 180 degree rotational axis and two planes of symmetry that include the axis of rotation.

Phosphine

The point group is C_{3v}. The molecule has a 120 degree rotational axis and three planes of symmetry that include the axis of rotation.

Character Tables

A point group has a character table. The rows are sets of Irreducible Representations and the columns include Symmetry operations (for the values for the irreducible representations) and a column listing functions for symmetry symbols for square and binary products.