1".“ a a .. v

Michigan State
University

 

This is to certify that the

thesis entitled

Analysis of Infrared Spectra of Asymmetric
Rotor Molecules with Application to HDSe,

325' and HZSe

presented by

James Ridgeway Gillis

has been accepted towards fulfillment
of the requirements for

 

 

 

Major professor

Date October 10, 1979

 

0-7639

 

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ANALYSIS OF INFRARED SPECTRA OF ASYMMETRIC
ROTOR MOLECULES WITH APPLICATION

TO HDSe, H S, AND H Se

2 2

by

James Ridgeway Gillis

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics

T979

.ABSTRACT

ANALYSIS OF INFRARED SPECTRA OF ASYMMETRIC
ROTOR MOLECULES WITH APPLICATION

TO HDSe, H23, AND HZSe

by

James Ridgeway Gillis

The infrared vibration-rotation spectra of the 2v1 band of HDSe in
the 2.2 um region, the 202, v],and v3 bands of H25 in the 4 pm region
and the 202, v], and 03 bands of H25e in the 4.5 um region were run on
the Michigan State University high resolution near-infrared spectro-

photometer at resolution limits near 0.05 cm'].

Data were recorded on
magnetic tape with the aid of an on-line PDP-lZ minicomputer. The
spectra were digitally smoothed before calibration and line position
measurement. Well resolved lines are believed to be measured to a
precision of :0.002 cm"1 relative to the calibration standards.

The analysis of the type B 2v1 band (Se-H stretch) of HDSe is the
first reported high resolution study of any vibration band of this
molecule. Since there are no nearby vibrational bands with which 201
can interact, the band is apparently unperturbed. Three hundred five
weighted transitions belonging to the five most abundant isotopes of
selenium (atomic weights 76, 77,78, 80, and 82 amu) have been assigned and
analyzed simultaneously using Typke's reduced Hamiltonian. Ground state
constants were obtained from a simultaneous least squares fit of our

ground state combination differences and published microwave data.

Upper state constants were obtained from a least squares fit of our

spectral lines with the ground state constants held fixed. The standard
deviation of observed minus calculated frequencies is 0.0044 cm‘].

The bands v1 and v3 of H25 and HZSe are coupled by a Coriolis
interaction,and the bands 202 and v] are coupled by a Fermi resonance.
Our analyses of H25 and HZSe have included the Coriolis interaction,
but because the band centers of 202 and v] are separated by over 250 cm‘1
for H25 and for HZSe, the effects of the Fermi interaction do not vary
in such a way that they can be determined from our data. Therefore, 202
was treated as an unperturbed band and v1 and 03 were treated as being
perturbed only by the Coriolis interaction. All rotational analyses
were done using Typke's reduced Hamiltonian. As with HDSe, ground state
constants were obtained from a simultaneous least squares fit of ground
state combination differences and microwave transitions. Upper state
constants were obtained from a least squares fit with upper state con-
stants allowed to vary and ground state constants fixed.

Three hundred fifty weighted transitions of 202 of H25, including

343 have been identified and fitted with a stan-

dard deviation of observed minus calculated frequencies of 0.0040 cm-].

45 transitions from H2

Approximately 260 transitions from v1 and l30 transitions from 03 were
simultaneously fit with a standard deviation of 0.0052 cm'1.
Five hundred thirty-seven weighted transitions from all five
isotopic species of 2v2 of HZSe were fit with a standard deviation of
0.0038 cm']. Approximately 900 transitions from all five isotopic
species of v] of HZSe and 600 transitions from all five isotopic species

of 03 were simultaneously fit with a standard deviation of 0.0082 cm‘].

TO MY PARENTS

ANN S. AND WILL M. GILLIS

ii

ACKNOWLEDGMENTS

I wish to express my appreciation to Professor T. H. Edwards for
his guidance, support, and encouragement throughout the course of this
research. I thank Professor P. M. Parker for an excellent molecular
spectroscopy course and for many helpful discussions. My fellow
graduate student Mr. D. E. Bardin has given me much help with the
spectrometer and has contributed to many useful discussions. The
Michigan State University Physics Department has supported me with
teaching assistantships throughout my graduate study. A special thanks
goes to Professor J. S. Kovacs for giving me teaching assignments which
have been both enjoyable and educational and have allowed me to budget
my time efficiently for doing research.

Scientific Gas Products, Inc. has generously donated the sample of
high-purity H25 used for the spectrum analyzed in this work.

Mrs. Delores Sullivan is responsible for the competent manner in
which this dissertation has been typed. All errors, of course, are the

responsibility of the author.

TABLE OF CONTENTS

Page
LIST OF TABLES . . . . . . . . . . . . . . . . . vi
LIST OF FIGURES . . . . . . . . . . . . . . . . . ix
INTRODUCTION . . . . . . . . . . . . . . . . . . l

CHAPTER
I. ASYMMETRIC ROTOR MOLECULE VIBRATION-ROTATION HAMILTONIANS 3

The Second Order Hamiltonian . . . . . . . . . . 3

Fourth Order Hamiltonians . . . . . . . . . . . 7

Coriolis Coupling . . . . . . . . . . . . . . ll

Fermi Coupling . . . . . . . . . . . . . . . 12

II. APPLYING THE HAMILTONIAN . . . . . . . . . . . 14
Evaluation of the Hamiltonian for Unperturbed

Vibrational States . . . . . . . . . . . . l4

Coriolis and Fermi Interactions . . . . . . . . . 2l

Isotopic Substitution . . . . . . . . . . . . 26

Fitting Observed Spectra: Computer Programs . . . . . 27

III. CALCULATION OF INTENSITIES . . . . . . . . . . . 30

Selection Rules . . . . . . . . . . . . . . 3O

Dipole Transition Intensities . . . . . . . . . . 3l

IV. DATA COLLECTION AND EXPERIMENTAL DETAILS . . . . . . 38

Experimental . . . . . . . . . . . . . . . 38

Data Processing . . . . . . . . . . . . . . 42

Calibration . . . . . . . . _. . . . . . . . 44

iv

CHAPTER Page

V. ANALYSIS OF 2V OF HDSe . . . . . . . . . . . . 52

1
General Comments about the Systematic Analysis of

Asymmetric Rotor Molecule Spectra . . . . . . . 69

VI. ANALYSIS OF 2v2, 0], AND 03 OF H23 . . . . . . . . 75

VII. ANALYSIS OF 202, 0], AND 03 OF H25e . . . . . . . . l06

VIII. CONCLUSION . . . . . . . . . . . . . . . . l26

REFERENCES . . . . . . . . . . . . . .1 . . . . l28
APPENDICES

A. NONVANISHING ANGULAR MOMENTUM MATRIX ELEMENTS . . . . 131

B. COMPUTER PROGRAM INTCALl . . . . . . . . . . . l35

C. ASSIGNED TRANSITIONS OF 201 OF HDSe . . . . . . . . l8O

D. ASSIGNED TRANSITIONS OF 202, 0], AND v3 0F H25 . . . . 188

E. ASSIGNED TRANSITIONS OF 20 AND 0 OF H Se . . . . 205

2’ Vi’ 3 2

Table

TO

IT

l2

l3

l4

l5

16

LIST OF TABLES

Molecular Axes Identification
Wang Symmetrized Basis Functions

+, and 0-

Classification of the Submatrices E+, E', 0
Selection Rules by Parity Change of K_ and K+ .
Symmetric Top Direction Cosine Matrix Elements
HDSe 201 Experimental Conditions

HZSe 202, v], and 03 Experimental Conditions

H25 202, v], and 03 Experimental Conditions

Molecular Constants for 2v1 of HDSe for Typke's Reduced

Hamiltonian

Partial Correlation Coefficients of HDSe Ground State
Constants for Typke's Reduced Hamiltonian

Partial Correlation Coefficients of HDSe 2v1 Constants
for Typke's Reduced Hamiltonian . . . . .

Molecular Constants for 201 of HDSe for the Planar Form
of the Hamiltonian

Partial Correlation Coefficients of HDSe Ground State
Constants for the Planar Form of the Hamiltonian .

Partial Correlation Coefficients of HDSe 20] Constants
for the Planar Form of the Hamiltonian . . .

Molecular Constants for 2v1 of HDSe for Watson's
Reduced Hamiltonian

Partial Correlation Coefficients of HDSe Ground State
Constants for Watson's Reduced Hamiltonian .

vi

Page

l7
19
BI
34
49
50
ST

6O

61

62

63

64

65

66

67

Table Page

l7 Partial Correlation Coefficients of HDSe 2v1 Constants

for Watson's Hamiltonian . 68
l8 Transitions to High J, High K_ Levels of 03 of H25. . . . 79
T9 Molecular Ground State Constants for H25. . . . . . . 83
20 Partial Correlation Coefficients for the Ground State 84

of H25. . . . . . . . . . . . . . . . . .
2l Molecular Constants for 2v2 of H25. . . . . . . . . 86
22 Partial Correlation Coefficients for 202 of H28. . . . . 87
23 Molecular Constants for v] and v3 of H28. . . . . . . 9O
24 Partial Correlation Coefficients for v] and v3 of H28. . . 9l
25 Molecular Constants for 202, v], and v3 of H25 with

FER = l5. . . . . . . . . . . . . 95
26 Partial Correlation Coefficients for 202, v1, and v3 of

H23 with FER = l5. . . . . . . 96
27 Molecular Constants for 202, v], and v3 of H25 with

FER = 30. . . . . . . . . . 98
28 Partial Correlation Coefficients for 202, v], and 03 of

H25 with FER = 30. . . . . . . . . 99
29 Molecular Constants for 2v2, v], and 03 of H23 with

FER = 45. . . . . . . . . . . . . . 101
30 Partial Correlation Coefficients for 202, v], and 03 of

H25 with FER = 45. . . . . . . . l02
3l Calculated Energy Levels in cm-1 and Wave Function

Mixing for H25 for J = 9 and FER = 30. . . . . . . . l04
32 Calculated Energy Levels in cm.1 and Wave Function

Mixing for H20a for J = 9. . . . . . . . . . . . lOS
33 Molecular Ground State Constants for HZSe. . . . . . . ll3
34 Partial Correlation Coefficients for the Ground State

of H Se. . . . . . ll4

2

35 Molecular Constants for 202 of HZSe. . . . . . . . . ll6

vii

Table

Page
36 Partial Correlation Coefficients for 202 of HZSe. . . . ll7
37 Molecular Constants for v] and 03 of HZSe. . . . . . . 120
38 Partial Correlation Coefficients for v] and v3 of HZSe . . lZl

viii

Figure

TO.

ll.

LIST OF FIGURES

Energy Level Diagram .

The Total Hamiltonian for a Given J for Fermi and
Coriolis Coupled Bands 0 , v , and 20 of H S 0r

1 3 2 2
HZSe . . . . . . . . . . . . . . .
The Form of the Hang transformed total Hamiltonian
for Fermi and Coriolis coupled bands 0], v3 and 202
of H25 or H25e . . . . . . . . . . . .

The Form of the E3 E F Wang Submatrix
for J = 4 . . . .

F

 

 

E202
Spectrometer Signal Processing Electronics
Schematic representation of a typical spectrum with
calibration gases and fringes. Fringe spacing
exaggerated . . . . . . . .

Observed-calculated values for a linear calibration fit

of H Se run l9. Standard deviation of fit = 0.004l cm‘1

2

Observed-calculated values for a quadratic fit of HZSe
run 19. Standard deviation of fit = 0.0017 cm-l.

l

I to 4750 cm- .

The spectrum of HDSe from 4500 cm'

Molecular geometry and principal axes of HDSe as
inferred from HZSe geometry

Absorption lines of the isotopic species of HDSe for

the unresolved doublet 9 7 3 - 8 6 2 and 9 7 2 - 8 6 3
near 47l4 cm' . . . . . . . . . . . .

ix

Page
20

22

23

24

41

45

46

46
53

55

58

Figure

12

T3

T4

15

T6

The 6 3 4 - 5 3 2 ground state combination difference
from some type 8 band transitions

The spectrum of 202, v], and 03 of H23 from 2220 cm-
to 2830 cm']. Impurities in the sample are identified
as CO 0, 002 A, and HCl ' .

The form of the Hamiltonian matrix for 03, v1 and 202 .

The spectrum of 202, v], and 03 of HZSe from I930 cm’]
to 2620 cm'l. . . . . . . . . . . . . .

Absorption lines of the isotopic species of 5 O 5 -
6 l 6 of 202 of HZSe near 2009 cm' . . . .

.l.

Page

71

77

81

107

Ill

INTRODUCTION

The infrared spectra of bent triatomic asymmetric rotor molecules
have been of interest for many years. Analysis of these spectra allows
determination of much useful information, including a positive identifi-
cation standard for the molecules studied, values of molecular energy
levels, and fundamental physical information about the molecule such as
molecular geometry, dipole moment, potential functions, and force con-
stants. Practical application of this information ranges from con-
struction of gas lasers to atmospheric pollution monitoring to identifi-
cation of molecules in interstellar space. However, only for the last
fifteen or so years have experimenters been able to carry out detailed
and precise analysis of the vibration-rotation bands of these molecules.
During this period Hamiltonians have been developed which permit the
precise and accurate prediction of energy levels and high speed digital
computers necessary to do the extensive calculations necessary have come
into widespread use.

In this dissertation the vibration-rotation spectra of the 2v1 band
of HDSe in the 2.2 pm region, the 202, v], and 03 bands of H28 in the
4 pm region, and the 202, v1 and 03 bands of HZSe in the 4.4 pm region
are analyzed.

The analysis of 201 of HDSe is the first high-resolution study of
any vibration-rotation band of HDSe. The band is not affected by any

resonance-type perturbations, which somewhat simplifies its analysis.

2

However, since selenium has five stable isotopes with abundances ranging
from 8 to 50 percent, each transition in the spectrum has five components.
A sufficient number of these components have been measured to allow
simultaneous analysis of the transitions of all five isotopic species.

The 01 and 03 bands of both H25 and H28e are coupled by a Coriolis
resonance and 202 and 01 are coupled by a Fermi resonance. The effect
of these resonances is to shift vibration-rotation energy levels and,
hence, spectral line positions, thus complicating the analysis. In
addition, because selenium has five isotopes, the H25e spectrum has a
great many lines.

The steps needed for the analysis of the spectra in this disserta-
tion start with an outline of the development of suitable Hamiltonians
in Chapter I. The procedure for using these Hamiltonians is described
in Chapter II. The method for calculating spectral transition intensi-
ties for unperturbed vibration-rotation bands is developed in Chapter III.
Chapter IV contains the particulars of experimental detail and data
collection. The analysis of the spectra of HDSe, H25, and H2Se and the
molecular constants determined from the analysis are given in Chapters

V thru VII.

CHAPTER I

ASYMMETRIC ROTOR MOLECULE VIBRATION-ROTATION HAMILTONIANS

In order to analyze the vibration rotation spectra of the bent
triatomic molecules studied in this dissertation, Hamiltonians capable
of predicting ground and excited state energies to a few thousandths of
a wavenumber are necessary. The development of such Hamiltonians is

sketched in this chapter.

The Second Order Hamiltonian

(1)

Darling and Dennison showed that the vibration-rotation

Hamiltonian for a general polyatomic molecule may be given by

l

NI"

H:

NI

ale WPa-paiuasu‘ (PB-paini + ;- g nipgoui + v (1-1)
where
a,8 correspond to the x, y, or z axes of the equilibrium inertia
tensor of the molecule with the origin at the center of the
mass of the molecule;
P is an operator corresponding to the a component of the total
angular momentum vector of the molecule;

is an operator corresponding to the a component of the vibra-

tional angular momentum of the molecule;

3

pgc is an operator for the component of linear momentum conjugate
to the normal coordinate 050 such that p50 = 2%T'gfiggf;
pas are certain functions of the instantaneous moments and products
of inertia;
p is the determinant of the “d8 ;
V is the vibrational potential energy of the molecule.
Since Schroedinger‘s equation Hw = Ew can not be solved analytically for

any Hamiltonian for asymmetric rotors, the Hamiltonian is normally

expanded in orders of magnitude:

_ 2
H - H0 + AH] + x H2 + . . . (1-2)

where HO approximately represents the rigid-rotor, harmonic-oscillator

Hamiltonian,
2 2
P P
1 0t 1 i so 2
H =— Z _+—hx2 X -—+q (1-3)
0 2 a=x,y,z la 2 s so ‘fiZ so]

 

where the A: are the normal frequencies of the molecule. The Hamiltonian
is then subjected to one or more unitary contact transformations of the

MSHe'mswo transform successive orders of the expansion of the

form e
Hamiltonian such that the matrix elements of that order are vibrationally
diagonal in a harmonic oscillator basis. Goldsmith et al.(2’3) have
shown in detail how this procedure can be carried out. It is found that
one transformation is necessary to transform the rotational Hamiltonian
through order two (terms through fourth power in angular momentum com—
ponents), but a second transformation is necessary to transform the

rotational Hamiltonian through order four (terms through sixth power in

angular momentum components).

4)

Chung and Parker( have shown that the asymmetric rotor Hamiltonian

through order two may be expressed as

H = HV + xpi + YP$ + 2P3
+ 4'Txxxxpi + 4'Tyyyypg + 4'TzzzzP:
+ it ‘yyzz<P§P§+P§P§> + i Txxzz<P§P§+P§P§>
+ 211. Txxyy(PiP32/+Pyzlp>2<) + % Tyzyz(Psz+PzPy)2
+ ‘4’WL-xzxzwxpzwsz)2 + 4'Txyxy(PXPy+PYPX)2 (1.4)

where

H is the pure vibrational Hamiltonian, considered to be constant
for a given vibrational state;

X,Y, and Z are inversely proportional to the principal moments of

inertia of the molecule; i.e. X== 3 , etc.;

8n CIX

 

and the T's are equilibrium second order centrifugal distortion
constants.
For planar asymmetric rotors only seven of the nine taus are non-zero,
and of these, only four are linearly independent. To facilitate reduc-
tion of (1-4), a set of body-fixed axes (a,b,c) is conventionally
associated with the molecular (x,y,z) axes such that A:>B>>C where

A = g1 , etc. For planar molecules, fiL-+ éL-= éL-where the subscript
e e e

8n CIa

 

e refers to the equilibrium configuration of the molecule and the mole-
cule lies in the ab plane. Evaluating momentum operators in the rigid

rotor wave function basis wJK and applying the commutation relation

6

[Px’Py] = - iPz and the planarity relations of Dowling(5) and Oka and
(6)

Morino leads to the planar form of the second order Hamiltonian
described by Moncur,(7) viz.,
- 2 2 2
H - Hv + APa + BPb + CPc

+ Taaaaoaaaa + Tbbbbobbbb + Taabboaabb + Tababoabab (175)

where
aaaa = 4'[P4+FZP4+T(P§PE+ PEPETJ
Obbbb =‘% [P4+52P4+s(p§p% nggi]
0aabb=i£2rspfifip§P§P PPE PEWPEE PP: innpfipiwipin
Oabab =‘% [2(PEP6+PEP§)‘2P2+5PE]
and
= cg/A: S = 62/3:

When working with this Hamiltonian, the momentum operators must be
identified in terms of (x,y,z) with the appropriate permutation of
(a,b,c). Thus, the momentum operators will have a different form
depending on whether the molecule is oblate (K = g%§%§E-> l) or prolate
(K < l). Now, (a,b,c) may be associated with (x,y,z) in six possible
ways as shown in Table l. Conventionally, the Ir representation is
chosen for prolate molecules and the IIIr representation for oblate

molecules because they yield right hand coordinate systems and diagonal

Hamiltonian matrices in the prolate and oblate symmetric top limits,

Table 1

Molecular Axes Identification

 

 

 

Body-Fixed Axis Molecular Axis
x b c c a a b
y c b a c b a
z a a b b c c
Representation 1" IP IIP 119' In" 1111

 

 

respectively. This is an advantage because the more nearly diagonal the
Hamiltonian matrix is, the more quickly and accurately it may be diago-
nalized numerically. Unfortunately, when applying the planar Hamiltonian,
A , B , and Ce usually are not known so most workers use ground state

e e
values for calculating r and 5.

Fourth Order Hamiltonians

 

Kneizys, Freedman, and Clough(8) showed that the asymmetric rotor
Hamiltonian for the orthorhombic point groups (02v, 02, and 02h) through

sixth power in angular momentum can be written in the form

H = xpi + vpi + ZPE (1-6)
+ TXXP: + Tny3 + TZZP: + Txy(PiP§+P§Pi)
+ < + opinion
+ ¢xxx g + ¢yny$ + $222 2 + ¢xxy(P:P§+P§P:)
+ ¢XXZ(P:P§+P§Pfi) + a yx(P3Pi+PiP§) + dyyZ(P:P§+P§P§)
waxwipiwipfi) + thaw + Mindanao .
Watson(9) later showed that this Hamiltonian may be used for asym-

metric rotors of any point group. However, not all the constants in
(1-6) are linearly independent of one another; only five of the six T's

and seven of the ten o's are linearly independent. Using two contact

transformations, Watson(]0) reduced (1-6) to a Hamiltonian containing

the requisite five P4 terms and seven P6 terms:

_ ~ 2 ~ 2 ~ 2
H - XPX + YPy + sz (1-7)

4 2 2 4 2 2 2
AJP - AJKP PZ - AKPZ - 26JP (PX-Py)

2 2 2
0K[PZ(Px-Py) + (P

6
HJP + HJK

4 2

4 2
P Pz + H

PZP + HKP

6

+

KO

4 2 2 2 2 2 2 2 2 2
ZhJP (PX-Py) + hJKP [Pz(Px-Py) + (PX-Py)PZ]

+

4 2 2
hK[PZ(PX-P )

+

2 2 4
+ (PX-Py)PZ] .

This reduction is, however, not unique and several other versions have
appeared in the literature. The Hamiltonian (I-7) has nonzero matrix
elements <K|K> and <K1K:2> in the symmetric top basis function set wJK‘
The symmetric form of (1-7) and the fact that it involves only diagonal
and second off diagonal matrix elements have given it widespread popu-
larity. However, Watson(10) points out that this reduced Hamiltonian
may not converge to a stable set of coefficients for molecules in which
(i-Y) is approximately equal to or less than the magnitude of the coef-
ficients of the P4 terms. This condition corresponds to near symmetric
rotor molecules. For such molecules, Watson suggests that another
reduction be used. In fact, we have found that it converges very slowly
in other cases, too.

(ll)

Recently, Typke has given a different reduction of (1-6) which

is especially suitable for fitting near-symmetric rotor molecules:

H = X'Pi + Y'Pi + Z'Pi (1—8)
- 05R4 - oprzpi - DkP: - 205P2(Pi P3) + 2R60
+ HJP6 + HJKP4P2 + HKJP2P4 + HKP6 + H5P4(P2- P5)
+JZ-H6 HP 20 + H10(Pi- P3,)3
where
0 = P: + pfi - 3(PX Mi pipi) .

Since this Hamiltonian involves nonzero matrix elements of the type

<K|K>, <K}K:2>, <KlKi4>, and <K)K:6>, numerical diagonalization of the

TO

Hamiltonian matrix is not quite as rapid as for Watson's Hamiltonian.

However, we have found that Typke's Hamiltonian converges to a stable

set of parameters more quickly than does Watson's for the molecules

H23 (oblate, K==0.5), HZSe (oblate, K==0.8) and HDSe (prolate, :=-O.5).
A few comments about the determinability of Hamiltonian parameters

when fitting bent triatomic molecules are in order. Necessarily, such

molecules have planar equilibrium configurations. In that case,

(5)

Dowling and Oka and Morino(6) showed that three planarity conditions
can be given to reduce the number of tau coefficients in the Hamiltonian
from seven to four. While such relations are exact for the second-order
Hamiltonian, they are only approximate for the Hamiltonians which include

6 4 terms then include a

P terms(]2) because the coefficients of the P
number of fourth-order contributions. Thus, the errors in the P4 terms
when introducing the planarity conditions may be of the order of magni-
tude of the coefficients of the P6 terms. Even though the P6 coefficients
are usually much smaller than the P4 coefficients, the planarity relations
lead to significant errors and should not be used in general. The fact
that these errors are usually small means that one of the coefficients

of the P4 terms is nearly a linear combination of the other P4 coef-
ficients. This leads to high correlations among the centrifugal dis-
tortion coefficients when fitting the spectra of bent triatomic molecules
even when a wide variety of transitions is assigned. These high corre-
lations would not be expected for molecules which are not planar.

For planar rigid rotors IA + IB = IC or %-+ %-= %-. For real bent
triatomic molecules with centrifugal distortion, the Hamiltonian para-
meters A,l3,and C include contributions from the centrifugal distortion
l l l

terms in the Hamiltonian and A'+Ԥ z-E . The difference from equality

IT

is on the order of 0.00l of the rotational constants (as can be seen,
for example, from the rotational constants for HDSe, H25, or HZSe given
in this thesis). As in the case of the centrifugal distortion para-
meters, the three rotational constants are nearly dependent upon one

another and high correlations among them result.

Coriolis Coupling

 

For molecules like H25 and HZSe, the rotational levels of two
vibrational bands with vibrational quantum numbers (V],V2,V3) and
(VliT,V2,V3iT) may be coupled by a Coriolis perturbation. Snyder and

(13)

Edwards have derived the operator form of the Coriolis interaction

term of the Hamiltonian as

HC = 1G2(qlq3-q3qlwz + nyqlq3(PxPy+Pny) (1-9)

which has matrix elements of the form

l l _ =
(I-TO)
. l %
[TGZPZ + 2 ny(PxPy+Pny)][(V]+l)V3]
and
' _ :
(1-11)
I 1- %
[-lePZ + 2 ny(PXPy+PyPX)][VT(V3+])] .

The total Hamiltonian for two Coriolis coupled vibration rotation bands
is

H = H + H + H

1 3 C (1-12)

12

where H1 and H3 are the vibration rotation Hamiltonians of the
type described earlier for the two interacting vibrational
states.

The presence of the Coriolis perturbation has three effects on the
observed infrared spectrum of interacting levels. First, levels with
appropriate symmetry which would be close together if there were no
perturbation will "repel" one another. Second, the value of the
effective rotational constant C in each of the interacting vibrational

bands is altered slightly from its unperturbed value.(]3)

Third,
intensities are altered due to the mixing of wavefunctions so a transi-
tion from the weaker band may ”borrow" intensity from the stronger.

The stronger transitions will then be weakened.

Fermi Coupling

 

Two vibration-rotation bands with vibrational quantum numbers

(Vl’VZ’VB) l 2

and Overend(]4) give the matrix element of this interaction as

and (V -l,V +2,V3) may be coupled by Fermi resonance. Smith

k V
+2,V > = 122

i _ __l_ i -
<v v JBIHF1V1-1,V 3 2 [2(V2+l)(V2+2)] (113)

1’ 2’ 2

where k122 is an anharmonic force constant. The complete Hamiltonian

for states coupled by Fermi resonance is then

H = H1+ H2 + HF (I-l4)

where H1 and H2 are the vibration rotation Hamiltonians of the two

interacting vibrational bands.

13

The Fermi interaction has three general effects on the observed
infrared spectrum of interacting levels. First, the observed band
centers are split farther than they would be if there were no inter-
action. Second, the interaction causes small changes in the effective
rotational and centrifugal distortion constants. And, finally,

intensity "borrowing" can also occur.

CHAPTER II

APPLYING THE HAMILTONIAN

Observed absorption spectra are formed when a molecule absorbs
photons and undergoes transitions from lower state energy levels to
upper state energy levels. The spectra considered in this thesis
involve transitions from the rotational levels of the ground vibrational
and electronic states to rotational levels of an excited vibrational
state, also in the electronic ground state (for brevity the ground
vibrational state will be referred to as the ground state hereafter).

If the appropriate molecular constants are known, the Hamiltonians given
in the preceding chapter may be used to calculate the ground and upper
state rotation energies. This chapter will outline the method for
evaluating the Hamiltonians and determining energy levels. Once the
energy levels are known, the predicted spectral transition frequencies

may be calculated as differences between the upper and ground state
energies. First, the evaluation of the Hamiltonian for unperturbed
vibrational bands will be considered, and then the method will be expanded

to account for bands perturbed by Coriolis and Fermi resonances.

Evaluation of the Hamiltonian for Unperturbed Vibrational States
In the absence of resonance-type perturbations, the vibration-rota-

tion Hamiltonians given in Chapter I are diagonal in all vibrational

14

15

quantum numbers VS (this is, only matrix elements of the type
<V1V2V3|HIV1V2V3> are nonzero) and are also diagonal in the total
angular momentum quantum number J. However, the Hamiltonians are not
diagonal in the projection of the total angular momentum along any set
of orthogonal molecular axes; that is, for asymmetric top molecules K

is not a good quantum number. Therefore, it is necessary to diagonalize
the Hamiltonian numerically for each value of J. Since Schroedinger's
equation Her = EOJT cannot be solved analytically in general for these
Hamiltonians, the wave functions are expanded in the basis of symmetric

J

top wave functions wJK = lJK> such that th = 2: CT

JKPJK and
T=-J

J
Z (CJKIZ = l and the Hamiltonian matrix is formed in terms of sym-
T=-J

metric top matrix elements <JK1H|JK'>. Only elements of the type
<JK|H|JK>, <JK!H[JK:2>, <JKlHlJK:4>... are nonzero. These matrix

elements are listed in Appendix A. The matrix elements are evaluated
(15)

using the phase conventions of King, Hainer, and Cross, viz.
<JK|P2!JK> = J(J+l) (II-l)
<JK1PZ|JK> = K

~1—

<JK|Py1JK+l> (%)[J(J+l) - K(K+l)]

<JK|PX|JK+1> (%)[J(J+l) - K(K+l)]P .

Here, the matrix elements are taken to be dimensionless and all

. . . . -l
Hamiltonian constants are expressed in cm .

16

Since the values of K range in integer steps from -J to J, the
resulting matrix is (2J+l)x(2J+l) and has only diagonal, second off
diagonal, fourth off diagonal, ... nonzero matrix elements. Such a
matrix rapidly becomes large and difficult to diagonalize numerically
as J increases. Since <JK|H|JK'> = <J-K]HlJ-K'> and the Hamiltonian
matrix has a ”checkerboard" pattern, Wang(]6) observed that the
Hamiltonian matrix could be block diagonalized by forming suitable linear
combinations of the symmetric top wave functions. The wave functions in

the Wang symmetrized basis set are

is : - Y -
TJKY aivJK + ( i) tJ_K) (II 2)
where
2'% for K f 0
5 = 1
‘2— TOVK=O
Y = 0, l .

These wave functions are of four types; and when the Hamiltonian matrix
is formed from matrix elements of these wave functions, four submatrices
of approximately equal size result. The overall Hamiltonian matrix is
block diagonal. Table 2 lists the wave functions, their designation,
and the dimension of the submatrices. The designations E and 0 refer
to the evenness or oddness of K.
A direct calculation shows that the matrix elements of the Hamiltonian

S

H in the Wang basis can be calculated from the matrix elements of the

Hamiltonian H in the symmetric top basis as follows:

‘5 S l = 6' .. Y .-
<VJKYiH [\DJK'Y') 60 {EJKKI + ( 1) EJK‘K' (II 3)

+ (-])YEJ-KK'

17

Table 2

Wang Symmetrized Basis Functions

:__—
I

Dimension of Submatrix

 

 

 

Designation Wave Function Even J Odd J
5+ PSKO ‘ ‘2(P00+Pdo) ‘ Poo P°P K = 0 2'+ ' 921‘
2-i(oJK+wJ_K) for even K f O
E‘ 03K] = 0 for K = 0 %- -i%l
2"%(OJK-OJ_K) for even K # O
o‘ ijl = 2'%(oJK-oJ_K) for odd K %— le
0+ ijo = 2%(PJK+Pd-K) for Odd K 2' 921'
where E = <JK|H|JK'>. For vibrationally diagonal Hamiltonians

JKK'
containing only even powers of components of angular momentum,

E = EJ-K-K' = EJK'K = EJ-K'-K' , and (II-3) reduces to

JKK'

.s ‘s = . _ r _
|H 'PJK'Y> 206 [E + ( l) E (II 4)

S
(PJKY JKK' JK-K'] '

Thus, for such Hamiltonians, K and K' are either both even or both odd.
As is the full (2J+1)x(2J+l) Hamiltonian matrix, each Wang block is
Hermitian (in fact for noninteracting vibrational bands, each block is
a real symmetric matrix). The eigenvalues of the Wang blocks are

identical to those of the full Hamiltonian matrix. Each Wang block

18

EJKY may be diagonalized separately by applying a unitary similarity

. _ -l . .
transformation such that EJT - SJTEJKYSJT . When such an Operation 15
performed, the elements of the diagonal matrix EJT are the energy

eigenvalues and the columns of the similarity transform S are the

Jr
eigenvectors of the energy eigenvalues in the space of the Wang trans-

formed basis; that is,

HSISJT> = EJTISJT> (11-5)
and
(SJIlHSISJt> = EJT '

Since K is not a good quantum number for asymmetric rotors, the
energy eigenvalues may be identified by an index T. By convention, the
eigenvalues of all four Wang blocks for a given J are arranged in
descending magnitude. The index 1 takes the values from +J to -J in
integer steps and is associated with the eigenvalues such that the
highest energy eigenvalue has the highest T index and the lowest eigen-
value has the lowest T index. A more common indexing scheme is to use
the indices K_ and K+. K_ and K+ refer to the K quantum numbers in
prolate and oblate symmetric top limits, respectively. K_ and K+ are
related to r by r = K_ - K+. King, Hainer, and Cross(15) have given
the identification of the energy eigenvalues with the various Wang
blocks. This ordering is shown in Table 3. As the asymmetry of a
hypothetical molecule is varied from the prolate to the oblate limit,
the energy levels for a given J vary smoothly and without crossing from
the prolate to the oblate symmetric top energy levels, respectively, as
shown in Figure 1. Although no level crossing occurs for levels with
the same J, levels involving different J may be interleaved with one

another.

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3

 

 

19

 

_ a _ a o a F ..a
N\A_+sv N\s Ame -o
o o o w m o o o
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N\l_+qv N\e New +0
o m o o o o m o
N _-w N Fig N Fifi F a
N\A_,sv N\s lav -m
m m w o m m o m
o a o a _ Pia o a
N\A_+sv _ + N\s APV +m
m o m o o m m m
+¥ -¥ +¥ -x +¥ -¥ +¥ -x
a two a co>m w coo a :m>m a uno a cm>m «Aomav
chumsnzm co mem Ac A y .mum—nov Ao v y .momFOLQV chumsnzm
:o_umu:mmmcawm LHHH co_pmocmmmcamm CH

 

 

-o see .+o .-m .+m mae_eee22=m age to colonele_mme_u

m wpamp

20

 

 

 

J K=K Ir J ”Ir K=K J
- Submatrix K_K+ Submatrix +
3 E+ _________.O -1
O-/ 30/0- 1—
__. ae—-3 -—~* 7“ ::::
...3___2 0+-—* 3l +

3 .
21 - 2 “
E
E+/3 /+7-

 

 

+ ___.____3—

 

 

 

 

 

 

 

 

2
2 11
07/ E- ”—2—;
e—i--—”-/—o+* 212/E+
L._O—-—“""'E+/202
E‘“'-—-"""""'0 i
0_ ‘——"——__’110 _————""Cr- ===______']:]
i—-—-'=0+ *— “11176'
1 [: +/l
.L i l i i
K -1.0 -O.5 0.0 0.5 1.0
Prolate Oblate
Limit Limit
8 = C B = A

Figure 1. Energy Level Diagram

21

Coriolis and Fermi Interactions

The H25 and H25e vibrational bands 202 and v] are coupled by a
Fermi resonance as shown in Equation (I-l3) and v] and 03 are coupled
by a Coriolis resonance as shown in Equation (I-10) and (I-ll).

Flaud and Camy-Peyret(]7)

also report a Coriolis resonance between 202
and 03. We believe that this interaction is small enough to be neg—
lected for H23 and HZSe, and, therefore do not include it in our analysis.
Because both the Fermi and Coriolis interactions have matrix elements
which are diagonal in total angular momentum, the total Hamiltonian
matrix in the symmetric top basis for a given J is as shown in Figure 2.
This matrix is a 3(2J+l)x3(2J+l) square matrix. As in the case of the
unperturbed Hamiltonian, it is convenient to transform this Hamiltonian
matrix from the symmetric top basis to the Wang symmetrized basis. An
examination of the matrix elements in the Wang basis shows that the
Coriolis interaction couples only Wang submatrices E+ to E' and 0+ to

0‘ where in each coupled pair of submatrices one belongs to v] and one
to 03. The Fermi interaction couples only submatrices of the same sym-
metry for v1 and 202; i.e., E+ to E+, E' to E‘, 0+ to 0+, and 0‘ to 0‘.
Therefore, the total Hamiltonian becomes block diagonal as shown in
Figure 3. The dimension of each of these triple Wang blocks is the

sum of the dimensions of each individual vibrational band Wang block.
For example, the dimension of the E:3 + 5;] + E202 block is the '

dimension of E: plus the dimension of E; plus the dimension of
3 1

Figure 4 shows the form of one of the triple Wang submatrices

EZVZ'
for J = 4. If no perturbations are present, the three vibrational
blocks in each Wang submatrix are uncoupled and each vibrational block

has the same form as in the unperturbed case.

22

 

 

 

v3 0] 202
v H H O
3 v3 C
.f.
0] HC H01 HF
2v2 0 HF szz

 

 

 

 

 

i = Hermitian conjugate.

Figure 2. The Total Hamiltonian for a Given J for Fermi and Coriolis

Coupled Bands 01,03, and 202 of H25 or HZSe.

23

 

 

 

 

EU
3
+
+E
“i
+
+E2V2
0.?
3 i
+
+00]
+
+0
202
+
0
P3
+0:
’1
+0

 

 

 

 

 

 

Figure 3. The form of the Wang transformed total Hamiltonian for Fermi
and Coriolis coupled bands 0], v3, and 202 of H25 or H2Se.

24

 

 

 

 

 

 

 

 

+ + +
E E E E 0
0300 V302 0304 C02
+ + +
E E E E E
0320 0322 0324 022 024
+ + +
E E E E E
0340 0342 0344 C42 C4
i i i - -
EC20 E022 E(:24 E0122 E0124 F 0
+1. .-
0 EC42 EC44 E0124 E0144 0 F
F 0 E' E'
20222 20224
0 F E' E‘
20242 2v244
+ _ S S S
Ev3KK' - (wJKOIHv3leK'O>
" _, S S S
E01KK' ‘ (wJKlIHvlleK'l>
' _ S S
EZvZKK' ' (PdKilHszlwdk'i >
= ..S 1 S S
ECKK' (P3PJK0'HC'PiPdK'i>
S S S
T i = <0 0 1H Iv w . >
ECKK l JKl c 3 JK 0
S S
F = <011HF103> = <v3|HF101>
+
EV3 EC
Figure 4. The form of the E: E; F Wang submatrix for J=4.
i
F E2v2

 

 

25

As in the unperturbed case, the triple Wang submatrices EJir'i'

may be diagonalized to yield energy eigenvalues by applying a unitary

similarity transformation SJ . . such that
TT T

S -
H ISJii'r'> _ EJtr't‘lsJii'i'> (11-6)

and

<s .|H5|s = E

>
Jit'i Jti'i' Jtr't'

The columns of S.J .
r

r T. form the eigenvectors associated with the energy

eigenvalues E Each of the three vibrational states in the triple

Jit'i"
Wang block contributes one component to the eigenvectors:

(SJir'i') = SVBJT (II-7)

vlJr

520 Ji

2

where the SvJ are (nvxl) column vectors, and nv is the dimension of

T

the Wang vibrational subblock and v is 0], v3, or 202. Since the SJTT'T'

are normalized such that

2 2

2
l JT'i

(s = [s + |s )2 + is = l (II-8)

. .I .
Jii T V3JT V1JT 202

the fractional contribution to the total wavefunction from one of the

vibrational states 0 is iSVJle- This provides a convenient method of

classifying the energy eigenvalues. Each eigenvalue EJir'r' is

associated with the vibrational state which makes the largest contri-

bution to its eigenvector. For states whose eigenvectors have a

majority contribution from one vibrational state, this scheme associates

26

exactly nv eigenvalues with each of the three vibrational states 0.
When a state is so mixed that none of the three vibrational states has
a majority contribution to its eigenvector, assignment to a vibrational
block becomes more arbitrary. In this case, all other eigenvalues must
be assigned and the remaining state is associated with the vibrational
state to which nv-l other eigenvalues have been assigned. When several
badly mixed levels are present, assignments become still more arbitrary.

The above method of assigning eigenvalues was employed in our three
band fitting computer program SPFT3 but was discarded because of dif-
ficulties with properly assigning badly mixed levels. A method which
seems to assign energy eigenvalues consistently to the proper vibrational
block results when it is assumed that the presence of a perturbation
does run: move an eigenvalue from the vibrational block in which it
would be if no perturbation were present. Examination of the eigen-
vectors for a large number of states confirmed that the method gives
meaningful results.

Once the eigenvalues are assigned to the correct vibrational states,
rotational levels are assigned in the same manner as for unperturbed
states. That is, the eigenvalues of each vibrational subblock are
arranged in descending order and T or K_ and K+ are associated with the

levels as previously described.

Isotopic Substitution

When several isotopic species of a molecule are present as in the
case of HZSe and HDSe, each isotopic species produces a separate absorp-
tion line for a given transition. If a large enough number of transi-

tions can be observed from each isotopic species, individual fits of

27

the spectrum of each species may be made. An alternative to this is to
express the Hamiltonian parameters of the less abundant species in
terms of the most abundant species as a function of the mass difference

(18) and us.(19)

of the various isotopes, as was done by Willson et al.
Both linear and quadratic mass dependent terms are assumed for the band
center 00, and nonzero linear mass dependencies are assumed for the

rotational terms A', B', and C'. With these assumptions, the frequency

of a transition is given by
= m mm 2 i i i _
F 00 + EOAM + E0 (AM) + 12(xa+€ AM)<X >a (I17)

Z +E AM)<X>

1 b

where for HZSe and HDSe a and b refer to the upper and ground states,
respectively. AM = (BO-M), where M is the mass of the selenium isotope
involved in the particular transition and xi and <Xi> are respectively
the Hamiltonian parameters and the expectation values of the associated

momentum operators in the Hamiltonian space of the 80 isotope.

Fitting Observed Spectra: Computer Programs

A number of computer programs for fitting and predicting observed
spectra have been inherited from previous graduate students in this
lab and several others have been written by me. The general method of
operation of these programs and of the least squares procedure for
determining Hamiltonian constants has been described in detail by

(20)

Willson. Basically, all of these programs calculate energy levels

using the methods described in this chapter and calculate transitions

28

as the difference between two energy levels. Two major differences in
these programs from those described by Willson are that all of the
programs now incorporate Equation (II-7) to allow several isotopes to
be fitted simultaneously, and all of the programs incorporate Typke's
Hamiltonian Equation (I-8) as an option. The following paragraphs
briefly describe the function of our major asymmetric rotor computer
programs.

Program ICDFIT. Estimated ground state molecular constants and
observed ground state combination differences are input. A weighted
least squares fit of the difference between the observed and calculated
ground state combination differences in performed and the molecular
constants which have been selected to vary are adjusted to improve the
fit. These constants are then used as starting values and the fit is
repeated. This process continues until the fit converges to stable
values or until the number of least squares fits specified by the
operator has been performed..

Program CDCALC. Ground state constants and either a range of

 

ground state combination differences to be formed or quantum numbers of
ground state combination differences are input. The values of the
ground state combination differences are calculated and may be punched
in a format usable by ICDFIT.

Program USEN. Ground state constants and observed transitions are

 

input. Upper state energy levels are calculated by adding the calcu-

1 to the observed transition frequency.

lated ground state energy in cm-
All transitions involving the same upper state are grouped together for
comparison and the average observed upper state energy is calculated.

USEN will handle up to six isotopic species and transitions from bands

29

v], 202, and v3 simultaneously. If desired, the average upper state
energies may be punched in a format usable by other asymmetric rotor
fitting programs.

Program ISPECFIT. Ground and upper state constants and observed
transitions from a single unperturbed vibrational band are input. The
operator selects which molecular constants are to be varied. As in
ICDFIT, a weighted least squares fit of the observed transitions is
performed and the molecular constants are adjusted to improve the fit.
Any combination of ground and upper state constants may be varied.

Program SPFTZ. Ground and upper state constants and observed
transitions from two vibrational bands coupled by Coriolis resonance
are input. Least squares fits of the observed transitions are performed
to improve the estimates of the constants selected to be varied by the
operator. Any combination of ground and upper state constants may be
varied.

Program SPFT3. Ground and upper state constants and observed

 

transitions from three vibrational bands coupled by Coriolis and Fermi
resonances are input. Least squares fits of the observed transitions
are performed to improve estimates of the constants selected to be
varied. As with the other fitting programs any combination of constants

may be varied.

CHAPTER III

CALCULATION OF INTENSITIES

Knowledge of upper and lower state energy levels alone is not
sufficient to allow the analysis of complex asymmetric rotor spectra.
One must also know the selection rules for transitions; that is, which
upper state energy levels can be reached from a particular lower state
level. In addition, it is useful to be able to predict the intensity
of the transitions because several possible transitions may have simi-
lar frequencies. The correct assignment of a such spectral lines thus
also depends upon knowledge of the transition intensities.

The following discussion of selection rules and intensities

follows the presentation of Cross, Hainer, and King.(2])

Selection Rules

As is the case for symmetric top molecules, for asymmetric top
molecules the selection rule for the change in total angular momentum
quantum number during an electric dipole transition is AJ = 0,:1.
The selection rules for changes in K_ and K+ are given in Table 4. It
follows that for transitions involving no parity change in one of the
K's, AK = O,:2,:4, ... and for transitions involving a parity change
in one of the K's, AK = :l,:3,:5.... An additional restriction placed
on K_ and K+ is that for any level with total angular momentum quantum

number J, K_ + K+ = J or J + l.
30

31

Table 4

Selection Rules by Parity Change of K_ and K+

m I

 

B d Axis Parallel Allowed Transitions The Parity
Tan t0 DTPOIE K K +,, K K Change is
ype Moment Change - + - + In
e e + + e o
A a K

 

 

Dipole Transition Intensities

 

The intensity of a spectral absorption transition from state n to

state n' is given by

3

8n N En/kT

 

-E )kT vgn (l-e'hV/kT)e lfwgfiwn.dv|2 (III-l)

3thgne

where

En is the energy of the lower state;

gn is the lower state statistical weight factor;

v is the transition frequency;

3

8n N

 

-E /kT is a constant involving the gas density N in

3thgne n -E /kT

molecules/cm3 and the partition function Zgne n ;

fpgfiwn.dv is the electric dipole transition matrix element.

32

Because only transitions between vibrationally diagonal (unperturbed)
vibrational states are considered in this treatment, the total wave
function p may be expressed as the product of a rotational wave function

PR and a vibration-electronic wave function wVe

w = vRvVe . (111-2)

Then, the transition matrix element may be factored as
fwguvn.dv = g TwaingR.dvIvgeung€dv (III-3)

where
waeugPVedv represents the contribution of the vibration-electronic
dipole transition element. This is considered to be a constant for
a given vibration-electronic band and must be nonzero if the band
is to be infrared active.

¢Fg are the direction cosines between the space-fixed F(X,Y,Z) axes
and the body-fixed rotating g(x,y,z) axes. Conventionally, the
axis system (x,y,z) is associated with the principal axes of
inertia (a,b,c).

For a symmetric rotor molecule, the rotational part of the dipole matrix

element may be factored into three parts:

f¢§¢Fg¢RidV = <JKM|¢Fg|J'K'M'> = <J|oFg|J'> (III-4)

.<JM|¢Fg|J'M'><JK|¢Fg|J'K'> .

The first factor is independent of M and K and is constant for given AJ.

The second depends on J and M, the projection of the total angular

33

momentum on the space—fixed Z axis. The symmetric top line strength

is then

2 2
I |Iv*¢ w .dvl == 2 |<JKM|¢ IJ'K'M'>| (III-5)
F M M' R F9 R FMM' F9

9 9

I2 iiz II2
= 3|<dl¢zgld >l KK.I<JMIRZQIJ M >I I<JK|¢ZglJ K >1 .

The factor of 3 in the right hand side occurs because the X, Y, and Z
axes are equivalent in the absence of external fields. The nonzero
matrix elements used in (III-5) are tabulated in Table 5.

For an asymmetric top the line strength is

g M' |<JTM|¢FglJ'T'M'>|2 = 3|<J|¢Zg|J'>|2 (III-6)

~MTK' |<JM|¢Zg|J'M'>|2|<Jrl¢§gld't'>lz
Because the asymmetric top wave functions are linear combinations of
the symmetric top wave functions, the first two factors on the right
hand side of (III-6) are identical to the corresponding factors in the
symmetric top line strength expression (III-5). The asymmetric rota-
tional wave functions

|Jr> = Z S lJKv> (III-7)
K

T S _ T
JKY Pde ‘ E SJKy

are the eigenvectors of the rotational Hamiltonian in the Wang sym-

metrized basis. Because lJr> is a function of the Wang symmetrized

+

wave functions from only one of the Wang blocks E+, E', O , or 0',

 

34

 

 

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mN
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Apn¥s_xae_xsv_n u
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. i . Na
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mucmsmpm chumz mcwmou cowuomc_o gob owcuwssam

m o—nmh

35

K ranges from O or 1 to J-l or J in steps of two. The ij are given

by Equation (II-2). A simple calculation shows that

i .
i i = T T i i I _

i , ,
3i: sdkst.K.Y. ad [<JK|+( l) <J K|]¢Zg[|J K >+( l) [J K >]

i . i
T T i i I _ Y I_ I
2K. SJKYSJ'K'y' 65 {<JK|¢Zg|J K >+( l) <JK1¢Zg|J K >

+(-l)Y<J-K|¢Zg|J'K'>+(-l)YTY'<J-K|¢Zg|J'-K'>}

where |JK> are the symmetric top wave functions. The amount of calcu-
lation necessary to evaluate <Ji|¢zg|J'i'> may be reduced by observing
that the only nonzero matrix elements <JK|¢Zg|J'K'> are those for which
AJ = 0,:1 and AK = 0 if g==z or AK = :l if g = x or y where AK = K-K'
or K+K'. For unperturbed vibrational bands, all SOKY are real. If
mixed bands (bands in which the change in dipole moment is not parallel
to one of the molecule fixed principal axes) are not considered, com-
plex arithmetic is not needed to evaluate the line strength (III-6)
because, even though some elements in Table 5 are imaginary, the matrix
elements <Jil¢zg|J'i'> will be either pure real or pure imaginary and
the line strength depends onl<J<l¢Zg|J'r'>|2 which is necessarily real.
The assignment of the molecule-fixed axis 9 to x, y, or 2 may be
determined from the band type and the representation in which the
Hamiltonian has been evaluated. As shown in Table 4, the molecular

axis along which the dipole moment changes determines the band type.

36

For example, for a prolate molecule (Ir representation) with a type A
vibrational band, 9 = a = 2. For bent triatomic molecules type C
transitions, which correspond to out of plane vibrations, cannot occur.
However, type A and type 8 transitions are allowed. For molecules like
“25 and HZSe, type A bands occur only for transitions to or from vibra-
tional levels (V],V2,V3) when V3 is odd. All other bands for these
molecules are type B.

If a molecule contains two equivalent nuclei, for example, the two
hydrogen nuclei in H25, nuclear spins and nuclear Spin statistics affect
the population of the ground state, and, hence, the transition inten-

sities. Townes and Schawlow<22)

show that for H25 or HZSe there are
three times as many asymmetric or odd levels (K_+K+ = odd integer) as

symmetric or even levels (K_+K+ = even integer). Thus, for H S and

2
H25e the statistical weight factor gn is three for odd levels and one
for even levels. The observed spectra of H25 and H25e Show this 3:l
intensity ratio for transitions originating from odd and even levels.
For example, the H25 0] transition 4 l 4 - 5 O 5 may be observed to have
three times the intensity of 4 O 4 - 5 l 5. Molecules with no equivalent
nuclei, such as HDSe, have gn equal one for all levels.

Because one is usually interested only in relative transition
intensities within an asymmetric rotor vibrational band, both the
vibration- lectrgnjfiTdipole matrix element fwveungedv and the partition

function Z gne are set to arbitrary constant values, giving the

relative intensity

-E /kT
_e‘hV/kT)e n

EiM.'<JTMl¢Eg|J'i'M'>I2 (III-9)

37

where Z l<JTMl¢Fg|J'I'M'>|2 is defined by (III-6) and (III-8).
FMM'

A description and listing of computer program INTCALl, which
calculates absorption transition intensities and frequencies for type A

and type B bands, is given in Appendix B.

CHAPTER IV

DATA COLLECTION AND EXPERIMENTAL DETAILS

During the past two years we have run spectra of HDSe 201,
HZSe 202, v1, and v3 and H25 202, v], and 03 on the Michigan State
University high resolution spectrometer. This chapter describes the
data collection and experimental details. Since the procedure for
acquiring spectra is similar for all three molecules, the general pro-
cedure is described and specific comments for the individual molecules
are made as required. The process of acquiring spectra comprises sample
preparation, spectrometer setting and computer assisted data acquisition,

data processing, line measurement, and calibration of the spectra.

Experimental

 

Samples of HZSe and DZSe were purchased from the Matheson Company,
Inc. HDSe was prepared by mixing HZSe and 025e in the sample cell.
Such a mixture rapidly reaches an equilibrium mixture of HZSe, 025e,
and HDSe. The proportions of each component of the mixture may be
calculated as follows. Consider a mixture containing fraction x of HZSe
and fraction (l-x) of DZSe. Then, the probability that an individual
atom attached to a selenium is H or D is respectively x or (l-x).

2

Therefore, the probability that a molecule is HZSe is x , HDSe is 2x(l-x),

and DZSe is (l-x)2. We used a mixture of one part H25e to nine parts

38

39

DZSe which yields an equilibrium mixture of 8l percent 025e, 18 percent
HDSe, and l percent H2Se. This ratio was chosen because it gives rea-
sonable HDSe absorption in the 2v1 region, while giving absorption by
only a few of the strongest lines of the HZSe bands 201, 01+v3, and 203
which are in the same region. There are no interfering 025e bands in
this region. An impurity present in the sample of DZSe obscured a small
number of HDSe lines in the low frequency region of the spectrum. How-
ever, this impurity caused little difficulty during analysis of the
spectrum.

The sample used for the H2Se 202, v],and v3 spectrum showed no
evidence of any impurities in the region of interest.

After several attempts to obtain a spectrum of H28 202, v] and 03
free from contamination from strongly absorbing CO2 bands in the 4.3 pm
region, Scientific Gas Products, Inc. donated to us a 35 gm sample of
electronic grade H25 (99.99 percent purity, less than 50 ppm C02). In
our spectra of their sample, a small amount of C02 contamination was
still present but, was sufficiently small so that only a few H25 lines
were obscured. Ultimately, the CO2 contamination served one useful
purpose. The recent analysis of (00°l) of C02 by Baldacci et al.(23)
allowed us to use this band as a calibration standard.

All spectra were run on the Michigan State University high resolu-
tion near infrared grating spectrometer. The spectrometer, which has

(24) (25) uses a l-m focal

been described in detail by Aubel and Keck,
length Littrow—Pfund monochromater with 300 line/mm and 600 line/mm
gratings mounted back to back on a turntable. Infrared radiation was
provided by a carbon rod source. The radiation was mechanically

chopped at 90 Hz.

40

The samples were contained in a White type multiple traverse cell
maintained at room temperature (22 to 26°C). A liquid nitrogen cooled
InSb photovoltaic detector was used to detect the HZSe and “25 spectra
and a dry ice cooled PbS photoconductive detector was used to detect
the HDSe spectrum.

Visible light from a 100 W Zr arc lamp chopped at 450 Hz was used
to produce Edser-Butler fringes used for calibration. The white light
fringes were detected by a dry ice cooled RCA 7265 photomultiplier tube
(PMT). Dry ice cooling provides two benefits: First, improved signal
to noise ratio (which was, however, not needed for most of the runs
most of the time); and, second, cooling prevents intermittent spikes
from appearing on the output signal of the PMT. The PMT was usually
operated in the neighborhood of 1500 V applied bias and 60 dB gain on
the Keithley 823 amplifier. These conditions seem to give the best
overall signal to noise ratio.

The signal processing electronics of the spectrometer are shown
schematically in Figure 5. The infrared dectector output was fed to a
Princeton Applied Research HR-8 lock-in amplifier. The lock—in output
was fed through an adjustable gain amplifier to a chart recorder and to
an analog to digital converter on a POP-12 minicomputer. The PMT output
was routed through a Keithley 823 amplifier and a Keithley 822 phase
sensitive detector before being fed through an adjustable gain amplifier
to a second analog to digital converter on the PDP-l2. Time constants
on both the HR-8 and 822 were set at 0.3 sec, about one-tenth the time

required to sweep through a line or fringe in a typical run.

41

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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42

Data Processing

 

Alternate samples of spectral data and visible light fringe signals
are stored on magnetic tape under the control of program SYSTEM.(20)
SYSTEM is an interactive program to sample data and manipulate them.

As recommended by Willson and Edwards,(26) the data sampling rate was
set to provide 30 to 60 points per full width at half height of a line.
To improve signal to noise ratio and prevent aliasing of high frequen-
cies, groups of 32 instantaneous samples of the spectral data and of
the fringes were averaged to provide each point stored on magnetic tape.
SYSTEM displays the data as they are being acquired.

At the start of each run, the offset on the infrared variable gain
amplifier was set to provide a suitable zero transmission baseline.
Usually the zero transmission level was set to correspond to near the
analog to digital converter maximum value of 20008. For the weakly
absorbing HDSe spectrum, the zero transmission level was set at about
twice the maximum of the analog to digital converter. After initial
setting, the zero transmission level was not varied during a run. The
zero absorption baseline was adjusted throughout a run to be approxi-
mately lOO8 on the analog to digital converter. Because the gain and
offset of the variable gain amplifiers do not interact with each other,
this adjustment did not alter the position of the zero transmission
baseline. The fringe variable gain amplifier was adjusted during each
run to keep the fringe amplitude approximately constant at 12008 on the
analog to digital converter.

After spectral data had been recorded, the spectral data and white
light finges were copied onto separate magnetic tapes. The data and

fringes were smoothed using a four times quartic smoothing function.

43

For this function, Willson and Edwards(26) recommend a smoothing range
equal to the full width at half height of a single well-resolved line.
Because of some misunderstanding of the conditions necessary for reli—
able deconvolution, our spectra were run at too high a noise level for
reliable deconvolution; and, therefore, the spectra were not deconvoluted.
Fringes and spectral lines were measured using the interactive line

measurement program CENTER.(27) Since a detailed account of the opera-
tion of CENTER and the line measuring process is given by Hurlock and

Hanratty,(27)

only a brief description is given here. CENTER displays
the spectrum or fringes on the PDP-l2 CRT display. The operator may

move the spectrum forward or backward on the display. The displayed
portion of the Spectrum can be reflected about a cursor displayed on

the CRT. The center of a line is determined by minimizing the difference
between the displayed portion of the spectrum and its reflection. The
vertical and horizontal coordinates of this point on the spectrum tape
are recorded on magnetic tape.

