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Microwave spectrum and structure of pentafluorosulfur bromide and infrared spectrum of arsenic pentafluoride

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MICROWAVE SPECTRUM AND STRUCTURE OF
PENTAFLUOROSULFUR BROMIDE
and
INFRARED SPECTRUM OF ARSENIC PENTAFLUORIDE
A D is s e rta tio n
By
ERWIN W ILL IA M NEUVAR
S ubm itted to th e G raduate School o f the
A g ric u ltu ra l and M e c h a n ic a l C o lle g e o f Texas in
p a rtia l fu lfillm e n t o f th e re q u ire m e n ts fo r th e degree o f
DOCTOR OF PHILOSOPHY
A ugust 1962
M a jo r S u b je c t:
C h e m is try
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UMI Number: DP16324
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MICROWAVE SPECTRUM AND STRUCTURE OF
PENTAFLUOROSULFUR BROMIDE
and
INFRARED SPECTRUM OF ARSENIC PENTAFLUORIDE
A D is s e rta tio n
By
ERWIN W ILLIA M NEUVAR
A pproved as to s ty le and c o n te n t b y:
li U
^
v .
C ha irm a n o f Comrrfifefee
&
Head o f D ep a rtm e n t
A u g u s t 1962
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ABSTRACT
MICROWAVE SPECTRUM AND STRUCTURE OF
PENTAFLUOROSULFURIBRQMIDE
and
INFRARED SPECTRUM OF ARSENIC PENTAFLUORIDE
by
E rw in W illia m N euvar
B . S ., A g ric u ltu ra l and M e c h a n ic a l C o lle g e o f Texas
M . S . , A g ric u ltu ra l and M e c h a n ic a l C o lle g e o f Texas
D ire c te d b y : D r . A lb e rt W . Jache
R o ta tio n a l s p e ctra o f p e n ta flu o ro s u lfu r brom ide o bserved w ith a v id e o
m icro w a ve sp e ctro m e te r in th e re g io n 5 1 -5 4 Kmc w ere fitte d to th e fo llo w in g
m o le c u la r c o n s ta n ts and s tru c tu ra l p a ram eters:
S
32
F_Br
5
79
— B =
o
79
1172.153 + 0 .0 0 2 M e , DT = 0 .0 6 7 2 + 0 .0 4 0 0 K c, D Tir = 0, eQq (Br ) =
J
JK
37
81
800 + 5 M e ; S F r Br
— B = 1159 .8 7 5 + 0 .0 0 2 M e , DT = 0 .1 6 1 2 +
—
5
O
~
J
—
0 .0 4 0 0 K c, Drir = 0, eQq (Br81) = 705 + 5 M e ;
JK
—
_ _ , . n = 88° (assum ed),
F -S -F (a x ia l;
d 0 _ = 2 . 1902 + 0 .0 0 6 5 A , ‘d 0 „ = 1 .5 9 7 0 + 0.0025 A .
S-Br
—
S -F
—
S te ric in te ra c tio n
be tw ee n the brom ine atom and th e F^ group re s u lts in a lo n g S-B r bond
d is ta n c e , a lth o u g h the v a lu e o f th e q u a d ru p o le c o u p lin g c o n s ta n t su g ge sts
some io n ic c h a ra c te r.
<
The stro n g a b s o rp tio n peak a t 704 cm ^ in the in fra re d sp e ctru m o f
a rs e n ic p e n ta flu o rid e is a w in d o w band due to a re a c tio n p ro d u c t o f a rs e n ic
p e n ta flu o rid e and the sodium c h lo rid e c e ll w in d o w s .
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ACKNOWLEDGMENTS
I w a n t to e xp ress my g ra te fu l a p p re c ia tio n t o . . . .
D r . A lb e rt W . Jache fo r h is e x c e lle n t te c h n ic a l g u id a n c e , in s p ir a ­
tio n , and m oral su p p o rt th ro u g h o u t my g ra duate s c h o o l c a re e r.
M y G raduate C o m m itte e , D r . R. M . H ed g e s, D r . J . K . G la d d e n ,
D r . E . C . K lip p le , D r . N . C . R ose, and D r . R. D . W h e a ly fo r th e ir
in te re s t and a s s is ta n c e th ro u g h o u t the in v e s tig a tio n and p re p a ra tio n
o f the d is s e rta tio n o
The W e lc h F o u n da tio n fo r the fin a n c ia l s u p p o rt.
D r . C la u d e I . M e r r ill and D r . G eorge H . C a d y , U n iv e r s ity o f
W a s h in g to n , w ho g ra c io u s ly p ro v id e d th e sam ple o f p e n ta flu o ro s u lfu r
brom ide used in th is s tu d y .
M y p a re n ts , who have a lw a y s encouraged me to seek h ig h e r
e d u c a tio n .
J a c k ie , my w if e , andK im m y and B illy , my c h ild r e n , w ho c h e e rfu lly
(w e ll, m ost o f th e tim e !) gave up new h a ts , sw in g s e ts , puppy d o g s ,
w eekend o u tin g s , and many o th e r e s s e n tia l ite m s d u rin g th e p a s t fo u r
y e a rs .
IV
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TABLE OF CONTENTS
MICROWAVE SPECTRUM AND STRUCTURE OF
PENTAFLUOROSULFUR BROMIDE
C h a p te r
I.
Page
INTRODUCTION
..........................
1
Ge n e r a l . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Theory o f th e S ym m etric Top R o ta tio n a l Spectrum .
N u c le a r Q u a d rup o le H y p e rfin e S tru c tu re ................. .
The S ig n ific a n c e o f e Q q ................
R e la tiv e In te n s itie s o f H y p e rfin e C om ponents . . .
C o n s id e ra tio n s in th e S e le c tio n o f C e ll
Tem perature and Frequency R egion . ...............
P re d ic tio n o f U n p e rtu rb e d R o ta tio n a l F re q u en cie s
o f SF..Br . . . . . . . . . . . . . . . . . . . . . . . . .
b
II.
III.
LITERATURE SURVEY
................
EXPERIMENTAL PROCEDURE . . . . . . . . . . . . . . . . . . .
RESULTS « . . . 0 9 . S O . O O O . . . . . . .
A n a ly s is o f
C a lc u la tio n
C a lc u la tio n
C a lc u la tio n
V•
DISCUSSION
.00. 0. 0 .0.0
th e H y p e rfin e S tru ctu re . . . . . . . .
o f eQq and U np e rtu rb e d F requency
o f D j and U pper L im it o f D j^ . . . .
o f M o le c u la r D im e n s io n s . . . . . .
• o. . . . . . . . . . s . . . . .
. .
. .
. .
. .
. . . . . . . . . .
R e la tio n s h ip Betw een Bond D is ta n c e and N atu re
o f the C h e m ic a l Bond . . . . . . . . . . . . . . . . .
Z e ro -P o in t V ib ra tio n E ffe c ts . . ........................
V I.
8
9
11
A pparatus . . . . . . . . . . . . . . . . . . . . . . . . . .
The Search fo r A b s o rp tio n L i n e s ...................................
A b s o lu te Frequency M easurem ents
...............
P re c is io n o f Frequency M e a surem ents
.............
IV .
1
2
4
6
7
C ON C L U S I O N S . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
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12
12
13
15
16
18
18
21
27
28
33
33
37
38
INFRARED SPECTRUM OF ARSENIC PENTAFLUORIDE
In fra re d Spectrum o f AsF,. . . . . . . . . . . .
o
. . . . . . . . .
A tte m p ted P re p ara tio n o f AsF^O . . . . . . ................
APPENDICES
REFERENCES.
•
®
o
o
o
0
.
o
o
o
»
.
.
.
. . . . .
.. . . . . . .
.
40
42
.
43
. .................... . . . . . . . . . . . . . .
47
9
.
.
o
.
.
.
o
o
o
.
.
o
o
a
a
o
.
.
vi
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»
LIST OF FIGURES
Figure
P age
1.
R e s o lu tio n o f the
2.
M o le c u la r D im e n s io n s D e fin e d .
30
3.
In fra re d Spectrum o f AsF,. .
41
Zi
„
ZZ
T ra n s itio n
v ii
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20
LIST OF TABLES
Page
T ab le
1.
P re d ic te d F re q u en cie s o f J T ra n s itio n s in the
R egion 5 0 -6 0 Kmc . . ,
10
A p p roxim a te F re q u en cie s and Proposed A s s ig n m e n ts
o f O bserved L in e s . . . . . . . .
..,»»»,
15
3,
R e su lts o f the C a lc u la tio n o f eQq and V
22
4,
C a lc u la te d and O bserved H y p e rfin e C om ponents o f
oo
7Q
th e v = 0 , J„.,
T ra n s itio n o f S F cBr
(DT = 0,
2.
Li
Z£
eQq = 800 M e , V
0
. . . . . .
J J\
= 51, 5 7 1 .8 7 M e )
23
C a lc u la te d and O bserved H y p e rfin e C om ponents o f
32
81
th e v = 0 , J21 ^ 22 T ra n s itio n o f S FgBr
( D ^ = 0,
eQq = 705 M e . V
o
= 51, 0 2 7 .6 2 M e ) ...............................
24
C a lc u la te d and O bserved H y p e rfin e C om ponents o f
32
79
th e v= 0 , J 2 2 —* .23 T ra n s itio n o f s F 5Br
(D jK= 0,
eQq = 800 M e , V
o
= 5 3 ,9 1 5 ,7 7 M e )
25
C a lc u la te d and O bserved H y p e rfin e C om ponents o f
32
81
th e v = 0 , J 2 2 —» 23 T ra n s itio n o f s F 5 Br
^D j k = 0,
eQq = 705 M e ,
8.
9.
10.
= 5 3 ,3 4 6 ,3 9 M e )
................
26
R o ta tio n a l C o n s ta n ts from R ig id R otor A p p ro x i­
m a tio n
27
B
28
o
and D_ from S e m i-rig id R otor T reatm ent . . . . . .
J
S tru c tu ra l Param eters C o n s is te n t w ith O bserved
M om ents o f In e rtia . . . ..................
.
31
11,
Proposed S tru c tu ra l Param eters o f SFcBr,
h
32
12.
Some O b served and C a lc u la te d S -F Bond D is ta n c e s
34
v iii
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T able
Page
13,
V alues o f 3K2/ J (J + 1) - 1 = X (J , K)
44
14
14.
V
V alues
alues o
o ff & & 2 (2 J + 3 )(2LJ -1 )I(2 I-1 ) = Y
15 .
V alues o f P h y s ic a l C o n s ta n ts and A tom ic M a s s e s
U sed in C a lc u la tio n s [ 3 , 2 8 ] . . . . . . . . . . , , . . . . .
(F)
fo 3r /12=. 3 ./2. .
1 ;0
IX
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45
45
46
MICROWAVE SPECTRUM AND STRUCTURE OF
PENTAFLUOROSULFUR BROMIDE
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CHAPTER
I
INTRODUCTION
G e n e ra l
The extrem e s e n s it iv ity o f m o le c u la r ro ta tio n a l s p e ctra to changes
in th e m o le c u la r g e om e try and m asses o f c o n s titu e n t atom s and the v e ry
a c c u ra te means a v a ila b le fo r a b s o lu te fre q u e n c y m easurem ents make
m icro w a ve s p e c tro s c o p y the m ost p re c is e means fo r d e te rm in in g the
s tru c tu re o f s im p le m o le c u le s o b ta in a b le in the gas p h a s e .
In order to
show a pure r o ta tio n a l sp e ctru m the m o le c u le m ust obey the g ro ss s e le c ­
tio n ru le ; th a t is , th e m o le c u le m ust p o sse ss a perm anent d ip o le m om ent.
M o le c u le s o f in te re s t to th e m icrow a ve s p e c trs c o p is t are d iv id e d
g e n e ra lly in to tw o c a te g o rie s : a s y m m e tric to p s and sym m e tric to p s .
M o le c u le s w ith th re e d iffe r e n t p rin c ip a l moments o f in e rtia are c la s s ifie d
as a sy m m e tric to p s .
