Microwave Spectroscopy

Introduction to microwave spectroscopy

1. MICROWAVE MICROWAVE
SPECTROSCOPYSPECTROSCOPY
Prof. V. Krishnakumar
Professor and Head
Department of Physics
Periyar University
Salem – 636 011, India

2. Summary of information from microwave spectroscopySummary of information from microwave spectroscopy
It is mainly used to get information about gas It is mainly used to get information about gas
molecules, such asmolecules, such as
1. Accurate bond lengths and angles.1. Accurate bond lengths and angles.
2. Electric dipole moments.2. Electric dipole moments.
3. Centrifugal distortion constants.3. Centrifugal distortion constants.
It can also be used to study relaxation times, It can also be used to study relaxation times,
dielectric constants, dipole moments in liquids and dielectric constants, dipole moments in liquids and
solutions, and potential energy barriers to rotation.solutions, and potential energy barriers to rotation.

3. In some cases, we can get information about the In some cases, we can get information about the
mechanism of chemical reactions, such as the mechanism of chemical reactions, such as the
decomposition:decomposition:
1515
NHNH
44
1414
NONO
33 ®®
1515
NN
1414
NONO
  
The requirements to get a microwave spectrum are:The requirements to get a microwave spectrum are:
Substance must have electric dipole moment (or Substance must have electric dipole moment (or
magnetic dipole moment) magnetic dipole moment)
Its vapour pressure > 10Its vapour pressure > 10
-3-3
mmHg.  mmHg. 

4. Characteristics of microwave spectroscopy, Characteristics of microwave spectroscopy,
compared with other techniques are:compared with other techniques are:
It has a high resolving power. It has a high resolving power.
It analyses the WHOLE molecule (not like nmr, or ir It analyses the WHOLE molecule (not like nmr, or ir
spectra, which fingerprint selected parts).spectra, which fingerprint selected parts).
It detects isotopic species, and conformational It detects isotopic species, and conformational
isomers.isomers.
Only a few ng of gas are required.Only a few ng of gas are required.
It is a non-destructive technique.It is a non-destructive technique.
It can be used remotely, such as for interstellar It can be used remotely, such as for interstellar
analyses.analyses.
The spectra of large molecules are very complex. The spectra of large molecules are very complex.
AbsoluteAbsolute absorbance is difficult to measure. NBS has absorbance is difficult to measure. NBS has
list of microwave spectra for qualitative analysislist of microwave spectra for qualitative analysis..

5. Basic conceptsBasic concepts

Rotational energies of molecules are quantized (i.e. Rotational energies of molecules are quantized (i.e.
only have definite energies) only have definite energies) E = hE = hnn
E, energy in J; h Planck’s constant, Js; E, energy in J; h Planck’s constant, Js; nn rotational rotational
frequency, Hz.frequency, Hz.
  
The range of rotational frequencies is about 8x10The range of rotational frequencies is about 8x10
1010
- -
4x104x10
11 11
Hz, which corresponds to wavelengths, Hz, which corresponds to wavelengths, ll ~ ~
0.75 - 3.75 mm. These wavelengths fall in the 0.75 - 3.75 mm. These wavelengths fall in the
microwave region of the electromagnetic spectrum. microwave region of the electromagnetic spectrum. 

6. By absorption of microwave radiation, transitions can By absorption of microwave radiation, transitions can
occur between rotational or inversion energy levels occur between rotational or inversion energy levels
of molecules. of molecules.
N.B. Molecule must have N.B. Molecule must have permanent dipole momentpermanent dipole moment
(D.M.) if it has a rotational spectrum.(D.M.) if it has a rotational spectrum.

7. DIRECTION DIRECTION
OF DIPOLE OF DIPOLE
VERTICAL VERTICAL
COMPONENT COMPONENT
OF DIPOLE OF DIPOLE
(along z)(along z)
Rotation of a Rotation of a
polar diatomic polar diatomic
molecule molecule
showing D. M. showing D. M.
along z versus along z versus
timetime
t
+
-
- + - +
- +
+
+-
-

8. To an observer, there is a change in dipole moment To an observer, there is a change in dipole moment
along z when the molecule rotates. The oscillating along z when the molecule rotates. The oscillating
electric field of microwave radiation, incident upon electric field of microwave radiation, incident upon
the molecule, can therefore make this rotation the molecule, can therefore make this rotation
occur (i.e. the radiation is absorbed).  occur (i.e. the radiation is absorbed).  

