1? H f f 3“,”?

 

I r" u e ‘ 4'
his «Hr-"o o. i
9-. ..-... rflg-‘Ifi‘

' an" ’...-.' 4] . “if! Ehre-

 

 

 

This is to certify that the

dissertation entitled

Infrared Radiofrequency Double Resonance Spectro-
scopy Outside the Cavity of CO2 Laser; Pure Nuclear

Quadrupole Resonances of CF31 and CF3Br.

presented by

Wafaa Mahmoud Fawzy

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Chemi stry

 

 

(QM "% LLu‘sCug lz‘l'I‘w'k \-

Major professor
Richard H. Schwendeman

Date April 17, 1986

 

MS U i: an Affirmative Action/Equal Opportunity Institution 0-12771

 

 

MSU

LIBRARIES

m

 

 

RETURNING MATERIALS:
Place in book drop to
remove this checkout from
your record. FINES will
be charged if book is
returned after the date
stamped below.

 

 

 

 

INFRARED RADIOFREQUENCY DOUBLE RESONANCE SPECTROSCOPY

OUTSIDE THE CAVITY OF CO LASER; PURE NUCLEAR QUADRUPOLE

2

RESONANCES OF CF31 AND CF3Br.

By

Wafaa Mahmoud Fawzy

DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1986

w

INFRARED RADIOFREQUENCY DOUBLE RESONANCE SPECTROSCOPY

OUTSIDE THE CAVITY 0F CO LASER; PURE NUCLEAR QUADRUPOLE

2

RESONANCES OF GASEOUS CF31 AND CFaBr.

BY

Wafaa Mahmoud Fawzy

Pure nuclear quadrupole resonances have been observed
for CF31 by applying the infrared radiofrequency double
resonance (IR—RF DR) technique with a stripline
radiofrequency sample cell outside the cavity of a semi-
sealed CO2 laser. The spectra were observed with the
9R(12), 9R(14), 9R(16), 9R(18), and 9R(20) laser lines of
120160

2 and with 9P(12), 9P(l4), and 9P(16) laser lines of

1201802 and recorded at fixed infrared frequency as a
function of radiofrequency in the range 1-500 MHz. It was
found that strong well-resolved spectra could be obtained
with the sample cell outside the laser cavity. 0f the 471
resonances recorded, 142 were assigned to pure nuclear
quadrupole transitions in rotational levels of many
vibrational states, 6 of which were identified. The center

frequencies of the double resonance effects were determined

by fitting the spectra to sums of Lorentzian lineshape

Wafaa Mahmoud Fawzy

functions. Quadrupole coupling constants and magnetic
hyperfine parameters were determined by least squares fits
of experimental frequencies to frequencies calculated by
direct diagonalization of the energy matrices. From the
laser coincidences with the assigned transitions, the v1
band center has been determined. The results of the present
work contribute data and help to resolve existing
controversies concerning the interpretation of the infrared

spectrum of CF31 in the important 9.3 pm region.

Pure nuclear quadrupole resonances in the ground, v1,

v6, and v1+v6 vibrational states of CF37QBr and in the

ground and v1 vibrational states of CF3813r have been
observed in the 1-300 MHz region by applying the infrared
radiofrequency double resonance technique. The 9R(28) and
9R(30) 002 laser lines were used for pumping. In addition
to the quadrupole hyperfine structure, Al-A2 splitting in

79

the v6 and vl+v6 vibrational states of CF3 Br have been

observed. Quadrupole coupling constants, determined by the
least squares fits of experimental frequencies to
frequencies calculated by direct diagonalization of energy

matrices, have been obtained for the ground, and

V1! V6!
v1+v6 vibrational states of CF37QBr and for the ground and

v1 vibrational states of CFSBIBr. The l-doubling constants

have been determined for the V6 and vl+v6 vibrational states

Wafaa Mahmoud Fawzy

79
3

vibration-rotation transitions, the centers of VI and

of CF Br. From the laser coincidences with the pumped
v1+v6 . V6 vibration-rotation bands have been estimated.

The results of this work demonstrate the very high
resolution and sensitivity achieved by applying the infrared
radiofrequency double resonance technique with the sample
cell outside a 602 laser cavity. In the present study of
the v1 region of CFafir, which shows a very crowded vibration
rotation structure, the bromine hyperfine components of
rotational states of very high J (67) and K (41) quantum
numbers, which are separated by less than 1 MHz, have been
resolved. The results of this work also provide new
parameters for the v1 and v1+v6 vibration-rotation bands of

CFzBr.

DEDICATION

T0

Tmy wonderful mother"

Gazebja Y. Kbalaf-allab

I found this as one special way of saying

Thank you mother;

I appreciate you and I love you.

and

"The memory of my father"

Mahmoud M. Fa wzy

Even though he departed this world a long time ago,

his love has always been in my heart.

_§NOWL§DGMENTS

I would like to express my sincere appreciation and
thanks to my advisor Professor Richard H. Schwendeman for
his openminded and enlightening discussions, and for his
support throughout this study. I also thank him for making
computer facilities available to me both for typing this

thesis and for making the figures and diagrams.

I would like to thank Professor James F. Harrison for
his willingness to be the second reader of my thesis while
Professor Katharine C. Hunt was on sabbatical leave and for
his concern and encouragement. My thanks are extended to
the other members of my committee, Professor John Allison
and Professor Harry A. Rick. I also like to thank Professor
Katharine C. Hunt for her service on my committee and for

her concern and kindness.

My deep appreciation and gratitude are directed to the
Chemistry Department at Michigan State University for
financial support through a teaching assistantship and to
the National Science Foundation for a research

assistantship.

I thank the members of the Infrared Laser and Microwave
Spectroscopy research group for their discussions and

concern about the progress of this work.

I would like to direct my thanks to everybody in the
Chemistry Department at Michigan State University, faculty
members, graduate students, members of the Electronics Shop,
Glassblowing Shop, the Machine Shop and Secretaries for
their help whenever it was needed. Their kindness and
friendly attitude helped me towards the progress of this

work and made me feel like being at home.

I am greatly indebted to the Chemistry Department at

Alexandria University in Egypt.

Finally, my thanks and appreciation are directed to my
family for their support and encouragement throughout my

stay away from home. To "my mother" I dedicate this thesis.

TABLE OF CONTENTS

CHAPTER

LIST OF TABLES .........................................
LIST OF FIGURES ........................................
CHAPTER I. INTRODUCTION ............................
CHAPTER II. THEORY ..................................
Molecular Motion .............. . ....................
Rigid Rotor and Rotational spectra .................
Energy levels ............ . .........................

The Electric Dipole Moment and ”Pure”
Rotational Spectra ....... . .........................
Vibration-Rotation Interaction.... .................
a- Non-degenerate vibrational states ...........
b- Degenerate vibrational states ...............
Types of Infrared Bands..... ..... .... ..... .........

Infrared Selection Rules ...........................

a- Parallel infrared bands .....................

b- Perpendicular infrared bands ................
The Nuclear Electric Quadrupole Moment.. ..... . .....

The L-Type Doubling and A -A Splitting ............

l 2

CHAPTER III. CF I ....................................

Page

V

VII

15
17
18
18
20
21
22
34

37

II

CHAPTER Page

CHAPTER IV. INFRARED-RADIOFREQUENCY DOUBLE

RESONANCE SPECTROSCOPY ..... . ............ 43

Infrared Radiofrequency Double Resonance

Spectrometer ....................................... 43
Infrared pumping radiation ..................... 43
Radiofrequency radiation ....................... 46
RF modulation ............................ . ..... 46
RF sample cells ................................ 47
Operation of the Spectrometer .................. 47

Operation of the IR-RF Outside a CO2

Laser Cavity ....... ..... .......... ....... .......... 50

CHAPTER V. METHOD OF CALCULATION AND ANALYSIS ..... 57

I- Method of Calculation..... ...................... 57

The quadrupole interaction energies ........... 57

Intensities of the hyperfine transitions...... 62

The main computer program ..................... 64
11— Method of Analysis... ............. . ............ 65
Rotational assignment ......................... 65

Determination of qu and the
magnetic parameters ........................... 66
Vibrational assignment ........................ 66

The vibrational dependence of qu ............. 67

III

CHAPTER Page
The rotational dependence of qu .............. 68
Infrared band centers .............. .... ....... 68
CHAPTER VI. RESULTS AND DISCUSSION .................. 71
Introduction..... .................................. 71
Results and Discussion ............................. 86
v1 . G.st ..................................... 88
v6+v1 ~ v6 ; °a(2o,16) ........................ 91
v3+v1 ~ v3 ; QR(23,20) ........................ 93
IR transitions in unidentified vibrational states... 94
”a . G.st; 00(18,16) .......................... 94
vx . G.st; °p(6,5) ............................ 95
vc ~ vb ; °o(43,24) .......... . ............... 96
vi ~ ”a ; °P(31,9) ........................... 97

vi ~ vh ; °o<44,34) and
v2 . v6 ; °o<34,29)... ....................... 99
vf ~ "e ; °P(22,9) ........................... 102
Unassigned transitions ............................. 102
CHAPTER VII. CFaBr ................................... 126
I- INTRODUCTION... ................................ 126
11- RESULTS AND DISCUSSION ......................... 129
9R(28) co2 laser line: 1083.47878 cm-l ........ 138

99(30) co2 laser line: 1084.63514 on” . ....... 14o

IV

CHAPTER Page
APPENDIX I ............................................. 153
APPENDIX II .................. . ......................... 165

REFERENCES ............................................. 168

LIST OF TABLES

1- Tables For CF I

3
Table Page
1 9R(16) 12c1602 Laser Line ................ 105
2—3 9P(14) 1201802 Laser Line ................ 106-107
4-6 9R(14) 12c1602 Laser Line ................ 108-110
7 9R(18) 12c1602 Laser Line ................ 111
8 9R(12) 1201602 Laser Line ................ 112
9 99(20) 1201602 Laser Line ................ 113
10-11 9P(12) 12c1802 Laser Line ................ 114-115
12 9P(16) 12c1802 Laser Line ................ 116
13-15 Summary of Results in Tables (1-12) ...... 117-119
16 Rotational Dependence of qu ............. 120
17 The Magnetic Parameters .................. 121
18 Comparison of Vibration-Rotation

Assignment of the Present Work with

the Previous Reported Results ............ 122-123
19 Vibrational Dependence of qu ............ 124
20 The v Band Center ...................... 125

l

II- The

Table

21-23
24
25

26

VI

79 81

Results for CF3 Br and CF3 Br
Page
9R(28) 1201602 Laser Line ................ 144-148
99(30) 12c1602 Laser Line ................ 149-150
Vibrational Dependence of qu ............ 151

Infrared Band Centers .................... 152

VII

LIST OF FIGURES

Figure
l The lower rotational energy levels
for a symmetric top molecule .................
2 The lower rotational energy levels for
a prolate symmetric top molecule in a
totally symmetric vibrational state ..........
3 The lower rotational energy levels for
a prolate symmetric top molecule in a singly
excited doubly degenerate vibrational state.
{ has been assumed to be positive ............
4 A vector diagram for the I and J coupling...
5 A schematic energy level diagram for "pure"
nuclear quadrupole resonances and nuclear
quadrupole resonances in CF31. ...............
6 A schematic energy level diagram for
the l-type doubling in CF38r .................
7 The intracavity experimental setup
for the IR-RF DR spectrometer ................
8 The extracavity experimental setup
for the IR-RF DR spectrometer ..... .........
9 A cross section in the coaxial RF

sample cell ..................................

Page

16

19

31

32

36

44

45

48

Figure

10

ll

12

13

14

15

16

17

VIII

A cross section in the stripline RF

sample cell ........ ............. .............
A schematic diagram for the IR-RF DR
operation at low IR power and at low

sample pressure..................... ........ .
A schematic energy level diagram shows the
"pure" nuclear quadrupole resonances and

the pumped IR transitions in CF31. ...........
IR-RF DR in CF31 recorded with the
intracavity setup. Laser line: 9R(16) C02;
sample pressure: 5 mTorr.....................
IR-RF DR in CF31 recorded with the
intracavity setup. Laser line: 9R(16) 002;
sample pressure: 10 mTorr....................
IR-RF DR in CF31 recorded with the
intracavity setup. Laser line: 9R(16) 002;
sample pressure: 2 mTorr....... ..............
IR-RF DR in CF31 recorded with the
extracavity setup. Laser line: 9R(16) 602;
sample pressure: 20 mTorr..... ............ ...
IR—RF DR in CF31 recorded with the
extracavity setup. Laser line: 9R(16) C02;

sample pressure: 20 mTorr....................

Page

49

51

53

72

73

74

76

77

Figure

18

19

20

21

22

23

IX

Page
Comparison of the intracavity spectra
in Figure 13 with the extracavity spectra
in Figure 16.
Solid lines: the intracavity spectra;
dots: the extracavity spectra ................ 78
Comparison of the intracavity spectra
in Figures 14 and 15 with the extracavity
spectra in Figure 17.
Solid lines: the intracavity spectra;
dots: the extracavity spectra ................ 79
The effects of laser frequency on
the IR-RF DR spectra.
Laser line: 9R(18) C02;
sample pressure: 17 mTorr .................... 81
IR-RF DR in CF31 recorded with
the extracavity setup.
Laser line: 9R(l4) 002;
sample pressure: 10 mTorr .................... 82
High resolution record for the first quartet
in Figure 21. sample pressure: 10 mTorr..... 83

High resolution record for the
second quartet in Figure 21;

sample pressure: 10 mTorr .................... 84

Figure

24

25

26

27

28

29

Page

IR-RF DR in CF3I recorded with the

extracavity setup. Laser line: 9R(18) C02;
sample pressure: 17 mTorr .................... 85
An example of a spectrum crowded

with different Q branches.

Laser line: 9P(12) 12C1802;

sample pressure: 15 mTorr .................... 100
An example of high resolution records
for Fig. 25.
12C18o

Laser line: 9P(12) 2;

sample pressure: 15 mTorr .................... 101
An example of unassigned IR—RF DR

transitions. Laser line: 9R(18) C02;

sample pressure: 17 mTorr .................... 103
A schematic energy level diagram for the

PNQR resonances and the laser pump

in CF38r ..................................... 131
The recorded FTIR spectrum in the

v1 band region of CF3Br.

Sample pressure: 0.9 Torr;

resolution: 0.02 cm’1 ........................ 132

Figure

30

31

XI

Page

The synthesized spectrum of CF3Br.

(as reported in Ref. (81)) ................... 134
An example of a resolved quartet in CF3Br.

Laser line: 9R(28) COZ;

sample pressure: 10 mTorr... ....... .. ........ 137

CHAPTER I

INTRODUCTION

The infrared radiofrequency double resonance (IR-RF DR)
technique with the sample cell placed inside a C02 laser
cavity has previously been established in other laboratories
as a powerful tool for radiofrequency (RF) spectroscopy (a
summary of previous work is given in Chapter IV). This
technique transfers the advantages of IR laser spectroscopy
to the RF region of the spectrum. However, the IR-RF DR
technique had not previously been applied at Michigan State
University (MSU).

The goal in this work has been the development of the
IR-RF DR technique at MSU and its application to the study
of the RF and ro-vibrational spectrum of the many different
vibrational states involved in the v1 region of the CF31 and
CF38r symmetric top molecules.

The first step in the present study was to assemble an
IR-RF DR spectrometer. This process was assisted
considerably by the availability of computer programs and
sample cells used by Dr. A. Jacques. The next step was the
successful observation of some of the previously reported
phenomena with a coaxial RF sample cell placed inside a

semi-sealed CO2 laser cavity. However, when the

spectrometer was applied to the study of CF31 and CF3Br, the
observed spectra showed complicated structure, distorted
lineshapes, and low resolution (examples are shown in
Chapter VI). 0n the other hand, high resolution spectra
with symmetric lineshapes were obtained by performing the
experiment with a stripline sample cell outside a CO2 laser
cavity (as shown in Chapter VI). In this work the
application of the IR-RF DR technique with a sample cell
outside a CO2 laser cavity is reported for the first time.
This method has been applied successfully to the study of
”pure" nuclear quadrupole resonances and to the
identification of several vibrational states in the very
complicated v1 regions of the CF3I and CF3Br molecules. The
results of this work demonstrate the usefulness of IR-RF DR
with an external cavity sample cell. The high resolution
and clean lineshapes make it not only a powerful tool for RF
spectroscopy, but also for identification of infrared bands
and strongly perturbed states in complicated IR spectra.

The high resolution and clean lineshapes also strongly
suggest that this method should be a powerful tool for the

study of lineshapes and relaxation in favorable molecules.

CHAPTER II

THEORY

Molecular Motion
Molecular motion is classified into 3 main categories:

1- Translational motion of the molecular entity.

2- Internal motion.

3- Electronic motion.
The first kind of motion can be understood classically
whereas the second and third types of motion can only be
understood with the aid of quantum mechanics. The solution
for the Schrodinger equation is simplified by the Born-
Oppenheimer approximation, in which the electronic and the
nuclear motion are separated (1). This thesis is concerned
with the internal motion which represents the relative
motion of nuclei with respect to the center of mass and
includes rotation about the center of mass and relative
vibrational motion. In the rigid rotor-harmonic oscillator

approximation the internal motion can be written as (2)

(2.1)

This separation of vibrational and rotational motion makes
it possible to discuss the energy levels for each motion

separately.

Rigid Rotor and Rotational Spectra

The rigid rotor Hamiltonian can be written as (3)

.. 1 2 1 2 ..1 2
Hr - 2T Pa + 21 Ph + 21 Pc (2'2)
a b c
where
P2 = P2 + P2 + P2
a b 0
Here 2 is the total angular momentum; Pa , Pb , and Pc are

components of P referred to molecule-fixed coordinates; and

Px , Py , and P2 are components of 2 along space-fixed axes.
The quantum mechanical properties of angular momentum

are governed by commutation relations of the operators for

the angular momentum and its components. These commutation

relations can be summarized as follow (4):

_ . , 2 - .
[Pi , Pj] - leijk Pk , [P , Pi] - o ,
- _ . 2 = .
[Pa , PB] — ”may PY , [P , Pa] 0 , (2.3)
[Pi , Pa] = 0.

In these Equations the indices ijk indicate space-fixed
axes, xyz, whereas a, B and Y indicate molecule-fixed axes,

abc. The tensor eijk has the following properties:

eijk = 0 if any two indices are identical;
eijk = 1 if ijk is a cyclic permutation of x, y, z;
eijk = -1 otherwise (anticyclic permutation).
e is defined in the same way as e.. but for the
«BY 13k

molecule-fixed axes, abc.

These commutation relations can be used to derive the
matrix elements for the total angular momentum, P , and its
components along the z and a axes, respectively (5). A
basis is chosen such that:

“2

9 ’ D _ 2 o
<ka| P IJ k m > — J(J+l)h sJJ.skk,s.m. ,

<ka|Pz|J’k’m’> mfiS (2.4)

JJ’skk’smm’ ‘

9 ’1: =
<ka|Pa|J k m > kfisJJ’skk’smm’

In Equation (2.4), J(J+1)fi2 is the square of the total
angular momentum where J = 0, 1, 2, 3.......,~; kh is the
projection of the total angular momentum on the molecular a
axis, where k = J, J-l, J-2,..,—|J|; and mh is the angular
momentum along the space fixed 2 axis and m is restricted to
integers such that -J g m S J . For the symmetric top
molecules studied in this thesis the molecular a axis is

taken to be the symmetry axis. The remaining matrix

elements have to be considered for asymmetric molecules and
they are given elsewhere (1).

Polyatomic molecules can be classified according to the
values of moments of inertia and the relations among them as
l- spherical tops I = I = I e.g., CH

2- linear molecules I = 0, Ib = I e.g., 008;

3- symmetric tops

a- prolate Ia < Ib = Ic e.g., CF31, CF3Br;
b- oblate I8 = Ib < IC e.g., NH3;
4- asymmetric tops Ia < Ib < IC e.g., H20.

The eigenvalues of the Hamiltonian (2.2) can easily be
obtained for each of the above mentioned classes. Since our
interest in this thesis is in symmetric top molecules, the
energy levels and rotational spectra for this class of

molecules are discussed in the next section.

Energy Levels

The rigid rotor energy levels for symmetric top
molecules can be easily derived from Equation (2.2).
However, rotation is associated with centrifugal forces

which cause an increase in the effective moments of inertia

which in turn affect the rotational energy levels as a power

series in J(J+l) and k2. For a prolate symmetric top

molecule (6)

E(J,k) = BJ(J+1) + (A-B)k2 - DJJ2(J+1)2 — Dkk4
2 3 3
DJkJ(J+l)k + HJJJJ (J+1) (2.5)
2 2 2 4 6
+ HJJkJ (J+l) k + HJkkJ(J+1)k + Hkkkk + .....

Explicit formulas for the distortion constants are given in
References (7,8). The quartic centrifugal distortion terms
are adequate for many cases, especially for levels of low J
and k quantum numbers. However, for energy levels of high J
and k the effect of the sextic and higher order terms is
important.

The energy is seen to be independent of the sign of k
and, accordingly, the energy levels for k a 0 are doubly
degenerate whereas those for k = 0 are non-degenerate in k.
On the other hand, each level is (2J+l) fold degenerate in
m. Typical energy level patterns for oblate and prolate

symmetric top rigid rotors are shown in Fig. (l).

4
J
3 3
2 2
1 1
O 0
O 1 2 0 1 2 K
3"" prolate symmetric top b- oblate symmetric top

Fig. l. The lower rotational energy levels for a symmetric

top molecule.

The Electric Dipole Moaent and ”Pure” Rotational Spectra
"Pure" rotational spectra are observed as a result of
interaction between the molecular electric dipole moment, 2
and the oscillating electric field associated with
electromagnetic radiation. The details of this interaction
can be determined by means of time-dependent perturbation
theory. In this derivation the molecular system is
described quantum mechanically whereas the electric field is
expressed classically. The result of this semiclassical
treatment for the absorption coefficient, Y(m), for a
transition from a rotational eigenstate In) to an upper

state In) is (4)

3 N N
F. l .2

C gm 31]

)l<nlgll>|28(u.unn)

where (2.6)

N 8

n n e-(En-El)/kT
N s

m m

in which Nm and gn represent the population and degeneracy
for the level In), respectively, whereas ND and gn are the
corresponding values for the level In). Also, S(u,un.) is
the line shape function.

The 1th component of the electric dipole moment matrix

elements connecting rotational states in a given vibrational

10

manifold may be written as (4)

(kalpilJ’k’m’> = ua<ka16ui|J’k’m’) (2.7)

where the repeated a indicates summation over a, b, and c
principal inertial axes of the molecule; the u“ are the
components of the electric dipole moment in the direction of
the molecular principal axes, the pi are the components in
the space—fixed axes, and the so‘i are the direction cosines
between the molecular axes and the space-fixed axes.

