\.
!

 

‘L‘

\

 

 

Nathan Lankford Nichols
candidate for the degree of
Doctor of Philosophy

Final examination, November 24, 1953, 1:50 P.9L Con-
ference room, Physics-Mathematics Building

Dissertation: The Near Infrared Spectrum of Nitric Oxide
Outline of Studies

Major subject: Physics
Kinor subject: mathematics

Biographical Items
Born, November 16, 1917, Jackson, Michigan

Undergraduate Studies, Jackson Junior College, 1935-37;
Western Michigan College, 1937-39

Graduate Studies, University of Michigan, 1940-45 (part-
time), Michigan State College, 1946-49, continued
1949-53 (part time)

Experience: High School Science and Mathematics, Barnard,
S. D. 1939-40, Milford, Michigan, 1940-43; Instruc-
tor, Illinois College, 1943-44, University of Mich-
igan, 1944-45; Graduate Assistant, Michigan State
College, 1946-48; Professor, Alma College, 1949-

Member of American Physical Society, American Association
of Physics Teachers, American Association of Univer-
sity Professors, Sigma Pi Sigma, Pi Mu Epsilon

THE NEAR INFRARED SPECTRUM
OF NITRIC OXIDE

by
Nathan Lankford Nichols

AN ABSTRACT

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1953

Approved (9. (/0 W

L
w 1 v

PLYSICS-ldni‘d. L33.

 

Nathan L. Nichols

ABSTRACT

A study has been made of the overtone rotation-
vibration absorption bands of nitric oxide occurring in
the near infrared. Complete rotational analysis was pos-
sible for the 2-0 and 3-0 bands but not for the 4-0 band
as the envelope only was obtained. The infrared data con-
firms the data from the electronic transitions involving
the ground state.

An absorption cell containing a multiple traverse
mirror system of the J. U. White type was constructed with
the mirrors separated 35 centimeters. The absorption cell
was used in conjunction with a vacuum infrared spectro-
graph built by R. H. Noble which consisted essentially of
a rock-salt fore-prism monochromgter and a plane grating
to provide the dispersion for the lead sulfide photocon-
ducting detector.

The 2-0 and 3-0 bands were obtained with absorbing
paths of about four meter-atmospheres. The 4-0 band re-
quired an absorbing path of about 60 meter-atmospheres.
The ground state of N0 is a doublet II state and each
branch of a band consists of two components. It was pos-
sible to resolve the P components for both overtone bands,

but not all the R components.

Nathan In Nichols

Careful reduction of the data gave values for the
rotational constants as: Bo - 1.6965 cm'l; 32 - 1.6631
cm'l; and B3 - 1.6408 cm'l. The equilibrium rotational
constant Be was determined as 1.7060 cm.“1 which gave the
equilibrium moment of inertia Io as 16.404 x 10-40 gm-cm8
and the equilibrium separation of the atoms as 1.1503 x ‘
10'8 cm. The band origins were determined as 3724.16 cm'1
and 3723.48 cm"1 for the two 0 omponents of the 2-0 band,
and as 5544.28 cm'1 and 5543.69 cm"1 for the two compo-
nents of the 3-0 band.

There were no evidences of any extreme perturbations
to the rotational structure of the N0 molecule nor was
there any evidence of a transition from one coupling
scheme to another. It is felt that the molecular con-
stants presented here are more representative of the

molecule than those previously determined from the elec-

tronic data and from the infrared fundamental band.

THE NEAR INFRARED SPECTRUM
OF NITRIC OXIDE

by
Nathan Lankford Nichols

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1953

(FF

-jZ-S'S/
[1

ACKNOWLEDGMENTS

The author wishes to express his sincere thanks to
Dr. C. D. Hause who suggested the original project and
has given constant and helpful guidance throughout its
entire developement. He is also greatly indebted to
Dr. R. H. Noble for his generous help and for the use
of his spectrograph, without which this work could not
have been completed. The writer deeply appreciates the
financial support offered by a Hinman Fellowship during
the year 1948-49.

354.78 '

TABLE OF CONTENTS

INTRODUCTION
General
History of NO Spectra
THEORY
“Ground State of N0
Vector iodels
Potential Curves
Hill and VanVleck Energy Relations
P, Q, and R Branches
Determination odevfi
Determination of Bv'
Determination of Be'°‘e9 Ie, and re
Electronic Confirmation of Infrared Data
Band Origins
APPARATUS
dultiple Traverse Mirror System
Construction of mirror mountings
Optical alignment
Absorption cell
Vacuum Infrared Spectrograph

Optical alignment

Page

COQCJer-IPNH

ll
15
19
20
21
22
24
24
24
27
31
32
32

Rotation of prism and grating
Detector, amplifier, and recorder
vacuum'tank
Absorption cell positioning
EXPERIMENTAI.DETAILS
3-0 Band
2-0 Band
4-0 Band
5-0 Band
RESULTS AND DISCUSSION
wave Numbers for 3-0 and 2-0 Bands
Rotational Constants
Evaluation of B0
Evaluation of B3
Evaluation of B2

Evaluation of BevG‘e» I8, and re

Vibrational Constants
3-0 band origins
2-0 band origins
4-0 band origins
we, ”exe: and “eye
Conclusion

BIBLIOGRAPHY

Page
36

39
42
43
44
44
47
49
51
52
52
59
59
66
7O
74

76
76
81
81
84
84

Figure
l.
2.
3.
4.
5.
5'.
7.
8.
9.

10.
ll.
12.
13.
14.
15.
16.
17.
18.
19.
20.

LIST OF FIGURES

Hund's Coupling Cases

NO Potential Curves

P, Q, and R Branches
Combination'Differences

Optical System of Absorption Cell
Absorption Cell

Absorption Cell Mirrors
Half-mirror Mountings

Optical System of Spectrograph
Spectrograph with Absorption Cell
Spectrograph Close-up

3-0 Spectrogram

2-0 R Branch Spectrogram

Tracing of 4-0 Spectrogram
Grating Equation Angles

Infrared and Electronic Bo(1)

Electronic VDetermination of B0 and DO

Infrared and Electronic 80(2)
Infrared and Electronic B3(1)
Infrared and Electronic 83(2)

Page

12
17
25
26
28
3O
33
34
37
46
48
50
52
61
63
65
68

69

Figure Page

21. Infrared and Electronic B2(1) 72
22. Infrared and Electronic B2(2) 73
23. Graphical Determination of Be 75
24. 3-0 Band Origins 80

25. 2-0 Band Origins 83

LIST OF TABLES

Table Page
I WAVE NUMBERS FOR THE 3-0 BAND 56

II WAVE NUMBERS FOR THE 2-0 BAND 58
III Bo COMBINATION DIFFERENCES 60
IV Bo INFRARED AND ELECTRONIC VALUES 60
v 83 COMBINATION DIFFERENCES 67
VI 83 INFRARED AND ELECTRONIC VALUES 67
VII Ba COMBINATION DIFFERENCES 71
VIII B2 INFRARED AND ELECTRONIC VALUES 71
II Bo TO B13 INFRARED AND ELECTRONIC VALUES 77
I Be, «e, 1,, AND r, VALUES 77
II 3-0 COMBINATION SUMS 78
III s-o BAND ORIGINS 7e
XIII 2-0 COMBINATION SUMS . 82

XIV 2-0 BAND ORIGINS 82

INTRODUCTION
General

Nitric oxide is a colorless, slightly heavier-than-
air gas which is toxic in very small quantities and poison-
ous in moderate quantities. Upon exposure to air, it im-
mediately becomes reddish-brown nitrogen dioxide (N02),
which is also a poisonous gas. The nitric oxide molecule
is diatomic (NO), has a molecular weight of 30.01 and the
sum of the atomic numbers is 15. Its normal freezing and
boiling points are -161.0°C and -151‘C.

Molecular constants for the nitric oxide molecule have
been determined from fine structure analyses of the elect-
ronic transitions occufing in the ultraviolet, but only the
fundamental vibration transition has been done with suffi-
cient rotational fine-structure resolution to yield these
constants. The object of the present work has been to in-
vestigate the rotational fine structure of as many of the
Vibrational overtones as possible to re-evaluate the rota-
tional constants for the ground state and to determine
these constants for the upper vibrational states. A criti-
cal re-examination of the electronic data involving transi-
tions to the ground state has been carried through and cal-

culations have been made using the electronic data in order

to determine the rotational constants. The presently ac-
cepted vibrational constants for N0, computed largely from
the electronic data, have been checked against the results

of the present work.

History of NO Spectra

The infrared spectrum of NO was first observed by
Warburg and Leithauserl when they obtained the envelope of
the fundamental rotation-vibration band and located its
center at 5.3 microns. In 1929, Snow, Rawlins, and Ridealg
were able to resOlve 42 lines in both P and R branches of
the fundamental but apparently used only six lines in each
branch in determining the rotational constants. Their work
on the first overtone3 confirmed the existence of P,Q, and
R branches but gave no measurable quantities. In 1939,
two papers appeared dealing with the fundamental band of'
NO, one by Nielsen and Gordy,4 the second by Gillette and
Eyster.5 The rotational constants for NO accepted by
Herzberg6 are taken from the work of Gillette and Eyster,
which seems to be the most thorough infrared work done on
NO to date.

The electronic transitions have been studied in great
enough detail to make NO one of the best known molecules.
In this present work, only the transitions involving the

ground state are of interest as they Irovide a check on the

a“

 

data from the infrared transitions. The electronic sys-
tems involving the grrund state are known as the 1,p ,p’,
5, and 6 systems and are described later. In the follow-
ing references to these electronic systems, only those are
included for which a rotational anaylsis was made, and
which have actually been used here. The )'system was first
studied in detail by Guillery,7 then redone by Schmid,8
who published 30 pages of tables giving frequencies, com-
bination differences, and other constants. Two years
later, Schmid, Kdnig, and Farkas9 reviewed the two earlier
works, redid some of the bands and obtained new bands and
recomputed all the combination differences and rotational
and vibrational constants. Two new‘y'bands and one‘r band
reviewed appeared several years later in.a paper by GerU
and Schmid.1°

The first comprehensive study of thep bands was by
Jenkins Barton, and Nulliken11 who published the rotational
lines for 18 different bands and computed combination dif-
ferences and empirical coefficients. Schmid, Kdnig, and
Farkas9 included in their comprehensive study a re-evalua-
tion and some additional work on thep bands. The J sys-
tem has been studied, but only the band head frequencies
have been published, so are of no value here. The e sys-
tem has been analyzed by Gard, Schmid,aand von Szilylz and
by Gaydon,13 although they were able to obtain only four

bands in the two investigations.

