Introduction to Basics of Raman Spectroscopy

Introduction to Basics of Introduction to Basics of Raman SpectroscopyRaman Spectroscopy

Chandrabhas NarayanaChandrabhas NarayanaChemistry and Physics of Materials

Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India

[email protected]://www.jncasr.ac.in/cbhas

Lecture at Lecture at MASTANI Summer School, IISER, Pune, June 30, 2014 to July 12, 2014MASTANI Summer School, IISER, Pune, June 30, 2014 to July 12, 2014July 11, 2014July 11, 2014

What happens when light falls on a material?

Transmission

Reflection

Absorption

Luminescence

Elastic Scattering

Inelastic Scattering

Raman SpectroscopyRaman Spectroscopy1 in 101 in 1077 photons is scattered inelastically photons is scattered inelastically

Infrared(absorption)

Raman(scattering)

v” = 0

v” = 1

virtualstate

Exc

itat

ion

Sca

tter

ed

Rotational RamanRotational RamanVibrational RamanVibrational RamanElectronic RamanElectronic Raman

Raman visible through unaided eye

Raman, Fluorescence and IRRaman, Fluorescence and IRScattering

Absorptionand emission Absorption

Concept of normal modes in a molecule

• There are 3N possible movements in a molecule made of N atoms, each of which moving in one of three directions, x, y and z.– There are three transitional movements: all atoms in the

molecule moving in x, y or z direction at the same time.– There are three rotational movements around x, y or z-axis

• Linear molecules are exceptions because two axes that are perpendicular to the molecular axis are identical.

– The rest of movements are vibrational movements• For linear molecules, 3N – 5 movements• For non-linear molecules, 3N – 6 movements

– All vibrational movements of the sample can be described as linear combinations of vibrational normal modes.

Vibrations in MoleculesVibrations in MoleculesHClHCl HFHF

HH22OO

NHNH33

SFSF66

Sym. StretchingSym. Stretching

Asym. StretchingAsym. Stretching Sym. BendingSym. Bending

Asym. BendingAsym. Bending

1 = 3835 cm-1 2 = 1648 cm-13 = 3939 cm-1

= 2991 cm-1 = 4139 cm-1

1 = 3505.7 cm-1 2 = 1022 cm-13 = 3573.1 cm-1

1 = 774.55 cm-1 4 = 523.56 cm-13 = 947.98 cm-1

5 = 643.35 cm-1 6 = 348.08 cm-12 = 615.02 cm-1

4 = 1689.7 cm-1

8086 cm-1 = 1 eV

Vibrational SpectroscopyVibrational Spectroscopy

re = equilibrium distance between A and B

re

For a diatomic molecule (A-B), the bond between the two atoms can be approximated by a spring that restores the distance between A and B to its equilibrium value. The bond can be assigned a force constant, k (in Nm-1; the stronger the bond, the larger k) and the relationship between the frequency of the vibration, , is given by the relationship:

DAB

rAB0

DAB = energy required to dissociate into A and B atoms

k

2

ck

or, more typically

where , c is the speed of light, is the frequency in “wave numbers” (cm-1) and is the reduced mass (in amu) of A and B given by the equation:

m m

m mA B

A B

Vibrational Spectroscopy

Molecule (cm-1) k (N/m) (amu)

HF 3962 878 19/20

HCl 2886 477 35/36 or 37/38

HBr 2558 390 79/80 or 81/82

HI 2230 290 127/128

Cl2 557 320 17.5

Br2 321 246 39.5

CO 2143 1855 6.9

NO 1876 1548 7.5

N22331 2240 7

2

ck

can be rearranged to solve for k (in N/m): k 5 89 10 5 2.

For a vibration to be active (observable) in an infrared (IR) spectrum, the vibration must change the dipole moment of the molecule. (the vibrations for Cl2, Br2, and N2 will not be observed in an IR experiment)

For a vibration to be active in a Raman spectrum, the vibration must change the polarizability of the molecule.