M o le c u le s in w h ic h tw o o f th e p rin c ip a l moments o f
in e rtia are e q u a l, b u t d iffe r e n t from the th ir d , are sym m e tric tops . L in e a r
m o le c u le s re p re s e n t a s p e c ia l c a s e o f a sym m e tric to p in w h ic h the
m oment o f in e r tia about the in te rn u c le a r a x is is z e ro .
The m o le c u le
SF,_Br, w h ic h w as c h o s e n fo r th is in v e s tig a tio n , is a m o n o -s u b s titu te d
o c ta h e d ro n , and is an exam ple o f a sym m e tric to p .
The ro ta tio n a l
sp e ctru m o f an a sym m e tric to p is v e ry c o m p lic a te d , w hereas th a t o f a
sym m e tric to p is r e la t iv e ly s im p le and r e a d ily in te rp re ta b le .
1
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2
Theory o f th e Sym m etric Top R o ta tio n a l Spectrum
The c h a ra c te ris tic e n ergy v a lu e s fo r th e r ig id s y m m e tric a l to p ro to r
are g iv e n b y the fo rm u la C1]
( 1)
w here
I
a
= M om ent o f in e rtia a b o u t th e fig u re a x is
= M om ent o f in e rtia a b o u t an a x is p e rp e n d ic u la r to the
fig u re a x is
-2 7
h
= P la n c k 's c o n s ta n t (6 .6 2 5 x 10
e rg -s e c )
J
= R o ta tio n a l quantum num ber re fe rrin g to an e n d -o v e r-e n d
ro ta tio n o f th e m o le c u le . J ca n assume*-the v a lu e s 0, 1 , 2 , 3 . . .
K
= R o ta tio n a l quantum num ber re fe rrin g to a ro ta tio n a b o u t th e
fig u re a x is . K ca n assum e v a lu e s o f 0, + 1, + 2, . . . + J .
E q u a tio n (1) a ris e s as a c o n d itio n fo r the a c c e p ta b le s o lu tio n o f the
S ch ro d in g e r w ave e q u a tio n fo r the sym m e tric to p r o to r .
The tw o quantum
num bers J and K o c c u r because o f th e tw o typ e s o f ro ta tio n w h ic h a sym m e tric
to p ca n u n d e rg o . K is a s s o c ia te d w ith the ro ta tio n o f th e m o le c u le a b o u t
th e fig u re a x is . No a b s o rp tio n o f ra d ia tio n ta ke s p la c e due to ro ta tio n
a b o u t th e fig u re a x is because th e re is no change in d ip o le m oment w ith
r e s p e c t to th e d i r e c t i o n of i n c i d e n t r a d i a t i o n .
fo r K is AK = 0.
H e n c e , th e s e l e c t i o n ru le
H o w e v e r, the e n d -o v e r-e n d ro ta tio n re s u lts in an a b s o rp ­
tio n o f r a d ia tio n , and th e s e le c tio n ru le fo r J is AJ = + 1.
N um bers in b ra c k e ts re fe r to th e R eferences .
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E q u a tio n (1) is u s u a lly re p re se n te d in th e s im p le r form [ l ]
Ejk = h CB0T (J + l ) + (Aq - b q )k 2 ]
2
w he re A = h /8 rr I
a
(2)
2
and B = h /8 rr L .
o
b
As the m o le c u le ro ta te s the atom s tend to f ly a p a rt.
To c o rre c t fo r
th is c e n trifu g a l s tre tc h in g E q u atio n (2) ta ke s the form
E
* h ’['BoJ (J + l ) + (Ao - B q )K2 - D jJ2 (J + l ) 2
- D jk J (J + 1 )K 2 - D k K4 ] ,
w he re
D
(3)
= A term re s u ltin g from th e d is to r tio n due to the e n d -o v e r-e n d
ro ta tio n o f the m o le c u le
= A term re s u ltin g from th e d is to r tio n ca u sed b y ro ta tio n
a b ou t the fig u re a x is
D
JK
= A term re p re s e n tin g an in te ra c tio n o f the tw o m o tio ns .
Bearing in m ind th a t fre q u e n c y o f ra d ia tio n and e n ergy
th e e q u a tio n E = h V
/ w here V
are re la te d by
is the fre q u e n c y , and u s in g th e s e le c tio n
ru le s fo r energy a b s o rp tio n , one ca n show th a t th e fre q u e n c y o f a ro ta tio n a l
tr a n s itio n is g iv e n b y [ 1 ]
V
= 2B (J + l ) - 4D (J + l ) 3 - 2D
(J + 1)K2 ,
o
J
->k
(4)
w here J is the quantum num ber o f the lo w e r le v e l o f the tr a n s itio n .
D and D
i
JK
are v e ry s m a ll com pared to B
th e tre a tm e n t o f lo w J s p e c tra .
V =
O
and are o fte n n e g le c te d in
E q u a tio n (4) is s im p lifie d , th u s ,
2B (J + l ) .
o
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(5)
The moments o f in e rtia o f m ost gaseous m o le c u le s are such th a t pure
r o ta tio n a l sp e ctra are e x h ib ite d in the re g io n o f the e le c tro m a g n e tic spectrum
in c lu d in g w a v e le n g th s o f a b o u t 1 m illim e te r to s e v e ra l c e n tim e te r s - th e m ic ro ­
w ave re g io n „ Since the quanta o f e nergy in th is re g io n are n o t s u ffic ie n t ly
e n e rg e tic to e x c ite e le c tro n ic and v ib r a tio n a l energy s ta te s , pure ro ta tio n a l
s p e ctra are o b s e rv e d .
A c c o rd in g to E q u atio n (4) th e ro ta tio n a l spectrum o f a sym m e tric top
m o le c u le c o n s is ts o f a s e rie s o f lin e s separated by a fre q u e n c y d iffe re n c e
o f v e ry n e a rly 2Bq . The sp a cin g o f the lin e s co n verg e s s lig h tly in p a ssin g
to h ig h J v a lu e s w hen the c o n trib u tio n from c e n trifu g a l d is to r tio n term s in
E q u a tio n (4) becom es s ig n ific a n t .
N u c le a r Q ua d rup o le H y p e rfin e S tru ctu re
The e le c tr ic q u ad ru p ole moment c a n c o u p le th e n u c le a r a x is to the
m o le c u la r a x is th ro u gh th e e le c tr ic f ie ld g ra d ie n t o f th e m o le c u le e ffe c tiv e
a t the n u c le u s .
A n u c le u s p o ss e s s e s a q u ad ru p ole moment w hen its s p in
has a v a lu e o th e r th a n 0 or 1 /2 .
In v e c to r n o ta tio n the a n g u la r momentum
v e c to r ~I = v/1 ( I + 1) h /2 rr due to n u c le a r s p in and th e a n g u la r momentum
v e c to r J - J J (J + l) h /2 r r due to m o le c u la r ro ta tio n add to produce a re s u lta n t
a n g u la r momentum ~F = J F (F + 1) h / 2 T T , The quantum num ber F may assum e
v a lu e s [ 2 ]
F = (J + I) , (T + I - 1), . . .
J ~ I
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Each K le v e l o f a sym m e tric to p is re s o lv e d in to 21+1 s u b - le v e ls o f
d iffe r e n t e nergy; h o w e ve r, th e num ber o f s u b -le v e ls ca n n o t exceed the
d e g e n e ra c y , 2J + 1, o f the pure ro ta tio n a l le v e l „ Energy tr a n s itio n s ,
m a n ife s te d as com ponents o f the h y p e rfin e s tru c tu re o f pure r o ta tio n a l
s p e c tra , ca n ta ke p la c e b e tw ee n th e se s u b -le v e ls in a cco rd a n ce w ith th e
s e le c tio n ru le s A j - + 1, AK = 0, AF = 0, + 1, AI = 0.
Br
79
and Br
a x is o f SFgBr„
81
, each w ith a n u c le a r s p in o f 3 /2 , are on th e fig u re
The n u c le a r q u a d ru p ole energy fo r a s in g le n u c le u s w ith
s p in I on th e fig u re a x is o f a sym m e tric to p is g iv e n b y quantum m e c h a n ica l
f i r s t order p e rtu rb a tio n th e o ry to be [ 2 ]
Eq = eQq
w here
eQq
3K
jd + D
1
3 / 4 C (C + 1) - I (I + 1) I ( I + 1)
. 2(2J - 1) (2J + 3 ) I (2 1 - 1)
(6 )
= Q u a d rup o le c o u p lin g c o n s ta n t, a p ro d u c t o f th re e fa c to rs ,
e = E le c tro n ic charge
Q = E le c tric q u a d ru p o le m om ent, a p ro p e rty o f a p a r ti­
c u la r n u c le u s w h ic h m easures the d e v ia tio n o f the
n u c le a r charge from s p h e ric a l sym m etry
_ 2,,,
q
= -— 'd z
= E le c tro n ic fie ld g ra d ie n t e ffe c tiv e a t the
n u c le u s a ris in g from th e e x tra n u c le a r
charges
C = F (F + 1) - 1 (1 + 1 ) - J (J + 1).
N u m e ric a l v a lu e s fo r the f ir s t and second fa c to rs in b ra c k e ts o f
E q u a tio n (6) ca n be fo u n d ta b u la te d th ro u gh J = 20 and J = 21, re s p e c tiv e ly ,
in R eference 1.
F a cto rs fo r h ig h e r J le v e ls w ere c a lc u la te d and are p re ­
sented in the A p p e n d ix .
E q u atio n (6) is used to c a lc u la te th e fre q u e n c y
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
d e v ia tio n s w h ic h are added to th e un pe rtu rb e d fre q u e n c y
h y p e rfin e com ponents o f a J tr a n s itio n .
o
) to g iv e the
The u n perturbed fre q u e n c y is the
fre q u e n c y o f a J tr a n s itio n w h ic h w o u ld be ob serve d i f eQq = 0 .
The
u n pe rtu rb e d fre q u e n c y is not o b s e rv a b le as a se p arate a b s o rp tio n lin e , b u t
is a th e o r e tic a l q u a n tity d e te rm in e d fro m the re s o lu tio n o f th e h y p e rfin e
s tru c tu re „
The S ig n ific a n c e o f eQq
Is o to p e s in a p a rtic u la r com pound w i l l e x h ib it d iffe r e n t v a lu e s o f
eQq because each is o to p e has a d iffe re n t Q » S ince q depends on the
e le c tro n ic e n viro n m en t o f the n u c le u s , a p a rtic u la r is o to p e in d iffe re n t
com pounds w i l l have d iffe re n t v a lu e s o f eQq because th e e le c tro n ic
e n viro n m e n t g e n e ra lly is d iffe r e n t in each com pound „ By co m paring the
o b se rve d eQq v a lu e fo r a p a rtic u la r is o to p e w ith eQq v a lu e s fo r th a t is o to p e
in know n e le c tro n e n v iro n m e n ts , c e rta in in fe re n c e s about th e na tu re o f the
b o nding o rb ita ls can be made „
Because o f s p h e ric a l sym m etry o f s_ o r b ita ls , e le c tro n s in th e v a le n c e
s h e ll w h ic h have s_ c h a ra c te r do n o t c o n trib u te to q . E le c tro n s in d or
h ig h e r o rb ita ls have l i t t l e p e n e tra tio n and do n o t in flu e n c e the n u cle u s
s ig n if ic a n t ly .
O n ly £ e le c tro n s ca n c o n trib u te s ig n ific a n tly to q 121 .
For e xa m p le , c o n s id e r the bonded brom ine atom „ The n a tu re o f the
b o nd in g o rb ita ls o f brom ine ca n be d is c u s s e d w ith re fe re n c e to th re e s ta te s
o f kn o w n e le c tro n c o n fig u ra tio n :
the brom ine atom (B r°), brom ine a n io n
(Br ), and brom ine c a tio n (Br+ ) „ The fre e brom ine a to m , or the brom ine
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
atom in th e brom ine m o le c u le , (3b)5 e le c tro n ic c o n fig u ra tio n , re p re s e n ts
a s ta te in w h ic h th e re is an u n b a la n ce o f one £ e le c tro n , a "p u re "
c o v a le n c y .
