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This is to certify that the
dissertation entitled

AN ANALYSIS OF THE DIGITALLY ENHANCED HIGH
RESOLUTION INFRARED SPECTRA OF

CD3Br AND CHSCN

presented by

Dale Edward Bardin

has been accepted towards fulfillment
of the requirements for

_EIL_D_._ degree in 2111.11515—

WW

Major professor

 

Date W /{L A“ 83

MSU is an Affirmative Action/Equal Opportunity lmtttuuon 0-12771

 

 

MSU

LIBRARIES

 

 

 

RETURNING MATERIALS:
Place in book drop to
remove this checkout from
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AN ANALYSIS OF THE DIGITALLY ENHANCED HIGH
RESOLUTION INFRARED SPECTRA OF
CD Br AND CH CN

3 3

By

Dale Edward Bardin

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1983

ABSTRACT
AN ANALYSIS OF THE DIGITALLY ENHANCED HIGH

RESOLUTION INFRARED SPECTRA OF
CDBBr AND CH3CN
By

Dale Edward Bardin

A signal averaging procedure has been developed to make
short segments of digital high resolution infrared grating
spectra linear in frequency and to sum the segments in phase.
Signal averaging can be used to increase the signal to noise
ratio, to increase the resolution limit, or a combination of
the two.

Combining signal averaging with other signal processing
techniques, the resolution limit of the v4 band of CD3Br was
increased enough to warrant a reanalysis that included an
x-y Coriolis interaction. The final resolution limit for
the v4 band was approximately 0.025 cm-l.
Signal averaging also increased the "signal strength"
of the weakly absorbing 2v5(i) band of CH3CN enough to
analyze it simultaneously with the v5 band. Analysis of
eighty (80) lines from the 2v5(l) band and one hundred

sixty (160) lines from the v5 band improved the values of

several molecular constants.

To my wife,

Linda

ii

ACKNOWLEDGMENTS

I wish to express my appreciation and gratitude to

Professor T. H. Edwards for his guidance, encouragement,

axui patience during the years of my graduate education.
Fkxllow graduate students James R. Gillis and William C.

Lane provided much help and many useful discussions. I

would like to give special thanks to Professor Paul Parker
‘for’teaching an excellent Molecular Spectroscopy course,

‘taught in addition to his normal teaching load.

I would like to thank the Michigan State University

Physics Department for providing me with a teaching assis-

tantship. I am grateful to The Timken Company for providing

unlimited computer services during the final stages of my

dissertation. Mrs. Delores Sullivan was very helpful with

both the typing and the format of this dissertation.

I especially wish to express my love and appreciation

to my wife, Linda, for her support and patience throughout

the course of this endeavor.

iii

TABLE OF CONTENTS

List of Tables
List of Figures

List of Appendices

Chapter
I Introduction
II The Symmetric Top Hamiltonian
III Digital Signal Averaging
Types of Noise to be Processed
Spectral Linearization
Choice of Alignment Trigger
Alignment Procedure
Effectiveness of Signal Averaging .
IV Experimental Configuration and Procedure
Experimental Configuration
Infrared Spectrophotometer Configuration
Infrared Pathway
Visible Pathway
Configuration Changes
Experimental Procedures

Experimental Procedure for a Calibrated Run

Run

Digital Signal Processing

iv

Experimental Procedure for a Signal Averagingi

vi

. vii

ix

24
25
32
34
35
38
42
42
42
43
44
45
47

47

51

55

Chapter

V

VI

VII
VIII

The Analysis of the v5 Band of CHBCN

Analysis
Weighting Scheme
Results
The Analysis of the 2v5 Band of CHBCN
Introduction
Procedures
Calibration
Analysis
Parallel Component of 2v5 of CH3CN
Results
A Review of Our Analysis of the v4
Conclusion

Appendix

I

II

III

IV

A Listing of the Focal- 12 Programs used to Signal

Average Spectra

A Copy of the Publication of Our Analysis
of CD33r . . . . . . . .
The Frequencies and Assignments of the v

4
of CD38r . .

The Frequencies and Assignments of the us
of CH3CN . .

The Frequencies of the 2v5(i). Band and the
2v5(fl) Band of CHBCN . . .

List of References .

3

of v

Band of CD Br

4

Band

Band

63
64
73
82
84
84
85
90
91
100
105
108
111

113

138

148

152

162

171

Table
Table

Table
Table

Table

Table

Table

Table

Table

Table

Table
Table

Table

LIST OF TABLES

The Darling-Dennison Hamiltonian.

Upper state energy levels (matrix) and
ground state energies.

Symmetric top selection rules.
Axially symmetric energy expression.

Generalized frequency expression (transitions
from the ground vibrational state).

Simultaneous frequency expression for v5,

2v 1, and 2v H of CH CN. . .
5 5 3

Summary of signal averaged N20 (120) data

versus single scan N20 (120) data. .

Experimental conditions used for the v5 band
of CHSCN data.

Single band Fit of v of CH CN.

5 3
Experimental conditions used for the 2v5
band of CH3CN data. .

Single band fit of 2v5(l) of CH CN.

3

Comparison of the K = 2 and K = 3 assign-
ments of the 2v5(fl) band of CH3CN.

Simultaneous fit of v5 and 2v5(l) of CHBCN.

vi

13
15
16

19

22

41

65
83

86
102

104
107

.Figure

Figure

Figure

Figure

Figure

Figure
Figure

Figure

Figure
Figure

Figure

Figure

LIST OF FIGURES

The v vibrational normal mode of CH3X
type Holecule is an unsymmetric C- H
stretch.

Deconvolution of two independent ”noisy"
scans of the same region of the (120)
band of N20 (deconvoluted in the same
manner). . . . . . . . .

Spectrophotometer noise at various stages
of processing. Real spectral lines, raw
and deconvoluted, at the same scale are
provided in G and H respectively for
comparison.

Two independent deconvoluted spectra, each
an average of eight scans, of the same
region of the (120) band of N20 (decon-
voluted in the same manner).

Illustration of data recorded on magnetic
tape and on chart paper during a typical
calibrated run, not to scale. . .

Data near the band center of the (120) band

of N20, shown with fringes.

Original, smoothed, and deconvoluted
spectra from the v band of CD3Br.

4
Survey spectra of the v5 band of CH3CN.

Q branch positions of us of CH3CN versus
KAK.

Residuals (Q branches minus quadratic fit)

for v5 of CHSCN.

cg versus KAK for v5 subband fits of CHBCN.

Residuals (calculated - quadratic fit) of
subband origins versus KAK.

vii

26

30

39

49
50

52
66 ‘

68

69
71

72

Figure
Figure

Figure

Figure

Figure

Figure
Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

RQ3(J) of us of CH3CN calculated from P.

RR3(J) and RP3(J) versus J for v5 of CH3CN.

Residuals from linear fits of RR3(J) and

R
P3(J) Versus J for us of CH3CN.

RR 6(J) versus J for us of CH CN.

3
Residuals from linear fit of REG (J) versus
J for us of CH3CN. . . . . . .

Survey spectra of the 2v5 band of CHBCN.

Q branches of 2v of CH CN versus KAK.

5 3
Residuals from a linear fit of low Q
branches of 2v5 of CHBCN.

B

as versus KAK for 2v5 of CHBCN.

Calculated subband origins of 2v5 of CH3CN
versus KAK. . . . . . . . .

Hot band frequencies near 2v5 of CH3CN Q
branches minus quadratic fit. . .

Hot band frequencies minus Q branch fre-

quencies of 2v of CH CN superimposed on
. 5 3

Figure 6.6. . . . . . .

of CH

RQ3(J) of 2v CN versus J(J+l).

R5 3

Residuals Q(J) of 2v of CH 3CN minus
linear fit) Rvgrsus J(J+I). .

viii

75
77

78
80

81
87

92

93
94

95

97

98

99

101

Appendix

Appendix

Appendix

Appendix

Appendix

I

II

III

IV

LIST OF APPENDICES

A Listing of the Focal Programs used to
Signal Average Spectra

A Copy of the Publication of Our Analysis

of v of CD Br . . . . . .
4 3

The Frequencies and Assignments of the v4

Band of CD3Br .

The Frequencies and Assignments of the v

Band of CH3CN .5

The Frequencies of the 2v5(i) Band and
the 2v5(u) Band of CH3CN . . .

ix

113

138

148

152

162

CHAPTER I

INTRODUCTION

With the development of quantum mechanics during the
1920's came rapid advances in many fields, including molec-
ular spectroscopy. Treating molecules as rigid rotors and
uncoupled harmonic oscillators, theorists were able to
model the spectra of many molecules. As the size of the
molecules studied increased and the experimental resolution
and precision improved, so did the complexity of the
required theory.

The basic theory of molecular spectroscopy has been
retumd over the years to match eXperimental and computa-
tional advances. Calculations of perturbed bands have been
particularly difficult. Only relatively recently have
Coriolis perturbed bands been analyzed with more than
marginal success.

All three bands studied in this dissertation, the v

4

band of CD Br, and the v5 and 2V5 bands of CH CN, belong

3 3
to the same vibrational normal mode (an unsymmetrical C-H

stretching mode, see Figure 1.1), and are Coriolis perturbed
by nearby levels. To analyze the data, we adopted the basic

theoretical approach used by P. M. Wilt of Centre College,

Kentucky. Wilt calculates the frequencies of the

1

 

Figure 1.1 The v vibrational normal mode of CH X type
molecfile is an unsymmetric C-H stret h.

transitions with the DiLauro and Mills Hamiltonian (1),
together with the Fermi matrix elements of Matsuura et
a1. (2), if needed.

Chapter II presents a brief development of the
Hamiltonian used to analyze the v4 band of CD3Br, and lists
the upper and lower state energies for v4 of CDBBr. Chapter
II also gives the single band and simultaneous frequency
expressions applied to us and 2v5 of CH3CN, as well as the
selection rules for infrared transitions.

Progress in theory inevitably requires progress in
experiment, and vice versa. Technological improvements led
to probably the two most important experimental developments
in molecular spectrosc0py in recent years, tunable lasers
and Fourier transform spectrometers. The application of
tunable lasers to molecular spectroscopy vastly improved
resolution, while the development of the ultra high resolu—
tion Fourier transform spectrometer, by Connes (3) of France,
enabled experimentalists to obtain a whole band with a resolu-
tion limit almost comparable to that of the tunable laser.
Unfortunately, tunable lasers are not able to obtain spectra
over a very large range and high resolution Fourier trans-
form spectrometers are very expensive (2$200,000). Because
of these limitations, grating spectrometers continue to be
the mainstay for much of high resolution infrared spectros-
copy, despite an order of magnitude lower resolution.

During the past two decades, computers have become very

sophisticated and relatively inexpensive. This has led to

the development of digital data processing methods by
several investigators. The techniques for use with high
resolution grating spectrometers include an improved means
of measuring line positions (4), sampling and smoothing (5)
to improve the signal-to-noise ratio (S/N), and deconvolu-
tion (6-8) to improve the resolution limit by as much as a
factor of three. However, one of the limitations of decon-
volution has been that the spectra must have a high S/N
initially (:50).

Chapter III discusses a signal averaging procedure
whereby spectra, having a S/N of 10-15 initially, can be
processed and then deconvoluted successfully. The signal
averaging procedure that we have developed makes short seg-
ments (12 to 20 cm-l) of a run linear in frequency,then sums
several linearized segments (scans) of the same region of
the spectrum. Ideally, the signal will add coherently and
the noise incoherently, improving the S/N by approximately
n5, where n is the number of scans summed. We normally sum
sixteen scans, improving the S/N by approximately a factor
of four. The new spectrum may be normalized to a desired
amplitude and then deconvoluted.

The results of signal averaging are impressive, but
many hours were spent determining the best procedure for
signal averaging. For this reason, our step by step recipe
to obtain and process the data is presented in Chapter IV.
The FOCAL programs used to process the data are included

in the appendices.

Peterson and Edwards (9) had previously analyzed the
v4 band of CDaBr, with the exception of the portion perturbed
by a Coriolis resonance. Signal averaging enabled us to run
the band at higher resolution and to resolve previously
unresolved transitions. This permitted an improved analysis
that, when coupled with an analysis of the perturbed portion,
improved the values of the constants for this band. Chapter

VII contains the new analysis of the v band of CD Br.

4 3

Barnett and Edwards (10) believed that they had devel-
oped a method to calculate A0 for symmetric tops by simulta-
neously analyzing a degenerate fundamental and its first
overtone. This particular rotational constant is difficult
to isolate. Peterson and Edwards (11) later showed that the

coefficient isolated was actually A0 - % Both of the

“tt °
above groups applied the simultaneous band analysis method
to various methyl halides (9,12-14). Until the development
of the signal averaging technique (in this instance, signal
adding would be a more descriptive name), the 2V5 band of
CH3CN was too weak to measure and assign a sufficient num-
ber of transitions to be analyzed simultaneously with the v5
band. The v5 and 2v5 simultaneous band analysis is the
subject of Chapters V and VI respectively.

Chapter VIII summarizes the results and offers sugges-

tions for future research.

CHAPTER II

THE SYMMETRIC TOP HAMILTONIAN

This chapter briefly outlines the development of the

band of CD Br

Hamiltonian used for the analysis of the v4 3

and of the v5 and 2v5 bands of CH3CN.

Historically, using the Schrodinger equation in other
than Cartesian coordinates was a non-trivial task. In 1928,
Podolsky (15) formulated a Hamiltonian in generalized
coordinates for a conservative system as:

—l n -i irs -&
H = (2n) 2 g prg g psg + U
r,s=l

where u is the reduced mass, {grs} is the coordinate system
metric, g is the determinant of {grS}, and the pa (where a
is either r or s) are the conjugate momenta of the particles.
This Hamiltonian was specialized to a semi-rigid rotating
polyatomic molecule by Wilson and Howard (16). Darling and
Dennison (l7) reformulated the Wilson-Howard Hamiltonian
into a Hermitian operator, which is usually more convenient

to apply. The Darling-Dennison Hamiltonian is listed in

Table 2.1.

Table 2.1

The Darling-Dennison Hamiltonian

 

u-% i

H = i I u&(Pa -pa >110,B

(P -p )u
a,B B B

-5 i
+ i u p*O u p*0u + V(Q )
$20 so

where, using the notation of H. H. Nielson (4),

a and 8 range over x, y, and z, the equilibrium prin-
cipal axes of inertia of the molecule,

Pa and p are the components of total and internal
angular momentum, respectively,

pgo are the momenta conjugate to the normal

i. e. p*O = -ifi a ,

so’ 3Qs so
(8 enumerates the normal 0mode and

o enumerates the degenerate mode)

 

coordinates Q

“a8 are the inverse moments and products of inertia

u is the determinant of {udB}

and
V(QS o) is the potential energy of the molecule as
a function of the normal coordinates Qso
a
= *
Also note that pa 3; Cso,s'o'Qsops'o' where Cso,s'o'
Slot

are the Coriolis constants for a given molecule.

 

An exact solution to the Schrodinger wave equation for
a rotating vibrating polyatomic molecule using the Darling-
Dennison Hamiltonian has not been found. Perturbation
theory through the fourth order provides sufficient accu-
racy for the cases presented here, however, the algebraic
complexities involved are formidable.

The Darling—Dennison Hamiltonian has been transformed
(18) to a form more convenient for perturbation theory by

first expanding H, V(QSO), and “as in orders of magnitude:

2

H = H0 + 1H1 + A H2 + °--
V(Q )=v +V +V +...=.:_L_ {AQZ
so 0 l 2 2 s s
so
+ X kso,le-l,SHGHQsoQSYOVQSHO" + ...
so
s'o'
SHOH
and
_ e e -l (0)aB (l)dB
u(1.8 - (10:18) [9 + ZQso Qso
so
(2)aB .0.
4' Z nso,s'o'Qson'o"+ ]
so
slot
where
(0)08 = e
9 IGBGGB

(1)aa _ aa = _ a o e 0 Y
Qso ' 'aso 2 E mi(Bi£iso+Yi£iso)’

(l)dB - a8 = Q 0 B a
S2so - 'aso E m1(aiziso+81£iso)’ a I B’

and a, B, y are cyclic,

and
(2)aB _ a B a B
Qso,s'o' Z ziso is'o' *- ,;,, z;so,s"o"‘:s'o' s"o"

1 s o
d6 86
so s'o'

+ I I

6 66

After expansion, a contact transformation of the form

113(1) -iAS(1)
e H e

I

_ — ' ' 2 ' .0. .
- H — HO + 1H1 + A H2 + is made.

This similarity transformation, first performed on the
Hamiltonian for polyatomic molecules by Shaffer, Nielsen and
Thomas (18), will generate expressions for the allowed
energies to second order by choosing the function 8(1) such
that the operator H6 + lHi will have only diagonal matrix
elements, with respect to vs, in the representation that
diagonalizes Ho.

During the mid 1950's, experimentalists improved
resolution sufficiently to require better than a second order
analysis. To obtain vibration-rotation energies to fourth
order, Goldsmith, Amat, and Nielsen (19-20) and Amat and

Nielsen (21-23) applied a second contact transformation to

the once transformed Darling-Dennison Hamiltonian such that

. 2 (2) _. 2 (2)
eil S H' e 11 S = H

n n + AH" + AZH" + ABH” + ...

= Ho 1 2 3

where 8(2) is chosen to diagonalize H3 + AH; + 12H; with

respect to the quantum number vS in the representation that

diagonalizes H0. Amat and Nielsen (21-22) list the

u...-

I.

*~---

 

 

.
4
\

 

 

10

coefficients of the S function as well as the explicit form
of the twice transformed Hamiltonian.

Usually nondegenerate perturbation theory can be used
with both contact transformations. There are, however,
denominators in the coefficients of 8(1) and 8(2) of the form
anus + boos, - cons" . These terms arise when the first order
anharmonic term in the potential energy of the Hamiltonian
is transformed. But when two frequencies such as aws + bw ,

s
and cm ,. are nearly equal, i.e., accidentally degenerate,

s
ruandegenerate perturbation theory is no longer valid and
degenerate perturbation theory must be used (24).

The approach of DiLauro and Mills (11) was adopted to

apply the Darling-Dennison Hamiltonian to the v band of

4
CI)33r and the v5 and 2v5 bands of CHBCN, both molecules are
(If the C3v point group. DiLauro and Mills approximate the
nm>lecular Hamiltonian as a rigid rotor, Hr’ a collection of
simple harmonic vibrators, RV, and the appropriate cross

txarms to take into account the Coriolis interaction, H':

H = Hr + HV + H

Where
_ 2 2 2
Hr - B(Jx + Jy) + AJZ
__ 2 2
HV - Z Mpr + ArQr)
r
H' =

-2B(prx + pny) - 2Asz2

and where Jo and Pa (d ranges over x, y, and z of the

appropriate molecular axes) are the components of total and

Vibrational angular momenta respectively, A and B are the

 

 

 

I..‘
*ua

 

,

b.
‘v

.

.-
- ~
v

 

 

 

ll

prolate symmetric top rotational constants, Pr,=-ifi Sér' is
the momentum conjugate to the normal coordinate Qr’ and
Ar = 4n2c2v: is the force constant in that coordinate.

When two vibrational normal modes of the same symmetry
:Lre degenerate, or nearly so, the resulting motion consists
«of both vibration and rotation. This Coriolis coupling
manifests itself in the Hamiltonian as H' , which mixes the
\hibrational and total angular momentum operators. The

nuatrix elements are obtained from degenerate perturbation

theory and are of the form, ny[J,k],

‘where
.. 1 . y 9: it
ny - 7?- B CrSEWr/VS) +(VS/Vr) ]
anti
[J.k] = [J(J+1)-k(k+1>]*

Another term was added to the DiLauro and Mills
Hanultonian to allow for a coupling of vibrational states
tnirough the first anharmonic term in the potential energy
(a.Fermi Resonance). Following Matsuura et. al. (2), J

dependent Fermi matrix elements of the form

k I
W = —S—l—$—+aJ(J+l) were used.

2/2'

A third resonance that should be considered is that due
to Z-type doubling. Grenier-Besson (25) showed that the
lvt,£t+l;J,k+1> and |vt,£t-1;J,k—l> states are coupled by
the héz term in the second order contact transformed
Hamiltonian. Non—zero matrix elements occur when A£t= :2

and Ak==22 and have the form (26):

 

12

<vt,£t+l;J,k+1|H'Ivt,£t-1;J,k-l> =

[%]qé+)[(vt+1)2_£f]é{[J(J+1.)—k(k+l)][J(J+1)-k(k-1)]}é

These terms are usually negligible because of the size of
q£+). The exception occurs when the two coupled states are
degenerate, i.e. for the K==l, |£|==l states. However, for

C molecules, only one subband of the perpendicular band

3v
is affected, as shown by Anderson and Overend (27). If the
affected subband is excluded from the analysis, the matrix
that must be diagonalized is greatly simplified.

With this model, i.e., the Hamiltonian used by
DiLauro and Mills plus allowance for a Fermi interaction,
F. W. Hecker and P. M. Wilt wrote a computer program to
Predict the spectrum, given the molecular constants. The
uPper state energy levels were calculated by diagonalizing
a 4X4 matrix for each value of J', with k==J', J'-l, ...,
‘J'. Table 2.2 lists the 4X4 matrix and the expression for
““3 spectrum of the v4 band of CD3Br. The requisite
SYHunetric top selection rules are listed in Table 2.3
The same Hamiltonian was applied to the v5 and 2v5

bands of CH CN. To simplify the analysis and allow a simul-

3
ta-Ileous fit of the two bands, transitions that were perturbed
wereeexcluded, leaving only diagonal matrix elements. The
generalized energy expression in Table 2.4 is obtained by

replacing the equilibrium rotational constants with the

corresponding effective rotational constants as follows:

nVF-l

k

Q

o

awn-an

 

«.1.

Cu...

..t.\

V

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o'>sI-

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unsighA-~

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.\ Dupi.

.AH+wos + a u a .Amu+muVu n

13

 

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0 “you .AHinusu "mu cons hmBOH .Huuawnumw cons some» mcmfim soaosv

 

 

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v m N m
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Ax.s.s~>.s~>. >vm
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as I ass I we .
«a .a NEAH+svwv .o NAH+svms .o
0 0
wiw: + vwaH+nvch + fiwxvu <m I Nwamlw<v + Aa+wvhwm + W9 u M onmna
m A2.s..~>cm
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A - ....~..\ mu .3 .‘........

14

x

ass I msfifl+svsxmo I «Afi+scmsma I mxA:mI:<o + Aa+svszm I on

w
a co: m

31h.

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museum one .H n x< sons .nH+x_ 09 com H“ u x< dons omBOHHd mam .Am_ 09 mnofipamddhp mafia?

HAH+scx I Aq+svsu u fix.sm .Hmaa>\m>v + «Am>\s>cumMu.m u as:

A.ssooc w.m sfisas

 

15

Table 2.3

Symmetric Top Selection Rules

 

 

 

Parallel band:

Perpendicular band:

for v

for th:

 

AK
AJ

AJ

AK

AJ

AZ
AK

 

 

21

22

23

31

32

41

42

43

4.4

16

Table 2.4*

Axially Symmetric Energy Expression

- BeJ(J+1) + (Ae-Be)l(2 + zsms(vs+gs/2)

a -2AeZt§tthK

= -D:J2(J+1)2 -D:KK2J(J+1) 0:13

- —zsa:(vs+gs/2)J(J+l) -£s(a:-a:)(vs+gs/2)K2
' 2

ss' xss'(vs+gs/2)(vs'+gs'/2) +Iztt' thLtILtLt'

sSs' tst'
. J
ZtntttJ (J+l)1(

K 3
a zanLtK +'ZtEnt+zsnt,s(vs+gs/2)3th

2
=- 259‘; (vs+gs/2)J2(J+1)2 +283:K(vs+gs/2)x J(J+l)

x A
+£sBs(vs+gS/2)K
B
a {288' YSSI(Vs+gs/2) (Vst‘l'gsI/2)+Zttt YL L .LCLC'
I s C C
858 CSC
2 A
We}[J(J+1)'K] + {288' YSS'(VS+83/2) (VSI'l‘gsI/Z)
sss'
2
+2cc' Ytttt.Lth'+AAe}K
tst'
= HgJ3(J+l)3 mibczlzunf + HgJK4J(J+1) +R§I<6
" XSS isIIYss 'S"(vs+88/2) (Vs I+85 t/z) (Vsu'l'gsn/Z)
SSS'Ss"
+DEstt'ysLtLt.(vs+gs/2)Ltét' + Esaws(vs+gs/2)

tSt'
(cont. on next page)

*T
akeTl from reference (28).

