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  Home > JCE Print > Journal of Chemical Education > Issues > 2005  > January  >
Information • Textbooks • Media • Resources
JCE SymMath: Symbolic Mathematics in Chemistry
Learning Molecular Geometry and Symmetry through Quantum Computations and Mathcad Exercises
Franklin M. C. Chen
Department of Chemistry, University of Wisconsin–Green Bay, Green Bay, WI 54311-7001
Cover
January 2005
Vol. 82 No. 1
p. 174
Full Text
This Mathcad template is intended to help students learn about molecular geometry and symmetry through calculations based on the coordinate data that are generated from quantum computation software such as HyperChem. Typically, students taking a quantum mechanics class in their junior year have been exposed to vector calculus and matrix algebra. Molecular coordinate data serve as excellent real-world materials for students to appreciate the applications of linear algebra and to refresh their linear algebra skills, especially linear transformations. In working with molecular linear transformations through the document’s hands-on exercises, students will learn about fundamental properties of quantum and symmetry operators. By using a series of exercises, students study the mathematics required to perform symmetry operations such as rotation and reflection through a mirror plane. They then apply these techniques by performing the symmetry operations on water, ammonia, methane, and benzene.

Methane in Cartesian coordinates as shown in the Mathcad template.
Supplement
Fully interactive computer algebra files are available in the JCE SymMath collection of the JCE Digital Library Only@JCE Online.
More Information
*  Citation
 Chen, Franklin M. C. J. Chem. Educ. 2005 82 174.
*  Keywords

Physical Chemistry; Computer-Based Learning; Group Theory / Symmetry, Mathematics / Symbolic Mathematics, Quantum Chemistry
*  History
 Created:
Last Updated:		 November 29, 2004
December 14, 2004
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