C om bined brom ine u t iliz in g e s s e n tia lly pure £ bonding o rb ita ls
w o u ld have an eQq v a lu e v e ry c lo s e to th a t o f the brom ine a to m .
Br
has
a s y m m e tric a l c lo s e d v a le n c e s h e ll (unbalance o f zero £ e le c tro n s ); h e n ce ,
eQq = 0 .
C om bined brom ine w ith an eQq v a lu e s m a lle r th a n th a t fo r a
brom ine atom w o u ld have some a n io n ic c h a ra c te r.
e xtre m e , Br
4*
H o w e v e r, th e o p p o s ite
+
O
has an u n b a la n ce o f tw o £ e le c tro n s and eQq (Br ) = 2eQq(Br ) .
o
I t fo llo w s th a t com bined brom ine w ith an eQq v a lu e g re a te r than eQq(Br )
w o u ld have some c a tio n ic c h a ra c te r.
A lo w e rin g o f eQq (com bined atom ) w ith re s p e c t to eQq (free atom )
ca n a ls o be a ttrib u te d to the £ c h a ra c te r o f h y b rid iz e d o rb ita ls in v o lv in g
£ and £ o rb ita ls . As the £ c h a ra c te r o f th e h y b rid iz e d o r b ita l in c re a s e s ,
eQq d e crea se s C l, 2 l .
R e la tiv e In te n s itie s o f H y p e rfin e C om ponents
R e la tiv e in te n s itie s o f h yp erfin e com ponents are u s e fu l in the p re­
d ic tio n of the h yp erfin e structure of a J tr a n s itio n .
For v a lu e s of J larg er
th an 10, th e ca s e in this in v e s tig a tio n , the more in te n s e com ponents are
t h o s e for w h ic h AF = AJ ( i . e . , J —> J + 1, F —> F + l ) .
The r e l a t i v e
in te n s itie s o f these com ponents are ap p ro xim ately proportional to F .
The
o th e r w e a k e r com ponents have in te n s itie s re p re s e n tin g o n ly a v e ry s m a ll
fra c tio n (about 1/2J
2
or le s s ) o f th a t o f the e n tire tr a n s itio n .
O n ly the
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
J
J + 1, F
F + 1 tra n s itio n s w i l l be c o n s id e re d in the r e s o lu tio n o f
the h y p e rfin e s tru c tu re o f SF Br ro ta tio n a l sp e ctra [ 3 ] .
C o n s id e ra tio n s in th e S e le c tio n o f C e ll Tem perature and F requency R egion
S e ve ra l fa c to rs m ust be c o n s id e re d in s e le c tin g the m ost a p p ro p ria te
a b s o rp tio n c e ll tem perature and fre q u e n c y re g io n to be s tu d ie d .
W hen th e o b je c tiv e of; a m icrow a ve s tu d y is s tru c tu ra l d e te rm in a tio n
from ro ta tio n a l s p e c tra , th e ro ta tio n a l tra n s itio n s in the ground v ib r a tio n a l
s ta te (v = 0) are o f the greatest: in te r e s t.
To enhance the p o p u la tio n o f
m o le c u le s in the ground v ib ra tio n a l s ta te , th e re b y in c re a s in g th e in te n s ity
o f a b s o rp tio n a t a g iv e n path le n g th and gas p re s s u re , th e w ave g u id e
a b s o rp tio n c e ll is c o o le d to a te m perature a t w h ic h th e va p o r p re ssure o f
th e com pound s tu d ie d is a t le a s t s e v e ra l m icron s o f Hg p re s s u re .
The p o p u la tio n o f m o le c u le s in v a rio u s J ro ta tio n a l le v e ls passes
th ro u g h a m axim um , the lo c a tio n o f th is m axim um be in g g iv e n b y [2 ]
o
- 1 /2 ’
w here k = B o ltz m a n n 's c o n s ta n t (1 „380 x 10
(7)
“ 16
e rg /d e g )
T = A b s o lu te tem perature (®K)
B = R o ta tio n a l c o n s ta n t o f m o le c u le
o
-2 7
h = P la n c k 's c o n s ta n t (6 .625 x 10
e rg -s e c )
E q u a tio n (7) show s th a t as th e te m p e ratu re is lo w e re d , the m ost
p o p u lo u s J le v e l w i l l be s h ifte d d o w n w a rd , u s u a lly in to th e more a c c e s ­
s ib le re g io n o f the m icrow a ve s p e c tru m .
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
The in te g ra te d in te n s itie s o f ro ta tio n a l lin e s are d ir e c t ly p ro p o rtio n a l
to th e th ird pow er o f the fre q u e n c y .
The J le v e l in c re a s e s r a p id ly w ith
fre q u e n c y fo r a m o le c u le w ith s m a ll B , and w ith an in c re a s e in J a c o n ­
c o m ita n t in c re a s e in the m u lt ip lic it y o f the h y p e rfin e s tru c tu re a ls o ta ke s
p la c e .
In th e s tu d y o f m o le c u le s w ith q u a d ru p o le in te ra c tio n one trie s to
o b se rve lo w J tra n s itio n s w here the h y p e rfin e s tru c tu re is le s s c o m p le x .
The lo w e s t a tta in a b le fre q u e n c y and s e n s it iv ity are fu n c tio n s o f the d e s ig n
o f the spe ctro m ete r .
In p ra c tic e one a rriv e s a t some co m prom ise betw een
to le ra b le c o m p le x ity o f the h y p e rfin e s tru c tu re and adequate s e n s it iv ity ,
c o n s is te n t w ith c a p a b ilitie s o f the a v a ila b le in s tru m e n t.
P re d ic tio n o f U np e rtu rb e d R o ta tio n a l F re q uencies o f SF 5 Br
A search fo r ro ta tio n a l s p e ctra is more f r u it f u l i f i t is preceded by a
c a lc u la tio n o f the u n pe rtu rb e d lin e fre q u e n c ie s based upon th e b e s t a v a ila b le
s tru c tu ra l d ata fo r the m o le c u le under in v e s tig a tio n , o r fo r s im ila r m o le c u le s .
The s tru c tu re o f a s im ila r m o le c u le , SF C l , has been d e te rm in e d b y m ic ro 0
w a ve s p e c tro s c o p y by K e w le y [ 4 ] .
The m o le c u la r d im e n s io n s are re p orted
as fo llo w s :
©
dc
=
O“ 1
1,5 7 6 + 0 ,0 1 0 A
o
d c _ = 2 .0 3 0 1 + 0 .0019 A
D
1
^ F -S -F (a x ia l) = 88° 22‘ ± 10'
One ca n assum e re a s o n a b ly th a t th e S -F d is ta n c e s and F -S -F a n g le s
in S F g C l and SF^Br are a p p ro x im a te ly e q u a l.
I t is a ls o n o te w o rth y th a t
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
10
d
b -G l
is eq ua l to th e sum o f P a u lin g 's s in g le -b o n d c o v a le n t r a d ii o f S and
o
C l [ 5 ] . T h e re fo re , a re a s o n a b le e s tim a te o f d
b -Br
is 2 .1 8 A , th e sum o f
S and Br s in g le -b o n d c o v a le n t r a d i i . *
The r o ta tio n a l c o n s ta n ts o f the tw o m ost ab un d a n t is o to p ic s p e c ie s
o f SFj.Br w ere c a lc u la te d by in s e rtin g the assum ed bond d is ta n c e s and bond
32
79
a n g le in to th e e q u a tio n s o f K ra itch m an [ 6 ] . For S F Br
the c a lc u la te d
0
nn
p|
B is 1191 M e ; fo r S F r Br , B is 1178 M e . The p re d ic te d lin e fr e o
5
o
^
q u e n c ie s in the re g io n 5 0 -6 0 Kmc show n in Table T w e re c a lc u la te d by
u s in g E q u a tio n (5 ).
U n iq u e sp e ctra a ls o e x is t fo r the le s s a bundant m o le c u la r s p e c ie s
33
34
c o n ta in in g S
(0.75% n a tu ra l abundance) and S
(4.2% n a tu ra l a b u n d a n c e ).
The le s s abundant is o to p ic s p e c ie s are n o t e xp ecte d to be o bserved w ith
the m o d e ra te ly s e n s itiv e s p e ctro m e te r used in th is re s e a rc h .
TABLE 1
P re d icte d F re q uencies o f J T ra n s itio n s in the R egion 5 0-6 0 Kmc
T ra n s itio n
J —* J + 1
Frecjuency (M e )* *
S3 W
0
9
S32F ocB r81
20 —» 21
50, 022
4 9 ,4 7 6
21 —» 22
5 2 ,4 0 4
5 1 ,8 3 2
22 —» 23
5 4 ,7 8 6
5 4 ,1 8 8
23 —* 24
5 7 ,1 6 8
5 6 ,5 4 4
24 —> 25
5 9 ,5 5 0
5 8 ,9 0 0
^ F re q u e n c ie s are o fte n exp ressed s im p ly as c y c le s , k ilo c y c le s , m e g a cycle s —
the "p e r se cond" be in g u n d e rs to o d . T his c o n v e n tio n w i l l be fo llo w e d th ro u g h ­
ou t th e d is s e r ta tio n .
o
o
©
* r = 1 .0 4 A , r _ T = 0 .9 9 A , r_ = 1 . 1 4 A [ 5 ] .
b
GL
Br
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
CHAPTER
II
LITERATURE SURVEY
SF Br is n o t y e t d e s c rib e d in th e lite r a tu r e .
0
The com pound has been
prepared re c e n tly by M r . C la u d e I . M e r r ill in the la b o ra to ry o f D r . G . H .
C ad y o f th e U n iv e r s ity o f W ashington,, to whom th is in v e s tig a to r is in d e b te d
fo r the sam ple used in th is re s e a rc h .
A lite ra tu re search re v e a le d th a t o n ly one m o le c u le o f the m ono­
s u b s titu te d o c ta h e d ra l ty p e (SF C l) has been s tu d ie d by m icrow a ve
0
s p e c tro s c o p y [4 ] .
S e ve ral lite ra tu re v a lu e s o f S-F bond d is ta n c e s have been c o m p ile d
and are p resented in Table 12 .
11
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
CHAPTER
III
EXPERIMENTAL PROCEDURE
A pparatus
A s im p le v id e o m icrow a ve s p e c tro m e te r, th e d e ta ils o f w h ic h can
be found in R eferences 1 and 3 , w as used in th is in v e s tig a tio n .
EMI
and R aytheon r e fle x k ly s tro n s c o v e rin g the range 2 0 -4 0 Kmc w ere used as
th e m icro w a ve energy s o u rc e , and as d riv e rs for a K - to I-b a n d (G ordy's
d e s ig n a tio n ) d o u b le r.
A P o ly te c h n ic Type 801-A K ly s tro n Power S upply
w ith a b u ilt - in a u d io fre q u e n c y sa w to o th g e n e ra to r w as used to e n e rg ize
th e k ly s tr o n .
M o d u la te d by a 6 0 -1 2 0 Cps s a w to o th v o lta g e , the fre q u e n cy
o f the k ly s tr o n w as v a rie d p e r io d ic a lly o ver a narrow ra n g e .
The same
s a w to o th v o lta g e w as a p p lie d to the h o riz o n ta l p la te s o f tw o o s c illo s c o p e s .
A B e th e -h o le d ir e c tio n a l c o u p le r c o u p le d th e k ly s tr o n to th e fre q u e n c y
d o u b le r, w h ic h w as a tta c h e d th ro u gh a K - to I-b a n d tr a n s itio n s e c tio n to a
4 -m e te r lon g K -b a nd b ra ss w a v e g u id e a b s o rp tio n c e l l .
