Chapter 10, Problem 10C.4P

(a)

Interpretation Introduction

Interpretation:

Whether the transition from the ground state ${\text{A}}_{\text{1g}}$ to ${\text{T}}_{\text{2g}}$ or ${\text{G}}_{\text{g}}$ is allowed or not has to be stated.

Concept introduction:

The selection rules for molecular transitions can be made on the basis of group theory by knowing the symmetry species of the wavefunctions.  The intensity of transition depends on the electric transition dipole moment.

(b)

Interpretation Introduction

Interpretation:

The change that might occur in the transition when the molecule ${\text{C}}_{\text{60}}$ is distorted slightly so as to remove its center of inversion 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.

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