ABSTRACT
SIMULTANEOUS ANALYSIS OF THE FIRST POSITIVE

BAND SYSTEM OF N2 IN THE NEAR INFRARED
EXCITED BY A HOLLOW CATHODE DISCHARGE

BY

Lamar E. Bullock

A flowing gas, double-ended, water-cooled hollow
cathode discharge tube has been designed and constructed
to operate in a longitudinal magnetic field. This source
was used to excite the first positive system of N2, and high
resolution spectra of the bands between 1 and 1.5 microns
were recorded.

A non-linear least squares analysis using the existing
theory of the excited electronic A32: and Bsflg states was
made to determine a set of simultaneous constants for the
first positive system of N2. A systematic difference between
the theory and experimental data for the spin-orbit inter-
action energy was found. The effect of this discrepancy
on this analysis and its relationships to previous analyses
are discussed.

Two sets of simultaneous constants and their 95%
simultaneous confidence intervals are given and discussed.
One set came from the analysis of the near infrared data

presented here and the other from the analysis of energy

Lamar E. Bullock

level data found in the literature. The vibrational
dependence of the spin-orbit coupling constant A and the
spin-splitting constant A are calculated for the first time.
Computer programs were written to calculate and identify
the transition frequencies and to perform a least squares
fit of the theory to the experimental data. A complete
description of their function and use is included. The
appendices contain listings of the computer programs and a
complete list of the identified frequencies with their

weights and deviations from the calculated values.

SIMULTANEOUS ANALYSIS OF THE FIRST POSITIVE
BAND SYSTEM OF N2 IN THE NEAR INFRARED

EXCITED BY A HOLLOW CATHODE DISCHARGE

BY

Lamar E} Bullock

A THESIS

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

DOCTOR OF PHILOSOPHY
Department of Physics

1969

To Patricia

ii

ACKNOWLEDGMENTS

I am thankful to Professor C. D. Hause for his guidance
and encouragement throughout the course of this research
projecc. The freedom he has given me to make decisions on
mv own, coupled with his patience and understanding, has
provided a very educational research experience. Professor
J. A. Cowen has been most helpful in supplying equipment
and advice at various times. Discussion with Professors
T. H. Edwards and P. M. Parker concerning various aspects
of this work have been very useful.

The cooperation and guidance of former graduate student
and close friend Dr. Donald Keck, on projects of mutual
interest and responsibility, have been helpful and is
greatly appreciated. I also wish to express my gratitude
to fellow graduate student Richard Peterson for his as—
sistance and advice on many projects. The cordial re-
lationships of all members of the Molecular Spectrosc0py
group have been a great asset.

The staff of the Michigan State Computer Center
have been very c00perative in providing assistance and
facilities necessary for the completion of this work.
Members of the staff of the Glass Shop and Physics machine

Shop, as well as Mr. Mercer of the Cyclotron Shop,have

iii

provided the skill and patience necessary to construct the
equipment described herein and their willing cooperation
has been helpful.

Several undergraduate students, paid on an hourly
basis, have contributed greatly to this project by
assisting in a wide range of tasks from measuring, tabulating
and checking data; to designing, constructing and operating
equipment; also in helping to write, check out and use
computer programs. I am indebted to these students for
their willing and skillful assistance and to the MSU
Breakthrough Research Committee as well as the Work Study
program for providing funds for their support. The
Breakthrough grant was also helpful in providing funds for
the purchase of the necessary supplies and equipment.

The support of my graduate studies through a National
Aeronautics and Space Administration Traineeship is
sincerely appreciated.

The dedication of this thesis to my wife is appropriate
because without her understanding, cooperation and assistance
throughout my graduate education, this thesis would not
exist. Also her patience, care and diligence in the

preparation of the many drafts of this work was invaluable.

iv

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

LIST OF APPENDICES

INTRODUCTION

Chapter

I.

II.

III.

DOUBLE ENDED HOLLOW CATHODE DISCHARGE TUBE
Gas Handling

Electrical Power

Magnetic Field

Initial Discharge Tube

Redesigned Discharge Tube

THEORY FOR THE FIRST POSITIVE SYSTEM OF N2
Electronic Term

Vibrational Term

Rotational Term

A32: Energy Levels

B3Hg State of N2

Selection Rules

Frequency Determination

NEAR INFRARED SPECTRUM OF N2

SHAFT

Page
vii

viii

10
14
19
20
20
20
22
23
25
27
29

33

Chapter Page

III. Cont.

Structure of Data Deck 42

IV. ANALYSIS OF N2 SPECTRUM 54

Linearized Least Squares 55

Analysis Programs 56

Structure of Data Deck 57

Observed Data Cards 62

D3SIG 63
Simultaneous Constants from the Near

Infrared 64
Simultaneous Constants from the Data

of Dieke and Heath 65

SUMMARY AND CONCLUSIONS 77

LIST OF REFERENCES 79

APPENDICES 81

vi

Table

LIST OF TABLES

Experimental Characteristics of the Near
Infrared Spectra

Sample Tabulated Output from SHAFT
1

Simultaneous Constants in cm- for the
A32 State of N2
_1
Simultaneous Constants in cm for the
B3n State of N2
_1
Molecular Constants in cm for the

A52 State of N2 from the Literature

_1
Molecular Constants in cm for the

BJH State of N2 from the Literature

P Branches of the (0,0) Band

Q
R

"U ”0 'U 2310 W

O

Branches
Branches
Branches
Branches
Branches
Branches
Branches
Branches
Branches
Branches

Branches

of
of
of
of
of
of
of
of
of
of

of

the
the
the
the
the
the
the
the
the
the

the

(0,0)
(0,0)
(0,1)
(0,1)
(0,1)
(1,2)
(1,2)
(1,2)
(0,2)
(0,2)

(0,2)

vii

Band
Band
Band
Band
Band
Band
Band
Band
Band
Band

Band

Page

32

4O

66

67

69

70
140
142
144
146
148
150
152
154
156
158
160
162

Table
19.
20.
21.
22.
23.

24.

’U FUD

IO

Branches
Branches
Branches
Branches
Branches

Branches

of
of
of
of
of
of

the

the

the
the

the

(1,3)
(1,3)
(1,3)
(2.4)
(2,4)

(2,4)

viii

Band
Band
Band
Band
Band

Band

Page
164
166
168
170
172

174

LIST OF FIGURES

Figure
1. Gas Distribution System
2. Electrical System
3. Magnet Characteristics
4. Water Cooled Stainless Steel Hollow Cathode
5. End Window and Anode Assemblies
6. End Window-Anode and Gas-Coolent
Feedthrough Assemblies
7. Water Cooled Hollow Cathode
8. Allowed Rotational Transitions from a 3Hg
State to a Eu State
9. (0,0) Band of First Positive System of N2
10. Block Diagram of SHAFT
11. SHAFT Input for Averaging Two Groups
12. SHAFT Input for Calculating and Using
Calibration Constants
13. SHAFT Input for Calculating and Using
Calibration Constants and for Identifying
the Resulting Frequencies
14. Ban Energy Levels for v=4 Lower A-Doublet
15. Ban Energy Deviations for v=4 Lower A-Doublet
16. Deviations from the 13400 Band of PH Reported

by Gilbert

ix

Page

11
12

13

16

17

21
30
35
51

52

53

72
73

75

INTRODUCTION

Hollow cathode discharge tubes have been used as
spectral sources for many years and recently as lasers (1,2).
This thesis describes the design, construction, and testing
of a double ended hollow cathode discharge tube and the
analysis of the molecular spectra excited using this dis-
charge tube. The discharge tube was designed such that it
could be used as an excitation source for gaseous laser
studies.

The hollow cathode source consisted of a cylindrical
stainless steel cathode with stainless steel anodes at each
end. The gas handling system was designed to allow the use
of any gas in either a flowing or non-flowing configuration.
The electrical system contained separate water cooled
ballast resistors for each end and a meter system for moni-
toring the electrical characteristics of the discharge.

End window assemblies were mounted coxial with the cathode
to allow the use of Brewster angle windows for laser appli-
cation.

The first positive system of N2 was excited by the
hollow cathode source and high resolution spectra in the
near infrared were recorded. An analysis of the bands

between 1. and 1.5 microns was performed. The first positive

2

3
system of N2 consists of transitions from the B Hg electronic

state to the A32: electronic state. Extensive analysis of
bands at wave lengths below 1 micron appear in the literature
(3, 4, 5, 6, 7). However, all previous analyses have been
done using combination difference methods. This study
determines the simultaneous values of the molecular constants
and their 95% simultaneous confidence intervals (SCI).
Simultaneous values of the molecular constants means that
set of estimators of the molecular constants for which the
weighted sum of the squares of the deviations is a minimum.
All the vibration bands were fit simultaneously so that the
least squares techniques used gives the best set of constants
for all the bands studied. The meaning of the 95% SCI is:
the probability that all the true constants are within a
range of i SCI of the estimated values is .95, assuming they
were determined from one sampling of a normally distributed
infinite population of similar sets of data.

The molecular model of the first positive system of
N2 is described in Chapter II. This model is non-linear in
the molecular constants; thus, a linearization technique
was employed so that linear regression analysis combined
with an iteration procedure could be used to determine the
molecular constants.

Determination of simultaneous molecular constants in a
model with 26 variables using in excess of 2000 transitions
requires a tremendous number of calculations. One of the

reasons this was not done in the earlier works was that

3
high speed digital computers were not available at that time.
This study required extensive development of computer pro-
grams both for determining and identifying the transition
frequencies and for determining the molecular constants.
Descriptions of these programs and instructions for their

use are included.

CHAPTER I

DOUBLE ENDED HOLLOW CATHODE
DISCHARGE TUBE

A double ended, hollow cathode discharge-tube was
designed and constructed so that it could be used both as
a spectral source and as a laser. The laser application
placed several design restrictions on the discharge tube
which might not be included in the design of a hollow
cathode for use as a spectral source; however, the two
applications were not found to be incompatible. The hollow
cathode was designed to have a continuously flowing gas
system and to operate in a longitudinal magnetic field.

Two different designs were tried. The first was a
very compact, stainless steel, water cooled device with
rapidly interchangeable discharge tubes and side mounted
anodes. Heating problems restricted this design to rela-
tively low current levels. The second design used a cy-
lindrical pyrex vacuum chamber with an axially mounted,
water cooled, stainless steel cathode and end mounted
anode assemblies. Again the system was designed to allow

for rapid interchangeability of the discharge tube.

Gas Handling

The gas was distributed through a manifold system as

5
illustrated in Figure 1. When mixtures were used, the
gas was mixed and stored in a #1A nitrogen cylinder, which
was cleaned by pumping to 10-“ torr for several days. Also
during the process of testing the discharge tube, the cylinder
was flushed several times with ultra high purity helium
at a pressure of approximately 500 torr. During operation of
the discharge, the gas flowed back into the manifold from
the cylinder through a Gilmont 3230-10 flowmeter. The gas
flow from the manifold was controlled by a Gilmont 3235
micrometer capillary valve. The reservoir gas pressure was
measured by means of a mercury manometer attached to the
manifold. The pressure on the input and output side of the
discharge tube was measured using an oil manometer. From
the capillary valve, the gas flowed through the anode, into
the discharge area, and out through the cathode into a
Welch 140 liter/minute Duo-Seal mechanical pump.

The establishment of a stable discharge proved to be
quite difficult. In general, a new discharge tube was very
unstable until it had operated for several hours. It was
also unstable for some time after being exposed to air at
atmospheric pressure. The stability problem was attributed,
at least in part, to the release of trapped gas by sputtering
action in the cathode. This would also explain the decrease
in stability when the discharge characteristics were changed,
as the discharge would then be acting on a different pro-
portion of the surface. Examination of the discharge tube

after several hours of operation revealed a considerable

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7
redistribution of metal, indicating that a great deal of
sputtering occurred.

This problem with stability made a study of discharge
characteristics, with respect to gas parameters, difficult.
However, some general trends were observed. There was a
very broad range from about .5 to 7 torr, over which gas
pressure had very little effect on the output energy. At
lower pressures the energy dropped off considerably; and at
higher pressures, the discharge became unstable. It was
also found that the percent concentration of N2 had very
little effect on the energy output between about 5 percent
and 100 percent; however, the discharge current was slightly
higher at large concentrations, and the stability was not
as good. Argon was also used as a carrier gas. It seemed
to provide a stable operation with a somewhat lower current
and voltage than with helium. However, the excitation of
the N2 first positive system was not as pronounced with
argon. Mixing a small percentage of argon with the helium
had no apparent effect on the discharge characteristics or
the nitrogen excitation; thus it was useful as an internal
calibration standard. An increase in gas flow caused a
momentary increase in output; but this returned to near the

previous value when equilibrium was reached.

Electrical Power
Electrical power-for the discharge was obtained from
five 0-150 volt D. C. generators connected in series. The

output voltage of each generator was controlled by a

8
rheostat in series with the field windings of the generator.
The series output from these generators provided the input
to the electrical system shown in Figure 2. With this
system it was possible to control the discharge current,
both by variations in the input voltage, and by adjustment
of the ballast resistors. The meter system monitored the
total current, total voltage, and the voltage drop across
either end of the discharge tube.

Again the instability of the discharge made it impos-
sible to get reliable plots of output energy, as a function
of discharge conditions. However, it was necessary to have
a total voltage of about 300 volts in order to maintain a
continuous discharge.9 This corresponded to a current of
about .6 amperes. With this and most voltages used, it was
necessary to start the discharge using a hand held Tesla
coil. By increasing the voltage to 650 volts, the current
increased to about 2 amperes. Above this current, excessive
heating of the end window assemblies occurred, and the O-
ring seals failed. There was a slight increase of out-
put with current. The energy output and current also in-
creased when the ballast resistance was decreased from 148
to 111 ohms. Decreasing the ballast also had a detrimental

effect on stability.

Magnetic Field

 

The magnetic field was provided by two air core solenoids.
They were made by winding six layers of Anaconda fiber?

glass coated rectangular copper tubing on an aluminum mandrel

 

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10
and then potting them in thermo-setting epoxy. The six
windings were connected electrically in series, mainly
because of power supply characteristics. However, the
cooling water was fed into each winding in parallel for
maximum cooling efficiency. The size of the tubing was
dictated by what was available, and the length and diameter
of the coil was determined by the size of the discharge
tube with which it was to be used. The additional re-
quirements established in designing the magnet were: a
field of at least 2000 gauss with a maximum current of 600
amps, maximum voltage of 160 volts, and maximum temperature
rise of the cooling water of 60 degrees centigrade. The
requirements indicated we would need the six layers, and
could obtain a 2000 gauss field, with 200 amps and 73 volts,
with the rise in water temperature being about 50 degrees
centigrade. As can be seen from the data in Figure 3,
the actual characteristics of the magnet, especially the
electrical resistance, varied somewhat from the calculated
values. However, the magnets met the nominal requirements

indicated above.

Initial Discharge Tube

 

Components of the hollow cathode discharge tube are
shown in Figures 4 and 5. The stainless steel discharge
tube was sealed into the stainless steel water jacket with
O-ring seals. The four discharge tubes were tested under
various discharge conditions, to find a combination which

‘would produce a stable high intensity hollow cathode

Field (Kilo Gauss)

11

 

 

 

 

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x’ u
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__.—~ " 3
' ' u
'2
0 0 a:
l I T I
0 100 200
Current (Amperes)
Size
Tubing 3/15" sq. l/u" dia. hole
Coil Length 12"
Coil Diameter 81/» " O.D. by 43/. " I.D.

Test results at 200 amps with coils in series

Field 2600 gauss
Voltage Dr0p 96 volts
Inner Wall temperature 45 oC
Outer Wall temperature 36 oC

Exit water temperature 44 oC
Water flow rate 2 gal./min.

Figure 3. Magnet Characteristics

12

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14
discharge. With this setup, the 10 mm diameter tube was
found to be the most useful. The 3 mm and 5 mm tubes became
unstable when the discharge was increased above about 1 amp.
In the 3 mm tube, the silver solder joint, which bonded the
end flange to the discharge tube, failed with a current of
about 1 amp. The instability of these small tubes was at-
tributed, in part, to the large stainless steel surface area
at the end of the discharge tube. The 15 mm tube provided
a very stable discharge; but when the current was increased
to obtain a higher current density in the plasma, the end
window assemblies overheated and the seals failed.

The end window assemblies were made from 19 mm 0. D.
quartz tubing, with a 15 mm Salv-Seal quartz joint sealed
into the tubing as a side port. A window was attached to
one end of this assembly using sealing wax. Silicone 0-
rings were used in the 3/4 inch Veeco quick couplings,
which sealed the end window assemblies to the discharge
tube. Silicone was used because the discharge heated the
quartz tubing above the melting point of butyl rubber.

The anodes were water cooled stainless steel cylinders
machined to seal into the 15 mm Salv-Seal joints. The

anodes were symmetrical so that the other end of the cylinder
would fit into another Salv-Seal joint for connection to

the gas handling system.

Redesigned Discharge Tube
In order to eliminate some of the problems with stability

and heating, which were encountered with the original

15
design, a new discharge tube was designed and constructed.
The vacuum chamber was a 4% in. O. D. by 4 in. I. D. by
28 in. long pyrex cylinder. Two holes were drilled in the
walls of this cylinder for entrance and exit of the gas. A
18/7 stainless ball joint soldered into a brass flange was
epoxied to the wall around one of these holes for connection
to the vacuum line.

A more complicated assembly for handling cooling water
and gas inlet was epoxied to the wall around the other hole.
This assembly, shown in Figure 6, consisted of a double
walled cylinder. The outer section was Split axially into
two sections, to handle both water inlet and outlet. The
outer section was again terminated by a 18/7 stainless steel
ball joint for connection to the gas handling system. The
water cooled discharge tube, shown in Figure 7, was attached
to this assembly by means of a double O-ring seal.

The fine ground ends of the pyrex cylinder were sealed
with water cooled stainless steel flanges, which also
acted as anodes. These anode assemblies had an axially
mounted stainless cylinder, terminated at Brewster's angle,
for mounting an exit window by means of an O—ring seal.

The magnets were designed to fit over this assembly, pro-
viding an axial magnetic field.

Two water cooled discharge tubes were available for
this apparatus. They consisted of a 25 mm 0. D. outer
cylinder, and either a 8 mm or 15 mm I. D. inner cylinder.

The end flanges connecting these two stainless steel tubes

16

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18

were sealed with high temperature silver solder. However,
the intense discharge vaporized the solder and produced a
metal vapor arc when the joint was left unprotected. Fuzed
quartz shields were designed to slip over each end of the
discharge tube. These quartz pieces were about 18 inches
long and protected the stainless steel tube inside and out,
for this distance, on each end.

With this design, it was found that a magnetic field of
about 2000 gauss was required to maintain a stable discharge.
Stable discharges in argon, helium, N2, and mixtures were
obtained with currents up to 10 amps. Instability was a
problem at higher currents. Other characteristics of the
discharge were much the same with this setup as with the
former one, except no heating problems were encountered with

the present operating currents.

CHAPTER I I

THEORY FOR THE FIRST POSITIVE
SYSTEM OF N2

Born and Oppenheimer (8) have shown that, to a good
approximation, the energy of a diatomic molecule can be
expressed as the sum of electronic, vibrational, and roe

tational energies, viz.,
E = E + E + E .
e v r

Even when this is not sufficiently accurate, additional terms
can be added to account for small interactions between the
electronic, vibrational, and rotational motions.

The first positive system of N2 consists of transitions
between two excited electronic states, the upper state being
the Bang state and the lower the A32: state. A theory for
these states was first presented by Hebb (6) in 1936.

Several other authors (9,10,11,12) have reported theoretical
models of these states. The model used in this study, to
determine numerical values and 95% confidence intervals of
all the molecular constants, was based on the work of Schlapp
(12) for the 32 state and that of Hebb and Gilbert (10) for

3
the H state.

19

\’ ‘

20

Electronic Term

 

The electronic energy of an excited state is given by

Te1 = TO + AAZ

where To is the electronic energy measured from the ground
state of the molecule and AAZ represents the spin-orbit
interaction energy for multiplet states. A is the component
of the electronic orbital angular momentum along the inter-
nuclear axis, and Z is the component of the spin angular
momentum along the internuclear axis. Since the spin-

orbit interaction energy is not completely independent of
the rotational state, it will be included in the rotational
energy expression. Thus, the electronic energy To will be

considered simply as an additive constant for each state.

Vibrational Term

 

The vibrational energy is given by (13):
2 3 u
G(v) - we(v+%) - wexe(v+k) + weYe(v+k) - weze(v+k)

where wexe’ weYe’ and weze are small constants to allow for
the anharmonic character of the molecular vibrations.
Rotational Term
3 3
The A 2: and B Hg states have different rotational

3
energy expressions. Each rotational state of the 2 state is
split by the spin-rotation interaction into three closely

spaced but not equally spaced levels as shown in Figure 8.

21

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22
3
In the H state the spin-orbit interaction splits the state
into three states designated by 0 = 0, l, 2 separated by
_1
approximately 40 cm . In addition, each of these states
is split into two levels by A type doubling, also shown in

. 3
Figure 8. Thus, for each value of J in the H state there

are six energy levels.

3
A 2: Energy Levels

 

The formula for determining the spin-split energy
levels of a 32 state as developed by Kramers (ll),and
later by Hebb (5) appear to fit observed data quite well
for large K values. Schlapp (12) reported a more accurate
formula, which takes into account the fact that the rotation
does not completely decouple the spin from the axis of the
molecule. Schlapp showed that this gave excellent agreement

with experimental data. The energy levels are given by:

I
>1
I

F1(K) = BVK(K+1) + (2K+3)Bv

2 2 2 g
_ + +1
[(2K+3) BV + AV ZAVBV] Y(K )

F2(K) = BVK(K+1)

xv +

2 2 2 1% K
[(ZK-l) BV + AV - ZAVBV Y

F3(K) = BVK(K+1) - (2K-1)BV

where F1, F2, and F3 refer to the levels with J = K+l, K
*
and K—l respectively, and where A and y are constants.

Assuming that the effect of centrifugal distortion on the

 

* For K = 0 the sign in front of the square root of F3
must be reversed.

23
spin splitting will be negligible, we modified the above
equations by adding a centrifugal distortion term DvK (K+1)2.
A rotation-vibration interaction is implied in the above
equations by the subscript v. The explicit vibrational
dependence of the rotational and spin splitting constants

is given by:

2
EV = Be - aB(v+%) + BB(V+%)

Av = Xe - ax(v+k).

Combining the above equations into a single equation (where
the possible subscripts of F are indicated by the letter N)

we obtain:
2 2 }
FN(K) — BVK(K+1) - DVK (K+l) - (N-2){(2K+(s-2N) BV +
, 2 2 2 1% +
[(N-2)lv- (2K+(5-2N) BV + 1V - 213v (K+l.5 - .5)yV

as the complete description of the rotational energy levels

3
of the A 2 state of N2.

3
B H State of N2
___2

 

The B3H state of N2 is a state with coupling intermediate
(15) between Hunds cases (a) and (b). Hill and Van Vleck
(16) have considered the general equations for-intermediate
coupling of multiplet states. Hebb (6) used their work to
study 3H - 32 transitions and developed a formula for the A-
type doubling in 3H states. This work was extended by Gilbert

(12) to include centrifugal distortion terms. He specifies

24
the apprOpriate Hamiltonian as the real symmetric matrix

*
with elements

H(H0;H0) = BV[J(J+1)+1] - AV - D[J2(J+1)2 + 6J(J+1) + 5/3]
H(H1;H1) = BV[J(J+1)+1] - D[J2(J+1)2 + 8J(J+1) + 2/3]
H(H2;H2) = BV[J(J+1)-3] + AV - D[J2(J+l)2 - 2J(J+l) + 17/3]
H(H1;H0) = H(H0;H1) = [av - 2D{J(J+1) + 1}]{2J(J+1)}is
H(H2;H1) = H(H1;H2) = [BV - 2D{J(J+1)—l}]{2J(J+1) - 4}’5
H(H2;H0) = H(H0;H2) = -ZD{J(J+1)-2}l’{J(J+1)}l5

A similarity transformation on H is then performed to obtain

the diagonalized Hamiltonian HD'

Here the diagonal elements of H represent the energy levels

D
3 0

of the H state not including the A-type doubling. Let us

again designate them by F1, F2, F3 corresponding to the

Ho, H1,H2 states. Hebb shows that the A-type doubling shift

of energy level F can be expressed in terms of the matrix

I
elements of the transformation matrix as:

2 %
AVI = C0 S(HO;HI) + C1[2J(J+1)] S(H1;HI)S(H0;HI) +

2
C2{J(J+1)S(H1;HI) + 2[(Jsl)J(J+l)(J+2)]%S(H2;HI)S(H0;Hi)}

‘where C0, C1, C2 may be treated as empirical constants.

 

* The sign of the centrifugal distortion terms has been
changed to conform to modern convention.

25
3 I I I 0
Again as in the E state the v subscript implies a rotation-

vibration interaction which is explicitly given by:

B

2
v Be - aB(V+%) + BB(V+%)

A

2
v Ae - aA(V+%) + BA(V+%) .

3
The complete rotational energy of the B H state is then
given in terms of the eigenvalues of the energy matrix

and the A-type doubling as:
FI(J,V) i %AVI(J,V).