Kel~F w ax #41 w a s
u se d to s e a l the m ica w in d o w s o nto the w a ve g u id e fla n g e s . The s ig n a l
tra n s m itte d alo n g the w a v e g u id e a b s o rp tio n c e ll w as d e te c te d by S y lv a n ia
and P b ilc o 1N26 d io d e s , a m p lifie d by a d iffe r e n tia l a m p lifie r , and a p p lie d
to th e v e r tic a l p la te s o f one o f the scopes . The o u tp u t o f the d e te c to r on
th e a u x ilia r y g u id e o f the B e th e -h o le c o u p le r was fed to th e v e r tic a l p la te s
o f th e o th e r s c o p e .
The o s c illo s c o p e tra c e re p re se n te d a p lo t o f fre q u e n c y
12
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
13
(x - a x is ) ve rsu s energy ( y - a x is ) . *
W hen the k ly s tr o n is tuned m a n u a lly
o ve r a fre q u e n c y w here a b s o rp tio n ta ke s p la c e , a s m a ll p ip (a b s o rp tio n
lin e ) appears on the d is p la y s c o p e . Rough fre q u e n c y m easurem ents w ere
made by c a v ity w ave m e te rs FXR Type U410A and H e w le tt-P a c k a rd M o d e l
K 532A .
The Search fo r A b s o rp tio n L in e s
P ast e x p e rie n c e has in d ic a te d th a t the optim um s e n s it iv ity o f the
sp e ctro m e te r is in the re g io n o f 52 K m c.
T h e re fo re , the search fo r
a b s o rp tio n lin e s was c o n c e n tra te d in th is re g io n .
SF Br w as a d m itte d a t a p re ssu re o f a b ou t 20 m icron s in to an
D
e va cu a te d bra ss w ave g u id e c e ll a t - 7 8 ° C p re v io u s ly tre a te d w ith BrF
to d e a c tiv a te the m e ta llic s u rfa c e .
0
D u rin g th e se a rch fo r SFj.Br lin e s
p re d ic te d in the v ic in it y o f 52 Km c, s e v e ra l lin e s w ere o b serve d w h ic h
proved to be due to SF^ (or S O F ^).
The lin e s d id n o t appear im m e d ia te ly
upon the in tro d u c tio n o f sa m p le , b u t w o u ld appear a b ou t fiv e m inu tes
th e re a fte r, in c re a s in g in in te n s ity w ith tim e .
T h is o b s e rv a tio n c o n ­
firm e d the s u s p ic io n th a t SF Br is u n s ta b le in a b ra ss s y s te m .
0
The same
e ffe c t w as observed in a c o in s ilv e r w a v e g u id e c e l l . The ra te o f decom ­
p o s i t i o n o f SF Br w as s u c h t h a t i t w as n e c essa ry to change the sam ple
o
a t 10 m in u te in te r v a ls .
* A c tu a lly , the p lo t is tim e ( x - a x is ) v e rs u s the f ir s t tim e d e riv a tiv e o f
the e nergy ( y - a x is ) . S in ce fre q u e n c y is e s s e n tia lly a lin e a r fu n c tio n
o f tim e , fo r a ll p r a c tic a l purposes the p lo t ca n be c o n s id e re d fre q u e n c y
ve rs u s e n e rg y .
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
14
In order to e lim in a te the n e c e s s ity fo r ch a n g in g th e s a m p le , an in le t
p o rt w as in s ta lle d a t one end o f th e bra ss w a ve g u id e c e l l .
The sam ple
flo w e d th ro u g h th e c e ll and w as c o lle c te d in a c o ld tra p a t th e o p p o s ite
end o f th e c e l l . T h is te c h n iq u e proved v e ry s a tis fa c to ry w he n th e sam ple
in p u t ra te w as a d ju s te d to c o rre sp o n d to a 3 -5 m ic ro n /m in p re ssure ris e
in the c lo s e d s y s te m , and the c o n d e n s a tio n ra te w as c o n tro lle d to m a in ta in
a s te a d y -s ta te p re ssure o f 20-3 0 m icron s o f Hg in th e s y s te m .
Two s e rie s o f lin e groups w ere o b s e rv e d .
Each s e rie s e x h ib ite d
an e s s e n tia lly c o n s ta n t fre q u e n c y d iffe re n c e b etw een in d iv id u a l lin e
g ro u p s , a p ro p e rty c h a ra c te ris tic o f a sym m e tric to p ro ta tio n a l spectrum
w ith n u c le a r qu ad ru p ole in te ra c tio n s . Each m u ltip le t c o n s is te d o f a strong
broad peak surrounded by m any, much w e a k e r, s a t e llit e s .
The fre q u e n c ie s
o f th e stro n g p e a k s , m easured w ith a c a v ity w a v e m e te r, co rresp o n d ed q u ite
c lo s e ly w ith the p re d ic te d SF,_Br lin e s in Table 1.
The observe d lin e fr e ­
q u e n c ie s w ith proposed a s s ig n m e n ts are show n in T a b le 2 .
W ith th e im proved v a lu e s fo r B the o th e r tra n s itio n s w ith in the
o
fre q u e n c y range o f the s p e c tro m e te r w ere lo c a te d v e ry e a s ily a t the n e w ly
p re d ic te d fre q u e n c ie s .
H o w e v e r, because o f the a p p a re n t optim um s e n s i­
t i v i t y and re s o lu tio n o f the in s tru m e n t in the 5 0 -54 Kmc re g io n , the
J 2 1— 22 anc* ^22~-* 23 tra n s itio n s w ere s e le c te d fo r d e ta ile d a n a ly s is .
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15
TABLE 2
A p proxim ate F re q u en cie s and Proposed A ssig n m e n ts
o f O bserved L in e s
T ra n s itio n
J —4 1 1 1
O bserved Frequency (M e )*
S32F5B r79
B
o
S3 % B r 81
B
o
22
5 1 ,5 6 0
1172
51, 03 0
1160
22—4 23
5 3 ,9 2 0
1172
5 3 ,3 5 0
1160
2 3 -4
5 6 ,2 8 5
1172
5 5 ,6 7 0
1160
21—*
24
O bserved d iffe re n c e b e tw ee n Bq ' s fo r th e tw o is o to p ic s p e c ie s — 12 Me
C a lc u la te d d iffe re n c e (Table 1)™11 Me
* C a v ity w avem eter m easurem ents
A b s o lu te Frequency M easurem ents
A ll lin e fre q u e n c ie s w ere m easured by an e le c tro n ic fre q u e n c y s ta n d a rd .
The h e a rt o f the fre q u e n c y sta ndard is a o n e -m e g a c y c le o s c illa to r (K night
M o d e l FS 1000A) w h ic h is s ta n d a rd iz e d a g a in s t the N a tio n a l Bureau o f
S tandards S ta tio n WWV . The sta ndard o s c illa to r d riv e s a VHF in te rp o la to r
(G ertsch M o d e l A M -1 A ) w ith a fu n d a m e n ta l fre q u e n c y range o f 2 0 -4 0 M e ,
w h ic h ca n be lo c k e d on p h a s e -fo r-p h a s e w ith a m icro w a ve fre q u e n c y m u lti­
p lie r (G e rtsch M o d e l F M -4 ) w ith a fu n d a m e n ta l fre q u e n c y range o f 5 00 -10 0 0
M e.
By b e a tin g the fre q u e n c y m u ltip lie r a g a in s t the k ly s tr o n fu n d a m e n ta l
fre q u e n c y , a fre q u e n c y m arker is ge ne ra te d and d is p la y e d on the m o n ito r
o s c illo s c o p e o
By u t iliz in g a d u a l-b e a m o s c illo s c o p e , one ca n superim pose
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
16
th e fre q u e n c y m arker upon th e a b s o rp tio n lin e by a d ju s tin g th e fre q u e n c y
o f th e in te rp o la to r.
Since the e n tire c h a in o f fre q u e n c y m u ltip lie r s is
lo c k e d in p h a s e -fo r-p h a s e w ith the sta n d a rd o s c illa to r , the frequency
o f the k ly s tro n is some in te g ra l m u ltip le o f the fre q u e n c y o f the in te r ­
p o la to r . The fre q u e n c y o f th e in te rp o la to r is co u n te d b y an e le c tro n ic
c o u n te r (H e w le tt-P a c k a rd M o d e l 524B).
P re c is io n o f Frequency M easurem ents
A lth o u g h the e le c tro n ic fre q u e n c y sta ndard is c a p a b le o f e x tre m e ly
h ig h a c c u ra c y (on th e o rd er o f 1 p a rt in 10'7) in a b s o lu te fre q u e n c y
m easurem ents, th e p re c is io n ca n v a ry c o n s id e ra b ly . Among th e fa c to rs
w h ic h d e te rm in e th e p re c is io n o f fre q u e n c y m easurem ents a re :
(1) lin e
in te n s ity , (b) lin e w id th , (c) sharpness and w id th o f fre q u e n c y m a rker,
and (d) S k ill o f operator .
Four fre q u e n cy m easurem ents w ere made on each a b s o rp tio n lin e .
A fte r a re a d in g w as ta k e n , the fre q u e n c y m arker w as c o m p le te ly rem oved
from the lin e and re p o s itio n e d fo r th e n e x t r e a d in g . The average o f the
fo u r d e te rm in a tio n s w as ta k e n as th e fre q u e n c y o f the lin e .
The range o f u n c e rta in ty a s s o c ia te d w ith a n ave rag e is exp resse d
in term s o f c o n fid e n c e lim its w h ic h ca n be c a lc u la te d by s ta t is t ic a l
m ethods . The c o n fid e n c e lim its e n c lo s e th e range w it h in w h ic h w e ca n
e xp e c t to fin d th e tru e v a lu e o f the average w ith a g iv e n p r o b a b ility j:7 ] .
C a lc u la tio n o f the c o n fid e n c e lim its a t the 9 0% le v e l fo r fo u r w ea k
h y p e rfin e com ponents c h o s e n a t random in th e re g io n o f 53 Kmc g iv e s the
fo llo w in g re s u lts : + 0 .1 3 7 , + 0 .0 7 8 , + 0 .0 8 4 , + 0 .0 5 8 M e , A re a s o n a b le
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
17
e s tim a te o f the c o n fid e n c e lim its a t th e 90% le v e l fo r a ll lin e s is the
average o f th e se fo u r q u a n titie s , or a b o u t+ 0 .0 9 Me .
I t is d if f ic u lt to com pare th is v a lu e fo r the c o n fid e n c e lim its w ith
th o se q u ote d by o th e r w o rk e rs in th e fie ld because th e y g e n e ra lly n e g le c t
to d e s c rib e the m ethod by w h ic h th e y a rriv e d a t th e ir v a lu e . It sh o u ld be
n o te d , h o w e v e r, th a t th e h y p e rfin e com ponents w ere v e ry w e a k , w ith
s ig n a l- to - n o is e r a tio a p p ro a ch in g u n ity in m ost ca se s . O fte n th e fr e ­
q u e n c y m arker w as broader than th e lin e , m aking d if f i c u lt the s u p e r­
p o s itio n o f c e n te r o f m arker upon th e c e n te r o f the l in e .
U n d o u b te d ly ,
the c o n fid e n c e lim its are c o n s id e ra b ly s m a lle r fo r m easurem ents o f lin e s
o f a t le a s t m oderate in t e n s ity .
The c o m p u ta tio n o f a ll propagated e rrors w i l l be based upon the
+ 0 .0 9 M e c o n fid e n c e lim its . The lim its o f e rro r q uoted fo r the v a rio u s
m o le c u la r c o n s ta n ts are th o s e w h ic h w o u ld a lte r a t le a s t one o f the
c a lc u la te d fre q u e n c ie s by 0 .0 9 M e .
U n c e rta in tie s in the m o le c u la r
d im e n s io n s are d e te rm in e d p rim a rily by fa c to rs o th e r than e x p e rim e n ta l
error in fre q u e n c y m easurem ents as w i l l be show n in su b seq u e n t d is c u s ­
s io n s .
