Molecular spectroscopy-final engineering.pdf

Spectroscopy

1. Molecular UV-Vis
Spectroscopy
Prof. C. K. Mondal
Department of Chemistry
JadavpurUniversity

6. WHAT IS SPECTROSCOPY?
•Atoms and molecules interact  with electromagnetic 
radiation (EMR) in a wide  variety of ways.
•Atoms and molecules may absorb and/or emit EMR.
•Absorption of EMR stimulates different  types of 
motion in atoms and/or molecules.
•The patterns of absorption (wavelengths  absorbed 
and to what extent) and/or emission (wavelengths 
emitted and their respective intensities) are called  
‘spectra’.
•The field of spectroscopyis concerned  with the 
interpretation of spectrain terms of atomic and 
molecular structure (and environment).

7. Electromagnetic spectrum

8. Physical 
stimulus
Moleculeresponse
Detecting 
instrument
Visual (most common)
representation, or
Spectrum
SPECTROSCOPY  ‐Study of spectral information
Upon  irradiation with  infrared  light, certain bonds respond by 
vibrating  faster.This  response can be detected and translated  
into a visual representation called  a spectrum.

12. Spectroscopy
•The analysis  of the EM radiations emitted,  absorbed or 
scattered  by atoms, molecules  or matter
•Photons  of the radiation bring information to us about the atom, 
molecule  or matter.
•The difference between molecular and atomic spectroscopy:  a 
molecule  can make a transition between its electronic,  
rotational and vibrational states.
•The rotational and vibrational spectroscopy of a molecule  can 
provide information about the bond lengths, bond angles and 
bond strength in the molecule.

13. General features of spectroscopy
Emission spectrum: A molecule returns to a state of lower energy
E
1
from an excited state of energy E
2
by emitting a photon.
Absorption spectrum: A molecule is excited from a lower energy
state to a higher energy state by absorbing a photon as the
frequency of the incident radiation is swept over a range
c
EEh
ν
=
λ
=ν
−
=ν
1 ~
||
21
is called the wavenumber of the 
photon and gives the number  of 
complete wavelengths per centimeter. It 
is in the unit of cm
‐1
.
ν~

14. Stimulated and Spontaneous emissions 
Spontaneous emission:
A molecule in an excited state will decay  to a lower 
energy state without any stimulus from the outside.
Stimulated emission:
As an EM radiation incident upon a molecule in an 
excited state can cause the molecule to decay  to a lower 
energy state. If the incoming photon has the same  
frequency  as the emitted photon, the incident and 
emitted photons have  the same  wavelength and phase 
and travel in the same  direction. The incoming photon is 
not absorbed by the molecule but triggers emission  of  a 
second photon. The two photons  are said  to be coherent.
The stimulated emission  is the fundamental physical  
process of the operation  of the laser.

15. Raman spectrum
A monochromatic radiation is incident and scattered by the molecule. The
frequency of a scattered radiation is different from the frequency of the
incident radiation. The spectrum of the scattered radiation is called the
Raman spectrum.
Stokes Raman spectrum : The frequency of the scattered radiation is
lower than the frequency of the incident radiation.
Anti-Stokes Raman spectrum: The frequency of the scattered radiation is
higher than the frequency of the incident radiation.

16. Transition dipole moment and selection rules
•Transition dipole moment integral
The strength with which individual molecule s are able to interact with the EM
radiation and generate or absorb photons. The transition dipole moment
depends on the initial and the final states of the molecules
dτψμψμ
i
*
f fi ˆ
∫
=
: Electric dipole moment operator
μˆ

18. The Beer-Lambert law for absorption
L
A
c
II
Lc
I
I
A
I
I
T
Lc
⋅
=
=
=≡
=
−
ε
ε
ε
][
10
][ log
][
0
0
0
I
0
andI : Intensities of the incident and transmitted radiations
A : Absorbance of the sample, T: Transmittance
L : Length of the sample
[c] : Concentration of the absorbing species in the sample
ε
: Molar absorption coefficient or the extinction coefficient
The intensity of radiation transmitted by an absorbing sample decreases
exponentially with the path length through the sample.
ε
depends on
wavelength of the
incident radiation.

