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THE MICROWAVE SPECTRA OF SULPHUR DICHLORIDE, DICHLOROSILANE AND PROPIOLYL CHLORIDE

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♦
THE MICROWAVE SPECTRA OF SULPHUR DICHLORIDE,
DICHLOROSILANE AND PROPIOLYL CHLORIDE
by
R ober t W e l l i n g t o n D a v i s
B.Sc.,
Memorial
U n i v e r s i t y o f N e w f ou n d l an d ,
1973
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
in
THE FACULTY OF GRADUATE STUDIES
( D e pa rt m e n t o f C h e m i s t r y )
We a c c e p t t h i s
required
t h e s i s as c o nf or mi ng t o t he
standard
THE UNIVERSITY .OF BRITISH COLUMBIA
December
©
Robert
1980
W e llin g to n
D a v is ,
1980
In presenting this thesis
in partial fulfilment of the
requirements for an advanced degree at the University
of British Columbia,
I agree that the Library shall make
it freely available for reference and study.
I further
agree that permission for extensive copying of this thesis
for scholarly purposes may be granted by the head of my
department or.by his or her representatives.
,
It is
understood that copying or publication of this thesis
for financial gain shall not be allowed without my written
permission.
Department of
t
The University of British Columbia
2075 Wesbrook Place
Vancouver, Canada
V6T 1W5
Date
ABSTRACT
The mi crowave s p e c t r a and s t r u c t u r e s o f
been i n v e s t i g a t e d ;
t hese a r e :
sulphur d i c h l o r i d e
t h r e e m o l e c u l e s have
(SC19 ) ,
(SiH^Cl^)
and p r o p i o l y l
chloride
( H-C C-COC1 ) .
32 35
S Cl^ i n t h e ground and
S u lp h ur D i c h l o r i d e : The mi crowave s p e c t r a o f
v2
dichlorosilane
C
*
= 1 excited
state
vibrational
states,
have been, measured i n
and o f
t h e 12 -
32 35
37
S Cl
Cl
i n t he ground
40'GHz f r e q u e n c y r e g i o n .
o f t he ground s t a t e s p e c i e s have been an a ly se d t o y i e l d
rotational
a partial
tional
constants,
t he q u a r t i c c e n t r i f u g a l
set o f s e x tic c e n t r i f u g a l
constants
values f o r
d isto rtio n
d is t o r t io n constants.
have been o b t a i n e d
The s p e c t r a
the
c o n s t a n t s and
Precise r o t a ­
f o r t h e v^ = 1 e x c i t e d s t a t e o f
32 35
S C l ^ * A c omp let e s e t o f harmonic f o r c e c o n s t a n t s has been d e t e r m i n e d
from t he q u a r t i c
the i n e r t i a l
vibrational
centrifugal
d i s t o r t i o n c o n s t a n t s and t h e v a r i a t i o n
d e fe c t with v ib r a t io n a l
state.
of
The wavenumbers o f t he t h r e e
f u n d am e n t al s o f ' s u l p h u r d i c h l o r i d e have been p r e d i c t e d ,
and
a r e in e x c e l l e n t agreement w i t h t he observed v a l u e s . An e f f e c t i v e and a
p artial
su b s titu tio n s tru c tu re for
from t he ground s t a t e
rotational
s u l p h u r d i c h l o r i d e have been e v a l u a t e d
constants.
The harmonic f o r c e c o n s t a n t s
have been used t o o b t a i n t h e a v e r ag e s t r u c t u r e s
and v^ = 1 s t a t e s .
of
32 35
S C l ^ i n the ground
The ground s t a t e av e ra g e s t r u c t u r a l
p ar a me t e r s o f
32 c 35r ,
S C1^ . a r e :
r
(S-Cl)
= 2.01525 + 0.00008 A
The e q u i l i b r i u m
and
< ( C l - S - C l ) = 102.730 + 0.005°
s t r u c t u r e o f s u l p h u r d i c h l o r i d e has a l s o been e s t i m a t e d .
D i c h l o r o s i l a n e : The microwave s p e c t r a o f ^ S i H ^ C l ^ ,
29
SiHg
35
C l2
have been measured i n t h e 8 - 4 0
2®SiH 2 ^5Cl^^Cl
GHz f r e q u e n c y r a n g e .
The
and
s p e c t r a have been a n a l y se d t o y i e l d
quartic c e n trifu g a l
d isto rtio n
coupling c o n s ta n ts ,
as w e l l
Debye.
f o r t he r o t a t i o n a l
c o n s t a n t s and c h l o r i n e
quartic c e n trifu g a l
ing v i b r a t i o n a l
values
have been o b t a i n e d
f o r t he r o t a t i o n a l
d i s t o r t i o n constants
1.129 + 0.0 2 0
Effective
and
fo r d ichlorosilane
constants.
Further,
t he
have been combined w i t h , e x i s t ­
d a t a to d e t e r m i n e a harmonic f o r c e f i e l d
has been used t o d e r i v e
constants,
n u c l e a r q u ad r u p o l e
as the m o l e c u l a r d i p o l e moment,
structures
usi ng t h e e x p e r i m e n t a l
(
«
The m o l e c u l e has been shown t o have C^v symmetry.
partial' su b stitu tio n
of
values
which,
t h e ground s t a t e av er ag e s t r u c t u r a l
in t u r n ,
p ar a me t e r s
28c . u 3 5 . ,
T,
SiH^ C1^ - These a r e : .
r z (S i-C l)
= 2.0352 + 0 .0 0 0 3 A
,
< ( C l - S i - C l ) = 109.68 + 0.03°
r
= 1.4726 + 0 .0025 A
,
< (H-Si-H)
(Si-H)
the e q u i l i b r i u m
Propiolyl
s t r u c t u r e o f d i c h l o r o s i l a n e has a l s o been e s t i m a t e d .
C h l o r i d e : The mi cr owave s p e c t r a o f HCC CO ^C l,
DCCCO^Cl and DCCCO^Cl
f o r DCCC0
= 1 1 2 .4 4 + 0 .2 8 °
37
C l,
have been measured i n , t h e ground and,
t he v^ = 1 v i b r a t i o n a l
values f o r the r o t a t i o n a l
t a n t s and c h l o r i n e
HCCCO^Cly
constants,
states.
quartic
The s p e c t r a
centrifugal
n u c l e a r q u ad r u p o l e c o u p l i n g c o n s t a n t s ,
e x ce pt
have y i e l d e d
distortion
as w e l l
cons­
as t he
m o l e c u l a r d i p o l e moment, 2 . 7 1 7 +_ 0-.035 Debye. The q u a r t i c c e n t r i f u g a l
d i s t o r t i o n c o n s t a n t s have been combined w i t h e x i s t i n g
t o d e t e r m i n e an a pp r o x i m a t e harmonic f o r c e f i e l d .
reasonable s t r u c t u r e fo r
the ethynyl
group,
vibrational
Havi ng assumed a
t h e f o r c e f i e l d was used
to o b t a i n t h e , g r o u n d s t a t e a v e r a g e s t r u c t u r e o f p r o p i o l y l
These r e s u l t s
su g g es t t h a t t h e carbon c h a i n
d e v i a t i o n from l i n e a r i t y o f
less
dat a
in p r o p io ly l
than one d e gr e e .
chloride.
c h l o r i d e has a
iv
TABLE OF CONTENTS
CHAPTER
•
PAGE
*
1.
INTRODUCTION
............................................................................ ...................................*.
1.1,
Energy Le ve ls
o f t he Asymmetric Ro to r
.
. » > .......................
1.2
N u c l e a r Quadrupole C o u p l i n g
1.3
The Asymmetric Rot or S t a r k E f f e c t
1.4
M olecular S tru c tu re s
1.5
C e n t r i f u g a l D i s t o r t i o n C o n st a nt s and t h e Harmonic
For ce F i e l d .................................................................................................. 23
.....................................
. . . . .
Spectra
*14
. . . . . .
16
B i b l i o g r a p h y ..................................................................
2.
2.2
‘ 3.
25
EXPERIMENTAL M E T H O D S .............................................................................. ' .
2.1
The Mi crowave S p e c t r o m e t e r
3
10
.......................
from R o t a t i o n a l
1
.
28
.............................................................
29
............................................... ....
. 32
The Microwave S t a r k C e l l s
.
2.3
Dipo le , Mo men t Measurements
....................................................................32
2.4
O r i g i n o f Samples and Running C o n d i t i o n s
............................
Bibl i o g r a p h y
. •............................... 36
THE MICROWAVE SPECTRUM OF SULPHUR DICHLORIDE
..................................
37
...............................................
40
3.1
Observed Spectrum and Assignment
3.2
A n a l y s i s o f t h e Sul phur D i c h l o r i d e S p e c t r a
3.3
The Harmonic P o t e n t i a l
3.4
The M o l e c u l a r S t r u c t u r e o f Su l ph u r D i c h l o r i d e
3.5
Comments on t h e Sul phur D i c h l o r i d e P o t e n t i a l
3.6
Comments on t h e M o l e c u l a r S t r u c t u r e o f Su l p h ur
D i c h l o r i d e ..................................................................
Bibliography
.
33
.......................
47
F u n c t i o n o f Su l p h u r D i c h l o r i d e .
60
...................
• i
Function .
^3
81
91
.............................................................................................95
•*
4
V
TABLE OF CONTENTS
*
CHAPTER
4.
PAGE
ThjE MICROWAVE SPECTRUM OF D I C H L O R O S I L A N E
Assignment o f t he D i c h l o r o s i l a t t e S p e c t r u m .........................100
4.2
A n a l y s i s o f the D i c h l o r o s i l a n e Spectrum .................................
102
4.3
The D i p o l e Moment o f D i c h l o r o s i l a n e
119
4.4
The E f f e c t i v e and S u b s t i t u t i o n S t r u c t u r e s o f
D i c h l o r o s i l a n e ........................................................................................... 124
■4.5
The Harmonic Force F i eT d o f D i c h l o r o s i l a n e
..........................................
......................-.
132
4.6
The Av er ag e S t r u c t u r e o f D i c h l o r o s i l a n e ..............................139
4.7
The E q u i l i b r i u m S t r u c t u r e o f D i c h l o r o s i l a n e
4.8
Comments on t he S t r u c t u r e and For ce F i e l d of-..
Dichlorosilane
. • ................................................................................... 143
..........................
143
................................................................................................
THE MICROWAVE SPECTRUM OF PROPIOLYL CHLORIDE
150
. . . . . . . .
152
5.1
Assignment o f t he S p e c t r a ............................................................... 155
5.2
D e t e r m i n a t i o n o f t h e R o t a t i o n a l C on s t a n t s and (|
C e n t r i f u g a l D i s t o r t i o n Constants
. . . . . . . . . . .
5.3
N u c l e a r Quadrupole C o u pl i ng i n P r o p i o l y l
Chloride .
5.4
The D i p o l e Moment o f P r o p i o l y l
.
5.5
The E f f e c t i v e S t r u c t u r e o f P r o p i o l y l
5.6
The Harmonic Force F i e l d o f P r o p i o l y l
5.7
The Ave r ag e S t r u c t u r e o f P r o p i o l y l
5.8
Comments on t he S t r u c t u r e o f P r o p i o l y l
Bi b! i o g r a p h y ........................ :
I
99
4. 1
Bibliography
5.
’ . .
Chloride
.
Chloride
.
173
.....................
179
.
„
.
.
157
.
Chloride . . . .
Chloride
............................
..........................
Chloride. . . .
. 191
195
206
209
212
vi
TABLE OF CONTENTS
APPENDIX
PAGE
/
1.
A R e p r i n t o f a R e p o r t o f t h e Mi crowave Spectrum o f
P r o p i o l y l F l u o r i d e ...................................... .... ..
..................................... . 2 1 5
2.
A R e p r i n t o f a R e p o r t o f t h e Micr owave Spectrum o f
P r o p i o l i c A c i d .........................................................
3.
A R e p r i n t o f a R e p o r t o f t h e Micr owave Spectrum o f
Formic A c i d ....................................................
225
232
11
4.
5.
A R e p r i n t o f a R e p or t o f t h e Mi crowave Spectrum o f
P y r r o l e - 2 - c a r b o n i t r i l e .........................................................
250
A R e p r i n t o f a R e p o r t o f t h e Microwave Spectrum o f
D i f l u o r o s i l a n e ......................................................................................................... 256
•
•
!>
vi i
L I S T OF TABLES
TABLE
3.1
PAGE
Examples o f H y p e r f i n e S t r u c t u r e
in T r a n s i t io n s
of
3 2 S35C137C 1 ............................
3.2
44
R o t a t i o n a l C o ns t a nt s and C e n t r i f u g a l D i s t o r t i o n C o nst an ts
o f Sul phur D i c h l o r i d e ...................................................................
49
3.3
Observed R o t a t i o n a l T r a n s i t i o n s ■(MHz) o f S u lp h ur
. D i c h l o r i d e .....................................................................................................................51
3.4
R e l a t i o n s h i p s Between Q u a r t i c C e n t r i f u g a l D i s t o r t i o n
C o n s t a n t s ................................................................................................................ 62.
3.5"
A l t e r n a t e ‘Ground S t a t e M o l e c u l a r C on s t a n t s o f 3^S3 ^C 1 ^
3.6
V a l ue s o f W a t so n' s Q u a r t i c P l a n a r i t y Sum f o r 3^S3^C12
3.7
Rotational
of
3.8
3.9
C o n st a nt s and C e n t r i f u g a l
3.11
3.12
3.13
3.14
65.
• •
66
D i s t o r t i o n C o ns t an ts
3^S3 ^C 1^ Obta'ined f r om V a r i o u s F i t s ...........................................
68
Q u a d r a t i c P o t e n t i a l C o n s t a n t s , V i b r a t i o n a l Fundamentals and
C o r i o l i s C o u p l i n g C o ns t an t s o f S u l ph u r D i c h l o r i d e
71
Principal
Moments o f
In ertia
and I n e r t i a l
°2
(uA )
V a r i o u s Su l p h u r D i c h l o r i d e Sp ec i es
3.10
•
• •
E ffective,
P artial
Defects of
. ( ............................
S u b s t i t u t i o n and Aver ag e S t r u c t u r e s
74
for
The E q u i l i b r i u m Bond Lengths i n Su l ph ur D i c h l o r i d e and
R e l a t e d M o l e c u l e s ................................................................................................
79
Summary o f P r e s e n t and P r e v i o u s Su l ph ur D i c h l o r i d e
P o t e n t i a l F u n c t i o n s and R e l a t e d E x p e r i m e n t a l Dat a ....................
83
Observed and C a l c u l a t e d I s o t o p e S h i f t s f o r t he S t r e t c h i n g
Fundamentals o f Su l p h u r D i c h l o r i d e .....................................................
89
The S-Cl
Bond Lengths and x ^ f ^ C l )
D i c h l o r i d e and R e l a t e d * M o l e c u l e s
.
V al ue s f o r Sul phur
...................................................... 92
r
vi i i
L I S T OF TABLES
TABLE
3.15
4.1
4.2
PAGE
S
E s t i m a t e d S t r e t c h i n g Force C o nst an t s o f Some S u l p h u r
C h l o r i n e Bonds
. . ....................................................................................................94
*
C h l o r i n e N u c l e a r Quadrupole C o u p l i ng C on s ta nt s (MHz) o f
Dichlorosilane
..................................................................................................... 104
Some R e p r e s e n t a t i v e T r a n s i t i o n s
(MHz) o f ^ S ^ ^ C ^
Showing N u c l e a r Quadrupol e H y p e r f i n e S t r u c t u r e
Transitions
........................
4.3
Observed R o t a t i o n a l
4.4
R o t a t i o n a l C o n st an ts and C e n t r i f u g a l D i s t o r t i e n C o n s t a n t s
o f D i c h l o r o s i l a n e ................................................................ •.................................. 117
4.5
Stark S h i f t s
4.6
Stark C o e f f i c i e n t s
4.7
In ertial
4.8
The E f f e c t i v e
4.9
S u b s t it u t io n Coordinates o f D i c h lo r o s ila n e :
4.10
The S u b s t i t u t i o n . S t r u c t u r e o f D i c h l o r o s i l a n e
4.11
in D ic h lo r o s ila n e :
(MHz) o f D i c h l o r o s i l a n e
of D ichlorosilane:
Par ame te rs o f D i c h l o r o s i l a n e
^ S iH ^ C l^
4.15
4.16
. . . . .
................................................
123
126
S t r u c t u r e o f D i c h l o r o s i l a n e * ..........................................127
°
(A)
130
............................
131
I n t e r n a l C o o r d i n a t e s and Symmetry C o o r d i n a t e s o f
-—
D ichlorosilane
.....................................................................................................
133
4 . 1 2 "The Harmonic For ce F i e l d o f D i c h l o r o s i l a n e
4.14
. 110
^ S i H ^ ^ ^ C l ^ ..................................... 121
\
4.13
.
106
TR
S i C l ^
...................................
’136
Observed and C a l c u l a t e d V i b r a t i o n a l Wavenumbers (cm- ^) of
D i c h l o r o s i l a n e ............................................................................
137
Observed and C a l c u l a t e d C e n t r i f u g a l D i s t o r t i o n C o ns t a nt s
( kHz) o f D i c h l o r o s i l a n e ....................................................
138
Par ame t e rs D e s c r i b i n g t he I s o t o p i c V a r i a t i o n i n t h e
Average Bond Lengths o f D i c h l o r o s i l a n e
...........................................
140
Average R o t a t i o n a l
C o ns ta n ts o f D i c h l o r o s i l a n e and Average
S t r u c t u r e o f ^ S i H ^ C l ^ .................................................................................142
1
ix
L I S T OF TABLES
TABLE
'•
'
PAGE
*
4.17
The E q u i l i b r i u m S t r u c t u r e o f D i c h l o r o s i l a n e
4.18
A Comparison o f t h e D e r i v e d S t r u c t u r e s «f< D i c h l o r o s i l a n e
4.19
A Comparison o f Bond Lengths and S t r e t c h i n g F o rc e C o ns t an ts
i n t h e F l u o r o s i l a n e s and C h l o r o s ^ l a n e s ............................................... 148
5.1
Observed R o t a t i o n a l
5.2
R o t a t i o n a l C o n st a nt s and C e n t r i f u g a l D i s t o r t i o n Con st an t s
o f P r o p i o l y l C h l o r i d e .......................................................................
169
R e p r e s e n t a t i v e P r o p i o l y l C h l o r i d e T r a n s i t i o n s (MHz) used
in t h e N u c l e a r Quadrupol e C o u p l i ng Ana l ys es . . . . . . . . . .
175
5.3
Transitions
..................................
(MHz) o f P r o p i o l y l
144
. 146
Chloride
159
■<r
5.4
C h l o r i n e N u c l e a r Quadrupol e C o u p l i n g C on s t a n t s o f PropioTy.l
C h l o r i d e .......................................................................
5.5
Stark S h ifts
5.6
Cell
_ 5.7
i n Car bonyl
Sulphide:
C a l i b r a t i o n w i t h Carbonyl
Stark S h ifts
in P r o p io ly l
160 12C32 S
Sulphide:
Chloride:
of Propiolyl
...
.
...
^ 0 ^ 2C32 S
.
.
HCCC03^CT
. 184
.
.1 8 5
.............................
HCCC03^C1
186
5.8
Stark C o e ffic ie n ts
5.9
The D i p o l e Moment o f P r o p i o l y l
5.10
Ground S t a t e
5.11
The E f f e c t i v e S t r u c t u r e o f P r o p i o l y l
5.12
I n t e r n a l C o o r d i n a t e s and Symmetry C o o r d i n a t e s o f P r o p i o l y l
C h l o r i d e ......................................................................................................................... 196
In e rtia l
Chloride:
.
178
C h l o r i d e ......................................
P a ra me t e r s o f P r o p i o l y l
'
. . . .
Chloride
Chloride
189
.1 9 0
.
. 192
.............................
i
194
f
5.13
The Harmonic Force F i e l d ' o f P r o p i o l y l
Chloride
..........................' 1 9 8
5.14
Observed and C a l c u l a t e d V i b r a t i o n a l Wavenumbers (cm” ^) o f
Propiolyl Chloride
. .
.................................................................................201
5.15
Observed and C a l c u l a t e d C e n t r i f u g a l D i s t o r t i o n Const ant s
( kHz ) o f P r o p i o l y l C h l o r i d e ............................................................................203
5.16
Observed and C a l c u l a t e d
Propiolyl C h l o r i d e
On
In e rtia l
Defects
(uA ) o f
. 205
X
L I S T OF TABLES
TABLE
,
. PAGE
•
.
4
5.17
Ground S t a t e Ay^r age R o t a t i o n a l C on s t a n t s (MHz) o f
P r o p i o l y l C h l o t f d e ........................ . . . . . . . . . ........................... 207
5.18
The Ave r ag e S t r u c t u r e o f P r o p i o l y l
5.19
The S t r u c t u r e s o f P r o p i o l y l
Chloride
..................................
208
C h l o r i d e and R e l a t e d M o l e c u l e s .
211
♦
xi
H
L I S T OF FIGURES
•
%
.FIGURE
PAGE
3.1
The K
4^1
An Example o f N u c l e a r Quadrupole Hyper^fine S t r u c t u r e i n
t h e Spectrum o f D i c h l o r o s i l a n e ...............................................................
a
= 2 •*- 1 Q-Branch T r a n s i t i o n s o f S C I 0
c
r
1
’
.................................... 46
108
'
xi i
ACKNOWLEDGEMENTS
The i n v e s t i g a t i o n s
under t h e d i r e c t i o n
Col umbi a.
I would l i k e
stim ulating
f o r h is
o f Dr.
described
M.C.L.
t h e s i s were c a r r i e d o ut
Gerry a t the U n i v e r s i t y o f B r i t i s h
i n t r o d u c t i o n to t h e t f i e l d
Ger r y f o r p r o v i d i n g a
d f M o l e c u l a r Sp ec t r o s co p y and
i n v a l u a b l e a s s i s t a n c e and encouragement .
As w e l l ,
I further
for specific
E lectronics
i n many ways
U . B . C . an e n j o y a b l e one.
e xt en d my thanks t o s e v e r a l
contributions
t o t h i s wo r k.
c o l l e a g u e s a t U . B . C.
The C h e m i s t r y Department
Shop and e s p e c i a l l y Zol Germann a r e acknowledged f o r t h e i r
patient e ffo rts
Green and D r .
vibrational
I would l i k e
Gerr y f o r a l l o w i n g me c o n s i d e r a b l e
i n t h e c h o i c e o f r e s e a r c h t o p i c s and f o r h e l p i n g
t o make my s t a y a t
Ijn e
this
v er y much- to t h a nk D r .
t o ex p r ess my g r a t i t u d e t o D r .
la titu d e
in
in
A.G.
taming a somewhat r e c a l c i t r a n t a p p a r a t u s .
Robiette afforded
problems and Gary L i t t l e
Dr .
R.
i l l u m i n a t i n g discussions of
p r o v i d e d an asymme tr ic top
s t r e n g t h program.
F in ally,
I am d e e p l y g r a t e f u l
t o my p a r e n t s
which t h ey have g i v e n me t h r o u g h o u t m y * s t u d i e s .
f o r the s u p p o r t
I n no small measure
t h e y a r e r e s p o n s i b l e f o r any successes which I m i g h t h a v e . a c h i e v e d .
Chapter 1
Introduction
The microwave r e g i o n o f t h e e l e c t r o m a g n e t i c spect rum l i e s
between t h e r a d i o r e g i o n and t h e f a r
infrared,
encompassing a f r e q u e n c y
range o f r o u g h l y 1 - 1 0 0 0 GHz. A cc o r d i n g t o t h e w a ve l e ng t h o f t h e r a d i a ­
tion
this
region
is f u r t h e r d iv id e d
s u b m i l l i m e t e r r an g e s .
Spectroscopic
c
i n t o t h e c e n t i m e t e r , ' mi 1 1 i m e t e r and
investigations,
t ho ug h,
have l a r g e l y -
been c o n f i n e d t o f r e q u e n c i e s below 40 GHz, because microwave hardware
becomes i n c r e a s i n g l y s o p h i s t i c a t e d and c o s t l y a t s h o r t e r w a v e l e n g t h s .
Al t h o u g h a v a r i e t y o f a t om ic and m o l e c u l a r phenomena can g i v e
rise
to microwave s p e c t r a , t h e s t u d i e s made a t t he se f r e q u e n c i e s have
al m o st e x c l u s i v e l y been o f t r a n s i t i o n s
between m o l e c u l a r s t a t e s
having
*
d ifferen t
rotational
energies.
This
is
t r u e t o such an e x t e n t
terms Microwave S p e ct r osc o p y and R o t a t i o n a l
v irtu a lly
synonymous.
In
spite of th is
ground v i b r a t i o n a l
state
low r e s o l u t i o n g r a t i n g
in a r u b b e r bag.
in terest
l ed t o t he
*
i n s t r u m e n t a t i o n used i n modern s p e c t r o ­
Since molecular r o t a t i o n
f o r t h e gas phase.
i n v o l v e d a s t ud y o f t he
s p e c t r d g r a p h and an ammonia gas sample c o n t a i n e d
Subsequently,
is usually.quenched
(1),
observed microwave
i n v e r s i o n spectrum o f ammonia. They used a
development o f t h e e l e c t r o n i c
meters.
Spect r oscopy have come t o be
the f i r s t
sp ect rum, o b t a i n e d by C l e e t o n and W i l l i a m s
t h a t t he
in solids
i n r a d a r t ec h n o l o g y
is t o t a l l y
randomized i n l i q u i d s
pu re r o t a t i o n a l
and
spectra are studied only
Very low gas p r e s s u r e s a r e used t o o b t a i n maximum
r e s o l u t i o n and measurement a c c u r a c y .
ex amp le ,
it
is o f t e n
possible
At a p r e s s u r e o f O.b Pa,
to r e s o l v e
lines
separated
0 . 5 MHz and t o measure them w i t h an a c c ur a c y o f b e t t e r
for
by l ess
t han
t ha n 50 kHz.
At
t h e f r e q u e n c i e s o f the p r e s e n t st ud y t h i s c or r es po nd s t o a measurement
p r e c i s i o n o f about 1 p a r t
in
10^.
%
Modern microwave t e c h n i q u e s ena-ble a t
be seen f o r a l m o s t a l l
m o l e c u l e s which e x h i b i t
Exceptions are the f i r s t
This
l a t t e r molecule,
mi crowave r e g i o n ,
in itia l
it
spectra.
however , does have a A - d o u b l i n g spect rum i n t he
firs t
seen by Dousmanis,
transitions
led i n d i r e c t l y
pu re r o t a t i o n a l
to
row e l em e nt monohydrides such as HF and OH.
microwave study o f a f r e e
fo r rotational
l e a s t some t r a n s i t i o n s
radical
Sanders and Townes ( 2 ) .
stimulated
of other free radical
to s tu d ies of the r o t a t i o n a l
successful
species
(3).
spectra of
Th is
searches
As w e l l ,
in terstellar
m o l e c u l e s by r a d i o a s t r o n o m y , c u r r e n t l y an a re a o f v i g o r o u s . i n v e s t i g a t i o n
(4).
Mi crowave s p e c t r a
have been used t o p r o v i d e a c c u r a t e i n f o r m a ­
t i o n a b o u t a wi de v a r i e t y o f m o l e c u l a r p r o p e r t i e s .
been used as a t o o l
rotational
moments o f
As a r e s u l t ,
it
in ertia,
is often
analysis of a ro ta tio n a l
possible to c h a ra c te r iz e
spect rum can a l s o y i e l d
d is t o r t i o n constants, C o r io lis
'field s;
The
i n t er ms o f
are a fu n c tio n o f the v i b r a t i o n a l
i n m o l e c u l a r s t r u c t u r e wh ich r e s u l t from v i b r a t i o n a l
rotation
t h e y ’ have
fo r determining precise molecular s tru c tu re s .
c o n s t a n t s , which d e f i n e t h e m o l e c u l a r s t r u c t u r e
the p rin c ip a l
state.
Prim arily
t he changes
excitations.
values
The
for centrifugal
c o u p l i n g c o n s t a n t s and o t h e r v i b r a t i o n -
p ar a me t er s which a r e used t o e v a l u a t e
intram olecular force
f o r some v e r y s i m p l e m o l e cu l e s c omp l et e p o t e n t i a l
been o b t a i n e d u si n g microwave d a t a o n l y .
functions
have
I n f o r m a t i o n a bo u t t h e e l e c t r o n i c
3
s t r u c t u r e o f a m o l e c u l e can be o b t a i n e d from t he S t a r k and Zeeman e f f e c t s
and fronw t h e values
This
molecules,
and,
o f n u c l e a r q u a dr up ol e c o u p l i n g c o n s t a n t s .
thesis
r e p o r t s microwave i n v e s t i g a t i o n s o f s e v e r a l
namely t h e
as w e l l ,
the v a r i o u s
isoelectronic
propiolyl
individual
chloride.
s u l ph u r d i c h l o r i d e and d i c h l o r o s i l a n e
The s p e c i f i c aims
m o le cu le s a r e dis cu sse d a t
r e l e v a n t c h a p t e r s . . The b a si c t h e o r y r e q u i r e d
in i n v e s t i g a t i n g
t h e b e g i n n i n g o f the
t o i n t e r p r e t microwave
*
rotational
spectra
ted i n s e v e r a l
is
not d evel oped h e r e s i n c e
good t e x t s
by Gordy and Cook ( 9 ) .
considered
1 .1
(5,
...,
10).
it
i s e x t e n s i v e l y documen­
P articu larly
useful
Only t h e p e r t i n e n t e q u a t i o n s and n o t a t i o n a r e
t he Asymmetric Ro to r
The r o t a t i o n a l
Hamiltonian f o r a r i g i d
r o t o r can be w r i t t e n as
H = APa + BPb + CPc
(1J ^
where P , P ^ , . a n d Pc ( i n u n i t s o f h / 2 tt) a r e t h e components,
m o l e c u l e f i x e d a xe s,
in ertial
the r o t a t i o n a l
o f t he t o t a l
axes a ,
rotational
b and c have been l a b e l l e d
t o t he c o r r e s p o n d i n g p r i n c i p a l
i n such a way t h a t
The r o t a t i o n a l
moments o f
inertia
I b and I c by
I x A * I b x B * I x C *
R i g i d r o t o r s can be c l a s s i f i e d
h/8,.2
in to several
a c c o r d i n g t o r e l a t i o n s among t h e moments o f
constants.
I
r e f e r r e d to
a n g u l a r momentum P_. The
c o n s t a n t s f o l l o w t he o r d e r A >_ B >_ C.
constants a re r e l a t e d
Ia.
t h e book
in th is c hapter.
Energy L e v el s o f
principal
is
Thus one has
in ertia
(1.2)
distin ct
t ypes
or r o t a t i o n a l
4
(1)
Li n ear m ol e c ul es
(2)
Spherical
(3)
P r o l a t e symmetri c tops
1.
(4)
O b l a t e symmetric tops
Kb " 1c
(5)
Asymmetric tops
Kb '
0,
tops
I
b
c
I
Jb =
= I
c
c
1c
Except f o r
t he asymme tr ic top case t he r i g i d
r o t o r H a m i l t o n i a n can be
e x p licitly
d i a g o n a l i z e d t o g i v e c l o se d forrpe x p r e s s i o n s
energies
(11).
F or p r o l a t e symmetri c t o p s , f o r
E = BJ( J
while for oblate
+ 1)
+ (A -
for
rotational
e xa mp l e, one o b t a i n s
B)K2
(1.3)
symmetric tops
E = BJ( J
+ 1)
+ (C -
B)K2
*
*
Here J i s
the
t he quantum number d e n o t i n g
t he t o t a l
(1.4)
rotational
angular
W
momentum and K g i v e s t he m o l e c u l e f i x e d component; a t h i r d
number M, which g i v e s t h e space f i x e d component o f
a n g u l a r momentum, w i l l
later
dependence o f t h e r o t a t i o n a l
a r e u s u a l l y den ot ed as
value;
are,
t he t o t a l
rotational
be needed t o d e s c r i b e t he e l e c t r i c
energies.
t o +J.
field
The symmet ri c top w a v e f u n c t i o n s
|JKM> where J can assume any p o s i t i v e
K and M r an ge from -J
however,
quantum
integral
The symmetric top r o t a t i o n a l
i n d ep e nd en t o f M a t z e r o f i e l d
and,
as w e l l ,
energies
do not depend
on t h e si gn o f K.
*
The i n t r o d u c t i o n o f asymmetry s p l i t s
which a r e d o u bl y d e g e n e r a t e ,
Hamiltonian m a t r ix
a basis set of
that is ,
the
those w i t h
Symmetric top l e v e l s
|K|
f o r t h e asymmetr ic top can s t i l l
^ 0.
However,
the
be c o n s t r u c t e d u si ng
symmetric r o t o r w a v e f u n c t i o n s . The n o n - z e r o m a t r i x ele men ts
|T
are,
tops
i n t he
I
representation
(12)
u s u a l l y chosen f o r p r o l a t e asymmetr ic
5
<J KM | H | JKM> = Jj(B + C ) J ( J + 1) + [A - ^ ( B + C ) ] K 2
(1/5)
<JK t 2M|
H |JKM> = »t(B - C ) { [ J ( J + 1)
[ J ( J + 1)
-
-
K(K *
(K ± 1 ) ( K
1)]
x
t 2)]}^
S i nce t h e r e a r e no m a t r i x e l e m e n t s c o n n e c t i n g even and odd K t h e
H a m i l t o n i a n m a t r i x blocks
Further fa c t o r iz a t io n
immediately
i n t o an u l t i m a t e
p o s s i b l e t hr o u g h a p p l i & t i o n
into
two t r i d i a g o n a l
s u b ma t r ic es
f o u r i n de p en de n t s u b m a t r i c e s
o f t he Wang t r a n s f o r m a t i o n
( 13) '.
is
Because
f o r an asymmetr ic t o p K i s no l o n g e r a good quantum number t he l e v e l s
a r e l a b e l l e d by
in the l i m i t i n g
^ . Here
and K, a r e t he |K|
a c
p r o l a t e and o b l a t e symmetri c l i m i t
asymme tr ic r o t o r f u n c t i o n s ,
v a l u e s which o b t a i n
respectively.
The
o b t a i n e d as a l i n e a r c o m b i n a t i o n o f t he
symmetri c top w a v e f u n c t i o n s a f t e r d i a g o n a l i z a t i o n o f t h e H a m i l t o n i a n
m atrix,
a r e d enot ed by |JtM>
The r i g i d
where
i
= K a
K .
c
r o t o r H a m i l t o n i a n can be r e c a s t i n o t h e r forms
thr ough t he i n t r o d u c t i o n o f s o - c a l l e d asymmetry p a r a m e t e r s .
. t h e Ray asymmetry par a me t er *
One has
( 1 4 ) and t he Wang asymmetry p a r a m e t e r bp
( 1 5 ) where
k
= 2B - A
A -
and
bp =
- C
(1.6)
C
C - B
(1.7)
2A - B - C
The
v a l u e o f k v a r i e s from -1
in
t he p r o l a t e
the
o b l a t e symmet ric l i m i t ; bp v a r i e s c o r r e s p o n d i n g l y from
Using t h e Wang asymmetry p a r a m e t e r ,
symmet ri c l i m i t
f o r e xamp l e,
t he r i g i d
t o +1 i n
0 to - 1 .
rotor
H a m i l t o n i a n t a k e s t h e form ( 1 3 )
Hr = »s(B + C)P2 + [ A -
>s(B
+ C)]H(bp )
(1.8)
1
6
Using t he known m a t r i x e l em e nt s o f H(b ) t he H a m i l t o n i a n
to o b t a i n
is d ia g o n a liz e d
(13)
L r = U(B + C ) J ( J
+ 1) + [A - ',(B + C) ]Wj
(b
)
(1.9)
i
where Wj
(b ) is t he Wang reduced e n e r g y , a d i m e n s i o n l e s s q u a n t i t y . The
i
.
Wang reduced energy Wj (b ) can be r e g ar d ed as the r o t a t i o n a l e n er g y o f a
i
r i g i d r o t o r havi ng the r o t a t i o n a l c o n s t a n t s 1, - b
and +b .
P
The s im pl e r i g i d
fu lly
to f i t
centrifugal
transitions
P
r o t o r H a m i l t o n i a n can o f t e n be used s u c c e s s ­
involving
low J s t a t e s .
f o r c e s become i m p o r t a n t .
Essentially
At h i g h e r v a l u e s o f J
t h e y cause d i s t o r t i o n s
o f t h e m o l e c u l a r s t r u c t u r e which a r e ,
in t u r n ,
t h e i n s t a n t a n e o u s moments o f i n e r t i a .
The r o t a t i o n a l
in g ly are s h ifte d
considered
from t h e i r
in d e ta il
a non-rigid
rigid
rotor positions.
by W i l so n and c o - w o r k e r s
where t h e x' 0 i i a r e q u a r t i c c e n t r i f u g a l
actpp
m
K
constants A ' ,
B'
and C'
s are d i r e c t l y
related
equation 1 .1 0 contains
^
T 'aacc*
T'bbcc^’ ^
r
a,
6
They d ev el o pe d
six
t'
nn
(=
aaBB x
was s ^own
terms.
t '
aaaa
,
(20,21):
i ' . kkk,
bbbb
r'
Watson t t i a t o n l y f i v e
t h i s case t h e r o t a t i o n a l
is w r i t t e n
(1.10)
c o n s t a n t s and t h e
t o t he harmonic f o r c e f i e l d
and which was' used t h r o u g h o u t t h i s w o r k ,
d e g r ee t e r m s ,
x'
P 2 P 2
aioiBB c t
B
distortion
«
The v a r i o u s
(18).
cccc
,
A l t h o ug h
x'
k k ,
aabb
combinations o f
spectrum ( 1 9 , 2 0 ) .
p o s s i b l e c o mb i n at i o n s whi ch can be w r i t t e n ,
In
accord­
T h i s problem was
(16,17,18).
centrifugal
them can be d e t er m i n ed f r om a r o t a t i o n a l
(20,21).
transitions
a r e d i s t i n c t from t hose o f t h e r i g i d
r o t o r as t h e y now have absorbed s ma ll
r'
by changes o f
r o t o r H a m i l t o n i a n which f o r an asymmetr ic top has t he form
H = A' P 2 + B'P 2 + C ’ P 2 + '4
a
D
C
rotational
reflected
Of t he many
one o f t h e s i m p l e s t t o use ,
is the s o - c a lle d A red uction
Hamiltonian,
now i n c l u d i n g h i g h e r
The r o t a t i o n a l
constants s t i l l
quartic d is to rtio n
of the t '
Q
HjK’ H ^j,
H^,
constants A j ,
given e a r l i e r
u
aapb
hj,
contain
(20).
h j K and h^,
intram olecular force f i e l d
Aj ^,
small
a ^,
averaging e f f e c t s
expected to
va ry
el e me n ts o f
J
It
t o t he c u b i c p a r t o f t he
should be emphasized t h a t
the.values of a ll
f rom one v i b r a t i o n a l
same t e c h n i q u e s .
state;
of
this
is
because o f
t he c o n s t a n t s a r e
s t a t e to the next.
have a l r e a d y been g i v e n .
those o f Hp and H p , ,
and t he
Aj and A^ a r e c o mb i n at i on s
an e f f e c t i v e H a m i l t o n i a n f o r a g i v e n v i b r a t i o n a l
vib ratio n al
terms,
The s o - c a l l e d s e x t i c c o n s t a n t s H . ,
are re la te d
(21).
correction
The a d d i t i o n a l
The m a t r i x
m a trix elements,
have t he same f orm and can be e v a l u a t e d usi ng t he
A g a in i n t he
I
representation
<JKM|H0 + Hd ,|JKM> = - Aj J 2 (J + l ) 2 -
they are:
Aj k J ( J + 1 ) K2
(1.12)
j
- Ak K4 + Hj J 3 (J + l ) 3 + Hj k J 2 (J
+ i ) 2 k2
+ Hk j J ( J + 1)K4 - + Hk K6
<JK + 2M|H d + Hp, | JKM> = { - A j j ( J + 1)
- ,i 6 |<[ ( K + 2 ) 2
+ K2 ]
V hJ J 2 (J + l ) 2 + ishJ K (J + 1 ) [ ( K + 2 ) 2 + K2 ]
+ ',hK[ ( K + 2 ) 4 + K4 ] }
{[J(J
+ 1)
-
x
K( K- + 1 ) ] [ J ( J
+ 1)
-
(K + 1) (K + 2) ] }'‘
8
Diagonalization of this
functions
|JxM>
functions.
Hamiltonian again gives
as l i n e a r c om bi nat i on s o f
The s i m p l e t r i d i a g o n a l
the asymmetr ic r o t o r
t h e symmetric r o t o r w ave­
m a t r i x o f t he A r e d u c t i o n Hami1 t o n i a n
can u s u a l l y be c o n s t r u c t e d and d i a g o n a l i z e d
faster
m atrix o f the a l t e r n a t i v e
the S redu ctio n
S reduction
(21);
t han the h e p t a d i a g o n a l
is,
howe ver ,
t h e n ec es sa r y c ho i ce f o r m o le cu l es which a r e o n l y s l i g h t l y asymmetr ic
f
The most e l e g a n t way o f f i t t i n g
the eigenvectors obtained
reduced H a m i l t o n i a n
from t he
is
t o use
e x a c t d i a g o n a l i z a t i o n o f Wat son' s
SE/3Ak = <Pa ^ > > • • •
e s t i m a t e d v a l u e s o f t he r o t a t i o n a l
b e g i n t he f i t t i n g
spectra
t o g e n e r a t e t h e r e q u i r e d Ja co bi an s
3E/dA = <Pa ^ > » 9E/3B = ‘ P ^ N
o f course,
rotational
(21).
process.
etc.
In itia lly ,
c o n s t a n t s were used to
L i n e a r v a r i a t i o n s o f t he r o t a t i o n a l
constants
and any chosen s e t o f q u a r t i c and s e x t i c c o n s t a n t s wer e s u b s e q u e n t l y
allowed.
Because t h e v a r i o u s Jac o b i an s a r e n o t q u i t e
v a l u e s o f A,
B, C, A j ,
determine^the f i n a l
Aj^
...
an i t e r a t i v e
in d e t a i l
approach was r e q u i r e d
spectroscopic constants;
produced conver gence o f t h e f i t .
by K i r c h h o f f
Fitting
three it e r a tio n s
In the e a r l i e r
(
fits ,
however,
usually
schemes f o r d e t e c t i n g
/
t he c e n t r i f u g a l
d i s t o r t i o n was
t r e a t e d as a p e r t u r b a t i o n on t he r i g i d
r o t o r e n e r g i e s as o u t l i n e d by
H e l m i n g e r , Cook and De L u c i a
is po ssib le to w r i t e a f i r s t
expression
f o r t he r o t a t i o n a l
(23).
It
e n e r g i e s as
E = e r + e d + ed -
t 1 - 13*
where
Er = 4 ( B + C ) J ( J
+ 1)
+ [A -
4(B,+
C)]Wj
(b
)
T
, En = - A , J 2 (J + l ) 2 - A , „ J ( J + 1 )<P 2 > - A„<P 4 >
U
I
to
c o n s i d e r a t i o n s a r e d i scu sse d
( 2 2 ) who a l s o d i s c u s s e s
mi sas si gn ed t r a n s i t i o n s .
i nd ependent o f t he
J
J J\
d
I\
d
order
/
9
- 26j 0
J ( J + 1)[W
(b ) T
^
- 2V Wj <bp> <Pa2> ED'
=
HJj 3 ( J
* V
+ 1 ) 3 + HJKj 2 ( J
Pa6> + 2V
j 2 <J *
■+ 2oh
T
^Pa 2 > ]
"
+ 1 ) 2< Pa 2> + h k j j ( j + 1 ) < P a 4>
1 >2 CWJ <bp> T
(b ) <Pa 2 > r
<pa2 > l
<Pa4 > ]
+ 2° \ [ “j <bp)<pa4> - <Pa6>J
. T
Here o = -1 / b ; W, (b ) , t h e Wang reduced e n e r g y , has been p r e v i o u s l y
P
t
P
discussed.
I n usi ng t h e f i r s t o r d e r e n e r g y e x p r e s s i o n t h e obser ved
f r e q u e n c i e s were i n i t i a l l y
fit
t o t he q u a r t i c c e n t r i f u g a l
c o n s t a n t s and t o changes i n t h e r o t a t i o n a l
a f t e r the f i r s t
i t e r a t i o n where t h e t r i a l
constants.
distortion
In each c a s e ,
v a l u es used f o r t he r o t a t i o n a l
V- '
c o n s t a n t s were e i t h e r guessed v a l u e s o r t hose o b t a i n e d from a r f g i d
analysis,
changes i n t h e r o t a t i o n a l
As v a r i a t i o n s
t
i n t he r o t a t i o n a l
the d i s t o r t i o n
c o n s t a n t s were s mal l
rotor
but s i g n i f i c a n t .
constants a f f e c t the values obtained f o r
c o n s t a n t s an i t e r a t i v e
approach was a g a i n used to a r r i v e
i
a t t he f i n a l
recent f i t
results;
Unfortunately,
e f f e c t s can be i m p o r t a n t when t h i s
Essentially
2
<Pfl > = dE/aA,
this
Hamiltonian.
firs t
higher o rder d i s t o r t i o n
ord er energy expression is
i s because t h e v a r i o u s e x p e c t a t i o n v a l u e s
2
<P^ > = 3E/3B,
eigenvectors o f the r i g i d
rotational
v a l u e s i n t h e n e x t sequence o f
The co nver gence was s w i f t w i t h chahges b e i n g i n s i g n i f i c a n t
the second i t e r a t i o n .
employed.
c o n s t a n t s d e r i v e d from the most
s er ve d i n each case as t r i a l
the i t e r a t i o n .
after
the r o t a t io n a l
...
etc.
have been c a l c u l a t e d u s i n g ’ t he
r o t o r H a m i l t o n i a n and n o t
t h e compl ete
To a c c ou n t f o r h i g h e r o r d e r d i s t o r t i o n e f f e c t s
V
the r o t a t i o n a l
c o n s t a n t s and c e n t r i f u g a l
usi ng t h e above p r o ce d ur e were i n s e r t e d
distortion
constants determined
i n t o t he c o m p l e t e H a m i l t o n i a n ,
10
equation
"exact"
1.11,
which Was then n u m e r i c a l l y d i a g o n a l i z e d
t r a n s it io n frequencies.
The d i f f e r e n c e s
between t h e s e e x a c t
f r e q u e n c i e s and t hose c a l c u l a t e d u si ng t he f i r s t
order energy expression
r e p r e s e n t the h i g h e r o r d e r d i s t o r t i o n c o n t r i b u t i o n .
were s u b t r a c t e d
This
“ H i g h e r O r d e r ' were r e f i t
needed t o ’ a t t a i n
I n such cases s e v e r a l
c o n ver gen ce;
achieve a constant value.
that -H ,
distortion
constants;
ite ra tio n s
i t e r a t i o n s were r e q u i r e d .
p r oc ed u re was expanded t o
again i t
may be
before the higher o rd e r c o rre c tio n s
Here two t o f o u r
When deemed n ec es sa r y t h e f i t t i n g
order e ffe c ts .
u s i " 9 t he f l > s t o r d e r e n e r 9 ) '
p ro ce du re i s u s u a l l y employed o n l y when h i g h J l i n e s
have been i n c l u d e d i n t h e f i t ' .
sextic
These f r e q u e n c i e s
from t h e observed f r e q u e n c i e s and the r e s u l t a n t f r e q u e n -
c 1 e s ' “Observed ‘
expression.
to y i e l d a set of
in clude th e
was n e c e s s a r y t o a c c o u n t f o r h i g h e r
The s p e c t r o s c o p i c c o n s t a n t s o b t a i n e d usi ng e i t h e r o f t h e
two p o s s i b l e f i t t i n g
p r oce du re s were i n each c a s e ,
of course,
ultim ately
identical.
1.2
N u c l e a r Q ua dr upol e C ou p li n g
A n ucleus w i t h a s p i n quantum number g r e a t e r t ha n 1 / 2 possesses
a nuclear e l e c t r i c
fie ld
q u ad ru po le moment which can i n t e r a c t w i t h
the e l e c t r i c
g r a d i e n t produced a t t h a t n u cleus by t h e m o l e c u l e ' s e x t r a q u a d r u p o l a r
charges.
I n e f f e c t t h e n u c l e a r s p i n a n g u l a r momentum I_ c o u p l e s w i t h t h e
rotational
a n g u l a r momentum
F =
t o g i v e a n e t a n g u l a r momentum £
+ J
I
where F ranges from J + I t o
is to s p l i t a r o t a t i o n a l
|J -
level
introduce hyperfine structure
.
(1.14)
I|.
The e f f e c t o f t he i n t e r a c t i o n
i n t o 21. + 1 l e v e l s and,
in to the r o t a t i o n a l
h y p e r f i n e s t r u c t u r e observed i n t h e p r e s e n t
a firs t
order Hamiltonian;
that
is ,
4
in t u r n ,
s p ect rum.
A ll
to
of the
st ud y coul d be t r e a t e d w i t h
a Hamiltonian diagonal
in J.
The q u a d r u p o l e H a m i l t o n i a n f o r a mol ecu le' c o n t a i n i n g one quadr u p o l a r n uc le u s can be w r i t t e n
■ Hq =
eQqj
2J(2J -
where eQ i s
[3 (I-J )2 + |
1)1(21
-
1_-J -
f t 2]
(1.15)
1)
t he c h a r g e - w e i g h t e d n u c l e a r q uad ru p o l e moment, a c o n s t a n t f o r
a given n u c l e u s ,
projection of
J.
(24)
and q j
i s a c o u p l i n g c o n s t a n t obse rv ed f o r t he maximum
along a s p a c e -fix e d a x i s ,
t h a t is f o r the s t a t e w ith M =
For an as ymmetr ic r o t o r
q j = <J t M = J 1 3 2V/3 Z2 | J t M = J>
where V i s
the e l e c t r i c
the s p a c e -fix e d a x i s .
*
where xaa i s
yy
(1.16)
f i e l d a t t h e q u a d r u p o l a r n u c le us and Z d e f i n e s
A l t e r n a t i v e l y one can w r i t e
-------------- L _ _
(J + 1 ) ( 2 J + 3)
£
g = a,b,c
x g g ' Pg2>
c a l l e d a n u c l e a r q u ad r up o l e c o u p l i n g c o n s t a n t .
( , ' ,7)
As a
consequence o f La P l a c e ' s e q u a t i o n t h e r e a r e o n l y two i n dep en d en t Xgg's
since
xaa + x bb + x cc = 0
’
-
{1J8)
And, f o r a p r o l a t e asyfnmetric top a n u c l e a r q u ad ru po le c o u p l i n g asymmetry
paramter,
n,
i s d e f i n e d by
n = ( x bb “ x c c )!/ x aa
1
"
!
