Introduction

Group theory is a very powerful tool in quantum chemistry. By analyzing the symmetry properties of molecules, we can easily make predictions such as whether a given electronic transition should be allowed or forbidden, whether a molecule should have dipole moment, whether a given vibrational mode should be visible in the infrared or not, etc. Here we will assume a basic familiarity with point groups and discuss how group theory can be used to determine the symmetry properties of molecular vibrations.