Question

5. Consider the PF5 molecule.

b) How many stretching vibrations does the molecule have, and what are their symmetries? Which ones appear in an IR spectrum? Which ones appear in a Raman spectrum?

c) How many bending vibrations does the molecule have, and what are their symmetries? Which ones appear in an IR spectrum? Which ones appear in a Raman spectrum?

Answer 1

Ans .) PF₅ has Trigonal Bipyramidal Symmetry.Point Group for this molecule is D_3h.

All the calculations are Calculated by means of Character Table. :

For the D3h the order is 12 .

We know that ,

Γ_total = Γ_Vibration+ Γ_Translation + Γ_Rotation

and

Γ_Vibration =Γ_Stretch + Γ_Bend

Now from The caharacter we find that.

The Irreducible representation, Γ_Total is calculated as

Γ_Total = 2A₁' + A₂' + 4E' + 3A₂" + 2_E"

Γ_trans = E' + A₂" (x,y,z)

Γ_rot = A₂' + E" ( R_x, R_y, R_z)

Γ_vibration =  Γ_tot - Γ_trans- Γ_{rot =}  2A₁' + 3E' + 2A₂" + E"

So these are VIbrational modes in PF₅.

5. b) ans. Γ_stretch = 2A₁' + E" + A₂''  = 4 Stretching Vibrations ( calculated from Character table ) .  

IR active= 2 = E" +  A₂''

Raman Active= 2 = 2A₁'

5.c) ans. 4 Bending vibrations are there in the Molecule.   Γ_Bending = A₂'' + 3E'

IR active = 1 = A₂'' + 3E'

Raman Active = 3E'