INFRARED SPECI‘RUM OF HYDROGEN
SULFIDE IN THE 3795 CM“1 REGION

THESIS FOR THE DEGREE OF M. Sn
MICHIGAN STATE COLLEGE

CARLETC‘N MCNEAL SAVAGE
1955

0-169

"I” “H" ‘MIiI'H'fiWISiA1lE i'iRIARIES _

31293 01774 5591

 

LIBRARY
Mlchfgan State I
Universlty

 

 

 

This is to certify that the

thesis entitled

Infrared Spectrum of Hydrogen
Sulfide in the 3795 cm-1 Region

presented by

Carleton McNeal Savage

has been accepted towards fulfillment

of the requirements for

M. S. degree in PhYSiCS

8. L9. 74%

Major professor

Date_A_plil ‘5’ 1955

 

 

 

w- x-)-

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1/98 cJCIRCJDateDue.p65-p.14

lNFRARED SPECTRUM OF HYDROGEN SULFIDE

1

IN THE 3795 cm‘ REGION

by

Carleton MCNeal Savage

A THESTS

Submitted to the School of Graduate Studies of Michigan
State College of Agriculture and Applied Science
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE

Department of Physics and Astronomy

1955

To Joan

354781

ACKROWLEDGEMENTS
The author wishes to express his thanks to Dr. H. C.
Allen, Jr. for suggesting the problem. He is also greatly
indebted to Dr. C. D. Hause and Dr. T. H. Edwards for their
guidance and assistance in carrying out the work. The writer
deeply appreciates the financial support of the Research

Corporation during the Fall and Winter of 1954—55.

WMSa/maé

INFRARED SPECQRUM OF HYDROGEN SULFIDE

IN THE 3795 our; REGION

by

Carleton.McNeel Savage

.AN'ABSTRAC!
Submitted to the School of Graduate Studies oflMichignn
State College of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of
MASEER OF SCIENCE

Department of Physics and Astronomy
1955

Approved" 51. (S): )§/;L¢4¢1‘£;=1

Carleton M. Savage

ABSTRACT

The absorption.of hydrogen.sulfide in the region from
3730 to 4030 cm-1
The absorption has been assigned partly to an.A-type.band
(n1, n2, n3) 3 (0,1,1) and partly to a.B-type band.(1,l,0).

The absorption was measured at pressures between 8 and

has been.measured under high resolution .

14 cm of Hg with a path length of 285 cm.using a.mnltiple
traverse cell. The spectral slit width was between .15 and
.20 cmTl. The spectrograph was a self-recording, vacuum,
grating insturment built by R. H. Noble and recently improved
by the installation of a new Bausch and Lomb 15,000 line per
inch grating and a Baird Associates 450 cycle amplifier and
phase-sensitive detector. The source was an argon filled
zirconium concentrated arc lamp. The detector was.an.Eastman
Kodak lead sulfide photcondueting detector.

Calibratfh.was made using‘Fabry-Perot interference
fringes to give divisions of equal wave number spacing
between two argon lines used as standards.

The analysis was made through the use of published
energy tables for the rigid rotor. A classical centrifugal
distortion correction was applied to the rigid.rotor energy
levels. A least squares fit of observed lines to assigned

transitions, assuming known ground state energy levels, gives

for the excited state inertial parameters (0,1,1) band, A =

10.517 cm'1 1 1

cm'lg (1,1,0) band, A = 10.595 emf

4.603 cm'1,'Vb = 3779.23 cm’l.

, a = 9.124 cm‘ , c = 4.619 cm?

1

9 yo = 3789.07
, a = 8.985 cm‘l, c =

TABLE E CONTENTS

Introduction
Apparatus
Grating
Auxiliary vacuum tank
Arc lamp
Absorption cell
Interferometer
Chopper motor
Detector
Cathode follower
Amplifier
Experimental
Calibration
Measurement of lines
Ground state energies
Calculations and results
Trial constants
Energy level calculations
Centrifugal distortion correction
Calculation of d, p, and 6’ .
Transition calculation
Symmetry and selection rules
Intensity

Assignment of transitions

Page

-4 ~J <r ox r> .e

TABLE OF CONTENTS
(CONT'D)

Least squares calculation
Calculation of B band
Conclusion

Tables of results

Bibliography

Page
36
39
41
42
61

LIST 9; FIGURES

H S Molecule

2
Normal vibrations of the H28 molecule
The Optical system of the spectrometer

The Optical system of the absorption cell in use.

The Optical system of the Fabry-Perot interfer—
ometer in position.

Cathode follower circuit.

Block diagram of the 450 cycle amplifier.

Comparison of observed and calculated spectra.

Page

CDUTVJ

13
15
38

LIST OF TAELBS.
Table Page

I. Constants of the H28 molecule 42

II. Rotational energy levels (cm-l) of the
(000), (011) and (110) vibration states 43

III. Comparison of Observed and calculated

Spectra in the 2.5}.region 48
PHOTOGRAPHS
Photo
1. Typical fringes 10
2. Spectrometer 16
3. Auxiliary tank and absorption cell 17
l

4., 5., 6. H28 Spectra from 3730 to 4030 cm— 19

7., 8. .Typical sections of spectra as measured. 23

INTRODUCTION

Hydrogen sulfide (H28) is an asymmetric top rotator simi-
lar to the H20 molecule. Much work has been done with both
low and high resolution in the photographic infrared and
the nearinfrared region1 to 7.

The absorption near 2.5 microns was observed and re—
ported in 1931 by H. H. Nielsen.l Since no analysis has been
reported in the literature, the purpose of this paper is to
present an analysis of the rotational fine structure in this
region.

The absorption has been assigned to the combination
bands (011) and (110). This notation represents the vibra-
tional quantum numbers of the upper state involved in the
transitions.- The lower state would be designated (000).

Thus the (011) band consists of transitions from the ground
vibrational state to a vibration of theV2 andifs modes.

An alternate method of labeling found in some papers gives
the vibrations in the order (V5,L’1,1’é) and the vibrational
quantum numbers are designated by Ina, n”, n5) following the
vearly notation used in the studies of H20.

The accepted molecular model for H28 is shown in Figure l.
The three fundamental modes of vibration are shown in Figure 2.

The modesif andtfé are symmetric and)!”3 is antisymmetric with

1
respect to rotation about the symmetry axis (B axis).

B (Symmetry axis)

 

 

 

 

 

2

Constants for ground state .
e = 92° 20'
r = 1.345 A
IA = 2.667 x 10"40 g cm2
IB = 3.076 x 10’40 g cmz
IC = 5.845 x 10-40 g cm2

Figure 1. H28 Molecule.

\\/ \/

V’Or ‘W VE or é,

/

1

2635 cm- 1189 cm—

/ \

Vora—
2651 cm-

Figure 2. Normal vibrations of the H23 molecule (not to scale)

APPARATUS

A self-recording, vacuum, prism-grating spectrometer
constructed by R. H. Noble8 and described in a thesis by
N. L. Nichols9 was used for this work. The portion of the
Optical system enclosed in the principal vacuum tank is shown
in Figure 3. It includes a foreoptic section, monochromhter
and detector. The foreprism was not used, being replaced by
a plane, front surfaced mirror. Under these circumstances,
the second order argon emission lines used in calibration
appeared directly on all the records.

