Raman XI

XI

References

DC Harris o ch MD Bertolucci Symmetry and Sp ectroscopy Oxford University

Press

J M Hollas Mo dern Sp ectroscopy Wiley Chichester

Handb o ok of vibrational sp ectroscopy J M Chalmers P R Griths Eds Wiley

G Herzb erg Infrared and Raman Sp ectra Van Nostrand

K P Hub er o ch G Herzb erg Constants of Diatomic Van Nostrand

PW Atkins Molecular Oxford University Press

LA Wo o dward Intro duction to the Theory of Molecular Vibrations and Vibrational

Sp ectroscopy Clarendon Press

EB Wilson JC Decius o ch PC Cross Molecular Vibrations McGrawHill

En ny upplaga Dover

S Califano Vibrational States Wiley

EFH Brittain WO George o ch CHJ Wells Academic Press

MD Harmony Intro duction to Molecular Energies and Sp ectra Holt Winston

CRC Handb o ok of Sp ectroscopy

T Hase Sp ektrometriset taulukot Otakustantamo CRC Press

B Schrader Ramaninfrared atlas of organic comp ounds VCH Weinheim

D A Long The Raman eect A unied treatment of the theory of

by molecules Wiley Chichester

XI Molecular spectroscopy

XI The Raman phenomenon

The Raman sp ectroscopy measures the vibrational motions of a like the infra

red sp ectroscopy The physical metho d of observing the vibrations is however dierent

from the infrared sp ectroscopy In Raman sp ectroscopy one measures the light scat

tering while the infrared sp ectroscopy is based on absorption of photons A summary

of the scattering theory is given in App endix I Scattering is also discussed in advanced

textb o oks in quantum mechanics

The Raman phenomenon was detected in by the Indian Sir Chandrasekhara

Venkata Raman and Kariamanikkam Srinivasa Krishnan Indep endently of this work the

phenomenon was also rep orted by Grigory Landsb erg and Leonid Mandelstam However

the phenomenen was predicted theoretically even earlier by using the classical mo del

After the end of s the metho d was forgotten for several decades b ecause the signal

is very weak Raman sp ectro copy exp erienced a renaissance in the s when the lasers

were invented and started to b e used as light sources in sp ectroscopy

The basics of the Raman scattering can b e explained using classical physics but a more

comprehensiv theory requires quantum mechanical treatise Both the classical and quan

tum mechanical formulations are schetched b elow

Classical description of the Raman phenomenon

Consider a molecule for the sake simplicity one without a p ermanent dip ole moment The

eect of a p ermanent dip ole moment can b e easily incorp orated An oscillating electric

eld

F F cos t XI

induces a dip ole moment

F cos t XI

The quantity is the p olarizability of the molecule The p olarizability is not a constant

but varies with every vibrational motion of the molecule Let the fundamental vibration

C V Raman and K S Krishnan A new typ e of secondary radiation

C V Raman and K S Krishnan Indian Journal of Physics A new class of

sp ectra due to secondary radiation I

C V Raman was made a knight in and received the Nob el pro ce for his invention in

G Landsb erg and L Mandelstam Naturwiss

A Smekal Naturwiss

Raman spectroscopy XI

frequences of the molecule b e k M Then

k

M

X

cos t XI

k k k

k

A phase factor has b een included in the formula The induced dip ole moment is

k

M

X

p F cos t F cos t cos

k k k

k

F cos t XI

M

X

F cos t cos t

k k k k k

k

The classical theory of electromagnetism states that an oscillating dip ole emits radiation

of the intensity

jpj XI I

c

A simple insertion gives the result

4

0

I F cos t Rayleigh

3

c

0

P

M

F f cos t anti Stokes

3

k k k

k

k

c

XI

0

cos t g Stokes

k k k

An oscillating dip ole moment emits therefore with the of the incident eld Ray

leigh scattering in phase with the incident eld In addition the molecule radiates with

two that are mo dulated by the frequency of the excited normal vibration and

phase shifted Raman scattering The Raman scattered light has a lower frequency

than the incident light Stokesraman scattering or a higher frequency antiStokes

Raman scattering

One of the failures of the classical picture is that the ratio of the Stokes and antiStokes

intensities should theoretically b e

I Stokes

k

XI

I anti Stokes

k

which is not the case exp erimentally

XI Molecular spectroscopy

The quantum mechanical description of the Raman eect

The relevant quantum mechanical system is the molecule plus the eld Usually the time

dep endent Schrdinger equation of the system is solved by using p erturbation theory

basically in the same way the Einstein transition rate is calculated but in this case to

second order The intensities are then according to App endix I

e

nm

j njm jm j XI I

k i

i

c

with the matrix elements of the induced dip ole moment

X X

nj jr r j F jm

i i

j

njm jm f

i

h

r m

r

j

XI

nj F jr r j jm

i i

j

g

nr

The momentaneous dip ole moment is determined also here by the p olarizability The

i

meaning of this expression is illustrated in Fig XI In addition to the free molecules

eigenstates somewhat p erturb ed the system also has an innite numb er of virtual states

r Very schematically one can say that the molecule is excited to a virtual state where

