DETERMINATION OF A0
FOR DEUTERATED ME‘z‘HYL HALIDES

Thesis far the fisgree of Ph. D.
MICHEGM STATE UNWERSETY '
RiCHARD WAYNE PETERSON
1969

 

0.169

F] LIBRARV “-

Michigan SLHU

i
L: University

   

This is to certify that the

thesis entitled

DETERMINATI ON OF A0

FOR DEUTERATED METHYL HALIDES
presented by

Richard Wayne Peterson

has been accepted towards fulfillment
of the requirements for

PhoDo degree inPhYSiCS

W

Major professor

Date W 3g /;/;

ABSTRACT

DETERMINATION OF
FOR DEUTERATED METHYL HRLIDES

By

Richard Wayne Peterson

and 2v

V4 4

vibration - rotation bands of CD31, CD3C1, and CD3Br have been

obtained with the Michigan State University near-infrared spectro-

High resolution absorption spectra of the

meter.

Molecular parameters have been determined by least squares
fits of observed frequencies to generalized frequency expressions
for symmetric top molecules resulting from the theoretical work
of Amat and Nielsen. A simultaneous analysis of the v4 and 2v4

bands of CD31 led to a value of A0 = 2.5788 : 0.0004 along with

other molecular parameters. A similar analysis of the unperturbed

lines of CD301 yielded the value A0 = 2.5930 : 0.0006. The A0

values obtained for CD31 and CD3Cl were compared to those from
zeta-sum work and were found to be an order of magnitude more pre-

cise. A0 could not be obtained by a simultaneous analysis for

4; however a

single-band fit of v4 resulted in values of DE, a2, 02, and

CD38r because of the highly perturbed nature of 2v

other linear combinations of parameters.
Systematic perturbations have been observed on the low fre-

quency side of the band of each molecule. Individual line

V4

shifts due to these perturbations have been listed in all cases

Richard Wayne Peterson

where definite assignments were possible. Other perturbations were

observed in 2v4(u) of CD3Cl and in 2V4(L and H) of CD3Br.

DETERMINATION OF A0

FOR DEUTERATED METHYL HALIDES
By

Richard Wayne Peterson

A THESIS
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Physics

1969

€é/770’
7%, 2.7-”

TO MY PARENTS

ii

ACKNOWLEDGMENTS

I would like to thank Professor T. H. Edwards for the guidance
and encouragement which he has provided throughout the course of
this work. His dedication to teaching and research has had a
significant effect on my current goals and aspirations: l have
enjoyed the experience of teaching under the direction of Professor
C. D. Hause, and the experience gained has greatly affected my
future plans for research and teaching. The excellent course on
molecular structure which has been presented by Professor P. M.
Parker has been very valuable in this work.

I would particularly like to thank Dr. Lamar Bullock for
the many times he provided assistance with experimental and computer-
related phases of this research. The advice and assistance of
fellow students Richard Blank, Paul Willson, and Peter Willson
have also been real assets in this work.

The excellent CDC 3600 and 6500 computer facilities of
Michigan State University have been very valuable in many parts
of this work. The Physics Shop staff has provided invaluable
assistance with some of the experimental problems which have been
encountered. A number of undergraduates in the Work-Study Program
have made significant contributions. Donna Deming, Nancy Nickerson,
and Jeannine Stetz all Spent many hours with theirfriendthe HYDEL
machine. Jack Bosworth has provided competent assistance with the
final changes in program SYMFIT and with the final analysis

iii

procedure.

The financial assistance provided by a National Aeronautics
and Space Administration fellowship was greatly appreciated. The
National Science Foundation has also provided support through grants
to Professors T. H. Edwards and C. D. Hause.

Finally I would like to express an loveand appreciation to
my wife, Donna, whose patience and moral support have helped bring

this work to a successful conclusion.

iv

LIST OF
LIST OF
LIST OF
Chapter
I
II
III

IV

VI
VII
VIII
IX

LIST OF

TABLE OF CONTENTS

TABLES
FIGURES

APPENDICES

INTRODUCTION
DEVELOPMENT OF SYMMETRIC TOP THEORY

METHODS OF A0 DETERMINATION

EXPERIMENTAL PROCEDURE
ANALYSIS OF DATA

v4 AND 2v4 OF‘CD3I

ANALYSIS OF v4 AND 2v4 OF CD3C1

v4 AND 2v4 OF CD38r

ANALYSIS OF

ANALYSIS OF

CONCLUSION

REFERENCES

APPENDICES

Page

vii

viii

22
29
38
45
56
66
74
77

79

Table

WNNNNN

0‘ r~ ¢~ D~
Hump—a

HU‘bWNt—J

LIST OF TABLES

Parameters of the D-D Hamiltonian
Axially Symmetric Energy Expression
Description of Energy Parameters

Generalized Frequency Expression

Single-Band Frequency Expression for v4 or 2vA
Frequency Expression for a Simultaneous Fit

of v4 and 2v4

Experimental Conditions - CD I

3
Experimental Conditions - CD3C1

Experimental Conditions - CD38r

Molecular Constants of CD I Obtained from Single

3
Band Fits

Molecular Constants Resulting from Simultaneous

Fit of v4 pand 2v4 of CD31

Second Order Molecular Constants of CD3C1 from
Single Band Fits
Molecular Constants Resulting from a Simultaneous

Fit of v4 and 2v4. of CD3Cl
Molecular Constants from a Single Band Fit of
v4 of CD3Br

Summary of Constants for CD3X Molecules

Page

11
12
14
17

23
3o
31

32

51

52

58

64

69
75

F igure
1.

l.

1

LIST OF FIGURES

CD3X Structure

Normal Modes of Methyl Halides
Detector Assembly

Bias Circuit

Block Diagram of SYMFIT

Survey Spectra of v4 and 2v4
Survey Spectra of v4 and 2v4
Effective 04 from Subbands of
of CD3C1

Deviations of Perturbed Subbands

Survey spectra of V4 and ZVZ+
, B
Effective 04

Subbands of CD3Br

ValuesDetermined from

of CD31

of CD3C1

v4 and 2v4

v4 of CD3C1

of CD3Br

of

2V4(l)

Page

36
36
41
47

57

61

67

71

[\ppendix
A.

B.

LIST OF APPENDICES

Listing of SYMFIT and Typical Data Set
Least Squares Fits and Associated Statistics

Results of a Simultaneous Fit for CD I

3

Results of a Simultaneous Fit for CD3C1

Results of a Single Band Pit of v4 of CD3Br

viii

Page
79
97

100

111

121

CHAPTER I

INTRODUCTION

The birth of quantum mechanics in the late 1920's led to a
renewed interest in the near-infrared absorption spectra of small
rnolecules. It was found that many features of infrared Spectra
could be predicted by a quantum mechanical model of the molecule
consisting of a rigid rotator and a set of uncoupled harmonic
(oscillators. Symmetric top molecules (where IXX = Iyy * Izz)
allow an exact determination of vibration-rotation energy levels
for the zero-order model described above. Because of this, some
of the first molecules studied experimentally and theoretically
‘Jere the methyl halides.

The basic form of a deuterated methyl halide molecule (CD3X,
‘where X = F, Cl, Br, or I) is shown in Figure 1.1. In addition to
their classification as symmetric tOps, the methyl halides have
C3v symmetry, which means they have a threefold axis of symmetry
and three vertical planes of symmetry. Figure 1.2 illustrates the
atomic motions involved with each of the vibrational modes Of a

thethyl halide molecule. The modes v4, v5, and v are doubly

6
degenerate.

In Chapter II a summary is given of the modern quantum
mechanical development of a fourth-order energy expression for a
vibrating and rotating symmetric top molecule. This general model

includes such effects as anharmonic forces, changes of moments of

l

 

 

X
la
la 0 0. fi
0 47013
= fl
D D o 4wclg
D

FIG l-l CDBX STRUCTURE

is we

FIG l-2 NORMAL MODES OF METHYL HALIDES

inertia with vibration, centrifugal distortion, and vibration-
rotation interactions. Different frequency expressions of particular
importance to this work are introduced and compared.

Because of the selection rules which govern symmetric top
transitions, the determination of the ground-state constant

A .
(where I is the principal moment of inertia about

A
A = h/4nc I 0

0 0

the unique symmetry axis) is a difficult but important problem.
(Shapter III describes and compares the two most commonly used

rnethods of determining A This work involves an application of

0'
the more accurate of the two methods to CDBX molecules.

The experimental procedures used in recording the v4 and

2v bands of CD I, CD Cl, and CD Br are described in Chapter IV.

4 3 3

Chapter V describes the computer programs used in determining accurate

3

frequencies of spectral lines recorded and in obtaining molecular
parameters, Such as A0, from the observed frequencies.

The remainder of the thesis describes the details of the
analysis of the spectra for each of the three molecules. Molecular
parameters obtained from the analysis are recorded and compared
with those obtained from lower resolution spectra. In the cases of

CD Cl and CD Br (Chapters VII and VIII) a number of Spectral lines

3 3
are found to correspond to transitions to perturbed upper-state
energy levels. Whenever possible the magnitudes of these energy
level shifts are determined.

The concluding chapter summarizes the molecular parameters

determined for each molecule and includes suggestions for future

work.

CHAPTER II

DEVEIDPMENT OF SYMMETRIC TOP THEORY

Among the problems which confront the beginner in high
resolution spectroscopy is the complexity of an accurate analytical
exqaression which is able to specify the energy of the quantum levels
of a vibrating and rotating polyatomic molecule. The situation is
further complicated for the experimentalist by the variety of expres-
sions which have been used to predict the frequencies of radiation
whixzh are absorbed when the molecule is excited to higher energy
states. For example, some frequency expressions are convenient for
the: rapid computation of approximate molecular parameters from gross
features of the spectra, others apply only to small portions of a
given absorption band, and Still others are general enough to allow
a IJarge scale computer analysis of more than one band under very
‘11831 resolution. The goal of this chapter is to introduce a few
0f the frequency expressions which are presently used for symmetric
tops and to facilitate their comparison.

A brief development of a general energy expression which re-
sults from the fourth-order Hamiltonian as developed by Amat and
Nielsen is given first. After applying appropriate selection rules,
tine generalized frequency expression for symmetric top molecules

is cflatained. This complicated expression is then compared to fre-
quency expressions which are commonly used experimentally at low

to medium resolut ion .

The development of a correct quantum mechanical form of the
fiamiltonian has been presented in detail by H.H. Nielsen (1) in his
(:omprehensive paper of 1951. Details of this development have been
ggiven at Michigan State University in the lectures on molecular
s;tructure by P.M. Parker, and an excellent summary is given in
(Shapter I of a theoretical thesis by R.L. Dilling (2). The re-
sxiltant Hamiltonian is commonly called the Darling-Dennison (D-D)
llandltonian (3,4) and is written as follows:

2/ = gin}: 2(PQ, - Pam—10898 - pan}

GB
(2.1)

1 l
12; ‘K
A 2 p50”
50

+ psgu%] + V

NIr—A

TFat31e 2.1 contains a brief description of each of the quantities
Lused.in the D-D Hamiltonian. More detailed information concerning
tile basic relationships between these constants may be found in
rezferences (1,2,3,4).

In principle, the D-D Hamiltonian is quite applicable to any
t)rpe of molecule. It is unfortunately a grievous task to solve the
S<2hroedinger equation for this complex Hamiltonian to high orders
Of? accuracy. The usual systematic approach is to first expand H

if! the manner,

H = H0 + H1 + H2 + H3 + .......

wllere expansions of V and ”a are

S

V=V +V +V +...

O l 2
=1- 2 + K Q Q Q +
V 2 Si XSQSC SE 50 SO’ Stat 8"0'"
Slot 5 O"
H n SIIOII
S U

(atlant it‘y’

“GB

30'

30'

we”)

Table 2.1

Parameters of the D-D Hamiltonian

Description

 

the inverse moments of inertia matrix,

2 de
At t (0:08)

range over (x,y,z) of the rotating coordinate
system attached to the molecule in a manner
Subject to the Eckart conditions (4,5)

(5) is an index ranging over all normal modes;
(0) ranges over the components of degenerate
normal modes

displacement of the a component of the normal
mode (5), does not appear explicitly in H

component of total angular momentum

component of internal angular momentum; (p )
may be expressed as a linear combination 0
components of internal angular momentum as
expressed in normal coordinate space:

= fa
pd E :58152 52

momentum conjugate to Q30

7% \
= - i a —Q——

so aQSc

P

potential energy of the molecule

a nd

_ 1 [Q(0)a3 3(1)GBQ + ...]

50‘

+

QM

where, if x,y,z are principal axes,

3(O)ap = I 6 -
O’O’D
WTith these, one can write for H0 (1,2)
=H +H
HO R V
(2.2) F2
1 y 1 r 2 2
2 E I 2 Z LPso stso]

CY 50
This Hamiltonian of a rigid rotor (HR) and a set of uncoupled

harmonic oscillators (HV) is very important in the development

e
Which follows. The Schroedinger equation of H (where Ie = I )

0 xx yy

. . a
has the well-known eigenfunctions

YT _ YR Yv
Where
Y = K t>
R \J t
and =
YV \vl>\v2> \VSLS>
Where vl,v2 vS are the vibrational quantum numbers of the

UI‘lcoupled harmonic oscillators, and J,K,M, and Ls are angular

momentum quantum numbers defined by

The quantum mechanics problem of the rigid symmetric rotor
Was first solved by Dennison via matrix mechanics (6). Solutions
by both wave mechanics and matrices are given in his paper of

1931 (7).

PZYR = J(J+l)h2yR
PZYR = K h YR
(2.3) PZYR =Mh‘1’R
‘QsoYV = $8 h YV
In the case of a symmetric top in zero order, vs, J, and \Kl are

(Konsidered primary quantum numbers since they determine distinct
eigenvalues; (,5, M, and the Sign of K are secondary quantum
numbers and in zero order only designate degeneracies.

A method of arriving at energies beyond zero order which has
often been used is that of the contact transformation. This is
essentially the perturbation approach as presented by Born, Heisen-
berg, and Jordan in 1926 (8,9), and it was applied by Van Vleck in
1929 to higher order terms of diatomic molecules (10). Shaffer,
Nielsen, and Thomas were the first to use the technique in the
Case of polyatomic molecules (11), and in his paper of 1951 (l)
Nielsen summarized first and second-order contributions to the
energies of symmetric tops. One applies the transformation to the

general D-D Hamiltonian as expanded to at least second-order,
21' =TIVT-1 =1v' +N’ +1V' +
O 1 2
aruj one attempts to choose T such that

u = v I = l
(1) NO NO and (2) <nlfillln> 0 for ni‘n

In this way the transformation does not invalidate the highly prized

eigEnfunctions of H but does remove the off-diagonal elements of

0)

Hi- Detailed application of the T transformation necessitates that

tine resulting terms be rearranged according to expected orders of

«magnitude. The rearranged matrix is written as

‘I = I I
h Nb +~h1 + h2 + ...

. . - . , 0
Ifliern Since H0 has known eigenfunctions Y( ), we may apply second—

()rcier perturbation theory which states that if

a) Y<0> z E<0>Y<0>

 

0 n n n
then
E50) = <nlflbln>
Eé1)==<nlhihfi>
I II 2

(2) - ' ' l<nlhlln >l

En ~ <nlhzln> +'Z E(O) (O)

n n - n"

but: by virtue of the contact transformation,

<nlhiln"> = O for all n f n"

anti therefore

E<2)

= <nlh'ln)
n 2

- . . . O
Cdlce nmst be taken in the case of degeneraCies in E( ) In such a

CaESe, one nmst use perturbation-adapted zero-order wave functions to

fiJid Eél) before proceeding to Biz).

The above method is described in great detail in two papers

by Nielsen, Amat, and Goldsmith (12,13). Amat and Nielsen (14,15,16)

tTNEn went on to perform an analogous second contact transformation

which removes the matrix elements off-diagonal in the principal

quantum numbers vS from hi. This procedure results (after no

Small amount of labor) in a doubly-transformed Hamiltonian,

10

+=vj Ire-1: + + + + +
A! .A/ . VO+N1+IVZ+IV3+V4+

:0 ! Il- + T
MO +Vl +£{2 +213 +i/a

[\fter another regrouping, the new Hamiltonian is written,

h+

=R0+h'+h++h +h

+ +
l 2 3 A

hiith 10 + hi + h: diagonal in the vibrational quantum numbers v ,
aggain in a representation which has as its zero-order wave functions,
tlie eigenfunctions of Ht. However, for a symmetric top, h: is not
ciiagonal in the angular momentum numbers Ls and K, and therefore
ternns off-diagonal in these quantities can contribute to fourth-
orxjer energies, or even to lower order in the case of certain
rwzsonance perturbations.

Table 2.2 contains the energy expressiOn from double contact
trwansformation theory of an axially symmetric molecule complete
ttrrough third-order, with partial contributions from fourth-order.
T3162 explicit form of the terms of the Hamiltonian may be found in
tile-thesis by W.E. Blass (17). Table 2.3 is a list of all the new
qkbantities which appear in the energy expression with their des-
Cr‘iptions.

We are usually concerned with the energy absorbed as the
trlOlecule is excited from its ground vibrational state (all v5 = 0)
Cf) an upper state where some vS # 0. This puts the range of
‘radiation absorbed in the near-infrared region where our spectro-
meter Operates. The general frequency expression is thus obtained
by Subtracting the ground-state energy expression from the upper-

State energy.

(+23

41+

11

Table 2.2
Axially Symmetric Energy Expression
B J(J+l) + (A B )K2 + w ( /2)
e e e 2s s vs+gs

-2A 2 g 22 K
e t t t

2 2 2
-DJJ‘(J+1) -DJKK J(J+l) -DKKA
e e e
B A B 2
.. 9 .. ...
2808(vs+gS/-)J(J+l) 25(as JS)(vS+gS/2)K

Ess' Xss'(vs+gs/2)(vs'+gs'/2) + Ztt' X L £ '
sss' tSt

J
EtfltLtJ(J+l)K
2 “K K3 + In +2 n ( /2)“I K

tgt£t ZtL't s‘t,s\%+gs J“

t

2
£88:(vs+gS/2)J2(J+l)2 +£SB:K(vs+gS/2)K J(J+1)

K , 4
+£sBs(Vs+gs/2)K
B
{ZSSI YSS'(VS+gS/2)(VS'+gS'/2)+£tt' Y6 L ,Lt&t'
sss' tst' t t
+AB ‘[J(J+i)-K27 + {z A (v +g /2)(v +g /2)
e3 J 53' Yss' s s s' s'
535'
2
+2tt' Vt t 'tttt.+AAe}K
. t t
tSt
4 K 6
H3J3(J+l)3 +HiKK2J2(J+1)2 + HSJK J(J+l) +HOK
ZSSISHYSSISH(VS+gS/2)(Vst+gS'/2)(VSH+gSH/2)
SSS'SS"
+ 7 ~
+ zstt'ysLtLt.(vs-ligs/zfl’tét' ”saws(vs+gs/2)

tsr'

 

Quaritzity
Sfi1,t
B , At

e re
0J8: gs

2

gt

a 3 GA

3.

D ’ I)e:’ De

88' ’ xtttt.

ySS' ’ ySLtLt.

J JR K

83’ BS ’ 8S

J

lit. 11‘:

A A

Yss" 'Y

Lttt.

B B

vssu y

J LtLt'
K KJ

Rodi ’Ho ll:

MS

we.me

12

Table 2.3

Description of Energy Parameters

Description

 

s is an index of a given vibrational mode.
n will refer to 8 Specifically non-degenerate
mode; t, the degenerate modes.

 

Bea—l—E. A: fie
Anal 9 Anal
x z
e e . .
where IX = I where z is the axis

of symmetry

designate a purely harmonic frequency w
of a normal mode 8 having degeneracy gs.

coriolis coupling constant about the symmetry
axis.

coefficients of vibrational corrections to
B and A
e e

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 g:

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 A8 and Be’
having same quantum dependence at Ae and B

13

Table 2.4 is a general expression (including partial fourth-
order terms) which gives the frequency (in cm-l) of radiation absorbed
as the molecule is excited from its ground vibrational state to an
upper state where some of the set Vs are not zero. The vibrational
terms have been grouped at the beginning of the expression and these
will be constant for a given vibrational excitation. In the notation
of the frequency expression, changes in the rotational quantum numbers
K and J are Specified by giving initial values (K,J) and their
changes (AK and AJ). Particular transitions will therefore often

be Specified by the notation

AKAJ‘K‘U) where K and J are initial values

where P implies AK or A] =-l

Q implies AK or A] = O

R implies AK or AJ = +1
For example, an RQ3(4) tran51tion implies Kinitial = 3 Kfinal = 4
= " 4

Jinitial 4 innal '
The vibrational transition from (all vS = O) to (1,0,0,0,2,0) is

called the band v1 + 2v5. This thesis is largely concerned with

the analysis of the v4 and 2v!+ bands of CD3X molecules.
Three important substitutions have been made in going from

the energy expression to the frequency expression. They consist of

applications of the following definitions,

.. A A
(2.4) Av - Ae - 2 as(vs+gS/2) + z vss.(vs+gS/2)(vs.+gS./2)

3 58'
555'
+ 2 YA L L + AA
I
tt' LtLt' t t e

tSt'

14

Table 2.4

Generalized Frequency Expression

A

K _
(vn’vn+1,"°)vt)M/t,vt+17Mt+l)'°°) AJK(J)

+ .
23(ws Aws)vs +

ZSZS'XSS'[Vs*gg/2)(st+gs'/2>‘gsgs'/41 +

535'

ALtAL , +

Z 2 IX
t t LELE' t

tSt'
ZSZS.ZSnySSvSnl(VS+gS/2)(VS:+85u/2)(Vsu+88n/2)-gsgsugSu/8] +

sgs'SS”

Z Z 2 .y
s t t sittt.

tSt'

(vSmS/DMtMC. +

AO[ (K+AK) 2-K2] +

BOE(J+AJ)(J+1+AJ)-J(J+1) - (mmzflzj +

z .m . r
[-ZAeztgt Mt+£twt+£sntsws+gsn>IM’t1LK+AK1 +
2
-DOJ[ (J+AJ) 2 (J+1+AJ) 2-J 2 (J+1) ] +

2 2
-D3K[(K+AK) (J+AJ)(J+1+AJ)-K J(J+1)] +

-DOK[(K+AK)A-K4] +

A A
[-23% vsfizszs 'Yss' (vSvS.-+vsgs./2+vs ,gS/Z)

335'

A 2
F
+Zt2tuYLtLt'MCMCJJK‘tAK) ] +

tSt

(continued on next page)

15

Table 2.4 (cont.)

Generalized Frequency Expression
F‘—Z a BV +£ Z V B (v v +v g /2+v g /2)
L s s s s 5' 83' S s' S s' s' s
B 2
+2: 2 .v MCM,tu]l(~.l+AJ)(J+1+AJ)-CK+AK) 1 +
l

ZcfltJMJ (K+AK) (J+AJ) (J+1+AJ)3 +
K 3
:tnt MtUKfliK) ] +

J 2 2
23535 vs[(J+AJ) (J+1+AJ) ] +
.JK 2 _
:SBS vS[(K+AK) (J+AJ)(J+1+AJ)J +
z; a Kv [(K+AK)4] +
S S S
HOJ E (J+AJ)3(J+1+AJ)3-J3 (J+1)3] +
HgKE (K+AK)2(J+AJ)2 (J+l+AJ)2-K2J2(J+l)2] +

HS‘JE (K+AK)4(J+AJ) (J+l+AJ)-K4J (J+1)] +

HEE (K+AK) 6-K6]

16

= _ B B
(2.5) Bv Be Easws‘th/Z) + SE! vss.(vs+gs/2)(vs.+gS./2)
953'
+ + B
til YLt£t1£t£t' A e
tst'

m _ m m =
(2.6) I)v De-Eas(vs+gs/2) for m J,K,JK

Substitutions have been made for A0, B0, and D3 since these ground—

state effects each have distinct rotational quantum dependencies

which are quite independent of the upper-state vibrational level. n
It will be noticed that the equilibrium constants Ae’ Be’ and D: [L

still are not readily available even if their ground-state values
are known -

Well-known selection rules (18) specify that for symmetric
tops,

‘ .

AK = O for 1'} bands
AK =il for .L bands
and for both types of bands
[3.1 = 0, 131
except that J = 0 to J = 0 transitions do not occur.
In addition, selection rules on Lt can be inferred from

symmetry considerations. In particular, for v4

m4 =Ax=il

and for 2x)4

M4 = "ZAK = O, :2
Table 2.5 (19) shows the form which the generalized frequency
expreSSion takes when it is applied to v or 2v . The effect of

4 4

the salad: ion rule on (Mt) has been put in terms of the parameter

17

Table 2.5

Single Band Frequency Expression for v4 or 2v4

,
AKAJKU) = +{BO[(J+AJ)(J+1+AJ)-J(J+1) - (K+AK)2+K‘]

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

“D3K[(K+AK)2(J+AJ)(J+1+AJ)-K2J(J+1)ll +

M!

