Selection Rules for IR and Raman Spectra Guide

Selection Rules for IR and Raman Spectra
Raman versus IR Spectroscopy
Depolarization Ratios for Raman Spectra
Master student: Đặng Thị Xuân Diễm
Lecturer: Nguyễn Văn Định, PhD

Contents
08/01/2017 Đặng Thị Xuân Diễm 2
Selection Rules for IR and Raman Spectra1
Raman versus IR Spectroscopy2
Depolarization Ratios for Raman Spectra3
Selection Rules for IR Spectra1
Selection Rules for Raman Spectra2
The mutual exclusion principle33
The advantages of Raman versus IR Spectroscopy1
The limitations of Raman versus IR Spectrosocpy2
Definition1
Calculations2

1. © Copyright http://www.aanda.org.
Problems
Figure 1.1 IR and Raman spectra
of 𝑆𝑖, 𝐶𝐻4, 𝐻2 𝑂, 𝑁2
1
“How can we determine
whether a vibration is
active or prohibited in
IR and Raman spectra?”
“Selection Rules for IR
and Raman Spectra”

Contents
Definition1
Calculations

2. Bernath P. (2005), Spectra of Atomics and Molecules, Oxford University Press, England.
3. Ferraro J., Nakamoto K. and Brown W. (2003), Introductory Raman Spectroscopy, Academic Press, USA.
4. Raymond S. and John J. (2013), Physics for Scientists and Engineers with Modern Physics, Brooks / Cole Cengage Learning, USA.
Selection Rules for IR SpectraSelection Rules for IR and Raman Spectra1
Dipole moment4
𝑃 = 𝑄𝑑Diatomic
molecules
Examples IR
Homopolar 𝐻2, 𝑂2 … not active
Heteropolar 𝐶𝑂, 𝑁𝑂 … active
a vibration is IR-active if the dipole moment
is changed during the vibration3

3.Ferraro J., Nakamoto K. and Brown W. (2003), Introductory Raman Spectroscopy, Academic Press, USA.
5. © Copyright http://www.fractalnomics.com
Figure 1.2 Normal modes of vibration in 𝐶𝑂2
3
𝜈1vibration is not IR-active
𝜈2 and 𝜈3 vibrations are IR-active
+ +.
𝜈1
𝜈2𝑎 𝜈2𝑏 𝜈31340 𝑐𝑚−1
667 𝑐𝑚−1 667 𝑐𝑚−1
2350 𝑐𝑚−1

Figure 1.4 Change in dipole moment
for 𝐻2 𝑂 molecule during each normal vibration3
All vibrations are IR-active!
𝝂 𝟏 𝝂 𝟐 𝝂 𝟑

Contents
Definition
Calculations

4. Raymond S. and John J. (2013), Physics for Scientists and Engineers with Modern Physics, Brooks / Cole Cengage Learning, USA.
6. Schrader B. (1995), Infrared and Raman Spectroscopy, Weinheim, Germany.
7. Bonin K. and Kresin V. (1956), Electric-dipole Polarizabilities of Atoms, Molecules and Clusters, World Scientific, USA.
𝑃 = 𝛼𝐸
Figure 1.5 The polarization
of the molecules
in an electric field6
Polarizability7
Figure 1.6 The polarization of the molecules
in an electric field4
𝑃 𝐶. 𝑚 : dipole moment
𝐸 (
𝑉
𝑚
): electric field strength
𝛼 (
𝐶𝑚2
𝑉
)

𝑃 = 𝜶𝐸
• In Descartes coordinates3
𝑃𝑥 = 𝛼 𝑥𝑥 𝐸 𝑥 + 𝛼 𝑥𝑦 𝐸 𝑦 + 𝛼 𝑥𝑧 𝐸𝑧
𝑃𝑦 = 𝛼 𝑦𝑥 𝐸 𝑥 + 𝛼 𝑦𝑦 𝐸 𝑦 + 𝛼 𝑦𝑧 𝐸𝑧
𝑃𝑧 = 𝛼 𝑧𝑥 𝐸 𝑥 + 𝛼 𝑧𝑦 𝐸 𝑦 + 𝛼 𝑧𝑧 𝐸𝑧
Polarizability tensor
• In normal Raman scattering, polarizability tensor is symmetric3
• In matrix form3
𝑃𝑥
𝑃𝑦
𝑃𝑧
=
𝛼 𝑥𝑥 𝛼 𝑥𝑦 𝛼 𝑥𝑧
𝛼 𝑦𝑥 𝛼 𝑦𝑦 𝛼 𝑦𝑧
𝛼 𝑧𝑥 𝛼 𝑧𝑦 𝛼 𝑧𝑧
𝐸 𝑥
𝐸 𝑦
𝐸𝑧

𝐼 𝑅𝑎𝑚𝑎𝑛~
𝜕𝛼
𝜕𝑞 0
2
“How can we know components of polarizability tensor
changes during the vibration? “
The vibration is Raman-active if the size, shape or orientation
of polarizability ellipsoid changes during the normal vibration3
“we plot
1
𝛼 𝑖
, we have polarizability ellipsoid”
The vibration is Raman-active if one of these components
of the polarizability tensor is changed during the vibration3

