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The microwave spectroscopy of ions and other transient species in DC glow and extended negative glow discharges

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T h e m icrow ave sp e ctro sc o p y o f ions a n d o th e r tra n s ie n t species
in D C glow a n d e x te n d e d n e g ativ e glow d ischarges
Warner, Hugh Edward, Ph.D.
The University of Wisconsin - Madison, 1988
UMI
300 N. Zeeb Rd.
Ann Arbor, MI 48106
A d is s e r t a t io n e n t it le d
THE MICROWAVE SPECTROSCOPY OF IONS AND OTHER
TRANSIENT SPECIES IN DC GLOW AND EXTENDED
NEGATIVE GLOW DISCHARGES
submitted to the Graduate School o£ the
University of Wlsconsin-Madlson in partial fulfillment of
the requirements for the degree of Doctor of Philosophy
by
HUGH EDWARD WARNER
88
Degree to be awarded:
December 19_____
May 19_____
August 19
Approved by Dissertation Readers:
Feb 3> 1988
Major Professor
fete of Examination
C-
^
—t/s—.
Dean, Graduate School
T H E M IC R O W A V E S P E C T R O S C O P Y O F IONS A N D O T H E R
T R A N S IE N T SPECIES IN DC GLOW A N D E X T E N D E D
N E G A T IV E GLOW D IS C H A R G E S
by
HU GH EDWARD W ARNER
A thesis s u b m itte d in p a r t i a l f u l f i l l m e n t o f the
r e q u i r e m e n ts f o r the d e g re e o f
D o c to r o f P h ilo so p h y
(C h e m is try )
a t the
U N IV E R S IT Y O F W ISCO N SIN -M A D ISO N
1988
ii
TABLE OF CONTENTS
Page
C H A P T E R I. IN T R O D U C T I O N
1
C H A P T E R II. T H E D E T E C T IO N O F T H E l u - l 10
T R A N S IT IO N S O F H ,D + .
14
C H A P T E R III. T H E SPE C T R O SC O PY O F X 2/71/2 SO+.
25
C H A P T E R IV. T H E M IC RO W A VE SPE C T R O SC O PY O F a 3H CO.
82
C H A P T E R V. T H E M IC RO W A V E E Q U IL IB R IU M S T R U C T U R E
OF HCN
105
C H A P T E R VI. T H E E Q U IL B R IU M S T R U C T U R E O F HNC.
209
C H A P T E R VII. T H E E Q U IL IB R IU M S T R U C T U R E O F HCO+.
268
C H A P T E R VIII. M IC RO W A V E S U B S T IT U T IO N S T R U C T U R E S
OF H N N+ and HOC+
A P P E N D I X 1. T H E M IC RO W A VE D E T E C T IO N O F K rD + .
348
398
A P P E N D I X 2. T H E D E T E C T IO N O F T H E l n - l 10
T R A N S IT IO N S O F H 2D+.
403
A P P E N D I X 3, P R O G R A M D O U B P I.F O R
405
A P P E N D I X 4. P R O G R A M S IM U L A T E .F O R
410
Nr
iii
A P P E N D IX 5. P R O G R A M SO L E V E L .F O R
419
A P P E N D IX 6. P R O G R A M U N IT Y .F O R
423
A P P E N D I X 7. P R O G R A M N E W C IN T E R A C .F O R
436
A P P E N D I X 8. P R O G R A M B O ND LS4.FO R
452
CHAPTER I.
IN T R O D U C T IO N .
2
T h e p r im a r y o b je c tiv e o f o u r re s e a rc h g ro u p is the s tu d y o f
m o le c u la r ions a n d o th e r tr a n s ie n t species in gas phase d isc h a rg e s by
m ic r o w a v e spectroscopy.
M ic ro w a v e sp ectroscopy c a n p r o v id e p recise
f r e q u e n c ie s to g u id e r a d io a s tr o n o m e r s , it c a n serve as a p ro b e o f th e
e le c tr o n ic s tr u c tu r e o f f r e e ra d ic a ls, it can p r o v id e a c c u r a te m o le c u la r
ge o m e trie s, a n d it can even se rv e as a tool fo r plasm a d iag n o stic s.
All
o f these a p p lic a tio n s w ill be m e n tio n e d in w ork in this thesis.
T h e m o le c u la r ion H s+ is a n e x tre m e ly im p o r ta n t
c o n s ti tu e n t o f the in te r s t e ll a r m ed iu m .
It is im possible to o b s e rv e the
r a d i o f r e q u e n c y s p e c tru m o f th is ion, b ecause its dip o le m o m e n t is zero.
D a lg a rn o et a l1, how e v e r, p o in te d o u t t h a t its isotopic v a r i a n t H 2D+ has
a n o n -ze ro d ip o le m o m e n t a n d r o ta tio n a l c o n s ta n ts th a t w o u ld p e rm it
o b s e rv a tio n in th e m ic ro w a v e.
A m a n o a n d W atson2 th en o b s e rv e d the
ion in th e i n f r a r e d , a n d o b t a i n e d an estim a te o f th e f r e q u e n c ie s o f the
m ic r o w a v e tra n s itio n s . G u id e d by th is w ork, w e3 (or A p p e n d ix 2 o f this
thesis) a n d Bogey el al.4 s im u lta n e o u s ly o b se rv e d th e 1j j —110 tr a n s it io n
a t 372421.38 MHz. Because o f these m ic ro w a v e o b s e rv a tio n s , P h illip s
et a l.5 w e re a b le to te n a tiv e ly obse rv e H 2D+ in th e i n te r s te lla r m ed iu m .
T h e l a b o r a to r y d e te c tio n o f this a s tro p h y s ic a lly i m p o r ta n t ion will be
d isc u sse d in C h a p t e r II o f th is thesis.
We shall also em ploy th is c h a p te r
to discuss ou r m o d if ic a tio n s o f th e sp e c tro m e te r a n d the d is c h a r g e system ,
e s p e c ia lly the d e v e lo p m e n t o f th e e x te n d e d n e g a tiv e glow d is c h a r g e by
W. T. C o n n e r.6
A p p e n d ix 1 is o u r p a p e r on the d e te c tio n o f K r D +.7 We shall
not in c lu d e a c h a p te r f o r this w o rk , b u t shall b r ie f ly discuss it in this
3
in tr o d u c ti o n .
T h e ion was p ro d u c e d in a 9-14 m T o rr K r b u f f e r w ith
1 m T orr D 2 added.
We m e a s u re d th e J=0-»1 t r a n s it io n f r e q u e n c ie s o f
all six iso topic species in n a t u r a l a b u n d a n c e , a n d we m e a s u re d th e q u a d r u p o le
c o u p lin g c o n s ta n t f o r th e 83K r nucleus. T h e m ost a b u n d a n t isotopic species,
84K r D + , was o b se rv e d in b o th n o rm a l a n d a b n o rm a l d isc h a rg e s , a n d a
s lig h t re v e rs e D o p p le r s h i f t was noted. T h is n e g a tiv e D o p p le r s h i f t p r o v id e d
e v id e n c e o f a sm all m ac ro sco p ic e le c tric f ie ld in o u r a b n o rm a l discharges.
In C h a p t e r III, we shall re p o r t th e m ic ro w a v e sp e ctro sc o p y o f
th e r a d i c a l ion SO+. Because o f o u r l a b o r a to r y m e a s u re m e n ts , it was
possible f o r Woods et al.8 to o b serve th is ion in th e i n te r s t e ll a r m edium .
We h a v e o b se rv e d b o th p a r i t y c o m p o n e n ts o f th e J = 3 / 2 —*5/2 a n d 9 / 2 —*11 /2
r o ta t io n a l t r a n s it io n s a n d one o f the J= 1/ 2 —*3/2 tr a n s it io n in th e la b o r a to r y
w o rk , a n d o b ta in e d im p ro v e d v alues o f B0, D 0, a n d p 0. A n e specially
in te r e s tin g asp ec t o f o u r w o rk is t h a t we h a v e m e a s u re d th e Z e e m a n
e f f e c t f o r th is m olecule, whose g ro u n d s ta te is a 2n 1/ 2 sta te , w h ic h w ould
h a v e no Z e e m a n e f f e c t a t all in a p u r e H u n d ’s case a. We h a v e d e v e lo p e d
a m odel f o r th is e f f e c t , w h ic h is in f a i r a g re e m e n t f o r all f iv e o b se rv e d
tr a n s itio n s .
In o r d e r to c a li b r a t e th e m a g n e tic fie ld , we m e a s u re d th e
Z e e m a n e f f e c t o f X 8E~ SO. T h e c a lc u la tio n o f th e f ie ld fro m th e m ea su red
AM =-1 c o m p o n e n ts will also be d iscussed in th is c h a p te r.
T h e a 3/7 s ta te o f CO has been th e su b je c t o f c o n s id e ra b le
e x p e r i m e n t a t i o n in th e r f reg io n by K le m p e r e r a n d his c o w o r k e rs 9 a n d
in th e m ic ro w a v e reg io n in o u r l a b o r a t o r y 10. T h e sp e ctro sc o p y o f this
sta te is esp ec ially o f in te r e s t, b ecause it is an open-shell e le c tro n ic system
p e r t u r b e d by th e n e a rb y a ' 3Z state.
T h e r e h a d been e a r l ie r m ic ro w a v e
4
spe ctro sc o p y o f th is system , b u t it w as w ith a f re e r u n n in g k ly stro n ,
a n d w as r e s tr ic te d to J = 0 —
*•1 tr a n s itio n s .10 In o u r w o rk , d e s c rib e d in
C h a p t e r IV, we h a v e used a phase lo ck e d k ly s tro n to re p e a t th e e a r lie r
m e a s u re m e n ts , a n d o b ta in m ore a c c u r a te fre q u e n c ie s .
In a d d itio n , we
h a v e e x te n d e d th e J = 0 —*1 w o rk to th e v=6 s ta te , not in c lu d in g th e v=5
sta te . We h a v e also e x te n d e d th e m ic ro w a v e m e a s u re m e n ts to J=4->5,
a n d to 12=1 a n d 12=2 tra n s itio n s . O u r pressu re b ro a d e n in g e x p e rim e n ts
rev e a l s im ila r lin e w i d th vs p ressu re r e la tio n s h ip s as HC N .
By u sin g m o le c u la r
g f a c to rs o b ta in e d f ro m laser m a g n e tic re s o n a n c e e x p e r im e n ts 11, we h a v e
a c c u r a te l y p r e d ic te d o b served Z e e m a n c o e ff ic ie n ts .
O ur p relim inary
w o r k suggests t h a t the p a r i t y d e p e n d e n c e o f th e Z e e m a n e f f e c t is m ea su rab le .
A m a n u s c r i p t 12 d e s c r ib in g these m e a s u re m e n ts on th e m ain isotopic species
a lo n g w ith a new le a st-sq u a re s a n a ly s is o f th e sp e ctral p a ra m e te rs c a r r ie d
o u t by N. C a rb a llo , has been s u b m itte d fo r p u b lic a tio n . C h a p te r IV also
d e s c rib e s an e x te n s iv e series o f m e a s u r e m e n ts f o r the 13CO isotopic fo rm ,
f o r w h ic h th e a n a ly s is is still in progress.
T h e m e a s u r e m e n t o f m o le c u la r s tr u c tu r e is one o f the m ajo r p urposes
o f m ic ro w a v e spectroscopy. F or a p o ly a to m ic , the f o r m u la r e la tin g Bv
(an e f f e c t i v e r o ta t io n a l c o n s ta n t in a given v ib r a tio n a l sta te ) to Be (the
t r u e e q u il ib r i u m r o ta tio n a l c o n s ta n t) is
Bv = Be -
E a i(v i+ d i/ 2 )
i
+
E 7 ij( v i+ d i/2 ) ( v j+ d :/2 )
ij
+
( 1)
E €ijk(v i+ d i/ 2 ) ( v j+ dj/ 2 ) ( v k+ d k/2 ) + 7 / // 2.
F o r a l in e a r tria to m ic , Be is a f u n c t i o n o f both bond distances.
Therefore,
5
a s t r u c t u r e c a n be c a lc u la te d i f Be’s f o r tw o isotopic species a re know n.
T w o r e la te d f u n d a m e n t a l q u e s tio n s are: (1) a t w h a t level o f t r e a tm e n t
o f th e v i b r a t io n - r o t a ti o n i n te r a c t io n ( a , a 7 , c*7e ?) does Be co n v e rg e
a n d (2) how c o n s is te n t a re th e bond d ista n c e s c a lc u la te d f r o m all p a irs
o f isotopom ers. C. S. G u d e m a n 13 a tte m p te d to a n s w e r these q u e s tio n s
f o r H C N u s in g o n ly J = 0 —1 d a ta , a n d was not a ble to o b ta in c o n v e rg e n c e
o f th e sum in E q u a t io n (1). In a d d it io n , he also obse rv e d t h a t th e r e was
g r e a t e r c o n s is te n c y o f s tr u c tu r e s a t th e a level th a n a t th e a 7 level.
H e d id , h o w e v e r, show t h a t a c c id e n ta l v i b r a t io n a l reso n a n c e e f f e c t s w ere
n o t a fa c to r.
B ecause H C N c a n be p ro d u c e d in a b u n d a n c e , a n d because
it is f r e e o f a c c id e n ta l reso n a n c e s, th is m olecule is an ideal c a n d id a te
f o r th e s tu d y o f th e e q u il ib r i u m s tr u c tu r e .
In C h a p t e r V o f th is thesis,
we discuss th e e x te n s io n o f G u d e m a n ’s12 w ork to h ig h e r v alues o f J a n d
to H 13C 15N.
We h a v e m e a s u re d Be f o r H C N a n d H 13CN to th e a y e level
o f E q u a t io n (1), d e te r m i n in g the most c om plete a n d a c c u r a te e q u il ib r i u m
s t r u c t u r e y e t o b ta in e d f o r a n y p o ly a to m ic molecule.
Because we w ere
w o r k in g a t h ig h e r J valu e s, we w ere a ble to observe v i b r a t io n a l satellites
w ith / - t y p e re s o n a n c e (/ ^ 0), such as the 0 ^ 0 , 0220, a n d 0 3 ^ sa te llite s
(/ is th e su p e rs c rip t).
O u r o b s e rv a tio n o f th e 0220 s ta te e n a b le d us to
m e a s u re 7» d ire c tly .
I n c lu d in g th is term , we note t h a t Be’s c a lc u la te d
a t th e a f level h a v e n e a rly th e sam e v alue
as Be’s c a lc u la te d a t the a 7 c
level, a v e ry s a ti s f y i n g re s u lt t h a t h a d not been o b ta in e d in e a r l ie r w o rk
by G u d e m a n .10 In a d d it io n , we h a d s o m e w h at b e tte r c o n sisten c y o f s tr u c tu r e s
a t th e a y level th a n a t th e a level, also u n lik e R e f e re n c e 10. A m eth o d
o f u sin g K r a i t c h m a n ’s 14 e q u a tio n s on Be’s has re s u lte d in a m eans o f
6
a c c u r a te l y d e te r m i n in g b o n d d ista n c es, even w h e n th e d i r e c t in te r s e c tio n
m e th o d gives in c o n s is te n t b o n d lengths. A m ethod o f p lo ttin g r CH vs
r CN d e v e lo p e d by M o rin o a n d N a k a g a w a 15 has been em p lo y e d to g e n e ra te
plots, in w h ic h both c o o rd in a te s c a n be re a d d ir e c tly o f f th e grap h .
When
o u r d a ta f o r th e h y d r o g e n c o n ta i n in g isotopom ers is c o m b in e d w ith th e
D C N Be d a t a o f W innew isser, M aki, a n d J o h n s o n 16, it is possible to note
t h a t d i f f e r e n t m o le c u la r s tr u c tu r e s r e s u lt fro m u sing H X Y - H X 'Y ' p a irs
t h a n f r o m u s in g H X Y - D X 'Y ' pairs.
In th e lim it o f th e B o rn -O p p e n h e im e r
a p p r o x i m a t io n th e r e sh o u ld have been no d i f f e r e n c e b e tw e e n these in te rsections.
T h e r e f o r e , it seems t h a t th e a p p r o x im a tio n b rea k s d o w n f o r d e u te r iu m
s u b s titu tio n .
A n i m p o r ta n t s id e lig h t o f o u r w o rk on H C N has been the o b s e rv a tio n
o f S ta r k p e r t u r b a t i o n in th e 0220 a n d 0330 states. T h e d ip o le m om ent
m a tr ix c le m e n t is p r o p o r tio n a l to J ' 2 - / 2. T h e r e f o r e , we sh o u ld have
seen 0 2 20 /0 2 °0 peak i n te n s ity r a tio s o f 5 /9 , 3 /4 , a n d 2 1 /2 5 f o r the J = 2 —3,
J=3-*4, a n d J=4-»5, resp e c tiv e ly . T h e a c tu a l ratio s o b se rv e d w ere c o n s id e ra b ly
sm a lle r, a n d th e 0 2 20 lines w ere c o n s id e ra b ly b r o a d e r th a n th e 02°0 lines.
O u r p r e l i m i n a r y o b s e rv a tio n s o f the S ta rk e f f e c t e n a b le d W. T. C o n n e r 6
to e x a m in e th is e f f e c t m ore th o ro u g h ly , a n d m odel it on a m icroscopic
e le c tr ic f ie ld d u e to th e m o tio n o f c h a rg e d p a ritic le s in th e d isc h a rg e ,
i.e., a H o lts m a rk field.
We h a v e m ea su red th e f ir s t m ic ro w a v e e q u il ib r i u m s tr u c tu r e o f
the u n s ta b le species H N C , a n d h a v e re p o rte d the w o rk in C h a p t e r VI.
We h a v e m e a s u re d Be’s at th e a level o f e q u a tio n 1 f o r H N C , H N 13C,
H 1BN C , a n d H 15N 13C o b s e rv in g J = 0 — 1, J=2-*3, a n d J=3-*4 tra n s itio n s
7
f o r th e g r o u n d v i b r a t io n a l sta te , a n d th e 100, 02°0, a n d 001 states.
In
a d d it io n , J = 0 —*•I t r a n s it io n s h a v e been o b se rv e d f o r th e D N C a n d D 15NC
isotopom ers.