The new Bausch and Lomb 15,000 line per inch grating,
purchased by the Research Corporation, was used for this work.
The grating has a ruled area of about 6" x 8" and is blazed
at about 27°. The first order wave length at the blaze is
1.5 microns. At first it was not expected that this grating
could be used in the region of 2.5 microns (an angle of 490
to 55°); however, it was found to give better results than
the 7,200 line per inch grating originally tried. (The 7,200
line grating is blazed at 15° and has a useable ruled area
of 4” x 5".)

Although the vacuum feature of the spectrograph greatly
reduced the atmOSpheric water vapOr absorption inside the
tank, much absorption was found to take place in the Optical
path before entering the Spectrograph proper. A cardboard

box was constructed around the external Optical section, and

parabaloidal mirrors

t F’ ,
‘ grating :::>

 

 

l
' l
chOpper ‘ \
motor / ‘
ii! .
flat
% (mirrors
~./‘ ‘» . exit
entrancgiiiis::3' C::;;ig;$Lfilit
, fix} _' detector

 

\

J

 

4 ' ‘(nri‘s'ni'
parabaloida I. ¢
collimati ,
mirror’ l ;’ Figure 3. The Optical system

/ of the spectrometer.

a solution of CO2 dissolved in acetanewas put into a copper
vessel designed to freeze out the H20 in this part of the appa-
ratus. This was found to reduce the water absorption greatly
and showed that most of the absorption took place in the
Optical path outside the tank. An auxiliary steel tank was
constructed to house the absorption cell and its necessary
lenses. Two quartz windows were placed in the tank and were

so designed that the concentrated zirconium arc lamp used as

a source could be placed in contact with the window. This
allowed the lamp to be Operated outside the vacuum system where
it might be cooled easily and moved for slight optical adjust-

ments without introducing additional atmOSpheric absorption.

Provision was made so that the absorption cell might be
filled without removing it from the spectrOgraph, thus making
it unnecessary to let air into the tank whenever the pressure
or material in the cell was to be changed.

The auxiliary tank was connected to the main spectrograph
at the light entrance port of the spectrograph. The quartz
window was removed, thus making it possible to evacuate the
auxiliary tank with the same pump as that used to evacuate
the spectrograph. A pressure Of about .2 mm of Hg could be
maintained throughout the system when pumping steadily.

A zirconium concentrated arc lamp was used to obtain the
spectrum. This lamp is argon filled, and the argon emission
lines were used for calibration. An attempt was made to use
a carbon are as a source but it was found to be too unsteady

for this type of instrument.

The absorption cell, a multiple reflection system, is
also described by Nicholsg, The absorption cell is made

of brass and the inside is readily attacked by the H S. To

2
minimize this, the inside was painted with clear glyptal and
baked to give a hard surface. Several coats of glyptal were
applied and baked. The absorption cell had been previously
used with D01 and the mirrors were badly corroded. It was
therefore necessary to re-aluminize the mirrors before this
work could be carried out. Figure 4 shows the absorption cell
as used in the work. The source is shown at the side window
of the auxiliary tank.

For calibration of the spectrograph, interference fringes
produced by a Fabry-Perot interferometer were used. The
Optical setup of the interferometer is shown in Figure 5.

The source is shown at the end window of the auxiliary tank.
Typical fringes are shown in Photograph 1. The plates of the
interferometer were adjusted for parallelism by use of
Haidinger fringes. That is, the interferometer is placed

in front of an extended monochromatic source, and by looking
toward the source through the interferometer a ring pattern
of fringes is observed. If the plates Of the interferometer
are parallel, this pattern will not change as the eye is
moved vertically or horizontally across the field of view. If
the plates are not parallel, the fringes seem to "expand out
of" or "collapse into" the center of the pattern as the eye

is moved across the field.

mirrors
2 \m

(mm

(8 traversals)

   

12.5 cm
. uartZ‘s
Qb-K q p
\ 7 lenses
kmirror
concentra -d

 

arc lamp \

i
-[fore slit of
c::rc::i spectrOgraph

Figure 4. The Optical system of the absorption cell in use.

 
  

concentrated
arc lamp

R~ 7.5 cm
quartz
lens

g Fabry-Perot
,’ I. etalon

 

0‘ K20 cm quartz
I / lens

fore slit Of
Spectrograph

The optical system of the Fabry-Berot
interferometer in position.

Figure 5.

mmozEu 29.25340 Adoit

The 2.88. _ I.

10

For proper alignment in the tank, the interferometer
is placed in position without the lenses. By looking at the
source through a circular hole at the spectrograph slit,
multiple images of the source can be seen if the interferometer
is at an angle with the line of light (five images could be
seen with this setup). The interferometer is rotated about a
vertical axis until the multiple images are in a vertical line.
Then by rotating about a horizontal axis, the images may be
made to overlap. The lenses are then put into place. The
light is collimated for visible light. This does not colli-
mate it for the infrared however. Therefore, the lenses are
moved by amounts calculated from the indices of refraction
of quartz for visible and infrared.

Although the chopper motor was not designed to operate
in a vacuum, it was decided to install it inside the
evacuated spectrograph. The grease was removed from the
bearings and replaced with Dow Corning high vacuum grease
(a silicone lubricant).

At one stage of the work considerable trouble was
experienced with the fuses blowing for the circuits connected
to the apparatus in the evacuated tank. Photographic film
was placed at various places in the tank near motors, termi—
nals, etc. where are discharges might occur. A number of the
film strips were blackened when the spectrograph was evacuated
and the fuses purposely blown. A complete rewiring job was

done on the spectrograph. The electrical equipment inside

11

the tank consists of a selsyn1x>adjust the slit widths, a

selsyn to rotate the prism table, a selsyn to rotate the grating,
the chopper motor and the cathode follower circuit. Although

it helped, the rewiring did not completely eliminate the

fuse blowing. The chOpper motor was suspected and removed,

and the area near the starter coil switch was cleaned and
painted with clear glyptal. The apparatus has worked satis-
factorily thereafter.

From previous work on the instrument, it was found to
ihave a nonlinearity of about .4 percent between the marker
signals placed every .10 on the record. The transmission
on the grating drive was dismantled and a badly worn fiber
gear was replaced. The cone bearing on which the grating
rotates was also removed and relapped. This gave an improve-
ment by a factor of four.

The detector, amplifier and recorder now in use con-
sists of an Eastman Kodak lead sulfide cell with a cross-
sectional area of 1/2 by 10 mm, together with a new 450 cycle
amplifier which replaced the original 10 cycle equipment 9
and a Speedomax recorder.

The detector has two matched sections of about 5 megohms
impedance each, one to be used as a photoconductive detector
and the other section as a load resistor. This has the
advantage that when the cell is cooled the two sections re-
main matched. The impedance of the PbS cell did not match

the impedance of the amplifier and it was therefore necessary

12

45V+

PbS
cell

oC4

 

 

'001/ifd

 

33 K
45 V +

.25 llfd

 

Meg. 50

Meg.

 

680 K

“AAAAAAL
V'V‘VV

.3ilpfd

out put

 

..|‘.

Figure 6. Cathode follower circuit.

13

a
45v-

to construct a cathode follower circuit as shown in Figure 6.
This was constructed to be Operated inside the vacuum tank

as near as possible to the PbS cell. Tests were run on the
effects of cooling the lead sulfide cell, and it was found
that cooling did not help in this particular installation.

The signal was increased by about 50 percent during the initial
stages of cooling, but when equilibrium was reached the energy
was actually less than at room temperature. It was there-
fore decided when the cathode follower was constructed not

to cool the cell and to use only half of the PbS cell as a
detector and to use a White resistor as a load resistor.

This was done in an attempt to minimize inherent noise from
the PbS Cell.

