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MSU In An AMrmdive AotlonlEquel Opportunity Institution

 

 

Hlfll RESOLUTION INFRARED SPECTROSCOPY

0F Cfléf, CD31, AND CD Dr AND

3
INFRARED—RADIOFREQUENCY DOUBLE RESONANCE SPECTROSCOPY
0F CD31 AND CD3Br
By

Han—Gook Cho

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1989

moonw-

ABSTRACT

HIGH RESOLUTION INFRARED SPECTROSCOPY
OF CR3F, CD31, AND CDBBr AND
INFRARED-RADIOFREOUENCY DOUBLE RESONANCE SPECTROSCOPY

0? CD31 AND CD3Br

BY

Han-Cook Cho

The v3+v6-v6 band of CH3F and the v2 bands of CD31 and CD3Br have
been recorded by means of an infrared microwave sideband laser (IMSL)
spectrometer and analyzed by vibration-rotation theory including
coupling with nearby vibrational states. The frequency measurement and
analysis were performed in order to obtain frequency information for
subsequent double resonance studies as well as to investigate the effect
of various energy couplings. It has been possible to record the
lineshapes of high J and K transitions at Doppler-limited resolution and
to use the measured frequencies to determine molecular constants
including high order centrifugal distortion constants for the ground and
excited vibrational states. In the infrared spectrum of CHBF the high
resolution allowed, in addition to the measurement of conventional
transitions, the observation of 14 l-type doublets between two
degenerate vibrational states. As a result, the infrared frequencies in
the 03+96-v6 band can be reproduced with the molecular constants to

within a few MHz, which is accurate enough for most double resonance

studies. In CD31 and CDBBr analysis of the v2 vibration-rotation

ii

structure also led to molecular constants that can predict the
frequencies to within a few MHz. These frequencies were used for double
resonance experiments in this work.

Infrared-radiofrequency double resonance, which has already been
recognized as a very sensitive and precise method for the observation of
various hyperfine energy structures, was used to record pure quadrupole
transitions of CD31 and C038r for the ground and the v2 vibrational
states. The data were analyzed by means of exact diagonalization of the
total Hamiltonian matrix composed of the rotational and quadrupole
interaction parts. The IMBL spectrometer employed as the infrared
pumping source had sufficient tunability to make it possible to select
for study an appropriate set of transitions without having to depend on
accidental coincidences with laser lines. Consequently, it was possible
to make precise measurements of a large number of transitions and to
determine the spin-rotation constants as well as the centrifugal
distortion constants for the quadrupole coupling in these molecules.

During the fitting of the frequencies of the pure quadrupole
spectra, it became evident that some effect was causing an apparent
shift of the transitions, especially at low RF-frequencies. The shift
has been traced to a double—resonance effect that appears in
calculations when four interacting levels are taken into account, but is
not evident in calculations based on the usual three-level system
employed for double-resonance theory. An appropriate linear equation
was set up in the density matrix fbrmalism for the four-interacting-
level system, and solved at each RF-frequency for a sequence of values
of the molecular velocity and for a fixed value of the laser frequency.

The agreement between the experimental and the calculated spectra

iii

obtained for both the frequency shift and the distorted lineshape

strongly confirms the four-interacting-level double-resonance effect.

iv

To the Memory of Bo-Kyoung

ACKNOWLEDGMENTS

I would like to thank Dr. R. H. Schwendeman for his guidance and
encouragement throughout the course of this study and the preparation of
this thesis. I wish to thank the other members of our group for their
cooperation in the laboratory.

The partial support from the National Science Foundation is

gratefully acknowledged.

vi

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . x
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . xii

CHAPTER I INTRODUCTION . . . . . . . . . . . . . . . . . . . 1

CHAPTER II HIGH RESOLUTION INFRARED STUDY OF THE D +v -v

12 3 6 6
BAND OF CH3F . . . . . . . . . . . . . . . . . . 6
11-1 Introduction . . . . . . . . . . . . . . . . . . . . 6

11-2 Theory . . . . . . . . . . . . . . . . . . . . . . . 10
II-2-l Hamiltonian for Harmonic Oscillator-Rigid Rotor
Approximation . . . . . . . . . . . . . . . . . ll
II-2-l-l Harmonic Oscillator . . . . . . . . . . . . 12
II-2-l-2 Rigid Rotor . . . . . . . . . . . . . . . . 16
II-2-2 Selection Rules . . . . . . . . . . . . . . . . 22
11-2-3 Nonrigid Symmetric Top Molecules . . . . . . . . 27
II-2-3-l Centrifugal Distortion . . . . . . . . . . 27
II-2-3-2 Coriolis Interaction . . . . . . . . . . . 3O
II-2-3-3 Rotational l-type Resonance Interaction . . 35
11-3 Experimental . . . . . . . . . . . . . . . . . . . . 40
II-3-l White-Type Long Path Cell . . . . . . . . . . . 40
II-3-2 Infrared-Microwave Sideband Laser Spectrometer . 43
11-4 Results . . . . . . . . . . . . . . . . . . . . . . . 49
II-4-l Term Values and Selection Rules . . . . . . . . 49
11-4-2 Analysis . . . . . . . . . . . . . . . . . . . . 52
11-5 Discussion . . . . . . . . . . . . . . . . . . . . . 65
11-6 Appendix . . . . . . . . . . . . . . . . . . . . . . 69
11-? References . . . . . . . . . . . . . . . . . . . . . 71

CHAPTER III HIGH RESOLUTION INFRARED SPECTROSCOPY OF THE v2
BANDS 0? CD31 AND CD3Br . . . . . . . . . . . . . 73
III-l Introduction . . . . . . . . . . . . . . . . . . . . 73
III-2 Theory . . . . . . . . . . . . . . . . . . . . . . . 79

III-2-l Term Values . . . . . . . . . . . . . . . . . . 79

vii

III-2-2 Coriolis Interaction
III-2-2-l CD31
III-2-2-2 CD38r . . . . . . . . . . . . .
III-2—3 Effect of Nuclear Quadrupole Coupling .
III-2-4 Hypothetical Unsplit Frequencies
III-2-4-1 CD31 .
III-2-4—2 CD33r
III-3 Experimental .
III-4 Results
III-4-l CD I

3

III-4-2 CD3Br .

III-5 Discussion .
III-5-1 CD31

III-5-2 CDBBr .

III-6 References .

CHAPTER IV INFRARED-RADIOFREQUENCY DOUBLE RESONANCE OF CDBI
AND CD3Br
IV-l Introduction
IV-l-l CD31 .
IV-l-2 CD3Br
IV-2 Theory
IV-2—l IR-RF Double Resonance .
IV-2-2 Nuclear Quadrupole Coupling
IV-2—3 Irreducible Tensor Method
IV-2-4 Quadrupole Interaction Energy
IV-2-5 Quadrupole Coupling of CD31 and CD38r
IV-3 Experimental
IV~4 Results and Discussion
IV-4-l CD I .

3
IV-4-2 CD3Br
IV-4-3 Other Aspects
IV-5 Appendix

IV—6 References

viii

79
80
82

EEEEB

91
91
97
121
121
124
125

127
127
131
132
135
135
137
141
142
145
148
155
155
163
173
177
178

CHAPTER V FOUR-INTERACTING-LEVEL DOUBLE RESONANCE . . . . . . 181
V-l Introduction . . . . . . . . . . . . . . . . . . . . . 181
V-2 Theory . . . . . . . . . . . . . . . . . . . . . . . . 185
V-3 Results and Discussion . . . . . . . . . . . . . . . . 192
V-4 References . . . . . . . . . . . . . . . . . . . . . . 198

ix

LIST OF TABLES

Table
2-1 Observed Transition Frequencies from R-type Doublets of
12
the v3+v6 ”6 Band of CH3F
2-2 Comparison of Observed and Calculated Frequencies in
12
the v3+v6 v6 Band of CH3F

1 State of 12CH3F

2-3 Molecular Constants of the v6

2-4 Molecular Constants of the v3

4 State of lzcngr

1, v6 = 1 Vibrational

2-5 Coincidences between Calculated Frequencies for the

12

v3+06-v6 Band of CH3F and Laser Frequenc1es

3-1 Comparison of Observed and Calculated Frequencies in
the v2 Band of CD31

3-2 Comparison of Ground State Rotational Constants of
CD31 . . . .

3-3 Molecular Constants of the v2 1 State of CD31 without

Coriolis Correction

3-4 Molecular Constants of the v2 1 State of CD31 with

Coriolis Correction

3-5 Coincidences between Calculated Frequencies for the v2

Band of CD31 and Laser Frequencies .

3-6 Comparison of Observed and Calculated Frequencies in

the v Band of CD 79Br . . . . . . . . . . . . .

2 3

Page

55

58

63

64

67

92

98

99

100

101

104

3-8

3-9

3-10

3-11

4-6

4-7

4-8

4-9

Comparison of Observed and Calculated Frequencies in
the 0 Band of CD 81Br .

2 3

Molecular Constants of CD37gBr .

Molecular Constants of CD3813r .......

Coincidences between Calculated Frequencies for the v

Band of CD37QBr and Laser Frequencies

2

Coincidences between Calculated Frequencies for the v2

Band of CD381Br and Laser Frequencies

Pure Quadrupole Frequencies of CD31

Infrared Pumping Frequencies for IR—RF Double

Resonances of CD31 . . . . . . . . . . . . .

Quadrupole and Spin-Rotation Interaction Parameters of

CD31 .

Pure Quadrupole Frequencies of CD37gBr

Pure Quadrupole Frequencies of CD38lBr

Quadrupole and Spin-Rotation Interaction Parameters of

79
CD3 Br .......................

Quadrupole and Spin-Rotation Interaction Parameters of

81
CD3 Br . . . . . . . . ..........
F = J+1/2 . F = J-1/2 Transitions of CD37QBr .
F = J+1/2 . F = J—1/2 Transitions of CD 81Br .

3

xi

109

114

115

117

119

157

161

162

164

.1167

170

171

174

175

LIST OF FIGURES
Figure Page

2-1 Symmetry properties of rotational levels of molecules
with a three-fold axis; (a) in a totally symmetric
vibrational state, (b) in a degenerate vibrational state.

The arrows show allowed transitions. . . . . . . . . . . 28

2-2 The rovibronic levels with K = 1 and J = 1,2 for vibronic
E-states of a molecule of symmetry C3v' The transitions
indicated by solid arrows are allowed; those indicated by

dashed arrows are not. . . . . . . . . . . . . . . . . . 29

2-3 Coriolis forces during the degenerate vibration of an X3

molecule. . . . . . . . . . . . . . . . . . . . . . . . 32

2-4 Diagrammatic representation of the x,y—Coriolis coupling
of the states with J = 3 and with the same k-lt. The
dotted line connects states exhibiting giant l-type
doubling. . . . . . . . . . . . . . . . . . . . . . . . 32

2-5 qé+), qé-), and rt l-resonance in an It = :1 degenerate
state of an oblate symmetric top. The levels are labeled
by K, with (+1) to the left of (-1); interactions are

shown by broken lines. . . . . . . . . . . . . . . . . . 39

2-6 Mirror arrangement of a White-type cell. The small
circles on mirror surface are the centers of curvature of

the mirrors. . . . . . . . . . . . . . . . . . . . . . . 41

2-7 Modified optical arrangement for a White-type cell. The

numbers show the sequence of reflection. . . . . . . . . 41

2-8 Block diagram of the infrared microwave Sideband laser

xii

2-10

2-11

3-1

3-2

used in this study. . . . . ............ . . . 44

Portion of the spectrum of the v3+v6-v6 band Observed in

the present work. The horizontal axis is the microwave

frequency to be added to (+) or subtracted from (-) the
12 16

frequency of the 9P(12) C 02 laser to obtain the

infrared frequency of the transition. . . . . . . . . . 46

Portion of the spectrum of the v3+v6-06 band observed in
the present work. The horizontal axis is the microwave
frequency to be added to (+) or subtracted from (-) the
frequency of the 9P(6) 12C16O2 laser to obtain the
infrared frequency of the transition. The transition
marked 2123 is in the 2123-1)3 band and completely absorbs

the positive sideband power. ........... . . . 47

Energy-level diagrams showing higher frequency

(solid lines) and lower frequency (dashed lines) allowed
transitions between rotational levels belonging to two
vibrational states of E symmetry for C3v. For each of

the diagrams, the J value of the levels in the lower

state is assumed to be odd and the qv value of the lower
state is assumed to be positive; the sign of the qv value

(qu) for the rotational levels of the upper state is

indicated above each diagram. ........ . . . . . 51

Block diagram of the infrared microwave sideband laser
spectrometer used to record the Doppler-limited vibration-

rotation spectra in this work. ...... . . . . . . 88

A portion of the infrared spectrum of the 02 band of CD31

recorded by the infrared microwave sideband laser

spectrometer. The microwave frequency on the horizontal

axis is added to (+) or subtracted from (-) the frequency
12 16

of the 10P(28) C 02 laser to obtain the infrared

xiii

3-3

frequency. The sample pressure was 0.3 Torr and a l-m

path length was used. ....... . ...... . . . 89

A small portion of the spectrum in the v2 band region of
CD3Br showing the typical lineshapes and signal/noise
obtained for the spectra reported. The horizontal scale
is the microwave frequency that must be subtracted from
the frequency of the 12C1602 10(28) laser to obtain the
infrared frequency of the transitions. Transitions of

CD379Br and CD3BIBr occur approximately alternately
everywhere in this region. .............. . 90

Three level system showing double resonance technique.
The infrared radiation pumps molecules from ll) to l2)
according to the Doppler shift resonance condition v12 =
vIR(1tv/c) which appears as "holes" in the Maxwellian
velocity profile of ll) and "spikes" in |2>. The
radiofrequency will then transfer the "spikes" from |2>
to [3) creating deeper "holes" in ll). This causes an
increase in the molecular absorption. The radiofrequency
transition from l2) to l3) can thus be observed by

detecting the infrared radiation. . . . . . . . . . . . 136

Block diagram of the infrared radiofrequency double-
resonance spectrometer used to record the pure quadrupole
transitions in this work. An infrared microwave sideband
laser in the cavity mode serves as the infrared pumping
source. A radiofrequency synthesizer whose output is
chopped by a double-balanced mixer and amplified serves

as the radiofrequency source. ....... . . . . . . 149

A portion of the infrared radiofrequency double resonance
spectrum obtained by pumping the P(22,5) transition in
the v band of CD I. The F quantum numbers of the

2 3
transitions in the upper and lower states of the

xiv

4-4

5-1

vibration-rotation transition are shown. The horizontal
axis is the absolute radiofrequency. the sample pressure

was 3 mTorr and l-m path length was used. ..... . . 152

Example of infrared radiofrequency double resonance
spectra obtained in the present study for CD3798r. For
these transitions, the infrared sideband laser source was
tuned to the center frequency of the Doppler-limited
lineshape of the P(22,6) transition in the 02 hand. For
the infrared microwave sideband laser source, the 10R(26)
1201602 laser was used with a microwave frequency of

11726 MHz; the lower frequency sideband was used. . . . 153

Example of infrared radiofrequency double resonance
spectra obtained in the present study for CD3alBr. For
these transitions, the infrared sideband laser source was
tuned to the center frequency of the Doppler-limited

2 hand. For
the infrared microwave sideband laser source, the 10R(18)

1201602 laser was used with a microwave frequency of 9747

lineshape of the P(30,6) transition in the v

MHz; the lower frequency sideband was used. . . . . . . 154

Typical energy level pattern for the infrared
radiofrequency double resonances observed for CD31. In
most cases, a single infrared frequency pumps all of the
allowed infrared transitions by interacting with molecules

in different velocity groups. . . . . . . . . . . . . . 156

Typical energy level pattern for the infrared
radiofrequency double resonance observed for CD3Br. A
single infrared frequency pumps all of the allowed
infrared transitions by interacting with molecules in
different velocity groups. In general, four high-
frequency an two low-frequency double resonances were

observed for each infrared transition. . . . . . . . . . 182

XV

5-2

5-3

Energy level diagram for the four-interacting-level double

resonance system. . . . . . . . . . . . . . . . . . . . 183

Comparison of observed and calculated infrared
radiofrequency double resonance spectra for a four-
interacting—level double resonance system. The upper
trace is the calculated spectrum and the lower trace is
the observed spectrum. The points below each trace are
the residuals obtained when the lineshape is fitted by
least squares to a sum of two Lorentz lineshapes. The
experimental spectrum was observed with a sample pressure
of 4 mTorr, infrared power ~2 mW, and radiofrequency power
~20 aw. The theoretical spectrum was calculated by means
of Equation (5-26) with all xi = 20 kHz and with kd = k0 =
100 kHz. For the experimental spectrum, the infrared
frequency was set at the center frequency of the Doppler-
limited lineshape of the P(26,4) transition in the v2 band
of CD37QBr; the 10R(22) 12C1602 laser was used with the
lower frequency sideband generated by a microwave

frequency of 12632 MHz. . . . . . . . . . . . . . . . . 194

Plot of the frequency shift caused by the four-
interacting-level double resonance effect against the
assumed frequency splitting between the two lower
frequency hyperfine transitions for the conditions
described in Fig. 5-3. The vertical axis is the
difference in frequency between the center of the best
Lorentz line approximation to the calculated lineshape
and the assumed hyperfine frequency for the lower-
frequency component of the infrared radiofrequency
double resonance doublet. All of the conditions for
the calculated lineshape in Fig. 5—3 apply, except that
the difference between the hyperfine frequency in the

upper vibrational state (vcd) and that in the lower

xvi

vibrational state (vba) is varied. This difference

is plotted on the horizontal axis. . . . . . . . . . . . 196

xvii

CHAPTER I

INTRODUCTION

Studies of the vibrational-rotational spectra of polyatomic
molecules in the gaseous phase provide considerable information
including intermolecular distances and angles, the vibrational
frequencies and force constants, dissociation energies, and other data
concerning the structures of the molecules. The information attainable
from studies of the vibrational-rotational spectra of polyatomic
molecules has recently been greatly increased by the advent of laser
spectroscopy and by considerable progress in the theoretical and
experimental studies of the fine structure of the vibrational-rotational
spectra of molecules. For the research reported in this dissertation,
high resolution spectroscopy was performed for the purpose of Obtaining
frequency information for subsequent double resonance studies as well as
for examination of the effect of various energy couplings. The purpose
of this "Introduction" is to provide an outline of the organization of
this dissertation. More details concerning the reasons for carrying out
the work, results of previous studies, etc., are given in the chapters
describing each project.

Chapter 11 presents the high resolution infrared spectroscopy of
the v3+06-v6 band of 12CH'3F by means of an infrared microwave sideband
laser (IMSL) spectrometer. This band is located in the vibrational

spectrum of CH3F in the important 10 pm region, which has been the
l

subject of many high resolution studies. Moreover, this band is of
interest because it appears to be the first example of a high-resolution

infrared study of an E~E band in a prolate C symmetric top. More than

3v
200 transitions with J and K values up to 20 and 10, respectively, have
been identified and their frequencies measured to an accuracy of a few
MHz. Among the identified transitions are the components of 14 l—type
doublets in this hot band of E~E symmetry. The spectra have been fit to
experimental accuracy by adjusting rotational parameters including
centrifugal distortion constants through the sixth order as well as
Coriolis coupling and l-resonance parameters.

In Chapter III, high resolution infrared studies of the v2 bands of

79

CD 1, CD3 Br, and CD38lBr are described. About 200 transitions for

3
each species have been recorded and the frequencies have been determined
to an accuracy of few MHz. The frequencies in these parallel bands have
been fit by least squares to an energy expression containing centrifugal
distortion parameters up to the eighth order. The strong Coriolis
interaction with the 05 band has been taken into account in each case by
using previously-reported parameters for the interaction and for the 95
band (for CD3I, interaction with the 2173 state has been also included).
The resulting combination of the v2 parameters obtained in this work and
the parameters from previous work is sufficient for each molecule to
predict the vz-band frequencies up to high J and K (~40 and ~10) within
a few MHz.

Radiofrequency spectroscopy is known to be a powerful tool for
investigation of various hyperfine energy structures. However, the

scope of the technique has been seriously limited by the density of the

spectra and the poor signal-to-noise ratio. When infrared-

radiofrequency double resonance was introduced, which involves the
simultaneous application of two fields of radiation to the sample,
radiofrequency spectroscopy could be performed with greatly enhanced
sensitivity and selectivity. In infrared-radiofrequency double
resonance, hyperfine resonances are observed as a steady-state change in
absorption of laser power simply due to the change in the population
difference between the excited and ground states as the RF frequency
passes through resonance. A molecular population change is made
possible by pumping molecules from the ground state to the upper
vibrational state by means of a strong infrared laser field which is
resonant with an infrared transition. When the RF-field is resonant
with the hyperfine levels, infrared absorption is increased by
equilibrating the populations of the hyperfine energy states.

The development of IR-RF double resonance spectroscopy in the last
two decades has made it possible to determine the values of a large
number of parameters for hyperfine states, and many of these can be used
for the investigation of the electron distribution in molecules. These
parameters are usually measures of weak interaction occurring between
atomic nuclei having electric quadrupole moments and electrons, and as
such yield information about the electronic structure of the molecule.
As will be seen in Chapter IV, the nuclear quadrupole coupling energy is
given as the inner product of the nuclear quadrupole tensor and the
electrostatic field-gradient tensor evaluated at the nucleus. Such an
inner product depends on the mutual orientation of the two axis systems
to which the two tensors are referred; for the nuclear quadrupole
tensor, the natural system is one in which one axis coincides with the

spin axis of the nucleus. The interest in quadrupole coupling constants

4

lies in the different values of the field gradient seen by a given
nucleus in different molecular environments. The electric field
gradient at the nucleus may be extracted from the quadrupole interaction
energy represented by the quadrupole coupling constants, by dividing by
the appropriate nuclear quadrupole moment.

The IR-RF double resonance technique has been applied to the v2 and
3798r, and CD381

IMSL as the infrared laser pump. The tunability of the laser allowed

the ground vibrational states of CD31, CD Br by using an
the selection of an appropriate set of transitions with a wide range of
J and K quantum numbers without having to depend on accidental
coincidences with laser lines; more than 150 pure quadrupole transitions
for each species have been observed. To improve the accuracy of the
frequency measurement, the RF radiation power was kept as low as is
consistent with reasonably good signal-to-noise ratio, because IR-RF
spectra are easily RF power broadened. The typical half width at half
maximum for the transitions was as low as 70 and 100 kHz for 003I and
CDBBr, respectively. As a result, it was possible to determine the
spin-rotation constants as well as the centrifugal distortion constants
for the quadrupole couplings in these molecules. The theoretical and
experimental details are described in Chapter IV.

During the IR-RF double resonance study stated above, it was
realized that some effect was causing an apparent shift of the
transitions that occur at low RF frequencies. This effect could be
easily shown through the adjustment of parameters to fit the frequencies
of the pure quadrupole spectra; experimental values for the two lowest
radiofrequency transitions were found to be much closer together than

predicted by the best values of the parameters. These shifts were

5

traced to a double-resonance effect that appears in calculations when
four interacting levels are taken account, but is not evident in
calculations based on the usual three-level system employed for double-
resonance theory. The nature of the problem is described in detail in
Chapter V. Essentially, it results from the fact that the hyperfine
splittings in the upper state are not greatly different from those in
the lower state for the double resonances in this work. As a result,
quadrupole transitions of the upper and the lower vibrational states are
often overlapped, and, generally, the lower frequencies are more
seriously overlapped than the higher frequencies. Since both the upper
and the lower states of the RF transitions are pumped by the strong
infrared radiation and the RF radiation connects the hyperfine levels,
the four levels must be considered as a four-interacting-level system.
An appropriate linear equation was set up in the density matrix
fermalism for the four-interacting-level system, and solved at each RF
frequency for a sequence of values of the molecular velocity and a fixed
value of the laser frequency; the resulting contributions to the
absorption were multiplied by the appropriate Doppler weight and summed.
The frequency shifts obtained by fitting the spectra calculated with
estimated parameters show good agreement with the shifts observed

experimentally. The details are described in Chapter V.

CHAPTER II

HIGH RESOLUTION INFRARED STUDY OF THE D - v BAND OF 12CH'3F

3””6 6

II-l Introduction

Methyl fluoride and ammonia, with their relatively simple
rotational structure and strong spectra, have been considered as model
compounds in the development of infrared high resolution spectroscopy.
Especially, the vibrational spectrum of CH3F in the 10 pm region has
been the subject of a number of recent high-resolution infrared studies
because the many strong transitions in this region include several that
are in coincidence with 002 lasers, and therefore provide pumping
sources for far-infrared lasers and for double-resonance effects. For
this molecule, a series of spectroscopic works have been performed by
means of infrared-microwave two-photon and infrared-microwave laser
spectroscopy in our laboratory (1-3). As a result of extensive
analyses for the v3 fundamental and 2123 - v3 hot bands of 12CH3F and
13CH3F, transition frequencies can be calculated to within a few MHz
with the reported molecular constants. The obtained information has
been successfully applied to an infrared-infrared double-resonance study
of collisional energy transfer including a determination of the change
in velocity upon collision (4).

This chapter is concerned with a high resolution infrared study of
l

O-

the v3 + v6 v6 band (1039.1 cm- ) of 12CH3F carried out with infrared

7

microwave sideband laser spectroscopy. Like other XY23 type symmetric
top molecules, CHBF has three totally symmetric and three doubly
degenerate vibrational bands. Among these, O3 is the totally symmetric

C-F stretching band (1048.6 cm-l), vs the degenerate CH3 rocking band

1

(1182.7 cm‘l), and v3+v6 the combination band (2221.8 cm- ). Although

the upper and lower state energy levels of the v3 + OS - band in CH3F

”6
have been studied previously during investigations of other bands by
infrared and microwave spectroscopy (5—9), the present work is the first
extensive high-resolution study of this hot band.

Values for the vibrational energy and primary rotational parameters
(A, B, and A!) of the v6 = 1 state were obtained by Smith and Mills from
grating spectra taken at 0.2 - 0.4 cm.1 resolution (5). Hirota and his
co-workers later determined B, A{nK, and |q6| by means of microwave
spectroscopy (6,2). Later, Hirota, by means of diode laser
spectroscopy, observed Q-branch transitions in the v6 band for J and K
values up to 14 and 3, respectively (8). The frequencies of these
transitions were used together with rotational frequencies to determine
A, A{, A{nK, the band center (D0 + Afz), and the sign of qv for v6 = l.

A set of constants for the v3 + OS state was determined by Nakagawa
gt g1. from grating spectra taken at 0.06 cm-1 resolution (2). However,
they were unable to assign Ak = -1 spectra and could not determine an
accurate value for the l-doubling constant qv. A final piece of
information on the spectrum of interest in the present work is the
assignment of the QQ(6,4) transition in the v3 + OS - v6 band by an
optical-optical double resonance method by Duxbury and Kate (19).

In addition to its importance for double resonance experiments, the

D3 + OS - ”6 band is also of interest because it appears to be the first

8

example of a high-resolution infrared study of an E - E band in a
prolate C3v symmetric top. Previous high-resolution studies of
transitions between doubly-degenerate vibrational states have included
analyses of the 03h molecule BF3 (11) and the oblate 03v molecules CF3H
(lgfimd CF30 (Li) .

In the present study, infrared spectra of the v3 + OS - ”6 band in
12CH3F have been recorded at Doppler-limited resolution (ADD 5 34 MHz)
by an infrared microwave sideband laser spectrometer with a White-type
long path absorption cell. The frequencies of more than 230 transitions
have been measured to an accuracy of a few MHz. The measured
frequencies include transition frequencies from 14 l-type doublets which
allow the determination of l-type doubling constants for both the upper
and the lower vibrational states. For this work, it was first necessary

to identify all of the transitions of the fundamental v3 bands of 12CH3F

and 13CH3F (which occurs in natural abundance) and of the 2v3 - 9 hot

3

band of 12CH3F; the absorption lines in these bands dominate the spectra
in this region. All of the observed transitions in the 03 + OS - v6
band that were assigned in the present study follow the selection rule,
Ak = 0, A1 = 0. Spectra obeying other selection rules may also occur as
a result of rotational R-type resonances, but they have not yet been
identified, probably because of exceedingly weak transition intensities.
The spectra were fit to experimental accuracy by adjusting rotational
parameters, including centrifugal distortion constants through the 6th
order, diagonal Coriolis coupling parameters, and l-doubling constants.

It is expected that the results of the present work will be applied

to a subsequent energy transfer study between nearby vibrational states

with predicted 002 laser coincidences. For this purpose, resolved I-

9

type doublets may provide ideal two level systems which are similar to
ammonia inversion doublets. The general theory for the present study is
described briefly in the next section. The experimental details,
analysis of the spectra, results of the study, and a discussion of the

results follow in subsequent sections.

10

II-2 Theory

Investigations of the vibration-rotation spectra of polyatdmic
molecules in the gas phase have been of importance for determining
precise molecular geometry and energy structure. With the advent of
laser spectroscopy, both the resolution and feasibility of various types
of experiments have been greatly improved. As a result, the importance
of studies of the rovibrational states of polyatomic molecules has
increased.

The quantum mechanical description of the electronic and nuclear
motions should yield the vibrational, rotational, and electronic energy
levels as well as the corresponding wave functions for the systu.

Since the electronic motion is so fast in comparison with the nuclear
motion, at each point the electronic energy may be considered to have
reached its equilibrium value corresponding to the nuclear geometry.
Therefbre, we are normally justified to employ the Born-Oppenheimer
approximation which treats the nuclear and the electronic motion
separately.

As a further approximation, the rigid rotor-harmonic oscillator may
be employed to divide the Hamiltonian of nuclear motion into the

vibrational and rotational parts, as follows:

Hn = Ht + Hr + Hv , (2-1)

where Ht is the Hamiltonian fer molecular translation, Hr the rotational

Hamiltonian, and Hv the vibrational Hamiltonian. With these

ll

approximations, the energy of a molecule may be expressed simply by a
sum of electronic, vibrational, rotational, and translational
contributions;
E = E + E + E + E
e v r

t r (2_2)

r’ and Et are the electronic, vibrational, rotational,

and translational energies. Since this thesis is concerned with the

where Ee’ Ev, E

vibration-rotation transitions in one electronic state, the electronic
and translational parts will not be discussed further.

The rigid rotor approximation is of course not sufficient to
analyze experimental data on vibrational-rotational transitions.
Higher-order corrections for the vibrational-rotational interactions,
the centrifugal effect of molecular rotation, and the anharmonicity of
molecular vibrations must be introduced to utilize fully the wealth of
information involved in the data of high resolution experiments.

The theoretical details will be discussed in this section

especially for symmetric top molecules.

II-2-l Hamiltonian for Harmonic Oscillator-Rigid Rotor Approximation

To a good approximation, the electronic and vibrational-rotational
motions are normally separated in molecular spectroscopy. However, it
is necessary to introduce further approximations because the SchrOdinger
equation is still too complicated to be solved exactly. Although these
approximations are much cruder than the Born-Oppenheimer approximation,

they are very important, since the known eigenfunctions will be used to

12

form the basis vectors for higher variation or perturbation
calculations.

As the first approximation, it is assumed that the vibrational
displacements of the atomic nuclei in rigid molecules are limited in a
small region around the equilibrium configuration. Hence the molecule
keeps the equilibrium moment of inertia by neglecting the vibrational

dependence:

2 (J 4092/ 2123+ 2 91/2 + v (2—3)

H = _
vr m-x,y,z m k

where PR is vibrational momentum, J“ and as are rotational and
vibrational angular momenta, and.I;u is a moment of inertia along a
molecular principal axis. As a further approximation, both the
vibrational angular momentum and the anharmonicity are neglected. The

obtained Hamiltonian operator for this case is

2 2 2

o 1 Jx J1 J2 l 3N-6 2 2
Hvr = 2 [ _3_ + o + _3— + 2' g [ Pk + ka ] ' (2-4)
I I I k-l
xx yy 22

II-2—1-l Harmonic Oscillator

The harmonic oscillator leads to a wave equation for the nonlinear

molecule that can be written in the form

13

—- 2
2k=l

 

1 3N‘6 [62 OZWV

-Eoo _
802 Mk V] - Ev wv (2 5)

where 0k is the normal coordinate of the k-th mode of frequency

1/2
"k"‘k

wave function depending on the normal coordinates.

/2n, E3 is the vibrational energy, and 03 is the vibrational

It is convenient to introduce dimensionless normal coordinates qk
and corresponding operators of linear momenta pk which are defined by

the equations

_:k 1/2Q

pk(=—i§ —q—k)= *1. ”4 fi‘l/Z P1. (2—7)

where =4n2v 2 and P =-iha/ao . So that Eq. (2-5) becomes
’1: k k k

--1-:g_6( 2)( 2+ 2w°< )-s° w°< ) (2—8)
2 ”‘1.“ pquvqk'vvqk°

It is well known that the solutions of Eq. (2-5) are the vibrational

energy levels Ev for which

E(k)= hD k(v k+l/2) v : 0,1,2,.... (2'9)

The eigenfunctions of the linear harmonic oscillator equations

(Eqs. (2-2)~(2-5)) are

14

2
W - N; e k k HV (Yk GR) (2 10)

”k k k

where rkf4nzvk/h and Hv,(yt{2 0k) is the hermite polynomial
k

of order of v expressed as a function of r1/2 0 ; N is a
k k k vk
normalization constant

N =

vk (2-11)

(5‘) v

[ Yk 1/2 1 1/2
2 k(vk!)

For a doubly degenerate normal vibration, the SchrOdinger equation can

be written in the form,

%<hx1/2>[(paz+pb2>+<qaz+qb2)1wv= 84w . <2-12)

V

It is convenient to introduce polar coordinates p and O by the

equations,

qa = pcosO (2-13)
and

qb = psinO . (2-14)

where 0 s p < a and 0 S O < 2n. It holds that

15

-_- 1-21.299... _
pa - 1[cosO an 0 so] . (2 15)
P1. = -i[sinOg-6+9§flg;1 . (2%)
and Eq. (2-12) then assumes the form,
2 2 23
[%+%§—5+1—23—§+{m—"— 2}]wv(p.¢)=o. <2—17)
an O aO

The wave function that is the solution of Eq. (2-17) depends on p and O
as variables and two vibrational quantum numbers v and 1 to label the
states. It can be shown that this function can be written as a product

of radial(p) and angular(¢) wave functions

2 .
_ -p /2 III III 11¢ _
Wv’1(0.¢) - Nv’, e p [ L(v+|1|)/2(p)][e 1 - (2 18)

The vibrational quantum number v assumes the values,

v = 0,1,2,... , (2-19)

and the quantum number 1 assumes the v+l values,

1 = v,v-2,....,-v+2,-v . (2-20)
The function Litilll)/2(p) is the associated Laguerre polynomial (14),

and Nv is the normalization factor,

16

1/2/{[v+l1|)/2]!}3/2 . (2-21)

NV”. = [(V’|1|)3]
The expressions for the energy levels of the two dimensional

isotropic harmonic oscillator can be written in the form:
0!) _ . _
Ev — hvk(vk+l) , (2 22)

i.e. Ev is independent of 1. Each energy level of this oscillator for a
given v has (v+l)-fold degeneracy corresponding to the (v+l) values that
quantum number 1 can assume according to Eq. (2-20).

The fact that exp(i1¢) appears in the expression of the
wavefunction 0v’£(p,¢), Eq. (2-18), indicates the presence of a
vibrational angular momentum; 1 is therefore the so-called vibrational
angular momentum quantum number. Classically, the vibrational angular
momentum can be interpreted as arising through superposition of the

normal vibrations Q8 and Qb with 900 phase shift.

II-2-l-2 Rigid Rotor

II-2-l-2-l Moment of Inertia

The moment of inertia tensor is defined as
'1‘ = 2 m.(r§ I — Fm.) (2-23)

in which the moment of inertia tensor is written in the notation of a

dyadic which is an expression of a second rank tensor. In the three

1?

dimensional Cartesian coordinates,

- 2_ 2 _ 2 2 _
Ixx - E mi(ri xi) - E mi(yi+ zi) , (2 24)

where Iyy and Izz can be expressed by the permutation of x, y, and z.

The off-diagonal elements are given by

Ixyz -§ mixiyi. (2-25)

Since the inertia tensor is real and symmetric, it may be diagonalized
through suitable rotations of axes. The diagonal elements of the
diagonal form are called principal moments of inertia (Ia S Ib s Ic)’
and the axis system is termed the principal axis system.

For some molecules, two moments of inertia such as Ia and Ib or Ib
and IC may be the same, in which case the molecule is called a symmetric
top molecule. From the point of symmetry, if a molecule has an axis of
three or more fold symmetry, then it is always a symmetric top. If a

molecule has an axis of symmetry, the axis lies on a principal axis of

the molecule.
II-2-l-2-2 NOnvanishing Matrix Elements of Rigid Rotor

From Eq. (2-4), the rotational Hamiltonian operator in the rigid

rotor approximation is given by

18

o _ 2 o 2 o 2 o _
Hr ~ (Jx /Ixx + Jy /Iyy + Jz /Izz) (2 26)

where Jx’ Jy, Jz are the angular momentum components along the principal

O O

axes x, y, z and I0 , I , I are the moments of inertia about the
xx yy 22

principal axes. The matrix elements of operators Ji, J5, and J: can be

obtained by matrix multiplication

<J’,k',m'|J§|J,k,m>
= z <J',k',m'IJaIJ”,k",m"><J",k",m"lJalJ,k,m> . (2—27)
JV. ’ k7. ’ m"

Only the diagonal matrix elements of the operator, J5, are nonzero,

<J,k,mlJ:|J,k,m> = h2k2 . (2-28)

On the other hand, Jx and Jy have diagonal as well as off-diagonal

matrix elements. From the relations,

(h/2)[(J:k)(J:h+1)11/2 <2-29)

<J,ktl,m|Jle,k,m>

<J,k11,mlJy|J,k,m> t(ih/2)[(J:k)(J:k+1)]1/2 , (2—30)

the diagonal elements of J: and J: are

<J,k,mlJi|J,k,m> = <J,k,m|J:|J,k,m>

= (52/2)[J(J+1)-k2] (2—31)

and the off-diagonal elements are

19

<J.k:2.Ile2|J.k.-> = -<J.kt2.nlJy2lJ.k.->

= (ha/4)[J(J+l)—k(ktl)]1/2[J(J+1)-(kil)(kt2)]1/2 . (2-32)

Hence there are the following nonzero matrix elements of H: in the

J, k, m representation:

2 2

<J,k,m|H°|J,k,m> = fl—[{-l— + -l—}[J(J+1)-k2] + 25—] , (2-33)
r 4 Io IO 0
xx yy 22

<J,k,mlHr°|J,k12,m>

: gi[_l_ _ _l_][J(J+1)-k(k:1)]1/2[J(J+1)—(k:1)(k:2)11/2. (2-34)
1° 1°
XX YY

II-2-l-2-3 Rotational Energy Levels of Symmetric Top Molecules

. o _ o
For a symmetric top molecule, Ixx - Iyy

lies along the axis of symmetry. As a result, H: has only diagonal

if the principal axis 2

nonvanishing matrix elements in the J, k, m representation; that is, the

angular momentum quantum number k becomes a good quantum number:

<J,k,m|H°|J,k,m> = fi— {iiiill + —l- - -1— k2} . (2—35)
r 2 Io Io Io
w 22 w

The molecular rotation constants A, B, C can be introduced by the
following relations:

A = fiz/(4ncIa), a = fiz/(4ncl c = fiz/(4nc1c) , (2-36)

b).

20

where c is the speed of light. In terms of the rotational constants,

the rotational energy levels of the prolate symmetric top are given by

the expression,

Eg/hc = BJ(J+1) + (A—B)k2 ; (2—37)

for an oblate top molecule,

Eg/hc = BJ(J+1) + (c-B)k2 . (2-38)

Hereafter, we will express all energies in multiples of hc, so that
Er/hc = Er'

II-2-l-2-4 Symmetric Top Rotational Wavefunctions

In terms of the Euler angles a, O. x, the Schrodinger equation for

a rigid prolate symmetric top can be written in the following form

 

 

o 2 o 2 o
1 §_ [sine ——5] + l a wr [:osze A] 6 mr
sine as a sm2e 802 in2e B ax2
2 o o
2cose 6 gr + Er 0° 0
sinze a¢ax B r

(2-39)

Variables in Eq. (2-39) can be separated and the wave function, W , can

21

be written as a product

O:(e,¢.x) = 8(6) aim” eikx . (2-40)
Since w: must be single valued if'o and.x are changed to ¢+2nn and.x+2nn
(n=0,l,2,...), k and m in Eq. (2-39) can assume only integral values
0,11,:2,...

Because variables O and x occur only in the derivatives in Eq. (2-
39), they appear in Eq. (2-40) in simple exponential terms. Function
8(a) is more complicated because it is the solution of the following

equation:

sine as . 2
in a sin e

2 2
1 a . 88 e I m cos a A 2
O

- 399§9km - —§5 ] 8(a) = o . (2-41)
sin e

Physically acceptable solutions of Eq. (2-41) exist only if 8? satisfies

the following conditions:
0 _ 2
Er - BJ(J+l) + (A-B)k , (2-42)

where J is a positive integer with J 2 lkl or lml, i.e.,

J = 0,1,2,..., (2-43)
k = 0,11,12,..., J, (2-44)
m = 0,:1,32,..., J. (2-45)

22

Rayefunctions Bka(e) corresponding to eigenvalues E:(J,k) for
k=m=0 are the Legendre polynomials P§(cose), whereas for m s 0 they are
the associated Legendre polynomials (15). The function 8300(9) can be

written as

[<2J+1)/<8n2>11/2] dJ

J (cosze-l)J . (2-46)
2 J!

8 (e) = [
J00 (dcose )

II-2-2 Selection Rules

If the molecule is in a free space, the isotropy of the space makes
it possible to consider any one of the three space-fixed principal axes.

The electric dipole moment operator is given by

N+Ne o
= 2 ei(Zi-Zi) (2-47)

p
2 i=1

where ei and 21 are the charge and space-fixed coordinate of the ith
particle in the molecule; 2: is a coordinate of the molecular center of
mass. We express pz in terms of the components ”x’ my, pz of 5 along

the molecule-fixed axes:

”z = pxXZx + pyny + “2"22 (2‘48)

where xZX, xzy, x22 are the direction cosines.

