Spectroscopy 6 Topics to be covered - NUI · PDF fileCocaine hydrochloride ... (liquid/solid) they overlap. Not seen at r.t. but if cooled down to LN2 . ... Fourier-Transform (FT)

2 year Spectroscopy Handout: 2008.

Page 1

1

Spectroscopy3 lectures leading to one exam question� Texts: � “Elements of Physical Chemistry” 4th ed.

– by Atkins & de Paula, Chapter 19& Chapter 20

� “Foundations of Spectroscopy”– By Duckett & Gilbert, Chapter 2-3-4

� Various Specialist texts in Hardiman Library� Need this for CH205 in second semester.� Need this for 3, 4 year chemistry.� Notes & Links available on my website.

– http://www.nuigalway.ie/chem/AlanR/– http://www.nuigalway.ie/nanoscale/undergraduate.html

– This version 22/11/2010: minor errors corrected.

2

6 Topics to be covered

� Introduction to Spectroscopy.

� Quantitative Spectroscopy:

– Beer-Lambert.

� Electronic spectroscopy.

� Vibrational Spectroscopy:

– FT-IR and Raman spectroscopy.

� Energies of Vibrational transitions.

� Polyatomic Vibrational spectroscopy.

3

2Y Spectroscopy: Topic 1

� Introduction to spectroscopy:– Electromagnetic spectrum.

– Quantisation of energy & energy levels.

– Selection rules.

– Bohr condition.

– Absorption, Emission, & Scattering Spectroscopies.

� Need to Know: EM spectrum, how to interconvert from wavelength, wavenumber, or frequency to energy, and the different types of spectroscopy.

4

What is spectroscopy?

� Interaction of electromagnetic radiation with matter:– Absorption.– Emission. – Scattering.

� Many different scales:– Astronomy (single stars).– Microscopy (single molecules).

� Everything from forensics to living cells


Page 2

5

Spectrum (pl. spectra)

� “Map” of the energy states of a compound or

molecule.

� In principle, each spectrum is unique.

� Spectrum is a molecular “fingerprint”:

– Tool for qualitative analysis (FT-IR, Raman).

� Also ideal for quantitative analysis via the Beer-

Lambert Law:

– UV-Vis (exp. 2)………..protein conc. in biochemistry.

– FT-IR, NIR, Raman spectroscopies in industry.

6

The Electromagnetic Spectrum

Region Frequency s–1

Wavelength

Radio F 10610

8 3003 m

Micro Wave 101010

12 300.3 mm

IR 10121014 3001 µm

UV-VIS 10141016 100030 nm

X-RAY 101610

19 10030 pm

γ-RAY 101910

22 300.03 pm

7

Wavenumber (cm-1)

500 nm = 0.5 x10-4 cm = 20,000 cm-1_______Visible (high energy)

1000 nm = 1 x10-4 cm = 10,000 cm-1

2000 nm = 2 x10-4 cm = 5,000 cm-1

5000 nm = 5 x10-4 cm = 2000 cm-1__________IR (low energy)

Near IR

8

Quantisation of energy……….� Quantum Theory….molecules exists in discrete energy

levels (electronic, vibrational, rotational).

� Transitions between allowed energy states….

� Spectra reflect these defined changes (band structure).

10000

20000

30000

300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

1458

1273

1024

894341

393

488

784613

868

1019

998

1599 1715

Cocaine hydrochloride

raman shift, cm-1

.

INT

EN

SIT

Y (

arb

. un

its)


Page 3

9

Schematic molecular energy levels

ELECTRONIC VIBRATIONAL ROTATIONAL TRANSLATIONAL

E

UV-VISIBLE INFRARED MICROWAVE

10

Selection Rules

� There are rules for each type of spectroscopy.

� In general:

– Interaction between oscillating electric (or magnetic

field) with the dipole moment of the molecule.