Selection Rules

 

In order to determine which transitions from the 3H
state to the 32 state will be observed, we must consider
the applicable selection rules (17). In the absence of A-
type doubling, transitions from any of the 3H states to
any of the 32 states are allowed as long as the selection
rule on total angular momentum AJ = 0, i1 is not violated.
This results in a total of twenty-seven allowed branches.
These will be designated as R

and PI corresponding

IN' QIN’ N

th

3
to AJ = +1, 0, -1 transitions from the I H level to the

3
th 2 level. The question still remains, which of the A-

N
3
doublet levels of the H state is involved in a given trans-
ition.
The two components of the A-type doublet have different

symmetry with respect to reflection at the origin. The

lower energy component of the A—type doublet is +(-) when

26
J' is even (odd). For the A32: lower state, the even
numbered (K) rotational levels are positive and the odd are
negative. Since transitions between states of the same
symmetry are not allowed, it is possible to determine which
component of the A-type doublet is to be used in each tran-
sition. If, for example, K is even, then we have a positive
32 state and need a negative 3H state; thus, we use the upper
(lower) component of the A-type doublet, if J' is even (odd).
The reverse is true for K odd.

In addition, since N2 is a homonuclear molecule, a
rotational state is either symmetric or antisymmetric with
respect to interchange of the identical nuclei. For a
given electronic state, either the positive rotational levels
are symmetric and the negative are antisymmetric throughout,
as is the case for the BSHg state of N2; or the positive are
antisymmetric, and the negative are symmetric, as is the
case for A32: state of N2. Since the nitrogen atom has a
nuclear spin I = 1, the total nuclear spin quantum number of
the molecule (T) can be 2, l or 0, i.e., the corresponding
statistical weights are 5, 3 and 1. The even T values
correspond to symmetrical states and the odd T values to anti-
symmetrical states, thus, the probability of the occurrence
of the two states is in the ratio 6:3. Therefore, alternate
rotational lines appear with an intensity ratio of 2:1.

(Herzberg (18) gives a more complete description of intensity

alternation.

27

Frequency Determination

 

Using the energy expressions and selection rules
established above, it is possible to obtain a single
expression for the observed transitions in the first
positive system of N2. Standard spectrographic notation
will be used to identify the quantum dependence of each
transition. Let X denote either R, Q or P for AJ = +1,
0, -1 respectively. Let I = 1, 2, 3 represent the three
triplet states for the upper (3H) level as discussed above,
and N = l, 2, 3 represent the triplet states of the lower
(32) level. K =-K" is the rotational angular momentum
quantum number of the molecule in the final state. Thus,
using single prime to represent the initial state, and
double prime to represent the final state, a complete
expression for the transition frequency in terms of the

energy relationships develOped above is given by:
I
f<xIN(K,v',v">) = FI'<J'.v') + %(-1)K+J AvI<J'.v') -

FN"(K",V") + G(v') - G(v") + v0

where v0 To' - To". Since I is l, 2, 3 for J' = K' + 1,

K', K'-l respectively, we have for the upper level:

J'=2_I+Ko

In the same manner for the lower level,

J"=2_N+K"'

28

and since

we can write

CHAPTER III

NEAR INFRARED SPECTRUM OF N2

Data Acquisition

 

The Spectra of the N2 first positive system between
1 and 1.5 microns were excited in the first of the two
discharge tubes described in Chapter I. They were recorded
using the Michigan State University high-resolution near-
infrared vacuum Spectrometer. Details on the construction
of the instrument have been given elsewhere (19, 20, 21).

The spectra obtained with this instrument were recorded
on a dual pen strip chart recorder. One pen recorded the
infrared spectra, and the other recorded Edser-Butler bands
of visible 1ight——in a higher grating order-—from an etalon
with fixed Spacing incorporated in the spectrometer. Fre-
quencies are determined by a linear interpolation between
calibrated interference fringes (22). In order to calibrate
the fringes, it was necessary to know frequencies of at
least two lines in the infrared spectrum. In practice it
is desirable to do a linear least squares fit, using a sub-
stantial number of calibration lines. In the present work
argon lines were used for calibration. A computerized
Iprocedure for performing this calibration is described below.

Figure 9 shows an example of a high speed run of the

29

30

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com

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mo

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mam

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53

a
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o.
co

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00

 

 

 

ed

 

 

 

 

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a co m 3.01

 

 

o1

31

(0,0) band with the grating turning at one degree/minute.

At this speed it is possible to see the overall structure of
the band and the positioning of some of the calibration
lines. The high resolution infrared spectra were recorded
in the first order with the grating turning at .01 degrees/
minute and the paper moving at 4 inches/minute. Thus,

some of the charts were as long as 40 yards. These spectra
were photographed in 15 inch sections using a 35 mm Nikkon F
camera with a special minimum distortion copying lens. The
photography was done on a specially constructed copying
stand where the camera was rigidly mounted in such a way
that the plane of the chart paper and that of the film

were parallel. Bulk loaded high contrast copy film was
used.

In order to accurately determine the position of the
infrared lines with respect to that of the fringes, the
position of the fringes and infrared lines were measured
on a Hydel semi-automatic digitized film reader, connected
to an IBM 526 printing summary card punch. This instrument
punches x—y coordinates of any desired point on the film,
to an accuracy of one micron. The line positions measured
in this way were then converted to frequencies by the
computer program SHAFT, described below.

The region from 1 to 1.5 microns contains the (0,0),
(0,1), (0,2), (1,2), (1,3), (2,4) bands. This was broken
up into three subregions as shown in Table 1. Three

calibrated runs of each subregion were made so that the

32

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33

observed frequencies could be averaged to reduce experimental
errors. Because of difficulities with the Hydel system,

and to guard against large random errors by the Hydel Oper—
ators, each record was measured twice, usually by different
operators. Thus, there were from two to six measurements

of each frequency depending on whether or not it appeared

on all three charts. The tabulation and averaging of these
multiple measurements was also performed by SHAFT as described

below.

TEES.

This program was specifically designed to be applicable
to the work performed in this laboratory. Its purpose is
to perform, as completely as possible, the task of reducing
raw Hydel data to a tabulated output of the identification
average fringe number, weighted average frequency, weighted
standard deviation, individual measurements and coded
weights, for up to eight measurements of each line in a
band. In addition, the program generates the frequency and
quantum dependence inputs for any of the many analysis
programs used in this laboratory. The general concept for
forming this program was to minimize Operator inputs, but
at the same time, to cover all possible Options the operator
might desire with the maximum data capability and the
minimum time requirement. Quite obviously, the final outcome
was a compromise among these goals. The versatility of
tasks was accomplished by means of a list of option para-

meters. Overlays and large multi-purpose variable dimensioned

34

data blocks increased the data capabilities. The run time
was minimized by ordering of the data, so that repeat
searching was kept to a minimum, and also by careful planning
of the sequence of operations.

Figure 10 shows the overall structure of the program.
The main program SHAFT is a driver program which contains
the required common storage blocks, and controls the overall
operation of the program. Program IDENTIFY reads in and
stores information for identifying the measured frequencies.
-ThlS information can be used for calibration purposes, as
well as for identification. SCAN is a program (written by
M. D. Olman (23)) that uses line positions measured on the
Hydel, to determine the positions of the spectral lines
relative to the fringes. AVFRQ is a tabulating and averaging
program. It takes lists of information provided by the other
programs or read in directly, and performs the necessary
weighted averaging. Subroutine IIDENT compares the average
frequencies to the identification list. Function CWT converts
the code weights to actual weights. Program SEARCH reads in
two or more initially identified calibration lines, and
using fringe numbers generated in SCAN along with calibration
data read in by IDENTIFY, calculates initial values of the
calibration constants. These constants are then used to
convert the remaining fringe numbers to frequencies. As
each frequency is formed, it is compared to the calibration
data to locate additional calibration lines, which are then

used to update the calibration constants. When all the

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36

calibration lines have been identified, CALFIT is used to
obtain final values of the calibration constants, as well as
statistics of the linear fit. This gives a very general
description of the program function. The details of how
these Operations were accomplished, will be given in the
following paragraphs.

AS indicated, the main program SHAFT is a driver
program which controls the Operations to be performed.
It reads in* the option card which contains the required
control information and.search tolerances. It also contains
the overlay calling sequences which are executed according
to the input control information, and the common storage
blocks which are used by more than one overlay.

Program IDENTIFY reads in a l6-character identification
and a frequency for up to 2000 lines.~ If the grating
order in which these are to be used, is different from that
in which they were measured, information must be entered
to convert them to the same order. Both orders are assumed
to be 1 unless input otherwise. This input identification
material may be used for either calibration, or identification,
or both.

SCAN, in its present form, is a modification of the
version reported by Olman. Even though some modifications

have required additional inputs, the present program contains

 

* Input formats for all inputs are described at the end of
this chapter.

37
options such that data measured prior to these revisions,
can be processed along with the new data.

The first card read by SCAN contains the Operators
name, and an indication of whether NEW SCAN or OLD SCAN
procedures are to be used. All data cards produced on the
Hydel machine contain six pairs of x-y coordinates, each
followed by a code-weighted number. At the end of each
card is an operation code and frame number, followed by
an unread nine column identification field.

Data read into SCAN allows it to correct the position
measurements for the separation between the I-R and fringe
recording pens, and to rotate the position measurements
from the Hydel reference frame to the chart reference
frame. If the fit of the rotation data for any frame is
in error by more than 10 microns on the film, or the
rotation angle is greater than .005 radians, a warning
error message is printed out. The fringe position of each
I-R line on a given frame is found by performing a linear
interpolation between adjacent fringes. If calibration
constants have been input, the fringe number will be
converted to frequency by a linear calibration formula.
Any fringe separations in a given frame, which differ
from the average separation for that frame by more than
10%, will cause a warning error to be printed out. Fre-
quencies calculated by SCAN can be punched out for later
processing by SHAFT and/or can be stored for immediate

processing.

38

Program AVFRQ orders and tabulates frequencies sup-
plied directly from SCAN and/or read in separately from
punched frequency cards. If for some reason the calibration
constants have been updated since the punch frequencies
were generated, it is possible to read in the new constants
and the old constants, so that all punched frequencies
read in after the old calibration constants will be changed
to the proper value for the new constants. Also Change and
Delete cards may be read in to change incorrectly measured
frequencies, and to delete unwanted frequencies. Up to
10,000 frequencies can be handled; and by the use of variable
dimensions of the frequency and weight storage areas, these
can be distributed in from one to eight groups. In each
group these frequencies are ordered from lowest to highest,
which is the normal order in which they are generated from
SCAN. This is done to simplify the following search and
averaging procedures and to make for an orderly output.

Measurements within a single group, which differ by
less than TOth are assumed to be duplicate measurements
of the same spectral line and are averaged. Measurements
from group to group which differ by less than TOL2, from
smallest to largest, are assumed to be duplicate measurements
of the same line, and a weighted average is performed.
Function CWT contains a weight-code correspondence table

in which the code-weight of each line is looked up to

 

* TOLl, TOL2, TOL3, and TOL4 are tolerances input by the
user as specified at the end of this chapter.

39

determine that line's weight. If an identification of the
line is desired, subroutine IIDENT compares the average
frequency to the ordered frequencies read in by IDENTIFY,
until a frequency with TOL3 of the measured value is found,
or until the identified frequencies are larger than the
measured value. If a match is found, the identification is
printed out along with the tabulation of the average frequency,
approximate fringe number, weight, standard deviation of
average minus individual measurements, individual measure-
ments and code weights as shown in Table 2. If desired, the
identification, average frequency and weight are also punched
out for later use. If no match is found, the tabulated
information minus the identification is printed and the
identification search is started, with the last line checked
the next time IIDENT is called. By using this method, it
is necessary to make only one pass through the identification
list. In addition to the tabulated list, AVFRQ calculates
statistics, such as weighted standard deviation of average
minus individual frequencies, and weighted average deviation.
These values are printed at the end of the tabulation of
frequencies.

SEARCH performs the nearly-automatic calibration of
the infrared lines. It is used in conjunction with SCAN,
IDENTIFY, and AVFRQ to determine the calibration constants,
which are then used to convert the fringe numbers from
SCAN to frequencies. The tabulated output from AVFRQ

then shows the prOperly identified calibration lines.

40

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41
Initially, a minimum of two calibration lines must be
correctly identified. The identification, exactly as it
appears on the calibration deck read in by IDENTIFY, and the
approximate fringe number (i.e. i TOL4), is then read in
as an initial identification. SEARCH orders these fringe
numbers and compares the identification to those in the
calibration deck until a match is found. Then it searches
the averaged fringe numbers from AVFRQ until a match to the
input fringe number is found. Using the calibration
frequencies and the averaged measured fringe numbers of the
initially identified lines, a least squares linear fit is
made to find initial values of the calibration constants.
These constants are then used to convert the average fringe
numbers to frequencies which are compared, one by one, to
the input calibration frequencies, to identify additional
calibration lines. Each time a new calibration line is
found, the calibration constants are updated and the search
is continued. When the end of the list is reached, all
calibration lines, for which the average measured value is
not within TOL3 of the input value, are rejected; and the
remaining list is transferred to CALFIT, which performs
an additional least squares fit, with full statistics, to

determine final values of the constant.

Structure Of Data Deck

 

I.
Col.
1
2

3

4

7

Option Card

Name
NGPS
IOP(l)

IOP(2)

IOP(3)

IDNT

IICAL

IDON

Field
I1
11

11

11

II

11

Value
<8
#0
#0
=2

42

Function

Number of groups to be averaged.
SCAN is desired.

AVFRQ is desired.

Punch of identification
average frequency and weight
in the identification deck

format is desired.

Lets input fringe numbers
be changed to frequencies
using calibration constants

determined in previous case.

Punch frequencies and weights
(8/card) are desired from SCAN.

Identification Option desired.
Identification deck(s) will be
input.

Calibration is desired.
Calibration deck to be input.

Allows conversion of fringe
numbers to frequencies using
calibration constants determined

in the previous case.

Allows single as well as
averaged frequencies to be
printed out in the single
group tabulation..

Omits punching weights as
provided in IOP(2) = 2.

Col.

11-20

21-30

31-40

Name Field
VISIBLE I1

TOLl FlO.8
TOL2 F10.8
TOL3 F10.8

Value

#0

43

Function

Indicates average desired

only if weights are the same.

Indicates input identifications
which are not found will be

printed out in final tabulation.

Indicates frequencies will1

be in excess of 10,000 cm

and adjusts input and output

of punched frequencies ac-
cordingly. It also adds wave
length in air, calculated from
Edlen's Formula (24) formula, to
the tabulated output.

Frequencies within a group
which differ by less than TOLl
are considered to be separate
measurements of one line, and
their non-weighted average is
formed, TOLl is preset to 0.05.

Frequencies in the various
groups which differ by less
than TOL2 are considered to be
measurements of the same line.
TOL2 is preset to TOLl.

Frequencies which differ by

less than TOL3 from input ident-
fication frequencies are
assigned the corresponding
identification. If two ident-
fications within TOL3 are

found, as asterisk field is
printed in the identification
area, if IOP(2) = 2. If TOL3

44
Col. Name Field Function

is greater than 100 the asterisk

field is suppressed and the same
identification may be punched and/or
printed for all lines. TOL3 is preset
to 0.04 if ICAL = 0 and 0.01 if ICAL # 0.

41-51 TOL4 F10.8 Average fringe numbers which differ
by less than TOL4 from the initially
identified calibration fringe numbers,

are identified as calibration lines.

*
II. IDENTIFY data deck

8 IR A8 Order in which the unknown radiation

was recorded.

16 IICAL A8 Order in which the identification or

calibration line would appear.

76-80 ORDER A8 ORDER specifies an order card.

The ORDER card can appear anywhere in the identification
deck, and all frequencies between it and the next order card
will be converted on the basis of its information. If no

order card appears IR and IICAL are assumed to be one.

1-8 NAMEl A8 These two fields contain the ident-
9-16 NAME2 A8 ification title that is deSired to be
printed and/or punched beside the

corresponding frequency.

20-32 XNU F13.4 Frequency of identification or

calibration line.

73-80 ORDER A8 ENDADATA specifies the end of the
IDENTIFY data deck.

 

* This section handles both identification and calibration
decks and appears if and only if IDNT or ICAL are equal
to 2.

Col.

III.

Name Field

SCAN data deck
This section appears if and only if IOP(l) # 0.

45

Function

A. Operator Name Card.

1-16

73-80

NAME 2A8

IFDONE A8

B. Heading Cards.

1-72

73-80

IHEAD 9A8

IFDONE A8

C. Data Cards.

1-5
6-10
11

12-66

67

ICODE

ICODE

ICODE

XM(l) F5
le) F5
WT(l) R1
ICODE Il

Reads in operators name.

NEWASCAN indicates new version is to
be used.
OLDASCAN indicates older version is

to be used.

Heading to be printed out at start
of SCAN section, last card will be
printed at top of each page.

END.HEAD indicates last heading card.

x coordinate of reticle on Hydel.
y coordinate of reticle on Hydel.

Code weight of preceeding point set
on code box 5 additional repetions of
above information.

Operation code indicating function of

this card as follows:

0 No operation is performed, the card is printed

out and program skips to next card.

1 Special Operation Card.

Nonzero XM(3) acts as a switch to either begin

or end punching and frequency storing. YM(3)

contains the fringe correction to be added to

all fringe numbers until it is changed.

2 Rotation Card.

This is the first card of each frame and it

ICODE

ICODE

ICODE

ICODE

ICODE

ICODE

3

46

contains the coordinates of six points on a

vertical grid line.

Pen Separation Card.

As many as necessary may be used, each will
contain up to 3 measurements of fringes recorded
by the I-R pen, alternating with 3 measurements
of fringes, recorded by the fringe pen. Two pen
separation frames are required at the beginning
of each SCAN data deck.

Calibration Constants Card.

A = YM(l) + XM(2)*0.00001 and B = XM(3) + YM(3)*
0.00001. From this card on fringe numbers will be
converted to frequencies using v(x) = A + Bx.

Fringe Separation Card.

XM(l) of the first 5 card in each frame contains

the fringe number of the first fringe used on

that frame. Subsequent xy pairs are the coordinates
of successive fringes. As many 5 cards as needed
may be used.

I-R Line Card.

Each xy pair gives the coordinate of a I-R line
duplicate measurements of the same line are
permissible. As many cards as are needed may
be used. WT(I) following each measurement
gives the coded weight of that line.

Comment Card.
The following card is read and printed by 10A8.
No other information on the code 7 card is used.

Continuation Card.

It indicates the end of a single group of SCAN
data, and returns to start of SCAN for a new
set of data.

47

ICODE = 9 Termination Card.
It indicates the end of the last group of SCAN

data, and returns to SHAFT for further processing.

Col. Name Field Function

68-71 IFR I4 Frame number.

IV. AVFRQ Data Deck
This section appears if and only if IOP(2) y 0.

A. Heading Cards.

1-72 ICHEAD 9A8 Heading to be printed out at start
of AVFRQ section. Last Card will be
printed at top of each page.

73-80 IFDONE A8 If IDNT 7! O IDN HEAD indicates the first
32 columns on the card are to be used
as a two line column heading over the
identification field. When this card
doesn't appear, the word IDENTIFICATION
is used. END HEAD indicates the last
card of the heading.

B. Group Identification and Data (full section appears NGPS
times).

Column Heading Card.
1-8 IHEAD(l) A8 First line of group column heading.

9-16 IHEAD(2) A8 Second line of group column heading,
and it is also used as a control card
as follows:

If 11-16 contains DELETE Frequency in C01. 21-35 will be

deleted from previous group.

If 11—16 contains CHANGE Frequency in Col. 21-35 will be
changed to frequency in C01.
36-50 with code weight in
Col. 52.

48
Col. Name Field Function

If 12-16 contains PUNCH Average frequencies, code
weights of previous group,
including changes and excluding
deletes will be punched in

8/card format.

21-35 A E15.10 Calibration constant. If A # 0 it
and B will be treated as updated
calibration constants for converting
input frequencies.

36-50 B E15.10 Calibration constant A and B are also
used for change and deletes as

described above.
52 IWT Rl Weight on change card.
Punch Frequency Cards.
1-8 FRQT(l) 4PF8 Frequency x101+ without decimal point.
9 WTT(1) R1 Code weight of line.

10 KO(1) R1 1-4 indicates the weight should be
changed to this value. D indicates
this frequency should be deleted.

The above is repeated 7 more times to make a total of
8 data sets per card. Additional operations performed for
special values on these cards are as follows:

FRQT(l) = 0 Indicates a caligration constants change.

FRQT(Z) a! O AZERO=FRQT(2)*10 + WTT(2)--g FRQT(3)*.1 -6
AONE = FRQT(4) + WTT(4)*1O + FRQT(5)*10 .
These are the old calibration constants which
are used, in conjunction with A and B, from
the column heading card, to convert input
frequencies. If the input values are fringe
numbers set FRQT(Z) very small (i.e. 10- )
and FRQT(4) = 1, all the rest = 0.

49

FRQT(l) = 0 Indicates a new weight-code correspondence
FRQT(2) = 0 for this group.
FRQT(3) # 0 Code 1 = FRQT(6)
2 = FRQT(S)
3 = FRQT(4)
4 = FRQT(3)
Blank = FRQT(7)
FRQT(l) = 0 Indicates end of punch frequency deck. The
FRQT(2) = 0 next read statement is a column heading card.
FRQT(3) = 0 If all NGPS groups have been read in A and B

from the next column heading, they will be
used to convert frequencies back to fringe
numbers for output.

V. Search Data Deck
(This section appears if and only if ICAL # O)

A. Number of Lines Card.
Col. Name Field Function

l-lO NUMLINES IlO Estimate of number of calibration
lines to be found. The search
procedure is carried out twice
unless the number of lines found
is é'NUMLINES.

B. Initial Identification Cards.

1-8 NAME 1 A8 Identification exactly as it
9-16 NAME 2 appears on the calibration cards
input to IDENTIFY.

30-39 Fringe number of calibration line.

As many initial identification cards as desired may be
used; but the program will not function with less than two
properly identified calibration lines. End of the initial

identification deck is signaled by a blank card.

50
Col. Name Field Function
C. Calfit Heading Cards.

1-80 IH 10A8 Heading cards printed out until
IH(10) = ENDAHEAD.

D. End of Case Card.

73-80 IFDONE A8 NEWACASE causes reading of new
option card to start another case.
AAAASTOP ceases execution.
Anything else is assumed to be an
error; and cards in the data string
are read until exhausted, or NEWACASE
or AAAASTOP is found.

A complete fortran listing of SHAFT is given in
Appendix A. The comment cards in this listing identify
the various sections of the program as related to the above
description. In order to illustrate the various tasks
this program will solve, Figures 11, 12, and 13 give
examples of the input deck structure for three of the

programs typical operations.

51

 

 

 

 

 

 

 

 

 

 

 

 

 

 

’e]21767 Lullu.

  

 

 

 

 

 

 

HYlgb DATA 1',

 

1234.5 0.1234

 

  

 

1 1

END HEADV

L

 

 

 

JOHN DOE

.a 1.1! S CAN

 

 

212100:

0.0&.

0.060

 

nun, 5,2100

 

 

/

 

 

 

 

 
    

~11.

JLATT PHLGHAH L?flI

 

 

 

 

 

 

2nd Group

lst Group

AVFRQ Data

Line Measurements

Cal. Constants

SCAN Data

Option Card

Figure 11. SHAFT Input for Averaging Two Groups

52

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

STOP
0 i ‘ I 3rd Group
‘ ‘5
2nd Group
I"? lst Group
END HEAD ‘
V MOL BR J IDN HEAD AVFRQ Data

 

 

42 ~*—* ~ Cal. Constants
7// ° ' I 2nd Group
T97ROSIE NEW SCAN _j lst Group

o'—-—-
.’

 

 

 

 

 

 

 

-—.. .....'l

flcyinnr——‘—"‘THNTIREEF‘j SCAN Data

  
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

W 1 .
iiCIDENTIFY DATA DECK
“311123 ‘ . Option Card
,V NEW CASE ‘ CALFIT Heading
' / END HEAD u F“
214. ‘1 Identification Deck
11in}
I
END HEAD 1m
.1 _ ‘ :14. . .
/* -2 l I Fringe Correction
(E/BEV RUN 63 NEW SCAN—l SCAN Data
1‘: 1 1; *1
l 2 ORDER 1 2nd Order
1 -57; '
I 1 ORDER ! ; lst Order
1110221 .4 .05 ijalibration Deck
Option Card
RUN

 

 

 

 

Figure 12. SHAFT Input for Calculating and
Using Calibration Constants

53

 

TNT

 

1234.567

0.12345

 

L

 

 

 

I

PUNCH FREQUENCY DECK --

 

 

 

6/7/68 JOB D.

 

 

 

 

 

 

END HEAD U

 

/

 

 

 

 

 

 

 

1111031 0.05

 

NEWCASD‘ ll

 

 

 

 

EWDIEMD

 

.1

 

 

 

1-0 00 P 7

1234.

1
]

 

 

15

mu“

CONSTANTS CARD

 

 

Bnnm.oum

 

 

'6f7/68 JOE D.

 

 

ImDIEMD

 

 

SCAN DATA 1E6:

 

1
fit
1

 

1-0 CO P 7

2115.6 Jj

 

 

 

 

 

 

 

K 1 3

1110020

mama

 

 

RUN. 5.9999

 

 

 

Figure 13.