9. Some definitions about rotation. Some definitions about rotation. For simplicity, we For simplicity, we
consider a diatomic molecule throughout. consider a diatomic molecule throughout.
   
QQ P P
¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾ 
  
moment of inertia, I = moment of inertia, I = SS m m
iirr
ii
22
r = distance of atom i from rotation axis (m); m in kg.r = distance of atom i from rotation axis (m); m in kg.
  
Angular momentum = IAngular momentum = Iww, where the angular frequency , where the angular frequency
(radian s(radian s
-1-1
),),ww = 2 = 2pnpn

10. Classification of molecules according to I values

1. Linear molecules

I
A
= 0;I
B
= I
C
 
22. Symmetric tops
 
I
A
¹ 0;I
B
= I
C
 
Q P
B
C
A
H C F
H
H

11. H Cl
H H
3. Spherical tops3. Spherical tops
  
II
AA = I = I
BB = I = I
CC
This is type of molecule has no rotational This is type of molecule has no rotational
spectrum.spectrum.

4. Asymmetric tops4. Asymmetric tops
  
II
AA ¹¹ I I
BB ¹¹ I I
CC
H C H
H
H
C = CO
H








H

12. Rotation spectra of diatomic moleculesRotation spectra of diatomic molecules
  
Consider molecule with nuclear masses mConsider molecule with nuclear masses m
11 and m and m
22
r
0
m
2
m
1
r
2
r
1
c
(C is centre of mass)(C is centre of mass)

13. Assume a rigid (not elastic) bondAssume a rigid (not elastic) bond
   rr
00 = r = r
11 + r + r
22
For rotation about center of gravity, C :For rotation about center of gravity, C :
   mm
11rr
1 1 = m= m
22rr
22( = m( = m
22 (r (r
00 - r - r
11) )) )
/ \/ \
21
02
1
mm
rm
r
+
=
21
01
2
mm
rm
r
+
=

14. Moment of inertia about C:Moment of inertia about C:
II
CC = m = m
11rr
11
22
+ m + m
22rr
22
22
= m = m
22rr
22rr
1 1 + m+ m
11rr
11rr
22
= r= r
11rr
22 (m (m
11 + m + m
22))
  
mm = reduced mass, = reduced mass,
2
0
2
0
21
21
μrr
mm
mm
I =
+
=Þ
21
m
1
m
1
μ
1
+=

15. More detailed derivation:More detailed derivation:
  

[ ]
[ ]
2
0
21
21
21
21
02
21
01
2121
2
11
22
1
22
11
r
mm
mm
mm
mm
rm
mm
rm
mmrr
m
rm
rm
m
rm
rm
+
=
+
ú
û
ù
ê
ë
é
+
ú
û
ù
ê
ë
é
+
=
+=
ú
û
ù
ê
ë
é
+
ú
û
ù
ê
ë
é
=
2
22
2
11C rmrmI +=

16. From the Schrödinger equation:From the Schrödinger equation:
Rotational energy of level J,Rotational energy of level J,
J(J+1) JoulesJ(J+1) Joules
I8π
h
E
2
2
J
=

17. Where J is the rotational quantum number, having Where J is the rotational quantum number, having
the values 0, 1 , 2….Note that J = 0 is the lowest the values 0, 1 , 2….Note that J = 0 is the lowest
level, and the molecule is not rotating in this level. level, and the molecule is not rotating in this level.
Now the rotational frequency is the same as the Now the rotational frequency is the same as the
frequency of the microwave radiation need to cause frequency of the microwave radiation need to cause
the rotation: the rotation:
nn / Hz = / Hz =

or in energy units:or in energy units: , where c is in cms , where c is in cms
-1-1
..

SoSo J(J+1) cm J(J+1) cm
-1-1
= BJ(J+1) = BJ(J+1) cmcm
-1-1
B is called the rotational constant for a given B is called the rotational constant for a given
molecule. Its units are cmmolecule. Its units are cm
-1-1
, since J is just a quantum , since J is just a quantum
number (label).number (label).
h
ΔE
hc
ΔE
/cmν
1
=
-
Ic8π
h
E
2J
=

18. Appearance of microwave spectrumAppearance of microwave spectrum
  
Microwave absorption lines should appear atMicrowave absorption lines should appear at
J = 0J = 0®® J = 1 : J = 1 : = 2B - 0 = 2B cm = 2B - 0 = 2B cm
-1-1
J = 1J = 1®® J = 2 : J = 2 : = = = 4B cm = 4B cm
-1-1
  
