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The portion of the infrared region most useful for analysis of organic compounds is not immediately adjacent to the visible spectrum, but is that having a wavelength range from 4000 to 600 cm-1, with a corresponding frequency range.

Infrared Spectroscopy

RegionWavelength (λ)

Range, μmWavenumber (νbar)

Range, cm-1Frequency (ν)

Range, Hz

near 0.78 - 2.5 12800 - 4000 3.8 x 1014 - 1.2 x 1014

middle 2.5 - 50 4000 - 200 1.2 x 1014 - 6.0 x 1012

far 50 - 1000 200 - 10 6.0 x 1012 - 3.0 x 1011

most used 2.5 - 15 4000 - 670 1.2 x 1014 - 2.0 x 1013

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Displacement, y0-A +A

-A

+A

0

Mechanical model of Stretching VibrationConsider the vibration of a mass attached to a spring.If the mass is displaced a distance y by application of a force, the restoring force is proportional to the displacement (Hooke’s Law)

y

where k is the force constant

The potential energy of a vibrating spring ( a harmonic oscillator) is

parabolic

The potential energy of a vibrating spring ( a harmonic oscillator) is given by

For a system consisting of two masses m1 and m2 connected by a spring ( which approximates two atoms connected by a bond),

- the mass m above is replaced by reduced mass, µ.

F = -ky

E = (1/2) ky2

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νm =12π

km

The vibrational frequency for such a system is given by

Quantum Mechanical Treatment of Vibrations

Solutions of the equations for PE of harmonic oscillator is given by

where h is Planck’s constant and v is vibrational quantum number (v = 0, 1, 2 ...)

Thus QM vibrators can take only certain discrete values.

Note that the last two terms (less h) is equal to the natural frequency, νm.

Thus,

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µ =m1m2

m1 + m2

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νm =12π

kµ

=12π

k m1 + m2( )m1m2

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E = v +12

h2π

kµ

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E = v +12

hνm

The transitions in vibrational energy levels can be brought about by radiation, provided the energy of radiation exactly matches the difference in energy levels (ΔE) between vibrational quantum states.

(and provided the vibration causes a fluctuation in dipole)

If we wish to express the radiation in wavenumber (vbar) in unit of cm-1,

k is about 500 N/m for single bonds1000 N/m for double bonds1500 N/m for triple bonds

N = kg m/s2

ExampleCalculate the approximate wavenumber of the fundamental absorption peak due to the stretching vibration of a carbonyl group (C=O).

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Eradiation = hν = ΔE = hνm =h2π

kµ

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ν =12πc

kµ

= 5.3x10−12 kµ

The mass of the carbon atom on kilograms is given bySolution

Similarly, for oxygen

and the reduced mass µ is given by

The force constant for the typical double bond is about 1 x 10³ N/m.

Substituting this value and µ

v = 1600 cm-1

The carbonyl stretching band is found experimentally to be in the region of 1600 to 1800 cm-1.

mC = 12 x 10-3 kg/mol x 1 atom = 2.0 x 10-26 kg 6.0 x 10²³ atoms/mol

mO = 16 x 10-3 kg/mol x 1 atom = 2.7 x 10-26 kg 6.0 x 10²³ atoms/mol

µ = (2.0 x 10-26 kg) x (2.7 x 10-26 kg) = 1.1 x 10-26 kg (2.0+2.7) x 10-26 kg

v = 5.3 x 10-12 s/cm x sqrt[(1 x 10³ N/m)/1.1 x 10-26 kg

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0

Dissociation energy

SELECTION RULES

The only transitions that can take place are those in which the vibrational quantum number changes by unity

Since the vibrational levels are equally spaced, only a single absorption peak should be observed for a given molecular vibration.

In reality, as two atoms approach each other, coulombic repulsion between them occurs, thus the PE rises as r approaches zero.

At the other extreme, as the two atoms move away from each other at distances where the dissociation occurs, the PE does not rise continuously.

The curve takes the anharmonic form.

Δv = ±1

ANHARMONIC OSCILLATOR

Anharmonicity leads to deviations of two kinds:

These are responsible for the appearance of overtone lines.

1. At higher quantum numbers, ΔE becomes smaller and the selection rule is not rigorously followed.

Δv = ±2 or ±3 are observed

Overtone lines occur at frequencies 2 to 3 times that of fundamental line; but low in intensity and may not be observed.

2. Two different vibrations in a molecule can interact to give peaks with frequencies that are sums or differences of their fundamental lines.