17

Table 2.4 (cont.)

Description of Energy Parameters

Quantity
s,n,t

B ,, A.

e e
ms, 8s

2
C:
B A
as: as
J JR K
De. De ,pe
88', x
LtLtI

3' .

33' ystttt.
SJ JK K
8’ BS ’ as
J

11:. 11‘:

A.

Y

Description

5 is an index of a given vibrational mode.
n will refer to a specifically non-degenerate
mode; t, the degenerate modes.

 

Be - h e A . 'fi e
Am C I e do c I
x z
e e . .
where Ix ' Iy where z is the ax1s

of symmetry

designate a purely harmonic frequency w
of a normal mode 3 having degeneracy gs.

coriolis coupling constant about the symmetry
axis.

coefficients of vibrational corrections to
Be and Ae

corrections due to centrifugal distortion
of equilibrium configuration.

first-anharmonic corrections
second-anharmonic corrections

third-order changes in centrifugal terms due
to vibration.

third-order corrections to ;:

fourth-order corrections to Ae

fourth—order corrections to Be

fourth-order corrections due to centrifugal
distortion.

fourth-order correction to w having the
same quantum dependence as ms

fourth order corrections to A and B ,
having same quantum dependence at A8 3nd B

 

 

‘

18

_ A A
Av — Ae - g ascvs+gS/2) + 828' vss.<vs+gS/2><vs.+gS./2>

s<s '

A
+ Z y ,££ , +AA
tt, tt tt
tst'
B = B -za3(v +g/2)+ z YB (v +g/2>(v +g m
V e s s s , ss‘ 8 s s' s'
s 5,8
sss'
+ Z YEt' ltlt, + AB
tt'
tgt'
and
Dm

a m_ m =
v De g Bs(vs+gS/2) where m J, k, or JR.

The frequency of a particular transition may be calculated

£
E(V 5,J’k) E d(J:k)
from _ 15m " ill—r— . The generalized single band

 

freQuency expression is given in Table 2.5. The simultaneous
ireQuency expression may be obtained by inserting the
appropriate selection rules into the generalized single

band frequency expression. Peterson and Edwards (11) give
the Correct expression for the v4, the 2V4 (II), and the

2v4 (i) bands of CD31. Since the v5 and 2v5 perpendicular
and parallel bands of CH3CN are the same normal modes as
the V4 and 2v4 perpendicular and parallel bands of CD31, a
Simple substitution of 5 for 4 in the subscripts will yield

th
e Correct simultaneous frequency eXpression for CHBCN

 

 

o n
5-"
unit.

19

TABLE 2.5
Generalized Frequency Expression (cm-1)

(transitions from the ground vibrational state)

 

AK =
(vnivn+1a'°'rvtamt’vt+lsmt+la"°) MK(J)

Es (ms + ALIJs)vs +
ZSZSIXSSIEVSms/Z) (vs,+-gS,/2)-gsgs'/41 +
sSs'

tht'xt. Lt.
csc' t

+
ALgME.

28:3 tzsuyss ISHE (Vs'l'gs/Z) (VS l+gs 1/2) (Vsn'IBsn/z) ‘gsgs igsli/B] +

853.53"
zsztztss, , .cvsargs/zmtat. +
tst' t t

AOI<K+AK)2-K2] +
301 (J+AJ)(J+1+AJ)-J (J+1) - (K+AK)2+K2] +
s z .
I uezttt utmtmtmsnts(vsms/ZHMEJIHAK] +

‘9th (J+AJ)2(J+1+AJ)2-J 2 0+1) 2] +

 

l angt (K+AK) 2 (J-l-AJ) (J+l+AJ)-K2J(J+1)] +

l ‘DOKI (mama-K4] +

[-2 A A
Sas vs‘."‘-':s£s 'Yss ' (vsvs 'ngs ' /2+vs ,gS/Z)

355'

A 2
fitztwfi,’ 'MtMtJUK-t-AK) ] +
tst'
(Cont. on next page) ‘

*T
aken from reference (28)-

III-IIII-___

20

TABLE 2.5 (cont.)

Generalized Frequency Expression

- B B
L 2503 VS+ZSZS.VSS.(vsvs.+vsgs./2+vs,gs/2)

535'

a 2
+2tzt. LtLt'MtMtJUJ'l'AJ)(J+1+AJ)-(K+AK) 1 +

tSt'

ztntJMtI (MAX) (J+AJ) <J+1+AJ)3. +
x 3
Stilt acid-tax) 1 +

ZsBszs[(J+AJ)2(J+1+AJ)2] +

xsaivaL (K-i-AK) 201w) (um-M )1 +
£538Kv8[(K+AK)4] +

HOJY, (1w) 3 (may) 3-13 (1+1) 3] +

H311 (K+AK) 2 (J+AJ) 2 (J +1+AJ) 2 -K2J 2 0+1) 2] +
II13JUI<+AK>4<J+AJ> (J+1+AJ>-K“Jo+1>] +

RISE (K+AK) 6-x6]

21

[Table 2.6). The program SYMFIT (28) uses the simultaneous

frequency expression to determine the molecular constants.

 

22

Table 2.6

Simultaneous Frequency Expression for

a:
v5, szfl, and 2v5L of CH3CN

 

KAJK(J) -{Bo[(J+AJ)(J+l+AJ) - J(J+l) - (K+AK)2 + K2

-Dg[(J+AJ)2(J+1+AJ)2 - J2(J+l)2]
-DgK[(K+AK)2(J+AJ)(J+1+AJ) - K2J(J+l)] =
’OCVS) or
' (2v .L) or + [A - 1-n S][(K+AK)2 - K2]
0 5 o 3 5

c,(:ZHo5fl)

_. z 1 5
2Ae‘5 + n5 + [22'] g "ssgs + [§]n55][A£5(K+AK)]

__ it 1 A A 2 A 2
€155 + [§]5§5Y85 + S§5y55][Av5(K+ K) ] + 735(Av5+2)Av5(K+AK)
£8 2 2

Y AI. ) K+AK)
£5£5][( 5 ( J

~Q§ +.;. Z 73 + 2 y ]Av5([J+AJ][J+1+AJ] - [K+AK]2)

A; s<5 Ss s>5 5s
58 ( Av5+2)Av5[(J+AJ)(J+1+AJ) - (K+AK)2]

E3 { Az )2[(J+AJ)(J+1+AJ) (K+AK)2] + (-DK)[(K+AK)4 K4]
€5£5( 5 - O - "

s A£5(K+AK)3 + mg A£5(K+AK)(J+AJ)(J+1+AJ)

K 4 JK 2
s Av5(K+AK) +35 Av5(K+AK) (J+AJ)(J+1+L\.J)

I 2 K 6
5 Av5(J+AJ) (J+1+AJ) + Ho[(K+AK) — K

p»
L.
D

61

J
E(K+AK)4(J+AJ)(J+1+AJ) - K4J(J+1)]

-E:
E (K+AK)2(J+AJ)2(J+1+AJ)2 - K2J2(J+1)2]

(cont. on next page)

23

Table 2.6 (cont.)

Hg[(J+AJ)3(J+1+AJ)3 - J3(J+1)3]

l k Av

2
2 q56061 5(J+AJ)(J+1+AJ)(2 J -1)

 

 

Taken from reference (11).

CHAPTER III

DIGITAL SIGNAL AVERAGING

The averaging of repeated scans, or signal averaging,
has long been recognized and routinely used as a powerful
technique to enhance the signal-to—noise ratio (S/N) in many
areas of the physical sciences. To our knowledge, signal
averaging has not been applied routinely to high resolution
infrared spectra obtained on grating spectrophotometers
llecause of the special difficulties, which will be discussed
below.

Peter Jansson briefly mentioned the possibility of
fisignal averaging high resolution infrared data in his Ph.D.
(iissertation at Florida State University in 1968, but he did
not discuss procedures or applications.

Paul D. Willson stated in his 1973 Ph.D. dissertation
Sit Michigan State University that "... averaging of repeated
ruins has not been possible because our monochromator is not
ciriven sufficiently linearly and reproducibly," i.e., the
:frequency spectrum is neither linear nor reproducible.
frhese have been the major obstacles to signal averaging with

grating spectrophotometers.

24

This chapter will describe an algorithm to render
linear in frequency a short section (scan) of digitally
recorded spectra obtained on our high resolution grating
spectrophotometer. Several trigger mechanisms to align

scans for averaging will also be discussed.

lypes of Noise to be Processed
Developments of digital signal processing techniques,
such as multiple sampling (5), followed by smoothing (5),
and deconvolution (7), make possible an increase in the
resolution limit by a factor of from 2.5 to 3.0 for
digitally recorded high resolution infrared spectra,
assuming a sufficiently high initial S/N (e.g., S/N ~ 50).
A S/N of 50, however, is not always possible, such as when
-increasing the resolution limit by decreasing the slit width
111 an effort to resolve closely spaced lines.
Figure 3.1 demonstrates the inconsistencies that
Occurred when an attempt was made to deconvolute two
idadividual "noisy" scans of the same region of the spectrum

()f N 0. We believe these unsatisfactory results are due

2
Ixrimarily to low and medium frequency noise, low frequency
ruoise being noise with features having a "full width at half
Ineight" (FWHH) comparable to that of a single line. In all
(bf our spectra, high frequency noise has been reduced

(effectively by RC smoothing, multiple sampling, and digital

smoothing ( 5 ) .

26

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mo :oflwos beam one go madam :zmfios: acmpsmaoosa 03p 90 cofipaao>=oowa H.m ohswfih

 

 

 

 

 

 

¢
no
“<r
N

 

 

 

 

 

é

 

 

 

 

 

 

 

 

 

 

 

 

 

28

In principle, there are two possible solutions to the
problem of low and medium frequency noise. The first is to
scan at a slower rate and change the RC constant, sampling
rate, etc., appropriately. Scanning at a lower rate is
effective for noise with a white power spectrum, is com-
pletely ineffective for f.1 noise, and is somewhat effective
for other types of noise (29). Unfortunately, we normally
scan our grating spectrophotometer at as slow a rate as can
be tolerated without introducing nonuniform frictional
problems, associated with rotating the grating, that cannot
be solved with our present equipment.

The second possible solution is to average repeated
scans of the spectrum, i.e., to signal average. Although
Signal averaging is ineffective for some kinds of noise,
Such as noise that is correlated with the signal, the
Jajority of noise power distributions can be signal averaged
effectively. Ernst (29) has shown that for several kinds of
loise (such as white noise, certain types of low pass RC
filtered white noise, and f"1 noise) the signal-to-noise
ratio increases approximately as the square root of the
lumber of scans averaged together. Furthermore, for noise
from non-recurring events, such as transients due to the
opening or closing of a switch, the S/N increases even
faster, viz., directly as the number of scans averaged
together.

The effectiveness of signal averaging for improving the

3/N in a given situation can be tested experimentally. To

29

test the effectiveness of signal averaging for our spectro-
photometer and procedure, we evacuated the sample cell after
a typical run and continued recording the output of the
system. Since there was no absorption of the signal by a

sample, the recording consisted only of real spectrophoto-

meter noise on top of a presumed fairly steady signal,

processed with our normal RC and sampling settings.

Figure 3.2 shows scans of our spectrophotometer noise
at various stages of processing. The top row shows a single
scan (3.2a), an average of four scans (3.2b), and an average
of sixteen scans (3.2c). The noise for the average of four
scans (3.2b) has a measured root mean square (RMS) deviation
from the baseline (2.10-1) times that of a single scan,
whereas, the noise for the average of sixteen scans (3.2c)
has an RMS deviation (3.94-1) times that of a single scan.

IFigures 3.2d, 3.2e, and 3.2f are the results of digitally

:smoothing Figures 3.2a, 3.2b, and 3.2c respectively.

13.2g shows a short section of a signal averaged spectrum;

3u2h shows the same section after digital deconvolution.

Some actual spectral lines are shown at the bottom to

provide both vertical and horizontal scales for comparison.
A visual comparison of parts 3.2a and 3.2d reveals that
digital smoothing significantly reduces high frequency noise,
‘but is not very effective on low and medium frequency noise.
In contrast, signal averaging not only reduces low frequency
noise (compare f with d), but also reduces high frequency

noise (compare 0 with a). We both digitally smooth and

' Signal average to reduce noise on our spectra.

¥+

 

 

 

30

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m was 0 ca pmcfi>ona was mason meow map as .cmpsao>:ooms use any .mm:HH

Haapomqm Hwom

.wswmmoooss yo momsum muoHns> pd omfioa nmuosoaongoapooam N.m ossmflm

 

 

32

Inspection reveals that there are several noise features
in the single scan (3.2a and 3.2d) whose height and width are
comparable to the weakest real spectral lines shown in 3.2g.
Such noise features would be enhanced by the deconvolution
program in the same manner as the weak real spectral lines
(compare 3.2g and 3.2h). Thus, the average of sixteen scans
may be deconvoluted more reliably than the single scan be-

cause the low frequency noise features are much reduced.

§pectra1 Linearization
To signal average effectively, the noise must add

incoherently but the signal must add coherently. To add the

signal coherently, the scans must be reproducible (excepting

noise) and must have a reliable trigger to align the scans.

'The more reproducible the scans are, and the more reliable

‘the trigger is, the better the results from signal averaging.
()ur original data are not accurately reproducible and often
«do not have an obvious, reliable trigger.

Our data are sampled linearly in time and calibrated as

‘i function of frequency in cm-l. Our data are not linear in

1frequency, however, because of grating dispersion, which
Vtiries monotonically with grating angle, and nonlinearities
ill the grating drive. The nonreproducible grating drive
l1<>nlinearities have two basic causes, cyclical errors in the

grating drive train gears, and a drive system that is not

1>€3rfect1y rigid. The undesirable effects of the grating
(ilfive nonlinearities must be counteracted in some way to

ac}; ieve reproducibil ity .

¥

33

In our spectrophotometer, visible light interference
fringes are sampled digitally and recorded on magnetic tape
alternately with the infrared data. The fringes provide a
coordinate system to measure infrared frequencies as described
in Rao, Humphreys and,Rank (30). This process intimately
couples the two signal records such that any nonlinearity
that occurs in the infrared data also occurs in the fringe
data in essentially the same way. Thus, should the fringe
spectrum be made linear and reproducible, the infrared
:spectrum would also be made linear and reproducible by the
same operation.‘

In principle, the interference fringes are equally
spaced in frequency. The number of data points recorded
laetween fringe peaks, however, varies due to the causes
Inentioned above by as much as four percent of the average
liumber of points between fringes. Since the fringe peaks
tare equally spaced in frequency, the region between the
:fringes should be sufficiently linear in frequency. The
(iata are nonlinear and not reproducible, because of the
Inonlinearities in sampling as a function of frequency. If
1111 regions between fringes could be made to contain the
Same number of data points, the scans would be linear in
II‘equency.

In practice, the fringes themselves need not actually
IDES reconstructed. The fringe spectrum is separated from the
itlfrared spectrum by the computer program SYSTEM (see

czklapter IV) so that a data point and its associated fringe

¥

 

34

point would have the same magnetic tape coordinate, but on
different tapes. The fringe positions are measured in tape
coordinates and linear interpolation is then used on the
infrared spectrum to construct the desired number of points
between adjacent fringe positions. In this manner, the
individual scans of infrared data are rendered both

reproducible and linear in spectral frequency.

goice of Alifignment Trigger

In addition to linearity and reproducibility, successful
signal averaging requires that the signal must have some con-
Sistent feature (a trigger) to align the scans, allowing the
Signal to add coherently.

Since our fringes generally have a high S/N, one logical
choice of trigger is a fringe (method A). Unfortunately,
the etalon generating the fringes increases in temperature
during operation so that in subsequent scans the position of
each fringe changes slightly in frequency, relative to the
infrared spectrum. Hence, when fringes are used to trigger
the sum, the successive scan signals will add more and more
Out of synchronization.

Another logical choice for a trigger is a single prominent
line in the infrared spectrum (method B). Often, however, the
8/N is not large enough to ensure the reliability of such a
1:I‘igger, resulting in reduced resolution and a broadening of

the signal averaged lines.

 

 

 

 

 

‘o

‘--

 

35

A trigger comprising many lines in the scan would
statistically increase the reliability for triggering on
lines (method C). A least squares fit of the line positions
in one scan versus the line positions of another should
provide a more reliable trigger.

Method C was not used until late in my analysis, but
was then used very successfully on a region of the spectrum
where every other method had failed. The region had many
tweak lines whose apparent shapes changed from scan to scan.
'This method was not applied to any other spectral regions
and so remains incompletely tested. Based on this single
zipplication, however, I would use this triggering mechanism
as my first choice in the future.

If the scans were sufficiently linear and reproducible,
the entire scan could be used as the trigger by employing
(aross correlation (method D) or the method of least squares
(nmmhod E). The time to process the data would probably be
Iprohibitively long, however, if the processing were done on

a.uucrocomputer or a minicomputer. Hence, we selected only

£1 portion of the linearized scan to trigger on. A suitable
Portion of the spectrum should have no incompletely resolved
SDectral lines and the lines should not be susceptible to

lJlrge changes of intensity with small changes of pressure.

£13;1gnment Procedure

Once the scans have been linearized and a suitable

t:1?igger chosen, the scans are ready to be summed.

 

36

As a first approximation, the position of a particular
strong line is found for each scan and each scan is roughly
aligned by compensating for any differences in the position
of that line. This usually aligns the scans to better than

20.005 cm'1

, but the fit needs to be improved before summing.
The method of refinement depends on the type of trigger.

If the actual spectrum is the trigger, in whole or in
part, then either a cross correlation or the method of least
squares can be used to determine the relative displacement

that optimizes the fit between two scans. The discrete form

of the cross correlation integral is given by:
G=Zg.={2[f.*h..]
11 ij 3 3+1

th

where fj is the value of the ordinate at the j point of

scan f and hj+i is the value of the ordinate at the (j+i)th
point of scan h. The subscript i is varied to provide a
relative displacement between the two scans. The two scans
fit together best when the maximum value of gi occurs.

The method of least squares, when applied to the
spectrum (or a portion of the spectrum), determines the best
fit by finding the smallest value of g1, where now

2
= C - h . f O , . .
.gi’ g [fJ j+1] , h and 1 hav1ng the same

J J'+i’
(definitions as given in the previous paragraph.

If the rough fit is refined using the position of many
J;ines, the method of least squares is used. As usual with

the method of least squares, the best fit occurs when

Eg'- = X [f. - h. .]2 is a minimum, where j identifies a
1 j J 3+1

37

particular line position in scan f and scan h, and i is
again an index to move the scans relative to each other. In
all of our cases, the index i is moved about 0.02 cm.1 above
and below the position of the rough fit by increments of
0.001 cm-l.
When averaging more than two scans, the procedure is
as follows:
1. A copy of the first scan is made in an empty file.
2. The best refined fit is found between the second
scan and the first scan.
3. The second scan is then added to the first scan,
appropriately displaced.
4. The third scan is then compared to the normalized
sum of the first two, assuming the trigger is a
region of the spectrum. If the trigger is the
position of several lines, all scans are compared
to the first scan (the best choice would be to
remeasure the position of all lines after adding
in each scan, but this requires a prohibitively
long time for our system). The third scan is then
added to the sum of the first two, appropriately
displaced.
5. Step 4 is repeated for each remaining scan.
6. The sum is then normalized to the desired signal

strength for further signal processing.

38

Effectiveness of Siggal Averagigg

To examine the effectiveness of signal averaging, the
region near the band center of the (1,2,0) band of N20 was
studied. Two single scans and two averages of eight scans
were deconvoluted identically and compared.

Figure 3.1 compares two single scans of N20 that have
been deconvoluted. Even though each scan was deconvoluted
in an identical manner, there are considerable differences
in the appearance of the two scans. Figure 3.3 also shows
two scans that have been deconvoluted in an identical man-
ner, except each scan is an average of eight independent
scans (sixteen total). It is clear that a factor of approxi-
mately lg'higher S/N in the two averaged scans, deconvoluted,
led to a substantial improvement in consistency and apparent
line shapes.

The reliability of these results was also examined by
comparing them with higher resolution interferometer measure-
ments (31). Seventy-two spectral lines of N20 were measured

in the 2462-2476 cm-1 region of the spectrum for four cases:
a single smoothed scan, a single deconvoluted scan, an
average of sixteen scans smoothed, and an average of sixteen
Scans deconvoluted.

The seventy-two lines were compared to the higher
1Nesolution data for each of the four cases. A comparison of
1the signal averaged data to the higher resolution data yields
1

El fit with a standard deviation of 0 = 0.0013 cm- Table 3.1

5summarizes the results. Column 1 lists the four cases and

 

39

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.aspomam pmusao>coomc pampsmampsfi 039 m.m madman

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

41

column 2 lists the number of lines of the original seventy—

two that lie within 0.0039 cm’1 (30) of the higher data. It

should also be noted that 0 for sixty-three lines of the
single scans was calculated to be approximately 0.0040 cm‘l.

We conclude from these comparisons that the averaged

snzans yield appreciably better results. Furthermore, the

zrveraged scan may be deconvoluted to enhance the resolution

Wtith assurance that the frequencies measured are reasonably

accurate .

[sable 3.1 Summary of signal averaged N20 (120) data versus
single scan N20 (120) data.

Number of Lines Out of
72 within 0.0039 cm‘1
of Reference 31

Case

 

‘

Single scan, smooth 45
Single scan, deconvoluted 46
Ikverage of 16, smooth 63

63

Average of 16, deconvoluted

-\

CHAPTER IV

EXPERIMENTAL CONFIGURATION AND PROCEDURE

Chapter IV is divided into three parts, experimental
cc>nfiguration, experimental procedure, and signal processing
P1?ocedure. Part one briefly describes the configuration of
tile spectrophotometer and changes in the configuration.
l<>re detailed descriptions of the spectrometer can be found
-II the dissertations of J. L. Aubel (32), D. B. Keck (33),
LIld J. R. Gillis (35). The experimental procedure used to
?£ecord the high resolution spectra on the Michigan State
Jtliversity near infrared spectrophotometer is discussed in
thrt two. Part three describes the algorithms used to

Dlrocess the infrared data digitally.

Eecperimental Configuration

Iggfrared Spectrophotometer Configggation

The Michigan State University high resolution infrared
sDectrometer (references 28, 32—35) is composed of eight main
SSubsystems categorized by function: the infrared and visible
SiOurces, pre— and post-optics of each” the White type multiple
tiraverse cell, the Littrow-Pfund monochromator, the fringe

‘System, the detectors, the electronics, the PDP-12

42

43
minicomputer. All mirrors in the discussion that follows are

front surface mirrors.

_Igfrared Pathway
An electrical current of approximately 350 amps is sent

through a carbon rod with a small wedge shaped cavity that

acts as a blackbody radiator in the infrared region of the

SIJectrum. The carbon rod is mounted in a pure argon atmos-

Pllere and surrounded with a water-cooled housing (28, 33).

A series of four mirrors reflects the infrared radiation into

the White type multiple traverse cell and changes the f/#

from f/5 to f/20. Several mirrors focus the radiation not

absorbed by the sample in the multiple traverse cell onto
the entrance slit of the monochromator and change the f/#
back to f/10. A mechanical chopper located between the

multiple traverse cell and the monochromator chops the

infrared at 450 Hertz. The 1.08 meter focal length Littrow-

Pfund monochromator contains three plane mirrors, a parabolic
mirror, and two diffraction gratings (a 300 line/mm grating

blazed for 5 microns, and a 600 line/mm grating blazed for

1 .6 microns) mounted back to back on a turntable. The

design allows either a single pass or a double pass configu-

I‘ation. The monochromator was used only in the single pass

Configuration for this work. The infrared post-optics

focuses the radiation onto the detector housed in a small

evacuated chamber with a Can window. The v4 band of CD3Br

Occurred in a region where our liquid nitrogen cooled

 

 

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44

photovoltaic indium antimonide detector was the most sensi-
tive, while the v5 and 2v5 bands of CH3CN occurred in a

region where our dry ice cooled photoconductive lead sulphide

detector was most sensitive.