Or generally:Or generally:
J J ®® J + 1 J + 1 = B(J+1)(J+2) - BJ(J+1) = B(J+1)(J+2) - BJ(J+1)
= 2B(J+1) cm= 2B(J+1) cm
-1-1
Note that the selection rule is Note that the selection rule is DDJ = J = ±±1, where + 1, where +
applies to absorption and - to emission.applies to absorption and - to emission.
ν
ν
ν

19. This diagram shows the rotational energy levels of This diagram shows the rotational energy levels of
a diatomic molecule. Fill in the ???a diatomic molecule. Fill in the ???
Here are some data for carbon monoxide:Here are some data for carbon monoxide:
EnergyEnergy
42B42B
30B30B
?B?B
?B?B
6B6B
2B2B
0B0B
J levelJ level
J = 6J = 6
J = 5J = 5
J = 4J = 4
J = 3J = 3
J = 2J = 2
J = 1J = 1
J = 0J = 0

20. 1414
13 13









12 12









11 11










10 10










9 9










8 8










7 7











6 6











5 5











4 4













3 3













2 2


















1 1

















0 0

















00
100100
200200
400400
F
(
J
)

c
m
F
(
J
)

c
m
-
1
-
1
.14 .14
.18 .18










.23 .23











.29 .29










.36 .36











.43 .43










.51 .51









.59 .59











.67 .67












.75 .75












.81 .81












.89 .89













.95 .95

















.98 .98


















1.0 1.0
















29 29
27 27










25 25









23 23










21 21









19 19










17 17










15 15










13 13











11 11











9 9












7 7













5 5













3 3

















1 1
















4.0 4.0
4.9 4.9










5.8 5.8










6.6 6.6










7.5 7.5











8.1 8.1









8.6 8.6











8.9 8.9










8.8 8.8












8.3 8.3












7.5 7.5












6.3 6.3













4.7 4.7
















2.9 2.9


















1.0 1.0
















53.8
50.0
46.1
42.3
38.4
34.6
30.8
26.9
23.1
19.2
15.4
11.5
7.69
ν(cm
-1
)
J 2J+1 eJ 2J+1 e
-E/kT-E/kT
N N
JJ/N/N
oo

21. F(J) = energy of levels as a function of J.F(J) = energy of levels as a function of J.
2J+1 = degeneracy of J level.2J+1 = degeneracy of J level.
ee
-E/kT-E/kT
= Boltzmann temperature factor. = Boltzmann temperature factor.
NN
JJ//N//N
oo = population of level J compared with = population of level J compared with
level O.level O.
= transition wavenumber= transition wavenumber
Rotational Energy Levels of CORotational Energy Levels of CO
ν

22. This is part of the rotational (far infrared) This is part of the rotational (far infrared)
spectrum of CO. You can see that the separation, spectrum of CO. You can see that the separation,
2B, is roughly 4 cm2B, is roughly 4 cm
-1-1
. Assign the lines.. Assign the lines.
15 20 25 30 35 40
n (cm
-
1
)
1212
CC
1616
O (major species)O (major species)
1313
CC
1616
O and O and
1212
CC
1818
O linesO lines
%

%
t
r
a
n
s
m
i
s
s
i
o
n
t
r
a
n
s
m
i
s
s
i
o
n

23. ApplicationApplication
  
The measurement of a microwave spectrum The measurement of a microwave spectrum
enables us to determine bond lengths and angles enables us to determine bond lengths and angles
accurately for gaseous molecules.accurately for gaseous molecules.
  
Example for CO:Example for CO:
(J=0 (J=0 ®® J=1) for J=1) for
1212
CC
1616
O is at 3.84235 cmO is at 3.84235 cm
-1-1
..
C = 12.0000 ; C = 12.0000 ;
O = 15.9994 O = 15.9994 amuamu
1 amu = 1 atomic mass unit = 1.6605402 x 101 amu = 1 atomic mass unit = 1.6605402 x 10
-27-27
kg kg
h = 6.6260755 x10h = 6.6260755 x10
-34 -34
JsJs
c = 2.99792458 x 10c = 2.99792458 x 10
1010
cm s cm s
-1-1

24. Find Find r(Cr(C¾¾O)O)
  
= = mmrr
22
B = 1.921175 cmB = 1.921175 cm
-1-1
; ; mm = 1.1386378 x 10 = 1.1386378 x 10
-26-26
kg kg
ÞÞ = 1.131 x 10= 1.131 x 10
-10-10
m m
ÞÞ 0.1131 nm0.1131 nm
Answer: C-O bondlength is 0.1131 nm. Answer: C-O bondlength is 0.1131 nm.
2
46
2
kgm
B
102.7992774
Bc8π
h
I
-
´
==
μ
I
r=

25. Intensities of rotation spectral lines Intensities of rotation spectral lines
  
Now we understand the locations (positions) of Now we understand the locations (positions) of
lines in the microwave spectrum, we can see which lines in the microwave spectrum, we can see which
lines are strongest.lines are strongest.
  