O u r D N C w o rk ha s e n a b le d us to observe a n o th e r possible
b r e a k d o w n o f th e B o r n - O p p e n h e im e r a p p ro x im a tio n , because, th e r e s tr u c tu r e s
( a level) v a r y b e tw e e n those c a lc u la te d w ith H X Y - H X 'Y ', H X Y - D X 'Y ',
a n d D X Y - D X 'Y ' pairs.
We h a v e also o b se rv e d th e 0220 states o f th e
m a in iso topic species a n d note t h a t as e x p e cte d , th ey a re c o n s id e ra b ly
less S ta rk p e r t u r b e d t h a n the H C N 0220 lines.
A n o t h e r i m p o r ta n t resu lt o f o u r H N C w ork was th e o b s e rv a tio n
o f a gross d i s p a r it y b e tw e en th e bond d ista n c e s c a lc u la te d f ro m th e in te rse c tio n
o f th e p a ir s o f s in g ly - s u b s titu te d isotopes a n d those o b ta in e d f r o m in te rse c tio n s
f o r a n y o t h e r isotopic p a ir. T h is d is c r e p a n c y was s im ila r to th e d is c r e p a n c y
ob se rv e d by G u d e m a n 12 in his H C O + w ork. O u r possible e x p la n a ti o n
f o r th is e f f e c t in H N C is th e s im ila r ity o f the slopes o f the tw o m em bers
o f th e o u tly in g p a ir.
It is also t r u e t h a t the singly s u b s titu te d species
of H C O + h a v e r CH vs r c o c u rv e s o f n e a rly e q u a l slope. T h u s we have
a possible e x p la n a ti o n o f G u d e m a n ’s 12 d isc repancies.
O u r w o rk on th e ion, H C O +, a n d its isotopom ers is d iscussed
in C h a p t e r VII. We h a v e e x te n d e d C. S. G u d e m a n ’s 12 o b s e rv a tio n o f the
g r o u n d v i b r a t io n a l s ta te a n d th e 02°0 s ta te to the J=4->5 tr a n s it io n f o r
the m a in iso topic species, H 13C O +, a n d H C 180 +. We have also e x te n d e d
th e o b s e rv a tio n s o f th e 100 a n d 001 v i b r a tio n a l s a te llite s to th e J = 3 —4
t r a n s it io n f o r these isotopom ers. G u d e m a n ’s 12 o b s e rv a tio n o f th e 002
sta te f o r th e m a in isotope has been c o n f ir m e d a n d e x te n d e d to th e H 13C O +
a n d H C lsO + isotopom ers. T h e 0 1 11, 0 3 ^ , 04°0, 0 2 20, 0330 v i b r a t io n a l
8
s a te llite s h a v e b e e n o b se rv e d f o r th e f i r s t tim e, e n a b lin g us to o b ta in
th e m ost a c c u r a te e q u il ib r i u m s tr u c tu r e f o r a m o le c u la r ion to date.
T h e o b s e rv a tio n o f th ese s a te llite s e n a b le d us to v i r t u a ll y e lim in a te the
in c o n s is te n c y in the s tr u c tu r e s th a t G u d e m a n 12 h a d observed.
A n o th e r
i m p o r t a n t p o in t to com e o u t o f th is re se a rc h w as th e d e m o n s tra tio n o f
th e p o w e r o f th e K r a i t c h m a n e q u a tio n -s e c o n d m om ent m ethod.
A p p ly in g
th is m e th o d to th e a level Be’s re s u lte d in a c a lc u la te d e q u il ib r i u m s tr u c tu r e s ,
v e ry s im ila r to th e m o re a c c u r a te ot7partiai s tr u c tu r e s .
In th e f u t u r e , if
in c o n s is te n t e q u i l i b r i u m s tr u c tu r e s resu lt f ro m m ic ro w a v e d a ta , th is m eth o d
w ill p r o v id e a p o w e r f u l a p p r o a c h to deal w ith th e problem . In o u r o b s e rv a tio n s
o f th e 0220 sta te , we n o te d c o n s id e r a b ly g r e a te r S ta rk p e r t u r b a t io n th a n
fo r H C N , w h ic h w as v a lu a b le in u n d e r s t a n d in g th e n a tu r e o f th e e le c tric
fie ld s in o u r d isc h a rg es.
F in a lly , we have n o te d in th e H C O + c h a p te r
a so rt o f B o r n - O p p e n h e im e r b r e a k d o w n , d i f f e r e n t fro m t h a t in th e p re v io u s
c h a p te rs , d u e to th e m issing e le c tro n mass.
A n e x a c t t r e a tm e n t o f th e
B o r n - O p p e n h e im e r b r e a k d o w n is a c o m p lic a te d pro b le m , a n d we d id not
a tt e m p t it.
We c a lc u la te d s tr u c tu r e s based on sim ply re m o v in g the e le c tro n
f r o m i n d i v i d u a l atom s. T hese c a lc u la tio n s re v e a le d some s tr u c tu r e d e p e n d e n c e
on th e lo c a tio n o f e le c tro n rem o v a l a n d p e rm it one to at least e s tim a te
th e m a g n itu d e o f th e e f f e c t.
T h e f i n a l c h a p te r o f this thesis, C h a p t e r V III, d e a ls w ith
th e s p e c tro sc o p y o f N 2H + a n d H O C +. We m e a s u re d the N 2H + g r o u n d
v i b r a t io n a l s ta te t r a n s it io n s to J=4-*5, a n d o b se rv e d the 01 ^
satellites.
T h e y w e re a p p r o x i m a t e ly th re e tim es w e a k e r w ith respect to the g ro u n d
sta te th a n t h e i r H C O + c o u n te r p a r ts .
A tte m p ts to observe o th e r s a te llite s
9
w e re u n s u c c e s s fu l. T h e s e w e re s u rp r is in g results, be c au se we w e re a ble
to o b se rv e sa te llite s f o r HCO+. We h a v e also o b se rv e d th e J=0-*1 t r a n s it io n s
o f N 2D+, 15N N D + , a n d N 15ND+.
T h e se m e a s u re m e n ts w e re c o m b in e d
w ith e a r l ie r m e a s u re m e n ts o f th e J = 0 —*1 tr a n s it io n o f 15N 2D+ by S za n to
et a l.11 a n d th e J = 0 —►
1 tr a n s itio n s o f th e H 16N N +, H 1BN 15N +, a n d H 15N 15N +
iso to p o m ers by G u d e m a n 12 to p r o v id e c o m p le te s u b s ti tu t io n s tr u c tu r e s
o f H N N + t h a t a re c o n s id e r a b ly im p ro v e d w ith respect to th e p u b lis h e d
one. T h e d i f f e r e n c e b e tw e e n th e s u b s titu tio n s tr u c tu r e s o f h y d ro g e n
c o n ta i n in g isotopom ers a n d th e d e u te r a t e d isotopom ers has been show n
to be c o n s is te n t w ith th e o th e r H X Y m olecules d iscussed in th is thesis
(H C N , H N C , a n d HCO+).
O u r w o rk on H O C + in c lu d e s th e o b s e rv a tio n o f th e J=2-»3
a n d 3-»4 t r a n s itio n s o f the H O C +, H 18O C +, H 0 13C + iso topom ers a n d
th e J=2->3 tr a n s it io n o f H 180 13C+.
We h a v e used th e d a ta o f Bogey et
a t.18 f o r D O C + to o b ta in a c o m p le te s u b s titu tio n s tr u c tu r e f o r H O C +
a n d we o b t a i n f o u r c o n s is te n t v alues o f rB(CO) fo r d i f f e r e n t p a r e n t species
f r o m o u r o w n m ea su rem e n ts.
T h e c h a p te r is c o n c lu d e d by c o m p a r in g
a n e s tim a te d r e s t r u c t u r e f o r H O C +16, a n i n f r a r e d r e s t r u c t u r e f o r N 2H +19
a n d o u r m ic ro w a v e r e’s fo r H C N , H N C , a n d H C O + w ith th e c o r r e s p o n d in g
r B a n d r 0 s tr u c tu r e s .
T h e r e was no d i f f e r e n c e b e tw e e n th e r 0 a n d r B s tr u c tu r e
f o r th e r XY’s, a n d th e d i f f e r e n c e b e tw e e n both s tr u c tu r e s a n d th e e q u il ib r i u m
s t r u c u t u r e is n e a rly c o n s ta n t f o r all th e m olecules in th e series.
We have
also sh o w n t h a t a p p ly in g K r a i t c h m a n ’s e q u a tio n s (r B m e th o d ) p r o d u c e s
lo w e r c a lc u la te d r HX’s th a n th e r 0 a p p ro x im a tio n .
T h is m ea n s t h a t the
r B’s only giv e a n im p ro v e d a p p r o x i m a t io n to th e e q u il ib r i u m s tr u c tu r e ,
10
( r e l a t iv e to th e r 0’s) w h e n th e r0
is g r e a t e r th a n th e e q u i l i b r i u m v a lu e .
11
REFERENCES
1 A. D a lg a rn o , E. H e rb s t, S. N o v ick , a n d W iiliam K l e m p e r e r , Ap.J.
183, L131 (1973).
2 T. A m a n o
a n d J. K. G.W atson, J. C hem . Phys. 81, 2689 (1984).
3 H. E. W arner, W. T. C o n n e r, R. H. P e trm ic h l, a n d R. C. Woods, J.
Chem . Phys. 81, 2514 (1984).
4 M. Bogey, C. D e m u y n c k , M. D enis, J. L. D estom bes, a n d B. L em oine,
A stro n . A stro p h y s. 137, L15 (1984).
5 T. G. P h illip s, G. A. B lake, J. K e e n e , R. C. Woods,
a n d E. C h u r c h w e ll, Ap. J. 294, L45 (1985).
6 W illiam T. C o n n e r, Ph.D. Thesis, U n iv e r s ity o f W isconsin-M adison
(1988).
7 H. E. W arner, W. T. C o n n er, a n d R. C. Woods, J. Chem.
Phys. 81, 5413 (1984).
8 R. C. Woods, E. C h u rc h w e ll, W. M. I rv in e , a n d R. L. D ic k m a n ,
to be p u b lis h e d .
9 B. G. Wicke a n d W. K le m p e re r, Mol. Phys. 30, 1021 (1975).
10 R. J. S a y k a lly , T. A. D ixon, T. G. A n d e rs o n , P. G. S z a n to , a n d
R. C. Woods, J. Chem. P h y s 87, 6423 (1987).
11 R. J. S a y k a lly , K. M. E venson, E. R . C om ben, a n d J. M. B row n,
J. Mol. Spec. 58, 735 (1986).
12 N. C a rb a llo , H. E. W arner, a n d R. C.Woods, s u b m itte d f o r
p u b lic a tio n , 1987.
13 C. S. G u d e m a n , Ph. D. T hesis, U n i v e r s i ty o f W isconsin, M a d iso n , 1982.
14 J. K r a i t c h m a n , Am. J. Phys. 21 17 (1953).
15 Y. M o rin o a n d T. N a k a g a w a , J. Mol. Spec. 26, 496(1968).
16 G. W innew isser, A. G. M aki, a n d D. R. J o h n so n , J. Mol. Spec.
39, 149 (1971).
12
17 P. G. S z a n to , T. G. A n d e r s o n , R. J. S a y k a lly , N. D. P iltch,
T. A. D ix o n , a n d R. C. Woods, J. Chem . Phys. 75, 4261 (1981).
18 M. Bogey, C. D e m u y n c k , a n d J. L. D e stom bes, J. Mol. Spec.
115, 229 (1986).
19 J. C. O w r u t s k y , C. S. G u d e m a n , C. C. M a r t n e r , L. M. T a c k , N. H.
R o s e n b a u m , a n d R. J. S a y k a lly , J. C hem . Phys. 84, 605 (1985).
13
C H A P T E R II.
T H E D E T E C T I O N O F T H E I n - l 10 T R A N S IT I O N O F H 2D+.
14
Shy, F a r le y , a n d W ing1 f ir s t o b se rv e d H 2D + in the i n f r a r e d in
1981, b u t th e y m a d e no a ssig n m en ts f o r th e tra n s itio n s .
T h e n e x t o b s e rv a tio n
o f H 2D + in th e i n f r a r e d w as by A m a n o a n d W atson2, w ho e s tim a te d the
1n ~ 110 t r a n s i t i o n f r e q u e n c y to be 372383(106) MHz.
U s in g th is e s tim a te
as a g u id e we o b se rv e d th e lin e a t 372421.34 M Hz.3 Bogey et al.* also
o b s e rv e d this tr a n s it io n a t a p p r o x im a te ly th e sam e tim e as we d id.
The
l a b o r a t o r y m e a s u r e m e n ts e n a b le d P h illip s et al.5 to m ak e a t e n a t iv e a s sig n m e n t
o f th e t r a n s i t i o n in th e i n te r s te lla r m edium . S a ito et al. 6 o b se rv e d th e
220- 2 21 t r a n s it io n a t 155987.185 MHz. T h is c h a p te r is i n te n d e d to a u g m e n t
R e f e r e n c e 3, w h ic h is A p p e n d ix 2 o f th is thesis, a n d to w h ic h th e r e a d e r
is r e f e r r e d . T h is c h a p te r p ro v id e s f u r t h e r d e ta ils c o n c e r n in g th re e topics:
(1) th e e s tim a tio n o f th e a b s o rp tio n c o e f f ic ie n t, (2) th e m o d if ic a ti o n o f
th e d is c h a r g e cell a n d s p e c tro m e te r, a n d (3) th e disc u ssio n o f f u t u r e w o rk
on th e m olecule.
P r io r to th e s e arc h , in d e e d , p r io r to r e c e iv in g A m a n o a n d W atson’s2
p a p e r, c a lc u la tio n s o f the a b s o rp tio n c o e f f ic i e n t w e re u n d e r t a k e n f o r
these t h r e e t r a n s it io n s in th e m icrow ave: th e 11X—110» t *ie ^ 20 ~ ^ 2 i> anc*
th e 3so- 3 31 a r o u n d 44 GH z. 7 T ow nes a n d S c h a w lo w 8 give the f o r m u la
(page 24)
7
Sn^NJlM
ij|V
=
-------------------------------- -—
3ckTA v
—
’
(])
' '
w h e r e N is th e n u m b e r d e n s ity o f th e a b s o rb in g species, / is the f r a c ti o n a l
a b u n d a n c e o f th e lo w e r sta te , l/Xyl2 is th e t r a n s it io n d ip o le m a t r ix e le m e n t
b e tw e e n the u p p e r a n d low er sta te , v0 is the tr a n s it io n f r e q u e n c y , A v
15
is th e l in e w i d th , a n d T is th e r o ta t io n a l te m p e r a tu r e .
We assu m e d t h a t
N w as 1010 c m -3, a n d T w as ta k e n as 77 K ( liq u id n itr o g e n co o lin g ) a n d
300 K ( w a te r cooling).
T h e v alues o f A, B, a n d C o f D a lg a rn o e t al.9
w e re used as in p u t f o r th e A S Y M R O T p ro g ra m , w h ic h c a lc u la te d th e
e n e rg y levels a n d lin e s tre n g th s . T h e f r a c t i o n a l a b u n d a n c e s , / , o f the
r o t a t i o n a l levels w ere c a lc u la te d u sin g th e fo rm u la , m o d if ie d f r o m T ow nes
a n d S c h a w lo w 8 (page 101)
" J K_1K1(2 J + I ) e x p
kT
f ------------- — --------------------- W--------JK-1K1
^ ,,jK_1K1(2 J + , )c x PkT
.
w h e r e th e W’s a r e th e c a lc u la te d e n e rg y levels, a n d th e n ,
(2 )
K -iKl
’s a r e the
n u c le a r sp in d e g e n e ra c ie s , w h ic h a re 3 w h e n K _ j is o d d a n d 1 o th e rw is e .
It w as assu m e d t h a t v i b r a t io n a l d i lu t io n w o u ld be n e g ligible, i.e., / v was
set e q u a l to one. In T a b le I, th e f r a c t i o n a l a b u n d a n c e s o f the lo w e r states
a re sh o w n f o r b o th 77 K. a n d 300 K. T h e c a lc u la tio n o f |/Ltjj|2 w as r e la tiv e ly
s t r a i g h t f o r w a r d u sing the f o rm u la (R e f. 7, p. 24)
th e v a lu e o f .60 D e b y e f o r the d ip o le m o m e n t fro m D a lg a rn o et al.9, a n d
c a lc u la t e d line s tr e n g th s (S) o f 1.5, 3.16, a n d 5.10 f o r th e l n - l i o > t *ie
220- 2 21, a n d th e 380- 3 31 t ra n s itio n s , resp e c tiv e ly . T h e reason t h a t H 2D+
has a d ip o le m o m e n t is t h a t th e c e n te r o f mass is no longer e q u a l to the
c e n te r o f c h a rg e u p o n s u b s ti tu t io n o f D f o r H in H s+.
16
T h e c a lc u la t io n o f A v w as s o m e w h a t m o re e la b o ra te .
T h e n a t u r a l l in e w i d th , g iv e n by T o w n e s a n d S c h a w lo w 8 (p ag e 336) is
( 4>
3hc3
w h ic h is a b o u t 10-4 H z, a n d th e r e f o r e , q u i te negligible. T h e sam e r e f e r e n c e 8
(p ag e 337) gives th e D o p p le r w i d t h to be
(5 )
w ith T in K a n d M in am u.
E s tim a te d D o p p le r w id th s f o r th e tra n s itio n s
w ill be p r o v id e d in T a b le II. C. S. G u d e m a n 10 has sh o w n t h a t the pressu re
b r o a d e n i n g r a t e o f a n ion in a n e u tr a l b u f f e r closely fo llo w s the L a n g e v in
ra te , i. e., th e p r e d o m i n a t e i n te r a c t io n is th e m o n o p o le -in d u c e d dipole.
We c a n , t h e r e f o r e , c o m b in e his e x p re ssio n f o r th e c o llisio n a l ra te c o n s ta n t 9,
f dAv \ 2nkT
1333 ’
(6)
w ith the e x p re s s io n f o r th e L a n g e v in ra te c o n s t a n t 10,
(7 )
to o b ta in
17
T h e q u a n t i t y a ( c m 3) is th e p o la r i z a b i li ty o f th e b u f f e r gas, jU(gm) is the
r e d u c e d m ass o f th e io n -n e u tra l collision p a ir , e is the c h a rg e o f th e e le c tro n
(4.8 x i o -10 esu), a n d k is th e B o ltzm a n n c o n s ta n t (1.38 x i o -16 e rg K _1).