Classical Picture of RamanClassical Picture of Raman

Stokes RamanAnti-Stokes Raman

Induced Polarization Polarizability

Mutually exclusive principleMutually exclusive principle

max 0

max max 0

max max 0

( ) cos 2

1cos 2 ( )

21

cos 2 ( )2

equilz zz

zzvib

zzvib

t E t

dr E t

drd

r E tdr

www.andor.comwww.andor.com

Selection rule: Selection rule: v = ±1v = ±1Overtones: Overtones: v = ±2, ±3, …v = ±2, ±3, …

Raman ScatteringRaman Scattering

Must also have a change in polarizabilityMust also have a change in polarizability

Classical Description does not suggest any difference Classical Description does not suggest any difference between Stokes and Anti-Stokes intensitiesbetween Stokes and Anti-Stokes intensities

1

0

vibh

kTN

eN

Calculate the ratio of Anti-Stokes to Stokes scattering Calculate the ratio of Anti-Stokes to Stokes scattering intensity when T = 300 K and the vibrational frequency is intensity when T = 300 K and the vibrational frequency is 1440 cm1440 cm-1-1..

Are you getting the concept?Are you getting the concept?

h = 6.63 x 10h = 6.63 x 10-34-34 Js Jsk = 1.38 x 10k = 1.38 x 10-23-23 J/K J/K

1

0

vibh

kTN

eN

~ 0.5

Energy diagram and Energy diagram and Quantum pictureQuantum picture

Vibrational statesElectronic states

Virtual states

g

ex

photon

<eg,p2|Her|p2,eb> <eb,p2|Hep|p1,ea> <ea,p1|Her|p1,eg>

|Es-Eb|x|Ei-Ea|a,b

Raman cross section

If Ei = Ea or Es = Eb

We have Resonance Raman effect

Intensity of Normal Raman Peaks

The intensity or power of a normal Raman peak depends in a complex way upon

• the polarizability of the molecule, • the intensity of the source, and • the concentration of the active group. • The power of Raman emission increases with

the fourth power of the frequency of the source; - photodecomposition is a problem.

• Raman intensities are usually directly proportional to the concentration of the active species.

Raman Depolarization Ratios

Polarization is a property of a beam of radiation and describes the plane in which the radiation vibrates. Raman spectra are excited by plane-polarized radiation. The scattered radiation is found to be polarized to various degrees depending upon the type of vibration responsible for the scattering.


The depolarization ratio p is defined as

Experimentally, the depolarization ratio may be obtained by inserting a polarizer between the sample and the monochromator. The depolarization ratio is dependent upon the symmetry of the vibrations responsible for scattering.

pI

I


Polarized band: p = < 0.76 for totally symmetric modes (A1g)

Depolarized band: p = 0.76 for B1g and B2g

nonsymmetrical vibrational modes

Anomalously polarized band: p = > 0.76 for A2g vibrational modes

Raman spectra of CClRaman spectra of CCl44

Isotope effectCl has two isotopes 35Cl and 37ClRelative abundance is 3:1

CClCCl44 Spectra Spectra

• 461.5 cm-1 is due to 35Cl4C

• 458.4 cm-1 is due to 35Cl337ClC

• 455.1 cm-1 is due to 35Cl237Cl2C

• What are the two question marks?

• Why are these bands weak?

Raman Spectra of Methanol and EthanolRaman Spectra of Methanol and Ethanol

20000

15000

10000

5000

0

500 1000 1500 2000 2500 3000 3500

OHstretching

CHstretching

CO stretching

CH3

deformation

Raman Shift (cm-1)

Ram

an Intensity (a

rbitrary unit)

CCOstretching

CH3 and CH2

deformation

Significant identification of alcohols which differ just in one CH2-group

CASR

Peak position – Chemical identity – Peak position – Chemical identity – Similar StructuresSimilar Structures

3,4-Methylenedioxymethamphetamine (MDMA) Methamphetamine

500 1000 1500 2000 2500 3000 3500

Raman Shift (cm-1)

Ra

ma

n In

ten

sity (arb

itrary

un

it)

CASR

ecstasy

1200

1000

800

600

400

200

0

Inte

nsit

y (c

ount

s/s)