For a prolate symmetric top molecule, the a axis is the
unique symmetry axis so that pb = pc = 0; therefore, the

only surviving term in Equation (2.7) is

(JkllpilJ’k’m’> = pa(kaleailJ’k’m’> (2.8)

The selection rules for "pure" rotational spectra of
symmetric top molecules can be deduced from Equations (2.6)-
(2.8) as follows:

1- in order to obtain a non-zero absorption coefficient,
Y(m), the matrix element of at least one component of the
electric dipole moment, given in Equation (2.7), must be
non-zero. As a consequence of Equation (2.8), the electric

dipole selection rules for a symmetric top molecule in the

ll

absence of an external static field, where the m-degeneracy

is preserved, are

for k = 0: aJ = :1; ak = 0; Am = 0;
(2.9)

for k t 0: aJ = 0, 11; ok = 0; Am = 0.

Plane-polarized radiation with go in the space-fixed z
direction is assumed.

2- The Bohr frequency condition must be fulfilled,

hm = ho = E - E (2.10)

"Pure" rotational transitions can be observed
throughout the microwave into the far-infrared region of the
spectrum. The rotational spectra is grouped into three

branches according to the aJ selection rule as following:

oJ = -l P— branch transitions;
AJ = 0 Q- branch transitions;
oJ = +1 R- branch transitions.

The frequencies of P, Q, and R branches are usually

and v respectively. These

V0! R9

frequencies can easily be calculated from Equation (2.5).

designated as vp,

The observation of "pure" rotational transitions by

12

microwave spectroscopy has been used as a powerful tool for
accurate determination of molecular dipole moments, bond

distances, moments of inertia, bond angles, ....... etc.

l3

Vibration:§atation Interaction

It has been stated (Equation (2.1)) that the
Hamiltonian for internal motion can be separated
approximately into rotational and vibrational parts. In
this rigid rotor-harmonic oscillator approximation, the
interaction of vibrational and rotational motions is
included in effective values of the rotational and
centrifugal distortion constants. In this section,
vibrational and rotational energy levels, including
vibration-rotation interaction and vibration-rotation
spectra, are discussed for a symmetric top molecule.

Vibrations may be non-degenerate or degenerate.
Vibrations of a degenerate vibrational mode in a molecule of
03v symmetry produce an angular momentum {15 about the C3
symmetry axis. The vibrational angular momentum quantum
number 1 = v., v. -2, ..... , —vi, whereas ltl S 1. The

1 1

general formula for vibrational energy levels is (9)

d.
— 11
E(vl , v2 ,...) - hf vi(vi+ 2 ) +

hf f xik(vi + »2 )(vk + W2 ) + (2.11)

h)? Zgi

9.. 9.
1 kzi 1

k

Here, xik is an anharmonicity constant, (11 is the degeneracy

th

of the i vibration, and gik is a small constant of the

14

order of xik' For non-degenerate vibrations, d1 = dk = l,

and 1i = 1 = 0.

1:311.

In the rigid rotor-harmonic oscillator approximation,
the moments of inertia are considered constants. However,
in a symmetric top molecule Ia and Ib change periodically
during vibration and accordingly, the rotational constants
and B contain contributions from averaging over the

vibration and from Coriolis effects. This leads to changes

in A and B with vibrational state, which are expressed as

(9)

d.
- - -1
Bv _ Be f 0‘1 (v1 + 2)’
(2.12)
A di
and Av = Ae - E 0‘1 (v1 + ~""2" )

In these Equations, Av and RV are the effective values of A

and B for vibrational state v and a:

and a: are called the
vibration-rotation constants.
The total energy of vibration and rotation of a symmetric

top molecule is given by (9)

E(g,J,k) = 11(3) + Ev(J,k) (2.13)

On the other hand, the rotational energy levels in a

15

vibrational state of a symmetric top molecule, Ev(J,k),
depend on the degeneracy of that vibrational state. As a
consequence, the fine structure of the vibration-rotation
also depend on the symmetry of the vibrational states
involved in the infrared transition. In the next section,
the rotational energy levels of non-degenerate and

degenerate vibrations will be discussed.

a- Non-degenerate vibrational states
In this case, the rotational energy levels for a

prolate symmetric top molecule are given as (9)

_ _ 2
Ev(J,k) - BvJ(J+1) + (Av Bv)k + ........ (2.14)

The centrifugal distortion contribution to Equation (2.14)
is the same as that in Equation (2.5). The contribution of
a non-degenerate vibrational state of A1 species in the 03v
group with the rotational energy levels of a symmetric top
molecule yield vibration-rotation levels of species A1 or A2
for rotational levels of species A (levels with k = 3n) or
of species E for rotational energy levels of species E
(levels with k = 3n11). The rotational energy levels of a

prolate symmetric top molecule in a totally symmetric

vibrational state are shown in Fig. (2).

16

A2
A
E 1
J E
5 A2
A1
A
E 2
E
E A1
E
3 A2
E
E
2 A1
A2
0 A1
K=O K-1 K=2 K=3

Fig. 2. The lower rotational energy levels for a prolate

symmetric top molecule in a totally symmetric vibrational

state.

17

b- Degenerate vibrational states
The rotational energy levels of a prolate symmetric top
molecule in which one degenerate vibration V1 is singly

excited are given as (9)

- _ 2 _
Ev(J,k) - BvJ(J+1) + (Av Bv)k + 2AvriK|1| + ........ (2.15)

Here, I is the previously introduced quantum number of
degenerate vibrations. The - sign applies if the
vibrational and rotational angular momenta are in the same
direction whereas the + sign applies if they are in opposite
directions. Equation (2.15) differs from (2.14) only by the
term $2Av{iK|£|. This additional term in Equation (2.15)
includes the Coriolis interaction (9). The result of this
Coriolis interaction is a first order splitting in the
rotational energy levels into +1 and -1 sublevels; this
splitting increases linearly with increasing k and is called
the l-splitting. The interaction of a singly excited
degenerate vibrational state of E species with the
rotational energy levels of a symmetric tap molecule of A
species characterized with lk-ll = 3n11 gives rise to levels
of E species, whereas this contribution yields levels of

E+A1+A2 species for rotational levels with Ik-ll = 3n.

18

The rotational energy levels of a prolate symmetric top
molecule in a degenerate vibrational state are shown in

Figure (3).

Types of Infrared Bands

There are two different types of infrared transitions
for symmetric top molecules. The first type is called a
paaallel band (fl). In this case the vibrationally induced
dipole moment, ”V, is u to the unique symmetry axis or the
near symmetry axis. The second type of infrared band shows
a more complicated vibration- rotation structure and is
called a perpendicular band (1). For a 1 band, the
vibrational transition moment is l to the symmetry axis.

In this work, only parallel infrared bands have been

identified for CF31 and CF3Br.

Infrared Selection Ralaa

Vibration-rotation transitions occur throughout the far-
infrared to the infrared region of the spectrum, from 810 to
= 10,000 cm—l, and obey selection rules which may be derived
from identification of non-vanishing transition moments.

The vibration-rotation transition moment, [Mun], for a

transition from a state m to another state n is expressed as

19

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 E E
.411 2/
A
2
2 E 1 5
A2_____
1 E A1
0 E
k - 0 k - 11 k - *2 k - :3

Fig. 3. The lower rotational energy levels for a prolate
symmetric top molecule in a singly excited doubly degenerate

vibrational state. { has been assumed to be positive.

20

nm _ r v r v
[M 1 - <11n inuvli’. 9.3 (2.16)

where pv is the vibrationally induced dipole moment; the
superscripts r and v indicate rotation and vibration,
respectively.

For a symmetric top molecule, the selection rules
depend on the type of the infrared band and on the
degeneracy of the vibrational states involved in the
infrared transition. These selection rules are given as

follows:

a- Parallel infrared bands
For transitions between non-degenerate vibrational
states, 1 = 0 and the selection rules for a parallel band

are

for k s 0 : AJ

11
C
1+
H
D
r

11
O

(2.17)

II
C

for k = 0 : oJ = 11 ; 0k

For infrared transitions in a parallel band involving two
degenerate vibrational states in a symmetric top molecule

the selection rule a! = 0 is added to those given in (2.17).

21

b- Perpendicular infrared bands
For a symmetric top molecule, a perpendicular band requires
that at least one of the vibrational states be degenerate;

the selection rules in this case are

0k

11
1+
1...
D
L4

11
O

11 ; olk-ll = 0. (2.18)

22

The Nagleaa_§lectric Quadrupole Moaent
In the early days of the atomic theory, nuclei were

considered to be simple point charges. We now have more
detailed knowledge of nuclear structure. Nuclei have radii
near 10_12 cm and consequently they may involve a charge
distribution. Some nuclei possess angular momentum
characterized by the nuclear spin quantum number I; nuclei
with odd mass number have a half-integer value of I whereas
nuclei with even mass number have an integer value of I.
Nuclei with an even number of protons and an even number of
neutrons have I = 0. Protons of nuclei with non-zero
nuclear spin I are in motion about the nuclear spin axes,
this motion of the protons (positively charged particles)
produces a magnetic field and sweeps out a charge
distribution giving the nucleus an angular momentum 15 and
electric and magnetic moments. Nuclear moments depend on
the value of I where the highest order which can occur is
given by 221. Thus nuclei with I = 1/2 may possess a dipole
moment, whereas those with I 2 1 may have quadrupole moment,

...etc. Poles of various orders may be magnetic or
electric depending upon the symmetry of the involved states.
Nuclei with nuclear spin I have (21+l) degenerate states
where this degeneracy can be lifted upon application of an
external field or molecular interaction into (21+l) states
of different orientations and energies. In this section,

the nuclear electric quadrupole moment, its interaction with

23

electronic charges in the molecule, and the consequences of
this interaction are discussed for the case of a symmetric

top molecule.

The system to be considered is a symmetric rotor
gaseous molecule with rotational angular momentum J and one
atom on the symmetry axis with nuclear spin I 2 1.

Since the rotation of charges in the nucleus about the
nuclear spin axis is fast compared to the rotational motion
of the molecule, in a space-fixed coordinate system the
nuclear charge distribution can be considered continuous.
One further assumes that the relative positions of the atoms
in the molecule are fixed and that the electronic charges
outside the nucleus may be described by a static charge
distribution relative to the molecular axes. With these
assumptions, the energy of the interaction between the
charges in the nucleus and those outside it can be expressed

as (10)

E = Ip(§)V(§)dg (2.19)

Here, 9(5) is the nuclear charge distribution within the
nucleus with nuclear spin I; V(§) is the electrostatic
potential witnessed by the nucleus due to the electronic and

nuclear charges external to the nucleus of spin I; d; is the

24

nuclear volume element dxdydz, where the integration is over
the entire nuclear size.

Upon expansion of V(§) about the nuclear center of mass,

+ El 2 z r.r.( aV + .... (2.20)
. i J

-——-— )
1 J ariarj 0

where ri is the component of g in the direction of the ith

cartesian axis.

Then

E = V0 Jp(r)dr + 2 (2 ;)o Ip(r)ri dr +

(2.21)

av2

1
g (SFTSFT)0 19(5)r1’jd5

2!

qu

In this expansion, only terms which depend on nuclear
orientation need to be considered. The first term is a
monopole moment which gives ZeVo, where Z is the atomic
number of the nucleus and Ze is the total charge. This term
is independent of the nuclear orientation (size and shape)
and hence it can be neglected (it is included in the
electronic energy of the molecule). The second term is the
nuclear electric dipole moment and is an inherent property

of the nucleus. This term is zero (11,12), because

25

integrals of the type:

Iwnuc pi wnuc d5 = 0 (2°22)

vanish because nuclear eigenstates posses a definite parity
(11,12) and pi is an odd operator. The rule is rather more
general as all electric multipole moments of odd order are
zero for a nucleus in a spin eigenstate. The third term in
Equation (2.21) involves the electric quadrupole moment
which does depend on molecular orientation. The next non-
zero higher order term in the expansion involves the
electric hexadecapole (16-pole) moment. This involves the
fourth derivative of the potential and accordingly its
contribution to the energy is expected to be smaller than
that of the quadrupole term by a factor of roughly 108. As
a consequence, the effect of the hexadecapole is too small
for experimental detection and can be ignored in the

expansion. Therefore, the power series in Equation (2.21)

can be truncated at the quadrupole term and written as

Ip(£)rirjdg = g f E V.. F.. (2.23)

26

where

=(azv

lj 3F;3F3)0 and F.. = Ip(§)rirjd§

1.]

Equation (2.23) can be simplified by considering some of the
properties of Cartesian second-rank tensors. Complete
discussions of Cartesian tensors have been given by Racah
(13-15), Wigner (16), Tinkham (l7), and Rose (18). In
general, a Cartesian second-rank tensor, with general

element Tij’ is reducible and can be expressed as

_ 1 s
Tij - § 8..T + T.. + T.. . (2.24)

In this equation ng is an antisymmetric second-rank tensor

as follows:

T = % (T..-T..) ; i, j, k cyclic. (2.25)
Also, the trace, Tt, which is independent of orientation, is

ii

27

Finally, T13 is a symmetric second-rank tensor,

.T . (2.26)

Then the interaction energy E in Equation (2.23) can be
decomposed into a combination of the effects of traces,
antisymmetric, and symmetric tensors. The interaction
energy involving the antisymmetric tensors vanishes because
vij = VJ1 and Qij = Q
the combination of traces of the Qij and vij tensors can be

ji' The interaction energy involving
neglected for the following reasons:

1- Only the s electrons have non-negligible charge
distribution inside the nucleus. However, the charge
distribution for s electrons is spherically symmetric and
consequently the interaction energy is zero in this case.
2- The Laplace Equation holds inside the nucleus for an
electronic potential due to charges outside the nucleus;
i.e., 02V = Vt = 0.

Thus, as a result of these considerations, the interaction
Hamiltonian, Ho, can be obtained from Equation (2.23) and

expressed as the scalar product of the symmetric second-rank

tensors, V7. and 07. , as follows:
1J 1J

28

- l s s
“o - g E 2 vij Qij (2.27)
1 .1
where
s _ s _ _ 2
015 - arij - Ip(£)[3rirj Sijr ]dr . (2.28)

The interaction energy is therefore between ng, the nuclear
electric quadrupole moment symmetric tensor (an inherent
property of the nucleus), and vgj, the second derivative of
the molecular electrostatic potential V(£) or the molecular
electric field gradient, -9E , at the nucleus due to the
potential V(5) (a molecular property).

s

Qij

and they are characterized by I in the nuclear space and J

and VEJ are reducible spherical tensors of rank 2

in the molecular space, respectively. Consequently, the

diagonal matrix elements of H can be calculated by

Q

transforming the components of V: to the principal inertia

J
axes and applying the Wigner-Eckart theorem (4) in the

uncoupled representation, I and J. The resulting diagonal

matrix elements for a symmetric top molecule are (10)

322

373:1) - 1]f(I,J,F), (2.29)

<JkIF|HQ|JkIF> = qu[

29

where
q = vaa’ the molecular electric field gradient at the
nucleus in the direction of the molecular symmetry axis

averaged over the states |J,m=J>;

f(I,J,F) is the Casimir’s function, which is defined as

(3/4)C(C+l) — I(I+1)J(J+1)

 

f(I'J'F) = 2I(2I-l)(2J-l)(2J+3) '
where

F = I+J, I+J—1, ................ ,II-Jl
and

C = F(F+1) - I(I+l) - J(J+1).

Q is the nuclear electric quadrupole moment and is a measure
of the deviation of the nuclear charge distribution from
spherical shape.

For many purposes, the matrix elements in Eq. (2.29),
which give the first-order perturbation contribution for the
energy, are a sufficiently accurate representation of the
quadrupole interaction energy. For large qu, however,
higher order effects are important. These are described in
Chapter V.

The electric nuclear quadrupole moment, Q, may be zero

30

or have a positive or negative value depending on the shape

of the nuclear charge distribution as follows:

 

 

value of Q agape of nuclear chaagg diatribution

zero spherical

positive prolate (elongated along the nuclear axis)
negative oblate (flattened along the nuclear axis)

qu is called the quadrupole coupling constant and is a
measure of the interaction of the electric nuclear
quadrupole moment with the molecular electric field gradient
at the nucleus. Both the value and the sign of qu depend
on Q and q.

As a result of the I.I coupling, the rotational energy
levels with k x 0 of a symmetric top molecule split into
(2J+1) states for J < I while they split into (21+l) states
for J > I. These splittings are very small and accordingly
the resulting energy levels are called the hyperfine
structure. Fig. (4) shows a vector diagram for the coupling
between I and I angular momenta.

The hyperfine structure for the system described
earlier and one of its nuclei with I = 5/2 (e.g., CF31) is
shown in Fig. (5) where the allowed transitions are

indicated by arrows.

 

31

 

32

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P
6.5
l 5.5
J-6 7.5
kiO K RF 4.5
8.5
T 3.5
MW MW
AF-O AF-ti
AJ-ii AJ-i1
F"
5.5
I 4.5
J-S V 6.5
“0.1.! RF 1! 3.5
7.5
12 2.5
Fig. 5. A schematic energy level diagram for the "pure"

nuclear quadruploe resonances and nuclear quadrupole

resonances in CF31.

33

The electric dipole selection rules for rotational
transitions in a symmetric top molecule allow "pure" nuclear

quadrupole resonances (PNQR) with

as well as nuclear quadrupole resonances which arise as a
result of changes in rotational energy coupled with nuclear

quadrupole energy levels, as follows:

dk = 0 , OJ = 11, AF = 0, 11 and + «a -

The "pure" nuclear quadrupole resonances normally occur in
the radiofrequency (RF) region of the spectrum and they are
indicated in Fig. (5) by RF while nuclear quadrupole
rotational energy resonances are normally observed by
microwave spectroscopy and they are indicated in Fig. (5) by
MW. From Eq. (2.29) it can be seen that if first-order
perturbation is sufficient then the frequencies of the
"pure" nuclear quadrupole resonances are directly
proportional to qu and the scaling factor ([3k2/J(J+l)] -
1). As a consequence, direct measurement of the frequencies
of PNQR allows accurate determination of qu. Knowing the
value of qu makes it possible to calculate directly the

molecular electric field gradient at the nucleus due to all

34

charges outside the nucleus. This quantity, q, reveals
information about the molecular electronic structure; e.g.,
the valence electrons, distortion of closed shell electrons,
and charge distribution of adjacent atoms or ions. This
information has been used to estimate the ionic character
and hybridization of bonds to nuclei with I 2 1 (19-22).

For reasons having to do with the intensity of the spectrum,
"pure" nuclear quadrupole resonances, which occur in the
radiofrequency region of the spectrum, are normally observed
in solid samples where a large number of nuclei give rise to
a small number of resonances (23). An extention of this
method to gases (24) showed two main difficulties:

1- very low intensity of the RF absorption.

2- high spectral density due to the appearence of many lines
corresponding to different rotational levels.

For these reasons this method (24) has not been pursued
further. On the other hand, as will be shown in Chapter IV,
these problems were solved by application of infrared-
radiofrequency double resonance (IR-RF DR).

The 1-Type Doubling and A

-A Splitting

l 2

 

As has been mentioned earlier in this Chapter, the
rotational energy levels in a degenerate vibrational state
of a symmetric top molecule split into +1 and -1 components.

Furthermore, the normally degenerate Al-A2 species of a

35

given 1-component with lk-1I = 3n split into A1 and A2
species. This splitting which is due to various higher-
order vibration-rotation effects and is called the 1-type
doubling (25), is related to the splitting of the degenerate
(k = 1, 1 = 1) and (k = -l, 1 = -1) states by an amount
qu(J+l), where qv is called the 1-doubling constant. In
the case of Al-A2 splitting, direct RF transitions are

possible between the following states:

,Jv-OJ,F~~FandF°-~F11

If the 1-doubling is large the AF = 0 transitions
predominate because they have higher intrinsic intensity
(normally AF = AJ for highest intensity). If the 1-doubling
is very small only the AF :1 transitions can be seen because
the AF = 0 transitions occur at very low frequency.

The energy level scheme and allowed direct RF transitions in
case of Al-A2 splitting in a degenerate vibrational state of
a symmetric top molecule and one of its atoms with I = 3/2

(e.g., CF3Br) are shown in Fig. (6).

36

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AF-e1 AF-O 41""1 6F5
71? 7h" '
A m 5-5
A2
—7‘
7.5
4 5
fii 7? '
1-typs doubling
V L__ 5 5
V: ¥' 5.5
)/
A1
\iL L7 5
AIL L45

Fig. 6. A schematic energy level diagram for the 1-type

doubling in CF Br.

3

37

CHAPTER III

CF I

The first microwave spectrum of the ground state of
CF31 was reported by Sheridan and Gordy in 1952 (26). They
determined the rotational constant B and the quadrupole
coupling constant qu for the ground state.

In 1954, Edgell and May (27) reported the conventional

infrared and Raman spectra of this molecule. The v band

1

1

(CF3-symmetric stretch) was measured at 1074 cm-
In 1955, ”pure" nuclear quadrupole spectra of CF31 were
studied by Streezer and Beers (24). This was the first
report of the observation of "pure" nuclear quadrupole
resonance (PNQR) in the vapor phase. The experimental
investigation employed a Stark modulated spectrometer with a
3 inch x 1.5 inch x 20 ft absorption cell. Details of the
instrument itself were given elsewhere (28-30). In this

experiment, only one "pure" nuclear quadrupole transition

was observed. The transition belonged to a rotational state
of J = k = 3 in the ground vibrational state. For this
transition, J = k, and consequently the intensity is maximum
(24).

Recently, the CF31 molecule has been found to be an

important model system for the use of CO2 lasers in the

38

study of photochemical phenomena induced by intense infrared
laser radiation.