23

If the rovibronic wavefunctions are considered in the approximation

as the product of electronic, vibrational, and rotational functions, we

can write

000 nor")
<Oewver|pzleéwdwr>

I n H i N) _
=rx2y ZOD'eWVIpal wee ><e My...” (2 49)

because ”a depends only on the vibronic coordinates and x2“ on the

rotational coordinates. we can integrate over the electronic

coordinates by writing

or n n _ o n N _ r n n) _
<Oéwv|pa|méwv> - (O' [ODe In“ IOe >]Ov > - (WV In“ (e’ ,e )|@v> (2 50)

where pa(e',e") depends still on the nuclear coordinates. we expand

pa(e ,e") in terms of the normal coordinates of the electronic states

about the point of the equilibrium configuration of the atomic nuclei of

that state,

ua(e' .e") = u:(e' .e") + i<auu(e' .e")/<3f-)k)o Q

+ <1/2) 2 (a2 u (e .e")/aokao ) oo

. (2-51)
k,l k 1

By substituting the first two terms of Eq. (2-51) into Eq.(2-49), we

obtain

24
l l 0 90 '9 fl
(OeWQWrIpZIOéOJOr>
- O 0 n r n v n r r n r n __
— §[pa(e ,e )(Wv|0v> + 2(apa(e ,e )/an)°<Wv|Qk|Wv>](Orlx2a|0r>. (2 52)
The first term is responsible for pure rotational transitions where (O;
= 0;, O; = O3). The intensities of such spectra are proportional to
0 r n 2
[pa<Wr|x2a|Wr>] , the product of the square of a component of the
permanent dipole moment and the square of the corresponding direction-
cosine matrix element. Vibrational transitions within a given
electronic state are controlled by the second term in the square
brackets. From the harmonic oscillator approximation, <0;|Qkhws> # 0
only if Avk = :1.
For the case of vibration-rotation transitions, we must consider
the matrix elements of x2“ together to specify selection rules on the

rotational quantum numbers J,k. It is convenient to write Eq. (2-49) in

the form

I l D N N N - 0 ' N N D I.
<Oemvwr|pz|eewvmr> - (Ovlpz(e ,e )IOvXOrlxlzltDr)

+ (1/2)<W;|px(e',e )-ipy(e',e )IW3><0;|xzx+ixzy|0;>

+ (l/2)<W;Ipx(e',e")+ipy(e',e")|@3><@£lx2x-ixzy|0;> . (2-53)

It turns out that the only non-zero elements of>~zz are

0 n - v_ n ._.._ _
<wr|xzz|or> ,. 0 1f Ak k k 0 (2 54)

and

II
l+
H

v - n ' _
(Wr'xe'thylwr) ,. 0 1f Ak (2 55)

25

The general selection rules may be applied to symmetric top
molecules by taking account of the fact that p: = p; = 0, p: x 0. For
the pure rotation spectra of non-degenerate vibrational states of

symmetric tops:
Ak = 0, AJ = 0, :1. (2-56)

Selection rules for the allowed vibration-rotation transitions can be
obtained by combining the selection rules for vibrational and rotational
transitions. There are two different types of allowed transitions in
symmetric top molecules (16). When the electric dipole moment
oscillates in a direction which is parallel to the z axis (parallel

band),
Griz/80190 # 0. (aux/0k)o = (my/3°90 = 0. (2-57)

In this case, selection rules for the rotational quantum numbers are

E

0, AJ 0, :1 for k s 0 , (2-58)

g

0, AJ

:1 for k = 0 . (2-59)

When the electric dipole moment oscillates in a direction that is

perpendicular to the z axis (perpendicular band),

(apz/aok)o = o. (aux/30k)o . o, (any/aok)O . o. <2-60)

Selection rules for the rotational quantum numbers are then

26

Ak = :1, AJ = 0, :1 . (2-61)

In addition to the above selection rules for the rotational quantum
numbers, there are also selection rules which are concerned with the
symmetry properties of the rotational levels. Hougen derived general
selection rules for electric dipole transitions by consideration of the
fact that rovibronic energy levels can be classified according to
certain symmetry species (11). The dipole moment operator is invariant
to a permutation of the coordinates of identical particles since the
operator pz is simply the sum of the charges ei of all the particles in
the molecule multiplied by their 2 coordinates. It may be noticed that
the transformation properties of ”Z are identical with those of the
product Tsz, where T2 and R2 represent a translation and a rotation
about the z axis (11).

Selection rules may be formulated from the transformation
properties of pz, which lead to the conclusion that the electric dipole
transition between two rovibronic states, of species F' and r", is

T x FR . Here FT and. FR
2 z z z

allowed if and only if F'x F" contains F

are the irreducible representations of T2 and R2 for the corresponding
permutation-inversion group. Application of this rule to a C3v molecule
leads to the consideration that the dipole moment operator is classified

under A2 species from r x FR = A1 x A2: A2. Therefore, the allowed
2

T
2

transitions ought to be such that F'x F" contains A2. As a result, we

may add two more selection rules:

27

AleaAZ and EvaE . (2-62)

The principally allowed transitions are shown in Fig. 2-1 and Fig. 2-2.

Hougen (11) introduced a convenient quantum number, G = Gev-k (for
the ground electronic state, G = 1-k), which may replace the 1-
designation originally proposed by Herzberg (16). This quantum number
allows influence of the symmetry species of rovibronic energy levels to
be specified without additional quantum numbers. The selection rule due
to symmetry considerations may be described with the quantum number G as
follows: An electric dipole transition between two states is allowed if
and only if G'- G" 5 AG = 0 mod n, where n is the highest-fold axis of
rotation in the molecule. As a result, the electric dipole transition
selection rules, Ak = 0 for parallel transitions and Ak = :1 for
perpendicular transitions, are proved by the fact that the connected
states have the same symmetry as shown in Fig. 2-1.

This rule may also be applied to the additional transitions allowed
by Coriolis interactions, which need not obey the selection rules on k.
Such transitions will normally be exceedingly weak compared to
vibronically allowed transitions. It should be pointed out that the
quantum number G by itself contains no more information than is

contained in the symmetry species label of the rovibronic level.

II-2-3 Nonrigid Symmetric Top Molecules

II-2-3-1 Centrifugal Distortion

Rotation about any axis in the molecule is accompanied by

centrifugal forces which tend to alter the effective moments of inertia.

 

Homemaker:-

 

 

-
.
1v
i
I
V
e

.h
I‘m

”-7
6

9 .un “owing...

 

28

on.
Fl
a
I...
r
‘1
Fl
3

 

7 E
6 E Ar: 5 z E E ‘—
2 a ‘ E3232
~_’ E
3 E up?
2 E N—
6 E ‘
J J
-’ 8—-—E J 7 E J
8 5 J E 7—____.—:.l E 6———E
7 6
7—5 5
7 IN 6 EC 5 E 6 {I S E
6 g E 3 “I O E
b) 5——E 5 ‘___‘
5 N ‘ E 4 E 3——*¢_.___~
4 a 3 E 3 E
3 0. 53—5 2 E
5 a.
K 3 0 K 3 1 K 3 2 K = 3 K = 4 K = 5

Figure 2-1. Symmetry properties of rotational levels of molecules
with a three-fold axis; (a) in a totally symmetric vibrational state,
(b) in a degenerate vibrational state. The arrows show allowed

transitions.

29

 

 

 

 

 

KL.
Hi}.

 

 

Figure 2-2. The rovibronic levels with K = l and J = 1,2 for
vibronic E-state of a molecule of symmetry C3v° The transitions
indicated by solid arrows are allowed; those indicated by dashed

arrows are not.

30

The resulting dynamic effect forces the atoms away from an axis of
rotation and increases the moment of inertia about that axis. The
centrifugal effects introduce into the energy level expression terms

with high powers of J(J+l) and K2. For a prolate top molecule,

E = BJ(J+1) + (ArB)K2 - DJJ2(J+1)2 - DKK4 - DJKJ(J+1)K2 +... , (2-63)

where D D and DJK are the quartic centrifugal distortion constants.

J! K!
The correction terms for centrifugal distortion are found to depend only
on even powers of the angular momentum because the distortion effects do

not depend on the direction of rotation about any axis.
II-2-3-2 Coriolis Interaction

Coriolis resonance interactions in symmetric top molecules have
been studied by Nielson and coworkers (lg-29) and later by diLauro and
Mills (g1). According to Jahn’s rule (22), if the product of the
symmetry species of two vibrational modes contains the species of
rotation, P(Qk) x P(Qk.) = P(Ru), Coriolis interaction takes place
between the vibrational nodes (11). The Coriolis force is represented
in classical mechanics as the cross product of the linear velocity of
the particle relative to the molecule-fixed axis system and the angular

velocity of the rotation;
= 2m; x u . (2‘64)

Fig. 2-3 illustrates the effect of the Coriolis interaction between

31

 

 

Figure 2-3. Coriolis forces during the degenerate vibration of an X3

molecule.

 

Figure 2—4. Diagrammatic representation of the x,y-Coriolis coupling
of the states with J = 3 and with the same k-lt. The dotted line

connects states exhibiting giant l-type doubling.

32

components of the v2 degenerate vibrational mode of the tri-atomic
molecule X3. For a counter-clockwise rotation of the molecule the
Coriolis forces are as shown by the short arrows (Fig. 2-3). It is
noticed from the figure that they tend to excite the other component of
the degenerate vibration. The result of this Coriolis interaction is a
splitting of the degenerate vibrational levels into two levels whose
separation increases with increasing rotation (K) about the top axis and
is zero for K = 0.

Coriolis interaction may be explained in quantum mechanics as the
interaction between the vibrational and rotational angular momenta about

the appropriate molecular axis:

_ 2 _ 2 _ _ _
Hcor - (2A/h )< szz) + (zn/h )< Pxe pny) , (2 65)

where A,B are the rotational constants of a prolate top molecule and Jx’
J . 32 and px. p

Y Y
angular momentum about the corresponding molecular axis. Eq. (2-65)

, pz denote the components of over-all and vibrational

indicates that there are basically two kinds of effects: (i) interaction
due to the rotation about the top axis 2 (in a symmetric top molecule,

interaction of two degenerate modes v and vt.), and (ii) interaction

t
due to the rotation about the x, y axes (in a symmetric top molecule,
interaction between nondegenerate mode vs and the degenerate mode vt).

When vt=v£, the z-axis Coriolis coupling contributes to the energy
in the first order by the term

_ z 2 _
2[ 232;t + ntJJ(J+l) + nth Jitk (2 66)

33

where the term -ZBZ{:1tk represents the primary effect of the Coriolis
interaction and the other terms describe the rotational dependence of
the Coriolis coupling. The subscript t denotes a degenerate vibrational
state. The result of this strong Coriolis interaction is a splitting of
the degenerate vibrational levels into two levels whose separation
increases with increasing rotation about the top axis. Hence the
formula for the rotational energy levels in a vibrational level of a

symmetric top molecule in which a degenerate vibration v is singly

t
excited, may be represented by

_ _ 2 - _
E(v)(J,K) - B(V)J(J+1) + (A(v) 8(v))K + 2A(v){iK1 + .... (2 67)
which differs from Eq. (2-42) only by the term 2A(v){iK£.

Coriolis interactions due to rotation about the x, y axes appear as

off-diagonal components:

(vs-l,vt,£t;J,k|H Iv ,(vt-l),ltil;J,kil>

cor s

_ y - 1/2 - 1/2 _

- _nst{stBy[vs(vt+1t)] [(J+k)(th+l)] (2 68)
where

_ 1/2 _

nst- [(vs+vt)/2(vsvt) ] . (2 69)
For simplicity, let us consider states with v8 = vt = 1. Since Ak =
Alt = 11, the matrix elements given in Eq. (2-68) connect only the state
|0,l+1;J,k+l) with the state |1,0;J,k> which is further connected to the
state |0,l-1;J,k-l> (Fig. 2-4). Thus for each value of J the energy

34

matrix factorizes in separate blocks, each block being characterized by
a particular value of (k-Rt). It is noticed that k is not a good
quantum number any more whereas (k-lt) still remains as a good quantum
number (ii). We can obtain the eigenvalues by building and

diagonalizing the following 3x3 matrix for given J and Rent;

 

 

|0,1 ;J,k+1> |l,0;J,k> |0,1 ,J,k-1>
"'0 +F(J k+1)—ZB {2(k+1) 21/23 9 {V [J k] 0 l
t ’ z t x st st ’
_ l/2 y _
ms+F(J,k) 2 B£n8t{st[3,k 1]
L (Hermitian) mt+F(J,k-l)+282{:(k-l) J
(2-70)
where
_ _ 2 _
F(J,k) - BXJ(J+1) + (82 Bx)k , (2 71)
[J,k] = [J(J+1)-k(k+l)]1/2 . (2-72)

Because for each rotational state Ikl g J, there are only two identical

2x2 blocks for the special case (k-lt) tJ, and only two identical lxl

blocks (unperturbed states) for (k-lt) :(J+l). In addition, Garing gt

a; (£3) showed that for k-lt = 0 the matrix given by Eq. (2—70) can be

factorized by the transformation

|A+> = 2'1/2[|o,1+1;J,1> t |0,1‘1;J,-1>] . (2—73)

The transformed matrix has the form,

35

|A+> |1,0°;J,o> |A_>
' _ Z
mt+F(J,1) zazat o o 1
y
mS+F(J,0) ZBzflst{8t[J(J+1)]
. . Z
L (Hermitian) mt+F(J,l) 282!t j

 

 

(2-74)

Thus the pair of degenerate levels with k = it = :1 of the ”t state
splits into two components A+ and A_. The A_ sublevel interacts with
the k = 0 level of us but the A+ sublevel is unperturbed, that is, only
one of the two energy levels (A1, A2) is affected by the Coriolis
interaction. Nielson called this splitting "giant l-type doubling"
(g3). Since l-type doublings provide a very good information source for
Coriolis interactions, they have been probed to study existing Coriolis
interactions (§,Z). Note that for odd J the species of A+ is A1 and
that of A_ is A2, while for even J the species of A+ is A2 and A_ is Al.

The effects of l-type doubling will be discussed in more detail in the

following section.

II-2-3-3 Rotational R-type Resonance Interaction

Wilson showed by symmetry considerations that rotation-vibration
interaction might split degenerate rovibrational energy levels of
symmetric top molecules into a number of components (g5). For example,

in a symmetric top molecule with C3v symmetry, if ken # 3n, then the

36

rotational and the vibrational wavefunctions belong to the degenerate
species B and the total rovibrational wavefunctions should form bases
for the irreducible representations of ExE = A1+A2+E. The splitting
into an E level and AlAZ pair results from first order Coriolis coupling
(see section II-2-3-2).

The splitting of the AlAz pair into separate levels, however, is of
higher order and explained by a more detailed treatment of vibration-
rotation interaction (gg). There are off-diagonal matrix elements in
the quantum numbers l and k which split and shift the zeroth—order
energy levels. The most familiar example of the splitting of the A
levels is R-type doubling. The associated effects, which are called
rotational l-type doubling or l-type resonance, were first discussed by
Nielson (g§,gz) and later described in detail by Grenier-Besson (gg).
Selection rules for the matrix elements can be obtained from Amat’s rule

(2_9)

-Ak + E “t Alt = pN (2-75)

where the value of N is determined by the N—fold principal symmetry axis
of the point group; p is an arbitrary integer which is positive,
negative or zero; and nt=l for 81 (or E) species, nt=2 for 82 species
etc. This relation gives off-diagonal matrix elements of three types
which, in the notation of Cartwright and Mills (39), are given as

follows:

37

(Vt,1t+l;J,k+lIH/hclvt,£t-1,J,k-l>

(p/4)qt*[<vt+1>2-n,211/2{[J(J+1>-k<k+1)1[J(J+1)—k<k-1)1}1/2 (2-76)

(Vt,1t+l;J,k-llH/hclvt,1t-1,J,k+l>

2]1/2{[J(J+1)-k(k+1)][J(J+1)—k(k¢l)]}1/2 (2—77)

<p/4)qt’[(vt+1)2-1t

(Vt,1t;J,klfi/hclvt,!tiZ;J,k¥1>

= prt[(vt+1)2-(£t¥1)2]1/2[J(J+l)-k(k+l)]1/2(2ktl) . (2—78)

The Hamiltonian fl is obtained by the appropriate contact transformation
and the constant p in Eqs. (2-76) - (2-78) is equal to either +1 or -1,

depending on the sign of the constants qt and r Cartwright and Mills

t’

(39) refer to the effects associated with the matrix elements as qt+ (or

:2,i2)-type , qt_ (or tZ,¥2)-type, and rt (or t2,$l)-type interactions.
According to Eq. (2-75), qt+ interactions occur for all El(or E,

E Elu’ E'l, etc) type vibrational species in all symmetric top

lg’
molecules; the qt- interactions occur for all Em species in symmetric
top molecules with an even principal axis of symmetry (Cn or 8D with n

even) when m=(n-2)/2 (E in DZd’ E in D4h’ etc.); the rt type

3,11
interaction occurs for El species in molecules with an odd principal
axis of symmetry Cn if m = (n-l)/2 (E in 03v, E2 in CSv’ etc). Since
this thesis is concerned with C3v molecules, qt— interactions will not
be discussed further.
we will follow the sign convention that Cartwright and Mills

t = k = :1 levels
leads to the rovibrational A1 level lying above the rovibrational A2

introduced; qt > 0 when the 1~type doubling in the 1

38

level for J even. In the (vt,llt )= (1, +1) vibrational state the

doubling is thus given by the formula

T(A1)-T(A2) qt+J(J+1) for J even (2-79)

qt+J(J+l) for J odd (2-80)

where T(A1), etc., denote the term values. The general formula for qt+
in terms of the vibration-rotation interaction parameters also has a

definite sign if we follow these conventions (2§,§Q). Thus,

31)2 2
+ : 2—2{— 01: +128 {y2 + flj—v—s. { X2
g3 v2 v2 st g v2 2 st
vs t s ”t
2
_ xz o l/ _
sat /4122 + 2w(C/h) 220, t t. at.v / 3/2} (2 81)
”t
where
_ -l 3 2 _

is a cubic anharmonic constant, qr is a dimensionless normal coordinate,

_ 1/2 yy _
qr - 2n(vr/h) or’ and at —

The effects of k-resonances are illustrated in Fig. 2-5. The

(aIyy/aot)o.

reason that l-type doubling is large compared to other Al-Az splittings
can be explained by the fact that the l-resonances take place between
the two degenerate levels (k = 1t = :1). Finally, since subscripts s
and t have been used here to denote the nondegenerate and degenerate
vibrational states only for clarification, they will be dropped or
switched with notation of the corresponding vibrational modes for

convenience in the following sections.

39

+l -l H -l H

1
2 .. 3 ° 3
3 I. 1 1 J a 1:??- a
1 8 3 a a
3 3 3 4

S 5

(+) (-)

Figure 2—5. qt , qt , and rt R-resonance in an 1t = :1 degenerate

 

state of an oblate symmetric top. The levels are labeled by K, with

(+2) to the left of (-£); interactions are shown by broken lines.

40

II-3 Experimental

II-3-l White-Type Long Path Cell

White-type cells have been applied to a number of applications in
spectroscopy to provide long absorbing paths (31,32). This type of cell
is useful for many cases: (1) inherently weak transitions, for example,
combination and overtone bands; (2) low concentration samples such as
transient molecules and reaction intermediates; (3) high resolution
spectroscopy that needs to keep the pressure low for small pressure
broadening. In 1942, White introduced the design which accomplished the
desired result (33). The essential parts of the equipment are three
spherical, concave mirrors that all have the same radius of curvature.
The setup is shown in Fig. 2-6, where two mirrors A and A' are placed
close together at one end and the third mirror B at the other end. The
centers of curvature of A and A' are located on the front surface of B,
and the center of curvature of B is half way between A and A'. Later
Bernstein and Herzberg introduced a useful variation in the shape of the
front mirror (B), which, in the case where the size of the source is
appreciable, doubles the number of traverses obtainable without
overlapping images (35). Fig. 2-7 shows the shape of a front mirror of
this type together with the image location on it.

In a multiple-reflection system, astigmatism can limit the maximum
attainable number of passes even more than reflectivity. This
aberration causes an increase of the size of each successive image and
eventually image overlapping. In the double row alignment (Fig. 2-7),
the tangential image elongation is the main result of the astigmatism.

The general fOrmula for the image increase has been derived by Edward

41

——
—-——

—~_.
——__-

Figure 2-6. Mirror arrangement of a White-type cell. The small

circles on mirror surface are the centers of curvature of the mirrors.

 

Figure 2—7. Modified optical arrangement for a White—type cell. The

numbers show the sequence of reflection.

42

z hb

4
( N — ‘) (2‘83)
12122 N

4 _
AL N N) —

__§__(
T 12Rfv
where b is the total separation between the entrance and exit images, N
the number of traverses, h the height of mirror, R the radius of
curvature, and fv the vertical f number (h/R). From Eq. (2-83), it is
clear that b should be as small as possible. For a source of width ws
the minimum value of b which will give distinct images on the front
mirror and, will allow the entrance and exit images to clear the mirror
edges, is bmin=N/4ws and the corresponding width of the upper portion of
the front mirror is (N/4-l)ws (3Q). One may wish to cut down the wide
front mirror to reduce ALT. Reflectivities of mirrors also limit the
number of traverses. For example, forty traverses with 98* reflectivity
reduces energy to about 45% of that incident.

The homemade White type cell used in this work includes three
spherical mirrors with 1 m radius of curvature, two one inch diameter
mirrors and a two inch diameter front mirror. Three micrometers provide
required fine adjustment for appropriate alignment of each mirror. The
cell body consists of a 6 inch glass cylinder, 1 inch Can windows
located horizontally at the level of the center of the front mirror, and
aluminium end plates, which are tightened with O-rings for seals. The
whole structure is supported by the customized aluminium frame, and the
actual volume of the cell is estimated to be about 11 liters. The

windows provide enough room to adjust the incoming and outgoing laser

for double row alignment (Fig. 2-7). Without particular difficulty, a

43

24 m path-length can be obtained with a 2 mm diameter He/Ne laser beam
entering parallel. Throughout the study of the pa + v6 - 06 band of
CH3F, the mirrors were arranged to give 8 m path-length, which is enough
to provide the necessary signal to noise ratio when the cell is filled

with CH3F to 0.5 Torr pressure.
II-3-2 Infrared-Microwave Sideband Laser Spectrometer

Fig. 2-8 is a block diagram of the infrared microwave sideband
laser spectrometer used to record the spectra for this work. It is very
similar to the spectrometer used for previous studies from this
laboratory (2,2) except for the use of the White-type long path sample
cell. Since the instruments used in the spectrometer have been
described in detail elsewhere (2,2), only a brief explanation of the
components will be given. The semisealed CO2 laser includes a 1.7 m
plasma discharge tube with ZnSe Brewster angle windows in a 2.2 m laser
cavity with a rotatable plane grating at one end and a partially
transmitting (95X reflection) spherical concave mirror on a
piezoelectric translator (PZT) at the other end. Microwave radiation
was generated by a synthesizer (HP 8671B) and amplified by a traveling

wave tube amplifier (Varian Model VZM-6991Bl) at specific frequencies in
the 8-18 GHz region. Approximately 1 W of CO2 laser power (frequency
v!) is mixed with ~20 W of microwaves (frequency vm) in a CdTe
electrooptic crystal that is mounted in an impedance-matched housing. A
detailed description of the CdTe electrooptic crystal and the
electrooptic effect can be found in Shin-Chu Hsu’s thesis (2§). Since

the generated sidebands (frequency ”1 1 um) are polarized in a vertical

44

CE]a LASER

  

  

He/Ne Los
Muthposs Ceu

  
 

Coll

 
 
  

  
  

  
   

 
 
  

Focusmg
Lens

Bean

Polariza-
Sputter-

  
      

DET

  
 

PREAMP

 
  
   

 
  
 

PIN
CONTROL

 
 
   

PSD

  

33.3kH2
Mod.

    
 
 

COMPUTER

  

Figure 2-8. Block diagram of the infrared microwave sideband laser

used in this study.

45

plane, they are efficiently separated from the horizontally—polarized
carrier by means of a polarizer and later divided by a beam splitter
into two portions. One of the beams is used as a reference while the
other is allowed to pass through the White—type sample cell. Both beams
are monitored by liquid N2 cooled HngTe detectors (Infrared Associates,

Inc. HOT-100) cooled by liquid N The sidebands are 100% amplitude

2.
modulated by chopping the microwave power with a PIN diode, and the
detector signals (signal and reference) are processed by lock-in
amplifiers at the modulation frequency (33 kHz). The signal from the
reference lock-in amplifier is sent to a feedback circuit to stabilize
the total sideband power by controlling the microwave power. The CO2
laser carrier reflected from the polarizer passes back and forth through
a cell that contains CO2 and the 4.3 pm fluorescence signal that results
from the additional vibrational excitation is detected at 90° angle to
the beam by a liquid N2 cooled InSb photovoltaic detector (Judson
Infrared, Inc. JlOD). The saturation dip in the fluorescence from this
cell is used to stabilize the laser frequency. For this purpose the
laser frequency is modulated at 100 Hz by means of a sinusoidal voltage
applied to the PZT. The residual jitter in the laser frequency is
estimated to be ~150 kHz, which is also the expected accuracy of the
frequencies of the sidebands. The sidebands were not separated, but the
spectra were recorded a second time with the CO2 laser locked at the
edge of the fluorescence saturation dip in a known direction. The shift
in the apparent center frequency of each spectral line (5-10 MHz) was
enough to identify whether the positive or negative sideband had been

absorbed.

Figs. 2-9 and 2-10 are examples of spectra of the hot band of

46

 

    

Intensity(orb. units)

 

 

 

‘53 R(9,5.—1)‘

‘ R 8,—1,—1 R 8.1.1 ‘

452 ( ) ( ) d

.1 .1

45* ‘2C‘602 9P(12) ‘
“‘35 I T FT* 1 I

12.0 12.5 13.0 13.5 14.0 14.5 15.0
Frequency(GHz)

Figure 2-9. Portion of the spectrum of the v3+v6-v6 band observed in
the present work. The horizontal axis is the microwave frequency to
be added to (+) or subtracted from (-) the frequency of the 9P(12)

1201602 laser to obtain the infrared frequency of the transition.

47

 

 

 

 

35 1* I I I I
25- 1
E 15‘ + V ‘
'E — + —
3 '1 .,
d 5_ V R(12,6,-1) d
S 4R(12,5,_1) 4
+
'6 R(12,2.1)
C '1
.8 -15~ ~
g * 2V3 R(17,0—6)
-25~ .
. 12C1602 9P(6) ,
-35 I 1 l 1 l
8.0 8.5 9.0 9.5 10.0 10.5 11.0
Frequency(GHz)

Figure 2-10. Portion of the spectrum of the 03+v6-06 band observed
in the present work. The horizontal axis is the microwave frequency
to be added to (+) or subtracted from (—) the frequency of the 9P(6)
l201602 laser to obtain the infrared frequency of the transition. The
transition marked 2v3 is in the 2123-123 band and completely absorbs the

positive sideband power.

48

interest in this work plotted as a function of the microwave frequency,
which must be added to or subtracted from the appropriate laser
frequency to obtain the infrared frequency of the transition; the laser
frequencies were obtained from the report of Freed g2 g1. (21). Fig. 2-
9 is an example of a relatively clear region of the spectrum that shows
a well-resolved B-doublet. Fig. 2-10 shows a portion of the spectrum
that includes a 2D3 * v3 hot-band transition that is sufficiently strong
to absorb the entire positive sideband power.

Spectra were recorded for microwave frequencies from 8 to 18 GHz in
4-MHz steps for more than 40 laser lines. The frequencies of the
transitions were obtained by fitting the spectra by least squares to
Gaussian lineshapes; for overlapped transitions, the Doppler halfwidths
were constrained to the appropriate value (~34 MHz). A commercial
sample of CH3F from Peninsular Chemical Research was used as received
with only the usual freeze-pump—thaw cycling. The spectra were recorded

at room temperature (~29? K).

49
II-4 Results

II-4-l Term Values and Selection Rules

As mentioned in the introduction, both the upper and the lower
vibrational states of the 03 + 06 — ”6 band in CH3F belong to E-type
symmetry for 03v point group. The spectra were analyzed by calculating
the frequencies as differences in term values E(v,J,k,£) for degenerate

vibrational states (22,29) as follows:

E(v,J,k,£) = W(v,J,k,1) + wq(v,J,k,£) (2-84)
where
W(v,J,k,£) = v0 + av J(J+1) + (Av- 3v) k2 - 211.v {k1
- n} J2(J+l)2 - DEX J(J+1)k2 - n; k4
+ n} J(J+l)k9. + 1.; R39.
+ H} J3(J+1)3 + 33K J2(J+l)2k2 + HEJ J(J+1)k4
+ a; k4 (2—85)

In Eq. (2-85), ”0 is the vibrational band center; Av and Bv are the

. , v v v v v v v .
rotational constants, DJ, DJK’ DK’ HJ, HJK’ HKJ’ and HK are the quartic
and sextic centrifugal distortion constants; and f. n}. and n; are
Coriolis coupling constants. In Eq. (2-84), wq(v,J,k,1) is the 1-

resonance contribution which, except when k = I, was taken into account

explicitly as a second order perturbation:

wq(v,J,k,£) = [qu(J+1) + q;J2(J+l)2]2f(v,J,k,£) for k , 1 (2-86)

50

where

(J:k)(J:k-1)(J:k+1)(J:k+2)
4[W(v,J,k,£=:l) - W(v,J,k$2,£=$1)]

 

f(v,J,k,1=il) = (2—87)

When k = B = :1, the l-resonance term becomes l-type doubling:

wq(v,J,k,1) = % [qu(J+l) + q;J2(J+1)2] for k = i . (2-88)

The l—resonance term described above is referred as the (12,32)-
interaction (29). Another possible l-resonance in a 03v symmetric top,
the ($2.11) interaction, can not be included in the least squares
fitting of the frequencies because of linear dependence. The details
will be described later.

During the vibrational transition, 03 + v6 ~ ”6’ the dipole moment
may be considered to change parallel to the principal axis of symmetry.
Therefore the selection rules for allowed transitions were taken to be
AJ = 0 or 11, Ak = 0, and.A1 = 0 (11). Since off-diagonal l-resonance
elements mix the rotational levels (Ak = Al = 12 and Ak = :1, A1 = $2)
of degenerate vibrational states, in principle, other transitions, (Ak =
AI = $2,.A(k<1) = :3), are also allowed, but they are expected to be
much weaker and no attempt has been made to assign them. The primary
selection rules were used for all of the transitions except those for
which k = 1, for which k and 1 are not good quantum numbers because of
the linear combination of the states. For these transitions, it was
necessary to use the fundamental selection rule A1 .. A2, where the
identification of A1 and A2 levels is shown in Fig. 2-11 for odd J and

qv > 0 for the ”6 state (q6 is known to be positive (2)) and for the two

51

qu>0 qu<0 qu>0 qu<0

 

 

 

 

Aa-w— A1 fir- A1 ‘7"- AZT—
A1 ‘7‘ Aan— A2 "5"!— A1 "'1?
i i i 1
i E i 1
A2 -LJ— A2 —-J— A2 ——L A2 ——-1—
A1 4— A1 4—— A1 —— A1 ——

Q-Bronch P,R-Bronc:h

Figure 2-11. Energy-level diagrams showing higher frequency (solid
lines) and lower frequency (dashed lines) allowed transitions between
rotational levels belonging to two vibrational states of 8 symmetry
for C3v‘ For each of the diagrams, the J value of the levels in the
lower state is assumed to be odd and the qv value of the lower state
is assumed to be positive; the sign of the qv value (qu) for the

rotational levels of the upper state is indicated above each diagram.

52

possible signs of qv for the v3+v6 state. As indicated in Fig. 2-11, we

followed the sign convention suggested by Cartwright and Mills (22).

II-4—2 Analysis

The most tedious part of the assignment of the spectra was the
identification and labeling of the many transitions from the 03
fundamentals of 12CH3F and 13CH3F and the 203 - v3 hot band of 12CH3F,
all of which were considerably stronger than the transitions desired for
the present study. Fortunately, we had precise constants available
(2,2) for the interfering bands and were able to calculate the
frequencies of the overlapping transitions to high accuracy (within few
MHz). A first attempt at assignment was made by combining the reported
frequencies of the D6 and v3+v6 bands, as reported by Hirota (2) and
Nakagawa (2) g: 22., respectively. This method led to the assignment of
three J = 6+5 transitions about 500 MHz from their predicted values.

The Q(6,4) transition, in which 0 denotes the transition J~J and the
numbers are the J and K quantum numbers, was also found near the value
reported by Duxbury and Kato (lg), although it was seriously overlapped
with another transition which was assigned later as the Q(lO,lO).
However, assignment of higher J and k transitions by this method was not
possible because a limited number of experimental frequencies were
reported. We then calculated energy levels of the two states by using
the parameters reported by these workers and obtained frequencies from

differences in the energies. This procedure was also not useful because

the calculated frequencies were far from the experimental values. The

53

problem was traced to the fact that rather different ground state
constants were used in Refs. 2 and 2. Successful assignment of the v3 +
v6 - v6 band transitions was obtained when the constants in the paper by
Hirota (2) were used to calculate frequencies of the 06 band and the
constants in the paper by Nakagawa (2) were used to calculate
frequencies in the 03-1-1)6 combination band. Then the desired frequencies
of the v3+06-06 band were obtained as combination differences of the
calculated frequencies. This procedure led to assignment of additional
transitions for 1 = +1, but the 1 = -1 transitions could not be assigned
with confidence until after several iterations of least-squares fittings
of the l = +1 frequencies with proposed assignments of the 1 = -1
transitions gave better values of the constants. Strong correlations
between A! and the centrifugal distortion constants DK and DJK could not
be broken until the 1 = -1 transitions were included. The Coriolis

terms in the energy expression give contributions to the energies that

are large enough to cause the transitions for adjacent k values for a

given J to be separated by about 3 GHz. The 1 = +1 and.k -1

transitions spread out in different directions from the k 0 transition
for each J; the separation between 1 = +1 components for adjacent k is
somewhat larger than for the corresponding 1 = -1 components. In case
of oblate top molecules one can actually observe a series of doublets (1
= +1, -1) with k for a given J because the Coriolis interaction term,
|C{l is smaller than the term, |(C-B)k2| (22).

As shown in Fig. 2-11, both components of the l-type doublets occur

for P, Q, and R transitions according to Al-A2 selection rule. It can

be seen that the va+v6-06 band frequencies are sensitive to the absolute

54

magnitudes and the relative signs of qv for the upper and lower states,
but cannot be used to determine the absolute signs of the qv’s. We took
the sign of qv for the 126 state from Ref. 2. Fig. 2-9 shows the 1-
doublet pair for the QR(8,l) transition, which was the first pair found.
By using the splitting for this pair and constraining the qv constant
for the 06 state to that determined by Hirota (2) it was possible to
identify one or both components of 13 P- or R-branch l-type doublets for
3 S J S 20 and one Q-branch pair, QQ(4,1); the frequencies of these
transitions are shown in Table 2-1. Additional Q—branch transitions
were not identified because of the density of the Q—branch region and
the low intensity of Q-branch transitions for k = 1. In the final
1 fitting, which included the microwave frequencies for the direct 1-
doublet transitions in the 06 state (1), the qv constants for both
states were adjusted (q6 was constrained to be positive) and it was
necessary to include the higher-order constant q; for high J l-doubling
transitions as shown in Eq. (2-88).

In principle, the contribution of l-resonance to the energy
includes rv-dependent terms that result from the following matrix

elements (22,29):

<v,J,k,1=+ll H |v,J,k+l,1=-l>

= 2rv(2k + l)[(J - k)(J + k + 1111/2 . (2-39)

An attempt was made to include the effect of these terms for both states
at the level of second-order perturbation, but unstable fittings with
unpredictable correlations were obtained. In order to trace the origin
of the problem, the data were fit, including rv for the v6 state only,

by means of a least-squares routine that calculates the eigenvalues of

55

TABLE 2-1

Observed Transition Frequencies 12

from l-type Doublets of the 03+ vs— vs Band of 083F

 

 

Trans.a Laserb v.c v/Mflz O—Cd Uhc. v/cm l f
P(17, 1, 1) 1301602 9P(12) -13 805.5 30 199 220.6 2.5 5.0 1007.337 57( 8)
P(l7,-l,-l) 1301602 9P(12) -10 667.9 30 202 358.2 2.1 5.0 1007.442 22( 7)
P(l5,-1,-1) 1301602 9P( 8) 9 081.4 30 324 127.7 0.2 5.0 1011.504 01( 1)
P( 7, l, 1) 1201602 9P(40) -15 094.5 30 785 048.2 -0.3 5.0 1026.878 67( -l)
P( 7.-l.-l) 1201602 9P(40) -14 513.9 30 785 628.8 4.4 10.0 1026.898 04( 15)
P( 5,-1,-1) 1301602 9R(18) -17 955.5 30 894 523.2 0.9 3.0 1030.530 36( 3)
P( 3, l, 1) 1301602 98(22) 13 210.6 31 000 682.6 0.4 5.0 1034.071 45( l)
P( 3,-1,-1) 1301602 98(22) 13 324.5 31 000 796.4 -3.4 5.0 1034.075 26( -11)
O( 4, 1. 1) 1201602 9P(28) -11 040.4 31 148 467.8 -3.4 5.0 1039.001 05( -11)
O( 4,-l,-1) 1201602 9P(28) -10 908.2 31 148 600.0 -0.2 5.0 1039.005 46( -1)
R( 4, 1, 1) 1201602 9P(20) 15 308.6 31 399 209.0 -3.7 5.0 1047.364 87( -12)
R( 5,-1,-1) 1201602 9P(18) 8 229.4 31 446 289.5 3.5 5.0 1048.935 31( 12)
R( 8, l, 1) 1201602 9P(12) -13 892.7 31 581 939.0 2.8 3.0 1053.460 09( 9)
R( 8,-l,-l) 1201602 9P(12) -13 072.6 '31 582 759.1 -0.1 3.0 1053.487 45( 0)
R(ll. l, 1) 1201602 9P( 8) 14 634.8 31 711 696.3 1.1 5.0' 1057.788 33( 4)
R(ll,-1,-l) 1201602 9P( 8) 16 115.8 31 713 177.2 1.1 5.0 1057.837 72( 4)
R(lZ,-1,-1) 1201602 9P( 6) 8 815.6 31 755 299.4 0.3 3.0 1059.242 77( 1)
8(18, 1, 1) 1201602 9R( 4) -13 901.0 31 990 116.4 -l.9 5.0 1067.075 41( -6)
R(18,-l,-1) 1201602 SR( 4) -10 192.3 31 993 825.1 -0.9 5.0 1067.199 12( -3)
R(19,-1,-1) 1201602 98( 6) -17 028.8 32 031 207.5 0.6 3.0 1068.446 06( 2)
8(20, 1, 1) 1201602 98( 6) 15 166.7 32 063 403.0 2.0 5.0 1069.519 99( 7)

 

 

8Numbers are J, k, and l of the lower vibrational state.
lower energy components of the l-type doublets.

bLaser line used; laser frequencies were taken from Ref. 21.

cMicrowave frequency in MHz. The signed microwave frequency was added to the laser

frequency to obtain the absorption frequency.

Levels with k,1 = -1,-1 are the

dObserved minus calculated frequency in MHz; the parameters for the calculation are in
Tables 2-3 and 2-4.

eEstimated uncertainty in the observed frequency in MHz.

fCbserved wavenumber in cm.1.
wavenumbers in units of 0.00001 cm

The 9

umbers in parentheses are observed minus calculated

56

the normal equations matrix after scaling. It is known that the
occurrence of one or more small eigenvalues in this procedure is
evidence of linear dependence (22); we found one small eigenvalue for
which the corresponding eigenvector contained a substantial contribution
from the parameter r6. The origin of this problem then became obvious
when we expanded the second-order perturbation contribution from the
matrix element in Eq. (2-89) and found that the contribution to the

energy, wr, could be written as

 

wr(v,J,k,1) = r'[-J(J+l) + 3k2 + ki - 2J(J+l)k1 + 2k31] (2—90)
where
4r:
r' = . (2—91)

Av — Bv + ZAV;

The detailed derivation of this equation is in the Appendix.
Apparently, at this level of approximation, by redefining the parameters

v v . . .
B Av Bv, Av" nJ. and "K to include a contribution from rv, the

v’
effects of the matrix elements in Eq. (2-89) are included completely.

It is therefore not surprising that a linear dependence was encountered
when rv was included as a parameter in the fitting. A linear dependence
involving rv was already implicit in the equation given by Grenier-
Besson and Amat for the rotational frequencies in an E state of a 03v
molecule (29).

Ultimately, the measured frequencies of’more than 220 transitions

in the v3+v6-v6 band were assigned and used to obtain vibration-rotation

parameters for the two states. The final least squares fitting included

57

the rotational frequencies reported in Refs. (2,1), in which each data
point was weighted by the inverse of the squares of the uncertainty. In
order to avoid linear dependence, vo, (Av-Ev), DK’ Av{, andnK of the
v6=1 state were constrained to the values reported by Hirota (2), and HK
for this state was constrained to zero. The standard deviation for an
object of unit weight and the root-mean-square deviation are calculated
1.05 and 8.05 MHz, respectively. The frequencies of assigned
transitions are compared in Table 2-2 to calculated frequencies that

were obtained from the determined vibration-rotation parameters in

Tables 2-3 and 2-4.

