,4 ' PHYSICS {15.7

 

 

ABSTRACT

ROTATION-VIBRATION SPECTRA OF AXIALLY
SYMMETRIC MOLECULES WITH
L0 CALIZED PERTURBATIONS

by Hillian.Errol Blass

The developnent ot the molecular rotation-vibration
Haniltonian.is reviewed especially as it applies to sole-
cules belonging to the point group 03'.

Problens involved in the analysis or the large nunber
of observable transitions in one (or sore) rotationdvibration
bands are discussed. A.generalised expression which sinul-
taneously represents all observed unperturbed transitions
of a particular nolecule is given, and the application or
this expression to the nunerical analysis or rotation-vibra-
tion spectra is discussed in considerable detail. the general-
ised expression is applied in the analysis of a perpendicular
band, v3 + v4, of 033?.

In.addition. an expression.is given which sinultaneously
represents all observable ground-state oonbination.di£terenoes
or a particular solecule. this expression was applied to
v) . v1. or on}: at 4058a", v1 + v2 of can3 at 5134“". and
v2 + v, o: CHBD at 3500ca7‘, to obtatn'values of Bo' DoJ and
D041. Sinilar expressions for upper-state conbination
differences are also discussed.

The work of Dr. G. Anat of the university of Paris on
an orderly seni-quantitative approach to perturbations in
infrared spectra is reviewed. Additional considerations

 

 

 

 

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William Errol Blass

which nay facilitate the experinentalist's analysis of local-
ised perturbations in the spectra of axially synetric sole-
cules are presented. Several well-substantiated perturbations
were found in v3 4- v‘ of 0331?. the nest cospletely substan-
tiated perturbations are a Coriolis resonance which lifts

the degeneracy of the K' = l = *1 levels. and an accidental
resonance affecting the K' 2 i=2, 1 = 1:1 and the K' = *2,

s = 1:1 levels. the analysis of these perturbations was

carried as far as currently possible.

ROTATION-VIBRATION SPECTRA OF AXIALLY
SYMRETRIC MOLECULES WITH
LOCALIZED PERTURBATIONS

BY

William Errol Blass

A THESIS

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

DOCTOR OF PHILOSOPHY
Department of Physics and Astronomy

1963

 

81% 39
MAMA

TO MY WIFE
1205mm

ACKNOWLEDGEMENT

I wish to thank Dr. T. Harvey Edwards for the many
helpful suggestions and discussions and for his continuing
patience and encouragement in the direction of my work. I
also wish to thank Dr. Gilbert Amat of the University of
Paris for several helpful discussions and for a helpful set
of unpublished lecture notes and other information given to
us in the course of this work. I should like to thank a
fellow graduate student, Dr. John Boyd, for many interesting
discussions and acknowledge that the computer program DAEA‘
was written in collaboration with Dr. Boyd. I also wish to
thank Dr. Paul M. Parker, Dr. C.D. Hause and fellow graduate
students Dr. Ronald A. Hill, Mr. Joseph Auble and Mr. Melvin
Olman for many stimulating discussions during the time this
work was in progress. I also wish to express my gratitude
to the Woodrow Wilson Foundation and the National Science
Foundation whose generous support by fellowships made this
work possible. I would also like to thank the National
Science Foundation for the indirect support by grants to
Dr. Edwards which made the experimental aspects of this work
possible. I also thank the staff of the'hichigan State
University Computer Center for their help and patience in
the numerical analysis of data. In addition I am grateful
to Miss Mary Douglas and Mr. Stephen Parker for the prepara-
tion of many of the tables and figures in the thesis.

I am deeply indebted to my wife for the four years of

patience and encouragement during which this work was in
iii

progress and thank her for the typing and assistance in the
preparation of this thesis.

iv

TABLE OF CONTENTS

ACKNO‘qI‘EDGEMNT O O C C O O O C -. C O 0

LIST OF TABLES . . . . . . . . . . . .

LIST OF FIGURES . . . . . . . . . . . .

LIST OF APPENDICES O O O O O O O O O O 0

INTRODUCTION 0 O O O O O O O O O O O 0

Chapter
1.

2.

3.

ROTATION-VIBRATION ENERGY OF THE AXIALLY
SHMETRIC MOILECULE O O O O O O O 0

Summary of the Development of the
Rotation-Vibration Hamiltonian . .

Rotation-Vibration Energy Through
Fourth order s e

Discussion of the Orders of Magnitude
of Contributions to EVRO . . . .

SYMMETRY PROPERTIES AND SELECTION RULES .

Selection Rules on Infrared Rotation-
Vibration TranBitiom e e e e e
Selection Rules on fi‘t‘ . . . . .

GENERALIZED EXPRESSION FOR THE SIMULTANEOUS
REPRESENTATION OF ALL TRANSITION FREQUENCIES
OF AN AXIALLY SYMMETRIC MOLECULE . . .

COI‘IBINATION DIFFERENCES e e o e a e

Definition of Ground State Combination
Differences. . . .
Simultaneous Representation of all
"Nine" Types of Ground State
Combination Differences. . .
Calculated Ground State Combination
Differences for Use in the Assignment
Of Transitions e e e 0 av e e e
Simultaneous Representation.of Upper
State Combination Differences. . .

iii
viii

xii

13
21

23
23

26
46

47

53
54

Chapter
5.

6.

7.

Page

ANALYSIS OF ROTATIONAVIBRATION SPECTRA OF
AXIALLY SYMMETRIC MOLECULES USING A

COMPUTER PROGRAMMED ANALYSIS SCHEME. . . 57
Analysis Scheme and Computer Program . 59
Method of Analysis and Generalized

Transition Frequency Expression
Suitable for Analysis. . . . . . 65

PERTURBATIONS IN THE SPECTRA OF AXIALLI

SYMMETRIC MOLECULES . . . . . . . . 73
Origin of Anomalies in Observed Spectra 74
Previous Work on Perturbed Spectra . . 74
Review of the Approach to Analysis of

Perturbed Spectra . . 75
Systematic Approach to the Analysis of:

Perturbed Spectra . . 78
Rules That Determine Which.:Levels May

Perturb One Another . . 82
Method of Determining if a Particular

Perturbation Element Exists in.h+. . 83
Expression for the Separation of

Unperturbed Energy Levels . . . . 89
Accidental Resonances . . 93
Systematic Approach to Perturbation

Couplings. e e e 94

Hypothetical Example of an Accidental
Resonance. e e e e 100

Intensities in Perturbations
"Borrowed Inten81ty " e e e e e e 102

Essential ReSOanCQSe e e e e e e 106

Summary e e e e e e e e e e 107

EXPERIMENTAL DETAILS AND CALIBRATION OF
RECORDS O O O O O O O O O O O O 108

SPGCtrometer e e e e e e e e e '08
Calibration Of CH F Bands e e e e e 109
Calibration Of CH3 0 a e e e e 115
Calibration 0f CH 3 e e e e e e e 1'5
Sample Preparatlo CH Fe 0 e e e e 115
CHD3 and CH3D Samples e e e e e e 122

PERTURBED PERPENDICULAR BAND 9} + v4
0F CHBF O C O C . O C O O C O 0 121‘

General Features and Vibrational

Assignment of the Observed Spectrum . 124
Assignment of Transitions . . . 125
Analysis of Ground State Combination

Differences e e e e e e e e e 146

vi

Chapter

Search for Possible Perturbations. . .
Analysis of the Unperturbed Transitions'

Of V + V4 e e e e e e e e e e
Coriolis Resonance. . . .
Additional Observed Perturbations. . .

Accidentally Strong Resonance
Affecting the K' = :2, A = :1 and

= *2. ‘ =IF1 Levels e e e
Perturbation of Levels with High J
find Low K. e e e
Weak Coriolis Resonance in the
negative Subbands . . . .

Perturbation Affecting the +5
Subband e e e e e e e .e -e

conCIusion e 0 e e e e e e e e

0 SIMULTANEOUS ANALYSIS OF COMBINATION
DIFFERENCES APPLIED TO V1 + V2 0F CHD3 AND
V2 + V3 OF 033D. e e e e e e e e e

V1 + V2 Of CHDBe e e e e e e e e

Ground State Combination Differences
0f V‘ + V2 e e e e e e e e

v2 + v3 of CH3D. . . . . . . . .

Ground State Combination Differences

Of V2+92 Of CH3D e e e e e e
J

Analysis of Upper State Combination

Differences and Unperturbed
Transitions of v2+v3. . . . .
Conclusion . . . . . . . . . .
10. CONCLUSION . . . . . . . . . . .
LIST OF PLEFERENCLS I O I I O O O O O O O

APPENDICES O O O O O O O O O O O O O 0

vii

148
154

156
186

186
204
213
218
218

221

221

228

230

231

234

1‘.)
\J
a]

PO
to
LL

h)
L‘-
(3

246

Table
1.1

1.2

1.8
2.1
3.1
3.2
3.3

3-4

3-5

3.6

3.8

LIST OF TABLES

Symmetric top transformed Hamiltonians
and energy a o o o e o e o o 0

List of symbols from Table 1.1 with
-deacr1pt10n. o e o o o o o o 0

Contribution to symmetric top energy
from h; e o o o o o o o e o 0

Fourth order transformed Hamiltonian . .

Description of contributions of terms in
h4 t0 EVE o o o o o o o o o 0

List of symbols from Table 1.3 with
descriptions o o o o o o o o 0

Approximate magnitude of the formal orders.
or magnitude 0 o o o o o o o 0

Order of magnitude of constants. . . .
seleCtion Rules on ‘t o o o o e o o
Generalized transition frequency expression
Description of symbols found in Table 3.1
Formal order of magnitude of the
contribution to the transition frequency
of terms a,b,c,d,e in Table 3.1 forvSa/A

Order of magnitude of terms for AK = 0,
AJ ='1, 1.6., QPK(J)O o o o o o 0

Order of magnitude of terms for AK = 0,
AJ: 0, 103., QPK(J)0 o o e o o 0

Order of magnituds Of terms for AK = O,
R

AJ = *1, 1030, K(J) o o o o o 0

Order of magnitude of terms for AK = 1,
AJ =’1, 1090, RPK(J)o o o o o o 0

Order of magnitude of terms for AK: 1,
AJ = 0, 1.80. RQK(J)- o o o o o 0

viii

10

12
14

15

16

18
2O
24
28

31.

35

37

38

39

40

Table
3.9

3.10

3.11

3.12

5.1

5.2

5.3

6.1

6.2

6.3
6.4

6.5
6.6
6.7
6.8

7.1

7.2

7.3

Order of magnitude of terms for
AK =1, AJ = +1. i.e., RRKU). . . . In

Order of magnitude of terms for
AK = 1' AJ = -1, 1080’ PPK(J)O O O o 42

Order of magnitude of terms for
AK = -1, AJ = o, i.e., PQK(J). . . . 43

Order of magnitude of terms for
AK = -‘, AJ = *1, 10°C, PRK(J) O O O 44

Normal equations for Eq.(5.1) (all sums
over 1 from 1 to n) a o. o- 0- 0- o 0 6O

Generalized transition frequency
expression suitable for the least
squares analysis of vn+vt . . . . . 67

First approximation of the expression
in Table 5.2 for the preliminary analysis

of Vn+vto o o o o o o o o o o 7‘

Matrix elements for the one dimensional
harmonic OSCillator o o o o o o o 84

Matrix elements (v,£lflv',i) for the two
dimensional harmonic oscillator . . . 85

Matrix elements of Pa and PQF . . . . 87

Generic form of elements in h+ capable of

producing an accidental resonance . . 9O
Perturbation couplings for p >/ 3. P1551 . 96
Perturbation couplings for p) 2, pt=1 . 97

Perturbation couplings for p=2,pt=2 . . 98

o
\i
\O

Perturbation couplings for p=2, pt=O . 2

Calibration of Fabry-Perot fringes of

V3+V4 CH3F Chart II o o o o o o o 110

Calibration of CH F Chart II vs.frequencies
of absorption lines from Chart I. . . 111

Calibration of CH F Chart II vs.frequeneies
of absorption 1 es from Chart II . . 113

ix

fiLA-v -'
«

 

Table
7.4

7.5
7.6
7.7
7.8

7.9

7.10

8.1

8.2

8.4

8.5

8.6

8.7

Experimental conditions for records of
V3+V4 Of CH3F at 20$}! 0 o o o 0

Calibration of Fabry-Perot fringes of
CHD3 Chart I vs. Neon emission lines.

Calibration of Fabry-Perot fringes of
CHD3 Chart II vs. Neon emission lines

Experimental conditions for records of
V1+V2 0f CED} o o o o o o o 0

Calibration of Fabry-Perot fringes of
033D Chart I vs. HCN absorption line.

Calibration of CH D Chart II vs.
frequencies of bsorption lines from
Chart I O O O O O O O O O 0

Experimental conditions for records of
V2+V3 Of C33D o o o o o o o a

Results of simultaneous analysis of all
observed ground state combination
differences from v +v and v +v of

3 4 1 3
CH3F O O O O O O 0 O O O 0

Summary of rotation-vibration constants
from references (58). (101), (102),
and (103). a o o o e o o o e

Overtone and combination levels as sums
of fundamentals in the vicinity of

V3+V4 . o o o o o o o o o 0

Principal perturbation couplings between

levels near V3+V4 o o o o o o 0

Results of a simultaneous least squares
analysis of,y +v4 of CHBF including

transitions om the -3,- ,-1,0,+1,+2,

+3,+4,+6,+7,+8, and +9 subbands (in

cm- -. '0 O O O O O -. O O 0

Results of a simultaneous least s uares
analysis of RRO(J). RPow) and Q0(J)
tran31t10n8 Of V3+V4 o o o o o o

(é-Ev)forK'=i2,£-:t1 and
K. g *1, t = ¥ 1 levels a o o o o

I

114

116

117

118

119

120

121

147

149

151

152

185

198

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.
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Table
8.8

8.9

8.10

8.11

8.12
8.13
9.1
9.2

9.3
9.4

Page

Summary of the results of the analysis
of the perturbation affecting the
K' = 12, z = :1, and the K' .-.-. :2,
‘= #:1 levels or V3+v40 o o o o o 200

P(AJ) (J) frequencies in the region of
ree'onance o e o e o o o o o o 206

PQ (J) frequencies in the region of
esonance e o o o o o o o o o 207

Summary of results of the analysis of

the perturbations affecting the -

K'.=:h2,£ =t1, andK' =u, z==F1

levels of V3+V4 o o o e o o o o 212
Subband origin analysis results (cm’1) . 216
Subband analysis resultafl(cm-1)e o o o 217
Ground State Conatants Of CED} e e o o 229

Comparison of available results for CED}
ground state constants . . . . 231

Molecular constants for CH3D (in cm") - 235

Comparison of ground state constants
for CHBD (in Cm-1) e o o o o o o 236

xi

Figure
4.1
6.1
6.2

7.1

8.1
8.2

8.3
8.4

8.5

8.6

8.7

8.8

8.10

8.11

LIST OF FIGURES

Page
Ground state combination differences. . 49
Two level perturbation relations . . . 91

Hypothetical perturbation with coupled
levels indicated by dashed lines . . 101

Position of the Q branches for
unperturbed v4(solid lines) and
v +v¢ (dashed lines) and the resul
s ectrum observed (hypothetical) due
to a perturbation of type I . . . . 103

Laboratory set up for the production of
CHBFO O 0 O O O O 0 O 0 0 0 ‘23

‘

Spectrum of v3+v4 and v‘+v3 of CHBF . . 126

v 3+v4 and v of C Fwith assignment
3of the principa Fsitions. . . . 133

Perturbation couplings near 4100cm". . 153

Observed minus calculated frequencies
from entire band analysis for P(AJ)9 (J) 157

. Observed minus calculated frequegcies9

from entire band analysis for (AJ)8(J) 158

Observed minus calculated frequegcies
from entire band analysis for (AJ)7(J) 159

Observed minus calculated frequeBcies
from entire band analysis for (AJ)6(J) 160

Observed minus calculated frequegcies
from entire band analysis for (AJ)5 (J) 161

Observed minus calculated frequencies
from entire band analysis for P(AJ)4(J) 162

Observed minus calculated frequegcies
from entire band analysis for (AJ)3(J) 163

Observed minus calculated frequencies
from entire band analysis for (AJ)2(J) 164

xii

Figure

8.1:

14

 

 

811’
5.1

'V.

 

Figure
8.12

8.13
8.14
8.15
8.16
8.17
8.18
8.19
8.20
8.21
‘ 8.22

8.23
8.24
8.25

8.26

8.27

8.28

Observed minus calculated frequegcies
from entire band analysis for (AJ)1(J)

Observed minus calculated frequencies
from entire band analysis for R(AJ)0(J)

Observed minus calculated frequencies
from entire band analysis for R(AJ)1(J)

Observed minus calculated frequencies
from entire band analysis for R(AJ)2(J)

Observed minus calculated frequencies
from entire band analysis.for R(AJ)3(J)

Observed minus calculated frequeficies
from entire band analysis for (AJ)4(J)

Observed minus calculated frequencies
from entire band analysis for R(AJ)5(J)

Observed minus calculated frequencies
from entire band analysis for R(AJ)5(J)

Observed minus calculated frequeficies
from entire band analysis for (AJ)7(J)

Observed minus calculated frequencies
from entire band analysis for R(AJ)8(J)

Observed minus calculated frequencies
from entire band analysis for R(AJ)9(J)

Secular equation for the K'=t=a1 levels .
Factored secular equation. . . . . .

Level structure for R(AJ)O(J)
transitions e e e e e e e e e e

K=0 AK=+1 observed minus calculated
ground state combination differences .

Expanded graph of R0 (J). RR (J). 3P01J)
indicating the eff ct of C riolis
resonance .

Observed transitions of Ho (J) indicating
the effect of the pertur ation . . .

xiii

Page

165

166

170

171

172

173

174

175
177
178

180

183

184

187

Figure

8.29

8.30

8.31

8.32

8.33

8.34

8.35

8.36

8.37

8.38

8.39

9.1
9.2

Observed transitions of Po (J) indicating
the effect of the perturgation . . .

R0 (J) transitions vs. J'(J'+1) indicating
the effect of an accidental resonance .

P (J) + 0.01 J'(J'+1)cn" vs. J'(J'+1)
indicating the effect of an accidental
resonance 0 e e e e e e e e e

Perturbation hyperbole for the K'=i2,
‘=*1 137.1Be e e e e e e e e e

Perturbation hyperbole for the K'=i2,
‘=:F‘ levels e e e e e e e e e

An hyperbole with its center at the
coordinate origin. . . . . . . .

Level structure of J=0 levels for the
perturbation of the K'=a2, 1:11 and
K.=t2,l=¥1 levels or V3+v4e e e e e

RQ (J) transitions vs. J'(J'+1) indicating
the effects of two accidental resonances

PQ (J) transitions va. J'(J'+1) indicating
ghe effect of an accidental resonance .

.Perturbation hyperbole for the K'=a2,

13*1 IOVQlfie e e e e e e e e e

Perturbation hyperbole for the K'=t1,
l=$1 levelse e e e e e e e e e

V1+V2 0f CED}. e e e e e e e e e

V2+V3 0f CHBD. e e e e e e e e e

xiv

Page
188

189

191
195
196

199

202
208
209
'210

211
222
232

Appendix .

I.

II.

III.

IV.

V.

VI.

VII.

VIII.

IX.

XI.

XII.

XIII.

XIV.

XV.

LIST OF APPENDICES

Page

SYMMETRY SPECIES OF ROTATION-VIBRATION
LEVELS OF MOLECULES BELONGING TO THE
POINT GROUP C3V' . . . . . . . . 246

LIST OF CALCULATED GROUND STATE COMBINATION
DIFFERENCES FOR CH3F . . . . . . . 249

LIST OF CALCULATED GROUND STATE COMBINATION
DIFFERENCES FOR CHD3 . . . . . . . 265

LIST OF CALCULATED GROUND STATE COMBINATION
DIFFERENCES FOR CH3D . . . . . . . 281

LIST OF ASSIGNMENTS AND FREQUENCIES OF
OBSERVED TRANSITIONS FOR v3+v4 0F CH3F . 297

LIST OF OBSERVED GROUND STATE COMBINATION
DIFFERENCES FOR V3+V4 0F CHBF e e e e 313

LIST OF ASSIGNMENTS AND FREQUENCIES 0F
OBSERVED TRANSITIONS FOR v1+v3 0F CH3F . 32S

LIST OF OBSERVED COMBINATION DIFFERENCES
FOR V +V 0F CH F e o e e e e e e 330
1 3 3
COMPARISON OF THE OBSERVED AND CALCULATED
FREQUENCIES OF V3+V4 OF CHBF . . . . 334

COMPARISON OF THE OBSERVED AND CALCULATED
FREQUENCIES OF K"=0 SERIES OF v3+v4 OF
CHBFe e e e e e e e e e e e e 350

LIST OF ASSIGNMENTS AND FREQUENCIES OF
-OBSERVED TRANSITIONS FOR v1+v2 OF 0RD3 . 352

COMPARISON OF THE OBSERVED AND CALCULATED
GROUND STATE COMBINATION DIFFERENCES OF
V1+V2 0F CHD} e e e e e e e e e 356

COMPARISON OF THE OBSERVED AND CALCULATED
GROUND STATE COMBINATION DIFFERENCES OF
92+V3 OF CHBD e e e e e e e e e 359

COMPARISON OF THE OBSERVED AND CALCULATED.
UPPER STATE COMBINATION DIFFERENCES OF
V2+V3 OF CH3D e e e e e . e e e 363

COMPARISON OF THE OBSERVED AND CALCULATED
TRANSITION FREQUENCIES OF v2+v3 OF CH3D. 367

IV

INTRODUCTION

During the past ten years the spectroscopy of small
molecules in the near infrared region has advanced to such
an extent that smaller and smaller effects are being observed
in ever-increasing detail. Attendant with this advance in
the experimental aspect of the art, the number of anomalies
which are observed in spectra has increased rapidly (1-11).
In fact, many of the effects deemed unimportant or listed as
unobserved by Herzberg (12) in 1951 are now of great interest
or have at least by now been observed.

Furthermore, with the improvement of resolution and pre-
cieion of infrared spectrometers a single rotation-vibration
band may exhibit up to a thousand observed transitions.
Meaningful values for many molecular parameters may be obtain-
ed. Together these two facts make the problem of data analy-
sis in molecular spectroscopy quite formidable, and lead
quite naturally to the use of an electronic computer in the
analysis of spectra. We have written and regularly used pro-
grams which obtain values of the molecular parameters and
also give statistical information on the accuracy of the
xnolecular parameters obtained.

In Chapter 1 we review Amat and Nielsen's (13-21) develop-
ment of the Hamiltonian of the molecular vibrating-rotor
while attempting to cast the results into a form immediately
usable by the experimentalist in the analysis of axially

symmetric molecules.

In Chapter 2 we comment briefly on the symmetry of
rotation-vibration wave functions, and set down several
selection rules which are useful in the anaLysis of spectra.

The simultaneous representation of all infrared transi-
tions of a particular molecule is discussed in Chapter 3 and
some of the ramifications of such a representation are dis-
cussed.

Another data analysis consideration makes up Chapter 4,
i.e., the simultaneous analysis of all observed ground state
combination differences. This method, to our knowledge, has
not specifically been used before, whereas it appears to be
the method to use to obtain the statistically most favorable
values of 30’ DoJ and DoJK from infrared data. -It is especial-
ly valuable when applied to the many molecules whose micro-
wave pure rotation spectra has not been observed.

Chapter 5 contains a "how to do it"'discussion of the
data analysis problem.

In Chapter 6 we have gathered together much of the work
of Dr. G. Amat on the orderly semi-quantitative analysis of
perturbed spectra. We have attempted to embellish the dis-
cussion with several additions to extend its usefulness for
the experimentalist.

The experimental details regarding the collection and
calibration of the spectra of v} + v4 of CHEF, v1 + v2 of

‘ and v2 + v3 of CHBD makes up Chapter 7.

CHD3

The application of the first six chapters to v3 + v4

of CH F is presented in Chapter 8. This perpendicular band

3
contains several interesting perturbations. Especially in-

teresting is an accidentally strong resonance affecting the
+1 and -3 subbands and a Coriolis resonance which lifts the
degeneracy of the K' = t = *1 upper state levels. For both
the Coriolis resonance and the accidentally strong resonance
affecting the K’: :2, t = *1 levels, we believe that we have
one of the most detailed and substantiated examples for both
types of resonances since we have in almost every instance
found the three individual transitions to each perturbed
upper state level.

In Chapter 9 we have applied the results of Chapter 4
on ground state combination differences to a parallel band

of CHD and a parallel band of CH3D to obtain values of 30’

JK
DO

3

DoJ and . This is especially interesting since the

microwave spectra of CH3D and CHD3 has not been observed and

J and DoJK represent a valuable

as a result our values of BO,Do
addition to the spectroscopic data on CH3D and CHD}.

In summary, existing theory and procedures for analysis
are reviewed and original contributions are made to the analy-
sis by line frequency, by combination differences and in the
analysis of perturbed spectra. These methods are applied in
the analysis of bands of CHBF, CHBD and CHD}. Even so, the
complexity of the situation,especially in the case of CH3F,

has not permitted a complete solution at this time.

CHAPTER 1

ROTATION-VIBRATION ENERGY OF THE AXIALLI SIMMETRIC MOLECULE

In this work, Amat and Nielsen's development of the
rotation-vibration Hamiltonian is used. We have attempted
to use this formalism especially as it applies to the analy-
sis of rotation-vibration spectra of axially symmetric mole-

cules belonging to the symmetry group 03v’

Summagy of the Deyelopment of the
Rotation-Vibration Hamiltonian

Briefly, one begins with a classical Hamiltonian and
converts it into a quantum mechanical Hamiltonian (22,23,24).
Then, this Hamiltonian is expanded in a power series in the
normal coordinates (13) and the resulting terms are grouped
according to the estimated order Of magnitude of the contri-
bution to the energy of rotation-vibration. The expanded
Hamiltonian is diagonal with respect to J and H but may con-

tain terms Off-diagonal with respect to vs, ts, ms, and K. 1

 

‘One defines the following symbols:

J: quantum number associated with the total angular

momentum.

M: quantum number of the projection of the total

angular momentum on a space-fixed axis.

K: quantum number of the projection of the total
angular momentum on the body-fixed symmetry axis
of the molecule.
quantum number of the s-th normal vibration.
second quantum number of doubly degenerate normal
vibrations (associated with internal angular
momentum)
third quantum number of threefold degenerate
normal vibrations (not needed for axially
symmetric molecules).

4

a4
mm

B

At this point a contact transformation (25,26,27) is
made on the Hamiltonian (14)

R.-=Ro +111 +H2+... (1.1)
such that the resulting Hamiltonian

h' = Ho + h'1 + h'2 + h' +... (1.2)
is diagonal, through h'I' with respect to all quantum numbers
for axially symmetric molecules. (This is valid only in the
absence of accidental resonances. In the event of such re-
sonances a special transformation must be performed on H to
preserve the contact transformation (19).) For axially
symmetric molecules, since HO and h'1 are diagonal, and as
the first non-diagonal terms occur in h'2, the energy of any
particular level is given through third order by the diagonal
elements of He + h" + h'2 + h'3 (21), i.e., in the absence
of accidental resonances, off-diagonal terms of h'2 will not
contribute to the energy before fourth order.

Amat and Nielsen performed a second contact transforma-
tion (15) which diagonalized h' through second order with
respect to the vibrational quantum number vs. For axially
symmetric molecules the twice transformed Hamiltonian

hi = Ho + h'1 + h; + h; + hZ't...
is diagonal with respect to the vibrational quantum numbers
VS through h§. However, hi has off-diagonal terms with
respect to K and 2.8. In addition hg, hf“... have terms
off-diagonal with respect to v 8. X8 and K.

For symmetric tOps, i.e., axially symmetric molecules,

the twice transformed Hamiltonian, h+, yields energies good
through third order since the terms in h§ which are off
diagonal in K and R s do not in general contribute before
the fourth order. Since h+ is diagonal with respect to vS
through hg, terms off—diagonal with respect to vS in h; will
not contribute to the energy before sixth order.

Rotationefiibration Energy
Through Fourth Order

The twice transformed Hamiltonian
h+ = Ho + h'1 + h§ + h; + n: + ... (1.3)
may be used to obtain the rotation-vibration energy of
axially symmetric molecules by solving the secular equation
det [<JMK...vS, 2'3“"Ho + 114+ 115+ 11; + h: + ...]
Ji-LK,...*I§, 2;... ) -g;,_;,._r... g‘~'s‘~'£”° 51.21,:"°EVR] = O
(1.4)
where Sii' is the Kronecker symbol and EVE is the energy of
rotation-vibration which we wish to obtain.

For energies through third order, in the absence of
accidental resonances, the secular equation which must be
solved is simple enough since h+ is diagonal and the energy
of rotation-vibration is given by the diagonal elements of
Ho + h; + h; + h;. Table 1.1 presents the terms in the
Hamiltonian and the resulting contribution to EVR (28,29,30)
in this case. In Table 1.1 the operators are taken from
h' rather than from h+ since the second transformation does

net add any new quantum dependence to the energy through

 

 

 

 

 

 

 

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.eesereee ... as:

third order but, in so far as diagonal terms are concerned,
it changes slightly the interpretation of spectroscopic
constants in terms of the basic molecular constants Ida

30,": , 5:5, , and the force constants, the ks1sg"'sm (14),
of the molecule. Table 1.2 gives a list of symbols found_
in Table 1.1 with appropriate definitions.

From these tables the energy of rotation-vibration to
any desired order through the third may be obtained. In
addition, a partial fourth order correction to the energy
is given in Table 1.3. However, it is necessary that one
be cognizant of the fact that this is a partial correction
and that an added correction may come from the off-diagonal
terms of hg, and also from other terms in h4 which are
diagonal in J, K, 2's and vs. Specifically, the off-diago-
nal lines (Tabletyj) which can contribute to fourth order
are: 21’ K-type resonance and doublingo(31); hég, rotation-
al X-type resonance and doubling (28); and héj, vibrational

L-type doubling and resonance (28).

hi also contains operators which may contribute further

to fourth order. No results of any study of these terms has

been published for the case of an axially symmetric molecule.2

‘—

2Chung and Parker (32) have studied the terms of h;3
for the asymmetric top case. In addition Benedict (33)
found it useful to gee a lumped sixth power cogrection of2
the form -1.0 x 10- {C J(J+1)-R2J 3 + J(J+1) K [J(J+1)-K J}
to fit an NH overtone band.. Ramadier and Amat (34) have
studied the Sixth power terms of hi} in the special case
Of a linear molecule.

10

Table 1.2 List of symbols from Table 1.1 with description.

Symbol
a

Description
x,y,z (likewise for fl andl') (body-fixed)
index for the normal vibration

index for specifically non-degenerate
normal vibration

index for specifically 2-fold degenerate
vibration

dummy index for s

ordering index for the two components of
a degenerate vibration

constant coefficients (generally complicated)
of the transformed Hamiltonians

rotational angular momentum Operator
normal coordinate operator
momentum operator conjugate to q8

principal equilibrium moment of inertia
about the d axis

2
h/(aTT ax). 1x ..- 1y

2 .
: h/(STT ch) IZ is unique 12% Ix = I

Y

harmonic frequency (cm'I) of sth normal
mode

: (27Tcw )2
s
degeneracy of the sth normal mode

Coriolis coupling constant - a function
of molecular geometry

m : J,K,JK: equilibrium centrifugal
distortion constant

correction to Be due to vibration

correction to Ae due to vibration

11,

Table 1.2 Continued.

Symbol Description

XSSI,X&‘9 anharmonic vibrational constants
tt’ 7

'It,m m = J,K,S or nothing: third order

constants

12

 

 

 

 

 

 

 

.59 5.: Eo: cozaetecoo 0 9:39. 030 mecoemcoo sweep t:
N m m m
TE ; 34 w
I.
e . ..w ..m Name .5
me; $3 .W iRemit.3...; ..w .
w — .Jx —« “WM. N m N m .mm ...»me
«X A h3<<+ ..d x (\A N + HWIO+>HZHdW+ >H (\A v
a.
7.x J .lm. .mmwm +c
. . .mm
+ ANxITIthVASHm 4+ J a. ex W + QthTNmUL ex v
m .m N m m m N m m ... ...
.eehw..:_+asehirsmw ..Tihmirhw .e
3.20 2.8205. .23
.He ES» 385 no. 023883 2 cozaetecoo m._ Bee»

 

15

However as Maes pointed out in his study of third order
terms (29), from the point of view of spectral analysis,
it is the quantum dependence which is important from third
order on since there seems to be no simple connection
between the constant coefficients of these high order terms
and the molecular parameters. The constants are in
general complicated combinations of molecular parameters
and force constants.

Table 1.4 lists the operators found in hz (16) which

we subdivide into five parts:

' ‘39
n; = n31 + hag + hz3 + n14 + h: (1.5)

such that n1“ contains only terms off-diagonal in v8 (16)
and in the absence of accidental resonances is able to
contribute to the energy only in the eighth or higher orders.
Table 1.5 gives a description of the contribution of the
various terms of h; to EVR’ Table 1.3 presents the contri-
bution of hi1, hZ2 and hZ4 to EVE (35). Table 1.6 is a
description of the constants used in Table 1.3.

The contribution of hZB cannot yet be given since no
results of a systematic study of its contribution to EVR have

been published for the case of an axially symmetric molecule.

Biscussion of the Orders of

Magnitude of Contribution: ‘tg EVE—
The expansion of the Hamiltonian is effected with an

assumed expansion parameter on the order of 1/30. It is
assumed that a zero order contribution to the energy is

approximately IOOOcm". One should realize that order of

14

 

sWs

 

no
fisssseNi +ossseNi w + Tsosssssosostsosssossssess sosans;
cor—
.wowwwuwsws .wowsswwwsws +
Assosssssaostsosssossssgwoososdi w + TossaosssssoososswstsosssosssssnsoeNi w
Fwwkmd mt:

foams :dnd a NEETQW +

 

 

swsoolmws

ndsd Nins+ losssssosorssossssgws ossNgns W +
. «3..
swoowwws as +
u o o c u n a vase
. T ass ssossNE s+ s s s s Nsnsgs “ms Ww
nlo

..v. no

.v
ma :dmdaflsasansNimesss scsassNmest W W + c

 

 

 

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.co..:o:_.EoI ucEnfimco: nacho 5.50“. v._ ~30...

 

15

Table 1.5 Description of contributions of terms in h: to EVR'

Diagonal Contribution to EVR

hZ1 correction to centrifugal distortion; due to
vibration

hie second correction to inverse moments of inertia;
due to vibration

hZB correction to centrifugal distortion; due to
rotation

h:4 . additional anharmonic contributions to

vibrational energy

16

Table 1.6 List of symbols from Table 1.3 with descriptions.

Description

m = J,K,JK; correction to D 21 ‘due to
vibration

correction to Be due to vibration
correction to Ae due to vibration
anharmonic vibrational constants
"correction" to Be and Ae which has
exactly the same quantum dependence
as Be and Ae

"correction" to a: which has exactly
the same quantum Sependence as we

17

magnitude considerations are approximations and are not to be
taken too literallfi and therefore,they should serve as a
helpful guide rather than as restrictions in the analysis

of spectra. For convenience Table 1.7 lists the eXpected
approximate magnitude of a contribution to the energy of
terms of order m.

In the following, the orders of magnitude of only the
diagonal contributions to the energy are discussed. For a
further discussion of this case and of the order of magnitude
of off-diagonal contributions the work of Amat and Nielsen
(18) is fundamental.

At this point it is useful to use simpler notation by
following the convention (18) that operators in the Hamil—
tonian having the forms qaqb, papb or qapb be called r 2,.
etc., that Pa, 1?,3 P, be called P3, etc., and that the sub-
and superscripts on the Y's and 2’s be dropped. Thus
hi2 = (2)Yr2P2.

The order of magnitude expansion of the Hamiltonian is
valid for J :3 K 2: 30. For other values of J and K a term
may be demoted or promoted from its present formal order
to a different order which we would then call the "true"
order of magnitude of its contribution.

A relatively simple approach to the problem leads us
to discuss first the order of magnitude of a given constant
appearing in hE. Consider the generic term

(mJZrnPs

Which is a term (from the m-th order transformed Hamiltonian)

18

Table 1.7 Approximate magnitude of the formal orders of

magnitude.
Order Magnitude in cm"

In
0 1000
1 30
2 1
3 3 x 10"2
4 1 x 10"3
5 3 x 10'5
6 1 x 10'5
7 3 x 10-8
8 1 x 10‘9
9 3 x 10"11

1o-‘2

d
O
N

19

with the constant coefficient (£132, a product of n vibrational
operators and s rotational operators. The order of magnitude
of the constant mm is m + s. For example D: is of order 6
since m = 2 and s = 4. Table 1.8 lists the order of magnitude
of the constants in h"' from Tables 1.1 and 1.3.

The computation of the "true" order of magnitude of
the contribution of steam in EVR may be carried out with
the aid of Tables 1.1, 1.3, 1.7, and 1.8 by substituting the
values of J and K in question into the contribution of the
term to EVR in Tables 1.1 or 1.3 using the approximate
magnitude of the constant from Table 1.8 and comparing the

answer with the list in Table 1.7. For example, from
Table 1.8, D"; is of order 6 but the term from Table 1.1, of
which 132 is the constant coefficient) is of order 2 for

J z 20, Km 0 or K x 30. At times a more meaningful order

of magnitude of the contribution of a term to EVE may be

comPuted if one has available the actual value of the constant
inVOlved. Some applications of these concepts will be

found in the following chapters.

20

Table 1.8 Order of magnitude of constants.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+ Order of Approximate
hm Operator Constant t ' Magnitude
Cons an at Constant
(0)sz ws O 1000 cm"'
Ho
101x132 Ae , Be 2 I
h .' erZP 2A,Z§,‘£. 2 |
t
'6
ha: (212 P‘ a: .13.“: a,K e 1 x 10
112; 12)Zr2P2 as“ , 053 4 I x IO'3
ha; (2)Zr‘ xss', x 1111' 2 - I
(3)2r2P3 77.3 6 I X 10’6
h; s12r2P’ 77:“ 6 IX 10"
13)Zr“P “’71 , 771.15 4 1 x lo".
J JK k _
h...’ 14)Zr2P‘ BS , BS , BS 8 I x IO”
2 A a A e '5
14)Zr“P yss. ,yss. '71,£,~'7£,1,- 6 IX IO
ho; 2 _6
(4)219 AA, , AB, 6 | x 10
“)er Yss's" 1 Ysltlr‘ 4 ‘ix '0‘3
+
h“ _3
(MD2 A0); 4 I x 10

 

 

 

 

 

 

 

CHAPTER 2
SYLR‘JIETRY PROPERTIES AND SELECTION RULES

In this chapter we comment briefly on the symmetry species
in: which a given energy level may belong and tabulate selection
rnxles on the quantum number i in infrared absorption spectra.

At the time this work was in progress no complete treat-
ment of the symmetry species of the molecular wave functions
was available. Scattered through the literature one finds
nxunerous partial treatments of the problem (36-47). However,
the problem has not been fully resolved and many subtle consi-
derations enter into the full treatment (48). The specific
Problem applied to XYZ3 molecules which belong to the point
group 03v is the problem of classifying. the full molecular wave
function including vibration, inversion, rotation and nuclear
apiai according the species A1,A2 or E1. If the rotational
functions only are considered, they may be classified according
to the rotational subgroup C3 which has species A or E.

For the work which we have done, it is sufficient to know
the symmetry species of the levels according to the rotational
subgroup 03. These may be found for the rotational wave func-
1319118 in reference 12. Very simply, the species in a pure
rotational state or an A1 vibrational state are given by

K = 3p: species A

(2.1)
K # 3p: species E

21

22

where p = 0,1,2, ....

In the case of degenerate vibrational statesthe problem
is more complex. A very simple method of finding the result
is given in Appendix I. We find that for all rotation-
vibration levels of 03v molecules, if

K - Kit 2 $3p (2.2)
the levels are of species A under the point group C3
(i.e., an A1A2 pair according to the 03v point group),
whereas if

K - th = i(3p t 1) (2.3)
the levels are of species E1. In Eqs (2.2) and (2.3) p
takes the values 0,1,2,...as in Eq (2.1).

He do know, however, that the total overall symmetry

012‘ the molecular wave function including the electronic,
vibrational, rotational, and nuclear spin contribution
must be A? for Elm?) molecules or A1 for 2X33 molecules for
those energy levels which can be populated (38,39,40).3

Due to the restrictions on the overall symmetry of
the molecular wave functions, there is a well-known effect
observed in the spectra of ZXY3 molecules. For ZXH:5

m(ll-eczules, the effect is the 2:1 intensity enhancement

01‘ transitions originating from ground states in which

 

 

3These restrictions arise from the fact that the
ZXH3 molecules obey Fermi-Dirac statistics whereas the

'7

«X33 molecules obey Bose-Einstein statistics.

23

[f z,- jp, p = O, 1, 2 ... over those which originate from states
where K ;E 3p. For 2X33, the effect is the same but the en-

hancement is only 11:8 (12),

Selection Rules on Infrared
Rotation-Vibration Transitions

There are a number of selection rules which are well
known in the study of absorption spectra of axially symmetric
molecules (12). These are the symmetry selection rules on
molecular energy level symmetries apart from nuclear spin
under the rotational subgroup C3

A<-A,:E«~<B, A‘t'E, (2.4)
the inversion symmetry selection rule

+0-, “t": +4~+, (2.5)
the selection rule on J
AJ.= 21,0; (2.6)
and on K
AK = o A or H bands (2.7)
AK = £1 E or.L bands (2.8)

with the restriction that J = 0, AI = O is forbidden.

“Selection Rules on £14;

Making use of Eq. (2.4). anqu. (2.8) and the results
°f Appendix I, the selection rules on tit may be deduced
for any case of interest. The selection rule on ‘éfit for
Several cases is given in Table 2.1 with the restriction that
only +IKI values be considered. This restriction is general-

1y adhered to in spectroscopic work. This restriction

Table 2.1 Selection rules on r.

24

 

 

 

 

 

 

 

 

 

 

 

 

 

Absorption §£t Vibration 1'1: Lt a it” .10180tl on
Band Rule
V1:1
vn + Vn, + Vnn A] ‘ O O O AL:AK=O
‘ Vt 1:] E1 121 O O AI=AK=i1
vt + Evn :h‘l E1 dd 0 0 A£=AK::1:1
2V1; 0 A1 0 O O A£=AK=0
2V1; i2 E1 i2 0 O A£=-2AK:::1:1
Vt + vt. 0 A1 $1 $1 0 A£=AK=O
“t + at. 52 12:1 s1 :1 o ' A£=-2AK=:I:1
vt + vt' + Vt" as; A1 s1 r1 r1 M=AK=0
E1 :1 i1 =F1
Vt 't Vt' + Vt" *1 E1 *1 #1 i1 A£=AK=11
; E1 :1 t1 t1

 

 

 

25

simplifies the selection rules without reducing generality.
The selection rules of Table 2.1 are given for transitions

from the ground state where all t are identically zero.

t
The subscript index n corresponds to a specifically non-
degenerate normal vibration, while t corresponds to a two-

fold degenerate vibration.

CHAPTER 3

GENERALIZED EXPRESSION FOR THE SIMULTANEOUS REPRESENTATION
OF ALL TRANSITION FREQUENCIES OF AN AXIALLY

SYMMETRI C MOLE CULE

In this chapter we develop a single expression which
simultaneously represents all allowed rotation-vibration
transitions of a particular molecule. The generalized tran-
sition frequency expression is of special value to the
spectroscopist since it enables him to perform a simultaneous
least squares analysis of all unperturbed transitions, or
any subset of transitions, of a particular molecule. This
then results in a consistent set of molecular constants and
accordingly, as more and more transitions are analyzed
simultaneously, the statistics involved 4 become more and

more favorable .

Consider the energy levels of an axially symmetric mole-
cule with a negligible inversion probability. These energy

levels are given by the energy expressions of Chapter 1 and

are Specified by-the quantum numbers vn, vn” ""Vt’ ‘t?
th| . , ‘t + 1,000J,K,M05

~

#cf. Boyd, (50).

5In the absence of external electric or magnetic fields
we 8hall omit M since the energy EVR is then independent of M.

 

27

Consider the transition

'vn4H3‘Gn,ooevt+Avtgtt+A‘tgoo0J+AJ,K+AK‘P‘vn,ooovt,‘t,...J,§3 4‘
which is a transition6 between the lower state

it ‘
EVR(vn'vn+1"”"t"t"’t+1"t+1""J'K) (3.2.
and the upper state

EGR(Vn+AVn,...Vt+AVt,1t+A1t,...J+AJ,K+AK). (3.3)

A generalized transition frequency expression is obtained

in a straight-forward manner when the upper and lower levels

are written as in Eq. (3.3) and Eq. (3.2) respectively. Alter-
nate forms of the transition frequency corresponding to the

transition given by Eq. (3.1) are

(vn’vn+1,OOOVtO‘t,OooAvn ’ o g . Avt,A‘t’...AK’AJ,K’J) =

”11.171144 ’ o ..vt,‘t...Avn.. oAvtCA‘t" ' )AEJK (J) = (301*)

. .
EVR(vn+Avn, o 0 °Vt+Avt"t+A‘t ’ . . .J+AJ 'KMK)-.

E" (v ,ooov

VR n tg‘toooJK)o

Table 3.1 presents the generalized transition frequency

expression7 defined by Eq- (3.4) for the case glvsl= ° 1" E31;

h

6For each transition the set Av ,Av ,...Av 'Mt"”
AK'A are determined by the selectioB rage; for that parti-
cular transition.

7The terms in Table 3.1 are grouped according to the

Various molecular constants. However, special considerations,
“Wild in Chapter 5 must be taken into account before using

the GXpressions given in this chapter in the numerical analy-
3 3 Of spectra in order to avoid linear dependence or a poorly
Conditioned set of normal equations.

28

 

. so...:.;..smts..sw + 5% .. .a new .3-

 

 

+ flux... NA¥<+V$ IA_+bvblAb<+_+bX.—u<+b; 0m
4

+ TV. 1~Ax<+xLo

 

:W
..a J. fum+o>vcx ...; ”WWVHW

 

...an

...._H..1wnulllo.e.mo.o.oi.nmw+..>x.ml+. m>ZdNI.+ m>:w..m.mm ..HWNV

w»;

 

. + ..«Jw: “AWN

 

Va
Vw

..del 121+. Ed]. is. ...x xWW

 

+ Ao3<+o3vo> W

 

 

nous.

 

H x .....i 21>: ..>...._+c>.:> 3
E 3&1 s q

 

60.30.98 3:33: 5:55.: me=Eoco0

_.m sass

 

29

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. o m o
_ m m _ m
on o .333: > on w n + Taoiézsfssxxsim > ohm. w -
m
s . + 7Q41+3o§<+efi>mm W
o o p
c . , Jessie «saw
. a p
c +Q<+_+bzs<+§x<+xc «as. w
. ..w.
....qé... m N so ooooooo
E + T353:Ab<i+3¢n<+2=m « a. m% N... as .o>+.o o>+. > 3.m»AN+ >mUW1.._
..w. .
a u 3a; .: N N m m mm .mm m - m
_ + 73.43:: a. a 4% W iflf o >+. > 3 .ax W+ Knew;
x + To. 1.52;; “a-
_ + risesx lasiézsfs «32;; swoon
_ + rc+bv~bnugdi+3«34+vath1 L
.ooaczcoo _.m «.32.

 

 

 

30

complete (in the absence of accidental resonances) through
the contributions of h; 8; Table 3.1 also contains a partial
contribution of hi.9

The definitions given in Eqs. (3.5) identify some of the
constants appearing in Table 3.1 with those found in the

literature and in papers on analysis of spectra.

BO=B.mBe-§(gs/2)a§+§ g, (gs/4) XESHABe

s\< s'
B ng . V lg B
.. I- -
Bv-B ...Bo §V8a8+§ §.'(v8v81++ Pig—fl) ray-r
ass
B
g £1 X‘t‘t"t‘t'
tst'
A‘
ao=A"=se-§(s,/2)a§+g gt.(gs/4)Iss'+AAe (3.5)
sss
V g 1 V 1g
_ u- _ A s s s s A
Av—A —A {Weds-1%: §.'(VBVB+T +T) yssH'
sss
A
p23. 7‘ ‘ .ttlt
’0 t t
tst'
m m .'
p‘gngfle-gmB/a )Is 8 m=J ,h ,JK
m_n'_ m- m ‘ _ "
:Dv—um—Do EVSFS . ma-oJ.I\,JK

Table 3.2 contains descriptions of symbols found in Table
3.1 but not defined in Table 1.2 or Table 1.6.

‘

80f. Table 1010

9cf. Table 1.5.

 

31

Table 3.2 Description of Symbols found in Table 3.1.

Symbo l . De scrip tion

Bo ground state constant corresponding to Be

cg, a. 2 coefficients of the correction to Ae and
Be,res1:activelyJ due to vibration

115.1%ng ground state centrifugal distortion

. constants

s refers generically to any vibrational
mode

n refers specifically to non-degenerate
vibrations

t refers specifically to two-fold degenerate
vibrations

V8 vibrational quantum number for the sth
mode, e.g., if three quanta of Y4 are
excited, V4 = 3

‘1; internal angular momentum quantum number
associated with two-fold degenerate
vibrations where it may take on values
vtsvt-2g vt"4,oooo or I

J total angular momentum quantum number

K quantum number associated with the

’ projection of J on the symmetry axis of

the molecule

M change in J in the transition being
considered, i.e., if st-JI, thenAJ: J2-J1

AK

similarily, for Ker-K1, AK = K2-K1

 

32°

There is an important restriction to be observed regard-

111g the expression in Table 3.1. The quantum number K may

properly take the values thI . However, in Table 3.1, one

need only take +IK| values into account, and in fact,if one

desires to retain simplicity in selection rules, only +IK|
should be used.

Returning to the significance of the general transition

frequency expression of Table 3.1, it is important to note

.that simply by specifying, for a given transition, v1,v2...vn,

Vt ’ Vt...‘ ' Q . .‘t"t+1’AvI’Av2 ’ O O .Avn’AVt,A‘t ,AVt+1’A‘t+1O 0 OJ,
AJ ,K , and AK as independent variables , the transition fre-
quency stands, in relation to these , as the dependent variable.

Thus , a simultaneous least squares analysis of all unperturbed

transitions of a given molecule may be obtained.

Quite often this is impractical especially if any of
the levels involved are perturbed but the fact remains that it
is OtherWise possible. Of course, any subset of transitions
believed to be unperturbed may be analyzed using an appron

Priate modification of the generalized expression of Table

3.1 . 10 For example, the sum of the purely vibrational

°°ntributions in Table 3.1 may be called v0, and all the

8P6 ctral lines of a given rotation-vibration band may be

Simultaneously analyzed. An example of this may be found in

‘

10One must of course be careful to avoid linear depen-
dence in the expression used in the actual analysis. This
18 further discussed in Chapter 5.

33

Chapter 8. Another case, where both parallel and perpendi-
cular components of a first overtone of an axially symmetric
molecule were analyzed simultaneously, may be found in a
thesis by Boyd (50). In the particular case of some diatomic
molecules it appears quite feasible to analyze simultaneously
all observed bands of a particular molecule since the addi-
tion of each band requires only the inclusion of a single
new term, the vibrational frequency of the added band.2O

Another consideration in the analysis of spectra involves
the expected order of magnitude of the contribution of any
Particular term found in Table 1.1 and Table 1.3 to the vibra-
tion-rotation energy. However, since the transition frequency
results from the difference of El'IR and EGR, certain of the
15911113 in the transition frequency expression are demoted to
a higher order of magnitude than they had in the energy
exPression. Furthermore, as mentioned in Chapter 1, the
for“Isl order of magnitude of some contributions to the energy
are "correct" only for Max:530. For J¢3O or K¢ 30 various
tame are demoted or promoted from their formal order of
m‘Etel'iitude to a higher order or lower .order.