Fringe positions are measured automatically. The operator measures
the first three fringe positions manually and CENTER measures and
records the remaining fringe positions on the tape. Actually, a bug in
CENTER causes it to crash after measuring anywhere between 10 and lOOO
fringes so frequent restarts are necessary when measuring fringes.

The usual routine for measuring line positions is to first record
fringe positions. Then, line positions are measured manually by the
operator and the fringe number of the line is interpolated by CENTER.
Conversion of the tape position of spectral lines to fringe numbers is
necessary because the spectrum is recorded linearly in time, but not

linearly in frequency.

44

Calibration

 

Calibration of the spectra presented some problems. The normal
procedure is to put a calibration gas in the sample cell at the begin-
ning of a run and another calibration gas in the sample cell at the end
of the run. The spectrometer is run continuously while gases are
changed. The spectra of the calibration gases and fringes are recorded
along with the spectrum and fringes of the sample. This is shown sche-
matically in Figure 6. Ideally, the Edser-Butler visible light fringes
Should be equally spaced in frequency, so they could be calibrated with
the calibration gases with the frequency of any spectral line given by
the linear relation

v = A + Bf
where v = frequency, f = fringe number, and A and B are constants deter-
mined from a least squares fit of observed fringe numbers of calibration
gas lines to their accepted frequencies. Upon attempting to calibrate
in this manner, we discovered systematic errors between the observed
and accepted values of the calibration gases (Figure 7). Also, an
discovered inconsistencies in line frequencies measured in overlapping
regions of different runs.

The nature of these errors suggested that rather than being equally
spaced in frequency, the fringe spacing was increasing with time. We
conjecture that this is because of thermal expansion of the Fabry-Perot
etalon used to generate the fringe. Because our air conditioner does
not have the capacity to keep the spectrometer room and equipment at
constant temperature, temperature usually increased 2 to 4°C during the
course of a run. A test run showed a fringe shift of 0.0l cm'1 during

a four hour run. This Shift is consistent with the Shifts predicted by

45

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47

using the calibration gas at one end of a spectrum to predict the
calibration gas frequencies at the other end of the spectrum.

To obtain more accurate calibration, we assume that the fringe
shift varies linearly with time so that frequencies can be calculated
using the quadratic formula
v = A + Bf + sz .
where A, B, and C are determined by a least squares fit of observed
fringe number to accepted calibration line frequency. Figure 8 shows
a dramatic improvement in calibration compared to Figure 7. Figure 8
shows no evidence of systematic errors and the fit has a much smaller

1

standard deviation (0.0017 cm- vs. 0.0041 cm'1). Typical values of

C are on the order of 10-7

cm'l/fringe.

Since at least three points are necessary to fit a parabola,
ideally a calibration standard should be available near the center of
the spectrum. For most reliable results, the calibration gases should
be mixed with the sample and should have lines which span the region
being run. Unfortunately, this can not often be done because the sample
spectrum and the calibration gas spectrum often obscure each other. In
such cases, the calibration regions at both ends of the sample should
be as long as possible. If several runs are necessary to span a spectral
region, the runs should be overlapped so that sample lines near the ends
of one run lie near the middle of another run. Well resolved lines
near the middle of the spectrum should be used as secondary standards.
If the spectral region of interest can be spanned in one run and it is
not practical to mix a calibration gas with the sample because too many
lines would be lost, a second run should be made with the calibration
gas mixed in specifically to obtain sample lines as secondary calibra-

tion standards.

48

Standard deviations of (observed-accepted) values of calibration
lines range from 0.0015 to 0.0034 cm.1 for the runs of HDSe, HZSe, and
H25 which were used for line measurement. This suggests that we can
measure the positions of well-resolved single spectral lines relative
to the calibration lines with a similar precision. Since the frequen-
cies of lines in most of the bands of the gases used as calibration

have been measured to stated precisions of less than i0.0005 cm"l

, the
absolute wavenumber accuracy of frequencies of well-resolved spectral
lines should be essentially the same as the calibration accuracy.
Exceptions to this are the absolute wavenumber accuracies of HDSe which
was calibrated with HBr (accuracy :0.005 cm'1) and the portion of H25
from 2280 to 2274 cm'1 which was calibrated with C02 (accuracy
$0.003 cm'l). Absolute wavenumber accuracy of well-resolved single
lines in these spectra should be in error less than $0.006 cm'l.
At least two runs of each region of the spectra of HDSe, HZSe, and
H25 were made. Runs of the HZSe and HZS spectra were arranged to over-
lap each other as suggested above. After the spectra were run and
calibrated, they were examined and the best run in each region was
chosen for line measurement and analysis. Tables 6, 7, and 8 give
experimental and calibration details for these runs of HDSe, HZSe,

and H S.

2

49

 

 

 

Table 6
HDSe 21% Experimental Conditions
Run 27 32
Region (cm“) 4470-4740 4250-4750
Cements Used to calibrate run 27.
Sample and calibration gases
mixed together.
Sample Pressure HZSe 10 HZSe 10
(torr) D S
2 e 90 DZSe 90
HDSe l8 HDSe 18
N20 3

Path Length (m) 12.6 12.6
Carbon Rod Current (A) 360 360
Fringe Order 8 8
Slit Hidth (um) 15 15
Resolution (cm‘1) 0.04 0.04
Digital Sampling 2 2
Interval (ms)
Samples Per Data Point 32 32

Calibration Gases
(Band)(Grating Order)
(Reference)

Standard Deviation 0
Calibration Fit (cm’ )

C0(2-0)(2)(28)
HBr(2-O)(2)(29)

CD(2-O)(2)(28)
HBr(2-0)(2)(29)

HDSe(2v1)(2)(Run 32) N20(12°l)(2)(30)
(20°1)(2)(30)
0.0023 0.0034

 

 

Note: Both spectra of HDSe were run using the 300 line/mm grating in second
order and a dry ice cooled PbS detector.

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CHAPTER V

ANALYSIS 0F 20 0F HDSe

1

Little previous work has been done in analyzing the vibrational

or rotational spectrum of HDSe. In 1939 Cameron, Sears, and Nielsen(35)
ran low resolution spectra to determine the values of the three normal
modes of vibration. Some 20 years later Veselago(36) observed ten
microwave transitions each for most of the stable isotopes of selenium,
but was not able to observe enough different types of transitions to
determine a complete set of rotational constants. We believe this
analysis of the 201 band (Se-H stretch) in the 2.2 pm region is the
first published high resolution study of any vibration band of HDSe.

1 to 4750 cm.1 is shown

The spectrum of 20] of HDSe from 4500 cm-
in Figure 9. The spectrum is a horizontally compressed plot of our
digitally smoothed data. An impurity at the low frequency end of the
spectrum obscures some lines below 4500 cm']. This impurity has not
seriously hindered analysis of the band because the spectrum of 20]
becomes quite weak below 4500 cm']. Nevertheless,e1even transitions

1 and 4500 cm".

were identified between 4470 cm' A quick examination
of Figure 9 shows that the spectrum of 20] has the characteristics of
a type 8 band: P and R branches and a gap at the band center (the

small group of lines near the band center is due to HZSe).

52

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54

Our analysis of any vibrational mode of HDSe began with an exami-
nation of the molecular geometry. Since isotopic substitution causes at
most small changes to the molecular equilibrium geometry, the structure
of HDSe (Figure 10) is, to very good approximation, the same as that of
H28e(37) with a deuterium atom substituted for one of the hydrogen atoms.
Because of the large mass of selenium compared to the masses of hydrogen
and deuterium, and because of the near right angle between the Se-H and
Se-D bonds, the principal axes of the molecule lie essentially along
the bonds. As a result, the Se-H stretching mode of v] and its over-
tones result in essentially pure type 8 bands. After completing line
assignment of the spectrum, we predicted frequencies and intensities
for strong type A band lines. A search of the observed spectrum for
these predicted lines failed to show any evidence for the presence of
type A band transitions, thus confirming our assumption of a pure type 8
band. In addition, there are apparently no nearby levels with which 201
interacts, so perturbations are not a problem.

Veselago's microwave 1ines(36) do not include enough types of
transitions to determine A, B, and C individually, but can be used to
determine the difference A-C and Ray's asymmetry parameter
K = (ZB-A-C)/(A-C). To get initial estimates of A, B, and C in the
ground and upper states, we assumed that HDSe has the same structure as
H25e in its ground state except that deuterium is substituted for one
of the hydrogens. Since A m 1/IA, B a 1/13, and C a 1/IC and since the
principal moments of inertia I are proportional to mr2 where m is
approximately the mass of H or D and r is approximately the Se-H or
Se-D distance, it follows that B x A A x 1/2 BHZSe’ and

HDSe HZSe’ HDSe
%- %~+-% . These crude estimates of the HDSe rotational constants were

55

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56

further adjusted so that A-C and K were equal to Vesalago's microwave
values. Examination of the molecular geometry shows that HDSe is a
near-prolate (A: B and K<0 and A>B>C) asymmetric rotor; that is,
x = b, y = c, z = a. This choice of association of the a, b, and c
principal axes with the x,y,z body fixed axes defines the Ir representa-
tion. All Hamiltonians were evaluated in this representation. Most of
the analysis was done by using Typke's reduced Hamiltonian. A11
Hamiltonians were evaluated through terms of the fourth power in angu-
lar momentum. Higher order terms were neither needed to fit the
observed spectrum, not were they found to be statistically significant.
The estimated values of A, B, and C, were used in our computer pro-

80$e. With this

gram INTCALl to predict and plot the spectrum for HD
predicted spectrum, we were able to identify the strong "zero" series

(Ad = AK+ = :1 and J = K+) lines as well as a few other strong lines.
Ground state combination differences were formed from these lines, which,
combined with the microwave lines, allowed us to improve our estimates

of the ground state constants. Keeping these ground state constants
fixed we then made a weighted least squares fit of the assigned transi-
tions to determine better upper state constants and predicted the
spectrum again. Several iterations of this procedure were necessary

to assign most of the HD8OSe 1ines. Because of the density of the
spectrum, many observed lines were found to be made up of several unre-
solved transitions. Such lines, although assignable, were not used in
fitting the spectrum. In particular, lines from the "first" series

(AJ = AK = :1 and J = K+ + 1) are often so close to lines from the zero

series that the lines can not be resolved. Also the even and odd

57

components of lines in a series1 are often split by small amounts. If
the splitting was greater than a few thousandths of a wavenumber but too
small to be resolved, the lines were not used in the fit. Because HDSe
has no symmetry axis, even and odd components of a transition have equal
intensities, so measurement of such an unresolved transition will give
the average of the two transition frequencies.

When most of the H0805e lines had been assigned, the assignments of
lines from the other four isotopic species of selenium was straightfor-
ward because of their characteristic spacing and intensity. Figure 11
shows an example of this for comparison with the natural abundances of
the Se isotopes. The ratio of intensities is seen to be roughly pro-
portional to the abundance of the Se isotopes. As a side comment, the
presence of a large amount of foreign gas (in this case the DZSe pressure
was approximately five times the HDSe pressure) seems to cause weak
lines to have less observed intensity than expected relative to stronger
lines.

We found that,as did Willson et al.518) assuming a linear mass
dependence in the rotational constants A, B, and C, and linear plus
quadratic mass dependences of the band center allowed us to fit all five
isotopes simultaneously. This method uses fewer parameters than do
separate fits of each isotope, i.e. 11 parameters vs. 5 sets of 8 para-
meters for the ground state and 13 parameters vs. 5 sets of 9 parameters
for the upper state. Further, the parameters we have chosen are physi-
cally significant and much better determined than many of the parameters

would have been if each isotope were fit individually.

 

1Evenness or oddness is defined by the evenness or oddness of K_ + K+.
An example of an even and odd pair of zero series lines is 2 0 2 - 3 l 3
and 2 l 2 - 3 0 3.

58

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59

For our final determinations of molecular constants, we formed all
possible ground state combination differences from observed transitions.
These ground state combination differences were fit simultaneously with
Veselago's microwave lines. The microwave lines were weighted 400 times
the weight of the combination differences (relatively lightly in compari-
son to their precision relative to the infrared combination differences)
in order to reduce highly correlated and poorly determined individual
ground state constants. Our final ground state constants were determined
from a least squares fit of the microwave lines and ground state combi-
nation differences, with all ground state constants varied simultaneously.
The standard deviation of the infrared ground state combination dif-
ferences is 0.007 cm'1 and the standard deviation of the microwave lines
is 0.001 cm'].

Our final upper state constants were obtained from a least squares
fit of all observed 201 transitions, with ground state constants fixed
and all upper state constants varied simultaneously. Most fits of the
spectrum were done using Typke's reduced Hamiltonian which we have found
causes the fits to converge quickly to stable values. Table 9 lists the
final set of constants obtained for the assigned transitions determined
from our fitting procedure using Equation (II-7) with Equation (I-8).
Tables 10 and 11 list partial correlation coefficients for the ground
and upper state constants. Tables 12 thru 17 list the sets of constants
obtained for the assigned transitions and correlation coefficients for
the constants for planar and Watson's forms of the Hamiltonian. All
constants are listed to two figures beyond the 96 percent simultaneous
confidence interval to reproduce our predicted frequencies. By using

linear mass dependencies for A, B, and C and both a linear and quadratic

60

Table 9

Molecular Constants for 20] of HDSe for Typke's Reduced Hamiltonian

 

 

 

Ground 95% Upper 95%
State (cm‘l) 501° (cm-1) State (cm-l) 5013 (cm-1)
A' 7.953039 20.00103 7.50341] 20.00021
0' 4.017408 20.00050 4.016749 20.00030
C' 2.532836 20.00047 2.585322 20.00015
05 0.00002227 20.0000035 0.00001736 20.0000015
05K 0.000949] 20.000023 0.00096662 20.0000060
“k -0.0005859 20.000022 -0.00061178 :0.0000055
55 0.00001796 20.0000012 0.00001812 20.0000011
R6 -0.000017200 20.00000069 0000019280 20.00000047
0.001268 20.00065 0.0011777 20.000056
53 0.00108, 20.00053 0.001075 20.00013
5C -0.000607 20.00060 0.000659 20.00017
)0 4617.8923o 20.0038
:3 0.32757 20.0043
:3” 0.00387 20.0016

 

 

;tandard deviation of fit of 305 weighted transitions = 0.0044 cm"

l95% SCI (simultaneous confidence intervals), here

1

* 6 standard deviations.

61

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63

Table 12

Molecular Constants for 2v1 of HDSe for the
Planar Form of the Hamiltonian

 

 

 

Ground 95% Upper 95%

State (cm‘l) SCIa (cm‘l) State (cm‘l) SCIa (cm'l)
A 7.952138 20.00096 7.502444 20.00021
8 4.017562 20.00047 4.016979 20.00030
c 2.633586 20.00043 2.586093 20.00014
‘aaaa -0.0015528 20.000042 -0.00149787 20.0000080
Tbbbb -0.0003826 20.000011 -0.0003854 20.000016
Taabb 0.0000938 20.000040 0.0001292 20.000042
Tabab -0.0017324 20.000045 -0.0017442 20.000029
5“ 0.001213 20.00063 0.0011432 20.000066
63 0.001047 20.00051 0.00106] 20.00012
5C 0.00058 20.00058 0.000638 20.00011
00 4617.89220 20.0038
6: 0.32706 20.0042
cg” 0.00394 20.0016

 

 

Standard deviation of fit of 305 weighted transitions = 0.0046 cm- .

1

a95% SCI (simultaneous confidence intervals) 5 6 standard deviations.

64

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Table 15

Molecular Constants for 201 of HDSe for
Hatson's Reduced Hamiltonian

 

 

 

Ground 95% Upper 95%
State (cm‘l) SCIa (cm’l) State (cm‘l) SCIa (cm'])
3 7.952806 20.00100 7.503162 20.00021
6 4.018509 20.00048 4.017926 20.00032
E 2.632075 20.00046 2.58459] 20.00016
aJ 0.000057]5 20.0000025 0.00005684 20.0000021
53x 0.0007403 20.000018 0.000733o4 20.0000088
AK -0.0004104 20.000018 -0.00041606 20.0000074
6J 0.00001794 20 0000012 0.0000183] 20.0000011
6K 0.0004613 20.000018 0.000455] 20.000011
0.001246 20.00063 0.0011632 20.000062
23 0.001084 20.00051 0.001075 20.00013
5C 0.000612 20.00058 0.000655 20.00012
v0 4617.89180 20.0038
62 0.32760 20.0043
6:” 0.00392 20.0016

 

 

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67

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69

mass dependence for 00, all three Hamiltonians gave similarly excellent
fits of the data for all isotopes with standard deviations of less than

0.005 cm“.

Whereas the planar form of the Hamiltonian and Typke's
Hamiltonian converged to stable values well before final assignments
were completed, this form of Watson's Hamiltonian converged only after
nearly all assignments were correct.

Appendix C lists the observed transitions and their differences
from values calculated using Typke's Hamiltonian. The weights listed
are those used in determining the constants by the least squares
fitting procedure.

We believe that for HDSe a simultaneous analysis of five isot0pic
species, including linear mass dependencies for A, B, and C and linear
and quadratic mass dependencies for V0’ leads to a more significant set
of molecular parameters than would individual fits of each isotopic
species. We note that the Typke, Watson, and planar Hamiltonians all
predict the spectrum equally well. Further, all three Hamiltonians pre-

dict very similar mass dependencies for the molecular parameters, thus

confirming their significance.

General Comments about the Systematic Analysis of Asymmetric Rotor
Molecule Spectra

 

 

In the course of fitting the molecules analyzed in this thesis, a
systematic procedure has been developed for analysis of asymmetric rotor
spectra. This procedure is discussed below.

1. First, ground state molecular constants should be used if
available. Often ground state constants are available from microwave
spectra or from infrared analysis of other bands of the molecule. If

other bands have been analyzed, it is useful to form or calculate ground

70

state combination differences. Ground state combination differences are
formed by taking the difference between two transition frequencies to
the same upper level. This difference is the difference between the

two ground state energy levels involved. The same ground state com-
bination difference may be formed from transitions to more than one
upper state level. Figure 12 shows an example of this. The ground
state combination differences and the observed transition frequencies

of the band to be analyzed can be used with our computer program LINESRT
to assign transitions. LINESRT compares the differences between all
possible pairs of observed transition frequencies to the calculated or
observed ground state combination difference frequencies. Pairs of
lines whose frequency differences match a combination difference fre-
quency are presumed to have the same upper state and the same ground
states as the combination difference. When one line is involved in
several different combination differences, the upper state can be deter-
mined. If good values for the ground state combination differences are
available, many lines can be assigned by this procedure. The lines
assigned by LINESRT should be examined carefully before an attempt is
made to fit them. If the spectrum contains many lines, some lines may
be incorrectly assigned because the frequency difference between two
lines may accidentally be the same as a ground state combination dif-
ference. Inspection of the assignments (for example, checking that a
transition assigned to a frequency in the R-branch of the spectrum
actually has quantum numbers corresponding to an R-branch transition)
will enable one to eliminate many misassigned lines. If LINESRT yields
a number of probable line assignments, these lines may be fit to give

estimates of upper state constants. The next paragraph suggests methods

for estimating starting values of upper state constants.

71

K K

 

 

 

 

 

 

 

5 0 5
L A
6 3 4

 

 

 

 

Figure 12. The 6 3 4 - 5 3 2 ground state combination difference from
some type B band transitions

72

2. Estimate upper state Hamiltonian constants. This may be done
initially by examination of available constants for other bands of the
molecule, by examination of constants of similar molecules (e.g., one
would expect similar variations between upper state and ground state
constants for 201 of HDTe and HDSe), or; if neither of these options is
available, by assuming equal upper and ground state constants.

3. Using the estimated Hamiltonian constants, predict the spectrum
of the band. For unperturbed bands, program INTCALl is very useful. It
plots both calculated line position and calculated line intensities.

For initial assignments of perturbed bands, INTCALl may be of some use.
It is best to arrange predicted transitions by series.

(20)

Cross et 81. give a good discussion of intensities of asymmetric
rotor transitions. For both type A and type B bands the zero series

(AJ = 21, K; = J', K = J) is usually one of the strongest series in

+
both the P and R branches of the band for both prolate and oblate mole-
cules. This series also is usually one of the least perturbed series

in perturbed bands. Although the inverse zero series (AJ = 21, K: = J',
K_ = J) has large line strengths for oblate type A and 8 bands, transi-
tion intensities fall off rapidly for high J values because of the

Boltzmann factor (e-Eg/kT,

E9 = ground state energy) in the intensity
formula. As a general rule, upper state energies in perturbed bands
are more strongly perturbed as J and K_ increase, making the high J,
high K_ levels the most difficult to predict accurately.

As the molecular constants are improved and energy levels are calcu-
lated more accurately, Q branch transitions and other series of transi-
tions should be predicted. It is often most fruitful to add transitions

in order of decreasing expected intensity, especially at early stages

of the analysis.

73

4. Using the predicted spectrum, identify transitions in the
spectrum to be analyzed. Lines within a series may often be identified,
even if they are poorly predicted,by looking for systematic intensity
variations and systematic differences between observed and calculated
lines. The spectra of molecules with several abundant isot0pic species
(for example, selenides and tellurides) often have clusters of lines
showing systematic structure for each transition, each line in the
cluster due to a different isotopic species. When analyzing such spec-
tra, care should be taken to make sure that transitions are assigned
to the proper isotopic species. Lines which do not show the proper
isotopic signature can often be attributed to impurities in the sample
or spectrometer.

5. Fit the assigned lines to improve the estimation of upper state
constants. Delete obviously incorrectly assigned lines from the fit.

6. Form ground state combination differences from the assigned
transitions. Combine these with other ground state combination differ-
ences and microwave lines if available. Fit these data to improve the
estimation of the ground state constants. An observed ground state
combination difference which is not equal to other observed ground state
combination differences between the same levels usually indicates that
one or both lines are misassigned. Moreover, ground state combination
differences which fit poorly often indicate incorrectly assigned lines.
Because the ground state levels are unperturbed, fits of correct ground
state combination differences usually converge to stable values of
Hamiltonian parameters which predict ground state levels accurately.

A line which is used to form several ground state combination differences

which do not fit is almost surely misassigned.

74

7. Using the ground state constants, use computer program USEN to
form upper state energies for all assigned transitions. Program USEN
calculates upper state energies by adding the calculated ground state
energy to the observed transition frequency. All lines involving the
same upper state are grouped together. Examine the upper state energies.
If accurate ground state constants are available and the lines are cor-
rectly assigned, all lines involving the same upper state should have
the same upper state energy within measurement error. When used with
ground state combination differences, this provides a powerful tool for
detecting incorrect assignments.

8. Refit the assigned transitions to improve the estimates of the
upper state constants.

9. Iterate steps 3 thru 8 until all lines are assigned and a good

fit of the spectrum is obtained.

CHAPTER VI

ANALYSIS OF 202, 0 AND 0 OF H S

1’ 3 2

In 1956 Allen et al.(38) identified and analyzed about 35 strong
lines of the v] and 202 bands of H25, identified some lines as being
due to 03, and estimated the position of the v3 band center. In 1969,

Edwards et al.(39)

reported values for the band centers of v], 202, and
03 based on a partial analysis of these three bands. The spectra run
by Edwards et al. were not used in the present investigation. Examina-
tion of their data showed systematic calibration errors of approximately
0.01 cm"1 from run to run. It is conjectured that these errors were
due in part to the lesser accuracy of frequency measurement of calibra-
tion gases then available and in part to the fringe shift problems
discussed in Chapter IV. In any event, the spectra of 202, v], and 03
were rerun for the present investigation. The Coriolis coupled bands
0] and 03 were analyzed simultaneously, while 202 was analyzed as a
single band by ignoring its Fermi interaction with v]. This work is
the completion of that investigation. In a manner similar to the

analysis Of 292, v1 and 03 of H20 by Flaud and Camy-Peyret(40)

, we have
investigated the effects of the Fermi interaction between 202 and 0].
However, unlike them, we have not been able to determine a value for

the Fermi interaction term for H25.

75

76

The spectrum of 202, v1, and v3 of HZS is shown in Figure 13.
This figure is a horizontally compressed plot of our digitally smoothed
data. Because several runs at various pressures were necessary to
record the complete spectrum, the absorption intensities shown in
Figure 13 do not necessarily reflect the true absorption intensities
from region to region for these bands of H25. In general, 202 is a
less strongly absorbing band than 01 and the actual absorption inten-
sities at the high and low frequency ends of the spectrum are smaller
relative to the absorption in the center region of the spectrum than
shown in Figure 13. The band v3 is weakly absorbing compared to v].
A number of the observed 03 transitions have borrowed their intensity
from 0] through the Coriolis interaction between the two bands. This
is particularly true of transitions to high J high K_ levels of 03.
For example, Table 18 lists a few transitions to the highest J and K_
levels of 03 together with their relative intensities and the contri-
bution from v] to the v3 wave functions. Generally, lines to less
perturbed levels of 03 with similar J and K_ either are not observed
or are weaker than those listed in Table 18. Since the Coriolis inter-
action couples levels of the type J K_ K+ in one band to levels of the
type J K_+l K+ in the other band where K_+K+ = J, the complementary
levels in 01 should be weaker than would be expected if no perturbation
were present. It has not been possible to make a good check of this
because only four 0] transitions ending on two upper state levels com-
plementary to those listed in Table 18 have been observed. They are
8 8 l - 7 7 O, 8 6 3 - 7 3 4, 8 6 3 - 7 5 2 - 7 5 2, and 8 6 3 - 8 5 4.
Of these transitions, two, 8 8 l - 7 7 0 and 8 6 3 - 7 5 2, are quite

strong and the upper state wavefunctions include 6 and 13 percent

77

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Table 18
Transitions to High J, High K_ Levels of 03 of H25
. . Observed Relative % Contribution from
Trans1t1on Frequency (cm' ) Intensitya v1 Wavefunction
871 - 770 2741.512 40 7
862 - 761 2746.957 60 15
963 - 862 2761.469 45 47
1073 - 972 2774.893 40 24
853 - 734 2799.285 30 11
981 - 862 2815.404 15 8

 

 

6Height of the strongest observed lines in the spectrum of v] and 03
is approximately 100. Line height is taken to be proportional
to intensity.

80

contributions from the 03 wavefunctions, respectively. The other two
transitions are of moderate intensity. Without detailed knowledge of
the predicted intensity for these lines, the amount of intensity donated
to the v3 transitions cannot be determined.

The bands 202, v] and 03 are coupled by Fermi (Eq.I-l3) and

(40) The form of the Hamiltonian matrix

Coriolis (Eq.I-ll) interactions.
for these interacting states is shown in Figure 14. In their analysis
of 202, v1 and 03 of H20, Flaud and Camy-Peyret found that their Coriolis
interaction coefficient between 202 and 03 was about one-fourth that of
the Coriolis interaction coefficient between 01 and 03. Because 202
and 03 are separated much more than 01 and 03, the interaction between
202 and 03 will be much weaker than between 0] and v3. Since the band
centers of 03 and 202 of H25 are separated by x260 cm'1 compared to
03 - 01 z 14 cm'], we have assumed that the Coriolis perturbation between
202 and 03 may be neglected.

Many of the observed transitions in 2v2, v1 and v of H23 had been

3
(39) .
Therefore, fa1rly good start-

previously assigned by Edwards et a1.
ing values for the Hamiltonian parameters were available. In our
initial analysis of these bands, we assumed the type B band 202 could
be treated as a single unperturbed band and that the type 8 band 01 and
the type A band v3 could be treated as being affected only by the
Coriolis interaction between them. This treatment assumed that the
only effect of the Fermi interaction is to move the observed positions
of the band centers of v] and 202 from the positions they would have

if no perturbation were present. All analysis were done using Typke's

Hamiltonian Eq.(I-8) and Eq.(I-ll) for the Coriolis interaction. Since

H2S is an oblate asymmetric rotor molecule, the rotational Hamiltonian

81

 

 

 

 

 

 

 

H H H
03 C C
.1-
HC Hv HF
1
i i
“0 HF ”202

 

Figure 14. The form of the Hamiltonian matrix 03, v] and 202.

82

is evaluated in the IIIr representation (a = x, b = y, c = z) with the
molecule in the xy plane.

We obtained ground state constants from a simultaneous least
squares fit of the 39 H25 microwave transitions of Helminger et al.(41)
together with our ground state combination differences combined with

(42) The microwave lines were

those obtained by Snyder and Edwards.
weighted approximately 60 times the weight of the ground state combina-
tion differences (relatively lightly in comparison to their precision
relative to the infrared combination differences) in order to reduce
high correlations among ground state constants and to better determine
them. Our final ground state constants were determined from a least
squares fit of the combined ground state combination differences and
microwave transitions, with all ground state constants varied simulta-
neously. These constants and their partial correlation coefficient
matrix are shown in Tables 19 and 20, respectively. The standard devia-
tion for the fit of the infrared ground state combination differences

is 0.003 cm"1 and for the microwave lines is 0.0001 cm'].

The fits for
ground state constants rapidly converged to a stable set of values. As
discussed in Chapter 1, several of the centrifugal distortion parameters,
v12. DJ, DJK’ and DK’ are highly correlated.

Our initial analysis of 2v2 was done by treating it as an unper-

2325 and H2345 isotopic species were fit simultaneously

turbed band. The H
using Eq.(II-7) with 52m set to zero. Because only two sulphur isotopes
are present, the band center does not involve the quadratic dependence
on mass difference.

Our fit of 202, considering it as a single unperturbed band,

quickly converged to a stable set of constants and fit with a standard

83

Table 19

Molecular Ground State Constants for H25

 

 

 

Constant (cm'l) $6125%cm-1)

A' 10.361528 0.00031
8' 9.016079 0.00029
0' 4.731214 0.00013

05 1.10011210“3 0.0079210"3
05K -l.9652x10'3 0.013x10‘3
”k 0.92695x10'3 0.0081x10'3
65 0.20845210‘3 0.00482210'3
R6 -0.2779]x10'3 0.0069210'3
H5 0.4244x10’5 0.093x10‘5
ij 4.536210“6 0.2800"6

k0 1.865x10‘5 0.35210'6
Hk -0.755x10'5 0.15210'6
Hg 0.325210'6 0.13210'6
H6 0.885x10’5 0.16210'6
H50 0.2412210"6 0.070x10‘5
5A 19.16x10'3 3.2210'3
53 0.697210'3 0.56210'3
15C 3.674x10'3 0.57210'3

m

Standard deviation of 353 ground state combination differences = 0.0030 cm'].

Standard deviation of 39 microwave transitions = 0.0001 cm'].

a95% SCI (simultaneous confidence intervals), here 5 6 standard deviations.

84

as... 2...... 2...... .8... us... 3......- 8.....-

m3... 8.....- 48...- 3.....- 8o... 3...- 8.....-

5...- .3... m3... .8... 2o... 82... 3....

3...- 3.....- m......- 2.....- 8.....- .8...-

3..... .3... 8.... ...... .8...-

.aa.o ~ma.° .No.a ..o.o-

82... NS... 8....

as... .8...

.2...

...... ...: 3.... ...... ...: o.. ...2
N

m
cm o—nuh

avo.01
coo.o
nmo.ou
m—o.o
mnm.oi
www.ci
www.c-
pcm.o-
ovo.o
omo.o

x

mvo.O1
eno.c
mmc.oi
_mo.o
mw~.91
pma.01
swo.o-
ovm.oi
wmo.c1
pno.o
omm.°

2d

omo.cc
~oo.oi
voo.o-
oo—.o

¢m~.c-
mam.c-
pww.91
oom.o1
ouc.o-
owo.oi
vom.o

~mm.°

: ... 33m v.59... 05 ..8 3:32:08 532883 2.3.3..

ppo.o

nvc.ci

moo.o
noo.oi
omn.o
mme.o
msv.o
ovv.o
omo.o
mvo.oi
—-.o-
o—m.oi
mmo.o-

.u

moo.o-
mo—.o1
mo~.o
mco.o-
~o°.o-
so—.o-
so—.c1
ovo.o-
oo~.c
mon.o
mon.o
oo~.o
mac.c
ovc.c-

~oo.o
c-.o
o—v.o-
nom.o
ovo.o-
mmo.co
ooc.o-
o_c.oi
Nov.o-
op~.01
ow—.°
map.o
ooc.c
—mm.o-
_wm.c-

85

l

deviation of observed minus calculated values of 0.004 cm- . In this

fit, all upper state constants for 202 were allowed to vary simulta-

32

neously. The fit includes over 300 observed transitions for H2 5 and

45 observed transitions for H2345. The H2345 transitions were fitted

32

simultaneously with the H2 S transitions using linear mass dependencies

34

for N, 0, cu and v . Because of the limited number of H2 5 transitions

0
observed, ground state combination difference were not used to deter-
mine isotopic mass effects; instead both upper and ground state EA, EB,

34

and EC were varied independently in the line fit. The H2 5 transi-

325 transitions.

tions fit with about the same precision as do the H2
The Hamiltonian parameters and partial correlation coefficients for 2v2
are shown in Tables 2l and 22, respectively. All assigned transitions
and frequencies for 202, v1, and 03 of H25 are listed in Appendix 0.
Most of the effective centrifugal distortion constants for 202 are
larger in magnitude than those of the ground state. This is to be
expected because of the relatively large deformations from equilibrium
in the bending mode. In contrast, the distortion constants for v1 and
03 are much closer to the ground state values.

We initially fit 01 and v3 considering only the Coriolis perturba-
tion between them. The fit converges to stable values for most transi-
tions for which we were able to form ground state combination differences.
However, levels involving high 0 or moderate to high J and high K_ are
very sensitive to small changes in Hamiltonian parameters. This occurs
because these levels are most strongly perturbed by the Coriolis inter—
action; thus, what would be a small change in energy if the levels were
unperturbed becomes a large change in energy because of the perturbation.

Obtaining a stable fit for u] and 03 is further complicated because a

536

Table 21

Molecular Constants for 2v of H S

2

 

 

Constant (cuf‘)

95: -1
SCIa (cm )

 

 

 

 

A' 11.1161] 0.0014
3' 9.442,, 0.0012
0' 4.500067 0.00036
05 1.05.53003 0.018x10‘3
05K -3.2789x10'3 0.037;:10‘3
”k 1.692x10-3 0.025x10'3
55 0.:1886x10"3 0.0215x10‘3
Ré 4.3999110“3 0.010x10‘3
H5 0.849x10'6 0.19x1o‘5
H3K -3.229x10'5 0.57x10'6
Hid 4.2051110“6 0.69x10‘5
Hk -1.826x10'6 0.29:00‘6
H5 1.1:”;110'6 0.50::10'6
Hg 2.285x10'6 0.72;:10‘6
Hi0 0.443xl0'6 0.27x10'5
5‘ 19.8x10‘3 5.1x10'3
53 1.3]xlo'3 2.7x10'3
ac 3.545x10'3 1.211103
00 2353.90710 0.00075
5” 1.0646 0.014
Isotope Standard Deviation Number of
of Fit (cm ) Weighted Lines
A11 .0040 335
H2325 .0040 291
112345 .0038 45

aoss SCI (simultaneous confidence intervals) here § 7 standard deviations.

87

000.0-
000.0-
000.0-
000.0-
.00.0-
000.0

000.0-
000.0

000.0-

.00.0-
000.0-
000.0-
000.0-
000.0-
000.0

000.0-
000.0

000.0-
000.0

0x

000.0-
000.0-
..0.0-
.00.0-
000.0-
0.0.0
000.0
000.0
000.0-
000.0
000.0

......

0.0.0-
000.0-
0.0.0-
..0.0-
.00.0-
0.0.0
000.0
000.0
000.0-
000.0
..0.0
000.0

000.0
000.0-
000.0-
000.0-
.00.0-
000.0-
000.0-
0.0.0
00..0-
000.0
000.0
000.0
00..0

000.0-
000.0
..0.0-
..0.0
.0..0
000.0
000.0
00..0
000.0-
00..0
0.0.0
000.0
0.0.0
00..0

0.0.0
0.0.0
000.0
0.0.0
000.0
0.0.0-
.00.0
.00.0-
000.0
000.0-
0m0.0-
000.0-
000.0-
.00.0-
000.0-

...5

0.0.0
0.0.0
000.0
0.0.0
000.0
.00.0-
0.0.0-
0.0.0-
000.0
000.0-
000.0-
000.0-
000.0-
000.0-
000.0-
000.0

x0

00 0.00.

000.0
000.0
000.0
.00.0
000.0
000.0-
000.0-
.00.0-
000.0
000.0-
000.0-
.00.0-
.00.0-
.0..0-
.00.0-
000.0
000.0

.00.0-
000.0-
..0.0-
000.0-
000.0-
000.0
000.0
000.0
.00.0-
00..0
0.0.0
000.0
000.0
000.0
0.0.0
..0.0-
000.0-
000.0-

.0

000.0-
000.0-
000.0-
0.0.0-
000.0-
00..0
000.0
00..0-
..0.0-
00..0
00..0
000.0
000.0
0.0.0-
000.0
000.0-
000.0-
.00.0-
0.0.0

mN: mo NDN ..0.0 mucmmuw&wmou comuu—egou .0wugan—

0.0.0-
00..0-
.00.0-
000.0-
00..0-
000.0
00..0
00..0-
.0..0-
.0..0
00..0
00..0
000.0
0.0.0-
000.0-
.00.0-
000.0-
000.0-
000.0
000.0

0.0.0-
00..0-
000.0-
000.0-
000.0-
000.0
.00.0-
0.0.0
..0.0-
000.0
000.0
0.0.0
..0.0
0.0.0
0.0.0
000.0-
000.0-
000.0-
0.0.0
000.0
000.0

MU
w‘

..0.0-
00..0-
.00.0-
000.0-
.00.0-
....0
000.0-
000.0
000.0
000.0
000.0
000.0
..0.0
000.0
000.0-
0.0.0-
0.0.0-
.00.0-
000.0
000.0
000.0
000.0

....

..0.0-
00..0-
000.0-
.00.0-
000.0-
.0..0
.00.0-
0.0.0
000.0
000.0
000.0
000.0
000.0
000.0
00..0-
.00.0-
000.0-
000.0-
000.0
000.0
00..0
000.0
000.0

...
a.

3....
....

0

....

0

...:

....
...5
.5
...
...
w...
....

88

m

0

..0.0 0.0.0 ..0.0 0.0.0
00..0 000.0 0.0.0

000.0 000.0

000.0

x .o N». La. m.=o.u...~o. co..u.at.ou ......m

.....eoa. NN 0....

q.

0.0.0-
00..0-
000.0-
0...0-
00..0-

0

000.0-
000.0
000.0
000.0
000.0
000.0

0.

000.0

..0.0-
0.0.0-
000.0-
0.0.0-
000.0

000.0-

0.0.0

0.0.0-
0.0.0

000.0-
.00.0-
.00.0-
000.0-
.00.0-

00<0

89

number of additional Hamiltonian constants are highly correlated. Most
of these new high correlations occur because we are not able to observe
and identify enough different upper state levels (about 160 for v] and
about 80 for 03) to determine all the individual constants well. In
particular, more high 0 energy levels are needed, especially for 03, to
determine a unique set of Hamiltonian constants. Because of this, the
constants shown for v] and v3 are principally effective constants which
accurately predict transitions of similar upper and lower state 0'5
and T'S (T = K_ - K+) to those observed and reported here. Tables 23
and 24 show Hamiltonian parameters and their partial correlation coef-
ficient matrix for v] and 03, respectively.

In an attempt to determine the size of the Fermi coupling constant
between 01 and 202, we made several simultaneous three-band fits of the
spectrum, starting with four different trial values for the Fermi inter-

1

action constant: FER = 0, l5, 30, and 45 cm' (FER = 0 corresponds to

treating 202 as an unperturbed band). Kuchitsu and Morino(43)

l 1

give

k for H20 and H28 as 255.4:3.4 cm' and 102.7:l3.2 cm'

(40)

122 , respectively.

Flaud and Camy-Peyret give their Fermi interaction term

1

FER = (3/2)”2 k = 47.87 +0.70 cm-1 or their k122 = 39.088i0.57 cm'

122 3'

is approximately l5 percent of the value of Kuchitsua and Morino. If
we assume the ratio of k122 determined by the Fermi interaction for
H25 to that given by Kuchitsu and Morino is the same as for water, we

estimate kl22 ~ l5.7 cm"1 and, hence, FER z l9 cm'1.

Our trial values
bracketed this value.

Upon fitting our observed transitions, we found that, if we fix
FER and allow A', B', C', and 00 to vary from their FER = 0 values for

all three bands and allow the P4 coefficients to vary from their

90

Table 23

Molecular Constants for v] and v3 of H25

 

 

 

 

 

-1 95: -1 _] 95: _.
Constant (cm ) SCIa (cm ) Constant (cm ) SCIa (cm )
N 10.200119 00015 10.14577 0.0053
0' 8.393784 0.00099 3.93949 0.0031
0' 4.662438 0.00046 4.678863 0.00032
03 1.000248-00‘3 0.00093 1.1685x10'3 0.013--10'3
°3x -1.936]x10'3 0.015x10'3 4.9572-00'3 00:32:003
”i 0.920831110'3 0.000631-10‘3 0.8792x10'3 0039-003
55 0.1972x10‘3 0.015-110'3 0.2318-‘10‘3 0015-003
06 -0.27992x10‘3 0.0072x10'3 -0.2830x10‘3 0.023-110‘3
H5 03581-00”6 0.016x10‘3 1.4204-‘10'6 0.052x10'5
H5K -l.47l]ox]0-6 0.0067x10‘5 086-00“6 1.8x10'6
HkJ 1.8792x10’6 0.031x10'6 -0.3490x10'6 0.24x10'5
Hi -0.7550x10‘5 -0.755x10'5
Hg 01065-006 0.021--10'6 1.873xl0'6 0.13x10'6
Hg 0.9763x10'5 0.003-110‘6 1.82:10'5 1.5x10’6
Hi0 0.2412-110'6 0.2412x10‘5
0° 2614.40990 0.0066 2628.44020 0.0072
02 0.13885 0.0040
xy -0.306240 0.00087
Band Standard Devia ion Number of
of Fit (cm‘ ) Heighted Lines
All 0.0052 368
v1 0.0041 233
03 0.0070 13s

695% SCI (simultaneous confidence intervals) here . 8 standard deviations.
the constant was fixed to the ground state value.

If no value is listed,

c.

CALC

0.855

0.517
-0.810
-0.444
~0.284

0.403
-0.176

0.593

0.377

0.249
-0.343
-0.100
.829
.124
.059
.203
.104
.027
-0.102
-0.023
-0.012
-0.116
.002
.086
.020
.012
.111
.038
.108

00000000

.014

0

-0.
.0_

00000

0000000

.482
849
413
.250
.788
.217
.738
.348
.218
.690
.269
.800
.128
.170
.147
.091
.021
.071
.016
.006
.041
.097
.052
.012
.005
.030
.059
.095
.003

91

Tab1e 24

Partial Correlation Coefficients for 01 and 03 of H25

”3

0.1K ”1': 5.1

-0.776

-0.943 0.787
-0.885 0.644 0.957

0.269 -0.632 -0.255 -0.145

0.097 -0.152 -0.104 -0.080 0.622
0.750 -0.971 -0.816 -0.689 0.597
0.875 -0.749 -0.984 -0.956 0.227
0.820 -0.620 -0.937 -0.988 0.132
-0.238 0.585 0.242 0.144 -0.965
0.109 -0.202 -0.122 -0.091 0.682
0.633 -0.685 -O.465 -0.349 0.424
0.182 -0.161 -0.159 -0.150 0.147
0.052 -0.104 -0.041 -0.028 0.323
0.039 -0.174 -0.042 -0.018 -0.006
0.033 -0.105 -0.038 -0.020 0.048
0.029 ~0.040 -0.040 -0.039 0.006
.110
.039

-0.036 .049 0.035 0.003

0 0
-0.028 0 0.041 0.040 -0.001
-0.026 0.026 0.038 0.041 0.007
-0.001 0.087 0.001 -0.006 0.122
0 0.006 -0.002 -0.237

0.031 -0.098 -0.046 -0.034 -0.020

-0.010 .031
0.026 -0.036 -0.040 -0.039 -0.004
0.025 -0.027 -0.039 o0.041 -0.009
0.000 -0.087 -0.001 0.006 -0.139

-0.004 -0.008 -0.001 -0.003 -0.226
0.032 -0.089 -0.C32 -0.020 0.031
0.026 -0.010 -0.029 -0.009 -0.001

.185
.102
.075
.612
.955
.009
.180
.001
.047
.074
.017
.011
.015
.005
.189
.280
.003
.012
.004
.187
.270
.012
.008

0

-0.

OOOOOOO

0030000

-0,

.809
.685
576
.229
.547
.138
.061
.210
.118
.052
.147
.055
.038
.134
.011
.140
.055
.041
.142
.058
.092
001

-0

0000000

00000000

”0K

.962
.226
.121
.366
.135
.031
.048
.043
.051
.064
.056
.051
.002
.001
.064
.058
.054
.002
.008
.034
.021

-0.

0000000

"-2.-

137
.089
.282
.130
.024
.021
.024
.049
.046
.053
.053
.009
.004
.047
.054
.054
.009
.006

.023
.001

R6
”3
”5K
”k0
“5
”6

v0

CALC

-0.723
-0.341
-0.183
-0.389

0.062
-0.046
-0.001
-0.029
-0.006
-0.012
-0.210

0.309

0.049
0.011
0.016
0.232
0.322
-0.014

0.009

53

-0.501
0.055
0.235
0.177

-0.974

-0.628
0.129
0.001

0.056
-0.111

-0.090
0.093
0.022
0.005

-0.020

-0.006
0.315

-0.413

-0.026
0.017
0.005

-0.329

-0.427
0.017
0.016

0.229
0.115
0.114
0.570
0.963
0.053
0.023

S92

Table 24 (cont'd.)
Partial Correlation Coefficients for v1 and 03 of H25

“1
0° 62 ny A' B' c' 05 03K 0*
0.128
0.077 0.518

0.108 -0.433 -0.314

0.059 -0.490 0.112 0.747

0.017 -0.673 0.101 0.419 0.553

-0.044 0.625 0.027 -0.746 -0.782 -0.836

-0.013 0.641 -0.092 -0.390 -0.509 -0.963 0.866

-0.007 0.620 -0.059 -0.266 -0.345 -0.942 0.742 0.962

-0 032 -0.103 0.599 -0.298 0.355 0.238 -0.101 -0.240 -0.167
-0.040 -0.190 -0.426 0.232 -0.019 0.110 -0.186 -0.115 -0.115
0.030 -0.666 -0.045 0.662 0.665 0.779 -0 970 -0.861 -0.732
0.010 -0.590 0.082 0.361 0.467 0.891 -0.852 50.977 -0.920
0.006 -0.591 0.058 0.268 0.345 0.901 -0 762 -0.967 -0.981
0.021 0.069 -0.572 0.330 -0.251 -0.210 0.053 0.230 0.166
-0.021 -0.l78 -0.464 0.336 0.003 0.111 -0.245 -0.124 -0.118
0.085 -0.513 -0.026 0.698 0.768 0 597 -0.623 -0.484 -0 409
-0.000 0.001 -0.027 -0.031 -0.001 -0.065 0.064 0.075 0.073
11
“5 ”ix ”la ”5 ”6 8°
0.891
0.787 0.966
-0 024 -0.240 -0 185
0.295 0.129 0.123 0.701
0.496 0.409 0.368 -0.074 0.070
-0.o78 -0 085 -0.082 0.020 0.009 -0.014

93

FER = 0 values for v] and 202, all four trial values of FER fit the

spectrum approximately equally well. For FER = 45 cm'1

, A' and B' for
v] and 202 are changed about 0.3 percent from the FER = 0 values.

Tables 25 thru 30 show Hamiltonian parameters and their partial correla-
tion coefficients for 202, 0,, and 03 with FER = 15, 30, and 45 cm“.
Because our fitting program deletes from the fit lines whose observed
minus calculated deviations are greater than 3.5 standard deviations

of the fit, slightly different numbers of lines are included in the fits
with the various values of FER.

An examination of the predicted energy levels and the fractional
contributions of each of the three bands to the total wave functions
gives some indication why we can fit the spectrum using arbitrary
values of FER. Both mixing of the v] and 202 wave functions for a
given level and the shifts of the v] and 202 band centers due to the
Fermi interaction are observed to increase as FERZ. More importantly
for any of our trial values of FER, the mixing increases smoothly as
the upper state J increases, and for given J the mixing increases
smoothly as T = K_ - K+ increases for all levels which we assigned. We
refer to this as smooth mixing. This may be contrasted with the non-
smooth mixing calculated for H20 by Flaud and Camy-Peyret. For exam-
ple, Tables 31 and 32 show the calculated energy levels and wavefunc-
tion mixing for J = 9 for H25e and H20. Smooth mixing of wavefunctions
mostly results in a uniform shift of the band centers of u] and 202
because of the Fermi interaction, whereas nonsmooth mixing indicates
strong accidental resonances between individual rotational levels. In

the case of smooth mixing, 0], 202 and FER are linearly dependent and

cannot be determined uniquely. However, when individual rotational

94

levels are perturbed in a nonsmooth manner, 0], 202 and FER become
determinable. Since we have identified no such levels, we are unable

to determine a value for the Fermi interaction constant.

95

Table 25

Molecular Constants for 202. v], and v3 of H25 with FER = 15

 

 

20

 

 

 

2 ”3
_, a95: _‘ -1 a95% -1 -1 a95: _,
Constant (cm ) SCI (cm ) Constant (cm ) SCI (cm ) Constant (cm ) SCI (cm )
A' 11.117656 0.00088 10.197776 0.00075 10.146279 0.00091
8' 9.444445 0 00075 8.89126 0.00082 8.938856 0.00069
0' 4.607906 0.00020 4.662157 0.00038 4.679392 0.00052
05 1.61887x10°3 0.0055x10'3 1.08686x10'3 0.0029x10‘3 1.1635,..10'3
03K -3.20Hx10'3 0.0121210'3 -1.94904x10'3 0.0065x10'3 -.1.9572xio‘3
0k 1.6437xio‘3 0.00741110‘3 0.9279,..10'3 0.00431210'3 0.8792x10°3
65 0.36422x10'3 0.00731210‘3 0.19843x10'3 0.00251‘10'3 0.2318100‘3
96 .0.39108x10‘3 0.0028x10’3 -0.27833x10'3 0.00221110‘3 0283;210‘3
H5 0.5246100“6 0.3581x10'6 1.42;.10'6
85K 2061.106 1471.10“6 -1.86x10‘5
HRJ 2.627x10'6 1.879x10'5 0.849x10'6
Hk 4.241.10‘6 -0.755x10‘6 -0.755x10'6
Hg 0.63x10'5 0.10651210'6 1.873.210‘6
Hg 1.6mx10‘6 0.97531210'6 1.82x10'5
Hi0 0528;210“6 0.24123210'6 0.2412,;210'6
6° 2354.83620 0.0061 2613.54280 0.0054 2628.44140 0.0099
02 0.1085 0 027
xy -0.30117 0.0051
Band Standard Deviation Number of
of Fit (cm'l) Weighted Lines

All 0.0055 701

61 0.0044 264

v3 0.0066 132

.62 0.0061 305

a95% SCI (simultaneous confidence intervals) here ; 7 standard deviations.
constant was fixed to the value detennined in the FER = 0 fit.

If no value is listed. the

CALC

0

Partial Correlation

.853

0.514

.831
.070
.063
.192
.098
.018
.042
.012
.009
.106
.001
.102

0.002

.001
.000
.000
.000
.000
.002

0.000

-0

.001
.003

0000000

”3
Bl

.478

.078
.175
.143
.089
.012
.029
.007
.004
.036
.098
.091

.001

.001

.000
.000
.000
.000
.001

.001

.000
.011

000000

CI

.633
.033
.053
.048
.044
.085
.091
.092
.093
.011
.007
.050
.001
.001
.000
.001
.001
.001
.000
.001
.000
.005

96

Table 26
Coefficients for 202. v], and 03 of H25 with FER = 15
"1
00 62 ny A' 8' C' 03 DJK

0.069

0.079 0.354

0.104 -0.403 -0.284

0.056 -0.449 0.119 0.771

0.013 -0.848 0.079 0.367 0.453

-0.021 0.833 -0.029 -0.454 -0.500 -0.958

-0.009 0.823 -0.055 -0.271 -0.328 -0.955 0.973

-0.008 0.809 -0.042 -0.216 -0.259 -0.931 0.946 0.993

-0.028 -0.184 0.579 -0.194 0.415 0.275 -0.229 -0.229
-0.039 -0.290 -0.393 0.263 0.044 0.252 -0.278 -0.244
.081 -0.518 -0.013 0.713 0.778 0.531 -0.492 -0.389
.001 ~0.002 -0.002 0.011 0.008 0.003 -0.004 -0.002
.000 -0.003 0.001 0.008 0.009 0.004 -0.004 -0.003

0 0

.000 -0.004 0.001 0.003 .004 .008 -0.007 0.006
.000 0.006 0.000 -0 006 -0.006 -0.009 0.009 0.009

.000 0.006 -0.001 -0.003 -0.004 -0.009 0.009 0.009

0000000

.000 0.006 0.000 -0.002 -0.003 -0.009 0.008 0.009
-0.001 -0.001 0.010 -0.007 0.005 .004 -0.002 -0.003
0.000 -0.002 -0.005 0.002 -0.001 .002 -0.002 -0.002

0.000 -0.002 0.000 0.006 0.006 .004 -0.003 -0.002

0000

-0.005 -0.017 -0.042 -0.010 -0.040 .008 0.001 -0.007

CALC

Partional Correlation Coefficients for 299. v]. and v3 of H25 with FER = 15

-0.190
-0.236
-0.348
-0.002
-0.002
-0.006

0.008

0.009

0.009
-0.002
-0.002
-0.002
-0.013

-0.046
-0.005

.404
.190
.003
.003
.002
.002
.002
.002
.019
.006
.001
.021

.007

.118
.002
.001
.002
.003
.002
.002
.009
.013
.000
.013

.008
.008
.005
.006
.004
.004
.002
.000
.008
.010

97

Table 26 (c0nt'd.)

Bl

.474
.542
.346
.266
.513
.222
.785
.019

-0

-0

0000

.943
.940
.912
.383
.246
.589
.018

0.969
0.936
-0.391
-0.149
-0.537
-0.027

0.992
-0.325
-0.248
-0.424
-0.018

-0.262
-0.250
-0.377
-0.015

()7

0.131
0.219
0.032

Holecular Constants for 202. v], and v3

98

Table 27

of H S with FER - 30

2

 

 

 

 

 

262 v] 03
Constant (cm'I) SC1251cm-l) Constant (cm-1) SCIa ?2;']) Constant (cm'I) 5C1251cm'l)

A' 11.126940 0.00092 10.188617 0.00058 10.146169 0.00093
8' 9.449938 0.00082 8.885926 0.00055 8.938893 0.00066
c' 4.6073758 0.000085 4.662744 0.00041 4.679350 0.00055
05 1.59352500'3 0.0056x10'3 1.1132,):10‘3 0.00331110‘3 1.1685x10'3
05K -3.1504x10'3 0.011x10'3 -2.00092x10'3 0.0071xio’3 -1.9s7x10'3
0k 1.61827x10'3 0.0070x10'3 0.953475210'3 0.0043100"3 0.8792x10'3
65 0.359551210'3 0.00771210'3 0.20:1981110'3 0.0028x10'3 0.2318x10-3
96 -0.39187x10'3 0.00315210‘3 -0.27812x10'3 0.00231210’3 -0.283x10'3
85 0.52461210’6 0.3581x10'6 1.42.2106
HjK 4.055.10‘6 -l.47x10'6 -1.86x10‘5
”k0 2.767.210‘6 1.879x10'6 0.849x10'6
Hi 4.241.10‘6 -0.755x10‘5 07553110"6
85 0.531(10'6 0.10651410'6 1.873x10°6
Hg 1.601x10'6 0.9763x10'5 1.82.210'6
Hi0 0.5281210‘6 0.2412x10'6 0.24121210'6
.0 2357.4737o 0.0059 2610.90350 0.0062 2628.4415 0.011
5; 0.11159 0.0042
xy -0.30376 0.0042

Band Standard Deviation Number of

of Fit (cm ) weighted Lines

411 0.0056 680

v1 0.0045 252

63 0.0057 124

262 0.0065 304

a95% SCI (simultaneous confidence intervals) here 3‘7 standard deviations.

constant was fixed to the value determined in the FER ' 0 fit.