THEORY
Ground State of Nitric Oxide

Mbst diatomic molecules have an even number of elec-
trons (e.g. CO, N3, H2, HCl, eth, indicating that the to-
tal electron spin S of the molecule must be zero or inte-
gral, since the electron spin unit is $(h/27). Since the
resultant electronic orbital angular momentum vector L
could be 0, 1, 2, etc., it can be seen that the lowest pos-
sible energy state, or gr und state, for a molecule having
an even number of electrons, would involve zero spin and
zero orbital angular momentum, resulting in what is called
a I: state which is a singlet state.

The nitric oxide molecule is the only stable diatomic
molecule to have an odd number of electrons (15) indicat-
ing that the resultant spin, and therefore its projection
on the internuclear axisE, must be half-integral. Since
this spin vector can combine with.A, the projection of L
on the internuclear axis, in either of two directions, the
ground state of NO must be a doublet state, or 'IIl/g,
21713/2 state, indicatingza A value of 1. The separation

of the two substates is 121 cm’l.

Vector Models

Lfthe rotation of the molecule_about a perpendicular
to its internuclear axis is considered along with the above
discussion of electronic orbital angular momentum and spin,
it becomes possible to combine in several different modes
the vectors for the total electronic orbital angular mo-
mentum L (and therefore its projection on the internuclear
axisA ), the total electron spin S, and the angular momen-
tum of nuclear rotation N, all of which combine to give a
final resultant J which is fixed in space. This was first
done by Hund, so the different coupling schemes are known
as Hund's cases "a", "b", "c”, etc.

In case "a" coupling,14 the electronic and nuclear
rotations are weakly coupled in such a manner that the to-
tal spin vector S is coupled to the internuclear axis (see
figure la) and combines with the electronic orbital angular
momentum vector A.to form a resultant‘! which in turn com-
bines with the nuclear rotation vector N to give a final
resultant J which is the total angular momentum of file
molecule including electron spin. Since J is constant in
magnitude and direction, the internuclear axis must rotate
about this vector (nutation) and the vectors L and S must
precess about the internuclear axis. (The precession of L
and S is much faster than the nutation of the axis about J

for case "a" coupling).

Hund's Coupling Cases

 

 

b. Case b Coup-ling

Figure 1.

In case ”b" coupling, the revolution of the nucleii
about a common center is enough greater so that the spin
vector S no longer couples with the internuclear axis but
instead couples to the resultant of the electronic orbital
angular momentum vector.A.and the nuclear rotation vector
N. This resultant ofA and N is called K and is illus-
trated in figure lb. The resultant of K and S is J, the
total angular momentum of the molecule and is represented
by a vector which is fixed in space. (The nutation of!\
about K is much faster than the precession of K and 8
about J). The nitric oxide molecule is between cases "a"
and "b", although for low rotation, it has practically

pure case "a" coupling.
Potential Curves

The natal energy of a diatomic molecule is determined
by both the kinetic and the potential energies, where the
potential energy depends upon the internuclear separation
of the two atoms, which in turn depends upon the vibration
of the molecule. Since the vibration of a diatomic mole-
cule is essentially that of an anharmonic oscillator, the
usual potential "well" for the simple harmonic oscillator
must be modified, as was first done by Morse. to better fit
the observed data. Gaydon15 has developed the potential
wells for NO as shown in figure 2. The state labeled X is

the ground state, the one of primary interest here. The

 

 

Energy Curves

Potential

NO

for

8" 02%

"' i

; 2
‘6’"

" EAZY ’7’

g.

g

Bfn

i

4

 

 

 

 

 

 

 

 

 

l

ix‘n

I 1 I

2

Internucleer
Distance, A‘

 

Figure 2.

 

ground state actually consists of two potential curves sepa-

rated by 121 cm'1

, making the separation too small to be
shown with the scale used. Transitions from fine K 3II
ground state to the A “2" state give the electronic ‘7
bands; to the B ‘II state give the electronicp bands; to
the C is? state give the electronic 6 bands; and to the

D '2‘“ state give the electronic 6 bands. The dissociation
limits are shown at the right. The present problem has
been to investigate the absorption transitions from the
zero vibrational level of the K 8II ground state to the 2,
3, 4, and 5 vibrational levels within this same ground
state. All of these transitions occur in the near infra-
red spectral region.

Since the molecule is rotating at U18 same time it is
vibrating, the_rotational levels are superposed on the vi-
brational levels, just as the vibrational levels are su-
perposed on the electronic levels. The vibratianal transi-
tions from any upper vibrational level to a lower level
will show, if there is sufficient resolution, rOtational
fine structure, an analysis of which leads to the rotational

constants of the molecule.
Hill and VanVleck Energy Relations

Hill and VanVleck16 have derived an expression for the
energy of a molecule which is intermediate between cases

"a" and "b" which may be written, neglecting the small term

f(K, J-K), as:

10

T1(J,v) - Te+Gi(v)+BvS(J+%)2-1+(-l)i[(J+%)'-A/BV+A‘/4Bvi9}

”DvJ2(J+1)2+‘°°‘ . eq 1
in which Ti represents the total energy term value, J is
the rotational quantum number, v the vibrational quantum
number, T8 the term value for the equilibrium position, Bv
a rotational constant which is inversely prOportional to
the moment of inertia of the molecule and approximately
half the separation of successive rotational levels (and
one of the important constants to be determined here), A
the separation.of the two substates. The ratio A/B gives a
measure of the type of coupling, a large number indicating
case "a", a small value, case "b". D represents the cen-
trifugal stretching term, which.arises because of the non-
rigidity of the rotating molecule. When i is 1, equation
1 refers to the first component, “111/3; when i is 2, the
equation refers to the second component, 8IT‘S/2. The sub-
script 1 is also added to the Vibrational energy term C(v),
since the two substates are not necessarily identical.
Since NO is represented by almost pure case "a" coupling,
it is oossible to make exhansions of the Hill and VanVleck
relation which represent the energy adequately:5

Tl - Te-A/2+G1(V)+BV(1)/4+Bv(1)J(J+l)-Dv(1)J2(J+1)3+..

eqs 2
T2 - Te+A/2+Gg(v)-7Bv(2)/4+Bv(2)J(J+l)-DV(2)J‘(J+1)8+..

The constants of equations 2 are related to those of equa-

tion 1 by:

11

E, - [Bv(l)+Bv(2)] /3. and Dv - [Dv(l)+DV(2)] /2 eq :5
(i.e. the averagosof his Bv and Dv values for the two com-
ponents). .

The actual transitions would involve the difference
between two such terms as given in equations 2 with differ-
ent Te values for the electronic tranétions, different v
values for the vibrational transitions, and different J
values for rotatrsnal transitions. For example, in the NO
3-0 rotation-vibration band in the near infrared (the band
done in the most detail here), the two terms would belong
to the same electronic system so Te would drop out; one
term would have v equal to three, the other v equal to
zero; and J would assume all possible half-integral values
within the restrictions set up by the selection rules that

AJ can be zero or plus or minus one.
P, Q, and R Branches

The rotational fine structure of a vibrational band
consists of three branches, the so-called P, Q, and R
branches, which correspond to the selection rules J'-J" -
-1, J'-J" - 0, and J'-J" - +1, resoectively, where J' is
the upper state, and J" is the lower state. The numbering
of the linesof the three branches is determined by the low-
er state level (6.g. P(3/2) is a transition from J' - 1/2
to J" - 3/2, etc.). Figure 3 shows the transitions in-

volved in these three branches. The fact that NO has a

12

Formation of P, Q, R Branches

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.

l3

resultant electronic angular momentum along U18 internucle-
ar axis causes it to be dis only stable diatomic molecule
to exhibit a Q branch in the infrared, since for a 1 2
ground state (as found in most molecules) the transition

AJ - O is forbidden. For uie ‘II3/2 component, the first

R line, R(l/2) and his first P line, P(3/2), are missing
since, fer the second component, the lowest J levels in the
upper and lower states are J - 3/2.

The structure of the N0 molecule corresponds essen-
tially to a symmetric top with the two moments of inertia
about an axis perpendicular to the internuclear axis equal
and very much greater than the moment of inertia about the
internuclear axis. The vove equation solution for the sym-
metric top then should be sufficient for N0 if modified to
account for the facts that the NO molecule is also vibrat-
ing and (due to this Vibration) is a non-rigid rotator.

The wave equation for the symmetric top was first solved
by Reiche and Rademacher17 and by Kronig and Rabi18 giving
for the rotational term values the following:

F(J) - BJ(J+1)+(A-B)A' eq 4
in which A - h/(8N‘CIA) and B - h/(8D‘CIB). IA is the mo-
ment of inertia abOut flie internuclear axis and IB is the
moment of inertia about a line perpendicular to the inter-
nuclear axis. Since IE is very much larger than IA’ the

value of B is very much smaller than A.

14

To account fiar the non-rigidity of U18 molecule, a
centrifugalstretching term -8DJ'(J+1)' has to be added to
equation 4, and since this non-rigidity (caused by vibra-
tion) is different for different Vibrational levels, the
B and D of equation 4 must be replaced by effective values
Bv and Dv which are slightly different for different Vib-
rational levels. Equatirh 4 then becomes:

FV(J) - BVJ(J+1)+(A-Bv)A‘-DVJ'(J+1)‘°‘+°-°- eq 5

The term containing A2 is constant fb r any one vibra-
tional level, and die infrared spectrum occurs within one
electronic system, so this term may be ignored provided
Fv(J) is understood to be the rotational term value meas-
ured from the rotational level having J . 0 (rather than
the lowest J value of 1/2 in One case of NO).

For the determination of die rotational constants this
relatively simple relation.is adequate in place of the Hill
and VanVleck relation of equations 2, since these constants
are based on differences between values in upper and lower
states, which means that electronic and vibrational pecu-
larities cancel.

The actual rotational translthlSlNill yield frequen-
cies (in cm‘l) for file P, Q, and R branches of:

PM) -vO+Fv'(J-l)-Fv"(J) -vO-(Bv'+Bv")J+(Bv'-BV")J‘
QM) '”o+Fv'(J)-FV"(J) "90+(Bv'-Bv")J+(Bv'-BV")J‘ eqs 6
R(J) - vo+Fv'(J+l)-FV"(J) - DO+ZBV'+(3BV'-Bv")J+(Bv'-Bv")J‘.

J is die rotational quantum number for his lower state, and

15

v'o is die band origin or zero line, corresponding to the.
(unrealileble) transition J' - O to J" - O.