V_isible Pathway

The visible light foreoptics focused the output for a

1(30 Watt zirconium arc lamp, mechanically chopped at 90 Hertz,

Ollto the entrance slit of the monochromator slightly above the
Jilnfrared. The visible ran "downhill" through the monochro-
flmator slightly below the infrared. ‘Appropriately placed
lltirrors and lenses directed the light to an etalon to produce
Edser-Butler band "fringes". A Littrow prism order sorting
Expectrometer selected the desired order to be detected by
‘tJae dry ice cooled RCA 7265 photomultiplier tube (PMT).

A general description of the electronics can be found
113 the dissertation of James R. Gillis (35); a summary is
provided here.

A Princeton Applied Research HR-8 lock-in amplifier
ifirst suppresses most frequencies output from the infrared
cletector, except those near 90 Hertz, then amplifies the
1?emaining signal. An adjustable gain amplifier further
Sumplifies the signal into the voltage range of an analog-to-
(ligital converter (ADC) for a PDP-12 minicomputer.

The visible light fringes were processed in a similar
Inanner. The PMT converted fringe intensities into electrical

'V01tages. A Keithley 822 phase sensitive detector and a

45

Keithley 823 amplifier passed only those frequencies near

450 Hertz and amplified that signal. An adjustable gain

amplifier made the signal suitable for an ADC.

An interactive program named SYSTEM (36) samples and
stores the data on magnetic tape to await further processing.
The SYSTEM data sampling rate is adjusted to sample between

30 to 60 magnetic tape data points per full width at half

height of a single spectral line (5). Each of these magnetic

taupe data points is a multiple sample, averaging 32 consecu-

tive data readings. Multiple sampling is the digital analog

of electronic integration in that it sums data points to

improve the signal to noise ratio and to help to prevent

the aliasing of higher frequencies.

Conf igurat ion Changes
The configuration of the spectrophotometer as described

above was used to collect the CD33r data. The 2v5 band of

CH3CN, however, is weakly absorbing. In preparation for

recording the 2v5 band of CH3CN, we realigned the spectro-
photometer to optimize the signal strength, and corrected

Some minor problems before running the spectra.

The multiple traverse cell (MTC) was disassembled and

the mirrors replaced with a spare set. The old set was then

Sent to be resurfaced. An extra mirror was installed at the

end of the MTC nearest the foreoptics to allow observation
of the intensity distribution on the other two mirrors. At

sOllie point during the reassembly of the MTC, stress caused a

¥

46

flake to break away from the CaF2 entrance window. Realignment
of the foreoptics to avoid the flake was very difficult, and
probably not optimum. All mirrors in the foreoptics were
cleaned with non-flexible collodion (37) prior to realign-
ment.

The entrance and exit slits to the monochromator required
<11eaning and recalibration. Minor physical changes were then
made to permit the slits to open dependably and reproducibly.
Wllen reinstalled, however, the previous optic axis could not
13£e recovered for some unknown reason. This changed the entire
alignment of the system.

Unfortunately, at this stage of the realignment procedure,
the circuit breaker to the vacuum pump of the evacuated main
tank (i.e., the monochromator) tripped, turning the pump off.
TUhis resulted in oil from an overfilled oil reservior in the
Irump spraying back into the main tank, mostly onto the
300 line/mm grating, the large flat mirror, and the small
IJickoff mirror. The mirrors were coated with several applica-
tzions of non-flexible collodion to remove any oil. However,
1Ihe diffraction grating was not so easily cleaned. As
lPecommended by Bausch and Lomb, Xylene was dripped vertically
(iown the face of the grating with the grating remaining in
‘the mount. After treatment the grating appeared much cleaner,
IDut the effect on its efficiency is not known with certainty.

The small pickoff mirror at the center of the large flat
llad been dropped, necessitating replacement. The parabolic

Inirror had to be adjusted to accomodate the new optical axis.

IIIII-_._

47

The elliptical mirror in the post optics was cleaned
and realigned to optimize the amount of energy leaving the
Inonochromator and reaching the infrared detector.

It is not known how much the realignment process actually
inmroved the performance of the spectrophotometer. When one
compares CH3CN data from 1967 with current data, the data
:from 1967 has a superior resolution limit and signal to noise
Ifatio. The probable cause for the poorer performance is the
cLeterioration of the spectrophotometer components. Contami-
Ilation of the sample gas or basic changes to the configuration
<>f the spectrophotometer could also be major contributors.
The main advantage with the present CH3CN data, however, is
1:hat signal processing techniques allow more information to

1>e extracted. The data from 1967 cannot now be processed

vvith digital techniques.

Iflxperimental Procedures

figxperimental Procedure for a Calibrated Run

The procedure for collecting the data of a calibrated
:run is well documented (28, 30, 34, 35). The following
ssection will briefly review that procedure.

Some lower resolution surveys of the region of interest
are run to find the necessary experimental conditions, such
as highest and lowest frequencies, grating angles, etc.
High resolution trials are also necessary to determine such

IDarameters as gas pressure, slit width, signal to noise ratio,

etc.

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Suitable calibration gases (usually a simple linear molecule)
'whose frequencies are well known and bracket the region of
interest are chosen, again performing preliminary tests to
determine necessary parameters. The fringe order must be
chosen and the fringes in the region of interest must be
<3hecked to ensure the S/N is large enough and that there are
no anomalies.

To start a calibrated run, a calibration gas whose
Ifrequencies are well enough known to use as secondary standards
is let into the multiple traverse cell. Several calibration
].ines are then recorded. With the spectrophotometer still
nrunning continuously, i.e., with the diffraction grating
trurntable rotating and the output from both detectors being
Jrecorded, the multiple traverse cell is evacuated and then
:filled with the sample. The sample is removed from the cell
sifter the region of interest has been recorded. In the man-
tler described previously for the first calibration gas, several
].ines of second calibration gas are recorded. The entire run
:is simultaneously recorded on chart paper in real time to
nmonitor the progress. Figure 4.1 is an illustration of the
<>utput of the detectors and of what is recorded on magnetic
izape. The upper trace consists of calibration gas 1, the
ssample gas, and calibration gas 2; the lower trace is the
Ifringes. Figure 4.2 shows actual N20 data with fringes.
Iqotes can be made on chart paper to mark noise spikes, angle

‘Versus tape position, etc.

 

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The fringe spectrum is sampled alternately with the
infrared spectrum and continuously recorded throughout. The
fringe spectrum therefore provides a system of coordinates
that enables interpolation between the calibration frequencies
to determine the unknown frequencies because Edser-Butler
bands are equally spaced in frequency.

Standard processing is performed on the data, viz.,
digital smoothing and, if necessary, digital deconvolution.
The upper portion or trace of Figure 4.3 is original CD3Br
data as recorded on magnetic tape and then output to an
analog chart recorder; the center trace shows the data corres-
ponding to the data at the top after having been digitally
smoothed; the bottom trace shows the data corresponding to
the data at the center after having been digitally deconvolu-
ted. The positions of the lines of the calibration gases are
then measured in fringe numbers. A second order linear least
squares fit of the measured fringe numbers to the calibration
frequencies determines the scale of the coordinate system.

The line positions of the sample gas under study are then
measured in fringe numbers and converted to frequencies from

the relationship determined by the least squares fit.

Eéperimental Procedures for a Sigpal Averaging Run

The process of collecting data to be signal averaged
differs from collecting data for a calibration run. The
following section describes our method for collecting the
data in cases where the data is to be averaged to improve

the signal to noise ratio (S/N) sufficiently for deconvolution.

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Numerous tests must be run on the spectra of interest to
determine the best conditions for optimum resolution and S/N.
To increase the amount of absorption of the "blackbody"
radiation by the sample gas, the number of traversals in the
MTC may be increased. However, as the number of traversals
goes up, the signal loss due to multiple reflections with a
reflection coefficient less than one also goes up, and
eventually becomes larger than the ”increase in absorption".

A test on R of 20 of CH CN determined that the optimum

Q 5 3
number of trgversals for CHBCN runs was between 20 and 24.
The relative slit orientation must also be considered when
trying to increase signal strength. Because the image is
parabolic and the entrance slit is straight, the entrance
slit must be continually rotated as the angle of the grating
changes to maximize resolution. The resolution can also be
controlled by varying the width of the entrance and exit
slits: the narrower the slit widths the better the resolu-
tion. Unfortunately, as the slits become narrower, the
signal gets weaker while the noise remains the same, thus
reducing the S/N.

Finally, the resolution can be increased by as much as
a factor of 3 by digitally deconvoluting the spectrum (7, 38,
39). Tk>deconvolute reproducibly, however, it is necessary
to have a S/N of approximately 50 or better. The S/N can
be increased by approximately a factor of 4 by averaging 16
scans together. When the data is to be signal averaged, the

slit width can be decreased until the S/N is approximately

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12, without decreasing the final S/N necessary for effective
deconvolution.

In principle, the S/N improves approximately as n%, where
n is the number of scans averaged. However, there is not much
advantage to be gained by averaging more than approximately
16 scans. For example, the S/N can be improved by approxi-
mately a factor of 5 by averaging 25 scans, but the time
required to obtain 25 scans is 25/16 times longer than the
time required to obtain 16 scans. Thus, if 16 scans require
approximately 8 hours, 25 scans would require approximately
12.5 hours. Furthermore, the minimum S/N that can be tol-
erated in a single scan for effective deconvolution is only
reduced from 12 to 10. We have found that 16 scans is a
good compromise between S/N enhancement and the time necessary
to collect the data.

In principle, the interference fringes are equally spaced
in frequency. In practice, however, the interference fringes
are not quite equally spaced. For our purposes, scanning a
range of no more than approximately 20 cm.1 will assure a
sufficiently linear scan.

Some overlap between scans to check the calibration of
the two scans is desirable. For CH3CN, each scan contained
approximately 0.18 degrees (the grating turntable is rotated
by 0.18 degrees) scanned at a rotational rate of 0.01
degrees/minute. This permitted an overlap of approximately
0.025 degrees at each end of the scan.

To ensure that each scan contains the same region of

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should start at precisely the same angle. If one watches the
computer monitor while moving to the starting point, one can
start each scan at the same fringe, or at worst plus or minus
one fringe from the nominal. The end point of the scan is
not so critical, as long as one drives past the predetermined
stopping point.

Adjustments to the system are to be avoided during a
scan. The detector will need to have the coolant replenished
periodically, but this should be done only between scans so
as not to introduce unnecessary noise into the scan.
Amplifier and gain adjustments usually can be set so that
adjustment during a scan is not necessary.

Exceptions do occur however. For 2v of CH

5 3
of the fringes was relatively low and minor adjustments had

CN, the S/N

to be made continually to the order sorter.

With generally stable conditions the scans need not be
recorded on chart paper. Should some of the controls be
sensitive, the progress may need to be monitored over a long
period of time. A simple means of doing this is to record
the detector output on chart paper simultaneously, but at

a very slow paper feed rate.

Digital Signal Process

The procedure for collecting data to be processed was
described in the previous section. This section will describe
our method of processing the digital data. The types of

processing include frequency linearization, smoothing,

56

averaging (summing and then normalizing the signals to a
desired amplitude), and deconvolution. Digital smoothing and
digital deconvolution have been described elsewhere (refer—
ences 5 and 7 respectively).

The digital infrared signal is intially recorded alter-
nately with the digital fringe spectrum on magnetic tape. To
do any kind of digital processing at all, the two signals must
be separated.

The "Copy" option of the program SYSTEM is used to
separate the data. Several questions must be answered inter-
actively when this option (or any Option) has been invoked.
Two of the questions may require further clarification, viz.,
which points are to be copied and where to start copying.
When separating the data and fringes, every second point is
copied, since every other point belongs to the same data set.
Usually the infrared data are the even numbered points and
the fringes are the odd numbered. Thus to copy the infrared
data, the first point to be copied would be point zero, the
fringes would begin at point one.

The infrared data and the fringe data are copied onto
corresponding blocks of separate tapes. For example, sup-
pose the originaldata, both infrared and fringe, are on a
tape named 8A. Each tape consists of 2000 octal blocks plus
leaders on each end. If all 2000 blocks of tape 8A contained
data, there would be 1000 blocks of infrared data and 1000
blocks of fringe data. The infrared data might, for example,

be c0pied onto blocks 2 to 1001 of tape 8B. The fringe data,

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then, would also be copied onto blocks 2 to 1001, but on
tape 8C.

After separating the data, it is desirable that the data
be linearized in frequency. Over a 20 cm-1 range, the fringe
separation for our system varies from linearity by approxi-
mately 0.0003 cm_1. Thus, if two fringes at the beginning of
a scan are separated by 0.2000 cm'l, two fringes at the end
of the scan would be separated by 0.2003 cm—l. Since the
fringe peaks are theoretically equally spaced in frequency,
the fringe spectrum may be linearized simply by constructing
the same number of points between any two fringe peaks. Any
non-linearities in the frequencies of the infrared data and
the fringe data are closely correlated, hence, the infrared
data are linearized by following the same steps used to
linearize the fringes.

The fringe data and the infrared data are digitally
smoothed using the "Smooth" option of SYSTEM. The four-times-
quartic running average is applied over a length determined
by the full width at half height (FWHH) of the narrowest
single line of the spectrum. This is easy to determine for
the fringe spectrum since all lines have nearly the same shape
and FWHH. The infrared spectrum is a little more difficult
to smooth because the FWHH of the best single line must be
chosen.

After the fringes have been smoothed, a second order

linear least squares fit of the intensity of the highest

2n+l points (where n is usually 14) to their positions

58

determines the fringe position. The point at which the calcu-
lated slope is zero defines the fringe's position. Knowing
the spacing of the fringes, the number of points between
fringes is usually chosen to give either 0.001 cm—l/point or
0.0005 cm-l/point .

For example, suppose we have a set of fringes that are
spaced 0.2000 cm"1 apart. The sampling rate yields a range
of from 140 to 170 data points recorded between fringes. To
construct a spectrum in which each point represents 0.001 cm"1
requires 200 points between fringes (400 points per fringe
would represent 0.0005 cm'l/point). Because the actual num—
ber of points between fringes is approximately 155, we would
choose to construct 200 points between all fringes.

In practice, the interpolated fringe data points are not
actually constructed. There is a one to one mapping between
the fringe spectrum and the infrared spectrum so we linearize
the infrared spectrum directly by linearly interpolating
between points to construct 200 points per fringe. Let us
suppose that the positions (measured in tape coordinates) of
two consecutivezfiringes relative to the start of the scan are
points 451.623 and 609.488. The intensity of the fringe
spectrum at these points is found by linear interpolation.
The value at 453.202 is found by linear interpolation between

the points at 453 and 454. The height at 453.202 [h(453.202)]

is determined from:

[h(453.202) - h(453)]/[453 202 — 453] =
[h(454) — h(453)]/[454 - 453]

59

The infrared data point corresponding to the fringe data point
at location 453 also has the coordinate 453. Thus, there is
no need to construct 200 data points per fringe and then per-
form the same operations on the infrared data, simply perform
the construction directly on the infrared data.

To average n scans, each of the n scans must contain
essentially the same portion of the spectrum. This can be
accomplished by finding the largest portion of the spectrum
that is common to all n scans, i.e., the largest subset of
points contained in all n sets of data points. I did this
visually by recording the position of the first few fringes
in my notes and counting the number of fringes in the scan.

I then sorted and assigned the first few fringes an absolute
number corresponding to their position relative to the
infrared spectrum. For example, say the first scan had ten
fringes before the first Q branch. The first fringe would
be given the label 1, the second 2, and so forth. Another
scan might have eleven fringes before the same Q branch, in
this case the first would be labeled 0, the second 1, etc.

A third scan may have only nine fringes before the Q branch.
The first fringe would be labeled 2, etc. If the largest
labeled first fringe of all scans is labeled two, and if

the smallest labeled last fringe of all scans is eighty-three,
then the largest portion of the spectrum that each scan con-
tains is the region beginning with the fringe labeled two
and ending with the fringe labeled eighty-three. In this
iway, the largest spectral region contained by all n scans

can be found.

60

The spectral regions are examined to find as many good
peaks as possible, where "good" means those that are clearly
peaks on all scans and a precise measurement can be made.
Ideally, the peaks would be distributed throughout the scan.

Run 11 of 2v of CH3CN used 37 positions. Each of the posi-

5
tions are measured relative to the beginning of the scan.
For perfect data, each peak would have the same position
within each scan, e.g., peak 1 located at point 82 in scan 1
would also be located at point 82 in every other scan. For
real data, these positions change because of noise. Since
the distribution of noise is essentially gaussian in nature,
an approximation to the true position of a particular peak
can be found by measuring that position many times. Alter-
natively, it is hoped that by measuring many peaks at one
time, as opposed to one peak many times, a good approximation
to the "true" offset can be determined. Thus, using the
methOd of least squares to fit the peak positions of each
scan to the average of all of the preceding scans, an offset
can be determined for the individual scan and that scan
averaged into the total.

To illustrate, assume the average contains 3 peaks
(yl, y2, y3) at 182, 324, and 646, while the single scan
registers these peaks (x1, x2, x3) at 194, 320, and 641.
What is the constant, k, necessary to add to all points in
the single scan to obtain the best fit to the average? We
wish to minimize:
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with respect to k, i.e. dR/dk = 0. This implies that

Z yi = 2X1 + kn, or k = [Zyi _ ZXiJ/n = L1152§11551 = -1

To optimize the fit, each point in the scan should be moved
to the left by one point, i.e., the peak at 194 should become
the peak at 193, etc. After the scan has been displaced
appropriately, it is added to the sum of the previous scans.

My summing method is to take the first scan and place
it directly into an empty sum file. The chosen peaks of scan
two are compared to those of scan one, then scan two is added
to the sum file appropriately displaced. Scan three, and each
succeeding scan, is then compared to scan one and added to the
sum file appropriately displaced.

An improvement to this approximation is to remeasure the
chosen peaks of the sum file after each new scan is added into the
sum file, then compared each new scan to the remeasured values.

Finally, the sum of n scans:k3normalized to some desired
signal strength and deconvoluted. The lines in the deconvolu-
ted spectrum are then measured in terms of tape coordinates
or points relative to the beginning of the scan.

To convert these positions to frequencies, a method
similar to the one used for averaging is employed. A number
of prominent lines are chosen to compare the averaged decon-
voluted spectrum (line positions in tape coordinates) with
the calibrated spectrum (same line positions in frequency
units of cm'll The positions of these lines are compared
with a linear least squares fit to determine a conversion

from position to frequency.

62

The procedures described in this chapter should not be
considered as ”cast in concrete”, but rather considered as
guidelines. Considerable flexibility exists to customize the
procedures to a particular problem. Improvements are pos-
sible, as well as desirable. Probably the most significant
improvement would be to transmit data to and from the M.S.U.
mainframe. The result would be a significant reduction in
the real time required to perform the signal processing.
Hours and days would be reduced to minutes or seconds, limited
primarily by baud rates for data transmittal. Using the
mainframe also permits usage of more sophisticated signal
processing algorithms, such as a cubic spline interpolation
instead of the simple linear interpolation.

In general, the procedures described in this chapter
are not "user friendly”, but the benefits far outweigh the
associated problems when the user is trying to extract the

most information from the available data.

CHAPTER V

THE ANALYSIS OF THE v5 BAND 0F CH3CN

Most of the symmetric top molecules studied by the M.S.U.
Infrared Lab were Methyl Halides (CH3X), which belong to the
C3v point group. The axially symmetric molecule Methyl
Cyanide (CH3CN) also belongs to the C3v point group, with
the CN radical replacing the halogen (X) along the axis of
symmetry. Because Methyl Cyanide has three more vibrational
normal modes than the Methyl Halides (3N-6 total vibrational
normal modes), the vibrational normal mode named us of Methyl
Cyanide has essentially the same atomic motions as the vibra-
tional normal mode name 04 of the Methyl Halides, viz. an
unsymmetric C-H stretch, and occurs at a frequency near
that of 04.

With one exception, the infrared investigations of
gaseous Methyl Cyanide prior to this study were of low to
medium resolution. Venkateswarlu (41) used a prism spectro-
meter to find the band centers of the vibrational normal modes
of CH3CN and to assign and measure the Q branch positions of
v of CH3CN. Parker et. a1. (42) measured the Q branch

5

positions of us and also determined c, cg, v0, [(A'-A")-(B'-B")],
and 2[A'(l-—c5)-B'] with a combination prism-grating spectro-

meter. Duncan et. a1. (43) determined fundamental vibrational

63

64

frequencies with heavy isotopic substitution, identified Fermi

resonances, and measured harmonic potential constants.

5 of CH3CN at a resolu-
The results of the

T. L. Barnett (34) investigated 0
tion limit of approximately 0.04 cm-l.
present study will be compared to Barnett's investigation,
the only known study at high resolution prior to this one.

This chapter will present the single band analysis of
the v5 band of CH3
weights of spectral lines, and compare the results of the

CN, detail a technique to adjust relative

analysis with the results Barnett obtained. Appendix IV

contains the frequencies and assignments for us of CH3CN.

Analysis

The M.S.U. high resolution grating spectrophotometer
system was used to record the spectra of the v5 band of CH3CN
under the experimental conditions listed in Table 5.1. Sur-
vey spectra of the region are shown in Figure 5.1. It was
not necessary to signal average the v5 band, although it
could have been done.

Barnett had previously analyzed this band, hence many of
the spectral lines already had their quantum dependencies
assigned. His assignments were carefully checked and some
additional assignments made. Several features characteristic
of symmetric top molecules helped in determining the assign-
ments. For any particular subband (i.e., for any particular
value of KAK) JzzK, in both the upper and lower states. Thus,

for KAK = 5, the J = 0 through J = 4 transitions are absent

65

Table 5.1 Experimental conditions used for the v5 band

of CH3CN data.

 

Region: 2973-3149 cm-1
Pressure: 2 - 4 torr
Path Length: 15 meters
Detector: PbS @ 77K
Grating: 300 lines/mm
Calibrated Gases: HCl(l—0)
HCN(001)
Standard Deviation _1
of Calibration: 0.0055 cm
1

Resolution Limit: ~0.032 cm-

 

66

 

 

 

 

 

 

 

 

 

.1 L;
A A W
. .. MW WWW.

 

Figure 5.1 Survey spectra of the 05 band of CH3CN.

1.,

n».

.
, ....
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shunt

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67

for AJ = 1, while the J = 1 through J = 4 transitions are
absent for AJ = —1. These criteria provide a check on Q
branch assignments as well as on the P and R branch assign-
ments. Subbands with K a multiple of three are theoretically
twice as intense as subbands with K not equal to 3n for CHSCN
due to C3v symmetry and nuclear spin statistics. Within a
subband, the transitions having AK = AJ = :1 are more intense
than those having AK==—AJ== i-l; this advantage becomes greater
as K increases. Herzberg (44) gives an excellent illustration
of the relative positions and intensities of the transitions
in a perpendicular band of a symmetric top molecule, both by
subbands and the whole band.

The fitting routine SYMFIT (28) only fits the unperturbed
subbands of symmetric top molecules. Thus to obtain a good
fit, all subbands that are perturbed must be excluded from
the whole band fit.

There are several aids to help recognize perturbed sub-
bands or misassigned lines. A plot of the approximate posi-
tion of the Q branches (1 used the sharp high frequency side
of the Q branch whenever possible) versus KAK provided an
initial approximate indicator of perturbed subbands (Fig. 5.2).
If the Q branches are fit to a quadratic in K, the residuals
(measured - calculated) can be plotted (Figure 5.3) to show
the Q branch plot on a more sensitive scale. It seems
evident from the Q branch fit that the subbands KAK = -3,

-2, 6, 12, and 13 should be regarded with some suspicion.

The single band frequency expression (Table 2.5) with the

68

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appropriate quantum dependencies can be used to fit the Q
branches. The Q branch fit of us of CH3CN was also useful
as an approximate indicator of which subbands might be
perturbed and to calculate an approximate value for 02.
Unfortunately, most of the Q branches for KAK < 0 are
obscured by the strongly absorbing parallel band vl, so
this method was of limited use.

