1. No category

2 year Spectroscopy Handout: 2008.
Spectroscopy
6 Topics to be covered
3 lectures leading to one exam question
Texts:
th ed.
“Elements of Physical Chemistry” 4
– by Atkins & de Paula, Chapter 19 & Chapter 20
– Beer-Lambert.
“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.
Introduction to Spectroscopy.
Quantitative Spectroscopy:
Electronic spectroscopy.
Vibrational Spectroscopy:
– FT-IR and Raman spectroscopy.
– http://www.nuigalway.ie/chem/AlanR/
– http://www.nuigalway.ie/nanoscale/undergraduate.html
– This version 22/11/2010: minor errors corrected.
1
Energies of Vibrational transitions.
Polyatomic Vibrational spectroscopy.
2
What is spectroscopy?
2Y Spectroscopy: Topic 1
Introduction to spectroscopy:
– Electromagnetic spectrum.
– Quantisation of energy & energy levels.
– Selection rules.
– Bohr condition.
– Absorption, Emission, & Scattering Spectroscopies.
Interaction of electromagnetic radiation with
matter:
– Absorption.
– Emission.
– Scattering.
Many different scales:
– Astronomy (single stars).
– Microscopy (single molecules).
Need to Know: EM spectrum, how to interconvert
from wavelength, wavenumber, or frequency to
energy, and the different types of spectroscopy.
3
Everything from forensics to living cells
4
Page 1
2 year Spectroscopy Handout: 2008.
The Electromagnetic Spectrum
Spectrum (pl. spectra)
Region
Radio F
“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).
Wavelength
106108
3003 m
10
12
Micro Wave
10 10
300.3 mm
IR
10121014
3001 µm
14
16
UV-VIS
10 10
100030 nm
X-RAY
10161019
10030 pm
γ-RAY
19
22
10 10
300.03 pm
Also ideal for quantitative analysis via the BeerLambert Law:
– UV-Vis (exp. 2)………..protein conc. in biochemistry.
– FT-IR, NIR, Raman spectroscopies in industry.
5
6
Wavenumber (cm-1)
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).
30000
500 nm = 0.5
x10-4
cm = 20,000
cm-1_______Visible
1000 nm = 1 x10-4 cm = 10,000 cm-1
998
Cocaine hydrochloride
(high energy)
INTENSITY (arb. units)
Frequency s–1
Near IR
2000 nm = 2 x10-4 cm = 5,000 cm-1
20000
868
1019
1024
1599
10000
341
393
784
1273
488
5000 nm = 5 x10-4 cm = 2000 cm-1__________IR (low energy)
300
400
500
1458
600
700
800
900
1000
1100
1200
-1
raman shift, cm .
7
8
Page 2
1715
894
613
1300
1400
1500
1600
1700
1800
2 year Spectroscopy Handout: 2008.
Schematic molecular energy levels
UV-VISIBLE
INFRARED
Selection Rules
MICROWAVE
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).
E
two electric charges +q and −q
separated by a distance R
ELECTRONIC
VIBRATIONAL
ROTATIONAL
TRANSLATIONAL
9
10
Absorption spectroscopy
The Bohr frequency condition:
∆E (molecule) = E (photon)
Can refer to the absorption of any frequency of
radiation, most common are:
– UV-visible absorption (electronic)
– IR absorption (vibrational)
– Microwave absorption (rotational)
PHOTON
ENERGY
BEFORE
DURING
These are all types of molecular spectroscopy.
Energy of the radiation ≅ energy of transition.
AFTER
ε = hν = hc / λ = hcν
11
12
Page 3
2 year Spectroscopy Handout: 2008.
Absorption spectrometer
Emission spectroscopy
Light absorbed by
sample.
Grating/frequency
analyser
Single channel (PMT) or
multichannel (CCD)
detectors (visible)
Emission of any frequency of radiation.
Concerned with the properties of emitted
photons.
UV-VIS-NIR (electronic transitions):
– Fluorescence, Phosphorescence,
Chemiluminescence, photoluminescence.
13
Fluorescence underpins nearly all of modern
biology.
Based on chemistry & physics.
14
Scattering spectroscopy
2Y Spectroscopy: Topic 2
We look at how light scatters from molecules:
Quantitative spectroscopy:
–
–
–
–
–
– 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.
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)
www.umich.edu/~morgroup/virtual/
15
16
Page 4
Beer-Lambert Law.
Absorbance & Transmittance.
Molar Absorption co-efficient.
Calculations.
Limitations.
2 year Spectroscopy Handout: 2008.
Beer-Lambert Law: Quantitative
Sample, Concentration C
I0
IT
Pathlength, l
17
Beer Lambert Law
IT = I0 × 10 (− e l C ) .....at constant Temp. and a single wavelength (λ )
At a fixed temperature
and a single wavelength:
e molar absorptivity, l pathlength, C concentration of absorbing species
– the intensity of light, IT,
transmitted through a
sample depends upon:
– the pathlength or sample
thickness, l
– the concentration of the
absorbing species, C
– the incident light intensity,
I0
log(IT ) = log(I0 ) − e l C.........rearrange to:
a
log(IT ) − log(I 0 ) = − e l C......we know: log ( a ) − log ( b ) =log   ⇒
b