If no value is listed. the

€99

0P0.0
~00.0
~00.0-
~_0.0
m-0.01
0—0.01
000.01
000.0
~00.0
0~0.0

«00.0
.00.01
—00.0
000.0
~—0.0-
~—0.01
000.01
0—0.0
000.0-
000.01
«00.0

000.0-
0—0.0
000.0
000.0
~_0.01
0.0.0-
000.0-
0—0.0
000.0
000.0
n~v.0
000.0

n~o.o m_o.o ooc.o-
aoo.o- o_o.o- m_o.o-
Noo.o- ~oo.o- mo¢.o-
o.o.o- ~_o.o- m_o.o-

.mo.o eno.o mmo.o
m2; m8... Rod
.mo.o mmo.o “mo.c
mmc.o- owo.o- “No.c-
moo.o- ..c.o- ~_o.o-
~oo.c- moo.o- q_o.o-
nmm.o- nam.o- .o..°-
o.n.o- n~n.o- mm~.o-
a_m.o- mam.o- «53.0-
nam.o —mm.o

m~o.o

do em as

—>

on. x02 g._z WN: .6

000.0-
0.0.0
000.0
0.0.0
000.01
“00.0-
000.0-
—00.0
0.0.0
n_0.0
«00.0
000.0
000.0
000.0-
000.0-
000.0-

.0

000.0
000.0
000.0-
m~0.0
——0.01
m—0.01
000.01
0—0.0
000.0
000.0
000.0
000.0
mvm.0
«00.0-
000.01
000.0-
000.0

.0

000.0
000.0
000.01
000.0
——0.01
0—0.01
000.01
m—o.0
000.0
000.0
mmm.0
000.0-
000.0
000.01
m—n.01
000.0-
mwv.0
000.0

.<

00 m—nah

000.0
000.0
000.0-
~_0.0
000.0-
000.0-
000.0-
000.0
000.0
~00.0
000.0
.0—.0-
000.0
~00.01
000.0-
000.0-
000.0
0~_.0
000.01

xx

000.0
000.01
000.01
000.01
~00.0
000.0
v~0.0
0—0.01
—p0.01
000.0-
m~m.0-
000.01
000.0-
o_0.0
~00.0
~00.0
~00.0a
pov.01
000.01
000.0

a use ..9 .~s~ c30 mu:a_u_0goo0 co_~c_mgcou

«00.0
~00.0
~00.01
.00.01
000.0
000.0
—00.0-
000.0
000.0
000.0
000.0
~00.01
000.0-
000.01
0—0.0-
000.0-
n-0.0
000.0
~0—.0
~00.0
000.0

...3288

_00.0
_00.0
000.01
000.0-
000.0
000.0-
000.01
~00.0
~00.0
000.0
000.0
000.0
000.0
N00.01
~00.0-
000.0-
000.0
000.0
—mo.0
000.0
000.0
000.0

000.0
000.0
000.0-
—00.01
000.0
000.0
~00.0u
000.0
~00.0
000.0
~00.0
00..0-
-0.0-
«00.0-
000.0-
000.0-
~—0.0
000.0
Pv—.0
00—.0
000.0
000.0
000.0

000.0
000.0
000.0-
_00.01
000.0
000.0
—00.01
000.0
000.0
000.0
v00.0
000.0-
000.0-
0p0.01
0—0.0-
000.0-
0_0.0
~00.0
50—.0
00..0
p~0.0
000.0
m~m.0
000.0

.<

00<u

o>

60
x

x0
0

.0
.0

.0
.0
.<
0
0
>
.0
.0

100

000.0- 000.0- 000.01 000.0
.m00.0i o—N.0 000.0-

00..0 pm~.01

_0~.01

000.0
000.01
oc~.0u
n~m.0i
000.0

x0

0—0.0-
000.0-
.0..0-
000.0-
000.0
000.0

~>~

on . mum =3_z mm: 06 ms use ..6 .~>~ 26. mo=8_uw2.mou =o_ua_gttou _a_3caa

A.u.u=oov mm m_gap

000.0-
000.0
~v~.0
000.0
~—0.01
0v0.0-
mv0.0-

000.0-
000.0
.00.01
n—m.0
mo~.01
000.0-
000.0-
000.0

~00.0-
005.0
—0~.0-
—00.01
00N.0-
vo~.0-
000.0-
p00.0
000.0

.<

x0

.0
.0

101

Table 29

Molecular Constants for 202. v1. and 03 of H25 with FER - 45

 

 

 

 

 

262 6, v3
-1 95: _, . _, 35: _, _] 95: _,
Constant (Cl ) SCI' (c- ) (Constant (c- ) SCI (0- ) Constant (cm ) SCI' (0- 1

N 11.14402 0.0010 10.17188 0.0011 l0.l46” 0.0010
3' 9.460523 0.00089 8.87558, 0.00098 8.988488 0.00074
0 4.6053 0.00021 4.6636“ 0.0041 4.679485 0. 00054
05 1.551381210'3 0.0074x10'3 1.1604‘x10'3 0.00541210'3 1.116%:110‘3
03K -3.07mx10‘3 0.016.:10‘3 -2.09‘6x10'3 0.011,:10‘3 4.9572100'3
0k 1.57959xio‘3 0.0097x10'3 1.000351110'3 0.0061100'3 0.8792x10'3
65 0.34755x10'3 0.0082x10‘3 0.213‘5x10'3 0.0067x10‘3 0.2318x10'3
26 -0.39422x10‘3 0.00:111210‘3 -0.27508x10‘3 0.032;:10'3 -0.283x10°3
83 0.5646x10'6 0.3581x10'6 1.42x10'6
"5‘ -2.06x1o'° mum“6 4.86100"6
Hid 2.767x10'6 1.879x10°6 0.849x10'6
Hi 4.24.110'6 07551.10"6 -0 755x10 5
a; 0.63x10“ 0.10651110'6 l.873x10'6
Hg 1.601x10'6 0.9763xl0'6 1.82x10"
Hi0 0.528x10“ 0.2412x10'6 0.2412x10'6
6° 2361.98960 0.0010 2606.38580 0.0089 2628.4422 0.010
5; 0.1028 0.028
Bx, -o.30548 0.0054

.. 59:28.53: 1°" .011-.5211.

All 0.0057 661

”1 0.0051 247

v3 0.0062 125

262 0.0058 289

'95: SCI (simultaneous confidence intervals) here ; 7 standard deviations.
constant was fixed to the value determined in the FER - 0 fit.

If no value is listed. the

CALC

Partial Correlation Coefficients for sz. v]. and v

A.

0.870
0.531
0.843
0.072
0.136
0.158
0.092
0.017
-0.030
-0.011
-0.008
-0.021
-0.113
0.090
0.009
0.006
0.001
-0.003
-0.001
-0.001
-0.003
-0.008
0.004
0.012

“3
Bl

0.487
0.806
0.058
0.176
0.135
0.069
0.010
~0.019
-0.005
-0.004
-0.035
-0.129
0.080
0.007
0.005
0.001
-0.002
0.000
0.000
-0.003
-0.008
0.004
0.020

c'

0.634
0.036
0.065
0.049
0.041
0.084
-0.091
-0.091
-0.092
0.026
0.005
0.047
0.006
0.005
0.004
-0.006

-0.006‘

-0.006
-0.001
-0.007
0.003
0.005

0.065
0.093
0.110
0.052
0.012
-0.018
-0.009
-0.008
-0.026
-0.066
0.077
0.006
0.004
0.001
-0.002
-0.001
0.000
-0.003
-0.006
0.004
0.009

102

Table 30

0.370
-0.447
-0.461
-0.854

0.845

0.825

0.810
90.421
-0.303
-0.515
-0.019
-0.025
-0.038

0.053

0.052

0.050
-0.024
-0.011
-0.019

0.034

-0.050
0.127
0.088

-0.072

-0.059

-0.045
0.279
0.038
0.036
0.005
0.014
0.007

-0.009

-0.006

-0.004
0.018

-0.002
0.006
0.043

3 2

A' 8'
0.874

0.416 0.431
-0.448 -0.458
-0.293 -0.296
-0.234 .-0.232
0.456 0.789
~0.116 0.056
0.782 0.778
0.089 0.066
0.083 0.087
0.035 0.036
-0.051 -0.050
-0.031 -0.031
-0.024 -0.024
0.016 0.055
-0.022 -0.009
0.062 0.055
-0.019 -0.011

of H S with FER ' 45

CI

-0.962
-0.951
-0.929
0.444
0.355
0.522
0.028
0.037
0.071
-0.086
-0.085
-0.082
0.037
0.021
0.035
-0.032

”1

”5

0.981
0.958
-0.475
-0.312
-0.468
-0.029
-0.037
-0.061
0.082
0.080
0.077
-0.035
-0.014
-0.029
0.034

0.1K

0.994
-0.353
-0.338
-0.371
-0.017
-0.023
-0.058

0.078

0.080

0.079
-0.028
-0.018
-0.021

0.028

V
0

CALC

103

Table 30 (cont'd.)

Partial Correlation Coefficients for 2v . \l'. and 1)., of H25 with FER - 45

-0.292
-0.329
-0.333
-0.013
-0.017
-0.056
0.074
0.078
0.078
-0.024
-0.017
-0.018
0.015

R6

-0.029
0.024

0.371
0.467
0.016
0.058
0.033
-0.044
-0.033
-0.027
0.087
0.021
0.024
o0.022

-0.015

0.093
-0.020
-0.009

0.024
-0.023
-0.030
-0.029

0.029

0.093
-0.001
-0.085

0.065
0.073
0.046
-0.052
-0.039
-0.034
0.031
-0.002
0.075
-0.017

AI

0.797
0.363
~0.444
-0.265
-0.206
-0.069
-0.249
0.752
-0.015

0.478
~0.532
-0.347
-0.269

0.504
-0.179

0.791
-0.021

c.

~0.946
-0.940
-0.912
0.388
0.272
0.589
-0.032

2"2

DJ

0.972
0.941
-0.385
-0.196
-0.534
0.028

0.1K

0.992
-0.328
—0.273
-0.423

0.025

-0.267
-0.272
-0.376

0.026

0.175
0.219
o0.027

1(311

5.55
5.55
5.55
5.55.
5.55
5.55
5.55
5.55
5.55
5.55
5.55
5.55
5.55
5.55
5.55
5.55
5.55
5.55
5.55

> a

0.0
0.0
0.0
0.0
5.0—
0.0—
—.0v
—.0
p.—
0.—
0.0
5.0
0.0
0.0
0.0
0.0
0.0
0.0
0.—

FDR

0.0
0.0
0.0
0.0
0.0
0.0
..—
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
..0
0.0
0.0

~>~ 5

555.5555
555.5555
.555.5555
555.5555
555.5555
555.5555
5555,5555
555.5555
5...5555
555.5555
555.5555
555.5555
555.5555
5.55.5555
555.5555
5555.5555
5.5.55.5
..55..555
5..55..555
5;

0.0
0.0
5.0—
0.0—
0.5
0.00
0.0
0.0
0.—
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
«.0
0.0

09 a

0.—o
—.—0
0.50
5.00
0.00
0.00
0.00
5.00
0.00
0.50
0.50
5.50
5.50
0.50
0.50
0.50
5.00
0.00
0.00

—> a

0.0
0.0
—.0
0.0
0.0
0.—
0.0
0.0
0.0
0.—
0.—
0.—
0.—
5.—
5.—
5.—
0.—
v.—
0..

~55 5

.00 n 000 0:5 0 u 0 go» 00: 555 0:55.: co55ucau o>53 use

555.5555

555.5555
5.55.5555

555.5555
5555,5555

555.5555
.55..5555
55.5.5555
5.55.5555
55.5..555
5555.5555
5555.5555
5.55.5555
5.55.5555
.555.5-5
5.55.5555

.55.55.5
5.55.5555
5.55.5555

.5

_

—0 0—055

0.0
0.0
0.0
0.0
0.0
0.0
0.0
—.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

0: a

0.0
0.0
0.0
0.0
0.0
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—.0
0.0
0.0
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0.—
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5.—
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0.—
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v.—

_> 0

05555555 .0505 55:5 55 55.5.55555

0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.00
0.00
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0.00
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-50 :. 555>55 5055eu 0555.55.50

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55.5.5555

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X

00004

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'3

105

.000 500555555 5055 50505

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5.55 5.. 5.5 555.5555 5.5 5..5 5.5 555.5555 5.5 5.5 5.55 555.5555 . 5 5
5.55 5.. 5.5 555.5555 5.5 5..5 5.5 555.5555 5.5 5.5 5.55 555.5555 5 5 5
5.55 5.5 5.5 555.5555 5.5 ..55 5.5 55..5555 5.5 5.5 5.55 555.5555 5 5 5
5.55 5.5 5.5 555.5555 5.5 ..55 5.5 55..5555 5.5 5.5 5.55 555.5555 5 5 5
5.55 5.5 ..5 555.5555 5.5 5.55 5.5 555.5555 5.. ..55 5.55 555.5555 5 5 5
5.55 5.5 ..5 555.5555 5.5 5.55 5.5 .55.5555 ..5 5.5 5.55 555.5555 5 5 5
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.
00 0.5.0..

CHAPTER VII

AND v OF H Se

ANALYSIS OF 2v2, v 3 2

‘l’

(35)

In l939 Cameron et al. determined the frequencies of the three

fundamental modes of vibration of HZSe. Twenty years later Palik(44)
analyzed the rotational structure of the three fundamental vibrational
bands of HZSe. Their analysis was hampered by low resolution and
inability to include the Coriolis interaction between v] and v3. In

the mid-l960's Hill(45)

, then with this laboratory, started an analysis
of the high resolution infrared spectra of v], 2oz, and v3 and con-
siderably extended the line assignment of Palik. This provided a con-
venient starting point for our analysis.

The spectrum of 2oz, v], and v3 of H23e is shown in Figure l5.
This figure is a horizontally compressed plot of our digitally smoothed
spectral data. As was the case with H25 discussed in the previous
chapter, several runs at different sample path lengths and pressures
were necessary to record the complete spectrum. Because of this, the
absorption intensities shown in Figure l5 do not reflect the true
absorption intensities from region to region of the spectrum. In
general, the true relative absorption intensities are less than de-
picted at the high and low frequency ends of the spectrum.

Just as with H25, the bands 2v2,v], and v3 of HZSe are coupled by

40)

Fermi and Coriolis interactions.( The results of our analysis of

l06

107

p

..5 88 cu

p-5u ommp Seem mmu: do m> new ._> .N>~ mo Ezguumam as» .m_ mg=m_u

..Eo oo_~ .dev

 

TEo omON

I

7:8 OOON

 

J

4

.-..5 Onm.

l08

.A.e.a=oov

2.0.9 750 00mm 8.0.:

4 u 4

IR. OO¢N

..Eu CONN _.Eu 405

.m. aa=o_a

109

.A.u.b=ouv .m. ae=m_a

13 00mm ..5 comm

‘

 

7.5 on ¢N

ll0
H25 led us to assume that the Fermi interaction between sz and v] and
the Coriolis interaction between 2V2 and v3 could be neglected. Our
excellent fit of 2oz supports this assumption. Under this assumption,
we have analyzed 2V2 by treating it as a single, unperturbed band and
have analyzed v] and v3 simultaneously. We have not attempted to
analyze 2oz, v], and v3 simultaneously.

All analysis was done using Typke's Hamiltonian Eq.(I-8) and
Eq.(I-ll) for the Coriolis interaction. Since H25e is an oblate asym-
metric rotor molecule, the rotational Hamiltonian is evaluated in the
IIIr representation (a = x, b = y, c = z) with the molecule in the xy
plane.

As noted in the discussion of 2v1 of HDSe, six stable isotopes of
selenium exist naturally, but the absorption lines of only the five
most abundant isotopic species of H25e could be identified and analyzed.
Figure l6 shows the characteristic splitting of the isotopic species
of HZSe. Equation (II-7) was used to analyze all isotopic species
simultaneously. Although this expression is strictly applicable only
to unperturbed bands, we have successfully used it in our analysis of
v] and v3. More will be said later about the conditions under which
Eq.(II-7) may be used in the analysis of perturbed bands.

Approximately 500 transitions in 2V2 from all isotopic species of

HZSe and approximately 300 transitions in v] and v3 from HZBOSe had

(44) and Hill(45).

previously been assigned by Palik Consequently,
fairly good starting values for the Hamiltonian parameters were avail-
able for all three bands.

We obtained ground state constants for H25e from a simultaneous

least squares fit of the lO9 microwave transitions of Helminger and

lll

 

 

l
l

W V

 

 

 

 

ISOTOPE 82 80 78 77 76
Kfifififififice 9 SO 24 8 9

Figure 16. Absorption lines of the isotopic species of 5 0 5 - 6 l 6
of 2V2 of HZSe near 2009 cm' .

112
(46)

De Lucia and the 879 distinct ground state combination differences
for all selenium isotopes formed from the assigned lines of sz, v1,
and v3. The microwave lines were weighted approximately 250 times the
weight of the ground state combination differences (rather lightly in
comparison to their precision relative to the infrared combination dif-
ferences) in order to reduce high correlations among ground state con-
stants and to better determine them. All ground state constants were
varied simultaneously.

To account for isotopic mass differences, the ground state rota-
tional levels were modified using Eq.(II-7) by the introduction of 5A
and 5C. Since the selenium is located on the b axis of the molecule,
EB was fixed to zero. A later fit in which 58 was allowed to vary
yielded a statistically insignificant value for it, supporting the
validity of setting 58 to zero. The ground state constants and their
partial correlation coefficient matrix are shown in Tables 33 and 34,
respectively. The standard deviation for the fit of the infrared
ground state combination differences is 0.0059 cm'1 and for the micro-

wave lines it is 0.0008 cm'].

The fits for ground state constants
rapidly converged to a stable set of values. The standard deviation

of the fit of the microwave lines is somewhat larger than was expected
on the basis of our analyses of the ground states of HDSe and H25. In
both of these cases the simultaneous fit of microwave lines and ground
state combination differences yielded standard deviations of the micro-

wave lines of approximately 0.000l cm'].

We have no explanation for
our inability to fit the H25e microwave lines as well as we fit the
H25 or HDSe microwave lines. Nonetheless, we believe that our ground

state constants perdict all H25e rotational levels through J = l0 for

113

 

 

Table 33
Molecular Ground State Constants for HZSe

Constant (cm-1) SCIgS%cm'1)
A' 8.170982 0.00026
3' 7.725612 0.00028
0' 3.901885 0.00021
05 0.76341x10'3 0.0040x10'3
05K -l.38l]3xl0'3 0.0095x10'3
DR 0.66107x10‘3 0.0060003
53 0.07556x10'3 0.0017x10'3
R5 -0.196384x10’3 0.00070x10'3
H5 0.1484x10'6 0.027x10'6
HjK -0.4926x10'6 0.0623x10‘6
de 0.5364x10‘6 0.044x10‘6
Hk -0.igox10'6 0.16x10'6
Hg 0.0955xio‘6 0.030x10‘6
Hé 0.5342x10’6 0.039x10'6
Hi0 «0.062x10'6 0.070x10'6
5A 2.5425x10’3 0.015x10'3
£0 0.574700"3 0.054x10“3

 

 

l

Standard deviation of 879 ground state combination differences = 0.0059 cm- .
Standard deviation of l09 microwave transitions = 0.0008 cm'].
a95% SCI (simultaneous confidence intervals), here 5 6 standard deviations.

.904
.298
.051
.060
.042
.900
.132
.005
.025
.028
.031
.781
.185
.284
.483
.186
.007

.027
.019
.002
.000
.020
.044

.069
.069
.008
.047
.917
.086
.009
.019
.034

.814
.152
.262
.444
.081
.004

.341
.492
.313
.089
.012

CC

-0.490
-0.658
-0.619
.152
.140

0
0
0.502
0.518
0.503
0.490
-0.121
0.134
0.110
-0.142
0.437

0.028

0.874
-0.199
.112

0

DJ

0.877

0.779
-0.019
-0.007
-0.912
-0.812
-0.754
-0.722

0.040
-0.028
-0.014
-0.024
-0.078
-0.035

”10

-0.212
0.094

114

Table 34
Partial Correlation Coefficients for the Ground State of HZSe
”ix ”x 50 R5 ”3
0.977
-0.034 0.007
-0.04l -0.007 0.226
-0.962 -0.93l 0.004 0.005
-0.963 -0.973 0.00l 0.010 0.974
-0.942 —0.973 -0.008 0.003 0.946
-0.925 -0.967 -0.009 0.003 0.927
0.028 -0.020 -0.966 -0.295 -0.008
-0.057 -0.024 0.277 0.982 0.026
-0.033 -0.004 0.407 0.823 0.011
0.017 0.004 -0.396 -0.l66 0.0ll
-0.l04 -0.07l 0.l09 0.l26 0.036
-0.044 -0.04l -0.005 0.038 0.048
5:“ ac
-0.382
-0.00l 0.001

O

.046

0.039

OOOOOOOO

"0K

.994
.986
.009
.027
.007
.000
.031
.047

“k0

0.998
0.023
0.020
0.002
0.000
0.024
0.046

115

for all isotopes to an accuracy of :0.0l cm.1 or better. We believe
that our constants predict rotational levels for J = ll through 20 and
K_ less than approximately J/2 to similar accuracy.

The high correlations among the sextic distortion constants H for
the ground state of H2Se suggest that they are effective constants,
that is, ones which allow us to predict our spectral data rather than
constants which can be related to more fundamental molecular parameters.
To a somewhat lesser extent, the remaining ground state constants are
also effective ones, as are the constants for 202, v], and v3. To
reduce the number of highly correlated constants, only the upper state
H's which differed significantly from the ground state values in pre-
liminary fits were allowed to vary in the final fits. All other
H's were held fixed to the ground state values. All molecular
constants are quoted to two digits beyond their 95 percent
simultaneous confidence intervals in order to reproduce our
calculated values.

Our fit of all isotopic species of the type 8 band 202 of H23e
quickly converged to a stable set of constants with a standard devia-

tion of observed minus calculated frequencies of 0.0038 cm'].

In

this fit the ground state constants were fixed and all upper state
constants (except H', HjK’ HkJ and Hk which were fixed to ground state
values) were allowed to vary simultaneously. Isotopic mass differences
were accounted for by using Eq.(II-7) and allowing £2, 53m, EA, and ac
to vary. The constants determined from this fit and their partial
correlation coefficients are given in Tables 35 and 36. Assigned
transitions of 202 are listed in Appendix E. The standard deviation

of the fit of 202 is somewhat smaller than the standard deviations of

1'16

Table 35

Molecular Constants for 202 of HZSe

 

 

95%

 

 

 

Constant (cm‘l) SCI“ (cm'])
A' 8.585143 0.00054
8' 8.100205 0.00058
0' 3.809932 0.00012
05 1.09894x10'3 0.0038x10'3
05K -2.20958x10'3 0.0084x10'3
”k 1.1525900“3 0.0047x10'3
85 0.12mx1o'3 0.011x10'3
R6 -0.25969x10‘3 0.0080x10‘3
H3 0.1356x10‘6
HJK -0.461x1o'6
de 0.5162mo'6
Hk -0.190x10'6
Hg 0.069x10'6 0.2ox1o‘6
Hé 0.650x10'6 0.59x10'6
Hi0 0.233700'6 0.30x1o'6
5A 2.754x10'3 0.11x10'3
ac 0.5496x10‘3 0.023x10'3
00 2059.96580 0.0027
52 0.l6497 0.0013
83” 2.0631(10‘3 0.36x10'3
Isotope Standard Deviation Number of
of Fit (cm‘l) Weighted Lines
All 0.0038 516
75 0.0042 52
77 0.0041 50
78 0.0030 117
80 0.0039 220
82 0.0033 57

695% SCI (simultaneous confidence intervals), here

6 standard deviations.

If no value is given, constant was held fixed at ground state value.

8' o
c' 0
05 -0
05K -0
”k -0
85 -0
R5 0
H5 -0
H5 0
Hi0 0.
v0 0
5A 0
EC 0
a: 0
:g"' 0
CALC -0
, 0
5C 0
a: 0
:2” 0

CALC -0.

AI

.851
.428
.494
.337
.282
.002
.052
.085
.169

.742
.476
.210
.324
.316
.007

.432
.329
.530
.568

004

COCO

BI

.444

.347
.288
.481
.129
.447
.211
.092
.748
.405
.217
.319
.319
.006

.494
.740
.641
.008

00000000

Partial Correlation Coefficients for Zv

Cl

.943
.943
.924
.218
.424
.345
.687
.008
.562
.240
.523
.282
.302
.000

.622
.549
.008

0.979
0.955
-0.234
-0.394

-0.710
-0.032
-0.490
-0.227
-0.443
-0.208
-0.197

0.003

«515

0.870
0.001

11 7

-0.

Table 36

03x

.994
.193
.411
.348
.739
.003
.408
.164
.451
.180
.170
.002

° 3

003

DI

-0.164
-O.409

0.309
-O.741

0.001
-O.376
-0.140
-0.450
-0.168
-0.157

0.002

I
O 0

00000000

.174
.908
.157
.000
.195
.004
.092
.069
.075
.005

ofHSe

2 2

-0.168
0.880
-0.254
0.154
0.031
0.218
0.069
0.089
0.003

-0.199
-0.004
-0.213
-0.041
-O.130
-0.070
-0.071
-0.008

-0.211
0.260
0.077
0.328
0.111
0.108
0.002

”10

0.037
0.128
0.011
0.049
0.037
-0.024

118

the fits of the ground state combination differences and of the line
fit of v] and v3 for several related reasons. First, the absorption
of 2v2 is less intense than that of v1 and 03. This gives fewer (and,
therefore, a larger proportion of well-resolved) lines than are present
in the spectrum of v] and 03. As a consequence,the measurement preci-
sion of these lines is estimated to be somewhat better than for the
more densely packed lines in v] and v3. Also, because 2v2 is less
strongly absorbing there are fewer lines involving high J, high K_
levels. These levels are the most difficult to calculate accurately.
And, last, 202 has no detectable Coriolis perturbations. This makes
accurate prediction of energy levels and transition frequencies more
reliable than for perturbed bands. We were able to assign virtually
all of the observed lines in the 202 region of the spectrum. However,
only unblended lines were used in the fit of 202.

Starting with the approximately 300 H280

(44) 45)

Se transitions of v] and

and Hill(
80

v3 assigned by Palik we were able to assign approxi-

mately 400 more lines from H2 Se. In addition, we assigned approxi-
mately 850 lines to the other four isotopic species. In the initial
fitting process only the HZSOSe lines were fit. When most of the H2805e
lines had been assigned, Eq.(II-7) was used to predict the transition
frequencies for the other four isotopic species of these lines. Before

a line for any of the five isotopic species was included in the final
fit, its intensity was checked for consistency with other isotopic

lines for that transition. In addition, all "observed" values for upper
state energies were calculated by adding calculated ground state energies

to observed transition frequencies. All transitions terminating on the

same upper energy level were grouped together. Transitions were

119

eliminated from the fit if their "observed" upper state energies dis-
agreed with upper state energies formed from other transitions to the
same level. In this manner many incorrect assignments were avoided.
The final fit of the data included lines from all isotopic species.
Equation (II-7) was used to make a simultaneous fit of all isotopic
species. As in the fit of 202, g3, 22m, a“, and 5C for both v1 and 03
were varied to account for selenium isotopic mass differences. All
isotopic species for assigned lines of v] and 03 of HZSe were fit with
a standard deviation of observed minus calculated frequencies of
0.0084 cm']. The molecular constants determined from this fit and
their partial correlation coefficients are given in Tables 37 and 38.
Assigned transitions of v] and 03 are listed in Appendix E. All iso-
topic species fit approximately equally well.

Individual test fits of H28OSe and H278

Se have standard deviations
which are approximately the same as the standard deviations for these
isotopic species when all species are fit simultaneously. In the fit
78

2 Se, 0 , A; C: and the five centrifugal distortion terms for each

of H 0

band were varied; all other constants were fixed to the values deter-

80Se fit. The results of these fits indicate that the

mined in the H2
use of Eq.(II-7) is valid for predicting energy levels and transition
frequencies for the isotopic species of v] and 03 of HZSe. The Coriolis
interaction most strongly perturbs pairs of levels of the type J K_ K+
and J K_+l K+ with one of the levels belonging to v1 and the other to 03.
A check of a number of observed transitions to pairs of levels of this
type for several different J values reveals that the 03 levels lie
approximately l3 cm'1 or more above the 0] levels and that the sepa-

ration of most of the pairs of 03 and 01 energy levels increases

1220

Table 37
Molecular Constants for v] and 03 of HZSe

 

 

 

 

 

,1 g3
_] 9s: _, _] 95: _]
Constant (cm ) SCIa (cm ) Constant (cm SCIa (cm )
4' 8.058028 0.00093 7.9949] 0.0015
8' 7.512833 0.00075 7.5575 0.0014
C' 3.845509 0.00075 3.857799 0.00078
05 0.75179x10‘3 0.0049x10‘3 0.73316x10'3 0.0042x10'3
05K -1.3786x10'3 0.0059x10'3 -1.33479x10'3 0.0051x10‘3
0k 0.55104x10'3 0.0042x10‘3 0.5450710“3 0.003.4x10'3
55 0.08120x10’3 0.0034x10‘3 0.04758x10’3 0.0052x10'3
R5 -0.19827x10'3 0.0053x10’3 -0.33945x10‘6 0.0084x10’3
H3 0.1466100”6 0.018x10’6 0.1251x10'6 0.011;:10'6
85K -0.49]0x10'6 0.022x10'6 -0.4575x10‘6 0.0141(10‘6
HkJ 0.5364x10'6 0.5364x10'6
HR -0.190x10‘6 -0.190x10‘5
Hg 0.0955x10‘6 0.0955100'6
Hé 0.7647(10’6 0.18x1o'6 0.744x10'6 0.241(10'6
Hi0 -0.062x10'7 -0.062x10'6
~:A 2.490x10‘3 0.11x10'3 2.484.00‘3 0.12x10'3
:5 0.5520100'3 0.049;:10'3 0.5358100“3 0.0411(10‘3
vo 2344.35240 0.0079 2357.5519 0.011
a: 0.1528] 0.0032 0'17915 0 0044
:5” 2.086x10'3 0.85x10‘3 1.52x10‘3 1.1x1o'3
oz 0.1857 0.024
ny -0.199820 0.0012
Standard deviation of fit of 1540 weighted transitions = 0.0084 cm.].
. J1 3’3 .
Standard Deviation Number of Standard Deviation Nunber of
Isotope of Fit (cm-l) Weighted Lines of Fit (cnr‘) Weighted Lines
All 0.0075 925 0.0095 514
75 0.0058 87 0.0111 58
77 0.0068 89 0.0088 54
78 0.0081 241 0.0095 150
80 0.0078 411 0.0095 284
82 0.0054 98 0.0102 58

6957. SCI (simultaneous confidence intervals), here = 8 standard deviations.

If no value is given.

constant was held fixed at ground state value.

121

Table 38
Partial Correlation Coefficients for v] and 03 of HZSe
"3
A' 8' C‘ 05 DJK 0k 05 R5 H3

0.959

0 504 0 509

-0.S96 -0.600 -0.915

-0.348 -0.349 -0.922 0.947

~0.246 -0.243 -0.889 0.893 0.987

0.240 0.480 0.222 -0.301 -0.179 —0.124

0.285 0.245 0.266 -0.319 -0.245 -0.216 -0.070

0.397 0.399 0 833 -0.958 -0.963 -0.930 0.234 0.277

0.254 0.253 0.825 -0.904 -0.977 -0.975 0.145 0.217 0.975
0.363 0.315 0.394 -0.505 -0.422 -0.387 «0.013 0.942 0.481
0.781 0.793 0.604 -0.509 -0.377 -0.314 0.236 0.198 0.330
0.304 0.287 0.658 -0.573 -0.592 -0.573 0.036 0.230 0.519
0.226 0.314 0.113 -0.159 -0.072 -0.043 0.356 -0.043 0.101
0.360 0.374 0.229 -0.180 -0.128 -0.091 0.074 —0.014 0.091
0.245 0.247 0.470 -0.337 -0.332 -0.313 0.079 0.107 0.255
0.345 0.370 0.303 -0.192 -0 147 -0.121 0.108 0.071 0.095
0.415 0.449 0.326 -0.228 —0.157 -0.126 0.171 0.117 0.119
0.119 0.091 0.019 -0.042 -0.015 -0.010 -0.078 -0.028 0.025
0.080 0.057 0.022 -0.035 -0.017 -0.012 -0.059 0.074 0.023
0.018 0.025 0.051 -0.050 -0.051 -0.050 0.044 0.020 0.048
-0.052 -0.044 -0.054 0.066 0 059 0.055 -0.002 -0.041 -0.063
-0.017 -0.023 -0.059 0.062 0.066 0.065 -0.044 -0.020 -0.066
-0.014 -0 018 -0.061 0.064 0.070 0.070 -0.038 —0.017 -0.068
-0.030 -0.024 0.032 -0.022 -0.030 -0.023 0.054 0.253 0 027
-0.019 0.071 0.017 -0.023 -0.014 -0.010 0.415 —0.495 0.018
0.033 0.031 0.055 -0.067 -0.066 -0.063 O 019 0.035 0.071
0.015 0.019 0.057 -0.065 -0.069 -0.068 0.040 0.018 0.072
-0.022 0.087 0.026 -0.038 -0.026 -0.019 0.506 -0.524 0.035
0.054 0.048 0.020 -0.025 -D.015 -0.012 -0.012 0.000 0.016
0.041 0.044 0.008 -0.015 -0.006 -0.005 0.021 -0.075 0.008
0.009 0.015 0.024 -0.024 -0.023 -0.022 0.034 0.011 0.024
0.021 0.023 0.008 -0.009 -0.005 -0.004 0.012 -0.017 0.005
0.024 0.025 0.009 -0.010 -0.005 -0.004 0.010 -0.014 0.006
0.047 0.047 0.093 -0.115 —0.111 -0.101 0.027 0.034 0.125

00000000000

1 u o
O O 0

0000000000

0

HJK

.407
.265
.523
.048
.079
.247
.080
.087
.012
.013
.048
.058
.066
.070
.027
.011
.068
.073
.023
.011
.005
.023
.004
.004

.116

-0.
-0.

-0.

-0.

000000

H3

122

Table 38 (cont'd.)

Partial Correlation Coefficients for v] and 93 of HZSe

00 52 ny 5‘ 5c 52 2:” A' 8' c' 03
0.399
0.159 -0.105
0.394 0.150 0.057

0.370 0.325 0.050 0.529

0.550 0.215 0 072 0.792 0.555
0.598 0.227 0.099 0.558 0.513 0.865

0 070 -0.347 -0.001 0.047 0.010 0.033 0.032

0.045 -0 285 0.043 0.025 0.011 0.019 0.022 0.917

0.024 -0.687 0.072 0 008 0.022 0.010 0 010 0.555 0.527
-0.034 0.592 -0.057 -0.015 -0.024 -0.013 -0.013 -0.540 -0.515 -0.915
-0.021 0.508 -0.051 -0.008 -0.025 -0.008 -0.007 -0 410 -0 375 -0.912 0.951
-0.020 0.580 -0.038 -0.007 -0.024 -0.007 -0.005 -0.307 -0 277 -0.874 0.895
-0.012 -0.055 0.045 -0.022 0.014 -0.012 -0.003 0.333 0.555 0.241 -0.338
0 018 -0.105 0.075 0.024 0 004 0.015 0.024 0.100 0.230 0.153 -0.175
0.023 -0.503 0.044 0.010 0.025 0.008 0.008 0.403 0.377 0.785 -0.929
0.017 -0.493 0.035 0.007 0.025 0 005 0.005 0.284 0.257 0.750 -0.878
0.020 -0.171 0.115 0.005 0.005 0.008 0.023 0.121 0.220 0.228 -0.259
0 048 -0.350 0 022 0 024 0 010 0.023 0.025 0.809 0.791 0.550 -0.502
0 033 -0.201 -0.024 0.081 0 015 0.054 0.045 0 514 0.553 0.323 -0 375
0.013 -0.373 0.054 0.017 0.043 0.021 0.018 0.427 0.400 0.549 -0.589
0 023 «0.174 0.014 0.044 0 017 0.041 0 034 0.489 0.482 0.275 -0.255
0 025 -0.157 0.009 0 038 0.015 0.035 0.041 0.505 0.511 0.270 -0.255
0.035 0 057 0 040 0 014 0.037 0.010 0.010 0.003 -0.005 -0.015 0.015

0.3x

.985
.194
.141
.954
.953
.246
.359
.235
.540
.168
.149
.016

.145
.127
.928
.952
.234
.297
.168
.479
.122
.104
.013

Partial Correlation Coefficients for v

0000000

.007

00000000

1
O

.132
.115
.957
.097
.155
.091
.087
.103
.002

123

Tabie 38 (cont‘d.)

-0.

0000000

0.231
0.230
0.174
0.519
0.111
0.089
-0.016

0.123
0.164
0.143
0.101
0.112
-0.004

1 and u

3

00000

of H

.494

.004

2Se

‘3»

0.643
0.819
0.738
-0.011

C m mm
5 £0 £0
0.578
0.481 0.872
0.002 -0.003 -0.004

124

smoothly as isotopic mass decreases. For most of the pairs of Coriolis

76Se levels

interacting levels checked, the separation of the pairs of H2
is larger than the separation of the pairs of H2825e levels by less

than 0.1 cm']. Because the levels of 01 and 03 for all isotopes of
selenium are shifted by approximately equal amounts by the Coriolis
interaction, Eq.(II-7) may be used to evaluate the transition frequencies
for all isotopic species. Since Eq.(II-7) is satisfactory in this

case, its use in a simultaneous fit of all isotopic species is prefer-
able to individual fits of each isotopic species because eight additional
constants (8:, 52m, 5A, and 5C for each band) predict the transitions

for all isotopic species rather than 16 additional constants for each

species (as in the fit of H278

Se, five sets of V0’ A', C', and five
quartic centrifugal distortion terms).

Despite our successful use of Eq.(II-7) to evaluate transitions
from all isotopic species of u] and 03 of HZSe, Eq.(II-7) cannot be
used successfully to evaluate all isotopic species in all perturbed
bands. This expression would be expected to give inaccurate predictions
if the perturbed energy levels are in close resonance (that is, if they
would be separated by only small amounts in the absence of perturbations)
or are otherwise strongly perturbed. In such cases, the isotopic species
of a particular level will probably not be shifted in a smooth manner.
The 0, transition 13 12 l - 12 ll 2 near 2528 cm'1 apparently shows
evidence of this breakdown. The observed minus calculated value is

-0.004 cm'] for the 80 isotope, -0.074 cm—1

1

for the 78 isotope, and

approximately -0.04 cm' for the other three isotopes.

Approximately 150 lines from H28OSe in the v] and v3 region of the

spectrum, most of them strong and well resolved, could not be assigned.

125

Since we are able to accurately predict most 0] and 03 energy levels
through J = 10 and most low K_ energy levels for J = 11 through 20, we
believe most of these lines may be transitions ending on high J, high

K_ levels. These levels tend to be strongly perturbed by the Coriolis
interaction. Predicted values of these energy levels are very sensitive
to small changes in the Hamiltonian constants. As an example of this
sensitivity, in one fit with a standard deviation of approximately

1 80

0.01 cm' the H2 Se v3 transition 15 14 2 - 14 14 l was assigned to

1

the line at 2536.441 cm' . On a subsequent fit with some new lines

added and a standard deviation of approximately 0.03 cm'], this transi-

1, a shift of over 28.6 cm'].

tion was predicted to be at 2565.096 cm-
0n the next iteration of the fit of this set of data, the predicted
transition frequency returned to within 0.1 cm of its assigned value.
While this is an extreme example, it illustrates the difficulty in
assigning and fitting very strongly perturbed levels. In less extreme
cases, shifts of several tenths to several cm'1 from fitting iteration
to fitting iteration are common. Because this is usually much larger
than the spacing between lines on the observed spectrum, we were unable
to assign these lines. This is unfortunate because knowledge of these
high J, high K transitions would help to determine higher order distor-
tion constants (the H's) well. Although it would be complicated to
develop, a computer program to predict the intensities of the lines of
v] and 93 including the effects of the Coriolis interaction would be
very useful. It would predict frequencies and intensities, both of
which may be very different from the non-interacting cases. At present

we have no feel for which high J, high K‘ levels should be strong and

which should be too weak to be observed.

CHAPTER VIII
CONCLUSION

The development of Hamiltonians suitable for predicting the energy
levels of asymmetric rotor molecules has been sketched. A procedure
has been given for applying the Hamiltonians to predict the energy
levels and transition frequencies of vibration rotation bands which are
unperturbed and which are perturbed by Fermi and Coriolis interactions.
In addition, a systematic procedure has been developed to assign
observed transitions in such bands.

We obtained the high resolution infrared spectra of 201 of HDSe,
202, v] and 03 of H25 and 202, v1, and 03 of H2Se. The analysis of the
201 band of HDSe<19> (accepted for publication in J. Mol. Spectrosc.)
is the first published high resolution study of any vibration rotation
band of this molecule. Molecular constants were obtained from simul-
taneous least squares fits of transitions from all five observed
isotopic species of selenium. The bands 202 and 01 of H25 and H25e
are coupled by a Fermi resonance interaction and the bands 0] and 03
of H25 and HZSe are coupled by a Coriolis interaction. We were unable
to determine the size of the Fermi interaction from our attempted three-
S and treated 20

band analysis of H 2 of H25 and 202 of HZSe as unper-

2
turbed bands. We analyzed the Coriolis interacting bands 0] and v3

simultaneously for H S and also for HZSe. Using our analysis procedure,

2
126

127

we were able to determine molecular constants which can be used to
accurately predict most of the observed transitions in our spectra

S and H Se.

of H2 2

10.
11.
12.
13.
14.
15.

16.
17.

B. T.

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J. M.

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Kneizys, J. N. Freedman, and S. A. Clough, J. Chem. Phys.

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L. E.

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Hil1, New York, 1955, pp. 102-105.
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p. l.
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(1974).

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C. Amiot and G. Guelachvili, J. Mol. Spectrosc. 81, 475 (1974).
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in the Infrared, Academic Press, New York, (1966) p. 118.

 

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APPENDICES

APPENDIX A

NONVANISHING ANGULAR MOMENTUM

MATRIX ELEMENTS

Listed below are the nonvanishing matrix elements
for the angular momentum operators of the various
Hamiltonians evaluated in the symmetric top basis 0(J,K).

<x|px1xtl> = 51/2 [f-x1x51113

<Klpylxtl> = 1/2 [f-K(z<.+.1)]ls

1'3
11

J(J+1)
j = f-K
9+: [(Jxx—1)(J;K)(th+1)(J3K+2)17

m = [(J¥K~2)(Jt}<+3)(J;K-3)(J1K+4)1!59+

. . - i , i .
Tne diagonal terms, <K1x 18> where x is equal to:

P = K
Z
2 2 .
Py = PX = .153
P2 = f
2 2
P = K
' .. 1 '3 s) a
(PHP: + pfr;) = (ngf + 939;) = jK4
J 4 I ‘- a

131

132

4 _ 4 _ 4.2_ . 2
PY - Px — (3] 23+3K )/8
p4 = £2
4 _ 4
22 — K
2292 = sz
2
(P2P2 + P2 P2) = (P2P 2 + P2 22) = sz
x z PX y z PPz y
2 2 2 2 _ .2 . 2
(Pxp y + PyP x) — (3 +23—3K )/4
4 P4_ 2P 2 + 2P 2 g _ .+ K2
PX+P y 3(2)?y exp y1 23 3
p; = P: = (Sj3-10j2+25jK2+8j-20K2)/16
26 = £3
96 = x6
2
2422 = 22x2
2
2 4 _ 4
2 P2 - fK
2 4 4 P2 2P 2 . 2
+ - P: + P = -2 +3K )
2 [ex 9y 3( xPy y Px)] f( 3
2 4 4 2 _ 2P 4 4 2 _ 2 .2_ . 2
(pzpy + pypz) — (222 x + 9x22) — K (33 23+3K )/4
2 4 4 2 _ 2P 4 4 2 _ .3 .2_ ."2_ . ,2
(PxPy + Pny) (PyP x + Px:y) — (j +6] 193A 83+208 )/8
2 2 2 2 2P _ lP.2,2_ 2 2 ,
(PXPZPY + PyP 2P :1 - ,3 h [(x+2) g+ + (1-21231/8

The off-diagonal terms, <K|x11K12> where x1 is equal to:

133

4 4 P2 P2 3
px + Py 3(P? xy+ P: PX) % mi
4 4 . -
PY =—Px = 8(3-2+2K)93
2P 2 P2 P2 _ 2P 2 2 2 _ 2 .
(PyP 2 P2 Py) — (PXP Z + PZPX) — 8(K 2.214219i
P2 2
(P: - Py) =-8fgt
[P2(P2 - 22) + (P2 - P21P2] =-(xz+2x+2)
z x y x y z ' gt
5 5 .2_ . .
Py =-Px = [153 +503x-703+105K(K:1)
1125K+136]g+/64
2P 4 4P 2 _ 2P 4 4 2 _ .2 . ._ 2-
(PXP y + PYP x) - ~(PYP x + PxPy)- (3 $43K+63 4114,102x-7219 /32
2P 4 4P 2 _ _ 2P 4 P4 2
(FY? z + PZP y1 - (PX? z + Psz1= 81K 4+(K+2) 19.
2P 4 4P 2 _ _ 2P 4 4P 2 _ 2 ,
(pzp y + PyP z) — (sz x + Px Pz)- L(x2 +2K+2)[f—( x 324+21192
4 2 2 _ 2
P (Px - Py) - -8f 93
2 2 2 2 2 2 2 __ 2
P [P 2(Px - Py) + (Px- Py)Pz] — (x 12k+2)£gi
4 2 2 2 2 P4 - 4 4
[Pz(Px - Py) + (Px- Py) P2] —-[x +(K22) lei/2

The off-diagonal terms, <K|x1|Kt4> where x1 is equal to:

P; = P: = mi/l6
(Pip p; + Pipi) =-mt/8
P3 = Px 6=(3j 4128-201m /32
(Pi? P; 4 P3P') = (P2P 2 + Pi? :)= (K 214K+8)mi/8
(Pip :P p; + 93930 I: =-(K22)2m1/8
(Pip: + PSPi) = (P3P: + 9:25: = (-j+4K+4)mt/16
P2[P; + P; - 3(PiP; + P3P21] = 8 fmt

134

The off-diagonal terms, <K|xllKi6> where x1 is equal to:

P: =-P: = [(J;K-5)(J:x-4)(J:x+5)

(J1K+6)]%mi/64

2 4 4 2 _ 2 4 4 2 __ _ _ _
(PxPy + Pny —-(Pny + PxPy) — EJ;K_5)(J+K 4)(JiK+S)
(J1K+6)]%m+/32
2
(P: - Pj)3 = - %{[J2-<x:1)ZJEJZ-(x:2)2][J2-(K:3> J

[J2-<K:4)2][J2-(x:5)2][J2:K]

[Jt(K:6)]}%

APPENDIX B
COMPUTER PROGRAM INTCALl

Computer program INTCALl calculates intensities for unperturbed
type A or type B (but not mixed) vibrational bands. Transition fre-
quencies and relative intensities for up to six isot0pic species of the
same molecule and up to lOOO transitions may be predicted. INTCALl
comprises a driver and l2 subroutines and functions. The operation of
the program is outlined below.

The user inputs a series of cards which control program operation,
specify Hamiltonian parameters, and specify the transitions to be
predicted. The user may specify which of several forms of output is
desired, the Hamiltonian to be used for calculating energy levels, the
band type, isotopic species and relative abundances, the range of fre-
quencies and intensities to be plotted, and other conditions necessary
for intensity calculations.

As transitions are read in, their quantum numbers are encoded by
subroutines IQN and INDOUT to minimized core storage requirements. To
minimize redundant calculations, the transitions are sorted in order
of ascending upper and ground state quantum numbers.

Function CAPPA, which is used by many other of our asymmetric
rotor programs, prints Hamiltonian constants and the Hamiltonian

selected.

135

136

The major portion of INTCALl is devoted to calculation of spectra.
This takes place in three steps: calculation of upper state energies
and energy eigenvectors, calculation of ground state energies and energy
eigenvectors, and calculation of transition frequencies and transition
intensities.

Starting with the smallest upper state J, the upper state energies
and eigenvectors of all levels involving the same upper state J value
are calculated. This is done in the same manner as employed in our
other asymmetric rotor programs. Subroutine PMAKE forms the symmetric
top matrix elements of the Hamiltonian. These symmetric top matrix
elements are Wang transformed by subroutine WANGT. Subroutine SYMDIG
diagonalizes and forms eigenvectors of the resulting Hang transformed
energy matrix. Subroutine FORMPIl selects and saves energy eigenvalues
of upper state levels involved in transitions and calculates angular
momentum expectation values to be used with Equation (II-7) when calcu-
lating energies of the various isotopic species. Subroutine HANGDIM
calculates the storage location of the eigenvectors for each of the
four Wang blocks for a given J.

Next, ground state energy levels and eigenvectors are calculated.
The method is the same as for calculation of upper state energies and
eigenvectors. To avoid redundant calculations, the program remembers
which ground state energies have been previously calculated and only
calculates new ground state energies and eigenvectors. Some ground
state levels may already have been calculated because the selection
rule AJ = 0,:l allows transitions from upper state J' to ground state
J = J', J'-l, or J'+l. For example, if transitions to upper states
J'-l were previously calculated, ground state levels J = J' or J'-l

may have been calculated.

T37

Third, the transition frequencies and relative intensities of the
transitions are calculated. Transition frequencies are calculated as
the difference between upper and ground state energy levels, using
(II-7) to account for isotopic substitution. Subroutine LSTR forms the
symmetric top direction cosine matrix elements listed in Table 5 between
the upper and ground states. The rotational matrix elements
<JK|¢Zg|J'K'> are Wang transformed by subroutine NANGCOS. INTCALl then
calculates the asymmetric top line strength (II-6) using (III-8). The
line strength, statistical weight 9”, temperature, transition frequency,
and ground state energy are substituted into (III-9) to give the rela-
tive transition intensity.

This procedure for calculating energy levels and intensities con-
tinues until all transitions have been calculated. After all transitions
are calculated, subroutine OUT and PRINTO print or plot the spectrum in
the form selected by the operator. Intensities may be printed in order by
quantum number or by frequency, or in order of input. Or, intensities
may be plotted. For plotting the operator selects the frequency range,
minimum intensity, and percent absorption to be plotted. All lines not
plotted are listed at the end of the plot of the spectrum. Finally,

if desired, predicted transitions may be punched in order of frequency.

nnnnnnnnnnnnnnnnnnnn

n

138

PROGRAM INTCAL1(INPUT,OUTPUT,PUNCH=STS)

CONNONIRLPR/ PRS(2)

COMMON/8LKP/P(19,4,13),PI(2,13),NP(3),PH(4,13)

COMMONIBLKEVIA(13,13),S(13,13),JIN(4,51),IHDEX,NVAR(24,2),IBN

COMMON NAP,NAI,IAN,AP(408,4),
1SE(26,26,4),FRE0(1000),10N(1000),
25TREN<1000>,C(51,3),ABSN,IBAND

OMMON /PMAK/HAM,VIDZ,VIDXY,HSPM,LPS

DIMENSION IHEAD(10),NGU(2),LUPS(2),GL(2)

CHECK DIMENSIONS IN THE FOLLOUING THREE CARDS UHEN CHANGING

ANY ONE OF THEM

DINENSION PAR1<19),PAR2<19),PGD1(19),PGDZ(19),NPAR1(48),NPAR2(43)

COMMON/5LK1/ PAR(19,4),voc3),NPAR<24,4)

EGUIVALENCE (PAR(1,1),PAR1(1)),(PAR(1,2),PGD1(1)),
1(PAR(1,3),PAR2(1)),(PAR(1,4),PGDZ(1)),(NPAR(1,1),NPAR1(1)),
2(NPAR(1,3),NPAR2<1)) '

DIMENSION JLPREV(4),IJPREV(4),IJDEL(4),JDEL(4),ISTDP<6),ABUN(6)

INTEGER HAM

CONSTANTS HHICH DEPENT ON THE MAXIMUM ARRAY IN COMMON

DATA VIBZ,VIBXY/2*0.0I,V0/3*0.0/,PAR/76*0.0/,NPAR/96*0/

DATA NISO/1/,ISTOP(1)l32/,A8UN(1)l1.0/

DATA JEOU,JEOLI2*1I

CALL NOBLANK

NAP=408

NMAx=13

JMAXA=25

IP=24

100 CONTINUE
READ 500, IFHEAD,IFHAM,IFISO,IFRA1,IFPDT,IFPA2,IFP02,IFDATA,
11PRT,IFPAv,IFRINT,IFSE,IFORD,IFTRAN,IOUT
500 FORNAT (2012)
IF(EOF(SLINPUT).NE.O) GO TO 101
IFHEAD=O READ HEADING CARD
IFHAM=O READ HAMILTONIAN CARD
IFISD=0 READ ISOTOPE CARD
IFPA1=O READ THREE GROUND STATE PARAMETER CARDS
IFPDT=0 READ THREE ISOTOPE GRD STATE PAR) CARDS
IFPA2=O READ THREE UPPER STATE PARAMETER CARDS
IFPDZ=O READ THREE ISOTOPE UPR STATE PAR) CARDS
IFDATA=0 READ FREQUENCY CARDS UNTIL END DATA IS FOUND
IPRT=1 PRINT THE ENERGY MATRICES
IFPAv=0,1,2,3 SEE COMMENTS IN FDRMPI1
IRINT = 1 PRINT LINE STRENGTHS
IF IFSE=1 PRINT SE EIGENVECTOR MATRICES
IFOR0=1 PRINT FREQUENCY CARDS AFTER ORDERING BY 0N
IFTRAN=1 PRINT EIGENVECTORS AND HANG TRANSFORMED DIRECTION Cos MATRIX
IOUT= 1 PRINT INTENSITIES ARRANGED EY DUANTUM NUHBER
0,2 PRINT INTENSITIES IN ORDER OF INPUT
3 PLOT STRONG LINES
4 PLOT SPECTRUM NITH ADDED INTENSITIES OF OVERLAPPING LINES
S PRINT INTENSITIES OF STRONG LINES IN ORDER OF FREQUENCY
6 PUNCH DECK CF STRONG LINES
IF (IFHEAD.NE.0) GO To 608

l39

READ 525, (IHEAD(N),N=1,10)
525 FORMAT(10A8)
608 CONTINUE

IF (IFHAM.NE.O) GO TO 610

READ 530,HAM,ISO,JTYPE,T,PRS(1),PRS(2),GL<1),GL(2),RESO,ARSN,
1T0PFRE,eOTFRE,NKSTREN,IRAND
530 FDRMATCZIs,AXA1,3F10.0,2F5.0,2F10.0/3F10.0,A5)
NGU(1)=NGU(2)=1
IFPRS=0
IF((RRS(1).ED.0.D).AND.<PRS(2).ED.0.0)) IFRRS=1
IF(HAM.LT.1) HAM=1
IF(ISO.E0.0) Iso=32
IF(JTYPE.EQ.1H ) JTYPE=1HD
IF(T.EG.O) T=293 ,
IF(ABSN.EG.O) ABSN=.5'
IF(TOPFRE.EQ.O) TOPFRE=1ES
IF(<GL(1).NE.0).0R.(GL(2).NE.0)) GO TO 610
GL(1)=1
GL<2)=3
C GL(1) GOES HITH EVEN (KN+KP=EVEN) GS ROTATIDNAL LEVELS
C GL<2) GOES NITH ODD (KN+KP= 000) GS ROTATIONAL LEVELS
610 CONTINUE
IF(IFISO.NE.0) GO TO 618
READ 612,(ISTOP(I),AEUN(I),I=1,6)
612 FORMAT(6(IS,FS.O))
00 615 1:1,6
IF(ISTOP(I).EQ.O) Go TO 618
615 NISO=I
618 CONTINUE
IF<IFPA1.NE.0) GO To 600
c READ GROUND STATE PARAMETERS
READ 505, ( PARCI,1),I=1,19)
NGU(1)=1
600 CONTINUE
IF (IFP01.NE.0)GO TO 601
c READ GROUND STATE ISOTDPIC CORRECTION PARAMETERS
READ 505, ( PAR(I,2),I=1,19)
505 FORMAT (3E15.0/6E10.0/10E8.0)
NGU(1)=1
601 CONTINUE
IF (IFPA2.NE.0)GD T0 602
c READ UPPER STATE PARAMETERS
READ 506,(PAR1I,3),I=1,3),V0(1),(PAR(I,3),I=4,19)
506 FORMAT (4E1s.0/6E10.0/10E8.0)
NGU(2)=1
602 CONTINUE
IF (IFPDZ.NE.O)GO TO 603
C READ UPPER STATE ISOTOPIC CORRECTION PARAMETERS
READ so? ,(FARCI,4),I=1,3),v0<2),v0(3),(RAR<I,4),I=L,19)
SO? FORMAT (SETS.O/6E‘l0.0/1OE8.0)
NGU(2)=1
603 CONTINUE
NVAR<20,1)=NVAR(20,2)=NVAR(21,1)=NVAR(21,2)=0

12

13

15

17

140

00 12 I=1,19

DO 12 J=2,h,2

IJ=JIZ

NVAR(I,IJ)=O
IF(PAR(I,J-1).NE.0) LUPSIIJ)=I
IF (PAR(I,J).NE.O.) NVAR(I,IJ)=1
CONTINUE

N1=N2=o

DO 15 1:1,19

IF (NVAR(I,1).E0.0)GO TO 13
N1=N1+1 S NVAR(I,1)=N1

IF (I.GT.LUPS(1)) LUPS(1)=I

IF (NVAR(I,2).E0.0) GO To 15
N2=N2+1 S NVAR(I,2)=N2

IF (I.GT.LUPS(2)) LUPS(2)=I
CONTINUE

IF(IFDATA .NE.0) Go To 660

00 17 I=1,204

JIN(I)=0

NGU(1)=NGU(2)=1

C READ AND SORT TRANSITIONS BY UPPER STATE QUANTUM NUMBERS
C UP TO 1000 LINES MAY BE USED

510

1004

115

120
117
502
503

MVAR=0

JHAXA=25

DO 502 M=1,1000

MVARzMVAR+NISo

READ S10,JU,KNU,KPU,JL,KNL,KPL,LAST

FORMAT<2XS(IZ,1X),IZ,S3XA8)

IF(LAST.EO.8HEND DATA) GO TO 503
IF((JU.LE.JHAXA).AND.<JL.LE.JMAXA)) GO TO 115

PRINT 1004,JMAXA,M

FORMAT(* MAXIMUM ALLDVED VALUE OF J =*IS*IS EXCEEDED AT DATA CARD*

1I5* PRINTED BELOH*)

PRINT 510,JU,KNU,KPU,JL,KNL,KPL
MVAR=MVAR-NISO

GO TO 502

CONTINUE .
INDU=JU**2+JU+KNu-KPU+1
INDL=JL**2+JL+KNL-KPL+1
ION(MVAR)=1000OOOOO*INDU+10000*INOL+MVAR
IF(MVAR.EO.NISOJ GO TO 502

MV=MVAR-NISO

DO 120 I=NISO,MV,NISO

MI=MVAR~I

HII=MI+NISO

IF(10N(MI).LE.IDN<MII)) GO TO 117
ITEMP=ION<MII) SIQN(MII)=IQN(MI) s ION(MI)=ITEMP
CONTINUE

IF(MVAR+NISO.GT.1000) GO TO 503

CONTINUE

CONTINUE

MVAR=HVAR~NISO

IF(NISO.EG.1) GO TO 660

C SETUP FOR ISOTOPE LINES

nnnn

141

NISL=NISO-1
DO 508 N=NISH,MVAR,NISO
D0 508 I=1,NISL

508 IGN(M-I)=IQN(fl)-I

660 IF(IFORD.EQ-D) GO TO 606

PRINT 652
652 FORMAT(*10RDERED INPUT DATA*I* JU KN KP JEOU JL KN KP*
1* JEOL LINE*)

CAPPL=CAPPU=T
IF(PAR(1,1).LT.PAR(3,1)) CAPPL=~1
IF(PAR(1,3).LT.PAR(3,3)) CAPPU=-1
00 650 I=1,MVAR
CALL INDOUT(ION(I),INDU,INDL,LIST)
CALL aN(INDL,JL,KNL,KPL,JEOL,CAPPL)
CALL DNCINDU,JU,KNU,KPU,JEOU,CAPPU)
650 PRINT 655,JU,KNU,KPU,JEOU,JL,KNL,KPL,JEOL,I
655 FORMATCZ<6XAI3),I10)
606 CONTINUE
PRINT GS AND US PARAMETERS AND KAPPA
JBAND=8H GROUND
IF(IFPRS.EQ.0) GO TO 25
PRS(T)=PAR(1,1)
PRS(2)=PAR(Z,1)

25 CAPPL=CAPPA(PAR1,JBAND,HAM,IHEAD,NPAR1,PGD1,ISO,IP)
JBAND=8H UPPER .
CAPPU=CAPPA(PAR2,JBAND,NAN,INEAD,NPAR2,PGD2,ISO,IP)
IF(VO(1).NE.0) PRINT 19?,V0(1)