Wavenumber (cm-1)

1000

800

600

400

200

Inte

nsit

y (c

ount

s/s)

Wavenumber (cm-1)

Mg - SO4

Na2 - SO4

The Mass Effect on Raman SpectraThe Mass Effect on Raman Spectra

Significant identification of salts (SO42-) which

differ just in the metal ion employed

CASR

Peak positions – Chemical identity Peak positions – Chemical identity DiasteromersDiasteromers

PseudoephedrineEphedrine

500 1000 1500 2000 2500 3000 3500Raman Shift (cm-1)

Ra

ma

n In

ten

sity (arb

itrary

un

it)

CASR

Peak Position – Crystal Phases – Polymorphs

200

400

600

800

1 000

1 200

1 400

1 600

1 800

2 000

2 200

2 400

Inte

ns

ity

(c

nt)

200 400 600 800 1 000 1 200 1 400Raman Shift (cm-1)

Both Anatase and Rutile are TiO2 but of different polymorphic forms - identical chemical composition, different crystalline structures.

Rutile

Anatase

Peak Shift – Stress and StrainPeak Shift – Stress and Strain

Nasdala, L., Harris, J.W. & Hofmeister, W. (2007): Micro-spectroscopy of diamond. Asia Oceania Geosciences Society, 4th Annual Meeting, Bangkok, Thailand, August, 2007.Nasdala, L., Raman barometry of mineral inclusions in diamond crystals. Mitt. Österr. Miner. Ges. 149 (2004)

CASRLarnite ( – Ca2SiO4) inclusion in Diamond

Bandwidth – Crystallinity – Bandwidth – Crystallinity – Structural order/disorderStructural order/disorder

Raman spectra of zircon, showing typical amorphous (blue) and crystalline (red) spectra.

CASR

Intensity – ConcentrationIntensity – Concentration4-Nitrophenol dissolved in CH2Cl2

0

500

1 000

1 500

2 000

2 500

3 000

3 500

Inte

nsi

ty (

cnt/

sec)

1 200 1 400 1 600Raman Shift (cm-1)

4-Nitrophenol in CH2Cl2_0,1 M4-Nitrophenol in CH2Cl2_0,01 M4-Nitrophenol in CH2Cl2_0,001 M

13

41

.0

CASR

Raman technique – what Raman technique – what requirements are needed? requirements are needed?

Requirements for Raman technique to determine peak position, peak shift, bandwidth and intensity

- Laser Excitation- Reduction of stray light- Collecting Optics- Spectral resolution and spectral coverage- Spatial resolution and confocality- Sensitivity: subject to detector- Light flux: subject to dispersion

CASR

What do we need to make a What do we need to make a Raman measurement ?Raman measurement ?

LaserSample

Filter

Grating

Detector

•Rejection filter (A way of removing the scattered light that is not shifted( changed in colour).

(A way of focusing the laser onto the sample and then collecting the Raman scatter.)•Sampling optics

•Monochromatic Light source typically a laser

•Spectrometer and detector(often a single grating spectrometer and CCD detector.)

CASR

Demonstration of the very high Demonstration of the very high spectral resolution obtained in the spectral resolution obtained in the triple additive modetriple additive mode

8000

6000

4000

2000

Inte

nsit

y (a

.u.)

1520 1540 1560 1580

Wavenumber (cm-1)

Triple additive modeSlit widths= 30 m

Rotation-Vibration Spectrum of O2

Triple subtractive mode . Slit=30 m

CASR

Laser excitation – Laser Selection to Laser excitation – Laser Selection to avoid fluorescence avoid fluorescence

Laser wavelength, 1

Raman shift, 1-1+

Laser wavelength, 3 Raman shift, 3-1+

Laser wavelength, 3 Fluorescence

Laser wavelength: 3 < 2 < 1

CASR

Laser excitation – Laser selection to Laser excitation – Laser selection to avoid fluorescence avoid fluorescence

0

10 000

20 000

30 000

40 000

50 000

60 000

Inte

ns

ity

(c

nt)