U s in g a v a lu e o f 1.60 x io -24 c m 3 f o r th e p o l a r i z a b i li ty o f A r ,u we o b ta in
p re s s u re b r o a d e n in g p a r a m e te r s o f 8 M H z / T o r r a t 300 K a n d 32 M H z / T o r r
a t 77 K.. A s su m in g 8 m T o r r o f a rg o n , we h a v e pressu re b r o a d e n i n g lin e w id th s
o f 64 k H z a t 77 K a n d 256 kH z a t 300 K. T h e to ta l lin e w i d th s w ere
th e n c a lc u la te d u sin g th e f o r m u la (see T o w n e s a n d
S c h a w lo w 8, page
375)
&
“ [ ^ D o p p le r J 2 + ( A v coUitionW /2 .
(9 )
T h e resu lts a re d isp la y e d in T a b le III.
H a v in g c a lc u la te d / , l/ii^l2, a n d A v, we a rc p r e p a r e d to use
E q u a t io n (1) to c a lc u la te 7 miix. T h e c a lc u la te d v alues f o r th e a b s o rp tio n
c o e f f i c i e n t a r e d isp la y e d in T a b le III.
t h a t th e 1
T h e s a lie n t f e a t u r e to no te is
1x0 is s tro n g ly f a v o r e d by l iq u id n itr o g e n co o lin g , th e 220- 2 21
is s lig h tly f a v o r e d by liq u id n itro g e n cooling, a n d the 3S0- 3 31 is m uch
b e tte r w ith only w a te r cooling.
Most o f the e x p e rim e n ta l d e ta ils a re in A p p e n d ix 2 a n d w ill not
be re p e a te d here. A b r i e f discussion o f th e m o d if ic a tio n s o f th e s p e c tro m e te r
a n d d is c h a r g e system , w h ic h w ere used f o r th is a n d s u b s e q u e n t e x p e rim e n ts
18
in th is thesis w ill be given. T h e S-band p h a se lock loop a n d to n e - b u r s t
m o d u la tio n schem es o f C. S. G u d e m a n 10 h a v e been r e t a in e d .
H o w e v e r,
R. H. P e t r m ic h l 12 has r e d e s ig n e d the phase d e te c to r, th e S -b a n d pow er
s u p p ly , a n d th e o p tic a l c o u p le r; d e ta ils o f th is w ill be p r o v id e d in his
thesis. W. T. C o n n e r 13 has a d d e d a M illitech h a rm o n ic g e n e ra to r , so t h a t
o u r f r e q u e n c y c o v e ra g e has gone f ro m the 80-95 G H z r a n g e to the th ir d ,
f o u r t h , f i f t h , a n d o c c asio n ally even sixth h a rm o n ic s o f th is range.
F u r th e r m o r e ,
he ha s in s ta lle d a liq u id h e liu m cooled in d iu m a n ti m o n i d e d e te c to r.
D e ta ils o f these w ill be in his thesis.
We h a v e c o n s tr u c te d a 17 —” x22
—" a lu m in u m p l a t f o r m a n d sev era l w a v e g u id e m ounts.
2
2
T h e la r g e r p l a t f o r m
p r o v id e s room f o r a f e r r i t e isolator, w h ic h red u c e s r e f le c tio n s , a n d f o r
a t h e r m is to r m o u n t, w h ic h e n a b le s th e e x p e rim e n te r to m e a s u re th e k ly s tr o n
p o w e r o u t p u t d ire c tly .
A f u r t h e r a d v a n ta g e is t h a t w a t e r co o lin g blocks
c a n be in sta lle d on th e k ly stro n . T h e 4" d isc h a rg e cell a n d p u m p in g sy ste m
a r e th e sam e as d e sig n e d by N. N. H a a s e 14, b u t the l a t t e r has been m o d if ie d
as well.
T h e m e c h a n ic a l p u m p s h a v e been m oved a b o u t n in e fe e t a w a y
f r o m th e m a n if o ld s , a n d m o u n te d on large a lu m in u m blocks.
T h e ju n c tio n
w a s m ad e w ith fle x ib le PV C tu b in g (1.5" d ia m e te r ) a t th e p u m p a n d m a n i f o ld
ends, m a te d w ith r ig id U -s h a p e d PV C tu b in g bolted to th e ceiling. T h is
h a s the d u a l a d v a n ta g e o f p r o v id in g v ib r a tio n iso la tio n b e tw e e n th e p u m p
a n d d e te c to r , a n d p r o v id in g m ore room fo r liq u id n itr o g e n D ew ars.
A f a r m ore s i g n i f ic a n t m o d if ic a tio n , the c o n s tr u c tio n o f th e e x te n d e d
n e g a tiv e glow d is c h a r g e w as acco m p lish e d by W. T. C o n n e r .13 D e ta ils
o f th e c o n s tr u c tio n w ill be p r o v id e d in his thesis. A v e ry b r i e f a c c o u n t
w ill be p r o v id e d here.
A stainless steel hollow c y li n d r ic a l e le c tro d e w as
19
in s e r te d in th e m ic ro w a v e p a th a d ja c e n t to the source p l a t f o r m , r e p la c in g
th e old t u r r e t e le c tro d e , w h ic h w as o u tsid e th e m ic ro w a v e p a th . In a d d it io n ,
a solenoid, c a p a b le o f p ro d u c in g up to 280 G auss w as p lac e d a r o u n d th e
d is c h a r g e tube.
When low pressures o f b u f f e r gasses w e re a d d e d , on
th e o r d e r o f 10 m T o rr, a v e ry f a i n t d is c h a r g e resu lte d . T h e r e was no
o b s e rv a b le re a d in g on the pow er s u p p ly c u r r e n t m eter. Such d isc h a rg e s
w ill be r e f e r r e d to as "abnorm al" d isc h a rg e s f o r th e rest o f th is thesis.
C o n v e n tio n a l DC glow d isc h a rg e s will be r e f e r r e d to as "norm al" d isc h a rg es.
A b n o r m a l d isc h a rg e s have several a d v a n ta g e s o v e r n o rm a l d isc h a rg e s
f o r ion spectroscopy. F irs t a n d fore m o st, the signals a r e m u ch s tr o n g e r
fo r g r o u n d v i b r a t io n a l sta te ions. L a te r c h a p te r s w ill e x p lo re this in
m ore d e ta il; only a b n o rm a l disc h a rg es w e re used in this e x p e rim e n t.
In a d d i t i o n , m u ch sm a lle r p a r t i a l pressu res o f in p u t re a c tiv e gas c a n
be used, on th e o r d e r o f .20 m T o rr. T h e r e f o r e , isotopic s u b s ti tu t io n becomes
m ore fea sib le .
F in a lly , w hen they a re f u n c t i o n i n g sm oothly, a b n o rm a l
d isc h a rg e s a re c o n s id e ra b ly q u ie te r, an o r d e r o f m a g n itu d e less noise
is n o t a ty p ic a l.
T h e d is a d v a n ta g e is th a t w hen th e y a re not f u n c t i o n i n g sm oothly,
a b n o r m a l d is c h a r g e s h a v e severe noise problem s.
T w o p ro b le m s caused
by a b n o r m a l d is c h a r g e noise a re spikes in th e d a ta , a n d c o m p u te r hangs.
T h e r e a r e tw o m ore serious problem s.
O ne is t h a t s p u rio u s d a ta c a n be
w r i tt e n on th e m a g n e tic ta p e , w r itin g o v e r v a lid d a ta , so t h a t c a u tio n
m u st be e x e rc ise d w h e n w o rk in g w ith tapes.
It is re c o m m e n d e d t h a t
th e u se r w r ite his file s to th e c o m p u te r a f t e r e a ch d a y ’s run.
F in a lly ,
th e m ost im p o r ta n t p o in t to note is t h a t th e a b n o rm a l d is c h a r g e is se verely
20
d a m a g in g to th e H u g h e s d io d e de te c to rs. O ne s h o u d alw ays use th e liq u id
h e liu m d e te c to r w h e n r u n n i n g th e a b n o rm a l d ischarge.
C le a rly , th e one m a jo r e x p e rim e n t le f t is th e d e te c tio n o f the
330- 3 31 t r a n s itio n e s tim a te d by F oster, et al., 7 to be 44234*100 M Hz, s u re ly
a t r a c ta b l e range. T h e a b s o rp tio n c o e f f ic i e n t is 450 tim es w e a k e r th a n
th e a b s o rp tio n c o e f f ic i e n t f o r th e l n - I io» w h ic h w as seen w ith a signal
to noise r a t i o o f 7 a f t e r a b o u t th re e m in u te s o f a v e r a g in g (11 scans).
T h is w o u ld seem hopeless, b u t it m ust be rea liz e d t h a t o u r sig n a l to noise
o f 7 w as o b ta in e d w i t h o u t a c u t o f f f i l t e r a n d a t 5 k G a u ss d e te c to r m a g n e tic
f i e l d - f a r f ro m o p tim u m c o n d itio n s. Since th e l n _ lio w as seen as a f o u r t h
h a r m o n ic a n d w i t h o u t a c u t o f f f ilte r , th e e x a c t p o w e r o f so u rc e r a d i a ti o n
is n o t k now n. It c a n , how e v e r, be e s tim a te d by a ssu m in g th e a b s o rp tio n
c o e f f ic i e n t to be 9 x 10-6 c m -1, th e p a th len g th to be 300 cm., a n d the
a b s o rp tio n to be 0.1 /uv.
All o f this results in a so u rc e p o w e r o f 30 juv
a t th e d e te c to r as m e a s u re d on a P rin c e to n A p p lied R e s e a rc h lock-in
A m p lif ie r .
m ag n e t.
As m e n tio n e d , this was d o n e w ith 5 A c u r r e n t on th e d e te c to r
P re se n tly , w ith a c u t - o f f a n d h ig h e r f ie ld , we c a n o b ta in 2 m V olt
a t th e f o u r t h h a rm o n ic , a b o u t 60 tim es b etter. Since th e 330- 3 sl occurs
a r o u n d 44 G hz, a k ly s tro n can be used d ire c tly , r e s u ltin g in a f u r t h e r
ga in o f 10. T h e a b s o rp tio n sh o u ld be ro u g h ly e q u a l to th e re c e n t m e a s u re m e n t,
since we a re t r a d i n g o f f a p p r o x im a te ly a f a c t o r o f 450 in re d u c e d a b s o rp tio n
c o e f f ic i e n t fo r a f a c t o r o f 600 in h ig h e r source pow er.
L o n g e r signal
a v e r a g in g w ill im p ro v e th e noise, a n d the e x p e rim e n t sh o u ld , th e r e f o r e ,
be q u ite feasible.
It is, o f course, v ita l th a t f u t u r e e x p e r im e n te r s rea liz e
th e y m u st use w a te r cooling, a n d not liq u id n itrogen.
21
T a b le I. - F r a c t i o n a l A b u ndances.
77 K
300 K
2.90x 10-1
8.95x 10~2
^21
8.54x 10~3
2 .3 4 x l 0 - 2
^31
4.08x10-*
3.11x10-2
T r a n s i t io n
22
T a b l e I I . - E s t i m a t e d Line W id th s(k H z ).
T =300 K.
T R A N S IT IO N
^ ‘'Doppler
^ ‘'Pressure8
U r* *10
1150
64
1150
2 20- 2 2 i
483
64
485
^ S lT ^ S l
130
64
145
T=77 K
T R A N S IT I O N
^ D o p p le r
^ P re ssu re 3
Av
l a - l 10
580
256
630
220- 2 21
250
256
360
3S0- 3 31
70
256
265
a A p re s s u re o f 8 m T o r r A r is used f o r these c a lc u la tio n s.
23
T a b l e I l l - M a x i m u m a b s o rp tio n C o e f f ic ie n ts ( c m -1)
T ra n sitio n
77 K
300 K
l n - l 10
9 x l0 -6
4 x l 0 -7
2 20- 2 21
l x l O -7
6 x l 0 -8
330- 3 31
6 x 1 0 '10
2 x l0 -8
24
REFERENCES
1 J. T. Shy, J. W. F a r le y , a n d W. H. Wing, Phys. R ev. A 24,
1146(1981).
2 T. A m a n o
a n d J. K. G.W atson, J. Chem . Phys. 81, 2689 (1984).
3 H. E. W arner, W. T. C o n n e r, R. H. P e trm ic h l, a n d R. C. Woods, J.
C h e m . Phys. 81, 2514 (1984).
4 M. Bogey, C. D e m u y n c k , M. D enis, J. L. D estom bes, a n d B. L em o in e ,
A stro n . A stro p h y s. 137, L I 5 (1984).
5 S. S a ito , K. K a w a g u c h i, a n d E. H ir o ta , J. C hem . Phys. 82,
45 (1985).
6 T. G. P h illip s , G. A. B lake, J. K e e n e , R. C. Woods,
a n d E. C h u r c h w e ll, Ap. J. 294, L45 (1985).
7 S. C. F o s te r, A. R. W. M c K e lla r, I .R. P e te r k in , J. K. G. W atson,
F. S. P a n , M. W. C r o f to n , R. S. A ltm a n , a n d T. O ka,
J. C hem . Phys. 84, 91 (1986).
8 C. H. T o w n e s a n d A. L. S chaw low , M icrowave Spectroscopy, (D o v e r
P u b lic a tio n s , Inc., N ew Y o rk , 1975).
9 A. D a lg a rn o , E. H e rb st, S. N o v ic k , a n d W iiliam K le m p e r e r , Ap.J.
183, L131 (1973).
10 C. S. G u d e m a n , Ph.D. T hesis, U n i v e r s i ty o f W isconsin-M adison, 1982.
11 J. B. H a s te d , Physics o f A tom ic C ollisions, ( B u tte r w o r th s , L o n d o n ,
1972) p732.
12 R. H. P e trm ic h l, Ph.D. T hesis, U n iv e r s ity o f W isconsin-M adison.
13 W. T. C o n n e r, Ph.D. Thesis, U n iv e r s ity o f W isconsin-M adison, 1988.
14 N. N. H aase, Ph.D. T hesis, U n i v e r s i ty o f W isconsin-M adison, 1981.
25
C H A P T E R III.
T H E S P E C T R O S C O P Y O F X 2J71/2 SO+.
26
Wu a n d Y e n s h a 1 f i r s t o b se rv e d S O + in 1977, in a f lo w in g a fte rg lo w .
L a te r ,T s u ji, et al.2 o b se rv e d th e ion, also in a n a fte rg lo w .
Both sets o f
a u th o r s , h o w e v e r, t h o u g h t th e y h a d seen S 0 2+. L a te r , T s u ji et al.3 re a liz e d
t h a t it w as SO+, t h a t h a d , in fa c t, been o bserved.
All o f these w e re low
re s o lu tio n e x p e rim e n ts , a n d p r o v id e d no s t r u c t u r a l in f o r m a t io n .
C ossart,
et a l* o b ta in e d th e f ir s t m e d iu m re s o lu tio n sp e ctra o f SO +, in t h a t th e y
w e re a b le to see r o ta tio n a l s tr u c tu r e . T h e y w ere, h o w e v e r, u n a b le to resolve
the la m b d a d o u b lin g . S u b s e q u e n tly , C oxon a n d F o s te r 5 o b se rv e d m e d iu m
re s o lu tio n sp e c tra w ith im p ro v e d a n a ly s is o f the r o ta tio n a l c o n s ta n ts,
b u t th ey , too, w ere u n a b le to s e p a r a te th e la m b d a d o u b lin g com p o n e n ts.
In 1984, H a r d w ic k et al.3 obse rv e d th e f ir s t high re s o lu tio n e le c tr o n ic
s p e c tr u m o f the ion, a n d w e re able to resolve la m b d a d o u b lin g .
L a te r
we o b s e rv e d th e m ic ro w a v e lines.7 R e c e n tly , M ilk m a n et al.8 o b se rv e d
h ig h re s o lu tio n em ssion sp e c tra o f SO+.
F in a lly , th e re h a v e been a s tr o n o m ic a l
o b s e rv a tio n s o f SO +, u s in g th e f re q u e n c ie s o b ta in e d in the p r e s e n t w o rk .9
T h is c h a p te r w ill discuss the m ic ro w a v e spe ctro sc o p y o f th e ion in the
la b o r a to r y .
T h e w o rk m e n tio n e d in this c h a p te r was d o n e in c o lla b o ra tio n
w ith Dr. N o r b e r t C a rb a llo .
T h e lock loop w as as d e s c rib e d in C h a p te r II o f this thesis, e x c ep t
t h a t th e t h ir d h a rm o n ic o f th e k ly stro n w as used f o r th e J = 9 /2 - * J = l 1/2
tr a n s itio n s , a n d th e o th e r lines w ere o b se rv e d w i t h o u t m u ltip lic a tio n .
A v a r i e ty o f d isc h a rg e s w ere used.
a rg o n w as th e b u f f e r gas.
F o r n o rm a l d isc h a rg es, a b o u t 20 m T o rr
E ith e r 2 m T o r r S 0 2 or 2 m T o rr e a c h o f H 2S
a n d 0 2 w ere em p lo y e d as r e a c tiv e gases.
it g a v e s ta b le r d ischarges.
We p r e f e r r e d to use S 0 2, since
N o rm al d isc h a rg e s w ere u su a lly r u n a t 400
27
m A. T h e f i r s t a b n o rm a l d isc h a rg e w as a tt e m p t e d w ith a n a rg o n b u f f e r
a n d 0.2 m T o rr S 0 2, b u t th e signal to noise r a t i o w as q u i te p o o r f o r the
J = 9 /2 - * J = l 1/2 line. It w as f o u n d t h a t c o n s id e r a b le im p r o v e m e n t was
r e a liz e d w ith p u re S 0 2, w h ic h gave q u ite s ta b le d isch arg es.
F igure I
o f f e r s a co m p a riso n o f s p e c tra o b ta in e d w i t h th e tw o types o f discharges.