Cal. Constants Card

AVFRQ Data

SCAN Data

Option Card

Initial Ident. Deck

Number of Lines Card

AVFRQ Data

SCAN Data

Calibration Deck

Option Card

SHAFT Input for Calculating and Using

Calibration Constants and for Identifying
the Resulting Frequencies

CHAPTER IV

ANALYSIS OF N2 SPECTRUM

The previous chapter indicated how averaged and
weighted experimental values of the frequencies of six
vibrational bands of N2 were determined. Chapter I
described the molecular model which can produce a theoe
retical value of the frequencies of these six vibrational
bands, provided the molecular constants are known. This
chapter describes a linearized least squares method of
determining the constants, and their 95% confidence intervals
from the experimental data.

The energy levels of the 33H and A32 states of N2,
as reported by Dieke and Heath (4), were used to calculate
transition frequencies. The program SHAFT was used to
compare these frequencies to the experimentally determined
values for initial identification. Further identifications
were made by extending the-branches to higher rotational
quantum numbers, once molecular constants were determined
for the initially identified lines.

Since the data published by Dieke and Heath covered
a larger range of vibrational levels, and because simul-
taneous values of all the molecular constants based on
these data were not previously reported, the linearized

54

55
. . 3
least squares technique was also applied to their B Hg

3
and A 2: energy level data.

Linearized Least Squares

 

The least squares technique requires that the obser-
vation equation be linear in the constants to be determined.
Since this is quite obviously not the case for the equation
deve10ped in Chapter I, the technique must be modified
slightly for this application. Since the literature
(3, 4, 6, 7, 9) provides reasonably accurate values of the
molecular constants, it is possible to use a linearized
least squares technique (25) by expanding the frequency
expression in a Taylor series about these values of the
constants. LetCi represent the molecular constants, C;
represent their initial values, and Sk represent the
observed values of the frequencies. To first order, the
observation equations can then be written as:

8f

_. . k
s = f (c. 1=l,r) + 2‘ —— AC

‘where r is the number of constants to be determined. This
equation is linear in the unknowns ACk, and a least square
fit on the frequency error Skffk(53) and first partial
derivatives of the frequency with respect to the initial
values of the constants, can be made to determine the error
ACk in the initial values of the constants. By using this

to update the constants, an iteration procedure is used

until insignificant corrections to the constants are obtained.

56

Analysis Programs

 

Three computer programs, MOLCON, DBSIG, and D3PI,
have been developed for analyzing the spectrum of N2.
They are all closely related and employ the same least
squares routine, based on the work of M. A. Efroymson (25).
for fitting the experimental data to the theoretical
expressions. The programs have been especially adapted for
use on a third generation computer (CDC 6500). Because of
the time sharing nature of the computer, it is sometimes
an advantage to use peripheral storage devices in order
to free central memory for other users. Sufficient detail
on the computer programs will now be given so that they may
be understood and used by other researchers.

MOLCON fits transition frequencies between the Ban
and A32 states. DBSIG and D3PI fit the energy levels of
the A32 and Dan states respectively. MOLCON and D3PI use
SUBROUTINE EIGEN to determine the diagonalizing matrix
of the Hamiltonian matrix of the Ban state. EIGEN is a
Fortran subroutine which finds the eigenvalues and eigen-
vectors of a real symmetric matrix. It was written by
Burton S. Garbow of Argonne National Laboratory, Lemont,
Illinois and obtained from the Michigan State computer
laboratory library. All three programs use SUBROUTINE
STEPFIT, to perform a linearized least squares fit based on
the molecular models described in Chapter II.

In brief summary of what was said above, these programs

use input initial values of the molecular constants to

57
calculate an approximate value of the measured quantity.
The linearized least squares technique is then used to
determine corrections to the initial values of the constants.
A specified portion of this change is then used to correct
the initial values of the constants, and the process is
repeated in an iterative manner until further steps no
longer improve the fit of the observed minus calculated

results.

Structure of Data Deck

 

 

I. Heading Cards

Columns l-72 are printed until END HEAD is encountered
in column 73-80. The last card is printed at the top of
each page of the tabulated output. If STOP is found in
columns 77-80, control is returned to the monitor.

II. Option Card
Options which control the flow of the program are
input on this card.

Col. Field Name Description
1-16 2A8 IDENT Identification used in stepfit output.

17 Il ITRYS Indicates number of iterations
desired.

18 Il INFOl # 0 suppresses the printout of the
raw sums of squares and cross products
matrix.

19 Il INF02 # 0 suppresses the printout of the
parital correlation coefficient
matrix.

20 Il INF03 # 0 suppresses the printout of the

intermediate regression steps.

Col.

21

22—36

46-47

48-52

53-57

58-62

63-67

68-72

Field

I1

11

I2

F5

F5

F5

F5

F5

Name

INFO4

NK(I)

NDELMAK

XDEVMAX

TOL

TOLF

*
EFIN

*
EFOUT

 

58
Description

# 0 suppresses the printout of
individual frequencies on all but
the last fit.

# 0 indicates the corresponding
constant (for ordering of constants
see below) will not be used in

the fit.

Indicates number of lines to be
eliminated from the fit if the
observed, minus predicted value
of the frequency, is greater than
XDEVMAX.

NDELMAX explained above.

If the diagonal element of the
inverted matrix for a particular
xn is smaller than TOL, that Xn
will be omitted from the fit.
Preset to 0.001.

If the observed minus predicted
value of the frequency is greater
than TOLF, the line will be given
a weight of zero.

If the variance reduction, due to
adding the next most significant
variable is greater than EFIN, the
next variable will be entered.

If the variance contribution of
a variable is less than EFOUT,
that variable will be removed
before adding another variable.

* EFINZFFOUT typical values are .5 to .005.

59

Col. Field Name Description

73-80 A8 ICASE Controls Operation of the program

as follows:

NEWACASE Forms a completely new problem

by reading in all data.

NEWACONS Reads in new initial values of
the constants, but continues fitting
the same observed data as the last
case.

ADDACONS Uses previous observed data and

molecular constants, but changes

which constants enter the fitting

process as controlled by other

variables on this card.

III. Initial Constants Cards
These molecular constants are read in by a 8F10.2

format in the order indicated below.

Name Location Description
MOLCON DBPI D3SIG

API 1-10 1-10 Spin coupling constant for
B H state.

3

BPI 11-20 11—20 Rotational constant for B H
state.

DPI 21-30 21-30 Centrifugal distortion 3
rotational constant for B H
state.

CO 31-40 31-40 A type doubling constants for

C1 41-50 41-50 the B H states.

C2 51-60 51-60

3

BSIG 61-70 1-10 Rotational constant for A 2

state.

Name

DSIG

LAMDA
GAMMA

NUZERO

ZEROE

WU

XU

YU

ZU

WL

XL

YL

ZL

ALAPI

Location
MOLCON D3PI
71—80
Card 2

1-10
11-20
21-30
61—70
31-40 71-80
Card 2
41-50 1-10
51-60 11-20
61-70 21-30
71-80
Card 3
1-10
11-20
21-30
31-40 31-40

60

D3SIG

11-20

21-30
31-40

41-50

51-60

61-70

71-80

Card 2

1-10

Description

Centrifugal distortion 3
rotational constant for A E

state.

Spin spligting constants
for the A 2 state.

Band origin for the first

positive system.

Energy of the F2(0) level
above some arbitrary origin
(origin nearly at F2(0) of
A Z).

Vibrational energy constants
for the B H state.

Vibrational constants for
the A 2 state.

Constant for linear vibrational
dependence of API.

61
Name Location Description
MOLCON D3PI DBSIG

BAAPI 41-50 41-50 Constant for quadratic
vibrational dependence of API.

ALBPI 51-60 51-60 Constant for linear vibra-
tional dependence of BPI.

BABPI 61-70 61-70 Constant for quadratic
vibrational dependence of BPI.

ALBSIG 71-80 11—20 Constant for linear vibra-
tional dependence of BSIG.

 

Card 4

BABSIG 1-10 21-30 Constant for quadratic
vibrational dependence
of BSIG.

ALLAM ll~2n 31-40 Constant for linear vibra-
tional dependence of LAMDA.

DELAPI 21-30 71-80 Change to be made in API to
numerically calculate g: '

TT
Card 4
DELBPI 31—40 1-10 Change to be made in BPI to

numerically calculate gg— .
n

IV. Fractional Change Cards

These cards contain the fraction of the predicted
error in the constants to be used in the iteration process
(i.e. constants will be changed by ACi*Fi). The fractional
change appears in the same columns on these cards, as the
variables themselves appeared on the "Initial Constants
Cards". If the first fraction change is zero, it will be

set equal to unity. If any of the other fractional changes

62
are zero, they will be set equal to the first fractional
change. Thus, if all fractional changes are left blank on
the fractional change cards, they will be set equal to

unity.

Observed Data Cards

 

MOLCON

Col. Field Variable Description

3 Il VU Vibrational level of the upper state.
5 I1 VL Vibrational level of the lower state.
8 R1 IBR P, Q or R to designate branch.
9 I1 I Subscript on F for B3H level.
10 I1 N Subscript on F for A3H level.
12-13 12 K
18-30 F13.4 FOBS Observed transition frequency.
38-41 F4.2 WT Assigned weight factor.

73-80 A8 IFDONE END DATA indicates last observed

data card.

D3PI

Observed values of the energy levels of the B3H state
are read in eight per card (Format 8F10.4), until an energy
of 8888.8888 is encountered in the eighth field. This
signals the end of the input for a particular vibrational
level and the vibrational quantum number is given in the
first field of the card with the 8888.8888. If this card
is followed by one with 9999.9999 in the eighth field,

reading of observed data is complete. The order of entry,

63
starting with J = 0, is F1(J), F1(J), F2(J), F§(J), F3(J),
F§(J) where the prime indicates the upper level of the A

doublet.

222139.
Observed values of the energy levels Of the A32 states
are read in eight per card as above. In this case, the order
of entry is F2(K), F1(K), F3(K). The termination of vi—
brational levels and data reading is the same as for D3PI.
When reading of the "Observed Data Cards" is completed,
the program calculates molecular constants according to
the instructions given by the above Option cards. When these
operations are completed, the computer returns to read in
heading cards for the next case.
Each of these programs has a SUBROUTINE PRINTOUT
which is called from SUBROUTINE STEPFIT. PRINTOUT prints
out in tabulated form the identification, observed, calcu-
lated and predicted values and their differences, for each
of the data points entered. MOLCON writes a COMMON FILE of
the identification, observed frequency, observed minus
calculated frequency and weight for each. PRTDATA then sorts
this data and prints the tabulated data shown in Appendix C.
A complete listing of the Fortran programs, with enough
comment cards to locate the various Operations Of the
program, are given in Appendix B. Although each program
uses a slightly different version of STEPFIT a listing is
given only for the program MOLCON. There are several places

where it will be noticed that it has been necessary to code

64
the programs in a rather unusual fashion because of

idiosyncrasies of the then current Fortran compiler.

Simultaneous Constants from the Near Infrared Data

Dieke and Heath have performed a rotational analysis
of a sufficient number of bands to determine the energy
levels of the A32 state for v up to 9 and K up to 13
(K = 21 for v = 0) and most of the energy levels of the B3H
state for v up to 12 and J up to 12 or higher. Using the
selection rules given in Chapter II these energy levels
were used to calculate expected values of the frequencies
for the infrared bands discussed in Chapter III. These
frequencies were then compared to the observed frequencies
using SHAFT and initial identifications made. Since the
separation of some of the transition frequencies was less
than the resolution limit of the spectrometer many of the
Observed frequencies were blends Of several lines. If the
blending caused Visible broading Of the recorded spectral
lines, the lines were given a smaller weight and thus had
a smaller influence in determining the molecular constants.
However, in the first stages of determining molecular
constants all lines identified by SHAFT were assumed to be
correct and were used in the fitting programs. After a
reasonably good fit was found using these frequencies the
molecular constants determined from them were used to calcu-

late frequencies with K up to 20. The identification and

65
fitting procedure was again used to get new values Of the
constants. As a final automatic identification step these
constants were used to calculate all transition frequencies
from K = l to 30 for the six bands studied. SHAFT was again
used to match these frequencies with the Observed values.
Using the tabulated output of observed frequency, observed
minus calculated frequency and weight, as shown in Appendix C,
each line was checked for proper identification. After all
changes were made, a final fit of 2372 transitions with a
standard deviation of .106 cm"1 gave the molecular constants
given in Tables 3 and 4.

A systematic difference between the Observed and
calculated values of the frequencies was found. The average
deviation of the observed minus calculated values of the
frequencies for all transitions originating from the Q = 1
level of the BBH state is +. 089 cm-1. While the respective
average deviation Of the transitions originating from the
$2 = 0 and 2 levels is -. 049 cm.1 and -. 043 cm-2 A systematic
difference was also found using the data Of Dieke and Heath

and will be discussed further in the following section.

Simultaneous Constants from the Data of Dieke and Heath

 

As mentioned in the previous section Dieke and Heath
have reported a large number of energy levels in the A32
and BBH state of N2. Since their data extend to higher
vibrational levels than were observed in the infrared it
was possible to obtain more accurate values of the vibra—

tionally dependent constants using their data. Information

66

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5000.0”
smo.on
ma.on

mmo.oH

 

Hum wmm

mDde

e m was new
n

w

h

«woo.o-
mo~.s
oe~.ma
hm.smha
maooo.o
mmoo.ou
mm.~
nonxom.m-
noaxmm.flu
mamao.o
ommm.n
moo.o
ssoo.o

Hmm.mv

 

me¢>

Qmm<mmZH m<mz

mmoooo.ow

1 O
1-l

Nooo.o

[x
O
+l

oo.
mo.

5

+l

o
moooo.on
eao.on
ma.on
Snoaxe.nn
muonxm.an
Hmooo.OH
aaooo.OH
omoo.on
mmo.on

mmo.ow

 

How wmm

Nz mo muwpm
.qu ca mucmumcou msowcmuasEHm

vmmooo.o

mmmoo.ou
NN¢.vH

NO.VM>H
mooo.o

mmao.o

HH.N

-oaxmm.m

0

nl

oaXmm.ml
namao.o
ommm.a
mmoo.o
mmma.o
mmv.m¢
mmmmw

«Eda mmmHQ

.v magma

68

concerning the relative accuracy of these energy levels was
not given, and therefore they were all weighted equally.

Using the 12 molecular constants for the model Of the
A32 state, presented in Chapter II, 436 energy levels were
fit to a standard deviation of .0212 cm-1, and all Observed
values were within .06 cm.1 of the calculated values.
Dieke and Heath indicate their frequency determinations
are accurate to approximately .01 cm"1 thus the fit is good
to the same order of magnitude as the experimental error of
the data. In the final iteration for the constants the
predicted corrections were all at least an order of magnitude
smaller than their respective standard errors. The resultant
constants and corresponding 95% SCI's are given in Table 3.

These constants include a the vibrational dependence

1’
of the spin-splitting constant A. Since this vibrational
dependency is only about three times its 95% SCI, it would
be difficult to Observe in a study using a limited number Of
vibrational levels and/or a less accurate molecular model.
Dieke and Heath determined the constants given in Table 5
using combination difference methods on one band at a time.
This simultaneous analysis includes D and 7, which were not
determined by Dieke and Heath.

After correcting the few obvious typographical errors
in the data of Dieke and Heath and eliminating the F1 (17)
level for which the Observed minus calculated values was

_1
-8.7 cm , there remained 1138 energy levels to fit to the 15

3
molecular constants of the B H state. As was the case with

69

Nbaoo.o
mm.ma
om.om¢a

em.al

muoaxve.w-

mtho.o
mvmv.a

flammav
mMmHo

omoo.o- moo.ou
mm.H- Hm.H-
noaxm.m -oaxm.m
m m
mmao.o mao.o
omme.a osv.a
Ammaac Aammav
qqommmo mosmz

.Oudumumuflq map Eoum NZ «0

mumum w « may now ISO ca mucmumcou HMHDOOHOE .m OHQMB

m

H

70

ml

mmao.o
th.o
mmH.mH
Nv.mmwa
Ioaxm.m
o
oaxmm.h
vmhao.o mmao.o
wvnmm.a wmmw.a
Ammmav Ammmav
mmmH Q Aqommdu

mumnm e m may now
m

H

mmooo.o
mmoo.o
n~.m
suoaxm.m suoaxm.m
mwao.o mmo.o
memm.a om.H
N.Ne m.~e
remade immmav flammai
mmmm comm mosmz

mudumnwqu map Eoum Nz mo
:80 ca mucmumcoo HMHDOOHOS

.m OHQOB

71
the infrared data, a systematic difference between the
Observed and calculated results was found. The average
deviation of the Q = 1 level is +.155 cm-1 while that of
the Q = O and Q = 2 levels is -.157 cm“1 and -.001 cm"1
respectively. The overall standard deviation Of the fit
is .198 cm"1 and the molecular constants are shown in Table 4.

To a first approximation the spin-orbit interaction
constant A gives the separation Of the F1, F2 and F3 levels.
In Figure 14 the solid line represents the theoretical
energy for the F1, F2 and F3 levels. The broken line shows
the deviation of the observed data from this theoretical
line with the scale increased by a factor of 100. This
shows a systematic deviation in the separation of the levels
which decreases with increasing rotational energy. It thus
appears that the asymmetry of the F1 to F2 and F2 to F3
separation is not adequately described by the theory. Figure
15 shows the Observed minus calculated deviation for the
three levels with V = 4. All other vibration levels showed
the same general trend.

The larger number Of degrees Of freedom in the simul-
taneous fits resulted in a different distribution Of the
deviations in each vibrational level. However, for each
vibrational level at least one of the following two state-
ments was found to be true: 1) The observed energy sepa-
ration of the F1 and F2 levels was greater than predicted.
2) The observed energy separation of the F2 and F3 levels
was less than expected. It is not possible to improve the

fit by varying A.

Energy Above F2(0) of A 2 (cm

72

   
  
 

16800 ‘
Theoretical Energy

--— Observed Energy Deviation

(Scale increased 100 times)

 

16600 '

16400 ‘

16200 '

 

 

2 4 6 8 10 12 14 16 18
Rotational Quantum Number (J)

3
Figure 14. B H Energy Levels for v=4 lower
A-Doublet

73

umandonl< HUBOH ¢n> How wGOflumH>ma mmumcm m m .ma
m

any Honesz Esucmso accoflumuom

musmflm

 

«a ma NH HA OH m m b m m v N
F _ _ _ L _ t _ u _ _ l
+
+ + +
+ L...
+ + + +
+ 4
i +
O
O 0 1H.
AU 0
Hm>ma mm + o 0
V IN.
Hw>0H .m o O
O
Hm>ma 1m < o
O

 

 

mo) Abieug penetnotea-peAxesqo

(T-

74
3

Gilbert (10)has calculated the energies of the H
state of PH and compared these to the values determined
from the A 3400 band (3H + 32 transition) data reported
by Pearse (26). He used a combination difference method
to determine these energies. The deviation of the experi-
mental and theoretical results are shown in Figure 16.

As with the N2 data, the experimental data indicate a
larger asymmetry in the spin-orbit interaction than the
theory predicted. Professor I. Kovacs (27) has indicated
that these deviations might be due to either a spin-spin
interaction or a spin-rotation interaction.

The above discussion would seem to indicate that it
would be difficult to obtain a reliable value for Av and
therefore to calculate the vibrational dependence of the
constant Av‘ However, the change in Av as v increases is
quite large, and although GA and BA are probably not as
accurate as their 95% SCI's indicate, a decrease in A as v
increases is certainly apparent. BudO (9) also determined
AV for several vibrational levels between v = 0 and v = 12
and although his values are not monotonically decreasing,
his result A0 = 42.3 and A12 = 41.3 also suggests a vibra-
tional dependence of A.

When theory is incapable of producing agreement to
within the experimental error Of observed data, the results
of a least square fit based on this theory must be interpreted
‘with caution. As stated earlier the 95% SCI's are calcu-

lated assuming one sampling of a normally distributed

75

.uumnawo an pmuuommu
mm no team oovm< Dav Eoum mcowumw>mo .OH Ousmwm

any umnasz Enhance Hmcofiumuom

 

NH Ha ca m m b m m e m N H
¢. *1 _ P t m A) _ _ _ L a
a.
Q.
Q Q
G.
0
no
0
O
o Cos
no no q + .+ +
+ q.
.+
+
+ Hm>mH mm +
Hm>wa mm o
+. Hm>ma is <
+.

 

m.l
v.1Mw
S
e
. M
m I e
m.
D
N I w
o
n
. a
H I 1
e
p
. 3
o u
e
1
5
H. .A
m,
m
N. .
m.
v.

76
infinite pOpulation of similar sets of data. When this is
not the case the 95% SCI's give sgmg_indication of the match
between the theory and experiment but it does not mean that
there is a probability of .95 that the estimators are within
a range of i SCI of the true values of the constants.

Tables 5 and 6 Show the values of the molecular
constants of the A3Z and B3H states of N2 obtained by
previous workers. These constants were found using combi-
nation difference techniques On one band at a time. For a
simultaneous fit different results might be expected even-
when the theory is adequate. When, as in this case, the
theory has shown to be inadequate, one might expect even
larger variations in the results of a single band and
simultaneous fits. Tables 3 and 4 show for the first time
in a single work all the constants describing the first

positive system Of N2.

S UFDLARY AND CONCLUS 1 ONS

A newly designed double-ended hollow cathode has been
develOped and stabilized for use as a spectral source. It
has been used to excite the Np first positive system in the
near infrared.

Computer programs for efficiently handling large
quantities of spectrographic data have been develOped,
tested and described in detail. These include a program
for calculating and identifying transition frequencies
and programs for non—linear least squares fits of the
experimental data to the existing theory Of the A32 and B3H
excited electronic states comprising the first positive
system of N2. A method of using punched cards to communi-
cate between the fitting and identifying programs has been
described to make the analysis semi-automatic. This process
could be improved and further automated by elimination of the
punched card interfacing.

The reported analysis of the first positive
system of N2 represent the first case in which all the
molecular constants have been determined from a single set
of data. This work also constitutes the first reported
simultaneous analysis of this system. The analysis has
indicated an inadequacy in the theory of 3H states. The

77

78
major portion of the discrepancy appears to be in the
description of the asymmetry of the energy separation of

the F1, F2 and F3 levels.

LI ST OF REFERENCES

14.
15.
16.
17.
18.
19.

20.

LIST OF REFERENCES

I. Agarbiceanu, A. Agafitei, A. Preda and V. Vasilio,
Rev. Roum. Phys. 11, 649 (1966).

D. A. Huchital, and J. Dane Rigden, IEEE J. Q.E. QE-3,
378 (1967).

P. K. Carroll, Proc. Phys. Soc. 54, 369 (1962).

G. H. Dieke and D. F. Heath, John Hopkins Spec. Report
#17, (1959).

M. W. Feast, Proc. Phys. Soc. 63, 568 (1951).

M. H. Hebb, Phys. Rev. 42, 610 (1936).

S. M. Naude, Proc. Roy. Soc. 136, 114 (1932).

M. Born and R. Oppenheimer, Ann. Physik. 84, 457 (1927).
A. Budo, Zeits. f. Physik. 26, 219 (1935).

Cecil Gilbert, Phys. Rev. 42, 619 (1936).

H. A. Kramers, Zeits. f. Physik. 53, 422 (1929).

Robert Schlapp, Phys. Rev. 51, 342 (1937).

G. Herzberg, S ectra of Diatomic Molecules, 2nd Ed,
D. Van Nostrand, (I950).

 

Ibid., p. 106.

Ibid., p. 231.

E. Hill and J. H. VanVleck, Phys. Rev. 32, 250 (1928).
G. Herzberg, Op. cit., pp. 240-245.

G. Herzberg, Op. cit., pp. 133-135.

J. L. Aubel, Thesis. M. S. U. (1964).

D. B. Keck, J. L. Aubel, T. H. Edwards, and C. D. Hause,
"Symposium on Molecular Structure and SpectroscOpy",

Paper H-2, Columbus, Ohio, (1966).

79

21.

22.

23.

24.

25.

26.

27.

80
D. B. Keck, Thesis. M. S. U. (1967).

K. N. Rao, C. J. Humphreys, and D. H. Rank, Wavelength
Standards in the Infrared. Academic Press, New York.

pp. 160-1627 W TI'_)"966 .—

M. D. Olman, Thesis. M. S. U. (1967).

 

 

C. D. Coleman, R. Boxman, W. F. Meggers, Table gf
Wavenumbers, National Bureau of Standards Monograph 3,

p. III (1960).

J. Mandel, The Statistical Analysis of Ex erimental Data,
Interscience Publishers, New York, pp. 147-150 (1964).

R. W. B. Pearse, Proc. Roy. Soc. A129, 328 (1930).

I. Kovacs, Dept. of Atomic Physics, Polytechnical Univ.
Budapest, Hungary. Private Communication.

APPENDICES

MAIN
C
S
10
C
C
C
15
20
C
C
C
25

APPENDIX A

FOPTPAM LISTING OF PROGRAM SHAFT

ppOGQAM SHAFT

SCAN HYDFL AVFWAGF FPEQUFNCIES IARULAIE

COWMON /l/ IOP(3)9IL§(R)QTOLIQTOLgoTOL-‘IGAORQLDOIDNTQICAL.
IIIONJQJLNWD

COMMON /2/ NoVISAQLF

COMMON /3/ NQMFI(2000)CNAMEZ(POOO)9NU(?000)9NMAX9TOL4

COMMON /S/ MUM

COMMON /R/ ICHEADIQ)QIHFAD(992)CIDN(4)

COMMON /Q/ CCWI(RQQ)

DIMENSION FPQ(1910000)0 WTS(1010000)

INTEGFQ WTI9WT9WTS¢VISAQLE

QEAD c509 NGPSOIOPOIDNTQICALQ IDONQVISARLFQIOLI cTnL70T0L39

l TOL4-IFDONE

IF (IFDONF.FO.8H STOP) STOP
IDN(1):RH

IDN(?)=RH

IDN(3)=RH

IDN(A)=8H

JUMP:0

NGPSZ:HGPS

IF (ICAL.FQ.O.OQ.ICAL.FQ.3) GO TO 10
NGPSP=NGDS+2

IDEM:10000./NGPSP

READS IN CALIPQATION OP IDFNTIFICATION DECKS

IF (IDNI.FO.2.OP.ICAL.FQ.2) CALL OVFPLAY (1.9109)
IF (IDNT) 90915920

Lp=l

NAMF?(1)=RH

NAME1(])=NAMEZ(I)

CONTINUE

N21

D0 25 I=I9NGPS

GIVES TOLFQANCFS PPFSET VALUES IF THEY ARE NOT PFAD IN

IL5(I)=1
IF (TOL4.FQ.O.) TOL4=1.
IF (TOL1.F0.0.) TOLI=.050

RI

000

000

8?