600 800 1 000Wavelength (nm)

Green spectrum: 532 nm laserRed spectrum: 633 nm laserDark red spectrum: 785 nm laser

Fluorescence is wavelength dependentOrdinary Raman is wavelength independent

0

10 000

20 000

30 000

40 000

50 000

60 000

Inte

ns

ity

(c

nt)

1 000 2 000 3 000Raman Shift (cm-1)

CASR

Commercial Hand Cream

785 nm – 633 nm – 473 nm

x10 3

5

10

15

20

25

30

35

40

45

Inte

nsity

(cn

t)

500 1 000 1 500 2 000 2 500 3 000 3 500Raman Shift (cm-1)

Reduction of Fluorescence

CASR Laser excitation – Laser selection to Laser excitation – Laser selection to avoid fluorescence avoid fluorescence

Laser excitation – laser radiation Laser excitation – laser radiation power power

Laser wavelength: 473 nm

Laser power at sample: 25.5 mW

Objective N.A. Laser spot size

(µm)

Radiation power

(kW/cm2)

100× 0.90 0.64 ~7900

50× 0.75 0.77 ~5400

10× 0.25 2.31 ~600

Laser wavelength: 633 nm

Laser power at sample: 12.6 mW

Objective N.A. Laser spot size (µm)

Radiation power (kW/cm2)

100× 0.90 0.85 ~2200

50× 0.75 1.03 ~1500

10× 0.25 3.09 ~200

CASR

Laser excitation – laser radiation Laser excitation – laser radiation powerpower

• Keep in mind: the usage of high numerical objective lenses causes a very small spot size of the laser which results in a high power density

• To avoid sample burning radiation power has to be adapted INDIVIDUALY to the sample

CASR

Collecting OpticsCollecting Optics

Sampling volumeSmall for high N.A. lensLarge for low N.A. lens

Laser spot sizeSmall for high N.A. lensLarge for low N.A. lens

Collection solid angleLarge for high N.A. lensSmall for low N.A. lens High N.A. lens

θ

Low N.A. lens

θ

NA = n · sin ()

n: refraction index

: aperture angle

Wo

rkin

g

dis

tan

ce

Wo

rking

d

istance

CASR

Collecting Optics – Overview on Collecting Optics – Overview on common objectivescommon objectives

Objective N.A.Working distance

[mm]

x100 0.90 0.21

x50 0.75 0.38

x10 0.25 10.6

x100 LWD 0.80 3.4

x50 LWD 0.50 10.6

CASR

Collecting Optics – what objective Collecting Optics – what objective should be used?should be used?

A distinction between opaque and transparent samples has to be made

For opaque samples, high N.A. lens works better because there is almost no penetration of the laser into the sample. High N.A. lens enables

- High laser power density (mW/m3) increases sensitivity- Wide collection solid angle increases sensitivity

0

5 000

10 000

15 000

20 000

25 000

30 000

Inte

ns

ity (

cnt

/sec

)

460 480 500 520 540 560 580 600 620Raman Shif t (cm-1)

Siliconx100 – NA = 0.9 – 31.350 C/sx50 – NA = 0.75 - 21.995 C/sx10 – NA = 0.25 - 1.462 C/s

100 %

70 %

5 %

-20

0

20

Y (

µm

)

0X (µm)

10 µm

Example for an opaque sample:Silicon wafer

CASR

Collecting Optics – what objective Collecting Optics – what objective should be used?should be used?