( 1 - 19)
^
The two i n d e p e n d e n t c o n s t a n t s which can be d e t e r m i n e d from a f i r s t
order
a n a l y s i s o f a spect rum h a vi n g n u c l e a r q u a dr u p o l e h y p e r f i n e s t r u c t u r e a r e
u s u a l l y chosen as x , , and n- I t
act
i s t hen
p o s s i b l e to w r i t e a f i r s t
order
e x p r e s s i o n f o r t h e q u a d r u p o l e energy as ( 2 5 )
( 1. 20)
12
where f ( I , J , F ) ,
Casim ir's
f ( I , J.F)
function,
= 3C(C + .1 ) / 4
2 1 (2 1 -
with
C = F( F +
1)
i s d e f i n e d by
-
1(1+
1 ) ( 2J -
- J ( J + 1)
-
1 ) J ( J + 1)
1 ) ( 2 J + 3)
1(1 + 1)
Again,
t h e Wang reduced e n er gy Wj (b ) has been used p r e v i o u s l y
T
discussing the r i g i d
asymmetr ic r o t o r probl em.
,
It
is ,
o f course, po ssib le f o r a molecule to
n u c l e a r q u ad r u p o l e c o u p l i n g .
in
e x h ib it plural
The s i m p l e s t p o s s i b l e case i n v o l v e s two
•
q u a d r u p o l a r n u c l e i where one c o u p l es much more s t r o n g l y than t h e o t h e r .
In t h i s
case f t
i s p o s s i b l e to d e r i v e a f i r s t o r d e r e x p r e s s i o n f o r t h e
q u ad r u p o l e e n e r g i e s s i m i l a r t o t h a t
ca se;
it
a l r e a d y g i v e n f o r t h e one nucl eus
t h e t h e o r y has been o u t l i n e d by Bardeen and
case where two n u c l e i
have equal
*
o r n e a r l y equal
Townes( 2 6 ) .
couplings,
In t he
however,
i s n e c e s s a r y t o d i a g o n a l i z e t h e H a m i l t o n i a n m a t r i x o f Hq .
When a m o l e c u l e possesses two q u a d r u p o l a r n u c l e i
n u c l e a r s p i n a n g u l a r momenta o f
p o s s i b l e c o u p l i n g schemes.
1^ and
h av i ng
r e s p e c t i v e l y t h e r e a r e two
For example one can have
0-2 D
-1
where a g a i n
+
-2
is
=
|J -
'
the r o t a t i o n a l
a n g u l a r momentum.
.,
-
1^1
■
a n g u l a r momentum and £ i s t h e t o t a l
Then F-j and F can assume t he v a l u e s J + 1^, J + I-j
and F1 + I 2 , Fj
+ I2 -
1,
...
| F1 -
A l t e r n a t i v e l y one can use t h e scheme
k
+
I
+ J
h
=
I 2 | respectively.
.
l-
( 1. 22)
In t h i s
I
= F
case t h e quantum number I which d e s c r i b e s
the t o t a l
nuclear
-
1,
^
\
13
s p i n a n g u l a r momentum can have the v a l u es
|l.|
-
I-|
+ ^
I-| + I ^ -
I ^ 1 and F c ov er s t he r ange J + I . J + I - l , . . . .
* sepond o f t h e s e two schemes i s t he most u s e f u l
since i t
,
1,
jJ -
....
11.
,
The
a l l o w s one to
d e t e r m i n e by i n s p e c t i o n t he symmetry o f t h e n u c l e a r s p i n w a v e f u n c t i o n s .
This
cal
is
t h e d e s i r e d c o u p l i n g scheme f o r a m o l e c u l e which c o n t a i n s
nuclei
s i n c e i n t h i s c a s e the r e q u i r e m e n t s o f n u c l e a r s p i n p e r m u t a t i o n -
symmetry d i c t a t e t h a t
are d i f f e r e n t .
t he s t a t i s c a l
w e i g h t s o f t he v a r i o u s s p i n f u p c t i o n s
In cases such as t h a t o f
■ zero are pos s ib le .
practice,
id en ti­
however,
l e n t nuclei' case;
O nl y t h i s
32 35
S C l^ s t a t i s t i c a l
l a t t e . r case w i l l
weights o f
be c o n s i d e r e d h e r e .
In
t h e f o r m e r scheme was sometimes used f o r t he i n e q u i v a ­
t he r e q u i r e d computer program was w r i t t e n by R ober t L.
Cook u s i n g t h e m a t r i x e l e m en t s in t h e form g i v e n by Cook and De L uci a
Plural
n u c l e a r q u a d r u p o l e c o u p l i n g was o bse r ve d i n t h i s
o n l y f o r m o le cu l es c o n t a i n i n g two c h l o r i n e atoms.
= 3/2.
(27).
st ud y
For t h i s case I-| =
The r e q u i r e d m a t r i x e l em en t s o f ( H q ) j o t a ^ where
(1.23)
(V T o t a l
have been e v a l u a t e d by F l y g a r e and Gwinn i n
methylene c h lo r id e
(28).
th eir
l andmark s t u d y o f
As a f i r s t o r d e r t r e a t n # n t was s u f f i c i e n t
t h e p r e s e n t s t u d y o n l y t he e le me nt s d i ag o n a l
i n J were r e q u i r e d .
for
The
m a t r i x e le me nt s have t h e f orm
(1.24)
S p e c i f i c a l l y one has f o r t h e v a r i o u s cases
1.
_r ’
J ’ = J and I '
.<Hq > = 3 X* ( I
T
= -I
+ 3 ) ( I - 2 )____________ [ A( A + 1)
16J ( 2J -# 1) (21 \
(28)
1) (21 + 3)
- 4 i(i
+ i)j(j
+ i)]
14
with
2.
A = f(F + 1 )
J'
<h
q
-
1(1 + 1)
= J and I '
= I + 1
> = x ~ [I(I
+ 2)
T
- J ( J + 1)
+ J(J + 1 )
16 J ( 2 J
-
J and I '
J
+ 5),(-
I +, 3)
I + J)(F + I - J + 1)(
-
F + I + J + 1)]'
= 1 + 2.
3 2 J( 2 J -
where t he
U
1 )]
(21 + 1) (21 + 3)
(I
V
F(F +
1)
x [ ( F + I + J + 2) ( F 3:
-
1 ) ( 2 1 + 3)
I + 3)(-
I + 2 ) (F + I + J + 3)
(21 + 5) (21 + 1)
x (F + I
+ J + 2)(F
x (-
I + J + 1)(F -
F +
+ 6 ) ( I + 5)(-
+ I -
J + 2)(F + I - J + 1 )(-
I + J)CF -
I +J -
c o u p l i n g c o n s t a n t s x + and x ” ar e g i v e n i n
F + I + J +
2)
1)
terms o f p r e v i o u s l y
d e f i n e d c o n s t a n t s by
+
-X = (eQ
),
qJ
+ (eQ
1
)? if
qJ
I'
= I or
I'
= I ± 2
(1.25)
c
and
x" = (eQ
)1 '
(eQ
)2 if
I * = I ± 1
(1.26)
qJ
For a m o l e c u l e c o n t a i n i n g two c h l o r i n e s ,
1^ =
^
, it
i s a s i mp le
m a t t e r t o c o n s t r u c t and d i a g o n a l i z e t h e 16 x 16 H a m i l t o n i a n m a t r i x o f
Hn
Ql
1.3
+ Hn .
No l e a s t squares f i t s
Q2 -
though we re made u si ng t h i s
H am iltonian.
The Asymmetric R o t or S t a r k E f f e c t
The S t a r k e f f e c t o f an asymme tr ic r o t o r has been d e s c r i b e d
by Golden and Wi lson
ele ctric
fie ld
(29).
When a m o l e c u l e i s p l a c e d i n a u n i f o r m
E ( d i r e c t e d along the s p a c e -fix e d Z - a x i s )
a t o r q u e which p e r t u r b s
t he r o t a t i o n a l
it
experiences
energies o f the molecule.
S t a r k H a m i l t o n i a n i s g i v e n by
H =
S
1
- u ■ E= - E
-
n _l
,
r * 7.
g= a , b , c
Zg
u n
g
(1.27)
The
15
where ^
i s the d i r e c t i o n c o s i n e between t h e s p a c e - f i x e d Z - a x i s
m olecule-fixed g -axis.
If
S t a r k e ne r gy f o r a g iven
le vel
second o r d e r p e r t u r b a t i o n
S
EJ x ^
g =Ea , b , c
t h e r e a r e no n e a r d e g e n e r a t e l e v e l s
J^ i s M dependent and i s g i v e n by the
t t j -
(4J
( 1 .28)
£ .N - T |* rg
.f )
-
1)
T '
Ej
-
E°
_
1
T
T'
M
71
4J ( J
+
1)
+ (J + l^)
2
E0
ug
*
E°
- M2
--------
4(J + i r ( 2 J
x
then t h e
sum
4J
+
and t h e
+ 1) ( 2 J * 3)
T 1
E°
J + 1
2C2
E
where E ° j
is
i
an e l e c t r i c
t he r o t a t i o n a l
field .
e ne r gy o f t he l e v e l
|Jx > i n t he absence o f
The d i r e c t i o n c o s i n e m a t r i x e l e m en t s can be e xpr essed
i n terms o f t h e l i n e s t r e n g t h s
I < j T l $Z g l J +
1
(Jt ; J ' t ')
= 4(J
,T ,> i
I < j T l <tZgl J t ' H ‘
4J(J
+
1)
+
1 )A
X
(J
(Jt;
u si ng
t
;
J
+
J
T *)
1 ,
t
')
(1.29)
2J + 1
4J Xg ( J x ;
The l i n e s t r e n g t h s
Xg
(Jt;
J ' t ' )
J - 1jt
1
)
depend o n l y on t he degr ee o f asymmetry
o f a m o l e c u l e and have been t a b u l a t e d as a f u n c t i o n o f k , t he asymmetry
p a r a m e t e r o f Ray ( 1 4 ) .
The use o f t h es e t a b l e s
p o l a t i o n between a p p r o p r i a t e v a l u es o f <.
(30)
may r e q u i r e
A lternatively
t he l i n e
inter­
strengths
can be e s t i m a t e d u s i n g t h e e i g e n v e c t o r s o f t h e asymmetr i c r o t o r H a m i l t o n i a n
and t h e r e l a t i o n
\
(31)
16
Ag ( J x ;
J'-t * ) -
Z j ^ M,
j <JxMhPZg | J ‘ t ‘ M* > | 2
The e i g e n v e c t o r s o f t h e r i g i d
^
(1.30)
r o t o r H a m i l t o n i a n a r e u s u a l l y adequat e as
S t a r k e f f e c t measurements a r e a l mo st al ways made u si ng
low J t r a n s i t i o n s .
The e x p r e s s i o n used above t o c a l c u l a t e t h e S t a r k e n e r g i e s
f o r a pure second o r d e r or q u a d r a t i c
d e s c r i b e t h e s h i f t s measured h e r e ,
ative
t r e a t m e n t s may be r e q u i r e d i f
y
levels or i f
This l a t t e r
a tra n s itio n exhibits
problem i s
Stark e f f e c t ,
w h i l e adequat e t o
is not g e n e r a ll y a p p l i c a b l e .
A ltern ­
t h e r e a r e n ea r d e g e n e r a t e r o t a t i o n a l
n u c l e a r q u ad r u p o l e h y p e r f i n e s t r u c t u r e .
d is cu s se d f o r p r o p i o l y l
chloride
i n Ch ap t er 5.
Near d e g e n e r a c i e s a r e most f r e q u e n t l y o f the a p p r o x i m a t e symmetric r o t o r
type.
V er y f a s t S t a r k
effects
can t he n occur p r o v i d e d
a p p r o p r i a t e d i p o l e moment component i s
1.4
that
the
non-zero.
M o l e c u l a r S t r u c t u r e s from R o t a t i o n a l
Sp e c t r a
Both o f the methods commonly used t o d e t e r m i n e t he m o l e c u l a r
structures
o f gaseous m o l e c u l e s ,
namely microwave s p e c t r o s c o p y and
electron d i f f r a c t i o n ,
have i n h e r e n t l i m i t a t i o n s .
gations,
several
f o r exa mpl e,
order to s p e c ify
ies
s p e c i e s must o f t e n be s t u d i e d
t he m o l e c u l a r ge o met ry;
in d e t e r m i n i n g a c c u r a t e l y
near i n e r t i a l
isotopic
axes,
because o f i n a d e q u a t e l y r e s o l v e d r a d i a l
i m p u r i t i e s and complex c o n f o r m a t i o n a l
th e re are d i f f i c u l t -
t he e l e c t r o n d i f f r a c t i o n method
d istrib u tio n
eq u ilib ria.
%
determinations
inadequate treatm ent o f v i b r a t i o n a l
effects.
o f v i b r a t i o n are manifested d i f f e r e n t l y
t ypes o f s t r u c t u r a l
in a d d i t i o n ,
in
t he c o o r d i n a t e s o f atoms which a r e s i t u a t e d
Problems a r i s e w i t h
the accuracy o f the s t r u c t u r a l
I n microwave i n v e s t i ­
p a r am et e rs a r e used.
n o r m a l l y d e r i v e d from r o t a t i o n a l
curves,
sample
In bo th c a s e s , however,
is often
l i m i t e d by an
I n p a r t because t he e f f e c t s
i n t h e two e x p e r i m e n t s s e v e r a l
Here o n l y t hose p ar amet er s
spectra w i l l
be c o n s i d e r e d ; a more
17
d e t a i l e d discussion
is g i v en by Gordy and Cook ( 3 2 ) .
o f t he t h e o r y r e q u i r e d
to r e l a t e
a r e g i v e n by R o b i e t t e
To a f i r s t
collection
a^,
of rigid
b,j and c ^.
in ertia
I
a
,
structures
(34).
a p p r o x i m a t i o n A m o l e c u l e can be t h o u g h t o f as a
p o i n t masses, m^, h a vi n g p r i n c i p a l
Then t he e q u a t i o n s d e f i n i n g
axis coordinates
the p r i n c i p a l
moments o f
I. and I
can be w r i t t e n :
b
c
¥ ™1
l b
i mi ^a i
=
(bi ?
Ic = ^
in ertia
Good ove r v ie ws
s p e c t r o s c o p i c and d i f f r a c t i o n
( 3 3 ) and by K uch it su and Cyvin
‘a =
For a r i g i d
I
+ ci 2>
+ ci 2)
2
(a7
^ ,31)
* b ,2)
p l a n a r m o le cu l e t h e r e a r e o n l y two i n dep en d en t moments o f
since a l l
■c -
o f t h e c^ a r e
'a -
id en tically
z e r o and
!b ■ 0
Real m o l ec u l es a r e not r i g i d ,
(1.32)
however,
and do not conform t o
idealized
picture.
As a r e s u l t a g iven moment o f i n e r t i a
constant)
is a fu n ctio n o f the v i b r a t i o n a l
t
p a r t i c u l a r consequence o f t h i s
d e fects f o r p la n a r molecules;
by t h e obs er ve d p r i n c i p a l
is
state of
this
(or rotatio n al
the molecule.
t he o b s e r v a t i o n o f s o - c a l l e d
fo r a vibrational
moments I
v
,
1
v
^
state,
and I
v
A
in ertial
v, c h a r a c t e r i z e d
the i n e r t i a l
defect
A v i s d e f i n e d by
!C V - !a V - Ib V = S
The i n e r t i a l
d e f e c t depends m a i n l y on t h e harmonic p a r t o f t h e i n t r a ­
molecular fo rc e f i e l d
t h e r e a r e s mal l
rotation
<>.33)
b u t , as i s
contributions
interactions.
t he case w i t h
from c e n t r i f u g a l
U s u a l l y one w r i t e s
(35)
t he p r i n c i p a l
moments,
terms and f rom e l e c t r o n -
18
A
= A ., + A
v
Thi\ j i ground s t a t e
in ertial
s t a t e moments I ° ,
a
I
c
. + A ,
cent elec
vib
-
0
I
a
I, 0
b
0
-
defect,
arnd I
I,°
b
c
= A
(1.34)
aq , i s o b t a i n e d from t he observed ground
usi ng
0
3
(1.35)
o
For a p l a / i a r m ol e c ul e t h e ground s t a t e
and p o s i t i v e .
In f a c t ,
such a n j ^ b s e r v a t i o n
p la n a r m olecular s t r u c t u r e ,
especially
slig h t
S trictly
isotopic v a ria tio n .
be compared w i t h
but often
this
is
in e rtia l
t hose c a l c u l a t e d
if
d e f e c t s a r e u s u a l l y small
is o fte n
t ak en as p r o o f o f a
t he i n e r t i a l
d e f e c t e x h i b i t s only
t he observed i n e r t i a l
d e f e c t s should
from a good harmonic f o r c e
field
(35,
im possible.
The most m e a n i n g f u l
structural
p a r a me t e rs a r e t ho se which
c h a r a c t e r i z e t he geometry o f a m o l e c u l e i n
s t a t e or e q u i l i b r i u m c o n f ig u r a t i o n .
Oppenheimer a p p r o x i m a t i o n
its
Within
hypothetical
the l i m i t a t i o n s
vibrationless
o f t he Born-
t h e e q u i l i b r i u m o r r g s t r u c t u r e has t he i m p o r t a n t
p r o p e r t y o f bei ng i s o t o p i c a l l y
i nd e p en d en t
s t r u c t u r e which i s c a l c u l a t e d by
a b
i n i t i o
(37).
As w e l l ,
methods.
this
is
the
To o b t a i n an r
6
structure
t he c o r r e s p o n d i n g e q u i l i b r i u m v a l u e s o f t he r o t a t i o n a l
a r e needed.
36)
For d i a t o m i c m o le cu l es t he r o t a t i o n a l
ex p re ss e d as a f u n c t i o n o f
t he v i b r a t i o n a l
,
constants
c o n s t a n t s can be
quantum number
v usi ng a
q u i c k l y c o n v e r g i n g power s e r i e s
B v = B e - a ( v + 1s ) + Y ( v + li ) ^ + . . .
(1.36)
He re B i s
e
t he e q u i l i b r i u m
rotational
wh ic h g i v e
t he v i b r a t i o n a l
dependence o f t h e r o t a t i o n a l
s i m i l a r e q u a t i o n s can be w r i t t e n
Keeping o n l y t hose terms l i n e a r
for
c o n s t a n t and a and y a r e c o n s t a n t s
t he g e n e r a l
constant.
Three
polyatomic molecule.
i n t he v i b r a t i o n a l
quantum number we have
o
19
G
Here
3N Z
i =
= G e
a
1
a r e t he v i b r a t i o n a l
which s p e c i f y t h e s t a t e
v, d.
all
o f the
G
e
3N' = G +
Z
o
. =
6
however.
c o n s t a n t s can be
usi ng a s i m p l i f i e d
c o n s t a n t s and thus t he r g s t r u c t u r e
is often
state
rotational
i m p o s s i b l e to o b s e r v e e x c i t e d
by h i g h e r o r d e r v i b r a t i o n - r o t a t i o n
(38)
c o n s t a n t s must be
-
4e -
is o f te n complicated
moments I a e ,
< ' - 39)
0
f o r a given v i b r a t i o n a l
Th is
I ^ e and I c e have
the r e l a t i o n
A second p h y s i c a l l y w e l l - d e f i n e d s t r u c t u r e
s t r u c t u r e which,
i s t he a ve r ag e
s t a t e v , gives
i s u s u a l l y denoted by an r o r
f o r an e x c i t e d v i b r a t i o n a l
this
For a p l a n a r m o l e cu l e one
been c o r r e c t l y c a l c u l a t e d s i n c e t hese must s a t i s f y
l b
spectra
i n c r e a s e d use o f
may somewhat a l l e v i a t e
interactions.
can check t h a t t he e q u i l i b r i u m p r i n c i p a l
! ae -
therefore
state rotational
t he a n a l y s i s o f t h e s e e x c i t e d s t a t e s p e c t r a
■ce -
is u s u a l l y
i s much worse f o r more complex m o l e c u l e s .
i n f r a r e d microwave d oubl e resonance
and by r z
the
T h i s method o f e x t r a p o l a t i n g to o b t a i n
r
a
ispecies ar e need t o o b t a i n a s t r u c t u r e ;
The s i t u a t i o n
o f t h e atoms.
form o f
(1.38)
because o f u n f a v o u r a b l e Boltzmann f a c t o r s a l t h o u g h t h e
p robl em;
constants
Even f o r a s i m p l e m ol ec u l e such as a b ent XYZ
two i s o t o p i c
it
normal mode
vibration-rotation
r
a ■ d./2
s i x ground s t a t e and e i g h t e e n e x c i t e d
Further,
ith
normal modes
1
the e q u i l i b r i u m r o t a t i o n a l
determined.
6
namely
Here G i s e i t h e r A , B o r C .
o
o
o
o
im practical,
3N -
va l ues o f t h e r o t a t i o n a l
from t h e ground s t a t e c o n s t a n t s
above e q u a t i o n ,
(1.37)
1
i s t he de gener acy o f t he
If
a.j a r e known t h e e q u i l i b r i u m
triatom ic
d ./2 )
quantum numbers f o r t h e
and G i s e i t h e r A, B o r C.
obtained
r
(v • +
i
1
6
state
v.
*r>
t he mean p o s i t i o n s
f o r t he ground s t a t e
The c o r r e c t i o n s
required
20
to o b t a i n
the average r o t a t i o n a l
c o n s t a n t s depend o n l y on t h e harmonic
Q
part o f the
in tra m o le c u la r force
used p r e v i o u s l y can be s e p a r a t e d
ou
G
= a.j
G
( Har moni c)
field
(39).
Since t he ut..
i n t o harmonic and anharmonic p a r t s as
G
+
( Anharmoni c)
(1-40)
one^ can w r i t e e q u a t i o n s anal agous t o those used to d e f i n e
rotational
constants.
the e q u ilib r i u m
For example
3N -
Gz = G q +
constants
r
6
d^ot^ ( Har moni c)
l
(1-41)
Here G^ i s any one o f t h e ground s t a t e a v e r a g e r o t a t i o n a l
constants Az ,
Q
Bz ^or C z and Gq and d^ have been d e f i n e d p r e v i o u s l y .
The u .
are r e a d i l y c a l c u l a t e d
is a v a i l a b l e
if
a good harmonic f o r c e f i e l d
A d i f f i c u l t y w ith average s tr u c t u r e s
w ell-defined,
invariant.
able to c a l c u l a t e
the
consequent on i s o t o p i c
therefore,
i s o t o p i c v a r i a t i o n o f t h e a v e r ag e s t r u c t u r e
substitution
ed by K u ch i ts u and c o - w o r k e r s
variations
calculated
t hey a r e n o t i s o t o p i c a l l y
f o r complex m ol e c u l e s one needs to be
b e f o r e t h e av er a g e s t r u c t u r e o f a
g iven i s o t o p i c s p e c i e s can be d e t e r m i n e d .
isotopic
(40).
i s t h a t a l t h o u g h t h ey a r e p h y s i c a l l y
because o f anharmonic e f f e c t s ,
S tric tly ,
( Harmoni c)
(41,
42).
T h i s probl em has been c o n s i d e r ­
They have suggest ed t h a t
o f t he bond l e n g t h s a re most i m p o r t a n t .
the
They have
t he se and a l s o e s t i m a t e d t he e q u i l i b r i u m bond d i s t a n c e s u si ng
t he e q u a t i o n s
r z = r e + 3 a u 2/ 2 and
6
K
(1.42)
rz = 3a6(u2 )/2 - K
(1.43)
2
Here
r Q
and r z a r e t h e e q u i l i b r i u m and a v e r ag e bond l e n g t h s ,
z e r o - p o i n t mean s q u a r e a m p l i t u d e o f t he bond i n q u e s t i o n ,
u
K is
is- the
the
2
corresponding p e rp e n d ic u la r amplitude c o r r e c t io n
(both u
and K ar e
21
read ily calculated
from the harmonic f o r c e
field
(43)),
and a i s
the
Morse a n h a r m o n i c i t y p a r a m e t e r ; where p o s s i b l e v a l u e s o f a a r e o b t a i n e d
from t h e cor res' pondi ng d i a t o m i c m o l e c u l e .
When no c o r r e c t i o n s
structural
p ar a m e t e r s a r e u s u a l l y a d j u s t e d
' s t a t e moments o f
inertia
I °,
a
has a v e r y nebulous p h y s i c a l
C oriolis
for vibrational
I. 0
b
and I ° .
c
meaning f o r
effects
to f i t
a r e p o s s i b l e t he
the e f f e c t i v e
The r e s u l t i n g
r
3
o
ground
structure
p o l y a t o m i c m o le cu le s because o f
effects.
J
F in ally
t h e r e i s t h e s u b s t i t u t i o n o r r s s t r u c t u r e based on t he
e q u a ti o ns o f Kr ai t ch ma n
are c a lc u la te d
(44).
In t h i s method t h e c o o r d i n a t e s o f an atom
f rom t he changes i n t h e moments o f i n e r t i a
t o p i c s u b s t i t u t i o n o f t h a t atom.
caused by i s o ­
C o s t a i n has suggested t h a t t h e r g
method g i ves an improvement o v e r t he r Q s t r u c t u r e because when d i f f e r e n c e s
i n t he moments o f
i n e r t i a a r e used v i b r a t i o n a l
are la r g e ly cancelled
(45).
contributions
t o t he
1
1s
For a p l a n a r asymmetr ic t o p K r a i t c h m a n ' s
e q u a t i o n s have a p a r t i c u l a r l y
simple form.
The a $ and b g c o o r d i n a t e s
of
t h e s u b s t i t u t e d atom a r e o b t a i n e d from
2
as
= *b
-
<b
1
+ *a
I
b
where t h e
stituted
1
s
= I
a
-
^ and
I
a
1
*
-
*a
I,
*b
~ *b
V
!a
a r e t he p r i n c i p a l
(1.44)
moments o f i n e r t i a
and s u b s t i t u t e d s p e c i e s r e s p e c t i v e l y .
o f t h e unsub­
The reduced mass
u is
d e f i n e d by
u = MAm
M + Am
(1.45)
22
where M and M + Am r e s p e c t i v e l y
s u b s t i t u t e d molecules.
molecule.
a r e the masses o f t h e u n s u b s t i t u t e d and
The u n s u b s t i t u t e d s p e c i e s
is c a l l e d
S u b s t i t u t i o n o f each atom i n t u r n e n a bl e s a l l
coordinates
to be d e t e r m i n e d .
coordinates
o f the r
s
The c o o r d i n a t e s o f atoms such as f l u o r i n e ,
phosphorus and i o d i n e c a n n o t be c a l c u l a t e d
o n l y one s t a b l e
the parent
i n t h i s way because t h e y have
isotope.
In a d d i t i o n , C o s t a i n has shown ( 4 6 ) t h a t at omi c
O
s m a l l e r t h an about 0 . 1 5 A c annot be r e l i a b l y e s t i m a t e d using
t h e s u b s t i t u t i o n method.
Both o f t h e s e l a t t e r d i f f i c u l t i e s
can be m i t i -
i
ga ted by use o f t h e c e n t e r o f mass c o n d i t i o n s
Ei mi a i = Li mi b i = Ei mi c i
o r t he p r o d u c t o f i n e r t i a
!
( 1 - 4 6)
0
conditions
E.m.a.b. = E.m.a.c. = E.m.b.c. = 0
liii
iiii
iiii
For o v e r - d e t e r m i n e d systems Watson has shown t h a t an r
(1.47)
'
m
'
structure
o b t a i n e d from
V
2I s - ‘ o
y - 0 ' 48’
is in many cases an excellent approximation to the r g structure ( 4 7 ) .
23
li
1.5
C entrifugal
D i s t o r t i o n C o ns t a nt s and t h e Harmonic F o rc e F i e l d
The q u a r t i c c e n t r i f u g a l
d i s t o r t i o n constants
i n f o r m a t i o n about 'the hanjtonic f o r c e f i e l d .
check t h e v a l i d i t y
additional
force constants.
They can be used e i t h e r to
o f a proposed f o r c e f i e l d
to t h a t o f
t he v i b r a t i o n a l
F o r a C2 v t r i a t o m i c ,
o r to p r o v i d e d a t a ,
wavenumbers,
however,
c o n s t a n t s can be used to d e t e r m i n e c o m p l e t e l y
S tric tly
provide useful
usually
f o r the e v a l u a t i o n ; o f
the c e n t r i f u g a l
distortion
t h e harmonic f o r c e f i e l d .
t h e e q u i l i b r i u m v a l u es o f t he c e n t r i f u g a l
d i s t o r t i o n constants
shoul d be used f o r f o r c e c o n s t a n t d e t e r m i n a t i o n but t h e s e a r e seldom
available.
The q u a r t i c c e n t r i f u g a l
d i s t o r t i o n constants are r e l a t e d t o 't h e
e l e m en t s o f t h e i n v e r s e harmonic f o r c e c o n s t a n t m a t r i x .
W i ls o n and Howard ( 1 6 )
can be w r i t t e n
c o n s t a n t s using t h e e q u a t i o n
V v v
Here A , a a r e r o t a t i o n a l
0
(J ^ ) k
of
s
/i/in \
(1.49)
^
constants
°2
in ertia
'
in verse force
„ ), (F ^ ) , t ( J „) ,
aB k
kl
1
i n MHz;
I OQ, I
pp
of
t
(18)
R 'E (J
T , r = "AA
a&-y<5
i n terms o f t h e
The
i n uA ; R = 2h x 10
17
are p rin c ip a l
YY
with h in erg -sec.
moments
The q u a n t i t i e s
v
= ( 9 l a g / 3 S)
in ertia
0
dre the p a r t i a l
derivatives
tensor w ith respect to the k - t h
o f t h e components o f tfie
internal
c o o rd in a te ,a n d are
g i v e n by
‘O
J
The l - t h
k =M
m<{6^
(6)+
^
<Y)’
( , ' 5° ’
.
V jJ' miV k i <a) + J8 V?* mi“ipki*6),/IvY
V,atom has mass m. and c o o r d i n a t e s a . ,
1
a components o f
the
i-th
1
«
(
6
1
-,
y-J
1
the p . .
K1
atom o f P o l o ' s p - v e c t o r f o r t h e k - t h
\
'
are
internal
24
coordinate
(49).
If
the
in e rtia l
derivatives
have u n i t s
o f uA and uA
r a d ^ f o r a s t r e t c h and a b en d , r e s p e c t i v e l y , and t h e j p r c e c o n s t a n t s
0 _I
°
*
/
have u n i t s o f mdyn A , mdyn A rad and mdyn rad f o r aj s t r e t c h , a bend
and a s t r e t c h
bend i n t e r a c t i o n ,
The e x p e r i m e n t a l
Aj,
c o mb i n at i o n s o f t h e
A j K> a ^ ,
t
'
s
6
respectively,
j
and
6
t hen t h e \ r
^ can be o b t a i n e d as l i n e a r
u si ng e q u a t i o n s due t o Watson ( 2 0 ) ;
r e l e v a n t e q u a t i o n s f o r W at so n ' s A r e d u c t i o n H a m i l t o n i a n
p
I
„ r a r e i n MHz.
r e p r e s e n t a t io n are given
in Table 3 .4 .
>
*
/
(21)
the
i n t he
25
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C l e e t o n and N. H.
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v
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i •
1
28
Chapter 2
Experimental
Methods
A l t h o u g h t he i n s t r u m e n t a t i o n and t e c h n i q u e s used i n t h i s work
were q u i t e c o n v e n t i o n a l
given here.
a b r i e f ac co un t o f t h e e x p e r i m e n t a l
In microwave s p e c t r o s c o p y h i g h s p e c t r a l
Experimental
lim i­
r e l a t e m o s t l y to t h e i n h e r e n t weakness o f t he s i g n a l s which i s
<»
u s u a l l y a r e s u l t o f small
l e v e l s o r a small
easily
is
r e s o l u t i o n and
a c c u r a t e f r e q u e n c y measurement a r e r e a d i l y a c h i e v e d .
tations
pr ocedur es
lost
population d iffe re n c e s
d i p o l e moment.
between t h e r o t a t i o n a l
O f t e n s i g n a l s a r e so weak t h a t t h ey a r e
in t h e d e t e c t o r n o i s e o r masked by power f l u c t u a t i o n s
caused
f
by r e f l e c t i o n s
in the c e l l .
A p a r t i c u l a r l y s i m p l e method o f enhancing t he s e n s i t i v i t y
of a
microwave s p e c t r o m e t e r i s t h e S t a r k m o d u l a t i o n t e c h n i q u e suggest ed by
Hughes and Wi ls on
(1).
The a b s o r p t i o n c e l l
is c u s t o m a r i l y a long s e c t i o n
o f r e c t a n g u l a r waveguide havi ng a t h i n m et a l
<IL
A ra d io frequency e l e c t r i c
the c e n te r .
connecting
fie ld
fie ld
strip
o r septum mounted a t
is ap p lied to the c e l l
t h e septum to a z e r o - b a s e d s q u ar e - wa ve g e n e r a t o r .
i s on,
t he r o t a t i o n a l
transition
is
s p lit
by
When the
in t o a s e r ie s o f Stark
components which a r e s h i f t e d away from t h e z e ro f i e l d
lin e.
The use o f
a phase s e n s i t i v e d e t e c t o r thus a l l o w s one s e l e c t i v e l y t o mo d ul at e t he
rotational
power.
fact
t r a n s i t i o n s and a l m o s t e l i m i n a t e t h e e f f e c t s o f r e f l e c t e d
The second i m p o r t a n t b e n e f i t o f S t a r k m o d u l a t i o n r e s u l t s
from t he
t h a t t h e n o i se power o f t h e s o l i d s t a t e d e t e c t o r s g e n e r a l l y used i s
inversely proportional
to t h e m o d u l a t i o n f r e q u e n c y .
Thus, d e t e c t o r n oi se
29
is
r e a d i l y r educed by u s i n g h i gh f r e q u e n c y m o d u l a t i o n .
frequencies are
i n t he range 5 -
100 kHz; a t
Typical
higher fre quencies
b r o ad en in g becomes an a p p r e c i a b l e and u n d e s i r a b l e f a c t o r
The S t a r k m o d u l a t i o n t e c h n i q u e
centim eter-w ave studies but several
modulation
description
to F o u r ie r transform sp ectrometers,
of the various
literatu re.
regions r a d i a t i o n
r an gi ng
suited fo r
from source
<^re a v a i l a b l e .
t ypes o f micrbwave s p e c t r o m e t e r s
(3)
lin e
( 2 ).
s i m p l e and w e l l
altern atives,
has been g i v e n by Roussy and C h a n t r y
the r e l a t e d
is
modulation
A b rief
and components
together with a b ib lio graph y of
I n the m i l l i m e t e r - w a v e and s u b m i l l i m e t e r - w a v e
i s u s u a l l y produced by harmonic g e n e r a t i o n ,
hi gh f r e q u e n c y backward wave os ci l l a t o r s . The e x p e r i m e n t a l
t h e s e methods have been d i s c u s s e d by De L u ci a
(4)
or from
aspects of
and Krupnov ( 5 )
respectively.
2. 1
The Microwave S p e ct r o me t er
The e s s e n t i a l
el ement s o f a c o n v e n t i o n a l
a r e a t u n a b l e sour ce o f mi crowave r a d i a t i o n ,
s ys t e m, an a b s o r p t i o n c e l l
and a d e t e c t o r .
i n s t r u m e n t o f t h e Hug he s- Wi 1 son t y p e
cial
(1)
microwave s p e c t r o m e t e r
a f r eq u e n c y measurement
In t h i s work a S t a r k modu la t ed
was used;
it
employed a commer­
microwave s o u r c e . The r e c e n t monograph o f Varma and Hrubesh
describes a very s i m i l a r
i n some d e t a i l .
This
spectrometer,
latter
t h e H e w l e t t Packard Model
(6 )
84 60 A,
i n s t r u m e n t f e a t u r e s a microwave b r i d g e and
a mor5^ s o p h i s t i c a t e d sweeping system.
The sour ce o f microwave r a d i a t i o n
for a ll
o f t he e x p e r i m e n t s
d e s c r i b e d h e r e was a H e w l e t t Pa ck ar d 84 00 B p h a s e - s t a b i l i z e d microwave
spectroscopy source.
T h i s c o n s i s t e d o f an HP H 81 - 8 69 0 A sweep o s c i l l a t o r ,
an HP 8466 A r e f e r e n c e o s c i l l a t o r ,
HP 8 7 09 A s y n c h r o n i z e r .
an HP 8467 B power a m p l i f i e r and an
Most o f t h e 8 - 4 0
GHz f r eq u e n c y r an g e c o u l d be
30
co ver ed w i t h an a p p r o p r i a t e backward wave o s c i l l a t o r
X-band
-
( 8
1 2 . 4 G Hz ),
P-band ( 1 2 . 4 -
plug-in u n it.
18 GHz) and R-band ( 2 6 . 5
In t he
- 40 GHz)
ranges r e s p e c t i v e l y mi crowave power was o b t a i n e d using HP H81 - 8694 B,
HP H81 - 8695 A and HP 8697 A p l u g - i n u n i t s .
D ur in g o p e r a t i o n o f t h e mi crowave source t he s y n c h r o n i z e r was
used t o
tor.
l o c k t h e sweep o s c i l l a t o r
To a c h i e v e a s t a b l e
R- band,
firs t
t o a harmonic o f t he r e f e r e n c e o s c i l l a ­
p h a s e - l o c k i t was o f t e n n e c e s s a r y , e s p e c i a l l y a t
to r o u t e t h e o u t p u t o f t he r e f e r e n c e o s c i l l a t o r
power a m p l i f i e r : An HP 5246 L e l e c t r o n i c
f r e q u e n c y o f t he m i cr owa ve s .
correct
it
had been m o d i f i e d t o d i s p l a y •
t h e microwave f r e q u e n c y o f the sweep o s c i l l a t o r
l o ck p o i n t was chosen.
us in g a c a l i b r a t e d
next section.
The p r o p er harmonic l o c k p o i n t was s e l e c t e d
used f o r t h e measurement
described
i n the
The sweep o s c i l l a t o r was mated t o one end o f the chosen c e l l
u si n g a p p r o p r i a t e w avegui de t r a n s i t i o n
o f f l e x i b l e wa ve g u i de.
s e c t i o n s a nd , when r e q u i r e d , l e n g t h s
A power a t t e n u a t o r and a f e r r i t e
i n s e r t e d between t h e sweep o s c i l l a t o r
needed t o p r e v e n t r e f l e c t e d
which o f t e n
p l u g - i n when t h e
s c a l e on t h e sweep o s c i l l a t o r .
The S t a r k c e l l s
also
c o u n t e r was used to d e t e r m i n e t h e
A lt ho ug h t h e c o u n t e r measured the r a d i o f r e q ­
uency o u t p u t o f t h e r e f e r e n c e o s c i l l a t o r
directly
t h r o u gh t he
i s o l a t o r were
and t h e c e l l .
The i s o l a t o r was
power from r e a c h i n g t h e s o u r ce - a phenomenon
l e d to l e s s s t a b l e p h a s e - l o c k i n g .
The d e t e c t o r s used a t X-band
and P-band were HP H06-X422A and HP H06-P422 A back d i o d e s r e s p e c t i v e l y
w h i l e an HP 11586 A p o i n t c o n t a c t d i o d e was employed a t R-band.
tran sitio n
s e c t i o n s were a g a i n used t o j o i n
t h es e d e t e c t o r s
•
Waveguide
to t h e c e l l .
A
s i m p l e p h a s e - s e n s i t i v e d e t e c t i o n system was used t o m o n i t o r t he a b s o r p t i o n
lines.
An I n d u s t r i a l
Components I n c o r p o r a t e d
1 0 0 kHz s q u a r e wave g e n e r a t o r
was used t o a p p l y a h i g h v o l t a g e t o t h e septum o f t h e S t a r k c e l l
reference signal
t o a P r i n c e t o n A p p l i e d Research Model
and a
120 l o c k - i n a m p l i f i e r .
31
The d e t e c t o r s i g n a l
lock-in am p lifier.
was f i r s t
passed t hr ou gh a p r e a m p l i f i e r and t h e n t o t h e
The o u t p u t o f
the l o c k - i n
s e r v e d as t h e y - a x i s
e i t h e r an o s c i l l o s c o p e o r an HP 680 s t r i p c h a r t
was t aken f rom the sweep o s c i l l a t o r .
f r e q u e n c y was m o n i t o r e d usi ng an
Typical
the x - a x i s
input
For c h a r t p r e s e n t a t i o n the mi crowave
8429 A m a r k e r system.
was t aken t o a voi d s a t u r a t i n g any t r a n s i t i o n s
was seldom measured.
recorder;
input f o r
A l t h o ug h c a re
t h e power l e v e l
d e t e c t o r bias c u r r e n t s ,
in
the c e l l
however , wer e 40 wa
a t R-band and 80 ua a t X-band and P-band.
The s p e c t r a were m o n i t o r e d u si ng bot h a u t o m a t i c and manual
S i n c e S t a r k m o d u l a t i o n was used both t h e f i e l d
on and f i e l d
d i s p l a y e d s i m u l t a n e o u s l y on o p p o s i t e s i d es o f t h e base l i n e .
o f most l i n e s w'ere measured by m a n u a l l y t u n i n g
off
sweeps.
l i n e s were
The p o s i t i o n s
t o t he a b s o r p t i o n maximum
u si ng an o s c i l l o s c o p e d i s p l a y and 'reading d i r e c t l y
t he c o u n t e r f r e q u e n c y .
Weaker l i n e s were d i s p l a y e d on c h a r t r e c o r d i n g s and measured by i n t e r p o ­
latin g
between f r e q u e n c y m a r k e r s .
Measurement ac c ur ac y was e s t i m a t e d t o be
50 kHz or b e t t e r f o r most s i g n a l s and 100 kHz o r b e t t e r , f o r weak l i n e s .
32
2.2
The Mi cro wa ve S t a r k Cel 1s
Two d i f f e r e n t
Stark c e l l s ,
bot h c o n s t r u c t e d from l e n g t h s o f
r e c t a n g u l a r b rass w a ve gu i de , were used in t h i s
X-band c e l l
h av i ng o u t e r c r o s s - s e c t i o n a l
study.
The f i r s t
di me ns i ons o f
1.00 in x 0 .5 0
The c o r r e s p o n d i n g di mensions o f t he l a r g e r S-band c e l l
in;
both c e l l s were 10 f t
usi ng t he X-band c e l l
employed.
in l e n g t h .
slotted
teflon
frequencies
t he S-band c e l l
The septa wer e h e l d
was
in p l a c e a t
and i n s u l a t e d from t he brass wavegui de w i t h
the
thin,
runners.
The S t a r k c e l l s
equipped w i t h m e ch an i ca l
were mated t o a c o n v e n t i o n a l
and d i f f u s i o n
vacuum p o r t a t b o th ends t o f a c i l i t a t e
to be f l o w e d t h ro u gh them;
and t h i n
in x 1 . 5 0
c o n t a i n e d a t h i n copper septum o r i e n t e d p a r a l l e l
t o t h e l a r g e r f a c e o f t h e wave g u id e.
c e n t e r o f each c e l l
were 3 . 0 0
in.
Measurements below 40 GHz were made
w h ile a t higher
Each S t a r k c e l l
was an
s he et s o f m i c a .
more o f t e n w i t h
the c e l l s
g l a s s vacuum system
pumps. Each c e l l
had a brass
r a p i d pumping and t o e n a b l e samples
t he ends o f t h e c e l l s were s e a l ed u si ng
Measurements were made a t
wrapped w i t h
0
-rings
room t e m p e r a t u r e b ut
s t yr o f o a m t r ou g h s f i l l e d
with dry
t
ice.
P r e s s u r e s wer e measured w i t h a N o r t o n Model 801
2.3
D i p o l e Moment Measurements
A t high v o l t a g e s
nents
t h er mo co up le gauge.
'
t he waveform produced
by t he
\
Industrial
I n c o r p o r a t e d squa re wave g e n e r a t o r was q u i t e d i s t o r t e d .
Compo­
T h i s had
the e f f e c t o f b r o ad e n i n g S t a r k components and making a c c u r a t e measure­
ment o f t h e S t a r k f i e l c k i m p o s s i b l e .
t h e r e f o r e a small
I
large a c c u r a te ly
For p r e c i s e S t a r k measurements
s qu ar e wave m o d u l a t i o n v o l t a g e was f l o a t e d on t op o f a
known DC b i a s p o t e n t i a l .
m i xe r c o n s t r u c t e d by C. R.
Parent (7 )
T h i s was done u si ng a v o l t a g e
a c c o r d i n g t o a d e si gn by Mu en t er
\
( 8 ).
33
The DC b i a s p o t e n t i a l
Model
was o b t a i n e d f rom a John F l u k e M a n u f a c t u r i n g Company
412 B DC power s u p p l y .
of t h i s
The c a l i b r a t i o n a c c u r a c y and r e s e t a b i l i t y
s u p p l y were g i v e n as + 0.25°/ and + 0.05% r e s p e c t i v e l y .
For t h e s e
measurements t h e m o d u l a t i o n v o l t a g e was d e t e r m i n e d using an o s c i l l o s c o p e .
2.4
O r i g i n o f Samples and Running C o n d i t i o n s
a.
Sulphur D ic h lo r id e
A sample o f s u l p h u r d i c h l o r i d e ,
o b t a i n e d c o m m e r c i a l l y from
Matheson, Coleman and B e l l , was f u r n i s h e d by P r o f e s s o r N . L .
Paddock o f t he
C h e mi st r y D e p a r t m e n t , U n i v e r s i t y o f B r i t i s h Co lu mb i a. The i n v e s t i g a t i o n
o f t h i s m o l e c u l e was b e s e t by s e v e r a l
osition.
250 ml
15 -
d iffic u ltie s
due t o sample decomp­
The sample was s t o r e d under vacuum a t room t e m p e r a t u r e
round bottom f l a s k .
in a
B e f o r e making each s e t o f measurements a
20 ml sample was t a ke n and f r a c t i o n a t e d
in o r d e r t o remove t h e more
v o l a t i l e c h l o r i n e formed by d e c om p o s i t i o n o f t h e sample and a l s o a small
amount o f s u l p h u r d i o x i d e , whose microwave spect rum i s e x t r e m e l y s t r o n g
relative
to sulphur d i c h l o r i d e .
absorption c e l l
it
occasions,
t h e sample
a t a p r e s s u r e o f about 5 Pa f o r s e v e r a l
f u r t h e r f l o w i n g was r e q u i r e d
on s e v e r a l
usi ng a d r y i c e wrapped
was not p o s s i b l e t o see any s i g n a l s u n t i l
had been f l o w e d t hr ough t he c e l l
h ou rs;
Even t h e n ,
t o o b t a i n good s i g n a l s .
a f t e r rewarming t o room t e m p e r a t u r e i t
As w e l l ,
was found
V
t h a t the c e l l
c o m p l e t e l y a t t e n u a t e d microwave r a d i a t i o n .
then n e c es sa r y t o d i s m a n t l e t h e c e l l
t he mica windows.
cell
Eventually
and c l e a n
it
as w e l l
I t was
as t o r e p l a c e
t he c oppe r vacuum, p o r t s co nnect ed t o t h e
became c l o g ge d and i t was n e c e ss a r y t o p l a c e t h es e i n an u l t r a s o n i c
cleaner fo r several
All
days t o c l e a n s e them o f a b l a c k , g r a n u l a r m a t e r i a l .
measurements f o r s u l p h u r d i c h l o r i d e were made w i t h
t he gas
34
f l o w i n g s l o w l y t hro ug h t he S t a r k c e l l
good s i g n a l s
made.
had been o b t a i n e d runs
None o f
a t pressures o f 0 .4
i n excess o f t h i r t y
2 SC 1 2
-
hours c o u l d be
is d isu lp hu r d i c h l o r i d e
(9).
S2 C1 2 + C l 2
S^Cl^ i s t o o i n v o l a t i l e a t dr y i c e
and c h l o r i n e
Once
t he d e c o m p o s i t i o n p ro d uc t s gave r i s e t o d e t e c t a b l e s i g n a l s .
One o f t he p r o b a b l e d e co m p o s i t i o n p roduct s
However,
- 4 . 0 Pa.
has no microwave spect rum.
'
t e m p e r a t u r e to g i v e s i g n a l s
No a t t e m p t was made t o
identify
«
t h e b l a c k subst ance which formed i n t he wavegui de and vacuum p o r t s .
yi
Dichlorosilane
b.
A sample o f
McLean,
Dr .
N.P.C.
normal
d i c h l o r o s i l a n e was p r o v i d e d by Dr .
Westwood and D r .
U n i v e r s i t y o f B r i t i s h Co lu mb i a.
t e m p e r a t u r e when n o t
i n use.
u si ng p r e s s u r e s o f 0 . 2
D.C.
F r o s t of the Chemistry Department,
The sample was s t o r e d a t
A ll
- 3 . 0 Pa.
R . A. N.
liq u id
nitrogen
s p e c t r a we re run a t d r y i c e t e m p e r a t u r e
Under t h e s e c o n d i t i o n s
t h e sample was
s t a b l e f o r a b o u t an hour a f t e r which t he i n t e n s i t y o f t h e d i c h l o r o s i l a n e
l i n e s was a p p r e c i a b l y d i m i n i s h e d b u t no new s i g n a l s were a p p a r e n t .
practice
this
c.
sample d e t e r i o r a t i o n
Propiolyl
were both s u p p l i e d by Dr.
propiolyl
W.J.
Balfour,
Chemistry Department,
chloride-d
U niversity
p r o p i o l i c a c i d and p r o p i o l i c a c i d - d ^ r e s p e c t i v e l y
a c c o r d i n g t o t h e method o f B a l f o u r ,
HCiCCOOH + PCI
stored
c h l o r i d e and p r o p i o l y l
These m o l e c u l e s were p r ep a r ed by r e a c t i n g phosphorus p e n t a -
c h l o r i d e w i t h normal
As p r o p i o l y l
p r o v i d e d no d i f f i c u l t i e s .
Chloride
Samples o f normal
of V icto ria.
In
5
G ri e g and V i s a i s o u k
(10).
•> HC=CC0C1 + P0C1 3 + HC1
c h l o r i d e r e a d i l y decomposes a t
room t e m p e r a t u r e t h e sampl es,
i n a p yrex t u b e , were kep t immersed i n l i q u i d
n i t r o g e n when not i n
35
use.
For m a n i p u l a t i o n s on t h e vacuum l i n e
main tain ed
propiolyl
in a Dewar f i l l e d
with dry
ice.
c h l o r i d e were measured w i t h
P r ess u r es used we re i n t h e range 0 . 3
t h e sample was q u i t e s t a b l e
t he s t o r a g e v e s s e l s were
All
rotational
t he S t a r k c e l l
-
3 . 0 Pa.
spectra of
wrapped i n d r y i c e .
Under t h e s e c o n d i t i o n s
i n t he a b s o r p t i o n c e l l ;
broad band sweeps
r e q u i r i n g about an hour t o compl et e w e re c a r r i e d o u t w i t h o u t n o t i c e a b l e
sample d e t e r i o r a t i o n .
A l t h o u g h t he i n f r a r e d and Raman s p e c t r a o f t h ese
samples showed t h e p r es en ce o f a POCl^ i m p u r i t y
experimental
low f o r
it
conditions
u sed,
t o be d e t e c t e d
t he v o l a t i l i t y
(
1 1
),
under t h e
o f t h i s m o l e c u l e was too
i n t h e mi cr owave spect r um.
36
Bibliography
1.
R.H.
Hughes and E.B.
Wilson,
J r.,
Phys.
Rev.
7J_, 562 ( 1 9 4 7 ) . ,:
2.
W. Gordy and R . L . Cook, Mi crowave M o l e c u l a r S p e c t r a , pp.
I n t e r s c i e n c e P u b l i s h e r s , New Yor k, 1970.