JJ ¾¾¾¾¾¾¾¾¾¾¾¾¾¾ BJ(J+1) BJ(J+1)
  
J=0J=0¾¾¾¾¾¾¾¾¾¾¾¾¾¾ 0 0
Intensity depends upon initial state population.Intensity depends upon initial state population.

26. Greater initial state population gives stronger Greater initial state population gives stronger
spectral lines.This population depends upon spectral lines.This population depends upon
temperature, T.temperature, T.

kk = Boltzmann’s constant, 1.380658 x 10 = Boltzmann’s constant, 1.380658 x 10
-23-23
J K J K
-1-1
((k k = R/N)= R/N)
  
We conclude that the population is smaller for We conclude that the population is smaller for
higher J states.higher J states.
÷
ø
ö
ç
è
æ
-=÷
ø
ö
ç
è
æ
-µ
kT
νhc
exp
kT
E
exp
N
N
J
0
J
cmK1.52034
k
hc
=
÷
ø
ö
ç
è
æ
-µ
T
ν1.52034
e
N
N
o
J

27. Intensity also depends on degeneracy of initial
state.
(degeneracy = existence of 2 or more energy states
having exactly the same energy)
Each level J is (2J+1) degenerate
Þ population is greater for higher J states.
To summarize: Total relative population at energy
E
J
a (2J+1) exp (-E
J
/ kT) & maximum population
occurs at nearest integral J value to :
 
Look at the values of N
J
/N
0
in the figure, slide #27.
2hcB
kT
2
1
J +-=

28. Plot of population of rotational energy levels versus Plot of population of rotational energy levels versus
value of J. value of J.
B = 5cmB = 5cm
-1-1
B = 10cmB = 10cm
-1-1
max. pop.max. pop.
J
0
P
o
p

P
o
p
aa

(
2
J

+

1
)

e

(

-
B
J
(
J

+

1
)
h
c
/
k
T
)

(
2
J

+

1
)

e

(

-
B
J
(
J

+

1
)
h
c
/
k
T
)

29. At maximum population value, At maximum population value,
slope = 0: Putting x = hc/slope = 0: Putting x = hc/kkTT
Slope = 0 at maximumSlope = 0 at maximum
What is J value?What is J value?
J = 0 J = NJ = 0 J = N
J J ®®
(
2
J

+

1
)
e

–
x
B
J
(
J
+
1
)
®®

30. ( )[ ]
[ ][ ]
[ ]21)xB(2Je0
2e1)(2JxBe1)(2J0
0e12J
dJ
d
slope
21)xBJ(J
1)xBJ(J1)xBJ(J
1)xBJ(J
++-=
++×-+=
=+=
+-
+-+-
+-
So:So:
2hcB
kT
2
1
J
2xB
1
2
1
J
021)xB(2J
2
+-=
+-=
=++-

31. Effect of isotopesEffect of isotopes
  
FromFrom
1212
CC
1616
OO®®
1313
CC
1616
O, mass increases, B O, mass increases, B
decreases (decreases (µµ 1/ 1/II), so energy levels lower.), so energy levels lower.
2B 4B 8B 12B2B 4B 8B 12B
cmcm
-1-1
spectrum spectrum
J = 6J = 6
55
44
33
22
11
00
1212
COCO
1313
COCO
EnergyEnergy
levelslevels

32. Comparison of rotational energy levels of Comparison of rotational energy levels of
1212
COCO
and and
1313
COCO
  
Can determine: Can determine:
(i) isotopic masses accurately, to within 0.02% of (i) isotopic masses accurately, to within 0.02% of
other methods for atoms in gaseous molecules; other methods for atoms in gaseous molecules;
(ii) isotopic abundances from the absorption relative (ii) isotopic abundances from the absorption relative
intensities. intensities.
Example:Example:
for for
1212
CO CO J=0 J=0 ®® J=1 J=1atat 3.84235 cm3.84235 cm
-1-1
for for
1313
COCO 3.67337 cm 3.67337 cm
-1-1
Given : Given :
1212
C = 12.0000 ;C = 12.0000 ; O = 15.9994O = 15.9994 amu amu