A distinction between opaque and transparent samples has to be made

For transparent samples, low N.A. lens works better because of penetration of the laser into the sample. Low N.A. lens enables

- Large sampling volume increases sensitivity

x103

0

2

4

6

8

10

12

14

Inte

nsity

(cn

t)

740 760 780 800 820 840 860 880Raman Shift (cm-1)

cyclo_100xLWDcyclo_macroSample: Cyclohexane

Instrument: ARAMISRed: x100LWD, 7,000 cts/sBlue: Macro lens, 14,500 cts/s

100 %

48 %

CASR

Spectral resolution and spectral Spectral resolution and spectral coveragecoverage

Slit

Detect

or

Focal Length

Collimating mirror

Focusing mirror

Grating

Schematic diagram of a Czerny-Turner spectrograph

CASR

Spectral resolution and spectral Spectral resolution and spectral coveragecoverage

• Spectral resolution is a function of 1. dispersion, 2. widths of entrance slit and 3. pixel size of the CCD

• Dispersion is the relation between refraction of light according to the wavelength of light

• Dispersion is a function of the 1. focal length of spectrograph the 2. groove density of the grating and 3. the excitation wavelength

• In general, long focal length and high groove density grating offer high spectral resolution.

CASR

Dispersion as a function of the focal Dispersion as a function of the focal lengthlength

Same gratingSame excitation wavelength

CC

D D

ete

cto

rC

CD

Det

ect

or

Long focal length

Short focal length

CASR

Dispersion as a function of the focal Dispersion as a function of the focal length vis-a vis wavelengthlength vis-a vis wavelength

Dispersion in cm-1 / pixel1800 gr/mm GratingLabRAM (F = 300 mm)LabRAM HR (F = 800 mm)

CASR

200 400 600 800 1000 1200 1400 1600 1800

244 - 269 nm (25 nm) 325 - 371 nm (46 nm) 457 - 553 nm (96 nm) 488 - 599 nm (111 nm) 514 - 639 nm (125 nm) 532 - 667 nm (135 nm) 633 - 833 nm (200 nm) 785 - 1119 nm (334 nm) 830 - 1210 nm (380 nm) 1064 - 1768 nm (704 nm)

Horizontal lines indicate a relative Raman Shift of 3800 cm-1

Wavelength [nm]

Dispersion as a function of excitation Dispersion as a function of excitation wavelengthwavelength

Long wavelengthShort wavelength

Same focal lengthSame grating

CC

D D

ete

cto

r

CC

D D

ete

cto

r

CASR

Spectral coverage - dependence from Spectral coverage - dependence from excitation wavelengthexcitation wavelength

Length of CCD Chip

x10 3

0

2

4

6

8

10

12

14

16

18

20

22

Inte

nsi

ty (

cnt/

sec)

500 600 700 800 900 1 000Wavelength (nm)

Relative Raman shift of 3100 cm-1

corresponds to 81 nm

Relative Raman shift of 3100 cm-1

corresponds to 154 nm Relative Raman shift of 3100 cm-1

corresponds to 252 nm

473 nm – 633 nm – 785 nm

Same focal lengthSame grating

Length of CCD Chip

Length of CCD Chip

CASR

Dispersion as a function of groove densityDispersion as a function of groove density

High density groove grating

Low density groove grating

CC

D D

ete

cto

r

CC

D D

ete

cto

r

Same focal lengthSame excitation wavelength

CASR

Spectral resolution as a function slit Spectral resolution as a function slit widthwidth

Slit Slit Slit

One of parameters that determines the spectral resolution is the entrance slit width. The narrower the slit, the narrower the FWHM (full width at half maximum), and higher the spectral resolution.

When recording a line whose natural width is smaller than the monochromator’s resolution, the measured width will reflect the spectrograph’s resolution.

CASR

Spectral resolution as a function of pixel Spectral resolution as a function of pixel sizesize

• Because a CCD detector is made of very small pixels, each pixel serves as an exit slit (pixel size = exit slit width)

• For the same size CCDs, the CCD with a larger number of smaller pixels produces a larger number of spectral points closer to each other increasing the limiting spectral resolution and the sampling frequency

• 26 m pixel vs. 52 m pixel (simulation)

Inte

ns

ity

600 650 700Raman Shift (cm-1)

Detect

or

Detect

or

CASR

Choice of Laser for RamanChoice of Laser for Raman

The choice of laser will influence different parameters:

• Signal Intensity: (1/4 rule applies to Raman intensity.

• Probing volume: spot size and material penetration depth.

• Fluorescence: may overflow Raman signal.

• Enhancement: some bounds only react strongly at a certain wavelength.

