Molecular spectroscopy-Pure rotational (Microwave) spectra-Vibrational (Infrared) spectra -Electronic (UV) Spectra- Raman Spectra

1. Associate Professor and Head
Department of Chemistry
Saiva Bhanu Kshatriya College , Aruppukkottai 626101,
Tamilnadu ,India .

2. Molecular Spectroscopy
 The study of interaction of electromagnetic radiations with matter is called
Molecular spectroscopy.
Types of Molecular spectroscopy:
 Pure rotational (Microwave) spectra
 Vibrational (Infrared) spectra
 Electronic (UV) Spectra
 Raman Spectra
 Nuclear Magnetic Resonance (NMR) spectra
 Electron Spin Resonance (ESR) Spectra

3. Rotational spectra of diatomic molecule
• Definition:
The interaction between rotational energy levels of a gaseous
molecule and microwave radiation causes transition between the rotational
energy levels by the absorption of microwave radiation is called rotational
spectra
• Condition:
Molecules possess permanent dipole moment shows molecular
spectra .The microwave spectra occur in the spectral range of 1-100 cm-1
• Example :
HCl , CO ,H2O , NO ,etc.

4. .Explanations :
consider a diatomic molecule rotating about its center of gravity (C.G)
.Where,
r is the bond length
m1 is the mass of one atom
m2 is the mass of another atom
r1 is the distance of the atom 1 from the CG
r2 is the distance of the atom 2 from the CG
.At center of gravity :
m1r1 = m2r2 ---------- ( 1 )
Rotational spectra of diatomic molecule

5. Rotational spectra of diatomic molecule
. The moment of inertia I of a molecule is
I = μr2 ------- (2)
where , μ = reduced mass of the molecule =
𝑚1
𝑚2
𝑚1
+𝑚2
.According to classical mechanics , the angular momentum (L) of a rotating molecule is
L = Iω ------- (3)
where , ω = angular velocities

6. Rotational spectra of diatomic molecule
.According to quantum mechanics
L = 𝐽 ( 𝐽 + 1)
ℎ
2𝜋
------- (4)
where , J = rotational quantum number = 0,1,2,3,…….
.The energy of rotating molecule is
EJ =
1
2
𝐼𝜔2 =
𝐼2
𝜔2
2𝐼
=
𝐿2
2𝐼
=
𝐽 𝐽+1
ℎ
2𝜋
2
2𝐼
EJ =
𝐽 𝐽+1 ℎ2
2𝐼4𝜋2
EJ =
ℎ2
8𝜋2
𝐼
𝐽 𝐽 + 1 ------- (5)

7. Rotational spectra of diatomic molecule
The equation (5) is divided by hc in order to express the energy in cm-1
𝐸 𝐽
ℎ𝑐
=
ℎ2
8𝜋2
𝐼ℎ𝑐
𝐽 𝐽 + 1 cm-1
EJ =
ℎ
8𝜋2
𝐼𝑐
𝐽 𝐽 + 1 cm-1 ------- (6)
EJ = BJ( J+1) cm-1 -------- (7)
Where , B =
ℎ
8𝜋2
𝐼𝐶

8. Rotational spectra of diatomic molecule
Substituting the rotational quantum number (J = 0 , 1 , 2 , 3 , ….) in the equation (7) we
gets the quantized rotational energy levels of the rotating diatomic molecule
when ; J = 0 , E0 = 0
J = 1 , E1 = 2 Bcm-1
J = 2 , E2 = 6 Bcm-1
J = 3 , E3 = 12 Bcm-1
J = 4 , E4 = 20 Bcm-1
J = 5 , E5 = 30 Bcm-1
Since the rotational energy levels falls on the microwave region , the transition between
rotational energy level takes place by the absorption of microwave radiation as per the
selection rule ΔJ = ±1