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
CHAPTER
IV
RESULTS
A n a ly s is o f the H y p e rfln e S tru ctu re
The a n a ly s is o f the h y p e rfin e s tru c tu re in v o lv e s the d e te rm in a tio n
o f v a lu e s fo r eQ q, V
o
, and D
JK
such th a t the c a lc u la te d fre q u e n c ie s o f
h y p e rfin e com ponents co rre sp o n d to th e o bserved fre q u e n c ie s w ith in the
lim its o f e x p e rim e n ta l e rro r.
In th e tre a tm e n t o f lo w J sym m e tric to p
ro ta tio n a l sp e ctra the c e n trifu g a l d is to r tio n term 2D
JK
(J + 1)K
2
in
E q u a tio n (4) is o fte n n e g le c te d . A lth o u g h th e r ig id - r o t o r tre a tm e n t is
u s u a lly a v a lid one fo r lo w J s p e c tra , an a p r io r i a s s u m p tio n th a t the
c e n trifu g a l d is to r tio n term s w i l l be n e g lig ib le fo r h ig h J s p e ctra is not
n e c e s s a rily a good o n e .
For e x a m p le , i f D
r e c tio n te rm is 9 .7 M e fo r J = 2 1 , K = 2 1 .
JK
is o n ly 0 .5 K c , the c o r -
I t is a p p a re n t fro m E q u ation
(4) th a t th e c e n trifu g a l d is to r tio n e ffe c t s h ifts lin e fre q u e n c ie s tow ard
th e lo w e r fre q u e n c ie s , th e am ount o f s h if t b e in g dependent upon the s iz e
of D
JK
, J, and K .
The d e v ia tio n from the u n pe rtu rb e d fre q u e n c y (F tr a n s itio n s ) fo r
eQq v a lu e s o f 500 and 1000 Me w ere c a lc u la te d u s in g E q u atio n (6 ).
d e v ia tio n s from V
o
The
fo r the tw o v a lu e s o f eQq w ere p lo tte d on the h o r i-
z o n ta l s c a le re a d a b le to th e n e a re s t 0 .0 5 M e , and s tra ig h t lin e s
c o n n e c tin g the d e v ia tio n s fo r the tw o eQq v a lu e s w ere p lo tte d on the
v e r tic a l s c a le re a d a b le to th e n e a re s t 5 Me . F requency s h ifts w ere
com puted fo r D v v a lu e s o f 0, 0 .0 0 0 1 , and 0 .0 0 0 5 Me and p lo tte d on the
JK.
18
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
19
same g ra p h .
The observed lin e fre q u e n c ie s w ere p lo tte d on se p arate
s trip s o f graph paper o f the same s c a le , and the s trip s w ere superim posed
upon th e graph to o b ta in b e s t co rre sp o n d e n ce b e tw ee n ob serve d and c a l­
c u la te d lin e fre q u e n c ie s . W hen s a tis fa c to ry agreem ent b e tw ee n o bserved
and c a lc u la te d lin e fre q u e n c ie s fo r each lin e group w as a c h ie v e d , F
quantum numbers w ere a s s ig n e d to each ob serve d lin e from th e g ra p h .
B est g ra p h ic a l f i t w as o b ta in e d fo r D
and 800 Me fo r S
32
F Br
0
79
JK
= 0, eQq = 705 Me fo r S
32
F Br
5
81
(Figure 1 ).
The p lo ts o f d e v ia tio n s o ve r a range o f eQq v a lu e s re v e a le d u s e fu l
in fo rm a tio n about the n a ture o f th e h y p e rfin e s tr u c tu r e . The p lo t showed
th a t many lin e s separated by o n ly a s m a ll fra c tio n o f a m e g acycle o ccu r
w it h in a b o u t 2 m e g acycle s o f the un pe rtu rb e d fre q u e n c y .
M a n y o f the
lin e s c lu s te re d around the u n pe rtu rb e d fre q u e n c y are u n re s o lv a b le and
are o bserved as the b ro a d , strong p e a k .
The u n pe rtu rb e d fre q u e n c y lie s
a p p ro x im a te ly in the c e n te r o f the broad p e a k . T his c h a ra c te ris tic o f the
sp e ctru m re s tric te d c o n s id e ra b ly the range o ve r w h ic h th e p lo t o f observed
fre q u e n c ie s c o u ld be v a rie d a lo n g th e d e v ia tio n a x is in the se a rch fo r a
fit.
A re a s o n a b le f i t is a c h ie v e d o n ly i f th e u n pe rtu rb e d fre q u e n c y fa lls
w ith in a b o u t 1 Me o f the stro n g p e a k .
Any o th e r f i t , no m a tte r how good
i t may a p p e a r, n e c e s s a rily w o u ld be a c c id e n ta l.
The fre q u e n c y s e p a ra tio n b e tw ee n lin e s d is p la c e d s e v e ra l m ega­
c y c le s from th e un pe rtu rb e d fre q u e n c y is la rg e r th a n th e s e p a ra tio n b e tw een
lin e s near th e m ain p e a k .
A much g re a te r degree o f c o n fid e n c e in the
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
20
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21
a ss ig n m e n t o f th e se lin e s e x is ts b ecause o f th e d im in is h e d p r o b a b ility
o f an a c c id e n ta l f i t in the re g io n s o f le s s c ro w d in g .
A ls o , th e c a lc u ­
la tio n o f eQq and ~\J re q u ire s the ta k in g o f a d iffe re n c e b e tw een the
o
fre q u e n c ie s o f o b s e rv a b le com ponents o f the h y p e rfin e s tru c tu re .
As
th is d iffe re n c e is in c re a s e d , th e p re c is io n o f the c a lc u la te d q u a n titie s
is in c re a s e d .
T h e re fo re , e ffo rts w ere c o n c e n tra te d to ob serve and
m easure lin e s as fa r as p o s s ib le from th e u n perturbed fre q u e n c y .
C a lc u la tio n o f eQq and U np e rtu rb e d Frequency
The fre q u e n c ie s o f the h y p e rfin e com ponents m ust s a tis fy the
syste m o f lin e a r e q u a tio n s [ 2 ] ,
+ AEq (eQq) = lJ
w he re
V
AE
0
(8)
= U np e rtu rb e d fre q u e n c y
= The d iffe re n c e b e tw ee n th e p ro d u cts o f fa c to rs w ith in
b ra c k e ts in E q u a tio n (6)
~U — O bserved fre q u e n c y .
A syste m o f lin e a r e q u a tio n s w as s e t up fo r each lin e g ro u p .
The
s o lu tio n o f each s yste m o f e q u a tio n s in tw o v a ria b le s eQq and 1 / w as
a c c o m p lis h e d by the method o f le a s t squares [ 8 ] . The le a s t squares
s o lu tio n fo r v *
had to be a d ju s te d s lig h tly to g e t b e s t co rresp o n d en ce
b e tw ee n c a lc u la te d and o bserved fre q u e n c ie s .
The re s u lts are sum m arized
in Table 3 . These v a lu e s o f eQq and V* w ere used to c a lc u la te the
o
fre q u e n c ie s o f h y p e rfin e c o m p o n e n ts .
T a b les 4 , 5, 6 , and 7 c o n ta in
proposed assign m ents and com parisons betw een observed and c a lc u la te d
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fre q u e n c ie s » O n ly th o se c a lc u la te d h y p e rfin e com ponents w h ic h re la te to
o b serve d fre q u e n c ie s are show n in th e t a b le s .
TABLE 3
R e su lts o f the C a lc u la tio n o f eQq and
S3 W
T ra n s itio n
J ->
J+ l
21—» 22
VQ
(M e)
o
C!32p n 81
9
eQq (M e)
V Q (M e)
eQq (M e)
5 1 ,0 2 7 .6 2 + 0 .0 9
5 1 ,5 7 1 „8 7 + 0 .0 9
800+5
22—» 23
53, 915 „ 77+ 0 o09
705+5
5 3 ,3 4 6 .3 9 + 0 .0 9
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
23
TABLE 4
C a lc u la te d and O bserved H y p e rfin e C om ponents o f the v = 0 , J_.
32
79
T ra n s itio n o f S F_Br
(D = 0, eQq = 800 M e , V
= 51, 5 7 1 .8 7 M e)
O
K
JJs.
T ra n s itio n
F
F+ 1
O
C a lc u la te d
Frequency (M e)
O bserved
F requency (M e)
The th e o re tic a l com ponents o f th is broad lin e
p ro b a b ly in c lu d e a ll F com ponents fo r K = 0
to 4 . Range: 51, 5 7 0 .7 7 to 5 T ,5 7 3 .0 2 Me
5 1 ,5 7 1 .6 8
5
4 3 / 2 - * 4 5 /2
5 1 ,5 7 3 .1 3 ^ )
5
4 1 /2 —* 4 3 /2
5 1 ,5 7 3 .4 7
6
4 5 /2 —> 4 7 /2
5 1 ,5 6 9 .7 5
6
4 3 / 2 - * 4 5 /2
5 1 ,5 7 3 ,82 s!