The importance of the order of magnitude of various terms
in the transition frequency expression is discussed in
Chapter 5. The basic idea is that one does not wish to ex-
clude terms which should make larger contributions than

‘

20Olman, Hause, and HoNe s (51) are simultaneously
analyzing bands of 1311-0 and N 0 in this manner.

34

others which have been included.

Table 3.3 indicates the theoretical order of magnitude
of"the five terms in the transition frequency expression of
Table 3.1 which are independent of J, K, AJ and AK. Tables
3.1: 'to 3.12 present the theoretical magnitude and order of
magnitude of the terms in Table 3.1 which do depend on
J, SKI, AJ and AK for the transition AK = 0, AJ = -1, 0, +1;
AK == (+1, AJ = -1, 0, +1; and AK = -1, AJ 2 -1, 0, +1 for
several values of J and K. These tables were constructed by
substituting the theoretical magnitude of the molecular
constants from Table 1.8 and the values of J and K indicated
in Tables 3.4 to 3.12 into the individual terms in Table 3.1
anti (:alculating the approximate magnitude of the contribution
0f 'tllat term to EVR‘ The order for the various values of.

J anarltx was obtained using this calculated magnitude and
Table 1.7. 3

These tables may be used by spectroscopists in deter-
mining which terms from Table 3.1 contribute sufficiently
t0 the transition frequency to be used in an analysis.
Hm”Fever, it is necessary to take two factors into account;
itriis necessary to consider the accuracy and reproducibility
ofr‘the spectral data involved,and it should be noted that
13°? a given band, promotion or demotion of one order of
magnitude is not unusual. In this respect, we would expect

that terms whose laggest contribution to any of the transi-
tions used in the analysis is less than the accuracy and

reproducibility of the data would be statistically and

 

35

Table 3.3 Formal order of magnitude of the contribution to
the transition frequency of terms a,b,c,d,e in

Table 3.1 for vsz1.

 

 

Coefficient Table 3.1 Order Approximate
Descriptive Index J any Magnitude
of Term K any (cm’ )

‘08 a 1 30

x33, b 2 1

Kick, c 2 1

yes, 3,, d 4 1.1: 10-3
rut!“ e 4 1 x 10-3

 

 

 

 

 

 

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45

perhaps physically insignificant or meaningless. One should

remember especially that order of magnitude considerations
are a guide, and at times only a rather approximate guide.

None the less, order of magnitude considerations serve as a

starting point and often can be time and effort saving if
properly applied. In Chapter 5 some of these considerations

are discussed in more detail.

CHAPTER 4
COMBINATION DIFFEREN CES

Combination differences are a powerful analytical tool
available to the spectroscopist (12). In this chapter
various uses of combination differences in the analysis of
axially symmetric molecules (symmetric due to a three-fold
or higher axis of symmetry) are considered. Perhaps the
most significant development is that all ground state combina-
tion differences can be described by a single analytical
function of the ground state quantum numbers and the changes
in the quantum numbers for the transition involved, 1.8.,
in terms of J, K, AJ and AK. As a result,a relatively
Simple least squares analysis of all observed ground state

combination differences for a given molecule provides statis-

tically favorable values of 30’ Di and Dix for the molecule.

However, in so far as the other ground state constants
A0. DOK,... are concerned, the spectroscopist must still
rely on analysis of spectral lines or other means in order
t0 obtain values of these constants as they cannot be obtained
from "true" combination differences.

In the event that good values of Bo’ DoJ and DoJK are
aJuneady available from analysis of microwave spectra of
Pure rotation transitions, or from a good analysis of infra-
red data, numerical values of the ground state combination
C1ifferences can be calculated and used as an invaluable aid
in the assignment or verification of assignment of transitions

46

1+7

in infrared spectra.

Where a molecule has only at best a small permanent
dipole moment, and the pure rotation spectra is not observed,
the method of simultaneous analysis of all available ground
state combination differences can provide the statistically
most favorable values of 30' Dc,J and D'JK available. CH3D
and CDBH fall into this category, and application of the
method of this chapter to these molecules is discussed in
Chapter 9.

It is also possible to represent simultaneously all
observed upper state combination differences from an indivi-
dual parallel band or from a perpendicular band.11 However,
the expressions obtained are applicable only in the absence

01’ Perturbations .

Definition of Gro (1 St t8
Lombination Differences
Consider a generic binary combination of transitions

with. a common upper state:

AK AK
'AJ, (J,-AJ,)- 2AJ2 (J2-AJ2)
K1 K2

where in order that the two transitions have a common upper
81581:8 it is necessary that K1 = K2. AK1 = 15sz With J, = J2,
and with AJ1 and AJ2 standing in relation to each other

\

11For a parallel band the expression is simple and
quite similar to the ground state combination difference
e3KDression. For a perpendicular band the expression is
mOre complicated.

48

as (+1,-1), (O,-1), (+1,C). That these provide the conditions
required for a common upperstate in the absence of perturba-
tion is evident since:
AK AK
AJ1K(J-J1)- AJ2K(J-J2) =

F'(K+AK,J)-F"(K,J-AJ1)-F'(K+AK,J)+F"(K,J-AJ2) (4.1)

F"(K,J»AJ2)-F"(K,J-AJ,),
where F" is the ground state term value and F' is the upper
state term value. If one refers to Fig.4.1 where examples
of each type of allowed transition for parallel and perpen-
dicular bands are shown, one can see that the conditions
given above insure that the binary combination of Eq.(4.1)
does have a common upper state and is therefore a true
ground state combination difference.

Some care must be exercised in the event that the
transition terminateson an (A1A2) degenerate upper level.
Since it is possible that a perturbation may split the upper
level, the various transitions terminating on the degenerate
(A1A2) level might now terminate on two different (energy-
wise) levels.12 An example of this occurrence is found in
Chapter 8 where a Coriolis resonance splits the KézziI

upper levels.13

 

1airmen possible one modifies the expression for the
ground state combination differences to take such a perturba-
tion of known form into account.

13For details in this instance refer to Chapter 8.

49

Fig. 4.| Ground stole combination differences.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

      
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

K1. KE
K1. _ "
- K+l
...< <
Perplndlculor K'H ' + +
Bond Levels + A
ll
- K C
- K
K o + C 1 %+ +
- K-I< '4'.
K-|< +
you.)
O
K+|
Parallel
Bond Levels 0
K
‘i
1; 0
1i K-l \
" Rn J-I) F
K‘ Ro (J)
/ K PP (3+1)
Vo(ll) PRKGI-I) K
p
on”) °PK(J+i)
RPKGH'I)
QR (J-l) 0K”)
K
K-H 0
l l
Ground ' K.”
Stole Levels
K O
K K
K-l O
-|
K-I K

J-l 3' (PH

50

Furthermore, when a molecule has a non-zero inversion
splitting, the ground state combination differences associat-
ed with the + inversion vibrational ground state only (or
the - inversion ground statel,should be fit simultaneously
since effectively the B°,DoJ and DoJK are different in the
+ and - inversion ground states.

In the event that the "ground state" is the lower level
of a hot band (12),care must be exercised since the .ex-
pressione relative to ground state combination differences
in this chapter apply, strictly, only to the case where the
ground state is the vibrational ground state, the so called

"zero vibrational state".

Sim it eou R 8 ant tion of 1
Nine Zypes of Ground State
Combinat on Differgncgs _
In the literature one generally finds distinct indivi-
dual expressions for the "different" ground state combination

differences given,e.g. as

AKRK(J)-AKQK(J+1) = 2<Bo-K293K>(J+ll-4D3(J+"3 (4'23)

AKQK(J)-.AKPK(J+1) = 2(Bo-K2DgK)(J+1)-4D2(J+ll3 (“'2”)

AK AK _ 2 JK J J 3

PK(J-1) PK(J+1) _ [4(Bo-K Do )-6D01(J+%)-8D°(J+§24.26)
On the surface it appears that one has at least two

irreconcilable expressions,and that if one had,for example,

ten combination differences represented by Eq.(4.2a) and

51

two represented by Eq.(4.2c), the two represented by Bq.(4.2c)
could not be combined with the other ten. Or in another
instance, if one had data for ground state combination
differences from two bands, one of which yields' data repre-
sented by Eq.(4.2a) and the other represented by Eq.(4.20)
it would seem that there was no way, other than by averaging
the resulting values for the constants, of combining the
data to get the best ground state constants. A different
mistake is sometimes made regarding ground state combination
differences, i.e., one might think that since
(R-P) = (R-Q) + (Q-P)

(for appropriate J values), no new information is contained
in the third possible difference (e.g. Q-P, where R-P and
E-Q are also known). This neglects to take into account the
manner in which the data is fit, i.e., the way in which the
three members enter into the normal equations involved in
the least squares fitting of the data.

We have been able to write a single expression which
represents simultaneously all possible ground state combina-

tion differences. This relation is given by:

AK
A"<K.AK.J.AJ,.AJ2) = AKAJ1K(J-AJ1)- AJ2K(J-AJ2) =
2 JK “J } __ .
{Bo-K Do -"o [2J€J+1)- elf-£2] (.S1 52) (4.3)
where
51 =-. (2J+1-AJ1)AJ1 , 1 = 1 or 2. (4.3a)

This expression simultaneously represents all "nine"
types of ground state combination differences; this

\T‘l
h)

expression allows the simultaneous least squares analysis
of all ground state combination differences of a particular
molecule thus leading to the statistically most favorable
results available from a particular set of data.

In making use of Eq.(4.3) it is necessary that the
values of J given below in Eq.(4.5) and Eq.(4.6) be used;
i.e., calling the combination difference

AK

A"(K,AK,J,AJ1,AJ2)=AKAJ1K(J-AJ1}- AJ2K(J-AJ2)
=AJ‘,AJé,K,J (4.4)
we have from parallel bands
QRK(d-1) - QQK(J) = RQK,J a
QQK(J) - QPK(J+1) = QPK,J b (4.5)
QRK(J-1) - QPK(J+1) = RPK,J c
and from perpendicular bands
RQK(J) - RPK(J+1) = QPK,J a
RRK(J-1) - RQK(J) = RQK,J b
RRK(J-1) - RPK(J+1) = RPK,J c (4.6)
PQK(J) - PPK(J+1) = QPK,J d
PRK(J-1) - PQK(J) = RQK,J e
PRK(.r-1) - PPK(J+1) = RPK,J. r

53

It should be noted that these differ from Eq.(4.2a) in
the J value used relative to Eq.(4.2b) and Eq.(4.2c); also,
we point out that A" is independent of AK except that both
transitions used in the binary combination must have the
same AK. 14

Equation (4.3) then allows one to make full use of each
ground state combination difference obtainable for a parti-
cular molecule and leads thereby to the statistically most
favorable set of molecular constants Bo,Dg, Dix which can
be obtained from a given set of infrared spectral data. In
Chapter 8 the methods described in this chapter are applied
to a perpendicular band of CHEF. In this case however, good
values of the constants 30’ Di and Dix are already available
from the microwave spectra of pure rotation transitions.
However, if the pure rotation spectra is not observable in
the microwave region as is the case for CHD3 and CHBD
(which have a very small permanent dipole moment),we can
obtain statistically favorable values of 30' D: and DgK
following the method outlined in this chapter. This was
done for two parallel bands, v2 + v of CHBD and v1 + v2

3
of CHD3,and is discussed in Chapter 9.

 
     

Ass cut 0 Tr

In the case of axially symmetric molecules which possess

 

14That is, both transitions in a given combination
difference must come from the same subband.

 

54

a permanent electric dipole moment, analysis of the pure
rotation spectra in the microwave region yields very accurate
values of some of the molecular parameters for the ground
state, i.e., so, Di, DgK. The methyl halides, a family of
molecules of particular interest in this work, have been
thoroughly investigated by microwave spectroscopists (52-59),

and accurate ground state constants are available. In these

J

cases, as well as in cases where good values of Bo’ Do' and

Dix are available from infrared data, the ground state
combination differences may be computed and the numerical
values used as a valuable aid in the assignment of transi-
tions in complex spectra. This was done in the case of the
perturbed band v3 + v4 of CHEF discussed in Chapter 8 and
proved to be very valuable in assignment and analysis. Any
modest size computer may be programmed to perform this com-
1, AJ2)
may be obtained. Appendix II contains such a table for

putation so that complete tables of A" (K, J, AJ

15

CH F, Appendix III, for CHD}, and Appendix IV, for CH3D.

3

Simultagegus Rgpresentgtion of

Upper Stgte Compingtion Diffiggencgg

In the event that one has an unperturbed band or bands
of an axially symmetric molecule which allows one to obtain
a number of upper state combination differences, one can

perform a simultaneous least squares analysis. The appropriate

_‘._

15por C p, Bo , Dg,and D JK were takenC from the results

of microwave psctralm ysig (58). For CHBD and CHD the
values of B , DE , and Dg were obtained from our analy is

(Cf. Chapter 9 ) e

-mr'hnfi ‘ ....AI.

55

combination differences are
AK AK
A'(K,AK,J,AJ,AJ2)= AJ‘K(J)- AJ2K(J):AJ1,AJ2,K,J (4.7)

and the resulting expression for the upper state combination

differences may be written as
AKm,)K(J,)-AK(AJ2)K(J2)=
{[so-§.gvs].[§llglt3 [K+AK]+ (4.8)
[43319.2 FsJKVs] f(K+AK)2J +
[-Dg+§PsJV33 [2mm ). 5,. 521] ( 51-52)

with g .
61:(2J+1+AJ1 )AJi , 1:1 or 2. (4.9)

Thus, using Eq.(4.8) one may analyze simultaneously the

three "types" of upper state combination differences from

a parallel band, i.e.,

Q, -Q -

RK(J) QK(J)—RQK.J - a
QQK(J)-QPR(J):QPK,J ' b (4.10)
QRK(J)-QPK(J)=RPK,J c

or the six from a perpendicular band
RQ (J)-RP (J)=QPK J a
K K ’
R. R _
EK(J) QK(J)—RQK,J b

ER (J)-RP (J)=RPK,J c
K K

 

56

PQK(J)-PPK(J)=QPK,J d (4.11)
PRK(J)'PQK(J)=RQK,J e

P _p _

RK(J) PK(J)_RPK.J r

One must of course realize that due to the difference
of the various upper state constants from band to band,
upper state combination differences from only one band may
be fit simultaneously.

In the case of a parallel band with all A = O in the

t
upper state 16 the term containingrzi is identically zero
and must not be included in an analysis of parallel band
upper state combination differences.

In the event that a band is perturbed by a perturba-
tion of known form,it may sometimes be possible to modify
Eq.(4.8) to include the effect of the perturbation and
still carry out the upper state combination difference

analysis.

 

16An exception to this is the case of a parallel band
which is one component of the band Vt + vt' for example.
Here the lzfl term must be retained.

 

CHAPTER 5

ANALYSIS OF ROTATION-VIBRATION SPECTRA OF AXIALLY
SYRMETRIC MOLECULES USING A COMPUTER
PROGRAMMED ANALYSIS SCHEME

The analysis of rotation-vibration spectra is facili-
tated by the use of electronic computers. We use a computer
in our analysis scheme because of the ease, speed, precision,
and accuracy with which the computer can carry out the varied
and often quite complicated numerical calculations required.
However, many of the considerations discussed in this
chapter should also be useful for an analysis carried out
with a desk calculator. None of the computations are
impossible to perform on a desk calculator, although it
would be a rather Herculean task in some cases.

Before one begins to make use of the computer it is
necessary to identify the observed transitions in the
spectrum, i.e., to assign the quantum numbers of the ground
state, and the changes in the quantum numbers for the
transition being considered. The discussion which follows
is based on the assumption that one uses only transitions
which have been correctly identified and that the numerical

values of the frequencies of the observed transitions are

 

58

available.17

In order to perform an analysis it is necessary to set
down an expression for the transition frequencies which
will be used in the analysis of the spectrum; the analysis
is then carried out by the method of least squares (50,60,61)
which gives the best unbiased linear estimator of the

).18 From the analysis

transition frequency expression (50
we can also determine certain statistical information about
the molecular constants which are determined.

The description which follows is divided into two
parts; the first concerns the computer analysis scheme,
the second concerns the transition frequency expression to

be used.

 

17In the process of'assignment, several specific aids
(apart from experience) are available. The absence of
transitions for which Kj> J in either the lower or upper
state is an aid to unequivocal assignment of the quantum
numbers of the observed transitions (12). Relative inten-
sities also provide an aid to assignment (12); however,
they cannot be considered to be of the same quality as
considerations relative to missing lines since intensity
anomalies are not a rarity. A great aid to assignment is
the use of grounSKstate Sombination differences. If good
values for B , Do and D are available, the various ground
state combination differences can be calculated. Then, if
one transition of the binary pairs in qu.(4.5) and (4.6)
has been identified, the frequency of the second member of
the pair may be calculated.

18The transition frequency is assumed to be a linear
function of the molecular parameters, an assumption borne
out in all the expressions we have used.

.- .-—~ “...—- -- m. I I'

. -. “...—V

a1 sis Scheme d
Computer Pregrap

In this section we assume that a specific transition
frequency has been selected. 8.8..
' I v=a+b(JAJ)+c(J+AJ)2+d(KAK) (5.1)
where a, b, c, and d are molecular constantsisuch as
30' D3, etc.) or combination of molecular constants. Further-

more, we have n sets of data labeled

{K1, J1, AKi, AJ1, v1} (5.2)

for. the n observed transitions of frequency v1.

The mechanics of the analysis scheme involves comput-
ing the normal equations (50) given in Table 5.1 for a least
squares analysis based on Eq. (5.1) (or whatever equation is
to be used). Then, the normal equations must be solved ‘9
for the numerical values of the constant coefficients
(e.g., a, b, c, d in Eq. (5.1)). In the process of the solu-
tion of the normal equations it is valuable to find the
inverse of the normal equation matrix (50) since the inverse
is utilized in the statistical interpretation of the results.
The numerical values of the constants obtained from the
least squares analysis (e.g., a, b, c, d in Eq. (5.1) ) are
used in the line frequency expression (e.g., Eq. (5.1) ) to
CalCfilate a value for each observation, viobs' The calculat-

ed value 13 called vicalc’ and the difference

 

 

‘9 The normal e uations for a frequency expression used
to find p constants e.g., a, b, c, d in Eq.(5.l)) form a
set of p simultaneous linear equations.

6O

 

 

Ag}; SW u

«A 6 8+5 a w

_b<_b_sw u -

SW n

«33;: N e + A_v.<_5«A_b<+..3 N o + rainbow N a + .82; No
Axexeafew 8 + agatewo + «12.8225? + «eatewo
Afflxzeqeew e + «A_b<+_BA_.2_3W o + «EVEN h + ..bqb We

._x<_x W e + NAH<+§W o + HQHW a + AWo L

 

.A: 2 _ Eat _ .26 2:3 =3.A_.mv.aw .8 9.2833 .2502 _.m 29o...

 

61

A1(o-c) = v, -v, (5.3)

obs calc

is computed. The sum of the squares of the A1(o-c) is also
formed for use in statistical analysis.20 If n observations

v1 are used, and p constants determined, then

= Elmo-e12
n-p

 

A2 (5.4)

is an unbiased estimator of the variance of the parent
statistical distribution of the errors in the observations
(50)e We 0811

(Ci-0)] 2 e

P

 

E f.
n-

the standard deviation of the points, i.e., of the obser-

vations v1.

In addition, if the generic constant determined is
b3. then the corresponding diagonal element of the inverse
of the normal equation matrix, 113?, is related to the

Standard deviation of the constants determined as (50)

Aha: $2N351 (5-6)

and the simultaneous confidence interval (50) for the
"true" value F 3 of the constant estimated by b: with a

k

 

20The statistical considerations described in this
ghepter have been taken from a recent Doctoral thesis by

62

confidence coefficient (50) of (l—o) is given by

where

s = pFa(p,n-p) (5.8)

p is the number of constants determined, n is the number of
observations used, and Fa(p,n-p) are tabulated values of the
F distribution (62, 63, 64). One interpretation which may
be made regarding the confidence interval b3 i Shh is that
if we consider the data used, 1.8. a particular spectrum,
to be a sampling of an infinite sample population, i.e., all
conceivable records of the spectrum obtained by whatever
observer, wherever, whenever, the probability that b: :tSA-D
will contain the "true" value of the constant /8 3 for our,
data is (l-a). 21

Furthermore, Doyd (50) points out that the test to
determine whether a particular b, is significant in the fit
Of the data, i.e., whether the data depends significantly
“Pm the term of which a particular b: is the coefficient,
is Performed by comparing the ratio lb3 l/Ab with S. If

, b
El > She significant
b") (5.9)
[1535' ( 13$ not significant
1

21Boyd (50) presents a more detailed discussion of the

use Of simultaneous confidence interVals in the analysis of
SDi:ctral data.

then a term is found to be significant it is of course

retained in the fit. If it is insignificant it should be

dropped from the fit.22 In this case there are two possible

interpretations. They are, that no such term should be in

the expression used or that the data used is not sufficient

to determine the constant coefficient of the term.

The foregoing analysis scheme has been programmed for
the Michigan State University digital computer, MISTIC (65).
The program DAEA embodies a flexible symmetric top analysis
scheme patterned after the above discussion.

Data is punched
on IBM cards as

AK AJ K,J frequency Av weight
E Q 0,5 0000.0000 .0000 00.00
where weighting (50) may be effected using either the weight
or the Av taken, of course, from the appropriate card columns.
The latter is assumed to be related to the weight w as

.1» 2
w = ill-3% (5.10)
Equation (5.10) implies the assumption that the errors in
the observations, i.e., in the v1, are statistically random-
1y distributed and all removable or known biases removed.
The N‘orm simply allows one to. obtain an average weight of l

regardless of the quality of observations used in a least
I3(mares fit.

E

22"For a derivation of these results as well as a more
detailed discussion, of. Boyd (50).

64

The polynomial to which the data is to be fit is
specified by the program user. For example, Eq. (5.1) may
be specified with punched tape input to the computer as

FO.= 1.

F1 = 3x5.

F2 = 3x3+3x5+315+5x5. (5.11)
F} = 2x4.

N = 6.

where the indices 1,2,3,4,5,6 refer to 1,K,J,AK,AJ,v,
respe ctively.

Upon input of the polynomial specification tape and
the data cards, the computer executes a least squares fit
of the data, and outputs the least squares estimators of the
constant coefficients,23 the standard deviations of the
constants, i.e., the Ab 's, the calculated v and the observ-
ed V for each point fit,‘ the A1(o-c) for each point fit, and
the standard deviation of the points, i.e., the A.

In addition, provision is made to compare other observa-
tions not included in the least squares fit and also to
calculate additional transition frequencies.

The use of the computer programmed analysis scheme
allows the spectroscopist to take advantage of the generalized

*

23The program employs double-precision floating point
erlthmetic which is equivalent to approximately 20 decimal
d1Sits. Solution of the normal equations is accomplished
by a Grant reduction (66) and round-off error for a well
conditioned set of equations has been found to be insignifi-
cent for a 13x13 normal equation matrix. .

65

transition frequency expression in Table 3.1 to analyze
simultaneously, for example, all transitions observed in a
single Perpendicular band. In general, if one were forced
to rely on a desk calculator, it would not be feasible to
attempt to simultaneouslyenalyze all transitions of a
given band, determining for example nine constants from
315 transitions as was done by Boyd (50) in a simultaneous
analysis of both'the parallel and perpendicular components
of 2v), of CD31. In addition, as was pointed out in
Chapter 3, simultaneous analysis insures consistency of
analysis since it prevents one from obtaining and using

several values (however nearly equal these may be) for the

same constant, as happens when one analyzes one subband at
a time (4).

Method of awsig apd ggneraiizgd

Tr sition Ire uenc 83-
Suitable {or Emel-

We shall outline the approach we use in the analysis
°f a Perpendicular band vn + Vt of an axially symmetric
m°leeule of the form ZXY3. The very same approach may be
used for a parallel band or a combination of bands.

The first point to consider is the question of linear
independence of the terms to be fit to the date.“ Essen-
tially, linear dependence, which makes the solution of the
normal equations impossible or meaningless, results when

—._

24For a detailed discussion of linear independence in
reference to 2V4 ll and J. of CD31 cf. Boyd (50).

Ire-.- nob-M—~
all "y

66

a given quantum dependence of a constant to be determined

is a. linear combination of any of the quantum dependences

of the other constants to be determined. For example,

because of linear dependence it is not possible to determine

individually A0, aA, Ci, v0, r13: and D0K from a single per-

pendicular band of the type Vn + Vt. One can only obtain

linear combinations of these constants from such an analysis.

Using the generalized transition frequency expression
from Table 3.1, taking care to avoid linear dependence, the
most general transition frequency expression suitable for
analysis of Vn + Vt is given in Table 5.2. The selection
rule Al. :AK, from Table 2.1, is incorporated in the expres-
sion given in Table 5.2. In addition, all sums appearing
in Table 3.1 except the one involving ntfi are written out
explicitly.

Using the expression in Table 5.2 it is possible to
perform a least squares analysis of the assigned transitions
and frequencies of the band Vn + Vt. We have found that an
efficient way to proceed is to fit the data to a first
approximation to the expression of Table 5.2 to check assign-
ments and measurements of frequencies. The reasoning is
that a "low order fit" of the data will indicate errors of
this sort since there are only a few variables available to
the least squares fit to be adjusted to best represent the
data. On the other hand, if the full expression of Table
5.2 is used in preliminary analyses, there are so many

Variables to be adjusted that errors in assignment or measure-

67

 

+7 2+3N b+ Ab<+.+.2 A2753 .5

 

LAISBba x + Abni+bxh<+3~§<+xv f

 

+ Tb<+_+BAb<+bT=:maxs“ex? “Km- “Knmnws

 

 

 

 

 

 

LAN x<+x<x~T -.oAb<+.+3Ab<+3:

 

 

 

 

+9 x+ Agni; “=54:

 

+ TAx<+xT:hAe.m:2%A+MNN+ me+mXW+md maizaxu SWAN: 4.8m exm.

 

 

+T x4+x3£7 9m: AMw+ ..3.5W_ Wench; “u < 04

 

 

a

a

i

m:
:efé a:
a:

I

i

i

+_H.?._IIA.«N|~.V.+»33FW IN..+ gel _+ ”mum .4:

 

xenc.

 

 

x
"E 23

 

 

 

 

..A + a; .0 stress 3.33 Boo. 2: 3. 23:3 57.3.98 3:33: c .

9:26: 33.2280 Nd 03o...

68

 

_H~Ah<+_+.3~Ab<+3H=.. “Q + “QH

 

+ mAh¢+IBAb<+B~Ax<$2me Jami

 

 

 

+ T<Ax<+xxb<i+bxb<+£AMA;

 

swatcoo ND Eco...

 

69

ment may easily be concealed.25

Using the theoretical order of magnitude Tables 3.1 -
3.12 for the appropriate types of transitions involved, it
is a straightforward process to obtain a first approximation
to the expression in Table 5.2. Assume that we have transi-
tions up to K5510 and Jzzo and of the type RRKU) and
PPK”). Then, from Tables 3.3, 3.9 and 3.10, taking terms
through third order,26 the appropriate expression to begin
with would be the sum of the terms a,b,c,f,g,h,i from
Table 5.2.

If as mentioned in Chapter 4, good values of the con-
stants Bo’ DE), D3} are available from microwave spectroscopy
studies, these values should be substituted into the
expression from Table 5.2 which is used and the value of

the terms for each transition subtracted from the observed

frequencies.27

‘

2E‘Admittedly, the value of the constants obtained from
8“Ch an erroneous high order fit could indicate the presence
°f errors. Even so, the deviations of the observed and the
calculated transition frequencies would not indicate which
I~‘a.nsitions were in error as readily as in low order fit.

26These are expected to make a contribution to some
t'I‘ansitions of approximately O.O2cm"’1 or greater on the
Essie of the theoretical magnitude of the constants in
able 1.8. .

27In the event that one uses a desk calculator to carry
Out an analysis, the observed frequencies can be modified
in this manner one time only, and the resulting modified
frequencies used in all subsequent calculations.

 

.. It

It‘-

I v

‘

7O

whenever, as for many molecules of the 03v family,

J JR
D DO

30’ o

and are known from microwave work, we shall
assume that the dependence of the observed frequencies on
these constants can be eliminated. Thus, as a first appro-
ximation in the analysis of Vn + Vt the expression given in
Table 5.3 would be suitable.

J

Since we assume Bo’ Do and DJK

o to be available, the

first approximation used contains only four variables which
may be adjusted to obtain the best fit, i.e., Vo‘AeCi’
Ao-AeCi, cfiwfi, and sang. Under these conditions errors
in assignment and measurement have been found to be readily
located by scanning the A1(obs-calc) results.
After all obvious errors have been eliminated, and
the results of a fit to the expression of Table 5.3 have
been obtained, the constants determined should be tested
for significance as indicated by Eqs.(5.9). We shall assume,
as is usually the case, that all constants from the fit
based on the expression of Table 5.3 are significant. (If
any are insignificant, they should be dropped and the data
refit to the remaining expression.)
At this point, one proceeds by fitting the data to the
exDression of Table 5.3 plus each of the remaining terms
in Table 5.2, one term at a time. That is, we would fit the
expression of Table 5.3 plus 6. from Table 5.2, then Table
5.3 plus e, then plus 3, then plus 1:, then plus 1. The
significance of d,e,3,k, and l is then tested with

71

 

$313332 ..E s+ a:

 

+7333: E d: “on :6...

 

 

an
+ TafvaxNZM m. .4 33
+..“: -..;

 

u Talus?«Ab<+_+2~Ab<+bLo ea

 

+ TIE so.+Ab<+_+BAb<+B~qu+xLawe

 

Tlll
xotc.

 

 

+ Taxq+x<x3+ As<+_+3A2+sLom

Il'lllllllllII'II'IIIIIIIIII

 

. .a + as ho mAmzoco >3£E=2a 2: .8 No 232. s 5.33..qu 2: no 3.58??qu Ame... men rich

 

Eqs.(5.9)28 and the most significant term (largest
ijl /1lb ) added to the expression of Table 5.3. Assume

that d wasjthe most significant new term and call the
expression of Table 5.3 plus d from Table 5.2, Eq.(x). The
process is now repeated fitting Eq.(x) plus e, Eq.(x) plus
3, etc. Then e,J,k,l are tested for significance, adding
the most significant term to Eq.(x), and repeat the process
uurtil no new significant terms remain after the last fit
performed.

When all significant terms have been included in the
analysis, we may assume that we have gone as far as we can
if the spectrum is unperturbed. In the case of perturbations,
the best procedure to follow is not as straightforward and
will be discussed in the following chapters.

At the termination of the analysis one has the estima-
tors of the molecular constants, their simultaneous confi-
dence intervals, the standard deviation of the points
1Jicluded in the analysis, and a table of the calculated and
obsorved frequencies and the difference A1(obs-calc).

One of the advantages of proceeding as outlined lies in
the fact that a consistent analysis will be obtained in a
BYstematic fashion and that the confidence intervals for
the molecular parameters are obtained in a systematic,-

Statistically based, reproducible manner.

__ A__‘_

28Note that as each new term is added to the fit, p

in Eq.(5.8) increases by 1 and thus the value of S changes.

CHAPTER 6
PERTURBATIONS IN THE SPECTRA OF AXIALLY SYMITETRIC MOLECULES

With the advent of higher and higher resolution of
infrared spectrometers, more and more anomalies have been
noticed in the near infrared spectra of small molecules.
Particularly in the region from about 3000cm"1 up, in which
overtone and combination bands normally occur (12), many
pexrturbations giving rise to anomalous spectra have been
seen (1). A major cause of these anomalies appears to be
accidental resonances between overtone and combination levels.
Since, for the most part, accurate anharmonic constants are
not available for ZSXY3 molecules, and since in general each
of these molecules have several.low lying fundamentals on
the order of lOOOcm"1 or less, the a priori calculations
needed to sort out unambiguously the possible resonances,
are at best difficult to perform satisfactorily.

As a result, one desires a systematic approach to the
PrOblem of anomalous spectra which will allow the maximum
1111‘ ormation about the form and cause of the perturbation which
has to be obtained from the meager amount of a priori infor-
mation which is, available.

In this chapter a brief review of rigorous perturbation
treatments applied to axially symmetric molecules is presented,
followed by a description of the method due to Amat (7) of
systematically treating the anomalous, i.e., perturbed,

spectra which are observed.

73.

Origin of Anomalies in
Observed Spectra

These anomalies are due in general to essential or acci-
dental resonances between energy levels of the molecule. An
essential resonance is a resonance between energy levels of
a molecule due to the symmetry of the molecule. Essential
resonances only occur within a single rotation-vibration
band, i.e., 2: “’5 = o for the matrix element Causing the
perturbations. For example, lo-type rotational resonance 29
between the K'=:I:1, t=i1 levels of a doubly-degenerate funda-
mental of a 2X!3 molecule is an essential resonance. This
resonance can exist for all ZXY3 molecules due to symmetry,
independent of the character of the constituent atoms. An
accidental resonance, on the other hand, is a resonance
between energy levels of the molecule due to the fortuitous
cOmbination of molecular parameters. For example, the Fermi
resonance between v1 and 2v5 of some ZXY3 molecules is an
aJ-“Z‘idental resonance. Accidental resonance may occur within
a Single rotation-vibration band or more commonly between

two or more different rotation-vibration bands.

‘2? evious flop]: on Perturbed Spectra

There have been many perturbed spectra found and some
have been analyzed in the past. In the spectra of C3w,mele-
cules, one of the more striking perturbations, due to a

Coriolis resonance, has been illustrated by the work of

29This is generally called t-type doubling.

 

75

Nielsen and his ce-workers on XY} molecules (8-11,67-69).
Nielsen and co-workers have lately referred to this effect

as giant L-type doubling since it is similar to A-type doubling
observed for linear molecules. The effect manifests itself
in a shift of the RR‘,(J) and RP°(J) lines relative to the
Room) lines. An example of this splitting in the K'=t=ii
levels of v3 4- v4 of CHEF is discussed in Chapter 8..

Other work on rotational resonances has been done by

Benedict and co-workers on the NH3 molecule (33,70,71,72).
In addition,considerable other work. has been done on perturba-
tions both theoretical and in the interpretation of spectra

(7 , 1 8-21,24,28-31 .73-84).

Reziew of the Approach to Analysis
of Perturbed Spectra

The general problem of perturbed spectra is complex
and, although the theory is relatively straightforward, the
application in particular cases is often discouragingly
Cu~1'ficult. At this point we review the general problem of
mOlecular spectra and show in general how one arrives at and
t”Pests perturbations in spectra. Recall that we began with
a classical Hamiltonian (22,23) of the non-rigid vibrating
I'O‘tor developed from a model of nuclear point masses in an
anharmonic potential field due to the atomic electrons.

The classical Hamiltonian was then transformed into a
quantum mechanical Hamiltonian and subsequently expanded in
a power series of the normal coordinates of the harmonic

vibrator ( 13 ) .

’3
Ct

Then, after collecting terms of the same order of magni-

tude, the Hamiltonian of Eq.(1.1) results. As pointed out

in Chapter 1, this Hamiltonian is diagonal with respect to

J and M but may have elements which are off- diagonal in

vs, ‘8’ m8, and K. However, H0 in Bq.(1.1) is diagonal with
respect to all quantum numbers. The first contact transforma-
tion performed on Eq.(1.1) results in Eq.(1.2) such that the
first order Hamiltonian is now diagonal with respect to v8.
The second contact transformation performed on Eq.(1.2)
results in Eq.(1.3) such that the twice transformed Hamil-

tonian h" is diagonal with respect to vs through terms of

the second order of magnitude. As pointed out in Chapter 1,
terms in h; which are off—diagonal will not be expected to
contribute before sixth order, etc. Thus in the absence of
essential or accidental resonances, the diagonal elements

of the twice transformed Hamiltonian give a good representa-

tion of EVR through third order.

For axially symmetric molecules, h; and h; are diagonal

with respect to all quantum numbers. ha, however, may have

elements which are off-diagonal with respect to K and ‘s (16)
While higher order Hamiltonians h; may have elements which
are off—diagonal with respect to vs"s and K. Since the first
part of the twice transformed Hamiltonian in which off-diago-
nal elements occur is h; (as indicated in Chapter 1), the
lowest order to which these may contribute in the absence of
essential or accidental resonances is the fourth order (21).

Thus, in the. unperturbed case, i.e., in the absence of

77

essential or accidental resonances, the diagonal elements
of h+ are a good representation of EVR through third order.
However in the event of essential or accidental resonances
this is no longer the case, so that the secular equation
given by Eq.(1.5) must be solved.

There is, however, an important point to consider. In
performing the contact transformation, certain resonance
denominators appear in the transformed Hamiltonian (19,20,24).
These are of the form 1/(CUS-'aé.) and in the event that any
cosaeco§.,-the transformed Hamiltonian "becomes infinite".

In these instances, Nielsen has shown (19,20,24) that the
transformation function used in the contact transformation
may be modified to eliminate the resonance denominator and
preserve the contact transformation. In many other instances
however, these resonance denominators are not the problem

and a resonance results not from we ”ws' but from
EVR(v8,£s,...J,K)2$EVR(vsytac,...J,K+AK). (6.1)

In the latter instance, the secular equation of Eq.(1.5) may
be solved without using a special transformation function to
preserve the contact transformation.

A detailed resume of the exact treatment of accidental
or essential resonances is beyond the scope of this work and
reference is made to the work of Nielsen, Amat and co-workers
(8,11,18-20,24,28-31,67-69,73-77). The exact treatment is
very complex and quite often requires the solution of secular

equations of order three and higher.

78

In these instances it is not generally possible to
solve the secular equation in closed form. One may either
substitute approximate (or "guessed") values of the required
constant coefficients into the secular equation and solve
it numerically, and then perform iterative solutions, or as
is possible in some cases, obtain approximate solutions in
closed form by neglecting certain terms in the secular
equation which are assumed to be small. In general, the best
that can be done is to demonstrate that a given off-diagonal
element(s) could produce the effect seen,and an approximate
form of the perturbation may sometimes be found. One notable
exception is the case of a first order Coriolis resonance

which will be discussed in detail in Chapter 8.

S te tic A 0 ch h l
o Pertur ed Spectra

In 1962 at the Symposium on Molecular Structure and
Spectra, Professor G. Amat presented a systematized approach
to the treatment of perturbed spectra (7) which, while not
possessing the complete rigor of some approaches, makes it
possible to attack the problem of anomalies in the observed
spectra of axially symmetric molecules 30 in an orderly
manner. However, while approaching the problem in this
orderly manner does not guarantee a complete solution of a
perturbed spectrum, it does provide a good method which will

F

3°Parts of the following discussion are the result of
several discussions with G. Amat,and much of thds chapter
follows rather closely an invited paper by c. Amat. (7)

79

enable an investigator to proceed as far as the available
data will allow. Ior ZXY3 molecules, the lack of good an-
harmonic constants makes a complete solution of a perturbed
spectrum at best a very difficult task.

Consider two energy levels which perturb each other, viz.

621

6b

where E3 and Eb are the unperturbed energies, and 6&3 and

6b are the resulting energies of levels a and b when the
perturbation is taken into account. In order for a perturba-
tion to exist, there must be some matrix element of h+

coupling the two states a and b such that
E: <a|h+|b># 0, (6.2)
Thus, the resulting secular equation, giving the perturbed

energies is

a . __—--_ o (6.3)
“s, Eb "’ é

 

 

which has the solution in closed form.

 

1

313' 13-352
6 :: a bi: \/(a b) +112 (6'4)

 

 

2 2 .

As yet unexplored are considerations regarding the possible

80

states a,b,c... which may be coupled by a perturbation, as
well as the form of W as a function.of the quantum numbers
of the levels coupled by the perturbation, and any possible
analytical expression for Ea'Eb as a function of the molecular
constants and the quantum numbers of levels Ba and Eb’

In the following, it will be found that from a knowledge
of the form of the unperturbed energy levels, as presented
in Chapter I, a relatively simple expression, as a function
of the relevant quantum numbers, can be given for the separa-
tion of the unperturbed energy levels, i.e., Ea-Eb. A prac-
tical problem.arises, even though the expression is relatively
simple, since at the present time, very Often the molecular
constants involved in the expression Ea-Eb are not known
with sufficient accuracy. Furthermore, the large number of
accidental resonances possible in the 3000-6000cm" region
complicates the matter further since this means that we do
not know the position of the unperturbed levels and makes
the extraction of the "unperturbed" molecular constants
difficult if not impossible.

The possible couplings of levels which may enter into
a perturbation will be explored so that all those disallowed
by symmetry considerations may be eliminated. This is
especially helpful since without these rules many couplings
would also be considered which in fact are identically zero
due to the symmetry of the molecule. The possible forms of
K as a function of the quantum numbers are also presented

according to the scheme of Amat (70,and an orderly approach

 

.Ivllv..l.-‘ vvt,ob|.'ln.4w.v.l‘.b ‘
e. >. , .

..w.
u .‘ PFH

\

L I.

81

for obtaining information about perturbed spectra is indicated.
It should be noted, however, that the problem is so complex,
and so many considerations are involved, that each perturbed
spectrum is somewhat of a special case,and that proceeding

in the manner outlined in this chapter does not guarantee

a complete solution.

If [Ea-Ebl << lWI,the resonance is said to be a strong
resonance, whereas if IEa-Eb|)>[WLthe resonance is said to
be a weak resonance. The order of magnitude of W is said to
be the order of the resonance.* However, the order of magni-
tude of w is not necessarily the order of the Hamiltonian
h; in which the perturbation matrix element occurs (7).
Considerations regarding the order of magnitude of a perturba-
tion are rather intricate and reference is made to the paper
of Amat and Nielsen (18) for a clear presentation of these
considerations. As mentioned above however, an estimate of
the magnitude of the perturbation may be obtained by consider-
ing the magnitudes of 'Ea'Ebl and le in Eq.(6.4).

In the event that three energy levels perturb one
another, the secular equation is more complex, with no simple
solution. Let the levels a,b,c be involved in the perturba-
tion. Then, it is possible that the coupling elements are

(a |h+| b)

I:
II

(a |h+| C) (6-5)

W = (b If” c)

82

which results in the secular equation

 

 

Ea—é 3:1 B2
w] Eb-e w} = 0. (6.6)
W2 W3 EC‘E

This case will not be pursued further at this time.

Rules Thgt Determine Which Levels
ng Perturb One Another

An important consideration is the question of a parti-
cular coupling of energy levels. For example, if E8 and Eb
are the two levels in question, under what conditions is a
perturbation possible? First, only levels of the same J
value may perturb each other, since h+ (and in fact H and
h') is diagonal in J, i.e., <?a_lh*I J5) = w SJan whore
SJan is the Kronecker symbol. Second, Amat's rule (49)
indicates specifically which matrix elements of h+ are
identically zero due to the symmetry of the molecule, so that
the matrix elements of h+ which may result in a perturbation
are indicated. When applied to a given symmetry group Amat's
rule establishes the conditions on Ka'Kb"a"b in order that
a perturbing matrix element (a lh“ b)’ may exist. Amat's

rule applied to 03v molecules 3' may be written as

‘1;

—A

31Care must be exercised here since the rule takos on a
different form for different point group symmetries.

8}

where AK 2 K‘-Kb and A‘t 3' ita-‘tb and where P = 091,2939ooo
Thus the conditions on the levels E8 and Eb under which

a perturbation is possible are:

Ja = Jb (6.8)
and for 03v molecules
(Kg-Kb)-§(Lta-£tb) = iEp (6.9)
or equivalently
AK'§A‘t = iEP. (6.9a)

In addition, there must be a term in h+ which has
matrix elements corresponding to the coupling conditions.
Method of termin i P ticul

tion E ment E ists n h+

In order to ascertain the possibility of a given
coupling in so far as the terms of h+ are concerned, it is
necessary to have tables of the matrix elements of q8,pB and
Pa as well as tables of the terms in h*. Table 6.1 contains
the matrix elements of q8 and p8 for the one-dimensional
(non-degenerate) harmonic oscillator (85,86), Table 6.2
contains the matrix elements of q8 and p8 for the two-dimen-
sional (doubly-degenerate) harmonic oscillator (86). Table
6.} contains the‘matrix elements of Pa and PQPP (86).

From Table 6.3 higher order matrix elements of Pa may be
found directly by multiplication.

Chapter 1 contains a partial list of elements in h‘.
Many additional elements which have only off-diagonal ele-
ments are available in the literaturo (13-17). A list of

Table 6.1 Matrix elements for the one—dimensional harmonic
oscillator.a'

 

 

 

 

 

v operator f element (vl fl v')
v-1 q, p/ih [v/2] 4;
v+1 q.-P/ih [(v+1)/2]%
V <12 . 132/112 (we)
v-2 <12 , -p2/‘1‘12 [v(v-1 )] 1' /2
v+2 q2.-P2/h2 [(v+1)(v+2)]§/2
v M . -qp -1f1/ 2
v-2 pq . on 115 [v (v-1 )3 aé/a
v+2 pq . qp -ih[(v+1 ) (v+2 )1 ’é/e
v-3 (13 . -I>3/1f13 [v(v-1 ) (v-2 )/8] %
v-1 q3,p3/ih3 3[v/2]3/2
v+1 q3,-p3/ih3 3[(v+1)/2]3/2
W3 q3,p3/1e3 [(v+1)(v.2>(v+3)/8]*
v q9.p4/54 [3/2(v+%)2+3/83
v p2q2 . can? to (we )2-3/ 83112

 

 

8‘From N. Shaeffer, Revs. Mod. Phys.

bFor simplicity the index s (from vs) is omitted throughout

the table o

 

Table 6.2 Matrix elements

harmonic oscillator.a

(v,llflv;t') for the two-dimensional

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Operator f
v' ) t' q1 Q2 1),/h pZ/fi
l
{m m emf-2% engage wily-W «27¢
Fv+‘1 21...: efl'mfi’ e<V——"+2)% e(V———“*2)% e<"“*2)%
. 2 .2 2 2
v-1 m sat-2A2 Jed-21f} awed—2&2 ecgifi
v-1 5 M 42-min +£(V—+‘)’1’ seems .%(V+£)%
‘ 2 2 2 2
Operator f E
' 2 2 2 7
Lv. " Jr; Q1 9.2 Q1QZ 131/112 IDS/112 papa/{12 !
v . l é(v+1) %(v+1) O %(v+1) ‘%(v+1) 0 ;
v . t +2 -B +13 ~13 -B +13 -iB *
v , 1-2 -C +0 +10 -C +0 +iC )
. (
v+2; i -D -D 0 +13 +1) 0 ;
. (
v+2' 1+2 +E -E +iE -E +E ~1E j
' v+2 1-2 +F -F -iF -F +F +iF i
v-2 1 -c -c o +G +G o f
v-2 1+2 +H -H +iH -H +11 -iH ;
:
v-2 L-2 +J -J -iJ -J +J J +iJ {

 

 

 

 

 

o—J

9‘For simplicity the index 8 has been omitted throughout the
table.

Table 6.2 Continued.

86

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

"Operator f
V' " qug/h qug/n ‘11P1/‘5 p1q1/‘fi rrum/”f1 page/an
v 1' +t‘ é! a 4: 4% -%
f v 1+2 0 o o o o o
E v z-2 o o o o o g o
3v+2 1 O O +iD +iD +iD E +iD
v+2 1+2 +E +E -iE -iE .+iE 3 +13
v+2 t-2 -F -F -iF -iF +iF +1?
|v-2 1. o 0 -1c' -iG -iG f; ~19
f v-2 1+2 -H -H +13 +13 -iH -iH
g‘v-Z 5-2 +J +J +iJ +iJ -iJ i -iJ
where
B = §[(v+++2)(v-z)]%
c = :1,-[(v--l:+.’2)(v-I~afi)]é
D = i[(v+.&+2)(v-£+2)] 12‘
E = 1/8 [(v+£+2)(v+l.+4 )] %‘
F = 1/8 [(v-£+2 > (v-M )1 f
G = {FEW-+1. )(v-l. 3%
n = 1/8[(v-A-2)(v-1.)]%
J = 1/e[(v+z-2)<v+z)]%

 

Table 6.3.Matrix elements

(K lle Ke1)
(K Ihyl Kt1)
(K lel K)
(K (PEI K)
(K IP§I K)
(K IPEI'K)
(K lPil K12)
(K IP2| Ki2)

y

(K IPxPyl Ki2)

(K IPnyl Kt2)

(K lPxPyl K)

(K lele K)

87

a
of Pa and P

ap'

 

E7,— (f-K(K:h1)

 

$123;— Vf-K(Kt1)

5117,- K
§€§§'(f-K2)

nip?
8772 ( K )

.EE_.K2
47/2

 

2
h Vf-K KtI
1672 ( )

 

 

-£EL—- f-K
167r2 V (Kid)

 

2
$172???) (f-K(Ki1)

1.2...

 

16772 (Emma)
2
-1_h__.K
87f2

+1-hg— K
8772

3For simplicity, f.§E.J(J+1).

 

lf-(Ki1)(K¢2)

 

Vf-(Ki1)(Ki2)

 

Vf-(Ka1)(K:2)

 

Vf-(Ki1)(Ki2)

 

88

Table 6.3 Continued.

 

 

(K 11> le Ken xi 112 (Ken (Ir-mun

 

 

 

 

 

y 8772
(K lePyl KM) = “81):? K Vf-K(K=t1)
(K lele K11) = 513—2 K [If-K(Ki1)
(K 'PxPy' K11) = 817:2 (K11) Vf-K(Ki1)

 

 

(K lPxPy+Pny| K12) = “513;? Vf-K(K=h1) Vf-(Ki1)(K:t2)

 

2
| = L n
(K lePz-q-PzPy Kit) $18772 (21m) Vt mm)

 

2 _
(K lePz+PzPyl KM) .-.- 3%; (21m) Var-mun

89

the elements of h+ in the generic form used in Chapter 1 is
given in Table 6.4.

From Tables 6.1-6.4 it is possible to ascertain whether
a given coupling is possible as regards the existence of an
appropriate element in h*. Thus, combining the information
contained in Eqs.(6.8) and (6.9) and the information con-
tained in Tables 6.1-6.4,it is possible to determine whether
a given coupling may possibly produce a perturbation in the

spectra.

Egpregsion for the Se tion
of Unperturbed Energy Levels

Recall again the case of two levels Ba and Eb coupled

 

by some matrix element (a lh+| b) = N such that

 

Ea
Eb \\\
E
’b
where the secular equation, Eq.(6.3), has roots
E +E 2
.. .32.); S .2

where ea is 6 using the + sign, 6 b is G using the - sign

and
8.2-z. Ee’Eb (6.11)

is the separation of the unperturbed levels. Fig. 6.1
illustrates the effect of the perturbation W on the levels

Ba and Eb and indicates certain magnitudes of shifts which

90

Table 6.4 Generic form of elements in h+
an accidental resonance. Capable °f PTOdu01ng

 

 

 

 

 

 

 

 

 

 

4..
hm OPerator
h+
4
h; r r3P r2?2
h; r5 r4? r3P2 r2P3
h+ r6 5 4 2

 

91

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e N (e
N3+1lml .l. Qm+0m .I m //
N v /
la.) ~3+~1m1 /
pm llllllll Fl LI l1 l1 / aw
v N 1 N
~3+wd1\. .ml1nMIow
1| N
.w w , am+ow
v N N
~3+~dl lwln nwlow
ow )))))))) .71 1L) 1) I.) \ ow
\\
1m11 «aim. \\
v N 10 A \
N3+mlwl\ 1T Qwrfcw I m
.8286. 3:09:23 .96. 03... ..m .2...

 

KO
F0

will prove useful in the following.

