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Infrared and Microwave Spectroscopy. Lecture Date: February 6 th , 2013. The History of Infrared Spectroscopy. Infrared (IR) Spectroscopy: Herschel first recognized the existence of IR and its relation to the heating of water First real IR spectra measured by Abney and Festing in 1880’s

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Infrared and microwave spectroscopy
Infrared and Microwave Spectroscopy

Lecture Date: February 6th , 2013

The history of infrared spectroscopy
The History of Infrared Spectroscopy

  • Infrared (IR) Spectroscopy:

    • Herschel first recognized the existence of IR and its relation to the heating of water

    • First real IR spectra measured by Abney and Festing in 1880’s

    • IR spectroscopy became a routine analytical method as spectra were measured and instruments developed from 1903-1940 (especially by Coblentz at the US NBS)

    • IR spectroscopy through most of the 20th century is done with dispersive (grating) instruments, i.e. monochromators

    • Fourier Transform (FT) IR instruments become common in the 1980’s, led to a great increase in sensitivity and resolution

J. F. W. Herschel

W. Coblentz

W. Abney, E. R. Festing, Phil. Trans. Roy. Soc. London,1882,172, 887-918.

Infrared spectral regions
Infrared Spectral Regions

  • IR regions are traditionally sub-divided as follows:

After Table 16-1 of Skoog, et al. (Chapter 16)

What is a wavenumber
What is a Wavenumber?

  • Wavenumbers (denoted cm-1) are a measure of frequency

    • For an easy way to remember, think “waves per centimeter”

  • Relationship of wavenumbers to the usual frequency and wavelength scales:

  • Converting wavelength () to wavenumbers:

Image from

Vibrational Spectroscopy: Theory

  • In IR spectroscopy, IR photons is absorbed and converted by a molecule into energy of molecular vibration




  • A simple harmonic oscillator is a mechanical system consisting of a point mass connected to a massless spring. The mass is under the action of a restoring force proportional to the displacement of the particle from its equilibrium position and the force constant k of the spring (under the classical Hooke’s law)

Vibrational Spectroscopy: Harmonic Oscillator

  • The quantum version of the classical oscillator (spring):

m is the natural frequency of the oscillator (a.k.a. the fundamental vibrational wavenumber)

k is the Hooke’s law force constant (now for the chemical bond)

v is the vibrational quantum number

h is Planck’s constant

  • v must be a whole number, so:



  • The potential energy function is:


r is the distance (bond distance)

re is the equilibrium distance

Vibrational spectroscopy theory
Vibrational Spectroscopy: Theory

  • The potential energy of vibrations fits the parabolic function fairly well only near the equilibrium internuclear distance.

  • The anharmonic oscillator model is a more accurate description for the overall motion

Figure from Skoog et al.

Anharmonic corrections
Anharmonic Corrections

  • Anharmonic motion: when the restoring force is not proportional to the displacement.

    • More accurately given by the Morse potential function than by the harmonic oscillator equation.

    • Primarily caused by Coulombic (electrostatic) repulsion as atoms approach

  • Effects: at higher quantum numbers, E gets smaller, and the ( = +/-1)selection rule can be broken

    • Double ( = +/-2), triple ( = +/-3), and higher order transitions can occur, leading to overtone bands at higher frequencies (NIR)

Deis the dissociation energy

Rotational spectroscopy theory
Rotational Spectroscopy: Theory

  • Vibrational spectra of condensed phases appear as bands rather than lines.

  • When vibrational spectra of gaseous molecules are observed under high-resolution conditions, each band can be found to contain a large number of closely spaced components resulting from rotational energy levels.