33. What is isotopic mass of What is isotopic mass of
1313
C ?C ?
B(B(
1212
CO) = 1.921175 cmCO) = 1.921175 cm
-1-1
B(B(
1313
CO) = 1.836685 cmCO) = 1.836685 cm
-1-1
Now Now

ÞÞ ((
1313
C) = 13.0006 amuC) = 13.0006 amu
μ
1
I
1
B µµ
1.04600
1.836685
1.921175
CO)μ(
CO)μ(
12
13
==Þ
15.999412
15.999412
15.9994C)(
15.9994C)(
1.046
13
13
´
+
´
+
´
=Þ

34. Refinements to theory for diatomic moleculesRefinements to theory for diatomic molecules
Rotation spectrum of hydrogen fluoride in the far IR Rotation spectrum of hydrogen fluoride in the far IR
region region 
JJ
00 41.0841.08 41.1141.11
11 82.1982.19 82.1882.18 41.1141.11 20.5620.56 0.09290.0929
22 123.15123.15 123.14123.14 40.9640.96 20.4820.48 0.09310.0931
33 164.00164.00 163.94163.94 40.8540.85 20.4320.43 0.09320.0932
44 204.62204.62 204.55204.55 40.6240.62 20.3120.31 0.09350.0935
55 244.93244.93 244.89244.89 40.3140.31 20.1620.16 0.09380.0938
66 285.01285.01 284.93284.93 40.0840.08 20.0420.04 0.09410.0941
77 324.65324.65 324.61324.61 39.6439.64 19.8219.82 0.09460.0946
88 363.93363.93 363.89363.89 39.2839.28 19.6419.64 0.09510.0951
99 402.82402.82 402.70402.70 38.8938.89 19.4519.45 0.09550.0955
1010 441.13441.13 441.00441.00 38.3138.31 19.1619.16 0.09630.0963
1111 478.94478.94 478.74478.74 37.8137.81 18.9118.91 0.09690.0969
)(cmν
1
obs
-
)(cmν
1
calc.
-
)(cmνΔ
1
obs
-
ν(1/2)ΔB= r(nm)

35. note:note: r r increases with increases with JJ because the bond is not rigid because the bond is not rigid
but elastic.but elastic.
H-F atoms are pushed apart at higher rotational H-F atoms are pushed apart at higher rotational
speed by centrifugal force.speed by centrifugal force.
  
For an elastic bond : For an elastic bond :
wherewhere k k is the bond force constant (Nm is the bond force constant (Nm
-1-1
). Smaller ). Smaller kk, ,
less rigid bond.less rigid bond.
Note also that Note also that r r and and BB vary during a vibration. vary during a vibration.
μcν4πk
2
2
2
=

36. We can refine the theory by adding a correction We can refine the theory by adding a correction
term, containing the centrifugal distortion constant, term, containing the centrifugal distortion constant,
D, which corrects for the fact that the bond is not D, which corrects for the fact that the bond is not
rigid. Assuming harmonic forces:rigid. Assuming harmonic forces:
EE
JJ = BJ(J+1) - DJ = BJ(J+1) - DJ
22
(J+1)(J+1)
22
cm cm
-1-1
where is bond stretch wavenumber. where is bond stretch wavenumber.
  i) can find J values of lines in a spectrum - fitting 3 i) can find J values of lines in a spectrum - fitting 3
lines gives 3 unknowns: J, B, D.lines gives 3 unknowns: J, B, D.
ii) We can estimate from the small correction ii) We can estimate from the small correction
term, D.term, D.
1
224
3
cm
kcrI32π
h
D
-
=
2
vib
3
ν
4B
=
vibν
vibν

37. Polyatomic moleculesPolyatomic molecules
  
Things get much more complicated, but the general Things get much more complicated, but the general
principles are the same.principles are the same.
  
e.g. OCSe.g. OCS HCHCººCClCCl II
cc = I = I
BB; I; I
A A = 0= 0
  
* I greater than for diatomic molecule, * I greater than for diatomic molecule, \\ B smaller; B smaller;
lines more closely spaced.lines more closely spaced.
  
* Remember that the molecule must have D.M. for * Remember that the molecule must have D.M. for
microwave spectrum.microwave spectrum.