A b n o r m a l d isc h a rg es w ith H 2S a n d 0 2 w e re n e v e r sta b le e n o u g h to p e rm it
spectro sc o p y , reg a rd le ss o f w h e th e r or not a rg o n w as th e b u f f e r . T h e
a b n o rm a l d isc h a rg e s w e re r u n a t 1800 V.
A m a jo r c o m p lic a tio n is th a t S 0 2 a n d H 2S a r e n o t v o la tile a t
liq u id n itro g e n te m p e ra tu re s . S t r a i g h t f o r w a r d liq u id n itr o g e n cooling
re s u lte d in th e c o n d e n s a tio n alo n g th e w alls o f all th e r e a c tiv e gases.
It w as not th o u g h t possible (la ter, c o n f i r m e d by e x p e rim e n t) to see the
lines a t room te m p e ra tu re .
T h e r e f o r e , th e fo llo w in g p r o c e d u r e w as a d o p te d .
L iq u id n itro g e n was se n t t h ro u g h 2 o f th e 4 cooling lines u n t il S 0 2 or
H 2S fro z e out.
At th is p o in t, one o f th e 2 cooling lines w as d isc o n n e c te d ,
a n d the tu b e was a llo w e d to w a rm up.
O nce the r e a c tiv e gas m a d e it
t h ro u g h , the liq iu d n itr o g e n was a d m i tt e d t h ro u g h th e one r e m a in in g
cooling line. T his, a d m i tt e d ly sloppy, p r o c e d u r e p o in ts o u t a pro b le m
in o u r la b o r a to r y , t h a t f u t u r e e x p e rim e n te r s should a d d re ss, n am ely ,
t h a t c u r r e n tl y we can use only liq u id n itr o g e n or w a te r cooling.
M any
in te r e s tin g ions, such as SiF+ a n d CC1+, r e q u ir e p re c u rs o rs w h ic h are
n ot v o la tile a t liq u id n itr o g e n te m p e r a tu r e , a n d t h e r e f o r e , a system o f
i n te r m e d ia t e cooling, su ch as a fre o n p u m p , w ould be d e sira b le .
28
F ig u re 1-The J»4.5-*5.5 (+) p a r i t y tra n s itio n o f SO+ is m ore in te n se in
a n S 0 2 b u f f e r , a b n o rm a l d isc h a rg e th a n a n a rgon b u f f e r d ischarge. T h e
solid line s p e c tr u m was o b ta in e d w ith 6 m T o rr S 0 2 a n d r e q u i r e d 113
scans. T h e d a s h e d line sp e c tru m was o b ta in e d w ith 8 m T o rr A r an d
O.S m T o rr S 0 2 a n d re q u ir e d 135 scans. C o n d itio n s com m on to both spe ctra
a r e 10 javolt lock-in scale, 15 m se c /p o in t, 10 msec tim e c o n s ta n t, InSb
d e te c to r (7 T o r r H e p ressure a n d 5 kG auss field), f a s t flow , p a r t i a l liq u id
n itro g e n cooling (see text), 1600 kH z FM, 30 kH z AM, 2 baseline suppressions
(533 kHz), a n d 31 p o in t sm oothing.
29
S 0 + 4.5-5.5(+) ABNORMAL
.10
.05
-.05
-.10
85113. 0
85116. 0
8 5119. 0
FREQUENCY/3.
SOLID LINE-PURE S02 DASHED-Ar BUFFER
30
F ig u re 2 -T h e Z e e m a n e f f e c t o f th e J=4.5—5.5 (+) t r a n s it io n o f S O + is
s tr i k in g l y d e m o n s t r a t e d in this c o m p a rs io n o f tw o n o rm a l d is c h a r g e scans.
T h e lo w e r tra c e is w i t h o u t a n a p p lie d m a g n e tic f ie l d a n d th e u p p e r tra c e
is w i t h a 100 G a u ss f ie ld a p p lie d to th e d is c h a r g e tube. T h e SO + lin e
in th e c e n te r o f th e g r a p h is c o n s id e r a b ly b r o a d e n e d by th e a p p li e d fie ld ,
b u t t h e c o m p a n io n lin e , a t the r ig h t e n d o f th e scale, is n o t a f f e c te d .
T h e e x p e r i m e n t a l c o n d itio n s com m on to b o th s p e c tr a a re as follow s: 24
m T o r r A r, 2 m T o r r SOa, 400 m a d is c h a rg e , p a r t i a l L N 2 cooling, f a s t flo w ,
100 scans, 15 s e c /s c a n , 2400 k H z FM , 30 k H z AM, 3 b a s e lin e su p p re ssio n s
(800 k H z), a n d 11 p o in t sm ooth.
31
S 0 + 100GAUSS AND OGAUSS J= 4.5-5.5
.40
.30
.20
.10
-.10
-.20
85113.0
85116.0
85119.0
FREQUENCY/3.
85122.0
32
F ig u re 3 -T h e Z e e m a n lobes o f th e
J*4.5-»5.5 (-) tr a n s it io n w ere o b s e rv e d
in a p u r e S 0 2 a b n o r m a l d isc h a rg e .
T h e e x p e r i m e n t a l c o n d itio n s a r e as
follow s: 10 juvolt lo ck -in scale, 15 m s e c /p o in t, 10 msec tim e c o n s ta n t,
InSb d e te c to r (7 T o r r He p re s s u re a n d 5 k G a u s s fie ld ), 6 m T o r r S 0 2, a b n o rm a l
d is c h a r g e (1800 volt), f a s t flo w , p a r t i a l l iq u id n itr o g e n cooling, 1600
k H z FM , 30 k H z AM, 3 b a s e lin e supp re ssio n s (533 kHz), 160 scans, a n d
11 p o in t s m o o th in g .
33
S 0 + J=4.5-5.5(-)ABNORMAL
.10
0
-.10
84990.0
84996.0
FREQUENCY/3.
34
F ig u re 4 -T h e J=4.5-*5.5 (-) t r a n s it io n o f SO+ a t was o b s e rv e d a t a k ly stro n
f r e q u e n c y o f 84992.6 M H z (ro u g h ly th e m id p o in t o f th e g r a p h ) , in a n o rm a l
d is c h a r g e u n d e r th e sam e c o n d itio n s as th e F ig u r e 2 zero f i e l d sp e ctru m .
T h e o t h e r f e a t u r e is a n u n i d e n t i f i e d i n t e r f e r i n g line.
35
S 0 + OFIELD J = 4 . 5 - 5 . 5 H
.15
.0
-.15
84990.0
84995,0
FREQUENCY/3
36
F ig u re 5 -T h e J=1.5-»2.5 (+) tr a n s it io n a t 116179.8 M Hz as o b se rv e d in
a n o r m a l d is c h a r g e is p r e s e n te d in this fig u re . T h e e x p e r im e n ta l c o n d itio n s
a r e as follow s: 21 m T o rr A r, 3 m T o rr SO a, 300 mA d is c h a r g e , p a r t i a l
L N 2 cooling, f a s t flow , 150 scans, 15 s e c /s c a n , 800 kH z FM, 30 k H z AM,
3 b a s e lin e su p p re s s io n s (800 kH z), H u ghes d iode d e te c to r , a n d 51 p o in t
sm ooth.
37
S 0 + J=1.5-2.5(+)NORMAL
i | ■
.24
.18
.12
.06
-.06
-.12
-.18
116175.0
116180.0
FREQUENCY
■ ■
38
F ig u re 6-T he J=1.5—2.5 (-) t r a n s it io n a t 115804.4 M Hz is o b se rv e d u n d e r
th e sam e c o n d itio n s as F ig u re 5, ex c ep t t h a t 140 scans w e re r e q u ir e d .
39
S 0 + J=1.5-2.5(-)NORMAL
.16
.12
.08
. 04
.0
-.04
-.08
-.12
115800.0
115805.0
FREQUENCY
40
F ig u re 7 -T h e tw o lobes o f th e J » 1.5—*2.5 (-) t r a n s it io n a r e o b se rv e d in
a n a b n o r m a l d is c h a rg e . T h e e x p e r im e n ta l c o n d itio n s a r e as follows: 6
m T o r r S 0 2, 250 G auss n o m in a l f ie ld , 1900 volt d is c h a rg e , p a r t i a l LN 2
co o lin g , f a s t flo w , 400 scans, 15 s e c /s c a n , 800 k H z FM, 30 k H z AM, 3
b a s e lin e s u p p re s s io n s (800 kH z), H u g h e s d io d e d e te c to r , a n d 51 p o in t
sm ooth.
S 0 + J=1.5-2.5(-)ABNORMAL 250 GAUSS
.08
.08
.04
.02
.02
.04
.08
115800.0
115805.0
FREQUENCY
42
F ig u re 8 -T h e low er f r e q u e n c y lobe o f J=1.5—2.5 (+) t r a n s it io n a t 116178.5
M H z a n d a n in te r lo p i n g lin e a t 116183.4 M H z a r e o b s e rv e d u n d e r the
sam e c o n d itio n s as F ig u r e 7, e x c e p t t h a t 200 scans h a v e b e e n a v e ra g e d
a n d th e r e h a v e been 2 b a s e lin e suppressions.
43
SO* J=1.5-2.5(+) ABNORMAL AND INTERLOPER
.GO
.40
.20
-.20
-.40
116175.0
116178.0
116181.0
FREQUENCY
116184.0
44
F ig u re 9 -T h is a tra c e o f the s p e c tru m o f both Z e e m a n lobes o f th e J*0.5—1.5
(-) t r a n s it io n in a n a b n o rm a l d isc h a rg e w ith th e sam e e x p e r i m e n t a l c o n d itio n s
as in F i g u r e 7, e x c e p t th a t we h a v e a v e ra g e d 376 scans.
45
S 0 + 27r1/2 J = 0 .5 -1 .5
. 015
.0
-.015
-.030
69405.0
69410.0
FREQUENCY
46
F ig u re 10-T he J=0.5-*1.5 (-) t r a n s it io n a t 69408.4 M Hz ( f e a t u r e in th e
c e n te r) c a n b a r e ly be seen in a n o rm a l d isc h a rg e.
T h e e x p e r i m e n t a l c o n d itio n s
a re as follow s: 25 m T o rr A r, 3 m T o rr S 0 2, 300 m a d is c h a rg e , p a r t i a l LN 2
c ooling, f a s t f lo w , 382 scans, 15 s e c /s c a n , 800 k H z FM, 30 kH z AM, 3
b a s e lin e su p p re s s io n s (800 kHz), H u g h e s d io d e d e te c to r , a n d 51 p o in t
smooth.
-.060
j __ j— »— *-
69405.0
i
■
69410.0
FREQUENCY
■
- j —
i—
-j—
*-
48
T a b le I. O bserved T r a n s itio n Frequencies.
J
1/ 2 —►3/2(-)
v(MHz)obgerved v(MHz)calculateda
69408.371(100)
O bs.-C alc.
69408.378
0.007
3 / 2 —►5/2(-)
115804.445(48)
115804.455
0.010
3 / 2 —5/2(+)
116179.835(45)
116179.845
0.010
9 / 2 —11/2(-)
254977.815(26)
254977.814
0.001
9/2-* 11/2(+)
255353.208(40)
255353.205
0.003
a C a lc u la te d fro m pro g ra m , D O U B P I.F O R (see text) w ith
the M icrow ave(M ) c o n s ta n ts in T a b le II a n d
A 0=365.2 c m -1 (R e fe r e n c e 11).
49
F iv e tr a n s it io n s o f 2n 1/ 2 SO + w ere obse rv e d . E x a m p le s o f s p e c tra
f o r th e m a r e giv en in F ig u re s 2-10. T h e i r f r e q u e n c ie s a re given in T a b le
I.
We also p r e s e n t f re q u e n c ie s c a lc u la te d w ith o u r p ro g ra m , D O U B P I.F O R ,
w h ic h w ill be discussed in m ore d e ta il l a t e r in th e c h a p te r. T h e e x c e lle n t
a g r e e m e n t is n o t s u rp r is in g f o r th e J = 9 / 2 —►
11 / 2 a n d J = 3 / 2 —*5/2 tr a n s itio n s ,
s in c e the c a lc u la te d c o n s ta n ts w ere v a rie d to give th e best a g re e m e n t
w ith th e o b se rv e d fre q u e n c ie s . T h e close a g re e m e n t f o r th e J= 1/ 2 —*3/2
is a s o m e w h a t o f a s u rp rise ; a g lan c e a t F ig u re s 9 a n d 10 rev e a ls t h a t
th e sig n a l to noise r a tio is r a t h e r poor f o r th is tra n s itio n .
Because we
h a d o n ly one n o rm a l d isc h a rg e scan, a n d b ecause th e signal to noise was
poor, we fee l t h a t 100 kH z is not a n u n r e a s o n a b ly large e rr o r lim it fo r
th is t ra n s itio n .
T h r e e p roblem s e n c o u n te r e d in th is e x p e rim e n t s h o u ld
be a p p a r e n t f r o m these spectra: (1) SO+ lines a re c o n s id e ra b ly w e a k e r
t h a n th e i r H C O + c o u n te r p a r ts , (2) i n t e r f e r i n g lines a re f a i r ly p r e v a le n t,
a n d (3) a b n o r m a l d isc h a rg e s do not m a r k e d ly im p ro v e th e signal. T h is
w ill be d iscussed in g r e a te r d e ta il l a te r in th e c h a p te r.
th e 2n s/ 2 SO+ lines w ere n o t successful.
A tte m p ts to observe
T h e o t h e r J = I / 2 —*J=3/2 t r a n s itio n
a t 69783.7 M H z w as not obse rv e d b ecause o f i n t e r f e r i n g lines.
T h e sam e p ro b le m also o c u rr e d in th e s e a rc h f o r the J= 1 3 /2 —*J=15/2
tra n s itio n s .
A m a jo r i n t e r f e r i n g lin e w as seen a t 347741.564 MHz.
F ig u re
11 d e p ic ts a n u n s u c c e s s fu l a tt e m p t to use the Z e e m a n e f f e c t a n d b a seline
s u b tr a c ti o n to o b serve th e line.
a b o u t th e a tte m p t.
A f e w c o m m e n ts a re p e rh a p s in o r d e r
To begin w ith , b a s e lin e s u b tr a c tio n is e x p la in e d in
d e ta i l in the thesis o f N. D. P i l t c h 10, b u t e s se n tia lly it consists o f N scans
b e in g a d d e d in th e n o rm a l w ay, a n d th e n N m ore scans b e in g s u b tr a c te d .
50
F ig u re 11-O ur a tt e m p t s to obse rv e the J=*6.5-»7.5 (-) t r a n s itio n f a ile d ,
b e c au se o f th e larg e i n t e r f e r i n g line a t 347740 MHz. T h e top tr a c e is
a s p e c tr u m a t 250 G auss n o m in a l f ie ld n o rm a l disc h a rg e.
N e i th e r line
is d u e to SO+. T h e m id d le tra c e is 100 scans a t 50 G auss f o llo w e d by
s u b t r a c t i o n o f 100 scans a t 250 Gauss. T h e lo w e r tra c e is 100 s c an s a t
50 G a u ss s u b tr a c te d by 100 scans a t 50 Gauss, w h ic h sh o u ld h a v e re s u lte d
in no o b s e rv e d signal.
Both m id d le a n d low er tra c e a re e x p a n d e d by
a f a c t o r o f 5 r e l a ti v e to th e u p p e r trace. C le a rly , we c a n n e v e r get rid
o f th e i n t e r f e r i n g line.
51
S 0 + J=6.5-7.5(-)SEARCH
-
2.0
-
4.0
v*i,/**A,*’V
i v:
8 6928.0
86934.0
FREQUENCY/4.
86940.0
52
T h e t r i c k is to a lt e r c o n d itio n s in such a w a y t h a t th e line o f in te r e s t
is n o t visible in th e s u b tr a c tio n phase, b u t th e i n te r f e r i n g line is. T h e r e
a re , h o w e v e r, d i f f ic u l ti e s . T h e f ir s t is t h a t th e signal goes d o w n by a
f a c t o r o f two, n o t a n e gligible c o n c ern w ith poor signal to noise. T h e
se co n d is th a t w h e n th e i n t e r f e r i n g line is c o n s id e ra b ly stro n g e r th a n
th e lin e o f in te re s t, it is not n e c essa rily rem oved.
It should be p o in te d
o u t t h a t th e i n t e r f e r i n g line was re d u c e d by a f a c t o r o f 10. T h u s th e
m e th o d s h o u ld w o rk w hen i n t e r f e r i n g a n d d e s ire d lines a re o f c o m p a r a b le
in te n s ity .
T h e r e a re a t least th re e reasons w hy we o b ta in e d poo rer signals
f o r S O + th a n f o r HCO+.
A c c o rd in g to K. A. P e te r s o n 11 th e d ip o le m o m e n t
o f SO + is 2.3±0.1 D ebye, w h e re as th e dip o le m o m e n t fo r H C O + is 4.1 ±0.2
D e b y e a c c o r d in g to Haese a n d Woods.12
Because th e in te n s ity o f a m ic ro w a v e
t r a n s i t i o n d e p e n d s on the s q u a re o f th e d ip o le m o m e n t (see, f o r e x a m p le,
T o w n e s a n d S c h a w lo w ,13 page 24), the f a c t o r o f 2 r e d u c tio n in th e dip o le
m o m e n t causes a f a c t o r o f 4 r e d u c tio n in the signal stre n g th . T h e la m b d a
d o u b l in g causes a n a d d it io n a l r e d u c tio n o f 2.
F in a lly , th e p a r t i a l cooling
re s u lts in a w a r m e r d isc h a rg e, w h ic h f u r t h e r re d u c e s signal s tre n g th .
In o r d e r to c a lc u la te th e c o n s ta n ts a n d e x a m in e the Z e e m a n e f f e c t,
it is necessary to e x a m in e the th eory. T h e e le c tro n ic g ro u n d s ta te o f
SO + is th e 2f7 sta te .
A H a m ilto n ia n can be f o u n d in V eseth’s 14 p a p e r,
b u t we sim p ly em p lo y e d the e n e rg y level f o rm u la s o f G o rd y a n d C o o k 15
a n d M iz u s h im a 16. G o rd y a n d C o o k 16 propose the fo llo w in g f o r m u la f o r
th e e n e rg y levels,
53
E * = Bv( l - ^ - ) J ( J + 1 ) ± i p ( J + I ) - D V[ ( J - i ) ( J + y )2 (J + -|)+1]. (1)
T h is f o r m u la is b a sed on th e a p p r o x i m a t io n A / 4 » B .