a photon has transferred from the electric eld to the molecule dressed molecule and

then go es back to one of the initial states In the gure it is also shown that the energy of

the incident photon must not b e equal to any of the electronic excitation energies of the

molecule b ecause the photon is absorb ed in that vase The upp ermost whole line in the

gure indicates an electronically excited state

hν hν hν hν hν hν 0 0 0 UVvis absorption

ν k

ν ν ν ν ν ν ν ν h = h 0 h = h 0 - h k h = h 0 + h k

Rayleigh scattering Stokes scattering Anti-Stokes scattering

Fig XI Schematic representation of the Raman eect

Raman spectroscopy XI

In the quantum mechanical mo del the intensity dep ends on the o ccupation of the initial

state This is determined by the Boltzmann distribution Thus the intensity ratio is

I Stokes

k

hc k T

k

e XI

I anti Stokes

k

This ratio dep ends on the temp erature T Therefore one can determine the temp erature

of the sample by measuring the intensities of b oth the Stokes line and the corresp onding

antiStokes line The temp erature is given by the formula

k

XI T

I antiStokes

0

k

lnf g lnf g

I Stokes

0

k

An example of the Raman sp ectrum is shown in Fig XI 22479 22624 22720 Raman intensity -> 23156 22148 22176 23252 23397 22938 23700 23728

-800 -400 0 400 800 Raman frequency (cm-1) 218 218

314 314

459 459

762 762

790 790

Fig XI An example of a Raman sp ectrum Carb on tetrachloride

Intensity of the scattered light

The most common pro cess in light scattering is that the photon do es not interact at all

with the sample but simply passes through it Only one photon of or is scatteted

XI Molecular spectroscopy

An overwhelming ma jority of the scattered photons show Rayleigh scattering where the

frequency of the scatteted light is the same as that of the incident light Only one of a

thousand or ten thousand scattered photons will have a mo dulated frequency ie will b e

Raman scattered Therefore the intensity of the Rayleigh signal is a thousandth of the

intensity of the incident light and intensity of the Raman signal is a millionth of the

intensity of the incident light

In the ab ove gure the Rayleigh band is shown in the middle Its frequency is used as

the origin of the Raman sp ectrum The p ositions of the Raman bands are Their

k

displacements from give the frequencies of the normal vibrations The Rayleigh band is

very intense as compared to the Raman bands on b oth sides of it The StokesRaman bands

on the lowenergy side are stronger than the antiStokesRaman bands on the highenergy

side of the central Rayleigh band but their distances from the central band are the same

as those of the StokesRaman bands In practical measurements one wishes to remove the

strong rayleigh band in order to b e able to observe the Raman signals Therefore only the

StokesRaman part of the sp ectrum is usually shown The infrared and Raman sp ectra of

carb on tetrachloride are shown in Fig XI

2000 1500 1000 500

Fig XI Infrared and Raman sp ectra of carb on tetrachloride

The intensity of the signal is determined by the scattering cross section by

the frequency of the incident light and by the Boltzmann factor The scattering cross

section dep ends on the molecular p olarizability see App endix I From this follow

the selection rules in the Raman sp ectroscopy The eect of the incident light is imp ortant

b ecause the intensity dep ends on the fourth p ower of the frequency If the is

Raman spectroscopy XI

halved eg from to nm the intensity of the scattered light will increase by a

factor

XI Molecular spectroscopy

XI The Raman sp ectrometer

The light source

The light source of a Raman sp ectrometer must give very intense radiation for the scattered

light to b e strong enough to b e observed In addition the light should b e as mono chromatic

as p ossible so that the Raman bands would b e as narrow as p ossible

In the old instruments a mecury vap or lamp is commonly used It has several strong

emission bands and nm If one do es not use

a lter to select one of the bands all of them will generate a sp ectra that may partly

overlap The emission bands also have quite large widths which will b e convoluted into the

resulting Raman sp ectrum and result in quite broad Raman bands The emission bands

of a mercury lamp lie in the range from UV to visible green light This is very favorable in

Raman sp ectroscopy b ecause the intensity of the scattered light inreases with the fourth

p ower of the frequency On the other hand one risks to hit on an electronic absorption band

which will result in uorescence The uorescence in Raman sp ectroscopy is discussed in

detail later In mo dern sp ectrometers a laser is used as the light source b ecause it gives a

high intensity and the light can easily b e fo cused in a small sp ot in the sample Laser light

is also p olarized and this can b e used to determine the dep olarization ratio Gas lasers in

particular the argon laser that has two stron emission lines at and nm have b een

p opular In FTRaman sp ectrometers NdYAG lasers with an emission wavlength of

nm are p opular To day also dio de lasers are gaining p opularity Dio de lasers can have

one of several emission wavelength in particular and nm are p opular The

emission p ower of mo dern dio de lasers is typically several hundred milliwatts

The sample

The scattered light is distributed in all directions Two observation geometries are



particularly p opular For liquid samples observation at angle to the incident light

b eam is used most often This geometry is shown schematically in Fig XI Ine can also



observed light that is scattered in angle back scattering This is normally the

only p ossibility for solid samples Both geometries have their go o d p oints The optical



arrangement is simpler in the geometry Also the p ortion of Raman scattering of all