– Transitions only between allowed energy levels (QChem).

two electric charges +q and −qseparated by a distance R

11

The Bohr frequency condition:

ε ν λ ν= = =h hc hc/

∆E (molecule) = E (photon)

PHOTON

BEFORE DURING AFTER

ENERGY

12

Absorption spectroscopy

� Can refer to the absorption of any frequency of

radiation, most common are:

– UV-visible absorption (electronic)

– IR absorption (vibrational)

– Microwave absorption (rotational)

� These are all types of molecular spectroscopy.

� Energy of the radiation ≅ energy of transition.


Page 4

13

Absorption spectrometer � Light absorbed by

sample.

� Grating/frequency analyser

� Single channel (PMT) or multichannel (CCD)

detectors (visible)

14

Emission spectroscopy

� Emission of any frequency of radiation.

� Concerned with the properties of emitted

photons.

� UV-VIS-NIR (electronic transitions):

– Fluorescence, Phosphorescence,

Chemiluminescence, photoluminescence.

� Fluorescence underpins nearly all of modern biology.

� Based on chemistry & physics.

15

Scattering spectroscopy

� We look at how light scatters from molecules:

– Not absorbed, doesn’t have to pass thru.

– Can use everything from neutrons to x-rays etc.

� Most Important is Raman spectroscopy:

– Molecular technique.

– Great for forensics etc.

www.umich.edu/~morgroup/virtual/

16


� Quantitative spectroscopy:– Beer-Lambert Law.

– Absorbance & Transmittance.

– Molar Absorption co-efficient.

– Calculations.

– Limitations.

� Know the Beer-Lambert law & calculations, how to interconvert from transmittance to absorbance. Limitations of method.

� Sec. 10.1 & 19.2: Atkins (Elements of Phys. Chem, 4ed)


Page 5

17

Beer-Lambert Law: Quantitative

Pathlength, l

I0 IT

Sample, Concentration C � At a fixed temperature and a singlewavelength:

– the intensity of light, IT, transmitted through a sample depends upon:

– the pathlength or sample thickness, llll

– the concentration of the absorbing species, C

– the incident light intensity,I0

18

Beer Lambert Law

T 0

T 0

( )at constant Temp. and a single wavelength ( )

molar absorptivity, pathlength, concentration of absorbing species

log(I ) = log(I )

log(I )

rearrange to:

log(I

e l CT 0

.....

e l C........

e l C

.

I I 10 λ−

−

−

= ×

( ) ( )

0T

0 T

0

T

awe know: log a log b =log

b

rearrange to:

) =

IIlog = log =

I I

Iabsorbance, A = log

I

A = e l C

e l C......

e l C... e l C,

−

−

− ⇒

⇒

19

Application of Beer-Lambert law (1)

� Calculate: Molar abs. Co-eff. of Tryptophan (comp. of proteins)– Radiation @ 280 nm

– 1 mm pathlength Needed Info

– Aqueous solution, 0.50 mmol L-1

– 54% of light passes through

� A = - log T = ε l C ----- step 1, write eqn.

� ε = - log T / l C --------- step 2, rearrange eqn.

4

2

3

1

1 1

1 1

log 0.54 =

(5.0 10 ) x (1 )

= 5.4 10 , or

= 5.

molL mm

Lmo

4 10 ,

l mm

Lmol cm

ε

ε

ε

− −

− −

− −

×

×

×

Step 3, put in values.

20

Application of Beer-Lambert law (2)

� What is the Absorbance for 1 mm & 5 mm?

� For 1 mm: A = -log T = -log 0.54 = 0.27

� For 5 mm, A = ε l C

� A = (5.4 x102 Lmol-1mm-1)(5 mm)(5.0 x 10-4 mol L-1)

� = 1.35

� Simple equation, always check the units

� Defined wavelength


Page 6

21

Limitations of Beer-Lambert law

� Works with relatively dilute solutions

� Does not work with turbid samples

� Need to avoid scattering

� Fixed single wavelength / fixed temperature

� Most commonly used with UV-Visible absorption

spectroscopy.

– Can be used with FT-IR……etc.

22


� Electronic Spectroscopy:

– UV-Visible absorption.

– Franck-Condon Principle.

– Fluorescence.