In 1976, Petersen, Ties, and Witting (31) reported the
observation of laser induced multiphoton molecular
absorption in CF3I. They used a pulsed CO2 TEA laser, tuned

1 and producing 3x105 W cm-z, for pumping and a

to 1075 cm-
low pressure continuous-wave 002 laser (operating at 1052
cm-1) to probe the transient absorption induced by the
pumping radiation. The possibility of application of this
phenomenon to laser isotope separation (LIS) was also
reported. One year later, a quite efficient and selective
multiphoton dissociation of CF3I was achieved and applied to
carbon-isotope separation (32). For this purpose, 0.1 Torr

of CF I was irradiated with the 9R(l4) 002 laser line at

3
laser fluences of 1.2 J/cmz. Also, a kinetic scheme for the
infrared photochemical reaction CF3I a CF3 + I was reported
(32). The efficiency of C-13 separation was shown to
increase by ~ 33% upon addition of HI to CF31 (33). The
bond rupture reaction in multiphoton dissociation of CF31
was established by a molecular beam study in 1979 (34).
These results for the CF31 molecule have been used in the
establishment of a theory of photochemistry induced by
intense infrared laser radiation (35-38). The reaction CF31
~ CF3 + I was one of the first infrared photochemical

reactions for which a rate constant could be evaluated (37-

40). The rate constant of this reaction was found to be

39

1.6x108 s.1 for a laser intensity of 100 MW cm—2 (40). This

high value of the rate constant is a result of the large
absolute value of the vibrational transition moment,
corresponding to an integrated band strength of 8.8xlO-20
cm2 (41). Of further experimental and theoretical
investigations in the IR-laser chemistry of CF31 (42-48),
particular mention is given to C-l3 isotope separation
(44,45).

Despite the large number of theoretical and
experimental studies of the IR multiphoton excitation and
dissociation of CF31, the theoretical details of these
phenomena are not yet known; only a semi-empirical approach
has been reported (44). Detailed understanding of these
phenomena requires a quantum mechanical treatment (49). The
difficulty in the theoretical approach is due primarily to
the lack of spectroscopic data for the highly excited
vibrational states; e.g., rotational constants, quadrupole
coupling constants, ..... .etc.

An appreciable effort has already been made by
spectroscopists in order to understand and analyze the
complex spectrum of CF3I in the v1 region.

In 1975, the infrared-microwave double resonance
technique was applied to the study of CF31 by Jones and
thler (50). They showed that the 9R(16) C02 laser line

pumps the QR(7,2) infrared transition of the v1 fundamental

40

band. They were able to determine the rotational constant B
and the centrifugal distortion constants DJ and DJk for the
ground state and v1 = l excited state.

In 1979, Bedwell and Duxbury invented "single side band
Doppler free double resonance Stark spectroscopy using an
acousto-optic modulator" (51). They applied this new

technique to the study of CF I and showed that the 9R(14)

3
CO2 laser line pumps the QQ(18,16) transition of the
v6+v1 v ”6 hot band.

In 1980, Kohler et a1. reinvestigated the infrared-
microwave double resonance of CF31 with three CO2 laser
lines, 9R(12), 9R(14), and 9R(18) (52). It was shown that
the v1 region of CF3I is a complex mixture of hot bands of
the type vi+v1 « Vi involving the following low-lying
vibrational states (vi): v3 (C-I stretch, 286 cm-l), V6

(CF3-rock, 265 on'1

1

), and v5 (CFa-degenerate deformation,

540 cm- ). In addition to these hot bands, the overtone and

1).

+3.,6 (1081 on‘l), and 4.6 (1060 en’l) should be expected

combination bands, 2v5 (1080 cm-1), v5+2v6 (1070 cm-
"3
in this region. All of these states are in such close
proximity to the v1 = 1 state that ”intensity borrowing"
from this state may significantly increase the importance of
the high order states. Seven different infrared transitions
were observed with the three mentioned 602 laser lines. The

rotational and centrifugal distortion constants B, D and

J!

41

DJk were determined for the observed vibrational states.
However, the quadrupole coupling constant for each of the
seven different vibrational states was constrained to the
value obtained by Sheridan and Gordy for the ground state in
1952 (26).

In 1980, the microwave spectrum of CF31 was
reinvestigated (53). Rotational parameters and the
quadrupole coupling constant were improved for the ground
state.

In 1982, Ritze and Stert applied Lamb-dip saturation
spectroscopy to the investigation of the nuclear hyperfine
structure of the CF31 vibration-rotation spectrum (54).

They used the 9R(16), 93(14), and 9R(18) 120150

2
9P(24), and 9P(12) 1201802 laser lines and reported a semi-

and the

quantitative analysis of the rotational and vibrational
states observed.

In 1982, Ibisch and Andresen applied the infrared-
microwave double resonance technique to the study of CF31
with the 9R(12) CO2 laser line (55). They reported that
this laser line pumps the QQ(8,5) transition of the v1
J, and DJk and

the quadrupole coupling constant for the ground and v1

fundamental. The rotational constants B, D

vibrational states were determined.
Also in 1982, a medium resolution infrared spectra of

CF31 was reported (56).

42

In 1983, the rotational spectrum of CF3I was studied by
Walters and Whiffen (57). They used the microwave-
radiofrequency double resonance technique in their study.
From this experiment, the rotational constants and the
quadrupole coupling constants were determined for the
ground, v3, and v6 vibrational states.

A very interesting observation for CF3I was reported in
1983 (58). This was the observation of laser radiation in
the mm region (0.8-l.25 mm) achieved by pumping CF3I vapor
with a low-pressure CO2 laser of average output power up to
10 Watts. The most intense mm laser lines were generated by

1). This

CO2 pumping in the v1 region (1070-1080 cm-
observation demonstrated that the CF31 molecule is a
promising source for laser radiation in the millimeter
region of the spectrum.

In 1985, a high resolution (0.01 cm_1) FTIR spectrum of
CF3I was reported (59). Only J clusters of the v1 band were
resolved.

In spite of all these studies of CF31, the nature and
molecular constants of all of the rotational and vibrational

states involved in absorption in the v1 region are still not

well known nor understood.

43

CHAPTER IV

INFRARED-RADIOFREQUENCY DOUBLE RESONANCE SPECTROSCOPY

Infgagad-Radiofreqaencyagaable Reaonance Spectroaeter

A schematic diagram for the IR-RF DR spectrometer used
in this work arranged with the sample cell inside the CO2
laser cavity is shown in Figure (7), while that with the

sample cell outside the laser cavity is shown in Figure (8).

Infrared pumping radiation

Infrared pumping radiation for the systems in Figures
(7) and (8) is generated by a low pressure (~ 12 Torr) semi-
sealed COZ laser which was assembled at MSU. The length of
the laser cavity, which is determined by the distance
between the plane grating and the focusing end mirror, is
3m. The individual laser lines are selected by slight
rotation of the plane grating and can be identified by using
a 002 spectrum analyzer. The latter is a simple grating
spectrograph with fluorescent screen detection. The
frequency of each laser line can be tuned 125 MHz within the
Doppler width of the CO2 transitions by applying a D. C.
Voltage to a piezo-electric translator (PZT) attached to the
focusing end mirror of the laser. The application of D. C.
Voltage to the PZT causes a small (0-15 pl) change in the

length of the laser cavity and consequently in the resonant

44

.aouQIOLaoonm m: hmlmn 0:0 mom maven Hmvmolfihomxo huw>mosmasu use .b .muh

         

was» <§w<mm

023(10
east. «as

       
      

3:309 muN_mu:h2>m u!

zwhamaoo

45

.souoloaaoonm an mzlmu on» new haven aoumOIamomxo hufi>momeuxo one .Q .muh

 

 

\AQ \ / \

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\\ use» <2m<me // \\
eNh r+L r+L H+L ezzaee
H — See...» some; L
:_ ....uo uzzhiem So
u_\ E34... :9
Y V a _ r2 _ 52.3325 .3 f w— Jmo In: 1.: ...:

 

Jog—ZOO anci—

 

 

 

 

 

_ 5e 4.: «.3 ...:

_ a: l 55.58

 

 

 

fooo e1. 6.”

 

 

  
 

 

 

 

 

 

 

 

 

46

laser frequency.
The output power of the laser ranges from 1-10 Watts,

depending on the operating conditions.

gaaiofreqaency radiation

The radiofrequency waves were generated by an RF
synthesizer (Programed Test Sources Model PTS 500) operating
in the range 1—500 MHz with +3 to +13 dBm output. Both the
amplitude and the frequency of the radiowaves generated by
the RF synthesizer are controlled by a Digital Equipment
Coperation PDP8E computer. The RF power at the output of
the sample cell is terminated by a 30 dB attenuator (ATT)
and the output of this attenuator is monitored by a power
meter (PMT). The computer reads the output of the power
meter and controls the output of the synthesizer in order to
keep the RF ouput power fixed during the sweep. In this way

the RF power variations were minimized.

RF modulation

The RF radiation is amplitude-modulated (usually at 10
kHz) by means of a double-balanced mixer (DBM) at the output
of the synthesizer. The square-wave output of a 10 kHz
oscillator (10 kHz Osc.) is used to switch the RF on and
off. A TTL output from the computer acts as a switch for
the RF power. The infrared radiation is detected by a

liquid-N2 cooled Hg-Cd-Te photoconductive detector whose

47

10 kHz output is amplified and processed by a phase-
sensitive detector (PSD) and recorded by the computer. The
switched RF output from the DBM is amplified by an
Electronic and Navigation Industries, Inc. Model 525LA broad
band power amplifier (RF AMP), before being sent to the
sample cell. The RF amplifier has a maximum gain of 40 db
and maximum ouput power of 25 Watts. All of the RF

connections were made with double shielded coaxial cables.

RF sample cells

A 60 cm long coaxial sample cell is used for the
intracavity experimental setup whereas a 130 cm long
stripline cell was used for the extracavity experimental
setup. Figure (9) shows a schematic diagram for a cross
section of the coaxial sample cell while Figure (10) shows

that for the stripline sample cell.

Operation of the Spectrometer

 

Optical alignment of the laser and the infrared path
through the sample cell and on to the infrared detector is
achieved with the aid of a visible He/Ne laser. The
infrared laser line that is in coincidence with the
molecular absorption is chosen by a combination of
adjustment of the angle of the plane grating and of the
Voltage applied to the PZT. If more than one molecular

transition is in near resonance with the laser, variations

48

R1 - 0.5 Cm

 

 

 

Fig. 9. A cross section in the coaxial RF sample cell.

49

d1

 

 

 

 

 

 

 

/\
(——— 1.0cm ——->
fiTeflon
A ‘—_‘ _
1.. 1—-'
d d-.08cm
2.54cm 2-29cm k—B'N’

Brass fl (—-8ross

. —}1—
Teflon

1.27cm —__1
V/ LP

 

 

 

 

 

 

 

 

 

 

Fig. 10. A cross section in the stripline RF sample cell.

50

of the PZT will normally optimize pumping of one or another
of the near-resonant transitions. The laser radiation
passes through the sample while the RF field in the sample
cell is stepped by the computer. For the intracavity
experimental setup the laser output is detected, while for
the extracavity experimental arrangement the laser radiation
at the output of the sample cell is detected. As a result
of the phase-sensitive detection, the PSD output is
proportional to the difference in the IR intensity with the
RF on and off. Thus, the spectrometer output is a direct
measure of the double resonance effect. At low gas pressure
the double resonance effect is an increase in the infrared
absorption or, in other words, a decrease in the laser
power. The PSD output is displayed on an oscilloscope
(SCOPE) as it is measured and also recorded by the computer
for ultimate storage on a flexible disk.

Operation of IR-RF DR Outside a CO Laser Cavity

2

 

An explanation of the IR-RF double resonance effect in
a low pressure sample in a cell outside a 002 laser cavity
can be given with the help of Figure (11).

The laser pumping (at frequency v v42) depopulates level

1=
2 and populates level 4 simultaneously. This creates a

partial saturation of the v transition. When the RF

42

frequency is swept and brought into resonance with either

51

 

 

 

 

 

4
yr ”43
3
v..v
1 42
2
v v
r 21

1

 

Fig. 11. A schematic diagram for the IR-RF DR operation at

low IR power and at low sample pressure.

52

v21 or v43 saturation of the v42 transition is reduced
resulting in increased absorption of the laser beam. The
result is that the radiofrequency transitions v21 and v43
are each observed as an increase in the infrared absorption
(v42). By using the same population argument all the RF
transitions at low sample pressure are expected to be
observed as an increase in the IR absorption.

The energy level structure for the IR-RF double

0'

resonance observation of pure" nuclear quadrupole
resonances is sketched in detail in Figure (12).

A symmetric top molecule with one atom with nuclear spin I =
5/2 on the symmetry axis (e.g., CF3I) has been assumed. The
dipole selection rules AJ = 0, 11, AF = 0, 11, Ak = 0, and
parity + ~~ - apply to ro-vibrational transitions in a
symmetric top molecule. The dipole selection rules Ak = 0
and parity + o» - allow radiofrequency transitions with AJ =
0 and AF = 11 between the hyperfine levels with k x 0.

These allowed RF transitions are indicated in Figure (12) by
(a", b", c", d”, e") and (a’, b’, c’, d’, e’) for the lower
and upper vibration-rotation states, respectively.

The IR transitions with AF = AJ are very close in
frequency because the hyperfine splitting pattern in the
lower and the upper states is similar. Consequently, they
normally lie within the Doppler profile of the pumped

infrared transition, so that one laser line can often pump

all of the transitions. Therefore, all ten PNQR resonances

53

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fl
J+0.5
' 1°. J 0 s

v b1 .
.1 , J+1.5
c .1-1 s

:tk d, .
. J+2.5

e

J—2.5
Loser pump Loser pump

AF’AJ AF-AJ

F"

1 ‘14 J+O.5

" a“

J-O.5

3' .-- .... 5

COO .

*k d" J-1.5

J+2.5

N

——L ° 1’ J-2.5

Fig. 12. A schematic energy level diagram shows the "pure"

nuclear quadrupole resonances and the pumped IR transitions

in CF31.

54

in the lower and the upper states of these pumped infrared
transitions can be observed. However, if the hyperfine
splitting in the lower and the upper ro-vibrational states
is not comparable the frequencies of all of the IR
transitions with AF = AJ do not lie within the CO2 Doppler
width and consequently PNQR are only observed for the
directly pumped hyperfine energy levels. On the other hand,
for AF # AJ, the laser may not be able to pump all of the
infrared transitions because they show a large spread in
frequency. As a consequence, only one or a few PNQR
resonances can be observed in this case.

The difficulties associated with observation of PNQR
for gases, which are discussed in Chapter II, are avoided in
the IR-RF DR technique inside a COz laser cavity for the
following reasons:

1- Detection of the IR laser radiation provides a much more
energetic photon for the detection process.

2- Production of a non-equilibrium distribution by IR laser
pumping overcomes the problem of small population difference
for RF spectroscopy.

3- Placement of the sample cell inside the CO2 laser cavity
uses the non-linearity of the laser gain to increase the
sensitivity of the method.

4- High spectral density is avoided because the laser pump
singles out the pair of ro-vibrational states involved in

the pumped IR transition.

55

The disadvantages of this technique are:
1- It gives information only at isolated points in a narrow
region of the infrared spectrum (9-11 pm).
2- Line shapes may be broadened and distorted by the high IR
power inside the CO2 laser cavity.
3- In complicated and crowded ro-vibrational structure such

as in CF31 and CF Br, the resolution may not be sufficient

3
to separate all of the transitions.

In spite of these disadvanages, IR-RF DR inside a 002
laser cavity has been established as an extremely sensitive
technique for radiofrequency spectroscopy. It has been
applied successfully to studies of Vpure" nuclear quadrupole
resonances (60,61), Al-A2 splitting and 1-type doubling (61—
64), two photon and multiphoton processes (65), ”forbidden"
rotational transitions (66-68), A-doubling (69), and k-
doubling (70,71).

The effect of the second and third disadvantages of the
intracavity experiment listed above have been reduced in
this work by placing the sample cell outside the CO2 laser
cavity, where the laser output power is about 108 that
inside the laser cavity. This eliminates Advantages No. 2
and 3 listed above, but the sensitivity for the samples in
this work has been sufficient to observe spectra with very
high signal/noise. Elimination of disadvantages No. 2 and 3
listed above and the high signal/noise not only allowed us

to observe PNQR but also made it possible for the first time

56

to do lineshape analysis for the "pure" nuclear quadrupole
resonances.

The first of the listed disadvantages of the IR-RF DR
technique can be avoided by applying the technique with
tunable lasers. Takami used a tunable diode laser as the
source of IR radiation in IR-RF DR to determine the
vibration induced dipole moment in the v3 = 1 state of CF4
by observation of "pure" rotational spectra (66,67). Oka et
a1. applied the IR-RF DR technique to the observation Al-A2
splitting in OsO4 by using a 002 laser-microwave sideband

system for IR pumping (64).

57

CHAPTER V
METHOD OF CALCULATION AND ANALYSIS
1- Method of Calculation

Thegqaadrapole interaction energiaa

The quadrupole hyperfine contributions to the
rotational energies were calculated in this work by using
the formulation of Bauder et al. (72). This method requires

the exact diagonalization of the total Hamiltonian matrix,
Hzfl +H (6.1)

Here H is the total Hamiltonian, Hr is the rigid rotor

Hamiltonian, and H0 is the quadrupole Hamiltonian.

Bauder et al. used extensively the Wigner-Eckart

theorem (16) to calculate the matrix elements of H0 for

symmetric and asymmetric rotors. The matrix elements were

shown to be (72)*

We have been informed by A. Bauder, that there is
misprint in Eq. (6.2). Therefore, I derived this energy
expression and determined that the phase factor given as
(-1)J*J'+K*I+F*1 in Ref. (72) should be (-1)J+J'+K+I+F.
This correction has been taken into account in the

computer program used to calculate the energies.

58

(J.k.I.FIHQ|J’,k’,I,F> e (-1)J+J +k+1+p

J 2 J’

 

1/2 F I J (’k ’9 k.)
x 1(2J+1)(2J'+1)1 12 J.I} 2 (x_q/4) (6.2)
I I
(—I 0 I )

In Eq. (6.2), xq = eQVq is a quadrupole coupling constant in
spherical tensor form in the molecular frame; these

constants may be expressed in Cartesian coordinates as

:(2/311/2<xxztixyz).

(1/6)1/2(xxx—xyy121xxy).

In Eq. (6.2) the symbols in the arc brackets are Wigner 3j
symbols (16) while those in the curly brackets are Wigner 6j
symbols (16). Algebraic expressions for most of the needed
3j and 6j symbols are tabulated (73) and expressions for the
untabulated ones can be easily derived by using the symmetry
properties of these symbols (73).

Matrix elements of H for a prolate symmetric top

0

molecule, in which x+1 = x+2 = 0, are given by

59

_ 2_
<J,k,I,F|HQ|J,k,I,F> — e1[3k J(J+l)]xzz (6.3)

2 1/2

—_ 2—
<J,k,I,F|HQ|J+l,k,I,F> — 3e2k[(J+1) k .22 (6.4)
<J,k,I,F|H°|J+2,k,I,F> =

3e31((J+1)2-k2)((J+2)2-k2)]1/2xzz (6.5)

with the abbreviations:

e1 = [(3/4)C(C+l)-I(I+1)J(J+l)]/21(ZI-1)J(J+l)(2J-l)(2J+3),

C : F(F+l)-I(I+l)-J(J+l),

: [F(F+1)”I(I+l)—J(J+2)11/2

 

 

 

2 [(2J+1)(2J+3)]1/2
[(F+I+J+2)(J+I-F+1)(F+J-I+1)(F+I_J)]1/2
* 81(2I-l)J(J+1)(J+2) .
e : [(F+I+J+2)(F+I+J+3)(I-F+J+l)(I—F+J+2)]1/z
3 1/2

[(2J+l)(2J+5)]

[(F-I+J+1)(F—I+J+2)(F+I-J-l)(F+I_J)]l/2
161(2I-l)(J+1)(J+2)(2J+3) .

 

X

Also, qu = xzz .

The total Hamiltonian, H, is diagonal in F, MF and k.

60

Because of the very large spacing of nuclear energy states,
elements off diagonal in I may be ignored. It can be seen
from Equations (6.3)-(6.5) that the matrix elements of HO

are off diagonal in J for a given F and are independent of

the quantum number M which represents the projection of F

F’
on the space fixed z-axis. It is therefore possible to
calculate the energies for individual sets of quantum

numbers F, M I and k. The rotational energies used in

F 9

our calculations for a prolate symmetric top molecule are

Er(J,k) = BJ(J+1) + (A-B)k2 - DJJ2(J+1)2

— DJkJ(J+l)k2 - Dkk4 + ............. (6.6)
Sextic and higher order centrifugal distortion constants
were ignored for the calculation of ”pure" nuclear
quadrupole spectra because they are not known for CF31 and
CFaBr. Their contributions are negligible in any case since
they only affect second and higher order effects of the
coupling. The total Hamiltonian matrix, which is off
diagonal only in J, can then be diagonlaized to produce the
eigenvalues and the eigenvectors for the Hamiltonian
including the electric nuclear quadrupole interaction in the

coupled representation.

In this work , the "pure" nuclear quadrupole resonances

61

were first calculated by using the eigenvalues of the total
Hamiltonian given in Eq. (6.1). However, fitting of the
experimental to calculated frequencies was considerably
improved by adding the iodine spin-rotation interaction term
to the calculated frequencies. Consequently, the magnetic
interaction contribution to the hyperfine structure
frequencies was included for CF3I. Since the magnitude of
the spin-rotation interaction energy is small, only the
first-order perturbation contribution is needed (61) and is

given as

2
k )][F(F+l)-I(I+l)-J(J+l)] (6.7)

.. 1 _ __
w ‘ 2 [CN+(Ck Cu) J(J+l

mag
Then, contribution of the spin-rotation interaction to the
frequencies of the ”pure" nuclear quadrupole resonances with

the selection rules, AF = :1, AJ = 0, and Ak = O is

2
_ _ k
Avlag - t[CN+(Ck CN) 3(3:171(F+1) (6.8)
Here, wmag and ovmag are the spin-rotation energy and

contribution to the rotational frequency, respectively. OR

is the principal value of the nuclear spin-rotation coupling

along the molecular symmetry axis and C is the principal

N

value normal to the molecular symmetry axis.

62

Intenaitiaafof the hyperfine transitions
The electric dipole moment matrix elements were also
calculated by Bauder et a1. (72). By use of the Wigner-

Eckart theorem, they may be written as

<J,k,I,F,MF|pr|J’,k’,I,F’,M’> =

r
(-1)F*F'+"r+I+k+1 [(2J+1)(2J’+l)(2F+l)(2F’+l)]1/2

J r 1 r 1 r' J 1 J’
X {Ft J’ 1 }(_MF r Mi.)("k q 1‘2)an (609)

Here, pr is the rth spherical tensor component of the
permanant electric dipole moment in the space fixed axes,
whereas pq is the qth component of the permanant electric
dipole moment in the molecular fixed axes. As before, the
spherical tensor components are related to the Cartesian

components as

u;1 = 111/2)1/z<ux:iuy).

