Mathematica Programs for Physical Chemistry by W. H. Cropper

Reviewed by
Sally Chapman
Barnard College, Columbia University, New York, NY 10027
schapman@barnard.columbia.edu

Mathematica Programs for Physical Chemistry. W. H. Cropper, Springer, New York, 1998, ISBN 0-387-98337-6.

William H. Cropper's book and CD-ROM of Mathematica programs elegantly demonstrate what he asserts in his preface: with modern software tools "the tedium of calculation work [in physical chemistry] has largely been overcome." The Mathematica programs are easy to execute, and many take full advantage of the impressive graphical capabilities of this software package. Designed to be used as a companion volume to a regular textbook, this book covers a wide range of topics in physical chemistry, including many examples in thermodynamics, kinetics, quantum chemistry, spectroscopy, and statistical mechanics. The presentation is clear; each equation explored in the CD-ROM is introduced succinctly in the text. The programs can be run as is, or are easily altered as interactive exercises, most-obviously by introducing new parameters. The book contains many exercises based on the programs; the results are included on the CD-ROM. The depth of coverage in many areas often goes beyond most conventional junior-year physical chemistry courses, but this allows instructors to go more deeply into their favorite topics. I believe that any physical chemistry instructor will enjoy using the programs.

But how well will it work for students? Here I am a little less confident. Some of this comes from my own experiences writing educational software. Something I find challenging, interesting, and great fun to prepare, all too often doesn't excite the students nearly as much as it did me. Why? Because when they use it, the process is all too automatic. I found this to be the case with some of Cropper's 140 Mathematica programs. Take, for example, the program "Acetate." Using extended forms of the Debye&endashHückel theory to obtain the activity coefficients, it calculates pH values for acetic acid&endashacetate buffers. This is a tedious hand calculation. Instead you open the notebook, execute the program, and the result appears. But if you are not familiar with or not interested in Mathematica, you are not likely to examine the underlying code to see how it all works, and you simply have a pH calculator, which is convenient but not particularly instructive.

Mathematica's excellent graphics make the curve displayed in a program like "Morse" pretty to look at, but not more informative than a graph found in a textbook. Some students may benefit from seeing the curve change as the parameters are altered, but each plotted separately on differently scaled axes looks pretty much the same. Many of the 2-D graphical results (in programs like "X-ray1", "Leps", or "Aorbital") are lovely. Is seeing them at the end of a Mathematica notebook more instructive than seeing the same equations and figure in a book? For some students, the answer will be yes.

It is often argued that to motivate a student, a computer exercise should be interactive, dynamic, seriously use the computer's power, or be an obvious timesaver. Many of the Cropper's Mathematica examples nicely satisfy one or more of these criteria.

Some of my favorites:

The program "Pattersn" gives a pretty and very clear graphical explanation of the relationship of peak-to-lattice positions in a Patterson map.
The pair of programs "Symtop1" and "Symtop2" effectively use color graphics to explain the pattern of overlapping P, Q, and R branches, which explain the bandshapes in perpendicular and parallel transitions in the IR spectra of symmetric tops.
"Coil1" generates a polymer random coil; it is fun to see the different coils generated each time the program is executed.
"Nmrft" and "Irft" use the computer's power and nicely demonstrate the concept of Fourier transforms.

I experienced only a few problems.

Two versions of each program are included, "name.ma" for Mathematica 2.0, and "name.nb" for Mathematica 3.0. If Microsoft Windows 95 is set to not display filename extensions (often the default), this can be confusing since the files then appear to be the same.
When using the programs, one frequently has the opportunity to alter data: the program instructs the user to change the data in line n. I found it a little frustrating that one had to guess how the unnumbered lines were being counted. On the other hand, it is pretty easy to figure out where to make changes.
Some of the programs use separate data files on the CD-ROM. When I tried to run these by first starting Mathematica and then loading the programs, they failed to run, since the program looked in the wrong place for the data. The problem disappeared when Mathematica was launched using the program name on the CD-ROM.

I am only an occasional Mathematica user, so these minor and easily resolved problems suggest that this collection of programs is very user-friendly. I didn't have the software to run the QuickBasic programs.

I used the CD-ROM on a 200-MHz Pentium machine with 32 MB of memory. It still took a little time to display some of the graphics. My previous experience with Mathematica on slower machines suggests that some of these programs might try the patience of the user. But given the cost of Mathematica, chances are good that people using it today are probably also using quite new hardware.

Instructional programs written in languages like Fortran or Basic can be designed so users can be totally unaware of the underlying code; they simply execute the application. With Mathematica programs the opposite is true; the code is always there. This is a mixed blessing. On the one hand, one could argue that this is better pedagogy; the package is not a mindless black box. But it can also be imposing; if you are not familiar with Mathematica, there is a lot of code, some of it quite imposing, between you and the answer. Some is important to understanding the chemical problem, but quite a bit is not. Looking at it may be a good way to learn Mathematica, but if that is not the objective, it may be an unfortunate distraction. Nevertheless, Mathematica is being used as an important instructional tool in many disciplines. Students in a modern physical chemistry lecture or laboratory may be perfectly comfortable scrolling through the code, and will probably learn a great deal as they do so. Where physical chemistry students are already familiar with Mathematica, this book is a natural and very welcome contribution. But even for those for whom Mathematica is new, it is well worth the effort to use at least some of these lovely programs.