1. 6. Vibrational Spectroscopy
6.1 Diatomic spectropscopy
1 aJ Å-2 = 1 mdyne Å-1 = 100 N m-1

2. 6.1.1 Infrared spectra

4. 6.1.2 Raman spectra
Figure 6.2 Variation of the mean polarizability 𝛼 with internuclear distance r in a diatomic molecule

5. V(x) = De [1 – exp(-ax)]2 (6:23)
6.1.3 Anharmonicity
Morse Potential, 1929
De: dissociation energy
V(x) = De [1 – exp(-ax)]2 (6:23)
D0: zero-point energy

6. Anharmonicity
Electrical anharmonicity: (electrical properties, dipole moment and polarizability).
Mechanical anharmonicity: (nature of molecular vibration).
Selection rule because of the effect of anharmonicity:
Δv = ± 1, ± 2, ± 3, …

7. Types of Vibrational Transitions
The intensity of Δv= ±1 transitions is stronger than that for Δv= ±2, ±3, … transitions.
Both electrical and mechanical anharmonicity contribute to the intensities of Δv= ±2, ±3, … transitions.

9. Dissociation Energy from Spectroscopic Data

10. Birge-Sponer Diagram

11. Birge-Sponer Diagram

12. 6.1.4 Vibration–rotation spectroscopy
Infrared spectra

13. Infrared spectrum
ΔJ = ±1
Raman spectrum
ΔJ = 0 , ±2
Figure 6.7 Rotational transitions accompanying a vibrational transition in
(a) an infrared spectrum and (b) a Raman spectrum of a diatomic molecule

14. Vib-Rot Infrared Spectrum of Nitric Oxide
P-branch
Q-branch
R-branch
R. H. Gillette and Eugene H. Eyster, Phys. Rev. 56, 1113, 1939
Exceptions to the infrared ΔJ ≠ 0 selection rule are found for some diatomic molecules such as NO, which have electronic angular momentum in the ground electronic states.

16. 35Cl: 75.76
37Cl: 24.24

17. HCl isotopes, from SJ. Chem. Educ. 40, 245(1963)

18. 1H35Cl

19. Vib-Rot Infrared Spectrum of the DCl Molecule
νvib(HCl) > νvib(DCl) because of the differences in force constants and reduced massed between the two molecules.
B0 = cm-1
B1 = cm-1

21. 6.2 Polyatomic molecules
6.2.1 Group vibrations : 3N – 5(linear) or 3N-6(non-linear) group vibrational modes.

22. Figure 6.11 (a, b) Fundamental and overtone and (c) combination tone transitions involving vibrations νi and νj

23. Figure 6.12 2-Chlorofluorobenzene

25. (c) scissoring
(b) twisting
(a) rocking
(d) wagging
(e) the torsional
(f) the ring-breathing
inversion, or umbrella,

26. IR OH stretching vibration of Phenol
phenol in hexane solution 𝜈 =3622 cm-1.
phenol in diethylether
𝜈 = 3344 cm-1.

28. 6.2.3.1 IR Vibrational selection rules

29. Acetylene, D∞h

30. Naphthalene m=0, mxy=0, mxz=0, myz=4, m2x=0, m2y=0, m2z=1, m0=0. z
modes: 3N-6(non-linear) = 3(18) – 6 = 48 y
D2h
m=0,
mxy=0, mxz=0, myz=4, m2x=0, m2y=0, m2z=1, m0=0.

31. Naphthalene

32. 6.2.3.2 Raman vibrational spectra

33. 6.2.4.1 IR spectra of linear molecules
D∞h or C∞h
Allowed vibrational transitions:
in D∞h :
in C∞h :
For Σ 𝑢 + − Σ 𝑔 + (D∞h), the rotational selection rule
P branch : ΔJ = -1
R branch : ΔJ = +1

34. Parities for D∞h molecules 1. Σ + − Σ +

35. 3 0 1 , Σ + − Σ + infrared band of HCN
Figure 6.25 The , Σ + − Σ + infrared band of HCN and two weaker, overlapping bands.