The cathode follower feeds into a 450 cycle amplifier
and phase-sensitive detector, Model CM 2—3, made by Baird
Associates, Inc. A block diagram of this instrument is shown
in Figure 7.

Its input impedance is on the order of 0.68 megohms.
Included but not shown in the diagram of the amplifier is a
voltage regulated power supply and a high voltage power
supply for a photomultiplier tube. The reference input
signal is generated by a small synchronous generator mounted
on the shaft of the light chopper motor such that by

rotating the generator with respect to the chopper the phase

between the signal and reference voltages can be adjusted
for best rectification of the signal. The output of the

amplifier is fed into the Speedomax recorder.

14

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Twin "T“
filter
' A
Signal 6SJ7 6SJ7 G 68J7
in ah _,ya .J
amplifier__. amplifierp_.i mg amplifier
L i n
G
6SJ7 a
amplifier i
n
6SN7
h
Phase R c pus
fie pull a»
COHIPB~IVEUSOI‘—1 filter jfower to recorder
amplifij?"

 

 

 

 

6SH7

reference
amplifier

H

reference signal
in

 

 

 

Figure 7. Block diagram of 450 cycle amplifier.

15

 

 

Spectrometer 15

   

 

Auxiliary tank and Absorption cell
17

EXPERIMENTAL

The hydrogen sulfide was obtained from the Matheson
Company. As the cylinder was nearly empty, we were limited
in the amount of H23 that could be put into the absorption
cell. The maximum pressure that could be obtained was 14 cm
of Hg. As the H23 contained a considerable amount of water
vapor, the shipping container was cooled in an acetone and
dry ice bath; and the H28 was passed through a similarly cooled
U-shaped trap filled with glass beads. Even with these pre-
cautions an appreciable amount of water absorption was
recorded.

For the absorption expected in the region of 2.5 microns,
little energy was available with this apparatus. There are
several reasons for this. First, the black body radiation
of the arc is rapidly falling off. Second, the glass
envelope of the arc lamp, although thin, transmits less in
this region. Third, the angle of the grating used (490 to
550) results in less energy. Fourth, the sensitivity of the
PbS cell is decreasing. As mentioned before, cooling did not
result in the expected increase in signal.

The total effect of the aforementioned resulted in a
spectrum of inn; ”downhill" type as shown in Photographs4 ,
EBandéS. For the narrow slit widths necessary to resolve these

1

lines, the energy was so low below 3730 cm- that a suitable

spectrum could not be recorded. In addition, water absorption

18

a NO. v.02 0 ”k.”

 

- q u

7.6%.. 1.5.3 .EJm Admhomam
SommN Ea ZOEQm—Ommd
or 3v. wmnmmmma

zoCamomme mu:

 

 

 

 

 

 

 

 

19

 

 

who»

 

 

 

 

 

n~mn

21

in this region is especially intense. For these reasons,
much of the low frequency side of the bands could not be
observed.

The spectrum was obtained under the following conditions.
Eight traversals in the absorption cell gave a path length
of 285 em. Five runs were made with pressures from a to 14
cm of Hg (14 was the total pressure obtainable). The slit
widths were from 95 to 135 microns. The grating was turned
at a speed of about 1.25 degrees of are per hour. The chart
paper_was fed at 120 inches per hour. A run from 5750 to
4030 cm"1 took about five hours and resulted in a record
fifty feet long.

Sections of a typical run as they were used for

measurements are shown in PhotOgraphs 7 and a.

22

-- was? :55, 5m gum—am

:

iuao

aha

TI:...L u4<ou

.5 mmm TEE zofiamommq
fa: mmammmma
zoEmommq mwx

23

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v.2 to:

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4.3.. Em .5 elm

24

 

CALIBRATION

Previous work with the instrument shows a cyclic
variation of one degree length. No constant "grating constant”
could therefore be calculated. Because of this, other means
had to be used to obtain the frequencies of the lines.

Two prominent second order argon lines appeared on
either end of the spectrum in all records. These lines were
used as standards. The wave numbers used for these lines

are those measured and reported by Humphreys and Kostkowski.10

The values are 7478.84 cm"1 and 8060.43 cm-l. Their second

order positions appear at 5759.42 cm“1 and 4030.215 cm.-1
respectively. The region between these two lines was
divided into divisions of equal wave number spacing with the
use of a Fabry—Perot interferometer. The interferometer was
placed in the Spectrograph as shown in Figure.5, and was
allowed to reach equilibrium with its surroundings. Records
made on successive days reproduced within limits of linearity
of the recorder. The spacing of the etalon was therefore
considered constant throughout these runs.

The fringe run was compared with the runs containing the
argon emission lines. The frequency difference between the
argon lines divided by the number of fringes between them
gives an approximate wave number separation of the fringes.
The fractional part of a fringe between one of the argon lines

and the nearest fringe was measured and an approximate fre—

quency of the fringe was computed using the relationship

25

V: MAV' (Av: 1/2t) (l)
where V'is the frequency of the fringe, M is the order of
the fringe and zaV'the separation of the fringes, M was
determined for the fringe. As this should be an integral num—
ber, the nearest integer was assumed to be the correct one.
From this selection the order of the two argon lines were
calculated. From equation (l)<0v'is calculated from the order
and frequency of the two argonlines.

The two values of.AV’thus obtained were averaged giving

nor: 1.608047 i .000007 car1

This uncertainty would result in a difference of about .01 om‘l

in the computed values of the two argon lines.

The order of the argon line at 4050.22 cm—1 was measured
to be 2506.28. The order of the argon line at 3739.42 cm"1 was
measured to be 2325.44.

The fringe pattern as shown in Figure 1 contains both
first and second order fringes. This accounts for the alternate
intensity of the fringes. The large peaks contain both first
and second order, while the small peaks contain only the second
order. The large peaks were used in calibration. As the

etalon was used in a vacuum, no displacement of the first

and second order fringes would be expected.

26

Measurement of Lines

The wave number of the absorption lines were found
by the following method. Using the two argon lines as
reference points, an absorption run was compared with the
fringe runs. Assuming a constant separation of the fringes
and linear interpolation between them, the fringe run was
used as a ruler to assign an order number to the absorption
lines. The wave number was then found by direct multipli-
cation using relation (l). (Using ziV’z 1.608047)

Five runs were measured and averaged. The center
of the runs gave excellent agreement,the variation being
less than i .01 cm-l. The region near 4000 cm"1 had a deviation
of': .06 cm7l. None of the lines in this region were used
in the final analysis so this deviation caused no concern.

Photographs 4,5, and 6 show the complete region measured,
these were taken especially for this paper at a much compressed
scale. The argon reference lines are marked on either end
of the record. Many of the lines are due to atmospheric
‘water absorption, these lines were not measured,being sub-
tracted by comparison with a run of water absorption only.
Photographs 7 and 8 show sections of the runs as they were
measured. The spectrum was Spread out to reduce errors in the
width of the pencil lines used to mark the centers of the

lines being measured. (4% cm on the paper represented about

one cm-l )

27

GROUND STATE ENERGIES

The ground state rotational constants used are those
given by Crossz. Although the work was done in 1935 the
results are accepted by later workers in the field. The
constants were derived from analysis of photographic infrared
data and therefore considered reliable.

The values of the constants as given by Cross are

A = 10.373 .005 cm

H-

B 8.991 + .004 cm

C 4.732 1: .003 cm

Where A, B, and C are the reciprocal moments of inertia given

 

 

b h h h
y s 2e 8 20 8 20
A 2 _._JL__._... ’ B = ——-n-——-- , C :: ——-n-—-—-— 0
IA IB Ic
IA’ IB’ IC are given about the axes as shown in Figure l.

