SymMath Application

Finding Molecular Vibrational Frequencies from HCl to SO₂©

Franklin M.C. Chen
Department of Chemistry
University of Wisconsin-Green Bay
Green Bay, WI 54311-7001
United States
mail to: chenf@uwgb.edu

Theresa Julia Zielinski
Department of Chemistry, Medical Technology, and Physics
Monmouth University
West Long Branch, NJ 07764-1898
United States
mail to: tzielins@monmouth.edu

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 complicate 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 algebric skills to diagonalize both potential and kinetic energy quadratic terms to find corresponding vibrational frequencies.

Commentary

Editor's Commentary

Keywords

Audiences:	Upper-Division Undergraduate
Pedagogies:	Computer-Based Learning
Domains:	Physical Chemistry
Topics:	Chemometrics, Group Theory / Symmetry, Mathematics / Symbolic Mathematics, Quantum Chemistry

Documents

File Name	Description	Software Type	Software Version
FindingVibrationFrequencies.mcd	Requires Mathcad 11 or higher.	Mathcad	11
FindingVibrationFrequencies.pdf	Read-Only Document

JCE Subscribers only: name and password or institutional IP number access required.

Citations

Chen, Chen, F. M. C.; Zielinski, T. J. J. Chem. Educ. 2006 83, 1726.

Comments to: chenf@uwgb.edu