19. UV‐Visible Spectroscopy
•THE BEER‐LAMBERT 
LAW •For a light absorbing  
medium,  the light 
intensity falls 
exponentially with 
sample depth.
•For a light absorbing  
medium,  the light 
intensity falls 
exponentially with 
increasing  sample 
concentration.
100x
I
I
T%
I
I
T
o
t
o
t
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
= =
I
o
I
t
l
cuvette
light intensity (I)
Sample depth
I
o
I
t
l

27. UV‐Visible Spectroscopy
Absorbance
Concentration
TAclA
10
log
−
=
=
λ
ε
¾The negative logarithm of Tis called the 
absorbance (A) and this is directly  
proportional  to sample depth (called 
pathlength, l) and sample concentration 
(c). The equation is called the Beer‐
Lambert law.
εis called the molar 
absorption coefficient 
and has units of dm
3
mol
‐1
cm
‐1

28. UV‐Visible Spectroscopy
•Beer‐Lambert  Law 
limitations
–Polychromatic  Light
–Equilibrium shift
–Solvent
–pH

30. Rotational energy levels of a rigid rotor
πcI
B
J
JJBhcE
J
4
~
.... 3, 2, 1, 0,
),1(
~
h
=
=
+=
For a linear or spherical rigid rotor with a
moment of inertia I
z
z
y
y
x
x
I
J
I
J
I
J
E
222
2 2 2
++=
The kinetic energy of a rigid rotor with angular momentum J
x
, J
y
and J
z.
with respect
to the three principal axes of the rotor.
222 2
2
,
2
zyx
JJJJ
I
J
E++= =
Classical 
description
Quantum
description
)1(
~
2
1
+=
−=Δ
+
JBhc
EEE
JJJ

31. Rotational spectroscopy
•Gross selection rule: The molecules must have a permanent electric dipole
moment so that the molecules are polar.
To an observer, a rotating polar
molecule has an electric dipole that
appears to oscillate. This oscillating
dipole can interact with the EM field.
Rotational-inactive molecules : Molecules
without rotational spectrum
Homonuclear diatomic molecules: N
2
, O
2
Symmetric linear molecules: CO
2
Tetrahedral molecules: CH
4
Octahedral molecules: SF
6,
C
6
H
6
Rotational-active molecules : Molecules
with rotational spectrum
Heteronuclear diatomic molecules: HCl
Less symmetric polar molecules: NH
3
, H
2
O
Classical description 

32. Specific selection rules for rotational transition
•Conservation of angular momentum for ΔJ = ±1 
A photon is a spin-1 particle. When the molecule
absorbs one photon, the angular momentum of the
molecule must increase to conserve the total angular
momentum, so Jincreases by one. When the
molecule emits a photon, the angular momentum of
the molecule must decreases, so Jdecreases by one.
•Forsymmetric rotors , ΔK= 0
The dipole moment of a polar molecule does not
move when a molecule rotates around its symmetric
axis and, therefore, there is no absorption or
emission of the EM radiation by the rotation of the
molecule about the axis.
ΔJ = ±1 and ΔK= 0
Quantum description

33. Absorption of allowed rotational transitions
)1(
~
2
1
+=−=Δ
+
J BhcEEE
JJ )1(
~
2
~
+=ν J B
A rigid molecule with K=0 makes a 
transition  from J to J+1
•The rotational spectrum consists of a series of lines at frequencies 
separated by 2     .
•The rotational spectra of gas‐phase samples are microwave spectroscopy.
•We can use the value of     obtained  from the rotational spectrum to 
estimate  the bond length  of a heteronuclear diatomic molecule. 
B~
B~
Rigid‐rotor model
B~

34. INFRARED SPECTROSCOPY
•Only vibrations that cause a change in ‘polarity’ give rise to 
bands in IR spectra –which of the vibrations for CO
2
are 
infrared  active?
OCO
OCO
OCOOCO
Symmetric stretch
Asymmetric stretch
Bending (doubly
degenerate)