– Phosphorescence.

– Stokes shift, Lifetimes, Quantum yield.

� Understand and be able to explain the different

spectroscopies.

– Chapter 20, Elements of Physical Chemistry Sections 20.1,

20.3, 20.4, and 29.5

23

Visible spectrum

� Complementary colours

opposite ----

� Numbers = nm (wavelength)

– Absorb Red looks Green

– Absorbs blue looks orange

� Useful rule of thumb, but

not accurate enough for scientific purposes

� Observer dependant

24

Absorption spectrum

Absorption spectrum of chlorophyll in the visible region. Absorbs in the red and blue regions, green light is not absorbed.


Page 7

25

UV-Vis absorption

� 190 to 1000 nm

� Organic Chromophores

absorb in UV/Vis/NIR

– C=C, C=O, C=N

( )2 1E E E h photon∆ ν= − =

26

Franck-Condon Principle

� Nuclei are much more massive

than electrons, so Electronic transitions take place faster than nuclei can respond.

� most intense vibronic transition is

from the ground vibrational state

to the vibrational state lying

vertically above it.

� Transitions to other vibrational

levels also occur, but with lower

intensity.

27

Absorption in gaseous state

� The electronic spectra of

some molecules show

significant vibrational

structure.

� UV spectrum of gaseous SO 2at 298 K.

� Sharp lines in this spectrum

are due to transitions from a

lower electronic state to

different vibrational levels of a

higher electronic state.

28

Absorption in solutionVery broad, ill defined


Page 8

29

Fluorescence � Jablonski diagram

� Excitation of electron from ground to excited state – S0 to S1 (or S2)

� Vibrational Relaxation

� Emission of a photon of light – S1 to S0

30

Phosphorescence

� Sometimes electron can cross over to triplet level (not allowed transition)

� Takes much longer for T1

to S0, not allowed.

� Triplet state…..2 parallel electron spins (��)

� Singlet…paired spins (��)

31

Fluorescence Spectrometer

� Single channel

� Right angle excitation

� 200-900 nm usually

� Quartz cuvettes

� Light source; lamps, LED,

laser,

� Excite with a narrow band

� Photoluminescence

� Bioluminescence

� Chemiluminescence

32

Fluorescence spectra

� Most spectra don’t have

features…..energy gaps between vibrational levels

is too small and if in condensed phase (liquid/solid) they overlap.

� Not seen at r.t. but if

cooled down to LN2 temps…can be observed


Page 9

33

Stokes Shift

� Born in Sligo

� Emission @ longer

wavelength than absorption

� Difference = Stokes Shift

� Sensitive to environment

– polarity

– Ion concentration

34

Fluorescence Lifetime

� Average time a molecule

spends in the excited state:

– Nanosecond (10-9 s) to

Picosecond (10-12) range

– Anthracene = 5.2 ns in

cyclohexane solution

� For T1 to S0 transition lifetime can be seconds

35

Quantum yield (Q)

� Measure of the efficiency with which absorbed

light produces an effect:

– Ratio of No. of photons emitted to the No. of photons absorbed

– Good fluorophores have Q close to 1

– Q ~ 0, means no fluorescence (or phosphorescence)

� Tricky to measure experimentally:

– Have to integrate the absorption and emission bands

36


� Vibrational Spectroscopy:

– Vibrations of molecules (stretching, bending, etc,)

– Selection rules.

– FT-IR absorption spectroscopy.

– Raman spectroscopy.

� Know the key concepts underlying vibrational

spectroscopy, and the differences between Raman and IR absorption spectroscopy.

– Chapter 19, Elements of Physical Chemistry, Sections 19.9-

19.13 and 19.15


Page 10

37

Concepts

• Wavenumber: 5000 nm = 5 x10-4 cm = 2000 cm-1

� Molecules have bonds they can vibrate…

� Some bonds are stronger than others:

– C≡C / C=C / C-C.

� Electronegativities……..some atoms like electrons more than others…….

– Stronger / weaker bonds.

– H+F- ………………C-H

– Ionic………………..Covalent character.

