CHEM 3523 - Supplementary Problems

Vibrational Spectroscopy

Question 1

a. SiCl₄

3N = 15
3N-6 = 9

T_d	E	8C₃	3C₂	6S₄	6σ_d
Γ_total	15	0	-1	-1	3

Reduces to: A₁ + E + T₁ + 3T₂

IR = 2T₂
Raman = A₁ + E + 2T₂

b. trans-SF₂Cl₄

3N = 21
3N-6 = 15

D_4h	E	2C₄	C₂	2C₂'	2C₂"	i	2S₄	σ_h	2σ_v	2σ_d
Γ_total	21	3	-3	-3	-1	-3	-1	5	5	3

Reduces to: 2A_1g + A_2g + B_1g + B_2g + 2E_g + 3A_2u + B_2u + 4E_u

IR = 2A_2u + 3E_u
Raman = 2A_1g + B_1g + B_2g + E_g

c. SbCl₅

3N = 18
3N-6 = 12

D_3h	E	2C₃	3C₂	σ_h	2S₃	3σ_v
Γ_total	18	0	-2	4	-2	4

Reduces to: 2A₁' + A₂' + 4E' + 3A₂" + 2E"

IR = 3E' + 2A₂"
Raman = 2A₁' + 3E' + E"

d. CH₂Cl₂

3N = 15
3N-6 = 9

C_2v	E	C₂	σ_v	σ_v'
Γ_total	15	-1	3	3

Reduces to: 5A₁ + 2A₂ + 4B₁ + 4B₂

IR = 4A₁ + 2B₁ + 2B₂
Raman = 4A₁ + A₂ + 2B₁ + 2B₂