35. INFRARED SPECTROSCOPY
What  is a vibration in a molecule? •Any change  in shape  of the molecule ‐stretching  of bonds, 
bending of bonds, or internal  rotation around  single  bonds What vibrations change  the dipole moment of a 
molecule? •Asymmetrical stretching/bending and internal  rotation change  
the dipole moment of a molecule. Asymmetrical 
stretching/bending are IR active.  
•Symmetrical stretching/bending does not. Not IR active

36. Vibrations of diatomic molecules
BA
BA
eff
eff
f
n
e f har
mm
mm
m
m
k
nE
RRkRV
+
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=ω
=ω+=
−=
,
..0,1,2,3,.. n , )
2
1
(
)(
2
1
)(
2/1
2h
Harmonic  approximation around the equilibrium 
A diatomic molecule has three 
translational modes,  two rotational 
modes and one vibrational mode.
k
f 
:  force constant of the bond,
the curvature  of the potential  at R
e
⋅⋅⋅+−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
2
0
2
2
)(
2
1
)(
e
RR
dR
Vd
RV

0
2
2
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
dR
Vd
k
f

37. Infrared spectroscopy: Vibrational transitions
•Gross selection rule
The molecule need not to have a permanent dipole moment but
the electric dipole moment of the molecule must change during
the vibration. The rule only requires a change in electric dipole
moment, possibly from zero.
The typical vibrational frequency of a molecule
is about 10
13
~10
14
Hz. The vibrational
spectroscopy of molecules is in the infrared
region, which normally lies in 300 ~ 3000 cm
-1
.
Homonuclear diatomic molecules are infrared
inactive, because their dipole moments remain
zero as they vibrate.
Heteronuclear diatomic molecules are infrared
active, because their dipole moments change as
they vibrate.
Bending  motion of CO
2

38. Specific  selection  rules for infrared spectroscopy
•Molecules with stiff bonds joining atoms
with low masses have high vibrational
wavenumbers.
•The bending modes of a linear molecule
are usually less stiff than stretching modes.
So, the bending modes usually occur at
lower wavenumbers than the stretching
modes in a spectrum.
•At room temperatures, almost all molecules
are in their vibrational ground states (n = 0).
So, the most probable transition is from n =
0 to n = 1.
•For Δn= 1, the molecule absorbs one
photon and, for Δn= -1, the molecule emits
one photon.
⋅⋅⋅+ ⎟
⎠
⎞
⎜
⎝
⎛μ
+μ=μx
dx
d
x
0
0
ˆ
ˆ)( ˆ
⋅⋅⋅+ ⎟
⎠
⎞
⎜
⎝
⎛μ
+=
=
∫
∫
dτψ xψ
dx
d
μ
dτψμψμ
i
*
f
i
*
f fi ˆ
ˆ

ˆ
0
0
Electric dipole moment
Transition dipole element

2
1 ~
,
~
,1
2/1
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
π
==Δ±=Δ
eff
f
m
k
c
νvhcEn

39. Vibration-rotation absorption spectrum
Pbranch: ΔJ= -1 Qbranch: ΔJ= 0 Rbranch: ΔJ= +1
JBJ
P
~
2
~
)(
~
−ν=ν
ν
=
ν
~
)(
~
J
Q
)1(
~
2
~
)(
~
++ν=ν JBJ
R

40. Vibration‐rotation spectrum of HCl
Each line of the high-resolution
vibrational spectrum of a gas-
phase heteronuclear diatomic
molecule is found to consist of a
large number of closely spaced
components in the order of 10
cm
-1
, which suggests that the
structure is due to the rotational
transitions accompanying the
vibrational transitions.
•There is no Q branch.
•The lines appear in pair, 
because both H
35
Cl and 
H
37
Cl contribute in their 
abundance ratio 3:1.

41. Vibration-rotation Raman spectrum of CO
ΔJ=+2
ΔJ=‐2
ΔJ=0