I
−  log  T
 I0

I 
absorbance, A = log  0 
 IT 
Radiation @ 280 nm
1 mm pathlength
Aqueous solution, 0.50 mmol L-1
54% of light passes through
Needed Info
A = - log T = ε l C ----- step 1, write eqn.
ε = - log T / l C --------- step 2, rearrange eqn.
ε=
log 0.54
(5.0 × 10−4 molL−1 ) x (1 mm)

  = e l C ,

⇒ A=elC
Application of Beer-Lambert law (2)
Calculate: Molar abs. Co-eff. of Tryptophan (comp. of proteins)
–
–
–
–

 I0
 log  I
 T

18
Application of Beer-Lambert law (1)

  = e l C...rearrange to:

Step 3, put in values.
ε = 5.4 × 102 Lmol−1 mm −1 , or
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
ε = 5.4 × 103 Lmol−1 cm −1 ,
19
20
Page 5
2 year Spectroscopy Handout: 2008.
Limitations of Beer-Lambert law
2Y Spectroscopy: Topic 3
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.
Electronic Spectroscopy:
–
–
–
–
–
– Can be used with FT-IR……etc.
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
21
22
Visible spectrum
Absorption 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
Absorption spectrum of chlorophyll in the visible region.
Absorbs in the red and blue regions, green light is not absorbed.
23
24
Page 6
2 year Spectroscopy Handout: 2008.
UV-Vis absorption
Franck-Condon Principle
190 to 1000 nm
Organic Chromophores
absorb in UV/Vis/NIR
– C=C, C=O, C=N
∆ E = E2 − E1 = hν (photon)
25
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.
26
Absorption in gaseous state
Absorption in solution
Very broad, ill defined
The electronic spectra of
some molecules show
significant vibrational
structure.
UV spectrum of gaseous SO 2
at 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.
27
28
Page 7
2 year Spectroscopy Handout: 2008.
Fluorescence
Phosphorescence
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
29
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
()
30
Fluorescence Spectrometer
Fluorescence spectra
Single channel
Right angle excitation
200-900 nm usually
Quartz cuvettes
Light source; lamps, LED,
laser,
Excite with a narrow band
Photoluminescence
Bioluminescence
Chemiluminescence
31
32
Page 8
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
2 year Spectroscopy Handout: 2008.
Stokes Shift
Fluorescence Lifetime
Born in Sligo
Emission @ longer
wavelength than
absorption
Difference = Stokes Shift
Sensitive to environment
– Nanosecond (10-9 s) to
Picosecond (10-12) range
– Anthracene = 5.2 ns in
cyclohexane solution
– polarity
– Ion concentration
33
2Y Spectroscopy: Topic 4
Measure of the efficiency with which absorbed
light produces an effect:
Vibrational Spectroscopy:
–
–
–
–
– 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)
For T1 to S0 transition
lifetime can be seconds
34
Quantum yield (Q)
Average time a molecule
spends in the excited
state:
Tricky to measure experimentally:
– Have to integrate the absorption and emission bands
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 19.919.13 and 19.15
35
36
Page 9
2 year Spectroscopy Handout: 2008.
