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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.

An IR spectrum is characteristic of an entire molecule and is 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.

Important concepts in IR spectroscopy

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Types of Molecular VibrationsStretching or bonding vibrations (ν) 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(δ) and out-of-plane modes (γ); 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.

out-of-plane in-planein-plane

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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 modesbecause 3 of all the modes result in a translation and 2 in a rotation.

ν(s) C=OIR inactive, Raman active

1285 cm-1

2349 cm-1

666 cm-1δ(s) O=C=O

IR active, degenerated

ν(as) C=OIR active, Raman active

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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.

ν(s) O-HIR active3657 cm-1

3756 cm-1

1595 cm-1δ(s) H-O-H

IR active, degenerated

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.

ν(as) O-HIR active

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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 σv (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 σ’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.

13-19Γtot

σ’v (yz)σv (xz)C2EC2V

Example, the vibrational modes of water.Vibrational Spectroscopy and Symmetry

H O H

C2

HO

H

H O H

HOH

H O Hσv (xz)

H O H

HOH

σ’v (yz)

z y

x

59-250, notes 6, Macdonald

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yzy, Rx1-1-11B2

xzxy

x2,y2,z2

x, Ry

Rz

z

-11-11B1

-1-111A2

1111A1

σ’v (yz)σv (xz)C2EC2V

From the Γtot and the character table, we can figure out the number and types of modes using the same equation that we used for bonding:

( ) ( )[ ]n 1order

# of operations in class (character of RR) character of XX = × ×∑

( )( )( ) ( )( )( ) ( )( )( ) ( )( )( )[ ]n 14A1

= + − + +1 9 1 1 1 1 1 3 1 1 1 1

This gives:

( )( )( ) ( )( )( ) ( )( )( ) ( )( )( )[ ]n 14B1

= + − − + + −1 9 1 1 1 1 1 3 1 1 1 1

( )( )( ) ( )( )( ) ( )( )( ) ( )( )( )[ ]n 14B2

= + − − + − +1 9 1 1 1 1 1 3 1 1 1 1( )( )( ) ( )( )( ) ( )( )( ) ( )( )( )[ ]n 14A2

= + − + − + −1 9 1 1 1 1 1 3 1 1 1 1

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.

Vibrational Spectroscopy and Symmetry

13-19Γtot

σ’v (yz)σv (xz)C2EC2V

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An IR active vibrationalmode must result in a change of dipole moment of the absorbing group;

The requirement for a Raman active vibrationalmode is a change in polarizability of the absorbing group;

Almost every chemical bond between different elements has a dipole moment but dipole moments of a functional group or molecule might cancel out due to symmetry!

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Stretching and Bending vibrations of CH2

+ +

-

ν(as) 2926 cm-1 ν(s) 2853 cm-1 δ(in-plane) 1465 cm-1 δ(out-of-plane) 1350-1150 cm-1

+ -Out-of planebend or twist1350-1150 cm-1

In-plane bend or rocking 750-710 cm-1

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trans-methylstyrene

2-methoxyphenol (Guaiacol)

CH3

OCH3

OH

HH

HH

H

a

b

c

de

f

gh

ik

1

23

4

5

6

7

8

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IR of Normal Alkanes

C-H StretchCH3 (as) 2962CH3 (s) 2872CH2(as) 2924CH2(s) 2853

C-H BendCH2 (s) 1467CH3 (as) 1450CH3(s) 1378 C-H Rock

CH2 721

dodecane

C-H twistCH2 1350-1150(weak)

νC-C1200-800 (weak)δC-C bendbelow 500

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IR of Alkenesν C=C Stretch in simple alkenes 1670-1640ν C=C in conjugated alkenes near 1650 and 1600 (why lower?)

ν C=C1640 (s) w

ν C=C1598(as) s

=C-Hstretch

C-H stretchC-H bend (aliphatic &alkene in-plane) C-H bend

(out-of-plane)

isoprene

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IR of Alkynes

C≡C stretch2119≡C-H stretch

3310

C-H stretch

≡C-H bendovertone 1250

≡C-H bend630

1-hexyne

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Aromatics

Prominent (strong) absorptions:

ν C-H stretch 3100-3000 cm-1

δ in-plane C-H bend 1300-1000 cm-1

δ out of plane C-H bend 900-675 cm-1

(characteristic for substitution pattern)

ν C=C ring stretches 1600-1585 and 1500-1400 cm-1

δ out of plane C=C bend 450-400 cm-1

Overtone and Combination bands 2000-1650 cm-1

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combination bands

ν C=C ring

δ out of plane C-H bend

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Aromatic overtone and combination bands