50-53,
•k
3.
G. Roussy and G.W. C h a n t r y , i n Modern A spect s o f Microwave Spec­
t r o s c o p y , (G.W. C h a n t r y , E d . ) , pp. 1 - 6 3 , Academic P r e s s , London,
1979.
4.
F . C . De L u c i a , i n M o l e c u l a r S p ec t r o s co p y : Modern R e s e a r c h , ( K . N .
Rao, E d . ) , V o l . I I , pp. 6 9 - 9 2 , Academic P r e s s , New Y o r k , 1976.
5.
A . F . Krupnov, i n Modern As pe ct s o f Mi cr owave S p e c t r o s c o p y ,
C h a n t r y , E d . ) , pp. 2 1 7 - 2 5 6 , Academic P r e s s , London, 1979.
6
. R. Varma and L.W. Hrubesh, Chemical A n a l y s i s by Mi crowave R o t a t i o n a l S p e c t r o s c o p y , pp. 3 5 - 3 9 , John W i l e y and Sons, New Y o r k ,
1979.
7.
8
(G.W.
C.R.
. J.S.
9.
A. H.
Parent,
P h. D.
Muenter,
Spong, J .
Thesis,
U n i v e r s i t y o f B r i t i s h C o l u mb i a ,
P h . D. T h e s i s ,
Chem.
10.
W.J. B a l f o u r ,
(1974).
11.
W.J. B a l f o u r , R . H .
31, 967 ( 1 9 7 5 ) . *
Soc.
Stanford U n i v e r s i t y ,
1 972.
1962.
1283 ( 1 9 3 4 ) .
C . C . G r i e g and S.
M itchell
Visaisouk, J.
and S. V i s a i s o u k ,
Org. Chem.
3 9,
725
S p ec t r o c hi m . A c t a A
♦
C hapter 3
The Mi crowave Spectrum o f S u l p h u r D i c h l o r i d e
The r o t a t i o n a l
a special
attractio n
s p e c t r a o f v e r y s i m p l e m o l e c u l e s have long h e l d
for spectroscopists.
These have been o f
interest
not o n l y as a source o f p r e c i s e m o l e c u l a r c o n s t a n t s b ut a l s o as
fundamental
tests
of v ib r a t io n - r o t a t io n
theory.
asymmetri c t o p t r i a t o m i c s a r e p a r t i c u l a r l y
transitions
For mi crowave s t u d i e s
suitable
b e ca u se,
f o r non­
hydrides a t
least,
accessible.
Such s p e c t r a have been a n a l y s e d t o p r o v i d e v a l u e s f o r a
v a r ie t y of molecular constants,
and h i g h e r o r d e r c e n t r i f u g a l
coupling co n s ta n ts ,
As w e l l ,
including ro ta tio n a l
distortion
o f t e n been o b t a i n e d ;
0#F 2
(4),
SF2
n u c l e a r q u ad r u p o l e
intram olecular p o te n tia l
f u n c t i o n has
in a f ew f a v o u r a b l e ca?es t h e c u b i c as w e l l as t h e
constants
have been d e t e r m i n e d .
C2v symmetry, where t he p o t e n t i a l
has been done f o r ,
constants,
constants, q u artic
d i p o l e moments and bond l e n g t h s and bond a n g l e s .
i n f o r m a t i o n about t h e
harmonic p o t e n t i a l
i n v o l v i n g a l a r g e range o f J v a l u es a r e
amongst o t h e r s ,
( 5 ) and O3
For m ol e c u l e s o f
f u n c t i o n has a v e r y s i m p l e form t h i s
t h e m o l ec ul e s S0 2
(6 ,7 ).
(1 ,2 ),
Se0 2
(3),
-
The p r e s e n t st udy o f s u l p h u r d i c h l o r i d e was u n d er t a k e n w i t h
two p a r t i c u l a r aims i n mi nd.
tia l
function
The f i r s t was t o o b t a i n a harmonic p o t e n ­
f o r t h e m o l e c u l e using r o t a t i o n a l
w o r t h w h i l e as t h e v a r i o u s
unacceptable v a r i a t i o n .
published p o t e n t i a l
For exampl e,
data alo n e.
functions
T h i s seemed
(8-15)
show an
values o f the s t r e t c h i n g fo rc e
38
°-l
r a ng i ng f r o m 1 . 8 mdyn A
constant
been r e p o r t e d .
This s i t u a t i o n
as si gn men t o f t h e s t r e t c h i n g
( 8 ),
the v i b r a t i o n a l
°-l
t o 2 . 6 4 mdyn A
(15)
have
i s t h e r e s u l t o f an a m b i g u i t y i n t h e
\
f u nd am en t al s and o f i n s u f f i c i e n t
d e t e r m i n e u n i q u e l y t he p o t e n t i a l
values f o r
(14)
constants.
d a t a to
The most commonly q uot ed
f u n d am en t al s a r e those o f Stammreich e t a j _ . ,
namely 5 1 4 , ' 2 0 8 and 535 cm"^ f o r
only th re e pieces o f d a ta a v a i l a b l e
and
x> y
respectively.
Wi th
to s p e c if y the fo u r q u a d r a tic
n
potential
c o n s t a n t s , some assumptions were r e q u i r e d and t h e subsequent
variations
d etailed
observed a r e h a r d l y s u r p r i s i n g .
s t u d y Savoi e and Tr emblay
p r e v i o u s l y a s si gn e d as
(15)
As w e l l ,
suggested t h a t t h e 535 cm ^ band
of sulphur d i c h l o r i d e
caused by a d i s u l p h u r d i c h l o r i d e
^ C ^ ')
i n a more r e c e n t and
( 8 ) m i gh t have been
im purity.
Their resu lts
not a l l o w an unambiguous assignment o f t h e s t r e t c h i n g
although p o l a r i z a t i o n
refinements
o scillato r
data
fundamentals
and
( f o r t h e l i q u i d o n l y ) and f o r c e c o n s t a n t
f a v o u r e d t h e c ho i ce
approximation,
did
>
-J y
Because,
i n t h e harmonic
the d e s i r e d q u a d r a t i c f o r c e c on st an ts - can be
exp re ss ed e x p l i c i t l y
constants,
i n terms o f t h e q u a r t i c c e n t r i f u g a l d i s t o r t i o n
,
)
an a t t e m p t t o o b t a i n a c c u r a t e v a l u e s f o r t h e d i s t o r t i o n c o n s t a n t s
appeared t o be w a r r a n t e d .
th a t of Murray,
were l i m i t e d
vibrational
L ittle ,
In t h e o n l y p r e v i o u s mi crowave i n v e s t i g a t i o n ,
W i l l i a m s and W e a t h e r l y
t o seven low J l i n e s o f t h e
state.
From t h i s
(16),
the data obtained
32 35
S C l^ s p e c i e s
in i t s
ground
l i m i t e d d a t a s e t v a l u e s f o r t h e r o t a t%
ional
c o n s t a n t s o n l y were d e t e r m i n a b l e .
M ur r ay et^ a j [ . , d i d ,
however, measure
t h e m o l e c u l a r d i p o l e moment and o b t a i n a c c u r a t e v a l u e s f o r t h e c h l o r i n e
nuclear quadrupole coupling co nstants.
T h eir study,
i n v e s t i g a t i o n , was p la gu e d by sample d e c o m p o s i t i o n .
like
the present
v
.
39
'V
_
t
*
The second aim o f t h e p r e s e n t s t ud y was a r e f i n e m e n t o f t h e
m olecular s tr u c tu r e .
T h e r e have been t h r e e e l e c t r o n d i f f r a c t i o n
g atio n s o f the sulphur d i c h l o r i d e molecule St ev en so n and Beach ( 1 7 ) and by Pal mer ( 1 8 )
two v e r y e a r l y
in v e s ti­
s t u d i e s by
and t he seldom quoted work
o
of Morino, M urata,
(4)
I t o and Nakamura ( 1 4 ) .
o b t a i n e d f r om t h i s
The r^ bond l e n g t h o f 2 . 0 0 6 A
l a s t s t ud y i s somewhat s h o r t e r t ha n t h e r Q
o
value o f 2.014
(5)
A d e r i v e d from t h e microwave r es u l .t s o f Mur ray e t a l .
(15).
I t was f e l t
that additional
isotopic,
a nd ,
if
p o s s ib le , excited
state,
d a t a , w o u l d e na bl e a s t r u c t u r e d e t e r m i n a t i o n o f much improved
precision.
In th e present study r o t a t i o n a l
is o to p ic species,
32 35
S Cl^,
s t a t e and up t o J -
32 35
37
S Cl
Cl
species,
and a p a r t i a l
14 i n t he v^ = 1 e x c i t e d
ground s t a t e
ments ext ended up t o J = 4 0 .
the r o t a t i o n a l
constants, qu a rtic c e n trifu g a l
determ ined.
including v ib r a tio n a l
c o n s t a n t s and i n e r t i a l
results e ffe c tiv e ,
partial
For t h e
t h e se me a su r e­
The d a t a have been a n a l y s e d t o y i e l d
distortion
values
constants
A harmonic p o t e n t i a l
f u n c t i o n has been d e r i v e d which i s c o n s i s t e n t w i t h a l l
d isto rtio n
state.
l i n e s o n l y were a s s i g n e d ;
s e t of s e x tic d is t o r t io n constants.
spectroscopic d a t a ,
o f t h e most abundant
have been measured up t o J = 60 i n t he ground
vibrational
for
transitions
of the a v a ila b le
wavenumbers, q u a r t i c c e n t r i f u g a l
defects.
Using o n l y t he microwave
s u b s t i t u t i o n and a v e r a g e s t r u c t u r e s have been
F u r t h e r , w i t h some a s su m pt i o n s ,
s t r u c t u r e has been e s t i m a t e d .
the e q u i l i b r i u m molecular
40
3. 1
Observed Spectrum and Assignment
In t h e i r
s t u dy o f s u l p h u r d i c h l o r i d e M u r ra y e t a j . ( 1 6 )
noted
th a t the
observed spectrum c o n s i s t e d o f t x t y p e t r a n s i t i o n s o n l y .
Therefore
the K Ks e l e c t i o n
a c
r u l e s a r e ee-»-K) 0
and eo-f-K)e where
r e s p e c t i v e l y d enot e even and odd v a l u e s o f K
a
t h e usual
a J=0,+1
lines exhibited
selection
ru le applies.
and K
In a d d i t i o n , many o f
required
In the present i n v e s t i the m e t h o d s ^ o u t l i n e d
Because o f t h e m o l e c u l a r symmetry s p i n s t a t i s t i c s
For s p e c i e s ^ c o nt a i n i n g e q u i v a l e n t c h l o r i n e
t h a t t he t o t a l
vibratio nal,
t he
n u c l e a r q u ad ru p o l e h y p e r f i n e s t r u c t u r e due to t h e
g a t i o n t h e h y p e r f i n e s t r u c t u r e was a n a l y s e d u si ng
im po rtant.
( 1 9 ) ; as w e l l ,
C
pr esence o f the two s p i n 3 / 2 c h l o r i n e n u c l e i .
i n C h a p t e r 1.
and o
e
*
rotational
wavefunction -
nuclei
it
were
was
t he p r o d u c t o f e l e c t r o n i c ,
and n u c l e a r s pi n w a v e f u n c t i o n s
- be a n t i -
symmetric w i t h r e s p e c t t o i n t e r c h a n g e o f t he two c h l o r i n e atoms by
rotation
about t h e
symmetry a x i s
he re t he e l e c t r o n i c and v i b r a t i o n a l
rotational
60
and J
Oc
s pe c i e s s t u d i e d
w a v e f u n c t i o n s were s y m m e t r i c ^ The
J
levels
(21).
ee
and J
f o r ee+-*oo r o t a t i o n a l
ee+-K)o l i n e s were e s p e c i a l l y s i m p l e ,
oo
transitions
transitions.
b ei ng t r i p l e t s - w i t h
component a t t h e u n s p l i t l i n e
position.
have been di sc u sse d by Murr ay et^ al_. ( 1 6 )
/""'X
sbmewhfct d i f f e r ^ t t .
levels^ n d
Thus o n l y symmetric spi n
had to be c o n s i d e r e d f o r ecH-»oe r o t a t i o n a l
antisymmetric spin fun ctions
central
For a l l
w a v e f u n c t i o n s were symmetri c f o r J
antisymmetric f o r J
functions
(20).
c o n s t a n t s o f Mur ray e t a j . ( 1 6 ) .
The
a strong
These c o n s i d e r a t i o n s
b ut t he n o t a t i o n they used i s
*
The p r e s e n t i n v e s t i g a t i o n was begun by p r e d i c t i n g r i g i d
f r e q u e n c i e s and h y p e r f i n e p a t t e r n s f o r
and
the
32 35
S Cl2
The 1^ + L, = I_,
species using
rotor
the
I_ + J. = F c o u p l i n g
41
scheme was used whenever^a v a l u e o f I was r e q u i r e d ;
w a v e f u n c t i o n s were symmet ric f o r
I
= 0 or 2.
I = 1 o r 3 and a n t i s y m m e t r i c
1
for
F i v e o f t h e seven p r e v i o u s l y measured t r a n s i t i o n s were
a c c e s s i b l e u si ng t h e H e w l e t t - P a c k a r d s p e c t r o m e t e r .
• t h e se
t h e n u c l e a r sp in
An e x a m i n a t i o n o f
i n e s ^ q u i c k l y c o n f i r m e d t h e p r e v i o u s as si gn men t and t he p r e c i s i o n
o f t he r e p o r t e d q u a d r u p o l e c o u p l i n g c o n s t a n t s .
Additional
low J l i n e s
s u f f i c i e n t t o b egin a b o o t s t r a p as si gnment p rocess were r e a d i l y found.
P ro mi ne n t among t hes e wer e Q- branch l i n e s o-f t h e s e r i e s ^
which formed a bandhead a t a p p r o x i m a t e l y 2 9 . 9 GHz.
u s i ng t h e H a m i l t o n i a n o f e q u a t i o n 1 . 1 1 ,
fugal
d istortion
constants,
predict fu rth e r tra n s itio n
predicted
lines,
fittin g
j
^
_ 2
j
]»
These l i n e s were f i t
now i n c l u d i n g
the q u a r t i c c e n t r i ­
and t h e r e s u l t i n g
c o n s t a n t s were used t o „
i
'
The pr ocess o f measuring w e l l -
frequencies.
t he d a t a and p r e d i c t i n g a d d i t i o n a l
f r e q u e n c i e s was r e p e a t e d s e v e r a l
transition
times wdth t h e measurements g r a d u a l l y
\
b ei ng ext ended t o hi gh J .
The low v a l u e o f t h e d i p o l e moment, 0 . 36 D
*
( 1 6 ) , made many l i n e s d i f f i c u l t
>
to modulate.
o f t he weak and v e r y h i g h f i e l d
low K
t h e 21^
2 ^2
18 t r a n s i t i o n .
J h i s was t r u e E s p e c i a l l y
‘
P- and R- branch l i n e s
such as
These could be measured o n l y f rom c h a r t
recordings.
Subsequent t o t h e assi gnment o f the
sear eh was made f o r v i b r a t i o n a l
4
0 1
j_i
«- Jq j
transitions a ll
32 35‘
S Cl2
s a te llite s .
ground s t a t e
The 1 ^
lines
«- Oqq and
had high f r e q u e n c y s a t e l l i t e s which
e x h i b i t e d t h e ‘same s p i n s t a t i s t i c s
as t h e ground s t a t e
lines.
Their
/
i n t e n s i t y a t d r y i c e t e m p e r a t u r e was r o u g h l y
lines.
They were t h e r e f o r e a s si g n ed t o t he v 0
C-
'
state.
A fter a rigid
rotor f i t
T ran sitio n s o f the
% o f t h e ground s t a t e
= 1 or
(010)
excited
\
some f u r t h e r l ow J l i n e s were f o un d.
A sear ch f o r l i n e s o f a d d i t i o n a l
next.
2 0
32 35
37
S Cl
Cl
i s o t o p i c s p e c i e s was a t t e m p t e d
s p ec i e s wer e e a s i l y
l o c a t e d usi ng
42
rotational
constants c a lc u la t e d
e t aJL. ( 1 6 ) .
principal
A fte r estimating
in e rtia l
axis
system consequent on i s o t o p i c s u b s t i t u t i o n
were t r an s f o r m e d
a x i s system.
and t h e i r
inverses
=
x zz
For t h i s c a l c u l a t i o n
2
t o t he ^ S ^ C l ^ C l
t he f o l l o w i n g e q u a t i o n s -
* a a cosS a
6
~ »bbs i " 2|iZa
. 2
Za - s i n 9Za
_
* a a s l A Za ' * b b c o A Za
. 2'
T T
sir, eZa - cos e Za
=
y
xx
yy
t e n s o r and e^a i s
(3.,,
cc
Here x v ¥ » x uv/ and x ,
xx
yy
7
are the p r i n c i p a l
v a l u e s o f t h e q u ad r u p o l e c o u p l i n g
t h e a n g l e between t h e Z p r i n c i p a l
r u p o l e t e n s o r ( t a k e n to be c o i n c i d e n t w i t h t h e S-Cl
tial
axis;
xaa * x ^
in t h e bond a x i s
t he
moments o f ^ C 1
in e rtia l
system t h e
35
of
»
37
Cl
and ^ C 1
nucleus.
32 35 37
S Cl
Cl
37
a x i s system.
bond) and t h e £ i n e r ­
It
was t hen assumed t h a t
Cl c o u p l i n g c o n s t a n t s coul d be o b t a i n e d
Cl v a l u e s by 1 . 2 6 8 8
(23)).
and n = 1 . 5 2 9 f o r t h e ^ C 1
fo r the
axi,s o f t h e quad­
and x cc a r e t h e components o f t h e q u a d r u p o l e t e n s o r
r e f e r r e d t o t he p r i n c i p a l
by d i v i d i n g
t he
) - were needed:
cos
y
y
(2
s t r u c t u r e o f Murray
t he r o t a t i o n o f t h e m o l e c u l e i n t he
coupling constants o f
in ertial
from t he e f f e c t i v e
(the r a t i o of
the q u a d r u p o l e
T h i s c a l c u l a t i o n gave x = = - 3 7 . 8 5 MHz
da
n ucl eus and x
aa
-
-31.61
MHz and n = 1 . 3 8 6
Because o f t he l oss o f symmetry no spi n f u n c t i o n s
had a z e r o s t a t i s t i c a l
weight.
The r e s u l t i n g h y p e r f i n e
p a t t e r n s were t hus more complex and^measurement d i f f i c u l t i e s
caused by S t a r k components o v e r l a p p i n g t h e z e r o f i e l d
ft
lines
were o f t e n
- especially
at
low J . --The ^2 J
^1 J 1 Q'
^
r a n c *1
l i n e s were a g a i n p r o m i n e n t w i t h
a bandhead n e a r 2 9 . 8 GHz, v e r y c l o s e to t h a t o f t h e
F ig u re 3.1
2
illu strates
t he bandheads f o r
and ^ S ^ C l ^ C l
transitions.
species.
t h e ground s t a t e s o f t he
sp e ci es t o g e t h e r w i t h
the r e la t e d ^
A b o o t s t r a p as si gnment p ro ce ss e n a bl e d f u r t h e r
J
1 ^
J
1
J
l i n e s up to
J = 40 t o be l o c a t e d .
A summary o f t he obs er ve d and c a l c u l a t e d h y p e r f i n e
structure
two o f t h e s e in T a b l e 3 . 1
is given f o r
F_^ + L , = £ c o u p l i n g scheme has been used.
where t h e J + L| = F ^ ,
In a l l
cases t h e d i f f e r e n c e s
between t h e c a l c u l a t e d and observed f r e q u e n c i e s a r e l e ss
than t he measure­
ment e r r o r .
It
m o l e cu le s
detect.
should be mentioned f i n a l l y
in
t he v-j =
1
and v^ =
T h i s was t r u e as w e l l
species.
T r a n s it io n s o f the
1
th at transitions
excited
s t a t e ' w e r e too weak to
f o r ground s t a t e
32 37
S C l2
involving
lines of
substituted
s p e c i e s were v i s i b l e on c h a r t
r e c o r d i n g s b u t few were ass i gned as t hey were weak and p r o v i d e d no
additional
structural
information.
44
T a b l e 3.1
Examples o f H y p e r f i n e S t r u c t u r e
F'
Fi
Fa
F1
in T ra n s itio n s o f
Calculated(MHz)
Frequency
Observed(MHz)
Frequency
1 5 ( 2 , 1 3 ) <- 1 5 ( 1 , 1 4 }
13.5
12
13.5
12
35763.38
35763.44
13.5
15
13.5
15
35763.78
35763.85
16.5
15
16.5
15
35763.90
35763.85
16.5
18
16.5
18
35764.26
35764 .21
14.5
13
13.5
13
35767.23
35767.25
13.5
14
13.5
14
35767.63
35767.73
16.5
16
16.5
16
35767.77
35767.73
15.5
17
16.5
17
35768.14
b
13.5
13
14.5
13
35768.54
b
14.5
16
14.5
16
35768.89
35768.92
15.5
14
15.5
14
35769.00
35768.92
16.5
17
15.5
17
35769.38
35769.42
14.5
14
14.5
14
35772.40
35772.46
J
I
14.5
15
14.5
15
35772.73
35772. 81
15.5
15
15.5
15
35772.88
35 772 . 81
15.5
16
15.5
16
35773.25
35773.27
45
T a b l e 3.1
Examples o f H y p e r f i n e S t r u c t u r e in T r a n s i t i o n s
3 2 S35C 1 3 7 C1
. F'
Fi
(continued)
Fa
F 1
16(2,14)
of
. Calculated(MHz)
Frequency
bserved(Mh
Frequency
0
16(1,15)
14.5
13
14.5
13
3 8 5 5 3 . 71
38553.73
14.5
16
14.5
16
38554.14
38554.24
17.5
16
17.5
16
38554.27
38554.24
17.5
19
1 7. 5
19
38554.65
38554.66
15.5
14
14.5
14
38558.10
38558.13
14.5
15
14.5
15
38558.54
38558.67
17.5
17
17.5
17
38558.68
38558.67
16.5
18
1 7. 5
18
38559.07
b
14-. 5
14
15.5
14
38559.60
b
15.5
17
15.5
17
38559.97
38560.03
16.5
15
16.5
15
38560.09
38560.03
17.5
18
16.5
18
3 85 60 . 51
,38560.57
15.5
15
15.5
15
3 85 64 .0 1
38564.06
15.5
16
15.5
16
38564.37
38564.46
16.5
16
1 6. 5
16
38564.52
38564.46
16.5
17
16.5
17
38564.92
38564.93
✓
a D a t a is g i v e n o n l y f o r t h o s e h y p e r f i n e components w i t h an i n t e n s i t y
g r e a t e r t h a n 2 % o f t he t o t a l i n t e n s i t y t h a t i s , t h e ( 2 I-| + 1 ) ( 2 1 2 + 1 )
s t r o n g e s t components.
Unprimed and primed F l a b e l s r e f e r r e s p e c t i v e l y
t o t h e i n i t i a l and f i n a l s t a t e s .
k Observed b u t o ver l a pp e d by i n t e r f e r i n g
S t a r k components.
46
o
CVJ
cvj
CD
rO
o
O0
o
to
c
o
CVJ
CO
c
(Vi
(0
O
o
o
c
ra
C O
M—
I
cr
CO
4CNJ
<o
CVJ
a;
aj.
S-
3
Cn
CVJ
CVJ
47
3.2
Analysis of
t h e S u l p hu r D i c h l o r i d e S p e c t r a
A fte r prelim inary cen trifu g al
y i e l d e d good v a l u e s f o r
t he r o t a t i o n a l
distortion
a n a l y s e s had
constants,
the h y p o t h e t i c a l
unsplit
l in e frequencies of a l l
f o r the
32 35
S C1^ s p e c i e s t he q u a d r u p o l e c o u p l i n g c o n s t a n t s of
Mur r ay e t a l .
32 35 37
S Cl
Cl
(16),
namely
x .
da
t he v a l u e s d e r i v e d
t r a n s i t i o n s were c a l c u l a t e d using
= - 3 8 . 9 8 MHz and n = 1 . 4 5 8 , and f o r
in the previous
section.
The A r e d u c -
ir1
t i o n o f Wat son' s H a m i l t o n i a n
1.11,
was used t o f i t
of the
32 35
S C12
in the
t he u n s p l i t
representation,
lin e
frequencies.
way t h e d a t a c o u l d be f i t
t ha n r o u g h l y 30 were used.
distortion
adequately i f
resulted
than t h e o t h e r s .
in a s t e a d i l y
At t h i s
constants o n l y .
in creasing standard d e v ia t i o n o f
When h^,
made w i t h a l l
included
a
The
i s shown i n
constant,
indeterm inate
o f H^ gave t h e r e s u l t s shown i n T a b l e 3 . 2
U n f o r t u n a t e l y the choice o f s e x t i c constants
t o be r e t a i n e d
r e f i n e m e n t s e s s e n t i a l l y as good as t h o s e o f F i t 2
can be had i f e i t h e r HJK> H^,
I
the f i t ;
t o t h e most p o o r l y d e te r m i n e d q u a r t i c
c o n s t a n t was HK; t h e removal
In a l l
to higher J
t he r e f i n e m e n t p r o c e s s .
s e x tic constants
l e ss
1; most o f t he s e x t i c c o n s t a n t s a r e i n d e t e r m i n a t e .
the " c o r r e c t i o n "
was s u b j e c t i v e ;
with J greater
A c c o r d i n g l y t he
and s u b s e q u e n t l y Hj were removed t h e o n l y r e m a i n i n g
as F i t 2.
In t h i s
was d e t e r m i n e d r a t h e r
The a d d i t i o n o f f u r t h e r d a t a
s e x t i c c o n s t a n t s were i n t r o d u c e d i n t o
T a b l e 3 . 2 as F i t
analyses
p o i n t good v a l u e s had been o b t a i n e d
maximum v a l u e o f 0 . 5 6 MHz was reached a t J = 6 0 .
resu lt of a f i t
In itia l
no t r a n s i t i o n s
o f the q u a r t i c c o n s t a n t s a l t h o u g h
precisely
equation
ground s t a t e d a t a were made u sing the r o t a t i o n a l
c o n s t a n t s and t h e f i v e q u a r t i c
for a ll
I
c a s e s , however,
h j and h K o r HJ|(, ,
I
hj,
hJK and hK a r e k e p t .
t h e v a l u e s o f t h e q u a r t i c c o n s t a n t s agr eed
48
w ithin
t h e e s t i m a t e d s t a n d a r d d e v i a t i o n s . A ls o g i v e n a r e t h e r e s u l t s
of a refinem ent,
exclu ding a l l
F it
3 , made u s i n g .onty t he d a t a
up to J = 30 and
sextic constants.
A few comments should be ma9|? about t h e v a r i o u s
S
C1^
refinements.
Wi th t h e p o s s i b l e e x c e p t i o n o f t h e p o o r l y d e t e r m i n e d
constant a l l
o f t he q u a r t i c d i s t o r t i o n
variation
from one f i t
to the n ext.
constants
a r e t o be used t o d e r i v e a mea n i ng f ul
As w e l l ,
is e vid en t t h a t
it
measurements beyond J = 30.
little
potential
if
function.
has been g a i n e d by e x t e n d i n g t he
T h i s would n ot have been t he case i f
more v a r i e d d a t a s e t had been o b t a i n e d .
transitions
,.
I\
show o n l y a s l i g h t
This of course is e s s e n t ia l
the r e s u l t s
6
In p a r t i c u l a r ,
a t h i g h e r v a l u e s o f J and K
a
a
Q branch
and P and R branch l i n e s a t
#•*
t h e same o r h i g h e r J b ut w i t h
No a d d i t i o n a l
l ow er K v a l u es woul d have been u s e f u l .
a
Q branch l i n e s were a c c e s s i b l e ,
R branch l i n e s were e i t h e r
howev er , and t h e P and
too weak t o measure o r
i m p o s s i b l e to
modulate.
The d a t a f o r ^ S ^ C l ^ C l
were f i t t e d
d i s t o r t i o n c o n s t a n t s as were r e t a i n e d
The r e s u l t i n g c o n s t a n t s a r e a l s o g i v e n
v^ = 1 e x c i t e d
state of
and t h e c e n t r i f u g a l
32 35
S
u s i n g the same s e t o f
for Fit 2 of
t he
in Table 3 . 2 .
3? 35
S C 1^ l i n e s .
F in ally,
f o r t he
o n l y a few low J l i n e s , were measured
d i s t o r t i o n c o n t r i b u t i o n s were assumed equal
t o t h ose
i
o f t h e ground s t a t e .
A summary o f t h e obse r ved and c a l c u l a t e d u n s p l i t
■f
l i n e freq uen cies o f the various
Table 3 . 3 .
sulphur d i c h l o r i d e species
For t h e ground s t a t e o f
were o b t a i n e d u si n g t h e F i t
• 32 35
S Cl ^ t he c a l c u l a t e d
is given
in
fre quencies
2 constants o f Table 3 . 2 .
«
49
Table 3.2
R o t a t i o n a l C o ns t an t s and C e n t r i f u g a l
o f Sulphur D i c h l o r i d e
D i s t o r t i o n C o ns tan ts
32s 35c i 2 (Ground S t a t e )
F it
F it
2
F it
3
14613.5968(52)
14613.5985(67)
2920.8703(13)
2920.8702(11)
2920.8694(15)
2430.6943(12)
2430.6943(10)
2430.6930(13)
1.3249(46)
1.3249(25)
1.3232(35)
A(MHz)
14613.5966(59 )b
B(MHz)
C(MHz)
Aj(kHz)
AJ K ( kHz)
-14.597(55)
-14.604(37)
-14.516(48)
AK(kHz)
138.012(83)
138.027(70)
137.808(85)
6
j(kHz)
<$K(kHz)
0.33991(82)
0.33968(50)
0.34120(44)
3.913(59)
3.927(24)
3.811(21)
H j(H z)
-0.0007(98)
HJK( Hz )
-0.15(16)
-0.209(14)
c
0.12(50)
0.345(22)
c
HKJ( Hz )
Hk (H z )
0.48(172)
hj(Hz)
-0.0023(13)
hJ K (Hz)
hK(Hz)
^Hax
Std. D e v ia tio n
o f F i t (MHz)
I
la
0.14(25)
c
0.048
c
c
-0.00282(33)
c
c
0.198(29)
1.3(45)
60
c
c
60
0.047
c
30
0.052
50
Table 3.2
R o t a t i o n a l C on s t a n t s and C e n t r i f u g a l
o f Sulphur D i c h l o r i d e ( c o n tin u e d )
3 2
A(MHz)
S3 5 C1 3 7 C1
(Ground S t a t e )
14490.169(21)
3 2
D i s t o r t i o n C o n st a nt s
S3 5 C1 0
( vn = 1 S ta te )
14732.830(10).
B(MHz)
2841.1929(47)
2918.3174(34)
C(MHz)
2371.9634(3$)
2426.1032(34)
A j(kHz)
d
1.239(13)
AJK( kHz)
-14.40(13)
d
a k ( kHz)
135.68(18)
d
6
j(kHz)
0.3168(35)
d
6
K(kHz)
3.62(21)
d '
VH
z
)
-0.256(68)
d
0.36(13)
d
Hk j (H z )
d
-0.0050(22)
hj(Hz)
0.27(10)
hK(Hz)
40
J Max
St d. D e v i a t i o n
o f F i t (MHz)
a The v a r i o u s f i t s
_
d
17
0.035
0.063
a r e d i s cu s s e d i n t h e t e x t ,
k Errors c i t e d are standard e r r o r s .
c C on s t an t was c o n s t r a i n e d t o z er o .
^C en trifu g al
state.
distortion
c o r r e c t i o n s assumed t o equal
t h o se o f t h e ground
51
Table 3.3
Observed R o t a t i o n a l
Transition
O b se r v ed 3
Frequency
3 2
S3 5 C1„ ( gr ound v i b r a t i o n a l
11
, 1
" °0
'
2 0 , 2
2 2 , 0
"
2 1 , 1
3
- 2
1,3
2,2
-
\,3
4 \
2
5
0,2
3
1,3
0,4
12688 .1 1
-0.09
0.03
35091.60
-1.77
0 . 1 0
26527.86
-0
0.09
37291.67
-1.64
14573.30
-0
0 . 1 0
17881.46
-0.54
"
31828.24
1 ,7 \
1,7 ‘
7 2 , 6
8
2,6 "
7
3 ,5
"
8
1 ,7
2,7 "
9
1, 8
8 2 , 6
1 0
2,8 '
1
° 1 ,9
1 0
1,9 ‘
9
2,8
1 0
1,9 "
1 0
1 2 2 , 1 0
?
2,10
0.03
-0
. 0 2
0 . 1 1
, 6
6 ] } b
7
-0.05
t
0.05
0,4
0.05
. 1 0
35143.10
2,4 "
0 . 0 0
. 0 1
- 4
8
1
-
-1.04'
8 0 , 8
9
17044.19
33615.87
1,5
Deviation
state)
- 4
,\ \
1.3
6 1 ,5 ‘ ^0
6
D istortion^
Correction
, 0
2 1 , 1
3
1
T r a n s i t i o n s ’ (MHz) o f S u l p hu r D i c h l o r i d e
0 , 10
"
1 2 1 , 1 1
-
11
"3 ,9
0.05
0 . 1 2
35128.04
-3.28
-
15253.30
-4.52
-0.06
-14560.68
1.95
0 . 0 1
30370.45
1. 31
-0.05
29983.31
1.65
-0.04
29930.42
1.60
-
0 . 1 1
1 0 . 1 2
-
0 . 0 2
30046.23
-6
-0
31088.97
-0.52
0 . 0 1
13435.39
-16.20
0 . 1 1
29837.68
-
. 0 1
0 . 0 2
. 0 2
c
52
Table 3 .3
(continued)
Transition
D istortion
Correction
Observed
Frequency
Deviatior^
/ 1
»
32 35
S C ln
( gr o u n d v i b r a t i o n a l
state)
lit
1 2
3,9 '
1 3
3, 1 1
1 3 2 , 1 1
1
] 4,8
“
1 2
4,8
"
1 3 1 , 1 2
1 4
2 , 12 " 1 4 1 , 1 3
1 4
4, 1 1
“
1 3
5,8
16 2 , 1 4 " 16 1 , 1 5
174 , 14 "
1 6
5 ,11
174 , 1 3 "
1 6
5,12
172 , 1 6 '
1 63 , 1 3
17 1 , 1 7 " 16 2 , 1 4
185 , 1 3 “ -
1 7
<6,12
* 193 , 1 7 " 184 , 14
192 , 1 8
'
183 , 1 5
'
2 0 2 , 18
215,17 '
206 , 1 4
215,16 '
208 , 1 5
224 , 1 9 '
215,16
22 6 , 1 6 '
217 ,1 5
22 6 , 1 7 '
217 ,1 4
3,21
22 4 , 1 8
2 1 1 , 2 1
2 3
'
A
I
-17384.24
2.16
-0
-13429.93
0.15
-
32406.93
-3.09
-0.03
34274.37
-7.03
0 . 0 1
-31552.96
17.99
0 . 0 2
39766.13
-
. 0 2
0 . 0 2
2 0 . 1 2
-
-14808.74
-5.26
-0.04
-13908.38
-9.29
-
12849.70
5.12
-14716.81
40.68
0 . 0 1
-33460.09
22.36
0.08
1 5 7 1 0 . 32
-25.55
0 . 0 0
1 2 8 6 7 . 07
24.86
0 . 0 1
-36110.07
97.93
-16553.83
-15.11
0.03
-16216.57
-17.97
0.07
12753. 01
-55.49
-0.04
-35509.10
25.32
0.04
-35535.71
25.62
0 . 0 1
27811.12
-6.45
0 . 0 0
0 . 0 0
-0.03
-
-
0 . 0 1
0 . 0 1
53
Table 3 .3
(continued)
Transition
32 35
_S
C l2
Observed
Frequency
(ground v i b r a t i o n a l
236 , 1 7 * 2 2 7 , 1 6
2 3
4,20 '
2 2 5 , 17
2 4
4 , 2 0 ~ 235,19
2 5
4,22
2 6
6 ,2 0 " 257,19
2 6
5, 21
"
2 5
2 6
6,21
'
2 5 7 , 18
" 245,19
6,20
2 7 3 , 25 '
2 6
4,22
274 , 2 4 "
2 6
5, 21
275,23 ‘
2 6
6,20
285 ,2 3 "
2 7
6,22
295 , 2 4 " 2 8 6 , 2 3
307 ,2 4 ‘
2 9 8
30 5 , 2 6 ‘
29 6 , 23
318 , 2 3 “
3 0
9,22
318 , 2 4 '
3 0
9,21
316 , 2 6
,21
" 307,23
328 , 2 4 " 319 , 2 3
328 , 2 5 "
3 1
9,22
336 , 2 7 '
327,26
'
D istortion
Correction
Deviation
state)
-29835.67
7.98
0 . 0 1
17982.04
• -65.03
0 . 0 2
34379.69
-159.28
-0.03
27800.80
-78.94
-0.09
-12501.47
-54.89
-0.04
14795.95
-131.99
-12691.58
-51.95
0.05
28319.52
102.47
0
36337.36
-79.02
0 . 0 1
1 79 3 2 . 9 2
-119.05
0 . 0 0
.2 8694 .74
-207.84
-0.03
36136.75
-255.82
0.03
-14652.50
-80.96
34598.95
-170.63
-33867.00
-10.98
-33872.14
-10.82
16668.24
-184.59
0 . 0 1
.0
2
0 . 0 2
-0
. 0 0
-0.04
0 . 0 0
f
0 . 0 1
-28158.19
-44.64 '
-0.08
-28166.70
-44.37
-0
31414.74
-313.44
. 0 2
-0.04
'
54
Table 3 .3
(continued)
Transition
D istortion
Correction
Observed
Frequency
Deviation
i
3 2
S3 5 C1„
( gr ou nd v i b r a t i o n a l
33 6 , 2 8 “ 327 , 2 5
>
337 , 2 6
348 , 2 6 '
339 , 2 5
35
34
'
7,29
359,27 '
-16653.32
8,26
3 5 7 , 2 8 " 348 , 2 7
3 7 7,31
3510 , 2 5
" 368 , 2 8
387,32 '
378 , 2 9
3 9 8, 3 1
'
389 , 3 0
3 9 9,31
" 3810,28
4 2
4
8,34 "
“ 3911 ,2 8
9,33
?10,33 " 4211 ,3 2
4 3
1 0 , 3 4 ” 4 2 1 1, 31
4 3
8,35 ‘
4 2
9,34
•
-0
. 0 0
-0
. 0 2
-16631.11
-119.06
-0
. 0 1
14852.58
-260.67
-35876.03
-29.61
15381.94
-277.61
-30172.34
-72.19
26923.09
-347.30
32997.62
-392.99
13003.43
-356.76
-0.03
-
-215.65
-
'
-216.26
0 . 0 1
-348.18
0 . 0 1
12816.52
39 1 1 , 2 9
4 1
-118.28
-276.29
-12861.39
398 , 3 2 “ 389 , 2 9
4 0 10 , 31
• ’
0.05
34429.35
-12873.02
399 ,3 0 " 3810,29
4 0 10,30 '
-245.73
« *•
341 0 , 2 4
369 ,2 8 '
state)
'28529.79
348 , 2 7 " 339 , 2 4
346 ,29 '
>
’
>
0 . 0 0
■
-0
. 0 1
-0
. 1 0
-
0 . 1 1
0 . 0 2
■ -0
.
. 0 0
0 . 0 2
-32184.14
-108.67 .
-32185.13
-108.61
31591.85
-550.46
0.09
-149)4.83
-284.32
0.04
rl4918.62
-284.06
0.03
37984.19
-627.84
0.08
,
0 . 1 0
0 . 0 2
*
55
Table 3 .3
(continued)
Transition
(ground v i b r a t i o n a l
43 8 , 3 6 '
4 2
9,33
449 ,3 6 "
4 3
10 , 3 3
4 3
10 , 3 4
4 5
10 , 3 5
4 4
9,35 '
489 ,3 8 "
4 6
9 , 3 7 " 4 5 1 0, 36
4 7 11 , 3 6 "*
4 7
4 6
12 , 3 5
9 , 3 9 _ 4 6 10 , 3 6
479 ,3 8 "
4 6
4810,38 "
4 8
10 , 37
4 7
1 1 ,37
1 0 , 3 9 " 4 7 11 , 3 6
5 0 10»40 "
4 9
5 0 1 0, 41
‘
4911,38
5 1 1 0, 41
" 5 0 1 1 , 40
T1 ,39
561 1 ,4 6 "
5 5
1 2, 4 3
' 5611 ,45 "
5 5
1 2, 4 4
5714,43 '
56l £ , 4 2
12 , 4 5 '
56 1 3 , 4 4
5712 ,4 6 '
5 6 13 , 4 3
5 7
5 8 14 , 4 5 " 57J 5 , 4 2
5 9
D istortion
Correction
Deviation
<r
32 35
S Cl o
„
Observed
Frequency
1 2 , 4 7 “ 581 3 , 4 6
state)
37162.20
-582.86
16697.03
-515.61
-
16792.23
-521.91
-0.03
28823.14
-660.03
0.04
29027.53
-674.74
-16974.70
-365.33
0.03
34954.22
-737.81
-0.03
35249.19
-759.89
-
14550.75
r 646.84
-0.03
14518.69
-644.01
-0.04
26635.54
-822.33
-
26565.42
-815.61
32 75 5 .9 1
-918.91
-0.08
36412.35
-1208.95
36462.65
-1215.69
0.03
^*
-0.01
-34645.95
-468.92
*
16059.53
-1066.87
-
16 05 4 .41
-1066.08
-28944.96
-580.21
28017.72
-1307.84
0 . 0 2
0 . 0 1
0.Q3
e
0 . 0 1
0 . 0 0
0 . 0 0
0 . 0 1
-
0 . 0 1
0 . 0 0
-0.06
0 . 0 2
-
56
Table 3 .3
(continued)
Transition
3 2
S 3 5 C1„
Observed
Frequency
(ground v i b r a t i o n a l
59 1 2 , 4 8 '
5813,45
6 0 14 , 4 7 '
5915,44
6 0 1 2 , 4 8 " 5 9 13 , 4 7
6 0
12 ,4 9 '
3 2
S3
5
59- l 3 , 4 6
8
2,6 '
8
1,7
9
2,7 "
9
1,
1 0 2 , 8
'
1 0 1
,9
] 2,9 " ^ l . l O
1
Z2
'
-1305.96
0.03
-17483.10
-815.62
0.04
34052.96
-1436.90
-0.04
34036.27
-1434.04
-
0 . 0 0
state)
30324.62
1.34?
-0.05
29897.89
1.74
-
0 . 0 1
29778.18
1.79
-
0 . 0 2
30031.16
1.31
0.08
3 071 2 .7 1
0.08
0 . 0 1
33545.53
-5.65
-0
1 0 . 6 8
-o.oi
1 2 1 , 1 1
2,12 :
1 4 1 , 13
152 , 1 3 ‘
151,14
162 , 1 4 '
161 ,15
174 , 1 3 "
1 6
1 4
28006.35
8
1
, 1 0
Deviation
state)
(ground v i b r a t i o n a l
C1 3 7 C1
D istortion
Correction
5 , 12
193 , 1 7 " 184 , 1 4
225 , 1 8 " 216 , 1 5
225 , 1 7 " 21 6 , 1 6
224 , 1 8 " 2 1 5 , 1 7
. 0 1
35768.34
-
38559.36
-17.49
-16009.25
-7.30
-0.03
13894.23
-25.69
0.03
-13477.44
-26.58
-
-13041.75
-30.52
-0
15504.54
-88.87
0 . 0 1
0 . 0 1
. 0 1
0 . 0 1
,
57
T ab le 3.3
(continued)
Transition
3 2
S3 5 C1 3 7 C1
Observed
Frequency
(ground v i b r a t i o n a l
236 , 1 7 " 227 , 1 6
236 , 1 8 "
2 3
2 2
7,15
4 , 2 0 " 225 , 17
24 6 , 1 9 '
237 , 1 6
2 6
6 , 2 0 “ 25 7 , 1 9
2 6
6,21
" 257 , 1 8
2 7
7,21
“ 268 , 18
2 7
7,20 ‘
2 8
7 , 2 2 " 278 , 1 9
2 8
7, 21
'
268 , 1 9
2 7
8,20
305,26 '
296 , 2 3
317 , 2 5 '
3 0
8,22
316 , 2 6 " 307 , 2 3
358 , 2 7 '
349 , 2 6
358 , 2 8 " 349 , 2 5
356 , 3 0 " 347 , 2 7
3 6 7 , 3 0 " 358 , 2 7
* 367 , 29 " 358 , 2 8
37 9 , 2 9 “ 3 6 1 0 , 2 6
379 , 2 8 " 3 6 1 0 , 2 7 ^
D istortion
Correction
Deviation
state)
-32495.98
11.42
0.04
-32531.56
11.85
0 . 0 2
15316.52
-62.87
0 . 0 2
-27005.38
-5.86
-15694.40
-48.03
0 . 0 1
-15845.02
-45.76
0 . 0 1
-35007.09
7.20
0 . 0 2
-34995.32
6.98
0.04
-29471.72
-17.11
-0
-29452.33
-17.51
-0.06* 4©
30936.25
-165,74
-12655.17
-101.16
12663.09
-172.70
-15122.18
-143.36
0 . 0 2
-15147.64
-142.42
0 . 0 2
35707.97
-292.54
0 . 0 2
16144.68
-282.52
0 . 0 1
16735.47
-302.06
-0.03
-28874.54
-99.69
-28871.30
-99.84
-0.08
. 0 2
-0.05
0 . 0 1
u
0.03
-0
. 0 1
0 . 0 0
\
58
Table 3 .3 . (c o n tin u e d )
Transition
3 2
S3 5 C1 3 7 C1
Observed
Frequency
(ground v i b r a t i o n a l
399,30 " 3810,29
399, 31
3 9
‘
3 8 10 , 2 8
7 , 3 3 " 388 , 3 0
39 7 , 3 2 ‘
388 , 31
408 , 3 2 “ 3 9 9,31
4 0
8 ,3 3 " 399,30
Deviation
state)
-17651.92
-193.33
0 . 0 0
-17660.11
-192.91
0 . 0 0
33832.47
-414.50
35523.78
-478.78
13806.35
-382.95
13603.10
-373.35
-
0 . 0 0
0 . 0 0
-0
. 0 1
0 . 0 1
•
3 2
S3 5 C1„
’ C
( v0 =
u
^ .l
■ °0
2 1 , 1
■
2 0 , 2
2 2 , 0
"
2 1 , 1
2,2 ‘
3
1 ,3
4
1 ,3 *
4
0,4
4
0,4
8
1 ,7
Sl,5
‘
9
00
«#
^*si
1
00
B2 , 6 "
2,7 "
9
1
excited
vibrational
state)
0.08
17158.90
-
12813.97
-0.09
0.06
35456.89
-1.77
0.06
37666.03
-1.64
-
1 4 7 0 5 . 97
-0
-0.04
0 . 1 1
, 0
3
o
«#
'
D istortion
Correction
-l, 8
1 0
2,8 "
1
° 1 ,9
1 0
1,9 ‘
1 0
1 4
2,12 " 141,13
0,10
35214.68
. 1 0
0 . 1 1
0 . 0 1
« '
° - 0 5
-0.03
30 69 7 .11
1.32
34980.00
-3.28
30299.14
1.65
0.03
30234.66
1.60
-0.03
6 . 0 1
-0.04
30225.48
-
34532.63
-7.03
-
0 . 0 2
0.07
59
Table 3 .3
(continued)
a The "obser ved"
unsplit
freq uencies given
lin e frequencies.
in t h i s Table a r e the h y p o th e tic a l
The h y p e r f i n e s t r u c t u r e o f t h e measured
t r a n s i t i o n s w^s s u b t r a c t e d u s i n g t he methods o u t l i n e d
3. 1
and 3 . 2 .
k The c e n t r i f u g a l
Table 3 .2 .
c o r r e c t i o n s were c a l c u l a t e d u s i n g the c o n s t a n t s o f
The c o r r e c t i o n s
assumed t o be e q u a l
c
in sections
"Observed" u n s p l i t
for
t h e v^ = 1 s t a t e o f
were
t o t hose o f t h e c o r r e s p o n d i n g g round s t a t e l i n e s .
l i n e f r e q u e n c y minus t h e f r e q u e n c y c a l c u l a t e d
u si n g t h e c o n s t a n t s o f T a b l e 3 . 2 .
60
3.3
The Harmonic P o t e n t i a l
A fundamental
potential
functions
o f the v i b r a t i o n a l
F u n c t i o n o f Su l p h ur D i c h l o r i d e
d iffic u lty
in
from v i b r a t i o n a l
t he d e t e r m i n a t i o n o f harmonic
data alone
is
f u nd a m e n t a l s c o n t a i n c o n t r i b u t i o n s
terms and sometimes a r e p e r t u r b e d by v i b r a t i o n a l
it
is n ot p o s s i b l e t o make t h e c o r r e c t i o n s
desired
apply to t h e q u a r t i c d i s t o r t i o n
I n what f o l l o w s
effective
v a l u es o f
it
t he wavenumbers
from anharmonic
r e s on a n ce s .
I n g en e r a l
n e ce ss a ry to o b t a i n t h e
harmonized o r e q u i l i b r i u m wavenumbers.
spectra.
that
S im ila r considerations
c o n s t a n t s o b t a i n e d from r o t a t i o n a l
has been n e ce ss a ry t o use t h e obser ved or
t h ese c o n s t a n t s d i r e c t l y .
From the f i t s
described
in the previous
s e c t i o n v a l ue s
have
v
been o b t a i n e d f o r t h e f i v e
Hamiltonian.
the f o r c e
q u a r t ic d i s t o r t i o n constants
However i t
p l a n a r as ymme tr i c r o t o r
has been shown by Dowl ing t h a t f o r a
in i t s
equilibrium configuration
only f o u r
i n de p en den t ' q u a r t i c c o n s t a n t s
constants
greatly
followed here.
sim plifies
For t h i s
A
(24).
fundamentals.
constituted
Of t h e s e ,
. A potential
t h e most u se f u l
function w r it te n
Tbbbb’ Tc c cc anc* Tabab us1n9 r e l a t i o n s
(26)
t
CCCC
choice.
has t h r e e
t h e asymmetric s t r e t c h ,
i n t erms o f symmetry
The el ement s o f
c o n s t a n t m a t r i x can be e xp r es s ed
Jackson and M i l l e n
tkkkk,
DDDD
t w o , t h e symmetric s t r e t c h and
c o o r d i n a t e s t h e r e f o r e has f o u r f o r c e c o n s t a n t s .
inverse p o te n tia l
dddd
such as s u l p h u r d i c h l o r i d e
symmetric berrd a r e o f s p e c i e s A^ and t h e t h i r d ,
is of species
approach has been
purpose t he f o u r c o n s t a n t s
triatom ic
there a re
The use o f f o u r q u a r t i c
t h e problem and t h i s
and T^bab o f Wilson and Howard ( 2 5 )
Herberich,
Wat son' s
These c o n s t a n t s coul d have been used d i r e c t l y to s p e c i f y
fie ld .
vibrational
n f
i n terms o f
t he
t
dddd
,
r e a d i l y d e r i v e d from t h o s e o f
by use o f D o w l i n g ' s e q u a t i o n s
(24).
