1. Important concepts in IR spectroscopy
Vibrations that result in change of dipole moment give rise to IR absorptions. The oscillating electric field of the radiation couples with the molecular vibration to cause an alternating electric field produced by the changing dipole.
Absorption bands in vibration spectra appear as broad bands (not a single energy) if the rotational states of the molecules are not resolved as it is usually the case in liquid or solid phases.
IR absorptions are characteristic of an entire molecule and are as unique as a fingerprint (molecular fingerprint). Many “localized vibrations” help to identify functional groups.
Band intensities are expressed as either transmission (T) or absorption (A)
A = log10(1/T)
In addition to fundamental transitions, IR spectra can contain overtone bands, due to excitation into higher vibrational states, and combination bands, due to coupling of two or several “group” vibrations. Group vibrations can couple if their frequencies are similar and they share a common atom. A special case of coupling occurs when a fundamental vibration couples with an overtone or combination vibration. This phenomenon is known as Fermi resonance.

2. Molecular Vibrations
Stretching or bonding vibrations (n) alter the bond lengths;
Bending or deformation vibrations alter the bond angles, while the bond lengths remain unchanged; They can be subdivided into in-plane (d) and out-of-plane modes (g); These modes are often referred to as twisting, wagging, and rocking vibration of a fragment;
Torsional vibrations involve an alternation of the torsion angle;
A further division into symmetric (s), antisymmetric (as), and degenerated (e) vibrations is possible.
in-plane
out-of-plane
in-plane

3. IR and molecular symmetry
Every atom has a translational freedom of 3 because it can move in one of the three orthogonal directions (i.e. in the x, y, or z direction). There are a total of 3N possible motions for a molecule containing N atoms and each set of possible atomic motions is known as a mode.
Linear molecules, such as CO2, have 3N-5 vibrational modes because 3 of all the modes result in a translation and 2 in a rotation.
n(s) C=O IR inactive, Raman active
1285 cm-1
n(as) C=O IR active, Raman active
2349 cm-1
d(s) O=C=O
IR active, degenerated
666 cm-1

4. d(s) H-O-H IR active, degenerated
Bent molecules, such as H2O, have 3N-6 vibrational modes because 3 of all the modes result in a translation and 3 in a rotation.
n(s) O-H IR active
3657 cm-1
n(as) O-H IR active
3756 cm-1
d(s) H-O-H IR active, degenerated
1595 cm-1
All IR absorptions result not only in a vibrational excitation but also in transitions between different rotational states. Those rotational transitions can be resolved in gas phase IR spectroscopy. Rotational spectroscopy specifically measures transitions between rotational states and involves microwave radiation. It is an important method in gas phase chemistry.

5. Vibrational Spectroscopy and Symmetry
59-250, notes 6, Macdonald
Vibrational Spectroscopy and Symmetry
Example, the vibrational modes in water. z y
The E operation leaves everything where it is so all nine vectors stay in the same place and the character is 9.
The C2 operation moves both H atoms so we can ignore the vectors on those atoms, but we have to look at the vectors on the oxygen atom, because it is still in the same place. The vector in the z direction does not change (+1) but the vectors in the x, and y directions are reversed (-1 and -1) so the character for C2 is -1.
The v (xz) operation leaves each atom where it was so we have to look at the vectors on each atom. The vectors in the z and x directions do not move (+3 and +3) but the vectors in the y direction are reversed (-3) so the character is 3.
The ’v (yz) operation moves both H atoms so we can ignore the vectors on those atoms, but we have to look at the vectors on the oxygen atom, because it is still in the same place. The vectors in the z and y directions do not move (+1 and +1) but the vectors in the x direction is reversed (-1) so the character is 1. x C2
v (xz)
’v (yz)
C2V E C2
v (xz)
’v (yz)
tot 9 -1 3 1

6. Vibrational Spectroscopy and Symmetry
C2V E C2
v (xz)
’v (yz)
tot 9 -1 3 1
C2V E C2
v (xz)
’v (yz) A1 1 z
x2,y2,z2 A2 -1 Rz xy B1
x, Ry xz B2
y, Rx yz
From the tot and the character table, we can figure out the number and types of modes using the same equation that we used for bonding:
This gives:
Which gives: 3 A1’s, 1 A2, 3 B1’s and 2 B2’s or a total of 9 modes, which is what we needed to find because water has three atoms so 3N = 3(3) =9.

7. An IR active vibrational mode most result in a change of the dipole moment of a molecule;
The requirement for a Raman active vibrational mode is a change in the polarizability of the molecule.

8. Bending vibrations of CH2+ + -
n(as) 2926 cm-1 n(s) 2853 cm-1 d(in-plane) 1465 cm-1 d(out-of-plane) cm-1 - +
In-plane bend
or rocking
cm-1
Out-of plane
bend or twist
cm-1

9. IR of Normal Alkanes dodecane C-H Stretch CH3 (as) 2962 C-H Bend
C-H twist CH
weak
C-H Rock
CH2 721
dodecane

10. IR of Normal Alkenes C-H bend (in-plane) C-H bend (out-of-plane)
C=C Stretch in simple alkenes
C=C in conjugated alkenes near 1650 and 1600
C-H bend
(in-plane)
C-H bend
(out-of-plane)
C-H stretch
1640 (s) w
isoprene
=C-Hstretch
1598(as) s

11. IR of Normal Alkynes
C-H stretch
ºC-H bend
630
CºC stretch
2119
ºC-H bend
overtone 1250
ºC-H stretch
3310
hexyne