38

Dipole Moment

� two electric charges (or partial charges)

� +q and −q separated by a distance R

For IR, the atoms can be

Slightly different…

Carbon & OxygenNitrogen & Oxygen

39

Molecular Potential Energy Diagram

Plot of energy versus internuclear distance:Minimum = equilibrium bond distance (Re)0 = dissociation, atoms far apart.

MPE diagramFor 2 different diatomics….

Strong bondWeak bond

40

Molecular vibrations 1

� All molecules capable of vibrating.

� Many different types of vibration (modes):

– Stretching, Bending, Wagging, Twisting

� The bigger the molecule, the more vib. modes

– Diatomics (1 mode)

– Proteins…10’s of thousands

� Vibrations excited by absorption of EM radiation of the right energy.


Page 11

41

Molecular vibrations 2

� Observing the frequencies of vibration can be used to ID

molecules: Molecular Fingerprints.

� FT-IR and Raman spectroscopy used in this way for:

– Forensics (drugs, explosives, hazmat)

– Monitoring progress of reactions

0

2500

5000

7500

500 600 700 800 900 1000 1100Raman shift, cm

-1

Intensity (arb. units)

MDMA

HeroinCocaine

42

Selection Rules

� Very important in vibrational spectroscopy.

– Used to predict which vibrations you should see.

– Rules are different for IR-Absorption and Raman

scattering.

– Sometimes we see bands in IR and not in Raman …..and visa-versa.

– Raman good for non-polar molecules.

– IR good for polar molecules.

43

IR-absorption spectroscopy

� Light absorbed by molecule:

– passes light through the sample

– Measure how much absorbed.

� Vibrational transitions (lowish energy)

� IR radiation (2 µm – 1000 µm)

� (5000 cm-1 to 10 cm-1)

� Spectra from ~400-600 cm-1 to 4000 cm-1

� Obeys Beer-Lambert (linear with conc.)

44

IR spectrometer

http://www.chemistry.adelaide.edu.au/external/soc-rel/content/ir-instr.htm

Dispersive, like UV-visible,Light passes thru….scan across different wavelengths to make spectrum.

Most modern IR spectrometers are Fourier-Transform (FT) based and use a Michelson Interferometer.All light frequencies at once.Faster than scanning


Page 12

45

Typical IR spectrumPlot of % TransmittanceVersusWavenumber

Vibration type V/cm−−−−1

C–H 2850−2960

C–H 1340−1465

C–C stretch, bend 700−1250

C=C stretch 1620−1680

C≡C stretch 2100−2260

O–H stretch 3590−3650

C=O stretch 1640−1780

C≡N stretch 2215−2275

N–H stretch 3200−3500

Hydrogen bonds 3200−3570

46

Raman spectroscopy (I)� Light interacts with vibrational modes of molecule.

� A very small amount is scattered at longer/shorter

wavelength.

Stokes shift…to longer

wavelength

Anti-Stokes to shorter

wavelength.

Photon

hνννν0000

Virtual State

Photon

h(νννν0000−ν−ν−ν−ν1111)

Photon

hνννν0000

Photon

h(νννν0000+ν+ν+ν+ν1111)

Virtual State

Stokes anti-Stokes

Electronic Ground State

ν ν ν ν = 4

ν ν ν ν = 3

νννν = 2

νννν = 1

ν ν ν ν = 0

ν ν ν ν = 4

ν ν ν ν = 3

νννν = 2

νννν = 1

ν ν ν ν = 0

47

Raman spectroscopy (II)

RAYLEIGH

RAMAN(STOKES)

RAMAN(ANTI-STOKES)

υυυυ0000((((υυυυ0000−−−−υυυυ1111)))) ((((υυυυ0000 ++++ υυυυ1111))))

Frequency, cm-1

� Stokes lines:- ~103 times weaker than Rayleigh scattering

� - shorter wavelength, gain of energy : Anti-Stokes lines:- ~ weaker than Stokes at ambient temps.