• Coverage range and Resolution: grating dispersion varies along the spectral range.

0,001

0,01

0,1

1

10

100

200 300 400 500 600 700 800 900P

en

etr

ati

on

de

pth

(µ

m)

Wavelength (nm)

Silicium

CASR

Spatial resolution: penetration depthSpatial resolution: penetration depth

0

500

1000

1500

2000

2500

3000

244 nm 325 nm 457 nm 488 nm 514 nm 633 nm

Wavelength [nm]

Dep

th p

en

etr

ati

on

[n

m]

General: The larger the excitation wavelength, the deeper the penetration.

The exact values depend on material.

Penetration depth in Silicon0

2

4

6

8

10

12

244 nm 325 nm

CASR

250 300 350 400 450 500 550

Inte

nsi

ty [a

.u.]

Raman shift (cm-1)

785 nm


Uniform layer of SiGe

Gradient SiGe layer

Pure Si substrate

Strained silicon layer

250 300 350 400 450 500 550

Inte

nsi

ty [a

.u.]

Raman shift (cm-1)

325 nm 488 nm 785 nm

The higher the excitation wavelength, the deeper the penetration.

488 nm

250 300 350 400 450 500 550

Inte

nsi

ty [a

.u.]

Raman shift (cm-1)

325 nm

Strained Si of top layer

Si of silicon substrate

Si of SiGe layer

~nm

~nm

~µm

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EXAMPLE

325nm laser results

The strain is not homogenous.

A characteristic, cross-hatch pattern is observed.

CASR

D = 1.22 / NA

Laser spot size D is defined by the Rayleigh criterion:

excitation wavelength ()

objective numerical aperture (NA)

With NA=n sinα

Spatial resolution and spot sizeSpatial resolution and spot size

Spatial resolution is half of the laser spot diameter

CASR

Sample

Length ofLaser Focus

Nearly closedconfocal apertur

P P '

P '

P P 'P

Image P ' of laser focus P matchesexactly the confocal hole.

Confocality and Spatial ResolutionConfocality and Spatial ResolutionCASR

CASR

Axial resolution of a Confocal Raman Microprobe Axial resolution of a Confocal Raman Microprobe

Confocal z-scan against siliconwith different hole aperturesexc = 633 nm

Sampling Volume

Wide Hole Laser focus waist diameter

Depth of laser focus(d.o.f)

Narrow Hole

Narrow Hole: Collecting Raman radiation that originates only from within a diffraction limited laser focal volume with a dimension of:

Focus waist diameter ~ 1.22 / NADepth of laser focus ~ 4 / (NA)2

Confocality and spatial Confocality and spatial ResolutionResolution

CASR

Example of application using the confocality Example of application using the confocality principle : depth profile on a multilayer polymer principle : depth profile on a multilayer polymer sample sample

5000

4000

3000

2000

1000

0

Intensity (a.u.)

1000 1200 1400 1600

Wavenumber (cm-1)

3000

2500

2000

1500

1000

500

0Intensity (a.u.)

1000 1200 1400 1600

Wavenumber (cm-1)

75 m

Polyethylene

Polyethylene

nylon

z

x

CASR

Thank you for your attention!

Symmetry – Identity (E)Symmetry – Identity (E)Identity operation (E)This is a very important symmetry operation which is where the molecule is rotated by 360º. In otherwords a full rotation or doing nothing at all.This appears in all molecules!!!

Symmetry – Rotation (CSymmetry – Rotation (Cnn))Rotations (Cn)These are rotations about the axes of symmetry. n denotes 360º divided by the number for the rotation.

C2 = 180º C3 = 120º C4 = 90º C5 = 72º C6 = 60º

Symmetry – Symmetry – Reflections (Reflections ())Reflections (h, d and v) These are reflections in a symmetry planes (x, y and z).

h - Horizontal Plane (y)perpendicularto the highest rotation axis

v - Vertical Plane (z)parallelto the highest rotation axis

d - Diagonal (dihedral) Plane (x)the Diagonal Plane that bisects two axes

Symmetry – Inversion (i)Symmetry – Inversion (i)

Inversion centre (i)These are where the molecule can be inverted through the centre of the molecule (atom or space).

