Point Group Symmetry
Point group symmetry is a way to categorize molecules based on their shape, as described by valence shell electron pair repulsion (VSEPR) theory, and the symmetry that is observed in the molecule. When analyzing the compound for symmetry, the two axes that are looked at are the vertical and horizontal axis with respect to the central atom.
For example, in ammonia (NH3), nitrogen is the central atom in this compound and is trigonal pyramidal in its VSEPR shape due to the lone pair of electrons. Because the molecule is not linear, there are no multiple high order axes, no low symmetry or only even degrees of S axes, and no C2 axes which are perpendicular to the axis which the central atom is being rotated then the molecule falls under a Cn group. A Cn group is a cyclic group that has n number of rotations around the axis for symmetry.
When rotating ammonia around its horizontal axis, it takes a full 360 degrees to find a match so there is no symmetry on this axis. Looking at the vertical axis when rotating the molecule in a circle around the central atom, you find a match to the starting position every one hundred and twenty degrees. Because it is being rotated on the vertical axis to find symmetry it is Cnv. Finally, because there are matches to the original position every 120 degrees, three matches in total, ammonia is classified as C3v.
Point group symmetry takes practice to get a solid grasp on the concept. There are many commonly occurring structures that are highly recommended to just memorize to speed up the process of classifying molecules. These common structures will be covered later.