**Introduction**

Why study symmetry?

(i) One of the fundamental reasons for learning about molecular symmetry is that the notation gives us the ability to precisely and accurately describe a structure. For example, the point group D_{4h} for the structure of [Ni(CN)_{4}]^{2-} conveys precise, unequivocal structural information that would otherwise require a very lengthy description.

(ii) The notation (Schönflies notation) uses symmetry symbols which are now commonplace in the chemical literature and familiarity with it will allow a much fuller comprehension of research papers found in the literature.

(iii) From a knowledge of symmetry alone, it is often possible to reach useful, qualitative conclusions about molecular electronic structure and to draw inferences from spectra as to molecular structures.

The last point is perhaps the most far reaching and useful application of symmetry. Thus, knowledge of the symmetry properties of a molecule, combined with the mathematics of group theory, can be used to understand and predict a host of molecular properties, including vibrational modes, electronic spectroscopy, and bonding. The mathematics behind group theory can be complex, and a comprehensive treatment is beyond the scope of this course. (We do offer an excellent graduate level course on the chemical applications of group theory, which takes a more rigorous and thorough approach to the subject.)

In this section we will cover the basic ideas of symmetry in chemistry, and the nomenclature that is used to describe molecular shapes (Point Group or Schönflies Notation). We then introduce Character Tables and more notation which is used to describe the symmetries of molecular properties. Finally, we cover the use of Symmetry and Character Tables to deduce the fundamental modes of vibration for a molecule as well as the selection rules for infrared and Raman spectroscopy.

**Learning Objectives**

- Symmetry elements
- Symmetry operations
- Point group notation
- Systematic methods to identify point groups of molecules
- Character tables
- Fundamental modes of vibration
- Selection rules for infrared and Raman spectroscopy

We all have an inherent understanding of symmetry. For example, snowflakes have a beautiful six-fold symmetry, and butterflies have a mirror plane.

Symmetry is also found in art. For example, the famous graphic artist M.C. Escher (1898 - 1972) used symmetry in many of his creations.

Next: Symmetry Elements and Operations

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