Point Group Assignment Practice

Symmetry Resources at Otterbein University

Welcome to the world of symmetry! The resources contained within this web site are designed to help students learn concepts of molecular symmetry and to help faculty teach concepts of molecular symmetry. The materials are designed for a variety of levels, so look around and see what we have to offer. Choose from the following pages:

  • Symmetry Tutorial - An interactive point group symmetry tutorial. Guides students through all of the symmetry elements and operations, with interactive displays and animations.
  • The Symmetry Gallery - A collection of nearly 70 unique molecules with interactive display of all symmetry elements and animation of all operations. The molecules are organized by point group, so you can select examples to demonstrate particular symmetry elements. Includes links to the chemical literature when available.
  • The Symmetry Challenge - Using the same set of molecules from the Gallery, the Challenge includes a flow chart that details the process of determining the point group of each molecule. A great way to practice the point group determination process.

Updates: July 2016 - A new web site for displaying crystallographic symmetry in selected spacegroups is now live. (Presented at the 66th Annual Meeting of the American Crystallographic Association, Denver, CO).

March 2014 - A new mobile optimized version of the Symmetry Gallery can be found at symmetry.otterbein.edu/mobile. Compatible with iOS and Android - please test and send feedback!

January 2014 - Updated Jmol and underlying code to allow full operation without Java. All pages now default to HTML5 (JSmol) operation. If you prefer using Java, click the Java link on the bottom of the left panel. Testing is ongoing.

August 2011 - New pages on crystallography and crystallographic symmetry now at crystals.otterbein.edu.

August 2009 - Try out the new CSDSym search function. You can search the CSD for molecules with particular point groups or space groups.

April 2009 - Some errors in various structures have been corrected (thanks Andy!). The “flickering” during animations in Safari has been fixed.

System Requirements: All pages require a modern browser with Javascript enabled (Java no longer requred = see note below under updates). These pages have been tested with Chrome (OS X, Windows, iOS, Android), Safari (OS X, iOS), Firefox (OS X, Windows, Linux, Android), and Internet Explorer (Windows, IE v9 required for HTML5 mode).

Point Groups

Chemists classify molecules according to their symmetry. The collection of symmetry elements present in a molecule forms a “group”, typically called a point group. Why is it called a “point group”? Because all the symmetry elements (points, lines, and planes) will intersect at a single point.

So let's look at a specific example, say water. What symmetry elements does water possess? Identity, E; two reflection planes, σxz and σyz; and one 2-fold rotation axis, C2. In the common notation (aka Schoenflies notation), this is known as the C2v point group.

Another molecule that also belongs to the C2v point group is cyclohexane in the boat conformation. Look at the two figures below and see that they do contain the identical set of symmetry elements, even though their overall shapes are quite different.

Determining Point Groups

So how does one determine the point group of a molecule? One possible approach is simply to find all the symmetry elements and then look at a set of tables (something called character tables will work) until you find a matching set. While this would not be hard for something as simple as the example above, molecules like methane that contain 24 symmetry elements would be more tedious!

So chemists have developed various flowcharts that make the process as simple as answering a serious of yes/no questions. If you would like some practice in this process, you can go to the Symmetry Challenge page of this web site and find out how it works.

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