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Of the computer visualization packages available to help students learn symmetry and group theory, most can be categorized as tutorials (1–2), multimedia presentations (3–4), or computer-assisted instruction (5–6), and possess little user interactivity. Others incorporate sophisticated Web tools including the Chime (7) and Shockwave (8) browser plugins, or Java applets (9) but, again, are only modestly user interactive. The most instructive and versatile of these (8) lists all of the symmetry elements for each of the 47 molecules available in its internal library, and allows the user to run an impressive Shockwave animation illustrating the corresponding symmetry operation. Although such programs are helpful in familiarizing students with the concepts, once the fundamentals have been taught, students should be able to practice their skills in a visualization environment that is free from the kind of predetermined flow of information that characterizes these programs. Specifically, they should be able to define a symmetry element anywhere in any molecule and determine the effect of the corresponding symmetry operation. Such freedom allows students to capitalize on the most important aspect of interactive learning—to make mistakes and to learn from them. In this context, we have developed SymmetryApp, a new visualization program characterized by a high level of user interactivity. The program is built upon the framework of software written in Java and available under the GNU general public license (10), providing three-dimensional molecular representations from a simple Cartesian coordinate file (Figure 1). To this framework we have added algorithms exploiting standard linear algebra techniques to carry out user-selected symmetry operations directly on the Cartesians, once symmetry elements have been uniquely defined (11). Executing the symmetry operation yields a second image of the molecule, and a new visualization window is automatically opened wherein two images of the molecule are displayed (Figure 2): those corresponding to the molecule before and after the symmetry operation is performed. If the specific symmetry element is indeed present as defined by the user, the two images are identically superimposable and appear indistinguishable from the image of the molecule in the original visualization panel. However, if the symmetry element is not present, the two molecules are not identically superimposable, and appear, instead, as a sort of double exposure. In either case, users get clear visual feedback regarding the validity of their choices. As a secondary check, the program automatically compares the Cartesian coordinates of both molecule images and displays information regarding the comparison in a message bar. 
Figure 1. The chair conformation of cyclohexane is displayed in the main visualization panel along with two user-defined dummy atoms (without connecting lines) to define a proper rotation axis: the centroid and perpendicular to a ring. Dynamic messaging appears within the Rotation Axis Options window to assist the user in defining the symmetry element. Here, a C2 axis has been defined and the Rotate button has been activated.
Figure 2. A second visualization window, containing a superposition of the molecule images before and after the symmetry operation has been executed, appears when a symmetry operation is executed. The text at the bottom of the superposition window confirms, from a comparison of the Cartesian coordinates of the two molecule images, that the C2 symmetry element is not present as defined in this example.
In many cases, the user can define the symmetry element, e.g. a point, axis, or plane, by selecting various constituent atoms in the molecule. However, certain symmetry elements cannot be defined from the constituent atoms, and our program allows different types of dummy atoms to be placed within the molecule to aid in the definition. Dynamic messaging assists the user with all aspects of the procedure (Figures 1 and 2). Care has been taken to ensure that the program contains sufficient flexibility for the user to easily define symmetry elements in nearly any location, regardless of validity. A platform-independent Java Jar file, a library of 35 molecules, and a User Guide are available for download. The included Documentation provides a more thorough explanation of the program features. Literature Cited- Potillo, L. A.; Kantardjieff, K. A. A Self-Paced Computer Tutorial on the Concepts of Symmetry. J. Chem. Educ. 1995, 72, 399–400.
- Korkmaz, A.; Harwood, W. S. Web-Supported Chemistry Education: Design of an Online Tutorial for Learning Molecular Symmetry. J. Sci. Educ. Tech. 2004, 13, 243–253.
- Lee, A. W. M.; Leung, K. M.; Kwong, D. W. J.; Chan, C. L. Symmetry Elements and Operations. J. Chem. Educ. 1996, 73, 924–925.
- Vining, W. J.; Grosso, R. P. Symmetry and Point Groups. J. Chem. Educ. 2003, 80, 110.
- Kastner, M. E.; Leary, P.; Grieves, J.; DiMarco, K.; Braun, J. Point Group I, II, and III. J. Chem. Educ. 2000, 77, 1246–1247.
- Nedwed, K.; Gatterer, K.; Paulson-Fritzer, H. SYMAPPS 1.0: A Software Packet for Group Theoretical Applications to Molecular Symmetry. Comput. Chem. 1994, 18, 371–376.
- Johnston, D. Symmetry tutorial (accessed Jun 2007).
- Charistos, N. D.; Tsipis, C. A.; Sigalas, M. P. 3D Molecular Symmetry Shockwave: A Web Application for Interactive Visualization and Three-Dimensional Perception of Molecular Symmetry. J. Chem. Educ. 2005, 82, 1741–1742.
- Cass, M. E.; Rzepa, H. S.; Rzepa, D. R.; Williams, C. K. An Animated Interactive Overview of Molecular Symmetry. J. Chem. Educ. 2005, 82, 1742–1743.
- Lee, C.; Bartolotti, L. J. MolStart (accessed Jun 2007).
- Meyer, D. E. Computational Tools in Chemistry: From Software Development for the Advancement of Chemistry Education to Classic Quantum Chemical Research. M.S. Thesis, East Carolina University, Greenville, NC, 2004.
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