Chapter 11, Problem 11E.2ST

Interpretation Introduction

Interpretation:

The symmetry species of the normal modes of ammonia has to be stated.

Concept introduction:

The characters of the irreducible representations of the given point group can be multiplied by each other.  The only condition is the characters of the same symmetry operations are multiplied together.  The multiplication of the characters is commutative.

The great orthogonality theorem for the reducible representation can be expressed as shown below.

  $a_{\Gamma }=\frac{1}{h}{\displaystyle \sum _{\begin{array}{l}\text{all}\text{classes}\\ \text{of}\text{point}\text{group}\end{array}}N\cdot {\chi }_{\Gamma }\cdot {\chi }_{\text{linear}\text{combo}}}$