A m ore e x a c t t r e a tm e n t
is in M iz u s h im a .16 H is m a t r ix e le m e n ts a r e as follow s:
< 2f73/2| HI 2f73/2> = Av/ 2 + Bv- D v[ ( J + l / 2 ) 2+ 3 J + l],
( 2)
< 2/71/2| HI 2n 3/2> = - (BV+ p v/ 4 - 2 D V ( J + l / 2 ) 2[ J ( J + l) - 3 / 4 ] i/ 2 , ( 3 )
and
< 2/71/2| H| 2n 1/2> = - A v/ 2 + Bv( ( J + l / 2 ) 2) - D v[ ( J + l / 2 ) 2)2 + 3 ( J + l / 2 ) 2] ( 4)
± p/2(J+l).
A p ro g ra m , D O U B P I.F O R , ( A p p e n d ix 3 o f th is thesis) was w r itte n , w h ic h
c a lc u la te d th e e n e rg y levels fo r each p a r i t y o f e a c h J state, in both th e
zero f ie ld a n d Z e e m a n cases.
T a b le II is a c o m p ila tio n o f c o n s ta n ts c a lc u la te d
by both th e G o r d y a n d C o o k 16 m eth o d a n d th e M iz u s h im a 16 m eth o d , a n d
a c o m p a ris o n w ith o p tic a l d a ta .
It sh o u ld also be n o te d th a t th e re is
c o n s id e r a b le f r e q u e n c y d i f f e r e n c e (a b o u t 4 M H z f o r th e J = 9 / 2 - » l l / 2
t r a n s it io n ) d e p e n d in g on w h e t h e r th e A v v a lu e o f M ilk m an el al.s o r t h a t
o f H a r d w ic k et al .6 is used ( h o ld in g th e o t h e r p a r a m e t e r s co n sta n t). T h e
p o in t o f all th is is t h a t to o b ta in t r u e m ic ro w a v e a c c u r a c y f o r the Bv
a n d Dv c o n s ta n ts, it w ill be n e c essa ry to o b se rv e th e 2/73/ 2 state.
In T a b le
III, p r e d ic tio n s a r e listed f o r the u n o b s e rv e d 2f i x/ 2 S O + lines a n d f o r
th e
2n s/ 2 SO + lin e s f o r th e b e n e f i t o f f u t u r e e x p e rim e n te rs .
O ne o f th e m ost in te r e s tin g a n d i m p o r ta n t aspects o f this
w o rk w as o u r s tu d y o f th e Z e e m a n e f f e c t.
T h e f a c t , t h a t we w ere able
54
T a b le II. Spectroscopic C o n sta n ts.
B0
M icrow ave(G C )
M icrow ave(M )
O ptica l
23248.597MHz
23248.935MHz
23251.6M Hza
D0
32.489kHz
33.105kHz
31.8kH za
p0
375.387MHz
375.390MHz
264.0M Hza
A0
assum ed
assum ed
a R e fe re n c e 8.
b R e f e re n c e 11.
365.2 c m -1 b
55
T a b le I I I . P r e d ic te d T ra n sitio n F req u en c ies.3
P A R T I. 2J71/2 States
J
1 / 2 —3/ 2
3 / 2 —5/ 2
5/2-1/2
1 / 2 —9/ 2
9/2-11/2
1 1 /2 -1 3 /2
1 3 /2 -1 5 /2
1 5 /2 -1 7 /2
1 7 /2 -1 9 /2
KMHz)
69783.768
116179.845
162573.966
208965.957
255353.205
301736.757
348115.221
394487.423
440853.752
K M H z)
69408.378
115804.455
162198.576
208589.346
254977.814
301361.367
347739.831
394112.423
440478.362
P A R T II. 2f l 3/ 2 States
J
3 / 2 —5/2
5/2-1/2
1/2-9/2
9 /2 -1 1 /2
1 1 /2 -1 3 /2
1 3 /2 -1 5 /2
1 5 /2 -1 7 /2
1 7 /2 -1 9 /2
KMHz)
116491.898
163085.832
209676.939
256264.413
302847.446
349425.231
395996.962
442561.828
a T hese w e re c a lc u la te d using D O U B PI.FO R (see Text), the
M icrow ave(M ) c o n s ta n ts in T a b le II, a n d a v a lu e o f 365.2 c m -1
f o r A 0 (R e fe r e n c e 11).
56
to m easure sim ila r c h a ra c te r is tic Z eem an e ff e c ts f o r each o f th e fiv e
observed tra n s itio n s , p ro v id e d the c o n f ir m a tio n t h a t th e ir c a rr ie r was
SO+. T h e Z e e m a n e f f e c t also e n a b le d us to d i f f e r e n t i a t e betw een lines
due to SO+ a n d i n te r f e r i n g lines (see F ig u re 1). P e rh ap s th e most in te re s tin g
aspect o f ou r Z e e m a n e f f e c t m ea su rem e n ts is t h a t th ey w ere f o r a 2fT1^r2
molecule, w hich in a p u re H u n d ’s case a, is n e a rly zero. T he reason f o r
this is th a t if we com bine term s fro m M iz u sh im a ’s 16 fo rm u la s, we o b tain
the fo llo w in g results:
< 2n 3/2| H z| 2/73/2> -
u b HM
—
|.^ 3g, + 3 /2 g , - g n (J+ l/2 )* ]
(5)
< 2(71/2| H z| Jn 3/2> -
jiioHM
I ^ J - ^ g #[(J+ l / 2 ) 2- l ] i / 2
(6)
< 2n 1/2i f t zi 2n 1/2> -
u b HM
■jJfjTTj1281" 8' 4 M J+1/ 2>2 - « n ( J + i / 2 ) 2]. ( ?)
T h e values o f g! a n d g, a re 1 a n d 2.0023, w h ile gn a n d gp a re a p p ro x im a te ly
th re e o rd ers o f m a g n itu d e sm aller. T his m eans t h a t the < 2n x/ 2| H z| 2i7x/ 2>
m a trix elem ents a re q u ite sm all, a n d th a t a s ig n i f ic a n t c o n trib u tio n to
the Z e e m a n e f f e c t comes fro m th e < 2f7x/ 2| H z| 2n 3/ 2> terms. T h u s the
observed SO+ lines show Z e e m a n s h ifts o f only 1-3 M Hz f o r m agnetic
fie ld s up to 300 Gauss, w hile ty p ic a l lines o f o th e r p a ra m a g n e tic species
w ould show s h if ts o f h u n d r e d s o f MHz.
We h a v e a tte m p te d to q u a n it a ti v e ly u n d e r s ta n d a n d f it the
o bserved p a tte rn s by c a rr y in g o u t a series o f c alculations.
In these sp littin g
c a lc u la tio n s, g( a n d g, ha d th e ir usual values o f 1 a n d 2.0023, respectively,
56
to m e a s u re s im ila r c h a r a c te r is t ic Z e e m a n e f f e c ts f o r e a ch o f th e f iv e
o b se rv e d tr a n s itio n s , p r o v id e d th e c o n f i r m a ti o n t h a t th e i r c a r r i e r w as
SO+. T h e Z e e m a n e f f e c t also e n a b le d us to d i f f e r e n t i a t e b e tw e en lines
d u e to SO+ a n d i n t e r f e r i n g lines (see F ig u re 1). P e r h a p s th e most in te r e s tin g
a sp ec t o f o u r Z e e m a n e f f e c t m e a s u re m e n ts is t h a t th e y w ere f o r a 2n l / 2
m olecule, w h ic h in a p u r e H u n d ’s case a, is n e a rly zero. T h e rea so n f o r
th is is t h a t i f w e c o m b in e term s f ro m M iz u sh im a ’s 16 f o rm u la s , we o b ta in
th e f o llo w in g results:
< 2/T3/2l H z| 2n 3/2> =
( 5)
2 J ( - - | )[3g, + 3 /2 g . - g n ( J + l / 2 ) 2]
u bHM
< 2n 1/2i h zi 2n 3/2> =
< 2rTi/2| f t z| 2n 1/2> =
( 6)
J + i / 2 ) 2- ! ] 1/ 2
/abHM
2J(J+- 1)[2g, - g, ± gp( J + l / 2 ) 2 - g n ( J + l / 2 ) 2]. ( 7)
T h e v a lu e s o f gj a n d gg a r e 1 a n d 2.0023, w hile gn a n d gp a re a p p r o x im a te ly
th re e o r d e r s o f m a g n itu d e sm aller. T h is m eans t h a t th e < 2n i / 2| H z| 2U 1/ 2>
m a t r ix e le m e n ts a re q u ite sm all, a n d th a t a s ig n i f ic a n t c o n tr i b u ti o n to
th e Z e e m a n e f f e c t comes f r o m the < 2/7j/2I H z| 2/7a/ 2> term s.
T h u s the
o b se rv e d SO + lines show Z e e m a n s h if ts o f only 1-3 M Hz f o r m a g n e tic
f ie ld s up to 300 G auss, w hile ty p ic a l lines o f o t h e r p a r a m a g n e tic species
w o u ld show s h if t s o f h u n d r e d s o f MHz.
We h a v e a tt e m p t e d to q u a n it a ti v e ly u n d e r s t a n d a n d f i t the
o b s e rv e d p a tt e r n s by c a r r y i n g out a series o f c a lc u la tio n s.
In these s p littin g
c a lc u la tio n s , gj a n d g8 h a d th e i r usual values o f 1 a n d 2.0023, re s p e c tiv e ly ,
57
a n d gn a n d gp w ere t r e a te d as a d ju s ta b le p a ra m e te rs . B ecause th e m ag n e tic
f i e l d a n d m ic ro w a v e p o la r iz a tio n v e c to r w ere p e r p e n d i c u l a r A M = -1,+ 1
se le c tio n rules w e re used.
A c o n s ta n t h o m ogeneous f ie ld w as assum ed.
T h e n th e r e w as th e u su a l p r o c e d u r e o f d ia g o n a liz in g th e z e ro - fie ld m a trix ,
fo llo w e d by c a lc u la tio n o f the t r a n s f o r m a t io n m a tr ix , w h ic h w as th en
a p p lie d to th e Z e e m a n m a trix . T h e re la tiv e in te n s itie s , I, o f e a c h M c o m p o n e n t
w e re c a lc u la te d f ro m th e s ta n d a r d (see T o w n es a n d S c h a w lo w 13, p 256)
f o r m u la f o r AM = 1, AJ = 1 t r a n s itio n s
I = (J'+ M '- 1 ) ( ( J '+ Nf),
(8)
w h e re th e p rim e s c o rre s p o n d to th e u p p e r sta te q u a n t u m n u m b ers.
For
th e J = l / 2 —3 /2 c o m p o n e n t the M = - l / 2 - » l / 2 c o m p o n e n t is c o n s id e ra b ly
d i f f e r e n t in f r e q u e n c y f ro m the M“ l / 2 - * 3 /2 c o m p o n e n t ( a b o u t 1.5 MHz),
a n d is th re e tim es w e a k e r, so to c a lc u la te t h a t s p littin g the s e p a r a tio n
o f th e M = l / 2 —3 /2 was s im p ly m u ltip lie d by two.
F o r th e o t h e r low er
J ’s, 3 /2 a n d 9 /2 , a s lig h tly m ore c o m p lic a te d p r o c e d u r e w as used because
th e M c o m p o n e n ts w ere closer.
F or these a w e ig h te d a v e ra g e w as tak e n ,
th e f o r m u la is given by
EAi/j Ij
^ aVg “ ---------
.
( g)
PI ,
a n d th e s p littin g was ta k e n to be tw o tim es this term .
o f c a lc u la te d Z e e m a n s p littin g s vs. obse rv e d sp littin g s.
T a b le IV is a c o m p ila tio n
B ecause o f an
i n t e r f e r i n g lin e a t 116183.3 M Hz, the e x p e r im e n ta l s p li t ti n g f o r th e J = 3 / 2 —
58
5/2(+) t r a n s it io n w as sim p ly ta k e n as tw ice th e d is p la c e m e n t o f th e low er
c o m p o n e n t f r o m th e u n s p lit line. O u r d a ta is sim ply not good e n o u g h
to p e rm it g r e a te r t h a n c r u d e a c c u ra c y in th e Z e e m a n p re d ic ito n s . T h e
c o n s ta n ts c a n be m a n i p u la t e d to r e p ro d u c e some p a r t i c u l a r sets o f tra n s itio n s ,
b u t n o t a ll o f th e tr a n s it io n s a t the sam e tim e. T a b le V is a c o m p ila tio n
o f term s f o r a s a m p le c a lc u la tio n , w h e re U n a n d U 12 a re t r a n s f o r m a t i o n
c o e f f ic i e n t s , th e H ’s a r e the Z eem an H a m ilto n ia n m a tr ix e le m e n ts c a lc u la te d
f r o m E q u a tio n s 5 t h r o u g h 7, a n d A E /M is th e c a lc u la te d s h if t.
T h e f o r m u la
r e l a ti n g th e q u a n ti ti e s is
A E /M =
U n 2( H Z22/M ) + 2 U n U ia( H zia/M ) + U 122( H ZU/M ). ( 10)
F in a lly , a s p e c tra l sim u la tio n ro u tin e , S IM U L A T E .F O R ,
(A p p e n d ix 4) w as w r itte n .
T h e p ro g ra m w as d e r iv e d fro m o f W. T. C o n n e r ’s17
S ta rk E f f e c t s im u la tio n p rogram .
E sse n tia lly all t h a t was c h a n g e d w as
th e w a y o f c a lc u la t in g f r e q u e n c y shifts. S am ple o u t p u t f o r th e v a rio u s
J t r a n s it io n s is sh o w n in F ig u re s 12-14.
In all cases, the - p a r i t y is th e
low er lin e a n d th e + p a r i t y is the u p p e r line. T h e u n s p lit line is in th e
c e n te r.
F o r th e s im u l a t io n gp=0.007 a n d gn=0.0002 w ere a r b i t r a r i l y chosen,
a n d th e l i n e w i d th w as assum ed to be 200 kH z. Since T is not k n o w n ,
b u t is s u re ly c o n s id e r a b ly h ig h e r th a n 77 K, a n d d A v / d P has a 1 /T d e p e n d e n c e
(see C h a p t e r II), a p re s s u re b ro a d e n in g p a r a m e te r o f 10 k H z / m T o r r is
a r e a s o n a b le guess. T a k i n g in to a c c o u n t source m o d u la tio n , etc., 200 kH z
is p r o b a b ly n o t u n re a s o n a b le .
A tte m p ts to o b t a i n e x p e r im e n ta l lin e w i d th s
w ere f r u s t r a t e d by th e f a c t th a t th e lin e w id th is v e ry d e p e n d e n t on sm o o th in g ,
Table IV. Experim ental and C alculated Zeem an Spittings (M H z).
tra n s itio n
ex p e rim ental
gp=0
gp*0.007
gn=0
gn=0
gp*0.007
gp=0.007
gn=*-.0002 gn=.0002
j5p-.009
g n=.0002
1 /2 —3/2(-)
4.318
4.165
4.513
4.677
4.385
4.489
3 / 2 —5/2(-)
4.199
3.370
3.919
4.076
3.763
3.919
3 / 2 —5/2(+)
3.060
3.370
2.822
2.978
2.665
2.508
9 / 2 - 1 1/2(-)
3.633
3.336
3.618
3.775
3.462
3.533
9 / 2 - 1 1/2(+)
2.807
3.336
3.118
3.276
2.962
2.891
<50
T able V. Terms In Zeeman C alculations.*
J
Un
U 12
H ZX1/M
H Z12/M
l/2 ( + )
1.00000000
0.00000000
0.
0.
1.528
1.528
l/2 (-)
1.00000000
0.00000000
0.
0.
-2.129
-2.129
3/2(+)
0.99999312
0.00370861
313.693
181.214
0.671
2.019
3/2(-)
0.99999312
0.00370835
313.693
181.214 -0.791
0.557
5/2(+)
0.99998166
0.00605594
134.439
126.824
0.445
1.985
5/2(-)
0.99998167
0.00605532
134.439
126.824 -0.496
1.048
9 /2(+ )
0.99994500
0.01048794
47.529
77.659
0.268
1.902
9/2(-)
0.99994502
0.01048613
47.529
77.659 -0.286
1.347
ll/2 (+ )
0.99991981
0.01266425
32.905
64.927
0.224
1.873
1 1/2(-)
0.99991984
0.01266164
32.905
64.927
-0.236
1.412
a F o r 280 G auss, gp = 0.007, gn - 0.
h
Z22/ m
A E /M
61
F ig u re 12-Model s p e c tr a f o r th e J=0.5-»1.5 tra n s itio n s a re p re s e n te d .
The
c e n te r tr a c e is th e zero f ie ld s p e c tru m , the u p p e r tra c e is th e + p a r i t y
t r a n s it io n , a n d th e lo w e r tr a c e is the - p a r ity t ra n s itio n .
The - p arity
s p li t ti n g is s lig h tly g r e a te r , b u t th e re is no s i g n i f i c a n t d i f f e r e n c e in c a lc u la te d
p e a k in te n s it it e s b e tw e e n th e tw o p arities.
Also no te t h a t th e p e a k i n te n s ity
o f th e Z e e m a n c o m p o n e n ts is p r e d ic te d to be a lm o st one h a l f th e p e a k
in te n s it y o f th e u n s p lit line. T h e m odel is based on 1 b a selin e s u p p re s s io n
o f 800 kHz.
62
2 8 0 Gauss J = 0 .5 - 1 . 5
.15
.0
-.15
-
4.0
-
2.0
.0
2. 0
Zeeman Shift (MHz)
4.0
63
F ig u re 13-We d isp la y m odel s p e c tra f o r th e J = l . 5—2.5 tra n s itio n s . T h e
c e n te r tra c e is th e zero f ie l d s p e c tru m , th e u p p e r tra c e is th e + p a r i t y
t r a n s it io n , a n d th e low er tra c e is the m in u s
p a r i t y tr a n s it io n .