The P and R branches actually form a single series ac-
cording to the relation:

1) - 'DO+(B‘,'+Bv")m+(B,,'-Bv")m‘B eq 7

where m is -J for the P branch and m is- J+Iror the R
branch. The P and R lines of any one of the NO vibrational
bands form a single series with two missing lines at the
positions for which m would be -l/2 and +l/2. These waild
correspond to P(1/2) and R(-l/2) which of course are non-
existent. The second component has a gap in the center
with four missing lines at m . -3/2, -1/2, +l/2, and +3/2
since for this component there is no P(3/2) line and no
R(l/2) line. The lines net Closer together in passing
throujh the P branch toward the center and on into the R
branch. This direction of convergence, which is called
degrading toward the red in this case, is caused by the
fact that Bv" is greater than Bv' for NC. This convergence

is shown in the spectrogram for the 3-0 band, figure 12.
Determination of RV"

While it would be possible to determine the rotational
constants of equation 7 (and therefore equations 6) by get-
ting an empirical relation of fine form 12- a+bm+cm', where
the a, b, and c correSpond to the constants in equation 7,

more accurate results are had by obtaining the upper and

16

lower state constants separately by a method using the so-
called combination differences. The lower state constant,
BV", may be fiaund from the combination differences formed
by subtrccting die freouencies (in cm‘l) of the P lines
from the frequencies of the R lines which have the same up-
per state levels. Thus. the first R line, R(l/2), has the
same upper level as the second P line, {(5/2); the second
R line R(3/2) has the same upper level as the third P line,
I(7/2), etc. Figure 4a shows that the difference between
these corresponding R and P lines gives the separation of
alternate rotational levels in the lower state -- (e.g. the
first R line frequency minus the second F line frequency
gives the separation of the two lower state levels with
J - 1/2 and J - 5/2). This combination difference relation
may be written as:
A2F1"(J) - R(J-1)-P(J+l) - Fv"(J+l)-Fv"(J-l). eq 8
By substituting the values flar Fv" from equation I in-
to equation 8, the fiallowino relation is obtained:
A3F"(J) - [Bv"(J+l)(J+2)-Dv"(J+l)2(J+2)2]
$v"(J-l).T-Dv"(J-l)’J2] eq 9
which reduces to:
AZF"(J) - (4Bv"-6Dv")(J+,13-)-8Dv"(.T+%)5. eq 10
Since Dv" is very much smaller than Bv", it may be neglec-
ted in the first term of equation 10, giving:
42F"(J) - 4BV"(J+§)-8Dv"(J+,§)3. eq 11

If the value of Dv is known from other sources, such as the

1'7

Combination Differences

J

_§_
2

 

 

 

 

 

 

 

 

 

 

 

v. mv
3.2 I_2 "J 5_2 3.21.?
«x» m iv
A.!. IAN: mvll .II....1 Ill .v
alluuxn n. +—
A «\m a v

 

1.. I3)... “3!. I.

 

AIIII|N\_ m

 

 

 

 

 

Upper

Lower
State

State

Figure 4;

18

data of the electronic transitions, die last tenn,
8Dv(J+§)3, may be added to the left hand member so that

the slope of the curve of his new left hand member plotted
against J+§ will give directly 48v": If Dv" is negligible
(as was found to be true for N0 for the first component),
then, of course, the second term of equationll may be omit-
ted.

A second method for determining Bv" would be to aver-
age the values of [d2F"(J)+8DV(J+%)3]/4(J+g) for the indi-
vidual cases. However, a method which gives more accurate
results than either of those mentioned, is to assume an ap-
proximate Bv" value, 5;", which is close to the expected
value, and then make use of the equation:

AZF"(J) I (4g,"+4ABV")(.J+%)-8DV(J+%)3 eq 12
inxwhich the EV" of equation 11 has been replaced by
§;“+ABV". ‘Rearranging then gives:

ABF"(J)-4§;"(J+g)+anv(J+g)3 - 4ABV"(J+§). eq 13
The subtraction of the term 4é‘;"(J+g.) from the left hand
member of equation ll allows plotting to a much larger
scale and gives, from the slope, the corrective term ABV"
which, when added to 5;", results in the true value of Bv".

The above procedure is applied in the same manner to
both the “III/2 and “113/2 components yielding two differ-
ent values with the second value larger than the first.

The average of these two values gives the true Bv" with

the splitting effect due to the resultant electronic angu-

19

lar momentum about the internuclear axis removed; that is,
it gives the value for rotation only,without any elec-

tronic effects.
Determination of Bv'

The upper state rotational constants are determined
by'a similar graphical means except that the combination
differences used here must be the difference between the
frequencies of R lines and I lines having a common lower
state level. Thus, the second R line, R(5/2), minus the
first } line, P(3/2), gives the separation of the upper
levels for which J equals l/2,and 5/2. Figure 4b shows
the method byxwhich the separation of alternate levels in
the upper state is obtained. Equation 8 for the upper
state then becomes:

AZF'U) - R(J)-P(J) - Fv'(J+l)-Fv'(J-l). eq 14
When.flhe values fiar Fv' are substituted from.equaticn 5 in-
to equation 14, the resultant equation is identical to e-
quation 9, which reduces to equation 10, except, of course,
the superscripts must now refer to the upper state.

The determination of Bv' then becomes the same as for
Bv"' Eouotions ll, 12, and 13 all apply to the treatment
of the combination differences, and the slape of the graph
again determines the correction ABV' to be added to the
approxinate g:' to get the true Bv'. Two values are ob-

tained, one for each component as before, with the second

20

component value the larger. Again file average of the two
component values gives the true rotational constant with

the electronic influence removed.
Determination of Be,O¢e. 16, and re

After the Bv values are obtained for two or more vi-
brational states, it then becomes possible to determine the
equilibrium constant, Be, from the relation:

Bv - Be“ e(v+g-) eq 15
where “e is a measure of the change in the rotational con-
stant Bv with changes in vibration, and Be is given by the
relation:

Be - h/(BV“cIe) - h/(Bv‘cpre‘) eq 16
where I6 is the moment cf inertia for the equilibrium sepa-
ration of the two atoms, 0 is the velocity of light, h is
Planck's constant, and.p.is the reduced mass of the NO mole-
cule (in grams) and is equal to the product divided by the
sum of the individual masses of the two atoms. The usual
method for determining Be is to plot the various Bv values
against (v+§), the Y intercept giving directly Be, and the
slope giving ate. An examination of equation 5 in which the
small Dv term is neglected, [FV(J) - BvJ(J+l)+-~°], shows
that the difference between two energy term values, each
given by this equation, one with J - 3/2, the other with
J - 1/2, gives 5Bv. This monstant (Bv) could then be de—

fined as one-third the separationrof his first two NO rota-

21

tional levels. It usually is defined as one-half the sepa-
ration of the natational levels with J - l and J I O,
which, of course, has no significance for NO with its half-
integral values of J.

Once the value of Be has been determined, the compu-
tation of the equilibrium moment ofinertia is a simple
matter, using the first part of equation 16. From the val-
ue of the moment of inertia, the internuclear equilibrium
distance may then becietermined from:

1° - pre‘. eq 17
Electronic Confirmation of Infrared Data

The NO combination differences can be checked from
any rotational fine structure data involving the ground
state and having the proper vibrational level. For example:
BO" could be determined from any of the following sets of
combination differences: 1-“, 2-0, 3-0, 4-0, etc. bands
of the infrared; also the-l-O, 2-0, 3-0, etc. bands of ggy
of the electronic transitions involving the ground state,
such as the V’P , 5, and é systems. B3' could be deter-
mined from the combination differences of any of theaabove
electronic systems involving the ground state with the low-
er vibrational level v ' 5, such as the 0-3, 1-3, 2-5, 5-5,
4-3, etc. bands. BZ' could be checked by electronic bands
involving 0-2, 1-2, 2-2, etc. transitions to tme ground

state.

22

Band Origins

Of the various vibrational constants, the only ones of
real interest in this problem are the band origins for the
3-0 and 2—0 bands. The band origin represents the energy
level term value for the upper state which has the rota-
tional quantum number zero. In the case of NO, the band
origin has no physical significance, since the lowest J
value is one-half. It also represents the energy involved
in the unrealizable transition between J - O in the upper
state and J - O in the lower state.

A band origin could he determined from the relations
of equations 6 using the values for the frequencies of the
P and R lines arm setting up as many equations as the num-
ber of known lines. This would obviously be a tedious task

and would require a precise Knowledge of the rotational

The usual (and much simplier) way to determine the
band origin is a graphical method making use of combina-
tion sums which involve only the frequencies of the lines
and does not require an exact knowledge of the rotational
constants. The combination sums needed involve the addi-
tion of the frequencies (in cm‘l) of corresponding P and R
lines, the first P plus the first R; the second P plus the
second R, etc. Substituting fnaa equations 6, the combina-
tion sums simplify to the following:

R(J-l)+P(J) - 2v0+2(Bv'-Bv")J‘. eq 18

lirlotof‘ttn left hand member aeaintt J8 gives 2L6 as the
Y intercept. A refinement'“hich dds much to the accuracy
of the result is to assume an afiproximate value for
(Bv'-Bv") which is close to the expected value ani then
make use of the relation:

R(J-l)+P(J) - 2110+2.[(3V"‘i‘.‘1'3.';,'?)+-A(av:-13V")]J2 eq 19
in which the Bv'-Bv" of equation 18 has been replaced by
an approximate value plus a corrective term shown in the
brackets of equation 19. Rewriting equation 19 and divid-
ing by 2 gives:

§[R(J-l)+P(J)-2(W)J‘] -V0+A(Bv'-Bv")J‘. eq 20
The left band member can now be plotted to a much larger
scale and the Y intercept gives the band origin directly.
Actually the effect of non-rigidity, the D correction,
should add a corrective term involving (Dv'-Dv") to the a-
bove, but for NO, the D values for the different vibration-
al states are practically identical and the term may be

neglected.

24

AFPnRiTUS
Multiple Traverse Mirror System

Construction of mirror mountings. In absorption spec-
troscopy, there are two ways of increasing the amount of
absorption, one by increasing the length of the light path
in the gas, the other by increasing the pressure. Both
methods effectively increase the number of gas molecules
encountered by the beam of light. But increasing the pres-
sure causes "pressure broadening" of the lines and the res-
olution of the lines is lowered. Increasing the path length
has obvious physical limitations. However, it is possible
to get a long path length in a short tube by using an in-
genious multiple reflection system of concave mirrors orig-
inally devised by White.19

The multiple traverse mirror system as used here con-
sists of three mirrors with identical radii of curvature,
one of 4 3/4 inch diameter with two ledges cut from its
edge as sheen in figure 5b, the other two formed by sawing
a 4 3/4 inch mirror in two as shown in figure So. The mir-
rorsasre aounted withir a 6 [/2 inch brass cylinder, as
shown in figure 6, at a distance of 35.7cm apart, this dis-
tance being the radii of curvature of tMe mirrors. The top

of the cylinder is cut to facilitate visual observation dur-

25

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Figure 5

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27

ing adjustment of the mirrors. The mirrors themselves are
mounted on brass rings held to the cylinder with Allen
screws. The front mirror (figure 7a) has one-half inch
notches cut from each side above the center to allowrthe
beam of light to enter and leave the system. The cuts were
made with a diamond impregnated rock saw made available by
the Geology Department. The mirror is supported at three
points by six soft-solder-tipped screws, to give adjustment
frcm either face of the mirror. The back "half" mirrors
are supported on.aluminum semicircular supports as shown in
figure 8. These in turn are mounted on a three-sixteenths
inch steel rod fastened to a br ss ring which just fits
within the cylinder. The steel rod coincides with the pole
of the mirrors when they are adjusted to have the same cen—
ter of curvature. Screws through the brass ring, plus
spring tension, allow the adjustment of the rotation of the

mirrors about the steel post, (figure 7b).

thical alignment. The optical arrangement is shown
in figure be for the simple case of four traversals. A
source placed at 31 forms an image at $2 on the edge sf Use.
mirror ledge as shown in figure 5b. With the center of
curvature of half-mirror A at CA, the cone of light 1 re-
flects as cone 2 from the mirror A and converges to point
83 which is as far below the center of the mirror as 82 is a-
bove. Point 83 then is a source giving cone 3 which reflects

from mirror B as cone 4, converging to S4. Finally, 35 repre-

28

 

Figure 7} Absorption Cell Mirrors

sente the slit of the spectrograph. The extreme upper and
lower parts of the mirrors actually are not used. In the
initial adjustment, cone 1 of light is made large enough
to slightly overlap mirror B, giving a faint image which
falls outside the front mirror beyond 84, greatly facili-
tating the adjustment of mirror B.