IF(VO(2).NE.0) PRINT 198,V0(2>
IF(VO(3).NE.0) PRINT 199,Vo(3>
197 FORMAT(/3X* V0 = *F11.4,27X*8AND CENTER*)
198 FORMAT(*+*29XE12.S)
199 FORMAT(2X*CDVO = *21XE12.5)
PRINT 202,(ISTOP(I),ABUN(I),I=1,NISO)
202 FORMAT(///* INTENSITIES ARE CALCULATED FOR THE FOLLONING ISOTOPES*
1/l8x*ISDTOPE AaUNDANCE*//(Sx11o,r1o.3/))
START CALCULATION OF INTENSITY
SEARCH QUANTUU NUNBERS FDR LEVELS UITN SAME JU.
REMEMBER THE ARRAV INDEX OF LEVELS OF THIS JU, LAST TVO JU, AND NEXT
TVO JU FOR USE RNEN es LEVELS ARE CALCULATED
NLINE=NISO
IUPREZ=IUPREV=IUTHIS=IUNEXT=IUNEX2=NISO
CALL INDOUT(IQN(NLINE),INDU,INDL,LIST)
JUPRE2=JUPREv=JUTNIs=JUNEXT=JUNEx2=SORTCFLOATCINou-T))
IUEN=NISO
DO 29 L=2,A
JLPREV(L)=-2
29 IJPREV(L)=L
300 CONTINUE
CALL INDOUTCION(NLINE),INDU,INDL,LIST)
J=SDRTCTLOAT<INou-1))
IF(J.NE.JUNEXZ) 60 T0 320
IULAST=NLINE
IFCIULA$T.GT.NVAR) IULAST=NVAR
NLINE=NLINE+NISO

non

142

IF(MVAR-NLINE)320,300,300

320 CONTINUE
IF(IUNEXT.EO.IUTHIS) GO TO 545
IUEN=IUNEXT-NISO
DO 28 L=1,51

28 JIN(1,L)=0
LPS=LUPS(2)
DO 325 I=IUTHIS,IUEN,NISO
CALL INDOUT<IQN(I),INDU,INDL,LIST)

325 JIN(1,INDU~JUTHIS**2)=1
J=JUTHIS

FORM UPPER STATE ENERGY LEVELS
IF((IPRT.NE.O).OR.(IFPAV.NE.O)) PRINT 327,JUTHIS

327 FORMAT(/II* UPPER STATE ENERGIES J = *ISI)
NAI=0
IAN=N2+1
INDEX=O
IBN=2
DO 340 JEO=1,4
N=O
NP(1)=J
IF((JEO.EO.1).OR.(JEO.EQ.3)) JAGAIN=O

SET SIZE OF HANG BLOCK
CALL HANGDIM<J,JEO,NP(3),IROU,ICOL,CAPPU,KTU)

350 ISAV=INDEX

DETERMINE HHICH LEVELS HILL BE CALCULATED
CALL FDRMPIT(-1,NMAX,JEO,PAR2,P,NP,CAPPU,1)
IF(ISAV.EG.INDEX) GO TO 340
INDEX=ISAV
IER=IPRT

CALCULATE P OPERATOR MATRIX ELEMENTS IN JK SPACE
IF(JAGAIN.EQ.0) CALL PMAKE(J,JEO,NHAX,PAR2,P,PI,NP)

HANG TRANSFORH IT
CALL HANGT(A,N,JEO,JAGAIN,NMAX,PAR2,PH,P,NP)

DIAGONALIZE THE UPPER STATE HAMILTONIAN
CALL SYMDIG(N,IER)_

STORE THE EIGENVECTORS IN $E(I,L,1)= (E+ * E-)

(tittttt)
(D- * 0+)
IBK=NP(3)
DO 355 II=1,IBK
DO 355 I=1,IBK

355 SE(I+IROH,II+ICOL,1)=S(I,II)

FORK THE EXPECTATION VALUES OF THE P OPERATORS AND STORE IN AP(L,1)
CALL FORMPI1(IFPAV,NMAX,JEO,PAR2,P,NP,CAPPU,1)
JAGAIN=1

340 CONTINUE
IF(IFSE.EG.O) GO TO 370

PRINT SE EIGENVECTOR MATRIX
PRINT 360,J

360 FORMAT(///* UPPER STATE EIGENVECTOR MATRICES FOR JU = *13)
DO 363 JEO=1,4
CALL UANGDIN(J,JEO,NP(3),IROH,ICOL,CAPPU,KTU)
PRINT 362,JEO

nnnnn

143

362 FORMAT(I* JEO = 1All“)
363 PRINT 364, <(SE(I+IRON,II+ICOL,1),II=1,13),I=1,13)
364 FORMAT<13E10.3/)
370 CONTINUE
DETERMINE NHICH GS LEVELS CAN BE REACHED FROM THE UPPER STATE LVEELS
JDEL INDICATES GS J HHICH CAN BE REACHED FROM US J.
JLPREV INDICATES PREVIOUSLY CALCULATED GS J LEVELS.
ENERGIES AND EIGENVECTORS FOR GS J ARE STORED IN AP(I,IJDEL(L)) AND
SE(I,II,IJDEL(L))
JDEL(2)=J-1
JDEL(3)=J
JDEL(4)=J+1
IF((IPRT.NE.O).OR.(IFPAV.NE.O)) PRINT 357
357 FORMAT(///* GROUND STATE ENERGIES*I)
DO 400 L=2,a
CHECK IT GS LEVELS ARE ALREADY CALCULATED. IF DONE DO NOT RECALC.
DO 405 LL=2,4
IF(JDEL(L).NE.JLPREV(LL)) GO TO 405
IJDEL(L)=IJPREV(LL)
GO TO 403
405 CONTINUE
FIND PREVIOUSLY CALCULATED GS J UHICH CAN NOT BE REACHED FROM THE US
PUT THE NEH Gs J LEVELS HERE
DO 415 LL=2,4
IF((JLPREV(LL).EG.JDEL(2)).OR.(JLPREV(LL).EO.JDEL(3)).OR.
1<JLPREV<LL>.E0.JOEL<4)))GO TO 415
IJDEL(L)=IJPREV(LL)
JLPREV(LL)=JDEL(L)
IF(JDEL(L).LT.O) GO TO 403
GO TO 403
415 CONTINUE
408 00 407 LL=1,51
407 JIN(IJDEL(L),LL)=O
DO 410 I=IUPRE2,IULAST,NISO
CALL INDOUT<I0N<I),INDU,INDL,LIST)
J=SQRT(FLOAT(INDL-1))
IFCJDELCL).E0.J) JIN(IJDEL(L),INDL-J**2)=1
410 CONTINUE '
DO 412 1:1,408
412 AP(I,IJDEL<L))=0
FORM Gs ENERGY LEVELS. THE PROCEDURE IS THE SAME As FOR FORMING
US LEVELS
NAI=0
IAN=N1+1
INDEx=0
IBN=1
J=JDEL(L)
LPS=LUPS(1)
DO 420 JEO=1,4
N=0
NP(1)=J
IF((JEO.EQ.1).OR.(JEO.EQ.3)) JAGAIN=0
CALL HANGDIM(J,JEO,NP(3),IROU,ICOL,CAPPL,KTL)
43o ISAV=INOEx

no

144

CALL FORMPI1(-1,NMAX,JEO,PAR1,P,NP,CAPPL,IJDEL(L))
IF(ISAV.EG.INDEX) GO TO I.20
INDEX=ISAV
IER=IPRT .
IFCJAGAIN.E0.0) CALL PNAKECJ,JEO,NMAX,PAR1,P,PI,NP)
CALL HANGT(A,N,JEO,JAGAIN,NMAX,PAR1,PH,P,NP)
CALL SYMDIG(N,IER)
IBK=NP(3)
DO 435 II?1,IBK
00 435 I=1,IBK
43S SECI+IROH,II+ICOL,IJDELCL))=S(I,II)
CALL F0RNPIT<IFPAV,NHAX,JEO,PAR1,P,NP,CAPPL,IJDEL(L))
JAGAIN=1
420 CONTINUE
IF(IFSE.EQ.O) GO TO 380
PRINT 371,J _
371 FORNATC/I/t GROUND STATE EIGENVECTOR MATRICES FOR JL = *13)
00 373 JEO=1,6
CALL HAHGDINCJ,JEO,NP(3),IROV,ICOL,CAPPL,KTL)
PRINT 362,JEO
373 PRINT 364,((SE(I+IROH,II+ICOL,IJDELCLJ),II=1,13),I=1,13)
380 CONTINUE
403 CONTINUE
400 CONTINUE
DO 411 L=2,4
IJPREVCL)=IJOEL(L)
411 JLPREV(L)=JDEL(L)
CALCULATE TRANSITION FREQUENCIES AND INTENSITIES FOR EACH ISOTOPE
JLL=-1
Ju=JUTHIS
DO 540 I=IUTHIS,IUEN,NISO
CALL INDOUT(IQN(I),INDU,INDL,LIST)
JL=SORT(FLOAT(INDL-1))
PICK THE PROPER MATRIX OF ENERGY EIGENVALUES FOR JL
DO 550 LL=2,4
IF(JL.EQ.JDEL(LL)) IJDL=IJDEL<LL>
550 CONTINUE
FORM SYNHETRIC TOP JK PART OF DIRECTION COSINE NATRIX ELEMENTS
(JU,KU/DIR COSIJL,KL)
IF(JL.EQ.JLL) GO TO 555
JLL=JL
CALL LSTR(JU,JL,JTYPE,CAPPL,CJM)
SSS CALL 0N(INDU,JU,KNU,KPU,JEOU,CAPPL)
CALL 0N(INDL,JL,KNL,KPL,JEOL,CAPPL)
HANG TRANSFORN THE DIRECTION COSINE NATRIX ELEMENTS AND STORE IN A
CALL VANGCOSCJEOU,JEOL,JU,JL)
LOCATE THE PROPER EIGENVECTOR MATRIX
CALL HANGDIHCJU,JEOU,NPU,IRONU,ICOLU,CAPPU,KTU)
CALL HANGDIHCJL,JEOL,NPL,IRONL,ICOLL,CAPPL,KTL)
DO 480 MI=1,NPU .
IFCKTU.NE.Kuu-KPU> GO TO 480
IU=NI+ICOLU
GO TO 482
480 KTU=KTu-4

nnn

145

482 D0 484 NI=1,NPL
IF<KTL.NE.KNL-KPL) GO TO 484
IL=MI+ICOLL
GO TO 486
484 KTL=KTL-4
486 CONTINUE
CALCULATE (JU,KNU,KPU/DIR COS/JL,KNL,KPL)
PHITAU=0
IF(IFTRAN.EG.O) GO TO 588
PRINT 582,JU,KNU,KPU,JEOU,(SE(M+IROHU,IU,1),N=1,NPU)
582 FORMAT(*0UPPER STATE QN*3IS* AND JEO*IS/5X*EIGENVECTOR*I
1Sx13E10.3)
583 FORMAT(*OGROUND STATE QN*3IS* AND JEO*IS/SX*EIGENVECTOR*I
1SX13E10.3)
PRINT 583,JL,KNL,KPL,JEOL,(SE(N+IRONL,IL,IJDL),N=1,NPL)
PRINT S15,JU,JL
515 FORMAT(/* HANG TRANSFORNED DIRECTION COSINE MATRIX FOR JU = A
113* JL = *I3/)
00 516 M=1,NPU
516 PRINT 517,(A(H,N),N=1,NPL)
517 FORMAT<SX13£10.3)
PRINT 520, CJM
320 FORMAT(ZSX* CJN = *E10.3/)
588 CONTINUE
00 S85 N=1,NPL
DO 585 N=1,NPU
585 PHITAU=PHITAU+SE<N+IRONU,IU,1)*A(M,N)*SE<N+IROHL,IL,IJDL)
PHITAU=PHITAU**2*3
RELINT=PHITAU*CJM
IF(IFRINT.NE.0) PRINT 586,JU,KNU,KPU,JL,KNL,KPL,RELINT
586 FORMAT(*O JU KN KP JL KN KP LIVE STRENGTH*/
12(6X3I3),5XE16.3)
DETERMINE THE STATISTICAL HEIGHT OF GS LEVEL
GL(1) MEANS KNL+KPL = EVEN
GL(2) MEANS KNL+KPL = ODD
G=GL(1)
IF(MOO(KNL+KPL,2).NE.O) G=GL(2)
DO 540 L=1,NISO
ISTP=ISO-ISTOP(L)
CALCULATE THE GS ENERGY
IUL=JIN(IJDL,INDL-JL**2)
EL=AP(IUL,IJDL)
ISOTOPIC CORRECTIONS TO GS ENERGY
DO 64 II=1,19
IF<NVAR(11,1).E0.0) GO TO 64
NA=IUL-NVAR(II,1)
EL=EL+ISTP*AP(NA,IJDL)*PAR(11,2)
64 CONTINUE
CALCULATE THE us ENERGY
EU=VO(1)+V0(2)*ISTP+VO(3)*ISTP**2
IUL=JIN(1,1NDU-JUTHIS**2)
EU=EU+AP(IUL,1)
00 6S II=1,19
IF(NVAR(II,2).E0.0) GO TO 65

65

CALCULATE THE J,KN,KP INDEPENDENT PART OF THE INTENSITY

146

NA=IUL-NVAR(II,2)

EU=EU+ISTP*AP(NA,1)*PAR(11,4)
CONTINUE

IL=I+L~NISO

FREO(IL)=Eu-EL

G*FREG*(1-EXP(-FREO/T))*EXP(‘EL/T)*ABUN*CJH

STREN<IL)=G*FREQ(IL)*(1-EXP(-FREQ(IL)/(.69SO3*T)))
1*EXP(-EL/(369503fT))*ABUN(L)*CJM

CALCULATE INTENSITY

540
SET
545

S90

S95

STREN(IL)=STREN(IL)*PHITAU
CONTINUE

UP PARAMETERS FOR NEXT ITERATION

CONTINUE

IUPRE2=IUPREV

IUPREV=IUTHIS

IUTHIS=IUNEXT

JUPRE2=JUPREV

JUPREV=JUTHIS

JUTHIS=JUNEXT

IF(IUTHIS.GT.MVAR) GO TO 595
IUNEXT=IUNEX2

JUNEXT=JUNEX2

IF(NLINE.GT.MVAR) GO TO 590
IUNEX2=NLINE

CALL INDOUT(ION(NLINE),INDU,INDL,LIST)
JUNEX2=SQRT(FLOAT(INDU‘1))

GO TO 300

IUNEX2=MVAR+NISO

CALL INDOUT(ION(MVAR),INDU,INDL,LIST)
JUNEX2=SQRT(FLOAT(INDU‘1))

GO TO 320

CONTINUE

PRINT INTENSITIES

101

CALL OUT(IOUT,MVAR,NISO,RESO,ISTOP,TOPFRE,BOTFRE,UKSTREN)

GO TO 100
CONTINUE
END

147

FUNCTION CAPPA (PAR,JBAND,HAM ,IHEAD,NPAR,PGDEL,ISO,IP)
COMMON/8LPR/PRS(2)

DIMENSION XCZS),D(11,25) -

DIMENSION PAR(IP),IHEAD(10),PGDEL(IP),NPAR(IP,2)

TYPE INTEGER HAN,D,X

DATA ((XCI),I=1,19)=8HOA = X =,8H B = Y =,8H C = Z =,8H

18H T2 =,8H T3 =,8H T4 =,8H TS =,8H T6 =,8H
28H H2 ;,8H H3 =,8H , H4 =,8H H5 =,8H H6 =,8H
38H H8 =,3H H9 =,8H H10 =,8H0<X+Y)/2 ,8H (X-Y)/2 )

DO 10 I=1,11
DD 10 J=1,IP

10 D(I,J)=8H
D(1,1)=8HPX2 S D(1,2)=8HPY2 S D(1,3)=8HP22
D(4,1)=8HPLANAR
X(IP-1)=8HO(X+Y)/2 $X(IP)=8H (X-Y)/2
IF(IP.LE.21) GO TO 15
X(20)=8H0 V0 = S X(IP-2)=8H DDVO =
D(1,20)=8H8AND CEN S D(2,20)=3HTER

15 CONTINUE
IPT=IP

C FINDS CAPPA AND PRINTS OUT THE STATE CONSTANTS
IF (PAR(1).GE.PAR(2))GO TO 428
PRINT 221
AP=PAR(2) S PAR(2)=PAR(1) S PAR(1)=AP
428 CONTINUE

AP=PAR(1)
B=PAR(2)
C=PAR(3)
X(1)=8HOA = X = $X(2)=8H 8 = Y = S X(3)=8H C = Z =
D(5,1)=8HOBLATE
420 IF (8.5T.C) GO TO 426
C=8 S B=AP S AP=PAR(3)
X(1)=8H08 = X = S X(2)=8H C = Y = S X(3)=8H A = Z =

D(5,1)=8HPRDLATE
IF (B.LE.AP) GO TO 426
PRINT 221
PAR(3)=PAR(1) $PAR(1)=AP
B=AP S AP=PAR(3)

426 CAPPA=(2.*B-AP-C)/(AP-C)
IF (J8AND.EO.8H UPPER) GO TO 20
PRINT 217
PRINT 218,(IHEAD(N),N=1,10)

20 GO TO (21,22,23,24) HAM
21 PRINT 121

121 FORMAT (*OPLANAR-7 PARAMETER HAMILTONIAN,MDNCUR-THESIS *)
0(3,1)=8H
D(10,4) = 8HXE= S D(10,5) = 8HYE=
ENCODE(16,230,0(10,4))D(10,4),PRS(1)
ENCDDE (16,230,0(10,5)) D(10,5),PRS(2)

230 F3RMAT(A4,E12.6)
ENCODE(8,240,D(11,4)) D(10,4),D(11,4)
ENCDDEC8,240,D(11,S)) D(10,S),D(11,S)

240 FORMAT<R2,A6)
GO TD 40

I
I

H1
H7 ,

148

22 PRINT 122
122 FORMAT (*OKFC-REDUCED,FORD{YALLABANDI,PARKER,J.M.S.,30,241(1969)*)
D(3,1)=8HKFC-NON
GO TO 40
23 PRINT 123
123 FORMAT (*0 H-FORM,YALLABANDI AND PARKER,J.C.P.,49,410(1968)*)
D(3,1)=8H H¢NDN
GO TO 40
24 PRINT 124
124 FORMAT(*0 TYPKE REDUCTION OF UATSON HAMILTONIAN, J.H.S. 63,170(19
176)*)
D(3,1)=8H H-NDN
40 PRINT 250,J8AND,ISO
250 FORMAT (1X,A8* STATE*9X
1 *VARI (*I3*-ISOTOPE VARI-*I* CONSTANT VALUE*9X*ABLE MA
1SS)EFFECT ABLE OPERATOR*)
GO TO (41,42,43,44) HAM
41 IF (CAPPA.LT.O) GO TO 51
C PLANAR OBLATE
D(1,4)=8H(1/4)*(P S D(2,4)=8HX4 + R2* 3 DC3,4)=8HPZ4 + R*
D(4,4)=8H(PX2*PZZ S D(S,4)=8H + P22*P S D(6,4)=8HX2))
D(7,4) = 8HR= (YE/( S D(8,4) 3 8HXE+YE))2
D(1,5)=8H(1l4)*(P S D(2,5)=3HY4 + 82* S D(3,5)=8HPZ4 * 8*
D(4,5)=8H(PY2*PZZ S D(5,S)=8H + P22*P S D(6,5)=8HXZ))
D(7,5) = 8H8 =(XE/( S D(8,5) = 8HXE’YE))2
D(1,6)=8H(1/4)*(2 S 0(2,6)=8H*R*S*PZ4 3 DC3,6)=8H + (PX2*
D(4,6)=8HPY2 + PY S D(5,6)=8H2*PX2) + S D(6,6)= 8H S*(PX2*
D(7,6)=8HPZZ + Pl 3 D(8,6)=882*PX2) + S D(9,6)=8HR*(PY2*P
D(10,6)=8H22+PZZ*P S D(11,6)=4HY2))

0(1,7)=8H(1I4)*(2 S D(2,7)=8H*(PX2*PY 3 D(3,7)=8H2 + PY2*
D(4,7)=8HPX2) - 2 S 0(5,7)=8H*P2 + 5* S D(6,7)=8HPZZ)
D(1,10)=8HP6 S D(1,11)=8HP4*PZZ S DC1,12)=8HP2*PZ4
D(1,13)=8HPZ6

GO TO 60

51 CONTINUE

c PLANAR PROLATE
D(1,4)=8H(1/4)*(P s D(Z,4)=8HZ4 + R2* 3 DC3,4)=8HPV4 + R*
D(4,4)=8H(P22*PY2 s DCS,4)=8H + PY2*P s D(6,4)=8HZZ))
047,4) = EHR =CCXE- s DC8,4) = 8HYE)/XE)2
D(1,S)=8H(1/4)*(P s D(2,5)=8HX4 + 52* s D(3,S)=8HPY4 + 5*
D(4,5)=8H(PXZ*PY2 s DCS,5)=8H + PY2*P s DC6,S)=8HX2)
0C7,5) = GHS = (YEI s D(8,S) =8HXE)2 -
0(1,6)=8H(1/4)*(2 s D(2,6)=8H*R*S*FY4 s D(3,6)=8H + (PZZ*
0(4,6)=8HPX2 + RX 3 D<S,6)=8H2*PZZ) + s 0(6,6)= 8HS*(PZZ*
D(7,6)=8HPY2 +‘PV s D(8,6)=8H2*PZZ) + s D(9,6)=8HR*(PXZ*P
D(10,6)=8HY2+PYZ*P s 0(11,6)=4Hx2))
D(1,7)=8H(1l4)*(2 s D(Z,7)=8H*(PZZ*PX s DC3,7)=8H2 + Px2*
D(4,7)=8HPZZ) - 2 s D(S,7)=8H*P2 + 5* s DC6,7)=8HPY2)
DC1,10)=8HP6 ' S D<1,11)=8HP4*PZZ s D(1,12)=8HP2*PZ4
DC1,13)=8HP26
GO TO 60

42 CONTINUE

c PHI-PORN

D(1,4)=8HPX4

43

D(1,5)=8HPY4

149

S D(1,6)=8HPZ4

D(1,7)=8H(PY2*P22 S D(2,7)=8H + P22*P S
D(1,8)=8H(PX2*PZZ S D(2,8)=8H + PZZ*P S
D(1,9)=8H(PX2*PY2 S D(2,9)=8H + PY2*P S

D(1,10)=8HPX6
D(1,13)=8H(PX2*PY4
D(1,14)=8H(PY2*PX4
D(1,15)=8H(PY2*PZ4
D(1,16)=8H(P22*PY4
D(1,17)=8H(P22*PX4
D(1,17)=8H(PZZ*PX4
D(1,18)=8H(PX2*PZ4
D(1,19)=8H(PX2*P22
D(4,19)=8HX2)

GO TO 60

CONTINUE

C H-FORM

44

D(1,4)=8HP4

Hflfififififlflfi

D(1,11)=8HPY6

D(2,13)=8H + PY4*P
D(2,14)=8H + PX4*P
0(2,15)=8H + PZ4*P
0(2,16)=8H + PY4*P
D<2,17)=8H + PX4*P
D(2,17)=8H + PX4*P
0(2,18)=8H + PZ4*P

D(2,19)=8H*PY2 + P

S D(1,5)=8HP2*P22

D(1,7)=8HP2*(PX2- S D(2,7)=8HPY2)
D(1,3)=8H(P22*(PX S D(2,8)=8H2-PY2) + S

D(4,8)=8H2)*PZZ)
D(1,10)=8HP6
D(1,13)=8HPZ6
D(1,1S)=8HP2*(PZZ*
D(4,1S)=8H-PY2)*PZ
D(1,16)=8HPZ4*(PX2
DI4,16)=8H)*PZZ

GO TO 60

CONTINUE

C TYPKE REDUCTION

60

126

214

D(1,4)=8H-P4

““60““

D(1,11)=8HP4*P22
D(1,14)=8HP4*(PX2'
D(2,1S)=8H(PX2-PY2
D(5,15)=8H2)
D(2,16)=8H-PY2) +

S D(1,5)=8H-P2*P22 S
D(1,7)=8H-2*P2*(P S D(2,7)=8HX2 “ PYZ

M

D(1,8)=8H2*(PX4 + SD(2,8)=8H PY4 - 3 s

D(4,8)=8H2 + PY2*
D(1,10)=8HP6
D(1,13)=3HP26

D<1,1S)=8H1/2*P2*(S
D(4,15)=8HX2*PY2 +s
D(1,19)=8H(PX2 - PS

CONTINUE
DD 64 N=1,20

S

D(1,11)=8HP4*P22

D(5,8)=8HPX2))

IF((IP.E0.21).AND.(N.EQ.20))GO TO 65
IF((IP.EG.24).AND.(N.EQ.20)) GO TO 70

IF (N.EG.4) PRINT 126

IF (N.EQ.10) PRINT 126

FORMAT (*0*)

0(3,7)=8HY2)
D(3,8)=8HX2)
D(3,9)=8HX2)

S

MMHMMHMM

S

D(1,12)=8HPZ6
D(3,13)=8HX2)
D(3,14)=8HY2)
O(3,1S)=8HY2)
D(3,16)=8H22)
D(3,17)=8H22)
D(3,17)=8HZZ)
D(3,18)=8HX2)
D(3,19)=8HY2*PZZ*P

D(1,6)=8HPZ4

D(3,8)=8H (PXZ'PY

S
S
S

S

D(1,12)=8HP2*PZ4
D(2,14)=8HPY2)
D(3,15)=8H) + (PXZ

D(3,16)=8H(PX2-PY2

D(1,6)=8H-PZ4
D(3,7)=8H)
D(3,8)=8H*(PX2*FY

$0(1,12)=8HP2*PZ4
D(1,14)=8HP4*(PX2 S D(2,14)=8H- PY2)
D(2,15)=8HPX4 + FYS D(3,15)=8H4 - 3*(P
D(S,15)=8H PY2*PX2$ D(6,15)=8H))
D(2,19)=8HY2)**3

IF ((NPAR(N,1).EG.0).AND.(NPAR(N,2).EG.O).AND.(PAR(N).E0.0).AND.

1(PGDEL(N).EQ.O)) GO TO 64

PRINT 214,((X(N),PAR(N),NPAR(N,1),(D(J,N),J=1,11)))

FORMAT

( A8,1X,E15.8,I3,2X,15X,3X,11A8)

IF((NPAR(N,2).NE.0).OR.(PGDEL(N).NE.O)) PRINT 216,PGDEL(N),

1NPAR(N,2)

216 FORMAT (*+*29X,E12.5,I3)
64 CONTINUE

150

IF((NPAR(IP-2,2).EG.O).AND.(PGDEL(IP-2).EG.0)) GO TO 65
PRINT 214,X(IP-Z),PGDEL(IP-2),NPAR(IP'2,2)
GO TO 65

7O IP=21

65 IF(NPAR(IP-1,1).E0.0) GO TO 66
PRINT 212,X(IPT-1),NPAR(IP-1,1)

66 IF(NPAR(IP,1).E0.0) GO TO 68
PRINT 212, XCIPT),NPAR(IP,1)

68 CONTINUE

212 FORMAT ( A8,16X,I3)
PRINT 220,CAPPA

220 FORMAT(//* KAPPA = *F14.7)
IP=IPT
RETURN

217 FORMAT(*1*)

218 FORMAT (10A8)

221 FORMAT (6H*******0NLY TYPES I-R AND III-R WORK PROPERLY IN THIS PR
1OGRAM ---- THEREFORE THE VALUES X AND Y OR X AND Z HILL BE EXCHANG
2ED*)

END

151

SUBROUTINE PMAKE(J,JEO,NMAX,PAR,P,PI,NP,PF)
COMMON lPMAK/HAM,VIBZ,VIBXY,MSPM,LP$
C THIS PROGRAM CALCULATES THE MATRIX ELEMENTS OF THE OPERATORS IN J,K S
C THE DIMENSION OF P MUST BE 19*4*(JMAx/2+1)
DIMENSION P(19,4,NMAX),PI(2,NMAX),NP(3),PF(4,NMAX)
DIMENSION PAR(3) '
COHMON/BLPR/PRSCZ)
TYPE INTEGER HAM
C ZERO THE P MATRIX
M=1
MM=NMAX*19*4
DO 6 I=M,MM
6 P(I)=0.0
MM=2*NMAX
DO 8 I=1,MM
8 PI(I)=D.O
MM=4rNMAx
DO 9 I=1,MM
9 PF(I)=O
N=0
IF(J.EQ.O)GO TO 380
THE K EVEN ELEMENTS ARE CALCULTED AND STORED SEPATRATE FROM THE ODD
GO TO (2,2,4,4) JED
K IS EVEN
KEO=(J/2)*2
GO T0 5
K 15 ODD
KEO=((J+1)/2)*2-1
PPF=J*(J+1)
K = KEO +2
NK=KEOIZ+2
N=NK-1
GO TO (3S9,10,260,110) HAM
C KENT MONCURS HAMILTONIAN
359 CONTINUE
IF (PARC1). LT.PAR(3)) GO TO 370
C OBLATE PLANAR FORM
R = PRS(Z)I(PRS(1)+PRS(2))

NOD

\n$~n

R=R*R
S = FRS(1)I(PRS(1)+PRS(2))
S=S*S
360 NK = NK-1
K=K-2
PK=K*K
KN =1-K

IF (KN.LT.1) KN=1
IF (KN.GT.4) KN =4
GO TO (362,364,366,380) KN
362 PPK = PPF-PK ,
C CALCULATE THE DIAGONAL TERMS
IF (NK.LE.0) GO TO 380

P(1,1,NK) = .5*PPK
P(2,1,NK) = .5*PPK
P(3,1,NK) = PK

364
365

152

P<4,1,NK) .25*(PPK*(.375*PPK-.25)+.37S*PK+R*PK*(PPK+R*PK))
P(5,1,NK) .25*(PPK*(.375*PPK-.25)+.375*PK+S*PK*(PPK+S*PK))
P(6,1,NK)=.25*((R+S)*PK*PPK+2.*R*S*PK*PK+.25*PPK*(PPK+2.)-.7S*PK)
PC7,1,NK) = .25*(S.*PK-2.*PPF+.5*PPK*(PPK+2.)-1.S*PK)

P(10,1,NK) = PPFtPPF*PPF

P( 11,1,NK) = PPF*PPF*PK
P(12,1,NK) = PPF*PK*PK
P(13,1,NK) = PKtPK*PK

PI( 1,NK)=K*VIBZ
PF(1,NK)=.5*(PPF-PK)

PF(2,NK)=PPF
PF(3,NK)=.5*PPF-1.5*PK

IF (KED.E0.0) GO TO 380

IF (KEO-K) 365,360

PPK=PPF°PK

G = (J-K-1)*(J-K)*(J+K41)*(J+K+2)
PPG =-SGRT(G)

C CALCULATE THE K,K+2 TERMS

366

368

NK=NK+1

IF (NK.LE.O) GO TO 380

P(1,2,NK) = .25*PPG

P(2,2,NK) = -.25*PPG

P(4,2,NK) = .0625*PPG*(PPK-2.-2*K+2.*R*(PK+2.+2*K))
P(5,2,NK) =-.0625*PPG*(PPK-2.-2*K+2.*S*(PK+2.+2*K))
P(6,2,NK) = .125*PPG*(s-R)*(PK+2.+Z*K)

PPG=-PPG

PI(2,NK) = O.5*VIBXY*PPG
PF(4,NK)=-.25*PPG

NK=NK-1

IF (KEO.EQ.1) GO TO 380

IF (KEO-K-Z) 368,360

PPK=PPF-PK

G = (J-K-1)*(J-K)*(J+K+1)*(J+K+2)
PPG = SGRT(G) _

PM = (J-K-3)*(J-K-2)*(J+K+3)*(J+K+4)
PPM = PPG*SORT(PM)

C CALCULATE THE K,K+4 TERMS

C

NK=NK+2

IF (NK.LE.0) GO TO 380
P(4,3,NK) = .015625*PPM
P(5,3,NK) = .015625*PPM
P(6,3,NK) = -.03125*PPM
P(7,3,NK) ='.0625*PPM
NK=NK'2

IF (K.GT.“1) GO TO 360
GO TO 380

PROLATE PLANAR FORM
370 R=(PRS(1)-PRS(2))IPRS(1)

371

R=R*R J
S=PRS(2)IPRS(1)
S = S*S

NK=NK'1

K=K~2

PK=K*K

372

153

KN=1 -K

IF (KN.LT.1) KN=1

IF (KN.GT.4) KN=4

GD TO(372,374,376,380) KN
PPK=PPF-PK

C CALCULATE THE DIAGONAL TERMS

374
375

IF (NK.LE.0) GO TO 380

P(1,1,NK) = .5*PPK

P(2,1,NK) = .5*PPK

P(3,1,NK) 3 PK
P(4,1,NK)=.25*(PK*PK+R*R*.125*(3.*PPK*PPK‘2.*PPK+3.*PK)+R*PPK*PK)
P(5,1,NK)= .25*(($*S*1.)*.125*(3.*PPK*PPK-2.*PPK*3.*PK)+S*.25*(PPK

1*PPK+2*PPK-3*PK))

P(6,1,NK) = .25*( R*S*.25 *(3*PPK*PPK-2*PPK+3*PK) +PPK*PK+$*PPK*PK

1+R*.25 *(PPK*PPK+2*PPK-3*PK))

P(7,1,NK) = .25*(2*PK*PPK-2.*PPF+2.S*PPK)
P(10,1,NK) = PPF*PPF*PPF

P( 11,1,NK) = PPF*PPF*PK
PC12,1,NK) = PPF*PK*PK
P(13,1,NK) = PK*PK*PK

PI(1,NK) = K*VIBZ
PF(1,NK)=.5*(PPF-PK)

PF(2,NK)=PPF
PF(3,NK)=.5*PPF-1.5*PK

IF (KE0.E0.0) GO TO 380

IF (KEO-K) 375,371

PPK=PPF-PK

G = (J-K-1)*(J-K)*(J+K+1)*(J+K+2)
PPG=SRRT(G)

C CALCULATE THE K,K+2 TERMS

376

378

NK=NK+1

IF (NK.LE.0) GO TO 380

P(1,2,NK) = -.2$*PPG

P(2,2,NK) = .25*PPG

P(4,2,NK) = .25*R*PPG*(R*.25*(PPK-2.*K-2.)*.5*(PK+2*K+2))
P(5,2,NK) = .25*((S*S-1.)*.25*(PPK-2*K-2))*PPG

P(6,2,NK) = .125*(R*S*(PPK-2.“2.*K)+(S-1.)*(PK+2.*K+2.))*PPG
P(7,2,NK) = .ZS*PPG*(1.25-(PK+2.*K+2.))

PI(2,NK) = 0.5*VIBXY*PPG
PF(4,NK)=-.25*PPG

NK=NK'1

IF (KEO.EQ.1) GO TO 380

IF (KED-K-Z) 378,371

PPK=PPF-PK

G: (J-K-1)*(J-K)*(J+K+1)*(J+K+2)
PPG= SQRT(G)

PM = (J-K-3)*(J-K-29*(J+K+3)*(J+K+4)
PPM = PPG*SORT(PM)

C CALCULATE THE K,K+4 TERMS

NK=NK+2

IF (NK.LE.0) GO TO 380

P(4,3,NK) = 0.015625*R*R*PPM
P(5,3,NK) = .03125*PPM*(.5-S+.5*S*S)

P(6,3,NK)= .03125*R*PPM*(S-1.)

154

NK=NK-2
IF (K.GT.-1) GO TO 371
GO TO 380
C HATSONS HAMILTONIAN
260 NK=NK~1
K=K-2
PK=K*K
KN=1-K
IF (KN.LT.1) KN=1
IF (KN.GT.3) KN =3
GO TO (262,264,270) KN
262 PPK=PPF-PK
c CALCULATE THE DIAGONAL TERMS
P(1,1,NK)=0.5*PPK
P(2,1,NK)=O.S*PPK

P(3,1,NK) = PK

P(4,1,NK) = PPF*PPF
P(5,1,NK) = PPFAPK
P(6,1,NK) = PK*PK
P<10,1,NK) = PPF*PPF*PPF

P( 11,1,NK) = PPF*PPF*PK
P(12,1,NK) = PPFtPK*PK
P(13,1,NK) = PK*PK*PK

PI( 1,NK)=K*VIBZ
PF(1,NK)=.5*(PPF-PK)
PF(2,NK)=PPF
PF(3,NK)=.5*PPF-1.5*PK
IF ( KEO . EQ.0) GO TO 380

IF (KEO-K) 266,260

264 PPK=PPF-PK

266 G=(J-K-1)*(J~K)*(J+K+1)*(J+K+2)
PPG=$QRT(G) '

NK=NK+1
P(1,2,NK) =-.25*PPG
P(2,2,NK) = .25*PPG

P(7,2,NK)=PPF*PPG*(‘.5)
P(8,2,NK) =*PPG* (PK+2*K+2)
P(14,2,NK) =—PPG*.5* PPF*PPF
P(15,2,NK)=PPG*PPF*(PK+2*K+2)*(-1.)
PC16,2,NK)=0.5*PPG*(PK*PK+(K+2.)*(K+2.)*(K+2.)*(K+2.))*(-1.)
PI(2,NK) = O.5*VIBXY*PPG
PF(4,NK)='.25*PPG
NK=NK-1
IF(K.GT.O) GO TO 260
270 GO TO 380
C KFC HAMILTONIAN
10 NK=NK-1
LP=LPS'8
K=K'2
PK=K*K
KN =1-K
IF (KN.LT.1) KN=1
IF (KN.GT.5) KN=5
GO TO (12,14,18,22,380) KN

155

12 PPK=PPF-PK
IF(LP.LT.2) GO TO 40
41 CONTINUE
P(19,1,NK) = .5*PPK*PK-.125*(2*PPF*PPF*(PK+4)-PPF*(2*PK*PK+26*PK
1+8)+PK*PK*PK+24*PK*PK+28*PK)
PDUM =.25*PK*(3*PPK*PPK-2*PPK+3*PK)
P(16,1,NK) =P(17,1,NK)=POUM
PDUM=PPK*PK*PK . _
P(1S,1,NK) =P<18,1,NK)=PDUM
PDUM = .125*(PPK*(PPK*(PPK+6.)-8.-19.*PK)+20.*PK)
P(13,1,NK) =P<14,1,NK)=POUM
P(12,1,NK)= PK*PK*PK
PDUM (PPK*(25*PK+8-10*PPK+S*PPK*PPK)-ZD*PK )*.0625
P(10,1,NK) P(11,1,NK)=PDUM
40 CONTINUE ,
P(9,1,NK) = .25*(PPK*PPK+2.*PPK-3.*PK)
P(8,1,NK)=PPK*PK
P(7,1,NK)=PPK*PK
P(6,1,NK)=PK*PK
PDUM = .25*(1.5*PPK*PPK-PPK+1.S*PK)
P(4,1,NK) = P(S,1,NK) = PDUM
P(3,1,NK)=PK
P(2,1,NK)=.5*PPK
P(1,1,NK)=.S*PPK
PI( 1,NK)=K*VIBZ
PF(1,NK)=.S*(PPF-PK)
PF(2,NK)=PPF
PF(3,NK)=.5*PPF-1.5*PK
IF (KEO.E0.0) GO TO 380
IF (KEO - K) 16,10
14 PPK=PPF-PK
16 G = (JoK-4)*<J-K)*(J+K+1)*<J+K+2)
PPG = SQRT(G)
NK=NK+1
IF(LP.LT.2) GO TO 50
51 CONTINUE

PDUM = (PK*2.*(PK+4*K+12J+32*K+16)*.25*PPG

P(18,2,NK) =-PDUH

P(15,2,NK) = PDUM

PDUM = .S*PPG*(PK+2*K+2)*(PPK-2*K-2)

P(17,2,NK) =-PDUM

P(16,2,NK) = PDUM

PDUM = .O3125*PPG*(PPK* (PPK-4*K+6)-41*PK-102*K-72)
P(14,2,NK) =-PDUM I

P(13,2,NK) = PDUM

PDUN = PPG*(1S*PPK*PPK-60*PPK*K-70*PPK+105*K*(K+1)+125*(K+1)
1+11)*.015625

P(11,2,NK) PDUM

P(10,2,NK) = -PDUH
50 CONTINUE

PDUM =.5*PPG*(PK*2*K+2)
P(8,2,NK) = 'PDUM
P(7,2,NK) = PDUM

PDUM =.S*PPG*(.25*(2*PPK-4*K-4))

18

20

61

60

22

24

71

70

110

156

P(S,2,NK) PDUM

P(4,2,NK) -PDUM

PDUM: .25*PPG

P(2,2,NK) = PDUM

P(1,2,NK) =-PDUM

PI(2,NK) = O.5*VIBXY*PPG
PF(4,NK)=-.ZS*PPG

NK=NK-1

IF (KEO.E0.1) GO TO 380

IF (KEO -K -2) 20,10

PPK=PPF-PK

G = (J-K-1)*(J-K)*(J+K+1)*(J+K+2)
FPG = SQRT(G)

PM = (J-K-3)*(J-K-29*(J+K+3)*(J+K+4)
PPM = PPG*SGRT(PM)

NK=NK+2

IF(LP.LT.Z) GO TO 60

CONTINUE

P(19,3,NK) = —.125*(PK+4*K+4)*PPM
PDUM =PPM*(PK+4*K+8)*.125
P(17,3,NK) = P(16,3,NK) =PDUM
PDUM =PPM*(4-PPK+K*4)*0.0625
P(14,3,NK) = P(13,3,NK) = PDUM
PDUM =PPM*(3*PPK-12*K-20)*.03125
P(11,3,NK) = P(10,3,NK) = PDUM
P<9,3,NK) = -.0625*PPM

CONTINUE

P(5,3,NK)=.0625*PPM
P(4,3,NK)=.O625*PPM

NK=NK-2

IF (KED.EO.2) GO TO 380

IF (KED -K-4 ) 24,10

PPK=PPF-PK

G = (J-K-1)*(J-K)*(J+K+1)*(J+K+2)
PPG = SORT(G)

PM = (J-K-3)*(J-K-2)*(J+K+3)*(J+K+4)
PPM = PPG*SQRT(PM)

PM = (J-K-5)*(J-K-4)*(J+K+S)*(J+K+6)
IF(LP.LT.2) GO TO 70
CONTINUE

PPN = PPM*SQRT(PN)

NK=NK+3

P(10,4,NK) = -.S*PPN*.03125
P(11,4,NK) = -P(10,4,NK)
P(14,4,NK) = .03125*PPN
P(13,4,NK) = -P(14,4,NK)
NK=NK~3

CONTINUE

IF (K.GT.-2) GO T0 10

GO TO 380

c TYPKE HAMILTONIAN
NK=NK-1
LP=LPs-8

K=K-Z

157

PK=K*K
PPK=PPF-PK
PD=-2*PPF+5*PK
G=(J-K-1)*(J-K)*(J+K+1)*(J+K+2)
PPG=SORT(G)
KN=1-K
IF(KN.LT.1) KN=1
IF(KN.GT.5) KN=5
GO TO (112,114,118,122,380) KN
c CALCULATE DIAGDNAL ELEMENTS
112 IFCLP.LT.2) GO TO 140
P(10,1,NK)=PPF**3
P(11,1,NK)=PPF*PPF*PK
P(12,1,NK)=PPF*PK*PK
P(13,1,NK)=PK**3
P(1S,1,NK)=.S*PPF*PO
140 P(1,1,NK)=.S*PPK
P(2,1,NK)=.S*PPK
P(3,1,NK)=PK
P(4,1,NK)=-PPF*PPF
P(5,1,NK)=-PPF*PK
P(6,1,NK)=-PK*PK
P(8,1,NK)=2*PD
PI(1,NK)=K*VIBZ
PF(1,NK)=.5*(PPF-PK)
PF(2,NK)=PPF
PF(3,NK)=.S*PPF-1.S*PK
IF(KEO.EQ.O) GO TO 380
IF(KEO.EO.K) GO TO 110
C CALCULATE (K, K+2) TERMS
114 NK=NK+1
IF(LP.LT.2) GO TO 150
P(14,2,NK)=-.S*PPF*PPF*PPG
P(19,2,NK)=-.125*PPG*3
150 P(1,2,NK)=-.25*PPG
P(2,2,NK)=.25*PPG
P(7,2,NK)=PPF*PPG
PI(2,NK)=.S*VIBXY*PPG
PF(4,NK)=-.25*PPG
NK=NK-1
IFCKED.E0.1) GO TO 380
IFCKED-K-2.E0.0) GO TO 110
C CALCULATE (K, K+4) TERMS
118 PM=(J-K-3)*(J-K-2)*(J+K+3)*(J+K+4)
PPM=.5*SGRT(PM)*PPG
NK=NK+2
P(8,3,NK)=2*PPM
P(15,3,NK)=.S*PPF*PPM
NK=NK-2 _
IFCKED.E0.2) GO TO 380
IF(KED-K-4.E0.0) GO TO 110
c CALCULATE (K, K+6) TERM
122 IF(LP.LT.2) GO TO 170
PN=J*J

158

PN=CPN-(K+1)**Z)*(PN-(K+Z)**2)*(PN~(K+3)**2)*(PN-(K+4)**2)
1*(PN-(K+S)**Z)*(J-K)*(J+K+6)
PPN=SORT(PN)
P(19,4,NK+3)=-.125*PPN
170 IF(K.GT.’Z) GO TO 110
380 CONTINUE
NP(1)=J
RETURN
END

159

SUBROUTINE HANGT (A,NN,JEO,JAGAIN,NMAX,PAR,AH,P,NP)
DIMENSION PAR<19),P(19,4,NMAx),AH(4,MMAX),NP(3)

DIMENSION A(13,13)
t t a a t t t t t t t * t t i *
IF JAGAIN =O,A NEH INTERMEDIATE

JEO=1 *raK IS Even, use SUM or

JEO=4 ***K Is 000 , use sun OF
*tii’ifitii’ttii’iifi

nnnnnnnnnnn

J=NP(1)
so 10 <10,1o,12,12) JED
1o KEO=(J/2)*2
co T0 14
12 KEO=((J+1)/2)*2-1
14 ~=xsozz+1
1r (J.EQ.O) N=O
~913>=u
IF (N.LT.O) RETURN
1r (J.LE.0) RETURN
212:1.414213542
1r (JAGAIN) 24,26
24 so 10 <40,64,68,72)Jco
co 120:1
50:2
so 10 so
64 420:2
eo=-2
so TO 31
68 120:3
ED=-2
50 TD 40
72 420:4
50:2
so TD 40
26 CONTINUE
NEND=L*NMAX
oo 20 I=1,NEND
20 AH(I)=0.0

THE DIFFERENCE BETWEEN THE JEO=

*i'ki’iit'kititfi‘kititi

THIS ROUTINE FORMS THE HANG TRANSFORMED HAMILTONIAN AND STORES IT IN‘

HAMILTONIAN IS ALNAYS FORMED,IF NOT,TH
1 OR 2 AND JEO=3 OR 4 ARE HADE.
THE BASIS FUNCTIONS

JEO=2 ***K IS EVEN, USE DIFFERENCE OF THE BASIS FUNCTIONS
JEO=3 ***K IS ODD , USE DIFFERENCE OF THE BASIS FUNCTIONS

THE BASIS FUNCTIONS
* t t i * a t t t a t t t i t t * t t

C FORM THE HAMILTONIAN IN J,K SPACE

DO 13 L=1,6
DO 13 LL= 1,N
DO 13 I=1,19

13 AH(L,LL)=AH(L,LL)+PAR(I)*P(I,L,LL)

GO TO (28,29,36,37) JED
C FORM THE HANG TRANSFORMATION
28 JEO=1
EO=1
30 11:0
DO 36 I=2,4

160

AH(I,I)=RT2*AH(I,I)
34 CONTINUE
GO TO 32
29 JEO=Z
EO=-1
31 CONTINUE
N=N-1
NP(3)=N
IF (N.EQ.O) RETURN
I1=1
32 CONTINUE
AH(1,2)=AH(1,2)+EO*AH(3,2)
AH(2,3)=AH(2,3)+EO*AH(4,3)
GO TO 50
36 JEO=3
EO=-1
GO TO 40
37 JEO=4
EO=1
40 DO 42 1:1,3
L=I+1
AH(I,I)=AH(I,I) +EO*AH(L,I)
42 CONTINUE
AN(1,2)=AN<1,2)+EO*AN(4,2)
I1=0
so CONTINUE .
C STORE THE TRANSFORMEO MATRIX INTO A
00 $2 I=1,N
II=NN+I
DO 52 M=I,N
IJ=M+I1
L=M+NN
K=M-I+1
IF (K.GT.4) GO TO 51
A(L,II)=AH(K,IJ)
A(II,L)=AH(K,IJ)
GO TO 52
s1 CONTINUE
A(L,II)=A(II,L)=0.0
52 CONTINUE
NN=NN+N
RETURN
ENO

nnnnnnnnnnnnnnnn

mm

161

SUBROUTINE SYMDIG (N,ITN)

i‘kiiiiitit******.*********fl*********

THIS ROUTINE DIAGONALIZES THE SYMMETRIC MATRIX A AND COHPUTES ITS
EIGENVECTORS, STORING THEM IN S. THE COLUMNS OF S ARE THE EIGENVECTORS
CORRESPONDING TO THE EIGENVALUES HHICH ARE ALONG THE DIAGONAL OF A.
THE ROUTINE USES ONLY THE UPPER RIGHT CORNER OF A FOR THE OFF DIAGO

ELEMENTS OF A AND STORES THEIR SQUARES IN THE THE LOHER LEFT HAND CORN

THE ORDER OF ARITHMETIC OPERATIONS IS SET UP SUCH THAT THE METHOD OF
IZATION WORKS ONLY HHEN THE DIFFERENCE OF THE DIAGONAL ELEMENTS IS NOT
AND WORKS BEST IF THAT DIFFERENCE IS GREATER THAN THE OFF DIAGONAL EL
NAGNITUOE. ‘

IF ITN IS NOT ZERO ON ENTRY THE MATRIX ELEHENTS ARE PRINTED BEFORE AN
DIAGONALIZATION.

HE HILL CALL B=A(I,J) AND 8$=CONJG(A(I,J))
A t t a i t * t * t * t t t t t * t t * t t t t t t t t i t t i t A *

COHNON/BLKEV/A(13,13),S(13,13)
TYPE DOUBLE BAB,R
PRECN MUST BE APPROX = TO 2**(-N) UNERE N IS THE NUXBER OF BITS USED
THE FLOATING HRNTISSA IN THE COMPUTER
IPRT=ITN
PRECN=1.OE-11
ITN = NUMBER OF ITERATIONS THRU ALL OF A.
ITN = o
8(1,1)=1.0
IF (N.LE.0) RETURN
INITIALIZE THE S MATRIX

DO 2 I =1,N
S(I,I) =1.D
II=I+1

DO 2 J=II,N
NOTE I + 1 BECOMES LARGER THAN N
2 S(I,J) = S(J,I) = 0.0
IF (IPRT.EQ.O) GO TO 1
PRINT 200,((A(J,I),I=1,11),J=1,N)
1 CONTINUE -
IF (N.LE.1) RETUR
BAVE = 0.0
COMPUTE B*BS AND STORE THEM IN THE LOHER RIGHT OF A
DO 5 I=1,N
II=I+1
IF (II .GT. N) GO TO 5
DO 4 J=II,N
TEHP = A(I,J)
BB=TENP*TEHP
A(J,I) = 88
4 BAVE = BAVE * BB
5 CONTINUE
FN = N
BAVE=BAVE*(Z.O*FN/(FN-1.0))
FN=FN*FN
INVER=0
NH=N-1

162

IF (A(2,1).LT.A(N,NM)) INVER=1
C THIS ENTRY SHOULD BE USED ONLY IF THE CALLING PROGRAM IS NOT SATISFIED
C THE DIAGONALIZATION AND HISHES TO CYCLE THRU MORE ITERATIONS ON THE SA
C MATRIX.

ENTRY DIGMOR
CNOTE...
c+-+-+-+-+-+-+-++-+-+-+-+-+-+-++-+-+-+--+-+-+-+--+-+-+y-+--+-+-+-+-+-+—+
C BAVE SHOULD NOT BE ZERO UNLESS.THE MATRIX T 0 BE DIAGONALIZED HAS ITS
C ELEMENT IN THE UPPER LEFT OR LOWER RIGHT OFF THE THE DIAGONAL AND THE
C OF THE THE ELEMENTS COME IN DECREASING ORDERUP OR DOHN AWAY FROM THE T
C ONE
c+-+-+-+-+-+-+-++-+-+-+-+-+-+-++—+-+-+-—+-+-+-+--+-+-+--+--+-+-+-+-+-+-+

BAVE=0.0

ITN=O

IND=T
C AFTER EACH ITERATION THRU THE WHOLE MATRIX, RETURN HERE
C COMPUTE THE AVERAGE VALUE OF THE SQUARES OF THE OFF DIAGONAL ELEMENTS
C THIS LOOP IS SET UP FOR C1 AND C2 GREATER THAN ONE, IFTHEY ARE LESS TH
C PRECN SHOULD BE SET SMALLER BY THE SAME FACTOR

6 IF ((IND.EQ.D).AND.(BAVE.LT.PRECN)) GO TO 60
BAVE=BAVEIFH
IND = 0
M330
ITN = ITN’T
IF (ITN.GT.100) GO TO 50
1O LL=0
M = M+1
IF (M.GE.N) GO TO 6

00

C THE ROUTINE IS SET UP TO CHECK AND ROTATE MATRIX ELEMENTS SEQUENTIALLY
C PARALLEL TO THE DIAGONAL,HORKING DOWN AND TO THE RIGHT.
C CR HORKING UP AND TO THE LEFT WHEN INVER=1
12 LL=LL+1
L=LL
IF (INVER.EQ.1) L=N-L
K = L+M

IF (L.LE.0) GO TO 10
IF (L.GE.N) GO TO 10
IF (K.GT.N)GO TO 12
BAB = A(K,L)
C IF 8*83 IS LESS THAN THE AVERAGE 3*83 GO TO THE NEXT ELEMENT,OTHERHISE
IF (BAB.LT.BAVE) GO TO 12
IF (BAB.LT.PRECN) GO TO 12

C1 = A(L,L)
C2 3 A(K,K)
B = A(L,K)

CDF = (C1‘C2)/2.0
R=CDF*(1.0-DSQRT(1.0+BABI(CDF*CDF)))
IF(DABS(R).LT.PRECN) GO TO 12
ALFA = 1.0/DSORT(1.0 + R*R/BAB)
IF (ALFA.E0.1.0) GO TO 12
C IND IS A FLAG WHICH IS SET WHEN A ROTATION IS DONE
C IND ALSO CONTAINS THE NUMBER OF ROTATIONS DONE AFTER EACH TIME THRU TH
IND = IND+1
C A ROTATION HILL NON BE DONE UHICH HILL SET THE VALUE OF A(L,K) TO ZERO

nnnnn

:1 non on

nnnn

163

BETA = (R*ALFA)/B
DO 40 I = 1,N
ROTATE THE UNITARY TRANSFORMATION MATRIX
TEMP = ALFA*S(I,L) - S(I,K)*BETA
S(I,K) = BETA*S(I,L) + S(I,K)*ALFA
S(I,L) = TEMP
ROTATE THE HERMITIAN MATRIX
IF (I-L) 20,24,28
20 TEMP = ALFA*A(I,L) - A(I,K)*BETA
A(I,K) = TEMPZ = BETA*A(I,L) + A(I,K)*ALFA
A(I,L) = TEMP
COMPUTE B*BS AND STORE THEM IN THE LOHER RIGHT OF A
A(L,I) = TEMP*TEMP
A(K,I)=TEMP2*TEMP2
GO TO 40
24 A(L,L) = c1 - R
A(K,K) = c2 + R
NITHOUT ROUNDOFF ERRORS A(L,K) NOULD BE ZERO AS CALCULATED BY THE FULL
NE SHAL SET IT EQUAL TO ZERO
TEMP:(ALFA*ALFA-BETA*BETA)*B+ALFA*(C1-CZ)*BETA
A(L,K)=TEMP
A(K,L)=TEMP*CONJG(TEMP)
A(L,K)=A(K,L)=0.0
GO TO 40
28 IF (I-K) 30,40,34
so TEMP = ALFA*A(L,I) - BETA*A(I,K)

A(I,K) = TEMPZ = BETA*A(L,I) + ALFA*A(I,K)
A(L,I) = TEMP
A(I,L) = TEMP*TEMP
A(K,I) = TEMP2*TEMP2
GO TO 60
34 TEMP = ALFA*A(L,I) ' BETA*A(K,I)
A(K,I) = TEMPZ = A(L,I)*BETA + ALFA*A(K,I)
A(L,I) = TEMP
ACI,L) = TEMP*TEMP
A(I,K) = TEMP2*TEMP2
40 CONTINUE
GO TO 12

THE ROTATION IS COMPLETED ,GET THE NEXT ELEMENT

60 CONTINUE
THE DIAGONALIZATION HAS COMPLETED TO THE DESIRED ACCURACY.
THE FOLLOHING SORTS THE EIGENVALUES INTO DESCENDING ORDER
THE EIGENVECTORS ARE ALSO SHITCHED TO CORRESPOND TO THEIR EIGENVALUE
IF (IPRT.EQ.O) GO TO 110

50 CONTINUE

THE DIAGONALIZATION HAS NOT COMPLETED SATISFACTORILY AFTER 100 ITERATI
THRU THE COMPLETE MATRIX. THE CALLING PROGRAM MAY RETURN ENTERING AT
TO COMPLETE THE DIAGCNALIZATION.