It may be shown by considering the differences of the
unperturbed energy levels given (in Chapter 1) as a function
of the several quantum numbers, that through third order

contributions, for Jz 20, K2510, 5 may be expressed as

S =.a+bK+cK2+dJ(J+1) (6.12)
where,for most cases which we will consider,the term cK2
may be neglected.32 The term dJ(J+1) may be important
especially in cases where (a2 - mg) is of the sale order of
magnitude as the resolution of the spectrometer used. This
will become apparent in Chapter 8 where the term dJ(J+1)
plays an important role in the perturbations observed. As
mentioned above, Eq.(6.12) may be obtained as the difference

between the two levels in question, i.e.,
S = Ea(v8‘80ongKa) " Eb(v3"s"°°J’Kb) . (6o13)

for which a particular example is given in Chapter 8. Note
however that since E3 and Eb are functions of the molecular
constants and the quantum.numbers K and J, the differences
will obviously be a function of K,J and the molecular con-
stants. A practical difficulty arises however5because the
molecular constants involved in S are often not known with

A—

32For a AK = 0 coupling, the term 0K2 is negligible in
nearly all cases. For a AK 2 $1 or greater coupling, CK2
may occassionally be important.

sufficient accuracy to be useful, so that the required
a priori calculations are very difficult (if not impossible)
to perform effectively. At this time we shall consider only
the form of Eq.(6.12) simplified by neglecting the term 0K2,
i.e.,

S: a + bK + dJ(J+1). (5.14)

Up to this point we have given the rules needed to

ascertain the possible existence of a given perturbation
coupling, the method of ascertaining whether an appropriate
term exists in 11+ to provide the perturbation element(s),

and the form of the separation of two levels involved in a

perturbation.

Accidental Resonances

First, we consider the problem of accidental resonances
between the energy levels of two different vibration-rotation
bands. Subsequently we shall consider the problem of essen-
tial resonances, since in so far as the approach used is
concerned, essential resonances appear as a special case.

If we again consider two levels E8 and Eb, belonging
to the same J value, with E8 having v8,v8'... excited whereas
Eb has vs 3
Possible couplings exist between Ba and Eb’ we find the

u,v nu...excited, and seek to ascertain what

answer given by Amat (7).
Considering only the vibrational portion of the problem,
if the vibrational coupling is expressed as

(vn,...vt,... |h+| Vn+AVn,...Vt+AVt,...> (6o15)

.b..-. 1

O

94

let us call

g lAvnl = pn (6.16)
and

§ lAvtl = Pt (6.17)
and

pt + pn = p (6.18)

so that p is the total number of (differences of ) vibra-
tional quanta involved in the resonance, pn the total number
of non-degenerate quanta,and pt the total number of doubly-
degenerate quanta involved in the resonance. For example,if
we are considering a resonance between v1 + 2v3 + v4 and

v2 + v} + v5 + V6 of CHEF 33 thenlAv1l- = 1, Iszl = 1,

)Av3l = 1, [Av4l = 1, IAvSI = 1 andIAv6] = 1 so that
p=6.pn=3.pt=3.

S st ti A ch t P tu b t n
Cou 1

Using the approach discussed in the beginning of this
chapter, Tarrago and Amat (87) have found the possible
couplings for several values of p,pn and pt. The possible
types of couplings are (7,87):

I W
I' w + w'J(J+1) + w"K2
:1 w V?(J+1)-K(Ke1)

 

A

335For the numbering of the fundamentals of xrz molecules
we follow Herzberg (12) where v , v , and v3 are nog-degenerate
and v , v5 and V6 two-fold degenerage, each3 in order of
decreasing frequency.

4wri...'
a ..

1.1.. I. 19.11. 11

III wK .
111 w VE(J+1)-K(Kr1) (/J(J+1)-(Ks1)(Ke2)
v w VJ(J+1)-K(Kr1) fi(J+1)-(Ks1)(Ks2) x

 

 

 

 

 

V5(J+1)-(Ki2)(Ki3)

where W is a constant coefficient for terms in h+ through
rnP3 terms. These include all terms through those contained
in h; (14-17). Tables 6.5-6.8 give the principal coupling34
of each type for several values of p,pn,pt (87). The tables
are self-explanatory except for the subscript on the w, i.e.,
h(n),which indicates the estimated order of the perturbation
for J25K251. The column entitled "Order of Magnitude" gives
the order of the perturbation for JszSO unless otherwise
indicated. AK is simply the required difference in K Values
between the perturbing levels; §A£t is the sum of Alt for
the degenerate modes involved in the perturbation, i.e., for

those modes which have a Avt f C; the Z'AL is the sum of

I
t t
Alt for those degenerate modes not involved in the perturba-

tion, i.e., those for which Avt = O. In those instances for

which §Att or E'Alt, is given as 0*, the notation indicates
z 2111' 1. z = .
that the §IA tl or tI t.l¢ 0 but the EA t or %.A t. o

The heavy box lines enclose the largest effects.
In summary, up‘to this point we have found how to deter-
mine whether or not a particular perturbation coupling is a

—— g

34The author is indebted to G. Tarrago and G. Amat for
these tables. (87)

 

, +..!” 1““. n’.|lvtn ‘
1 hi

P. ,-

96

Table 6.5 Perturbation couplings for 623, p'ail.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Order of
p Matrix elemems AK 2A1) 2A2. Cplng Mogmtude
' - 1 1' ' p=3 p=4 p=5
0 WW2,” o o I 1 2 3
w o 0* o I 1 2 3
(1,2,3)
w(“)~/J(J+I)-K(1<i1) 11 $2 0 11 2~ 3—-
.1.
2 Wm o _2 $2 I 3
w(5)/J(J+1)-K(Kil) x
:2 :2 o 11 3..
JJ(J+1)-(1<i1)(1<:21 .
w o is o I 1 2 3
(1,2,3)
w(3 4)..[111:r+1)-1<(1<11) 21:1 1:1 0 n 2~3 3—
+ +
3 Wu,” 0 -1 -2 I 3
w(5)J.fiJ+1)-K(Kt1) X
:2 ’il 0 m 3‘-
,/J(J+1)-(Kil)(Kt2)
w o 0* o I 2 3
(2,3)
4 r a
W(4)JJ(J+I)‘K(KiI) i1 i4 0 II 3‘-
5 w o :3 o I 3
(3)

 

 

 

 

 

 

 

 

 

 

 

 

 

97

 

 

 

 

 

 

 

Table 6.6 Perturbation couplings for p22 , p,=l.
Sweats;

. agmu
Matnx elements AK A511 24A” Cplng p=2 p=3 p=4
w(é’3’4)‘/J(J+I)'K(K+l) :1 :1 0 II I~2 2*3 3—

{ o 13 o } 2 3
was) a .+.1 :2 1
- x
“'14,” ‘Nw‘m “(Kim :2 :t1 0 m 2‘- 3‘-
J J(J+ 1)-(1<:l:1)(1<t2)

 

 

 

 

 

 

 

 

 

 

4......

4 ‘93.: .

 

Table 6.7 Perturbation couplings for p=2, p52.

 

 

 

 

 

 

 

 

 

- ' Order of
Matnx elements AK ;A*t 25131,. Magnitude
w(2),/J(J+1)-K(Ki1) it :2 0 1~2
w K 0 0* 0 .... 2

(2) (Kzsouxzn
0 0* 0
W12) 0 :2 :2 2
w“) fl1J+1)-1«1<:1) X
:2 i 2 0 2 ‘-
fi(J+1)-(Ki1)(1<i2) . '
w(6)JJ(J+I)’ Ktxtn X

JJ(J+I)-(Ki1)(1(i2) X :3 0* 0 3°-

fiJt-ll-(KiZNKiIS)

 

 

 

 

 

 

 

99

Table 6.8 Perturbation couplings for p=2, pfO.

 

 

 

 

 

 

 

 

. . Order of
Motnx elements AK ;A2,- Couplmg Magnitude
“'12) 2

| 2 O O I 2...
w(‘)J(J+I)+W(4)K . (wa)
w(‘)JJ(J+I)‘K(K:tI) 1:1 :2 n 3 .-
w(6,./:11;1+11-1<'11(i1) x

JJ(J+I)-(KiI)(Kf2) X :3 0 1 3 .-
fi(J+1)-(K:2)(K:3)

 

 

 

 

 

 

”tolerate ,1 (...-new
.wa ..p

’1

.l

13C

possible coupling. he have also discussed the form of the
analytical expression, 8 , for the separation of two unper-
turbed levels as a function of molecular constants and J
and K. Additionally, Tables 6.5-6.8 contain the principal
perturbation couplings and their functional form due to
terms contained‘in h+ through hg.

Hypothetical Exggple of an
Accidental Resonggce

At this point we shall consider a hypothetical example
to indicate the relevance of the foregoing. Assume that
v2 + V5 and v4
other. Here, p = 3, p

of CHBX, where X is a halogen, perturb each
n = 1, pt = 2,and from Table 6.5 we
see that the principal coupling is of type I,i.e.,0f the
form w, and of first order of magnitude.

The separation of the unperturbed energy levels is given
by

8‘: (v2+v5)-v4+2Ae (Ci-CS)K-(a§ -a, B)J (J+1) (6.19)

MB
+(15
which is obtained by finding the difference between EVR for

v2 + v5 and v4 (neglecting small terms). If in addition,
(Cg + Q? - a2) is negligible, then

8: (V2+V5)-V4+ 2A 8(C4-12Z)K ' (6.20)

which leads to a level scheme given in Fig. 6.2 for

(112 + 05) - V4” --10cm"1 and 2Ae(gg - Cg)zjcm-1. we further
assume v2+vs is of such a low intensity as to be normally
unobserved, and that, in the absence of the perturbation,

only v1 would be observed. From Table 6-5 we “Qt? that the

'101

Fig. 6.2 Hypothetical perturbation with coupled levels
indicated by dashed lines.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Kg 14, yaw/5 KI,
cm"'
5+ ”\
\\
100'- \
\ O
\
\
x 5—
4" \
\\
... 4+
4’xflfifl
4+ \
\
\
\
\
\
\ 4-
50— 3— fl
\\
3+ 7—‘C‘“‘ 3+
\
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1172

t

of v4 couple to the K£+ levels of v2 + v5 and the K2" to the

K£-. It is apparent from Fig. 6.2 that the separation of the

coupling is a AK : O, §A1 = 0 case so that the K1* levels

unperturbed levels is smallest near the K = 3 levels of
these upper states and the perturbation should be the strong-
est here. These levels correspond, for the case considered,
to the RQ2(J) lines of v4. Fig. 6.3 presents in the top
row the position of the Q lines for v4 (solid lines) and
v2 + v5 (dashed lines) in the absence of a perturbation.

The second row shows the resulting spectrum which would be
observed (drawn for an arbitrary W). Notice that in the
vicinity of the maximum perturbation, the lines of v4 are
not only shifted, but several additional lines appear due

to the mixing of wave functions of v4 and v2 + us when the
perturbation is a maximum. The relevant theory involved

in the intensity considerations and the "borrowed" inten-
sity of the extra lines will be discussed below. Chapter 8

contains an actual example of the effect of a perturbation

of type II and is discussed in detail.

Intensities in Perturbgt10n§--
Bogrowgd Intensitx_

When a perturbation is observed, intensities are an

 

important factor to consider. Assume that two levels are
resonating, a and b, with zero order (unperturbed) wave
functions Y: and Y3. Let the matrix element of the perturba-
tion be W. Then in the notation used in this chapter, the

new wave functions are

103

 

 

 

 

 

 

 

 

 

 

 

 

 

o c n N . OOm _ N n c 0 00¢
_ _ _ _ _ _ _ _
_ _ . _ _ _ _ ._ _ _
_ _ ._ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _

m c n N . OO _ N n t a a0
0 t n N . m 001 . N nCQ l

.H on?

so c2692.: o 2 26 28.55035 umtmmno Eatooam 9.533. of 9.6 Amos.
3563 S+~x~ ecu 53:: 2.03 on 35.25%: .8 35:95 o 9: no cosmos m.w .9“.

 

 

Ya = at: + (mg (6.20)
Yb = —/3Y: + curb (6.21)
where
a = [A +2 8(2]%
A
(6.23)
_. /_l._:__§12*lr
P" 2A
and
A5. V82/4 + W2 (6.24)
8 .5. Ba .. Eb. (6.25)

It has been shown (88) that for the transitions va<—-v"
and vb4P-v" where a perturbation W exists,the intensity of
two perturbing transitions in the perturbed absorption bands

may be given by

H
C
II

[M13838 + pugbfir (6.26)

H
II

[naugf + (1(1ng (6.27)

tuners 131 is the unperturbed intensity of a v1 transition.
Thus the intensities in a perturbation may be calculated,
Sidren the information required by Eqs.(6.26) and (6.27).
HoWever, even if all of the information needed to calculate
thfi? intensities is not available, some information may be
elt‘lnracted.
Considering the case where the rotation-vibration band

belonging to level b is not. normally observed, i.e., 13b = O)

33‘

105

Ivb : p 2 A- 8/2

'1— T A+ 5/2

V O.

—1
= 1-5;Bfl§é/4 + W2’+ S/é].

(6.28)

(D

 

Thus if W = O, (IVb/Iva) = O,Whereas (Ivb/Iva) = 1 if (S- : O),
i.e., at the position of exact resonance.

Another view is also interesting. From Fig. 6.1 the
magnitude of the shift of the perturbed level from its

unperturbed position is

 

X— -§+\/61/+ HM" (6.29)

which when substituted into Eq.(6.28) results in the

expression
I
v 1
b = 1 - .._—_....-
fg; [Hr/6] (6°30)

trhich proves to be helpful in the analysis of perturbed
sifJectra.

Eq.(6.30) implies that when the shift of the observed
liJae from its unperturbed position is the greatest, the in-
tensity sharing by the transitions of the unobserved level
318 “the greatest. This is seen in the hypothetical example
illustrated by Fig. 6.3 for the RQ2(J) levels. The intensi-
13343‘s of extra lines is proportional to the shift from the
un-I.>erturbed positions. Eq.(6.30) also indicates that as the
Shduft goes to zero, so does the intensity sharing.

- war

1J6

It is apparent then that in a perturbation, transitions
normally not observed may borrow intensity from the transi-
tions which they perturb. In Chapter 8 an example of this
intensity borrowing will be seen in several instances.

In the event that both levels involved in the perturba-
tion have non-zero intensities in the unperturbed case, the
problem is even more complex and the intensity sharing is
not easily described. However, when applicable, the calcula-

tions using Eqs.(6.16) and (6.17) are straight-forward.

 

Essential Resonances
Although essential resonances have not been treated in

(detail in this chapter, they can be important in the inter-
pretation of spectra.

In an essential resonance, the resonance occurs between
levels in the same rotation-vibration band. It is necessary
to be clear about the term "same rotation-vibration band"
since it is used here in a broad sense. By the same rotation-
vibration band we mean the entire band which has the same
Vibrtitional quantum numbers. For example, for ZXY3 molecules,
the same rotation-vibration band is taken to mean the entire
complex for which v‘,v2,...v6 are identical. However, 1.4,
£5 axui ‘6 may be different, e.g., an essential resonance
may occur between the parallel and perpendicular components
01’ 2V4 of a ZXY3 molecule.

III treating essential resonances the same considerations
°f thits chapter apply with the restriction that the perturba-

t1°n matrix elements satisfy the rule ElAvSIE 0'

C)
'\]

Summary

In general, there are several points which should be
systematically considered when analysing perturbed spectra.
These are:

1) the order of magnitude of W

2) the type of coupling (I,II...)

3) the number of auanta involved in the resonance,

i.e., p, pn, pt

4) the order of magnitude of a,b,c,d (Eq.(6.12))
5) the number of resonating levels

6) observed intensities.
{the appearance of the perturbation is governed by considera-
‘ticumt,2,4,5, and 6 while 3 presents a systematic approach

tn) the consideration of the couplings possible. In Chapter 8,

these considerations are applied to v3 + v4 of CHBF.

55'

.,—_

—...—T.--—.

CHAPTER 7

EXPERIMENTAL DETAILS AND CALIBRATION OF RECORDS

Spectrometer
The spectra of CHBF, CHD3 and CH3D were obtained with a

high resolution vacuum recording spectrometer employing an

f/ 5 Pfund-Littrow monochromator of focal length 1 meter (89-91)
and one of two Bausch and Lomb "certified precision" echelette
gratings, a 600 line/mm, 212x158mm, grating blazed at 1.6;1

and a 300 line/mm, 254x128mm, grating blazed at §/¢. The gas
samples were contained in a White type multiple traverse cell
(92,93). Two entrance optics arrangements were used, one em-
‘ploying three calcium fluoride lenses and several front surface
zrluminized mirrors, the other employing an all mirror system.

The infrared energy was detected using Eastman-Kodak

leaui sulfide detectors, type P and type N. The detectors were
cocfiled to one of two temperatures, -50°C by a circulating dry
leer-acetone mixture and -175°C by a pressure driven liquid
aix' cooling system. The infrared beam was chopped at 90 cycles
pex~ second and the lead sulfide detector outputs amplified

by a Tektronix Type 122 preamplifier followed by a phase sen-
sitive amplifier. The amplifier output was recorded by a
Leeds and Northrup Model G two-pen recorder.

Cadibration was effected by interpolation between the

V1~81bll.e fringes from a Fabry-Perot interferometer following

the method of Douglas and Sharma (94). The Fabry-Perot

108

‘vw"

fringes which are equally spaced on the chart with respect
to frequency are calibrated by a least squares fit of the
fringe position of well known standard lines versus their
frequency in cm". The standard lines are normally recorded
simultaneously with the infrared absorption record. Several
types of standard lines are used in the calibration of the
fringes. The best standards available for calibration of
infrared absorption spectra are the carefully measured ab-
sorption lines of CO, N02, HCl and HCN measured by Rank and
co-workers(95-97). These standards are recorded simultaneously
'with the spectra by including the calibration gas with the
sanple gas in the multiple traverse cell. In addition, well
lanown Argon emission lines (98) due to the Argon carrier gas
331 the 300 watt Zirconium arc, which we use as an infra-
:reCI source, provide another source of standards; and an end-
on.]Neon lamp inserted in the entrance optic train by a

movxible mirror also provides a source of standard lines (98).

Calibration 9f CHEF Bands

The v; + v4 band of CHBF discussed in Chapter 8 was
calibrated using secondary infrared standards as follows.
Sevexl CO lines (95), one Argon emission line (98) and one
Neon emission line (98) were recorded simultaneously with
15116 best infrared absorption lines of v} + v4. Subsequently
the Fabry-Perot fringes of the record CH3F Chart I were
calibrated using these standard lines. The results of this
linear least squares fit are given in Table 7.1. Table 7.1

_u E -.-." '3-

 

HO

Table 7.1 Calibration of Fabry-Perot.fringes of
V} 4’ V4 CH3F Chart I.

Std. Fringe Position Freguency Calculated Hts A1(?-c)
cm-

of Standard 'cm’ Frequency
cm'

Ne ~134.1973 3903.8008 .7992 2 +0.0016
P(22) 661.2890 4159.5609 .5603 1 +0.0006
P(21) 677.7175 4164.8423 .8423 1 0.0000
P(18) 725.7604 4180.284} .2889 1 -0.0046
P(17 741.3288 4185.2971 .2943 1 +0.0028
P(16 756.7080 4190.2424 .2390 1 +0.0034
P(14 786.8532 4199.9298 .9311 1 -0.0013
P(12) 816.1305 4209.3454 .3442 1 +0.0013

V : a + b(f#)

a = 3946.94567cm'1

b = 0.3215154em-1

s :.-.’c0.0026cm--'1 Std. dev. of points

111

Table 7.2 Calibration of CH F Chart II vs frequencies

Fringe Position

Chart II

211.503
212.112
278.657
279.522
280.302
301.133
302.053
306.272
347.422
348.453
349.378
350.230
352.275
352.826
416.372
419.225
420.075
514u786
515.324
515.995

Standard Fr
Chart I cm'

4014.9496
4015.142}
4036.5384
4036.8182
4037.0704
4043.772?
4044.0705
4045.1620
4045.3114
4045.4187
4058.6532
4058.9814
4059.2782
4059.552}
4060.2131
4060.3869
4080.8260
4081.7442

4082.0153 _

4112.4689
4112.6414
4113.1838

v

a
b
a

‘1‘1'

a + b(f#)
3946.93827cm'1
0.3215543cm-1
$0.0032cm-1

of absorption lin s from Chart 1.

Calculated Freq.
Chart II cm-1

.9480
.1438
.5416
.8198
.0706
.7689
.0647
.1554
.3085
.4214
.6533
.9848
.2823
.5562
.2138
.3910
.8245
.7419
.0152
.4699
.6429
.1803

$11-91“)

+0 .0016
-0.0015
-0.0032
-0.0016
-0.0002
+0.0038
+0.0058
+0.0066
+0.0029
-0.0001
-0 00034
-0.0041
“000039
-0.0007
+0.0015
+0.0023
+0.0001
-0.0010
-0.0015
+ .0035

Std.dew of points

112

presents the intemal calibration of CH3}? Chart II against
the frequencies of infrared absorption lines obtained from
CH3F Chart I.

The initial analysis was carried out using Chart II.
Subsequently, the resolution of the spectrometer was improved
by cooling the PbS detectors to -175°C. The CH3F was rerun
in the double pass configuration of the Pfund-Littrow mono-
chromator. A difficulty arose, however, since the Fabry-Perot
fringes were single passed. As a result of the different dis-
persion at which the infrared and fringes were obtained on
Chart III, it was found that a quadratic fit of the fringe
position of the best lines on Chart III vs the frequencies
of these same lines from Chart II was required to obtain a
good calibration of Chart III. The results are given in
Table 7.3. .

Secondary internal calibration was used on these records
due to the difficulty of using primary standards in this
region. As is apparent from Table 7.1, there is a lack of
accurate and observable standards in this region and since
the internal calibrationfits were as good as they turned
out to be, secondary internal calibration was used. The
Principal effect of this approach would be to introduce a
small error in absolute accuracy of frequencies. However,
the relative accuracy should be extremely good.

Table 7.4 presents a summary of experimental conditions
. f°r all usable records of V} + v4 for CHBF which were run.

Unfortunately, the last three records listed in Table 7.4

..‘r‘ik‘ U- .1"

s:

'1'

.1 1.1.1 .I. 1.. .... I. ...... LI Vsiiflh

Table 7.3 Calibration of CH F Chart III vs.frequencies
of absorption lin s from Chart I.

Fringe Position Standard Fre . Calculated Freq. A.{€-c)

Chart III Chart 11 cm- Chart III cn-1 s;
158.219 3989.8449 .8437 +0.0012
200.099 3995.5406 .5437 -0.0031
215.684 4003.0261 .0223 +0.0038
231.132 4010.4369 .4362 +0.0007
265.710 4027.0310 .0348 -0.0038
277.953 4032.9120 .9131 -0.0011
291.014 4039.1807 .1848 -0.0041
300.564 4043.7696 .7711 -0.0015
315.877 4051.1280 .1258 +0.0022
326.836 4056.3899 .3900 -0.0001
335.160 4060.3946 .3887 +0.0059
345.477 4065.3513 .3453 +0.0060
366.376 4075.3857 .3872 -0.0015
372.535 4078.3466 .3470 -0.0004
416.574 4099.5142 .5150 -0.0008
442.455 4111.9603 .9590 +0.0013
4530489 411702560 .2652 +OOOOOB
474.552 4127.4023 .3957 +0.0066
1485.544 4132.6861 .6833 +0.0028

v = a + me!) + c7177)?

3 : 3899.61773cm'

b.= 0.1‘1>7896060111"‘l

c = 0.0000021 9cm-1

3 :zt.0040cm' Std.dev;of points

.1 .‘~

 

114

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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1‘15

proved to be impossible to calibrate since satisfactory

Fabry-Perot fringes were not obtained.

Cglibrgtion of CHD;

Three high resolution records of v1 + v2 of CHD} were
calibrated and measured. Later, several other records were
run for details not obtainable on a calibrated run. CHD3
charts I and II were calibrated against Neon emission lines
(98) recorded intermittently with the absorption spectrum
while fringes were recorded continuously. The results of
the calibration fits are given in Tables 7.5 and 7.6. Chart
III was internally calibrated against average frequencies
of infrared lines from Charts I and II with a standard devia-

tion for 11 points fit of $0.0014cm’1.

C ibr tion H

Two records of we + v3 of CHBD were run. CH3D Chart I
Was run for a primary calibration against HCN standards (95).
0331) Chart II is a second high resolution run for second mea-
surement of lines and was internally calibrated against
absorption lines contained on Charts I and II. Table 7.8
preGents the calibration fit of Chart I vs. HCN standards.
Table 7.9 presents the calibration fit of Chart II vs. absorp-
t1011 line frequencies from Chart I. Table 7.10 lists the

eKPeximental conditions for the two ‘records.

3.213233 Preparation 01132

The CHEF was prepared by transferring 97.6g (0.524 mole)

'\ 3'

 

116

Table 7.5 Calibration of Fabry-Perot fringes of CHD}

Neon Line
Fringe
Position
Chart I

9.157
80.810
230.051
357.120
616.086
655.142

Standard Calculate
Freq.cm-1 Freq. cm’
4961.132 .131
4989.930 .930
5049.912 .913-
5100.984 .985
5205.071 .070
5220.768 .768

1’: a + b(f¢*)

a = 4957. 450cm-1

b = 0. 4019239

3‘ :10. 001cm"

Chart I vs. Neon emission lines.

Al£0-0)
031

+0.001
0.000
-00001
-00001
+0.001
0.000

m’
1 Std. dev of points

“...-am

(‘1’; g: p.

117

Table 7. 6 Calibration of Fabry-Perot:fringes of CHD}

Neon Line
Fringe
Position

9.212
80.864
230.098
616.164
655.228

Chart II vs. Neon emission lines.

Standard Calculated 81(0-0)
Freq.cm-1 Freq.cm‘ 0111‘1
4961.132 .134 +0.002
4989.930 .931 +0.001
5049.912 .909 -0.003
5220.768 .770 . +0.002

v = a + b(f#)

a = 4957. 431cm"1

b = 0. .4019036Cm

s =i0. 002cm" Std. dev. of points

118

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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3.0 0.00 1 alga 2050 . _ 000 0. 00. or, a
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119

Table 7.8 Calibration of Fabry-Perot fringes of CHBD
Chart I vs.HCN absorption lines.

HON Line Standard Calculated 4; (o-c)
Fringe Position Freq. cm"1 Freq. cm" on"1
R(9) 770.899 3339.8843 .8817 +0.0026
12(10) 779.385 3342.6077 .6108 -0.0031
12(18; 844.672 3363.6134 .6065 +0.0069
R(19 852.562 3366.1405 .1438 -o.0033
R(20) 860.350 3368,6455 .6484 -0.0029
R221 ) 868.042 3371.1283 .1221 +0.0062
a 23; 883.332 3376.0271 .0392 -0.o121
M25 898.252 3380.8366 .8373 -o.0007
M26) 905.619 3383.207? .2065 +0.0012
M27) 912.910 3385.5563 .5512 +0.0051

v = a + b(f#)

a = 3091.9675em-‘

b = 0.3215911on-1

s ==to.oo6ocm-1

Table 7.9 Calibration of CH D Chart II vs. frequencies of
absorption lines Erom Chart I.

Fringe position Standard Freq. Calculated Freq. 81(0-0)
Chart II Chart I cm" Chart II cm" cm“
937'.191 .3393.339 .327 +0.012
945 - 347 3395.942 .951 -0.009
9463.173 3396.213 .217 -0.004
952 . 794 3398.345 .346 -0.001
980 . 529 3407.284 .265 +0.019
1012.551 - 3417.559 .565 -0.006
1022. 952 3420.909 .909 0.000
1025 . 281 3421.669 .658 +0.011
1059 .052 3432.511 .519 -0.008
1146.345 3460.576 .593 -o.017
1248.465 3492.459 .437 +0.022
1264.519 3498.602 .600 +0.002
1265.531 3498.926 .925 +0.001
1379 . 838 3535 . 682 . 687 -0 .005
1396.580 3541.066 .071 -0.005
1398.879 3541.814 .811 +0.003
1417.119 3547.687 .677 +0.010
1434.659 3553.311 .318 -0.007
1437. 801 3554. 326 . 328 -0.002
'44 1 . 840 3555. 628 . 627 +0.001
1454.526 3559.719 .707 +0.012
495.721 3572.945 .956 -0.011
1497.845 3573. 644 .639 +0.005
)) = a + b(f#)
a = 3091.91889 cm-1
b = 0.321610337 cm-1
s = a. 0.0096 cm"

IiivI

. :1. ..

121

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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of methyl p-toluenesulfonate and 62.7g (1.08 mole) of dehy-
drated potassium fluoride into a flask. The pressure was
reduced to 500mm Hg and the temperature raised to 250°C over
a period of 1% hours and maintained at 250°C for 3 hours.

The reaction product was passed through a dry ice - acetone
cooled trap to remove any water present and subsequently
collected in a liquid air cooled trap. Fig. 7.1 illustrates
the apparatus set-up used for the production of CHEF. Yields
were on the order of 85% with a small amount CO2 contamina-

tion.

CHD3 32d CH3D Samples
The samples of CHD3 and CHDD were obtained from Volk

Padiochemical Co. and used without further purification.

123

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5:3? 2

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836065.:

E. .9“.

CHAPTER 8
A PEFTURBED PERPENDICULAR BAND v3+v4 OF CHEF

In the past, the infrared spectrum of CH3F has been
investigated in several laboratories. Bennet and Meyer
first reported the spectrum of CH3F (99). Subsequently Yates
and Nielsen analyzed the fundamental bands with resolution
2:0.3cm"(100). The bands v1, v3, v4 and 2v5 were examined
by Pickworth and Thompson with somewhat higher resolution
250.1cm"(101). Smith and Mills have recently re-analyzed
the rotational structure of v3 and V6 with resolution
230.2cm"(102). A low resolution (2:1.5cm") study of all
perpendicular fundamentals was performed by Andersen, Bak,
and Brodersen (103) who found the G: constants from the
zeta sum rule (12) and thus also obtained a value for A0.
The microwave spectra of CH3F has been reported (52.53.58),

J JK

and excellent values of B0, Do and D0 are available.

Warm
A 1 ent of th Ob e ed S r

In the region from 3900 - 4500 cm“ the infrared absorp-
tion spectrum of CHBF is very complex, with a number of
overlapping bands. The subject of this chapter is a perpen-
dicular band at 4058cm'1 which we have assigned to v3+v4.
We have also found, overlapping the low wave number and
of v3+v4, numerous transitions belonging to the parallel
band v1+v at 4011cm’1. Another parallel band which may be

3

2V2 + v is observed at 3905cm". We also observe several

3
124

I-’Ael . '| ;k h r: . at! k! I..-Ll..v.\ .
'4. . .

125
Q branches of a perpendicular band near 4138cm'1 which may
belong to v1+v5.

The band v3+v4 spans approximately 230cm‘1 and we have
measured approximately 1000 absorption lines in this region.
About 700 have been assigned to v3+v4 and about 200 have
been assigned to v1+v3. v3+v4 is particularly interesting
since individual transitions of the types RRK(J), RPK(J),
RQK(J), PRK(J), PPK(J), and PQK(J) have been resolved.35
Fig. 8.1 is a slow speed "slave" recording of a high resolu-
tion record of the spectrum of v3+v4.

The resolution limit of the spectrometer in this region
isz 0.04on'1 and CHBF Chart III (of. Chapter 7) was obtained
with this high resolution. Charts I and II were obtained
earlier with an apparent resolution of R: 0.06cm’1. The
working records were approximately 17 meters long and the
Fabry-Perot fringes were separated by 95 0.32m"1 which is
x 25mm of chart so that 1cm‘1avs 7.5cm of chart.

W

The assignment of rotational quantum numbers to indivi-
dual lines was complicated by the large number of transitions
observed, the relatively large rotational spacing (23:51.7cm'1)
and the rapid quadratic convergence and divergence of

A

35in the perpendicular bands of the other members of
he methyl halide family we have not seen Q branches, i.e.,
and QK lines, resolved into individual J transitions.

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series of lines of fixed K. The latter effect is due to
the large (:3 ($80.01cm") in this band.

Making use of calculated intensities of the six possible
types of transitions and the criterion of missing lines for
J<IK as discussed in Chapter 5, the Q branch transitions
for several values of K were located. Then, following the
procedure outlined in Chapter 4, calculated values of the
ground state combination differences (using microwave values

J and DOJK) (52.53.58) were used to complete the

36

of B0, Do
assignment of the unperturbed levels.

It is apparent from inspection of Eqs.(4.2a) and (4.2b)
that, provided the proper K value has been assigned to a
series of RQK(J) (or PQK(J)) lines, the calculated ground
state combination differences unequivocably fix the assign-
ment of the corresponding RR and HP (or PP and PR) lines
for the same K value.

At this point it is convenient to establish a convention
of notation to be used in the following. We shall call the
RRKU), RQKU) and RPKU) lines, the +le subband and the
PRK(J), PQK(J) and PPK(J), the -lKl subband, i.e., we shall
designate the subbands by KAK.

In the manner described above, the -6,-3,-2,-1,0,+2,+3,
+4,+5,+6,+7,+8 and +9 subband lines were assigned without
undue difficulty. The assignment of the -9,-8,-7,-5,-4, and
the +1 subband lines, as well as the -3 subband lines above

36The values of the ground state constants used are from
the work of Thomas, Cox, and Gordy (g8):1Bo = 0.851793,
cm

DoJ = 1.98 x 10-5, DOJK = 1.48 x 10'

 

132

J = 10, presented a more complicated problem.

The +1 subband was obviously perturbed (as was the -3
subband) by a perturbation which varied in magnitude with
J. The -9,-8,-7.-5. and -4 subbands were more difficult to
locate due to less obvious perturbations and also because
of the overlap of this region by the QRK(J) lines of v1+v3.
The transitions in these subbands were successfully assigned
when it was found that a large empirical K3 term was needed
to fit the subband origins from -3 to +9. The assignments
were then made and verified in the -9,-8,-7,-5. and -4
subbands using the calculated ground state combination
differences.

After all but the -3 and +1 subbands were assigned, it

was possible to assign the transition in these two subbands

from the remaining unassigned lines with reasonable certainty,

again using the ground state combination differences to
verify the assignments.

Fig. 8.2 is a medium resolution record of a large portion'
of the band v3+v4. Assignments of the principal series are
indicated for v3+v4 and also v1+v3. The high resolution
records are considerably expanded (a factor of 5:1) and
show more detail.

All assigned transitions from v3+v4 are listed in
Appendix V. The list contains the assignment, frequency,
fringe number (for which the calibration given in Table 7.2
may be used to obtain the frequency), Av and weight (the
weight = .0001/(dv)2), the observed line height, and line

133

 

 

 

 

 

 

 

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146

number. The observed ground state combination differences
are listed in Appendix VI. This list presents the combina-
tion difference assignment in the notation of Eqs.(4.6),
the observed combination difference, the combination
difference calculated from microwave values of B0, DoJ
and DoJK from Table 8.1, the Av and the A1 (obs-calc).

All assigned transitions from v1+v3 are listed in
Appendix VII,and the observed and calculated combination
differences are listed in Appendix VIII.

AE§%§§l§12£.§£2%EQ_§Ea£2
Com at on Dif egenceg

All of the ground state combination differences which
were observed for v3+v4 and v‘+v3 and which received a
non-zero weight 37 were simultaneously analyzed by the
method of least squares using the method described in
Chapter 4. A single exception is the ground state combina-
tion differences for the zero subband, i.e., the
Rcow) - RPO(J+1) and the RRO(J-1) - RQO(J) combination
differences. These were not included in the simultaneous
analysis since the K' = L = *1 upper levels have had their
degeneracy removed by a Coriolis resonance and the combina-

tion differences mentioned are not "true" ground state

 

37The ground state combination differences were weight-
ed by using the square root of the sum of the squares of
the AV's assigned to the individual lines as_the Av for
the combination difference.

147

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combination differences in that they do not go to upper
levels of equal energy. This will be discussed in a later
section. °

The results of the simultaneous analysis are given in
Table 8.1 together with a comparison with the microwave
results (58). A detailed listing of the observed minus
calculated value of each combination difference fit is not
included in this work since the equivalent data is listed
in Appendices VIII and X and we feel the microwave results

are likely to be more accurate. 38

8 ch 0 Possible P b t on

When it became apparent that the band was perturbed,
it was necessary to investigate the possible perturbation
couplings with'nearby rotation-vibration levels as dis-
cussed in Chapter 6, and to investigate the possible essen-
tial resonances.

Before one begins to look for possible perturbation
couplings it is almost imperative that the results of any
available investigations be gathered for reference since a
search for possible couplings depends largely on a priori
calculation of nearby rotation~vibration levels. Table
8.2 presents a summary of past work on CHBF from a paper
by Smith and Mills (102).

A;

38The difference between our calculated value of B0 and
the microwave value may lie in the calibration of the
spectral record of v3w 4and v ‘+v3. Some difficulty was
encountered due to a lack of suitable calibration standards
over a large portion of these bands. See note added in proof,
p.220.

149

Table 8.2 Summary of rotation-vibration constants from
references (58), (101), (102) and (103).

.A3381gno

2v2(?)

, w p-
II M

Vibration
Symmetry

500810m-1

0.8517930m"1
1.98 x 10"6cm”1

1.48 x 10"5cm"1

Ref.

(101)
(103)
(102)
(101)
(103)
(102)

(102)
(101)
(102)
(100)
(101)

-1
vocm

2964.54
1464

1048.60.

3005.8
1466.5
1182.35

1032.76
2081.42
2222.6
2818
2863.22

(103)
(58)
(58)
(58)

B
s

a cm"1

-o.o017

aAcm"
s

(not analyzed)

+0.0113

+OOO‘1
+0.00&

(not analyzed)

+0.0043

+qu223

+000047

-0001}

+00091
'00290
+0.284

 

150

Using the information in Table 8.2, the sums of funda-
mentals were formed forall possible overtone and combina-
tion bands in this region. These frequencies are not very
accurate because they neglect anharmonicity, the effects
of which may be quite large. However, the anharmonic
constants are not available except for a few special cases,
so that we had to use the sums of fundamentals. Table 8.3
lists all nearby rotation-vibration levels as sums of funda-
mentals. Then using Tables 6.5-6.8 a compilation of the
principal perturbation couplings between all of these levels
may be built up. Such a table- is presented in Table 8.4.
Listed in the table are: the formal order of magnitude of
the coupling, the type of coupling described in Chapter 6.

Fig. 8.3 has the levels from Table 8.3 drawn to scale,
and the perturbation couplings of expected order of magni-
tude 1 indicated in the left and right hand columns. The
two. center columns indicate the principal couplings of
tYDe I and type II between v3+v4 and the nearby bands.
There is some overlap in the information shown in two outer
columns and the two inner columns.

Examination of Fig. 8.3 leads to the conclusion that
insufficient vibrational information is available to make pos-
‘a‘ible a rigorous treatment at the present time. However,
the possible couplings are indicatediand some correlation
With observation is possible. We shall return to the
Perturbation considerations a number of times in the

to llowing dis cussion.

W -‘9— ‘7 m‘ ‘mmfi-fl

151

Table 8.3 Overtone and combination levels as sums of
fundamentals in the vicinity of v3+v4.

Level Sum of
Fundamentals (cm"1 )
4v3 ' = 4194.40
v4 + v6 = 4188.15
v1 + v5 = 4146.84
2v5 + v6 = 4115.35
v2 + v5 + v6 = 4112.85
2v2 + V6 = 4110.35
V3 4 V4 = 4054.40
v1 + v} = 4013.14
v} + 2v5 = 3981.6
v2 + v3 + v5 = 3979.1

V3 '1' 2V = 3976.6

152

Fig. 8.3 Perturbation couplings near 4|OOcm-'.

cm"
4200—-

 

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F

Analysis of the Unperturbed
Transitions of vjflh

Once the majority of the perturbed transitions were
found and excluded from the data, the remaining lines, which
are assumed to be either unperturbed or only slightly per-
turbed, were simultaneously analyzed, following the proce-
dure outlined in Chapter 5. The equation !

‘ {(AK)(AJ)K.(J)}°bs-Bo[(J+AJ) (J+1+AJ) - J(J+1 )1.

DOJ [(J+AJ)2(J+1+AJ)2 -J2(J+1)2] +

DOJK [(K+AK)2(J+AJ)(J+1+AJ) -K2J(J+1)] =

(Vo‘Ae C42 'i‘Q4K) + (Ac-A9 CZ 812410 [2111111 + (11102] +
((1311 + (1411 _ (133 _ “4B _(3/2),24K) [41945102] +

(QB+aB‘=

3 z, 1 [-(J+AJ) (J+1+AJ)] +

(DOK fling) [-(K+AK)4 + K4] +

(r241?) [(11.1.1) (mm) (11.11:) ax] (8.1)

was, found to represent the data adequately, and no other
terms were found to be significant. The results of the
81multaneous least squares analysis of 156 transitions are

Presented in Table 8.5 with their simultaneous confidence

1,11
1J1

Table 8.5 Results of a simultaneous least squares analysis
of V} + v4 of CHBF including transitions from
the -3, -2, -1, 0, +1, +2. '1’}, M. +6’ +7, +8
and +9 subbands (in cm’1).

4057.2074 t 0.0074

2 K
Vo -Aec4 ”knit

4.6684 i 0.0018

K
A 'Aeclzi ““14

0
A A B K -2 -2
(13 + 0.4 - 0'3 - 0.2 -(3/2)’24 10390110 * 0.097110
B
3

a, + a2 = 1.08161c10”2 a 0.0980x1o‘2
DOK - irZ4K = 4.46::10"4 s 0.21xic"4
J 5

4-7x10" t 1.2x10-5

r:S
4:-
ll

Std. dev. of observations

included in the analysis $0.01 1cm"1

1"

156

intervals (discussed in Chapter 5). The computer output is
contained in Appendix IX which consists of three sections;
the first is a summary of the observed and the calculated
frequencies, the Av (Weight = (Norm)2/(Av)2), and the
A1(obs-calc) discussed in Chapter 5. The second section is
a similar listing for lines which were not included in the
analysis because of perturbations, while the third section
is the same type of listing for all zero weighted lines
(usually badly overlapped with other lines).

Figs. 8.4 - 8.22 are graphs of the observed minus
the calculated frequencies39 based on the results in
Appendix IX. In principle each would be a horizontal
straight line if no perturbations were present. From
Figs. 8.4 - 8.22 it is possible to obtain a qualitative
idea of the nature of several perturbations which are
present in this band. In the following sections we discuss
these perturbations and our analysis of some of the pertur-

bations o

W
An interesting perturbation affects the zero subband

of v3+v4. The effect of the perturbation.may be seen in
.Fig. 8.13. The perturbation is ascribed to a first order
-chiolis resonance between v3+v4 and v3+v3, although an
appropriate coupling with another vibration band of

L

39110 distinction in Figs. 8.4 - 8.22 is made between
AJ = +1, 0, -1 transitions since this information is contain-

ed in detail in Appendix IX.

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176

symmetry species A1 would cause a similar effect.

The Coriolis resonance splits the K' = £ 0 :1 levels
in v3+v4, i.e., the resonance lifts the degeneracy of the
K' =.£ = *1 levels. The effect on the observed spectrum
will be discussed below.

Nielsen has studied extensively the first order Corio-
lis resonance especially as applied to XY3 molecules of
the ammonia type (8-11.67-69). We shall use the results
of these investigations in the following as well as the
results from Chapters 2 and 6.

From the work of Nielsen (as well as from the considera-
tions of Chapter 6) the secular equation for the Coriolis
resonance is given in Fig. 8.23 where X = aim
From the work of Nielsen, assuming that the perturbing

band is v1+v3,

a = 2(c1§)2382. (8.2)

By using a symmetrized set of wave functions the
secular equation in Fig. 8.24 results. Thus the levels

corresponding to the wave function

. Y

1 +1 -1]
——- Y - Y
0L1
are unaffected by the Coriolis resonance while the energy
levels described by the wave function

_1__ 1+1 +Y-1] ._._. Y+
VE' +1‘ -1

are affected by the perturbation as are the YJ’ levels of

177

 

 

 

 

 

 

 

 

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179

v1+v3. The resulting solutions of the secular equation

thus are

1

6 = E1 (803’)

 

e = E11 + E00 1%“ " E9°)2 + 2a(J(J+1)) (8.4)
2 4

where, in the event of a weak resonance, an approximate

solution corresponding to Eq.(8.4) may be used. In the

event that the parallel band is at a lower frequency than

the perpendicular band (as is the case for v3+v4_and v‘+v3),

the approximate solutions corresponding to Eq.(8.4) are

60 E0 OJ
° ° 3.130 (8.5)

and

1 _ '1 2aJ§J+1l
6‘ ”E1 U: ° (8.6)

where 611 is a function of J, as are 1311 and E00.
Although, as mentioned in Chapter 2, the complete
symmetry classification of the rotation-vibration levels
for C3v molecules has not been worked out (48),it has been
found that the Rcow) transitions terminate on the 1"
levels while the RR0(J) and RPO(J) transitions terminate
on the Y+ levels. This leads immediately to the level
structure shown in Fig. 8.25 (8.9.11). Only levels of
overall symmetry A2 are shown since these are the only

levels which may be populated due to the fact that the

180

Fig. 8.25 Level structure for R(AJ)0(J') transitions.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

J \P’

3‘ \II' 5 +

5 ..
4 _

4 +
3 +

3 _
2 ..

2 +
I +

I _.

K'=.t| R
2 =01 Rom
R0013) R1313)
R
R0012) R012)
R1312)

5 +
4 ._
3 +
2 _
| +
O _

’38:

three identical H atoms sbey Fermi-Dirac statistics~ (38,
39.40).

The + and - indicate the overall inversion symmetry.
Due to the + 0—0 - selection rule and the existence of
levels of either (but not both) + or - inversion symmetry
for each K”: 0 level of different J, no doubling of transi-
tions is observed.40

Thus in a Coriolis resonance, the RQO(J) lines are
unaffected while the energy of the RRON) and BPO”) upper
states is given by Eq.(8.6). This is in contrast to E-type
doubling in which both upper levels are shifted by the per-
turbation.

Immediately one may deduce that the observed ground

state combination differences are now given by“

[Reorr-r) - 315000)] c .-. [ReorJ-r) - RPO(J+1)] (8.7)
[R11 1.1-1) - RQ m] = [RR 1.1-1) - HQ (“1001“,; <8 8)
o O c O 0 °

[Reom - Rp01J0)]c = [Rqom - RPO(J+1)]-2qJ(J+1). (8.9)

 

 

4OK”: 0 levels are a special case in this respect since
for all other K values each J level has both + and - inver-
sion components. It is interesting to note that even
though inversion doubling is me 11 ible, i.e., the levels
are still degenerate, for CH3F F??? the inversion symmetry
still plays an important r013

41Equations of the same form also apply for the
1. -type doubling case .

182

Iieferring to Appendix-VI it is evident that Eq.(8.7) is
ssatisfied. Fig. 8.26 is a plot of the observed Coriolis
(sombination difference minus the calculated value taken
:from.Appendix II. The resulting function should be
2qJ'(J'+1). It is apparent that through J' = 15 the
expected result is found. The added curvature above J' = 15
Inay be due to a J6 perturbation discussed in a later sec-
tion.

Fig. 8.2? shows an expanded effective Q branch plot
'vs.J'(J'+1) for the zero subband. The splitting of the
li' =.£ = *1 levels is apparent as a difference between the
<2 branch curve and the R and P branch curve. The rapid
(livergence of both curves to low wave numbers as J exceeds

6 perturbation discussed below.

10 is due to the J
A simultaneous least squares analysis was made on the

IRRO(J), RQO(J) and RPO(J) to the equation given as follows:

R(AJ)O(J) - Bo(2J+1+AJ) AJ + DOJK(J+AJ) (J+1+AJ) +

DOJ [{(JwJHJ-o-HAH} 2 - {J(J+1)} 2] = Vsub + (8.20)

B

(a3 +a4B)(J+AJ)(J+1+AJ) + 2q (AJ)2(J+AJ)(J+1+AJ) +

f:[(J+AJ) (J+1+AJ)] 3

Where q is the Coriolis resonance constant and f is the

constant coefficient of a J6 perturbation discussed below.

Table 8.6 presents the results of this simultaneous analysis

7)

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Table 8.6 Results of a simultanefius least squares analysis

of 1now), RPO(J) and 00(J) transitions of
V3+V4. '

4060.987 a 0.014 em"

sub

03B + a B = 0.01057 a 0.0016 em“
q = 2.75 x 10"4 a 0.57 x 10'4 cm"
5:: 1.06 x 10'8 a 0.10 x 10"8 on"

S

0.015 cm“1 std. dev.

where q is the.Coriolis resonance constant,

f is constant coefficient of [J'(J'+1)J 3

 

4v:- ..'1I.lfl ..IuM? ...dv:.u.. ..fl! . I ...hvhl .....kfl

with their simultaneous confidence intervals (of. chapter 5)
and Appendix X contains the computer output from the analysis.

Additional Observed Perturbations

Accidentally Strong Resonance Affecting
the K'=i2, 121:1 and K':=h2, £=$1 Levels

The perturbation which affects the K'ziZ, Eztt and
the K'=:1:2, 1:31 levels42 is interesting since it is an
‘example of a localized perturbation involving a single,
fixed K' value and showing up as a J dependent shift
of the levels for this particular K. Fig. 8.28 shows a
relatively high resolution record of the RQfiJ) lines.
Included in the figure are a calculated (unperturbed) spect-
rum, and an observed spectrum. The shift of the various
lines from their unperturbed positions is indicated. (The
tails of the arrows mark the unperturbed positions of the
lines, while the heads of the arrows indicate the observed
Position of the line.) Fig. 8.29 presents the same results
for 1DQ3(J). The double transitions, i.e., transitions for
which J has the same value in either one figure or the
other result from the "mixing" of wave functions of the
Observed band and the perturbing band as discussed in
Chapter 6. Fig. 8.30 is a graph of the R(21(J) transitions
Vs. J' (J'+l) after modifying the RQ,I (J) frequencies by

M
L

p 42These are the terminal levels of the R(AJ)1(J) and
(AJ )3(J) transitions.

 

...... ....-.;.3..av....._?y....JT...,Ayl. i

 

187

Fig. 8.28 Observed transitions of RQ.(J) indicating the effect of
the perturbation.

 

 

 

 

 

 

 

 

I am"
Observed positions 10
0 LL L 17 1 1
I 12 1 11 IO 3 7 s 5432
.—--—'Q O-Q O O O I. 5% _:
. 3 f : vo-O 0‘ o
Calculated positions
1 i L
(unperturbed) 20 19 $ ' 11 s 1 11 4

 

188

Fig. 8.29 Observed transitions of P030) indicating the effect of
the perturbation. ‘

 

 

 

 

 

 

 

 

lcm"
Observed positions 20 19 1e 17 IS 15 L 1 1 1 1
fits! T l 141 13 12,11 109976543
0 0 CU ... 0‘
C————‘Q 0-1 .0 ‘
Calculated positions _L 1 1 1 1 1 L 1 1 1 1

 

1111111
(unperturbed) * 20 19 1s r7 is 15 1413 12 "109016643

 

gunhaflalle . ...1.u.....¢. ...l- 1w,” «In... 2.1-2*

 

4069.0

4068.0

R0,(J)+0.01.I‘(.1'+11 in cm“'

4067.0

efllJl l l l l

189

Fig. 8.30 RQIU) transitions vs. J'(J'+l) indicating the
effect of an accidental resonance.

+— ”Eav"

 

 

@234 5 6 7 8 9 l0 ll l2 l3 l4 l5 l6

J'(J'+1)

adding 0.01 J'(J'+1)om"1 to each transltlon‘B in order to

expand the scale of the graph. Fig. 8.31 is a similar graph

for the PQ3(J) lines.
The assignments which we have made are fairly certain

since for most transitions among those included, AKPK(J)
and AKRK(J) lines were found which give good agreement with

the calculated ground state combination differences in

Appendix II .
If we now assume that the perturbation involves two

levels, as in Chapter 6, then Eq.(6.3) is the secular equa-
tion and Eq.(6.10), the solution of the secular equation.
Plotting the unperturbed energy levels of two bands

assumed to be in resonance, we have
Ea

Energy

 

Eb

 

J(J+l)

‘43rhe AKQK(J) frequencies are equivalent to an expanded
set or upper state energy levels as may be seen by compar-
ing the Q branch line position expression with the upper
8tate energy level. expression. Since that is the case we
Shall speak of energy levels and Q branch frequencies inter-

Chang e ably .

