Why Use Mathcad in Physical Chemistry?

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 the traditional course is rather rudimentary. Typically one finds, on the one hand, simple linear least squares curve fitting and, on the other hand, elaborate thermodynamic derivations using partial derivatives. Neither side of this spectrum 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.

The three major symbolic mathematics software products used by practicing chemists and chemical engineers are Mathematica (1), MAPLE (2), and Mathcad (3). Each of these software packages has its own supporters and each has been adopted as the software of choice at a variety of college campuses for both calculus courses and in the chemistry curriculum. Mathematica and MAPLE are interpreted programs. Instructions are entered one line at a time and performance is reminiscent of BASIC. Mathcad, on the other hand, is an electronic whiteboard where data, variables, constants, equations and graphs appear on the screen in much the same form as they would on paper. All three programs perform symbolic manipulations. Mathcad has an additional feature. It permits free form placement of text with the data, equations, variables and graphs. This makes the construction of interactive instructional documents very easy (4). The ease with which documents are constructed and the shallow learning curve for students make Mathcad an excellent choice for development of instructional materials.

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 a quantum chemistry course as a mathematical tour de force that has little relevance to 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. This 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 we will focus on the UV-vis spectrum of iodine and various mathematical models used to analyze an iodine UV-vis spectrum.

There are five Mathcad documents in this collection. They 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 contains student exercises designed to promote learning-based reflection and the integration of concepts drawn from the laboratory experience and mathematical models developed in lecture. In the following sections the abstract of each document describes goals and objectives of the document.

In the Classroom

The five documents presented here form 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 of the significant spectroscopic concepts available through the experiment. The algorithm approach may be avoided by giving students the detailed template contained in the IodineSpectrum.mcd document. One might say that the template approach substitutes a blackbox for the algorithm mechanism used by students. Although one cannot prevent misuse of a template, 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 document questions and exercises.

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 (5). 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.

These Mathcad documents require Mathcad PLUS 6 or higher. The documents and complete articles described in these abstracts can be obtained from the following JCE Internet address, http://www.jce.divched.org/JCEWWW/Features/McadInChem/ .

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

1. Mathematica is a registered trademark of Wolfram Research, Inc.; 100 Trade Center Drive; Champaign, IL 61820-7237; USA.

2. Maple and Maple V are registered trademarks of Waterloo Maple Software, 450 Phillip Street, Waterloo, Ontario, Canada N2L 5J2.

3. Mathcad is a registered trademark of Mathsoft, Inc., One Kendall Square, Cambridge, MA 02139; USA.

4. 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; Chapter 10.

5. 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., in press.

Mathcad in the Chemistry Curriculum: Mission Statement

The goal of the Mathcad in the Chemistry Curriculum column is to promote creation, dissemination, and utilization of well-crafted Mathcad documents that span the chemistry curriculum. We are soliciting exemplar Mathcad documents in physical chemistry, analytical chemistry, and instrumental analysis. A mix of shorter more focused documents along with longer fuller treatments of content are welcome. All documents will be peer reviewed. This column will also serve to exchange or suggest ideas and experiences about the use of its Mathcad documents.

The highest priority for acceptance for publication via this column will be given to those documents that include significant opportunities for students to interact with the material so that they can practice the chemical skills and develop deep understanding of the concepts featured in the document. The documents accepted will support independent student learning of the content or in class demonstration of advanced chemical concepts.

Succinct descriptions (abstracts) of the Mathcad documents published here will appear in the Information, Textbooks, Media, Resources section of the Journal. Such abstracts will contain the title, author information, and the URL where the document may be obtained and explain the scope of the document, its target audience, and its place in the chemistry curriculum.

Mathcad documents and abstracts may be sent to the JCE editorial offices or to the feature editor, Theresa Julia Zielinski. Instructions for authors of Mathcad documents for this column can be found at JCE Online at http://www.jce.divched.org/JCEWWW/Features/McadInChem/Authors/index.html.