PRINT 201,((A(J,I),I=1,11),J=1,N)
PRINT 202,((S(J,I),I=1,11),J=1,N)
PRINT 203,1TN

203
110
120
130
141
149

150

155

160
1140
200

201
202

164

FORMAT (///* ITN = *I8)

M=N

N=M/2

IF (H) 130,140,130

K=N-M

J=1

I=J

L=I+M

a=A(I,I) s B1=A(L,L)

IF (8-81)1SO,160,160

TEMP=A(I,I)

A(I,I)=A(L,L) s A(L,L)=TEMP

DO 155 LL=1,N

TEMP=S(LL,I) s S(LL,I)=S(LL,L)

S(LL,L)=TEMP

I=I-H

IF <I-1) 160,149,149

J=J+1

IF (J-K) 141,141,120

CONTINUE

RETURN

FORMAT (*OA BEFORE DIAGONALIZATION*I( 1X,11E12.S))
FORMAT (*OA AFTER DIAGCNALIZATION*I( 1x,11E12.5))
FORMAT (*os AFTER DIAGONALIZATION*I( 1X,11E12.5))
END

FOR

’1'

nonnnnnnnnnnnnnn

40

IFPAV > 3

165

SUBRCUTINE FORMPI1(IFPAV,NMAX,JEO,PAR,P,NP,CAPP,IJDEL)
COMMON/BLKEV/A(13,13),S(13,13),JIN(4,S1),INDEX,NVAR(24,2),IBN

COMMON NAP,NAI,IAN,AP(408,4)

DIMENSION P(19,4,NMAX),PAR(19),AVEP(19),NP(3)

*ttttttttiti‘ktiiiti’fiiitii'kt'kt*******

THIS ROUTINE SORTS THE EIGENVALUES AND DETERMINES THE QUANTUM NUM

EACH STATE. THE DIAGONAL ENERGIES FROM A ARE STORED IN AP AT
LOCATION (JIN(J+KN+1'KP9,IJDEL)'

THE AVERAGE VALUES ARE CALCULATED BY USING THE TRANSFORMA
MATIX AND APPLYING IT TO THE UNDIAGONALIZED OPERATOR VALU

OPTIONS ARE
IFPAV =0,1 THE DIAGONAL AND AVERAGE ENERGIES ARE PRINTED ONLY IF
EXPECTATION VALUE OF THE ENERGY IS DIFFERENT FROM THE

ENERGY BY MORE THAN E-9.

IFPAV=2,>4 THE DIAGONAL AND AVERAGE ENERGIES ARE PRINTED
THE NORMALIZED EXPECTATION VALUES OF EACH OPERATOR IS

*********************************A*

EXPECT=1.0E-9
RT2=1.414213562

NT =0

MT=0

J=NP(1)

NL=NP(3)

IF (NL.GT.0) GO TO 10

IF ((J.NE.0).OR.(JEO.NE.1)) RETURN
IND=JIN<IJDEL,1)

IF (IND.EQ.0) RETURN
INDEX=INDEX+1

IF (IFPAV .EQ.'1) RETURN
DO 40 I=1,IAN

NAI=NAI+1
AP(NAI,IJDEL)=0.0
JIN(IJDEL,1)=NAI

RETURN

C INITIALIZE QUANTUM NUMBER IDENTIFICATION

10
C FOR
21
22
23
26
C FOR

28
121

CONTINUE

IF (CAPP.LT.O) GO TO 28

GO TO(21,22,23,24) JED

3-R NOTATION USE,OBLATE
K2=-2 s K1=J+2

GO TO 30

K2=O S K1=J+1

GO TO 30

K2=-1 s K1=J+2

GO TO 30

K2=-1 S K1=J+1

GO TO 30

1-R NOTATION USE ,PROLATE
GO TO (121,122,123,124) JED
K1=(J/2)*2+2 S K2=((J+1)l2)*2-J-2
GO TO 30

TH
DI

PRI

C
C

C

166

122 K1=(J/2)*2+2 S K2=((J-1)/2)*2-J+1
GO TO 30

123 K1=<<J+1)I2)*2+1 s K2=(JlZ)*2-J-1
GO T0 30

124 K1=((J+1)/2)*2+1 s K2=(J/2)*2-J

3o CONTINUE
KP=K2 S KN=K1
DO 65 NN=1,NL

DERIVE THE OUATUN NUMBERS FOR THE STATE
KP=KP+Z S KN=KN-2
IND=J+KN+1-KP
ITAR=JIN<IJDEL,IND)
IF (ITAR.EQ.0) GO TO 65
INOEx=INOEx+1
IF (IFPAV.EQ.-1) RETURN
NAI=NAI +IAN ' -
IF (NAI.GT.NAP) GO TO 242
JIN(IJDEL,IND)=NAI
DO SO NZ=1,19

So AVER(NZ)=O.0

FORM THE EXPECTATION VALUES OF THE P OPERATORS IN H SPACE

THE AVERAGE 0F R(N,N)=SUH OVER I,J 0F S*(I,N)*P(I,L)*S(L,N)
VSOSUN=o.o
DD 60 I=1,NL
SINN=S<I,NN)
OO 59 L=I,NL
Ho=L-I+1
IF (MD.GT.4) GO TO 60
VSQ=SINN*S(L,NN)

FORM THE SQUARE OF THE DIAGDNAL ELEMENTS
IF (Ho.En,1) VSOSUM=VSOSUH+VSR
IF (MD.NE.1) VSQ=VSQ*2.0
H=L
IF (JEO.EO.2) M=M+1
IF <(JEO.ER.1).ANO.(ND.EO.H).ANO.(MD.ST.1)) VSO=RT2*VSQ
DO 32 LI=1,19
AVEP(LI)=AVEP(LI)+VSQ*P(LI,MD,M)
IF (M.GT.4) GO TO 32

THE FOLLOHING TRANSFORMS THE MATRIX ELEHENTS BY THE HANG TRANSFORM
GO TO (94,98,102,104) JED

94 EO=1

96 IF((MD.E0.1).AND.(M.EG.2))AVEP(LI)=AVEP(LI)+ED*VSQ*P(LI,3,2)
IF((MD.EG.2).AND. (M.EQ.3))AVEP(LI)=AVEP(LI)+ED*VSQ*P(LI,4,3)
GO TO 32

98 EO=-1
GO TO 96

102 ED=-1

106 HDL=H0+1
IF((MD.LT.4).AND.(M.EG.MD))AVEP(LI)=AVEP(LI)+ED*VSQ*P(LI,HDL,M)
IF((HD.EO.1).AND.(M.EQ.2))AVEP(LI)=AVEP(LI)+E0*VSG*P(LI,6,Z)
GO TO 32

104 60:1
60 T0 106

32 CONTINUE

167

S9 CONTINUE
6o CONTINUE
C CHECK FOR INCORRECT EXPECTATION VALUES
AVEE =0.
DO 62 LI=1,19
AVEE=AVEE+PAR(LI)*AVEP(LI)
62 CONTINUE
AA=A(NN,NN)
DIFF=(ABS(AA-AVEE))IAA
IF ((IFPAV.Eo.2>.OR.(IFPAV.GE.4)) GO TO 48
IF (DIFF.LE.EXPECT) GO TO 64
48 VSOSUM=VSQSUM-1
IF <NT.Eo.o) PRINT 226,EXPECT
NT=NT+1
PRINT 227,J,JED,NN,KN,KP,AA,AVEE,DIFF, vsosun
6A CONTINUE
DO 70 MI=1,19
NAPI= NAI-NVAR(MI,IBN)
AP(NAPI,IJDEL)=AVEP(MI)
7o CONTINUE
AP(NAI,IJDEL)=AA
IF (IFPAV.LT.3) GO TO 65
IF (MT.EQ.O) PRINT 222
HT=MT+1
DD 58 LI=1,19
58 AVEP(LI)=AVEP(LI)/AA
PRINT 220,J,KN,KP,JED,(AVEP(LI),LI=1,19)
GO TO 65
242 PRINT zao,INDEx,INo
6s CONTINUE
RETURN
220 FORMAT (1x,313,14,2x,15Ea.1/(1x,1068.1))

222 FORMAT (*0 J KN KP JEO*6X*X/E Y/E Z/E T1/E T2/E
1T3/E TAIE TSIE T6/E H1/E H2/E H3/E HAIE HS
2/E H61E*)

226 FORMAT (1* J JED NN KN KP DIAGDNAL ENERGY AVERAGE ENERGY DI
TFF/ENERGY *2X,12HU*U DIAG ' 1* DIFF GREATER THAN *

2E10.3)
227 FORMAT (1X,5I3,2X,E16.9,2X,E16.9,3X,E1D.3,3X,E10.3)
240 FORMAT (/*INDEX OVERFLON, INDEX =*I7* IND = *I?)
END

168

SUBROUTINE DN(IND,J,KN,KP,JEO,CAPPL)
c THIS SUBROUTINE OECOOES THE QUANTUM NUMBERS AND HANG BLOCK OF LEVELS
C IF JED=0 FIND ONLY QUANTUM NUMBERS
RJ=IND-1
J=SORT<RJ)
KPART=INO-J**2-J-1
J1=J+1
DO 10 I=1,J1
KN=1-1
KP=J-KN
IF(KN-KP.E¢.KPART) GO TO 20
KP=KP+1
IF<KN-KP.E0.KPART) GO TO 20
10 CONTINUE
20 IF(JED.EQ.O) RETURN
C DETERMINE CLASSIFICATION E+, E-, O-, 0+ OF THE LEVEL
JED=A
IF(CAPPL.CE.0) GO TO 40
C 1-R REPRESENTATION
IF(HOD(J,2).NE.0) GO TO 30
C EVEN J
IF((MOD(KN,2).EQ.0).AND.(MDD(KP,Z).EG.0)) JEO=1
IF((MOD<KN,2).Eo.0).AND.<MOD(KP,2).NE.o)) JED=2
IF((MOD(KN,2).NE.O).AND.(MOD(KP,2).NE.O)) JEO=3
RETURN
C 000 J
30 IF((MOD(KN,2).E0.0).AND.(MOD<KP,2).NE.0)) JEO=1
IF((MOD(KN,2).EQ.O).AND.(MOD(KP,2).EQ.O)) JEO=2
IF((MOD(KN,2).NE.0).AND.(MOD(KP,Z).EQ.O)) JEO=3
RETURN
c 3-R REPRESENTATION
40 IF<MOD(J,Z).NE.O) GO TD 50
c EVEN J
IF((MDD(KN,2).EG.0).AND.(MDD(KP,2).EG.0)) JEO=1
IF((MOD(KN,2).NE.0).AND.(MOD(KP,2).E0.0)) JEO=2
IF((MDD(KN,2).EQ.0).AND.(MDD(KP,2).NE.O)) JEO=3
RETURN
c 000 J
50 IF((MOD(KN,2).NE.O).AND.(MOD(KP,2).EQ.0)) JEO=1
IF((MOD(KN,Z).ER.0).AND.(MOD(KP,2).E0.0)) JEO=2
IF((MOD(KN,2).NE.O).AND.(MOD(KP,2).NE.O)) JEO=3
RETURN
END

nonnnn

169

SUBROUTINE LSTR(J,JL,JTYPE,CAPPL,CJM)
COMMON NAP,NAI,IAN,AP(ADB,A),
15E<26,26,A),FREDITDoo),IaN(1000),
2$TREN(1000),C(S1,3)
THIS SUBROUTINE FORMS SYMMETRIC TOP DIRECTION COSINE MATRIX ELEMENTS
BETHEEN STATES JU,KU, AND JL,KL AND STORES THEM IN C. THE MATRIX
ELEMENTS ARE THE SAME FOR 3-R A- AND 1-R B-TYPE BANDS.
3-R A- AND B- AND 1-R B-TYPE BANDS USE DIRECTION COSINES PHI z,x OR Y.
1-R A-TYPE BANDS USE PHI 2,2.
C(I,L) MEANS L=1 DELTA K=-1, L=2 DELTA K=o, L=3 DELTA K=+1
DO 5 1:1,153
S C(I)=O
JJ1=2*J+1
IF(<CAPPL.GE.O).OR.(JTYPE.EO.1HB)> GO TO 40
1-R A-TYPE MATRIX ELEMENTS
IF<J-JL)1o,zo,30 -

JL=JU+1
10 DD 15 I=1,JJ1
K=I-1-J
15 C(I,2)=2*SQRT(FLOAT((J+K+1)*(J*K+1)))
GO T0 57
JL=JU
20 DO 25 I=1,JJ1
K=I-1-J
ZS C(I,2)=2*K
60 TD 67
JL=Ju-1
30 DO 35 I=1,JJ1
K=I-1'J
3S C(I,2)=-2*SQRT(FLOAT(J**2-K**2))
GO TO 77
1-R B-TYPE AND 3-R A- AND B‘TYPE MATRIX ELEMENTS
40 EO=1.0
IF((CAPPL.LE.D).OR.(JTYPE.EQ.1HA)) EO=-1.0
IF(J-JL) 50,60,70
JL=JU+1
50 DO 55 I=1,JJ1
K=I-1-J
C(I,1)=EO*SDRT(FLOAT((J-K+1)*(J-K+2)))
55 C(I,3)=-SORT(FLOAT((J+K+1)*(J+K+2)))
57 CJM=1IFLOAT(12*(J*1))
RETURN
JL=JU
60 DO 65 I=1,JJ1
K=I-1'J
C(I,1)=EO*SGRT(FLOAT((J+K)*(J-K+1)))
65 C(I,3)=SGRT(FLOAT((J-K)*(J+K+1)))
67 CJM=(2*J+1)/FLDAT(12*J*(J+1))
RETURN
JL=Ju-1
70 DO 75 I=1,JJ1
K=I-1’J

C(I,1)=-EO*SGRT(FLOAT((J+K)*(J+K-1)))
75 C(I,3)=SQRT(FLOAT((J-K)*(J-K-1)))

170

77 CJ.‘1=‘T/ FLOAT (12*J)
RETURN
END

171

SUBROUTINE NANGCOS (JEOU,JEOL,JU,JL)
COMMON/9LKEV/A(T3,13)
COMMON NAP,NAI,IAN,AP(408,4),
1SE<26,26,A),FREO(1C00),ION(1000),
23TREN(TOOO),C(31,3)
C THIS SUBROUTINE HANG TRANSFORMS THE DIRECTION COSINE MATRIX ELEEENTS
c OETNEEN HANS BLOCKS JEUU AND JEOL
CAMUzGANL=1
PT2=1ISQRT(2.0)
IF((JEOU.EO.3).SP.(JEOU.EO.3)) GAHU=-1
IF((JEOL.EG.Z)SOR.(JEOL.EQ.3)) GAML=~1
KUST=1
I?<(JEOU.EO.3).OR.(JEOU.EO.4)) KUST=2
IF(JEOU.EG.2) KU3T=3
KU£H9=JU+1
KLST=1
IF((JEDL.EG.3).OR.(JEOL.EQ.A)) KLST=2
IF(JEDL.EO.2) KLST=3
KLEND=JL+1
DD 20 IaKUST,KUEND,2
KU=I-1
M=(I+1)/2
IF(KU$T.EG.3) H=M-1
DELU=RT2
IF(KU.ER.0) OELU=.S
C FORM ANO STORE THE HANG TRANSFORHEO DIRECTION COSINES IN A(H,N)
DO 10 L=KL5T,KLEND,2
N=(L+1)l2
1f(KLST.EG.3) N=N~1
A<M,N)=o
FL=L~1
DELL=RT2
IF(KL.E0.0) DELL=.S
IF(KU.EG.KL-1) A(H,N)=A(H,N)+C(KUEND-KU,T)+GAMU*GAML*C(KUEND+KU,3)
IF(KU.EQ.KL ) A(M,N)=A(M,N)+c(KUEND-KU,2)+GAMU*GAML*C(KUEND+KU,2)
IF(KU.EQ.KL+1) A(M,N)=A(M,N)+C(KUEND°KU,3)+GAMJ*GAML*C(KUEND+KU,1)
IF(KU.EQ.-KL-1)A(M,N)=A(H,N)+GANL*C(KUEHD-KU,1)+GAMU*C(KUEND+KU,3)
IFCKU.EO.-KL )A(M,N)=A(M,N)+GAML*C(KUEND-KU,2)+GAHU*C(KUENDPKU,2)
IF((U.EQ.-KL+1)A(M,N)=A(M,N)+GAML*C(KUEND-KU,3)+5AMU*C(KUEHD+KU,1)
To A<M,N)=DELL*DELU*A(M,N)
20 CONTINUE
RETURN
END

172

SUBROUTINE HANGDIM(J,JEO,N,IROV,ICOL,CAPP,KT)
C THIS SUBROUTINE CALCULATES HANG BLOCK SIZE N, POSITION HHICH
C EIGENVECTORS HILL BE STORED IN SE MATRIX IRON AND ICOL, AND TAU OF
C HIGHEST ENERGY LEVEL IN HANG BLOCK
GO TO (2,4,6,8) JED
2 N=le+1
IROH=ICOL=D
KT=J
IF((MOD(J,2).NE.O).AND.(CAPP.LT.0)) KT=J-2
RETURN
lo N=Jl2
IROH=D s ICOL=13
KT=J-3
IF<(MOD<J,2).EB.0).AND.(CAPP.LT.D>) KT=J-1
RETURN
6 N=<J+1>IZ
IROH=13 s ICOL=o
KT=J-1
IF<CAPP.GT.D) RETURN
KT=J-2
IF<MOD(J,2).NE.0) KT=J
RETURN
8 N=<J+1>Iz
IRCN=ICOL=13
KT=J-2
IF(CAPP.GT.0) RETURN
KT=J-3
IF<MOD(J,2).NE.D) KT=J~1
RETURN
END

THIS
IOUT

1
2

NORM

105

110

SORT
200

275
278
280
100

1

630

173

SUBROUTINE OUT(IOUT,MVAR,NISO,RESO,ISTOP,TOPFRE,BOTFRE,NKSTREN)
SUBROUTINE HANDLES OUTPUT

= 1 PRINT INTENSITIES ARRANGED BY QUANTUM NUMBER

PRINT INTENSITIES IN ORDER OF INPUT

PLOT SPECTRUM USING DELTA FUNCTION LINE SHAPE NITH ADDED
INTENSITIES FOR OVERLAPPING LINES
PRINT INTENSITIES IN ORDER OF FREQUENCY
PUNCH DECK OF LINES OF INTENSITY GREATER THAN HKsTREN
COMMON NAP,NAI,IAN,AP(408,4),
SE(26,26,A),FREG(1000),IGN(1000),
STREN<1000),C(51,3),ABSN,IBAND

COMMON lBLKP/KNT(1000)

DIMENSION ISTOP(6)

ALIZE INTENSITIES TO A MAXIMUM OF 10

SNORM=0

DO 105 I=1,HVAR

IF(STREN(I).GT.SNORM) SNORM=STREN(I)
CONTINUE

SNORM=10ISNORM

DO 110 I=1,MVAR
STREN(I)=SNDRM*STREN(I)

IF(IOUT.EQ.O) IOUT=2

IF(RESO.EG.O) RESO=.03

GO TO (100,200,300,300,300,300) IOUT

DATA INTO ORDER OF INPUT

DO 280 M=2,MVAR
Mv=M-1
DO 275 I=1,MV
MI=M-I
MII=MI+1
LISMI=MOD<IGN(MI),10000)
LISMII=MOO(IGNCMII),10000)
IF(LISMI.LT.LISMII) GO TO 278
ITEMP=IGN<MII) SIQN(MII)=IGN(MI) S IQN(MI)=ITEMP
TFRE=FREG<MII> S TSTR=STREN(MII)
FREG<MII)=FREO(MI) S STREN<NII)=STREN(MI)
FREQ<MI)=TFRE S STREN(MI)=TSTR
CONTINUE

CONTINUE
CONTINUE
CONTINUE

O‘UI bWN

PRINT INTENSITIES

DO 620 I=1,MVAR,NI$O

CALL INDOUT(ION(I),INDU,INDL,LIST)
CALL :N(IVDU,JU,KNU,KPU,0,CAPPL)
CALL ON(INDL,JL,KNL,KPL,0,CAPPL)
DO 620 L=1,NISO

M=I~1+L .
IF(MOD(M-1,80).EG.D>PRINT 625

625 FORMAT (*1 JU KN KP JL KN KP ISOTOPE*12X*FREQUENCY*

7X*INTENSITY*AX*LINE*/)

620 PRINT 630,JU,KNU,KPU,JL,KNL,KPL,ISTOP(L),FREO(M),STREN(M),M

FDRMAT(2(6X3I3),6XI3.SX2F16.3,4XIA)

PLOT STRONG LINES IN SPECTRUM HITH DELTA FUNCTION LINE SHAPE

174

RETURN
C SORT DATA INTC ORDER OF INCREASING FREQUENCY
:00 DO 380 M=2,MVAR
MV=M~1
DO 375 I=1,MV
RI=N-I
WII=RI+1
TF(FREG MI).LT.FPEO(“II)) GO TO 373
ITENF= GNiNIL) S'ION(MII)=IOM(HI) S ICN(NI)=ITENP
TFRE=FREO<MII> S TSTR=STREN€NII)
FREQ<HIIJ=FREQ(RI) S SIREN<MII)= TREN(NI)
FREQ<MIA=TFRE S STREN(HI)=ISTR
375 CONTINUE
T75 CONTINUE
1&0 CONTINUE
IFLICUT.LT.5) GO TO 600
K=0
C PRINT BY FREQUENCY
DO 330 I=1,NVAR
1F(STREN(I).LT.NKSTREN) GO TO 333
'{:K+’g
CALL INDOUT(IQN(I),IHDU,INOL,LIST)
CALL ON(IVEU,JU,KNU,KFU,O,CAPPL)
CALL GN(INOL,JL,KNL,KPL,0,CAPPL)
JISO=HOO<LIST,HISO)
IF<JISO.:0.0) JISO=NISO
{F(MOD(K-1,EO).EG.0) PRINT 625
IF(ICUT.EU.S PUNCH 3AO,JU,ENU,KPU,JL,KNL,KPL,FREQ(I),STFEN(I),
{STOP(JTSD),13AND
340 FORMAT(2XS(IZ,1X),I2,F1S.3,TSD,F5.1,T65,I$,AS)
325 PRINT 630,J!J,.\.‘UJ,KFU,JL,KNL,KPL,ISTOP(JISO),FREQ(I),STREN(I),I
330 CONTINUE
RETURN
(000 :GNTINUE
C PLOT THE SPECTRUN
PRINT 603,RESO,ABSN
403 FORMAT(*OTHE SPECTRUM IS PLOTTED FOR A DELTA FUNCTION LINE SHAPE*
1/1OX*RESGLUTIOH = *F10.3/10X*ABSCRPTICN = +£10.3) .
IF((TOPFRE.NE.1ES).AND.(BOTFRE.HE.0)) PRINT 402,80TFRE,TOPFRE
402 FORNAT(*OCNLY LINES HITH FREQUENCIES BETVEEN-F10.3* AND*F10.3
1* ARE PLOTTEO*)
IF‘(EOTFRE.NE.O).AND.(TOPFRE.EO.1ES)) PRINT 406,80TFRE
A06 FORMAT<POONLY LINES WITH FREQUENCIES GREATER THEN*F10.3
1k ARE PLOTTEDi)
IF((BOTFRE.EQ.O).AND.(TOPFRE.NE.1ES)) PPINT 407,TOPFRE
407 FORMAT(*OONLY LINES NITH FREQUENCIES LESS THAN*F10.3
1* ARE PLOTTED*)
PRINT 404
404 FORNAT<1H1)
PRINT 405
405 FORMAT(*O JU KN KP JL KN KP FREQUENCY INTENS ISO 0*44X*S*43X
1910*II)
N=O
SPACE=.5*RESO

...)

175

HSPACE=.S*SPACE
MV=O
ENFRE=FREQ(NVAR)+3*RESO+HSPACE
IF(IOUT.EQ.4) GO TO 655
SET END OF PLOT ON LAST STRONG LINE
ENFRE =0
00 650 I=1,MVAR
MV=MVAR+1-I
IF(STREN(HV).GE.UKSTREN) GO TO 655
650 CONTINUE
655 IF(MV.NE.O) ENFRE=FREQ<MV)+3*RESO+HSPACE
IF(TOPFRE.NE.1ES) ENFRE=TOPFRE+HSPACE
SFRE=FREQ(1)‘3*RESO
IF(BOTFRE.NE.O) SFRE=BOTFRE
NLINE=O
PFRE=SFRE~HSPACE
RFRE=SFRE+HSPACE
IFRE=O
BRITE=O
CHECK FOR LINES UITH TOO LOU FREQUENCY TO BE PLOTTED
NLO=NHK=NHI=O
470 N=N+1
IF(N.LE.HVAR) GO TO 473
471 PRINT 472
472 FORMAT(/I/l* THERE ARE NO LINES IN THE SELECTED FREQUENCY RANGE*
1/l* JU KN KP JL KN KP FREQUENCY INTENSITY’I)
GO TO 459
473 IFIFREQ(N).GE.BOTFRE) GO TO 474
KNT(N)=NLO=NLINE=NHK=N
GO TO 470
474 IFCN.GT.MVAR) GO TO 471
RFRE=FREQ(N)-3*RESO
IFCIOUT.EQ.4) GO TO 500
IF(STREN(N).GE.HKSTREN) GO TO 413
NLINE=NHK=NLINE+1
KNT(NLINE)=N
N=N+1
GO TO 474
DO NOT START PLOT UNTIL SUFFICIENTLY STRONG LINE IS FOUND
PLOT DELTA FUNCTION LINE SHAPE
410 N=N+1
411 IF (N.GT.HVAR) GO TO 437
IF(FREQ(N).GT.ENFRE) GO TO 437
IF(STREN(N).GE.UKSTREN) GO TO 413
IF LINE T0 HEAK TO PLOT, SAVE IT FOR PRINTOUT
NLINE=NUK=NLINE+1
KNT(NLINE)=N
GO TO 410
413 IF(FREQ(N).GT.RFRE) GO TO 436
PLOT LINE AT PROPER POSITION ALONG FREQUENCY AXIS
BRITE=9*ABSN*STREN(N)
430 CONTINUE
IF(BRITE.GT.90) BRITE=9O
IBRITE=BRITE*1

176

PLOT LINE
CALL INDOUT(IGN(N),INDU,INDL,LIST)
JISO=MODCLIST,NISO)
IF(JISO.EQ.O) JISO=NISO
CALL QN(INDU,JU,KNU,KPU,O,CAPPL)
CALL 3N(INDL,JL,KNL,KPL,O,CAPPL)
PRINT 440,JU,KNU,KPU,JL,KNL,KPL,FREQ(N),STREN(N),ISTDP(JISO),
1IBRITE
440 FORMAT(1X313,3X3I3,F10.3,F8.3,I3,1X=(1H*),T136,1Hl)
GET NEXT LINE
IFRE=O
GO TO 445
PLOT BLANK
536 IFRE=1
437 PRINT 43S _
43S FORMAT(44X1H*,T136,1HI)
INCREASE FREQUENCY AXIS
44$ RFRE=RFRE+SPACE
BRITE=O
IF<IFRE.NE.O) GO TO 411
IF(RFRE.LE.ENFRE) GO TO 410
PRINT 405
GO TO 459
PLOT DELTA FUNCTION LINE SHAPE HITH ADDED INTENSITIES FOR OVERLAPPING
LINES
Soo CONTINUE
IFRE=O
515 IF<FRED(N).LE.RFRE) GO TO 520
RFRE=RFRE+SPACE
PRINT BLANK LINE
PRINT 435
IF(RFRE.LE.ENFRE) GO T0 515
PRINT 405
GO TO 459
520 NC=NCS=N
BRITE=STREN(N)
521 NC=NC+1
MORE THAN ONE LINE IN PLOTTING INTERVAL
IF(NC.GT.MVAR) GO T0 550
IF(FREQ(NC).GT.RFRE) GO TO 550
NLINE=NLINE+1
IFRE=1
IF<NC.NE.NCS+1) GO To 525
SAVE FIRST OF SEVERAL LINES IN INTERVAL
KNTINLINE)=N
NLINE=NLINE+1
SAVE OTHER LINES IN INTERVAL
525 KNT(NLINE)=NC
BRITE=8RITE+STREN<NC)
IF(STREN(NC).LE.STREN(N)) GO T0 521
SAVE STRONGEST LINE FOR PLQTTING
N=NC
GO TO 521
550 CONTINUE

177

C PLOT LINE

nn

BRITE=9*ABSN*BRITE
IF(BRITE.GT.90) BRITE=90
IBRITE=BRITE+1
CALL INDOUT(IQN(N),INDU,INDL,LIST)
JISO=N80<LIST,NISO)
IFIJISD.EQ.0) JISO=NISO
CALL QN(INDU,JU,KNU,KPU,0,CAPPL)
CALL QN(INDL,JL,KNL,KPL,0,CAPPL)
IF(IFRE.EQ.0) PRINT 440,JU,KNU,KPU,JL,KNL,KPL,FREQ(N),STREN(N),
TISTOP(JI$0),IBRITE
IF(IFRE.EQ.1) PRINT 441,JU,KNU,KPU,JL,KNL,KPL,EREQ(N),STREN(N),
1ISTOP(JISO),IBRITE
441 FORMAT<1x3I3,3x3I3,F10.3,F8.3,13,1x=(1H=),T136,1HI)
RFRE=RFRE+SPACE
N=NC
IF((N.LE.HVAR).AND.(RFRE.LE.ENFRE)) GO TO 500
PRINT 405
LIST LINES NOT PLOTTED
Lou FREQUENCY LINES
459 IF(NLO.EQ.O) GO To 450
IF(NLO.LT.MVAR) PRINT 451,80TFRE
451 FORMAT(////* THE FOLLONING LINES HAVE FREQUENCY LESS THAN*F10.3
1* AND ARE NOT PLQTTED*/)
CALL PRIVTO(KRT,IST0P,NTSO,1,NLO)
450 IF<NLD .EQ.NNK) GO TO 452
NL=NLO+1
PRINT 4S3,BQTFRE,TOPFRE,HKSTREN
453 FORMAT(IIII* THE FOLLONING LINES IN THE FREQUENCY RANGE*F10.3
1* T0* F10.3l* HAVE INTENSITY LEss THAN*F10.3
1* AND ARE NOT PLOTTED*/)
CALL PRIVTO(KNT,ISTOP,NISO,NL,NRK)
452 IF(ICUT.NE.4) GO TO A55
IF(NLINE.GT.MVAR) NLINE=MVAR
NLO=NLO+1
PRINT 456
456 FORMAT(////* THE FOLLORING LINES ARE T00 CLOSE TOGETHER TO BE*
1* RESOLVED*/)
CALL PRINTO(KNT,ISTQP,NISO,NLO,NLINE)
ASS IF(N.GT.HVAR) RETURN
NHI=NLI~E+1
DO 640 I=N,MVAR
NLINE=NLINE+1
640 KNT(NLINE)=I
PRINT 4S4,TOPFRE
454 FDRMAT(IIII* THE FOLLOUING LINES HAVE FREQUENCY GREATER THAN*
1F10.3* AND ARE NOT PLOTTED*/)
CALL PRINTO(KNT,ISTOP,NISO,NHI,NLINE)
RETURN
END

10

30

40

178

SUBROUTINE FRINTO(KNT,ISTUP,NISO,IFROM,ITO)
C THIS SUBROUTINE PRINTS LINES NOT PLOTTED BY SUBRCUTINE OUT
COMMON NAP,NAI,IAN,AP(408,4),SE(26,26,4),FREG(1000),ION(1000),

TSYREN(1000)

DIMENSION KHT(1000),I$TUP(6)

PRINT 10
FORMAT(* JU KN KP

DD 30 N=ITRDN,ITD
L=KNT<N>

1L KN KP ISCTGP

I'l

“12X

1*FREQUERCY*77*INTEHSITY‘NK*LINE*/)

CALL INDOUT(IGN(L),INDU,INDL,LIST)

JISO=HOD(LISF,NISD)
IFCJI$3.EQ.O) JI$O=NISO

CALL 0N<INDU,JU,KNU,KPU,0,CAPPL)

CALL 3N(INDL,JL,KNL,KFL,C,CAPPL)

PRINT 60,JU,KNU,KFU,JL,KNL,KPL,ISTCP(JISO),FREJ(L),STREN(L),LIST
F3RMAT(Z(DXTIE),6XI3,SX2F16.3,4X14)

RETURN
END

T79

SUBROUTINE INDOUT(IQN,INDU,INDL,LIST)
C THIS SUBROUTINE OECOOES INDU,INDL, AND LIST FROM ION
C IGN=100000000*INDU*10000*INDL+LIST

INDU=IGNITCOOOOOOO

IPART=IQN-INDU*TOOOOOOOO

INDL=IPARTI10000

LIST=IPART-INDL*1000O

RETURN

END

APPENDIX C

ASSIGNED TRANSITIONS OF 2v OF HDSe

T

UPPER

t...
x
I
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180

OBSERVED
(CM-1)

4474.553
4467.335
4467.950
4482.186
4482.186
4488.767
4488.767
4495.436
4496.071
4496.383
4498.605
4505.496
4509.396
4509.396
4510.019
4510.019
4512.358
4512.682
4515.492
4516.099
4516.727
4517.374
4519.132
4519.132
4519.748
4525.816
4525.816
4526.437
4526.746
4532.891
4535.290
4535.910
4535.910
4536.546
4536.546
4536.872
4536.872
4537.220
4537.220
4537.382
4538.015
4538.314
4538.931
4539.537
4540.759
4540.962
4541.395
4542.154
4542.403
4543.043

OBS'CALC
(CM-1)

-0.013
-0001 5
'0.019
0.002
-00008
-0.013
0.010
0.015
-00013
-0.022
0.001
‘0.004
0.006
-0.015
0.004
0.005
'0.002
0.016
0.009
0.000
“0.038
0.011
-0.012
“0.019
0.020
0.014
-0 .002
0.006
0.014
0.007
'0.002
“0.001
-0 .009
-00002
0.006
0.003
-0000?
0.013
0.002
’0.006
0.005
0.002
-0.00Z
'0.010
'0.002
‘0.007

WEIGHT

0.00
0.40
0.00
0.01
0.01
0.00
0.00
0.40
0.00
0.01
0.00
0.10
0.01
0.01
0.01
0.01
0.01
0.10
0.40
0.00
0.00
0.01
0.10
0.10
0.00
0.00
0.00
0.00
0.00
0.10
0.01
0.04
0.04
0.0‘
0.04
0.01
0.04
0.01
0.01
0.50
0.04
0.04
0.10
0.00
0.20
0.20
1.00
0.40
0.40
0.04

157

78
80
78
80
80
80
8O
80
78
80
80
80
80
80
78
78
80
80
80
80
50
78
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80
78
80
80
78
80
80
82
80
80
78
78
77
77
76
76
80
78
80
80
78
80
90
78
80
80

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d ....) ...L A... -—i

ét‘dOOOOUTOOROOVV—P
OW-bl‘.‘NNN¥‘O-DO¥‘-.ObNtNNN-‘OdumdmmNNLI-IMLNUTT‘JNLN‘u-‘Olflw-‘d-HDON—ON—I

.3

u-b

.h «A...
'4!!meNV‘INNOOOKNO‘O‘WWObb‘JVV-‘UJWUTUTOAONNNNNVWObOOU‘W

U10 anuououowyoooooomenLnquwmmoo-UNP

5‘0-me‘JONOML‘TMO‘U‘IMO‘LdO"C‘J‘OO(PNLD

181

OBSERVED
(CM‘1)

4545.321
4545.321
4545.953
4546.276
4551.638
4551.638
4551.929
4552.268
4554.525
4555.181
4557.882
4557.882
4558.055
4558.855
4562.211
4563.191
4563.834
4567.019
4567.242
4567.659
4567.889
4568.259
4568.911
4569.687
4570.330
4570.711
4572.760
4573.183
4575.971
4576.153
4576.622
4577.485
4577.834
4579.603
4581.015
4581.267
4581.545
4581.702
4581.935
4582.166
4582.365
4582.825
4584.817
4585.661
4586.327
4586.327
4586.492
4587.197
4587.477
4587.638

OBS-CALC
(CM'1)

0.015
0.000
“0.025
0.002
0.005
-0.002
-0.017
-0.019
0.003
0.012
‘0.010
“0.006
0.001
0.005
'0.002
0.018
0.003
'0.002
“0.003
-0000}
0.001
0.002
0.009
“0.001
0.001
0.001
0.004
-00012
0.001
0.002
‘0.011
0.005
‘0.003
'0.005
0.000
0.004
“0.005
0.012
0.002
0.007
0.000
“0.004
-0.002

HEIGHT

0.00
0.04
0.00
0.01
0.10
0.10
0.10
0.01
0.00
0.10
0.00
0.00
0.10
0.00
0.10
1.00
0.10
0.10
0.40
1.00
0.20
0.20
1.00
0.04
0.04
0.00
0.00
0.10
0.40
1.00
0.20
0.10
0.01
0.10
0.10
0.10
0.10
0.01
0.50
0.40
0.40
0.10
0.40
0.40
0.01
0.01
0.20
0.04
0.20
0.04

ISC

80
80
78
77
80
80
20
78
80
78
80
80
80
77
30
80
78

80
80
78
78
80
78
80
78
78
80
80
80
80
78
78
77
80
80
80
82
50
78
80
78
78
30
80
80
7.

80
80
80
RE

\-

UPPER

(...
7‘
I
7‘
...

TuNu).....ALNUl"(ul““f‘)\fl\fl\fll>J‘NI‘JO‘O‘NUIONVWBJUITVU‘ICDF’J‘WLNLHVWKNKNkflk-‘mwmo«1%va

(DOQU-J—booaa-fiuida—‘doO-‘J—‘NN8‘I‘JPJNO[\DOON").JJJJ'JOONONJNT‘JWO-fi-Ad

r‘JNl’UmfiQWKHWNWW-‘I-"bb?NNUT“UTNPMWNIANUTOKNl-‘WLNLA’OWMNUWO‘P‘bWO‘AS‘4‘

NNNNNUJUJ-bwbbNUTUTVIJ‘t‘WNOON00 NwTMLnummt-bbbtth‘WS-kmmmooommm

dd-‘OOd-‘NNNNNNNN-fi-fioNNMMMWWW—‘Lfl-l-JQNWKIOOONddUJ-IwNumb—bmoo

dAdNNNNNdNNOWWHMMlfl-‘FMbMWJ‘NMNWl‘UT-‘mbb4‘UTb<P-‘8‘N-OMUJ¥‘WOUTUT

182

OBSERVED
(CM-1)

4588.268
4588.926
4589.229
4589.423
4589.788
4590.019
4590.665
4590.951
4591.672
4592.329
4592.613
4592.991
4593.308
4593.665
4593.954
4594.594
4595.246
4595.456
4595.771
4595.924
4596.261
4597.149
4597.511
4597.803
4598.186
4598.340
4598.670
4598.850
4599.004
4599.339
4599.507
4601.291
4601.291
4602.454
4603.133
4603.482
4604.148
4604.487
4605.284
4605.501
4606.168
4606.571
4606.878
4607.379
4608.035
4608.338
4608.988
4610.061
4610.691
4611.362

OBs-CALC
(CM-1)

0.001
0.003
-00012
'0.006
0.004
-0 .01 S
-0 .012
-0.001
0.001
0.003
0.003
‘0.022
0.004
-0 .010
0.002
0.015
0.002
-0.00Z
0.000
-0 .002
-00009
0.003
0.006
0.003
-0 .007
0.006
‘0.004
‘0.008
0.008
0.002
0.002
‘0.005
0.001
0.001
0.012
“0.009
-0.019
0 .003
-0 .012
0.00?
0.000
0.003

HEIGHT

0.20
0.20
0.20
0.01
0.00
0.10
0.00
0.00
0.20
2.00
0.04
0.40
0.04
0.40
0.10
1.00
0.20
0.10
0.04
0.20
0.10
0.20
0.20
0.10
0.20
0.20
0.10
0.00
0.01
0.00
1.00
0.01
0.01
1.00
0.04
2.00
0.20
0.04
1.00
0.10
0.10
0.01
0.01
0.01
0.00
0.20
0.00
0.01
1.00
0.40

ISO

78
80
80
80
80
78
80
80
80
80
78
77
80
82
30
78
80
80
80
80
80
80

78
80
80
80
78
78
80
80
80
80
78
80
78
77
80
'80
78
78
76
80
78
8O
78
82
80

Q
U

ID

(...

.3
O'xl‘xltr111anUTO~L’).S‘NU'INUI-AbKDObO‘O‘bO‘OOO‘JOVTOD'NlUTUTUIr‘bbIU'ANNFUi‘JIU—L-i-J-h~54

uh

UPPER

7V
1

7S
+

Nhbbbb-LQNFUTO4‘AbdwN4‘6‘W“8‘04“bidtflwNétJNNNNNNN-nfiodad-badooCO

U‘II“bl..dfi?~b-t'bNUT-DINFWLNO‘LNJ‘O—‘O‘Wwa‘m‘RMh)4‘LNPUJWWNhiN-v‘PJN-R'J-‘QORD-«fi-J-‘wb

LOHER

c.
7"
I
K
+

....s
O\\J"~JO‘WUIOUTOOLJNM‘JN-Jt‘CUOJ‘O‘OPO‘0LX309VTO~$"‘\IUTU1UT6“#‘bWUJdNNNN-Q'v’d—i-‘wb

"-5
O‘UIU'T6‘LMNKHU'TLNOUmebN~meVNVO~NNO()O'ALNUTbUTJ‘S‘S‘U-ILNWNUl-JNNNN-‘JOOOO

dwiflkJ-IWL-JT‘J—‘Wfi-DWOUObAWWR1WWNWWNT‘JNdON—l—‘d-I-I—‘dO-EOOCOCO-044‘

183

OBSERVED
(CM-1)

4612.526
4613.188
4613.543
4613.883
4622.758
4623.440
4623.756
4624.394
4625.070
4625.765
4626.756
4627.271
4627.485
4627.704
4628.368
4629.079
4629.214
4629.888
4630.224
4630.694
4631.452
4632.198
4632.479
4632.890
4633.572
4633.981
4633.981
4634.193
4634.661
4634.661
4634.868
4635.003
4635.363
4636.881
4637.068
4637.551
4637.551
4637.976
4638.222
4639.324
4639.504
4639.729
4640.231
4640.586
4641.333
4642.385
4642.385
4642.770
4643.419
4644.070

OBS'CALC
(CM-1)

0.000
0.002
-0 .012
“0.003
0.008
0.001
-00003
0.000
-0.009
0.000
0.001
“0.003
0.005
-0.004
0.003
0.005
0.004
”0.010
-00011
-00033
-0.004
-0.004
-0.00L
-0.001
0.006
0.003
‘0.003
0.014
0.006
0.001
-00001
0.018
0.018
'0.005
0.004
‘0.011
0.004
0.004
-0.00S
0.001
‘0.008
-00006
0.010
0.002
'0.034
“0.003

HEIGHT

0.50
0.00
0.01
0.01
0.10
0.10
0.00
1.00
0.40
0.04
0.10
0.40
0.40
0.50
0.10
0.04
1.00
0.10
0.10
0.01
0.00
0.10
0.40
0.20
0.40
0.04
0.04
0.00
0.01
0.01
0.00
0.04
1.00
0.04
0.00
0.01
0.01
0.00
0.00
1.00
0.01
0.00
0.10
0.00
0.00
0.01
0.01
0.40
0.00
0.10

ISO

80
78
77
76
80
78
82
80
78
76
80
80
80
80
78
76
80
78
77

9‘)
0..

80
80
80
80
78
80
80
80
78

Q
U

78

,
80
8O
80
so
80
76
78
80
80
80
80
80
so
80
80
73
80

ID

UPPER

c.
7'5
I
7"
...

A

(3‘3“ 6‘ombmt‘mb.$\00$~VVO‘OU-I'\IINL~ILIJ‘OU~I\IUINV‘NIUIOLAIOS‘ WODO‘OO"O-3LNLN'\J\D‘ONKDI‘J

1:13‘$‘R1rdtflNWI‘Juw-‘WNRJNT‘IW—SWHMRDWOI‘JA-‘ONWNLNI‘JT‘JN-0..¢_AOWOANNU'IObNOIU
Pi)A®~JJNdVfldVNOOMMOOC30dM-‘VPVV‘J-lmdemeT)O‘O‘NO‘NNLNU‘GOUTO

LOHER
K- K+

‘-

a.)

.a
L’T‘,.~1£NOC‘\JUI\AM‘~IL~JMVMO~0‘UTUTTVOANNN‘ON06‘000‘IVONowmommmm‘odNNN4‘O-‘b-fi

I")(MIN-3d“:dN-‘NNNN—h—td—bNNNNNdN-fi-fioOJdN-‘N-fi—IJNOO‘NU‘l-b-‘fi-‘UJ-‘d-‘I-
l.\I-OC)‘\IO‘NO~NO~NNO-—¥WUT¥‘b-AUI-‘w‘oOOOWOOONON‘ONm0©\flmmm\l~‘—‘S‘P\I-‘¥“

184

OBSERVED
(CM-1)

4644.261
4644.706
4644.946
4645.252
4645.382
4647.273
4647.612
4648.306
4648.457
4649.502
4649.649
4650.171
4650.853
4651.067
4651.946
4652.455
4652.624
4653.211
4653.444
4653.896
4654.132
4654.331
4654.539
4655.215
4655.493
4655.742
4656.052
4656.724
4656.724
4657.071
4657.764
4658.004
4658.478
4658.626
4659.312
4661.661
4662.347
4662.557
4662.682
4663.730
4664.391
4664.932
4665.088
4665.624
4665.797
4665.985
4668.489
4670.610
4671.002
4671.344

CBS’CALC
(CM-1)

-00006
0.007
-00001
‘00003
-00004
-00015
“0.016
-0000“
-00015
0.017
0.000
'0.005
-00012
0.008
‘0.024
0.003
0.017
0.003
0.003
'0.006
0.005
0.009
-0.003
‘0.020
-00011
0.002
-00012
“0.008
0.007
-0.008
0.001
’0.007
0.000
0.002
0.000
0.000
’0.005
-00011
-0.00Z
-0.007
-0000}
0.005
0.005
0.002
'0.005
0.004
“0.004
0.005
-00016
0.000

HEIGHT

0.00
0.40
0.50
0.10
0.10
0.10
0.00
0.10
0.00
0.00
0.50
0.10
0.00
0.04
0.00
0.20
0.01
0.00
0.10
0.00
0.10
0.25
0.25
0.00
0.20
0.20
0.01
0.01
0.01
0.10
1.00
0.00
0.10
0.10
0.10
0.10
0.10
0.01
0.00
0.01
0.20
0.10
0.10
0.01
0.01
0.50
0.40
0.01
0.01
0.40

ISO

30
30
78
80
78
78
80
78
80
30
80
80
78
80
80
80
78
80
80
78
78
80
80
78
80
76
82
80
80
80
78
78
76

Q
(..-

78
80
78
80
80
82
80
80
78
78
76
77
80
77

50

ID

«S

000017-3-‘VNIV

UPPER

K-

owynuo~orvc~rl>nracpc-b-atn»1>:~bwnLnUTbLnunuc:—-0LNDI:u>J>wa;~mhac>nuNL~uwawu-a~ho

K+

at...
”6.4

...—i... c—I—J-A

J...

..l-hut
O—Ab-OOIVL’JLH”M‘AUTDNJ‘IUC‘RIWLA'Od-‘UI'¢OOO'JJUIU~I\I\I°*N—b..s0:aONNmUYNN‘OF‘vO

LOWER

J K- K+

10 1 10
10 0 10
9 2 8

5 2 3

9 2 8

4 2 3

4 2 3

6 2 4

9 3 7

11 1 11
11 0 11
10 1 9
4 3 2

10 4 7
4 3 2

4 3 2

4 3 1

4 3 2

8 2 6

8 2 6

12 1 12
12 0 12
12 1 12
9 2 7

4 4 1

4 4 0

5 3 2

4 4 0

4 4 0

4 4 1

5 3 2

5 3 2

5 3 3

13 0 13
5 3 3

13 0 13
5 3 3

6 3 3

14 1 14
13 2 12
13 1 12
6 3 3

6 3 4

6 3 4

13 3 11
5 5 1

S 5 0

5 1 5

5 5 0

5 5 1

185

OBSERVED
(CM-1)

4671.553
4671.553
4671.785
4672.035
4672.478
4672.784
4673.472
4674.270
4674.471
4675.585
4675.585
4676.101
4676.282
4676.976
4676.976
4677.318
4677.318
4677.682
4678.412
4679.109
4679.520
4680.218
4680.396
4681.339
4681.339
4681.830
4682.027
4682.386
4682.386
4682.530
4682.873
4683.260
4683.357
4683.951
4684.063
4684.687
4686.892
4687.097
4687.371
4687.371
4687.587
4690.965
4691.672
4691.785
4692.150
4692.150
4692.411
4692.839
4692.839

CBS-CALC
(CM-1)

0.005
0.001
-00004
0.001
-0 .015
-0000?
-0000?
-0.009
0.001
-00001
0.004
0.001
'0 .013
0.004
-0 .012
-0.016
“0.013
0.002
0.003
0.000
'0.001
'0.022
-0.003
0.003
-00001
0.000
0.002
-00004
0.004
-0.011
0.004
0.000
‘0.019
0.007
’0.004
0.003
0.010
-0.00Z
'0.005
'0.004
0.001
0.003
0.004
‘0.005
-0.001
'0.002

HEIGHT

0.05
0.05
0.40
0.20
0.00
0.20
0.40
0.20
0.10
0.40
0.40
0.00
0.10
0.01
0.01
0.00
0.00
0.00
0.20
0.10
1.00
1.00
0.00
0.20
0.10
0.10
1.00
0.40
0.04
0.04
1.00
0.01
0.10
0.10
0.01
0.00
0.01
1.00
0.50
0.00
0.00
0.01
0.00
0.01
0.00
1.00
1.00
0.00
1.00
1.00

ISO

80
80
80
78
78
80
78
80
80
80
80
80
80
80
78
77
76
76
80
78
80
80
78
80
80
80
80
78
77
77
78
77
80
80
78
78
76
80
80
8

80
78
30
78
80
80
80
80
78
78

ID

ummmmmflflflflfldflflwflfluoo

OOVVVVVVVVVVODMCFU‘OOO00WVVVV‘.HUIVVVV\1VU1\AUI\A(‘OOO‘O‘Ol‘VIMMWU'IU‘OO

.“\)W C 4

Cor-JN-v-bUVm—‘O JOJLVLNILN‘F“fihJéf‘II‘J—INLNFJR’LN

i-gl‘JIQIDulwu-l bObaOLq-‘O

nil-J

.a\)'

osacmuJmammyxcnamw~q~Jm-u~qawv-q\rV-v~qmcmo~ow>o~oc>\rv-uxrflc>o~oc>o~o<>o~o<>o~oxn01

VOOUOOO‘O000~VVMVNUIVVO~O~OO~D50000003‘bbbumMMUMU-bbk559mm

“ital"Jthl‘NPJKMI’VMRJOAWOfl-‘bo-‘T‘J—JJI‘J-P‘l‘O—‘O—IOJ5‘PWWK'1-bNd4NNNULNNUIN—bo

186

OBSERVED
(CM-1)

4693.201
4693.201
4694.048
4694.317
4694.747
4695.010
4695.384
4695.462
4696.132
4698.508
4698.508
4699.199
4699.559
4699.559
4700.025
4700.025
4700.734
4701.012
4701.705
4702.002
4702.002
4702.699
4702.699
4703.070
4703.070
4705.348
4708.252
4708.252
4708.950
4708.950
4710.907
4710.907
4711.180
(0711.604
4711.604
4711.716
4712.336
4712.336
4713.799
4713.799
4714.471
4714.471
4715.175
4715.175
4715.528
4715.528
4715.914
4715.914
4717.028

08$‘CALC
(CM-1)

0.002
0.002
0.001
-00001
0.001
“0.007
0.006
‘00014
0.003
0.002
0.009
0.001
“0.006
0.001
-00008
0.002
0.009
0.010
‘0.001
“0.001
'0.001
-00001
0.010
0.010
'0.006
“0.006
-00002
“0.001
‘0.005
“0.005
0.006
0.006
“0.007
0.004
0.0010
0.004
0.006
0.006
0.006
0.001
0.004
0.002
‘0.003
-0.009
-0.015
0.005
-0.001
‘0.005

HEIGHT

0.20
0.20
1.00
0.10
0.00
0.00
0.00
0.01
0.00
0.01
0.01
0.10
0.01
0.01
0.01
0.01
1.00
0.01
0.10
1.00
1.00
1.00
1.00
0.10
0.10
0.10
0.10
0.20
0.20
0.10
0.10
0.10
0.10
0.04
0.10
0.10
0.10
0.01
0.01
0.01
0.01
0.20
0.20
0.10
0.10
0.01
0.01
0.02
0.02
0.40

150

77
77
80
80
78
78
77
76
80
80
80
78
77
77
80
80
78
80
78
30
80
78
78
77
77
80
78
80
80
78
78
80
80
8O
78
78
78
76
74

5‘1

22
82
80
80
78
78
77
77
76
76
80

ID

UPPER
J K- K+
9 8 1
9 9 0
9 9 1
9 9 0
9 9 1
9 9 O
9 9 0
11 6 6
10 8 2
10 8 2
10 9 1
10 9 1
10 10 O
10 1O 1
10 10 1
10 10 O
11 7 5
11 7 5

11 O

11 0

LOHER
J K- K+
8 7 2
8 8 1
8 8 0
8 8 1
8 8 0
8 8 1
8 8 1
10 5 5
9 ‘7 3
9 7 3
9 8 2
9 8 2
9 9 1
9 9 O
9 9 0
9 9 1
10 6 4
10 6 4
1O 10 1
1O 10 1

187

OBSERVED
(CM-1)

4717.730
4718.833
4718.833
4719.536
4719.536
4719.901
4720.273
4722.548
4723.133
4723.835
4724.839
4725.542
4725.795
4725.795
4726.494
4726.494
4726.745
4727.447
4731.782
4732.486

OBS'CALC
(CM-1)

-0.001
”0.001
0.001
0.001
0.003
0.005
0.003
-0.003
0.005
0.003
-00001
“0.001
‘0.005
-00005
0.007
'0.005
0.002
0.002

HEIGHT

0.04
0.04
0.04
0.10
0.10
0.01
0.01
0.00
0.40
0.20
1.00
0.10
0.40
0.40
0.20
0.20
0.00
0.01
0.20
0.10

ISO

78
80
80
78

77
76
80
80
78
80
78
80
80
78
78
80
78
80
78

IO

APPENDIX D

ASSIGNED TRANSITIONS OF 202, v AND 03 OF H S

1 2

UPPER
J K- K+
14 14
13 13
13 12
12 12
12 11
12 1O
12 10
12
7
7
11 1
11
11

4...)

“A
«Juan-41s“) c~4-1 \INOOOOpouobUIUOOI.mO'II‘OO'OknOJ-“OOCBOOVKP-

b (7.

(4150-3.(NJN'NJ‘bL‘U'IL-JN—‘A'4MbPkflUIf‘erdtdo«“WNLHNOO-‘LHWKNN-‘O‘VbNWN-‘JO—h

...wVVNo‘mug)...pwp-qwmoN-Amwbxl—stoo-0NCouo~ooaoNN00~OOdO©

LOWER

(...

7\
I

7<
...

— a.)
$‘U1

..qu-oh—A-fi-b
COCfiWWUJUJLNP

A
\nwmmuoom-qmmoomcxmooo01.110‘0‘000m

boa-ac:bmwbmmwbb—amomewbtwo-4bammubawwooobwmqoomwN-nom—so

J-J—DJHJ-)JHJ
dO-bdNLNWbm

c-h—I

DJDOOINUJVO‘b—OOU‘bUIOOm‘CV—ANCFOMOOO‘OVOAOPJVO-"DC4461-5004“)

188

OBSERVED
(CM-1)

2192.478
2204.404
2212.446
2216.121
2222.652
2227.115
2227.115
2229.744
2230.158
2230.300
2232.670
2235.777
2237.130
2237.196
2238.767
2238.939
2240.634
2241.008
2242.502
2242.811
2243.794
2244.254
2248.071
2250.027
2251.198
2252.137
2252.517
2252.517
2255.332
2257.764
2258.120
2258.549
2259.548
2260.588
2260.894
2261.569
2261.569
2263.641
2263.876
2265.047
2265.621
2267.342
2268.057
2268.384
2270.788
2271.031
2271.539
2271.539
2272.865
2275.160

CBS'CALC
(CM-1)

0.018
0.015
0.009
0.008
0.010
-0000?
'0.006
0.004
-0 .003
0.006
-0.001
0.007
-00001
-0000}
0.006
0.008
0.010
0.006
0.006
-0.009
0.006
0.015
0 .006
-0.006
0.005
0.004
0.000
0.002
’0.004
0.001
0.005
0.009
-00003
0.003
0.005
0.005
0.003
-00001
0.004
0.006
0.006
0.002
0.003
0.003
0.004
0.001
3.001
0.000
0.006

HEIGHT

0.10
1.20
0.10
0.50
0.10
0.10
0.01
0.04
0.10
0.01
0.50
0.25
0.00
0.00
0.01

0.50
0.10
0.05
1.50
0.25
0.01

0.01

0.01

2.50
0.01
2.50
0.25
0.25
0.00
0.01

0.30
0.50
0.05
0.75
1.50
0.25
2.50
0.30
0.01

0.01

1.50
0.30
0.06
0.10
1.25
1.50
0.05
1.50
1.50
0.40

ISC

32
32
32
32
32
32
32
32
32
32
32
32
32

32
32
32
32

73
JL-

32
32
2

7

3.

32
32
32
32
32
32
7?

a-
'2?

db

32
32
32
32
32
32
32
32
32
32

‘)
1..

b

32
32
32
32
32
32

.u.’.

ID

020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
023
020

L.

F~)#“»J‘O<D'\)$‘OmmF—fiCOLNWVF‘Jb“ *lUOle-éynLN'fltho1‘23‘1\J$‘k4”1\l1u1bf‘UMWHdU‘O‘00“}00‘

UPPER
K- K+

OLNN ;C.A_¢nJ-§bN.¢OOI‘JFJQCQJNNO—DONlrlo§-aNN—bf\lb~‘hloN-‘N-JMbUPJMIOfUU‘LN‘N

Nwaomwbwmw-hoowbombboamw—«ban-JmbCOL-«mamawbbwmumowmo-mmbb

LOWER

G...
7‘
I
7"
+

.uphqun-..l\)&‘0Ofimbfuflwm‘JUJb&\ruL~O‘bl‘nlkflbb&‘-\nOU\U1u5UI$‘O~O~OwwOObOVN‘Q‘JNV
awaaNNwomwoa-amacarumawamaammowamuNwA—amwwmwbwo~44er
g-aawr..AruuumJhnuu~qnnfl~qUHNULAhubnbcabtunnwxnbeJ~OLNnJO\nunfl-hk\N—a¢~V~JOLNUNm

189

OBSERVED
(CH-1)

2275.821
2276.224
2276.614
2279.799
2281.957
2281.957
2282.464
2283.132
2283.429
2284.205
2285.582
2287.702
2288.524
2288.607
2292.151
2292.789
2293.533
2295.040
2296.874
2297.327
2300.374
2302.115
2304.374
2306.291
2306.436
2309.883
2311.317
2311.801
2317.007
2317.375
2319.302
2320.042
2320.308
2321.527
2424.310
2325.805
2330.924
2431.164
2331.669
2333.575
2333.884
2434.172
2334.816
2336.798
2337.788
2338.871
2439.084
2339.236
2341.210
2341.429

OBS-CALC
(CM-1)

0.005
0.004
-00001
0.002
‘0.002
-0.003
0.001
0.002
'0.001
0.003
-00004
0.001
0.000
'0.001
-0 .001
0.001
0.000
‘0.001
0.002
0.002
-0.011
-0.002
0.001
-00002
0.000
0.004
“0.003
0.005
‘0.001
0.001
0.000
“0.003
“0.002
‘0.005
‘0.001
-0.002
'0.002
0.000
0.001
0.001
”0.007
'0.003
“0.004
'0.006
0.000
“0.005
‘0.004

HEIGHT

0.30
1.50
0.10
0.10
0.25
2.50
0.50
0.05
0.01
0.06
0.01
0.25
0.10
0.01
1.25
1.25
1.25
1.25
1.25
1.25
1.25
0.10
1.25
0.01
0.25
0.01
0.05
0.01
0.01
0.25
1.25
0.25
0.01
0.01
0.25
0.05
0.05
0.25
0.25
0.05
0.01
0.05
0.01
0.25
0.01
0.01
0.25
0.01
0.01
0.25

ID

020
020
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
023
020
020
023
020

’ 020

020
020
020
020
020
023

.020

020
020
023
020
020
020
020
020
020
020
023
023
020
020
023
020
023
020
023

C...