If the mirrors A and B are rotated so that their cen-
ters of curvature CA and CB are closer together, the number
of traversals is increased in steps of four with the dis—
tance between these two points always giving twice the sepa-
ration of successive images either above or below the cen-
ter. Figure 5d shows the conditions for 16 traversals with
the numbers by the images representing the number of trav-
ersals of the light beam. In this case, the separation of
the centers CA and CB would be twice the separation of two
images such as 6 and 10. It is not necessary to have the
images below the center spacvd exactly between the ones a-
bove the center; in fact, the final adjustments have always
been nade~with mirror A only.

Since the initial beam enters the mirror system far
off axis, the astigmatism is very great, causing a vertical
enlargement. This actually is a welcome feature, allowing
a point source to give a vertical image to illuminate the
Slit of the Spectrograph.

There are two limiting factors restricting the number

of traversals in this type of optical system. .First, there

30

 

Figure 8. Half-mirror Mountings

31

is a loss of energy at each reflection (e.g. a 5% loss on
each of lOO reflections would result in a final image hav-
ing an intensity of only about 0.6 of 1% of the initial in-
tensity!). The seocnd limiting factor is the minimum sepa-
ration of images 0 and 4 (figure 5d). If the edge of the
ledge is rough or chipped, or if the source does not give

a narrow image, some intensity will be lost.

 

Absorption;ggll. The cylinder containing the mirror
system is so fixed that it slides into a second, larger,
seven inch cylinder (the absorption cell itself), as shown
in finure 6b. This outer cylinder is fitted with two legs
at the back and one at the frant, all three being adjust-
able. The front face is eouioned with two two inch diame-
ter cuertz windows to allow the light to enter aid leave,
and a half-inch brass tube leading to a brass-to-glass ta-
pered joint connected to a mercury manometer and a stop-
cock, the stopcoox in turn being connected to a vacuum
pump. The manometer is fastened to the cell itself so that
the cell may be moved without danger-of breaxing flue glass
tubing. The absorption cell is made vacuum-tight by means
of a brass disk at U16 back end, which fits over a collar
having a groove with an eight inch neoprene "0" ring. The
back is held on by means of six large machine screws. A
half-inch brass tube with a brass-to-glass tapered joint

connects the back of the cell to the cylinder containing

the gas.

32

The nitric oxide gas was obtained from the Matheson
Gas Company and was claimed by them to be better than 99
percent pure. The chief impurity was found to be nitrous
oxide (N20). The gas was used without further purification,
although it was found that upon standing for several weeks
in the brass absorption cell, it gradually deteriorated,

presumably into N20.
Vacuum Infrared Spectrograph

Optical alignment. The vacuum infrared spectrograph
was designed and constructed by Dr. Robert H. Noble20 and
consists essentially of the following parts: rock salt
prism to serve as a monochromlter; grating to give the dif-
fraction; lead sulfide detector to detect the radiation from
the grating; amplifier and recorder to give a permanent re-
cord of the absorption spectrum; plus the necessary mirrors
used in conjunction with the prism and grating.

Referring to figure 9, the initial slit 31 corresponds
to the final image $5 from the absorption cell (figure 5a)
and is the entrance slit to the monochromator section of
the spectrograph. This slit lies Just within the wall of
the steel vacuum chamber which houses the spectrograph prop-
er (see figure 10). The cone of light from the slit 81 re-
flects from the plane mirror M1 to the off-axis parabaloidal
collimating mirror M2 (of six inch diameter), which is
placed so that 31 is at its principal focus, the focal

 

 

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34

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35

length of M2 being 49.7 centimeters. The parallel light

from M2 strikes the rock salt prism which acts essentially

as a monochromator passing only a small band of wave lengths
and eliminating the troublesome over-lapping of several diff-
erent orders. The prism is of the Littrow type withxthe

back side aluminized to effectively double the prism angle,
and to return the light very nearly along its incident path.

The parallel light returning to M2 is de-collimated
and focussed at the slit 32' This slit is both the exit
slit of the monochromator section, and the entrance slit to
the spectrograph section of the instrument. If all the
light traveled through the monochromator as horizontal rays,
a straight entrance slit 31 would produce a straight image
in the plane of the exit slit. However, some of the light
enters the prism at a slight angle to the horizontal and
travels farther through the prism material than a similar
horizontal ray. Thus, the prism angle "seems" greater to
this oblique ray and a curved image results. This effect
is minimized by using a very short slit.

The large plane mirror M4 has a three-fourths inch hole
in its center which allows the cone of light from $2 to pass
through to the parabaloidal mirror M3. Since the incident
and reflected beams have the same axis, the pole of the mir-
ror M5 is at its center and not near the edge as withing.
The distance from $2 to M3 is the focal length of M3 (100.4

centimeters), so the beam is collimated by'Ms, returns to

36

the plane mirror M4, and is reflected to the grating. The
mirrors M3 and M4 have diameters of eight inches. Figure 9
shows the grating in position for the central image.

The parallel beam of light coming from the grating is
reflected from plane mirror M5 (identical to M4) to paraba-
loidal mirror Md (identical to M3) which decollimates the
beam and focusses it through the hole in M5 onto the slit
83, which is the exit slit for the grating section. The
slit $3 is at the far focal point of an ellipsoidal mirror
M7 so that the cone of light from S3 is re-focused to the
detector placed at the near focal point of the ellipsoidal
mirror. The ellipsoidal mirror has a diameter of six inches
and focal lengths of 7.7 centimeters and 40 centimeters. It
has been found that the sensitized area of the lead sulfide
detector (about 1.5mm3) used in all the present work is
large enough so that the ellipsoidal mirror can be elimina-
ted and the sensitive surface placed directly at the posi-
tion 83. The chief advantage in using the ellipsoidal mir-
ror is to diminish the size of the image in going from the
far to the near focal points. This ratio would be the ratio
of the focal lengths, viz. 40 to 7.7. In using a thermo-
couple detector, where the radiation must fall on a very

small area, the ellipsoidal mirror would be a necessity.

Rotation of prism and grating. The prism is rotated
by means of a Selsyn motor mounted inside the spectrograph

tank and controlled by i similar motor mounted outside the

37

 

Figure 11. Spectrograph Close-up

38

tank behind the control panel and connected to a mechanical
counter. The Selsyn inside the tank is lubricated with
vacuum oil to avoidthe high vapor pressure of ordinary mo-
tor oil. The prism measures three and one-half by five
inches for its aluminized back, and is approximately a 30-
60-90 degree triangle. In measuring the 5-0 band, it has
been found that there are no over-lapping orders in the re-
gion of sensitivity of the lead sulfide detector, and that
the prism can be replaced by a plane mirror.

The grating is also rotated by means of a Selsyn motor
mounted inside the spectrograph tank, and controlled from
outside. The grating circle is so arranged that two grat-
ings placed back to back may be used interchangeably, with-
out opening the vacuum tank, by simply rotating the entire
mount 180 degrees. A cam on the worm gear driving the grat-
ing circle actuates a micro-switch which discharges a con-
denser in such a way as to put a "pip" on the recorder paper
for each revolution of the worm gear, corresponding to a
tenth of a degree of rotation of the grating. This pip has
very greatly facilitated the calibration of the instrument
and the analysis of the spectrograms. The grating may be
rotated at six different speeds by means of gears, each suc-
cessive speed being 1/6, l/6, 1/6, 1/4, and l/4 of the pre-
ceding speed. These six values correspond to grating rota-
tions of 1080, 180, 50, 5, 1.25, and 0.5125 minutes of are

per minute of time. It is interesting to note that the

39

gears causing the slowest rotation would require approxi-
mately 48 days for a complete revolution, whereas at the
fastest speed a complete revolution may be had in a matter
of 20 minutes. A mechanical counter is attached to the
control panel indicating the rotation in one-hundredths of
a degree.

Two plane gratings have been used with the instrument
so far, one 1800 lines per inch, the other 7200 lines per
inch. The 1800 grating has a useable surface area of six
by eight inches, implying a total number of lines of about
14,000. It is blazed at 27 degrees so was used in the high-
er orders so as to take advantage of the blaze. The 7200
grating is on loan from the University of Michigan by the
courtesy of Dr. E. F. Barker and has a useable surface area
of four by five inches. It is blazed at 15 degrees which
fortunately corresponds to the 3-0 region of nitric oxide

in the first order.

. Detector, amplifier, and recorder. The electronic
circuit associated with the detector consists essentially
of three parts, a pre-amplifier, a lO-cycle tuned amplifier,
and a lock-in amplifier. The beam of light entering the
spectrograph at the entrance slit is "chopped" by a sector-
ed circle which allows light to pass half the time, the
successive pulses being one-tenth of a second apart. The
detector, then, receives lO-cycle pulses of light which
have passed through the spectrograph. The pre-amplifier

..
yrs-i“!

40

is placed as close to the detector as possible, outside

the vacuum tank, so as to make possible short lead wires

to minimize stray pick up. The second component is a con-
ventional plate-tuned amplifier which is designed to pass
only the lO-cycle signal. The chopper has a small flash-
light-size bulb and a photocell attachment connected so
that the photocell receives lO-cycle pulses of light of the
same duration as those received by the detector.

