WEB TUTORIAL - Group Theory

H₂O Worked Example

The Number of Unchanged Bonds ( _R)

Ensure that you have not mixed up the number of unchanged bonds (_R Values) with the values for N.

• N Values (all 1 in this case) are the numbers preceding the symmetry element and are important for use in the Reduction Formula.

• The listed Symmetry Elements are all of the elements present in the point group.
A good way to check you have assigned the correct point group is to check the character table off against your molecule and make sure all of the elements in your molecule are present in the character table and vice-versa.
• The h term is a summation of all of the N terms and varies for each character table.
• _I Values are the entries into the table which are used in the Reduction Formula.
• Normal/Quadratic Terms refer to mathematical properties in the table. However, if there is a Normal Term, the row vibration will be IR active. If there is a Quadratic Term it is Raman active.
• Row Names are the labels given to each mode of vibration of the molecule.

Consider each symmetry element in turn, and answer how many unchanged bonds there are in each case after the symmetry element has been completed and pick one of the following answers.

The first number indicates the number of unchanged bonds for E, the second number
indicates the number of unchanged bonds for the C₂ rotation and so forth.

• 1 0 1 0
• 1 1 1 1
• 0 2 0 2
• 2 0 2 0
• 2 0 2 2
• 3 1 3 1