 

the scattered light is larger in geometry than in geometry For gaseous

Raman spectroscopy XI

5

the ratios are

I I

Raman Raman

XI

I I

Ray leig h Ray leig h

In the geometry one only needs to have access to one surface of the sample which

may make the practical exp eriment easier The scattering intensity is also highest at

For gaseous nitrogen

I

Raman

XI

I Raman

Monochromator

Fig XI Raman exp eriment at geometry

The estimates ab ove are based on the following scattering probabilities at angle

2

P cos

Ray leig h

 

  XI

2

P cos

Raman

Here is the dep olarization ratio For nitrogen when the wavelength of the

incident light is nm One can also derive for nitrogen gas the relation

I

Raman

4

XI

I

Ray leig h

The sample cell is often an nmr tub e or a capillary tune that is made of suitable glass

grade The laser light is fo cused on the sample so that the glass wall of the cell do es not

disturb the exp eriment The scattered light is collected by using a large condensing lense

and directed to a mono chromator or an interferometer and thence to the detector

5

N M Reiss J Appl Phys

XI Molecular spectroscopy

Mono chromator and interferometer

In the infrared sp ectoscopy the interferometric technique has completely replaced the dis

p ersive technique In Raman sp ectroscopy however the disp ersive sp ectrometers ha

ve certain advantages over the interferometry The largest manufacturers of FTRaman

sp ectrometers also pro duce disp ersive Raman sp ectrometers The disp ersive instruments

are signicantly more sensitive by a factor of ten to hundred than the FTRaman sp ectro

meters Therefore smaller laser eects can b e used and thereby sensitive samples are aec

ted less They also have a lower noise level indicating a lower detection limit In an FT

Raman sp ectrometer the dominating source of noise is the detector noise while in mo dern

disp ersive Raman sp ectrometers the shot noise ie random uctuations of the charge

carriers in the electronic circuits dominates It is also easier to change the wavelength of

the incident light in a disp ersive sp ectrometer than in an FTRaman sp ectrometer in case

the measurement is disturb ed by eg uorescence To day CCD detectors are common

They make the measurements fast b ecause the whole sp ectrum or a large p ortion of it

can b e measured simultaneously

One of the great challenges in Raman sp ectroscopy is to remove the Rayleigh signal

This is accomplished in the old sp ectrometers by using very large double or triple

mono chromators with large fo cal lengths up to m and very high resolution This

allows the recording of sp ectra quite close to the central burst without the Rayleigh signal

reaching to the detector The optical arrangement of a typical double mono chromator is

6

shown in Fig XI The two gratings must b e turned in phase and therefore the structure

of the mono chromator is such that b oth gratings are xed to a common axis

Gratings

Fig XI A double mono chromator schematically Solar TI I DM

A traditional triple mono chromator is shown in Fig XI The illustration shows schema

7

tically McPhersons McTriple LE mono chromator the two rst stages of which are cm

ononchromators with gratings that are rotated simultaneously by a connecting ro d The

6

httpsolartiicom

7

httpwwwmcphersoninccomramansp ectroscopyMcTripleLEhtm

Raman spectroscopy XI

Fig XI A triple mono chromator schematically McPherson McTripple LE

fo cal length of the third stage is either or cm The ap ertures are f and f

resp ectively

The success of the interferometric technique in infrared sp ectroscopy has also led to ma

nufacturing of commercial FTRaman sp ectrometers They are often accessories to

infrared sp ectrometers One such construction is shown schematically in Fig XI Pu

re FTRaman sp ectrometers are also pro duced They are often mo dications of existing

FTIR sp ectrometer b enches The interferometric technique is demanding in the short wa

velength range and in particular in the UV region The FTRaman sp ectrometers are

usually equipp ed with an NdYAG laser emitting near infrared light and with an eect of

up to W Dio de lasers are b ecoming more p opular They work ususally at or

nm An instrument may b e equipp ed with several dio de lasers in order to b e

able to avoid uorescence

The most critical comp onent in an FTRaman sp ectrometer is the lter that damps the

Rayleigh scattered light as the interferometer cannot do this If the Rayleigh light reaches

to the detector the detector will b e overown On the other hand the the Raman signals

close to the Rayleigh band must b e observed This p oses high requirements on the lter

8

and a bandwidth of A holographic notch lter with an optical denisty of at least

1

cm is used Each laser typ e must have a lter that is sp ecically optimized for the

appropriate laser wavelength A typical transmission curve is shown in Fig XI

8

Opticalsk density is dened here as OD log T r ansmission An alternative denition is OD

10

log T r ansmissionl 10

XI Molecular spectroscopy

Mirror scanner

Input beam Filter

D Interferometer Raman 2 sample

S 1 S 2 YAG laser Sample

Exit D 1 beam

Raman

detector

Fig XI FTRaman mo dule attached to Bruker IFS

0

1

2

3

4

5 Optical density

6

7

8 610 620 630 640 650 660

Wavelength (µm)