IF (TOL?.FU.0.) TOLP=TOL1
IF (TOL3.NF.O.) GO TO 30
IF (ICAL.NF.0) TOL3=.03
TOL3=.04-TOL3

CALLS SCAN

30 IF (IOP(I).NF.0) CALL OVERLAY (29 9P9J9FRQ9WIS9NGDSo
1 NGDSP-IDFM)

CALLS AVFRQ

35 IF (IOP(2).NF.0) CALL OVERLAY (39 939J9FPQ9WT89NGPS9
1 NGPSP9IDEM)
IF (ICAL) 40945940

CALLS SEARCH AND CALFII

40 CALL OVFDLAY (49949J9FQ09NGPS?9IDEM)
JUMpzl
ICAL=0
IONI=1
GO I0 35
45 RFAD 559 IFDONE

SKIPS NEXT CASF IF SFI UP WPONG

IF (IFDONF.FQ.RH ) GO TO 45
IF (IFDONF.FQ.RHEND HEAD) GO TO 45
IF (IFDONE.FQ.RHNFW CASF) GO TO 5
IF (IFDONF.FQ.8H STOP) STOP

50 FORMAT (9II9?X94F10.R9??X9AR)
55 FORMAT (72X9AR)
END

OVERLAY 1

000

PPOGQAM IDENTIFY
PFADS IN CALIRHATIOM OP IDFNIIFICAIION DFCKS

COMMON /I/ 1013(3) 9ILS(8)9T0L19IOL29IOL39A9ROLP9IIINI9ICAL0
1 IDON9JUMP

COMMON /3/ NAMEI(2000)9NAMF2(?000)9NU(?000)9NMAX9IOL4
DEAL NU

INTEGFQ OQDFQ

N=1

NTzl

ASSUMFS OPDFPS APF I UNLFSS GIVFN

83

IICAL=1
IP=IICAL

S DEAD 3§9 INAMFIOINAMCPQXNUQURDFD
IF (OROFQ.FO.RH OQOEP) GO TO 10
GO TO 15

10 IR=IMAMFl-8H 0
IICAL=INAMF?-RH 0
GO T0 5

15 CONTINUE

C
C CONVFQTS FQFQUENCIFS TO PPOPFR VALUF DEPENDING 0N OPDFPS USED

C
XNU=XMU*IQ/IICAL
IF (N.EO.1) GO TO 25
C
C OPUFPS FREQUENCIES LOW TO HIGH
C
20 IF (NU(NT-l).LF.XNU) GO TO 25
NU<NT)=NU(NI-1)
NAMF1(NT)=NAMF1(NT-l)
NAME?(NT)=NAMF2(NT-l)
NT=NT-l
IF (MI-l) 25.25.?0
25 NU(MT)=XNU
NAMFI(NT)=INAMF1
NAMF?(HT)=INAME?
M=M+1
NT=N
IF (ORDEQ.NF.8HEMO DATA) GO TO 5
NMAX:N-1
IF (TOL3.GT.100.) GO TO 30
NAME1(NMAX+P)=8H
NAMFz(MMAX+1)=MAMF1(NMAXoE)
NAME)(NMAX+1)=NAMFP(NMAX+1)
MAMF?(NMAX+2):RH ***
NU<NMAX+1)=0.0
QFTUPN
30 NAMF1(NMAX+2)=NAMF1(I)
NAME?(NMAX+2):NAME2(1)
PFTUDN
3Q FORMAT (9A993X9F13o4940X9AR)
FND
OVFRLAY 2
PROGRAM ALLSCAN(FPOoWT89N6959NGPS29IDFM)
C
C OFTFQMINFS FQINGF NUMRFQS FROM HYDFL DATA
C

COMMON /I/ 109(3)9]LS(R)9I0Ll9IOLPOIOL39A999LP9IDNI9ICAL9
I IDON9JUMP
COMMON /?/ NAVF9VISARLF

84
OIMFNSION IFST(10)9XM(6)OYMIO)9FQNGX(100)9PSFP(100)0
1 FOSFP(100)9II(P)9I°(?)9IHFAO(9)9NAME(?)9NHFAO(10)9
2 OELx(6)9IpFQ(3)9PFN(?)9WT(6)9WTT(R)

ALLOCATFS F90 ANO WIS STORAGE ACCOQDING TO NUMRFQ OF GROUPS

COO

0053

000

("300

10
IS

20

25

30

35

40
A5

50

DTMFNSION FPO(NGPS?-IDEM)9 WTS(NGPS?9IOFM)
OATA (IPFN:RH6FIPST 9PH65FCOND )

INTFGFP WIT.NT9WIS9VISARLE

PRINT 450

QFADS In OPFPAIOR NAME

DFAO 3309 NAMF9IFOONF

IF (IFDONF‘RHNFW SCAN) 10995910
IF (IFDONE-HHOLO SCAN) 15970915
DQINT 335

GO TO 25

INFW=O

GO TO 30

INFW21

QEAOS IN HEAOING CAPOS

QFAO 3759 IHEAO9IFOONE
PRINT 3759 IHFAO

IF (IFOONF-RHFNO HFAO) 30935930
NIP:]

IH=NIP

IF (IOP(3)) 40945940
DUNCH 3759 IHFAO
CONTINUE

IPUNCHzo

IFROOzlpUNCH
ICAQOS=IFQOO

IszCAPOS

NCAL=ID

NFRMzNCAL

IL5(NAVF)=1
IL=IL5(NAVF)

ILT=IL

IHZILT

M031

FPCOP=0.0

FSED=FQCOQ

XFSFPzFSFP

ASSIGN 175 TO NGO

IF (ICAL) 50955950

IF (ICALoFO.3) GO TO 105

SFTS UP OFCK FOQ CALIBRATION

A=0.0

SS
60

OS
70
75
80
85

90

100

105

110
115

120

125

130
135

140

85

9:1.0

NCAL=1

IF (.NOToIOP(3)) GO TO 55
[AzA

IXA=(A-IA)*I.F5

IS=B*1.E5

X535519F5

IXH=1X5-I5)*1.E5

PUNCH 3609 IA9IXA9IR9IXR
CONT I NUE-

QFAO 3509 (XM(119YMII)9WT(I)9I=196)¢ICOOE91FQ
IF (ICODE-6) 70995965

IF (ICOOF‘R) 32592359PR5

IF (A-ICOOE) 2159190975

IF (ICODE-2) 909140995

IF (‘ICOOE1 120985995

pRINT 3559 (XM(I19Y”(I)9I=195)
GO TO 60

DQINT 450

PETUQN

NCOOQO=6

IF (XM(61) 11091009110

00 105 I=195

NCOOPD=NCOOPO-l

IF (XM(NCOOPO).NF.0) GO TO 110
CONTINUE

GO TO 60

DO 115 I=I9NCOOPO
XM(I)=OMT2*XM(I)-THFTA*YM(I)
IF (ICOOF‘5) 165920592?5

IF (INFW.NF.O) GO TO 125
XFRM:XM

XFRNfizYM

FPNG:XFPNG-l,0

SFTS UD FRINGF COQPFCTION

IPP=XM(2)

FPCOP=YM(3)

PRINT 340. FPCOQ

IF (IPUNCH.NF.0) GO TO 130
IPUNCH=XM(3)

GO TO 135

IF (XM(3).NF.0) IPUNCH=O
CONTINUE

GO TO 60

THIS QECTIOM DFTFPMINES ROTATION ANGLE

SUWYX=0.0
SUMYYzSUMYX
SUMY=SUMYY
SUMX:SUMY

149

150

160

165

170

175

180

86

GO TO NGO

CONTINUF

NOFQzI

IFPNSzO

ASSIGN 230 T0 NIP

00 150 I=1~h

SUMY:SUWY+YM(I)

SUMX:SUNX+XM(I)
SUMYYzSUMYY+YM(I)*YM(I)
SUMYX:SUMYX+YM(I)*XM(I)
THFTA=(SUMYX-SUMY*SUMX/6.)/(SUMYY-SUMY*SUMY/O.)
THETA2:O.S*IHFTA*THFTA

OMT2=1.0-THFTA2

IBAO=0

DO 155 1:1 915
OFLX(I)=(SUMX-THFTAFSUMY)/6.*THFTA*YM(I)-XM(I)
IF (ARSF(OELX(I)).GT.10.O) IRAO=1
CONTINUE

GO TO (60.160). IH

IF (.NOT.INFW) FNCOOE (49345.1FP) XFRM
PRINT 4159 IHEAO.IFQ.NAME

IF (THETAP.GT.0.0000125) PPINT 410

IF (IHAO.NF.0) pPINT 405

GO TO 60

THIS SECTION OFTEPMINFS pEN SEDAPATION

no 170 J=29NCOOPD92

IP=ID+1

XFSFP=XFSEP+1.0

PSFP(IP)=XM(J)-XM(J-l)

FSEP:PSFP(IP)+FSFP

CONTINUE

no T0 60

NFPMzNFQM91

IPFP(NFRM)=IFH

IF (.NOI.INFN) FNCOOE (49345919FR(NFRM) )XFPM
no TO (145.190). NFQM

FSFP=FSEP/XFSFP

N1=NFPM-l

PPINT 350. IDFNTNI).TPFD(N1).NAMeoTHETAanLxc(DSFD(I)-

l I=N1991P)

MIP:IP+1

IF (THEIA?.OT.0.00001251 PQINT 410
IF (IRAO.NF.O) pQINT 405

pQINT 3559 FSFP

XF5FP=0.0

F5FP:XF5ED

IF (MFQM.F().?) GO TO 145

IH=P
ASSIGN 145 TO NGO
DSEPSUM=0

00 195 J=19ID

GOO

IRS

190

195

200

205

210

(\J
H
d1

87

PSEDSUM:PSEPSUM+DSFD(J)
DFNSFP=PSFPSUM/ID

PRINT 4209 PFNSFD

GO TO 145

THIS SFCTION PFAOS IN CALIRPATION CONSTANTS

CONTINUE
A=YM(1)+XM(?)*0.00001
R=XM(3)+YM(3)*0.00001

IF (YM12).LT.0.0) Rz-R
R:YM(2)*5*0.0000I

pRINT 4259 AQR

NCAL=1

IF (.NOT.IOP(3)) GO TO 60
IA=A

IXA=(A'IA)*1.F5
1535*].F5

XR:R*1 0E8
IXB=IXH‘15)*1.F5

IF (IL.EO.1) GO TO 900
GO TO 290

pUNCH 3609 IA9IXA9IQ9IXQ
GO TO 60

THIS SFCTION OFTFPMINES FRINGE SPACINGS

DO 210 J=19NCOOPO
FPNGX(NOFP)=XM(J)
FasED(NOFQ)=FPNGX(NOFQ)-FPNGX(NOFP-I)
NOszNOFQ+l

CONTINUE

GO TO 60

IF (IFQN5.NF.O) GO TO 95
IF (.NOT.INFW) GO TO 95
IFRNS=1

XFPNszM

FPNG=XFRNG-l.0

DO 220 1:195
XM(I)=XM(I+1)
YM(I)=YM(I91)

YM(6)=0.0

XM(6)=YM(6)

GO TO 95

THIS SECTION DFTFHMINFS FRINGF NUMRFRS

GO TO NIQ

NOszNOFP-l

PRINT 430~ XFPNGoTHFTA.OELX9(FGSFP(I)9I=29NOFP)
ASSIGN 240 TO NIP
AVESEP:(FQNGX(NOFP)-FRMGX(1))/(N0FP-1,)
FASFP=0.1*AVFSFP

0000

n

735

740

p45

250

255

260

265

270

779

290

285

HR

I5AO:O

DO P35 1:29NOFR

IF (ASS(FGSF9(I)-AVFSEP).GToEASFp) IRAO=IRAO+I
CONTINUE

IF (IRAO.NE.0) POINT 4009 ISAO
M:O

IF (NCAL.NF,O) DQINT 4359 A98
PRINT 445

IF (IOP(3).ANOoIpUNCH) pQINT 355
DO 320 J=19NCOOPO

NFXT:RN

XI4=PFNSFP+XM(J)

00 245 IzloNOFP

IF (XIQ.LF.FRNGX(I)) GO TO ?50
CONTINUF

N=NOFR-l

L=N

NFXTzRHEX SIGHT

GO TO 260

L=I'1

GO TO (2559?50)9 I

NFXTzRHEX LEFT

L=1
FPNOleQCOP+FPNG+L+(XIQ-FRNGX1L))/FGSFD(L*11
IF (.NOT.NCAL) GO TO 315

CALCULATFS FQFOUFNCIFS IF CALISQATION CONSTANTS AQF KNOWN

FQF01=A+R8FRNO1
PPINT 440. NFXToFRNO19WT(J)9FQFQl
IF (.NOT.IPUNCH) GO TO 320

IF (NFXT.NF.FH ) GO TO 120

ORDEPS ANO STOHFS FDFOUFNCIES ANO wFIGHTS FOR AVFRQ OP
FOR PUNCHING

IF (ILT.FO.1) GO TO 279

IF (FQOINAVFqlLT-l).LE.FREOl) GO TO 270
FPO(NAVF9ILT)=FPO(NAVF9ILT-1)
WTS(NAVF9ILT)=WTS(NAVF-ILT-l)
ILT=ILT-1

IF (ILT.FO.1) GO TO 270

GO TO 255

FRO(NAVF9ILT)=FPFOI
WTSINAVF9ILT)=WT(J)

GO TO 280

FQO(NAVF9ILT)=FPF01
NTS(MAVF91LT)=WT(J)

IL=IL91

ILT=IL

GO TO 320

IF (.NOT.IOP(3)) GO TO 110

290

295
300

305

310

315
320

325

330
335
340
345
350

355

160
355
970

375
380
3R5

390
305
400
405
410
415

420
425

PUNCHFS FQFOUFNCIFS ANO

MM:IL-1
(VIOAqLFONFOO)
DUNCH 3909

IF

Sq

NEIGHTS R PFP CARD

GO TO 795
(FPO(NAVF9JJ)9WTS(NAVF9JJ)9JJ=MO9MM1

GO TO 300

DUNCH 3959

(FpO(NAVF9JJ)9WT5(NAVF9JJ)9JJ=MO9MM)

(NNJTIAUJF

MO=IL
IF

(ICOOF.OT.A)

GO TO 305

GO TO 200
ICAPOS=(IL96)/S
ILL=IL-l

PRINT 3709
pUNCH 3709

ILL9ICAQO5
ILL9ICAQOS

CTVUTIAHJF
ILS(NAVF)=ILT
NAVF=NAVF+1

GO TO

POINT 4409

(599019

ICOOF-7
NFxI,FPN019WT(J)

CONT INUF
GO TO GO

DFAO 3759
PQINT 3759

NHFAO
NHFAO

GO TO 60

FOPMAT
FORMAT
FQDMAT
FOPMAT
FORMAT

1 3H RY
2 17H ROTATION
1 254 OASFPVFO PFN

FORMAT

1 FO.19

FOPMAT
FORMAT
FOPMAT

FORMAT
FORMAT
FOPMAT

FORMAT
FORMAT
FORMAT
FORMAT
FOPMAT
FORMAT

1 4X912HMFASUPFO PY

FORMAT
FORMAT

(PA8956x9A8)

(81x9 31H—N0 NAMF CARO-ASSHMTNG NFw SCAM)

(41x. PSHFRINGF COPPFCTION IS NOW 9F5.1)

(F4)

(A89 P7HPFNSFPAPATION FPAME IS NO..A4/ 0H MpAquFn
~2AH/ 18H ROTATION ANGLF ISoFIO.69 8H DAOIANS./
FITS T096(F3.091H9)9 RH MICPOMS/
SFPAPATIONS9(?0F5.O))

( 41H AVFPAGF PEN SFDAQATION FOR THIS FDAMF 18.

RH MICR‘ONS)

(15X9I49X9I59RX9I69X9I5)
(14+.4ox. BSHTHFSF FREQUFNCIFS APF RFING PUNCHFO)
(TS. 3PHFPFOUFNCIES HAVF RFFN PUNCHEO 0N915.

1 20H CARDS FOR THIS CASE )

(10AS)
(6(2F59R1)9I19AA)
( 35H0THIS CAQO HAS A PLANK OP 7FRO COOF95X9

1 6(PF5.091X)/)

(8(4PF89919XI)

(5(3PF99DI9X11

(15+990X912935H FRINGE SPACING VAPIATIOMQ
(81X9 ?8HQOTATION FIT .GT. 10 MICRONS)

( 1H+980X9 97HTHETA IS .GT. 0.005 PAOIANS)

(IHS/ 1H199AS/ 25H LINE POSITIONS FOP FDAMF.A4.
92A5)

(PQHBPFN SEPARATION ON THF FILM =.F6.1.AH MICDONS)
( AIHGTHF FOLLOWING CALIRPATION CONSTANTS HAVF

.GT. 10%)

90

I 19H PFFN INPUT A =9F11.598H R =9Fl3.10)

430 FOPMAT ( 205 FIRST FPINGF IS NO.9F7.196X99%POTATION
1 RHANGLF IS9F10.698H PAOIANS/ 17H POTATIONS FITS TO.
2 6(F3.091H-).8H MICRONS/30HOFRINGE SEPARATIONS IN MICRONS
3 / (5x910F5.O))

435 FORMAT ( 30HCALIPDATION CONSTANTS USED APE95X. 3HA z.
1 F11.595X93HH =9F13.10)

440 FORMAT ( 1HQ9A99F10.49X9R19F13.4)

445 FOPMAT (/10x9 25HFRINGF NUMRER FPFOUFNCY)

450 FOPMAT ( 1H59/9 1H19QAR)
FND

OVFPLAY 3

O

0530

DQngAM AVFPO(FQOowTSoNGPSoNGPS29IOFM)

COMMON /1/ IOP(3)9ILS(8)9TOL19TOL29TOL39A9R9LP.IONIoICALo
1 IOOAh‘NNJP

COMMON /?/ N9VISADLF

COMMON /3/ NAMFI(2000)9NAMF2(200019NU(2000).NMAxoTOLA
COMMON /5/ MUM

COMMON /7/ LL91PPToTOCNT

COMMON IR/ ICHFAO(9)91HFAD(992)9ION(4)

COMMON /9/ CCWT(8-5)

OIMFNSION FFOT(10)9I(8).SIG(8)oSWT(8)9WIT(8)9OFV(8)9
1 WTT(R)9F(10)

ALLOCATFS FQO AND WIS STORAGE ACCOPDING TO NUMRFR OF GPOUPS

OIMENSION FHO(NGPS?9IOEM)9 WT5(NOP5?9IOFM)9 K0(10)
FOUIVALFNCF (F9FPOT)

INTEOFR NTT9WT59WOT9NIT9VISA5LE
NGPSlzmaosg-l

TOL=0.1*TOL1

IF (TOLoLT.0.0002) TOL=0o000?
IOCNT=0

MDUNCHzl

LL31

AZEPOzA

ACNEzP

AVLA5T20.

NOS=0

N=NGPS*1

IF (_HNAD.NE.0) (V7 TO PR5

POINT 415

IF (IONT.NE90) GO TO 35

PFAOS IN HFAOING CADOS

5 PFAO 420. ICHFAO9IFOONF
IF (IFDONE.FO.RHION HEAO) GO TO 25
DPINT 4209 ICHFAO
IF (IFDONF.NF.RHFNO HEAO) GO TO 5

000

10

15

?0

40

45

55

91

Nzl

Nljw'lzn

PFAO 5109 (IHFAO(N9J)9J=197)9A9R9INT

IF (Nquol) GO TO 45

IF (IHFAO(N92).FO.RH OFLFTF) GO TO 370
IF (IHFAO(N9?).FO.RH CHANGF) GO TO 385
IF (IHFAO(N92).FO.SH D(INCH) GO TO 15
GO TO 40

ILIM=ILS(NM1)

KO=1D

IF (VISARLF.NF.0) GO TO 20

PUNCHFS FQFO‘JFNCIF59 WFIGHT59 AND NOS ()F GQOUP JUST CDMDLETFU

PUNCH 4459 (FPO(NM19J)9WTS(NM19J)9KO(1)9J=19ILTM)
GT) TO 10
PUNCH 4509 (FPO(NMI9J)9NTS(NM19J)9KO(1)9J=l9ILTV1
GO TO 10

SETS UP IOENTIFICATION HFAOINGS

OO 30 J=199
ION(J)=ICHFAO(J)

GO TO 5

ION(3)=SH IOFNTIF
ION(4)=HHICATION

GO TO 5

CONTINUE

IF (N.GT.NGPS) GO TO 235
C(HJTIAHJE

SFTS UP STANOAPO WFIGHT COOF COPRFSPONOANCE

CCwT(N9l)=.016
CCWT(N92)=.062
CCWT(N93)=.PS
CCNT(N.4):1,0
CCWTIN'S):190

IPRINT=55

IF (A) 50955950

IA=A

IXA=(A-IA)*1.F5
IR=9*I.F5

X8=H*1.ES
IX5=(XR-IR)*1.F5

PUNCH 4259 IAoIXA9IP91XP
ILT=ILS(N)

IL=ILT

SIG(N)=O.

OFVIN)=0.0

SWT(N):O.

IF (ICAL.NF.O) GO TO 60

O

60
65
7O

7;
80

9‘3
90
<95

100

105

11%

1?0

12%

130
133
140

9?

QFAUQ IN CntUMN HFAOING CADDS

PPINT Slqs ICHFA09(THFAD(NoJ)9J:lo?)
praog IN PUNCHED FPFQUFMCIFS

TF (quapLFoNFon) GO TO 65

9:130 4309 (FRQT(J)Q‘ATTTTJ)9K0(J)OJ=198)
GO TO 70

9.7130 43C§9 (FQQT(J)OWTT(J)9KO(J)onlcg)
CONTTNUF

IF (FRQT) 11Q975911§

IF (FRQT(2)) ROQTOQQQO

TF (.NQT.VISAQLF) GO TO 90

DO 95 J2295

FQQT(J)=FRQT(J)/10

§FTS up NEH CALIRPATIOM COMSTANTS

AZFQO=1.E§*FQOT(2)+NTT(?)+FQQT(3)*.T
A0w5:FRQT(4)+1,F—S*WTT(A)+I.F-6*FPOT(§)
TF (A) QQolOOoQR

§LOPF=R/AUMF

DRINT 4400 TLQAQR

GO TO 60

DPIVT 4409 ILOAZFPOQAONF

GO TO 60

IF (FTWJT(?)) 11(391709110

QFADS IN MONSTAMDARD WFIGHT-CODE COPRF§PONDANCF

CCWT(N¢1)=FPOT(6)
CC“1T(N97)=FWUT(‘S)
CCWT(N93)=FPOT(A)
FCNT(N94):FPQT(3)
CCWT(N05)=FPQT(7)
GO TO 60

CONTINUE

TF (A) 12091409120

CALCULATFS Aufl PUNCHFS FQEQUEHCIES USING NEw CONSTAMTS

DO IPR J=l~9

IF (FRQT(J).€Q.O.) GO TO IPS
FDOT(J)=A+(FQOT(J)-AZFRO)*SLOPF
COi~~£TINUE

IF (VISARLF.MF.0) GO TO 130

PUNCH 44%. (FRQT(J)oNTT(J)oKO(J)oJ=19R)
GO TO 138

PUNCH 480» (FPOT(J).WTT(J).KO(J)9J=198)
CONTINUF

DO 165 J=loP

O

5') ('37)

(7’70

14%

150

199

160
16?

