Operations of C3v Symmetry Group Applied to Ammonia

This Demonstration shows the effect of successive symmetry operations of the group applied to the ammonia molecule and how this corresponds to the multiplication table of the group.
Set the buttons to apply one of these group operations: , the identity operator; , clockwise rotation by 120°; , counterclockwise rotation by 120°; and the three reflection operators , and , corresponding to the plane going through the three N-H bonds.
You can apply two symmetry operations successively and show that the combined operations generate another operation, in accordance with the multiplication table of the group. The direct application of the product operator is shown in the lower row of the diagram.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Snapshot 1: clockwise rotation followed by counterclockwise , with resulting effect the identity operation
Snapshot 2: counterclockwise rotation followed by reflection , with resulting effect a reflection
Snapshot 3: reflection followed by reflection , with resulting effect a counterclockwise rotation
[1] W. M. McClain, Symmetry Theory in Molecular Physics with Mathematica: A New Kind of Tutorial Book, New York: Springer, 2009.
[2] W. J. Moore, Physical Chemistry, New York: Prentice-Hall, 1950.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+