58

TABLE 2-2

Comparison of Observed and Calculated Frequencies in the v3+ v6- ”6 Band of 12CH3F

 

 

Trans.a Laserb v-c v/MHz O—Cd U’nc.e v/cm l f
P(17, l,-l) 1301602 9P(12) —17 765.8 30 195 260.3 -2.1 3.0 1007.205 46( -7)
P(l7, 0, 1) 1301602 9P(12) -15 063.0 30 197 963.2 0.1 5.0 1007.295 62(
P(17, l. 1) 1301602 9P(12) -13 805.5 30 199 220.6 2.5 5.0 1007.337 57(
P(17,-1,-1) 1301602 9P(12) -10 667.9 30 202 358.2 2.1 5.0 1007.442 22(
P(17. 2. 1) 1301602 9P(12) -9 277.2 30 203 748.9 5.3 5.0 1007.488 61( 18)
P(16, 5,-1) 1301602 9P(10) -17 314.9 30 247 154.2 4.7 3.0 1008.936 46( 16)
P(16. 4,-1) 1301602 9P(10) -15 158.6 30 249 310.5 4.7 5.0 1009.008 38( 16)
P(16, 3.-1) 1301602 9P(10) -12 865.7 30 251 603.3 -2.2 3.0 1009.084 87( -7)
P(16, 2.-l) 1301602 9P(10) -10 431.8 30 254 037.3 -6.4 5.0 1009.166 06( -21)
P(16, 5, 1) 1301602 9P(10) 10 431.8 30 274 900.8 -0.1 5.0 1009.861 98(
P(16, 7, 1) 1301602 9P(10) 17 708.2 30 282 177.3 -ll.7 5.0 1010 104 70( —39)
P(15, 9,-1) 1301602 9P( 8) -14 201.7 30 300 844.6 0.1 5.0 1010.727 38(
P(15, 8,-1) 1301602 9P( 8) -12 708.1 30 302 338.2 4.7 5.0 1010.777 19( 16)
P(15, 7.-1) 13C1602 9P( 8) -11 039.2 30 304 007.1 1.5 5.0 1010.832 86(
P(15, 6,-1) 1301602 9P( 8) -9 186.5 30 305 859.8 11.0 30.0 1010.894 67( 37)
P(15,-1,-1) 1301602 9P( 8) 9 081.4 30 324 127.7 0.2 5.0 1011.504 01(
P(15, 2. 1) 1301602 9P( 8) 10 826.9 30 325 873.2 1.1 3.0 1011.562 23(
P(15. 3. 1) 1301602 9P( 8) 13 952.5 30 328 998.8 0.6 5.0 1011.666 50(
P(15, 4, 1) 1301602 9P( 8) 17 220.8 30 332 267.1 -0.8 5.0 1011.775 52( -3)

9. 5.-1) 1201602 9P(44) -16 006.7 30 658 439.0 -3.8 5.0 1022 655 44( -l3)
9. 2.-1) 1201602 9P(44) -9 045.1 30 665 400.7 1.5 5.0 1022.887 65(

9, 4, 1) 1201602 9P(44) 8 739.0 30 683 184.8 -22.1 30.0 1023.480 87( -74)
9, 5, 1) 1201602 9P(44) 12 253.1 30 686 698.8 0.7 3.0 1023.598 08(

9, 6, 1) 1201602 9P(44) 15 917.4 30 690 363.2 7.7 5.0 1023.720 32( 26)
8, 3.-l) 1301602 9R( 8) 9 306.3 30 719 078.4 -2.7 3.0 1024.678 15( -9)
8, 1,-1) 1201602 9P(42) -13 484.1 30 724 172.6 3.2 20.0 1024.848 07( 11)
8, 3, 1) 1301602 98(10) -16 001.5 30 736 057.4 1.4 3.0 1025.244 51(

8, 4, 1) 1301602 9R(10) -12 664.1 30 739 394.8 -0.8 3.0 1025 355 83( -3)
8, 5, 1) 1301602 9R(10) —9 161.6 30 742 897.3 4.0 5.0 1025 472 67( 13)
8, 6, 1) 1201602 9P(42) 8 917.0 30 746 573.7 16.4 20.0 1025 595 29( 55)
8, 7, l) 12C1602 9P(42) 12 765.2 30 750 421 9 24.0 10.0 1025 723 66( 80)
7, 6,-1) 1301602 99(10) 16 001.5 30 768 060 4 18.4 20.0 1026.312 02( 61)
7. 2.-1) 1301602 98(12) -16 422.5 30 777 049.4 0.6 3.0 1026.611 85(

7, 0, 1) 1201602 9P(40) -17 696.7 30 782 446.0 13.5 20.0 1026.791 87( 45)
7, 1, 1) 1201602 9P(40) -15 094.5 30 785 048.2 -0.3 5.0 1026.878 67( -l)
7.-1.-1) 1201602 9P(40) -14 513.9 30 785 628.8 4.4 10.0 1026 898 04( 15)
7, 2, 1) 1201602 9P(40) -11 743.0 30 788 399 7 16.3 20.0 1026 990 46( 54)
7, 3, 1) 1201602 9P(40) -8 555.1 30 791 587 6 10.8 20.0 1027.096 80( 36)
6, 3, 1) 1201602 9P(38) -15 467.0 30 846 430.5 -3.3 5.0 1028.926 16( -11)
6, 3, 1) 1301602 98(14) 12 421.6 30 846 433.6 -O.2 3.0 1028 926 26( -l)
6. 4, 1) 1201602 9P(38) -12 116.2 30 849 781.3 -0 7 5.0 1029.037 93( -2)
6, 4, 1) 1301602 9R(14) 15 771.0 30 849 782 9 0 9 3.0 1029.037 99(

6, 5, 1) 1201602 9P(38) -8 608.0 30 853 289.5 1 7 5.0 1029.154 96(

5, 3,-1) 1301602 9R(16) 9 876.0 30 883 556.4 -8.6 10.0 1030.164 55( -29)
5, 2,-1) 1301602 9R(16) 12 375.5 30 886 055.9 1.9 3.0 1030.247 92(

5, l,-l) 1301602 9R(16) 15 003.6 30 888 684.0 -1.4 3.0 1030.335 58( -5)
5, O, 1) 1301602 99(16) 1? 778.0 30 891 458.4 0.8 3.0 1030.428 13(

5.-1,-l) 1301602 9R(18) -17 955.5 30 894 523.2 0.9 3.0 1030.530 36(

5, 3, 1) 1301602 9R(18) -11 855.8 30 900 622.9 -2.2 5.0 1030.733 82( -7)
5, 4, 1) 1301602 99(18) -8 504.4 30 903 974.3 -l.3 5.0 1030.845 62( -4)

 

 

59

TABLE 2-2 (cont’d)

 

 

Tranl.a Laserb v-C v/Mflz 0—0d Uhc. D/CI-l f
P( 4, 3,-l) 1201602 9P(36) 14 150.8 30 937 066.3 1.1 5.0 1031.949 45( 4)
P( 4, 2,-1) 1201602 9P(36) 16 647.5 30 939 562.9 2.7 5.0 1032.032 72( 9)
P( 4, 1,-1) 1301602 98(20) -8 207.4 30 942 201.1 4.3 5.0 1032.120 73( 15)
P( 3, 2,-1) 1201602 9P(34) 9 209.7 30 992 400.5 0.8 3.0 1033.795 20( 3)
P( 3, 1,-1) 1201602 9P(34) 11 852.5 30 995 043.3 1.9 3.0 1033.883 36( 6)
P( 3, 0, 1) 1201602 9P(34) 14 631.5 30 997 822.3 0.4 3.0 1033.976 05( 1)
P( 3, 1, 1) 1301602 98(22) 13 210.6 31 000 682.6 0.4 5.0 1034.071 45( l)
P( 3,-1,-1) 1301602 98(22) 13 324.5 31 000 796.4 -3.4 5.0 1034.075 26( -11)
P( 3, 2, 1) 1301602 98(22) 16 328.5 31 003 800.4 0.0 5.0 1034.175 45( 0)
0(17, 8,-1) 1201602 9P(32) -12 184.2 31 030 533.9 20.0 OMIT 1035.067 19( 67)
0(17, 7,-1) 1201602 9P(32) -10 201.3 31 032 516.8 10.2 20.0 1035.133 34( 34)
0(16, 9,-1) 1301602 98(24) 16 510.3 31 040 181.7 23.2 OMIT 1035.389 01( 77)
0(16, 7,-1) 1301602 98(26) -15 065.0 31 043 944.3 -4.2 5.0 1035.514 51( -14)
0(19, 7, 1) 1301602 98(26) -12 374.6 31 046 634.6 0.7 5.0 1035.604 26( 2)
0(15,12,-1) 1301602 98(26) -12 374.6 31 046 634.6 2.2 5.0 1035.604 26( 7)
P( 2, 1,-1) 1301602 98(26) -11 791.9 31 047 217.4 -0.2 5.0 1035 623 70( -1)
0(15,11,-1) 13C1602 98(26) -11 109.9 31 047 899.4 2.4 5.0 1035.646 44( 8)
0(16, 5,-1) 1301602 98(26) -10 734.8 31 048 274.4 5.2 5.0 1035.658 95( 17)
P( 2, 0, 1) 1301602 98(26) -9 011.5 31 049 997.7 -4.1 5.0 1035 716 43( -14)
0(15, 5,-1) 1201602 9P(32) 16 284.0 31 059 002.0 -6.5 10.0 1036 016 78( ~22)
0(l4, 5,-1) 1301602 98(26) 10 063.5 31 069 072.8 -9.4 20.0 1036.352 72( -31)
Q(13,10,-1) 1301602 98(26) 10 063.5 31 069 072.8 13.1 20.0 1036.352 72( 44)
0(13. 8,-1) 1301602 98(26) 13 368.5 31 072 377.7 5.5 5.0 1036.462 96( 18)
0(13, 7,-1) 1301602 98(26) 15 261.1 31 074 270.3 0.7 5.0 1036 526 09( 2)
0(16, 5, 1) 1301602 98(28) -17 173.7 31 076 314.8 -7.7 5.0 1036 594 28( -26)
0(13, 6,-1) 13C1602 98(28) -17 173.7 31 076 314.8 2.9 3.0 1036.594 28( 10)
0(12,11,-l) 1301602 98(26) 17 532.7 31 076 541.9 -3.6 5.0 1036.601 85( -12)
0(15, 4, 1) 1201602 9P(30) -17 664.3 31 083 827.9 8.2 10.0 1036.844 89( 27)
0(11,11,-1) 1201602 9P(30) -16 759.0 31 084 733.1 -6.3 5.0 1036.875 09( -21)
0(12, 6,-1) 1201602 9P(30) -16 426.0 31 085 066.1 1.8 5.0 1036 886 19( 6)
0(11, 9,-1) 1201602 9P(30) -13 926.2 31 087 566.0 -16.9 20.0 1036.969 57( -56)
0(12, 4,-1) 1201602 9P(30) -11 968.7 31 089 523.5 -0.2 5.0 1037.034 87( -1)
0(15, 6, 1) 1201602 9P(30) -10 939.4 31 090 552.8 -8.5 5.0 1037.069 21( -28)
0(16. 9, 1) 1201602 9P(30) -10 751.5 31 090 740.7 -37.2 40.0 1037.075 47("124)
0(11, 7,-1) 1201602 9P(30) -10 361.5 31 091 130.7 -6.2 5.0 1037.088 49( -21)
0(12, 3,-1) 1201602 9P(30) -9 545.7 31 091 946.5 3.7 5.0 1037.115 70( 12)
0(11, 6,-1) 1201602 9P(30) -8 349.0 31 093 143.2 -4.3 5.0 1037.155 61( -14)
0( 9, 9,-1) 1301602 98(28) 8 337.1 31 101 825.6 -9.8 20.0 1037.445 23( ~33)
0(14, 7, 1) 1301602 9R(28) 10 828.9 31 104 317.3 -6.9 3.0 1037.528 35( -23)
0(10, 4,-1) 13C1602 98(28) 11 489.4 31 104 977.9 -2.0 20.0 1037.550 37( -7)
0(15,10, 1) 1301602 98(28) 12 313.9 31 105 802.4 28.0 OMIT 1037.577 88( 94)
0(13, 5, 1) 13C1602 98(28) 13 235.3 31 106 723.8 -2.7 5.0 1037.608 61( -9)
0( 9, 6,-1) 1301602 98(28) 13 805.0 31 107 293.5 -8.6 10.0 1037.627 61( -29)
Q( 9, 5,-1) 1301602 98(28) 15 941.1 31 109 429.6 -4.0 5.0 1037.698 86( ~13)
O( 8, 8,-1) 1301602 98(28) 16 092.9 31 109 581.3 -6.0 5.0 1037.703 92( -20)
0(13, 6, 1) 1201602 9P(30) 8 719.7 31 110 211.9 -0.9 5.0 1037.724 96( -3)
O( 8, 7,-1) 1201602 9P(30) 9 903.1 31 111 395.3 -4.2 3.0 1037.764 43( -14)
0( 9, 4,-1) 1201602 9P(30) 10 208.8 31 111 700.9 -3.4 5.0 1037.774 64( -11)
0(14. 9. 1) 1201602 9P(30) 10 510.2 31 112 002.4 10.3 5.0 1037.784 68( 35)
0(12. 4. 1) 1201602 9P(30) 10 654.3 31 112 146.5 -0.6 5.0 1037.789 50( -2)

 

 

60

TABLE 2-2 (cont’d)

 

 

Trans.a Laserb v-C v/Mflz 0-0d Unc.e D/CI-1 f
0( 8, 6,-1) 1201602 9P(30) 11 877.5 31 113 369.7 -2.2 5.0 1037.830 30( -7)
0( 8, 5,-1) 1201602 9P(30) 14 012.5 31 115 504.7 10.3 10.0 1037.901 51( 34)
0( 7, 7,-1) 1201602 9P(30) 15 307.5 31 116 799.7 -7.4 5.0 1037.944 70( -25)
0(13, 8, 1) 1201602 9P(30) 16 131.3 31 117 623.5 -4.3 5.0 1037.972 18( —14)
0( 8, 4,-1) 1201602 9P(30) 16 265.2 31 117 757.4 -1.2 5.0 1037.976 66( -4)
0( 7, 6.-l) 1201602 9P(30) 17 275.3 31 118 767.4 -1.8 3.0 1038.010 35( -6)
O( 5, 2,-1) 1301602 98(30) 9 699.6 31 136 811.7 4.3 10.0 1038.612 23( 14)
0( 8, 3, 1) 1301602 98(30) 10 111.6 31 137 223.8 0.8 5.0 1038.625 99( 3)
0( 4, 3.-1) 1301602 98(30) 10 542.3 31 137 654.5 6.6 5.0 1038.640 34( 22)
Q( 9, 5. 1) 1301602 98(30) 10 748.0 31 137 860.2 1.7 20.0 1038.647 22( 6)
0(10, 7, 1) 1301602 98(30) 11 239.1 31 138 351.3 9.0 5.0 1038.663 60( 30)
0( 5, 1,-1) 1301602 98(30) 12 340.8 31 139 452.9 -11.0 5.0 1038.700 34( -37)
0( 7, 2, 1) 1301602 98(30) 12 340.8 31 139 452.9 0.9 5.0 1038.700 34( 3)
0( 4, 2,-1) 1301602 98(30) 13 057.7 31 140 169.9 -1.4 20.0 1038.724 25( ~5)
Q( 3, 3,-1) 1301602 98(30) 13 248.8 31 140 360.9 20.6 20.0 1038.730 63( 08)
0( 8, 4, 1) 1301602 9R(30) 13 403.4 31 140 515.6 -3.5 5.0 1038.735 78( -12)
0( 9, 6, 1) 1301602 98(30) 14 322.3 31 141 434.5 6.5 5.0 1038.766 44( 22)
0( 7. 3. 1) 1201602 9P(28) -16 891.7 31 142 616.5 -5.7 10.0 1038.805 86( -19)
O( 3. 2.-1) 1201602 9P(28) -16 644.0 31 142 864.2 1.3 10.0 1038.814 12( 4)
0( 2. 2.-1) 1201602 9P(28) -14 625.1 31 144 883.1 1.3 5.0 1038.881 48( 4)
0( 9, 7, 1) 1201602 9P(28) -14 338.9 31 145 169.3 15.5 5.0 1038.891 02( 52)
0( 7, 4, 1) 1201602 9P(28) -13 579.8 31 145 928.4 -0.3 3.0 1038.916 33( -1)
0( 6, 3, 1) 1201602 9P(28) -12 163.1 31 147 345.0 -2.9 3.0 1038.963 60( -10)
O( 2, 1,-1) 1201602 9P(28) -11 970.7 31 147 537.4 -1.3 20.0 1038.970 01( -4)
Q( 8, 6, 1) 1201602 9P(28) -11 970.7 31 147 537.4 -4.4 20.0 1038.970 01( -15)
Q( 5, 2, 1) 1201602 9P(28) -11 293.4 31 148 214.8 ~1.4 3.0 1038.992 61( -5)
0( 4, 1, 1) 1201602 9P(28) -11 040.4 31 148 467.8 -3.4 5.0 1039.001 05( -11)
0( 4,-1,-1) 1201602 9P(28) -10 908.2 31 148 600.0 -0.2 5.0 1039.005 46( -1)
0( 1, 1.-1) 1201602 9P(28) -10 615.6 31 148 892.5 7.6 30.0 1039.015 21( 26)
O( 9, 8, 1) 1201602 9P(28) -10 426.2 31 149 082.0 34.7 30.0 1039.021 52( 116)
O( 7. 5. 1) 1201602 9P(28) -10 130.8 31 149 377.4 -0.6 5.0 1039.031 39( -2)
O( 6, 4, 1) 1301602 98(32) -9 213.6 31 150 670.0 6.6 10.0 1039.074 50( 22)
Q( 8, 7, 1) 1201602 9P(28) -8 207.8 31 151 300.4 14.0 10.0 1039.095 53( 47)
0( 5, 3. 1) 1201602 9P(28) -8 113.1 31 151 395.0 -4.6 5.0 1039.098 69( -15)
0( 4, 2, 1) 1301602 98(32) -8 293.9 31 151 589.8 1.6 5.0 1039.105 18( 5)
R( 0, 0, 1) 1201602 9P(26) -14 243.5 31 202 517.8 4.6 5.0 1040.803 95( 15)
R( 3, 3,-l) 1201602 9P(22) 11 965.4 31 340 926.9 3.8 5.0 1045 420 78( 13)
R( 3. 2.‘1) 1201602 9P(22) 14 516.3 31 343 477.8 3.8 5.0 1045 505 87( 13)
R( 4, 1, 1) 1201602 9P(20) 15 308.6 31 399 209.0 -3.7 5.0 1047 364 87( -12)
R( 5,-1,-1) 1201602 9P(18) 8 229.4 31 446 289.5 3.5 5.0 1048 935 31( 12)
R( 5. 2. 1) 1201602 9P(18) 11 088.4 31 449 148.6 -1.6 3.0 1049 030 68( -5)
R( 5, 3, 1) 1201602 9P(18) 14 249.7 31 452 309.8 -3.9 3.0 1049 136 13( -13)
R( 5. 4. 1) 1201602 9P(18) 17 538.8 31 455 599.0 -5.3 3.0 1049 245 84( -18)
R( 6, 6,-1) 1201602 9P(16) -17 196.3 31 474 241.1 20.4 20.0 1049.867 68( 68)
R( 6. 5.-1) 1201602 9P(16) -15 009.9 31 476 427.5 4.5 5.0 1049.940 61( 15)
R( 6, 4,-1) 1201602 9P(16) -12 678.5 31 478 758.9 3.2 3.0 1050.018 37( 11)
R( 6. 3.-l) 1201602 9P(16) -10 227.3 31 481 210.1 -2.0 5.0 1050.100 14( -7)
R( 6, 4, 1) 1201602 9P(16) 10 227.3 31 501 664.7 -6.1 5.0 1050.782 42( -20)
R( 6. 5. 1) 1201602 9P(16) 13 640.0 31 505 077.4 -0.4 5.0 1050.896 25( -1)
R( 6. 6. 1) 1201602 9P(16) 17 196.3 31 508 633.7 11.4 20.0 1051.014 88( 38)

 

 

61

TABLE 2-2 (cont’d)

 

 

Trans . a Laserb v“: v/Mflz O-Cd Unc . p/cn-l f
B( 7, 3,~1) 1201602 99(14) ~17 414.9 31 526 614.0 0.2 3.0 1051.614 64( 1)
R( 7, 2,~1) 1201602 9P(14) ~14 825.3 31 529 203.6 5.5 5.0 1051.701 02( 19)
E( 7, 1,~1) 1201602 9P(14) ~12 132.0 31 531 896.8 2.7 3.0 1051.790 86( 9)
R( 7, 0, 1) 1201602 9P(14) ~9 329.4 31 534 699.5 ~1.2 3.0 1051.884 35( ~4)
R( 7. 6. 1) 1201602 9P(14) 9 938.3 31 553 967.1 4.3 3.0 1052.527 04( 14)
R( 8, O, 1) 1201602 9P(12) ~16 395.6 31 579 436.2 1.6 3.0 1053.376 61( 5)
R( 8. 1. 1) 1201602 9P(12) ~13 892.7 31 581 939.0 2.8 3.0 1053.460 09( 9)
R( 8.~1.~l) 1201602 9P(12) ~13 072.6 31 582 759.1 ~0.1 3.0 1053.487 45( 0)
R( 3. 2. 1) 1201602 99(12) ~10 469.0 31 585 362.8 ~5.8 5.0 1053.574 29( ~19)
R( 9, 8,-1) 1201602 9P(12) 8 209.2 31 604 041.0 ~34.4 OMIT 1054.197 32(-115)
E( 9, 7,-1) 1201602 9P(12) 10 247.7 31 606 079.4 ~2.7 3.0 1054.265 32( ~9)
R( 8, 8, 1) 1201602 9P(12) 10 247.7 31 606 079.4 42.5 OMIT 1054.265 32( 142)
R( 9, 6.~1) 1201602 9P(12) 12 393.7 31 608 225.5 1.7 3.0 1054.336 90( 6)
R( 9, 5,-1) 1201602 9P(12) 14 661.7 31 610 493.4 2.9 3.0 1054.412 55( 10)
R( 9, 4,-1) 1201602 9P(12) 17 040.0 31 612 871.8 ~3.1 3.0 1054.491 89( ~10)
R( 9, 2. 1) 1201602 9P(10) ~17 439.9 31 629 403.5 ~3.6 3.0 1055.043 33( ~12)
R( 9, 3, 1) 1201602 9P(10) ~14 321.4 31 632 522.0 ~4.6 3.0 1055.147 35( ~15)
R( 9, 4, 1) 1201602 9P(10) ~11 091.2 31 635 752.2 ~4.7 3.0 1055.255 11( ~16)
8(10, 4,-1) 1201602 9P(10) 9 373.4 31 656 216.8 2.5 3.0 1055.937 73( 8)
8(10, 3,-1) 1201602 9P(10) 11 883.3 31 658 726.7 3.1 3.0 1056.021 44( 10)
8(10, 2,~1) 1201602 9P(10) 14 494.1 31 661 337.5 2.5 5.0 1056.108 53( 8)
R(10, 1,~1) 1201602 9P(10) 17 204.6 31 664 047.9 2.7 3.0 1056.198 94( 9)
8(10, 6, 1) 1201602 9P( 8) ~11 214.8 31 685 846.6 ~0.5 3.0 1056.926 07( ~2)
8(11, 1,~1) 1201602 9P( 8) 9 677.3 31 706 738.7 10.1 20.0 1057.622 95( 34)
8(11, 0, 1) 1201602 9P( 8) 12 478.7 31 709 540.1 3.6 3.0 1057.716 40( 12)
8(11, 1, 1) 1201602 9P( 8) 14 634.8 31 711 696.3 1.1 5.0 1057.788 33( 4)
R(11,~1,~1) 1201602 9P( 8) 16 115.8 31 713 177.2 1.1 5.0 1057.837 72( 4)
8(12, 8,-1) 1201602 9P( 6) ~14 767.6 31 731 716.2 1.1 3.0 1058.456 12( 4)
8(11, 7, 1) 1201602 9P( 6) ~14 516.1 31 731 967.7 2.3 3.0 1058.464 51( 8)
8(11, 8, 1) 1201602 9P( 6) ~10 832.4 31 735 651.4 13.2 10.0 1058.587 37( 44)
8(12. 6.~1) 1201602 9P( 6) ~10 437.5 31 736 046.2 ~10.8 10.0 1058.600 55( ~36)
8(12, 5,-1) 1201602 9P( 6) ~8 080.2 31 738 403.6 6.6 5.0 1058.679 19( 22)
R(12,-1,~l) 1201602 9P( 6) 8 815.6 31 755 299.4 0.3 3.0 1059.242 77( 1)
8(12, 2, 1) 1201602 9P( 6) 10 927.2 31 757 410.9 0.2 5.0 1059.313 20( 1)
8(12, 3, 1) 1201602 9P( 6) 14 002.6 31 760 486.4 ~0.4 3.0 1059.415 79( -l)
8(12, 4, 1) 1201602 9P( 6) 17 174.2 31 763 657.9 ~0.7 5.0 1059.521 58( ~2)
8(13, 6,~1) 1201602 9P( 4) ~17 814.1 31 777 294.6 0.1 20.0 1059.976 45( 0)
8(12, 8, 1) 1201602 9P( 4) ~17 653.5 31 777 455.2 7.6 5.0 1059.981 80( 26)
8(13, 5,-1) 1201602 9P( 4) ~15 448.3 31 779 660.4 ~0.4 3.0 1060.055 37( ~1)
8(13, 4,-1) 1201602 9P( 4) ~12 991.0 31 782 117.7 ~6.0 20.0 1060.137 33( ~20)
8(13, 3,~1) 1201602 9P( 4) ~10 431.7 31 784 677.0 ~0.4 3.0 1060.222 70( ~1)
8(13, 4, 1) 1201602 9P( 4) 9 804.0 31 804 912.6 -3.0 5.0 1060.897 69( ~10)
8(13, 5, 1) 1201602 99( 4) 13 054.0 31 808 162.7 0.6 10.0 1061.006 10( 2)
R(14,10,~1) 1201602 9P( 4) 14 245.1 31 809 353.8 8.5 5.0 1061.045 83( 28)
8(14, 9,-1) 1201602 9P( 4) 16 182.4 31 811 291.1 2.9 5.0 1061.110 44( 10)
8(13, 6, 1) 1201602 9P( 4) 16 398.6 31 811 507.3 ~4.9 3.0 1061.117 65( ~16)
8(16, 9, 1) 1201602 98( 2) ~17 740.2 31 941 255.8 ~15.4 5.0 1065.445 60( ~51)
8(17, 3,~1) 1201602 9R( 2) ~15 986.7 31 943 009.4 ~9.l 5.0 1065.504 10( ~30)
R(16,10, 1) 1201602 98( 2) ~14 069.6 31 944 926.5 ~25.7 30.0 1065.568 05( ~86)
8(17, 1,-1) 1201602 98( 2) ~10 559.4 31 948 436 7 ~5.7 3.0 1065.685 14( ~19)

 

 

62

TABLE 2~2 (cont’d)

 

 

Trans.a Laserb -c v/MHz 0-0d Unc. v/cm 1 f
8(18, 8,-1) 1201602 98( 2) 9 385.3 31 968 381.4 18.9 30.0 1066.350 41( 63)
8(17, 6, 1) 1201602 98( 2) 10 380.0 31 969 376.0 5.3 3.0 1066.383 59( 18)
8(18, 7,-1) 1201602 98( 2) 11 749.6 31 970 745.7 22.5 30.0 1066.429 29( 75)
8(18, 6,~1) 1201602 QR( 2) 14 169.2 31 973 165.3 2.0 5.0 1066.509 99( 7)
8(18, 5,-1) 1201602 98( 2) 16 674.9 31 975 671.0 ~3.8 5.0 1066.593 57( ~13)
8(17, 8, 1) 1201602 98( 2) 17 041.8 31 976 037.9 ~4.8 5.0 1066.605 81( ~16)
8(18, l,~1) 1201602 98( 4) ~17 696.5 31 986 320.9 ~5.9 5.0 1066.948 82( ~20)
8(18, 0, 1) 1201602 98( 4) ~14 902.2 31 989 115.2 ~12.6 20.0 1067.042 03( ~42)
R(18, 1, 1) 1201602 98( 4) ~13 901.0 31 990 116.4 ~1.9 5.0 1067.075 41( ~6)
H(18,~1,~l) 1201602 QR( 4) ~10 192.3 31 993 825.1 ~O.9 5.0 1067.199 12( ~3)
8(18, 2, 1) 1201602 98( 4) ~9 141.0 31 994 876.4 6.1 3.0 1067.234 20( 20)
8(19, 5,-1) 1201602 98( 4) 8 795.5 32 012 812.9 ~1.6 3.0 1067.832 49( ~5)
8(18, 8, 1) 1201602 9R( 4) 9 640.6 32 013 658.0 ~11.3 10.0 1067.860 68( ~38)
8(19, 3,~1) 1201602 9R( 4) 14 041.3 32 018 058.7 ~11.1 10.0 1068.007 47( ~37)
8(19, 2,~1) 1201602 98( 4) 16 741.5 32 020 758.9 ~14.5 20.0 1068.097 54( ~49)
R(19,~1,~l) 1201602 98( 6) ~17 028.8 32 031 207.5 0.6 3.0 1068.446 06( 2)
8(19, 2, 1) 1201602 QR( 6) ~16 187.3 32 032 048.9 10.8 3.0 1068.474 14( 36)
8(19, 3, 1) 1201602 98( 6) ~13 240.9 32 034 995.4 15.3 5.0 1068.572 41( 51)
8(20, 2,~1) 1201602 98( 6) 9 030.6 32 057 266.8 ~12.8 10.0 1069.315 31( ~43)
8(20, l,~1) 1201602 QR( 6) 11 788.4 32 060 024.6 ~10.4 3.0 1069.407 31( ~35)
8(20, 0, 1) 1201602 98( 6) 14 588.8 32 062 825.1 ~7.2 10.0 1069.500 72( ~24)
8(20, 1, 1) 1201602 98( 6) 15 166.7 32 063 403.0 2.0 5.0 1069.519 99( 7)
8(20, 4, 1) 1201602 9R( 8) ~17 229.4 32 074 423.3 24.6 10.0 1069.887 60( 82)
8(20, 5, 1) 1201602 98( 8) ~14 222.9 32 077 429.8 17.9 10.0 1069.987 87( 60)

 

 

The

aNumbers are J, k, and 1 of the lower vibrational state. -l,~1 level is the

lower energy component of an l-type doublet.

k,1 =

bLaser line used; laser frequencies were taken from Ref. 31.

cMicrowave frequency in MHz. The signed microwave frequency was added to the laser
frequency to obtain the absorption frequency.

dObserved minus calculated frequency in MHz; the parameters for the calculation are in
Tables 2~3 and 2~4.

eEstimated uncertainty in the observed frequency in MHz. An "OMIT" means that the
frequency was omitted from the least squares fits.
f0bserved wavenumber in cm-l. The numbers in parentheses are observed minus calculated

wavenumbers in units of 0.00001 cm

63

 

 

TABLE 2-3

Molecular Constants of the v6 = 1 State of 1201135‘8
Parameterb This Workc Hirotad
av /GHz 35 455.736 0e 35 455.736 0(240)
av /MHz 25 418.931 7(144) 25 416.92(48)f
(Av-8v) /MHz 130 491.1e 130 491.1(42)
DJ /kHz 61.613 5(4190) 59.669g
nJK /kHz 457.251(4225) 440.27g
nK /kHz 2 108.e 2 108.8
HJ /Hz 1.961(1061)
HJK /Hz 7.231(8791)
HKJ /Hz ~160.30(3447)
HK /Hz o.h
A( /MHz 46 279.8 46 279.(33)
nJ /kHz 1 146.40(454) 1 120.(60)f
“2 /kHz -9 600.e -9 600.(6600)
qv /an 8.720 5(396) 8.70(13)f
q'v /kHz -2.147 7(258)

 

 

8Values in parentheses are one standard deviation in multiples
of the last digit in the parameter.
bVibration-rotation parameters.

cObtained from a fit of the vibration-rotation frequencies
listed in Table 2-2.

dRef. g, Table 2—3.

eConstrained to the value reported in Ref. 8.
tRef. 1, Table I.

gAssumed to be the same as in the ground state (Ref. g).

hConstrained to zero.

64

TABLE 2-4

Molecular Constants of the v3=1,v6=1 Vibrational State of 83F

12C 3

 

 

Parameterb This WorkC Nakagawa gt _1.d
Ev /GHz 66 608.085 00(109) 66 605.04(36)
Bv /MHz 25 082.214 8(305) 25 080.(39)
(Av-8v) /MHz 130 557.989 9(961) 127 452.(60)
DJ /kHz 58.076 9(4107) 55.2(45)
DJK /kHz 519.867(3725) 528.(6)
DK /kHz 2 039.099(2173) 2 370.(30)
HJ /Hz 1.166(855)

HJK /Hz 8.966(6712)

11KJ /Hz ~186.89(3241)

AHK /Hz 13.26(1270)

A! /MHz 44 850.096(97) 41 800.(150)
nJ /kHz 942.86(433) 1 020.(60)
“K /kHz ~9 479.44(41) 3 900.(300)
qv /an -2.204 7(50) -90.e

q’ /kHz ~0.959 8(207)

 

 

8Values in parentheses are one standard deviation in multiples

of the last digit in the parameter.

bVibration-rotation parameters.

cObtained from a fit of the vibration—rotation frequencies listed

in Table 2~2.

dRef. g, Table 1.

eRef. 9, constrained.

65

II~5 Discussion

The frequencies of the transitions in Table 2~2 were fit without
consideration of Coriolis interaction with other vibrational states. It
is known that the levels of the v6 = 1 state are in mild Coriolis
resonance with the levels of v3 = 1 (1,21) and presumably a similar
resonance occurs between (v3,v6)=(l,l), (2,0), and (0,2). As was
discussed in the studies of the v3 band from this laboratory (1,2), the
mild v3~v6 Coriolis resonance in CH3F can be taken into account for
reasonable J and k by adjustment of the rotational and centrifugal
distortion constants for the states involved. As can be seen in Table
2~2, the transitions in the present work are limited to J S 20 and K i
10, and for K = 10 the residuals are beginning to show Coriolis effects
that cannot be simulated by adjustment of the parameters. Since the
necessary frequency information was not available for the v6 = 2
vibrational state, we did not examine the Coriolis interaction with
nearby vibrational states in detail. The comparisons in Table 2~2 show
that the frequencies of the transitions in the v3+v6~v6 band can be
computed from the parameters in Tables 2~3 and 2~4 to within a few MHz
for lower J and K and to within :10 MHz for J S 20, K S 10.

In Tables 2~3 and 2~4 the parameters obtained in the present study
are csmpared to previously-determined values. Except for the 1-doubling
constant, the newly-determined constants agree with the older values to
within the experimental accuracy of the latter. However, the new
constants are much more precise, as the older data led to predictions of
the frequencies that differed by as much as 1 GHz (0.03 cm-l) from the

experimental values. Coriolis parameters for 03+v6 have been also

66

determined from the frequencies of the assigned 1=~1 transitions of
v3+v6~06 band. Finally, the parameters in Tables 2~3 and 2~4 have been
used to predict coincidences within 100 MHz of laser lines for the
various isotopes of 002. The predicted coincidences are in Table 2~5,
which may be helpful for various studies such as infrared-infrared
double resonance.

There are intriguing aspects of this work that suggest interesting
topics for future study. First, there are unanswered questions about
the effects of Coriolis coupling, or possibly Fermi resonance, in the
1234-1)6 state. Two pieces of evidence suggest that such effects should
not be ignored: (1) the qv constants in the v6 and v3+v6 states differ
not only in magnitude, but in sign, whereas they are expected to be of
similar value (Eq. (2~81)); and (2) the ratio of the intensities of the
transitions in the 203-v3 band to those in the v3+v6~96 band, although
not measured, seemed to be greater than the value of ~2 that is inferred
from the Boltzmann factor. A second interesting subject for future
research would be an attempt to observe transitions in the 03+06-v6 band
that obey selection rules other than the AR = 0, A1 = 0 rules observed
in this work. In principle, transitions with Ak = :2, AI = :2 and with
Ak = :1, A9. = :2 are allowed via the (1.2.:2) and (12,71) type 9.-
resonances, respectively. However, their intensities may be as much as
two orders of magnitude or more below the intensities observed in this
study as inferred from the fact that frequency corrections due to 2-
resonances are usually less than 20 MHz except for 1~type doublets.
Nevertheless, the molecular constants reported here are sufficiently
accurate to predict these frequencies to within a few MHz for low J and

k, so that it may be possible to observe them if a region can be found

67

TABLE 2~5

Coincidences between Calculated Frequencies for the v3+v6~v6

Band of

1

201131? and Laser Frequencies

 

 

Trans.a Frequencyb vo~v Laserd
P(12, 8,-1) 30 480 581.7 54.7 1201602 BAND II P(50)
P(10, 3,~1) 30 606 125.4 14.9 120160180 BAND II P(58)
P(10, 7, 1) 30 637 314.3 ~19.4 120160180 BAND II P(57)
P( 8, 1, l) 30 730 197.3 74.3 120160180 BAND II P(54)
0(18, 3,~1) 31 029 621.8 ~78.6 120160180 BAND II P(44)
0(20, 6, 1) 31 029 700.6 0.3 120160180 BAND II P(44)
0(17, 3,~l) 31 041 668.1 ~35.l 1301802 BAND II R(12)
0(18, 4, 1) 31 049 480.4 0.5 1201802 BAND II P(58)
0(15, 5,~1) 31 059 008.1 ~1.l 1301602 BAND II R(26)
0(13, 1, 1) 31 093 513.9 25.4 1301602 BAND II R(28)
Q(lO,lO,-l) 31 093 552.5 64.0 1301602 BAND II R(28)
P( l, 0, 1) 31 101 511.4 19.2 1201602 BAND II P(30)
0(13, 5, l) 31 106 726.8 ~25.7 1201802 BAND II P(56)
Q( 9, 2,~l) 31 116 638.7 42.8 120160180 BAND II P(4l)
0(11, 6, l) 31 127 170.8 58.6 1301602 BAND II R(30)
Q( 9, 7, 1) 31 145 153.8 ~96.6 120160180 BAND II P(40)
Q( 5, 1, l) 31 145 263.9 13.5 120160180 BAND II P(40)
Q( 6, 4, l) 31 150 663.4 1.7 1301802 BAND II R(18)
R( 8, 6, l) 31 598 614.4 58.3 1201802 BAND II P(38)
R( 9, 5,~1) 31 610 490.6 ~43.4 1301802 BAND II R(48)
R(10, 2,~1) 31 661 334.8 ~96.8 1301802 BAND II 8(52)
R(10, 9, l) 31 696 998.2 ~63.3 1201602 BAND II P( 8)
R(15, 3, 1) 31 882 260.9 ~45.9 120160180 BAND II P(12)
R(18, 5, 1) 32 003 944.4 ~73.0 1201602 BAND II R( 4)

 

 

a . . . 12 ,
Transition in the v3+v6~v6 band of CH3F, J i 20, k S 10.

cFrequency of the v

d

frequency in MHz.

3+v6~v6 band transition minus the laser

bFrequency of the 03+v6~v6 band transition in MHz.

Identification of the CO laser; Band II is the 9 pm band.
Laser frequencies were 0 tained from Ref. 31.

68

in which the transitions are not strongly overlapped.

69

II~6 Appendix

The contribution to the energy of the state |v,J,k,1=+1> from the
(12,11) interaction given in Eq. (2~89) can be represented by a second

order perturbation,

4r3(2k+1)2[J(J+1)-k(k+1)1
W(v,J,k,1=+1)~W(v,J,k+1,£=-1) °

 

Wr(v,J,k,£=+1) = (2~92)

The energy difference between the corresponding rotational levels may be

calculated approximately by
W(v,J,k,1=+1) ~ W(v,J,k+l,£=-l)

= vo+BJ(J+1)+(A~B)k2~2A{k

~[vo+BJ(J+1)+(A-B)(k+l)2+2A{(k+l)]
= ~(2k+l)(A—B+2A{) . (2~93)
By substituting Eq. (2~93) into Eq. (2~92),

4r2

wr<v.J.k.1=+1) = -<;:§;§X;>(2k+1)[J<J+1>—k<k+1)1
2

= r'[~J(J+1)-2kJ(J+1)+k+3k +2k3] . (2—94)

where

r' = 4r3/(A~B+2A() (2-95)

70

If the contribution to the energy of the state |v,J,k,1=~1> is
calculated in similar fashion, it will be seen that the result is the
same except that the signs of the terms including odd powers of k are
reversed. Therefore, since 1 = :1 only for v = l, we can write for the

energy of either state,

2

w (v,J,k,£=tl) = r'[-J(J+l)+3k +k1-2J(J+1)k1+2k31] . (2—96)

71

II-7 References

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72

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E. B. Wilson, Jr., J Chem. Phys. 3, 818-821 (1935).

T. Oka, J. Chem. Phys. 47, 5410-5426 (1967).

H. H. Nielsen, Phys. Rev. 75, 1961 (1949).

H. H. Nielsen, Phys. Rev. 77, 130-135 (1950).

M. L. Grenier-Besson, J. Phys. Radium 21, 555-565 (1960).
G. Amat, Compt. Rend. 250, 1439 (1960).

G. J. Cartwright and I. M. Mills, J. Mol. Spectrosc. 34, 415-439
(1970).

A. Biernacki, D. 0. Moule, and J. L. Neale, Appl. Spectrosc. 26,
648-650 (1972).

D. Horn and G. 0. Pimental, Appl. Opt. 10, 1892-1898 (1971).

J. U. White, J. Opt. Soc. Am. 32, 285-288 (1942).

H. J. Bernstein and G. Herzberg, J. Chem. Phys. 16, 30-39 (1948).
T. H. Edwards, J. Opt. Soc. Am. 51, 98-102 (1961).

S. 0. Hsu, Ph. D. Thesis, Michigan State University, 1988.

C. Freed, L. 0. Bradley, and R. G. O’Donnell, IEEE J. Quantum
Electron. QE~16, 1195- 1206 (1980).

R. M. Lees, J. Mol. Spectrosc. 33, 124-136 (1970).

M. L. Grenier-Besson and G. Amat, J. Mol. Spectrosc. 8, 22-29
(1962).

CRBPTER III

HIGH RESOLUTION INFRARED STUDY OF THE v BANDS 0F

2

CD31 AND CD38r

III—l Introduction

The fundamental halides, CD I and 0D Br, have been the subject of a

3 3
number of spectroscopic studies in the microwave and infrared regions.
Especially the 02 bands are of importance because they occur in the CO2
laser region and have therefore provided considerable spectroscopic
information by means of linear and nonlinear spectroscopic techniques.
The 02 band is identified to be the symmetric deformation of symmetry
A1, a parallel band, among the six fundamental bands of the 03V prolate
symmetric top. The v2 bands for both molecules appear in almost the

1, v2(0D3Br)=991.4cm_1), and were reported

same region (92(CD3I)=949.4cm-
to have sufficient intensity that a long path cell is not necessary for
observation of the spectra as long as the sample pressure is higher than
0.1 Torr (l—Z).

This chapter is concerned with high resolution infrared studies of
the 02 bands of these molecules by means of an infrared-microwave
sideband laser spectrometer. As for other methyl halide molecules, the
Coriolis interactions between the v2 bands and the v5 bands (asymmetric
deformation) of these molecules have been long-standing subjects of

study (2,§,§,z). A question concerning the effects of the Coriolis

coupling for these bands was one of the reasons for our interest in

73

74

studying the molecules. The main reason for studying them, however, was
to determine the magnitude of the nuclear quadrupole coupling constants
of the iodine and bromine atoms by the method of infrared-radiofrequency
double resonance. The presence of a single nucleus of spin I > 1 in
each of these molecules causes each rotational level to be split into
2I+l sublevels. As a result, the lineshapes of transitions in the
infrared spectra of these species are distorted and sometimes,
especially in CD31 spectra, even split. Direct observations of pure
quadrupole transitions by means of infrared-radio frequency double
resonance allowed us to determine the magnitude of the quadrupole
interaction between the nuclear quadrupole and the electric field
gradient at the I or Br nucleus. However, in order to perform the
double-resonance study, it was first necessary to have accurate
frequencies for linear infrared spectra for the vibration-rotation
bands. The experimental frequencies and parameters are reported in this
chapter; the infrared-radiofrequency double resonance results are

described in the next chapter.

79
3 3

recorded at Doppler-limited resolution. About 200 transitions for each

In this work, the v2 bands of 0D I, CD Br, and CD381Br were
species, including transitions of high J,K (higher than 40,8), were
recorded and the frequencies measured to an accuracy of few MHz. The
effect of the quadrupole interaction has been observed for some
transitions in the infrared spectrum and the infrared frequencies have
been converted to hypothetical unsplit frequencies where necessary. The
frequencies in these parallel bands have been combined with frequencies

reported from previous microwave, millimeter, and infrared studies and

fit by least squares to an energy expression containing centrifhgal

75.

distortion parameters up to the eighth order. The Coriolis interaction
with the v5 band has been taken into account in each case by using
previously-reported parameters (1,1) for the interaction and for the v5
band. The resulting combination of the 02 parameters obtained in this
work is sufficient to predict the frequencies within a few MHz for the
appropriate range of J and K. The determined parameters have been used
to calculate coincidences with CO2 laser frequencies.

In a series of microwave studies of the ground vibrational state of
CD31 by Simmons and co-workers (8—19) the rotational constant 80 and the

centrifugal distortion constants D and DJK were determined. Kuczkowski

J
(11) extended this microwave work to transitions in the low-lying
vibrational states v2, v3, v5, v6, 2v3, and v3+v6. More recently,
higher J transitions have been recorded in the millimeter wave region
and more accurate quadrupole constants were reported for low-lying
vibrational states by Demaison 91 g1. (12) and by Wlodarczak g1 g1.
(13.) .

The first vibration—rotation spectra of 0D3I were taken by Jones
_1 21. (1) with grating spectrometers in the 500-5000 cm.1 region. A
series of studies of several bands by different investigators followed
(14-19). In 1976 Matsuura and Shimanouchi reported a study of Coriolis
coupling of the ”2’ v5, and 2v3 bands (2). Then, as a result of laser-
Stark and laser-microwave double resonance spectroscopy, Kawaguchi g;
91. (3) obtained the rotational constant B2, the centrifugal distortion
constants DJ and DJK’ and the quadrupole coupling constant qu for the
02 vibrational state in a study in which they found no need to include

Coriolis coupling to other states for the rather low J transitions that

they recorded. In addition to the vibration-rotation parameters

76

obtained by infrared studies of deuterated methyl iodide, the rotational
constant A0 and the centrifugal distortion constant DK were determined
by studying the 124 band by Raman spectroscopy (19).

Sakai and Katayama (11,11) have performed level-crossing and
level-anticrossing experiments in CD31 by using the coincidence of the
band with the CO

°P(4,1) transition of the v 10P(16) laser line. They

2 2
determined the dipole moments of the ground and v2 vibrational states in
this laser Stark study. An intracavity cell and an external cavity
White cell were used by Caldow g1 g1. (11) to record laser Stark Lamb
dips for this molecule. Infrared radio frequency double resonance at 1-
MHz resolution was reported by Rackley and Butcher (14) as part of a
study of Stark-tuned non—linear spectroscopy. Mbre recently, Demaison
g1 g1. (11) used infrared-radiofrequency double resonance to measure the
frequencies of pure quadrupole transitions in the ground state of this
molecule with 100 kHz accuracy. Vibrational energy transfer has been
studied in CD31 by using coincidences with Q-switched 002 laser lines
and detecting fluorescence from v1, v4, ”6’ and 2v5 levels (1Q). The
influence of nuclear quadrupole coupling on rotational relaxation has
been investigated by means of microwave double resonance (16). Finally,
submillimeter wave laser emission has been observed from CD31 pumped by
a number of CO2 laser lines (11).

