Fourier Transforms of Molecular Vibrations©
W. Tandy Grubbs Department of Chemistry Stetson University DeLand, FL 32720 United States mail to: william.grubbs@stetson,edu
Abstract
These Mathcad documents permit students to explore the relationship between the time and frequency representations of vibrational motion in a simple molecule. The classical harmonic oscillator model, CHO, is the basis for the exploration in the first document. Although the equations of motion for the CHO can be easily solved, the Runge Kutta method is used to prepare students for the following two documents in the set. A Fourier transform produces the spectrum for the CHO case. The second document extends the study to a Morse potential and gives the students additional practice with the Runge Kutta method. In this document the students can see the difference between the Morse Potential and Classical Harmonic Oscillator in both the amplitude plot and the frequency spectrum for the oscillator. In the third document students examine the effect of a damping term on the harmonic oscillator equation of motion and learn about 'lifetime broadening' in a vibrational spectrum. All three documents are suitable for a first year course in physical chemistry or an instrumental analysis course. Student exercises are included in each document. Development of this document was made possible by the NSF supported 1997 "Workshop for Integration of Numerical Methods into the Undergraduate Physical Chemistry Curriculum Using the Mathcad Software" at the University of South Alabama, Mobile Alabama.
Commentary
Editor's Commentary
Keywords
Audiences: Upper-Division Undergraduate Pedagogies: Computer-Based Learning Domains: Analytical Chemistry, Laboratory Instruction, Physical Chemistry Topics: Fourier Transform Techniques, Mathematics / Symbolic Mathematics, Quantum Chemistry, Spectroscopy
Documents
File Name Description Software Type Software Version Part II-Morse Oscillator Mathcad Computational Document Mathcad Part I-SHO Mathcad Computational Document Mathcad Part III-Lifetime Broadening Mathcad Computational Document Mathcad Part II-Morse Oscillator Read-Only Document Part I-SHO Read-Only Document Part III-Lifetime Broadening Read-Only Document JCE Subscribers only: name and password or institutional IP number access required.
Citations
Grubbs, W. T. J. Chem. Educ. 1999 76, 286.
Comments to: W. Tandy Grubbs at william.grubbs@stetson.edu.
©Copyright 1999 Journal of Chemical Education