; v0(v4) or
v (2v ») or 2 - r-k(AK)2(A Q z-l/Z+T‘ K)1 +
O 4 * g L 84 Z J
tv0(2v4 H)

2 2
[A0 - kAegaz - l/2kn4K3[(K+AK) -K j +

K

[-DO - l/Akflax][(K+AK)a-K I +

41
J
[‘aaA + 3/2kn4Kll(Av4)(K+AK)2] +
['aaB][(AV4){(J+AJ)(J+1+AJ) - (K+AK)2}] +
[“4J31(kAK)(K+AK)(J+AJ)(J+1+AJ)] +
E J [(Av )(J+AJ)2(J+1+AJ)2] +
34 3 4
JR 2
[84 JEAv4)(K+AK) (J+AJ)(J+1+AJ)] +
[64km (Ava) (“no") +
[HOJ][(J+AJ)3(J+1+AJ)3-J3(J+1)3] +

[HgKlE(K+AK)2(J+AJ)2(J+1+AJ)2—K2J2(J+1)2] +

4
[H§J3[(K+AK)4(J+AJ)(J+l+AJ)-K J(J+1)] +

[HOK][(K+AK)6-K6]

1 for v4

k = -2 for 2v4

‘me‘wr - -
P.“ l A. j

18

(k), thus allowing the one expression to apply to both
(1 or H). The expression is written in a form making

for a large-scale computer fit of individual transition

K A

to obtain the unknown constants (A - kAegz, -DO, -a4,

0

Chapter V covers the computerized analysis procedure in

One form of the single-band frequency expression

v4 and 2v4

it convenient
frequencies
B etc )
-0 o o o o o
4

detail.

which is

often used at lower resolution is that in which AJ = 0, and third

and fourth-order terms are ignored (20,21,22). This expression allows

an approximate analysis from the Q branches of perpendicular bands

(AK =.il) from symmetric top molecules. If, in addition, centrifugal

distortion is ignored, the second-order frequency expression for

these RQK and RQK lines is

v(J,K,AK) = v + (Bv - BO)J(J+1)

O

T' _ r _
+ ZLAV(1 gv) BVJKAK

2
+ [(AV - A0) - (BV - 30)]K

where the small second term determines the extent of the spreading

of the unresolved lines. The usual approach is to fit

branch peak to the formula,

(2.7) v(K,AK) = v0 + ZEAV(1 - gv) - BV]KAK

2
+ [(Av - A ) - (BV - BO)]K

0

where v0 contains all the non-rotational terms.

A careful comparison of this expression for Q

wit?) the general single-band expression as applied to

the Q

branch peaks

or 2v

V4 4

(Table 2.5) indicates that the two are compatible. Unfortunately,

coefficients obtained from fits of the two forms are very difficult

g!“-

19

to compare. For example, v0 of (2.7) contains all the terms which
have constant quantum coefficients involving AK é :1; the generalized

2

v0 has put some of these (AK) terms in the coefficients of a4
and aaB. Likewise, the coefficient of KAK contains effects which
become art of the coefficients of A -A Q 2 a A and B in the

p - 0 e 4 ’ A ’ a4
generalized equation. The third term of (2.7) is equal to (GAB-04 ),
but does not allow a determination of 04A or 04 separately.
Such mixing of terms requires that great care be taken in comparing
results of fits using the two forms.
Two combination relationships from (K,AK) are often used in

Q branch analyses. These result directly from the AK dependence

of the second term. They are

RQ +PQ 2ivO+Av<1-gv) -B]

2
+ 2[(AV - A) - (13V - 30)]K

O
(2.8)

R P
- F - - 2

These combination relationships are most commonly found in papers
written before the computer era, since they allow a simple graphical'
deternfination of approximate molecular constants.

Analysis of the parallel bands (AK = O) of symmetric tops is
usually a difficult process due to difficulties in assigning the
overlapping lines. The most common approach has been to measure
series of QRK(J) and QPK(J) lines without attempting to identify
true (hopefully) constant K value of the particular series (21,22).

1?“? resultant frequency expressions for QP‘K(J) and QRK(J) are
1

 

20

Q _ .2
_ . + - - +
PK(J) v0 (AV A0 Bv BO)K
-(B +3 -21<21) )J+(B -B)J2+4D J3
v 0 JK v 0 JJ
Q J =~ +A -A - + 2
RK( ) VO ( v 0 Bv BO)K + Bv
+ (38 - B )J + (B - B )J2 — 4(J+1)3D - 2K2(J+1)D
v 0 v 0 JJ JK

If a given K series is followed (K = constant), then the two equa-

tions can be put in compact form, viz.,

2 3
(2.9) v(J) - a1 + blm + clm + dlm

-J for the P branch

where m

m = J + l for the R branch

2
and a1 - v0 + (Av - AO - BV + BO)K
b = B + B - ZKZD
l v 0 JK
_ B
c - B - B = a for fundamentals
l v 0 v
(11 - ~4DJJ

The QQK(J) lines (AJ = 0, AK = O) in the center of a parallel band

are seldom completely resolved because of the small magnitude of a:
A

for the methyl halides; but, because of a much larger av, often they

can be identified in K. This allows them to be described by the

equation,
2
(2.10) v(K) = a + b K
2 2
where = _
a2 v0 + (Bv BO)J(J+1)
= - - +
b2 (Av A0 Bv BO)

A
- QB - a for fundamentals.
v v

 

1r

in. j: '. ' ' l.-

—"‘ w" use
i

Thus from a complete analysis of a parallel band one can determine

A B .
av, av, and v0(h).

Equations (2.7 - 2.10) have all been used extensively for
moderate resolution spectra where it is difficult to resolve the
R P . ‘ Q Q .
R (J), P (J) lines of L bands and P (J) and R (J) lines
K K K K
of H bands. They can also be usefully applied where computer
facilities are minimal, or where approximate molecular constants
are desired without Spending much time and effort assigning in-
dividual lines. When it is possible to resolve the individual
R P Q Q . . .
R (J), P (J), P (J), R (J) lines, it is best to use the
K K K K
appropriate form of the generalized frequency expression. The
latter approach has been used exclusively in this work, except
where a comparison of accuracies with previous work and differing
methods has been made.
The next chapter is concerned with differing methods of find-
ing the ground-state constant A0. Two methods are treated in de-
tail: the first uses a generalized frequency expression, the

second uses the peak Q branch formula (2.7) and some of its

equivalent forms.

 

CHAPTER III

METHODS OF A0 DETERMINATION

A definition of A0 in terms of Ae is given in Eq. (2.4),

and this definition is then used in a development of a single-band

frequency expression as applied to V4 or 2v4 (Table 2.5). The
n

expression shows clearly that AO cannot be determined from a if

single band. Two methods of obtaining A are the main topic of

0

this chapter. The first involves the use of frequencies of a

fundamental band and its first overtone (e.g. v4 and 2v4); the

second uses information from the three fundamental perpendicular

bands of a methyl halide (i.e. v4, v5, and v6). In the analysis

chapters which follow, a statistical study is included from experi-

mental applications of both methods.

If single—band fits of v4 and 2v4 are made, the particular

combination of AO-Aegz and A + ZAEQZ can be obtained. These

0
constants can then be combined to determine a value of A0. An
alternative approach is to fit the bands simultaneously to a fre-
quency expression generalized to include both bands. This simul-
taneous equation has been given by T.L. Barnett (l9) and is con-
tained in Table 3.1. Barnett and Edwards applied the simultaneous
fit approach to find A0 for CHBBr and CHBI (23,24,25). Barnett

has also shown that A0 can be obtained by fitting a combination

band of the form Vt + Vn simultaneously with 2vt (19). The

simultaneous approach has a number of advantages over the method of

combining two Single-band fits. These advantages are discussed in
22

23

Table 3.1

Frequency Expression for a Simultaneous Fit of v and 2v

4 4

meg) - {EOE (J+AJ)(J+1+AJ)-J (J+1)-(K+AK)2+K2]
-DOJ[ (J+AJ) 2 (J+1+AJ) 2 -J 2 0+1) 2]
433% (1(+Ax) 2 (HM ) (J+1+AJ) ~K2J (J+1)]} =
‘30 (v4) 0;
”00% ,) org
\20(2v4 H) _:
[AO1[(K+AK)2—K2] +
[-2Aeg42+n4][(m.4) (K+AK)1 +
[-DOK][(K+AK)4-K4] +
[-a4A1[(Av4)(K+AK)2] +
[xi/4831. (Av4){ (J+AJ) (J+1+AJ> ~ <K+AK> 2}] +
mfn (up (MK) 31 +
magi (Av4+1) (M4) (mam +
[MIR (M4) (mar) (J+AJ) (J+l+AJ)] +
[afficmp u+m2<J+1+m>23 +
[aixli (Ava) new 2 (HM) (J+1+AJ)] +
[afiumpmuxf‘] +
[HOfiE(K+AK)6-K6] +
[HOJ] [ (J+AJ)3 (J+1+AJ) 35.13 (J +1) 3] +

2-K2J2(J+1)2] +

ugh: (K+AK) 2 (J+AJ) 2 (J+1+AJ)
[11ng [ (Ki-£3104 (J +AJ) (J +1+AJ) -K"J (J+l)] +
[“21 (mp (Av4+2) <1<+m<>23 +

A. 2 2
[yuan (M4) max) 1 +
[YAZJE (4V4) (AV4+2){ (J+AJ) (J+1+M) - (K+AK) 2}] +

[Y B ][(M )2{(J+AJ)(J+1+AJ)-(K+AK)2}]
44‘4 4

 

24

the chapters involving the A0 determination of CD31 and CD3C1.

The method of a simultaneous analysis of individual transi-
tions of a well-resolved vt and 2Vt(i) is believed to be the
most accurate way to determine A0 for axially symmetric moelcules.
However, for purposes of comparing statistical accuracy and method-
ology, one needs to consider the time-honored procedure of obtaining
A0 from the zeta-sum rule.

Historically, for accidentally symmetric-top molecules, it
was possible to predict infrared spectra without consideration of
vibration-rotation interaction. The classic paper of D.M. Dennison
(7), published in 1931, summarized the theoretical work up to that
time which was done without considering Coriolis interactions. In
1934, E. Teller (26) pointed out that many features of the perpen-
dicular bands of true symmetric tops can be explained if one con-
siders the Coriolis interaction between rotation and the vibratiOnal
motions of degenerate normal modes. Since the eigenvalues of in-
ternal angular momentum are not necessarily integers, Teller intro-
duced the constant Q as a proportionality factor in the expression

for the component of internal angular momentum which results as a

consequence of degenerate vibrations,

_ z
pzh’svs> . {’s‘Ti gslsZ ‘sts>

‘Teller then presented a theorem which States that the sum of the
Q's for all the degenerate first-excited vibrational states is a
function of only the individual masses and their relative distances
in the molecule. Most important, Teller succeeded in Showing that
this sum is not a function of the force field which binds the atoms

in the undecule. By using this result, Johnson and Dennison (27)

were able to Show that in the harmonic approximation,

,

2 g: = (# of atoms on symmetry axis) -2 + Be/ZAe
t

 

or for methyl halides,
(31) Z’z=B/2A
° t tat e e

The theory behind the zeta-sum rule has since been more rigorously

"1

developed by Boyd and Longuet-Higgins (28).

Most zeta-sum work with the methyl halides has involved an

Pact-t 2.4- HF?-

application of an equation of the form (2.7), utilizing only the

—-

Q branches of v4, v5, and v6. Eq. (2.7) can be put in the form,

(3.2) v = Cl(v) + C2(v)KAK + C3(v)K2

where C1(v) all terms independent of K

02(v) ZEAV(1 - c3) - Ev]

c3(v) = [(Av - A0) - (av - 30)]

If Q branches of v4, v5, v6, are fit, the constants Ci(v) for
'v = 4,5,6, can be obtained.
Then,

.. _ Z-
2 C2(V) - 2 ZCAV Avgv B
v v

1

V

‘This sum can be approximated as

at Z
(3-3a) z C2(v) - 2 zEAv - BO - Aogv]
v v
or can,be approximated still further as

~ 2
(3.31:) 3:]: 02(v) - 2 EEAO - Bo 5A0Cv]

26

First consider the form (3.3a) which has been used in recent

work on the methyl halides (20,21). It requires further information

from C3(v) in order to arrive at A0,
~ A
ZC3(V)-ZA-3A=-£or;
v 0 v
v v v

substituting into (3.3a),

= f' + _ _ Z
5 C2(v) 2L5 03(v) 3AO 3BO A0 5 fiv]

but the zeta-sum rule may be approximated as

2 Be BO
zg=.—__:.—_
v v 2 e 2 0
and thus,
_ l.
(3.4) A0 - €15 C2(v) - 2 E C3(v) + 7B0]

The further approximation (3.3b)was used in earlier work on
the methyl halides and is presented in standard reference books on
the subject (18,29). The older treatments often obtained the value

of C2 for each band by means of the combination relations (2.8)

and graphical techniques. The expression for A0 which results

from (3.3b) is identical to Eq. (3.4) if 2 C3(v) = 0. This

V
approxinmtion corresponds to a change in A0 of about 0.005 cm-l.

Approxihmtions involved in arriving at Eq. (3.3a) are not as large

as that described above. For example, in the case of CD3X molecules,

the error in A0 which results is approximately 0.0002 cm-l.

There is one other important source of error (apart from the

harmonic approximation of the zeta-sum rule itself) and this involves

the problem of where to measure Q branch peaks. Y. Morino and

J. Nakamara consider this problem in their zeta-sum paper (20).

‘1

27

In Appendix I of that paper, an estimate of the change in Jmax

corresponding to a Q branch peak is given as a function of the K.
The uncertainty caused by this dependence is further complicated

by the slit function of the instrument. They were only able to
estimate the maximum effect on C2(5) to be‘: 0.04 cm“.1 for

CD3C1 us (which was the poorest band they analyzed). Such a change

in C2(5) corresponds to a change in A0 of i .006 cm-1. Morino

and Nakamura concluded they could ignore any Jmax dependence on

K since in most cases this systematic error would be less than their

...—fm;3‘mfij

random experimental error.

In summary, a zeta-sum determination of A0 under low to
moderate resolution depends on the following approximations:

(l) The zeta-sum rule is derived in the harmonic approximation.

(2) The approximation,

2

z
2 Ava - A0 2 gv
v v

is made in obtaining Eq. (3.3a).
(3) In all applications to CHSX or CD3X, Jmax has been

assumed not to be a function of' K.

The approximations (2) and (3) above could be removed by a
high resolution study of v4, v5, and v6. Such a single-band
analysis would yield the constants:

2‘
‘erca Ca
A-Az=c o 3A-A(z+gz+;z)=c+c +c
o 255 5 r o e C4 5 6 4 5 6

z
AO-Aéc6 C

‘Therefore, by summing these terms and by making the very small

approximation B 3 Be’ a value of A. would be immediately avail-

0 0

able. However, the harmonic approximation (1) would remain; indeed

28

v4, v5, and V6

of the magnitude of this approximation if the resultant A.O were

a high resolution study of could provide a measure
compared to that obtained from a simultaneous analysis.

It is apparent that even though the zeta-sum technique could
gain accuracy under high resolution, it would still be subject to a
source of systematic error which currently cannot be estimated. In

comparison, the accuracy of A from simultaneous fits of unperturbed

0
bands is largely determined by the resolving power of the spectrometer
.which is used.

In much of this chapter the assumption has been made that un-
perturbed Spectra are available. In practice, the chances of finding
a pair of. vt and 2vt bands which are completely unperturbed is
Slight (likewise for v4, v5, and v6). Accidental resonances are
found to play a critical role not only in determining whether A.O
can be obtained by a given method, but also in determining the
accuracy of its value when it can be found. Examples of the effects

of perturbations in particular cases are given in Chapters VII and

VIII.

 

CHAPTER IV

EXPERIMENTAL PROCEDURE

High resolution spectra of the v4 (4.5u) and 2v4 (2.2u)

3Cl, and CD3Br have been recorded on the

Michigan State University near infrared spectrometer. Experimental

regions of CD31, CD

ll

conditions for the individual runs are given in Tables 4.1, 4.2,

and 4.3. Two or three spectra were recorded for each of the six

A

bands. The averaging procedures and results of individual cali-
brations will be discussed for each of the molecules individually
in the analysis chapters (VI, VII, and VIII).

The Michigan State University spectrometer has continually
been improved during the past 15 years, and consequently it bears
the imprints of many contributors. The present state of the
instrument has been particularly affected by the work of former
graduate students, J.L. Aubel and D.B. Keck. The most current
report on the major features of this instrument is given in the
thesis of D.B. Keck (30), which includes references to earlier
work. In this chapter a summary of recent changes made on the
instrument is given, along with a description of some of the-
problems unique to this work.

Because of the expense of samples of CD3X gases, great
care had to be exercised in handling them. If ordinary freeze-
'out procedures failed, the gases were slowly pumped out of‘the,
labsorption cell through a liquid nitrogen cold trap. Memories of

these freeze-out difficulties are less than fond, since they often

29

Experimental Conditions - CD

Grating

Calibration

Paper Speed

Detector

Date of Runs

Rod Current

Pressures (torr)

Path lengths

Slits (approx. width)

Best Chart Resolution

30

Table 4.1

v (44° - 38°)

4

300 grooves/mm
lst Order - S.P.
@500/1

CO (1-0)
N20 (1,2,0)

4"/min

PbSe - Type El
@770K

Chart #1 — 7/11/68
Chart #2 - 11/23/68

#1 - 360 amps
#2 - 375 amps
#1 - 19

#2 - 19,10,20
#1 - 3.2 m

#2 - 6.4 m

#1 - 60 microns
#2 - 35 microns
#2 - .05 cm”1

3

I

2vA (45° - 39.s°)

300 grooves/mm ,
2nd Order - S.P.
@500/1

CO (2-0)
N 0 (2,0,1)
2
4"/min
PbS - Type 0
@77°K
Chart #1 - 6/20/68
Chart #2 - 7/24/68
Chart #3 - 12/11/68
#1 - 360 amps
#2 - 360 amps
#3 - 380 amps
#1 - 20
#2 - 19
#3 - 25,19,30
#1 - 9.6 m
#2 - 9.6 m
#3 - 9.6 m
#1 - 16 microns

#2 - 11 microns
#3 - 8 microns
#3 - .04 cm’1

 

Experimental Conditions - CD

Grating

Calibration

Paper Speed

Detector

Date of Runs

Rod Current

Pressure (torr)

Path Lengths

Slits (approx. width)

Best Chart Resolution

31

Table 4.2

64 (44° - 38°)

300 groves/mm
lst Order - S.P.
@500/1

CO (l-O)
N20 (1,2,0)

4"/min

PbSe - Type El
@ 77°K

Chart #1 - 7/12/68
Chart #2 - 11/25/68

#1 - 360 amps
#2 - 375 amps
#1 - 8,4,8
#2 - 15,9,15
#1 - 3.2 m
#2 - 3.2 m

#1 - 62 microns
#2 - 35 microns

#2 - .05 cm"1

3

Cl

2v4 (45° - 39.5°)

300 grooves/mm
2nd Order . S.P.
@500/1

00 (2-0)
N20 (2,0,1)

4"/min

PbS - Type 0
@770K

6/19/68
7/24/68
12/11/68

Chart #1
Chart #2
Chart #3

#1 - 360 amps
#2 - 360 amps
#3 - 375 amps

#1 - 18
#2 - 24,18,24
#3 - 25,19,25

#1 - 9.6 m
#2 - 9.6 m
#3 - 9.6 m

#1 - 16 microns
#2 - 11 microns
#3 8 microns

#3 .04 cm-1

 

Experimental Conditions - CD

Grating

Calibration

Paper Speed

Detector

-Date of Runs

Rod Currents
Pressures (torr)
Path Lengths'

(Slits (approx. width)

Best Chart Resolution

32

Table 4.3

84 (44° - 38°)

300 grooves/mm
lst Order - S.P.
@500/1

CO (1-0)
N20 (1,2,0)

4"/min

PbSe - Type El
@77°K

Chart #1 — 8/19/68
Chart #2 - 11/25/68

#1 360 amps
#2 - 375 amps

#1 - 21,15,9,15
#2 - 20,15,20

#1 - 3.2 m
#2 - 3.2 m

#1 - 54 ndcrons
#2 - 35 microns

l

#2 .05 cm-

3

Br

284 (45° - 39.s°)

300 grooves/mm
2nd Order - S.P.
@500/1

00 (2-0)
N20 (2,0,1)

4”/min

PbS - Type 0
@77°K

Chart #1 - 8/09/68
Chart #2 - 10/30/68

#1 - 360 amps
#2 - 375 amps

#1 - 25,40

#2 - 20,40

#1 - 12.8 m

#2 - 9.6 m

#1 - 13 microns
#2 - 9 microns
#2 - .05 cm-1

w'P-mf 1707—1. . . »

 

33

resulted in rather frantic glassware assemblage in the small time
available between CD3X removal and calibration gas insertion.
Initially a study of' CD3F was to be included in this work,
but it was found that the only sample of this very expensive gas
which remained in the laboratory was very small and impure. Moderate
resolution runs were made using that sample, but a new sample arrived
too late for any more runs during the winter of 1969. Future p1ans

do include a study of 04 and 2v of CD F. Samples of CD CN

4 3 3

have also been obtained and could be studied in the future.

The source of near infrared radiation in both.wavelength
regions was an ohmic-heated carbon rod. The associated assembly
has been described by D.B. Keck. The only changes were in the
operation of the source:

(1) It was found that the use of #17 copper wire for hold-
ing the carbon rods provided trouble free starting.

(2) If the rod being used had been exposed to the a‘tmOSphere,
it was beneficial to flush the rod housing with argon
after the rod has been heated for 10 or 15 minutes.

This rids the chamber of the CO and 002 which are formed
soon after the rod is heated. 00 lines, which were uSed
in the calibration of both bands, could be seen to be

considerably broadened by 00 in the housing. The lines

immediately narrowed after flushing with argon.

The White type multiple traverse cell as described by T.H.
Edwards (31) was completely disassembled and cleaned. The spherical
mirrors were stripped and realuminized by Liberty Mirror (anti-

corrosive quartz finish No. 749). The foreoptics and cell system

"“f. I: =‘ H
: "'n ‘i.

34

were then carefully realigned and focused on the entrance Slit of
the monochromator.

All of the spectra eventually used were recorded with the
monochromator in a single-pass configuration, using the 300 groves/mm
grating between 450 and 380 (first-order for v4 and second-order
for 2v4). The calibration fringes were an immense problem in this

region. An apparent grating anomaly causes a sharp decrease in the

intensity of ninth-order fringes between 43.50 and 430 and a similar

Imu'v‘al‘lh “—5.3 I

effect in the case of eighth-order fringes between 42.70 and 42.30.

*3

This effect has been noticed by others and was certainly verified
far too many times in the course of this work. Fortunately the bad
fringes occurred in a region lying largely between our low-fre-

quency calibration and the CD X region. It did however cause some

3
- "only fair" fringes on the extreme low-frequency Side of a few
charts. This fringe problem was much worse in the case of double
passing the grating. The already weak fringes became much weaker
and could not be used. The infrared double-pass resolution was
very good in the 2v4 region and so these spectra were run without
fringes as high resolution references - if needed.,

(The problems associated with the previous detector system
were described bereck. A new detector housing was designed which
(allows a mounting of three detectors simultaneously in'a manner
allowing a rapid transition from one to another while maintaining
a temperature of 770K. The three detectors were mounted on a tri-
angular head attached to the bottom of the liquid N2 dewar.* The
dewar assembly can be rotated at leasf 1200 left or right of the

center position. The dewar is supported by a knurled stainless

steel top which keeps the critical top O-ring seal as isolated as

35

possible from the N2. The cold O-ring maintains a good seal under
rotation from one detector to another, but does stick and cause a
difficult transition from one detector to another if it is not
lubricated periodically (approximately every 10 cold turns). When-
ever possible, the detector should be changed before cooling.
Sketches of the assembly are Shown in Figure 4.1 along with
the variable bias system (Figure 4.2) which was constructed to allow

the choice of a bias resistance to match the impedance of the detector

currently in use. Although it is advisable to periodically check and

r'V!‘ "Vati‘hg'a’ !. r ‘ '3
.8

record the cold detector resistances, the correct choice of bias
resistance can be simply made by maximizing the recorder signal.
Even though the recorder signal seems greatly dependent upon bias
choice, it should be realized that the effect on S/N is quite small.

Heat shields have been designed to limit the field of view
of each of the mounted detectors. The shields slide into the large
circular apertures in front of each detector and provide an adjust-
able rectangular opening. They have been found to be particularly
necessary for the type E detectors; typically raising the cold
resistance from around 3 MD to 10 M0 and significantly increasing
the detectivity.

The detectors which are currently available are the same
' types that are deScribed by Keck. A new type E (PbSe) detector has
been purchased from Kodak; however, its detectivity does not seem
ito~match that of the previously used E type. The tri-detector system
as described should be operated with a set of detectors to cover the
entire 1 to 6 micron region. This can be accomplished by means of
an N or 0 type in one position (1 to 2.8u), a P type in another

(2.8 to 4.2u), and a type E (4 to 6p) in the third position. Such

36

 

 

 

 

 

 

 

 

 

Figure 4.1 Detector Assembly

0N~OFF

1

TYPE 0
(1+2.8 u) :.>_.o

 

 

 

 

TYPE E 2
(4+6 u)

 

 

.+
TYPE P

(2.8+4.2 u)

 

 

 

JL —
Cr 1"—

 

.5 M9
7° . 10 M9 2-5 M“
PREAMP

 

 

Figure 4.2 Bias Circuit

9 VOLTS

 

37

a system was used during the summer and fall of 68’ and allowed runs
of emission Spectra in the lu region by L.E. Bullock, separated only

by hours from some of these absorption runs around 4.5g.

 

Plans are being made for the purchase of an InSb detector
which operates with peak detectivity in the 4 to 6 micron region.
The present type B PbSe detector for that region has a significantly
lower detectivity than any of our PbS devices or the InSb. The new ‘
detector should allow excellent resolution in the 5 micron region

in comparison to the present maximum of 0.05 to 0.07 cm-1. Un-

fortunately, the new detector will necessarily be mounted in an [
evacuated dewar which will not have immediate compatibility with the
present system.

Other plans for the near future include an improvement in
the fringe detection system. Professor C.D. Hause's plans include
use of a newly introduced phototube, the correSponding power supply,
and a more sophisticated preamp. In addition Professor T.H. Edwards
is investigating a tunable lock-in amplifier for the IR signal along
with a digital voltmeter which will sample at least four channels
of information and record them on magnetic tape. The advantages of
such a data acquisition system would be numerous. Some of these
advantages are discussed briefly in the first part of the next

chapter which summarizes our current data analysis system.