Rotational spectroscopy theory1
Rotational Spectroscopy: Theory

  • Rotational energy levels can be described as follows:

For J = 0, 1, 2, 3…

The rotational constant:

The centrifugal distortion coefficient:


c is the speed of light

k is the Hooke’s law force constant

r0 is the vibrationally-averaged bond length

 is the reduced mass

h is Planck’s constant

Example for HCl:

B = 10.4398 cm-1

D = 0.0005319 cm-1

r0 = 1.2887 Å

c = 2990.946 cm-1 (from IR)

k = 5.12436 x 105 dyne/cm-1

R. Woods and G. Henderson, “FTIR Rotational Spectroscopy”, J. Chem. Educ., 64, 921-924 (1987)

Rovibrational Spectroscopy: Theory

  • A vibrational absorption transition from  to +1 gives rise to three sets of rotational lines called branches:

    • Lower-frequency P branch: =1, J=-1

    • Higher-frequency R branch: =1, J=+1

    • Q branch: branch: =1, J=0

The selection rules allow transitions with D= +1 and J = ±1 (the transition with J = 0 is normally not allowed except those with an odd number of electrons (e.g. NO)).



Molecular vibrations total modes
Molecular Vibrations: Total Modes

  • How many vibrational modes are possible in a molecule? A molecule has as many degrees of freedom as the total degree of freedom of its individual atoms. Each atom has three degrees of freedom (corresponding to the Cartesian coordinates), thus in an N-atom molecule there will be 3N degrees of freedom.

  • Translation: the movement of the entire molecule while the positions of the atoms relative to each other remain fixed. There are 3 degrees of translational freedom.

  • Rotational transitions: interatomic distances remain constant but the entire molecule rotates with respect to three mutually perpendicular axes. There are 3 degrees of rotational freedom in a nonlinear molecule and 2 degrees in a linear molecule.

Vibrational modes and ir absorption
Vibrational Modes and IR Absorption

  • For a molecule with N atoms the number of vibrational modes is:

    • Linear: 3N – 5 modes

    • Non-linear: 3N – 6 modes

  • Types of vibrations:

    • Stretching

    • Bending

  • Examples:

    • CO2 has 3 x 3 – 5 = 4 normal modes


No change in dipole



Change in dipole



Change in dipole


  • IR-active modes require molecular dipole moment changes during rotations and vibrations.

Vibrational coupling
Vibrational Coupling

  • Vibrations in a molecule may couple – changing each other’s frequency.

    • In stretching vibrations, the strongest coupling occurs between vibrational groups sharing an atom

    • In bending vibrations, the strongest coupling occurs between groups sharing a common bond

    • Coupling between stretching and bending modes can occur when the stretching bond is part of the bending atom sequence.

    • Interactions are strongest when the vibrations have similar frequencies (energies)

    • Strong coupling can only occur between vibrations with the same symmetry (i.e. between two carbonyl vibrations)

Vibrational modes examples
Vibrational Modes: Examples

  • IR-activity requires dipole changes during vibrations!

  • For example, this is Problem 16-3 from Skoog (6th edition):








Ir spectra formaldehyde
IR Spectra: Formaldehyde

  • Certain types of vibrations have distinct IR frequencies – hence the chemical usefulness of the spectra

  • The gas-phase IR spectrum of formaldehyde:

(wavenumbers, cm-1)

  • Tables and simulation results can help assign the vibrations!

Formaldehyde spectrum from:

Results generated using B3LYP//6-31G(d) in Gaussian 03W.

Ir frequencies and hydrogen bonding effects
IR Frequencies and Hydrogen Bonding Effects

  • IR frequencies are sensitive to hydrogen-bonding strength and geometry (plots of relationships between crystallographic distances and vibrational frequencies):

G. A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford, 1997.

Instrumentation for vibrational spectroscopy
Instrumentation for Vibrational Spectroscopy

  • Two IR Absorption methods:

    • Dispersive methods: Scanning of wavelengths using a grating (common examples are double-beam, like a spectrometer discussed in the optical electronic spectroscopy lecture).

    • Fourier-transform methods: based on interferometry, a method of interfering and modulating IR radiation to encode it as a function of its frequency.














Ir emission spectroscopy
IR Emission Spectroscopy

  • Emission is seldom used for chemical analysis

  • The sample must be heated to a temperature much greater than its surroundings (destroying molecules)

  • IR emission is widely used in astronomy and in remote sensing applications on heated materials.