The third component contains three additional stages
of amplification, a phase-splitter stage, and a lock-in
amplifier stage. The lock-in stage consists of two double
tubes (63N7's), the first of which has the two cathodes
tied together and with one grid connected to the chopper
photocell, and the second connected through the amplifiers
to the detector. The first grid receives a lO-cycle square
wave pulse from the chopper, the second a lO-cycle signal
upon which is superposed the variations caused by the
grating. The two plates of this tube are connected to the
two grids of another 68N7. The cathodes of this second
tube are tied together, as are their plates. Therefore,
if the two grids receive signals that are out of phase,
each will nullify the other. However, if the two grids
receive signals that are in phase, the two will add and
amplification will result. This implies that the first
of the above tubes must have signals on the two grids that

are in phase, or that the square wave signal from the chop-

41

per must be in phase with the signal from the detector.
Stray noise that is not in phase with the chopper signal
will be minimized, since the lock-in amplifier will pass

a signal only during the half of each cycle that the chop-
per is allowing light to enter the spectrograph. The lock-
in amplifier is connected through a resistive-capacitive
filter to a Leeds and Northrup Speedomax recorder which has
a paper speed of one-half inch per minute.

The detector itself is a lead sulfide photo-conducting
tube which has a small area that is eXposed to the radiation.
A 45 volt battery causes a very small current to flow
through the high resistance of the lead sulfide surface.
This current changes as the conductivity of the surface
changes due to variations in the light beam coming from
the grating. These fluctuations in current cause changes
in voltage which are amplified by the above-mentioned am-
plifiers. The detector is many times more sensitive at low
temperatures so is cooled by running chilled acetone
through the brass block supporting the cell. This acetone
"pump" is self-acting, the acetone running in to the de-
tector by gravity. As it warms slightly, some of the dis-
solved carbon dioxide from the dry ice comes out of solu—
tion causing bubbles which actually force the acetone
above its original level and back into the container hold-

ing the dry ice.

42

Vacuum tank. ‘The vacuum tank which holds the spectro-
graph proper is essentially a steel cylinder 42 inches in
diameter and about six feet long with the ends rounded,
(volume of about 55 cubic feet). It is sliced in a hori-
zontal plane about eight inches above the center and fitted
with flat steel pieces, one of which contains a rectangular
groove. A square neoprene gasket fits into the groove and
provides the vacuum seal. The tank is supported at three
points on a cement pier with two additional supports which
contact the cement only when the heavy lid is open. The
lid is raised by an electric motor about its hinge, which
runs along one side of the tank, as may be seem at the ex-
treme right of figure 10.

The inside of the tank is criss-crossed with steel
supports at the tOp and bottom, the bottom cross pieces
acting as the supports for the aluminum table upon which
the optical system is fastened. This table is approximate-
ly three feet by five feet and one inch thick with one and
one-half inch channel aluminwm around the four edges. It
is supported at only three points, these points being di-
rectly above the points of support of the tank. This coin-
cidence of supporting points is necessary, as evacuating
the tank causes some distortion, and changes in the optical
alignment must be avoided. The connecting wires to the
Selsyn motors, chopper, etc. are sealed through the side

of the tank, as are the tubes which supply the cold acetone

43

to the detector. The vacuum tank window is a circular
piece of quartz fastened with piecine to the flat end of

a section of 2 inch brass pipe which has a tapered thread
and screws into the side wall of the tank. The tank is
evacuated with a megavac pump which pumps out most of the
air and water vapor in a matter of a half hour. Up to the
present time, it has not been found necessary to install a
diffusion pump, although one would be necessary if an ex-

tremely high percentage of water vapor were to be removed.

Absorption cell positioning. The initial alignment of
the entire system, absorption cell and spectrograph, is done
as follows: the inner cylinder containing the mirrors is re-
moved, and its adjustment made out in the room'where the
images formed on the front mirror can be seen. The mirror
system is then replaced in the absorption cell. Next, a
small source (such as an auto head light) is placed inside
the spectrograph somewhere along the optical axis of the
spectrograph. With no lenses in the system, the absorption
cell is moved until the beam from this source enters at the
proper angle. The real source is then placed in line with
this beam.where it emerges from the absorption cell. The
.lenses are then positioned and the final adjustments are

Inade on them with no further changes in the mirrors.

44

EXPERIMENTAL DETAILS
3-0 Band

The 3-0 band which was known to be near 1.8 ,i was ob-
tained by adjusting thermirror system to 40 traversals and
the N0 pressure to about 25 centimeters of mercury,giving
an absorbing path of about 4% meter-atmospheres. With the
slits set at 20 microns (0.4 cm’l) the absorption was about
15-20 percent.

The source used for this region was a Western Union
100 watt concentrated zirconium oxide are operated at 6.25
amperes. Since this type of arc has a negative temperature
resistance coefficient, it was necessary to insert a large
ballast resistor in series with the arc. A large induct-
ance coil (actually a heavy-duty auto-transformer) was
placed in series with the arc in an attempt to minimize
fluctuations in the current. The total voltage drop was
about 80 volts from the D C generators, approximately 60
volts being the drop in the ballast resistors. The glass
envelope around the arc was air cooled. Since the arc op-
erated in an atmosphere of argon, the argon emission lines
“were present on every spectrogram, aiding in the analysis.

With the grating rotating at speed 6 (0.3125 minutes

<3f are per minute of time), the linear dispersion on the

45

recorder paper was about 0.0002 degree per millimeter, cor-
responding to about 0.08 cm“1 per millimeter. It was pos-
sible under the conditions used to get lines in the P and R
branches out to J values of 37/2.

This spectral region at 1.8‘p was favorable in three
respects: the 7200 lines per inch grating was blazed at 15
degrees which corresponded to 1.8‘p in the first order; the
100 watt concentrated arc source had its maximum radiation
at 1.6 p; and the lead sulfide detector had very high sensi-
tivity in this region.

Figure 12 shows a typical 5-0 spectrogram taken at a
fairly fast grating speed making the spectrogram more eas-
ily photographed. The doubling of the lines due to the
doublet nature of the ground state is evident for all the
lines of the P branch and for some in the R branch. The
‘IIl/g component can easily be identified by its relative-
ly greater intensity. In the spectrograms actually meas-
ured, taken at slower grating speeds, the doubletswere re-
solved for all J values beyond 13/2 in the R branch and for
all the P lines. Only the envelope of the Q branch was ob-
tained. High orders of well known visible argon and neon
lines were superposed on the spectrograms to aid in the cal-
1bration. It was necessary to have the neon source off at
one side and to use a hinged.nurror so that the beam from
the neon replaced that through the N0 gas only in regions

‘where known neon lines existed, as determined by prelimin-

.NH shaman

......21 .1... ..x... 1:112 ... 2.1:: :c;:::.n< 3 fl

1. . . .
......:._...,:._..I; 1, 3111...... .. 11..., 11.1.11...

......1. ... ...... .1... .. ...... 11.11.... 1

1.1... .. 1

 

47

ary trials. The NO lines missing in these regions were
then determined from another tracing on the spectrogram

taken without superposing the neon.
2-0 Band

The 2-0 band at 2.69 p.presented difficulties because
of the fact that glass becomes opaque beyond about 2.7 pm
It was found that the best results for the R branch were
obtained with the 100 watt concentrated are using the 7200
grating, but that it was necessary to change to a carbon.
arc and to the 1800 grating for the P branch.

For the R branch, the spectrOgraph slits were set for
50 microns, corresponding to 0.4 cm"1 with the 7200 grating,
and the absorption cell was set for 40 traversals with the
pressure at 14 centimeters of mercury. With the grating
rotating at speed 5 (1325 minutes of are per minute of time),
the linear dispersion on the recorder paper was about
0.0008 degree per millimeter or 0.11 cm‘1 per millimeter.
It was possible to get R lines with good resolution to J
values of 159/2. Figure 15 shows a typical spectrogram of
the 2-0 R branch but at a faster grating rotation speed
than used on the spectrograms measured. It is readily seen
that the glass envelope on the source became opaque soon
latter passing through the Q branch.

In order to obtain the P branch of the 2-0 band, it

‘Nas necessary to change all the glass lenses and the win-

48

.na magmas

2pm

 

49.

dows on the absorption cell and the spectrograph to quartz,

and to eliminate the glass surrounding the source by using

a carbon arc. It was also found that better results were

obtained with the 1800 grating which was used in the fifth
order to take advantage of its blaze at 27 degrees. With
the 1800 grating it was necessary to use the fore-prism
monochromator. With the slits set at 200 microns (6‘42 cm'l),
it was possible to get P lines out to J values of 33/2 be-

fore the thin glass envelope on the lead sulfide detector

became completely opaque.

4-0 Band

In an attempt to resolve the 4-0 band at 1.36 p, an

estimate was made from the absorption in the 3-0 band as to

the necessary absorbing path. This was of the order of 100

xneter-atmospheres to give even 5—10 percent absorption.
TPhe mirrors were adjusted for 100 traversals and the press-

llre was increased to almost two atmospheres, giving an ef-

fective absorbing path of about 60 meter-atmospheres.
Since this region was off the blaze of the 7200 line grat-

1413, it was necessary to open the slits to 400 microns

(Q15 cmfl) to get much indication of absorption. Figure 14

13 a tracing made from a spectrogram and shows that the en-,

velope of the 4-0 band only was obtained . Two argon emis-

sion lines from the 100 watt arc, one on each side of the
band, aided in the location of its center 'at 7337 cm'l.

It ‘

k l 1 l l

7200 7300 7400 7500 Cm"

 

4-0 Envelope of NO 0? I.36/u, Slit 400/4.

51

5-0 Band

An attempt was made to obtain the 5-0 band in the
photographic infrared region at 1.10 p, but with the ab-
sorption cell mirrors silver-plated and set for 120 tra-
versals and the NO pressure at two atmospheres (an absorb-
ing path of about 80 meter-atmospheres), no absorption was
evident even with 48 hour exposures. The spectrograph used
for this part was a photographic, concave-grating instru-
ment built by C. F. Clarke.‘2l Its concave grating is an
original made by R. W. Wood and has a radius of curvature
of 100 centimeters. It has 30,000 lines per inch over a
two inch by four inch surface. The grating was used in an
Eagle mount on a Rowland circle of one meter diameter.

The photographic plates ware Eastman Z plates which were
hyper-sensitized with a 4 percent ammonia solution immedi-
ately before exposure in the spectrograph. The background

fogging was found to be rather intense, so that the time

of exposure had to be limited.

52

RESULTS AND DISCUSSION
wave Numbers for the 5-0 and 2-0 Bands

The determination of the actual wave number for a
line involved knowing the angle through which the grating
rotated in giving the line. This can be seen from the
grating equationzzg

fink - d(sind+sinfi) eq 21
in which n is the order number, d is the separation of
successive grating rulings,akis the angle of incidence,
and fl is the angle of diffraction.