Subband fits can also reveal perturbed subbands and
poorly fitting lines. A subband fit provides a calculated
value for a: and the subband origin for each subband, which
are plotted versus KAK to provide a more sensitive indicator
of perturbed subbands (Figures 5.4 and 5.5 respectively).
These plots add KAK = 11 to the list of subbands to care-
fully consider before including in the final fit to
determine constants.

Comparing the calculated frequency of a line with the
measured frequency also gives some indication of the fit of
the line as well as the assignment. This comparison can be
done with either a subband fit or a whole band fit. The
better the Hamiltonian parameters are known, the more con-
fidence one has in the assignments and the fit. Thus, the
subband and whole band fits are done in an iterative fashion,
using the results from a previous fit to guide the new fit.

In a manner similar to that of the subband fit, the
whole band fit can also be used to reveal perturbed subbands.
Q branch positions and subband origins can be calculated,
then compared to the measured values of Q branch positions

and subband origin positions to reveal any perturbations.

71

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73

Determining perturbed subbands and poorly fitting lines
is an iterative process, as previously stated. SYMFIT was
run 40 to 50 times before obtaining satisfactory values for

the parameters of v5 of CH3CN. Even then, some parameters
k
0’
correlated. More data, better data, or an alternate method

like AO-Aec, D and a? for us of CH3CN can remain highly
must be used to better separate the effects of these para-
meters. For the aforementioned example, a? was determined
from a fit of the Q branches of 2v5. Decoupled parameters,
such as a2, are not varied in SYMFIT, then, until the final
fit, if at all.

The results of the whole band fit were disappointing,
however. The subband fit showed that the subbands fit very

nicely individually, but the whole band fit was poor.

Weighting Scheme

Examining the outputs from whole band fits suggested
a possible means of improvement in the analysis, viz., by
using a revised method of assigning relative weights to the
transitions. The primary criteria for assigning initial
iweights were the line shape and intensity, admittedly
qualitative criteria. Some additional criteria were needed
to better quantify the weighting scheme.

Ground state combination differences had been used to
Check line assignments and to make further assignments.
T1lis suggested a modified weighting scheme, in particular,

weight the transitions according to the reasonableness of

74

the measured frequency. To check the reasonableness of the
measured frequency, the customary ground state combination

differences for CH3CN were used, viz.,

A

AKRK(J) - AKQK(J+1> = AKQK(J) - KPK(J+1) =

2 J

K J 3
2(BO-K DO )(J+1) — 4DO(J+1)

3K, and D: are microwave constants (45). Given

where Bo’ D
a measured value of the P or R branch lines of a particular
subband, the expected locations of Q branch lines can be
calculated without much loss of accuracy since the values
for ground state microwave constants are orders of magnitude
more accurate than our frequency measurements. These Q
branch lines are then plotted versus J(J+l) and should fit

a straight line with a slope of -2ag and an intercept of

sub

v0 (the subband origin), neglecting higher order terms.

A reasonable line is drawn through these data points accom-
panied by a reasonable error region ($0.010 to 0.020 cm‘l,
see Figure 5.6) such that any data points falling outside
this region are excluded from the least squares fits. The
residuals (measured - calculated) are then put into bins

and assigned weights according to the magnitude of the

residual. The following scheme was used in this study:

75

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bin (cm—1) weight
.000-.002 8
.002-.OO4 4
.004-.006 2
.006-.008 1
.008-.012 .5
.012-.016 .25
.016-.024 .13
.024-.032 .06

For the most part, as the worst residual in the range doubles,
the weight quarters. The weight of a spectral line whose
residual lies on the border between two bins is determined
by line shape and intensity.

One would argue that a plot of the P or R branch lines
versus J would yield similar information. To some extent
this argument is valid. Figure 5.7 shows a typical subband
plot of RR3(J) and RP3(J) versus J. From Figure 5.7 only,
it is not obvious that there are any lines that should be
excluded from a fit to determine weights. To examine this
in more detail, these data were fit to straight lines. The
resulting calculated frequencies were subtracted from the
measured frequencies and plotted versus J, as in Figure 5.8.
Clearly, the poorly fitting lines are now easier to exclude
by examining a plot of the residuals before determining line
weights. The disadvantage to this method is that the plot

of the measured frequencies versus J is not, in principle,

77

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79

a straight line. To discern anything but a straight hori—
zontal line in the residuals is more difficult, making the
task of assigning weights less accurate.

Futhermore, the perturbed subbands, such as the KAK = 6
subband, are more difficult to see from a plot of RRK(J) or
RPK(J) versus J (Figure 5.9), than from a plot of the
residuals (Figure 5.10) obtained by fitting a line to
the data in Figure 5.9.

The residuals of either method are of comparable
magnitude, however, and either method of calculating weights
may be only of small benefit if the calculated weights are
changed substantially. Some are of the opinion that weights
should be changed to improve the fit until there is no longer
an apparent change in the fit. The weights in this study
were changed by no more than two bins to improve the fit,
and then only if justified by the line shape and intensity.
The justification for a change in weight at all is that there
is some uncertainty involved in measuring the line position,
especially for incompletely resolved lines. For bins having
a small range (near zero residuals), any error at all can
easily change a weight by two bins. For bins having a large
range, there is so much uncertainty already that if line
shape and intensity warrant, changing the weight by a
relatively small amount can easily be justified. These
guides have been strictly adhered to in this study.

It should also be noted that ground state combination

differences work best for unperturbed subbands and some

80

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82

perturbed subbands. Should a perturbation transform the
Q branch plot into a smoothly varying line, for example,
the ground state combination difference method could still

be used.

Results

Utilizing the methods described in this chapter, the
molecular constants for us of CH3CN were determined from a
single band fit of 160 lines from the KAK = 0,2,3,4,5,8,
and 9 subbands. These constants are compared in Table 5.2
with the constants obtained from a single band fit by
Barnett (34). Most of the uncertainties in the present
study are smaller than those given by Barnett. In addition,
two more parameters were determined in the present study.

The 95% simultaneous confidence interval (95% SCI)
given in Table 5.2 can be found in many statistics texts.
John Boyd (46) has a nicely written section that describes
the method used at the M.S.U. I.R. lab. Boyd describes the
95% SCI as approximately /2510, where p is the number of
parameters varied to obtain the standard deviation of the
fit, 0 is the standard deviation of the parameter, and 2
is an approximation to F0 975(p,n-p), F being the F dis-
tribution of reference (46) and n the number of data points.

The analysis of the parallel and perpendicular com-

ponents of 2v5 and the simultaneous fit of us and 2v of

5

CH CN will be presented in Chapter VI.

3

83

Table 5.2 Single Band Pit of v of CH CN

5 3

 

(A) All parameters allowed to vary

Parameter Barnett Bardin
v0 3008.697(15) 3008.7183(59)
Ao-Aec 4.96707(67) 4.9606(18)
ag + 0.0323(22) 0.0301(10)
cg 0.54(32)E—4 l.93(56)E-4
fig -0.27(1l)E-4 -0.52(21)E—4
Hg 0.77(4l)E-8
Std. Dev. of Fit 0.009 0.0052
(B) 0A and dB constrained to values consistent with simul-

tgneous fit of v5 and 205, Q branch fit, and parallel
component fit.

Parameter Barnett Bardin
v0 3008.697(15) 3008.7142(6l)
Ao—Ae; 4.9607(67) 4.9606(18)
D: 1.04(57)E-4
mg + ... 0.0323(22) 0.02891(63)*
a: 0.54(32)E-4 1.27(10)E-4*
3% -0.27(1l)E-4 -0.49(18)E-4
Hg 0.77(4l)E-8

Std. Dev. of Fit 0.009 0.0056

 

*These were known from two independent fits and thus held
constant here.

CHAPTER VI

THE ANALYSIS OF THE 205 BAND OF CHBCN

Introduction

 

The 2v band of CH3CN is the first overtone of the

5
vibrational normal mode of us. The ideal model of 205 would
vibrate at twice the rate of us, and in practice this is
nearly so. The vibrational angular momentum for 05 is
{V5 = l or A£v5 = :1, while for 295, £2v5 = 2, or Aflzvs = :2.
This not only allows for a perpendicular component A£=-12,
but also for a parallel component, AL = 0.

To date, the previous work on 295 has been sparse.

Venkateswarlu (41) determined that 295 (parallel and perpen-

dicular) occurred near 5972 cm-1. Parker et.al. (42) were
able to obtain v0 = 6006.99 cm-l, c5 = 0.042, :55 = -0.084,
[(A'-A")-(B'-B')] = -0.055r0.006 cm-l, and the g55, x35, and
o

“5 force constants. Parker et.al. also identified the
parallel component of 2v5. T. L. Barnett (34) was able to
study 2v5 at a resolution limit of about 0.2 cm"1 and deter-
mined several rotational constants. Unfortunately, there

were too few unperturbed subbands to obtain a good single

band fit.

84

85

The 2v5 band is a weakly absorbing band, which probably
accounts for the sparseness of literature. To obtain a suf-
ficient number of unperturbed subbands, and thus avoid the

problems Barnett had to contend with, the 2v band was signal

5
averaged. Signal averaging had been effective on "dense"
spectra and extending the averaging technique to include

weak spectra seemed feasible.

Details of how the signal averaging technique was
specifically applied to 2v5 will be presented in this chapter,
as well as the analysis of the parallel and perpendicular
components of the 2V5 band. Both components presented
problems that will be addressed in this chapter. The results
from a single band fit and a simultaneous fit of us and 2v5
will be compared to the results Barnett obtained. Appendix
V’ contains the frequencies and assignments of the 205 band
of CH3CN.

Procedures

 

The spectra of 2v5 of CH3CN were recorded on the Michigan
State University high resolution grating spectrophotometer
under the experimental conditions listed in Table 6.1.

Survey spectra of the region are shown in Figure 6.1.

The perpendicular component of 2v5 from 5988 cm"1 to

1

6153 cm' to R ) was divided into about six equal

(P
Q2 Ql3
regions. Each region was signal averaged, independent of

the other regions. Each scan of a particular region was

86

Table 6.1 Experimental conditions used for the 20 band of

 

CHBCN data. 5
Region 5988-6153 cm-1
Pressure 10 - 15 torr
Path Length 15 meters
Detector PbS @ 193K
Grating 600 lines/mm
Calibrated Gases N20(3,0,l)

HCN(0,0,2)
Standard Deviation _1
of Callbratlon 0.0059 cm
1

Resolution Limit ~0.055 cm-

 

87

 

 

 

 

 

“I“ 75“

parallel component

 

 

 

J 1 WM

Figure 6.1 Survey spectra of the 2v band of CH CN.

5 3

88

linearized in the manner described in Chapter IV. To average
effectively the scans must be properly aligned. To align the
scans, the first scan was carefully examined and a suitable
short segment was chosen as a trigger for other scans. The
corresponding segment of each successive scan was then fit
to this trigger using a least squares method to best align
the scans. The scans were then summed and normalized
appropriately for deconvolution.

The alignment method described above was not effective
When a

for the region that includes R through R

Q10 Q13.
single scan was compared to the average, there were many
differences. Consequently, no assignments could be made.

In an attempt to improve the results, an alignment scheme
that had been previously considered was tried with great
success. Several positions of peaks and valleys (for well
resolved lines) distributed approximately evenly throughout
the scan were selected from the first scan to serve as the
triggering mechanism to align the remaining scans with the
first. These same line positions from each successive scan
were compared to the positions in the first scan, using the
method of least squares, to determine the relative offset.

In principle, several measurements of a line that changes

its apparent position because of noise should give a good
approximation to the "true” position of that line. Similarly,
as the number of line positions (measurements) in a com-

parison of two scans increases, the error associated with

measuring the relative offset between the two scans should

89

decrease. Based on the success of this one trial, this error
assumption appears to be valid. There is an additional assump-
tion implicit in all line measurement schemes; any systematic
errors that are present in one region, are also present in all
other regions, including the calibration run, and thus do not
affect the frequency measurements. After aligning the scans,
they were summed and normalized appropriately.

Assignments were subsequently made for KAK = 10 and 11.
Unfortunately, none of the assignments were used in the final
fit; either these subbands were perturbed or the triggering
method was not successful. Barnett's data seems to support
the argument that the subbands above KAK = 8 are perturbed.
An analysis that includes perturbations would hopefully
remove any doubts.

After signal averaging, the regions were deconvoluted
to try to rid the spectra of the broadening effects of the
instrument function. Although convolution is unique, decon-
volution is not, and, at times the spectra were excessively
deconvoluted. When this occurred, the original spectra were
later deconvoluted in a slightly different manner in an
attempt to acquire a more meaningful spectrum.

The parallel component frequencies and the Q branch
frequencies were taken directly from the calibration run

and were neither signal averaged nor deconvoluted.

90

Calibration

A secondary calibration method was necessary to calibrate

the averaged spectra. The 2v5 calibration run consisted of

two well known bands bracketing the 2v band of CH CN. The

5 3
frequencies of 2v5 were obtained by interpolation between
lines from N20(3,0,l) and HCN (0,0,2). These interpolated
frequencies then calibrate the averaged spectra in a manner
similar to that used in averaging the weak region of the

).
Q10 Q13
For each region, a number of well resolved lines were

spectrum (R to R
selected, distributed approximately evenly throughout that
particular region. The positions (in tape coordinates) of
these well resolved lines were matched to their counter parts
in the calibrated run via a weighted least squares fit. Once
the relationship between the calibrated run and the uncali-
brated averaged region had been determined, the remaining
frequencies of the averaged region could be calculated.
Most of the region fit the calibrated run to between 0.002
and 0.006 cm-l.
To provide some check of calibration between regions,
each region overlapped neighboring regions by from three to
four wavenumbers. Although it was thought at the time that
this overlap would be sufficiently long, frequently there

were not enough clearly resolved lines of high enough

intensity to unambiguously provide this check.

91

Analysis

Barnett had made many transition assignments in the

region KAK = -2 to 7 of 2v of CH CN, and, as with v these

5 3 5’
were carefully checked. In addition to his assignments, this
study enabled assignments to extend through KAK = 11, enabled
Q branch assignments from -7 to 13, and to some extent
facilitated the parallel component assignment.

The 2v5 band was analyzed in the manner described in
Chapter V. Figure 6.2 shows the approximate Q branch posi-

tions plotted versus KAK, including both parts of R The

Q .

8

effects of the pertubation near RQ are shown by the splitting
8

of the Q branch, illustrated by the two points at R Also

Q .
shown in Figure 6.2 is a fit of the frequencies of tge Q
branches PQ7 through RQ8 versus KAK and a fit of RQ8 through
RQ13 versus KAK. The two lines obtained from these fits are
not parallel, but intersect at approximately KAK = 13 and
illustrate in“; effects of the perturbation on the rest of
the band. A plot of the residuals obtained from fitting all
of the Q branches to a line (Figure 6.3) illustrates the
perturbation even more dramatically, and further suggests
another perturbation near RQS.

A good guess at a; can be obtained if only the unper-
turbed Q branches are included in a Q branch fit using
SYMFIT. To determine which subbands were perturbed, plots

of 0% versus KAK (Figure 6.4), subband origins versus KAK

(Figure 6.5), and subband fits were used in addition to the

information in Figures 6.2 and 6.3. The subband fits showed

92

 

 

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93

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96

that each of the subbands were good fits and self-consistent.
The ag's generated in these fits were plotted versus KAK but
were not too helpful, probably because good values for

A0 + 2Aec, DE, and a? were not yet available. The subband
origins served to confirm the Q branch plots. When all sub-
bands were included in the whole band fit, the fit was poor.
Each subband suspected of being perturbed was excluded from
the fit, one at a time, to see how the fit changed. Several
possible combinations were tried, but still difficulties
remained and the expected good fit did not occur.

In an effort to help determine perturbed subbands, we
tried comparing the hot band line positions that occurred
as a neighbor to the Q branches with the Q branches positions
themselves to see how the relative positions changed.

Figure 6.6 shows the hot band positions (minus a quadratic
fit) versus KAK and indicates that the hot band in that
region is less perturbed. Figure 6.7 shows the hot band
position minus the nearest neighbor Q branch position.
Notice that a straight line can be drawn through the sub-
bands KAK = -l,1,2,3, and 6, these are the subbands that
were eventually chosen to comprise the "whole band" fit.

As with us, ground state combination differences
(GSCD's) were used to assign weights to line positions for
the whole band fit and were somewhat helpful for determining
new transition assignments. Figure 6.8 illustrates a typical

subband plot of calculated R verus J(J+l) where the

Q3(J)

were calculated from the R

RQ3(J) R3(J) using GSCD's.

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100

Excluding the obviously non-fitting lines, fitting the
remainder to a straight line, and then plotting the residuals
verus J(J+l) (Figure 6.9) allows a quantitative weight
assignment to the line position using the method described
in Chapter V.

A single "whole band" fit was performed on 79 lines with
the results given in Table 6.2. These results were then com-

pared to the results of the single band fit of v to test

5
somewhat for internal consistency of the two sets of data.
Barnett's single band fit of 2v5 was not available for
comparison.

The v5 and 2v5 bands were then combined to provide a

simultaneous fit. The simultaneous fit gave fairly good

results when compared to Barnett's results.

Parallel Component of 2v5 of CH3CN

 

If the parallel component could be analyzed, SYMFIT
would provide a value for the band origin of the parallel
component and a value for cg. The parallel component was
very difficult to analyze, however, as the R and P branches
were not resolved and the Q branch was only partially
resolved.

As a first approximation one might guess that the two

strongest lines in the center would correspond to K 3 and

K = 6 of the Q branch (~5965 cm.1 of Figure 6.1), K

6 being
the lower of the two in frequency. Thus, the parallel com-

ponent band origin might be taken to be at the high frequency

101

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Table 6.2 Single Band Fit of 2v5(l) of CHSCN
Parameter Calculated Value (cm'l)
v0 6007.700(23)
AO-Aec 5.790(14)
A
as + ... 0.0643(20)
B
as 7.63(13.72)E-5
k
Ho -7.47(17)E-5
k
Do -0.60(39)E-3
k
85 0.001543(12)

Std. Dev. of Fit 0.0083

 

103

edge of the central portion. If the parallel component band
origin was provided for SYMFIT, the simultaneous fit would
calculate parallel component frequencies. This was, in fact,
attempted, with poor results, indicating a need for more or
better information.

It has been noted from studies of other molecules that
one value of K is usually stronger than the other for a
particular value of J. Thus, it was assumed in this analysis
that the measured line positions all belonged to the same K
value. A better model would be to assume that the measured
line position is a combination of two or three neighboring
K values.

To determine which K fit best, GSCD's were computed
from measured line positions assuming K to be 1, 2, 3, ..., 9
and compared to the calculated GSCD's using microwave con-
stants. The "true" K value would be expected to yield the
best fit to the GSCD's calculated from microwave constants.
Once K is determined, the QQK(J) are calculated using GSCD's
and plotted versus J(J+l). The weights were again assigned
according to the size of the residual. The weighted lines
and appropriate constants were input to SYMFIT to obtain
a: and vo(u)

When these calculations were performed, all K except
K = 2 and K = 3 were eliminated. The results of a fit of
the parallel component tend to support setting K = 3 (Table

B

6.3). as obtained in the fit using K = 3 was closer to the

value obtained the simultaneous fit than the value obtained

104

Table 6.3 Comparison of the K = 2 and K = 3 assignments

 

 

of the 2v5(u) band of CH3CN.
B Standard
05 Deviation
of Fit
K = 2 l.350(51)E-4 0.0224 cm‘1
K = 3 l.289(42)E-4 0.0133 cm“1
Simultaneous Fit l.268(23)E-4 0.0083 cm-1
of v5 and 2v5(i)

 

in the fit using K = 2. The variation in 02's
band fits, however, reduces the reliability of
an indicator. Finally, the standard deviation
using K = 2 was about 60% larger than when K =

and since the K = 3 lines would be expected to

intensity, the natural choice is for K = 3.

from the sub-

. B
u31ng 05 as

of the fit

3 was used,

have more

On the other hand, several circumstances recommend

1. The fit for K = 2 predicts the parallel band origin
on the high frequency edge of the central portion
identified as the Q branch, the expected position.
The fit for K = 3 predicts the band origin 0.25 cm-
lower than for K = 2, and to the low frequency side
of the Q branch line at that edge, and unexpected
position. Changing the J assignments only changes

the band origin, by approximately 0.61 cm-

1

9

and

thus does not remove the 0.25 cm"1 difference.

1

105

2. The simultaneous band fit predicts the 205 (perpen—

dicular) Q branch positions to approximately 0.1 cm-1
of the measured positions, thus indicating a capabil—
ity of predicting to 0.1 cm-l. When the simultaneous

band fit is used to predlct the QQK(O) lines, the

results match the results obtained assuming K = 2

1, but only to 0.34 cm-1

to better than 0.02 cm-
when K = 3 is assumed.

3. Prediction of QQK(O) line positions using K = 2 gives
reasonable assignments for the two highest intensity

lines, i.e., K = 3 and K = 6. The fit assuming K = 3

gives less reasonable assignments for these two lines.

It should also be mentioned that predicting the perpendicular
component Q branches from the parallel component fit did not

discriminate between K = 2 and K = 3, primarily because a:

is not significantly different for the two cases.

Results

Because of the uncertainty as to whether K = 2 dominates
the R and P branches or whether K = 3 dominates, the parallel
component was not included in the final simultaneous band fit.
The final fit contained approximately 240 lines, about 2/3 of
which were from the v5 band and the remainder from 2v5.
Consideration was given, however, to the Q branch fit of
2v5 in the determination of a: and to the parallel component

fit of 2v5 in the determination of the parallel component

band origin.

106

The results of this analysis are compared to Barnett's
results in Table 6.4. Most of the constants are similar to
Barnett's values, while every 95% SCI improved relative to
that given by Barnett. Where there were disagreements in
the values of the constants, the values were checked against
values obtained on a similar molecule, under the presumption
that similar molecules should have similar values for con-
stants. The values of constants obtained in this study are
comparable in magnitude to the values of constants obtained
by Barnett for the simultaneous fit of 04 and 2V4 of CHaBr
(34), whereas the values obtained by Barnett for CH3CN for
those constants that differed were farther from the CHaBr

values.

107

Table 6.4 Simultaneous Fit of v and 205(i) of CH CN

5 3

 

1

Parameter (cm' ) Barnett Bardin CHSBr
05 3009.111(15) 3008.9721(58) 3056.3525(40)
205(i) 6005.96(23) 6007.143(12) 6095.3793(88)
A0 5.026(64) 5.2125(10) 5.12909(97)
Aec + ... 0.328(21) 0.25311(45) 0.30493(71)
DE 0.0238(16) -9.42(54)E-5 0.37(33)E-4
02 + ... -0.143(27) 0.02891(63) 0.02849(39)
a: 0.79(14)E-4 l.27(10)E-4 -1.844(62)E-4
n: 0.0248(15) -6.04(30)E-4 -0.83(37)E-4
a: 0.00656(28) -63(19)E—6 -1.62(93)E-5
H: -4.54(l9)E-5 77(34)E-8 11(9)E-8
3g 68(49)E-9
2v5(u) 5966.366(12)

Std. Dev. of Fit 0.008 0.0075 0.006

 

CHAPTER VII

A REVIEW OF OUR ANALYSIS OF THE v4 BAND OF CD38r

Our study and analysis of an x-y Coriolis interaction
between v4 and v3+vgl+vél of CD3Br was published in 1981 in
the Journal of Molecular Spectroscopy (40). A copy of this
paper appears in Appendix IV. The measured frequencies and
assignments for v4 of CD33r appear in Appendix V. This
chapter will review our contributions to this publication.

Professor Marshall Wilt, F. W. Hecker, and J. D.
Fehribach of Centre College, Kentucky, wrote a computer
program (CORIFERM) to calculate the intensities and frequen-
cies of transitions in axially symmetric C3v molecules. The
diagonal part of the Hamiltonian is the Hamiltonian for
axially symmetric molecules as described in Chapter II.
Additional terms are added to this Hamiltonian to allow for
an x-y Coriolis interaction and a Fermi interaction between
vibrational states. These additional terms connect different
vibrational states and thus are off-diagonal. An iterative
technique (similar to a force constant calculation) is used
to solve this system for the parameters. A parameter is
changed slightly to determine how the frequency of each
transition changes. This is repeated for each parameter.