Even with all of these spectroscopic studies, there has been no
systematic study at Doppler~limited resolution of high J and K
transitions in the very important v2 band region of CD31. Such a study
would be expected to provide more precise frequency information and to
allow investigation of the effect of Coriolis coupling in the

calculations of the energies of the levels in the v =1 state. It would

2

77

also allow accurate calculation of possible coincidences between v2~band
transitions and CO2 laser lines.
The infrared and microwave spectra of CD3Br are rather complicated

compared with CD31 for two reasons: First, CD38r consists of two

isotopes with almost the same natural abundance (CD37QBr = 50.54%,

81
3

same J,K appear about 500 MHz apart, depending on the value of J and K.

CD Br = 49.46%); thus, the transitions of the two species with the

Second, the Coriolis interaction between the v2 (991.4 cm-l) and the v5
(1055.5 cm-l) bands is much more serious than in CD31 since the bands
lie only 64 cm-1 apart and the Coriolis coupling constants are about 1.5

times larger than that of CD31. As a result, CD Br has not been studied

3
previously in as much detail as CD31.

Infrared spectra of the v2 bands of CD379Br and CD381Br recorded
with grating instruments have been reported by Morino and Nakamura (4)
and by Jones _5 _1. (5). More recently, Betrencourt-Stirnemann £1 _1.
(6) analyzed the 02 and v5 bands recorded by Fourier transform
spectroscopy at a resolution of 0.01 cm_l. Also, Harada _1 91. observed
low J,K transitions and investigated the Coriolis coupling between
the 02 and v5 hands by laser—Stark spectroscopy (1) and Edwards and
Broderson determined the rotational constant AG by analysis of Raman
spectra of the v4 band (18). Microwave spectra in the ground states of
CD379Br and CD3818r have been reported by Garrison g1 g1. (19) and have
been extended to low—lying excited states by Morino and Hirose (gg).
Frequencies reported by these workers (6,1,19,19) were included in our

analysis.

band of CD Br

As implied by the studies performed to date, the 02 3

78

has been one of the major concerns and the Coriolis interaction between
the v2 and the 05 bands is very important for analyzing the
corresponding rotational energy structure. However, for possible double
resonance studies, the previous FT-IR (6) and laser-Stark (1) studies
had not provided precise enough frequency information because of the
limited resolution as well as a frequency calibration problem.
Therefore, experimental frequencies and rovibrational parameters were

obtained in this study and are reported for both species.

79

III-2 Theory

III-2~l Term Values

2 = 1 states of CD31 and both CD37QBr and CD381Br are

The v
nondegenerate, so the vibration-rotation energy levels of these states
and the ground states of these species can be expressed as the usual

power series in J(J+l) and K2, as follows:

- _ 2
WR(v,J,K) - vv + Bv J(J+l) + (Av Bv) K

J2(J+l)2 - DEX J(J+1)K2 — n” K4

_D K

J3(J+l)3 + H3

94¢ Ltd

2 2 2 v 4 v 6
K J (J+1) K + HKJ J(J+1)K + BK K

4 4 3 3 2 v 2 2 4
J (J+1) + L J (J+1) K + LJJKK J (J+1) K

v
JJJK
v 8

6
+ LJKKK J(J+1)K + LK K . (3-1)

<‘-1<

In this expression, ”v is the vibrational energy of the state V (v0 =
0), Av and Bv are rotational constants for the state v, and the D’s,
H’s, and L’s are quartic, sextic, and octic centrifugal distortion
constants for the state v, respectively. The frequencies corresponding
to the experimental frequencies were computed by taking differences in
energy levels calculated with the term value written above; the usual
selection rules for a parallel band, AJ = 0, :1 and.Ak = 0 (K = lkl)

were used.

III-2~2 Coriolis Interaction

In order to include the effect of the Coriolis coupling on the

fitting of the frequencies reported here, we calculated the effect of

80

the coupling for each of the transitions in the fitting and subtracted
these effects from the experimental frequencies before completing the
fitting. For this purpose, the appropriate matrix was set up for each
transition and the eigenvalue was obtained by diagonalizing each matrix;
the second order perturbation method is considered not to be adequate
because of the large Coriolis effect and the accuracy of frequency
determination of this work. The zero-order energy was subtracted from
the desired eigenvalue and the difference was subtracted from the
experimental frequency. The coupling effects and the subtracted zero-
order energies were calculated with the parameters, including the
parameters for v2 = 1, reported in previous works where the Coriolis
interaction constants are derived. This was done to insure a treatment
of the Coriolis effects that was equivalent to the previous analysis,
since we do not have any additional data for the other vibrational

states involved.

III-2~2-l CD3I

There are three vibrational states, v2=1 (A1, 949.4 cm-l), v5=l

(B, 1049.3 cm_1), and v =2 (A1, 999.0 cm-l), involved in the mid-

3
infrared Coriolis interaction system in CD31 (1). In order to calculate
the effect of the Coriolis interaction, the appropriate matrix was set

up for each transition as discussed in Ref. (1):

81
|0,0,1,~1;J,k~1> l1,0,0,0,J,k> |0,2,0,0;J,k> |0,0,l,+l;J,k+l>
rEo(v5=1,15=~1;J,k~l) ~£25f(J,k~1) ~4335f(J,k~1) ~q5f(J,k-1)f(J,k+1)/27
Eo(v2=1,J,k) 0 £25f(J,k+1)

Eo(v3=2;J,k) £335f(J,k+l)
(Hermitian) E (v :1’1
0 5

 

 

5=l;J.k+1)_

(3-2)

In this equation, Eo denotes the unperturbed energy, the "ket" notation
is |v2,v3,v5,15;J,k>, the ~q5f(J,k~l)f(J,k+l)/2 term accounts for the
(22,12) interaction in the v5=l state, and

f(J,ktl) = [J(J+1)~k(ktl)]1/2 . <3-3)

For K=0, the matrix is reduced to 3x3 matrices; for the A+ species

 

 

|1,0,0,0;J,0> l0,2,0,0;J,0> |0,0,l,tl;J,l>
E (v =l'J k=0) 0 e {2[J(J+1)]}1/2
I o 2 ’ ' 25 l
E (v =2°J k:0) e {2[J(J+l)]}1/2
o 3 ’ ' 335
1 (Hermitian) Eo(v5=l,15=1;J,k=l)+q5J(J+l)/2J
(3‘4)

and for A_ species that do not affect the v2=l state,
. _ O - — o — _ _
|0,0,1,tl,J,1> - E (vs—1,15—1,J,k-l) q5J(J+l)/2 . (3 5)

The parameters used in our calculation are given in Table II of

Ref. (1). The only ambiguity in this procedure was the specific value to

82

use for B{éfg which affects the value of £25. In Table II of Ref. (1)
only the value of [{éfgl is given; the value of B used to obtain the
desired product is not mentioned. A value of 3106.495 MHz was used for
the combined constant B‘éf; by using the B2 rotational constant of the
v2=1 state in the following equation.

:25 = <1/2>1/2[(vs/.2)1/2+<.2/.5>1/2]a.;fg . (3-6)

The resulting value of £25 was 4398.7 MHz.

III-2~2-2 CD3Br
The Coriolis coupling between the v2 and v5 bands in these

molecules is, as indicated before, somewhat stronger than that between
the same bands in CD31 and it was necessary to include this interaction

in order to obtain a satisfactory fitting of the frequencies. For this
purpose, the effect of the coupling was calculated for each of the
transitions by setting up, for the upper state of the transition, the
appropriate matrix with elements defined by Eq. (4), (5) and (7) in Ref.
(1). The matrix is essentially the same as the one in Eq. (3-2) except
that the v3=2 state (1154cm_1) is not included because its effect has
been considered to be satisfactorily included in the usual Coriolis
contribution to the molecular constants (1). The energies needed to
compute the Coriolis contribution were calculated with the parameters,

including the parameters for the v2 = 1 state, given in Table V of Ref.

(1).

83

III-2~3 Effect of Nuclear Quadrupole Coupling

In order to obtain the frequencies of rotational and ro-vibrational
transitions, it is necessary to subtract the effect of nuclear
quadrupole interactions from the spectra. In order to calculate the
effect of quadrupole coupling, the appropriate energy matrix was set up
and diagonalized. In this matrix, we also included the effects of
centrifugal distortion of the quadrupole coupling and the nuclear spin
rotation interaction. To carry out this calculation the energy matrix

was written

H = HR + H0 + H0 + H8 . (3—7)

The matrix HR was assumed to be diagonal with diagonal elements equal to
the rotational energies given in Eq. (3-1). The elements of H6, the
nuclear quadrupole coupling, were taken to be the elements proportional
to er = xzz in the Appendix of the paper by Benz g1 g1. (19); the
matrix elements are listed in the Appendix of Chapter IV.

The matrices HD and H were also assumed to be diagonal with non—

8

zero matrix elements as follows:

<J,K,I,F|HD|J,K,I,F> e1{[3K2~ J(J+l)][xJJ(J+1) + xKKZ]

+ *6 K2(4K2~1)} (3-8)

2
_ _ l _ ___§__ _
<J,K,I,F|HS|J,K,I,F> — 2 [cN+(cK cN) J(J+1)] G . (3 9)

In these equations F is the total angular momentum quantum number and

e1 is the Casimir function divided by J(J+l);

34
61: [(3/4)G(G+l)-I(I+1)J(J+l)]/[2I(21~1)J(J+1)(2J~1)(2J+3)] (3-10)

with

G = F(F+1) ~ I(I+l) ~ J(J+1) . (3-11)

The constants xJ, XK’ and xd are centrifugal distortion constants for
the quadrupole coupling (11,11), whereas CN and CK are spin-rotation
constants (11). The signs of the spin rotation constants are taken to
be consistent with the signs in the previous work on CD31 (11).
Inclusion of the spin-rotation and the centrifugal distortion of the
quadrupole coupling terms on the diagonal before the diagonalization was
done for convenience. This is almost equivalent to what is desired ~ a
first-order perturbation treatment of these terms in a zero-order basis
which diagonalizes the quadrupole coupling effects. The only difference
is that the distortion and spin-rotation terms have a small effect on
the diagonalization. The matrix H, as defined, is diagonal in F, I, and
K; therefore, submatrices with rows and columns indexed by J (usually
6x6 for CD3I and 4x4 for CD3Br) were set up and diagonalied to obtain

the energy levels. The nuclear quadrupole coupling is discussed in

greater detail in the next chapter.

III-2~4 Hypothetical Unsplit Frequencies
III-2~4-l CD3I

In order to obtain the experimental frequencies of the infrared
transitions, each experimental lineshape as a function of microwave
frequency was fitted by least squares to a sum of Gaussian functions.

The relative intensities and separations of the Gaussians were

85

constrained to the values calculated with the highest quality set of
quadrupole parameters available at the time of the fitting. Since there
was little change in quadrupole parameters and since the quadrupole
splittings of many of the transitions were rather small, the
hypothetical unsplit frequencies obtained did not depend on the specific
set of quadrupole parameters used. Each experimental infrared frequency
was obtained by adding or subtracting the resonant microwave frequency
to or from the appropriate laser frequency; the laser frequencies were
obtained from the report of Freed g1 g1. (15).

The microwave and millimeter-wave frequencies measured in previous
studies were also converted into hypothetical unsplit frequencies by
subtracting the frequency shifts caused by the quadrupole couplings.

The frequency shifts were calculated with the same set of quadrupole
parameters used for the frequency determination of infrared transitions.
The rovibrational parameters were adjusted by a least squares fitting of
the modified experimental frequencies including, in addition to the
present measurements, microwave and millimeter wave frequencies from

Refs. (§~11) and infrared frequencies from the laser-Stark study (1).

III-2~4-2 CD3Br

In order to obtain the experimental frequencies of the infrared-
micrave sideband-laser transitions, each experimental lineshape as a
function of microwave frequency was fitted by least squares to a single
Gaussian function. Because the shifts in frequency resulting from the
hyperfine splitting were less than 5 MHz in nearly every case, it did

not seem necessary to fit the lineshapes to a sum of Gaussians, one for

86

each hyperfine component, as was done for CD31 (15); there was no
apparent evidence of hyperfine splitting in the Doppler-limited spectra
recorded in this work. Each experimental infrared frequency was
obtained by adding or subtracting the resonant microwave frequency to or
from the appropriate laser frequency, which was obtained from the report
of Freed _1 _1. (14).

On the other hand, the microwave and millimeter wave frequencies
were converted into the corresponding hypothetical unsplit frequencies
with the quadrupole coupling constants reported in Ref. (11). The
rovibrational parameters were adjusted by a least squares fitting of the
experimental frequencies including, in addition to the present
measurements, converted microwave and millimeter wave frequencies from
Refs. (19) and (11) and infrared frequencies from the FTIR (6) and
laser-Stark (18) studies. Each experimental frequency was given a

weight equal to the reciprocal of the square of its estimated

uncertainty.

87

III-3 Experimental

All of the spectra in this work were recorded with an infrared
microwave sideband laser spectrometer that has been assembled in our
laboratory. Fig. 3~l shows block diagram of the spectrometer used in
this study. The design of the electrooptic modulator used is that of
Magerl g1 g1. (16) and a detailed description of our spectrometer has
already been given in Chapter II. As examples, portions of the spectra

of the v bands of CD I and CD38r are shown in Figs. 3~2 and 3~3. The

2 3

horizontal axes of Figs. 3~2 and 3~3 are the microwave frequencies that
must be added to or subtracted from the laser frequency to obtain the
sideband frequency depending on the sign. The overall accuracy of the
frequency scale is limited entirely by our ability to reproduce the
known laser frequencies; we estimate this accuracy to be 1150 kHz. The
accuracy of the reported frequencies of the transitions was limited by
our ability to determine the center frequency of the Doppler-limited

absorption lines (Av = ~18.5 MHz); this uncertainty ranges from 2~10

D
MHz.

The sample cell was a l~meter glass tube with NaCl windows and the
samples were obtained from Merck & Co. and used as received except for
the usual freeze-pump-thaw cycles. Sample pressures, which were about
0.3 Torr for CD31 and 0.5 Torr for CD3Br, were measured with a

capacitance manometer. All spectra were recorded at room temperature

(~297 K).

88

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘ P27
5 EH!” ‘~ , X
DET
@ CUE LASER V
: - 0C.
sou “m. 1.1m ln Sample Cell +
\ x j
DOD. LI Bean \ J
[cos I Splrttor :i:
REF DET DET
PR AMP - -
w... m
"" PSD PSD
' comm 33.3kHz ,
PIN Mod. 1 . .
W m. COMPUTER Eli

 

 

 

 

 

Figure 3-1. Block diagram of the infrared microwave sideband laser

spectrometer used to record the Doppler-limited vibration-rotation

spectra in this work.

88

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F27
I n Y 1
4: Hr” P J k
DST
my (:02 LASER v
% - oc.
Coll :' Mm 1n Sample Cell
Y: ‘—7
F'cumng uni 3,un“—~ 11
L:ns Splitter
REF DET
PREAMP
.___i__,.
"" PSD
’cm‘rnm. 33.3kHz ‘
Mod.

 

 

 

 

 

 

 

 

 

 

 

COMPUTER *4: m

Figure 3~1. Block diagram of the infrared microwave sideband laser
spectrometer used to record the Doppler-limited vibration-rotation

spectra in this work.

89

 

 

 

 

35 r 1 r 1 . 1 T—
25 - «
A
3 1s -
cg _-
- +
£5 5- .J
o + +
V
g, -5)- P(31,8)
‘.’:’
.2 ~15 ~P(2a.0) P(28.1) P(28.2)-
-25- -
Laser Line: 1201602 10P(28)
._3 . 1 . 1 . L . L, .
154.0 14.2 14.4 14.6 14.8 15.0

Microwave Frequency (GHz)

Figure 3~2. A portion of the infrared spectrum of the v2 band of
CD31 recorded by the infrared microwave sideband laser spectrometer.
The microwave frequency on the horizontal axis is added to (+) or
subtracted from (~) the frequency of the 10P(28) 1201502 laser to
obtain the infrared frequency. The sample pressure was 0.3 Torr and a
l~m path length was used.

90

 

 

  

 

 

 

35 1 1 r 1 a .
254 .v _ 7
1; 4 \N
=°-'-' 15- -
C
3 4 .1
.9' 5-1 -
o 1 .
v
>4 ~5- -‘
3:1 61
2 J co; Br man) J
0 -15-4
g . co;"8r P(2o.3) cofar P(20.1) :
~25- "0“02 10R(28) -
J .
-35 . . . , . , . r .
15.0 15.2 15.4 15.6 15.8 16.0

Microwave Frequency (MHz)

Figure 3~3. A small portion of the spectrum in the 02 band region of
CD38r showing the typical lineshapes and signal/noise obtained for the
spectra reported. The horizontal scale is the microwave frequency
that must be subtracted from the frequency of the 1201502 10(28) laser
to obtain the infrared frequency of the transitions. Transitions of

CD379Br and CD381Br occur approximately alternately everywhere in this
region.

91

III-4 Results

The Coriolis effects were eliminated from all the experimental
frequencies, including the new, more precise infrared frequencies for
each species, and the modified frequencies were fit to the differences

in energy levels calculated by Eq. (3~1). In the least squares

g, H;, and L; were

constrained to zero or to the previously-reported values. This was done

fittings, the ground-state parameters A0, D

to avoid the linear dependence, which is a result of the selection rule,
AK=0 for a parallel band. In addition, it was found that all of the L
constants for the ground states were too small to affect the calculated
frequencies significantly; consequently, these parameters were

constrained to zero in the fittings for all three species.

III-4-l CD31

Approximately 175 vibration-rotation transitions were recorded with
J’s up to 43 and K’s up to 10. Some transitions of higher K were
recorded, but these frequencies show the effects of a resonance that
cannot be fully accounted for by a power series expansion in J(J+l) and
K2; this appears to be the Coriolis resonance with us and 2v3 reported
by Matsuura and Shimanouchi (1). A small portion of the infrared
spectrum is shown in Fig. 3~2.

The frequencies of the infrared transitions measured in this work
are shown in Table 3~l with their estimated uncertainties. Also shown
in Table 3~l are the observed minus calculated frequencies for the

parameters derived in this work. The rotational and centrifugal

£32

 

 

TABLE 3~1
Comparison of Observed and Calculated Frequencies in the v2 Band of CD31
a b c -1 e
Trans. Laser 1:. v/MHz O—C Unc v/cm
P(43, 8) 10P(34) ~16 281.8 27 894 439.0 ~l.4 2.0 930.458 33( ~4)
P(43, 9) 10P(34) ~14 549.9 27 896 170.9 1.2 2.0 930.516 10( 4)
P(43,10) 10P(34) ~13 276.1 27 897 444.7 ~O.8 2.0 930.558 59( ~2)
P(42, 0) 10P(34) ~11 245.0 27 899 475.8 ~0.1 2.0 930.626 34( 0)
P(42, 1) 10P(34) ~11 065.0 27 899 .8 0.0 2.0 930.632 34( 0)
P(42, 2) 10P(34) ~10 523.8 27 900 .0 1.8 2.0 930.650 40( 5)
P(42, 4) 10P(34) ~8 427.0 27 902 .8 0.3 2.0 980.720 34( 1)
P(4l, 7) 10P(34) 11 582.2 27 922 .0 ~1.7 2.0 931.387 77( ~5)
P(41, 9) 10P(34) 15 616.4 27 926 .2 3.0 2.0 931.522 34( 9)
P(4l,10) 10P(34) 17 209.9 27 927 .7 0.2 2.0 931.575 49( 0)
P(40, 0) 10P(34) 17 931.4 27 928 .2 ~0.2 2.0 931 599 56( 0)
P(39, 8) 10P(32) ~15 410.7 27 954 .l ~0.5 2.0 932 446 38( ~1)
P(39, 9) 10P(32) ~13 208.4 27 956 .4 0.8 2.0 932 519 84( 2)
P(39,10) 10P(32) ~11 300.8 27 958 .0 .9 2.0 932 583 47( ~6)
P(38, 0) 10P(32) ~11 854.6 27 957 .2 .3 2.0 932 564 99( ~1)
P(38, 2) 10P(32) ~11 076.9 27 958 .9 .5 2.0 932 590 94( ~5)
P(38, 4) 10P(32) ~8 788.5 27 960 .3 .2 2.0 932 667 27( 0)
P(37, 6) 10P(32) 9 350.3 27 978 .1 .9 10.0 933 272 31( ~2)
P(37, 8) 10P(32) 14 007.1 27 983 .9 .6 2.0 933 427 65( ~2)
P(37, 9) 10P(32) 16 427.3 27 985 .1 .7 OM T 933 508 38(-25)
P(36, 0) 10P(32) 16 854.0 27 986 .8 .2 2.0 933.522 61( 0)
P(36, 1) 10P(32) 17 055.9 27 986 .7 .2 2.0 933.529 35( 0)
P(35, 7) 10P(30) ~17 386.1 28 010 .8 .0 2.0 934.314 56( 3)
P(35, 8) 10P(30) ~14 815.2 28 012 .7 .2 2.0 934.400 31( 0)
P(35, 9) 10P(30) ~12 168.2 28 015 .7 .5 2.0 934.488 61( 1)
P(35,10) 10P(30) -9 654.9 28 017 .0 .5 2.0 934.572 44( ~1)
P(34, 0) 10P(30) ~12 657.9 28 014 .0 .8 2.0 934.472 27( ~2)
P(34, 1) 10P(30) ~12 448.6 28 014 .3 .2 2.0 934.479 26( 0)
P(34, 2) 10P(30) ~11 823.6 28 015 .3 .1 2.0 934.500 10( 0)
P(34, 3) 10P(30) ~10 789.0 28 016 .9 .2 2.0 934.534 61( 4)
P(34, 4) 10P(30) ~9 363.5 28 018 .4 1.2 2.0 934.582 16( ~3)
P(33, 6) 10P(30) 8 860.2 28 036 .1 0.8 0.0 935.190 04( 2)
P(33, 7) 10P(30) 11 352.8 28 038 .7 0.2 2.0 935.273 18( 0)
P(33, 9) 10P(30) 16 941.7 28 044 .6 1.9 2.0 935.459 61( 6)
P(32, 0) 10P(30) 15 576.1 28 043 .0 0.5 2.0 935.414 06( l)
P(32, 1) 10P(30) 15 790.6 28 043 .5 ~0.1 2.0 935.421 21( 0)
P(32, 2) 10P(30) 16 429.3 28 043 .2 ~5.4 2.0 935.442 52(-l7)
P(32, 3) 10P(30) 17 502.3 28 044 .2 1.5 2.0 935.478 31( 5)
P(3l, 7) 10P(28) ~17 404.3 28 067 . ~0.9 2.0 936.223 20( ~2)
P(3l, 8) 10P(28) ~14 522.9 28 070 ~0.4 2.0 936.319 32( ~1)

 

 

533

Table 3~1 (cont’d)

 

 

Trans . Laser“ vlb v/MHz O-Cc Unc v/cm 1 e
P(31, 9) 10P(28) ~11 463.1 28 073 206.7 ~0.1 2.0 936.421
P(3l,10) 10P(28) ~8 384.2 28 076 285.6 ~0.5 2.0 936.524
P(30, 0) 10P(28) ~13 669.8 28 071 000.0 ~0.1 2.0 936.347
P(30, l) 10P(28) ~13 448.8 28 071 221.0 ~0.2 2.0 936.355
P(30, 2) 10P(28) ~12 784.6 28 071 885.2 1.9 2.0 936.377
P(30, 3) 10P(28) ~11 689.7 28 072 980.1 ~0.3 2.0 936.413
P(30, 4) 10P(28) ~10 166.3 28 074 503.5 1.1 2.0 936.464
P(30, 5) 10P(28) ~8 238.5 28 076 431.3 ~1.7 2.0 936.528
P(29, 7) 10P(28) 10 818.0 28 095 487.8 ~0.1 2.0 937.164
P(29, 8) 10P(28) 13 843 l 28 098 512.9 0.4 2.0 937.265
P(29, 9) 10P(28) 17 095.8 28 101 765.6 0.9 2.0 937.374
P(28, 0) 10P(28) 14 084.6 28 098 754.4 3.4 2.0 937.273
P(28, 1) 10P(28) 14 308.5 28 098 978.3 0.6 2.0 937.281
P(28, 2) 10P(28) 14 987.7 28 099 657.5 0.7 2.0 937.303
P(28, 3) 10P(28) 16 115.2 28 100 785.0 1.7 2.0 937.341
P(28, 4) 10P(28) 17 678.4 28 102 348.2 ~0.3 2.0 937.393
P(27, 7) 10P(26) ~17 720.3 28 123 445.7 ~0.9 2.0 938.097
P(27, 8) 10P(26) ~14 559.0 28 126 607.0 0.0 2.0 938.202
P(27, 9) 10P(26) ~11 124.4 28 130 041.6 ~0.4 2.0 938.317
P(26, 0) 10P(26) ~14 908.7 28 126 257.3 ~1.2 2.0 938.190
P(26, l) 10P(26) ~14 676.6 28 126 489.4 ~l.l 2.0 938.198
P(26, 2) 10P(26) ~13 979.0 28 127 187.0 1.4 2.0 938.221
P(26, 3) 10P(26) ~12 826.5 28 128 339.5 ~0.1 2.0 938.260
P(26, 4) 10P(26) ~11 221.0 28 129 945.0 ~0.2 2.0 938.313
P(26, 5) 10P(26) ~9 176.3 28 131 989.7 ~1.4 2.0 938.382
P(25, 7) 10P(26) 9 975.2 28 151 141.2 1.0 2.0 939.020
P(25, 9) 10P(26) 16 869.6 28 158 035.6 0.3 2.0 939.250
P(24, 0) 10P(26) 12 355.6 28 153 521.6 0.4 2.0 939.100
P(24, 1) 10P(26) 12 592.1 28 153 758.1 0.0 2.0 939.108
P(24, 3) 10P(26) 14 480.2 28 155 646.2 ~1.4 2.0 939.171
P(24, 4) 10P(26) 16 126.1 28 157 292.1 1.1 2.0 939.226
P(24,ll) 10P(24) ~16 992.6 28 179 930.0 ~4.8 OMIT 939.981
P(23, 8) 10P(24) ~14 950.7 28 181 971.9 ~1.3 2.0 940.049
P(23, 9) 10P(24) ~11 182.7 28 185 739.9 ~1.3 2.0 940.175
P(22, 0) 10P(24) ~16 385.3 28 180 537.3 ~0.3 2.0 940.001
P(22, l) 10P(24) ~16 143.2 28 180 779.4 0.4 2.0 940.009
P(22. 2) 10P(24) ~15 421.2 28 181 501.4 ~1.2 2.0 940.033
P(22, 3) 10P(24) ~14 215.7 28 182 706.9 1.0 2.0 940.073
P(22, 5) 10P(24) ~10 388.8 28 186 533.8 3.6 2.0 940.201
P(21, 7) 10P(24) 8 800.3 28 205 722.9 ~0.1 2.0 940.841

 

 

94»

Table 3~1 (cont'd)

 

a b ~1 e

Trans. Laser 0 u/MHz

O

E
O
c
\
8

 

P(Zl, 8) 10P(24) 12 316. 28 209 239.3 ~0. 940.958 94( ~1)

7 4 2.0
P(21, 9) 10P(24) 16 234.9 28 213 157.5 0.8 2.0 941.089 64( 2)
P(20, l) 10P(24) 10 628.1 28 207 550.7 ~l.l 2.0 940.902 61( ~3)
P(20, 2) 10P(24) 11 365.9 28 208 288.5 0.5 2.0 940.927 22( 1)
P(20, 4) 10P(24) 14 301.8 28 211 224.4 1.4 2.0 941.025 15( 4)
P(20, 5) 10P(24) 16 491.1 28 213 413.7 0.5 2.0 941.098 18( l)
P(19, 8) 10P(22) ~15 718.6 28 236 223.1 ~2.1 2.0 941.859 02( ~7)
P(19, 9) 10P(22) ~11 664.3 28 240 277.4 ~1.4 2.0 941.994 26( ~4)
P(18, l) 10P(22) ~17 867.0 28 234 074.7 ~0.3 2.0 941.787 36( ~1)
P(18, 2) 10P(22) ~17 119.7 28 234 822.0 ~0.6 2.0 941.812 29( ~1)
P(18, 3) 10P(22) ~15 874.7 28 236 067.0 0.0 2.0 941.853 81( 0)
P(18, 4) 10P(22) ~14 135.8 28 237 805.9 ~0.1 2.0 941.911 82( 0)
P(18, 5) 10P(22) ~11 905.3 28 240 036.4 0.1 2.0 941.986 22( 0)
P(l7, 9) 10P(22) 15 162.6 28 267 104.3 ~0.3 2.0 942.889 11( ~1)
P(16, 0) 10P(22) 8 153.0 28 260 094.7 ~0.2 2.0 942.655 29( 0)
P(16, l) 10P(22) 8 406.6 28 260 348.3 0.8 2.0 942.663 75( 2)
P(16, 2) 10P(22) 9 179.5 28 261 121.2 16.1 OMIT 942.689 53( 53)
P(16, 3) 10P(22) 10 425.2 28 262 366.9 ~0.1 2.0 942.731 08( 0)
P(16, 4) 10P(22) 12 190.9 28 264 132.6 0.7 2.0 942.789 98( 2)
P(16, 5) 10P(22) 14 456.3 28 266 398.0 0.2 2.0 942.865 55( 0)
P(16, 6) 10P(22) 17 220.9 28 269 162.6 0.3 2.0 942.957 76( 1)
P(15, 8) 10P(20) ~16 881.2 28 289 343.7 ~0.4 2.0 943.630 93( ~1)
P(15, 9) 10P(20) ~12 599.2 28 293 625.7 ~6.0 2.0 943.773 77(-20)
P(l4, 3) 10P(20) ~17 813.8 28 288 411.1 ~0.5 2.0 943.599 83( ~1)
P(l4, 4) 10P(20) ~16 026.6 28 290 198.3 ~0.8 2.0 943.659 44( ~2)
P(l4, 5) 10P(20) ~13 729.2 28 292 495.7 ~0.8 2.0 943.736 07( ~2)
P(14, 6) 10P(20) ~10 923.4 28 295 301.5 ~1.7 2.0 943.829 66( ~5)
P(12, 4) 10P(20) 9 781.8 28 316 006.7 0.3 2.0 944.520 32( 0)
P(12, 5) 10P(20) 12 106.5 28 318 331.4 0.6 2.0 944.597 86( 2)
P(12, 6) 10P(20) 14 948.9 28 321 173.8 ~0.1 2.0 944.692 67( 0)
P(10, 5) 10P(18) ~15 872.4 28 343 901.4 2.0 2.0 945.450 78( 6)
P( 9, 0) 10P(18) ~9 728.1 28 350 045.7 ~l.5 2.0 945.655 73( ~4)
P( 9, 1) 10P(18) ~9 467.5 28 350 306.3 ~1.9 2.0 945.664 43( ~6)
P( 9, 2) 10P(18) ~8 683.1 28 351 090.7 ~0.6 2.0 945.690 59( ~1)
P( 7, O) 10P(18) 15 400.3 28 375 174.1 ~0.7 2.0 946.493 93( ~2)
P( 7, 1) 10P(18) 15 662.7 28 375 436.5 ~0.7 2.0 946.502 68( ~2)
P( 7, 2) 10P(18) 16 450.7 28 376 224.5 ~0.2 2.0 946.528 97( 0)
P( 7, 3) 10P(18) 17 764.3 28 377 538.1 ~0.1 2.0 946.572 78( 0)
P( 5, 0) 108(16) ~12 543.2 28 400 046.5 0.6 2.0 947.323 58( 2)
P( 5, 2) 10P(16) ~11 491.8 28 401 097.9 ~1.9 4.0 947.358 65( ~6)

 

 

95

Table 3~1 (cont’d)

 

 

Trans. Lasera v-b v/MHz O—Cc Dnc v/cm 1 e
P( 5, 3) 10P(16) ~10 167.9 28 402 421.8 3.1 2.1 947.402 81( 10)
0(16,10) 10P(14) 12 199.1 28 476 872.8 5.0 2.0 949.886 23( 16)
0(15, 9) 10P(14) 8 835.1 28 473 508.8 ~0.5 2.0 949.774 02( ~1)
0(15,10) 10P(14) 13 516.7 28 478 190.4 0.5 2.0 949.930 18( 1)
0(14, 9) 10P(14) 10 001.5 28 474 675.2 1.9 10.0 949.812 93( 6)
0(14,10) 10P(14) 14 757.4 28 479 431.1 0.3 2.0 949.971 57( 0)
0(13, 9) 10P(14) 11 087.6 28 475 761.3 0.7 2.0 949.849 16( 2)
0(13,10) 10P(14) 15 918.9 28 480 592.6 2.2 2.0 950.010 31( 7)
0(12, 9) 10P(14) 12 096.0 28 476 769.7 ~1.4 2.0 949.882 79( ~4)
0(12,10) 10P(14) 16 996.0 28 481 669.7 1.4 2.0 950.046 24( 4)
0(11, 8) 10P(14) 8 621.4 28 473 295.1 ~1.9 2.0 949.766 89( ~6)
0(11,10) 10P(14) 17 990.2 28 482 663.9 ~0.4 10.0 950.079 40( ~1)
0(10, 8) 10P(14) 9 438.0 28 474 111.7 ~0.5 2.0 949.794 13( ~1)
0(10, 9) 10P(14) 13 886.2 28 478 559.9 ~0.9 2.0 949.942 51( ~3)
0( 9, 8) 10P(14) 10 177.8 28 474 851.5 ~2.2 2.0 949.818 81( ~7)
0( 9, 9) 10P(14) 14 666.1 28 479 339.8 0.0 2.0 949.968 52( 0)
0( 8, 8) 10P(14) 10 848.7 28 475 522.4 1.1 2.0 949.841 19( 3)
R( 5, 1) 10P(12) 16 448.8 28 532 475.5 0.1 2.0 951.740 94( 0)
R( 5, 2) 10P(12) 17 233.2 28 533 259.9 0.8 2.0 951.767 10( 2)
R( 7, 0) 10P(10) -ll 252.3 28 555 396.9 ~1.9 2.0 952.505 51( ~6)
R( 7, 1) 10P(10) ~10 992.5 28 555 656.7 ~1.5 2.0 952.514 18( ~4)
R( 7, 2) 10P(10) ~10 211.9 28 556 437.3 0.9 2.0 952.540 22( 3)
R( 7, 3) 10P(10) ~8 915.9 28 557 733.3 ~0.8 2.0 952.583 45( ~2)
R( 9, 0) 10P(10) 11 672.2 28 578 321.4 ~0.4 2.0 953.270 19( ~1)
R( 9, 1) 10P(10) 11 929.9 28 578 579.1 0.2 2.0 953.278 79( 0)
R( 9, 2) 10P(10) 12 701.2 28 579 350.4 0.1 2.0 953.304 52( 0)
R( 9, 3) 10P(10) 13 986.8 28 580 636.0 ~0.2 2.0 953.347 40( 0)
R( 9, 4) 10P(10) 15 789.5 28 582 438.7 1.1 2.0 953.407 53( 3)
R(1l, 0) 10P(8) ~15 560.0 28 600 981.8 ~0.9 2.0 954.026 06( ~3)
R(ll, 1) 10P(8) ~15 306.5 28 601 235.3 ~l.8 2.0 954.034 52( ~6)
R(ll, 2) 10P(8) ~14 542.2 28 601 999.6 ~0.8 2.0 954.060 01( ~2)
R(ll, 3) 10P(8) ~13 269.7 28 603 272.1 ~0.3 2.0 954.102 46( O)
R(ll, 5) 10P(8) ~9 200.1 28 607 341.7 ~1.2 2.0 954.238 21( ~3)
R(13, 3) 10P(8) 9 100.3 28 625 642.1 ~0.2 2.0 954.848 64( 0)
R(13, 4) 10P(8) 10 860.5 28 627 402.3 3.0 2.0 954.907 35( 10)
R(13, 5) 10P(8) 13 119.0 28 629 660.8 4.5 2.0 954.982 69( 15)
R(13, 6) 10P(8) 15 877.0 28 632 418.8 7.0 2.0 955.074 69( 23)
R(14, 0) 10P(8) 17 940.5 28 634 482.3 0.2 2.0 955.143 52( 0)
R(14, 8) 10P(6) ~15 337.9 28 650 366.7 ~0.8 2.0 955.673 36( ~2)
R(14, 9) 10P(6) ~11 154.5 28 654 0.1 ~0.8 2.0 955.812 91( ~2)

 

 

S36

Table 3~1 (cont’d)

 

 

Trans. Lasera v-b v/MHz O—Cc Uncd v/cm 1 e
R(15, 3) 10P(6) ~17 959.0 28 647 745.6 ~0.1 2.0 955.585 93( 0)
R(15, 4) 10P(6) ~16 229.2 28 649 475.4 ~0.3 2.0 955.643 63( ~1)
R(15, 5) 10P(6) ~14 008.4 28 651 696.2 0.5 2.0 955.717 71( l)
R(15, 6) 10P(6) ~11 304.5 28 654 400.1 ~1.7 2.0 955.807 90( ~5)
R(16, 0) 10P(6) ~9 217.4 28 656 487.2 0.6 2.0 955.877 52( 2)
R(16, l) 10P(6) ~8 972.9 28 656 731.7 ~0.8 2.0 955.885 68( ~2)
R(16, 2) 10P(6) ~8 238.0 28 657 466.6 ~3.3 2.0 955.910 19(-10)
R(16,10) 10P(6) 14 915.2 28 680 619.8 21.7 OMIT 956.682 50( 72)
R(17, 6) 10P(6) 10 408.6 28 676 113.2 1.2 2.0 956.532 18( 3)
R(17, 8) 10P(6) 17 084.6 28 682 789.2 ~0.8 2.0 956.754 86( ~2)
R(18, 0) 10P(6) 12 524.0 28 678 228.6 0.4 2.0 956.602 74( 1)
R(18, l) 10P(6) 12 766.5 28 678 471.1 1.2 2.0 956.610 83( 3)
R(18, 3) 10P(6) 14 696.9 28 680 401.5 0.6 2.0 956.675 22( 2)
R(18, 4) 10P(6) 16 381.8 28 682 086.4 1.7 2.0 956.731 42( 5)

 

 

aCO2 laser line used (1201602); laser frequencies were taken from Ref. 34.

bMicrowave frequency in MHz. The signed microwave frequency was added to the
laser frequency to obtain the absorption frequency.

cObserved minus calculated frequency in MHz; the parameters for the calculation
are in the second column in Table 3~2 and the second column of Table 3~4.

dEstimated uncertainty in the observed frequency in MHz. An "OMIT" means that
the frequency was omitted from the least squares fits.

eObserved wavenumber in cm-l. The numbers in parentheses are observed minus
calculated wavenumbers in units of 0.00001 cm 7

97

distortion constants obtained by least squares fitting of the
hypothetical unsplit rotation and vibration-rotation frequencies are

given in Tables 3~2 and 3~3 for the ground and v = 1 states,

2
respectively. In Table 3~3 the Coriolis effects described above were
ignored. Table 3-4 contains the corresponding parameters for v2 = l for
fittings in which the Coriolis coupling to us and 2v3 was included.
Finally, the parameters in Tables 3~2 and 3~3 have been used to
calculate coincidences within 1200 MHz of CO2 laser frequencies for
transitions with J S 40 and K S 10 in the v2 band of CD31, and these are

listed in Table 3~5. For this calculation, the laser frequencies were

taken from Refs. (14) and (18).

III~4~2 003Br

The infrared frequencies measured in this work are given in Tables

3~6 and 3~7 for CD 7gBr and CD

3

fitting was done with more than 1200 experimental frequencies for each

3818r, respectively. The least squares

species, including approximately 230 and 190 new, more precise infrared
frequencies for CD37QBr and CD3818r, respectively. For both species,
ground state molecular parameters A0 and DK were constrained to the
values reported by Edwards and Broderson (11). H; and L; are
constrained to zero so that only AHK and ALK for v2 = l are reported.
The determined molecular constants are shown in Tables 3-8 and 3~9 for

3798r and CD381Br, respectively. Although the values in these tables

CD
are approximations to deperturbed parameters, with the effects of the

v2~v5 Coriolis coupling removed, until a complete fitting of both bands

 

98

TABLE 3~2

Comparison of Ground State Rotational Constants of CD318

 

 

Parameter This Workb This Workc Wlodarczakd

Bo /MHz ’6 040.297 40 (47) 6 040.297 77 (22) 6 040.297 28 (38)
DJ /kHz 3.722 63 (60) 3.722 60 (32) 3.721 88 (30)
DJK /kHz 48.294 8 (40) 48.294 5 (16) 48.296 3 (36)
BJ /Hz ~0.001 346(145) ~0.001 358(78) ~0.001 530(60)
HJK /Hz 0.043 41 (320) 0.033 47(152) 0.037 75(192)
HKJ /Hz 0.998 5 (108) 1.017 8 (38) 1.008 0 (63)

 

 

8Values in parentheses are one standard deviation in multiples of the

last digit in the parameter.

bObtained from fit of vibration-rotation frequencies listed in

Table 3~1 and hypothetical unsplit rotational frequencies calculated

from References (1,11-11).

cObtained from fit of rotational frequencies from references (11-11)

and pure quadrupole frequencies in Table V of Ref. 5 and in Table 4-1.

dFrom Table VI in Ref. 6.

Molecular Constants of the v2

539

TABLE 3~3

Coriolis Corrections

= 1 State of CD I Without

 

 

Parameterb This Workc This Workd Kawaguchie

Ev /GHz 28 461.093 3 (9) 28 461.093 3 (15) 28 461.093 8(14)
Bv /MBz 6 007.878 0 (28) 6 007.878 4 (46) 6 007.873 (8)f
6(Av-Bv) /MHz 264.71 (13) 264.71 (22) 266.4 (4)
DJ M12 3.557 4(171) 3.557 4(287) 3.6‘ f
DJK /kRz 102.265 (249) 102.263 (421) 106. (2)
ADK /kHz 19.6 (58) 19.6 (98) 121. (34)
BJK /Bz 1.374 (182) 1.362 (309)

HEJ /Hz ~186.01 (400) ~185.95 (677)

AH: /Bz 1136. (93) 1136. (157)

LJJJK /mHz ~0.242 (57) ~0.242 (96)

LJJKK /mHz 48.77 (157) 48.78 (27)

LJKKK /mBz ~1988.5 (243) ~1988.4 (411)

ALK /mBz ~3562. (475) ~3563. (804)

 

 

.Values in parentheses are one standard deviation in multiples of the last

digit in the parameter.

b

Vibration-rotation parameters. AP = P(v2=l) - P(v2=0).

constrained to zero in both fits in this work.

HJ and LJ were

cObtained from a fit of the vibration-rotation frequencies listed in

Table 3~3 and hypothetical unsplit rotational frequencies calculated
from References (1,11~_l_3_).

dObtained from a fit of the frequencies described in previous footnote with

the ground state parameters constrained to the parameters in Table 3~2

(Column 2).

3Obtained from Table V in Ref. 1.

f

Obtained from Ref. 11 (Tables VIII and X).

‘Assumed to be the same as in the ground state.