CHAPTER‘V

ANALYSIS OF DATA

After a high resolution spectrum has been obtained from the
Spectrometer, a large amount of data reduction must be completed
before observed frequencies are available from the chart. Part of
this process involves an analog to digital conversion of the in-

formation on the chart; the rest involves obtaining observed fre-

 

quencies from this digital data. Thus it is the first step of this
process which could be almost eliminated with a digital voltmeter to
magnetic tape data acquisition system.

Presently our data is digitized to five-place accuracy by
the HYDEL system. A description of this process has been given by
T.L. Barnett (19) and briefly by L.E. Bullock (32). The encoders,
which are the heart of this digital process, were often unreliable
during the past year. They were carefully cleaned a number of times
but still cannot be completely trusted. Since the system had already
seen considerable use when first acquired by this laboratory in the
early 60's, the encoders may in fact simply be worn out. The tight
financial situation has made overhauling the system quite infeasible
at the present time. The state of the HYDEL system is thus another
reason the magnetic tape system currently seems very inviting.

The computer program SHAFT as developed by D.B. Rack (30) and
lnE. Bullock (32) has been very helpful in this work. Its major
purpose is to help obtain the best possible set of observed fre-

quencies from many records of HYDEL digital data output., SHAFT
38

39

takes the recorded line and fringe positions, along with the input

 

calibration frequencies, and from these determines the coefficients

(A and B) of the linear equation,
Line Frequency (cm-1) = A (Fringe #) + B

Observed frequencies are calculated for all measurements of chart
lines, and these are then averaged and output in formats useable
in our other programs. The other options available in SHAFT are
manifold and their usefulness is matched only by the initial

complications in using them. However, for anyone who is about to

 

Start a project which involves many charts and measurements, learn-
ing to use the program is time well spent.

Two HYDEL measurements were made of two individual charts for
each of the six bands. Thus, four sets of data were available for
each band. Unfortunately, the first charts which were run during
June and July 68' were almost invariably significantly poorer in
resolution. Only in the case of 2v4 of CD33r was it possible
to average frequencies between charts without reducing frequency
accuracy. In each case, however, the two HYDEL measurements were
averaged. Because of the unreliable condition of the HYDEL system
during the past year, the two HYDEL measurements were very necessary
since the occasional HYDEL errors were erratic and usually ranged

from 0.04 to 0.07 cm-l.

The observed (averaged) frequencies are then ready to be fit
'by a frequency expression given in terms of molecular constants,
(quantum.numbers, and changes in these quantum numbers. The fre-
(quency expressions which have been used most extensively in this

work are the single—band frequency expression (Table 2.5), the

40

v4 and 2v4 expression (Table 3.1), and to a much

lesser degree, the Q branch frequency expression (Equation 2.7).

simultaneous

Program SYMFIT has been written to conveniently provide for the
above fits. The remainder of this chapter is devoted to a des-
cription of this program and instructions for its use.‘

The major goals in the construction of SYMFIT were:

(1) It must be a general symmetric top fitting program - thus it
must fit single bands, Subbands, double bands, Q branches,
etc.

(2) SYMFIT should Operate with formats compatible with the in-
puts and outputs to program SHAFT.

(3) It should be able to perform fits in less than 45 seconds
(Priority 5 on the CDC 3600 at MSU).

(4) For the convenience of other researchers, SYMFIT should
utilize subroutine STEPFIT in order to lessen confusion
when comparisons are made to other fitting programs
currently in use in this laboratory.

(5) SYMFIT should be compatible with the CDC 3600 and 6500.

A Simplified block diagram of the final SYMFIT version which
.accomplishes these goals is shown in Figure 5.1. A listing of
SYMFIT along with a typical data set is given in Appendix A.

The set up of a SYMFIT deck is described below. After a
Fortran‘ IV or binary copy of SYMFIT (and the associated control
cards), the following cards are read:

(1) Option gggd - reads the variable IBAND in the last 8 columns

(73-80)

 

41

 

eHezsm mo snowman xuoam H.m magmas

 

 

 

 

 

0» ooxmo we
codum>ummoo umouoOQ use msouca

 

mcofiumasoamo
Hmouumuumum can use

no muflsmou use museum
I BDOBZHMm NZHfibommDm I

*

 

 

 

 

.ouo roam uo
noduofi>oo oumocmum .wucofloflwwooo
mo muouuo oumocmum neonasoauo

 

 

i

   

 

mm>Hma Bthwm LUHB COEEOU

ca some means mofloconooum usdcw
ou moaomwum> oofiuwuomm mo uflm
monsoon unmoa omwsmoum m mEhOwuom
coco .mCOMumsoo Hmsuo: meson

 

51g one cocwum o .mc

L moaomHuo> no sumo no muom wuoe

E o: 3 new a: . one 35 5 cum: 3

cu sum moanmfium> unaccomoocw scans momma

 

 

MCOMuosuumcw mcwuouomo umzuo
can .mmcwpooc .moocmuoaou uwu momma

mucoumcoo usmcfi Enuw
mowucooooum neonaaodoo

 

 

:o«umofiuaucovw some HOu moaomfium>
ucoocomoo one unaccoQOVCa
wo xHuuME oumwudoummn do muom

+

   
  

 

 

so mu m u one: monusu use
comm sou .uaauummoc anon - Ave couudo
uom .coHum>uomoo powuwucoow some now

 

 

< ucmwoz muw can oo>uwmoo hucwsooum momma
.\ +
owuwaflu: mcfion nodumo ecu
u0w mucmumcoo Hows» am momma
+

uwm mwaofluou Ave

 

 

 

one econ wansoo Ame
sou ecmnasm
so scan museum lac

 

 

 

 

mZHBDOmmDm BHhmmBm

ucouuno 688m

 

 

 

mm>Hmn BHmZNm

BHEZNm z<moomm

 

42

(a) If IBAND = 8HSINGLEBD8, the program assumes it is to use
the single band frequency expression of Table 2.5. The
expression also will allow a fit of subbands when the only

. . . B i
variables put into fit are a and the subband origin.

4

(b) If IBAND = 8HDOUBLEBD, the simultaneous frequency
expression is assumed (Table 3.1).

(c) If IBAND = 8HQ BRANCH, a fit is made to the expression
of Eq. 2.7.

(d) If IBAND = 8HCORIOLIS, a residual analysis of the type
described by W.E. Blass (33) is performed.

(2) Constant card - if g_card reading CONSTANT in the last 8

 

columns (73-80) is read next, the program assumes initial
values of some variables will be read into the fit.

(3) END HEAD card - if a CONSTANT card was provided, the

 

opportunity to insert a heading to describe these constants
is provided. The program will print a heading until a card
with END HEAD in the last 8 columns (73-80) is found.

(4) Initial values pf constants are then expected to follow the

 

END HEAD card. These are read in the order indicated by
their quantum dependencies as shown in their reSpective
Tables or in the Fortran listing. Values are read until an
§§2_gQN§T_is found in columns (73-80). Thus if only three
values are read in (e.g. microwave values of 30’ D3, and
Dgx), then the END CONST card should follow the third
constant (all other initial values are automatically set
- 0.0).

(5) Next, a NEW DATA card will start the reading of sets of

Av, AK, AJ,K,J, observed frequency, and line weight for

 

7? The Fortran notation, IBAND = 8HSINGLEBD implies the variable
IBAND contains the 8 characters SINGLEBD.

films-“#091

43

each identified transition. The identification format used

in SYMFIT is compatible with the identification format of

 

SHAFT. This format is given in statement 185 of the SYMFIT
listing.

(6) An §_i_ column 19 will stop the reading of frequencies and
identifications.

(7) The next card reads in control data for the fitting sub-

’4.

routine STEPFIT. Variables read in here are: INFOl,

 

INFOZ, INF03, NDEIMAX, XDEVMAX, TOL, EFIN, EFOUT, and
ILEVEL. The format here is Specified in statement 190.
Definitions of these terms and their functions have been
given in the MSU IR Laboratory writeup of STEPFIT and are
given by Keck (30).

(8) The next card reads in values of the one-dimensional array
N§(_), NK(I) = 0 unless the Ith variable is to be varied
in the fit, in which case NK(I) = l. The associated format
is given in statement 195.

(9) END HEAD - Another heading may be read in at this point.
Headings are listed until END HEAD is found in columns
(73-80).

(After reading the END HEAD card, the subroutine STEPFIT is
called, and a least squares fit is performed. STEPFIT performs a
stepwise least squares regression, in which variables are individually
entered or removed from the fit after they are tested for statistical
(significance. Appendix B briefly describes the method used in this

fit and the manner in which the associated statistics are calculated.

44

(10) After the fit is performed, STEPFIT will perform a refit after
removing the poorest line depending upon its instructions on
card (7). After performing the correct number of refits and
corresponding line throwouts, control is restored to the
driver program. If a LAST FIT card (last 8 columns) is found,
the entire program will terminate.

(11) If a refit using a new set of variables (using the same data) m

Mfr

is desired, the LAST FIT card should be replaced by a new

1...-

card (8) which gives the new NK(I) array. Another END HEAD
card (9) will then Start the next fitting sequence.

(12) If an entirely new set of data is to be fit, the LAST FIT
should be replaced by a NEW DATA card (5) followed by the
sequence of cards: (6), (7), (8), and (9). This is most
commonly used in the SINGLEBD Option for subband fits in
which each set of subband data is separated by cards (5),

(6). (7). (8). and (9)-

The program is designed to print out the fit results in
formats corresponding to the various options. Single-band fits of
200 to 300 lines require 10 to 15 seconds per fit (fitting with 5
or 6 independent variables). Double-band fits of 400 or 500 lines
require 30 to 40 seconds each (fitting with 7 or 8 independent
variables). The very simple fits of options 3 and 4 require only
3 to 5 seconds each.

The next four chapters include applications of various
SYMFIT options to the cases of CD31, CDBC1, ®3Br and to studies

of the accuracy of molecular constants obtained for each of them.

 

CHAPTER VI

ANALYSIS OF 04 AND 2vA 0F CD31

Consideration of which molecule to study first is important
in light of the experience which is necessarily gained from the first
bands analyzed. In this case CD31 was chosen because it was known
to have a relatively unperturbed 2V4, and because its v4 band
showed no obvious perturbations. This chapter summarizes previous
work on CD31, and then presents the results of this work under high
resolution. Since many steps of the CD31 analysis procedure are the
same for the other two molecules, many of the details are given in
this chapter.

Infrared absorption spectra of CD31 have been studied by a

number of workers at lower resolution. Morino and Nakamura (20)

included CD I in their comprehensive study of the degenerate

3

- fundamentals of CHBX and C03}: molecules at a resolution ranging

from 0.6 to,0.8 cm-l. In addition, Jones, Popplewell, and Thompson

(21) studied many bands 0f CD31 between 3 and 20p at a resolution
of approximately 0.2 cm-l. In each of the above studies, a value

of A0 was calculated by a zeta-sum analysis of unresolved Q branches

of the three perpendicular type fundamental bands.

2v4 of CD31 is the only one of the six bands under investiga-
tion which has previously been studied under high resolution. Joffrin,
Van Thanh, and Barchewitz (22) studied the unresolved Q branch

structure of the perpendicular component along with the parallel

45

 

 

46

component at a stated resolution limit of 0.07 cm-1. However, it

does not appear that their path length was sufficiently long to
resolve any non - Q branch lines of the perpendicular component.

J. W. Boyd (34) studied 2v4 of CD31 at sufficient resolution

(2 0.07 cm-l) and path length (8 m) to resolve many of the PPRU)

and RRK(J) lines of the perpendicular component. Boyd's original

charts are present in the laboratory and provided useful checks on

2v4 assignments for the lines which he was able to resolve.

Experimental conditions for the recorded Spectra of CD31 are

given ianable 4.1. The spectra were calibrated and frequencies were
averaged by use of program SHAFT in the manner described in Chapter V.

The standard deviations of the calibration fits are 0.002 and 0.003
cm- for v4 and 2v4 respectively. Survey spectra of the two
regions are shown in Figure 6.1. A series of 002 lines is in

evidence on the high-frequency Side of v4, but under high resolu-
tion these lines are far enough apart to allow identification and

use of most of the CD31 lines in the region. The v4 and 2v4
surveys of CD31 exhibit low intensity "secondary Q branches" which
can be attributed to the hot bands v4 +*v6 - V6 and

2v 6 - 06.

A number of characteristics of symmetric top spectra aid in

4‘”

.the initial assignment of spectral lines. For example, subband
identification is greatly aided by the J 2 K requirement which
gives rise to a number of "missing lines". In addition, nuclear
spin statistics for CDBX molecules predict that all spectral lines
involving transitions from levels having ground state K values

*which are any integral multiple of 3 will be 11/8 times as strong

48

as the other lines. Thus every third Q branch is noticeably more
intense, even though the change in intensity is considerably less
than the 2/1 ratio for CH3X molecules. An excellent diagram of the
expected intensities in a perpendicular band of a symmetric top
molecule (disregarding the above mentioned spin statistics) is

given by Herzberg (36). It will be noticed that RRK(J) and Ppk(J)
lines tend to dominate the fine structure for high K, but for very
low K values one can expect to find both R and P branches of a given
subband (e.g. RR0(J) and RP0(J)).

With a basic knowledge of the above Spectral features it is
possible for even the beginner to assign a number of lines of a
band such as 284 of c931. In 2v4, 70 to 80 RRK(J) lines had
obvious assignments, and these lines were immediately put into a
single-band fit. Such a fit was used to predict more RRKU)
lines (by giving the unidentified transitions zero weights) and
then the list of observed frequencies was searched for lines which
are predicted by the fit. By such an iterative process most of the
RRK(J) lines of 204 were assigned. It was expected that with,
inost of these RRK(J) lines already assigned, one would be able
t1) predict PPRU) lines to a high degree of accuracy. However,
tfliis was not the case, because, in order to accurately determine
the set of constants A0 + 2Aegz, a2, and D: (all of which have
quantum coefficients which are dependent only on K and AK), it
is :imperative that some lines with a negative AK be included in
the fit. By further impaction of the chart, some PPIC!) and

PPZ (J) lines were found along with a few PP90) lines on the

low—frequency side of the parallel component. Once these were

“I.“ (KIWI—j
I .

49

found, the fit was able to predict more PP10 and PP11 lines.

It was later discovered that much time and trouble can usually be
saved in this assignment process if a few Q branch frequencies are
initially included in the fit in order to help determine more accurate
values of the terms having coefficients dependent on only K and AK.
In all the fits which were done after 2v4 of CD31, rough Q branch
frequencies were included during the initial assigning process.
Once the perpendicular component of 2v4 was successfully fit,
it was found that the resultant constants could be used to predict
"the frequencies of the parallel component which overlaps the
KAK ' -8, -7, -6, -5, -4, and -3 subbands of the perpendicular com-
ponent. Three distinct series of lines can be seen in the parallel
component, although many of the lines are too broad to be included
in the fit. The broad lines are the result of the overlapping of
transitions of differing K values. For example the K = 2, K - 6,
and K.= lO subbands all overlap. Over 60 narrow lines from the
parallel component were included in the final 2V4 fit, and were
givennweights appropriate to the line shape and expected intensity
'(3f the assigned K value. For example, the series of lines formed
by overlapping of the K = 3 and K = 5 subbands were assigned
as K .- 3 lines because this series is approximately twice as
strong as that made up of K - 5 lines. A study of the single-
band frequency expression shows that parallel component lines of
high J are very valuable in determining a precise value of 012.
and in the case of 2v4 of C031 this effect was very apparent.
The final single-band fit of 2v had a standard deviation of

4

0.007 cut-1 and determined the most precise set of constants of

50

all the bands analyzed. The results of this fit are given in Table

6.1 along with the results from previous work on CD31. The micro-

J
wave values of BO, DO’ and Dgx which have been used in all the

CD31 fits are included in Table 6.2.

Many RRK(J) lines of the v4 band could be immediately

identified. However, the low-frequency side of this band was char-
acterized by an overlapping of lines from different subbands. For 1
‘example, the PP9(J) lines fall on top of Pp (J +-10) lines. 1

8
This greatly limited the number of negative AK lines which could

 

be included in the fit. In addition, it was found that the PPlZ’ ‘ l

P
10, and P9 lines which could be identified did not fit well

with the rest of the band. These lines were therefore suspected of

P
P

being perturbed and were given zero weights. The results of the
v4 fit.of unperturbed lines is given in Table 6.1, and the pre-
cision.of the reSpective constants as determined by the two single-
band fits may be compared. The wide range of KAK values available
in the 2v4 perpendicular component together with a: and or:
information from the parallel component are the major reasons for
the greater precision of constants found in the fit of 2v4'
At this point in the analysis procedure, one must try to

decide how to determine the best value of A0 from the available

data. As Chapter III points out, the results of single-band fits

of v4 and 2v4 can be combined directly to obtain A0. In this
case,

A0 - Aegz - 2.1324 from VA

A0 + 2116;: . 3.4726 from 2v“
and thus 3Ao " 7.7374 .

A0 ' 2.5791 cm;-1

51

Table 6.1

Molecular Constants of CD31

Obtained from Single Band Fits (in cm-l)

 

 

This work: v4(k=l) 204(k=-2)
vo-k(AK)2AeQZ 2298.087:0.006a 4581.387:0.005 (,)
4546.115:0.006 (n)
Ao-kAegZ 2.132410.0005 3.472610.0005
03 (23300) x 10‘° (34:2) x 10’6
A‘ -3 -3
04 (13.510.4) x 10 (12.891.04) x 10
a: (86110) x 10“6 (8218) x 10‘6
aQuoted uncertainties are 95% s.c.i. (See
Table IV)
Previous work:
(A) Morino and Nakamura (20) (B) Jones, Pepplewell, and Thompson (21)
00(04) = 2298.1 00(04) = 2298.53
A A B
" . 1 .. c .
a4 0 0 4 a4 a4 0 015 (from 04)
A = 2.586 GA - B = 0.012 (from 20 )
0 4 4 4
g: - 0.178 A0 = 2.586
g: - 0.178
(C) Joffrin, N. Van Thanh, (D) J. W. Boyd (34)
and Barchewitz (22)
v0(2v4)i ' 4580.23 vo(2v4)i 8 4581.397
v0(2v4)u - 4546.10 00(204)n - 4546.14
at - 0.01310.003 Ao(l+2§:) - 3.472
a: - 0.000171000001 a2 - 2 - 0.01268
CZ ' 0-206 DE - 0.000038
a: - 0.000091

”H

“garment-n L-u

52

Table 6.2

Molecular Constants Resulting from Simultaneous Fit

 

of v4 and 2v“ of CD31 (in cm-1).
Constant V3133 95% 3.0.1.8

00(04) 2298.526S 0.003

00(204i) 4580.4948 0.005

00(204n) - 4546.1156 0.005 p
A0 2.57882 0.0004 E
Aer: 0.44676 0 0002 i
0% . ’ 0.0000358 0.000002

«2 0.01290 0.00004

a: 0.000083 0.000002

Standard Deviation of fit = 0.008 cm.1

Input Microwave Values of Ground State Constants (37)

 

Constant “ Value (cm-1)
30 0.2014822
03 1.197 x 10'7
03K 1.612 x 10’6

aSimultaneous confidence intervals (95%) for the eight constants

determined. In this case 3 4 x standard error of the coefficient.

53

This approach has three obvious difficulties:

(1) The manner of combining these two constants is uniquely
determined by their algebraic forms. Thus, as in the
case above, if one constant comes from a rather in-
completely assigned band, it is Still not possible to
give it a lower weight in combining it with the results
from the better band.

(2) A final result of such an analysis is to find two values 1
of each of the constants aA B, and DK, even though

4 4 0 .~

there is certainly only one true value of each. i

, or

 

(3) While it is possible to calculate the Standard error
of the AO which results from combining the sets of
constants, the calculation of any sort of a meaningful
simultaneous confidence interval (s.c.i.) (see Appendix
B) would be most difficult.
The first two of these difficulties can be overcome by per-
forming a weighted average of the two sets of constants from VA
and 2v4. Weights should be given which are inversely proportional

to the variance of the individual constants. The new averaged

constants (usually D13 av’ 0'2 av’ and 0!: av) must then be held
constant in new fits of v4 and Zva in order to determine the
best values of A0 - kAegZ (k = l and k =5 -2).

IFor example, in the case of a2 from v4 and 2v4 of CD31.

 

 

1 1 ‘1 A 1 A 1 A
+ a = a(V~)+"—"- 07(29)
[(10)2 (1)2,J “V (10)2 “ “ (1)2 “ “

Therefore in this case,

54

A N A
0’4 av ' °’4‘2"4)

O O a O O K
The Situation 13 Similar for a: and D0" If the average values
A a” and 0K are held consta c ' th f‘ h
0‘4 av’ 4 av’ 0 av n 1“ e v4 lt’ t e

new value of A0 - Aegz is 2.1321. If this is combined with the

z .
Ao +2Aeg4 from 2v4, one obtains

A0 = 2.5789

This should be the most precise AO value which can be obtained

by combining single-band fits. However, the difficulty of obtain-

ing the correct s.c.i. still remains.

 

A simultaneous fit of v4 and 204 with the generalized
frequency expression of Table 3.1 provides a more direct way to
overcome the above difficulties. The results of such a fit for this
case are given in Table 6.2 along with previous values of A0
obtained by the method of zeta-sums. The Standard deviation of
this fit of 464 lines (0.008 cm-l) is only slightly larger than
that of the single-band fits (0.007 cm-l).l The final assignments,
observed frequencies, and the line weights are given in Appendix C.

The sixteen apparently perturbed lines of v4 were given
zero weights in the simultaneous fit, and their observed minus
calculated frequencies are shown along with the other lines in
Appendix C. The simultaneous fit indicated the lines were indeed
perturbed since they clearly did not fit well with the other lines
in either band. The observed minus calculated (OBS-CALC) values
are almost independent of J, but increase rapidly with K. The

ability of the simultaneous fit to help find perturbed subbands

and the corresponding energy level shifts is more clearly

55

illustrated in the case of the more extensive perturbation in v4

of CD3C1 (see Chapter VII).

The A resulting from the zeta—sum analysis of Morino and

0
Nakamura (20), as shown in Table 6.2, was obtained from an analysis

using the Q branches of 04, v5, and V6 by fitting the frequencies

with Eq. (3.3a). By refitting their data, the standard error of

the resultant A0 has been calculated by SYMFIT to be approximately . #1
1 .

0.001 cm- , which is an order of magnitude larger than the standard ‘

_error resulting from a simultaneous fit of v4 and 2V4. This is

 

the standard error of the constant due to random errors in observed
frequencies and is theoretically quite independent of various
approximations made in zeta-sum method (see Chapter III). The
standard error of the zeta-sum A0 could be considerably lowered
in the case of a fairly complete set of v4, v5, and v6 bands.
In practice, for CD3X molecules it is found that the strongly
absorbing 02 parallel band overlaps the low-frequency Q branches
of us (20).

In summary, the determination of A0 for CD31 by a simultaneous
fit has proven to be precise and direct. The advantages of this
method over either determination by single-band fits or by the method

of zeta-sums have been illustrated.

CHAPTER VII

ANALYSIS or 04 AND 204 OF 013301

Survey Spectra of the 04 and 2v4 bands of CD301 are shown
in Figure 7.1. Except for the RQ14 and Rle lines of v4, which
seem rather perturbed, the general appearance of both bands is quite
2 lines which appeared strongly in CD31 are much

weaker in this case and do not Show on the survey spectra of Va.

normal. The CO

The calibration fits of the averaged frequencies result in standard
deviations of 0.002 cm”1 for v4 and 0.003 cm.1 for 2v4. A
The analysis procedure started with the 2v4 band and pro-
.ceeded in a manner similar to that used in the case of C031. The
first new problems which arose involved the 2v4 parallel component
which could not be predicted with the constants obtained by fitting
the RRK(J) and PPK(J) lines of the perpendicular component. The
effect of a perturbation in the parallel component is very obvious
in the QQK lines at its center. Identifications for K s 6 are
uncertain for both the QQK lines and for the RQK and RQK

Q

lines, even though the QR. line positions are quite normal for
K.> 6. It is possible that a further study could result in a better
understanding of this perturbation; however, since the perpendicular
component did fit well, no more time was Spent on the parallel com-

ponent in this study. The results from the final single-band fit

(201 lines) are given in Table 7.1. As in the case of C031, only

second-order terms were found to have statistically significant values.

56

 

 

m a ,
#0 no mo 9N com a; mo muuoonm xo>uom ~.m ouswwm

 

 

HUEC On.oe 001mv omoe 80v
6 n .
aviatiije1Wy S~.u oo
......W. aeaeeessssesee ‘ ......53
~_oW WW _ W W. . . .. .W ”W. ...; WWW WWW), W so
c .. W .1.. .W W. W .. .— ...WWEr — a
W W W . .. .1. ... W W .W .W. ... g1 .. ,3 W
Ooe , W W . W W. _ W W W aW
WM co W W W W W W W co m
a no: cox non A
750 ...oanr... 8.3 . on:

W

W .... W..W..

W. .
We W fifivskxéja4

;ess. . Wee:..... _.;.Wes.

.... W .. W 3.}... WWEW. WWWWWW WWWWW WWW WWWWWWW WWWW. WWWWWWWW W WWWWWWWWWWWWWWW: W. .W.
~..W _ . .... W W ... .W W W ..W. W. W W. W W .. .. W. 1 W w. a
.._._WWW..W.._.W5.W ... ..

a: so... no: co... no mm. A

58

 

 

Table 7.1
Second Order Molecular Constants of CD3C1 from Single
Band Fits (in cm-l)
Constant v4(k = l) 204(k = -2)
vo-k(AK)2(AeCZ) 2283.001:0.009 4552.175jp.006
A0 - kAegz 2.138:0.002 3.500Lj0.0006
K -6 17‘?"
D (from 2v ) (28+4) X 10
0 4 —. i
A -3 -3 5
a4 (12.110.2) X 10 (12.47i0.06) X 10 ;,_
a2 (101317) x 10'° (117:4) x 10'6 I
Standard Deviations of Fits: v4 a 0.010 cm.1
20 - 0.008 cm'1
4
Average Microwave Values of Ground State Constants (37)
-l
Constant Value (cm 4)
B 0.360127
0
J
D0 0.000000359
DJK 0.00000339

59

In the 04 and 204 bands of CD3C1 there is little evidence

of the two naturally occurring chlorine isotopes (Cl35 and 0137).