Figure 1.7 Changes in polarizability ellipsoid during
normal vibrations of 𝐶𝑂2 molecule3
• 𝜈1 is Raman-active
(the ellipsoid size is changing)
• 𝜈2 and 𝜈3 is not Raman-active
𝝂 𝟏
𝝂 𝟑
𝝂 𝟐

Figure 1.9 Changes in polarizability ellipsoid
during normal vibrations of 𝐻2 𝑂 molecule3
(the ellipsoid size is changing)
(the ellipsoid shape is changing)
(the ellipsoid orientation is changing)
𝝂 𝟏
𝝂 𝟐
𝝂 𝟑

Contents
Definition
Calculations

In a centrosymmetry molecule, a vibration may be
either IR active or Raman active but not both3
3. Ferraro J., Nakamoto K. and Brown W. (2003), Introductory Raman Spectroscopy, Academic Press, USA
1 Mutual exclusion principle
𝑪𝑶 𝟐
band IR Raman
𝑣1 Not active active
𝑣2 active Not active
𝑣3 active Not active
→ 𝐶𝑂2 is centrosymmetric

→ 𝐻2 𝑂 isn’t centrosymmetric
→ is valuable in the determination of
molecule structure
• Notes: holds if a molecule has no
atom at the center of symmetry3
1 Mutual exclusion principle
𝑯2 𝑶
band IR Raman
𝑣1 active active
𝑣2 active active
𝑣3 active active

Problems
What’s the matter?
I wanna determined 𝐻𝑂𝑂𝐻
solution’s spectra, but I don’t
know I should measure
IR or Raman spectra.
So, why don’t you compare
the Raman versus IR spectroscopy?
Cool dear!

Contents
Definition
Calculations

The advantages of Raman versus IR
Spectroscopy
IR
 Sample cannot aqueous
 Thorough sample
preparation
 Not measure of
depolarization ratios
 Not measure spectra of
hygroscopic and
air-sensitive
Raman
 Sample can aqueous
 Little and no sample
preparation required
 Measure of depolarization
ratios
 Measure spectra of
hygroscopic and air-sensitive

Spectroscopy
𝐻𝑂𝑂𝐻

Spectroscopy
IR
 Sample can not aqueous
 Thorough sample
preparation
 Not measure of
hygroscopic and
air-sensitive
Raman
ratios

Spectroscopy
Prepar
sample
for
IR
spectra

Spectroscopy
IR
 Thorough sample
preparation
 Not measure of
hygroscopic and
air-sensitive
Raman
ratios

Spectroscopy
IR
 Thorough sample
preparation
 Not measure of
hygroscopic and
air-sensitive
Raman
ratios
hygroscopic and
air-sensitive

8. © Copyright http://www.americanphotonics.com.
9. © Copyright http://www.globalopticsuk.com.
10. © Copyright http://www.alibaba.com.
Spectroscopy
Figure 2.1 Types of prism, lens made of 𝐶𝑎𝐹2
8
Figure 2.2 Types of prism, lens made of 𝑍𝑛𝑆𝑒9
Figure 2.3 Types of prism made of glass10

Spectroscopy
IR
 Large quantity
 Optical instruments must
be changed to cover the
same region
Raman
 Advantageous in vibrational
studies of large biological
molecules containing
chromophoric groups
 Small quantity
 Can be covered by a single
recording

Spectroscopy
IR
 Large quantity
same region
Raman
chromophoric groups
 Small quantity
recording

The limitations of Raman versus IR
SpectroscopyRaman versus IR Spectroscopy2
Raman
 Damage sample by using
high-powered lasers
 Some compounds will
fluoresce when irradiated
by laser beam
 More difficult to obtain
rotational and rotational-
vibration spectra with high
solution
 Expensive
IR
 Less expensive

Raman versus Infrared Spectroscopy2
Raman
high-powered lasers
by laser beam
solution
 Expensive
IR
 Less expensive
Spectroscopy

Raman
high-powered lasers
by laser beam
solution
 Expensive
IR
 Less expensive
Spectroscopy

Problems
???
Input: frequency
polarizability
Intensity
Output: frequency
polarizability
Intensity
Reaction of ???
=> Contain information of ???

Contents
Definition
Calculations

11. Sathyanarayana D. (2004), Vibrational Spectroscopy: Theory and Application, New Age, India.
Definition3 Depolarization Ratios for Raman Spectra
• Depolarization ratios measured only in the form of gases, liquids and
amorphous solids11
• Depolarization ratios cannot be measured for IR spectrum11
Figure 3.1 Model experiments
measuring depolarization ratio3

12. Allemand C. (1970), Applied Spectroscopy 24 (3), pp. 348 – 353.
Definition3 Depolarization Ratios for Raman Spectra
• 𝜌 𝑝 if incident light is
polarized light
• 𝜌 𝑛 if incident light is
natural light
Figure 3.2 Parallel and perpendicular components
of Raman scattering radiation2
𝜌 =
𝐼⊥ 𝐼 𝑦
𝐼∥ 𝐼𝑧

