1. Rotational Spectra
Simplest Case: Diatomic or Linear Polyatomic molecule
Rigid Rotor Model: Two nuclei joined by a weightless rod
J = Rotational quantum number (J = 0, 1, 2, …)
I = Moment of inertia = mr2
= reduced mass = m1m2 / (m1 + m2)
r = internuclear distance m2 m1 r

2. Rigid Rotor Model In wavenumbers (cm-1):
Separation between adjacent levels:
F(J) – F(J-1) = 2BJ

3. Rotational Energy Levels
Selection Rules:
Molecule must have a permanent dipole.
DJ = 1
J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

4. Rotational Spectra J” → J’ F(J’)-F(J”) 3 → 4 2(1.91)(4) 15.3 cm-1
4 → 5
2(1.91)(5)
19.1 cm-1
5 → 6
2(1.91)(6)
22.9 cm-1
6 → 7
2(1.91)(7)
26.7 cm-1
7 → 8
2(1.91)(8)
30.6 cm-1
8 → 9
2(1.91)(9)
34.4 cm-1
9 → 10
2(1.91)(10)
38.2 cm-1
J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

5. Intensity of Transitions
cm-1
J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

6. Are you getting the concept?
Calculate the most intense line in the CO rotational spectrum at
room temperature and at 300 °C. The rigid rotor rotational
constant is 1.91 cm-1.
Recall:
k = 1.38 x J/K
h = x Js
c = 3.00 x 108 m/s

7. Account for the dynamic nature of the chemical bond:
The Non-Rigid Rotor
Account for the dynamic nature of the chemical bond:
DJ = 0, 1
D is the centrifugal distortion constant
(D is large when a bond is easily stretched)
Typically, D < 10-4*B and B = 0.1 – 10 cm-1

8. More Complicated Molecules
Still must have a permanent dipole
DJ = 0, 1
K is a second rotational quantum number accounting for rotation around a secondary axis A.

9. Vibrational Transitions
Simplest Case: Diatomic Molecule
Harmonic Oscillator Model: Two atoms connected by a spring.
in Joules
in cm-1
v = vibrational quantum number (v = 0, 1, 2, …)
n = classical vibrational frequency
k = force constant (related to the bond order).

10. Vibrational Energy Levels
Selection Rules:
Must have a change in dipole moment (for IR).
2) Dv = 1
J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

11. Anharmonicity Selection Rules: Dv = 1, 2, 3, …
Dv = 2, 3, … are called overtones.
Overtones are often weak because anharmonicity at low v is small.
Ingle and Crouch, Spectrochemical Analysis

12. Rotation – Vibration Transitions
The rotational selection rule during a vibrational transition is:
DJ = 1
Unless the molecule has an odd number of electrons (e.g. NO).
Then,
DJ = 0, 1
Bv signifies the dependence of B on vibrational level

13. Rotation – Vibration Transitions
If DJ = -1  P – Branch
If DJ = 0  Q – Branch
If DJ = +1  R – Branch
Ingle and Crouch, Spectrochemical Analysis

14. Rotation – Vibrational Spectra
Why are the intensities different?
J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

15. Are you getting the concept?
In an infrared absorption spectrum collected from a mixture of
HCl and DCl, there are eight vibrational bands (with rotational
structure) centered at the values listed below. Identify the
cause (species and transition) for each band.
Band Location
Species/Transition
2096 cm-1
2101 cm-1
2903 cm-1
2906 cm-1
4133 cm-1
4139 cm-1
5681 cm-1
5685 cm-1
Atomic masses
H → amu
D → amu
35Cl → amu
37Cl → amu

16. Raman Spectra Selection Rule: DJ = 0, 2
J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

17. Only those that have a change in dipole moment are seen in IR.
Polyatomics
If linear  (3N – 5) vibrational modes
(N is the # of atoms)
If non-linear  (3N – 6) vibrational modes
Only those that have a change in dipole moment are seen in IR.

18. Linear Polyatomic How many vibrational bands do we expect to see?
J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

19. Nonlinear Polyatomic (Ethylene)
J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

20. Infrared Spectroscopy
Near Infrared: 770 to 2500 nm
12,900 to 4000 cm-1
Mid Infrared: to 50,000 nm (2.5 to 50 mm)
4000 to 200 cm-1
Far Infrared: 50 to 1000 mm
200 to 10 cm-1

21. Ingle and Crouch, Spectrochemical Analysis
Infrared Spectroscopy: Vibrational Modes
Ingle and Crouch, Spectrochemical Analysis

22. Group Frequencies Estimate band location: Pretsch/Buhlmann/Affolter/
Badertscher, Structure Determination of Organic Compounds

23. Are you getting the concept?
Estimate the stretching vibrational frequency for a carbonyl
group with a force constant, k, of 12 N/cm. If a C=S bond
had the same force constant, where would its stretching
band appear in the infrared absorption spectrum?
Recall:
1 amu = x kg
1N = 1 kg*m*s-2
Atomic masses
C → amu
O → amu
S → amu

24. Infrared Spectroscopy
Near Infrared: 770 to 2500 nm
12,900 to 4000 cm-1
* Overtones
* Combination tones
* Useful for quantitative measurements
Mid Infrared: to 50,000 nm (2.5 to 50 um)
4000 to 200 cm-1
* Fundamental vibrations
* Fingerprint region 1300 to 400 cm-1
(characteristic for molecule as a whole)
Far Infrared: 2.5 to 1000 um
200 to 10 cm-1
* Fundamental vibrations of bonds with heavy
atoms (useful, e.g., for organometallics)

25. Example of an Overtone Wagging vibration at 920 cm-1.
Overtone at approximately 2 x 920 cm-1 = 1840 cm-1.

26. Fermi Resonance
N.B. Colthup et al., Introduction to Infrared and Raman Spectroscopy, Academic Press, Boston, 1990.

27. Example of a Fermi Resonance
Stretching vibration of C-C=(O) at 875 cm-1.
Overtone at approximately 2 x 875 cm-1 = 1750 cm-1
coincides with C=O stretch

28. Light Source: Globar Silicon Carbide Rod (5mm diameter, 50 mm long)
Heated electrically to 1300 – 1500 K
Positive temperature coefficient of resistance
Electrical contact must be water cooled to prevent arcing
Ingle and Crouch, Spectrochemical Analysis

29. Ingle and Crouch, Spectrochemical Analysis
Sample Preparation for IR Spectroscopy
Ingle and Crouch, Spectrochemical Analysis

30. Liquid Samples: Cell Thickness
Ingle and Crouch, Spectrochemical Analysis

31. Ingle and Crouch, Spectrochemical Analysis
Window and Cell Materials
Ingle and Crouch, Spectrochemical Analysis

32. Solvents
Pretsch/Buhlmann/Affolter/Badertscher, Structure Determination of Organic Compounds

33. Suspension Media for Solid Samples
Pretsch/Buhlmann/Affolter/Badertscher, Structure Determination of Organic Compounds

34. Interferences Pretsch/Buhlmann/Affolter/
Badertscher, Structure Determination of Organic Compounds