In the Noble spectrograph, the directions of the incident
and diffracted light remain fixed in space and the grating

is rotated. In Figure 15 the grating is shown in the pos-

 

Grating

Figure 15. Grating Equation Angles

53

ition for the central image by the dotted lines and rotated

through an angle 0 by the solid lines. No is the normal

for the central image and N is the normal for the grating

after being rotated through the angle 9. From the figure

it can be seen that d- G-pO, and that P- 9+Po. With
these substituted into equation 21, and the usual expansion
of the sine of the difference of two angles and the sins of

the sum of two angles, the grating equation becomes:
Inl.‘ 2dcospbsin9 eq 22

from which the wave number becomes:

‘1}- l/a - n/(Zacosposing) ' Kv/sino eq
The angle of rotation of the grating for each line

23

W8 8

determined as follows: One of the ”pips" near one end of

the spectrogram was selected as the zero meter stick read-

number of millimeters to each of the spectral
The count-

ing and the

lines from this zero was observed and recorded.

er>on the spectrograph indicated the number of degrees (or
'tenths of a degree, since the pips were one-tenth of a de-

gree apart)from the zero meter stick reading to the pip

Imearest to the central image. For the 3-0 band this was

about 15 degrees: for the 2-0 it was about 22 degrees for
‘tdne 7200 grating and 29 degrees for the 1800 grating. The
églrating angle for the 4-0 band with the 7200 grating was
Eibout 11 degrees. The linear dispersion in degrees per
litillimeter was then computed by dividing the linear dis-

ihilnce on the recorder paper into the number of degrees be-

54

tween the pips used. Averaged values were always used.
The spectrograph counter reading corresponding to the cen-
tral image was then computed from this linear dispersion,
and the distance from several pips to the central image.
With the counter reading for the central image known, a
simple subtraction then gave the accurate angle from the
central image to the pip which was taken as the zero meter
stick reading (i.e. the angle of grating rotation for the
zero meter stick reading was then known). The linear dis-
persion in degrees per millimeter was then used to deter-
mine the angles from the meter stick zero to each line and
these were added to the angle of grating rotation for the
zero of the meter stick, so that the results then gave the
angles of grating rotation from the central image to each
of the lines on the spectrogram. It was then a simple mat-
ter to look up the sines of the angles.

The grating constant for each line was determined from
a graph of K‘;vs. G where the values of Ky were determined
from the spectrograms of mercury, neon, and argon in this
region. Most of these lines were higher orders of well-
known visible lines so that the11's were accurately known
and with the anglesc) determined as above, equation 23
gave the values of K1,. Equation 22 would indicate that Kv
should be the same for all angles of rotation of the grat-
ing; however, it was found that there was a periodic varia-

tion occufling with a period of one degree caused by the

55

worm gear which drove the wheel upon which the grating was
mounted. The teeth on the wheel are one degree apart, so
with the shaft of the worm gear very slightly off-axis, the
periodic error was introduced, necessitating the correction
graph. The sines of the angles for each line divided into
their grating constants (equation 25) than gave the wave
numbers of the lines.

It was noted that the humidity of the air was an impor-
tant factor in the linear dispersion of a spectrogram as
the paper stretched noticibly on moist days. However, if
all readings were taken at one time, this introduced no error.

Table I shows the wave numbers for the 3-0 band, the
erl/Z lines being labeled R1 and P1 and the 2II3/3 lines
being labeled R2 and P2. The parentheses indicate that the
R lines were unresolved for J values up to 13/2. Although
the envelopes of most of these unresolved lines showed asym-
metry, only those for which the two peaks were visible were
actually separated into the two components. Three of the R2
lines (lg/2, 21/2, and 25/2) were masked by amplifier noise
so were omitted. It was discovered that maximum resolution
‘was obtained for the P branch lines on a spectrogram dated
4-7-53, whereas maximum resolution for the R lines occurred
on a spectrogram dated 5-29-53. Since the P line frequencies
for the spectrogram dated 5-29-55 were higher on the average
by 0.39 cm'”1 than the corresponding lines on the spectrogram

dated 4-7-53, the final values were obtained by subtracting

56

TABLE I

WAVE NUMBERS FOR 3-0 BAND

(R components are from spectrogram dated 5-29-53)
(P components are from spectrogram dated 4- 7-53)

 

 

J+§ R1”) P1(J) 112(1) Pg”)

1 5548.81 ---- ---- ----

2 (5551.81)* 5558.95 (5551.81)* ----
5 (5554.79) 5555.69 (5554.79) 5554.80
4 (5557.81) 5552.19 (5557.81) 5551.11
5 (5560.65) 5528.40 (5560.65) 5527.50
6 (5565.41) 5524.64 (5565.41) 5525.44
7 (5565.97) 5520.80 (5565.97) 5519.59
8 5568.26 5516.80 5568.51 5515.28
9 5570.64 5512.55 5570.92 5510.78
10 5572.71 5508.22 ---- 5506.50
11 5574.88 5505.88 ---- 5502.05
12 5576.89 5499.46 5577.45 5497.49
15 5578.92 5494.92 --—- 5492.85
14 5580.71 5490.15 5581.18 5488.05
15 5582.45 5485.57 5582.90 5485.15
16 5584.01 5480.48 5584.52 5478.05
17 5585.41 5475.41 5585.80 5472.90
18 5586.79 5470.50 5587.50 5467.51
19 5588.04 5465.50 5588.51 5462.52

 

*Two R components unresolved.
Maximum of unresolved Q1 and Q2 branches at 5543.0

57

0.19 cm"1 from the R lines and adding 0.20 cm"1 to the P
lines as they were computed from their separate spectro-
grams.

Table II shows the wave numbers for the 2-0 band, the
parentheses indicating that the two R components were unre-
solved for values of J up to 25/2. It was impossible to
resolve the first of the P lines. The P lines were obtain-
ed from a spectrogram dated 2-21-52 for which the 1800 lines
per inch grating and the 196% are were used‘.
The R lines were obtained from a spectrogram dated 2-8-53
for which the 7200 lines per inch grating and the angzz‘trc
were used. As was mentioned previously, it was possible to
measure R lines out to J values of about 139/2, but P lines
only to about 33/2.

Upon comparing the data from the 3-0 and 2-0 bands and
making use of Gillette and Eyster's data on the 1-0 band,5
it was discovered that the average separation of the two P
components was greatest in the 3-0 band, less in the 2-0 and
least in the 1-0 band; also that the separation of the R
components was least in the 3-0 band, more in the 2-0, and
greatest in the 1-0 band. This would indicate that a grat-
ing with much greater resolution.would be necessary if an

attempt is to be made to obtain the fine structure of the
4-0 R branch.

58

TABLE II
WAVE NUMBERS FOR 2-0 BAND

(P components from spectrogram 2-21-53 using 1800 grating)
(R components from spectrogram 2- 8-53 using 7200 grating)

!

 

 

J24 R1(J) P1(J) R2(J) P2(J)
1 5729.10 ---- ---- ----
2 (5752.09)* 5719.28 (5752.09)* ----
5 (5755.14) (5715.71)* (5755.14) (5715.71)*
4 (5758.18) 5712.65 (3738.18) 5711.85
5 (5741.10) ' 5708.95 (5741.10) 5707.87
6 (5744.26) 5704.88 (5744.26) 5705.67
7 (5746.96) 5700.97 (5746.96) 5699.77
8 (5749.66) 5697.26 (5749.66) 5696.08
9 (5752.57) 5695.29 (5752.57) 5692.01
10 (5755.11) 5689.57 (5755.11) 5687.92
11 (5757.56) 5685.18 (5757.56) 5685.75
12 (5760.01) 5681.07 (5760.01) 5679.29
15 (5762.59) 5676.95 (5762.59) 5675.15
14 5764.85 5672.87 5765.65 5670.95
15 5767.02 5668.59 5767.74 5666.60
16 5769.25 5664.09 5770.07 5661.98
17 5659.86 5771.85 5657.54

3771523

 

*Two components unresolved.

maximum of unresolved Q1 and Q2 branches at 3724.0

59

Rotational Constants

Evaluation of B0. The combination differences

 

‘A2F(J) - R(J-l)-P(J+l) which were used to determine Bo"

for both components are shown in Table III for the 3-0

and 2-0 bands. The average of the 3-0 and the 2-0 bands

for each component is also given in Table III with the

3-0 values having been given a weight of two and the 2-0

values a weight of one, since the 3-0 data, in general,was

much better than the 2-0. The parentheses indicate the

combination differences which involve unresolved R lines.
Figure 16 shows the graphical solution of equation 13

for Bo"(19 in which 33(1) was taken as the final value pro-

posed here for Bo"(1), namely 1.6706 cm"1

, and Do was con-
sidered negligible. With the approximate value equal to
the final value, the slope, or 4480,13 zero and the line
becomes horizontal. Also shown in Figure 16 are the re-
sults from Gillette and Eyster for the fundamental5 and
from Gerd and Schmid for the electronic‘flso and 2-0

bands.10

The dotted line in the 1-0 graph represents the
line corresponding to Gillette and Eyster's final value,
1.6696 cm'l. Beyond the first few points the scattering
in the 3-0, 2-0 data is less than for either of the other
two. All three lines represent the best fit through the

zero ordinate as determined by least squares calculations.

60

TABLE III

B COMBINATION DIFFERENCES

0

(R lines from spectrogram 5-29-53; P from 4-7-53)

 

 

 

 

 

 

 

J”: A2F1 52F 1 A2F1 A21"2 A2F2 A2F 2
(5-0) (2-0) (Avg)a (5-0) (2-0) (Avg)
2 13.12 13.39 13.21 ---- ---- ----
5 (19.62)b (19.46) 19.57 (20.70)b (20.24)b 20.55
4 (26.39) (26.21) 26.33 (27.49) (27.27) 27.42
5 (33.17) (33.30) 33.21 (34.37) (34.51) 34.42
6 (39.83) (40.13)' 39.93 (41.24) (41.33) 41.27
7 (46.61) (47.00) 46.74 (48.13) (48.18) 48.15
8 (53.44) (53.67) 53.52 (55.19) (54.95) 55.11
9 60.04 (60.29) 60.12 62.01 (61.74) 61.92
10 66.76 (67.19) 66.90 68.89 (68.62) 68.80
11 73.25 (74.04) 73.51 ---- (75.82) 75.82
12 79.96 (80.61) 80.18 ---- (82.43) 82.43
13 86.76 (87.14) 86.89 89.40 (89.08) 89.35
14 93.35 (93.80) 93.50 ---- (95.79) 95.79
15 100.23 100.74 100.40 103.15 103.65 103.32
16 107.02 107.16 107.07 110.00 110.20 110.07
17 113.51 ---- 113.51 117.01 ---- 117.01
18 120.11 ---- 120.11 123.48 ---— 123.48
a(3-0) values given weight 2; (2-0) given weight 1.
bTwo R components unresolved.
TABLE IV
Bo INFRARED AND ELECTRONIC VAIUES
30(1) 30(2) Bo Source
1.6680 1.7222 1.6951 Infrared 3-0
1.6762 1.7207 1.6985 Infrared 2-0
1.6706 1.7224 1.6965 Infrared 3-0,2-0a
1.6696 1.7200 1.6948 Infrared 1-0
1.6703 1.7182 1.6943 Electronic 1 l—O,2-O
1.6706 1.7239 1.6973 Electronic 7 0-0,1-0

 

61

 

f)

 

 

 

 

 

 

a.
3 :0
2:3 0
44-? 1;! Bo Comp. l
S 'I.‘ e.(I)= (.6706 cm"
"35 2° NHN'IR (2,0)(3,0)
4 m a 9 oo
()1 C) ()CD (3
.. o°
"F
H" o e.(l)- l.6696 cni"
'ooo GE'IR(I,0)
o 0 oo
0 — —°o—° —G.°_o.ao _______
...)-
+I- B.(I)= (.6705 6113'
o e 5 11.70.61 (2,0)
’°oo° 000° 00 °0 0‘0
0 go 4) DEL—3.9.6.9330
o0 o
b <3 (3
. J++
”'.CL_|_|__LLL1__L|_]__|_L_|__|J_111111111l1111l11111
5 l0 I5 20 25 30

 

 

 

 

Figure 16.