170

179
130

93
7FRO FREDUFWCIFS SKIPPFD
TF (FPOT(J).FO.0) Gn TO 169
D FOLLOWING HFIGHT MFANQ SKID THIS FPFOHFNCY

TF (KO(J).F0.IDn) GO TO 109
IF (KO(J).MF.IP ) WTT(J)=K0(J)
TF (TLT.F0.1) GO TO 155

OPDFPS FQFQUFNCTES LOW TO HIGH

IF (FQQ(N.ILT-1T.LF.FROT(J)) GO TO 150
FQO(MOTLT)=FQQ(NQTLT’1)
WTS(M9TLT)=WTS(M91LT-1T

ILT=ILT-l

IF (ILT.FO.1) GO TO 180

GO TO 145

FPO(M.ILT):F40T(J)

WTS(M.ILT)=wTT(J)

GO TO 160

FQ0(N.ILT):FQOT(J)

wT§(N.ILT):wTT(J)

IL=IL+1

ILT=TL

IF (FPQT.ME.O) GO T0 60

CONTTNHF

DQINT 48%. (CCwT(NoJ)oJ=lv%)

TLT=TLT-1

IF (ICAL.NE.3.0D.IOP(2).NE.3) GO TO 180

CALCULATES FHFOUFNCTFS FQOM CALFIT PROQUCFD CONgTANTg

D0 175 J=10TLT

FPO (NQJ) =AZFQO+A0NF*FPO (NoJ)
CONTINUE

FTOT=F§Q(N91)
FPO(NQTL)=1.F3O

TSAMF=1

TDROpzo

DFRFOQMS IN GROUP AVFQAAIMG AND PPTNTS RESULTS

00 290 J=l~ILT

WGT=WTS(N9J)

TF (FRQ(N~J*1)~FPQ(MoJ).GT.T0L1) GO TO 190
TF (TDON.NE.4) GO TO 189

cLTMINATES AVFPAGTNG IF CODF WFIGHTS APF DIFFEDFNT
TF (WT§(N0J+1).NF.WTS(N9J)) GO TO 190

FTOT=FQQ(N9J*1)+FT0T
T§AMF=ISAME+1

190

195
200
P05
210

215

??0

225

?30
235

240

245

94

IDPQD:1;)DOP+1

GO TO 290

AVF=FTQT/TSAMF

JTTZJ-ISAME+1

TF (TPQINT.LT.§0) GO TO 200

TPDINTZO

TF' (.T‘J‘TT.A) (30 T0 19‘;

PPINT 4600 TCHFADQ(IHEAD(NQL)0L=192)9A999TOL1
GO TO 900

DQINT 4609 ICHFATM(IHEAD(NoL)9L=192)9AZFRO9A0NF9TOLI
TF (TQAMF'l) 210,?nq,210

TF (TDON.NF.1) GO TO 215

DQIMT 4659 (FDO(N9KToWTS(N9K)9K=JTT9J)
{PRINTleRINT+(JTT-J+4)/5

PPINT 4709 AVF

FPU(MqJ-IDQOP):AVF

WTS(N9J-TDQOD):WGT

TSAMle

FT”T:FRO(M9J+1)

CONTINUE

TLTzILT-IDQOD

TLS(N)=ILT

TL=TLT+1

FRQ(NQTL):10F?0

|\lMl:r\|

ru=N+1

GO TO 10

CALCULATFS FPFQUFNCTFS USING CALFTT CONSTANT§

CONTINUE

DO ??0 MI=19NGP§
NIL§=TLS(NT)

DO ?30 J=1~NTLS
FPO(MI-J)=A+Q*FDQ(M19J)
MzN-l

TF (TCALoFQ.3) TCAL=O

TF (ICAL.NE.0) GO TO 249

DQTNTS AVFPU PAGE HFADINGS

199T20

POINT SIS. ICHFAD

IF (VISARLF.NF.O) GO TO 240 _
PRINT 8369 (IDN(1)9I0N(2)a(IHEAD(IH~l).IH=1.N))
PRINT 6489 (IDM(3).IDN(4).(IHEAD(IHo2)oIH=l-N))
DQINT 589

GO TO 24% _
PPINT Ran. (IDNII).TDM(P)~(IHFAD(IH-l)oIH=1-N))
PRINT §Sn~ (IDN(3)sION(4)~(IHFAD(IHo2)oIHzloN))
PQINT 838

CONTINUE

IF (A.EQ.0.) A:A7EPn

OCWF)

PR0
P95

260

269

270

?75

?80

PRS

P90

99

IF (Qquono) RZAOMF
lezm—l

FOLLOWTMG SFCTIHM PFRFOQMS QFTWFEM GROUP AVFRAQTNG

00 PRO J=19N

T(\J)=l

F(l)=F99(lol(l))

F§=F(l)

STGT20.
WIT(1)=WTS(191(1))
TWS=WTT(1)

no 260 K329N
F(K)=F43(K91(K))
WIT(K)=NTS(K91(K))

TF (F(K).GT.FS) GO TO 760
FS=F(K)

1W82NIT(K)

CFYJTIIHIE

A\/#:0

AVG=AVN

ICNT=0

no 290 K=ToN

TF (F(K)-F9.LF.TOL?) GO TO 270
F(K)=1.F?0

WIT(K)=49

GO TO ?RO

IF (IDON-NEo4) GO TO 279

FLIMINATES FRFQUFNCY FQOM AVFRAGE IF WFIGHTS DIFFFP

IF (WTT(K).NF.IWS) GO TO 265
XCWT=CWT(KQWIT(K))
AVG=AVG+F(K)*XCNT
AVW=AVW+KCNT

I(K):I(K)+l

TCNT=ICNT+1

CONTTNUE

AVG=AVG/AVN

IAVGzAVG

DO 290 KzloN

TF (F(K).GT.1.EIO) GO TO 290
IF (TCNT.LF.1) GO TO 2R5
KCNT=CNT(K9WTT(K))
UFVT=(AVG-F(K))
QTG§T=DEVT**P*XCWT
SIG(K)=§IG(K)+9TGST
qTGT:STGT+STG§T
DEV(K)=UFV(K)+DFVT*XCWT
SWT(K)=SNT(K)+XCWT
FTKTZFTKT-IAVG

TF (F(K).LT.0) F(K)=1.+F(K)
CONTTNUE

GOO

0730

("700

P99

300

309
310
319

320

3?9

330

339

340

349

96

9IGT=SQQT((9IGT*ICNT)/((ICNT-l)*AVW))
IF (ICAL.NF.0) CO T0 300

IDQT=IDPT+I

IF (IPRT.LF.90) GO TO 300

PPINTS AVFRQ PAPE HFADINGS

PQINT S30. TUL?

PQINT 9199 ICHFAO

IPHT=I

IF (VI9ARLF.NF.O) GO TO 299

PQINT 9390 (IUNII)9ION(?)9(IHFAO(IH91)9IH=ION))

DPIVT 9490 (IDNI3IQIDN(Q)9(IHEAD(IHOZIOIH319NI)

PRINT 959

GO TO 300

DRINT 9409 (ION(I)9ION(?)9(IHEAO(IH91)9IH=19N))

pDINT 9909 (IONT3)QION(4)9(IHFAO(IH92)QIH=ION))

PQINT 999

CONT INUF.

FPNG=(AVG‘AI/R

IF (IONT) 30993109309

CALL IIDFNT (AVGOAVWI

IF (ICAL) 315937093I9

NUMzNUM+1

FPQ(NGPSIONUM)=AVG

FQQ(MGPSZONUM)=AVW

GO TO 390

IF (VISARLE.NF.0) GO TO 329

DPINT 9909 NAMFI(LDIQNAVE2(LP)oFRNGqAVGoAVNo9TGTo(F(J)¢
WITIJIOJ=19NI

GO TO 330

CALCULATFS AI? WAVFLFNGTH FROM VACUUM FPEOUFNCY

XKVT=AVG*I.F-4

XKVTS=KKVT**2

XN=(6432.R+?949R10/(lhfi-XKVTS)+29940/(41-XKVTS))*I.E-R+I

XKAT=XKVT*XN

WL=1.F4/XKAT

PRINT 9290 NAWEI(LPIQNAME2(LP)oFRNGoWLqAVGsAVWoSIGTo
(F(J)9NIT(J)0J=I¢N)

IF (IOP(2).NE.?) GO TO 345

IF (IDON.FO.2) GO TO 339

GO TO 340

PUNCHES AVEPAGF FREQUENCY wITH IDENTIFICATION

PUNCH 670. NAMFI(LP)9NAMF2(Lp)9AVG

GO TO 349
IF (NAMFI(LP).FO.RH ) GO TO 749
PUNCH 970. NAMEI(LPIoNAMF2(Lp)oAVGoAVW
CONTINUE

IF (AVG-AVLA9T.GT.TOL2) GO TO 390

on")

350

399

360

365

370

379

380

«‘27

PRINT 960

CONTIAHHI

AVLASTzAVG

DO 399 J=19N

IF (I(T).LF.ILS(J)) GO TO P99
CONTINUF

IF (ICAL.NF.O) GO TO 410

CALCULATFS AND PQINTS STATISTICS

GSIGT=O.

GAVN=Oo

NUHR=O

OO 360 J:I¢N

NUVR=OHNM3*ILS(JI
OFV(J)=OFV(J)/9WT(J)
GSIGT=OSIGT+9IG(JI
GAVik‘zGAVW+9WT (J)
9IG(JI:SOPI(9IGIJ)*ILS(J)/IILS(J)-II/SWT(J)I
GSIGT=SQDT(GSIGT*NUWR/(NUMR-II/GAVW)
IF (VISARLE.MF.0) GO TO 369
PQINT 4790 (DFV(J)!J:19N)

PQTNT 4900 GSIGT9(SIG(J)9J=IQN)
pPINT 489v (ILS(J)9J=IQNI

PQINT 9099 IOCNTQNMAX

DRINT F3300 TOLZ

GO TO QIO

PQINT 4909 (OFV(J)0J=19N)

DDINT 4999 G9IGT~(9TO(J)9J=19N)
PRINT 9000 (ILS(J)9J=19N)

POINT gag, IOCNTQNMAX

PQTMT 9309 TOL2

GO TO 410

FOLLOWING SFCTION OFLETFS UNWANTFO FREQUENCIFS

CONTINUF

OO 3R0 KzloILT

IF (ARS(FPO(NM19K)-A).GT.TOL) GO TO 380
DO 375 J=K.ILT
WTS(NMl-J):WTS(NM19J+I)
FPO(NM19J)=FRO(NM19J+1)
TLS(NM1)=ILS(NMl)-l

IF (IOp .NF. RH9URTITLF) GO TO 30
DRINT 906. LIST

ILT=IL9IMMII

GO TO 10

CONTINUE

PQINT 9599 AoIHFAO(M92)

GO TO 10

FOLLOWING SFCTION CHANGFS FQEOUFNCIFS

98

389 CONTINUF

390

399

400

409

410

419
420
4?9
430
439
440

449
450
499

460

469
470
479
4R0
«RS

PO
TF
IF
no
IF

409 K=IQILT
(ARS(FQU(NWIQK)-A).OToTOL)
(qoLT.FRO(NMl-K)I
300 KOKquILT

(9.9T.FRQ(NMIQKOK+I)I

GO TO 409
GO TO 399

GO TO 390

WTS(NM19KOK)=IMT
FQO(NM19KOK):R

GO TO 10
FQJ(MM19KOK)=FHO(NMIoKOK+1I
WTS(MM19KOK):WTS(NMIcKOK+I)
FPO(NMIQILTI=R
wT9(MM19ILT)=TwT

GO TO 10

KM1=K-1

O0 400 KOR=I~KMI
KQMzK—KQK

IF

(9.LT.FRO(NM19KQM))

GO TO 400

FQU(NM19KQ%§1):D
WTS(NMIQKQW+I):IWT

GO TO 10
FRQ(NM19KQM*I)2FQO(MM19KOM)
WT9(NM1oKQV+l)=wI9(MM19KOM)
FQ0(HM191):H

WTS(MM101)=IMT

GO TO 10

C(VJTTAMJE

pQIMT 5550

A.THFAO(N~2)

GO TO 10
CONTINUE

PFTUDN

FOPMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT

? I7H CALCULATFO

FORMAT
FOQMAT
FORMAT

I 6KOIH199X9IHPQQXQIH399XQIH497X99H9LANK/ 10H
2 9F10o4)

FOHMAT

ZHA=9FII.9-9H
P AHwITHIN.F7.3.24H

FORMAT
FORMAT
FORMAT
FORMAT
FODMAT

(lHO/IHI)

(IOAA)

(15x.IA.x.IR.9x.IS.x915)

(R(FF.4q?Hl))

(9(FH.3¢PQ1))

( 34HOFPFOUFNCIF9 BEGINNING WITH NUMRFQ.149§H wFPF
USING / 29H THF FOLLOWING CONSTANTS. A:
P:gFl?.IO)

(9(4DFRo?Ql))

(8(3PFRo2Ql)T

( 27HOWFTGHT-COOF CORPF9DONOFNCFo/9XQ9H COOF.
WFIGHT

(1H199AR/IHOoPAR/ ETHO CALIRPATION CONSTANTS
R:.FIP.IO/ 29H0 IHESF FREOUFNCIFS ADF
NAVF NOQ. OF FACH OTHEQoQX97HAVFQAGF/)
(S(F11.4quPlI)

(1H+~67XF10.4)

( IOHO AVFPAGF DFVIATIOM93OX98(3XF7.4))

( 19H STANOADO OFVIATTON.?4XF7.492XF7.497(3XF7.4))
( 22H NO. OF LINFS MEASURFD.?6X.R(6XIA))

067?)

90

490 FORMAT ( IMHO AVFPAGF OFVIATIOM.41X.R(3XF7.4))
R39 FOHVAT (1H0.2AR.?X.16HFPINGF AVERAGF-lflxo 4H§TO..?XRAIO)
San FODMAT ( IHOq2A992X9 PTHFQINGF WAVFLFNGTH AVFPAGEQIOXQ
I 4H9TO.92X9RAIOI
94S FOPMAT (1X?A%.?Xo3OHNUM9FR FPFOUFNFY WGT. nFv..PXRA10)
990 FOUMAT (IXRARoBXo 37HNUMRFQ IN AID FRFOUFMCY WGT.
I 4HOPV..?X.RAIO)
955 FOFMAT (1H )
960 FOQMAT ( 1H+o39XolH*)
969 FOQMAT (IPHFQFOUFNCY OF9F10.4919H WAS NOT PQFGFMT TO9A9)
970 FOQMAT (2A9.3XOF13.497XOF4.2)
FNO

FUNCTION CWT (IA9I9)
CONVFPTS COOF-WFIGHTS TO NUMFRICAL WEIGHTS

COMMON /9/ CCWT(8o9T
IF (I9.E0.0) GO TO 9
IF (I9.(¥I.4) (HT TO IT)
CMT=CCNT(IA~IR)
DFTUQN

9 CWT=1.F-?O
PFTUPN

IO CszCCVT(IA99)
PETIJDM
FNO

SUPPOUTINF IIOFNT (AVFPFOgAVW)
COPPFLATFS AVFQAGF FPFOUFNCIFS WITH IDFNTTFTCATTONS

COMMON /1/ IOP(3)9TL9(R)~TOLIoTOLZoTOL3-A9R9L0oIONTqICALo
1 IFWYdoJUWP
FOHMON /3/ NAME](2000)oNAMF?(POOO)oNU(?OOO)oMMAX.TOL4
FO%MON /7/ LL~IDHT0TOCNT
QFAL NH
IFRGTzO
LD:NMAX +1
9 X:AVFPFO-NU(LL)
IF (AP9(K).LF.TOL3) GO TO 30
GO TO 10
IO IF (X) 19919.20
19 PETUQN
?O IF (TOON.NE.9) GO TO P9
IF (LL.FO.LASTL) GO TO ?9
IF (AR9(NU(LL)-AVFL).LF.TOL3) GO TO 25
IDHT:IPQT+]
DQINT 90. NAMFI(LL).NAMF?(LL)9NU(LL)
29 CONTINUE
LL=LL+1
IF (LL.GT.NMAX) IONT=O
GO TO 9

3O

3?

(J
J“:

40

90

100

LD=LL

LASTL=LL

TOCHTzIOCMT+l

AVFLzAVFHFO

LLplzLL+I

IF (AD§(AVFFFO-NH(LLDIT).GT.TOL3) QFTUDN

IFPSTzIFN§T+1

IF (TOD(?).NF.?) PFTUQN

IF (IOON.FO.?T GO TO 39

GO TO 40

BUNCH 999 MAMFI(ILPI)9NAME?(LLP1)9AVFQFO

LLPI=LLPI+I

IF (IFQST .NF. 1) GO TO 32

DUNCH 999 NEWFI(LLI9WAMFEILLI9AVFQEO

GO TO 3?

pUWCH 959 NA“F1(LLDI)9NAME?(LLDI)9AVFPF09AVN

LLDI=LLPI+1

TF (TFHST .hF. I) GO TO 32

DUNCH 99- NAMFI(LL).NAMP2(LL)oAVFPEOoAvw

GO TO 32

FORMAT (IX~?AR-QX~FII.49 RRH THIS INPUT IOFNTTFICATIOM
13HWAS NOT FOUND)

99 FORMAT (2A993X9FI3.497X9F4.2)
FNO
OVFPLAY 4

00:5

DQOGDAA SFAPCH(FRO9NGD9?OIOEMI
COMMON /I/ I’)D(3) 9I'-9(R) 9TOLI9TOL29TOL39A999LP9IONTOICALO

1 IOOkuxflyAQ

COMMON /3/ MAMFl(2000)oNAMF2(2000).NU(?000)~NMAX~TOL4
COVMON /4/ FMHM(100)9FPFQ(IOO)9WT(IOO)oSUMWHToMODATAoINOATA
COMMON /9/ MOM

ALLOCATE9 FRO 9TOQAGF ACCOPOING TO NUMRFR OF GDOUPS

DIMENSION FPO<MGP§?.IDFM)
DTMFMSION IOTNTIISOI- IOINT2(9“T
PFAL NU

NGPSI=NGP§2-l

PEAO 16S. NUMLIMFS

TNOATA20.0

MnnATA:INOATA

QUMWHT=NOOATA

L=1

LT=1

QFADQ IN ANO QQGFPS ASQIGNFO LINES
DFAD 160. IIOFNTIoITOFNTEoXFNUM

TF (XFMUM,P0,n,o) GO TO 20
IF (L.FO.1) GO TO 1:

00F)

IO

19

PO

2%

3O

39
4O

50
99

60

101

IF (FNOM(LT-I).LF.XPNUMT GO TO 19
FMUM(IT)=FNOM(LT-l)
IOINT1(LT)=IOTNT(LT-l)
IOIMT2(LT)=IOINT2(LT-I)
LT=LT-1

IF (LT-l) 19.19.10
F“«IM(IQT)=XFIAIM
IOINT1(LT)=IIDFMT1
IOINT2(LT)=IIOFNT?
L=L+I

LT=L

GO TO 9

LMAX:L—1

[LzLMAX

IF (LMAX.LT.?) GO TO 190
9H9X?:O.O

9UMXY=9JMXP

GUMY:§U AXY

9U4X29JMY

II=O

LL=1

9FAQCHF9 CALIRQATION OFFKS FOR INITIALIY ASSIGMFO LINF9

OO 70 L=19LMAX

OO G9 '-‘\J=I9I‘\|'V.AX

IF (TOIMTI(I).FO.NAMF1(M)) GO TO 2%
GO TO 69

IF (IOTNT2(LT.FO.NAMF2(M)) GO TO 30
GO TO 69
X:FNUM(LT-FDOU‘JGPSI.LL)

IF (ARS(X).IE.TOL4) GO TO 49
GO TO 39

IF (X) 99959.40

LL=LL+1

IF (LL.GT.NUM) GO TO 79

GO TO '30

II=II+1
FNOM(TI)=FRO(MGDSI.LL)
vT(II)=FDO(NaPS?oLL)
FDFOIII)=NO(W)
9UMNHT=9UMWHT+WTIIII

IF (WT(IIIT 90.99.90
NIIJITATA="~J’)T)AT,A+I

AMFAZNU“-I

CALCULATF9 INFOPHATTON FOP INITIAL LEAGT soqura FIT

OO GO K=LL.NHM
FPO(NGPGI.K)=FPO(NGD9I-K+l)
FQQ(MGDS?.K):FQQ(NGDSZOK*II
cgu4ngumx.TIMJM(II)
SUWYzSUWY+FPFOIII)

(3530

69

7O
7%

102
QUMXY=Sd1XY+FNUV(II)*FPFO(II)
QUMX228UMX2+FNUM(II)*FNUW(II)
GO T0 70
CONTINUF
IL=IL-1
IF (IL.LT.P) GO TO IQO
CONTINUF
IF (II.LT.?) GO TO 190

CALCULATFS INITIAL CONSTANT§

O=II*9UMx2-SOMX*SUMX
A:(gUMY*§UMX?-§HMX*9HMXY)/D
R=(II*SUMXY-SUMX*SHMY)/O
LL=1

SFAQCHFQ FRQ MATQIX F09 MQQF CALIRQATION LINFS

90

R9
90

as

100
105

]?O

“0 140 IT=l-?

no 119 I=loNHM
FQOP=A+H*FQQ(N60919I)
Xszfip-NU(LL)

IF (fiR3(K).LE.IOL3) GO TO 99
GO TO 95

IF (X) 1159119900

LLzLL*l

IF (LLofiT.NMAX) GO TO I70

00 TO 90

II=II+1

FPFQ(II)=NU(LL)
FMHM(II)=FRG(NGDSIQII
WT(II)=FQQ(NGPS?QI)
QUMWHT:SU%MHI+WT(III

IF (WT(II)) IOOQIOSQIOO
NHUATthQDATA+1

NUMzNHM-l

IV) 110 K=I0NUM
FQQ(NGPSI9K)=FRQ(NGDSloK+1)
FQQ(NGPSRQK)=FPQ(NGDS29K*1)
I=I‘I

§HMX=SUMX+FNUM(II)
QUMY=SUMY+FPFO(II)
§UWXY=§HMXY+FNUMIII)*FPFQ(II)
§UMX7:SUMX?+FNUM(II)*FNUM(II)
0=II*SUMK2-SHMX*SUMX
A:(SUMY*SUMX2-SUMX*QUMXY)/D
R=(II*§UMXY-§UMX*SUMY)/D
CONTINUE

ELIMINATF9 LINE9 WHICH APF OUT OF TOLEPANCE

OO 11g 1:1.MOOATA
FPQP:A+R*FNU“(I)

0000

000

10?

IF (APS(FPQD‘FRFO(I)).LF.IOL3) no In 135
DPIVT 199. Fuum(1)
II=II-1
SHMwHT=SUMIHI-NT(I)
IF (VT(I).FU.O.) 60 TO 199
NOUATAzwflnATA-1

1?9 (VINTIIMIF
O0 130 K:1.11
FPFQIK):FPFO(K.])
FNUM(K)=FNHM(K+1)
NT(K)=WT(K+1)

110 CONTINHF

11?; C(rJTIhHIF
IF (II-LT.WHMLIME9) an TO Ian
GO TO 149

140 CONTINJE

149 IMDATA=II

TPANSFFR FQFOUFMCIF9 AMO COPRF9DONOING FQINGF MHMRFD§
FOR FINAL CALIRQATION CONSTANIS

CALL CALFIT
DQINT 170. INDATAomHMLINES
QFTURN
190 DDIMT 179
DFIINDN

199 FOPMAT ( 11% FRIMGF NO..F10.4. PIH WAS IOFNTIFIFO A9 A
1 PQHCALIRPflIION LINF RHT REJECIED)

160 FOPMAI (?AR.IBX.F10.33X.A8)

169 FORMAT (I10)

170 FORMAT ( 3H? .19. 14H LINFS OUT OF 919. 11% HAVF PEFN
1 17HFOUNO AMO FNTFPFD)

179 FOQMAT ( 49H?A WQONO IDFMTIFICATION OR FRINGE NUMREP HAS
1 IOHPFFV INDUT)
FIN)

SUBROUTINE CALFIT
LINEAR LFAST 90HAPF9 PPOGRAM

COMMON /1/ IOP(3).ILSIa).TOLI.T0L2.T0L3.A.R.Lo.ran.ICAL.
1 IOOM.JOMP

COMMON /4/ FQINaF1100).FPFQ(100).WHT(1001.9UMNHT9NOOATA~INOATA
DIMFNSION COFN(1).DATA(1>.IH(10).INOEX(3).SIGMA(1).

1 SIGMCO(3).VFCTOP(4.4)oIHEAOIBI

OATA (IMFAOzaH COMST.RH SLOPF)

DOUHLE DQFCISIOH COFN.919MA.SIGY.VECTOQ

DDINT P60

ppqnq IN HFADING CADDS

9 PFAD 2799 IH

104

IF (IH(10).F0.RHLA§T FIT) 9TOD
IF (IH(10)-94FNO HFAD) 10.19.10
10 PQINT 779. IH
GO TO 5
19 PRINT 279. (IH(I)~I=1¢Q)
NUFL=O
70 VAPzfl.n
FLFVFL=VAQ
UFVMAX2FLFVFL
MOMAX:O
NOMIM=MQMAK
NOFNTzHOMIV
KzNOFNT
MOIM=K
AVGNHT=SUMth/NDDATA
00 2‘3 1:1916
29 VFCTOP(I)=O.O
DATA:1.0
IV) 30 "|=101’\”7AIA
NT:WHT(M)/AVGWHT
DATA (P):FRIVGF(N)
DATA (3)=FHFO(N)
DO 30 1:193
VFCI0P(I94)=VFCIOR(I94)+DATA1119WT
DO 10 J=193
30 VFCTOR(19J)=VFCTOW(I.J)¢DATA(I)*DATA(J)*WT
VFCIOP(Q.4)=NODATA
PQINT 3009 NOOATAoAVGWHToVFCTOQ(P94)oVFCTOQ(3oh)o
DDINT 3009 NODATAoAVONHTsVFCTOP(?.4)oVFCTORI39h)0VFCTOQ(?9?)9VFFTI
1 VFCTOQ(992.9VFCTOP(?93)QVFCTOP(307)
NOSTFp=-1
DFFQ:VFCTOR(4.4)‘1.0
DO 50 1:193
IF (VFCTOD(191)) 39.40945
35 ORINT 3109 I
GO TO ?99
#0 PQINT 3199 I
SIGMA(I)=1.0
GO TO 90
45 SIGMA(I)=USQQT(VFCTOQ(I¢I))
90 VFCTOQ(IoI)=1.0
U0 Q5 1:192
Ipl=I+l
DO 9; JIIDIOK
VFCTOQIIoJ1=VFCTOP(IoJ)/SIGMA(I)/SIGMA(J)
95 VFCTOP(JoI)=VFCT0F(19J)
DQINT PRO. VFCIOP(?.1).VFCTOP(3QI)oVECTOP(3o?)
60 MOSTrpszSTFP+1
IF (VFCTOP(3.?)) 69.69.70
69 NSTPMI=N0§TFP-l
PQINT R30. N9TPM1
GO TO ?29
70 §IGY=SIGMA(3)”DQOQTIVFCTOR(393)/DVFP)

79

115
120
129
130
139
140

149

190
199

160

109

DFFQ=DFFQ-l.0

IF (“FF”) 79979.90

DPIMT 3199 N09IFD

GO T0 ??9

VMAX:0,0

VMIN=VMAX

MOIH=0

00 130 1:19?

