Operations of C3v Symmetry Group Applied to Ammonia

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.


Contributed by: D. Meliga and S. Z. Lavagnino (November 2016)
Open content licensed under CC BY-NC-SA



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.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.