� Vibrational spectrum similar to an IR spectrum,·

� Based on chemical structure of molecules,

� Spectra are unique…….molecular fingerprints,

48

Raman spectroscopy (III)

� Raman looks at the scattered light relative to the excitation line.

� Can use any wavelength excitation.

IR A b s o rp t io nb a n d s

R a y le ig h s c a t te r in g

R a m a n s a c t te r in gb a n d s

P h o to nE n e rg y

0 - 4 0 0 0 c m- 1

1 5 ,6 0 0 + / - 4 0 0 0 c m-1

- 6 3 2 n m H e N e

1 8 ,7 9 7 + / - 4 0 0 0 c m-1

- 5 3 2 n m

2 0 ,4 9 2 + / - 4 0 0 0 c m-1

- 4 8 8 n m A r io n


Page 13

49

Raman spectrometer

50

Typical Raman Spectra

0

500

1000

1500

2000

2500

3000

3500

4000

200 400 600 800 1000 1200 1400 1600 1800

Pure Cocaine taken using aBattery operated portable system

10000

20000

30000

300 500 700 900 1100 1300 1500 1700

Cocaine hydrochloride, pure.

Raman shift, cm-1

.

INT

EN

SIT

Y (

arb

.)

A11AUG13:11/8/97.

Pure Cocaine taken using aLaboratory system

51

Gross selection rule: IR-Absorption

� The dipole moment, p, of the molecule must change during the vibration for it to IR active.

• Does not have to have a permanent dipole…can move

• Some vibrations cause no change in dipole moment (homonuclear diatomics)

Transitions are restricted to single-quantum jumps to neighboring levels……e.g. from v=0 to v=1, from v=1 to v=2, etc

52

Changing dipole moment

– Original molecule AB; 2

atoms + “bond” ⇒ electron

cloud.

– Draw bond dipole.

– Distort molecule.

– Draw new bond dipole.

– Has dipole changed?

+q -qr

p→→→→

p→→→→

+q -qr

A Br


Page 14

53

Gross selection rule: Raman spectroscopy

� Has to be a change in the polarizability for a vibration

to be Raman active:

Distortion of the electron cloud of a molecular entity by

a vibration. Good for Homonuclear diatomics (N2, O2 etc.)

C OO O C O C OO

CO2 symmetric Stretch

54

Exclusion Rule:

� More exact treatment of IR and Raman activity of normal modes leads to the exclusion rule:

� If the molecule has a centre of symmetry (like CO2), then no modes can be both infrared and Raman active:– A mode may be inactive in both.

– often possible to judge intuitively if a mode changes the molecular dipole moment,

– use this rule to identify modes that are not Raman active

� Group theory is used to predict whether a mode is infrared or Raman active (3rd year)

55

IR vs. Raman spectra

FT-IR…….

Raman……..

56

Raman vs. IR spectroscopy

� How do the 2 different vibrational techniques

compare?

� How do the selection rules work in practice for polyatomic molecules?

� What are the advantages/disadvantages?

� How can we use the techniques for advanced studies?


Page 15

57

Ethanol (C2H5OH)

O-Hstretch

O-Hbend

Scales not exact match

Polar groups give strongIR bands….weaker in Raman

Different selection rules

Data from: ww.aist.go.jp/RIODB/SDBS

Weak O-H bands mean can use OH containing solvents

58

Applications in Microscopy

� Can use IR and Raman in microscopy.

� IR radiation = long wavelength = large spot size

– In practice spot ~10 µm.

� UV-Vis = shorter wavelength = smaller spot size

– For 488 nm excitation, spot < 1 µm.

� Water is a weak Raman scatterer:

– Can use Raman for analysis of cells & tissue.

59

IR versus Raman: comparison

IR-absorption Raman

Selection rule Change in Dipole moment Change in polarizability

Good for Polar molecules (e.g. HCl) Non-polar molecules (e.g. N2)

Water Very strong absorption Very weak scattering

Wavelength IR region of spectrum Any region

Spectra Same (100-4000 cm-1) Same (100-4000 cm-1)

Sensitivity Good Very weak

60


� Vibrational Energies:– Spring Model.