The ground state vibrational levels given in Table I,

are also from Cross' work.

28

CALCULATIONS AND RESULTS

The general method of analysis used by Cross 2 was
followed. This consists of the following steps. The excited
state inertial constants were estimated on the assumption
that the observed A-type structure arose from the (011)
vibrational band. By comparing the reciprocal moments of
inertia of previously analyzed bands, it can be seen that the
effect of theAQ vibration changes the constants by the

following amount.

AB = -.19 cm-1
A c = —.068 cm"1

Subtracting these changes from the values already computed
for the (111) band 7, we get the trial values for A, Bland
C. With these trial values of A, B and C, a spectrum is
calculated. The energy levels were computed with the aid

of published energy tables of king, Hainer and Cross.11

For completeness, a typical energy level is calculated

_below. The energy of a given level is given by

E = A_§_Q (J2 + J) + (5—5—9) E (K) (2)
For the 43 level, we use A = 10.51, B = 9.14 and C = 4.62.

J, the rotational quantum number, = 4. E (K) is taken from

the published tables. K is defined as

2B - A - C
K = A-C (3)

29

Using the above values of A, B and C we get from equation(5)

K = +.5348

E (K) is found by quadratic interpolation between the
values listed in the tables. The values from the tables are
for negative K, however

E1 (K) = -Ei.<-K> (4)
where T is the sublevel of the J quantum state. There are
2J + 1 values of T running from.T = -J to 1': +J.

We can find the values for positive K as follows. Since
K is positive, we use the value of 4_3. For this level the

energies from the table are given as

E (K) = E (—.4) = -15.63481
E (-.5) = ~15.98528
E (-.6) = -l6.35224

so that by relation (4)

s (.4) = 15.65481
E (.5) = 15.98528
E (.6) = 16.55224

Using quadratic interpolation between these three points, we
get

43 = a(x) + Mac)2 (5)
where.e,is the difference between two given E (K) values.

x is 10 times the difference between the K's. To find a and b

A]. = a + b (X z 1)
A2 = 2a 4» 4b (x = 2)
Al is the difference between E (.4) and E (.5); A2 is the

30

difference between E (.4) and E (.6). Hence
.35047 = a + b

Solving these two equations one gets

a = +.342225
b = +.008245
s (K) = r (.4) + a(x) + b(x)2 (6)
ForK = .5348, x = 1.348 = 10(.5348- .4)
E (.5348) = 16.111 cm'l

From equation (2)

E = (——-—A‘2*C)(J2+J) + (———1A'2'C E(K)

E 198.747 cm.1 (for 4 level)

3
At this point a classical centrifugal distortion correc-

 

tion is applied. Using the method of Cross 2 , it is assumed
that the molecule is rotating as would a classical rotator
having the same values of o< , p and K ;where 0< , f3 and X
represent the component of the square of the angular momentum
along the A, B and 0 axis respectively. Hence

o<+ fl+ X = (J2+J)
Thus the energy may be divided into three components.

E = o(A + p B + X'C

and
' _ «BE - as -ee
°<" 311' (3" 3B and 'ac

Since the center of gravity is so near the sulfur atom,
the further assumption is made that the rotation takes place

about the S atom. Using these assumptions, the total change

31

in energy due to rotational distortion is shown to be

.2
_ E («A tan 4:— p B cot ck )2 ~16

 

where

-16 —1)

1.963 x 10 = ho (to reduce to dimensions cm

E = energy as calculated from equation (2)

PT
ll

1 4.2 x 105 dynes cm.1 (molecular force constant)

 

 

 

k3 = 4,1 x 104 dynes cm-l (molecular force constant)
r = 1.361 A
([3 =460 30'
<x,(3, and X may be expressed in terms of
E = A 3 C (J2 + J) + E(K).
The simplest of these is 2/3. By definition
6E
63- 5'5
Differentiating the above equation gives
aE _Q_E_ g5 __ A-C aE(K).
313’ 3K 313 " 2 3K 513?
and K: 2BA--AC- C 3%- =A—:2-—C from relation (3),
therefore
-QE. _. M1
F'oB " eK

From equation (6) for E (K) one can also obtain
/3 = a + 2b (X) (actual equation used to find/3)
Performing similar differentiations, collecting terms and

simplifying gives
2 .
QE _ J + J E (K) K + 1
°<=eA" 2+2K’/3(2)

2
aE J + J E21 - 2K

 

Summing these values for o<, 2p, and Y, one gets

0( +fl + X = (J2 + J) as previously stated.
32

For the 4 level, /3 = 3.6, o<= 15.3 and X: 1.1.

3

After calculation Of the energy levels for a rigid
rotator (only values up to J = 10 were calculated, this is
the limit of the published tables) and application of a
classical correction for centrifugal distortion, a trial
spectrum was calculated, using the published ground state2
and the calculated energy levels for the excited state. The
transition energies in cm-1 were calculated from the equation

Ecal = V0 + E (#1) - E (Jr) (a)
where Ecal is the calculated wave number Of the transition,

V0 is the band center, E (J%l) is a rotational energy level
Of the excited state, and E (Jr) is a rotational energy level
of the ground state.

Table II lists the rotational energy levels used in the
final analysis Of the band. Column one gives the energy
level, column two the symmetry, column three the energy of
the ground state and column four the energy of the excited
state (011).

The symmetries of the rotational levels and the selection

13 An Operation of

rules are those formulated by Dennison.
180O rotation with respect to the C axis is indicated by the
first sign and an Operation Of 1800 rotation with respect to
the A axis by the second sign. A + in either column indicates
that the wave function is symmetric for this Operation and

-a - indicates that the wave function is antisymmetric for

the operation.

33

For type A bands, the selection rules are
+

AJ = 0, - 1
and
+ — 4+9 ——
-‘+ «a 44-
For type B bands, the selection rules are
lkJ = O, t l
and
++ «av ——
+— ¢+ —+

NO type C band can occur for plane triatomic molecules
as there can be no restoring force fOr out of plane vibrations.
With the complicated Observed bands, it is not only
necessary to calculate the position of the transitions, but
one also needs to have some idea of their relative intensities
before the calculated spectrum can be compared with the Observed
spectrum. The relative intensities of the lines can be cal-
culated with the aid of tables published by Cross, Hainer,

and Kingll- . The approximate intensity of a transition is

given by E

ET (9)

I = e Vg‘MZ’

where E is the rotational energy level Of the ground state;
V'is the frequency Of the transition in cm’l; g is a nuclear
spin factor, (g = 3 when T is Odd in the ground state and

g = 1 when T is even in the ground state); k is the Boltzmann

constant; T is the Kelvin temperature; and )le is the "line

34

strength" or probability of the transition. The values of
[M2) are obtained frOm the published tables. Using K = +.5
will give intensities with sufficient accuracy for this work
and eliminates the need for interpolation.

The calculated positions and intensities were plotted
from i V'O, Vb as yet being unknown. This was thencnmpared
with the Observed spectrum. The "collected Q"branches Of the
Observed and calculated spectra were matched, and )fo assigned.
From comparison of locations and intensities a number of
transitions were assigned to the observed spectrum. For each
assigned transition, an equation of the form

.AE = Avo+ac><+ bp+ OX (10)
was set up, where ZXE is the difference betwaalthe Observed
and calculated value of the transition energy in cm-1. .AL/o

is a change in the band center, and

SE: _ ép _ «53
SA fi‘ 513 X‘S'é

(for explicit expressions, see page 32 ). a, b, and c are

(X:

changes in the rotational constants. (‘3VO’ a, b, and c are
undetermined coefficients.)

