Character tables and applications
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What is a character table?
Each point group has one It describes how directional properties such as vectors or orbitals transform under the symmetry operations of that point group
What are the parts to a character table?
Point group Symmetry operations Order of group Symmetry label Mathematical functions
What is every row of the character table referred to as?
Irreducible representation
What does irreducible representation mean?
They are directional properties for a particular point group
What is the order of group?
Total number of operations in point groups
What are characters (X)?
The main part of the table and they show how an object or mathematical function is affected by the corresponding symmetry operation of the group
What does the character being -1 mean?
The function changes sign
What does the character being 1 mean?
Function appears unchanged
What does the character being 0 mean?
Function undergoes a more complicated change
What is an example where the character is 1
Rotation of Pz orbital about z axis
What do all operations of the same class have?
The same character
In general, what will a set three interacting orbitals produce?
One bonding (a1) One nonbonding (a1nb) One antibonding (a1*)
When will orbitals only react?
If they belong to the same irreducible representations of the point group