F’<.131ar1+o.01 JiJ'+11 in cm '

Fig. 8.3I PQ,(J)+0.01J'(J'+1) cm" vs. J'(J'+1) indicating the
resonance.

effect of an accidental

 

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is}:

where the slope of the lines is the unperturbed value of
Bo-gagvs if the energy levels themselves are plotted or
—§a§vs if the Q(J) line frequencies are plotted.

Since the two cases are equivalent we shall assume that
it is the Q(J) frequencies which are plotted as is the case
in Figs. 8.30 and 8.31. Below, the levels are redrawn with

the corresponding solution of the secular equation from

EQe(6e1O)9 10809

 

E: = Ea"'Eb :t ¢ea-Eb)2+ W2
q

2

01‘

 

G = Eav :i: “82/4 + W2

where Eav is the average energy of the two unperturbed sets
of levels whose individual separations from Eav are given

by 8/2 = (8/2). + (b/2)J(J+1).

Energy

 

 

313+!)

 

In the diagram above, y is the energy separation of Rev and
either leg of the hyperbola and is given by
=|e~ Eavl" V32/21 . we (8.21)
while x is equivalent to y but is equal to it only at the
point of exact resonance44'where
X = W (8022)

since at this point 5.: 0.
That 6 describes an hyperbola may be shown as follows.
Consider the case of a type II coupling (cf.Chapter 6) where

 

the perturbing matrix element has the form w VJ(J+1)-K(Kt1).
Then, in order to simplify the following, we assume without
loss of generality, that we have transformed coordinates
such that saw = 0 and is parallel to the J(J+1) axis (identi-
_ 45
cal to the J(J+J) axis since Eav _ 0%
Then
‘ 2 l 2 n2 .2
6 = ‘(a+bJ(J+1)) +h J(J+1)-h K(K+1)
where (8.23)
S =.a + bJ(J+1)

44As we shall see below, this figure must not be taken
too literally, since E and Eb are not always the asymptotes
of the hyperbolae and thus, 8 = 0 does not occur exactly at
the intersection of Ba, Eb and Eav'

4SIn the event that Bay is not a straight line vs.
J(J+1) we take the J(J+1) axis to be the tangent to Eav at
exact resonance.

which may be written as

2 _ [£(J-1-1) + (a/b)+ 2112/11?- 32 = ‘ (8.2M

.5.
D (4/b2)D

where

D = w?- [( 412/112) -K(K+1) - a/b]
Eq.(8.24) is the equation of an hyperbola with its origin
at -(a/b + Fee/be), 0 and asymptotes whose slope is b/2.
For a type I coupling (i.e., w = constant) the center is at
-(a/b), 0 so that for a type II coupling the asymptotes are
not exactly equal to the unperturbed energy whereas for a

type I coupling they are equal to the unperturbed energy.

For a type IV coupling, i.e.,

 

 

w {J(J+1) -K(K=l:1) Wan) - (K:H)(K:t2)

the asymptotes have a different slope as well as a different
Origin from that of the unperturbed energy levels.

From the expanded version of the graphs in Figs. 8.30
and 8.31 we have obtained values of ( E - Eav) for several

Values of J(J+1). Using these values, the hyperbolae in

Figs. 8.32 and 8.33 were constructed.46

h—h

46The existence of two points for each J value in
Figs. 8.32 and 8.33 does not imply that two lines were actual-
1y observed in all cases. However, from Eq.(8.24) it is
8J’Parent that the branches of an hyperbola are symmetric
about the major axis and those in Figs. 8.32 and 8.33 were

8 0 c one tructe d .

E-EW in cm"

195

Fig. 8.32 Perturbation hyperbola for the K'=:t:2, .Q=:I:i levels.

N

o - .
ommhmooo'mxrooro'soooomc'mooo
T

 

 

N

 

7 s 9 1o 11 12 13
J'(J'+1)

196

Fig. 8.33 Perturbation hyperbola for the K'=:t:2, 1:411 levels.

N

 

6-Eav in cm"

 

0 .
Omwbmo'mmb'mblvlb'm'm'ombmmo
I

N

 

65.363

 

197

The data used to plot Figs. 8.32 and 8.33 is presented
in Table 8.7.

Figure 8.34 shows an hyperbola in its principal axis
system; the equation of such an hyperbola is given by

l
6 _ f 1H1]2 ..
._2 $1.32.)... ..1 (8.25)

c
where c and d are the lengths of the semi-axes of the
hyperbola which has its origin at (x(x+1), 6 ) = (0,0). In
Fig. 8.34) x(x+1) is equivalent to J(J+1) but is measured
from the J(J+1) value at exact resonance, i.e., x(x+1) = 0

at exact resonance. As shown in Fig. 8.34, the equation of

the asymptotes is given by

e = i (c/d) x (1+1). (8.26)

From Figs. 8.32 and 8.33. the value of 0 may be obtained
immediately since it is a well defined quantity. Then using

Eq.(8.25) written as

E; -1 = (1/d2) [x(x+1)] 2 (8.27)
the value of 11 may be found from a least squares analysis
01' several points on the hyperbola. Thus, the asymptotes
01’ the hyperbola are well defined when the perturbation data
is reduced in this fashion. 0n the other hand, the asymptotes
are not well defined in any suple way in Figs. 8.30 and 8.31.
From Figs. 8.32 and 8.33, using the results of the above
cu~8<2ussion, we find the results given in Table 8.8, where

198

Table 8.7 (E-Eav) for Kfzee, t=e1 and K'=i2, 1:;1 levels.

K'ziQ, £=i1 levels

J' 6 -an(cm")
1.38
1.14

9 0.88

10 0.72

11 0.79

12 1.04

13 1.44

lit-J2, 1.1-«i=1 levels

J' 6 -Eav(cm")
16 1.40
17 ’ 0.96
18 0.61
19 0.54
20 1.50

22 2.09

 

199

Fig. 8.34 An hyperbola with its center at the coordinate
ought

 

 

 

 

 

6
o—asymptote
6 = fi- x (x+ I)
(0,C)
(-d,01 (d,0)
x(x+D
(O,-Cl

 

200

Table 8.8 Summary of results of the analysis of the
perturbation affecting the K'=:i 2, L = i 1, and
the K' = t 2, t =<¥ 1 levels of v3 + v4.
Equation of the perturbation hyperbola

%:-zi§§1l=1

x(x+1) = 0 at resonance

For H': :2, t = 11 levels

J'(J'+1) = 117 at resonance
C = 0e62 01n-1
d = 30
- -1
easym _ ¢0.0206 x (x+1) cm (asymptotes)

3:.- 4.82-0.0412 J'(J'+1) on"1
For K’: 22, L :1? 1 levels

J'(J'+1) = 207 at resonance
c = 0.50 cm"1 I
d = 24
6 = $0.0206 x (x+1) cm"1 (asymptotes)

asym
8: 8.52-0.0412 J'(J'+1) c111’1

c and d are the semi-axes of the hyperbolae,

5 = :1: (c/d) x (x+1) is the equation of the asymptotes, and
5 is the resulting equation for the separation of the two
perturbing levels in each case. Using the information in
Tables 8.5 and 8.8 we obtain the relative energy level
positions of the 22+ and 2" lines of v3+v4 and the perturbing
levels.47 These results are given schematically in Fig. 8.35
and include the symmetry species of the levels under the
rotational subgroup C3 (of. Chapter 2).

The question of the assignment of the perturbing band
is a perplexing one since there are so many possible
resonances between nearby bands, as depicted in part by
Fig. 8.3 and Table 8.4, so that in this instance we are not
certain of the location of the levels of the unobserved bands.
In fact, as mentioned earlier, for most molecules at present
the anharmonic constants are unknown and thus accurate
Placement of even the unperturbed rotation-vibration levels
is nearly impossible in a majority of the cases.

We have investigated the possibility of the perturbing
levels belonging to the overtone and combination levels
believed to be in the vicinity of VB“:4 (of. Table 8.3).

It is indeed unfortunate as well as frustrating that
We have not been able to find a complete explanation for the

Observed data. Several levels have provided interesting

¥

A

47For brevity, the K': :2, L = 11 levels are designated
as 2+ levels and the K': :2, 1: :4” levels as 2" levels.

202

Fig. 835 Level structure of J =0 levels for the perturbation
of the K'=:t2,f=rl and K'=12, £==Fl levels of

 

 

 

 

 

 

113+ 14 .
V3.11- 14 Perturbing levels
_ ... T) ______ A
8.52 cm" 7.00 cm"I
E
A 2 -
4.82 cm"
3.30 cm"
E 2+ ( ______ _ .lL. _ __

Jug...» .. -

h)
0
Ln!

possibilities but have not separately been able to account
for the perturbations in the K': 12, l = i1 and the
K': 1:2, I = 11 levels without giving rise to apparent con-
tradictions. From the results of our study of the possible
perturbing levels, it is quite likely that the perturbations
observed in \13-w4 are the result of an interaction between
v3+v and two or more overtone or combination levels. This
is quite plausible since although we do not know the anhar-
monic constants and thus cannot place the vibrational origins
0f the other nearby levels accurately, we can calculate the
=0 levels for the various K values in a given set of
combination or overtone levels quite accurately (to within
7:5 :h 2cm”) if they are unperturbed. Even so, by making
the most favorable assumptions about the vibrational origin
(1 -e., the J=0, K=0 level), we still cannot arrive at a
consistent explanation based on a single perturbing overtone
or combination level. However, a mutual interaction between
V3+v4 and two or more other overtone or combination levels
c(Duld easily invalidate the considerations which we have
meuie while considering one perturbing overtone or combina-
tion level at a time. However, with the current data avail-
able on the anharmonic constants for CH3F, the problem of

a resonance involving two or more unobserved overtone or

coInbination levels with V3+V4 is nearly impossible to solve

'5 ati sfactorily .
At this point we shall describe several other perturba-

t1011:5 we have observed and whose effects may be seen in the

Gian . . 1

 

observed minus calculated graphs in Figs. 8.4-5.2;

O

Perturbation of Levels With
High J and Low K

In Figs. 8.11-8.17 for the -2 through the +4 subbands
the effect of a perturbation on the high J levels is apparent.
We have examined two possible interpretations of this per-

turbation. The first is that an accidental resonance involv-

ing a coupling of type V, i.e., a

 

 

 

v; {Tram «(new 51.1.1) -1xe111xa2) 7mm -(Kt2)(Kt3)

coupling, with nearby overtone or combination levels causes
the rapid divergence to low wave numbers with high J values.
If this is the proper interpretation, it appears that in
151118 case there is no crossing of levels in contrast to the
Situation for the K'=2 levels described in the previous
Section. Under these assumptions, one would expect the
lfielding term of the second order non-degenerate perturbation
eXpansion to be a (J+l!iJ)3(J~1»1+AJ)3 term. A least squares
analysis of the subband lines for the -2,-1,0,+2,+4 subbands
including such a term resulted in a good fit of the lines
13 or each subband analyzed. The coefficients of the
(J~t-A.J)3(J+1+AJ)3 term ranged. from 4x10'9 to 11x10'9cm".
An example of the "goodness of fit" is given in Appendix X
for the K"=O subband which was mentioned previously in the
Seetion dealing with Coriolis resonance.

A second possible interpretation is that the rapid

divergence to low wave numbers is caused by a crossing of

m
0
\j‘l

unperturbed energy levels in the same manner as for the
K'-:t2,£ = i1 and L = :1 levels discussed in the preceding
section. In these cases the crossing must be for a value
of J above 15. Indeed, we have been able to find partial
sets of lines for the +1 and the -2 subbands which might
represent such an effect. However, since these occur at such
high J values where the lines are very weak, we cannot be
certain that the lines observed actually belong to the
subbands in question. However we present the data here for
the sake of completeness and with an eye to further work

on this band.

It should be noted that the +1 subband involves the
K' = 12, 1. .-..- :1 levels where we observed another, more certain,
crossing of unperturbed energy levels. This portion of the
discussion was not mentioned at that point because 'of its
speculative nature. Tables 8.9 and 8.10 list the Q(J)
(and corresponding R(J-1) and P(J+1) where found) transition
frequencies in the region of resonance. Those marked with
an asterisk are of uncertain assignment and are not included
in Appendix V. Figures 8.36 and 8.37 Present the Q(J)
frequencies vs. (J+AJ)(J+1+AJ) for the +1 and -2 subbands
respectively. In Figs. 8.38 and 8.39 the perturbation
IWperbolae for the +1 and -2 subbands are reproduced and
Table 8.11 presents the results of an analysis of these
hyperbolae.
Although we have not been able to find the corresponding

transitions for the -1,0,+2,+3 and +4 subbands, we feel that

206

Lower Frequency Brancha

Assignment

R01m
16
17
18
19
20

Frequency

4065.76
4065.34
4064.82
4064.44
4063.97

Higher Frequency Branch

Assignment

R01(18)
R121(17)
RP,(19)

F121(19)
R31(18)
R191(20)

RQ,(2o)
R12,09)
R13(21)

RQ,(21)
RQ,(22)
RQ‘(23)

a Corresponding RR1(J) and RP1(J) lines are found
in Appendix V

Frequency

4066.05*
4096.69*
4033.76*

4065.08*
4097.41*
4030.99*

4064.52*
4098.54*
4028.77*

4064.01“
4063.51*
4063.16*

Table 8.9 R(AJ)1(J) frequencies in the region of resonance.

Line

536
563
531
527
520A

Line

5383
6T4
376

532A
677A
362’.

529A
681A

3503

527A
525A
521A

207

Table 8.10 PQ2(J) frequencies in the region of resonance.

.P
02(J)

1:2
125
144
155
1(5
1'?
153
1S?
2%)
221
222
223

a

Higher Freq. Branch

Frequency

4044.79*
4044.49*
4044.07*
4043.57*
4043.12*
4042.62*
4041.14«
4041.67*
4041.20*
aoa'o.76*
4040.24*
4039.72*

Appendix V.

Line

430
428
426 \
424A
4223
419

.417

414A
412A
4103
408A
406*

lower Freq.

Frequency

4044.06
4043.77
4043.44
4043.09
4042.71
4042.28
4041.84
4041.38
4040.76
4040.08
4039.39

Brancha
Line

426
425
423A
422A
420
417B
415
413
410B
407C
404A

Corresponding PR2(J) and PP2(J) lines are found in

 

Ids-1... ... ism-shenafllawqasaz. shone

 

 

208

2+.3 .5

 

 

VN MN NN _N ON 9 0. h. w. n. S m. N. Z O. m m N w m @mNa
_ _ . _ _ _ _ _ q _ .n.__fi___n:w.
/ .. ..
I ONmO¢
1 N.
I. V.
J m.
J o.
l Od¢0¢
L N.
o o o o 1 c.
Q m.
I... m.
l O.m@OV
1 N.
I c.
1 w.

 

noses. 320208 2: no use: 2. 3.8.2 23% .2 uses: 3.? one .5

 

..wo U! (l+,f‘),1‘|0'0+(1‘)'03

 

 

§.W)r. ,. fill; and”. ‘vanln: «We: adult-l ".

 

209

 

2+.va

 

 

 
  
 
  

¢N mm mm .N ON m. m. t w. o. v. m_ N. : O. m m N w memgo

a n _ _ _ __44_4444:4¢.

1 m.

1 w.

s.

m.

m.
omvov

_.

N.

m.

e.

m.

m.

s.

m.

m.
onooo

_.

N.

l m.

m o.

 

.8588. .25280 no ho 83$ 9: 056205 A538 .m> mcozfico: ENoa mm. .. .Ew

‘

..wo U! (l+,f‘),I‘IO'O +(r)zod

210

2.1.28

 

 

 

_N ON m. m. t w_
1 w
L ¢.
-w . ....
. 0..
1 m.
1 w.
. a. a
3
1 N. D
A
a . as m.
. N. 3 .
n n.
. m.
. o._
.o . N.
r V.
. w.

 

.326. fine. .Nfluw. of .0. 0.3.8.... 8:35th mm.m .9...

211

ON

23.2%,

 

 

 

 

 

 

 

m_ m. ... n. n. v. n.

1?.

O 3

>0
0 O . N.
.o ....
Law.
.326. .4 q .3 .0.. 23.3.3 5:35th QMQ .31..

212

Table 8.11 Summary of results of the analysis of the
perturbations affecting the K = i2, 1 = i1,
and K' = i1, 1 = ¥ 1 levels of v3+v4.

Equation of the perturbation hyperbola
2
5 x x+ _

For K': i2, A = t1levels

J'(J'+1) = 363 at resonance
c = 0.44cm'1
d = )3
easym : i0.0136x(x+1) (asymptotes)
8‘ = 9.081 - 0.0272 J'(J'+1)cm"1
For K'- *1, A = ¥=1 levels
J'(J'+1) = 313
c = 0.1550m"1
d = 66
easym = 10.0023x(x«1-1)cm"1 (asymptotes)

09
n

1.44 - 0.0046 J'(J'+1)cm'1

2.

\N

this second interpretation of the high J low K perturbation
is made plausible by the transitions found for the +1 and
-2 subbands.

In either case, we cannot.at the present time decide
between the two possible interpretations.

Weak Coriolis Resonance in the
Negative Subbands

 

Figures 8.4»8.8 indicate the presence of a weak Coriolis I

 

type resonance, quite likely of the form W V3(J+1)-K(Kt1) 1
which if the separation of the perturbing levels is large
enough will give rise to an added term in EVR for the upper

state, of the form

6 ,_. 11'2J'(J'+1) ~112(K'(K'a1)l (8.28)
where, as before, 8' is the energy separation of the per-
turbing levels. In general 8 is a function of J and K as
discussed in Chapter 6. From our analysis it is possible
to obtain approximate values of (112/8 ). We find:

subband (112/8 )(cm-1 )
(K"AK)
-9 +0.0021 a 0.0001
-8 +0.0012 a 0.0003
-7 +0.0008 a 0.0001
-5 40.0018 a 0.0004

-4 -0.0002 t 0.0001

-‘ SHEA

ll .-

214

The uncertainties indicated above are the simultaneous
confidence intervals of the type discussed in Chapter 5.

In the list above, no results are given for the -6
subband since it is perturbed quite strongly and the coef-
ficient of (J'(J'+1) is not well defined. This is easily
verified by noting the form of the perturbation of -6
subband lines in Fig. 8.7. It appears quite likely that
the -6 subband is perturbed by the same form of perturbation

as the other negative subbands discussed above but the

 

resonance is probably accidentally strong so that the 1

energy levels have the added correction here of

 

6’ = Eav .tW82/4)+112[J'(J'+1)-K'(K'a1)] (8.30)
where S is very small.

At this point we interject a word of caution concerning
the analysis of subband origins.

For the purpose of comparison, the -9 to +9 subband
origins were obtained graphically from expanded graphs of
effective Q branch lines vs.J'(J'+1) (cf. Fig.8.27, for
example). The subband origins were also obtained by a
computer analysis of the individual subband lines using
the equation (for a fixed K and AK):

{AK(AJ)K(J)}°bs-Bo[(J+AJ)(J+1+AJ)-J(J+1)]+
DJ[(J+AJ)2(J+1+AJ)2-J2(J+1)2]+
° (8.31)

DgK[(K+AK)2(J+AJ)(J+1+AJ)-K2J(J+1I]:

vsub(K)-[a 2+0, E-QiM-MKMK] (J+AJ)(J+1+AJ),

215

J JK is

where the dependence of the lines on B0, Do , and Do

subtracted off using microwave values of B0,.DoJ and DOJK
(58). In both cases the obviously perturbed high J lines
were ignored (graphical method) or not fit (computer method).
The subband origins (Vsub) obtained in the two methods
agreed to 0.01cm'1.

These subband origins were further analyzed graphically
and those which were thought to be perturbed (+5,+1,-3,-4,
-5,-6,-7,-8,-9) were not included in the subsequent least
squares analysis. The results of a least squares analysis

of the subband origins to the equation

Vsub = a + bKAK + cK2 + dK3AK (8.32)

are given in Table 8.12 where the coefficients a,b,c,d
(assuming that the subband origins included in the

analysis are unperturbed) are interpreted in that
order in the table. Table 8.13 lists the results of the
analysis for each subband origin. Those points enclosed

in parenthesis were not included in the analysis since they
were thought to be perturbed. We notice particularly that
from -4 to -9 there appears to be a K dependent perturbation

of the subbands. In this respect, remember that the sub-

band origins used here are actually appggent subband origins
obtained from an analysis based on Eq.(8.31). However
Figs. 8.4-8.9 indicate that the low J lines (J’a‘! K) in the
.4 to -9 subbands do indeed appear near their calculated

values. The apparent discrepancy is due to the use of

 

216

Table 8.12 Subband origin analysis

V
O

2(110 -Aeg -B°

Std. dev.

- - - A
2AeC +Ao B0 a +0

B K K
+rl4 “Do

’QA + 0B) +3'1E

1‘- 1:

+0“ +3114 -63K

0
K K
--4Do +04

of observations

results (cm'I).

4060.99 i

7.5954 t

-0.0110 i

-0.0089 a

0.0062

0.015

0.0067

0.0029

0.0027

217

Table 8.13 Subband analysis results (cm'1).

Vsub(obs) vsub(calc) (obs-calc)
4127.80 .80 0.00
4113.31 .31 +0.00
4105.98 .97 +0.01
(4098.11) .58 {-0.47)
4091.14 .14 0.00
4083. 65 .66 “0.0‘
4076.14 .13 +0.01
(4068.57) .58 (-0.01)
4053.39 .39 0.00
4045.76 .76 0.00
(4022.69) .85 (-0.16)
(not defined) 4015.22

(3999.48) .98 (-0.50)
(3991.64) 2.40 (-0.76)

 

.. "01.. ~
, 4"!

218

extrapolated subband origins in the -4 to -9 subbands.
However, there is no other way of obtaining the subband
origins "accurately" on the basis of an analysis of lines

only from a particular subband. Thus, there is the additiion-

 

a1 effect of a perturbation of the type W VJ(J+1)-K(Kt1)
which leads one to false subband'origins, by changing the
coefficient of the J'(J'+1) term in the upper state energy
expression.

Perturbation Affecting
the +5 Subband

The final major perturbation affects the +5 subband
as indicated in Fig. 8.18. Its principal effect is a shift
of the subband lines to lower wave numbers by about 0.55cm"1
at the subband origin, plus a small change in the coefficient
of J'(J'+1) in the upper state energy expression. The
first effect is probably due to a perturbation of type I or
III, i.e., a coupling of the form W or WK while the second
is probably due to a coupling of type II, i.e.,
1: 1511.1) -K(Ki1).

 

genslssian
we have obtained, under high resolution (€50.04cm'1),

a perpendicular band which has, in addition to the usual
RR, RP, PR, and PP “fine structure", numerous resolved
RQK(J) and PoK(J) transitions. In fact, this is the first
example of such‘highly resolved structure in the molecules

of the methyl halide_family_of which we are aware. We have

‘ ‘99» ...—1g: Fania-11’

'31.!- I
.-.... .1311...
, 3.4913545.th

219

simultaneously analyzed 207 ground state combination
differences according to the method of Chapter 4 and 156
"unperturbed” transitions according to the method described
in Chapter 5 to find the molecular parameters for this
rotation-vibration band.

In addition, we have observed several perturbations in
this band. he have identified one as a Coriolis resonance
which lifts the degeneracy of the K'=n£=ri1 levels. Our ob-

servations are somewhat unique since we have here resolved

the individual RQO(J) as well as the RRO(J) and RPO(J) transi-
tions making possible a full analysis of this perturbation.
Another interesting perturbation is the accidental resonance
which shows up as a crossing of the K': 12, 1 = a1 and

K‘: :2, 4 ==F1 unperturbed energy levels of 93+v4 with those
of another band. Due to our observation of the Q(J) lines
involved in these resonances as well as the R(J) and P(J)
lines, we have well substantiated data on these resonances.
Using the method of Chapter 6 we have searched for a complete
quantitative solution to the perturbation. However, we

have not been able to assign the perturbing levels to a
single rotation-vibration band and have reason to believe
that the actual perturbation may involve the levels of two
or more rotation-vibration bands. We have not been able
to.investigate this possibility due to the non-availability
of.anharm0nic constants for CHBF. We have however obtained

some quantitative results because of the manner in which we

 

4.1

,FEUFFMLVJJa

220

have treated the data from our observations of these perturb-
ed transitions.

Several other perturbations were also observed and some
information obtained from our observations.

We have treated this band according to the methods
outlined in the first six chapters of this work and have
carried the analysis as far as we believe it may be readily
taken at the present time.

The analysis of unperturbed spectra itself is a complex

 

problem when treated properly as described in Chapters 3,4
and 5,due in part to the huge volume of data one observes
and the small effects which must be taken into account

.5

(conservatively, as small as 0.050m"1 or'2=6.2x10 electron-

volts). When one steps into the realm of perturbed spectra
the problem is several times more complex, a point which is
borne out by the large number of perturbed spectra which

have been observed and the very few which have been complete-

ly solved.
Note added in 2:99; - We have been able to recalibrate

v3 +-v4 against 17 Neon lines using the 300 li/mm grating.
The results of this calibration indicate that the frequencies
should be corrected according to the formula:

”new = «10.2989 + 0.9999193 Vold' For the ground state con-
stants, this leaves DoJ and DoJK unchanged and gives the
-va1ue 0.851872cm'“1 for Bo which differs from the microwave
results by 0.0000780111"1 which lies within our simultaneous

confidence interval of a0.000087cm".

- Jessi.

ti- ..

 

 

CHAPTER 9

SIMULTANEOUS ANALYSIS OF COMBINATION DIFFERENCES
APPLIED TO v1+v2 OF CHD3 AND v2+v3 OF CH3D

The high resolution spectra of two parallel bands,
v1+v2 of CEID:6 and v2+v3 of CHBD, were obtained as described
in Chapter 7. Upon investigation both were found to be
perturbed and we shall discuss this briefly in this chapter.
However, the principal reason for this chapter is to illus-
trate the application of the results of Chapter 4 to two
molecules whose pure rotation spectra have not been observed
by microwave stpectroscopists because of the extremely small
permanent dipole moments which these molecules possess. As
a result of our work we have found good values for Bo, DoJ

and DoJK for both molecules, even though the upper levels

are perturbed.

v14~2 of CHD1

 

The observed spectrum of CHD:5 which we have assigned
to v1+v2 is shown in Fig. 9.1, with assignment of the
principal transitions indicated. The QQK(J) transitions,
:hn particular, are well resolved on the high resolution
‘woakdng records. Appendix XI lists the observed transitions
:for v1+v2. We observed, upon attempting to analyze the
spectrum, that it is perturbed and have not definitely found
spay large subset of apparently unperturbed lines (as was the
«case for v3+v4 of CHBF in Chapter 8). The first striking
suspect of'the perturbation, apart from an apparent J

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dependent perturbation, is that the J':K' levels in the
upper state appear to be displaced from their expected
position (on the basis of other levels of the same J) by a
nearly constant amount (68 O.2Ocm"’1 higher than expected).
If one assumes that the K'zJ' transitions are perturbed,
while the others are not as strongly perturbed, then

v04: 5135.04cm" whereas if one assumes the K'aJ' are
unperturbed, then ”a” 5134.84cm"'. In addition, an
apparent J dependent perturbation shows up when one attempts
to analyze a single K subband. We have not been able to
find an explanation for the perturbation at this time.

Ground State Combination

Differences of v1+v2

The ground state combination differences of v +v

1 2

were, however, analyzed simultaneously following the method
described in Chapter 4. The perturbation affects only the
upper state of v1+v2 and therefore the ground state combina-
tion differences give good values for Bo' DOJ, and DOJK.
Table 9.1 lists the results of this simultaneous analysis
with the simultaneous confidence intervals 48 for each

constant (cf.Chapter 5) from an analysis of 54 ground state

 

48The more meaningful simultaneous confidence intervals

used throughout differ by the factor S =[pFa(p, n -p)J'/"‘£rem +11.“

usually quoted (e.g.reference 107). In this work S ranged
from 2.5 to 3.5. An a of 0.05 was used throughout this work.

 

 

 

 

 

a...”
. ..
u.

229
Table 9.1 Ground state constants of CIID3

Bo : 3.27944 1 0.00062cm"1

 

DOJK: -4.8 x 10’5 a 1.4 x 10"'5cm-1
'DOJ = 5.22 x 10'5 a 0.61 x 10'5cm"

s = 0.010c1m"1 std. dev.

 

230

combination differences. The comparison of observed and
calculated combination differences is given in Appendix XII.
Table 9.2 compares the results of this study with results
of analyses of several other infrared bands (2,3,104,105).
We believe our values to be the best presently available

for this molecule.

 

v2+v3 of CH D

3

The observed spectrum of v2+v3 of CHBD is shown in

Fig. 9.2. The structure of the band is similar to that of

 

v1+v2 of CHD3 due in part to the similarity of B0 between

the two bands and particularly due to the large a5 and dB
in both bands.

We find that v2+v3 is also perturbed,particularly for

J > 10 or 12 and K >’6 or 7. Part Of the perturbation shows
up as a divergence to high wave numbers with large K and J.49

Ground State Combination

Differences of V2+v3 of CHBD

As with v1+v2 of CHD3 we have simultaneously analyzed

all observed ground state combination differences of v2+v3

of CHBD following the method presented in Chapter 4. The

 

49W.B. Olson (6) of the National Bureau of Standards
(105) has communicated the information that v2+v3 also
shows a perturbation in the K":O and 1 series of lines. He
adds that the probable perturbing levels belong to 396, a
band which is too weak to be observed.

231

Table 9.2 Comparison of available results for CHD3

ground state constant3°(cm")

 

 

 

 

 

 

 

 

Bo DoJK DoJ v0
v1+v2(a) 3.2794 -4.8r10"5 5.2x1o'5 513:;84 *
5135.04b
2v (C) -3.2777 -4 x10'5 3.91m"5 5865.02
3v'(d) 3.2784 5 210-5 8623.31
4v,(d) 3.2787 -3.5x10'5 4.6x10'5 11266.94
v1(e) 3.2792 4.6x10'5 2992.3
2v5(f) 3.278 . 1+ x1o'5 2592.6
a This Study.
b of. text ‘
c From an analysis of transitions (2).
d

From an analysis

From an analysis

f From an analysis

of combination
of combination

of combination

differences (104),

differences (3).

differences (105).

 

 

 

 

 

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The results of our analysis of 108 ground state combination

differences for we“):5 are given with their simultaneous
The

confidence intervals (cf.Chapter 5) in Table 9.3.
comparison of observed and calculated combination differences

is given in Appendix XIII. Table 9.4 compares our results
with two other studies of CHBD, one infrared absorption

study (105) and one Raman study (107).

Analysis of Upper State Combination
Differences and Unperturbed

Transitions of vew3

For those upper state levels which are not measureably

perturbed, we have simultaneously analyzed 83 upper state
The method

combination differences involving these levels.
of analysis is described in Chapter 4. The results are

listed, with their simultaneous confidence intervals
The comparison of the observ-

(of. Chapter 5). in Table 9.3.
ed and calculated upper state combination differences are

listed in Appendix XIV.
JK J

Using the values of B0, DOJ, and DC
from Table 9.3) 99 "unperturbed" transitions of vew3 were

malyzed using the expression:
AKAJK (J)}obs-Bo [(J+AJ) (J+1+AJ)-J(J+1 )] +-

0‘ 3+ Q§)(J+AJ)(J+1+AJ) + Di [(J+AJ)2(J+1+AJ)2-J2(J+,)2] +‘
'KIKQUMJ><J+1+AJ)-K2J(J+1)] f(/Bg+/3g)(J+AJ)2(J+1+AJ)2 ..

PgK+flgK)K2(J+AJ)(J+1-+AJ) = V. -(u12+01§)1<‘

. m... ”1.111,
.2:‘e/3’v...13o Dv

 

Table 9.3l101ecular constants for CHBD (in cm'1 ).

From Ground State Combination Differencesa

Bo 3.88107 i 0.00031

3gK 1.192 x 10-4 a 0.070 x 10"4
pg 5.28 x 10"5 i 0.18 x 10’5

From Upper State Combination Differencesb
Bv 3.74260 : 0.00035
DgK 2.51 x 10-4 a 0.16 x 10"4

D3 ’1.52. x 10"5 i 0.2! x 10-50'

From Analysis of Transition Frequenciesc
v 3499.6291 1 0.0026

0
aA-aB 0.151718 t 0.00020

a Std. dev. = 0.012 cm'1 for 108 points included in the analysis.

3

Std.

’ Std.

dev. = 0.012 cm"1 for 83 points included in the analysis.
dev. = 0.007 cm"1 for 99 points included in the analysis.

 

 

 

Table 9.4 Comparison of ground state constants for
C141 D (in cm'I),

 

 

 

 

 

 

3 ..
x12 + vjia) v2(b) v4“)
v0 2499.63 2200.03 5016.59
Bo 3.88107 5.8800 5.877
DOJK 1.192 x 10'4 1.2 x 10'“ 5 x 10‘5
DOJ ?.28 x 10"5 5 x 10'5 4.7 x 10"SJ

 

 

 

 

a This study, from 108 ground state combination differences.

b From an analysis of ground state combination differences (105).

c From an analysis of transitions (107),

 

 

 

257

The results are given with their simultaneous confi-
dence intervals (of. Chapter 5) in Table 9.3. The comparison

of the observed and calculated frequencies of the lines
included in the analysis make up the first part of Appendix
The second part of Appendix XV is a comparison of the

XV.
calculated and observed frequencies of all other lines we

have assigned but which were not included in the least

squares analysis.
The effect of the perturbation may be seen by scanning

the observed minus calculated column of Appendix XV.

Conclusion

Using the method of Chapter 4 we have obtained statis-

tically favorable values of 30’ DoJ and DOJK. This is

especially valuable for molecules whose pure rotation spectra

has not been observed in the microwave region. This was

the case for the two molecules discussed in this chapter.
In addition, from our results for CHBD, it appears 4-

although not surprisingly - that if possible one should use
combination differences to obtain the molecular constants

which can be found from combination differences.

 

 

 

CHAPTER 10
CONCLUSION

In this work we have gathered together many facets of
the theory of molecular spectras particularly as applicable

to molecules belonging to the point group ij.
2n have also set down a number of important considera-

tions and practical methods, usable in the analysis of spectra,
which have evolved over the four year period this work was
in pragress, particularly, the simultaneous representation

of all possible transitions50 (Chapter 3). the simultaneous

analysis of all observable ground state combination
differences (Chapter 4); and a reasonable approach to the

analysis of the large quantities of data involved in mole-

cular spectra51 (Chapter 5).
We have also attempted to gather together many of the

salient features of the remarkable work of Dr. G. Amat of

the University of Paris on the semi-quantitative study of

perturbations in molecular spectra (Chapter 6). Using all

of the foregoing we have analyzed the perturbed band, 123+”;

of CHBF, (Chapter 8) where we have. found several perturba-
tions and have come to a somewhat better understanding 0-

_¥

50This result evolved from a rather extensive study of

data analysis schemes applied to molecular spectra carried
A similar result,

3111: in collaboration with J.'1'.'. Boyd.
11though not carried as far was, obtained independently by

Brodersen and Richardson (61).
51These results are in part taken from a thesis by Boyd
50) and in part the result of the data analysis studies

arried out with J.'v.*'. Boyd.
238

 

 

239

several of these perturbations. However, the problem
involving this single band is not completely solved although
we feel that we have carried the problem about as far as it
can readily be taken at present. We have found a good
example of a Coriolis resonance which lifts the degeneracy
of K': 12, t = 11 levels. We.have, in this case, resolved
all of the K"=0 transitions involved in the resonance, i.e.,
RPOW). RQO(J). RRO(J). and have obtained a value for the
Coriolis constant q from a simultaneous analysis of all
observed K"=0 transitions. Additionally, we have observed
several accidentally strong resonances,and for at least
two cases have well substantiated data on the effect of
these resonances on the observed spectrum. These accidental
resonances provide a fine example of applied quantum
mechanical perturbation theory.

In Chapter 9 we have applied the method of Chapter 4
to two parallel bands (CHBD and CHDB) in order to demonstrate
the principle and to obtain good values of 30' DoJ and DoJK
for two molecules whose microwave spectra has not been
observed. The upper states of both parallel bands are
perturbed and we have not yet reached an understanding of

those perturbations.

 

 

1.

2.

3.

9.

10.

11.

12.

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T.A. Wiggins, Jo Opt. SOCo Mo 59—, 1275 (1960)

98. erican Institute of P sics Handbook, D.P. Gray,
editor (McGraw-Hill, New York, 1957).
2, 888 (1928).

Bennett and C.F. Meyer, Phys. Rev.

"1'. 0 PI 0

\5
o

245

100. LJL Yates and H.H. Nielsen, Phys. Rev. ll, 349 (1947).

1C”. J. Pickworth and H.H. Thompson Proc. Roy. Soc. (London)
A222. 443 (1954).

102. W.L. Smith and I.M. Mills, to be published, J. Mol.
Spectroscopy.

103. F.A. Andersen B.Bak and S. Brodersen, J. Chem. Phys.
24. 989 (1956).

104. L. Bovey, J. Chem. Phys. 21, 830 (1953).

105. H.C. Allen Jr. and E.K. Plyler, J. Res. National Bureau
of Standards 635, 145 (1959)

106. W.B. Olson, private communication.

107. E.H. Richardson, 8. Brodersen, L. Krause, and H.L. Welsh,
J. Mol. Spectroscopy 8, 406 (1962).

 

APPENDIX 1

SYMMENWTSPECIES or ROTATION-VIBRATION LEVELS OF MOLECULES
BELONGING TO THE POINT GRCEI C45”

In the systematic analysis of molecular spectra, it is
helpful to know the symmetry species of the rotation-vibration
levels of‘the absorption bands under study.

A simple, though not fundamental method of determining
the symmetry species of the rotation-vibration levels of
axially symmetric molecules belonging to the point group 03v

is presented in this appendix.

The point group 03v has symmetry species A1,A2 and E1;
the latter is a two dimensional representation and for the
axially symmetric molecule corresponds to an essential de-
generacy of the levels which are of symmetry E1(12). This
degeneracy may only be lifted by a perturbation of lower
symmetry than that of the Hamiltonian of the molecule. Levels
of species A, and A2 also occur in degenerate pairs; however
the degeneracy of'species A.levels is not essential, i.e.,
the degeneracy may be lifted by a perturbation of symmetry
equal to that of the Hamiltonian, i.e., a term contained in

the Hamiltonian of the molecule may lift such a degeneracy(12).

Since A, and A2 levels occur in degenerate pairs, we

shall only speak of levels of symmetry A and we shall drop

the subscript on the E.
Amat has found a convenient rule (49) that allows one to

determine which matrix elements of the transformed Hamiltonian
246

 

 

 

247

h' or h” are not necessarily zero due to symmetry considera-

tions. Specialized to the case of the C3,, axially symmetric

molecule the rule may be written
AK-thzt = 3p
where p is an interger 0, t1, i2,...and where the matrix

(AI.1)

elements may be written as
.5.
(oongoool‘toooIhmloooK+AK,ooo‘t+A‘tooo) (111.2)

Since only levels of species A may be split, i.e., may

have their degeneracy lifted, consider a generic segment of

 

 

the Hamiltonian matrix for a given vibrational state as

shown below.

 

 

 

 

-21 +21
-K t +K t
-K
+21t P(h+) o(h*)
+K

 

 

In the matrix, the Q(h"‘) elements are the diagonal
elements of h‘” corresponding, in the absence of off diagonal
elements, to the energy of the level with K = K and zztzzmt.

The two diagonal elements shown form a degenerate pair

either of species B or A. If the level is of species A it

may have its degeneracy lifted by a perturbing term indicated
by P(h"); if the level if of species E, the element P(h")
will necessarily be identically zero due to the symmetry

of the Hamiltonian.
Therefore, if P(h*) is identically zero the level

K, but is of species E, whereas if P(h+) is not necessarin

zero due to symmetry the level is of species A.

 

R)
L»
(0

Applying Amat's rule to the matrix element
(coo-Kooo-zttoeolP(h+)'eco+Keoo+zztooo) (A103)

it is apparent that in this instance AK = 2K and th:221t.

Therefore if P(h+) is not necesgagily zero then
2K-2 zzt =3p =0, i3,i6,t9,i12,...

 

or, after dividing by 2 and recalling that K and Lt must

necessarily be intergers,
K-2‘t :31} =O,i3’i6, o o o

where n may take on the values O,i1,i2,t3,....

 

Quite generally for a 03v molecule the A species level
are those which satisfy the relation
K-ut =3p; p =0,11,i2,... (AI.4)
Consequently the E species levels are those which satisfy

the relation
K-ut =3pi1 (AI.5)
This approach may also be used for molecules belonging
to other point groups and in fact the results obtained here

depend only upon the fact that the top axis is a three fold

axis.

 

APPENDIX II

LIST OF CALCULATED GROUND STATE COMBINATION

DIFFERENCES FOR CHBF

The following pages contain ground state combination
differences (in cm'1) computed on the Michigan State Univer-
sity Digital Computer, MISTIC. The values of the constants
used are (in cm"):

B = 0.851793

DJK = 1.48 I 10-5

DJ = 1.98 x 10'5
These constants are taken from the results of the pure
rotation spectra observed in the microwave region (58).

In order to use the tables one should note that the
designation of the combination differences in this appendix
is that used in Chapter 4. Note also that

QPK,J = RQK,J+1.

249

 

 

 

 

ASSIGN-
MENT

R0
RQ
R0
R0
RQ
90
R0
R0
R0
90
R0
R0
R0
R0
R0
R0
90
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
90
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0

09
09
09
3, ,
O9
09
O,
09
09 ,
0910
0911
0912
0913
0914
0915
0916
0917
0918
0919
0920
0921
0922
0923
0924
0925
0926
0927
0928
0929
0930
0931
0932
0933
0934
0935
0936
0937
0938
0939
0940
19
19
19
19
19
19
19
19
1910
1911

omxlOuimeH

\OQNO‘U‘wa

CA

LCULATED
GSCD

197036

394071

591105

698138

895169
1092198
1199224
1396246
1593265
1790279
1897289
2094293
2291292
2398285
2595271
2792250
2899221
3096185
3293139
3597022
3793948
3990864
4097769
4294663
4491545
4598415
4795272
4992115
5098945
5295761
5492562
5599348
5796118
5992873
6099610
6296331
6493034
6599719
6796386

394070

591104

698137

895168
1092196
1199221
1396244
1593262
1790276
1897286

ASSIGN-
MENT

R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0 1
R0 2912
R0
R0
R0 2915
R0
R0
R0
R0
R0
R0
R0 2922
R0 2923

1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
29
29
29
29

\omqombm

251

CALCULATED

GSCD

2094290
2291288
2398281
2595266
2792245
2899216
3096179
3293134
3490079
3597015
3793942
3990857
4097762
4294656
4491537
4598407
4795263
4992107
5098936
5295752
5492553
5599338
5796108
5992862
6099600
6296320
6493023
6599708
6796374

591102

698133

895163
1092191
1199215
1396237
1593254
1790267
1897276
2094279
2291277
2398268
2595253
2792231
2899201
3096163
3293117
3490062
3596997
3793922
3990837

ASSIGN-
MEMT

R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0

2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
39
39
39
39
39
39
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922
3923
3924
3925
3926
3927
3928
3929
3930
3931
3932
3933
3934
3935
3936

\OOJNCPUTP

252

CA

LCULATEO
GSCD

4097741
4294633
4491514
4598383
4795238
4992381
5098910
5295724
5492524
5599309
5796078
5992831
6099568
6296287
6492989
6599673
6796339

698127

895156

092182
1199205
1396225
1593241
1790252
1897259
2094261
2291257
2398247
2595231
2792207
2899176
3096137
3293089
3490032
3596966
3793889
3990803
4097705
4294596
4491476
4598343
4795197
4992038
5098865
5295678
5492477
5599260
5796028
5992779

099514

ASSIGN-

MFMT

99
R0
9.0
R0
R0
R0
9.0
R0
R0
R0
R0
R0
R0
Ra.
R0
R0
R0
R0
R0
R0
9.0
R0
R0
R0
R0
R0
Rd
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0

3937
3938
3939
3940
49 5
49
49
49
49 9
4910
4911
4912
4913
4914
4915
4916
4917
4918
4919
4920
4921
4922
4923
4924
4925
4926
4927
4928
4929
4930
4931
4932
4933
4934
4935
4936
4937
4938
4939
4940
59 6
59 7
59 8
59 9
5910
5911
5912
5913
5914
5915

O‘TDNJO‘

TU

UT
U0

CALCULATED

GSCD

6296232
6492933
6599615
6796279

895145
1092169
1199190
1396208
1593222
1790232
1897237
2094236
2291239
2398218
2595200
2792174
2899141
3096099
3293049
3399990
3596922
3793844
3990755
4097655
4294544
4491422
4598287
4795139
4991978
5098803
5295614
5492410
5599191
5795957
5992706
6099439
6296155
6492854
6599534
6796196
1092153
1199172
1396187
1593198
1790205
1897207
2094204
2291196
2398181
2595160

33.. ii. 50m...“ in .

 

ASSIGN-
RENT

R0 5916
R0 5917
RC 5918
93 5919
90 5929
R0 5921
R0 5922
R0 5923
90 5924
R0 5925
R0 5926
R0 5927
R0 5928
R0 5929
R0 5930
R0 5931
R0 5932
R0 5933
R0 5934
R0 5935
R0 5936
R0 5937
R0 5938
R0 5939
R0 5940
R0 69 7
R0 69 8
R0 69 9
R0 6913
R0 6911
R0 6912
R0 6913
R0 6914
R0 6915
R0 6916
R0 6917
R0 6918
R0 6919
R0 6920
R0 6921
R0 6922
R0 6923
R0 6924
R0 6925
R0 6926
R0 6927
R0 6928
R0 6929
R0 6930
R0 6931

CALCULATED

GSCD

2792131
2899095
3096051
3292998
3399937
3596866
3793785
3990693
4097591
4294478
4491352
4598214
4795064
4991900
5098723
5295531
5492325
5599103
5795866
5992613
6099343
6296056
6492752
6599430
6796089
1199149
1396161
1593169
1790172
1897171
2094165
2291153
2398135
2595111
2792079
2899040
3095992
3292936
3399872
3596797
3793713
3990618
4997513
4294396
4491267
4598126
4794972
4991805
5098625
5295430

 

ASSIGN-

MF M T

R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0

~10\O\0\O‘O\O\O\(h<l\
4>wmwwwwww
O) C)\003~JO‘UIJ>UJI\J

.-.--.OOOO

\lxl
.-
9.4
"\0

7911
7912
7913
7914
7915
7916
7917
7918
7919
7920
7921
7922
7923
7924
7925
7926
7927
7928
7929
7930
7931
7932
7933
7934
7935
7936
7937
7938
7939
7940
89 9
8910
8912
8911
8913
8914
8915
8916

1\)
U1

U1

CRL

TED

(
nC
nr'

A
0

‘5

x

K

1

5492229
5598995
5795755
5992499
6099226
6295936
6492628
6599303
6795959
1396130
1593134
1790134
1897129
2094119
2291103
2398081
2595053
2792017
2898974
3095923
3292863
3399794
3596716
3793628
3990533
4097420
4294300
4491167
4598022
4794864
4991694
5098509
5295310
5492097
5598868
5795624
5992364
6099087
6295793
6492481
6599152
6795804
1593094
1790089
2094065
1897080
229 045
2398019
2594986
2791946

.53.

 

 

ASSIGN‘
.‘4 E N T

R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0

8917
8918
8919
8920
8921
8922
8923
8924
8925
8926
8927
8928
8929
8930
8931
8932
8933
8934
8935
8936
8937
8938
8939
8940
9910
9911
9912
9913
9914
9915
9916
9917
9918
9919
9920
9921
9922
9923
9924
9925
9926
9927
9928
9929
9930
9931
9932
9933

.9934

9935

[\J

UT
0‘

CALCULATED

GSCD

2898898
3095843
3292779
3399705
3596623
3793530
3990427
4097313
4294188
4491051
4597902
4794740
4991564
5098375
5295172
5491954
5598721
5795473
5992208
6098926
6295628
6492312
6598978
6795626
1790039
1897024
2094005
2290980
2397948
2594910
2791865
2898813
3095752
3292683
3399604
3596517
3793419
3990311
4097192
4294062
4490920
4597766
4794599
4991418
5098224
5295016
5491793
5598555
5795301
5992031

 

ASSIGN-
FflEPJT

257

CALCULATED

GSCD

R0
.90
R0
R0
80
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RD
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP

9936
9937
9938
9939
9
09
09
09
O9
09
09
09
09
09
09
0910
0911
0912
0913
0914
0915
0916
3917
0918
0919
{3,20
0921
0922
0923
0924
0925
0926
0927
0928
0929
0930
0931
0932
0933
0934
0935
0936
0937
0938
0939
09490
19 1
19 2
19 3
19 4

o
4}
.3

\Om'xlO‘WbWNHC);

6998745
6295441
6492121
6598782
6795424
197036
591107
895176
1199243
1593307
1897367
2291421
2595470
2899511
3293544
3597568
3991582
4295586
4599577
4993556
5297521
5691471
5995436
6299324
6693225
6997107
7390970
7694812
7998633
8392432
8696208
8999960
9393686
9697387
10091061
10394706
10698323
11091910
11395466
11698991
12092483
12395941
12699365
13092753
13396105
13699420
591106
895175
1199241
1593305

ASSIGN-
MENT

RP 19
RP 19
RP 19
RP 19
RR 19
RR 1910
RP 1912
RP 1913
RP 1914
RP 1915
RP 1916
RP 1917
RP 1918
RP 1919
RP 1920
RP 1921
RP 1922
RP 1923
RP 1924
RP 1925
RP 1926
RP 1927
RP 1928
RP 1929
RP 1930
RP 1931
RP 1932
RP 1933
RP 1934
RR 1935
RR 1936
RP 1937
RP 1938
RP 1939
RP 1940
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP

\OUJKJO‘UT

258

CALCULATED

1
1
1
1
1
1
1
1
1

GSCD

1897364
2291417
2595465
2899506
3293538
3597562
4295578
4599569
4993547
5297512
5691461
5995396
6299313
6693213
6997095
7390957
7694799
7998619
8392418
8696193
8999944
9393670
9697370
0091043
0394688
0698304
1091891
1395446
1698970
2092462
2395920
2699343

13092731

1
1

3396082
3699396

895170
1199235
1593297
1897354
2291406
2595452
2899491
3293521
3597543
3991555
4295556
4599545
4993521
5297484
5691432

 

ASSIGN-
MENT

RP
RD
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP

2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
39
39
39
39
39
39
39
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922
3923
3924
3925
3926
3927
3928

00049099169»

25

C

C

/

ALCULATED
GSCD

5995364
6299280
6693178
6997058
7390919
7694759
7998578
8392374
8696148
8999897
9393621
9697319
19090991
13394634
10698248
11091833
11395387
11698909
12092399
12395855
12699276
13092662
13396011
13699324
1199225
1593283
1897338
2291387
2595430
2899465
3293493
3597512
3991521
4295519
4599505
4993478
5297438
5691383
5995312
6299225
6693121
6996997
7390855
7694692
7998508
8392302
8696072
8999818
9393539
9697235

ASSIGN-
MENT

(P
(7

CALCULATED

GSCD

RP
RP
RD
RP
RP
RD
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP

RP

3929
3930
3931
3932
3933
3934
3935
3936
3937
3938
3939
3940
49
49
49
49
49
49
4910
4911
4912
4913
4914
4915
4916
4917
4918
4919
4920
4921
4922
4923
4924
4925
4926
4927
4928
4929
4930
4931
4932
4933
4934
4935
4936
4937
4938
4939
4940
59 5

\OCDNO‘W-P

10090903
10394543
10698155
11091736
11395287
11698807
12092293
12395746
12699165
13092548
13395894
13699203
1593265
1897315
2291360
2595398
2899430
3293454
3597468
3991473
4295467
4599449
4993418
5297374
5691314
5995240
6299148
6693040
6996912
7390766
7694599
7998410
8392200
8695966
8999708
9393425
9697116
10090780
10394417
10698324
11091601
11395148
11698663
12092146
12395595
12699009
13092388
13395730
13699035
1897285

 

ASSIGN-
MENT

RP 59
RP 59
RP 59.
RP 59
RP 5910
RP 5911
RP 5912
RP 5913
RP 5914
RP 5915
RP 5916
RP 5917
RP 5918
RP 5919
RP 5920
RP 5921
RP 5922
RP 5923
RP 5924
RP 5925
RP 5926
RP 5927
RP 5928
RP 5929
RP 5930
RP 5931
RP 5932
RP 5933
RP 5934
RP 5935
RP 5936
RP 5937
RP 5938
RP 5939
RP 5940
RP 69 6
RP 69 7
RP 69 8
RP 69 9
RP 6910
RP 6911
RP 6912
RP 6913
RP 6914
RP 6915
RP 6916
RP 6917
RP 6918
RP 6919
RP 6920

\O(D\l()

261

CALCULATED

1

GSCD

2291325
2595358
2899385
3293403
3597412
3991412
4295400
4599377
4993341
5297291
5691226
5995146
6299050
6692935
6996803
7390651
7694478
7998285
8392069
8695830
8999567
9393278
9696964
0090623

10394254
13697856
11091428

1
1
1

1394969
1698479
2091956

12395400
12698809
13092182

1
1

3395519
3698819
2291282
2595309
2899329
3293341
3597344
3991337
4295318
4599289
4993246
5297190
5691119
5995032
6298929
6692808
6996669

 

mwuruw=

ASSIGN-
MENT

262

CALCULATED

GSCD

RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP

6921
6922
6923
6924
6925
6926
6927
6928
6929
5930
6931
6932
6933
6934
6935
6936
6937
6938
6939
6940
79 7
79 8
79 9
7910
7911
7912
7913
7914
7915
7916
7917
7918
7919
7920
7921
7922
7923
7924
7925
7926
7927
7928
7929
7930
7931
7932
7933
7934
7935
7936

7390510
7694331
7998131
8391909
8695663
8999394
9393099
9696778
13090430
10394354
13697650
11091216
11394750
11698254
12091724
12395161
12698564
13091931
13395261
13698554
2595251
2899264
3293268
3597263
3991248
4295222
4599184
4993134
5297070
5690991
5994897
6298786
6692658
6996511
7390344
7694158
7997950
8391720
8695466
8999189
9392887
9696558
13090203
19393819
13697407
11090965
11394492
11697987
12091450
12394880

 

 

ASSIGN-
MENT

RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP

7937
7938
7939
7940
89 8
89 9
8910
8911
8912
8913
8914
8915
8916
8917
8918
8919
8920
8921
8922
8923
8924
8925
8926
8927
8928
8929
8930
8931
8932
8933
8934
8935
8936
8937
8938
8939
8940
99 9
9910
9911
9912
9913
9914
9915
9916
9917
9918
9919
9920
9921

CALCULATED
GSCD

12698274
13091634
13394956
13698242
2899188
3293183
3597169
3991145
4295111
4599064
4993005
5296932
5690844
5994741
6298621
6692484
6996328
7390153
7693957
7997741
8391502
8695239
8998953
9392642
9696304
9999940
10393548
10697126
11090675
11394194
11697680
12091134
12394555
12697940
13091291
13394605
13697881
3293087
3597063
3991029
4294985
4598928
4992859
5296776
5690678
5994564
6298435
6692287
6996121
7299936

264

ASSIGR- CALCULATED
MENT GSCD
RP 9922 7693730
RP 9923 7997504
RP 9924 8391254
RP 9925 8694982
RP 9926 8998686
RP 9927 9392364
RP 9928 9696317
RP 9929 9999642
RP 9930 10393243
RP 9931 13696809
RP 9932 11090347
RP 9933 11393856
RP 9934 11697332
RP 9935 12090776
RP 9936 12394186
RP 9937 12697562
RP 9938 13090902
RP 9939 13394206
RP 9940 13697473

 

or

-19.. «.