1. n 0 U1 3‘ b 4.4 m .. 0 00 u; U1 0‘

~1UIbL/‘IJ-“Ime01'bOb-L‘vJLAU‘l bHJU‘aLNblqr-JO‘PJbWVUJ-aOhJNAVOOV

V

UPPER

7‘
I
K
...

LII—85".».thr-JAMWS‘NUb-éCDUINRIF“PUIJNOMNN—l—IJNJWNO‘WUJ“NtflN-‘Om‘n-DN“

[JIJIN4‘NIJJ-5LNO ANOCN-itQWNNN-vNOQI‘JMNdfi-‘Q‘O-JOOl-Jé—éfUL.~I—.N-¢-§-B-¢I‘I6"NLNW

LDHER

‘—
K
I
7"
...

VF‘JU'ILNU'it‘-O<I-‘U10‘0‘VOJ‘bFVI‘JLn-PL'JVIWJ‘Lfl-‘m—luF'NUJOCNNQNWNmowfi‘t‘LJI‘JQOmwmo

bl‘J—DQLN—O-JObbUIUJNUIOANA-J-UJOWI‘UOUl-JN-S-‘ONOQOGOOV3‘J‘MW3‘WN-AO‘O‘NUJM

UJ-b-I-‘UJUJFO6‘ANWNLNNNPJLNLNUINLN-‘N-ON-JY‘QNNOCGI‘J-i-‘dOO—iNO-‘OOCO-JL'I-ubNN

190

OBSERVED
(cm-1)

2342.857
2343.866
2345.423
2346.730
2347.270
2348.641
2349.072
2349.365
2349.449
2349.449
2351.292
2353.057
2353.739
2358.255
2358.577
2360.775
2364.812
2369.423
2469.607
2369.683
2371.700
2374.132
2375.923
2377.481
2378.392
2379.206
2380.236
2380.793
2381.366
2382.689
2383.112
2383.954
2387.051
2387.680
2388.021
2388.326
2388.456
2490.424
2391.430
2392.382
2392.574
2392.964
2393.055
2393.364
2395.550
2397.021
2397.393
2397.630
2397.993

UBS'CALC
(CM-1)

-0.004
0.000
0.000

“0.005
0.000
0.002
0.002

“0.009
0.004

-0.002

-00001
0.001
0.002

'0.009
0.001

‘0.001

'0.002
0.001
0.000

‘0.004
0.001

“0.003

’0.002

-00002

“0.018

-0.001
0.001
0.000

‘0.002
0.001
0.001
0.000

’0.003

‘0.004
0.000

'0.002

-0000“
0.002
0.000
0.000

'0.003

-0.015
0.001
0.001

'0.002

HEIGHT

0.01
0.40
0.25
0.01
0.05
1.25
0.01
0.10
0.01
0.01
0.10
0.05
0.01
0.00
0.25
0.04
1.25
0.05
0.25
0.01
0.25
1.25
1.25
0.01
0.25
0.01
1.25
0.25
0.05
1.25
1.25
1.25
1.25
1.25
1.25
1.25
0.05
0.05
0.25
0.25
0.25
1.25
0.00
0.05
1.25
1.25
0.01
1.25
1.25
1.25

ISO

ID

020
020
023
020
020
020
023
020
020
020
023
023
020
020
023
020
023
020
023
020
020
020
023
020
020
020
020
020
020
020
023
023
020
020
023
020
020
020
020
023
020
020
023
023
020
023
020
020
020
020

{A \IflmmmVVO(X§l-3N¢‘VNO()~‘43‘033‘006mUIO-VO‘WUJO'"JL'I‘JI

WL'I‘OWUICOOWI‘U‘JW1NOlNOOV

mun)NNMN-ILNbuanxluaAwOV8~NaNNVNNI-‘NmoAmmmmamoxoot‘omamL-Jrvmm

-51“ c.“p.30ugoorumm—bbmboQV-AbbwaxJ-tehbmbh—.>O'flwwwul4\-+Nmbl~RIwaOW-l

LOWER

FI;U1‘\]UJ(£@N©CUCO\JI\JO‘\JO33‘$ VN‘JJL‘OI‘ON1N‘J‘JU'10"QL‘iC‘DKNO‘O‘ml-‘CANO‘U‘NOQVIUI L.
K
I
7"
4.

F'Cm1‘~

a

Vt-\fl-‘UI-bo-bOI‘UuN-‘bO‘bON-J'ON‘N—iN—DOOO-NLNLAII‘JU‘IO-‘b-‘bNI‘Jmm-JWU‘IbCcard-9N“

NJwOONVP\I-‘O‘ONU'IIAUIV-‘O'Nwwwo~“(NH'OUI-AWUIUIO‘#NbNWNthhJWW—ibAl‘N

191

OBSERVED
(CH-1)

2398.261
2398.861
2400.864
2401.806
2403.437
2403.785
2404.478
2405.005
2405.596
2405.917
2407.452
2409.761
2410.095
2410.744
2410.913
2412.486
2413.773
2414.199
2414.583
2415.225
2416.040
2416.758
2417.202
2418.259
2419.991
2420.168
2420.365
2421.328
2421.710
2422.062
2422.226
2422.569
2422.999
2423.631
2424.310
2425.306
2427.644
2427.967
2428.457
2429.002
2429.305
2429.506
2431.164
2431.924
2432.503
2433.644
2434.172
2434.536
2434.733

OBs-CALC
(CM-1)

0.007
0.005
0.001
0.000
0.001
0.002
'0.006
'0.005
“0.003
-00002
0.006
'0.010
'0.001
0.000
'0.004
0.000
'0.001
“0.005
-0.002
'0.002
0.005
'0 .017
0.000
0.000
0.036
-00002
0.000
0.002
0.000
‘0.006
0.002
“0.001
0.001
0.000
'0.002
0.011
0.000
0.000
’0.005
'0.002
-0.002
'0.007
0.003
0.002
0.001
0.020
0.000

HEIGHT

0.25
0.25
0.25
0.25
0.25
0.01
0.25
1.25
1.25
0.05
0.01

.25
0.25
1.25
0.10
0.25
0.25
0.05
1.25
0.05
1.25
0.01
0.25
1.25
0.01
0.05
0.25
0.04
1.25
1.25
0.01
0.01
1.25
0.10
0.50
1.25
0.01
0.05
1.25
0.01
0.05
0.25
1.25
0.04
1.25
0.25
0.05
0.01
0.05
0.01

ID

020
020
020
023
020
020
020
020
020
020
020
023
020
020
020
023
020
020
020
023
020
020
020
023
020
020
020
023
023
020
020
020
020
020
020
020
020
020
020
020
020

’ 020

020
023
020
023
020
020
023
020

A

A

AC.

-.. .I

UPPER
J K- K+
9 8 1
9 4 s
9 s s
3 3 1
s 3 3
9 0 9
9 z. 6
7 1 6
9 3 7
9 2 7
9 1 s
z. z. 1
o 7 4
0 0 10
6 2 4
o 6 s
4 4 3
6 3 z.
4 3 1

s 6
8 2 7

3 a

011
6 3 3
o 9 2
1 a 4
s 4 2
7 2 s
7 3 s
9 1 3
- 112

110

3 9

2 9

z. a.

3 s
r. 3 2
6 4 3
4 4 1
3 o 13
7 s 2
a 3 6
o 2 9
2 211
7 3 4
s 4 1
s s 1
s 5 0
4 114
2 s 6

-.O

a.)

A

..5 7...

~54
Cl0‘04>~§OkflC>O'VCDUHflUHown!)OtflihO‘OO‘CWhC‘NHOV)O

...

a

-‘4

LOWER

L
K
I
K
+

‘flt‘bHA\nLdfiJC\OOK\HULN~3O£fl<3U1O‘OOOaHfl~anMf0050flv

“(3;>;~U‘§.a-§h;osAHAINCDPULM—bhlc>OIQIU4NLN‘JGJ#deU-¢$‘thJUHflLN-§O\UICH¢IU[VFU*’hJCL§IN‘J

11
11
1O
10
9
3
5
3
2 1
6
7
q
2 1
6
4
L
4
3 1

‘0LA-‘QIULHRJUWfl—AAHVTUUJO

192

OBSERVED
(CM-1)

2436.408
2436.923
2437.898
2438.610
2438.783
2439.084
2441.248
2441.679
2443.353
2443.353
2443.782
2444.903
2445.089
2446.758
2446.944
2447.201
2448.101
2448.356
2449.866
2450.668
2451.225
2453.939
2454.186
2455.620
2456.376
2456.955
2457.294
2458.530
2458.834
2460.534
2461.370
2462.281
2464.268
2464.268
2464.579
2465.448
2467.237
2468.305
2468.644
2469.517
2469.607
2471.183
2472.150
2472.458
2472.557
2474.253
2475.003
2475.582

OBS-CALC
(CM-1)

0.014
'0.004
0.012
'0.002
-00001
'0.001
0.002
'0.006
“0.001
0.002
0.064
0.003
-00002
0.038
0.001
0.002
-00002
0.008
-0 .006
0.009
0.002
0.020
‘0.017
-00003
'0.002
-0.003
0.001
0.018
0.002
'0.006
-00006
0.000
0.004
“0.004
-0 .003
0.000
0.025
-0.010
“0.010
0.000
O .011
-0.004
‘0.004
0.004
0.042
0.032

WEIGHT

0.01
0.01
0.05
0.01
0.25
1.25
0.10
0.25
0.25
0.25
1.25
1.25
0.01
0.25
0.25
0.05
1.25
0.05
0.10
0.05
1.25
0.25
1.25
0.01
0.01
0.25
1.25
1.25
1.25
0.05
1.25
0.40
0.01
0.25
0.00
0.01
0.25
1.25
0.25
0.25
0.25
0.04
0.10
0.10
0.25
0.20
0.10
1.29
1.25
0.00

ID

020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
023
020
020
020
023
020
020
020
020
020
020
020
020
020

’ 020

020
023

. 023

..x .o ...)...1.
\JI‘O-OSJNN

I1

\

....
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......L
1ON0004W

...-uh
VN(D\Jm-‘N‘OON‘JVOOOONO-V-JIJ-KJOONOOWCROéVO‘O ‘sJO‘~LN\flU|U

Obflt/JNUIPWOPVVOU1“U|UIO‘MPGWxflLNML‘OONb‘Nknm-‘MNC‘WNFM‘NWUON-it‘8‘04

.6

an.
f‘Jl‘r-C‘fi.JVLib-'OO-JLNO‘O [\Jb-‘COWPJWMO#NO#000WaNL4UNOO-OU1NU1-3NU1VO3"O‘O

cub

O 0~Vorwowcomaoaw~o~oomoouxomooawmmmooowOthbe—aflm

Q.

.4 ...—t
OO-NN

...» a
VW‘“¥‘00

LOWER
K- K+

W-‘O‘NOJ‘UJUIMLNO‘OV‘J‘mt‘OmeMNL‘BJPWMkflHW-bbbNO—h-‘N-OLNJNl‘NN-bUJNLdDIN

..5-L

Lqmwmaos‘wruoaaoNmmmeVb-avbbound-JoOommNN-hbbuNOb-aJ-‘NmboowOO

193

OBSERVED
(CM-1)

2475.793
2475.793
2476.220
2478.458
2480.074
2481.454
2481.977
2484.183
2485.623
2486.506
2486.725
2487.080
2490.424
2491.804
2493.431
2494.941
2495.476
2496.705
2497.005
2497.775
2498.036
2500.539
2500.978
2501.807
2503.557
2505.953
2510.444
2515.856
2516.462
2516.704
2520.514
2520.712
2522.880
2525.354
2525.865
2526.396
2527.278
2528.515
2530.066
2530.446
2531.765
2533.923
2537.597
2538.863
2539.285
2547.439
2549.914
2550.844
2551.141
2552.081

OBS-CALC
(CM-1)

0.015
0.014
.00005
0.008
0.002
0.058
0.001
“0.005
“0.007
-00002
0.014
'0.004
‘0.001
‘0.001
“0.007
0.016
“0.007
“0.007
'0.011
‘0.008
“0.006
0.000
0.007
0.000
'0.001
0.004
0.007
0.003
’0.004
'0.014
0.008
“0.002
‘0.001
0.001
0.012
0.014
0.008
0.001
0.001
0.008
3.006
0.022
0.018
0.000
“0.004
0.004
‘0.005
0.000

HEIGHT

0.00
0.10
0.10
0.40
1.25
0.01
1.25
0.01
0.05
1.25
1.25
1.00
0.05
0.01
0.25
0.06
0.25
0.25
0.05
0.05
0.25
0.25
1.25
0.25
0.05
1.25
0.25
0.01
0.01
1.25
0.01
1.25
0.25
0.05
0.25
0.01
0.05
1.25
1.25
1.25
0.10
0.05
0.01
0.25
0.01
0.25
0.25
1.25
0.00
0.05

ID

020
020
020
020
020
023
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
023

L.

-jWU10030~NU1§be 1‘1J'JI‘J\.Nkrl..JL,-5‘-Nb PUIMOO‘ \JVfin‘O‘C‘OfflmmCflCDOOJOCV

o~60604>3~wkn03r

A1'~J1‘~.!1:44‘4\wilf‘JNL‘loPJ-‘AJV-JMNQNNWO—DNI‘UO404700-3~OI\)O-*-¢O(hl‘~n1JJI‘Q-IO‘fiflmmfl’

00V! a)“C—OO‘UJO‘R"J¥‘I‘O*VI$‘NW?LQ-‘FJL'JNAJQNLNJ‘MVIJ‘O'NJUVOCX"UO\bO-WWKA4‘11NWOU1

O~NU1UJ¢44‘N-JLN4N-JUJJ‘V1U1CJ‘O"Q‘JOCOO‘UOOGW‘Q‘JV‘VV1'DVVO‘

LOWER

g
N
I
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0c 1.) w w w w o 43 on L4 0‘ 4* #2 1440‘

NLN-JNWWNUJ-éN-h—DNCJONde-i-‘N-‘O“DJ-#N-‘O-fi—JNQ-‘w-DNCdNfiC-‘NLNLNO‘b'VJ

\l1‘0VJ-‘OWTUV—AOLNLNWO‘MUIbL-JbOMN-‘NQO~0bmb‘0kflVO-WNOONWNOOb‘Lan-‘O-

194

OBSERVED
(CM‘1)

2555.737
2559.905
2561.076
2574.399
2576.391
2581.936
2582.254
2586.028
2597.946
2613.165
2248.071
2258.916
2268.791
2269.546
2277.781
2279.944
2286.501
2290.127
2295.271
2300.067
2309.739
2343.281
2346.547
2347.389
2369.561
2377.013
2385.506
2386.212
2390.798
2391.166
2394.832
2395.245
2395.736
2407.878
2411.944
2412.356
2419.479
2419.801
2420.763
2427.123
2430.241
2431.504
2439.400
2442.452
2445.723
2446.014
2448.934
2456.227
2458.230

OBS“CALC
(CM-1)

0.003
-0.020
0.005
0.031
‘0.008
0.007
'0.008
‘0.002
“0.003
0.001
'0.009
0.010
0.004
“0.002
0.004
-00009
-00003
-0.007
0.005
-0 .009
-0.005
-0.006
'0.008
0.005
“0.007
0.007
“0.003
-00001
0.005
“0.001
0.011
'0.004
0.005
0.005
0.013
‘0.003
-OIOOS
0.004
“0.003
0.001
‘0.004
0.017
0.006
“0.002
0.002
-0.002
0.302
‘0.002
'0.006
0.001

HEIGHT

0.10
0.01
0.01
0.05
0.01
1.25
0.10
0.25
0.25
0.05
0.01
0.00
0.05
0.01
0.10
0.01
0.01
0.01
0.10
0.01
0.25
0.01
0.01
0.10
0.00
0.01
0.05
0.05
0.01
0.01
0.02
0.01
0.05
0.01
0.01
0.25
0.01
0.10
0.01
0.25
0.00
0.01
0.01
0.05
0.25
0.01
0.04
0.10
0.10
0.02

180

32
32
27

J5

32
32
32
32
32
32
32
32
34
34
34
34

9
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34
34

,
J

34
34

7.
J

34
34
34

ID

020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
023
020
020
020
023
020
023
020
020
020
020
020

‘—

m7VC>OH7~OLG

UPPER
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195

OBSERVED
(CM-1)

2471.774
2477.729
2483.888
2498.356
2499.231
2527.764
2544.653

OBs-CALC
(CM-1)

0.000
0.001
‘0.002
0.009
0.000
0.013

wEIGHT

0.25
0.01
0.05
0.25
0.02
0.05
0.01

ISO

34
34
34
34
34
34
34

ID

020
020
020
020
020
020
020

14J-ALNK‘Q‘..HO~\I(7‘£‘0N1Uk.’1\1M-€‘O~l;lb‘00~00'-

[\IUNI1UC‘C) b1N1‘r-aknm03 :-b-A~J;\\J‘J01\)rubb-bm0~0~

UPPER
J K- K+

..Nrgzuowmbabmtsam—aobmunnao0......N1-1N—ao-aommbr4-4NNooN;~.4m;~..wau1

...)
.24Nh:CArum—IdLNtNNWdfifikdfdtdi‘Jh)b4‘C’ t‘fib-JJW-ikflkanIl‘O‘OdWVd-i’)oQONO-J

.... —b
I‘del‘dl‘abtdo NMWC‘bbNNJ$‘-\JO’JL~1(AJ>4‘FJV‘IO 0WN9LMUTO~\IUJUJOMUJOVJ‘MNéMG‘J-JN

LOVER
J K- K+

T‘)Ud-*U!-¢$‘UJMOUIW“¥‘N-‘UTLNO‘O‘O—8~3NNNWP-IN-’N-¢MWU10h.'LNU~l—$-5WL~|O“MOJ>OO~

A

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CJO«JJ-JO~19“thNDJJNNNNdf‘JWHLNkN-J'WWWNOJ‘N’t‘b#‘J‘WU‘I—‘OO‘ONN-J-‘OOL’I—DN

196

OBSERVED
(CM-1)

2476.516
2497.373
2508.068
2508.229
2509.660
2534.557
2540.007
2542.597
2546.255
2546.606
2550.338
2551.323
2556.626
2557.381
2560.551
2563.154
2565.872
2566.698
2568.063
2568.414
2570.603
2570.909
2573.671
2575.373
2578.036
2578.178
2578.344
2578.480
2578.739
2580.414
2580.710
2585.462
2586.249
2586.657
2588.869
2589.660
2590.046
2590.046
2590.341
2590.475
2591.143
2591.256
2592.543
2594.016
2597.629
2599.313
2599.641
2600.723
2602.831
2606.442

OBS’CALC
(CH-1)

0.004
“0.005
0.005
0.003
-0 .001
0.002
'0.002
0.011
-0000?
0.006
0.006
-00003
-0.004
“0.004
’0.009
’0.005
0.000
0.008
0.001
-00001
0.001
0.003
0.001
-0.013
0.008
‘0.002
0.007
0.002
-00002
0.004
0.000
0.003
0.001
0.002
0.007
0.005
‘0.001
'0.007
0.000
'0.001
0.000

HEIGHT

0.25
0.10
0.04
1.25
0.01
0.01
0.01
1.25
0.05
0.25
0.01
0.01
0.01
0.01
1.25
0.10
0.01
0.05
0.10
0.01
0.25
1.25
0.05
0.25
0.01
0.01
0.05
0.01
0.05
1.25
1.25
0.05
0.25
1.25
1.25
0.01
0.10
0.10
0.01
0.25
0.01
0.01
1.25
0.01
0.25
0.05
0.25
0.10
1.25
0.05

ID

100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
103
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100

8

0144'CDNNertNLNJ‘mm05001'xJOONt-IO~\lI‘RJUJO‘OI‘OkmOOuJUIhJ‘Jlu—JINO‘ONbflo‘ldoob-NN-Aa

UPPER

11..
7‘
I
K
+

14.41:»bwmmao-aumbmmooamowwoamoomobmwwwNm-aObo-akmmwowwN—‘o

beUIbb-i'S-‘LNLNLNLAUWI‘WI‘v'NIUIU-JOPJN‘NNd-I‘UOdw~bdNJO-l-¥N(N~.Ol\lv‘-§NdoOil—‘3

LOVER

G-
75
I
7‘
+

\IOO-JUJO‘NJ-‘dL/QO‘CFC)bCEUOUIU‘NVION00N4‘N0‘w003‘INN-3-4

....
owvtaxru—smruanxnuwo~oo

NNk'ILNN—i8‘CAOI‘J-ALN-PNUIUIO-‘L'IO‘N-‘Ob‘fl-‘MWJ‘O'NNé’OWUMOUbb-‘MNN-écd

LII-JO-UIU‘OU‘INN“4““9U!“UIb-‘WN-‘W-‘WWNW—DNhNk’UlU-JONUI‘PN-‘DJNNWI‘J-‘d-‘O

197

OBSERVED
(CM-1)

2608.582
2619.753
2620.820
2622.859
2624.086
2624.864
2625.168
2625.432
2625.666
2625.975
2626.794
2627.756
2627.911
2628.121
2629.268
2629.861
2630.427
2631.001
2631.524
2631.665
2632.099
2632.370
2633.876
2634.148
2635.285
2635.936
2636.662
2636.769
2637.292
2637.424
2637.767
2637.884
2638.387
2639.317
2639.432
2640.857
2641.721
2643.181
2643.993
2644.880
2646.203
2646.468
2646.799
2648.079
2649.352
2650.120
2650.729
2651.873
2652.937
2653.136

OBS‘CALC
(CM-1)

-0.003
0.000
0.003
0.001
0.000
0.006
0.005

'0.001

-0 .018
0.003
0.008

”0.002
0.001

'0.001
0.000

-0.00Z
0.006
0.005
0.003

'0.006

-0.001
0.002

‘0.004

-03011

“0.002

“0.003

“0.002

-0 .002

-00003

‘0.014
0.006
0.003

-0000}

-0.003

-0.001

’0.005

‘0.002

'0.014

“0.001

‘0.001
0.002
0.004

-0.009
0.008

'0.003

HEIGHT

1.25
1.25
1 .25
1.25
1.25
0.25
1.25
1.25
0.05
1.25
1.25
0.25
1.25
1.25
1.25
0.25
1.25
1.25
0.25
0.01
0.01
1.25
0.01
1.25
0.01
0.25
0.10
0.05
0.25
0.01
0.01
0.01
1.25
0.05
0.01
0.25
0.10
1.25
1.25
1.25
0.25
0.25
1.25
1.25
1.25
0.25
1.25
0.05

.25
1.25

ISO

ID

100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
1C3

UPPER

B
7‘
I
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+

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00.;~._.r_).o.-\Joo(‘ooomL-10~—6V\J(XIoomutbO‘OmC)OMVIOOVVJUJbOmeOOVdmmmmb‘o

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JL‘JJ‘NLQPJ—S-‘O(NNLNNPJLAJO-oéhJ—ONUUJPJWW“(NNvd-JOJNbWNIflNO-‘h’mwo.kaNN-os.§

()wOObvooowuzoow-Jsmccxl \JVNKNNNNVO"~1~J&\4~O~O~O~OM-¢N0~wmmmomommmobu‘.

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Ol‘J-301AL4U1VV‘O‘ONN3‘OO‘O-Ot-CCN-l-vJ-OOOOAOOOOWUJMVININODO—‘NDJfiO‘O‘NO‘NO‘O-fi-‘WO‘

03‘w—‘NINNO—Oiv—lN-fiu‘N-‘O‘OMFN—DNIULQNJNOdOJWNWNJ-JC-‘b-AMWNQ-‘OU’

-..
—-h

198

OBSERVED
(CM-1)

2654.962
2655.458
2656.871
2658.212
2658.464
2658.593
2658.811
2661.414
2662.776
2663.899
2663.899
2664.114
2665.566
2666.355
2666.952
2669.561
2669.992
2672.431
2672.431
2672.632
2672.632
2673.104
2673.421
2673.979
2673.979
2675.063
2677.574
2677.574
2678.354
2678.680
2680.246
2680.798
2680.798
2680.998
2680.998
2681.377
26 1.623
26 1.921
2684.810
2685.373
2685.373
2689.218
2689.218
2689.801
2690.157
2691.398
2692.985
2693.283
2694.669
2697.040

OBS-CALC
(CM-1)

0.006
-00015
0.002
0.001
0.007
0.001
0.000
0.010
0.001
-00005
0.001
0.002
-0 .003
0.006
0.003
0.011
0.005
'0.003
‘0.003
'0.003
0.004
'0.001
0.000
-0.003
“0.002
0.010
0.002
-0.004
‘0.004
‘0.004
-0 .004
'0.007
-0 .008
-0 .005
-0.004
-0.003
'0.003
-00003
0.001
“0.001
0.001
-0.009
“0.001
0.003
-0 .008

HEIGHT

0.25
0.05
1.25
0.25
0.01
0.05
0.01
1.25
0.10
0.25
0.05
1.25
1.25
0.05
1.25
0.05
0.01
0.01
0.05
0.05
0.25
0.05
1.25
0.05

.25
1.25
0.01
0.05
0.25
0.25
1.25
0.05
0.25
0.05
0.25
0.05
0.25
0.25
0.25
0.05
0.25
0.25
1.25
1.25
1.25
1.25
0.25
1.25
1.25
0.01

ID

100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
103
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
103
100
100
100
100
100
100

(—

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4.3

199

OBSERVED
(CM-1)

2697.040
2697.286
2697.286
2697.853
2698.040
2698.594
2698.870
2700.418
2704.589
2704.915
2705.198
2705.198
2705.752
2706.232
2706.599
2706.741
2709.739
2710.248
2711.536
2712.956
2713.506
2713.506
2713.854
2714.294
2715.079
2716.009
2717.969
2720.554
2721.100
2721.856
2721.856
2722.883
2723.094
2724.654
2725.923
2728.003
2728.524
2728.728
2728.975
2729.260
2729.668
2729.749
2730.335
2730.725
2733.123
2733.353
2735.287
2735.802
2736.514
2736.721

OBs-CALC
(CM-1)

“0.008
-00001
’0.001
“0.004
0.000
-0 .015
-00002
’0.011
-00010
-00002
'0.002
-0.005
0.005
-00014
0.002
-00003
-00001
-0.003
0.002
O .002
0.001
0.002
0.002
0.000
-00001
'0.008
0.004
-0.001
“0.003
0.003
0.000
‘0.004
-0000}
“0.006
‘0.009
0.002
'0.006
O .002
-00002
0.005
'0.001
0.001
-00009
“0.010
-C.OO4
3.004

WEIGHT

0.05
0.25
1.25
0.25
0.05
0.05
1.25
0.05
0.25
0.25
0.25
1.25
0.01
1.25
0.05
0.05
1.25
1.25
1.25
0.25
0.25
1.25
1.25
1.25
1.25
1.25
1.25
0.25
0.25
0.25
1.25
1.25
1.25
1.25
0.25
1.25
1.25
1.25
1.25
1.25
0.10
0.05
0.25
1.25
0.01
1.25
1.25
1.25
1.25
1.25

ISO

32

ID

100
100
100
100
100
100
100
100
100
100
100
100
103
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
103
100
100
103
103
100

"J‘O‘OV‘JO‘VO‘

LNNWO‘knbt‘w-QUIO‘UIWOCUIJ-QOJ‘C‘JN001AU1WMWOMJJCINVO‘hmt‘tfiNNOO‘t‘Nmt‘8‘00

‘da

-54.;
doumwouommom

4......
045000

--b

t~N.4iJuHNLN:~b<»h)O

J

10

.3
O\ntHO<JO

15

—3 ..s
NVHVN

Cr--at‘.00"O~MC"UI‘O

LOUER

K.-

(VO‘\IUUI‘JWUJOO.O‘WbVNNthLNWUS-l-AMNO‘bfiPUINNO\HOOmmOWWWJ-¢WW45MDJ“

K+

ALMbwnqu-u

a.;
an

4...)... .3
demUJ-QON06‘CDNO

' do...)
VIMVULNS‘meWNW‘OdOWW‘JNmFJboml‘MW-fl‘o

200

OBSERVED
(CM-1)

2737.515
2737.515
2738.663
2739.378
2740.032
2740.032
2740.924
2742.411
2742.918
2743.606
2744.289
2744.565
2745.072
2745.847
2745.998
2747.173
2747.503
2748.306
2749.371
2749.872
2750.537
2751.300
2751.458
2752.720
2753.530
2753.709
2755.511
2755.728
2756.170
2756.669
2757.310
2759.393
2761.911
2762.516
2763.307
2763.911
2764.786
2764.936
2765.918
2766.906
2767.453
2767.942
2768.397
2769.482
2771.191
2775.176
2776.289
2779.093
2780.620
2783.994

OBS-CALC
(CM-1)

0.002
-0.008
0.001
-00001
0.001
0.017
'0.007
-00010
-00002
“0.017
0.002
0.013
-00005
'0.002
“0.006
‘0.026
-0.013
0.011
-00001
‘0.040
0.000
'0.009

0.003,

‘0.004
0.042
‘0.054
-0.020
'0.008
-0.004
-0.073
-0.044
-0.001
0.002
-0 .007
0.004
'0.009
-0.001
0.004
0.001
0.005
0.009
0.003
“0.007
0.003

HEIGHT

0.25
0.05
1.25
1.25
0.05
0.05
0.25
1.25
1.25
0.25
1.25
1.25
0.01
0.05
0.25
1.25
1.25
0.25
1.25
1.25
1.25
0.25
0.05
0.05
0.25
0.05
0.05
0.05
0.25
0.25
0.05
0.01
0.25
0.00
0.05
0.01
0.25
0.05
0.01
1.25
0.05
1.25
0.25
1.25
0.01
0.05
0.01
1.25
1.25
0.25

ID

100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
103
103
100
100
100

‘ 100

100
100
103
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
103
100
100
100
103

10

UlL-l‘flf) \IobOhmox~VONusmemmmmmmwmo~o~NoNoooooooo-booooooo

A...

MFJPL‘NWI‘)U1UJI\)ONU'iLOJS‘tNO‘h)W¥‘UJU1-A&‘NO‘ulml-‘D‘JIMWOJ‘N-‘UII‘UV'I’OONNWO‘omb

AN-JtMmLNNN—‘OOWU‘JWNNLAI‘JJUWI‘N910m#MWNINthvioObU1b#Jome\,-JUJ$‘¥‘

LOVER

...)
m‘flCDO 9-
K
I
K
...

-I

O~b47NJm'VUINLnirflkhOJOChCrGW)CU0~0~OONO(>VDOHV‘QGWNC3130VO‘JOCD‘WV‘QITO(f9‘0

Utt‘J-‘bNWJ‘LflU’INO‘bmWJ‘mO‘vL‘mO‘MWWObombO‘ONVVmo—DOb-‘NW‘O‘O—IOONU‘MN-J

N-ONt‘O“JMONdN-I-‘OOh—JUJNMONbudwwaNN-bNN-bbNAMOU‘U‘OdOVLMI‘me

201

OBSERVED
(CM-1)

2784.655
2786.043
2792.163
2793.411
2794.925
2795.464
2795.808
2798.314
2798.314
2798.610
2800.480
2811.543
2811.697
2814.254
2823.111
2407.120
2416.860
2432.890
2433.457
2452.750
2454.694
2457.907
2461.697
2467.620
2472.330
2476.516
2478.343
2479.336
2480.788
2481.331
2484.308
2490.557
2493.147
2497.255
2497.373
2501.326
2501.643
2503.201
2503.671
2511.105
2512.362
2512.930
2516.292
2519.423
2522.571
2522.977
2523.577
2525.729
2527.635
2531.296

OBS'CALC
(CM-1)

-00006
0.024
-0.013
-00014
0.060
-0 .003
-0 .008
0.020
-00006
“0.004
0.005
'0.005
0.000
-0.004
-0 .018
0.006
'0.005
'0.010
0.006
-00005
0.004
0.000
'0.005
0.007
-0.003
0.001
“0.011
-0 .001
'0.006
'0.003
-0 .010
-00008
'0.001
0.002
‘0.002
0.002
-0.005
'0.012
0.013
'0.003
0.011
'0.005
0.003
0.011
-0.002
G .003
0.005
0.004

HEIGHT

0.01
0.05
0.05
0.01
0.05
0.05
0.05
0.01
0.05
0.01
0.25
0.01
0.05
1.20
0.01
0.10
0.05
0.25
0.25
0.01
0.05
0.05
1.25
0.25
0.05
0.25
0.01
0.05
0.25
0.25
0.05
0.05
0.25
0.01
0.10
0.01
0.01
0.05
0.25
0.05
0.00
0.01
0.01
0.25
1.25
0.01
0.00
0.01
0.05
0.05

ID

100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001

C.-

‘xlOdL‘J-‘UI-f‘lkn4‘0 :‘JS‘KN’LBUlt‘UJUJO‘V‘I‘ I‘WVIO‘O‘O‘N‘NI'}m'.N$“-NN\I-I‘N‘Obb¥‘bJ-‘U'IML-JKAQ‘JI

UPPER
K- K+

t‘t‘NJkabNb—AWNJ‘WNJOUl-k 3OaANFJdNNOI‘JW—bf‘J-AJNOLNUJNJ‘UJJ‘UI'JNbNLN

4“£‘~UJ‘.NKNUIL~JvaN-IAIUWINWLQWRJJ‘P‘3‘4‘U1-5‘UIUIU1BJU‘OJMJJ‘JWNNNN-fi-‘OWU—DNFN

L.

“1008“bmo"JULPO-NJ-‘LdO‘UIJ‘tNMVVb-I‘UIWO-O‘O~\JJ‘O‘GJJ‘UIPLNVDM‘OMWWWMO‘O‘;‘O~\IOI

LOWER

n
I

x
+

[\18‘0JJNLQNNJ‘JUN8‘WNANUJdeu-‘I‘NUJbNPJ-I‘MJNUJ-‘OhILNWN6‘LNJ-‘WNI‘3‘IVLN

WUIAC‘b5"3‘3‘WWWNNdI‘JNNNNWMlNLJWbWbbfilflWMNbNOOP—‘O‘WWNN-‘I‘bowmw

202

OBSERVED
(CM-1)

2532.745
2533.463
2535.556
2537.822
2543.666
2544.073
2544.502
2545.868
2549.490
2553.420
2555.098
2558.004
2558.646
2660.609
2561.485
2561.630

564.293
2564.402
2567.756
2568.885
2572.043
2574.871
2579.596
2581.180
2581.409
2589.568
2582.541
2591.468
2592.797
2593.078
2593.272
2594.147
2602.575
2603.951
2604.452
2605.478
2606.811
2615.932
2635.634
2640.728
2641.116
2648.353
2651.583
2656.045
2657.327
2659.004
2660.446
2660.609
2661.086
2665.033

OBS-CALC
(CM-1)

0.001
0.008
0.005
-0.001
“-0.002
‘0.002
-0 .003
'0.003
0.015
-00002
0.001
-0.001
0.009
'0.008
0.042
0.007
0.004
-00005
‘0.001
0.005
0.011
-00002
0.010
0.006
0 000‘
0.002
'0.013
’0.002
-0 .005
.00005
’0.006
0.019
-0 .019
-0.001
'0.005
“0.006
0.009
'0.009
0.012
0.003
0.005
0.008
-0.006
-00004
‘0.001
”0.008
-0 .022
-0000}

HEIGHT

0.05
0.05
o .25
0.01
0.01
0.05
1.25
1.25
0.25
1.25
0.01
0.00
0.25
0.01
0.00
0.05
0.01
0.01
0.10
0.05
0.25
0.01
0.01
1.25
0.01
0.01
0.25
0.05

.25
0.01
0.05
0.05
0.05
0.25
0.01
0.25
0.05
1.25
1.25
0.01
0.05
0.25
0.01
0.25
0.01
0.25
0.25
0.05
0.01
1.25

ISO

32
32
32
32

32
32
32
32
32
32
32
32

n)
‘-

32
32
32
32
32
32
32
32
32
32
32
32
32
32

a,
I.

‘3
1‘.

32
32

‘5
L

32
32
32
32
32
32
32
32
32
32
32

3
L

32
32
32
32
32

ID

001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001

001

001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001

‘—

(XJOCCK)U(D-\J\JLD'\IVVC)OO ~00~Q~moommmVV uOOObVO0006001s11m~0bb~xjooms~xjmmo~o

UPPER

7‘
I

K
...

bwonr.bwwmmpowasmoovuObmwmommwwwm-aovwmbkwwwwgwmwwwmwm

UiUICr 49mmk/JWLNNWINN1NCJNWNNQIUN1‘1MW-AUJ-fimC(JLNNJ‘JNLNV-‘NO‘DONU1ON3‘b

monomwo‘o-Naocrewmoowuarwrbbooooommuococombmbbbowu-qoooom-uumoo

C...

LOWER

75
\nOOr'J-hOlNLdN-bV-ALN03‘PP—hoNw—émommmw-‘w-‘OPWth‘wdwN-A-‘NLd-l-fih'dh) I
7‘
+

:

br~01~amo~0~t~s~bwmt~wmawt Aumtud-ANNONNpmmm-auodNOoo-wa-v-aou-Amm

203

OBSERVED
(CM-1)

2667.328
2667.455
2668.129
2672.431
2675.934
2684.145
2684.276
2684.276
2687.091
2689.394
2692.220
2692.483
2695.255
2699.260
2704.364
2705.598
2706.599
2711.144
2712.486
2712.486
2713.127
2714.548
2716.710
2717.307
2720.820
2726.041
2727.144
2734.088
2741.113
2745.229
2746.507
2746.957
2755.039
2757.140
2760.408
2761.469
2765.288
2770.234
2774.893
2784.353
2784.985
2788.764
2799.285
2810.334
2810.334
2813.493
2815.417
2533.923
2577.589
2579.849

OBS‘CALC
(CM-1)

'0.002
0.004
0.000
0.006
0.012

-0 .004
0.008
0.005
0.009

-00004
0.002
0.003
0.000
0.003
0.009
0.009

-0.012
0.002

-0000?

“0.007
0.000

-00006
0.001
0.009
0.012

-0 .005
0.004
0.001

“0.006
0.019
0.007
0.004

'0.005
0.004

‘0.024

'0.019
0.030
0.003

-00011
0.003
0.009

‘0.020
0.000
0.023
0.005

‘0.019
0.062

“0.058

-0.015
0.010

HEIGHT

0.25
0.01
1.25
0.01
0.01
0.05
0.25
0.05
0.25
0.05
1.25
1.25
0.05
1.25
0.05
0.01
0.05
0.05
0.05
0.25
0.01
0.01
0.25
1.25
0.01
0.05
1.25
1.25
0.01
0.01
0.05
1.25
0.01
1.25
0.05
0.10
0.01
0.05
0.10
0.00
0.01
0.01
1.25
0.01
0.05
0.10
0.00
0.00
0.00
0.01

188

32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32

a)
‘-

32
32
32
32
32
32
32
32
32
32

32

32
32
32
32
32
32
32
32

32
32
32
32
32
32
32

ID

001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001
001

LOWER
J K- K+
9 0 9
7 6 2
7 7 O
7 4 3

204

OBSERVED
(CM-1)

2720.554
2740.032
2741.512
2741.747

OBS-CALC
(CH-1)

0.025
-0.020
-0 .038
-0000?

HEIGHT

0.00
0.00
0.25
0.05

158

32
32
32
32

ID

001
001
001
001

APPENDIX E

ASSIGNED TRANSITIONS OF 202, 0], AND 03 0F H25e

J

UPPER
K- K+

NVUNmOA-fi-J-‘LNLHO‘O‘I‘N—J-4*‘-JU1‘\I‘\I1D¢3OOOININNNhJN‘Dm—t-IJV—bfiLDOCNN-$400

1O

A-JdJ-‘NOOOO#‘J-‘NVUIWNNNNO‘WCOJ—A—hd—fiNN—i-bub-“O‘OOOOCDNNmi—i—D-fi-N‘OO'44

12

..5
N

..5
h)

N

«ha-*NNNRJN—b-fi

...;
A—JI

205

OBSERVED
(CM-1)

1918.253
1918.549
1928.051
1928.340
1934.796
1935.083
1937.698
1937.995
1938.309
1943.278
1943.566
1943.346
1947.189
1947.487
1947.803
1948.953
1949.251
1951.611
1951.911
1952.079
1952.235
1954.565
1954.869
1956.218
1956.521
1956.822
1956.980
1957.145
1958.496
1958.775
1959.211
1959.810
1960.111
1960.283
1960.438
1961.713
1961.826
1961.991
1962.247
1962.361
1962.678
1965.398
1965.694
1966.003
1966.160
1966.273
1966.889
1967.566
1967.862
1968.173

OBS'CALC
(CM-1)

“0.002
0.003
-0.003
‘0.009
0.010
‘0.002
-D.002
-00003
‘0.005
0.014
0.000
0.004
“0.001
'0.005
-0.007
0.014
0.017
0.005
0.001
0.010
0.003
'0.022
'0.025
‘0.015
-0.001
-0.005
“0.004
-0000“
'0.002
-0.005
0.004
0.010
0.001
-0.017
0.005
0.006
-0.005
0.000
0.000
'0.003
“0.010
'0.006
‘0.001
0.001
0.002

HEIGHT

0.05
0.05
0.05
0.01
0.05
0.01
0.25
0.25
0.05
0.05
0.05
0.05
0.25
0.01
0.01
0.05
0.01
1.25
0.05
0.01
0.01
0.01
0.01
0.01
1.25
1.25
0.01
0.01
0.25
0.25
0.10
1.25
0.05
0.05
0.01
0.01
0.01
0.00
0.05
0.05
0.01
0.25
1.25
0.05
0.05
0.01
0.01
0.01
1.25
0.05

80
78
80
78
80
78
80
78
76
80
78
80
80
78
76
80
78
80
78
77
76
80
78
82
80
78
77
76
80
78
80
8O
78
77
76
80
80
80
78
80
78
82
80

78

77
8O
80

q
(-

80
78

ID

020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020

qwmmbb p.b-xpnwxjmm..hm'bmm-q-xjm-qmtnanxnb1700000\J1'0~O~O~O~O~O~O~O‘O‘O~O~O~O‘JO\J

'J'JmU‘F-I‘bkl'lbbWJ-‘(db‘flid “Jim/8‘4‘8‘JFUIUIMLNUIKAbk}!AN-aN-JOOOIAJOINO'.AOMLN1.NLM

”1UINNnb-A—A—515-‘bfi-JUNNO‘D‘mfifiwm‘fiwmkDOQNbeJ’OVMV‘DO‘OOQ‘Ofb‘001NFJOO1n-‘Xi

11
H.

11

1O
10
10
10
10
1O
1O
‘0
10
1O
1O
1O

{1.0-"0\jN\H\nU'IU10)-7~mm0\~0‘4\050‘0‘Om~D~OOO~OO‘O~O-U1‘OO

LOuER
J K- K+

{MLN4‘4‘\flU‘IwMDUtINPUINmNI‘QNNAbWUJUILNO‘0‘018‘3‘1-‘U10‘NLNNLNN—Bd-‘P—bb-5DWONNN

C‘..

nr‘rwwoooommwmruumVN-sjwbbobov-s-A—a-smmmoomcmOOOONo-uowbwoo‘o

206

OBSERVED
(CM-1)

1968.723
1969.037
1969.366
1971.412
1973.034
1974.235
1974.409
1974.557
1974.703
1974.876
1975.014
1975.177
1975.338
1975.471
1975.588
1975.770
1975.897
1976.078
1976.163
1976.244
1976.569
1976.888
1978.543
1978.762
1979.028
1979.308
1979.931
1980.188
1980.255
1980.799
1981.498
1981.997
1982.296
1982.612
1982.768
1982.832
1982.944
1985.329
1985.394
1985.489
1985.617
1985.708
1986.612
1986.912
1987.231
1987.394
1987.509
1987.858
1988.539
1988.839

OBS'CALC
(CM-1)

‘0.009
'0.008
‘0.006

0.003
“0.009

0.000
'0.001
“0.001
‘0.002
‘0.001
'0.006

0.001
'0.005

0.005
'0.001
-0.010
‘0.034
'0.001

0.002
”0.001
'0.001
“0.004
-0.014
‘0.005
-0 .005
'0.008
-O.D10
'0.003
'0.003
-00003
‘0.011
'0.013
'0.003
-00005
‘0.004
-0.010

0.003
'0.004

0.003

0.000
‘0.002
“0.005
“0.002
-0.002
‘0.003
‘0.004

HEIGHT

1.25
0.25
0.01
0.25
0.01
0.25
0.25
0.05
1.25
0.01
1.25
0.05
0.05
0.25
0.25
0.25
0.25
0.00
0.00
0.25
0.05
0.05
0.01
1.25
0.10
0.01
0.01
0.01
0.05
0.05
0.25
1.25
1.25
0.05
0.05
0.25
0.05
0.05
0.05
0.25
0.25
0.05
1.25
0.25
0.05
0.01
0.25
0.25
1.25

ISO

80
78
76
80
8O
80
82
78
80
76
78
77

82
80
80
78
78
80
80
80
80
82
80
78
8O
80
78
76
80
82
80
78
77
80
76
80
80
8O
78
78
82
80
78
77
80
78
82

9"}

ID

020
0.30
020
026
626
620
020
020
026
626
020
026
626
026
020
620
626
020
020
020
026
020
020
020
626
620
620
020
026
020
026
020
020
020
026
023
626
620
020
020
023
620
026
626
020
020
020
329
020

‘50.
iv

anxru-JV-0\Hm~do-vn~b~00~b~00-u\rfl L

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UPPER

7‘
I

K
4.

...)..sakungutuummkuarJaa...gNrerNTULNb-L"JJUJWUJOOOOO-abuibw—bt‘8"hbatflf‘d'dN

pabbuoomoowwrmwo-o(has'.n\nvvu1\.n~‘-t~.‘mbbNNNVVMNOHOMOWOOWOO‘N‘0WV'

O‘OO‘O\nb$‘4\t‘$‘OO‘“~JOV \J‘JNV‘JVNNUIU‘O \rqoxocoma;oooocowoa-vmwmoonQo-xlmmoo

'vNNrQ‘qbkphbun.OU(y(-)QoAdug—bbngmyvppAa-AA-ANUJIVLNNUJUINLNU'II‘JJ‘UJUJUJ

anmxnmagg-...g~b-jpVNNVooooonuuwmmwmmmmoomflb-ubxlh-a-qbdw>000

207

OBSERVED
(CH-1)

1989.158
1989.322
1989.492
1990.487
1990.807
1990.930
1991.024
1991.112
1991.214
1991.344
1991.427
1991.517
1991.590
1991.679
1991.763
1991.926
1992.226
1992.544
1992.708
1992.877
1994.370
1994.652
1995.717
1995.887
1997.092
1997.409
1998.132
1998.238
1998.544
1998.862
1999.026
1999.201

200004337

2000.737
2001.053
2001.221
2001.328
2001.396
2001.510
2001.645
2003.586
2003.871
2004.169
2004.330
2004.478
2005.314
2005.500
2005.805
2006.127
2006.29?

CBS‘CALC
(CM-1)

“0.002
-0000}
-00002
0.001
0.003
'0.002
0.000
-0.003
’0.004
0.002
‘0.004
‘0.007
0.000
‘0.001
-0.002
-0.001
'0.002
“0.005
“0.005
-0.00S
-0.005
0.004
-0 .015
-0.003
‘0.001
0.001
-00001
'0.003
0.002
'0.001
0.0C0
“0.005
‘0.003
0.000
0.002
‘0.001
'0.002
0.000
0.002
0.000
0.005
“0.007
‘0.001
0.003
0.002
0.302
0.005

HEIGHT

0.25
0.05
0.05
0.05
0.01
0.25
0.10
0.25
0.01
0.05
0.25
0.05
0.05
0.05
0.25
0.01
0.25
1.25
1.25
1.25
0.05
0.25
0.05
0.05
0.25
0.05
0.01
0.10
1.25
0.25
0.25
0.25
0.25
1.25
0.25
0.05
0.05
0.01
0.25
0.10
0.01
1.25
1.25
0.25
0.25
0.25
0.05
0.05
0.05
0.05

180

78
77
76
8O
82
80
80
80
78
78
78
77
77
76
76
82
80
78
77
76
82
50
77
76
80
78
80
82
80
78
77
76
82
80
73
77
80
76
8O
78
82
80
78
77
76
80
83
80
78

-,-9
1

ID

020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
023
023

(—

”0101.11,; a m dun m Hummus ~14 1,»: MN 0‘ r) b b 0‘ mm (N O- 0 041-11.» '01er)an Nmmmmuub b 4‘ b b 4‘ U1

......ooo—sc.aoo-zhan)N—s-b.awm-¢N—>JamwwnamammwwmmrvmfliooooOL-ILNLNLMTON-A

__‘_._.(J..(}.a..3-;.).A—a.~b.aAmmMWMNNNNNN§

-041.404144LN-‘k’1WO‘U~NNIU1\J1U(DC) 4‘ (UPI-‘8‘

LOWER

g

7‘
I

7‘
'0'

l-ILNI‘4‘J.‘NI-‘I‘JU'ILD'Q‘JC‘bbbl‘LNL-Jknkukflkl‘lkflt‘J‘JFO‘O‘J‘bPL-JJ‘LdJ-‘UJLNONO‘O‘O‘O‘kflmmmkflmo

I'QN—‘O-th~JN—4—8NPJ—a—IKJK‘hJL'JWOLNOOONN'JNthNWU1WWMkr-‘L4Wd—fiafid-‘NNNNWU‘N

rumbbboborbmmwwwwwaaw-‘mmmmNmmmmmmoNoNOoooooowwwwtumm

208

OBSERVED
(CM-1)

2006.466
2006.883
2007.205
2007.644
2007.955
2008.285
2008.448
2008.768
2009.076
2009.398
2009.564
2009.735
2010.825
2011.131
2011.299
2011.460
2011.594
2011.801
2011.900
2012.057
2012.229
2015.057
2015.378
2015.718
2016.073
2016.245
2016.932
2017.239
2017.564
2017.740
2017.904
2018.060
2018.241
2019.312
2019.623
2020.110
2020.488
2020.646
2021.436
2021.764
2023.644
2023.974
2024.755
2024.917
2025.080
2025.229
2025.553

2025.397 1

2026.001
2026.171

DBS’CALC
(CM-1)

0.002
'0.003
0.005
0.004
0.001
0 .001
-0 .007
’0.001
0.000
0.000
-00002
-0000}
0.005
0.000
‘0.003
0.002
0.000
0.000
’0.001
“0.005
0.003
'0.004
“0.007
-0000}
0.000
“0.010
0.000
‘0.002
’0.012
‘0.004
‘0.003
0.017
“0.005
0.006
‘0.010
0.002
0.003
'0.002
0.301
‘0.001
0.003
-0.005
0.004
0.000
0.000
0.002
0.006

HEIGHT

0.25
0.05
0.01
0.25
0.25
0.25
0.05
1.25
1.25
1 .25
1.25
1.25
0.05
1.25
0.05
1.25
0.05
0.05
0.25
0.05
0.05
0.05
0.01
0.25
0.05
0.05
1.25
1.25
1.25
0.00
1.25
0.05
0.01
0.25
0.25
0.25
0.01
0.05
0.25
0.01
0.01
0.05
0.05
0.05
0.01
0.05
0.05
0.05
0.05
0.01

ISO

76
80
78
82
80
78
77
82
80

77
76
82
80
82
78
80
76
73
77
76
80
73
80
78
77
82
78
8O
76
78
77
82
80
77
77
76
80
73
80
78
80

' L.

78
80
78
76
78
77

ID

020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020

€-
‘-

-A;J‘O\n\n[\JV")L‘OI-‘O‘d—l‘é'". ‘L‘JU‘U’IUIUWU‘U‘NI‘J!\)|\)IJI‘JNI\’IU~3‘5bO‘OWU-WNFJIUIQNI‘J
t.~anUl~0Un\n!\JVN-“~ObO-IQNNruR'U1m\I1mm\n\J1\wawuxtuwtuqurumbpooooooogngwugggu;
bh)WNLflUJW-¢L‘P\J\HUJWFOOAfldNNFJNU‘NWkUOAOJO‘OaNNNNkMLfl’WJ‘A-‘dd—‘hl

b (N! ‘N
:.

UJ«bl‘i..§b1UfUO1N-31’JNNL‘J-‘u-IOC)O—i-J«9JIU-‘N’XI-O’DJ0-30‘044-54NNL‘JRI1NNI‘JNNNd

Nmrummwmmbl‘UUJOLNb-h-aJambwbPbbbbquNNNNNNI-uoO-b-bmmomov-b-i4.4-*4
AVA-Jabruw—bw-JNONUHJNNmrumwuduhfllALflbwwwtuwwxqaug—awuqbbmmeNNNNN

209

OBSERVED
(CM'1)

2026.327
2027.331
2027.649
2027.988
2028.168
2028.346
2028.555
2028.764
2028.878
2029.074
2029.402
2031.742
2032.057
2032.147
2032.458
2033.004
2033.076
2033.330
2033.405
2033.493
2033.571
2033.676
2033.747
2035.648
2036.536
2036.628
2036.862
2036.963
2037.137
2037.298
2040.207
2040.372
2040.701
2040.876
2041.007
2041.339
2041.776
2043.637
2043.738
2043.960
2047.697
2048.354
2048.965
2049.065
2049.416
2050.040
2051.705
2049.717
2052.031
2052.418

OBs-CALC
(CM-1)

-00008
0.005
-0 .001
'0.003
0.001
-0.002
0.006
3.008
0.005
0.004
0.003
0.005
‘0.006
0.000
0.001
0.002
'0.002
0.000
'0.010
“0.005
'0.002
“0.005
“0.001
0.008
0.003
0.002
0.004
0.005
-0.011
'0 .007
-00003
-0.004
0.000
0.002
'0.002
-00001
0.002
0.000
0.004
0.005
‘0.001
0.022
0.002
0.000
-00001
-0.001

HEIGHT

0.01
0.10
1.25
1.25
0.05
0.10
0.25
0.01
0.05
0.01
0.01
0.01
0.01
0.10
0.25
0.01
0.25
0.01
0.25
0.01
0.10
0.01
0.25
0.01
0.01
1.25
0.05
0.25
0.05
0.01
0.05
0.05
0.10
0.05
0.01
0.10
0.25
0.25
0.25
0.25
0.25
0.05
0.25
1.25
0.25
0.01
0.10
0.25
1.25
0.00

ID

020
020
023
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
020
020.
020
020
020
020
020
020

C...

“‘1 N IJ N r») n) O. —* a a ...x fr \n \r. cr- UT 0'1"; N b b \J p kn \fl U1 0 m 0s U10 w w Id (,5 4:4 1".) “J N _. .. -4 .. b .4- u 00 0. b1).

U1Unh)Nh)l‘Im-’—D-5—i$‘¥‘$‘0*~3‘“(“b41404DWWINUU‘LMU‘LMMNNR’NNJ-J—DOOOCJNCthknl-‘b-l“

--~C)k.)OONM-Jkr.'4ALdeé-hLfldFUNfQIVNNNIU-‘oJ-Jd'4-’-¢-3-‘~3-*°4N-3LHJ>UINUJ

)0 C.) 2.) O

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C...

.64-...ommoomm-qwbbfibmmmomowoawtdmwwmwm-h-J-J—b«baquOOJ-‘w

\J M Ix: N ru r0 (:9

LOWER

75
I

K
...

