 There seems to be a gap in the physical chemistry curriculum. Although physics and calculus are prerequisites for physical chemistry and the course is the first one in which numerical methods can be used to compute physical and chemical quantities from measurable data, the actual level of computation in a traditional course is rather rudimentary. Typically one finds, on the one hand, simple linear least squares curve fitting and , on the other hand, elaborate thermodynamics and quantum mechanics derivations using partial derivatives. Neither extreme represents the dynamics of physical chemistry as practiced by modern physical chemists. Neither side of this dichotomy makes use of modern software tools such as symbolic mathematics software that would permit students to engage in complex numerical analysis and exploration of mathematical models for chemical systems. Young, Madura, and Rioux wrote, in a recent paper, an excellent review of numerical methods used in chemistry (2).
A Focus on Quantum Chemistry
Of particular interest in physical chemistry is the study of quantum chemistry by undergraduates. Even in quantum chemistry one often finds an emphasis on derivation and a concurrent lack of numerical analysis and exploration of mathematical models beyond the simplest calculations. Consequently students often view the course as a mathematical tour de force that seems to have little connection with modern chemistry. A quantum chemistry course need not be the mathematical equivalent of trekking the high Himalayas. We can offer students instructional materials that would foster more efficient and effective learning by using a commercial symbolic mathematics program.
A Link to Spectroscopy
An important role for quantum chemistry in the curriculum is to forge the connection of mathematical models to measurable spectroscopic quantities. Too often text books and quantum chemistry courses lose sight of this intrinsic connection as one after another mathematical equation is introduced. The premier issue of the Mathcad in the Chemistry Curriculum column describes a collection of instructional materials that can be used by students and teachers to construct a stronger link between spectroscopy and mathematical models. The emphasis is on the connection to spectroscopy not on derivation. Specifically the focus is on the UV-vis spectrum of iodine and various mathematical models used to analyze an iodine UV-vis spectrum.
The five Mathcad documents in this collection are:
- Exploring the Morse Potential: MorsePotential.mcd
- Introduction to Franck-Condon Factors: FranckCondonBackground.mcd
- The Franck-Condon Factors: FranckCondonComputation.mcd
- Vibronic Spectra of Diatomic Molecules and the Birge-Sponer Extrapolation: Birge-Sponer.mcd
- The Iodine Spectrum: IodineSpectrum.mcd
These documents address concepts ranging from examination of Morse potential functions through computation of Franck-Condon factors and use of the Birge-Sponer plot to determine the dissociation energy of the electronic excited state of iodine. Along the way students use the harmonic oscillator wave functions, compute overlap integrals, and use the Franck-Condon factors to simulate a UV-vis spectrum. Each of the documents is highly annotated to facilitate learning. Each document contains student exercises designed to promote learning based on reflection and the integration of concepts drawn from the laboratory experience and mathematical models developed in lecture.
In the Classroom
The five documents are a suite of integrated yet independent units. The suggested order for use in the classroom is MorsePotential.mcd, BirgeSponer.mcd, IodineSpectrum.mcd, FranckCondonBackground.mcd, and FranckCondonComputation.mcd. Through the suggested order students first are given an opportunity to explore the Morse potential including detailed unit analysis. This can be part of an early discussion of bonding or as a topic that follows harmonic oscillator lectures. At about the same time students may be measuring the UV-vis spectrum of iodine or bromine in the laboratory. The BirgeSponer.mcd document will give students a clear introduction to what is expected of them as they analyze their own iodine or bromine spectral data. Often the full data reduction required for analysis of an iodine spectrum is accomplished by students through algorithm techniques that lead to lower level or incomplete learning. The algorithm approach may be avoided by using the IodineSpectrum.mcd template. One might say that the template substitutes a blackbox for algorithms. Although one cannot prevent template abuse, the potential gains far outweigh the risk. First, by using a template students quickly complete the routine labor intensive parts of the data analysis. Second, the time saved can be used constructively in discussion of the spectroscopic concepts embedded in the experiment. It is here that the time in the curriculum to include a meaningful treatment of Franck-Condon factors can be found. Here also the importance of classroom time set aside for group work and cooperative learning becomes clear as students step through the detailed questions and exercises in the document.
The entire sequence of lessons is brought to closure through use of the FranckCondonBackground.mcd, and FranckCondonComputation.mcd documents. The set of five documents described here have all been classroom tested by the authors (3). Student and faculty reactions are very positive. The faculty who used these materials in their classes observed clear increases in learning as demonstrated by the quality of laboratory reports and the in class discussions among students.
Acknowledgment
The editor acknowledges partial support for development of this column from the New Traditions project at the University of Wisconsin-Madison through the National Science Foundation's Division of Undergraduate Education grant DUE #9455928.
Literature Cited
- Mathcad® is a registered trademark of Mathsoft Engineering & Education, Inc., 101 Main Street, Cambridge, MA 02142-1521; USA.
- Young, S. H.; Madura, J. D.; Rioux, F. Software for Teaching and Using Numerical Methods in Physical Chemistry. In Using Computers in Chemistry and Chemical Education; Zielinski, T. J., Swift, M. L., Eds.; American Chemical Society: Washington, DC, 1997; pp 163-185.
- Long, G.; Sauder, D.; Shalhoub, G. M.; Stout, R.; Towns, M. H.; Zielinski, T. J. The Iodine Spectrum: a New Look at an Old Topic. J. Chem. Educ. 1999, 76, 841-847.
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