Again, the intensities of combination and difference peaks are low.

Vibrational Modes

The number of possible vibrations in a polyatomic molecule is

normal modes = 3N - 6where N is the number of atoms in the molecule.

A molecule containing N atoms is said to have 3N degrees of freedom.The location of each atom requires three coordinates (x, y, z). Thus to fix N atoms requires 3N coordinates.

For a linear molecule, rotation about the bond axis will not count (it will not affect the energy of the molecule)

Four Factors that tend to produce fewer peaks

1. The symmetry of the molecule is such that no change in dipole results from a particular vibration. (no dipole change, no IR absorption)

normal modes = 3N - 5

The six degrees of freedom subtracted from 3N is due to the translational and rotational motions of the molecule.

The molecule may move along x, y, or z (translation) or rotate about x, y, or z (rotation) for a total of 6 degrees of freedom.

2. The energies of two or more vibrations are identical or nearly identical.

3. The absorption intensity is so low as to be undetectable,

4. The vibrational energy is in a wavelength region beyond the range of the instrument.

Factors that tend to produce more peaks1. Overtone lines2. Combination bands

Vibrational coupling possibly occurs when there is common atom or bond involved between vibrating groups and their energy and symmetry are favorable.

ExampleConsider the IR spectrum of CO2. Normal modes = 3(3) - 5 = 4

If no coupling occurs, a band is expected at 1700 cm-1 for vC=O.Experimentally two peaks are observed (at 2330 cm-1 and 667 cm-1).

The peak at 2330 cm-1 is due to asymmetric stretching vibration of two C=O bonds which are vibrationally coupled.The peak at 667 cm-1 is due to two bending vibrations (scissoring) which are degenerate.

The 4th mode is symmetric stretch, which is IR inactive.

Different Vibrational Modes

Gas Phase IR Spectrum of Formaldehyde, H2C=O

Infrared spectrum of a compound is a unique reflection of its molecular structure.

An example of such a spectrum is that of the flavoring agent vanillin, shown below.

The inverted display of absorption, compared with UV-visible spectra , is characteristic. Thus a sample that did not absorb at all would record a horizontal line at 100% transmittance (top of the chart).

Some General Trends:i) Stretching frequencies are higher than corresponding bending frequencies.

(It is easier to bend a bond than to stretch or compress it.)

ii) Bonds to hydrogen have higher stretching frequencies than those to heavier atoms.

iii) Triple bonds have higher stretching frequencies than corresponding double bonds, which in turn have higher frequencies than single bonds. (Except for bonds to hydrogen).

Functional Class

Stretching Vibrations Bending Vibrations

Range (cm-1) Intensity Assignment Range (cm-1) Intensity Assignment

Alkanes 2850 - 3000 strong CH3, CH2 & CH 2 or 3 bands

1350 - 14701370 - 1390

720 - 725

mediummedium

weak

CH2 & CH3 deformation

CH3 deformationCH2 rocking

Alkenes3020 - 31001630 - 16801900 - 2000

mediumvariablestrong

(=CH) and =CH2

C=C (sym)C=C (assym)

880-995780-850675-730

strongmediummedium

(=CH) and =CH2

(out-of-plane bending)

cis-RCH=CHR

Alkynes 33002100-2250

strongvariable

C-H C≡C 600-700 strong C-H deformation

Arenes 30301600 & 150

variablemed-weak

C-H (sevrl bands) C=C (2 to 3 bands) 690-900 strong-med C-H bending &

ring puckering

Alcohols and

Phenols

3580-36503200-3550970-1250

variablestrongstrong

O-H (free) O-H (H-bonded)

C-O1330-1430

650-770mediumvar-weak

O-H (in-plane)O-H (out-of-plane)

Amines3400-35003300-34001000-1250

weakweak

medium

N-H (1o) 2 bands N-H (2o)

C-O1550-1650

660-900med - strong

variableNH2 (sciss, 1o)NH2 N-H (wag)

Typical Infrared Absorption Frequencies

Functional Class

Stretching Vibrations Bending Vibrations

Range (cm-1) Intensity Assignment Range (cm-1) Intensity Assignment

Aldehydes and

Ketones

2690-28401720-17401710-1720

169016751745

mediumstrongstrongstrongstrongstrong

C-H (aldehyde)C=O (satd ald)C=O (satd ket)aryl ketoneα, β-unsaturationcyclopentanone