F o r this
t r a n s i t i o n th e - p a r i t y c o m p o n e n ts a re p r e d ic te d to be 1/4 th e h e ig h t
o f th e u n s p lit line, a n d th e + p a r i t y c o m p o n e n ts a r e p r e d i c te d to be 1/2
th e h e ig h t o f th e - p a r i t y co m p o n e n ts.
Also, th e + p a r i t y c o m p o n e n ts
a r e p r e d i c te d to h a v e v e ry d i s t o r te d line shapes. T h e m odel is based
on 1 b a s e lin e su p p re ssio n o f 800 kHz.
64
280
Gauss J = 1 .5 _2 .5
.5
.0
.5
-
4.0
-
2.0
0
2.0
Zeeman Shift (MHz)
4.0
65
F ig u re 14-Model s p e c tr a f o r th e J=4.5-»5.5 t r a n s it io n s a r e d is p la y e d w ith
th e c e n te r tr a c e b e in g th e zero f ie ld s p e c tru m , th e u p p e r tr a c e b e in g
th e + p a r i t y t r a n s it io n , a n d th e low er tra c e be in g th e m in u s
p a r i t y tra n s itio n .
T h e - p a r i t y c o m p o n e n ts a re p r e d ic te d to be alm ost one h a l f th e p e a k
i n t e n s i t y o f th e u n s p lit line a n d to h a v e s h a r p lin e shapes.
T he + p arity
c o m p o n e n ts a r e p r e d i c te d to be h a v e less p e a k in te n s it y t h a n th e - p a r i t y
c o m p o n e n ts a n d to h a v e m ore d is to r te d lin e shapes.
2 8 0 Gauss J = 4 .5 “5.5
1.0
0
1.0
Zeeman S h ift/3 (MHz)
67
F ig u re 15-The lo w e r lobes o f the J=1.5-*2.5 (-) tr a n s it io n a n d o f th e J=1.5-»2.5
(+) t r a n s i t i o n a r e c o m p a re d in this fig u r e , w h ic h has th e e x p e r im e n ta l
c o n d itio n s as F ig u re s 7 a n d 8, e x c e p t th a t we h a v e o n ly 1 b a s e lin e su p p re ssio n
a n d no sm o o th in g . T h e - p a r i t y c o m p o n e n t(lo w e r tra c e ) has a g r e a te r
p e a k i n te n s ity t h a n th e + p a r ity c o m p o n e n t ( u p p e r tra c e ) as o u r m odel
p re d ic ts . T h e d i f f e r e n c e , h o w ever, is not a f a c t o r o f two.
It is also s o m e w h a t
f a r t h e r a p a r t f r o m th e u n s p lit f r e q u e n c y , as p r e d ic te d by th e model.
I "
'■
>
I1
"
lll"
,ll
I
T
I■
■
■
I
I
I"
I
f
I
r
I "
T
—!
■
—
T
. 05
it #•»
i
i
*
«»i
.0
.05
.10
3.0
-
1. 5
0
1. 5
ZEEMAN SHIFT(MHz)
2 8 0 Gauss Exper J= 1 .5 -2 .5
69
(see N. D. P i lt c h ’s thesis 10) a n d the sig n a l to noise is not good. O u r m odel
p re d ic ts t h a t f o r b o th p a ritie s th e J = l / 2 - * 3 / 2 a n d J = 9 / 2 —►
11 / 2
t r a n s itio n s
w ill be split in to tw o Z e e m a n c o m p o n e n ts, ea ch a b o u t 1/2 th e peak in te n s ity
o f the u n s p lit line.
A m ore c o m p lic a te d p a tt e r n is p r e d ic te d f o r the J = 3 /2 -* 5 /2
t r a n s itio n . T h e - p a r i t y is p r e d ic te d to split in to tw o b r o a d e n e d c o m ponents
ro u g h ly one f o u r t h th e p e a k in te n s ity o f the u n s p lit line, a n d th e + p a r ity
is p r e d ic te d to f o r m tw o even m ore b ro a d e n e d c o m p o n e n ts, one h a l f th e
p e a k in te n s it y o f th e - p a r ity com ponents. T h e + a n d - p a r i t y e x p e rim e n ta l
lines f o r th e 9/2 -* 11/2 a re ro u g h ly c o m p a r a b le in in te n s it y to each o th er,
in a g re e m e n t w ith th e sim u la tio n , as can be seen by c o m p a r in g F ig u re s
I a n d 3. T h e y a r e also c o m p a ra b le to th e p e a k in te n s ity o f th e un sp lit
n o r m a l d is c h a r g e lin e (co m p a re F ig u re 3 a n d 4). T h is c o rre s p o n d s to
a f a c t o r o f tw o in c re a s e in th e [SO+] in th e a b n o rm a l d isc h a rg e , a c c o rd in g
to ou r m odel. T h e - p a r i t y t r a n s it io n f o r th e J = 3 / 2 —5 /2 is s o m e w h at
m ore in te n s e t h a n th e + p a r i t y tr a n s it io n , a lth o u g h by no m ea n s by a
f a c t o r o f 2 ( F ig u r e 15). T h e - p a r i t y c o m p o n e n ts h a v e a p p r o x im a te ly
one h a l f th e p e a k in te n s ity o f the u n s p lit n o rm a l d is c h a r g e t r a n s itio n
(see F ig u re s 6 a n d 7). T his, also, c o rre s p o n d s to a n in cre ase in SO+ a b u n d a n c e
by a f a c t o r o f tw o in th e a b n o rm a l d isc h a rg e, b ecause o u r m odel ha d
p r e d ic te d these c o m p o n e n ts to have one f o u r t h the p e a k in te n s ity o f th e
u n s p lit line.
In the case o f the J = l / 2 —3 /2 the Z e e m a n c o m p o n e n ts fo r
th e - p a r i t y t r a n s it io n h a d a p p r o x im a te ly one h a l f th e p e a k in te n s ity
o f th e u n s p lit lin e (see F ig u re s 9 a n d 10), w h ic h c o rre s p o n d s to equal
a b u n d a n c e o f the ion in the n orm al a n d a b n o rm a l d isc h a rg e s , a d e f i n i te
c o n tr a d ic t io n o f th e results f ro m th e o th e r J states. It is e a sily possible,
70
g iv e n th e n a t u r e o f o u r cooling, t h a t th e ra tio s m ay h a v e v a rie d f ro m
d a y to d a y . It also t r u e t h a t o u r sig n a l to noise r a tio w as r a t h e r poor
f o r b o th sets o f c o n d itio n s f o r th e J = l / 2 - * 3 / 2 tr a n s itio n , a n d t h a t one
sh o u ld be s c ep tica l o f i n te n s it y ra tio s b e tw e e n tw o such w e a k signals.
A n in te r e s t in g s id e lig h t o f th e SO + se arc h was th e c a li b r a t io n
o f th e m a g n e tic f ie ld , by th e o b s e rv a tio n o f the Z e e m a n e f f e c t o f 3r ~
SO. T h e t r a n s it io n o b se rv e d w as th e J=6,N=7-»J=7,N =8 lin e a t 340714.5
M Hz.
A t y p ic a l e x a m p le o f th e sp e c tra t h a t w ere ta k e n a t v a rio u s m a g n e tic
f ie ld s is sh o w n in F i g u r e 16. T a b le VI is a c o m p ila tio n o f th e
f it s o f
th e Z e e m a n c o m p o n e n ts , a n d F ig u r e 17 is a plot o f th e s h if t s v e rs u s M.
H a v in g e x p e r i m e n t a l l y d e te r m i n e d th e Z e e m a n s h if t s fo r
d i f f e r e n t f ie ld s , we w ish to c a c lu la te th e o r e tic a lly th e f ie ld s r e q u i r e d
to p r o d u c e th e o b se rv e d e f f e c ts , in o r d e r to h a v e a c a lib ra tio n .
F ro m
Bogey et a /.18, we o b t a i n th e H a m ilto n ia n
H = Bv N 2 + 2/3A v(3Sz2 - S 2) + 7 V( N S ) -
1 / 3 D a[N 2,3Sz 2 - S 2]+ -
Dv N< ( 11)
D 7N 2( N S),
f o r th e zero f ie ld case, w h e re th e [ ]+ is th e a n tic o m m u ta to r. T h e only
c o m p lic a tio n is the e v a lu a ti o n o f th e m a tr ix ele m en ts o f (3SZ2 - S 2). M iz u s h im a 16
gives these as
- 3 X ( X + 1 ) + 4S(S+1)N(N+1)
<JSN|3SZJ - S » |J S N > ---------------2 ( 2 N - l) ( 2 N + 3 ) ---------- •
(12)
76
w h e re
X = J( J + 1) - N ( N + 1)-S ( S + 1),
( 13)
<JSN+1|3SZ2 - S 2|JSN> = 0,
( 14)
and
<JSN+2|3SZ2 - S 2|JSN> =
( 15)
3[(J+ S + N + 2)(J+ S + N + 3)(-J+ S + N + 1 )(-J+S+N+2)]1/ 2
4(2N + 3)[(2N + 1X2N +5)]1/ 2
x [(J -S + N + 2 )(J -S+ N + 1X J+ S - N -1X J+ S - N ) ] 1/ 2
F o r a 3Z~ s ta te S = l, a n d the o n ly v a lu e s
N can h a v e a re 3- 1, J, a n d J + l.
T h u s , th e a b o v e m a t r ix e le m en ts r e d u c e
to th e follow ing:
< J,1 ,J-1 |3 S Z2 - S 2|J,1 ,J-1 > = I ^ j p
( 16)
<J,1,J|3SZ2 - S 2|J,1,J> = 1,
( 17)
<J,1,J+1|3SZ2 - S 2|J,1,J+1> =
( 18)
and
<J1 J+1|3SZ2 - S 2|J 1 J -1 >
( 19)
F in a lly , giv en t h a t J= N + S , it is f a i r l y s t r a i g h t f o r w a r d to d e te r m i n e th a t
<J,S,N| N S |J ,S ,N > = [J (J + 1) - N ( N + 1) -S ( S + 1)]/2 .
All o f th is re s u lts in a m a t r ix o f the fo rm ,
(20)
77
N '/N
J-l
J
J+l
J-l
a
0
b
J
0
c
0
J+l
b
0
d
w h e re
( 21)
a=
Bv J(J+ 1) - D v J 2(J+ 1)2 - 2J [Av+(J-1)2D a/3 ]/(2 J + 1 ) + 7 J + D 7J (J - 1 ) 2,
b= 2[J(J+1)]X/ 2 [Av+ (J2+ J + 1 )D a]/(2J+1),
( 22)
c= (Bv + ( 2 D A/3 ) - D 7)J(J-1)- D v J 2(J+1)2,
( 23)
and
d=
Bv (J + l)( J + 2 ) - D v ( J + l ) 2(J+2)2 - 2(J+1) [Av+(J+2)2D a/3 ]/(2 J + 1 )
- 7J+
( 24)
D 7( J + l) ( J + 2 ) 2.
A c o n s ta n t te rm o f 2Av/ 3 - 7 V has been o m itte d f r o m th e d ia g o n a l term s
a, c, a n d d.
A p r o g ra m , S O L E V E L .F O R , has been w r i tt e n , w h ic h steps
in J, c a lc u la te s a, b, c, a n d d, th e t r a n s f o r m a t io n m a t r ix U n e e d e d to
d ia g o n a liz e it, th e e n e rg y levels o b ta in e d f r o m the d i a g o n a l iz a ti o n , a n d
th e t r a n s it io n f re q u e n c ie s . T h e p ro g ra m is listed in A p p e n d ix 5.
O n c e , th e t r a n s f o r m a t io n m a tr ix has been o b ta in e d , it is a s t r a i g h t f o r w a r d
p r o c e d u r e to c a lc u la te th e e n e rg y level s p littin g s, by u sin g th e m a t r ix
e q u a ti o n Z ' s l ^ Z U , w h e re U is the t r a n s f o r m a t io n m a t r ix , c a lc u la te d
e a r l ie r , U ‘ is its tra n sp o se, a n d Z is th e Z e e m a n m a t r ix in th e id e a l case
b lim it.
T h e o f f d ia g o n a l ele m en ts a re zero, a n d th e d ia g o n a l e le m en ts
78
a r e giv en by the f o r m u la ( R e f e r e n c e 13, page 286),
AW = 1.001 15HM/ ub
[J( J + 1)+S(S+1) -N (N + 1)]
J(J+1)
w h e r e H is th e m a g n e tic f ie ld a n d jUB is the B ohr m ag n e to n .
( 25)
A g a in we
c a n s im p lif y m a tte r s by n o tin g t h a t i f N=J-1 a n d S=1 th e q u o t ie n t re d u c e s
to ( 2 /J ) a n d th a t i f N=J+1 it r e d u c e s to - ( 2 / J + l ) .
F o r a (6,7)-*(7,8) t r a n s it io n
th e r e le v a n t e q u a tio n becomes
AW = 2.0023H M fiB( - U n 2/ J + l + U 122/J ) .
( 26)
F o r J = 6 ,U U=0.96495802 a n d U 12=0.26240431, a n d f o r J=7, U n =0.97290623
a n d U 12= 0.2 3 120005. F or AM=+1 tra n s itio n s th is leads to
Av= (-0.31018 + 0.03044M)H,
( 27)
w h e re M is th e q u a n tu m n u m b e r o f the low er state. O n e can th e r e f o r e
o b ta in th e f ie ld by p lo ttin g Av vs. M. T a b le VII is a c o m p ila tio n o f n o m in a l
f ie ld s v e rsu s a c tu a l fields. W hat sh o u ld be n o te d is t h a t th e a c tu a l f ie ld
is a b o u t 30 gauss h ig h e r th a n th e n o m in a l f ie ld , e x c ep t w h e n th e n c u t o f f
is r e a c h e d a t a b o u t 290 gauss.
79
T a b le V II. M agnetic Field C a lib ra tio n .
N o m in al F ield(G auss)
slope(MHz)
C a lc u la te d Field(G auss)
100
4.062
133.4
150
5.623
184.7
200
7.038
231.2
250
8.609
283.2
280
8.787
288.6
80
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15 W. G o r d y a n d R. L. C ook, M o lecular M icrow ave
S pectroscopy. (Jo h n Wiley & Sons, N ew Y ork, 1984).
16 M. M iz u s h im a , T h e T h e o r y o f R o t a ti n g D ia to m ic M olecules. (Jo h n
Wiley & Sons, N ew Y ork, 1975).
81
17 W. T. C o n n e r , Ph.D. T hesis, U n i v e r s i ty o f W isconsin-M adison,
1988.
18 M. Bogey, C. D e m u y n c k , a n d J. L. Destombes,
Chem . Phys.,66, 99 (1982).
83
The
a 3H s ta te o f CO has been th e s u b je c t o f e x p e rim e n ts
in h ig h r e s o lu tio n sp e ctro sc o p y f o r a n u m b e r o f years, b ecause o f the
im p o r ta n c e o f CO, a n d b ecause th e r e is a p a u c ity o f d a t a on open shell
e le c tr o n ic states. T h e
a 3/7 s ta te is o f f u t h e r in te re s t, be c au se some o f
th e v i b r a t io n a l levels, n a m e ly v=4, 5, a n d 7 a re s tro n g ly p e r t u r b e d by
th e n e a r b y
a ' 3£ s ta te , w h ile o th ers (v= 0,l,2,3, a n d 6) a re only s lig h tly
p erturbed.
T h e f i r s t h ig h re s o lu tio n e x p e rim e n ts w ere by K le m p e r e r
a n d c o w o r k e r s 1' 8, w ho p e rf o r m e d a series o f m o le c u la r beam e le c tric
r e s o n a n c e e x p e rim e n ts f ro m 1965 to 1975, w h e re th e y m e a s u re d th e 12=1
a n d 12=2, AJ=0 la m b d a d o u b lin g tra n s itio n s fo r several v i b r a t io n a l sta te s
o f th e m a in isotope a n d th e 13CO isotopic f o r m a n d d e te r m i n e d
d ip o le m o m e n ts f o r th e
a 3/7 1 a n d
a p p r o x im a te
a/3Z 5 states a n d a tr a n s it io n dip o le
m o m e n t b e tw e e n th e sta te s.6 E f f a n t i n et al .9 o b se rv e d F o u r ie r t r a n s f o r m
i n f r a r e d s p e c tra o f th e
a ' 32T- a 317 system in 1982. T h e y a n a ly z e d the
p e tu r b a ti o n s b e tw e e n th e
a ' 3Z a n d
a 3/7 levels a n d o b ta in e d c o n s ta n ts
f o r se v era l v i b r a t io n a l levels o f both e le c tr o n ic states. S a y k a lly et al.10
r e p o r t e d o b s e rv a tio n o f laser m a g n e tic reso n a n c e sp e ctra o f h ig h J p u r e
r o t a t i o n a l tr a n s it io n s in the 12=1 a n d 12=2 s ta te s in 1986, a n d o b ta in e d
im p r o v e d v a lu e s f o r m o le c u la r p a ra m e te rs o f the v=0 state.
The
a 3H sta te o f CO has also been th e su b je c t o f m ic ro w a v e spe ctro sc o p y
in th is l a b o r a to r y f o r a n u m b e r o f years.
In 1977, S a y k a lly et al. n -12
o b s e rv e d p u r e r o ta t io n a l t ra n s itio n s in th e m ic ro w a v e f o r J=0-»1 o f the
v=0 to v=4 states. T h e y also d e m o n s tra te d t h a t it w as n e c essa ry to ta k e
a ' 3r - a sn i n te r a c t io n s in to a c c o u n t d ir e c tly to f i t th e v=0, 1, 2, a n d 3
m ic r o w a v e d a ta s a ti s f a c to r il y .11-12 In 1982 C. S. G u d e m a n 13 f ir s t o b se rv e d
84
th e Z e e m a n e f f e c t o f th e J = 0 —►
1 sta te , a lb e it p r im a r i ly as a n a d ju n c t
to his H O C + w ork. We h a v e o b se rv e d th e sam e t r a n s it io n s as S a y k a lly
et
b u t w ith th e phase-lo ck e d sp e c tro m e te r.
In a d d i t i o n , th e v=6
tr a n s it io n s w e re o bserved. F in a lly , th e w o rk has been e x te n d e d to in c lu d e
J = 2 —3, J= 3-"4, a n d J=4-»5 tra n s itio n s .