To bring the Observed and calculated frequencies into
agreement, the set Of equations Obtained from equation (10)
was solved for zavb, a, b, and c by the least squares method.

These increments were added to the original assumed values
and new rotational energy levels were calculated. A new
calculated spectrum was prepared and compared with the Observed
spectrum. Many lines in the calculated band were shifted in

35

 

location so that more transitions could now be assigned and
another least squares fit carried out. The process should be
repeated until the change in the increments is negligible.
The number of times depends on the original estimate of
the rotational constants and on the correct assignment Of
lines. In each case here it was done twice.

For a molecule for which the ground states were unknown,
equation (10)becomes

AE=£wb+a}u' +bfl3'+c'K'-ad—bfi—OX
where the primed values are for the excited states and the

unprimed for the ground state.

Least Squares
To solve a series of equation Of the type
AE =AV0+O<a + {3b +b’c by least squares
one first Obtains the following set of equations where

n
Z: Z , n is the number of equations.
.=1 .
ZAEi = nAV'o + azc<i + bZ/ai + chi
2
ZAEiOCi =AVOZdi + aZoti + bzo‘ifli + 02%)}
2
ZAEi/3i = Adi/31 + alz"’i/3i + bZPi + CZBiXi
2
ZAEin = AVoZYi + affixi + bzflixi + czb’i
These sums can be computed readily with the aid Of a Friden

Calculator. A typical result is given below for 23 lines in

the A band.

36

-1.26 23‘3V6 + 146.72 a + 182.09 b + 419.19 0

146.724V6 + 1650.70 8 + 1999.40 b + 2848.49 0
-23.32 = 182.09.3Vb + 1999.40 a + 3006.56 b + 4879.44 c

1

—30.57 = 419.19.0Vb + 2848.49 a + 4879.44 b + 19882.55 c
The above set Of equations was solved using determinates

for.gyb, a, b, and c. These values are given below.

a. = + 0006 CHI-1 AVE) = .01 CID-1
b = - .013 om-l
c = + .001 cm“1

 

Table III is a comparison of the Observed and calculated
spectra. Column one gives the line number assigned in original
measurements. Column two gives the observed intensity; it is
prOportional to the percent absorption of the center of the
line and thus not strictly comparable. Column three gives the
wave numbers Of the observed lines. Column four the assigned
transitions; the rotational energy level of the excited state
is given first and that of the lower or ground state is given
second.: Column five lists the calculated wave number of the
transitions of the A band (011). Column six lists the cal-
culated wave number of the transitions Of a B band (110) to
be explained shortly.

Figure 8 shows a line drawing of the Observed spectra,
with the water absorption removed, compared with the calculated
A and B bands.

Only the strongest transitions are drawn to reduce confu-

sion. The B band was calculated for the following reason.

37

Figure 8. Comparison of Observed and calculated spectra.

 

 

 

 

 

 

Observed Calculated Calculated scale
'spectra A band B band ‘
A.
1
:. J
O
.___ h
—_. ‘“<n
"I
m ——4
4
.. '5
‘. d O
__J
t O
_: _. O
00
IV.
fit 1
D 3° ‘
-a
a 8.
f‘
m

 

 

 

 

 

38

After as many lines as possible were assigned for the A type
band, quite a number of strong lines were still unaccounted
for. Since Vi and V3 are of nearly the same frequency
(2635 cm"1 and 2651 cm-l), it is logical that a B type band
(110) also occurts in this region.

.Assuming that most of the additional absorption was due
to the (110) band, trial rotational constants were estimated

as before. The effect of the V3 vibration<x1the rotational

constants is

AB = - .034 cm-1
AC = - .046 curl

Using the trial energylevels for the (110) band and the
known ground state levels and B type selection rules,a B
band was compiled. The procedure is the same as used for
the A type band. Table II gives in column five the rotational
energy levels for the (110) band used in preparation of
Table III. Table III includes,in addition to the A band as
mentioned, the transitions of the B band in column six.
Figure 8 shows a calculated B band compared wifllthe Observed
spectrum.

Some difficulty blessigning the band center of the B
band was eXperienced. Because of the H20 absorption and the
small energy available below 3730 cm-1, only the R branch of
the B band was Observed. The method of matching Observed and
calculated spectra was as follows. The strongest series cal-

culated for the B band is of the type

J - (J - 1)
-J J—2
39

That is

6-6 ‘ 5-4
This series was matched to a series of strong Observed lines.

Only V; = 3779.23 gave a good fit to the Observed spacing

and intensities.

40

CONCLUSION

The absorption in the 3795 cm-1 region has been assigned
to the bands,(011) and (110). The rotational constants and
band centers are given in Table 1.

NO strong predicted lines were unaccounted for, however
some Observed lines were not assigned transitions. These
unassigned lines are probably for the most part due to transi-
tions Of J2710 and the piling up of weak transitions not
calculated.

The accuracy of the Observed lines are believed to be

within .03 cm-l. The mean deviation for the strongest transi—

tions is about .1 cm-l. The classical centrifugalndistortion
correction may be responsible for some Of the large deviations.
Also, many of the listed peak positions cannot be attributed
to single transitions. The overlapping of tWO or more transi-
tions will give an Observed peak that will not be the true
frequency Of any one transition.

The Observed intensities Of the A and B bands are about

the same.

41

TABLE I

CONSTANTS OF THE H28 MOLECULE

 

 

 

(011) (110)
A cm-l 10.517 10.595
B cm‘1 9.124 8.985
C cn'l 4.619 4.603
210 cm'1 3789.07 3779. 23
IA g cm2 2.6615 x 10’40 2.6417 x 10'40
IB g cm2 3.0676 x 10‘40 3.1151 x 10"40
IC g cm2 6.0595 x 10"40 6.0806 x 10"40

h _. —40
,g— — 27.989 X 10
17 C

42

TABLE II

ROTATIONAL ENERGY LEVELS (cm'l) OF (000) (011)

(110) VIBRATION STATES

 

 

 

Jr Symmetry (000) (011) (110)
00 ++ 0 0 0

11 +- 19.36 19.64 19.58
10 -- 15.11 15.14 15.20
1__l —+ 15.72 15.74 15.59
22 ++ 58.37 59.19 59.10
21 -+ 55.20 55.79 55.94
20 -- 51.06 51.61 51.12
2_1 +- 38.29 38.12 37.99
2_2 ++ 38.01 37.84 37.62
33 +- 117.48 119.09 119.15
32 -- 115.44 116.87 117.23
31 -+ 107.24 108.61 107.68
50 ++ 96.36 97.02 96.72
3-1 +- 95.00 95.69 94.97
3_2 -- 71.46 70.86 70.58
3_3 -+ 71.42 70.83 70.52
44 ++ 197.08 199.75 200.14
43 -+ 195.92 198.44 199.13
42 -- 182.56 184.98 183.62
41 +- 173.98 175.73 175.23

TABLE II (CONT 'D)

 

 

 

