Lecture 5

Lecture 5

1. Numbers of normal modes

   • non-linear molecule
     • 3N-6 normal modes
     • 3 translations and 3 rotations
   • linear molecule
     • 3N-5 normal modes
     • 3 translations and 2 rotations (none about the lone it lies)

2. Whole molecule method

   • use all motions of all atoms as a basis
   • Γall=Γvib+Γrot+Γtrans
   • +1 for each axis that stays the same
   • -1 for each axis that becomes negative
     • then reduce from tables
       • this gives Γall
         • from the table work out Γrot and Γtrans
           • whatever is left is Γvib
   • 0 for each axis that moves
   • this works out the contribution of the old axis to the new axis

3. IR spectroscopy

   • a normal mode must result in a change in dipole moment
   • if it has these symmetry labels then it is IR active
     • Tz or z
     • Ty or y
     • Tx or x

4. Raman soectroscopy

   • Requires a change in the molecular polarisability
   • if it has these symmetry labels then it is Raman active
     • x^2
     • y^2
     • z^2
     • xy
     • xz
     • yz

5. if a molecule has an inversion centre then none of its normal modes can be both IR and Raman active