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  Home > JCE Print > Journal of Chemical Education > Issues > 2006  > November  >
Information • Textbooks • Media • Resources
JCE SymMath: Symbolic Mathematics in Chemistry
Finding Molecular Vibrational Frequencies from HCl to SO2
Franklin M. C. Chen
Department of Chemistry, University of Wisconsin–Green Bay, Green Bay, WI 54311

Theresa Julia Zielinski
Department of Chemistry, Medical Technology, and Physics, Monmouth University, West Long Branch, NJ 07764

Cover
November 2006
Vol. 83 No. 11
p. 1726
Abstract
This Mathcad worksheet is intended to help students learn about finding molecular vibrational frequencies through normal mode analysis and numerical solutions for a simple molecule, such as HCl, and more complicated molecules, such as CO2 and SO2. Students will learn various coordinates such as displacement coordinates, internal coordinates, symmetry coordinates, and their relationship. Students will also learn how to write sets of differential equations, quadratic terms of potential and kinetic energies using most convenient coordinates. This exercise will help students develop algebraic skills to diagonalize both potential and kinetic energy quadratic terms to find corresponding vibrational frequencies.

Figure 1. The symmetric and anti symmetyric stretching modes for CO2.

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.; Zielinski, Theresa Julia J. Chem. Educ. 2006 83 1726.
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Keywords
Chemometrics; Computer-Based Learning; Group Theory / Symmetry; Mathematics / Symbolic Mathematics; Physical Chemistry; Quantum Chemistry; Upper-Division Undergraduate
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History
Created:
Last Updated:
9/19/2006
9/20/2006
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