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Finding Molecular Vibrational Frequencies from HCl to SO₂

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

Figure 1. The symmetric and anti symmetric stretching modes for carbon dioxide.

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Mathcad 11	VibFreq.mcd

Version	Download
Mathcad 11	VibFreq.pdf

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Keywords

Audience: Upper-Division Undergraduate;

Domain: Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Chemometrics; Group Theory / Symmetry; Mathematics / Symbolic Mathematics; Quantum Chemistry;

JCE Citation