Fig XI Transmission curve of a notch lter It is assumed here that the wavelength of

the laser light is nm

The detectors used in the FTRaman sp ectroscopy dep end on the laser wavelength The

Raman signal is extremely weak and therefore the detector must b e sensitive and its noise

level low The most common detector typ e is the germanium detector the must however

b e co oled down wit liquid nitrogen It is excellent when used with a NdYAG laser

Examples of detector typ es that can b e used in the near infrared region are shown in Fig

Raman spectroscopy XI

1014

1013 Ge (77 K)

1012 *

D PbS (196 K) InAs (77 K) 1011 InGaAs (300 K) InSb (77 K)

1010 PbS (77 K)

PbSe (196 K) 109

108 PbSe (300 K) 1 2 3 4 5

Wavelength (µm)

Fig XI Examples of detectors for the NIR region

XI

The mo dern disp ersive sp ectrometers use lters similar to those in FTRaman sp ectro

meters Then one can use a rather small mono chromator as it do es not need to separate

away the Rayleigh band On the other hand the lter is optimized for a particular laser

typ e If one wishes to have several lasers to cho ose among then one also has to implement

all the necessary lters in the sp ectrometer The most common detector typ e is a CCD

detector that allows a fast uptake of the whole sp ectrum At low resolution one do es then

not need any moving parts in the sp ectrometer The whole sp ectrum is recorded simul

taneously This technique is also excellent for new measuring metho ds such as mapping

The principle of such sp ecttrometers is illustrated in Fig XI

CCD detector

Transmission grating Filter

Raman and Rayleigh signal

Raman signal

Fig XI Disp ersive Raman sp ectroscopy using a transmission grating

XI Molecular spectroscopy

XI Selection rules in Raman sp ectroscopy

Raman sp ectroscopy measures molecular vibrations The actual vibrations are the same

as in infrared sp ectroscopy and their symmetries can b e determined in the same way as

in infrared sp ectroscopy This pro cedure has b een discussed in chapter VI I The selection

rules can thus b e derived from the theory of p oint groups The physical interaction me

chanism in infrared sp ectroscopy is absorption of photons That pro cess is determined by

the uctuations of the electric dip ole moment of the molecule In Raman sp ectroscopy the

photons are scattered The physical quantity that governs scattering is the p olarizability

In all other resp ects the analysis is similar to that in infrared sp ectroscopy The principles

for b oth exp erimental techniques have b een discussed in chapter VI I The basic principles

for interpretation of Raman sp ectra are discussed b elow

The intensity of the scattered light dep ends on the dierential scattering cross sec

tion Molecules with an easily p olarizable electron cloud have a high scattering

cross section In Raman sp ectroscopy the vibrations aect the p olarizability and therefore

dierent vibrational mo des give dierent band intensities The intensity of the Raman

signal is strongly aected by the frequency of the incident light Therefore one often uses

4

the reduced scattering cross section The reduced scattering cross

0 k

sections of a few liquids are shown in the table b elow Wavelength of the incident light is

nm

1 4 48 6

Molekyl Vibration cm cm sr

0 k

C H

6 6

C H CH

6 5 3

C H NO

6 5 2

CS

2

C C l

4

C H C l

3

C H

6 12

Molecules with aromatic or conjugated functional groups show a high Raman intensity

b ecause the delo calized electrons are easily p olarizable Molecules with double b onds or

free electron pairs often show hifh Raman signals However water is a notable exception

There the free electron pairs form hydrogen b onds and their p olarizability is reduced

Water is a good solvent in Raman spectroscopy The complexes of transition metal ions

often give strong Raman signals

Raman spectroscopy XI

Molecules can rotate and the rotational transitions can b e observe b oth in absorption and

scattering sp ectra The term rotational sp ectroscopy refers to absorption sp ectroscopy

b ecause the pure rotational bands are dicult to observe in Raman sp ectroscopy as they

are very weak and lie very close to the Rayleigh band This is shown schematically in Fig XI

Raman

Fig XI Raman rotations schematically

The rotational motions can also b e observed as ne structure of the vibrational bands

Normally one can only observe that the vibrational bands are broad The rotational levels

have so low energies that the ambient thermal energy can cause transitions The band

width is determined by the Boltzmann distribution If the sample is co oled down to K

the vibrational bands are quite narrow b oth in infrared and Raman sp ectroscopy

In infrared sp ectroscopy the for the rotational transitions is J

which give rise to the P Q and R branches In Raman sp ectroscopy the corresp onding

selectiion rules are J and the lab els of the branches are then O Q and S

XI Molecular spectroscopy

XI Interpretation of Raman sp ectra

The selection rules of Raman sp ectroscopy are dierent from those of inrared sp ectroscopy

b ecause the physical pro cesses givin rise to the sp ectra are dierent However the actual

molecular vibrations are the same Therefore the basic principles of assignment are the

same in infrared and Raman sp ectroscopy If a vibrational motion is active in b oth infrared

and raman sp ectroscopies the band p osition is obviously the same in b oth sp ectra The

dierence of the selection rules can result in bands that are strong in the infrared sp etrum