Concepts
Dipole Moment
• 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.
two electric charges (or partial charges)
+q and −q separated by a distance R
For IR, the atoms can be
Slightly different…
Electronegativities……..some atoms like
electrons more than others…….
– Stronger / weaker bonds.
– H+F- ………………C-H
– Ionic………………..Covalent character.
Carbon & Oxygen
Nitrogen & Oxygen
37
38
Molecular Potential Energy Diagram
Molecular vibrations 1
MPE diagram
For 2 different
diatomics….
All molecules capable of vibrating.
Many different types of vibration (modes):
– Stretching, Bending, Wagging, Twisting
Strong bond
Weak bond
The bigger the molecule, the more vib. modes
– Diatomics (1 mode)
– Proteins…10’s of thousands
Plot of energy versus internuclear distance:
Minimum = equilibrium bond distance (Re)
0 = dissociation, atoms far apart.
39
Vibrations excited by absorption of EM radiation
of the right energy.
40
Page 10
2 year Spectroscopy Handout: 2008.
Molecular vibrations 2
Selection Rules
Observing the frequencies of vibration can be used to ID
molecules: Molecular Fingerprints.
FT-IR and Raman spectroscopy used in this way for:
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.
– Forensics (drugs, explosives, hazmat)
– Monitoring progress of reactions
MDMA
In
te
n
s
ity(a
rb
.u
n
its
)
7500
5000
2500
0
Cocaine
Heroin
500
600
700
800
-1
Raman shift, cm
900
1000
1100
41
42
IR-absorption spectroscopy
IR spectrometer
Dispersive, like UV-visible,
Light passes thru….scan across
different wavelengths to make
spectrum.
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.)
Most modern IR spectrometers are
Fourier-Transform (FT) based and
use a Michelson Interferometer.
All light frequencies at once.
Faster than scanning
43
44
http://www.chemistry.adelaide.edu.au/external/soc-rel/content/ir-instr.htm
Page 11
2 year Spectroscopy Handout: 2008.
Typical IR spectrum
Raman spectroscopy (I)
Plot of %
Transmittance
Versus
Wavenumber
Vibration type
V/cm−1
C–H
2850−2960
C–H
1340−1465
Light interacts with vibrational modes of molecule.
A very small amount is scattered at longer/shorter
wavelength.
anti-Stokes
Stokes
Virtual State
700−1250
Photon
C=C stretch
1620−1680
h(ν
ν0 −ν1)
C≡C stretch
2100−2260
C–C stretch, bend
O–H stretch
3590−3650
C=O stretch
1640−1780
C≡N stretch
2215−2275
Photon
N–H stretch
3200−3500
hν
ν0
Hydrogen bonds
3200−3570
Stokes
shift…to
longer
wavelength
Virtual State
Photon
h(ν
ν0+ν1)
ν=4
Photon
ν=4
ν=3
ν=2
ν=1
hν
ν0
ν=3
ν=2
ν=1
ν=0
Anti-Stokes to
shorter
wavelength.
ν=0
Electronic Ground State
45
46
Raman spectroscopy (II)
RAYLEIGH
RAMAN
(STOKES)
RAMAN
(ANTI-STOKES)
(υ0−υ1)
υ0
Frequency, cm-1
(υ0 + υ1)
Raman spectroscopy (III)
R a y le ig h s c a t t e r in g
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,
I R A b s o r p t io n
bands
R a m a n s a c t t e r in g
bands
P h o to n
E n e rg y
0 - 4000 cm
-1
1 5 ,6 0 0 + /- 4 0 0 0 c m
1 8 ,7 9 7 + /- 4 0 0 0 c m