Because of this, the values of BO, D3, and Bax which are avail-

able for both isotopes from microwave work (37) were averaged with

weights given according to the natural abundance of Cl35 and 0137

' (approximately 3 to l).

The PPRU) and RRK(J) assignments were easily made in
the v4 band. However, when these 250 lines were put into a Single-
band fit, the disappointing result was a standard deviation of over
0.02 cm-l, even though no lines seemed to be obviously perturbed.
In an effort to determine the cause of the problem, the RRK(J)
and PPk(J) lines were separated. It was found that the two halves
of the band fit well separately (to about 0.008 cm-l) in each case.
The major difference in the sets of constants determined by the two
fits was in GE, which was much larger in the case of the PRKCJ)
lines. The a: as determined by the RRK(J) lines was approx-
imately equal to that found in the case of 2v4, whereas that from
the PTk(J) lines was about twice as large. At this point one
might guess that the PPK(J) lines of 04 are subject to a.J-
dependent perturbation which shifts the upper states in such a way
as to produce a new "effective 012".

To further study this effect, the subbands of Va and 2v4

were analyzed individually. In such fits, the single-band frequency

expression (with K and AK constant) takes the form,

v B 00 (subband origin)
+ (microwave determined terms)

- “2W0 (J + 1 + (mo + M)

r-r‘

1-97.-
I

 

60

when third and fourth-order terms are ignored. To determine a
statistically significant a: from a subband, approximately 10 to
20 lines of differing J values are required. All the subbands of

v4 and 204 having a sufficient number of lines to individually

. B . . .
determine 04 were fit with the above expre381on, and the results

of these fits are shown on the graph of Figure 7.2. It will be

noticed that a: values determined by the RRKU) lines of v
B

and those from 204 are compatible; however, the effective a4 5

4 1!:

values from the KAK s 0 subbands of 04 are clearly quite i

 

different. The error bars given on the graph are‘: (Standard 3
errors of a2) and are therefore somewhat optimistic.

Another effective and perhaps more direct way to determine
exactly which subbands are perturbed is to perform a simultaneous
fit of all the identified lines of 04 and Zva. When the perturbed
lines of v4 are fit with the many unperturbed lines of both bands,
they no longer have such a large effect on the constants from the
fit. Therefore the perturbed lines no longer fit well, and the
OBS-CALC values from the fit clearly indicate which subbands are
perturbed. These lines are then given zero weights in the simulo
taneous fit, and their OBS-CALC values from the fit indicate the
magnitude and direction of the shifts in the upper levels:

Figure 7.3 indicates the OBS-CALC values in the case of the
four subbands on the far left of Figure 7.2. These deviations are
seen to have a consistent J dependence, and also gradually become
larger for higher K values. The V4 section of Appendix D in-
cludes the smaller deviations of the other perturbed subbands. In

P P

the case of the P3 (J s 12) and P1 (J S 12) subbands, the

61

 

m
Ho :0 «0 «pm one e) no monsooam scum Mo o>wuoomwm N.n ousmfim

v>~ no man

 

 

 

 

 

 

a+

all. I'll. ill in":
. . . W W . .

v

o

a NO K<K

 

1

 

.13..
H.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(1.1-- +14--IH.. I W..- 2. - ,-
. ,. .
Hsn~ ~.. {II 7 .
Fifi.“ H 1 W. W
I .II VI Ill 141! 11 l I I‘ll? Ill. III]. 1' ll ( ‘ lIni.’ V II I'll PI In| h lpLW ”HI 1.. l I AW. I lwluIMI .v‘.
IIIIII . 1. -- . . , ..
I, .I 1 2A - I III: .I( I r a .. 1|.er
. , w .W. . .w . _. w- m- r
II lull: I II I. . (II IZIIITIIII I... ~ .
.. W, H . . .. ... ...
. . a: :I.:z. . . .W;
.IWIH] I 1. Ill I I | I I I Ill . w .
)I . ..II.I . . ...m M Il(I chIH 1 I. y l . (I IIIIII I {I I ....
.....WgW ... . .Ii. .. .
. a ...W . . 1 .IIII In: .
W W W I I- A.
In- .-- .141; .III. I , . - - - . (I. II
a.

 

 

 

oou

omN

con

62

'0 . I
. I
lill‘ll' | '
i-llill
c

Ho

m

I
ELF: ...lnll \llzui

nu uo q; no

mvcwnnsm wmnusuumm mo mcowumfipmn m.~ wuswfim

 

 

--I- .... -- ....m: - .-..I .23.... ---I...II..-.I.I
I 4 .

.Ih

 

Ia

 

 

 

 

 

..- - - I.
I I I..- IIIIILIIIIIIIIII-‘ {III-I . I
. .
I
. . I
I
. I H

 

 

 

 

 

 

 

 

 

 

 

 

 

9
. In" .
I I I I .l I“ .

 

 

 

 

 

  

p ... .. .
o I . .
. -00. WI. I III, I «III: III-III .III. III IIIIIIIOOo
. . M!“- .
_ . * I.

 

on.

 

 

s. I.

 

 

. . - . _
. . . . . .
0'. II ' 'Ikuu 'III I I . I
I I r .I.. ..IIIIII.III.-IIII. .II‘I «III . II.
. . . . .
. . . . -
C
.III 0 III-I. lo. . IIIII
. I II II... II- . .IIII‘I: III
l ’i'...’ - l-..‘
.
.
II I I- .| '3 I ‘ III II . la.II.? ' O
IIIII. II. .oIIII-I . I

II. III- NH 0

 

63

deviations were sufficiently small so that these lines could be
given some weight in the fit.' This was advantageous since both

v4 and 2v4 had very few usable negative AK lines, and thus

these lines were very valuable in determining better values of

A

K
04 and D0 in the Simultaneous fit.

The results of a single-band fit of the 130 largely unperturbed
lines of v4 are given in Table 7.1. A fit of these lines was not

able to determine a statistically significant D3 (i.e. the 95%

~L

s.c.i. was larger than the determined DE), and thus this constant

was taken from the fit of the 2v4 band and was held constant in

‘2 scar-ii 5.qu
.- I

the v4 fit.
The constants resulting from the simultaneous fit of v4 and
2v4 are given in Table 7.2. The resultant A.O is seen to be less

precise than that obtained for CD31, but still appears to be an order

’of magnitude more precise than the AO value from zeta-sums. _The

zeta-sum A0 of CD301 as determined by Morino and Nakamura is quite

uncertain because the v2

this case than for the other CD3X molecules (20). This overlapping

band overlaps us to a larger extent in

affects the A0 determination in two ways:

(1) it limits the precision of AD by reducing the number
of data points in v5; therefore C1(5), C2(5) and C3(5)
are the major contributors to the variance of A0. By
use of SYHFIT, the resultant standard error in A0 was
determined to be 0.002 cm-1.

(2) The large number of RQK lines compared to the small

number of PQK lines lowers the accuracy of A0 by

increasing the effect of the systematic error resulting

64

Table 7.2

Molecular Constants Resulting from a Simultaneous

Fit of v and 2v of CD Cl (in cmfl)

a , 4 3

Constant '. Value 95% s.c.i.
00(04) ' 2283.455 ‘ 0.008
00(204) 4551.275 0.006
A0 . 2.5930 0.0006

2 - ‘ .
Aega . . 0.4532 0 0002
pg 23 x 10'6 2 x 10"6
a: 12.53 x 10'3 0.06 x 10'3
a: 114 x 10'6 5 x 10'6

Standard Deviation of Fit = 0.009 cm“1

A0 from g-Sum Approximation = 2.613 (20)

1!

“#flg‘?

 

65

from the assumption that the Q branch peaks all

correspond to the same J value.

In summary, a simultaneous analysis of v4 and 2v4 of CD3C1

has resulted in an accurate value of A0 which is statistically
different from and superior to that obtained by zeta-sum methods.
The simultaneous fit was useful in determining the location and
magnitude of a systematic perturbation in the low-frequency half of
the

04 band. The perturbation is seen to increase the magnitude

of the effective a

r ...-anamn‘ as???
\

Z in the perturbed region.

CHAPTER VIII

ANALYSIS OF v4 AND 2v4 OF CD3Br

Survey spectra of these two bands are shown in Figure 8.1.
Several irregular features occur in both 04 and 2v4 of CDaBr,
not all of which can be readily seen in the figure. The more
obvious abnormalities in the v4 band are the perturbed Q branch

on the low-frequency side (PQB) and the strong fine structure

‘1': ”11m... . ans-war
.

between RQ6 and RQ12. In 2x24, perturbations are obvious in
P .
Q12 and RQ7. The Q branches to the right of RQ7 are narrower
and closer together (which hints of a shift in the effective values
of an and A + 2A (,2). Another characteristic of 2v under
4 0 e 4 4

higher resolution is a splitting of almost all lines, with the
splittings differing in magnitude from one subband to another.

High resolution spectra were recorded under the experimental_
conditions given in Table 4.3. The measured spectra were calibrated

and averaged with program SHAFT, with calibrations fitting to 0.002
1 .

cm for v4 and to 0.003 cm- for 2v4.

Over 240 lines were assigned in v4 without undue difficulty.
The only problem encountered in the RR.“ lines (for 3 < K < 9)
was an overlapping of lines which results in the many strong
absorptions which may be seen on the rapid survey of Figure 8.1.
The previously mentioned perturbation in the KAK - -8 subband
made it impossible to assign any PP8(J) lines. The same pertur-
bation would also seem to be responsible for the smaller shifts

(less than 0.05 cmd) in the line positions of the adjacent
66

b7

 

 

 

 

 

 

 

 

ammoo mo q>N pom q) mo muuomam xm>unm H.w ouswwm
7.5 on: come on? 32.
v; tune
.. .... 3.3. 3.3:...) ._
at. .. . w. _ N
mo a... ..: .. .71.. y..-
.. .
cm on ._ . w.
n Aas
o co
m c nfl»
7:8 09$ 83 om-
. : . «A smog
:.. up A .
:... ;.. .... egg... ......
: .. .. . .. .. ...... .3... i. . .. . . . ....
. . . . . . . __ _ . i .. _. . a
. -. _. - ..
. . . . . . .. .. . -. . .60
~_ . _- .. w . . . .. .. .. a
om_ _ .. _ R. g . _ _ we
a m cm ox a a

68

subbands (KAK = -9 and -7).

When the Pp7 and P99 lines were given zero weights, the
constants resulting from a single-band fit of the 209 unperturbed
.lines are given in Table 8.1. The OBS-CALC values for the perturbed
subbands along with those of other lines are given in Appendix E.

Assuming that the splittings of lines due to the isotopes of
bromine (Br79 and Bral) would not be resolved, the microwave values
0’ D3, and Dgx

to natural abundance. These average values were used in the v4

of B for the two isotopes were averaged according

fit described above and are recorded in Table 8.1. We did, however,

notice the effects of 339 and, 831 for high values of J in

K

series of PPI, PP2 and P93 subbands. For J > 20 the lines are

broad and in some cases are split. The calculated line splittings
for these cases is approximately 0.04 cm-1, and therefore this effect
is barely resolved by the spectrometer. Because of this isotopic
broadening, no lines of J > 28 were included in the v4 fit. The
limited number of high J values reduces the precision of the a:
value determined by the fit.

Even before attempting to analyze the 2v4 band, the follow-

ing characteristics were noted:

(1) Host of the lines of the 2v4 band are split into two
components of nearly equal intensities.

(2) In the perpendicular component, the Q branch separations
on the left side of 0Q? are different from those on the
right.

(3) Because of the overlap of subbands in the parallel com-

ponent, our resolution is too low to determine if the

 

69

Table 8.1

Molecular Constants from a Single Band

 

Fit of 04 CD33r
Constant yglgg- 95% s.c.i.
00 - Aecz 2295.986 0.005
A0 - Act: 2.1289 0.0005
0% 10 x 10'6 2 x 10"6
«2 13.19 x 10‘3 0.07 x 10'3
a: 129 x 10"6 16 x 10"6
Standard Deviation of Fit = 0.009 cm“1
Average Microwave Values of Ground State Constants (37)
Constant 22123
30 0.256775
03 0.0000001965
03K 0.000002115
.Previoua Results (cm-1):
(A) Merino and Nakamura (20) (B) Wiggins, Shull, and Rank (38)
A0 - 2.589 00(204u) = 4541.05
vo(v4) ' 2296.3 vo(2v41)= 4579.9
62 - 0.013 a: - o2 - -0.012

-. _ i

70

ka and QRK lines are Split; consequently line

identifications are uncertain. The QQK lines are

distinctly Split for K.< 6.
The combination of these unusual features has prevented a satisfactory
analysis of 204. A description of the methodology used in trying
to analyze the band follows.

The analysis started with an emphasis upon individual subbands

of the parallel and perpendicular components. ISubband fits were made
inthe perpendicular component using the lower frequency component

of the double lines. values resulting from the more completely

B
“A

assigned subbands are shown in Figure 8.2 with the "error bars"

‘1. m :oW‘I'q

indicating standard errors. With the exception of the two subbands
close to the RQ7 perturbation (0Q5 and RQ6)’ the a: values
are concentrated in the region between (200 - 300) X 10"6 cm-l.

If lines from these supposedly compatible subbands are then put

into a single-band fit, the results (in cm-1) are:

90 +2Aegz = 4577.8 :1: .4

A0 + neg: = 3.5 1- .1
0:; = (201 i 120) x 10'6
a: = (20 i 10) x 10'3
0'2 =- (239 1 30) x 10’6

,‘The poorly determined constants from this fit are the result of a
.shift in. Q branch separations on different sides of the ‘07
perturbation. There appears to be no way to fit these lines (with
our molecular model) without identification and inclusion of the

Ieffects of the perturbation. In this case the perturbation seems

 

 

71

 

a...

smmmo mo mvcmnnsm A4V¢?N Eouw omcflEumqu mw3Hm> No 0>Huoomwm ~.w mugwflm
Amumum pmzofiv m
0H «H Na OH w o a N
I4. q . I II _ I . ooa

 

. CON

., com

 

I ooq.

A.IEuV

ea
c m

6>asoouam

OH x

72

to be general enough to make it difficult to treat.
Analysis of the parallel band has depended on the rather un-
certain assignments of QRK lines. Present assignments result in

the following a: determinations from the subbands indicated.

 

 

a: X 106 cm-1(9SZ.s.c.i.)
QR2 - 203 :t 10
QR3 - 235 i 14
QR6 - 181 j; 20
These a: values are not greatly different than those determined

from RRK subbands, but a single-band fit of all the parallel-
component lines results in a large standard deviation and very
poorly determined coefficients of K dependent terms. Similar
single-band fits were attempted using various combinations of
lines from the parallel and perpendicular components without much
success.

The above analyses of the perpendicular and parallel com-
ponents were repeated with the hypothesis that the lower frequency
components of the double lines correspond to Br81 (using its
associated microwave values). This lowers a: for each subband

6

;‘by approximately 20 x 10- cm-l, but does not help the basic

fitting problem with K-dependent terms.

The following conclusions can be drawn from the above attempts
to analyse 2V4:

(l) a: values determined for major portions of the band..

vary smoothly in areas away from centers of perturbations

 

 

 

73

(see Figure 8.2). Except for subbands very close to
strong perturbations, a: values obtained from dif-
ferent parts of the band are not greatly different,
but are considerably larger than those from the sub-

bands of of CD Br or those of any other CDBX

V4 3
molecule in this study.
(2) Much higher resolution is needed to make assignments

in the parallel component more certain.

(3) The perturbation (or perturbations) which affects the

 

band has a strong K dependence which makes a fit of I"

the 2v4 frequencies impossible with the usual fre-

quency expression.

As a consequence of the perturbed nature of 2v4, an A0

value cannot be obtained by a simultaneous fit. The results of the

zeta-sum work of Merino and Nakamura on CD Br (20), as quoted in

3
Table 8.1, include a value of A0 = 2.589 which is currently-the
only value available in the literature. The value of a: from our
analysis of v4 is believed to be an order of magnitude more
accurate than the values previously determined at lower resolution
(20, 38). Even though the values of a: and D: from our analysis

are somehwat lacking in precision, they do have some significance

since to our knowledge they have never been previously obtained.

CHAPTER IX

CONCLUSION

Table 9.1 is a comparative summary of the best available
;,va1ues for the molecular constants which may be determined from
V4 and 2v4 for the three molecules investigated. Except for l

the cases indicated by superstripts, they are the results of single

 

or double-band fits with program SYMFIT (see Chapters VI, VII, and 9 I
VIII). Uncertainties specified in the table correspond to 95%
simultaneous confidence intervals.

For CD I, all the constants were well determined from a

3
simultaneous fit of v4 and 2V4. In the case of C03Cl, the con-

;stants are somewhat less precise because of a perturbation affect-
ing the low frequency half of VA. A second perturbation in the
parallel component of CD3Cl 2v4 prevents an accurate measurement
of vo(u). The least well determined parameters are those of
CDaBr. The band origins for both the perpendicular and parallel
components of Zva could not be accurately determined because of
the large effect of K-dependent perturbations. Because 2v“ is
liighly perturbed, A0 of CDBBr is limited in accuracy by the nature
of the zeta-sum technique (see Chapter III).

A possible method of confirming the accuracy of the A0
values would be to perform a simultaneous analysis of other wt

and 2v: bands of a synrnetric top.' Thus A0 as obtained from v“

and 204 could be confirmed or disproved by a simltaneous analysis

74

75

 

Anny as as .ueumwwzv
Aouv auoaaxuz new ocuuoxu

Nuo< I 0) mo 03Ha> neon caucus use scuba

 

 

Amoewa xad cw cowumnusuuoo On our aIEU N.Qflv uusno uso Bonn ouuaewxouanda
6-0. x “mummy oIOH x Aeaflwmav o-o~ x Anflaaav N6
m-oH x Aso.oflo¢.-v «.03 x Aeo.qflma.nav nIoa x 16o.Qflmn.~Hv N8
0.03 x Amflomv oIOH x ANHoHV 6-0. x Amflmwv ma
Nooo.Qfleoas.o uos.o Nooo.ofl~mns.o mama
sooo.QHmmem.~ 6mmm.~ sooo.qflommm.~ o<
moo.qflmsa.osms emo.sams 63.6Hma Asa>uvo>
moo.9flsms.owms as.6ems oo¢.gfln-.amns “aspavo5
moo.QHo~m.ms- ems.so- woo.qwmms.mm~a Aspvo>
mmmw cameo dunno

“HIEUV moaauoao: unno sou nanosecoo uo assassm

H.m manna

76

of high resolution spectra of 06 and 2V6. Such an approach has
“recently become feasible with the advent of Fourier transform
spectrometers which can offer excellent resolution over wide spectral
ranges (e.g. 2% to 20p).

A considerable amount of theoretical work has recently been
done (33, 39, 40, 41) which may be applicable to the perturbations
observed and recorded in this work. The perturbations found on the
lower frequency sides of the 04 bands of each molecule appear to
have very systematic deviations. The question as to whether these
effects could be caused by the nearby fundamental v1 must be

thoroughly investigated. Now that shifts in energy levels for all

three v bands have been determined, such an investigation would

4
be feasible.
Finally it should be possible to use the results of this

work to determine certain of the anharmonic constants, and to im-

prove the values of the structural parameters of these molecules.

L...,_,|

 

REFEREN CBS

~10.

11.

12.

13.

14.
15.
16.
17.

18.

19.

LIST OF REFERENCES

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B. T. Darling and D. M. Dennison, Phys. Rev., 51, 128 (1940).
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W. Heisenberg, The Physical Principles of the Quantum Theory,
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G. Herzberg, Molecular Spectra and Molecular Structure 1;;
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T. l“ Barnett, thesis, Michigan State University, 1967.

77

 

20.
21.
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23.
24.
25.

26.
27.

28.
29.

30.
'31.
32.
’ 33.
34.

35.

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37.
38.

39k
440;
41.

78
Y. Morino and J. Nakamura, Bulletin of Chemical Society of
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E. W. Jones, R. J. L. Popplewell, and H. W. Thompson, Proc.
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C. Joffrin, N. Van Thanh, and P. Barchewitz, Journal de
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T. L. Barnett and T. H. Edwards, J. Mol. Spectry., 29) 347
(1966). ‘

'1‘. L. Barnett and T. H. Edwards, J. Mol. Spectry., _2__(_)_, 352
(1966). '

T. L. Barnett and T. H. Edwards, J. Mol. Spectry., 23, 302
(1966).

B. Teller, Handb. J2. Chem. Phys., 9 II, 43 (1934).

 

M. Johnson and D. M. Dennison, Phys. Rev., 48, 868 (1935).

D. R. J. Boyd and H. C. Longuet-Higgins, Proc. Roy. Soc.,
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H. C. Allen, Jr. and P. C. Cross, Molecular Vib-Rotors, John
Wiley and Sons, Inc., New York, 1963.

D. B. Keck, thesis, Michigan State University, 1967.

T. H. Edwards, J. Opt. Soc. America, 21, No. l, 98 (1961).
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W. E. Blass, J. Mol. Spectry., 24, 38 (1967). 2
J. W. Boyd, thesis, Michigan State University, 1962.

A. Ralston and H. S. Wilf (eds), Mathematical Methods for
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G. Herzberg, see Reference 18, p. 425.

A. K. Garrison, J. W. Simmons, and C. Alexander, J. of Chem.
Phys., 42, 412 (1966).

T. An‘Wiggins, B. R. Shull, and D. H. Rank, J. of Chem. Phys.,

2;, 1368 (1951).

D. di Lauro and I. M.‘Mills, J. Mol. Spectry., 31, 339 (1966).
R. L. billing and P. M. Parker, J. Mol. Spectry., 22, 178 (1967).

R. L. billing and P. M. Parker, J. Mol. Spectry., 22, 340 (1968).

APPENDICES

| I

COCO

0000

000

APPENDIX A

P R 0 O R A M S Y M F I T

PROGRAM SYMFIT (INPUT:OUTPUT)
COMMON /12/ INFOIoINFOZIINFCS.VUMCUNoaUMPotFINaEFOUToT
10L:IDENT(2)

COMMON /125/ IMPLIES USE IN valves. STEPFIT, AND
PHINlOUT.

COMMON /123/ NK(JO).NDELMAXaXDEVMAX,CCNST(JO)4ILEVtL
COMMON /A/ NAME<30).INL(30).IEAMO

COMMON /100/ JJ<650)aKK(850):uDFL<850),KOEL(850).NUDEL
1(860)

DIMENSION CON<18,850). FOBS<dSD>a FCALC(650). wT(850),
1 NUSECBSO)

DIMtNSION IH<10)

NAME CORRESPONDts T0 NAMES CF vARIARLES IN A SINGLt
BAND FLT, 1NL 15 THE SAME FOR a DOURLtBAND r1?

DATA (NAME=2HBOp6HDOJp4HDOJK:54NOZRO.EHAZRO-AEZ.
16H-DZROK,6H-ALFAA.6H-ALFAB,4HETLJ.5HBETAJ;6H8ETAJK.
ZbHBtTAK,5HHZROJ:6HHZROJK,6HHZRJKJ.5HHZROK.7HNUZR0PL)

DATA (INL=2HBO.3HDOJ;4HDOJK;7HVUZONU4o8HNUZOZNU o
14HAZRO,7HAEZETA+.
16H~DZR0K.8H-ALPHA4A.BH-ALPHA4B,SHETA4K,6HBETA4K,
25HHZR0K.4HETAJ.5HBETAJ.6HBETAJ<,7HNUZROPL)

NUMCON=17

NCONP1=NUMCON+1

OPTION LABEL IBAND IS LABELED COMMON

READ 180: IBAND

11(IBAND.NE,8HO BRANCH,AND.IBAND.NE.8PCOHIOL15)GO T0 5
NUMCON=5

NCONP1=18

INL(1)=4HC0N1

NAM&(1)=INL(1)

INL(2)=4HC0N2

NAME(2)=INL(2)

INL(3)=4HCON3

NAME(3)3INL(3)

79

 

OOOO

OOOO

OOOOO

OOOCOO

10
lb
20

25
30

35

4U

45
50

55
60

65

80

INLC4)=4HCUN4
NAME(4)=1NL(4)
INL(5)=4HCON5
NAME(b)=INL(5)

JUMP = 1 ONLY NHtN NEW CONSTANTS (TPIAL) ARE
BtING READ IN

 

JUMP=0

RtAD 200, IH

STATEMENTS 10. 15. AND 20 ARE THE MAIN DIVIDING

PTS. FOR THE DRIVER LT
IF (IH(10).EQ.8HLAST FIT) GO TO 175 !
GO TO 15 5
IF (IH(10>.EO.8HCONSTANT) GO T3 25 g _
GO TO 20 i 1
IF (IH(10).EO.BHNtw DATA) GO T3 65

GO TO 175

JUMP=1

READ 200: 1H

PRINT 200: (IH(I):I=109)

1F (IH(10).EQ.8H:ND HEAD) GC 73 55
GO TO 30

PRINT 205

DO 60 J1=1aNUMC0N

1F (IH(1U),EQ.&HCNDCONST) G0 73 45
GO TO 40

READ 215: CONST(J1)oIH(10)

GO TO 50

CUNST‘J173090

1F (IBAND.EQ,8HSINGLEBU) GO TC 59

PRINTS READ IN CONSTS AND THEIR LABFLS FOR SINGLE
0R DOUBLE BAND FITS. HILL SET ALL consTS,
ZERO AFTER AN ENUCONST IS FOUND IN COLS. 73s80

PRINT 220: INLCJ171C0NST(J1)
GO TO 60

PRINT 220: NANE(J1)aCONST(Ji)
CONTINUE

READ 200: 1H

60 TO 10

M=1

HERE WE READ IN CMANGE IN QUANTUM MUPBEHS,
GROUND STATE QUANTUM NUNBERSA OBSERVED
FREQ. AND RELATIVE WEIGHT FOR EACH SPECTRAL LINE.