9. Rotational spectra of diatomic molecule
So, the energy for a transition
J = 0 J = 1 is
ΔE = E1 – E0
ΔE0-1= 2B – 0 = 2B ; Since ΔE = γ
γ0-1 = 2B ;where, γ is frequency in cm-1 of the microwave causes transition
Similarly for,
J = 1 J = 2 is
γ1-2 = E2 – E1
γ1-2 = 6B – 2B = 4B
Similarly ; γ2-3 = 6B , γ3-4 = 8B

10. Rotational spectra of diatomic molecule
• The rotational spectrum of a rigid diatomic molecule appear at the following rotational
frequencies 2B, 4B, 6B, 8B .etc.. And each are appeared as a lines in the detector . These lines
are equally spaced by 2B
i.e. the interspaceial distance of the spectral lines is 2B and it shown in the diagram

11. Relative intensities of rotational spectral lines
• The plot of
𝑁 𝐽
𝑁0
versus J for a rigid diatomic molecule at room temperature is
• The value of J corresponding to the maximum in population is
Jmax = (
𝑘𝑡
2ℎ𝑐𝐵
)1/2
– ½

12. Vibrational spectra of diatomic molecule
• Definition : The interaction between the vibrational energy levels of a molecule and the
infrared radiation causes transition between the vibrational energy levels by the absorption of
infrared radiation is called infrared radiation
• Condition: The vibrations of a molecule involving changes in the dipole moment are IR active.
These spectra occur in the spectral range of 500-4000 cm-1
• Example : hetero diatomic molecule like CO , NO , CN , HCl ,(dipole moment) shows changes
in dipole moment during vibration.
i.e.. Homodiatomic molecule (H2 , O2 , N2 etc.) are IR-inactive but hetero diatomic molecules
are IR-active

13. Vibrational spectra of diatomic molecule
• Explanation : consider a vibrating diatomic molecule and the vibration is assumed to be
simple harmonic vibration
Where m1 and m2 are the masses of the atoms
re = equilibrium distance
x = displacement of the atom during vibration(expansion and compression) from the
equilibrium distance

14. Vibrational spectra of diatomic molecule
• The vibrational frequency of the vibrating molecule in term of cm-1 is
γ =
1
2π𝑒
𝑘
𝜇
cm-1 ---------(1)
Where ,
k = force constant , it is the restoring force acting on the molecule in order to come to
original position during expansion and compression
μ = reduced mass =
𝑚1
𝑚2
𝑚1
+𝑚2
According to Hooke's law , the potential energy (Vx) of the vibrating molecule is a function of
‘x’
i.e.. V(x) = ½ kx2 --------(2)
where x = r - re

15. Vibrational spectra of diatomic molecule
• The plot of potential energy (Vx) versus x gives parabolic curve
On solving the Schrodinger wave equation for a simple harmonic vibrator gives the
vibrational energy level
EV = ( v + ½ )h γ ----------(3)
where v = vibrational quantum number
= 0,1,2,3,……..
γ = vibrational frequency

16. Vibrational spectra of diatomic molecule
Equation (3) is divided by hc to get the energy in cm-1
𝐸 𝑣
ℎ𝑐
= (v + ½)
ℎγ
ℎ𝑐
= (v + ½)
γ
𝑐
Ev = (v + ½) ωe -----------(4)
where ωe = equilibrium vibrational frequency
By putting the value of v in equation (4) we get the energy of various vibrational level
When ; v = 0 , E0 =
ωe
2
called zero point energy
v = 1 , E1 =
3ωe
2
; v = 2 , E2 =
5ωe
2
v = 3 , E3 =
7ωe
2
; v = 4 , E4 =
9ωe
2
v = 5 , E5 =
11ωe
2

17. Vibrational spectra of diatomic molecule
• This shows the vibration energy levels are equally spaced by ωe . Since the vibrational
energies are falling into IR region , the transition between vibrational energy levels takes
place by the absorption of IR radiation as per the selection rule Δv = +1