An a d v a n ta g e o f th is e x tr a d a ta
is t h a t m ore p a r a m e te r s can be d i r e c tl y d e te r m in e d , i n c l u d in g th e c e n tr if u g a l
d i s t o r ti o n c o n s ta n t, a n d the c e n t r i f u g a l d is to r tio n c o rr e c tio n to th e s p in - o r b it
c o u p lin g c o n s ta n t.
is t h a t
A f u r t h e r b e n e f i t o f e x a m in in g th e h ig h e r J tra n s itio n s
1 a n d 2 lines w ere o bserved. T a b le I is a c o m p ila tio n o f the
f r e q u e n c ie s o f the t ra n s itio n s o b se rv e d , w ith tra n s itio n s f i r s t o b se rv e d
by S a y k a lly et al. n -12 d e n o te d w ith a n a ste risk .
s p e c tr a o f v=4 sta te s o f d i f f e r e n t h a rm o n ics.
c a r r i e d o u t a d e ta ile d new a n a ly s is o f th e
d a t a , t h a t tre a ts c e n tr if u g a l d is to r tio n a n d
o f th e a ' sr sta te .
F ig u re s 1-3 a rc sam ple
Dr. N o r b e r t C a r b a llo has
a s/7 state, i n c l u d in g o u r new
p e r t u r b a t io n s by v' =0-10
A p a p e r d isc u ssin g th e new m e a s u re m e n ts a n d a n a ly s is
f o r th e m a in isotopic species has been s u b m itte d f o r p u b l i c a t i o n ,14 an d
w o r k by Dr. C a r b a llo on the a n a ly s is o f th e new m e a s u r e m e n ts on the
13C O species is still in progress.
A n i m p o r ta n t m eans o f d is tin g u is h in g b e tw e e n ion a n d n e u tr a l
sig n a ls is th e lin e w id th ; ion lines a re ty p ic a lly 3-5 tim es b r o a d e r th a n
n e u tr a ls .
The
a sfl CO lines are, h o w e v e r, a n o m a lo u s ly b r o a d f o r n e u tr a ls
b e c au se o f u n re s o lv e d Z e e m a n s p littin g , as p o in te d o u t in C. S. G u d e m a n ’s
th e sis.13
It w as th e r e f o r e d e c id e d to do a p ressu re b r o a d e n in g e x p e rim e n t
to c o m p a r e
a 3I7 CO w ith H C O + a n d HC N .
In o r d e r to m in im iz e the
Z e e m a n e f f e c t th e E a r t h ’s m a g n e tic f ie ld w as c a n c e le d by a p a ir o f
85
T a b le I. O b served
a s /7 CO Lines
n
J
p arity
V
V
n
J
p arity
o
0 -1
+
92889.911*
0
0
0-1
-
92499.121
o
2-3
+
279170.079
0
0
2 -3
-
278089.830
o
3 -4
+
372779.776
0
0
3-4
-
371435.416
o
4-5
+
466814.345
0
0
4 -5
-
465271.190
2
2-3
+
330805.290
0
2
2 -3
-
330831.961
2
3-4
+
439834.371
0
2
3 -4
-
439893.155
0
0-1
+
1
0
0-1
-
91509.899
0
2-3
+
276160.713
1
0
2-3
-
275103.072
0
3-4
+
368750.084
1
0
3-4
-
367432.634
0
4 -5
+
461751.665
1
0
4-5
-
460237.431
2
3-4
+
434573.403
1
2
3-4
-
434630.055
0
0-1
+
2
0
0-1
-
90512.693
0
2-3
+
273124.785
2
0
2 -3
-
272092.795
0
3-4
+
364685.809
2
0
3-4
-
363398.785
0
4 -5
+
456646.646
2
0
4 -5
-
455165.738
2
3-4
+
429287.905
2
2
3-4
-
429342.875
0
0-1
+
3
0
0-1
-
89506.887
0
2-3
+
270056.143
3
0
2-3
-
269057.193
0
3-4
+
360579.045
3
0
3-4
-
359331.733
0
4 -5
+
451490.410
3
0
4 -5
-
450052.737
1
2-3
+
287501.346
3
1
2 -3
-
288478.980
2
3-4
+
423967.420
3
2
3-4
_
424020.235
91892.027*
90885.144*
89866.824*
V
86
V
a
j
p arity
V
V
12
J
p arity
V
4
0
0 -1
+
88792.239*
4
0
0-1
-
88413.716*
4
0
2 -3
+
266829.308
4
0
2 -3
-
265759.224
4
0
3 -4
+
356272.706
4
0
3 -4
-
354913.478
4
0
4 -5
+
446100.750
4
0
4 -5
-
444497.549
6
0
0-1
+
86800.369
6
0
0-1
-
86413.453
a 3/7 13C O Lines
v
n
J
F
P
V
V
n
J
F
P
0
0
0 -1
0.5—0.5
+
89082.116*
0
0
0 -1
1.5—1.5
+
89164.941
0
0
0-1
0
ui
1
©
O bserved
-
88738.742*
0
0
0-1
1.5 —1.5
-
88801.342
0
0
2 -3
1.5—2.5
+ 267803.205
0
0
2 -3
2.5—2.5
+ 267663.729
0
0
2 -3
2.5—3.5
+ 267856.470
0
0
2 -3
1.5—2.5
-
266814.855
0
0
2 -3
2.5—2.5
-
266710.392
0
0
2 -3
2.5—3.5
-
266854.959
0
0
3 -4
2.5—3.5
+ 357548.076
0
0
3 -4
3.5—3.5
+
357355.332
0
0
3 -4
3.5—4.5
+ 357598.367
0
0
3 -4
2.5—3.5
-
356309.220
0
0
3-4
3.5—3.5
-
356164.600
0
0
3 -4
3.5—4.5
-
356347.240
0
1
2 -3
1.5—2.5
+
284744.043
0
1
2 -3
2.5—2.5
+
284709.510
0
1
2 -3
2.5—3.5
+
284746.107
0
1
2 -3
1.5—2.5
-
285719.913
0
1
2 -3
2.5—2.5
-
285650.409
0
1
2 -3
2.5—3.5
-
285734.274
1
0
0 -1
0.5—0.5
+
88226.234*
1
0
0-1
1.5—1.5
+
88144.654
1
0
0-1
*/■>
o’
t
v-i
O
-
87870.341*
1
0
0-1
1.5 — 1.5
-
87809.036
1
0
2 -3
1.5—2.5
+
264975.816
1
0
2 -3
2.5—2.5
+
264838.491
1
0
2 -3
2.5—3.5
+
265028.385
1
0
2 -3
1.5—2.5
-
264007.776
I
0
2-3
2.5—2.5
_
263905.281
1
0
2 -3
2.5—3.5
.
264047.154
V
J
F
P
V
V
a
J
F
P
V
1
0
3 -4
2.5—3.5
+
353763.444
1
0
3-4
3.5—4.5
+
353813.216
1
0
3 -4
2.5—3.5
+
352549.116
1
0
3 -4
3.5—4.5
-
352586.640
1
1
2 -3
1.5—2.5
+
281652.801
1
1
2-3
2.5—2.5
+
281615.220
1
1
2-3
2.5—3.5
+
281654.214
1
1
2 -3
1.5—2.5
-
282608.265
1
1
2-3
2.5—2.5
-
282538.482
1
1
2 -3
2.5—3.5
-
282621.984
2
0
0 -1
0.5—0.5
+
87279.352
2
0
0 -1
1.5—1.5
+
87199.113
2
0
0-1
0.5—0.5
-
86872.064
2
0
0 -1
1.5—1.5
-
86931.946
2
0
2 -3
1.5—2.5
+
262124.367
2
0
2-3
2.5—2.5
+
261989.565
2
0
2 -3
2.5—3.5
+
262176.120
2
0
2-3
1.5—2.5
-
261179.319
2
0
2-3
2.5—2.5
-
261079.332
2
0
2 -3
2.5—3.5
-
261217.878
2
0
3 -4
2.5—3.5
+
349948.112
2
0
3-4
3.5—4.5
+
349996.796
2
0
3 -4
2.5—3.5
+
348761.240
2
0
3 -4
3.5—4.5
-
348797.592
3
0
0-1
La
+
86243.499
3
0
0-1
1.5—1.5
+
86322.522
3
0
0 -1
0.5—0.5
-
85927.409
3
0
0-1
1.5—1.5
-
85985.826
3
0
2 -3
1.5—2.5
+
259244.211
3
0
2-3
2.5—3.5
+
259294.926
3
0
2 -3
1.5—2.5
-
258328.209
3
0
2 -3
2.5—3.5
-
258365.820
3
0
3 -4
2.5—3.5
+
346094.488
3
0
3-4
3.5—4.5
+
346142.720
3
0
3 -4
2.5—3.5
344943.252
3
0
3-4
3.5—4.5
1
O
n
La
V
0
87
* L in e s o rig in a lly seen by S a y k a lly 11'12 et al.
344979.236
88
F ig u re 1-T he t r a n s it io n show n in this f ig u r e is th e v=4, J = 0 —1, + p a r i t y
a t 88792.213 MHz. T h e
e x p e rim e n ta l c o n d itio n s a r e as follow s: 1 baseline
s u p p re s s io n (800 kHz), 11 p o in t s m o o th in g , 18 m T o rr a rg o n b u f f e r , f a s t
flo w , l i q u i d n itr o g e n cooling, 0.6 m T o rr CO, 150 m A d is c h a r g e , 800 kH z
AM, 100 k H z FM, E a r t h ’s f ie ld c a n c e le d , 110 scans, 10 fivolt scale lock-in
a m p l i f i e r , 1 m s e c /p o in t, 1 msec tim e c o n s ta n t, H u g h e s S c h o ttk y d io d e
d e te c to r.
1000 .
T h e d a s h e d line is th e least s q u a re s f i t b e tw e e n p o in ts 1 a n d
89
v=4 J= 0~1 +parity
88790
88795
FREQUENCY(MHz)
90
F ig u re 2-T he v=4, J*3-*4, - p a r i t y tr a n s it io n a t 354913.478 M Hz is obse rv e d
w ith th e fo llo w in g e x p e r im e n ta l co n d itio n s:
1 b a selin e s u p p re s s io n (600
kH z), 11 p o in t s m o o th in g , 20 m T o rr a rg o n b u f f e r , f a s t flo w , l iq u id n itro g e n
cooling, 0.5 m T o r r CO, 150 m A d isc h a rg e , 2400 k H z AM, 30 k H z FM,
E a r t h ’s f i e l d n o t c a n c e le d , 11 scans, 10 fivolt scale lock-in a m p l if i e r ,
15 m s e c /p o in t, 10 msec tim e c o n s ta n t, InSb d e te c to r a t 11 k G a u s s f ie ld
a n d 26 T o r r H e pressure.
p o in ts 150 a n d 500.
T h e d a s h e d line is th e least s q u a re s f i t b e tw e e n
91
v=4 J= 3~4 -parity
354900
FREQUENCY(MHz)
354940
92
F ig u re 3-T h e s p e c tr u m o f th e v=4, J = 4 —5, - p a r i t y tr a n s it io n a t 446100.750
M H z is o b s e rv e d w i t h th e sam e e x p e r im e n ta l c o n d itio n s as in F ig u r e
2, e x c e p t t h a t t h e r e a r e 72 scans a n d we h a v e used a b a s e lin e su p p re ssio n
o f 480 kH z. T h e d a s h e d lin e is the least s q u a re s f i t b e tw e e n p o in ts 1
a n d 1000.
93
v=4 J = 4 - 5 +parity
446080
446120
FREQUENCY(MHz)
94
H e lm h o ltz coils. T h e p re s s u re was m e a s u re d w ith a M K S B a r a tr o n c a p a c ita n c e
m a n o m e te r.
T h e d is c h a r g e was r u n "fast flow ", i. e., w ith th e d i f f u s i o n
p u m p t h r o t t l e d back. T h e flo w ra te w as k e p t c o n s ta n t, as w e re th e in p u t
CO p re s s u re (0.5 m T o rr) a n d th e d isc h a rg e c u rr e n t( 1 5 0 m iliam ps).
The
a rg o n p re s s u re was v a r ie d f r o m 7 to 85 m T o rr. T h e line e x a m in e d w as
th e v=2, + p a r i t y t r a n s it io n a t 90885.14 MHz.
vs. pressure.
F ig u re 4 is a p lo t o f lin e - w id th
T h e slope w as 4.89 M H z /T o r r , w h ic h is f a i r ly close to G u d e m a n ’s
v a lu e o f 5.2 M H z / T o r r f o r H C N in an A r b u f f e r a t liq u id n itr o g e n te m p e ra tu re s ,
a n d c o n s id e r a b ly d i f f e r e n t f r o m th e 18 M H z / T o r r v a lu e f o r H C O + in
the sam e ty p e o f d is c h a r g e .13 T h e zero pressu re i n te r c e p t w as 96 kHz.
A c a lc u la tio n o f th e D o p p le r lin e w id th by (see, f o r ex a m p le, C h a p t e r
II or T o w n e s a n d S c h a w lo w 15, p337),
Av= 3 . 5 8 1 X 1 0 - M T / M ) 1/ 2
(])
yields a c a lc u la te d lin e w id th o f 53 kH z. Since the AM f r e q u e n c y was
30 kH z, a n d o th e r sources o f b r o a d e n in g n e g ligible, we can re a s o n a b ly
c o n c lu d e t h a t th e r e is still re s id u a l Z e e m a n b r o a d e n in g , a n d t h a t c o m p le te ly
c a n c e lin g o u t th e E a r t h ’s f ie ld is a most d i f f i c u l t task.
In o r d e r to e s tim a te th e e f f e c t o f th e E a r t h ’s f ie ld on th e lines,
a n a c c u r a te v a lu e o f th e Z e e m a n c o e f f ic i e n t is necessary.
C. S. G u d e m a n 13
c a lc u a te d a Z e e m a n s h i f t o f 226 k H z / G a u s s f o r the J= 0 —l,v = 0 tr a n s itio n ,
a n d m e a s u r e d an e f f e c t o f 240 k H z /G a u s s u sin g th e old H e lm h o ltz coils
f o r th e - p a r i t y line.
T h e f ie ld m e a s u re m e n ts f r o m th e coils w e re f a i r l y
c ru d e , a n d in a n y e v e n t o n ly v e ry low f ie ld v a lu e s w ere possible, i.e.,
on th e o r d e r o f a f e w Gauss. S u b s e q u e n tly , W. T. C o n n e r 15 d e v e lo p e d
a so lenoid c a p a b le o f p r o d u c in g u p to a p p r o x im a te ly 290 Gauss.
97
W ith th is h ig h e r f ie l d it w as d e c id e d to re d o G u d e m a n ’s e x p e rim e n t,
u sin g th e + p a r i t y in s te a d o f th e - p a r i t y .
T h e c o n d itio n s w e re s im ila r
to th e p re s s u re b r o a d e n i n g e x p e rim e n t, in t h a t "fast flow", liq u id n itr o g e n
cooling, 150 m illia m p d isc h a rg es, a n d 1.0 m T o rr o f CO w ere used.
In
a d d i t i o n , th e A r p re s s u re w as ke p t c o n s ta n t, a t 28 m T o rr, b u t th e f ie ld
was v a r ie d f r o m 0 to 200 Gauss. F ig u re 5 is a plot o f f r e q u e n c y vs. n o m in a l
m a g n e tic fie ld .
T h e slope is 224.9 k H z /G a u s s , a n d the in te r c e p t is -0 .2 8
G auss, w h ic h is in c o n tr a s t to the in te r c e p t o f 30 G auss in th e th e p re v io u s
c h a p te r , b u t it sh o u ld be p o in te d out th is w o rk was d o n e in la te 1983,
w h e re a s th e SO + w o rk w as do n e in 1985, so th e p o ssib ility o f " d rift" in
th e m a g n e t p o w e r s u p p ly is not u n re a s o n a b le .
A r e s id u a l f ie ld o f 0.2
G a u ss w o u ld c a u se th e e x tr a b r o a d e n in g , d e s c rib e d in th e p re v io u s se ctio n
on p re s s u re b r o a d e n in g . T o redo the c a lc u la tio n s we use th e m ore a c c u r a te
v a lu e s o f S a y k a lly et al. 10 f o r th e m a tr ix e le m en ts a n d th e g fac to rs.
T h e m o re a c c u r a te U c o e f f ic i e n t s o f C a r b a llo a n d Woods a re e m p lo y e d .14
T h e Z e e m a n c o e f f ic e n ts as listed by S a y k a lly et al. 10 a re
< 3/70|H z| 3n 0> = - g rMBBMj
( 2)
/igBMj
< 3J70|H Z| 3/7x> =
< s/TjIHgl 3/7x> =
J(J+1)
{ 2 J (J + 1){1 / 2 ( g 8+gr+gl) t 1/2 ( g / - g f ) \\l ^ 3 )
Mb BM j
J(J+1) [8 l ~ 8 j J ( J + 0 - l ]
* g ? J (J + l)],
(4 )
w h e re g,=2.002, gL' = 1, gr= - .7 7 X 1 0 -3, a n d g1= -.2 2 6 6 X 1 0 -3. T h e u p p e r
a n d low er signs in the Tterms r e f e r to th e e a n d f p a r i t y term s, resp e c tiv e ly .
T h e r e m a in i n g p a r a m e t e r s a re assum ed to be zero. F o r th e + p a r i t y lines,
C a r b a llo a n d Woods’14 v alues a re U 00=.9968915 a n d U 01=-.0787486.
For
th e - p a r i t y lines, th e ir v alues a re U 0O=.9966016 a n d U ol= -.0823354.14
95
F ig u re 4-In th is p lo t o f Av(HWHM)
vs
to ta l p re s s u re f o r th e v=2, J = 0 — 1,
+ p a r i t y tr a n s it io n o f a 3I7 CO a t 90885.144 M Hz, th e CO p ressu re was
k e p t c o n s ta n t a t 0.6 m T o rr, a n d we em p lo y e d no s m o o th in g in f i t t i n g
th e d a ta .