36. Parities for D∞h molecules 2. Π 𝑢 − Σ 𝑔 +
Level splitting in the Π state

37. Figure 6. 27 The 1 0 1 5 0 1 , Π 𝑢 − Σ 𝑔 + infrared band of acetylene
Figure 6.27 The , Π 𝑢 − Σ 𝑔 + infrared band of acetylene. (The unusual vertical scale allows
both the very intense Q branch and the weak P and R branches to be shown conveniently)

38. 6.2.4.2 IR spectra of symmetric rotors
C3v
Ex, methyl fluoride
For a parallel band(A1 − A1)
ΔK = 0 and ΔJ = ±1; for K = 0
ΔK = 0 and ΔJ = 0, ± 1; for K ≠ 0
Figure 6.28 The , A1 − A1 infrared parallel band of C2H3F.

39. 6.2.4.2 IR spectra of symmetric rotors
C3v
Ex, SiH3F.
For a perpendicular band(E − A1)
ΔK = ±1 and ΔJ = 0, ± 1
Figure 6.29 The , E − A1 infrared perpendicular band of SiH3F. (Robiette, A. G., Cartwright, G. J., Hoy, A. R. and Mills, I. M., Mol. Phys., 20, 541, 1971)

40. 6.2.4.3 IR spectra of spherical rotors
for regular Td as CH4, the only type of allowed infrared vibrational transition is T2 − A1.
for regular Oh as SF6, the only type of allowed infrared vibrational transition is T1u − A1g.
ΔJ = 0, ± 1
similar to a Π–Σ type of band in a linear molecule.

41. 6.2.4.4 IR spectra of asymmetric rotors
,(type A), ,(type B), , (type C).
ΔJ = 0, ± 1
Ethylene (H2C=CH2) is a prolate asymmetric rotor
type A; type B; or type C

42. Figure 6.34 Part of the infrared spectrum of fluorobenzene showing typical type A, B and C bands

43. 24B=67 cm-1
𝐸 𝑟 = ℏ 2 2𝐼 𝐽 𝐽+1 =𝐵𝐽 𝐽+1

51. Exam 2
1. ethylene(C2H4) 분자의 진동모드
H H C x y z

52. C=C str
CH2 s-str
CH2 twis
CH2 rock
H H C x y z
CH2 wag
CH2 rock
CH2 a-str
CH2 twis
CH2 a-str
CH2 sci
CH2 s-str
CH2 wag

53. m=0, mxy=0, mxz=0, myz=1, m2x=0, m2y=0, m2z=1, m0=0.
Hollas p.423
Hollas p.423
m=0, mxy=0, mxz=0, myz=1, m2x=0, m2y=0, m2z=1, m0=0.
Hollas p.416

54. 3ag+au+2b1u+b2g+2b2u+2b3g+b3u
Hollas p.423
m=0, mxy=0, mxz=0, myz=1, m2x=0, m2y=0, m2z=1, m0=0.
ag = = 3.
au = = 1.
b1g = – 1 = 0.
b1u = – 1 = 2.
b2g = = 1.
b2u = – 1 = 2.
b3g = – 1 = 2.
b3u = – 1 = 1.
3ag+au+2b1u+b2g+2b2u+2b3g+b3u

55. H H C x y z ag
b1u
b2u au
b3g
b3u
b2u ag ag
b2g
b1u
b3g

56. CH2=CH2 # 대칭종 cm-1 (*) 1 CH2 s-str (A1)ag 3022 2 C=C str 1625 3
CH2 i-p sci
1343 4
CH2 o-p twis
(A2)au
1026 5
CH2 o-p wag
(B1)b2g
940 6
(A1)b1u
2989 7
CH2 a-str
(B2)b2u
3105 8
CH2 i-p rock
826 9
1444 10
(B2)b3g
1222 11
3083 12
(B1)b3u
949
위 표와 그림에서 B1과 B2는 서로 바뀌어져 있음