Fourier transform ir spectroscopy rationale
Fourier Transform IR Spectroscopy: Rationale

  • Advantages of FT methods:

    • The Jacqinot (throughput) advantage: FT instruments have few slits, or other sources of beam attenuation

    • Resolution/wavelength accuracy (Connes advantage): achieved by a colinear laser of known frequency

    • Fellgett (multiplex) advantage: all frequencies detected at once, signal averaging occurs and thermal noise grows more slowly than signal (good with IR detectors)

  • These advantages are critical for IR spectroscopy

  • The need for FT instruments is rooted in the detector

    • There are no transducers that can acquire time-varying signals in the 1012 to 1015 Hz range – they are not fast enough!

  • Why are FT instruments not used in UV-Vis?

    • The multiplex disadvantage (shot noise) adversely affects signal averaging – it is better to multiplex with array detectors (such as the CCD in ICP-OES)

    • In some cases, there are technical challenges to building interferometers with tiny mirror movements

Inteferometers for ft ir and ft raman
Inteferometers for FT-IR and FT-Raman

  • The Michelson interferometer, the product of a famous physics experiment:

Figures from

  • Produces interference patterns from monochromatic and white light


  • For monochromatic radiation, the interferogram looks like a cosine curve

  • For polychromatic radiation, each frequency is encoded with a much slower amplitude modulation

  • The relationship between frequencies:

  • Where:

  • is the frequency of the radiation

    c is the speed of light in cm/s

    vm is the mirror velocity in cm/s

  • Example: mirror rate = 0.3 cm/s modulates 1000 cm-1 light at 600 Hz

  • Example: mirror rate = 0.2 cm/s modulates 700 nm light at 5700 Hz

Ftir spectrometer design
FTIR Spectrometer Design

  • It is possible to build a detector that detects multiple frequencies for some EM radiation (ex. ICP-OES with CCD, UV-Vis DAD)

  • FTIR spectrometers are designed around the Michelson interferometer, which modulates each IR individual frequency with an additional unique frequency well suited to the time response of IR detectors:

Fourier Transform - IR Spectrum

IR Source







Fixed Mirror

Moving Mirror

The basics of the fourier transform
The Basics of the Fourier Transform


  • The conversion from time- to frequency domain:


Time domain

Frequency domain



Ir sampling methods absorbance methods
IR Sampling Methods: Absorbance Methods

  • KBr/CsI pellet: a dilute (~1%) amount of sample in the halide matrix is pressed at >10000 psi to form a transparent disk.

    • Disadvantages: dilution required, can cause changes in sample

  • Mulls: Solid dispersion of sample in a heavy oil (Nujol)

    • Disadvantages: big interferences

  • Salt plates (NaCl): for liquids (a drop) and small amounts of solids. Sample is held between two plates or is squeezed onto a single plate.

  • Cells: For liquids or dissolved samples. Includes internal reflectance cells (CIRCLE cells)

Common IR Solvents

The horizontal lines indicate regions where solvent transmits at least 25% of the incident radiation in a 1 mm cell.

Ir sampling methods reflectance methods
IR Sampling Methods: Reflectance Methods

  • Specular reflection: direct reflection off of a flat surface.

    • Grazing angles

  • Attenuated total reflection (ATR): Beam passed through an IR-transparent material with a high refractive index, causing internal reflections.

    • Depth is ~2 um (several wavelengths)

  • Diffuse reflection (DRIFTS): a technique that collects IR radiation scattered off of fine particles and powders.Used for both surface and bulk studies.



Figures from

Hybrid hyphenated techniques interfaces
Hybrid/Hyphenated Techniques: Interfaces

  • Interfaces between vibrational spectrometers and other analytical instruments are possible

  • Example: In GC-FTIR, gaseous GC column effluent is passed through “light pipes”

  • Another Example: TGA-IR, for identification of evolved gases from thermal decomposition

Figure from Skoog et al.

Ir detectors
IR Detectors

  • Thermal transducers

    • Response depends upon heating effects of IR radiation (temperature change is measured)

      • Slow response times, typically used for dispersive instruments or special applications

  • Pyroelectric transducers

    • Pyroelectric: insulators (dielectrics) which retain a strong electric polarization after removal of an electric field, while they stay below their Curie temperature.

    • DTGS (deuterated triglycine sulfate): Curie point ~47°C

      • Fast response time, useful for interferometry (FTIR)

  • Photoconducting transducers

    • Photoconductor: absorption of radiation decreases electrical resistance. Cooled to LN2 temperatures (77K) to reduce thermal noise.