61
(The r e l a t i o n s
1.49 a f t e r
o f H e r b e r i c h e_t a l . ( 2 6 )
f o l l o w d i r e c t l y from e q u a t i o n
some e x t e n s i v e b u t s t r a i g h t f o r w a r d m a n i p u l a t i o n s ) .
These a r e :
( F ' 1 ) i ! = -R s i n 2 4 > cos2 <j
5 _ S £ L ± ± Taaaa +
.
Tbbbb + 55. Tcccc
A3
B3
C4
-
(3.2)
(F
~
^
= "R s i n %
(A+B)
cos^
Taaaa
Tbbbb
A3
B3
AB
t
cccc
(3.3)
(F"^).j2
= -R s i n %
B(tan<j) -
cos%
cot$)
-
2A c o t i
t
aaaa
2 ( 2 )**
+ A(tan<fr -
cot<t>) + 2B tan<)> t ^ b b
_
AB t a n $ - cot<t> t
cccc
(3.4)
1
( r l >33 * ± %
2
+
2
M
sin
abab
m
These r e l a t i o n s
f o r m u l a XY,,.
m
have been w r i t t e n
for
Her e R = r^ x 10“ ^ ,
+ 2my.
t he g e n e r a l
with
o n e - h a l f t h e Y - X- Y bond a n g l e ; M i s
m
(3.5)
AB
C2
triato m ic of
r t h e X-Y bond l e n g t h ;
the m olecu lar w e ig h t with M =
With P l a n c k ' s c o n s t a n t h i n e r g seconds and r
t he p o t e n t i a l
constants
F^,
F^»
^
$ is
anC*
2
^ 3 3
i n Angstroms
° b t a ^ned by i n v e r t i n g
o
t he m a t r i x c a l c u l a t e d above a r e i n mdyn/A.
phasized t h a t w h il e these r e l a t i o n s
Ag ai n i t s ho u l d be em­
are s t r i c t l y
v a l i d only f o r the
e q u i l i b r i u m Va lu e s o f t h e m o l e c u l a r c o n s t a n t s a good a p p r o x i m a t i o n
can be o b t a i n e d u si ng t h e obs er ve d ground s t a t e
B e f o r e using e q u a t i o n s
3.2 -
3.5
f u n c t i o n t h e v a l u e s o f f a a a a , Tbbbb* TCCCc*
values.
to determ ine a p o t e n t i a l
T 1
ancl
r 2
may be c a ^c u ^a t ed
62
TABLE 3 . 4
R e l a t i o n s h i p s Between Q u a r t i c C e n t r i f u g a l
v
-
,
—
D i s t o r t i o n Constants3
-
-
-
i
-
-
■ -
- -
9
—
-
E v a l u a t i o n o f Wat so n ' s d e t e r m i n a b l e p a r a m e t e r s
—
V*
(I
—
-
—
—
representation)
'aaaa = - 4 ( \ ] * AJK + V
Tbbbb “ - 4 ( \ ) +
'cccc = - 4 (4 J - 26J>
Ti
1
=
t
'
,,
aabb
+
t '
aacc
+
T'
bbcc
-
- 4 ( A 1u, +
JK
t 2 = A' T 'bbcc+ B‘ T'aacc+ .C‘ 1 aabb =
3 A ■.)
J'
4 ( 2 6 J + 2 6 K- a A J ) +
Flanar Relations
Tacac ~ Tbcbc
'aabb ' ^
,
aacc
■
'bbcc -
a 2 c2
— 7f-
bV
=
0
aaaa
Tbbbb
cccc
aaaa
Tbbbb
cccc
aaaa
Tbbbb
cccc
“ F
By d e f i n i t i o n
I
t'.
+
2
Tj
ffg g ~ Tffg g ' t l fg fg
63
as l i n e a r combinations o f the e x p erim en tally determined q u a rtic
constants using r e la tio n s given in Table 3 .4 .
The p o t e n t ia l constants
o f species A^, th a t i s , F ^ , F.^ and F2 2 ,were obtained d i r e c t l y from
the values o f
t. kK.
aaaa
bbbb
and x
cccc
thus derived.
In other cases
s i m il a r methods have provided good p re d ic tio n s f o r the corresponding
v ib r a tio n a l fundamentals, to w ith in 5% or b e t t e r f o r the very l i g h t
molecules H20 (27) and H2S (28) and r a t h e r b e t t e r f o r heavier molecules
such as C120 (2 6 ).
The F^^ force constant fo r the
e a s ily evaluated.
v ib r a tio n was not so
I t is r e la te d by equation 3.5 to T^bab,
one o f Watson's determinable parameters.
not
A value f o r Tflbab can be
calculated in a number of ways (27, 2 9 -3 1 ) from
and/or
t2
using
Dowling's planar r e la tio n s ( 2 4 ) , which are also given in Table 3 .4 .
U n fortunately
t.-j
and
t2
are not very s e n s itiv e to the value of Tatjab ’
th a t i s , t abab does not make a larg e c o n trib u tio n to e i t h e r
or
t2 .
Because of experimental u n c e rta in ty and v ib r a tio n a l e f f e c t s the values
o f xabab thus obtained vary w id e ly , depending on the method used to
determine them.
As a r e s u l t the derived value of F .^ is ra th e r un­
c e r t a in , and the p re d ic tio n o f the B^ fundamental is usually much
worse than those o f the A^ funcfomentals.
The f i v e determinable parameters o f
32 35
S C l2 in i t s ground
s t a t e , c a lcu lated from the experimental d is t o r tio n constants using
the equations of Table 3 . 4 , are given in Table 3 .5 .
t
aaaa
t.... , t _
and x, were obtained d i r e c t l y .
bbbb
cccc
.1
J
The constants
To evaluate t 0
2
the r o t a tio n a l constants A ' , B' and C' o f Kivelson and Wilson (32)
were req u ire d ; these are r e la te d to Watson's constants by (27)
64
A'
= A -
16Rg
B ‘ = B + 16Rg (A'
-
C‘ V ( B ' - C ' )
C'
-
B* V ( B ' - C‘ )
= C -
16Rg (A*
The q u a r t i c c o n s t a n t Rg = - ( 4 Aj + Tb bc c) / 3 2
For l i g h t
*
(3.6)
was d e f i n e d
m ol e c u l e s such as H^O wher e t he c o r r e c t i o n s
by N i e l s e n
i n v o l v e d are
v e r y l a r g e t h e s e e q u a t i o n s must be s o l v ed i t e r a t i v e l y
(27);
fo r sulfur
d i c h l o r i d e t h i s was n o t t h e c as e.
Having c a l c u l a t e d xbbcc from the
planar re la tio n s
B'
derived;
t he v a l u e s o f A ' ,
and C' g i v e n
(33).
in T a b l e 3 . 5 were
t h es e d i f f e r by a t most 0 . 0 1 2 MHj f r o m t h e e x p e r i m e n t a l A , B . C .
Four d i f f e r e n t methods we re used t o c a l c u l a t e
32 35
S Cl2 -
These we r e:
planar re la tio n s ;
re latio n s;
(iii)
(ii)
(i)
from t h e
v a l u e o f x-j and a l l
from t h e v a l u e o f x 2
from t he p l a n a r r e l a t i o n s
•
and a l l
for
t
t
. . for
abab
o f Dowling's
o f t he p l a n a r
... t
, x. .
and
a a b b ’ acac
bcbc
Tbbcc and simu^taneous s o l u t i o n o f t h e e q u a t i o n s
f o r x-j and x2 -
The
v a l u e s d e t e r m i n e d show a f a i r l y w i d e range and a c c o r d i n g l y a r e o f
4
. d u b io u s v a l u e f o r a f o r c e c o n s t a n t d e t e r m i n a t i o n .
o b t a i n e d from F i t
3 (see Table 3 . 2 )
t ho se d e r i v e d usi ng t h e F i t 2
form a more s e l f - c o n s i s t e n t s e t than
results
even though t he s t a n d a r d e r r o r s
are
smalle r f o r the l a t t e r s e t.
F it
1r e s u l t s are e s s e n t i a l l y
identical
F it
2 c o n s t a n t s and hence a r e
n ot g i v e n 1n T a b l e
Several
authors
( The Tabab v a l u e s
c a l c u l a t e d usi ng
the
t o t ho se o b t a i n e d f r o m ' t h e
3.5).
have c o n s i d e r e d t he p r o b l e m o f choosi ng t h e
c o r r e c t v a l u e f o r Tabab w i t h o u t ,
subject.
The ^abab va lu es
i n g e n e r a l , t h r o w i n g much l i g h t on t h e
(See f o r example Yamada and Wi n n ew i ss er ( 3 0 ) ) .
Watson has
*
shown t h a t f o r t he e q u i l i b r i u m v a l u e s o f t h e m o l e c u l a r c o n s t a n t s
(34)
65
TABLE 3 . 5 :
A l t e r n a t e Ground S t a t e M o l e c u l e Co n st an ts o f ^ 2 S 3
5
C12
Fi t 2 a
Fi t 3
-498.99(32)b
-498.46(39)
Wat so n' s D e t e r m i n a b l e P a r a m e t e r s
xa a a a (kHf >
’ b b bb * kHz)
'
xc c c c ( k H z >
T y
( kHz)
t
(MHz )
2
Kivelson-Wilson
2
Rotational
-8.017(11)
-8.023(14)
-2.582(11)
-2.563(14)
42.51(15)
42.18(19)
58.866(42)
57.829(53)
C on st a nt s and Rfi
A'
(MHz)
14613.5973(52)
14613.5990(67)
B'
(MHz)
2920.8586(11)
2920.8577(15)
C'
(MHz)
2430.7054(10)
2430.7042(13)
R6
( kHz )
-0.0292
-0.0294
Val ues o f Tabab C a l c u l a t e d by D i f f e r e n t Methods (KHz)
Method ( i )
-5.98(20)
-6.62(25)
Method ( i i )
-5.80(22)
-6.56(28)
Method ( i i i )
-6.89(65)
-6.96(82)
-6.02(22)
-6.64(28)
Method ( i v )
*
D istortion
Co ns t an ts Ev al u ed U si ng t he P l a n a r R e l a t i o n s
Taabb ' W z >
Tbbcc (kHz:>
' a a c c . (ktlz)
42.92(30)
-4.365(
8)
-4.353(10)
15.92(21)
16.31,(26)
^ C a l c u l a t e d from t h e c o n s t a n t s o f T ab l e 3 . 2 .
^Errors c i t e d are standard e rro h s .
43.47(38)
66
^ p l a n a r " 4CaJ " (B~C) AJK "
2
( 2 A+b+C ) 6 j
+ 2(B-C)6K = 0
(3.7)
The e f f e c t i v e
ground s t a t e v a l u e s do n o t s a t i s f y
th is expression;
t h e s e s o - c a r l l e d p l a n a r sums d e r i v e d u si n g t he r e s u l t s o f F i t 2 and
F i t 3 are given in Table 3 .6 .
F it
The mag ni t ud e o f
3 than f o r F i t 2 and accounts f o r
F it
3.
If
6
j
is sm aller f o r
t he more s e l f - c o n s i s t e n t s e t
o f Tabab v a l u e s o b t a i n e d using t he F i t
m o s t l y t he d i f f e r e n t e s t i m a t e s o f
z
3 results;
and
6
this
reflects
^ d e r i v e d from F i t 2 and
t h e r e s u l t s o f T a b l e 3 . 6 a r e t aken t o i n d i c a t e
q u a r t i c constants o f F i t
3 constitute
t h a t t he
t h e more r e a s o n a b l e s e t t he n
t h e s e x t i c c o n s t a n t s o f F i t 2 must be r eg ar de d w i t h s u s p i c i o n .
all
o f t he d a t a b ei ng f i t
o n l y one s e t o f s e x t i c c o n s t a n t s - H ^ j ,
and h j - was found whose use would g i v e val ues
f or , t he q u a r t i c
constants e s s e n t i a l l y
identical
expense o f a s l i g h t l y
h i g h e r s t a n d a r d d e v i a t i o n o f the f i t f ?
TABLE 3 . 6
Wi th
to those o f F i t 3 ( a l b e i t a t the
However
Values o f Wat son' s Q u a r t i c P l a n a r i t y Sum f o r
R ef i n e m e n t
Valuea
F it 2 *
0.400(53)
MHz2
F it 3
0.120(56)
MHz2
C a l c u l a t e d usi ng e q u a t i o n 3 . 7 and t h e c o n s t a n t s o f T a b l e 3 . 2
t h e r e was no process o f l o g i c a l
and s e q u e n t i a l
s e x t i c c o n s t a n t s whioh would l e a d t o HKJ,
elim in atio n of other
and h j b ei n g r e t a i n e d .
A g a i n , whereas Ta a a a . Tbbbb, t cccc w e r e i n s e n s i t i v e
and t h e d e t a i l s o f t h e
r e f i n e m e n t p r o c e d u r e the v a l u e s o f Ta b a b , "
though i m p r e c i s e , v a r i e d w i d e l y .
)
to t h e d a t a s e t
.
67
t)
In a f i n a l
re fin e m e n t o f the
32 35
S C l2 ground s t a t e data
D o w l i n g ' s p l a n a r i t y r e l a t i o n s - ( 2 4 ) w e r e u s e d t o e l i m i n a t e on e o f t h e
f i v e q u a r t i c d i s t o r t i o n c o n s t a n t s , and a f i t was made t o f o u r c o n s t a n t s ,
♦
chosen
£ 0
be ^ a a a . ^ bbbb> i aabb and t a b a b .
been made f o r t h e
F2 O ( 3 5 )
The f i t was a f i r s t
the r o t a t i o n a l
S i m i l a r a n a l y s e s have
and C l ^0 ( 2 6 ) m o le c u l e s amongst o t h e r s .
order f i t
i n a r i g i d as ymme tr ic r o t o r b . as i s, and
c o n *s t a n t s used i n
the p
r l a• n a r r e l a t i o n s were t he
e f f e c t i v e ground s t a t e c o n s t a n t s o b t a i n e d e a r l i e r .
w i t h J < 2 5 were used i n t h i s
c o n t r i b u t i o n s were i g n o r e d .
Only t r a n s i t i o n s
r e f i n e m e n t as p o s s i b l e s e x t i c d i s t o r t i o n
The s t a n d a r d d e v i a t i o n o f t he f i t
0 . 0 5 5 MHz w i t h an av er ag e d e v i a t i o n o f 0 . 0 4 4 MHz.
was
The r e s u l t s o f t h i s
¥
refinem ent, F i t 4 ,
2 and 3 ,
a r e compared t o those o f p r e v i o u s a n a l y s e s ,
in Table 3 . 7 .
Fits
E x c e l l e n t agreement i s o bs er ve d f o r t he d i r e c t l y
determ inable constants A ' , B1, C ' , t
aaaa
and xuu. . .
bbbb
The v a l u e s o f
Tcccc and Taabb have been comPar ec * usi ng t h e p l a n a r r e l a t i o n s
T a b l e 3 . 4 , t h e a gr eem en t her e i s
of
less s a t i s f a c t o r y w it h the values
of
Taabb ° b t a‘' ned ^rom F i t 2 and F i t 4 d i f f e r i n g by more* than t h e sum o f
t h e i r stan4ard e r r o r s .
F in ally,
t h e v a l u e s o f xabflb have been compar ld.
For F i t 2 and F i t 4 t h e agreement i s v e ry p o o r ; t h e d i s c r e p a n c i e s
between t he F i t
3 and F i t 4 x abab v a l u es a r e r a t h e r s m a l l e r .
Because
t h e d i f f e r e n c e s between t h e v a r i o u s va l u e s o f xabab a r e l a r g e t h i s
c o n s t a n t was n o t used t o d e t e r m i n e F ^ .
The t h r e e
-species f o r c e c o n s t a n t s were c a l c u l a t e d usi ng
t h e v a l u e s o f xa a f i a , xbbbb and t c c c c from T a b l e 3 . 7 i n e q u a t i o n s 3 . 2 3.4;
the r e s u lt s are given in Table 3 .8 .
T a b l e 3 . 8 were d e r i v e d assuming t h e e r r o r s
t o be t hose g i v en
T h e ‘u n c e r t a i n t i e s
in t , , ,
aaaa
i n T a b l e 3 . 7 and t h e e r r o r s
g i ve n i n
x . . k. and t
bbbb
cccc
in the r o t a t i o n a l
4"*
\
68
TABLE 3 . 7
Rotational
and C e n t r i f u g a l
D i s t o r t i o n Constants o f ^ S ^ C l ,
**
O b t a i n e d from V a r i o u s F i t s
P ar am et e r
Fi t
2 a >'
F i t 3b
.
F i t 4C
A'(MHz)
14613.5973(52)
14613.5990(67)
14613.6041(73)
B' (MHz )
2920.8586(11)
2920.8577(15)
2920.8598(18)
.C'(MHz)
2430.7054(10)
2430.7042(13)
2430.7054(18)
-498.99(32)
-498.46(39)
-498.47(26)
-8.017(11)
-8.023(14 )
-8.050(24)
-2.582(11)
-2.563(14)
-2.574(13) '
42.92(30)
43.47(38)
43.55(15)
-5.9a(20)
-6.62(25)
) -5.80(22)
\ -6.56(28)
) -6.89.(65>
1 -6.96(82)
W
kHz)
,
Tc c c c ( k H z >
V a b b (kHz>
,
Tabab^kH
z^
aUaU
' -6 .0
2
(2
2
)
-
\
-6^58(76)
-6.64(28)
-at
The i n i t i a l f i t was made u s i n g Wat son' s H a m i l t o n i a n .
A ll quartic •
c o n s t a n t s and a l l s e x t i c c o n s t a n t s e x c e p t H j ,
and hK w i r e i n c l u d e d .
See T a b l e s 3 . 2 a n d * 3 . 5 .
Ref i nemen t was made u s i n g Wat son' s H a m i l t o n i a n w i t h a l l
no s e x t i c t erms i n c l u d e d .
See T ab le s 3 . 2 and 3 . 5 .
q u a r t i c but
' F i t was made t o A' , B ' , C ‘ , t
, x..
, t
. . and t . . .
*
’
aaaa’
b bb b ’ aabb
abab
S.____
J
c o n s t a n t s t o be t h e d i f f e r e n c e s between t h e e f f e c t i v e ground s t a t e
' v a l u e s and t hose c a l c u l a t e d f rom the* av e ra ge ground s t a t e moments
r
o f i n e r t i a o f Table 3 .9 .
These l a t t e r e r r o r s a r e s e v e r a l
magni tude l a r g e r t ha n t h e e x p e r i m e n t a l
some i n d i c a t i o n ' o f t h e model e r r o r .
using the various f i t s
u n c e r t a i n t i e s but s ho ul d g i v e
The p o t e n t i a l
constants derived
a r e i n good agreement a l t h o u g h t h e v a l u e o f
F^-j o b t a i n e d f rom F i t *2 i s s l i g h t l y
f rom F i t s
orders o f
3 afid 4 .
s m a l l e r than t ho se c a l c u l a t e d
-
As has been a l r e a d y m e n t i o n e d , because o f t h e r an g e o f
experimental
v a l u e s f o r ^ bab
constant F ^ .
The i n e r t i a l
1
t was n ot used t o c a l c u l a t e t h e f o r c e
Instead i n e r t i a l
defects o f a l l
d e f e c t d a t a was used f o r t h i s purpose
species studied are given in Table 3 .9 .
f
The f a c t t h a t t h e ground s t a t e i n e r t i a l
d e f e c t s a r e small
* numbers s h o e i n g s l i g h t i s o t o p i c v a r i a t i o n
is
positive
c o n s i s t e n t w i t h t he
molecule having a p la n a r s t r u c t u r e .
The i n e r t i a l
#
d e f e c t s d e te r m i n e d e x p e r i m e n t a l l y a r e t h e sum
o f v ib r a tio n a l, centrigual
vibrational
a n d > e l e c t r o n i c c o n t r i b u t i o n s o f whi ch t h e
p a r t 1 s . u s u a l l y by f a r t h e l a r g e s t ( 3 6 ) .
«
contributions
(0
•
0 0
to the i n e r t i a l
) s t a t e and t h e v ^ =
1
or (0
harmonic p a r t o f ‘ t h e p o t e n t i a l
.« * » .
V IS
4K
<‘ u >2/ l C
U1
defects o f
1 0
1
S
C
Cl2
3
function
(36,
U l.+ t d .
“
t he ground o r
) s t a t e depend o n l y . u p o n t h e
37) and a r e g i v e n by ( 1 ,
I - _ L _ V u 23»2( i ♦ I
C0o
in
The v i b r a t i o n a l
1
k W 2
-1
“3 V
(3.8)
w3,
(010) , . (000) s 4
2
Her e
A V1b
A Vib
and c 2
3
•
(s tric tly
(3.9)
u2 +a,3
and c2 3 ^ ) a r e C o r i o l i s c o u p l i n g co-
70
efficien ts;
and
are the e q u ilib riu m v ib r a tio n a l
(assumed h e r e t o d i f f e r n e g l i g i b l y f ro m
2
°9
K = h / 8 n c has t he v a l u e 1 6 . 8 5 7 6 3
o k
and v ^ ) and t h e f a c t o r
cm
-1
t he d i f f e r e n c e between t he ground and v^ =
The c e n t r i f u g a l
contribution
wavenumbers
.
I n e q u a t i o n 3 . 9 A^
1
state in e r tia l
is
defects.
t o t he K i v e l s o n - W i l s o n c o n s t a n t s
is
gi ve n by
‘ cent = -
W
( 3 , ' c / 4 C '> + ( ‘ V
Where I ' a> 1 ' ^ and I '
from A ' ,
B'
and C'
assumed t h a t
28'*
are the p rin c ip a l
respectively.
t h e s mal l
(3.10)
moments o f i n e r t i a
e l e c t r o n i c and c e n t r i f u g a l
o f t h e e l e c t r o n i c and c e n t r i f u g a l
t h an
( > ‘ a7 2 A ' ) ]
In w r i t i n g equation
same f o r t h e ground and v^ = 1 s t a t e s .
sensitive
*
3.9
it
obtained
has been
c o n t r i b u t i o n s a r e t he
Because o f t h e c a n c e l l a t i o n
c o n t r i b u t i o n s and( because
t o t h e v a l u e o f u ^ , and hence F ^ ,
it
i s more
has been
used t o c a l c u l a t e F ^ .
B e f o r e u si n g a ^ t o o b t a i n
c a l c u l a t e v a l u e s f o r u)-|, u>2 ,
^
was f i r s t n e c e s s a r y t o
and
Values of
and
were
2 2 2
o b t a i n e d f rom t he r o o t s
= 4n c u> ^ o f t he A^ b l o c k o f t h e usual
secular equation (38)
**
*
|FG -
*
XE|
= 0
.
(3.11)
T h i s was c o n s t r u c t e d u sj ng t h e f o r c e c o n s t a n t s
o f T a b f e 3 . 8 and
the G m a t rix
(39).
i n t h e f orm s p e c i f i e d by C a l i f a n o
The e q u a t i o n s
k
o f
Meal and Po l g ( 4 0 ) wdte used t o c a l c u l a t e
constants.
F o r an XY^ m o l e c u l e 1
(c,
3
) 2
-
[X,
- F1
I
I
the C o r i o l i s coupling
1
/{G "1 ) 1 , ] / ( x
1
- x2 )
(3.11b)
•
I
71
TABLE 3 . 8
Q u a d r a t i c P o t e n t i a l C o n s t a n t s , V i b r a t i o r r a l Fundamentals
and C o r i o l i s C o u pl i ng C o ns ta n ts o f S u l p h u r D i c h l o r i d e
Potential
C on s t an t
o
F-j i (mdyn/A)
O
F 1 2 (mdyn/A)
F i t 2a
Fit
3
F it 4
2.913(90)
2.994(95)
2.986(96)
0.0926(55)
0.0913(55)
0.0891(57)
0.2624(21)
0.2611(21)
0.2606(23)
2.421(41)
2.479(45)
2.470(44)
u j ( cm” ^)
514.8(84)
521.9(88)
521.6(89)
u 2 (cm” ^)
2 06 .9(
206.5(
2 0 6 . 2(
u3 (cm J )
523.8(62)
530.0(68)
529.0(66)
0.3241(26)
0.3221(28)
0.3231(27)
0.6759(26)
0.6779(28)
0.6769(27)
0
F2
2
(mdyn/A)
0
F3
3
(mdyn/A)
«
Vibrational
Fundamental
7)
8
)
8
)
C o u p l i n g Co n st an ts
'
( t 13)2
(c2 3 ) z
p
a F i f s a r e d e s c r i b e d 1n T a b l e 3 . 7 .
^The e r r o r s a r e d i s c u s s e d i n t h e t e x t .
'
72
U l 3 )2 + U 2 3 ) 2 = 1
An e x p r e s s i o n f oV ( G ~ ^ i
(3.12)
has been g i v e n by Pol o
(41).
These
e q u a t i o n s were s o l v e d i n an i t e r a t i v e manner u s i n g i n i t i a l l y
effective
structural
p a r a m e t e r s and f i n a l l y
discussed i n Sec tio n 3 . 4 .
s e t o f A1 s p e c i e s
3.8.
“ 3* ( ^ 1
3
)
a r e a ^so 9"*ven
0.52198 (38)
0 2
uA
(F ^ ,
and F2 2 ) g i v e n i n T a b l e
as t h e c o r r e s p o n d i n g v a l u e s o f
Table 3 . 8 .
is very p re c is e ;
r e f l e c t almost e n t i r e l y
t he a v e r ag e p a ra m e te r s
A v a l u e o f F33 was t hus o b t a i n e d f o r each
fo rc e constants
These r e s u l t s as w e l l
the
The e x p e r i m e n t a l
, w2 ,
value o f
t he e r r o r s q uot ed f o r F33 and <u3
the estim ated u n c e r t a i n t i e s
in ^ 2 and
U 23)
The e r r o r s quot ed f o r t h e A^ s p e c i e s f o r c e c o n s t a n t s , A-j v i b r a t i o n a l
wavenumbers and C o r l o l i s c o u p l i n g c o n s t a n t s a r e r o u g h l y t w i c e what
woul d be o b t a i n e d 1 f o n l y t h e e x p e r i m e n t a l
d istortion
uncertainties
in the
c o n s t a n t s had been c o n s i d e r e d ; t h e l a r g e s t c o n t r i b u t i o n s
t o t h e s e e r r o r s come f rom t h e u n c e r t a i n t i e s a s s i g n e d t h e r o t a t i o n a l
constants.
T a b l e 3 . 8 shows t h a t t h e p o t e n t i a l
u s i n g t h e F i t 3 and F i t 4 r e s u l t s
a re almost i d e n t i c a l ;
f u n c t i o n d e r i v e d from F i t 2 has s l i g h t l y
stretching
fo rce constants
_
F^
functions
and F 3 3 .
/
v
derived
the p o te n tia l
l o we r v al u e s , f o r t he
4
73
3.4
The M o l e c u l a r S t r u c t u r e , o f Su lp hu r D i c h l o r i d e
The e f f e c t i v e p r i n c i p a l
moments o f i n e r t i a
of the variou s sulphur d i c h l o r i d e species studied
3.9;
t h e s e p a r a m e t e r s were d e r i v e d u s i n g
Table 3 . 2 .
The ground s t a t e e f f e c t i v e
and i n e r t i a l
are c o lle c te d
t he r o t a t i o n a l
structural
in Table
constants of
parameters,
were c a l c u l a t e d u s i n g t h e p r i n c i p a l moments o f t h e
defects
r Q and eQ ,
32 35
S C l? species.
a
Because t h e i n e r t i a l
d efect is non-zero,
somewhat d i f f e r e n t
o b t a i n e d when t he t h r e e p o s s i b l e p a i r s o f moments I a , 1^;
I
were, used.
These r e s u l t s a r e summarized i n T a b l e 3 . 1 0 ;
ground s t a t e e f f e c t i v e
A s im ilar calculation
p a r am et e rs
is id e n tic a l
and I ^ ,
t h e mean
t o t h a t o f Murr ay e t a l . ( 1 6 ) .
Because t h e i n e r t i a l
defect
is
larger
t h e r e s u l t s o b t a i n e d using d i f f e r e n t p a i r s o f
moments show a w i d e r v a r i a t i o n
A p artial
Ia, I
has y i e l d e d v a l u e s f o r t h e e x c i t e d s t a t e e f f e c t i v e
and 6 ^g-jg^-
fo r the e x c ite d s t a t e
principal
structure
r e s u l t s were
substitution
ground s t a t e . E q u a t i o n s
s t r u e t g r e has a l s o been o b t a i n e d f o r t h e
1 . 4 4 and 1 . 4 5 wer e used t o c a l c u l a t e t h e a^and
32 35
S C12 as t h e p a r e n t s p e c i e s .
b c o o r d i n a t e s o f c h l o r i n e usi ng
c e n t e r o f mass c o n d i t i o n ,
t han t he ground s t a t e v a l u e s .
m. b. = 0 ,
1 1
i
i
The
gave t h e b^ c o o r d i n a t e o f s u l p h u r ;
i t s a^ c o o r d i n a t e i s z e r o by symmetry.
D i f f e r e n t s t r u c t u r e s corresponding
t o changes i n t h e t h r e e p o s s i b l e p a i r s o f . p r i n c i p a l
moments were c a l c u l a t e d .
*
These r '
p a r am e t er s a r e a l s o p r e s e n t e d i n T a b l e 3 . 1 0 and a r e seen t o be
more s e l f c o n s i s t e n t t h a n £he e f f e c t i v e
(
vajues.
74
Table 3 .9
Principal
Moments o f
In ertia
and I n e r t i a l
Defects of
<>2
a
V a r i o u s Su l ph u r D i c h l o r i d e Sp ec i es (uA )
¥
3 2 s3£* c i 2
32 s35c i 37 ci
Ground S t a t e v 2 = 1 S t a t e
Ground S t a t e
\\.
1
E f f e c t i v e V a l ue s3
•.
«vb
34.58279(1)
34.30291(2)
34.87737(5)
173.0 2 344(7)
173.17479(20)
177.8 7 564(30)
207.91549(9)
’208.30895(30)
213.06357(32)
0.83125(35)
0.31056(44)
0.30926(11)
Average Values^
>c
a
.
34.7366
34.5889
173.3086
173.8166
208.0466
208.4068
*
0,0 014
0 .Opi3
Calculated
u s i n g t he r o t a t i o n a l
c o n v e r s i o n f a c t o r 5 0 5 3 7 9 . 0 uA2 .
•
c o n s t a n t s o f T a b l e 3 . 2 and t h e
For t h e ground s t a t e o f 3 2 S3 5 C12 t he
F it 2 results
we r e used.
k
u s i n g e q u a t i o n s 3 . 1 3 - 3 . 1 5 and t h e F i t 2 f o r c e c o n s t a n t s
Calculated
o f Table 3 . 8 .
*
75
As w e l l , , t h e p h y s i c a l l y w e l l - d e f i n e d a v e r a g e s t r u c t u r e s
43)
o f 32S35C12 have been c a l c u l a t e d
tional
states.
For a C2v t r i a t o m i c
I z = I v + 3 K ^ (2 v 1 + 1)
a
a
s i n 2x
f o r bot h t he ground and ( 0 1 0 )
vibra­
such as SC 1^ one has ( 4 3 ) :
+ ( 2 v ? + 1) c os 2 x + ( 2 v . + U i l a/ I
-a'
► O).
J1
(42,
1
]
(3.13)
I 2 = I v + 3K |~( 2 v-j + 1) c os2 x + ( 2 v 2 + 1)
lb
s i n 2x + ( 2 v 3 + 1
xb
L
w2
W1
J
w3
(3.14)
Ic
= Ic
+ 3 K [(2V.,
- 4K ( 2v - |
+
1)
+ 1 )/o>1 + ( 2 v 2 + 1 )/u>2 + ( 2 v 3 + 1 )/o>3 ]
w3 3
c132
+
(2
v
2 +
1)'
U) -j (\ (i)3 2 “ CjlIi 2 )/
-
(2v3 +
in ertia,
Here
(3.15)
’ 23
2
2 )
3 -w2 ]
a r e t h e a v e r a g e and e f f e c t i v e moments o f
f o r the v i b r a t i o n a l
(43)
state
in q u e s tto n ,
and
(42)
I n g en e r a l
The p a r a m e t e r x i s d e t e r mi n e d
,
C0S x + c23
i s n e g a t i v e by c o n v e n t i o n
I 2 notation
(43).
(
u3
has been e v a l u a t e d e a r l i e r .
x + 2 ^23^ W
L
2 )\
(^ 2 2 /\
»
f rom t h e e q u a t i o n
cos
OJ,
+
2 -
; 23
2
K (= h/87T c )
t
; 13
and I v e t c .
a
respectively,
•
2 A
^1—
i| w 3 ((u>3 2 - t o ,
where I 2 e t c .
a
{
oj ^ \ ^ 3
2
1)|
w3
"
W
(44).
(3.16)
= °
In equations
has been used i n s t e a d o f t h e
3 . 1 3 - 3 . 1 5 Ok a' s
•»
I * o f Herschbach and L a u r i e
t h e use o f e q u a t i o n s 3 . 1 3 - 3 . 1 5
requires £ h a t
( u ^co -, )
*
and ( u>3“cu2 )
are
fa irly
large.
approximately equal.
Here t h i s
For t h e ground and v 2 -
e q u a t i o n s a r e v a l i d because f a c t o r s o f
a v e r a g e moments o f i n e r t i a
i s n ot t he case s i n c e w3 and
and i n e r t i a l
( uj3 - o>-| ) a l l
1 states,
cancel.
howe ver , the
The r e s u l t i n g
d e fects are also presented
in
V
76
♦
Table 3 . 9 ;
the average i n e r t i a l
d e f e c t s are e f f e c t i v e l y
In t h e a v e r a g e moment c a l c u l a t i o n s
t h e val ue s o f
zero,
as r e q u i r e d .
, u ^ , to ,
and
were t h o se p r e d i c t e d u si ng t h e F i t 2 f o r c e c o n s t a n t s o f T a b l e
essen tially
identical
3.8;
a v e r a g e moments were c a l c u l a t e d when t h e F i t
3 or
F i t 4 f o r c e c o n s t a n t s were used.
A
In t h e c a l c u l a t i o n o f t h e a v e r ag e moments t h e n e g l i g i b l e
centrifugal
c o r r e c t i o n s and n e c e s s a r i l y
have been i g n o r e d .
states o f
The smal l
the unknown e l e c t r o n i c c o r r e c t i o n s
v a l u es o f
o b t a i n e d f o r both v i b r a t i o n a l
32 35
“ ’
S C l ^ d e m o n s t r a t e , h o w eve r ,
cannot be l a r g e and a r e ,
uncertainties
in
fact,
in the v i b r a t i o n a l
th at the e le c tro n ic
on t h e o r d e r o f o r s m a l l e r than the
corrections.
The a v e r a g e bond l e n g t h s and a n g l e s ,
average p r in c ip a l
moments o f T a b l e 3 . 9 ,
both t h e ground and
= 1 vibrational
using the three po ssible p a irs
is
s lig h tly
larger
It
obtained u s in g ,th e
ar e g i v e n
states
of principal
As mi gh t be e x p e c t e d f o r d i f f e r e n t
a v e r ag e bond l e n g t h
contributions
in T a b l e 3 . 1 0 .
the s t ru c t u re s
For
calculated
moments a r e v e r y s e l f - c o n s i s t e n t .
s t a t e s o f a bending v i b r a t i o n ,
is e s s e n t i a l l y constant w h ile
the
the a v e r a g e bond a ng l e
i n the e x c i t e d s t a t e .
is w o rth w h ile ,
in p a r t i c u l a r ,
o f t he ground s t a t e a ver ag e . s t r u c t u r e .
estimating
Using t h e F i t
t he r e l i a b i l i t y
2 r e s u l t s o f Table
$
3 . 8 the e rr o rs
I. Z b
I.°
b
i n t h e harmonic v i b r a t i o n a l
and I z c
respectively.
I 0 we're c a l c u l a t e d
c
t h e s e e r r o r s seem r a t h e r s m a l l .
i n a s t r u c t u r e d e r i v e d from
A and 0 . 0 0 1 ° f o r r 2 and e
Even i f
I °,
a ’
*
both
I
a
z -
a r e assumed to be i n e r r o r by 3%, h ow ev er , t hen r
at
I z a
t o be 0 . 6 % , 0.5% and 1.1%
The suggested u n c e r t a i n t i e s
I flZ and I ^ z a r e t h e r e f o r e p . 00002
corrections
2
respectively;
I 0 and I.
a
b
and 0
z
-
I.0
b
can change by
most 0 . 0 0 0 0 8 A and 0 . 0 0 5 ° from the I z , I / z s t r u c t u r e ' o f T a b l e 3 . 1 0 .
a
d
77
Table 3.10
E ffective,
f
for
P artial
32c 35r l
S Cl
S u b s t i t u t i o n and Aver age S t r u c t u r e s
2
('a -
>b>
Ic)
<‘ b ’
‘ c>
Mean
>
Ground V i b r a t i o n a l
State
r 0 (A)
2.0125
2.0136
2.0 160
2.0 140
90 ( D e g . )
102.81
102.86
102.56
102.74
r s (A)
2.0138
2.0135 j r .
2. 0 15 1
2. 01 41
102.66
102.70
' 102.56
102.64
2.01524
2.01524
2.01526
2.01525(8)
102.730
102.730
102.729
102.730(5)
2.0099
2.0128
2.0 193
2.0 140
1 0 3 . 06
103.19
102.39 ■
102.88
2.01537
2.01538
2.01538
2.01538
102.931
«. 102. 931
102.930
102.931x.
e$ (D e g .)
fsi
ez (D eg.)
'
*
v0 = 1 E xcited State
r ( 0 1 0 ) ( ®*
e ( 0 1 0 ) ( De g- 5
r 2 ( 0 1 0 ) (S)
3 E st i m a t e d o u t s i d e l i m i t s o f e r r o r .
See t e x t .
*
78
These a r e r e a s o n a b l e o u t s i d e e r r o r l i m i t s
f o r t h e ground s t a t e av er ag e
structure.
F in ally,
t h e e q u i l i b r i u m v a l u e o f t h e s u l p h u r - c h l o r i n e bond
d i s t a n c e was e s t i m a t e d .
1.42;
and K,
The r g bond l e n g t h was p r e d i c t e d u s i n g e q u a t i o n
2
v a l u e s o f u , t he z e r o - p o i n t mean squar e a m p l i t u d e o f t h e S-Cl
«
bond,
t h e c o r r e s p o n d i n g p e r p e n d i c u l a r a m p l i t u d e c o r r e c t i o n wer e c a l c u l a t e d
using^the F i t 2 fo rc e constants o f Table 3 . 8 .
The magnitude o f a ( S - C l ) ,
the Morse a n h a r m o n i c i t y p a r a m e t e r , was t aken as t h e mean o f t h e va l u e s
g iv en f o r t he
and C l^ m o l ec u l es
p er fo rmed f o r s e v e r a l
in a l l
,,
(45).
m o l e cu le s whose e q u i l i b r i u m s t r u c t u r e s
cases t he v a l u e o f a was c a l c u l a t e d
f o r d i a t o m i c m o l ec u l es
(45).
c a l c u l a t e d usi ng e q u a t i o n
uncertainty
in r
The same c a l c u l a t i o n
has been
a r e known;
u si ng t h e a v a i l a b l e
results
The e r r o r a s si gn e d t o each o f t h e r g v a l u es
1 . 4 2 was t h e d i r e c t sum o f t he e x p e r i m e n t a l
and one q u a r t e r o f t he r - r
difference.
z .
z e
s u b j e c t i v e e r r o r was chosen because i n a l l
cases
it
T h i s somewhat
exceeds t h e d i f f e r e n c e
between t h e s p e c t r o s c o p i c o r observed r & v a l u e and t h a t c a l c u l a t e d usi ng
equation
mental
1.42.
The d e v i a t i o n s a r e ,
i n f a c t ’, on t h e o r d e r o f t h e e x p e r i ­
e r r o r f o r t h e m ol e c u l e s w i t h s i n g l y bonded atoms.
the a gr eement i s
poorer;
this
reflects
For t h e o x id e s
the f a c t t h a t t h e v a l u e o f t he
Morse a n h a r m o n i c i t y p a r a m e t e r d e r i v e d from t h e c u b i c f o r c e c o n s t a n t s o f
ozone,
f o r exampl e,
i s s l i g h t l y higher, than t h a t
found f o r t h e
<
molecule
(6).
-
A
4 *
0 ^
<79
T a b l e 3.11
The E q u i l i b r i u m Bond Lengths i n Su l ph u r D i c h l o r i d e and
Related Molecules
P a ra me t e r
SC12
u2(S2)
0.00195
sf2
so2
0.00173
0.00123
%
0.00060
K(«)
0.00062
*
0.00059
J
a(jr’ )
1.71
2.06
r z («)
2.0153(1)
1.5921(1)
r e ( C a 1 c . )(S)b
2.0109(12)
1.5874(13)
1.4317(9)
1 .5875(1 )
1.4308(2)
2.07
.
1.4349(1 )a
\
r e(0 bs .)( A)C
-
41
i
R e f er en c e
*
T h i s work
(5)
(1)
T a b l e 3..11
The E q u i l i b r i u m Bond Lengths i n S u l p h u r . D i c h l o r i d e and
Related Molecules
(continued)
of2
P a ra me te r
Si F2
°3
#.
V
0.00225
0.00191
0.00172
0.00076
0.00067
0.00069
2.45
2.48
1.88
r z (A)
1.4124(1 ) a
1.2792(1)
1.5946(2)
re (C alc.)(A )b
1.4049(20)
1.2728(17)
1.5904(14)
re (0 b s .)
1.4053(4)
1.2717(2)
1.5901(1)
u2 ( A 2
)
K(fi)
a(A- 1 )
0
'
{ K ) C
*
R e f er en c e
( 2 9 , 46)
(6)
(4)
J
\
a No e r r o r „ w a s g i v e n .
b C a l c u l a t e d from r
This
J
is a reaspnable u n c e r t a in t y .
u si n g e q u a t i o n 1 . 4 2 .
c The s p e c t r o s c o p i c a l l y ' d e r i v e d r
bond l e n g t h .
-
t
81
3.5
Comments on t h e S u l p h u r D i c h l o r i d e P o t e n t i a l
The harmonic p o t e n t i a l
been based e n t i r e l y
fu n c tio n obtained in
on mi crowave d a t a .
F irst,
consistent w ith a l l
as w e l l
is
it
o f t he v i b r a t i o n a l
possible
to r e f i n e
a combination o f r o t a t i o n a l
is
i n v e s t i g a t i o n has •
and v i b r a t i o n a l
fie ld
va lid ity
the p o te n tia l
as
the p o t e n t i a l
i n q u i r e w h e t h e r t he p r e s e n t f o r c e
this
In a s s e s s i n g i t s
ob vi ou s q u e s t i o n s s ho u l d be an swer ed.
Second,
Funct i on
function
the r o t a t i o n a l
function
results?
two
data?
f u r t h e r by using
As w e l l
one*should
i s d emons t r abl y b e t t e r than those
previously obtained.
Despite the f a c t t h a t several
studies of
the v ib r a tio n a l
o f s u l p h u r d i c h l o r i d e have been made, d i f f i c u l t i e s
.appropriate
va lu es
for
v a l u e s q u ot ed f o r
lie
t he v i b r a t i o n a l
are in
wavenumbers.
the range 202-211
between 514 cm’ ^ and 535 cm
Al t hough
have gas phase v a lu es
The
(neglecting
do n o t a l l o w
f o r the various
it,
results
%
t he s t r e t c h i n g
v^
fund ame n t al s o f t h e
due a t
and
coupling).
to
32 35
. S Cl2
f o r e xa m p l e ,
least p a rtly
to
f unda me nt al s a r e o v e r l a p p e d and t h e i s o t o p i c
s t r u c t u r e o f t h e band i s u n r e s o l v e d ;
structure of this
though
for c r y s t a llin e
*
r e g i o n o f t he i n f r a r e d spect rum o f t h e g a s ,
fact that
rotational
cases
i d e a l l y one would l i k e
•» shows or\ly one band w i t h a complex c o n t o u r ( 1 5 )
t he
In a l l
( 1 5 ) whi ch show e v i d e n c e o f v i b r a t i o n a l
the p r e s e n t r e s u l t s
species.
i n choosing
cm ^ and those f o r
3
sulphur d i c h l o r i d e
arise
spectrum1
i t ’ is
a l s o p o s s i b l e t h a t the
' ♦
band mi gh t be a f f e c t e d by a C o r i o l i s
<
perturbation:
The i n f r a r e d spect rum o f matr. ix i s o l a t e d s u l p h u r - d i c h l o r i d e
probably gives
the best e stim ate
this
f o r t he s t r e t c h i n g f undamenT&l s; i n
case t h e i r i s o t o p i c s t r u c t u r e
A g a i n , however ,
and H a r r i s o n
t he a ss i gn me n t o f
i s a t 1e a s t - p a r t i a I T y ^ r e s o l v e d ( 1 5 ) .
and ^
^
uncertain.
Frankiss
-1
(47-) a s c r i b e a gas phase Raman band a t 528 cm
to
*
1
t
r
'
'
■
'
*
'
r
but do n o t r e pr od uce t he spec t rum o r d e s c r i b e
and Tremblay found an as ymme tr ic band i n
a t 519 cm ^ ( 1 5 )
t h e bandshape; Sav oi e
t h e Raman spec t rum o f t h e l i q u i d
and i n t e r p r e t e d t h e - p o l a r i z a t i o n
p r o p e r t i e s as i n d i c a t i n g
t h e i n t e n s i t y a r o s e m a i n l y from the v. f u n d a m e n t a l .
$
I
fundamental
has been obser ved in
an asymmetr ic b ^ d
The e a s i l y a s s i g n e d
t h e Raman spect rum o f
a t 211 cm ^ ( 15 )
and i n
t he gas a t 205 cm ^ ( 4 7 )
the l a t t e r r e p o r t a g ai n does n o t d e s c r i b e t he tjaedshape.
^ 2
fundamental
with
Also g i v en a r e
distortion
t hose o f S a v o i e and Tremblay
wavenumbers.
t h i s work a r e
f o r the c e n t r i f u g a l
in e rtia l
defects
and
and v i b r a t i o n a l
.
All
fo r the v i b r a t i o n a l
the mi cr owa ve - ba s ed r e s u l t s , h ow ev er ,
data.
'
we r e
t hese' ' have been compared d i r e c t l y
t he e x p e r i m e n t a l e f f e c t i v e wavenumbers
rotational
(48).
The e s t i m a t e d e q u i l i b r i u m wavenumbers
f u n c t i o n s g i v e good p r e d i c t i o n s
t he
and Oka and Morino ( 1 1 ) .
v a l u es
ground and e x c i t e d s t a t e
p r e d i c t e d u si ng e f f e c t i v e microwave d a t a ;
with
(15)
t he c a l c u l a t e d and e x p e r i m e n t a l
constants,
vibrational
fun ction s d e riv e d in
although
Further,
has been obse rv ed i n an argon m a t r i x a t 208 cm
In T a b l e 3 . 1 2 t he p o t e n t i a l
compared
the l i q u i d a s. ^
o f the p o te n tia l
f u n da me n t al s. ,,
Onl y
a r e c o n s i s t e n t w i t h bot h t he
The f o r c e c o n s t a n t s o f S a vo i e and
Trembl ay ( 1 5 ) ,
♦
which a r e based on t h e most comprehensive v i b r a t i o n a l
provide b e t t e r
predictions
f o r the d i s t o r t i o n c o n s t a n t s and i n e f t i a l
d e f e c t s / t h a n any p r e v i o u s p o t e n t i a l
t hough,
f unct -ion
estimates
c o n s t a n t s and i n e r t i a l
f o r t he p o t e n t i a l
constants
defects
they v ar y
V
I
a more r e p r e s e n t a t i v e
*
F^,
*
F^,
The p r e s e n t
,
the s t r e t c h i n g force c o n s ta n t,
constant,
v a lu es o f
from t hose p r e v i o u s l y o b t a i n e d i n h av in g a l a r g e r v al u e
4
for
i s poor .
are c le a r ly
fe '
set;
( 8 - 1 5 ) ; e v e n ^ i n ' t h i s c^se
t he agreement between t h e c a l c u l a t e d and e x p e r i m e n t a l
the d i s t o r t i o n
data,
and a p o s i t i v e
*
a s m a l l e r v a l u e f c ^ t he bending
/
r a t h e r than n eg ative value 'for the
/'
i
Table 3 .1 2
Summary o f P r e s e n t and P re v i o u s S u l p h u r D i c h l o r i d e P o t e n t i a l
F unct ions and R e l a t e d E x p e r i m e n t a l
Data.
*
C a l c u l a t e d Values
Fit 2
Fit
3
F it 4
O
F ^ (mdyn/ A)
2.913
2.994
O
F1 2 (mdyn/A)
0.0926
0.0 913
0. 08 91
F2 2 (mdyn/A)
0.2624
0. 2 6 11
0.2606
O
F3 3 (mdyn/A)^
2. 4 21
2.479
2.4 70
-499.0
-498.5
-498.5
-8.017
-8.023
-8.050
-2.582
-2.563
-2.574
-6.728
-6.571
-6.595
'
2.986
o
%
Ta a a a ( k H z )
Tbbbb( k H z )
Tc c c c ( k H z )
t , k (kHz)
ababv
'
0. 324 1
0. 3 2 21
0 . 3 23 1
0.6759
0.6779
0.6769
(cm* "*)
514.8
521.9
521 .6
aj2 (cm~^)
206.9
206.5
206.2
w3 (cm
523.8
530.0
529.0
A<0 0 0 >(uA2 ) f
0.3086
0. 3081
0.3 084
a 2 (uAz )
0.5220
0.5220
0.8306
0. 83 01
^
/
■
U 23)
)
A<01° ) ( u A 2 >f
•
•
0.5 220
0.8304
84
Table 3.12
Summary o f P r e s e n t and P r e v i o u s S u l p h u r D i c h l o r i d e P o r e n t i a l
*
F unct ions and R e l a t e d E x p e r i m e n t a l
...... -
r
-
-M
Data
■"
■
(continued)
•
C a l c u l a t e d Values
Sa vo i e and
Trembl ay ( 1 5 )
Exper iment *
Oka and
Mor ino ( 1 1 )
0
F ^ (mdyn/A)
2 . 6 41
2.52
-
F] 2 (mdyn/A)
-0.029
-0.055
-
F2 2 (mdyn/A)
0.303
0.305
-
2.433
2.52
-
O
o
F3 3 (mdyn/A)
-404
’ aaaa(KHz>
W
KHz>
W
KHz>
'abab(KHz>
-397
-4 9 8 .6a
-8.22
-8.52
-8.0263
-2.88
-3.04
- 2 . 574a
-6.69
-6.46
- 6 . 58b
1
'
0.415
<‘ 13>2
^23*
co-j ( crri“ 1 )
'
0.440
-
0.585
0.560
-
517.1
514
5 1 8 .0C
d
e
, 2 ir
w2 (cm
)
211
208
205
/
-1
LO3 \ cm
)\
525.3
535
5 2 5 . 5C
0.290
0.287
0.3077f
0.446
0.427
0.5220
0.736
0.714
op
a2
(
uA
)
4 ( ° , 0 >(uA2) f
'
0.8297f
85
Table 3.12
Summary o f P r e s e n t and P r e v i o u s S u l p h u r D i c h l o r i d e P o t e n t i a l
Funct ions and R e l a t e d E x p e r i m e n t a l
Final
C alcu lated Values
P o t e n t i a 1 Const ant s
Data ( c o n t i n u e d )
Experimentaj
o
2.949
-
F12 (mdyn/A)
0.0 916
-
O
F2 2 (mdyn/A)
0.2618
-
O
F3 3 (mdyn/A)
2.439
-
F ^ (mdyn/A)
Q
'a a a a (kHz>
Tbbbb(kHz)
, c c c c ( kHz )
’ a b a b (kHz )
-498.6
- 4 9 8 . 6a
-8.023
-8.0263
-2.575
- 2 . 574a
-6.679
-6.58b
k 1 3 >2
0.3234
-
u 23>
0.6766
-
u)^ ( cm
)
518.0
5 1 8 . 0C
w2 ( c m
)
■206.7
2 0 5 d , 211
aj3 ( c m _ 1 )
525.7
5 2 5 . 5C
4 <000>(uA2 )
0.3085
0.3077f
4 2 ( u A2 )
0.5 222
0.5220
A(010>(uA2 ) f
0.8307
0.8297f
I
86
Footnotes to Table 3.12
a
Wei ghted a v e r a g e o f t h e t h r e e val ues
were i n v e r s e l y p r o p o r t i o n a l
k
in T abl e 3 . 7 .