 

APPENDIX III

LIST OF CALCULATED GROUND STATE COMBINATION
DIFFERENCES FOR CHD}

The following pages contain calculated ground state
combination differences (in cm") computed on the Michigan
State University Digital Computer, MISTIC. The values of
the constants used are (in cm“):

B0 = 3027944

pi = 5.22 x 10'5
These constants were obtained from an analysis of v1+v2 of
CHD3 discussed in Chapter 9.

In order to use the tables one should note that the
designation of the combination.dif£erences in this
appendix is that used in Chapter 4. Note also that

QRK,J = RQK,J+1.

265

 

gil- ...9. J“!fhuwtllr I .mgck u. 99. u‘

 

 

ASSIGN-
MENT

R0 09
R0 09
R0 09
R0 09
R0 09
R0 09
R0 09
R0 09
R0 09
R0 0910
R0 0911
R0 0912
R0 0913
R0 0914
R0 0915
R0 0916
R0 0917
R0 0918
R0 0919
R0 0920
R0 0921
R0 0922
R0 0923
R0 0924
R0 0925
R0 0926
R0 0927
R0 0928
R0 0929
R0 0930
R0 0931
R0 0932
R0 0933
R0 0934
R0 0935
R0 0936
R0 0937
R0 0938
R0 0939
R0 0940
R0 19 2
R0 19 3
R0 19 4
R0 19 5
R0 19 6

7

8

9

\OfiD-xlO‘U‘ImeH

R0 19
R0 19
R0 19
R0 1910
R0 1911

266

CALCULATED

GSCD

695587
1391161
1996710
2692222
3297683
3993082
4598406
5293642
5898777
6593801
7198699
7893459
8498069
9192516
9796788
10490871
11094755
11698426
12391871
12995078
13598035
14290729
14893147
15495278
16097107
16698624
17299815
17990668
18591171
19191310
19791073
20390449
23899423
21497984
22096120
22693817
23291063
23797846
24394154
24899972

1391163

1996713

2692225

3297688

3993088

4598412

5293649

5898786

6593810

7198709

 

v1

 

 

267

ASSIGN- CALCULATED
MENT 65C
R0 1912 7893470
R0 1913 8498081
R0 1914 9192529
R0 1915 9796802
R0 1916 13490887
R0 1917 11094771
R0 1918 11698443
RC 1919 12391889
R0 1920 12995098
R0 1921 13598055
R0 1922 14290750
R0 1923 14893170
R0 1924 15495301
R0 1925 16097132
R0 1926 16698649
R0 1927 17299841
R0 1928 17990695
R0 1929 18591199
R0 1930 19191339
R0 1931 19791103
R0 1932 20390480
R0 1933 20899455
R0 1934 21498017
R0 1935 22096154
R0 1936 22693852
R0 1937 23291099
R0 1938 23797883
R0 1939 24394191
R0 1940 24990011
R0 29 3 1996722
R0 29 4 2692237
R0 29 5 3297702
R0 29 6 3993105
R0 29 7 4598433
R0 29 8 5293673
R0 29 9 5898812
R0 2910 6593839
R0 2911 7198741
R0 2912 7893505
R0 2913 8498119
R0 2914 9192570
RD 2915 9796846
R0 2916 10490933
R0 2917 11094821
R0 2918 11698495
R0 2919 12391945
R0 2920 12995156
R0 2921 13598116
R0 2922 14290814
R0 2923 14893236

 

ASSIGN-
HE N T

R0 2924
R0 2925
R0 2926
R0 2927
R0 2928
R0 2929
R0 2930
R0 2931
R0 2932
R0 2933
R0 2934
R0 2935
R0 2936
R0 2937
R0 2938
R0 2939
R0 2940
R0 39
R0 39
R0 39
R0 39
R0 39
R0 39
R0 3910
R0 3911
R0 3912
R0 3913
R0 3914
R0 3915
R0 3916
R0 3917
R0 3918
R0 3919
R0 3920
R0 3921
R0 3922
R0 3923
R0 3924
R0 3925
R0 3926
R0 3927
R0 3928
R0 3929
R0 3930
R0 3931
R0 3932
R0 3933
R0 3934
R0 3935
R0 3936

\OCDflO‘U'b

268

CALCULATED

GSCD

15495371
16097204
16698725
17299920
17990777
18591283
19191426
19791193
23390573
23899551
21498116
22096255
22693957
23291207
23797994
24394305
24990127

2692256

3297727

3993134

4598467

5293711

5898856

6593888

7198794

7893563

8498182

9192638

9796918
13491011
11094903
11698583
12392037
12995253
13598218
14290921
14893348
15495487
16097325
16698851
17390051
17990912
18591423
19191571
19791344
23390728
20899711
21498281
22096425
22694131

 

269

ASSIGR- CALCULATED
MENT GSCD
R0 3937 23291386
R0 3938 23798178
R0 3939 24394494
R0 3940 24990321
R0 49 5 3297761
R0 49 6 3993175
R0 49 7 4598514
R0 4’ 8 52.03766
R0 49 9 5898917
R0 4910 6593956
R0 4911 7198869
R0 4912 7893645
R0 4913 8498270
R0 4914 9192733
R0 4915 9797020
R0 4916 10491119
R0 4917 11095019
R0 4918 11698705
R0 4919 12392165
R0 4920 12995388
R0 4921 13598361
R0 4922 14291070
R0 4923 14893504
R0 4924 15495650
R0 4925 16097495
R0 4926 16699027
R0 4927 17390234
R0 4928 17991102
R0 4929 18591620
R0 4930 19191775
R0 4931 19791554
R0 4932 20390945
R0 4933 20899935
R0 4934 21498511
R0 4935 22096662
R0 4936 22694375
R0 4937 23291637
R0 4938 23798435
R0 4939 24394758
R0 4940 24990592
R0 59 6 3993227
R0 59 7 4598575
R0 59 8 5293835
R0 59 9 5898995
R0 5910 6594043
R0 5911 7198965
R0 5912 7893749
R0 5913 8498384
R0 5914 9192855
R0 5915 9797151

 

270

ASSIGM- C4LCULATED
MENT GSCD
R0 5916 10491259
R0 5917 11095167
R0 5918 11698862
R0 5919 12392331
R0 5920 12995563
R0 5921 13598544
R0 5922 14291262
R0 5923 14893704
R0 5924 15495859
R0 5925 16097713
R0 5926 16699254
R0 5927 17390469
R0 5928 17991346
R0 5929 18591873
R0 5930 19192036
R0 5931 19791824
R0 5932 20391224
R0 5933 23990222
R0 5934 21498808
R0 5935 22096968
R0 5936 22694689
R0 5937 23291960
R0 5938 23798767
R0 5939 24395098
R0 5940 24990941
R0 69 7 4598650
R0 69 8 5293921
R0 69 9 5899091
R0 6910 6594149
R0 6911 7199082
R0 6912 7893877
R0 6913 8498522
R0 6914 9193004
R0 6915 9797311
R0 6916 10491429
R0 6917 11095348
R0 6918 11699053
R0 6919 12392534
R0 6920 12995776
R0 6921 13598768
R0 6922 14291496
R0 6923 14893950
R0 6924 15496115
R0 6925 16097979
R0 6926 16699531
R0 6927 17390757
R0 6928 17991645
R0 6929 18592182
R0 6930 19192356
R0 6931 19792155

 

271

ASSIGN- CALCULATED
MENT GSCD
R0 6932 23391565
R0 5933 269.0574
R0 6934 21499170
R0 6935 22097341
R0 6936 22695073
R0 6937 23292354
R0 6938 23799172
R0 6939 24395514
R0 6940 24991367
R0 79 8 5294021
R0 79 9 5899205
R0 7910 6594275
\0 7911 7199221
R0 7912 7894028
R0 7913 8498686
R0 7914 9193180
R0 7915 9797500
R0 7916 10491631
R0 7917 11095562
R0 7918 11699280
R0 7919 12392773
R0 7920 12996028
R0 7921 13599032
R0 7922 14291773
R0 7923 14894239
R0 7924 15496417
R0 7925 16098294
R0 7926 16699858
R0 7927 17391097
R0 7928 17991998
R0 7929 18592547
R0 7930 19192734
R0 7931 19792545
R0 7932 20391968
R0 7933 20990990
R0 7934 21499598
R0 7935 22097781
R0 7936 22695526
R0 7937 23292820
R0 7938 23799650
R0 7939 24396005
R0 7940 24991871
R0 89 9 5899336
R0 8910 6594421
R0 8912 7894203
R0 8911 7199381
R0 8913 8498875
R0 8914 9193384
R0 8915 9797718
80 8916 13491864

 

272

ASSIGN- CALCULATED
mENT GSCD
R0 8917 11095809
R0 8918 11699542
R0 8919 12393049
R0 8920 12996318
R0 8921 13599337
R0 8922 14292093
R0 8923 14894573
R0 8924 15496766
R0 8925 16098658
R0 8926 16790236
R0 8927 17391489
R0 8928 17992404
R0 8929 18592969
R0 8930 19193170
R0 8931 19792995
R0 8932 20392433
R0 8933 20991469
R0 8934 21590093
R0 8935 22098290
R0 8936 22696049
R0 8937 23293358
R0 8938 23890203
R0 8939 24396572
R0 8940 24992453
R0 9910 6594585
R0 9911 7199562
R0 9912 7894400
R0 9913 8499089
R0 9914 9193614
R0 9915 9797965
R0 9916 10492127
R0 9917 11096089
R0 9918 11699838
R0 9919 12393362
R0 9920 12996648
R0 9921 13599683
R0 9922 14292455
R0 9923 14894952
R0 9924 15497161
R0 9925 16099069
R0 9926 16790665
R0 9927 17391934
R0 9928 17992866
R0 9929 18593446
R0 9930 19193664
R0 9931 19793506
R0 9932 20392960
R0 9933 20992013
R0 9934 21590653
R0 9935 22098867

 

ASSIGN-
MENT

R0
R0
PQ
R0
R0
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
RD
PP
RD
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP

RP '

RD
RP

RR ‘

PP
PP
PP
PP
RD
RD
PP
PP
PP

9936
9937
9938
9939
9940
O9
O9
O9
O9
O9
O9

\OCDNIO‘U‘bUJNIv-‘O

273

CALCULATED

GSCD

22696642
23293967
23890829
24397214
24993111
695587
1996748
3297871
4598932
5899905
7290765
8591487
9892047
11192419
12492578
13792499
15092157
16391527
17690584
18899303
20197659
21495626
22793181
24090297
25296949
26593113
27798764
29093876
30298425
31592385
32795732
33998439
35290484
36491839
37692480
38892383
40091522
41199872
42397407
43594104
44699937
45894880
46998910
48192000
49294126
50395262
1996750
3297876
4598938
5899913

 

274

ASSIGN- CALCULATED
MFNT GSCD
RR 19 5 7290776
RP 19 6 8591500
RD 19 7 9892062
RP 19 8 11192436
RP 19 9 12492597
RP 1910 13792520
RR 1912 16391552
RP 1913 17690611
PP 1914 18899331
RP 1915 23197689
RP 1916 21495658
RP 1917 22793215
RP 1918 24090332
RP 1919 25296987
RP 1920 26593153
RP 1921 27798806
RP 1922 29093920
RR 1923 30298471
RP 1924 31592433
RR 1925 32795781
RP 1926 33998491
RR 1927 35290537
RP 1928 36491894
RP 1929 37692538
RP 1930 38892442
RP 1931 40091583
RP 1932 41199935
RP 1933 42397472
RP 1934 43594171
RP 1935 44790006
RP 1936 45894951
RP 1937 46998982
RP 1938 48192075
RD 1930 49294202
RP 1940 50395341
RP 29 2 3297890
RP 29 3 4598959
RP 29 4 5899939
RP 29 5 7290807
RP 29 6 8591538
RP 29 7 9892105
RP 29 8 11192485
RP 29 9 12492652
RP 7910 13792581
RP 2911 15092246
RP 2912 16391624
RP 2913 17690689
RP 2914 18899416
RP 2915 20197779
RP 2916 21495754

 

[\J
\1
U1

ASSIGN- CALCULATED

mng GSCD
RP 2917 22793316
RD 2918 24090440
80 2919 25297109
RR 2920 26593272
RP 2921 27798931
89 2922 29094051
89 2923 30298607
RP 2924 31592575
RP 2925 32795929
RP 2926 33998645
RP 2927 35290697
RP 2928 36492060
RD 2929 37692709
RP 2930 38892619
RP 2931 40091766
RP 2932 41290124
RP 2933 42397667
RP 2934 43594372
RP 2935 44790212
RP 2936 45895163
RP 2937 46999200
RP 2938 48192298
RP 2939 49294432
89 2940 50395576
RP 39 3 4598993
RP 39 4 5899983
RP 39 5 7290861
RP 39 6 8591601
RP 39 7 9892178
RP 39 8 11192567
RP 39 9 12492744
RP 3910 13792682
RP 3911 15092358
RP 3912 16391745
RP 3913 17690820
RP 3914 18899556
RP 3915 20197929
RP 3916 21495914
RP 3917 22793486
RP 3918 24090619
RP 3919 25297289
RP 3920 26593471
RP 3921 27799139
RP 3922 29094269
RP 3923 30298835
RP 3924 31592812
RP 3925 32796176
RP 3926 33998902
RP 3927 35290963

 

(9-

 

4910
4911
4912
4913
4914
4915
4916
4917
4918
4919
4920
4921
4922
4923
4924
4925
4926
4927
4928
4929
4930
4931
4932
4933
4934
4935
4936
4937
4938
4939
4940

[‘0

O‘

CALCULATFD

GSCD

36492336
37692995
38892915
40092071
41290438
42397992
43594706
44790556
45895517
46999564
48192671
49294815
50395969

5990044

7290935

8591689

9892280
11192683
12492873
13792825
15092514
16391915
17691303
18899753
20198139
21496138
22793723
24090870
25297554
26593749
27799431
-9094574
33299154
31593145
32796522
33999261
35291336
36492722
37693395
38893329
40092498
41290879
42398446
43595174
44791037
45896012
47090072
48193194
49295350
50396518

 

ASSIGN-
MENT

RP 5
RP 5
RP 6
.903
PD 5
RP 5910
RP 5911
RP 5912
RP 5913
RP 3914
RP 5915
RP 5916
RP 5917
PP 5918
RP 5919
RP 5920
RR 5921
RP 5922
RP 5923
RP 5924
RP 5925
RP 5926
RP 5927
RR 5928
RP 5929
RD 5930
RP 5931
RP 5932
RP 5933
RP 5934
RP 5935
RP 5936
RP 5937
RP 5938
RP 5939
RP 5940
RP 69 6
RP 69 7
RP 69 8
RP 69 9
RP 6910
RP 6911
RP 6912
RP 6913
RP 6914
RP 6915
RP 6916
RP 6917
RP 6918
RP 6919

277

CALCULATED

GSCD

7291031

8591802

989241"1
11192831
12493038
13793008
15092714
16392133
17691238
18990006
20198410
21496426
22794028
24091193
25297894
26594106
27799896
29094966
39299563
31593572
32796967
33999723
35291816
36493219
37693909
38893861
43093048
41291446
42399030
43595775
44791657
45896649
47090726
48193865
49296039
50397224

8591941

9892570
11193012
12493241
13793232
15092960
16392399
17691526
18990315
20198740
21496777
22794401
24091587
25298309

 

278

ASSIGN- CALCULATED
MENT GSCD
RP 6920 26594543
RP 6921 27890264
RP 6922 29095446
RP 6923 30390064
RP 6924 31594094
RP 6925 32797510
RP 6926 34090288
RP 6927 35292402
RP 6928 36493827
RP 6929 37694538
RP 6930 38894511
RP 6931 40093719
RP 6932 41292139
RP 6933 42399744
RP 6934 43596511
RP 6935 44792413
RP 6936 45897427
RP 6937 47091526
RP 6938 48194686
RP 6939 4929683
RP 6943 50398087
RP 79 7 9892759
RP 79 8 11193226
RP 79 9 12493480
RP 7910 13793496
RP 7911 15093249
RP 7912 16392714
RP 7913 17691866
RP 7914 18990680
RP 7915 20199131
RP 7916 21497193
RP 7917 22794842
RP 7918 24092053
RP 7919 25298801
RP 7920 26595060
RP 7921 27890805
RP 7922 29096013
RP 7923 30390656
RP 7924 31594711
RP 7925 32798153
RP 7926 34090956
RP 7927 35293095
RP 7928 36494545
RP 7929 37695281
RP 7930 38895279
RP 7931 40094513
RP 7932 41292957
RP 7933 42490588
RP 7934 43597380
RP 7935 44793308

 

279

ASSIGN- CALCULATED
MENT GSCD
RP 7936 45898346
RP 7.37 473.2470
RP 7938 48195655
RP 7939 49297876
RP 7940 50399108
RP 89 8 11193473
RP 89 9 12493756
RP 8910 13793801
RP 8911 15093583
RP 8912 16393078
RP 8913 17692259
RP 8914 18991101
RP 8915 20199581
RP 8916 21497673
RP 8917 22795351
RP 8918 24092591
RP 8919 25299367
RP 8920 26595656
RP 8921 27891430
RP 8922 29096667
RP 8923 30391339
RP 8924 31595423
RP 8925 32798894
RP 8926 34091726
RP 8927 35293894
RP 8928 36495373
RP 8929 37696139
RP 8930 38896165
RP 8931 40095428
RP 8932 41293902
RP 8933 42491562
RP 8934 43598383
RP 8935 44794339
RP 8936 45899407
RP 8937 47093560
RP 8938 48196774
RP 8939 49299024
RP 8940 50490285
RP 99 9 12494069
RP 9910 13794147
RP 9911 15093962
RP 9912 16393489
RP 9913 17692703
RP 9914 18991579
RP 9915 20290092
RP 9916 21498216
RP 9917 22795927
RP 9918 24093200
RP 9919 25390010
RP 9920 26596331

 

f\)
(O
")

ASSIGN- CALCULATED
MENT GSCD
RP 9921 27892139
RP 9922 29097408
RP 9923 30392113
RP 9924 31596231
RP 9925 32799734
RP 9926 34092599
RP 9927 35294800
RP 9928 36496312
RP 9929 37697111
RP 9930 38897170
RP 9931 40096466
RP 9932 41294973
RP 9933 42492665
RP 9934 43599519
RP 9935 44795509
RP 9936 45990609
RP 9937 47094796
RP 9938 48198043
RP 9939 49390325
RP 9940 53491619

APPENDIX IV

LIST OF CALCULATED GROUND STATE COMBINATION

DIFFERENCES FOR CH3D

The following pages contain calculated ground state
combination differences (in cm'1) computed on the Michigan
State University Digital Computer, MISTIC. The values of

the constants used are

B 3.88107

0

DgK = 1.192 x 10’4

pi 5.28 x 10'5

These constants were obtained from an analysis of v2+v3 of

0333 discussed in Chapter 9.

In order to use the tables one should note that the
designation of the combination differences in this appendix
is that used in Chapter 4. Note also that

QPK,J = RQK,J+19

281

 

ASSIGN-
M. E M T

R0 09
R0 09
R0 09
R0 09
R0 09
R0 09
R0 09
R0 09
R0 09
R0 0910
R0 0911
R0 0912
R0 0913
R0 0914
R0 0915
R0 0916
R0 0917
R0 0918
R0 0919
R0 0920
R0 0921
R0 0922
R0 0923
R0 0924
R0 0925
R0 0926
R0 0927
R0 0928
R0 0929
R0 0930
R0 0931
R0 0932
R0 0933
R0 0934
R0 0935
R0 0936
R0 0937
R0 0938
R0 0939
R0 0940
R0 19 2
R0 19 3
R0 19 4
R0 19 5
R0 19 6

7

8

9

\omxlmmbmmn—a

R0 19
R0 19
R0 19 ‘
R0 1910
R0 1911

f\)
(D

CALCULATED

GSCD

797619
1595226
2392807
3190350
3897843
4695272
5492624-
6199888
6997051
7794099
8591020
9297802
10094432
10890896
11597183
12393279
13099173
13894850
14690300
15395508
16190462
16895150
17599559
18393676
19097488
19890983
20594148
21296970
21999437
22791536
23493255
24194580
24895499
25595999
26296067
26995692
27694859
28393558
29091773
29699494

1595221

2392800

3190341

3897831

4695257

5492608

6199869

6997029

7794075

8590994

283

ASSIGN- CALCULATED
MRNT GSCD
R0 1912 9297773
R0 1913 10094401
R0 1914 10890863
80 1915 11597147
R0 1916 12393241
R0 1917 13099132
R0 1918 13894808
R0 1919 14690254
R0 1920 15395460
R0 1921 16190412
R0 1922 16895098
R0 1923 17599504
R0 1924 18393618
R0 1925 19097428
R0 1926 19890921
R0 1927 20594083
R0 1928 21296903
R0 1929 21999368
R0 1930 22791465
R0 1931 23493181
R0 1932 24194503
R0 1933 24895420
R0 1934 25595918
R0 1935 26295984
R0 1936 26995606
R0 1937 27694771
R0 1938 28393467
R0 1939 29091680
R0 1940 29699399
R0 29 3 2392779
R0 29 4 3190312
R0 29 5 3897795
R0 29 6 4695214
R0 29 7 5492558
R0 29 8 6199812
R0 29 9 6996965
R0 2910 7794004
R0 2911 8590915
R0 2912 9297688
R0 2913 10094308
R0 2914 10890763
R0 2915 11597040
R0 2916 12393127
R0 2917 13099011
R0 2918 13894679
R0 2919 14690119
R0 2920 15395317
R0 2921 16190262
R0 2922 16894940
R0 2923 17599339

ASSIGN-
MENT

R0 2924
R0 2925
R0 2926
R0 2927
R0 2928
R0 2929
R0 2930
R0 2931
R0 2932
R0 2933
R0 2934
R0 2935
R0 2936
R0 2937
R0 2938
R0 2939
R0 2940
R0 39
R0 39
R0 39
R0 39
R0 39
R0 39
R0 3910
R0 3911
R0 3912
R0 3913
R0 3914
R0 3915
R0 3916
R0 3917
R0 3918
R0 3919
R0 3920
R0 3921
R0 3922
R0 3923
R0 3924
R0 3925
R0 3926
R0 3927
R0 3928
R0 3929
R0 3935
R0 3931
R0 3932
R0 3933
R0 3934
R0 3935
R0 3936

\OmxlO‘U1F

284

CALCULATED

GSCD

18393447
19097249
19890735
23593890
21296703
21999161
22791250
23492959
24194275
24895184
25595675
26295734
26995349
27694507
28393195
29091402
29699113

3190264

3897735

4695143

5492474

6199717

6996858

7793885

8590784

9297545
10094153
10890596
11596861
12392936
13098808
13894464
14599892
15395079
16190012
16894678
17599065
18393161
19096952
19890425
20593569
21296370
21998815
22790893
23492590
24193893
24894791
25595269
26295317
26994920

ASSIGN-
MENT

285

CALCULATED

GSCD

R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0

3937
3938
3939
3940
49 5
49 6
49 7
49 8
49 9
4910
4911
4912
4913
4914
4915
4916
4917
4918
4919
4920
4921
4922
4923
4924
4925
4926
4927
4928
4929
4930
4931
4932
4933
4934
4935
4936
4937
4938
4939
4940
59 6
59 7
59 8
59 9
5910
5911
5912
5913
5914
5915

27694066
28392742
29090937
29698636

3897652

4695043

5492357

6199583

6996708

7793718

8590601

9297344
10093936
10890362
11596611
12392669
13098524
13894164
14599575
15394745
16099661
16894311
17598682
18392760
19096534
19799991
20593118
21295903
21998331
22790392
23492073
24193359
24894249
25594702
26294733
26994319
27693449
28392109
29090286
29697969

4694914

5492207

6199412

6996515

7793503

8590365

9297087
10093657
13890062
11596289

286

ASSIGN- CALCULATED
MENT 60CD
R0 5916 12392326
R0 5917 13098160
R0 5918 13893778
R0 5919 14599168
R0 5920 15394316
R0 5921 16099211
R0 5922 16893839
R0 5923 17598188
R0 5924 18392246
R0 5925 19095998
R0 5926 19799434
R0 5927 23592539
R0 5928 21295302
R0 5929 21997709
R0 5930 22699749
R0 5931 23491408
R0 5932 24192673
R0 5933 24893532
R0 5934 25593973
R0 5935 26293982
R0 5936 26993547
R0 5937 27692655
R0 5938 28391294
R0 5939 28999450
R0 5940 29697111
R0 69 7 5492024
R0 69 8 6199202
R0 69 9 6996279
R0 6918 7793241
R0 6911 8590077
R0 6912 9296773
R0 6913 10093316
R0 6914 10799695
R0 6915 11595896
R0 6916 12391907
R0 6917 13097714
R0 6918 13893306
R0 6919 14598670
R0 6920 15393792
R0 6921 16098660
R0 6922 16893263
R0 6923 17597585
R0 6924 18391616
R0 6925 19095343
R0 6926 19798752
R0 6927 20591831
R0 6928 21294568
R0 6929 21996949
R0 6930 22698963
R0 6931 23490595

287

ASSIGN- CALCULATED
MENT GSCD
R0 6932 24191834
R0 6933 24892667
R0 6934 25593082
R0 6935 26293064
R0 6936 26992603
R0 6937 27691685
R0 6938 28390297
R0 6939 28998427
R0 6940 29696063
R0 79 8 6198954
R0 79 9 6996000
R0 7910 7792931
R0 7911 8499736
R0 7912 9296401
R0 7913 10092913
R0 7914 10799261
R0 7915 11595431
R0 7916 12391411
R0 7917 13097188
R0 7918 13892748
R0 7919 14598081
R0 7920 15393172
R0 7921 16098010
R0 7922 16892581
R0 7923 17596873
R0 7924 18390873
R0 7925 19094568
R0 7926 19797947
R0 7927 20590995
R0 7928 21293700
R0 7929 21996051
R0 7930 22698033
R0 7931 23399635
R0 7932 24190843
R0 7933 24891645
R0 7934 _25592028
R0 7935 26291980
R0 7936 26991488
R0 7937 27690539
R0 7938 28299120
R0 7939 28997219
R0 7940 29694823
R0 89 9 6995678
R0 8910 7792574
R0 8912 9295972
R0 8911 8499343
R0 8013 10092449
R0 8914 10798761
R0 8915 11594895
R0 8916 12390839

288

ASSIGN- CALCULATED
MENT GSCD
R0 8917 13096583
R0 8918 13892105
R0 8919 14597402
R0 8920 15392457
R0 8921 16097259
R0 8922 16891795
R0 8923 17596051
R0 8924 18390015
R0 8925 19093675
‘ R0 8926 19797017
80 8927 20590030
R0 8928 21292700
R0 8929 21995014
R0 8930 22696961
R0 8931 23398526
R0 8932 24099699
80 8933 24890465
R0 8934 25590813
R0 8935 26290729
R0 8936 26990201
R0 8937 27599216
R0 8938 28297762
R0 8939 28995825
R0 8940 29693393
R0 9910 7792169
R0 9911 8498897
R0 9912 9295486
R0 9913 10091922
R0 9914 10798193
R0 9915 11594287
R0 9916 12390191
R0 9917 13695891
R0 9918 13891376
R0 9919 14596632
R0 9920 15391647
R0 9921 16096408
R0 9922 16890903
R0 9923 17595119
R0 9924 18299043
R0 9925 19092662
R0 9926 19795964
R0 9927 20498936
R0 9928 21291565
R0 9929 21993839
R0 9930 22695745
R0 9931 23397271
R0 9932 24098402
R0 9933 24799128
R0 9934 25499435
R0 9935 26199311

289

ASSIGN- CALCULATED
MENT GSCD
R0 9936 26898742
R0 9937 27597717
R0 9938 28296222
R0 9939 28994245
R0 9940 29691773
RP 09 0 797619
RP 09 1 2392845
RP 09 2 3898033
RP 09 3 5493157
RP 09 4 6998193
RP 09 5 8593114
RP 09 6 10097896
RP 09 7 11692513
RP 09 8 13196939
RP 09 9 14791150
RP 0910 16295119
RP 0911 17798822
RR 0912 19392234
RP 0913 25895328
RP 0914 22398079
RP 0915 23990462
RR 0916 25492452
RP 0917 26994023
RP 0918 28495150
RP 0919 29995808
RP 0920 31495970
RP 0921 32995612
RP 0.22 34494799
RR 0923 35993234
RP 0924 37491163
RP 0925 38898471
RP 0926 43395131
RP 0927 41891118
RP 0928 43296407
RP 0929 44790974
RP 0930 46194791
RP 0931 47597834
RP 0932 49090078
RP 0933 50491497
RP 0934 51892066
RP 0935 53291759
RP 0936 54690551
RP 0937 55998417
RP 0938 57395331
RP 0939 58791268
RP 0940 60096202
RP 19 1 2392838
RP 19 2 3898021
RP 19 3 5493141
RR 19 4 6998171

N
\1’)
()

ASSIGN- CALCULATED
MENT GSCD
RP 19 5 8593088
RR 19 6 13097865
RP 19 7 11692477
RP 19 8 13196899
RP 19 9 14791104
RP 1910 16295069
RP 1912 19392174
RP 1913 20895263
RP 1914 22398010
RP 1915 23990388
RP 1916 25492373
RP 1917 26993940
RP 1918 28495062
RP 1919 29995715
RP 1920 31495872
RP 1921 32995510
RP 1922 34494602
RP 1923 35993122
RP 1924 37491047
RP 1925 38898349
RP 1926 40395004
RP 1927 41890987
RP 1928 43296272
RP 1929 44790833
RP 1930 46194646
RP 1931 47597684
RP 1932 48999923
RP 1933 50491338
RP 1934 51891902
RP 1935 53291590
RP 1936 54690377
RP 1937 55998233
RP 1938 57395147
RP 1939 58791080
RP 1940 60096009
RP 29 2 3897985
RP 29 3 5493091
RP 29 4 6998107
RP 29 5 8593009
RP 29 6 10097772
RP 29 7 11692370
RP 29 8 13196777
RP 29 9 14790969
RP 2910 16294919
RP 2911 17798603
RP 2912 19391995
RP 2913 20895070
RP 2914 22397802
RP 2915 23990167

291

ASSIGN- CALCULATED
MENT GSCD
R 2916 25492137
RP 2917 26993689
RP 2918 28494797
RP 2919 29995436
RP 2920 31495579
RP 2921 32995202
RR 2922 34494283
RP 2923 35992786
RP 2924 37490696
RP 2925 38897984
RP 2926 43394625
RP 2927 41890594
RP 2928 43295864
RP 2929 44790411
RP 2930 46194210
RP 2931 47597234
RP 2932 48999459
RP 2933 50490859
RR 2934 51891408
RP 2935 53291082
RP 2936 54599855
RP 2937 55997702
RP 2938 57394597
RP 2939 58790515
RP 2940 60095430
RP 39 3 5493007
RP 39 4 6998300
RP 39 5 8592878
RP 39 6 13097617
RP 39 7 11692191
RP 39 8 13196574
RP 39 9 14790742
RP 3910 16294669
RP 3911 17798329
RP 3912 19391697
RP 3913 20894748
RP 3914 22397457
RP 3915 23899797
RP 3916 25491744
RP 3917 26993272
RP 3918 28494356
RP 3919 29994971
RP 3923 31495091
RP 3921 32994690
RP 3922 34493744
RP 3923 35992226
RP 3924 37490112
RP 3925 38897377
RP 3926 40393994
RP 3927 41799938

292

ASSIGN- CALCULATED
MENT GSCD
RP 3928 43295185
RP 3929 44699708
RP 3930 46193483
RP 3931 47596483
RP 3932 48998684
RP 3933 50490060
RP 3934 51890586
RP 3935 53290236
RP 3936 54598985
RP 3937 55996808
RP 3938 57393679
RP 3939 58699573
RP 3940 60094465
RP 49 4 6997850
RP 49 5 8592695
RP 49 6 10097400
RP 49 7 11691941
RP 49 8 13196291
RP 49 9 14790425
RP 4910 16294319
RP 4911 17797945
RP 4912 19391280
RP 4913 20894298
RP 4914 22396973
RP 4915 23899280
RP 4916 25491194
RP 4917 26992689
RP 4918 28493739
RP 4919 29994320
RP 4920 31494407
RP 4921 32993973
RP 4922 34492993
RP 4923 35991442
RP 4924 37399295
RP 4925 38896526
RP 4926 4C393110
RP 4927 41799021
RP 4928 43294234
RP 4929 44698724
RP 4930 46192465
RP.4931 47595432
RP 4932 48997600
RP 4933 50398942
RP 4934 51799435
RP 4935 53199052
RP 4936 54597768
RP 4937 55995557
RP 4938 57392395
RP 4939 58698255
RP 4940 63093113

ASSIGN-
ME N T
R P

59 5
RP 59 6
RP 59 7
RP 59 8
RP 59 9
RP 5910
RP 5911
RP 5912
PP 5913
RP 5914
RP 5915
RP 5916
RP 5917
RP 5918
RP 5919
RP 5920
RP 5921
RP 5922
RP 5923
RP 5924
RP 5925
RP 5926
RP 5927
RP 5928
RP 5929
RP 5930
RP 5931
RP 5932
RP 5933
RP 5934
RP 5935
RP 5936
RP 5937
RP 5938
RP 5939
RP 5940
RP 69 6
RP 69 7
RP 69 8
RP 69 9
RP 6910
RP 6911
RP 6912
RP 6913
RP 6914
RP 6915
RP 6916
RP 6917
RP 6918
RP 6919

293

CALCULATED

GSCD

8592459
10097121
11691619
13195926
14790018
16293868
17797452
19390744
23893719
22396351
23898615
25493486
26991938
28492946
29993484
31493527
32993050
34492028
35990434
37398244
38895432
43391973
41797841
43293011
44697458
46191157
47594081
48996206
53397505
51797955
53197529
54596202
55993948
57390743
58696561
60091376
10096781
11691226
13195481
14699520
16293318
17796849
19390089
23893011
22395591
23897802
25399621
26991020
28491976
29992462

ASSIGN-
MENT

RP 6920
PP 6921
RP 6922
RP 6923
RP 6924
RP 6925
RP 6926
RP 6927
RP 6928
RP 6929
RP 6930
RP 6931
RP 6932
RP 6933
RP 6934
RP 6935
RP 6936
RP 6937
RP 6938
RP 6939
RP 6940
RP 79 7
RP 79 8
RP 79 9
RP 7910
RP 7911
RP 7912
RP 7913
RP 7914
RP 7915
RP 7916
RP 7917
RP 7918
RP 7919
RP 7920
RD 7921
RP 7922
RP 7923
RP 7924
RP 7925
RP 7926
RP 7927
RP 7928
RP 7929
RP 7930
RP 7931
RP 7932
RP 7933
RP 7934
RP 7935

294

CALCULATED

GSCD

31492452
32991923
34490848
35899202
37396959
38894095
40390583
41796399
43291517
44695912
46099558
47592429
48994502
53395749
51796146
53195668
54594288
55991982
57298725
58694490
59999253
11690761
13194954
14698931
16292667
17796137
19299314
20892175
22394692
23896842
25398598
26899936
28490829
29991253
31491182
32990591
34399454
35897746
37395441
38892515
40298941
41794695
43199751
44694084
46097668
47590477
48992488
53393673
51794008
53193468

ASSIGN-

9.].
mE

RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP

NT

7936
7937
7938
7939
7940
89 8
89 9
8910
8911
8912
8913
8914
8915
8916
8917
8918
8919
8920
8921
8922
8923
8924
8925
8926
8927
8928
8929
8930
8931
8932
8933
8934
8935
8936
8937
8938
8939
8940
99 9
9910
9911
9912
9913
9914
9915
9916
9917
9918
9919
9920

295

CALCULATED

GSCD

54592027
55899659
57296339
58692042
59996743
13194346
14698252
16291916
17795314
19298420
20891209
22393656
23895734
25397419
26898685
28399507
29899859
31399717
32899054
34397845
35896066
37393690
38890692
40297047
41792729
43197714
44691975
46095487
47498225
48990164
50391278
51791542
53190930
54499417
55896978
57293587
58599218
59993848
14697482
16291066
17794383
19297408
20890115
22392481
23894478
25396082
26897267
28398008
29898279
31398055

1720
RP
QD
no
96
60
RP
RP
RP
PP
DP
90
60
60
RP
60
60
pa
po

\- I) \O

~O \O \J) ‘4’.)
w
\J
I1

w) ‘0 '0 KO ‘0 x0
9
N
0

32897312
3439692?
35894161
37391794
38798626
(90294900
41790501
43195404
44599584
46093016
47495673
48897531
59398564
51698746
53098053
54¢;961159
55893939
57290467
58596018
59990565

APPENDIX V

LIST OF ASSIGNMENTS AND FREQUENCIES 0F OBSERVED
TRANSITIONS FOR v3+v4 OF CH3F

The following pages contain a list of the observed
transitions of v3+v4 of CH3F. The columns of the list,
left to right, are: the assignment (AK,AJ.K,J); the observed
frequency (in cm"); the observed fringe number (from which
the frequency may be calculated - of. Chapter 7); the Av
(weight = (NORM)2/(Av)2); the weight; observed line height;

and the line number.

297

ASSIGN-
MENT

PP 99 9
PP 9910
PP 9911
PP 9912
PP 9913
PP 9914
PP 9915
PP 9916
PP 9917
PD 9918
PP 9919
PP 9920
PP 9921
P0 99 9
P0 9912
PO 9913
PO 9915
P0 9916
P0 9917
PO 9918
P0 9919
P0 9920
PR 99 9
PR 9910
PR 9911
PR 9915
PR 9916
PR 9919
PP 89 8
PP 89 8
PP 89 9
PP 8910
PP 8911
PP 8912
PP 8913
PP 8914
PP 8915
PP 8916
PP 8917
P0 89 8
P0 89 9
P0 8910
PG 8912
P0 8913
PO 8913
P0 8914
PR 89 8
PR 8912
PR 8913
PR 8914

OBSERVED
FREQUENCY

397597390
397399180
397290460
397091670
396892650
396693600
396494370
396295090
396095590
395895740
395696220
395496280
395296370
399099020
399093650
399091840
398997250
398994280
398991880
398898710
398896090
398893020
400797510
400992680
401097750
401696630
401890390
402292300
398593710
398594280
398395320
398196630
397997830
397798700
397599650
397490370
397291070
397091670
396891290
399898380
399896570
399894980
399890590
399798610
399798190
399795970
401398630
401999400
402193310
402298340

298

FRINGE
NUMEER

8996480
8399030
7890310
7292410
6693250
6094010
5494200
4394220
4293600
3691870
3091153
2399150
1797230
13697210
13590540
13494910
13390610
13291390
13193910
13094050
12995930
12896370
13991220
19398380
19895260
21698370
22191160
23491490
11995230
11997000
11398020
10799890
10291430
9691930
9092710
8492750
7892270
7292410
6599020
16194020
16098410
16093460
15899790
15893640
15892340
15795420
20891280
22790290
23193550
23690270

DELTA
NU

90140
90200
90140
90140
90140
90200
90140
90140
90140
90140
.0200
90200
90200
99999
90200
90200
99999
99999
99999
99999
90200
.0200
90200
99999
99999
99999
99999
99999
90200
90200
90200
90100
90140
90140
90200
90140
90200
90200
99999
99999
99999
99999
90200
99999
99999
99999
99999
99999
99999
99999

WEIGHT

950
925
950
950
950
925
950
950
950
950
925
925
925
900
925
925
900
900
900
900
925
925
925
900
900
900
900
900
925
925
925
1900
950
950
925
950
925
925
900
900
900
900
925
900
900
900
.00
900
900
900

INT

HfidPJH
m-b£~b

943m

9.9
C

~ooau

9.9

H

9...:

R)H
ocruam—40~®<Dq)mtfistxfi£~mxfioxw.DC3br0$~b-Pfiab—quw

H94 th Hbd 94
w940~fl~4$‘PCD

Wkfi

LINE

3
z.
-Dm)m\flu9o O

kthmkanPLfiO‘®~4Q)®
N\OO‘

G)W\UJ‘

1664
164
163A
161
160
159
157A
155
154
236A
244
2524
289
295A
316
139
139A
130
119
109
100
91
84
75A
68
61
200
199
198
195C
1954
195
194
275A
304
311A
318

ASSIGN-
MENT

PP 79 7
PP 79 8
PP 79 9
PP 7910
PP 7911
PP 7912
PP 7913
PP 7914
PP 7915
PP 7916
P0 79 7
P0 79 8
PO 7910
0 7911
PO 7912
P0 7913
PO 7914
PO 7915
PR 79 8
PR 7910
PP 69 7
PP 69 8
PP 69 9
PP 6910
PP 6911
PP 6912
PP 6913
PP 6914
PP 6915
PP 6916
PP 6917
PP 6918
PP 6919
PP 6920
PP 6921
PG 69 6
P0 69 8
PG 69 9
PO 6910
P0 6912
PO 6913
P0 6914
P0 6915
P0 6916
PO 6917
P0 6918
PO 6919
PO 6920
PR 69 7
PR 69 8

OBSERVED
FREQUENCY

399499820
399391480
399192950
398994280
398795260
398596180
398397050
398197930
397997830
397798700
400697690
400696130
400692430
400690280
400598010
400595980
400592870
400590950
402197430
402497560
400390220
400191710
399993010
399794220
399595440
399396510
399197530
398998440
398799340
398690300
398491220
398292340
398093740
397895640
397697650
401499440
401496203
401494420
401492570
401398630
401396530
401394420
401392310
401390329
401298340
401296790
401295400
401294480
402892280
402997830

299

FRINGE
NUMBER

14994120
14397070
13799460
13291390
12692250
12092900
11493420
10893930
10291430

9691930
18690670
18595820
18494320
18397630
18390580
18294250
18194590
18098300
23296340
24290040
17494150
16896570
16298430
15699990
15191580
14592720
13993680
13394310
12794920
12195710
11596363
10997660
10399810

9893540

9297570
21194900
21094840
20999300
23993540
20891280
20794770
20698190
20691640
20595440
204993C0
20494480
20490140
20397280
25299040
25796380

DELTA
NU

90140
90140
90200
90200
90140
90140
90200
90140
90200
90200
99999
99999
99999
99999
99999
99999
99099
99999
99999
90200
90100
90140
90140
90200
90100
90140
90140
90100
90100
90200
90140
90200
90200
99999
99999
90140
90100
90100
90200
90100
90100
90140
90140
90140
90200
90140
90140
90140
99999

99999

WEIGHT

950
950
925
925
950
950
925
950
925
925
900
900
900
900
900
900
900
900
900
925
1900
950
950
925
1900
950
950
1900
1900
925
950
925
925
900
900
950
1900
1900
925
1900
1900
950
950
950
925
950
950
950
900
900

INT

9.9

9.9
U)HCDJ)$\O%)O\»G)0(DQJOCFGJN(D¢)N

9.9

LINE
NO

182
174
168
160
130
140
131
120
109
100
231
230A
229A
228
227
226A
225
224
313
327
216
208
201
193
184
176
169
162
151
142
134
123
112
103
94
281
279
278
276A
275
273
272
271
270
260
259
258
257
348A
356

ASSIGN-
MEMT

PR 6911
PR 6915
PR 6916
PP 59 6
PP 59 7
PP 59 8
PP 59 9
PP 5910
PP 5911
PP 5912
PP 5913
PP 914
P0
P0
P0
P0
P0
P0
P0
P0
PR
PR
PR
PR
PR
PP
PP
PP 49
PP 49
PP 4910
PP 4912
PP 4913
PP 4914
P0 49 6
P0 49 7
P0 49 8
P0 49 9
PO 4910
PO 4911
PO 4912
PO 4913
PR 49 6
PR 49 7
PR 4910
PR 4912
PP 39
PP 39
PP 39
PP 39
PP 39

Ul
‘.

U1 U1U|U1 U‘IUIU"
9.000.000.9909.

...;
O‘N\OFD\IO‘\»NO‘O(D\IO‘U1

HHF-I'

U1 U1 U1 ‘J1 U1

U1

IP45
o.
TONI

(

O

\

mqomp

ORSERVED
FREQUENCY

403492790
404092360
4041.7400
401292110
401094360
400895470
400697690
400498930
400191710
399993010
399793130
402294230
402293420
402292300
402291060
402199500
402197430
402193310
402191540
403491820
403597000
403792290
40 397750
404392440
401998560
401890390
401691740
401492960
401293880
400895470
400696130
400496070
402999260
402997830
402995890
402994020
402991570
402899140
A02896740
402894000
404197400
404392440
404797390
405095770
403191380
402993500
402795470
402597030
402398420

300

FRINGE
NUMBER

27196210
29091490
29498280
20299920
19794720
19198380
18690670
1839234C
17494150
16896570
16298430
15696600
23497490
23494990
23491490
23397630
23392780
23296340
23193550
23098040
27193180
27690390
23097960
28596070
29995050
22697660
22191160
21593170
20994730
20395420
19195960
18595823
17993450
25890839
25796380
25790360
25694550

N
U
U
C
0
C‘
9...:
3

I

254993"
254918;

‘U
OCJC

(

C)

(D

C)U1(D~J
C)

l C.) (.7)

25692930
25096840
24499510
23991640

DELTA
NU

99999

.QCQO

JJ/

.0200
.0200
99999
99999
90200
99999
90100

9999

90100

900
900
925
925
900
900
925
900
1.00
950
.00
925
900
925
900
900
900
900
900
900
900
900
900
900
900
950
925
950
900
950
925
925
925
900
900
900
1900
900
925
900
925
925
900
900
925
925
1900
950
950
1900

....

INT

LINE
NO

379A
408A
414A
256
251
241
231
223A
216
208
201
192
3165
316A
316
315
314
313
311A
310
3783
3854
392A
401
423
303
295A
288
277
256A
240A
230A
222
356A
356
355
354A
353
351
350A
349
414A
423
444
4593
353
354
343
333
323

ASSIGN-
MENT
PP 39 9
PP 3910
PP 3911
PP 3912
PP 3913
PP 3914
PP 3916
PP 3915
PP 3917
PP 3918
PP 3919
PP 3920
PP 3921
P0 39 3
P0 39 4
P0 39 5
P0 39 6
P0 39 7
P0 39 8
P0 39 9
P0 3 10
P0 3911
P0 3912
PO 3913
PO 3914
P0 3915
PR 3913
P0 3914
PO 3915
P0 3916
PO 3917
P0 3918
P0 3919
PO 3920
PR 39 3
PR 39 4
PR 39 5
PR 39 6
PR 39 7
PR 39 8
PR 39 9
PR 3910
PR 3911
PR 3912
PR 3916
PR 3917
PR 3918
PR 3919
PP 29 3

PP 29 4

ORSFRVED
FREQUENCY

402199500
402090340
401890890
401691020
401490600
401290740
400697690
401097750
400690280
4004.0010
400198540
399996990
399795970
403799480
403798670
403797630
[1037.62QO
AC3794650
403792839
403790760
403698240
403695260
403691900
403599000
403592440
403399560
403797940
403695470
403594309
03499359

C
p
O
\J‘
\O

D
u

()0C)

ox 0 Ch 1;: u: U7 m m m D .P «P 4? Lu W W W

O
[—9
"(D
'\9
k4

<5C>O
bLoub

0
w -

o

o

\J

(D

C) U!
U1 H \J 00 k» u)
1.“) Q ‘ ’

\J (1‘ D 610) UN 01 U.) m 1) \O

o o o. .0.... o
co UINC) (.10 LfitDG‘N'

O\

C) (7) C) C) O C.) (D C) (D C) (3 f)

b-) «L‘ 0‘
C)

P‘DJ>b-P#\P£>PJ>$~PJ>P~PJ>£~DJ>P~D
\OfilJ‘fiP-‘t—JN

C) Q Q L) g) Q Q

N 01 O\ I)

C)
CD .

U)
C)
l—‘

FRINGE
NUM8ER

23392780
22793210
221927C0
21590920
20897430
20295660
18690670
19895260
1839763C
177945O
173971~
16490<
157954-”
28390340
28297830
23294550
2829038:
281953:0
99640

, \
1

J)
J C) 1-4 \
C) C ('7

\
I

U‘
)

\
L

N m '\1
(D

1') L.) C)
O
U)
H
)
( \

.\..

\fi _.
C) Q.

9 m

\l \J

p m

0 O

m 17m
:1) 0" Q 41 m l-‘ .u m 0‘ a) 09

N
\1
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O
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j-) l—--‘ ‘N \0 m ‘r.