    • Mid-IR: Mercury cadmium telluride (MCT)

    • Near-IR: Lead sulfide (NIR)

Interpretation of ir spectra
Interpretation of IR Spectra

  • General Features:

    • Stretching frequencies are greater (higher wavenumbers) than corresponding bending frequencies

      • It is easier to bend a bond than to stretch it

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

      • Hydrogen is a much lighter element

    • Triple bonds have higher stretching frequencies than double bonds, which have higher frequencies than single bonds

  • Strong IR bands often correspond to weak Raman bands and vice-versa

Interpretation of ir and raman spectra
Interpretation of IR and Raman Spectra

Characteristic Vibrational Frequencies for Common Functional Groups

See also Table 17-2 of Skoog, et al.

More detailed lists are widely available. See R. M. Silverstein and F. X. Webster, “Spectrometric Identification of Organic Compounds”, 6th Ed., Wiley, 1998.

Ir and raman spectra of an organic compound
IR and Raman Spectra of an Organic Compound

The diamond ATR IR spectrum of tranilast (polymorphic Form I):

Ir and raman spectra of an organic compound1
IR and Raman Spectra of an Organic Compound

The diamond ATR IR spectrum of flufenamic acid (an analgesic/anti-inflammatory drug):

Far ir spectroscopy in condensed phases
Far IR Spectroscopy in Condensed Phases

  • Far IR is used to study low frequency vibrations, like those between metals and ligands (for both inorganic and organometallic chemistry).

    • Example: Metal halides have stretching and bending vibrations in the 650-100 cm-1range.

    • Organic solids show “lattice vibrations” in this region

  • Can be used to study crystal lattice energies and semiconductor properties in solids via phonon modes.

  • The far IR region also overlaps rotational bands, but these are normally not detectable in condensed-phase work

Terahertz spectroscopy
Terahertz Spectroscopy

  • A relatively new technique, addresses an unused portion of the EM spectrum (the “terahertz gap”):

    • 50 GHz (0.05 THz) to 3 THz (1.2 cm-1 to 100 cm-1)

  • Made possible with recent innovations in instrument design, accesses a region of crystalline phonon bands

P. F. Taday and D. A. Newnham, Spectroscopy Europe, ,

G. Winnewisser, Vibrational Spectroscopy 8 (1995) 241-253

Applications of ft microwave spectroscopy
Applications of FT Microwave Spectroscopy

  • Under development for: real-time, sensitive monitoring of gases evolved in process chemistry, plant and vehicle emissions, etc…

    • Current techniques have limits (GC, IR, MS, IMS)

    • Normally use pulsed-nozzle sources and high-precision Fabry-Perot interferometers (PNFTMW)

Diagram from

For more information, see E. Arunan, S. Dev. And P. K. Mandal, Applied Spectroscopy Reviews, 39, 131-181 (2004).

New methods in ft microwave spectroscopy
New Methods in FT Microwave Spectroscopy

  • A new method using a “chirp” pulse (which excites a wide range of frequencies) has been developed by the Pate group at U. Virginia Charlottesville

    • The CP-FTMW (chirped pulse FT microwave) method enhances sensitivity by 100 to 10000 times and allows for studies of molecular shape changes (occurring on picosecond timescales)

Diagram from B. H. Pate et al., Science, 2008, 320, 924

See C&E News:

Applications of near ir spectroscopy
Applications of Near IR Spectroscopy

  • Near IR (NIR) is heavily used in process chemistry and materials identification

  • Amenable to quantitative analysis usually in conjunction with chemometrics (calibration requires many standards to be run)

  • While not a popular qualitative technique, it can serve as a fast and useful quantitative technique especially using diffuse reflectance

  • Accuracy and precision in the ~2% range

  • Examples:

    • On-line reaction monitoring (food, agriculture, pharmaceuticals)

    • Moisture and solvent measurement and monitoring

      • Water overtone observed at 1940 nm

    • Solid blending and solid-state issues

Near ir spectroscopy
Near IR Spectroscopy

Figure from For more information see:

1. Ellis, J.W. (1928) “Molecular Absorption Spectra of Liquids Below 3 m”, Trans. Faraday Soc. 1928, 25, pp. 888-898.

2. Goddu, R.F and Delker, D.A. (1960) “Spectra-structure correlations for the Near-Infrared region.” Anal. Chem., vol. 32 no. 1, pp. 140-141.