Weight s g i v e n
t o the q u ot ed e r r o r s .
Mean o f t h e F i t 4 v a l u e and t h e a v e r ag e F i t 2 and F i t
Ta bl e 3 . 7 .
3 val ues o f
Th is c o n s t a n t i s o n l y p o o r l y d e t e r m i n e d .
£
M a t r i x v a l u e from S a v o i e and Tremblay ( 1 5 ) .
^
Gas phase v a l u e from F r a n k i s s
and H a r r i s o n
(47).
L i q u i d phase v a l u e f rom Savoi e and Tremblay ( 1 5 ) .
^
Values f o r
t he K i v e l s o n - W i l s o n
experim ental
regardless
value of
A ',B ',C '
as g i v e n
i s h i g h e r than a ^ ^
3.7.
The
by 0 . 5 2 2 0 uA^
o f w h e t h e r Watson o r K i v e l s o n - W i l s o n c o n s t a n t s ar e used.
The Watson va lu es o f
and A ^ l ^
a r e 0 . 3 0 9 3 uA^ and
Op
0 . 8 3 1 3 uA
in T a b l e
respectively
(from Table 3 . 8 ) .
87
interaction
constant,
F in ally,
F^-
the q ue st i on - a r i s e s
microwave and v i b r a t i o n a l
constants.
as
to w h e t h e r a c o m b i n a t i o n o f
dat a would improve
Any me an i n g f u l
refinement
t he a ccu rac y o f
is u n l i k e l y s i n c e the d i f f e r e n c e s
between the observed and c a l c u l a t e d ; wavenumbers a r e l e ss
observed upon a change o f phase from,
(15).
Nevertheless
val ues
for
one notes
t he s t r e t c h i n g
from F i t
constants
"Final
t h a t t he
gives
for
32 35*
S C l2 while
the r e s u l t s
listed
Constants".
for
measured v a l u e o f 205
o f t he
(1)
the p r e d i c t i o n s
function
band, however,
predictions
o f T abl e
constants,
as g i v e n
in T a b l e
then
t he p r e d i c t e d
*-1
(10)
cm
, in
3.12.
•
32 35
S C l2
If
No
the
"center of
fundamental
good agreement w i t h
t he
3.12.
isolation
potential
fu nction is
dat a o f S av o i e and Tremblay
i s o t o p i c s t r u c t u r e o f the s t r e t c h i n g
those c a l c u l a t e d u s i n g t he " F i n a l
The agre eme nt is a g a i n
Potential
very good a l t h o u g h
(15)
was m o s t l y
a re compared t o
C o n s t a n t s" o f T a b l e 3 . 1 2 .
the p r e s e n t i n t e r p r e t a t i o n
band i s somewhat d i f f e r e n t
S a vo i e and Tremblay
also confirmed
( 1 5 ) , where the
f un d am en t al s v-| and
I n Tabl e 3 . 1 3 t he observed i s o t o p e s h i f t s
the s t r u c t u r e o f the
t he w e i g h t e d -
t he gas phase v a l u e f o r
The acc u ra c y o f t he p r e s e n t
by the m a t r i x
obtained
is e s s e n t i a l l y
cm ^ i s assumed to c o rr e s po n d to t h e
is e s t i m a t e d to o cc u r a t 2 0 6 . 2
e a rlie r.
low when
i n T a b l e 3 . 1 2 under the h ea d i ng
a t t e m p t has been made t o r epr oduce
resolved.
predict
A m i n o r a d j u s t m e n t o f t he f o r c e
This p o t e n t i a l
the d i s t o r t i o n
the s h i f t s
to s o li d
t o t h a t whi ch would be o b t a i n e d t hr ough t h e use o f
average v a l u es
gravity"
liq u id
F i t 2 force constants
3 and F i t 4 a r e s l i g h t l y h i g h .
Potential
identical
f o r e x a mp l e ,
than
fund amen tal s which a r e s l i g h t l y
compared to t he m a t r i x data
the f o r c e
of
from t h a t given
a s s i g n e d a v er y weak f e a t u r e ~ 1 0 cm ^
v-
88
32 35
away from t h e
t he
S'
Cl^ peak as b e i n g due to the symmet ri c s t r e t c h
34 35
S Cl,, s p e c i e s .
The microwave r e s u l t s ,
howe ve r , suggest
of
t h a t the
32 37
34 35
S Cl^ and
S Cl ^ s p e ci e s
symmetric s t r e t c h i n g f un d ame n t al s o f t h e
are overlapped.
It
is o f some i n t e r e s t
t he i s o t o p i c s h i f t s
Cl-S-Cl
bond a ngle
o f the
raj
Voj^ /
( 4 9 ) where
uncertainty
s h i f t and 1 0 4 . 5 °
o f even 0 .1
approximately 2.0°
with
is h a l f t h e
t h e e s t i m a t e d bond a n g l e is 1 0 5 . 2 °
u si n g t he ^ S ^ C l ^
t he measured s h i f t s
vibrational
c o n sisten t with
because an
an e r r o r o f
i n t he p r e s e n t work an improved p o t e n t i a l
o f t he r e l a t e d
centrifugal
distortion
i n t he v i b r a t i o n a l
has n o t been p o s s i b l e to d em on st r at e t h a t - f o r
> v^both
this
defects,
wavenumbers and i s o t o p i c s h i f t s
While i t
t h e gas phase ^
These
i n t h e bond a n g l e .
data i n c l u d i n g i n e r t i a l
fundamentals.
s h ift.
introduces
f u n c t i o n has been d e r i v e d which i s c o n s i s t e n t w i t h a l l
constants,
the microwave and m a t r i x
choice.
isolation
Thi s i s s u e c o u l d be s e t t l e d
d a t a are
unambiguously
by mea su ri ng t he microwave spect rum o f t h e v^ = 1 a n d / o r the v^ e x c i t e d s t a t e s bec ause, as f o r SF^ ( 5 ) ,
v er y s e n s i t i v e
Cl-S-Cl
a '
t h e microwave v a l u e o f 1 0 2 . 7 ° ,
cm ^ i n
In conclu sion,
experim ental
the
( 3 . , 6)
Using t he d at a o f T a b l e 3 . 1 3
agrpe ver y w e l l
n
K
,
m^ rn^i ' \m<. + 2m^.^sin
u si ng t he ^ S ^ C l , ,
estim ates
me,
t he asymmetr ic s t r e t c h
s pe c i e s can be used to e s t i m a t e
through t he e q u a t i o n
,
bond a n g l e .
to n ot e t h a t f o r
to t he d i f f e r e n c e ^
showed c o n c l u s i v e l y
that
the i n e r t i a l
- w-| •
(5);
1
d e f e c t s w o u l d be
For SF£ t he microwave r e s u l t s
c o r r o b o r a t i o n has been p r o v i d e d by
89
Table 3.13
Observed and C a l c u l a t e d
Isotope.Shifts
For t h e S t r e t c h i n g
Fundamentals o f S u l p h u r D i c h l o r i d e .
•
Symmetric S t r e t c h
Speci es
C a l c u l a t e d Value
3 2 s 35 c i 2
.
Calculated S h i f t
518.0
Observed S h i f t
0.0
0.0
%
32 s 35 c i 37 ci
a
513. 3
4.7
4.5
3 2 s 37c i 2
511.0
7. 0
7.5
3 4 S35C12
510.3
7. 7
7.5
Calculated S h i f t
Observed S h f i t
Asymmetric S t r e t c h
Sp ec ie s
C a l c u l a t e d V alue
32S 35C12
525.7
0.0
0.0
32S3 5 C137C1 a
523.8
1.9
3.2
3 2 S 3 7 C12
519.6
6.1
6.0
3 4 S3 5 C12
516.8
8.9
9.0
3
The r e q u i r e d G m a t r i x e le me n t s
a r e given by C a l i f a n o
(33).
f o r t he
32 35
37
S Cl
Cl s p e c i e s
(C
symmetry)
90
m a trix i s o l a t i o n data f o r
32
SF^ and
34
SF^ ( 5 0 ) .
In itia l
•
results
infrared
f o r s u l p h u r d i b r o m i d e and s u l p h u r d i i o d i d e have been ta-ken to s u g g e s t ,
however,
ing t h a t
t h a t i n bo th cases
ar,d
su l p h u r d i h a l i d e s
av er ag e v a l u e .
(48).
Therefore
i n SCl^ a r e n e a r l y d e g e n e r a t e .
t h e two s t r e t c h i n g
f un d am en t al s
it
is h a rd ly s u r p r i s ­
In f a c t fo r a l l
lie
w ithin
2%
four
of th e ir
91
3.6
Comments on t he M o l e c u l a r S t r u c t u r e o f S u l p h u r D i c h l o r i d e
I n T a b l e 3 . 1 4 t he v a r i o u s
in
r
this
s u l p h u r - c h l o r i n e bond l e n g t h s d e r i v e d
s t u d y a r e compared t o t h e p r ev i o u s e s t i m a t e s .
, r s and r g v a l u es a r e a l l
quite
A slig h t error
,
s i m i l a r and a r e c l e a r l y more p r e c i s e
t h an t he e a r l y e l e c t r o n d i f f r a c t i o n
and Beach ( 1 7 ) .
The microwave r
r e s u l t s o f Pal mer
(18)
and o f Stevenson
in t he e l e c t r o n d i f f r a c t i o n
results of
Mo r in o e t a_l_.. ( 1 4 ) must a l s o be suspect ed because t h e r^ d i s t a n c e i s
e x p e c t e d to exceed t h e r z o r r g bond l e n g t h
S- Cl
bond l e n g t h
is
identical
Al so g i v e n
for
(51).
t o t h a t g i ve n by Mur ray ert al_.
i n T a b l e 3 . 1 4 a r e t he S-Cl
some r e l a t e d m o l e c u l e s .
have quoted e r r o r s o f
The r Q e s t i m a t e o f t he
(16).
bond l e n g t h s d e t e rm i n e d
Exc ept f o r SO^CIF ( 5 2 )
these d i s t a n c e s a l l
less
t han Q . 010 ft and o n l y f o r NSC1 ( 5 3 ) is t h e
't
o bs er ved bond l e n g t h v e r y d i f f e r e n t from t h e sum o f P a u l i n g ' s s i n g l e
0
bond r a d i i ( 2 . 0 3 A) ( 6 6 ) . The e s t i m a t e d p r i n c i p a l v a l u e o f t h e c h l o r i n e
n u c l e a r q u ad ru po le c o u p l i n g
tensor,
t h e s e m o l e c u l e s ; where n e c e s s a r y ,
NQR f r e q u e n c y
(67).
x z z > i s p r e s e n t e d as w e l l
x zz has been c a l c u l a t e d
f o r each o f
by d o u b l i n g t he
These' numbers should be r e g a r d e d w i t h some d e t a c h ­
ment as t h e v a r i a t i o n s
to a larg e e x te n t r e f l e c t
changes
in the h y b r i d i ­
z a t i o n o f t h e s u l p h u r atom ( 6 3 ) .
Nevertheless,
i n c r e a s e i n t h e S-Cl
i s p a r a l l e d by a d ecr eas e i n the
bond l e n g t h
ma gnit ude o f t h e c o u p l i n g c o n s t a n t x z z - T h i s
is
fo r divalent
illu s tra te d
s u l p h u r an
by t he
,
results
f o r S C ^ , CH^SCl and S^Cl^ where bond l e n g t h s o f 2 . 0 1 5 A, 2 . 0 3 0 A
0
and 2 . 0 5 7 A a r e a s s o c i a t e d w i t h x zz v a l u es o f - 9 1 . 9 MHz, - 7 8 . 9 MHz and
- 7 1 . 6 MHz r e s p e c t i v e l y .
The f i r s t
o f t hese v a l u e s
in p a r t i c u l a r
c l o s e to t h a t o f t h e c h l o r i n e atom ( 1 0 9 . 7 4 MHz ( 6 8 ) )
e v i d e n c e f o r p r i m a r i l y c o v a l e n t s i n g l e bond c h a r a c t e r
is q u ite
and p r o v i d e s s t r o n g
(69).
92
Table 3.14
The S- Cl
Bond Lengths and x '2 ( ^ C l )
V a l ue s
f o r S ul phur
D i c h l o r i d e and R e l a t e d M o l e c u l e s
Molecule
SCI
x Zz(MHz)a
r ( S-C1 ) ( A )
r z 2.01525(8)b
T h i s work
r s 2.0141(10)
T h i s work
2
-91.9
r Q 2.014(2)
r e 2.0109(12)
T h i s work
T h i s work
r Q 2.014(5)
-89.9
(16)
r g 2.006(4)
(14)
r g 2.00(2)
(17)
r g 1 . ? 9( 2 )
(18)
S02C12
r g 2.011(4)
-75.4
(54,
S02C1F
r Q 1.985(15)
-74.7(7)
(52)
S2C12
r g 2.057(2)
-71.6
(56,
r s 2.055(1,:)
•
R e fe re n c e
CH3SC1
r
SFcC1
0
r $ 2.0392(2)
55)
57}
(58)
2.030(1)
»
)
r z 2.045(3)
-78.9(14)
(59)
-85.4
(60)
j
(61)
CH3 S02C1
r g 2.046(4)
-66.5
(62,
63)
CcHcS0oCl
6 5 2
r
2.047(8)
-66.0
(64,
63 )
S0C12
r g 2.077(6)
-64.0
(54,63)
NSC 1
r s 2.161
-43.4
(53)
■
a Principal
9
r g 2.159(3)
value, p a r a lle l
k The quoted e r r o r
molecules.
(65)
lim its
to t h e S- Cl
bond,
have d i f f e r e n t meanings f o r
t he v a r i o u s
93
/
It
is
interesting
and t h e r e l a t e d
force constant
ingful
as w e l l
stretching
t o compare t h e S-Cl
force constants.
i s s i m p l y t h e mean o f
bond d i s t a n c e s
For SC 1^ t he r e q u i r e d v a l e n c e
and F ^ .
Agai n t h e most mean­
comparisons i n v o l v e m o l ec u l es where s u l p h u r e x h i b i t s
hybridization.
T he r e a r e s u r p r i s i n g l y
t h e same
few good d a t a a v a i l a b l e
.
pur pose.
A l t h o u gh s e v e r a l
are presented
e s t i m a t e s o f t he S-Cl
in Table 3.15
in a l l
n e ces sa r y t o make c o n s t r a i n t s
v a l u e s should t h e r e f o r e
I
stretching
fo r this
m
f o r c e constants
c as es e x c e p t t h e p r e s e n t i t
in e v a lu a t in g
t he p o t e n t i a l
be r e g ar de d as t e n t a t i v e .
was
function.
These
94
Table 3.15
Estimated S tr e tc h in g
Force C o n st an t s o f Some Su l p h ur
C h l o r i n e Bonds
Molecule
F ( S- C1 ) (mdyn/A)
r ( S-C1 ) (A)
Reference
%
SCI 2
2.015
2.69(7)a
T h i s work
S2 C12
2.057
1.97
(70)
S0C12
2 . 0 77
1.79
(71)
3.26
(72)
*
w
S02C1F
1 .9 85
»
'
S02 C12
2.011
2.52
(72)
*
s f 5c i
2.030
2.76
(61)
NSC1
2.161
1.49(15)b
(73)
a E r r o r e s t i m a t e d f rom t h e T a b l e 3 . 8 r e s u l t s .
*
b E r r o r quoted i s one s t an d a r d e r r o r .
Not a s t a n d a r d e r r o r .
95
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34,
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(1978).
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S o c i e t y , London, 1 973.
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T.
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G l e ms er , J .
Mol .
CHAPTLR 4
The M i c r owave Spectrum o f D i c h l o r o s i l a n e
*
Al t ho ug h t h e r e have been many microwave i n v e s t i g a t i o n s o f
various
halomethanes and h a l o s i l a n e s .
m o s t l y t o symmetric top s p e c i e s .
t hese s t u d i e s have been l i m i t e d
Whereas p r i o r
to t h i s
s p e c t r a had been observed f o r d i f 1uoromethane ( 1 ) ,
(2,3)
and dibromomethane ( 4 )
the q u a r t i c
st udy r o t a t i o n a l
d i ch lo n o met han e
centrifugal
d i s t o r t i o n con­
s t a n t s had been measured o n l y f o r d i f l u o r o m e t h a n e ; even f o r d i f l u o r o ­
met hane,
however,
in a fo rc e f i e l d
one d i h a l o s i l a n e ,
no c e n t r i f u g a l
t he c e n t r i f u g a l
refinement.
d istortion
More s u r p r i s i n g l y ,
namely d i f l u o r o s i l a n e ,
distortion
c o n s t a n t s were not used
t he spectrum o f o n l y
had been s t u d i e d
c o n s t a n t s were d e t e r m i n e d .
C2 V m ol ec u l es t h e d i s t o r t i o n
(5)
and a g a i n
For t hese s i m p l e
c o n s t a n t s can be combined w i t h v i b r a t i o n a l
d a t a to e v a l u a t e t h e f o r c e f i e l d w h i c h , i n t u r n , can be used to r e f i n e
«
•*
the molecular s t r u c t u r e .
The p r e s e n t s t ud y o f d i c h l o r o s i l a n e was
undertaken .p r i m a r i l y
to determine a p r e c is e m ole cula r s t r u c t u r e ,
complement the e a r l i e r work on c h l o r o s i l a n e
(7,8)
and,
hopefully,
(6)
to
and t r i c h l o r o s i l a n e
to p i n p o i n t any s y s t e m a t i c v a r i a t i o n s
in the
s tr u c t u r e s of these molecules.
A l t h o ug h d i c h l o r o s i l a n e has not been p r e v i o u s l y s t u d i e d u s i n g
microwave s p e c t r o s c o p y ,
it
has been t he s u b j e c t o f s e v e r a l
s p e c t r o s c o p i c and s t T u c t u r a l
investigations.
Its
bond l e n g t h s and
a n g l e s were d e t e r mi n e d
i n an e a r l y e l e c t r o n d i f f r a c t i o n
Several
vibrational
studies o f i t s
other
st ud y ( 9 ) .
spectrum have been made ( 1 0 - 1 2 )
and
ion
t h ese d a t a have been used to d e t e r m i n e
molecule.
Recently
al ong w i t h
t hose o f o t h e r h a l o s i l a n e s ,
force f i e l d s
(13-17)
for
t h e p h o t o e l e c t r o n spectrum o f d i c h l o r o s i l a n e ,
used t o p r o v i d e e v i d e n c e f o r
has been i n v e s t i g a t e d
( p ~k J) tt back bonding to s i l i c o n .
( 1 8 ) and
The
n u c l e a r g u ad ru po le r esonance spectrum o f d i c h l o r o s i 1ane is a l s o
(19)
and suggests as w e l l
halosilanes
that
is quite d i f f e r e n t .
isotopic
species o f d i c h l o r o s i l a n e ,
n^m^i /
namely,
2 8 c . u 35r l
28c . 35~,37r l
, 29 c . u 35 r l
,
.
SiH^ C ^ .
S i C l
Cl and
SiH^ C1 ^ have been
gated.
The a c c u r a t e v a l u es o b t a i n e d f o r
been used t o d e t e r m i n e e f f e c t i v e
Val ues have a l s o been o b t a i n e d
coupling constants,
with e x is tin g
the r o t a t i o n a l
c o n s t a n t s have
and s u b s t i t u t i o n m o l e c u l a r s t r u c t u r e s .
f o r the c h l o r i n e
n u c l e a r q u ad r u p o l e
vibrational
The d i s t o r t i o n c o n s t a n t s
number o f f o r c e c o n s t a n t s and s t r u c t u r a l
more complex t han t h a t o u t l i n e d
cen tri­
have been combined
dat a t o e v a l u a t e the Harmonic f o r c e
subsequently the average m o le c u la r s t r u c t u r e .
fie ld
and
Because o f t h e l a r g e r
pa ra me te rs
t h i s p r oc e d u r e was
f o r sulphur d i c h l o r i d e
in C h a p t e r 3.
Assignment o f t he D i c h l o r o s i l a n e Spectrum
The r o t a t i o n a l
dense w i t h many l i n e s
spectrum o f d i c h l o r o s i l a n e was found t o be q u i t e
havi ng complex h y p e r f i n e s t r u c t u r e .
the a s si gn me nt o f t he spectrum r i g i d
predicted fo r
fic a lly ,
t he
ro to r transition
To f a c i l i t a t e
f r e q u e n c i e s were
low J l i n e s u s i n g a model m o l e c u l a r s t r u c t u r e .
Speci­
C2 v symmetry was assumed w i t h s i l i c o n - c h l o r i n e and s i l i c o n -
hydrogen bond d i s t a n c e s equated t o t h e i r
all
.
.
in vesti­
t h e m o l e c u l a r d i p o l e moment and t h e q u a r t i c
d i s t o r t io n constants.
4.1
known
t h e bonding in t h e hal omethanes and
In t h e p r e s e n t study t h r e e
f ug al
the
val ues
bond a n g l e s were assumed t o be e q u a l .
th at only b-type lin es
should be seen.
in c h l o r o s ila n e
Ihese c a l c u l a t i o n s
(6;;
indicated
A p r e d i c t i o n o f the n u c l e a r
TO 1
q u a d r u p o l e h y p e r f i n e s t r u c t u r e was a l s o r e q u i r e d .
hyperfine patterns even tu ally
ment.
In itia lly
principal
Cl
t he v a l u e s
p a t t e r n s were c a l c u l a t e d
32 35
S C12
to be the
having
x
as f o r
one o b t a i n s
X a a = ' X c c = - 2 0
using
32 35
S C^.
t h i s was not t he case f o r
28
MHz
the I-j + ^
spin s t a t i s t i c s
some s p i n w a v e f u n c t i o n s
35
28
for
SiH^
and
= I ,
- ~ 2 \
= -2;<
=
xx
yy
is
- 3 9 . 7 MHz
zz
( t h e c o r r e s p o n d i n g v a l ue f o r c h l o r o s i l a n e
angles)
scheme because,
for
t h e s i l i c o n - c h l o r i n e bond was assumed
T h e r e f o r e u si ng e q u a t i o n 3.1
tetrahedral
fine
35
t h e observed
the means o f making t h e a s s i g n ­
a x i s o f a symmetric q u a dr up o le t e n s o r
- 4 0 MHz f o r
(6)).
provided
Indeed,
35
C1^ (assuming
MHz. The h y p e r ­
I + J = F coupling
were i m p o r t a n t .
had a s t a t i s t i c a l
Whereas
w e i g h t o f zero
C l^ because o f t he pr esence o f a
second p a i r o f e q u i v a l e n t f e r m i o n s ,
t he hydrogen atoms.
These gave the
%
even and odd I h y p e r f i n e components s t a t i s t i c a l
weights of
1 and 3
r e s p e c t i v e l y f o r K K =ee«->oo t r a n s i t i o n s and t he r e v e f s e f o r K K =ecn-K)e
a
transitions.
C
a
The same s i t u a t i o n
C
has been obser ved i n m e t h y l e ne c h l o r i d e
( 2 ).
The model
spectrum i n d i c a t e d
low J t r a n s i t i o n s
and i r r e g u l a r .
o f the s e rie s
In a c a re fu l
j
t h a t t h e h y p e r f i n e p a t t e r n s o f the
j
should be e s p e c i a l l y complex
e x a m i n a t i o n o f t h e 1 4 - 1 8 GHz r e g i o n t h r e e
t r a n s i t i o n s were found whose h y p e r f i n e p a t t e r n s a l m o s t e x a c t l y matched
t hose c a l c u l a t e d
f o r t h e J = 5 , 6 and 7 members o f t h i s
t r a n s i t i o n s were too s t r o n g t o bel ong to a symmetric
species.
As w e l l ,
n e a r 16 GHz a s e r i e s o f u n s p l i t
high f r e q u e n c y S t a r k components were found.
l i n e s was as si gne d as t h e
a rigid
rotor f i t
t o t he
29
Si,
30
lin es with
t hese
Si
or
37
Cl
single
The s t r o n g e s t o f t hese
l i ne o f t h e
A s s i g n i n g the Q- br anch l i n e s as w e l l
series;
2b
28
SiH^
SiH^
35
35
Cl^ s p e c i e s .
Cl ^ s p e c i e s enabl ed
t o be made which a c c u r a t e l y p r e d i c t e d
t he p o s i t i o n s o f
102
many o t h e r t r a n s i t i o n s w i t h J < 10;
in a l l
cases t h e obser ved h y p e r f i n e
s t r u c t u r e was c o n s i s t e n t w i t h t h e p r e d i c t e d s p l i t t i n g s .
number o f t hese low J t r a n s i t i o n s
bootstrap c e n trifu g a l
higher J lines
distortion
being assigned.
A su fficien t
were measured to b eg in t h e usual
a n a l y s i s which r e s u l t e d
For
28
SiH^
35
in su ccessively
Cl^ t r a n s i t i o n s
ha vi ng a
maximum J v a l u e o f 34 were measured a l t h o u g h h i g h e r J l i n e s wer e seen.
28
Having made t he ass i gn men t f o r
S i^
35
C l^
( 46. 6% f r a c t i o n a l
*
abundance)
pO
OC
SiH^
t he l i n e s o f a d d i t i o n a l
s p e ci e s were s o u g h t .
The
77
Cl
and i t s
isotopic
Cl
species
( 30.4% f r a c t i o n a l
l i n e s were e a s i l y
identified;
abundance) was s t u d i e d f i r s t
because t h e two c h l o r i n e n u c l e i
were now n ot e q u i v a l e n t s l i g h t l y more complex h y p e r f i n e p a t t e r n s were
observed.
Transitions
28 *
35 37
SiH^ Cl
Cl.
for
hav in g a maximum J v a l u e o f 29 were measured
Using t h i s
29
was r e f i n e d and l i n e s o f t he
abundance) were s ear ch ed f o r .
i s o t o p i c data the m o le c u la r s t r u c t u r e
SiH^
35
C^
species
Agai n t h e s e were q u i c k l y
a ss ig nme n t was c o n f i r m e d by t he r e l a t i v e
compared t o t hose o f
statistics
28
35
( 2.37% f r a c t i o n a l
C^.
in ten sities
located;
o f t he t r a n s i t i o n s
t he h y p e r f i n e s p l i t t i n g s ,
and t h e S t a r k e f f e c t o f the
lin e.
for fu rth e r
isotopic
iH^^^C1 2 » were o b s e rv ed .
t h e y p r o v i d e d no a d d i t i o n a l
species,
sp ecifically
28
29
SiH^
S i^
37
These were n o t measur ed, h ow ev er ,
information.
35
C^
Cl.,.
and
because
No a t t e m p t was made t o assi gn
excitqd
state lin e s .
4.2
A n a l y s i s o f t he D i c h l o r o s i l a n e Spectrum
a.
spin
Only e i g h t
t r a n s i t i o n s w i t h a maximum J v a l u e o f 17 were measured f o r
Transitions
the
. N u c l e a r Quadr upol e C o u p l i n g
In an i n i t i a l
unsplit
a n a l y s i s o f t he
28
l i n e f r e q u e n c i e s o f the v a r i o u s
SiH^
35
C l^ d a t a
t he h y p o t h e t i c a l
t r a n s i t i o n s were c a l c u l a t e d
103
u si n g the model
section.
n u c l e a r q u ad r u p o l e c o u p l i n g c o n s t a n t s o f t h e p r e v i o u s
A centrifugal
d isto rtio n
v a l u es f o r t h e r o t a t i o n a l
then y i e l d e d
c o n s t a n t s and c e n t r i f u g a l
The model c o u p l i n g c o n s t a n t s ,
observed h y p e r f i n e s t r u c t u r e .
the r e l a t i v e
analysis
d i s t o r t io n constants.
howev er , d i d n o t p r e c i s e l y
F or t he
prelim inary
p r e d ic t the
tran sitio n ,
f o r e x am p l e ,
spacing o f t h e h y p e r f i n e components was a l m o s t p e r f e c t l y
pred icted but
t he a b s o l u t e s p l i t t i n g s were about f i v e ,per c e n t s m a l l e r
than t he obse rv ed s p l i t t i n g s .
P recise values f o r the
stants of
28
SiH^
35
35
Cl
n u c l e a r q u a d r u p o l e c o u p l i n g c on -
Cl ^ were o b t a i n e d by comparison o f t he observed
h y p e r f i n e p a t t e r n s w i t h t ho se o b t a i n e d from a s e r i e s o f guessed v a l u e s .
T h is was done by d i a g o n a l i z i n g t h e c o u p l i n g H a m i l t o n i a n f o r
rupolar nuclei
as d e s c r i b e d
c o n s t a n t s used f o r t h i s
prelim inary ro ta tio n a l
the coupling
in s e c t i o n
1 . 2 o f C h a p t e r 1;
purpose were t he v a l u e s o b t a i n e d f ro m the
analysis.
To a ccount f o r t he sp in s t a t i s t i c s
m i n i ng the v a l u e s o f t he c o u p l i n g c o n s t a n t s ,
»
t he 1^ + J_ =
however,
■*
, F_^ + l 2 = L scheme because o n l y
components we r e used f o r comparison purposes;
o f t he q u a d r u p o l a r H a m i l t o n i a n were needed.
a n a l y s i s one m ig h t a t t e m p t
In d e t e r ­
t h i s was used
t hose obs er ve d f r e q u e n c i e s which cor r es p o n d ed t o i s o l a t e d
partially
the r o t a t i o n a l
scheme 1-j + L> = L» I + ^ = F had t o be used.
interchangeably with
two quad-
hyperfine
thus o n l y t he e i g e n v a l u e s
In a more s o p h i s t i c a t e d
to make use o f t h e d a t a c o n t a i n e d
resolved p ortions o f the absorption
necessita te a lineshape s im u la tio n ,
lines;
in t he
t h i s would
i n which case t h e s t a t i s t i c a l
w e i g h t s o f t h e v a r i o u s components would have t o be acco un ted f o r .
The b e s t v a l u e s o f t h e c o u p l i n g c o n s t a n t s o b t a i n e d by v a r y i n g
x aa and n ^
pQ
x b b" xc c ^ x aa^ t 0 r e Produce t h e b y p e r f i n e s t r u c t u r e o f t he
OC
SiH^
C1 2
species are given
in T a b l e 4 . 1 ;
the e r r o r
lim its
represent
104
\
Tabl e 4 , 1
C h l o r i n e N u c l e a r Quadrupole C o u p l i n g Co nst an t s
Dichlorosilane
(MHz) o f
28 Si H2 3 5 C l 2
-21.13 (3 5 )a
xaa
-20.88(30)
x bb~x cc
2 8 S i H 2 35C l 37Cl
Xa a ( 35C l )
xbb( 35ci ) _xcc(35cl)
Xa a ( 3 / C l )
* b b < 3 7 c , ) - * c c ( 3 7c' >
-20.70b
' 21- 30
- 1 6 . 99b
- ' 6-n
Estimated o u ts id e e r r o r l i m i t s .
O b t a i n e d by t r a n s f o r m i n g t he
OC
OQ
SiH2
Xz z (
28
SiH~
07
Cl
,C1 p r i n c i p a l
^
in ertial
C l ) = 1 . 2 6 8 8 XZ Z ( 37 C 1 ) .
35
Cl ~ v a l u e s t o t he
^
axes system and usi ng
105
estimated outside l im i t s
28
35
forS i C ^ *
transitions
splittin g s
a r e g i ve n
calculated
along with
t h e i r assi gnment s and the
One o f t h e s e ,
the
tran sitio n ,
is also
a l on g w i t h t he c a l c u l a t e d h y p e r f i n e p a t t e r n .
29
To a n a l y s e t he d a t a f o r
d e r i v e d above were used;
pQ
Some r e p r e s e n t a t i v e obse rv ed
u s i n g t he d e r i v e d q u a d r u p o l e c o u p l i n g c o n s t a n t s ,
in T a b l e 4 . 2 .
shown in F i g u r e 4 . 1
of error.
SiH^
35
C1 2
the coupling constants
, 29
t he h y p e r f i n e s p l i t t i n g s
for
S il^
35
Cl^ and
«
SiH2
C1 2 were s l i g h t l y d i f f e r e n t ,
however, because t he r o t a t i o n a l
po
c o n s t a n t s a r e i s o t o p i c a l l y d ep en d en t.
estimating
the r o t a t i o n
o f t he m o l e cu l e
system consequent on i s o t o p i c
^®SiH 2 ^^C1
sy st em.
For
I t was assumed t h a t
i n t h e bond a x i s
gave x
o f t h e q u a dr u po l e moments o f
aa
28
Cl
the
and
= - 2 0 . 7 0 MHz and n=1 . 0 2 9 f o r t he ^ C 1
37
and n = 0 . 94 8 f o r t h e
the
35
SiH^
35
Cl
37
Cl
nucleus.
C l,
after
in ertial
axis
the coupling constants o f
were t r a n s f o r m e d t o t h e ^ S i H ^ C l ^ C l
2
07
Cl
i n t he p r i n c i p a l
substitution,
c o n s t a n t s co ul d be o b t a i n e d by d i v i d i n g
ra tio
or
Sil^
in ertial
37
system t he
35
37
axis
Cl c o u p l i n g
Cl
val ue s by 1 . 2 6 88
Cl
(20)).
(the
This c a l c u l a t i o n
n u cl e u s a n d ' x = , = - 1 6 . 99 MHz
aa
The h y p e r f i n e
p a t t e r n s observed f o r
Cl s p e c i e s were a c c u r a t e l y p r e d i c t e d using
t hese v a l u e s
f o r the coupling con stan ts.
b.
Rotational
C o ns t an t s and C e n t r i f u g a l
D i s t o r t i o n Co ns t an ts
A f t e r t h e h y p e r f i n e s t r u c t u r e was ac count ed f o r
f r o m each r o t a t i o n a l
transitio n.
The r e s u l t i n g
unsplit
it
was s u b t r a c t e d
lin e
w e re used t o c a l c u l a t e
the r o t a t i o n a l
d istortion
The A r e d u c t i o n o f Wat son' s H a m i l t o n i a n in t h e
Ir
constants.
c o n s t a n t s and q u a r t i c
frequencies
r e p r e s e n t a t i o n , e q u a t i o n 1 . 1 1 , was a g a i n used.
c o n s t a n t s were r e q u i r e d
^ S ^ ^ C l^ C l.
to f i t
t h e d a ta f o r e i t h e r
centrifugal
No s e x t i c d i s t o r t i o n
28
The d a t a s e t o b t a i n e d f o r ^ S ^ ^ C ^
SiH^
35
C1 2 or
was too l i m i t e d
*
106
Table 4 .2
S o m e ' R e p r e s e n t a t i v e T r a n s i t i o n s (MHz) o f 2 8 SiH2 35C l 2
showing N u c l e a r Quadr upol e H y p e r f i n e S t r u c t u r e
I*
P
Calculated
Observed^
_______________________________Frequency_________________Fr equency_________
6(1,5)
- 6(0,6)
3c
3
15706.64
15706.67
0
6
' 15707.57
15707.57
1
6
15707.57
15707.57
3
9
15 70 8 .3 1
15708.29
3
4
15709.22
15709.16
3
5
15710.73
15710.97
1
7
15710.98
15710.97
2
8
15711.15
15710.97
2
7
15711.15
15710.97
2
5
15711.15
15710.97
2
4
15711.15
15710.97
3
8
15712.57
1
5
15713.90
15714.17
3
6
15714.22
15714.17
2
6
15714.73
15714.17
3
7
15715.32
15715.31
-
1, 6)
15712.60
'
- 7(0,7)
3
4
17200.83
0
7
17201.64
17201.63
1
7
17201.64
17201.63
3
10
17202.30
'17202.31
3
5
17204.67
17205.26
3
6
17204.98
1
8
17205.14
17205.26
2
9
17205.28
17205.26
2
8
17205.28
17205.26
2
6
17205.28
17205.26
2
5
17205.28
17205.26
3
9
17206.56
17206.56
1
6
17208.17-
17208.94
3
7
17208.53
17208.94
2
7
17208.93
17208.94
3
8
17209.48
.
<v
17205.26
17208.94
107
Table 4 .2 (c o n tin u e d )
a The I and F l a b e l s a r e t h e same f o r bot h r o t a t i o n a l
' b Repeat ed f r e q u e n c i e s
S tric tly ,
I
levels.
i n d ic a t e unresolved h y p e r fin e s t r u c t u r e .
i s n ot a good quantum number;
it
used t o s p e c i f y t he symmet ri es o f t h e v a r i o u s
can
, however,
hyperfine
I
be
levels.
108
“ SiHftl*
6
, 5-
6
^
R e c or d e r t r a c i n g
■»;
Calculated pattern
1 5 7 1 1 . 1 6 MHz ( u n s p l i t
Figure 4.1
An Example o f N u c l e a r Quadr upol e H y p e r f i n e S t r u c t u r e i n t h e
Spectrum o f D i c h l o r o s i l a n e
I
lin e frequency)
f
109
to enable the q u a r t i c c e n t r i f u g a l
For
29
SiH2
35
refinement,
C l^ th e re fo re ,
F it
1,
'
frequencies;
rotational
or
'
<
SiH„ C l 0and was s u b t r a c t e d f r o m t he
2
2
ther e s u lt in g
constants.
centrifugal
-■
I n an i n i t i a l
two approaches were t r i e d .
t h e d i s t o r t i o n on each t r a n s i t i o n was assumed t o be
po
t he same as f o r
d i s t o r t i o n c o n s t a n t s t o be d e t e r m i n e d .
measured
f r e q q e n c i e s were then f i t
to t h e
three
I n a subsequent a n a l y s i s , F i t
2, th e
quartic
d i s t o r t i o n constants o f ^ S i H ^ C ^
v a l u e s c a l c u l a t e d u si n g t h e harmonic f o r c e f i e l d
we re c o n s t r a i n e d t o
o f T a bl e 4 . 1 2 .
Both
o f t h e s e r e f i n e m e n t s gave v e r y s i m i l a r v a l u e s f o r t h e r o t a t i o n a l
constants although the standard d e v i a t i o n of the f i t
was s m a l l e r f o r
*
'
Fit 2 A summary o f t h e t r a n s i t i o n s measured f o r ^ S i H ^ ^ C ^ .
and
29
SiH2
35
The r o t a t i o n a l
w i t h h y p e r f i n e s t r u c t u r e removed,
c o n s t a n t s and q u a r t i c c e n t r i f u g a l
c a lc u la t e d using t h i s
is given in Table 4 . 3 .
distortion
d a t a a r e gtven i n T a bl e 4 . 4 .
^ S i^ ^ C l^ C l
constants ■
no
Table 4.3
Observed R o t a t i o n a l T r a n s i t i o n s
a
Observed
Frequency
Transition
(MHz) o f D i c h l o r o s i l a n e
D istortion
Correction
Deviation
■
28Si H, 35 C1
! — 2—
’ l.l
'
°0,0
2 2,1
'
2 1,2
3 1 ,2 '
30 ,3
3 2,1
'
3 1 »2
42 ,2 '
41,3
4 1 >4
30 , 3
5 1.4 “ 50,5
52 , 4 " 5 1 *5
50 , 5 '
4 1 »4
5 1 »5 " 4 0»4
60,6
62,5
6 1 ,6
6 1 »6
50 , 5
7 1 .6
-
92,7 '
9 1,8
*
00
O
00
1
8 2 , 6 " 8 1 .7
?1,7
90 ,9 "
0.03
35705.26
-1.88
' -0.04
12787.20
-0.03
-0.01
34213.14
-1.51
-0.00
33615.07
-1.08
-0.06
29269.93
0.06
0.04
14494.45
-0.04
-0.0V
37780.27
-1.06
o.oi
43763.62
-0.77
0.02
33266.36
0.12
0. 01
-8654.58
0.56
0.04
15711.15
-0.19
-0.02
0. 01
37140.59
-0.75
*
0.16
0 . 01
17205.28
-0.51
0.04
31449.25
0 . 91
-0.06
30753.37
1.71
-0.00
30170.15
-2.99
0.02
30154.89
2.47
-0.04
3 88 26 . 71
7 1 »6 " ?0 , 7
72 ,5 '
-0.11
*
51,4 " 42 ,3
61 , 5 -
16367.54
.
4'
3 5 64 4 .4 1
■i ( -- .
■J, ■ - -
*
-4.04
*
0.05
‘
Ill
Table 4 .3
(continued)
Transition
Observed
F requency
1Q2 , 8 " J ° l , 9
11 1 , 1 0 '
]1 2,9 ‘
^ 0,11
102 , 9
• ^ lf O
'
120 , 1 2
122 , 1 0 " ‘1 2 1, 11
131 , 1 2 '
130 , 13
132,T1
'
131 , 1 2
142 , 1 2 -
141,13
U 2,12 '
13 3 , 11
143 , 1 2 -
134 , 9
143 , 11 '
134 , 1 0
152 , 1 3 " 15 1 , 14
162 , 14 '
^6 1 , 1 5
162 , 15 " 153 , 12
172 , 1 5 -
171 , 1 6
172 , 1 5 " 163 , 1 4
182 , 1 6 '
1 8 1 , 17
18J , 1 5 -
175 J 2
184 , 1 4 -
175 , 1 3
.
Deviation
29 70 5 .4 1
3.09
-0.01
26424.00
-5.54
0.00
3.43
-0.03
28014.83
-11.62
0.06
29596.24
-8.23
-0.04
29 44 3 .0 1
3.36
0.02
33101.16
-11.64
-0.04
29713.18
2.68
0.02
30297.99
1.22
0.03
16682.58
-24.19
0.08
-14378.03
-2.24
0.05
-13158.87
-5.19
0.05
31227.00
-1.27
0.01
32525.80
-5.00
0.03
11425.18
-9.93
0.03
34215.43
-10.23
0.02
3,7379.40
-51.44
0.03
36311.53
-17.15
-0.03
-17999.50
-7.11
0.02
-17643.17
-9.02
0.01
29453.38 .
1 ^1 , TO
D istortion
Correction
112
'
,
Table 4 .3
(continued)
Transition
Observed
Frequency
D istortion
Correction
Deviation
38822.66
-26.02
0.01
15781.69
-56.55
0.02
-13015.99
-16.34
0.02
-12473.76
-19.53
-0.02
13432.88
-35.42
- o : oi
17 632 . 81
-39.97
-0.00
29008.99
-91.27
-0.01
-26846.69
-1.82
0.01
36023.77
-112.23
-0.07
-16873.55
-28.56
-0.04
28781.05
-44.05
-0.03
11837.58
-72.12
0.01
-11823.35
-43.86
-0.06
-11599.51
-46.46
-0.02
-35886.15
11.36
-0.03
16713.56
-84.21
-0.05
-30897.89
-5.90
0.04
-30882.65
-6.13
-0.01
-30404.24
157.07
-0.00
9555.52
-131.34
-0.07
2 8 S i H 235C l 2 :
192 , 17 “ 19 1 ,18
193 , T 6 " 1 84 , 1 5
194 , 1 6 " 1 8 5 , 13
194 , 1 5 " 1 8 5 , 1 4
2 0 3 , 1 8 " 19 4 , 1 5
2 1 3 , 1 9 " 2 0 4 , 16
213 ,1 8 ‘
2 0 4 , 17
2 1 5 , 1 6 " 2 0 6 , 15
22 3 , 19 " 2 1 4 , 1 8
23 5 , 1 9 ‘
226 , 16
243,22 " 234,19
244 , 21
‘
2 3 5 , 18
245,20 " 236,17
245,19 ‘
236,18
246 , 1 9 ” 2 3 7 , 1 6
25 4 , 2 2 " 2 4 5 , 1 9
25 6 , 2 0 ‘
2 4 7 ,17
2 5 6 , 19 '
247,18
261 ,26 " 252,23
2 8 5 , 23 ‘
2 76 , 22
Vl
1 13
Table 4 .3
(continued)
Transition
Observed
Frequency
286,23 " 277 ,20
286 ,22
2 77-v21
2 9 5 , 24 '
286 , 2 3
296,24 '
2 8 7 ,21
29
6,23
28 7 , 2 2
336 , 2 8 * 3 2 7 , 25
3 3 7 ,27 '
337 , 2 6 "
346,29 "
346 , 2 8 "
34 7 , 2 8 '
3 4 7 ,27 ‘
32
32
33
33
33
33
8,24
8,25
7,26
7,27
8,25
Deviation
-15801.15
-65.70
-0.03
-15742.85
-66.81
-0.05
15071.88
-159.23
-0.05
-10721.06
-88.50
-0.02
-10633.01
-90.29
-0.03
9851.46
-195.21
0.03
-14760,28
-122.39
0.02
-14738.05
-123.08
0.01
15054.40
-225.78
0.03
15612.68
-241.05
0.05
-9668.23
,-154.08
0.04
-155.18
0.04
16212.28
-0.11
0.05
3 5 56 7 .2 1
-1.85
0.03-
13409.58
-0.00
-0.01
13130.49
-0.72
0.04
15488.80
-0.T5
-0.04
16909.15
-0.45
0.03
-9634.73
8,26
D istortion
Correction
.,
28 Si H2 35C l 37C1:
] 1,1 - ° 0 , 0
2 2,1
" 21.2
4 1 ,3 " 40 ,4
50,5 " 41,4
61 ,5 -
60 ,6
7 1»6 ' 7 0 , 7
«
114
Table 4 .3
(continued)
Transition
Observed
Frequency
D istortion
Correction
Deviation
28 S'iHo35C l 37C 1 :
72 , 5 '
71 ,6
9 2 , 7 " 9 1 *8
92,7 '
8 3 ,6
102 , 8 '
1° 1 , 9
102 , 9 '
93,6
112 , 9 " ^ I J O
122 , 1 0 " 12 1 ,11
132 , 11 '
131,12
142 , 1 2 '
14 1 , 13
143 , 1 2 " 134 , 9
‘
162 , 1 4 " 16 1 , 15 .
172 , 1 5 " 1 7 i ; i 6
172 , 1 6 '
3 6 3»13
182 , 1 6 " 1 8 1 , 17
193 , 16 '
184 , 1 5
194 , 1 6 " 1 8 5 , 1 3
194 , 1 5 " 18 5 , 1 4
2 0 3 , 18 '
194 , 1 5
244 , 21
" 2 3 5 , 18
24a
“ 2 3 r 1Q
on
31454.12
0.86
-0.02
30159.00
2.42
0.04
-14665.44
0.88
-0.04
29687.33
3.08
-0.03
-12496.89
0.45
O'. 05
29395.50
3.49
-0.02
29325.82
3.53
-0.00
29516. 01
3.02
0.00
29999.17
1.78
0.02
-15855.35
-1.67
0.03
31956.06
-3.76
-0.02
33476. 11
-8.52
-0.00
13058.£7
-9.86
-0.03
35380.84
-14.89
0.02
13095.86
-52.51
-0.03
-15101.44
-14.54
0.05
-14639.54
-17.19
0.02
11406.02
-34.45
-0.00
9 13 7. 2 1
-68.73
-0.02
1 1 88 9 .2 5
-92.57
-0.02
115
Table 4 .3
(continued)
Transi t io n
D istortion
Correction
Observed
Frequency
Deviation
28 Si H23 5 C137C1
2 4 5 , 2 0 * 23 6 , 1 7
245 , 1 9 ‘
236 ,18
255,20 '
2 46 , 1 9
2 9 2 , 28 '
283,25
295,25 '
286 , 2 2
29 5 , 2 4 ‘
286,23
•
-14507.72
-39.79
-0.04
-14324.44
-41.88
-0.01
-58.90
-0.02
924 6. 21
.,200. 75
0.00
10307.50
-129.18
0.02
11444.95
-147.55
0.03
16114.23
-0.11
0.18
32947.58
0.12
-0.04
29016.89
3.09
-0.04
28814.00
3.43
-0.06
28866.79
3.36
0 . 01
29214.36
2.68
0.04
30925.93
-1.27
0.04
34167.56
-10.23
-0.03
-9305.05
,
2 9 S i H „ 3 5C l 2
o
0
o
1
51 ,5 '
40 , 4
102 , 8 " 1° 1 , 9
1 ]2,9 '
111,10
122 , 10 '
1 2 1 ,11
132, 11
‘
1 3 1 , 12
152 , 1 3 '
1 5 1 ,14
17, ic 2,15
17,
1 , 16
116
Table 4 .3
(continued)
a The "obse r ve d"
unsplit
lin e
frequencies given
frequencies.
in t h i s Table are the h y p o th e tic a l
The h y p e r f i n e s t r u c t u r e , , o f t h e measured
t r a n s i t i o n s was s u b t r a c t e d u si n g t he q u a d r u p o l e c o u p l i n g c o n s t a n t s
o f Table 4 .1 .
b
For t h e
29
SiH^
t o be equal
35
C1^ s p ec i e s
to those o f t h e
t h e d i s t o r t i o n c o r r e c t i o n s were assumed
2R
SiH^
t h e o bs er ve d f r e q u e n c i e s were c a l c u l a t e d
Table 4 . 4 .
species.
The d e v i a t i o n s
u si ng t h e F i t
from
1 co n s ta n ts of
117
Table 4 .4
R o t a t i o n a l C on s t a n t s and C e n t r i f u g a l
of D ichlorosilane
D i s t o r t i o n Co ns t an ts
28 S i H 2 35C l 2
2 8 Si H2 35C137C1
A(MHz)
14135.0061(41)a
14034.3404(73)
B(MHz)
2573.58084(80)
2504.4799(16)
C(MHz)
2232.61326(80)
2177.9966(13)
Aj(kHz)
1.0223(18)
0.9691(29)
AJ|(( k H z )
-15.464(27)
-14.912(43)
AK( k H z)
142.107(54)
139.46(11)
6j(kH z)
0.24100(20)
0.23335(35)
6K( k H z )
3.117(16)
2.490(59)
Std. D e v ia tio n
o f F i t (MHz,)
0.036
0.033
No. o f T r a n s i t i o n s
72
32
118
Table 4 .4
R o t a t i o n a l C o n s t a nt s and C e n t r i f u g a l
o f D ichlorosilane
29
F it
1
Si H2
35
D i s t o r t i o n Con st an ts
C1 2
F it
2
A(MHz)
13887.8035(182)
B(MHz)
2573.6076(97)
2573.6278(50)
C(MHz)
2226.3566(93)
2226.3496(48)
A j(kHz)
b
1 . 0 1 6C
Aj
b
-1 5 . 0 2 °
AK( kHz )
b
1 3 8 . 7C
6j(kHz)
b
0.2470°,
6 k ( kH z)
b
2.895°
k
( I cH z )
Std. D eviatio n
o f F i t (MHz)
, 13 8 8 7 . 9 2 5 5 ( 9 4 )
0.092
0.048
8
8
*
No. o f T r a n s i t i o n s
Errors c i t e d
Centrifugal
t hose o f t h e
are standard e r r o r s
distortion
c o r r e c t i o n s assumed t o be equal
to
species.
