Character tables and applications

Question 1

What is a character table?

Answer 1

Each point group has one
It describes how directional properties such as vectors or orbitals transform under the symmetry operations of that point group

Question 2

What are the parts to a character table?

Answer 2

Point group 
Symmetry operations 
Order of group 
Symmetry label 
Mathematical functions

Question 3

What is every row of the character table referred to as?

Answer 3

Irreducible representation

Question 4

What does irreducible representation mean?

Answer 4

They are directional properties for a particular point group

Question 5

What is the order of group?

Answer 5

Total number of operations in point groups

Question 6

What are characters (X)?

Answer 6

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

Question 7

What does the character being -1 mean?

Answer 7

The function changes sign

Question 8

What does the character being 1 mean?

Answer 8

Function appears unchanged

Question 9

What does the character being 0 mean?

Answer 9

Function undergoes a more complicated change

Question 10

What is an example where the character is 1

Answer 10

Rotation of Pz orbital about z axis

Question 11

What do all operations of the same class have?

Answer 11

The same character

Question 12

In general, what will a set three interacting orbitals produce?

Answer 12

One bonding (a1) 
One nonbonding (a1nb) 
One antibonding (a1*)

Question 13

When will orbitals only react?

Answer 13

If they belong to the same irreducible representations of the point group