2 0 ,4 9 2 + /- 4 0 0 0 c m
47
-1
-1
- 632 nm H eN e
- 532 nm
- 4 8 8 n m A r io n
Raman looks at the scattered light relative to the
excitation line.
Can use any wavelength excitation.
48
Page 12
-1
2 year Spectroscopy Handout: 2008.
Raman spectrometer
Typical Raman Spectra
Pure Cocaine taken using a
Battery operated portable
system
4000
3500
3000
2500
2000
1500
A11AUG13:11/8/97.
1000
30000
0
200
400
600
800
1000
1200
1400
1600
1800
Pure Cocaine taken using a
Laboratory system
INTENSITY (arb.)
500
Cocaine hydrochloride,
pure.
20000
10000
300
49
Gross selection rule: IR-Absorption
500
50
700
900
1100
1300
-1
Raman shift, cm .
1500
Changing dipole moment
The dipole moment, p, of the molecule must
change during the vibration for it to IR active.
r
– Original molecule AB; 2
B
A
atoms + “bond” ⇒ electron
• Does not have to have a
permanent dipole…can move
cloud.
r
-q
+q
– Draw bond dipole.
• Some vibrations cause no
change in dipole moment
(homonuclear diatomics)
→
p
– Distort molecule.
– Draw new bond dipole.
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
– Has dipole changed?
51
52
Page 13
r
-q
+q
→
p
1700
2 year Spectroscopy Handout: 2008.
Gross selection rule: Raman spectroscopy
Exclusion Rule:
Has to be a change in the polarizability for a vibration
to be Raman active:
CO2 symmetric Stretch
O
C
O
O C O
O
C
O
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
Distortion of the electron cloud of a molecular entity by
a vibration.
Good for Homonuclear diatomics (N2, O2 etc.)
53
Group theory is used to predict whether a mode
is infrared or Raman active (3rd year)
54
IR vs. Raman spectra
Raman vs. IR spectroscopy
FT-IR…….
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?
Raman……..
55
56
Page 14
2 year Spectroscopy Handout: 2008.
Ethanol (C2H5OH)
O-H
stretch
Applications in Microscopy
Scales not exact match
O-H
bend
Polar groups give strong
IR bands….weaker in Raman
Can use IR and Raman in microscopy.
IR radiation = long wavelength = large spot size
– In practice spot ~10 µm.
Different selection rules
UV-Vis = shorter wavelength = smaller spot size
– For 488 nm excitation, spot < 1 µm.
Weak O-H bands
mean can use OH
containing solvents
Water is a weak Raman scatterer:
– Can use Raman for analysis of cells & tissue.
57
58
Data from: ww.aist.go.jp/RIODB/SDBS
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
Spectra
Sensitivity
IR region of spectrum
Any region
Same (100-4000 cm-1)
Same (100-4000 cm-1)
Good
Very weak
2Y Spectroscopy: Topic 5
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 19.919.9 and 19.10
59
60
Page 15
2 year Spectroscopy Handout: 2008.
Modelling vibrations
Force Constant K
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)
61
62
m1
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
63
Effective Mass (µ)
m2
H3C
Measure of the strength
of the bond
Parabola gets steeper as
k increases…….
CH3
K
ν=
1
2π
k
µ
µ=
, µ = effective mass
mA mB
,
mA + mB
 M A  M B 