These c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s have been c a l c u l a t e d
from t he f o r c e f i e l d g i v e n i n T a b l e 4 . 1 2 .
119
4.3
The D i p o l e Moment o f D i c h l o r o s i l a n e
The e l e c t r i c d i p o l e moment o f
m o l e c u l a r symmetry, c o i n c i d e s w i t h
28
S i^
35
C^,
t he b - p r i n c i p a l
because o f the
in ertial
axis.
Thus t h e d i p o l e moment can be d e t e r m i n e d by measur ing S t a r k s h i f t s
f o r j u s t one S t a r k component.
sition
of
28
S i^
35
The S t a r k e f f e c t on t h e l ] , i +-Oo0 t r a n -
C l ^ was used t o measure t h e d i p o l e moment because
both t h e z e r o - f i e l d and S t a r k - s h i f t e d
hyperfine stru ctu re.
As w e l l ,
lines
showed no e v i d e n c e o f
the Stark e f f e c t o f t h is
though s e c o n d - o r d e r , was m o d e r a t e l y f a s t .
component was measured up t o f i e l d s
tran sitio n ,
The f r e q u e n c y o f t h e S t a r k
o f a bo u t 1000 V cm'^
in th e c e l l .
U n f o r t u n a t e l y t h e p r e c i s i o n o f t h e f r e q u e n c y measurements was g r e a t l y
degraded by i n t e r m i t t e n t
d riftin g
shorting
in t he S t a r k c e l l
in t he p o s i t i o n o f t he S t a r k l o b e ;
r e p e a t t h e se measurements l a t e r .
impossible to o b ta in
However, t h e c e l l
In a d d i t i o n
t h e h igh f i e l d s
was n ot p o s s i b l e t o
t h e s h o r t i n g made i t
n e c e ss a r y t o c a l i b r a t e
had been p r e v i o u s l y c a l i b r a t e d
measurement f o r p r o p i o l y l
chloride
t he e l e c t r o d e sp a ci n g o f 0 . 4 6 8 9 ( 4 )
was used h e r e .
it
The c a l i b r a t i o n
which caused
( see s e c t i o n
the c e l l .
i n a d i p o l e moment
5.4 o f Chapter 5 );
cm d e t e r m i n e d
in t h a t experiment
p r oc ed u r e i s d is cu s s e d in d e t a i l
in
C h a p t e r 5 along w i t h t he d e t e r m i n a t i o n o f t h e a p p l i e d e l e c t r i c
field
from t h e s i m u l t a n e o u s l y impressed DC and m o d u l a t i o n v o l t a g e s ,
Here i t
i s not ed o n l y t h a t a m o d u l a t i o n v o l t a g e , „ 2 V ^ ,
throughout.
The observed
28
SiH^
35
C l2
f r e q u e n c i e s a r e given t o g e t h e r
. w i t h t h e square o f t h e a p p l i e d S t a r k v o l t a g e s
Table a ls o contains the re s id u a ls
o f the d a ta .
o f 30 v o l t s was used
in Table 4 . 5 ;
from a l i n e a r
this
l e a s t squares a n a l y s i s
f
The r e s u l t s o f T a b l e 4 . 5 show t h a t t h e S t a r k e f f e c t f o r t he
120
11 1
+ Oqq t r a n s i t i o n
expression f o r
of
28
SiH^
35
C l^ i s second o r d e r .
The second o r d e r
t he S t a r k e ne r gy has been found usi ng e q u a t i o n 1 . 2 8 t p
be
& v ( l 1 1 ,M=0 ^ 0 Q0,M=0)
= 1 . 8 2 2 9 x 1 0 ' 5 u^E2
where Av i s t h e f r e q u e n c y s h i f t
(4.1)
and E i s t he e l e c t r i c
field
i n V cm \
L i n e a r l e a s t squares a n a l y s i s o f t h e S t a r k d a t a gave t h e r e s u l t s
presented in Table 4 . 6 .
The s l o p e A v / V 2 = 1 . 0 5 6 ( 1 2 )
x 10“ 4 MHz V o l t " 2
has been converted to the r e q u i r e d Av/E2 v a l u e of 2 . 3 2 2 ( 2 6 )
Volt
-2
-2
cm
u si n g t h e e l e c t r o d e sp a ci n g o f 0 . 4 6 8 9 ( 4 )
2
f o r p b and ub r e s p e c t i v e l y v a l u e s o f 1 . 2 7 4 ( 1 5 )
value f i n a l l y
adopted f o r ^b i s
1.129(20)
ponding t o t h r e e s t a n d a r d e r r o r s ,
re fle c t
possible systematic e r r o r s
cm. T h i s g i ves
?
D and 1 . 1 2 9 ( 7 ) D. The
D where t h e e h r o r ,
corres­
has been i n c r e a s e d s u b j e c t i v e l y t o
i n t he d e t e r m i n a t i o n .
f o r t h e d i p o l e moment ag ree s e x t r e m e l y w e l l
T h is value
w i t h t h e p r e v i o u s v a l ue o f
1 . 1 7 3 D, o b t a i n e d using d i e l e c t r i c measurements
9
x 10"5 MHz
(9).
121
Table 4 . 5
Stark S h ifts
in D i c h l o r o s i l a n e :
Transition
10“ 2xV2
l^ ,
^ S i ^ 38^
M=0*-0QO, M=0
O bs.-C alc.b
Observed Frequency3
•
0.00
16367.54
-0.23
27.25
16367.86
-0.20
102.25
16368.75
-0.11
227.25
16370.15
-0.02
402.25
16372.16
0.13
508.50
16373.08
-0.07
627.25
16374.67
0.27
758.50
16375.75
-0.04
902.25
16377.70
0.39
1058.50
16378.84
-0.12
1227.25
1 6 & 1 .16
0.42
1408.50
16382.38
-0.27
/
Table 4 .5
Stark S h ifts
in D.ichlorosilane:
^ S i ^ 35^
v
1 0 " 2 x V2
Observed Frequency
O bs.-C alc.b
•
1638^.18
0.48
1808.50
16386.47
-0.41
2027.25
16389.62
0.43
2164.50
16390.00
-0.63
1602.25
.
a Given i n MHz.
b C a l c u l a t e d f r e q u e n c i e s ' a r e o b t a i n e d using t h e c o n s t a n t s o f T a b l e 4 .
123
Table 4 .6
Stark C o e ffic ie n ts o f D ic h lo ro s ila n e :
T ra n s itio n
vQ
A v/V 2
^ S iH g ^C lg
1 ^ , ,M=0+-0oo, M=0
=
1 6 3 6 7 . 77(14)MHz
=
1.056(12 ) x 'lb-4 MHz
V- 2
*
&
i k.
4.4
The E f f e c t i v e and S u b s t i t u t i o n S t r u c t u r e s o f D i c h l o r o s i l a n e
It
partial
i s c o n v e n i e n t t o d i s c u s s the e v a l u a t i o n o f e f f e c t i v e and
substitution
stru ctu res f o r d ic h lo ro s ila n e before considering
/
t h e d e t e r m i n a t i o n o f t h e harmonic f o r c e f i e l d .
described
i n t h e n e x t s e c t i o n has,
The f o r c e f i e l d
however, been used h er e t o h e l p
s p e c i f y t h e c o o r d i n a t e s o f t h e hydrogen at oms.
S ufficient
o f the s t r u c t u r a l
i s o t o p i c dat a have been o b t a i n e d t o c a l c u l a t e a l l
parameters o f the molecule.
The r o t a t i o n a l
s t a n t s o f T a b l e 4 . 4 have been c o n v e r t e d t o t h e p r i n c i p a l
in ertia,
4.7.
which a r e g i v e n a l o n g w i t h
some r e l a t e d
A lt h ou g h t h e - e f f e c t o f t he s p i n s t a t i s t i c s
con­
moments o f
p a ra me t er s
in Table
on t h e h y p e r f i n e s t r u c -
t u r e has a l r e a d y c o n f i r m e d t h e e xp e c te d C2 v - m o l e c u l a r symmetry, a d d i t i o n a l
c o r r o b o r a t i o n i s p r o v i d e d by t he r e s u l t s o f T a b l e 4 . 7 .
t h e hydrogen at oms^from t h e S i C l 2 p l a n e , c ^ ,
W
'
a nd, n e g l e c t i n g smal l
for a ll
' a + *b *
i s g i v e n by
lc
zero-point v ib ra tio n a l
th ree species.
The d i s t a n c e o f
<4' 2>
effects,
As w e l l , f o r t h e two a x i a l l y
shoul d be t o n s t a n t
symmetric s p e c i e s ,
^ ® S i 1 2 and ^ ^S iH ^ ^ ^ Cl 2 * t h e d i s t a n c e o f t h e c h l o r i n e atoms from
t h e S iH 2 p l a n e , aQ-j, i s g i v e n by
*
1
^
.
4mC1aC 1 = *b + *c ~ *a
and should a l s o be e s s e n t i a l l y c o n s t a n t f o r
t h e s e two s p e c i e s .
the r e s u l t s o f Table 4 . 7 s a t i s f y both of these requirem ents.
Clearly
Fin ally,
28
35
C2v symmetry would r e q u i r e t h a t I b be c o n s t a n t f o r t h e ■ S iH ^ C l 2 and
29
SiH2
35
C l 2 species since in
on t h e ^ - I n e r t i a l
axis;
thfs
t hese two cases t he s i l i c o n atom must l i e
requirement is also met,
Thus, t h e m o l e-
125
c u l a r symmetry i s w e l l
established.
The s i m p l e s t m o l e c u l a r s t r u c t u r e t o c a l c u l a t e i s
or r Q s t r u c t u r e .
field
T h i s s t r u c t u r e was s u b s e q u e n t l y employed i n t he f o r c e
determ ination;
in e rtia
its
use ensures
used i n c a l c u l a t i n g
t h a t the th e o r e tic a l
the d i s t o r t i o n constants
c l o s e l y as. p o s s i b l e t h e ground s t a t e moments.
l e a s t squar es f i t
n a me l y ,
moments o f
r ep r od u c e as
In t h e p r e s e n t case a
t o f o u r i n d ep e n d e nt s t r u c t u r a l
t he S i - H and S i - C l
bond a n g l e s .
the e f f e c t i v e
p a r a me t e r s was made,
bond d i s t a n c e s and t he H - S i - H and C l - S i - C l
The d a t a used were the n i n e i n d ep e nd e nt r o t a t i o n a l
constants o f Table 4 . 4 .
In d e r i v i n g t h i s
The r e s u l t s
s t r u c t u r e the
29
SiH^
o f this
35
fit
are'given
rotational
in Table 4 . 8 .
constants o f F i t
were u se d. When t h e F i t 2 v a l u e s were used i n s t e a d t h e f i t t e d
was i n s i g n i f i c a n t l y d i f f e r e n t
- t he S i - H d i s t a n c e ,
cr ea se d t o 1.459?) A and t he S i - C l
f o r e xa mp le ,
and S i - H d i s t a n c e s ,
o
in
f o r e x amp l e,
o
t he s t a n d a r d e r r o r s were ± 0 . 0 0 0 3 A and ± 0 . 0 0 2 2 A r e s p e c t i v e l y .
small
s t a n d a r d d e v i a t i o n o f 1t h e f i t ,
reflects
The
0 . 0 3 2 MHz, a l m o s t c e r t a i n l y
the f a c t t h a t z e r o - p o i n t v i b r a t i o n s
the r o t a t i o n a l
The
a r e n o t quoted i n
the t a b l e as t h e y a r e t ho u gh t t o u n d e r e s t i m a t e t he u n c e r t a i n t y
For t h e S i - C l
in­
d i s t a n c e de cr ea sed t o 2 . 0 3 3 4 A.
s t a n d a r d e r r o r s o b t a i n e d from t h e l e a s t squares f i t
t hese p a r a m e t e r s .
structure
constants o f the various
s i m i l a r l y c o n t r ib u t e to
is o to p ic species s tu d ie d .
would c e r t a i n l y not be t h e case f o r a d e u t e r a t e d s p e c i e s .
*
This
1
126
4 .7
I n e r t i a l Param eters o f D ic h lo r o s ila n e 3
P a ra me t e r
‘a
'b
!c
t'
'c
4mHcH2
4mc i a ci
35.75372(1) b
36.01017(2)
196.37192(6)
2 0 1 . 79000(T3)
226.36209(8)
232.03847(14)
5.76170(20)
(.
386.9 8 029(10)
4mc i a ci
>b
28S i H 2 35C l 37Cl
5.76354(10)
4mHc H2
‘a
28 S i H 235Cl 2
29S i H 235C l 2 ( F i t
1)
29Si H2 35C l 2 ( F i t
36.39013(5)
36.38981(3)
196.36987(74)
196.36833(38)
226.99823(95)
226.9 9 894(49)
5.7618(12)
5.7592(6)
386.9780(12)
386.9775(6)
C a l c u l a t e d from t h e r o t a t i o n a l c o n s t a n t s o f T a b l e 414 u s i n g a
c o n v e r s i o n f a c t o r o f 5 0 5 3 7 9 . 0 MHz uA^.
A l l par amet ers g i v e n a r e
in ua2.
b E r r o r s quoted a r e s t a n d a r d e r r o r s .
2)
127
1
Table 4 .8
The E f f e c t i v e S t r u c t u r e o f D i c h l o r o s i l a n e
P ar am et er
V al ue
O
2.0336 A
, r o ( S i ' C1)
r 0 (Si-H)
1.4590 A
<
(C l-S i-C l) -
109.76°
<
(H-Si-H)
110.05°
.it
t
,1 .
'.
If *
128
The s u b s t i t u t i o n
next.
s t r u c t u r e o f d i c h l o r o s i l a n e was i n v e s t i g a t e d
Because no d e u t e r a t e d s pe c i e s were s t u d i e d a c o mp le t e sub­
s titu tio n
s t r u c t u r e c oul d n o t be o b t a i n e d .
atom c o o r d i n a t e s w e re a c c u r a t e l y d e t e r m i n e d .
Nevertheless,
The p a r e n t s p e c i e s
adopt ed f o r t he s u b s t i t u t i o n c o o r d i n a t e c a l c u l a t i o n s was
Because t he c h l o r i n e atoms l i e
ordinates
t h e heavy
28
SiH^
35
C^.
in a symmetry p l a n e and have z e r o ^ c o ­
t h e i r a and b^ c o o r d i n a t e s were d e t e r m i n e d using t h e method
outlined for
p la n a r molecules in Chapter 1 (e q u a tio n
because s i l i c o n
has both z e r o £ and c c o o r d i n a t e s
1.44).
And,
i t s b c o o r d i n a t e can
be o b t a i n e d from
.
b
s
2
=
where u has i t s u su al
given
in Table 4 . 9 .
(4.4)
u
meaning ( 2 1 ) .
These v a r i o u s c o o r d i n a t e s a r e
The hydrogen atoms had t o be l o c a t e d by a l t e r -
n a t i v e methods.
!
The b^ c o o r d i n a t e was c a l c u l a t e d u s i n g t he c e n t e r o f
mass c o n d i t i o n ,
e m.b.
= 0.
A c c u r a t e val ues o f t h e £ c o o r d i n a t e o f
hydrogen were h a r d e r t o o b t a i n .
T h r e e methods wer e t r i e d .
I n Method
1 t h e y were c a l c u l a t e d u s i n g e q u a t i o n 4 . 2 , and w e re thus r Q c o o r d i n a t e s ,
h a v i ng nebulous p h y s i c a l
meani ng.
They ar e a l s o g i v e n in T a b l e 4 . 8 ,
and a g r e e o n l y p o o r l y w i t h t h e c o r r e s p o n d i n g v a l u e s f o r d i f l u o r o s i l a n e ,
±1.220 A ( 5 ) .
In Method 2 an a t t e m p t was made t o improve t h e p h y s i c a l
meaning o f t h e s e c o o r d i n a t e s by u s i n g t h e a v e r a g e moments o f
d e r i v e d u si ng t h e f o r c e f i e l d
o f Table 4.12.
in ertia
One has
4™H<c^ 2 “ 'a + 'b - ’ c
<4 ' 5>
>»
These a v e r ag e c o o r d i n a t e s ,
however, a r e u s u a l l y l a r g e r t han t he
0
1
129
corresponding s u b s t i t u t i o n v alues.
(23) molecules,
c^ c o o r d i n a t e s a r e
I n t he r e l a t e d
Sil^F^
(22)
and
f o r e x am pl e,
t h e s u b s t i t u t i o n v a l ue s f o r the
O
i n each case 0 . 0 0 2 A s m a l l e r t h an t he a v e r a g e v a l u e s .
I n Method 3 t h e r e f o r e t h e p r e f e r r e d e s t i m a t e s f o r t h e c^ c o o r d i n a t e s
o
have been o b t a i n e d by a p p l y i n g t h i s 0 . 0 0 2 A c o r r e c t i o n .
The r e s u l t s
given
in Table 4 . 9
of in e rtia
for
29
have been o b t a i n e d u si ng t h e ground s t a t e moments
S i^
35
corresponding to F i t
1 (see Table 4 . 4 ) .
Usi ng i n s t e a d t he F i t 2 v a l u e s changes o n l y t h e b c o o r d i n a t e s o f s i l i c o n
'
0
0
and hydrogen to 0 . 8 0 1 7 A and - 1 . 6 3 9 9 A.
The " l a r g e " jump i n t h e bu
coordinate results
general
from t he use o f the f i r s t moment c o n d i t i o n .
In
t h e a c c ur a c y w i t h which an atom can be p l a c e d usi ng a f i r s t
moment c o n d i t i o n v a r i e s
i n v e r s e l y as i t s mass; a s ma l l c h a n g e - i n the
s i l i c o n c o o r d i n a t e causes a much l a r g e r s h i f t
The s u b s t i t u t i o n
in t h e hydrogen p o s i t i o n .
s t r u c t u r e o b t a i n e d f rom t he c o o r d i n a t e s o f T a b l e 4 . 9
. 29
96
Using t h e F i t 2 v a l u e s f o r
S i C 1 2 would
o
'
r e s u l t i n an S i - C l d i s t a n c e s h o r t e n e d by 0 . 0 0 0 1 A f r om t he v a l u e g iv en
o
and an S i - H d i s t a n c e i n c r e a s e d by 0 . 0 0 1 6 A.
is given
i n T abl e 4 . 1 0 .
%
130
Table 4 .9
S u b s t it u t i o n Coordinates of D ic h lo r o s i la n e :
Method 1
Method 2
Method 3
a
±■1.6622
±1.6622
±1.6622
b
0.3 680
0.3680
0.3680
c
0.0 000
0.0000
0.0000
a
0.0 000
0.0000
0.0000
b
-0.8019
-0.8019
-0.8019
c
0.0000
0,0000
0.0000
a
0.0000
0.0000
0.0000
b
-1.6372
-1.6372
-1.6372
c
±1.1957
±1.2240
±1.222
Atom
Coordinate
Cl
Si
H
28 c . u 35r ,
Si
C12 ( A )
131
Table 4 .1 0
The S u b s t i t u t i o n S t r u c t u r e o f D i c h l o r o s i l a n e 3
P ar amet e r
V al u e
\
r $(S i-C l)
2.0326 A
r s (Si-H)
1.4802 A
0
a
< (C l-S i-C l)
109.72° •
< (H-Si-H)
111.29°
O b t a i n e d u s i n g the Method 3 c o o r d i n a t e s o f T a b l e 4 . 9 .
f
132
4.5
The Harmonic F or ce F i e l d o f D i c h l o r o s i l a n e
S e ve r a l
(13-17)
have been p u b l i s h e d
o f which t he most d e t a i l e d and c o n v i n c i n g
and N i e l s e n
(17).
wavenumbers f o r
resolved)
sp e ci es
all
force fie ld s
t he normal
species
set f o r
However,
of the v ib r a tio n a l
(chlorine
t h a t of Christensen
i s o t o p e e f f e c t s we r e not
t h e s i n g l y and d o ub ly d e u t e r a t e d
as C h r i s t e n s e n and N i e l s e n
pointed o u t ,
wavenumbers were i n d e p e n d e n t ;
were f o r c e d t o use an assumed m o l e c u l a r s t r u c t u r e .
w o r t h w h i l e a t t e m p t i n g a new f o r c e f i e l d
microwave s t r u c t u r e and t he a d d i t i o n a l
distortion
is
They had a v a i l a b l e a c omp l et e s e t o f v i b r a t i o n a l
and a p a r t i a l
(12).
for d ichlorosilane
not
in a d d it io n
It
they
t h e r e f o r e seemed
r e f i n e m e n t u si ng the p r e s e n t
d a t a p r o v i d e d by t he c e n t r i f u g a l
constants.
The f o r c e f i e l d
r e f i n e m e n t program used he r e was one d ev el o p ed
i n t he C h e m i s t r y D e p a r t m e n t , U n i v e r s i t y o f Reading and k i n d l y s u p p l i e d
by Dr .
A.
fittin g
G. R o b i e t t e .
I t ,h a d a very f l e x i b l e weighted
l e a s t squares
r o u t i n e which a l l o w e d t h e use o f any number o f v i b r a t i o n a l
wavenumbers o r c e n t r i f u g a l
distortion
c o n s t a n t s as d a t a
(24).
Ref inement s
were in terms o f v a l e n c e f o r c e c o n s t a n t s u s i n g t he EG m a t r i x method o f
Wilson
(25).
The f o r c e f i e l d
r e f i n e m e n t f o r d i c h l o r o s i l a n e was c a r r i e d o u t
i n terms o f nonr edundant symmetry c o o r d i n a t e s .
o r d i n a t e s , which t r a n s f o r m as 4A^ +
^
+ ^
+
These s y i m e t r y c o ­
2
B£ i n t h e p o i n t group
"r
^2 v ’ are
9
^ven
Table 4 . 1 1 .
terms o f the i n t e r n a l
These a r e e s s e n t i a l l y
C h r i s t e n s e n and N i e l s e n
internal
coordinates in
w i t h t h e microwave r
o
displacement co ord in ates
t he symmetry c o o r d i n a t e s used by
(17) except t h a t the c o e f f i c i e n t s
and
structure.
in
o f the
have been changed t o be c o n s i s t e n t
133
Table 4.11
Internal
Internal
C o o r d i n a t e s and Symmetry C o o r d i n a t e s o f D i c h l o r o s i l a n e
Coordinates:a
ri
= r ( S i - H i ) = 1.459 A
C
= <H-Si-H
0
-
. i = <H. - S i - C l .
1J
*
110.05°
;
R.
= r(S i-C lj)
= 2.034 A
B
= <C1-Si-Cl
= 109.76°
= 109.25°
J
Symmetry C o o r d i n a t e s :
A-j
b lo ck
S-j
=
S2
= ( 1 / / ? ) ( a R 1 +aR2 )
Sg
= mAa-n ( A0-j i +A0 -j 2 + A02 1+A022 )
S^
= dA 8 - e ( A0-| i +A0 -j 2 +A02 i +A02 2 )
b l ock
55
= ( l / 2 ) ( - A 0 1 1 + A e 12+Ae2 1 - A e 2 2 )
B-j b l ock
56
= ( l / / 2 ) ( A r r Ar2 )
57
= ( l / 2 ) ( - A 6 11- A 6 12+Ae21+Ae2 2 )
Sg
= ( 1 / 2 ) (AR-,- a R2 )
Sg
= ( l / 2 ) ( - A 0 11+A612 - A 0 21+A02 2 )
A2
B2
a
13
b lo ck
( l / ^ /2 ) ( A r 1 + A r 2 )
The m o l e c u l a r s t r u c t u r e used i s t h e r 0 s t r u c t u r e o f T a b l e 4 . 8 .
Th is
ensures t h a t t h e t h e o r e t i c a l moments o f i n e r t i a used i n c a l c u l a t i n g
t he d i s t o r t i o n c o n s t a n t s - a r e as c l o s e as p o s s i b l e t o t h e ground
s t a t e moments.
So i s d e f i n e d as a pure HS>H bending c o o r d i n a t e w i t h no change in
C lSiC l.
The c o e f f i c i e n t s , c a l c u l a t e d from t h e assumed ge o met ry,
remove t he f i r s t o r d e r redundancy between t h e s i x a n g l e s and n o r m a l i z e
53 .
T h e ir values are:
m = 0.8947
c
n =0.2234
S4 i s d e f i n e d as a pure C l S i C l bending c o o r d i n a t e w i t h ho change in
HSiH.
The c o e f f i c i e n t s , c a l c u l a t e d from t h e assumed s t r u c t u r e ,
remove t he f i r s t o r d e r redundancy between t h e s i x a n g l e s and n o r m a l i z e
54 .
T h e ir values are:
d = 0.8956
.
e = 0.2229
134
Because no heavy atom i s o t o p e e f f e c t s were r e s o l v e d f o r
d i c h l o r o s i l a n e t he obse r ved wavenumbers o f t he n o r m a l ,
doubl y
d e u t e r a t e d and s i n g l y d e u t e r a t e d m o le cu les were a s s i g n e d t o the
28c .u
SiHg
35r ,
28c .n
C^,
vibrational
SlD 2
35-i
■ 2 8 - -un3 5 -i
C1 ^ and
SiHD
wavenumbers were a l l
w e i gh t e d l e a s t squares f i t .
the f i t
because t h i s
no a d d i t i o n a l
28
SiHg
35
C1 2
o f 3% as i t
i n t he f i t
inform ation.
of
]%
, .
SiHD
35
The-centrifugal
except f o r
is r e l a t i v e l y
i n the f i t ;
6
,
Tu
1
% in t h e
The
C l 2 wavenumbers were used i n
s p e c i e s has C$ symmetry and,
o n l y were i n c l u d e d
uncertainties
■
s pe c i e s r e s p e c t i v e l y .
a ss i gn ed u n c e r t a i n t i e s o f
28
No
C12
i n any c a s e , p r o v i d e s
d istortion
constants o f
t hese wer e a l s o a ssi gn ed
^ which was a ss i g n e d an u n c e r t a i n t y
poorly determined.
All
d a t a were w ei gh t ed
a c c o r d i n g t o t h e r e c i p r o c a l s o f t he squar es o f t h e i r
u ncertainties.
In an i n i t i a l
fitte d
r e f i n e m e n t the d i a g o n a l
to the v i b r a t i o n a l
wavenumbers a l o n e ;
f o r c e c o n s t a n t s were
the t r i a l
v a l u es f o r
t hes e f o r c e c o n s t a n t s were t a k e n from C h r i s t e n s e n and N i e l s e n
(17).
I t was found a t once t h a t a n o n - z e r o v a l u e o f Fgg was r e q u i r e d to
rep ro du ce Vg and v g f o r
t he two i s o t o p i c
species.
The d i s t o r t i o n
c o n s t a n t s wer e then i n c l u d e d as d a t a , and t h e o f f - d i a g o n a l
c o n s t a n t s were g r a d u a l l y
introduced.
The b e s t f i t s
force
we re o b t a i n e d
i n c l u d i n g F2 3 , F2 4 , F34 and F g g ;
F 1 3 ’ F14 and F 56 w e r e i n d e t e r ­
m i n a t e and we r e c o n s t r a i n e d t o z e r o .
In f a c t a l l
c o n s t a n t s between t h e S i - H ( Si
D)
the in te ra c tio n
s t r e t c h i n g c o o r d i n a t e s and the
r e m a i n i n g symmetry c o o r d i n a t e s have been c o n s t r a i n e d t o z e r o .
S i nc e
even t h e S i - D s t r e t c h i n g modes a r e a t l e a s t 900 cm~^ h i g h e r than any
others the in t e r a c t i o n s
force f i e l d
obtained
can p l a u s i b l y be e xp ect ed t o be s m a l l .
i s g i v e n i n T ab le 4 . 1 2 ;
all
The
o f the fo rc e constants
135
a p p e a r t o h a v e r e a s o n a b l e m a g n i t u d e s a nd s i g n s .
T a b l es 4 . 1 3 and 4 . 1 4 d e m o n s t r a t e how w e l l
r e pr o du ce s t h e obse rv ed d a t a .
the fo rce f i e l d
These t a b l e s g i v e t h e observed v i b r a t i o n a l
*•
wavenumbers o r d i s t o r t i o n c o n s t a n t s and t h e i r a s s i g n e d u n c e r t a i n t i e s ,
t o g e t h e r w i t h t h e d e v i a t i o n s between t h e observed v a l u e s and t h o s e
c a l c u l a t e d from t h e f o r c e f i e l d .
the v i b r a t i o n a l
T a b l e 4 . 1 3 shows t h a t t he f i t
wavenumbers i s s a t i s f a c t o r y , a n d ,
furthermore,
for'
the
f o r c e c o n s t a n t s g i v e e x c e l l e n t p r e d i c t i o n s o f t h e wavenumbers o f
SiHDC1^ which wer e n ot used i n t h e r e f i n e m e n t .
fo r the S i-H (S i-D )
stretching
The d e v i a t i o n
observed
f u n da me n t a l s i s h a r d l y s u r p r i s i n g
i n view
o f t h e f a c t t h a t no c o r r e c t i o n s f o r a n h a r m o n i c i t y have been made.
4 . 1 4 shows t h a t t h e f i t
although f o r
6
j
and
6
i s a l s o v e r y good f o r t h e d i s t o r t i o n
^ the d e v ia t io n s are s l i g h t l y
estimated u n c e r t a i n t i e s .
It
is
seen as w e l l
T ab l e
constants,
l a r g e r t h an t h e
t h a t the force f i e l d
g i ve s good p r e d i c t i o n s f o r t h e d i s t o r t i o n c o n s t a n t s o f t h e
species.
>
28
Sih^
35
Cl
37
Cl
136
i
Table 4.12
The H^Vmonic For ce F i e l d o f D i c h l o r o s i l a n e
Force C o n s t a n t s 3
S p ec i es
2.891(3 9 )b
_c
_c
-0.188(87)
0.180(52)
0.547(28)
-0.357(83)
_c
3.231(45)-
0.814(70)
a2
0.418(8)
2.862(38)
_c
B 1
0.723(10)
2.871(43)
-0.283(26)
B 2
0.607(11)
a
°-l
Bond s t r e t c h i n g f o r c e c o n s t a n t s i n mdyn A ; s t r e t c h - b e n d i n t e r a c t i o n
f o r c e c o n s t a n t s i n mdyn r a d - ' ; a n g l e bendi ng f o r c e c o n s t a n t s i n mdyn
A rad- 2 .
b Numbers i n b r a c k e t s a r e s t a n d a r d d e v i a t i o n s
s ig n ific a n t figures.
in u n its o f the l a s t
c These f o r c e c o n s t a n t s were c o n s t r a i n e d t o z e r o
%
r
137
Table 4 .1 3
O b s e r v e d a n d C a l c u l a t e d V i b r a t i o n a l Wavenumbers ( c m - ^)
o f D ich lo ro silan e
■»
2 8
28 S
c i-n
D2 35 c i 2a
S iH 2 35c i 2a
2 8 SiHD
35r i
Vibration
A1
V1
v3
v4
A2
v5
B1
v6
v7
B2
v8
v9
,
Obs.c
Dev.d
2224
-9.9
954
Dev.d
0
1608
7.4
2231
0.9
695
-0.7 '
527
-2.5
519
0.6
188
0.8
187
0.7
710
-0.2
2237
-11.7
602
-0.3
1
0
bs.c
bs.c
1637
466
Dev.d
-10.4.
885
2.0
-
.
-
1621
8.6
b
2
“
-
6.5
_
0.1
>
876
-1.2
663
0.8
590
0.0
566
. 1 . 1*
818
- 599
0.0
-0.1*
Wavenumbers f o r t h e s e i s o t o p e s were used t o d e t e r m i n e t he harmonic
force f ie ld .
In t h e l e a s t squares f i t s u n c e r t a i n t i e s were t akerr"}
t o be 1 % o f t h e measured v a l u e .
'
•%
k
These wavenumbers were- not used i n t h e l e a s t s q u ar es f i t s .
Since
t h i s s p e c i e s , has Cs symmetry t h e v i b r a t i o n s t r a n s f o r m as
A(=A-|+B] i n t h e symmet ri c m o l e c u l e s ) and A " ( = ^ 2 + B2 i n t h e symmetric
molecules).
C
*
Taken from C h r i s t e n s e n and N i e l s e n
(12).
Observed v a l u e minus v a l u e c a l c u l a t e d usi ng t h e f o r c e c o n s t a n t s o f
Table 4 . 1 2 . ,
138
Table 4 .1 4
O b s e r v e d a nd C a l c u l a t e d C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s
(kHz) o f D ie h lo r o s ila n e
Parameter
2 8
SiH2
3 5
Observed V a l u e 3
\
Cl2
V
AJ
•a j k
ak
t
1 . 0 2 2
0.15
-0.14
14 2.1
1..4
-0.49
0.2410
0.0024
-0.0032
3.117
0.093'
6k
Si H 2
3 5
ak
0.969
.
-0.003
-14.91
-
139.5
-
‘A
SK
cl
0.18
C l3 7 Cld
AJ
aj k
0.0014
0 . 0 1 0
-15.46
6J
2 8
D eviation0
Uncertainty^
-
1 . 1
t
0.2 334
2.490
Taken from T a b l e 4 . 4 .
0 . 0 2
0.0045
-0.34
-
r*
b
Estimated u n c e r t a i n t i e s
used i n t h e f o r c e c o n s t a n t f i t .
r
*
Observed v a l u e minus v a l u e c a l c u l a t e d f r o m t h e f o r c e f i e l d
Table 4 .1 2 .
d
V a l ue s f o r t h i s ^ i s o t o p e were n ot used i n t h e f o r c e f i e l d
of
refinement.
139
4 .6
The A v e r a g e S t r u c t u r e o f D i c h l o r o s i l a n e
The harmonic f o r c e f i e l d
o f T a b l e 4 . 1 2 has been used to
e v a l u a t e t h e ground s t a t e a v e r a g e s t r u c t u V e o f d i c h l o r o s i l a n e .
In
C h a p t e r 3 t h e av e ra g e s t r u c t u r e o f s u l p h u r d i c h l o r i d e was e v a l u a t e d ;
because t h i s
s t r u c t u r e c ou ld be d e t e r m i n e d using t h e r o t a t i o n a l
c o n s t a n t s o f only, one i s o t o p i c s p e c i e s i t
isotopic variations
however, a t
was p o s s i b l e to
i n t h e a v e r a g e bond l e n g t h s .
For d i c h l o r o s i l a n e ,
l e a s t two i s o t o p i c s p e c i e s a r e r e q u i r e d
molecular s t r u c t u r e ;
ignore
to e v a lu a te the
t h e r e f o r e t h e i s o t o p i c v a r i a t i o n o f t h e bond
d i s t a n c e s w er e c a l c u l a t e d u s i n g e q u a t i o n 1 . 4 3 . The v a l u e s used f o r t h e
Morse a n h a r m o n i c i t y p a r a m e t e r a wer e a ( S i H )
a(S iC l)
°
= 1 . 7 5 A"
1
and
°- 1
= 1 . 5 6 A" , bot h t a k e n from K uc h i t su and M or ino ( 2 6 ) .
calculated
i s o t o p i c changes
The
i n t h e a v e r a g e bond l e n g t h s a r e g i ve n
in
2
Table 4 .1 5 to g e th e r w it h the corresponding values o f
6
<u > ,
t he change
i n t h e mean square a m p l i t u d e o f v i b r a t i o n o f t h e bond in q u e s t i o n ,
6
and
K, t h e c o r r e s p o n d i n g change in t h e mean square p e r p e n d i c u l a r a m p l i t u d e
correction.
In a l l
cases t h e i s o t o p i c v a r i a t i o n s
;
are extrem ely s m a ll,
v a l u e s has
l e s s t h an 4 x 10
been g i v e n f o r f o r m i c
acid
-5°
A; a
For
29
28
isotopic
set of
6
rz
c o n s t a n t s A2 , Bz and Cz
species of d i c h l o r o s i l a n e
in T ab le 4 .1 6 .
'35
SiH 2
Table 4 . 4 ;
the
t he v a r i o u s
more t y p i c a l
(27).
The a ve r a ge v a l u es o f t h e r o t a t i o n a l
are given f o r
i n t h e bbnd. d i s t a n c e s
SiHg
C l 2 these have been c a lc u la te d using the F i t 2 constants of
fo r this
fit
is
l a r g e r than t h e c o r r e s p o n d i n g v a l u e f o r
35
C1 2 s p e c i e s by 0 . 0 4 7
0 . 0 7 6 MHz p r e d i c t e d u si ng t h e
6
MHz,
r z values o f Table 4 . 1 5 .
s t r u c t u r e o b t a i n e d by a l e a s t squares f i t
*
*
i n good a g re e m e n t ^ w f t i i ^ t h e
The m o l e c u l a r
t o t h e s e a ve r a ge r o t a t i o n a l
1 40
Table 4.15
P ar am et e r s D e s c r i b i n g t h e I s o t o p i c V a r i a t i o n
Average Bond Lengths o f D i c h l o r o s i l a n e
Parameter3
2 8
SiH2
3 5
C l 2 ->2 8 S i H 2
<5<u2 > ( S i H )
6
<u 2 > ( S i 3 5 C l )
6
<u2 > ( S i
6
K( Si H)
6
K (Si3
6
K( Si
6
r z (SiH)
5
3 7
3 7
C1)
3 5
C l 37 Cl
2 8
SiH2
i n the
3 5
C l 2 -^2
0 . 0
-0.4
0 . 0
-1.7
-2.4
C1)
3 5
Cl2
1.3
-
1 . 0
-
SiH2
-
0.9
Cl)
9
1 . 0
-
2 . 0
-0.9
^
-2.4
*
6
r z ( S i 3 5 Cl)
-
6
r 2 (S i3 7 C l)
-3.6
3
-
Par ame t er s g i v e v a l u e s f o r s u b s t i t u t e d s p e c i e s minus t h e v a l u e f b r t h e
28
35
2
parent o r
S i C l 2 species.
The u n i t s o f <5<u > , 6 K and 6 r z a r e
r e s p e c t i v e l y 10~^A^,
V
-3.0
1 . 0
l Qi ^A and 10 ”
8
A.
141
c o n s t a n t s , w i t h a l l o w a n c e made f o r t h e i s o t o p i c bond l e n g t h v a r i a t i o n s
is also given in T a b le 4 .1 6 .
A n e g l i g i b l y d i f f e r e n t s t r u c t u r e was
o b t a i n e d when t h e a v e r a g e r o t a t i o n a l
instead c a lc u la t e d
6
u s i n g t he F i t
constants f o r
OQ
S
i
1 v a lu es o f T a b l e 4 . 4 .
r^ v a l u e s were o m i t t e d from t h e f i t
a s lig h tly d iffe re n t
C
1 2 were
When t h e
structure
was o b t a i n e d ; t h e s i l i c o n - h y d r o g e n and s i l i c o n - c h l o r i n e bond l e n g t h s ,
o
i n c r e a s e d and d e c r e a s e d by 0 . 0 0 3 7 A an d 0 . 0 0 0 4 A
respectively.
The e r r o r s ^ q u o t e d f o r t he a v e r ag e s t r u c t u r a l
p ar amet er s
a r e t h e s t a n d a r d e r r o r s o b t a i n e d f rom t he l e a s t sq uar es f i t
and a l m o s t
c e r t a i n l y u n d e r e s t i m a t e t he t o t a l
re lia b ility
section 4 . 8 .
/
o
f o r e x a mp l e,
e r r o r in
t hese p a r a m e t e r s .
o f t he v a r i o u s d i c h l o r o s i l a n e s t r u c t u r e s
The
i s d i sc u sse d i n
142
Table 4 . 1 6
Av er ag e R o t a t i o n a l
C o n s t a n t s o f D i c h l o r o s i l a n e and
Aver age S t r u c t u r e o f
P ar am et e r
2 8
SiH2
3 5
2 8
C l2
Si H 2
2 8
3 8
SiH2
Cl2
3 5
C l 37Cl
29
SiH 2
3S
C l2
f
Az (MHz)
1 40 8 2 . 1 4 2
13 98 2 . 1 1 5
13836.076
B2 (MHz)
2570.078
2501.117
2570.120
Cz (MHz)
2231.376
2176.795
2225.130
r z (S i-C l)
2.0352(3)
r z (Si-H)
1.4726(25) A
<(C l- S i- C l)
109.68(3)°
< ( H-S i - H )
112.44(28)°
A b
a
O b t a i n e d usi ng t h e F i t 2 v a l u e s o f T a b l e 4 . 4 .
b
■*
E r r o r s quoted a r e s t a n d a r d e r r o r s .
These p r o b a b l y u n d e r e s t i m a t e
t h e t o t a l e r r o r f o r t h es e p a r a m e t e r s .
a
143
4.7
The E q u i l i b r i u m
Structure of Dichlorosilane
Havi ng e v a l u a t e d
silane,
it
structure.
seemed o f
the average m olecular s t r u c t u r e o f d i c h l o r o ­
i n t e r e s t t o c a l c u l a t e as w e l l
T h i s was done u si ng e q u a t i o n
a crude e q u i lib r iu m
1 . 4 2 and t he f o r c e f i e l d
of
{
Table 4 .1 2 to g e th e r w ith the r e s u l t s o f the previous s e c t io n ;
c a l c u l a t e d e q u i l i b r i u m v a l u e s o f t h e S i - H and S i - C l
g i ve n i n T a b l e 4 . 1 7 .
that
bond l e n g t h s a r e
I t was not p o s s i b l e t o e s t i m a t e t h e e q u i l i b r i u m
va l u e s o f t h e bond a n g l e s ;
however,
t he
results
f o r m et hyl en e f l u o r i d e
t h ese can be a p p r e c i a b l y d i f f e r e n t
(28)
suggest,
from t h e a v e r ag e v a l u e s .
The e q u i l i b r i u m s t r u c t u r e and o t h e r d i c h l o r o s i l a n e s t r u c t u r e s a r e
compared i n s e c t i o n 4 . 8 .
f
4.8
Comments on the~ S t r u c t u r e and For ce F i e l d o f D i c h l o r o s i l a n e
The v a r i b u s
molecular s t r u c t u r e s derived f o r d i c h l o r o s i l a n e
been compared i n T a b l e 4 . 1 8 .
It
is
seen t h a t t h e si 1i c o n - h y d r o g e n
have
bond
l e n g t h and bond a n g l e show a wide v a r i a t i o n f rom one s t r u c t u r e t o t he
next;
t he s i l i c o n - c h l o r i n e
s l i g h t v a r i a t i o n s a nd ,
p a r a m e t e r s , on t he o t h e r hand,
in f a c t ,
the r >r >r >r
trend t y p ic a l
z o s e
t h e s i l i c o n - c h l o r i n e bond l e n g t h s
o f d i a t o m i c m o le cu l es
o f T a b l e 4 . 1 8 a r e i n accord w i t h t h e g e n e r a l
neglect of v i b r a t i o n a l
show o n l y
effects w ill
(21).
'
observation
follow
The r e s u l t s
t h a t t he
introduce the g re a te s t e rro r
in
t h e c o o r d i n a t e s o f hydrogen atoms.
It
r
shoul d have a nebulous meaning.
(Si-H)
bond l e n g t h
in p a r t i c u l a r
Using t h e r e s u l t s o f T a b l e s 4 . 7 ,
i s easy t o u n d er st a nd why t h e
4 . 16 ' and 4 . 1 8 ,
and n e g l e c t i n g any
144
Table 4 .1 7 :
The E q u i l i b r i u m S t r u c t u r e o f D i c h l o r o s i l a n e 3
Par amet e r
Value
u2 ( S i - H ) ( A 2 )
0.00773
u2 ( S i - C l ) ( A 2 )
0.00190
K (si-H )(A )
0.01493
K ( S i - C l ) (A)
0.00076
a(S i-H )(A - 1 )
1.75
a(S i-C l)(A -1 )
1.56
r
1.4726
(Si-H)(A)
O
r ( S i - C l ) (A)
O
r (Si-H )(A )
O
re (S1-Cl)(A)
2.0352
1.4672
2.0315
V
2
3
Calculation
for
2 8
SiH2
using the fo rc e f i e l d
3 5
C l2 .
Va l ue s o f u
o f Table 4 .1 2 .
f rom t h e p r e v i o u s s e c t i o n .
and K were c a l c u l a t e d
Val ues o f a and r ^ wer e t a ke n
145
»»
anharmonic e f f e c t s ,
c h l o r i n e a t oms,
are,
28
for
•y
SiH2
t h e c o n t r i b u t i o n made t o
°,
f o r e xamp l e,
by t he
t he hydrogen atoms and t h e z e r o - p o i n t v i b r a t i o n a l
35
C l2 , calculated
°?
t o be 1 9 3 . 6 2 uA
7
(= 2mc l ( a ^ )
o
),
effects
3 . 0 2 uA
O o
0
(= 2mH ( c H ) ) and - 0 . 2 7 uA? ( = 1° point v ib r a t io n a l
coordinates.
1
effects
1^) r e s p e c t i v e l y .
C learly
can produce a l a r g e u n c e r t a i n t y
t he z e r o -
i n t he hydrogen
F o r t he example g i v e n one m i g h t e x p e c t t h e e f f e c t i v e a°-|
and c ° c o o r d i n a t e s t o d i f f e r
from t h e i r c o r r e s p o n d i n g w e l l - d e f i n e d
O '
O
a v e r a g e v a l u es by a t most 0 . 0 0 1 2 A and 0 . 0 5 6 A r e s p e c t i v e l y ; t he observed
O
O
d e v i a t i o n s a r e 0 . 0 0 0 5 A and 0 . 0 2 9 A. I t i s obvious t h en t h a t comparing
t he r
(Si-H)
b.ond l e n g t h s o f d i f f e r e n t h a l o s i l a n e s would be a m ea n i ng l ess
exercise.
Looki ng n e x t a t t h e s u b s t i t u t i o n
dichlorosilane,
it
is
and a v e r ag e s t r u c t u r e s o f
seen t h a t t h e r s ( S i - H )
bond l e n g t h , whi ch was e s t i ­
mated usi ng t h e c e n t e r o f mass c o n d i t i o n
(see section
larger
(28),
than r z ( S i - H ) .
d ifluorosilane
(22),
In d i f l u o r o m e t h a n e
however,
t h e r $ ( C- H)
1.4),
is a p p a re n tly
dichloromethane
and r ^ ( S i - H )
( 2 3 ) and
bond l e n g t h s ,
o b t a i n e d u si ng d e u t e r a t e d s p e c i e s d a t a , a r e a l l
s m a l l e r t han t h e c o r r e s ­
ponding a v e r a g e bond l e n g t h s .
has been p o i n t e d o u t t h a t
In t h i s
hydrogen atom c o o r d i n a t e s c a n n o t ,
usi ng a c e n t e r o f mass c o n d i t i o n
there i s ,
however,
little
regard
in g e n e r a l,
(2
1
it
be a c c u r a t e l y s p e c i f i e d
); w ith o u t d euterated species data
altern ative.
*
It
becomes c l e a r t h e n t h a t o n l y t h e w e l l - d e f i n e d a v e r a g e
s t r u c t u r e g i v e s an a c c u r a t e e s t i m a t e f o r t h e si
and bond a n g l e .
Table 4 . 1 8 .
i c o n - h y d r o g e n bond l e n g t h
Whereas a v e r a g e s t r u c t u r e s
other ch lorosilanes,
difluorosilane
1
(2
2
the r z ( S i-H )
) is
have not t e e n e v a l u a t e d f o r
Q
d i s t a n c e o f 1 . 4 7 2 3 A found f o r
i n e x c e l l e n t a g reement w i t h t h e v a l u e g i v en
Because t h e d i f f e r e n c e between t h e r Q( S i - C 1 )
in
bond l e n g t h
146
Table 4 .1 8
A Comparison o f the D e r iv e d S t r u c t u r e s o f D i c h l o r o s i l a n e 3
<(X -S i-X )(D eg.)
r(S i-X )(A )
>
. r
SiH
1.4590
110.05
SiCl
2.0336
109.76
S i Hb
1.4802
1 1 1 . 29
SiCl
2.0326
109.72
SiH
1.4726(75)°
112.44(84)
Si C l
2.0352(9)
109.68(9)
SiH
1.4672(89)d
Si C l
2.0315(18)
0
rs
r
r
z
e
a The r Q, r $ ,
_e
e
and r g s t r u c t u r e s a r e t a ke n from T a b l e s 4 . 8 ,
4.10,
4.16
and 4 . 1 7 r e s p e c t i v e l y .
b S tric tly,
t h e si 1 i c o n - h y d r o g e n p a r am et e rs g i v en a r e not s u b s t i t u t i o n
4
values.
No d e u t e r a t e d d i c h l o r o s i l a n e s p e ci e s were s t u d i e d .
See s e c t i o n
4.4.
c
Errors c i t e d
error.
for
the r p a r a m e t e r s
are estimated outside l i m i t s
of
See t e x t .
^ E r r o r s c i t e d a r e t h e d i r e c t sums o f t h e e r r o r s
one q u a r t e r o f t h e a p p r o p r i a t e r
-
i n t he r z v a l ue s pl us
r g difference.
e No e s t i m a t e o f t h e s e a n g l e s o b t a i n e d .
See t e x t .
147
and t h e r ^ ( S i - C 1) d i s t a n c e
i s o n l y 0 . 0 0 1 6 A and t he f or me r s t r u c t u r e
t a k e s no account o f v i b r a t i o n a l
effects,
it
seems e v i d e n t t h a t
t he
o
uncertainty
i n r ^ ( S i - C l ) must be l e s s
a ssi gn ed t h e a v e r a g e s t r u c t u r e
squares s t a n d a r d e r r o r s
outside
than 0 . 0 0 1 A.
The u n c e r t a i n t i e s
i n T a b l e 4 . 1 8 a r e t h r e e t i mes t h e l e a s t
o f Table 4 . 1 6 ;
these c o n s t i t u t e r e a s o n a b l e
lim its of erro r.
The f i n a l
are the r
c
(Si-H)
set of
and r
6
structural
(S i-C l)
p ar amet er s g i v e n i n T a b l e 4 . 1 8
distances.
