Lecture 4

Lecture 4

1. Reducible representation

   • a sum of irreps
     • Γ=c1Γ1+c2Γ2+.....
       • C1=1/h(Γ1*Γ)
         • this is the number of times Γ1 occurs
         • h is the order of the group
   • rows in the tables are irreps

2. When reducing a representation you should ALWAYS get a whole number

3. Vibrational spectroscopy

   • use the bonds in a molecule e.g. OH bonds in water, as a basis for a representation
   • find ΓOH
     • e.g. in water ΓOH=A1+B2
       • 2 stretching modes
         • asymmetric
         • symmetric
   • NH3
     • ΓNH=A1+E
       • symmetric
       • doubly degenerate
         • made up of 2 NH stretches that have the same energy