’HILL KEEP READING UNTIL AN F 13 FOUND IN COLUMN 10

OOOO

COO

81

70 READ 185. NDDEL(M>.KDEL¢M).JDE;<M).KK<M>.JJ(M).FOBS<M)

laWTIM)

IF (NUDEL(M),E0.0) NUDEL(M)=1

1F (KUELIM),EO.1HF) GO To 160

INDATA=M

1KDEL=KDEL<M)-1RO

IJDEL=JDEL(M)-1RO

DELTA1=KK(M)+IKDEL

DELTA2=KK(M)

DELTAJ=JJ(M)*1+IJDEL

DELTA4=JJ(M)¢1JUEL

DELTA5=JJ(M)*1

DELTA6=JJ(M)

1F<IBAND.NE.8HD URANCH.AND.TBAVD.NE.8FCORIOLIS)GOTUIOO
1F (IBAND.EO,8HCOHIOLIS) GO TC 75

THIS SECTION PROVIDES THE OPTION 0F FITTING
Q BRANCHES TO THE THREE VARIAfigES CONl, CONP. AND CONS.

 

CONI1aMI=100
CONIZaMI=KKIM)*IKDEL
CON(3.M)=KK(M)**2

GO T0 140

THIS SECTION PROVIDES A FIT OF THE DEVIATIONS SOUAHED

75 1F (KK(M)-8) 80:85.90
80 CON<10M)=FOBS(M)
C0N(21H180.0
CON(SoM)=D.0
GO TO 95
85 CONIZoMT=FOBS(M)
CONI11M73090
CON‘30M7=090
GO TO 95
90 CON(3;M)=FOBS(M)
CON(1;M)=D,0
CONIZIM7=090
95 CON(4aM)=JJ(M)'(JJ(MI‘lIiFOBS(M)
CON(5oM)=JJ(M)*(JJ(M)*1)*KK(M)«(KK(M)'1)
FOBS(M)=FOBS(M)**2
GO TO 140
100 IF (NUDEL(M)-1) 105:1054110
105 LDEL=IKDEL
GO TO 115
110 LDEL=*2*IKOEL
_ 115 CONIIpM)=DELTA4*OELTA5-DELTA6ADELTASqLELTAltt2+DELTA2*
1*2
CON(2,M)=-DELTA4**2*DELTA3tt2¢DELTAéttztDELTA5**2
CON(3;M)=~DELTA1**2*DELTA4ADELTA6*DELTA2**2*UELTA5*DEL
1TA6

OO

O‘ O

OOOO

125

130

135

82

I? (IBANU.EO.8HDOUBLEBD) GO TC 120

CONI4aM)=1.0

CONISoM)=DELTA1*u2-DELTA2tt2
CONI6.M)=DELTA1wt4-DELTA2¢AA
CONI7.M)=NUDEL(M)*DELTAit02
CONI8aM)=NUDEL(M)*(DELTA4iDELTA3-DELTAlti2I
CONI9aM)=LDEL*DELTA1*DELTA4tDELTA3
CONIlO.M)=NUDEL(M’iDELTA4**2*CELTA3**2
CON(11,M)=NUDEL(M)*DELTAlttZtEELTAAmDELTAS
CONI12.M)=NUOEL(MI*DELT41*O4
CONI15:MI=DELTA4**3*DELTA3**3-DELTA6**3*DELTA5**5
CONIl“:MI=UELTA1**2*DELTA4t¢2tDELTA3"290ELTAZ**2*UELT

1A6~DELTAS

CONI15,M)=DELTA1**4*DELTA4wEELTASFDELTA2ii4tDELTA6*DEL

1IA5

CONI16,M)=DELTA1**6'DELTA2**6
GO TO 155

THE SECOND CON MATRIX IS FOR DOUBLE BAND FITS.

IF (NUDEL(M),NE.1) GO TO 125
CONI4aMI=1.0

PROVIDES FOR TWO PERPENUICULAP BAND CENTERS

CON(5.M)=0.0

GO TO 130

CUN(5aM)=1,D

CUNI4’M)=090

CUNIboMI=DELTA1**2'DELTAZ**2
CON(7.M)=LDFL*DELTA1*(—2)
CONT8;M)=DELTA1tw4-DELTA2**4
CON(9oM)=NUDEL(M)'DELTA1**2
CONI10,M)=NUUEL<M)*(DELTA4*EELTA6vDFLTA1**2)
CON(11.M)=LDELtDtLTA1*t3
CUN(12.M)=NUDEL(M)tDELTA1*w4
c0N<13,M)=DELTA1**6-DELTA2*o6
CONI14,M)=LDELtUELTA1*UtLTA4*DELTAJ
CONI15,M):NUDEL(MItDELTA4fit2ttéLTA3wt2
CONI16,M)=NUDEL(MI*DELTAivtzrcELTAAADELTAJ

PROVIDES r09 PARALLEL BAND CENTER IF KDEL = 0
LINES ARE READ IN

CON(17'M)=1'0
IF (IKDEL.NE.D) CON(17.H)=0.0
IF (IKDEL.E0,0) CUN<5.M)=0,0

"GO T0 140

CONI17IMI=190
IF (IKDELQEQQO) CONI4aMI=0.0
1F (IKDEL.NE,O) CON<17.M)=0.0

 

OOOOOOO

OOOO

140

145
150
is:

160

165

170

175

180,

18b
390
195
200
205
210
21:
220

83

FCALCIMI=0,0
IF (JUMP) 145.155.145

HERE WE CALCULATE FREQS. FROM THE TRIAL CONSTS.
WHICH HAVE BEEN READ IN

DO 150 N=1pNuMCON
FCALCIMI=FCALC(M)*CDNSTINIOCON(N,M)
CONTINuE

M=M¢1

GO T0 70

HERE WE READ IN INSTRUCTIONS FOR THE FORTHCOMING

FIT. INFOI INDICATES DESIRE RAN SUMS AND CROSS PRODUCTS:
INF02*CORRELATION COEFFIENTS, INFOS THE DIAGONAL
ELEMENTS. SEE STEPFIT wRITEUP FOR REST

ILEVEL . 1 IMPLIES UPPER STATF ENERGY LEVELS ARE

DESIRED

READ 190. INF01:INFOZIINF03,NCELMAX,XCEVMAX,TOL,EFIN,E

IFDUTOILEVEL

TELLS RHIOR VARIABLES ARE TC 8; USED. USUALLY
5 vARIABLES FOR SINGLE BAND SEOONO ORDER F11,
7 FOR DOUBLE BAND FIT. FIRST THREE ARE
MICRORAVE, THEREFORE ARE NOT VARIED.

READ 195. INKIIIII=1II7IIIHIIO>

WILL TAKE NEW SET OF FREQS IF A (NEw DATA) CARD IS
SEEN. THEREFORE USABLE FOR SLSBAND FITTING

IF (IH(10)ONE08H ) GO TO 10

READ 2001 I“.

PRINT 2000 (IHIM90M3119I

IFLIIHI10IINELDHEND HEAD) GO T3 170

CALL STEPFIT (CONOFDBSoFCALCaNJSEpNTgkCONP1,INDATA)

90 To 165

CONTINUE
PRINT 210

FORMAT (72XIA8)

FORMAT (4Xo1104xoRloR10IZleoIZIJXIFISI4I7XIF402)
FORMAT I4I514F10910X;I3I

FORMAT I1711055XIA8)

FORMAT (IOABI

FORMAT (///)

FORMAT I 1H5)

FORMAT (FZOJSZXOABI

FORMAT IA200F3001U)

END

 

COCO

10

lb

20
25
60

35

4U

84

S U B R O U T I N E S T E P F I T

SUBROUTINE STEPFIT (DATA,FOES,FCALC.NLSE.NT.NCONP1.IND
IATA)

COMMON /12/ INFOIIINFOZIINFOS,VOMCON,.OMP,EFINFEFOUT.T
10LOIDENT(2)

COMMON /23/ NOOATA.NOVMI,AVERLT,STDY,NOSTEP,N.RTN,FREO
1PHD.YPREU.OEV.XAZHO.XOZHO

COMMON IA/ NAMEISOIIINLISOIFIPAND

COMMON /12$/ NK(SO).NDELMAX.XCEVMAx.cCNST(30IaILEVEL
DIMENSION N1(30); VECTOR(31.3III INDEXI30I. IDEX‘SU).
ISIDMAIEDIIC
10tNI30). SIGMCO<60Ia NOTINISOII XCONSTISOI

DIMENSION DATAINOONplaINDATA), FOBSIINDAIA), FCALCIIND
1ATAIINTIIND
1ATA), NUSEIINDATAI .SVECTOR(31ISIIISSIGMCOISDIFSCOEN(3
20)

DIMENSION XNENCONIJDI

TYPE DOUBLE VECTOR,SIOMA,cOFN.SIGrcD.SIGY.DEFRIVAR
II (IDENT(1)I SIIDFS

IOENTI1I=8HINPUT DA

IDENTIZI=2MTA

CONTINUE

IF(EFOUT.E0.0.DIEFOUT=1.0E-8

IF (EFIN.E0.0.DI EFIN=EFOUT=1.0E-R

IF (TOLqE0.0!D) TOL=0.001

NOVAR=1

DO 30 IzlaNUMCON

HEDEFINES NAME AND INI

IF (NK(I)) 15:30:15

N1INOVAR)=NAME(I)

IF (IBANOgEO.8HDOUBLEBDI N1INOVARI=INL(II
IF (JUMP) 20.25120

XCONSTINOVARI=CONSTIII

NOVARzNOVAR¢1

CONTINUE

NODATA=O

DO 45 N=1:INDATA

IF (HT(N)) 40:35:40

NUSE IN) IS AN INDEx OF ALL NON-ZERO wT, LINES
NODATA = TOTAL NUMBER OF NONvZERo LINES

NUSEINI=0
GO TO 45
NUSE(N)=1

E13

 

1 . III.| 4 l1 5 I‘ll-.IIIIIIIITIII‘III III. '
Ill‘ll‘l. III I4 [I‘ll-II

 

 

.JI [JON 1-1 ‘11:}. . . H

 

CO'DC

45

5O

55

60

65
7O
75
80

85

90

95

100

104

85

NODATAzNODATA¢1
CONTINUE
NDEL=O
FLEVEL=0.0
VAR=FLEVEL
NOMAX=VAR
NOMIN=NOMAX
NOENT=NOMIN
K=NOENT
NOIN=K
LOOP=U
NOVMI=NOVAH-1
NOVPL=NOVAR*1
DU 55 I=1DNOVPL
DO 55 J=1,NOVPL
VtCT0H(IIJ)=000
IF (NOEL) 80.60.50
SUMWHT=OOO
IDEXINOVARISNCONPl
DO 75 N=111NDATA
NUM=0 7 .
U0 70 I=1INUMCON
IF (NK(I)) 65.70.65
NUM=NUM¢1
IDEX(NUM)=1
‘ I N E
OgTIIINCONP1FN)= FOBS<NI~ FCALCIN)
SUMNHT=SUMNHT*WT(NI
AVENHT=SUMNHTINODATA
U0 95 N=1oINDATA -
IF (NUSEINI) 85:95:85
WHT=NTINIIAVEN3T

= OVA _ .
83CTORIITNOVPLI=VECTOR(I.N0VPL)+DATA(IDEX‘IIIN)*NHT
U0 9O J=IINOVAR

Q A
AT THIS POINT. VECTOR (IaJ) I.
GENERAL VARIABLE I INDEPENDENT OR DEPENDENTI

VECTORIIDJI=VECTOHII;J)*DATA(IDEXII).h)*DATAIIDEX(J).N

1)*NHT

VECTORINOVPL.NOVPLI=VECTOR(NOVDL.NOVPL)*WHT
CONTINuE _

IF (INF01I 100.130.100

PRINT 49o

NOMAx=NOVMI

IF INOVMI.GT,7I NOMAX:7’

R NT 500 <I.I=1.NOM x
:vECTORINOVAR.NOVPLI=VECTORINCDAR.NOVEL)

D0 104 I=1.NOMAx
SVECTORII.NOVPL)=VECTOR(I.NCVR;)

 

86

PRINT 505.5VECTOHINOVARINOVPL)3ISVECTCR(I.NOVPL),I=1.N
10MAX)
105 IF (NOVM1.EO,NOMAXI 60 To 110
MOMAx=NDMAx+1
NOMAx=MOMAx+7
IF (NOMAX.GT,NOVMI) NOMAx=NCVN1
PRINT 510. II.I=MOMAx.NOMAXI
DU 109 I=MOMAX,NOMAX
109 SVECTORII:NOVPL)=VECTORIITNOVP;)
PRINT 505. ISVECTORII.NOVPL).TERORAx,NoMAx>
GO TO 105
110 CONTINUE
NOMIN=1
NOMAx=NOVMI
NGO=5
115 II (NUvMI.GT,NDOI NOMAx=NGO
PRINT 5201 (IoIgNOMINDNOMAX)
DO 120 J=NOMIN,NOVMI
JJJ=J
IF (JJJ.GT.NOMAXI JJJ=NOMAX
DO 118 I=NOHIN,JJJ
118 SVECTORII.JI=VECTOR(ITJI
DO 119 I=N0MINFN0MAX
119 SVECTOR(I.NOVAR)=VECT0R(IINOVA?)
120 PRINT 525. JIISVECTORIITJ).I=NDMINFJJOI
PRINT 5301 (SVECTORII'NUVARIDIONUMIN,ROMAX)
IF (NOMAx.EO.NOVMII GO TO 125
NOMIN=NOMAX¢1
NGO=NOO¢5
NOMAx=NOVM1
GO TO 115
125 CONTINuE
SVECTOR(NOVAR,NOVAR)=VECTORIVCvARTNCVAR)
PRINT 535.SVECT0RINOVAR.NOVART
130 NOSTEP=~1
ASSIGN 310 T0 NUMBER
DEFR=VECTORINOVPLTNDVPLI-l.0
DO 150 I=1IN0VAR
1F IvEcToR(1.1)) 135,140,145
135 PRINT 550. I
_ GO TO 485
140 PRINT 585. I
SIGMAIII=1.D
GO TO 150
145 SIGMA(I)=DSORT(VECTORIIIII)
150 VECTORIIIII=1.0
LOO 155 I=1aNOVMI
IP1=I*1
DO 155 J=IP1,NOVAR
VECTORIIIJI=VECT0HIIIJIIISIGMAIIItSIDPAIJII
155 VECTORIJIII=VECTORIIIJI

 

160

165

168
170

109

175

180

185

190

195

200

205
210

215

87

IF IINFOZ) 160.175.160
NOMIN=1

NOMAx=NDvM1

NGO=15

NOMINP=2

1F (NOVMI.DT,NDDI NOMAx=NGO
PRINT 540. (IoI=N0MINaNOMAx)
DO 170 I=NOMINP.NOVM1
III=I~1

IF (III.GT.NDMAXI III=NOMAx
DO 168 4:1,111 f
SVECT0R(IDJI=VECTOR(IOJ)

PRINT 545. IITSVECTOHIITJ).D=1.III) L.I
DO 169 I=NOMIN,NOMAX :'
SVECTORII.NOVARI=VECTORII.NOVIRT E

PRINT 550. (SVECTORIITNOVARI.[ENOM1N,N0MAXT
IF (NOMAX.EQ,NOVMI) GO To 175 3 1
NOMIN=NOMAX+1 ' a

 

NOMINP=NOMIN*1

NUD=NOO+15

NOMAx=NOVMI

GO TO 165

NOSTEPzNOSTEP+1

IF (VECTOR(NOVAHINOVAR)) 180a150.185
NSTPMlzNOSTEP-l

PRINT 600. NSTPMl

GO TO 395
SIGY=SIGMAINOVAR)*DSQRT(VECTOR(NOVAP,AOVAR)/DEFR)
DEFR=DEFR-1.o

IF (DtFR) 19011900195

PRINT 605. NOSTEP

GO TO 395

NOIN=0

VMAX=NOIN

VMIN=VMAX

DO 245 1:1,NOVMI

IF (VECTORIIDIII 200.245.205

PRINT 6100 IDNOSTEP

GO TO 395

IF (VECTORIIIII-TOL) 245.210.210
VAR=VECTORIIoNOVAR)*VECTORINOVIR.IIIVECTORIITI)
IF (VAR) 215.245.265

NOIN=NOIN+1

INDEXINOINI=I
COENINOINT=VECTOHIIaNOVAR)*SIGWA(NOVAR)/SIGMAII)
SIDMCOINOIN)=ISIuY/SIGMA(1)).csORTIvECTORII,II)
IF (VMIN) 230.225a220

PRINT 590

GO TO 485

VM1N=VAR

NOMIN=I

250
235
240
245
250
255
260
265
270

275
280

285

290
295

300
7 so:
310

“515

620

525
330

635
640

545

350

GO TO 245

88

IF IVAR-VMIN) 245.245.225
IF (VAR-VMAXI 245.245.240

VMAX=VAR
NOMAX=I
CONTINUE

IF (NOIN) 250,2550260

PRINT 595
GO TO 485
STDY=SIGY
GO TO 320
IF (INFOS)
IF (NOENT)
PRINT 5700
GO TO 280
PRINT 575:
IF

PRINT 555a

ILOOR.NE.0T FLEVEL=FL
SSIGY=SIGY

?65p310o265
27002700275
NOSTEPJK

NOSTEPoK

 

KgFLEVELaSSIGY

DO 285 J=1ONOIN

N=INDEXIJI

SCOENIJISCOENIJ)
SSIGHCOIJIESIGMCOIJ)

PRINT 560:
IF
IF
PRINT 495

N.N1(N)aSCOENIJIISSIGMCOIJI

(JUMP) 290.305n290
(LOOP) 29503050295

DO 300 J= 1. NOIN
7 N=INDEXIJI
XNENCON(N)=COEN(JI¢XCONSTINI

SSIGMCO(JI=
PRINT 560:

GO TO NUMBER,

FL=FLEVEL

SIGMCO‘J)
N N1(N)p XNENCON‘N), SSIGMCOIJ)
(310. 400)

FLEVELEVMIN'DEFR/VEcTORINOVAR,NOVAR)
IF (EFOUTOFLEVEL) 320;320.315

K‘NOHIN

NOENTso

GO TO 335

FLEVEL=VMAXPDEFHIIVECTOR(N0VAR,NOVAPIFVMAX)

If (EFIN-FLEVEL)
590:3900330

IF (EFIN)
K=NOMAX

NOENT=K

IF (K) 340
PRINT 615:
GO TO 485
OD
IF
DO
IF (J'K)

(I'K)

650.325.390

340.545
NOSTEP

365 I=1ONOVAR
350;365,550
360 J=1aNOVAR
35503600555

 

555
660
$65

$70
675

680
$85

$90

395

400

401

405

410
415

420

425

430

89

VECTOHIIpJI=VECTORIIDJ)'VECTOR(IQK)*VtCTOR(KOJI/VECTOR

1(KDK)

CONTINUE

CONTINUE

DO 375 1:1,NOVAR

IF (I’K) 37013751570
VECTOR(I,K)=aVECIOR(InKI/VECTCRIKIK)
CONTINUE

DO 385 J=1pNOVAR

IF IJ'K) 380.385.580
VECTOR‘KIJ)=VECTUH(KQJ)/VECTOR(K'K)
CDNTINuE

VECTORIKIKI=1oO/VECTOR(K,K)

GO TO 175

PRINT 5651 IDENTI1)OIDEKTIZIIKDDATAJNCVMIINDELMAXIXDEV

1MAXDAVENHTDSTDYINOSTEP

CONTINUE

ASSIGN 400 TO NUMBER

LO0P=1

GO TO 265

CONTINuE

DU 401 L=1.NOVMI
SVECTURILILI=VECTORIL0LI

IF (INF03.NE,0) PRINT 6200 (L:SVtCTOR(LaLIaL‘1aNOVMI)
IF (IBAND.EO,8HCOHIOLISI GO TO 410
IF (ILEVELqNE.OI GO TO 405

CALL pRINT2

GO TO 415

CALL PRINT4 (DATA:FOBS,FCALC,NT.NUSE,DCONP1,INDATA)
GO TO 415

CALL PRINT6

XIR=OOO

SWT=XIR

DEVMAX=SHT

VFIT=DEVMAX

NOLINE=0

IF (IBAND.EO,8HDOU8LEBOI GO TO 420
XAZRO=CONSTISI

XOZRO=~XNENCON<JI

GO TO 425

XAZRO=XNEWCON(3)

XDZRO=5XNEWCONI5I

DO 470 N=1,INDATA
HTN=NUSE(N)*WT(N)

NHTBWTN/AVEWHT

YPRED=ODO

DO 430 I=1INOIN
LASSIE=IDEXIINDEXIIII
YPRED=YPRED*COENII)*OATA(LASSIEIN)
DEV=FOBS(N)'FCALCINIPYPRED

IF (10,.WT(N)) 4502450o435

90

435 VFIT=VFIT+HTN*DEV*'2
XIR=XIR+1.D
SNT=SNT¢NTINI
NOLINE=NOLINE+1
1F (NOLINE.LE.50) DO TO 450
NOLINE=O
IF (IBAND.EO,8ROUHIOLISI GO TO 445
IF (ILEVEL.NE.0I GO TO “40
CALL PRINTZ (DATAIFDBS.FCALC.NT.NUSE.NCONP1.INDATAI
GO TO 450
440 CALL PRINT4 IDATA.FODS.FCALC.RT.NOSE.NCONP1,INDATAI
GO TO 450
445 CALL PRINTO
450 FREOPRD=FCALC(N)+YPR&D
WHTszTtAVENHT
IF (ILEVEL.NE.0) GO TO 455
CALL PRINT6 IDATA.FOES.FOALO.NT.NDSF.NOONR1,INDATAT
GO TO 460
455 CALL PRINT5 (DATAIFOBSIFCALC.DT.NUSE.DCONP1.INDATA)
460 ADEV:ABS(DEV)*SORT(NHT)*NUSE(N3
IF (DEVMAX-ADEV) 465,465,470
465 NMAX=N
DEVMAX=ADEV
47D CONTINuE
VFIT=VFITRXIR/((XIRwNDINIASDT)
STDFIT=SORTIVFITI
PRINT 515. VFITISTDFIT
IF (NDELMAx-NDELI 485.485.475
475 IF IDEVMAx-XDEVMAXI 485.485.483
480 NUSEINMAXI=O
NDEL=NDELF1
NODATAaNODATA-l
SUMMHT=SUMRHT-NTINMAXI
PRINT 625. NMAx
GO TO 50
485 RETURN
_-49u FORMAT I 11HISUM 0F VARI/I
495 FORMAT I *ZFINAL CONSTANTS AFTER CORRECTIONS WERE *
1tADDEDv/I _u i _
500 FORMAT I 9H YI7I17O/I
‘505 FORMAT (X1P7E17.6oE16.6p//)
510 FORMAT (I10.6117./)
515 FORMAT I 29HOSTAT FROM LINES NATO LT 10.0a/. *UVARg =*
1.F1D.6. * STD. DEV Iw.F7.4/, 1R7)
520 FORMAT ( 15HRAN SSCP MATRIx./5126I
525 FORMAT (x12.1P5E26.10I
-530 FORMAT I_ OH Y.1P5E26.10I
:35 FORMAT I OH Y vS Y.F15,4)
540 FORMAT_( 21H9PARTIAL CORR. COEFF,.//16182
545 FORMAT (13.16F8.4I
550 FORMAT I OH Yo16F8.4)

 

91

55: FORMAT I 16H F LEVEL OF x-111.t10.2.9x. *STD DEV OF*
1. (O-P)*.F7.4
1//10x. 41HVARIABLE COEFFICIFNT STD ERROR./>

560 FORMAT(111.1X.A8.2F17.12)

565 FORMAT I 22H1LEAST SQUARES FIT PF ,2Aax. 5H FIT .14,
116H DATA POINTS T0 .12.10H VARIABLES./. * DELFTES UP .
2*TO t.12.23H POINTS IF IO~PI 15 GT .Fb,3/. . wHT NURMt
31x.F6.2/.17R SID DEV OF IO-CI,F8.4/, 11H COMPLETED .12
4: 6H STEPS,

57o FORMAT I BHOSTEP NO.I$/, 15H VAR, REMOVED.!3>

57b FORMAT BHOSTEP NOpISI, 15H VAR. ENTEREDAIS)
580 FORMAT 19H ERROR RESID SQ VARAISI 7H 13 NEG)
585 FORMAT 4H0VAR.151 9H IS CCVST)

I

I

I

:90 FORMAT I inOERRUR: VMIN P08)

:9: FORMAT I 15ROERROR NOIN NEG)

600 FORMAT I 18HOY SOOARE NEG STEPglb)

605 FORMAT I 22ROZERO DEG FREEDOM STEP.13I

610 FORMAT I 9HSOUARE x-.12. 14R NEGAYIVE STEP.IS>

615 FORMAT I 8HK=0 STEP,13I

620 FORMAT I 16H0 DIAG ELEMENTs./; 16H VAR NO VALUta/l
1IIA.E14.4II

o2: FORMATI 8H1LINE MO.IA.23R EEIIO DELETED FROM FIT )
END

 

92

S U B H O U T I N E P R I N T 0 U

SUdROUTINE PRINTUU (DATAIFORS.RCALC,NT,NUSE,NC0NP11IND
1ATA)

COMMON x123/ NKIAOI.NDELMAx.xDEVMAx.CONSTIsoI.ILEVEL

COMMON /23/ NODATA.NOVMI.AVERRT.STOY.AOSTEP.NIMTN.IREG
lpRDIYPREDIDEVQXAAHDOXDZRO

COMMON /100/ JJ(O50),KK(850),;QEL(850).KUtLI850).NUDEL
1I850)