1(10

TABLE 3~4

Molecular Constants of the v2

3

= 1 State of CD I with Coriolis Correctiona

 

 

Parameterb This Workc This Workd Matsuurae

Ev /GBz 28 461.095 4 (6) 28 461.095 4 (14) 28 461.094 7 (18)
Bv /M82 6 020.287 0 (33) 6 020.287 2 (75) 6 020.339 2 (180)
A( Av-Bv) /MHz 252 . 328 (47) 252 . 328 (105) 250 . 600 (180)
DJ /kHz 3.692 3 (50) 3.692 1 (113) 4.197 1(8894)
DJK /kHz 52.56 (16) 52.56 (37) 54.86 (60)
ADK /kHz 13.8 (5) 13.8 (12) 8.1 (15)
BJ /Hz ~0.006 4 (20) ~0.006 5 (46)

833 /Hz 0.454 (137) 0.439 (311)

HEJ /Hz ~13.46 (22) ~13.38 (50)

LJJJK /mHz ~0.059 (50) ~0.057 (113)

LJJEK /mHz 2.78 (106) 2.77 (240)

LJKEK /mHz ~77.9 (111) ~77.8 (251)

 

 

aEffects of Coriolis interaction with us and 203 states were subtracted from

the experimental frequencies before fitting.

The Coriolis parameters in

Table II of Ref. 1 were used except that (25 = 4398.7 MHz. Values
in parentheses are one standard deviation in multiples of the last digit in

the parameter.

b . . . _ _ _ _
Vibration-rotation parameters. AP - P(vz-l) P(vz-O). ABK, ALK, and
were constrained to zero for both fittings in this work.

LJ

cObtained from full fit of vibration-rotation frequencies listed in Table 3~1

and hypothetical unsplit rotational frequencies calculated from References

(gall-1:3.) .

dObtained from fit of frequencies described in previous footnote with the

ground state parameters constrained to the parameters in Table V (Column 2).

eObtained from Table 11 in Ref. 2.

101

TABLE 3~5

Coincidences between Calculated Frequencies for the 02

Band of CD31 and Laser Frequencies

 

 

Trans.a Frequencyb vO-DLC Laserd

P(40,10) 27 943 074.3 ~62.5 N20 P( 8)
P(39, 0) 27 943 156.3 19.5 N20 P( 8)
P(38, 8) 27 968 783.7 ~79.4 N20 P( 7)
P(34, 4) 28 018 067.4 ~140.9 1301802 BAND I R( 8)
P(34, 5) 28 019 870.2 ~142.8 N20 P( 5)
P(32, 6) 28 050 509.7 ~15.6 120160180 BAND P(36)
P(31, l) 28 057 251.8 7.2 1201802 BAND I P(38)
P(27, 2) 28 113 451.9 ~15.0 1201802 BAND I P(36)
P(25, 4) 28 143 652.0 ~192.6 1301602 BAND I R(36)
P(24, 7) 28 164 886.5 ~63.3 120160180 BAND P(32)
P(23, 4) 28 170 871.8 ~161.5 N20 R( 0)
P(20, 5) 28 213 414.7 ~90.7 1301602 BAND I R(40)
P(19, 0) 28 220 595.4 35.0 N20 R( 2)
P(19, l) 28 220 843.5 ~135.5 120160180 BAND P(30)
P(19, 8) 28 236 223.1 ~98.7 1301802 BAND 1 R(20)
P(l7, l) 28 247 241.6 ~145.5 1301602 BAND I R(42)
P(16, 8) 28 276 169.4 ~53.6 120160180 BAND P(28)
P(15, 4) 28 277 199.9 ~89.9 1201802 BAND I P(30)
P(12, 5) 28 318 329.9 ~59.0 N20 R( 6)
P( 9, 8) 28 366 860.0 171.8 N20 R( 8)
P( 8, 4) 28 366 837.5 149.3 N20 R( 8)
P( 4, l) 28 412 648.0 58.3 1201602 BAND I P(16)
P( 4, 3) 28 414 762.8 186.9 N20 R(lO)
P( 2, 1) 28 437 133.0 16.8 1301602 BAND I R(54)
Q( 2, 2) 28 461 956.9 ~94.1 N20 R(12)
Q( 4, 4) 28 464 662.3 ~ll.5 1201602 BAND I P(l4)
Q( 6, 3) 28 462 093.1 42.1 N20 R(12)
Q( 6, 5) 28 466 291.8 -138.9 1301602 BAND I R(56)
Q( 7, 4) 28 463 462.3 41.6 120160180 BAND P(21)
Q( 9, 2) 28 459 216.0 ~108.5 1301802 BAND I R(34)
Q( 9, 5) 28 464 664.9 ~8.8 1201602 BAND I P(14)
0(11, 3) 28 459 132.4 ~192.l 1301802 BAND I R(34)
0(11, 5) 28 463 242.3 ~178.4 120160180 BAND P(21)
0(13, 4) 28 459 266.8 ~57.7 1301802 BAND I R(34)
0(14, 6) 28 463 370.0 ~50.7 120160180 BAND P(21)
0(17, 7) 28 463 223.4 ~197.3 120160180 BAND P(21)
0(18, 7) 28 461 944.5 ~106.6 N20 R(12)
0(20, 7) 28 459 176.5 ~148.0 1301802 BAND I R(34)
0(20, 9) 28 466 547.9 117.2 1301602 BAND I R(56)

 

 

102

Table 3~5 (cont’d)

 

 

Trans.a Frequencyb vo~vLc Laserd

0(22, 8) 28 459 502.0 177.5 1301802 BAND I R(34)
0(22, 9) 28 463 233.7 ~187.0 120160180 BAND I P(21)
Q(24,10) 28 463 420.8 0.1 120160180 BAND I P(21)
Q(26,10) 28 459 271.3 ~53.2 1301802 BAND I R(34)
0(28, 4) 28 438 387.0 21.8 N20 R(ll)
0(29, 2) 28 433 887.0 1.6 1201802 BAND I P(24)
0(29, 5) 28 438 378.2 13.0 N20 R(ll)
0(33, 8) 28 437 044.5 ~7l.7 1301602 BAND I R(54)
0(34, 6) 28 429 733.7 160.7 1301802 BAND I R(32)
0(34, 9) 28 437 165.9 49.7 1301602 BAND I R(54)
0(35, 7) 28 429 619.7 46.8 1301802 BAND I R(32)
0(36, 8) 28 429 459.2 ~ll3.8 1301802 BAND I R(32)
Q(36,10) 28 433 976.2 90.8 1201802 BAND I P(24)
0(39, 1) 28 411 108.9 198.8 120160180 BAND I P(23)
0(39, 3) 28 412 554.7 ~35.0 1201602 BAND I P(16)
0(40, 5) 28 412 686.6 96.9 1201602 BAND I P(16)
0(40, 6) 28 414 451.0 ~124.9 N20 R(lO)
R( 3, l) 28 509 030.3 ~82.0 N20 R(l4)
R( 5, 1) 28 532 474.6 ~12.7 N20 R(15)
R( 7, l) 28 555 657.3 ~101.1 N20 R(16)
R( 8, 4) 28 571 030.1 ~156.3 1301802 BAND I R(42)
R(ll, 2) 28 602 001.0 13.0 N20 R(l8)
R(12, 4) 28 616 261.8 ~31.4 120160180 BAND I P(15)
R(15, 3) 28 647 747.7 ~52.3 N20 R(20)
R(17, 4) 28 671 284.9 ~136.7 1301802 BAND I R(50)
R(18, 7) 28 689 934.8 ~180.2 120160180 BAND I P(12)
R(19, 2) 28 689 958.4 ~156.6 120160180 BAND I P(12)
R(21, 4) 28 714 089.3 ~48.4 1201602 BAND I P( 4)
R(22, 6) 28 729 166.7 132.0 1301602 BAND II P(60)
R(22, 9) 28 738 957.4 169.5 1301802 BAND I R(56)
R(26,10) 28 782 703.7 ~12.0 N20 R(26)
R(30, 3) 28 805 022.6 190.4 N20 R(27)
R(31, 4) 28 816 383.4 ~17.l 1201802 BAND I P( 8)
R(32, 7) 28 832 413.2 ~127.6 120160180 BAND I P( 6)
R(35, 4) 28 855 419.2 ~183.2 120160180 BAND I P( 5)
R(36, 7) 28 870 580.4 36.0 N20 R(30)
R(37, 6) 28 877 919.1 16.7 1201602 BAND I R( 2)
R(39, 3) 28 892 201.6 ~33.9 N20 R(31)
R(3l, 4) 28 816 383.4 ~l7.1 1201802 BAND I P( 8)

 

 

aTransition in the v2 band of CD3I; J S 40, k S 10.

Frequency of the 02 band transition in MHz.

103

cFrequency of the v2 band transition minus the laser
frequency in MHz.

dIdentification of 002 or N20 laser. Band I is 10 pm
band; band 11 is 9 pm band. Laser frequencies were

obtained from Refs. 14 and 11.

104

TABLE 3~6

79

Comparison of Observed and Calculated Frequencies in the 02 Band of CD3 Br

 

 

Trans.a Laserb v-c v/MBz v/cm l f
P(45, 5) 1201602 10R( 4) 854.1 28 907 192.3 5.0 964.240 13( ~17)
P(45, 4) 1201602 10R( 4) 408.0 28 910 638.4 5.0 964.355 09( ~9)
P(45, 3) 1201602 lOR( 4) 318.5 28 912 728.0 5.0 964.424 79( 6)
P(44, 7) 1201602 10R( 4) ~9 531.6 28 913 514.9 10.0 964.451 04( 13)
P(45, 2) 1201602 10R( 4) ~9 098.0 28 913 948.4 5.0 964.465 50( 6)
P(45, 1) 1201602 10R( 4) -8 464.0 28 914 582.4 5.0 964.486 65( ~2)
P(45, 0) 1201602 10R( 4) ~8 269.5 28 914 776.9 5.0 964.493 14( ~12)
P(44, 4) 1201602 lOR( 4) 8 086.2 931 132.7 10.0 965.038 71( ~9)
P(44, 3) 1201602 lOR( 4) 029.2 933 075.6 5.0 965.103 52( 11)
P(44, 1) 1201602 lOR( 4) 729.7 934 776.1 20.0 965.160 24( 5)
P(43, 7) 1201602 10R( 4) 769.3 934 815.7 20.0 965.161 56( 35)
P(44, 0) 1201602 10R( 4) 909.3 934 955.8 5.0 965.166 23( 7)
P(43, 4) 1201602 10R( 6) 917.3 951 539.8 5.0 965.719 42( ~4)
P(43, 3) 1201602 10R( 6) 125.6 953 331.4 5.0 965.779 l7( 4)
P(43, 2) 1201602 10R( 6) 101.6 954 355.4 5.0 965.813 34( 5)
P(42, 7) 1201602 10R( 6) 435.7 956 021.3 5.0 965.868 91( 14)
P(38,10) 1201602 10R( 6) 085.6 958 371.5 5.0 965.947 30( 3)
P(41, 7) 1201602 10R( 6) 691.5 977 148.6 10.0 966.573 62( 13)
P(40, 8) 1201602 lOR( 6) 369.9 984 826.9 10.0 966.829 75( 5)
P(41, 6) 1201602 10R( 6) 513.5 984 970.6 5.0 966.834 55( ~13)
P(4l, 3) 1201602 lOR( 8) 557.5 993 575.5 .0 967.121 57( 5)
P(4l, 2) 1201602 10R( 8) 730.1 994 402.9 .0 967.149 18( 1)
P(41, 1) 1201602 10R( 8) 319.2 994 813.8 .0 967.162 87( ~5)
P(41, 0) 1201602 lOR( 8) 191.9 994 941.1 .0 967.167 13( 4)
P(40, 7) 1201602 10R( 8) 944.9 998 188.1 5.0 967.275 44( 10)
P(39, 6) 1201602 10R( 8) 013.3 026 146.3 20.0 968.208 02( ~17)
R(37, 9) 1201602 lOR( 8) 056.7 026 189.7 OMIT 968.209 47(-649)
P(38, 8) 1201602 10R( 8) 622.2 027 755.2 5.0 968.261 69( 0)
P(38, 7) 1201602 10R(10) 072.1 040 000.6 5.0 968.670 15( 14)
R(37, 6) 1201602 10R(10) 870.9 066 943.6 5.0 969.568 86( ~10)
P(36, 8) 1201602 10R(10) 283.9 070 356.6 5.0 969.682 72( 8)
P(33,10) 1201602 10R(10) 030.5 071 103.2 OMIT 969.707 62(-628)
R(37, 4) 1201602 10R(10) 958.3 072 031.0 5.0 969.738 56( ~1)
P(36, 7) 1201602 10R(12) 840.2 081 434.2 5.0 970.052 23( 8)
P(36, 6) 1201602 108(12) 082.8 087 191.6 5.0 970.244 28( ~15)
P(35, 6) 1201602 10R(12) 067.8 107 342.2 5.0 970.916 42( ~6)
P(35, 4) 1201602 10R(12) 145.5 111 419.9 5.0 971.052 44( ~4)
P(35, 3) 1201602 10R(12) 772.1 112 046.5 5.0 971.073 00( 5)
P(34, 8) 1201602 10R(12) 325.7 112 600.1 5.0 971.091 81( 3)
P(33, 9) 1201602 10R(12) 756.4 114 030.8 5.0 971.139 53( ~22)
P(34, 6) 1201602 lOR(l4) 350.5 127 385.6 5.0 971.585 00( ~10)
P(33, 6) 1201602 10R(14) 590.9 147 327.0 5.0 972.250 18( ~2)
P(33, 5) 1201602 10R(14) 737.2 149 473.3 5.0 972.321 77( 26)
P(33, 4) 1201602 10R(14) 662.6 150 398.8 5.0 972.352 63( ~23)
P(32, 8) 1201602 108(14) 727.7 154 463.8 5.0 972.488 23( 0)
P(32, 7) 1201602 10R(16) 357.0 163 098.6 5.0 972.776 25( 15)
P(32, 6) 1201602 10R(16) 301.0 167 154.7 5.0 972.911 56( ~14)
P(32, 5) 1201602 10R(16) 453.9 169 001.8 5.0 972.973 16( ~8)
P(32, 4) 1201602 10R(16) 714.9 169 740.8 5.0 972.997 82( ~6)
P(31, 5) 1201602 108(16) 9 978.9 188 434.6 5.0 973.621 38( ~3)

 

 

Table 3~6 (cont’d)

105

 

 

Trans.a Laserb v-c v/MHz O-Cd Unc.e v/cm‘.1 f

P(30, 8) 1201602 10R(16) 17 464.9 29 195 920.6 0.7 5.0 973.871 08( 2)
P(30. 7) 1201602 108(18) ~15 150.1 29 203 280.6 2.1 5.0 974.116 58( 7)
P(30, 6) 1201602 10R(18) ~11 945.7 29 206 485.0 ~5.8 5.0 974.223 47( ~19)
P(28, 7) 1201602 10R(20) ~14 656.4 29 243 002.1 0.1 5.0 975.441 55( 0)
P(28, 3) 1201602 10R(20) ~11 958.0 29 245 700.6 4.0 5.0 975.531 56( 13)
P(26, 0) 1201602 10R(22) ~14 206.7 29 281 929.7 ~4.4 5.0 976 740 04( ~15)
P(26, 1) ' 1201602 108(22) ~14 084.0 29 282 052.3 ~4.0 5.0 976 744 13( ~14)
P(26, 7) 1201602 10R(22) ~13 892.5 29 282 243.8 2.4 5.0 976 750 52( 8)
P(26, 2) 1201602 10R(22) ~13 728.0 29 282 408.3 2.0 5.0 976 755 99( 7)
P(26, 2) 1201602 10R(22) ~13 728.0 29 282 408.4 2.1 5.0 976 756 00( 7)
P(26, 3) 1201602 10R(22) ~13 205.8 29 282 930.6 3.7 5.0 976.773 42( 12)
P(26, 4) 1201602 10R(22) ~12 632.3 29 283 504.1 1.0 5.0 976.792 55( 3)
P(24, 8) 1201602 108(24) ~16 332.6 29 317 528.6 4.1 5.0 977.927 49( 14)
P(24, 0) 1201602 10R(24) ~15 405.9 29 318 455.2 ~1.3 5.0 977.958 39( ~4)
P(24. 1) 1201602 10R(24) ~15 254.7 29 318 607.0 0.5 5.0 977.963 46( 2)
P(22.10) 1201602 10R(24) ~15 071.8 29 318 789.4 27.1 OMIT 977.969 55( 90)
P(24. 2) 1201602 108(24) ~14 818.0 29 319 043.1 0.8 5.0 977.978 01( 3)
P(24, 3) 1201602 108(24) ~14 143.3 29 319 717.9 1.7 5.0 978.000 52( 6)
P(24, 7) 1201602 10R(24) ~12 883.9 29 320 977.3 3.8 5.0 978 042 53( 13)
P(24. 6) 1201602 10R(24) ~12 175.4 29 321 685.8 ~2.3 5.0 978 066 15( ~8)
P(22, 0) 1201602 10R(26) ~16 290.8 29 354 533.8 ~11.6 OMIT 979.161 84( ~39)
P(22, 1) 1201602 10R(26) ~16 109.7 29 354 719.9 ~1.5 5.0 979.168 05( ~5)
P(22, 2) 1201602 108(26) ~15 589.6 29 355 240.0 2.1 5.0 979.185 41( 7)
P(22, 3) 1201602 108(26) ~14 771.9 29 356 057.7 1.7 5.0 979.212 67( 6)
P(22, 5) 1201602 10R(26) ~12 622.9 29 358 206.7 ~0.5 5.0 979.284 36( ~2)
P(19,10) 1201602 10R(26) 15 422.9 29 386 252.5 ~28.8 OMIT 980.219 87( ~96)
P(20, 0) 1201602 lOR(28) ~16 845.0 29 390 193.3 ~0.9 5.0 980.351 31( ~3)
P(20, 1) 1201602 lOR(28) ~16 643.4 29 390 394.8 0.4 5.0 980.358 05( l)
P(20, 2) 1201602 lOR(28) ~16 050.7 29 390 987.5 1.6 5.0 980.377 82( 5)
P(20. 3) 1201602 lOR(28) ~15 096.5 29 391 941.8 3.3 5.0 980.409 65( 11)
P(20, 4) 1201602 lOR(28) ~13 839.5 29 393 198.7 9.7 5.0 980.451 56( 32)
P(20, 5) 1201602 lOR(28) ~12 422.2 29 394 616.1 .~1.3 5.0 980.498 84( ~4)
P(20, 7) 1201602 lOR(28) ~10 219.5 29 396 818.7 ~1.3 5.0 980.572 31( ~4)
P(19, 8) 1201602 lOR(28) 8 132.9 29 415 171.2 5.7 5.0 981.184 49( 19)
P(19, 7) 1201602 lOR(28) 8 386.4 29 415 424.6 ~2.8 5.0 981 192 94( ~9)
P(18. 0) 1201602 108(30) ~17 088.7 29 425 394.6 ~2.0 5.0 981 525 51( ~7)
P(18, 1) 1201602 10R(30) ~16 867.2 29 425 616.1 ~2.9 5.0 981 532 90( ~10)
P(18, 2) 1201602 10R(30) ~16 201.1 29 426 281.8 2.2 5.0 981 555 ll( 7)
P(18. 3) 1201602 108(30) ~15 119.7 29 427 363.6 7.7 5.0 981 591 18( 26)
P(18, 4) 1201602 10R(30) ~13 678.7 29 428 804.6 3.7 5.0 981 639 26( 12)
P(18, 5) 1201602 lOR(30) ~11 960.4 29 430 522.9 ~0.4 5.0 981 696 56( ~1)
P(18, 6) 1201602 10R(30) ~10 144.3 29 432 339.0 ~5.3 5.0 981 757 15( ~18)
P(18, 7) 1201602 10R(30) -8 599.5 29 433 883.9 ~3.5 5.0 981 808 67( ~12)
P(l7, 7) 1201602 10R(30) 9 710.7 29 452 194.0 ~3.0 5.0 982.419 44( ~10)
P(16,10) 1201602 10R(30) 11 564.0 29 454 047.4 ~42.3 OMIT 982.481 26(-141)
P(16, 0) 1201602 10R(30) 17 661.0 29 460 144.4 ~2.4 5.0 982.684 63( ~8)
P(16. 1) 1201602 108(32) ~16 774.0 29 460 386.9 ~2.4 5.0 982.692 72( ~8)
P(16, 4) 1201602 10R(32) ~13 251.0 29 463 909.8 ~13.5 10.0 982.810 24( ~45)
P(16, 6) 1201602 108(32) ~9 019.6 29 468 141.3 ~6.3 5.0 982.951 38( ~21)
P(15, 6) 1201602 10R(32) 8 671.3 29 485 832.1 ~6.2 5.0 983.541 48( ~21)

 

 

106

Table 3~6 (cont’d)

 

 

Trans.a Laserb v-c v/Mflz O—C Unc v/cm-1 f

P(15, 8) 1201602 10R(32) 13 251.0 29 490 411.9 ~6.4 20.0 983.694 25( ~21)
P(15, 9) 1201602 10R(32) 13 251.0 29 490 411.9 208.7 OMIT 983.694 25( 696}
P(14, 0) 1201602 108(32) 17 277.9 29 494 438.6 ~0.8 5.0 983.828 57( ~3)
P(14, 1) 1201602 10R(34) ~16 367.6 29 494 699.1 ~0.8 5.0 983.837 26( ~3)
P(14, 2) 1201602 10R(34) ~15 593.2 29 495 473.4 ~5.5 5.0 983.863 09( ~18)
P(14, 3) 1201602 108(34) ~14 295.4 29 496 771.3 3.1 5.0 983.906 38( 10)
P(14, 4) 1201602 10R(34) ~12 516.2 29 498 550.5 2.0 5.0 983.965 73( 7)
P(14,10) 1201602 10R(34) ~11 422.7 29 499 644.0 ~19.5 5.0 984.002 20( ~65)
P(14, 5) 1201602 108(34) ~10 287.2 29 500 779.5 ~1.3 5.0 984.040 07( ~4)
P(13, 6) 1201602 108(34) 9 716.6 29 520 783.3 ~6.3 5.0 984.707 34( ~21)
P(l3,10) 1201602 10R(34) 11 588.8 29 522 655.5 1.1 5.0 984.769 78( 4)
P(13, 7) 1201602 10R(34) 12 807.3 29 523 874.0 ~3.9 5.0 984.810 42( ~13)
P(l3, 8) 1201602 108(34) 15 922.6 29 526 989.3 10.1 OMIT 984.914 35( 34)
P(12, 0) 1201602 108(34) 17 201.1 29 528 267.7 ~1.7 5.0 984.956 99( ~6)
P(12, 1) 1201602 10R(36) ~15 652.7 29 528 543.6 ~1.9 5.0 984.966 18( ~6)
P(12, 2) 1201602 108(36) ~14 822.0 29 529 374.3 0.9 5.0 984.993 90( 3)
P(12, 3) 1201602 10R(36) ~13 444.4 29 530 751.9 1.6 5.0 985.039 85( 5)
P(12, 5) 1201602 10R(36) ~9 087.5 29 535 108.8 ~4.4 5.0 985.185 19( ~15)
P(ll, 6) 1201602 108(36) 10 942.5 29 555 138.8 ~18.6 OMIT 985.853 30( ~62)
P(lO, 0) 1201602 108(36) 17 433.5 29 561 630.1 ~2.4 5.0 986.069 83( ~8)
P(10, 1) 1201602 108(38) ~14 625.5 29 561 919.7 ~2.2 5.0 986.079 50( ~7)
P(10, 2) 1201602 108(38) ~13 754.1 29 562 791.0 0.0 5.0 986.108 56( 0)
R(10, 4) 1201602 10R(38) ~10 265.9 29 566 279.2 0.1 5.0 986.224 91( 0)
R( 3, 1) 1301602 9P(28) 11 473.0 29 782 141.2 ~0.9 10.0 993.425 29( ~3)
R( 5, 1) 1301602 9P(26) ~17 264.2 29 811 661.3 ~2.5 10.0 994.409 98( ~8)
R( 5, 2) 1301602 9P(26) ~16 353.0 29 812 572.5 -2.8 10.0 994.440 38( ~9)
R( 5, 4) 1301602 9P(26) ~12 653.6 29 816 271.9 7.0 20.0 994.563 77( 23)
R( 7, 0) 1301602 9P(26) 11 476.3 29 840 401.9 ~5.1 5.0 995.368 66( ~17)
R( 7, 1) 1301602 9P(26) 11 770.9 29 840 696.4 ~3.4 5.0 995.378 49( ~11)
R( 7, 2) 1301602 9P(26) 12 653.6 29 841 579.1 -l.0 20.0 995.407 92( ~3)
R( 7, 3) 1301602 9P(26) 14 127.1 29 843 052.6 0.1 5.0 995.457 08( 0)
R( 7. 4) 1301602 9P(26) 16 201.4 29 845 127.0 2.2 20.0 995.526 28( 7)
R( 9, 0) 1301602 9P(24) ~17 377.5 29 868 967.0 ~3.8 5.0 996.321 50( ~13)
R( 9, 1) 1301602 9P(24) ~17 105.1 29 869 239.4 ~ll.8 30.0 996.330 58( ~39)
R( 9, 2) 1301602 9P(24) ~16 249.5 29 870 095.0 2.6 20.0 996.359 11( 9)
R( 9, 3) 1301602 9P(24) ~14 849.0 29 871 495.5 0.8 10.0 996.405 84( 3)
R( 9, 4) 1301602 9P(24) ~12 889.4 29 873 455.2 ~1.0 10.0 996.471 19( ~3)
R( 9, 5) 1301602 9P(24) ~10 380.1 29 875 964.5 ~5.8 10.0 996.554 90( ~19)
R(10, 7) 1301602 9P(24) 9 719.0 29 896 063.5 9.2 20.0 997.225 33( 31)
R(11, 0) 1301602 9P(24) 10 709.4 29 897 053.9 ~0.0 10.0 997.258 37( 0)
R(ll, 1) 1301602 9P(24) 10 973.0 29 897 317.5 ~1.8 5.0 997.267 16( ~6)
R(ll, 2) 1301602 9P(24) 11 770.8 29 898 115.3 1.3 5.0 997.293 77( 4)
R(10, 8) 1301602 9P(24) 13 089.1 29 899 433.6 ~137.4 OMIT 997.337 75(-525)
R(11, 3) 1301602 9P(24) 13 089.1 29 899 433.6 1.1 20.0 997.337 75( 4)
R(11, 4) 1301602 9P(24) 14 918.9 29 901 263.4 1.4 10.0 997.398 78( 5)
R(1l, 5) 1301602 9P(24) 17 229.2 29 903 573.7 ~1.4 5.0 997.475 85( ~5)
R(13, 2) 1301602 9P(22) ~17 273.8 29 925 646.9 ~0.2 5.0 998.212 13( ~1)
R(13, 3) 1301602 9P(22) ~16 043.1 29 926 877.6 8.7 5.0 998.253 19( 29)
R(13, 4) 1301602 9P(22) ~14 374.0 29 928 546.8 0.5 5.0 998.308 85( 2)
R(13, 5) 1301602 9P(22) ~12 290.6 29 930 630.1 2.1 5.0 998.378 36( 7)

 

 

Table 3~6 (cont’d)

107

 

 

Trans.a Laserb one v/Mflz O-Cd Unc e 12/cm-1 f
R(13, 6) 1301602 9P(22) ~9 917.0 29 933 003.8 ~8.1 5.0 998.457 53( ~27)
R(15, 0) 1301602 9P(22) 8 864.7 29 951 785.4 ~l.l 5.0 999.084 02( ~4)
R(15, 1) 1301602 9P(22) 9 093.6 29 952 014.3 ~0.6 5.0 999.091 64( ~2)
R(15, 2) 1301602 9P(22) 9 774.0 29 952 694.8 ~0.1 10.0 999.114 34( 0)
R(15, 3) 1301602 9P(22) 10 890.8 29 953 811.6 4.0 5.0 999.151 61( 13)
R(15, 4) 1301602 9P(22) 12 393.2 29 955 314.0 0.5 5.0 999.201 72( 2)
R(15, 5) 1301602 9P(22) 14 214.6 29 957 135.3 ~0.0 5.0 999.262 47( 0)
R(15, 6) 1301602 9P(22) 16 195.5 29 959 116.3 ~4.7 5.0 999.328 54( ~16)
R(17, 4) 1301602 9P(20) ~17 080.8 29 981 569.3 0.4 5.0 1000.077 49( 1)
R(17, 5) 1301602 9P(20) ~15 546.2 29 983 103.9 ~0.6 5.0 1000.128 69( ~2)
R(17, 6) 1301602 9P(20) ~13 999.3 29 984 650.8 ~2.9 5.0 1000.180 29( ~10)
R(17, 8) 1301602 9P(20) ~13 193.0 29 985 457.1 3.8 5.0 1000.207 18( 13)
R(17, 7) 1301602 9P(20) ~12 869.1 29 985 780.9 ~4.2 5.0 1000.217 98( ~14)
R(19, 4) 1301602 9P(20) 8 672.2 30 007 322.3 4.0 5.0 1000.936 52( 13)
R(19, 8) 1301602 9P(20) 9 777.0 30 008 427.1 5.2 5.0 1000.973 38( 17)
R(19, 5) 1301602 9P(20) 9 894.8 30 008 544.9 1.5 5.0 1000.977 30( 5)
R(19, 6) 1301602 9P(20) 10 972.0 30 009 622.1 ~0.1 5.0 1001.013 23( 0)
R(19, 7) 1301602 9P(20) 11 363.2 30 010 013.3 1.5 5.0 1001.026 29( 5)
R(20, 9) 1301602 9P(20) 12 280.8 30 010 930.9 ~188.9 OMIT 1001.056 90(-630)
R(22, 8) 1301602 9P(18) ~11 813.1 30 041 715.6 ~0.1 5.0 1002.083 76( 0)
R(22, 0) 1301602 9P(18) ~10 504.2 30 043 024.5 ~6.1 5.0 1002.127 43( ~21)
R(22, 1) 1301602 9P(18) ~10 355.1 30 043 173.7 ~1.0 5.0 1002.132 39( ~3)
R(22, 4) 1301602 9P(18) ~8 519.7 30 045 009.1 1.0 5.0 1002.193 62( 3)
R(22, 7) 1301602 9P(18) ~8 275.9 30 045 252.9 ~0.3 5.0 1002.201 76( ~1)
R(24, 8) 1301602 9P(18) 9 666.5 30 063 195.3 2.4 10.0 1002.800 25( 8)
R(24, 7) 1301602 9P(18) 14 530.0 30 068 058.7 12.5 10.0 1002.962 48( 42)
R(24, 0) 1301602 9P(18) 14 530.0 30 068 058.7 0.6 10.0 1002.962 48( 2)
R(24, 1) 1301602 9P(18) 14 644.2 30 068 172.9 ~0.9 5.0 1002.966 28( ~3)
R(24. 2) 1301602 9P(18) 14 976.3 30 068 505.1 1.1 5.0 1002.977 36( 4)
R(24, 3) 1301602 9P(18) 15 467.2 30 068 995.9 4.4 5.0 1002.993 74( 15)
R(26, 9) 1301602 9P(18) 15 617.5 30 069 146.2 46.3 OMIT 1002.998 75( 154)
R(24, 4) 1301602 9P(18) 15 995.6 30 069 524.4 2.6 5.0 1003.011 37( 9)
R(24, 6) 1301602 9P(18) 16 131.0 30 069 659.7 ~0.8 5.0 1003.015 88( ~3)
R(24, 5) 1301602 9P(18) 16 347.7 30 069 876.5 ~3.5 5.0 1003.023 10( ~12)
R(26, 7) 1301602 9P(16) ~17 248.7 30 090 304.4 1.0 5.0 1003.704 52( 3)
R(26, 0) 1301602 9P(16) ~14 927.1 30 092 626.0 ~4.4 5.0 1003.781 96( ~15)
R(26, 2) 1301602 9P(16) ~14 597.8 30 092 955.3 1.0 5.0 1003.792 94( 3)
R(26, 4) 1301602 9P(16) ~14 007.6 30 093 545.5 -8.8 5.0 1003.812 63( ~29)
R(26, 5) 1301602 9P(16) ~14 007.6 30 093 545.5 9.9 5.0 1003.812 63( 33)
R(27, 8) 1301602 9P(16) ~13 138.4 30 094 414.7 ~2.0 5.0 1003.841 62( ~7)
R(29, 9) 1301602 9P(16) ~10 845.5 30 096 707.6 0.3 5.0 1003.918 09( l)
R(28, 2) 1301602 9P(16) 9 396.3 30 116 949.4 0.3 5.0 1004.593 29( l)
R(ZB, 3) 1301602 9P(16) 9 555.6 30 117 108.7 7.1 5.0 1004.598 61( 24)
R(28, 4) 1301602 9P(16) 9 555.6 30 117 108.7 ~4.5 5.0 1004.598 61( ~15)
R(30, 8) 1301602 9P(16) 16 990.6 30 124 543.7 ~2.2 5.0 1004.846 62( ~7)
R(31, 7) 1301602 9P(14) ~16 976.5 30 143 743.4 3.1 10.0 1005.487 04( 10)
R(32, 8) 1301602 9P(14) ~16 650.7 30 144 069.2 ~2.8 5.0 1005.497 92( ~9)
R(31, 5) 1301602 9P(14) ~10 155.6 30 150 564.3 ~2.6 5.0 1005.714 56( ~9)
R(3l. 4) 1301602 9P(14) ~9 138.2 30 151 581.7 ~0.3 5.0 1005.748 51( ~1)
R(31, 3) 1301602 9P(14) ~8 734.8 30 151 985.1 1.6 5.0 1005.761 96( 5)

 

 

Table 3~6 (cont’d)

108

 

 

Trans.’ Laserb v: v/MHz o—cd Unc.e v/cm 1 f
R(31, 0) 1301602 9P(14) -8 618.4 30 152 101.5 -2.1 30.0 1005.765 84( ~7)
R(31, 2) 1301602 99(14) ~8 618.4 30 152 101.5 2.0 30.0 1005.765 84( 7)
R(3l, 1) 1301602 9P(14) -8 618.4 30 152 101.5 -8.0 30.0 1005.765 84( —27)
R(33, 4) 13c1602 9P(14) 13 275.7 30 173 995.6 1.9 5.0 1006.496 14( 6)
R(34, 7) 1301602 9P(14) 13 675.0 30 174 394.9 3.9 5.0 1006.509 46( 13)
R(33, 3) 1301602 9P(14) 13 962.0 30 174 681.9 2.3 5.0 1006.519 04( 8)
R(33, 0) 1301602 99(14) 14 383.5 30 175 103.4 -20.8 15.0 1006.533 10( ~69)
R(33, 1) 1301602 9P(14) 14 383.5 30 175 103.4 7.4 15.0 1006.533 10( 25)
R(35, 4) 1301602 99(12) -17 065.6 30 195 960.5 -1.1 5.0 1007.228 82( -4)
R(35, 2) 1301602 9P(12) -15 590.9 30 197 435.3 6.6 20.0 1007.278 01( 22)
R(35, 1) 1301602 9P(12) -15 376.3 30 197 649.9 -1.4 10.0 1007.285 l7( -5)
R(35, 0) 1301602 9P(12) -15 314.5 30 197 711.6 —2.7 10.0 1007.287 23( —9)
R(38, 8) 1301602 9P(12) -12 788.1 30 200 238.0 0.4 5.0 1007.371 50( 1)
R(36, 6) 1301602 9P(12) -12 027.5 30 200 998.7 -2.4 5.0 1007.396 88( ~8)
R(38, 5) 1301602 99(12) 12 587.3 30 225 613.4 -2.5 5.0 1008.217 93( ~8)
R(38, 3) 1301602 9P(12) 16 494.9 30 229 521.1 2.4 5.0 1008.348 28( 8)
R(38, 2) 1301602 99(12) 17 276.7 30 230 302.9 2.0 5.0 1008.374 36( 7)
R(38, 1) 1301602 99(12) 17 679.5 30 230 705.6 16.8 0M T 1008.387 79( 56)
R(38, 0) 1301602 9P(12) 17 780.7 30 230 806.8 1.2 5.0 1008.391 16( 4)
R(40, 4) 1301602 9P(10) -15 472.8 30 248 996.3 -1.5 5.0 1008.997 91( -5)
R(40, 3) 1301602 9P(10) —13 751.7 30 250 717.4 3.6 5.0 1009.055 32( 12)
R(4l, 6) 1301602 9P(10) -13 507.3 30 250 961.8 —4.1 5.0 1009.063 47( -14)
R(40, 1) 1301602 99(10) -12 276.1 30 252 193.0 -0.3 5.0 1009.104 54( -1)
R(40, 0) 1301602 9P(10) -12 123.6 30 252 345.4 —1.1 5.0 1009.109 61( -4)
R(46, 6) 1301602 9P( 8) ~16 605.6 30 298 440.7 2.0 10.0 1010.647 19( 7)
R(45, 1) 1301602 99( 8) -10 871.0 30 304 175.2 ~6.3 10.0 1010.838 48( -21)
R(45, 0) 1301602 9P( 8) -10 626.9 30 304 419.4 ~8.3 10.0 1010.846 62( ~28)
R(46, 5) 1301602 9P( 8) -9 970.4 30 305 075.9 -0.3 5.0 1010.868 51( -1)
R(47. 2) 1301602 9P( 8) 8 340.0 30 323 386.2 0.2 5.0 1011.479 28( 1)
R(48, 5) 1301602 9P( 8) 8 917.2 30 323 963.5 -1.4 10.0 1011.498 55( -5)
R(47, 1) 1301602 9P( 8) 9 239.5 30 324 285.8 ~0.6 5.0 1011.509 30( -2)
R(47, 0) 1301602 99( 8) 9 522.3 30 324 568.6 —1.4 5.0 1011.518 73( —5)
R(48, 4) 1301602 9P( 8) 13 507.2 30 328 553.5 1.8 5.0 1011.651 65( 6)
R(48, 3) 1301602 9P( 8) 16 417.4 30 331 463.7 3.1 5.0 1011.748 72( 10)

 

 

aNumbers are J and E of

b

Laser line used; laser

the lower vibrational state.

frequencies were taken from Ref. 13.

cMicrowave frequency in MHz. The signed microwave frequency was added to the laser
frequency to obtain the absorption frequency.

d

eEstimated uncertainty in the observed frequency in MHz. An ”OMIT”

means that the frequency was omitted from the least squares fits.

fObserved wavenumber in cm-l.

The numbers in parentg
minus calculated wavenumbers in units of 0.00001 cm

Tses are observed

Observed minus calculated frequency in MHz; the parameters for the calculation are
in Table 3~8 of this work and in Table V of Ref. 7.