6
4 1 /2 —* 4 3 /2
5 1 ,5 7 4 .0 2 j
7
4 5 /2 —* 4 7 /2
5 1 ,5 6 9 .0 9 )
7
3 9 / 2 - * 4 1 /2
5 1 ,5 6 9 .1 4
7
4 3 / 2 - * 4 5 /2
5 1 ,5 7 4 .6 2
8
4 5 /2 —* 4 7 /2
5 1 ,5 6 8 .3 2 ')
.8
3 9 / 2 - * 4 1 /2
5 1 ,5 6 8 .2 0 J
10
4 1 /2 —* 4 3 /2
5 1 ,5 7 7 .2 4
5 1 ,5 7 7 .3 8
11
4 1 /2 —* 4 3 /2
5 1 ,5 7 8 .3 0
5 1 ,5 7 8 .3 5
12
4 1 /2 —* 4 3 /2
5 1 ,5 7 9 .4 6
5 1 ,5 7 9 .4 4
14
4 5 /2 —* 4 7 /2
5 1 ,5 6 1 .5 9
5 1 ,5 6 1 .5 6
15
4 5 /2 —* 4 7 /2
5 1 ,5 6 0 .1 1
5 1 ,5 6 0 .1 0
16
4 5 / 2 —* 4 7 / 2
5 1 , 558 .53
51,558 .40
17
4 1 /2 —* 4 3 /2
5 1 ,5 8 6 .7 5
5 1 ,5 8 6 .7 1
51, 573 .37
J
5 1 ,5 6 9 .64
51, 573 .97
5 1 ,5 6 9 .1 0
J
C o n fid e n c e lim its on a ll observe d fre q u e n c ie s
(9 0% p r o b a b ility le v e l) : + 0 .0 9 Me
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
5 1 ,5 7 4 .5 6
5 1 ,5 6 8 .2 8
24
TABLE 5
C a lc u la te d and O bserved H y p e rfin e C om ponents o f the v = 0 , J „
0 9 0 1
T ra n s itio n o f S
K
F_Br
_
i 4 ^4
= 5 1 , 0 2 7 .6 2 M e)
4
(D
T ra n s itio n
F— F + 1
= 0, eQq = 705 M e , V
C a lc u la te d
F requency (M e)
O bserved
F requency (M e)
The th e o re tic a l com ponents o f th is broad lin e
p ro b a b ly in c lu d e a ll F com ponents fo r K = 0
to 4 . Range: 51, 0 2 6 .6 5 to 51, 028 .63 M e
5 1 ,0 2 7 .2 3
6
4 5 /2 —4 4 7 /2
5 1 ,0 2 5 .7 5
5 1 ,0 2 5 .6 7
7
3 9 / 2 - 4 4 1 /2
5 1 ,0 2 5 .2 2
5 1 ,0 2 5 .4 7
8
4 5 /2 —4 4 7 /2
5 1 ,0 2 4 .5 0
5 1 ,0 2 4 .5 3
8
4 3 /2 —4 4 5 /2
51, 03 0 . 8 6 s)
8
4 1 /2 —4 4 3 /2
51, 03 0 .7 5 j
9
4 3 /2 —4 4 5 /2
51, 031.79
5 1 ,0 3 1 .7 4
10
4 1 /2 —4 4 3 /2
5 1 ,0 3 2 .3 5
51, 032.39
11
4 1 / 2 - 4 4 3 /2
5 1 ,0 3 3 .3 9
5 1 ,0 3 3 .29
12
4 1 /2 —4 4 3 /2
51, 0 3 4 .3 0
51, 0 34.39
12
3 9 / 2 - 4 4 1 /2
5 1 ,0 1 9 .9 7
5 1 ,0 1 9 .93
13
4 5 /2 —4 4 7 /2
5 1 ,0 1 9 .7 7
5 1 ,0 1 9 .8 2
14
4 5 /2 —4 4 7 /2
5 1 ,0 1 8 .5 6
5 1 ,0 1 8 .5 4
14
3 9 / 2 - 4 4 1 /2
51, 0 1 7 .1 0 s)
15
4 5 /2 —4 4 7 /2
5 1 ,0 1 7 .2 6 j
16
4 5 / 2 - 4 4 7 /2
5 1 ,0 1 5 .8 6
5 1 ,0 1 5 .7 7
16
4 1 /2 —4 4 3 /2
51, 039 .27
5 1 ,0 3 9 .2 8
17
4 5 / 2 - 4 4 7 /2
5 1 ,0 1 4 .3 8
5 1 ,0 1 4 .2 6
18
4 5 / 2 - 4 4 7 /2
5 1 ,0 1 2 .8 0
5 1 ,0 1 2 .7 5
C o n fid e n c e lim its on a ll o bserved fre q u e n c ie s
(9 0% p r o b a b ility le v e l) : + 0 .0 9 Me
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
5 i , 0 30.79
5 1 ,0 1 7 .2 2
25
TABLE 6
C a lc u la te d and O bserved H y p e rfin e C om ponents o f the v = 0 , J
T ra n s itio n o f S
K
32
F_Br
5
79
_
^
(DT„ = 0, eQq = 800 M e , V = 5 3 ,9 1 5 .7 7 M c )
JK
o
T ra n s itio n
F— -F + l
C a lc u la te d
Frequency (M e)
O bserved
F requency (M e)
The th e o re tic a l com ponents o f th is broad lin e
p ro b a b ly in c lu d e a ll F com ponents fo r K = 0
to 4 . Range: 5 3 ,9 1 4 .7 9 to 5 3 ,9 1 6 .7 9 Me
5 3 ,9 1 5 .9 8
6
4 1 /2 —4 4 3 /2
5 3 ,9 1 4 .1 2
5 3 ,9 1 4 .1 2
9
4 3 /2 —> 4 5 /2
5 3 ,9 1 9 .6 7
5 3 ,9 1 9 .6 1
10
4 7 /2 —> 4 9 /2
5 3 ,9 1 1 .0 3
5 3 ,9 1 1 .0 3
11
4 3 / 2 - 4 4 5 /2
5 3 ,9 2 1 .4 4
5 3 ,9 2 1 .3 9
12
4 3 /2 —4 4 5 /2
5 3 ,9 2 2 .4 5
5 3 ,9 2 2 .3 6
13
4 1 /2 —4 4 3 /2
5 3 ,9 06.86
5 3 ,9 0 6 .8 7
14
4 7 /2 —4 4 9 /2
5 3 ,9 0 6 .7 2
5 3 ,9 0 6 .7 6
14
4 1 / 2 - 4 4 3 /2
53, 905 .39")
15
4 7 /2 —> 4 9 /2
5 3 ,9 0 5 .4 2 J
15
4 3 / 2 - 4 4 5 /2
5 3 ,9 2 6 .0 4
15
4 1 / 2 - 4 4 3 /2
53 ,9 0 3 ,'8 l'|
16
4 7 /2 —4 4 9 /2
5 3 ,9 0 4 .0 3 j
C o n fid e n c e lim its on a ll o bserved fre q u e n c ie s
(90% p r o b a b ility l e v e l ) : '+ 0 . -09 Me
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
5 3 ,9 0 5 .4 6
5 3 ,9 2 6 .1 8
5 3 ,9 0 3 .91
26
TABLE 7
C a lc u la te d and O bserved H y p e rfin e C om ponents o f the v = 0 , J
on
T ra n s itio n o f S
K
o
FgBr
££■—“7
1
( D ^ = 0, eQq - 705 M e ,
T ra n s itio n
F— F + 1
= 5 3 ,3 4 6 .3 9 M e )
C a lc u la te d
Frequency (M e)
O bserved
F requency (M e)
The th e o re tic a l com ponents o f th is broad lin e
p ro b a b ly in c lu d e a ll F com ponents fo r K = 0
to 4 . Range: 5 3 ,3 4 5 .5 3 to 5 3 ,3 4 7 .2 8 Me
5 3 ,3 4 6 .5 4
6
4 1 /2 —►4 3 /2
5 3 ,3 4 4 .9 3
5 3 ,3 4 4 .9 8
8
4 5 /2 —> 4 7 /2
5 3 ,3 4 9 .2 0
5 3 ,3 4 9 .2 1
10
4 7 /2 —> 4 9 /2
5 3 ,3 4 2 .2 1
5 3 ,3 4 2 .1 4
13
4 1 /2 —►4 3 /2
5 3 ,3 3 8 .5 4
5 3 ,3 3 8 .5 8
14
4 7 /2 —> 4 9 /2
5 3 ,3 3 8 .4 1
5 3 ,3 3 8 .4 5
15
4 7 /2 —* 4 9 /2
5 3 ,3 3 7 .2 7
5 3 ,3 3 7 .3 1
15
4 1 /2 —* 4 3 /2
5 3 ,3 3 5 .8 6
5 3 ,3 3 5 .9 2
16
4 7 /2 —* 4 9 /2
5 3 ,3 3 6 .0 4
5 3 ,3 3 6 .0 8
16
4 3 /2 —» 4 5 /2
5 3 ,3 5 6 .65
5 3 ,3 5 6 .5 2
17
4 7 /2 —* 4 9 /2
5 3 ,3 3 4 .7 5
5 3 ,3 3 4 .6 7
C o n fid e n c e lim its on a ll o bserved fre q u e n c ie s
(90% p r o b a b ility le v e l) : + 0 ,0 9 Me
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C a lc u la tio n o f D j and U pper L im it o f P jK
The re s o lu tio n o f th e q u a d ru p o le h y p e rfin e s tru c tu re in d ic a te s th a t
th e fre q u e n c y s h if t due to D
JK
is u n d e te c ta b le .
C o n s id e rin g th a t K = 16
is the h ig h e s t K quantum number a s s ig n e d to a n y o b serve d lin e , one ca n
e s tim a te the h ig h e s t lim it fo r the v a lu e o f D
JK
. In o rd er to ca u se a f r e -
q u e n c y s h if t o f 0 . 09 M e (the u n c e rta in ty in fre q u e n c y m easurem ents) fo r
a J = 22, K = 16 lin e , D
JK
w o u ld have to exceed 7 .6 x 10
fo re , in su b seq u e n t c o n s id e ra tio n s , D
The ro ta tio n a l c o n s ta n ts fo r S
32
JK.
—
fi
M e . T h e re -
w i l l be c o n s id e re d z e ro .
F Br
0
79
and S
32
F Br
D
la te d u s in g the r ig id ro to r a p p ro x im a tio n (Equation ( 5 ) ) .
81
w ere e a le u -
The re s u lts
are show n in Table 8 .
TABLE 8
R o ta tio n a l C o n s ta n ts from R ig id Rotor A p p ro x im a tio n
T ra n s itio n
J —+ J + 1
B (M e)
o
S32F « r 79
0
S32F 5B r81
21—» 22
1 1 7 2 .0 8 8 + 0 .0 0 2
1 159.719 + 0 .0 0 2
22—* 23
1 1 7 2 .0 8 2 + 0 .0 0 2
1159 .70 4 + 0 .0 0 2
The s lig h tly la rg e r moment o f in e rtia (s m a lle r Bq ) fo r the h ig h e r J
tr a n s itio n su g ge sts th a t th e re is a m ea sura b le c e n trifu g a l d is to r tio n
e ffe c t governed by th e term D^, in E q u atio n (4 ). A d m itte d ly , th e c a lc u la te d
D j w i l l have a h ig h degree o f u n c e rta in ty s in c e the e ffe c t, e s p e c ia lly
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28
fo r the Br
79
m o d ific a tio n ,, is v e ry s m a ll.
A ssum ing D
= 0, s e ttin g up
J
E q u atio n (4) fo r J = 21 and 22, and re s p e c tiv e u n pe rtu rb e d fre q u e n c ie s ,
one can s o lv e th e s im u lta n e o u s e q u a tio n s fo r B and D _ . R e su lts are
o
J
p re sen te d in Table 9 .
TABLE 9
B and DT fro m S e m i-rig id R otor Treatm ent
o
J
Is o to p ic
M o d ific a tio n
B (M e)
o
DJ
o3 2 n „ 79
S F Br
0
1172.153 + 0 .0 0 2
0 .0 6 7 2 + 0 .0 4 0 0
o 32 F,_Br
d d 81
S
5
1 1 59.875 + 0 .0 0 2
0 .1 6 1 2 + 0 .0 4 0 0
Some ty p ic a l v a lu e s o f
(Kc)
fo r o th e r sym m e tric to p m o le c u le s a re :
C H I , 8 .0 K c [ 9 ] ; F G e C l, 0 .6 Kc [ 1 0 ] ; F C C C H , 0 . 2 4 K c [ l l ] .
0
0
o
C a lc u la tio n o f M o le c u la r D im e n s io n s
One is o to p ic s u b s titu tio n o f an atom is s u ffic ie n t to lo c a te th a t atom
w ith re s p e c t to th e c e n te r o f g r a v ity o f the m o le c u le .
M ic ro w a v e s p e c tro ­
s c o p ic data fo r the tw o brom ine is o to p ic s p e c ie s a llo w s one to c a lc u la te
the d is ta n c e o f th e brom ine atom from the c e n te r o f g r a v ity (r_ ) from the
Br
fo llo w in g e q u a tio n [ l ] :
1 /2
(1^ - E^) (m + A m ^)
rx
mAmv
A
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
(9)
29
w here
r
X
= D is ta n c e o f atom X fro m c e n te r o f g r a v ity
1^
= M om ent o f in e rtia o f is o to p ic m o d ific a tio n
^
= M om ent o f in e rtia o f o rig in a l m o le cu le
m
= T o ta l mass o f o r ig in a l m o le c u le
A m ^= M a ss d iffe re n c e b e tw e e n is o to p ic m o d ific a tio n and
o rig in a l m o le c u le
The moment o f in e rtia is g iv e n by [ 3 ]
5.05531
!b =
w he re 5 .0 5 5 3 1 x 10
5
X 105
B ( M e )'
o
.2
am U - A '
(10)
is a c o m p o s ite c o n s ta n t, in c lu d in g P la n c k 's c o n s ta n t
and c o n v e rs io n fa c to r s .
The moment o f in e rtia o f a sym m e tric to p m o le c u le o f th e typ e
XpYZ . . . Is g iv e n b y [ 1 ]
2
pm s
A A
1 = — j —
and
9
+ pny:
La
+
2 mr
1
La
pmx 1'x + ^ mi r i = ® °
/ *1 1
\
(11)
(12)
The v a lid it y o f the fo llo w in g re la tio n s h ip s ca n be v e r ifie d from
F ig u re 2:
rX = r S + r s - x = r s + r S - F ° OS e
r F = r S + dS-F
s
= d
S in «
w here 0 is the a x ia l F -S -F a n g le .
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
(13)
(14)
(15)
30
—j k —{ Br, \-
1—
S -Br
vl
cm '
_ d / ____
'IL
I
F ig u re 2 .
M o le c u la r D im e n s io n s D e fin e d
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31
There are three in d e p e n d e n t v a r ia b le s , rg , dg p , and Q, b u t o n ly
tw o e q u a tio n s ca n be w r it t e n .