After all have been done, the process is repeated substituting

108

109

the most recent values of the parameters for the previous
values. The iterations are stopped when the calculated
residuals are smaller than the experimental error. Wilt
used this iterative technique to analyze the Fermi and

I and for CH Br.

3 3
These successes suggested that analyses of other CH3X

x-y Coriolis interacting bands for CH

type molecules would also be successful. From the litera-
ture, Marshall Wilt picked CDBBr as a good candidate. The
experimental work done by Peterson and Edward (9), however,
did not quite resolve the transitions necessary for the
analysis of v4 of CD3Br using Wilt's procedure. Hence,
Wilt asked T. H. Edwards, one of the original authors, if

CD Br could be run at higher resolution using the M.S.U.

3
high resolution infrared spectrophotometer. Deconvolution
had recently been developed, so it was thought that the
CD38r spectrum could be deconvoluted to improve the resolu-
tion limit.

We reran the v4 spectrum of CD3Br under conditions
Optimum for deconvolution, which requires a high signal to
noise ratio (2 50). To improve resolution, the spectro-
photometer slits must be narrowed, which lowers the signal
to noise ratio. When the slits were widened to improve the
signal to noise ratio enough to deconvolute effectively,
there was not sufficient gain in the final resolution limit
to be helpful to Marshall Wilt.

The insufficient gain in resolution prompted an exami-

nation of possible means to signal average spectra. Signal

110

averaging spectra permits a higher initial noise level and
hence a higher initial resolution limit. Although signal
averaging had not been successful for high resolution
infrared spectroscopists in the past, a successful technique
was eventually developed at the M.S.U. high resolution
infrared lab.

The signal processing techniques described in previous
chapters were originally developed for this application to
CD3Br. Much time was spent trying various ideas and then
testing thoroughly before applying the final procedure to
CDBBr. Deconvoluting the spectrum then produced a more
resolved spectrum for v4 of CD3Br, especially in the region
of interest to Marshall Wilt. We assigned as many transitions
as we could, then gave the data and intermediate results to
M. Wilt. Wilt confirmed our assignments and made many more.
He then extended the analysis to include an x-y Coriolis
interaction and the possibility of a Fermi interaction,
although no Fermi interaction was found.

The extension of the usual method to include x-y Coriolis
and Fermi interactions resulted in the publication given in

Appendix IV.

CHAPTER VIII

CONCLUSION

A technique has been developed to signal average high
resolution infrared spectra. The band under study is run in
segments approximately 20 wavenumbers in length. Each
segment is scanned and recorded approximately 16 times.
These scans are linearized in frequency and summed using a
least squares fit of each scan to the first scan as an
alignment trigger. The averaged segments are calibrated
by fitting to a calibrated run using a least squares fit.

The signal averaging technique was successfully applied
band of CD

Br and the 20 band of CH CN. Each

4 3 5 3
band represents a different application. The v

to the v
4 band of
CD38r is a dense band where the transitions appear to be
many incompletely resolved lines. The 2v5 band of CH3CN

is a weak band in that the intensities of the individual
transitions are relatively small.

Signal averaging allowed us to obtain a higher resolu-
tion limit for v4 of CD3Br than had been obtained previously.
As a result, Marshall Wilt was able to extend the analysis
to include an x-y Coriolis interaction between 04 and
v3+vgl+vél. The analysis resulted in improved values of the

molecular constants not held constant in the calculation.

111

112

The v5 and 2v5 bands of CHBCN were rerun at a higher

resolution limit. The 2v5 band had to be signal averaged to
obtain sufficient signal strength for some parts of the band.
A Q branch fit of the 2v5 (perpendicular) band gave a signi—
ficant improvement in the value of 02. A simultaneous fit
of us and 2v5 (perpendicular) resulted in improved values of
most constants and significantly improved values of the
remaining constants. Although the P and R branches were
unresolved, and the Q branch only partially resolved, assign-
ment of the parallel component of 2v5 and the subsequent fit
yielded values for the band origin and 0:. The parallel
component was not included in the simultaneous fit, however,
because of the uncertainties in the assignments.

Signal processing and numerical techniques were necessary
for us to improve upon the work done in the past. In the
future, signal processing and numerical techniques will be-
come more and more useful, and general, as the limits of
instrumentation are reached. Signal processing can extract
information from spectra normally not subject to analysis.
Numerical techniques can bring computers to bear on problems,
such as resonances, where other techniques fail. With these
tools, the future will bring improved values of molecular
constants, and, in addition, allow analysis of larger and

more complicated molecules.

APPENDICES

APPENDIX I

A LISTING OF THE FOCAL-12 PROGRAMS USED
TO SIGNAL AVERAGE SPECTRA

APPENDIX I

A LISTING OF THE FOCAL-12 PROGRAMS USED
TO SIGNAL AVERAGE SPECTRA

LINQ
This program was last revised on March 12, 1982. LINQ

lensures that each point of a run, or a portion of a run,
:represents the same interval of frequency, i.e., to make
‘the run linear in frequency. The program was written in
‘the PDP-12 minicomputer interpretive language FOCAL-12.

.Availability of three tapes drives is assumed, units one,

‘two and three:

‘UNIT 1: Tape 424 blocks 2 through 23 contain the fringe

positions necessary for file "F1"

IINIT 2: Tape 423 blocks 2 through 744 contain the original

data necessary for file "F2"

UNIT 3: Tape 82-1 blocks 2 through approximately 1371
contain the data after it has been linearized

(i.e., the output) necessary for file "F3"
IFollowing is a list of symbols and their meanings:

4A. ratio of the number of points between fringes in
original scan to the number of points between fringes

in the linearized scan

113

El

132

I33

135

IFl

IFZ

:F3

1K1

132

IPC

114

the coefficient to the linear term in CALFIT, an

M.S.U. I.R. lab program

used in "FOR" loop as a temporary storage for

truncated D
value of B (B in "FOR” 100p) in original scan

the coefficient of the quadratic term in CALFIT.
2 * C gives the change in B for an increase in fringe

number of one.

pointer to mark point in original scan that corresponds

to the point being operated on in linear scan
first point of present fringe for the linear scan

position of the Rth fringe from the beginning of the

scan

position of the (R+l)st fringe from the beginning of

the scan

integer array containing fringe positions
integer array containing original data
integer array containing linearized data
pointer marking present point in linear scan
first point in the original scan

last point in the original scan

desired number of points per wavenumber

pointer marking present fringe (of either scan)

115

RIN first fringe of the portion to be linearized (i.e.,
first fringe preceding Kl). Note that only the first

two letters in name count for variable name)

RMAX last fringe of the portion to be linearized (i.e.,

first fringe beyond K2).
IX number of points between fringes (not constant)

‘Y floating point value of F3(K)

'The following code is stored on my tape under name "LINQ".
Spaces are added to improve clarity, they are not present

in actual code.

.44 IF < F1(RMAX) - K2 > 1.46, 1.46, 1.42

CL.

C . . OPEN FILES

CL.

1.1. L 0,F1,F,#2,1

1.20 L 0,F2,I,#2,2

1.30 L O,F3,I,#2,3

CL.

(2.. INITIALIZE VARIABLES
CL.

1.40 S RMAX = 1436; S PC = 500; S RIN = 0; S K2 = 67000
CL.

C.. DETERMINE LAST FRINGE
C..

1.42 S RMAX = RMAX - 1

1

1

.46 S RMAX = RMAX + 1

mmmoooooooooooonnooo

.10
.20
.25
.30
.40
.50
.70
.80
.90

116

SUBROUTINE TO CALCULATE LINEAR
POINT BY LINEAR INTERPOLATION

BETWEEN POINTS IN ORIGINAL SCAN

D3 = F1(R); S D5 = F1(R+1)

X + 2 * C * PC

( 05 - 03 ) / x; s 02 = 02 + X

D3 + ( K - D2 ) * A

FITR(D); S B1 = F2(B)

< F2(B+1) - B1 > * ( D - B ) + B1

U) 01 U) U) U) U) U)
N K: 03 U :9 >4
II

= K + 1
IF ( K - 02 — x ) 8.3

CONTINUE

117

FIND

This program was last revised on August 9, 1981. FIND
finds fringe positions by fitting a quadratic to the upper-
most 29 points using a least squares fit. The program is
‘written in the PDP-lz minicomputer interpretive language

FOCAL-12. Accessibility to two tape drives is assumed.

'UNIT 0: Tape containing fringes

'UNIT 2: Tape on which to store fringe positions

Following is a list of symbols and their definitions:

A. constant coefficient in quadratic for least squares
fit

IB linear coefficient in quadratic for least squares fit

(3 quadratic coefficient in quadratic for least squares
fit

IDB constant determined from least squares fit necessary

to determine point where slope is zero

DC constant determined from least squares fit necessary

to determine where slope is zero
F0 file containing original fringe data

F2 file that will contain fringe positions

QQ

Q1

SC

118

index for least squares fit
data point index

number of points between first point of scan n and first

point of scan n+1

marks first point of scan; increments by L after each

scan
counts number of scans completed

counter that increments by 85 thus allowing fringe
positions from each scan to be stored on a separate

block
fringe counter

number of points in data scan

The following code is stored on my tape and named "FIND".

Spaces are added to improve clarity, actual code does not

have these spaces.

INITIALIZE VARIABLES AND OPEN FILES

.10 S Q = 0; S QQ = O; S Q1 = O; S SC = 12032; S L = 12288

.20 L 0, F0, I, #2, O; L 0, F2, F, #2, 2

C
C
C...
1
1
1

.30 S K = Q; S R = Q1

(30000

FIND OUT WHERE POSITION K IS
RELATIVE TO PEAK OF FRINGE, THEN

FIND PEAK OF FRINGE.

119

1.40 IF < F0(K) - FO(K+1) > 1.6

C
C...
C

H

Hl—‘OOOl—‘OOOOOOOOO

.50 S K = K + 25;

.70 S K
.80 S K

OOOOOOO

IF < SC

CHECK TO SEE IF MUST GO TO NEXT SCAN

+ Q - K > 2.5, 2.5, 1.4

THE FRINGES ARE MANUALLY ADJUSTED
DURING THE RUN TO MAINTAIN AN AP-
PROXIMATE HEIGHT OF 1200 (OCTAL)
HENCE THERE SHOULD NOT BE ANY
FRINGES WITH HEIGHT LESS THAN 400,
S0 GO TO GREATER THAN 400 BEFORE
CHECKING FOR TOP POINT

.60 IF < F0(K) - 400 > 1.7, 1.7, 1.8

CHECK TO SEE IF MUST GO TO NEXT SCAN

K+5;IF<SC+Q-K>2.5,2.5,1.6
IF < F0(K) - FO(K+1) > 1.8

TOP POINT WAS FOUND IN 1.80 AND IS
POINT K. NOW INITIALIZE CONSTANTS
FOR LEAST SQUARES FIT OF 14 POINTS
TO LEFT AND 14 TO RIGHT OF TOP
POINT TO A QUADRATIC

120

1.85 s A

F0(K); S B = 0; S C = O

1.90 F I

1, 14; D 9

A QUADRATIC HAS THE FORM Y=A+BX+CX“2
THE POINT WHERE THE SLOPE IS ZERO,
OR THE PEAK OF THE QUADRATIC, IS AT
dY/dX = 0 = B + 2 c X(PEAK) OR
X(PEAK) = -3/20, WHERE HERE "B" = DB,

"C" = DC, AND X(PEAK)=F2(R).

32849.46 * B

.20 8 DB
.25 8 DC = -41209 * A + 588.7 * c
.35 s F2(R) = -DB / ( 2 * DC ) + K - Q; s R = R + 1; s K = K + 5

IF NOT AT LAST POINT OF SCAN, REPEAT
PROCESS UNTIL LAST POINT EXCEEDED

.40 IF<K-SC-Q>1.4

IF BEYOND LAST POINT OF SCAN, TYPE
OUT,NUMBER OF FRINGES IN SCAN, GO
TO NEXT SCAN, CHECK TO SEE IF DONE.
IF NOT, REPEAT PROCESS FOR NEW SCAN,
ELSE QUIT. FRINGES FOR SCAN 1 ARE
STORED ON BLOCK 2, FRINGES FOR SCAN
2 ARE STORED ON BLOCK 3, ETC.

OOOOOOOOONOOOONNNOOOOOCOO

(09000000103035)

.50
.10
.20
.30

.10
.20
.30

121

T R — Q1 - 1

S Q = Q + L; S Q1 = Q1 + 85

S QQ = QQ + 10; IF < QQ - 16 > 1.3
L C, F0; L C, F2; QUIT

SUBROUTINE TO COMPUTE MATRIX
ELEMENTS IN LEAST SQUARES FIT

S A = A + FO(K+1) + F0(K-I)
S B = B + < FO(K+1) > * I
S B = C + < FO(K+1) > * I ** 2

LIN2

122

This program was last revised on August 17, 1981. LIN2

linear
Of dat
interp

drives

UNIT 1:

UNIT 3:

UNIT 4:

izes several (usually 16 for our applications) scans
a. The program is written in the PDP—12 minicomputer
retive language FOCAL-12. Accessibility to three tape

is necessary.
Tape containing original data
Tape containing fringe positions

Tape containing linear data

Following is a list Of symbols and their definitions:

A

Bl

D2

D3

D5

F1

number of original points per new point (a combination

of constants to save momory)
truncated "D"

function "Fl" at "B"
interpolated data point
counter to count fringe points
the "Rth" fringe

the "(R+l)st" fringe

array containing original data

F3

F4

K1

L3

Q1

Q3

123
array containing fringe positions (previously measured
with "FIND")
array containing linearized data
counter to mark present original data point
counter to mark present linear data point
number of points between scans Of original data
number of points between scans of linear data
flag to allow file containing data to change tapes
original data point counter
fringe counter
linear data point counter
counter to mark present fringe

number of fringes minus 1 (only RM counts in variable

name)
number of points between fringes

new linearized data point, still in floating point

format

The following code is stored on my tape and named "LIN2".

Spaces are added to the code here to improve clarity.

INITIALIZE VARIABLES AND OPEN FILES

1-10
1.20

.35
.40

.16
.17

dooooooommoonOt-‘H

.20
.25
.30
.35

OOOONNNN

mr‘t-‘mm

UJUJUJUJ

124

RMAX = 63; S X = 267.958; S Q = 0; S Q1 = 0

Q3 = 0; S L = 12288; S L3 16896; S M = 0
0, F1, I, #2, 1; L 0, F4, I, #22, 4
0, F3, F, #2, 2

K = Q; S R = Q1; 8 D2 = Q; 8 K1 = Q3

CALCULATE NUMBER OF ORIGINAL POINTS

PER NEW POINT

03 = F3(R); s 05 = F3(R+l)
A=<D5-D3>/X

CALCULATE POSITION OF NEW POINT
RELATIVE TO ORIGINAL POINTS, THEN
CALCULATE HEIGHT AT THAT POINT BY
LINEARLY INTERPOLATING BETWEEN
HEIGHTS OF ORIGINAL POINTS

{ F4(Kl) }

D = D3 + ( K - D2 ) * A
B = FITR(D); S Bl = F1(B)
Y = < F1(B+1) - Bl > * (D - B ) + Bl

F4(K1) = FITR< Y + .5 >

INCREMENT COUNTERS, AND CHECK TO
SEE IF NEW FRINGE

wOOOwQWCCOwOOOwwOOONN

.40

.50

.10
.20

.30

.40
.50
.60

.80

SK=K+1,
SR=R+1,
SQ=Q+1.
IF < 03 + 10

S M

II
E
+

10;

L C, F4; L 0,

L C, F3; L 0,

125

S K1 = K1 + 1; IF < K - D2 - X > 2.20

S D2 = D2 + X; IF < R — RMAX - Q1 > 2.16
CHECK TO SEE IF NEW SCAN

S Q1 = Q1 + 85; S Q3 = Q3 + L3

- 8 * L3 > 1.40

CHECK TO SEE IF CHANGE TAPES

IF < 15 - M > 3.80

CHANGE TAPES

F4, I, #22, 2
F3, F, #2, 4

S Q3 = 0; G 1.4

L C, F1; L C,

CLOSE LIBRARIES AND GO HOME

F3; L C, F4

126

LSF

This program was last revised on August 14, 1981. LSF
performs a least squares fit between a particular region of
the average of scans (initially just scan number 1) and the
same region Of a remaining scan. The program is written in
the PDP-12 minicomputer interpretive language FOCAL-12.

Accessiblity to minimum of two tape drives is necessary:

UNIT 1: Tape containing scans of uniformly separated data

UNIT 2: Tape on which to store averaged data (floating
point)

Following is a list of symbols with definitions:

A Number Of points between beginning of first scan and
the beginning Of the trigger region (i.e., the region
on which the least squares fit will be performed,

hereafter referred to as "the LSF region")

B A constant used to skip a number of blocks after
Opening a file

F0 Averaged data (in floating point format)

F1 Original data, first point of each scan is separated

from the first point of its neighboring scan by a

constant number Of points

F3

F7

P6

RA

RB

W

X1

127

Final averaged data (in integer format)

File contains the Offset of each scan from the "average”
position Of the scans (a rough Offset usually determined

from some significant feature in the scan)
Index for data points

Counter tO count scans, used to find "average” height
Of LSF region and to access Offset for the scan being

fitted

Calculated number Of points needed to add to all points
of a scan for the "average" height of scan to match

that of the average Of all scans

"Average" height for the LSF region Of average Of scans
Index used to change tapes when data is on two tapes
Sum of residuals squared

Number of points in the LSF region

Number of points in total scan

Trial Offset between scan and average (used to fine

tune the fit of scan and average of scans)

Smallest sum Of residuals squared

Offset position Of smallest sum Of residuals squared
Index to locate the LSF region Of the scans

Approximate number of points needed to add to the
position Of a scan to move to "average" position Of

all scans

128

Y Index used to access all scans on the same tape

Y1 Number Of points between successive scans
The following code is stored on my tape and named "LSF".

Spaces are added to improve clarity, actual code does not

have these spaces.

C
C... INITIALIZE VARIABLES AND OPEN FILES
C
1

.05 L 0, F7, I, #22, O; S X1 = F7(1); S A = 10193; S Q = 0
1.07 S RA = 1834; S RB = 15810; S Y1 = 16384; S Y

ll
*4
...-l

1.10 S N = 1; S B = 256 * 21; S A = A + X1; S X = Y + A

H

.20 L 0, F1, I, #2, 1; L 0, F0, F, #777, 2

READ FIRST SCAN INTO FILE CONTAINING
AVERAGED DATA, INITIALLY EMPTY

H0000

.30 F I = 0, RB; S F0( I+B+X1 ) = F1( I )

DETERMINE AVERAGE HEIGHT OF AVERAGED

DATA

.10 S P6 = O; S X1 = F7 ( N+1 )

.20 F I = A, A+RA; 8 P6 = P6 + F0( I+B ) / N

DETERMINE AVERAGE HEIGHT OF NEXT SCAN

000NN0000

129

P + F1( I-Xl )

CALCULATE AMOUNT NEEDED TO COMPEN-
SATE FOR ANY DIFFERENCE BETWEEEN
AVERAGE HEIGHTS OF AVERAGED DATA

AND NEXT SCAN

CALCULATE THE SUM OF SQUARES OF
RESIDUALS BETWEEN THE AVERAGE AND
THE NEXT SCAN DISPLACED T POINTS,
THEN REPEAT FOR A DISPLACEMENT OF
T+l POINTS, ETC., FOR -16<T<16.
KEEP THE DISPLACEMENT THAT GIVES
THE SMALLEST SUM OF RESIDUALS
SQUARES

2.30 s p = 0

2.40 F I = x, X+RA; s p =
C..

C..

C..

C..

C..

C..

2.50 s p = ( p - P6 ) / ( RA + 1 )
C..

C..

C..

C..

C..

C..

C..

C..

C..

C..

3.10 s T=-15; s U=9 E 99
3.20 s R = 0

3.30 F I = x-x1, X-X1+RA; s R = R

.40
.50
.60

< F0 ( I+B+Xl-Y ) / N - FL( I+T) + P > ** 2

IF ( R—U ) 3.5; S T =
S U = R; S W = T; S T
IF ( T—16 ) 3.2

T + l; G 3.6

= T + 1

133-0000

00004:-

130

ADD SCAN (APPROPRIATELY DISPLACED)

INTO SUM OF PREVIOUSLY FITTED SCANS

.10 F I = Y + 15, Y + RB - 15;

S F0( I+B-Y ) = R0( I+B—Y ) + F1( I+W+Xl)

INCREMENT INDICES AND CONSTANTS.
CHECK TO SEE IF GO TO NEXT SCAN,
NEXT TAPE, OR IF DONE

.20 S X = X + Y1; S Y = Y + Y1; S N = N + 1
.25 IF ( Y + 10 - Y1 * 8 ) 2.1
.27 S Q = Q + 10; IF ( Q - 15 ) 5.1

CLOSE TWO FILES, OPEN FINAL
AVERAGED DATA FILE (INTEGER FORMAT),
CLOSE THE REST OF THE FILES, AND
QUIT

.30 L C, F1; L C, F7; L 0, F3, 1, #777, 2
.40 F I = 15, RB - 15; S F3( I+B ) =
FITR< F0( I+B) * .4 - 400.5 >

.50 L C, F0; L C, F3; QUIT

SUBROUTINE TO SWITCH F1 and F0

FILES, I.E., PUT ON OPPOSITE TAPES

131

5.10 L C, Fl; L 0, Fl, F, #777, 1
5.20 F I = 0, RB; S Fl( I+B ) = R0( I+B)
5.30 L C, F0; L C, Fl; L 0, F0, F, #777, l
.40 L 0, Fl, I, #2, 2; S Y = 0; S X = A; G 2.1

NOTE: I+W+X1 FROM STATEMENT 4.10

SECOND HALF; IF SO, SET Y = 256 IN
LINE 5.40 AND OPEN FILE ONE BLOCK

5
C
C
C... MAY BE A PROBLEM ON FIRST SCAN OF
C
C
C SOONER

C

132

PTLSF

This program was last revised on August 7, 1982. PTLSF
performs a least squares fit on line peaks between the first
scan and each succeeding scan, then sums the scans appro-
priately displaced in a separate file. The program is
written in the PDP-lZ minicomputer interpretive language
FOCAL-12. Accessibility to a minimum Of three tape drives

is necessary:

UNIT 0: Contains approximate Offsets for each scan. Also

contains the least squares fit calculation positions.
UNIT 1: Contains the original data.

UNIT 2: Contains the averaged data.

Following is a list Of symbols with definitions:
D1 Trial index used with the least squares fit

D2 Flag indicating when 'h) change tape and when to quit

D3 Constant containing numbercfi’scans on each tape
D9 Best relative displacement for scan being tested
F0 Array containing averaged data (floating point format)

Fl Array containing original data

1F7

M1

N1

RB

SS

S6

88

W1

133

Block 21, positions 1 through 16 contain approximate
offset for each scan relative to the position of a
strong line in scan 1; positions 17 through 53 contain
the positions at which the least squares fit will be

calculated (scan 1 positions).
Data point index

Average difference in intensities between scan to be

tested and the first scan (from S5 and S6)
Counter to count scans

Number Of positions at which least squares fit is to

be calculated (LSF points)

Counter to count scans on a particular tape; manually

reset to zero when tape is changed.

Counter to count scans

Total number of points per scan

Average intensity of averaged data at LSF points
Average intensity of trial data at LSF points

Minimum sum Of residuals squared (residuals are the
difference between averaged data at LSF points and

trial data at LSF points)
Marks first point of scan after accounting for Offset
Index to locate first point of trial scan

Position Of a least squares fit line (temporary)

134

2X1 Approximate number of points trial scan must move to

left (+) or right (-) to match first scan

X2 Position Of a least squares fit line (temporary)
X3 Position Of a least squares fit line (temporary)
X4 Position Of a least squares fit line (temporary)
Y1 Number Of points between first points Of successive

scans (scan separation)

Z Sum Of squares of residuals between first scans and

trial scan

The following code is stored on my tape and named "PTLSF".
Spaces are added to improve clarity, actual code does not

have these spaces.