Symmetry – Improper Rotation (SSymmetry – Improper Rotation (Snn))

Improper rotations (Sn)These are rotations about the axes of symmetry followed by reflections.

Vibrational SpectroscopyVibrational Spectroscopy

For polyatomic molecules, the situation is more complicated because there are more possible types of motion. Each set of possible atomic motions is known as a mode. There are a total of 3N possible motions for a molecule containing N atoms because each atom can move in one of the three orthogonal directions (i.e. in the x, y, or z direction).

Translational modes

Rotational modes

A mode in which all the atoms are moving in the same direction is called a translational mode because it is equivalent to moving the molecule - there are three translational modes for any molecule.

A mode in which the atoms move to rotate (change the orientation) the molecule called a rotational mode - there are three rotational modes for any non-linear molecule and only two for linear molecules.

The other 3N-6 modes (or 3N-5 modes for a linear molecule) for a molecule correspond to vibrations that we might be able to observe experimentally. We must use symmetry to figure out what how many signals we expect to see and what atomic motions contribute to the particular vibrational modes.

Vibrational Spectroscopy and SymmetryVibrational Spectroscopy and Symmetry

1. Determine the point group of the molecule.

2. Determine the Reducible Representation, tot, for all possible motions of the atoms in the molecule.

3. Identify the Irreducible Representation that provides the Reducible Representation.

4. Identify the representations corresponding to translation (3) and rotation (2 if linear, 3 otherwise) of the molecule. Those that are left correspond to the vibrational modes of the molecule.

5. Determine which of the vibrational modes will be visible in an IR or Raman experiment.

We must use character tables to determine how many signals we will see in a vibrational spectrum (IR or Raman) of a molecule. This process is done a few easy steps that are similar to those used to determine the bonding in molecules.

Finding the Point GroupFinding the Point Group

Example, the vibrational modes in water.

The point group is C2v so we must use the appropriate character table for the reducible representation of all possible atomic motions, tot. To determine tot we have to determine how each symmetry operation affects the displacement of each atom the molecule – this is done by placing vectors parallel to the x, y and z axes on each atom and applying the symmetry operations. As with the bonds in the previous examples, if an atom changes position, each of its vectors is given a value of 0; if an atom stays in the same place, we have to determine the effect of the symmetry operation of the signs of all three vectors.

The sum for the vectors on all atoms is placed into the reducible representation.


Make a drawing of the molecule and add in vectors on each of the atoms. Make the vectors point in the same direction as the x (shown in blue), the y (shown in black) and the z (shown in red) axes. We will treat all vectors at the same time when we are analyzing for molecular motions.

HO

H

H O Htop view

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. C2V E C2 v (xz) ’v (yz)

tot 9 -1 3 1

Example, the vibrational modes in water.


H O H

C2

HO

H

H O H

HOH

H O H

v (xz)

H O H

HOH

’v (yz)

z y

x

C2V E C2 v (xz) ’v (yz)

A1 1 1 1 1 z x2,y2,z2

A2 1 1 -1 -1 Rz xy

B1 1 -1 1 -1 x, Ry xz

B2 1 -1 -1 1 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:

n 1

order# of operations in class (character of RR) character of XX

n 1

4A 1 1 9 1 1 1 1 1 3 1 1 1 1

This gives:

n 1

4B1 1 9 1 1 1 1 1 3 1 1 1 1

n 1

4B 2 1 9 1 1 1 1 1 3 1 1 1 1 n

1

4A 2 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.



tot 9 -1 3 1


Now that we have found that the irreducible representation for tot is (3A1 + A2 + 3B1+ 2B2), the next step is to identify the translational and rotational modes - this can be done by reading them off the character table! The three translational modes have the symmetry of the functions x, y, and z (B1, B2, A1) and the three rotational modes have the symmetry of the functions Rx, Ry and Rz (B2, B1, A2).