T h e re fo re , one has %o assum e a v a lu e fo r
one o f th e v a ria b le s in o rd er to s o lv e fo r the o th e r t w o .
The F -S -F a n g le in SF^Br is not e xp ecte d to v a ry s ig n ific a h tly from
th e c o rre s p o n d in g a n g le in S F g C l, w h ic h has a v a lu e o f 8 8 °2 2 ' + 10' [ 4 ] .
S in ce th e moment o f in e rtia is le s s s e n s itiv e to changes in th e bond a n g le
th a n i t is to changes in bond le n g th s , th e s tru c tu re w as c a lc u la te d fo r
th re e v a lu e s o f the F -S -F a n g le , 8 8 °3 2 ‘ , 88° 2 2 ', and 88° , a range w h ic h
sh o u ld in c lu d e th e v a lu e o f the F -S -F a n g le o f SF Br w ith h ig h p r o b a b ility .
D
S u b s titu tio n o f E q u atio n s (13) and (14) w ith assum ed v a lu e s fo r Q in to
E q u a tio n (12) y ie ld s an e x p re s s io n fo r d
in r
b
b “T
in term s o f r
b
. The q u a d ra tic
re s u ltin g from the s u b s titu tio n o f the e x p re s s io n fo r d_
and
b -r
E q u atio n s (13), (14), and (15) in to E q u atio n (11) w as s o lv e d , and the
re a s o n a b le s o lu tio n fo r r
b
w as c h o s e n .
The Br-S d is ta n c e (dc
) is s im p ly
b -b r
r c + r „ . R e su lts are p re sen te d in Table 10.
b
br
TABLE 10
S tru c tu ra l Param eters C o n s is te n t w ith O bserved M om ents o f In e rtia
^ F -S -F (a x ia l)
(assumed)
d S~Br ^
dS -F <*>
88®
2 o1902
1 .5 9 7 0
88° 22'
2 o1967
1 .5945
88® 32'
2 .1 9 9 7
1.5936
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32
The lon g S-Br bond su g g e sts th a t the s te ric re p u ls io n e ffe c t in
SF,.Br is g re a te r th a n in S F g C l (see D is c u s s io n ) , and le a d s one to th e
re a s o n a b le c o n c lu s io n th a t the F -S -F a n g le in SF Br is som ew hat s m a lle r
0
th a n th e c o rre s p o n d in g a n g le in SFcC l .
0
For an assum ed a n g le o f 88°
proposed s tru c tu ra l param eters w ith c o n fid e n c e lim its e s tim a te d from
th e u n c e rta in ty in the assum ed a n g le are pre sen te d in Table 11.
TABLE 11
Proposed S tru c tu ra l Param eters o f S F.B r
0
0F -S -F (a x ia l) = 88° (assumed)
d
_ = 2 .1 9 0 2 + 0 .0 0 6 5
"""
d c _ = 1 .5 9 7 0 + 0 .0 0 2 5
b -r
~
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CHAPTER
V
DISCUSSION
R e la tio n s h ip Between Bond D is ta n c e and N atu re o f the C h e m ic a l Bond
I t is in s tr u c tiv e to com pare th e above s tru c tu ra l param eters w ith
v a lu e s fo r co rre sp o n d in g bond d is ta n c e s o b ta in e d from o th e r s o u rc e s .
Table 12 lis t s s e v e ra l S -F bond d is ta n c e s from th e lit e r a t u r e .
The observed d
O“ i
= 1 .5 9 7 is re a s o n a b le in lig h t o f th e o th e r
m easured S -F d is ta n c e s . The v a lu e is c o n s id e ra b ly lo w e r th a n th e sum
o f the s in g le -b o n d c o v a le n t r a d ii fo r s u lfu r and flu o r in e , and a ls o lo w e r
th a n dg ^ c a lc u la te d from th e S chom aker-S tevenson ru le [ 1 2 ] , w h ic h
a tte m p ts to c o rre c t fo r a d e crea se in bond le n g th due to io n ic c h a ra c te r.
Any a d d itio n a l d e crea se in bond le n g th is u s u a lly e x p la in e d by a ssum ing
th a t th e bond has d o u b le -b o n d c h a ra c te r [ 5 ] . In v ie w o f th e s t a b ilit y
o f d o u b le bonds in f ir s t- r o w e le m e n ts such as flu o r in e , th e s h o rt dg p
su g g e sts th a t re so n a n ce form s such as (I) c o n trib u te s ig n ific a n t ly to the
s tru c tu re „
Br
F+
(I)
33
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
34
TABLE 12
Some O bserved and C a lc u la te d S -F Bond D is ta n d e s
M o le c u le
dS -F <*>
M e th o d
R eference
s f 2 02
1 o57 + 0 ,0 1
M ic ro w a v e
[1 3 ]
s° f 2
1 .5 8 5 + 0.0 0 1
M ic ro w a v e
[1 4 ]
nsf3
1 .5 5 2 + 0.003
M ic ro w a v e
[1 5 ]
SF C l
1 .5 7 6 + 0 .0 1
M ic ro wa ve
[4 ]
1 .5 4 5 + 0 .0 0 3
(e q u a to ria l)
and
1 .6 4 6 + 0.003
(p o la r)
1 .56 + 0 .0 2
M ic ro w a v e
[1 6 ]
M ic ro w a v e
[1 6 ]
E. D .*
[1 7 ]
1 .5 6 + 0 .0 2
E. D .
[1 8 ]
1 .5 6 + 0 .0 2
and
1 .5 8 + 0 .03
E. D .
[1 9 ]
E. D o
[2 0 ]
1 .7 6
Sum o f S in g le -b o n d
C o v a le n t R a d ii
[5 ]
S ch o m ake r-S te ve n so n
Rule
[1 2 ]
SF4
S2F 10
S2F 10C>2
SF6
1 .6 4
SF Br
0
*
1 .5 9 7 0 + 0.0025
M ic ro w a v e
T h is In v e s tig a tio n
E le c tro n D iffr a c tio n
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35
O
The S -F d is ta n c e o f SFj.Br is a b o u t 0 .0 2 A lo n g e r th a n th e S-F d is ta n c e
o f S F,_C i. An e x p la n a tio n fo r th is d iffe re n c e in term s o f r e la tiv e io n ic and
d o u b le bond c h a ra c te rs o f th e S -F bonds o f these tw o m o le c u le s is n o t
o b v io u s o Perhaps the apparent d iffe re n c e is o n ly a r e fle c tio n o f the la rg e
u n c e rta in ty in the m easured S-F bond d is ta n c e c re a te d by the som ew hat
ha zardous a s s u m p tio n th a t th e a x ia l and e q u a to ria l S-F d is ta n c e s are e q u a l.
H ig h re s o lu tio n n u cle a r m a g ne tic re so na n ce s p e ctra o f th e -SF
5
group in GFgCF^SF^ re p o rte d by M u lle r [ 2 1 ] show s an e la b o ra te fin e s tru c tu re
in d ic a tin g th a t th e flu o rin e atom s are n o t in e q u iv a le n t p o s itio n s . A re c e n t
h ig h re s o lu tio n NMR s tu d y o f SF OF by G ady and M e r r ill [ 2 2 ] show s th a t
0
one flu o rin e atom in the -SF
fro m the o th e r fo u r .
0
group is d is t in c t ly d iffe r e n t m a g n e tic a lly
H e n c e , m a g ne tic n o n -e q u iv a le n c e im p lie s an e le c tro n
e n v iro n m e n ta l n o n -e q u iv a le n c e o f one o f th e flu o rin e n u c le i, w h ic h fu rth e r
im p lie s a n o n -e q u iv a le n c e o f c h e m ic a l b o n d in g .
I t s h o u ld be noted th a t a ny u n c e rta in ty in the S -F d is ta n c e in h e re n t
in th e a s s u m p tio n th a t d „
J
= d_
^
w i l l a ls o a ffe c t th e
S-F (a x ia l)
S-F (e q u a to ria l)
u n c e rta in ty in d0
be cau se o f th e inte rd e p e n d e n ce o f th e se s tru c tu ra l
o —Br
param eters .
The q u a d ru p ole c o u p lin g c o n s ta n ts fo r one u n b a la n c e d £ e le c tro n fo r
Br
79
and Br
81
are 769 and 643 M e , r e s p e c tiv e ly [ 3 ] .
The la rg e r eQq
o b serve d fo r SF Br in d ic a te s an u n b a la n ce o f s lig h tly more th a n one £
e le c tro n , s u g g e s tin g c o n trib u tin g io n ic form s such as (II) in w h ic h th e
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36
brom ine atom assum es a p a r tia l p o s itiv e c h a rg e .
(See page 6
fo r a d is ­
c u s s io n o f th e s ig n ific a n c e o f e Q q .) On the b a s is o f io n ic c h a ra c te r a
d e crea se in the S-B r bond le n g th is e x p e c te d , w hereas the bond le n g th is
(II)
a b o u t 0 .0 1 A lon g e r th a n p re d ic te d by th e S ch o m ake r-S te ve n so n r u le .
The
le n g th e n in g o f the S - C 1 bond in SF C l r e la tiv e to o th e r m easured S - C l
D
d is ta n c e s , was a ttrib u te d to th e s te ric re p u ls io n b e tw een the C l atom and
the fo u r e q u a to ria l flu o rin e a to m s . T h is v ie w is su p po rte d by th e d ecrease
o f the a n g le F -S -F (a x ia l) from 90° to 88° 22' [ 4 ] . The S-S bond d is ta n c e
o
©
0
o f S0F
is 2 .2 1 A [ 1 7 ] , as com pared to 2 .07 A fo r S [ 2 3 ] , and 1 .9 2 A
Z ID
O
fo r S^ [ 2 4 ] , d e m o n s tra tin g th a t s te ric re p u ls io n c a n r e s u lt in s ig n ific a n t
bond le n g th e n in g .
S im ila r ly , th e lo n g S-Br bond in SF^Br c a n be e x p la in e d .
Any d e cre a se in d c
due to io n ic c h a ra c te r is overshadow ed by th e much
o “ Br
more im p o rta n t s te ric re p u ls io n e ffe c t.
E le c tr o n d if f r a c tio n work of S t e v e n s o n a n d C o o le y [ 2 5 ] g a v e
d
0
= 2 .2 7 + 0 .0 2 A fo r SOBr . A co m p a riso n b e tw ee n S-B r d is ta n c e s fo r
S~Br
2
SOBr_ and SF^Br is n o t m e a n in g fu l be cau se o f the la c k o f s im ila r ity o f the
2
0
tw o m o le c u le s .
U n fo rtu n a te ly , no o th e r e x p e rim e n ta l S-Br bond d is ta n c e s
1
c o u ld be fo u n d in the lit e r a t u r e .
"
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37
Z e ro -P o in t V ib ra tio n E ffe c ts
Even in the ground v ib r a tio n a l s ta te a m o le c u le p o ss e s s e s 1 /2 h i /
o f v ib r a tio n a l e n e rg y, the s o - c a lle d z e ro -p o in t e n e rg y .
The v ib ra tio n a l
a m p litu d e o f an atom changes w ith the m a ss, and the a p pa re n t moments
o f in e rtia depend upon the v ib ra tio n a l, a m p litu d e s „ C o n s e q u e n tly , the
in te rn u c le a r d is ta n c e s in is o to p ic a lly s u b s titu te d m o le c u le s are not
e x a c tly eq ua l and u n c e rta in tie s g re a tly e x c e e d in g th e lim its o f e x p e rim e n ta l
e rro r may be p re se n t in s tru c tu ra l d e te rm in a tio n s w hen th e is o to p ic s u b ­
s titu tio n method is u s e d .
These z e ro -p o in t v ib r a tio n e ffe c ts are re s p o n ­
s ib le fo r the la rg e s t u n c e rta in tie s in s tru c tu ra l param eters c a lc u la te d from
m icro w a ve data [ 2 ] , fre q u e n c ly re s u ltin g in u n c e rta in tie s as h ig h as
0 „01 A [ 1] .