Errors
t o t h e s e p a r a me t e r s usi ng t he approach o u t l i n e d
dichloride
(see s ectio n
3.4);
v a l u e was t a k e n as t h e d i r e c t
that
is,
the t o t a l
have been assi-gned
p re v io u s ly f o r sulphur
uncertainty
sum o f t he u n c e r t a i n t y
r z v a l u e pl us one q u a r t e r o f t he r z -
r g d iffe re n c e .
in each r g
in the corresponding
Accepting^ t h e r g
d i s t a n c e s a t f a c e v a l u e and assuming t h a t t h e a v e r a g e and e q u i l i b r i u m
bond a n g l e s a r e i d e n t i c a l ,
one can c a l c u l a t e
^
bution o f the z e r o - p o i n t v i b r a t i o n s
)
°2
somewhat l a r g e r t han t h e - 0 . 2 7 uA
e a rlier.
to
t h a t t h e anharmonic c o n t r i -
o
I. , f o r e xamp le,
D
is 0 . 7 2 ( 3 7 )
harmonic c o n t r i b u t i o n e s t i m a t e d
These r e l a t i v e magnitudes and signs a r e c o n s i s t e n t w i t h r e s u l t s
f o r difluoromethane
Fin ally,
stretching
(28).
in Table 4 . 1 9 ,
t h e si 1 i c o n - h a l o g e n bond l e n g t h s and
f o r c e c o n s t a n t s o f t h e f l u o r o s i l a n e s and c h l o r o s i l a n e s
been compared; where p o s s i b l e c o n s i s t e n t bond l e n g t h d e f i n i t i o n s
.used.
0 2
uA ,
For t h e f l u o r o s i l a n e s
t he s t r e t c h i n g
t h e r e i s a s t r on g
inverse c o r r e l a t i o n
f o r c e c o n s t a n t s and t h e bond l e n g t h s
(22).
have
have been
between
The r e s u l t s
for
t he c h l o r o s i l a n e s a r e l e s s c l e a r - c u t . In p a r t i c u l a r , t h e s t r e t c h i n g
•% ,
•
f o r c e c o n s t a n t o f t r i c h l o r o s i l a n e appears t o be too s m a l l ; t h i s may
suggest t h a t t h e t r i c h l o r o s i l a n e
force f ie ld
requires fu rth e r a tte n tio n .
However, w i t h t h e p o s s i b l e e x c e p t i o n o f t he t e t r a h a l o s i l a n e s , t h e r e
is a
1 48
Table 4 .1 9
A Comparison o f Bond Lengt hs and S t r e t c h i n g Force
C o n s t a n t s i n t h e F l u o r o s i l a n e s and C h l o r o s i l a n e s
(a)
Fluorosilanes
Si H 3
F
r(S i-F )(A )
5.31
r
Si H 2 F 2
5.83
r
SiHF 3
6 . 0 1
r
6.52
r
SiF4
(b)
Fr ( S i - F ) ( m d y n A- 1 )
Chlorosilanes
F r ( S i - C l ) ( m d y n A” ^ )
e
e
e
a
R e f er en c es
= 1. 591
(24)
= 1.576
(2
= 1.562
(29)
= 1.552
2
)
(30,31)
r(S i-C l)(A )
R ef er e n ce s
(32,6)
SiH-jCl
2.98
r s = 2. Q48
Si H 2 C l 2
3.05
r
SiHCl3
2.92
rs =
SiC l.
4
3.37
r
s
= 2.033
2 . 0 2 0
= 2.019
9
T h i s work
(33,8)
(34,35)
d efin ite
s y s t e m a t i c s h o r t e n i n g o f t he s i l i c o n - h a l o g e n bond as t h e
number o f "halogen atoms i n c r e a s e s .
halogen bonds suggests
al o n g each s e r i e s ;
this
that th e ir
The s h o r t e n i n g o f t he s i l i c o n strength
increasing s l i g h t l y
i s s u pp o r t e d by t h e t r e n d
v a l u e s and i s c o n s i s t e n t w i t h t h e i n c r e a s e d
the s ilic o n -h a lo g e n
is
sigma bonding o r b i t a l s
i n the f o r c e c o n s t a n t
ionisation p o te n tia ls of
(18).
1 50
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152
Chapter 5
The Mi cr owave Spectrum o f P r o p i o l y l
The a c i d
#
been e x t e n s i v e l y
Chloride
h a l i d e d e r i v a t i v e s o f s i m p l e c a r b o x y l i c a c i d s have
s t u d i e d u si n g mi crowave s p e c t r o s c o p y .
whi ch have been i n v e s t i g a t e d
c h l o r i d e s o f f o r m i c ac i d
The mo le cu le s
in clu d e the acid f l u o r i d e s
(1 ,2),
a c e tic acid
(3 ,4 ),
and a c i d
cyclopropane%
carb oxylic acid
(5,6)
and p r o p i o n i c a c i d
"deriv atives of p r o p i o l i c
examined.
In f a c t ,
(7,8).
The c o r r e s p o n d i n g
( p r o p y n o i c ) a c i d have n ot been p r e v i o u s l y
t he p r e p a r a t i o n o f t h e p r o p i o l y l
r e c e n t l y been a c c o mp l i sh ed .
As p r o p i o l i c a c i d
These m o l e c u l e s a r e o f e s p e c i a l
halides
example,
seemed w o r t h -
i n t e r e s t .as t h e p a r e n t p r o p i o l i c
a c i d has a v e r y l a r g e a c i d d i s s o c i a t i o n c o n s t a n t
those o f a l i p h a t i c ,
has o n l y
i s one o f t h e two s i m p l e s t
p l a n a r c a r b o x y l i c acids a study o f the p r o p i o l y l
w hile.
halides
(9,10)
compaj ^l t o
o l e f i n i c or aromatic c a r b o x y l i c / a c i d s .
At 2 0 ° C ,
for
the acid d i s s o c i a t i o n constants of the th ree-carb o n propionic
and p r o p i o l i c a c i d s a r e 1 . 3 5 x 10
respectively.
-5
and 1 . 3 6 x 10
T h i s d i f f e r e n c e has' been a t t r i b u t e d
-? \
mol ^ l i t e r
-1
to the stro n g ^elec-
tron withdrawing properties of the ethynyl group ( l l V r e l a t i v e to those
o f O t h e r hydrocarbonr s u b s t i t u e n t s .
the simplest acid halides
carbon-carbon t r i p l e
bond.
As w e l l ,
the p r o p i o l y r halides are
i n which t he c a r b o n y l
Therefore i t
-COX groups i n t h e p r o p i o l y l
bond i s c o n j u g a t e t o a
would n o t be s u r p r i s i n g
if
t he
h a l i d e s had somewhat d i f f e r e n t s t r u c t u r e s
f r om t h o se found f o r o t h e r a c i d h a l i d e s .
"
153
T h is chapter deals w ith
o f one such d e r i v a t i v e :
d e a l t with
its
propiolyl
t h e mi crowave spectrum and s t r u c t u r e
chloride.
Several
recent reports
s y n t h e s i s and w i t h o t h e r s p e c t r o s c o p i c
have
investig atio n s.
t
Augdahl et^ aj_.
(12)
halogenation with
prepared p r o p i o l y l
dichlorodimethyl
1 , 1
Raman s p e c t r a and a s s i g n e d a l l
c h l o r i d e f r o m t h e p a r e n t a c i d by
ether,
vibrational
r ec o r d e d t h e
fundamentals.
i n f r a r e d and
Balfour,
Grieg
and V i s a i s o u k d e s c r i b e d a s y n t h e s i s from p r o p i o l i c a c i d and phosphorus
pentachloride
spect rum o f
(13).
S ub s eq ue nt l y B a l f o u r e t al_. a n a l y s e d t h e v i b r a t i o n a l
propiolyl
s p e c t r a o f t h e normal
chloride-d
(14)
and observed t h e n e ar u l t r a v i o l e t
and d e u t e r a t e d s p e c i e s
normal c o o r d i n a t e a n a l y s e s
(15).
Two r a t h e r i n c o m p l e t e
have been made f o r p r o p i o l y l
chloride.
In the
*
firs t
study t h e mean a m p l i t u d e s o f v i b r a t i o n were r e p o r t e d w i t h o u t
d e t a i l s of the corresponding fo r c e f i e l d
values f o r
(16).
A second a n a l y s i s
gave
t h e f o r c e c o n s t a n t s b u t u n f o r t u n a t e l y d i d not use non-
r ed un da n t symmetry c o o r d i n a t e s
The r o t a t i o n a l
to p r o p io ly l
(17).
s p e c t r a o f a few m o l e c u l e s s t r u c t u r a l l y
c h l o r i d e have been i n v e s t i g a t e d .
p r o p y n a l , was f i r s t
The c o r r e s p o n d i n g a l d e h y d e ,
s t u d i e d by Howe and G o l d s t e i n
few low J l i n e s o f t h e normal
isotopic
sim ilar
(18)
who a s s i g ne d a
s p e c i e s and measured t h e d i p o l e
moment. A c o m p l e t e s t r u c t u r e f o r p r op yn al was l a t e r d e t e r m i n e d by C o s t a i n
and Morton
p ro py n al
(19).
T h e i r microwave r e s u l t s
showed t h a t t h e carbon c h a i n
has a bend o f a p p r o x i m a t e l y 1 . 5 d e g r e e s . ' T h i s
in
r e s u l t has s i n c e
been c o n f i r m e d by a c o mb i n at i o n o f t h e microwave r e s u l t s w i t h e l e c t r o n
d iffractio n
data
(20).
The d e v i a t i o n f rom l i n e a r i t y ,
chains of o t h e r p r o p i o l y l - t y p e molecules
has n ot p r e v i o u s l y r e c e i v e d a t t e n t i o n .
1
I
if
a n y , o f t h e carbon
i s an i n t e r e s t i n g
problem which
O t h e r r e l a t e d microwave s t u d i e s
154
i n c l u d e t hose o f p r o p i o l i c
a c i d , which L i s t e r and T y l e r
be p l a n a r , and 2 - c h l o r o b u t e n - 3 - y n e
and i s o e l e c t r o n i c w i t h p r o p i o l y l
( 2 2 ) whi ch i s
fo r the r o t a t io n a l
structural
distortion
an a p p r o x i m a t e f o r c e f i e l d .
Again,
Further,
constants
f rom t he ground
the c e n t r i f u g a l
vibrational
group
d istortion
data to determine
havi ng assumed a s t r u c t u r e f o r t h e
t h e a v e r ag e r o t a t i o n a l
c u la t e the average s t r u c t u r e
values
The m o l e c u l a r d i p o l e moment
p ar a m e t e r s have been c a l c u l a t e d
c o n s t a n t s have been combined w i t h e x i s t i n g
g r ou p,
is o to p ic species
Usi ng an assumed s t r u c t u r e f o r t h e e t h y n y l
s t a t e e f f e c t i v e moments o f i n e r t i a .
ethynyl
c h lo rid e four
constants, quartic c e n trifu g a l
has a l s o been o b t a i n e d .
s i m i l a r to
T h e i r s p e c t r a have been a n a l y s e d t o y i e l d
and n u c l e a r q u a d r u p o l e c o u p l i n g c o n s t a n t s .
t he r e m a i n i n g
in e rtially
showed t o
chloride.
In t h e p r e s e n t s t u d y o f p r o p i o l y l
have been i n v e s t i g a t e d .
(21)
cbnstants
have been used t o c a l ­
i n t h e ground v i b r a t i o n a l
state.
•
w
no
155
5.1
Assignment o f th e S p e ctra
The g en e r a l method used t o a s s i g n t h e spect rum o f p r o p i o l y l
c h l o r i d e was v e r y s i m i l a r
dichlorosilane.
p ropynal
F i r s t a model
( 1 9 ) and a c e t y l
the r o t a t i o n a l
to t hose used f o r s u l p h u r d i c h l o r i d e and
s t r u c t u r e based on t h e known g e o m e t r i e s o f
chloride
constants;
( 4 ) was used t o p r o v i d e e s t i m a t e s
t h es e c o n s t a n t s ,
in t u r n ,
for
were* used to make an
>
a p p r o x i m a t e p r e d i c t i o n o f t he s p e c t r u m, and e s p e c i a l l y o f some key
t r a n s i t i o n s which co ul d be used f o r
in itia l
A maj or d i f f e r e n c e was e x p e c t e d ,
of propiolyl
propiolyl
c h l o r i d e and t he p r e v i o u s
a x es .
Thus,
t ype t r a n s i t i o n s ,
(The K K
a
however,
between the spectrum
two m o l e c u l e s .
Like propynal,
c h l o r i d e was e x p e c t e d t o be p l a n a r , w i t h C$ symmetry, and thus
to have n on -z er o -c o mp o ne n t s o f i t s
in e rtia l
a s si g n me n t s .
C
selection rules
oe -<— ► oo where a g a i n
s i m pl e p a t t e r n ,
principal
i n c o n t r a s t t o S C ^ and S i H ^ C l ^ , whi ch have o n l y b-
propiolyl
and odd v a l u e s o f
d i p o l e moment a l o n g two o f i t s
c h l o r i d e shoul d have b o t h a^- and b - t y p e s p e c t r a .
for a-type tra n s itio n s
—
a r e ee <— ► eo and
( s e e s e c t i o n 3 . 1 ) e and o r e s p e c t i v e l y d enot e even
and «c ( 2 3 ) ) .
The a - t y p e s p e c t r a f o l l o w ' a
relatively
t h e most p r o m in e n t p a r t o f which i s a s e r i e s o f e q u a l l y
spaced R branch l i n e s .
F or t h e t r a n s i t i o n s
shoul d be a t a f r e q u e n c y ^ ( B + C ) ( J + 1 ) .
(J + 1)
J*, t h e s e groups
They s h o u l d ,
f u r t h e r m o r e , have
h i g h l y c h a r a c t e r i s t i c lStark""”p a t t e r n s ; i n p a r t i c u l a r 1 t he c e n t r a l
t he g r o u p s , and v e r y l i t t l e
v e ry low S t a r k f i e l d s .
.
else
i n t h e sp ec t ru m,
shoul d be o b s e r v a b l e a t
They shoul d thus be u s e f u l
*
parts of
for in it ia l
a s si gn me nt s .
An i n i t i a l sweep o f t h e spect rum o f normal p r o p i o l y l c h l o r i d e
i
in t h e f r e q u e n c y range 2 6 . 5 - 4 0 GHz a t hi gh S t a r k f i e l d s showed i t t o be
*
v er y r i c h and compl ex, w i t h e v i d e n c e o f c h l o r i n e q u a d r u p o l e h y p e r f i n e
structure,
b ut no w e l l
resolved Stark p atte rn s .
T h i s was i n ke e pi n g w i t h
/
in itia l
predictions.
A t v e r y low m o d u l a t i o n f i e l d s ,
t y p i c a l l y 20-40 v o lt
1 56
cm
t h e d e n s i t y o f l i n e s was g r e a t l y
r e du ced .
Under t hese c o n d i t i o n s
two clumps o f l i n e s were found a t ^ 3 1 . 5 - 3 2 . 5 GHz and a t
frequency r a t i o o f .^ 6 : 7 .
6
«- 5 and 7 <-
6
They were a p p a r e n t l y
respectively.
3 7 . 0 - 3 8 . 2 GHz, a
t h e a^-type R br anches J =
Closer in s p e c tio n
r e v e a l e d t h a t each clump
contained
two groups o f l i n e s :
a s t r o n g high f r e q u e n c y group and an al mo s t
identical
group w i t h one t h i r d
t he i n t e n s i t y a t
were e a s i l y a s s i g n e d as £ - t y p e
r e s p e c t i v e l y , and t he o v e r a l l
lower f r e q u e n c y .
R branches o f HCCCO^Cl
a gi ven group u s i n g t h e i r S t a r k e f f e c t s ,
hi gh Ka t r a n s i t i o n s
6 4 3
5 4 2
and
6 4 2
*■
7g <5 4
6
and HCCCO^Cl,
ass i gn me n t was t a k e n as c o n f i r m e d .
I t was a l s o r e l a t i v e l y easy to a s s i g n
comparison w i t h t h e o r i g i n a l
They
and r e l a t i v e
predictions.
g , 7&
6
individual
&, 7 H
First
<-
6
43,
inside
in te n s itie s
in
to be a ssi gn ed were t h e
7 ^
«-
^, which were t hen used i n a f i t
c o n s t a n t s , which i n t u r n gave new p r e d i c t i o n s
lines
6
42,
55 ,
6 5
t o the r o t a t i o n a l
fo r further transitions.
The b o o t s t r a p p r o c e d u r e which had e a r l i e r been used f o r S CI 2 and S ^ C ^
was now employed t o a s si g n an i n c r e a s i n g number o f t r a n s i t i o n s ,
t y p e and t hen b - t y p e ,
f o r both i s o t o p i c
species.
Most t r a n s i t i o n s showed
t o some degr ee c h l o r i n e q u a d r u p o l e h y p e r f i n e s t r u c t u r e ,
po ssible to e v a lu a te the coupling constants
s t r u c t u r e confirmed the r o t a t i o n a l
t r a n s i t i o n s o f t h e DCCCO^Cl
hyperfine
inten sities
s u g g es t i ng t h a t tffe"
d i p o l e moment components were o f n e a r l y equal
The s p ec t ru m o f p r o p i o l y l
This
The r e l a t i v e
o f t he a_- and b_-type t r a n s i t i o n s were v e r y s i m i l a r ,
ua and
from w h i c h i t was
(section 5 . 3 ) .
a s s i gn m en t s .
f i r s t a_-
m ag n i tu d e.
c h l o r i d e - d was a l s o examined w i t h
and DCCCti^Cl
se cie s
b ei ng a s s i g n e d .
The
c h l o r i n e q u ad r u p o l e c o u p l i n g c o n s t a n t s o f t he two d e u t e r a t e d s p e c i e s were
I
f i r s t e s t i m a t e d u s i n g t h e normal
constants
s pe ci e s r e s u l t s .
These values o f the
p r e d i c t e d t he obser ved h y p e r f i n e p a t t e r n s w e l l
facilita te d
and g r e a t l y
the a s s i g n m e n t , which f o l l o w e d a c o u r s e s i m i l a r to t h a t
157
p r e v i o u s l y d e s c r i b e d f o r t h e normal
Fin ally,
lines of the J =
measured f o r
specific
excited s ta te
satellites
«- 5 and J = 7 «
6
ments t o be made.
predicted a t
vibrational
(12).
5.2
<3
a^-type'R branch gr oups.
6
From t he r e l a t i v e
lines
were observed f o r t he h ig h K
a t dry ic e
150 + 50 cm \
in tensities
o f t he ground and
temperature a v i b r a t i o n a l
T h i s agr ee s v e r y w e l l
a t 157 cm
(12).
t h e p r e d i c t e d r an g e a l t h o u g h
with
f un dament al
No o t h e r fundament al
224 cm ^ i s f a i r l y
No a t t e m p t was made t o a s s i g n any l i n e s o f o t h e r e x c i t e d
D eterm in ation o f the R o ta tio n a l
C o n s t a n t s and C e n t r i f u g a l
from each r o t a t i o n a l
tran sitio n
constants.
chloride
the r e s u l t i n g
unsplit lin e
equation
req u ired to f i t
t he d a t a .
1
.
1 1
c o n s t a n t s and q u a r t i c c e n t r i f u g a l
, was a g a i n used;
no s e x t i c c o n s t a n t s were
c o n s t a n t s and a l l
fiv e quartic c e n t r if u ­
d i s t o r t i o n [ . c o n s t a n t s . For t h e HCCCO^Cl and DCCCO^Cl
t h e r e were i n s u f f i c i e n t d a t a a v a i l a b l e
I n t hes e l a t t e r
excited
states,
to perform c e n t r i f u g a l
two cases t h e d i s t o r t i o n on each l i n e
was assumed t o be t h e same as t h a t c a l c u l a t e d
state tra n s itio n ,
Ir
For most s p e c i e s s t u d i e d t he d a t a were used to
o b ta in values f o r the r o t a t i o n a l
d is t o r t io n analyses.
frequencies
The A r e d u c t i o n o f Wat son' s H a m i l t o n i a n i n t h e
representation,
resulting
D istortion
A f t e r t h e h y p e r f i n e s t r u c t u r e was s u b t r a c t e d
were used t o c a l c u l a t e t h e r o t a t i o n a l
however,
states.
was ac count ed f o r usi ng t h e c h l o r i n e q u a dr u p o l e c o u p l i n g
constants o f Table 5 . 4 .
distortion
close
>
The h y p e r f i n e s t r u c t u r e o f t h e v a r i o u s p r o p i o l y l
transitions
was
t he measured
C o ns t a n t s
gal
These were
i s o t o p i c s p e ci e s and en ab l e d some f u r t h e r a s s i g n ­
f r e q u en c y o f t h e Vg f un dament al
lies w ithin
species.
f o r t h e c o r r e s p o n d i n g ground
and was s u b t r a c t e d f rom t h e measured f r e q u e n c i e s ;
f r e q u e n c i e s were f i t
t o the t h r e e r o t a t i o n a l
constants.
t he
158
A summary o f t h e “ observed"
transitions
tran sitio n
f r e q u e n c i e s and c e n t r i f u g a l
f r e q u e n c i e s o f t h e measured
t o g e t h e r w i t h t he c a l c u l a t e d
d isto rtio n
c o n s t a n t s and c e n t r i f u g a l
are given in Table 5 . 2 .
I
lin e
i s presen ted in T a b le 5.1
determined r o t a t i o n a l
N
unsplit
corrections.
The
d i s t o r t i o n constants
159
Table 5.1
Observed R o t a t i o n a l
Transition
HCCC08 8 C1
3
0,3
5
1,4
5
3,3
- 2
0,2
-
4
-
4
"
5
1 ,5
1,3
3,2
6
1, 6
6
1 ,5 ‘
5
1 ,4
6
2,5 "
5
2,4
6
2 ,4 *”
5
2,3
6
3,4 ”
5
3,3
6
3,3 "
5
3,2
6
1, 6
"
5
0,5
7
1, 6
"
6
1 ,5
7
2,6 '
6
2,5
?3 , 5
‘
6 3 , 4
? 3 « 4
"
7
Transitions
Observed
Frequency
(ground v i b r a t i o n a l
4,3
3,4
7
1,7
"
7
0,7
1 ,7 “
7
2,6
8
1,
8
1, 8
8
8
o
*
*
00
'
O
1
7
Deviation
15422.13
-0.08
-0
28253.37
-0.63
-0.05
27062.95
-0.24
0.04
28261.22
-0.28
-0.04
33278.70
-0.91
3134.1.46
-0.58
-
34666.16
-1.33
-0.07
32497.22
-0.62
-
33252.92
-0.90
-0.03
29075.06
-0
37944.99
-1.14
0.04
36214.00
-0.89
0 . 0 1
37873.60
-1.14
0 . 0 2
0 . 0 2
0 . 0 2
0 . 0 1
. 1 2
0 . 2 0
. 0 0
-
0 . 0 2
0.04
2,5
•Vj
CD
'
D istortion
Correction
Chloride
state)
17312.08
7
(MHz) o f P r o p i o l y l
29105.35
-1.34
0 . 0 2
37251.45
-0.56
0.03
37140.16
-0.59
-0.06
37355.33
-0.47
0.04
38796.04
-2.33
0.04
31381.27
-4.12
0 . 0 1
1 60
T a b l e 5.1
(continued)
Transition
HCCC038C1
*
C\J
00
in
CO
00
1
82,7
-
3,6
i
m
*
ro
00
CO
92,8 '
(ground v i b r a t i o n a l
CO
0
00
r-^
1
00
•
8 3,6 '
8 4
/> , 5c
Observed
Frequency
9 1 ,9
9 3,7 " 92 ,8
93 ,6 ‘
92,7
101 , 9 '
1 0 1 , 10
1° 2 , 8 " 1 0 1 , 9
] 1 2 ,9 " 111,10
1^ 4 , 8 '
]1 3,9
T15 , 6 -
1 ]4,7
12 4 , 8 " n 5 , 7
•
123 , 9 " 12 2 , 1 0
135,8 '
14 3,11
134 , 9
‘
143 , 1 2
1 4 5 , 9 " 144 , 1 0
‘
Deviation
state)
29541.94
-2.90
-0.02
28813.10
-1.85
-0.04
16954.97
-0.11
0.02
32032.24
-2.16
-0.04
27423.15
-0.12
0.04
35659.32
-2.68
0.00
31534.94
-2.77
-0.02
17688.25
-1.30
0.04
39198.13
-4.41
0.01
29159.19
-7.33
0.01
34607.49
-9.36
-0.00
36028.24
-4.17
0. 01
35100.25
1.50
0.00
34666.84
-14.20
0. 01
27 68 9 .1 1
-12.11
0.05
30293.78
6.19
0. 01
♦
1 4 3 , 1 1 " 14 2 , 1 2
154, 11
D istortion
Correction
15 3 , 12
\
38123.23
-23.72
-0.03
38913.77
-21.48
0. 01
28405.37
5.62
0.Q2
31099.80
-22.69
0.01
161
T a b le 5.1
(continued)
Transition
HCCC038C1
15 5 , 1 0 '
Observed
Frequency
(ground v i b r a t i o n a l
154 , 11
156 , 9 ‘
14 7 , 8
164 , 1 2 '
16 3 , 1 3
165, 11
'
164 , 1 2
175 , 1 2 '
174 , 1 3
176, 11
'
175,12
185 , 1 3 '
184 , 14
186 , 1 2 '
185,13
\
O
*
00
00
206,14 '
205,15
HCCC035C1
( v„
J
6 1,5 " 51 ,4
6 2 , 4 " 52 , 3
63 , 3 " 53,2
72 ,6 “ 62,5
73 ,4 " 72 ,5
0
70 , 7
8 3,5 " 82,6
1 ]4,8 " 1 ] 3,9
1
Deviation
s t a t e ).
27570.16
1.46
0.01
27673.54
-9.29
0.05
3 6 5 29 . 5 2
-32.50
0.03
28174.53
-6.97
-0.01
3 0 4 1 8 , 62
-19.81
-0.01
34636. 11
15.24
-0.00
34294.39
-35-16
-0.02
32962. 61
9.42
-0.02
• 36321.78
-21.78
-0.03
34165. 71
-24.00
0.00
1 excited vib ra tio n a l
state)
33332. 71
-0.83
0.03
34753.68
-1.25
-0.03
33337.35
-0.81
0.02
36267.03
-0.77
-0.03
17265.02
0.17
0.00
37279.27
-0.52
-0.00
37170.36
-0.55
-0.04
37380.14
-0.43
0.05
1 6 9 3 9 . 57
-0.15
0. 01
36094.39
-4.11
0.00
0*
1
00
o
CO
- 8 1 ,8 " 71 ,7
8 1 ,8 ‘
=
D istortion
Correction ,
1 62
T a b l e 5.1
(continued)
Transition
HCCC035 C1
13
5,8
-
13
Observed
Frequency
(v„ *
J
4,9
155 , 1 0 " 154 , 11
165 , 1 1 ‘
164 , 12
175 , 1 2
'
174 , 1 3
176 , 1 1 '
175 , 1 2
186 , 12 ‘
1 85 , 13
1^ 6 , 1 3 " 195 , 14
206 , 1 4 " 2 0 5 , 1 5
HCCC037C1
5
* H ,4
4
4 1,3
60 , 6 " 50 , 5
6 1 ,6 '
5 1 ,5
6 1 ,5 '
5 1 ,4
62,5 " 52,4
62,4 '
52 , 3
63,4 “ 53,3
6 1 , 6 " 50 , 5
7 a <7 * 6 a <•
0,7
0,6
7 1 , 7 " 6 1 ,6
1
1 excited vib ra tio n a l
D istortion
Correction
Deviation
state)
30136.37
6.05
-0.01
27527.17
0.96
0.00
28243.55
-7.64
- 0-.04
30619.49
- 20. 5-3
0.03
34426.43
14.64
-0.00
32842.36
8.39
0.02
32717.54
-5.06
o.oo.
3434 0 :1 1
-25.68
-0.01
27716.53
-0.62
-0.03
28149.22
: 0.28
0.05
27757.83
-0.29
-0.02
32666.33
-0.91
-0.01
30755.84
-0.56
0.04
33963.76
-1.30
-0.01
31863.00
-0.56
0.09
28596.52
^0 .11
0.02
32361.13
-0.40
0.04
32140.30
-0.43
-0.03
(ground v i b r a t i o n a l
state)
*>
1 63
T a b le 5.1
(continued)
Transition
HCCC08 7 C1
Observed
Frequency
( gr ou nd v i b r a t i o n a l
7 1 , 6 " 6 1 .5
72 , 6 " 6 2 ,5
6 3,3
7 1 »6 “ 6 2 , 5
?3 , 4 '
72,5
74 , 4 " 7 3 , 5
74 , 3 ” 7 3 , 4
"
1
00
o
00
70 , 7
8 1 , 8 ■ 7 i ,7
84 , 5 " 8 3,6
1
1
1
00
00
*
*
o
00
00
00
8 3,5
8 1 »‘7
72,6
7 1 .7
70 , 7
‘
90,9
92 , 8 '
9 1 »9
93,7 '
92 ,8
9 1,8
11 2 , 9
«1 2 a
Deviation
state)
37270.77
-1.14
0.04
35546.13
. -0.87
0.02
38558.10
-1.75
0.08
31913.76 '
-0.56
0.01
31928.92
-1.96
-0.02
17 28 1 .1 1
0.31
0.04
31376.17
. -2.27
0.00
29048.37
-1.34
0. 11
36600.92
-0.57
-0.13
36485.07
-0.61
31797.02
-2.04
0. 01
27430.51
-0.05
-0.07
3 6 3 7 4 . 41
-0.71
-0.06
36711.66
-0.47
-0.01
37959.35
-2.40
-0.04
33757.47
-3.53
-0.03
35 01 5 .1 1
-2.51
-0.03
31055.48
-2.53
-0.00
33741.53
-9.24
-0.03
• 33076.32
-14.04
0.03
6 1 >6
St
O
I
73 , 4 ‘
D istortion
Correction
o
^ l.lO
- 1 V 7
-
-^02
164
T a b l e 5.1
(continued)
Transition
Observed
Frequency
Deviation
D istortion
Correction
w
HCCCC037C1
(ground v i b r a t i o n a l
state)
< '
133 , 1 0 " 132, 11
154, 11
" 153,12
164 , 1 2 " 16 3 , 1 3
1 7 5 , 1 2 " 17 4 , 1 3
185,13 '
184 , 1 4
186 , 1 2 " 185 , 1 3
196 , 1 3 “ 195 , 1 4
206 , 1 4 ‘
71,7 '
61,6
70 , 7 '
60 , 6
30143. 61
-21.48
0.02
35329.74
-31.54
0.02
29721.53
-17.05
-0.04
33242.33
-33.35
33008.99
12.98
32450.44
1.04
/
-0.03
.
0.00
0 .0 2 *
-18.48
(v n = 1 excited vibrational
J
0.00
state)
32168.07
-0.42
-0.05
32385. 71
-0.44
36628.65
-0.57
-0.04
36514.92
-0.62
0.02
36407.26
-0.72
0.03
27220.32
-0.29
0.01
31431.45
-0.87
-0.04
29565.57
-0.57
-0.03
'
0.04
*
1
1
00
CO
*
00
CO
0.02
»
80 , 8 “ 70 , i
o
-16.72
33520.17
205,15
HCCC037 C1
32125.13
ft
DCCC035C1
60 , 6 '
(ground v i b r a t i o n a l
50 , 5
6 1 ,5 " 51 ,4
6 2 , 5 " 52 , 4
--- ------- —
r
■■
—
state)
*
•r*
165
T a b l e 5.1
(continued)
Transition
DCCC088 C1
Observed
Frequency
( ground ' v i b r a t i o n a l
62,4 " 52,3
70 , 7 ‘
60,6
'
? 1 ’ 7 " 6 1 ,6
7 1 >6 ‘
6 1 »5
.
72 ,6 “ 62,5
73,4 “ 63,3
7 1,7 -
60 , 6
7 2 , 6 " 7 1 »7
72,5
70 , 7 ‘
6 1 *6
00
*o
CO
1
73,4 ‘
?0 , 7
'
i
00
00
o
<0
7 1 »7
7 0 ,7
90 ,9 " 80 ,8
92,7 '
8 3,6
93 , 7 “ 9 2 , 8
95 ,4 ‘
state)
32426.90
-1.20
.-0.09
31286.97
-0.42
0.02
31028.19
-0.45
35957.32
-1.15
34 20 5 .01
-0.88
0.03
3 67 37 . 71
-1.63
0.06
31578.78
-0.30
0.02
26517.39
-1.20
-0.00
17897.98
0.03
0.04
30736.36
-0.57
0.01
35376.25
-0.6K
0.02
35233.36
-0.64
35084.42
-0.74
$>525.23
-0.51
o.oi
39489.08
-0.85
-^09
35045.08
-5.15
Q. 05,
30367.90
-2.62
0.01
39408.38
-4.19
0.01* ‘
36649.99
-10.56
28519.27
4.02
,
0.02
'
0.04
•*
**
8 1,& ■ ? 1 ’ 7
v*t
61,8 '
Deviation
' D istortion
Correction
94,5
122 , 1 0 '
121,11
155 , 1 0 -
154, 11
•
-0.05
*
’
o.oi
-0.01
0.00
T a b le 5.1
(continued)
T ransition
PCCC038C1
Observed
F r eq ue n cy
(ground v i b r a t i o n a l
16 4 , 12 '
164 , 1 3
1 6 5,11
'
164 , 1 2
175,12 ‘
174 , t 3
176 , 11
'
175 , 1 2
185,13 '
184 , 1 4
18 6 , 1 2 '
185 , 1 3
195,14 '
194 J 5
19 6 , 1 3 '
195 , 1 4
206 ,1 4 '
205 , 1 5
DCCC035 C1
i
52 , 4
6
6
3,4
-
80 , 8 '
70,7
8 1 ,8 '
7 1 ,7
81 ,8 "
70,7
-25.29
-0.02
27899.78
-0.72
0. 01
28608.40
-9.35
37485,52
13 .51
-0.01
30801.18
-21.96
-0.02
’ ,
34464.80
33415.47V
-
33059.76
J
***
0. 01
S
\
2
'
13.26
-0.00
-37.75
0.00
7.53
-0.01
-4.69
0.02
2724 ^. 71
-0.29
0.06
29616.06
-0.J57
-0.01
30589.93
-0.63
-0.10
31311.83
-0.43
0,02
-0.88
0.03
36841.02
-1.63
0.05
35404.30
-0.61
-0.01
35264.57 .
-0.64'
-0.03
35548.60
-0.51
-0.01
34258.96
-
‘
state)
V
72 , 6 r 6 2,5
63,3
32007.70
35031.99
70 , 7 “ 6 0 , 6
73 , 4 '
state)
( v n = 1‘ e x c i t e d v i b r a t i o n a l
3,3
Deviation
f*'
60 , 6 ■" 50 , 5
62 ,5 '
D istortion
Correction
.
167
T a b l e 5.1
(continued)
Transi tio n
Observed
Frequency
D istortion
Correction
Deviation
*
DCCC087C1
( gr ound v i b r a t i o n a l
6 0 , 6 " 50 , 5
6 1,5 " 51,4
62,5 \
52 , 4
6 2,4 " 52,3
6 3 , 3 " 53 , 2
70 , 7 " 6 0 , 6
71,7 '
6 1 ,6
72,6 ‘
82,5
7 3^5 ~ 6 3 , 4
63,3
o
1
00
o
00
73,4 '
8 T , 8 ~ *7 1 ,7
8 1,8 ‘
70,7
83,5
**
82,6
90,9 '
80 , 8
9 0 , 9 " 8 1,8
#
10 2 , 9
122,10 '
12 1, 11
143,11
142 , ^ 2
26753.09
-0.22
30861.99
-0.79’
-0.01
2 9 0 2 6 . 61
-0.46
-0.02
31796.35
-1.08
0.00
30477.66
- 0 ; 65
-0.06
30749.08
-0.31
0.00
30486.19
- 0 ‘. 34
0.03
33587.34
-0.72
0.02
34930.36
-0.89
-0.02
36013.1T
-1.38
0.05
34766.45
-0.44
0.06
34619.95
-0.48
-0.04
34921.53
-0.33
-0.10
0.05
0. 01
17089.68
91 , 9 " 8 1,8‘
103,8 ‘
state)
*
,
*
'
0.06
38806.98
-0.62
38729.39
-0.65
38651.73 ,
-0.73
0.02
32634.75
-3.47
-0.04
35816.05
-10.38
-0.02
33761.33
-18.81
0.06
0.03.
"•
-0.03
168
(continued)
PCCC087C1
Observed
Frequency
(ground v i b r a t i o n a l
154 , 11
" 153,12
155 , 10
154 , 1 1
176 , 1 1
17 5 , 1 2
185 , 13 '
185,14
186 , 1 2 -
185 , 1 3
196 , 1 3 '
195,14
.
205,15 - 204,16
206 , 1 4 '
205,15
a Hypothetical
6.19
0.05
-15.00
0. 01
28446.86
5. 31
0. 01
28191.16
-7.20
-0.03
37 565 . 51
14.86
-0.06
30130.00
-19.56
-0.01
35074.66
15.54
0.00
33328.16
10.79
0.07
38179.02
-52.89
-0.00
27043.66'
175 , 1 2 - 174 , 1 3
unsplit
Deviation
state)
30153.18
U 5 , 9 ‘’ 144 , 1 0
D istortion
Correction
32754.35
cn
00
Transition
1
o
T a b le 5.1
-0.03
lin e frequencies.
*
r
1 69
Table 5 .2
R o t a t i o n a l C o n s t a n t s a nd C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s
o f P ro p io ly l C h lo rid e
HCCC035C1
«
Ground S t a t e
Vg = 1 S t a t e
A(MHz)
7190.0143(30 )a
7190.3397(90)
B(MHz)
3149.2440(10)
3158.1194(85)
C(MHz)
2186.7459(11)
2188.0389(66)
A^(kHz)
1.2066(69)
AJ K ( kHz)
AK( k H z )
1.171(60)
-4.790(28)
-5.30(39)
22.69(11)
24.0(15)
6 j ( k H z)
0 . 4 9 4 8 (”21)
0.463(19)
6K( kHz )
2.325(30)
2.91(33)
St d. D e v i a t i o n
o f F i t (MHz)
0.031
0.033
•-
No. o f T r a n s i t i o n s
t
r
(
50
18
170
T a b le 5.2
R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s
of P ro p io ly l C h lo rid e (continued)
HCCC037C1
Ground S t a t e -
Vg = 1 S t a t e
A(MHz)
7111.7135(87)
7113.41(79)
B(MHz)
3084.7668(30)
3093.18(21)
C(MHz)
2148.3505(20)
2149.635(30)
A j(kHz)
1.197(15)
b
AJK( k Hz )
-5.338(81)
b
AK( k H z)
23.86(41 )
b
6j(kHz)
0.4837
P
6k ( k H z )
2.19(10)
b '
St d. D e v i a t i o n ^
of F i t (MHz)
0.050
No. o f T r a n s i t i o n s
I
0.061
\
5
38
t
171
T a b le 5.2
R o t a t i o n a l C o n s t a n t s a nd C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s
o f P ro p io ly l C h lo rid e (continued)
DCCC035C1
¥
Ground S t a t e
Vg = 1 S t a t e
A(MHz)
7075.1763(54)
7072.40(21)
B(MHz)
2943.0992(34)
2951.8115(82)
C(MHz)
2075.4480(26)
2076.8132(55)
A j(kHz)
aj k (
kHz)
AK( k H z )
1.080(23)
b
-3.413(58)
b
20.73(25)
b
6j(kHz)
0.4174(44)
b
6 K( k H z )
2.501(70)
b
Std. D e v i a t i o n
o f F i t (MHz)
0.038
No. o f T r a n s i t i o n s
32
0.056
9
172
'T ab le 5.2
R o t a t i o n a l C o n s ta n ts and C e n t r i f u g a l D i s t o r t i o n C o n s ta n ts
o f P ro p io ly l C h lo rid e (continued)
3
PCCC037C1
Ground S t a t e
A(MHz)
6990.1164(88)
B(MHz)
2885.5642(39)
C(MHz)
2039.4673(30)
Aj(kHz)
0.99(25)
AJ K ( k H z )
-4.30(14)
AK( k H z )
24.06(68)
6j(kHz)
0.4042(62)
6 K( kH z )
2.45(11)
Std. Deviatio n
o f F i t (MHz)
0.047
3
No.
of Transitions
30
a Errors c i t e d are standard e r r o r s .
k C e n t r i f u g a l d i s t o r t i o n c o r r e c t w n s ^ a s s u m e d t o be equal
t h e c o r r e s p o n d i n g ground s t a t e .
\
to those o f
173
5.3
N u c l e a r Qu ad r up ol e C o u p l i n g
in P r o p io ly l
Chloride
The n u c l e a r q u ad r u p o l e h y p e r f i n e s t r u c t u r e o bs er ve d in t h e
rotational
1.20,
spect rum o f p r o p i o l y l
which g i v e s ,
to f i r s t
c h l o r i d e was a n a l y s e d u s i n g e q u a t i o n
order,
t h e n u c l e a r q u a d r u p o l e energy o f a
p r o l a t e a sy mme tr i c r o t o r h av i n g one q u a d r u p o l a r n u c l e u s .
values f o r the r o t a t i o n a l
was used t o p r e d i c t
constants
had been o b t a i n e d ,
sp ittin g s
a l m o s t e x c l u s i v e l y on e i t h e r
x j or
x KK '
dd
we re r e a d i l y e s t i m a t e d .
°f
An a n a l y s i s o f t h e
ground v i b r a t i o n a l
studied.
equation
DD
on x
aa
some t r a n s i t i o n s depended
x
CC
rough v a l u e s f o r t h e s e
These e n a b l e d assi gnment s o f F
quantum numbers and s u b s e q u e n t l y l e a s t squar es f i t s
the
this
t h e dependence o f t h e observed s p l i t t i n g s
anc* nxaa = x bb ” xc c '
parameters
When good
t o be made.
h y p e r f i n e s t r u c t u r e was p er f or me d f o r
s t a t e o f each o f t h e f o u r i s o t o p i c
No l i n e s which e x h i b i t e d
v e r y smal l
splittings
-
species
typically
l e s s t han 0 . 3 0 MHz <- were used t o d e t e r m i n e t h e c o u p l i n g c o n s t a n t s as
*
in
t hese cases i t was i m p o s s i b l e t o d e f i n e t h e magni tude o f t he s p l i t ­
tings accurately.
For t he t r a n s i t i o n s
used i n t h e a n a l y s e s t h e s t r o n g e s t
*
h y p e r f i n e components were t h e f o u r w i t h
aF
= aJ + 1 components were o b s er v e d .
H
aF
t h a t of- t h e second and f o u r t h .
the hyperfine patterns
p a i r s o f sta ggered,
a "doublet"
structure,
is
can t h e r e f o r e
none o f
t he weaker
E q u a t i o n 1 . 2 0 shows t h a t f o r
« x p e c t e d q u a r t e t t he s e p a r a t i o n o f t h e f i r s t
eq ua l
= aJ ;
t he
and t h i r d components should
Neglecting
intensity
variations
be c o n s i d e r e d as c o n s i s t i n g o f two
e q u a l l y spaced d o u b l e t s .
For f i t t i n g
p u rposes, when
was observed because o f i n c o m p l e t e l y r e s o l v e d h y p e r f i n e
t h e s t a g g e r i n g o f t h e p a i r s o f components was i g n o r e d - T h i s
e q u i v a l e n t t o a s s u m i n g ' t h a t t h e measured s p l i t t i n g
4
s e p a r a t i o n o f say t h e f i r s t * a n d
s ho ul d eqdal
the
"
third
h y p e r f i n e components. As a l t e r n a n t
174
components o f t h e obser ved t r a n s i t i o n s
was a r e a s o n a b l e p r a c t i c e .
frequencies,
had n e a r equal
in ten sities
this
I n T a b l e 5 . 3 t h e observed h y p e r f i n e component
F quantum numbers and o bs er ve d and c a l c u l a t e d s p l i t t i n g s
a r e given f o r s e v e ra l
transitions
used i n
the f i t s .
The v a lu es o b t a i n e d
f o r the n u c l e a r q u a d r u p o l e c o u p l i n g c o n s t a n t s a r e p r e s e n t e d i n T a b l e 5 . 4 .
A planar molecular s t r u c t u r e f o r p r o p i o l y l
one o f t h e p r i n c i p a l
v a l u es o f t h e q u a d r u p o l e t e n s o r .
v a l u e must be i n v a r i a n t t o t h e i s o t o p i c
chlorine.
Further,
chloride requires
the r a t i o
xcc(
35
37
C l ) must equal
o f the q u a d r u p o l e moments o f t h e two c h l o r i n e n u c l e i
37
xcc(
C o n se q u e n t l y
its
s u b s t i t u t i o n o f any atom e x c e p t
C1 ) / x c c (
data o f T ab le 5 .4 s a t i s f y these c r i t e r i a
t h a t xcc be
(=
the r a t i o
1.269
(24)).
*
'
35
( e x p e r im e n ta ll y xc c (
C l)/
*
C l)
= 1.279)
an d,
in f a c t ,
provide strong evidence fo r a p la n a r
molecular s t r u c t u r e .
•
The
i
Table 5 .3
R ep resentative P ro p io ly l C hloride T ra n s itio n s
(M Hz ) u s e d i n
the N u c le a r Q uadrupole C ou p lin g A na ly se s
F* 3
HCCC035C1
F 3
Observed
Frequency ,
:: Ground V i b r a t i o n a l
Observed
Spli t t in g
Calculated
Spli t t i n g
State
5 33 ‘ 4 32
4.5
27061.58
. -1.39
-1.39
4.5
3.5 1
27062.35
-0.62
-0.62
6.5
5.5
27063.75
0.78
0.79
3.5
4.5
27064.55
1.58
1.56
532 " 4 31
'*
5.5
4.5
27365.95
-1.21
-1.22
4.5
3.5
27366.65
-0.51
-0.52
6.5 4
5.5
27367.85
0.69
3.5
4.5
27368.52
1.36
6.5
6.5
29539.16
- -2.78
-2.76
9.5
9.5
2 9 5 4 0 . 01
-1.93
-1 .9 4
7.5
7.5
29543.79
1.85
1.84
8.5 .
8.5
29544.62
2.68
2.67
6.5
6.5
28811.38
-1.72
-1.72
9.5
9.5
28811.90
-1.20
-1.20
7.5
7.5
28814.24
1.14
1.14
8.5
8.5
28814.76
1.66
1.66
0.68
J
1.38
1
00
o
00
00
5.5
8 36 ‘ 8 27
a
*
He re F and F
respectively.
a r e t he l a b e l s
fo r the i n i t i a l
and f i n a l
states
1 76
Table 5 .3
t
R ep resentative P ro p io ly l C h lo rid e T ran s itio n s
(M Hz ) u s e d i n
th e N u c le a r Q uad rupole C o u p lin g Analyses
1
F
F
Observed
Frequency
Observed
Spl i - t t i n g
Calculated
Spli t t i n g
9 28 “ 9 19
35657.13
-2.19
-2.21
10.5
10.5
35657.72
-1.61
-1.61
8.5
8.5
35660.86
1.54
1.55
9.5
9.5
35661.46
2.14
2.14
8.5
8.5
39196.00
-2.13
-2,13
11.5
11.5
3 919 6 .51
-1.62
-1.60
9.5
9.5
39199.70
1.57
10.5
10.5
39200.22
2.09
2.08
o
7.5
0
<£>
1
7.5
,10
HCCC037C1
9 18 '
ft
: Ground V i b r a t i o n a l
.
'
‘1 . 5 5
State
9 09
7.5
7.5
3 3 75 5 .7 1
-1.82
-1.83
10.5
10.5
33756.16
-1.37
-1.33
8.5
8.5
33758.81
1.28
-1.28
9.5
9.5
33759.33
1.80
1.78
t
9 28 " 9 19
7.5
7.5
3 501 3. 41
-1.71
-1.68
10.5
10.5
3 50 13 . 91
-1.21
-1.22-
8.5
8.5
35016.32
1.20
1.17
9.5
9.5
35016.74
1.62
1.63
*
,
Table 5 .3
R ep resen tative P ro p io lyl C h lo rid e T ra n s itio n s
(M H z ) u s e d i n
t h e N u c le a r Q uadrupole C o u p lin g A nalyses
1
F
F
Observed
Frequency
DCCC035C1 : Ground V i b r a t i o n a l
Observed
S plittin g
Calculated
S p littin g
State
P.
7 26 " 71 7
5.5
5.5
26514.49
-2.90
-2.91
8.5
8.5
26515. 41
-1.98
1.95
6.5
6.5
26519.25
1.86
1.82’
5.5 •
5.5
26520.14
2.75
2.78
10.5
10.5
36647.90
-2.08
-2.09
13.5
13.5 .
3 66 4 8 . 2 9
-1.69
-1.65
11.5
11.5
36651.63
1.65
12.5
12.5
36652.04
2.06
122 , 1 0 " 1 2 1 ,11
DCCC037C1 : Ground V i b r a t i o n a l
1.61
•
2.06
State
1038 " 1029
“8 . 5
8.5
32633.46
-1.29
-1.29
11.5
11.5
32633.76
-0.99
-0.97
9.5
32635. 71
0.96
0.94
10.5
32636.01
1.26
1.26
9.5
*
*
10.5
122 , 1 0 '
1 2 1 ,11
j
10.5
10.5
35814.49
-1.56
-1.56
13.5 '
13.5
35814.80
-1.25
-1.23
11.5
11.5
35817.27
1.22
1.20
12.5,
35817.57
1.52
1.54
12.5
'
/
Table 5.4
C h l o r i n e N u c l e a r Qu ad ru p o l e C oupl ing C o n s t a n t s o f P r o p i o l y l
Chloride
Species
Xa a ( M H z )
HCCC035C1
xc c (MHz)
* b b (MHz)
*
-2 0.56(6)a
-3.21(8)
Cl
-16.80(12)
-1.68(13)
d c c c o 35 c i
-16.43(15)
-7.20(18)
23.63(18)
d c c c o 37 c i
-14.43(32)
-4.14(33)
18.57(33)
HCCCO
37
23.77(8)
-
18.48(13)
a Errors c it e d are standard e r r o r s .
\
*
t
*
I
1 79
5.4
T h e D i p o l e Moment o f P r o p i o l y l C h l o r i d e
A d e t e r m i n a t i o n o f t he d i p o l e moment o f an a s y m m e t r i c _ r o t o r by
means o f t h e S t a r k e f f e c t r e q u i r e s
d ent on a l l
t h e measurement o f S t a r k s h i f t s
n o n - z e r o d i p o l e moment components.
For p r o p i o l y l
o b s e r v a t i o n o f s t r o n g a - and b - t y p e t r a n s i t i o n s
were both n o n - z e r o .
z e r o , h o we ve r,
The
yc
b ec^se of
depen­
c h lo r id e the
indicated th at
y
3
and
y.
D
component o f t h e d i p o l e moment i s n e c e s s a r i l y
t h e mol eci i. l e' s p l a n a r s t r u c t u r e .
When measuring t h e d i p o l e moment o f a m o l e c u l e c o n t a i n i n g a
q u a d r u p o l a r nucl eus
s p littin g
i s 'small
it
•*
- 4
i s d e s i r a b l e t o use t r a n s i t i o n s whose h y p e r f i n e
compared t o t h e obs er ve d S t a r k s h i f t s
t he s e p a r a t i o n between i n d i v i d u a l
S t a r k components.
and a l s o
to
Because i n t e r f e r e n c e
between t h e S t a r k components o f n e i g h b o u r i n g l i n e s s houl d a l s o be
avoided,,
t h e r e were few s u i t a b l e c a n d i d a t e s f o r S t a r k e f f e c t measurements
i n t h e dense p r o p i o l y l
tran sitio n s,
«
c h l o r i d e sp ec t ru m. The 3q^ «-
which have S t a r k s h i f t s
2 ^
and
6 2 4
6
^
s t r o n g l y dependent on both .y, and
3
«
y^,
3
were s e l e c t e d f o r t h i s
q3
2
q2
tran sitio n
purpose;
t h e low f r e q u e n c y component o f
and t h e two s t r o n g e s t
6 2
^ •*-
6
^
the
components* w e r e '
measured.