C..

C.. INITIALIZE VARIABLES AND OPEN FILES
C..

1.10 L0, F7, #21, O; L 0, F1, I, #22, l

1.20 L 0, F0, F, #700, 2

1.30 S X1 = 0; S N1 = 36; S D2 = l; S D3 = 8

1.40 S RB = 18944; S Y1 = 20480‘

1.50 S N = 1

C..

C.. PUT FIRST SCAN INTO "AVERAGED"
C..

1.60 F I = 0, RB; S FO(I) = F1(I)

co :9 u» 0: :0 To C) (3 O r) (3 (1 N! no to N! 53 to In N) (3 <3 C: C) (3 O

.10
.20
.30
.40
.45
.50
.60
.70

.10
.20
.40
.50
.60

$5 =0

135

DETERMINE AVERAGE INTENSITY OF POINTS
WHERE LEAST SQUARES FIT WILL BE
CALCULATED, FIRST FOR FIRST SCAN

THEN FOR TRIAL SCAN

I = 17, N1+16, 4; D 7

P = N — ( D2 - 1 ) * 8; S N = N + 1; S D1 = -30

W1 = Y1 * P; S W =

$6 = 0

W1 + Xl

I = 17, N1+16, 4; D 9

S
F
S
S X1 = F7( N ); S 88 = 9 E 30
S
S
F
S

M1 = ( S6 - ss ) / Nl

DO LEAST SQUARES FIT OF TRIAL SCAN
TO AVERAGE OF SCANS THAT HAVE BEEN
SUMMED TO FIND THE OFFSET FOR TRIAL
SCAN, BASED ON PRESELECTED LINE
POSITIONS

S Z = 0
F I = 17, N1+16, 2; D 8

IF < Z - 88 > 3.5, 3.6, 3.6

S D9 = D1; S 88 = Z

S D1 = D1 + 2; IF < D1 - 30 > 2.5

noonquooonmooommooombpnnopn

.10
.20
.10

.20
.30

.10

.10

.20

136

ADD TRIAL SCAN INTO AVERAGE OF SCANS
APPROPRIATELY DISPLACED. GO TO NEW
TRIAL SCAN, CHECK FOR NEW TAPE 0R END

F I = 0, RB-30; S FO(I) = FO(I) + F1( I + w + D9 )

IF ( N — D2 * D3 ) 2.1

IF ( l — D2 ) 5.1

GET REST OF DATA FROM OTHER TAPE

S D2 = D2 + l; L C, F7; L C, Fl

L 0, F7, F, #21, 1; L 0, F1, I, #22, 0

CLOSE FILES AND QUIT

L C, F7; L C, F1; L C, F0; QUIT

SUBROUTINE TO FIND AVERAGE

INTENSITY OF AVERAGED DATA

S X = F7(I): S X2 = F7(I+1); S X3

F7(I+2); S X4 = F7(I+3)
S 35 = SS + < F0(X) + F0(X2) + FO(X3) + FO(X4) > / N

SUBROUTINE TO CALCULATE SUM OF
RESIDUALS SQUARED, WHERE RESIDUALS
ARE DIFFERENCE BETWEEN AVERAGED

137

C.... DATA AND TRIAL DATA AT LEAST
C.. . SQUARES FIT POINTS
C.. -

8.10 SX=F7(I);SX2=F7(I+1);SQ=P+(D2-l)*8
8.20 SZ=Z+<F0(X)/Q-Fl(X+W+Dl)+Ml>**2+
< F0( x2 ) / Q - Fl( X2+W+Dl ) + Ml > ** 2

SUBROUTINE TO FIND AVERAGE DENSITY

OF TRIAL SCAN

@0000

.10 s x = F7(1); S x2 = F7(I+1); S x3 = F7(I+2);
S X4 = F7(I+3)
9.20 8 S6 = 86 + F1( X+W+Dl ) + F1( X2+W+Dl ) + F1 ( x3+w+ D1 )

+ F1( X4+W+D1 )

APPENDIX II

A COPY OF THE PUBLICATION OF OUR

ANALYSIS OF v of CD Br

4 3

APPEND IX I I

A COPY OF THE PUBLICATION OF OUR

ANALYSIS OF v4 of CD3Br

sou-NM. or MOLECULAR seecrnmcorv 90. 33-42 (198!)

An X-Y Coriolis Perturbation in u. Of CD,Br

P. M. WlL‘l‘, F. W. Hecxea, AND I. D. FBH’RIBACH
Department of Physics. Centre College. Danvilie. Kentucky 40422

AND

DALE B. BAan AND T. H. EDWARDS
Department of Physics. Michigan State University. East Lansing. Michigan 48824

The mam-2213 cm‘| ofthe v. band in CD.Br was remeasured at a resolution limit
of0.025cm". Uneassiutmentswereextendeduptol - SOinsomesubbands. Transitions
intheKAK - -8subbaodwereassigned.aodthepenurbationapparentinthisregionwas
attributed to the s-y Coriolis interaction with v, + r1" + PP. The s-y Coriolis coupling
parameter W... and the v, + of' + '3' band center (in cm") are 0.01960 and 2339.11 for
CD.”8r. while the corresponding values for CD.“Br are 0.0!956 and 2337.95.

INTRODUCTION

For several years it has been known from the infrared study of Peterson and
Edwards (1) and the Raman work of Edwards and Brodersen (2) that the k'l'
- -7 energy levels in v. of CD,Br are perturbed. The effects of the perturbation
are easily recognized from the appearance of 'Q. in Fig. l of (I), and of “Q4
and 0Q... in Fig. 2 of (2). A similar perturbation observed in the k’i' - +6 levels
of v. of CH.Br has been identified by Betrencourt-Stirnemann et al. (3) as an
x-y Coriolis interaction with the i, - l. - :l levels of v, + v, + v... Their analysis
also showed that while the resulting eflects were most pronounced in the K AK
- 5 subband,l the perturbation produced widespread effects that could not be
neglected in neighboring subbands.

Figure l is a plot of residuals from Peterson and Edwards‘ (1) analysis of the
K AK - -6. -7. -9. and -10 subbands; they were unable to assign transitions in
the KAK =- -8 subband. These residuals may be explained qualitatively by an
x-y Coriolis interaction with a nearby vibrational level P, with rotational levels
situated as shown in Fig. 2. From the fundamentals of CD;Br (4). no binary com-
bination. and only one ternary combination, v, + u, + u.. provides a probable
explanation for the perturbing vibrational state. Using C... = —(g, + c.) we cal-
culated the energy level pattern for is =- l. = 1- l and found that, with a downward
anharmonicity shin of about 5 cm" in the band center. the resulting levels of
v, + v, + u. fit the pattern in Fig. 2. it appeared from this evidence and the similar

' We use It as the signed quantum number for the projection of angular momentum on the molecular
symmetry axis. and K =- Ill.

33 0022-28538 lll mm. "502.0010
Copyright .3. lfilll by Aeademu: Press. inc.
All rights at teptmlut'lmn at any term reserved.

138

139

 

 

34 WILT ET AL.
9
4 @- gm 4. ~ ’.
our '1' m
, O. l . a. use Ff...

‘- . -

C. h . . . . — . ..‘7
3 » " ~ 0 use - tl
° “so. eo°0
‘1' ’ e“

4 -- . 1 1 J use -
3 °~v are an so -7— "' t‘
r L'o '9!" In 0 ‘0. _
2 t - , ’ , - .5

° . x-'rt.n aseo '. _

7 4
, '0 DJ."

 

6) ®

Fro. l. Wavenumber residuals vs 1' for the KAK - -6. —7. -9. and -10 subbands of CDgflr.
Values m from the analysis of Peterson and Edwards (1 ).

Fro. 2. Relative bositions of the levels of v. and the perturbing level a, necessary to explain the
residuals plotted in Fig. I. An r-y Coriolis interaction is assumd. I

case of CH,Br that the perturbing level in question for v. of CD,Br is most probably
”3 + ”f‘ + Vf‘.

We present below new experimental data and a quantitative analysis supporting
this conclusion. During the final stages of our work we learned that Graner (5 )
has also suggested that the perturbing vibrational state is v, + vf‘ + 9“.

EXPERIMENTAL DETAILS

The spectrum of v. of CD,Br was obtained using the Michigan State University
near-infrared grating spectrophotometer interfaced with a PDP-IZ minicomputer.

The experimental conditions are listed in Table I. The spectrum was run in
segments approximately 12 cm" long. Each segment was scanned 16 times using
an appropriate time constant, then multiply sampled in the manner recommended
by Willson and Edwards (6). Following this. each scan was baseline adjusted
and made linear in frequency. The 16 scans were subsequently averaged. im-
proving signal-to-noise ratio (SIN) by a factor of ~4. The averaged spectrum was
then digitally smoothed (6) and deconvoluted. improving the resolution limit by a
factor of ~2.5 to 0.025 cm".

The signal-averaged spectrum was calibrated via a complete run of the CD,Br
spectrum plus calibration gases. using Edser- Butler interference fringes as de-
scribed by Rao et al. (7).

The portion of the spectrum from 2255 to 2263 cm" is shown in Fig. 3.

A table listing the observed frequencies and transition assignments will be in-
cluded in the Ph.D. thesis of Bardin (8). These data have also been deposited in
the Editorial Office of the Journal of Molecular Spectroscopy. Please contact
the authors first for these data.

DESCRIPTION OF THE SPECTRUM

The u, region from 2242 to 2273 cm ' contains the Q branches "Q7 through
"Q... and "PM.“ lines for the KAK = —3 to -- l2 subbands. In general. the

140

 

PERTURBATION IN v. OF CD,Br 35
TABLE I
Experimental Conditions

Region: 2242-2273 an"
Pressure: 3-6 torr-
Path Length: 12.6 ll
Detector: lnSb 0 77 K
Grating: 300 ll-
Callbratlon Gases: CO (1-0)‘

~20 0.2.0)"
3?$¥§.3§11:‘}?2. 0.0026 an"

Resolution um: 0.02.0.0: an“

 

 

'Une frequencies taken fru Ref. (1_5_).

bLine frequencies taken from Ref. (L6).

appearance of the spectrum is that of a normal perpendicular band composed
of two isotopic components (CD,"Br. CD,"Br) of approximately equal abundance.
almost coincident band centers, and slightly difl‘erent B values. The Q branches
degrade slightly to lower wavenumber except for ”Q. which is much more strongly
red-degraded. The "Br—"Br isotopic splitting of HM.” lines in our spectrum be-
gins to be resolved around} = 20 for K AK - -3. -4, at which point the doublet.
spacing of =0.025 cm" can be predicted by the different B. values (5 ), an efl'ective
of for each species (I ). and an isotopic shin in the v. band center of less that 0.010
cm". Figure 3 shows a typical portion of the spectrum and gives many line
assignments. We observed no isotopic splittings for KAK s -7. -9. -10. —11.
or - 12 transitions.

The K AK = -6 and -8 transitions overlap for low J , and are first resolved
beginning at 2261.6 cm". The ’P.(J) series then appears as a well-resolved iso-
topic doublet which can be followed to about] = 50. The 'P.(J ) isotopic doublets
have anomalously large separations for] 2 12. and the "Br component. in contrast
to the situation in other subbands. is the lower-wavenumber member. The reason
for this inversion is discussed below. The wavenumber separation of lines in the
'P.(J) series is anomalously large and is larger for the "Br component than for the
7”Dr component. The series 'P.(.I) for "Br was assigned through J = 20, above
which point it merges with 'P,(J). while the corresponding "Br series was assigned
through J = 24. above which it merges with the ’P..(J) series. No convincing
assignments could be made for the extensions of the PP.(.I) series. The line
PP.(17) for "Br may be split into a doublet by an unidentified. localized perturba-
tion. No lines attributable to v, + v, + v. were observed.

141

 

 

 

 

 

 

 

 

 

 

 

 

36 WlLT ET AL.
.— 4 T . . f '3 - 'gm
H H .3: 5'7. r‘n r‘1 r'1 '-“'
L a T . 1 'gm
a h r‘r 3. n F}. g :m
I cite. I
a
2
.-
$
5 col.
0
C
‘ '0"
I U I U f I U I I r I I ' I I I V T U I 1
use ss 57 so use
I! ' I
'IJI
a r"! h .. f '
v v v ‘9 . r 'r'm
H—T'fi" 33 ‘ '5‘"
fl ' . u . ¥ . f h f 'mr
'1 a ‘1‘ H ‘1 r5 r5 'r'“
.... 7. U
l
i
3 eel.
U.
3 '0.
l— 1 V f I I ' I I I T T I I I l l U V I I
use so or 02 as:
Ice")

Fro. 3. Experimental and computer-calculated spectra of v. of CD,Br from 2263 to 2255 cm".
The experimental conditions are as stated in the text. and the calculation utilizes the constants in
Table II for v. and v, + v, + v..

THEORETICAL MODEL

We have attributed the anomalies described above to an x -y Coriolis interaction
between v. and v, + vf‘ + w.“ in which the k'l' = —7 levels of the former state
are nearly degenerate with the k'l' = +6 levels of the latter. We have allowed for
the possibility of Fermi resonance between these vibrational states. For each value
of J', the upper-state energy levels involved in the interaction may be calculated
by diagonalizing. for an appropriate range of k values. the 4 x 4 matrix shown
in Eq. (1).

142

37

PERTURBATION IN V. CE CD,Br

 

A— + « .‘Jl— " oflsn ._l— u «“3 .— " nsnvm

a a + «.7.-. a 3m
c 2 + «Sara:
2 + «5&3: c

A- + v5.5.7; rlr ads: .-I— n a? .— u as; A— + «.‘a.l— " owi—

252235

Aux $1....— 11. on; .2.—

35... n .«3 ....

" owsn .— rlr 63v”

‘3

u «a ._ u na—

3 (...L n «an
A«.\. ..+— H ow;—

 

143

 

 

 

 

38 err ETAL.

3““). f i
no.2? fi L - c ;
nouzr' semi

:
2 observed
1
seleeletad
I—* f ' T ‘ f I ' ' ' r ' I
14” 1470 1471

cull

Fro. 4. Comparison of the experimental and computer-generated spectra for the v.. v, + v. Fermi
and x-y Coriolis interacting bands in CI-IJ. Experimental data and constants are taken from Refs.
(9) and (12).

In Eq. (1). the diagonal elements are defined as follows:
[EM-.1. Ic)/lrc - v: + B;J(J + 1) + (A; - B;)k’ - 2A.;Jd. + 1,310 + Did.
+ nthk' - DLJ‘U + 1)’ - DL‘JU + l)lc' - th‘. (2)
E(v,. wk. ref. .1. kWrc ' v!“ + EMU + l) + (Ah. - 8;“)? «‘0: 2A,{.¢It
2: nS'VU + Di: 1: 113“” - DWI + l)’ - Damn] + I)!" - th‘, (3)

where the upper signs are to be taken when I, - l. = +1. and the lower when
I. - l. - -1. (... =- -(C. + is). and the Fermi resonance element (9)

W - W. + aJU + l). (4)

The x-y Coriolis matrix element (9. 12) is composed of a vibrational factor
W... and a rotational factor

F(J.It : l) I {J(J + l) - k(k :- l)}"‘. (5)

The dependence of the vibrational factor W ... on fundamental molecular constants
may be derived using the phase conventions and procedure of Di Laura and Mills
(10) as extended by Anderson and Overend (II ). For C..... molecules we have
performed these calculations for two interacting E fundamentals. and for the case
studied here: v. with v, + vf' + v.“ and. as cited below. as with v, -+ v.. The
results are available upon request; they agree with those quoted by Matsuura
er al. (12) for the case of the fundamentals.

The above theoretical model is adequate to explain the details observed in our
spectrum of v. of CD,Br in the region 2242-2273 cm“. The wavenumbers of the

144

PERTURBATION IN 9. OF CD,Br 39

observed transitions are calculated from the eigenvalues of the matrix in Eq. (1)
and the ground-state energies which are calculated from the expression

EmuU. k)/hc = BX] + l) + (A' - B")k‘
- DSJ‘U + l)’ - DSKJU + l)k‘ - fik‘. (6)

The intensities of the transitions are calculated from the eigenvectors of Eq.
(1). the appropriate vibrational transition moments M. and M3,. (10), rotational
line strengths. nuclear spin statistical weights, and Boltzmann factors. Transitions
to the states labeling the two left columns in Eq. (1) are allowed when Ak = +1.
while transitions to the states labeling the two right columns are allowed
when Alt - - 1.

We have written a computer program to perform the calculations described
above and to generate a computed spectrum composed of overlapping "Br and
"Br components. the ratio of whose intensities is equal to the ratio of the natural
abundances of the isotopes. This program was tested carefully and was found to
reproduce correctly the v. and v, + v. Fermi and x-y Coriolis-interacting bands
in CHJ (9) and the simpler case of v. and v, + v, + v. in CH,Br which does not
involve a Fermi interaction (3). As an example of the agreement between ob-
served and calculated spectra. we reproduce in Fig. 4 the region 1468- 1472 cm“
in CH,I (12). where the x-y Coriolis effects are strongest and are responsible
for the doubled Q—branch. The calculation of Fig. 4 is based on values quoted in
(9) and (12), and used a ratio of vibrational transition moments IM,./M,| = 0.10
2 0.05, which is somewhat lower than. but within the error limits previously
determined by Malti and Hexter (13). We have also confirmed that the sense of
the perturbation is negative. i.e.. W-MaoM, is negative. .

We have carefully investigated the effects on line intensities produced by the
signs of W. W... and the ratio of the vibrational transition moments. Our conclusion
is that the intensity perturbation depends on the sign of the product of W and the
vibrational transition moment ratio. and is independent of the sign of W”.

ANALYSIS OF THE SPECTRUM

The analysis of v. of CD,Br that we present here assumes that the x-y Coriolis
perturbation is localized in the KAK :- -6 to - 10 subbands and that the band
constants of Peterson and Edwards (1 ). obtained by assigning 0 weights to the
KAK a -7, -8. and -9 subbands. can be used in Eq. (1) to explain the other
transitions in the v. spectrum from 2242 to 2273 cm". This assumption was
modified slightly as our analysis progressed. and will be discussed below.

We have confined our analysis to the K AK = -3 to -10 subbands. for much
of which we have improved data (8). However. it became desirable to include
as many lines as possible in the KAK - —3. -4. and -5 subbands. and many
of these occur in the region 2273-2285 cm". Hence, we have combined some
data from (I) with the new measurements (8). Comparison of lines measured
in the two experiments shows that the results are consistent to about :6
x 10” cm".

We have detected no experimental evidence for a Fermi resonance between
v. and u, + uf' + vf'; thus our analysis assumes W = 0. Equation“) then factors

145

40 WlLT ET AL.

TABLE ll
Molecular Constants from the 17.. u, + vf' + u." Interaction in CDgBr

 

 

CD3798r c033‘sr
Plflfltlf' V4 VJ’VST’VS V4 VJWSTVG
6° 2296.460(5) 2339.17 2296.453(5) 2337.95
11' 2.58981 a 2.5963 (10) 2.58981 6 2.5963 (10)
8' 0.257199 a 0.2556 (25) 0.256088 a 0.2561 (25)
r -7 " '7 .
DJ 1.87 (6)1110 0J 1.89 (6)xlO 6 0J
. ‘6 re - I
”.111 2.115 xlO 0“ 2.45 (40)x10 0“
0K 0K 0K 0‘ 0‘
Ac 0.47422 0.31675 0.47422 0.36867
u 0.01960 (10) 0.01956 (10)
110 2.603 6 2.603 6
00 0.257328 c 0.256217 c
0: 1.945 x 10" 6 1.945 x 10'7 6
03" 2.115 x 10" 6 2.115 x 10" 6
0" 1.0 x 10'5 6 1.0 x 10'5 6

 

_________l_____

A11 para-stars meted in ca"

The errors quoted in parentheses are estieated uncertainties of the last
significant digits.

a Constrained by mm a: or a: m- m. (1_).

b Constrained to values fro- Ref. (1).

c Hicrouave values fro: Ref. (5).

into two 2 x 2 matrices. one of which is the central 2 x 2 block containing the
(2. 2) and (3. 3) diagonal elements of Eq. (1). Furthermore. the thirdoorder terms
1), and n. of Macs (14) were neglected.

The perturbing level u; + uf‘ + It.“ involves 17,. for which the "Br-"Br
isotopic shift (~ 1.3 cm") is appreciable (5 ). Consequently. the quantitative effects
of the perturbation on the v. "P..(.I) series will be different for each Br isotopic
species. The wavenumber separation between the (2. 2) and (3. 3) diagonal ele-
ments in Eq. (1) is smaller for CD,"Br than for CD,”Br. Since the (2. 2) element
is larger than the (3. 3) element. the effect in v. of the perturbation will be a
downward shift in the upper-state energy level for "P..(.I ) transitions. the shift being
significantly greater for CDamBr than for CDJ’Br. These statements are valid for
.I" s 24. the only values for which we have identified transitions. For "P.(20) this
downward shift is found to be ~0.22 cm" for CD.."Br and ~0.08 cm'I for CD37'Br.
The result is a strongly red-degraded K AK = -8 subband, and an inversion of the

146

PERTURBATION IN v. 0F CDaBr 41

0.05» O I'P,(Jl

72 t
. r
9: 0 Pol J)
..1 . ,
3 0.004 ‘. " . ~ .1
r . ‘g
a; 10 so so so
8 [ .- 'em
. "
NJ P.(Jl

 

Pro. 5. Wavenumber residuals vs J' for the KAK - -6. -7. -9. and -10 subbands of CD.Br.
Values are from the present analysis.

isotopic components in the isotopic doublets from the normal situation where the
CD,“Br component is higher in wavenumber.

Our analysis used the values from Ref. (1) for the ground-state constants. except
that we allowed for the isotopic variation in B. (5 ). We assumed no isotopic varia-
tion of ad. 04'. and A. - A,;.. but found that it was necessary to allow a small
isotopic variation in u‘.’ in order to reproduce the observed isotopic splitting. The
distortion constants for v, + vi‘ 4» 63‘ were constrained to ground-state values.
The band centers for this state were originally estimated to be near 2338 and
2339.3 cm" for the "Br and "Br species. respectively. The remaining parameters
in Eq. (1) were then varied in a least-squares fit of the assigned transitions.

The band parameters resulting from the least-squares fit are shown in Table II
along with the values of constrained constants used in the analysis. These constants
reproduce 277 lines in the K AK :1: - 3 to - 10 subbands with a standard deviation of
6 x 10" cm“. The new residuals shown in Fig. 5 are much reduced compared
to those in Fig. 1. Many of the parameters quoted here for v, + vf‘ + vf' have
large uncertainties and the values of 11.. Al}. (1‘. and a' are highly correlated.
As for CH3Br (3). A; and the isotopic shift in v. difier somewhat from values
predicted from measurements involving fundamentals (5). The uncertainty in v.
of v, + v, + v. is estimated to be at least 0.3 cm". This situation may be attributed
to the absence of assigned lines in u, + v, + v.. It is gratifying to find that W n, is
essentially the same for both isotopic species.

In order to reproduce observed wavenumbers for 40 5 J s 50 it was found
necessary to vary Peterson and Edwards' (1) values of D}, and D 3‘ in u.. (The
previous analysis was done for an average of the two isotopes and was limited to
J 5 35.) In addition. observable effects of the x-y Coriolis interaction extend
into the K AK = -3 subband. e.g., 'P,(50) is shifted by about 0.03 cm". Thus the
assumptions upon which our initial analysis was based. while very useful. are not
quite consistent with the observed data.

To improve matters significantly it would be necessary to remeasure the entire
band. preferably with a resolution appreciably higher than presently available to
us. and to reevaluate the V. band constants using data from throughout the band.

Using the results of the least-squares fit. we have calculated the u. spectnrm
and included part of the results in Fig. 3. The good agreement shown there is

42

147

WILT ET AL.

typical. and supports both the model used and the values of the molecular constants
given in Table II. Since no transitions attributed to u, + u?‘ + u.“ were observed.
we were unable to determine Mags/M4; our calculation assumes 0 for this ratio.