109

 

 

TABLE 3-7
Comparison of Observed and Calculated Frequencies in the v2 Band of 003813r
Trans.a Laserb vnc v/MHz O-Cd Unc. v/cm 1 f
P(45, 6) 1201602 lOR( 4) -17 835.0 28 905 211.4 9.4 5.0 964.174 07( 31)
P(45, 5) 12C1602 lOR( 4) -12 239.5 28 910 807.0 -6.2 5.0 964.360 72( -21)
P(45, 4) 12C1602 10R( 4) -8 825.6 28 914 220.8 -0.6 5.0 964.474 59( -2)
P(44. 5) 1201602 lOR( 4) 8 365.5 28 931 411.9 -4.9 10.0 965.048 01( -16)
P(44. 4) 12C1602 lOR( 4) 11 571.6 28 934 618.1 1.1 5.0 965.154 97( 4)
P(44, 3) 12C1602 lOR( 4) 13 485.0 28 936 531.4 1.0 5.0 965.218 79( 3)
P(44. 2) 12C1602 lOR( 4) 14 588.7 28 937 635.1 -l.9 5.0 965.255 61( -6)
P(44, l) 12C1602 lOR( 4) 15 162.4 28 938 208.8 0.2 5.0 965.274 73( l)
P(43, 7) 1201602 lOR( 4) 15 282.0 28 938 328.4 -2.7 5.0 965.278 72( -9)
P(44. 0) 12C1602 lOR( 4) 15 336.6 28 938 383.1 -1.8 5.0 965.280 56( -6)
P(39,10) 12C1602 lOR( 4) 16 336.2 28 939 382.7 374.0 OMIT 965.313 89(1248)
P(43, 5) 12C1602 lOR( 6) -15 531.4 28 951 925.7 -6.9 10.0 965.732 29( -23)
P(43, 3) 12C1602 lOR( 6) -10 765.0 28 956 692.1 1.8 10.0 965.891 28( 6)
P(43, 2) 12C1602 lOR( 6) -9 756.6 28 957 700.4 1.4 10.0 965.924 90( 5)
P(43, l) 12C1602 lOR( 6) -9 243.8 28 958 213.3 -1.4 10.0 965.942 01( -5)
P(42, 3) 12C1602 lOR( 6) 9 305.8 28 976 762.8 2.2 10.0 966.560 77( 7)
P(42, 2) 1261602 lOR( 6) 10 217.4 28 977 674.4 2.6 5.0 966.591 17( 9)
P(42, l) 12C1602 lOR( 6) 10 676.6 28 978 133.7 2.0 5.0 966.606 49( 7)
P(42. 0) 12C1602 lOR( 6) 10 814.4 28 978 271.5 -0.1 20.0 966.611 08( 0)
P(39, 9) 1201602 lOR( 6) 17 944.3 28 985 401.3 -68.1 OMIT 966.848 92(-227)
P(41, 4) 1201602 10R( 8) -15 867.4 28 995 265.6 -2.0 5.0 967.177 95( -7)
P(4l. 3) 12C1602 lOR( 8) -14 392.1 28 996 740.9 0.8 5.0 967.227 16( 3)
P(4l, 2) 1201602 lOR( 8) -13 577.9 28 997 555.1 0.9 5.0 967.254 32( 3)
P(41, l) 12C1602 lOR( 8) -13 175.0 28 997 958.0 -0.6 5.0 967.267 75( -2)
P(4l. 0) 12C1602 10R( 8) -13 052.4 28 998 080.6 0.1 5.0 967.271 84( 0)
P(40, 7) 12C1602 lOR( 8) -9 726.2 29 001 406.8 1.0 5.0 967.382 79( 3)
P(39, 7) 12C1602 lOR( 8) 11 122.1 29 022 255.1 -0.8 5.0 968.078 22( -3)
P(39, 3) 12C1602 lOR(lO) -17 650.7 29 036 422.0 0.6 5.0 968.550 78( 2)
P(39, 2) 1201602 lOR(lO) -17 030.5 29 037 042.2 -0.7 5.0 968.571 46( -2)
P(38, 7) 12C1602 108(10) -11 059.2 29 043 013.5 -l.4 5.0 968.770 65( -5)
P(37, 7) 1201602 lOR(IO) 9 608.9 29 063 681.6 1.2 5.0 969 460 05( 4)
P(37, 6) 12C1602 108(10) 15 733.9 29 069 806.6 ~5.l 5.0 969 664 36( -l7)
P(36, 7) 12C1602 108(12) -12 024.4 29 084 250.0 0.4 5.0 970 146 15( 1)
P(35, 7) 1261602 108(12) 8 448.9 29 104 723.3 2.8 5.0 970 829 07( 9)
P(35, 5) 12C1602 108(12) 16 430.7 29 112 705.1 -l.0 5.0 971 095 31( -3)
P(35, 4) 1201602 108(12) 17 756.4 29 114 030.8 -1.5 5.0 971 139 53( -5)
P(34, 7) 1201602 10R(14) -12 661.9 29 125 074.3 -16.0 OMIT 971 507 89( -53)
P(33, 6) 12C1602 108(14) 12 065.4 29 149 801.5 -0.4 5.0 972.332 71( ~1)
P(33, 5) 1201602 108(14) 14 168.3 29 151 904.4 -4.9 5.0 972.402 86( -16)
P(33, 4) 1201602 108(14) 15 092.3 29 152 828.4 -0.2 5.0 972.433 67( -l)
P(32, 7) 1201602 108(16) -12 987.8 29 165 517.9 1.9 5.0 972.856 95( 6)
P(31. 6) 1201602 108(16) 10 706.9 29 189 162.6 -0.3 5.0 973.645 66( -l)
P(3l, 5) 1201602 108(16) 12 234.5 29 190 690.1 -0.7 5.0 973.696 60( ~2)
P(29, 9) 1201602 108(18) -15 798.2 29 202 632.5 -228.0 OMIT 974 094 96(-760)
P(30. 7) 1201602 108(18) -12 922.0 29 205 508.7 3.5 5.0 974 190 91( 12)
P(28, 3) 1201602 108(20) -10 010.6 29 247 648.0 -0.9 5.0 975 596 52( -3)
P(27, 2) 1201602 108(20) 8 125.6 29 265 784.1 3.1 5.0 976 201 47( 10)
P(27, 3) 1201602 108(20) 8 566.9 29 266 225.4 -4.0 5.0 976 216 19( -l3)
P(27. 6) 1201602 108(20) 8 876.0 29 266 535.1 0.5 5.0 976 226 53( 2)
P(27, 4) 1201602 108(20) 9 033.0 29 266 691.5 0.2 5.0 976 231 75( l)

 

 

110

Table 3-7 (cont’d)

 

 

Trans.a Laserb vlc v/Mflz 0-6d Uhc. v/cm l f
P(26. 8) 1261602 108(22) -16 756.9 29 279 379.5 -3.9 5.0 976.654 97( -13)
P(26, 3) 1261602 10R(22) ~11 433.9 29 284 702.5 1.0 5.0 976.832 53( 3)
P(26, 4) 1261602 108(22) -10 849.5 29 285 286.9 0.5 5.0 976.852 02( 2)
P(25, 9) 1261602 108(22) -8 706.5 29 287 429.9 -229.0 OMIT 976.923 49(-764)
P(24, 3) 1261602 108(24) -12 545.4 29 321 320.8 5.1 5.0 978 053 98( 17)
P(24, 4) 1261602 108(24) -11 723.6 29 322 137.6 0.1 5.0 978 081 23( 0)
P(24, 7) 1261602 108(24) -11 228.8 29 322 632.4 3.0 5.0 978 097 72( 10)
P(24, 5) 1261602 108(24) -10 940.9 29 322 920.2 0.9 5.0 978 107 34( 3)
P(24, 6) 1261602 108(24) -10 544.5 29 323 316.7 -0.5 5.0 978 120 55( -2)
P(22. 9) 1261602 108(24) 16 078.7 29 349 939.9 -226.3 OMIT 979 008 60(-755)
P(22, 2) 1261602 108(26) -14 170.6 29 356 659.0 -1.2 5.0 979.232 74( -4)
P(22, 3) 1261602 108(26) -13 345.8 29 357 483.8 0.5 5.0 979.260 25( 2)
P(22, 4) 1261602 108(26) -12 296.2 29 358 533.4 4.8 5.0 979.295 25( 16)
P(22, 5) 1261602 108(26) -11 183.8 29 359 645.8 0.0 5.0 979.332 36( 0)
P(21. 6) 1261602 108(26) 8 143.5 29 378 973.2 2.4 5.0 979.977 06( 8)
P(21, 7) 1261602 10R(26) 8 623.0 29 379 452.6 4.6 5.0 979.993 05( 15)
P(20, 9) 1261602 lOR(28) -16 050.7 29 390 987.5 -228.7 OMIT 980.377 82(-763)
P(20, 0) 1261602 lOR(28) -15 595.8 29 391 442.5 -1.2 5.0 980.392 99( -4)
P(20. 1) 1261602 lOR(28) -15 393.5 29 391 644.7 -0.4 5.0 980.399 73( ~1)
P(20. 2) 1261602 lOR(28) -14 798.2 29 392 240.0 0.0 5.0 980.419 59( 0)
P(20, 3) 1261602 lOR(28) -13 839.5 29 393 198.7 2.2 5.0 980.451 56( 7)
P(20, 4) 1261602 lOR(28) -12 587.1 29 394 451.2 0.5 5.0 980.493 34( 2)
P(20, 6) 1261602 lOR(28) -9 773.0 29 397 265.2 3.4 5.0 980.587 22( ll)
P(20, 8) 1261602 lOR(28) -9 773.0 29 397 265.2 -4.5 5.0 980.587 22( -15)
P(20, 7) 1261602 lOR(28) -8 926.7 29 398 111.6 1.9 5.0 980.615 45( 6)
P(19, 8) 1261602 lOR(28) 9 362.8 29 416 401.1 ~4.0 5.0 981.225 51( -l3)
P(18. 0) 1261602 108(30) -16 002.1 29 426 481.3 -0.1 5.0 981 561 76( 0)
P(18. 1) 1261602 108(30) -15 776.9 29 426 706.4 1.5 5.0 981 569 26( 5)
P(18, 2) 1261602 108(30) -15 119.7 29 427 363.6 -4.8 5.0 981 591 18( -16)
P(18. 3) 1261602 108(30) -14 032.8 29 428 450.5 2.7 5.0 981 627 44( 9)
P(18. 4) 1261602 108(30) -12 585.1 29 429 898.3 .3.4 5.0 981.675 74( 11)
P(18, 5) 1261602 108(30) -10 865.6 29 431 617.8 -0.6 5.0 981.733 08( -2)
P(18, 9) 1261602 108(30) -10 865.2 29 431 618.1 -73.1 OMIT 981 733 11(-244)
P(18, 6) 1261602 108(30) -9 041.3 29 433 442.0 -0.6 5.0 981.793 94( -2)
P(l7, 8) 1261602 108(30) 11 705.3 29 454 188.6 -2.9 5.0 982.485 98( -10)
P(16, 1) 1261602 108(32) -15 846.0 29 461 314.9 1.3 5.0 982.723 67( 4)
P(16, 2) 1261602 108(32) -15 121.4 29 462 039.5 0.2 5.0 982.747 84( 1)
P(16. 3) 1261602 108(32) -13 929.3 29 463 231.1 0.8 5.0 982.787 59( 3)
P(16. 4) 1261602 108(32) ~12 314.9 29 464 845.9 —7.0 5.0 982.841 46( -23)
P(16, 5) 1261602 108(32) -10 317.3 29 466 843.5 0.8 5.0 982.908 09( 3)
P(15, 6) 1261602 108(32) 9 524.9 29 486 685.7 2.4 5.0 983.569 96( 8)
P(15, 7) 1261602 108(32) 12 043.8 29 489 204.6 -1.5 5.0 983.653 99( ~5)
P(15, 8) 1261602 108(32) 14 135.5 29 491 296.3 -2.2 5.0 983.723 75( —7)
P(15, 9) 1261602 108(32) 14 381.0 29 491 541.9 390.9 OMIT 983.731 94(1304)
P(14, 0) 1261602 108(34) -15 861.5 29 495 205.1 1.0 5.0 983.854 14( 3)
P(14, 1) 1261602 108(34) -15 593.2 29 495 473.4 7.9 5.0 983.863 09( 26)
P(14, 2) 1261602 108(34) -14 817.9 29 496 248.8 2.1 5.0 983.888 95( 7)
P(14, 3) 1261602 108(34) -13 523.1 29 497 543.5 6.1 5.0 983.932 14( 20)
P(14, 4) 1261602 108(34) -11 750.1 29 499 316.6 -0.5 5.0 983.991 27( -2)
P(14, 5) 1261602 108(34) -9 521.6 29 501 545.1 -l.0 5.0 984.065 61( ~3)

 

 

11.1

Table 3-7 (cont’d)

 

 

Trans.a Laserb vnc v/Mflz O—Cd Unc v/c:m"l f
P(13, 7) 12C1602 108(34) 13 523.1 29 524 589.8 28.0 OMIT 984.834 30( 94)
P(12, 0) 12C1602 10R(36) ‘15 318.3 29 528 878.0 ‘1.1 5.0 984.977 35( ‘4)
P(13, 9) 12C1602 108(36) ‘14 345.5 29 529 850.8 28.7 OMIT 985.009 80( 96)
P(12, 2) 12C1602 108(36) ‘14 210.0 29 529 986.4 0.8 5.0 985.014 31( 3)
P(12, 3) 12C1602 108(36) ‘12 833.6 29 531 362.7 ‘0.7 5.0 985.060 23( ‘2)
P(12, 4) 12C1602 108(36) ‘10 942.5 29 533 253.9 ‘26.5 OMIT 985.123 30( ‘88)
P(ll, 7) 12C1602 108(36) 15 071.5 29 559 267.9 ‘0.7 5.0 985.991 03( ‘2)
P(10, 0) 12C1602 108(38) ‘14 455.2 29 562 089.9 ‘0.5 5.0 986.085 18( ‘2)
P(10, 1) 12C1602 108(38) ‘14 156.9 29 562 388.2 7.7 5.0 986.095 13( 26)
P(10, 2) 12C1602 108(38) ‘13 295.6 29 563 249.5 ‘1.5 5.0 986.123 86( ‘5)
P(10, 3) 12C1602 108(38) ‘11 843.0 29 564 702.2 ‘0.5 5.0 986.172 31( ‘2)
P(10, 4) 12C1602 108(38) ‘9 808.9 29 566 736.2 ‘0.2 5.0 986.240 15( ‘1)
R( 3, 0) 13C1602 9P(28) 10 663.5 29 781 331.7 7.4 10.0 993.398 29( 25)
R( 3, 1) 13C1602 9P(28) 10 965.2 29 781 633.4 ‘1.9 10.0 993.408 36( ‘6)
R( 7, 0) 13C1602 9P(26) 10 729.8 29 839 655.3 ‘0.2 5.0 995.343 75( ‘1)
R( 7, 1) 13C1602 9P(26) 11 022.5 29 839 948.0 ‘1.2 5.0 995.353 52( ‘4)
R( 7, 2) 13C1602 9P(26) 11 903.5 29 840 829.1 ‘1.9 5.0 995.382 91( ‘6)
R( 7, 3) 13C1602 9P(26) 13 378.7 29 842 304.3 0.6 5.0 995.432 12( 2)
R( 9, 1) 13C1602 9P(24) ‘17 961.6 29 868 382.9 ‘0.8 5.0 996.302 00( ‘3)
R( 9, 2) 13C1602 9P(24) ‘17 105.1 29 869 239.4 12.7 OMIT 996.330 58( 42)
R( 9, 3) 13C1602 9P(24) ‘15 717.3 29 870 627.2 ‘2.7 5.0 996.376 87( ‘9)
R( 9, 4) 13C1602 99(24) ‘13 757.9 29 872 586.6 ‘2.6 5.0 996.442 22( ‘9)
R(10, 7) 13C1602 9P(24) 8 775.9 29 895 120.4 ‘0.7 5.0 997.193 88( ‘2)
R(11, 0) 13C1602 9P(24) 9 719.0 29 896 063.5 ‘8.7 5.0 997.225 33( ‘29)
R(11, 1) 13C1602 9P(24) 9 991.2 29 896 335.7 ‘2.8 5.0 997.234 42( ‘9)
R(11, 3) 13C1602 9P(24) 12 089.1 29 898 433.6 ‘21.8 OMIT 997.304 39( ‘73)
R(11, 4) 1301602 9P(24) 13 937.8 29 900 282.3 ‘1.6 5.0 997.366 05( ‘5)
R(13, 4) 13C1602 9P(22) ‘15 470.0 29 927 450.8 ‘9.8 5.0 998 272 29( ‘33)
R(13, 5) 13C1602 9P(22) ‘13 381.3 29 929 539.4 ‘0.9 10.0 998 341 96( ‘3)
R(13, 6) 13C1602 9P(22) ‘10 998.9 29 931 921.9 ‘0.7 5.0 998 421 43( ‘2)
R(15, 3) 13C1602 9P(22) 9 693.5 29 952 614.2 ‘1.9 10.0 999.111 67( ‘6)
R(15, 4) 13C1602 9P(22) 11 203.2 29 954 124.0 0.2 5.0 999.162 02( 1)
R(15, 5) 13C1602 9P(22) 13 023.3 29 955 944.0 ‘1.8 5.0 999.222 74( ‘6)
R(15, 6) 13C1602 9P(22) 15 013.9 29 957 934.6 1.8 5.0 999.289 13( 6)
R(17, 5) 13C1602 9P(20) ‘16 836.1 29 981 814.0 ‘2.7 5.0 1000.085 65( ‘9)
R(17, 6) 13C1602 99(20) ‘15 277.4 29 983 372.7 2.2 5.0 1000 137 65( 7)
R(17, 8) 13C1602 9P(20) ‘14 434.2 29 984 215.9 ‘5.5 5.0 1000 165 78( ‘18)
R(17, 7) 13C1602 9P(20) ‘14 130.0 29 984 520.1 3.8 5.0 1000 175 92( 13)
R(18. 1) 13C1602 9P(20) ‘8 220.0 29 990 430.1 ‘5.4 5.0 1000 373 06( ‘18)
R(Zo, 0) 13C1602 9P(20) 17 434.5 30 016 084.6 ‘6.5 5.0 1001 228 80( ‘22)
R(ZO, 1) 13C1602 9P(20) 17 614.8 30 016 264.9 1.8 5.0 1001 234 82( 6)
R(22. 0) 13C1602 9P(18) ‘12 048.4 30 041 480.7 ‘1.5 5.0 1002 075 92( ‘5)
R(22, 2) 13C1602 9P(18) ‘11 476.5 30 042 052.2 2.0 5.0 1002 095 00( 7)
R(22, 3) 13C1602 9P(18) ‘10 829.5 30 042 699.3 ‘1.1 5.0 1002 116 57( ‘4)
R(24, 2) 1301602 9P(18) 13 341.8 30 066 870.5 0.8 5.0 1002 922 85( 3)
R(24, 3) 13C1602 9P(18) 13 839.5 30 067 368.2 3.1 5.0 1002 939 44( 10)
R(24, 4) 13C1602 99(18) 14 374.9 30 067 903.6 ‘1.1 5.0 1002 957 31( ‘4)
R(26, 0) 13C1602 9P(16) ‘16 656.4 30 090 896.6 ‘2.1 5.0 1003 724 27( ‘7)
R(26, 1) 13C1602 9P(16) ‘16 566.2 30 090 986.9 0.1 5.0 1003.727 27( 0)
R(26, 6) 13C1602 9P(16) ‘16 458.0 30 091 095.0 4.6 5.0 1003.730 89( 15)

 

 

112

Table 3-7 (cont’d)

 

 

Trans. Laserb v/Mfiz v/cn 1 f
R(26, 1301602 9P(16) ‘16 .0 30 091 233.1 .4 5.0 1003.735 49( 8)
R(26, 13C1602 9P(16) ‘15 .7 30 091 562.4 .9 5.0 1003.746 48( ‘3)
R(26, 1301602 9P(16) ‘15 .9 30 091 850.2 .4 10.0 1003.756 07( -1)
R(26, 13C1602 9P(16) -15 .9 30 091 850.2 .9 10.0 1003.756 07( 13)
R(29, 1301602 9P(16) 13 .1 30 120 995.2 .2 5.0 1004.728 25( 27)
R(30, 1301602 9P(16) 15 .6 30 122 732.7 .4 OMIT 1004.786 20(-318)
R(29, 1301602 9P(16) 17 .3 30 124 687.4 .7 5.0 1004.851 40( 6)
R(31, 13C1602 9P(14) -l4 .0 30 146 475.9 .9 5.0 1005.578 18( ‘20)
R(31, 1301602 9P(14) ‘12 .9 30 148 677.0 .8 5.0 1005.651 61( ‘13)
R(31, 1301602 9P(14) ‘11 .8 30 149 674.1 .5 5.0 1005.684 88( ‘2)
R(31, 1301602 9P(14) ‘10 .0 30 150 058.9 .6 5.0 1005.697 71( ‘5)
R(31. 13C1602 9P(14) ‘10 .2 30 150 165.7 .9 10.0 1005.701 27( 3)
R(3l, 13C1602 9P(14) ‘10 .2 30 150 165.7 .9 10.0 1005.701 27( ‘6)
R(31, 1301602 9P(14) -10 .2 30 150 165.7 .5 10.0 1005.701 27( 22)
R(33, 1301602 9P(14) ‘8 .1 30 151 863.8 .9 5.0 1005.757 92( 10)
R(33, 1301602 9P(14) 9 .2 30 170 604.1 .4 5.0 1006.383 02( ‘1)
R(35, 13C1602 9P(14) 9 .2 30 170 604.1 .5 OMIT 1006.383 02(-342)
R(33, 13C1602 9P(14) 11 .3 30 172 011.2 .4 10.0 1006.429 96( 5)
R(34. 13C1602 9P(14) 11 .4 30 172 483.3 .9 5.0 1006.445 70( 16)
R(33, 1301602 9P(14) 12 .4 30 172 967.3 .2 5.0 1006.461 85( 1)
R(34, 13C1602 9P(14) l7 .5 30 178 311.4 .1 .0 1006.640 12( 4)
R(35, 13C1602 9P(12) ‘17 .9 30 195 553.2 .9 .0 1007 215 23( 3)
R(35, 13C1602 9P(12) ‘17 .8 30 195 612.3 .3 .0 1007 217 21( ‘1)
R(36, 13C1602 9P(12) ‘10 .5 30 202 652.7 .8 .0 1007 452 04( -9)
R(38. 13C1602 9P(12) 10 .7 30 223 478.9 .4 .0 1008 146 74( ‘11)
R(38. 1301602 9P(12) 12 .2 30 225 945.4 .5 .0 1008 229 01( 28)
R(38, 13C1602 9P(12) 15 .6 30 228 102.7 .2 .0 1008 300 97( 7)
R(38, 13C1602 9P(12) 15 .1 30 228 480.2 .5 .0 1008 313 56( 2)
R(38, 13C1602 9P(12) 15 .9 30 228 617.0 .4 IT 1008 318 12( 78)
R(40, 13C1602 9P(10) -17 .0 30 246 766.1 .5 .0 1008 923 52( ‘2)
R(40. 13C1602 9P(10) ‘16 .0 30 248 461.0 .7 .0 1008.980 05( 6)
R(41, 13C1602 9P(10) -15 .l 30 248 773.9 .9 .0 1008.990 49( ‘23)
R(40, 13C1602 9P(10) -14 .0 30 249 914.1 .1 .0 1009 028 51( 0)
R(41, 13C1602 9P(10) ‘10 .6 30 253 935.5 .8 .0 1009.162 65( ‘9)
R(48, 13C1602 9P(10) ‘9 498.1 30 254 970.9 .1 T 1009.197 19(1735)
R(43, 13C1602 9P(10) 9 263.4 30 273 732.5 .5 .0 1009.823 02( ‘8)
R(47, 13C1602 9P(10) 12 .6 30 276 592.7 .0 1009.918 41( 540)
R(45. 1301602 9P(10) 12 .6 30 276 592.7 .3 1009.918 41( 1)
R(44. 1301602 9P(10) 12 .5 30 277 449.5 .3 1009.947 00( ‘44)
R(43, 13C1602 9P(10) 14 .0 30 279 386.1 .3 1010.011 60( 4)
R(43, 13C1602 9P(10) 16 835.9 30 281 304.9 .1 1010.075 60( ‘7)
R(45, 1301602 9P( 8) ‘14 .9 30 300 961.3 .7 1010.731 27( ‘9)

 

 

113

Table 3-7 (cont'd)

aNulbers are J and K of the lower vibrational state.

bLaser line used; laser frequencies were taken from Ref. g5.

cMicrowave frequency in MHz. The signed microwave frequency was added
to the laser frequency to obtain the absorption frequency.

dObserved ninus calculated frequency in MHz; the paraneters for the
calculation are in Table 3-9 of this work and in Table V of Ref. 1.

eEstimated uncertainty in the observed frequency in MHz. An "OMIT"
leans that the frequency was omitted from the least squares fits.

f0bserved wavenumber in cn—l. The nulbers in parenthfses are observed

sinus calculated wavenumbers in units of 0.00001 c-

114

TABLE 3-8

79 a

Molecular Constants of CD3 Br

 

 

Parameterb v2 = 0C v2 = lC

Ev /GHz 0.8 29 721.322 4(12)
av /MHz 7 714.650 1(68) 7 690.278 7(90)
(Av-8v) /MHz 70 243.4d 7o 527.91(16)

DJ /kHz 5.797 8(96) 5.567 7(107)
DJK /kHz 65.026(452) 69.722(558)
0K ka2 450.d 382.742 5(68497)
HJ /Hz -o.002 30(303) -o.017 39(425)
HJK /Rz 0.174(121) 2.462(262)
HKJ /Hz -18.52(746) -27.58(924)
aux /R2 0.‘3 —1410.(115)
LJ./mHz o.e 0.00325(76)
LJJJK /mHz o.e -o.2999(533)
LJJKK /mHz o.e 18.34(218)
LJKKK /mHz o.e -435.3(291)

ALK /nHz o.e 6677.(633)

 

 

8Values in parentheses are one standard deviation in multiples of
the last digit in the parameter.

bVibration-rotation parameters. AP = P(v2=l) - P(v2=0).

CObtained from a fit of the vibration-rotation frequencies listed
in Table 3-6 and hypothetical unsplit rotational frequencies

calculated from the experimental frequencies reported in
References lg and gg.

dConstrained to the value reported in Ref. 2g.

eConstrained to zero.

115

 

 

TABLE 3-9

Molecular Constants of CD3alBra
Parameterb v = 0C v = 1c

2 2

Ev /GHz 0.e 29 721.073 2(12)
8v /MHz 7 681.278 0(106) 7 657.050 4(121)
(Av-8v) /MHz 70 276.8d 70 562.22(19)
DJ /kHz 5.580 2(124) 5.595 8(153)
DJK /kHz 63.030(1188) 67.955(1237)
0K /kHz 450.d 455.3(83)
HJ /Hz 0.013 15(394) -0.ooo 44(579)
HJK /H2 0.053(282) 2.227(384)
HKJ /Hz -18.85(l790) -23.86(2144)
ARK /Hz 0.8 -284.(120)
LJ /mHz 0.e 0.002 40(73)
LJJJK /mHz 0.e -0.416 5(518)
LJJKK /mHz o.e 15.03(324)
LJKKK /mHz 0.e -984.9(874)
ALK /mHz 0.8 3 441.(492)

 

 

8Values in parentheses are one standard deviation in multiples of
the last digit in the parameter.

bVibration-rotation parameters.

AP = P(v2=l) - P(v2=0).

CObtained from a fit of the vibration-rotation frequencies listed
in Table II and hypothetical unsplit rotational frequencies
calculated from the experimental frequencies reported in
References 19 and 29.

dConstrained to the value reported in Ref fig.

eConstrained to zero.

116

is performed, the parameters are best interpreted as constants for
frequency calculation only. The parameters have been used to predict
coincidences between C02 and N20 laser frequencies (§Q,§§) and the
frequencies of the v2 bands of both species of CD3Br. The predicted
coincidences are shown in Tables 3-10 and 3-11.

The differences between the observed and calculated frequencies
are shown in Tables 3~6 and 3-7, where it may be seen that the residuals
are usually well within the estimated experimental uncertainties; this
is confirmed by the values of the standard deviations for an observation

79

of unit weight, which were 0.86 and 0.83 for the Br and 81Br species,

respectively.

11

TABLE 3-10

7

Coincidences between Calculated Frequencies for the v2

 

 

Band of CD379Br and Laser Frequencies

Trans.a Frequencyb uo-vLc Laser
P(38,1) 29054033.96 -38.74 1201602 BAND I R(10)
P(38,0) 29054105.00 32.30 12C1602 BAND I R(10)
P(32,6) 29167161.93 48.06 12C1802 BAND I R( 8)
P(27,3) 29264366.87 183.54 N20 R(49)

-l41.27 1301802 BAND II P(60)
P(27,6) 29264630.?6 122.62 1301802 BAND II P(60)
P(26,6) 29283772.83 -3l.46 N20 R(50)
P(26,5) 29283920.64 116.35 N20 R(50)
P(23,5) 29339816.89 3.99 13C1602 BAND II R(42)
P(19,5) 29412634.09 36.19 12C1802 BAND I R(22)
P(15,0) 29477350.60 189.74 1201602 BAND I R(32)
P(13,7) 29523877.89 -103.50 12C160180 BAND I R(28)
P(12,2) 29529373.37 21.92 1301602 BAND II R(36)
P(12,5) 29535113.27 40.78 12C1802 BAND I R(30)
P(ll,6) 29555157.45 90.70 13C1802 BAND II P(50)
P(10,6) 29572119.06 115.97 120160180 BAND I R(3l)
Q(37,2) 29638806.15 -74.04 12C1602 BAND I R(42)
Q(37,l) 29639068.83 188.64 1201602 BAND I R(42)
P( 5.2) 29644222.22 -l79.72 1201802 BAND I R(38)
Q(35,5) 29644480.38 78.44 12C1802 BAND I R(38)
P( 5.4) 29648033.64 41.04 120160180 BAND I R(36)
Q(31,4) 29662655.62 76.51 12C160180 BAND I R(37)
Q(27,2) 29676834.52 ~126.07 12C160180 BAND I R(38)
Q(22,0) 29691147.43 10.93 12C160180 BAND I R(39)
Q(23,5) 29691209.84 73.34 120160180 BAND I R(39)
Q(22,l) 29691307.70 171.20 12C160180 BAND I R(39)
0(21,1) 29693916.35 -l58.96 12C1802 BAND I R(42)
Q(20,3) 29697831.03 -198.32 12C1602 BAND I R(46)
Q(21,6) 29698196.81 166.33 12C1602 BAND I R(46)
Q(17,3) 29704927.l3 -179.16 12C160180 BAND I R(40)
Q(16,0) 29705012.?2 -93.57 120160180 BAND I R(40)
0(19,7) 29705092.29 -11.00 120160180 BAND I R(40)
0(16,1) 29705243.25 136.96 120160180 BAND I R(40)
Q(13,2) 29711418.23 -l58.86 1301602 BAND II P(30)
Q(17,8) 29711677.82 100.75 13C1602 BAND II P(30)
0(11,4) 29717755.86 106.03 1201802 BAND I R(44)
0( 6,0) 29718790.12 -79.26 12C160180 BAND I R(4l)
0( 7,4) 29722778.40 119.92 13C1802 BAND II P(44)

 

 

118

Table 3-10 (cont’d)

 

 

Trans.a Frequencyb vo-vLc Laserd

0( 9,6) 29726342.55 -52.21 1201602 BAND I R(48)
Q(ll,7) 29726432.03 37.27 1201602 BAND I R(48)
0( 6,5) 29726532.18 137.42 1201602 BAND I R(48)
Q(lO,8) 29732378.36 -46.81 120160180 BAND I R(42)
R( 3.3) 29784647.36 84.16 120160180 BAND I R(46)
R( 4,1) 29796963.69 -109.55 12C160180 BAND I R(47)
R( 6,5) 29833516.22 182.26 12C160180 BAND I R(50)
R( 7,4) 29845124.?6 129.35 12C160180 BAND I R(Sl)
R( 8.2) 29855897.74 26.03 1261602 BAND I R(58)
R(13,5) 29930628.03 107.09 120160180 BAND I R(59)
R(26,3) 30093278.81 58.56 13C1802 BAND II P(30)
R(31,7) 30143745.44 -10.96 1301802 BAND II P(28)

 

 

798r; J < 40. K < 8.

8Transition in the v2 band of CD3
bFrequency of the v2 band transition in MHz.

CFrequency of the 0 band transition minus the laser
frequency in MHz.

dIdentification of the CO laser; Band II is the 9 pm band.
Laser frequencies were 0 tained from Refs. 34 and 38.

119

TABLE 3-11

Coincidences between Calculated Frequencies for the 02

 

 

Band of C0381Br and Laser Frequencies

Trans.a Frequencyb vo-vLC Laserd

P(39,5) 29033085.68 -52.19 120160180 BAND I R( 2)
P(37,3) 29075724.25 137.89 12C160180 BAND I R( 4)
P(37,2) 29076156.12 151.68 13C1602 BAND II P(50)
P(36,6) 29089962.67 198.43 12C1802 BAND I R( 4)
P(30,8) 29198208.41 -63.44 120160180 BAND I R(10)
P(27,?) 29264622.06 113.92 13C1802 BAND II P(60)
P(26,0) 29283694.97 -109.32 N20 R(50)
P(26,1) 29283819.06 14.77 N20 R(50)
P(25,7) 29303421.?2 108.04 N20 R(51)
P(24,?) 29322629.33 ~81.88 N20 R(52)
P(23,6) 29341996.45 -0.ll N20 R(53)
P(16,5) 29466842.77 -134.00 1301602 BAND II R(38)
P(12,1) 29529159.04 -195.42 13C1602 BAND II R(36)
P(10,7) 29576373.04 -l72.09 12C1602 BAND I R(38)
P( 7,1) 29611334.?5 -167.81 13C1802 BAND II R(48)
P( 5,2) 29644317.12 -84.83 1201802 BAND I R(38)
P( 5,4) 29648123.20 130.59 12C160180 BAND I R(36)
Q(34,2) 29651565.?8 -91.33 13C1602 BAND II P(32)
Q(34,l) 29651660.l4 3.03 13C1602 BAND II P(32)
Q(34,0) 29651681.13 24.29 1301602 BAND II P(32)
Q(29,6) 29668792.27 -63.56 12C1602 BAND I R(44)
Q(27,6) 29676880.16 -79.78 12C160180 BAND I R(38)
Q(27,2) 29676910.92 -49.67 12C160180 BAND I R(38)
Q(22,0) 29691114.52 -21.98 12C160180 BAND I R(39)
Q(23,5) 29691224.34 87.83 12C160180 BAND I R(39)
Q(22,1) 29691276.38 139.88 12C160180 BAND I R(39)
Q(21,6) 29698177.00 147.66 12C1602 BAND I R(46)
Q(19,7) 29705050.18 -56.11 120160180 BAND I R(40)
0(16,l) 29705113.37 7.08 12C160180 BAND I R(40)
Q(17,8) 29711623.55 46.48 1301602 BAND II P(30)
0(12,0) 297ll761.59 184.52 13C1602 BAND II P(30)
Q(11,4) 29717566.62 -83.21 12C1802 BAND I R(44)
0( 7,0) 29717722.63 72.80 12C1802 BAND I R(44)
0( 6,1) 29718863.80 -5.58 120160180 BAND I R(4l)
0( 7,2) 29718923.38 54.00 12C160180 BAND I R(41)
0(10,4) 29719007.12 137.74 12C160180 BAND I R(41)
0( 7,4) 29722552.17 -106.3l 1301802 BAND II R(44)
0( 4,3) 29722696.93 38.45 13C1802 BAND II P(44)

 

 

120

Table 3-11 (cont’d)

 

 

 

 

Trans.a Frequencyb vo-vLC Laserd
Q(ll,7) 29726232.07 —161.94 1201602 BAND I R(48)
0( 6,5) 29726290.57 -104.19 12C1602 BAND I R(48)
R( 8,3) 29856529.51 86.61 12C160180 BAND I R(52)
R(10,4) 29886501.57 157.06 13C1602 BAND II P(24)
R(14,2) 29938089.58 110.22 13C1802 BAND II R(36)
R(14,5) 29942810.38 -110.36 13C1602 BAND II P(22)
R(18,0) 29990238.92 -89.20 13C1802 BAND II R(34)
R(18,l) 29990435.49 107.38 1301802 BAND II P(34)
R(22,2) 30042050.23 -26.08 1301802 BAND II P(32)
R(32,4) 30160897.88 177.99 13C1602 BAND II P(14)
R(37.5) 30213122.03 95.90 13C1602 BAND II P(12)
8Transition in the v2 band of CDaalBr; J < 40, K < 8.

bFrequency of the v2 band transition in MHz.

CFrequency of the 02 hand transition minus the laser
frequency in MHz.

dIdentification of the C0 laser; Band II is the 9 pm band.
Laser frequencies were ogtained from Refs. 34 and 38.

121

III—5 Discussion
III-5-l CD3I

As seen in Table 3-1, the vibration-rotation parameters for the
ground and v2 = 1 states, including the Coriolis coupling, predict the
infrared frequencies for J S 43 and K s 10 to an accuracy of a few MHz.
As shown in the first two numerical columns of Table 3-4, the resulting
parameters are quite reasonable and convergent. In fact, ARK, ALK, and
LJ were so close to zero that they could be constrained to zero in the
fitting without significant effect on the standard deviation for an
observation of unit weight, which was ~0.7 for both fittings. The
corresponding fitting in which explicit Coriolis effects were omitted
also gave calculated frequencies that were in good agreement with the
experimental values (standard deviation = 1.5), but, as shown in Table
3-3, the higher-order parameters, especially those that multiply higher
powers of K, are rather large. This is the typical result of an attempt
to mimic the effect of substantial Coriolis coupling by means of a power
series expansion in J(J+1) and K2. An important conclusion is that it
is possible to predict the vibration-rotation frequencies for J $ 43 and
K s 10 in the 92 hand of CD31 to within a few MHz with the parameters in
Table 3—4 in a simple power series expansion without Coriolis
interaction. Above K = 10 the frequencies of the P, Q, and R branch
transitions for a given J, which increase in frequency as K increases
for lower K, reach a maximum and begin to decrease with increasing K.
small number of higher K transitions have been assigned and their

frequencies agree much better with the Coriolis-corrected calculated

values than with the values Obtained with the simple power series

122

expansion. It appears that many higher K transitions can be recorded
and assigned, but this was judged to be beyond the scope of the present
study. Combination of such frequencies with those for the v5 band given
in Ref. (2) should lead to an improved set of Coriolis parameters.

The parameters in Tables 3-2 and 3-4 were used to calculate the
vibration-rotation frequencies of the v2 band and the rotational
frequencies in the v2 = 1 state for J g 50 and K S 15 for an attempt to
assign the submillimeter laser transitions reported in Ref. (21). It
was possible to give a definite assignment for two of the transitions
and a provisional assignment for a third. The two assigned transitions
are pumped by the 10R(38) CO2 laser at 27851242 MHz (reported at 10.764
pm in Ref. (21)). This laser frequency is only 8 MHz above the
calculated frequency of the P(46,10) transition in the v2 band. In
addition, the two reported submillimeter wave frequencies (538347.3 MHz
and 526434.4 MHz) are only 0.9 and 2.7 MHz above the calculated values
for the R(44,10) and R(43,10) transitions in the v2 =1 state,
respectively. Since these calculated values should be within a few MHz
of the experimental frequencies, these assignments are probably
definite. The provisional assignment involves a submillimeter wave

laser pumped by the 10P(36) CO at 27791010 MHz (reported as 10.787 pm

2
in Ref. (21)). This frequency is ~426 MHz below the calculated
frequency of the P(49,13) transition in the v2 band. The reported
submillimeter wave frequency is 572772.l MHz, which is ~19 MHz below the
calculated value for the R(48,13) transition in v2 = 1. This agreement
is probably satisfactory considering the fact that the J and K values

for the transitions is outside the range of J and K for which the

parameters are known to be valid. For this reason and because of the

123

strange behavior of the levels in v2 = 1 for k > 10, this last
assignment must be viewed as provisional.

The ground state vibration rotation parameters obtained as a
result of this study are compared to the values obtained by microwave
and millimeter wave spectroscopy in Table 3-2, where it may be seen that
there is good agreement between the results of our fittings and that
obtained previously (12). Comparison in Table 3-3 of the parameters
derived in this work with the best previous infrared values, obtained
from a laser Stark study of a relatively small number of transitions,
shows that a much more complete set of centrifugal distortion constants
has been obtained in the present study. As mentioned above, the
inclusion of the effects of Coriolis coupling to the v5 and 2v3 states
improves the fit of the rotation and vibration-rotation frequencies; the
standard deviation for an observation of unit weight is reduced from 1.5
to 0.75. The resulting parameters are compared to the results given by
Matsuura and Shimanouchi (2) in Table 3-4, where it is seen that the
agreement is very good considering the small number of experimental
frequencies for the v2 band that were available to these authors. The
Corilis effects on the energy are substantial for this molecule,
reaching almost 30 GHz for the highest J and K studied in this work.
Therefore, the calculated vibration-rotation frequencies are very
sensitive to the values assumed for the Coriolis and vibration-rotation
constants. It is essential that the two sets of parameters be
consistent. The parameters in Table 3-3 do not include the effects of
the Coriolis coupling discussed in this paper. Comparison of the B

values for v2 = l in Tables 3-3 and 3-4, for example, show the large

124

contribution of this Coriolis coupling to the rotational constants.

III-5-2 CD Br

3
A substantial number of frequencies in the v2 bands of CD3798r and
CD381Br have been measured to an accuracy of a few MHz by the method of

infrared-microwave sideband laser spectroscopy and have been used to
evaluate vibration-rotation parameters for the ground and v2 = 1 states
for both species. The new parameters together with previously-reported
vibration—rotation constants for v5 = l and the 122-v5 Coriolis coupling
are sufficiently accurate to reproduce the experimental frequencies for
J S 48 and K S 8 to within ~ 5 MHz. The parameters have been used to
predict coincidences between CO2 and N20 laser frequencies (25,21) and
the frequencies of the v2 bands of both species of CD3Br. The predicted
coincidences are shown in Tables 3-10 and 3-11.

The frequencies of a number of transitions for K > 8 have been
omitted from the fittings and, as can be seen in Tables 3-6 and 3-7,
these show rather large residuals. We interpret this to be the result
of some problem with the accuracy of the Coriolis parameters and/or the
parameters for the v5 = 1 state used in the fitting. Since the Coriolis
corrections are very large, relatively small changes in these
parameters, perhaps even within the round-off errors, would be
sufficient to cause the difficulties observed. Since we do not have any
data of our own for the 95 hand, we did not pursue this problem any

further.

125

III-6 References

10.

ll.
12.

l3.

14.
15.

16.

17.

18.

. E. W. Jones, R. L. Popplewell, and H. W. Thompson, Proc. Roy. Soc.

London A288, 39—49 (1965).

. H. Matsuura and T. Shimanouchi, J. Mol. Spectrosc. 60, 93-110

(1976).

. K. Kawaguchi, C. Yamada, T. Tanaka, and E. Hirota, J. Mol.

Spectrosc. 64, 125-138 (1977).

. Y. Morino and J. Nakamura, Bull. Chem. Soc. Japan 38, 443-458

(1965).

.‘E. W. Jones, R. J. L. Popplewell, and H. W. Thompson, Spectrochim.

Acta 22, 639-646 (1966).

. C. Betrencourt-Stirnemann, R. Paso, J. Kauppinen, and R. Anttila, J.

Mol. Spectrosc. 87, 506-521 (1981).

. K. Harada, K. Tanaka, and T. Tanaka, J. Mol. Spectrosc. 98, 349-374

(1983).

. J. W. Simmons, Phys. Rev. 76, 686 (1949).

. J. W. Simmons and J. H. Goldstein, J. Chem. Phys. 20, 122-124

(1952).

A. K. Garrison, J. W. Simmons, and C. Alexander, J. Chem. Phys. 45,
413-415 (1966).

R. L. Kuczkowski, J. Mol. Spectrosc. 45, 261-270 (1973).

J. Demaison, D. Boucher, G. Piau, and P. Glorieux, J. Mol.
Spectrosc. 107, 108-118 (1984).

G. Wlodarczak, D. Boucher, R. Bocquet, and J. Demaison, J. Mol.
Spectrosc. 124, 53-65 (1987).

Y. Merino and L. Nakamura, Bull. Chem. Soc. Jap. 38, 443-459 (1965).

C. Joffrin, N. Van Thanh, and P. Bardewitz, J. Phys. Paris 27, 15-23
(1966).

R. W. Peterson and T. R. Edwards, J. Mol. Spectrosc. 38, 1-15
(1971).

H. Kurlat, M. Kurlat, and W. E. Blass, J. Mol. Spectrosc. 38, 197—
213 (1971).

D. R. Anderson and J. Overend, Spectrochim. Acta. A28, 1231-1251

19.

20.
21.
22.

23.

24.
25.
26.

27.

28.

29.
30.

31.
32.

33.

34.

35.

36.

37.

38.

126

(1972).

D. R. Anderson and J. Overend, Spectrochim. Acta. A28, 1637-1647
(1972).

C. Poulsen and S. Brodersen, J. Raman Spectrosc. 14, 77-82 (1983).
J. Sakai and M. Katayama, Chem. Phys. Lett. 35, 395-398 (1975).
J. Sakai and M. Katayama, Appl. Phys. Lett. 28, 119-121 (1975).

G. L. Caldow, G. Duxbury, and L. A. Evans, J. M01. Spectrosc. 69,
239-253 (1978).

S. A. Rackley and R. J. Butcher, M01. Phys. 39, 1265-1272 (1980).
Y. Langsam, S. M. Lee and A. M. Ronn, Chem. Phys. 15, 43-48 (1976).
W. Schrepp and H. Dreizler, Z. Naturforsch. 36a, 654-661 (1981).

S. F. Dyubko, L. D. Fesenko, 0. I. Baskakov, and V. A. Svich,
Zhurnal Prikladnoi Spektroskopii 23, 317-320 (1975).

T. R. Edwards and S. Brodersen, J. M01. Spectrosc. 54, 121-131
(1975).

Y. Morino and C. Hirose, J. M01. Spectrosc. 24, 204-224 (1967).

H. P. Benz, A. Bauder, and Rs. H. Gunthard, J. M01. Spectrosc. 21,
156-164 (1966).

J. T. Hougen, J. Chem. Phys. 57, 4207-4217 (1972).

M. R. Aliev and J. T. Hougen, J. M01. Spectrosc. 106, 110-123
(1984). ,

C. H. Townes and A. L. Schawlow, "Microwave Spectroscopy," Chap. 8,
McGraw-Hill, New York, 1955.

C. Freed, L. C. Bradley,and R. G. O’Donnell, IEEE J. Quantum
Electron. 08-16, 1195-1206 (1980).

H.-G. Cho and R. H. Schwendeman, J. M01. Spectrosc. 133, 383-405
(1989).

G. Magerl, W. Schupita, and E. Bonek, IEEE J. Quantum Electron. QB-
18, 1214-1220 (1982).

S. K. Lee, R. H. Schwendeman, and G. Magerl, J. M01. Spectrosc. 117,
416-434 (1986).

B. G. Whitford, K. J. Siemsen, H. D. Riccius, and G. R. Hanes, Opt.
Commun. 14, 70-74 (1975).

CHAPTER IV
INFRARED-RADIOFREQUENCY DOUBLE RESONANCE
OF CD31 AND CD3Br
IV-l Introduction

The radiofrequency spectroscopy provides a powerful tool for
investigation of various hyperfine energy structures such as nuclear
quadrupole splittings, Al-A2 splittings, x-doubling, K-doubling,
hyperfine rotational levels of tetrahedral molecules, and so on.
However, the scope of the technique is seriously limited by the density
of the spectrum, the poor signal-to-noise ratio caused by the negligible
population difference, and the low photon energy due to the small energy
gap between the levels. As a result, radiofrequency spectra are often
too weak to record properly or too complicated to analyze. In order to
overcome the limitations, the radiofrequency double resonance technique
has been invented which is a combination with another radiation of much
higher energy photons. By detecting a photon with much higher energy
than the radiofrequency photon, sensitivity and signal-to-noise ratio
are greatly enhanced; and, by requiring two near—resonant photons for
signal detection, the spectra are greatly simplified.

The radiofrequency-microwave (RF-MW) double-resonance method was
introduced by Autler and Townes (1). In their experiment, l-type

doublets in the J=l and 2 rotational levels of the v2=l vibrational

127

128

state of 008 were probed while the corresponding rotational transition
J=l~2 was pumped by microwave radiation. The RF-MW double resonance
technique was further developed by Wodarczyk and Wilson (2) for
assignment purposes in microwave spectroscopy. When the RF double
resonance method was later extended to the infrared region (IR-RF double
resonance), it became possible to observe RF resonances for higher
rotational quantum numbers and higher-energy vibrational states than had
been possible with RF-MW spectra.