– Force Constants.

– Effective mass.

– Vibrational Energy levels.

– Effect of bond strength on vibrational transitions.

� Understand the simple spring model. Be able to calculate force constants & energies of vibrational transitions. – Chapter 19, Elements of Physical Chemistry, Sections 19.9-

19.9 and 19.10


Page 16

61

Modelling vibrations

� Close to Re the MPE

curve….approximates to a parabola (y=x2).

� Potential Energy (V) can be written:

� V = ½k(R-Re)2

� k = force constant (Nm-1)

62

Force Constant K

� Measure of the strength

of the bond

� Parabola gets steeper as k increases…….

63

Diatomic Model:

� Both atoms move in a

vibration…..

� Need to use detailed

calculations:

– Schrödinger wave

equation (3rd year)

� υ = vibrational quantum

number.

� Specific selection rule:

∆υ = ±1

1, = effective mass

2

(frequency in H )

k

z

ν µπ µ

=

CH3 CH3

K

m1 m2

vE = ( +½)h , = 0,1,2,....υ ν υ

Vibrational Energy Levels:

1( ) , 2 2

(Energy in Joul

h

e

E

)

k

s

υ υπ µ

= +

64

Effective Mass (µ)

= ,

= in ,

= avogadros number

= Atomic

kg

kmass (in )g

A B

A B

A B

a a

A B

a a

a

m m

m m

M M

N N

M M

N N

N

M

µ

µ

+

+

� Important for calculating

vibrational energies

� Always a very small number:


Page 17

65

Vibrational energy levels (diatomics)

E

0

0

1

2

3

(1/2)(h/2ππππ)√√√√(k/µµµµ)

(3/2)(h/2ππππ)√√√√(k/µµµµ)

(5/2)(h/2ππππ)√√√√(k/µµµµ)

(7/2)(h/2ππππ)√√√√(k/µµµµ)

� Differences?

� Constant

� ∆E = (h/2π)√(k/µ)

� For photon

Therefore

66

Calculating the wavenumber of a vibration

� An 1H35Cl molecule has a force constant of 516 Nm−1.

Calculate the vibrational stretching frequency:

wher

The

e

wavenumber of a vibration can be calculated from the equation:

1, .

2

, = ,

0.0010079 0.

Step 1: Calculate the effective

=

ma s

s

H Cl

H Cl

1

a

ν is the vibrational wavenk

c

m m

m m

N

umber in mνπ µ

µ

µ

−=

+

��

27

03545

in , = avogadros number0.001

kg

kg [ ]

0079 0.03545

= 1.63 10

a

a

a a

Always write this out

NN

N N

longhandµ −

+

×

67

Calculating the wavenumber of a vibration

8 2

1

1 7

where

The wave

Nm[N = k

ms kg

number of a vibr :

1, .

2

1

ation can be c

(516 ),

2 2.997 10 1.63

alculated from the equation

Step 2: input the va

10

es:

lu

-1ν is the vibrational wavenumber in m

k

cν

π µ

νπ

−

− −

=

=× ×

�

�

�

9 27

2

2 1

1

229

9 1

1 1

1 (516 ),

1.88 10 1.63 10

13.165 10 ,

1.88 10

gms ]

kgms m

ms kg

sms

m

299, 246 2992 = cm

ν

ν

ν

−

− −

−

−

−

−

−

−

=× ×

= ××

=

�

�

�68

Calculating a force constant (step 1)

( )

2

2 2

2 2 2

2 2 2

wher

The force constant can be calculated from the equation:

1, .

2

1 1, , then:

2 4

4 k

k

Step 1: Rearrange the equat

e

= 4

n:

io

-1ν is the vibrational wavenum

k

c

k

ber

k

c c

c

c

in mνπ µ

ν νπ µ π µ

ν π µ

π ν

=

= =

=

�

��

�

�

� µ

�1H35Cl has a fundamental stretching vibration at 2991 cm-1, Calculate the force constant.