18. Vibrational spectra of diatomic molecule
• The energy of the IR radiation in term of cm-1 ( γ )that causes the vibrational energy
transition is equal to Ev+1 – Ev
i.e.. For v = 0 ----- v = 1 For v = 1 ----- v = 2
γ = E1 – E0 =
3ωe
2
–
ωe
2
= ωe γ = E2 – E1 =
5ωe
2
–
3ωe
2
= ωe
For v = 2 ----- v = 3 For v = 3 ----- v = 4
γ = E3 – E2 =
7ωe
2
–
5ωe
2
= ωe γ = E4 – E3 =
9ωe
2
–
7ωe
2
= ωe
This shows all vibrational energies transition as per the selection rule Δv = ±1 occurs
at only one frequency we called fundamental vibrational frequencies and gives only one
vibrational spectrum line

19. Vibrations of polyatomic molecules
• Total degree of freedom for polyatomic molecule = 3N
where N is number of atoms
• The translational degree of freedom for polyatomic molecule = 3
• The rotational degree of freedom for
linear molecule = 2
non linear molecule = 3
• So , the vibrational degree of freedom for
polyatomic linear molecule = 3N – 5
polyatomic non linear molecule = 3N – 6

20. Vibrations of polyatomic molecules
1. Linear CO2 molecule
N = 3
• The vibrational degree of freedom
= 3 N – 5
= (3 X 3) – 5
= 9 – 5
= 4
• The four types vibrations in CO2
molecule are IR active are shown
in figure

21. Vibrations of polyatomic molecules
2. Linear H2O molecule
N = 3
• The vibrational degree of freedom
= 3 N – 6
= (3 X 3) – 6
= 9 – 6
= 3
• The three types vibrations in H2O
molecule are IR active are shown in
figure

22. Electronic spectra
• Definition : The interaction between the electronic energy levels in a molecule and the
visible and ultra violet radiation causes transition between the electronic energy levels
by the absorption of the visible (or) u.v radiation is called electronic spectra
• Conditions : Components containing π – bond shows electronic spectra. The electronic
spectra in the visible region span 12,500-25,000 cm-1 ,those in the ultra violet region
span 25,000-75,000 cm-1
• Explanation :
The total energy of a molecule in the ground state is
E = Eelc + Evib + E rot --------(1)
(since Etrans is not quantized , it is not included in equation 1 )
The total energy of a molecule in the excited state is
E
,
= E
,
elc + E
,
vib + E
,
rot ---------(2)

23. Electronic spectra
• Equation (2) – (1) gives the energy required to make the electronic transition from E to
E
,
i.e.. E
,
– E = (E
,
elc – Eelc ) + (E
,
vib – Evib ) + (E
,
rot – E rot )
ΔE = ΔEelc + ΔEvib + ΔE rot ---------(3)
• Since , ΔEelc >> ΔEvib >> ΔE rot ; the two electronic states transition is accompanied by
simultaneous transition between the vibrational and rotational level.
• Divide equation (3) by hc we get the energy in terms of frequency for the electronic
transition in cm-1
ΔE
ℎ𝑐
=
ΔEelc + ΔEvib + ΔE rot
ℎ𝑐
= γ cm-1 ----------(4)
• The electronic energy levels transition will be governed by the Franck - Condon
principle

24. Electronic spectra – Franck Condon principle
• Franck Condon principle states that an electronic transition takes place without any
change in the internucler distance of the vibrating molecule .