but weak in the Raman sp ectrum and vice versa Therefore the infrared and Raman

sp ectra dier and the same correlation tables cannot b e used for b oth The two metho ds

complement each other

The Raman sp ectra are often simpler than the corresp onding infrared sp ectra The al

lowed fundamental transitions give very strong signals while the forbidden fundamental

transitions often give very weak signals in Raman sp ectroscopy This is typically not the

case in infrared sp ectroscopy

Certain functional groups are easily identied from the infrared sp ectrum and others in

the Raman sp ectrum One notable example of the dierences are the sceleton vibrations

of aromatic hydro carb ons Some examples are shown in the table b elow

Molecule Band p osition Intensity

1

cm Raman IR

Naphtalene w m

vs vw

vw m

vs ms

Anthracene ms ms

vs s

vs vw

Fenantrene m m

m s

s m

vs w

One application where Raman sp ectroscopy can b e particularly useful is identication of

inorganic comp ounds that often have low vibrational frequencies lying close to or even

1

b elow cm which is the limit for infrared sp ectroscopy Some examples of the Raman

sp ectra of inorganic three four and ve atom ions are shown in the table b elow The

Raman spectroscopy XI

symb ol p indicates that the band is p olarized

XI Molecular spectroscopy

1 1

band cm band cm

1 2

Molecule vibration symmetry vibration symmetry

puktgrupp

in H O p owder R IR in H O p owder R IR

2 2

+

D

h s

NO vs

3

+

NO vs

2

FHF vs m m

C

v

OCN s w m

SCN s w m m

C A A

2v s 1 2

NO s s m s

2

D A A

3h s

1 2

3

BO p vs s

3

NO p vs w s

3

2

CO p vs m

2

C A A

3v s 1 1

2

SO p vs s p w m

3

C l O p s p

3

B r O p s p

3

p s p IO

3

+

OH m vs

3

T A E

d s 1

+

NH p s

4

+

ND p s

4

3

PO p vs w m

4

2

p vs w m SO

4

C l O p vs

4

IO p vs

4

M nO p vs

4

C r O p vs

4

3

AsO p vs

4

Al H p s s w m

4

BF p vs s w s 4

Raman spectroscopy XI

1 1

band cm band cm

1 2

Molecule vibration symmetry vibration symmetry

puktgrupp

in H O p owder R IR in H O p owder R IR

2 2

+

D

h as

NO vs

3

+

NO vs

2

FHF vs

C

v

OCN p s s

SCN p vs s

C B

2v as 1

NO m vs

2

D E E

3h as

3

BO vs m m

3

NO m vs m w

3

2

CO w vs w m

2

C E E

3v as

2

SO m s s m

3

C l O m s

3

B r O m s

3

m s IO

3

+

OH m vs m s

3

T T T

d as 2 2

+

NH s s

4

+

ND s

4

3

PO s

4

2

w vs w SO

4

C l O

4

IO

4

M nO

4

C r O

4

3

AsO vs

4

Al H vs s s

4

BF s vs w s 4

XI Molecular spectroscopy

XI Dep olarisation ratio

A laser light source gives plane p olarized light The p olarization plane or the electric

vector of the incident radiation E lies p erp endicular to the optical axis of the sp ectrome

ter The Raman scattering may alter the direction of the p olarization plane This is known

as dep olarization By measuring the intensity of the scattered light in two p olarization

directions parallel with the p olarization plane of the incident light I and p erp endicular

k

to it I one can determine the dep olarization ratio as

I

XI

I

k

The p olarization directions are dened in Fig XI

Sample cell

Analyser Optical I⊥ axis I||

E

Laser in

Fig XI Denition of the parameters for dep olarization ratio

Every band has its characteristic dep olarization ratio that dep ends on the symmetry pro

p erties of the vibration If the vibration b elongs to the totally symmetric irreducible

representation it will not mo dify the p olarization plane and In that case the vibra

tion is p olarized If the vibration is asymmetric it will turn the p olarization plane and the

dep olarization ratio is Such vibrations are dep olarized Thus the symmetry of

the vibration can b e deduced from the dep olarization ratio This will help in assignment

of the sp ectral bands

1

The sp ectral bands of carb on tetrachloride at and cm show a dep olarization ratio

of The vibrations b elong to the irreducible representations E and T resp ectively

2

which means that the shap e of the molecule changes during the vibration The vibration

1

observed at cm b elongs to the irreducible representation A and has a dep olarization

1

ratio of That vibration do es not change the shap e of the molecule so the asymmetry

of the p olarization tensor cannot aect the scattering The parallel and p erp endicular

sp ectra are shown in Fig XI

Raman spectroscopy XI

I⊥

I||

2000 1500 1000 500

Fig XI The parallel and p erp endicular sp ectra of carb on tetrachloride

A more detailed analysis shows that when the incident radiation that propagates in the

i

z direction with n e unit vector in z direction the corresp onding electric vector

z

i i i i

lies in x or y direction The electric vectors are denoted as E k and E Let the

x y

incident radiation collide with a molecule that is placed at the origin of the co ordinate

s

system The light scattered at angle will propagate in the direction n e The

x

s

momentaneous electric dip ole moment emitted by scattering has comp onents p k and

z

s

p The scattered electric vector is parallel with or p erp endicular to the scattering

y

plane in this case xz The co ordinate system is shown in Fig XI One can write the

matrix elements of the transition moment in Placzeks approximation ie assuming

that the p olarizability tensor is adiabatic as

p E

y y y y

XI

p E

z z y y

for incident light that is p olarized in the y direction

Consider N freely rotationg ideal gas molecules in the vibrational ground state Intensity

of the scattered light is obtrained by taking the mean value of all orientations ie by