N
N
µ =  a  a  in kg,
 MA   MB 

+

 Na   Na 
(frequency in Hz)
E v = (υ +½)hν , υ = 0,1,2,....
V ibrational Energy Levels:
N a = avogadros number
h
Eυ = (υ + 1 )
2 2π
M = Atomic mass (in kg)
k
µ
,
(Energy in Joul e s )
64
Page 16
Important for calculating
vibrational energies
Always a very small
number:
2 year Spectroscopy Handout: 2008.
Calculating the wavenumber of a vibration
Vibrational energy levels (diatomics)
π)√
√ (k/µ
µ)
3 (7/2)(h/2π
E
Differences?
Constant
∆E = (h/2π)√(k/µ)
For photon
An 1H35Cl molecule has a force constant of 516 Nm−1.
Calculate the vibrational stretching frequency:
The wavenumber of a vibration can be calculated from the equation:
ν =
µ)
2 (5/2)(h/2π
π)√
√ (k/µ
1
2π c
k
µ
, where ν is the vibrational wavenumber in m −1 .
Step 1: Calculate the effective mass, µ =
1 (3/2)(h/2π
π)√
√ (k/µ
µ)
Therefore
 0.0010079   0.03545 



Na
Na 



µ=
in kg, N a = avogadros number
 0.0010079   0.03545 
+

 

Na

  Na 
0 (1/2)(h/2π
π)√
√ (k/µ
µ)
0
65
66
Calculating the wavenumber of a vibration
1
k
2π c
µ
1H35Cl
has a fundamental stretching vibration at 2991 cm-1,
Calculate the force constant.
, where ν is the vibrational wavenumber in m-1 .
The force constant can be calculated from the equation:
ν =
Step 2: input the values:
ν =
1
(516 Nm −1 )
, [N = kgms −2 ]
2π 2.997 × 108 ms −1 1.63 × 10−27 kg
ν =
1
1.88 × 109 ms −1
1
k
2π c
µ
, where ν is the vibrational wavenumber in m -1.
Step 1: Rearrange the equation:
ν =
(516 kgms −2 m −1 )
,
1.63 × 10−27 kg
1
k
2π c
µ
, ν 2 =
ν 2 4π 2 c 2 µ = k
1
ν =
3.165 × 1029s −2 ,
9
−1
1.88 × 10 ms
67
µ = 1.63 × 10−27 kg [Always write this out longhand ]
Calculating a force constant (step 1)
The wavenumber of a vibration can be calculated from the equation:
ν =
mH mCl
,
mH + mCl
k = ( 4π 2 c 2 )ν 2 µ
ν = 299, 246 m −1 = 2992 cm −1
68
Page 17
1
k
4π c µ
2 2
, then:
2 year Spectroscopy Handout: 2008.
Calculating a force constant (step 2)
(
Calculating a force constant (step 3)
)
k = 4π 2c 2 ν 2 µ .....................remember
Step 2: Calculate the effective mass, µ =
k = ( 2π c ) ν 2 µ......µ = 1.63 x 10−27 kg
2
mH mCl
,
mH + mCl
Step 3: Input values, [Always write this out longhand ]
k = ( 2π c ) ν 2 µ
2
 0.0010079   0.03545 



Na
  N a  in kg, N = avogadros number
µ= 
a
 0.0010079   0.03545 
+

 