Infrared-radiofrequency (IR-RF) double resonance was first used by
Shimizu to observe the Stark splittings of the P(3,2) transition of the
v2 excited state of PH3 by pumping the transition with the R(33) N20
laser line (2). This technique was further developed and applied to
various studies, mostly by workers at the Herzberg Institute of
Astrophysics. Curl and his coworkers studied hyperfine rotational
energy structures of CH4 by means of the laser coincidence of the 03
hand and He-Ne 3.39 pm laser line and intracavity radiofrequency cells
(4,5). The IR-RF double resonance technique is sensitive enough that
they succeeded in observing two rotational transitions weakly allowed by
the centrifugally induced electric dipole moment. Later, the 9P(36)
C1802 laser line was used for the investigation of the rotational energy
levels of CD4 by Kreiner (Q). Kreiner and Oka extended this technique
to observe forbidden rotational transitions of Sifld with P(5), R(4), and
R(6) N20 laser lines (1). Arimondo and his coworkers applied the
technique to the observation of pure quadrupole transitions in 003I by
using 002 and N20 laser coincidences (2) and later analyzed energy

transfer between rotational levels by means of collision-induced

resonances in the radiofrequency region (2). Dale g1 g1. and Lowe g; 21

129

used their C0 laser to study x-doublings of NO utilizing the close
coincidences of VI band transitions of NO in the 5.4 pm region (19,11).
They also applied the spectrometer to investigation of the spin-rotation
hyperfine structure of N02 (12) and of the Stark effect of H20 (12).
Recently Sakai and his coworkers observed Al-A2 splittings in the ground
state (K=3) and v5 state (K1=-2) of CDF3 by pumping the ”5 band with a
CO2 laser (14). Mito g1 g1. employed the coincidence of P(8,0)
transition of 07 band of CH3CN and 9P(30) CO2 laser line to search for
l-type doubling transitions including collisionally transferred
resonances and determined the effective l-type doubling constants q,7 and
q1 (1g). Ioli and his coworkers performed radiofrequency triple
resonance for CH3OH in order to study the K-doubling (1Q). Some k-type

doublets of the v state of CH3I were observed by Arimondo and P.

6
Glorieux (11). Man and Butcher studied pure quadrupole transitions (12-
2g) of halide compounds and K-doublings (21) of formic acid by means of
CO2 laser coincidences. Their precise experiment allowed determination
of quadrupole coupling constants including the centrifugal distortion
parameters and the spin-rotation constants.

The early IR-RF double-resonance measurements were performed with
the sample cell inside the laser cavity in order to apply the highest
available powers to the samples. As a result, the line broadening
caused by the power of the pump laser seriously restricted the accuracy
of the frequency measurement. Among the first demonstration of IReRF
double resonance outside the laser cavity were studies of CF31 and CF3Br
in our laboratory (22,22). The lower pumping power still provides

sufficient signal-to-noise ratio and many nuclear hyperfine structures

are well resolved as a result of the considerably smaller linewidth.

130

Line-tunable infrared lasers provide accurate frequency and enough
radiant power for saturating vibrational transitions; however, they
restrict the method to accidental coincidences between the laser
frequencies and the vibration-rotation frequencies of the molecule under
study; this severely limits the performance of the technique. More
recently, it has been shown that tunable infrared sources could be used
for IR—RF double resonance. Takami introduced IR-RF double resonance by
means of diode lasers in studying forbidden rotational transitions of
v3=l state of CF4 (24). The diode laser was intentionally focused
inside the coaxial radiofrequency cell used in the experiment in order
to overcome the low radiant power of the laser. In a series of works,
he and his coworkers investigated the hyperfine rotational energy

structure of CF4 (2Q), 13

CF4 (g), Sill4 (21,22), and 811114 (2g) and
determined the rotational parameters. The infraredemicrowave sideband
laser was first used by Oka to observe forbidden rotational transitions
of OsO4 (29) and Sifld (21). A color center laser was used to observe 1-
type doubling in HCN by DeLeon et a1. (22). Oka also employed a color
center laser to search for Al-A2 splittings of CH3F (22).

In recent studies, we discovered that our infrared microwave
sideband laser system operating in the cavity mode (24) had sufficient
power to saturate vibration-rotation transitions. In this thesis we
describe the use of our infrared-microwave sideband laser for the
measurement of pure nuclear quadrupole transitions in the ground and
v2=1 vibrational states of 003I and 003Br by the method of IR—RF double
resonance. Before carrying out the double resonance measurements, it

was necessary to determine the frequencies of the infrared transitions

in the v2 vibrational bands of these molecules. Frequencies of

131

transitions with J,K up to higher than 40,8 were measured and fit to
energy expressions for symmetric top molecules with centrifugal
distortion. The measured IR frequencies and spectroscopic analyses have
been described in Chapter III. The tunability of the infrared-
microwave-sideband laser source allows the selection of vibration-
rotation transitions over a wide range of J and k, which permits the
evaluation of centrifugal distortion effects on the quadrupole coupling
constants and spin-rotation interaction parameters, as well as the
precise measurement of the quadrupole coupling constant itself. In
addition to the advantages of tunability, the spectrometer is found to
have sufficient sensitivity to work at very low RF power, which together
with the very low power of the infrared—microwave sideband laser source
substantially increases the resolution compared to direct 002 laser-
pumped double resonance. As a result, it is possible to determine the
spin rotation constants as well as the centrifugal distortion constants

for the quadrupole coupling in these molecules.

IV-l-l CD31

In a series of microwave studies of the ground vibrational state of
CD3I Simmons and co-workers (25-21) resolved quadrupole components and
determed the primary quadrupole coupling constant as well as
rotational constants. Kuczkowski (22) extended this microwave work to
transitions in the low-lying vibrational states 02, v3, ”5’ v6, 203, and
03+ve. More recently, higher J transitions have been recorded in the
millimeter wave region and more accurate quadrupole constants were

reported for low—lying vibrational states by Demaison 41 Q1. (22) and by

132

Wlodarczak g1 g1. (49). Infrared radio frequency double resonance at 1—
MHz resolution was reported by Rackley and Butcher (41) as part of a
study of Stark-tuned non-linear spectroscopy. Demaison g1 g1. (22) used
infrared radio frequency double resonance to measure the frequencies of
pure quadrupole transitions in the ground state of this molecule with
100 kHz accuracy. The influence of nuclear quadrupole coupling on
rotational relaxation has been investigated by means of microwave double
resonance (42).

In the present study, about 150 radio frequency resonances, half
each in the ground and v2 = 1 states, have been recorded at 70 kHz
resolution and few kHz accuracy by using the infrared microwave sideband
system as a pumping source for infrared radio frequency double
resonance. In addition to demonstrating the usefulness of this
technique for systematic infrared radio frequency double resonance, the
radio frequencies have been combined with previous measurements of
microwave, millimeter wave, and infrared radio frequency double
resonance spectra to determine nuclear quadrupole coupling parameters,
including centrifugal distortion effects, and spin rotation parameters

for the iodine nucleus.

IVrl-Z CD38r

The splittings caused by Br quadrupole coupling in CD3798r and

381Br have been studied in the microwave region for the ground state

CD
by Garrison 91 Q1. (42) and in low-lying vibrational states by Morino
and Hirose (44). Consequently, values of the quadrupole coupling

constants for the ground and v2 = 1 states of the two species have been

133

reported. However, we are not aware of any previous measurements that
are sufficiently precise to include the effects of the centrifugal
distortion of the quadrupole coupling or of the spin-rotation
interaction.

An infrared microwave sideband laser source operating in the 10 pm
region has been used with the method of infrared radiofrequency double
resonance to record radiofrequency spectra in the ground and v2 = l

vibrational states of CD3Br. The frequencies of ~ 200 and ~ 160 pure

81
3 3 Br,

respectively, approximately half in the ground state and half in the v2

quadrupole transitions have been observed for CD 798r and CD
= l vibrational state of each species. The frequencies have been used
to determine the quadrupole coupling constants, including centrifugal
distortion parameters, and spin-rotation constants for the bromine
nucleus in each species.

During the fitting of the frequencies of the pure quadrupole
spectra, it became apparent that some effect was causing an apparent
shift in frequency for each of a pair of closely spaced double resonance
transitions that occur at low RF frequencies. This shift has been
traced to a double-resonance effect that appears in calculations when
four interacting levels are taken into account, but is not evident in
calculations based on the usual three-level system employed for double-
resonance theory. The nature of the shifts, a description of the theory
used to interpret them, and a comparison of observed and calculated
lineshapes is described separately in Chapter V.

The theory of vibration-rotation-quadrupole interaction is
outlined in the next section, whereas the experimental details of this

study are presented in the subsequent section. The last two sections

134

include a description of the spectra and a discussion of the results of

this work, respectively.

135

IV-2 Theory

IV-2-l IRrRF Double Resonance

The mechanism of IR—RF double resonance is easily understood by
considering a three-level system excited by laser and radiofrequency
fields. We assume that two levels in the excited state form the
hyperfine structure and that the laser frequency is much larger than
kT/h. An example of a three—level system is shown in Fig. 4-1, where
state ll) is a rotational level in the ground vibrational state and
states [2) and [3) are rotational levels in an excited vibrational
state. The laser radiation will interact with a group of molecules with
velocity v, which satisfies the Doppler shifted resonance condition 012
= ”IR (l-v/c). If the infrared radiation is strong and the gas pressure
low, molecules with the correct velocity will be "pumped" from state II)
to |2>. This occurs when the infrared Rabi frequency, xRabi(IR) =
pleIR/h, is comparable to or larger than the collisional frequency,
= (Av)p-p. Here ”12 is the transition dipole moment matrix

v 0 O
collision

element, E is the laser electric field, (Av)p is the pressure

IR
broadening parameter, and p is the gas pressure.

Due to the pumping, "holes" are burned in the Maxwellian velocity
profile of state II) and transferred to state l2) as "spikes." When the
radiofrequency radiation with sufficient power for saturation comes into
resonance with the transition between levels, the "spikes" in level I2)
are transferred to level [3). This causes an increase in infrared

absorption and is detected as a decrease in the infrared radiation

reaching the detector. The condition for saturation by the

136

I3) -———-—— _1...—

RF

 

_/_/_\__ A

IR PUMPING IR and RF
PUMPING

l1) —---

Figure 4~l. Three level system showing double resonance technique.
The infrared radiation pumps molecules from ll) to |2> according to
the Doppler shift resonance condition v12 = vIR(ltv/c) which appears
as "holes" in the Maxwellian velocity profile of ll) and "spikes" in
|2>. The radiofrequency will then transfer the "spikes" from |2> t0
l3) creating deeper "holes" in II). This causes an increase in the
molecular absorption. The radiofrequency transition from [2) to |3>

can thus be observed by detecting the infrared radiation.

137

radiofrequency is that its Rabi frequency, xRabi(RF) = ”23'ERF/h’ needs
to be comparable to or larger than the collisional frequency, where p23
is the transition dipole moment matrix element in the excited state, and
ERF is the radiofrequency electric field.

In terms of the absorption coefficient, the maximum value is

obtained when the saturation parameter pE/hv ~ 1 (2).

collision
According to Shimizu, the maximum attainable rf—induced absorption
coefficient in this technique is 13* of the linear absorption
coefficient for a Doppler-limited three-level system (2). The linewidth
increases with increasing field intensities. The best operating
condition is usually obtained when the saturation parameters of both
fields are around one. In case the saturation parameter of the rf field

is larger than that of the laser, the resonance line splits into a

doublet.

IV—2-2 Nuclear Quadrupole Coupling

12

Atomic nuclei have radii near 10_ cm, and hence are very small

compared with the size of electron orbits, which are approximately

-8 cm in diameter. Nuclei are also some 104 times heavier than

10
electrons. To a good approximation, therefore, electronic energies can
be obtained by considering nuclei to be positive point charges of
infinite mass. However, effects on electronic energy levels due to the
finite size and mass of nuclei, although small, often appear on
observation of atomic and molecular spectra. These effects are called

"hyperfine structure" because they produce a very small splitting of

spectral lines.

138

If a nucleus is to be considered other than a point charge, it must
be recognized that the nuclear particles may be in motion, producing a
magnetic field and giving the nucleus an angular momentum. The
interaction energy between a nuclear charge distribution pi(xi, yi, 21)

and an electron charge distribution pe(xe,ye,ze) is

 

p.p d£.dg
_ I 1 e R 1 e (4_1)

where

/2

:U
u

(r?+r2-2r.r cosm)1
1 e 1 e
Here, ri=vector from the origin of the coordinates of the nuclear center
of mass to the volume element dri, 5e the vector from the origin to the
volume element dge and m the angle between Ei and Ee'
Only s electrons have non-negligible charge distribution inside the
nucleus. However, the contribution of s electrons to the quadrupole

coupling energy vanishes because of the spherical symmetry of the

electron orbital. We therefore expand l/R in powers of ri/re to obtain

as r. 9.
_1- = Fl 2 [Fl] P (cosm) . (4-2)
e i=0 e 1

Where P1(cosm) is the Legendre polynomial of order 1. It is convenient

to use the spherical harmonic addition theorem in the form,

139

2
P1(cosu) = z (-1)"(§§ETJ Y1m(e£, ¢£)Yi,-m(°i’¢i) . (4—3)

m=-1

Substitution of Eq. (4-2) in Eq. (4-1) gives W as a series of integrals,

as follows:

Then,
9.0 p
- 1 e - .9 _
wo _ [I ;;——d§idre 2e] re dr (4 5)

where Z ' atomic number. This is the Coulomb interaction between the

nucleus and the electrons, which is independent of the nuclear
orientation and would be included in the determination of the
electronic energy.

The second term in the series of W is

”i
"I: II_;2 C080 pipedsidge
e

pe Ee
[I ”i EidEi] dEe ° (4'6)

 

=1

3
r
e

The quantity in square bracket is the nuclear electric dipole moment;

hence W1 is the nuclear dipole interaction energy. However, if the

140

nucleus has a dipole moment in one direction with respect to its angular
momentum, there must be a degenerate nuclear state, or one of the same
energy, with an oppositely directed dipole. Normally, such identical or
degenerate states of the nucleus are not encountered. Hence the nucleus
has no inherent dipole moment, and no effects from nuclear dipole
moments have been observed, so that we can assume that this term
vanishes. The rule is rather more general as all electronic multipole
moments of odd order are zero for a nucleus.

The third term in the series for W is the quadrupole interaction,

r .
= n -;;- WM

=22 (- —1)‘“(4—5") [p33 r 72.3“ (e. .0. )dr [0° 3 72 m(°e .0 )dr <4-7)

m=-2 re e
+2 m
or HQ: 2 (-l) va—m
m--2
_ g]1/2
where vm_&1%r3h2,m( e’¢i) dz:i
re
fll/Z
' (4 ‘2'] 1°11 13y2’_m(ei,¢i) d5i

VIII and Q_m are components of second-rank irreducible spherical tensors
since they are integrals of a spherical factor (~rn) times a spherical
harmonic (ref. (45), P. 115). They are characterized by 1 in the
nuclear space and g in the molecular space.

The quadrupole moment may be considered as a measure of the

141

deviation of the nuclear charge from the spherical shape. If the charge
distribution is somewhat elongated along the nuclear axis 2n, then 0 is

positive; if it is flattened along the nuclear axis, 0 is negative.
IV—2-3 Irreducible Tensor Method

If the interaction energy of two parts of any quantum mechanical
system is invariant under arbitrary rotations of the space-fixed axes,
then it can be written most generally as a contraction of two
irreducible tensors (gfi). Usually, the system may be divided into two
distinct parts, characterized by their angular momenta J1 and J2, so
that one tensor depends exclusively on one set of variables and the
other tensor on a set of variables in a different space. The matrix
elements of such a contraction of two commuting irreducible tensors A
and B of rank K are given in the irreducible representation where the
angular momenta of the two parts are coupled to form the resultant
J=J1+J2 as

(J1,J2,J,MIA:BIJ',Jé,J',M'>

J J J
_ _ J +J'+J 2 l , . _
-( 1) 2 l SJJ'SMM' {k Ji Jék <J1HAHJ1><J2HBHJ2> . (4 8)
The symbol in curly brackets is the Wigner 6j symbol. Eq.(4-8)
expresses the fact that each matrix element is proportional to constants

(JlflAflJl) and (JZHBHJZ) called reduced matrix elements which may be

determined by using the Wigner-Eckart theorem, as follows;

142

1; g) <J'IIT(i)llJ"> . <4-9)

° (1) H I _ _ aj-m .j
(J,m|Tq IJ ,m >-( 1) (—m

If any one of the matrix elements of an irreducible set of spherical
tensors Téi) of rank i is known in the representation with the angular
momentum quantum number j and the projection quantum number m, the
remaining elements can be determined. The symbol in parenthesis is the
Wigner 35 symbol, which contains the entire dependence of the matrix
elements on the projection quantum number.

The relation of a quantity, which refers to only one of the
interacting systems, between its reduced matrix element in the coupled

representation and in the original uncoupled representation is expressed

as

(i) J1+J2+J' +i
(J1,J2,JHT HJ',J2,J'> = (-1)

J1 J J

'[(2J+1)(2J'+1)]1/2 { . J. 12} <J HT(i)HJ'> (4—10)
1

where the tensor operator T(1) acts only in the J1 space. It is
therefore possible to calculate the matrix elements of any observable in

the coupled representation using Eq. (4—9) and (4-10).
IV-2—4 Quadrupole Interaction Energy
As shown above, the quadrupole interaction energy can be expressed

as a contraction of two irreducible tensors of rank 2: the electric

field gradient tensor V and the nuclear quadrupole moment tensor 0.

143

2
- _ m _

The quantity Q-m is the -m component of the nuclear quadrupole tensor,
9. The nuclear quadrupole moment, Q, is defined conventionally to be

the I, mI=i diagonal matrix element of the m=0 component of Q i.e.;
eQ = 2<II|Qo|II> (4-11)

where e is the electric charge. The matrix elements of HQ in the

coupled representation F = J+I are given according to Eq. (4-8). It

turns out that H6 may be factorized into blocks for the different

quantum numbers of the total angular momentum F and is independent of

the projection quantum number M From the Wigner-Eckart theorem

F.
<II|Q III) = I I '2 <I||Q||I>
o I -I 0
or

[(21+3)(21+2)(21+1)(2I)(ZI-l)]1/299
2[3IZ—I(I+1)] 2 '

 

<I||Q||I> = (4‘12)
The symbol in parenthesis is the Wigner 3j symbol, and <IHQHI> called
the reduced matrix elements.

The electric field gradient tensor V has constant components VA in
the molecular frame. Hence it is necessary to transform one component

of V to the principal inertial axes

144

2 (2)
v0 = Z 2noq (or,B,r)V_'_q (4-13)
q=- ’

(

where 00:)(u,8,r) is a matrix element of the five-dimensional
irreducible representation of the three-dimensional rotation group,
which depends on the Eulerian angles a, B, Y locating the molecular
frame in the space-fixed axes system. The matrix elements of 032) in

the symmetric rotor basis mé§)(a,8,r) c (2J+1)1/20é§)(a,8,r) are given

as

<J.k.mlné§)1j'.k'.m> = <—1)"“"“”q [(2J+l)(2J'+1)]1/2
J 2 J' J 2 J'
”(m o m)(-k -q 1..) (4-14)

using k for the projection quantum number in the molecular frame and m
for the same in the space-fixed system. Then, the reduced matrix
element of the V tensor is calculated with the aid of Rqs. (4-10), (4-

13), and (4—14) to yield

<J.kllVllJ' .k' >
J 2 J

= (-1)J+k[(2J+1)(2J'+1)]1/2(-k —q k;)v;q/2 . (4—15)

The matrix elements of the quadrupole Hamiltonian can be expressed in

the specified representation by introducing the reduced matrix elements

(4-12) and (4—15) into Eq. (4-8) for each F block

145

<J,k,I,F|Bb|J',k',I,F> = (_1)J+J +k+I+F+1

( J 2 a)
:E_:a__5_ x_q/4 (4-16)

.[(2J+1)(2J'+1)]1/2 iF I J] I 2 I
{—1 o I)

2 J' I

with the abbreviation xq = eQVé for the quadrupole coupling tensor. The
irreducible quadrupole coupling tensor may also be expressed in the

Cartesian axes

x0 - xzz’

xfl = $(2/3)1/2(sz x ixyz). (4-17)
_ 1/2 .

X12 - (1/5) (xxx - xyy : 21xxy).

The explicit expressions for the matrix elements of the quadrupole
interaction have been derived by Benz et a1. (gfi). The matrix elements

used in this study are listed in the Appendix of this chapter.

I and CD Br

IV—2-5 Quadrupole Coupling of C03 3

The interaction between a nuclear quadrupole and an electric field
gradient splits the rotational level into 21+l hyperfine levels if J 2
I, where I is the nuclear spin number. The complete Hamiltonian for
quadrupole interaction includes the rotation of the molecules since J is
no longer a good quantum number. Especially the quadrupole couplings of

Iodine (qu[CDaI] = ~-1930 MHz) and Bromine (qu[CD3Br79] = ~576 MHz,

81

qu[CD3Br ] = ~481 MHz) are large enough that calculation to the

accuracy of 1 kHz requires inclusion of the effect of centrifugal

146

distortion on the quadrupole interaction and the spin-rotation
interaction and diagonalization of the appropriate energy matrices. The
method used to calculate the quadrupole interaction energy has been
described in Chapter III in the discussion of the effect on the
vibration-rotation energies of the molecules. As mentioned, the matrix
H, as defined, is diagonal in F, I, and k; therefore, submatrices

indexed by the possible J’s (usually 6x6 for CD I and 4x4 for CD3Br)

3
were set up and diagonalized to obtain the energy levels; the
eigenvalues were indexed by the J value of the closest diagonal element.

For 0031, all of the microwave(§§-§Q) and radio frequency data for
the ground vibrational state(§g) were combined and used in a least
squares adjustment of the rotational, centrifugal distortion, quadrupole
coupling, distortion quadrupole, and spin rotation constants for the
ground state (21 parameters). In this calculation the unresolved
microwave data were included, but were assumed to have no quadrupole or
spin rotation contribution. In the corresponding fitting for the v2 = 1
state the centrifugal distortion constants and the rotational constants,
except the B value, were constrained to the values obtained from the
fitting of the vibration-rotation spectra because only a small number of
rotational frequencies in the v2 = 1 state have been measured.

For CD3Br, the least squares fitting was performed by adjusting
only the six quadrupole and spin-rotation parameters qu, xJ, XK’ xD,
and C

C the vibration-rotation parameters were constrained to the

N’ K‘
values determined in the analysis of the infrared spectra (Chapter III).
This was done because of a limited number of reported microwave

frequencies. The experimental data for the fitting included the

previously-reported microwave frequencies (fl§,flfl), in addition to all of

147

the measured IR—RF double resonance spectra. The calculated frequencies
of the IR—RF double-resonance spectra were obtained from the computed

energy levels by using the selection rules AJ = 0, Ak = 0, and.AF = t1.

148

IV-3 Experimental

Fig. 4-2 is a block diagram of the infrared radiofrequency double
resonance spectrometer used in the present study. The infrared
microwave sidebands are generated in a CdTe electrooptic crystal that is
irradiated simultaneously with the output of a frequency-controlled CO2
laser and the output of a ZO-W traveling wave tube amplifier. For IR-RF
double resonance, the sideband generator was operated in the "cavity
mode" (g3), in which the electrooptic crystal is made part of a tunable
microwave cavity. In order to provide a cavity resonance, a tunable
short was used which is adjustable anywhere in the 8-18 GHz range. In
this mode the sideband output was ~l mW per W of infrared power. Since
we normally used 2 W of 002 laser power, the typical sideband power was
2 mw, which is sufficient to saturate partially an infrared transition
in the molecules. In order to maintain highest power, the beam splitter
and reference detector used in traveling mode operation (g5), are not
employed in the cavity mode of operation. Also, the PIN diode is set
for maximum transmission. The sidebands were directed through a
radiofrequency cell which is made of a l-meter piece of X-band waveguide
with a centered septum in a stripline design (31). The RF cell was
matched to a 50 9 transmission line impedance and has Ban windows. The
infrared power was detected by a liquid-N2 cooled Hg-Cd-Te
photoconductive detector (Santa Barbara Research Center Model 40742),
whose signal was processed at the modulation frequency by means of a
lock-in amplifier and recorded by a computer. The frequency of the
infrared source was set at the center frequency of the Doppler-limited

infrared transition, especially for CD3Br. Because of the relatively

149

 

PZT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L I
4 1TH” X
D“ cu LASER
STAB 8 Vac
: , ~ '
Fluorescence
Cell Polorlzer Strlpllne Cell +
s e u————$
ATT.
53355 lam" .9
ower ATT.
Meter RF RF DET'
I SYN. AMP. q,
A/D DBM
TVTA PRC»?
1 \l/ l
DB" 33.344
W SYN. CDMPUTER °°""°‘ non. I 5 PSD.
(— A/D

 

 

 

Figure 4—2. Block diagram of the infrared radiofrequency double-
resonance spectrometer used to record the pure quadrupole transitions
in this work. An infrared microwave sideband laser in the cavity mode
serves as the infrared pumping source. A radiofrequency synthesizer
whose output is chopped by a double-balanced mixer and amplified

serves as the radiofrequency source.

150

small hyperfine splitting of the vibration-rotation transitions, all of
the expected double resonances could be recorded without retuning the
infrared frequency. However, when the frequency difference between the
component and the hypothetical unsplit frequency was calculated to be
more than 10 MHz, the frequency of the infrared sideband laser was fixed
at the frequency of the desired hyperfine component. we estimate the
accuracy of the time averaged infrared pump frequency to be 1150 kHz.
The frequency jitter of this source is also ~150 kHz, which is mostly
the intentional laser modulation for the frequency stabilization.

The radiofrequency was generated by an RF-synthesizer (Programmed
Test Sources Model PTS 500) operating in the range 1-500 MHz with +3 to
+13 dBm output. The frequency and the power of the radiowaves were
controlled by the computer through an interface built at MSU. The
radiowave was 100 X amplitude modulated at 33 kHz (Hewlett Packard 8428
C Modulator Control) by means of a double balanced mixer (DBM, Mini-
Circuit Laboratory Model ZAD-lSH) at the output of the synthesizer. The
switched RF output from the DBM was amplified by broadband power
amplifier (Electronic and Navigation Industries, Inc. Model 525 LA).
The amplified radiofrequency power from the computer-controlled
synthesizer was applied to the central electrode of the cell. The power
of the radiowave was monitored at the exit of the cell by a thermister
detector (Hewlett Packard 8478 Thermister Mount) and a power meter
(Hewlett Packard Model 432) after 30 dB attenuation. The signal of the
power meter was fed into the computer, which in turn sent a correction
voltage to the synthesizer in order to maintain constant power of the
radiowave. The computer increased the radiofrequency in steps of 20 kHz

within the range 1-500 MHz and recorded the output of the lock-in

151

amplifier, which consisted entirely of double-resonance effects. The RF
power at the sample cell was kept as low as is consistent with
reasonably good signal to noise ratio, because the spectra are easily RF
power broadened at the low sample pressures used. Typical RF powers
were of the order of a few milliwatts for CD31 and 5-50 milliwatts for
CD3Br. An example of an infrared radio frequency double resonance
spectrum of CD31 is shown in Fig. 4-3, where it is seen that the half
width at half maximum for the transitions is about 70 kHz. Figs. 4-4
and 4-5 show typical IR-RF double resonance spectra for CD379Br and
CD381Br, respectively, where it may be seen that the half width at half-
maximum for the transitions is about 100 kHz. The center frequencies of
the RF transitions were determined by fitting the observed lineshapes to
a Lorentz function or to a sum of Lorentz functions for overlapped
transitions; we estimate the RF accuracy of well-resolved transitions to
be 1-5 kHz.

The methyl iodide and the methyl bromide were fully-deuterated
samples obtained from Merck & Co. and used as received except for the
usual freeze-pump-thaw cycling. Sample pressures were 3-5 mTorr for the
double resonance measurements. All spectra were recorded at room

temperature (~297 K).

152

 

 

 

 

 

 

35 I ' I T I I T T
25 “'- d
A P(22,5)
3 .
15 15..
3
.d 5 - .1
s.
3
a -5 _ 4
'77)
C
3 ~15 - -
E
-25 L- Upper F - 45/2 - 43/2 Lower F I- 47/2 - 45/2 -I
_3 . 1 . 1 . L a 1 . L .
?05 106 107 108 109 110 111

Radio Frequency (MHz)

Figure 4—3. A portion of the infrared radiofrequency double
resonance spectrum obtained by pumping the P(22,5) transition in the
02 band of CD31. The F quantum numbers of the transitions in the
upper and lower states of the vibration-rotation transition are shown.
The horizontal axis is the absolute radiofrequency. the sample

pressure was 3 mTorr and l-m path length was used.

153

 

 

 

 

 

35 t j t I u r fi— I ' j
-I 7. '4
25 CD3 Br P(22,6)
A 4 l
9? 15-1 J
c
:3
.o'
L
o
V
>.
3:
0‘)
c
a)
'E
- r-n/z-os/z F-41/2-39/2 r-4s/2-47/2 r-u/z-u/z *
I l
-35 V l I r T I I F r I f
109 110 111 112 113 114 115

Radio Frequency (MHz)

Figure 4~4. Example of infrared radiofrequency double resonance
spectra obtained in the present study for CDs7gBr. For these
transitions, the infrared sideband laser source was tuned to the
center frequency of the Doppler-limited lineshape of the P(22,6)
transition in the ”2 band. For the infrared microwave sideband laser
source, the 10R(26) 1201302 laser was used with a microwave frequency

of 11726 MHz; the lower frequency sideband was used.

154

 

 

     

 

 

35 1 T f I F I r
4 I
ll
25- CD3 Br P(30,6) ..
A d d
:2 15
'E - q
3 1
.d 5— a
L
3 ‘i 'i
> -5-J _q
«H
'6 ‘ ‘
c
3 -15-' -I
E , F-57/2-55/2 r-59/2-57/2 .
_25_1 F-59/2-6l/2 F-51/2“63/2 _.
. V2=1 V2=O .
—35 . r . , . , .
125 126 127 128

Radio Frequency (MHz)

Figure 4—5.

spectra obtained in the present study for CD3818r.

Example of infrared radiofrequency double resonance

For these

transitions, the infrared sideband laser source was tuned to the

center frequency of the Doppler-limited lineshape of the P(30,6)

transition in the v2 band.

For the infrared microwave sideband laser

source, the 10R(18) 1201602 laser was used with a microwave frequency

of 9747 MHz; the lower frequency sideband was used.

155

IV-4 Results and Discussion
IV-4-l CD31

About 150 radio-frequency resonances in CD31 were recorded by the
IR—RF double resonance technique; 19 vibration-rotation transitions with
J’s between 4 and 31 and K’s between 1 and 9 were pumped. In many cases
all 10 of the possible RF resonances were measured. It was often
possible to observe all of the RF resonances with a single infrared
pumping frequency. This can be explained by the fact that each
quadrupole component is in resonance for some velocity group within the
Doppler profile for the transition frequency (Fig. 4-6), though the
intensities of the transitions vary because they depend on the
Maxwellian (Gaussian) weight. The results show that the IR—RF double
resonance method is very powerful for studying pure quadrupole
transitions, especially for high J transitions. For these transitions,
the quadrupole hyperfine splittings in the infrared spectrum are usually
very small (a few MHz), because the hyperfine shifts in the energies of
the upper and lower states are almost the same. However, the shifts in
energy for the hyperfine components of a single vibration-rotation level
are still very large for high J (up to 300 MHz). The AF = :1 selection
rules for the RF resonances allows the differences in these large shifts
to be observed directly. An example of RF transitions observed by IR-RF
double resonance is shown in Fig. 4-3.

Previously reported microwave and radiofrequency transitions are
also included in the least squares fittings with their estimated
uncertainties. The frequencies of the radiofrequency transitions

measured in this work are shown in Table 4-1 with their estimated

156

 

T JI+I-1
J’-I+8
v -1 J"K i "NH
3 ‘ I J’-I+1
J’+I
.J’-I

 

 

 

 

 

 

 

 

RF

F d
In rare " Tronsltlans

Tronsl‘tlons

K

 

- Whuh

F:
‘1' J+I‘1
J-I-l-E
J)K J+I-1
G'S' J-I+1

J+I
J-I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4-6. Typical energy level pattern far the infrared
radiofrequency double resonances Observed for CD31. In most cases, a
single infrared frequency pumps all of the allowed infrared

transitions by interacting with molecules in different velocity

groups.

157’

Table 4-1

Pure Quadrupole Frequencies of CD31

 

 

 

 

v = 0 v2 = l
J zr’ 2F” v/MHz o—ca nob J 2F’ 2?" 0/882 o—cc nob Pumpd
5 15 13 300.357 4 5 4 13 11 290.458 —17 5 1
13 11 57.337 -3 5 11 9 34.853 38 20 1
7 9 180.203 -29 20 5 7 179.019 18 5 2
3 5 175.589 0 5 2
5 15 13 199.185 2 5 3
13 11 38.939 -2 5 4 11 9 17.739 33 20 3
9 11 85.409 4 5 7 9 54.518 10 5 3
7 9 120.597 -1 5 5 7 85.115 20 5 4
3 5 82.945 -8 20 4
7 19 17 308.174 -29 20 8 17 15 304.872 20 20 5
17 15 83.897 -3 5 15 13 72.909 8 5 5
13 15 74.580 0 5 11 13 85.015 -1 5 8
11 13 177.185 12 5 9 11 179.245 -2 5 8
9 21 19 98.493 -8 5 8 19 17 92.248 8 5 7
15 17 173.113 7 20 13 15 175.258 —4 5 7
10 25 23 99.388 0 5 9 23 21 51.889 -17 5 8
23 21 34.354 -4 5 21 19 17.830 3 5 8
17 19 9.922 8 20 9
17 19 58.233 -1 5 15 17 30.194 -3 5 9
12 29 27 181.095 -8 5 11 27 25 134.888 0 5 10
27 25 59.083 0 5 25 23 48.010 0 5 10
23 25 23.980 -18 20 21 23 21.898 21 20 11
21 23 89.114 3 5 19 21 75.192 -7 5 11
19 21 137.522 -7 5 17 19 113.882 -2 5 11
14 33 31 149.473 -8 5 13 31 29 125.888 -2 5 12
31 29 57.578 —12 5 29 27 47.495 1 5 12
27 29 19.208 -21 5 25 27 17.297 21 20 13
25 27 81.852 -5 5 23 25 89.150 -8 5 13
23 25 130.498 -2 5 21 23 108.844 ~17 5 13
14 31 33 48.795 5 5 14
29 31 17.907 -33 20 14
27 25 28.241 35 20 15
25 23 41.181 5 5 15
17 39 37 257.732 -5 5 18
18 39 37 108.818 3 5 37 35 103.820 4 5 18
35 37 28.871 33 20 33 35 27.888 -12 20 18
33 35 140.217 -8 5 31 33 138.558 12 5 18
31 33 234.447 2 5 29 31 229.373 -2 5 18

 

 

1583

Table 4-1 (cont’d)

 

 

 

 

- 0 v2 - 1
J ZF’ 2F" v/MHz o—c‘ ucb J 2r' 2F” v/an o—c° ucb Pumpd

18 41 39 237.778 4 5 17 39 37 230.748 ~10 5 17
39 37 97.078 7 5 37 35 93.033 2 5 17

35 37 24.388 42 20 33 35 24.890 -20 20 17

33 35 127.383 0 5 31 33 124.079 4 5 17

31 33 213.015 5 5 29 31 205.491 -5 5 17

19 43 41 109.599 0 5 18 41 39 88.375 10 5 18
41 39 45.591 0 5 39 37 38.483 12 5 18

37 39 10.393 -8 20 35 37 8.788 22 20 18

35 37 58.573 7 5 33 35 47.445 7 5 19

33 35 99.173 4 5 31 33 79.738 8 5 19

22 49 47 273.529 8 5 21 47 45 271.587 -8 5 20
47 45 118.014 2 5 45 43 114.244 8 5 20

43 45 23.187 25 20 41 43 24.018 —8 20 20

41 43 144.731 -8 5 39 41 144.098 17 20 20

39 41 249.583 4 5 37 39 248.788 -2 5 20

22 49 47 257.427 10 5 21 47 45 253.879 -14 5 21
47 45 109.225 4 5 45 43 108.848 1 5 21

43 45 21.780 33 20 41 43 22.412 -14 20 21

41 43 138.217 —4 5 39 41 134.718 8 5 21

39 41 234.937 3 5 37 39 230.775 -10 5 21

23 51 49 189.077 -1 5 22 49 47 157.529 3 5 22
49 47 72.494 4 5 47 45 87.079 5 5 23

43 45 89.245 3 5 41 43 83.373 8 5 23

41 43 155.101 1 5 39 41 144.034 -7 20 22

28 57 55 288.894 —22 20 25 55 53 288.899 17 5 24
55 53 125.810 —10 5 53 51 125.002 10 5 24

51 53 20.818 22 20 49 51 21.588 -14 20 24

49 51 151.591 37 20 47 49 151.891 -24 5 24

45 47 288.084 8 5 24

28 57 55 279.957 3 5 25 55 53 278.978 —10 5 25
55 53 121.934 -4 5 53 51 120.819 3 5 25

51 53 20.155 25 20 49 51 20.821 -17 20 25

49 51 148.817 —32 20 47 49 148.847 28 20 25

47 49 258.814 -2 5 45 47 257.182 -5 5 25

27 57 55 89.484 —2 5 28 55 53 88.024 8 5 28
51 53 108.722 -10 5 49 51 103.352 12 5 28

49 51 189.181 -2 5 47 49 182.348 -3 5 27

 

 

1553

Table 4-1 (cont’d)

 

 

 

 

v = 0 v2 = 1
I O! a b g u C b d
J K 2F 2F v/bflz O-C 00 J K 2F 2F 1.7/m: 0-0 00 Pump
30 4 65 63 283.814 -4 5 29 4 63 61 283.358 -4 5 28
63 61 126.027 -5 5 61 59 125.297 5 5 28
59 61 17.743 34 20 57 59 18.261 -17 20 28
31 9 67 65 226.064 4 5 30 9 65 63 221.747 -8 5 29
65 63 100.904 -2 5 63 61 98.602 2 5 29
59 61 117.536 -10 20 57 59 115.485 10 5 29
57 59 211.477 2 5 55 57 207.037 -7 5 29

 

 

aObserved minus calculated frequency in kHz. The parameters
for the calculation are in the second column of Table 3-2
and in the first column of Table 4-3.

bEstimated uncertainty in the observed frequency in kHz.

cObserved minus calculated frequency in kHz. The parameters
for the calculation are in the first column of Table 3-3
and the third column of Table 4-2.

dPump transitions and frequencies are listed in Table 4-2.

160

uncertainties. Also shown in Table 4-1 are the observed minus
calculated frequencies for the parameters derived in this work. Table
4-2 lists the infrared transitions that were pumped for the RF double
resonances listed in Table 4—1. The quadrupole and spin rotation
parameters obtained from the radio frequencies and the resolved
microwave frequencies for both vibrational states are in Table 4-3. As
shown in the table, the centrifugal distortion parameters for the
quadrupole coupling and the spin—rotation parameters are well determined
in the present work although the previous microwave and radiofrequency
data could not determine all of these constants. This is a result of
the accuracy of the present radiofrequency data as well as the
tunability of our pump source which allowed selection of a wide range of
J and K for the double resonances.

Comparison of the observed and calculated radio frequencies in
Table 4-1 shows that the quadrupole and spin-rotation parameters in
Table 4-3 predict the combined quadrupole-spin-rotation splittings to a
few kHz. A comparison of the predicted uncertainties of the microwave
and radio frequencies with the observed residuals indicates that the
predicted uncertainties are approximately equal to the expected
accuracies for resolved transitions by each technique; the standard
deviations for an observation of unit weight are all within a factor of
2 of unity. Also, although the previous microwave and radiofrequency
data could not determine all of the centrifugal distortion parameters
for the quadrupole coupling, these parameters are all well determined in

the present work.

161

Table 4-2

Infrared Pumping Frequencies for IR-RF Double Resonance

 

 

27 P(27,9) -11 130.
28 P(30,4) -10 167.
29 P(31,9) -11 463.

10P(26) 28 130 035.
10P(28) 28 074 502.
10P(28) 28 073 206.

Index8 Transitionb v/Ml-IzC Laserd vP/MHze
1 P(5,1) -12 289.2 10P(16) 28 400 300.5
2 P(5,1) -12 249.3 10P(16) 28 400 340.4
3 P(5,2) -11 466.0 10P(16) 28 401 123.7
4 P(5,2) -11 444.0 10P(16) 28 401 144.9
5 P(7,1) 15 655.5 10P(18) 28 375 429.3
6 P(7,1) 15 678.9 10P(18) 28 375 452.7
7 P(9,1) -9 458.0 10P(18) 28 350 315.8
8 P(10,5) -15 861.2 10P(18) 28 343 912.6
9 P(10,5) -15 878.1 10P(18) 28 343 895.7
10 P(12,5) 12 111.0 10P(20) 28 318 335.9
11 P(12,5) 12 105.8 10P(20) 28 318 330.7
12 P(14,6) -10 919.4 10P(20) 28 295 305.5
13 P(14,6) -10 923.9 10P(20) 28 295 301.0
14 P(15,9) -12 582.9 10P(20) 28 293 642.0
15 P(15,9) -12 596.1 10P(20) 28 293 628.8
16 P(18,4) -14 138.4 10P(22) 28 237 803.3
17 P(18,5) -11 905.3 10P(22) 28 240 036.4
18 P(19,9) -11 659.0 10P(22) 28 240 282.9
19 P(19,9) -11 662.8 10P(22) 28 240 278.9
20 P(22,4) -12 539.3 10P(24) 28 184 383.3
21 P(22,5) -10 395.9 10P(24) 28 186 526.7
22 P(23,9) -11 191.1 10P(24) 28 185 731.5
23 P(23,9) -11 180.3 10P(24) 28 185 742.3
24 R(26,3) -12 825.8 10P(26) 28 128 340.2
25 P(26,4) -11 220.7 10P(26) 28 129 945.3
26 P(27,9) -11 123.1 10P(26) 28 130 042.9
1 9
5 3
8 0

 

 

aIndex number in Table 4-1.

bVibration-rotation transition pumped for IR-RF double
resonance.

cMicrowave frequency in MHz; the signed microwave frequency
was added to the laser frequency to obtain the pumping
frequency.

dCO2 laser line used; laser frequencies taken from Ref. 51.

ePumping frequency in MHz.

1152

 

 

 

Table 4-3
Quadrupole and Spin-Rotation Interaction Parameters of CD318
v = 0 v2 = 1
Parameter
. b c . d .e
This Work Wlodarczak This Work Kuczkowski

 

qu/MHz -1 929.008(14) -1 928.918(86) -1 930.886(3l) -l 930.30(26)

xJ/KHz -1.098(33) -1.615(19) -1.342(72)
xK/KHz -32.86 (40) -8.16(184) -45.81 (88)
xD/KHz 19.27 (27) 26.58 (35)
CN/KHz -13.64 (6) -14.94 (42) -l4.03 (ll)
CK/KHz -9.57 (52) -ll.3 (63) -7.09 (87)

 

 

8Values in parentheses are one standard deviation in multiples of the last
digit in the parameter.

bObtained from a fit of the rotational frequencies of the ground state from
the references shown in Table 4-1 and pure quadrupole frequencies in
Table III and in Table V of Ref. 39.

cObtained from Table VI in Ref. 49.

dObtained from a fit of the rotational frequencies of the v2 = 1 state from

Table II in Ref. 38 and pure quadrupole frequencies in Table IV.

eObtained from Table VIII in Ref. 38.