38. Microwave spectrum of carbon oxysulphide
J J ®® J+1 J+1 B(cmB(cm
-1-1
))
0 0 ®® 1 1 …… 2 2 ´´ 0.4055 0.4055 0.20270.2027
1 1 ®® 2 2 0.81090.8109 0.40540.4054 0.20270.2027
2 2 ®® 3 3 1.21631.2163 0.40540.4054 0.20270.2027 CalculateCalculate
3 3 ®® 4 4 1.62171.6217 0.40540.4054 0.20270.2027 II
BB
4 4 ®® 5 5 2.02712.0271 0.40550.4055 0.20270.2027
)(cmobsν
1-
N atoms N atoms ®® N-1 bond lengths, so for OCS must N-1 bond lengths, so for OCS must
determine rdetermine r
COCO, r, r
CSCS : that is, two bondlengths are : that is, two bondlengths are
unknown - not just 1 as in a diatomic molecule.unknown - not just 1 as in a diatomic molecule.
νΔ

39. \\ need 2 values for need 2 values for II
BB - the second can come from - the second can come from
an isotopically substituted molecule, which has same an isotopically substituted molecule, which has same
bondlength (almost), but different mass.bondlength (almost), but different mass.
  
e.g.e.g.
1616
OCOC
3434
S, S,
1818
OCOC
3434
S ….S ….
O O ¾¾ C C ¾¾ S S
mm
oorr
oo + m + m
CCrr
CC = m = m
SSrr
SS

I = mI = m
oorr
oo
22
+ m + m
CCrr
CC
22
+ m + m
SSrr
SS
22
  
In accurate work isotopic bondlengths differ, due to In accurate work isotopic bondlengths differ, due to
differences in zero point energy. differences in zero point energy.
r
0
r
c
r
s
centre of gravity

40. Microwave instrumentationMicrowave instrumentation
Schematic diagram Schematic diagram
of a microwaveof a microwave
spectrometerspectrometer
    S: source Klystron oscillator (few mW). S: source Klystron oscillator (few mW).
This is monochromatic, but can be tuned This is monochromatic, but can be tuned
mechanically or electronically. By using several mechanically or electronically. By using several
klystrons we can cover the spectral range 1000 Mc/s klystrons we can cover the spectral range 1000 Mc/s
(30 cm) - 37500 Mc/s (8 mm)(30 cm) - 37500 Mc/s (8 mm)
More recent instruments use solid-state microwave More recent instruments use solid-state microwave
sources.sources.
MICA WINDOWS
SAMPLE
VACUUM
S D

41. The waveguides are hollow metallic conductors The waveguides are hollow metallic conductors
through which the energy propogates. through which the energy propogates.
  
WM: wavemeter measures WM: wavemeter measures ll (or (or nn).).
  
Vacuum - prevents atmospheric (HVacuum - prevents atmospheric (H
22O) absorption.O) absorption.
  
Sample - 0.01 mm Hg pressure adequate, so liquids, and Sample - 0.01 mm Hg pressure adequate, so liquids, and
even some solids, as well as gases may be studied.even some solids, as well as gases may be studied.
  
D: Detector. Radio receiver or crystal detector.D: Detector. Radio receiver or crystal detector.
  
Output: absorption vs frequency.Output: absorption vs frequency.

42. Special cases of microwave absorptionSpecial cases of microwave absorption
a) Inversion spectrum of NHa) Inversion spectrum of NH
33
Pyramidal molecules Pyramidal molecules
not only rotate, but not only rotate, but
can turn inside out can turn inside out
(i.e. invert) because (i.e. invert) because
this has a low this has a low
potential barrier.potential barrier.

43. Rotation-inversion levels of NHRotation-inversion levels of NH
3 3 : Each level is : Each level is
split into two (+,-), which show the orientation of split into two (+,-), which show the orientation of
the molecule. Inversion energy (~ 23000 MHz the molecule. Inversion energy (~ 23000 MHz ´´ hh
Js) depends slightly Js) depends slightly onon rotational energy. rotational energy.
More generally, this type of phenomenon is useful in More generally, this type of phenomenon is useful in
studying the interconversion of conformers.studying the interconversion of conformers.
  
b)b) Microwave spectrum of OMicrowave spectrum of O
22
OO
22 has no permanent dipole moment, but in has no permanent dipole moment, but in
the electronic ground state has 2 unpaired the electronic ground state has 2 unpaired
electrons with parallel spins:electrons with parallel spins:
OO
22 11ss
gg
2 2
2 2ss
uu
22
3 3ss
gg
22
1 1pp
uu
44
2 2pp
gg
22