1. 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).

2. 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.

3. 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

4. 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

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

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

7. 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

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

9. 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.

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

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