The intensity of the M components (AM = 0 ) of a

F F

hyperfine transition 8 is given by the absolute squares

F~F’

of the elements of a matrix S which is given by (72)

FaF’

63

+ s a
F _. F, = T (1.1.)[51 Ur=o(FoF aMF)1T(F) (6.10)

F

Here, T(F) is the transformation matrix that diagonalizes
the Hamiltonian matrix H for a given value of F; this matrix
is independent of MP. Because the RF radiation is
polarized, only the r = 0 component of the space-fixed
dipole moment contributes to the intensity.

Explicit formulas for the dipole moment matrix elements

(6.9) for the "pure" nuclear quadrupole resonances of a

symmetric top molecule are given here without the common

factor (f),
+ ’
f=(—1)F"(_§ 1 ,5.)
r 9 F
as
<J,k,I,F,MF|pq|J,k,I,F+l,MF> = -f3kpz ,
(J k I r M 1 (3+1 k I F+1 M’) = -r [(J+l)21t2..]1/2
tIO’qu it, 91;- 41-32:

> = £5102- k ”JI/z (6.11)

_ a
<J,k,I,F,MF|pq|J 1,k,I,F+l,MF

64

The abbreviations are:

 

 

f3 = [(I+F+J+2)(F-I+J+1)(I+F—J+1)(I+J_F)/(F+l)11/2/2J(J+1)’
[(I+F+J+2)(I+F+J+3)(F-I+J+1)(F_I+J+2)11/2
f4 1/2 /2(J+1).
[(F+1)(ZJ+1)(2J+3)]
[(I-F+J-1)(I-F+J)(I+F-J+1)(I+F_J+2)11/2
f5 1/2 /2J-

[(F+l)(2J+l)(2J-1)]

The main computer program

A computer program has been written in which the total
Hamiltonian matrix for a given F, I, and R was generated by

using the matrix elements given for H in Eq. (6.3)-(6.5)

Q
and by using the rotational energies in Eq. (6.6) as the
non-zero elements in the diagonal matrix Hr' The Jacobi
rotation method used for the diagonalization procedure
simultaneously calculates the eigenvalues and the
eigenvectors of H. From the eigenvalues the program
calculates the "pure" nuclear quadrupole resonances
according to the selection rules, 01 = 0, AJ = 0, ok = 0, AF
= :1, and the rotational nuclear quadrupole resonances with
the selection rules, oI = 0, oJ = 11, ok = 0, AP = 0, $1.
The dipole moment matrix elements, given in Eq. (6.11), are

transformed by the aid of the eigenvectors to the eigenbasis

of the total Hamiltonian and the intensities of the

65

hyperfine structure were calculated according to the

previously mentioned procedure.

II— Method of Analysis

Rotational assignment

The assignment of rotational quantum numbers to the
observed vibration-rotation transitions was made from the
pattern of the hyperfine structure which is characteristic
for each J, k and F. The experimental frequencies were
determined by fitting the spectra to sums of Lorentzian line
shapes. The rotational constants of Ref. (52) and qu of
Ref. (26) for the ground vibrational state were used to
calculate the frequencies of the ”pure” nuclear quadrupole
resonances (a", b”, c”, d", e" in Fig. 12) by the method and
the computer program described in the previous section. The
calculated frequencies for each possible J and k were
compared, by the aid of a computer program, with all of the
experimental frequencies. In this way the J and k
assignment could be made. However, the hyperfine structure
of very high J and k values is insensitive to the rotational
quantum numbers and in this case a unique assignment
requires the knowledge of qu with a medium accuracy. In
some other cases, where highly excited states are overlapped
or strongly perturbed, the assignment needs values of

rotational parameters and qu with high accuracy.

66

Determination of e09 and the magnetic parameters

 

After the rotational assignment of each ro-vibrational
state was made, the least squares method was used to fit qu
and the total magnetic effect which is defined as CM =
[CN+(Ck-CN)k2/J(J+l)] to the experimental frequencies of the
lower (a", b", c", d", e") and upper (a’, b’, c’, d’, e’)
states to obtain (qu" and CM") and (qu’ and CM’) for the
lower and the upper states, respectively, within the
experimental accuracy (:20 kHz). The spin-rotation coupling

terms (C and Ck) were determined for only the ground and v1

N
vibrational states because the ”pure" nuclear quadrupole
resonances were observed for ro-vibrational states of

different J and k quantum numbers only in these vibrational

states.

Vibrational assignment

Since the IR-RF DR technique depends on a coincidence
between the frequency of an infrared transition and the
frequency of a 002 laser line, the vibrational assignment
should be easy and straightforward because one can assign
the frequency of the pumping 002 laser line to the pumped
infrared transition. This has been the case for all of the

previous IR-RF DR experiments.

67

However, this method of vibrational assignment could not be
applied in the present work on CF31 and CF3Br because of the
complexity of the ro-vibrational structure of these
molecules in the 9pm region and the lack of spectroscopic
data about all of these states. However, a very high
resolution could be achieved in our experiment and
consequently, precise values of qu for each vibrational
state could be obtained. The vibrational assignment was
then made with the aid of these accurate qu values and

their vibrational dependence.

The vibrational dependence of ng
The expression for the vibrational dependence of qu is

given as (60)

quZv. = quo + ;6(e0q)ivi (6.12)
. 1

1
1

where

6(e0q)i = (qu)v.- (e0q)o
1

and (qu)o is the quadrupole coupling constant for the

ground ro-vibrational state.

68

The rotgtionglidependence of egg

The rotational dependence of qu is given by (60)

qu(J,k) = quo + xJJ(J+l) + xkkz (6.13)

“J and ”k represent the rotational dependence of the nuclear
quadrupole coupling constant due to the centrifugal
distortion of the molecule. The determination of these
parameters and qu0 requires the knowledge of qu(J,k) for
at least three different rotational states with the same

vibrational quantum numbers.

Infggredpggnd centerg
Band centers (v0) of the observed and identified
infrared transitions can be estimated according to the

relations

’ v = v — J(B ,+B ”) - JZQB - k2(aA'aB)
P 0 v v

t2|k1|({"A"-{’A’)g

- J(J+1)aB — k2(aA‘aB

v0 v0 ) t 2|k1l({"A -( A ).

VB v0 + (J+l)(Bv’+Bv") _ (J+I)Z¢B _ k2(uA-q )

tZIkll({"A"-{’A’). (6.14)

69

Here, is the frequency of the laser line that is in

”9.
coincidence with the corresponding P or 0 or R branch
transitions between doubly degenerate vibrational states
with k t 1, where the Al-Az splitting and the l-type
doubling are very small.

For non-degenerate vibrational states, 1 = 0 and
consequently the last term in each of the above equations is

zero. Since the laser frequency, is known from the

V1,
laser experiment and the rotational constants are known from
microwave spectroscopy, the band center, ya, can be
calculated from equations (6.14). However, there are three
important sources of error in this calculation

1- Since our experiment is done with the laser operating

is

anywhere along the CO2 Doppler width (~ 25 MHz), then vi

v1 :25 MHz.
2- In Equations (6.14), the centrifugal distortion constants
are neglected because their values are known with only low
accuracy for CF31 and CFaDr. The effect of centrifugal
distortion terms can be significant, especially for high J
and k quantum numbers.

3- The hyperfine splittings are neglected in Equations
(6.14). Because of the complexity and the crowding of the
vibration-rotation spectra in the 9pm region, we have not
found a convenient way to determine which hyperfine level or

levels is or are pumped. The effect of the hyperfine

splittings on the ro-vibration frequencies is of order of

70

magnitude of 0.01 cm_1. However, the band centers could be
estimated within the uncertainty caused by these three

mentioned sources of error.

71

CHAPTER v1

_§SULTS AND DISCUSSION
Intrquction
Since the IR-RF DR technique had previously been
applied with the sample cell inside the 002 laser cavity, we
first tested our spectrometer with this method (Fig. (7)).

We successfully reproduced a number of reported

observations, e.g., velocity tuned multiphoton processes in
CH3F (65), "pure" nuclear quadrupole resonances in CHaI and
CH Br (60,61), and l-doubling in CH Br (61). Both the

3 3

sensitivity and the resolution of our spectrometer were
shown to be comparable to that obtained elsewhere. However,
distorted line shapes and low resolution were achieved when

we applied this method to the observation of PNQR for CF I

3
in the v1 region (9pm). Examples of the observed spectra in

12 16

CF I with the 9R(16) C 02 laser line at different sample

3
pressures are shown in Figures (13), (14), and (15). It is
clear from these spectra that not only are the line shapes
distorted and broadened, but also some effects other than
"pure" nuclear quadrupole spectroscopy are taking place.
Consequently, it is almost impossible to fit these records
to a line shape function in order to obtain frequencies for

analysis of the spectra. Since the ro-vibrational spectra

of CF31 is very complicated, we had to find a way to obtain

72

 

 

 

 

 

 

62.0 70.0 78.0 86.0 94.0
4000.0 : : : } .L § :
db “P
a
.2 1r
3
C
._ +
0
.2
l5 ..
0
(K
-L
1300.0 : i : i : : :
62.0 70.0 78.0 86.0 94.0

Frequency in MHz

Fig. 13. IR-RF DR in CF3I recorded with the intracavity

setup. Laser line: 9R(16) C02; sample pressure: 5 mTorr.

73

 

 

 

 

150.0 160.0 170.0 180.0 190.0 200.0
4000.0 ' : } + ', I. 1, : ', 1
.1- J)-
I?)
.6 q. Cli-
C
.9
.5
q. C.
0
.2
E ._ ..
0
0:
db T-
.. .41-
1 l 1 l 1 l 1 l 1
90000 17 I T ' l l I l I I
150.0 160.0 170.0 180.0 190.0 200.0

Frequency in MHz

Fig. 14. IR-RF DR in CF31 recorded with the intracavity

setup. Laser line: 9R(16) 002; sample pressure: 10 mTorr.

74

 

 

 

 

150.0 160.0 170.0 180.0 190.0 200.0
4000.0 ' 1 5 1 1 1 5 1 1 1
q- d-
.1 1L
3‘
.5 q_ -_
c
3
.E
0 7 .b
.2
:6 «1- .11-
0
m:
di- .1.-
11- 4f
I l j I l I l I I
900.0 I i t l I l I r l I
150.0 160.0 170.0 180.0 190.0 200.0

Frequency in MHz

Fig. 15. IR-RF DR in CF3I recorded with the intracavity

setup. Laser line: 9R(16) 002; sample pressure: 2 mTorr.

75

high resolution, good line shapes, and clean "pure" nuclear
quadrupole resonances. All of these properties were
obtained when we performed the experiment with the slight
modification of using a stripline cell outside the laser
cavity (Fig. (8)). With this experimental setup, very high
resolution and sensitivity were achieved. It was expected
that the resolution would be improved by this method,
because the infrared power was much lower, but we did not
expect to find such a high sensitivity that very good
signal/noise could be obtained with a sample pressure of
only 5-20 mTorr. Examples of the spectra obtained by the
extracavity experiment with the 9R(16) 120160z laser line in
the v1 region of CF31 are shown in Figures (16) and (17).
The differences in resolution, line shapes, and structure,
between the spectra recorded by the intracavity and the
extracavity experiments at comparable sample pressures are
easily seen in Fig. (18) which combines the spectra in
Figures (13) and (16). Similarly, a portion of the
intracavity and the extracavity IR-RF DR spectra in the v1
region of CF31 recorded with the 9R(16) 12C1602 at different
sample pressures is shown in Figure (19). This comparison
shows a dramatic change in the resolution, structure, and
line shapes. The complexity shown in the structure of the
intracavity spectra shown in Figures (l3), (l4), and (15)

and the low signal/noise are attributed to the following:

1- The very high IR power inside the laser cavity causes not

76

 

 

 

 

 

 

 

62.0 70.0 78.0 86.0 94.0
1 J 1 l 1 l 1
4000.0 17 l I l I j I
‘1— di—
3‘
.5 ..- .1!-
C
.8
.E
0 ..
.2
‘6
B ali- cil-
0:
.1. ..
-- 41-
150.0 1 1 1 1 1 1 1
62.0 70.0 78.0 86.0 94.0
Frequency in MHz
Fig. 16. IR-RF DR in CF31 recorded with the extracavity
setup. Laser line: 9R(16) C02; sample pressure: 20 mTorr.

77

 

 

 

 

 

 

 

 

150.0 160.0 170.0 180.0 190.0 200.0
1 l 4 L 1 l 1 4 1
3000.0 1 I r 1 1 1 1 1 1
.11. .1.
3‘
.5 fl 1.
E
.8
c
-- fl -1-
U
.2
o
71; ‘1 "-
0:
.1. J.-
1 l 1 l L l 1 l _1
10000 I l I l I l I I T
150.0 160.0 170.0 180.0 190.0 200.0
Frequency in MHz
Fig. 17. IR-RF DR in CF3I recorded with the extracavity
setup. Laser line: 9R(16) C02; sample pressure: 20 mTorr.

78

 

 

 

 

62.0 70.0 78.0 86.0 94.0
L l l L 1 1
4000.0 1 I 1 l 1 l 1
.. 11
d!- 41-
J1- ! 4|-
3‘
.6). ‘_ .41.
c
.3
C
.- q_ 1
0
.2
‘6
E 4- «1-
m:
41- .1.
41- '. ~11-
150. 0 '- 1 1 3"”? 1 1 1 1
62.0 70.0 78.0 86.0 94.0
Frequency in MHz
Fig. 18. Comparison of the intracavity spectra in Figure 13

with the extracavity spectra in Figure 16.
Solid lines: the intracavity spectra;

dots: the extracavity spectra.

79

 

 

 

 

 

 

 

 

 

 

150.0 160.0 170.0 180.0 190.0 200.0
4000.0 1 1 1 1 4 1 1 1 1
-11- .11.
2
3 .
.5
U
.2 ,
*0, A
B I
[Z ._
1
#1- V . 1'11-
‘In- 7". I'v: .1,’~'.'. , ._.’.~' '1...- .~
..I' “1' v.- s. ' s ... ‘imp .“
100.0 1 1 1 1 1 1 1 1
150.0 160.0 170.0 180.0 190.0 200.0

Frequency in MHZ

Fig. 19. Comparison of the intracavity spectra ianigures
14 and 15 with the extracavity spectra in Figure 17.
Solid lines: the intracavity spectra;

dots: the extracavity spectra.

80

only broadening and distortion of line shapes but also
induces the occurrence of complicated non-linear phenomena.
This is seen in the comparison Figures (18) and (19).

2- The tunability of the laser frequency with the sample
cell inside the laser cavity is less than that with the
sample cell outside the laser cavity. This makes it more
difficult to tune the laser to resonance.

3- The effect of tuning the laser off of the top of its gain
profile on the noise is more pronounced with the sample cell
inside the laser cavity. This is probably the result of the
laser running closer to the threshold of the laser action
when the sample is inside the cavity.

As a result of these experiments, we decided to carry
out our study by using an extracavity experimental setup.
Figure (20) demonstrates that our spectra maintain good
signal to noise ratio as the laser frequency is tuned
through several MHz.

Figure (21) indicates that the high sensitivity and
signal/noise of the IR-RF DR tecnique outside the laser
cavity is maintained even for transitions of high J and k
quantum numbers. Figures (22) and (23) show the high
resolution and signal/noise obtained for the IR-RF DR
spectra of high J and k in the v1 region of CF31.

Finally, Fig. (24) shows a very high resolution
spectrum (half-width at half-maximum ~ 0.3 MHz) where only

one ”pure" nuclear quadrupole component is resolved with a

.—-'—' ....._..,—..

81

 

 

 

 

20.0 25.0 30.0
3500.0 1 ' 1
11. 41
3
.g _U_ .11-
3
..c.
m ..
.2
:6 . ..
6‘2 1 .
1 5 K;
...o' .....‘v ...: - .... ....
‘V '\ /' ‘-. 1.
300.0 1 1 1
20.0 25.0 30.0

Frequency in MHZ

Fig. 20. The effects of laser frequency on the IR-RF DR

spectra. Laser line: 9R(18) 002; sample pressure: 17 mTorr.

82

 

 

 

 

10.0 20.0 30.0
4500.0 1 J, 1

.1- Vc " 1’b ..

._ M Qc1(4:'1.24) ..

4F 41-
3‘

“a w ..
C
B
.E

m U d.
.2
‘5

.5 ‘1- II!-
0:

.11-

 

 

 

 

1 1 1 _
' I
20.0 30.0

Frequency in MHZ

 

Fig. 21. IH-RF DR in CF31 recorded with the extracavity

setup. Laser line: 9R(14) 002; sample pressure: 10 mTorr.

4500.0

Relative intensity

0.0

Fig. 22.

Figure 21.

83

 

11.0 12.0 13.0 14.0 15.0 15.0
1 l L I 1 I 1 l 1
I I r I I T I '
._ ”c Vb 0-
”c 1’0
db “P
«1- 4-

. 1 . 1 if i 1 l 1 _
11.0 12.0 13.0 14.0 15.0 16.0

Frequency in MHZ

 

 

High resolution record for the first quartet in

sample pressure: 10 lTorr.

84

 

 

 

 

24.0 26.0 28.0 30.0
1 l l l J
4500.0 . I . l T
1’c Vb
4r- fin
.. Vc 4r.
.. Vb ..
3‘
.a ‘_ 4.
C
B
E
a, i-
.2
‘6
B " "
m
-. 4.
«a. .1-
1 l l I l
0.0 T l I l I -
24.0 26.0 28.0 30.0
Frequency in MHz
Fig. 23. High resolution record for the second quartet in

Figure 21.

sample pressure: 10 nTorr.

85

145.0 148.0 150.0 152.0
5000.0 : § : g :

 

Relative intensity

 

 

. l _
0.0 : { . ,
146.0 148.0 150.0 152.0
Frequency in MHZ

 

 

Fig. 24. IR-RF DR in CF31 recorded with the extracavity

setup. Laser line: 9R(18) 002; sample pressure: 17 nTorr.

86

clean line shape and fine base line.

Results and Discussion
By using the extracavity experimental setup (Fig. (8)),

471 RF transitions were observed with five 1201602 and three

1201802 laser lines. Of these, 142 resonances could be
assigned with confidence. 0f the many vibrational states
involved, six were identified unambiguously. As mentioned
above (in the discussion near Fig. (12)) ten frequencies,
corresponding to transitions between the quadrupole
hyperfine levels (Fig. 12) are observable in principle for
each double resonance. These frequencies are labeled a”,
b", c", d", and e" for the lower level and a’, b’, c’, d’,
and e’ for the upper level. For each of the assigned double
resonances, the experimentally observed frequencies (ve),
the corresponding calculated frequencies (we), the
difference between the experimental and calculated
frequencies (by), the standard error for each observed
frequency SE(ve), the quadrupole coupling constant for each
ro-vibrational state (qu), the standard error in the qu
fit (SE(e0q)), the magnetic term (CM), the standard error in
the CM fit (SE(CM)) and the root mean square deviation in
the observed frequencies (RMS(v)) are listed in Tables (1-
12). (The tables of data and results of the analysis begin
on page 104).

In some cases it was not possible to resolve a" and a’

87

because they lie close together at low frequencies; this is
indicated in the Tables (1-12) by a "u". In one case the a"
and a’ transitions were so weak that their frequencies could
not be fit to a line shape function. Consequently, the
frequencies of these transitions were not included in the
qu fit and they are indicated in Table (9) by a "w". In a
few other cases it was not possible to locate a" and a’ in
the presence of the large obscuring zero-frequency double
resonance signal (60); the entry for this frequency was
omitted when this occurred. In one case, it was found that
the hyperfine splitting pattern in the lower and the upper
vibrational states is different and consequently only "pure"
nuclear quadrupole resonances of the directly pumped
hyperfine levels were observed. As a result, only one
"pure" nuclear quadrupole resonance was observed in the
upper vibrational state (see Table 6) and accordingly only
qu was fit to the frequency of this transition to obtain an
estimate for the qu value of the upper vibrational state
involved in the pumped IR transition. Tables (13-15)
summarize the results for each laser line. The rotational
dependence of qu for the ground and v1 vibrational states
determined from this work is shown in Table (16). The

magnetic parameters (C and Ck) for the ground and v1

N
vibrational states are given in Table (17). A comparison of
the results of the analysis of the present observations and

those from other experiments is shown in Tables (18), (19),

88

and (20). Frequencies of unassigned transitions are listed
in Appendix I for each laser line. It is clear from Tables
(1-12) and Appendix I that each laser line pumped more than
one infrared transition at a time, which made each laser
line a case by itself. As a consequence, results will be
discussed and compared with those from other experiments for

each infrared transition separately.

v1 * G.st

 

As shown in Tables (13-15) (page 117-119), five IR

transitions involving the ground vibrational state of CF31

have been observed, one with the 9R(16) 12C1602 laser line

12 16 120180

and two each with the 9R(14) C 0 and the 9P(14)

2 2
laser lines. Three IR transitions involving the v1
fundamental have been observed, one with the 9R(16) 120160

2
laser line and two with the 9R(14) 1201802 laser line. The
rotational and vibrational assignment for our observations
in the v1 band with the 9R(16) 12C1602 laser line is in
agreement with those of References (50) and (54). Since the
qu value of the ground state has been determined accurately
from other experiments (57), it was easy to identify the
ground state double resonances in the present work from the
qu value. On the other hand, the qu value of the v1 state
was not known to us. It was first determined from our

observations with the 9R(16) 12C1602 laser line, where we

89

knew from the laser coincidence and from previous work (Ref.
50 and 54) that this laser line pumps the v1 fundamental.
With this information qu for the v1 state could be
determined and its value could be confirmed by our
observations in the v1 band with the 9P(l4) 12C1802 laser
line.

As shown in Table (20), the value of the frequency of
the v1 band center that has been determined from the
conclusion that the QR(7,2), QP(16,4) and °P(18,12)
transitions overlap CO2 laser frequencies is in good
agreement with the band centers reported in References (52)
and (59) (Table (20)). However, the v1 band center was
determined accurately from only the QR(7,2) IR transition
because this transition is of low J and k quantum numbers
and consequently the error in the calculated ro-vibrational
frequency of this transition, caused by the uncertainty in
the previously determined rotational parameters (52) and the
neglect of the centrifugal distortion terms in Eq. (6.14),
is expected to be negligible whereas the errors in the
calculated ro-vibrational frequencies increase significantly
with increasing J and k. This can be easily seen in Table

(20) where the v band center derived from the QP(16,4) IR

1
transition, which is of relatively high J value, shows a

moderate deviation (0.064 cm‘l) from the value of the v1

band center derived from the QR(7,2) transition while the v1

90

band center derived from the QP(18,12) transition, which
involves even higher J and K values, shows a large deviation
(~ 0.2 cm-l) from the value determined from the QR(7,2). 0n
the other hand, the v1 band center estimated by Ibisch et
a1. (55) is about 2 cm.1 below the value measured from three
different experiments (Refs. (52), (59)), and the present
work).