JT Symmetry (000) (011) (110)
40 ++ 170.27 172.10 170.60
4_1 -+ 148.41 148.92 148.24
4_2 -- 148.14 148.68 147.87'
4__3 +- 114.18 112.94 112.48
4_4 ++ 114.18 112.94 112.48
55 +- 297.29 501.29 502.18
54 -— 296.66 500.55 501.68
53 -+ 277.49 281.18 279.58
52 ++ 271.50 274.42 275.85
51 +- 265.75‘ 266.95 264.48
50 -- 244.48 246.59 245.26
5_l -+ 245.47 245.45 245.86
5_2 ++ 210.50 210.45 209.50
5_3 +— 210.26 210.42 209.44
5_4 -- . 166.57 164.24 165.60
5_5 —+ 166.57 164.24 165.60
66 ++ 417.96 425.41 425.06
65 -+ 417.52 425.02 424.82
64 -- 592.57 597.75 596.16
63 +- 588.46 595.16 592.59
62 ++ 575.68 580.49 577.07
61 -+ 559.65 565.50 561:67

44

TABLE II (CONT'D)

 

 

 

JT Symmetry (000) (011) (110)

60 - 356.96 360.68 357.81
6_1 +— 325.39 327.24 325.62
6_2 ++ 325.22 327.08 325.34
6_3 -+ 281.70 281.26 280.01
6_4 -- 281.69 281.25 280.01
6_5 +- 227.99 224.74 225.91
6_6 ++ 227.99 224.74 223.91
77 +- 558.89 565.98 568.46
76 -- 558.37 565.57 568.34
75 -+ 528.26 534.96 533.74
74 ++ 525.55 532.11 531.69
73 +- 506.59 513.17 509.03
72 -- 494.40 499.77 497.66
71 -+ 488.29 493.87 489.39
70 ++ 459.42 463.21 460.82
7_1 +- 458.71 462.63 459.87
7_2 -- 415.98 417.51 415.51
7_3 -+ 415.96 417.48 415.46
7_4 4+ 362.52 361.27 359.71
7_5 +- 362.52 361.27 359.71
7-6 -- 299.06 294.50 293.38
7 -+ 299.06 294.50 293.38

4 5

TABLE II (CONT'D)

 

 

 

Jz- Symmetry (000) (011) (110)
88 ++ 719.67 728.66

87 -+ 718.92 728.57

86 -- 684.77 692.97

85 +— 682.59 691.22

84 ++ 657.10 665.78

83 -+ 648.35 655.91

82 -- 637.49 645.19 649.28
81 +- 612.33 618.33 615.11
80 ++ 610.42 616.58 611.84
8_1 -+ 569.11 572.88 569.95
8”2 -- 568.95 572.77 569.73
8_3 +- 516.03 516.99 514.59
8_4 ++ 516.03 516.98 514.58
8_5 —+ 452.77 450.46 448.57
8—6 -- 452.77 450.46 448.57
8_7 +- 379.53 373.43 372.03
8_8 ++ 379.53 373.43 372.03
9_2 ++ 688.29 691.82 688.38
9_3 +4 688.29 691.82 688.58
9_4 -- 625.36 625.62 622.78
9_S —+ 625.56 625.62 622.78
9-6 ++ 552.38 548.82 546.54

46

TABLE II (CONT'D)

 

 

 

Symmetry (000) (011) (110)
552.58 548.82 546.54
469.59 461.54 459.85
469.39 461.54 459.85
744.11 743.18 740.06
744.11 743.18 740.06
661.38 656.54 655.66
661.58 656.54 655.66
568.67 558.82 556.75
568.67 ° 558.82 556.75

 

47

TABLE III

COMPARISON OF OBSERVED AND CALCULATED

SPECTRA IN 2.574 REGION

*Indicates Overlapping Water Absorption

 

 

 

L§§? Intensity SEEEiNS? Transition Calcglated w?¥§0§o'
.5 .7 4022.69 9_5 — 8_7 4022.48
1 1.6 4017.05
2 1.0 4015.05 9_3 - 8_5 4014.84
3 1.0 4011.13
4 1.1 4010.58
5 1.4 4007.72
6 1.1 4007.55 8_3 - 7_6 4007.00
7 1.0 4005.98
8 1.0 4005.52
9 1.0 4004.79
9.1 .5 4000.68
9.2 .5 5999.74 8_l — 7_4 5999.56
8-2 ' 7-5 5999.52
9.3 1.0 3998.62
10 .9 3997.48
10.6 1.4 3993.34
11 1.0 3990.10
12 1.4 3989.02
13 2.1 3988.08
14 1.0 3987.43
15 .8 3987.09
16 .7 5986.55 8_2 - 7_4 5986.44
17 .8 3985.05
18 1.2 3978.79 7_3 — 6_6 5978.56
7_2 - 6__5 5978.59
20 3.6 3973.39
21* 1.8 3972.47

48

TABLE III(CONT'D)

 

 

 

. Observed
Lfig? Intensity Wazg_¥o. Transition Calcgiated w?¥§0§°’
22 2.4 3971.31
23 3.4 3967.22 7_3 - 6_5 3966.70
24 2.8 3965.69
25* 2.0 3964.87
26* 3.0 3963.77 72 - 6_1 3963.45
27* 1.2 3961.68 74 - 61 3961.53
28 2.0 5961.04
29* 4.0 3954.74
30 1.6 3952.40
30.1 2.0 3951.60
31 5.6 3951.13
32 1.3 3946.12
55 2.2 33943.48 71 - 6_l 5945.24
35.1* 7.0 3942.51 61 - 5_2 3942.07
56 5.0 5959.92 60 - 5_3 3939.49
36.1 3.0 3938.90
37 2.2 3935.57
40 3.0 3931.63
41 2.6 3931.07
41.1* 4.5 3930.31 77 e 65 3930.17
44 4.5 3928.30 73 - 61 3928.61
45 2.8 3927.38 82 - 73 3927.67
45.1 2.0 3924.74

49

TABLE III (CONT'D)

 

 

 

L§§9 Intensity SEEEfES? Transition Calfgigged W9§§O§O-
45.2* 2.6 5924.57 75 — 63 5924.51
45.5* 1.5 5925.59 86 - 77 2925.15
50 7.0 3921.74 85 - 76 3921.92
51 2.8 3921.00
52 5.9 3918.97 74 — 64 5918.55
83 - 74 5919.45
55 5.9 5915.66 54 - 41 5915.62
54 5.7 5914.95
55 3.4 3914.23
56 1.4 5911.75 62 - 50 5911.82
9_2 - 8_1 5911.78
57 1.4 3911.14
58 6.8 5910.55
59 .8 3909.64 73 - 64 5909.67
60 1.0 5908.67 5_1 - 4__3 3908.91
61 5.8 3908.04 51 - 4_2 5907.88
54 — 42 5907.80
62 3.6 3907.76 66 - 54 3907.63
65 5.5 5907.02 71 - 62 5907.26
10_6 - 9_5 5906.89
10_5 - 9_4 5906.89
65 - 55 3906.76
63.1* 9.1 3906.25 75 - 66 3906.07
81 - 71 5906.05
64 4.1 3904.79 64 - 52 3904.09
64.1 2.2 5902.75 8_2 - 7_1 5905.15
82 74 3902.96
8_l — 70 5902.46
64.2* 5.1 5901.85 72 - 62 5901.21
64.5 2.5 5901.29

50

 

 

TAHLE III (CONT'D)
mm . 28587“" "'“
No. Inten81ty Wave_§o. Transition
cm

68 4.9 3900.35 72 - 63
9—5 ‘ 8-4
9-2 ’ 8—2

69* 3.2 3897.95

70 2.5 3896.69 80 - 72

71 9.1 3895.43
10_4 - 9_4

74 6.7 3892.60 10_8 - 9_7
10_7 - 9-6
7O " 61

74.1 4.0 3891.34 43 — 3O

75 3.9 3890049 8-1 " 7_1
8-4 ' 7--5
8—5 ' 7-2

76 6.1 3889.44 40 - 3_3
8-2 ‘ 70
64 ’ 55

77 4.0 3888.71

78 4.5 3888.43

79 4.3 3886.94

7901* 3885063 9_5 " 8-2
9-4 ' 8-4
55 " 45

79.2 7.2 3885.26 9-6 - 8 5
9 7 ' 8-6

 

- ”ww—

“u--w a“. .‘1

(011)

65900.58

3898.66
3898.66

3893.03
3893.03
3892.63
3891.15

3890.09
3890.08
3889.75

3889.51

3885.57

3885.12
3885.12

 

‘——

Calculated Wave No.