-.i_‘.: O C.)

)N
\1
)("J-
o
‘1

_I

(“h (’7)
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\
CL)
\ _
O
1’) U)
("3 1;

\DH L‘

I“\
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O\

013

m
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1),) \
O

U.) 1‘ ()\1\)

27192

N

0‘
'1) \O

.

\
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\’ Kn (2C)

J
L“ \(_.
C) C.) Q

9)
)
J)
O

K
I
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U)
Q
(X)
o

\J

U)
H
W
O

(‘) (,3 (I

TU \Q \j1 {\J ‘xl

'1» K
O

0‘ CHD 4‘ 0161mm

019-4 #0 0‘ NUWHOMv (331»:

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C) O O C)

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C) C) C)

N N U) U) '~.)) \_1) U.) U) U) U3

0) \O \l \l
I\) D) C) 0‘9 U“! (1) h)

C)

Oommp

\lU‘

\d

925

95

950
900
900
.00
.00
900
950
925
900
900
900
925
950
950
925
950

A
950

1900
950
900
900
900
900
900
900
900

F'.

017‘

925
925
900
950
900
900
925
950
950
953
.00
925
900
.00
925
925
925
900
900
925

1900

14

...—99.9
101‘!)

H m:
UJOODO\»()W(DO\fl\)

Hl—JH 9—9
(DwOO

LO

\0 \O

Dynasm

\O \O ‘0 \1) \L')

(I) (D 1

KQKJJKNWUJUJUJWUJUJWUJWWW
"D
3>>

('DLUxOxliD
U1'ZDO\O)J> 410009—an
.. 3)

WW

0303

F—‘N
.L‘

3783
376
373A
4298
4384
445
453
461
469
477
484
490
497
525A
531
5385
544
410
402

ASSIGN-
MENT

PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
pa
PP
PP
PP
PQ
PQ
PQ
P0
P0
PQ
P0
P0
P9
PG
P0
P0
P0
PQ
P0
PQ
P0
P0

29
29
29
29 8
29 9
2910
2911
2912
2913
2914
2915
2916
2917
2918
29
29
29
29
29
29
29
29
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919

\IO‘U)

(DNO‘U‘L‘UJN

\0

PR 29
PR 29
PR 29
PR 29
PR 29
PR 29

2
3
4
5
6
9

PR
PR
PR
PR
PR
PR
PR
PR

2910
2911
2912
2913
2914
2915
2916
2917

PP 19
PP 19
PP 19
PP 19

2
3
4
5

OPSERVED
FREQUENCY

403790240
403592120
403394083
403195420
402996390
402797610
402598330
402398900
402199530
40199940
40179722
40159875
4013.799\
4011.6668
4045.7000
404596510
404595450
404594280
404593070
404591510
404499740
404497899
404495630
404493210
404490670
404397710
404394370
4043.0900
404296880
404292870
404198060
404192050
405097960
405293450
405490640
405595200
405790800
4061.5950
406390570
4064949CO
406598990
406792860
406896260
406999360
407192160
407294280
404999580
404892090
404694413
404496240

(J C.) L)

Q

302

FRINGE
NUMBER

28091570
27495220
26899110
26391080
25791910
25193500
245.3540
23993130
23392780
22790290
22397523
21493350
20799290
20192960
307.1400
30699863
30696563
30692930
30599160
30594360
30498800
30493043
30396040
30298490
30290600
30191400
300.1000
29990230
29797730
29695230
29590290
29391590
32299870
32798050
33391513
33796770
34295300
35695710
36191170
36595750
36999560
37492700
37894370
38295100
38694900
39092590
32093790
31499430
309.A470
30397950

DELTA
NU

99999
99999
90200
99999
99999
.0200
90130
90140
99999
.0200
.0100
99999
90140
90200
99999
99999
90140
90100
99999
90200
.0100
.0200
.0140
.0100
90200
.0140
99999
.0140
99999
99999
.0100
99999
99999
99999
99999
90200
.0140
90200
90200
99999
.0140
90200
90200
99999
.0200
99999
90200
90140
99999
.0200

WEIGHT

.00
900
925
.00
900
925
1.00
950
900
925
1900
.00
950
925
.00
900
950
1900
.00
925
1900
925
950
1900
925
950
900
950
900
900
1.03
900
.00
.00
.00
925
950
925
925
900
950
925
925
900
925
900
925
950
.00
925

INT

LINE
NO

391A
3838
374A
365
3558
344
334
323A
314
304
295
286
274
253
436A
436
435
434
433
432
4314
430
429
427
426
425
423A
422A
420
4173
415
412A
460
4688
4788
485
453
516
522A
529
537
544
553
559
563
568A
4568
448
439A
429A

ASSIGN-
MENT
PP 19 6
PP l9 7
PP 19 8
PP 19 9
PP 1910
PP 1911
PP 1912
PP 1913
PP 1914
PP 1915
PP 1916
PP 1917
PP 1918
PP 1919
PP 1923
PP 1921
P0 19 1
PG 19 2
PG 19 3
PG 19 5
PG 19 6
PG 19 7
P0 19 8
PG 19 9
C 1910
PG 1911
PO 1912
PO 1913
PO 1914
P0 1915
P0 1916
PO 1917
PO 1918
PO 1919
PO 1920
PR 19 4
PR 19 5
PR 19 6
PR 19 7
PR 19 8
PR 19 9
PR 1912
PP 1913
PR 1914
PR 1915
PR 1916
PR 1917
PR 1918
PP 1919
99 09 3

oNl

OBSERVED
FREQUENCY

404298460
4C419C140
403991840
403796050
4C3594300
403394880
4C3195420
402995890
402796020
402595990
402395780
402195930
401994299
401793010
401591410
401299550
405393733
4053932l+0
30257v
39473'3
299400
297963
29626
294190
29208C
199790
19 7190
19 4330
191260

DJ-‘b
U‘Wk)

Pb D
C) C) C) C) (_) (u (3

DL‘
m
\J1\J1\J1 \I \J: U1 \fi Ln \fi

7 I
1 l
- .

C) (7) C) C)
()
.
.4
‘OI
U
(.-

09435

£‘b-DF‘D<P
C) 0

404991530
404896790
406195950
40639163"
406397220
406692550
406797490
406992400
4C739573O
407499530
407693273
407796610
407899610
408092430
408194630
408297010
405598515

303

FRINGE
NUMBER

2989263C
292.57C‘v
2869 3770
28199643
27592010
26991600
26391080
25790360
25098570
24496260
23893430
23198880
22594390
21898223
2129 1C 2C
2C593C

UJ
U)
H
o

k)

\D '7‘
O C-) 0‘)

3309
3339
3309‘
3299
3299-
3289
3289
3279
3269
925.
3249
3249
“229

a

)U‘

r) \I)

() C7 C) C) C) C)

9
c

1

00‘

CCU“ U) ()0:
U1 (2“ \l U1 \1 O \r 0‘ L.» p C.)
W.) ) () 000

f
\

H')(_)\1’)

A

b) ,0 U)
raw N
O ' H
O O
o

:1). p \n l\) m J) ‘4! «I \f) m m \I U)

U.)

K
N
(
O 0
(PL.
~JQ)-\JI'\)L\O‘CI)t—JO\

000 0000000

p

-,'-‘ (7‘ I} C) “J (D N P 0‘ I‘-‘ U) (D

C)

w w L0 U) U) UJ
'OGJN‘4®(PUM~
(D U) C) U1 H 0‘ H 0‘ (‘1‘

I} U) U) U)

WC>®

a] U) 0‘

.“\17L7\\JU)O) C)i\JD HG‘\O

\f)

\JNKflU‘WKHUHAUJN-QC)RLPKH$‘W\»

C) (:1 O (f) O C7 (.5 C.) C) O (3 C.)

1.;
\J

\O \I') \-

\O D (54> \O

r"
1.
v.

177
9—9
(3

HT

900
900
900
900
925
900
900
900
925
925
900
1900
900
900
900
925
900
950
950
1900
1900
950
950
925
925
1900
19 00
19 00
950
19 00
900
1900
953
950
930
925

925

14

LIME
NO

421
411
403
393
385
375
365
355
343A
332
321
312
301
292
282
658
475A
475
474A
473
472
471
470
459
468
467
465
454
462
460
459
457
455
452
450A
516
523
530
539
547
555A
571
576
566
592
596
603
606
612
487

ASSIGN-
MENT

RP 09

RP 09
RP 09
RP 09
RP 09
RP 0910
RP 0911
RP 0912
RP 0913
RP 0914
RP 0915
RP 0916
RP 0917
RP 0918
RP 0919
RP 0920
RP 0921
RP 0922
RP 0922
RP 0923
RQ 09
R0 09
R0 09
R0 09
(3

R0 09
R0 09
R0 09
R0 0’ .7
R0 0910
R0 0911
R0 0912
R0 0913
R0 0914
R0 0915
R0 0916
R0 0917
R0 0918
R0 0919
R0 0920
R0 0921
RR 09
RR 09
RR 09
RR 09
RR 09
RR 09
RR 09
RR 09

xomxlO‘lfi-F‘

OCDxJOLflbWfinJH

\JOLflk‘mPUP‘O

OBSERVED
FREQUENCY

405491170
405292620
405094670
404896530
404697950
40449924-O
4043.0230
404191330
403991840
403792290
403592440
403392500
403191990
402991570
402790120
402499160
402296290
402092660
401797510
451797510
401591410
406099780
406099320
406098640
406097830
406096730
4060.5440
406093893
406092170
406090320
405998000
405995520
405992880
405399960
405896650
405893040
405799020
405794660
405699640
405693900
405597240
405499590
406296880
406493420
406599860
406796000
406992100
407097860
407293550
407398920

m+-4w

C)

UJUJUJUJUJ
(DHHNNW

p
......

Q\fixnd)wmfl
QJKJDIuchfi‘H
0:) u) \1 1.31 Lu 1;) \1 U1

U)

I .
.J

C)OC)C)C)CJC)O

MN
‘00
N0)
.
01)
U)

28693770
28097960
27496200
26894190
26290420
25596910
24990200
24295010
23593890
22890410
22092190
22392190
21291020
35496520
354.5090
35492970
35490450
97040

93010

,1

N

L0
H
\O
L

MP0”
0 O C.) C.) C) “1

11:) i—«d I\) N U) h.)

\f) I—fi U) H (“17

DJ UJUJ DJUJUOUJ kUU)
UL) I\) \O

3~bkfiu1mxnu1wk
p
@CDwa-qup

- (D 4L) (J
.99. oa»o:-o 0

DJ

6

W

C
HKJOU)

KL)

6

4
00 0‘ m m m m U1

|\
'I"

61»
P.P
uwo
O

.1

D.)
p
m

A

\)

OCJOOC)OO

p
C
C
u

3
3389313
33599320
35999700
36591140
37092260
37592460
380.2520
38591520
39090340
39498120

)p(nq)b\n

O

DELTA
N0

.0200
90140
90200
99999
90200
.0100
90140
90200
90140
.0200
99999
99999
90200
90200
90140
99999
90140
90140
90140
9C140
99999
90140
90100
.0100
.0100
90100
90100
90070
.0070
99999
90140
90140
.0130
.0100
90140
90140
90200
90100
90140
90100
90100
.0100
90200
90100
.0140
90200
.0200
99999
99999
90200

WE 1 0H 7

1900
950
925
900
925

1900
950
925
950
925
.00
.00
925
925
950
900
953
950
950
950
900
950

1.00

1.00

1900

1900

1.00

2900

2900
900
950
950

1900

1.00
950
950
925

1900
950

1900

1900

1900
925

1900
950
925
925
900
.00
925

INT

16
21
24
19
18
17
15
23
19
17
27
22
20
19
17
19
11
16
19
1o
11
16
13
20
21
21
21
20
22
25
23
20
25
21
24
21
29
19
18
19
19
14

14
18
16
19
20
24

LINE

479
468A
459A
450
441
431
422
412
403
392A
384
373
363A
353
340
328
317
306

294
282
514A
514
513
512
511
510
509
508
507
505
504
503
501
500
499
496
495
492
489
486
483
521
528
538
546
555
561
568
572

ASSIGN-

MENT

RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0

09 8
09 9
09 9
0910
0911
0912
0913
0914
0915
0916
0917
0918
0919
0920
19
19
19
19
19
19
19
1910
1911
1912
1913
1911
1912
1913
1914
1915
1917
1918
1919
1920
1921

\OCDxIO‘U‘i-L‘U)

....9
O
~00)4(bu1bLnk9

OBSERVED
FREQUENCY

407593920
407698840
407698840
407893470
407997990
4C8192070
408296070
408399640
405592930
408695860
408798150
408899520
408999720
409098480
406393910
406498580
405998680
405890260
405691960
405493270
405294190
405094670
404893710
404599480
404299430
404996190
404790840
404499740
404299433
404099630
403698240
403497350
403294990
402992970
402698500
406895160
406894550
406893630
406892570
406891170
406799460
406797490
406795110
406791180
406693630
406590520
406893630
406795110
406791180
406697890

305

P

.—
I

~ '2

F“ C)
X1 m

1
\'

R
Uu—w

I'ID

Z

39994790
40491180
40491180
40896670
41391540
41795620
42199150
42691360
43092690
43492910
43891110
44196490
44498200
44795450
36291550
35697180
35192000
34594730
33997970
33399690
32890350
32199630
31594460
30799110
29895640
31993260
31194440
30498300
29895640
29294080
27995350
27390400
26690860
25892390
24895180
37890950
37799030
37796170
37792380
37698520
37693220
37597100
37499700
37397450
37193970
36793210
37796170
374.9700
37397450
37297240

DELTA
NU

90200
90140
90140
99999
90140
.0200
90140
90100
90140
.0100
.0140
90200
90100
.0100
99999
99999
99999
90140
99999
99999
99999
99999
90200
90200
90200
.0140
99999
.0230
90200
90200
99999
99999
99999
99999
.0290
99999
90200
90200
90200
90200
90140
.Gl/LO
90200
90200
90200
99999
99999
90200
90200

99999

WEIGHT

925
950
950
.00
950
925
950
1900
950
1900
950
925
1900
1900
900
900
.00
950
.00
900
.00
900
925
925
925
950
900
925
925
925
900
.00
900
900
925
900
925

’75;

94/
925
925
950
950
925
925
925
900
900
925
925
900

LINE
N0

579

589
594
599
600A
611
619
624
630
635
642
646
552
524
516A
506
497
488
480
469
459A
449
437A
4213
455
442
431A
4218
410E
391
381A
3703
357
339
552A
552
551
550
549
548
547
545
543
540
532
551
545
543
542

ASSIGN-
MENT

R0
R0
R0
R0
R0
R0
R0
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RP
RP
RP
RP
RP
RR
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
R0
R0
R0
R0
R0
R0

1914
1915
1916
1917
1918
1919
1920
19
19
19
19
19
19
19
19
19
1911
19 9
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
29 4
29 5
29 7
29 8
2910
2911
2912
2913
2915
2916
2917
2918
2920
2921
2922
2924
29
29
29
29
29
29

w>m~40~uupuamn~

mxlO‘U19Lx)

OFSERVED
FREQUENCY

406694960
406691400
406597590
406593440
406498150
406399680
406295260
407199250
407395730
407591820
407697700
407893470
407998720
408193830
408298250
40849 260
408594920
408594150
408692530
408795540
408899520

409492750
409594380
409692860
409695320
406992090
406794080
406397640
406199170
405891590
405692010
405493270
405293450
404893710
404693620
404493210
404292120
403799490
403597380
403395220
402990100
4076.0200
4075.9250
407598190
407596900
407595460
407593920

306

FRINGE
JUMBER

37198130
37097060
36995200
36392280
36695850
36399490
35994670
38896950
39398200
39898240
40397640
40896670
41394100
41891100
42295930
42696390
43098870
43096490
43392450
43792990
44196490
44599080
45990320
45492160
45892020
46198180
464.4400
46592220
38092520
37496490
36393160
35795720
34598850
33997970
33399690
32798050
31594460
30992000
30298490
26992910
28390340
27691590
26992650
25592340
401.4300
40191360
400.8070
43094290
39999560
39994790

DELTA
NU

.0140
90140
90140
90140
.0140
90200
99999
90100
90100
90200
90140
99999
90200
90200
90140
90140
90200
99999
90200
.0140
.0140
.0140
90100
.0200
.0200
90140
90200
99999
99999
99999
90200

.8148'

99999
99999
90200
90200
90140
90200
99999
90200
99999
99999
99999
90200
99999
90140

AHAQ
/

9999
.0100
.0140
99999

WEIGHT

950
950
950
950
950
925
900
1900
1900
925
950
900
925
925
950
950
925
900
925
950
950
950
1900
925
925
950
925
900
900
900
925
950
900
900
925
925
950
925
900
925
900
900
.00
925
.00
950
.00
1900
950
900

INT

LINE
NO

541
538C
536
533
531
527
5204
566
571
578
588
594
600
6058
6128
620
626
625
628
634
642
647
655
659
663
668
6718
673
555
5448
526
518
498
488
480
4683
449
439
427
417A
397
386
375A
352
584
583
582
581
580
579

ASSIGN-
MENT

R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR

29 9
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
29
29
29
29
29
29
29
2910
2911
2912
2913
2914
2915
2916
2917
2918
2920
2921
39
39
39
39
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922

\OxlO‘U‘J-‘UJN

«J U1

\0 CD

OBSERVED
FREQUENCY
407501823
407409500
407407530
407404910
407402060
407308920
407305730
407302250
407208260
407203710
407109250
407104210
407008930
407003470
406907930
408101510
408207390
408403340
408509180
408704740
408809970
409109640
409304790
409409150
409603370
409707360
409901060
410004460
410107460
410209980
4104.2330
410605833
410707360
407409500

406705500
406506880
406307640
406108270
405908630
405709020
405509240
405309170
405108960
404908850
404707390
404506510
404304770
404101340

307

FRINGE
NUMBER

39808240
39801040
39704950
39606740
39507900
39408120
34308200
39207370
39104960
39000340
38806950
38701290
38504870
38307370
38200650
41703880
42203250
42702870
43202000
43700500
44107880
45100150
45507260
46001910
46406140
46809650
47302250
47703730
48104350
48503280

8901690
49604780
50000650

39801040

U3 U.) DJ
\J (Y) (:0
\fl (2) Ch
. C O
C) \

(“

LL)

b)

O

\O

o

9 U)
' 1)) (1* <1) \() 4"
9 1 L) C) C) (L)

o
N

C)

C) '1. "

. U.)

U) U)

U1 U! 0‘

9—9 - w

o o

i\) U
:C)\.OI~—JC)OOI> _)

U’UJ
U)?
-U1
..

\OLL)
LOU.)
U14}
CO

CO 4} 0‘ (A)

DELTA
NU

00200
09999
00140
00200
00140
09999
09999
00100
00140
09999
00100
00200
00200
00200
00200
09999
00200
00100
00140
00140
00140
00140
00140
00200
00140
00140
00140
00200
.0140
00200
09999
00200
09999
09999
00200
00200
09999
09999
00200
00140
09999
09999
00140
09999
00140
09999
00140
09999
09999
09999

025
000
050
025
050
000
000
1000
050
000
1000
025
025
025
025
000
025
1000
050
050
050
050
050
025
050
050
050
025
050
025
000
025
000
000
025
025
000
000
025
050
.00
000
050
000
050
000
050
000
000
000

LINE
N0

578
576
575
574
573
572
571
570
569
568A
566
564
562
560
558A
605
612A
621
627
633
642A
656A
661A
6655
672
676
663
689
695
699
704A
714
7193
576
5635
556
543A
535
526
517
506
496
487A
478
466
456A
444
436
424
412

ASSIGN-
MENT

R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RP
RP
RP
RP
RP
RP

39
39
39
39
39
39
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922

39 3
39 4
39
39
39
39
39
3910
3911
3913
3914
3915
3916
3917
3918
3920
49 9
4911
4913
4914
4916
4917

\OG)Q(FU‘9

0(D\JOKfi

R0 49
R0 49
R0 49
R0 49

6
7

8
9

R0
R0
R0
R0
R0

4910
4911
4912
4913
4914

OBSERVED
FREQUENCY

408394400
408393370
408392120
408390620
408298880
408297013
408294910
408292630
408290120
408197330
408194630
408191510
408098200
408095000
408090870
407996560
407991700
407895310
407794940
409092563
409198650
409394320
409499790
409695320
409890350
409995150
410099910
410294710
410502760
410696720
410890440
410994260
411096690
411199590
411492250
407590540
407192530
406793400
406593440
406191420
405990920
409096900
409095400
409093740
409091840
408999720
408997250
408994620
408991630
408898140

308

FRINGE
NUMEER

42495050
42491860
42397960
42393290
42297900
42292090
42195540
42098470
42090660
41991970
41893570
41793880
41693590
41593630
41490790
41297380
41192260
40992390
40690140
44597030
45097080
45595810
46093920
46592220
46998940
47494970
47990870
48396890
49294150
49697550
50190213
50593200
50991860
51391970
52092430
39894250
38696050
37494360
36892280
35591630
34897870
44790530
44695850
44690700
44594800
44498200
464.0530
44392330
44293030
44192200

DELTA
NU

90140
90140
90140
90100
90100
90140
90140
90140
90140
90140
99999
90200
90100
99999
99999
90140
90140
99999
99999
90100
90200
90100
90100
90200
99999
90140
90100
99999
90100
90140
90140
99999
99999
90100
.0100
99999
99999
90200
99999
99999
90140
90140
99999
90140
90140
90200
90200
99999
90140
90100

950
950
950
1900
1900
950
950
950
950
950
900
925
1900
900
900
950
950
900
900
1900
925
1900
1900
925
900
950
1900
900
1900
950
950
900
900
1900
1900
900
900
925
900
900
950
950
900
950
950
925
925
900
950
1900

WEIGHT INT

10
14
17
17
21
25
19
18
19
19
23
25

8
14
15
16

13
12

p

9
20
21
20
24
24
23
21
22
30
19
16
16
21
15
14
12
11

6

8
14

4

7

7
15
14
13
16

9
12
13
10

LINE
N0

617
616
615
614
613
612
610
609
608
607
606
605
604
603
601A
598
597
595
591
648
656
661
666
673
679
686
692
697
710
715
721
728
732
737
745
577
563A
544A
533
515
502
651
650A
649A
647
646
645
644
643
641

ASSIGN-
MENT

R0 4915
R0 4916
RR 49 4
RR 49 5
RR 49 6
RR 49 7
RR 49 8
RR 49 9
RR 4910
RR 4911
RR 4912
RR 4913
RR 4914
RR 4915
RR 59 6
RR 59 7
RR 59 8
RR 59 9
RR 5910
RR 5911
RR 5912
RR 5913
RR 5914
RR 5915
RR 5916
RR 5917
RR 5918
RR 5919
R0 59 8
R0 59 9
R0 5910
R0 5911
R0 5912
R0 5913
R0 5914
R0 5915
R0 5916
R0 5917
R0 5918
R0 5919
R0 5920
RP 5915
RP 5917
RP 5919
RP 69 8
RP 6910
RP 6914
RP 6916
RP 6919
RP 6920

OBSERVED
FREQUENCY

408893560
408799690
409993470
410099090
410294710
410399910
410595020
410699950
410894590
410999120
411192920
411296440
411398760
411591990
410994260
411099730
411294850
411399420
411594130
411698490
411892710
411996610
412190440
412293890
412397350
412590390
412693030
412796060
407993670
409791410
409699250
409696380
409694300
409691480
409598480
409595290
409591800
409498040
409494170
409490060
409395730
407093470
406692560
406291060
409197300
408799690
408090870
407690200
406997930
406796600

309

FRINGE
NUMBER

43997930
43895920
47399740
47898340
48396890
45394160
49391163
49797590
50293110
50698320
51191240

593260

A

D
d
J

k

0
O
N,“
rv~Jm
Cypu
OC)(.

k.)
C.)
’ )

‘09 C) Ulw\"
......-
-D¢)w(nh0w

Wkns

C) U)

UHfianlmkfikfiU1mx
px09>w
() C) C) C)

wl‘urQHr—er 33109-49

I\) G.) U.)
o

w

M

\l

C

53791500
54194490
54596330
54998200
55398730
55798060
56198560
46798180
46791140
46694440
46597050
46499030
46490270
46390950
46291030
46190170
45998480
45896430
45793640
45690180
38397870
37190670
35891600
45092860
43895920
41490790
40194300
38390650
37594310

90140
90100
90140
.0100
99999
.0140
90100
90100
90100
90140
90100
90200
90200
90140
99999
.0200
99999
90140
99999
90140
90100
90200
99999
90200
99999
99999
90200
90200
90200
99999
90140
90140
90200
90140
90200
90140
90200
90200
90140
90200
90200
99999
99999
99999
90200
90200
99999
99999
99999
99999

925
950
925
925
900
900
900
925
925
900
900
900
900

INT

10

21

LINE
NO

638
636
685
691
697
703
711
716
723
729
734
740
744
748
728
733
739
744A
749
753
758
762
766
769
773
780
785
788
677
676
675
674
672A
671
670
669
667
665
664
662
661A
560
539
519
655A
636
601A
584
558A
546A

ASSIGN-
MENT

RP
RP
RP
RR
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RP
RP
RP
RR
RR
RR
RR

6921
6922
6925
6926
69 7
69 8
69 9
6910
6911
6912
6913
6914
6915
6916
6917
6918
6919
6920
6921
6922
6923
6924
6925
6926
6927
69 6
69 7
69 8
69 9
6910
6911
6912
6913
6914
6915
6916
6917
6918
6919
6920
6921
6922
6923
7910
7915
7920
79 7
79 8
79 9
7910

0
F

Him

m
IT) <
2'. HI
0 U

,1,)1)

Y

K)

406595300
406393910
405697530
405495010
410592760
410591660
413499613
413497340
410494750
413491993
410398990
410395810
410 392450
413 298 933
41020471.)
413293893
410196620
410192170
413097460
410092510
409997380
409992040
409896500
408990350
409794120
41179265-
411897770
412092740
412197540
412391930
412496180
412690240
412793960
412897570
413390860
413194050
413296840
413399530
413591940
413694190
413796220
413897920
413999490
409592740
408594150
407590540
412691120
412796060
412990850
413095300

49294150
49290700
49194340
43-3.7230
g9.07§©

Ahwonfi‘q

48591330

43791430
486909 60
485'9OC
403968
43295

48191
47997
47893
476978
475919
4739629
471.9 000
46998943
46799560
52996990
53493990
53990570
54396590
54891340
55295650
55699380
56192040
56594380
56995710
5739673‘3

57796500
58195970
58594550
58992640
59390060
59696460
60092430
46193 070
43096490
39894250
55792100
56198560
56694580
57099500

A)

NO‘JC)
9—4:JO\9-—00\1—J ()1
(J(‘LWLU

99999
90200
90140
90200
99999
99999
.0100
90100
.0140
90200

WEIGHT

900
900
900
900
900

50
O .2 '

1900
925
950
950
900

1900

1900
950
900

1900
925
950
925
900
950

:9

.JV

950
900
900
2900
950
1900
2900
1900
1900
950
1900
925
1903
950
950
1900
1900
950
900
925
950
925
900
900
1900
1900
950

925

A

Fay—9

N
\O'.p\1\1WL5C

NN
\JU)

Hrka
-QC)qur

HHr—JH
\IO‘NNO

9.4
\I‘

H F‘HFJFJ
\ONxOJ-‘NJ-‘D

11
13
16
11
13

LINE
N0

534
524
491
481
710
709
708
707
706
704
702
701
700
698
697
696
694
693
690
688
6873
534
682
679
677A
755
760
754
768
771
778
733
737
789
792
795
798
800
803
806A
808
311A
314
625
525
577
784
788
790
793

311

ASSIGN- OESER VED FRINCE DELTA WEIGHT INT LINE
MENT FREOU 'EHJC NUMBER N0 N0
RR 7911 413199590 57593943 90140 950 12 797
RR 7912 413393620 57997590 90140 950 13 799
RR 7913 413497433 58490540 90200 925 11 801
RR 7914 413501340 595.2850 .9999 .00 13 835
RR 7915 413794263 59293963 90140 950 10 807
RR 7916 413897380 59694780 90200 925 10 811
RR 7917 414090223 6039471‘3 90230 925 8 8144
RR 7918 414192980 60494393 90200 925 6 817
RR 7919 414295433 60893090 99999 900 10 821
R0 79 8 411294850 21498330 99999 900 8 739
R0 79 9 411293310 51492610 .999 900 7 738
R0 7910 411293620 31395163 925 5 7374
R0 7911 411198150 51297503 950 5 7365
R0 7912 411195550 5119940J 925 10 735
R0 7915 411096010 50899747 950 11 7314
80 7916 411092263 50798070 925 8 7304
R0 7919 4109.0090 50490.24J .00 5 7254
R0 7923 413894910 50294110 900 10 7234
R0 7922 410795890 49996060 950 7 709
R0 7923 410699953 49797590 900 16 716
RP 8915 409296760 453923C3 900 4 6580
RP 8917 408896500 44097090 950 5 640
R0 8911 411990940 53593570 900 5 7614
R0 8915 411798610 53195520 925 4 7573
R0 8916 411795 040 53092740 900 5 756
R0 8917 411791250 52992640 900 7 754
R0 8918 411697110 52799740 925 8 752
R0 8919 411692940 52696780 900 7 751
R0 8920 411598263 5259223'3 925 5 7508
RR 89 8 413498760 58494680 1900 - 802
RR 89 9 413693510 58990540 1900 806
RR 8910 413797980 59395530 1900 809
RR 8911 413992270 59799980 950 11 812
RR 8912 414096273 60293510 925 7 815
RR 8913 414290020 60696290 925 8 820
RR 8914 414393600 61J98520 1900 7 823
RR 8915 414497080 61590430 900 7 825
RR 8916 414599970 61990520 925 5 828
RR 8917 414793220 62391710 925 4 833
RR 8’21 415291250 63891C80 925 9 838
RP 9914 410199630 48496260 900 3 6958
RR 9918 409397350 45695210 900 4 6618
RP 9920 408995160 44394C’30 900 8 6446
R0 9910 412695370 55895330 950 8 786
R0 9911 412693030 5579,060 925 10 785
R0 9912- 412690240 55699380 900 19 783
R0 9913 412597300 55690233 925 4 7823
R0 9914 _412594200 55590600 900 5 782
R0 9915 4125906 60 55399590 900 12 7804
R0 9916 412496860 5529776C 900 11 779

ASSIGN-
MENT
R0 9917
R0 9018
R9 9019
R0 9022
RD 9023
R0 9924
R0 9926
R0 9927
R0 9929
RR 90 9
RR 9910
RR 9011
RR 9912
RR 9013
RR 9914
RR 9915
RR 9916

CBSERVED
FREQUENCY

412403190
412309040
412304713
412200370
412104950
412009660
411907980
411902383
411709110
414305510
41450OC40
414604203
414708213
414901993
415005463
415108883
415301893

312

FRINGE
NUMBER

(Jr-I

O)
O O F.) C.) C.) O

C)4>\J OWL» «)bw
m a,» C) 0) 0.) m m \o -p m

(g) d1 +..- r-I U) \l a-‘ N L‘
q) 4') \l \1 U" m 0.) U) x0 m 0‘
_'\

nob
00.000.000.000...

0‘ 0‘0“ 0‘ 0‘0‘ (P UT U1 U! U1 U‘ U1 U“ \B U‘
D\))r—‘O\lw

\l \O (0) {\J (3‘ 0‘

£~wwmmm~v—amwwppppmm
0)H\1\L)U1\]\u

(,1) (f) C) '1') (T) (_') C) (_'_) (") (’) (3

O\
HxlUJ
H

025
000
025
000
000
000
000
000
025
.50
1030
1030
1000
050
025
050

025

INT

._0

H
\OC)!—‘\))U)|—‘(T‘ wbwooxcbo‘omt—o

...:HHHHHH

LINE
NO

776
774
772
768A
7678
765A
763
7618
757C

w
N
p

07(DCDUJOJ

l} kpg) xJVu r\_){\)
Oxlul-L‘N\OO‘

0') (l)

APPENDIX VI

LIST OF OBSERVED GROUND STATE COMBINATION

DIFFERENCES FOR v3+v4 OF CH3F

The following pages contain a list of the observed
ground state combination differences for v3+v4 of CHBF.
The columns of the list, left to right, are: the assignment
(cf.Chapter 4); the calculated combination difference (in cm'1)
from Appendix II; the observed combination difference (in cm");
the Av (weight = (NORM)2/(Av)2); and the observed minus the

calculated difference.

313

ASSIGN-
MENT

R0 9012
R0 9016
R0 9017
R0 9020
RP 9010
RP 9011
RP 9012
RP 9016
RP 9017
RP 9020
GP 90 9
GP 9012
GP 9013
GP 9015
GP 9016
OR 9017
GP 9018
GP 9019
GP 9020
RP 8013
RP 8014
RP 8015
R0 8013
R0 8014
GP 80 8
GP 80 9
GP 8010
GP 8012
GP 8013
0P 8014
RP 70 9
RP 7011
R0 7011
GP 70 7
GP 70 8
GP 7010
GP 7011
GP 7012
GP 7013
GP 7014
GP 7015
R0 60 8
R0 60 9
R0 6012
R0 6016
R0 6017
RP 60 8
RP 60 9
RP 6012
RP 6016

CALCULATED

GSCD

200401
270187
280881
330960
350706
390103
420499
560068
590456
690612
170039
220098
230795
270187
280881
300575
320268
330960
350652
450906
490300
520693
220105
230802
150309
170009
180708
220104
230802
250499
320327
390125
180713
130613
150313
180713
200412
220110
230808
250505
270202
130616
150317
200416
270208
280904
280933
320334
420532
560112

314

OBSERVED

GSCD

2004100
2702350

808510
3309280
3507050
3901010
4205100
5601040
5904650
6905930
1608940
2200800
2308240
2702160
2808690
3006140
3202490
3309810
3506650
4509030

4902240 .

5206670
2201210
2307340
1503060
1609940
1807150
2200940
2308240
2504900
3203150
3901380
1807280
1306210
1503180
1807170
2004100
2200960
2308050
2505040
2702150
1306080
1503410
2004160
2702040
2809060
2809270
3203610
4205260
5601140

DELTA
NU

09999
09999
09999
09999
00245
09999
09999
09999
09999
09999
09999
00245
00283
09999
09999
09999
09999
00283
00283
09999
09999
09999
09999
09999
09999
09999
09999
00283
09999
09999
09999
00245
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
00283
09999
09999
09999
09999

085-
CALC

0009
0048
“0030
‘0032
‘0001
-0002
0011
0036
0009
-0019
‘0055
‘0018
0029
0029
“0012
0039
-0019
0021
0013
'0003
-0076
-0026
0016
-0068
-0003
‘0015
0007
'0010
0022
‘0009
-0012
0013
0015
0008
0005
0004
-0002
'0014
“0003
‘0001
0013
-0008
0024
0000
-.004
0002
-0006
0027
‘0006
0002

ASSIGN-
MENT

RP
0P
0P
0P
0P
0P
OP
0P
0P
0P
0P
0P
0P
0P
0P
0P
0P
0P
0P
0P
QP
RP
RP
RP
RP
RP
R0
R0
R0
R0
R0
R0
R0
R0
RP
RP
RP
RP
OP
0P
0P
0P
0P
OP
0P
OP
0P
0P
OP
GP

6017
60 6
60 8
60 9
6010
6012
6013
6014
6015
6016
6017
6018
6019
6020
50 5
50 6
50 8
50 9
5010
5012
5013
50 7
50 8
50 9
5010
5013
50 8
50 9
5010
5013
40 7
40 8
4011
4013
40 7
40 8
4011
4013
40 6
40 7
40 8
4013
30 3
30 4
30 5
30 6
30 7
30 8
30 9
3010

CALCULATED

GSCD

590503
110915
150317
170017
180717
220115
230813
250511
270208
280904
300599
320294
330987
350680
100215
110917
150320
170020
180721
220120
230818
250536
280938
320340
350741
450938
130619
150320
170021
220120
110919
130621
180724
220123
250540
280943
390147
450945
110919
130621
150322
230822

60813

80516
100218
110921
130623
150324
170025
180726

315

OBSERVED

GSCD

5905060
1109220
1503190
1700200
1807130
2201100
2308090
2505080
2702010
2809100
3006000
3203050
3309760
3506830
1002120
1109060
1503370
1700140
1807210
2201300
2308410
2506350
2809310
3203610
3507530
4509310
1305940
1503470
1700320
2200900
1109570
1306550
1808250
2201770
2505660
2809480
3901920
4509700
1108870
1306090
1502930
2307930

608100

805170
1002160
1109260
1306230
1503330
1700420
1807350

DELTA
NU

.0283
.0173
00173
00224
00224
00173
00141
00173
00245
.0200
00283
00245
09999
00245
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
00283
00245
09999
09999
00283
09999
09999
09999
00283
00283
00173
00200
00245
00173
00245
00173
00200

085-
CALC

0003
0007
0002
0003
-0004
'0005
'0004
'0003
'0007
0006
0001
0011
~0011
0003
~0003
~0011
0017
‘0006
0000
0010
0023
0099
‘0007
0021
0012
'0007
‘0025
0027
0011
“0030
0038
0034
0101
0054
0026
0005
0045
0025
‘0032
-0012
“0029
-0029
-0003
0001
‘0002
0005
0000
0009
0017
0009

ASSIGN-
MENT

0P 3011
GP 3012
GP 3013
0P 3014
GP 3015
GP 3016
GP 3017
GP 3018
OR 3019
OR 3020
R0 30
R0 30
R0 30
R0 30
R0 30
R0 30
R0 3010
R0 3011
R0 3012
R0 3013
R0 3017
R0 3018
R0 3019
R0 3020
RP 30
RP 30
RP 30
RP 30
RP 30
RP 30
RP 3010
RP 3011
RP 3012
RP 3013
RP 3017
RP 3018
RP 3019
RP 3020
OR 20
GP 20
OP 20
OP 20
GP 20
GP 20
OP 20
OP 20
GP 2010
GP 2011
OR 2012
0P 2013

ocn~00\n£~

\OGDQCFU‘?

mnn~00xn$~wrv

CALCULATED

GSCD

200426
220126
230825
250523
270221
280918
300614
320309
340003
350697

60813

80517
100218
110920
130622
150324
170025
180726
200426
220126
280918
300614
320309
340003
150328
180734
220139
250543
280947
320349
350751
390152
420552
450951
590531
620923
660312
690700

50110

60813

80516
100219
110922
130945
150325
170027
180728
200428
220128
230827

316

OBSERVED

GSCD

2004240
2201300
2308260
2507720
2702170
2809070
3005950
3203280
3400570
3507030

607930

805090
1002110
1109230
1306260
1503430
1700159
1807270
2004180
2201270
2809150
3006330
3202980
3309860
1503100
1807250
2201370
2505460
2809590
3203850
3507500
3901510
4205480
4509530
5905100
6209610
6603550
6906890

501060

607890

805210
1002160
1109330
1309300
1503350
1700280
1807310
2004460
2201330
2308310

DELTA
NU

09999
09999
09999
09999
09999
.0245
00283
09999
09999
09999
09999
00245
00245
00200
00173
09999
.0245
09999
09999
09999
00283
09999
09999
09999
09999
00245
00200
00173
00245
09999
00245
09999
09999
00283
00283
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
00283
00173
00173
09999
.0245

085-
CALC

-0002
0004
0001
0249

-0004

-0011

‘0019
0019
0054
0006

-0020

-0008

‘0007
.003
0004
0019

"0010
0001

‘0008
0001

-0003
0019

“0011

‘0017

“0018

-0009

-0002
0003
0012
0036

-0001

-0001

‘0004
0002

-0021
0038
0043

-0011

‘0005

‘0024
0005

'0003
0012

'0015
0010
0001
0003
0018
0005
0004

ASSIGN-
MENT

OR 2014
OR 2015
0P 2016
GP 2017
R0 20 3
R0 20 4
R0 20 5
R0 20 6
R0 20 7
R0 2010
R0 2011
R0 2013
R0 2014
R0 2015
R0 2016
R0 2017
R0 2018
RP 20 3
RP 20 4
RP 20 5
RP 20 6
RP 20 7
RP 2010
RP 2011
RP 2012
RP 2013
RP 2014
RP 2015
RR 2016
RR 2017
R0 10 5
R0 10 6
R0 10 7
R0 10 8
R0 10 9
R0 1010
R0 1013
R0 1014
R0 1015
R0 1016
R0 1017
R0 1018
R0 1019
R0 1020
0P 10
0P 10
OR 10
OR 10
0P 10
0P 10

OLD$>mtha

CALCULATED

GSCD

250525
270223
280920
300616

50110

60813

80516
100219
110922
170027
180728
220128
230827
250525
270223
280920
300616
110924
150330
180735
220141
250545
350754
390156
420556
450955
490352
520748

'560143

590536

80517
100220
110922
130624
150326
170028
220129
230828
250527
270224
280922
300618
320313
340008

30407

50110

60814

80517
100219
110922

317

OBSERVED

GSCD

2505150
2702160
2808900
3006210

501450

608010

806360
1002130
1109300
1700320
1807360
2201280
2308500
2505360
2702480
2809290
3006220
1109340
1503210
1808520
2201460
2505380
3507620
3901670
4205410
4509590
4903640
5207520
5601370
5905500

805220
1002230
1109250
1306290
1503300
1700300
2201400
2308250
2505330
2702420
2809180
3006260
3203090
3400020

304150

501160

608140

805230
1002270
1109240

DELTA
NU

09999
09999
09999
09999
09999
09999
09999
09999
00245
00245
00224
.0200
09999
00245
09999
09999
09999
09999
09999
09999
00283
09999
00224
00245
09999
00245
00224
09999
09999
00283
00224
00173
.0245
.0245
09999
09999
09999
09999
00173
09999
00173
09999
09999
09999
09999
00200
09999
09999
09999
09999

OBS-
CALC

-0010
'0007
-0030
.005
0035
“0013
0120
-0006
0008
0004
0009
0000
0023
0011
0024
0009
0005
0010
‘0008
0117
0005
-0007
0008
0011
“0015
0004
0012
0004
‘0006
0014
0005
0003
0003
0005
.004
0002
0011
-0003
0006
0018
‘0004
0008
~0004
0012
0008
0006
0000
0006
0008
0002

ASSIGN'
MENT

OP
OP
OP
OP
OP
OP
OP
OP
OP
OP
OP
OP
OP
OP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
OP
OP

10 7
10 8
10 9
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
10 5
10 6
10 7
10 8
10 9
1010
1013
1014
1015
1016
1017
1018
1019
1020
00
00
O0
00
00
00
O0
00
0010
0011
0012
0013
0014
0015
0016
0017
0018
0019
0020
0021
10 2
10 3

0CD~JOthwxn0

CALCULATED

GSCD

130624
150005
170028
180729
200429
220129
230828
250527
270224
280922
300618
320313
340008
350702
180736
220142
250547
280629
320354
350756
450957
490354
520751
560146
590540
620960
660322
690709

80518
110924
150331
180737
220142
250547
280951
320354
350757
390158
420559
450958
490356
520752
560147
590541
620932
660323
690711
730097

50110

60814

318

OBSERVED

GSCD

1306110
1500210
1609890
1807210
2004380
2201300
2308310
2505300
2702160
2809320
3006140
3203160
3400130
3507240
1807490
2201470
2505370
2806500
3203190
3507530
4509700
4903520
5207430
5601580
5905320
6209410
6603220
6907460

804910
1108690
1503380
1807430
2201330
2505600
2809680
3203640
3507510
3901630
4205610
4509630
4903570
5207650
5601360
5905740
6208990
6603230
6907060
7300970

501250

605970

DELTA
NU

09999
09999
00283
09999
09999
09999
00224
00245
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
00141
09999
09999
09999
09999
00224
00173
00245
00283
09999
09999
00224
00283
00245
09999
00245
09999
09999
00224
00245
.0173
09999
00245
00173
.0173
09999
09999

085-
CALC

‘0013
0016
'0039
‘0008
0009
0001
0003
0003
-0008
0010
0004
0003
0005
0022
0013
0005
‘0010
0021
'0035
-0003
-0013
-0002
"0008
0012
‘0008
-0019
0000
0037
-0027
‘0055
0007
0006
'0009
0013
0017
0010
‘0006
0005
0002
0005
0001
0013
‘0011
0033
-0033
0000
-0005
0000
0015
“0217

ASSIGN-
MENT

QD
OP
OP
OP
QD
OP
0P
0P
0P
OP
OP
0P
OP
OP
OP
OP
OP
OP
QD
RP
RP
RP
RP
RP
RD
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RO
RO
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0

10
10
10
10
10
10
1010
1011
1012
1010
1011
1012
1013
1014
1016
1017
1018
1019
1020
10
10
10
10
10
10
10
10
1010
1012
1010
1012
1013
1014
1016
1017
1018
1019
1020
10
10
10
10
10
10
10
10
1010
1012
1010
1011
1012

\omqombwm 0
\ (DNIO‘U‘P

\OGJQCFUTPKHRJ

CALCULATED

GSCD

80517
100220
110922
130624
150326
170028
180729
200429
220129
180729
200429
220129
230828
250527
280922
300618
320313
340008
350701

80518
110924
150330
180736
220142
250546
280951
320354
350756
420558
350756
420558
450957
490355
560146
590540
620931
660321
690710

30407

50110

60814

80517
100220
110922
130624
150326
170028
200429
170028
180729
200429

319

OBSERVED

GSCD

804950
1002310
1109160
1306190
1503300
1700440
1807470
2004150
2201090
1807440
2004270
2201440
2308460
2505330
2809350
3006090
3203160
3404700
3506760

805340
1107150
1503140
1807440
2201460
2505450
2809640
3203580
3507550
4205490
3507960
4205800
4600090
4903590
5601690
5905400
6209390
6607820
6906820

304090

501180

608190

805130
1002300
1109260
1306340
1503140
1700080
20044C0
1700520
1807390
2004360

DELTA
NU

09999
.0245
09999
09999
09999
09999
00283
00283
09999
09999
09999
00283
09999
00245
09999
09999
09999
09999
09999
09999
09999
09999
00200
09999
09999
09999
09999
00245
00283
09999
00245
00245
00245
09999
09999
09999
09999
09999
09999
00224
00283
00245
09999
00245
00245
00245
00245
09999
09999
00283
00245

085-
CALC

-0022
0011
'0006
‘0005
0004
0016
0018
-0014
'0020
0015
-0002
0015
0018
0006
0013
-0009
0003
0462
‘0025
0016
'0209
‘0016
0008
0004
~0001
0013
0004
‘0001
‘0009
0040
0022
0052
0004
0023
0000
0008
0461
‘0028
.002
0008
0005
‘0004
0010
0004
0010
~0012
-0020
0011
0024
0010
0007

ASSIGN‘
MENT

R0 1013
R0 1014
R0 1015
R0 1016
R0 1017
R0 1018
R0 1019
R0 1020
RP 20 3
RP 20 4
RP 20 6
RP 20 7
RP 2010
RP 2011
RP 2012
RP 2014
RP 2015
RR 2016
RP 2017
RP 2019
RR 2021
GP 20 3
OR 20 4
OR 20 6
OR 20 7
OR 20 9
OR 2010
0P 2011
OR 2012
OR 2014
OR 2015
OR 2016
GP 2017
OP 2019
0P 2020
OP 2021
OR 2023
R0 20
R0 20
R0 20
R0 20
R0 20
R0 20 8
R0 2010
R0 2011
R0 2012
R0 2013
R0 2014
R0 2015
R0 2016

\IO‘Ui-bw

CALCULATED

GSCD

220129
230828
250527
270225
280922
300618
320313
340008
110924
150330
220141
250545
350754
390156
420556
490352
520748
560143
590536
660318
730092

60813

80516
110922
130624
170027
180406
200428
220128
250525
270223
280920
300616
340006
350700
370392
400783

50110

60813

80516
100219
110922
130624
170027
180728
200428
220128
230827
250525
270223

320

OBSERVED

GSCD

2201630
2308260
2505240
2702340
2809310
3006230
3203120
3400060
1109410
1503290
2201500
2505560
3507630
3901510
4205690
4903650
5207430
5601190
5905340
6602840

300610

608100

805170
1109340
1306290
1700230
1804270
2004270
2201450
2505200
2702100

809040
3006140
3309760
3506830
3703720
4007830

501310

608120

805150
1002160
1109280
1306050
1700140
1807240
2004240
2201310
2308440
2505330
2702150

DELTA
NU

09999
00200
00173
.0245
00245
00200
00283
09999
09999
09999
00245
00200
09999
00245
00283
00200
00245
09999
00245
09999
09999
09999
09999
00224
00200
09999
09999
00245
00283
09999
09999
09999
.0245
09999
09999
09999
00283
09999
00245
09999
00173
.0200
09999
09999
00200
00283
00200
09999
09999
00224

OBS-
CALC

0034
~0002
'0003

0009

0009

.005
'0001
-.002

0017
“0001

0009

0011

0009
-0005

0013

0013
-.005
-0024
-0002
'0034
‘0031
-.003

0001

0012

0005
‘0004
'0021
‘0001

0017
‘0005
'0013
“0016
'0002
-0030
‘0017
-0020

0000

0021
‘0001
‘0001
‘0003

.006
-0019
-0013
-.004
‘0004

0003

0017

0008
‘0008

ASSIGN-
MENT

R0 2017
R0 2018
R0 2019
R0 2021
R0 2022
RP 30 4
RP 30 6
RP 30 7
RP 30 8
RP 30 9
RP 3010
RP 3011
RP 3012
RP 3014
RP 3015
RP 3016
RP 3017
RP 3018
RP 3019
RP 3021
R0 30 4
R0 30 5
R0 30 6
R0 30 7
R0 30 8
R0 30 9
R0 3010
R0 3011
R0 3012
R0 3014
R0 3015
R0 3016
R0 3017
R0 3018
R0 3019
R0 3021
OR 30 4
OP 30 6
OR 30 7
OP 30 8
OP 30 9
OR 3010
OR 3011
OR 3012
OR 3013
OR 3014
OR 3015
OR 3016
GP 3017
OR 3018

CALCULATED

GSCD

280920
300616
320312
350700
370392
150328
220139
250543
280947
320349
350751
390152
420552
490348
520744
560138
590531
620923
660312
730085

60813

80516
100218
110921
130623
150324
170025
180726
200426
230825
250523
270221
280918
300614
320309
350697

80516
110921
130623
150324
170025
180726
200426
220126
230825
250523
270221
280918
300614
320309

321

OBSERVED

GSCD

2809200
3006420
3203080
3506900
3703900
1503060
2202480
2505470
2809830
3203460
3507510
3901630
4206020
4903520
5207550
5601490
5905410
6209300
6603080
7300910

608160

805280
1002210
1109180
1306440
1503330
1700240
1807270
2004580
2308140
2505210
2702233
2809260
3006070
3203030
3506940

804890
1109270
1306290
1503380
1700130
1807270
2004360
2201440
2308310
2505380
2702340
2809260
3006160
3203230

DELTA
NU

00200
09999
09999
00283
09999
09999
00224
00224
09999
09999
00245
00173
09999
00173
09999
.0200
09999
09999
09999
09999
00173
00245
00173
.0141
00224
09999
00200
00173
09999
09999
00245
00173
09999
09999
00173
09999
09999
00245
00224
09999
09999
00245
00200
09999
09999
09999
09999
00173
09999
09999

OBS-
CALC

0000
0026
-0004
'0010
‘0002
-0022
0009
0004
0036
~0003
0000
0011
0050
0004
0011
0011
0010
0007
‘0004
0006
0003
0012
0003
‘0003
0021
0009
-0001
0001
0032
‘0011
‘0002
0002
0008
-.007
-0006
-.003
‘0027
0006
0006
0014
-0012
0001
0010
0018
0006
0015
0013
0008
0002
0014

‘0 10‘ .I. . 0.‘

 

ASSIGN-
MENT

GP 3019
GP 3020
0P 3022
0P 40 8
GP 4010
GP 4012
GP 4013
0P 4015
GP 4016
R0 40 6
R0 40 7
R0 40 8
R0 40 9
R0 4010
R0 4011
R0 4012
R0 4013
R0 4014
R0 4015
R0 4016
RP 40 8
RP 4010
RP 4012
RP 4013
RP 4015
RP 4016
R0 50 8
R0 50 9
R0 5010
R0 5011
R0 5012
R0 5013
R0 5014
R0 5015
R0 5016
R0 5017
R0 5018
R0 5019
R0 5020
RP 5014
RP 5016
RP 5018
GP 5014
GP 5016
0P 5018
R0 60 7
R0 60 8
R0 60 9
R0 6010
R0 6011

CALCULATED

GSCD

340003
350697
370389
150322
180724
220123
230822
270217
280914
100217
110919
130621
150322
170023
180724
200424
220123
230822
250520
270217
280943
350747
420547
450945
520737
560131
130619
150320
170020
180721
200420
220120
230818
250516
270213
280910
300605
320300
330994
490334
560123
620905
250516
280910
320300
110915
130616
150317
170017
180717

322

OBSERVED

GSCD

3400050
3506930
3703970
1503200
1807190
2201220
2308190
2702140
2808770
1002190
1202320
1306170
1503180
1700230
1807340
2004500
2201290
2308300
2505200
2702300
2809370
3507420
4205720
4509480
5207340
5601070
1306060
1503440
1700170
1807250
2004190
2201230
2308130
2505150
2702090
2809310
3006220
3202970
3400330
4903140
5601330
6209330
2505010
2809240
3109000
1109890
1306110
1503130
1700200
1807170

DELTA
NU

09999
09999
09999
09999
09999
09999
09999
09999
00173
00173
09999
00200
00173
00224
00224
09999
00173
00224
00245
00173
09999
09999
00245
09999
09999
00200
00283
09999
00200
09999
00245
00173
00283
09999
00283
09999
09999
00283
00283
09999
09999
09999
09999
09999
09999
09999
00200
00141
00212
00173

085-
CALC

0002
‘0004
0008
-0002
‘0005
-0001
-0003
‘0003
'0037
0002
0113
‘0004
~0004
0000
0010
0026
0006
0008
0000
0013
‘0006
“0005
0025
0003
-0003
'0024
‘0013
0024
'0003
0004
‘0001
0003
-0005
-0001
-0004
0021
0017
‘0003
0039
“0020
0010
0028
'0015
0014
-0400
0074
-0005
‘0004
0003
0000

ASSIGN-
MENT

R0 6012
R0 6013
R0 6014
R0 6015
R0 6016
R0 6017
R0 6018
R0 6019
R0 6020
R0 6021
R0 6022
R0 6023
R0 6024
GP 60 7
GP 60 9
OR 6013
GP 6015
OR 6018
GP 6019
GP 6020
0P 6021
OR 6024
OR 6025
RP 60 7
RP 60 9
RP 6013
RP 6015
RP 6018
RP 6019
RP 6020
RP 6021
RP 6024
R0 70 8
R0 70 9
R0 7010
R0 7011
R0 7012
R0 7015
R0 7016
R0 7019
R0 7020
0P 70 9
OP 7019
RP 70 9
RP 7014
RP 7019
R0 8011
R0 8015
R0 8016
R0 8017

CALCULATED

GSCD

200417
220115
230814
250511
270208
280904
300599
320294
330987
350680
370371
390062
400751
130616
170017
230814
270208
320294
330987
350680
370371
420440
440127
250531
320334
450929
520719
620893
660281
690667
730051
830191
130613
150313
170013
180713
200412
250505
270202
320286
330979
170013
330979
320327
490313
660266
180708
250499
270195
280890

323

OBSERVED

GSCD

2004190
2201250
2308150
2505120
2701930
2809340
3005950
3202910
3309770
3506730
3703710
3900540
4007450

1305460‘

1609920
2308120
2702250
3202960
3400020
3506870
3703550
4204510
4401490
2505350
3203050
4509370
5207370
6208910
6602930
6906640
7300280
8301960
1306270
1503050
1700230
1807150
2004040
2505030
2702000
3202890
3400520
1700270
3309550
3203320
4903280
6602440
1808900
2504990
2702040
2808720

DELTA
NU

00173
09999
00141
00224
00173
09999
00173
00224
00173
00245
09999
00245
00200
09999
00224
09999
09999
09999
09999
09999
09999
09999
09999
00212
00224
09999
09999
09999
09999
09999
09999
09999
09999
09999
00245
00245
00245
09999
00245
09999
09999
09999
09999
00224
09999
09999
09999
00224
09999
09999

085-
CALC

0002
0010
0001
0001
-0015
0030
‘0004
‘0003
'0010
-0007
0000
‘0008
'0006
‘0070
~0025
-0002
0017
0002
0015
0007
‘0016
0011
0022
0004
-0029
0008
0018
'0002
0012
-0003
‘0023
0005
0014
-0008
0010
0002
-0008
~0002
-0002
0003
0073
0014
“0024
0005
0015
'0022
0182
0000
0009
”0018

ASSIGN-
MENT

R0
R0
RP
RP
0P
0P
0P
0P
RP
RP
R0
R0
R0
R0
R0
R0
R0
R0

8018
8019
8014
8016
8016
9013
9017
9019
9013
9017
9010
9011
9012
9013
9014
9015
9016
9017

CALCULATED

GSCD

300584
320278
490301
560084
280890
230795
300575
330960
450893
590456
170004
180702
200400
220098
230795
250491
270187
280881

324

OBSERVED

GSCD

3006110
3202550
4903260
5600580
2808540
2307670
3005840
3309550
4508580
5904540
1700140
1807010
2003960
2200910
2307790
2504800
2702020
2808700

DELTA
NU

09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
.0200
00224
09999
00224
09999
09999
09999
00283

OBS-
CALC

0027
‘0023

0025
-0026
-0036
-0028

0009
~0005
-0035
‘0002

0010
“0001
‘0004
“0007
-0016
-0011

0015
-0011

APPENDIX VII

LIST OF ASSIGNMENTS AND FREQUENCIES OF OBSERVED

TRANSITIONS FOR v1+v3 OF CH3?

