Introduction to Basics of Raman Spectroscopy
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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
cbhas@jncasr.ac.inhttp://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.
Raman Depolarization Ratios
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
Raman Depolarization Ratios
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
Spatial resolution: penetration depthSpatial resolution: penetration depth
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
CASR
Spatial resolution: penetration depthSpatial resolution: penetration depth
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.
Vibrational Spectroscopy and SymmetryVibrational Spectroscopy and Symmetry
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.
Vibrational Spectroscopy and SymmetryVibrational Spectroscopy and Symmetry
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.
Vibrational Spectroscopy and SymmetryVibrational Spectroscopy and Symmetry
C2V E C2 v (xz) ’v (yz)
tot 9 -1 3 1
Vibrational Spectroscopy and SymmetryVibrational Spectroscopy and Symmetry
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.
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
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.
Vibrational Spectroscopy and SymmetryVibrational Spectroscopy and Symmetry
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
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.
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