DIMENSION DATA(NCUNPIIINDATA): FOBSIIADATAI. FCALCIIND
1ATA). NTIINDATA). NUSEIINDATAI

ENTRY PRINT2

PRINT 20

RETURN

ENTRY PRINT3

PRINT 25; NIKDELIN)IJDEL(N).KKINIIJJ(N)aNTN.FObSIN).FC
1ALCIN).FREOPRD.DATAINCONP1.AI.vaED.DEv

RETURN

ENTRY PRINT4

PRINT 5

RETURN

ENTRY PRINTS

XGRD=XAZRO*KK(N)**2+CONST(1)¢(JJ(N)0(JJ(N)*1)*KKIN)?*2
1I-CONSTI2)*J
2J<N)**2*(JJ(N)¢1)'*2-CONST(3)v<K(N)¢t2tJJIN)*(JJ(N>*1’
S-XOZROwKKINth4

XUPPER=XGRD+FREOPRD

PRINT 10a NOKDEL‘N)IJDEL(N>DKKfim’IJJ‘k,DWTNOFOBS(N"FC
1ALCIN),FREOP

1HDADATAINCONP1.N):YPREDIDEVIXGRDFXUPPER

RETURNV

ENTRY PRINT6

PRINT 15

RtTURN
5 FORMAT (*1 NO, NT OBS FREO CALC FREDA
1* PRED FREQ OUS-CALC FRED-SALC CBS-PREO GRD ENi
2*ERGY UP ENERGY*) _“

10 FORMAT (15.x.2R1;12:1HooI2.3X.=6.2.RF11.4)

15 FORMAT ( 33H1 N0, K J UP NT (O-C)05Ht*2 o
1* ZEROS PRE*
2*0(0'C)*o5H**2 1* IGNORE IGNORE FIT DEVi)
20 FORMAT (*1 NO. RT 083 FREQ CAL! FREQ *
1*PRED FREQ OBS-CALC FRED-SALE CBS-PRFD')

25 FORMAT (ISJXOZRllIzalHl.12'3x';6Q2O6F11Q4)
END

WW
,
‘v

T Y P I C A L

SINGLEBD '
CONSTANT -
THIS IS THE INITIAL

1

END HEAD -

0.660127

0.000000659
0.000006699

4000.00
2.594

tNOCONST -
Ntw DATA

CDOCZNu4
CDOCZNU4
cosczNUA
CD602NU4
CD6C2NU4
CDACZNUA
CDJCZNU4
CDSCZNU4
CDJCZNU4
CD3C2NU4
CD3C2NU4
coscaNUA
CD6C2NU4
CDSCZNU4
CDsczNUA
CDACZNUA
cosczNUA
CDJCZNU4
CDJCZNU4
CosczNUA
coaczNUA
CD6C2NU4

CDJCZNU4
'CDACZNUA
CDJCZNU4
CD5C2NU4
CDJCZNU4
CDSCZNU4
CD6C2NU4
cusczNuq
CDJCZNU4
CDAczNUA
CDSCZNU4
CDJCZNU4

P0
P0
P0
PO
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR

IN

IN

35 TO 37

IN

IN

COLUMNS
COLUMNS
FIT FOR

COLUMNS

COLUMNS
COLUMNS

93

D A T A

450308080
451094474
451619591
4536.3361
459306840
4594.3735
4595.1176
4595.825?
4596.5446
4597.9716
4598.6701
459903722
4600.0848
4600.7945
460194998
460201981
460219030
460305916
460432975
4605.0018
4596,7789
4598.2018
459899217
4599.6380
460093502
460190561
4601;7755
460294878
460398980
460406061
460595074
460600332
460607386
460794502

73-80
73-80 ‘
NANCYS CD3LL

73-80

73-80
73980

0.02
0.02
0.02
0.02
0.06
0.02
0.02
0.02
0.02
0.02
0.02
0.06
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.?5
0.06
0.06
0.06
0.06
0.02
0.06
0.06
0.06
0.06
0.06
0.02
0.02
0.06

CD3C2NU4
CDdCZNU4
CD3CZNU4
CDJCZNU4
CDdCZNU4
CD3CZNU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD302NU4
CD302NU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CDJCZNU4
CD3C2NU4
CD3C2NU4
CDJCZNU4
CDSCZNU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD302NU4
CDJCZNU4
C03C2NU4
CDSCZNU4
CD3C2NU4
CD3C2NU4
CDJCZNU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD3C2NU4
CD3CZNU4
CD3C2NU4
CDJCZNU4
CD3C2NU4
CDéCZNU4
CD3CZNU4
CD3C2NU4
CD3C2NU4

RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR

6.22
6.24
6.25
6.26
6.27
6.28
6.29
6.30
6.32
6.33
6.34
7. 8
7. 9
7.10
7.11
7.12
7.13
7.14
7.16
7.17
7.18
7.19
7.20
7.21
7.22
7.24
7.25
7.26
7.27
7.28
7.29
7.30
7.31
7.32
7.33
7.34
7.35
7.36
7.37
7.38
7.39
8. 8
8. 9
8.10
3.11
8.12
6.13
8.14
8.16
6.17
8.18

94

4606.1430
4609.5419
4610.2426
461009551
4611.6539
4612.3554
4613.0409
4613.7456
“615.1388
4615.6386
4616.5065
4604.1030
4604.8143
4605.5258
“606.2395
“606.9482
4607.6561
460603772
4609.7593
461094974
461192196
4611.9236
4612.6311
4613.3320
“614.0381
4615.4505
4616.1430
4616.8358
“617.5633
4618.2382
4616.9471
4619.6269
“620.3413
462190296
4621.7314
4622.4122
4623.1026
4623.7690
4625.1693

4625.8468_

4609.8933
461006864
4611.3611
4612.0740
4612.7757
“613.4896
4614.1926

74615.6419

4616.3578
4617.0569

0.02
0.06
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.06
0.06
0.06
0.06
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.06
0.02
0.02
0.02
0.06
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.25
0.02
0.06
0.06
0.06
0.06
0.06
0.06
0.02
0.02

 

CDJCZNU4
CDéCZNU4
CDSCZNu4
CDJCZNU4
C03C2NU4
CDSC2NU4
CDSCZNU4
CD3C2NU4
003C2NU4
CDJCZNU4
CDJCZNU4
CDSCZNU4
CDéCZNU4
CDéCZNU4
CDJCZNU4
CDJCZNU4
CDJCZNua
CDJCZNU4
CDSCZNU4
CDéCZNU4
CDJCZNU4
CDJCZNU4
CDJCZNU4
CDSCZNU4
CDJCZNU4
CDSCZNU4
CDSCZNU4
CDJCZNU4
CDSCZNU4
CDJCZNU4
CDJCZNU4
CDJCZNU4
CDJCZNU4
CDJCZNU4

CDJCZNU4
'CDACZNUR
CDJCZNU4
CD6C2NU4
CDJCZNU4
CDSCZNU4
CDSCZNU4
CDéCZNU4
CDJCZNU4
CDJCZNU4
CD6C2NU4
CDSCZNU4
CDJCZNU4
CDéCZNU4
CDJCZNU4
CDSCZNU4
CD302N04

RR
RR
HR
HR
HR
RR
RR
RR
RR
RR
RR
HR
RR
HR
RR
RR
RR
RR
RR
RR
RR
HR
RR
RR
RR
RR
RR
HR
RR
RR
RR
RR
HR
RR
RR
RR

8.19
8.20
8.21
8.22
8.24
8.25
8.26
8.27
8.28
8.29
8.30
8.32
8.33
8.34
8.55
8.36
9. 9
9.10
9.11
9.12
9.13
9.14
9.16
9.17
9.21
9.22
9.24
9.25
9.26
9.27
9.28
9.29
9.30
9.31
9.52
9.33

RR10.10
HR10.11
RR10.12
RR10.13
RR10.14
RR10.16
RR10.17
RR10.18
RR11.11
RR11.12

RR11.13_

RR11.14
RR11.15
RR11.16
RR11.17

95

4617.7591
“618.4612
4619.1712
“619.8733
4621.2750
4621.9649
462296756
4626.3726
4624.0716
“624.7559
4625.4673
4626.8525
4627.5446
4628.2278
4628.9217
4629.6255
461604211
4617.1314
461798425
4618.5613
4619.2750
4619.9827
462194097
4622.1151
“624.9363
4625.6402
4627.0488
4627.7620
“628.4484
4629.1599
4629.8485
4630.5741
4631.2631
4631.9642
4632.6922
“633.3350
4622.8531
4625.5619
4624.2472
462510039
4625.7264
4627.1279
4627.8380
4626.5651
4629.2432
4629.9569
“630.6602
4631.3779
4632.0803
4632.7622
4633.4894

0.02
0.02
0.02
0.02
0.06
0.02
0.02
0.06
0.06
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.00
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.06
0.06
0.06
0.06
0.06
0.06
0.06

 

96

C06C2N04 HH12.12 4665.5688 0.06
CD602N04 RR12.13 4636.27b1 0.06
C06C2~u4 RR12.15 4637,7007 0.06
C06Cz~04 RR12-16 4638-4068 0.06
CD6C2N04 RR12.17 4639.1136 0.06
CDSCZNU4 RR12.18 4639.8145 0.06
006C2004 RR12.19 4640.5095 0,06
CD3CZNU4 RR12120 464102024 0.56
f
1 1 1 4 0.00000001
11111
lHlS IS A FIT OF 2NU4 UF CU3CL ~tTHOuT THt PARALLEL
COMPONENT
END HtAD - IN COLUMNS 76-80
111111111
IHIS IS A CHECK FOR TH: SIGNIFICANCE OF mnRt VARIABLES IN
THE FIT

END HtAD - IN COLUMNS 75-80
LAST FIT - IN COLUMNS 73'80

 

APPENDIX B
LEAST SQUARES FITS

AND ASSOCIATED STATISTICS

The frequency expressions which concern us most (e.g. Table

2.5 or Table 3.1) are of the form,

= , + . +... +
y: x1151 x1232 “1po e1

where y ith observed frequency

i I 1, 2,... n

:3
II

number of observations

number of parameters to be determined

'0
I

xij = value of quantum coefficient of molecular parameter
Bj for the ith observation
ei - the random error associated with the ith measurement.
The resultant set of equations for the n observations can be

summarized in the vector-matrix form,

1=£fl+s

which is shorthand notation for

 

 

 

 

 

'qu C311 x12...xlj...x1p7 {3;} E elj
y2 x21 :52 gez
s - ' i W +
Y1 ' 53 e1
2 x11 x12.. x11...xip ° .

Lyn-J .xnl xnzu x J . xnpd LBP‘J LenJ

 

 

 

 

98

In the thesis of J. W. Boyd (34), it is shown that the best
estimate of the unknown parameter vector .fl is given by the least

squares estimate (2)

T25.

n
ms

and 2;, 5}; transposed

Thus the job of a least squares fitting program is to find a value

of §:1. This corresponds to solving the set of normal equations,

92"”

N

1.

II2

This is exactly what the subroutine STEPFIT does. It first calculates
the matrix g: and proceeds to invert it by the process of Gaussian
elimination as described by Orden in Chapter 2 of Mathematical
Methods £25.§igital Computers (35). The actual regression program
used in subroutine STEPFIT is that written by M, A. Efroymson and

. is described briefly in Chapter 15 of the same book. Once the

vector of molecular parameters (2) has been determined, it is

important to determine the statistical significance of the vector

2, The standard error (sb ) of any component bJ of ~2. is
‘ A J
given by,
2 2 -1
s . s N
bj JJ
2 l 2
where s - 3:3'E w1(y1-y1) n-p 3 degrees of freedom
with “x - g _b_
and w1 = normalized weight of ith measurement such that
z w = n
1 i

Boyd showed that a simultaneous confidence interval for all com;

Ponents of b_ is defined such that the probability is l - a for

 

99
all b. in {6.} that,
J J
b-
‘ J 83‘ S Sasb

where Sa is a function of the well-known Fa (p, n-p) distribution

 

SO! =pra(p. n-p)

 

This simultaneous confidence interval [1 83a] is the mean- I ‘
ingful statistic to quote for the results of a least squares fit E.
when variables are statistically dependent. The common test for the
statistical dependence of two variables xij and xiq is the i5.

correlation coefficient rjq’

’f‘xij'xj) (“1(2)

 

r I

Jq

 

/I£(xij-xj)§(xiq-iq)

Subroutine STEPFIT prints out rjq for all variables. The coef-

ficients (b) of variables having non-zero r are dependent

1‘!

upon one another. For example, A is highly dependent on the

0

value determined for «2 and DE. In such a case it is important '
to know that the probability is led that all three parameters
are simultaneously within a specified interval of their true values.
In our work.we have chosen a 8 0.05.

The manner in which standard errors of independent and
.dependent variables are calculated in STEPFIT is described on
pages 193 and 195 of Bfroymson's Chapter 17 (35). At first glance
(or even many glances) it appears his definitions differ from those
given above. However, when one carries through the normalization

factors of the correlation coefficients (r ) to the very end,

11

agreement is reached. ;

H t S U L T S

NU4
NU4
N04
N04
N04
N04
NU4
N04
N04
NU4
N04
N04
NLJ4
NU4
NU4
N04
NU4
N04
NU4
N04
NU4
N04
NU4
N04
N04
N04
NU4
NU4
N04
N04
N04
N04
NU4
N04
N04
N04
NU4

0 F

IDENT

PP12114
PP1?,16
PP12,12
PP11113
PP11.12
PP 9,19
PP 9115
PP 9,17
PP 9,16
PP 9,15
PP 9,14
PP 9,15
PP 9,12
PP 9,11
PP 9, 9
PP 8,16
PP 5,15
PP 5,14
PP 5,16
PP 5,12
PP 5,11
PP 5, 9
PP 5, 5
PP 5' 7
PP 5, 6
PP 5, 5
PP 4,28
PP 4,2/
PP 4,26
PP 4,25
PP 4,24
PP 4,25
PP 4,21
PP 4,19
PP 4,15
PP 4,10

0

R

APPENDIX C

S I M U

4
-

C D 3 I

085, FREE
2246,4937
2246,9074
2247,3034
2251,0347
2251.4425
2256,7635
2257.1704
2257,5683
2257.9765
2258,3804
2258,7847
2259,1862
2259,5872
2259,9934
2260,8079
2262.0221
2274.4411
2274,8471
2275,2569
2275.6610
2276.0695
2276,8709
2277.2833
2277,6790
2278.086}
2278,4992
2273.1313
2273.5429
2273.9424
2274.3437

2274,7492'

2275,1507
2275.5609
2275,9573
2276.7785
2277.1749
2277,9867

100

OSS'CALC

.0,2074
.0,1971
p0,2044
.0,1467
«0,1424
.o,o969
no.0942
-0.1004
«0,0963
“000994
.o,o961
$0,0984
F“00101-3
.o,o9ss
”000915
.0,0750
-0.0153
.o,0133
90.0054
90.0086
90.0043
40.0110
.0.0024
'000105
‘000068

0.0026
60.0000

0.0059
"000002
-o.0045
90,0055
.o,0064
,0.0036
90.0123
P040014
“000100
-0.0079

T A N E U U S

“T
0900
0000
0000
0400
0:00
0400
0000
0400
0:00
0100
0400
0900
0000
0.00
0000
0.00
0412
0012
0012
0903
0012
0,03
0403
0'03
0:03
0.03
0003
0003
0003
0903
0,03
0,03
0403
0903
0903
0903
0:03

N0.
38
39
40
41
42
46
44
46
46
47
48
49
60
61
62
53
64
66
66
67
66
69
60
61
62
63
64
66
66
67
66
69
70
71
72
7s
74
76
76
77
78
79
60
61
82
66
64
66
66
67

N04
N04
NU4
N04
NU4
N04
NU4
N04
N04
N04
NU4
NU4
N04
NU4
NU4
NU4
NU4
N04
N04
NU4
N04
N04
NU4
N04
N04
NU4
N04
N04
N04
NU4
N04
N04
N04
N04
NU4
NU4
N04
N04
NU4
N04
N04
NU4
N04
N04
NU4
N04
N04
N04
N04
NU4

IDFNT

Pp
Pp
Pp
Pp
Pp
Pp
Pp
Pp
Pp
Pp
PP
Pp
Pp
PP
Pp
pp
PP
PP
Pp
Pp
Pp
pp
PP
PP
Pp
Pp
Pp
PP
Pp
Pp
Pp
Pp
Pp
Pp
Pp
Pp
Pp
PP
PP
PP
Pp
PP
Pp
PP
PP
Pp
Pp
RR
Pp
pp

4,15
4,14
4,13
4,12
4,11
3,36
3,35
3,34
3,33
3,32
3,31
3,29
3,28
3,20
3,25
3,24
3,23
3,22
3,21
3,19
3,10
3,17
3,16
3,15
3,14
3,13
3,12
3,11
3, 9
3, 8
2,25
2,24
2,23
2,22
2,21
2,19
2,18
2,16
2,15
2,14
2,13
2,12
2,11
1:15
1,14
1013
1,12
1, 1
1, 2
1, 3

101

063, FRF]
2278,3883
2278.7913
2279.1925
2279.5892
2280.0017
2273,8050
2274,2093
2274,6182
2275,0222
2275,4196
2275,8377
2276,6493
2277,0584
2277,8648
2278,2714
2278,6885
2279,0789
2279,4877
2279,8791
2280,6929
2281.1037
2281,5041
2281,9113
2282,3280
2282,7357
2283.1301
2283.5271
2283,9316
2284,7417
2285,1639
2282,1609
2282,5623
2282,9702
2283,3794
2283,7853
2284.6019
2285.012?
2285,8244
2286,2272
2286,6300
2287,0393
2287,4459
2287,8464
2290,0854
2290,4830
2290,8818
2291,2858
2304,6125
2305.0276
2305.4366

DES-GALE

I'000105
-0.0126
“000159
90,0236
.0,0154
0.0047
0.0026
0.0022
0.0060
-0.0058
0.0061
000056
0.0088
0.0035
0.0044
0.0158
0.0006
0.0040
'040101
.0,0068
“0,0011
-0.0058
.0,0030
0,0084
0.0114
0.0012
00.0063
90,0062
P0.0045
0.0136
“000016
9000091
90.0039
9000004
-0.0000
0,0058
0.0108
0.0128
0.0107
0.0086
0.0137
0.0152
000113
90.0068
90.0111
60,0171
.0.0178
“000124
000003
0.0070

NT
0903
0:03
0403
0903
0903
0,03
0,03
0903
0012
0:12
0312
0:03
0,12
0903
0,03
0,03
0,03
0103
0,12
0,03
0,03
0903
0.12
0903
0,03
0903
0:03
0903
0,03
0903
0012
0,12
0012
0,12
0,03
0,03
0,12
0912
0,03
0,12
0012
0,12
0,03
0003
0,12
0,03
0903
0103
0.03
0903

 

N0.
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126

127.

126
129,
160
161
162
166
164
165
166
167

NU4
0U4
NU4
N04
N04
N04
NU4
N04
N04
NU4
NU4
N04
NU4
NU4
N04
NU4
N04
NU4
N04
NU4
NU4
N04
N04
N04
N04
NU4
NU4
N04
NU4
NU4
NU4
NU4
NU4
NU4
N04
NU4
NU4
NU4
N04
NU4
NU4
NU4
N04
N04
NU4
NU4
NU4
N04
N04
N04

IDENT

RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR

1, 4
1. 5
1, 6
1,12
1.16
1,14
1,15
1,16
2.19
2, 2
2, 3
2,20
2,21
2,22
2,23

3,14
3,15
3,16
3,15
3,19
3,20
3,21
3,22
3,23
3,24
3,25
3,26
3,30
3,31
3.52
4, 5
4, 6
4, I
4,10
4,12
4,13
4,15
4,16

102

OHS. FRED
2305,8387
2306,2496
2306,6543
2309,0478
2309.4353
2309,8304
2310.2353
2310.6363
2315.6368
2308.8106
2309.2150
2316.0421
2316.4492
2316,8395
2517.2358
2317.6306
2318.0135
2312,9852
2313.4001
2313.8063
2314.2038
2314,6076
2315.4188
2315.8030
2316.6101
2317.0044
2317.4006
2317.8006
2318.2028
2318.9815
2319,3846
2319.8115
2320.1908
2320.5917
2320.9925
2321,3856
2321.7816
2322,9836
2323,7695
2324,1556
2324,5592
2317,1452
2317.5387
2317.9355
2318,3417
2319.5398
2320.3326
2320,7471
2321.5383
2321.9445

Gas-CALC

0.0071
0.0101
0.0191
0.0067
60.0063
-0.0110
.0,0062
-0.0045
0.0043
“0.0120
-0.0098
0.0116
0.0204
0.0126
0.0111
0.0053
.o,0061
90.0070
0.0060
0.0101
0.0063
0.0058
0.0179
0.0014
0.00/7
0.0020
'0.0016
90.0012
0.0016
"0.0177
"0.0132
0.0153
"0.0055
“0.0005
0.0027
-0.0017
p0.0028
0.0094
0.0035
-0.0059
0.0024
0.0124
0.0042
v0.0005
0.0044
0.0000
.0,0077
0.0068
-0.0011
0.0058

01
0.03
0.12
0.12
0.12
0103
0.03
0.03
0.03
0.12
0.03
0.03
0.03
0.12
0.12
0.00
0.02
0.12
0.03
0.12
0.12
0.03
0.06
0.08
0.12
0.50
0.50
0.50
0.12
0.12
0.12
0.12
0.12
0.50
0.50
0.12
0.12
0.12
0.03
0.03
0.03
0.03
0.00
0.12
0.03
0.03
0.03
0.12
0.50
0.03
0.03

rf

 

N0.
138
139
140
141
142
143
144
145
146
147
146
149
150
151
162
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175

176
177
178
179
180
181
182
163
184

NU4
N04
N04
N04
N04
NU4
NU4
NU4
N04
N04
N04
N04
N04
N04
N04
N04
NU4
N04
N04
N04
N04
NU4
NU4
NU4
N04
NU4
NU4
NU4
N04
NU4
N04
N04
NU4
.NU4
N04
NU4
N04
N04

2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4

IUFNT

RR 4,16
RR 4,19
RR 4,21
RR 4,22
RR 4,23
RR 4,24
RR 4,25
RR 4,28
RR 4,29
RR 4,31
RR 4,32
RR 4,34
RR 4,35
RR 5,10
RR 5,12
RR 5,13
RR 5,14
RR 5,15
RR 5,16
RR 5,18
RR 6, 6
RR 6, 7
RR 6, 9
RR 6,13
RR 6,14
RR 6,15
RR 6,16
RR 8, 9
RR 9, 9
RR 9,10
RR 9,11
RR 9,12
RR 9,13
RR10014
RR10,15
RR10117
RR10115

QR 3,44
0P 3,45
OR 3,42
UP 3,41
QR 3,40
QP 3339
UP 3,35
QR 3,37
QR 3,36

103

085. FRED
2322,7433
2323.1373
2323.9416
2324.3197

2324.7312,

2325.1256
2325.5308
2326.3136
2326.714?
2327.114?
2327,8816
2323.2783
2329.0703
2329,4936
2323.2443
2324.0364
2324.4390
2324.8421
2325.9504
2325,6495
2326.4388
2325.3227
2325.7293
2326.5224
2323.1164
2328.5183
2328.9098
2329.3159
2333.7780
2337.3626
2337.7700
2338.1724
2338.5655
2338.9576
2342.9304
2343.3226
2344.1093

2344.5032

4527.8835
4528.2985
4528,7163
4529.1306
4529,5401
4529.9517
4530.3545
4530.7753
4531.181?

URS-CALC

0.0074

0.0024.