2 2

replacing by The isotropic mean value is expressed by using invariant

y y y y

quantities that can b e dened in several dierent ways We use here the quantities i

XI Molecular spectroscopy

z

O y p (||s) z (||i Ex ) (⊥s py ) (⊥i Ey ) x ns = e i

x n = ez

Fig XI The co ordinate system used to dene dep olarization

9

mean p olarizability

a XI

xx y y z z

ii



2 2 2 2

j al pha j j al pha j j al pha j

xx y y y y z z z z xx

XI



2 2 2

j j j j j j

xy y x xz z x y z z y

iii antisymmetric anisotropy



2 2 2 2

j j j j j j XI

xy y x y z z y z x xz

The intensity of an oscillating dip ole at the angle to the axis of the dip ole is

2

4 2

I K p sin XI

Here only scattering at angle is considered e Therefore

s i 4 2 2

I K N E XI

y y

y

Similarly one can obtain the intensity

s i 4 2 2

I k K N E XI

z y

y

Using the isotropic invariant quantities the intensities can b e written as

 

2 2

a

2 s i 4

E XI I K N

y

9

For a discussion of the invariant quantities and their relation to the p olarizability tensor see any advanced

text b o ok in electro dynamics or eg Long

Raman spectroscopy XI

and

 

2

2 s i 4

E XI I k K N

y

Using these notations the dep olarization ratio can b e written as

s i 2

I k

i

XI

s i 2 2

I a

XI Molecular spectroscopy

XI Lattice vibrations

Lattice vibrations are the molecules motions with resp ect to each other in the lattices of

a crystalline material These motions are also quantizised the quantum numb er is called

a phonon The motions dep end on the crystals symmetry which means that they ob ey

selections rules similar to those for ordinary vibrations

The masses are high in the lattice vibrations and therefore the motions are slow and the

frequencies low In the infrared sp ectroscopy they are in the far IR region and are seldomly

considered In Raman sp ectroscopy they are more easily accessible The example in Fig

10

XI shows ammonium p errhenate NH R eO

4 4

δ(ReO ) ν(ReO ) Lattice vibrations 4 4 NH4ReO4

ν(NH ) 4 Intensity (arbitrary units) Intensity (arbitrary units)

200 600 1000 1400 1800 2200 2600 3000 50 100 150 200 250

Wavenumber (cm-1) (cm-1)

Fig XI Lattice vibrations in ammonium p errhenate

10

Y S Park et al J Raman Sp ectr

Raman spectroscopy XI

XI Exp erimental metho ds

Gas samples are seldomly used in Raman sp ectroscopy In thin gases there are normally

to o few molecules in the fo cal p oint of the laser b eam This indicates that lasers with very

high p ower and extremely sensitive detectors must b e used On the other hand many gases

absorb only deep in the UV so that incident radiation with quite short wavelengths can

b e used This increases of course the scattering cross section

The highest p ossible laser intensities are obtained when the sample is placed in the laser

cavity

Liquid samples are easily handeled in the Raman exp eriment Raman is a form of

vibrational sp ectroscopy so similar rules for the sample as in infrared sp ectroscopy must

b e observed In particular the sample must b e a pure comp ound Each comp onent of a

mixture gives its own set of bands but the interpretation still is quite cumb ersome when

the numb er of partly overlapping bands is large

The sample cells are often nmr tub es or melting p oint capillary tub es The glass wall of

the cell do es not disturb the exp eriment when the incident light is fo cused on the sample

The typical incident laser p owers range from a few tens to a few hundresd of milliwatts

The measuring metho d for liquid samples is normally the geometry but back scattring

is also used in some cases

p owder samples can in most cases b e placed in a capillary or in a cavity on a metal

plate It is also easy to construct sample holders for solid samples bres and lms so that

they can b e places in the correct ngle in the sp ectrometer The suitable amount of sample

dep ends on how easily handeled the sample is and on the size of the fo cal p oint of the

incident laser b eam typically approximately m

Single crystals can b e attached to the xy table of a microscop e by using a nonuorescent

glue By using p olarized light and turning the crystal in dierent orientations it is p ossible

to determine all nine comp onents of the p olarization tensor

Thin lms can b e studied eg by using a sample holder where the light is reected on

the lm One such sample holder is shown in Fig XI In this way one can obtain

p erfectly acceptable Raman sp ectra of thick lms of longchained organic molecules

of thick phospholipids of nm thick titanium oxide lms or of m thick p olymer

lms

Strongly absorbing samples can b e problematic b ecause of strong uorescence or b ecau

se they are strongly heated Samples that normally would b e combusted by the strong

laser light can b e placed in a rotating sample holder Then one has continuously fresh