Page 18

69


( )2 2 2k = 4 .....................remember

, = ,

0.0010079 0.0354

Step 2: Calculate th

5

= in , = avogadros number0.0010079 0.03545

=

e effective ma

1

s

kg

s

.

H Cl

H Cl

a a

a

a a

c

m m

m m

N NN

N N

π ν µ

µ

µ

µ

+

+

�

27 kg 63 x 1 ]0 [Always write this out longhand−

70


( )

( )

2 2 27

2 2

8 2 2 27

1

1 1

2 2 10 28

k = 2 ...... = 1.63 x 10

,

k = 2

= (2 2.9

Ste

kg

[ ]

m

p 3: Input

97 10 ) (299,100 ) (1.63 10 )

= (3.54

values

s m

6 10 )(8.946 10 )(1

kg

m s m

Always write this out longhand

c

c

π ν µ µ

π ν µ

π

−

− −

− − −× ×

× ×

�

�

2 2

1

27.63 10 )

= (517 ) [1

kg

kgs kgmsNewton = 1 ]

= 517 Nm

− −

−

−×

71

Diatomic Molecules: V/cm−−−−1

Re/pm k/(N m−−−−1) D/(kJ mol−−−−1

)

1H 2

+ 2333 106 160 256

1H2 4401 74 575 432

2H2 3118 74 577 440

1H

19F 4138 92 955 564

1H

35Cl 2991 127 516 428

1H

81Br 2648 141 412 363

1H

127I 2308 161 314 295

14N2 235S 110 2294 942

16O2 158 121 1177 494

19F2 892 142 445 154

35Cl2 560 199 323 239

1

2

k

cν

π µ=�

p. 497, Atkins & DePaula, 4th edition.

72


� Polyatomic Molecules:– Mass effect.

– Number of vibrational modes.

– Anharmonicity.

– Predicting active modes.

– Analysis of vibrational spectra.

– Comparison between Raman and IR spectra.

� Understand mass effect and factors that influence spectra of polyatomic molecules. Be able to calculate the number of vibrational modes, & predict which bands are IR or Raman active.– Chapter 19, Elements of Physical Chemistry, Sections 19.12/13/15


Page 19

73

Polyatomic molecules……..N>2

� IR spectra are much more complex

� More than just stretching vibrations:

– Bending, wagging, twisting

– Combinations of vibrations

74

Polyatomics? N>2

� View polyatomic as collection of diatomics

� Force constants as per diatomics– Correlates with bond strength (right-hand column)

� Mass effect? Yes, next ovhd.

� Group frequencies or wavenumbers, i.e., all ketones have IR band/peak near 1800 cm−−−−1111

2

3

RC O 2140 1080

R C O 1770 740

R C-OR 980 380

≡

-1 -1Bond ν (cm ) Bond Energy (kJmol )

=

�

75

Mass effect: CHCl3 & CDCl3

( )( )( ) ( )

( )

3

3

3

3

-27 13

1 1, so

2

,

.001 0.11835 1 = in , = avogadros numbe

Step 1: Calculate the effective ma

r.001 0.11835

1 = 1.65

kg

kg x 10 2.46 10

.002 0.

, so...

118 =

s s

s e

H CCl a

a

H CCl

H CCl

D CCl

k

c

NN

ν νπ µ µ

µ

µµ

µ

−

−

−

−

= = ∝

×+

= ×

� �

( )( ) ( )

3

3

-27 13

3

3

kg, so...

35 1

.002 0.11835

1 = 3.266 x 10 1.75 10

H-CClRatio = 1.406

D-CCl

a

D CCl

D CCl

N

µµ−

−

×+

= ×

=Is this seenexperimentally?

76

Compare CHCl3 & CDCl3

� Peak at ~ 3,019 cm–1 due to C—H stretch

� Shifted to ~ 2,258 cm–1 for D—C stretch

� Ratio 3019/2300 = 1.34 (1.406 not bad….)


Page 20

77

How many vibrational modes?