In the present work, qu values for the ground state
have been determined from five different observations, while
values for the v1 state have been obtained from three
observations with the 9R(16) 1201602 12C1802

laser lines. The observed rotational states and their qu

and 9R(14)

values for the ground and v1 states are listed in Table

(16). The magnetic parameters (C and Ck) were also

N
determined and their values are given in Table (17). Values
of quo and the distortion constants ”J and “k were
determined for the ground and v1 states by substituting the
values of qu, J, and k for the ground and v1 states into
Equation (6.13) and applying the least squares method; the
results are listed in Table (16). The value of qu0
obtained for the ground state is in excellent agreement with
that of Ref. (57) and is in good agreement with that of
References (53) and (55) (Table (19)). However, qu for the
v1 state was estimated by Ibisch et a1. (55) to be about 16

MHz larger than that determined in the present work. We

believe that the qu value determined in the present work is

91

more reliable than that determined by Ibisch et al. for the
following reasons:

1- In the present work the v1 state was observed three times
with two different laser lines and the qu values of the v1
state for all of these observations are in very good
agreement (Table 16).

2- The v1 band center determined in the present work is in
excellent agreement with that determined by Kohler et al.
(52) and Burger et al. (59), while the v1 band center
determined by Ibisch et al. (55) is ~ 2 cm“1 below that of
References (52) and (59). It is probable that the infrared
transition studied by Ibisch et al. does not belong to the
v1 band, but is a transition in a higher order or a
perturbed band.

4 °a(2o,16)

v6 v1 * v6;

 

The QR(20,16) transition of the v6+v1 . "6 band was
observed with the 9R(18) 1201602 laser line. Our rotational
assignment for this transition is in agreement with that of
Refs. (52) and (54). The qu value determined for the lower
vibrational state of this transition is within 2 MHz of the
value for "6 given in Ref. (57) (Table 19). This 2 MHz

difference is attributed to the rotational dependence of

qu. If the lower state is assumed to be vs, the upper

92

vibrational state can then be identified as v6+vl from the
vibrational dependence of qu.
In the IR-MW DR experiment of Kohler et a1. (52) two

12C160

infrared transitions were observed with the 9R(18) 2

laser line. These were assigned as (a) the QR(20,16)
transition in the v3+v1 ~ v3 band, and (b) the QR(20,k)
transition with 0 S k S 4 in the v6+v1 ~ "6 band. However,
the rotational constants for the v3 and v6 vibrational
states have been determined from the MW-RF DR experiments by
Walters et al. (57). The constants obtained in this more
recent work (57) would agree with those measured from the
IR-MW DR experiment (52) if v3 and ”6 are interchanged in
the IR-MW DR study. Then, the rotational constants and the
vibrational assignment of Ref. (52) are in agreement with
the results of Ref. (57) and with our results.

The QR(20,k), 0 S k S 4, infrared transitions reported

by Kohler et al. (52) are attributed to the v3+v ~ band

1 "3
by the interchange of ya and v6. This transition has not
been observed in our experiment. We believe that this is a
result of the fact that K = 0 for these transitions ("pure"
nuclear quadrupole resonances that belong to rotational
states of k = 0 are not allowed). This confirms the
assignment of QR(20,0) given in Ref. (51) for this
transition. The center of the v6+vl ~ ”6 band was estimated

from our observations to be 1075.3 cm-1 by using the

rotational constants of Ref. (52) after interchanging v3 and

93

v6. It was estimated in Ref. (52) to be 1075.42 :13 cm'1

(after interchanging v3 and us). These two values are in
reasonably good agreement. Even though "6 is a degenerate
vibrational mode, the contribution of the n-term has not
been taken into account in calculating the band center,
because the pumped 1 component (+1 or -1) could not be
determined from our observations. The 1 term was also
ignored in Ref. (52) because "6 was treated as us which is a

non-degenerate vibrational state.

, 0
v3 + v1 9 v3, R(23,20)

 

Q

The R(23,20) infrared transition in the v3+v1 + v3

state was observed with the 9R(20) 12C1602 laser line. As
shown in Table (19), the lower vibrational state v3 was
found to be within 1.3 MHz of that reported in Ref. (57).
The ~ 1.3 MHz difference is attributed to the rotational
dependence of qu. The upper vibrational state was
identified from the vibrational dependence of qu to be
v3+v1. The center of the v3+v1 band was estimated from our
observations to be 1076.3 cm.1 whereas it is 1075.256 cm-1
in Ref. (52) after interchange of v3 and v6. The
difference between these two values (~ 1 cm-l) is large. We

attribute this large difference to the facts that: (l) in

Ref. (52), the v3+v1 4 v3 band center was calculated from

94

the infrared transition QR(20,k) with 0 S k S 4 where the k
value is low and its assignment was uncertain; and (2) in
Ref. (52) v3 was treated as a degenerate vibrational state
(ya) so that a contribution from an 1 term was included.
Since the transition actually involved the non-degenerate v3
state, the 1 contribution should not have been included in

the frequency calculation.
IR transitions in unidentified vibrational states

”a . G.st; °o<18,16)

 

We have observed very strong and well resolved "pure"
nuclear quadrupole resonances for an IR transition with the

12 16

9R(14) C 0 laser line. The hyperfine structure

2
associated with this IR transition has been observed in
three other experiments in Refs. (51), (52), and (54) with
the same laser line. The rotational assignment in our work
is QQ(18,16), which is in agreement with that of all of the
other experiments. The vibrational assignment of the upper
vibrational state is uncertain and we refer it as "Va"' In
Refs. (52) and (54) the transition was assigned to vy o G.st
where vy is unidentified. However, as a result of the
optical-optical double resonance experiments, Bedwell and

Duxbury (51) assigned the QQ(18,16) transition to the

v6+v1 v "6 band. We do not agree with this vibrational

95

assignment for two reasons:

1- The lower vibrational state of the Q0(18,16) transition
was identified in our work from its qu value and in Ref.
(52) from its rotational constants to be the ground state.
Consequently, the upper state can not be v6+v1.

2- As a result of the Lamb-dip experiment, Ritze and Stert
concluded that this transition belongs to the v1 band and is
not a hot band (51). From our work the qu value for the
upper vibrational state of the Q0(18,16) transition is
determined to be -2121.52 MHz. This value of qu is about
20 MHz below that of either v6+v1 or v1 (Table 19).
Nevertheless, we beleive that this infrared transition
belongs to the v1 band with the upper state being perturbed
by some resonance or coupling with another state. If the
coupled state has a different R value, this would explain
the large deviation in the value of qu from that observed

for any other state.

vx 4 G.St; °p(6,5)

 

The QP(6,5) IR transition is an example of a case in
which the hyperfine splitting pattern in the lower and the
upper vibrational states is so different that only "pure"
nuclear quadrupole resonances of the directly pumped
hyperfine components could be observed. As a consequence,

only three "pure" nuclear quadrupole resonances were

96

observed in the ground state whereas only one "pure" nuclear
quadrupole resonance was observed in the upper vibrational
state. Accordingly, the qu value could not be determined
with a reasonable accuracy for the upper vibrational state
(vx). However, the observed difference in the hyperfine
splitting in the ground and ”x vibrational states indicates
that vx is either an overtone or a highly excited
combination band. On the other hand, the QP(6,5) transition
was not observed at all in the Lamb-dip experiment (54), and
the upper vibrational state of this transition was not
rigorously identified in Ref. (52) but was tentatively

assigned as the v3+3v6 combination band.

, 0
so . vb. oc43.24)

 

"Pure" nuclear quadrupole resonances were observed in
our work at low RF frequencies (Table 5 and Fig. 21) with
the 93(14) 1201602 laser line. The doublets for both the
lower and the upper vibrational states could be resolved
(Figures (22) and (23)) and, therefore, the transition could
be assigned to QQ(43,24) and qu could be determined for
both vibrational states; the values are shown in Table (19).
The hyperfine structure for this transition was observed in
the Lamb-dip experiment (54) and the rotational assignment

for the observed hyperfine structure was reported to be that

of a Q-branch transition with J = 40 t4 and k = 25 :5. This

97

rotational assignment, within the uncertainity given in J
and k, is in agreement with our assignment. On the other
hand, Ritze and Stert (54) reported that this transition
belongs to the v1 band. In the present work, the
vibrational assignment could not be made for this transition
because the qu values for both vibrational states are 20
and 152 MHz lower than that of the ground state. Either the
states involved are high order in v1 or they are strongly

coupled to other vibrational states.

VJ . yd; °P(31,9)

 

A transition observed with the 9R(12) 12C1602 was

assigned as QP(31,9). The upper vibrational state of this
transition may be identified as ya from its qu value.
However, we were not able to assign the lower state from the
vibrational dependence of qu. Accordingly, we leave the
vibrational states of this transition as unidentified. This
laser line has been studied by two independent IR-MW DR
experiments in Refs. (52) and (55). The results of Ref.
(52), Ref. (55), and the present work are all in
disagreement with each other (Table 18). Our criticism of
Ref. (55) was discussed earlier in the section on I
transitions in the v1 v G.st band and will not be discussed
further in this section. The questions then are why we did

not observe the two transitions seen in the IR-MW DR

98

experiment by Kohler et al. (52) and why Kohler et a1. did
not observe the transitions observed in our work. The
answer to the second question is easy. The infrared
transition detected in our experiment, QP(31,9), involves J
values of 30 and 31. The frequencies of the J = 30 and J =
31 transitions are much too high to be observed by the
apparatus used by Kohler et a1. (52). The answer to the
first question is not obvious, but our explanation is given
as follows:

1- One of the assignments of Kohler et al. is to the
QR(18,8) transition in the 2v +v

Ill=2~2v I£I=2

6 l’ 6’
(52). This assignment is doubtful because the assignment of
v3 and V6 in this paper had to be interchanged for the
reasons mentioned in the discussion of v3+v1 + v3 and

v6+v1 ~ ”6 bands.

2- The second infrared transition observed in Ref. (52) was
assigned as QP(18,6); v5+v1 e vs. We have observed a few
weak hyperfine components which could belong to the
rotational states involved in a QP(18,6) transition.

However, we can not count on these few weak components to

make a confident assignment.

99

vi . vh ; °0(44,34) and v °o(34,29)

g ' ”6 ‘

 

Five different 0 branch transitions were observed with
the 9P(12) 12C1802 laser line. Part of the spectrum
observed with this laser line is shown in Fig. (25). The
"pure" nuclear quadrupole resonances of all these 0 branches
were observed as strong doublets. Most of these doublets
were resolved (Fig. 26).

The 9P(12) 12C1802 laser line was studied in the Lamb-
dip experiment by Ritze and Stert (54). They also observed
five different 0 branch transitions but the doublets of the
hyperfine structure for only one of these 0 branches were
resolved and were assigned to a rotational state with J =
3531. In the present work, the rotational assignment could
be made for only two of these 0 branch transitions and this
assignment is given in Table (18). Furthermore, only one
vibrational state could be identified from the qu values.
The quadrupole coupling constants were attributed to the "6
state and to unknown states "g’ vh’ and vi; the values are
given in Table (19). It is possible that these 0 branch
transitions belong to the v1 band because they are observed
at 1075.08599 cm-1 (the frequency of the 9P(12) 1201802
laser line) which is only 0.12 cm"1 below the v1 band

center. If this assignment is correct, the large deviations

in qu of the assigned transitions (Table 19) indicate that

100

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.ssoam mm "chansons summon “NomuomH ANvam "saga gonna
.nomosmsm a asosommav Au“: movzoso Issaooau a «o canasxo s< .mN .uwh
~12 c_ xenon?!“—
od: odn— odw. 0.0: 0.03 0.0m
- n D b — b - p D - [-loo
4 - d - q - d - d
4 .x
41 .1
. E : a .-
A u u u A u x u x 989
0.03 odn— adm— 062 0.00. 0.0m

Kigsuaiul aAgolag

101

1150 1225 1200
50000 t l :

 

V' ‘- Vh

Q0(44,34)

 

 

Relative intensity

 

   

h

 

 

0.0 4 l .
115.0 122.5 1290

Frequency in MHz

 

Fig. 26. An example of high resolution records for Fig. 25.

Laser line: 9P(12) 1201802; sample pressure: 15 mTorr.

102

the v band is either highly excited or strongly perturbed

l

in this region.

, Q
Vf "' Veg P(2299)

 

An infrared transition that could be assigned as
QP(22,9) was observed with the 9P(16) 1201802 laser line.
No previous study has been reported for this laser line.
The qu values obtained were again sufficiently different
from those obtained for known states that a vibrational

assignment could not be made (Table 19). Therefore, we have

attributed this transition to the vf e ve band.

Unassigned transitions

Many observed RF transitions could not be assigned to
either rotational or vibrational states. The frequencies of
these transitions are given in Appendix I for each laser
line. The reason for not being able to assign these
transitions is no doubt due to the complexity of the ro-
vibrational structure in the region of study. This region
is crowded with many highly excited and strongly perturbed
states. Consequently, we can not even be sure that all of
the unassigned transitions are "pure" nuclear quadrupole
resonances. As an example, Fig. (27) shows a very strong RF
spectrum observed at low RF frequency with the 9R(18)

1201602 laser line for which no assignment could be made.

103

 

 

 

 

12.0 15.0 20.0
4500.0 1 1 1
d1- .11-
dp "l‘
3
'3 tr ‘*
I:
.2
..c. .
U
.2
‘6
3 db .1.-
(K
#r 11-
0.0 1 1 1
12.0 15.0 20.0

Frequency in MHz

Fig. 27. An example of unassigned IR-RF DR transitions.

Laser line: 9R(18) C02; sample pressure: 17 mTorr.

Symbols are as follows:

we = The experimental frequency. The sign of we has been

chosen to agree with that of wC

E(J,k,F’) - E(J,k,F")

V

c
OV=V"'V
e c
SE(we) = The standard error in we derived from the fit of

the spectrum to a Lorentz lineshape.

qu = The quadrupole coupling constant.

CM: Includes the spin-rotation coupling terms and is defined
as [CN+(Ck-CN)k2/J(J+l)].

RMS(w) = The root mean square deviation in the we derived
from the fit of we to qu and CM.

SE(qu) and SE(CM) = The standard errors in qu and CM
derived from the fit of we to qu and CM, respectively.

CR and CN = The spin-rotation coupling constants along the
symmetry axis and in the direction normal to it,
respectively.

(CM)e and (CM)C: The experimental and calculated values of
CM, respectively.

oCM = (CM)e - (CM)C

105

Table l.

9R(16) 12C1602 Laser Line

 

IR Transition: e G.St; QR(7,2)

”1

Ground state transitions; J = 7 and k = 2

F" F’ ve/MHZ vC/MHZ 0v SE(ve)
4.5 5.5 -214.226 -214.218 -0.008 0.0006
5.5 6.5 -164.385 -164.372 -0.014 0.0016
6.5 7.5 -69.454 -69.507 0.053 0.0016
7.5 8.5 77.013 77.001 0.012 0.0008
8.5 9.5 280.408 280.411 -0.003 0.0004
qu = -2145.15 MHz
CM = 0.00690 MHz
RMS(w) = 0.025
SE(qu) = 0.08
SE(CM) = 0.00106
w1 state transitions; J = 8 and k = 2

F F ve/MHZ vC/MHZ 6v SE(ve)
5.5 6.5 -23l.903 -231.908 0.004 0.0006
6.5 7.5 ~169.495 -l69.551 0.056 0.0024
7.5 8.5 -64.841 -64.759 -0.083 0.0023
8.5 9.5 88.142 88.148 -0.006 0.0005
9.5 10.5 294.431 294.421 0.010 0.0007
qu = -2140.36 MHz

CM = 0.00603 MHz
RMS(w) = 0.045
SE(qu) = 0.10
SE(CM) = 0.00101

106

BILLIE—.24

9R(14) 1201802 Laser Line

 

IR Transition (I): e G.St; QP(16,4)

”1

Ground state transitions; J = 16 and k = 4

F" F’ ve/MHZ vc/MHZ 0v SE(ve)
13.5 14.5 -245.o13 -248.049 0.035 0.0016
14.5 15.5 -15l.650 -151.724 0.075 0.0024
15.5 16.5 -32.669 -32.603 -0.066 0.0015
16.5 17.5 110.697 110.724 -0.027 0.0012
17.5 18.5 279.598 279.585 0.013 0.0008
qu = -2144.90 MHz
CM = 0.00583 MHz
RMS(V) = 0.049
SE(qu) = 0.24
SE(CM) = 0.00146

w1 state transitions; J = 15 and k = 4

F" F’ ve/MHZ vc/MHZ 6v SE(ve)
12.5 13.5 -239.396 -239.393 -0.004 0.0006
13.5 14.5 -l48.242 -l48.203 -0.038 0.0019
14.5 15.5 -33.519 -33.592 0.073 0.0015
15.5 16.5 105.931 105.925 0.006 0.0012
16.5 17.5 271.687 271.695 —0.008 0.0007
qu ' -2140.13 MHz

CM = 0.00698 MHz
RMS(w) = 0.037
SE(qu) = 0.12
SE(CM) = 0.00081

IR Transition (II);

9R(14)

IZCIBO

107

Table 3.

2 Laser Line

 

”1

Ground state transitions: J =

F F we/MHZ
15.5 16.5 76.820
16.5 17.5 47.468
17.5 18.5 10.662
18.5 19.5 —35.303
19.5 20.5 -92.608
qu = -2144.57 MHz
CM = 0.00446 MHz
RMS(w) = 0.017
SE(qu) = 0.21
SE(CM) = 0.00033

w1 state transitions;

F F ve/MHZ
14.5 15.5

15.5 16.5 74.714
16.5 17.5 16.733
17.5 18.5 -54.971
18.5 19.5 -143.301
qu = -2140.61 MHz
CM = 0.00389 MHz
RMS(v) = 0.021
SE(qu) = 0.35

SE(CM) = 0.00083

J :

. G.St; °p<18,12)

18 and k = 12

vc/MHZ

76.
47.
10.
-35.
-92.

854
465
644
302
604

17 and k

vc/MHZ

-120.
74.
16.

-54.

-143.

975
717
766
994
288

Av

-0.034
0.002
0.018

-0.001

-0.004

-0.003
-0.033

0.023
-0.013

SE(v )

.0020
.0006
.0017
.0030
.0011

00000

SE(ve)

0.0006
0.0009
0.0005
0.0005

108

Table 4.

9R(14) 1201602 Laser Line

 

IR Transition(I): we . G.St; °o(15,15)

Ground state transitions; J = 18 and k = 16

F" F’ we/MHz wc/MHz Ow SE(ve)
15.5 16.5 375.251 375.249 0.002 0.0008
16.5 17.5 226.002 226.044 -0.042 0.0013
17.5 18.5 44.557(u) 44.766

18.5 19.5 -170.972 -l7l.047 0.076 0.0012
19.5 20.5 -423.975 -423.954 -0.021 0.0008

qu = -2144.31 MHz
CM = 0.00240 MHz
RMS(v) = 0.045
SE(qu) = 0.15
SE(CM) = 0.00135

wa state transitions; J = 18 and k = 16

F" F’ ve/MHZ vc/MHZ 6v SE(ve)
15.5 16.5 371.213 371.239 -0.026 0.0008
16.5 17.5 223.729 223.591 0.138 0.0015
17.5 18.5 44.557(u) 44.266

18.5 19.5 -169.310 -169.287 -0.023 0.0012
19.5 20.5 -419.470 -419.470 0.000 0.0004

qu = -2121.49 MHz
CM = -0.00036 MHz
RMS(V) = 0.071
SE(qu) = 0.16
SE(CM) = 0.00152

9R(14)

109

12C160

M

2 Laser Line

 

IR Transition (II): wc v wb ; QQ(43,24)

wb state transitions; J = 43 and k = 24

F" F’ we/MHZ vc/MHZ Ow SE(ve)
40.5 41.5 -28.154 -28.178 0.025 0.0009
41.5 42.5 -l4.718 -14.698 -0.020 0.0008
42.5 43.5 -00.958
43.5 44.5 13.054 13.076 -0.022 0.0009
44.5 45.5 26.938 26.916 0.023 0.0009
qu = -2124.37 MHz
CM = -0.00147 MHz
RMS(w) = 0.022
SE(qu) = 1.56
SE(CM) = 0.00036

wC state transitions; J = 43 and k = 24

F" F’ we/MHZ wc/MHZ Ow SE(ve)
40.5 41.5 -26.531 -26.559 -0.028 0.0011
41.5 42.5 -l3.982 -l3.963 -0.020 0.0008
42.5 43.5 -l.015
43.5 44.5 12.448(u) 12.104 0.0008
44.5 45.5 25.182 25.178 -0.004 0.0007
qu = -1995.27 MHz
CM = -0.00517 MHz
RMS(w) = 0.020
SE(qu) = 1.55
SE(CM) = 0.00039

110

W

9R(14) 12C1602 Laser Line

 

IR Transition (III): wx s G.St; QP(6,5)

Ground state transitions; J = 6 and k = 5
F" F’ ve/MHZ wc/MHZ Ow SE(ve)
3.5 4.5 200.707
4.5 5.5 165.479
5.5 6.5 82.354 82.400 -0.046 0.0054
6.5 7.5 -63.690 -63.707 0.017 0.0026
7.5 8.5 -297.036 -297.036 0.000 0.0003

qu = -2145.07 MHz“

on = 0.00550 Msz
RMS(w) = 0.028
SE(qu) = 0.24
SE(CM) = 0.00392

wx state transitions; J = 5 and k = 5
F" F’ ve/MHZ wc/MHZ Ow SE(ve)
5.5 6.5 -106.340 -106.340 0.000 0.0027

qu = -2139(1)°

was not included in the qu fit.

was not included in the CN and C1‘ fit.

was determine by fitting qu to a single transition.