XI Molecular spectroscopy

Laser in Film Glass Metal substrate

Prism Air Film

Glass

Fig XI Sample holder for thin lms

sample under the laser b eam and the sample do es not have time to heat so much that it

would b e destroyed

Raman microscopy is a p opular technique to day The most common metho d is to place

the sample on a xy table and move it so that the laser b eam is fo cused at a network of

p oints on the sample one p oint at a time Then one can store the raman sp ectrum for each

p oint to form a sp ectroscopic hyp ercub e One can also illuminate the whole surface at

one time and by diuse light and photograph the surface through a notch lter to see the

distribution of strongly scattering molecules on the whole surface However one cannot

have the sp ectra and identify the scatterers in this case

Raman sp ectroscopy can b e used for quantitative analysis b ecause the intensity of

the emission lines dep ends linearly on the concentration It is in fact often easier than in

infrared sp ectroscopy b ecause the calibration curve can b e linear in a broader concentration

range than in infrared sp ectroscopy On the other hand the exp erimental conditions aect

the intensity of the scattered light It is therefore customary to add an internal reference

to the sample in order to eliminate such errors The accuracy of the quantitative analysis

and the limit of determination dep end on the scattering cross section of the sample It

has b een rep orted that b enzene which is a strong scatterer has b een analyzed in carb on

tetrachloride down to concentrations of ca ppm The mo dern techniques in particular

resonance Raman and SERS have turned Raman sp ectroscopy to a sensitive metho d

Raman spectroscopy XI

XI Fluorescence

The purp ose of the traditional Raman sp ectroscopy is that the freauency of the incident

light do es not corresp ond to any electronic excitation in the molecule If this happ ens

the light may b e absorb ed The p ossible relaxation pro cesses are then uorescence or a

nonradiative pro cess where the incident p ower is converted to heat whereby the sample

may b e destroyed

Fluorescence is usually a phenomenon to b e avoided in Raman sp ectroscopy The probabi

lity of uorescence inreases when incident light with a short wavelength is used Therefore

UV or violetbluegreen light is not preferred even though the intensity of the scattered

light would b e quite high at such frequencies Instead infrared light is often used in par

ticular in FTRaman instruments b ecause of low probability of uorescence If uorescence

is observed its intensity is several decades higher than that of the scattered light and the

Raman bands are drowned

If uorescence o ccurs one should if p ossible switch to another laser wavelength Most

often the new wavelength do es not coincide with any of the molecules absorption bands

This is illustrated in Fig XI where the sample is p oly vinylcarbazol and the two

11

laser wavelengths are and nm

One common cause of uorescence is impurities and rest chemicals in the sample Fluore

scence is also a common phenomenon in bio chemical and pro cess chemical samples where

there are many comp onents If one can chemically remove the disturbing substances from

the sample the uorescence often vanishes One may also try to illuninate the sample at

high laser p ower for an extended p erio d of time whereby the disturbing substances are

burmed away This metho d is called bleaching If the sample itself emits uorescent light

one may try to use a high laser p ower and see the very weak Raman signals on top of the

strong broad uorescence band

One should also observe that scattering is an immediate pro cess while uorescence emission

starts several nanoseconds after the incident pulse A b oxcar integrator can therefore

separate the raman signal from the uorescence light

If the sample absorbs and is heated it will b e destroyed in a very short time under the

intense laser light The absolutely b est metho d to avoid this is to switch to another laser

wavelength that is not absorb ed If this is not p ossible one should use as low laser p ower

as p ossible and a short measuring time in order to reduce the heating One can also

defo cus the incident laser light in order to reduce the energy density Various rotating

sample holders have b een suggested so that there is constantly fresh sample in the laser

fo cus whereby the heating is minimized Examples of such sample holders are shown

11

httpwwwkanalysse

XI Molecular spectroscopy

514 nm Intensity (arbitrary units)

830 nm

200 400 600 800 1000 1200 1400 1600 1800

Wavenumber (cm-1)

Fig XI Raman sp ectrum of p oly vinylcarbazol at two incident laser wavelengths

of which one induces uorescence The scales for the uorescence and Raman light are not

the same

schematically in Fig XI In the rst sample holder the p owder is pressed to a gro ove

In the second one the liquid is driven to the edge of the sample holder by the

Raman spectroscopy XI

Sample

Sample

Slit Slit

Laser in Laser in

Fig XI Examples of rotating sample holders for Raman sp ectroscopy The rst one is

intended for p owder samples and the second for liquid samples

XI Resonance Raman sp ectroscopy

Sometimes one can delib erately cho ose to use a laser wavelength that will induce uore

scence Such a metho d is known as resonance Raman sp ectroscopy In resonance

2

Raman sp ectroscopy the intensity of the Raman signal is increased by a factor of

