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The Franck-Condon Factors: FranckCondonComputation.mcd

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Theresa Julia Zielinski

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

George M. Shalhoub

Department of Chemistry, La Salle University, Philadelphia, PA 19141

J. Chem. Educ., 1998, 75 (9), p 1192

DOI: 10.1021/ed075p1192.1

Publication Date (Web): September 1, 1998

Abstract

The goal of this document is to introduce some of the mathematical models that are used to describe vibronic spectra (vibration-electronic spectra) of molecules. After completion of a study of the material presented in this document and the exercises distributed throughout the document, students are expected to be able to describe the relationship between Franck-Condon factors and vibronic spectra, explain the key factors determining the magnitude of the Franck-Condon factors, compute Franck-Condon Factors, and construct a vibronic spectrum for a molecule from a knowledge of the wavelength of the electronic transition and the number and the relative intensity of the vibronic peaks. Along the way students are introduced to the idea of using a complete orthonormal set of functions, in this case the harmonic oscillator functions, as a linear combination to represent another function. The final focus of the document is the simulation of spectra in terms of the Franck-Condon factors. The document contains many student exercises and it is highly annotated for the novice Mathcad user. Faculty using this document can easily modify the document to increase student interaction with the mathematical content.

Keywords (Audience):

Upper-Division Undergraduate

Keywords (Domain):

Physical Chemistry

Keywords (Feature):

JCE Online: Mathcad in the Chemistry Curriculum

Keywords (Pedagogy):

Computer-Based Learning

Keywords (Subject):

Quantum Chemistry

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This article has been cited by 2 ACS Journal articles (2 most recent appear below).

Franck-Condon Factors and Their Use in Undergraduate Quantum Mechanics
John C. Wright , Theresa Julia Zielinski
Journal of Chemical Education1999 76 (10), 1367
- Franck-Condon Factors and Their Use in Undergraduate Quantum Mechanics
  John C. Wright , Theresa Julia Zielinski
  Journal of Chemical Education1999 76 (10), 1367
  Symbolic mathematics software makes it possible for undergraduates to model the expansion of a wave function using the Hermite polynomials of a simple harmonic oscillator. The probabilities for transitions between the vibrational states of two electronic ...
  Abstract | Hi-Res PDF | PDF w/ Links
The Iodine Spectrum: A New Look at an Old Topic
Deborah Sauder , Theresa Julia Zielinski , George M. Shalhoub , Roland Stout , Marcy Hamby Towns , George Long
Journal of Chemical Education1999 76 (6), 841
- The Iodine Spectrum: A New Look at an Old Topic
  Deborah Sauder , Theresa Julia Zielinski , George M. Shalhoub , Roland Stout , Marcy Hamby Towns , George Long
  Journal of Chemical Education1999 76 (6), 841
  This paper describes a new approach to the traditional iodine gas absorption spectrum experiment often performed in undergraduate physical chemistry labs. The approach is student centered and designed to emphasize the conceptual richness in this classic ...
  Abstract | Hi-Res PDF | PDF w/ Links