163

IV-4-2 CD3Br
More than 160 IR—RF double resonances have been observed for each

of the two naturally-occurring isotopic species of CD Br; it has been

3
possible to measure pure quadrupole frequencies for 10 S J $ 38 and 3 S
K S 8. The experimental values of the pure quadrupole frequencies
measured in this work are given in Tables 4-4 and 4-5. In each table
the v2 = 0 transitions are given on the left side and the v2 = 1
transitions are given on the right side. The pumped vibration-rotation
transition is identified by the J,K quantum numbers in the two
vibrational states. Since most of the quadrupole splittings in the
infrared spectra of CD3Br are within 5 MHz and the Doppler width is
~18.5 MHz, it was not necessary to adjust pump frequencies to observe
all of the pure quadrupole transitions for a given infrared transition.
Hence, the infrared frequency was set at the center frequency of the
Doppler-limited vibration-rotation transition. The infrared frequencies
were calculated from the parameters given in Chapter III and the
appropriate CO2 laser transition and microwave frequency for the IMSL
source were determined from the calculated frequency. The experimental
frequencies in Tables 4-4 and 4-5 were fit separately by least squares
to differences in energies calculated by diagonalization of Hamiltonian
matrices with different parameters for the two isotopic species. The
resulting parameters are shown in Tables 4-6 and 4—7 for C0379Br and
CD38lBr, respectively. Also shown in Tables 4-6 and 4-7 are the values
of qu determined by Marina and Hirose (44). It is seen that the newer

values are in good agreement with the less accurate values previously

reported. The observed minus calculated frequencies for the parameters

164

 

 

 

 

Table 4-4
Pure Quadrupole Frequencies of CD3793ra
v = 0 v2 = 1

2!“ 2r" v/MHz o—cb 00° J x 21“ 21'" v/MHz o—ob 00c
10 19 17 108.683 9 50 9 17 15 100.987 108 100

21 23 108.517 -62 50 19 21 100.807 -35 100
10 19 17 81.161 -6 50 9 17 15 67.508 170 200

21 23 81.161 10 50 19 21 67.272 ~12? 200
12 23 21 99.742 -10 40 11 21 19 91.853 31 50

25 27 99.568 -55 40 23 25 91.674 -69 50
14 27 25 125.543 -37 50 13 25 23 122.841 35 50

29 31 125.326 -9 40 27 29 122.629 36 50
14 27 25 111.183 -4 20 13 25 23 106.224 -22 30

29 31 110.979 2 20 27 29 106.056 -17 30
14 27 25 92.688 8 30 13 25 23 84.932 -51 30

29 31 92.515 4 30 27 29 84.788 -70 30
15 29 27 55.883 -63 OMIT

31 33 55.888 68 OMIT
15 29 27 28.928 -19 OMIT

31 33 28.928 73 OMIT
16 31 29 118.728 4 20 15 29 27 115.457 -3 20

33 35 118.451 2 20 31 33 115.214 -2 20
16 31 29 104.449 5 20 15 29 27 99.298 -51 30

33 35 104.201 3 20 31 33 99.092 -48 30
18 35 33 123.958 2 10 17 33 31 121.722 15 10

37 39 123.628 3 10 35 37 121.420 16 10
18 35 33 112.606 0 10 17 33 31 109.059 -25 20

37 39 112.297 0 10 35 37 108.784 -22 20
18 35 33 98.737 7 20 17 33 31 98.618 -63 50

37 39 98.453 6 20 35 37 93.372 -59 50
20 39 37 127.736 -2 10 19 37 35 126.154 11 10

41 43 127.355 —2 10 39 41 125.803 15 10
20 39 37 118.501 -0 10 19 37 35 115.977 -12 10

41 43 118.135 -3 10 39 41 115.641 -11 10
20 39 37 107.212 1 20

41 43 106.866 0 20

 

 

165

Tdfle 4-4 (cont’d)

 

 

 

 

= 0 v2 = 1
J 21" 21*" mm: o—ch 00° J 21" 21'" was: o-cb 00°
20 39 37 93.888 3 20 19 37 35 88.982 —21 20
41 43 93.542 2 20 39 41 88.873 -19 20
20 39 37 78.458 0 10
41 43 78.152 -5 10
22 43 41 122.907 5 10 21 41 39 121.082 -6 10
45 47 122.489 2 10 43 45 120.874 -4 10
22 43 41 113.537 0 10 21 41 39 110.874 -15 10
45 47 113.138 0 10 43 45 110.503 -13 1o
24 47 45 137.747 -3 20 23 45 43 137.310 -10 50
49 51 137.310 43 20 47 49 138.893 32 30
24 47 45 128.277 2 10 23 45 43 124.912 -5 10
49 51 125.814 2 10 47 49 124.474 —4 10
24 47 45 118.384 0 10 23 45 43 118.397 -11 1o
49 51 117.932 0 10 47 49 115.978 —8 10
24 47 45 109.052 -2 10 23 45 43 108.410 39 10
49 51 108.616 -1 10 47 49 105.995 34 10
28 51 49 138.717 -0 5 25 49 47 138.449 24 10
53 55 138.190 -3 5 51 53 137.947 23 10
26 51 49 134.434 3 10 25 49 47 133.815 -5 20
53 55 133.930 18 20 51 53 133.327 1 10
28 51 49 128.928 9 10 25 49 47 127.892 -14 20
53 55 128.419 9 10 51 53 127.424 3 20
28 51 49 122.180 0 10 25 49 47 120.889 -1 10
53 55 121.875 -6 10 51 53 120.215 0 10
28 51 49 114.210 2 10 25 49 47 112.220 42 30
53 55 113.722 -3 1o 51 53 111.758 42 20
28 55 53 139.483 -12 20 27 53 51 139.325 17 30
57 59 138.923 -6 20 55 57 138.783 17 30
28 55 53 135.773 -20 30 27 53 51 135.347 -8 50
57 59 135.229 -3 30 55 57 134.848 28 30
28 55 53 131.029 -2 10 27 53 51 130.255 -23 1o
57 59 130.485 7 10 55 57 129.745 -3 10
30 59 57 138.910 10 30 29 57 55 138.809 10 10
81 83 138.291 -6 3o 59 81 138.011 -9 10

 

 

166

Table 4-4 (cont'd)

 

 

 

 

v = 0 v2 = 1

J 8 2r' 2F" v/MHz o—cb 00° J x 27' 2t" v/an o—cb 00
30 59 57 132.724 ~23 3o 29 57 55 132.221 28 20
81 83 132.128 ~24 20 59 81 131.837 18 40

30 59 57 127.870 0 10 29 57 55 128.811 ~9 10
81 83 127.078 ~2 10 59 81 128.240 ~14 10

32 83 81 129.888 ~28 3o 31 81 59 129.097 35 50
85 87 128.984 ~78 80 83 85 128.455 3 40

34 8 87 85 131.389 ~13 20 33 8 85 83 130.883 ~42 50
89 71 130.721 18 40 87 89 130.259 ~13 30

35 8 89 87 132.128 5 20 34 8 87 85 131.719 ~23 4o
71 73 131.432 8 30 89 71 131.040 ~27 20

 

 

.Obtsined by infrared radiofrequency double resonance. The infrared transition
was between the J and K values across from each other in the left and right
halves of the table. For example, the infrared transition for the first four
double resonances was from (J,K) = (10.3) in v = 0 to (J,K) = (9,3) in V: = 1.
The infrared frequency used was the center frequency of the Doppler-limited
transition, as calculated from the parameters in Table 3-8.

bObserved minus calculated frequency in kHz. The parameters for the calculation

are in Tables 4-6 and 3-8.

cEstimated uncertainty in the observed frequency in kHz. An ”OMIT” means that
the frequency was omitted from the least squares fits.

Pure Quadrupole Frequencies of 003 Br

167

Table 4-5

81

 

 

 

 

= 0 v2 = 1

J 21" 21'” v/MHz o-cb 00° J 21" 21m o/mz o-cb 00°

12 23 21 111.089 ~28 4o 11 21 19 109.548 33 40
25 27 110.854 ~13 30 23 25 109.322 28 40

12 23 21 99.547 ~8 20 11 21 19 95.872 18 30
25 27 99.323 ~9 20 23 25 95.887 0 30

14 27 25 104.945 9 20 13 25 23 102.833 ~25 20
29 31 104.889 14 20 27 29 102.395 ~10 20

14 27 25 92.890 ~27 30 13 25 23 88.839 40 40
29 31 92.822 ~38 30 27 29 88.579 12 40

14 27 25 77.488 9 30 13 25 23 71.005 44 40
29 31 77.221 -4 30 27 29 70.787 35 40

18 31 29 108.499 11 20 15 29 27 108.992 ~18 30
33 35 108.181 7 30 31 33 108.892 ~9 20

18 31 29 99.228 13 50 15 29 27 98.518 4 20
33 35 98.913 18 50 31 33 98.239 19 20

18 31 29 87.274 ~14 30 15 29 27 83.029 22 30
33 35 88.988 ~3 30 31 33 82.750 22 30

18 35 33 110.959 2 10 17 33 31 109.977 18 10
37 39 110.572 ~2 10 35 37 109.810 4 10

18 35 33 103.585 ~3 20 17 33 31 101.718 ~28 30
37 39 103.223 7 30 35 37 101.381 ~18 10

18 35 33 94.123 14 3o 17 33 31 91.120 ~48 50
37 39 93.788 17 30 35 37 90.818 ~12 20

20 39 37 112.742 ~2 10 19 37 35 112.089 8 20
41 43 112.322 8 10 39 41 111.889 9 10

20 39 37 108.755 8 10 19 37 35 105.444 ~13 20
41 43 108.329 1 10 39 41 105.047 ~14 10

22 43 41 117.840 8 5o 21 41 39 117.514 34 50
45 47 117.187 15 40 43 45 117.054 22 30

22 43 41 114.087 ~15 10 21 41 39 113.881 50 20
45 47 113.570 ~37 10 43 45 113.192 28 20

22 43 41 109.118 5 10 21 41 39 108.175 ~15 10
45 47 108.848 8 10 43 45 107.735 ~12 10

 

 

168

Table 4-5 (cont’d)

 

 

 

 

:0 V231
J 2r' 2F” v/an o-cb 00° J 2F' 2F” v/an o—cb 00°
22 43 41 102.715 0 20 21 41 39 101.190 ~22 3o
45 47 102.225 ~30 20 43 45 100.750 ~23 20
24 47 45 115.118 8 10 23 45 43 114.799 9 10
49 51 114.591 0 1o 47 49 114.307 8 10
24 47 45 110.923 0 10 23 45 43 110.237 ~28 10
49 51 110.427 19 10 47 49 109.771 ~5 10
24 47 45 105.539 4 1o 23 45 43 104.419 ~17 10
49 51 105.032 8 10 47 49 103.931 ~20 10
24 47 45 98.948 1 1o 23 45 43 97.310 7 20
49 51 98.443 ~1 10 47 49 98.830 10 10
28 51 49 115.932 10 20 25 49 47 115.727 18 20
53 55 115.373 18 20 51 53 115.191 12 20
28 51 49 112.354 8 30 25 49 47 111.878 0 20
53 55 111.805 20 30 51 53 111.327 ~18 20
28 55 53 118.588 14 40 27 53 51 118.457 11 20
57 59 115.970 7 50 55 57 115.884 ~8 20
31 81 59 111.578 11 20 30 59 57 111.211 ~3 20
83 85 110.885 ~11 20 81 83 110.558 ~19 20
31 81 59 107.548 ~48 50 30 59 57 107.003 -16 20
83 85 108.883 ~47 50 81 83 108.398 17 20
33 85 83 109.122 ~17 20 32 83 81 108.720 -7 20
87 89 108.424 -4 20 85 57 108.041 ~3 20
34 87 85 105.895 ~13 30 33 65 83 105.400 28 20
89 71 105.170 ~8 30 87 89 104.714 48 20
38 71 89 107.508 ~13 20 35 89 87 107.188 21 20
73 75 108.738 -8 20 71 73 108.418 21 20
38 75 73 108.888 0 3o 37 73 71 108.835 ~11 20
77 79 108.089 20 20 75 77 107.854 0 20

 

 

169

Table 4—5 (cont’d)

IObtained by infrared radiofrequency double resonance. The infrared transition
was between the J and K values across from each other in the left and right
halves of the table.

bObserved minus calculated frequency in kHz. The parameters for the calculation

are in Tables 4-7 and 3-9.

cBatimated uncertainty in the observed frequency in kHz. An "OMIT” means that the
frequency was omitted from the least squares fits.

1370

Table 4-6

Quadrupole and Spin-Rotation Interaction Parameters of CD37gBr

 

 

 

 

v = 0 v2 = 1

Parameter

This Harka Morino & Hiroseb This Workc Merino & Hiroseb
qu/MHz 575.718(35)‘l 575.4(10) 575.811(41) 578.2(10)
xJ/kHz 0.224(53) 0.946(74)
xK/kHz 14.75(l32) 26.01(243)
xD/kHz 4.19(154) -52.76(402)
CN/kflz -10.02(15) -10.00(22)
Cx/kHz -9.12(259) -9.04(391)

 

 

.Obtained from a fit of the pure quadrupole frequencies in Table 4-4 and the
rotational frequencies for the ground state reported in Refs. 43 and 44.

bRef. g.

cbbtained from a fit of the pure quadrupole frequencies in Table 4-4 and the
rotational frequencies for the v2 = 1 state reported in Ref. 44.

dValues in parentheses are one standard deviation in multiples of the last
digit in the parameter.

171.

Table 4-7

Quadrupole and Spin-Rotation Interaction Parameters of CD3alBr

 

 

 

 

v = 0 v2 = 1
Parameter
This Worka Morino & Hiroseb This Workc Morino & Hiroseb

can/1012 480.922(24)d 479.5(10) 481.206(25) 478.5(10)
xJ/kHz 0.064(56) 0.480(64)
xK/kHz 14.73(127) 35.15(153)
xD/sz 0.e 0.°
CN/kHz -10.75(22) -10.45(25)
Cx/kHz -11.12(588) -17.61(612)

 

 

.Obtained from a fit of the pure quadrupole frequencies in Table 4-5 and the
rotational frequencies for the ground state reported in Ref. 44.

bRef. 44

cObtained from a fit of the pure quadrupole frequencies in Table 4-5 and the
rotational frequencies for the v2 = 1 state reported in Ref. 44.

dValues in parentheses are one standard deviation in multiples of the last
digit in the parameter.

eConstrained to zero.

172

in Tables 4-6 and 4-7 are shown in Tables 4-4 and 4-5, respectively,
where it is seen that the theoretical frequencies agree with the
experimental values for well—resolved transitions to within the
experimental uncertainty.

Examination of the centrifugal distortion terms for the quadrupole
coupling (Tables 4-6 and 4-7) shows that both xJ and XD are quite small
in the ground state. The residual for xD for CD381Br was larger than
the value obtained, and it was therefore constrained to zero. The
centrifugal distortion terms for the quadrupole coupling in v2 = l are
larger than in the ground state for both species. This may be the
result of the Coriolis interaction between the v2 = l and v5 = 1 states
(48), which should lead to some sharing of quadrupole effects between
the two vibrational states. Since this is a Coriolis interaction
involving states of A and E symmetry, the coupled levels differ by 11 in
k. Therefore, even if the quadrupole coupling is very similar in the
two vibrational states, an effect of the mixing is expected. The result
is that caution should be used in interpretation of the vibrational
dependence of the quadrupole parameters.

Since the values of qu obtained are quite precise, it is expected
that the ratio of these values should be nearly equal to the ratio of
the quadrupole moments of the two bromine isotopes. The experimental

7 81Br) obtained in the present work for the

value of qu(CD3 9Br)/qu(CD3
ground vibrational state is 1.197ll(9), which is the same within our
experimental error as the molecular beam values of 1.1971005(24) for
LiBr (49) and 1.1970568(15) for atomic bromine (59). The corresponding

ratio obtained by us for v2 = l in CD3Br is 1.19660(9). The difference

173

between this value and that for the ground vibrational state may result
from the effect of the Coriolis coupling.

As stated before, it has been found that some effect was causing an
apparent shift of the transitions especially at low RF frequencies. In
contrast to the residuals shown in Tables 4-4 and 4-5, the observed-
minus- calculated frequencies for the low radiofrequency transitions
shown in Tables 4-8 and 4-9 are often greater than the experimental
uncertainty and nearly always the same sign for a given vibrational
state; the residuals for v2 = 0 are positive while the residuals for v2
= l are negative. The reason has been traced to the result of a four—
interacting-level double—resonance effect that causes the lower
frequency transition of a pair to be shifted to higher frequency while
the higher frequency component is shifted to lower frequency. In fact,
the same effect has been observed in low frequency quadrupole
transitions of CD31, however, it is much more serious in CD3Br since the
transitions are located much closer (within 1 MHz). The details are
discussed in the next chapter. Since the low frequency transitions were
most strongly affected by the four-interacting-level double resonance

effect, they have been omitted from the least squares fittings.

V-4-3 Other Aspects

This is the first systematic application of an infrared microwave
sideband laser system to the use of IR-RF double resonance for studying
quadrupole transitions; previous studies of a few rotational transitions

in 0804 and SiH4 have been reported (39,31). Some unresolved questions

174

 

 

 

Table 4-8
- _ . . 79 a
F~J+l/2 ~ F-J-1/2 transitions of CD3 Br
v = 0 v2 = l
J x 21" 21'" v/MHz 0—0b 00° J 11 21" 2F” mm: 0-0" 00°

 

10 3 21 19 15.834 95 50 9 3 19 17 16.110 -76 50
14 3 29 27 13.225 81 60 13 3 27 25 13.741 -62 60
16 4 33 31 11.047 89 100 15 4 31 29 11.283 -55 100
18 4 37 35 10.292 71 30 17 4 35 33 10.545 -53 30
18 5 37 35 9 362 51 60 17 5 35 33 9.512 -17 60
20 5 41 39 8.915 54 60 19 5 39 37 9.067 ~40 60
20 6 41 39 8.036 -8 100 19 6 39 37 8.142 -23 100

19 8 39 37 5.744 -26 30
22 5 45 43 8.446 49 40 21 5 43 41 8.608 -35 40
22 6 45 43 7.820 41 20 21 6 43 41 7.922 -19 20
24 3 49 47 8.686 42 30 23 3 47 45 8.984 -31 30
24 6 49 47 7.513 40 40 23 6 47 45 7.625 -22 40
24 7 49 47 6.930 22 160 23 7 47 45 7.019 5 160
26 2 53 51 8.294 41 30 25 2 51 49 8.524 -28 30
26 3 53 51 8.129 39 30 25 3 51 49 8.331 -20 30
26 4 53 51 7.889 47 30 25 4 51 49 8.060 -34 30
26 5 53 51 7 587 53 60 25 5 51 49 7.722 -29 60
26 6 53 51 7.175 18 80 25 6 51 49 7.292 -40 80
28 2 57 55 7.768 37 20 27 2 55 53 7.954 -34 20
28 3 57 55 7.630 39 30 27 3 55 53 7.797 -39 30
28 4 57 55 7.445 46 60 27 4 55 53 7.588 -36 60
28 5 57 55 7.188 37 40 27 5 55 53 7.325 -25 40
30 4 61 59 7.039 35 50 29 4 59 57 7.172 -34 50
30 5 61 59 6.847 45 50 29 5 59 57 6.973 -12 50
30 6 61 59 6.590 35 50 29 6 59 57 6.704 -11 50
34 6 69 67 6.047 20 70 33 6 67 65 ' 6.153 -13 70
35 6 71 69 5.943 35 50

 

 

.Obtained by infrared radiofrequency double resonance. The infrared transition
was between the J and K values across from each other in the left and right
halves of the table.

bObserved minus calculated frequency in kHz. The parameters for the calculation are

in Tables 4-6 and 3-8.

cEstimated uncertainty in the observed frequency in kHz.

175

Table 4-9

F=J+l/2 . F=J-1/2 transitions of CD Br

 

 

 

J K 2F' 2F" v/MHz 0—0 00 J K 2F' 2F" v/Mflz O-Cb DC

 

12 2 25 23 13.591 94 50 11 2 23 21 14.383 -75 50
12 3 25 23 12.212 93 40 11 3 23 21 12.607 -82 40
16 3 33 31 10.147 114 100 15 3 31 29 10.437 -84 100
16 4 33 31 9.282 84 60 15 4 31 29 9.506 -11 60
18 3 37 35 9.272 93 40 17 3 35 33 9.537 -62 40
20 3 41 39 8.523 76 30 19 3 39 37 8.755 -52 30
20 4 41 39 8.062 48 50 19 4 39 37 8.248 -59 50
22 3 45 43 7.878 57 50 21 3 43 41 8.082 -47 50
22 4 45 43 7.569 75 50 21 4 43 41 7.708 -49 50
22 5 45 43 7.147 75 50 21 5 43 41 7.259 -20 50
24 3 49 47 7.333 50 50 23 3 47 45 7.510 -38 50
24 4 49 47 7.074 44 50 23 4 47 45 7.218 -46 50
24 5 49 47 6.753 49 50 23 5 47 45 6.888 -11 50
24 6 49 47 6.341 36 50 23 6 47 45 6.480 28 50
26 3 53 51 6.872 55 30 25 3 51 49 7.026 -21 30
26 4 53 51 6.665 48 50 25 4 51 49 6.798 -28 50
28 3 57 55 6.472 60 50 27 3 55 53 6.606 -6 50
30 7 61 59 5.349 40 50

31 5 63 61 5.647 22 60 30 5 61 59 5.792 25 60
31 6 63 61 5.456 18 100 30 -6 61 59 5.616 50 100
33 6 67 65 5.248 26 50 32 6 65 63 5.405 65 50

 

 

.Obtained by infrared radiofrequency double resonance. The infrared transition
was between the J and K values across from each other in the left and right
halves of the table.

bObserved minus calculated frequency in kHz. The parameters for the calculation

are in Tables 4-7 and 3~9.

cEstimated uncertainty in the observed frequency in kHz.

176

have arisen as a result of this work. For example, the narrowest lines
that we have obtained have a half width at half height of ~70 kHz for
CD31 and ~100 kHz for CD3Br. We have not yet analyzed sources of the
broadening, although the most likely candidates are some combination of
RF power broadening, beam transit time broadening, and pressure
broadening. It is also necessary to investigate the effect of the
nuclear quadrupole coupling of the deuterium nuclei in these molecules,
which could give additional linebroadening; however, further study may
require more theoretical development for the effect of interaction of
quadrupoles between different nuclei. In order to analyze the source of
line-broadening, CH3I is a very good candidate since the molecule
provides a strong vibrational band (02) in 002 laser region (3), and is
free from the perturbation of deuterium nuclei.

A second unresolved question is the source of the many weak
satellite lines that accompany the RF transitions. These could be the
result of collisional double resonance (3,43), but have not yet been
assigned. Probing the intensity and the frequencies of the satellite
lines may also shed additional light on energy transfer between
rotational levels as well as uusual double resonance effects. _An
additional interesting subject for future work is observation of Al-A2
splittings in the v5 doubly-degenerate vibrational bands of CD3I and
CD3Br. Pure quadrupole transitions of k = 1 = :1 states are not allowed
due to the single parity of the hyperfine levels, however, Al-A2
transitions are allowed for all of the quadrupole components by the
opposite parity and may provide further information about the Coriolis

interaction between the v2 and the 05 vibrational states.

177

IV-5 Appendix

For a symmetric top molecule the principal axes of the quadrupole
coupling tensor x lie along the principal inertial axes of the molecule.

Also, x Therefore, for xq, only x020, and the only non-zero

xx-xyy'

matrix elements of the quadrupole interaction are as follows:

= 3- _
<J,k,I,FIHQIJ,k,I,F> e1[3k J(J+l)]xzz (4 Al)

<J,k,I,F|H°|J+1,k,I,F> —3e2k[(J+l)2-k2]1/2x

22 (4—A2)

<J,k,I,F|H°|J+2,k,I,F> = 3e3[(J+l)2-k2)((J+2)2-k2)]1/2xzz (4—13)

The abbreviations are

e1: [3G(G+l)/4-I(I+1)J(J+l)]/2I(21-1)J(J+l)(2J-1)(2J+l), (4-A4)

G = F(F+l)—I(I+1)—J(J+1), (4—A5)

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

 

e =
2 8I(2I-1)J(J+1)(J+2) ’ (4‘A6)
[(F+I+J+2)(F+I+J+3)(I—F+J+1)(I-F+J+2)
e3 = -(F—I+J+l)(F-I+J+2)(F+I-J-1)(F+I—J)]1/2 (4-47)

 

16I(2I-1)(J+1)(J+2)(2J+3)[(2J+1)(2J+5)]1/2 ’

xzz is equal to qu for a symmetric-top molecule.

178

IV-6 References

M

10.
ll.
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l3.
14.
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CHAPTER V
FOUR-INTERACTING-LEVEL DOUBLE RESONANCE

V-l Introduction

As mentioned in the previous chapter, the preliminary fittings of
the pure quadrupole transitions of CD3Br revealed some problem with the
low-frequency RF spectra. The nature of the problem may be seen by
reference to the energy-level diagram in Fig. 5-1, which shows a typical
hyperfine pattern for a single J and k in the ground vibrational state
coupled by the infrared radiation to a typical hyperfine pattern for J'
and k' in the v2 = 1 state. It may be seen that the allowed RF
transitions include two transitions of relatively high frequency and one
transition of relatively low frequency for each of the two vibrational
states. Because the hyperfine splittings in the upper state are not
greatly different from those in the lower state for the double
resonances in this work and because of the near symmetry of the
patterns, the four upper frequencies are comparable and the two lower
frequencies are comparable. Generally, the two lower frequencies are
more severely overlapped than the higher frequencies. Finally, each
pair of comparable frequencies has an energy level pattern similar to
that shown in Fig. 5-2, in which it may be seen that both the upper and
lower states of both RF transitions are pumped by the infrared
radiation. The least squares adjustment of the hyperfine constants to

fit the experimental frequencies showed that the experimental values for

181

182

Rodlof‘requency
Tronsltlons

J’+1/2
TI; J’-1/2

 

 

 

L.“ J’+3/2
*3 J’-3/2

 

 

 

)F

 

Infrared 4+
Transltlons .. f

 

 

 

J+1/2
/ W: J-1/2

 

J,K
6.8.

 

 

 

4"- J-3/2

 

 

Figure 5-1. Typical energy level pattern for the infrared
radiofrequency double resonance observed for CD3Br. A single infrared
frequency pumps all of the allowed infrared transitions by interacting
with molecules in different velocity groups. In general, four high-
frequency and two low-frequency double resonances were observed for

each infrared transition.

183

 

 

 

 

 

 

 

Figure 5—2. Energy level diagram for the four-interacting~level

double resonance system.

184

the two lowest radiofrequency transitions were too close together; the
lower frequency of the pair almost always showed a positive residual
(observed - calculated) while the upper frequency showed a negative
residual. This was finally traced to a double-resonance effect that
appears to be unique to an energy-level pattern like that in Fig. 5-2, a
pattern that we refer to as a "four-interacting-level double resonance".
Double resonance for the four-level system in Fig. 5-2 has been treated
by Small gt El. (1), but in their case the millimeter wave frequency
(corresponding in our case to the IR frequency) was scanned while the RF
was fixed. In our study, it has been found that the magnitude of the
shift in frequencies depends on the difference in frequency of the two
overlapped lines, the Rabi frequencies for the IR and RF radiation, and

the pressure broadening.

185

V—2 Theory

The purpose of this section is to describe the density matrix
treatment used to calculate the lineshape of the double-resonance
spectra obtained for the case of four interacting levels. The energy
levels and allowed transitions for the four levels are shown in Fig. 5-
2. The procedure followed is to set up and solve numerically the
density matrix equations for the four levels in the presence of two
radiation fields. The equations are solved for a sequence of values for
the component of the velocity in the direction of the two beams and the
resulting lineshapes are weighted by the appropriate Boltzmann factor
and summed. Only the infrared frequencies are assumed to be affected by
the Doppler averaging, since the Doppler shifts at the radiofrequencies
involved are much smaller than the Lorentz widths of the double

resonances. The density matrix equation is as follows:

$3; = -% [H.p] - K (p - 0°) . (5-1)

Here, 9 is the density matrix, p0 is the density matrix at thermal
equilibrium, and K is a supermatrix of relaxation coefficients. The

Hamiltonian H is in two parts,
H = 11(0) + 11(1) , (5-2)

in which R(o) is the Hamiltonian for the rovibrational energy including

the quadrupole coupling, and R(l) describes the interaction with the two

186
(1)

radiation fields. A matrix element of H is
3(1) = R(1)= — p (2 cos 2wv t + 2 cos 2nv t) (5—3)
ij kj Jk l l 2 2 '

In this expression, £1 and £2 are the peak electric fields and v1 and v2
are the frequencies of the laser and radiofrequency fields,
respectively; 1t 18 assumed that v1 = vL-kv1 ~ EC-Ea ~ Ed-Eb and v2 ~ v1
u Eb—Ea ~ Ed—EC in which the E3 are eigenvalues of R(o) for the energy

levels shown in Fig. 5—2, v the infrared laser frequency, k = (vL/c)

L
and v is the component of molecular velocity in the direction of the
beam; Doppler effects are assumed to be negligible at the radiofrequency

v 0f the dipole transition moments, we assume that ”ba’ pea, ”db’ and

R'
“dc are all real and are the only non-zero elements.
For the four levels in Fig. 5-2, the density matrix contains 4

real diagonal elements and 6 complex elements above the diagonal that

are complex conjugates of the elements below the diagonal as follows;

+22>+..+..+22 +..+22 -+..++..
5bb=‘(i/m(“t(aWpab+fltg+11)°db‘°bang)‘°bd db)) kbbApbb (5’5)

.. ++22+..+..+22 ++.. +—22> +..++..
pdd i_(1/fi)(R(1)pbd+ndi)pcd_pdbubd ‘pch Héd))-kddApdd (5‘7)

_- (1)H(1)(1) _
a(i/m(fiba)p aa +1'lbd pda_pbcH ca -pbeba ) (ivba+ kba)pba (5 8)

' -_ + (1)‘J H(1) ”(1) (1)
pca- (l/h)(ncap aa+ Hcd pda_pccH ca chnba ) (ivca+ kca)pca (5-9)

+11(1)p Ha)

__ . (1) <1) __ _
pda- (I/fi)(Hdb 0be do pHca-pdc ca _pdeba ) (ivda+ kda)pda (5 10)

187

__ (1)p (1) (1)1(1) . _
(i/fi)(Hc pab +Had pdb-pcanab Tcdndb ) (lvcb+kcb)pcb (5 11)
_ (1) M(1) (1) H(1) _
pdb (1/H)(H& ”be dc ”cb’pdaHab pddH db ) (lvdb+kdb)pdb (5 12)
__ - (1) (1) (1) (1) _
”dc‘ (l/H)(Hdb pbc Hdc pcc ”daHac pddec ) (1”d ckdc)pdc ' (5 13)

To write Eq. (5-4) to (5-13), the relaxation supermatrix K has been
assumed to have a particularly simple form.

In preparation for using the rotating-wave approximation, which
assumes that the oscillating electric field of the radiation is too fast
to be detected by experimental apparatus, we make the following
substitution for the off-diagonal elements of p:
pjk Ejkexp(-2nivnt) . (5—14)

Here, ”n is v2, v1, v1+v2, vl-vz, v1, and v2 for jk 3 ba, cs, da, cb,
db, and dc, respectively. After this substitution and elimination of
common factors of exp(-2nivnt) , all terms that oscillate at

radiofrequencies or higher are eliminated. The resulting equations are;

paa:(i/z)[x2(dba_dab)+xl(dca-dac)1—kaaApaa (5‘15)
pbb=(i/2)[x2(dab- dba )+x3(ddb- dbd)]k bbApbb (5-16)
pmin/2)["1(dac‘dca)+"4(ddc‘d cd)] kccAp cc (5‘17)
Hdd:(i/z)[x3(dbd-ddb)+x4(dcd-ddc)]_kddApdd (5'18)

pba:(isba-kba)dba+(i/2)[x2(pas-pbb)+x3dda_xldbc)1 (5-19)

188

Sca:(isca-kca)dca+(i/2)[x1(pas—pcc)+x4dda—x2dcb)] (5-20)
gda:(isda_kda)dda+(i/2)[x3pba+x4pca)_xlddc-xzddb)1 (5‘21)
Hdb:(isdb‘kdb)ddb+(i/2)[x3(pbb‘pdd)+x4dcb'x2dda)1 (5‘22)
Sdc:(isdc—kdc)dba+(i/z)[x3dbc+x4(pcc_pdd)—xldda)1 (5'23)
Scb:(iscb-kcb)dcb+(i/2)[leab+x4pdb_x2dca—x3dcd)1 ° (5‘24)

In these equations, the non-oscillating part of each off-diagonal

element (Ejk) has been represented by

pjk: d.

Jk + 1 d3 (5-25)

k 9

where dsk’ and dgk are real numbers that account the real and imaginary
parts of the off-diagonal element. There are, therefore, 16 real
numbers that must be specified to define the density matrix. It is
possible to write the 4 diagonal elements and the 6 real and 6 imaginary
parts of the off-diagonal elements as a column matrix, in which case the
supermatrix K in Eq. (5-1) becomes an ordinary two-dimensional matrix,
which is diagonal for the form of the relaxation elements in Eq. (5-15)
- (5-24). For simplicity, we have made the further assumption that the
diagonal elements are kd and k0 for the relaxation rates for the
diagonal and off-diagonal elements of p, respectively. For the
calculations here, it was further assumed that kd = k0. The next step
is to make the steady-state approximation in which the time derivatives

of the pjj’s and the djk’s are set equal to zero. The result is a

189

linear system, as follows:
A D = B (5-26)

in which D is a vector of the diagonal elements of the density matrix
and the real and imaginary parts of the pjk' The order of the elements

in D is such that the transposes of D and B are

“muumuuuuumumuuuuw<W>

0 O
c O 0 Odd 0 0 0 0 0 0 ) . (5-28)

__ 0 O
' Hd (pan 0 ° pbb ° ° ”c

Finally, the matrix A is the following:

 

 

r-kd 0 -x2 0 0 -x1 0 o o o o o o o o o 7
2 0 -ko -s o o o o o o o o o o -x1/2 o -x3/2'
x2/2 52 -k -x2/2 o o o o o o o o -x1/2 o x3/2 o f
3 o 0 x2 -kd o o o 0 -x3 0 o o o o o o i
i o o o 0 -ko ‘51 o o o o o o o xz/Z o - 4/22
éxl/z o o o 51 -k -x1/2 o o o o o -x2/2 o x4/2 o i
i o o o o 0 x1 -kd o o o 0 -x4 0 o o o t
A = g o o o o o o 0 -ko -53 o o o o -x4/2 o xz/zg
o o o x3/2 o o o 53 -k -x3/2 o o x4/2 o -x2/2 o f
o o o o o o o 0 x3 -kd 0 x4 0 o o o E
o o o o o o o o o 0 -ko -s4 0 x3/2 o xl/Zé
. 0 0 0 0 0 0 x4/2 0 0 -x4/2 64 -k0 x3/2 0 -x1/2 0 i
i o o x1/2 o o x2/2 o o -x4/2 o o -x3/2 ~20 ‘2'51 0 o I
2 o x1/2 o o -x /2 o o x4/2 o o -x3/2 0 51“2 -k° o o
i o o -x3/2 o o -x4/2 o o x2/2 o o xl/Z o 0 -ko ‘52'53
\o x3/2 o o x4/2 o o -x2/2 o o -xl/2 o o o 52+53 -k° J

(5-29)

190

In the matrix, x1 = ucafil/h, x2 = ubaSZ/h, x3 = udbEI/h, and x4 =
“chZ/h' Also, 61 = v1(l—v/c) - vca’ 62 = v2 — vba’ 63 = v1(1-v/c) -
vdb’ and 64 = 02 - vdc' In these equations v is the component of the
molecular velocity in the direction of the laser beam, c is the speed of
light, and vjk = (Ej - Ek)/h'

In order to calculate the spectrum, the linear system is solved for
a fixed value of the laser frequency, v1, and sequences of values of the
velocity component v and the RF frequency v2. For each of these
solutions, the contribution to a quantity a, which is proportional to
the absorption of the laser radiation, is calculated as

a = x1 dga + x d . (5-30)

3 db

This equation is set by the fact that the infrared absorption is
proportional to the product of the Rabi—frequency (xi) and the imaginary
part of the corresponding off-diagonal element of the density matrix.
The calculation is repeated for x2 = x4 = 0 in which case Eq. (5-26)
becomes a 6x6 linear system since the hyperfine levels are not connected
any more. It is then possible to derive an analytical expression for a,

as follows:

191

.. no ”0
“o- xldca + x3d'db

 

k k
l o 2 2 2 2 o 2 2 2
E E; { x1D1[(53+Ho)+"3 E'] + X1D3(53+Ho)
k
2 2 2 2 o 2 2 2
+x393[(51+ko)+x1 kd] + X3D1(61+ko)}
: k k 9 (5-31)
2 2 2 o 2 2 2 o 2 2 2 2
{[(61+k0)+x1 E;][(63+k0)+x3 EEJ-(63+k0)(61+k0)
where D1 3 p28 - 02c and D3 = pgb - p§d° The intensities of the double-

resonance spectra are then proportional to the differences, An = a — do.
The values of Am for the v values for a given v2 are multiplied by the
Boltzmann weight factor exp(-v2/uz) and summed. Here, u2 = 2kBT/m where
RE is the Boltzmann constant and m is the molecular mass. For the
numerical integration, it is necessary to insure that the interval in v
is sufficiently small and that the range of v includes the important
contributions to the integral. It has been found that the interval in
vlv/c must be smaller than the smaller of kd or ko and that the range of
vlv/c must include at least several times the larger of kd or R0 on
either side of the v values for the resonant velocity groups (there are

in general two resonant values of v in the four-interacting-level case).

192

V-3 Results and Discussion

The effect of the four-interacting—level double-resonance was
discovered by calculating the lineshape for a selected doublet by means
of Eq. (5-9) under conditions as close as could be estimated to the
experimental conditions. An example of the comparison of observed and
calculated lineshapes is shown in Fig. 5-3. The conditions used for the
calculation are given in the caption for the figure. We have no value
for the transition moment for the infrared transition and could only
estimate the Rabi frequency to be about 20 kHz by assuming 0.01 Debye as
the transition dipole moment (2,§). The Rabi frequency for the
radiofrequency transition was calculated from the measured value of the
amplitude of the RF field and the known permanent dipole moment for
CD38r (1.83 D (4)) by using the dipole moment matrix elements given by
Benz gt g1. (Q). The only questionable point in this calculation is the
method used to average over the spatial degeneracy. We used an average
over the m states weighted by the expected intensity of the double
resonance and obtained values of 5-80 kHz for the various transitions.
Also needed for the double resonance calculation are the effective
relaxation parameters; we used the halfwidth at half-maximum for the
double resonances, 100 kHz.

The observed and calculated lineshapes in Fig. 5—3 were each fit
by least squares to a sum of two Lorentz functions and the resulting
residuals are plotted below each line. The agreement between the two
plots of the residuals in both appearance and magnitude provides strong
confirmation of the proposed four-interacting-level double resonance

effect. If conventional 3—level double resonance equations (3,6) are

193

Figure 5-3. Comparison of observed and calculated infrared
radiofrequency double resonance spectra for a four-interacting-level
double resonance system. The upper trace is the calculated spectrum
and the lower trace is the observed spectrum. The points below each
trace are the residuals obtained when the lineshape is fitted by least
squares to a sum of two Lorentz lineshapes. The experimental spectrum
was observed with a sample pressure of 4 mTorr, infrared power ~2 mW,
and radiofrequency power ~20 mW. The theoretical spectrum was
calculated by means of Equation (5-26) with all xi = 20 kHz and with
kd 3 k0 = 100 kHz. For the experimental spectrum, the infrared
frequency was set at the center frequency of the Doppler-limited
lineshape of the P(26,4) transition in the v2 band of CD37QBr; the
10R(22) 1201502 laser was used with the lower frequency sideband

generated by a microwave frequency of 12632 MHz.

 

 

 

Intensity (orb. units)

194

 

95

 

 

 

 

 

r l '
79P(26.4)
75- l
55- "
Wfiffififlw
35- "
154 H
-5- "
-25- r-53/2-51/2 F-51/2-49/2 _
—45 I I '
7.0 7.5 8.0 8.5 9.0

Frequency (MHz)

195

used to calculate the spectra, it is found for the conditions in this
work that the lineshapes are almost perfect Lorentz functions centered
at the predicted frequency. The two Lorentz functions obtained from the
fitting of the calculated lineshape in Fig. 5—3 are each shifted by 40
kHz from their expected value; the lower frequency transition is shifted
to higher frequency and vice-versa. Examination of the residuals in
Tables 4-8 and 4-9 shows that 40 kHz is of the correct order of
magnitude to explain the observed frequency shifts.

After discovering this effect, the next question was whether there
was a corresponding shift in frequency for the other double resonances,
because, as mentioned above, both the upper and lower levels of every RF
transition are pumped. Such a difficulty did not seem probable because
the residuals for the high-frequency double resonances were much smaller
than for the low-frequency transitions, even when the low-frequency
transitions were included in the fit. Nevertheless, a series of
lineshape calculations have been carried out with 20 kHz for Rabi
frequencies, with 100 kHz for the Lorentz widths, and with varying
values of the separation in frequency of the two double-resonance
transitions. The computed lineshapes were fit to a sum of two Lorentz
functions and the difference between the center frequency of the lower
frequency Lorentz component and the expected value is plotted in Fig. 5-
4 as a function of the separation of the two peaks. It may be seen that
the shift ranges from about 45 kHz for a separation of 0.3 MHz to less
than 5 kHz for separations greater than 4 MHz. These values were
surprising to us in view of the rather small Rabi frequencies involved.

A final point is that examination of the radiofrequencies obtained

for a single pumping frequency shown in Tables 4-4 and 4-5 will reveal a

196

50-

30-

20-+

Frequency Shift (kHz)

10-

 

 

 

‘ ”T

o ' i 4 ' 5 ' a ' 10
Frequency Split (MHz)

Figure 5-4. Plot of the frequency shift caused by the four-
interactingelevel double resonance effect against the assumed
frequency splitting between the two lower frequency hyperfine
transitions fer the conditions described in Fig. 5~3. The vertical
axis is the difference in frequency between the center of the best
Lorentz line approximation to the calculated lineshape and the assumed
hyperfine frequency for the lower-frequency component of the infrared
radiofrequency double resonance doublet. All of the conditions for
the calculated lineshape in Fig. 5-3 apply, except that the difference
between the hyperfine frequency in the upper vibrational state (vcd)
and that in the lower vibrational state (”ba) is varied. This

difference is plotted on the horizontal axis.

197

number of strongly overlapped lines, which might be expected to be
shifted. In these cases, however, the overlapped lines do not involve
four interacting levels, as shown in Fig. 5-1. We believe, and the
residuals in Tables 4-4 and 4-5 seem to confirm our belief, that the
shifts occur only when the two transitions occur between four
interacting levels. The calculation should probably be done for the
eight-level system, but the necessary algebra and computer time are both
formidable.

As has been shown, the frequency shifts of RF-transitions in low
frequency region have been traced to a result of a four-interacting-
level double—resonance. The amount of frequency shift and the distorted
lineshape were calculated numerically by the use of density matrix; the
calculated frequency shift and lineshape with the estimated input
parameters show good agreements with the experimentally obtained values.
Considering the amount of shift in frequency, the four-interacting-level
double-resonance effect must be taken into account in the assessment of
measured frequencies, especially for overlapped transitions in the low

frequency region.

198'

V-4 References

l. C. E. Small, J. G. Smith, and D. H. Whiffen, Mol. Phys. 37, 681-688
(1979).

2. J. W. Russell, C. D. Needham, and J. Overend, J Chem. Phys. 45,
3383-3398 (1966).

3. S. T. Sandholm and R. H. Schwendeman, J. Chem. Phys. 78, 3476-3482
(1983).

4. K. Harada, K. Tanaka, and T. Tanaka, J. Mol. Spectrosc. 98, 349-374
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