The S t a r k e f f e c t can Be q u i t e c o m p l i c a t e d when a n u cleus w i t h
■
/
*
q ua dr up ol e c o u p l i n g i s p r e s e n t . T h i s i s t r u e e s p e c i a l l y when t he S t a r k
and q u a d r u p o l e e n e r g i e s a r e s i m i l a r ,
must be s o l v e d
(25).
These d i f f i c u l t i e s
q u ad r u p o l e e n e r g y i s small
fie ld
i n which case s e c u l a r e q u a t i o n s
a r e l a r g e l y a l l e v i a t e d when t h e
compared 1 t o t h e S t a r k e n e r g y ;
in th is^ stro n g
l i m f t n u c l e a r s p i n - r o t a t i o n d e c o u p l i n g i s o bse r ve d and t h e b y p e r -
1
'
<s
'
/
*
1
V
180
i
fine s p littin g
can be t r e a t e d as a p e r t u r b a t i o n on t he S t a r k e n e r g i e s .
Howe and F l y g a r e have d is cu s s e d t h e e v a l u a t i o n o f t h e q u ad r u p o l e
energies
i n t h e h ig h f i e l d
components may be s p l i t
lim it
(26);
t h e y showed t h a t t h e S t a r k
t o g i v e h y p e r f i n e components f o r each
2
p o s s i b l e v a l u e o f M j , where Mj
is
Further,
t h e av e ra ge o f t he Mj = + / 1 / 2 and
f o r t he
Mj = + 3 / 2
I = 3/2 case,
t h e s p a c e - f i x e d component o f _I_.
h y p e r f i n e component f r e q u e n c i e s
i s t h a t which would be
observed f o r a m o l e c u l e w i t h o u t q u a dr u p o l e c o u p l i n g .
Therefore,
t h e s e a v e r a g e f r e q u e n c i e s , when e x t r a p o l a t e d t o z e r o f i e l d ,
the hypothetical
unsplit lin e
This strong f i e l d
chloride
Stark
frequency o f the t r a n s i t i o n
give
studied.
case o b t a i n e d f o r a l l measured p r o p i o l y l
sh ifts;
t h e S t a r k components.
no h y p e r f i n e s t r u c t u r e was obse r ved f o r any
of
The S t a r k d a t a were t h e r e f o r e t r e a t e d as i f
no q u a d r u p o l a r n u c l e u s were p r e s e n t .
When p e r f o r m i n g ’S t a r k e f f e c t measurements t he e l e c t r o d e
sp ac i n g and t he a p p l i e d v o l t a g e must both be measured p r e c i s e l y .
The
e l e c t r o d e spaci ng can be d e t e r m i n e d by o b s e r v i n g t h e S t a r k e f f e c t o f a
m o l e c u l e whose d i p o l e moment i s a c c u r a t e l y known; u s u a l l y c ar bo nyl
s u l p h i d e i s chosen.
♦
moment o f c ar bo nyl
Very a c c u r a t e measurements o f t he e l e c t r i c
s u l p h i d e have been made by Muent er ( 2 7 ) and by
R e i n a r t z and Dymanus ( 2 8 )
spectroscopy;
dipole
u si ng m o l e c u l a r beam e l e c t r i c
t he v a l u e o f Muent er
( 0 . 71 52 1
(20)
For t he S t a r k measurements a p o t e n t i a l
r esonance
Debye) was used h e r e .
V was o b t a i n e d by
mixing a la rg e
D C ' v o l t a g e and a s m a l l ,
f l o a t i n g AC v o l t a g e as d e s c r i b e d
in Chapter 2.
The AC v o l t a g e was a 100 kHz square wave o f peak t o
peak
181
amplitude 2 V ^ ;
the signal
c o n s i s t e d o f two l o b e s
and VQ£ -
2
value o f E
observed f o r each S t a r k component t h e r e f o r e ,
( h a v i n g o p p o s i t e phases) a t
respectively.
If
potentials
of
+
d i s t h e e l e c t r o d e s p a ci n g t hen the
which c or r es p o n d s t o t h e mean f r e q u e n c y o f t h e s e two l obes
i s g i v e n by:
[ 2 = (VDC + VAC) / d 2
=
v2/cj2
(5 J )
The use o f t h e s e mean f r e q u e n c y s h i f t s o b v i a t e d t h e need f o r a p r e c i s e
determination
of
a strong signal
because t h e m o d u l a t i o n v o l t a g e r e q u i r e d t o produce
was al ways small
compared t o t he DC b i a s v o l t a g e .
The second o r d e r S t a r k e n e r g y o f a l i n e a r m o l e c u l e such as
OCS i s g i v e n by ( 2 9 ) :
E
=
J W )
S
2hB
-
3M2
_
J ( J + 1 ) ( 2 J - 1 ) ( 2 J+ 3)
(5.2)
*
\
where B i s t he r o t a t i o n a l
constant.
component o f t h e J=l«-0 t r a n s i t i o n
The S t a r k s h i f t o f t h e l o n e M=0
is
2
= (0.50348)2
Av
thus
2
(5.3)
\
158
d
W i th B i n MHz, u i n Debye, d i n cm and V i n v o l t s t h e c o n v e r s i o n f a c t o r
0 . 5 0 3 4 8 MHz Debye"^ v o l t " ^
cm g i v e s A v i n MHz; t h i s v a l u e g i v e s con­
s i s t e n c y w i t h t h e r e s u l t s o f Muent er ( 2 7 ) .
2
versus V
should g i v e a s t r a i g h t l i n e
a ltern atively ,
a p l o t o f Av
passing throOgh t he o r i g i n o r ,
2
a p l o t o f t he observed f r e q u e n c i e s v e r s u s V
give a lin e with
fie ld
Therefore,
t he i d e n t i c a l
f r e q u e n c y Vq .
should
s lo pe b u t w i t h t he i n t e r c e p t a t t h e z e r o
The c a rb o ny l
sulphide c a l i b r a t i o n data a r e c o l l e c t e d
182
in Table 5 . 5 ;
was k e p t a t 20 v o l t s
least
of this
squares f i t
calculated
fie ld
(31)
intercept
is
The
the published zero
Usi ng t h e v a l u e o f 6 0 8 1 . 4 9 MHz
from t h e l e a s t squares
cm.
The p r o p i o l y l
again,
MHz ( 3 0 ) .
A linear
o f Table 5 . 6 .
i n e x c e l l e n t agreement w i t h
t he e l e c t r o d e s p a ci n g c a l c u l a t e d
s l op e i s 0 . 4 6 8 9 0 ( 4 0 )
measurements.
d a t a gave t h e r e s u l t s
frequency o f .1 2 1 6 2 .9 7 9 (1 )
f o r B,
for a l l
c h l o r i d e S t a r k dat a a r e c o l l e c t e d
was k e p t c o n s t a n t a t
S t a r k s h i f t s were o b s e r v e d .
20 v o l t s .
In a l l
in Table
5.7;
cases second o r d e r
The assi gnment o f M v a l u e s f o r t h e
6 ^
6^
<-
t r a n s i t i o n was i m m e d i a t e l y o bvious because f o r a Q branch t r a n s i t i o n
i n t e n s i t y o f a g i v e n M component i s p r o p o r t i o n a l
2
to M
(32).
t h e s i n g l e 303 " 202 component as t he M = 0 t r a n s i t i o n ,
firs t
energies o f a l l .three 3 ^
squares a n a l y s e s o f
*■ 2 ^
t he d a t a o f T a b l e 5 . 7 a r e g i v e n
c h lo r id e can,
was
the Stark
in Table 5 . 8 .
in r e t r o s p e c t ,
a s c r i b e d t o t h e use o f an e x c e s s i v e m o d u l a t i o n v o l t a g e ,
least
The
be l a r g e l y
which u n n e c e s s a r i l y
lobes.
The second o r d e r e x p r e s s i o n s f o r t h e p r o p i o l y l
e n e r g i e s , e v a lu a te d using e q u a tio n 1 . 2 8 ,
c h lo rid e Stark
are :
A v ( 3 Q 3 ,M=0
«-
2Q2,M=0)
=
(-1.2769
x
1 0 ' 6 u2 -
3.3736
x
1 0 ' 7y 2 ) E 2
A v ( 6 2 4 ,M=5
-
6 1 5 ,M=5)
=
(
1.1322
x
l ( f 6 p2 +
4.6451
x
10*6y2 )E2
A v ( 6 2 4 ,M=6
-
6 1 5 ,M=6) =
(
1.8425
x
1 0 ' 6 U2
+ 7.1915
x
1 0 ' 6 U2 ) E 2
Because t h e l a s t two e x p r e s s i o n s a r e a lm ost l i n e a r i l y
good s o l u t i o n s
it
components. The r e s u l t s o f l i n e a r
poorer data obtained f o r p r o p io ly l
broadened t h e S t a r k
To a s s i g n
however,
n e ce ss a ry t o e v a l u a t e t h e second o r d e r e x p r e s s i o n s f o r
the
to these equations are p o ssib le;
(5.4)
d ep e n d e n t , o n l y two
t h e s e a r e o b t a i n e d by
183
s o lv in g sim ultaneously the f i r s t
equations.
F or t h i s
by t h e f a c t o r d
2
mean v a l u e s o f p
and e i t h e r o f t h e two r e m a i n i n g
purpose m u l t i p l y i n g
the slopes o f T ab le 5.8
gave t h e a p p r o p r i a t e v a l u e s o f
d
and p.
D
were 2 . 0 4 4 ( 3 )
Av / E
2
.
The d e r i v e d
Debye and 1 . 7 9 0 ( 1 4 )
Debye
respectively.
The s i m i l a r p
t h e 3q 2» M=0
2
2 q £ , M=0 S t a r k e n e r g i e s depend p r i m a r i l y on p . The
a
spread o f t h e p^ va l ues
error;
v a l u e s r e s u l t from t h e f a c t . t h at o n l y
is a b e t t e r
i n d ic a t i o n o f the experimental
t h e somewhat a r b i t r a r y b u t r a t h e r
larger error
t o both pfl and p^ a r e + 0 . 0 2 5 Debye g i v i n g 2 . 7 1 7 ( 3 5 )
total
d i p o l e moment p.
l i m i t s assigned
Debye f o r t h e
A summary o f t h e e x p e r i m e n t a l
v a l u e s o f Av/E
t o g e t h e r w i t h t h os e c a l c u l a t e d u s i n g t h e d e r i v e d v a l u e s o f pfl and p^
i s g i ve n
in Table 5 .9 .
magnit udes o f p
results
are
a
It
and p.
D
shoul d be emphasized t h a t o n l y t he
have been d et e r m i n e d f rom t h e S t a r k e f f e c t ;
i n agreement w i t h t h e r e l a t i v e
type sp e c tra .
intensities
t he
o f t h e a - and b-
184
Table 5 .5
Stark S h ifts
1n Carbonyl
Sulphide:
Transition:
10
-2
2
x AT
J = 1
' 16o 12c 32s
0
a
Observed Frequency
Obs.-Calc.
^Frequency
0
12162.970
-0.016
29
12163.070
0.0 09
104
12163.260
0 .0 0 6
229
12163.580
0 . 001
404
12164.035
0.004
904
12165.330
0.0 06
1604
12167.135
0 . 001
2504
12169.460
0.002
3604
12172.305
-0.001
4765
12175.290
-0.019
6088
12178.695
-0.035
7573
12182.605
0.035
9220
12182.605
0 .0 61
11029
12186.890
-0.047
a Given 1n MHz .
^ C a l c u l a t e d u sing t h e c o n s t a n t s o f T a b l e 5 . 6 .
185
Table 5 .6
C e ll C a l i b r a t i o n w it h Carbonyl S u lp h id e :
Transition:
Av/V2
V
d
0
^W
J * 1 «- 0
2 . 5 8 6 0 ( 2 1 ) a x 10- 5
MHz V " 2
12162.986(10)
' MHz
0.46890(40)
cm
a Errors c i t e d are standard e r r o r s .
m
2S
186
Table 5 .7
Stark S h ifts
in P ro p io ly l
C hloride
: HCCCO^Cl
i
Transition
10
-2
2
x V-
c
M = 0
2^,
Observed . Freq ue n cy2
M = 0
Obs. - C a l c .k Frequency
i>
15422.13°
0 . 07
2504
15 41 4 .9 3
0. 18
3029
15 41 3 .2 4
0 . ,02
3604
1 5 4 1 1 . 34
- 0 . ,20
4036
15410.28
0. ,00
4100
1 5 4 1 0 . 06
- 0 . ,04
4493
1 5 4 08 . 7 9
- 0 . ,16
4904
15407.68
- 0 , ,07
5333
15 40 6 .4 9
- 0 , ,01
5644
15405.59
0. ,00
6277
15403.78
0. .03
6565
15402.94
0, .04
6943
15401.91
■ 0. .11
7400
15400. 51
0, .04
0
.
187
Table 5.7
Stark
Shifts
in P r o p io ly l
________________________
-2
x r
2
: HCCCO.^Cl
n____________________________________
Transition 6 .^ ,
io
Chloride
M = 5 «- 6 ^ ,
Observed Frequency3
12947.82°
0
M = 5
Obs. - C a l c . * 3 Frequency
-0.23
2029
12966.05
0. 11
2213
12967.65
0.07
2504
12970.35
0.20
2605
12971.09
0.05
2920
12973,88
0.06
3029
12974.83
0.04
12976.65
-0.11
3604
12979.88
0.02
4229
12985.48
0.10
4904
12991.05
-0.28
3253
'
*
188
Table 5.7
S t a r k Shi f t s
in P ro p io ly l
Chloride
: HCCC035C1
%
X
O
1
ro
T ran si t i o n
V2
6 2 4
>M =
6
«-
6
^ ,
Observed Frequency3
t
M = 6
O b s . - C a l c . k Frequency
/
•
0
\
-0.02
12947.82°
1604
12970. 61
0.12
1768
1 2 9 7 2 . 89
0.09
1940
12975.10
-0.13
2120
12977.83
0.05
12982.82
-0.38
1 2 9 8 6 . 35
0.27
'■
2504
2708
3 Given i n MHz .
b
Calculated
using t h e c o n s t a n t s o f T a b l e 5 . 8 .
c Hypothetical
un sp lit-lin e
i
f r eq u e n c y o f the z e r o - f i e l d
transition .
1
189
Table 5 .8
Stark C o e ffic ie n ts o f P ro p io ly l C h lo rid e
3
10J
Transi t io n
30 3 . M = 0
624, M = 5
62 4 , M = 6
20 2 *
" 6 15 ’
^ 6 15 r
Av/V
-2.918(14)C
M = 5
8.826(39)
M = 6
14.12(1)
CNJ
o
1
+->
ft
k Given i n MHz
c E rro rs c it e d are standard e r r o r s
I
2 3
M = 0
>
3 Measured i n MHz
X
: HCCCO^Cl
b
vo
15422.06(7)
12948.05(12)
12947.84(21)
1 90
T a b le 5.9
T h e D i p o l e Moment o f P r o p i o l y l
C hloride
5
2
1 0 3 x Av /E^
Transition
----------------------------------------------------------Observed
3
03’ ^
^ ^
^02’
*
M = 0
-0.642
6 24* M = 5 «- 6 ] 5 , M = 5
1.941(9)
1. 961
6 24* M = 6 ^
3.104(23)
3.074
6 1
5, M = 6
u
-
a
= 2 . 0 4 4 ( 2 5 ) c Debye
Ub = 1 . 7 9 0 ( 2 5 )
Debye
u = 2.717(35)
Debye
;
a Measured i n MHz v o l t ^ cm^
b S t an d ar d e r r o r s
c Assigned e r r o r s .
I
-0 .642(3)b
Calculated
See t e x t
191
5.5
The E f f e c t i v e S t r u c tu r e o f P r o p io ly l C h lo rid e
The ground s t a t e p r i n c i p a l
moments o f i n e r t i a
and i n e r t i a l
1
defects o f the four
g iven
*r
is o t o p ic species o f p ro p io ly l
in Table 5.10.
The ground s t a t e
in e rtia l
p o s i t i v e numbers which show o n l y small
c h l o r i d e stu d ied are
d e f e c t s a r e smal l
i s o t o p i c v a r i a t i o n s and t h e r e ­
f o r e c o n f i r m t h a t t h e m o l e c u l e has a p l a n a r s t r u c t u r e .
The l i m i t e d
is o t o p ic data obtained f o r p r o p io ly l
chloride
p r e c l u d e d t he c a l c u l a t i o n o f a s u b s t i t u t i o n s t r u c t u r e .
Therefore,
an i n i t i a l
effective
structural
r e f i n e m e n t , a c r ud e ground s t a t e
geometry was c a l c u l a t e d .
V a l ue s f o r f i v e
bond l e n g t h s and f o u r a ng le s
ar e r e q u i r e d t o d e f i n e t h e s t r u c t u r e o f p r o p i o l y l
ang l es can be chosen as < ( H - C hC ) ,
no d e v i a t i o n
from l i n e a r i t y
r e a s o n a b l e t o assume t h a t
structural
< ( C eC - C ) ,
v a l u e s ' f o r t w e l v e ground s t a t e
c h l o r i d e molecule
(two f o r each i s o t o p e ) a r e
= 180°;
principal
this
independent.
a c e t y l e n i c mo l e c u l e s
were i n i t i a l l y
and < ( C - C - C 1 ) .
(19,33-44)
group i t
As
is
Table, 5.10 contain s
in ertia.
Because
however, onl.y e i g h t o f t h e se
T h e r e f o r e f u r t h e r assumpti ons
structure.
d i s t a n c e s have been found t o be n e a r l y
the four
r educes the number o f
moments o f
is p l a n a r ,
were r e q u i r e d t o d e r i v e a m ea n i n g f u l
(34)
< ( C - C= 0)
p a r am et e rs t o be d e te r m i n e d t o e i g h t .
the p r o p i o l y l
chloride;
has been found f o r an e t h y n y l
<(H-C=C)
in
S i n c e t he C-H and C=C
identical
i n a wide r a ng e o f
v a l u e s o f 1 . 0 5 7 + 0 . 002A and 1 . 2 0 6 + 0 . 003A
assumed f o r t h e s e bond l e h g t h s ;
do t h e C-H and C=C d i s t a n c e s
lie
only f o r flu o r o a c e t y le n e
o u t s i d e t h e s e r an g es .
Using t h e assumed e t h y n y l ' group geometry a s e r i e s o f e f f e c t i v e
s t r u c t u r e s were c a l c u l a t e d
s t r u c t u r e was s u b j e c t i v e ,
for propiolyl
chloride.
h o we ve r , because d i f f e r e n t
when e i t h e r t h e A and B o r ,
The c ho ic e o f " be s t "
r e s u l t s we r e o b t a i n e d
a l t e r n a t i v e l y , t h e B and C r o t a t i o n a l
constants
192
4
Tablb 5.10
Ground S t a t e
P ar am et e r
In e rtia l
Parameters3 o f P r o p io ly l
HCCC035C1
Chloride
HCCC037C1
►
70.28901( 3 ) b
■b
‘c
71.06290(9)
160.47^29(5)
163.83053(16)
231.11006(12)
235.24048(22)
,
'
'
0. 3 47 7 )4 ( 2 9 )
0.34477(13)
/
d c cco 35 c i
1°
a
■b
- dccco 37 c i
71.42988(5)
72.29908(9)
171.71660(20)
175.14045(24)
.
N
1°
c
A
0
•
-
243.50357(31)
247.79951(36)
0.35709(37)
0.35998(44)
......
a C a l c u l a t e d from t h e r o t a t i o n a l
constants o f T a b le 5.2 using a
Op
Op
c o n v e r s i o n f a c t o r o f 5 0 5 3 7 9 . 0 uA. . A l l p a r a m e t e r s g i v en a r e i n uA .
b E r r o r s quoted a r e s t a n d a r d e r r o r s .
193
w e r e used i n t h e f i t .
5.11
Th e re fo re the e f f e c t i v e
should be r e g a r de d w i t h det ac h men t;
s t r u c t u r e given
in T a b l e
i t 'was o b t a i n e d u si ng
the.
grotind s t a t e A and B r o t a t i o n a l c o n s t a n t s and assuming f u r t h e r
< ( C =C-C) = 180° and r ( C - C )
ethynyl
= 1 . 4 3 5 A. When o n l y
t he geometry o f t h e
group was c o n s t r a i n e d somewhat d i f f e r e n t
F o r example,
by f i t t i n g
r ( C = 0 ) and r ( C - C l )
t h e A and B r o t a t i o n a l
d i s t a n c e s o f 1 . 4 3 0 A,
that
r e s u l t s were o b t a i n e d .
constants
r(C -C ),
1 . 2 0 0 A and 1 . 7 6 4 A r e s u l t e d ;
r
t h e c o r r e s p o n d i n g v a l u e s d e r i v e d from a f i t t o t h e B and C r o t a t i o n a l
O
o
ot
c o n s t a n t s wer e 1 . 4 5 0 A, 1 . 1 8 8 A and 1 . 7 6 0 A. F u r t h e r c a l c u l a t i o n s
showed t h a t ,
w ith th e present data s e t ,
are highly c o rre la te d ;
jjjrobably a l l e v i a t e
the r ( C - C )
i s o to p ic s u b s t i t u t i o n o f the carbonyl
this d i f f ic u lt y .
In both o f t h e s e l a t t e r
v e r y s i m i l a r v al ue s were o b t a i n e d f o r t h e < (C=C- C)
to
t h e A and B r o t a t i o n a l
and C c o n s t a n t s
c o n s t a n t s and 1 7 9 . 3 °
fie ld
-
179.4°
f ro m t h e f i t
( h e r e ' a n a n g l e l e s s t ha n 180°
gr ou p i s b ent away f rom t h e C-Cl
i n propynal
and r ( C = 0 ) d i s t a n c e s
group would
refinements
from t h e f i t
to the B
i n d i c a t e s t h a t the ethynyl
bond and towar ds t h e C=0 bond whereas
t h e o p p o s i t e was observed ( 1 9 )
).
It
was f e l t
th at a force
r e f i n e m e n t and a v e r a g e s t r u c t u r e c a l c u l a t i o n would be u s e f u l
to
d e t e r m i n e w h e t h e r t h i s a p p a r e n t bend o f t h e c a rb o n c h a i n was an a r t i f a c t
caused by z e r o p o i n t v i b r a t i o n a l
described in the f o llo w in g
effects.
These c a l c u l a t i o n s
two s e c t i o n s o f t h i s
chapter.
*
I
are
194
Table 5.11
The E f f e c t i v e S t r u c t u r e o f P r o p i o l y l C h l o r i d e 3
P a ra me t e r
>
j
V a l ue
r (C -H )(A J^
U
*
'N; ;
1.056
•F
r Q( C = C ) ( A ) b
V- .•
1.208
■- i
r 0 (C-C)(A)b
1.435
4
r o(C =0)(A)
1.207
r0 (C-Cl)(A)
1.753
<(H- C=C) ( D e g . ) b
180.0
<(C=C- C) ( D e g . ) b
180.0
<(C-C=0)(Deg.)
124.9
< ( C - C - C 1) ( D e g . )
113.0
a O b t a i n e d by f i t t i n g
of T a b l e 5 . 2 .
b Assumed.
I
'
t h e greund s t a t e A and B r o t a t i o n a l
constants
195
5.6
The H a r m o n i c F o r c e F i e l d o f P r o p i o l y l Chi o r i c l e
The f o r c e f i e l d
refinement fo r p ro p io lyl
c h l o r i d e proceeded
i n a manner an al ogous to t h a t d e s c r i b e d p r e v i o u s l y f o r d i c h l o r o s i l a n e
( see Ch ap t er 4 ) .
Again,
t he d a t a p r o v i d e d by t he c e n t r i f u g a l
distortion
c o n s t a n t s were used t o augment t he a v a i l a b l e v i b r a t i o n wavenumbers.
The chosen n o n re dundant symmetry c o o r d i n a t e s , which t r a n s f o r m as 9 A 1 + 3A"
i n the p o i n t group Cs , a r e o i v en i n terms o f t h e i n t e r n a l
coordinates
in
t he c ar b o n y l
T able 5 . 1 2 ;
displacement
the t r e a t m e n t o f t he a n g u l a r redundancy a t
carbon f o l l o w s
t h a t used f o r f o r m i c a c i d
(45).
From t he i n f r a r e d
vibrational
although
spectrum o f the gas ( 1 2 ) a c omp l et e s e t o f
v
wavenumbers was a v a i l a b l e f o r normal, p r o p i o l y l c h l d r i d e
the a ss i gn me n t o f
uncertain.
Except f o r
V j ,
(Tl-C C i n p la n e bend) was c o n s i d e r e d
which showed a complex hot band s t r u c t u r e ,
t hese wavenumbers were used d i r e c t l y w i t h no c o r r e c t i o n s
b ei ng made; t he Raman l i g u i d
v a l u e was adopted f o r v-,.
f o r anharmonicity
Unfortunately,
■*
results
i
for propiolyl
c h l o r i d e - d were l e s s c l e a r c u t ,
weaker spectrum was o b t a i n e d .
For t h i s
and gas phase v a l u e s f o r vq and
c o r r e s p o n d i n g gas and l i q u i d
d iffe re n t
c ar d e d ;
the
instead,
A dditionally,
lower in
Raman l i q u i d
t h e normal
value f o r p r o p io ly l
(14).
Because the
sp eci es were q u i t e
c h l o r i d e - d was d i s ­
a v a l u e was t aken from t h e u l t r a v i o l e t
spectrum ( 1 5 ) .
f ° r t h e d e u t e r a t e d s p e c i e s was t ake n to be 2 cm~^
t h e gas than i n t he l i q u i d
species i s
s pe ci es v-jq was n o t observed
were u n a v a i l a b l e
v a lu es f o r
p a r t l y because a
( ob ser ved s h i f t f o r t h e normal
3 crrf^) an d, as f o r the normal
v a l u e was adopted f o r
v-j.
species,
t he Raman l i q u i d
Except f o r vg (D-C^.C i n p l an e bend) the
the
1
196
If
Table 5 .1 2
Internal
A'
I n t e r n a l C o o r d i n a t e s and Symmetry C o o r d i n a t e s o f P r o p i o l y l
C hloride
Coordi n a t e s : a
bl ock
*
r 1 = r ( C - H ) = 1.0 56 A
r 3 = r(C-C)
= 1.435 A
r 5 = r(C -C l)
«
02 -
= 1.7 52 A
<(C:C-C)
e4 = <( 0 = C- C1 )
A" b lock
a }
=
= 180°
= 113.0°
= 1.208 A
'
0
r 4 = r(C=0) = 1.207 A
0 1 = '(H-C=C)
= 180°
0 3 = <(C-C=0)
= 124.9°
0 C = < ( C - C - C l ), = 1 2 2 . 2
b
a 2 = < (H-C :C) * 1 80 °
6 (CC0C1)b
a 3 = <(C£C-C)
r 2 = r ( C C)
= 180°
Symmetry C o o r d i n a t e s :
A'
b l ock
s 1 = Ar]
52 = A r 2
5 3 = Ar 4
%
S4 = A r 3
S5 = A r 5
S6 = A01
S? = ( 1 / / ? ) ( A 0 3 Sg = ( T / / 6 ) ( 2 A 0 4 -
A05 )
>
A03 - a e 5 )
Sg ~ A02
b lo ck
S10 = Aa2
S11 = Aal
S i«
Aa^
a
The m o l e c u l a r s t r u c t u r e
k The i n t e r n a l
I
i s t he e f f e c t i v e
c o o r d i n a t e c*^ d e f i n e s
s tru c tu re of Table 5 .11.
t h e A" d e f o r m a t i o n o f t he CC0C1 g r ou p.
197
wavenumbers used f o r
t he r e m a i n i n g p r o p i o l y l
were t he r e p o r t e d gas i n f r a r e d
t o a band a t 522 cm ^ ( 1 4 )
F irstly,
this
w ell,
(14).
propiolyl
seemed u n l i k e l y
chloride
v a l u es ar e 2 0 - 2 5 cm
the f o r c e f i e l d
o f p l a n e bend)
(12)
f u n d ame n t al s
The p r e v i o u s a ss i gnment o f
band showed no a p p r e c i a b l e gas
whereas f o r normal
liq u id
v a lu es
chloride-d
for several
to l i q u i d
frequency s h i f t
and pr opynal
(46)
h i g h e r than t h e gas i n f r a r e d
calculations
r ea s o n s .
the Raman
values.
suggested t h a t vg and
As
(D-C C out
should be n e a r l y d e ge n e r a t e and should occur a t a somewhat
high er frequency.
( a ss i g n e d to v ^ )
N o t a b l y , a gas i n f r a r e d
is
band observed a t
seen in t h e l i q u i d a t 570 cm
shows'this behaviour;
tentatively
therefore
547 cm ^
No o t h e r band
\
and
have been t aken
t o be d e g e n e r a t e .
The f o r c e c o n s t a n t s o b t a i n e d
in Table 5 . 1 3 .
in t h e p r e s e n t a n a l y s i s a r e g i v en
Because o f the l i m i t e d d a t a a v a i l a b l e
the v a l u e s o f s e v e r a l
f o r c e c o n s t a n t s were f i x e d anJ o t h e r s were c o n s t r a i n e d
addition,
t he c o r re sp o nd i n g f o r c e c o n s t a n t s d e f i n i n g
o u t o f plane h’-C C arid C T - C
values obtained fo r
lig h t of results
phosgene ( 4 9 )
for
t he v a r i o u s
and f o r m i c a c i d
°-1
(45,50);
The
propyne
(48),
(C-C
however, a p p e a r low i n comparison to the
v a l u e o b t a i n e d f o r propyne ( 4 8 ) .
r eproduce s the observed d a t a .
t he v i b r a t i o n a l
(47),
the v a l u e o b t a i n e d f o r
T a b l e s 5 . 1 4 and 5 . 1 5 d emo ns t r at e how w e l l
fie ld
p la n e and
f o r c e c o n s t a n t s appear r e a s o n a b l e i n
t he r e l a t e d mo l ecul es a c e t y l e n e
5 . 5 0 mdyn A
the in
In
d e f o r m a t i o n s were assumed to be e q u a l .
s t re t c h in g f o r c e constant) does,
corresponding
to z e r o .
wavenumbers, w i t h
the presen t force
Tabl e 5 . 1 4 shows t h a t t h e f i t
t he p o s s i b l e e x c e p t i o n o f v g ,
is
for
198
Table 5 .1 3
The H a r m o n i c F o r c e F i e l d o f P r o p i o l y l C h l o r i d e
Speci es
Force C o n s t a n t s
A'
11
22
33
44
55
66
77
88
99
A"
10
11
= 5.943(94)
= 15.79(29)
= 12.70°
= 4.66(13)
0
= 1. 50
; F35
: 0.50
= 0 15
; F48
-0 .8 4 (5 )
;
= 0.844(27)
;
= 1.249(22)
;
F69.
F79
F89
= 0 096(20)d
= 0 040(8)
=- 0 If93(9)
= 0.218(9)d
J0
n
= 0.263(6)
; F 10 , 1 2
= 0.096(20)
= 0.689(15)
= 0.218(3)
i n mdyn A"
; stretch-bend
in teractio n
i n mdyn r a d ; a n g l e bending f o r c e c o n s t a n t s
i n mdyn
-2
Uncertainties
cant f ig u r e s .
1
F45
= 0.2 6 3 (6 )d
Bond s t r e t c h i n g f o r c e c o n s t a n t s
A rad
F34
= 3.03
12,12
force constants
;
c i t e d a r e s t an d ar d e r r o r s
in u n it s of th e l a s t s i g n i f i ­
199
Table 5.13
(continued)
c No e r r o r c i t e d
in d ic a te s a constrained force constant.
For ce c o n s t a n t s
n o t c i t e d were c o n s t r a i n e d t o z e r o .
d The c o r r e s p o n d i n g f o r c e c o n s t a n t s d e f i n i n g
t h e A 1 and A" H-CsC and
C C-C d e f o r m a t i o n s were assumed t o be e q u a l .
c o n s t r a i n t s made were:
F66 ■ F10>10
S p ecifically,
t he
; F69 > F , 0 ) 2 and Fgg = F ] 2 J r
200
satisfactory.
centrifugal
T a b l e 5 . 1 5 shows t h a t t h e f i t
d istortion
constants.
F in ally,
i s a l s o v e r y good f o r
t he
a good harmonic f o r c e f i e l d
should a c c u r a t e l y p r e d i c t the v a l u e s o f t h e ground and e x c i t e d s t a t e
in e rtia l
here a n d ,
in e rtia l
defects;
the r e s u lt s
further,
defects
are very pleasin g
that
is well
o f Table 5.16
ac count ed f o r .
t he f o r c e f i e l d
given
t h e case
A l t h o u gh t he r e s u l t s o b t a i n e d
g i v e n i n T a b l e 5 . 1 3 shoul d be
w i t h t he many assumpt ions made,
the n e g le c t of anh arm o nicity,
uncertainties
is
t he i s o t o p i c dependence o f t h e ground s t a t e
r eg ar ded as a p r e l i m i n a r y r e s u l t ;
including
show t h a t t h i s
it
is evident th a t
in Table 5 .1 3 underestimate the t o t a l
t hese p a r a m e t e r s .
t
t he
errors
in
201
Table 5.1 4
O b s e r v e d a nd C a l c u l a t e d V i b r a t i o n a l Wavenumbers (cm
P ro p io ly l C h lo rid e
HCCCO 35C1
Vibration
Observed3
A'
v2
"3
v4
v5
v6
v7
v8
>v 9
A"
V10
V11
v 12
Deviation
Observed*3
Deviation
-11.1
2609
7.8
2131
-8.2
2000
8.9
1767
-3.6
1772
1.6
1003
0.0
994
-5.9
696
-3.3
653
3.9
655
-1.4
547
-0.6
478
2. 1
472
1.1
414
3.6
404
-1.2
157
5.2
147
2.8
703
3.2
665
1.4
547
3.8
224
-2.3
214
-2.2 *
e t al_.
(12).
i n f r a r e d v a l u e s e xcep t f o r
the f i t s
DCCC035C1
3326
a Taken from Augdahl
th e u n c e r t a in t y of
\> - j
of
(664)C
-
The obser ved wavenumbers a r e gas
which i s a Raman l i q u i d
was t a ke n t o be 1. 5%;
value.
all
In
other
f u n d a m e n t a l s were g i v e n u n c e r t a i n t i e s o f 1% o f t h e measured v a l u e .
I
202
r
)
Ta b le 5 .1 4
(continued)
k The o bse r ved wavenumbers a r e m o s t l y gas i n f r a r e d
a Raman l i q u i d
v a l u e and
(14)).
t a k en from t he u l t r a v i o l e t spectrum ( 1 5 ) .
were assumed to be d e g e r a t e b ut were g i v en
\>g and
5% r e s p e c t i v e l y ;
all
v-, i s
( 216
A v a l u e f o r Vg was
I n t he f i t s
vg and v-^
low w e i g h t s ;
were g i ve n u n c e r t a i n t i e s
of
see t e x t .
2% ,
5% and
o t h e r f u n d am en t al s were a s s i g ne d u n c e r t a i n t i e s
o f 1% o f t he measured v a l u e .
£
C a lc u la te d value.
(14);
"'s an e s t i m a t e d gas phase v a l u e
- cm ^ i n t h e Raman spect rum o f t he l i q u i d
In t h e f i t s
values
No e x p e r i m e n t a l
v a l u e was a v a i l a b l e .
2 03
Ta b le 5.15
O b s e r v e d and C a l c u l a t e d C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s
(kH z) o f P r o p i o ly l C h lo r id e
P ar am et e r
O b ser ved3
Calculated*3
Uncertainty
-
HCCC035C1
AJ
aj k
ak
6k
1.207
1.212
0 .0 21
-4.790
-4.717
0.084
22.69
2 2. 61
0.33
0.4948
0 .4 91 1
0.0 063
2.325
2.195
0 .^ 0
1.080
1.022
0.0 92
I
d c c c o 35 c i
AJ
aj k
ak
6J
6k
-3.41
-3.408
0.23
20.7
21.28
1.0
0.417
0.4082
0.018
2.50
2.4 24
0.28
f
1
c
204
T ab le 5.15
Observed and C a l c u l a t e d C e n t r i f u g a l D i s t o r t i o n C o n s ta n ts
(kHz) of P ro p io ly l C h lo rid e (continued)
P ar ame t er
Calculated
Observed
Uncertainty
HCCC037C1
-
1.201
'0.060
-5.34
-5.164
0.32
•23. 9
23.12
1.6
1.197
AJ
aj k
ak
6J
6k
0.484
0.4859
0.0 29
2.19
2.006
0.40
0.99
1.020
1.00
-4.30
-3.933
0.56
2 4. 1
21.89
2.7
d c cco 37 c i
AJ
<3
ak
'
6J
\
6k
a Experimental
0.404
0.4072
0.025
2.45
2.172
0.44
va lu es from T a b l e 5 . 2 .
k Va l ue s c a l c u l a t e d
using the fo rc e f i e l d
U n c e r t a i n t i e s used i n t he f o r c e f i e l d
cited un certain ties
refinement.
are t h r e e standard e r r o r s ;
' t h e assigned u n c e r t a i n t i e s
I
of Table 5 . 1 3 .
for
F o r HCCCO
4
Cl
the
th e o th e r isotopes
represent fo u r standard e r r o r s .
2 05
Table 5 .1 6
,op
O b s e r v e d a nd C a l c u l a t e d I n e r t i a l D e f e c t s (uA ) o f P r o p i o l y l
C hloride
S p eci es
Calculatedb
Obser ved3
Deviation
*
Ground V i b r a t i o n a l
State
-
HCCC035C1
0.3448(1 )°
0.3436
0.0012
KCCC037C1
0.3470(3)
0.3 460
0.0011
dccco 35 c i
0.3571,(4)
0.3560
0. 0011
dccco 37 c i
0.3600(4)
0.3587
0.0013
v^ = 1 E x c i t e d S t a t e
hccco 35 c i
0.662(1)
0.652
0.010
hccco 37 c i
0.669(14)
0.668
0. 001
dccco 3 5 c i
0.676(2)
0.683
-0.007
-
3 C a l c u l a t e d f rom t h e r o t a t i o n a l
b The v i b r a t i o n a l
field
constants of T ab le 5 .2 .
p a rt of the i n e r t i a l
o f T a b l e 5.13'.
c Errors c it e d are standard e r r o r s .
I
d e f e c t c a l c u l a t e d u si ng t h e f o r c e
5.7
The Av er ag e S t r u c t u r e o f P r o p i o l y l
I-
’
The harmonic f o r c e f i e l d
o f T a b l e 5 . 1 3 was used t o c a l c u l a t e .
r
t
t h e ground s t a t e a ve ra g d r o t a t i o n a l
species s tu d ie d ;
Chloride
constants of the fo u r
these are given in T able 5 .1 7 .
isotopic
Because t h e i n e r t i a l
d e f e c t s c a l c u l a t e d u si ng t h e s e A , B and C v a l u e s a r e e s s e n t i a l l y z e r o
J
z
z
z
■
J
(see Table 5 .1 6 ) a l l
twelve r o t a t i o n a l
t h e ground s t a t e a v e r a g e s t r u c t u r e .
wer e i n d e p e n d e n t ,
g r o up .
The r ( C - H )
Again,
since only e i g h t of these
it
was n e c es sa r y t o assume a s t r u c t u r e f o r t he e t h y n y l
O
bond l e n g t h was t a k e n t o be 1 . 0 5 5 A ( r & and r v a l u e s
°
for
c p AS ta n ts were used t o d e t e r m i n e
p r o p y n a l a r e 1.055 A (19)
0
and 1 . 0 5 4 A ( 2 0 )
respectively
) and t h e
o
* r(C~C)
are
l e n g t h was t a k e n t o be 1 . 2 0 7 A ( r $ and r^ v a l u e s f o r propynal
o
o
*
1 . 2 0 9 A ( 1 9 ) and 1 . 2 0 5 A ( 2 0 ) r e s p e c t i v e l y ) . The r e s u l t s o f a l e a s t
s quar es f i t
t o t he ground s t a t e a v e r ag e r o t a t i o n a l
in T able 5 .1 8 .
In t h e s t r u c t u r a l . r e f i n e m e n t s
c o n s t r a i n e d * a n d r ( C - C ) was v a r i e d by t r i a l
increments)
to f i n d the best f i t ;
were i g n o r e d .
constants are given
t h e < ( C - C e C) was not
and e r r o r
isotopic v ariatio n s
The s t a n d a r d d e v i a t i o n o f t h e f i t
c o n s t a n t s of' T a b l e 5 . 1 7 was 0 . 0 0 8 MHz,
O
( a t 0.0005 A
i n t h e bond l e n g t h s
to the tw elve r o t a t i o n a l
not s i g n i f i c a n t l y
•
l a r g e r t han
*
t h e e r r o r s q uot ed f o r t h e e f f e c t i v e ground s t a t e c o n s t a n t s o f "D|ble 5 . 2 ;
in view of the l i m i t e d
isotopic d a ta ,a v a ila b le ,
s t a n d a r d d e v i a t i o n may n ot be m e a n i n g f u l .
however,
As w e l l ,
thisw naTl
because p o s s i b l e
s y s t e m a t i c e r r o r s have been i g no r e d t h e l e a s t squares s t a n d a r d e r r o r s
almost c e r t a i n l y underestimate the t o t a l
parameters;
errors
i n tfhe s t r u c t u r a l
t h e u n c e r t a i n t i e s q uot ed i n T a b l e 5 . 1 8 r e p r e s e n t f i v e
s t a n d a r d e r r o r s b ut do not i n d i c a t e o u t s j d e l i m i t s
of e r r o r .
Table 5 .1 7
G r o u n d S t a t e A v e r a g e R o t a t i o n a l C o n s t a n t s (MHz) o f
P ro p io ly l C h lo rid ea
V
V
cz
\
B
Z
cz
3
hccco35ci
HCCC037C1
7175.153
7097
3145.260
3080.869
2186.696
2148.287
dccco35c i
DCCC037C1
7060.482
6975.728
2939.564
2882.102
jl63
*
2075.455
2039.460
V
Obtained using the effective*ground s t a t e r o t a t i o n a l constants of
Table 5.2 and the force f i e l d of Table 5.13.
208
T a b le 5.18
The Average S t r u c t u r e o f P r o p i o ly l C h lo r id e
P a r a me t e r
V al ue
r z (C-H)(A)'
1.055
r z ( C ~C ) ( A ) '
1.207
1.4415
r z (C=0)(A)
1 . 19 88(4 0 ) (
r z (C -C l)(A )
1.7587(37)
<(H-C=C)(Deg.)
180.0
<(CsC-C)(Deg.)
179.58(22)'
<(C-C=0)(Deg.)
125.19(30)
< (C -C -C l} (Deg.)
112.42(23)
Assumed.
V a l u e f ou nd by t r i a l
and e r r o r .
E r r o r s q uot ed a r e f i v e
lim its
See t e x t .
standard e r r o r s .
and may u n d e r e s t i m a t e t h e t o t a l
The e t h y n y l
These a r e a r b i t r a r y e r r o r
e r r o r in these par am eter s.
group i s ben t away from t h e C-Cl
bond.
2 09
5.8
Comments on t h e S t r u c t u r e o f P r o p i o l y l
A l t h o ug h t he p r e s e n t r e s u l t s f o r
d e fin itive
propiolyl
it
nevertheless
interesting
propiolyl
this
The r e s u l t s o f T a b l e 5 . 1 9 suggest t h a t
chloride
in view o f r e s u l t s
c h l o r i d e a r e not
t o compare the s t r u c t u r e s o f
c h l o r i d e and some r e l a t e d m o l e c u l e s ;
Table 5 .1 9 .
propiolyl
is
C hloride
has been done in
t h e C=0 bond in
i s s h o r t e r than t h a t i n p r o p y n a l .
Thi s
is reasonable
f o r H2C0 ( 5 2 ) ,
( 5 3)
where C=0
bond l e n g t h s o f 1 . 2 0 7 A
( r z )>
HC0C1 ( 2 )
1.188 A ( r
and C ^ C O
) and 1 . 1 7 9 A ( r
) have been
obtained;
as w e l l , f o r CH^CHO ( 5 4 ) and CH^COCl ( 5 1 ) t h e c o r r e s p o n d i n g
O
0
v al ue s a r e 1 . 2 0 7 A ( r ^ ) and 1 . 1 85 A ( r ) .
T h e r e f o r e t he 0=0 bond in
O
p r o p i o l y l c h l o r i d e mi gh t be- e xp ec t ed t o be 0 . 0 1 0 - 0 . 0 2 0 A s h o r t e r than
4
that
in propynal;
the r e s u l t s of Table 5 .1 9 ,
this
hypothesis.
More marked a r e t h e v a r i a t i o n s
essentially
identical
c h l o r i d e and p r o p i o l y l
rather
lo nger.
bond d i s t a n c e s
alb eit
imprecise,
i n t h e C- Cl
(55)
lengths;
have been d e t er m in e d f o r f or my l
c h l o r i d e w h i l e t h a t found f o r a c e t y l
Kagarise
su pp or t
chloride
suggested t h a t e l e c t r o n e g a t i v e
substituents
should l ower t he c o n t r i b u t i o n o f nonbonded r esonance s t r u c t u r e s
RC0+C1
; therefore
t h e l o n g e s t C-Cl
is ;
such as
bond would be e x p e ct e d f o r a c e t y l
c h l o r i d e due t o t h e p r ese n ce o f t h e " e l e c t r o n d o n a t i n g " me t hyl group.
S i m i l a r arguments have been used t o e x p l a i n t h e t r e n d
in t h e a c i d
d is s o c ia t io n constants of the parent c a r b o x y lic acids
(11).
b a si s one m i g h t e x p e c t t h e C- Cl
s h o r t e r than t h a t found i n
neglects,
however,
nearly e q u al.
f ormyl
chloride;
in.propiolyl
c h l o r i d e t o be s l i g h t l y
t h i s v e r y s i mp l e argument
possible conjugative e f f e c t s
The r e m a i n i n g bond l e n g t h s
ently
bond.in p ro p io ly l
.On t h i s
in p r o p io ly l
c h l o r i d e and p r o p y na l
chloride.
are appar­
210
L o o k i n g a t t h e bond a n g l e s i n a c e t y l c h l o r i d e and p r o p i o l y l
chloride
it
molecules;
is
seen t h a t
t h e < ( C- C = 0 )
the <( C - C - C l ) is e s s e n t i a l l y
is
i n each case ab o u t 14°
carbon c h a i n
in p ro p io ly l
in propynal.
A l t h o u g h t h i s may be an e x p e r i m e n t a l
structure calculations
conclusion.
larger.
c h l o r i d e i s more n e a r l y l i n e a r
outlined
in s ectio n 5.5
Less ambiguous s t r u c t u r a l
would r e q u i r e a d d i t i o n a l
results
isotopic data.
C and
18
0 la b e lle d p r o p io lic acid
to correspondingly label
I
propiolyl
than t h a t found
the r Q
for propiolyl
regard
Therefore i t
chloride.
t he
l e a d t o t he same
In t h i s
(56).
in b ot h
Apparently
a rtifa c t
t h a t v e r y r e c e n t s y n t h e t i c work has p r o v i d e d a v i a b l e
13
identical
it
chloride
i s wor t h n o t i n g
route to o b ta in in g
should be p o s s i b l e
211
Table 5.1 9
The S t r u c t u r e s o f P r o p i o l y l C h l o r i d e and R e l a t e d M o l e c u l e s 9
P ar am et e r
HCCC0C1b
HCCCHO
r ( C - H ) (A)
1 . 055
1.054(7)
r(C:C)(A)
1.207
1.205(6)
r ( C - C ) (A)
1 . 442
1.449(2)
r ( C = 0 ) (A)
1 .199(4)
1.212(5)
r ( C - C l ) (A)
1.759(4)
<(C-C=0)(Deq.)
125.2(3)
<(C-C-C1) (D e g .)
112.4(2)
<(CnC-C)(Deq.)
179.6(2)°
178.6 (3 )d
Reference
T h i s work
(20)
a
The HC0C1 s t r u c t u r e
r z structures.
k
Structure
I
c h 3 coci
1.188(2)
1.185(3)
1.760(2)
1.796(2)
124.2(2)
127.2(6)
111 . 6 ( 6 )
(2)
i s an r $ s t r u c t u r e .
(51)
The o t h e r s t r u c t u r e s
t aken f rom T ab l e 5..18.
*
r
d
HC0C1
E t h yn y l
group b ent aJay from C-Cl
bond.
%
E t h yn y l
group b e n t away from 0=0 bond.
i
212
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Cor.r, t a n t n , n ar m o n i c f o r c e f i e l d , ar. . M o l e c u l a r
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t 1 MHO)
Biographical
NAME:
Information
R o b e r t W e l l i n g t o n Davis
PLACE AND DATE OF BIRTH:
EDUCATION:
Memorial
St.
J o h n ' s , N ewf oundl and,
( C o l l e g e s and U n i v e r s i t i e s
February 27,
attended, dates,
U n i v e r s i t y o f Newf oundland,
The U n i v e r s i t y o f B r i t i s h Co lu mb i a,
1968-73,
1951
degrees)
B. Sc.
1 9 7 3 - 8 0 , Ph.D.
POSITIONS HELD:
PUBLICATIONS:
R.W. D a v i s , A.G.
(1980).
R.W.
R o b i e t t e and M . C . L .
Davis and M . C . L .
Gerry,
J.
Gerry, J.
Phys. Chem. 8 4 ,
R.W. D a v i s , A. G. R o b i e t t e , M . C . L .
‘ J . Mo l. S p e c t r o s c . 81_, 93 ( 1 9 8 0 ) .
Gerry,
Mol.
1767
Spectrosc.
(1980).
E. B j a r n o v and G. W i n n e w i s s e r ,
R.W.
Davis
and M . C . L . G e r r y , J .
Mo l.
Spectrosc. 65,
455 ( 1 9 7 7 ) .
R.W.
Davi s
and M . C . L . G e r r y , J .
Mol .
Spectrosc. 60,
117 ( 1 9 7 6 ) .
R.W.
Davi s
and M . C . L . G e r r y , J.
Mo l.
S p e c t r o s c . 59^,
407 ( 1 9 7 6 ) .
R.W.
Davis
and M . C . L .
M ol .
S p e c t r o s c . 57^,
118 ( 1 9 7 5 ) .
G erry, J.
R.W. D a v i s , M . C . L . G e r r y ,
L e t t . 2 6 , 561 ( 1 9 7 4 ) .
AWARDS:
S.
83^ 185
V i s a i s o u k and W.J.
B a l f o u r , Ch£m. Phys.
.
T h i s form i s t o be co mpl et ed by c a n d i d a t e s f o r t h e M a s t e r ' s o r h i g h e r
d e g r e e and s u b m i t t e d t o t h e U n i v e r s i t y L i b r a r y S p e c i a l C o l l e c t i o n s
D iv is io n w ith the th e s is .
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