 

62

The first column of Table IV gives a comparison be—
tween the Bo(1) values from the infrared data and the val-
ues determined from the electronic data. It is to be noted
that the 3-0 80(1) alone is lower than the others and that
the value from the 2-0 band alone is higher than the others
but that the average of the 3-0 and 2-0 is about the same
as the other three.

A graph of equation 13 using the electronic 71-0, 2-0
data of Gerd and Schmid (not included here) shows that for
values of J up to about 59/2, the centrifugal stretching
termDo is negligible. Beyond this value, the curvature
suddenly becomes great enough to indicate the possibility
of an additional term involving (J41)5 in equations 11 and
13. This would indicate the addition of a cubic term
H'J5(J+1)3 to equation 5 with Hy of opposite sign to Dv.

The centrifugal stretching term DO(2) is not a negli-
gible quantity so was computed from the 7'1-0, 2-0 electron-
ic data of Gerd and Schmid using equation 13 with 8; as
1.65 cm'l. Figure 17 shows the results for J values to
69/2 and the influence of this centrifugal stretching can
be seen to be appreciable. A least squares fit of equation
13 to the points indicated a value for Do(2) of 6.63 x 10'6
‘wave numbers. Similar graphs and least squares calculations
(not shown here) for the electronic 6.0-2 band of Gerd,
Schmid, and von Szily12 gave D2(2) as 6.88 x 10'"6 cm’l.

“The same treatment of the electronic 6.0-3 band of Gero,

l
1

l

m.
:9

63

 

[ROI-I) - 904-1)] - 4341+ )

 

/

/
/ o¢°°°o°°°oo°o°ooooo
7(I,0)(2,0) / .95,

B.

Comp.2

B.(2)= |.7|82 crri"

 

 

4.
(0., 44° Data from
‘ ' Gert and Schmid
. '°.
.’.
" . — — — — G.S.- 7(I,0)(2,0)
5...
.. Infra. (3,0)(2,0)
~1- J + .%
(0'20' '0 40 50 60'
Figure 17. Electronic 1 Determination of B0 and

 

64

Schmid, and von 8211y12 gave 03(2) as 6.85 x 10"6 cm'l.
In all the computations involving Dv(2), the value was
taken as 7 x 10’6 cm'l. The fact that D0, D2, D3 are all
practically identical indicates that Fe in the relation

D - De+ Pe(V+%) is negligible, or that Dv is practically

v
constant.

Figure 18 shows equation 13 plotted for BO"(2) with
g; as 1.65 cm'1 and 00(2) as 7 x 10"6 cm’l. The 36116
line is for the combined 3-0, 2-0 infrared data and the
three broken lines represent the infrared fundamental and
two electronic results. Table III shows that the average
AgFg for J values of 21/2, 23/2, and 27/2 are from the
2-0 band only and for J values of 33/2 and 35/2 are from
the 3-0 band only. These five points are shown in figure
18 with small horizontal lines through the circles desig-
nating the points, and all five were omitted in determin-
ing the final Bo"(2). Figure 18 illustrates that the 3-0,
2-0 curve matches well the infrared 1-0 curve of Gillette
and Eyster and the 1 0-0., 1-0 curve of Schmid, Kanig, and
Farkas.9 The 1'1-0, 2-0 curve of Gerd and Schmidlo is
seen to have a lesser slope.

The values of 80(2) determined from the slopes of
these four curves are given in the second column of Table
IV. The final Bo values are given in column 3 of Table IV
and indicate that the infrared 3-0, 2-0 value agrees as

well with the electronic data as the electronic dataagrees

among itself.

65

 

 

 

 

 

6 .-
.. '3‘ B 7
.4... O C O m p . 2 II
+ e
5" so; -I III/6'
8 _ (.7 224 cm .’ /
"- + 5: IV /
-T~ '3 '2
4'1" 1%; ": '1‘- ’/’//
tn .. .. ,1 /
“- I? n O I], 0,-0-
'? ’e .
3.. % ,"/’
if x.
1 ,//
.. z; [I /
2‘, ‘E-J III/
,/ Infre.(3,0)(2,0)
.... . '/. - --------- S.K.E-7(0,0)(|,0)
/
| .. -— G.E.'lnfre.(l,0)
—— - —— - —- G.S.'7(I,0)(Z,0)
' J + +
5 l0 l5

Figure 18.

 

66

Evaluation of 85. The combination differences AZFLI) -

 

R(J)-P(J) from the 3-0 data are given in Table V for both
the 3111/2 and the 2I13/2 components. Again, the numbers
in parentheses indicate values computed from R lines for
which the resolution was incomplete. The three combina-
tion differences for J values of 19/2, 21/2, and 25/2 are
missing in the second component since amplifier noise ob-
scured the R lines for these values (see Table I).

Figure 19 gives the graphical solution of equation 13
for the 3-0 determination of the first component of 83 with
.a value of 1.54 cm'1 for 83 and with D3(l) considered negli-
gible. The solid line represents a least squares fit of
points used to determine the ABS from which the final value
of B3(l) was calculated as 1.6150 cm’l. The dotted line re-
presents the electrohic 60-3 data of Gero, Schmid, and von
Szily12 and also the p and 1 electronic data of Schmid,
_K6nig, and Farkas.9 The two electronic lines would be
practically coincident so have not been drawn separately.

Table VI, column 1, shows a comparison of the final
B3(l) values for the infrared 3-0 with the corresponding
electronic values. The two electronic values agree but are
appreciably higher than the 3-0 value. However, the points
on the 3-0 graph show very much less scatter than either of
the electronic curves (not shown here). The 6.0-3 graph
shows D3(1) to be negligible for the low J values needed in

this present analysis.

85 COMBINATION DIFFERENCES

67

TABLE V

 

 

 

 

 

 

 

J+§ 4291(1) 4293(1)
2 (12.86)*
3 (19.10) (19.99)*
4 (25.62) (26.70)
5 (52.25) (55.55)
6 (38.77) (39.97)
7 (45.17) (46.58)
8 51.46 53.23
9 58.11 60.14
10 64.49 ----
11 71.00 ----
12 77.43 79.94
13 84.00 ----
14 90.58 93.15
15 96.86 99.77
16 103.53 106.49
17 110.00 112.90
18 116.29 119.79
19 122.74 126.19
*Two R components unresolved.
TABLE VI
B3 INFRARED AND EIECTRONIC VALUES
35(1) B3(2) 55 Source
1.6150 1.6665 1.6408 Infrared 3-0
1.6193 1.6651 1.6422 Electronic p v
(7 bands averaged)
1.6199 1.6629 1.6414 Electronic C 0-3

‘

68

 

L7

‘Ilb

-45

13.-1:154 cm"

 

(Ji'i)

l
3

N

[R(J)-P(J)]

83 Comp. I

L 6 (50 cm" /

   
  
   

3-0 hflrered

 

 

— —— EIecHonchye
J + t
j |'° I U U U '3 U I I 210

Figure 19.

 

69

 

I
f

3 DR

— 48508) ’6 802.0%?

>1

(J)"P(J

 

|.600m|

8

   
 
   
 

 

3- 0 Infrared

------------ 3,7 [leenenle

— ------ 60-3 "

 

I 0

Figure 20.

 

70

Figure 20 represents a least squares fit of [R(J)-P(J)]
-48é(J+§)+8D3(J+§)3 plotted against (J+§) from the 3-0 data
for the second component. 8; was taken as 1.60 cm'1 and
D3(2) as 7 x 10'.6 cm'l, giving the solid line. The broken
lines represent the electronic data of Schmid, Kanig, and

9 and Gera, Schmid, and von Szily.12 The 3-0 infra-

Farkas
red line is seen to have a slightly steeper slope than the
two electronic lines.

The second column of Table VI gives the values for
B3(2) and column 3 gives the final 83 values. It should
be noted that the 3-0 component 1 value is lower than the
electronic values, but that the component 2 value is higher,

so that the average or final B3 agrees well with the final

electronic 83.

Evaluation of 82. Table VII gives the combination dif-

 

ferences for the 2-0 data from which the values of 82(1) and
82(2) were found. The parentheses show that only four val-
ues of the combination differences and therefore only four
points on the curves of figures 21 and 22 involve R lines
which were completely resolved. However, the line of fig-
ure 21 for the first component shows very little scatter of
points after the first few. Component 2 (figure 22) shows
considerable scatter and the first two points are far enough
from the final curve that they were omitted in the least
squares calculation of 82(2). The values used in solving

for the ordinates are shown en the two graphs. The solid

71

 

 

 

TABLE VII
82 COMBINATION DIFFERENCES
5‘5 4231(3) A2F2U')
2 (12.81)*
5 (19.45) (19.45)*

4 (25.55) (26.55)
5 (52.17) (55.25)
6 (39.38) (40.59)
7 (45.99) (47.19)
8 (52.40) (55.58)
9 (59.08) (60.56)
10 (65.74) (67.19)
11 (72.58) (75.81)
12 (78.94) (80.72)
15 (85.44) (87.26)
14 91.96 94.70
15 98.45 101.14
16 105.16 108.09
17 111.57 114.29

*Two R components unresolved.

TABLE VIII

B2 INFRARED AND ELECTRONIC VALUES

 

 

82(1) 82(2) BB Source

1.6406 1.6855 1.6631 Infrared 2-0 7‘—
1.6390 1.6808 1.5599 Electronic 6 0-2
1.6342 1.6869 1.6606 Electronic p , v

(4 bands averaged)

 

72

 

 

 

 

 

cm"
2.: BE Comp. l
4.- 7' o a
"D /6(
V
m“ /
9' |.6 406 ...." /
q)- o /
I
(7:1 ° /
31- v /
O.
I /
A
‘r 3 °//
19.1.. /
/
~ /
25- B 8 l.58 /
z /.
./
/
club /
2'0 Infrared
i” ------ 6 Electronic
-1 °
0
. ° J + 4
o T I I I 51 I As a I '10 a r w I {a . ‘—

Figure 21.