The following pages contain a list of the observed
transitions of v1+v3 of CHBF. The columns of the list,
left to right, are: the assignment (AK,AJ,K,J); the observed
frequency (in cm"); the observed fringe number (from which
the frequency may be calculated - of. Chapter 7); the Av
(weight = (NORM)2/(Av)2); the weight; the observed line
height; and the line number.

325

ASSIGN-
MENT

0P

0R

0R

0R
0R
0R
OR
OR
0R
OR

(:30
co
0P
op
0P
0p
0p
op
op
0P
0P
on

0P

O0
O0
00
O0
00
O0
00
O0

._0
OVDm-JOFUI#PUh0

0011
0012
0013
0014
0015
0016
0017
0018
0020
0021
00

n
09

00
00
00
00
O0
O0
00

00

0010
0011
0012
0013
0014
0015
0017
0019
10
10
10
10
10
10
10
1010
1011
1012
1013
1014
1015

@(D‘QO‘U'PK»RJH‘O

©CD~JO‘U1va

OBSERVED
FREQUENCY

400902680
400705650
400400010
400202030
400003890
399805380
399606720
399407840
399208760
399009460
398809940
398700340
398500230
398300270
398100120
397809620
397608330
397205540
397004390
401206790
401402960
401509220
401705410
401901240
402006770
402202300
402307410
402502410
402607060
402801500
402905890
403009940
403203770
403307560
403500740
403706290
404000850
400705400
400309570
400201670
400003480
399804980
399606720
399407480
399208380
399009020
398809380
398609620
398409590
398209280

326

FRINGE
NUMBER

19308380
18805440
17704590
17108670
16602260
16004710
15406660
14807940
14208620
13608580
13007900
12406940
11804410
11202330
10509670

9905900

9209700

7906620

7300860
20404480
20904730
21405310
21905670
22404890
22903210
23401490
23808480
24305120
24800690
25205610
25700360
26104030
26507050
26909950
27400920
28200380
28906800
18804650
17703220
17107550
16600980
16003460
15406660
14806820
14207420
13607210
13006150
12404690
11802390
11109250

DELTA
NU

09999
00200
00200
00200
.0200
09999
09999
00140
00200
09999
09999
09999
.0200
.0200
09999
.0200
09999
.0200
09999
00140
00100
09999
00200
00200
09999
09999
00200
00140
00140
00140
09999
00140
00140
00200
00140
00200
09999
09999
09999
00200
00200
09999
09999
00140
00200
09999
00200
00200
09999
09999

WEIGHT

.00
025
025
025
025
000
000
050
025
000
000
000
025
025
000
025
000
025
000
050
1000
000
025
025
000
000
025
050
050
050
000
050
050
025
050
025
000
000
.00
025
025
000
.00
050
025
000
025
025
.00
000

INT

LINE
NO

244
235A
220A
212A
206
198A
190
181A
173A
167
158A
148
138
128
116
106
94A
77
70
259
277
286A
293
300A
308
316
322A
330A
338A
348
355
362
370
376
383
395
407C
135
220
212
205A
198
190
181
173
166A
158
147
137A
127

ASSIGN-

MENT

QD 1016
OR 1017
QP 1018
QR 1019
QP 1020
QR 1021
QR 1022
QQ 10 3
00 10 4
00 10 6
00 10 8
00 1010
00 1016
QR 10
QR 10
QR 10
QR 10

("D 1,

“J1\

QR 10
QR 10
QR 10
OR 10
OR 1010
QR 1011
QR 1012
QR 1013
QR 1014
QR 1015
QR 1017
QR 1018
QR 1019
QR 102C
QR 1021
0R 20
0R 20
QR 20
QR 20
QR 20
OR 20
QR 20
QR 20
QR
QR 2011
OR 2012
QR 2014
QR 2015
OR 2016
QR 2017
QR 2018
QR 2019

\OCD-xlO‘UT-L‘UJNH

0...:
O\OG)NCPU1b\»KJ

N
0.

0858RVED
FREQUENCY

398008700
397808030
397607030
397406080
397204560
397003050
396801290
401007750
401007150
401004360
401000960
400906240
400707140
401402570
401508760
401705020
401900920
402006440
402202300
402306970
402501940
402606530
402800990
402905130
403009130
403202990
403306240
403409350
403705290
403807750
403909930
404102040
404203770
401507550
401703660
401809660
402005220
402200630
402305780
402500830
402605710
402709860
402904020
403008140
403305220
403408540
403601900
403704650
403806920
403909200

327

FRINGE
NUMBER

10505230
9900970
9205650
8600490
7903560
7206670
6509020

19805260

19803390

19704720

19604130

19409460

18900060

20903540

21403850

21904450

22403900

22902170

23401490

23807110

24303680

24709050

25204020

25607980

26101520

26504640

26905830

27306600

28107280

28506070

28903950

29301590

29608070

21400140

21900230

22309980

22808380

23306290

23803430

24300210

24706490

25200500

25604550

26008460

26902650

27304080

27705630

28105300

28503480

28901670

DELTA
NU

09999
09999
09999
09999
00200
09999
09999
00200
00200
09999
00200
09999
00200
09999
09999
09999
00200
09999
09999
00130
00100
00140
00200
00200
00200
00200
.0140
00200
00140
0999

09999
09999
09999
00200
09999
00200
00200
00200
00200
00140
09999
09999
00100
00100
0020

09999
09999
09999
00200

09999

WEIGHT

.00
000
000
000
025
.00
.00
025
025
000
025
000
025
000
000
000
025
000
000
1000
1000
050
025
025
025
025
050
025
050
.00
000
000
000
025
.00
025
025
025
025
050
000
000
1000
1000
025
000
.00
000
025
000

INT

HH

N
~JO-4U1®(T~JP‘OO‘O

0—0 H
DO‘D

NrdkathhdH ha FJH
k-Nrdhawrdkawodh4kwv0d
N\fi~JH\fiF‘HChH‘D\OO‘N\fi4>h*HCDFJNP‘U’WCDKJW::O\:

0.00—0
\OH

N
._0

K1)
0

HFHK)
H190)

LINE
N0

115
105
93A
66
76c
69
61
252A
252
251
2491
246A
236
276A
286
2925
300
307C
316
322
330
338
347
2546
361
369
3756
382A
394A
401
4078
412A
418A
285
292A
299
307A
314A
321
329
337
346
354A
360
375A
382
388
394
400
407A

ASSIGN-
MENT
GP 29 3
GP 29 4
GP 29 5
GP 29 7
GP 29 8
GP 29 9
GP 2910
GP 2911
GP 2912
GP 2913
GP 2914
GP 2915
GP 2916
GP 2917
GP 2918
GP 2920
00 29 2
00 29 5
00 29 8

00 29 9
00 2911

00 2912
GO 2914
GP 39 4
GP 39 5
Q? 39 6
GP 39 7
GP 39 8
GP 39 9
OD 3910
09 3911
GP 3912
GP 3913
GP 3914
GP 3915
GP 3916
GP 3917
09 3918
GP 3920
OP 3921
GP 3922
00 39 3
00 39 4

Q 39 5
OO 39 6
Q 39 7
00 39 8
00 39 9
00 3912
00 3913

OBSERVED
FREQUENCY

400505980
400308190
400200530
399803820
399605180
399406230
399207250
399007860
398808300
393608580
398408540
389208330
398007860
397807240
397606310
397204030
401007150
401004360
400909480
400907670
400902680
400809980
400803400
400306290
409108540
400000240
39980193‘0
3996 03410
399404620
399205161LO
399006419
398807030
398607400
398407610
398207770
398007500
397807240
397606310
397204560
397003050
396801290
401004360
401003610
401002360
401000960
400909480
LC0907670
400905800
400808410
400805470

328

FRINGE
NUMBER

1820425 0
1760 893 9
1710 4025'
15909860
15401870
14802940

12401450
11709140
11106290
10502629
9808260
9203400
7901940
19803390
19704720
19509550
19503909
1Q _JI 38
19209990
19009540
17603029
17007810
16500910
15903980
15306370
14707950
14108920
3509110
12908830
12307808
1170:6260
11104'
10501

a

f'}
KO 0'

p
)C)OK)C)O(DC3

O
30
o
J
\)

/ J

92034
79035-
720 66
6509
1970472K
19702370
19608480
19604130
9509550
19503900
19408380
19205110
19105960

)

m9q<pc>m

k

DELTA
1U

09999
0999
09999
09999
09999
00140
00140
:ogo9
H9 9
00200
00140

nanfi

.thw

00200

00200
09999
09999
00233
09999
09999
09999
09999
09999
0020 0
00200
09999
00200
00140
09999
00140
00100
09999
00140
09999
00140
09999
00200
00200
09999
00230
09999
.gQQQ

09999

00200
00200
00200
09999
09999
09999
09999
09999

WEIGHT

000
000
000
000
000
050
050
000
000
025
050
025
025
025
000
000
025
000
000
000
000
000
025
025
000
025

an

02»-

000
050
1000
000
050
000
050
000
025
025
000
025
000
000
000
025
025
025
000
000
000
000
000

INT

0.0

H h» in kJHfd HrAkJ
N\fiRJ©(DKJNCDPJOFJU1HdeJm(DFJfl\fi\Jm

9494 H
OO-NINOON

HH
0.0..—0

hJHtAPJH
KOC)O<DC)H

0...:
f—J

LINE
NO

226A
219A
211
197
189
180
172
165A
157
146
137
126A
114A
104
92A
76B
252
251
248A
247
244
243
2388
218
210
203
196
188
179
171
165
156
145
136
126
114
104
924
76C
69
61
251
250A
250
249A
248A
247
246
242
240A

ASSIGN-
MENT
GO 3014
GO 3915
00 3016
GO 3917
Q 3918
GO 3919
Q0 3920
CO 3021
Q? 30 3
Q? 39 4
OR 39 5
OR 39 6
GP 39 7
OR 39 8
QR 39 9
Q? 3910
OR 1011
GR ’2912
CR 3913
OR 3014
OR 3015
OR 3916
OR 3917
O? 2918
OR 3919

ODSFQVED
FREQUENCY

400802800
4OC709720
400706073
400702160
4C0508533
403604843
ACC5.3283
493505613
4C1701720
401807590
4C2303273
402108820
402304070

AOBC0717O
403201120
403304830
4C34085¢O
403601909
403704550
403807750
403909930

329

FQIMGE
NUWBER

19007650
13908070
18806740
13704580
18603280
18501813
18307633
18203129
21804193
22303563
22902323
13300660

C) U) |\) |\) O‘

(J C) L.) O C-) t.) C) C) 7’

Q)

N
)\
p
o
\ . . (‘0
C) w (h F) O\ (‘1) .D I\) .1)

U”. \l C‘) D) 7D

L) C) C)

025
000
000
000
000
000
.50
.00
.50
025
025
000

1000

000
000
000
025
050
050
025
003
000
000
000
000

APPENDIX VIII

LIST OF OBSERVED COMBINATION DIFFERENCES
FOR v1+v3 0F CHEF

The following pages contain a list of the observed
ground state combination differences for v1+v3 of CH3F.
The columns of the list, left to right, are: the assignment
(cf.Chapter 4); the calculated combination difference
(in cm") from Appendix II; the observed combination
difference (in cm“); the Av (weight = (N0RM)2/(Av)2); and
the observed minus the calculated combination difference.

330

ASSIGN-
MENT

RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
R0
R0
Re
Re
R0
R0
0P
0P
0P
0.9
OP
0P
RP
RP
RP
RP
RP

09
O9
O9
09
09
O9
O9
O9
0910
0911
0912
0913
0914
0915
0916
0920
19
19
19
19
19
19
19
1910
1912
1913
1914
1915
1916
1918
1919
1920
1921
19 3
19 4
19 6
19 8
1910
1916
19 3
19 4
19 6
19 8
1910
1916
29
29
29
29
29

xooouombww

\OCDxlO‘UI-U-‘U’

mxlO‘J-‘w

CALCULATED

GSCD

50111
110924
150331
180737
220142
250547
280951
320354
350757
390158
420559
450958
490356
520752
560147
690711
110924
150331
180736
220142
250547
280951
320354
350756
420558
450957
490355
520751
560146
620931
660321
690710
730096

50110

60814
100220
130624
170028
270224

60814

80517
110922
150326
180729
280922
110924
150330
220141
250545
280949

331

OBSERVED

GSCD

501140
1109210
1503380
1807350
2201390
2505580
2809570
3203650
3507600
3901560
4205550
4509710
4903500
5207440
5601120
6906460
1109190
1503350
1807440
2201460
2505580
2809490
3203660
3507510
4205510
4509540
4903710
5207540
5601320
6209210
6603190
6906880
7300750

501010

607870
1002080
1306010
1700290
2702210

608180

805480
1109380
1503480
1807220
2809110
1109363
1503130
2201400
2505450
2809550

DELTA
NU

00245
09999
00283
00283
09999
09999
00245
00245
09999
09999
09999
00245
00245
09999
00245
09999
09999
09999
00283
09999
09999
00173
00224
09999
00283
00283
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
00224
09999
09999
09999
00283
09999
00245
09999
09999
09999
09999
09999
09999
00245

085-
CALC

0003
‘0003
0007
-0002
-0003
0011
0006
0011
0003
-0002
-0004
0013
“0006
-0008
‘0035
‘0065
‘0005
0004
0008
0004
0011
‘0002
0012
-0005
-0007
r0003
0016
0003
‘0014
'0010
-0002
'0022
'0021
~0009
0073
-0012
-0023
0001
‘0003
0004
0031
0016
0022
‘0007
-0011
0012
-0017
-0001
0000
0006

ASSIGN-
MENT

RP 29 9
RP 2910
RP 2911
RR 2912
RP 2913
RR 2915
RP 2916
RP 2919
R0 29 5
R0 29 8
R0 29 9
R0 2911
R0 2912
R0 2914
GP 29 2
GP 29 8
GP 29 9
GP 2911
GP 2912
GP 2914
RP 39
RP 39
RP 39
RP 39
RP 39
RP 39
RP 3910
RP 3911
RP 3912
RP 3913
RP 3914
RP 3915
RP 3916
RP 3917
RP 3919
RP 3920
R0 39 4
R0 39 5
R0 39 6
R0 39 7
R0 39 8
R0 39 9
R0 3912
R0 3913
R0 3914
R0 3915
R0 3916
R0 3917
R0 3918
R0 3919

«30040014:

CALCULATED

GSCD

320352
350754
390156
420556
450955
520748
560143
660318

80516
130624
150325
180728
200428
230827

50110
150325
170027
200428
220128
250525
150328
180734
220139
250543
280946
320349
350751
390152
420552
450951
490348
520744
560138
590531
660312
690700

60813

80516
100218
110921
130623
150324
200426
220156
230825
250523
270221
280918
300614
320309

332

OBSERVED

GSCD

3203580
3507850
3901560
4205440
4509600
5207360
5601300
6602890

805300
1306300
1503160
1807180
2004040
2309590

501170
1503250
1700420
2004380
2201400
2505070
1503180
1807350
2201340
2505410
2809450
3203520
3507580
3901520
4205550
4509560
4903350
5207380
5601300
5905590
6603190
6906880

608110

805230
1002310
1109340
1306400
1503360
2004540
2201700
2308320
2505160
2702470
2809740
3006120
3202910

DELTA
NU

00200
09999
09999
00224
00173
00283
09999
09999
09999
09999
09999
09999
09999
00283
09999
09999
09999
09999
09999
00283
09999
00283
00245
09999
00173
09999
09999
09999
09999
00200
09999
00283
00283
09999
09999
09999
00245
00283
00283
09999
09999
09999
09999
09999
00245
09999
09999
09999
09999
09999

OBS-
CALC

0006
0031
0000
'0012
0005
'0012
'0013
-0029
0014
0006
-0009
-0010
‘0024
0132
0007
0000
0015
0010
0012
‘0018
‘0010
0001
‘0005
-0002
‘0001
0003
0007
0000
0003
0005
'0013
'0006
~0008
0028
0007
-0012
‘0002
0007
0013
0013
0017
0012
0028
0014
0007
‘0007
0026
0056
-0002
-0018

ASSIGN-
MENT

RO
OP
OP
OP
OP
OP
OP
OP
OP
OP
OP
OP
OP
OP
OP
OP
OP

3920
39
39
39
39
39
39
39
3912
3913
3914
3915
3916
3917
3919
3920
3921

\OCDxIO‘U‘kUJ

CALCULATED

GSCD

340003
60813
80516

100218

110920

130622

150324

170025

220126

230825

250523

270221

280918

300614

340003

350697

370389

333

OBSERVED

GSCD

3309650
608070
805070

1002120

1109030

1306070

1503050

1700160

2201010

2307860

2505030

2702220

2808830

3005850

3400280

3507230

3704320

DELTA
NU

09999
09999
09999
00283
00245
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999
09999

088-
CALC

-0038
‘0006
-0009
-0006
'0017
-0015
‘0019
-0009
-0025
‘0039
'0020

0001
-0035
“0029

0025

0026

0043'

APPENDIX IX

COMPARISON OF THE OBSERVED AND CALCULATED
FREQUENCIES OF V3+V4 0F CHEF

The following pages contain a comparison of the observed
and calculated transition frequencies of v3+v4 of CHBF. The
analysis of 156 ”unperturbed" transitions resulted in the
following constants (in cm"):

190 -A'8C£ 4111i = 141.757.2074

A0 -Aecfi 411% = 4.6684
(1% +02 «1133 «12 -(3/2) 11% = 1.390 x 10"2
a; +a£ = 1.0816 x 10'2
DE "3,111: 1.46 110‘4
_ . '5
ng — 407 x ‘0
5(8td. dev.) = 00011

In the following list, the columns, from left to right,
are: the assignment (AK,AJ,K,J); the calculated frequency
(in cm"); the observed frequency (in.cm’1); the Av
(weight = (NORM)2/(Av)2); the observed minus the calculated
frequency; the observed line height; and the line number.

The first part of the list contains the transitions
included in the least squares fit, the second contains the
comparison of transitions not included in the analysis due
to perturbations, the third contains a comparison of transi-
tions not included in the analysis since they were assigned
a zero weight (i.e., Av 80.9999).

334

ASSIGN-
MENT

PR
PR
P0
P0
P0
P0
PP
PP
PP
PP
PR
PR
PR
PR

39
39
39
39
39
39
39
39
39
39
29
29
29 ,
2910

()0WfixlOkfiD<)U‘b\»Uflh

P0 29

P0 29
P0 29

P0 29
P0 29

4
5
7

8
9

P0
P0
P0
PP
PP
PP
PR
PR
PR
PR
PR
P0
P0
P0
P0
P0
P0
P0
P0
P0
P0
P0
P0
P0
RP
RP
RP
RP
R0
R0
R0

2910
2911
2912
2910
2911
2912
19 4
19 5
19 6
19 7
1914
19
19
19
19
19
19
19
1910
1911
1912
1913
1914
1915
O9
09
09
09
09
09
O9

0(D~J®\fiunv

‘NR)HCDO‘WLQ

CALCULATED
FREQUENCY

404602743
404708491
403709503
403708651
403707587
403706309
403101375
402903495
402705404
602507104
405505144
405700667
406105928
406300577
404505313
4045.4240
404501452
404409736
404407805
404405661
404403301
404400727
402707538
402508385
402309022
406105836
406301568
40640708

406602376
407603251
405303261
405302613
405300668
405209372
405207860
405206132
405204187
405202027
405109651
405107059
405104250
405101226
405007985
405508341
405202754
405004638
404607761
406009882
406009447
406008794

U.)
W
U‘

OBSERVED
FREQUENCY

404602735
404708404
403709491
403708684
403707629
403706288
403101383
402903504
402705468
402507034
405505198
405700803
406105952
406300570
404505449
404504281
404501506
404409738
404407886
404405635
404403207
404400670
402707610
402508329
40230890
4061059
4063016
406407217
406602549
407603273
405303242
405302567
405300734
405209396
405207962
405206261
405204258
405202084
405109795
405107190
405104332
405101258
405307946
405508510
405202625
405004669
404607954
406009782
406009322
406008640

4
2
8

1\) HI

DELTA
NU

00200
00140
00200
00140
00140
00200
00200
00100
00140
00140
00200
.0140
00200
00200
00140
00100
00200
00100
00200
00140
00100
00200
0020

.0100
00140
00200
.0140
00200
00200
00140
.0140
00140
00100
00100
.0140
00140
00200
00200
00100
00100
00100
00140
00100
00200
00140
00200
00200
00140
.0100
.0100

OBS- INT
CALC
"00008 5
'00086 7
'00012 9
00033 16
00043 18
‘00020 19
00007 23
00009 25
00064 17
-00070 18
00054 4
00136 9
00024 9
”00007 7
00136 11
00041 13
00055 14
00002 19
00080 18
‘00026 14
‘00094 17
‘00057 16
00072 13
-00055 14
‘00118 16
00116 9
00060 5
00135 8
00173 11
00021 8
"00018 15
“00046 17
00066 13
00024 15
.0102 13
00130 15
00071 23
00057 18
00144 12
00132 18
00082 15
00032 14
‘00040 15
00169 11
"00130 21
00031 24
00193 18
'00100 16
‘00125 18
‘00154 20

LINE
NO

438A
445
397
3968
396
395
363
354
343
333
485
493
516
522A
435
434
432
431A
430
429
427
426
344
334
323A
516
523
530
539
586
475
474A
473
472
471
470
469
468
467
465
464
462
460
487
468A
459A
441
514A
514
513

ASSIGN-
MENT

R0
R0
R0
R0
R0
RR
RR
RR
RR
RR
R0
R0
R0
RR
RR
R0
R0
R0
RR
RR
RR
RR
RP
RR
RR
DD

R0
R0
RQ
R0
R0

"3

.«r

| \

RR
RR
RR
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0

R0

n
! \T

09
09
09
09
O9
09
09
O9
09
09
19
19
19
19
19
29
29
29
29
29
29
29
39
391
39
39
39
39
39
39
39
49
49
49
49
49
49
69
69
6910
6911
6912
6914
6915
6916
6918
6919

«300(19memeooxlcnmoms-44x!)\lomxo\10~mmmbw4\mmw OOONOUTb

CALCULATED
FREQUENCY

406007924
406006836
406305531
406004008
406002267
406206918
406403518
406509899
406706062
406902005
406804680
406803803
406802708
407305784
407501941
407506926
407505381
407501630
408509117
408704597
408809853
409109692
407102887

06307279
409304275
409409743
408303426
408302093
408300537
408208760
408206760
409903347
4100.9029
410309712
410504712
409006859
409003503
410501649
410409608
410407340
410404845
410402124
413306901
410302599
410208970
410201033
410106724

336

OBSERVED
FREQUENCY

406007830
4050.5734
406005438
406003888
406002167
406206882
406403423
406509861
406706003
406902100
406 04546
406803627
406802569
407305728
407501819
407506980
407505459
407501819
406509141
408704736
408809971
409109641
407102843
406307641
409304323
409409793
408303371
408302117
408300616
408208883
408207014
409903467
410009094
410309906
410505019
409006901
409003740
410501655
410409610
410407340
410404758
410401993
413305812
4103.2446
410208931
410200886
410106625

DELTA
N U

.0100
00100
.0100
.0070
00070
00200
00100
00140
.0200
.0200
.0200
.0200
.0200
00100
00200
.0100
.0140
00200
00140
00140
00140
.0140
.0200
00200
00100
00100
.0140
00140
00100
.0100
00140
00140
00100
.0140
00100
00140
00140
00140
00100
00200
00140
.0140
.0100
00100
00140
00100
.0200

CALC

‘00094
‘00102
'00093
"00120
’00100
‘00035
-0OO95
~00039
‘00059
00094
-00133
‘00177
“00139
‘00056
'00122
00054
00078
00189
00024
00139
00119
-00050
-00044
00362
00049
00051
‘00054
00025
00078
00123
00254
00120
00066
00194
00307
00042
00237
00007
00002
00000
“00087
'00131
”00188
'00153
‘00039
‘00147
'00099

INT

21
21
21
20
22

5

8
14
18
16
16
20
19
21
17
11
11
17
16
14
18
11

7

9
20
24
14
17
17
21
25
18
21
20
14

7
14

8
ll
15
15
13
12
15
12
14
11

LINE
N0

512
511
510
509
508
521
528
538
546
555
552
551
550
571
578
581
580
578
627
633
642A
656A
5638
526
661
666
616
615
614
613
612
685
691
703
711
651
649A
709
708
707
706
704
701
700
698
696
694

ASSIGN-

ME

R0
R0
R0
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
R0
R0
R0
R0
RP
RP
R0
RR
RR
RR
RR

RR
RR
RR
RR
R0
R0
R0
R0
RR
RR

NT

6920
6921
6923
69 6
69 7
69 8
69 9
6910
6911
6912
6913
6914
6915
6916
6917
6918
6919
6920
6922
6923
69 8
79 7
79 8
79 9
7910
7911
7912
7913
7915
7916
7917
7918
7910
7911
7915
7916
7910
7915
8915
89 8
89 9
8910
8911
8912
8913
8914
8916
9910
9911
9913
9919
99 9
9910

CALCULATED
FREQUENCY

410102188
410007426
409907221
411702612
411807810
412002777
412107513
412302017
412406290
412600329
412704136
412807710
413001049
413104154
413207025
413309660
413502059
413604222
413807837
413909288
409107392
412601111
412706061
412900777
413005261
413109511
413303527
413407309
413704166
413807242
414000080
414102682
411209643
411108132
411005802
411002149
409502792
408504174
411708465
413408799
413603496
413707958
413902185
414006177
414109932
414303452
414509778
412605593
412603048
412507263
412304355
414305633
414500073

337

OBSERVED
FREQUENCY

410102172
410007461
409907380
411702653
411507766
412002744
412107542
412301932
412406180
412600241
412703959
412807573
413000863
413104053
413206842
413309533
413501939
413604187
413807924
413909490
409107297
412601116

_412706055

412900853
413005297
413109587
413303623
413407434
413704258
413307384
414300224
414102983
411200616
411108153
411006011
411302258
409502736
408504154
411708611
413403765
413603512
413707978
413902271
414006269
414200025
414303604
414509972
412605370
412603032
412507299
412304713
414305511
414500039

DELTA

NU

00140
00200
00140
00070
.0140
00100
00070
00100
00100
00140
00100
00500
00100
00140
00140
00100
00100
00140
00200
00140
00200
00100
00100
00140
00200
00140
00140
00200
00140
00200
.0200
00200
00200
00140
00140
00200
00200
09999
00200
00100
00100
00100
00140
00200
.0200
00100
00200
00140
00200
00200
00200
00140
.0100

055-
CALC

‘00017
00035
00160
00041

‘00044

-00033
00029

‘00086

-00110

-00088

-0Ol78

‘00136

-00186

'00101

‘00183

“00126

-00120

-00035
00087
00202

‘00005
00004

"00005
00076
00036
00076
00096
00125
00092
00142
00143
00300

'00027
00021
00209
00109

'00056

“00020
00146

‘00034
00016
00020
00086
00092
00092
00153
00193

'00223

'00016
00036
00358

-00122

‘00035

0....
O‘NCPi‘OCDU1NCDxl

Ht—J

LINE
N0

693
690
6878
755
760
764
768
771
778
783
787
789
792
795
798
800
803
806A
811A
814
655A
784
788
790
793
797
799
801
807
811
814A
817
737A
7368
731A
730A
625
625
7578
802
806
809
812
815
820
823
828
786
785
7828
772
824
826

ASSIGN-
MENT

RR
RR
RR
RR
RR
RR

9911
9912
9913
9914
9915
9916

EXCUDED

PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
P0
P0
P0
P0
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
P0
PP
PP
PP
PP
PP

99 9
9910
9911
9912
9913
9914
9915
9916
9917
9918
9919
9920
9921
9912
9913
9919
9920
99 9
89
89 8
89 9
8910
8911
8912
8913
8914
8915
8916
8912
79 7
79 8
79 9
7910
7911

CD

CALCULATED
FREQUENCY

414604277
414708244
414901973
415005464
415108716
415301730

397507558
397308734
397109711
397000489
396801069
396601452
396401638
396201627
396001420
395801018
395600420
395309627
395108641
399002050
398909401
398709231
398705157
400706776
398503395
398503395
398304753
398105910
397906867
397707623
397508180
397308533
397108697
396908658
399709226
399409052
399300596
399101938
398903077
398704013

338

OBSERVED
FREQUENCY

414604200
414708213
414901989
415005455
415108877
415301890

397507650
397309177
397200456
397001677
396802654
396603605
396404373
396205086

U)
0
O‘
L
O.
m n
an
bx!)
bk»

\0 \O -

a
0‘
N

1 9—9
\O

\0 \i)

\o g1 \j1 01 U"!
”Hu£ wcn
o
. 0‘ ,

N
0
w

\0 \O

4> L» L» L» \M L» L» LU Lu
1 (1) CO \I)

NDUOC)
.
(F
O
\D
01

<60)m<-
U
C
p
N
m
p

07513

J1
.

D.)
\J
....-
.L‘

w m U) W
' \O \O \O C) ~O \0

\3
CO
H
O
O\
‘ ‘ 0‘
[\J
0‘

DELTA
NU

00100
00100
00140
00200
00140
00200

FROM LEAST SQUARES ANALYSIS DUE

00140
00200
00140
00140
00140
00200
.0140
00140
00140
00140
00200
00200
00200
00200
00200
00200
00200
00200
00200
00200
00200
00100
00140
00140
00200
00140
00200
00200
00200
00140
00140
00200
00200
00140

088- INT
CALC
‘00077 11
-0OO3O 13
00016 13
‘00008 11
00161 10
00161 9

00092
00443
00745
01188
01584
02153
02735
03459
04173
04726
05799
06655
07731
01605
02443
06863
07864
00737
00320
00889
00565
00716
00962
01073
01473
01835
02228
03019
01361
00772
00883
01017
01205
01252

9—99—99—49—9
w4>$‘b

H

H

9.00.4

...—0
mNmflNpU’NNO‘QO‘O(D\fi\IO‘w-¥>D-Dpflmom-QOQCD

H

LINE
NO

829
832
834
835
837
840

TO PERTURBATIONS

90
83
75
68
62
54
46

Q
J

32
26
19
15

164
163A
155
154
236A
139
139A
130
119
109
100
91
84
754
68
195C
182
174
168
160
150

ASSIGN-
MENT

PP
PP
PP
PP
PP
PR
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
P0
P0
P0
P0
P0
P0
PC
PC)
P0
P0
.923)
P0
P0
PP
PP
PP
PP
PP
PP
P0
PP
PP
PP
PP
PP
PP
PP
PP
PQ
P0
P0

7912
7913
7914
7915
7916
7910
69 7
69 8
69 9
6910
6911
6912
6913
6914
6915
6916
6917
6918
6919
69 6
69 8
69 9
6910
6912
6913
6914
6915
6916
6917
6918
6919
6920
6916
59 6
59 9
5911
5912
5914
59 6
49 6
49 7
49 8
49 9
4910
4912
4913
4914
49 9
4911
4913

CALCULATED
FREQUE

NCY

398504749
398305283
398105616
397905749
397705683
402405997
400206222
400007752
399809077
399700198
399501116
399301830
399102342
398902652
398702760
398502666
398302372
398101878
397901184
401405372
401402246
401400371
401308288
401303496
401300787
401207870
401204745
401201412
401107870
4C1104120
401100161
401005994
40 4J06909
401201589
490606136

401908373
401800283
401601785
401403080
401204168
400805723
400606192
400406456
402904400
402809963
402804674

339

OBSERVED
FREQUENCY

398506181
398307055
398107925
397907828
397708696
402407557
400300222
400101707
399903012
399704220
399505438
399306511
399107527
398908436
398709339
398500300
398401216
398202340
398003738
401409438
401406203
401404422
401402570
401308628
401306534
401304418
401302312
401300 319
[LC '12.;8 344+
401206794

401205399
401204479
404107415
401202113
400607689
400300222
403101707
399703130
402203425
401908559
401800391
401601744
401402953
401203881
400805468
400606130
400‘406075

DELTA
NU

00140
00200
00140
00200
00200
00200
.0100
00140
00140
00200
00100
.0140
00140
00100
00100
00200
00140
00200
00200
00140
00100

,0100

00200
00100
00100
.0140
00140
00140
00200
00140
00140
00140
00200
00200

0200
.0130
0C140
00200
00200
00140
00200
00140
00100
00140
00200
00200
00200
00100
00200
00200

085-
CALC

01432
01772
02309
02079
03013
01560
04000
03955
03934
04022
04322
04681
05185
05784
6579
07633
08843
100462
102554
04067
3957
04051
04282
05132
05747
06548
07567
08907
100474
102675
105233
108435
100506
00524
01553
02083
02873
03520
00942
“00014
00108
“00041
‘00128
“00286
‘00255
"00062
"00381
‘00374
‘00822
‘00675

INT

\»()O\OO‘©

N
WUJNO‘W

LINE
N0

140
131
120
109
100
327
216
208
201
193
184
176
169
162
151
142
134
123
112
281
279
278
276A
275
273
272
271
270
260
259
258
257
414A
256
231
216
208
192
316A
303
295A
288
277
256A
240A
230A
222
354A
351
349

ASSIGN-
MENT

PR
PR
PR
PR
PR
PR
PR
PR
PC)
P0
P0
P0
P0
P0
P0
PQ
PP
PP
PP
PP
PP
PP

A0 6
4912
39 6
39 7
39 9
3912
3916
3017
30 7
39 8
39 9
3010
3915
3016
3917
3019
30 8
39 9
3910
3011
3917

3918

EXCUDED

PR
PR
PR
PR
PC
P9
P0
PP
PP
PP
PP
PP
PP
PP
PR
PR
P0
P0

2012
2013
2014
2016
2913
2015
2918
29 3
20 4
20 7
2914
2015
2917
2918
1915
1916
1917
1013

CALCULATED
FREQUENCY

404107184
405005905
404904023
405009339
405309321
405302659
406307374
406500301
403704818
403703114
403701198
403609068
403505226
403501819
403408199
403400319
402308593
402109873
402000945
401801809
400602644
400402363

406509216
406703204
406806971
407103841
404307939
404301719
404200779
404505712
403808037
403303733
401909671
401709683
401309086
401108478
407706773
407900072
405000856
404906968

340

ORSERVED
FREQUENCY

404107415
405005772
404903584
405009090
405308394
405300266
406305107
406408153
403704655
403702835
403700761
403608240
403504304
403409349
403405959
403307564
402308425
402109499
402000344
401800886
600600281
400400010

FROM LEAST SQUARES ANALYSI'

406508993
406702864
406806264
407102158
404307712
404300904
404108062
404005949
403308617
403304078
401909405
401709221
401307988
401106659
407706611
407809608
405000428
404906170

DELTA
NU

00200
.0200
00140
00140
00200
00200
00200
00200
00140
00140
00100
00140
00140
00200
00200
00140
00100
.0200
00140
00140
00140
.0200

(J)
U
C.
[11

00140
00200
00200
0C200
00140
00140
00100
00200
00100
00200
00200
00100
.0140
00200
00100
00140
00100
.0140

‘00223
“00340
"00708
‘01682
-00227
‘00814
-02718

00236

00580

00340
-00266
~00462
'01099
‘01819
‘00163
'00464
‘00429
‘00798

LINE
N0

414A
4598
453
461
477
497
525A
531
394
393
392
391
385
382A
381
376
323
314
305
296
228
220A

TO PERTURBATIONS

537
544
553
563
425
422A
415
410
402
374A
304
295
274
253
592
596
457
455

ASSIGN-
MENT

PQ
RP
RP
RP
RP
RD
RP
RP
RP
RP
RP
RP
RP
RP
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RP
RP
RP
RP
RP
RP
RP
RP
RP
R0

1919
09 4
00 9
0910
0911
0012
0913
0016
0017
0018
0920
0921
0922
0922
0013
0911
0012
0,13
0014
0015
0016
0917
0018
0019
0020
0021
00 7
O9 8
O0 9
00 9
0911
0012
0913
0014
0015
0016
0917
0018
0019
0920
19 6
1011
1912
1013
1011
1013
1014
1015
1021
10 6

CALCULATED
FREQUENCY

404902863
405400656
404409002
404100844
403901447
403701837
403101742
402901290
402700628
402208678
402007391
401805896
401805896
405908133
405905740
405903129
405900301
405807255
405803992
405800511
405706812
405702896
405608762
405604411
405509842
407308513
407503574
407608413
407608413
407907423

408101593.

408205540
408309262
408502760
408606032
408709079
408901900
409004494
409106861
405800512
404806658
404607244
404407616
404806658
404407616
404207776
404007723
402802970
406801393

341

OBSERVED
FREQUENCY

404901533
405401172
404409246
404300293
404101338
403901848
403702295
403101990
402901568
402700118
402206287
402002659
401707507
401707507
405907997
405905518
405902884
405809865
405806652
405803038
405709016
405704658
405609639
405603902
405507243
405409587
407308918
407503925
407608842
407608842
407907898
408102072
408206069
408309642
408502932
408605865
408708148
408809524
408909721
409008483
405800266
404803713
404509484
404209428
404906190
404409738
404209428
404009634
402608503
406801167

DELTA
NU

00140
00200
00100
.0140
00200
00140
00200
00200
00200
001.40
00140
00140
00140
00140
00140
00140
.0100
00100
00140
.0140
00200
00100
00140
00100
00100
00100
00200
.0200
00140
00140
00140
00200
00140
00100
00140
00100
00140
00200
00100
00100
00140
00200
00200
00200
00140
00200
00200
00200
00200
00200

085-
CALC

‘01330
00516
00244
00264
00494
00402
00458
00248
00278

‘00511

‘02392

‘04732

‘08390

'08390

‘00136

-00222

-00245

‘00436

-00603

‘00953

‘01495

-02153

‘03257

‘04860

-07168

”100255
00405
00351
00429
00429
00475
00479
00529
00380
00172

‘00168

'00931

-02376

'04773

‘08378

-00245

-02945

‘07760

‘108188
09531
02122
01653
01911

‘104466

-00226

INT

20

10

LINE
N0

452
479
431
422
412
403
392A
363A
353
340
317
306

294
505
504
503
501
500
499
496
495
492
489
486
483
572
579

589
599
600A
611
619
624
630
635
642
646
552
497
449
437A
4218
455
431A
4218
4105
339
549

ASSIGN-
MENT

R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RP
RP
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
RR
RR
RR
RR

19 7
l9 8
19 9
1910
1911
1911
1912
1914
1915
1916
1917
1918
1919
19
19
19
19
19
19
1911
1910
1911
1912
1913
1914
1915
1916
1917
1918
2912
2913
2915
2916
2918
2924
29 4
2911
2912
2913
2916
2917
2919
2920
2921
2922
2923
29 3
29 4
2910
2911

\oooxlmbr—a

CALCULATED
FREQUENCY

406709860
406708107
406706135
406703944
406701534
406701534
406608905
406602989
406509702
406506197
406502472
406408528
406404365
407109408
407607876
407909081
408104351
408209397
408404220
408703194
408508820
408703194
408807345
409001269
409104968
409208441
409401687
409504706
409607498
405402718
405203072
404803139
404602852
404201639
402902926
407509353
407406997
407404349
407401481
407301552
407207801
407109638
407105225
407100592
407005738
407000663
408207486
408403413
409304273
409408629

342

OBSERVED
FREQUENCY

406709463
406707495
406705115
406701176
406603626
406705115
406701176
406604964
406601404
406507591
406503436
406408153
406309677
407109249
407607704
407908721
408103834
408208249
408401259
408504919
408602501
408705537
408809524
409003219
409106641
409209934
409402751
409504379
409602810
405403275
405203454
404803713
404603629
403305300
402900099
407509253
407407545
407404905
407402063
407302246
407208255
407109249
407104213
407008933
407003306
406907930
408207387
408403343
409304790
409409147

DELTA
NU

00140
00140
00200
00200
00200
00200
00200
00140
00140
00140
.0140
00140
00200
00100
00140
00200
0020

00140
00140
00230
.0200
00140
00140
.0140
.0100
00200
00200
00140
00200
00200
00200
00143-0

00200

085-
CALC

'00397
"00612
‘01020
'02768
‘07908
03582
02272
01975
01702
01394
00964
-00375
“04688
‘00159
’00172
-00361
‘00517
“01148
“02961

‘108276

03632
02342
02180
01950
01673
01493
01064
-0O328
‘04688
00557
00382
00574
00777

“806339

~02827
“00099
00548
00556
00582
00694
00454
"00389
'01012
‘01659
‘02432
'02733
-90099
‘00070
00517
00519

INT

18
21
22
24
12
22
24
13
14
15
14
13
10
11
15
13
13
14

10
16
19
13
12
10

11
11
12
12

16
13
13

11
14

11

m~4©

q
C

13
21
16

LINE
NO

548
547
545
543
540
545
543
541
538C
536
333
531
527
566
588
600
6050
6123
620
626
628
534
642
547
55
659
663
668
6718
480
4688
499
A39
417A
352
583
575
574
573
570
559
566
564
562
560
558A
612A
621
661A
6658

ASSIGN-
MENT

RR
RR
RR
RR
RR
RR
RR
RP
RP
RP
RP
RP
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
R0
R0
R0
R0
R0
R0
R0
R0
R0
RR
RR
RR
RR
RR
RR
RR
R0
R0
R0
R0
R0
R0
R0
RP
RP
RR
RR
RR

2912
2913
2914
2915
2916
2917
2920
39,8
3912
3915
3917
3919
39 3
39 4
39 7
39 9
3910
3913
3914
3915
3918
3920
39 4
3911
3910
3912
3913
3915
3916
3919
3920
49 9
4910
4911
4912
4913
4914
4915
49 9
4910
4911
4913
4914
4915
4916
4913
4917
59 7
59 9
5911

CALCULATED
FREQUENCY

409692758
409796660
409990335
410093783
410197002
413299992
410697586
406994312
406197833
405598199
405197367
404795679
409092664
409198582
409694985
409994791
410099354
410591677
410695328
410798749
411197633
411492400
408394536
408292095
408294539
408109429
408196540
408190097
408096542
407994545
407990102
410699485
410894029
410998344
411192430
411296286
411399911
411593306
409091490
408999253
408996792
408991199
408898067
408894712
408891132
406792877
405991992
411193998
411493737
411792556

I" U‘
Din

15CY

”er (I

Q!
U

11C)
‘A‘I'D

409693369
409797360
409991058

406198274
405599243
405198962
404797392
409092560
409198654
409695324
409995149
410099908
410592765
413696723
410890438
411199590
411492247
408394397
408292635
408294908
408290123
408197329
408191512
408098203
407996560
407991698
410699949
410894586
410999123
411192924
411296436
411398758
411591993
(09091843
408999721
408997255
408991627
408398145
408893556
408799695
406793398
405990923
411099728
411399420
411698469

DELTA
NU

90140
9015790
90140
90200
90140
.0200
90200
.0200
.0140
90140
90140
90140
90109
90290
90200
90140
90100
90100
90140
90140
90100
90100
90140
90140
.0140
90140
90140
90200
90100
90140
90140
90100
90100
90140
90100
.0230
.0200
90140
90140
90200
90200
90140
90100
90140
90100
90200
90140

90200
90140
90140

OE) S“
CALC

90612
90700
90723
90614
90456
-90016
‘91757
‘90630
90441
91044
91595
91713
-90104
90072
9340
90357
90554
91087
91392
91689
91958
-90153
“90139
90540
90370
90695
90789
91415
91661
92015
91596
90464
90557
90779
90495
90150
‘91153
”91313
90353
90468
90463
90428
L078
‘91155
-91438
90521
-91069
‘94270
‘94317
"94067

2
.1

IX!

HHD—J

9.9

D—‘H
Hoxlr—Jr-JxOO‘xjmv-IOHHO‘

NNhJIV
H4?

HN
Dix)

9—99—49—99—2
“9990‘

9.4
L)

t—‘D—‘HH Nb—‘l—‘HH
WCJ‘WLDLDUI‘O“L‘)‘OU‘)

16
14
12
15

13
16

13
10
10

10
l (g.

10

LINE
NO

672
678
683
689
695
699
714
556
517
487A
466
444
648
656
673
686
692
710
715
721
737
745
617
609
610
608
607
605
604
598
597
716
723
729
734
740
744
748
647
646
645
643
641
638
636
544A
502
733
744A
753

 

 

 

J: ‘4... . :1

3n! illil

ASSIGN-
MENT

RR
RR
RR
RR
RR
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0

. A
RU

R0
R0
RP
R0
R0
RP
RP
R0
R0
RR
RR
RR
R0
R0

EXCUDED

P0
P0
P0
P0
P0
PR
PR
PR
PR
PR

5912
5913
5015
5918
5019
5910
5011
5012
5013
5014
5015
5916
5017
5018
5019
5020
6024
6925
6910
7012
7022
7920
8017
8018
8020
8915
8017
8921
9917
9929

FROM

CALCULATED
FREQUENCY

411806619
412000453
412207417
412606121
412708554
409703532
40970 354
409608351
409605423
409602269
409508899
4C9505287
409501457
409407403
409403123
4C9308618
409901778
4C9806103
408709435
4111.5392
410705435
407500326
4C8805889
411606742
411507778
414400734
414702585
415201423
412402917
411707664

398806770
398803102
4170901520
401006056
401602099
401705583
402104761

344

OBSERVED
FREQUEch

411802711
411906612
412203890
412603032

whu£~b

q

. IN
OCDC)O

409404169
409400357
409305729
409902353
4093065C5
403709595
411105548

414703216
415201247
412403139

411709113

LEAST SQUARES ANALYST

399009015
398907246
3989.4282
398901575
398808706
40C902577

401007752
401606632
401800391
402202299

DELTA
NU

00100
.0200
.0200
00200
.0200
.0140
.0140
00200
.0140
.0230
00140
.0230
.0230
.Clqo
.0200
.C_OO
.0140
00140
.0230
.0200
00140

U)
C)
C:
111

055- INT
CALC

-03907 13
-.3833 10
-03528 1

-03088 10
-.2495 16

-.4278 10
-.4176 9
‘04052 12
-.3941 12
-03734 9
-03595 9
‘03483 11
“03413 9
~03233 7
-03065 5
-02390 10
00580 7
00397 7
00250 8
00157 10
00452 7
00510 11
00613 5
.0354 3
.0482 5
00347 7
00631 4
-.0175 9
00273 11
01449 4

00242 12
03753 4
04048 12
05107 4
.5504 10
01157 5
01696 5
04533 4
.4308 15
.7533 22

TO ZERO WEIGHT

166A
161
160
159
157A
244
252A
289
295A
316

 

 

0 .11 . .II'3ll

ASSIGN-
!IENT

PP
P0
P0
P0
P0
P0
P0
PR
PP
PR
PR
P0
P0
P0
P0
P0
P0
P0
P0
PR
PP
PP
PR
PR
PR
PR
PP
PP
PP
PP
P0
P0
P0
P0
P0
P0
P0
PP
PR
PR
PR
PR
P6
P0
P0
P3)
P0
PR
PR
PR

8017
80 8
80 9
8010
8013
8013
8014
80 8
8012
8013
8014
70 7
70 8
7010
7011
7012
7013
7014
7015
70 8
6020
6021
60 7
60 8
6011
6015
50 7
50 8
5010
5013
50 5

40 8
4010
4012
40 7
4010
30 3

CALCULATED
FREQUENCY

396708422
399807847
399806000
399803947
399706557
399706557
399703684
401309094
401907603
402101703
402205591
400606727
400605072
400601143
400508868
400506386
400503698
403503802
400407700
402106345
397700291
397409198
402708407
402903540
403307661
403903491
401003311
400804827
400407240
399809324
402203742
402201014
402109335
402107446
402105347
402100520
402007791
403400186
403505522
403700644
403805552
404208987
402909474
402907994
402906302
402902235
402807423
404302511
404707197
404406779

U)
J}
u1

OBSERVED
FREQUENCY

396801294
399808378
399806574
399804983
399708609
399708191
399705966
401308628
401909405
402103315
402208338
400607689
400606130
400602432
400600281
400508014
403505978
433502872
400500850
402107428
397805645
397607647
402802285

402907829

,,‘\ A

.