IF (VFCTOQ(I9I)) 99.130.90

DQINT 3409 19NU9TFP

GO TO 229

IF (VFCTOP(I9I)-0.000l) 130999999
VAQ:VFCTOQ(I93)*VFCTOH(39I)/VFCT09(I911
IF (VAR) 10091309120

NOIN=N01M+1

INUFX(NOIV)=I
COFMINOIM)=VFCTOQ(I93)§916MA(31/SIGMA(I)
9IGMCO(U01N)=D9ORT(VFCTOR(19I))“SIGY/9IGMA(I)
IF (VMIN) 11991109109

PQIMT 380

GO TO ?99

VM1M=VAQ

“UNAINzI

60 T0 130

IF (VAR-VMIN) 1309130.110

IF (VAQ-VMAX) 17091309179
VMAX=VAR

NOMAX:I

COVTINHF

IF (NOIN) 13991409149

PQIMT 799

GO TO 299

PPINT 9999 SIGY

GO 70 170

1X=RHFNTFDING

IF (NOENT) 19091909199
IX=RHPFWOVFD

PRINT 3099 N09TFP9IX91HFADIK)
DpINT 2909 IHFADIK19FLFVFL9SIGY
DO 190 J=19MOIN

JK=INDFX(J)

DQINT 7699 IHFAD(JK)9C0FN(J)9SIGMC0(J)
A=COFN(1)

HzCOFN12)
FLEVFL=VMIN*DFFP/VFCIOQ(393)

IF (FLFVFL+0.0000001) 17091709169
K=NOMIN

NOFMT=0

GO T0 190
FLFVFL=VMAX*DFFQ/(VFCTOQ(393)-VMAX)
IF (FLFVFL-0.00000011 ??091799179
K=NOMAX

NOFMTzK

O

106

190 IF (K) 199.199.190
189 PRINT 349. NOSTFP
GO TO 299
190 VK=1.0/VFCTOH(K.K)
DO 205 1:193
IF (I—K) 199.209.199
199 O0 200 J=l.3
200 IF (J.NF.K) VFCTOQ(I.J)=VFCTOR(I9J)-VFCTOP(I.K)*
1 VFCTOQ(K.J)*VK
209 CONTINUE
O0 210 1:1.3
210 IF (I.ME.K) VFCTOD(I9K)=-VECTOQ(I.K)*VK
OO 219 J=1.3
?19 IF (J.MF.K) VFCTOQ(K9J)=VECTOP(K9J)*VK
VFCTOQ(K.K):VK
GO TO 60
220 PQINT 2999 NOSTFP
229 CONTINUE
PQINT 390. VFCTOQII91)9VECTOP(?.2)
VFIT=0.
DATAzl.
DO 240 N=191MOATA
NT=WHT(N)
OAIA (2)2FQIMGE(N)
YPPEO=0.0
DO 210 1:1.NOIN
230 YPRFO=YDDFO+C0FN11)*OATA(IMOFX(I))
OFV:FPFO(N)-YPHFD
VFIT=VFIT+wT*OFV*OFV
PPINT 360. N.OATA(2)-F9F0(N)9YPRE090EV.wT
AOEV=WT*DEV*OFV
1F (AOFV—OEVMAX) 240.239.239
239 NMAX=N
OFVMszAOFII
240 CONTINOF
VFIT=VFIT*NOOATA/(NOOATA—2.0)/VECTOD(4.4)
9TOFIT=O90~T(VFIT)
PRINT 270. VFIT.STOFIT
IF (9-NOFL) 299.299.249
249 IF (OFVMAX-0.000029) 299.299.290
290 NOEL=NOEL+1
MOOATAzNOOATA-l
gUMwHTzsnMWHT-WHTINMAX)
WHT(NMAX)=0.0
PQINT 399. NMAX
GO TO 20
299 QFTHQN

790 FORMAT ( 1H1)

769 FOQMAT (0179F1R.10.F16.10)

P70 FORMAT (11H0VARIANCF =9Fll.6/91?H 9T0. DEV. =9FR.4/91H7)
P79 FOPMAT (1008)

790 FORMAT ( 33HOPAPTIAL COPQFLATION COFFFICIENTS9OX9RHCONST

107

1 5HFDTMGF/?Rx.GHFDINGF.Fl2.4/29X.QHFQFOUENCY92FQ.4)
2R9 FORMAT ( 23H09IANOADO FDPOQ 0F Y 199Fl?.6)
790 FORMAT ( 11H F LEVFL OF9Q69F11.2/9 17H STD nFV OF (0-910
1 F11.2//10X9HVAPIADIF99X911HCOFFFICIENT96X910H9TO. EPDOQl)
299 FORMAT ( 10H0C0MPLFTED9129 20H SIFDS 0F RFGQF9910N)
300 FORMAT (IQH-CALIRDATION FIT 0F91496H LINFS/ RH0WFIGHT
1 13HNORMAL17ATION.F9.2/ 22H SUM OF FRINGF NOS. IS.F12.4/
2 2B SUM OF FPFQUFNCIFS IS9F12.4/ POHORAW SSCp MATQIX

3 21HFPIWGF FRFOHFNCY/ 11H FRINGE.FIR.7/ 9x
4 QHFPFOUFNCY.2F19.2)
309 FORMAT ( QHOSTFP NO..I?. 12H VAPIARLFsAqobq)

310 FORMAT ( 24HFQROP 9:310. SQUARF VAQ..12. 19H I9 NFGATIVF.
1 7HSO LONG)
319 FORMAT ( QHOVADIARLF9IP9 12H IS CONSTANT)
120 FORMAT 29H0FHDOD. VMIN PLUS. 90 LONG)
329 FORMAT 27HOFHDOR. NOIN MINU9. SO LONG)
330 FORMAT RJHOY 9OHADF NON-DOSITIVFo TFPMINATF 9TF9912)
339 FORMAT P9HnNO MOPF OFGQFFS FPEFOOM STFP91?)
340 FORMAT ( IOHOSOHAHF x-.119 1AH NFGATIVF. SO LONG912.
1 6H STFPS)
349 FORMAT ( QHOKzO STFP.12. 9H. 90 LONG)
190 FOQMAT ( IQHODIAGONAL ELEMENTS.SX. SHCONST.FQ.4/23X.
1 6HFD]NGF.FR.4/ 191.10x.7HDFSULTS/ 21H0 PUN FQINGF FPFO
2 30HORS FFFO CALC 099-CALC WHT/)
15; FORMAT ( IRH+OFLETIN9 LINE NO..14)
360 FORMAT (14.F10.4.2F11.4.FQ.4.F6.2)
FND

AAAA

PDOGQAM MOLCO

PQOGQAW
19QN2T9I
COMMON

1
COMMON
COMMQM
1
COMMON
1
P
3
COMMON
1
p
COMMON
DIMFMSI
FOUIVAL

013<5rJTD.J\J~

INTFGFR

C INITALI

DFAL LA
INFIT(1

APDFNUIX R

FORTQAN LISTING OF ANALYSIS PROGRAM9

N

MOLCON (IMDUI9UUTPUTQTAPE1QNEDAIAQTAPF73=NZDATA9
APFBPZSVM211
H1(1.?)9HPI397)9FPI(3)9NUSF(9000)9FOMCO
NII9000)9C0N9TNT(26)9FCONS(?6)9SCON(?5)

/A/ NAMF(?6)

/1?/ INF0191WF0291NF0391NFOA9NUMCON9JU“09

C0N9T(?fi)9FFIN9FF0UT9TOL9IDFNI(719TOLF

/17/ 1999(900)919(900)9IN(500)91K(5001OIHFAD(9)9

VU(19)9VL(19)9NV9V(15)9FOHS(90001QIIPY59ITQCNT9

IRAQQAY(1?0)oISAQQAY(120)OIMARRAY(120)’

IKARQAY(1?01
/21/ N1(?7)9VFCTOD(?R9RR)91NDEX1271910FX12719
SIGVA(?7)9C0FN(?7)9SIGMCO(?7)9N0T1N(?7).
XCON5112719N01N
/]?3/ NK(?619NDFLMAX9XDFVMAX
UN TFVP(960)9 COU(3)9 INFIT(2)

FNCF (C0M91NI1119API19 (C0NSTNI1219Rp119
(COM9INTI3)9DPI)9 (CON9TNT(4)9CO)9
(CUM9TNT(S)9C1)9 (CONSTNT1619C219
(C0M9TNTI7)9RSIG)9 (CONSTNT(8)9DSIG)9
(C0N9TNT(Q)9LAMDA)9 (C0NSTNT11019GAMMA)9
(CONSTNT(11)9NUZEPO)9 (CON91N1(1219WU)9
(CONSTNTI1319XU19 (CONSTNT(1419YU)9
(C0M9TNT(19)OZU)9 (C0MSTNT(16)9WL19
(CONSTNT(17)9XL19 (CONSTNT(18)9YL)9
IFDN9TNTI1919ZL19 (NUSE9TFMP)

VU9VLQTFMD

IFS NAME9 AND VADIAQLES

MOA.LAMOAV.NH7FPO
)23HNO

INFITIP):?HYFS

NAMETI)
MAMF(2)
NAM913)
NAMF(Q)
NAMFIS)
NAMF(6)

:4HEAQT
=4HFRPI
:QHIZNFNDI
=3HFC0
zthCI
=3HEC2

109

000

ad

109

NAMF(7)=9HF99IG
NAME(P)=9HFO9IG
NAMF(9)=6HFLAMOA
NAMF(10)=6HFGAMMA
NAMF(11)=7HFNUZFQO
NAME(12)=3HENU
NAME(13)=3HEXU
NAMF(14)=3HFYU
NAME(19)=BHFZU
NAM9(16)=3HEWL
MAMF(17):3HFXL
NAMF(19)=3HEYL
NAMF(10)=1HF7L
NAMF(20):AHFALAPI
NAMF(21)=6HFRAAPI
NAMF(22)=6HFALBPI
NAMF(?3)=6HFRARPI
NAMFI24)=7HEALHSIG
NAMFI26)=6HFALLAM
NAMF129)=7HFHAR919
NUMCON=26
NCON91=NUMCON+1
JK=1

KI=0

JHJP:O

CONTINUE

ITQCNT=0

DFAO9 In AND PRINTS OUT HEAOING

QFAD P69 IHFAO9IFDOMF

1F (IFDONF.F0.RH STOD) STOP
PQINT 269 IHFAD

1F (IFDONF.NE.8HFNO HFAO) GO TO 1

QFADS OPTION CAQD

READ 28. IOFNT.ITPY9.INF01.INFO29INF03. INFO4.
(NK1I).=l.26).NOFLMAX.XOEVMAx.TOL.TOLF.FF1N.FFOUT.ICASE
A9SIGN 4 TO MGO

IF (ICA9F.FO.RHNFW CASE) GO TO 2

IF (ICA9F.F0.PHNFW CONS) ASSIGN 14 TO MGO

IF (ICA9F.F0.RHADD CONS) GO TO 14

CONTINUE

IT=0

PFAOS IN CONSTANTS ANO FPACTIONAL CHANGFS

QFAD 299 FONSINTODFLAPIODELRPI
QFAO 299 FCONS

SFT9 FRACTIONAL CHANGE IF ANY OP ALL NOT DEFINFO

000

10

11

110

IF (FCON9(1).F0.0.0) FCONS(1)=1.0

DO 3 11:2926

IF (FCON9(II).F0.0.0) FCON9(II)=FCONS(1)
CONTINUE

[RUF20

I9FC=0

GO T0 “909 (1494)

CONTINUE

IT=IT+1

QFADS IN FPEOUFNCIF9 AND IDENTS

PFAD (73,30) VU(JK).VL(JK)OIRPOIQNQKQFOPS(IT)9WT1IT)9
IIFDONF

JOFL=I9R-IQO

J=K+?*N+JDFL

IF (J.NF.0) GO TO 9

IT=IT-1

GO TO 11

CONTINJE

IF (KI.NF.0) GO TO 6

IVUD=VU(JK)

IVLP=VL(JK)

GO T0 8

IF (VU(JK).NF.IVUP) GO TO 7

IF (VL(JK).FO.IVLP) GO TO 8

NVSVIJK1=KI

VU(JK+1):VU(JK)

VL(JK+1)=VL(JK)

VU (JK) =IVUP

VL(JK)=IVLp

JK=JK+1

TVUP:VU(JK)

IVLP=VL(JK)

KI=0

IF (1A9T1.EQ.1) GO TO 9

KI=KI+1

I9UF=IRUF91

IF (IROF.LE.240) GO TO 10

CONTINUE

IRUF=1

ISUR=2A*ISEC+1

ISFC=ISFC+1

FNCOOF (109319IRDS(I9U9) )(TFMP(M).M=19240)
FNCOOF (10.31919(I9HH) )(TFMP(M)9M=24194RO)
FNCOOE (10931.IN(ISHR) )(TEMPIM)9M=4RI.72O)
FNCOOF (10.319IK(ISHR) )(TFMP(M)9M=721.960)
TFMP(IRUF):IQQ

TFMD(IQUF+240)=I

TEMP(IBUF+490)=N

TFMP(19UF+7?0)=K

COHTINUF

IF (IFOONF.NF.8HFNO DATA) GO TO 4

111

IF (LAST1.EO.1) GO TO I?
LAST1=1
GO TO 7
12 CONTINUF
O0 13 II=19?6
l3 9CONI11)=0.
ITM=IT
14 CONTINUE

PDIMTS INITIAL CONSTANT9 AND VAPIARLES

PPINT 329 ICA9F9IIPYS9FFOUT9EFIN9IOLF9(NAMEIM19
1CON9TNT(M)9FCON9(M)9INFIT(NK(M)+I)9M=1916)
19I’\1FIT(NK(M)*1)9’4=I976)

l9 CONTINUE

I9U9=0

ISFC=0

IWOCNT=121

190030

FFRT=0.

PFwINO 1

NVSVT=0

JK=0

DO 24 Jp=19ITM

ASSIGN 20 TO NGO

IWDCNT=IWOCNT+1

IF (IWOCNT.LF.I70) GO TO 16

IWOCNT=1

I9UR=12FISFC+I

I9FC=ISEC*1

OFCOOF (109339IQQS(ISUR) )IRAQPAY

OFCOOE (10933913113UR) )ISAQRAY

OFCOOE (1093391N(ISU9) IINARRAY

OFCOOF (109339IKIISUR) )IKAPRAY

ISUR1=II9U9-11*5*I

I9UR?=ISURI+SQ

16 199=IPAQRAY(IWOCNT1

I=ISAPRAYIIWOCNTI

NzIMARRAY11WOCNT)

K=IKARQAY(1WOCNT)

IF (K.FQ.49) K20

JOELZIRQ‘IHQ

J=K‘2-N+JOFL

X=J*(J+1)

1M23I‘?

IF (NV9VT.E0.0) GO TO 17

CALCULATFS VIQPATIONAL DEPENDENT VAPIAqLES

NVSVTzNVSVT-l
GO TO 18

17 JK=JK+1
NVSVT=NVSV<JK)-1

112

IVUP=VU(JK)

IVLP=VL(JK)

VIBL=IVLP+.9

VIRL?=VIRL*VIRL

VIBL3=VIRL*VIRL2

VIBL4=VIRL*VIRL3

VIHU=IVUP+,5

VIBU?=VIRU*VIRU

VIRU3=VIRU*VIRU2

VIRU4=VIRU*VIRUB
VFL=WL*VIRL-XL*VIRL?+YL*VIRL3-ZL*VIRL4
VEU=WU9VI9U-XU*VIRU2+YU*VIRU3-ZU*VIRUQ
APIV=ApI-CON9TNT(201*VIPU+CONSTNT(21)“VIRU?
RPIV=RDI-CONSTNT(22)*V19U+CONSTNT(231*VIBU2
RSIGV=99IG-CONSTNT(241*VIRL+CONSTNT(29)“VIRL?
LAMOAV=LAMOA-CONSTNT(26)*VIRL
CON(12)=VIRU

C0N(13)=-VIRU2

CONI141=VIBUB

CONIIS)=-V19U4

CON(16)=-VIRL

CON(17)=VIHL2

CON(18)=-VIHL3

CON(19)=VIRL4

CONTINUE

COODI=(J+I-1.9)**4

SOR2X=SQQT(?.*X)

COZZ=-2.

PARO?=.S*(-l)**(J+K)

XM32X-3

SOPX12=SQPT(X*(J-l)*(J+?))

XP1=X+1

SQRX2M4=SOPI(2*X-4)

XK=K*(K+1)

COB=2*K9(S-?*N)

NM2:N-2

COGAM=K+1.9-.S*N

XKSQ=XK*XK
SQROO=SQRT((CORFRSIGV)“*2+LAMOAV”*2-2”LAMDAV*R9IGV)
IF (K.EQ.1.AND.N.EQ.3) SQRQD=-SQPOO
FL=BSIGV*XK-OSIG*XKSO-NM2*(COB*BSIGV+NM2*LAMOAV-SOQQO
1.COGAM*GAMMA).VFL

XSQ=X*X

OPIT2=DPI*2.
C000FJ=<XSQ+4.*X+1.666666666)
COO(1)=C000FJ+?.*X
COD(2)=C000FJ+4.*X-4.
COD(3)=COOOFJ-6.*X+4.

CONTINUE

H11191)=RPIV*XPI-APIV
H1(291)=RPIV*SOQ2X

H1(193)=0.0

(700

20

21

113

H11292I=9p1V*X91
“1(392)=RPIV*SOQX2M4
H1(393)=RPIV*XM3+APIV
H1(192)=HI(291)

H113.1)=0.0

H1(293)=H1(3921
H111911=H1(1911'OPI*COO(1)
H1(292)=H1(PoZI'OpI*COO(?)
HI(393)=H1(393)”DPI*COO(3)
H1129112H1(2911-ODIT2*SOQ2X*XPI
H1(192)=HI(2911
H1(392)=Hl(3921'OPIT?*SOQX?M4*IX-lo)
H1(293)=HI(39?)
HI(391)=H1(391)-OPIT2*SORT(X*(X-2.I)
H111931=H1(391)

INV=1

IF (IoEQ.21 INV=P

IF (I.EO.1) INV=3

CALL EIGEN (H19FPI9391939H2)
FI=FDI(INV)*VEU
COC0=PAR02*H1(INV91)”*2
COClszQO2*SQR2x&H1(INV92)§H1(INVQII
COC2=pAQ02*(X§Hl(INV92)**2+2“SORX12*H1(INV93)*H1(INVQIII
OFLNU=COCOFCO+COCIFC1*COCZFC?
FUC3F19OFLNU+NUZFPO

GO TO N609 (23922920)

CONTINUE

FOMC=FORS(JPI'FUC*FL

IF LINE IS OUT OF TOLEPANCE THEN WEIGHT IS SET TO ZERO

IF (ABS(FOMC).LF.TOLF) GO TO 21
IF (WT(JP).FQ.0.) GO TO 21
WT(JP)=OO

FCAL=FUC-FL

PPINT 349 JP9FORSIJP)9FCAL9FOMC
FFRTzFERT+FOMC

IRAO:IRAO+1

CONTINUE

THIS SECTION CALCULATES PAQTIAL DERIVATIVES

CON(3)=-COO(I)

CONT4)=COC0

CON(9)=COC1

CON(6)=COC2
CON(7)=-XK9NM?*(C09-(COR*COR*BSIG-LAMOAV)/SOQOO)
CON(8)=XKSO
CON(9):9NM2*(NM?9(R916-LAMOAV)/SOPQO)
CON(10)=NM2*(COGAN)

CON(11)=1.

FUCL=FUC

ASSIGN 22 T0 N60

005')

000

23

26
29
29
30
31
32

1

JDNJ‘JIJ-‘LJNH

RPIV=QPIV+OFLQDI

GO TO 19

(2001(2): (FUC‘FUCLI/OFLBPI
RPIVzRPIV’OFLRpI
ADIV=APIV*OFLAPI

ASSIGN 23 TO NGO

GO TO 19
CON(1)=(FUC’FUCLI/OFLADI
APIV=APIV‘OFLAPI 4
CON(20)=‘VIRU*CON(1)
CONI?II=VIHU2*CON(11
CON12212-VIQU*CON(?)
CON1731=VIHU2*CON(?I
CON12413-VIHL*CON(7)
CON(25)=VIHL2*CON(7I
CON12613-VIHLFCON(91
CON(?7)=FOMC

WQIIF (1) COM

CONTINUE

IF (IRAO.NF.OI DQINT 399 IRAOQFERT
CALL SIEDFII (COHoFOMCQFCALCONUSE9WT9NCONP19ITM)

CALCULATES NEW CONSTANTS FROM STEPFIT COPQECTIONS

OO 29 JP=I9NOIN

ICONG=INOFX(JP)

ICONGO=IOEX(1CONG)
CONSTNT(ICONGO)=CON9TNT(ICONGO)+COEN(JP)*FCONS(IC0NGO)
SCON(ICONGO)=SIGMCO(JP)

CONTINUE

ITQCNT=ITPCNT+1

PPINTS CONSTANTS AFTER EACH FIT

PQINT 369 IHEAO9ITQCNI91TPYS9(NAMEIM)9CONSTNT1M)9
SCONIM19M=19261

IF (ITQCNIoLFoIIQYS) GO TO 15

GO TO 1

FORMAT (10A?)
FORMAT (2A8931119129F3oO94F9.09A8)
FORMAT (8F10.2)
FORMAT (2X91191X9II92X99192I191X91296XF13.497X9F4.?929X9AR)
FORMAT (24(1091/11
FOPMAT I 7HOIHIS I9ARo 16H] CASE WILL MAKECIZQ
36H IIERAIIONS FOP MOLECULAR CONSTANng9/9
41H CONSTANIS WILL NOT RE USED IN THE FIT IF
PSH THEIR F-LEVFL IS GQEAIER9/9 5H THAN9F9.29
43H. OATA pOINTS FOP WHICH THE ORSFREVEO MINUS
11H CALCULAIEOc/o 19H VALUE IS LESS THAN9F6.29
14H WILL RF USFOo9/9 QHOCOMSTANT 99X95HVALUE96X9
17HFPACTIONAL CHANGE93X9 4HUSEO9/2X9RQ93X9F12.6
99X9F7.497X9A3))

33
34
I
39
1
36
1
2
3

119

FORMAT (12(10R1/)1

FORMAT ( 9H0LINE NO.9149 27H IS OUT OF TOLERANCE. FORS=9
9F10.49 6H CALC=9F10.A9 6H FOMC=9FIO.A)

FORmAT ( 16H TOTAL FRROQ FOR9149 18H REJECTFO LINES IS9
F11.4)

FORMAT (9A3//9 3HFIT9I39 3H OF9I39 93H ITERATIONS

42H IS COMRLFTFO WITH THE FOLLOWING CONSTANTS9//9
QH CONSTANT98X9 9HVALUE912X9 9HSTO FRROR9//(1XR99
2F20.l2))

FNO

SURROUTINF STEPFIT

000

000

1
1
2
3

1
2

1
l

SUBROUTINE STFPFIT (OATA9F0859FCALC9NUSF9WT9NCONPIOINOATA)

COMMON /A/ NAMF<261

COMMON /12/ INFO]OINFogfiINFO3OINFOAQNUMCONQJUMPQ
CONST(26)9FFIN9FFOUT9TOL9IOENTIZ)9TOLF

COMMON /17/ IQRS(500)9IS(500191N(500)9IK(90019IHFAO(Q)9
VUIIS)9VL(1519NVSV(19)sOUMRISOOOI91TQYSoITQCNT9
IRAQPAY(120)9ISARPAY(120)9INARRAY(12019
IKAQRAY112OI