(110)

3898.65
3896.67
3894.33

3893.93
3893.93

3890.47

3889.54

3885.98
3885.98

3885.49

TABLE III (COJT'D)

 

m “o-—

 

' c—.——v.-.-—-_ .--.. ‘,

 

L§Ef Intensity nggrfig? Transition Calculated Wave N0.
cm- (011) (110)
79.3 6.5 3884.86 53 - 41 3884.83
80* 5.0 3883.63 54 - 44 3883.83
45 ‘ 3-1 5885.56
81 3.1 3882.34
81.1 1.5 3881.73 44 -31 3881.58
81.2* 5.0 3881.03 7_3 - 6 2 3881.33
7_2 - 6-1 3881.19
61 - 52 3881.07
81.3* 5.0 3880.59 lO_7 —9_7 3880.51
10_8 - 9—6 3880.51
71 - 63 3880.17
81.4 5.0 3879.67 7_1- 61 3879.46
82 10.0 3878.55 lO_10- 9_9 3878.50
10_9 - 9-8 3878.50
40 - 3_2 3878.37
83 3.4 3877.52 8_4 - 7_2 3877.83
8_3 - 7_3 3877.86
61 - 51 3877.17
8—6 - 7_5 3877.01
8_5 - 7_4 3877.01
84 8.5 3876.78 lO_8 - 10_9 3876.74
10_7 - 10_lo 3876.74
84.5 1.5 3874.98
84.6* 10.0 3873.70 51 - 42 3873.46
85 4.4 3873.25 53 - 44 3873.17
85.1 2.7 3872.76 9—6 - 8-6 3873.00
9_7 - 8_5 3873.00
86 6.8 3872.27 6-2 - 5_1 3872.68

TABLE III (CONT‘D)

 

 

‘m..._’ -L-

 

-....- g ”a...“ -” “C -

 

LiEe . 3:3:r535 Transition Calculated Wave No.
0. Inten81ty cm‘1 (011) (110)
87 8.4 3871.07 9-8 - 8_7 3871.08
9_9 8_8 3871.08
10_5 - lO_8 3870.87
10-6 - 10_7 3870.87
87.1* 3 3870.09 7__3 - 6_1 3869.30
7_2 - 6_2 3869.52
88 7.6 3868.46 7_4 - 6_3 3868.64
7_5 - 6__4 3868.65
9-6 ' 9—9 3868.50
9_7 - 9_8 3868.50
89 5.3 3867.24 52 - 43 3867.57 '
52 - 2_1 5867.65
90 5.0 3866.48 10_9 - 9_9 3866.59
10_10- 9-8 3866.59
42 - 30 3866.49
91 5.3 3865.79 60 - 52 3865.74
8_5 - 7_5 3865.28'
8—6 ' 7-4 5865.28
92 6.0 3863.93 44 - 32 3863.93
10_7 - 10__9 3864.22
10-8 ‘ 10-10 5864.22
5_1 - 40 3864.25
93 8.6 3863.43 8__8 - 7_7 3863.44
8_7 - 7-6 3863.44
94 1.2 3862.61
95 5.1 3862.04 9_4 - 9_7 3862.31
9_5 - 9—6 3862.31

53

TABLE III (CONT'D)

 

-—-—‘-u .0

Calculaté‘c'iwfia'vE—Né‘.‘

 

 

.m‘:- "'1‘“ '-~N- a. r

 

 

Line Observed ( . .
No. Intensity WavelNo. TranS1t10n (011) (110)
CID
96 11.0 3861.00 6-1 - 5_1 3861.38
43 - 33 3860.88
97 9.2 5859.89 6_4 — 6__3 5860.06
6_2 - 50 5860.09
98* 7.0 5859.44 9_,9 - 8_7 5859.55
9-8 " 8'8 38590 53
9_6 - 9-8 3856 038
9_7 - 9_9 3856 038
7_6 - 6_5 5855.58
9_2 - 9_5 3855 053
9_3 "' 9_4 3855 o 53
101 8.5 5851.06 5_2 - 4_l 5851.11
5_3 " 4-2 3851 035
101.1 4.5 5849.84 9_4 - 9_6 5849.65
9-5 ' 9"7 5849.65
101.2 10.0 5849.55 5_1 - 41 5849.11
41 - 32 3849 .36
102 10.2 5847.47 6_6 - 5_5 5847.44

TABLE III (CONT'D)

_4_

 

 

Line Observed Calculated Wave No
Intensity . . '
No. Wag:_§o.t Tran81tion (011) (110)
102 10.2 5847.47 6‘6 - 5_5 5847.44
41 — 51 5847.22
105 1.5 5845.92 8_1 — 8_4 5845.85
8__2 - 8_3 5845.81
104 8.1 5844.59 7_7 - 6_5 5844.62
105 6.3 3843.30 22 - 1_1 3843.56
107 2.4 5842.20 6_4 - 6_5 3842.33
6-5 ' 6-6 5842.54
9-2 " 9_4 3842.25
108 5.5 5841.64 4_1 - 50 5841.65
109 .4.2 5840.61 5_2 - 4_2 5840.59
6_5 - 5_5 5856.77
80 — 8_1 5856.54
112 1.9 3835.76
113 2.8 3835.39
114 4.7 5854.07 6_2 - 6_3 3834.45
22 - 1.”1 5854.54
115 4.7 5855.74 5_1 - 20 5855.70

55

TABLE III (CONT 'D)

 

 

 

 

 

Lfige Intensity ggserved ‘ Transition "03161113188 Wave No.
ve-T°' (011) (110)
cm

116 7.4 5855.09 8__l - 8_3 5855.15

8__2 — 8_4 5852.95
5_2 — 545 5855.15
5_3 - 5_4 5855.12
116.5 7.4 5852.59 4_l - 5_l 5852.47
117 9.4 5851.05 50 - 21 5850.89
6_3 — 6_5 5851.25
6_4 — 6_6 3831.25
118 10.2 5850.69 4_4 - 5_3 5850.59
4_3 - 5_2 5850.55
4-2 ' 30 5850.74
119 1.2 5829.64 72 - 7_l 5850.15 .
120 7.8 3828.65‘ 5 5 - 4 3 5828.65
5_4 - 4_4 3828.65
121 1.. 3827.22 61 - 6_2 5827.15
122 5.2 5824.95 50 - 20 5824.89
81 — 8_1 5825.25
50 - 5_3 3825.20
125 7.0 5825.87 70 - 7.2 5824.05
124 6.4 5825.59 4 2 - 4 3 5825.57
71 - 70 5825.52 0
125 4.0 5822.67 76 - 74 5822.62
6_2 — 6_4 5822.88
5 2 - 5_4 5822.56
5_3 - 5 5 5822.50
125.1* 8.0 5821.65 20 - 11 5821.52
3-2 ' 2-1 5821.64
5_3 - 2 2 5821.89

56

TABLE III (CONT'D)

 

-. —-—'--.~—.—————-—p~ --~ --—-.— --— - -c .