()-0...:o-b-fiv-fiO‘OQOOMkfl\HVMU1\'-\flb4‘-\’ibbP-PO‘#015O-WL‘JUJUQKNFUI’OI’D‘dad-3.1.19"l‘O-MJ‘kfl

QNOQNNQOruo—‘dé-a-fié-Jo-boooo0000000CdorouJN-am

‘-A"~.A~C’QOJQ~¢~;A(J

210

OBSERVED
(CM-1)

2052.524
2052.735
2053.188
2054.264
2054.795
2055.664
2055.817
2055.980
2056.314
2056.662
2056.825
2057.140
2057.463
2058.508
2058.817
2059.137
2059.300
2059.473
2059.649
2059.798
2059.925
2060.126
2060.361
2060.474
2060.833
2060.949
2061.275
2061.409
2061.572
2061.654
2061.839
2063.247
2063.516
2063.706
2063.809
2064.110
2064.780
2065.123
2065.466
2065.642
2065.829
2066.553
2067.059
2067.384
2067.730
2067.914
2069.330
2069.633

OBS'CALC
(CM-1)

0.004
0.006
0.003
'0.005
'0.008
0.001
'0.004
0.002
‘0.004
'0.003
0.000
-00001
'0.005
0.001
0.002
“0.001
0.002
“0.000
‘0 .002
0.000
'0.001
0.000
0.003
0.004
0.002
‘0.004
'0.012
‘0.007
‘0.007
0.000
-00004
‘0.005
-0.005
0.006
0.003
0.002
0.007
0.000
0.000
'0.001
0.004
0.002
0.003
0.000
-0.003
0.000
0.004
0.004

HEIGHT

0.25
1.25
0.01
0.25
0.25
0.10
0.01
1.25
1.25
0.05
0.10
0.01
1.25
0.25
0.25
1.25
1.25
0.25
1.25
0.01
0.05
0.25
1.25
0.01
0.25
0.05
0.25
1.25
0.00
0.05
0.01
0.25
0.05
0.10
1.25
0.05
1.25
0.05
0.25
0.25
1.25
1.25
0.25
0.25
0.01
1.2.5
1.25
0.01
0.05

1.25

ID

020
020
020
023
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
023
020
020

<—

p O >0 1" bbLJt‘UJW’J‘IU‘LhU‘ItflUI1".)N|\"\)r\1NIJf\!l~Jbud$~ p 8* bad mullurom Nun—4.49101.» (5000\1‘4'»:

UPPER
K- K+

UIWLflknlNDJb-bb-fi5u‘11‘l‘bWUZ—é-‘JO-JC-JOMWWLNMbk‘rflNNh’f‘Jg-a-h.s—\UJ&~ILNUJNU1C>\D

a4—ha-a.A—b..a.a.aoc;) (,5 UI’UI‘J..3 [\3

N-aN-«Q'dl‘J-‘N-‘N-‘O«3440)CL‘I‘ONNhJIUNI‘JPJ-J-‘J-i-aoC

0-‘0~b0;‘«5““lN-bLNU'IUT\N\DLJ1\H\J:A—3—l—A.a—J-J_&UJbarbb{\Lq‘vLNVquhJNooowwlflwm~‘uqfl

IUDN~PPJAWOWOLN¢WWLNFJ~C>OO-‘O-‘OéNNNNNWLNw’d-‘d’éoooooNR’NNWO‘“V0

L-Jn)LNN1N(Nl\)l_-JI\DLNN—3FJNNéJ-A-J"iv-5d49*-3rUNNI'QPJ-‘-*NNNFJNI'\DNOO04-O—0—0-4a0a

211

OBSERVED
(CM-1)

2069.949
2070.158
2070.290
2070.411
2070.859
2071.220
2071.405
2071.598
2072.135
2072.460
2072.806
2073.390
2073.724
2074.745
2075.091
2075.336
2075.442
2075.837
2076.199
2076.392
2078.129
2078.462
2078.579
2078.812
2078.940
2079.847
2080.029
2080.189
2080.363
2080.553
2080.708
2080.888
2081.075
2081.301
2081.688
2081.925
2082.267
2082.437
2082.514
2082.615
2082.745
2082.816
2083.063
2083.178
2086.063
2086.669
2086.863
2087.006
2087.217

GBs-CALC
(CM-1)

0.001
0.005
0.006
0.005
0.001
0.000
‘0.002
0.000
0.004
0.000
0.001
0.002
0.000
-00008
0.003
0.001
0.002
'0.004
0.005
'0.003
'0.002
‘0.002
0.003
‘0.001
0.002
“0.003
‘0.003
'0.002
0.000
0.005
'0.001
0.002
0.003
-0.001
0.001
0.005
-00001
'0.006
'0.002
0.008
“0.001
0.000
0.002
0.003
0.004
‘0.001
0.007
0.001
‘0.002

HEIGHT

0.25
0.25
0.05
0.05
1.25
1.25
0.25
0.25
0.10
1.25
0.05
0.10
0.05
0.05
0.05
1.25
0.05
0.05
0.05
0.05
1.25
0.25
0.10
0.05
0.01
1.25
0.05
0.25
1.25
0.05
1.25
0.05
0.25
0.05
0.25
0.05
0.25
0.05
0.05
0.05
0.01
0.01
0.05
0.25
0.25
0.05
0.25
1.25
0.25
1.25

ISO

78
80
76
80
80
78
77
76
82
80
78
30
78
82
80
80
78
77
77
76
80
78
80
76
78
80
82
78
80
76
73
77
76
82
80
80
78
77
76
76
82
82
80
80

80

30
80
78
78

ID

020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
023

2 020

020
023
020

020

G—

9.» U1 3‘

.J‘l a! I.) {b 041.17.: Ld 1»! Nu)!“ N141")~ WWW-P ‘5 b p VVU‘UI ‘\ U! Nédl'u hJN UIUI 1." ”1:."

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UPPER
K- K+

V'WWHWUI\JHnUIwwmwwrdmwNrucmmmmwwmbb b p...-.NnjtgwadafldmmwMoog“,

‘—

U\O\N1\JNN'\J~F\JVTU(}MMUIUIIAkfltlJ‘JNKJ'Iva“\J1"’~3-§--‘-3ViWU‘WO‘O‘U'IJ‘

C» t» ‘4 L4 «0 -0 4~ s~ c- :> (r a)

"‘““4““““‘""“"“WWU‘“~’-‘-‘“4mebAN-aoounawmwm-Jw-saaaammwNmmbrm

crumb):-bbpbbbbbb-.s-4-z—AL.~J--aw-¢m;~bbwwwt--Jwr~1wmr~mooooo¢4mmuqaamu

212

OBSERVED
(CM-1)

2087.720
2088.823
2089.011
2089.436
2089.536
2089.867
2090.210
2090.359
2090.696
2091.051
2091.236
2091.421
2091.566
2091.830
2091.922
2092.312
2093.085
2093.662
2095.158
2095.158
2095.490
2096.028
2096.211
2096.374
2096.562
2097.110
2097.686
2097.921
2098.022
2098.272
2098.603
2099.353
2099.708
2099.899
2100.079
2101.375
2101.722
2101.902
2102.092
2102.558
2102.899
2103.428
2103.621
2105.704
2106.027
2107.733
2107.917
2108.107
2109.388

OBS-CALC
(Cm-1)

0.002
-0.004
-0.004
-0.018
-0.003
-0.002
‘0.003
‘0.005

0.005

0.002

0.001

0.001
-0.002
-0.002
”0.006
‘0.003

0.013

0.004

0.013

0.003
“0.001
-0.001

0.007
'0.001
-0.003

0.004
‘0.005

0.000
-0.003
'0.002

0.031

0.004

0.000

0 .006
“0.004

0.004
'0.001
-0.003

0.001
-0.003

0.004

0.001

0.008
-0 .003

0.001

0.001

0.002

0.004

0.006

WEIGHT

0.05
0.25
0.25
0.01
0.25
0.25
0.25
0.05
0.25
0.05
1.25
1.25
0.25
0.25
0.01
0.01
0.01
1.25
0.01
0.25
0.25
0.05
0.01
0.25
0.10
0.25
1.25
1.25
0.05
0.25
0.01
0.01
1.25
0.25
0.05
0.05
0.05
1.25
0.05
0.25
1.25
1.25
0.05
1.25
0.01
1.25
1.25
0.05
0.05
0.25

76
80
80
73
80
78
77
76
82
8O
78
77
76
80
82

76
80
77
82
82
80
77
80
8O
78
80
80
80
78
80
76
80
78
77
76
80
78
77
76
82
80

9
l

76
82
811
73
77
76
30

ID

020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
023
020
023
020
020
020
023

C.

.o\n\0~o~o\]\3\j\lt"i)t“$“n‘.'1U1U1\nC"OthJtnmmLDu)(«l‘r‘ bb-xj-xj-xHAJl-‘VVNOOQJWOOOOOOOOO

UPPER

K
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'quINOO-JOU'I

AwahJN-«a $44.50bbtflkrlIer-JIURHJRJVb4‘bbwthWLN—iOOmmlururgoouo0.3-64.3“;

(11h! )1"'\j\ll)~!'lf}‘v0‘ -D“L)-A—*'\N1)3U~3WUJ \INO‘-5U1\n‘JI\JI\fl(‘JNNf\INO‘\I‘VCJNU‘IWUIUJ‘JJ'

(..-

(91(k16JxN-F‘t‘ I“ I‘L‘U'Giml'vtlnWOV‘Y)‘-7"LM1N1.4LMlN\IO~O t-~vw-J\J-Joooooooomwwmmo

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m‘flnlowrcro~oua-¢-b-A-qo~c-A-ACh0 o~b3>t~r~bannU1UHm

('JbOv-b-JRIIUI‘xINw-fil/QLNIUIVLNLNUIA—IN-iU4LAJKNL2I16II’UNRINNO~‘flNw-9'5-JU1U'IU1MUTOOOO-fi

‘O-fi‘lL mCX‘UIU‘IUO‘J'I 1301 O C- 1‘3 1V FUNIU Cl

213

OBSERVED
(CM-1)

2109.926
2110.119
2110.471
2110.651
2110.842
2113.369
2113.705
2114.068
2114.252
2114.441
2114.797
2115.135
2115.489
2115.793
2116.514
2117.151
2117.506
2117.708
2119.054
2119.411
2119.784
2119.963
2120.171
2121.187
2121.528
2121.885
2122.067
2122.262
2122.773
2124.235
2125.863
2126.230
2126.596
2126.927
2127.465
2127.757
2128.117
2130.033
2130.399
2130.673
2130.785
2132.038
2132.397
2132.586
2132.775
2133.152
2133.702
2133.816
2134.002
2134.182

OBS‘CALC
(CM-1)

0.008
0.002
0.002
“0.001
0.004
0.014
0.304
0.005
0.001
’0.001
0.002
0.001
0.001
'0.002
0.002
'0.002
‘0.001
'0.002
3.003
3.004
0.034
‘0.010
0.001
-00010
’0.009
“0.008
'0.011
'0.004
’0.001
'0.008
0.011
0.020
0.004
0.000
0.003
0.001
“0.006
0.005
0.001
0.003
0.000
0.004
0.304
0.307
0.005
0.000
3.303
0.007
‘0.002
0.012

HEIGHT

0.01
0.05
0.05
0.05
0.05
0.10
0.25
0.25
0.05
0.01
0.10
0.25
0.25
0.01
0.25
0.25
0.05
0.00
0.25
1.25
0.25
0.25
0.25
0.01
0.01
0.01
0.01
0.01
0.25
0.01
1.25
0.01
0.25
1.25
0.05
0.05
0.25
0.05
0.25
1.25
1.25
1.25
1.25
1.25
0.25
0.25
0.05
0.25
1.25
0.01

180

77
80
78

76
82
80
78
77
76
82
80
76
80
80
80
78
80

9‘:
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80

G
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77
76
82

78
77

36
80
80
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7a
82
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so
78
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76
so
77
30
96

E

1)

ID

020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020

A
on.

b’Q‘JVVO*O~O‘OU1~OU1U1UI—bww#‘b

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o~4g~o~puphomunmbammxnmocoowooo'
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Oxnww—A-\.A-50”-,n1m-AoaruNr0NNVNbJ~b

214

OBSERVED
(CM-1)

2134.664
2135.590
2135.957
2136.321
2136.533
2136.661
2137.023
2137.151
2137.400
2137.509
2137.706
2137.891
2139.021
2139.604
2139.942
2140.306
2140.687
2140.901
2140.983
2141.596
2141.861
2143.450
2143.808
2144.003
2144.201
2145.660
2146.213
2146.408
2146.924
2147.669
2148.029
2148.413
2148.738
2149.103
2149.487
2149.558
2151.645
2152.207
2153.773
2154.561
2155.214
2155.568
2155.937
2156.130
2156.328
2157.956
2159.783
2160.991
2162.181

QES-CALC
(CM-1)

“0.008
0.022
0.000
0.004

-0.00Z
0.002
0.002
0.001

‘0.001

-0.002
0.009
0.004
0.017
0.012
0.004
0.006
0.009
0.007

-0.012
0.012

“0.008
0.000
0.006
0.013
0.000
0.000
0.003
0.006
0.005
0.001
0.004

‘0.005

“0.006

'0.006

“0.006

-00001
0.011
0.000

'0.004
0.002

“0.003

'0.003

-0.003
0.002

‘0.001
0.003

‘3.060

HEIGHT

0.10
0.01
0.25
0.05
0.01
0.05
0.01
0.25
0.25
0.10
0.01
0.05
0.01
0.00
0.01
0.05
0.25
0.05
0.01
0.10
0.05
0.25
1.25
1.25
0.05
0.05
0.05
0.05
0.05
0.01
0.25
0.05
1.25
0.01
1.25
0.05
0.05
0.25
0.00
0.05
0.25
0.25
0.25
0.05
0.25
0.25
0.00
0.05
0.05
0.00

020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
023
020
020
020
023
020
020
020
023
020

' 020

020
020
020
020
020
020
020
020
020
020
023
020
023
023
020
020

<—
K
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7'5
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‘~]O-’D\,I1F\DO\DN\o'WIUuIVO"0‘)03‘(”(D-fi-JO‘WDU'U-IO‘O‘O*JMUDUOCENO'O—b
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o#0.,¢wm{-J_\\O()Os...00.4..LWKI‘INNJL-Jbb'()0-‘O~IUNA-«OOCLNNNUIWLNN
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0mV‘40-O‘\Ib—D‘O‘OD~0‘0h'05U100UI‘OUJV'QOOU‘ICOIUNU‘UT‘O0‘fibVVommO

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‘0t‘VNNLflO‘v-JLMJF‘JIUIO‘OLNOI'U‘Jldw—i#bLH‘LN-I‘fil‘JNMMflJ¥*ANUWU‘MUN

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-3
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4

215

OBSERVED
(CM-1)

2162.592
2163.278
2163.651
2167.520
2168.009
2168.373
2168.582
2170.747
2171.439
2171.813
2173.628
2174.041
2176.839
2177.234
2177.614
2179.202
2180.183
2180.553
2180.772
2181.164
2183.725
2187.082
2187.965
2190.676
2195.776
2196.219
2196.425
2198.138
2198.545
2199.311
2201.063
2201.153
2205.463
2208.324
2209.341
2214.273
2217.558
2219.265
2220.529
2265.362
2266.792

CBs-CALC
(CM-1)

‘0.002
'0.002
0.001
0.000
0.000
“0.010
-0.003
0.005
-0.022
-00010
“0.002
-0.008
-0.001
0.022
'0.003
'0.003
'0.012
”0.017
-0000:
0.001
0.012
-00008
0.015
‘0 .012
0.015
0.017
.000.8
0.005
0.005
'0.003
'0.038
0.013
'0.036
0.006
0.010
'0.013
0.005
0.031
0.002
’0.001
-0.015

WEIGHT

0.05
0.05
0.05
0.25
0.00
0.00
0.05
0.01
0.01
0.05
0.25
0.25
0.25
0.05
0.01
0.01
0.01
0.00
0.25
0.05
0.01
0.00
0.05
0.00
0.05
0.05
0.00
1.25
- 0.25
0.05
0.01
0.25
0.00
0.25
0.05
0.00
0.01
0.00
0.01
0.00
0.00

IS?

V0101
(4100

at
80

k

80
80
80
80
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78
80

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80
80
80
78
80
78
80
80
30
80
80
80
80
80
78
80
80
80
80
80
SO
80
80
80
80
80
80

ID

020
020
020
020
020
020
020
020
023
020
020
020
020
020.
020
020
323
020
020
020
023
020
020
020
020
020
020
020
023
020
020
020
020
020
020
020
020
020
020
020

A‘s
UK.

UPPER
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11
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216

OBSERVED
(CM-1)

2079.214
2112.870
2118.166
2118.443
2120.724
2128.536
2128.812
2134.994
2142.579
2142.869
2144.774
2145.115
2145.366
2150.164
2151.116
2151.485
2152.942
2153.186
2153.463
2160.886
2160.991
2161.269
2161.569
2161.718
2162.181
2162.476
2163.651
2164.163
2166.394
2166.759
2167.035
2167.342
2169.978
2170.261
2170.423
2170.571
2170.747
2171.079
2171.250
2173.214
2173.498
2173.934
2174.483
2174.556
2174.643
2174.927
2174.927
2175.195
2175.260
2177.752

OBS‘CALC
(CM-1)

'0.008
0.016
0.002
0.005
0.005
0.012
0.009
0.010
0.000

'0.019
0.007
0.001

'0.008
0.000
0.014
0.014

‘0.005

'0.007

‘0.015

-0000}
0.005
0.003

-00001
0.016

-0.013
0.010

'0.006
0.002
0.006
0.004
0.003
0.009

“0.011
0.040
0.000
0.003
0.003
0.014
0.022

“0.002

-0.025

-0.012
0.021
0.005

'0.005

-0.005
0.006
0.003

HEIGHT

0.05
0.25
0.05
0.05
0.25
0.25
0.01
0.25
0.25
0.25
0.25
0.01
0.01
1.25
0.25
0.25
0.05
0.25
0.25
0.05
0.01
1.25
0.25
0.01
0.05
0.25
0.10
0.05
0.01
0.05
0.10
0.10
0.01
0.10
0.10
0.01
1.25
0.10
0.01
0.25
0.01
1.25
0.01
0.01
0.01
0.25
0.25
0.01
0.05
0.05

158

80
80
80
78
80
80
78
80
80
78
80
82
80
80
80
78
82
80
78
80
82
SO
78
77
80
78
78
80
30
80
80
78
80
78
82
80
8O
78
77
80
78
80
76
80
82
30
80
78
78
80

ID

100
100
001
001
100
100
100
001
001
001
100
100
100
001
100
100
100
100
100
100
100
100
100
100
100
100
100
103
100
100
001
001
100
100
100
001
100
100
100
100
100
100
100
001
001
100
001
100
001
100

UPPER
J K- K+

M-‘U‘PIVR'(FU'UIS‘WNVhJNUIAIUIUWI/‘WWLNJLNWOJ‘NMMO‘O‘bfibPJ‘Nv6‘N6‘Nh10wuh)pJ

dub
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J K- K+

8 5 4

8 5 4

17 3 14
17 3 14
9 7 2

17 1 16
16 3 14
15 3 12
8 4 5

15 3 12
8 4. 5

15 3 12
9 6 3

9 6 3

14 5 10
14 5 10
13 5 8
13 5 8
8 8 1

16 3 13
17 2 15
7 7 0

14 6 9
8 5 4

8 5 4

16 2 15
15 2 13
15 2 13
1S 2 13
14 4 11
14 4 11
14 4 11
13 4 9
7 3 4

13 4 9
7 3 4

7 3 4

11 6 5
11 6 5
8 6 2

8 6 3

3 6 2

8 6 2

8 6 3

16 2 14
16 2 14
8 6 3

14 5 10
17 1 16
14 5 10

217

OBSERVED
(CM-1)

2178.033
2178.345
2180.294
2180.407
2182.148
2182.499
2182.907
2183.352
2183.510
2183.625
2183.822
2183.912
2184.187
2184.721
2184.850
2185.013
2185.979
2186.272
2188.613
2189.404
2189.404
2190.043
2190.364
2191.425
2191.748
2192.123
2192.253
2192.526
2192.823
2193.215
2193.506
2193.656
2194.125
2194.315
2194.411
2194.577
2194.875
2196.667
2196.965
2197.517
2198.646
2197.862
2198.231
2198.350
2198.448
2198.736
2198.963
2199.104
2199.104
2199.410

OBs-CALC
(CM-1)

'0.002
0.008
0.024

-0 .017

'0.009
0.007

-0000?

'0.002
0.011
0.005
0.015
0.005

-0000?
0.008

‘0.017
0.009
0.000
0.007
0.020
0.008
0.014

‘0.005

'0.014

-00008
0.005

-00005
0.002
0.003
0.014

-0000?
0.001
0.008
O .017
0.022
0.002

-0 001‘.

'0.005

‘0.004

‘0.008
0.007
0.002
0.009
0.007
0.003

HEIGHT

0.01
0.01
0.01
0.01
1.25
0.25
1.25
0.01
0.05
0.25
0.05
0.10
0.01
0.25
0.10
0.05
0.25
0.01
0.05
0.05
0.05
0.05
1.25
0.25
0.05
0.10
0.01
0.25
1.25
1.00
1.00
0.05
1.25
0.05
1.25
0.01
0.01
1.25
1.25
0.25
1.25
0.01
0.25
0.05
0.25
0.25
0.05
0.25
0.10

ISO

78
76
78
77
80
80
80
82
82
80
80
78
80
77
78
77
78
76
80
80
80
80
80
80
78
80
82
80
78
80
78
77
80
82
78
80
78
80
78
80
80
78
76
82
82
80
78
80
8O
78

ID

100
100
001
001
100
100
100
100
001
100
001
100
001
001
100
100
100
100
100
001
001
100
001
001
001
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
001
100
100
001
001
001
001
001
001
001

UPPER
K- K+

VIN \JL’Ib’IblMWWUCdd‘OO-bOb5WNbJOOOOQOO‘O3‘bbUIII‘LNNNONNNONNOOwA

a
U145")

&\)t\)r\)u)mu1U\U1V\1~O-P\Obbwm.b

.18

..b
ChRJOthnu¢bxn

16

4‘ O (.3 0* 0‘ U4 ‘1’ U" Q

J

18
12
16
15
14

15
14

16

15

......) ...;
LN‘IW‘VV

..A

A...) ...}
wwwwwowmooocoa

LOWER

K-

($00003-bmbk'deWBioNOO-NO4‘DO‘NQ'VVVflmeU‘IU‘ImW‘U-‘MbUI-‘I-JMLN—D-DUJJ-3O‘Ul-i

K4-

ad

44

a.)
VéflxoxommNAAaAQOOOK‘»OOOMOUJMI-t‘ow

A

.3.) 4.3.3.3
ddt‘MmWV

"JVNO‘O

m4-4

218

OBSERVED
(CM-1)

2199.915
2200.155
2200.502
2201.601
2201.668
2201.759
2201.901
2201.962
2202.055
2202.126
2202.205
2202.276
2202.430
2202.581
2202.717
2202.872
2203.007
2203.596
2204.024
2204.622
2204.919
2205.077
2205.224
2206.049
2206.365
2206.693
2206.869
2207.860
2208.324
2208.398
2208.398
2208.717
2208.799
2208.799
2209.025
2209.096
2210.832
2211.048
2211.108
2211.227
2211.491
2211.777
2212.107

2212.410.

2212.955
2212.955
2213.237
2213.334
2213.572
2213.693

OBs-CALC
(CM-1)

0.020
0.006
0.013
0.001
0.000
-0.028
0.016
0.008
'0.002
0.017
0.019
0.006
0.006
0.000
0.007
0.002
0.004
‘0.007
‘0.011
“0.003
0.004
'0.004
'0.023
'0.024
'0.019
-0001?
0.001
0.008
0.002
0.005
0.010
0.007
-00006
0.017
“0.005
'0.001
'0 .003
’0.006
0.007
0.002
‘0.009
0.003
'0.008
0.004
-00006
‘0.014
-0.011
-0.024

HEIGHT

0.25
0.01
0.25
0.01
0.25
0.01
0.01
0.01
0.05
0.05
0.01
0.01
0.25
0.05
0.25
1.25
1.25
0.25
1.25
0.01
0.05
0.10
0.25
0.25
1.25
0.25
0.05
0.25
0.25
0.01
0.05
0.25
0.01

0.05

0.05
0.05
0.01
0.05
0.01
0.01
0.05
0.01
0.05
1.25
0.25
0.25
0.25
0.05
1.25
0.25

ISO

80
80
80
80
80
82
78
78
80
80
76
76
78
82
80
8O
78
80
77
80
78
77
76
82
80
78
77
82
80
78
80
78
82
80
80
80
82
80
80
80
8O
78
80
78
80
80
78
80
78
80

ID

001
001
001
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
001
100
001
001
001
100
001
001
100
100
100
100
100
103
100
100
100
100
100
100
100
100

é -.
...-b

~00“)deLNLNU'IUIWUJUJu-41NLANWU‘VVVVO‘0‘O—btdumbbJ‘Nb-aQMANOWVQJb3‘3‘8‘be
cub-b

on)

...-D...

....

NEMNONNNAgaooooombbbbbmmNNOOVNNNNaoodomwdmwumwwmmfl
...)

.34.) d—b-med—ba—J-a —b “‘44....
wawoommmmmwoooommooo‘owooo-A-a—bmuuoommmoom-qs‘m-q-omb—ammo
Nbmmwwmmuwummmmmommuwuwwwed—nomqubV-g-bVmu-bmwmbhumour:

bluowu~qo<yo~oc>o>o~o<>o~o~u
wcdh:ONPJNbbl-t~bbt 9400000000

A
4.).)
A

219

OBSERVED
(CM-1)

2213.828
2213.979
2215.671
2215.980
2216.393
2216.722
2217.172
2217.247
2217.320
2217.478
2217.558
2217.632
2218.121
2218.223
2218.362
2218.620
2218.959
2219.178
2219.265
2219.560
2219.722
2219.945
2220.110
2220.398
2220.454
2220.529
2220.809
2221.264
2221.416
2221.714
2222.022
2222.197
2222.638
2222.863
2223.463
2223.760
2224.070
2224.226
2224.396
2224.601
2224.913
2225.231
2225.464
2225.734
2226.003
2226.097
2226.199
2226.293
2226.377
2226.559

OBS'CALC
(CM-1)

-0.0Z4
0.005
-0000?
0.010
0.002
0.003
0.002
0.001
-0.003
0.006
0.015
0.031
0.015
0.015
0.003
-0.023
0.008
0.000
0.004
‘0.014
-o.002
-00001
’0.005
‘0.002
0.005
0.000
0.004
0.000
0.003
‘0.004
“0.006
0.011
0.015
0.014
0.009
0.013
0.001
0.001
‘0.004
0.004
0.008
‘0.007
'0.030
0.010
0.000
'0.008
0.000

HEIGHT

0.25
0.01
0.05
0.25
1.25
0.25
0.10
0.25
0.01
0.25
0.05
0.25
0.25
0.01
0.25
0.01
0.25
0.05
0.25
0.10
0.01
0.01
0.01
0.01
0.01
0.01
0.05
0.10
1.25
1.25
0.01
0.25
0.01
0.05
0.25
0.25
1.25
1.25
0.05
0.05
0.25
0.25
0.01
1.25
0.05
1.25
0.25
0.10
0.25
0.01

ISO

76
78
80
78
80
78
80
80
82
80
78
80
80
80
78
76
80
80
80
78
77
76
82
80
80
82
80
77
80
78
76
80
77
78
82
80
78
77
76
82
80
78
82
80
78
80
80
80
80
80

ID

100
100
001
001
001
001
001
001
001
001
001
001
100
001
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
001
001
001
100
100
100
100
001
001
001
001

J

10
11
13
1:.
1o
14

.3
p

.3
U1&-O

Ntrwommommmmmmmoooouom~o~OVVNV

UPPER
K- K+

bmwkk—hadumwdmw-ALAObbbe-«NNNNVILHU»bmbbwwmmv‘mwoUVOOJ‘ONbs‘

6
8
12
14
6
14

cu.
b

..5
N161.“

.a.sa
mVVNNwwuomO-bNO-bOHJNNNNMObbbbbfibvhbboowmmw

L.

“dub—b
Vl-t‘N-J

.h

a.

4......)
\JIOU‘U!

.3.)
'SU'VVVNUJO‘O‘Oxnxo\O'O‘O‘O‘O‘O‘OOOWOOOOOOO‘

an.

.0...»
hJUJN

«A
.5

...... 4.3—34.54....
()OOOObJ‘bNONW

LOUER
K- K+
7
9

1

1

(NMMUIUI—D-bfiUJUIUJ-‘Ulw—iwkfio‘o‘oo«fibbbbfib3‘bm3‘mmt‘boooooo\J‘OObOND‘k

‘d

uh

..5
moNObi-344%NWWHUMMU‘UMMWWVNL/«ltNUJUJ-DMUIU‘WNMU

cub-...)

4.3—3...: ...)...
Offload-AbkbOOON

220

OBSERVED
(CM-1)

2226.776
2226.870
2226.870
2226.949
2227.108
2227.237
2227.551
2227.618
2227.894
2228.300
2229.088
2229.332
2229.571
2229.830
2230.617
2230.909
2230.990
2231.273
2231.407
2231.567
2231.709
2231.865
2232.021
2232.179
2232.497
2232.807
2232.986
2233.274
2233.487
2233.994
2234.319
2234.491
2234.665
2234.824
2235.025
2235.257
2235.335
2235.453
2235.555
2235.649
2235.864
2235.980
2236.198
2236.519
2236.685
2238.081
2238.401
2239.158
2239.468
2239.710

OBS-CALC
(CM-1)

-00002
'0.005
0.016
0.005
0.004
0.006
0.024
0.001
'0.003
0.007
-0.005
-0001}
0.003
’0.002
’0.014
-00010
0.004
'0.011
0.006
0.007
0.003
0.002
0.006
-0001,
0.001
-0.009
-00012
0.006
'0.002
'0.001
-00001
-00016
'0.001
“0.004
-0 .001
-00001
’0.013
-0.010
0.002
‘0.014
-09002
0.002
0.005
‘0.004
'0.008
0.001

HEIGHT

0.25
0.05
0.05
0.01
0.01
0.01
0.01
0.01
0.01
1.25
0.25
0.05
0.05
0.05
0.01
0.01
0.05
0.01
1.25
1.25
0.25
0.25
0.25
0.05
1.25
0.25
0.05
0.25
0.05
1.25
1.25
1.25
1.25
0.05
0.25
0.01
1.25
0.25
0.05
0.25
0.05
0.05
0.05
1.25
0.01
0.01
0.25
0.05
0.25
0.05

80
77
78
82
78
80

78
76
80
82
80
78
76
80
78
82
80
80
78
78
77
76
82
8O
78
77
8C
78
80
78
77
76
80
82
82
80
30
80
78
80
76
80
78
77
82
80
80
78
80

ID

001
001
001
001
001
001
001
001
001
100
100
100
100
100
100
100
100
100
100
100
100
100
100
001
001
001
001
100
100
001
001
001
001
100
001
001
001
001
001
001
001
001
001
001
001
100
100
100
100
100

.3...
..LCJOOONOJ.—b—bu.

~b

A—b

UPPER

c.
7‘
I
7'1
4.

—8

AOU‘IVVU-‘dNNNNIUN-‘kt‘OfiC’tfiOONOONNS‘~$‘£‘1\IOC‘OOm—b-bfi-ILN—DUJLNMMWWU‘ILN

«3.3.3.3 a
mN-bO-JO\nmmmS‘UIJ-‘V~JVODNOJN
...-.5

our)

(ThatbhlihNVVm‘lm‘N \nLnOxnwquoooo
7a

JAtNtN‘.NO~OC)WMWWMMNl/JQNWMM‘AMMPUIWNObeONNNNMMmme-‘mmbl‘fil‘b
A...)

..5

A-JbQ—b-b
..5

IU—JOQOV-‘A‘JVNVO‘VNibmom‘O‘OGONG“O-MUQ‘OO‘OUJN—ON-‘O‘OO‘O‘U‘O‘MWQIOOVOW‘OOO
dun-h

a.)

..5
(V0O-C‘Dm-«bOOUUWLQJWOWUSNW°flVéJM-h-l-DUJV'IMUILN-Q‘OJ‘OOOOONONbbJ‘OJ-‘Ob

...-I
a.)

—b .-g
...)...

”Au—h
.JJW‘NUJO-‘Jth5m3‘WbbNJ-‘NBIO‘O‘U'IO‘O‘U10h§h0NNNNO~O~0090~5§hWWWMM

I.‘ A
“ so.

221

OBSERVED
(CM-1)

2239.996
2240.163
2240.269
2240.326
2240.420
2240.704
2241.015
2242.908
2243.046
2243.196
2243.330
2243.619
2243.771
2243.930
2244.010
2244.507
2244.636
2244.978
2245.102
2245.161
2245.334
2245.495
2245.757
2247.111
2247.208
2247.464
2247.656
2247.727
2248.004
2248.183
2248.499
2248.669
2248.822
2248.980
2249.290
2249.989
2250.511
2250.735
2250.825
2251.160
2251.330
2251.507
2251.999
2252.308
2252.636
2252.896
2253.209
2253.371
2253.371
2253.611

CBS-CALC
(CM-1)

0.010
’0.006
“0.007
’0.004
-0.007

0.006

0.009

0.007

0.001
-0 .001

0.006

0.000
'0.001

0.017

0.003

0.002
-0 .017

0.008

0.003

0.007

0.009

0.009

0.004

0.011

0.003

0.008

0.004

0.005
‘0.006

0.008

0.002
’0.007

0.005

0.000
'0.002
‘0.001
’0.004
-0 .004
‘0.010
‘0.003
'0.006

0.009

0.004

0.000

0.005

3.012

HEIGHT

0.01
1.25
0.01
0.01
0.25
0.25
1.25
0.25
0.05
0.05
1.25
1.25
1.25
0.05
0.01
0.01
0.25
1.25
0.01
0.01
0.01
0.01
0.25
0.05
1.25
0.25
0.05
0.10
0.05
0.01
0.10
0.25
1.25
0.25
0.25
0.25
0.25
‘0.25
1.25
0.25
1.25
0.25
0.25
0.10
1.25
0.25
0.25
0.05
0.01
0.1

so
77
7s
7s
77
80
78
so
as
7s
so
78
77
76
32
so
78
77
so
78
77
76
76
so
82
so
so
73
7s
so
7s
so
76
7s
76
so
82
so
so
78
77
7s
so
7s
so

q
‘1-

so
so
a e

an

,
-

ID

100
100
100
100
100
100
100
100
100
100
100
100
100
100
001
001
001
001
001
001
001
001
001
100
100
100
100
100
100
100
100
100
100
100
100
100
100
001
100
100
100
100
100
100
001
001
001
001
00”
001

UPPER

t...
7‘
I
7‘
+

.8

c.)

...)

«Joa-0000000bebmul-b-hbbwfiVNNOLflmmmm-fipun
"I

«6.;
ad

... —-‘

ub-A
IVCDO‘OOONN-J—DLNIMC)ULNKNLNUJU'IOW‘ON-DA—I-‘dfvlflw

bN|NultA-*UJ-J1N“-F“~t‘POOOORl4‘(\JNPJJ-élflwr't‘OO-Ov-DJ-Jb-DNLNNONP“?##MU‘U‘

10 10
1O 10
10 10
10 1O
4 0
12 9
4 0
4 0
3 2
5 2
8 3
5 2
8 8
6 4
6 4
6 4
11 9
5 2

LOWER
K- K+

.4
‘—

Ad
4‘

....

-3“
O‘QCJO‘COOmUlmVlb-P-D—IUWVINMmNOOOUJO‘U‘O‘O‘NUVOOm

A

...—5.5.:
(NOOUWU'IWONOMJ-‘flOO-A—i—‘A-‘VUJ‘OVV‘O‘C-‘dOONNVO‘ONNfiNO‘VOOKO-INNNNN-ébb

...l

O-*'\l'\l'\1~00-OU~J>UIUI
LNWNIVI‘JObo8‘kmmmmooOONS‘NNNNNU‘MV‘WWMNNWWWMWbM-INUIUIMLII-33*b1UI

222

OBSERVED
(CM-1)

2253.699
2254.044
2254.132
2254.242
2254.761
2255.028
2255.171
2255.311
2255.985
2256.816
2257.122
2257.579
2257.579
2257.806
2258.019
2258.176
2258.344
2259.062
2259.355
2259.448
2259.746
2260.044
2260.352
2260.821
2261.127
2261.260
2261.572
2261.723
2262.038
2262.167
2262.285
2262.358
2262.651
2262.978
2263.157
2263.334
2264.344
2264.521
2264.608
2264.887
2265.230
2265.502
2265.653
2265.789
2266.123
2266.234
2266.396
2266.561
2266.676
2266.792

OBS'CALC
(CM-1)

0.008
0.019
-0.003
0.004
0.004
0.000
0.001
“0.005
0.008
0.013
0.013
0.007
0.004
0.000
0.007
0.019
0.007
“0.004
0.000
0.002
0.012
0.010
0.010
-00016
-0.012
“0.010
0.016
0.009
0.013
0.002
-0.005
-0.00S
“0.007
0.002
0.007
0.007
-0.008
0.007
0.007
'0.004
0.012
0.006
0.006
0.006
‘0.004
“0.003
-0.003
0.003
“0.003

HEIGHT

0.25
0.25
0.25
0.05
0.25
1.25
1.25
1.25
0.05
0.01
0.01
0.01
0.05
0.05
0.25
0.25
0.10
0.01
0.25
0.01
o .05
0.25
0.25
0.25
0.05
1.25
1.25
0.25
0.25
0.01
0.05
0.05
o .25
0.25
1.25
1.25
0.25
0.05
1.25
0.25
0.10
0.25
0.05
0.05
0.25
0.10
0.10
0.10
0.01
0.05

ISO

80
78
80
78
80
78
77
76
80
80
80
78
77
8O
78
78
77
82
80
82
80
80
78
78
76
8C
78
82
80
8O
80
78
80
78
77
76
82
80
80
78
80
80
80
78
77
78
77
76
80

q-

66

ID

001
001
100
001
100
100
100
100
001
100
100
100
100
001
100
001
001
100
100
100
100
100
100
001
001
103
100
001
001
001
001
001
001
001
001
001
100
100
100
100
100
103
100
100
100
100
100
100
100
103

L.

xrlbtrlt‘6‘4"O‘ON(bm‘lln‘0LA‘Ofldkfl\nm&~

if».1)O~O‘O~'D\]O~NLN'-IDUJ 4‘14‘0‘0‘6‘41NlNWOmmW‘lO‘U‘V

OO‘NOLMO I‘J1NWN1‘38‘N3‘I‘U—sAMUMUWn‘hJNOIVPJCALQAUDJW—l-‘Lfltfl—Jlfl—bOh’On'bb5N

00005008‘!»{)8‘0N5u—DN—8NOOOO-J-fid-im“MWVUIKAVUJ-‘(NA—‘écOU1lA\lU1'\I~ON\ONhJNNN

Au.)

0‘0NOVkaDVNJ-‘L’7U'IbmbCOF¢§§OJ‘O~OL‘D'\IO~®bVIbU’IUI'UIOOmN‘Om‘O‘O-L‘OC‘OOO‘UI

OOU‘OWOh’lNU‘bOM-l‘kdt‘hJNt‘hb-l‘buMW-fi-‘lA-‘W3‘DJ“bbd-bL/JM—‘U-A-ALN-‘lflkdtuwb

u-l—fi

0‘OU‘C\fl(WV\nGhA-bmhAfiJ4”fl‘JOCDCDO'fl-*£~#CDO~hCDfiJnHUFUhJNHDCDO~bCDO~mWr-OahdLNUHN-fi

223

OBSERVED
(CM-1)

2267.027
2267.104
2267.590
2267.767
2269.805
2270.142
2270.306
2270.454
2270.551
2270.780
2270.876
2270.934
2271.119
2271.645
2271.832
2272.449
2272.726
2273.011
2273.164
2273.307
2273.494
2274.098
2274.300
2274.391
2274.391
2274.581
2275.214
2376.219
2276.317
2276.411
2276.728
2276.891
2277.059
2277.543
2277.844
2278.288
2278.442
2278.577
2278.801
2278.901
2279.047
2279.047
2279.447
2279.507
2279.595
2279.791
2279.918
7280.145
2280.241
2280.425

OBS'CALC
(CM-1)

“0.002
0.002
-0.005
0.001
0.000
“0.002
0.039
0.007
0.002
0.008
0.006
0.004
-0.012
0.004
0.004
0.002
'0.005
-00006
-00010
0.007
0.017
‘0.003
0.004
0.004
'0.002
0.014
0.001
0.000
0.001
0.000
0.000
-0.004
0.001
0.002
0.005
‘0.007
0.003
0.007
-0000?
'0.009
-0.003
0.002
0.005
0.001
0.003
0.002
-0.011
0.000

HEIGHT

0.05
0.10
0.25
0.05
0.01
1.25
0.01
0.01
0.01
0.25
0.01
0.01
0.10
0.25
0.25
0.01
1.25
1.25
0.05
0.25
0.05
0.25
0.01
0.05
0.25
0.25
0.01
0.01
0.05
1.25
1.25
0.25
0.25
0.05
1.25
0.05
0.25
0.25
0.01
0.05
0.01
0.01
0.01
0.01
0.25
0.05
0.01
0.01
0.05
1.25

ISO

80
8O
77
76
8O
82
77
80
82
80
80
80
78
78
77
82
80
78
80
76
73
82
82
80
80
80
76
80
78
80
78
77
76
82
8O
82
80
80
78
78
77
80
80
80
82
78
80
76
78
77

ID

001
100
100
100
100
100
100
100
001
001
001
001
001
001
001
100
100
100
001
100
001
100
100
100
100
100
100
001
100
100
100
100
100
100
100
001
100
001
100
001
001
001
001
001
001
001
001
001
001
001

UPPER

c.
7‘
I
K
...

(DOG064141-146)?gthJ‘OIU‘O‘nKNUIMVIOLNUJ‘J‘JVVVNUJCDWa'U‘ON‘O‘flVOU‘L‘ONML‘O‘Wbut-JIHLrJfiN-J'Io

JO4.6,ANNN-bmdtvm—xMN—J—IN—bdwwwwtdwwO

lNLfiOWLNOLNNNUJNfl/JOOOOOU‘NNO

o~o\()o—-~a-uc-a-s.ao «sommmmmo-A-bfl'fl\INV-JVVVNVNNUOONQPNObNOO0000510

LOWER

G...
7"
I
K
+

0000OO-C‘btx‘I‘LNt/J‘OLAOO‘O‘Osoo‘OPb‘JWNWWOJOOOOCDWOM‘OO‘00m~q0-u1xj0sm5g~gubb413

kaNNNh'MwbWJ‘dd-J-é-‘OWM-‘d-léd-‘HLNWNLNNwF—sblfloNMONWbJ-‘fibfiwo

mmumw-qmoomomoooooxrummomooommooo-boaowmwwumwumudaaaaw~o

224

OBSERVED
(CM-1)

2280.598
2281.203
2281.481
2281.760
2282.054
2282.199
2282.359
2282.577
2282.719
2282.719
2282.857
2283.016
2283.016
2283.163
2284.641
2284.965
2285.160
2285.270
2285.456
2285.578
2285.775
2286.657
2286.960
2287.275
2288.417
2288.767
2288.946
2288.946
2289.128
2289.128
2290.333
2290.629
2290.782
2291.239
2291.536
2291.855
2292.020
2292.191
2292.446
2292.553
2292.732
2292.877
2293.211
2293.593
2293.766
2293.938
2294.290
2294.290
2294.450
2294.766

OBS'CALC
(CM-1)

-0.003
0.005
0.002
0.004
0.006

-00002
0.002
0 .012
0.002
0.001
0.000

-0 .004

-0.003
0.009

-0 .008
0.009
0.000
0.001

-00009
0.003
0.002

-00003
0.001

-0.006
0.005
0.008
0.002

‘0.005

’0.011

“0.005

“0.009

‘0.008

‘0.008

'0.006
0.012

-0.003
0.000

-0.003
0.004

’0.004
0.006

'0.002
0.004
0.010
0.007

HEIGHT

1.25
0.10
0.01
1.25
1.25
1.25
1.25
0.05
1.25
0.25
0.25
0.25
0.25
0.25
0.25
0.05
0.01
0.25
0.25
0.05
0.01
0.10
1.25
0.25
0.01
0.05
0.25
0.05
0.25
0.05
0.05
0.05
0.25
0.25
0.05
0.25
0.25
0.05
0.01
0.25
0.25
0.25
0.05
1.25
0.25
1.25
0.05
0.05
0.25
1.25

ISO

76
80
82
80
78
77
76
82
82
82
80
80
8O
78
80
80
77
80
80
78
78
82
80
78
80
78
77
77
76
76
80
78
80
82
80
78
77
76
82
80
80
78
76
80
8O

76
77
80
78

ID

001
001
100
100
100
100
100
100
100
100
100
100
100
100
100
001
100
100
100
100
100
100
100
100
001
001
001
100
001
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
001
100
100
001
100
100

UPPER

c...
7‘
I
7‘
....

.qh—ui

OOVO‘X‘OJ‘IJIU‘J‘OUJbl/‘JONOORJIURJO‘ONUIObbmbkfvfl—I—IWF‘OO

-.. _4_.s...;\;-qt\)|q-.s..._sb.¢u;;\..s-a ...b .3paNAmN—h—thwU‘NOhlOOPJONUJBJNW-D-v‘VU‘UJMw

uummmmbmmww'flmwmm-V'q'qmflmbNNmNbNN-‘JU'IONQO~O~$~O~NN£~NNNO~UIVO~NO

muumoo‘OVNNVVinxjoaoomm

LOWER

(—
7K
I
7‘
+

“A

(>o~0(>o~o-V~qaru-qarwcnoomuno:ocn<3vnbssi>bun:w0~ocndLnurV~40~VanumxnUHu-q—xawn04m
.....a—Amwoo«Inna...Ann—abummumumoANO—nomwwowmwOONONwNNwWNOOMbNb

($005-meI‘O\O~O‘$‘O-I-‘b0~0~0~«I‘O‘bmuwt‘UMMO‘ObJ—ldVNUINMUU‘IMLNJVIFO‘UI-bm

225

OBSERVED
(CM-1)

2294.929
2394.999
2295.102
2295.363
2295.690
2295.983
2296.114
2296.292
2296.446
2296.547
2296.637
2296.788
2296.876
2297.075
2297.209
2297.571
2298.553
2298.779
2298.849
2298.849
2298.976
2299.309
2299.818
2299.961
2300.042
2300.132
2300.132
2300.366
2300.617
2300.810
2300.992
2301.160
2301.345
2301.531
2301.706
2301.942
2302.086
2302.177
2302.266
2302.508
2302.852
2303.033
2303.591
2303.910
2304.248
2304.934
2304.934
2305.230
2305.572
2305.742

085-CALC
(CM-1)

0.005
'0.002
0 .008
-0.014
'0.014
-0 .003
'0.010
0.005
'0.004
0.004
0.010
0 .002
-0 .001
0.005
'0.004
'0.003
0.003
0.001
0.009
0.009
0.003
'0.002
0.000
0.001
-0 .001
0.001
-0.003
-0 .006
'0.004
“0.003
0.004
0.013
0.009
0.000
0.001
0.002
“0.007
'0.007
-0 .003
0.009
0.005
‘0.018
0.014
0.000
0.005
0.000
'0.003

HEIGHT

1.25
0.10
1.25
0.05
0.25
0.25
0.25
0.05
0.05
0.25
0.01
0.01
0.05
0.01
0.10
0.10
0.05
0.01
0.05
0.05
0.01
1.25
0.25
0.10
0.01
0.01
0.01
0.01
0.05
0.01
0.25
0.01
0.25
0.03
0.01
0.25
0.10
0.05

0.25

0.10
0.25
0.05
0.05
0.05
0.05
0.01
0.01
0.05
1.25
0.01

ISO

77
30
76
80
80
80
80
80
80
80
78
78
80
78
76
82
80
80
80
82
80
80
80
80
80
78
78
76
78
80
76
78
77
76
80
8O
82
78
80
78
77
80
78
80
80

"r
LU

80_

78
77

ID

100
100
100
001
100
100
001
001
001
001
001
001
001
001
001
001
100
001
100
100
001
001
100
100
100
100
100
100
100
100
001
100
001
001
CO1
100
100
001
103
001
001
001
100
100
100
100
100
001
001
00*

L.

om-q-qmm-amaoobwoooov-banal-10NVNoNo-qoow-qoomoommwmumwmomoooomm

UPPER

7‘
I

7‘
...

AbM\nJ—3dlfl—bw~§NU‘IO~m-OOdN-‘UA‘AL’IU‘OWO—I‘L‘NRIUINMNONNOI‘JO-‘m-‘boC‘I‘OJ

m-iLNLAhJNC'UIOm50mwm¢5NNNbb§fio~§0~bfioo‘t‘ddeO-‘WIIW-‘LN-‘O‘J‘O‘O‘mm

LOWER

c.
7‘
I
7‘
+

O-C-V‘JLNLNPJO‘.NWbWOWOWM§¢§O~VVNO~VO~VmV’VWLNOOINDVLN4\UDS‘HOH‘O‘O‘O’OUION
bbNIULdUJ—bb—bbud-8‘NbLNUIUIWLNUII/JWUUIMU‘WLNMUISNNWNbUIkaflfiNNNU‘IUIU‘U'I1‘ON

INNO‘ONOONWA’MNNV‘IVWNO&N&k#h&FJ#‘NMUINNOJOJAN-‘A-fib-INONJ‘VI-‘F4-9

226

OBSERVED
(CM-1)

2305.937
2306.117
2306.236
2306.589
2306.912
2307.115
2307.539
2307.539
2307.857
2308.275
2308.275
2308.583
2309.086
2309.825
2308.926
2309.420
2309.420
2309.581
2309.581
2310.181
2310.362
2310.850
2310.937
2311.185
2311.309
2311.528
2311.633
2311.968
2312.318
2312.471
2312.906
2313.156
2313.244
2313.506
2314.153
2314.153
2314.424
2314.503
2314.719
2314.786
2315.604
2315.745
2315.960
2316.056
2316.481
2316.805
2317.041
2317.349
2317.989
2318.266

CBS‘CALC
(CM-1)

0.006
0.001
0.000
0.014
0.016
0.010
0.000
0.003
0.003
0.007
’0.003
0.010
“0.004
0.010
0.004
’0.002
0.000
0.005
0.008
“0.008
0.000
‘0.004
0.002
’0.009
0.006
0.005
0.002
0.002
0.004
'0.009
0.004
0.002
‘0.011
-00001
0.010
0.010
0.012
0.002
0.005
0.005
-00002
-0.006
'0.008
0.000
0.005
0.034
0.013

WEIGHT

0.01
0.01
0.01
0.01
0.05
0.01
0.25
0.25
0.10
0.25
0.25
0.05
0.25
0.05
0.10
0.05
0.05
0.05
0.05
0.10
0.05
0.01
0.05
0.10
0.05
0.05
0.25
0.01
0.25
0.25
0.01
0.25
0.05
0.05
0.01
0.25
0.01
0.01
0.05
0.01
0.25
0.25
0.01
0.05
0.05
0.05
0.05
0.10
0.05
0.01

ISO

76
80
82
80
80
77
80
80
78
8O
80
78
80
80
76
78
78
77
77
78
77
78
80
80
82
78
80
78
76
80
82
80
80
80
78
80
80
78
8O
80
80
80
78
78
80

80

”’Q

mm~
mo<

ID

001
100
001
001
100
001
100
100
100
100
001
100
100
001
100
100
100
100
100
001
001
100
100
001
100
001
100
100
100
100
001
001
001
001
100
001
100
001
001
100
001
100
001
100
100
100
100
100
001
001

UPPER

‘-
7‘
I
7‘
4.

4‘ 4‘ F't-VU‘INIW‘J‘O‘U‘O‘OOUlO‘O-J-JJV JINJKNI-‘KNLNO‘PI‘UJPU-JUIO‘O‘J‘J'KR‘OUIU1L'I‘0‘01}‘00‘0

OU4~Dwmr--..IUIu)-—-ht.4;\)LAMNbsz-D-towoooO-buowaN—aN—b—LVVbuumaua-bb..sboo-Aa

FNDNNJ-‘I‘JkfibbbbbNIvbaa—bD-aw-fiLNINUJUJNUJLNKNLNLNUIRJNHULNJ‘U‘IUIUILNUIW..LU'IUI

LDUER
J K- K+

b3‘5‘t-VU1NU1U10-U‘0‘C}(J‘W‘VO‘NNN'VNWNWFMMO‘P-t‘bt‘$‘-$“O\O"\IMU1‘OWVIOO‘O~O"00‘0‘
Nb1UPO‘R’O‘NLNLNNUJLflfimLNJ‘OO-Jm—I-a—tANNdONW—bwddmmmfibV-i-fiV'IMUIUI‘OUJUJ
w-JUI—iJWJMMWUMMW-‘WWNNNMNNNNNNNANNbka-QANNNW“bNN-I‘NO8‘8‘

227

OBSERVED
(CM-1)

2318.602
2318.953
2318.833
2319.191
2319.331
2319.519
2319.676
2319.789
2320.323
2320.517
2320.619
2320.925
2321.074
2321.187
2321.436
2321.708
2322.059
2322.249
2322.423
2322.584
2322.903
2323.244
2323.482
2323.581
2323.581
2323.800
2324.005
2324.151
2324.318
2324.433
2324.643
2324.804
2325.316
2325.650
2325.727
2325.829
2325.989
2326.296
2326.652
2327.034
2327.034
2327.261
2327.377
2327.542
2327.727
2327.838
2328.003
2328.318
2328.474
2328.669

OBS'CALC
(CH-1)

0.009
0.008
-0.001
-0 .005
0.022
0.011
0.005
-0.006
-00004
0.001
0.001
0.005
‘0.006
-0.003
‘0.009
0.006
0.003
‘0.008
0.002
0.003
0.006
0.002
0.006
0.002
-0.006
'0.006
-0.002
-00001
0.005
‘0.002
0.000
0.009
0.004
0.003
0.001
0.001
0.004
‘0.001
0.006
0.008
“0.009
0.004
0.006
'0.003
'0.007
’0.009
0.003
0.002
-0.001

HEIGHT

0.25
0.10
0.05
0.25
0.05
0.05
0.25
0.05
0.01
0.25
0.01
0.05
0.05
0.05
0.05
0.25
0.25
0.05
0.05
0.05
0.05
0.25
0.10
0.01
0.01
1.25
0.01
0.01
1.25
0.01
1.25
0.05
0.25
0.01
0.01
0.25
0.01
0.01
0.05
0.01
0.01
0.25
0.25
0.25
1.25
0.25
1.25
0.05
0.05
0.01

ISO

80
78
78
76
78
77
80
77
78
82
80
80
80
78
80
78
80
76
78
8O
80
80
78
76
78
82
76
80
80
78
80

82
82
80
80
80
78

82
76
80
80
80
78
78
80
80
77
78

ID

001
001
100
100
001
100
100
001
001
001
100
100
100
100
100
001
001
100
001
100
100
100
100
100
100
100
100
100
100
001
100
100
100
001
001
100
001
001
001
001
001
001
001
100
001
100
103
001
100
001

‘—

JRDO‘O‘I‘JO‘OFV'

tNtdek/Jml'fl mmbI“knbkkns)")~m0~m0m\.nx,1mv1mm0c)xub0bNUwaNUInngm-q“

PJ—E—DC-DONUJ-JUIIN-fiuwt‘brvbN5N##53‘0I-JLNO-‘NOwawdtN—A-bumdokMOL‘1‘00

deLflU‘tNLflMWW-‘ww-‘LflwNMNUJNLN‘J-A-i-DOIUWOIUDJONNNNIUNONIUONN-waNNb“

LOHER

J K- K+
3

3

(MbJLplk/Jtnlknlt‘m5‘$‘U1J‘3‘U10\O‘UICBLWO‘WU‘IUIMUINLNO—bw3‘de’UUINUIhJNU'IVNUIO‘O‘UDO~O~J-‘$‘
\NJ-bNdNRDWWS‘WWJ‘WJ-‘O6‘0-8‘0-4‘MMMWONWANMJUNbN¢NéPVdOU10OVIUINN

ONNNNhJNNNOR)NONNdN—bN—9NOOOO'VdN—fi-D-Jfi-‘J-l-‘dd-JJ-‘dUJ-‘OW—I-D

228

OBSERVED
(CM-1)

2328.847
2329.047
2329.276
2329.584
2329.798
2329.798
2329.911
2330.156
2330.350
2330.536
2330.643
2330.723
2330.803
2330.963
2331.107
2331.302
2331.594
2331.787
2331.983
2332.131
2332.224
2332.298
2332.427
2332.560
2332.681
2332.949
2333.221
2333.362
2333.507
2334.277
2334.451
2334.631
2334.701
2334.800
2334.975
2335.242
2335.401
2335.543
2335.668
2335.764
2335.836
2336.023
2336.138
2336.330
2336.686
2336.905
2337.037
2337.262
2337.451
2337.551

OBS-CALC
(CM-1)

‘0.005
0.010
0.005
0.003
0.004

‘0.013

-0 .013

-00011
0.004

-0.003

-00002
0.004

“0.003
0.006

-00005

‘0.004
0.003

‘0.001
0.001
0.007
0.005

“0.003
0.011
0.005
0.000

“0.003

'0.007
0.003
0.008
0.009
0.004
0.012

-0.015
0.003
0.002

-0.004

-00002
0.003

-0.005

-0.001
0.002

'0.006

“0.004

“0.009

'0.005

-0300}

HEIGHT

0.25
0.01
0.25
1.25
0.05
0.01
0.01
0.01
0.25
0.05
0.05
0.25
0.25
0.25
1.25
1.25
0.05
0.25
0.10
0.25
0.25
0.25
0.01
1.25
0.01
0.25
1.25
1.25
0.05
1.25
0.25
0.05
0.25
0.01
0.10
0.25
0.01
0.25
0.25
0.25
0.25
0.25
0.25
0.25
1.25
0.05
0.01
0.05
0.05
0.25

77
76
82
80
80
80
78
78
80
80
82
78
82
80
80
78
77
80
82
78
80
80
80
78
80
80
78
77
76
80
82
78
80
77
78
80
82
80
80
80

‘3'!

to
78
78
8O
80
80
78
78
77
80

ID

001
001
100
100
001
100
100
001
001
001
100
001
100
100
100
100
100
100
100
100
100
100
001
100
100
100
100
100
100
001
001
001
001
001
001
001
001
100
001
001
100
001
001
001
001
001
001
001
001
100

G-

a .3 a
buwo'uuqoom)eivwm—DOO-bOO-AOUJQPJOWQU1IMN\GI\JV£A1ALHOOW4‘4‘r-A-4A4N!\)'\JUIN‘R-bu:

...

-3

UPPER

7‘
I
7‘
+

8‘CbUJCflNLANN-JNNOOOOO‘OCx‘OONO-‘ON‘OJ‘OObOLNQJ-‘V‘NNPJOOOO—fid—bM-‘UI-bw

‘3OA~th-ONwhNONON—0NJNNNNN8‘NIUNNNNNIU-‘J-D-I-‘JdN-‘N-J—h

O—AO-¢OU-‘C)

LOHER

‘-
7‘
I
7‘
+

aha-b

... ...)

a.)

..5
t-VW‘OIULNOGN JR'Mm-fim-‘m-J-‘tfln-bfuoWOUINNMNWUWWWW“F‘b—h-A—I-JNNNWNUINLN

mmNVdNOdOAdmmmmmmONOAONObNNbNNuwMVWbbkddddNNNmdew
dwuaruAamaaaNouowow-aA-s-sN-sN-é—s-a—s-bw-aa-s—aa-s-adooooooo-ao-awo

229

OBSERVED
(CM-1)

2337.867
2338.030
2338.453
2338.691
2338.770
2338.997
2339.317
2339.485
2339.927
2340.252
2340.422
2340.600
2340.899
2341.226
2341.392
2342.654
2342.724
2342.973
2343.492
2343.670
2344.373
2344.433
2344.783
2344.783
2344.980
2345.166
2345.325
2345.569
2345.684
2345.744
2346.029
2346.331
2346.393
2346.513
2346.717
2346.888
2347.069
2347.250
2347.391
2347.574
2348.153
2348.406
2348.477
2348.640
2348.742
2348.821
2348.919
2349.098
2349.211

OBS-CALC
(CM-1)

0.000
0.017
0.001
‘0.007
90.007
0.002
-0.003
‘0.007
-0 000‘
0.007
0.003
-0000?
0.001
0.001
0.004
’0.004
0.006
-0 .005
0.011
-0 .003
0.006
0.007
-00009
'0.006
0.001
'0.006
-0000}
0.005
’0.009
‘0.017
'0.008
0.003
0.001
‘0.025
'0.002
-0 .001
-00023
’0.001
0.010
“0.002

HEIGHT

1.25
0.01
0.05
0.25
0.01
1.25
0.05
0.25
0.05
1.25
0.25
0.01
0.25
0.25
0.10
0.01
0.25
0.25
0.25
0.01
0.01
0.05
0.25
0.05
0.01
0.01
0.01
0.05
0.25
0.25
0.10
0.01
1.25
0.05
0.01
0.05
1.25
0.01
0.01
0.25
0.05
0.10
0.10
0.25
0.25
0.25
0.05
0.05
0.25
0.25

78
80
78
82
76
80

078

77
80
78
77
76
80
78
77
82
80
80
77
76
80
80
80
78
77
78
80
80
78
80
80
76
78
8O
32
78
80
76
78
80
82
80
80
80
80
78
73
78
80
80

ID

100
001
001
100
001
100
100
100
100
100
100
100
001
001
001
001
001
001
001
001
100
001
001
001
001
001
001
001
001
001
001
001
001
100
001
100
001
100
001
100
103
100
100
100
100
100
100
100
100
100

...)
awn-anNVMwourmoooowwoomawmbAVm-quummowmowmuobbt-|mmo~m~omo~c~pm

a.)