73

 

j

 

 

 

Figure 22.

o o
”A
+1
13 /
r :7 l. 6855 ..." /
O /
m
+ T '1 /
e a /
(.1: C) C)
... ... :0 . /°
:3 "' — /
“a (O )<
1200 _; p. /
q. a II /0
I 216 5 /
r--I ‘
A /
r 3 /
O.
A /.
-3 /
E /
'/ 0
° /
/
/ 2'0 Infrared
/
_ / ° _____ 6 Electronic
/
r o
J + l:
l l o l l l l l l #1 j. l J L l _L
5 no 15

 

74

lines represent the infrared 2-0 data and the dotted lines
represent the electronic 6.0-2 data of Gera, Schmid, and
von Szily.12 The electronic P and 1data of Schmid, Kdnig,
and Farkas9 shows so much scatter of points when plotted
as in figures 21 and 22, that no corresponding lines have
been inserted on the two graphs.

Table VIII shows a comparison of the B2(1), and 82(2),
and B2 values, as determined from the infrared 2-0, with
the two electronic studies. The final B2 value is slight-

ly higher then either of the two electronic values.

Evaluation of Be,cKe, I8, and re. Figure 23 shows a

 

plot of equation 15: Bv - Beddg(v+§) in which Bo, Ba, and
B5 are from the infrared 3-0 and 2-0 bands and the points
B6 through 813 are from the electronic fl study of Jenkins,
Barton, and Mulliken.ll A least squares fit of these nine
points, all taken with equal weight, determined Be (the Y
intercept in figure 23) as 1.7060 cm‘l, andcxe (the slope)
as 0.01797 cm'l. A separate determination was made using
only the data from the present investigation.with Bo given
a weight of three, B2 given a weight of one, and B3 given
a weight of two. These weights were determined from the
fact that the 3-0 data was considered to be much more re-
liable than the 2-0 data. Since Bo involved both the 3-0
and 2-0 data, it was given a weight of flaree. Be determin-
ed from this infrared data was 1.7060 cm'l, identical to

75

 

  
  
 

Be = L7060 cm"

‘a:e = C).C)|£3(J’ Cflfi'
|.65"

|.60"

|.55‘

j l
U V V f j I U

'50"

  
 

‘ BIZ
: Bus

l.45'r
" L 1 J 1 l 1 1V+iL l
2 4 6 8 l0 l2

Figure 23.

 

 

 

76

that determined using all nine points. The slope, however,
was slightly larger, being 0.01834 cm’l. The final values

1 and 0.0180 cm'1 and

proposed for Be ands!e are 1.7060 cm'
are shown in Table X compared with those presently accept-
ed as taken from Gillette and Eyster.5 It is to be noted
that the 3-0, 2-0 values are larger than the ones proposed
by Gillette and Eyster. Their curve was based on the same
six electronic points and two of their own infrared 1—0
points (Bo and B1). Since their Bo value was slightly low-
er than the 5-0, 2-0 value, it would be expected that their
Be and Q. would be smaller.

Once B6 was known, equation 16 readily gave Ie' the
equilibrium moment of inertia, and from the moment of iner-
tia, the equilibrium distance re was computed. These quan-
tities are shown in Table I along with those proposed by
Gillette and Eyster. Table IX gives the Bv results for both

components and the average Bv values that were used in

figure 23.
Vibrational Constants

3-0 band origins. The combination sums R(J-l)+P(J)
formed from the 3-0 data are shown in Table II for the
2I11/2 and 2I13/2 components. The numbers in parentheses
again indicate combinations involving R lines for which the
resolution was not complete. A plot of the left hand mem-

ber of equation 20 against J2 gives the graphs shown in

77

TABIE II

no T0 313 INFRARED AND ELECTRONIC VALUES

 

 

 

 

 

 

 

v Bv (1) EV (21 Bv Source
0 1.6706 1.7224 1.6965 Infrared 3-0,2-O
2 1.6406 1.6855 1.6631 Infrared 2-0
3 1.6150 1.6665 1.6408 Infrared 3-0
6 1.5649 1.6063 1 .5856 Electronic p
7 1.5539 1.5966 1.5753 Electronic p
8 1.5382 1.5711 1.5547 Electronic p
11 1.4744 1.5269 1.5007 Electronic p
12 1.4639 1.4916 1.4778 Electronic p
13 1.4469 1.4812 1.4641 Electronic p
TABLE I
3., 3., I., AND r. VALUES
Infrared 3-0, 2-0 Infrared l-O
(Plus Electroniop )
Be 1.7060 1.7046 cm'1
«6 . 0.0180 0.0178 cm-1
16 16.404 x 10-40 16.423 x 10‘40gm cmz
r 1.1503 1.1508 A

 

78

TABLE XI
3-0 COMBINATION SUMS

 

 

 

13-1/4 R1(J-1)+P1(J) 92(1-1)+92(J)
2 11087.76
6 (11087.50)* (11086.61)*
12 (11086.98) (11085.90)
20 (11086.21) (11085.11)
50 (11085.27) (11084.07)
42 (11084.21) (11082.80)
56 (11082.77) (11081.25)
72 11080.79 11079.29
90 11078.86 11077.42
110 11076.59 ----
152 11074.54 ----
156 11071.81 11070.28
182 11069.05 ----
210 11066.28 11064.51
240 11062.91 11060.95
272 11059.42 11057.42
506 11055.91 11055.51
542 11952.09 11049.62

 

*Two R components unresolved.

TABLE XII
3-0 BAND ORIGINS

 

 

 

3-0 (1) 3-0 (2) Source
5544.28 5545.69 cmrl Infrared 5-0 ‘
5544.21 5545.55 cm.’l Gillette, Eyster eq.6

 

79

figure 24, one for each of the two components. For the
2I11/3 component, the first five points (J2 from 2.25
through 30.25) are so far from the straight line formed
by the others that they were omitted in the least squares
computation of the band origin (Y intercept). The fact
that these few points are not regular is supported by all
the previous data for the Bv quantities in which the first
few points are all slightly off the straight line formed
by the others. The 2I13/2 component does not show this
peculiarity so all the points were included in the least
squares determination of this band origin.

The two straight lines, when plotted together as in
figure 24, should be parallel and therefore should have the
same slope. It is seen that there is a gradual divergence
as J2 increases, which apparently must be attributed to
experimental error. Since the data for the first component
is better than that for the second, it would seem that the
origin for the ZIIl/z substate is accurate, but that the
line for the 2I13/2 substate has too steep a slope and
that the origin for this component is too 2‘92: This inter-
pretation was substantiated by computing the band origins

from the two relations given by Gillette and Eyster5

as
equation 6. Reference to Table XII shows that the first
component band origin agrees almost exactly with the com-
puted value, but that the second component origin is much

larger than the computed origin.

cm"

80

 

5544 ~ -.

45-
42»
4| ._
40-»

ESE)“.

 

 

flaw-n+9”) - mar-8654‘]

.-

50

3- 0 Bond Origins

Comp.| 5544.28 cm”
Comp.2. 5543.69 cn'i'

(Comp. I

Comp. 2’

J

l l l l 1
I60 I50 200 250 30

Figure 24.

 

81

2-0 band origins. Table XIII gives the combination
sums for the 2-0 data with the parentheses showing that
only three of the sums were derived from completely resol-
ved R lines. Figure 25 shows two graphs of equation 20
from which the band origins were determined as the Y inter-
cepts. The two lines, as determined by a least squares fit
of the points in each case, are practically parallel, al-
though the scatter'of the individual points is fairly
great. For the second component, the first two points
would have been far from the straight line determined by
the other points so were omitted both on the graph and in
the computations. Table XIV shows the band origins as de-
termined from the infrared 2-0 data and as computed from
equation 6 of Gillette and Eyster. The agreement for each

component is exceptionally good.

4-0 band origins. Since the envelope only of the 4-0
band was obtained, it was, of course, impossible to deter-
mine the two band origins. However, the envelope of the Q
branch was visible on the spectrogram and the argon emission
lines on either side of it made it possible to locate the Q
branch quite accurately at 7337 cm-1. It will be necessary
to build a longer absorption cell in order to get enough

absorption to show any rotational fine structure for this

band.

82

TABLE XIII
2-0 COMBINATION SUMS

 

 

 

 

 

 

 

52-1/4 R1(J-l)*P1(J) R2(J-1)+P3(J)
2 7448.58 ----
6 (7447.80)* (7447.80)*
12 (7447.77) (7446.99)
20 (7447.11) (7446.05)
50 (7445.98) (7444.77)
42 (7445.25) (7444.05)
56 (7444.22) (7445.04)
72 (7442.95) (7441.67)
90 (7441.74) (7440.29)
110 (7440.29) (7458.86)
152 (7458;65) (7436.85)
156 (7456.96) (7455.14)
182 (7455.26) (7455.52)
210 7455.42 7452.25
240 7451.11 7429.72
272 7429.11 7427.61
*Two R components unresolved.
TABLE XIV
2-0 BAND ORIGINS
3-0 (1) 2—0 (2) Source
3724.16 3723.48 cm“l Infrared 2-0
5724.22 5725.51 omél - Gillette, Eyster eq.6

 

83

 

2 - 0 Bond Origins

. , Comp. I 3724.|60;Y')
Comp. 2 57 25.4866

 

 

 

 

50 I60 I50 200 250 500

' Figure 25.

84

are. 00x3, and Ueye. The term values for the anharmon-

 

ic oscillator relating to the various vibrational energy
levels are given by the relation:2:5
om - u,(v+4)- u.x.(v+4)2+ o.y.(v+4)3 e4 22
in which 6).. “axe: and maya are constants with the first
much larger than the second and the second very much larg-
er than the third. The difference between two such terms
with a v value of zero for one gives the vibrational band
origin. It can be seen that a determination of these three
constants is possible only if several of the band origins
are known. Gillette and Eyster, in their note-worthy study,
used the electronic 9 data of Jenkins, Barton, and Mulli-
ken11 for 7 values of four to ten, and determined these
three constants, arriving at the following relations for
the components:
Gl(v) - 1904.03(v+§)~13.97(v+§)2-0.00120(v*§)3
Gz(v) - 1905.68(v+§)-15.97(v+§)2-0.00120(v+;)5
eq 23
Since these were the equations used to check the infrared
3-0 and 2-0 band origins, and since the agreement is very

close, it would seem that the Gillette and Eyster values

for 9., “o‘er and anyo are accurate.
Conclusion

During this entire study of the N0 vibrational bands

in the near infrared, there were no evidences of any ex-

85

treme perturbations to the rotational structure of the
molecule. There also was no evidence of any noticeable
transition from one coupling scheme to another. It is
felt that the mol~cular constants presented here are more
representative of the molecule than those previously de-
termined from the electronic data and from the infrared

fundamental investigation of Gillette and Eyster.

10.

11.

12.

13.

86

BIBLICGRAPHY

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Show, C. P., and E. K. Rideal. Infrared investigations
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87

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Herzberg, G. reference 6, page 92.

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