0,0105
'0,0091
0.0049
0.0021
0.0104
0.0001
0.0051
0,0088
-0u0147
P0:01.25
“000101
0.0191
90.0041
'0n0123
q0,0096
“0.0060
0.0029
0.0030
"0.0052
POIOOOB
0.0047
“0.0038
90.0100
1"0.0070
90.0152
'010081
"000100
'0n0073
0.0000
0.0026
n0.0038
90.0110
0.0156
0.0092
0.0001
p0,0043

0.0009
0.0015
0.0061
0.0053
0.0010
.0.0010
.o.0114
”000049
-0.0102

WT
0.12
0.03
0012
0912
0.12
0:50
0.03
0.03
0.03
0103
0.12
0.12
0.03
0.03
0.03
0.12
0.12
0.12
0003
0:03
0903
0912
0.12
0.12
0.12
0.50
0912
0.00
0.12
0:12
0.03
0.50
0.50
0900
0906

_0.02

0.25
0.06

0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.12
0.03

NO.
186
186
187
188
189
190
191
192
193
194
196
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234

2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4

IuENT

UP
UP
UP
UP
UP
UP
QP
UP
UP
UP
UP
UP
UP
UP
UP
UP
OF
UP
UP
UP
UP
UP
UP
UP
UP
UP
UP
UP
UP
UP
UP
UP
UP
UP
UP
UP
UP
UP
0P
OF
UP
09
UP
UP
UR
UP
UR
UR
UR
UP

3,36
3,33
3,32
3,31
3,29
3,28
3,2/
3,26
3,26
3,24
3,23
3,22
3,21
3,20
3,19
3,18
3,17
3,16
3,16
3,13
6,39
6,38
6,33
6,32
6,31
6,30
6,29
6,28
6,27
6,26
6,26
6,24
6,23
6,21
6,20
6,16
6,16
6,14
6,13
6,10
3,18
3,19
3,20
3,21
3,22
3,23
3,24
3,26
3,26

104

Obs, FREQ
4561.5996
4632,0100
4532.4274
4532,9407
4533.2594
4534,0847
4534,4991
4534.6964
4565.2997
4535.7193
4636.1307
4536,5459
4566,9543
4537,3666
4537.7799
4538.1800
4568.5813
4539.0023
4539,4044
4539.8105
4540.6255
4529,2649
4529,6795
4531.7285
4532.1415
4532,5662
4532,9783
4633,3879
4533.7953
4564.2093
4564.6115
4565.0265
4565.4333
4535.8576
4636,6783
4567,0866
4566.7200
4539.1227
4539,5342
4539.9353
4641.1618
4553,4727
4553,8623
4554,2553
4554,6553
4555,0547
4555,4453
4655.8528
4556.2330
4666,6273

OPS'CALC

-0.0062
'0,0072
90.0021
-0.0008
0.0062
0.0087
0.0121
”0.0014
.0,0086

“090003_

0.0021
0.0076
0.0065
0.0096
0.0139
0.0054
-0.0017
0.0112
0.0054
0.0040
0.0048
0.0010
0.0027
'090113
9000105
0.0025
0.0032
0.0016
.0,0020
0.0014
«0.0069
10.0020
~0,0047
090095
0.0117
0.0131
0.0119
0.0071
0.0114
0.0062
0.0133
'0,0007
.0,0063
“090092
90.0043
0.0005
'0.0001
0.0106
“0.0026
p0,0013

”7
0950
0.12
0.12
0.12
0912
0.02
0902
0.02
0.12
0,12
0.12
0.12
0.12
0.12
0.03
0.12
0903
0.12
0.12
0.12
0912
0.03
0.03
0.12
0903
0.03
0.03
0.03
0.03
0903
0903
0.03
0.03
0903
0903
0.03
0.03
0.03
0903
0903
0.12
0912
0912
0.12
0.12
0112
0.12
0,03
0012
0.12

:1

—-—-"-
Ymfiim'fi

N0.
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
254

2NU4
2NU4
2NU4
2004
2NU4
2Nu4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2N04
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4

IDENT

QR 3,27
UP 3,29
PP11,15
PP11914
PP11913
PP11,12
PP11,11
PP10916
PP10,15
PP10,14
PP10913
PP10912
PP10,11
PP 9,13
PP 9,12
PP 9,11
PP 9,10
PP 9, 9
PP 2910
PP 2, 9
PP 2, 5
PP 2, 7
PP 1,19
PP 1,15
PP 1,14
PP 1913
PP 1,12
PP 1911
PP 1910
PP 1, 9
PP 1, 7
PP 1, 6
RR 0, 3
RR 0, 4
RR 0, 6
RR 0, 7
RR 0, 6
RR 0, 9
RP 0,10
PR 0,11
PR 0,12
RP 0,13
PR 0,16
PR 0,17
RR 0,16
PR 0,19
RR 0920
RR 0921

105

OBS, FREQ
4557.0090
4557,4055
4557,7949
4504,2293
4504,6497
4505,0527
4505,4639
4505,8670
4510.799?
4511.2185
4511.6289
4512.0343
4512.4367
4512,8363
4518.9842
4519,3777
4519.7819
4520.2048
4520.6024
4567,5155
4567.896?
4568.3163
4568,7171
4570,4055
4572.023}
4572,4315
4572,8452
4573,2579
4573,6752
4574.0726
4574,4934
4574,8849
4575,2851
4575,6946
4586,2455
4586,6521
4587,4492
4587,8579
4588.2453

I4588,647o

4589,0383
4589,4425
4539.836?
4590,2397
4991.4300
4591.8305
4592.2301
4592.6253
4593.0238
4593,4126

OBS-CALC

“090123
'090078
9090103
~0.0103
0.0054
0.0027
0.0084
0.0062
-0.0169
“0.00958
0.0003
090004
-0.0034
90.0092
0.0084
“090069
E090052
090124
0.0049
0.0053
no.01b3
00.0016
no.0064
no.0031
90,0171
'0,0160
9090094
60.0042
0.0076
.o,oo11
0.0139
-0.0000
80.0050
'0,0004
0.0035
090088
0.0044
0.0129
0.0005
0.0027
90.0052
090004
-0,0044
,0.0010
90.0005
0.0034
0.0069

0.0064-

0.0095
0.0033

wT
0912
0.12
0903
0902
0.03
0903
0.03
0.03
0903
0903
0903
0903
0903
0903
0902
0903
0.03
0903
0912
0903
0903
0903
0903
0903
0912
0903
0903
0912
0903
0903
0912
0912
0912
0912
0,12

_0.03

0903
0903
0903
0903
0903
0903
0903
0903
0,12
0,12
0912
0912
0903
0,03

' n.
4 h

NO.
255
286
287
258
289
290
291
292
295
294
295
296
297
298
299
500
$01
602
306
304
605
606
607
608
609
610
$11
612
616
614
315
616
617
318
619
320
621
622
523
624
325
326
627
528
629
630
561
652
666
664

2NU4
2004
2NU4
2NU4
2NU4
2NU4
zwua
2Nu4
2NU4
2~u4
2NU4
2NU4
2NU4
2NU4
2~u4
2NU4
2NU4
2~04
2Nu4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2Nu4
2NU4
2NU4
2NU4
2NU4
2NU4
2~U4
2Nu4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2Nu4
2Nu4
2NU4
2NU4

IDENT

RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR

RR '

RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR

0.22
0.26
0.24
0.25
0.20
0.27
0.26
0.29
0.50
0.52
0036
0.34
0.55
1: 7
1: 5
11 9
1.11

106

4593,8051
4594.2055
4594,5957
4594.9853
4595,3716
4595.7846
4596.1703
4596,5679
4596,9640
4597.759?
4598,1467
4598,5243
4598.9164
4594.306;
4594.7037
459500924
4595,8950
4596.3007
4599.9005
4600.3110
4600.7133
4601,1074
4601,5189
4601,9072
4602.316?
4602.7092
4603.1030
4604.3197
4604.7080
4605,8713
4606.2740
4606,6694
4607.076?
4607,4707
4607,8658
4608.2676
4608.6694
4609.0705
4609,4711
4610.250}
4610,6536
4611.0559
4611.4445
4611.8369
4613.793?
4614.1659
4614.9908
4615.3824
4615.7770
4616.1725

ORS'CALC

0.0013
0.0076
0.0039
0.0007
90.0065
0.0169
0.0075
0.0154
0.0132
0.0321
0.0296
0.0173
0.0205
90.0021
90.0051
'000158
no.0110
90.0066
90.0193
'000093
'000071
90.0127
-0.0006
-0.0113
90.0009
.0,0061
90.0101
0.0154
0.0014
90.0061
90.0059
90.0089
-0.0021
'000073
9000114
.000055
90.0052

-0.00ZSfi

0.0006
'0I0145
90'0077
“000016
n0.0086
-0.0117

0.0122
—0,0148

0.0129

0.0065

0.0065

0.0018

NT
0.12
0903
0.03
0.03
0.03
0903
0.12
0.12
0903
0:03
0.03
0.03
0.03
0.03
0903
0303
0.03
0.12
0.03
0.03
0.02
0.03
0.03
0.03
0903
0.03
0903
0903
0903
0912
0912
0.12
0.12
0.12
0003
0.03
0912
0:12
0.12
0:03
0.03
0.03
0:12
0:12
0:12
0.03
0.03
0,12
0.12
0.02

 

NO.
665
666
667
668
669
640
641
642
646
644
645
646
647
648
649
650
651
652
656
654
655
656
657
658
659
660
661
662
666
664
665
666
667
668
669
670
671
672
676
674
675
676
677
678
679
680
681
682
686
684

2N04
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4

IDENT

RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR

4'15
4,16
4,11
4,18
4.19
4,20
5.16
5.17
5,18
5,19
5,20
5,21
5.22
5,26
5.24
5,25
5.26
5,27
5,26

107

Obs. FREQ
4616.5560
4616,9551
4617,6482
4617,7471
4618.1691
4618.5684
4626.2279
4626,6151
4624.0147
4624,4015
4624,7960
4625,1764
4625,5761
4625,9681
4626.3620
4626.7553
4627.1646
4627.560;
4627.9668
4625.4211
4625.8159
4626.2275
4626.6252
4627,0244
4627,4245
4627,8172
4628.2194
4629.0170
4629,4076
4629,7969
4660.1991
4661,6880
4661.7774
4662.1768
4662,5626
4662,9544
4636.3431
4666.7648
4664.1223
4634.5152
4664,8907
4665,2957
4665,6860
4666.0698
4666.4557
4666.8506
4667.264?
4637.6121
4667,9961
4668,7869

URS'CALC

90.0116
“0.0089
.0.0118
'0.0055
”0.0117
'0.0071
0.0165
0.0079
0.0120
0.0069
0.0007
“0.0151
“0.0071
n0.0054
90.0044
P0.0069
90.0163
“0.0115
0.0003
-0.0017
«0.0067
0.0053
0.0042
0.0048
0.0067
0.0016
0.00b4
0.0105
0.0050
“0.0014
0.0055
0.0111
0.0069
0.0102
0.0065
0.0059
0.0028
0.0061
0.0002
0.0022
90.0126
0.0052
0.0044
'0.0004
p0,0026
0.0047
0.0018
-0.0077
P0.0129
0.0069

1"T
0.12
0.12
0.12
0.12
0.03
0.03
0.03
0.03
0.03
0.12
0.03
0.03
0.12
0.12
0.12
0.03
0.03
0.03
0.12

,0.12

0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.03
0.03
0.12
0.12
0.12
0.12
0.12
0.12
0.03
0.03
0.12
0.12
0.03
0.03
0.03
0.03
0.03
0.03
0.03

 

N0,
685
686
667
668
659
690
691
692
696
694
69b
69b
69/
698
699
400
401
402
406
404
405
406
407
408
409
410
411
412
416
414
415
416
417
418
419
420
421
422
426
424
425
426
427
428
429
460
461
462
466
464

2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4

IDENT

RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR

6.41
6.42
6.46
7. 7
7. 8
7. 9
7.10
7.11
7.12
7.16
7.15
7.16
7.17
7.18
7.19
7.20
7,21
7.22
7.26
7.24
7.25
7.26
7.27
8. 9
8.10
8.11
8.12
8.16
8.15
8,16
8.17
8.18
8.19
8.20
8.21
8,22
8.26
8,24
8.25
8.26
8.28
8.60
8.61
8.62
8.66
9. 9
9.10
9.11
9.12
9.16

108

DES, FRFQ
4669,1702
4669,5516
4669,9241
4661.9520
4662.6565
4662,7599
4666,1584
4666,5561
4666,9482
4664,6466
4635.1312
4665,5426
4665,9657
4666.6642
4666.7214
4667,1257
4637,5149
4667.9021
4668,2990
4668,6854
4669,0750
4669,4689
4669,8573
4668,8261
4669,2600
4669,6290
4640,0291
4640,4297
4641.2185
4641.6154
4642,0096
4642,4109
4642,7871
4646,1923
4646,5807
4646,9714
4644.3732
4644,7667
4645.1616
4645,5441
4646.6669
4647,0914
4647,4869
4647,8700
4648,2544
4644,8629
4645.2568
4645,6501
4646,0566
4646,4455

URS-CALC

0.0084
0.0056
’0.0057
“0.0061
“0.0009
0.0056
0.0067
0.0003
.0.0023
-0.0011
'0.0097
0.0057
0.0062
0.0066
“0.0009
0.0092
0.0045
'0.0016
0.0023
“0.0038
«0.0062
'0.0069
'0.0066
90.0076
00.0021
“0.0010
0.0016
0.0051
0.0009
0.0020
0.0008
0.0072
.000112
90.0000
90.0053
P0.0077
0.0013
90.0004
0.0054
no.0062
0.00:33
90.0167
P0.0132
n0.0156
'0.0193
0.0104
0.0061
0.0015
0.0106
0.0026

NT
0.03
0.03
0.03
0.12
0.12
0.12
0.12
0.12
0.12
0.03
0.12
0.12
0.12
0.03
0.03
0.06
0.06
0.06
0.03
0.12
0.12
0.03
0.03
0.12
0.12
0.12
0.12
0.06
0.12
0.12
0.12
0.12
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.06
0.03
0.12
0.12
0.06
0.03
0.03

N0.
465
466
467
468
469
440
441
442
446
444
445
446
447
440
449
450
491
452
456
454
455
456
457
458
459
460
461
462
466
464
465
466
467
466
469
470
471
472
476
474
475
476
477
478
479
480
481
482
486
484

2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4

IDENT

RR 9.15
RR 9.16
RR 9.1/
RR 9.18
RR 9.19
RR 9.20
RR 9.21
RR 9.26
RR 9.24
RR 9.2/
RR 9.25
RR 9.60
RR 9.61
RR 9.62
RR 9.66
RR 9.64
RR 9.65
RR 9.60
RR 9.67
RR 9.68
RR 9.69
RR10.11
R910.12
RR10.14
RR10.15
RR10.16
RR10.17
RR10p15
R910119
RR10.20
RR10.21
RR10.22
R910.26
RR10.24
RR10.25
RR11.12
RR11.16
RR11.14
Rpllplb
RR11.16
RR11.17
RR11.10
R911.19
RR12.12
RR12.14
RR12.15
RR12.16
RR12.17
R912.15

109

088. FRF]
4647,2276
4947.626.
4648.017}
4648,4101
4648,7989
4649,2113
4649,6119
4650.0045
4650,3968
4650,7837
4651.9661
4652,3463
4656.112}
4653,5081
4653,8939
4654,2728
4654,6748
4655.0602
4655,4557
4655.8379
4656.222“
4656.605}
4651.615?
4652.0099
4652,7915
4653.1885
4656,5954
4653.9858
4654,3783
4654,7848
4655.1716
4655,5584
4655,9492
4656,6433
4656,7391
4957.1293
4657.9075
4658,3005
4658,6873
4659.0910
4659,4878
4659,8777
4660,2766
4660,6692
4663,7376
4664,5512
4664,9396
4665,3448
4665.7356
4966.1172

OES'CALC

n0,0079
.0,0051
P0.0091
-U.0111
-0.0166
0.0019
0.0082
0.0087
0.0085
0.0066
0.0096
0.0029
-0.0106
-0,0066
-0.0060
90.0149
”0.0002
90.0016
0.0076
0.0069
0.0061
0.0012
0.0076
0.0051
"0.0094
-0.0055
0.0060
0.0013
-0.0005
0.0116
0.0047
"0.0017
.0,0067
—0.0014
0.0021
0.0009
0.0042
0.0005
-o.0089
90.0010
0.0005
”0.0044
0.0001
-0.0013
90.0066
0.0180
0.0109
0.0209
0.0171
0.0045

NT
0.12
0.06
0.06
0.12
0.12
0.06
0.1?
0.12
0.12
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.03
0.06
0.06
0.06
0.03
0.12
0.06
0.12
0.06
0.06
0.02
0.12
0.06
0.06
0.06
0.06
0.06

'6 l1'V“.'A'. L1

‘AI’ ~"-.'..
I

 

N0.
455
456
467
458
469

2NU4
2NU4
2NU4
2NU4
2NU4

IUENT
R912;19
RR12:20
R912;2l
R912:22
RRIZpZJ

110

OFS. FRFD
4666,5143
4666,9085
4667.282!
4667,6781
4608.071:

ch'CALC
0.0078
0.0058
“0.0105
-0.0068
“000052

“T
0.03
0912
0012
0.03
0103

 

 

APPENDIX 0

R t S U L T S 0 F A S I M U . T A N E 0 U S
F O R C D 3'C L
NU. IDENT OBS. FREQ UBSVCALC UT
1 NU4 P912.14 2230,5253 9001152 0:00
2 NU4 P912113 2231.2480 l091149 0.00
3 NU4 PP12112 2231.9615 00.1206 0000
4 NU4 P911p23 2227,8271 u0.1227 0.00
5 NU4 PP11.22 2228.5498 a0o1191 0100
6 NU4 PP11o21 222902721 0031161 0900
7 NU4 PP11120 2229.9916 90.1159 0,00
8 NU4 P911p19 2230.7185 c0.1083 0:00
9 NU4 PP11015 2231:4485 .000979 0'00
10 NU4 P911017 2232,1656 v0.1004 0:00
11 NU4 PP1131D 2233.617? 9000874 0.00
12 NU4 PP11¢14 2234,3433 90.0818 0.00
13 NU4 Pp11a13 2235.0669 90.0779 0.00
14 NU4 PP11a12 2235,7901 u0.0745 0p00
15 NU4 P911111 2236.5020 00.0824 0'00
16 NU4 PP10.28 2227,9706 u0.1424 0000
17 NU4 P910127 2228,6992 I0.1328 0.00
18 NU4 PP10.26 2229,4225 u0.1285 0.00
19 NU4 Pp10.25 2230.1444 0001260 0.00
20 ,NU4 PP10024 2230.8860 0001038 0.00
21 NU4 P910023 2231.5985 I0l1108 0:00
22 _NU4 PP10122 2232.3225 I0.1063 0:00
23 NU4 P910121 2233.0511 00.0974 0:00
24 NU4 PP10,20 2233,7759 30.0924 0.00
25 NU4 PP10a19 2234,5034 00.0847 0100
26 NU4 P910a18 2235,2278 o0.0802 0.00
27 NU4 P910017 2235.9490 .090790 0'00
28‘ NU4 PP10016 2236.6637 I0.0342 0000
29 NU4 PP10015 2237,4011 00.0669 0.00
30 NU4 PP10p14 2235,1252 I0.0628 0:00
31 NU4 P910013 2238.8467 0000614 0000
32 ANU4 PP10.12 2239.5738 90.0544 0:00
33 NU4 P910311 2240.2920 00.0563 0.00
34 NU4 P910110 -2241.01361 0000548. 0000
35 NU4 PP 9.31 2229.5606 .011327 0900
36 NU4 PP 9.30 2230.2844 90.1280 0.00
37 NU4 PP 9.29 2231.0173 I0.1139 0:00

111

rag-I

 

N0,
38
39
4o
41
42
43
44
45
46
47
48
49
so
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
7o
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87

NU4
N04
N04
NU4
NU4
NU4
NU4
N04
NU4
NU4
NU4
NU4
NU4
N04
NU4
NU4
NU4
NU4
N04
NU4
N04
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
N04
N04
NU4
N04
NU4
N04
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4

IDENT

PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP

9,28
9,27
9,26
9,25
9,24
9,23
9,22
9,20
9,19
9,18
9,17
9,16
9,18
9,14
9,13
9,12
9,11
9,10
9, 9
8,28
8,27
8,26
8.25
8,24
8,26
8,22
8.20
8.19
8,18
8,17
8,15
8,14
8.13
8,12
8,11
8,10
8, 9
8. 8
7,11
7.10
7, 9

7, 8,

3.20
3.19
3.18
3.17
3.16
3.14
3.13
3.12

112

OBS. PRES
2231,7392
2232,4486
2233,1767
2233,9007
2234,6251
2235,3534
2236,0787
2237,5256
2238,2515
2238,9772
2239,7076
2240,4442
2241,1583
2241,8862
2242,6123
2243,3342
2244,0610
2244,7748
2245,4983
2235,5280
2236,2055
2236,9259
2237,6393
2238,3620
2239,0835
2239,8059
2241,2647
2241,9965
2242,7244
2243,4509
2244,8896
2245,6223
2246,3538
2247,0696
2247,7983
2248,5135
2249,2309
2249,9560
2251,5033
2252,2431
2252,9578
2253,6841
2259,5767
2260,3035
2261,0304
2261,7508
2262,4768
2263,9323
2264,6567
2265,3797

Ops-CALC

'0.1119
u0.1220
.081135
ID.1092
F0.1047
90.0963
00.0910
90.0844
I0.o787
90.0752
'0.0651
'0.0469
90.0552
no.0456
no.0399
80.0384
o0.0320
I0.0356
90.0354
l0.0416
I060841
no.0858
90.0906
90.0881
20.0870
«0.0850
00.0673
no.0560
30.0488
no.0429
90.0456
60.0336
'000228
£0.0276
'0.0196
90.0250
00.0232
'0.0256
60.0191
no.0002
l0.0062
90.0007
I0.0481
00.0456
90.0409

no.0427'

9000358
60.0269
a000250
9010238

HT
0900
0000
0:00
0900
0000
0000
0000
0.00
0:00
0:00
0.00
0300
0100
0.00
0400
0000
0:00
0900
0900
0.00
0900
0900
0.00
0300
0900
0300
0.00
0300
0.00
0000
0.00
0900
0.00
0:00
0.00
0000
0900
0.00
0000
0.00
0.00
0000
0900
0900
0.00
0:00
0.00
0300
0900
0:00

 

NO.
88
89
90
91
92
93
94
9b
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137

N04
NU4
NU4
NU4
NU4
NU4
N04
N04
NU4
NU4
NU4
N04
NU4
NU4
N04
N04
NU4
NU4
N04
N04
N04
N04
NU4
NU4
N04
NU4
NU4
NU4
N04
NU4
N04
NU4
NU4
NU4
NU4
NU4
N04
NU4
NU4
N04
N04
N04
NU4

N04.

NU4
NU4
NU4
NU4
NU4
NU4

[DENT

PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
PP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RP
RR
RP
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
PP
RR

3.11

U
~
‘0-bCP‘JG

113

085, FRFD
2266,1055
2266,8419
2267,5602
2268,2871
2269,0043
2269,7428
2271.1857
2271,9029
2272,5482
2276,9011
2278,3273
2279,0525
2262,2811
2263,7356
2264,4675
2265,1934
2265,9132
2267,3679
2268,0972
2268,8178
2269,5499
2271,0067
2271,7360
2272,4559
2273,1833
2274,6486
2275,3783
2276,0970
2276,8292
2278,2813
2279,7223
2280,4419
2281,8765
2283,3277
2293,9625
2294,6755
2295,3784
2296,0863
2296,8321
2297,5648
2298,2868
2299,0001
2299,7132
2300,4418
2301,1468
2302,5955
2303,2944
2304,0138
2304,7348
2306,1620

OPS'CALC

90.0198
00.0050
I17000083
-080028
-0.0070

0.0104

0.0113

0.0073
-0.0192

0,0030
~0.0126
'010059
90.0935
.o,0856
.o,o771
90,0745
P060761
90.0701
no.06‘1
.o,o667
90.0578

'0.0473'

P000410
90.0440
90.0395
90.0196
Q0.0124
"000161
90.00b2

090018
l0.0007
90.0026
90.0104

-0.000833

0.0168
0.0106
00.0053
00.0154
0.0117
0.0265
080310
090271
0.0233
080354
080243
080418
000257
000305
000374
090375

WT
0:03
0103
0.03
0303
0:03
0.03
0103
0903
0103
0403
0.03
0:03
0.00
0.00
0000
0.00
0900
0:00
0.00
0.00
0.00
0000
0900
0.00
0.00
0.00
0003
0103
0903
0903
0.03
0103
0903
0.03
0903

.0.12

0:12
0903
0903
0:00
0900
0.00
0900
0100
0900
0.00
0100
0900
0900
0100

 

~8.
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178

f 179

180
”181
182
183
184
185

186'“

187

~84
~84
~84
~84
~84
~84
~84
~84
~84
~84
~84
~84
~84
~84
~84
~84
~84
NU4
~84
~84
~84
~84
~84
~84
~84
~84
NU4
NU4
~84
NU4
~84
~84
~84
~84
NU4
~84
~84
~84
~84

__NU4

N04
N04
N04
N04
NU4
NU4
NU4
N04
N04
N04

IDENT

RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR

2.20
2.21
39
3.

an

5.14

6.10
6.11
6.12
6.14
6.15
6.16
6.19
6.20
6.21
7. 9
7.10
7.11
7.12
7.14
7.15
7.16
7.18
7.19
7.20

114

08s, FPE3
2306,8718
2307,5908
2298,1453
2298,8638
2299,5843
2300,2992
2301.009?
2302.439}
2303,1541
2303,8818
2304,6077
2306.0276
2306.7300
2307,4343
2309,3015
2310.0153
2310,7342
2312,8809
2313,5913
2314.3023
2315,7332
2316,4496
2317,8863
2321.4334
2322.1387
2322,8415
2323,5401
2324.2586
2325,6562
2311.2253
2312.6814
2313.4030
2314.1201
2314.8336
2316.2534
2316,9835
2317,6930
2319,8257
2320,5397
2321,2457
2316,0348
2316,7496
2317,4589
2318.1785
2319,6148
2320,3188
2321,0314
2322,4604
2323,1805
2323,8929

OHS-CALC

0.0344
0.0409
090111
090109
0.0130
090093
090023
'090023
19090041
0.0073
090172
090065
n0.0059
90.0159
090044
090020
090050
090066
000028
090000
090043
090038
090222
090193
090163
090118
090032
090150
090010
9090245
#090015
0.0040
090055
0.0038
no.0055
090107
090067
090019
090044
9090007
“090053
90.0063
'090124
90.0077
090000
90.0096
90.0101
9090059
090025
0.0033

“T
0.00
0900
0912
0112
0.12
0912
0912
0912
0912
0912
0912
0.12
0912
0.12
0912
0912
0900
0912
0912
0912
0903
0912
0903
0903
0912
0903
0912
0912
0903
0903
0912
0912
0.12
0912
0912
0912
0903
0950
0912
0912
0912
0912
0912
0903
0912
0.50
0912
0903
0903
0.03

 

N0.
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237

NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4

IUENT

RR 7.21
RR 7.22
RR 7.23
RR 7.24
RR 7925
RR 8910
RR 8.11
RR 8.13
RR 8.14
RR 8.15
RR 8.16
RR 8.15
RR 8.19
RR 8.20
RR 8.21
RR 9. 9
RR 9.10
RR 9.11
RR 9.12
RR 9.16
RR 9.14
RR 9.15
RR 9.16
RR 9.17
RR 9.18
RR 9.19
RR 9021
RR 9.22
RR 9.23
RR 9.24
RR 9.26
RR 9.27
RR 9.28

RR 9.29_

RR10911
R810912
8810914
RR10.15
RR10916
8810.19
RR10.20
RR10.17
R811912
RR11.13
RR11.14
RR11.15
RR11917
8811918
RR11.19
RR11.20

115

085. FREE
2324.6060
2325.3123
2326.0145
252697239
2327.4320
2320.0683
2320.7808
2322.2317
2322.9483
2323,6633
2324,3679
2325,7921
2326,4970
2327.2015
2327.9211
2322.6566
2323.3769
2324.0893
2324,8019
2325,5163
2326.2244
2326,9312
2327.6577
2328,3515
2329.0830
2329.7897
2331.2222
2331.9255
2332,6522
2333,3479
2334.7535
2335,4637
2336.1627
2336.8596
2327,3515
2328,0773
2329,4980
2330,2135
2330.9432
2333,0780
2333.7864
2331,6488
2331,3144
2332.0213
2332.7416
2333,4550
233498748
2335,5884
2536.2920
233790143

ORS'CALC

0.0062
0,0024
.090052
.0,0047
-0,0051
.0,0152
-0.0178
0.0042
0.00/5
0.0058
0.0006
0.0007
.0,0057
'0.0120
90.0026
“090094
90.0044
90.0068
'090096
90.0061
“0.0154
"090196
90.0055
”0.02956
'0.0056
.0.0078
0.0045
-0.0015
0.0165
0.0040
no.0050
“090012
’090080
~0.0163
90.0117
0.0001
90.0059
.0,0030
0.0146
0.0163
0.0147
0.0086
090015
“090049
0.0027
0,0038
0.0007
0.0037
90.0028
0.0100

NT
0903
0.12
0.03
0.03
0.03
0903
0903
0.03
0912
0.03
0912
0912
0912
0903
0903
0912
0950
0912
0.12
0950
0.50
0.03
0.03
0903
0112
0.03
0903
0903
0912
0912
0.03
0903
0903
0903
0.03

,0.03

0903
0.03
0903
0903
0.03
0903
0903
0903
0.03
0912
0903
0903
0903
0903

 

N0.