UPPER
J K- K+

.3
u‘O‘OMb-JNOO‘“Ot‘bVNVUwN-ifl’w#émmdeNONNONO‘O‘WMWNbJ‘UIUINUIU'IS‘L‘0

O-API'Ut‘dOrdiuN-‘NPULAMLNddO-J-fi—bd—‘IQ—JN-D—‘AO-¥-50'JI\JI"J-|-J-DO-J-*~3Of\fi

LOWER

L.
7‘
I
7‘
+

.3
5N

AVWO\DINV\IOOOC‘OOOOUJLNNCDI‘JLNbOWIWNNNLN‘OUJWOL/JINCX}Pbb'flmmomomo‘k»

~5O‘NDIVNU'IUILN‘OUJWO‘O‘D‘RJNMO-JNU‘JOPbeC-fim—i—lm-‘U‘UINNNO‘WU-fi-‘FO‘53‘Nwm

dN—‘UJW-‘WMLANHWhWDNNWONNNOWNKNNNN-‘NN—DNWMNNN-JNNN—bwAN-l-bfi

230

OBSERVED
(CM-1)

2349.466
2349.662
2350.055
2350.121
2350.121
2350.623
2350.709
2350.825
2351.347
2351.675
2352.274
2352.405
2352.710
2353.041
2353.215
2353.511
2354.066
2354.178
2354.400
2354.564
2354.631
2354.736
2355.251
2355.565
2355.833
2355.965
2356.125
2356.252
2356.299
2356.442
2356.516
2356.603
2356.664
2356.794
2356.961
2357.041
2357.537
2357.653
2357.985
2358.268
2358.465
2358.591
2359.109
2359.463
2360.371
2360.371
2360.431
2360.735
2361.049
2361.249

OBs-CALC
(CM-1)

0.003
0.001
0.007
.00005
0.008
0.006
0.005
0.001
0.000
'0.002
0.001
'0.004
‘0 .008
”0.003
0.014
0.007
‘0.007
“0.021
-00001
-00006
“0.026
0.003
-00015
0.002
-00012
-0000?
0.001
'0.003
0.002
0.004
'0.006
'0.004
'0.006
-0.015
0.017
0.004
’0.010
0.025
0.000
‘0.010
-00012
0.008
0.000
‘0.001
0.012
0.022
“0.004

HEIGHT

0.05
0.01
0.05
0.25
0.25
0.25
0.01
0.25
0.25
1.25
1.25
0.05
0.25
0.25
0.25
0.25
0.05
0.25
0.25
0.25
0.05
0.05
1.25
0.01
0.10
0.01
0.05
0.01
0.01
0.25
0.05
0.25
0.25
0.05
0.01
0.25
0.25
0.05
0.10
0.05
0.25
0.25
1.25
1.25
0.01
0.25
0.05
0.05
0.10
1.25

ISC

80
78
76
80
80
80
77
76
80
78
80
82
80
78
80

80
8O
78
77
78
76
80
78
8O
80
78
80
80
80
80
78
80
78
77
8C
80
76
82
80
77
78
80
78
80
8O
80
80
78
80

ID

100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
001
103
100
001
001
001

UPPER

I...
7‘
I
7‘
+

mm!‘-)O~NO~0‘OC\O\U~IK~IO‘t‘UILNO‘L‘OU‘ILflflfl ~me~O~LrJO~O~wOCONVVOOOONQONN:AOO bbemmM
U1 hmbmbrupbmaomwaoommmwwowbhothWObc-boo—so-aammwuw-qbvo

bb-‘N-‘NPO-NFL/4L4bW‘Jde-b-bw-‘dHUMUJWW—h“[\SLNUUJLHLNPJUJNNNlNNNNUJNN~J

LOVER

L.
7‘
I
7‘
+

com—bom-bomocrmmmms~mmo~b~ommwomo~o~ruo~o~uomVN-Voooo-aoo-a—buoobbromm—q
bW-‘b-‘S‘UINJ‘UIO—smdo~15bdeN-fiCDNWWNWNRIUIOMINMWMOMOO-‘C‘NNNO‘UUO‘
WWOWOWJ‘OWJDJN-‘PNNNJ-‘WNDNO8‘L‘J‘O##Nkflblblt‘hbbdfd-9M5‘MLNLN3‘MNN

231

OBSERVED
(CM-1)

2361.400
2361.577
2361.919
2362.276
2362.583
2362.934
2363.113
2363.362
2363.449
2363.774
2364.110
2364.424
2364.480
2364.757
2365.118
2365.823
2366.165
2366.482
2366.541
2367.302
2367.508
2367.821
2368.048
2368.139
2368.387
2368.747
2369.534
2369.534
2369.629
2369.877
2370.125
2370.333
2370.785
2370.851
2370.912
2370.960
2371.121
2371.183
2371.246
2371.301
2371.481
2371.554
2371.612
2371.783
2371.882
2372.119
2372.235
2372.467
2372.552
2372.656

OBS'CALC
(CM-1)

0.023
'0.009
‘0.014
‘0.010
'0.001

0.000
-0000}
‘0.007

0.009

0.004

0.001

0.004

0.004

0.018
-0 .009
-0.017

0.000
-00011

0.001
’0.007

0.000

0.003
‘0.004
‘0.024
'0.001
'0.016

0.006
“0.006
“0.001
-0001. 1
-0.025
“0.009
“0.004
‘0.004

0.001
'0.008

0.005
.00005

0.001
'0.002
-00015

0.003

HEIGHT

0.10
0.01
0.05
0.25
0.25
1.25
0.10
0.10
0.25
0.25
1.25
0.05
0.01
0.25
1.25
1.25
0.25
0.01
0.05
0.25
0.01
0.01
0.25
0.25
0.25
0.25
0.01
0.01
0.01
0.10
0.01
0.05
0.25
0.01
0.01
0.01
0.25
0.01
0.01
0.01
0.05
0.05
0.10
0.25
0.05
0.25
0.10
0.25
0.05
0.25

ISO

76
80
78
80
80
78
77
80
80
80
78
80
76
78
76
80
78
76
8O
80
80
80
80
80
78
76
80
78
80
78
80
80
80
80
80
80
78
82
78
78
80
82
80
78
80
80
78
78
80
80

ID

001
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
001
100
001
100
100
001
100
100
100
001
001
100
001
100
100
001
100
100
100
100
100
100
100
001
001
100
001
100
001
100
100
100

a)

.3

...—aibm(D0Jadbsntflw‘o.bfflgq\lln\uOPMlN8‘U1LN‘JJNN‘JJI‘J'UWO‘NNWO‘OfibeNNM‘JI—DOOCOOJ

-b-3

mmcsbbbubmumbbwmbmmpaaaa—n-a-aod-AO-a-on—I—htNONNNMut/Juuo bmb

OO‘WKJ‘MVIOOOONMCaCDNW‘JII‘JU’I3‘9Nt‘J‘I‘JNNNNFUNNFNNNbWNNNfibbN'UUT“8‘3‘

«.3

A

.b-LCanO-'llUJbU'ILNfU\Ot‘kflN\l'flfl)\OWWNWWNNdawddWO—b-‘WO‘O##9VVNU‘Im-cb0000m

..5 ..5

LOHER

L.
7‘
I
K
4.

bJ‘WWMWOANOdw-JNAbO-5UJOONQONNOAdo—fi-‘NO—b-‘NU‘NNNNNNUWMWfiU‘
\I‘JO‘O‘OO‘UJUJUJUl—bD‘LAlN-J'blU—bOUJm-JLNU'I—bnbaALA-DAtdm-b-bLNWO‘U-IMMMMMUIWO‘MMU!

232

OBSERVED
(CM-1)

2372.895
2372.991
2373.072
2373.302
2373.909
2374.260
2374.694
2375.028
2375.202
2375.473
2375.840
2376.031
2376.296
2376.528
2376.639
2376.639
2376.741
2376.868
2377.012
2377.012
2377.095
2377.391
2377.391
2377.472
2377.563
2377.873
2378.074
2378.211
2378.211
2378.405
2378.553
2378.923
2379.081
2379.081
2379.306
2379.423
2379.529
2379.529
2379.635
2379.772
2379.772
2379.895
2379.895
2380.310
2381.296
2381.644
2381.824
2382.004
2382.139
2382.476

OBs-CALC
(CM-1)

'0.009
-00001
”0.006
'0.006
-0.005
-00011
0.003
“0.003
‘0.005
-0001“
'0.006
'0.004
0.000
-0.011
‘0.001
-00003
-0.006
0.003
'0.007
-0000?
0.003
0.002
‘0.004
0.002
-0.003
0.001
-00010
“0.004
'0.002
0.007
‘0.004
0.010
0.0110
0.004
0.000
0.013
0.010
‘0.004
0.005
0.000
-0000?
'0.001
0.001
‘0.001
0.007
0.004

HEIGHT

0.05
1.25
0.01
0.05
1.25
0.25
0.25
0.01
0.01
0.05
0.25
0.25
0.05
0.25
0.05
0.05
0.25
1.25
0.01
0.01
0.01
0.01
0.01
1.25
0.25
0.25
0.25
0.25
0.25
0.25
0.10
0.25
0.05
0.05
0.01
0.05
0.10
0.10
0.05
0.01
0.05
0.01
0.05
0.01
1.25
1.25
0.05
0.25
1.25
0.01

78
78
77
80
80
78
8O
78
77
80
78
77
80
80
80
80
82
78
78
78
80
76
76
78

82
80
80
80
78
78
78
80

4“
v".

76
8O
80
80

a
U

76
78
80
73
78
77
80
78
77
76
80
78

ID

100
100
100
100
001
001
100
100
100
001
001
001
100
100
001
001
001
100
001
001
001
001
001
001
100
100
100
103
100
100
100
103
100
100
001
103
100
100
100
103
100
100
100
100
100
100
100
100
100
100

(—

mo bx:bmpmmpboa-honmammow‘omowombebpbmbmbowOWNOmflkn\n_§

(J‘I'UO‘

UPPER

x
I

x
+

ANA-O.AO“ORIONNNONbUJNN’LNIURJW‘NULNLNINbNNm-JN"bNO*NON4033‘HNWUW

J~iJO~lV0~bOfibbl-‘IUI‘UI‘N‘VCPO‘#0411340‘dos40*#MWOUJMWbMMMWMWWJ-‘O‘LHMUJUO‘

L.

UldWiUVIMVLHMWMNWWN-DCNOO‘UO‘OO‘N‘OIU‘ONOWWWOWWWWMPWO‘DO‘NO‘OWVWU!“

LOWER

7‘
I
K
4.

(DOOdOOOOOOONLNONUJIMONNONNNNNNI’UJ‘fi-‘oN-DN4fi-h-aN-haa—hoxja—saab

mgm-Amw\lwmwzn-aaw-aoousomuovmo~40VOVmNNuNNNmNbNO~£~O~N~bLAbO~J~bw

233

OBSERVED
(CM-1)

2382.651
2382.899
2383.271
2383.404
2383.466
2383.720
2384.033
2384.340
2385.237
2385.363
2385.581
2385.757
2385.887
2385.998
2386.090
2386.276
2386.346
2386.458
2386.529
2386.529
2386.712
2386.836
2387.401
2387.568
2387.733
2387.907
2388.079
2388.659
2390.053
2390.129
2390.129
2390.420
2390.481
2390.481
2391.044
2391.220
2391.391
2391.465
2391.595
2391.595
2391.758
2391.980
2392.120
2392.255
2392.317
2392.393
2392.600
2392.748
2393.041
2393.111

OBS'CALC
(CM-1)

0.003
0.004
‘0.008
-00016
‘0.008
“0.009
0.00“
-00002
0.003
0.004
“0.003
-0.001
0.012
0.001
'0.002
0.000
'0.010
0.001
-0.001
0 .007
-00008
0.007
0.001
’0.002
0.013
0.006
0.012
-00005
0.000
'0.009
0.001
0.001
‘0.002
0.006
0.003
“0.012
0.003
0.000
-0.008
“0.008
‘0.003
-O .006
-0000?
0.002
0.013
0.001

HEIGHT

0.01
0.25
1.25
0.25
0.01
0.01
0.01
0.05
0.25
0.25
1.25
0.05
0.25
0.25
0.05
0.05
1.25
0.05
0.05
0.05
0.25
0.25
0.25
0.01
0.25
0.10
0.25
0.01
1.25
0.01
0.05
0.05
0.05
0.01
0.25
0.25
0.10
0.05
0.05
0.01
0.25
1.25
0.05
0.10
0.05
0.25
0.01
0.25
0.01
0.25

ID

100
001
001
100
001
100
100
001
100
100
100
100
100
100
001
100
100
100
100
100
100
001
100
100
100
100
100
100
001
001
100
001
001
100
100
001
001
100
001
001
001
001
001
100
001
100
001
100
001

- 100

uh

A

$\OO‘OL~IOxN‘OtNU‘IO'flknm\nU1O~U10~\lmo‘b-x3L~OOU'IKH~lOO~V\INI‘O~0\JVO‘OL‘b-t‘ulb$~w0001vu1

A.)

#01114 P'NJ-‘h’ f-NU-J'bNUJLNhlnlthth~5R1~DONN«ANObAideLNNfUWNNMLNWMMLNUthNA

1 aminodOdU‘AWO-a‘flflkflwumww\lmU'IUJVLNVm-OVO‘V‘IMUIW‘JNWV‘JNNNOI‘UNOVOC‘b

..8

A

{MCDOVONOIVONb‘Olvt-be‘VIS‘UIOC‘MWOvLNOODNOOO‘VNV‘O‘ON‘O‘OUMWNMMNOa-hb

~.

A

LOWER
K- K+

L.

thNNdN—l-lU—ONN—bNNMMdUl-fiéflé-‘o‘N-‘dN-fib-fi-‘A-‘é—D-‘é-bfilNNNNNNUJOON
O‘O‘ONNVNNNNNNNNNNkoObJ‘NO\Nm$‘OOVOO‘O‘O‘ODODOmm-‘a-I-baa—bm—Ddu

234

OBSERVED
(CM-1)

2393.243
2393.417
2393.815
2394.010
2394.401
2394.655
2394.997
2395.112
2395.355
2395.548
2395.741
2396.394
2396.722
2397.075
2397.075
2397.248
2397.444
2397.636
2397.841
2398.904
2398.904
2398.972
2398.972
2399.042
2399.174
2399.174
2399.301
2399.410
2399.474
2399.614
2399.667
2399.800
2400.166
2400.336
2400.517
2400.696
2400.916
2401.274
2401.514
2401.573
2401.653
2401.843
2401.949
2402.034
2402.142
2402.202
2402.348
2402.839
2403.171
2403.524

OBs-CALC
(CM-1)

0.012
0.010
0.017
0.002
0.002
0.001
-00005
0.001
-0.002
0.006
0.003
‘0.004
0.000
0.000
0.010
-00002
0.003
'0.007
-00008
'0.002
0.012
-0.010
0.002
0.004
0.003
0.007
-00004
-0.010
0.001
-0.004
-00003
‘0.001
0.000
0.003
-00001
0.004
'0.007
‘0.001
0.009
0.000
0.011
“0.001
'0.002
0.004

HEIGHT

1.25
1.25
0.25
0.01
0.10
1.25
0.25
0.10
1.25
1.25
1.25
0.01
1.25
0.05
0.05
0.01
0.01
0.25
0.05
0.01
0.01
0.01
0.05
0.25
0.25
0.05
0.25
0.25
0.01
0.01
0.25
0.05
0.01
1.25
0.25
1.25
0.25
0.25
0.10
0.25
0.10
0.25
0.25
0.01
0.01
0.01
0.05
0.10
1.25
1.25

78
78
76
80
80
82
80
76
78
77
76
82
80
80
78
77
78
77
76
80
8O
82
80
80
80
80
80
80
82
77
78
80
80
77
78
77
80
78
80
80
76
78
78
77
77
76
76
82
80
80

ID

100
001
001
100
100
100
100
100
100
100
100
100
100
001
100
100
001
001
001
001
001
100
001
001
100
001
100
001
100
001
100
100
100
100
103
100
100
103
100
001
100
100
001
100
001
100
001
100
100
103

UPPER

c.
7‘
I
7‘
4.

...}

5:)c~b<38-01)t~ow>C>0Mfl~u<H>I>UHwkn0>DCDP~

..5
mr~J"~)rom.¢LJ-a—au-samomb‘flbsrlldt‘thbthNNgthLQNNIANLNO—AN-fiowwwmmbfvlfi
LN‘n‘fltNUJ'JLNUIVLN‘I‘I‘JVOI)N1NT‘J‘~J‘ANN‘O\')~00‘~JNN\IIU$‘~L‘Nkbt‘offlomONNNNCfi-flo-fi

\AKJ‘JWU‘IVO‘O‘V‘AONOO OOVIOV'I‘OO'JI

LOUER

‘—
K
I
K
...

A
.3

...-8

1a
ndt~bwuru05hibcfithw$C>tflC>awsufiuvo-4-bo«Ac:~aflLa-aoaAHALA_6UHNLNLnqu~0gn_saha.3~qo-qc)

-.b

...-I
4‘00th‘U‘WD14‘U'IO‘Vl'DOC‘MF‘OUIFb-de-‘11MOUJLNO!N\nmwmmmmflflomw5b¥‘mwmw
NUIMNDJ—D#J-fiUJJ—S-i-A-mew-émwwaANAMl/INNUJNNWNRIMNOOOOOMbi‘bNWNw

235

OBSERVED
(CM-1)

2403.978
2404.290
2404.353
2404.844
2405.301
2405.458
2405.554
2405.880
2405.936
2406.100
2406.100
2406.244
2407.006
2407.231
2407.355
2407.523
2407.588
2407.707
2407.893
2408.074
2408.277
2408.689
2408.824
2409.268
2409.473
2409.615
2409.831
2410.147
2410.513
2410.622
2410.765
2410.892
2410.960
2411.288
2412.570
2412.765
2413.254
2413.348
2413.485
2413.607
2413.726
2413.856
2414.061
2414.125
2414.191
2414.274
2414.274
2414.466
2414.660

OBS’CALC
(CM-1)

0.002
0.006
0.005
0.005
0.003
0.002
'0.003
-00019
0.005
-0.004
'0.001
‘0.001
'0.007
'0.008
0.004
0.002
‘0.003
0.003
0.017
'0.004
0.010
0.002
0.004
'0.006
‘0.001
0.001
-0.003
“0.004
0.014
0.002
'0.004
0.006
“0.004
0.002
-00004
0.006
'0.006
0.009
-00022
“0.006
0.000
“0.015
0.004
'0.008
0.004
0.003
0.002

HEIGHT

0.25
0.25
0.05
0.05
0.25
0.25
0.25
0.10
0.05
0.10
0.25
0.25
0.25
0.25
0.25
0.01
0.05
0.05
1.25
0.25
0.01
1.25
0.05
0.05
0.25
0.25
0.25
0.01
0.01
1.25
0.05
0.25
0.25
0.01
0.05
0.25
0.10
0.05
0.25
0.25
0.01
0.05
0.01
0.05
0.05
0.25
0.10
0.05
0.05
1.25

ISO

78
80
76
78
80
77
76
78
82
8O
8O
80
80
82
80
80
82
78
78
80
80
78
76
76
80
80
78
78
99

L; a.

80
80
80
78
78
76
80
80
80
80
80
80
78
78
80
76
77

80
'79

C \-

77
78

ID

100
001
100
001
100
100
100
001
001
100
001
100
001
100
100
100
001
100
100
001
001
001
001
001
100
100
100
100
100
100
001
001
100
001
100
100
‘00
100
001
001
001
001
001
100
001
001
00‘
100
100
001

UPPER

c.
7‘
I
7‘
+

...

A

«I

«I

..5

..5...)
moomoowooooompomoomm»

.3...
“1100-5

..5 ..5
~O€~000

\AUIUIUIUV'QLHVVNIOVNIO‘NObN’flfl)

UlU‘ILNIUIUI-FUIFPUINUIbNLdNb‘IJNO-JhAA-DvIAJAAUIhJNUIN-blfllvt‘l‘fi-FUWbHHbNHJ8‘

J—h

.a
OOtleubNb4‘bbbbfibL‘d‘Ou)'Tiow-aomoamo'3amruoamrJ-Ioorucxwuo...ur)...»:fltguoo

...)

A

.A

8‘“4‘bbDPOOVJ‘WO‘O‘\J10\U1L4100\V03'1J‘0m‘0bOO‘OAbKDO4‘OU1NOUIU1UIMNLMU1NUIU11‘b4

...) c—l

LOWER
J K- K+

PfiWWW'NWWlMS‘N-I‘LHNJ‘NAMNON-AONO#‘NO'DbNNbNKfl-‘NMMWWNIUWNIVUNNIU

4a-JA'JUI-JLNIlNlNUI‘IJW'NLN‘NmtjU‘IV‘JTUOV‘OON‘O-fio0‘00‘O—DN‘O-JNNN—DNNANNNN‘O

236

OBSERVED
(CM-1)

2414.799
2414.859
2415.075
2415.438
2415.570
2415.633
2415.788
2415.900
2415.996
2416.161
2416.350
2416.554
2417.018
2417.079
2417.292
2417.439
2418.794
2417.832
2418.025
2418.430
2419.079
2419.315
2419.443
2419.585
2419.667
2419.789
2419.851
2420.056
2420.133
2420.364
2420.436
2420.644
2420.644
2420.879
2421.217
2421.456
2421.570
2421.570
2421.655
2421.762
2421.947
2422.105
2423.231
2422.316
2422.477
2422.840
2423.434
2423.996
2424.349

CBs-CALC
(CM-1)

0.007
0.003
0.018
0.007
'0.009
0.003
“0.009
0.001
0.004
0.001
0.009
0.014
0.005
“0.006
0.011
“0.002
'0.003
0.013
0.012
0.001
0.006
0.003
-0.00S
O .003
0.001
0.003
0.002
O .016
'0.005
0.009
'0.002
0.016
0.010
‘0.014
0.006
0.007
‘0.015
0.005
-0.006
0.023
‘0.006
“0.008
0.014
0.006
“0.009
'0.005
0.006
0.002

HEIGHT

0.05
0.01
0.05
0.25
0.05
0.05
1.25
0.01
0.01
0.25
0.25
0.25
0.10
0.01
0.05
0.01
0.25
1.25
0.25
0.01
0.25
1.25
0.10
0.10
0.01
1.25
0.25
0.01
0.10
0.25
0.05
0.25
0.05
0.05
0.05
0.05
0.25
0.01
0.05
0.10
0.05
1.25
0.25
1.25
0.01
1.25
1.25
0.25
1.25
0.25

IS?

78

’
I

76
82
80
80
80
78
78
78
77
76
80
82
80
78
80
80
78
77

A“
A!
-

Eo
80
82

q
I J

78
80
77
80
78
80
80
80
77
80
80
77
80
78
76
77

q
I

77

q
(8

r—\
I

.9-

8O
77
8C
:79

ID

001
001
001
100
100
100
100
100
100
100
100
100
100
001
001
100
001
100
001
001
100
100
100
103
100
100
100
100
100
100
001
001
001
100
001
100
001
100
100
001
100
100
100
001
103
001
001
001
100
100

G...

*4 A

...)

~O~J-qo'nth1-xj1nm0‘10110~OOOOO~OVD~1JO~O~O~OO$~0~OJPO~AO~PU!

UPPER

K
I
K
...

A

4.;
N01fl'3414.aw-bm\n‘\lOMWQOWVOUILAV‘OVNONN‘O-QNNANNO

-4.. Ta
“)0

..5
C)

.3
N

10

sqmouu‘uoo.‘ 3.3a-.04¢~m#\nmwt~wbm>4.§'flbAabubdwb-J-ARINNHMNOWMOMNU!
A 7).;
"bO—i-7DIU

J
u). as O U)

LOHER

:—
K
I
7‘
...

—I

«b

MOOOMPmbO‘V‘QmO‘sHVNV\IWOW'QWWW‘OD‘W‘OOMMOMM“
[UNNhJNN-i6‘0(”3‘NO-m#ONI'flbNOIEOOOO'JI—lOOOW-J‘O'JLNJ

DIVOIUI-‘OU1|VONONCJIUMI08‘8‘MWMWO’1U4-5LN«I>-D~O‘.N-3~5UJ1‘~9«¢UIM-§ObddOJ‘fibd-P

2 19
1

20 19
1 11
10 9
11 11
10 9
11 11
10 9
5 0
9 9
8 5
8 7
9 9
7 5
8 5

237

OBSERVED
(CM-1)

2424.719
2425.446
2425.519
2425.725
2425.889
2426.029
2426.090
2426.200
2426.282
2426.390
2426.562
2426.856
2427.221
2427.293
2427.293
2427.594
2427.594
2427.662
2427.662
2427.779
2427.869
2427.869
2427.990
2427.990
2428.069
2428.069
2428.132
2428.250
2428.898
2429.018
2429.209
2429.421
2430.655
2431.042
2431.520
2431.680
2431.875
2432.023
2432.142
2432.383
2432.487
2432.572
2432.854
2433.444
2433.745
2433.988
2434.045
2434.108
2434.294
2434.347

OBS‘CALC
(CM-1)

0.000
0.006
-00004
-0.007
-0.012
‘0.003
0.003
0.000
’0.014
'0.004
0.006
0.003
O .011
0.003
0.006
'0.004
-0.001
'0.007
-0000?
0.003
0.006
0.004
0.016
0.011
0.008
0.006
-00003
0.005
0.006
0.007
0.002
O .011
0.004
0.002
'0.012
0.031
-0.032
-0000?-
‘0.006
0.001
-0.002
0.005
0.008
”0.030
-0.001
0.001
‘0.007
’0.006
0.000
0.001

WEIGHT

0.01
0.05
0.05
0.25
0.05
0.01
0.25
0.25
0.25
0.05
0.05
0.25
0.01
0.25
0.05
0.01
0.01
0.01
0.01
0.05
0.05
0.05
0.05
0.25
0.05
0.05
0.01
0.05
0.25
1.25
1.25
1.25
1.25
1.25
1.25
0.05
0.25
0.10
0.10
0.25
0.25
0.05
0.05
0.05
0.01
0.01
0.25
0.01
0.05
0.01

ISO

76
80
82
80
80
80
78
80
78
78
78
80
78
80
80
8O
80
78
78
80
77
77
78
78
76
76
78
80
82
80
80
78
80
78
80
80
78
80
82
78
80
77
78
80
82
80
80
80
80
78

ID

100
100
100
100
100
100
100
100
100
100
100
100
100
001
001
001
001
001
001
100
001
001
001
001
001
001
100
100
100
001
100
001
100
100
001
001
001
100
100
100
100
100
100
100
001
100
001
001
001
100

UPPER

‘—
K
I
7‘
+

4..“
...-Ion)

«I
M.

-.I A
ab
04-.) ..L-b\nU'|U'lU\m\J‘-|‘OUJ-“OLN—§‘O‘J‘VLN‘ON‘ON-‘NAJOdidNNNIV§¢§5‘8‘6‘6‘fifit‘m

...)
5.!100-‘1n-athN0anxoawwmooVm'xlxlwflxho

.3
p

b .

1

0.4.4.)bUIMUILNLNUJ‘flflde—D'JAQL'I-Jd-bbinLhINUJNNNONO“Pt-FWMMkkoitd‘l‘b'fli‘N

.2
JN

‘

LOWER

L.
7‘
I
7‘
...

4*
A“

A
OxLIIU‘I‘JINJVVOO-flmo~01)O~Ofl~1j)C‘O-F‘VObO.de"JL14'UWUIM\flVC‘VO“JDO“)0‘O~m

.3

.3
«A

J...‘

an.

..s
JQ‘NMNNNNb4‘15“beOUNO'iflhJOmO‘lAIIUOO'.NOJIAIOlIJO-I|ON ¢JQALJBJUM1AMUINL41NV

q)

O‘NOObfiPJ‘wwxflbwPct-Jbfid'ékfl-JAL‘INO‘MNKHNQOaka—3.4“bbthJ‘U‘bLflt‘S‘Wl‘N
a—A-A-h

4.3.41
O-Nww

238

OBSERVED
(CM-1)

2434.441
2434.763
2435.071
2435.139
2435.339
2435.448
2435.609
2435.861
2435.980
2435.980
2436.176
2436.983
2437.356
2437.743
2437.946
2438.181
2438.303
2438.566
2438.649
2438.933
2439.015
2439.091
2439.275
2439.410
2439.639
2439.713
2439.764
2440.111
2440.354
2440.472
2440.654
2440.726
2440.839
2441.029
2441.117
2441.213
2441.298
2441.434
2441.691
2441.831
2442.037
2442.239
2442.470
2442.800
2442.975
2443.632
2443.873
2444.233
2444.685
2444.991

OBS-CALC
(C8-1)

0.006
-0.008
0.018
'0.013
-0.015
0.003
0.004
0.011
0.003
0.005
0.006
0.005
'0.001
“0.004
-00001
‘0.014
“0.006
‘0.003
‘0.002
0.007
0.005
0.002
0.000
‘0.007
0.004
'0.306
0.003
’0.002
0.005
0.000
‘0.003
‘0.001
0.011
0.012
‘0.003
-0.018
-0.001
0.010
0.006
0.012
0.011
0.003
0.003
0.006
0.019
“0.022
'0.004
-0.002
0.001

WEIGHT

0.01
0.25
0.01
0.05
0.05
0.05
0.05
0.01
0.25
0.25
1.25
0.25
0.25
0.25
0.25
0.05
0.01
0.25
0.05
1.25
0.05
0.01
0.10
1.25
0.05
0.01
0.05
1.25
0.05
0.05
0.01
0.05
0.05
0.01
0.10
0.05
0.01
0.05
0.25
0.01
0.01
0.01
0.25
0.25
0.01
0.25
0.00
0.25
0.05
0.01

ISO

78
80
80
78
77
78
80
76
78
80

82
80
78
77
80
8?
80
80
80
78
82
80
80
78
80

q
I-

20
82
82
82
80
8O
80
78
78
so
80
75?
75
77
76
80
78
77
80
82
80
80
76

1‘0

001
001
001
001
001
001
100
001
100
100
100
001
001
001
001
100
100
103
100
001
100
100
100
100
100
100
100
100
001
001
001
00‘
001
001
001
001
100
001
100
001
001
001
100
100
100
001
100
100
100
001

...
N

..s
000

I

,.
D—b

(

.3 .s ....ha-I-ah 4.3-8
~o-ango.a:)a.a.sa

‘OWU'IJO\0(JO’D‘(J‘.’1

'0 O

‘40

0b'fl‘x—haabu'WIFL‘bmbkflbNUIVUO‘~3IV-JONO'J~bObO15‘i‘b‘flbNC)I‘JfULflMMUWO~MWO~‘N

«b

a.

6..

4..

-L

Jc...b-§~b
4UI'U'I'JI-‘1NA‘JN")IU‘\I‘O.U‘OIV‘0‘. J-J‘NU'IL'JUI'IJUIC‘bm-fi4‘950-40070110'30‘m1nmmwm0tfl3

a)

w.

ama.a

(—

ab J-Jgh—h «.344 «l
o\oc>o<3<)~¢o..~¢e.

4..)
000.140

NNb‘Jfl) 4“an

[manaom

LOHER

7‘
I

7‘
+

U1.\\JI£‘Aa-dealflm‘flm1flmww\flflfl\l‘4~‘J-‘4U'IJ-‘JP‘J'IL‘L‘8‘UJJ‘NONN4‘4‘PFPM4‘IUU'IIU

—b

..b
umbumwummm\o-¢N~OU‘IV~JNNN-J~ON-o

.... ~§aI—I-§~§
.hONbNhN“

wfi

.¢.a
n1b3>bwanoc>uman~omxmsm.4000

..5

239

OBSERVED
(CM-1)

2445.294
2445.521
2445.662
2445.761
2445.924
2446.111
2446.476
2446.659
2446.845
2447.188
2447.291
2447.395
2447.458
2447.676
2447.836
2447.970
2448.211
2449.047
2449.447
2449.577
2449.648
2449.790
2449.868
2449.968
2450.148
2450.233
2450.520
2450.596
2450.713
2451.110
2451.183
2451.359
2451.559
2451.614
2451.744
2451.962
2452.152
2452.348
2452.648
2452.750
2452.995
2453.085
2453.560
2453.777
2453.999
2454.166
2454.962
2455.206
2455.352
2455.450

OBS-CALC
(CM-1)

'0.003
0.012
0.004

‘0.003
0.006
0.001
0.904

‘0.001

'0.006

-0.001
0.000

'0.010

'0.001
0.012

’0.031

“0.004
0.017
0.014
0.021
0.009

'0.019
0.020
0.023

“0.003

'0.018
0.009
0.001
0.016

“0.007

' .007
0.022
0.006

'0.019
0.020

-00078
0.028
0.004

“0.014

“0.008

“0.003

“0.004
0.013
0.004
0.017
0.004

“0.012
0.016

HEIGHT

0.05
0.25
1.25
0.01
0.25
0.10
1.25
0.05
0.05
0.05
1.25
0.05
0.01
0.05
0.01
0.01
0.25
0.05
1.25
0.05
0.25
0.01
0.25
0.25
1.25
0.01
0.05
0.05
0.01
0.05
0.25
0.05
0.25
0.01
0.05
0.01
0.00
1.25
0.05
0.01
0.10
0.05
0.01
0.01
1.25
0.05
1.25
0.25
0.01
0.01

ISO

80
80
78
82
78
80
78
77
76
80
80
80
80
78
80
80
78
80
78
80
77
82
76

s
It.

80
82
78
80
77
80
80
8o
78
82
78
8o
76
78
82
so
80
80
77
80
30
78
80
72
7g
80

ID

100
100
100
100
100
100
100
100
100
100
001
001
00‘
001
001
00’
001
001
001
100
001
100
001
100
100
100
100
100
100
100
100
001
100
100
001
100
001
100
100
100
100
001
100
001
001
001
00‘I
001
00‘
100

UPPER

J K- K+

9 4 5

16 1 16
8 7 2

16 1 16
15 1 14
14 3 12
15 1 14
13 3 1O
‘2 5 8
12 5 8
11 5 6
12 2 10
‘0 6 4
‘2 2 10
10 4 6
10 4 6
5 3 3

15 2 13
13 4 9
13 4 9
7 5 2

7 5 2

9 7 3

13 2 11
14 1 13
12 3 9
15 1 15
12 3 9
11 5 7
19 1 18
8 8 0

6 4 2

1R 1 18
6 4 2

10 6 5
16 3 14
15 3 12
15 3 12
7 4 4

6 3 4

9 8 1

6 3 4

6 3 4

14 2 12
14 2 12
‘5 2 14
14 2 12
16 0 16
‘6 0 16
17 2 15

LOHER
J K- K+
8 4 4

15 0 15
7 6 1

15 0 15

1 2 13

1.3 2 11

14 213

12 4 9

11 4 7

11 4 7

10 6 5

11 2 9
9 7 3

11 2 9
9 4 5
9 4 5
4 1 4

14 312

12 5 8

12 5 8
6 4 3
6 4 3
8 7 2

12 310

1 1 12

1.1 3 8

14 1 14

11 3 8

10 5 6

17 0 17
7 7 1
5 2 3

17 0 17
5 2 3
9 6 4

15 2 13

14 4 11

14 4 11
7 1 7
5 0 5
8 8 0
5 0 5
5 o 5

13 2 11

13 2 1

14 2 13

13 2 11

15 015

15 0 15

16 3 14

240

OBSERVED
(CM-1)

2455.564
2455.626
2455.737
2455.943
2456.379
2456.952
2457.081
2457.712
2458.361
2458.704
2459.972
2460.122
2460.504
2460.504
2461.020
2461.406
2462.597
2464.288
2464.668
2465.432
2465.756
2466.113
2466.304
2466.404
2466.499
2466.756
2466.896
2467.052
2467.124
2467.212
2467.330
2467.454
2467.843
2468.094
2468.816
2469.192
2471.012
2471.234
2471.503
2471.591
2471.948
2472.033
2472.402
2472.589
2472.799
2472.973
2473.363
2473.485

DBS-CALC
(CM-1)

0.006
0.031
‘0.026
0.005
0.004
"0.003
‘0.034
'0.011
-00040
-0007?
-0.002
0.016
-0 .001
0.009
'0.005
-0.015
0.000
0.006
“0.013
-0.001
‘0.004
-00002
0.015
'0.908
“0.001
’0.009
0.012
-0.005
0.007
'0.002
-0.003
‘0.CO9
-0 0032
0.005
'0.019
'0.002
“0.003
0.007
0.012
0.004
-00031
0.007
‘0.007
‘0.003
'0.012
0.019
'0.004
0.009
0.018
0.015

HEIGHT

0.01
0.05
0.05
1.25
1.25
0.25
0.01
0.25
0.01
0.05
0.01
0.05
0.01
0.05
0.25
0.25
0.25
1.25
0.25
0.01
1.25
1.25
1.25
1.25
0.25
1.25
0.01
1.25
0.05
0.25
0.10
0.10
0.25
0.01
1.25
0.01
0.25
0.01
0.25
0.10
0.25
0.25
0.25
0.01
0.05
0.05
1.25
0.25
0.05
0.01

159

77
82
8O
80
80
80
76
80

6
L

.80
80
80
78
78
80
78
80
80
80
78
80
78
80
80
80
80
80
78
80
80
80
77
78
76
80
80
80
78
80
82
80
80
78
82
80
80
78

80
78

n
(D

ID

001
100
100
100
100
100
100
100
100
100
100
001
100
001
001
001
001
100
100
100
100
100
001
001
00‘
001
001
001
001
100
100
001
100
001
001
100
100
100
100
100
001
100
100
001
001
001
001
001
001
100

L.

..5

...I -§.b_b-bbb
p1»u0mwu u~10wflknn~O-4-90

1‘ r0
«.71 *0 C'.) ‘0

UPPER

75
I

7‘
...

...)...
iUfUY‘JWtNUUJW-“UIbO‘O‘PO‘

...-b

A

-\JUJ-\JLHOOmtnuJObNhNVOD‘OmO‘OOV-Jtflmmmdvam'fi—bawo00s\nmmw4‘3‘3‘V001N0
LNanvud)b-b1>$~ 0

LA
.3.

-8... A ..5 ...)
OCDWJO 9-

‘J'QOOQWOPU‘O

LOWER
K- K+
6 5
7 3
6 5
6 5
7 3
3 12
5 10
3 4
1 4
2 4
2 I.
2 4
5 3
5 3
5 3
3 10
1 14
1 16
2 15
5 8
1 14
1 16
5 8
5 6
5 8
4 13
1 16
7 4
8 1
8 1
8 1
9 3
9 C
9 0
9 C
4 3
4 3
4 9
2 13
4 9
0 17
2 5
8 3
8 3
8 3
2 17
6 3
2 17
6 3
3 12

241

OBSERVED
(cm-1)

2473.800
2474.037
2474.196
2474.404

'2474.470

2474.530
2475.624
2476.167
2476.167
2476.390
2476.759
2477.120
2477.185
2477.497
2477.799
2478.457
2478.631
2478.716
2478.716
2478.832
2479.018
2479.094
2479.212
2479.575
2479.638
2479.775
2479.869
2480.416
2481.235
2481.636
2481.805
2482.106
2482.770
2483.069
2483.426
2483.644
2484.038
2484.578
2484.683
2484.966
2485.092
2485.295
2486.032
2486.416
2486.611
2488.82?
2483.971
2489.153
2489.262
2489.985

OBS-CALC
(CM-1)

0.002
-0.009
0.000
0.936
0.003
0.011
0.003
0.016
0.005
0.000
0.018
0.010
'0.002
0.001
0.006
0.005
0.011
0.903
0.015
'0.007
0.012
0.010
0.018
0.076
“0.032
“0.029
0.007
0.009
0.006
“0.010
0.019
‘0.016
“0.021
0.023
’0.007
0.014
0.003
0.004
0.010
0.021
0.021
0.029
0.003
‘0.007
“0.007

HEIGHT

0.25
1.25
0.05
0.05
0.01
0.05
1.25
0.25
0.05
1.25
0.25
0.01
0.25
0.05
0.05
0.01
0.01
0.01
0.01
0.25
0.05
0.25
1.25
0.25
0.01
0.10
0.25
0.01
0.25
1.25
1.25
1.25
0.25
1.25
0.25
0.01
0.25
0.25
0.05
0.01
1.25
0.25
0.01
0.05
0.01
0.25
0.01
1.25
1.25
0.05

ISO

80
80
78
77
78
78
77
80
80
82
30
78
82
80
78
80
80
97
80
80
78
80
78
80
76
78
76
80
80
78
77
80
80
78
76

80
80
78
78
80
80
80
78
77
80
80
78
78
80

ID

001
001
001
001
001
100
100
100
001
100
100
100
100
100
100
001
001
001
100
001
001
001
001
001
001
100
001
001
100
100
100
100
001
001
001
100
100
001
001
001
001
100
001
001
001
100
100
100
100

001

UPPER
J K- K+
17 315
8 6 3
9 4 5
8 7 1
19 1 19
19 1 19
8 7 1
11 1o 2
12 8 5
10 9 1
7 2 5
7 2 5
1010 0
17 4 14
‘8 21
19 21.8
19 2 18
20 O 20
9 8 1
9 8 2
7 4 4
8 4 4
8 5 4
7 4 4
7 3 4
8 4 4
8 5 4
7 4 4
7 4 4
10 8 2
1O 8 2
10 8 2
1O 8 2
10 8 2
9 6 7.
9 6 3
9 6 .7
12 8 4
1 8 4
7 6 1
19 4 16
1 4 16
19 416
8 4 s
7 3 5
8 4 5
11 11 1
9 8 2
11 11 1
9 8 2

LOWER

u
7‘
I

...—4.4.5...) ..5... ...—..5 ..5
'orncn~00wo<>c»<3-so'qcnooxro~qo~
4

~04
o-J—omfnma050<r0<30(h\JVC>O~V~00%nu5

...-b-fil‘filv‘wmCDUIUI‘JIVVVVVNNIUM-‘NNUJNUIOONNIUkO-‘dmmom—I-‘U‘JWW

7‘
4-

cu)

.5—2
AQONb—SNMOOI‘JP‘JI‘J‘

Adah—ta
Lit/JDb-fi‘lfltd Q'Nlfl\fl‘.flMmLflU'IUIMU1UJNOVVU‘M

(NOMIOOOWUIUIUIb

242

OBSERVED
(CM-1)

2490.101
2490.257
2490.385
2490.609
2491.005
2491.371
2491.576
2492.115
2492.528
2493.158
2494.241
2494.614
2495.116
2495.588
2495.803
2496.139
2496.582
2496.788
2497.667
2498.173
2498.433
2498.567
2498.666
2498.813
2498.813
2498.949
2499.051
2499.222
2499.642
2499.734
2500.018
2500.310
2500.469
2500.619
2500.808
2501.117
2501.611
2502.970
2503.447
2504.307
2506.063
2506.444
2507.237
2507.590
2507.908
2507.971
2509.022
2509.364
2509.726
2510.070

OBS-CALC
(CM-1)

0.019
0.008
'0.003
0 .008
0.012
-0.002
0.007
0.036
0.014
0.014
0.002
-00003
'0.026
0.003
0.050
0.027
0.036
'0.002
“0.020
-0 .005
“0.006
“0.018
-0.001
0.003
0.007
“0.013
“0.010
'0.008
-0 .003
’0.007
“0.002
-0.011
0.006
0.000
“0.011
0.014
0.029
0.022
0.004
0.005
0.000
“0.004
0.000
-0.003
0.018
0.007
0.014
-0.011

HEIGHT

0.01
0.10
0.25
1.25
0.05
0.05
0.01
0.25
1.25
1.25
0.25
0.25
0.01
0.25
0.01
1.25
0.25
0.25
0.05
0.25
1.25
0.01
0.25
0.05
0.01
0.25
0.05
0.25
0.25
1.25
1.25
1.25
1.25
0.01
0.25
1.25
0.05
0.05
0.25
0.25
0.05
1.25
0.25
0.25
0.01
0.10
0.25
1.25
0.05
0.01

ISO

80
80
8C
80
80
78
76
80
8O
8O
80
7.9
80
80
80
80
78
80
80
80
82
80
80
80
80
78
78
78
76
82
80
78
77
76
82
80
77

80
78
80
82
80
76
8O
80
78
80
80
76
77

ID

001
100
100
001
001
001
001
001
001
100
100
100
100
001
001
001
001
001
001
100
001
100
100
001
001
100
100
001
001
100
100
100
100
100
100
100
100
001
001
100
001
001
001
100
001
100
100
001
100
001

UPPER

J K- K+

11 9 2
11 9 2
9 5 4

9 6 4

9 5 4

8 4 4

8 4 4

8 4 4

3 4 4

13 12 2
13 12 2
13 12 2
8 3 6

9 7 3

8 3 6

8 3 6

10 1O 0
15 10 6
15 10 6
9 4 5

9 4 5

9 4 5

8 3 5

9 9 0

8 3 5

8 3 5

9 9 0

8 3 5

9 9 0

11 8 3
9 9 0

11 8 3
11 8 3
10 6 4
10 6 4
’0 6 4
‘3 12 1
13 12 1
13 12 1
‘3 12 1
13 12 1
9 3 6

9 3 6

8 2 6

9 3 6

9 3 6

8 2 6

8 2 6

8 2 6

8 2 6

LOUER
J K- K+
10
10
8
8
8
7
7
7
7
12 1
12 1
12 1
7

_)-8

—5

..5...
‘°<30<3C>“MDCUNJN'Q‘JW'QODmeS\b~O~J\Hw

V~uxrqoom1400m

...b—l
\flhnU1V‘QOVVC)~OO‘4H%L%~00HNLHC>OLDc)OEACDKHVPUhJNHVDJ#WN$fiGHN

OCDCDOthJOfURJ

”‘17"VVVVVVNNW’Nr‘JV‘V‘U‘“*WF‘NO‘UO‘O‘WOGO‘Omm-AKJ-qbNdaamwmmm1flmwu

243

OBSERVED
(CM-1)

2510.776
2511.079
2511.359
2511.627
2511.921
2512.112
2512.512
2512.711
2512.933
2514.728
2515.038
2515.247
2516.741
2516.959
2517.109
2517.530
2517.773
2519.917
2520.347
2520.519
2520.889
2521.101
2521.262
2521.481
2521.664
2521.878
2521.956
2522.096
2522.723
2522.796
2523.000
2523.235
2523.392
2523.580
2523.948
2524.319
2526.940
2527.415
2527.796
2528.066
2528.299
2529.672
2530.062
2530.177
2530.260
2530.472
2530.579
2530.990
2531.209
2531.435

OBs-CALC
(CM-1)

“0.001
-0.010
0.015
-00010
0.018
0.012
0.004
0.015
-0.007
“0.031
0.005
0.009
0.016
‘0.008
0.012
0.010
'0.016
0.014
0.002
'0.009
0.006
0.009
‘0.009
0.000
0.003
'0.021
0.008
'0.014
0.002
0.002
0.002
0.005
-O.C15
‘0.024
‘0.042
“0.004
-0.073
“0.034
'0.036
“0.008
‘0.005
0.008
’0.007
0.001
0.008
0.005
0.012
0.023

HEIGHT

1.25
0.05
0.25
0.25
0.10
0.05
1.25
0.01
1.25
0.25
0.05
0.01
0.05
0.05
0.05
0.25
1.25
1.25
1.25
1.25
0.25
0.05
0.25
0.01
1.25
0.01
0.25
0.01
0.05
0.05
0.05
0.05
1.25
0.10
0.25
0.01
0.00
1125
0.00
0.00
0.00
0.25
1.25
0.05
0.05
0.05
0.25
0.01
1.25
0.01

ISO

80

8O
80
77
80
78
77
76
80
78
77
80
76
78
76
80
82
8O
80
78
77

fl
’ U

82
78
77

80
7A

4 s.

77
80
76
77
76
80
78

76
97

~’.

80
78
77
76
80
78
82
77
76
80
78
77
76

ID

100
100
100
100
100
001
001
001
001
001
001
001
100
001
100
100
001
001
001
100
100
100
001
100
001
001
100
001
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
001
100
100
001
001
001
001

I 7‘3‘rn‘n'
It 1

mmmwwwwL~g~¢~bbmooo~oo~o~0~oo~bbbbbM\n\flm\nr~JNNNMO~VVV‘AMNMU’IOOO

17.1).04VV 54 qwuq\lufimmmmmmmmmo001010OH)0~1)~O~\J 'JVNVbbbbmmJ-‘WWUIUIVIO

‘-

ab

..5
03000000000130

.34.)
‘0000

...—3...)“;
mvnoam~o<>o50<r9430~o<hoc>o<>c>mcnawwrn<ho<>o~oauwcnmwn

9 .‘~‘

LOUER

7‘
I

7‘
...

kg~pna_;ah;—ha.a.bAC)$“#15F‘¢\AUHA\NKHVDJKHVDJNHV00Rh¢~bdw4~§#%>OH3LRUH)LHDHALNUJO

wuummmmmmmmmmoooooooomwwuwvwflfluflmmmmmWWWMOOMOOOO04

244

OBSERVED
(CM-1)

2532.186
2533.046
2533.423
2533.619
2534.175
2534.586
2534.799
2534.799
2535.017
2535.142
2535.479
2535.671
2536.726
2538.686
2539.060
2539.452
2539.657
2539.870
2541.822
2542.191
2542.575
2542.777
2542.983
2543.125
2543.513
2543.933
2544.148
2544.376
2544.613
2544.980
2545.358
2545.757
2546.257
2546.653
2547.069
2547.281
2547.499
2549.485
2551.191
2551.570
2551.965
2552.175
2552.379
2552.701
2553.104
2553.520
2553.733
2553.890
2554.263
2554.650

DBS'CALC
(CM-1)

0.021
0.016
0.009
0.007
-00010
“0.017
'0.009
“0.020
“0.010
‘0.021
0.002
0.002
0.003
9.006
0.013
'0.001
'0.010
“0.009
'0.007
0.013
“0.005
-0500}
'0.001
0.010
0.001
0.004
0.001
0.003
-00006
-0-015
'0.015
-0.016
'0.014
‘0.011
‘0.008
‘0.006
“0.005
0.002
-0.001
0.013
0.007
0.003
0.001
0.010
0.010
0.006

HEIGHT

0.05
0.01
0.25
1.25
0.25
1.25
0.01
0.01
0.05
0.25
1.25
1.25
0.05
0.01
1.25
0.25
0.01
0.05
0.25
1.25
0.25
0.25
0.25
0.05
1.25
1.25
1.25
1.25
0.25
1.25
0.25
0.05
1.25
1.25
1.25
1.25
1.25
0.05
0.01
0.05
0.25
0.25
0.25
0.25
1.25
0.25
0.05
0.01
1.25
1.25

ISO

80
80
78
77
80
82
77
76
80
78
77
82
82
80
78
77
76
82
80
78
77
76
82
M
73
77
76
82
80
78
76
82
8O
78
77
76
80
82
80
78
77
76
82
80
78
77
82
80
73

ID

001
100
100
100
001
001
100
001
001
100
100
100
001
100
100
103
100
100
100
109
100
100
100
001
001
001
001
001
100
100
100
100
001
001
001
001
001
00‘1
100
100
100
100
100
001
001
001
001
100
100
100

€—

11
11
1o
10
10

A

11
11
11
‘0
1O
10
11
11
11
11
11
1o
10
12
10
971
13
13

1.3
11
11
11
11
12
12

11
11
11
11
11
12
12
10
12
11
11

‘1
11
11
11

UPPER

7‘
I

7‘
1+

lUNNKHMMMONOO‘NM‘N‘NW'fimmO‘OOO‘mommU‘MNWUI45“bWJ‘WWN‘JNVVflbJ-‘t‘mm
~0~O~O ‘NJ‘JVVNJ'U \IVOOO?0030(flh1U1m01010101U10‘U1U1V'QO‘VVVVNVNOOOOWMV‘IMWKJIOOO‘fio

J

10
1O

10
1O
10
10
10

10

LOWER
K- K+

—a.a.-AKNL~JLNWUJOLNU~INNNNNO10‘O~4‘¥‘F-t‘VS‘VV4-Jb-‘4WUJWN1N0OOU’IUIUIU'IU'INNN“b
o(Dcuwcnaamcn<>mcn<roso<roc>o~0~0Nru~domflo~ownooxuxcnaamcnoom~O<DOC>O~0<50vw-u~rfl~q

245

OBSERVED
(CM-1)

2554.853
2555.058
2556.029
2556.440
2556.665
2558.280
2558.671
2559.083
2559.300
2559.522
2561.216
2561.609
2562.038
2563.265
2563.639
2564.036
2564.239
2564.451
2565.189
2565.612
2565.885
2566.033
2566.477
2567.257
2567.619
2567.691
2567.794
2568.094
2568.514
2568.729
2568.963
2569.792
2570.194
2570.599
2572.879
2573.270
2573.669
2573.876
2574.097
2574.892
2575.261
2575.488
2575.664
2577.683
2578.106
2578.331
2578.552
2582.815
2583.204
2583.819

OBS’CALC
(CM-1)

0.008
0.007
0.005
“0.005
0.005
0.007
‘0.009
“0.013
0.001
‘0.004
0.011
‘0.007
“0.005
‘0.007
“0.003
‘0.014
“0.003
0.036
-00006
0.002
0.023
0.018
0.025
0.003
O .017
0.013
0.012
0.026
0.001
“0.006
“0.009
’0.010
0.001
0.024
0.012
0.005
0.003
‘0.001
0.006
0.005
0.001
0.002
0.005

HEIGHT

1.25
1.25
1.25
0.05
0.05
0.25
1.25
0.25
0.25
1.25
0.01
1.25
0.01
1.25
1.25
1.25
1.25
1.25
1.25
1.25
0.00
1.25
0.25
0.25
0.01
0.05
0.01
0.25
1.25
0.25
0.25
0.05

1.25
o 9:

...J

0.05
1.25
0.05
0.25
0.25
0.05
1.25
1.25
1.25
1.25
1.25
1.25
0.05
0.25
1.25
0.05

ISO

77

w
I

80
78
77

82
80
78
77
76
80
78
76
82
8O
78
77
76

82
80
80
78
76
80
78
82
77
8o
78
77
76
82
80
78
82
80
78
77
76
82
80
80
7.8
80
78
77
76
82
80
77

ID

100
100
001
001
001
001
001
001
001
001
100
100
100
100
100
100
100
100
001
001
100
001
001
100
100
001
100
001
001
001
001
001
001
001
100
100
100
100
100
100
100
001
100
001
001
001
001
100
100
100

UPPER

«8534-5 baan~§JJvh.A hu—I

'AWWNNNNNWWWWNNNN (-
N
I
7‘
+

1

a
N

...; ¢..a~b 84344-»...4-» 5..
NNNNWMNNNNNN-ta...

.z
N

t

.5 ....)
U11 4‘

.3 .3—3 5
M‘O'VJNb

L

4.8;..5...a 3-.....3
.L‘bm;‘w4‘6‘bbm

mmb‘bwbmmwmmmmmmuowwwuwbbwhbbbbNNtummmxnb§§be~O~o~O~u1m\nm

~Om1'ut‘IJ-X) O‘OQO‘O'Q‘JVVCIDO) 0000

A

.3
0.1-“01'JU’J‘01D‘10‘0‘O‘0‘0‘0LDOO'O-JOOOODO‘O

.3

A

-.5—3.)» 8.3—5-¢.~b.A-A
f‘uNAOx-l‘;) 4-3-30

LOWER

J K- K+

11 2 9
11 2 9
11 2 9
11 2 9
12 5 8
12 5 8
12 5 8
12 5 8
11 1 1O
11 1 1O
11 1 10
11 1 10
11 1 10
12 4 9
1 4 9
12 4 9
12 4 9
10 0 1O
10 0 10
10 0 1O
11 2 9
11 2 9
11 2 9
11 2 9
11 2 9
11 0 11
12 3 10
12 3 10
11 1 10
11 1 10
11 1 10
11 1 10
12 2 11
13 3 10
‘2 2 11
13 3 10
11 0 11
12 3 10
8 1 7

12 3 1C
14 4 11
13 2 12
13 2 12
13 2 12
13 2 11
12 1 12
‘3 2 11
14 3 12
13 O 13
13 0 13

246

OBSERVED
(CM-1)

2584.483
2584.872
2585.273
2585.697
2586.416
2586.815
2587.030
2587.228
2594.386
2594.769
2595.182
2595.393
2595.616
2595.616
2596.010
2596.412
2596.627
2597.723
2598.160
2598.375
2598.748
2599.150
2599.577
2599.793
2600.037
2605.019
2605.882
2606.299
2608.887
2609.304
2309.734
2610.202
2616.085
2616.509
2616.509
2616.923
2619.833
2620.419
2620.587
2620.858
2636.781
2637.189
2637.618
2638.056
2641.508
2641.779
2641.937
2647.254
2648.122
2648.556

CBS-CALC
(CM-1)

-0.009
'0.006
'0 .007
0.048
0.048
0.058
0.046
'0.011
-0.018
'0.011
'0.001
0.006
0.013
0.010
0.017
'0.003
0.001
-0.005
0.028
0.009
0.003
-0.003
0.017
0.004
-0 .009
‘0.001
“0.003
“0.010
0.004
'0.013
0.006
“0.002
0.009
0.008
0.0C8
0.008
0.008
0.014
-O.CZ1
-0.011
’0.009
0.021
0.005
0.006
“0.005
0.009
0.020

HEIGHT

0.01
1.25
1.25
0.25
0.00
0.00
0.00
0.00
0.01
0.25
0.25
0.05
0.05
0.01
0.25
0.25
0.01
1.25
0.25
0.05
0.05
1.25
1.25
0.05
0.01
1.25
0.25
0.05
0.05
0.25
0.25
0.01
0.25
1.25
0.01
0.01
0.25
1.25
0.25
0.05
0.25
0.01
0.01
0.01
0.25
0.05
0.01
0.05
0.05
0.01

153

82
80
78
76
80
78
77
76
82
80
78
77
76
82
80
78
77

1“
El

78
77
82
80
78
77
76
80
8O
78
82
80
78
76
8O
80
78
78
80
80
80
79
8O
80
78
76
80
80
78
80
80
78

ID

100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
001
001
001
001
001
001
001
001
100
100
100
001
001
00‘
001
100
100
100
100
001
001
001
001
100
100
100
100
001
001
001
100
100
103

UPPER
J K- K+

1!. 311

LOHER
J K- K+

13 1 12

247

OBSERVED
(CM-1)

2652.307

UBS'CALC
(CM-1)

'0.026

HEIGHT

0.01

ISO

10

80 001