COMMON /21/ N1(27)9VECTOQ(2R029)OINOEXIP719IOFX127IO
SIGMA(?7) 9COFN(27) osIGMCO(27) 9NOTIN(27) 9
XCONST(27)9NOIN

COMMON /23/ NOOATA9NOVMI9AVEWHT95TOY9NOSTEP9IWOCNTo

NTN.FRFODRo.YPRFO.OFV9N9MS

FO9OEV9N9MS

COMMON /123/ NK(?6)9NDEL“AX9XOFVMAX

OIMFNSION OATA<NCON9119 WT(INDATA19 NUSF(INOATA1

pEWINO 1

SETS INITIAL VALVES IF NOT PRESENT

NOINL=O

IF (IOFNT(II.NF.RH 1 GO TO I
IOFNTIII=8HINPUT OA

IOENT(?)=?HTA

CONTINUE

IF (FFOUT.F0.0.) FFOUT=19E‘R

IF (FFIN.FQ.O.I EFIN=1.F‘R

IF (TOLoFQ.0.0) TOL=0.001

NOVAQzl

COUNTS AND RELARFLS VARIABLES TO BE USFO IN FIT

DO 9 I=I9NUMCON

IF (NKIIII 2999?
NIINOVA91=NAMF1I1

IF (JUMP) 39493
XCONST(NOVAPI=CONSTII)
NOVAP:NOVAH+I

CONTINUE

(WCVO

(7C7O

10

11

13

14
IS

16

NODATAZO

COUNTS NUMRFR OF MON ZFQO LINFS USFD IN FIT

DO 8 N=1QINOATA
IF (WT(N1) 796.7
NUSF(N)=O

GO TO 8
NUSE(N):1
NOOATAzNODATA+1
CONTINUE

NDEL=0
FLEVFL=0.0
VA4=FLFVFL
NOMAX2VAR
NOMINzNOMAx
NOENTzNOMIN
K=NOFNT

NOINzK

QFWIND l

LOOP:O
NOVMI:NOVAQ-1
NOVPLzNOVAQ+1

”0 10 I=1~NOVPL
OO 10 J=19NOVPL
VFCTOP(I,J):0.O
IF (NOEL) 15911915
SUMWHT:O.Q
IOFX(NOVAQ):NCOM01

SUMS WFIGHTS TO COMPUTF AVFRAGF WEIGHT

DO 12 N=191NOATA
SUMWHTZSUMWHT+WT(N)
NUM=0

CHECKS WHICH VARIARLFS ARE TO BE USED

O0 14 I=1¢NUMCON

IF (NKII)) 13914913
NUMzNUM +1

IOEXINUM1=I

CONTINUE
AVEWHT=SUMWHT/NOOATA

CALCULATES PAW SUMS OF SQUARES AND CROSS PRODUCTS

00 18 N=191NDATA

PFAD (1) DATA

IF (MUSE(N)) 16.18.16
WHT=WT(N)/AVEWHT

no 17 1:1.NOVAQ

VFCTOQII9NOVPL1=VECTOR(I9NOVPL)+OATA(IOFX(I)1*WHT

0

17

IR

19

20

21

23

Pa

25

OO 17 J=19N0VAP

I01=IDEX(I)

IORzIDFX(J)

XIHATthATA(IDI)
X?0ATA=DATA(IDP)
PX1XPW=XIOATA§XPOATA*WHT

CALL 904
VECTOR(I.J):PX1X?N+VECTOR(19J)
CONTINUF
VECTOR(NOVPL9NOVPL)=VECTOPINOVDL9NOVPL)*WHT
CONTINUE

DFwIND 1

IF (INFOI) 19.28919

PQINTS OUT PAW SUNS OF SOUAQFS AND CROSS PRODUCTS MATPIX

POINT 97

NOMAX=NOVMI

IF (MOVMI.GT.7) NOMAX=7

PRINT 1019 (191:19N0MAX)

PRINT 1029 VFCTOP(N0VAQ.NOVDL)9(VECTORIIoNOVDL1oI=loN0MAX)
IF (NOVMI.EO.NOMAX) GO TO 21
M0MAX=N0MAX+1

NOMAX=MOMAX97

IF (NOMAX.GT.NOVMI) NOMszNOVMI

PPINT 1039 (I9I:MOMAX9NOMAX)

PRINT 10?9 (VECTOP(I9NOVPL)91=MOMAX9NOMAX)
GO TO 20

CONTINUE

NOMIN=1

NOMAX=NOVMI

NGO=S

IF (NOVMI.GT.NGO) NOMAX=NGO

DPINT 1059 (IqlzNOMIN9NOMAX)

DO 23 J=N0MIN9NOVMI

JJJ=J

IF (JJJ.GT.NOMAX) JJJzNOMAX

POINT 1069 J9(VFCT0Q(I9J)9I=NOMIN9JJJ1
pQINT 1079 (VFCTOP(I9NOVAR)91=NOMIN9NOMAx1
IF (NOMAX.FO.NOVMI) GO TO P4
NOMINzNOMAX+1

NGO=M60+S

NOMAX=NOVMI

GO TO 22

CONTINUE

PRINT 1099 VECTOR(MOVAR.MOVAQ)
NOSTsz-l

ASSIGN 61 TO NUMREP
OFFR2VFCTOR(NOVPL9N0VPL1-1.0

CALCULATFS A PARTIAL CORRELATION COFFFICIENT MATPIX

OO 29 I=19NOVAR

000

26

27

29
20

30

31

32

33

34

BS

36

37

3%

118

IF (VECTORII9II) 26927929
DRINT 1179 I

GO TO 95

PRINT 1189 I

SIGMAIII=190

GO TO 29
SIGMA(I)=SQVTIVFCTOQ(I°1))
VFCTORII9I)=I.O

OO 30 1:19NOVMI

IPI=I+1

OO 3O J=IP19NOVAP
VECTORII9J)=VFCTOQ(I9J)/(SIGMA(11*SIGMA(J)I
VECTOQIJ9I)=VFCTOQ(I9J)

PRINTS OUT PARTIAL CORRELATION COEFFICIENT MATRIX

IF (INFO?) 31.34.31

NOMINzl

NOMAX:NOVMI

NGOzlS

NOM {Mpzz

IF (NOVMI.GT.NGO) NOMAX=NGO

PRINT 1099 (I9I=NOMIN9NOMAX)

no 33 I=NOMINP9NOVMI

III=I~1

IF (III.GT.NOMAX) III=NOMAX

DRINT 1109 I.(VFCTOQIIoJ)9J=NOMIN9III)
DQINT 1119 (VFCTOR(I9NOVAR).I:NOMIN9NOMAX)
1F (NOMAX.EO.NOVMI) GO T0 34
NOMINzNOMAK91

NOMINP:NOMIN91

NGO=NGO+1S

NOMAX=NOVMI

GO TO 32

N05TFP=NOSTFP+1

DETERMINES NFXT CONSTANT TO RE ENTEREO INTO THF FIT

IF (VFCTOR(NOVAR9NOVAR)) 35935936
NSTPH1=NOSTER-1

PRINT 1219 NSTPMI

GO TO 78
SIGYzSIGMA(NOVAR)*SORT(VECTOR(NOVAR9NOVAR)/OFFR)
DEFanFFQ*IoO

IF (OEFR) 37937938

PRINT 1229 NOSTFR

GO TO 78

NOINL=NOIN

NOIN=0

VMAX:NOIN

VMIN=VMAX

OO 4R I=19NOVMI

IF (VECTOR(I9I)) 39948940

COO

0000

39

4O

41

42

43

44.

4‘3

46
47

48

1.9

50

S1

S2
S3

S4
‘5‘;

56

S7
SS

SO
60
61

 

PRINT 1239 I9NOSTFP

NOINzNOINL

GO TO 77

IF (VFCTOR(I91)-T01) 49941941 _
VAP=VFCTOR(I9NOVAR)*VFCTOR(NOVAR9II/VFCTORII9IT
IF (VAR) 42949946

NOIN=NOIN+1

INOFX(NOIN)=I
COFN(NOIN)=V€CTOR(I9NOVAR)*SIGMA(NOVAR1/SIGMA(I)
SIGMCO(NOIN)=(SIGY/CIGMA(I))“SQRT(VFCTOR(I9I))
IF (VMIN) 45944943

PRINT 119

GO TO 96

VMIN=VAR

NOMIN=I

GO TO 49

IF (VAR-VMIN) 4R94R944

IF (VAR-VMAX) 4R948947

VMAX:VAR

KJOMAX:I

CONTINUE

IF (NOIN) 4Q9SO9S1

PRINT 120

GO TO 96

STOY=SIGY

GO TO 63

IF (INFO3) S29619S2

PRINTS OUT INTERMFOIATF REGRFSSION STERS

IF (NOENT) S39S39S4

PRINT 11S9 NOSTFP9K

GO TO 55

PRINT 1169 NOSTFR9K

IF (LOOP.NF.O) FLFVFL=FL

PRINT 1129 K9FLFVEL9SIGY

OO S6 J=19NOIN

N=INOFX(J)

PRINT 1139 N.N1(N)9COEN(J)9SIGNCO(J)
IF (JUMP) S79609S7

IF (LOOP) SHo6O9SR

DRINT 98

O0 SQ J=19NOIN

N=INOFX(J)

XNEWCON=COEN(J)+XCONST(N)

pRINT 1139 N9N1(N)9XNEWCON9SIGMCO(J)
GO TO NUMRFR9 (61970)

FL=FLEVFL

CHECKS TO SFF IF AOOING NEXT VARIARLE WILL MAKF A
SIGNIFICANT CHANGE IN THE FIT

FLEVFL=VWIN*OFFR/VECTOR(NOVAR9NOVAR)

120

IF (FFOUT+FLEVEL) 63.63962
6? K=NOMIN
NOFNT=0
GO 70 as
63 FLFVFL=VMAX*OFFR/(VFCTOR(NOVAR.NOVAR)-VMAX)
IF (EFIN-FLFVFL) 65964.77
64 IF (FFIN) 77.77.65
6S K=NOMAX
NOFNT=K
65 IF (K) 67967968
67 PRINT 124. NOSTFR
GO TO 96

CALcuLATES NFw MATRIX FOR NEXT STEP OF PROGRESSION

6R DO 72 I=19NOVAR
IF (I~K) 69972.69
69 O0 71 J=1.NOVAR
IF (J-K) 70.71970
70 VFCTORII9J)=VFCTOR(I.J)-VECTOR(I9K)*VECTOR(K.J)/VFCTOR(K9K)
71 CONTINUE
72 CONTINUF
OO 74 1:19NOVAR
IF (I-K) 73.74.73
73 VECTOR(I9K)=-VECTOR(I.K)/VECTOR(K.K)
74 CONTINUF
no 76 J=19NOVAR
IF (J-K) 79.76.75
7S VECTOR(K.J)=VFCTOR(K.J)/VECTOR(K.K)
76 CONTINUE
VFCTOR(K.K)=1.0/VECTOR(K9K)
GO TO 34
77 PRINT 1149 IOFNT(1).IOENT(2)9NOOATA.NOVMI9NOELMAX.
IXOEVMAK.AVEWHT.STOY.NOSTEP
78 CONTINUE
ASSIGN 79 T0 NUMRER
LOOle
GO TO S?
79 CONTTNJE
IF (INF03.NF.0) pRINT 1259 (L9VECTOR(L.L).L=19NOVMI)
LPRTzo
CALL PRINTB (DATA.FORS9FCALC9WT.NUSF.NCONP19INOATA)
VFIT3=0.0
VFIT?=VFIT3
XIR=0.0
SWT=XIQ
OFVMAXszT
VFIT=OEVMAX
NVSVT=0
VF1=0
VFP=0
VF3=0
IF1:O

OCOCU

90

81

82

S3

R4

RS

S6

87

121

TF2=0
IF3:O
INOCNT=121
ISUR=O
ISFC=0
MS:0

CALCULATES VALUES FOR TABULAR OUTPUT

OO 93 N=19INOATA

RFAO (1) DATA

FOBS:OATA(NCONP1)

uITN=NlJSF (N) *‘rlT (N)

WHT=WTN/AVEWHT

YPREO=0.0

OO 90 I=19NOIN
LASSIF=IOFXIINOFX(I))
YPREnzYPRFO+COFN(I)*OATA(LASSIE)
OFV=FOSS-YPPEO

IF (10.-NT(N)) R29RP991
VFIT=VFIT+wTN§OFV**?

XIR:XIR+1.0

SWTzSWT+NT(N)

FQFQPRD:YPQFD

OFVOWC=FOHS

OFVOMP=FRFOPQD
VFIT2=VFIT2+NTN*OFVOMC*OFVOMC
VFIT3=VFIT3+NTN*OFVOMP*OFVOMP
WHTszT*AVFWHT

IF ((INFO4.FQ.O).ANO.(ITRCNT.NF.ITRYS)) GO TO 91
LDQT:LDQT+1

IF (LPRT.LF.SO) GO TO 83

LRRT=1

CALL pRINT2 (OATA9FORS9FCALC9WT9NUSF9NCONP19INOATA)
CONTINUE

INOCNT=INOCNT+1

IF (IWOCNT.LE.120) GO TO 84
IWOCNT=1

ISUH=1?*ISEC+1

ISFC=ISEC+1

OFCOOF (10.99.IRRS(ISUR) )IHARRAY
OECOOF (109RQ.IS(ISUR) )ISARRAY
OFCOOE (109QQ9IN(ISUR) )INARRAY
OFCOOE (109999IK(ISUR) )IKARRAY
IF (NVSVT.E0.0) GO TO RS
NVSVTzNVSVT-l

GO TO R6

M§:M§9l

NVSVT=NVSV(MS)-1

CALL PRINT3 (OATA9FORS9FCALC9WT9NUSF9NCONP19INOATA)
IF (WHT.E0.0) GO TO 90

IF (TSARRAY(IWOCNT)-2) Q79RR9BQ
IF1=IF1*1

00:30

99

89

90
91

93

94
98

96

97
99

99
100

101
102

VF1=VF1+OEVOWC

GO TO 00

IF2=IF2+1

VF2=VF2+OFVOMC

GO TO 90

IF3=IF3+1

VF3=VF3+OFVOMC

CONTINUE
AOEvaQS(OFV)*SORT(NHT)*NUSE(N)
IF (OFVMAx-AOFV) 92.92993
NMszN

OFVMAX2AOFV

CONTIAHW7
VFIT=VFIT*KIR/((XIR-NOIN)*SWT)
QTOFIT=SORT(VFIT)

CALCULATES STATISTICS FOR RRINTOUT AT END OF TARULAR OUTPUT

COVFIT=XIR/((XIR-NOIN)*SNT)
VFIT=VFIT*COVFIT
VFIT?=VFIT2*COVFIT
VEIT3=VFIT3*COVFIT
STDFITPISOPIIVFIT?)
STOFIT3=SOQTIVFIT31

PRINT 1049 STOFIT?9STOFIT39STOFIT
VF1=VF1/IF1

VF2=VF2/IF2

VF3:VF3/TF3

DRINT 1009 VF19VF29VF39IFI9IF29IF3

CHECKS TO SEE IF NFW FIT IS TO RF MADE AFTER THROWING
OUT WORST LINE

IF (NDELMAX-NOFL) 96996994
IF IOEVMAX-XOFVMAX) 96996999
NUSEINMAXI=O

NOFL:N')EL91

NOOATA=NODATA-1
SHMWHTZSHMWHT*WTINMAX)

DRINT 1259 NMAX

GO TO 9

pETURN

FORMAT ( IIHISUM OF VAR9/)

FORMAT T 45H2FINAL CONSTANTS AFTER CORRFCTIONS WFRF AOOEO9/)
FORMAT <12<1091/>)

FORMAT ( 379 AVFPAGF DFVIATION OF LINES FROM F1=9FR.49

1 4H F2:9FR.49 4H F3=9FR.4/9 21H NUMBER OF LINES FROM9
2 13X9 3HF1=9IQ9 4H F2=9I99 4H F3=9I81

FORMAT ( 9H Y.7Il7./)
FORMAT (X97El7.69F16.6.//)

103 FORMAT (11097Il79/1
104 FORMAT(*OSTAT FROM LINFS WHTO LT 10.0“/*O*2SX*STANOARO*

123

1 *OFVIATION* 2F11.4.19XF11.4)

10$ FORMAT ( 16H pAw SSCP MATRIX9/5126)

106 FORMAT (X.1?.SE?6.101

107 FORMAT ( 3H Y.SE?6.101

10R FORMAT ( 8H Y VS Y.E?6.10)

109 FORMAT ( 21H-PARTIAL CORR. COFFF.9//1X.ISIR)

110 FORMAT (I3.16FR.2)

111 FORMAT ( 3H Y.16F9.2)

11? FORMAT (9 F LEVEL OF x-*I?.F10.2.QX*STO OEV OF (O-P)*
1 F12.4//10X *VARIARLF COFFFICIFNT STO FRROR*/)

113 FORMAT (Ill.A0.?Fl7.101

11467 FORMAT(*1LFAST SOUARFS FIT OF ”EAR /*FIT “14* OATIHt
1 ”FOINTS TO * I?” VARIARLFS*/* DELETES UP TO *1?“ POINTS*
2 *IF (O-P) IS GT “F6.3/* WHT NORM * F6.P/§ STD DEV OF“
3 *(O-C)*FR.4/* COMPLFTFO *12* STEPS*)

11S FORMAT ( RHOSTFP N0913/9 ISH VAR. RFMOVEO.I3)

116 FORMAT RHOSTFP NO9I3/9 lSH VAR. ENTEREO9I3)

117 FORMAT 19H FRROR QESIO SO VAQ.IB9 7H IS NFG)

119 FORMAT 4POVAR9IS9 9H 18 CONST)

119 FORMAT IOHOFRPOR. VMIM POS)

120 FORMAT ISHOFRROR NOIN NEG)

121 FORMAT 13HOY QOUAQF NFG STEP.IS)

12? FORMAT P2H07FRO OFG FRFEOOM STFP.13)

123 FORMAT IOH SQUARF X-.T2. 14H NFGATIVF STFP9I3)

124 FORMAT QH Kzfl STFP9I3)

12S FORMAT *0 OIAG FLEMENT§*/* VAR NO VALUF*//(14.Dl4.4))

126 FORMAT RH LINF NO.I4. 23H BFING OELFTED FROM FIT)
ENO
SURROUTINF SOP

C THIS ROUTINF NFFOEO TO KILL OVER OPTIMZATION

FNO

AAAAAAAAAAA

SURROUTINE RRNTOUT

SURROUTINE PHNTOUT (DATA9FOMC9FCALC9WT9NUSE9NCONP19INOATA)

COMMON /17/ IRPS(SOO)9IS(ROO)9IN(SOOIQIK(SOOIQIHEAOIQIO
VU(15)9VL11819NVSV115)9FORSISOOO)OITQYS9ITQCN19
IQAQPAYI1PO)9ISAQRAY(120191NARPAYI1ZO)9
IKARRAY(1?O)

COMMON /1?3/ NK12610NDELMAX9XOEVMAX

COMMON /23/ NOOATA9NOVMI9AVEWHT9STDY9NOSTEDOIWOCNT’

IWTN9FQFQDRO9YDPEO9DEV9N9MS

DIMENSION DATA(NCONDI)9 WT(INDATA)9 NUSEIINOATA)

ENTRY DRINT?

TFOONanH

RRINT 30 IHEAD

PQINT 3

RETURN

ENTRY PRINT3

FDRPO:FORS(N)-FQFQPDO

FRPMczFomc—FRFODRO

FRCALC=EOQS(N)’FOMC

.JNF‘

124

IF (ITRCNT.LT.ITRYS) GO TO 1

IF (N.FO.IHOATA) IFOONF=SHFNO OATA

IF (IKAQRAY(IP).FO.4S) TKARHAY(IP)=O

WRITE (9294) VUIMS).VLIMS).IHARRAY(IP)9ISARRAYIIP).
IINARRA((IP191KARRAYIIP).FORS(N)9WT(N).FOMC9IFOONE
1 CONTINUE

PRINT S9 N9VU(MS)9VL(MS)9IRARRAY(IR)9ISARRAY(IP).
lINARRAY(Ip).IKARRAY(IP).WT(N).FORS(N).FRCALC9FOMC.
P FRFOPROoFRPQO9FPPMC

RFT-JRN

2 FORMAT ( 1H199AS/1

3 FORMAT ( 65” N RANO TRANS. WT ORS FQFO CALC FREQ“
1* ORS‘CALC OPS-RQF0916X9 ZOHPRED FREQ PRED-CALC9/1

4 FORMAT (2X91191X91192X991971191X91296X9E13o494x9FR939
14X9F12.49I?X9A8)

S FORMAT (1X9149 ?H (9119 1H99119 2H) 99192119 1H(9
1129 1H)9F6.392(FQ.39?X)92(Fgo492X)914X92(FQ.492X)1
EMT)

SURROUTINF E I GEN

SURROUTINE F IOEN (A9VALU9N9N9IA9‘3)

FIGFNVALUES ANO EIGFNVFCTORS OF A RFAL SYMMETRIC MATRIX

001’.)

OIMENSION A(IA91)9 R(IA.1)9 VALU(3)9 DIAG(3)9 SUPFRO(2)9
1 O(2)9 VALL(3)9 S(2)9 C(219 O(3)9 IND(3)9 U(3)

CALCULATE NORM OF MATRIX

F300

1 ANORM2=O.O
OO 2 I=I9N
OO 2 J=19N

P ANORM22ANOWMP+A(I9J)**?
ANORMzSQRTIANORM?)

C GFNERATE IOFNTITY MATRIX

IE (“I 39793
3 OO 6 1:19N
OO 6 J=19N
IF (I‘J) 59493
4 RII9J1=190
GO TO 6
S 9(I9J)=O.O
6 CONTINUE
C ppppnpm QOTATTONS TO RFOUCE MATRIX TO JACOHI FOPM

7 IEXIT=1
Mszxl-P
IF (NN) 6S91598

(‘30

10

11

12

IS

16

17

19

19
20

21

23

24
PS
26

12S

OO 14 I=I9NN

1131+?

OO 14 J=II9N

T1=A(I9I*1)

T2=A(10J)

GO TO 66

O0 IO K=I9N
T?=COS*A(K91+11+SIN*A(K9J)
A(K9J)=COS*A(K9J)-SIN*A(K9I+1)
A(K9I+1)=T2

OO 11 K=I9N
T2=COS*A(I+19K)+SIN*A(J9K)
A(J9K)=COS*A(J9K)’SIN*A(I*19K)
A(I+19K)=T2 ‘

IF (”1 12914912

OO 13 (=19N
T2=COS*Q(K9I*1)*SIN*S(K9J)
Q(K9J)=COS*S(K9J1‘SIN*R(K91*1)
RIK9I+1)=T2

CONTINUE

MOVE JACORI FORM FLFMFNTS ANO INITIALIZF EIGENVALUF ROUNOS

OO 16 I=I9N
OIAG(T)=A(I9I)
VALUIII=ANORM
VALL(I)=-ANO9M

OO 17 I=P9N
SHDEQOII-1)=A(I’19I)
O(1’1)=(9UPFQO(I-I))**?

TAU=0.0

I=1

MATCH=O

T2=0.0

T1=I.O

OO 33 J=19N
D=OIAGIJ1‘TAU

IE (T2) 19921919
IF (T1) 2O924920
T=P*T1-O(J-1)*T2
GO TO 2%

IF (T1) 22923923
71=-1.o

Tz-p

GO TO 23

T1=1.0

sz

GO TO 23

IF (OIJ’111 2§97397S
1F (T?) 27926926
T=-1.0

(705')

29
P9
30
31
32
33

34
3S

36
37
38
39
40
41
42

43

44

45

46

47
49
49
60

SI
S2

S3

126

GO TO 29
T=1.0

COUNT AGREEMENTS 1N SIGN

IF (T1) 90.29.29
IF IT) 32.31.31
IF (T) 31.32.32
MATCH=AATCH+1
T2=TI

T1=T

FSTARLISH TIGHTFR gnumns ON EIGFNVALUES

OO 33 K=I9N

IF (K—MATCH) 34.34.36

IF (TAU-VALL(K)) 3R.3R.3S
VALL(K)=TAU

GO TO 3Q

IF (TAU-VALU(K)) 37.38.38
VALUIK1=TAU

CONTINUE

IF (VALUII)-VALL(I)-S.OF—R) 42942.40
IF (VALU(I)) 41.43941

1F (ARS(VALL(I)/VALU(I)-l.0)-S.0E-R) 42.42.43
I=I+1

IF (I-N) 39939.44
TAU=IVALL(I)+VALU(I))/P.0

GO TO IR

JACORI EIGENVECTORS RY ROTATIONAL TRIANGULARIZATION

IF (M) 4§9GC§94S

IEXIT=3

OO 46 1:19N

OO 46 J=19N

A(I9J13090

OO 6? 1:19N

IF (1'1) 50990947

IF (VALUII’I)-VALU(I)-q.0E-7) 56956949
IE (VALUII-111 499S0949

IE (ARSIVALUII)/VALU(1-1)-190)-§.0E*71 56996950
COS=1.0

RETA=0

SIN=0.0

OO 54 J=19N

IE (J-I) S39S39S1

GO TO GO

S(J-1)=SIN

C(J“1)=COS

O(J*1)=T1*COS+T2*SIN
TI=(OIAG(J)-VALU(I))“COS‘RETA*SIN
T2=SUPEQOIJ1

£39
94

57
SR
S9
60
61
62

C

C

C
63
64
6S

C

C

C
66
67
69

99059

127

DETA=OHPFRQ(J)*EOS
O(N)=T1

OO SS J=19N

10U3(\I)=(1

SMALLO=ANORM

OO GO J=19H

1E (II‘JO(J)-1) 579599S9
IE (ARS(SMALLO)’AOS(O(J))) 59959958
SMALLO=O(J)

MM3J

CONTINUE

INOU‘JN) =1

DROOS=1.O

IE (NN-I) h2962960

OO 61 K2794N

II=NN+1-K
A(11+19I)=C(TI)*PROOS
PROOSz-PQOOS*S(II)
A(19I)=DQOOS

FORM MATRIX L’ROOUCT OF ROTATION MATRIX WITH JAFORI MATRIX

Or) 64 11:1951

OO 63 K=I9N

U(K)=A(K9J)

OO 64 I=l9N

A(IQ.J)=OOO

OO G4 K=I9N
A(I9J):R(I9K)*U(K)+A(I9J)
QFTURM

CALCULATE SINF ANO COSINE OF ANGLE OF ROTATION

IF (T2) 67969967
T=SORT(T1**2+T2**2)
COSle/T

SIN=T2/T

GO TO (99SP)9 IFXIT
GO TO (1496719 TFXIT
ENO

AM 0391

DROGRAM 0391 (INPUT9OUTRUT9TAPE1)

COMMON 41(3.3)9H2I3o3)oFPII3).NUSFI130019CONIIF).FOMC.
1WT(SIO)9CONSTSTNT(1S)9FCONS(15)9SCON(15)

COMMON /A/ NAMFIIS)

COMMON /TFMP/ ONU(130019FONU(1300)

COMMON /1P/ INFOI9INF029INFO39INFO4.NUMCON9JUMP9CONST(1S)9
IEEIN9EEOUT9TOL9IOENT1219TOLF

COMMON /17/ 18(13001.INI1300).IJ(1300)o1HEAOI9).VU(IS).
INVSV(16)9RS(13OO)9ITRYS9ITRCNT

0(3F)

IPR

COVMQN /?l/ NT(16)9VFCTOP(17017)9INDEX(16)oIDFX(15)-
TSIGMA(16)~CUFN(16)9910MC0(16)9NOTIN(16)9XCONST(16)oNOIN
COMMON /123/ NK(lq)oNDFLMAXoXDFVMAX

DIMENSION FUT(R)- INFIT(2)9 COD(3)

DIMFNSION AFHN(3)~ DFUN(3)
VQUIVALENCE (COHQTNT( 1)9 API)9

l (COM§TmT( 3). UPI).
2 (CKNTSTNT( ‘3). C1)~
3 (CONgTNTT 7)! 2590?).
4 (CONSTNT( 9). XU)’
G (COM§INT(ll)o 2U).
7 (com§TNT(lS)o RAHPI)

TNTEGFQ VU
INITALIZES NAMFQ AND VAWIARLFS

TNFTT(1)=3H M0
IMFIT(9)=3HYFS
NAMF(1):QHFA91
NAMF(2)=4HFRDT
NA”F(3)=4HFUDT
NAMF(4)=3HFCO
NAMF(§)=3HFC1
NAMF(6)=3HECB
NAMF(7)=6HF2FPOF
NAME(R)=3HFWU
MAMF(Q):}HEXH
MAV€(10)=3HFYU
NAVF(11)=3HF2U
NA”E(12)=6HFALADT
MAMF(13)=6HFHAAPT
NAMF(14)=6HEALRDT
MAWF(15)=6HFRARDI
MUM-CON: 1‘5
NC0N01=JUMCOH+1
MVSV(1)=0

JK=1

KI=O

JHMD=0

TRAnzo

FFRTzo.