ACKNOWLEDGMENTS

Wilt. Hecker. and Fehribach wish to make acknowledgment to the Donors of the Petroleum
Research Fund. administered by the American Chemical Society. for the partial support of this research.
and to acknowledge generous support from Research Corporation of America. We also thank Pro-
fessorl. Overend for making available original spectra showing examples of: -y Coriolis perturbations.

Racerveo: March 26. 1981

WN~

you.

REFERENCES

R. W. PereasoN AND T. H. EDWAaDs. J. Mol. Spectrosc. 41. 137-142 (1972).
T. H. BDwAaDs AND S. BaooexsoNJ. Mal. Spectrosc. 54. 121-131 (1975).

. C. BETRENOOURT-S‘I’IRNBMANN. 0. Games. AND G. GUELACHVILI.J. Mol. Spectrosc. 51. 216-

237 (I974).

. E. W. JONas. R. J. L. Pomeweu. AND H. W. TrroursoN. Spectmclrr'nr. Am: 22. 639-

646 (I966).

. 6. Owen. J. Mol. Spectrosc.. in press.
. P. D. WILLsON AND T. H. EDWAxDs. Appl. Spectrosc. Rev. 12. 1-81 (1976).

K. NAaArrAar RAD. C. J. Huurrraavs. AND D. H. RANK. "Wavelength Standards in the infrared."
pp. 160. 161. Academic Press. New York. 1966.

. DALI E. BAaDrN. Ph.D. dissertation. Michigan State University. East Lansing. Michigan. to be

submitted.

. l-i. MA‘rsuuaA. T. NAxAOAwA. AND J. OveeeNo. J. Chem. Phys. 59. 1449-1456 (1973).
. C. DI LAUIO AND 1. M. MILLs. J. Mol. Specrmsc. 21. 386-413 (1966).

. D. R. ANDeesoN AND 1. Memo. Spectroclrinr. Acre 28A. 1231- 1251 (1972).

. H. MArsuuaA AND 1. OveaeND. J. Chem. Phys. 55. 1787-1797 (1971).

. A. MAxr AND R. Hexrea. J. Chem. Phys. 53, 453-454 (1970).

. S. Mans. J. Mol. Spec-nose. 9. 204-215 (1962).

. G. Guaucrrvrtr. J. Mol. Spectrosc. 75. 251-269 (1979).

C. Auror- AND G. GuaLAcrrvru. J. Mol. Spectrosc. so. 171- 190 (1976).

APPENDIX III

THE FREQUENCIES AND ASSIGNMENTS OF

THE 0 BAND OF CD Br

4 3

148

APPENDIX III

THE REQUENCIES AND ASSIGNMENTS OF

131'

 

 

 

 

 

THE 0 BAND OF CD
4 3
79 81
003 arr-CD3 6r v4 Observed Vacuun Havana-hers
(add 2200 en’1 to each value)
'2,(J1 'PatJ)

J 796: (unresolved) 816: 19!: unresolved 61’:
3 76.379

6 73.663 71.966

7 73.363 71.671

6 70.934

9 74.306 70.440

10 73.767 69.929

11 73.270 69.612

12 72.731 66.696

13 72.233 66.376

16 71.717 67.637

13 71.193 67.363
16 70.666 66.626
17 70.163 66.310

16 69.666 63.792

19 69.129 63.273

20 66.612 64.731

21 66.096 66.260

22 ‘63.721.

23

26

23 63.997

26 66.613

27 66.939

26 66.646

29 63.919 60.061 60.113
30 63.610 39.366 39.367
31 62.666 39.023 39.063
32 62.363 36.306 36.337
33 61.646 37.967 36.063
36 61.331 37.666 37.317
33 60.606 36.947 37.004
36 60.291 36.431 36.667
37 39.771 33.912 33.966
36 39.230 33.367 33.637
39 36.670 36.930
60 36.332 36.611
61 33.626 33.693
42 33.314 33.361
63 32.792 32.663
66 32.260 32.361
63 31.737 31.636
66

67 30.716 30.792
66 30.193 30.273

149

79

“’3

(add 2200 car

P
PaiJ)

 

La

79’

It (unsolved) 6"Ir:

..a
OOONO MON

135

73.131
72.606
72.066
71.370

70.327
70.006
69.666
66.970
66.432

67.931
67.617
66.696
66.373
63.639

63.336
66.616
66.296
63.776

62.732
62.222

66.300
66.012

63.669
62.974

61.939
61.626

”0’”
60.600
79.676
79.366

76.326
77.613
77.296
76.766
76.266

73.736
73.226

76.169
73.671

73.162
72.661
72.160
71.624

70.366
70.070
69.332
69.036
66.323

66.000
67.679
66.963
66.667
63.923

63.396
66.690
66.369
63.633

62.616
62.302
61.773
61.271
60.747

1

to each value)

lr-Cbsallr 0‘ Observed Vacuu- Havana-hers

P
r‘u)

 

I E6: (unsolved) 3r:

70.360

69.319
66.607
66.263
67.763
67.231

66.722
66.202
63.667
63.169
66.636

66.132
63.611
63.091
62.367
62.031

60.711
60.206

79.669
79.166

76.162

77.106
76.392
76.067
73.369

76.333
74.012
73.691
72.976
72.636

71.916
71.601
70.660

69.667

61

70.382

69.337

66.323
67.606
67.279

66.769
66.236
63.739
63.219
66.711

66.193

79
CD3 Br-CD3

61

150

v4 Observed Vocuus wavenumbers

(odd 2200 cu"1 to each value)

 

 

 

P P
67(3) POCJ)

J (unresolved) 796: '16:
7 67.363

6

9 66.366
10 66.037

11 63.320 61.363
l2 63.007 61.067 61.027
13 66.491 60.366 60.303
14 63.976 60.062 39.966
13 63.439 39.311 39.436
16 62.960 36.990 36.909
17 62.422 36.466 36.363
16 61.901 37.963 37.629
19 61.366 37.413 37.303
20 60.663 36.692 36.763
21 60.362 36.363

22 39.630 33.639

23

24 36.796 36.777

23 36.271

26 37.730

151

 

 

 

 

003796r-60381 v4 Observed Vacuu- Hevenunbers
(odd 2200 cn-l to such vslue)
P P
P9 (J) P10 (J)
J fluoresolved) (unresolved)
9 36.723
10 36.207 36.230
11 37.691 33.736
12 37.176 33.223
13 36.663 32.712
16 36.132 32.197
13 33.660 31.662
16 33.132 31.169
17 36.609 30.633
16 36.106 30.160
19 33.369 49.626
20 33.060 69.103
21 32.366 66.392
22 32.037 66.066
23 31.363 67.371
26 31.023 67.033
23 _ 30.313 66.336
26 49.999 66.026
27 69.676 43.311
26 66.971 46.990
29 46.636 46.661
30 67.949 63.936
31 67.433 63.633
32 66.916 42.927
33 66.403 62.429
36 43.666
33 63.373
36 66.663

APPENDIX IV

THE FREQUENCIES AND ASSIGNMENTS OF THE

v5 BAND 0F CH3CN

APPENDIX IV

THE FREQUENCIES AND ASSIGNMENTS OF THE

v5 BAND OF CHBCN

The frequencies from v5 of CHBCN given in this appendix
were part of the output from the program SYMFIT, a linear
least squares fit of v5 and 2v5(i) of C33CN. The columns

in the table are:

1. Assignment of each transition

(AKAJK(J) a AKAJ K,J)

2. The weight assigned each transition.
3. The observed frequency of each transition.

4. The frequency calculated after the least squares

fit.

5. The residuals, observed frequency minus calculated

frequency.

152

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0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
o .00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

153

‘OBS FREQ

2961.1620
2961.7820
2982.3760
2983.0090
2984.8940
2966.1560
2906.7610
2967.4070
2987.9930
2986.6330
2969.1870
2989.6840
2990.4860
2991.1240
2991.7400
2992.3660
2992.9930
2993.6050

3005.7330
3006.3600
3006.9710

3006.2060
3009.4450
3010.6960

2968.6330
2989.8840

, 2990.4860

2991.1240

CADC FREQ

2969.6281
2989.0158
2988.4034
2987.7908
2983.4970
2982.6829
2961.6562
2961.2016
2961.8165
2982.4316
2983.0468
2984.8932
2966.1243
2906.7399
2967.3554
2967.9706
2968.5662
2989.2014
2969.6165
2990.4315
2991.0463
2991.6609
2992.2754
2992.8697
2993.5037
2996.5709
2997.1636
2997.7962
2996.4066
2999.0207
2999.6327
3000.2465
3000.6561
3001.6676
3005.7451
3006.3561
3006.9671
3007.5761
3008.1893
3008.6006
3009.6121
3010.0237
3010.6357
2988.6842
2989.9140
2990.5292
2991.1467

OBS-CHDC

-0.0396
-0.0345
-0.0536
-0.0376
0.0008
0.0337
0.0211
0.0516
0.0222
0.0466
-0.0164
0.0675
0.0565
0.0777
0.0791
0.0926
0.1033
0.1013

-0.0121
0.0039
0.0039

0.0167
0.0329

0.0623
-0.0512
-0.0300
-0.0412
-0.0207

K J

PP 1,20
PP 1,19
PP 1,18
PP 1.17
PP 1,16
PP 1,14

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RP 0,16
RP 0,14
RP 0,13

‘WT

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
o .00
0.00
0.00
1.00

154

OBS FREQ

2991.7400
2992.3680
2992.9930
2993 .6050
2994.2540
2995.4790
2996.1030
2996.7390
2997.3420
2997.9500
2998.5380
2999.1560
2999.8150
3000.4270
3001.0310
3001.6430
3002.2710
3002.8920
3003.4870
3005.3310
3005.9420
3006.5720
3007.1850
3007.8060
3008.4120

3009.6430

2989.7390
2990.3840
2990.9920
2995.4790
2996.1030
2996.7390
2997.3420
2997.9500
2998.5360
2999.1560
2999.8150
3000.4270
3001.0310
3001.6430
3002.2710
3002.6920
3003.4670
3004.6980
3005.3310

CADC FREQ

2991.7604
2992.3761
2992.9920
2993.6080
2994.2240
2995.4559
2996.0719
2996.6877
2997.3035
2997.9192
2998.5347
2999.1500
2999.7652
3000.3602
3000.9950
3001.6096
3002.2240
3002.8381
3003.4521
3005.2924
3005.9053
3006.5180
3007.1305
3007.7427
3008.3546
3006.9666
3009.5782
3010.1896
3010.8006
2989.9373
2990.5479
2991 .1594
2995.4586
2996.0751
2996.6918
2997.3087
2997.9259
2998.5434
2999.1610
2999.7768
3000.3966
3001.0145
3001.6325
3002.2504
3002.6683
3003.4861
3004.7214
3005.3386

OBS-CADC

-0.0204
-0.0081
0.0010
-0 .0030
0.0300
0.0231
0.0311
0.0513
0.0385
0.0308
0.0033
0.0060
0.0498
0.0468
0.0360
0.0334
0.0470
0.0539
0.0349
0.0366
0.0367
0.0540
0.0545
0.0633
0.0572

0.0648

-0.1963
-0.1639
-0.1674
0.0202
0.0279
0.0472
0.0333
0.0241
-0.0054
-0.0050
0.0362
0.0304
0.0165
0.0105
0.0206
0.0237
0.0009
-0.0284
-0.0078

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RP 0,12
RP 0,11

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0.00
0.00
0.00
0.50
0.13
0.00
4.00
0.50
0.50
0.50
1.00
0.00
0.00
4.00
0.00
0.00
0.00
0.00
1.00
0.25
4.00
0.50
4.00
1.00
1.00
8.00

155

088 FREQ

3005.9420
3006.5720
3007.1850
3007.8060
3008.4120
3009.0410
3009.6430
3010.2680
3010.8710
3011.4770
3012.1320
3012.7100
3013.9540

3015.1850
3016.4130

3017.6350
3018.2460
3018.6600

3021.8620
3022.5340
3023.0660
3023.7240
3024.3210
3024.9550
3025.5620
3026.1660
3026.8000
3027.4060
3027.9790
3028.6300
3029.2240
3029.6640
3022.4340
3023.0810
3023.7240
3024.3210
3024.9550
3025.5620
3026.1660
3026.8000
3027.4080

CHDC EREQ

3005.9560
3006.5730
3007.1898
3007.8064
3008.4226
3009.0386
3009.6543
3010.2697
3010.8848
3011.4995
3012.1139
3012.7279
3013.9549
3014.5679
3015.1806
3015.7928
3016.4047
3017.0163
3017.6276
3016.2385
3018.6491
3019.4593
3020.0693
3020.6790
3021.2865
3021.8977
3022.5067
3023.1155
3023.7241
3024.3325
3024.9409
3025.5491
3026.1573
3026.7654
3027.3736
3027.9816
3028.5900
3029.1984
3029.8069
3022.4731
3023.0903
3023.7073
3024.3242
3024.9409
3025.5574
3026.1736
3026.7696
3027.4054

OBS-CHDC

-0.0140
-0 . 0010
-0.0048
-0.0004
-0.0106

0.0024
-0.0113
-0.0017
-0.0138
-0.0225

0.0181
-0.0179
-0.0009

0.0044
0.0083

0.0074
0.0075
0.0109

-0.0157
0.0273
-0.0295
-0.0001
-0.0115
0.0141
0.0129
0.0107
0.0346
0.0344
-0.0028
0.0400
0.0256
0.0571
-0.0391
-0.0093
0.0167
-0.0032
0.0141
0.0046
-0.0056
0.0104
0.0026

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0.00
0.00
0.00
0.00
0.00
1.00
4.00
4.00
4.00
4.00
4.00
4.00
0.00

156

088 FREQ

3028.6300
3029.2240
3029.8640
3033.5600
3034.1690
3034.7790
3035.3820
3035.9890
3036.6010
3037.2150
3037.8220
3038.4400
3039.0300
3039.6750
3042.0710
3042.6790
3024.1380
3024.7300
3025.3840
3025.9970
3026.6130
3027.2200
3028.4670
3029.0870
3029.7160
3030.3360
3031.5640
3032.1720
3032.7890
3033.3860
3034.0030
3034.6270
3035.2120

3043.2310
3043.8490
3044.4640
3045.0720
3045.6830
3046.2970
3046.9100
3047.4650

CALC FREQ

3028.0209
3028.6361
3029.2510
3029.8656
3033.5465
3034.1588
3034.7708
3035.3825
3035.9938
3036.6049
3037.2157
3037.8262
3038.4364
3039.0464
3039.6561
3042.0930
3042.7019
3024.1405
3024.7575
3025.3748
3025.9923
3026.6100
3027.2278
3028.4637
3029.0816
3029.69“
3030.3175
3031.5530
3032.1706
3032.7860
3033.4052
3034.0221
3034.6369
3035.2554
3035.8716
3036.4676
3037.1032
3037.7185
3036.3335
3038.9461
3043.2406
3043.8524
3044.4636
3045.0749
3045.6857
3046.2961
3046.9062
3047.5160

OBS-CRDC

-0.0061
-0.0270
-0.0016
0.0135
0.0102
0.0082
-0.0005
-0.0046
-0.0039
-0.0007
-0.0042
0.0036
-0.0164
0.0189
-0.0220
-0.0229
-0.0025
-0.0275
0.0092
0.0047
0.0030
-0.0078
0.0033
0.0054
0.0184
0.0205
0.0110
0.0014
0.0010
-0.0192
-0.0191
-0.0119
-0.0434

-0.0096
-0.0034
0.0002
-0.0029
-0.0027
0.0009
0.0038
-0.0510

K J

R 3,11
RR 3,12
RR 3,13

RR 3,14

333333
““647wa
““LL
8555mm

333333333

““““‘

RP 4,

QQ

““

Q‘

333333333

‘
....
O

833332333

WT
1.00

1.00
0.25
0.00
2.00
0.00
0.50
1.00
4.00
1.00
2.00

2.00
1.00
6.00
6.00
0.25
0.50
0.00
0.00
0.50
0.06
0.25
0.00
0.00
0.50
6.00
0.00
0.00
2.00
2.00
0.06
0.00
0.25
0.25
1.00
0.50
1.00
1.00
2.00
6.00
6.00
6.00
4.00
1.00
0.00
0.50

157

OBS FREQ

3046.1160
3046.7210
3049.3360
3049.9360
3050.5260
3051.1630
3051.7150
3052.3740
3053.0030
3053.6010
3054.2160
3054.6220
3055.4360
3056.0360
3056.6500
3057.2510
3057.6590
3059.0570

3059 .6640 '

3060.2660
3060.6610
3036.0670
3036.6740
3039.3360
3039.9450
3040.5640
3041.1670
3041.7960
3042.4470
3042.9990
3043.6430
3044.2600
3044.9120

3046.0990
3046.7140
3047.3340
3052.6740
3053.4610
3054.0930
3054.6660
3055.3060
3055.9130
3056.5250
3057.1260
3057:7470
3056.3350
3056.9440

CALC FREQ

3046.1255
3046.7346
3049.3436
3049.9526
3050.5611
3051.1695
3051.7776
3052.3659
3052.9939
3053.6016
3054.2097
3054.6175
3055.4254
3056.0334
3056.6415
3057.2497
3057.6561
3059.0757
3059 .6649
3060.2945
3060.9046
3036.0671
3036.7056
3039.3239
3039.9422
3040.5603
3041.1763
3041.7960
3042.4135
3043.0306
3043.6476
3044.2645
3044.6610
3045.4970
3046.1126
3046.7262
3047.3432
3052.6611
3053.4723
3054.0630
3054.6934
3055.3035
3055.9131
3056.5225
3057.1315
3057.7403
3056.3467
3056.9569

CEEFCELC

-0.0095
-0.0136
-0.0076
-0.0146
-0.0351
-0.0065
-0 .0626
-0.0119
0.0091
-0.0006
0.0063
0.0045
0.0126
0.0046
0.0065
0.0013
0.0009
-0.0167
-0.0209
-0.0265
-0.0236
-0.0001
-0.0316
0.0121
0.0026
0.0037
0.0067
0.0020
0.0335
-0.0316
-0.0046
-0.0045
0.0310

-0.0136
-0.0142
-0.0092
0.0129
0.0067
0.0100
-0.0074
0.0025
-0.0001
0.0025
-0.0035
0.0067
-0.0137
-0.0129

RP 5,

‘

---~L--- u
U UQNIO‘UUIO‘NO‘D

3:333

,24

‘
....
O

‘

“““

3333333333333333333333333333333

WT

0.00
1.00
1.00
0.13
o.“
0.50
0.00
0.00
0.00
0.00
0.00
0.00
0.50
1.00
0.25
6.00
0.13
0.13
0.13
2.00
0.00
6.00
6.00
0.25
2.00
1.00
1.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

158

088 EREQ

3059.5050
3060.1600
3060.7650
3061.4000
3061.9530
3046.2560

3062.4130
3063.0000
3063.6060
3064.2300
3064.6200
3065.4300
3066.0360
3066.6730
3067.2500
3066.4690
3069.1000
3069.7190
3070.3150
3070.9240
3071.5340
3072.1230
3072.7610
3073.3440
3073.9490
307 4.5420
3075.1510
3075.7400

3071.6360
3072.4630
3073.1100
3073.7340
3074.3510
3074.9760
3075.6140

3076.6060

CADC FREQ

3059.5649
3060.1726
3060.7602
3061.3675
3061.9946
3046.2539
3052.5602
3053.1971
3053.6137
3054.4299
3055.0456
3055.6613
3062.4036
3063.0142
3063.6242
3064.2336
3064.6431
3065.4519
3066.0604
3066.6666
3067.2765
3066.4913
3069.0964
3069.7052
3070.3116
3070.9162
3071.5245
307 2.1307
3072.7366
3073.3429
3073.9490
3074.5551
3075.1613
3075.7676
3061.4331
3062.0502
3062.6670
3063.2633
3063.6993
3071.6655
3072.4751
3073.0643
3073.6930
3074.3013
3074.9093
3075.5169
3006.1241
3076.7310

-0.0599
-0.0126
-0.0152
0.0125
-0.0416
0.0021

0.0092
-0.0142
-0.0162
-0.0036
-0.0231
-0.0219
-0.0224

0.0044
-0.0265
-0.0023

0.0016

0.0136

0.0032

0.0056

0.0095
-0.0077

0.0242

0.0011

-0.0131
-0.0103
-0.0276

-0.0295
-0.0121
0.0257
0.0410
0.0497
0.0667
0.0971

0.0770

RR 6,26
RR 9, 9

noooogco???
8018888313888

159

085 FREQ

3077.4260
3076.0470
3076.6500
3079.2720
3079.6950
3060.5430
3081.1530
3061.7690
3082.3750
3082.9960
3063.6630
3064.2260
3065.4500
3066.0610
3066.6450
3067.2430
3067.6900
3066.4440
3069.0410
3069.6350
3090.2110
3090.6520
3091.4640
3092.1090
3092.6540
3093.9370
3094.5470
3095.1450
3095.7150
3090.5320
3091.1390
3091.7610
3092.3560
3092.9720

3094.2070
3094.7900
3095.3650
3095.9690
3096.5970
3097.1670
3096.4220
3096.9650
3099.6390
3100.2440
3100.6520
3102.6120
3099.7670

CADC FREQ

3077.3375
3077.9436
3076.5499
3079.1556
3079.7612
3060.3666
3061.2447
3061.6534
3062.4616
3063.0694
3063.6767
3064.2836
3065.4963
3066.1022
3066.7077
3067.3126
3067.9176
3066.5224
3069.1269
3069.7312
3090.3353
3090.9396
3091.5433
3092.1472
3092.7511
3093.9591
3094.5632
3095.1676
3095.7722
3090.5420
3091.1496
3091.7566
3092.3635
3092.9697
3093.5755
3094.1609
3094.7660
3095.3906
3095.9949
3096.5969
3097.2026
3096.4093
3099.0124
3099.6153
3100.2161
3100.6206
3102.6266
3099.7606

0.0665

0.1032

0.1001

0.1164

0.1336

0.1764
-0.0917
-0.0644
-0.0666
-0.0734
-0.0137
4 005%
-0.0463
-0.0412
-0.0627
-0.0696
-0.0276
-0.0764
-0.0659
-0.0962
-0.1243
-0.0673
-0.0593
-0.0362
-0.0971
-0.0221
-0.0162
-0.0226
-0.0572
-0.0100
-0.0106

0.0042
-0.0055

0.0023

0.0261
0.0040
-0.0256
-0.0259
-0.0019
-0.0156
0.0127
-0.0474
0.0237
0.0259
0.0312
-0.0166
0.0064

.99????°°°
8883383888

000
O O
GO
GO

0
0
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

s s
CO
CO

160

OBS FREQ

3100.3590
3100.9760

3101.5730

3102 .7670
3103.3920
3103.9990
3104.6060
3105.1690
3105.6070
3106.4090
3106.9750
3107.6140
3106.2490
3106.6060
3109.4360
3110.0270
3111.2410
3111.7900
3112.4300
3113.0140
3113.6110
3106.6060
3109.4340
3110.0260

3111.2400

3112.4290
3113.0140
3113.6110
3117.9360
3116.5560
3119.1310
3119.7350
3120.3540
3120.9300
3121.5060
3122.1450
3122.7090
3123.2930
3123.9190
3124.5160
3125.0650
3125.6330
3126.2660

3127.4830

CADC EREQ

3100.3671
3100.9731
3101.5766
3102.1637
3102.7663
3103.3924
3103.9962
3104.5996
3105.2026
3105.6053
3106.4077
3107.0096
3107.6116
3106.2135
3106.6151
3109.4165
3110.0179
3111.2206
3111.6220
3112.4235
3113.0251
3113.6270
3106.9070
3109.5123
3110.1171
3110.7213
3111.3250
3111.9263
3112.5311
3113.1335
3113.7355
3117.9916
3116.5957
3119.1991
3119.6019
3120.4043
3121.0061
3121.6075
3122.2064
3122.6069
3123.4091
3124.0069
3124.6064
3125.2076
3125.6065
3126.4053
3127.0297
3127.6321

OBS-CADC

-0.0061
0.0029
-0.0056

-0.0013
-0.0004
0.0026
0.0064
-0.0136
0.0017
0.0013
-0.0346
0.0022
0.0355
-0.0071
0.0195
0.0091
0.0204
-0.0320
0.0065
-0.0111
-0.0160
-0.0990
-0.0763
-0.0911

-0.0650

-0.1021
-0.1195
-0.1245
-0.0556
-0.0397
-0.0661
-0.0669
-0.0503
-0.0761
-0.1015
-0.0634
-0.0999
-0.1161
-0.0699
-0.0904
-0.1426
-0.1735
-0.1393

-0.1491

‘WT

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

161

OBS EREQ

3126.6920

3131.6630
3133.4500
3134.6150
3135.6690
3136.4600

3137.6660
3136.2170
3136.6460

3140.6540
3141.6510
3142.4660
3143.6560
3145.4160
3146.0740
3147.2350

CALC FREQ

3126.2340
3126.6354
3129.4362
3130.0365
3130.6363
3131.2356
3131.6346
3133.6292
3134.6241
3136.0405
3136.6414
3137.2417
3137.6415
3136.4406
3139.0393
3139.6374
3140.2351
3140.6323
3142.0256
3142.6217
3143.6131
3145.6490
3146.2476
3147.4430
2947.0904
2956.7719
2966.3657
2965.3363
2994.7312
3004.0657
3013.3416
3022.5567
3031.7075
3040.7699
3049.7995
3056.7324
3067.5657
3076.3579
3065.0499
3093.6650
3102.2102
3110.6961
3119.1376
3127.5550

-0.1434

-0.1516
-0.1792
-0.2091
-0.1515
-0.1614

-0.1735
-0.2236
-0.1933

-0.1763
-0.1746
-0.1557
-0.1571
-0.2330
-0.1736
-0.2060

APPENDIX V

THE FREQUENCIES OF THE 205(l) BAND AND

THE 20 u) BAND OF CH CN

5‘ 3

APPENDIX V

THE FREQUENCIES OF THE 205(1) BAND AND

THE 20 H) BAND OF CH CN

5‘ 3

The frequencies of 2v5(i) of CH3CN were part of the
output of the program SYMFIT, a linear least squares fit
of v5 and 2v5(i) of CH3CN. The 2v5(n) frequencies were
calculated from a single band fit using most of the con-

stants determined by the simultaneous fit. The columns

in the table are:

1. Assignment of each transition

(AKAJK(J) a AKAJ K,J)

2. The weight assigned each transition.
3. The observed frequency of each transition.

4. The frequency calculated after the least squares

fit.