• 3n degrees of freedom (x, y, z)……different displacements• Take away the translational (change in x=y=z) so -3• 2 angles needed to specify linear molecules orientation (A)• 3 angles needed to specify linear molecules orientation (B)

78

Rule:

� The number of modes of vibration Nvib :

� 3N − 5 for linear molecules (e.g. CO2)

� 3N − 6 for nonlinear molecules (e.g. H2O) .

� Where N = number of atoms in molecule

� The bigger the molecule…the more vibrations

79

If ‘Linear’ H2O: Number of IR bands?

� How many vibrations?

� 3N-5 = 3××××3 -5 = 4

� Can only find three different:

– Symmetric stretch

– Asymmetric stretch

– 2 Bends (identical)

� Only two are IR active:

– Changes in dipole moment.

– But we see three experimentally!!

H O H

H O H

H O H

80

Linear triatomic water

� Symmetric stretch

� Asymmetric stretch

� Bend

http://science.widener.edu/svb/ftir/ir_co2.html


Page 21

81

Vibrational modes for ‘bent’ H2O� How many vibrations for non-linear molecule?

3N-6⇒ 3××××3-6 = 3 vibrations

� Sketch each mode & draw bond dipoles

� Sum to produce overall dipole

� Distort molecule for each vibration

� Redraw bond dipoles

� Sum to give overall dipole

� Has dipole changed during vibration?

82

IR Spectra of simple cyanidesLinear arrangement of atoms X-C-N

3N-5 vibrations; 3 different & all active

Emergent Concept; Group frequencies

X ↔ C C ↔ N B e n d

HC N 3 3 1 1 2 0 9 7 7 1 2

D C N 2 6 3 0 1 9 2 5 5 6 9

FC N 1 0 7 7 2 2 9 0 4 4 9

C lC N 7 1 4 2 2 1 9 3 8 0

B rC N 5 7 4 2 2 0 0 3 4 2

IC N 4 7 0 2 1 5 8 3 2 1

83

HCN Vibrational modes

� C-N stretch

� H-C stretch

� H-C-N bends

� All IR active

Isotopic substitution?

Identical structure

� D replacing H

– No change -8%

– Big change -20%

– Some change -20%

H C N

H C N

H−−−−C stretch

H C N H C N

H C N H C N

84

Band areas

Single bonds to H

O-H

C-H

Fingerprint region

Phenol…

Functional group region


Page 22

85

Analysis of vibrational spectra (I)

� Functional group region most important for

interpreting IR spectra.

– In IR it is the polar covalent bonds than are IR "active“

– In Raman spectra non-polar bonds are also “active”.

– In organic molecules these polar covalent bonds represent the functional groups.

� Hence, the most useful information obtained from

an IR spectrum is what functional groups are present within the molecule.

86

Analysis of vibrational spectra (II)

� Some functional groups are combinations of

different bond types.

– Esters (CO2R) contain both C=O and C-O bonds,

– Both are typically seen in an IR spectrum of an ester.

� In the fingerprint region, spectra tend to be more complex and much harder to assign.

– But very important in Physics, Materials Science,

etc………….properties of materials

� Now some examples:

87

Benzene vs Toluene, liquid

Spectra from: http://www.aist.go.jp/RIODB/SDBS

CH3

88

Environmental Influences (I)

� Covalent diatomic molecule HCl

Gas-phase 2,886 cm−1

Solid state 2,720 cm−1

Solution (aromatic solvent) 2,712 cm−1

Solution (ether solvent) 2,393 cm−1

� Conclusion?– NB: wavenumber of absorption ∝ √∝ √∝ √∝ √(force constant)

– weak intermolecular bonding R2O....HCl


Page 23

89

Environmental Influences (II)

� Vibrational bands are usually broader in

condensed media (solid liquid) than gas phase.

� Crystalline materials have sharper vibrational bands than amorphous materials.

– Can be used to distinguish polymorphs of

pharmaceutical products

Documents

Spectroscopy 6 Topics to be covered - NUI · PDF fileCocaine hydrochloride ... (liquid/solid) they overlap. Not seen at r.t. but if cooled down to LN2 . ... Fourier-Transform (FT)