3. Goddu, R.F. (1960) “Near-Infrared Spectrophotometry,” Advan. Anal. Chem. Instr. Vol. 1, pp. 347-424.

4. Kaye, W. (1954) “Near-infrared Spectroscopy; I. Spectral identification and analytical applications,” Spectrochimica Acta, vol. 6, pp. 257-287.

5. Weyer, L. and Lo, S.-C. (2002) Spectra-Structure Correlations in the Near-infrared, In Handbook of Vibrational Spectroscopy, Vol. 3, Wiley, U.K., pp. 1817-1837.

6. Workman, J. (2000) Handbook of Organic Compounds: NIR, IR, Raman, and UV-Vis Spectra Featuring Polymers and Surfactants, Vol. 1, Academic Press, pp. 77-197.

Near ir spectrum of acetone
Near IR Spectrum of Acetone


  • NIR taken in transmission mode (via a reflective gold plate) on a Foss NIRsystems spectrometer

  • Useful for quick solvent identification

Near ir spectrum of water 1 st derivative
Near IR Spectrum of Water (1st Derivative)


  • 1st derivative (and 2nd derivative) allows for easier identification of bands

Photoacoustic spectroscopy
Photoacoustic Spectroscopy

  • First discovered in 1880 by A. G. Bell

  • When radiation is absorbed, the energy is converted to heat, causing expansion and contraction of the sample at the modulation frequency which is transferred to the surrounding air. Can be detected with a microphone.

  • The IR “version” of photoacoustic sampling is generally applied to two types of system

IR Radiation

  • All gas (or all-liquid) systems:

  • The solid-gas system:


IR Radiation

IR-Transparent Gas


A. G. Bell, Am. J. Sci. 20 (1880)305.

A. G. Bell, Philos. Mag. 11(1881),510.

The photoacoustic effect for solid gas systems
The Photoacoustic Effect for Solid-Gas Systems

  • The photoacoustic effect is produced when intensity-modulated light hits a solid surface (or a confined gas or liquid).

Modulated IR Radiation

PA Cell









Thermal Wave (attenuates rapidly)

IR is absorbed by a vibrational transition,

followed by non-radiative relaxation

J. F. McClelland. Anal. Chem.55(1), 89A-105A (1983)

M. W. Urban. J. Coatings Technology.59, 29 (1987).

The thermal diffusion length solids
The Thermal Diffusion Length –Solids

  • The thermal diffusion length is:

0.15 cm/sec IR

1.2 cm/sec IR



  • The thermal diffusivity a is:

 - thermal diffusion length

 =  / 2 

  • The variable , the modulation frequency of the IR radiation, is directly proportional to interferometer mirror velocity, and is defined as:

Urban, M. W. J. Coatings Technology.1987, 59, 29

Quintanilla, L., Rodriguez-Cabello, J. C., Jawhari, T. and Pastor, J. M.. Polymer. 1993, 34, 3787.

The thermal diffusion length
The Thermal Diffusion Length

  • The mirror velocity is therefore inversely related to the thermal diffusion length, and therefore can be used to control the maximum sampling depth.

  • Typical thermal diffusion lengths for the carbonyl band (~1750 cm-1) of poly(ethylene terephthalate):

The thermal diffusivity was taken to be 1.3 * 10-3 cm2/sec, and the absorption coefficient of the carbonyl band was assumed to be 2000 cm-1.

Urban, M. W. and Koenig, J. L. Appl. Spec. 1986, 40, 994.

Quintanilla, L., Rodriguez-Cabello, J. C., Jawhari, T. and Pastor, J. M.. Polymer. 1993, 34, 3787.

A typical photoacoustic ftir spectrum
A Typical Photoacoustic FTIR Spectrum

A PA-FTIR Spectrum of a silicone sealant:

IR Modulation frequency is high

IR Modulation frequency is low

  • The spectrum shows peaks where the IR radiation is being absorbed due to vibrational energy level transitions.