6

This is a particularly useful technique for bio chemical or pro cess chemical samples

that are mixtures of a numb er of substances In such samples one can select one particular

comp onent that absorbs at the laser wavelength that is used Eg the active centre of an

enzyme often contains a metal ion that gives the complex a visible color while the rest of

the organic material do es not absorb In that case one can obtain the Raman sp ectrum of

just the active centre and nothing else At the same time one can obtain information of

the electronic state of the active complex

The enhancment aect exactly those parts of the molecule where the electronic absorption

takes place Not all vibrations of the molecule are enhanced equally much If one uses

eg the wavelength of an electronic transition the Raman signal of the stretching

vibration of the b ond will b e aected most Similarly the vibrations of the metalligand

b onds will b e enhanced if the incident wavelength is adjusted to the absorption band of

the metal complex The Raman sp ectrum and resonance Raman sp ectrum of paraethyl

phenols PEP in hexane are shown in Fig XI The Raman sp ectrum was pro duced

using laser light with nm wavelength and the resonance Raman sp ectrum with

nm The sp ectral bands of PEP are marked with strokes The most imp ortant bands

XI Molecular spectroscopy

of the solvent are marked with stars Their intensity is not aected very much by the

12 resonance

244 nm

* * Intensity (arbitrary units)

* *

*

* 514 nm

600 800 1000 1200 1400 1600

Wavenumber (cm-1)

Fig XI Raman and resonance Raman sp ectra of paraethyl phenol

The origin of the enhancement can b e read in the rst term of the KramersHeisenb erg

equation where the energy denominator contains the dierence of frequencies see App endix

I This dierence b ecomes small when the laser wavelength lies close to an absorption

band

12

M P Russel et al Biophys J

Raman spectroscopy XI

XI SERS

In surface Enhanced Raman Scattering SERS the sample is placed on a metal

surface with an ordered crystal lattice In this case the intensity of Raman scattering will

3 6

b e increased by a factor of as compared to liquid samples A silver surface gives

the b est results even though other metals gold in particular can also b e used

The phenomenon is explained by the fact that the easily p olarizable conduction electrons

enhance the electric eld of the incident light that a molecule in the sample feels It has

also b een claimed that the molecules or ions on the metal surface can form weakly b onded

electron transfer complexes which have an absorption band at the laser wavelength This

would then lead to a resonance enhancement

As an example consider the surface enhanced Raman sp ectrum of transbispyridyl

ethylene BPE that is a relatively strong Raman scatterer The sp ectrum is shown in Fig

XI The sp ectrum has b een created by using a frequency doubled NdYAG laser b eam

13

at nm The laser eect was mW and the measuring time s Intensity (arbitrary units)

800 1000 1200 1400 1600

Wavenumber (cm-1)

Fig XI The surface enhanced Raman sp ectrum of BPE on a AgFON silver surface

13

M A Young et al Can J Chem

XI Molecular spectroscopy

XI CARS

Two lasers are used in the Coherent AntiStokes Raman scattering CARS One

of them has a xed frequence and the other is a dye laser or another laser light source

1

with adjustable frequency The rst laser gives rise to a normal Raman phenomenon

2

At the same time the sample is also illuminated with the second laser that sweeps over the

whole antiStokesRaman sp ectrum When the frequency of the dye laser coincides with a

Raman transition the two intense electric elds will interact and a strong scattered laser

b eam with the frequency will b e emitted This phenomenon is based on the

3 1 2

nonlinear In principle the two laser b eams should b e aligned accurately so that

the electric vectors meet at the correct angle However for siquid samples the b eams can

usually b e parallel The exp erimental setup is shown schematically in Fig XI

Dye laser

Fixed laser

Sample

Scattered beam

Fig XI The CARS exp eriment schematically

The CARS technique is suitable also for samples with strong disturbances such as uore

scence One imp ortant eld of application is the vibration sp ectroscopy of molecules in

ames

A more detailed illustration of the principle of CARS sp ectroscopy is shown in Fig XIa

The two laser b eams and interact and create the two virtual states j a and j b

1 2

that coexist and are in coherence The whole pro cess involves four photons and is based on

(3)

the third order hyp erp olarizability The momentaneous induced dip ole moment

  

of the molecule is

X X X

0 (3)

p E E E E E E XI

       0   

   

     

0

Here is the molecules p ermanent static dip ole moment p olarizability or the linear





(1)

electric susceptibility multiplied with and is the rst hyp erp olarizability The

 

0  

Raman spectroscopy XI

quantity E is a comp onent of the external oscillating electric eld The CARS metho d is



based on the third order nonlinear optics In addition the wave vectors of the incident

and departing b eams must full the sum rule of Fig XIb

|b>

|a> ν ν 2 CARS

ν ν 1 Stokes

k Stokes k CARS |1> k k 1 2

|0>

Fig XI a Energy levels in the CARS exp eriment b sum rule of the wave vectors

CARS is to day available also in microscopy and in mapping teqchniques Timedep endent

CARS has also b een rep orted

XI Molecular spectroscopy

XI Timeresolved Raman sp ectro oscopy

Fast phenomena can b e observed by sending short laser pulses to the sample The pulse

characteristics and the sp eed of the detcting assembly determine how shortlived pro cesses

can b e observed In sp ecialized lab oratories one can reach a time scale of femtoseconds