111

 

Rifle—L
9R(18) 12C1602 Laser Line
IR Transition: v6 + ”1 . we ; °R(20,15)

w6 state transitions; J = 20 and k 16

F" F’ we/MHZ wC/MHZ Ow
17.5 18.5 249.922 249.913 0.008
18.5 19.5 148.601 148.593 0.008
19.5 20.5 27.491 27.511 -0.020
20.5 21.5 ~115.208 -115.252 0.044
21.5 22.5 -281.887 -281.883 -0.004
qu = -2142.91 MHz
CM = 0.00376 MHz
RMS(w) = 0.022
SE(qu) = 0.13
SE(CM) = 0.00054

w6 + w1 state transitions; J = 21 and k =

F F we/MHz wc/MHz Ow
18.5 19.5 199.543 199.607 -0.065
19.5 20.5 118.070 118.095 -0.025
20.5 21.5 21.344 21.272 0.073
21.5 22.5 -92.531 -92.517 -0.014
22.5 23.5 -225.210 -225.203 -0.007
qu = -2140.53 MHz
CM = 0.00491 MHz
RMS(w) = 0.046

SE(qu) = 0.39

SE(CM) = 0.00118

16

SE(we)

0.0011
0.0008
0.0006
0.0010
0.0006

SE(ve)

0.0012
0.0015
0.0008
0.0006
0.0007

112

 

Table 8.
9R(12) 12C1602 Laser Line
IR Transition: "3 ~ wd ; QP(31,9)

wd state transitions; J

F F we/MHz
28.5 29.5 -235.472
29.5 30.5 -l30.956
30.5 31.5 —15.462(u)
31.5 32.5 111.631
32.5 33.5 250.540
qu = -2148.15 MHz
CM = 0.00677 MHz
RMS(w) = 0.048
SE(qu) = 0.18
SE(CM) = 0.00060

"5 state transitions; J

F F we/MHz
27.5 28.5 a230.036
28.5 29.5 -128.488
29.5 30.5 -15.462(u)
30.5 31.5 108.939
31.5 32.5 245.089
qu = —2146.73 MHz
CM = 0.00644 MHz
RMS(w) = 0.049
SE(qu) = 0.13
SE(CM) = 0.00045

= 31 and k

vc/MHZ

-235.
-131.
-15.
111.
250.

= 30 and k

476
015
385
707
528

vc/MHZ

-230.

036

-128.409

-15.

533

108.881

245.

094

0.003
0.059

-0.076
0.012

-0.001
-0.079

0.058
-0.006

SE(ve)

0.0014
0.0068

0.0029
0.0014

SE(we)

0.0011
0.0057

0.0026
0.0010

113

 

M
9R(20) 12C1602 Laser Line
- . . . 0
IR Tran51tion. w3 + w1 t w3 , R(23,20)
w3 state transitions; J = 23 and k = 20
F" F’ we/MHz wc/MHz Ow
20.5 21.5 359.268 359.270 -0.002
21.5 22.5 208.477 208.474 0.003
22.5 23.5 33.3(w) 33.389
23.5 24.5 -167.527 -167.528 0.000
24.5 25.5 -395.894 -395.891 -0.002
qu = -2147.65 MHz
CM = 0.00291 MHz
RMS(w) = 0.002
SE(qu) = 0.01
SE(CM) = 0.00006
w3 + w1 state transitions; J = 24 and k = 20
F" F’ we/MHZ wC/MHz Ov
21.5 22.5 305.680 305.679 0.002
22.5 23.5 176.609 176.611 -0.002
23.5 24.5 27.55(w) 27.495
24.5 25.5 -l43.070 -143.075 0.005
25.5 26.5 -336.622 -336.619 -0.004
qu = -2143.80 MHz
CM = 0.00307 MHz
RMS(w) = 0.003
SE(qu) = 0.02
SE(CM) = 0.00009

SE(we)

0.0030
0.0034

0.0031
0.0054

SE(ve)

0.0074
0.0040

0.0056
0.0061

114

 

la_b_le_lL
9P(12) 1201802 Laser Line
IR Transition (1): wg * w6 ; QQ(34,29)
w6 state transitions; J = 34 and k = 29
F" F’ we/MHz wc/MHz
31.5 32.5 347.842 347.840
32.5 33.5 192.826 192.854
33.5 34.5 21.654(u) 21.746
34.5 35.5 -166.153 -166.204
35.5 36.5 -37l.750 -371.746
qu = -2142.54 MHz 1
CM = 0.00266 MHz
RMS(w) = 0.029
SE(qu) = 0.07
SE(CM) = 0.00032
wg state transitions; J = 34 and k = 29
F F we/MHz wc/MHz
31.5 32.5 343.415 343.438
32.5 33.5 190.502 190.389
33.5 34.5 21.654(u) 21.433
34.5 35.5 -164.165 -l64.139
35.5 36.5 -367.063 -367.062
qu = -2115.77 MHz
CM = 0.00178 MHz
RMS(w) = 0.059
SE(qu) = 0.16
SE(CM) = 0.00074

0.002
-0.028

0.051
-0.004

-0.024
0.114

-0.026
-0.001

SE(we)

0.0006
0.0013

0.0014
0.0005

SE(we)

0.0008
0.0015

0.0016
0.0005

115

TM

9P(12) 1201802 Laser Line

 

IR Transition (II): wi . wh ; °0(44,34)

wh state transitions; J = 44 and k = 34

F" F’ we/MHZ wc/MHZ Ow SE(we)
41.5 42.5 234.232 234.200 0.032 0.0022
42.5 43.5 127.287 127.302 -0.015 0.0010
43.5 44.5 12.040(u) 11.647
44.5 45.5 -113.l49 -ll3.181 0.032 0.0015
45.5 46.5 -247.667 -247.624 -0.043 0.0024
qu = -2137.85 MHz
CM = 0.00325 MHz
RMS(w) = 0.032
SE(qu) = 0.26
SE(CM) = 0.00043
wi state transitions; J = 44 and k = 34

F" F’ we/MHZ wc/MHZ Ow SE(we)
41.5 42.5 232.938 233.002 -0.064 0.0021
42.5 43.5 126.680 126.658 0.022 0.0010
43.5 44.5 12.040(u) 11.606
44.5 45.5 -112.592 -112.564 -0.028 0.0014
45.5 46.5 -246.269 -246.294 0.025 0.0023

qu = -2126.64 MHz
CM = 0.00376 MHz
RMS(w) = 0.038
SE(qu) = 0.31
SE(CM) = 0.00052

116

 

Table 12.
9P(16) 12C1802 Laser Line
IR Transition: wf ~ we ; QP(22,9)

we state transitions;

F F we/MHZ
19.5 20.5 ~159.844
20.5 21.5 ~92.321
21.5 22.5 -13.910(u)
22.5 23.5 73.752
23.5 24.5 172.322
qu = -2136.44 MHZ
CM = 0.00627 MHz
RMS(w) = 0.026
SE(qu) = 0.18
SE(CM) = 0.00052

wf state transitions; J

F F we/MHZ
18.5 19.5 -144.588
19.5 20.5 ~84.013
20.5 21.5 ~13.910
21.5 22.5 66.478
22.5 23.5 155.853
qu = -2119.95 MHz
CM = 0.00535 MHZ
RMS(w) = 0.046
SE(qu) = 0.46
SE(CM) = 0.00135

J = 22 and k

wC/MHZ

~159.
~92.
~14.
73.
172.

860
310
444
800
313

= 21 and k

wc/MHZ

~144.600
~83.950
~13.604
66.416
155.874

0.016
~0.011

~0.048
0.009

0.013
~0.063

0.062
~0.021

SE(we)

0.0015
0.0012

0.0036
0.0015

SE(we)

0.0009
0.0015

0.0017
0.0015

117

w

9R(16) 12C1602 Laser Line:

 

IR Transition: . G.St; QR(7,2)

I’1

Lower state transitions Upper state transitions

 

 

F" F’ we /MHz F" F’ we /MHz
4.5 5.5 ~214.226 5.5 6.5 ~231.903
5.5 6.5 ~164.385 6.5 7.5 ~169.495
6.5 7.5 —69.454 7.5 8.5 ~64.84l
7.5 8.5 77.013 8.5 9.5 88.142
8.5 9.5 280.408 9.5 10.5 294.431

9P(14) 12C1802 Laser Line:

IR Transition (I): w1 v G.st; QP(16,4)
13.5 14.5 ~248.013 12.5 13.5 ~239.396
14.5 15.5 ~151.650 13.5 14.5 ~148.242
15.5 16.5 ~32.669 14.5 15.5 ~33.519
16.5 17.5 110.697 15.5 16.5 105.931
17.5 18.5 279.598 16.5 17.5 271.687

IR Transition (II): w1 « G.st; QP(18,12)
15.5 16.5 76.820 15.5 16.5 74.714
16.5 17.5 47.468 16.5 17.5 16.733
17.5 18.5 10.662 17.5 18.5 -54.971
18.5 19.5 ~35.303 18.5 19.5 ~143.301
19.5 20.5 ~92.608

9R(20) 12C1602 Laser Line:
IR Transition: w + w r w ; QR(23,20)
3 1 3

20.5 21.5 359.268 21.5 22.5 305.680
21.5 22.5 208.477 22.5 23.5 176.609
22.5 23.5 33.3(w) 23.5 24.5 27.55(w)
23.5 24.5 ~167.527 24.5 25.5 ~143.070
24.5 25.5 -395.894 25.5 26.5 -336.622

118

Table 14.

9R(14) 12C1602 Laser Line:

 

IR Transition (I): wa . G.st; Q0(18,15)

Lower state transitions Upper state transitions
F F we /MHz F F we /MHZ
15.5 16.5 375.251 15.5 16.5 371.213
16.5 17.5 226.002 16.5 17.5 223.729
17.5 18.5 44.557(u) 17.5 18.5 44.557(u)
18.5 19.5 ~170.972 18.5 19.5 -169.310
19.5 20.5 ~423.975 19.5 20.5 ~419.470

IR Transition (II): wC v wb ; QQ(43,24)

 

40.5 41.5 ~28.154 40.5 41.5 ~26.531
41.5 42.5 -14.718 41.5 42.5 ~13.982
43.5 44.5 13.054 43.5 44.5 12.448(u)
44.5 45.5 26.938 44.5 45.5 25.182

IR Transition (III): wx r G.St; QP(6,5)
5.5 6.5 82.354 5.5 6.5 ~106.340
6.5 7.5 ~63.691
7.5 8.5 ~297.036

9R(18) l201602 Laser Line:

IR Transition: o6 + wl . we ; QR(20,15)
17.5 18.5 249.922 18.5 19.5 199.543
18.5 19.5 148.601 19.5 20.5 118.070
19.5 20.5 27.492 20.5 21.5 21.344
20.5 21.5 ~115.208 21.5 22.5 ~92.531
21.5 22.5 ~281.887 22.5 23.5 -225.210

9P(12)

12 18

119

C 02 Laser Line:

 

IR Transition (1):

9P(12)

wg * V6 ;

Lower state transitions

 

9P(16)

 

9R(12)

 

Table 15.

Q0(34,29)

Upper state transitions
we /MHz

F" F’ we /MHz F" F’
31.5 32.5 347.842 31.5 32.5
32.5 33.5 192.826 32.5 33.5
33.5 34.5 21.654(u) 33.5 34.5
34.5 35.5 -166.153 34.5 35.5
35.5 36.5 -371.750 35.5 36.5

12C1802 Laser Line:

IR Transition (II): wi r wh ; QQ(44,34)
41.5 42.5 234.232 41.5 42.5
42.5 43.5 127.287 42.5 43.5
43.5 44.5 12.040(u) 43.5 44.5
44.5 45.5 -113.149 44.5 45.5
45.5 46.5 ~247.667 45.5 46.5

12C1802 Laser Line:

IR Transitions: wf . we ; °P<22,9)

19.5 20.5 ~159.844 18.5 19.5
20.5 21.5 -92.321 19.5 20.5
21.5 22.5 ~13.910(u) 20.5 21.5
22.5 23.5 73.752 21.5 22.5
23.5 24.5 172.322 22.5 23.5

1201602 Laser Line:

IR Transition: "3 v wd ; QP(31,9)

28.5 29.5 ~235.472 27.5 28.5
29.5 30.5 ~130.956 28.5 29.5
30.5 31.5 ~15.462(u) 29.5 30.5
31.5 32.5 111.631 30.5 31.5
32.5 33.5 250.540" 31.5 32.5

343.
190.
21.
~164.
-367.

232.
126.
.040(u)
~112.
~246.

~144.
.013
~13.

66.
155.

230.
~128.
.462(u)
108.
245.

415
502
654(u)
165
063

938
680

592
269

588

910(u)
478
853

036
488

939
089

120

Table 16.

Rotational Dependence of egg
a- Xglues of egg

 

 

 

Ground state w1 state
Laser line (J,k) qu /MHz (J,k) qu /MHz
12 16
9R(16) C 02 (7,2) -2145.15(8) (8,2) ~2140.36(10)
12 18
9P(14) C 02 (16,4) -2144.90(24) (15,4) ~2140.13(12)
(18,12) ~2144.57(21) (17,12) —2140.61(35)
93(14) 1201602 (18,16) -2144.31(15)
(5,5) -2145.07(24)*
b- Values of xJ and xk
Ground state w1 state
quo/MHz ~2145.214(8) ~2140.464
XJ /kHz 0.992(72) 1.70
“k /kHz 2.195(95) -4.626
*

Not included in the fitting of ”J’ xk’

121

Table 17.

The Magnetic Paraaeters

 

 

 

The magnetic parameters for the ground state of CF3I

J k (CM)e/MHz (CM)c/MHz OCM SE(CM)

7 2 0.00690 0.00653 0.00037 0.00106

16 4 0.00583 0.00661 ~0.00078 0.00146

18 12 0.00446 0.00445 0.00001 0.00033

18 16 0.00240 0.00250 -0.00010 0.00135
CN = 0.00696 MHz
Ck = 0.00100 MHz
SE(CN) = 0.00040
SE(Ck) = 0.00060

The Magnetic Parameters for the wl

State of CF

I

 

 

 

3

J k (CM)e/MHz (CM)C/MHz OCM SE(CM)
8 2 0.00603 0.00665 ~0.00062 0.00101
15 4 0.00698 0.00657 0.00041 0.00081
17 12 0.00389 0.00390 ~0.00001 0.00083
CN = 0.00701 MHz
Ck = 0.00040 MHz

SE(CN) = 0.00058

SE(CR) = 0.00164

122

 

 

Table 18
IR-MW 05(52) Lamb—dip(54) IR-RF DR
9R(16) 12C1602 Laser Line; 1075.9878 cm-1
wle G.st; wlr G.st; wlr G.st;
QR(7,2) °R(7,2) °n(7,2)
9R(18) 1201602 Laser line; 1077.3025 em’1
1) V3 + VI“ V3 ; ------ V6 + V1. V6
°R<20,15) J = 25 :5, k = 10 +3 QR(20,15)
2) V6 + wlr w6 ------------
°R<2o,k), 0 z 1: 2 4 ————————————
90(14) 1201502 Laser line; 1074.5455 en'1
1) "x“ G.st; ------ "x“ G.st;
°P(5,5) ------ °P(5,5)
2) "y' G.st; wl band; "a“ G.st;
°0(18,15) °0(18.15) °0(18,16)
3) ~~~~~~ wl band; "c“ wb ;
------ 0 branch, °o(43,24)

J 40 14, k = 25

 

123

Table 18—Continued.

 

IR-MW 05(52) Lamb-dip(54) IR-RF DR
95(12) 1201602 laser line; 1073.2785 on”1
1) w5 + wlr w5 ; ------ wjr wd ;
°p<15,5) ------ °p(31,9)
2) 2V6 + wlr 2V6 ; ------------
111 = 2, °n<15,8) ------------
99(12) 1201802 Laser line; 1075.0599 on’1
I) ------------ w8 * we ;
------ a branch, °0(34,29)
J = 35 i1
2) ------------ vi r wh ;
------------ °0(44,34),
3) ------------------

------ four 0 branches three 0 branches

a- Results of theapraaent work

Vi

124

Table 19.

Vibrational Dependence of e09.

brational state

Ground state

1
"3
I’5
”5
w 4‘ w:l
w + w1
V
a
"h
V
C
”d
V
e
"f
”g
I’h

(J.k)

(23,20)
(20,16)
(34,29)
(24,20)
(21,16)
(18,16)
(43,24)
(43,24)
(31,9)
(22,9)
(21,9)
(34,29)
(44,34)
(44,34)
(30,9)
(5.5)

qu

~2145.
~2140.
~2147.
~2142.
~2142.
-2143.
~2140.
.49(16)
~2124.
~1995.
~2148.
~2136.
~2119.
-2115.
~2138.
~2126.
~2146.

~2121

~2139

Results of theaprevioaa work

Cox et al. (53)

MW

Walters et a1.
MW-RF DR

Ibisch et al.
IR—MW DR

Sheridan et a1.

(57)

(55)

(26)

/MHz
214(8)
464(12)
65(10)
91(13)
84(7)
80(2)
53(39)

4(1.6)
3(1.6)
15(18)
44(18)
95(46)
77(16)
29(85)
64(31)
73(13)

Vibrational state

Ground state

"3
"5

”1

Ground state

Ground state

Ground state

6(qu)/MHz

4.
—2.
.30
.37
.41
.68

23.

20.
149.
.94
.77
25.
29.
.92
18.
.52

151-1

qu

~2144.

~2145.
~2146.

~2144.

~2144.
~2156.

~2150

75
44

72
81
91

26
44

57

/MHz

7(6)

207(3)
49(11)

58(12)

66(52)
81(180)

125

T_&_|_b_1_<_3_2_0_-_

The w1 Band Center

 

a- Results of the preaent work

Laser line IR transition w1 band center /cm-l

92(15) 1201502 °R(7,2) 1075.191

99(14) 1201802 °P(15,4) 1075.255*
°P(15,12) 1075.485*

b- Comparison table for the values of the w1 band center

 

w1 band center /cm_1
l~ Hohler et al. (52) 1075.1915(10)
IR-MW DR
2- Burger et al. (59) 1075.20(l)
FTIR
3- Ibisch et al. (55) 1073.2785(3)
IR-MW DR
4- The present work 1075.191(10)
IR-RF DR
*

not included in determination of the w1 band center.

126

CHAPTER v11

CF38r

 

I- INTRODUCTION

The trifluoromethylbromide molecule is a prolate
symmetric top and belongs to the C3v symmetry group. This
molecule, commercially labelled as freon 13 B1, consists of
two main isotopic species, CF379Br and CF381Br, in roughly
equivalent natural abundance. Each species has six
fundamental vibrational modes, three non-degenerate and
three doubly-degenerate.

The pure rotational spectra of CF379Br and CF381Br were
previously studied by microwave spectroscopy and the values
of B, DJ, DJk’ and qu were determined for the ground
vibrational state (26,74).

Recently, rotational spectra in the ground vibrational
states of the C~13 and C~12 isotopic species of
trifluoromethylbromide have been investigated by using MW-RF
DR spectroscopy to obtain improved rotational constants and
an improved structure (53).

The rotational constants for excited vibrational states
in CF38r were first reported in 1976 by Jones et al. by the
aid of the IR-MW DR spectroscopy (75). In this report, they

indicated that all of the 9.44 pm CO2 laser lines that they

127

could generate were absorbed by CF37QBr at a pressure of

about 1 Torr. On the other hand, for pressures less than

100 mTorr only two C0 laser lines, 9R(28) and 9R(30), were

2

weakly absorbed. With these two laser lines, they observed
the hyperfine structure in the w6+w1 + w6 infrared band and

determined the rotational constants, B, D and D for the

J’ Jk’

w6 and w6+w1 vibrational states. For this analysis, the qu
value was constrained to the ground state value determined

by Sheridan and Gordy in 1952 (26).

The millimeter wave spectra of CF379Br and CF381Br have

recently been measured in the ground and low lying excited
vibrational states, w3, w5, and "6’ by Carpenter et a1.

(76). They determined the molecular constants, B, D D

J’ Jk’

and qu for the ground and w3 vibrational states and the

rotational constants B, I, q, D DJk’ and n for the w5 and

J:
w6 vibrational states. They also determined the value of
qu for the w6 state.

The first studies of low resolution infrared and Raman
spectra of trifluoromethylbromide were by Edgell and May in
1953 (27). A medium resolution IR analysis of the wl,

79 381Br

near 1100 cm—1 was reported in 1979 (77). In this study,

wl+w6 r w6 and wl+2w6 v 2w6 bands of CF3 Br and CF
only the J clusters could be resolved and the B rotational
constant was determined for the above mentioned vibrational
states.

An extensive investigation of the IR spectrum of CF3Br

128

in the range 400-1800 cm-1

at a medium resolution was
reported in 1982 (78).
In 1985, the spectra of the w5 fundamental near

550 cm"1 were obtained for CF379Br at a resolution of

0.05 on‘1

(59).

The CF38r molecule has recently been found to be a good
candidate for isotopically selective multiphoton
dissociation (31,79, and 80) and a good source for
generation of far-infrared, millimeter and submillimeter
laser lines by optical pumping (81-82).

Finally it is worth mention that molecules such as
CF3Br give rise to active forms of bromine which contribute
to the ozone depletion in the lower stratosphere and
consequently spectroscopic studies of such molecules may be
of some help in revealing the atmospheric pollutants. The
general interest in CF3Br together with the relatively poor
characterization of the infrared spectrum in the mid-

infrared region led us to examine the CO2 infrared laser

radiofrequency double resonance spectrum of this molecule.

129

II~ RESULT84AND DISCUSSION

Our goal in this part of the research program has been
to study the ro-vibrational spectra and to determine the

quadrupole coupling constant for the w1 infrared bands of

each of the CF37 381Br molecular species. Since
the w1 band centers for CF37QBr and CF381Br have been

9Br and CF

determined by Burczyk et a1. (77), to occur at 1084.763 and
1084.521 cm-l, respectively, we used in this work the 9R(28)
and 9R(30) 12C1602 laser lines because the frequencies of
the infrared radiation generated at these two laser lines
are very close to the w1 band centers. The IR—RF DR
experiment was tested by using both the intra- and extra-
cavity experimental arrangements. However, as with CF3I the
best results were obtained with the extracavity experimental
arrangement. The bromotrifluoromethane sample from the
Peninsular Chemical Research company was kindly provided by
Prof. G. E. Leroi of Michigan State University.

A fairly large number of Q-branch infrared transitions
were pumped with the 9R(28) and the 9R(30) CO2 laser lines.
The assignment of these infrared transitions has not been
straightforward for the following reasons:

1- The high resolution infrared spectrum in the wl region of
CF3Br has not been reported.

2- In the IR-RF DR experiment, for an infrared O-branch

transition in a molecule with one nucleus with I = 3/2, one

130

expects to observe three "pure" nuclear quadrupole
resonances for each of the pumped vibrational states. These
"pure" nuclear quadrupole resonances are indicated in Figure
(28) by (a, B, and r) and (a’, B’, and r’) for the lower and
upper vibrational states, respectively.