25. Electronic spectra – Franck Condon principle
• Since the bonding in the excited state is weaker than in the ground state , the minimum in
the potential energy curve for the excited state occurs at a slightly greater internucler
distance than the corresponding minimum in the ground electronic state
• So , when a photon falls on the molecule , the most probable electronic transition according
to Franck-Condon principle is v0 ----- v
,
2 and is shown in the above diagram as 0 ----- 2
• Application : The unsaturated molecules containing C=C and C=O (aldehydes and ketone)
are identified using electronic spectrum since they shows n – π* and π – π* electronic
transition

26. Raman spectroscopy
• Definition : It is the branch of molecular spectroscopy which deals about the scattering of
light radiation by the molecules in which the scattered light radiation will have either a
higher or a lower frequency than the incident light radiation and this effect is called
Raman effect
• Diagrammatically:
• Condition : Changes in polarisability of the molecule is the condition for getting Raman
spectrum. Raman spectra are observed in the visible region, 12,500-25,000 cm-1

27. Raman spectroscopy – Quantum theory
• According to quantum theory , a photon of frequency (γ) falling on a molecule ,
collision takes place between the molecule and photon .
• If the collision is elastic , then the scattered photon will have the same energy and
same frequency as the incident radiation . This scattering is called Rayleigh
scattering
• If the collision is inelastic , the scattered photon will have either higher (or) lower
energy and frequency then the incident radiation . This scattering is called Raman
scattering

28. Raman spectroscopy – Quantum theory
(a) (b) (c)

29. Raman spectroscopy – Quantum theory
• Figure b : when the molecule excited to the higher unstable vibrational energy level then
returns to the original vibrational energy level of the ground state we get Rayleigh scattering
• Figure a : when the molecule excited to the higher unstable vibrational energy level then
returns to the different vibrational energy level of the ground state we get Raman scattering
called stokes lines
• Figure c : when the molecule , initially in the first excited vibrational energy level of the
ground state is promoted to a higher unstable vibrational state and returns to the ground
state we get Raman scattering called anti stokes line
• The shifts in frequency (γ – γ
,
) is called Raman shifts and it fall in the range 100 – 4,000 cm-1

30. Comparison between Raman spectrum and Infrared spectrum

31. Application of Raman spectra
1. Using the mutual exclusion rule , it gives information about molecular vibrations which
are IR inactive
i.e.. Molecule having center of symmetry (H2 , O2 , CO2 …) IR active vibrations are Raman
inactive and IR inactive vibrations are Raman active
Example : In CO2 , the symmetric stretching vibration has no dipole moment so it is IR
inactive but it gives Raman spectra

32. Application of Raman spectra
2. The existence of cis and trans isomers in dichloro ethylene can be confirmed by
Raman's spectra
Raman active IR active
i.e.. if the compound has trans isomer only , it gives Raman spectra only but dichloro
ethylene gives both Raman and IR spectra. This indicates that the existence of cis and
trans isomers in equilibrium

33. Application of Raman spectra
3. All the vibrations for CS2 are Raman active and IR inactive . This indicates that the
structure of CS2 has center of symmetry like
4. All the vibrations for N2O are Raman active and IR active . This indicates that the
structure of N2O has no center of symmetry like

34. Experimental technique for Raman spectroscopy
• As shown in the diagram is the experimental set-up for the Raman spectroscopy

35. Experimental technique for Raman spectroscopy
Experiment :
• When a current discharge passes through the large spiral discharge tube emits intense
monochromatic radiation allowed to fall on the cell containing a gaseous (or) liquid
sample
• The scattered light is observed at right angles to the direction of incident radiation
and allowed to pass through the filter and monochromator then finally fall on the
detector
• The detector used is photographic plate

36. Pure Rotational Raman spectra
• The selection rule for Rotational Raman spectra is
ΔJ = 0 , ± 2
when
ΔJ = 0 → Rayleigh scattering
ΔJ = +2 → stokes lines
ΔJ = -2 → Anti stokes lines
Raman scattering

37. Rotation – vibration Raman spectrum
• The selection rule for Rotation - vibration
Raman spectra is Δv = +1 , ΔJ = 0 , ± 2
• The transition with Δv = +1 and ΔJ = 0
is called Q - branch lines
• The transition with Δv = +1 and ΔJ = +2
is called S - branch lines
• The transition with Δv = +1 and ΔJ = -2
is called 0 - branch lines

38. THANK YOU