Na

  Na 
= (2π 2.997 ×108 ms −1 ) 2 (299,100 m −1 ) 2 (1.63 × 10−27 kg )
= (3.546 ×1018 m 2s −2 )(8.946 × 1010 m −2 )(1.63 × 10−27 kg )
= (517 kgs −2 ) [1 Newton = 1kgms −2 ]
= 517 Nm −1
µ = 1.63 x 10−27 kg [Always write this out longhand ]
69
70
Diatomic Molecules:
2Y Spectroscopy: Topic 6
V/cm−
Re/pm
1
2333
106
160
256
1
4401
74
575
432
1
H 2+
H2
2
H2
k/(N m− )
1
D/(kJ mol− )
1
3118
74
577
440
1
19
4138
92
955
564
1
428
H F
35
2991
127
516
1
H81Br
2648
141
412
363
1
2308
161
314
295
14
235S
110
2294
942
16
158
121
1177
494
19
892
142
445
154
35
560
199
323
239
H Cl
H127I
N2
O2
F2
Cl2
ν =
71
p. 497, Atkins & DePaula,
4th
edition.
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
1
2π c
k
72
µ
Page 18
2 year Spectroscopy Handout: 2008.
Polyatomic molecules……..N>2
Polyatomics? N>2
ν (cm-1 ) Bond Energy (kJmol -1 )
Bond
RC ≡ O
2140
1080
R 2C = O
1770
740
R 3C-OR
980
380
IR spectra are much more complex
More than just stretching vibrations:
– Bending, wagging, twisting
– Combinations of vibrations
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−1
73
74
Compare CHCl3 & CDCl3
Mass effect: CHCl3 & CDCl3
ν =
1
2π c
k
µ
, so ν = ∝
1
µ
Step 1: Calculate the effective masses,
µH −CCl =
3
(.001)( 0.11835) × 1
(.001) + ( 0.11835) N a
µH −CCl = 1.65 x 10-27 kg , so...
3
µD −CCl =
3
in kg, N a = avogadros number
1
µH −CCl
= 2.46 × 1013
3
(.002 ) ( 0.11835) × 1
.002
( ) + ( 0.11835) N a
µD −CCl = 3.266 x 10-27 kg, so...
3
1
µD −CCl
= 1.75 × 1013
3
H-CCl3
Ratio =
= 1.406
D-CCl3
Is this seen
experimentally?
75
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….)
76
Page 19
2 year Spectroscopy Handout: 2008.
How many vibrational modes?
Rule:
• 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)
77
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
78
If ‘Linear’ H2O: Number of IR bands?
How many vibrations?
3N-5 = 3×
×3 -5 = 4
Can only find three different:
H
O
H
H
O
H
H
O
H
Linear triatomic water
– Symmetric stretch
Symmetric stretch
Asymmetric stretch
Bend
– Asymmetric stretch
– 2 Bends (identical)
Only two are IR active:
– Changes in dipole moment.
– But we see three experimentally!!
http://science.widener.edu/svb/ftir/ir_co2.html
79
80
Page 20
2 year Spectroscopy Handout: 2008.
IR Spectra of simple cyanides
Vibrational modes for ‘bent’ H2O
Linear arrangement of atoms X-C-N
3N-5 vibrations; 3 different & all active
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?
Emergent Concept; Group frequencies
81
X↔ C
C↔ N
Bend
HC N
331 1
2097
71 2
DCN
2630
1 925
569
FC N
1 077
2290
449
C lC N
71 4
221 9
380
B rC N
574
2200
342
IC N
470
21 58
321
82
HCN Vibrational modes
N
H
C
N
H
H
H
C
C
N
C
C
Fingerprint region
Identical structure
N
H−
− C stretch
H
Functional group region
C-N stretch
H-C stretch
H-C-N bends
All IR active
Isotopic substitution?
N
C-H
C
O-H
H
Band areas
N
D replacing H
– No change
-8%
– Big change -20%
– Some change -20%
Single bonds to H
Phenol…
83
84
Page 21
2 year Spectroscopy Handout: 2008.
Analysis of vibrational spectra (I)
Analysis of vibrational spectra (II)
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.
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.
Hence, the most useful information obtained from
an IR spectrum is what functional groups are
present within the molecule.
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
85
Now some examples:
86
Benzene vs Toluene, liquid
Environmental Influences (I)
Covalent diatomic molecule HCl
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?
CH3
– NB: wavenumber of absorption ∝ √(force
constant)
√
– weak intermolecular bonding R2O....HCl
87
88
Spectra from: http://www.aist.go.jp/RIODB/SDBS
Page 22
2 year Spectroscopy Handout: 2008.
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
89
Page 23