CONTINUF

ITPCNTz0

DFAD§ TV AND DRINTS OUT HFADING
DFAD 26o IHFADqIFDOMF

IF (IFDONE.FQ.HH STOP) QTOP
DPINT 269 IHFAH

IF (IFDUNF,ME.RHFMH HEAD) GO TO 1

QFAD§ ODTION CAQD

(CONQTNT( 2). RpI)9

(CONqTNT( 4). C0)9
(CONgTNT( 6). C2)9
(CONQTNT( R). WU).
(CONQTNT(10)¢ YU).

(CON§TNT(I?)o ALAPI)9

000

F)O:O

129

DFAO 279 IOFMT9ITWY§9INFO19INFO29TNFO39INFOQ9(MK(T)9

1T=191C5) 9"“)FL‘J‘AX0XflFVMAXOTUL'TOLFOEFINQFFOUT’ICASF

ASSIGN A TO MGO

IF (ICASF.F9.RHNFW CASE) GO TO 2

IF (ICASF.F0.QHHFW CONS) ASQIGN 13 TO “GO
IF (ICASF.FO.RHADU CONS) GO TO 13
CONTINUE

QFAOQ In CUNSTANTS AND FRACTIOMAL CHANGFS

QFAD 299 COM§THT9OFLAP19DELRDI
DFAU 789 FCOWS

DQINT 999 CONgTNT

TF (FCOVSTI).FQ.0.0) FCON5(1)=1.0
O0 3 TI=791§

§FTS FRACTIOMAL CHAMGF IF ANY OR ALL NOT DEFTNFO

TF (FCON§(TT).F0.0.0) FCONSTII)=FCONS(1)
C(VJTIAMJF

an TO “809 (1394)

CONTINUE

TJCT=0

IT=IJCT

J=IT

COMTTNUF

DFAOS IN EMFRGTFS

QFAU 309 FUT

CFVJTTKNHT

TF (FUT(R).NF.RRRR.QRRH) GO TO 7
VU(JK)=FUT(1)

NVSV(JK)=KI

DPTNT 319 JK9VU(JK)9NVSV(JK)
JK=JK+1

K120

J=0

TJCT=O

QFAL) 309 FWJT

TF (FUT(9).FO.QQQQ.QQQQ) GO TO 11
GO TO 6

CONTTNUH

O0 10 KRzloR

CALCULATES QUANTUM OFPFNOENCIES

KT=KI+1

IT=IT+1

IJCT=IJCT+I

1F (IJCT.L£.8) GO T0 8
IJCTzl

J=J+1

10

11

19
13

14

19

130

TF (J.NE.0) GO TO Q
TT=IT-1

KI=O

GO TO 10

COMTTNHF
FO*%S(IT)=FUT(KR)
T§(TT)=(TJCT+1)/?
TJ(TT)=J

L‘IT(IT):1.

IF (FUT(KR).F0.0.) WT(IT)=O.
C(WJTT’WJE

CO TO 5

CONTTNWF

ITM=TT

OO 12 M31015
§C(‘)T\T(M):Oo

CONTINUF

PQIVTS INITIAL CONSTANTQ ANn VAPIARLES

DPIMT 329 ICA§F9ITQYS9FFOUT9FFTN9TOLF9(NAME(M)9CONSTNT(M)9
lFCON§(W)9TNFTT(NK(M)+1)9M=l915)

CONTINUE

JK=0

”FWIND l
DDITP=DPI*2.
MVSVTzO

no 24 JD:191TM
ASSIGN IR TO NGO
T=IS(JP)
J=IJ(JD)
X=J*(J+l)
IMP=I-?

TF (NVSVT.E0.0) GO TO 19

CALCULATES VIRPATTONAL OEPFNOFNT VAPIARLES

NVQVT=NV§VT-l

GO TO 16

JKzJK+l

MVSVT=NVSV(J<)-1

IViN3=VLI(JK)

VIQU=IVUD+.S

VIEU?=VI%H%VIQ1
VIHU3=VIQU*VIRU?
VTRUA=VIRU9VIRU3
APIV:API-ALADI%VIRU+RAAPT*VIRU?
QDIVzRQI-ALHQT*VI%U+RARPI*VIHU?
VFUZWU*V[RU-XH*VIRU7+YU*VIQU3-2U*VIPU4
DRINT 339 VIKH-APIV9RPIV9VFU
CON(Q)=VIPJ

FON(Q)=-VI%U2

cnu(1n)=v{qua

7705')

16

17

19

COW(1])=-VIFUA

COMTINUF

POOPI=(J+I-1.R)**4
§OQ2X=SQPT(2.*X)

COZP=-2.

1F (I.FQ.?) COZ?=4.

1KK=(-l)**JP

DARO?:.5*IKK

XM32X-3
QORX12=SUQT(X*(J-1)*(J+P))
X91=X91
SOHX?M4=SORT(?*x-4)+1.5-RO
XQO=X*X
COOOFJ=(XSO+A.*X+1.666686666666)
COO(1)=CODOF)+2.#X
COD(?)=COOHFJ+A.*X-4.
COO(3)=COOUFJ-6.*X+4.

CONTIMuE

Hl(lol)=QPIV*XPI-APTV
H1(?91):4PIV*SOQZX

H1(391)=O.

H1(29?)=RDIV*X91
”1(392)=RPIV*SODX2MA
H1(393)=QPTV*XM7+APTV
H1(19?)=H1(291)

H1(193)=Oo

H1(293)=H1(39?)
H1(lo])=%l(191)-OPI*COO(1)
H1(?.2)=Hl(29?)-OPI*COO(?)
H1(393)2H1(J93)-ODI*COO(3)
H1(291)=H1(?9])-OPIT2*SOQEX*XP1
H1(19?.)‘-'Hl(291)
H1(1.2)=H1(392)-ODIT2*SQRK2M4*(X-l.)
H1(293)=H1(39?)
H1(3.1)=H1(3.1)-ODTT2*SORT(X*(X-2.))
H1(193)=H1(391)

1NV=1

IF (T.FO.?) INV22

IF (T.EQ.1) INV=3

CALL FTGQN (H19F919391939H2)
F1=FDI(IMV)*VFU
COCfiszQflP*H1(IMV9l)**?
COC1:DA&O?*9OQ2X*H](INV9?)*H1(INV91)
COC?:PAHO?*(X*H](INV92)**2+2*SOPX12*H1(INV93)*H1(INV91))
DFLMH2COC0*C0+COC1*C1+COC2*C?
FHC2FI+DELMu+ZEQOF

GO TO N909 (199209219??o?3)
CONTINUE

FOMC=FO?§(Jp)-FHC

TF LTNF IS OUT OF TOLFQANCF THFN WFIGHT IS QET TO ZFRO

TF (AQ§(FOMC).LF.TOLF) CO TO 19

013')

10

20

.72

23

24

132

IF (1-IT(JD).F_O.O) GO TO IQ
WT(JD)=O.

DPTNT 149 JP9FOR§(JD)9FOMC
FF9T=FE9T+FOWC

IQAO=IRAO+I

CONTTNOF

THIS SFCTION CALCULATES PARTIAL DFQIVATIVES

ONU(1P)=AG€(2*OFLNU)
FOOU(JD):AOS(FOR§(JD)-FORS(JP-TKK))-DNU(JP)
CON(3)=-COO(I)
COM<41=COCO
CON(§)=COC1
COM(A)=COC?
COH(7)=1.
CON(1?)=—VIPO*CON(1)
CON(13)=VIOUP*CON(1)
CON(14)=-VIWU*COM(2)
CON(15)=VTOU2*CON(2)
COM(16)=FOMC
FOCL=FUC

RFHM(1)=FUC
AFUM(1)=FUC
RDIVzRPIV+OFLRPI
ASSIGN 20 TO NGO

GO TO 17

CONTINUE

RFUN(P)=FUC
qDIV=RDIV+OFLBPT
ASSTGN 21 TO MGO

GO TO 17

CONTINUE

RFUN(3)=FUC
P°1V=RDIV-8*OFLPDI
APIV=APIV+OFLAPI
ASSIGN 2? TO NGO

GO TO 17

CONTINUF
APIV=APTV+OFLAPI
AFUM(2)=FHC

ASSIGN 23 TO NGO

GO TO 17

PONTIAMHZ

AFUN(3)=FHC
ADIV=APIV-2*OELAPI
CON(11=DFRIV(AFUN9OFLAPI)
CON(?)=OFQIV(RFUN9OFLRPI)
WRITF (1) COM
CONTINUE

1F (TRAO.NF.O) pRINT 3%. IRAncFERT

CALL STFPFIT (CON9FOMC9FCALC9NUSE9WT9NCONPI9ITM)

C

C
P5

C

C

C

C
26
27
ER
29
3O
31
3?
33
3A
35
36

DPOGQ

133
CALCULATES NFW CONSTANTG F904 STEPFIT CORRECTIONS

OO 29 JD=I9NOTN

ICONG=INOFX1JP)

ICONGO=IOFX(ICONG)
CONSTNT(ICONGO)=CON§TNT(ICONGO)+COFNIJD)*FCONS(ICONGO)
GCON(ICONGO)=SIGMCO(JP)

CONTINUE

TTQCNT=ITPCNT+1

POINTS CONSTANTS AFTFQ FACH FIT

PQINT 3G9 IHEAD9ITRCNT9ITRYS9(NAMEIM)9CONSTNT(M)9
1 SCON(M)9M=1915)

IF (ITQCNToLEolTRYg) GO TO 14

GO TO 1

FORMAT (1011“)
FORMAT (2AR920I199X9IP99F5.09AR)
VOQMAT (OF10.2)
FORMAT (RF15.7)
FORMAT (QFIO.4)
FORMAT ( 7H INDEX=9I39§X9 3HVU=9I39SX9 QHNV§V=9I41
FORMAT ( 7HOTHI§ I9A89 16H] CASE WILL MAKE9I29

3RH TTERATIONS FOQ MOLFCULAQ CONSTANT§.9/9

41H CONSTANTS MILL NOT RE USEO IN THE FIT IF

?QH THFIR F-LFVFL IS GQEATFR9/9 5H THAN9ER.29

43H. OATA POINTS FOP WOICH THF ORSFRFVED MINU9

11H CALCULATFD9/9 19H VALUE IS LFSS THAN9F6.29

14H WILL HF USFO.9/9 QHOCONSTANT 9RX9SHVALUE9GX9
17HFPACTIONAL CHANGF93X9 4HUSED9/2X99993X9E12.6
9HX9F7.497X9A3))
FOPMAT ( 6H VIHU=9F5.I9‘3X9 SHAPIV=9E1‘5.79‘3X9
IQHQDIV=9F15.79§X9 4HVEU=9Elso71

FOQMAT ( QHOLIN? NO.9I49 77H IS OUT OF TOLFRANCF. FORS=9
IF10.49 7H FOMC=9FIO.41

FORMAT ( 17H TOTAL FDPOQ FOR 9149 19H DEJECTED LINES IS
I F11.4)

FODMAT (QAR//9 3HFTT9119 3H OF9I39 51H ITFRATIONS
I 4?H IQ COWULFTFD WITH THE FOLLOWING CONSTANTS9//9
2 9H CONQTANT9RX9 RHVALHE912X9 QHSTn £99099I/(IX999
3 2F?O.l?))

FNO

DNJ‘JTT-‘JVH

AM O3§IG

PPOGQAM 03316 (INPUT9OUTPUT9TAPE11

COMMON HI(393)9H21393)9FpII319NUSEISIO)9C0NIIO)9FOMC9
IWTISIO)9COM§TNT(12)9FC0MS(12)99CON(12)

COMMON /A/ NAMF(12)

COMMON /1?/ INFUI9INFOP9INFO39INF049NUMCON9JUM99CONST(I?)9
1FFIN9FFOUT9TOL9IOFNT(2)9TOLF

000

134

IFOH§(GIU)9IT4YS9ITPCNT

COMMON /17/ IN(G10)9IK(510)9IHFAO(919VL(1519NV§V(1519

COMMON /?1/ NI(13)9VFCTOR(1491419INOEX(I319TOFX(1319

ISIGMA(13)9COFN(13)9§IGMCO(1319NOTIN(13)9XCONST(1319NOIN

JTL‘QJVH

COMMON /1?T/ NK(12)9NDFLMAX9XDFVMAX
OIMFWWSIOM FW1T(819 IAN7IT(81

FOUIVALFNCF (COMSTNTT 119 GSIGI9 (CONGTNT(

(COMSTNT( 319 LAMOA19 (CONQTNT(
(CONSTMT( 919 ZEPOF19 (CONGTNTI
(CONSTNT( 719 XL19 (CONOTNT(

(CONSTNT( Q19 7L19
(CONSTNTI1119HAHSIG19

PFAL LAWOA9LAMDAV
IMTFGFQ VL

INITALIZFS NAMFG ANO VAQIARLFS

INFITII1=3ONO
INFIT(?1=3HYES
NAMF11125HFGSIG
MAMF121=SHFO§IG
NAMF(3)=6HFLAMOA
NAMF(A):GHFGAMMA
NA%E(G)=6HF7FQOF
NAMF(A):1HCWL
NAME(7)=3HEXL
NAMF191=3PFYL
NAMF(Q)=3HF7L
MAMF1101=7HFALHSIG
MAWF1111=7HFRAHSIG
NA‘FII71=6HFALLAM
1J'WCON-Tl?
NCOlezmqucOw+1
JK=1

KI=0

IQAO=0

FFPT:0.0

JUWD=O

CONTINUE

TTWCMTIO

UFAO 209 IHEAO9TFOONF

pranq 1H A40 DHTNTS OUT HEAOING
1F (1FOOMF.FO.HH STOD) STOP
POINT P09 IHFAO

1F (TFOONF.NF.RHFMO HFAO) GO TO

QFAOO ODTION CAQO

1

?19
419
619
819

DSIGI9
GAMMAI9
WL19
YL19

(CONSTNT(1019ALRSIG19
(CONGTNT(1?19

ALLAM)

QFAO 219 IOFMT9ITQY99INFOI9INFO29IHFO39INFO49(NK(I19
11:]91219MDFLMAX9XOFVMAX9TOL9TOLF9EFIN9FFOUT9ICASF

A§§IGN 19 TO WIGO

07)?)

7100

135

IF (1CA$F.FO.RHMFw CASF) GO TO 2

IF (ICASF.EC.RHOFN CONQ) ASSTGM 13 TO MGO
TF (ICASF.LO.RHAOO CONS) GO TO 13
C(HJTTPMIE

”FAOG IN CONGTANTS AND FRACTIONAL CHANGFS

QFAO 229 COHSTWT
DEAD 7P9 FCCWg

qug FQACTIONAL CHANGE IF ANY OQ ALL NOT DEFINFO

IF (FCOIS(11.FO.O.O1 FCONSII1=19O

OO 3 11:2916

IF (FCONSIII19FO90901 FCON§(II1=FCONS(11
GO TO ”40(19 (119-591

CONTIKHFT

IJCT=0

IT=IJCT

K=IT

CONTINUE

PFAO 239 FUT

PFAOQ 1w ENEQGIFQ

CONTIANNE

PPINT 949 FJT

IF (FUTIR1.VF.ORQQ.QRRO1 GO TO 7
VL(JK1=FOT(I1

NVSV(JK1=KI

DQINT 239 J‘9VL(JK19NVSV(JK1
JK:JK91

KIZO

QFAO P39 FUT

IF (FUT(R1.FO.QQQQ.QQQQ1 GO TO 10
K=O

TJCT=O

GO TO 6

CONTINUF

00 Q KH:19R

KI=KT+1

CALCULATFG OOANTHM DFDFHDFNCIES

1T=IT+1

IJCT=IJCT+1

IF (TJCT.LF.T) GO TO 8
IJCT=1

K:K+]

FOOS(IT)=FUT(KP)
TN(IT)=IJCT

1K(IT)=K

WT(IT1=1.

0531')

000

OOUO

no

0

10

11

1?

13

1A

1%

136

IF (FUT1KQ),FO.O.) wT(IT)=0.
CONTINUE

GO TO 9

CONTTKOHT

ITO=1TI3+1

quTCHFs F1 nun F2

OO 11 I=19TTO
TQJR1=3*1-2

TOUR9=3*I-1
TFM92F04§(ISO91)
FORS(TQJQI)=FOR§(ISHRP)
FOHS(ISUR9)=TFMD
CONTINUE

ITM:TT

OO 1? M=191?
CCO\J(M)=O.O

DOINTS INITIAL CONQTANTQ ANO VARIARLES

CFHHTTFHJE
PRINT P69 ICA§F9ITPYS9FFOUT9FFIN9TOLF9(NAMF(M19CONSTNT(M19

1FCONS(M19INFIT(NK(H1+1)9M=19121

CONTINHF
JKIO
QFWINO 1
NVSVT=O

CALCULATFS ENFRGY VALUFQ AND PARTIAL PFPIVATIVFS WITH
DFGDFCT TO THF CONSTANTO

OO 19 JD=19ITM

M=IN<J91

K=IK1J01

1F (MV§VT.FO.O) GO TO 1%
MVSVT:UV§VT-1

GO TO 16

JK=JK+1

CALCULATF9 VIRPATIONAL OEPFNOFNT VAPIAQLFS

NVSVTzNV§V(JK)-l

TVLD=VL(JK)

VIOL=TVLP+.%

VIOL2=VIRL*VIRL

VIHL1=VIOL*VTPL2

V14LA=VIOL*VIQL3
VFL:1L*VTHL-Xl*VTQL?+Y1*VIRL3-ZL*V1HL4
OSIGV=OSIG-ALQSTG*VIRL+RAHSIG*VIRL2
LAMOszLAMOA—ALLAM*VIRL

DQIMT 27. HQIGV9LAMOAV9VIHL9VFL
COM(G)=VTGL

(300

000

16

17

IR

19

137

CON(7):~VIRL?

COM(Q)=VIHL3

COM(Q)=-VTHL4

CONTTNOF

XK=K*(K+1)

XK§O=XK*XK

N-‘~‘-?:'\j-P

FOQ:2*K+(q-P*N)
9OROO=SORT((COR*HSTGV)**2+LAMDAV*“?-2*LAMOAV*R§TGV)
TF (K.FO.O.AHO.N.FO.31 SOROOz-GOROO
COGAM=K+1.%-.S*M
FL=RQIGV*XK-OSIG*XKQO-NM?*(COR*RSIGV+NM?*LAMOAV-SOROO9

lrnanrfl‘:'a\;Ah-;A) +VF‘L

FOMC=F0H8(JR)-(FL+ZFROF1
IF LINF 1% OUT OF TOLERANCF THFN WEIGHT IS RFT TO ZERO

1F (AH§(FOMC).LF.TOLF) GO TO 17
1F (MT(JD).FO.0.1 GO TO 17
NT(JR)=O.

DRINT ?R9 JR9FORSIJD19FOMC
FFPTzFFRT+FOMC

TpAO:1AAO+1

COHTTANHZ

THIS SFCTION CALCULATFS PARTIAL DFRIVATIVES

CON(11=KK-NM)*(COR-(COR*COR*RSIG-LAMDAV1/SOROO1
CON(?)=-KKSO
CON(3)=-NM2*(NMP+(RQIG'LAMOAV1/SOROO1
CON(A)=-MM?*(COGAM)

COH(?)=1.

CON(IO)=-VIRL*COM(1)

CON(11)=VTRL?*COH(1)

COH(12):-VIHL*CON(3)

CON(13)=FOMC

WRIT? (1) COM

CONTIIHE‘

Ir (TQAO.NF.O) PRINT 20. IPAO9FFRT

CALL STEPFIT (COH9FOMC9FCALC9NUSF9WT.NFONRI9ITM)

CALCULATFO NFN CONSTANTG FROM STEPFIT CORRECTIONS

OO 19 J9=19MOTN

ICONG=TNOFX(JP)

TCONGO=IOFX(ICONG)
CONQTNT(ICONGO)=CON§TNT(TCONGO)+COFN(JR1*FCONSIICRNGOI
€CON(TCONGO)=SIGMCO(JR)

FOWTTNUF

TTRCNT=ITQCNT+1

POINTS CONSTAMT§ AFTFD FACH FIT

 

 

“ III ill-T Ill. 19" II

13R

D'm’IHT 3O9 IHFAO9TTRCNT9ITRYS9(NAMF(”)9CONSTNT(M)9

IQCU’VIM) 914219121

IF (ITRCNT.LF.ITRYS1 GO TO 14

GO TO 1
P0 FORMAT (IOAQ)
21 FORWAT (9AA9I7II91?X9I?9SFR.09A9)
?? FORMAT (OFIO.?)
RT FORMAT (RFIO.?)
PA FORMAT ( 1R4 OATA FARO PEAO9QFIS.R)
2‘3 FOPN‘AT I 7-1 IHOFX=9I39RX9 3HVL=9I395X9 SHNVQV=9I4)
P6 FORMAT ( 7HOTHIS [9AR9 16%] CASE WILL MAKE9I?9
3hH ITERATIONS FOR MOLFCULAR CONSTANT§.9/9
41H COISTAMTS WILL MOT OF USFO IN THF FIT IF
284 TAEIQ F—LFVFL IG GRFATER9/9 SH THAN9FR.?9
41H. OATA POINTG FOR WHICH THF ORSFPEVFD MINUG
11H CALCULATFO9/9 19H VALUF IS LESS THAN9F6.?9
14H WILL HF URFO.9/9 QHOCONSTANT 9RX9SHVALUE9GX.
17HFQACTIOMAL CHANGF93X9 AHUSED9/2x9RQ93x9Fl?.6
9RX9F7.497X9A311
27 FORWAT ( 7H RSIGV=.F15.R9RX9 7HLAMOAV=9EIS.R.SX9

IRHVIDL=9FIS.R.GX9 4HVE =9FIS.R)

DQJ‘JTL‘UJV-d

2R FORMAT I OHOLIMF NO.9I49 27H 1% OUT OF TOLFRANCF. FORS=9

1F10.49 7% FOMC=9FIO.41
PO FORMAT ( 17H TOTAL FRROR FOR 9149 19H RFJFCTEO LINFS IS
1 F11.41
30 FORMAT (OAR//9 3HFTT9I39 3H OF9I39 53H ITFRATIONS
1 42H 19 COMRLFTFO WITH THE FOLLOWING CONSTANTS9l/9
P RH CONSTANT9HX9 SHVALHF9IPX9 QHSTO ERROR9l/(1XRQ9
3 PF?0.1?11
FNO

APPENDIX C

The tables in this appendix contain all the identified
transitions which were used to obtain the simultaneous
values of the molecular constants. Each entry contains the
observed frequency, weight and observed minus calculated

frequency in the following manner:

observed

weight obs-calc.

An observed frequency of -0.0000 indicates that transition

was not identified.

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