 

 

 

'1'" him- '-

 

Line . OESerGEH
No. IntenSIty WavelNo. Transition
cm
126 6.8 3820.24 4_3 - 3_3
4-4 ' 3«2
52 ‘ 5—1
127 6.1 3819.46 77 - 75
3-1 ' 21
128 6.0 3818.40 82 — 80
132 10.0 3813.34 3_1 - 3_2
2—2 ' 1—1
4-1 ' 4-5
133 4.4 5812.87 40 - 4_1
5_1 - 5_3
4-5 ‘ 4-4
134 4.0 3812.25 2_1 - 1O
3-2 ’ 2-2
63 - 61
135 5.9 3811.44 3_3 - 2_l
S1 ’ 50
136 404 3810.84 32 - 3_1
62 - 61
138 6.6 3808.34 52 - 5O
41 "' 4-1
140 4.4 3804.49 30 - 3_2
43 - 41
141 6.6 3803.38 2-1 - 1_l
142 6.8 3802.52 3_1 - 3 3
20 ‘ 2—1

57

 

———v—rv “— #9‘ .&v'-—-—r—.Wa~u“’~_

Calculated Wave N0.

 

(011) (110)
3820.29
5820.25
5820.02
3819.43
5819.00
5818.09
5817.47
3814.67
3815.30
3813.19
5815.29
3812.76
3812.83
3812.92
5812.08
5811.80
3812.17
5811.46
5811.54
3810.94
5809.92
3809.91
5808.58
5806.58
5806.05
3804.49
5804.58
5805.50
5802.78
5802.59

TABLE III (CONT'D)

 

 

 

 

L557 Intensity 825;:N65 Transition
CID
142.1* 5801.70 2_2 - 0
4O - 4_2
'3-5 ‘ 22
143 6.6 3799.44 86 - 85
64 - 66
62 ' 60
7-1 ' 7-2
143.5 3.0 3798.45 64 - 63
88 - 87
41 - 54
75 - 74
144 8.2 3797.56 87 - 88
144.1* 5796.60 77 - 76
44 - 42
21 ‘ 2--1
145 6.2 5795.85 76 - 77
146 _ .9 5795.02 53 - 51
146.1 5.4 5794.54 66 - 65
65 - 66
1O — 00
147.1 3 3793.91
147.2 4 3793.72 11 - 1O
55 - 54
147.3 5 3793.38
147.4 8 5795.17 22 - 21
147.5 9 3792.79 74 - 75
42 - 40
53 - 52
147.6 10 3792.32 54 - 55

58

A n-‘M'-n.

Calculated Wave No.

 

(011) (110)
5801.74
5801.69
3801.53 ’
3799.45
5799.71
5799.54
5799.72
5798.54
3798.81
3798.43
5798.48 .
5797.97
5796.68
5796.81
5796.88
5795.75
' 5795.08
3794.96
3794.13
3794.43
5795.60
5795.70
5795.06
3792.90
5792.58
5792.70
5792.51

TABLE III (CONT'D)

 

 

 

‘(v-rPNDMr o'a-'|~--‘.'~O~'..-§'w #5.. ______

 

Calculated Wave No.

Line Observed Transition

 

 

59

No. Intensity Wave No. (011) (110)
cm -111111111111-1111-,1 11
150 5.5 3791.04 33 d 31 3791.14
151 4.8 3790.42 43 - 44 3790.43
152 8.3 3788.47 32 - 33 3788.46
155 2.8 3787.19 22 — 20 5787.27
154 4.9 3786.52 21 - 22 3786.49
155 5.1 3785.49 20 - 21 3785.48
11 — 1_1 5785.09
156 9.6 3784.94 10 - 11 3784.85
157 4.6 3781.93 41 - 42 3782.24
72 - 73 3782.25
158 5.6 3781.03
159* 5.3 3778.72 30 - 31 3778.85
159.1 2.9 3776.05. 2__l - 20 5776.15
160 6.7 5775.44 00 — 1_1 5775.55
161 5.0 5775.41 1_1 - 11 5775.46
162 4.2 3772.22
163 4.5 3771.84 20 - 22 3771.98
2_2 — 21 5771.71
164 4.8 3771.33 82 - 84 3771.41
165 6.6 5767.70 4 1 - 40 5767.72 .
166 5.4 3767.18 40 - 42 3767.27
5__l - 51 5766.96
.166.1* 5765.64 42 - 44 3765.77
10 ' 2—1 5765.92
40 - 43 3765.25
167 5.6 5764.89 5_2 - 5_1 . 5764.95
1_1 - 2_2 5764.80
1653 V5.1 5764.41 00 — 10 5764.12

TABLE III (CONT'D)

Vwflw _

Observed

A“ .-
me v—v w-w— w w-

‘__4_ --

Calculated Wave No.

 

 

Lfige Intensity WavelNo. Transition (011) (110)
CID
169 5'2 3763°67 70 ‘ 71 5765.99
21 — 5_3 5765.75
5_3 - 50 5765.54
170 6.6 5762.96 5_1 - 52 5765.22
171 2.9 3761.98 71 - 73 3762.04
2_1 - 21 5762.02
172 2 4 3761.11 60'. 63 3761.29
175 2.7 5757.70 11 - 20 5757.65
174 6.6 5756.14 5_2 - 5_1 5756.05
175 6 5 5755.61 2_.2 - 5__3 5755.49
2_1 - 5_2 5755.75
176 4.3 3748.55
177 2.5 5747.84 7_2 — 7—1 5747.87
178 9.5 5745.77 5_2 - 4_3 5745.75
5_3 - 4_4 5745.72
20 - 5_1 5745.68
2__1 - 5__3 5745.80
70 " 72 5745.65
179 4.8 5745.20 5_4 - 5_3 5745.52
4_3 - 4__1 5745.50
:179.5 5742.58 5_2 - 53 5742.45
:180 6.6 5757.65 50 - 4_1 5757.68
181 2.5 3729.59

60

10.

11.

12.

13.

BIBLIOGRAPHY

Nielsen, H. H., Phys. Rev. 31, 727 (1931).
Cross, P. C., Phys. Rev. 41, 7 (1935).

Sprague, A. D., and H. H. Nielsen, J. Chem. Phys. 5,
85 (1937)-

Innes, K. K., P. C. Cross, and E. J. Bair, J. Chem. Phys.
.21. 545 (1955).

Noble, R. H., and H. H. Nielsen, J. Chem. Phys. 18, 667
(1950).

Allen, H. C., Jr., and P. C. Cross, J. Chem. Phys. 19,
140 (1951). -

Allen, H. 0., Jr., and E. K. Plyler, J. Res. U. S. Bur.
0f Stds. 5g, 205 (1954).

Noble, R. H., J. Opt. Soc. Am..43, 550 (1955).
Nichols, N. L., Thesis (Michigan State College)(1953).

Humphreys C. J., and H. J. Kostkowski, J. Res. U. S. Bur.
of Stds. 49, 73 (1952).

King, G. W., R.M. Hainer, and P. 0. Cross, J. Chem. Phys.
11. 27 (1945).

Allen, H. C., Jru,P.C.Cross, G. W. King, J. Chem. Phys.
18. 1412 (1950).

Dennison, D. M., Rev. Mod. Phys. 3, 280 (1931).

61

 

“4411111474447; "1444 4 1444477 B

 

745591