The transitions B, r, B’, and r’ are very close to each
other in frequency and consequently are expected to be
observed as a closely spaced quartet. By contrast, the a

’ transitions occur at very low RF frequencies and

and a
accordingly they are expected to be observed as an
unresolved doublet. However, in most cases it was not
possible to locate a and a’. Also, not all the components
of the B, y, B’ and y’ quartet could be resolved and hence,
more often a doublet was observed instead of a quartet.

This means that we had to rely on only two hyperfine
components to determine the qu values for the lower and the
upper pumped vibrational states.

In order to overcome the first of the above mentioned
difficulties, I have recorded the infrared spectrum of CF38r
in the region 1068 to 1100 cm“1 by using the Bomem DA 3.01
FTIR spectrometer at Michigan State University with the

1). The obtained FTIR

highest available resolution (0.02 cm-
spectrum is shown in Fig. (29).
It is clear from Fig. (29) that the fine structure of the Q-

branch transitions could not be resolved and only the J

clusters of the R- and P- branch transitions could be

131

 

 

 

 

 

 

laser pump laser pump
OF-O AF-t1

 

 

 

 

 

 

 

A
p a
y A!— J-O.5

71
y! l, \’ J+1.5

 

 

 

 

 

 

 

Fig. 28. A schematic energy level diagram for the PNQR

resonances and the laser pump in in CF3Br.

132

. mo No.c “soflusuonos “whoa m.o “ossnoosa sun-mm

HI-
.hflMhO mo =o«u0h vac; H3 0:» ma Imhuoonm Guam vvvmoovh one .QN .uflh
:IEUV swaths: m>o>>
0.00: 0.0mm: odwo. odhop
_ n _ A . u . cod

 

 

 

BDUDQJOSQV

 

DON

 

 

0.00:

.11-

_
0.0mm: odwo— got:

133

resolved with the 0.02 cm-1 resolution. However, the FTIR
spectrum shown in Fig. (29) matches exactly the synthesized
infrared specrum in the 1068-1100 cm—1 region given in Ref.
(81). The synthesized infrared spectrum of Ref. (81) is
shown in Fig. (30) for a wider view of the ro-vibrational
structure in the w1 region of CF3Br.

As a consequence of the unresolved compact ro-
vibrational structure of CFaBr, the general procedure
followed in the ro-vibrational assignment of the observed
IR-RF DR spectra with each laser line has been as follows:
l~ By the aid of a computer program, the frequencies of the
infrared transitions for all of the previously identified
infrared bands (77) (w1+w6 r "6’ 2w6+wl « 2w6, and
w1 r G.St) for the 79Br and 818r isotopic species of the
bromotrifluoromethane, were calculated by using the infrared
band centers and the rotational constants given in Refs.
(75) and (77). Then, the computer program selected out the
infrared transitions which occur at frequencies comparable
to the frequency of the laser line under consideration. The
frequencies of the selected infrared transitions of low J
and k quantum numbers were restricted to lie within
0.01 cm.1 of the frequency the CO2 laser lines used in the
observations. The frequencies of the infrared transitions
of high J and k value were allowed to lie within 0.05 cm-1

of the frequency of the CO2 laser line.

134

“WV?" (1‘ 91 V; + V3
29,- I

M"/ "Ax 1.111% “1‘1

. L zillllllllnnim.
1050

1110 CPI":J

Fig. 30. The synthesized spectrum of CF3Br.

(as reported in Ref. (81)).

135

The computer program allowed a large deviation in
frequencies of the infrared transitions of high J and k
values because the distortion constants Dk’ HJJJ,
HJJk,...etc. are not known to us and the contribution of
these terms to the energies of the ro-vibrational states of
high J and k quantum numbers is significant.

2- By the aid of a computer program, the frequencies of the
"pure" nuclear quadrupole resonances were calculated by
using the qu value of the ground state of Ref. (76) for
each of the ro-vibrational states selected in step 1. Then,
each of the calculated "pure" nuclear quadrupole frequencies
(8 or 1) was compared to the experimental frequencies
observed with the particular laser line. This greatly
reduced the number of possible values of J and k picked in
step 1. In some cases, more than one pair of B and y
frequencies belonging to different J and k fit a given pair
of experimental frequencies. In such a case, the B and Y
splitting was calculated, by the aid of a computer program,
for each of the possible J and k values and compared with
the given experimental splitting. The calculated doublet (B
and r) that had the minimum deviation in the splitting from
the experimental splitting was chosen. In this way, the J
and k assignment could be made without ambiguity. Finally,
the calculated frequencies were adjusted to fit the
experimental frequencies to calculate the qu values. In

some cases, the fitting gave qu values which showed a

136

considerable deviation from the qu value of the previously
identified vibrational state in the region of study (77).
In this case, the IR-RF DR transitions involved in the
fitting were left as unassigned transitions and their
frequencies are given in Appendix II.

The second of the previously mentioned difficulties met
in determining the qu values has been avoided by the

following:

. 79
51 "6 3

r, and 7’ ”pure" nuclear quadrupole resonances could be

l~ For the w +w infrared band of CF Br, the B, B’,

resolved for two different infrared transitions. Similarly,

81
l 3

r’ quartet could be resolved for one transition which made

for the w r G.St infrared band of CF Br the B, B’, r, and
it possible to obtain accurate qu values for each of the
pumped vibrational states in this band. An example of a
resolved 8, B’, y, and y’ quartet is shown in Fig. (31).

2- The PNQR of the w1 and the ground vibrational states of
CF379Br were observed as doublets and consequently for each
observed infrared transition in this band, the qu value for
each of the vibrational states involved in the transition
was determined from only one "pure" nuclear quadrupole
resonance. However, the qu value for the w1 fundamental of

379Br was first estimated from the vibrational dependence

CF
of qu for the w6 and we+w1 vibrational states. Then, the
qu values which showed a considerable deviation (~ 1 MHz)

from the qu values of the ground and wl vibrational states

137

139.0 140.0 141.0 142.0 143.0 144.0 145.0
I

 

 

 

 

5000.0 1 , 1 1 1 1 1 1 1 1 1
.11. V6+V1 2" V6 .11-
Q0(12.10)
-. v6 ..
.11- 96+V1 V6+V1 .11-
V5
3:
'6 «1- 41-
C
33
.5 q
0
..>.
S -I
B -1- 1-
0:
db 1.
.11- .11.
1 l 1 l 1 l 1 I 1 l 1
000 1 I I I I I I l I I I
139.0 140.0 141.0 142.0 143.0 144.0 1450

Frequency in MHZ

Fig. 31. An example of a resolved quartet in CFaBr.

Laser line: 9R(28) C02; sample pressure: 10 mTorr.

138

were omitted and the PNQR transitions that led to these qu
values were left as unassigned transitions.

The vibrational assignment was confirmed by using the
vibrational dependence of qu. The vibrational dependence
of all of the determined qu values is given in Table (25).

In the next section, the results are discussed for each
laser line.

99(25) co2 Laser Line: 1083.47878 cn’l

 

Sixty six IR-RF DR transitions were observed with the
9R(28) C02 laser line by tuning the laser within its gain
profile while sweeping the RF from l~500 MHz. Some of the
infrared transitions pumped with this laser line were
identified as Q-branch transitions belonging to the
w6+wl r we 79

3 1
of CF381Br. On the other hand, some pumped infrared

infrared band of CF Br and the w ~ G.St band

transitions could not be identified for the two reasons
mentioned in the previous section.

The IR transitions involving the we+w1 « w6 band in

79

CF3 Br are listed in Table (21). These infrared

transitions were previously identified in the IR-MW DR

experiment with the 9R(28) CO laser line (75). On the

2
other hand, O-branch transitions involving the w1 « G.St of

CF381Br were first identified in the present work and they

139

are given in Table (22). These O-branch transitions were
not observed in the IR-MW DR experiment (75). As shown in
Table (22), they involve very high J values and consequently
the frequencies of these transitions are too high to be
observed by the apparatus used by Jones et al. for the IR—MW
DR (75). However, confirmation of the very high J values in
Table (22) is obtained from Ref. (81) where it is shown that

81

band of CF Br

the ro-vibrational state of J = 66 in the w1 3

is pumped by the 9R(28) CO2 laser line.

The QO(34,25) transition given in Table (23) represents
a special case in which the "pure" nuclear quadrupole
resonances could be fit only to the rotational quantum
numbers of J = 34 and k = 25 for upper and lower states.
The qu values for the lower and upper vibrational states
differ from the qu value of the ground and wl vibrational

379Br by only about 1 MHz. respectively.

states of CF
However, the ro-vibrational frequency of this O-branch
transition is not predicted for any of the previously
identified infrared bands in this region and consequently
the vibrational assignment could not be made. Therefore,
this transition and consequently the vibrational states

involved in this Q-branch transition are indicated in Table

(23) as wx and wy.

140

93(30) 002 Laser Line: 1054.53514 cm—l

 

Thirty strong IR-RF DR transitions were observed with
the 9R(30) CO2 laser line. Jones et al. studied the IR-MW
DR spectra of CF

Br with the 9R(30) CO laser line (75).

3 2
They observed quite weak double resonance signals with this
laser line, and effects were only observed for the directly
pumped levels which were identified as we+w1 ~ we; QR(7,2),
-1, F = 17/2 . F = 17/2 and °R(7,3), +1. F = 17/2 . F =
17/2. The ”pure" nuclear quadrupole resonances of the
rotational states of these pumped R—branch transitions have
not been observed in the present work. This is attributed
to either of the following:

1- The fact that the "pure" nuclear quadrupole resonances of
the rotational states of these R-branch infrared transitions
satisfy the selection rules OF = 0 and OJ = :1 (i.e., OF s
OJ) and accordingly these transitions are expected to be
very weak.

2- The possibility that Jones et al. k assignment could be k
= 1 instead of k = 2. If this were true, the IR-RF DR would
show A ~A

l 2
IR-RF transitions are interpreted as the Al-A2 splitting for

splitting rather than PNQR. In Table (24) two

J = 7, k = l, 1 = +1 in the w6 vibrational state and J = 8,

k = 1, 1 +1 in the we+wl vibrational state. Additional
evidence for this assignment is the fact that the computed

ro-vibrational frequency of the infrared transition

141

we+wl . we; QR(7,1), 1 = +1 is 0.0053 cm”1 above the
frequency of the 9R(30) CO2 laser line whereas the ra-
vibrational frequencies of the QR(7,2), 1 = ~1 and QR(7,3),
1 = +1 are 0.0089 and 0.0099 cm-1 above the 9R(30) CO2 laser
line, respectively. The q values for the we and we+w1
states obtained in Table (24) are compared with the
previously determined values for the we vibrational state in
Table (25).

The PNQR for several Q-branch transitions involving the

79

e G.St infrared band of CF3 Br identified in the present

”1
work are shown in Table (24). These transitions were not
observed by Jones et al., undoubtedly because the J values
and hence the microwave frequencies are too high.

The final qu values for the we and the we+w1
vibrational states of CF379Br were assumed to be the
weighted averages of the qu values determined from the
Q0(11,11) and °0(12,10) transitions (Table 21). The qu
values for the w1 and the ground vibrational states of the
81Br and 79Br isotopic species of bromotrifluoromethane were
assumed to be the average of the qu values given in Tables
(22) and (24), respectively. The final qu values obtained
in the present study are given and compared with the results
of previous work in Table (25).

The center frequencies of the we+w1 + we band in

79 79

CF3 Br and w1 e G.St band in CF3 Br have been determined

142

by using the frequencies of the lasers used for pumping, the
rotational assignment of the present study, and the
rotational constants of References (75) and (77). Their

resulting values are given in Table (26). The center of the

81
"1 3

because the observed transitions of this band are of

band in CF Br could not be determined by this technique

sufficiently high J and k values that knowledge of high
order distortion constants is essential for meaningful

calculation.

 

143

Tables 21 to 26.

Symbolagare as follows:

we The experimental frequency. The sign of we has been

chosen to agree with that of wC

wC = E(J,k,F’) ~ E(J,k,F")
Ow = we - wC
SE(we) = The standard error in we derived from the fit of

the spectrum to a Lorentz lineshape.

qu = The quadrupole coupling constant.

o(w) = The root mean square deviation derived from the fit
of we to qu.

SE(qu) = The standard errors in qu derived from the fit of

we to qu.

144

Eli—2L-

99<25) 12c1502 Laser Line

 

79

1- IR Transitions Involving the we+wl r we Band in CF3 Br
1- Q0(11,11)
Lower State Transitions
F" F’ we/MHz we/MHz Ow/MHz SE(we)

9.5 10.5 ~270.552 ~270.559 0.007 0.0016
10.5 11.5 ~35.393 ~35.336 0.057 0.0041
11.5 12.5 270.183 270.178 0.005 0.0016

e0q = 617.948 MHz
0(w) = 0.033
SE(qu) = 0.053

Upper State Transitions

" 3
F F we/MHZ we/MHZ Ow/MHZ SE(we)

9.5 10.5 ~269.581 ~269.636 0.055 0.0020
10.5 11.5 -35.307 ~35.217 0.090 0.0006
11.5 12.5 269.210 269.258 0.048 0.0017

qu = 615.842 MHz
a(w) = 0.047
SE(qu) = 0.076

 

145

2- °0<12,10)

Lower State Transitions

F" F’ we/MHz
10.5 11.5 ~143.140
11.5 12.5 ~16.607(u)
12.5 13.5 141.996
qu = 617.569 MHz
o(w) = 0.045
SE(qu) = 0.139

Upper State Transitions

F" F’ we/MHz
10.5 11.5 ~142.545
11.5 12.5 ~16.607(u)
11.5 12.5 141.400
qu = 615.093 MHz
a(w) = 0.030

SE(qu)= 0.092

3-°0(14,5)

r" F’ we/MHz
12.5 13.5 74.674(u)
13.5 14.5 ------
14.5 15.5 ~75.166(u)
4- °0<15,2)

F” F’ we/MHz
13.5 14.5 145.335
14.5 15.5 -------
15.5 16.5 -145.729
These

Table gl-Contiaged.

we/MHZ

~143.177
~16.643
141.943

we/MHZ

~142.600
~16.579
141.377

*
'7
we/MHZ

74.687
-7.927
~75.355

n *
we/MHZ

146.731
14.028
146.800

Ow/MHZ SE(we)
0.037 0.0007
----- 0.0011
0 052 0.0009
Ow/MHZ SE(we)
0 055 0.0010
----- 0.0011
0 024 0.0007

we/an* SE(we)

74.403 0.002
—7.595 -----
-75.053 0.002

*
’
wc /MHz SE(we)

146.171
13.975
~146.238 0.002

0.002

frequencies were calculated by using the qu

values determined from IR transitions 1 and 2.

146

112121212;

9R(28) 12c160

2 Laser Line

 

81

11- IR Transitions Involving the v1 . G.St Band in CF3 Br

1— °o(54,41)

Lower State Transitions

F" F’ ve/MHZ vc/MHZ
52.5 53.5 -90.188 -90.246
53.5 54.5 2.383
54.5 55.5 90.065 90.029

qu = 516.551 MHz
o(v ) = 0.048

SE(qu) = 0.195

Upper State Transitions

F F ve/MHZ vC/MHZ
52.5 53.5 -89.852 -89.920
53.5 54.5 2.375
53.5 54.5 89.736 89.705

qu = 514.690 MHz
0(v) = 0.038
SE(qu) = 0.153

Ov/MHZ

0.058

0.036

Ov/MHZ

0.069

0.032

SE(ve)

0.0006

0.0004

SE(ve)

0.0007
0.0004

147

Tableggz Continued.

2— °o(67,26)

Lower State Transitions

F F ve/MHZ vC/MHZ
65.5 66.5 71.565 71.565
66.5 67.5 1.604
67.5 68.5 -71.655

qu = 516.228 MHz

Upper State Transitions

F F ve/Mflz vC/MHz
65.5 66.5 71.285 71.285
66.5 67.5 1.598
67.5 68.5 -71.375

qu = 514.208 MHz

3- °o(64,25)

Lower State Transitions

F" F’ ve/MHz vC/MHz
62.5 63.5 70.988 70.940
63.5 64.5 1.640
64.5 65.5 -71.036

qu = 516.954 MHz

Upper State Transitions

F" F’ ve/MHz vC/MHz
62.5 63.5 70.714 70.667
63.5 64.5 1.659
64.5 65.5 -70.761

qu = 514.961 MHz

SE(ve)

0.0012

SE(ve)

0.0015

SE(ve)

0.0012

SE(ve)

0.0010

148

12212_2§;

12C160

9R(28) 2

Laser Line

 

III- IR Transition: vy . "x ; QQ(34,25)

Lower State Transitions

F F ve/MHZ vC/MHZ
32.5 33.5 -89.363 -89.359
33.5 34.5 88.859 88.863

qu = 619.178 MHz
o(v) = 0.00388
SE(qu) = 0.01907

Upper State Transitions

F" F’ ve/MHZ vC/MHZ
32.5 33.5 -88.692 -88.686
33.5 34.5 88.192 88.197

809 = 614.530 MHz
o(v) = 0.00377
SE(qu) = 0.01851

Ov/MHZ

0.004
0.003

Av/MHZ

0.006
0.00 5

SE(ve)

0.0009
0.0008

SE(ve)

0.0007
0.0007

149

 

Table 24.
9R(30) 12C1602 Laser Line
I- v6+v1« v6 in CF3793r; QR(7,1)
(J,k,£) Al-Az Splittiing/MHz q/MHz
”6 (7,1,1) 192.802 3.44
v6+vl (8,1,1) 238.896 3.32

II- IR Transitions Involving the v1 ~ G.St Band in CF37gBr

1- °o<24,5)
Lower State Transitions

" 9
F F ve/MHz vC/MHZ

22.5 23.5 135.196(u) 135.136
23.5 24.5 ---- 8.186
24.5 25.5 135.196(u) -135.247

qu = 618.020 MHz

Upper State Transitions

N 0
F F ve/MHZ vc/MHz

22.5 23.5 134.848(u) 134.743
23.5 24.5 ---- 8.162
24.5 25.5 134.848(u) -134.853

qu = 616.428 MHz

 

150

Table 24-Continued.

2- QQ(18,18)
Lower State Transitions

" ’
F F ve/MRz vC/MHz

16.5 17.5 284.638(u) -284.722
17.5 18.5 ----- 23.062
18.5 19.5 284.638(u) 284.557

qu = 618.063 MHz

Upper State Transitions

F" F’ ve/MHz vc/MHz
16.5 17.5 283.766 -283.848
17.5 18.5 ------- 22.992
18.5 19.5 283.766 283.684

qu = 616.169 MHz

3- Q0(19,7)

Lower State Transitions

F" F’ ve/MHz vc/MHz
17.5 18.5 94.877(u) 94.700
18.5 19.5 ------ 7.346
19.5 20.5 94.877(u) -95.073

qu = 618.949 MHz

Upper State Transitions

F F ve/MHz vC/MHz
17.5 18.5 94.595(u) 94.400
18.5 19.5 ------ 7.325

19.5 20.5 94.595(u) -94.79
qu = 617.115 MHz

151

 

 

 

Table 25. Vibrational Dependence of e09.
a- Results of the present work
79
1 CF3 Br
Vibrational state qu/MHz Squ q/MHz
Ground state 618.3(6)
v1 616.6(5) -l.7
V6 617.900(2) -0.4 3.44
"6 + v1 615.538(3) -2.76 3.32
81
2 CF3 Br
Vibrational state qu/MRz 6qu
Ground state 516.6(4)
v1 514.6(4) -2.0
b- Results of the previous work
79 81
CF3 Br CF3 Br
Vibrational state qu/MHz qu/MHz
Cox et al. (53) Ground state 618.2(3) 516.6(3)
Smith et a1. (76) Ground state 618.32(7) 516.65(6)
v6 618.07(5) 516.7(2)
Sheridan et a1. (26) Ground state 619 517(3)
79 79
CF3 Br CF3 Br
qu/MRz q/MHz
Jones et al. (75) Ground state 6198
v6 6198 3.44
a
v6 + v1 619 3.44

a Constrained.

Infr

a-Results of the presen

1- v6+v1 + ”5 in 033793

CO2 Laser Line IR
9R(28) l-
2-
3..
4—
9R(30) 5-
. 79
2 v1 1n CF3 Br
C02 Laser Line IR
9R(30)

b-Comparison table for

1- Jones et al. (75)
IR-MW DR

2- Burczyk et a1. (77)
IR Spectroscopy

3— The present work
IR-RF DR

152

Table 26.

ared Band Centers.

t work

r

transition Band center/cm—1
Q0(11,11) 1083.529
°0(12,10) 1083.528
°0<14,5) 1083.530
°0(15,2) 1083.531
°R(7,l) 1083.533
Transition Band center/c;1
Q0(24,5) 1084.757

the values of the IR band centers

band centers of CF73 Br
Vl/Cm-l v6+vl/Cm-1
1083.530(1)
1084.763(2) 1083.525(4)
1084.767(10) 1083.530(10)

 

153

APPENDIX I

This Appendix lists the IR-RF DR frequencies that were
measured for the CF31 molecule but could not be assigned to
specific transitions. The standard errors of the fit
(SE(ve)) are given. For those that could not be fit to
Lorentz lineshapes, approximate frequencies determined from
recordings are given. The intensities of all of the
transitions are estimated as weak (W), medium (M), strong
(S), or very strong (VS).