1350-13601400-1450

1100

strongstrong

medium

α-CH3 bendingα-CH2 bending C-C-C bending

Carboxylic acid and

derivatives

2500-3300 (acids)

1705-1720 (acids)

1210-1320 (acids)

1785-1815 ( acyl halides)

1750 & 1820 (anhydrides)

1040-11001735-1750 (esters)

1000-13001630-1695(amides)

strongstrong

med - strstrongstrongstrongstrongstrongstrong

O-H (very broad)C=O (H-bonded)O-CC=OC=O (2-bands)O-CC=OO-C (2-bands)C=O (amide)

1395-1440

1590-16501500-1560

medium

mediummedium

C-O-H bending

N-H (1¡-amide) N-H (2¡-amide)

Nitriles 2240-2260 medium C≡N (sharp)Isocyanates,Iso

thiocyanates,

Diimides,

Azides &

Ketenes

2100-2270 mediumN=C=O, -N=C=S-N=C=N-, -N3, C=C=O

Typical Infrared Absorption Frequencies

INFRARED SOURCESInfrared sources consist of an inert solid that is heated electrically resulting in continuous radiation approximating that of a blackbody.

Spectral distribution of energy from a Nernst glower operated at 2200 K.

1. Nernst Glower

Composed of rare earth oxides formed into a cylinder having a diameter of 1 to 2 mm and a length of 20 mm. It is heated to 1200 to 2200 K.

λ, µm

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it1 3 5 7 9 11

Platinum leads are sealed to the ends to permit passage of electricity.

2. Globar

Globar is a SiC rod, about 50 mm in length and 5 mm in diameter.

It is also electrically heated (1300 to 1500 K); has the advantage of positive coefficient of resistance.

Its spectral energy is comparable to that of Nernst glower except at 5 µm where Globar provides greater output.

3. Incandescent wire source

1. Nichrome wire (Ni + Cr)

- lower intensity but longer life.

2. Rhodium wire (Rh) - sealed in a ceramic cylinder; has similar properties.

- tightly wound spiral heated to 1100 K;

4. Mercury arc

This is for far IR region (λ > 50 µm); high pressure Hg arc is used;

The device consists of a quartz-jacketed tube containing Hg vapor at <1 atm pressure.

5. Tungsten lamp

An ordinary W filament lamp is a convenient source for NIR region (4000 to 12800 cm-1)

Passage of electricity forms an internal plasma source that emits far IR.

6. CO2 laser

A CO2 laser produces a band in the 900 to 1100 cm-1 range

Consists of about 100 closely spaced discrete lines; any one of these lines can be chosen by tuning the laser.

1. Thermal detectors

3 General Types

Thermal Detectors

The responses of thermal detectors depend on the heating effect of radiation.

A thermocouple consists of a pair of junctions fromed when two pieces of a metal (e.g. Bi) is fused to either end of a dissimilar metal (e.g. Sb).

INFRARED DETECTORS

2. Pyroelectric detectors 3. Photoconducting detectors

1. Thermocouple

A potential develops between the two junctions that varies with their difference in temperature.

A type of resistance thermometer constructed of strips of metals such as Pt or Ni, or from a semiconductor.

A well-designed thermocouple is capable of responding to T differences of 10-6 K.

Thermopile is composed of thermocouples connected in series; this enhances sensitivity.

These materials exhibit large change in resistance as a function of temperature.

2. Bolometers

Thermistors are bolometers constructed from semiconductors.

Pyroelectric Detectors

These are constructed from single crystalline wafers of pyroelectric materials, which are insulators (dielectric materials) with special thermal and electrical properties.

Example : Triglycine sulfate (NH2CH2COOH)3.H2SO4

A temperature-dependent capacitor is produced if a pyroelectric crystal is sandwiched between two electrodes.

Irradiating with IR changes the charge distribution across the crystal, which can be detected as current.

Photoconducting Detectors

They consist of a semicon material (e.g. PbS, HgCdTe, InSb) deposited on a nonconducting glass surface and sealed into an evacuated envelope.

Absorption of IR by these materials promotes nonconducting valence electrons to a higher E conducting state

electrical resistance decreases

A photoconductor is placed in series with a V source and load resistor, and the V drop across the resistor serves as a measure of the power of the beam.

Filter, modulator, amplifier

Pre-amp

Chopper

Monochromator

Grating

Detector

Synchronousmotor

Chart

Attenuator

Synchronousmotor

Reference

Sample

Source

Synchronousrectifier