5. The residuals, observed minus calculated frequency.

162

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wwbmmqwuufimmqqmm
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H
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33333889898888888888888

WT

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

ms

OBS FREQ

5935.0150
5946.4620
5957.7530
5969.1002
5960.1569
5991.3622
6002.0997
6013.1600
6023.5059
6034.1232
6044.7000
6055.6366
6064.1299
6075.3170
6067.0215

6112.1633
6122.3572
6132.2323
6142.0919
6151.6197

CELC FREQ

5934.6315
5946.3604
5957.6685
5969.1674
5960.3424
5991.3539
6002.2377
6013.0054
6023.6651
6034.2223
6044.6797
6055 .0367
6065.2993
6075.4609
6065.5226
6095.4652
6105.3469
6115.1169
6124.7941
6134.3664
6143.9112
5966.3305
5966.1566
5965.6613
5965.4367
5964.6716
5964.1520
5963.2600
5956.9565
5960.4643
5961.7995
5964.0190
5964.9266
5965.7169
5966.1446
5969.6470
5970.9770
5972.1520
5973.1662
5974.0907
5967.9944
5974.6734
5965.1975
5965.6150
5966.4320
5967.0466
5967.6651

0.3635
0.1216
-0.1155
-0.0672
-0.1855
0.0063
-0.1360
0.1546
-0.1592
-0.0991
0.0203
0.5999
-1.1694
-0.1439
1.4967

6.6344
7.2403
7 .4382
7.7035
7.7065

C..

QQQQQQQQQQQQQQQ

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mqmocwuwbmbuuHowmummfiwnnuom

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333333333333333333333333333333333333333333333333
DOOHHHHHHHHHHHHHHHHHHHHHHHHHHHNNNNNN~NNNNNNNNNNN N

QUOMNHOUQQO‘mbUNl-‘HNWbUI

Q

WT

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.50
0.13
4.00
1.00
0.50
0.13
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.06
0.00
0.06
0.00
0.00
0.00
1.00
0.00
0.00
0.06
1.00
0.13
0.00
0.00
0.00
0.00

m4

088 FREQ

5966.5636
5969.1659
5969.6265
5990.3662

5997.1101
5997.7459
5996.3223
5996.6915
5999.5547
6000.1947
6000.7664
6001.3729
5993.5924
5994.197 2
5994.6360
5995.4454
5996.0597
5996.6726
5997.2435

6003.4300
6004.0240
6004.6470

6005.6406
6006.4674
6007.1269
6007.6605
6006.3715
6006.9156
6009.5615
6010.1432
6010.6140
5994.4664
5995.0971
5995.7526

CALC EREQ

5966.2610
5966.6965
5969.5116
5990.1262
5993.1920
5993.6037
5994.4150
5995.0256
5995.6362
5996.2462
5996.6559
5997.4651
5996.0741
5996.6627
5999.2911
5999.6993
6000.5073
6001.1151
5993.6071
5994.2256
5994.6442
5995.4624
5996.0603
5996.6979
5997.3151
5997.9320
5996.5464
5999.1645
5999.7601
6000.3952
6001.0099
6001.6240
6003.4636
6004.0756
6004.6675
6005.2967
6005.9095
6006.5196
6007.1296
6007.7393
6006.3464
6006.9572
6009.5657
6010.1739
6010.7619
5994.4903
5995.1040
5995.7166

OBS-CADC

0.3026
0.2694
0.3149
0.2620

0.2542
0.2606
0.2462
0.2066
0.2636
0.2954
0.2611
0.2576
-0.0147
-0.0266
-0.0062
-0.0170
-0.0206
-0.0251
-0.0716
-0.0619

-0.0336
-0.0516
-0.0405

-0.0669
-0.0524
-0.0009
-0.0566

0.0231
-0.0414
-0.0042
-0.0307

0.0321
-0.0219
-0.0069

0.0340

QQ

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QQQQQQQQQQQQQQQQQQQQQ

:3

RP 1,13
RP 1,12
RP 1,11

WT

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

165

088 FREQ

5996.3537
5996.9637
5997.5664
5996.2471
5999.7653
5999.4676
6000.0795
6000.6713
6001.2576
6003.7660
6004.3695
6004.9906
6005.5740
6006.2209
6006.7627
6007.4162
6006.0614
6006.6646
6009.2456
6009.6514
6010.4957
6011.1220

6014.6273
6015.4769
6016.0429
6016.6752
6017.2644
6017 .6697
6016.5152
6019.0495
6019.6650
6020.3573
6020.9459
6021.5634
6025.2541
6025.6631
6026.4763
6027.0536
6027.6636
6015.1049
6015.7326
6016.3253

6016.9357 .

CADC FREQ

5996.3340
5996.9502
5997.5671
5996.1645
5996.6024
5999.4207
6000.0393
6000.6562
6001.2772
6003.7540
6004.3730
6004.9919
6005.6105
6006.2269
6006.6470
6007.4646
6006.0622
6006.6992
6009.3156
6009.9319
6010.5476
6011.1626
6011.7775
6012.3917
6013.0054
6013.6165
6014.2312
6014.6434
6015.4550
6016.0662
6016.6769
6017.2671
6017.6969
6016.5062
6019.1152
6019.7236
6020.3321
6020.9401
6021.5479
6025.1916
6025.7992
6026.4066
6027.0147
6027.6229
6015.0310
6015.6501
6016.2690
6016.6676

0.0197
0.0135
0 .0013
0.0626
0.9629
0.0469
0.0402
0.0131
-0.0194
0.0120
-0.0035
-0.0011
-0.0365
-0.0060
-0.0643
-0.0466
-0.0206
-0.0346
-0.0702
-0.0605
-0.0519
-0.0406

-0.0161
0.0239
-0.0233
-0.0017
-0.0027
-0.0272
0.0090
-0.0657
-0.0566
0.0252
0.0056
0.0355
0.0623
0.0839
0.0695
0.0369
0.0409
0.0739
0.0625
0.0563
0.0461

K J
RP 1,10
RP 1, 9
RP 1, 6
RP 1, 7
RP 1, 6
RP 1, 5
RP 1, 4
RP 1, 3
RP 1, 2
RP 1, 1
RR.1, 1
RR.1, 2
RR.1, 3
RR 1, 4
RR 1, 5
RR.1, 6
RR.1, 7
RR.1, 6
RR.1, 9
RR 1,10
RR 1,11
RR 1,12
RR 1,13
RR 1,14
RP 2,15
RP 2,12
RP 2, 9
RP 2, 6
RP 2, 7
RP 2, 6
RP 2, 5
RP 2, 4
RP 2, 3
RP 2, 2
RR.2, 2
RR 2, 3
RR.2, 4
RR 2, 5
RR.2, 6
RR 2, 7
RR 2, 6
RR 2, 9
RR 2,10
RR 2,11
RR 2,12
RR 2,13
RR 2,14

RR 2,16

771'

0.00
0.00
0.00
0.00
0.13
0.50
0.13
0.00
0.00
0.00
0.00
1.00
1.00
0.00
0.50

0.00
0.00
1.00
0.00
0.00
1.00
0.50
0.00
0.25
1.00
0.13
0.06
0.00
0.00
0.06
0.00
0.00
0.00
0.25
0.25
0.25
1.00
0.50
1.00
0.00
1.00
1.00
0.13
0.06
0.50
1 .00
1.00

166

OBS EREQ

6017.5300
6016.1460
6016.7695
6019.3960
6019.9936
6020.6272
6021.2256

6024.6664
6025.5303
6026.1443
6026 31%
6027.3756
6027.9669
6026.5564
6029.2196
6029.6102
6030.4347
6031.1132
6031.6370
6032.2496
6032.9345
6024.9751
6026.6193
6026.6531
6029.2615

6031.1132
6031.7627
6032.4055
6032.9530
6036.0465
6036.6576
6037.2531
6037.6745
6038.4969
6039.1064
6039.7390
6040.3117
6040.9194
6041.5151
6042.1210
6042.7509
6043.3476
6045.7660

CALC FRED

6017.5059
6016.1239
6016.7414
6019.3566
6019.9753
6020.5915
6021.2073
6021.6225
6022.4372
6023.0514
6024.6909
6025.5030
6026.1145
6026.7256
6027.3361
6027.9462
6028.5556
6029.1649
6029.7737
6030.3621
6030.9901
6031.5976
6032.2052
6032.6125
6024.9669
6026.8250
6026.6605
6029.2962
6029.9155
6030.5323
6031.1466
6031.7644
6032 .3797
6032.9944
6036.0596
6036.6713
6037.2622
6037.6925
6036.5024
6039.1116
6039.7207
6040 .3292
6040.9372
6041.5449
6042 .1523
6042.7594
6043.3662
6045.7920

0.0241
0.0221
0.0461
0.0394
0.0165
0.0357
0.0165

-0.0045
0.0273
0.0296

-0.0070
0.0395
0.0427
0.0026
0.0547
0.0365
0.0526
0.1231
0.0392
0.0446
0.1220
0.0062

-0.0057

-0.0274

-0.0367

-0.0354
0.0163
0.0256

-0.0414

-0.0133

-0.0135

-0.0291

-0.0160

-0.0035

4 .0054
0.0163

-0.0175

-0.0176

-0.0296

-0.0313

-0.0065

-0.0164

-0.0260

K J

R 2,19
RR 2,20
RR 2,21

:3
E:

RR.2,23

33
UN
w ‘
PM
0*

QQQQ

@OQQUIDUWbUIQNG‘O

QQQQQQQQQQQQQQQQQQQQQQQQQQQ

UUNWUWUUUNUUUWUUUJUUUNUWUUUQ’MMUNUU

b
----~
4””
FUN

33333338333333333333333333333333333333333

bébbfihfi
OWDQQM‘

Q
....

WT

0.25
0.25
0.00
0.00
0.00

0.00
0.00

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

167

088 EREQ

6046.4010
6047.0051
6047.5951
6046.2572
6046.7462
6049.4792

6039.7610
6040.3660

6047 .1371
6 047 .7341
6046.3561
6046.9771
6049.5762
6050.1532
6050.6262
6051.4061
6051.9901
6052.6611
6053.2110
6053.6170
6054.4359
6055.0629
6056.2447
6056.9407
6057.4726
6056.0765
6056.7274
6059.3063
6059.9352
6060.5251
6061.1109
6061.7056
6062.3247
6063.0145

6056 .7274
6059.4023

6060.6121

6061.6126
6062.4416

CADC RREQ

6046.3964
6047 .0046
6047.6114
6046.2162
6046.6253
6049.4327
6036.5192
6039.1375
6039.7554
6040.3726
6040.9697
6041.6061
6042.2219
6042.6372
6047.1262
6047.7369
6046.3491
6046.9567
6049.5676
6050.1764
6050.7646
6051 .3923
6051.9996
6052.6066
6053.2132
6053.6196
6054.4257
6055.0317
6056.2433
6056.6490
6057.4549
6056.0606
6056.6669
6059.2733
6059.6601
6060.4672
6061.0949
6061.7032
6062.3121
6062.9216
6055.0367
6056.0971
6056.7069
6059.3163
6059.9251
6060.5333
6061.1411
6061.7464

0.0026
0.0003
-0 .0163
0.0390
-0.0791
0.0465

0.0256
-0.0066

0.0069
-0.0046
0.0090
0.0164
0.0064
-0.0232
0.0416
0.0156
-0.0095
0.0545
-0.0022
-0.0026
0.0102
0.0312
0.0014
0.0917
0.0177
0.0157
0.0605
0.0330
0.0551
0.0379
0.0160
0.0026
0.0126
0.0927

0.6303
0.6954

0.6670

0.6717
0.6932

m 53-].

Q

.3
O‘DQNO‘UI

QQQQQ

LLLLLIIIIBLLLLLL
Huhqcfiagficumfiwup

Q
...o
O

QQQ

QQQ

3333333333333333333333333333333

WT

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.50
0.00
0.00
0.00
0.50
6.00
2.00
0.50
4.00
0.25
2.00
0.13
0.13
2.00
0.13
0.50
0.06

168

OBS FREQ

6063.0145
6063.6023

6064.6630
6065.5116
6066.1066
6066.6964

6066.4737
6069.0226
6069.6919
6070.2740
6070.6551
6071.5152
6072.1373
6072.7394
6073.3575
6073.9556
6076.3929
6077.0179
6077 .63”
6076.2071
6059.4023
6062.5606
6063.1755
6065.0009
6066.6610

6066.0150.

6066.6466
6069.9300

6071.7760
6079.7213
6060.3404
6060.9574
6061.5474
6082.1594
6062.7844
6063.3664
6063.9574
6064.6094
6065.1674
6065.6124
6066.3674
6066.2373

CADC FRED

6062.3553
6062.9616
6063.5660
6064.1736
6064.7794
6065.3646
6065.9900
6065.2993
6066.9662
6069.5752
6070.1836
6070.7915
6071.3966
6072.0057
6072.6121
6073.2161
6073.6237
6074.4269
6075.0339
6077.4519
6076.0562
6076.6606
6079.2651
6059.3622
6062.4665
6063.0903
6064.9555
6066.6192
6066.0600
6066.6796
6069.2992
6069.9160
6070.5364
6071.1541
6071.7713
6079.7349
6060.3429
6060.9503
6061.5572
6082.1635
6062.7694
6063.3746
6063.9797
6064.5643
6085.1666
6065.7926
6066.3964
6066.2070

OBSPCPLC

0.6592
0.6405

0.7092
0.7324
0.7236
0.7064

.1 .1015
-1.1606
-l.0996
-1.1246
.1615“
.1008“
.1 .073
-l.0216
.1 605m
0.0401
0.0921
0.0652
0.0454
0.0416
-0.0450
-0.0310

0.0120

0.0067
-0.0136
-0.0025

0.0071
-0.0096
-0.0041

0.0150
-0.0064
-0.0223

0.0251
-0.0012

0.0196
4 .00”

0.0303

WT

1.00
0.00
0.25
2.00
0.13
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

169

085 ERBQ

6066.6173
6069.4933
6090.0283
6090.6242
6091.2022

6091.6560
6092.4550
6093.0731
6093.6542
6094.2813
6094.6964
6095.4397
6096.1346
6096.7450

6097.9565

6106.4105
6109.0661
6109.6969
6110.3626
6111.0113
6111.5662
6112.6426
6113.3967

6116.9556
6119.5577
6120.1766

- 6120.6270

6121.3731

6124.4644
6124.9767
6125.6130
6126.2364

6127.4913

6129.7299
6130.3536
6130.9934
6132.7965
6133.4253
6134.6409

CADC FREQ

6066.6105
6089.4141
6090.0176
6090.6216
6091.2262
6065.5226
6090.4023
6091.0092
6091.6156
6092.2213
6092.6266
6093.4313
6094.0356
6094.6395
6095.2430
6095.6462
6096.4491
6095.4852
6100.9661
6101.5739
6102.1790
6102.7636
6103.3676
6103.9912
6105.1970
6105.7993
6105.3469
6112.0377
6112.6416
6113.2446
6113.6476
6114.4496
6116.2540
6116.6546
6117.4553
6118.0557
6116.6560
6119.2562
6119.6565
6120.4570
6121.0576
6115.1169
6121.6001
6122.4032
6123.0057
6124.6097
6125.4101
6126.6097

OBS-CALC

0.0066
0.0792
0.0105
0.0024
-0.0240

1.4557
1.4456
1.4575
1.4329
1.4547
1.4651
1.4041
1.4953
1.5020

1.5094

7.4424
7.5122
7.5179
7.5790
7.6237
7.5970
7.6456
7.5974

6.9179
6.9161
6.9340
6.9794
6.9233

7.0091
6.9230
6.9570
6.9602

7.0343

7.9296
7.9504
7.9677
7.9666
6.0152
6.0312

K J

RR10,19
RR10,21
RR10,23
RR10,24
9011 v.1
RR11,11
RR11,14
RR11,15
RR11,16
RR11,17
RR11,16
RR11,19
RR11,20
RR11,22
m2'—1
RR12,12
RR12,13
RR12,14
RR12,15
RR12,16
RR12,17
RR12,16
RR12,19
m3 1"].
RR13,13
RR13 ,14
RR13,15
RR13,16
RR13,17

WT

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

170

088 FREQ

6135.2966
6136.4955
6137.7362
6136.3071

6140.2340
6142.0799
6142.7160
6143.3320
6143.9110
6144.5391
6145.1411
6145.7663
6146.9605

CALC FRED

6127.2091
6126.4073
6129.6052
6130.2043
6124.7941
6132.0736
6133.6764
6134.4762
6135.0755
6135.6744
6136.2726
6136.6710
6137.4669
6136.6642
6134.3664
6142.2612
6142.6611
6143.4604
6144.0591
6144.6573
6145.2549
6145.6521
6146.4490
6143.9112
6152.3740
6152.9722
6153.5697
6154.1666
6154.7630

CBSFCPLC

6.0697
6.0662
6.1310
6.1026

6.1604
6.2035
6.2396
6.2565
6.2366
6.2663
6.2701
6.3194
6.3163

LI ST OF REFERENCES

10.

11.

12.

13.

14.

LIST OF REFERENCES

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P. Connes, Air Force Cambridge Research Laboratories,
Special Report Number 114, Aspen International Con-
ference on Fourier Spectroscopy, 1970, Vanasse, Stair,
and Baker, editors, p. 121.

S. C. Hurlock and J. R. Hanratty, Appl. Spectrosc. 22,
362 (1974).

P. D. Willson and T. H. Edwards, Sampling and Smoothing
of Spectra, Applied Spectroscopy Reviews, 12(1) (Marcell
Dekker, Inc.), (1976), p. 1.

P. A. Jansson, R. H. Hunt, and E. K. Plyler, J. Opt.
Soc. Am. 22, 596 (1970).

P. D. Willson, Ph.D. dissertation, Michigan State
University, 1973.

G. Halsey and W. E. Blass, Appl. Optics 22, 286 (1977).

R. W. Peterson and T. H. Edwards, J. Mol. Spectrosc. 31,
137 (1972).

T. L. Barnett and T. H. Edwards, J. Mol. Spectrosc. 29,
347 (1966).

R. W. Peterson and T. H. Edwards, J. Mol. Spectrosc. 22,
1 (1971).

T. L. Barnett and T. H. Edwards, J. Mol. Spectrosc. 22,
352 (1966).

T. L. Barnett and T. H. Edwards, J. Mol. Spectrosc. 22,
302 (1967).

R. W. Peterson and T. H. Edwards, J. Mol. Spectrosc. 22,
524 (1971).

171

15.

16.

17.

18.

19.

20.

21.
22.
23.

24.

25.
26.

27.

28.

29.

30.

31.

32.

33.

172

B. Podolsky, Phys. Rev. 22, 812 (1928).

E. B. Wilson, Jr. and J. B. Howard, J. Chem. Phys. 2,
260 (1936).

B. T. Darling and D. M. Dennison, Phys. Rev. 21, 128
(1940).

W. H. Shaffer, H. H. Nielsen, and L. H. Thomas, Phys.
Rev. 22, 895 (1939).

M. Goldsmith, G. Amat, and H. H. Nielsen, J. Chem. Phys.
22, 1178 (1956).

M. Goldsmith, G. Amat, and H. H. Nielsen, J. Chem. Phys.
.21, 838 (1957).

G. Amat, and H. H. Nielsen, J. Chem. Phys. 21, 845 (1957).
G. Amat, and H. H. Nielsen, J. Chem. Phys. 22, 665 (1958).

G. Amat, and H. H. Nielsen, J. Chem. Phys. 22, 1869
(1962).

M. L. Grenier-Besson, G. Amat, and H. H. Nielsen, J.
Chem. Phys. 22, 3454 (1962).

M. L. Grenier-Besson, J. Physique Rad. 22, 555 (1960).

G. J. Cartwright and I. M. Mills, J. Mol. Spectrosc. 22,
415 (1970).

D. R. Anderson and J. Overend, Spectrochimica Acta 28A,
1231 (1972).

R. W. Peterson, Ph.D. dissertation, Michigan State
University, 1969.

R. R. Ernst. Rev. Sci. Instrum. 22, 1689 (1965).

K. N. Rao, C. J. Humphreys, and D. H. Rank, Wavelength
Standards in the Infrared, Academic Press, New York,
(1966), p. 160.

C. Amiot and G. Guelachvilli, J. Mol. Spectrosc. 22,
171 (1976).

J. L. Aubel, Ph.D. dissertation, Michigan State
University, 1964.

D. B. Keck, Ph.D. dissertation, Michigan State
University, 1967.

34.

35.

36.

37.
38.

39.

40.

41.
42.

43.

44.

45.

46.

173

T. L. Barnett, Ph.D. dissertation, Michigan State
University, 1967.

J. R. Gillis, Ph.D. dissertation, Michigan State
University, 1979.

Michigan State University High Resolution Infrared
Lab Software Package.

Reference unknown.

W. E. Blass and G. W. Halsey, Deconvolution of Absorp-
tion Spectra, Academic Press, 1981.

J. Pliva, A. S. Pine, and P. D. Willson, Applied Optics
22, 1833 (1980). .

P. M. Wilt, F. W. Hecker, J. D. Fehribach, Dale E. Bardin,
and T. H. Edwards, J. Mol. Spectrosc. 22, 33 (1981).

P. Venkateswarlu, J. Chem. Phys. 22, 293 (1951).

F. W. Parker, A. H. Nielsen and W. H. Fletcher, J. Mol.
Spectrosc. l, 107 (1957).

J. L. Duncan, D. C. McKean, F. Tullini, G. D. Nivellini,
and J. Perez Pena, J. Mol. Spectrosc. 22, 123 (1978).

G. Herzberg, Molecular Spectra and Molecular Structure
11: Infrared and Raman Spectra of Polyatomic Molecules,
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D. Boucher, J. Burie, J. Demaison, A. Dubrulle, J.
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John W. Boyd, Ph.D. dissertation, Michigan State
University, 1963.

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