## Group Theory with Mathcad

### Frank Rioux

Department of Chemistry

Saint John's University

College of Saint Benedict

Saint Joseph, MN 56374

Abstract

**Mathcad** has
a powerful array of matrix manipulation commands that make it
an ideal programming environment for applying mathematical group theory to
chemistry problems. To illustrate this capability Mathcad will be used to
do symmetry analyses on a number of examples involving vibrational and
electronic spectroscopy, and chemical bonding.

The examples treated in this series will deal only with molecules that belong
to the finite point groups. Most examples will deal with molecules having
moderate to high symmetry - C_{2v} to I_{h}. Obviously all
finite groups will not be considered, but the most frequently encountered
symmetries will receive sufficient attention. Fortunately Mathcad worksheets
are easy to prepare and edit, so the worksheets included in this series can
serve as templates for a large number of additional exercises. Once a worksheet
has been created for a particular point group, it can be used for any molecule
with that symmetry after minor modifications are made.

Among the exercises included are:

For each of the major areas listed above, a number of additonal exercises have
been recommended. These exercises only require editing of the template Mathcad
worksheet.

**References**

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homepage.