# Week 1 review – molecular symmetry and an introduction to group theory

The focus this week has been on molecular symmetry, symmetry elements and operations, point groups and point group assignment, with a brief intro to character tables.

A few take home points:

- a molecule is considered to have symmetry if a transformation results in a new orientation indistinguishable from the original
- a
is an object (point, line, or plane) through which a symmetry operation is carried out,**symmetry element***e.g.*, rotation (operation) about a proper axis (element) - symmetry elements include: proper axis (C
_{n}), mirror plane (s), inversion center (*i*), improper axis (S_{n}*aka*rotation/reflection), and the identity (E) - molecules can be grouped and classified by symmetry elements (
)*point groups* - molecular and physical properties are often predicted and explained using symmetry and
*group theory* provide a mathematical basis for symmetry elements and operations*character tables*

I hope that I have impressed upon you the importance of drawing accurate Lewis structures *wrt* to identifying symmetry elements and making point group assignments. The molecule in the upper right is water, which belongs to the C2v point group. The molecule to the left is hydrazine, which is in the C2h point group. The images were created using Bio-Rad’s KnowItAll software package. I have a site license for the software; please contact me if you are interested.