The u n c e rta in ty in a s tru c tu ra l param eter due to the n e g le c t o f z e ro p o in t v ib r a tio n e ffe c ts d e crea se s as th e p e rcentage change in mass o f the
s u b s titu te d is o to p e d e crea se s and as the d is ta n c e o f th e s u b s titu te d
is o to p e from the c e n te r o f g r a v ity o f the m o le c u le in c re a s e s „ These e ffe c ts
are n o t e xp ecte d to ca u se a s e rio u s u n c e rta in ty in the d e te rm in a tio n o f the
d is ta n c e o f the brom ine atom from th e c e n te r o f g ra v ity o f SF^Br be cau se o f
the s m a ll percentage mass change in the s u b s titu tio n o f Br
81
fo r Br
79
and
©
th e r e la t iv e ly la rg e (1 „518 A) d is ta n c e o f th e brom ine atom from th e c e n te r
o f g r a v ity .
In the absence o f d e ta ile d k n o w le d g e o f r o ta tio n a l sp e ctra in
e x c ite d v ib r a tio n a l s ta te s , no a c c u ra te e s tim a te o f th e u n c e rta in ty ca n be
made „
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CHAPTER
VI
CONCLUSIO NS
SFgBr e x h ib its a ro ta tio n a l sp e ctru m c h a ra c te ris tic o f a sym m e tric
to p ro to r w ith n u c le a r q u a d ru p o le in te ra c tio n s . A n a ly s is o f the
and 1^2
^
^ 23 tra n s itio n s leacis 1:0 t ^e c o n c lu s io n th a t the gaseous SF^Br
m o le c u le is o f the m o n o s u b s titu te d (d is to rte d ) o c ta h e d ra l ty p e w ith th e
fo llo w in g d im e n s io n s :
= 88° (assum ed), d 0 _ = 2 =19 02 +
b -B r
r - o - r (a x ia l J
©
o
0 .0 0 6 5 A , d 0 _ = 1 .5 9 7 0 + 0 .0 0 2 5 A . The q u a d ru p o le h y p e rfin e s tru c tu re
o -r
~
79
w as fitt e d to : eQq (Br ) = 800 + 5 M e , D = 0 .0 6 7 2 + 0 „0 4 0 0 K c , and
oo
D
JK-
= 0, fo r S
yq
F Br
t>
q 1
; and eQq (Br
q o
+ 0 .0 4 0 0 K c , D
JK
= 0, fo r S
) = 705 + 5 M e , DT = 0 .1 6 1 2
J
q i
F Br
5
. C o n s id e ra tio n o f d
o -B r
and
eQq(Br) su g ge sts a " s tre tc h e d " S -B r bond o f p re d o m in a n tly c o v a le n t
c h a ra c te r w ith some io n ic c o n trib u tio n from re so na n ce in v o lv in g a p a rtia l
p o s itiv e ch arge on th e brom ine a to m .
C o n s id e ra tio n o f d_, _ su g g e sts th a t
o -r
th e S-F bond is a re so na n ce h y b rid w ith im p o rta n t c o n trib u tio n s from d o u b le
b o n d c o v a le n t, and io n ic fo rm s .
38
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INFRARED SPECTRUM OF ARSENIC PENTAFLUORIDE
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40
In fra re d Spectrum o f A s F ,.
M itr a [ 2 6 ] re p o rte d th e is o la tio n o f A sF ^O , some o f its p h y s ic a l
and c h e m ic a l p ro p e rtie s , and th e in fra re d s p e ctra o f AsF^O and AsFg
o b ta in e d u s in g a P yrex c e ll w ith N a C l w in d o w s . The IR sp e ctru m o f
AsFgO showed strong bands a t 7 04 and 811 cm * w h ic h he a ttrib u te d to
th e A s -F and A s -O s tre tc h , r e s p e c tiv e ly .
e x h ib ite d o n ly the 704 cm
-1
The re p o rte d AsF
band in th e 1 400-650 cm
-1
O
spectrum
r e g io n .
In c o n n e c tio n w ith a tte m p ts to prepare and is o la te A sF ^O , th e IR
sp e ctru m o f gaseous AsF
0
w as r e - in v e s tig a te d on a Beckm an IR -4
sp e ctro p h o to m e tb E u s in g 10 cm Pyrex c e lls w ith N a C l and KBr w in d o w s .
A fte r the c e ll w in d o w s w ere p o lis h e d to e lim in a te a ll w in d o w b a n d s,
c o m m e rc ia l* AsF
0
w as a d m itte d to 10 mm Hg p re ssure and fo u r scans
w ere ta k e n a t 10 m inu te in te rv a ls o ver th e 1 4 00-650 cm ^ r e g io n .
The
o b s e rv a tio n s are as fo llo w s :
The 7 04 cm
-1
band appeared o n ly m o d e ra te ly in te n s e in the f ir s t
s c a n , b u t in c re a s e d in in te n s ity w ith tim e .
1
-1
A w eak band a t 738 cm
in c re a s e d in in te n s ity w ith tim e .
The in te n s ity
o f the stro n g bands a t 784 and 811 cm
-1
decreased
w ith t im e .
The in te n s ity o f th e w ea k S iF^ band a t 103 0 cm ^ in c re a s e d w ith
tim e .
A fte r the c e ll was e v a c u a te d , the band a t 704 cm
-1
p e rs is te d
w ith an in te n s ity a p p ro x im a te ly equal to th a t show n by th e la s t scan o f
th e g a s -c o n ta in in g c e ll (Figure 3 ).
*A sF 5 sam ple fu rn is h e d g ra tis b y O z a rk -M a h o n in g C o . , T u ls a , O k la h o m a .
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Wavelength (Cm -i)
1500
1400
1300
1200
1100
1000
900
800
700
80 '
■
■60
;30
SiF 4
CONDITIONS:
Pressure: 10.mm Hg
Cell Windows: NaCl
Cell Length: 10 Cm
Wavelength (Microns)
Figure 3. Infrared Spectrum of Arsenic Pentafluoride
(Window Band)
650
42
Id e n tic a l re s u lts w ere o b ta in e d w ith N a C l and KBr w in d o w s .
These o b s e rv a tio n s d e m on stra te th a t gaseous AsF^ re a c ts w ith N a C l
and KBr to produce a n o n - v o la tile com pound w h ic h ab sorb s s tro n g ly a t
704 cm
cm
-1
-1
o PF
0
a ls o w as show n to produce w in d o w bands a t a b o u t 720
. E x te n s iv e e ffo rts to id e n tify th is com pound w ere not made . Sodium
h e x a flu o ro a rs e n a te and sodium flu o rid e w ere e lim in a te d b ecause o f an
ab sen ce o f a b s o rp tio n bands in the re g io n s tu d ie d .
I t is a p pa re n t th a t the IR s p e ctra w h ic h M itra la b e le d AsF^O and
A s F . a re , in fa c t, th e IR s p e ctra o f A sF _ , and a re a c tio n p ro d u c t o f
b
b
AsF
0
and N a C l, r e s p e c tiv e ly .
A tte m p ted P re p a ra tio n o f AsF^O
Num erous a tte m p ts w ere made to prepare AsF^O by d ir e c t f lu o r in a tio n o f an e q u i-m o la r m ix tu re o f A s C l^ and g la s s y As^O^ a c c o rd in g
to th e procedure d e s c rib e d by M i t r a . The p ro d u c t m ix tu re w as fra c tio n a te d
by a co p p e r c o - d is t illa t io n c o lu m n in a gas chro m a tog ra p h [ 2 7 ] .
C 1 „ , AsF , A sF . and SiF
2
5
3
4
O n ly
fra c tio n s w ere is o la te d as show n by m o le -
c u la r w e ig h t d e te rm in a tio n s and IR a n a ly s e s .
O th e r runs w ere made in w h ic h th e re p o rte d p rocedure w as m o d ifie d
b y v a ry in g the te m perature and m olar r a tio o f re a c ta n ts . A d e te c ta b le
q u a n tity o f AsF^O c o u ld n o t be is o la te d .
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APPENDICES
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APPENDIX 1
TABLE 13
V alues o f 3K2/T (J + 1) - 1 = X (J ,K )
K
x ( r , K)
K
X (T , K)
J = 23
J = 22
J = 23
0
-1
-1
12
-0 .1 4 6 2 5
-0 .2 1 7 3 9
1
-0 .9 9 4 0 7
-0 .9 9 4 5 7
13
0 .0 0 1 98
-0 .0 8 1 5 2
2
-0.97628
-0.97826
14
0 .1 6 2 06
0 .0 6 5 2 2
3
-0 .9 4 6 6 4
-0 .9 5 1 0 9
15
0 .3 3 3 99
0.22283
4
-0 .9 0 5 1 4
-0 .9 1 3 0 4
16
0 .5 1 7 79
0 .3 9 1 3 0
5
-0 .8 5 1 7 8
-0 .8 6 4 1 3
17
0 .7 1 3 44
0.5 7 0 65
6
-0 .7 8 6 5 6
-0 .8 0 4 3 5
18
0 .9 2 0 95
0.7 6 0 87
7
-0 .7 0 9 4 9
-0 .7 3 3 7 0
19
1.14031
0.96196
8
-0 .6 2 0 5 5
-0 .6 5 2 1 7
20
1.3 7 1 54
1.17391
9
-0 .5 1 9 7 6
-0 .5 5 9 7 8
21
1 .6 1 4 62
1 .3 9 6 74
10
-0 .4 0 7 1 2
-0 .4 5 6 5 2
22
1 .8 6 9 56
1 .63 043
11
-0 .2 8 2 6 1
-0 .3 4 2 3 9
23
J = 22
1 .8 7 5 0 0
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45
APPENDIX 2
TABLE 14
V alues Qf 3 / 4C_XC,+.,1.I,_~_L( I + .1)I ( J + 1? = Y (F) fo r , , 3 /2
V alues o f
2 (2 J + 3 )( 2J - 1) I (21 - 1)
Y (F) fo r I
3 /2
I
F
Y (F)
21
4 5 /2
0.116666
4 3 /2
-0 .1 3 3 3 3 3
4 1 /2
-0 .1 1 5 8 5 4
3 9 /2
0 .134146
4 7 /2
0.117021
4 5 /2
-0 .1 3 2 9 7 9
4 3 /2
-0 .1 1 6 2 7 9
4 1 /2
0.133721
4 9 /2
0.1 1 7 34 7
4 7 /2
-0 .1 3 2 6 5 3
4 5 /2
-0 .1 1 6 6 6 6
4 3 /2
0.133333
22
23
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46
APPENDIX 3
TABLE 15
V alues o f P h y s ic a l C o n s ta n ts and A tom ic M a sse s
U sed in C a lc u la tio n s [ 3 , 2 8 ]
m(Br
m(Br
79
)
= 78 .94365 a .m .u .
O1
)
= 8 0 .9 4 2 3 2
a .m .u .
no
m(S
m(F
19
)
= 3 1 .9 8 2 2 4 a . m . u .
)
= 19 .00446 a .m . u .
P la n c k 's co n sta n t;, h , == 6 .6 2 5 1 7 + 0.0 0 0 23 x 10
O
B x L = h /8 n
o
b
-27
C
= 5 .0 5 5 3 1 + 0.0003 0 x 10
—
e rg -s e c
^2
M c -a .m .u . -A
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REFERENCES
1.
W a lte r G o rd y , W . V . S m ith , and R . F . T ra m b a ru lo , M ic ro w a v e
S p e c tro s c o p y , John W ile y and S o n s , I n c , , N ew Y o rk , N ew York (1 9 53 ).
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
48
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S o c ie ty , 62, 247 7 (1 9 40 ).
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25, 691 (1953)»
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T h is d is s e r ta tio n w a s ty p e d and p rin te d
at
B I-C IT Y , IN C .
1001 S . C o lle g e Ave .
B ryan, Texas
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