4010.43

LU
‘ O\ \J \00

402107428
402103315
402101543
403401818
403506998
403702295
403307765
404302454
402909260
4029075
4029058'
4029015
402806739
404302454
404707392
404406609

C)“ \I) fx)
0) m \0

\O ")

‘ {J ‘1') ‘O

\0 ~13) ‘0
‘ \O \U \0 \O

I ‘0 KL)

\O \L
\O \L,

\O ‘43

\O\£)\O \I.)\1J\U\O\O\’)\Q\O
" \U \Q \1’.) 0 \D \L) \1’) \L) \O \U \L)
\O \O \O \0 xi) 0 k')

u) a") \O
u)

‘0 \O \O \O \f) \O \I) \O \O ‘0 \f) \O \O *0 \O \0 KO \0 \O \O \O \O \C! u \
V.) '0 x!) \O \L‘)

\O \O \O O \U \0 KC ‘0 \0‘0

\U \L) \L) \0

O 00 0-0 m m p
\L) m ‘0

wankfibu)
N004

01

CD L0 \O n) ‘31 \J U) 0) \1 .p

‘U\O\-$>

O
O
L
7' ()\(1J D.) O

...-...:

0—40—0
m-pUJO-ph4mCDUJQ‘OO‘WCDU1WKNFJO'N~JP(DO‘®

H

Hb—J

LINE
N0

61
200
199
198
195A
195
194
275A
304
311A
318
231
230A
229A
228
227
226A
225
224
313
103

94
3484
356
379A
408A
251
241
223A
201
3168
316
315
314
313
311A
310
3783
385A
3924

Lu£‘b
\J'I NO
(I Udlv—I
3‘2

D-Puawkyua

DPVUIW\BU1

Pkg()m\n0\\
p

429

ASSIGN-
MENT

PR
PP
PR
PR
PR
P0
P0
P0
P0
P0
PO
P0
P0
P0
PP
PP
PP
PP
PP
PP
[32)
PP
PP
PR
PR
PR
PR
PR
P0
P0
P0
P0
P0
P0
P0
PP
PP
PP
PP
PP
PP
PP.
PR
PR
PP
PR
PR
PP
P0
P0

30 8
3010
3011
3018
3019
3011
3012
3013
3014
3015
3013
3014
3018
3020
3012
3013
3014
3016
3015
3019
3020
3021
20 2
20 3
20 4
2011
2015
2017
20 2
20 3
20 6
2014
2016
2017
2019
20 5
206
20 8
20 9
2013
2016
10 8
10 9
1012
1013
1017
1018
1019
10 1
1016

CALCULATED
FREQUENCY

405204439
405503986
405608432
406603407
406706090
403606726
403604170
403601402
403508421
403505226
403601402
403508421
403404365
403306060
401602464
401402913
401203154
400803019
401003190
400201278
400000289
399709097
4 5007273
405203446
405309404
406405006
407000517
407206942
404506814
404506171
404502953
404304936
404208287
404204640
404106704
403700149
403502049
403105215
402906482
402109450
401509488
406707450
406902304
407305538
407409506
408003146
408105996
408208620
405303693
405004529

346

a ".0
.-

'\‘ CD

)1 (_fl

«1m
CXJ
n1<

710

E0
NCY

405204194
405502529
405606076
406600536
406702864
403605262
403601899
403508998
409905544
403309863
403707954
403605471
403401818
403303004
401601021
401400605
401200743
400607689
401007752
400108537
399906989
399705966
405007962
405203454

405400644
406404905
406909360
407204278
404507005
404506510
404503069
404304368
404206385
404202866
404102048
403700240
403502120
403105418
402906392
402109499
401508747
406707495
406902405

407305728

\00
J.

J

\0

\O U
~L

\I) \() \O \L) x[) x")

. . .
\O \O

L)

\1) ‘0 \U

\D \O ‘O R") \O ‘0

‘1) \C) *1) \O V

.40. o
«Dwxo
x!) \L) \0 =0 ‘0
\1’) \L) \D

r\fi f‘
UC,‘ 3"

CALC

-00245
-01456
"02356
‘02871
‘03226
‘01463
”02271
'02403
6307124
”105353
106552
07051
‘02548
‘03056
‘01444
'02308
‘02412
“105330
04562
‘02741
-03300
-03130
00689
00008
01241
“00101
“01157
‘02664
00191
00339
00116
‘00568
-01402
'01775
‘04656
00091
00071
00203
-00090
00048
‘00741
00045
00102
00190
‘00003
”00715
“01363
'01606
00035
'00175

INT

23
13
9

n
7

10
19
30
10
27

7
17
18

4
19
17

H N

0.00—.0de 0.00—00.4.0.0

NIdPJHrd
Lu J> \fi CP ~J 4> \fi ha ha C) F4 \fi C) C) no kn Ch 4> no \fi co 1: C\

NH
N

|\)0—0|\)0—0
Hub—INK“

QFJH
o£>b

h
L

Nr—a f\)
deU1

C) (3 \J ‘J Ul

@xnkjoprwAUl

L‘L‘U‘O‘U‘U‘IU‘U'
1)

Unfit-a

ASSIGN-
MENT

PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
R0
R0
R0
Po
R0
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
R0
Po
R0
R0
R0
R0
R0
PP
PP
PP

1920
09 7
0914
0915
0919
0923
O9 9
O9 5
O9 6
0910
19
19
19
19
19
19
1910
1912
1917
1918
1919
1920
19 2
1912
1910
1913
1920
19 5
19 9
1919
29 4
29 5
29 7
29 8
2910
2911
2917
2920
2921
2922
29 3
29 5
29 8
2910
2914
2915
2918
29 2
2918
2921

oarq\fi4>w

CALCULATE 0
F9500: éCY

404898543
404896307
403592016
403391984
402499758
401694194
406090309
407097729
407293231
407893029
406394233
406196543
405998636
405692172
405493616
405294844
405095858
404697244
403696981
403496294
403295396
403094287
406895337
4066989C5
406793944
406696056
406399983
407893590
408494220
4C9890061
406992102
406794189
406397710
406199144
405891363
405692148
404492352
403799578
403598230
403396672
407690235
407598249
4075 93616
407499424
407398392
407395082
407293839
408191337
410492753
410799657

347

710
AND
HIm

n3<

ED
NCY

(.70

E
0

404896791
404896533

403592436~

403392496
402499155
401591406

406090 325
407097856
407293554
40789 3469
406393908
406196425
405998682
405692015
405493275
405294194
405094669
404790845
403698240
403497355
403294994
402999762
406895164
406590520
406893627
406697893
406295265
407893469
408594154
Z C05 .5324
406992100
406794083
406397641
406199171
405391591
410.20.20.15
404493207
403799491
403597384
403395216
40'7690199

DELTA OBS-
NU CALC
99999 ‘91752
99999 90227
99999 90419
99999 90511
.9,99 ‘90602
99999 ‘192763
99999 90016
99999 90127
99999 90323
99999 90440
99999 ‘90325
99999 ‘90117
99999 90046
99999 -90157
99999 -00341
99999 '90651
99999 ‘91139
99999 93601
99999 91259
99999 91061
99999 ”90402
09999 ‘94526
99999 ‘90173
99999 “198385
99999 99683
99999 91837
99999 ‘194718
99999 '90120
99999 99933
99999 ”194736
99999 ‘90002

99999 ‘90106

90200 “90069
90140 90027
9999' 90223
99999 ‘90133
99999 90355
99999 -90087
99999 -00346
99999 ‘91456
99999 -90037
099540 "OOO'JQ'
99999 90309
99999 90080
99999 90526
99999‘1690131
99999 -90276
99999 90175
99999 '90426
09999 ‘92294

INT

0) HM F—‘H N IUNH H

H‘N
\JJCNO‘J-‘xjwDU‘OQDF-‘k-‘CI‘CI‘WC‘4-‘kdh-‘(DK7‘C‘U3

H
‘OI'\J‘O\1(D\IO

HN

H.) \l

qrrUt

xlxld

\op\jwnjp_.amos
)9

HC)()O\
CUP

4

ASSIGN-

99"-
:VII‘

RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RR
RR
RR
RR
R0
R0
R0
RQ
R0
RR
RQ
R0
RP
RP
RP
RP
RR
RR
RR
RR
RR
RR
RP
RP
RP
R0
R0
R0
R0
R0
RC
R0
R0
RR
RP
RP
RP
RP
RP

NT

39 5
39 9
3910
3913
3914
3916
3918
3920
3921
3922
39 8
3911
3916
3917
3914
3917
3918
3921
3922
49 6
49 7
4912
49 9
4911
4914
4916
59 6
59 8
5910
5914
5916
5917
5915
5917
5919
59 8
59 9
69 7
6913
6917
6922
6926
6927
6921
6914
6916
6919
6920
6921
6922

CALCULATED
FREQUENCY

407499380
406795519
406596508
405998171
405798293
405397891
404996630
404594515
404393138
404191549
409890091
410293690
410991941
411094902
408193430
408092765
407998766
407895436
407890548
410294484
409095293
408994127
407590281
407192016
406592981
406192533
410998785
411298982
411598261
412194050
412490552
412593453
407097110
406696192
406294405
409797811
409795784
410593463
410399176
410295115
410092437
409890212
409794089
413796148
408091040
407690523
406998097
406796854
406595393
406393715

348

OBSERVED
FREQUENCY

407499504
406795498
406596883
405998682
405799016
405399175
404998849
404596510
404394766
404191338
409890348
410294706
410994261
411096693
408194628
408095001
408090872
407895309
40779493

410294706
409095396
408994618
407590536
407192528
406593436
406191425
410994261
411294351
411594132
412190436
412397353
412590386
407093467
406692565
406291062
409793672
409791408
410592765
410398986
410294706
410092512
409590348
409794116
413796219
408090872
407690199
407091145
406796598
406595301
406393908

DELTA
NU

O O O O O O O

O \O \O \0 \0 x0 \0 ‘0

\O \1) \D \L) ‘1') *0

~L)~4) 1) u; u) d} u) no
\Ouaxooxoxoxoxom

o

O
‘0
\O

\I'.) \O ‘O \O
\O ‘0 \U \U \D \O
\C \O
\O \O \O \O NO \0

m

‘0 ‘0 ‘0 \D '0
‘0 KO ‘4')
‘0 KO \1) ‘4)

\O
\U
\0 \0 \LJ \0 \L') \i’) (-3 \1') ‘4) \O \O ‘1) Xx”) ‘0 \LJ \1) \0 ‘0 ‘1‘) C) \O

\O \O\O
‘£)\O\O
‘43 \D \O k0 \O \O

\0

‘0 \O \O C) \0

‘0

‘0 ‘1) \O \O \O ‘4) \C \0 ‘-O O

\ 0 KO \0

\O \O ‘O \0 KO \0 \U \0 \L) \O \O \O f‘x)
\O

\O \O ‘0 \O ‘0 ‘0 \1) \0

...-.....ooooocooooooo.......
1)
‘.O\L)\O\O

430’) ‘1)

\O \O

‘(J

\O ‘0

CBS“

CALC

90123
“90021
90376
90511
90723
91284
92219
91995
91628
“90211
90346
91016
92321
91791
91198
92235
92106
“90127
“95609
90222
90103
90510
90255
90512
90455
“91113
“94524
“94132
“94130
“93614
“93199
“93063
“93643
“93627
“93343
“94139
“94376
“90698
“90190
“90409
90076
90136
90027
90072
“90168
“90322
93048
“90256
“90092
90193

IN

\Jl—JHHNHl—‘HI—l
N(D()()U < P

l

N
00.)

L

I)

ks)

9...;

HNU)
HO

N

WU“

...—99...;
U19

H

HHt—I
fi‘QraRmeuuwm

}—-J

N

1

hjwri-J

070" UJU1~JU‘\O\OUJO(‘)O‘\C)CO

9—4 -.’>

CO

1

‘1) ~J

ME

RP
RP
RR
RR
R0
R0
R0
R0
R0
RP
R0
R0
R0
R0
RP
RP
RP
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0

NT

6925
6926
7914
7919
79 8
79 9
7919
7920
7923
8915
8911
8916
8917
8919
9914
9918
9920
9912
9914
9915
9916
9918
9922
9923
9924
9926
9927

CALCULATED
FREQUENCY

405697385
405494845
413690855
414295047
411294981
411292926
410899820
410895253
410790184
409296927
411990877
411794787
411790880
411692375
410199314
409397165
408994751
412690271
412594024
412590553
412496850
412398752
412199777
412194455
412098902
411997101
411990853

405697526
405495014
413691039
414295427
411294851
411293012
410990094
410894907
410699949
409296764
411990943
411794502
411791254
411692939
410297719
409397346
408995165
412690241
412594202
412590662
412496858
412399038
412290369
412194947
412099661
411997982
411992078

DELTA
NU

99999
99999
99999

C
{
x0490
\o u) w) \o
\o \o -~o \o \o

®\O%)®
\O \O
\O \O

‘0 \O \i) \0

IL) ‘0 \O \O x!)

\L') \O \0

00.000.00.00
\O\O

\O \O \O \O \0 t0 \0 \O \O \1’)
\O ‘0 ‘0 \0 \O ‘0 \C \O ‘~O

x!)

.0.
\OO
'04)
0430\0
\O\O\C

o

\O

‘0
7
1)

99999
99999

99999

086-

CALC

90141
90169
90184
90380
“90130
90085
90274
“90346
“90236
“90163
90066
“90285
90374
90564
98405
90181
90413
“90030
90179
90109
90008
90286
90591
90492
90759
90881
91225

INT

9.49...

9.49.9

{y—D

9—9H
wOO~O\O~Ufir—4me0mbwxlxlwmhoxomqooowwb

H

LINE
N0

491
481
805
821
739
738
725A
723A
716
6580
7614
756
754
751
6958
6618
6448
783
782
7804
779
774
768A
7678
765A
763
7618

APPENDIX X

COMPARISON OF THE OBSERVED AND CALCULATED FREQUENCIES OF
K"=0 SERIES OF v3+v4 OF CH3F

The following page contains a comparison of the observed
and calculated RRO(J), RQO(J), and RP°(J) transitions. The
analysis of this subband including a Coriolis resonance
constant q. and a J6 term whose coefficient is f resulted
in the constants (in cm"):

sub = 4060.987
ag+ag = 0.01057
q = 2973 x 10""4
y = 1.06 x 10-8
S (std. dev.): 0.015 cm"1

The columns of the list. left to right, are the
assignment (AK,AJ,K,J); the calculated frequency (in cm");
the observed frequency (in cm'1); the Av (weight =
(NORM)2/(AV)2), the observed minus the calculated frequency;

the observed line height; and the line number.

350

ASSIGN-
MENT

RP
RP
RP
RP
RR
RR
RR
RP
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
R0
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR

09 6
O9 8
09 9
0910
0911
0912
0913
0916
0917
09 1
O9

O9

09

O9

0920

CALCULATED
FREQUENCY

405094655
404697980
404499333
404390474
404191392
403992075
403792507
403192049
402991194
406099656
406099233
406098597
406097750
406096689
406095414
406093921
406092206
405998081
405995649
405992949
405899959
405896651
405892989
405798931
405794425
405699406
405693801
405597523
406296703
406493337
406599768
406992022
407398845
407594018
407698960
407698960
407998093
408192243
408296080
408399568
408592664

351

OBSERVED
FREQUENCY

405094669
404697954
404499246
404390293
404191338
403991848
403792295
403191990
402991568
406099782
406099322
406098640
406097830
406096734
406095438
406093888

405997997
405995518
405992884
405899865
405396652
405893038
405799016
405794658
405699639
405693902
405597243
406296582
406493423
406599861
406992100
407398918
407593925
407698842
407698842
407997898
408192072
403296069

408399642
408592932

24
18
17
15
23
19
17
20
19
16
18
20
21
21
21
20
22
23
20
25
21
24
21
29
19
18
19
19

14
16
24
21
58
18
19
23
18
16
15

LINE
N0

459A
441
431
422
412
403
3924
3634
353
514A
514
513

J‘IUIU‘IUTU'U‘
00(2)?)wa
D\POJO(:PJN

-bU1m\nuw
(3 0 9..)
(3 H k»

a
‘42)“)‘(90 _

O‘ HO i\) U7 0‘ \O

U.) i\) N 0) 1'1)

\ON‘JiGDLnf-d

\fiUMoxnunfiUMfikfi£mD$>b
-4~UJ

DUO
‘OKO

APPENDIX XI

LIST OF ASSIGNMENTS AND FREQUENCIES OF OBSERVED TRANSITIONS
FOR v1+v2 OF CHD3

The following pages contain a list of the observed
frequency (in cm"), together with the assignment (AK,AJ,K,J,)
and weight, of the observed transitions of v1+v2 of CHD}.

352

ASSIGN-
MENT

0P
0P
0P
GP
09
op
QD
OR
OR
OR
OR
QR
0P
0P
0P
0P
0P
OR
OR
0P
0P
0P
0P
0P
0P
0P
0P
0P
OR
OR
0P
0P
0P
0P
0P
QR
OR
0P
0P
0P
OR
OR
0P
0P
0P
0P
00

6910
7910
8910
9910
O9
19
29
39
49
59
69
79
89
O9
29
39
49
59
69
79
O9
29
39
49
59
69
09
19
29
39
49
59
O9
19
29
39
49
O9
19
29
39
09
19
29
O9
19
9912

mmwmm -
{>915PWU‘WU‘U‘O‘O‘O‘O‘O‘O‘NQ-fiflflflmcommmmCDOQQ\OO\O 000

0016916

00

7911

0010912

353

OBSERVED
FREQUENCY

506396030
506494700
506592130
506692700
506992690
506993980
506997000
507092030
507097540
507192970
507198270
507294500
507393890
507799340
507891150
507893680
507896670
507990900
507996190
508094650
508596320
508597610
508599900
508692950
508697430
508794660
509390640
509390640
509392160
509394420
509398320
509493760
510093970
510093970
510095580
510098560
510193810
510796150
510796150
510798350
510892130
511496830
511497630
511590170
512197680
512197680
512598610
512690100
512696180
512697200

WEIGHT

950
950.
950
925
925
950
950
950
950
950
950
925
900
900
950
1900
950
950
925

912
.00

950
1900
950
950
925
.00
.00
950
1900
950
912
900
900
1900
1900
912
.00
.00
1900
950
925
950
925
.00
.00
925
925
925
925

ASSIGN-
MENT

0015915
00 8911
00 6910
0014914
00 7910
OP O9 1
0013913
0010911
00 69 9
0012912
00 59 8
0011911
00 89 9
00 69 8
0010910
00 79
00 29
00 59
00 99
00 29
00 39
00 69
00 49
00 89
00 59
00 79
00 39
00 49
00 39
00 69
00 19
00 59
00 29
00 49
00 39
00 29
00 19
OR 09
0R 09
OR 19
OR 09
OR 19
OR 29
OR 09
0R 19
OR 29
0R 39
OR 09
OR 19
OR 29

bmb£>w\»UJwranmnakaorJAJmmbUme»O\b\fiunq($330-QO~O~O~JQCD

354

OBSERVED
FREQUENCY

512699250
512791190
512796580
512798510
512892540
512895050
512897600
512990450
512992630
512995980
513091940
513093500
513096560
513097270
513190660
513193700
513094790
513194580
513197170
513196200
513198220
513290190
513291580
513293150
513296080
513298540
513297680
513391570
513396340
513393310
513398750
513397260
513490769
513491640
513494390
513590890
513498770
514194250
514794800
514795410
515395120
515395120
515397360
515993850
515993850
515995480
515998570
516591490
516591490
516592980

WEIGHT

950
950
.00
950
925
950
925
912
925
925
925
1900
950
950
1900
950
912
925
1900
910
925
1900
950
1900
950
950
950
950
950
1900
912
950
925
950
1900
950
925
912
925
925
900
900
912
900
900
925
925
900
900
950

355

ASSIGN- OBSERVED WEIGHT
MENT FREQUENCY
OR 39 4 516595340 950
OR 49 4 516599220 950
OR 09 5 517097840 900
OR 19 5 517097840 900
OR 29 5 517099380 950
OR 39 5 517191460 1900
OR 49 5 517194700 1900
0R 59 5 517199090 925
OR 09 6 517691420 900
OR 19 6 517691420 900
0R 29 6 517693290 950
OR 39 6 517695850 1900
OR 49 6 517699000 925
OR 59 6 517793230 950
GR 69 6 517798770 950
OR 09 7 518095270 925
OR 19 7 518096400 925
OR 29 7 518099590 912
OR 39 7 518194610 1900
OR 49 7 518290250 1900
OR 59 7 518295780 1900
0R 69 7 518391180 1900
OR 79 7 518397630 950
OR 59 8 518696640 912
OR 69 8 518799060 925
OR 79 8 518898660 912
OR 89 8 518996230 912

APPENDIX XII

COMPARISON OF THE OBSERVED AND CALCULATED GROUND STATE
COMBINATION DIFFERENCES OF v1+v2 0F CHD}

The following pages contain a comparison of the observed
and calculated ground state combination differences of
v‘+v2
of these ground state combination differences. The constants

of CHBD from a simultaneous least squares analysis

determined are (in cm"):

B0 = 3.27944

DgK =-4.8 x 10-5

pg = 5.22 x 10'5

The columns, left to right, are the assignment (of.

Chapter 4); the calculated combination difference (in cm");
the observed combination difference (in cm"): the Av
(weight = (NORM)2/(Av)2); and the observed minus the cal-

culated combination difference.

356

ASSIGN-
MENT

0P
0P
0P
0.0
RP
RP
RP
RD
RP
QP
0P
0.9
GP
RP
RP
RD
RD
RD
R0
R0
R0
PP
RP
RP
RD
0o
0.0
0.0
R0
Po
PP
RP
RP
0P
0P
QP
R0
R0
PP
PP
RP
00
fiD

do
RE)
R0
RP
RP
GP

09

29
29
29
29
29
29
29
29
29
39
39
39
39
39
39
39
39
39
39
39
39
49
49
49
49
49
49
49
49
49
59
59
59
59
59
59
59
59
69
69
69
69
69
69
69
69
79
79
79
79

mfl‘ommflm40‘*0(n\lmflmflO‘mNO‘O‘UTO‘U!I-‘U)\JGWO‘kfibmflO‘m-DO‘U‘J-‘wmflkfiJ—‘UQNO‘UJN

CALCULATED

GSCD

1996722
2692237
4598433
5293673
4598959
5899939
7290807
9892105
11192485
2692256
3297727
3993134
4598467
5899983
7290861
8591601
9892178
11192567
2692256
3297727
3993134
7290935
8591689
9892280
11192683
3297761
3993175
4598514
3297761
3993175
8591802
9892410
11192831
4598575
5293835
5898995
4598575
5293835
9892570
11193012
12493241
4598650
5293921
5899091
4598650
5293921
11193226
12493480
5294021
5899205

357

OBSERVED
GSCD

1996702
2692412
4598595
5293638
4599017
5899896
7290814
9892145
11192590
2692255
3297777
3993254
4598318
5990008
7290923
8591556
9892165
11192574
2692231
3297668
3993238
7290907
8591745
9892330
11192714
3297833
3993254
4598631
3297652
3993114
8591657
9892330
11192807
4598651
5293683
5898971
4598647
5293835
9892575
11192915
12493030
4598651
5293996
5899003
4598579
5293912
11193124
12493958
5293892
5899192

DELTA
NU

90245
90224
90316
90316
90300
90224
90200
90200
90316
90173
90173
90173
90224
90224
90173
90140
90140
90173
90245
90200
90224
90200
90173
90245
90173
90316
90200
90200
90200
90173
90245
90200
90173
90200
90245
90245
90245
90224
90245
90173
90245
90224
90224
90200
90173
90173
90245
90316
90316
90245

085-
CALC

'90020
90175
90162

“90034
90059

-90044
90007
90040
90105

-90001
90050
90120

"90149
90025
90062

"90045

‘90013
90006

‘90025

-90058
90104

-90029
90056
90050
90032
90073
90080
90117

”90108

-90061

-90146

-90080

'90024
90076

‘90153

-90024
90072
90000
90005

-90097

‘90211
90002
90076

‘90088

'90071

'90009

-90102
90478

‘90130

‘90012

ASSIGN-
MENT

90
RP
90
GP

79
89
89
99

\O\O\OCD

CALCULATED
GSCD

5294021
12493756
5899336
6594585

358

OBSERVED
GSCD

5293932
12494107
5899675
6594477

DELTA
NU

90200
90316
90316
90224

055-
CALC

'90090
90351
90339

'90109

APPENDIX XIII

COMPAFISON OF THE OBSERVED AND CALCULATED GROUND STATE

COMBINATION DIFFERENCES OF v2+v3 OF CHDD

The following pages contain a comparison of the observed
and calculated ground state combination differences of
9924-v3 of CHBD from a simultaneous least squares analysis
of these ground state combination differences. The constants
determined are (in cm"):
B0 = 3.88107
DgK = 1.192 x 10"4
D3 = 5.28 x 10'”5
The columns, left to right, are: the assignment
(of. Chapter 4); the calculated combination differences
(in cm"); the observed combination difference (in cm“);

the Av (weight = (NORM)2/(Av)2); and the observed minus the

calculated combination difference.

559

ASSIGN-

MENT

RR 29
RP 29
RP 29
RP 29
RP 29
RP 29
RD 29

RR 291

R0 29
R0 29
80 29
80 29
80 29
R0 29

R0 291

OR 29
OR 29
OR 29
OR 29
OR 29
OR 29
RP 39
RP 39
RP 39
RP 39
RP 39
RR 39

\Omxlkfi-Pwrdfl'mflOKfi-L‘W

C.)

\OCDaIO‘U‘J-‘xOCDQUI-L‘w

RP 3911
RP 3912

R0 39
R0 39
R0 39
R0 39

a,
7
8
9

R0 3910
R0 3912

GP 39
OR 39
OR 39
OR 39

4
7

8
9

OR 3912

RP 49
RR 49
RP 49
RR 49

5
6
7
9

RP
RP
RR

4910
4911
4912

R0 49
R0 49
0P 49

6
9
6

CALCULATED

GSCD

5493091
6998107
8593009
10097772
11692370
13196777
14790969
19391995
2392779
3190312
3897795
5492558
6199812
6996965
7794004
3190312
3897795
4695214
6199812
6996965
7794004
6998000
8592878
10097617
11692191
13196574
14790742
17798329
19391697
3190264
5492474

. 6199717

6996858
7793885
9297545
3897735
6199717
6996858
7793885
10094153
8592695
10097400
11691941
14790425
16294319
17797945
19391280
4695043
6996708
5492357

360

OBSERVED
GSCD

5493210
6998068
8593030
10097837
11692351
13196792
14790972
19392103
2392878
3190454
3897733
5492605
6199508
6997161
794039
3190331
3897614
4695296
6199746
6997283
7793811
6998039
8592888
10097641
11692052
13196602
14790891
17798232
19391749
3190418
5492409
6199721
6996901
7793962
9297434
3897621
6199643
6996881
7793991
10094315
8592846
10097551
11691817
14790399
16294631
17797418
19391174
4695100
6996576
5492451

DELTA
NU

90122
90122
90122
90122
90100
90100
90212
90292
90122
90300
90212
90212
90212
90292
90346
90100
90292
90224
90212
90158
90346
90141
90141
90122
90122
90122
90158
90212
90300
90173
90141
90173
90100
90173
90173
90173
90122
90158
90158
90316
90122
90122
90100
90212
90292
90300
90245
90158
90122
90173

085-
CALC

90119
‘90039
90020
90065
‘90018
90015
90003
90108
90100
90142
‘90062
90047
'90304
90196
90035
90019
'90181
90082
'90066
90318
‘90193
90039
90010
90023
‘90139
90028
90149
‘90097
90052
90154
-90066
90004
90043
90077
'90111
‘90115
~9OO73
90024
90106
90162
90152
90150
-90123
‘90026
90312
“90527
-90107
90057
"90132
90093

ASSIGN-
MENT

09 49
R0 59
R0 59
R0 59
R0 59
R0 5910
R0 5911
R0 5912
R0 5914
RR 59 6
RP 59 7
RP 59 8
RP 59 9
RP 5910
RP 5911
QR 59 6
OR 59 7
GP 59 8
CR 59 9
09 5910
0P 5911
RP 69 7
RP 69 8
RP 6910
RR 6911
RR 6912
R0 69 7
R0 69 8
R0 6910
R0 6913
GP 69 7
GP 69 8
OR 69 9
OR 6910
RP 79 8
RP 79 9
RP 7910
RP 7911
RP 7912
R0 79 8
R0 79 9
R0 7910
R0 7911
R0 7912
OR 79 8
0P 79 9
00 7910
OR 7911
GP 7912
RP 8910

\OWNO‘KO

CALCULATED

GSCD

7793718
4694914
5492207
6199412
6996515
7793503
8590365
9297087
10890062
10097121
11691619
13195926
1479 018
16293868
17797452
5492207
6199412
6996515
7793503
8590365
9297087
11691226
13195481
16293318
1779 849
19390089
5492024
6199202
7793241
10093316
6199202
6996279
7793241
8590077
13194954
14698931
16292667
17796137
19299314
6198954
6996000
7792931
8499736
9296401
6996000
7792931
8499736
9296401
10092913
16291916

OBSERVED
GSCD

7793823
4694901
5492270
6199306
6996518
7793399
8590296
9297039
10890296
10097071
11691615
13195817
14790023
16293872
17797450
5492171
6199344
6996512
7793505
8590473
9297154
11691190
13195409
16293286
17796881
19299607
5491830
6199158
7793122
10093530
6199360
6996251
7793396
8590164
13194885
14698997
16292778
17796299
19298906
6198904
6996039
7793090
.8499785
9296479
6995981
7792958
8499688
9296514
10092427
16291762

DELTA
NU

90224
90158
90122
90100
90292
90122
90200
90158
90316
90122
90122
90212
90122
90292
90200
90173
90141
90212
90300
90300
90200
90158
90173
90245
90173
90300
90212
90346
90158
90245
90245
90300
90224
90212
90173
90173
90173
90200
90346
90224
90158
90224
90173
90283
90245
90122
90283
90173
.0346
90212

085-
CALC

90106
-90013
90063
-90106
90003
-90104
“90069
‘90049
90234
-90050
‘90004
'90109
90005
90004
‘90002
-90037
“90067
‘90003
90002
90108
90067
‘90036
-90072
“90031
90032
‘90481
-90194
-90044
‘90119
90214
90158
“90028
90155
90087
-90069
90066
90111
90162
“90408
“90050
90039
90159
90049
90078
*90019
90027
‘90048
90114
‘90486
‘90154

ASSIGN-

MENT

RP
R0
R0
0P
RP
RP

fl
2.?!

R0
OR

8911
8911
8912
8911
9910
9913
9911
9913
9913

CALCULATED

GSCD

17795314
8499343
9295972
9295972

16291066

20890115
8498897

10091922

10798193

u:
(h
{\J

OBSERVED
GSCD

17795292
8499389
9295964
9295903

16291064

20890710
8498730

10092562

10798147

DELTA
NU

90283
90224
90200
90224
90212
90346
90141
90346
90400

085-
CALC

‘90022
90046
‘90007
‘90068
-90001
90594
-90167
90640
“90046

EXCLUDED FROM LEAST SQUARES ANALYSIS DUE TO
ZERO WEIGHT

RP
R0
QD
RP
R0
0P
0P
RP
R0
R0
R0
R0
0P
0P
OR

OR

RP
09

R0
0P
RP
0P
RP
RP
R0
R0
0P
0P
R0

2910
2912
2910
3910
39 6
39 6
3910
49 8
49 5
49 7
4910
4912
49 5
49 7
4910
4912
5912
5912
6911
6914
6911
8912
8912
9911
9912
9912
9915
9911
9912
7915

16294919
9297688
8590915

16294669
4695143
5492474
8590784

13196291
3897652
5492357
7793718
9297344
4695043
6199583
8590601

10093936

19390744

10093657
8590077

10799695
9296773

19298420

10092449

17794383

19297408
9295486

11594287
9295486

10091922

11595431

16294808
9298949
8590769

16294656
4694901
5492746
8590695

13196441
3897624
5492209
7793061
9297090
4695222
6199608
8591570

10094084

19391084

10094045
8590318

10799598
9295984

19298524

10092559

17794353

19297774
9295476

11593356

9295624
10092299
11593562

99999
99999
9999

99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
90346

'90112
91261
-90147
-90012
‘90242
90272
“90090
90150
'90028
-90148
‘90656
‘90254
90179
90025
90969
90148
90339
90388
90242
‘90097
‘90789
90103
90110
-90029
90367
-90010
-90931
90138
90377
‘91870

APPENDIX XIV

COMPARISON OF THE OBSERVED AND CALCULATED UPPER STATE
COMBINATION DIFFERENCES OF 924-93 0F 083D

The following pages contain a comparison of the
observed and calculated upper state combination differences
of v2+v3 of CHD3 from a simultaneous least squares analysis
of these upper state combination differences. The constants

determined are (in cm"):

Bv = 3.74260
ngK = 2.51 x 10'“+
D3 =—1.5 x 10-5
The columns, left to right, are: the assignment
(of. Chapter 4); the calculated combination differences
(in cm“); the observed combination difference (in cm");
the Av (weight = (NORM)2/(Av)2); and the observed minus

the calculated combination difference.

36}

ASSIGN-
MENT

RP 29
RP 29
RP 29
RP 29
RP 29
RP 29
RP 29
R0 29
R0 29
R0 29
R0 29
R0 29
R0 29
0? 29
GP 29
GP 29
OR 29
GP 29
QR 29
0P 291
RP 39
RP 39
RP 39
RP 39
RP 39
RP 39 .
RP 391
RQ 39
R0 39
80 39
R0 39
R0 3910
GP 39 4
0P 39 7
OR 39 8
GP 39 9
OR 3910
0P 3912
RP 49 5
RP 49 6
RP 49 7
RP 49 8
RP 4910
RP 4911
OR 49 6
R0 49 6
R0 49 9
RP 59 6
7
8

000:)40mboomxlkj1bUJ~00)\jmpmxom~JO~mpw

\Omfl-D

RP 59
RP 59

CALCULATED

USCD

5293879
6793603
8293360
9793157
11293001
12792900
14292861
2999367
3794236
4499124
5998968
6793932
7498929
2294512
2999367
3794236
5294333
5998963
6793932
7498929
6793377
8293084
9792830
11292624
12792473
14292384
15792365
3794111
5998767
6793706
7498678
8293687
2999267
5293857
5998767
6793706
7498678
8998735
8292697
9792373
11292097
12791876
15791627
17291614
4498762
5293611
7498327
9791786
11291420
12791108

364

OBSERVED
USCD

5293688
6793616
8293458
9793206
11292964
12792963
14292881
2999348
3794390
4499187
5999031
6793693
7499066
'2294339
2999226
3794271
5293932
5999269
6793815
7498838
6793311
8293094
9792788
11292719
12792451
14292351
15792388
3794235
5998819
6793709
7498661
8293699
2998995
5293900
5998742
6793690
7498690
8998814
8292583
9792315
11292198
12791885
15791591
17291702
4498688
5293627
7498294
9791678
11291301
12791146

DELTA
NU

90122
90100
90100
90122
90122
90100
90212
90122
90292
90212
90212
90158
90346
90100
90292
90212
90224
90158
90292
90346
90141
90121
90141
90141
90100
90121
90158
90173
90141
90158
90122
90158
90173
90141
90158
90100
90200
90245
90122
90121
90121
90100
90224
90316
90173
90158
90122
90100
90122
90122

088-
CALC

'90192
90013
90098
90049

"90037
90063
90020

-90019
90154
90063
90064

-90239
90137

‘90173

‘90141
90035

'90101
90302

-90117

'90092

'90067
90010

-90043
90095

'90022

-90034
90023
90125
90052
90003

'90018
90012

'90272
90043

'90025

“90016
90011
90079

-90114

“90059
90101
90009

-90036
90089

'90074
90015

-90033

‘90108

'90119
90038

ASSIGN-
MENT

RP 59 9
RP 5910
RP 5911
RP 5912
R0 59 6
R0 59 7
R0 59 8
R0 59 9
R0 5910
R0 5911
R0 5912
R0 5914
0P 59 6
OP 59 7
OP 59 8
0P 59 9
OP 5910
0P 5911
0P 5912
RP 69 7
RP 69 9
RP 6910
RP 6911
R0 69 7
R0 69 9
R0 6910
R0 6913
R0 6914
OR 69 7
0P 69 8
OP 69 9
GP 6910
0P 6913

CALCULATED

USCD

14290858
15790678
17290575
18790555
5293295
5998125
6792983
7497875
8292803
8997772
9792784
11292955
4498491
5293295
5998125
6792983
7497875
8292803
8997772
11290591
14199809
15699518
17199305
5997683
7497323
8292196
10497071
11292126
5292908
5997683
6792486
7497323
9792066

365

OBSERVED
USCD

14290871
15790767
17290667
18790605
5293302
5998073
6793008
7497869
8292792
8997698
9792791
11292153
4498376
5293202
5998137
6793002
7497976
8292969
8997814
11290333
14199897
15699841
17199660
5997478
7497249
8292319
10496793
11291815
5292855
5997681
6792648
7497522
9791742

DELTA
NU

90212
90173
90292
90158
90158
90122
.0100
90292
90173
90158
90158
90400
90158
90141
90122
90346
90141
90316
90200
90200
90173
90224
90224
90245
90173
90122
90173
90200
90245
90316
90141
90212
90346

OBS-
CALC

90013
90089
90092
90049
90007
'90052
90025
-90005
"90011
‘90073
90007
‘90801
'90115
‘90093
90013
90019
90101
90166
90042
‘90258
90088
90323
90356
‘90205
‘90074
90123
~90277
-90311
-90054
-90002
90162
90199
‘90324

EXCLUDED FROM LEAST SQUARES ANALYSIS DUE TO

PERTURBATIONS OR ZERO WEIGHT OR BOTH

RP 2911
RP 2912
RP 2913
RP 3911
RP 4912
RP 49 9
RP 3913

17292999
18793191
20293474
17292422
18791685
14291717
20292796

17292400
18792624
20291466
17292249
18790598
14291949
20291321

99999
99999
99999
99999
99999
99999
90245

‘90599
'90566
-92008
‘90173
‘91087

90232
-91475

ASSIGN-
MENT

RP 3912
0P 39 6
R0 39 6
R0 3912
RP 4913
GP 49 5
OR 49 7
OP 49 8
0P 49 9
0P 4910
OR 4911
OR 4912
R0 49 5
R0 49 7
R0 49 8
R0 4910
R0 4911
R0 4912
RP 5913
R0 6911
R0 6912
GP 6911
0P 6912
RP 6912

RR 6913

CALCULATED

USCD

18792563

4498973
5293857
9793828

20291847

3793935
5293611

998486
6793390
7498327
8293300
8998314
4498762
5998486
6793390
8293300
8998314
9793371

20290627

8997109
9792066
8292196
8997109

18699175
29199136

366

OBSERVED

USCD

18791666

4499225
5293562
9793141

20291540

3794017
5293813
5998134
6793655
7499056
8293104
9090242
4498566
5998488
6793751
8292535
8998599
9792672

20290437

8997495
9792373
8292165
8997248

18699724
20198536

DELTA
NU

90212
99999
99999
90158
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
99999
90200
90224

OBS-
CALC

'90897
90252
”90295
'90687
“90308
90082
90202
'90352
90265
90729
“90196
91928
-90196
90002
90361
~90766
90285
'90699
‘90191
90387
90307
'90031
90139
90549
'90601

APPENDIX XV

COMPARISON OF THE OBSERVED AND CALCULATED TRANSITION
FREQUENCIES 0F v2+v3 OF CH3D

The following pages contain a comparison of the observed
and calculated transition frequencies of v2+v3_of CH3D from
a simultaneous least squares analysis of these transition
frequencies. The constants determined (of. Chapter 9) are
(in cm"):

v0 3499.6291

as +d§ -ag -a§ = 0.15718

The first set of transitions are those which were
included in the least squares analysis. The second set
contains those excluded due to perturbations or zero
weight, (i.e., Ava 0.9999).

The columns, left to right, are: the assignment
(AK,AJ,K,J); the calculated transition frequency (in cm");
the observed transition frequency (in cm"); the Av
(weight = (NORM)2/(Av)2); and the observed minus the

calculated frequency.

367

‘ASSIGN-

MENT

OR 29
OR 29
0P 29
GP 29
GP 29
OR 29
OR 29
OR 29
OR 29
OR 39
GP 39
0P 39
OR 39
0P 39
0P 39

H
O~0m\IO‘U‘-DU~)

12

\OOONO‘UT-D

GP 3910

OR 49
OR 49
OR 49
0P 49
0P 49

6
7

8
10

OR 4911
0P 4913

GP S9
GP 59
OR 59
OR 59

6
7

8
9

0P
0P
0P

5910
5911
5912

QR 69
GP 69
0P 69

7
8
9

0P
0P
0P
00
00
00
00
00
00
00
00

6910
6911
6912
29
29
29
29
29
29
2910
39 4

@004me

00 39
00 39
00 39

7
8
9

00 3910

00

00

3912
49 6

CALCULATED
FREQUENCY

347691485
346795685
345897257
344996278
344092844
343097064
342099067
341098995
339093282
346893513
345995044
345094011
344190510
343194650
342196559
341196380
346095945
345194837
344291242
343295269
341296719
340294445
338194777
345298757
344395040
343398923
342490533
341490013
340397522
339393238
344591905
343595611
342597015
341596260
340593506
339498929
349895997
349795052
349691492
349296876
349096031
348892997
348597922
349892779
349394366
349193416
348990263
348695056
348099147
349693599

368

OBSERVED
FREQUENCY

347691674
346795681
345897293
344996268
344092937
343097122
342099108
341099113
339092932
346893580
345995034
345094003
344190482
343194738
342196599
341196298
346095972
345194767
344291108
343295210
341296696
340294182
338194711
345298789
344394995
343398852
342490478
341399975
340397478
339393292
344592053
343595547
342596977
341596229
340593587
339499189
349896013
349794908
349691564
349296869
349096392
348892924
348597951
349892655
349394382
349193480
348990289
348694988
348098979
349693455

DELTA
NU

90070
90070
90070
90010
90100
90070
90070
90100
90200
90100
90100
90100
90100
90070
90070
90140
90100
90100
90100
90070
90200
90283
90200
90070
90100
90100
90200
90100
90283
90140
90140
90140
90100
90200
90200
90140
90700
90283
90200
90200
90140
90283
90283
90140
90100
90140
90070
90140
90140
90140

OBS-
CALC

90189
"90004
90036
“90010
90093
90058
90042
90119
-90350
90067
-90009
“90009
“90028
90088
90040
‘90082
90027
“90071
'90134
‘90060
-90024
‘90262
'90066
90032
-90046
'90071
'90055
“90038
‘90045
90054
90148
“90064
-90038
'90031
90081
90260
90016
‘90144
90072
-90007
90361
“90073
90029
-90124
90016
90064
90025
‘90068
‘90168
"90144

ASSIGN-
MENT

QQ
QQ
QQ
00
00
QQ
QQ
QQ
QQ
QQ
00
00
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR

49
59
59
59
59
5910
5911
5912
69 7
69 8
69 9

000400

0‘
C
5.9

N
o
\OWQOK”DW\OLD\IO‘W&WN(D

5910
5911
5912
69 6
69 7
69 9
6910

CALCULATED
FREQUENCY

349090436
349797247
349598334
349397047
349193515
348897886
348690323
348391007
349794813
349593293
349299500
349093581
352198775
352895364
353499287
354190615
354699433
355295842
355799961
356391924
352993043
353596889
354198126
354796840
355393132
355897120
356398940
356898740
357396690
353697532
354298641
354897209
355493337
355997143
356498761
356998342
357496053
354492161
355090541
355596458
356190028
356691388
357190687
357598092
358093787
355196836
355792494
356796821
357295775

369

OBSERVED
FREQUENCY

349090519
349797165
349598197
349396990
349193480
348897951
348690447
348391106
349794908
349593228
349299625
349093751
352198891
352895361
353499297
354190751
354699474
355295900
355890085
356391990
352993074
353596891
354198129
354796790
355393201
355897189
356398949
356898686
357396413
353697613
354298555
354897027
355493306
355997095
356498813
356998286
357495885
354492066
355090467
355596296
356099998
356691350
357190742
357598145
358093897
355196737
355792386
356796874
357296070

DELTA
NU

90100
90140
90100
90700
90283
90100
90140
90140
90200
90283
90100
90070
90100
90100
90700
90070
90070
90070
90070
90200
90100
90100
90070
.0100
90100
90070
90100
90070
90100
90070
90070
90070
90070
90070
90070
90100
90140
90070
90070
90070
90070
90070
90140
90070
90070
90070
90140
90140
90100

088-
CALC

90083
*90082
-90138
-90057
‘90035

90065

90123

90099

90095
'90065

90125

90170

90115
‘90002

90010

90136

90041

90058

90124

90065

90030

90002

90002
-9OOSO

90069

90069

90010
-90054
‘90276

90081
‘90086
“90182
-90031
‘90048

90053
‘90055
-90168
'90095
-90074
”90162
‘90030
“90038

90056

90053

90110
-90098
'90109

90053

90296

EASSIGR‘
MENT

CALCULATED
FREQUENCY

370

OBSERVED
FREQUENCY

DELTA
NU

OBS-
CALC

EXCLUDED FROM LEAST SQUARES ANALYSIS DUE TO

OR
OR
QP
QP
QR
QR
QP
QP
QP
QP
QP
QP
OR
OR
QP
QP
QP
QP
OR
OR
OR
OR
QR
OR
OR
OR
OP
QQ
00
00
GO
QQ
00
00
00
QQ
Q0
00
00
00
00

PERTURBATIONS OR ZERO WEIGHT OR 80TH

2913
4912
6913
O9
09
09
O9
09
09
09
O9
0910
0912
2911
3911
49 9
5913
79 8
79 9
7910
7911
7912
7913
8911
8912
8913
9911
39 6
49 7
49 8
4912
5914
6911
6913
6914
79 8
79 9
7910
7911
7912
7913

‘OCDQO‘U‘IJ-‘UJN

337998010
339290400
338492721
348398299
347595201
346699423
345891027
344990092
343996711
343090996
342093073
341093086
338997576
340097008
340194273
342297047
338297352
343795334
342796495
341795462
340792396
339697473
338690885
340994192
339898870
338891844
341198895
349592983
349494852
349293754
348198711
347697913
348795700
348194784
347892158
349792493
349498392
349292130
348993872
348693796
348392099

337997479
339290868
338493640
348399249
347596229
346790381
345891964
344991045
343997588
343091838
342093770
341093524
338997728
340097182
340194293
342296865
338297061
343795838
342796788
341795658
340792678
339698029
338692560
340994921
339899931
338893388
341290289
349593228
349494818
349293344
348198795
347697202
348795752
348195382
347892578
349792769
349498616
349292366
348994544
348694988
348393409

90283
90283
90283
99999
90200
90140
90140
90140
90200
90140
90140
90140
90200
99999
99999
99999
99999
90200
90140
90100
90140
90140
90283
90200
90200
99999
90200
99999
99999
99999
99999
90283
99999
90200
90140
90200
90070
90200
90100
90200
90283

-90531

90469
90919
90950
91028
90959
90937
90953
90877
90842
90697
90437
90152
90174
90020

'90183
-90291

90504
90294
90196
90282
90556
91675
90728
91061
91544
91394
90244

‘90034
-90410

90084

‘90711

90052
90599
90420
90276
90224
90236
90672
91192

91309

ASSIGN-
MENT

00
00
QQ
Q0
00
00
00
Q0
00
00
00
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
OR
OR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
OR
OR
QR
QR
QR
QR
QR
QR
QR
OR
OR

7915
89 9
8910
8911
8912
8913
8914
9911
9912

CALCULATED
FREQUENCY

347694709
349790190
349493533
349194840
348894289
348592079
348198420
349398603
349097515
348794722
348794722
351493233
352192580
352799220
353493206
354094606
354693508
355290011
355794234
356296312
356796396
357294651
357791263
358196430
358690368
357390002
357796467
357892971
358297785
358791346
357992078
358799884
359292114
358497972
358990862
359392691
357792806
358198098
358691850
359094280
359495618
355991447
356494391
356995060
357493606
357990195
358395010
358798252
359290136
359690896

371

OBSERVED
FREQUENCY

347694298
349792769
349494818
349195834
348895947
348594600
348198795
349399916
349097955
348795752
348890380
351494313
352193571
352890174
353494232
354095653
354694434
355290767
355794598
356296345
356796874
357296070
357791636
358195423
358597255
357299582
357795557
357892121
358295985
358697939
357991467
358797678
359197860
358497498
358899355
359299354
357793247
358198913
358692176
359094394
359494595
355991673
356494655
356995456
357494328
357991467
358396251
358890012
359197866
359690740

DELTA
NU

90200
90200
90140
90100
90100
90140
90283
90100
90140
99999
90200
.0140
90140
90140
90140
90140
90140
90140
90140
.0200
90140
90200
90200
90200
99999
90070
90200
90070
90200
90140
99999
90140
90200
90140
90283
90200
90130
90140
99999
90140
90140
90100
90140
90100
90140
90200
99999
.0140
90283
90200

085-
CALC

‘90411
92579
91285
90995
91658
92521
90375
91313
90439
91030
95658
91079
90991
90954
91026
91047
90926
90756
90364
90033
90478
91419
90374

-91006

-93113

-90419

‘90910

*90851

'91800

-93407

‘90611

‘92207

‘94255

“90474

“91507

“93337
90442
90815
90326
90114

“91023
90226
90264
90396
90722
91272
91241
91760

‘92270

-90156

ASSIGN-
MENT

QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR
QR

89 8
89 9
8910
8911
8914
8915
99 9
9910
9911
9912
9913
9914
9915

CALCULATED
FREQUENCY

356695867
357196105
357694180
358190259
359398433
359798524
357399957
357897498
358392998
358796641
359198626
359599169
359998502

372

TIC)
may
n1m

O m
[71 <

4. I”

R D
U PCY
6697341
7196683
7695223
3 8191911
359492604
359891625
357491353
357898646
358393430
358892942
359197860
359692335
360094852

\JJ U) U)
U1 U] U1 U1

DELTA
NU

90200
90070
90200
.0140
90200
90283
90070
90100
90140
90200
90200
90140
90140

 

 

“111111117111“