Contents
Definition1
Calculations

11. Sathyanarayana D. (2004), Vibrational Spectroscopy: Theory and Application, New Age, India.
Calculations3 Depolarization Ratios for Raman Spectra
• For polarizability tensor is symmetric11
𝛼 =
1
3
𝛼 𝑥𝑥 + 𝛼 𝑦𝑦 + 𝛼 𝑧𝑧 is isotropic part
𝛾2
=
1
2
𝛼 𝑥𝑥 − 𝛼 𝑦𝑦
2
+ 𝛼 𝑦𝑦 − 𝛼 𝑧𝑧
2
+ 𝛼 𝑧𝑧 − 𝛼 𝑥𝑥
2
+ 6 𝛼 𝑥𝑦
2
+ 𝛼 𝑦𝑧
2
+ 𝛼 𝑧𝑥
2
is anisotropic part
𝜌 𝑛 =
6𝛾2
45𝛼2 + 7𝛾2
𝜌 𝑝 =
3𝛾2
45𝛼2 + 4𝛾2
Note: from here on,
“polarizability tensor” means
“Quantum transition
polarizability tensor”

14. Nesto J. and Spiro T. G. (2003), J. Raman Spectrosc. 1,pp. 539–550.
𝛼 =
1
3
𝛼 𝑥𝑥 + 𝛼 𝑦𝑦 + 𝛼 𝑧𝑧
𝛾2
=
1
2
2
2
2
+ 6 𝛼 𝑥𝑦
2
+ 𝛼 𝑦𝑧
2
+ 𝛼 𝑧𝑥
2
Divided into 2 parts: symmetric 𝜸 𝒔
𝟐
and antisymmetric 𝜸 𝒂𝒔
𝟐
• In common literature, Placzek ‘s 𝒈 𝟎, 𝒈 𝒔, 𝒈 𝒂 are used instead of 𝜶, 𝜸 𝒔
𝟐, 𝜸 𝒂𝒔
𝟐
For polarizability tensor is antisymmetric14
𝛾𝑠
2
=
1
2
2
2
2
+
3
4
𝛼 𝑥𝑦 + 𝛼 𝑦𝑥
2
+ 𝛼 𝑥𝑦 + 𝛼 𝑦𝑥
2
+ 𝛼 𝑥𝑦 + 𝛼 𝑦𝑥
2
𝛾𝑎𝑠
2
= 𝛼 𝑥𝑦 − 𝛼 𝑦𝑥
2
+ 𝛼 𝑥𝑦 − 𝛼 𝑦𝑥
2
+ 𝛼 𝑥𝑦 − 𝛼 𝑦𝑥
2

• For polarizability tensor is antisymmetric2
𝑔0
= 3𝛼2
𝑔 𝑠
=
2
3
𝛾𝑠
2
𝑔 𝑎 =
2
3
𝛾𝑎𝑠
2
𝜌 𝑝 =
3𝑔 𝑠 + 5𝑔 𝑎
10𝑔0 + 4𝑔 𝑠
𝜌 𝑛 =
6𝑔 𝑠 + 10𝑔 𝑎
10𝑔0 + 5𝑔 𝑎 + 7𝑔 𝑠

𝜌 𝑛
𝜌 𝑝
6
7
3
4
0
0
PolarizedPolarizability Depolarized

𝜌 𝑛
𝜌 𝑝
6
7
3
4
0
0
totally
symmetric
vibration non-totally
symmetric

Figure 3.3 Raman spectra of 𝐶𝐶𝑙4 with
perpendicular and parallel polarization components3
• For vibration in 𝑣 = 459𝑐𝑚−1
we measured 𝜌 𝑝 = 0.02
→ this vibration is totally symmetric
• For vibration 𝑣 = 314𝑐𝑚−1 and 𝑣 = 218𝑐𝑚−1
we measured 𝜌 𝑝 = 0.75
→ these vibrations are non-totally symmetric

15. Spiro T. and Strekas T. (1972), 69 (9), pp. 2622 – 2626.
16. Fischer J. (2005), CERN Courier 45 (7), pp. 25 – 27
• In resonance Raman scattering, 𝜌 𝑝 >
3
4
• 𝜌 𝑝 → ∞ the vibration is called anomalous polarization
predicted theory by George Placzek (1934), observed
in the experiment of hemoglobin and cytochrome
by Thomas Spiro and Thomas Strekas (1972)15
Figure 3.4 George Placzek16
(1905 – 1955)

15. Spiro T. and Strekas T. (1972), 69 (9), pp. 2622 – 2626.
Figure 3.5 Resonance Raman spectra
of ferrocytochrome15
Figure 3.6 Resonance Raman spectra
of oxyhemoglobin15

Summary
• A vibration is IR-active if the dipole moment is changed and is
Raman-active if the polarizability is changed during the vibration
• In a centrosymmetry molecule, a vibration may be either IR active
or Raman active but not both
• 𝜌 =
𝐼⊥
𝐼∥
The measure depolarization ratios will help determine a vibration is
totally or non-totally symmetric

Thanks everyone for listening!

Selection Rules for IR and Raman Spectra Guide

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