Translational modes

Rotational modes

The other three modes (3(3)-6 = 3) that are left over for water (2A1 + B1) are the vibrational modes that we might be able to observe experimentally. Next we have to figure out if we should expect to see these modes in an IR or Raman vibrational spectrum.


A1 1 1 1 1 z x2,y2,z2

A2 1 1 -1 -1 Rz xy

B1 1 -1 1 -1 x, Ry xz

B2 1 -1 -1 1 y, Rx yz

Remember that for a vibration to be observable in an IR spectrum, the vibration must change the dipole moment of the molecule. In the character table, representations that change the dipole of the molecule are those that have the same symmetry as translations. Since the irreducible representation of the vibrational modes is (2A1 + B1) all three vibrations for water will be IR active (in red) and we expect to see three signals in the spectrum.

For a vibration to be active in a Raman spectrum, the vibration must change the polarizability of the molecule. In the character table, representations that change the polarizability of the molecule are those that have the same symmetry as the second order functions (with squared and multiplied variables). Thus all three modes will also be Raman active (in blue) and we will see three signals in the Raman spectrum.



A1 1 1 1 1 z x2,y2,z2

A2 1 1 -1 -1 Rz xy

B1 1 -1 1 -1 x, Ry xz

B2 1 -1 -1 1 y, Rx yz

The three vibrational modes for water. Each mode is listed with a (Greek letter ‘nu’) and a subscript and the energy of the vibration is given in parentheses. 1 is called the “symmetric stretch”, 3 is called the “anti-symmetric stretch” and 2 is called the “symmetric bend”.

The Geometry of the Sulfur Dioxide The Geometry of the Sulfur Dioxide Molecule Molecule

Cs structure: 3 normal modes, all having A' symmetry

The Cs structure should have 3 IR active fundamental transitions. These three fundamental transitions also should be Raman active. We would expect to observe three strong peaks in the IR and three strong peaks in the Raman at the same frequency as in the IR. All of the Raman lines would be polarized because they are totally symmetric (A' symmetry).

C2v structure: 3 normal modes, two with A1 symmetry, one with B2

The C2v structure should have 3 IR active fundamental transitions. These three fundamental transitions also should be Raman active.We would expect to observe three strong peaks in the IR and three strong peaks in the Raman at the same frequency as in the IR. Two of the Raman lines are totally symmetric (A1 symmetry) and would be polarized. One Raman line would be depolarized.

The Dooh structure should have two IR active fundamental transitions. It will have one Raman active fundamental transition at a different frequency than either of the IR peaks.. The Raman line will be polarized.

Experimental ObservationExperimental Observation

Fundamental 2 1 3

IR (cm-1) 519 1151 1336

Raman (cm-1) 524 1151 1336

The experimental infrared and Raman bands of liquid and gaseous sulfur dioxide have been reported in a book by Herzberg 7 . Only the strong bands corresponding to fundamental transitions are shown below. The polarized Raman bands are in red.

ConclusionConclusionThe existence of three experimental bands in the IR and Raman corresponding to fundamental transitions weighs strongly against the symmetrical linear (Dooh) structure. We usually do not expect more strong bands to exist than are predicted by symmetry. Group theory predicts that both bent structures would have three fundamental transitions that are active in both the IR and Raman. However all three of the Raman lines would be polarized if the structure were unsymmetrical (Cs symmetry). The fact that one Raman line is depolarized indicates that the structure must be bent and symmetrical (C2v symmetry).

The sulfur dioxide molecule has C2v symmetry.

Problems with Raman:a)Very Weak – for every 106 photons only 1 photon Ramana)Resonant Raman not feasible with every sample.b)Absorption a better process than scattering

Raman SpectrometersRaman SpectrometersMicro–Raman setupMicro–Raman setup

International and National Patent (2007), G.V. Pavan Kumar et al Current Science (2007) 93, 778.

Stage

Objective lens

Dichroic Mirror

CameraEdge filter

Focusing lens

Computer

Mono-chromatorCCD

Optical fiber

LASER

Introduction to Basics of Raman Spectroscopy

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