238
239
240
241
242
243
244
245

246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284

NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4

2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4

IDENT

RR12.15
RR12.16
RR12117
RR12.18
RR12019
RR12o20
RR12.21
RR12.22

RR 9.17
RR 9.16
RR 9.15
RR 9.14
PP 9.13
PP 9.12
RR 9.11
RR 9.10
RR 0. 9
RR 0.10
RR 0.11
RR 0.12
RR 0.13
RR 0.14
RR 0.15
RR 1. 5
RR 1. 6
RR 1. 8
RR 1. 9
RR 1.10
RR 1.11
RR 1.12
RR 1.13
RR 1.14
RR 2. 5
RR 2. 6
RR 2._8
RR 2. 9
RR 2.10
RR 2011
RR 2.12
RR 2.13
RR 2.14
RR 2.15
RR 2.17
RR 2.18
RR 2.19
RR 2.20
RR 3. 3

116

083, FRED
2336,6614
2337,3899
2338,0937
2338,7999
2339,4982
2340.2185
2340,9297
2341,6410

4484,9809
4485,7244
4486,4538
4487,1775
4487,8975
4488,6233
4489,3547
4490,0886
4562,4747
4563,1896
4563,9002
4564,6199
4565,3270
4566,0513
4566,7699
4565,8097
4566,5215
4567,9420
4568,6645
4569,3793
4570,1010
4570,8164
4571,5252
4572,2372
4571,9608
4572,6896

74574.1170

4574,8353
4575.538?
4576.255}
4576,9579
4577,6685

4578,3829,

4579,1013
4580,5310
4581.2310
4581.9358
4582,6496
4576,6255

ORS-CALC

0.0072
0.0244
0.0174
0.0134
0.0020
0.0133
0.0159
0.0193

00.0248
”0.0053
0.0003
0.0004
P000029
-0.0003
0.0082
0.0195
0.0047
0.0049
0.0014
0.0075
0.0017
0.0136
0.0204
0.0001
90.0048
no.0161
90.0087
n0,0084
.0.0007
0.0014
no.0026
90.0028
.0,0019
0.0103
0.0062
0.0096
90,0014
0.0015
.o,0091
-0.0110
.0,0086
90.0015
0.0074
80.0020

'0.00597

-0.0002
90,0045

WT
0.03
0303
0.12
0.12
0203
0.03
0.12
0.12

0.03
0.12
0.12
0.03
0.03
0903
0.03
0.12
0.03
0.03
0.03
0.03
0.03
0.12
0.03
0.12
0.12
0.12
0.12
0.12
0.12
0.03
0g12
0.12
0.03
0.03
0.03
0.03
0.03
0912
0.03
0.03
0.03
0.03
0.03
0103
0.12
0.03
0.50

 

NO.
285
286
287
288
289
290
291
292
296
294
295
296
297
298
299
600
601
602
606
604
605
606
607
608
609
310
611
612
613
314
515
616
617
318
619
620
621
622
626
624
625
626
627
_628
629
660
661
662
666
664

2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4

IUENT

RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR

3.
3.
3.
3.
3.
3.10
3.11

€020\Tb-

5.17
5.19

5.21

117

068, FREQ
4577,3433
4578,0579
4578,7714
4580,2016
4580.9248
4581.6371
4582,3548
4583,0684
4583,7833
4584,4892
4585.2070
4585,9162
4586,6264
4587,3246
4588,0407
4588,7469
4589,4586
4583,3854
4584,0991
4584,8264
4586.2600
4586,9730
4587,7021
4588,4057
4589.1240
4589,8452
4590,5452
4591.9598
4592,6623
4593,3679
4594,0921

,4594,7833

4595.5045
4596,1957
4596,9215
4599.0083
4590,1197
4590,8389
4592,2640
4592,9683
4593,6840
4595,1176
4595,8257
4596,5446
4597,9716
4598,6701
4599.6722
4600.0848
4600,7945
4601,4998

ORS'CALC

“000042
60,0067
.0,0096
“0.0107
I'000022
no.0041
0.0001
0.0007
0.0033
«0.0025
0.0042
0.0030
0.0064
.0,0075
0.0001
'0.0014
0.0032
”0.0124
40,0156
.0,0046
F000019
“0.0035
0.0116
0.0019
0.0075
0.0166
0.0051
-0.0012
.0,0082
'000114
0.0046
v0.0116
0.0029
~0.0120
0.005B
.0,0162
0.0072
0.0102
0.0048
.o,0056
.0.0034
0.0046
0.0009
0.0086
0.0152

.0.0045_

.0,0019
0.0029
0.0056
0.0045

NT
0.12
0:50
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.03
0.03
0.03
0.03
0.12
0.12
0.12
0.03
0.03
0.03
0912
0.12
0.12
0.12
0.03
0.12
0.12
0.12
0.03
0.12
0.03
0.03
0.03
0.03
0.03

A0903

0.12
0.12
0.12
0.12
0.12
0.03
0.03
0.03
0903
0.03
0912
0903
0.03
0.03

‘ twitm'iid. 2"}

NO.
665
336
667
656
639
640
641
642
545
644
645
346
647
648
649
650
691
652
653
654
655
356
357
358
659
660
661
662
665
664
665
366
367
668
669
370
371
672
573
574
675
676
677
678
579
680
661
382
685
384

2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4

IUENT

RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR
RR

5.22
5,26
5,24
5,25
5,26
6, 6
6, 8
6, 9
6,10
6,11
6,12
6,16
6,14
6,16
6,17
6,18
6,19
6,20
6,21
6,22
6,24
6,25
6,26
6,27
6,28
6,29
6,60
6,62
6,66
7, 8
7, 9
7,10
7,11
7,12
7,16
7,14
7,16
7,17
7,18
7,19
7,20
7,21
7,22
7,24
7,25
7,26
7,27
7,28
7,29
7,60

118

083. FRFD
4602,1981
4602,9030
4603,5916
4604,2975
4605,0018
4596,7789
4598,2013
4598,9217
4599,6380
4600,3502
4601,0661
4601,7755
4602,4878
4603,8980
4604,6061
4605,3074
4606,0332
4606,7386
4607,4502
4608.1430
4609,5419
4610,2426
4910,9551
4611,6569
4612,3554
4613,0409
4613,7456
4615,1388
4615,8385
4604,1033
4604.8143
4605,5258
4606,2395
4606,9482
4607,6561
4608,3772
4609,7893
4610,4974
4911.2196
4611.9236
4612,6311
4613,3320
4614,0381
4615,4505
4616,1430
4616,8358
4617,5633
4618,2382
4618,9471
4619,6269

ORS'CALC

“090029
'000029
9090155
'090160
.090144
090055
’090018
090059
090067
090060
090097
0.0075
090059
-0.0007
.0.0015
.090053
090100
090087
090143
0.0013
90.0075
9090098
090004
"090022
.000014
9090153
'090102
90.0127
E090095
090085
090059
0.0041
090052
090019
90.0015
090090
090019
090015
090159
090128
0.0140
0.0092
090105
0.0154
090054
“090056
0.0229
~0.0024
090071
~0.0116

WT
0903
0.03
0403
0903
0903
0950
0912
0912
0912
0912
0903
0912
0112
0912
0912
0912
0903
0903
0912
0903
0.12
0903
0903
0903
0903
0903
0903
0903
0903
0912
0912
0912
0912
0903
0903
0.03
0.03
0903
0:03
0903
0903
0903
0903
0903
0912
0903
0.03
0903
0912
0903

 

"h. _ _ ____

NO,
685
386
687
688
689
690
591
692
596
694
695
396
597
698
599
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
451
462
433
434

2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4

IUENT

RR 7.61
RR 7.32
RR 7.35
RR 7.64
RR 7.55
RR 8.10
RR 8.11
RR 8.12
RR 8.13
RR 8.14
RR 8.16
RR 8.17
RR 8.18
RR 8.19
RR 8.20
RR 8.21
RR 8.22
RR 8.24
RR 8.25
RR 8.26
RR 8.27
RR 8.28
RR 8.29
RR 8.60
RR 8.32
RR 8.36
RR 8.34
RR 8.55
RR 8.36
RR 9. 9
RR 9.10
RR 9.11
RR 9.12
RR 9.15
RR 9.14
RR 9.16
RR 9.17
RR 9.21
RR 9.22
RR 9.24
RR 9925
RR 9.26
RR 9.27
RR 9.28
RR10.16
R810.14
RR10.16

RR10.17,

RR10916
RR11911

119

085. FRED
4620,6416
4621.0296
4621,7314
4622,4122
4623.1026
4611,3611
4612,0740
4612,7757
4613,4896
4614,1926
4615,6419
4616,3578
4617,0569
4617,7591
4618.4612
4619,1712
4619,8733
4621,2750
4621,9649
4622,6766
4623,3726
4924,0716
4624.7559
4625,4676
4626,8525
4627,5445
4628,2278
4628,9217
4029.6255
4616,4211
4617.1314
4417,8425
4618,5613

4619,2750,

4619.9827
4621,4097
4922.1151
4624,9363
4625,6402
4627,0488
4627,7620
4628,4484
4629.159?
4629,8485
4625.0039
4625,7264
4627,1279
4627,8380
4628,5651
4629,2432

OHS-CALC

0.0020
-0.0066
0.0022
“090122
-0.0162
0.0031
0.0037
“090093
P090054
'030107
0.0201
0.0194
0.0149
0.0110
090158
090135
0.0086
90.0036
0.0038
0.0023
090016
40.0130
0.0004
90.0050
~0.0114
90.0228
00.0226
60.0117
90.0057
90.0081
-0,0091
90.0017
090013
90.0010
0.0051
0.0057
0.0032
0.0030
0.0060
0.0115
0.0061
0.0146
0,0040
0,0048
0.0176
0.0020
0.0046
0.0291
-0.0046

“T
0903
0103
0.03
0.03
0.03
0.12
0912
0912
0912
0.12
0912
0903
0903
0.03
0903
0903
0903
0912
0903
0.03
0.12
0912
0.03
0.03
0903
0.03
0.03
0.03
0.03
0912
0912
0912
0912
0912
0912

_0912

0.12
0.03
0903
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.12

 

N0.
465
458
467
466
469
440
441
442
446
444
445
446
447

2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4
2NU4

IUENT

RR11.12
R811116
RR11014
R811915
RR11916
RR11017
RR12.12
8812915
RR12.15
RR12916
RR12.17
RR12918
RR12.19

120

OBS. FREQ
4629,9569
4660.6602
4631.3779
4632.0803
4632.782?
4633.4894
4635,5683
4636,2751
4637.7007
4638.4083
4669.1136
4639,8145
4640.5095

ODS'CALC

.0.0017
.0.0084
-0.0001
’0.0062
-0.0121
“090120
-0.0032
.0.0066

0.0018

0.0025

0.0007
.0.0043
.-0.0144

9T
0912
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12

 

 

R E S U L T S

VOCDVO‘U‘bOJNO-‘O

NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4

0 F

IDENT

PP13.15
P913017
PP13.14
PP13.13
PP12027
PP12026
PP12.25
P912.22
P912021
P912gl9
PP12.18
PP12217
PP12915
PP12014
9P12.13
P912.12

N

A

PP11026 '

PP11125
PP11.25
P911022
PP11.21
PP11.20
PP11.18
PP11.17
PP11515
PP11114
P211015
P911012
PP11011
PP10127
P910026
PP10025
PP10.24
PP10.23
PplDozl
PP10020
P910019

U

A

4

PPENDIX

S I N G L
O F 3

085, FREQ
2238,1461
2238,6528
2240,2005
2240,7113
2237,5325
2238,0451

'2238,5516

2240,1022
2240,6178
2241,6404
2242,1611
2242,6710
2243,7338
2244,2154
2244,7375
2245,2479
2242,0391
2242,5653
2243,5893
2244,0991
2244,6169
2245.1193
2246,1568
2246,6706
2247,6988
2248,2099
2248,7185
2249,2431

”2249,7539

2245,5153
2246,0379
2246,5417

'2247,0601

2247,5686
2248,6023
2249.1150

'2249,6311

121 *

E

B A N D

D 3 B R

OBS'CALC

0.0108
0.0020

"0.0068

0.0037
0.0125
0.0093
0.0003
0.0047

0.0051"

I0.0027
0.0030
90.0021
0.0310
n0,0022

' "0.0054

0.0012
0.0056
010160
0.0086
000028
0.0050
90.0080
00.0012
00.0027
l0.°0‘6
.0.0085

I0.°147 --

I0.0048
00.0086
0.0234
0.0299
000176
000200
000125
000105
000115
000119

F

”T
0.03
0.03

0.03 w

0.03
0.03
0.03
0.03
0.03

0.12 '

0.03
0.03
0.03
0.03
0.03

0.03
0.03
0.03
0.03
0'03

I

.0‘03“

0:03'

0.03
0.03
0.03
0.03
0.12
0.12
0.03

0103 H

0.03
0.03
0.03

0.03'm

0.03
0.03
0.12
0.03

T

 

5

pm

 

 

NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4

NU4 PP

NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4

NU4'

NU4
NU4
NU4

NU4'

NU4
NU4
NU4
N04
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4

30”?

IDENT

PP10018
PP10017
PP10015
PP10.14
PP10013
PP10.12
PP10.11
PP10. 10
9. 35
PP 9. 34
PP 9.33
PP 9.52
PP 9.30
PP 9.29
PP 9.20
PP 9.27
PP 9.25
PP 9.26
PP 9.24
PP 9.25
PP 9.22
PP 9.21
PP 9.20
PP 9.19
PP 9.18
PP 9.17
PP 9.10
PP 9.14
PP 9.13
PP 9.12
PP 9.11
PP 9.10
9.29
PP 7.24
PP 7.22
PP 7.21

083, FREQ
2250,1420
_2350,6466
2251}679§
2252,1893
2252,6990
2253,2170
2253,7386
2254,2544
2245,3752
2245,8885
2246.404.
2246,9183
2247,9425
2248,4630

2240:9502.

2249,4615
2250,5143
2250,0025
2251,0234
2291,5490

'225230530"

2252,5354
2253,0302
2253,3034
2254,1055
2254,3153
'222221324‘
2256,1673
2253,3324
2257,1931
2257,7030
2253,2212

"225877339'222

2258,7936
2259,8382
2260,3463
2260:0664'
2261.3862
2262,4210
‘2262,9415
2263,9650

2263.456? ’W'
2364,4801
“”225!~

4
2265,5199
2266,0301
2266,5597
2271.1906

_3?!9;?i§i--

4 .o. 0009

' .0.024U’

_w:!:93}9__

 

OBS-CALC HT
0. 0075

.0. 0036 0.03

.030032270703“‘P

00.0066
.0,0140
I0.0009
.0. 0021

0.03

0112
0.12
0.12
0. 0559 0; 00
0. 0624 0. 00
0:061?
0.0587
0.0495
0005;,4
'2070320y
0.0308
0.0325
0.0434
0.0336 0.00
.0410 0. 00

0; 0295 ~0_00
0. 0251 0. 00
0:0240 0:00
000313 0000
0.0176
0.0122

0. 00
0:00
0100
0'00
0.00
0.00

0.037277

0.122

0. 00 7

 

FUTUU“'~

 

0.01322
0.0173
0.0172
000158
020103“
0.0111

0700
0.00

0.00
0.00

70.0077
0.00 ”’2

 

030021
'000301

0.00
0.00

.00027‘
.030238
.0. 0203

0'00
0. 00

.0. 0170 0. 00

' I0u0130' 01°0'**”“”"‘

I0.0206 0'00

0.12
I u I
I0I012a 0.12
.020097 0312
30.0031 0.12

"0.0037 0I03

Io.°139
“0

0?00"’2'V4—2

{02.01431 02.0Ti

3223“”

70700.7774222"’" W

“““236I79002 00.0??3"0. 00 '

 

NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4

NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4

PP
PP

IDENT

6.20
6.19
6.15
6.17
6.14
6016
6.12
6.11
6.10
6. 9
6. 7
6. 6
5.21
5.20
5.19
5.18
5.17
9.16
5.14
5.16
5.12
5.11
5.10
5. 9
5. 7
5o 6
5. 5
4.20
4.19
4.15
4.17
4.16

4.If "'"

4.15
4.12
4611
4. 9
4, 7
4. 6
4. 5
4. 4
3.28
3.27
3.26
3.25
3.24
3.22
3.21
3.20
3.19

123

083, 7883
2264,7451
2265,2741
2265,7814
2266,8114
2267,8472
2268,8711
2268,8852
2269,4048
2259,9172
2270,4825
2271,4642
2271,9765
2268,0980
2268,6186
“2269,1312
2269,6517
2270,1700
2270,6906
2271,7162
2272,2362

2273,2702
2273,7970
2274.3003
2275,3454
2275,8630
2270.37UF
2272,4568
2272,9743
2273,4914

2274,0123'

2274,5326
2275,5690
2276,0865
2276,5923
2277,1044
2278,1417
2279,1680
2279,6890
2280,2060
2280,7105
2272,1140
2272,6342
2273,1543
2273,6712
2274,1894
2275,2239
2275,7379
2276,2683
2276,7840

OBS-CALC

.0,0258
-0.0133
'000225
'0.°°88
9000211
I000129
.0,0144
00.0102
9000131
.0,0129
'0'0109
I0.0132
.0,0122

0.0020

0003

0.03
0103
0.03
0.03
0.03
0.03
0.03

0112
0.12

0112‘
0112

7 0103"

0112
0.03
0112
0112
0003
0.12
0.03
0103
0.12
0.03
0112
0.12
0112
0.12
0.03

 

 

 

 

N0,
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
153
157
158
159
160
161
162
183
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187

NU4
NU4
N04
NU4
NU4
~04
NU4
~04
NU4
NU4
NU4
NU4
~04
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
~04
NU4
NU4
NU4
N04
N04
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4

IDENT

PP 3015
PP 3,17
PP 3,16
PP 3,18
PP 3,13

A124

OBS, FRED
2277,2938
2277,8149
2278,3258
2279,8682
2279,8759
2280,3995
2280,9130
2281,4261
2281,9391
2282,9787
2283,4894
2284,0116
2284,5000
2276,9509

2277TI‘I0'"

2277,9812
2278.5071
2279,5345
2280,0495
2280,5578

ZESITUUFT‘

2281,5988

2282,1255'

2288,1596

2283,8737’

2284,1815

"2288;7007

2285,2247
2285,7294
2286,7684
2287,2823
2287,8034
228f'

I
2282,2605

2283,2810'

2283.812,

‘2284,3277_"‘

2284,8275
2283}
2289,8789

“2286,9121

2287,4272
2287,9286
2288,9817
2289,4868
2290,5250
2291,0302
2291,5511
2307,6975
2307,3015

OBS'CALC
'000052
00.0010
I0,0067

0,0038
.0'0057
080019
I0,000‘
no.0030
I0,0054
090059
'000003
0,0073
00,0107
000121

"7'0}0010"

080061
0101‘!
0,0061
0,0036

WT
0,12
0,12
0,12
0,12
0,12
0,12
0,03
0,12
0,03
0,03
0,0377
0,03
0,03
0,03
01:21,

0,03
0,03

0,03

 

 

N0.
188
189
190
191
192
193
194
199
196
197
198
199
200
201
202
203
204
205
206
207
“208
209
210
211
212
213
214
215
216
217
218
221
”222
223
224
225
226
244
227
228
229
230
231
232
233
234
235
236
237
238

NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4

125

IDENT 035, FREQ 085*C4LC WT

RR 2, 4 2307,7993 0,0063 0,12
RR 2, 5 2308,3107 0,0059 0,03
RR 2,'7 2309,3233 .0,0041 0,12
RR 2, 5 2309,8464 0,0051 0,12
RR 2, 9 2310,3478 00,0010 0,12
RR 2,10 2310,8660 0,0070 0,12
RR 2,11 2311,3728 0,0090 0,00
RR 2,15 2313,4089 0,0041 0,03
RR 2310 2513,9141 0,0011 0,03
RR 3, 4 2311,4487 0,0021 0,03
RR 3, 5 2311,9493 00,0070 0,03
RR 3, 7 2312,9699 00,0009 0,03
RR 3, 3 23(3,477SW 00,0120 0,03 W
RR 3, 9 2313,9926 00,0073 0,03
RR 6,17”Rmm“3325,8390mmfl—3090175 '0i12_m“97;(
RR 6,16 2323,3370 30,0124 0,12
RR 6,15_” —”2027,8275mw”m;0,0142 0,12H*
RR 6,14 2327,3105 '0,0177 0,12
RR 6,13 2326,5289 0,0007 0,12
RR 6,12 2326,3089 00,0106 0,12
RR 5,11‘“ ““232597039_uu—7090195 ”v.12.“
RR 6,10 2025,2724 00,0268 0,03
RR 6, 9 '2324,7024_‘WW;0,0071 0,123—
RR 6, 5 2324,2723 00,0072 0'50
RR 60—7 7 2323,7530 “90,0031 0,50_—
RR 8, 8 2331,3546 0,0209 0,12
RR 8,'9 2331,8585' .010131 “0112"“
RR 8,11 2332,8803 0,0104 0,12
RR 3,13 2333,8937 0,0150 0,12
RR 3,19 2304,9027 0,0162 9903
RR 8,15 932334,90030 03070004wm0112m“
RR 9, 9 2335,3496 0,0176 0,00
RR 9,1I_UM_“2336,3785ummwm070303—_0700_fl‘
RR 9,13 2337,3790 0,0100 0,00
RR 9,14’mmfimz337,8357_lW0m0,0155w_0,00 “
RR 9,15 2338,4011 0,0233 0,00
RR 9,16 2330,9180 —0,0319 0,00-r
RR 9,18 2039,9188 0,0224 0,03
RR 9,20 ' 2340,9374 000309” 0,00flu
RR 9,21 2341,4396 0,0279 0,00
RR 9,22 2341,9348 '0a0189 "0,00—
RR 9,23 2342,4344 0,0148 0,00
RR 9,24 7 2342,9363 0,0134 0,00—
RR 9,26 2343,9399 0,0117 0,00
RR 9,20 2344,9120 'I0g0195 'U,00“'
RR 9,29 2345,4149 I0o0176 0,00
RR 9,31 2346,4055 00,0275 0,00
RR 9,32 2348,9146 c0,0100 0,00
RR 9,33 2347,4038 ' 00,0278 0,00
RR 9,34 2347,9114 00,0187 0,00

 

 

mvcv- "c-u-wW—w- .0, . , ._

N0,
239
219
220
240
241
242
243
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265

NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4
NU4

IDENT

RR 9,35
RR10,11
RR10,13
RR10,14

0010,15—

RR10016
0010,17
RR11011
RR11a13
RR11,14
R911015
RR11016
RR11,19
RR11021
RR12,12
RR12J14
RR12015
RR12016
R012,17
RR12018
RR12,19
RR12,20
RR12,23
RR12a24
RR13,15
RR13a16
R913a10
R013o22

126

033. FREQ OBS-CALC
2348,3876 00,0406
2339.8142 0.0120
2340,8903 000228
2341,3327 0,0073
2391,8417 000098
2342.3456 0.0073
2992,5533 000037
23,3.2354 0.007s
2344.2572 0.0137
2344.7590 0.0083
23‘5-2595 * 0.0020
2345,7679 0,0041
2347:2805 0.0003
"mm, 2348.2927 0.0035
‘"?3?7.1013"“““:0.5254
23‘8-1422 -0.0051
2348.6535 .0.0004
2349.1612 0.0012
2349.6545 -0.0108
2350.1752 0.0044
2350,6586 .o.ou7u-
2351,1791 I0,0007
2352.697, 0.0072
2353,1904 00,0019
2352.023: 0.0024
2352,5269 0.000,
2353,5385 “ o,au,o
2355,5497 .o.oooz

HT
0,00
0,03
0,03
0,03

0,03"

0,03
0,03
0,03
0,03
0,03
0,03"
0,03
0,03
0,03
0,030"
0,03
0,12
0,03
0,12
0,03
0,03
0,03
0,03'
0,00
0,03'
0,03
0,03
0,03

 

 

 

   

”'TITI'IMIWIWMU]fiEflIlflflflW)flflMflj7fllT

1293