9R(16) 12C1602 laser line:

 

ve /MHz SE(ve)
79.39941 (W) 0.00524
84.12802 (W) 0.00259
93.26048 (W) 0.00451
236.09058 (W) 0.01500
246.81381 (W) 0.01988

Transitions which could not be fit to Lorentgilineshape:

3.3 (W)

7.1 (M)
17.9 (M)
19.7 (M)
62.7 (W)
71.4 (M)
72.8 (W)
79.3 (W)
81.1 (W)
82.2 (M)
107.3 (W)
110.6 (W)
113.6 (W)
114.9 (W)
122.1 (W)

124.
131.
132.
135.
147.
151.
157.
158.
160.
170.
172.
174.
181.
188.
191.
195.
203.
219.
223.
224.
233.
250.
256.
267.
277.
336.
338.
409.
411.

wouwwnocomwnNr-ammwmwocoombmqmmqu

(W)
(W)
(W)
(W)
(W)
(W)
(M)
(M)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(W)
(M)
(W)

154

APPENDIlil-Continued

 

155

APPENDIX I-Continued

 

9R(14) 12C1602 laser line:
we /MHz SE(ve)
10.78500 (M) 0.00108
16.09170 (M) 0.01161
18.87773 (S) 0.00295
20.28594 (S) 0.00306
41.02812 (M) 0.01979
48.29538 (M) 0.02732
61.14550 (M) 0.00432
64.98473 (W) 0.00693
67.30167 (W) 0.01299
80.75207 (M) 0.01473
81.82329 (M) 0.01406
83.43083 (W) 0.00614
84.26147 (8) 0.00354
85.12497 (VS) 0.00359
86.82925 (S) 0.00366
87.53918 (VS) 0.00561
88.09761 (M) 0.01036
90.34253 (VS) 0.00431
92.34129 (M) 0.00402
93.05558 (VS) 0.00624
93.77403 (S) 0.00235
95.01933 (S) 0.00372
95.98800 (M) 0.00767
97.01642 (M) 0.00559
98.63788 (W) 0.01985
102.03404 (S) 0.00532
103.76356 (S) 0.00388
108.90148 (VS) 0.00151
110.30164 (S) 0.00245
111.60356 (S) 0.00891
112.54088 (S) 0.00681
113.97908 (W) 0.01760
115.92814 (W) 0.01291
141.88249 (M) 0.00788
145.08009 (M) 0.00953
146.34389 (M) 0.00855
150.18216 (W) 0.01416
151.83208 (W) 0.03117
154.56088 (M) 0.02109
158.10130 (W) 0.06149
160.41559 (S) 0.00207
164.80739 (M) 0.00464

156

APPEEDIX I-Continued

196.52702 (W) 0.00843
346.78549 (S) 0.02251
354.65503 (S) 0.00289
365.51877 (M) 0.00915

Transitions which could not be fit to Lorentg lineshape:

ve /MHz

22.8 (W)
32.4 (M)
38.3 (M)
121.05 (W)
123.325 (S)
124.5 (W)
125.4 (W)
128.575 (S)
130.3 (W)
131.7 (W)
134.0 (W)
136 (M)

H
w
00
mo:
~10!
0'

(M)

 

157

APPENDIX I-Continued

 

9R(18) 12c1602 laser line:
we /an SE(ve)
1.75037 (S) 0.00248
2.54825 (8) 0.00584
3.15538 (S) 0.00453
3.55192 (S) 0.00528
5.19595 (8) 0.00455
5.55287 (S) 0.00188
5.49595 (S) 0.01405
5.77872 (S) 0.00455
7.43445 (S) 0.00172
7.52045 (S) 0.00490
8.35911 (S) 0.00239
12.95141 (8) 0.00329
14.37457 (S) 0.00400
14.78755 (VS) 0.00228
15.52705 (VS) 0.00188
17.23540 (VS) 0.00209
19.14153 (VS) 0.00224
20.58500 (M) 0.00915
22.07720 (M) 0.01298
23.39808 (M) 0.03114
24.25051 (S) 0.00245
25.31410 (S) 0.00143
102.75480 (w) 0.00395
114.02329 (S) 0.00198
143.31094 (S) 0.00223
155.48551 (S) 0.00259
157.29990 (W) 0.01302
194.72590 (VS) 0.00043
197.90349 (VS) 0.00125
208.16431 (w) 0.00327
221.51378 (v) 0.00538
228.92920 (u) 0.00474
236.44687 (W) 0.01092
238.55555 (M) 0.00504
241.22580 (M) 0.00553
244.48970 (M) 0.01139
244.55951 (M) 0.02971
247.97134 (W) 0.00705
253.81480 (W) 0.00459
255.31509 (W) 0.00942
282.95755 (W) 0.00157
284.28281 (W) 0.00729

 

285.
286.
290.
291.
293.
298.
300.
303.
306.
308.
324.
326.
328.
346.
358.
369.
384.
387.
395.
414.
419.
419.
462.

Transitions which could not be fit to Lorentg lineshape:

V
e

10.
10.
12.
13.
13.

41281
14536
46121
81931
77301
51389
76331
74579
00269
74060
71301
17700
15610
02280
71371
88211
86380
66849
33438
53110
05051
89511
32629

/MHz

05

775
325
175
875

(W)
(S)
(W)
(W)
(W)
(M)
(M)
(M)
(W)
(M)
(W)
(W)
(W)
(M)
(M)
(M)
(W)
(M)
(S)
(M)
(M)
(M)
(M)

(W)
(M)
(M)
(M)
(M)

APPENDIng-Continued

OOOOOOOOOOOOOOOOOOOOOOO

.00814
.00184
.00878
.00920
.01095
.00575
.00383
.00434
.00706
.00282
.00582
.00245
.01237
.00525
.00301
.00395
.03030
.00838
.00316
.00363
.00895
.00907
.00717

'L‘ 'Zli

 

159

APPENDIX I-Continued

9R(20) 12C1602 laser line:

 

we /MHz SE(ve)
10.03475 (M) 0.00731
11.03977 (M) 0.00845
12.66774 (M) 0.00961 ,
17.03045 (S) 0.00130 L
106.98467 (S) 0.00397 .
111.26041 (S) 0.00461
119.39971 (S) 0.00319 5
123.87475 (S) 0.00408 E
221.43030 (S) 0.00679
230.16936 (S) 0.00468
231.40173 (S) 0.00374
240.44530 (S) 0.00444
286.33121 (W) 0.02726
336.62222 (W) 0.00605
346.47000 (W) 0.03450
395.89395 (M) 0.00545

Transitions which could not be fit to Lorentz lineshape:
ve /MHz

3.1 (M)
5.9 (S)
7.9 (M)
23.65 (M)
26.85 (W)
27.55 (W)
29.85 (W)

33.3 (W)

160

Apggnnlx I-Continued

 

93(12) 12c1602 laser line:
”e /MHz SE(ve)
1.30595 (S) 0.00525
2.71443 (S) 0.00514
4.35928 (VS) 0.00158
5.48833 (VS) 0 00125

23.01504 (w) 0.01499
24.85480 (W) 0.00377
27.85545 (VS) 0.00085
30.77917 (S) 0.00109
32.57552 (VS) 0 00054
34.12805 (S) 0.00127
35.75944 (W) 0.02271
38.04951 (VS) 0.00114
44.49709 (S) 0.00275
48.99081 (M) 0.01288
51.41951 (M) 0.00866

105 08743 (M) 0.02718

114 52535 (M) 0.00802

118.97429 (3) 0.02387

124.31244 (M) 0.01203

134.90259 (M) 0.00954

137 33981 (S) 0.00547

144.50210 (8) 0.03990

145.58554 (W) 0.01735

175.55092 (S) 0.00284

197.25042 (S) 0.00315

202.77908 (W) 0.10380

205 22861 (W) 0.01008

207.51524 (8) 0.01007

224 21298 (n) 0.03275

228.12201 (W) 0.01757

237.20215 (M) 0.00425

239.25930 (W) 0.01405

242 55083 (M) 0.00771

248.03970 (w) 0.04385

253.91154 (M) 0.01492

255 37151 (M) 0.10730

258.54429 (S) 0.00290

330.47031 (8) 0.02183

337.19599 (W) 0.01281

355 99222 (VS) 0.00105

 

161

APPENDIX I-Continued

 

 

9P(14) 12C1802 laser line:
ve /MHz SE(ve)
3.48741 (S) 0.00301
5.27004 (W) 0.02869
6.06461 (S) 0.00409
7.73173 (S) 0.00693
20.24265 (M) 0.01001
21.43012 (M) 0.00664
23.03408 (M) 0.00587
34.42984 (W) 0.01213
51.90020 (VS 0.00078
52.68767 (VS) 0.00067
62.92550 (W) 0.00793
63.34703 (W) 0.00850
64.65009 (M) 0.00148
66.99109 (M) 0.00175
72.56429 (S) 0.00061
89.52404 (W) 0.01994
90.69505 (VS) 0.00145
91.77461 (VS) 0.00071
94.35982 (W) 0.01941
97.18348 (VS) 0.00077
155.68477 (VS) 0.00238
175.90494 (VS) 0.00405
176.08075 (VS) 0.00332
237.52930 (W) 0.00466
253.37816 (W) 0.00852
254.35886 (M) 0.00202
273.6346? (M) 0.00435
284.34473 (8) 0.00234

162

APPENDIX I-Continued

 

9P(16) 1201802 laser line:
we /MHZ SE(ve)
12.55701 (M) 0.02028
53.11254 (M) 0.00304
57.71825 (VS) 0.00253
78.51955 (M) 0.03094
85.33128 (w) 0.03952
85.40005 (w) 0.02888
88.52237 (W) 0.00954
131 59885 (VS) 0.00775
131.57915 (VS) 0.00571
134 39302 (W) 0.01135
148.49808 (W) 0.02857
152.75484 (w) 0.01302
153.04885 (W) 0.00898

163

APPENDIX I-Continued

 

99(12) 1201802 laser line:
ve /MHz SE(ve)
10.37225 (VS) 0.00301
19.88417 (VS) 0.00108
91.81348 (VS) 0.00084
94.38731 (VS) 0.00085
95.50073 (S) 0.00277
95.54290 (w) 0.00733
98.55257 (w) 0 00559
99.53514 (VS) 0.00101
100.1235 (S) 0.00091
101.11908 (S) 0.00205
102.18354 (W) 0.02055
103.51473 (VS) 0.00168
105.29781 (S) 0.00527
110.08083 (S) 0.00374
114.75524 (w) 0.00508
115.41879 (W) 0.04049
115.53754 (W) 0.01575
117 78757 (VS) 0.00285
118.22874 (VS) 0.00309
122 00111 (M) 0.01544
122.75554 (M) 0.02701
125.51309 (w) 0.00905
128.54539 (W) 0.00572
129.17454 (W) 0.01414
130.19170 (VS) 0.00122
130.57458 (VS) 0.00135
131.70044 (S) 0.00054
134 71931 (M) 0.00257
137.35423 (M) 0.00215
137.99854 (M) 0.00559
138.31319 (M) 0.74823
138.55471 (M) 0.00315
193 53792 (VS) 0.00195
194.15321 (VS) 0.00191
202.09349 (VS) 0.00193
202.74853 (VS) 0.00191
217.25403 (S) 0.00254
218.19589 (S) 0.00240
229.31429 (S) 0.00484
230 29955 (S) 0.00409
243.01157 (VS) 0.00255
243.39917 (VS) 0.00244

244.76527
249.79343
277.16916
277.61414

(W)
(W)
(VS)
(V8)

164

APPENDIX I-Continued

 

0.01831
0.03615
0.00198
0.00199

 

165

APPENDIX 11

 

This appendix lists the IR-RF DR frequencies that were
measured for the CF3Br molecule but could not be assigned to
specific transitions.

The standard errors for the fit SE(ve) are given. The

intensities from recordings are given. The intensities of

all of the transitions are estimated as very weak (VW), weak

(W), medium (M), strong (S), and very strong (VS).

 

 

9R(28) 12C1602 Laser Line:
ve/MHz SE(ve)
12.46505 (S) 0.00140
12.84320 (S) 0.00106
16.60721 (S) 0.00113
17.53615 (VW) 0.00293
22.98377 (VS) 0.00180
27.31055 (VS) 0.00086
29.17175 (M) 0.02645
30.14487 (M) 0.00811
31.06166 (W) 0.01559
31.42408 (W) 0.01863
32.95966 (M) 0.00711
33.49276 (M) 0.00370
34.83364 (M) 0.00571
45.58841 (VS) 0.00101
58.27822 (S) 0.00302
59.20430 (S) 0.00274
69.89377 (VS) 0.00083
88.19250 (VS) 0.00066
88.69616 (VS) 0.00071
88.85931 (VS) 0.00075
89.18907 (VW) 0.00589

APPENDIX II-Continued

ve/MHZ

89.
101.
101.
101.
102.
115.
116.
116.
117.
117.
118.
121.
127.
134.
135.
136.
137.
149.
163.
163.
174.
256.

36290
14641
41376
95217
21427
13242
63162
95482
49816
82005
60471
65781
85382
74397
13599
68994
04987
32027
21086
66090
49181
46246

OOOOOOOOOOOOOOOOOOOOOO

SE(ve)

.00086
.00147
.00134
.00146
.00134
.00867
.00124
.00120
.00119
.00132
.00656
.00341
.00501
.00330
.00273
.00431
.00490
.00118
.00171
.00164
.00224
.00131

 

APPENDIX II- Continued

167

 

 

9R(30) 12C1602 Laser Line:
ve/MHZ SE(ve)
6.56137 (M) 0.01179
7.63280 (M) 0.01085
8.36769 (VS) 0.00339
11.44670 (M) 0.00719
13.32852 (VS) 0.00244
16.68692 (VW) 0.08615
19.52195 (VS) 0.00384
22.88336 (VS) 0.00158
34.76738 (VS) 0.00142
44.83219 (VS) 0.00374
45.02621 (VS) 0.00155
49.48568 (VS) 0.00444
55.56409 (VS) 0.00425
63.93912 (VS) 0.00354
70.94064 (VS) 0.00052
71.15897 (VS) 0.00049
86.43337 (VS) 0.00073
91.16479 (M) 0.00077
93.28502 (VS) 0.00064
93.96255 (VS) 0.00068
95.40957 (VS) 0.00106
96.41935 (VS) 0.00121
100.41157 (VW) 0.01940
102.32102 (M) 0.00448
104.06727 (W) 0.00752
112.05141 (M) 0.00387
141.88127 (VS) 0.00072
142.32155 (VS) 0.00070
145.83374 (VS) 0.00070
146.79022 (VS) 0.00068
152.5367] (M) 0.00212
155.24998 (M) 0.00485
157.05867 (W) 0.00818
168.68321 (VS) 0.00121
172.42006 (VS) 0.00117
219.42909 (M) 0.00555
232.48306 (M) 0.00663
241.49028 (M) 0.00932

10.

11.

12.

13.
14.
15.

16.

168

REFERENCES

R. C. Allen and P. C. Cross, Molecular Vib-Rotors: The
Theory of Interpretation of High Resolution Infrared
Spectra (John Wiley and Sons, Inc., N.Y. 1963).

M. Born and J. R. Oppenheimer, An. Physik, 84, 457
(1937).

E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular
Vibrations: The Theory of Infrared and Raman Spectra
(McGraw-Hill Book Co., Inc., N.Y. 1955).

H. W. Kroto, Molecular Rotation Spectra (John Wiley,
Sons, N.Y. 1975).

R. Eyring, J. Walter, and G. Kimball, Quantum Chemistry
(John Wiley and Sons, Inc., N.Y. 1944).

A. C. Costain, J. Chem. Phys. 23, 2037 (1955).
E. B. Wilson, Jr. J. Chem. Phys. 21, 986 (1957).

R. C. Johnson, Q. Williams, and T. L. Weatherly, J.
Chem. Phys. 36, 1588 (1962).

G. Herzberg, Molecular Spectra and Molecular Structure:
Infrared and Raman Spectra of Polyatomic Molecules (D.
Van Nostrand 11 Company, Inc., N.Y. 1949).

C. H. Townes and A. L. Schawlow, Microwave Spectroscopy
(Dover Publications, Inc., N.Y. 1975).

N. F. Ramsey, Nuclear Moments (Wiley, Sons, New York,
1953).

L. D. Landau, and E. M. Lifshitz, Quantum Mechanics
(Pergamon, 1956).

G. Racah, Phys. Rev. 1, 186 (1942).

O)

G. Racah, Phys. Rev. 2, 438 (1942).

G. Racah, Phys. Rev. _3, 367 (1943).
E. P. Wigner, Group Theory and its Application to

Quantum Mechanics of Atomic Spectra (Academic Press,
N.Y. 1959).

17.

18.

19.

20.

21.

22.

23.

24.
25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

169

M. Tinkham, Group Theory and Quantum Mechanics (McGraw—
Hill, 1964).

M. E. Rose, Elementary Theory of Angular Momentum,
Wiley, N.Y. 1957).

C. H. Townes and B. P. Dailey, J. Chem. Phys. 11, 782
(1949).
B. P. Dailey and C. H. Townes, J. Chem. Phys. 23, 118

(1955).

B. P. Dailey, J. Chem. Phys. 3, 1641 (1960).

R. H. Schwendeman and G. D. Jacobs, J. Chem. Phys.
36, 1251 (1962).

T. P. Das and E. L. Hahn, Nuclear Quadrupole
Spectroscopy, Academic Press, N.Y. 1958).

F. Streezer and Y. Beers Phys. Rev. 100, 1174 (1955).

H. H. Nielsen, Phys. Rev. 11, 130 (1950).

J. Sheridan and W. Gordy, J. Chem. Phys. _0, 591
(1952).
W. F. Edgell and C. E. May, J. Chem. Phys. 2, 1808

(1954).

H. G. Dehmelt and H. Kruger, Naturwiss. _1, 111
(1950).

Y. Beers and S. Weisbaum, Phys. Rev. 91, 1014 (1953).

Weisbaum, Y. Beers, and J. Herrmann, J. Chem. Phys.
3, 1601 (1955).

N0)

B. Petersen, J. Tiee and C. Wittig, Optics. Commun.
, 259 (1976).

U! H>
o q.

Bittenson and P. L. Houston, J. Chem. Phys. 61,
4819 (1977).

C. N. Plum and P. L. Houston, Appl. Phys.
(1981).

4, 143

As. S. Sudbo, P. A. Schulz, E. R. Grant, Y. R. Shen,
and Y. T. Lee, J. Chem. Phys. 10, 912 (1979).

M. Quack J. Chem. Phys. 59, 1282 (1978).

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

170

M. Quack, Ber. Bunsenges. Phys. Chem. 33,757 (1979).

M. Quack, Ber. Bunsenges. Phys. Chem. 33, 1287
(1979).

M. Quack, Ber. Bunsenges. Phys. Chem. 82, 1252
(1978).

 

M. Quack, J. Chem. Phys. 13, 1069 (1979).
M. Quack and G. Seyfang, J. Chem. Phys. 13, 955
(1982).

W. B. Person, S. K. Rudys, and J. H. Newton, J. Phys.
Chem. 13, 2525 (1975).

M. Rossi, J. R. Barker and D. M. Golden, Chem. Phys.
Lett. 33, 523 (1979).

D. M. Golden, M. J. Rossi, A. C. Baldwin, and J. R.
Barker, Acc. Chem. Res. 13, 56 (1981).

V. N. Bagratashvili, V. S. Dolzhikov, V. S. Letokhov,
A. A. Makarov, E. A. Ryabov, and V. V. Tyakht, Sov.
Phys. TETP 59. 1075 (1979).

W. FuB and W. E. Schmid, Ber. Bunsenges. Phys. Chem.
33, 1148 (1979).

M. Quack, Chimia 33, 463 (1981).
T. G. Abzianidze, A. S. Egiazarov, A. K. Petrov, and
Nu. N. Samsonov, Sov. J. Quantum Electron. 1;, 343

(1981).

M. Quack and G. Seyfang, Chem Phys. Lett. _3, 442
(1982).

M. Quack and E. Sutcliffe, Chem. Phys. Lett. 33, 167
(1983).

H. Jones and F. Kohler, J. Mol. Spectrosc. 33, 125
(1975).

D. J. Bedwell and G. Duxbury, Chem. Phys.
(1979).

7, 445

F. Kohler, H. Jones, and H. D. Rudolph, J. Mol.
Spectrosc. 33, 56 (1980).

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66.

67.

68.

69.

70.

171
A. P. Cox, G. Duxbury, J. A. Hardy, and Y. Kawashima,
J. Chem. Soc. Faraday Trans. 2, 13, 339 (1980).

H. H. Ritze and V. Stert, J. Mol. Spectrosc. 33, 215
(1982).

E. Ibisch and U. Andresen, Z. Naturforsch. 37a, 371
(1982).

 

W. Fuss, Spectrochimia Acta 38A, 829 (1982).

S. W. Walters and D. H. Whiffen, J. Chem. Soc. Faraday
Trans. 2, 13, 941 (1983).

V. A. Bugaev and E. P. Shliteris, Sov. J. Quantum
Electron. 13, 404 (1983).

H. Burger, K. Burczyk, H. Hollenstein and M. Quack,
Mol. Phys. 33, 255 (1985).

E. Arimondo, P. Glorieux, and T. Oka, Phys. Rev. _1,
1375 (1978).

E. Arimondo, J. G. Baker, P. Glorieux, and T. Oka, J.
Mol. Spectrosc. 33, 54 (1980).

E. Arimondo, P. Glorieux, and T. Oka, J. Mol.
Spectrosc. 33, 559 (1980).

E. Arimondo, P. Glorieux, and T. Oka, J. Mol.
Spectrosc. 109, 412 (1985).

F. Scappini, W. A. Kreiner, J. M. Frye, and T. Oka, J.
Mol. Spectrosc. 106, 436 (1984).

S. M. Freund, M. Romheld, and T. Oka, Phys. Rev. Lett.
3_, 1497 (1975).

M. Takami, J. Chem. Phys. 11, 4164 (1979).
73, 2665 (1980).

M. Takami, J. Chem. Phys.

For a summary, see T. Oka, "Molecular Spectroscopy:
Modern Research, II" (K. Narahari Rao, Ed.), pp. 229-
253, Academic Press, N.Y. 1976.

R. M. Dale, J. W. C. Johns , A. R. W. McKellar, and M.
Riggin, J. Mol. Spectrosc. 31, 440 (1977).

E. Arimondo, P. Glorieux, and T. Oka, Opt. Commun.
33, 369 (1977).

 

71.

72.

73.

74.

75.

76.

77.

78.

79.

80.

81.

82.

172

P. Glorieux and G. W. Hills, J. Mol. Spectrosc. 13,
459 (1978).

H. P. Benz, A. Bauder, and Hs. H. Gunthard, J. Mol.
Spectrosc. 31, 156 (1966).

A. R. Edmonds, Angular Momentum in Quantum Mechanics
(Princeton, N.J., Princeton, University Press, 1960).

A. H. Sharbaugh, B. S. Pritchard and T. C. Madison,
Phys. Rev. 11, 302L (1950).

H. Jones, F. Kohler, and H. D. Rudolph, J. Mol.
Spectrosc. 33, 205 (1976).

J. H. Carpenter, J. D. Muse, and J. G. Smith, J. Chem.
Soc., Faraday Trans. 2, 13, 139 (1982).

7.

K. Burczyk and H. Burger, J. Mol. Spectrosc.
109 (1979).

A. Baldacci, A. Passerini, and S. Ghersetti, J. Mol.
Spectrosc. 31, 103 (1982).

M. Neve de Mevergnies and P. del Marmol, J. Chem. Phys.
13, 3011 (1980).

M. Gauthier, W. S. Nip, P. A. Hackett, and C. Willis,
J. Chem. Phys. Lett. 33, 372 (1980).

J. M. Lourtioz, C. Meyer, Rev. Infrared Millimeter
Waves 3, 53 (1984).

J. Pontnau, J. M. Lourtioz, C. Meyer, I. E. E. E. J.
Quantum Electron. QE-15, 1088 (1979).