  • Differences between a PA-FTIR spectrum and a regular IR spectrum:

    • IR modulation frequency effects (weak CH3 and CH2 bands)

    • Saturation of strong bands in the spectrum

Paroli, R. M., Delgado, A. H., and Cole, K. C. Canadian J. Appl. Spectr. 1994, 39, 7.

Photoacoustic saturation
Photoacoustic Saturation

A Saturated Band

  • Strong bands in PA-FTIR spectra often show saturation.

  • Saturation occurs when the vibrational transition is being pumped to its excited state faster than it can release energy.

  • A high absorption coefficient coincides with faster saturation.

Rosencwaig, A. Photoacoustics and Photoacoustic Spectroscopy. Wiley: New York, 1980.

Paroli, R. M., Delgado, A. H., and Cole, K. C. Canadian J. Appl. Spectr. 1994, 39, 7.

Depth profiling studies with pa ftir
Depth-Profiling Studies with PA-FTIR

  • Thermal diffusion length allows for IR depth profiling with PA-FTIR

  • Example: a layer of poly(vinylidine fluoride (PVF2) on poly(ethylene terephthalate) (PET)

0.15 cm/sec IR

1.2 cm/sec IR



PVF2 top layer is 6 micrometers thick.

The carbonyl band, due to the PET, is marked with a red dot ().

Data acquired with a Digilab FTS-20E with a home-built PA cell.

 - thermal diffusion length

 =  / 2 

Urban, M. W. and Koenig, J. L. Appl. Spec.1986, 40, 994.

Crocombe, R. A. and Compton, S. V. Bio-Rad FTS/IR Application Note 82. Bio-Rad Digilab Division, Cambridge, MA, 1991.

Ir microscopy
IR Microscopy

  • Most FTIR microscopes image using array detectors

  • IR spectra from a region are acquired at once, better S/N

    • However, this is at the expense of resolution (limited to ca. 10 um), in contrast with scanning techniques. Resolution in FTIR imaging is of course limited by the diffration limit, which is even worse for IR wavelengths.

Figure from J. L. Koenig, S. Q. Wang, and R. Bhargava, Anal. Chem.,73, 361A-369A (2001).

Ir microscopy image analysis
IR Microscopy: Image Analysis

  • Extraction of data from FTIR micrographs is done by color-coding peaks based on their IR frequency (a)

  • Suitable IR frequencies can be chosen via a scatter plot (c) of every point in the image vs. two (or more) frequencies, followed by location of the center-of-gravity and possible statistical analysis

  • False color images can then be constructed (b)

Figure from J. L. Koenig, S. Q. Wang, and R. Bhargava, Anal. Chem.,73, 361A-369A (2001).

Ir microscopy polymer chemistry applications
IR Microscopy: Polymer Chemistry Applications

  • FTIR microscopy can analyze compositional differences in material science, chemical and biochemical applications

  • Example – the study of time-dependent processes like dissolution of a polymer by a solvent

Figure from J. L. Koenig, S. Q. Wang, and R. Bhargava, Anal. Chem.,73, 361A-369A (2001).

Ir microscopy polymer chemistry applications1
IR Microscopy: Polymer Chemistry Applications

  • A complex, solvent-dependent dissolution, diffusion and molecular motion process is observed for polymers (e.g. polymethylstyrene) above their entanglement mwt:

Figure from J. L. Koenig, S. Q. Wang, and R. Bhargava, Anal. Chem.,73, 361A-369A (2001).

Vibrational circular dichroism
Vibrational Circular Dichroism

  • Analogous to electronic (UV-visible) circular dichroism (ECD), VCD measures the differential absorption of right and left-handed circularly polarized IR radiation

  • Much less sensitive than ECD, but much higher information content (many more bands show effects linked to chirality)

VCD of -pinene



Further reading
Further Reading


L. J. Bellamy, Advances in Infrared Group Frequencies, Methuen and Co., 1968.

R. M. Silverstein and F. X. Webster, Spectrometric Identification of Organic Compounds, 6th Ed., Wiley, 1998.

P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics, 3rd. Ed., Oxford, 1997.