96
Pressure Broadening v=2 + parity
.48
.42
Av(MHz)
.36
.30
.24
.18
.12
.06
10
20
30
40
50
60
70
Pressure(mTorr)
80
97
With this h ig h e r fie ld it was d e c ided to redo G u d e m a n ’s e x p erim ent,
using the + p a r i t y in ste a d o f the - p a r i t y . T h e c o n d itio n s w ere sim ilar
to the p ressure b r o a d e n in g e x p e rim e n t, in t h a t "fast flow", liq u id nitro g e n
cooling, 150 m illia m p discharges, a n d 1.0 m T o rr o f CO w ere used. In
a d d itio n , the Ar p ressure was ke p t co n sta n t, a t 28 m T o rr, b u t the field
was v a rie d f ro m 0 to 200 Gauss. F ig u re 5 is a plot o f fre q u e n c y vs. nom inal
m agnetic fie ld . T h e slope is 224.9 k H z /G a u ss, a n d the in te rc e p t is -0.28
Gauss, w h ic h is in c o n tra s t to the in te rc e p t o f 30 Gauss in the the previous
c h a p te r, b u t it should be po in te d out this w ork was done in late 1983,
w hereas the SO+ w ork was done in 1985, so the possibility o f "drift" in
the m agnet pow er su p p ly is not u n reaso n ab le. A re s id u a l fie ld o f 0.2
Gauss w ould cause the e x tra b ro a d e n in g , d e scrib ed in th e p revious section
on pressure b ro a d e n in g . To redo the c a lc u la tio n s we use the m ore a c c u ra te
values o f S ay k a lly et al. 10 f o r the m a trix elem ents an d the g factors.
The more a c c u r a te U c o e ff ic ie n ts o f C a rb a llo a n d Woods are em ployed.14
T h e Z eem an c o e ff ic e n ts as listed by S a y kally et al. 10 a re
(2)
< 3f7o|Hz| */7o> |Xd B M j
< s f7o|Hz|
3n 1> -
<»nliH^»n1>m
j ( j + 1 ) [2J(J+ 1)(1 /2 (g t+8r+g|) * l /2 ( g ,'- g ? )>]»/? J;
UdB M t
{gl; - g j j ( j + i ) - i ]
»gf j ( j + i ) ] ,
(4)
w here g,=2.002, gL'=»l, gr= -.7 7 X 1 0 -3, a n d gj=-.2266X 10_3. T he up p e r
a n d lower signs in th e Tterms r e f e r to the e a n d f p a r ity terms, respectively.
T h e re m a in in g p a ra m e te rs are assum ed to be zero. For the + p a rity lines,
C a rb a llo a n d Woods’14 values a re Uoo=.9968915 a n d U 0l=-.0787486. For
the - p a rity lines, th e ir values a re Uoo=.9966016 a n d U ol=-.0823354.14
98
F ig u re 5-T he d is p la c e m e n t o f the AM=+1 lobe f r o m th e z e ro - fie ld a 3f7
CO v=0, J = 0 — 1, + p a r i t y u n p e r t u r b e d f r e q u e n c y o f 92889.911 M H z is
p l o tt e d vs a p p lie d m a g n e tic fie ld .
99
92889.91-v(MHz)
Zeeman E ffect v - 0 +parity
50
100
150
200
Magnetic Field(Gauss)
100
F i n a ll y , M iz u s h i m a ’s 17 v a lu e o f 1.3996108 M H z / G a u s s is u s e d f o r /uB.
A p p l y i n g a ll o f t h is re s u lts in a c a lc u la te d Z e e m a n s h i f t o f 225.2 k H z / G a u s s
f o r th e + p a r i t y , in v e ry good a g r e e m e n t w i t h th e m e a s u r e d v a lu e o f
224.9 k H z / G a u s s .
T h e - p a r i t y is c a lc u la t e d to be a t 235.6 k H z / G a u s s ,
in r e a s o n a b le a g r e e m e n t w i t h G u d e m a n ’s c r u d e r v a lu e o f 240 k H z / G a u s s
f r o m th e H e l m h o l tz coils.13 T h e Z e e m a n e f f e c t a n d a n d p r e s s u r e b r o a d e n i n g
m e a s u r e m e n ts a r e also i n c l u d e d in R e f e r e n c e 14.
T h e e x p e r i m e n t w ith th e m ost p u z z lin g re s u lts w a s t h e s e a r c h
f o r th e v=5 a n d v=6 states.
F ir s t th e v=5 lin e s w e re s e a r c h e d f o r a r o u n d
th e p r e d i c te d v a lu e s o f F ie ld et al. 18 o f 87928(40) a n d 87167(55) M Hz.
N o t h i n g w a s seen e x c e p t th e v= l o f 13C O a t 87870 M H z, in " n a tu r a l"
abundance.
( T h is w o r k w as d o n e s h o rtly a f t e r w o rk i n v o lv i n g 13CO.
T h e r e w as s u re ly r e s id u a l 13C on th e w alls, e v e n t h o u g h n o n e w a s a d d e d
d ire c tly .)
A t t h is p o in t it w a s d e c id e d to s e a r c h f o r th e v= 6 lines, w h ic h
w e re n o t p e r t u r b e d by th e
a ' 3Z state.
S c a lin g th e d i f f e r e n c e s b e tw e e n
th e v=0, 1, 2, a n d 3 s ta te s y ie ld s p r e d i c ti o n s o f 86433 a n d 86723 M H z
f o r th e v=6 sta te .
T h e lin e s w ere seen a t 86413.43 a n d 86800.35 M H z,
a t a b o u t 1/10 th e in te n s it y o f the v=4 lines. T h i s r a t i o w a s to be e x p e c t e d ,
since t h e r e w as a f a i r l y c o n s ta n t d r o p o f a f a c t o r o f 3 p e r v i b r a t i o n a l
q u a n tu m num ber.
It w as th u s d e c id e d t h a t t h e u n c e r t a i n t y lim its q u o te d
m ay h a v e b e e n too sm all f o r the v=5, a n d th e s e a rc h w as r e n e w e d .
The
e n ti r e r a n g e b e tw e e n th e + p a r i t y v=4 a t 88792 a n d th e - p a r i t y v=6
a t 86413 w as s e a r c h e d .
N o t h i n g new w as f o u n d .
T h is r e s u l t r a is e s th r e e
p o ssib ilities: (1) we s im p ly m issed th e lines, (2) th e p e r t u r b a t i o n by th e
a ' 3r s ta te h a s s h i f t e d th e m b e y o n d th e v=4 to v=6 ra n g e , o r (3) t h e p e r t u r b a t i o n
101
has d i m i n is h e d th e p o p u la tio n o f th e v=5 states.
good a r g u m e n ts a g a in s t all th re e possibilites.
T h e r e are, u n f o r t u n a t e l y ,
P o s s ib ility (1) is u n l ik e ly ,
b e c au se two lin e s, w h ic h a r e th r e e tim es s tro n g e r t h a n s u c c e s s fu lly o b s e rv e d
lines, w o u ld h a v e h a d to be o v e rlo o k e d , a n d in a d d i t i o n a 13C O lin e w as
seen. P o s s ib ility (3) is n o t lik e ly , because th e v=4 lin e s a re p e r t u r b e d ,
a n d th e y f a l l in th e n o r m a l i n te n s ity p a tte r n .
A n a r g u m e n t a g a in s t p o s s ib ility
(2) is t h a t s c a le d d i f f e r e n c e s o f th e v=0, 1, 2, a n d 3 s ta te s p r e d i c t v=5
lin e s a t 87786 a n d 87467 Mhz; th e r e f o r e , F ie ld et al. 18 a re p r e d i c t i n g
p e t u r b a t i o n s o f a p p r o x i m a t e ly 150 M H z a n d 300 M H z f o r th e + a n d p a r itie s , r e s p e c tiv e ly .
Since th e y c o rr e c tly p r e d i c te d v=4 p e r t u r b a t i o n s
o f 43 a n d 78 M H z f o r th e v=4 lines, it w ould be s u r p r is in g i f th e y w e re
1000 M H z in e r r o r f o r th e v=5 lines.
103
18 R. W. F ie ld , S. G. T i l f o r d , R. A. H o w a rd , a n d J. D. Sim m ons,
J. Mol. Spec. 44, 347 (1972).
105
IN T R O D U C T IO N
H C N w as o n e o f th e f ir s t m olecules seen by m ic ro w a v e
sp e ctro sc o p y , th e J=0-*1 tra n s itio n o f th e g ro u n d v i b r a t io n a l s ta te be in g
o b s e rv e d by S m ith et al.1 in 1949. Because o f th e te c h n o lo g y o f th e tim e,
o n ly a v e ry c r u d e f r e q u e n c y was o b ta in e d , a n d no q u a d r u p o l e s p littin g
w as obse rv e d . S lig h tly late r, Sim m ons et al.2 o b s e rv e d th e h y p e r f i n e c o m ponents
o f t h is species a lo n g w ith those f o r H 1SC N , D C N , a n d D 13CN.
U n f o r tu n a t e l y ,
a m is r e a d in g o f th e w a v e m ete r re s u lte d in 30 M H z e rr o r s in the fre q u e n c ie s ,
as p o in te d o u t by th e a u th o rs in a la te r e r r a tu m .3 F u r t h e r im p ro v e m e n ts
in th e m u lt ip l ie r a n d a n d in the d e te c to r r e s u lte d in B u rru s a n d G o r d y 4
e x te n d i n g th e g r o u n d v ib ra tio n a l s ta te m e a s u re m e n ts to h ig h e r J tra n s itio n s
f o r H C N a n d DCN.
B h a tta c h a ry a a n d G o r d y 5 o b se rv e d S ta rk c o m p o n e n ts
o f th e J = 0 —1 tra n s itio n , a n d o b ta in e d a v a lu e f o r th e d ip o le m om ent.
S e n itz k y 6 r e p o r te d o b se rv a tio n s o f p u re r o ta tio n a l t r a n s it io n s o f H C 1BN
a n d D C 15N.
In a d d i t i o n to these m illim e te r w ave tra n s itio n s , low f r e q u e n c y
AJ=0 /-d o u b le t t ra n s itio n s betw een th e OUO levels w ere obse rv e d .
The
f ir s t su ch o b s e rv a tio n s w ere m ade in 1950 by S c h u lm a n a n d T o w n e s 7
f o r th e m a in isotope.
A n u m b e r o f a u th o r s e x te n d e d these m e a s u re m e n ts
to o t h e r J sta te s a n d to the DCN species as w ell.8*12 Y a r m u s 13 w as the
f ir s t to obse rv e h y p e r f i n e s tr u c tu r e a n d o b ta in a n eQ q f o r th e e x c ite d
v i b r a t io n a l state. T d r r i n g 14 e x te n d e d the m e a s u re m e n ts f o r H C N a n d
D C N , a n d he also observed d ire c t /-type d o u b lin g t r a n s it io n s f o r
H 13CN,
H C 16N, D 13C N , a n d D C 15N. F in a lly , he o b se rv e d /-type d o u b lin g t r a n s itio n s
f o r th e 03*0 a n d 05*0 states. M aki a n d L i d e 15 o b se rv e d h ig h J r o ta tio n a l
106
tr a n s it io n s f o r H C N a n d D C N , 0220 tra n s itio n s f o r b o th isotopes, a n d
0 3 ^ a n d 0330 lin e s f o r DC N . W innew isser a n d V o g t16 e x te n d e d th e m e a s u re m e n ts
to th e s u b s ti tu t e d isotopom ers H 13C 16N a n d D 13C 15N, a n d also obse rv e d
th e J = l- » 2 r o ta t io n a l tra n s itio n s .
R a d f o r d a n d K u r t z 17 used an e le c tric
re s o n a n c e b e a m m ase r s p e c tro m e te r to e x a m in e th e J=1 /-type d o u b lin g
t r a n s it io n f o r th e m a in isotope, a n d Fliege et al.18 used m ic ro w a v e F o u r ie r
t r a n s f o r m sp e ctro sc o p y to e x a m in e several J sta te s o f H C N a n d DCN.
R e c e n tly , M e h ro tra et al. 19 e x a m in e d the J -d e p e n d e n c e ot th e pressu re
b r o a d e n in g p a r a m e t e r s o f /-d o u b le t tra n s itio n s in H C 1BN.
M a rc u s e 20 o b se rv e d th e J = 0 —►
1 t r a n s it io n o f th e g r o u n d
v i b r a t io n a l sta te in a m aser e x p e rim e n t in 1961, a lth o u g h no a tte m p t
was m a d e to m e a s u re f re q u e n c ie s to high a c c u ra c y .
L a te r, D e L u c ia a n d
G o r d y 21 p e r f o r m e d h ig h ly a c c u r a te (1 kH z) beam m aser m e a s u re m e n ts
f o r th e H C N a n d D C N g ro u n d v ib ra tio n a l states. T h e y m e a s u re d B000,
D 000, c n> anc* ° Q q f ° r b o th n itro g e n a n d d e u te r iu m .
U sin g a m ore c o n v e n tio n a l
m ic r o w a v e s p e c tr o m e te r , W innew isser, M aki, a n d J o h n s o n 22 r e p o r te d o b s e rv a tio n
o f p u r e r o ta t io n a l t r a n s it io n s o f v i b r a t io n a ll y e x c ite d H C N a n d D C N ,
a n d o b t a i n e d th e f ir s t e x p e rim e n ta l e q u il ib r i u m s tr u c tu r e .
T h is was
not p u r e ly a m ic ro w a v e e q u ilib r iu m s tr u c tu r e , since i n f r a r e d d a ta was
used f o r th e 100 state. (In this thesis the h e a v y a to m - h e a v y a to m s tre tc h
is r e f e r r e d to as vs a n d th e light atom s tre tc h as v lt the rev e rse o f the
n o t a t io n in th e p a p e r o f W innew isser, M aki, a n d J o h n s o n 22.) In 1974,
M a k i 23 p u b lis h e d a c o m p ila tio n o f all the p re v io u s m ic ro w a v e results,
a lo n g w ith e x te n s iv e re fe re n c e s.
D e L u c ia 24 has r e p o r te d o b s e rv a tio n
o f m ic r o w a v e s p e c tra o f T C N , T 1SC N , a n d T C 15N in b o th th e g ro u n d
107
a n d 01*0 states.
P e a rso n et al.26 o b se rv e d g ro u n d v i b r a t io n a l sta te tra n s itio n s
f o r all e ig h t H C N a n d H N C isotopom ers, in a m ix t u r e o f a c tiv e n itr o g e n ,
c o n ta i n in g th e a p p r o p r i a t e isotopic fo rm s o f C H 3I a n d N 2. D e L u c ia a n d
H e l m i n g e r 26 o b ta in e d h ig h ly e x c ite d s ta te r o ta tio n a l c o n s ta n ts f r o m m ic ro w a v e
s p e c tr a f o r th e m a in isotope, s u f f i c i e n t to e x p e rim e n ta lly d e te r m in e Be,
b u t th e y only e x a m in e d th e m a in isotope, so no s tr u c tu r e c o u ld be d e te r m in e d .
R e c e n tly , C o lm o n t27 d e te r m i n e d the t e m p e ra tu re d e p e n d e n c e o f th e p re s s u re
b r o a d e n i n g p a r a m e t e r o f H C 1BN.
In o u r la b o r a to r y , G u d e m a n 28 d e te r m in e d
th e f i r s t c o m p le te m ic r o w a v e e q u il ib r i u m s tr u c tu r e o f H C N , o b s e rv in g
s a te llite s f o r H C N , H 1SC N , a n d H C 16N f o r J = 0 —1 tra n s itio n s .
It was
d e m o n s t r a t e d in th is w o rk t h a t such e f f e c ts as a n h a r m o n ic reso n a n c e
a n d C o rio lis c o u p lin g w e re sm all, m a k in g H C N a n ideal test case f o r
th e m e a s u r e m e n t o f e q u il ib r i u m stru c tu re s .
It w as d e c id e d to e x te n d
G u d e m a n ’s w o rk fo r the fo llo w in g tw o reasons : (1) he only o b se rv e d
J = 0 —*1 tra n s itio n s , w h ic h m e a n t he w as fo rc e d to e s tim a te c e n tr if u g a l
d i s t o r ti o n a n d w as u n a b le to see m odes w ith /-ty p e reso n a n c e , a n d (2)
he d id no w o rk f o r
H 13C 15N.
E X P E R IM E N T A L
T h e s p e c tr o m e te r s e tu p was c o n s ta n t t h r o u g h o u t th e w o rk in this
c h a p te r.
V a r ia n k ly stro n s fro m 82 to 96 G H z w ere em p lo y ed .
T h e y w ere
p h a s e -lo c k e d a n d so u rc e m o d u la te d as d e s c rib e d in C h a p t e r II o f th is
thesis. T h e M illitec h m u ltip lie r w as used to g e n e ra te th ir d , f o u r t h , f i f t h ,
a n d o c c a s io n a lly e v e n s ix th h a rm o n ic s o f the k ly stro n . T h e d a ta was
s to re d on a m a g n e tic ta p e a t 800 bpi, w h ic h w as th e n ta k e n to the M adison
A r e a C o m p u tin g C e n te r, w h e re it was copied to a n o th e r ta p e a t 6400
108
bpi. T h e d a ta w as th e n f i t on a d e p a r t m e n t a l V A X /8 6 0 0 c o m p u te r by
a least s q u a re s p ro g ra m w r i tt e n by N. D. P i l t c h 29 a n d m o d if ie d by W.
T. C o n n e r.30
T h e l iq u id h e liu m cooled InSb d e te c to r w as used f o r all th e w o rk
m e n tio n e d here. T h e d e te c to r w as o p e r a te d a t 5 kG auss a n d 10 T o r r
h e liu m p re s s u re f o r th e 13C isotopom ers; l a t e r it w as rea liz e d t h a t m u ch
b e tte r signals c o u ld be re a liz e d by r u n n i n g a t 26 T o r r h e liu m p ressu re
a n d 10 kG auss. T w o f a c to r s r e s u ltin g in g r e a t e r signal a t th e d e te c to r
w ere h ig h e r d e te c to r m a g n e tic f ie l d a n d lo w e r He pressure, i.e., lo w e rin g
the c ry s ta l te m p e r a tu r e .
U n f o r t u n a t e l y , b o th c o n tr ib u te d to noise o sc illa tio n s
r e f e r r e d to as "ringing".
It w as d isc o v e re d , h o w e v e r, th a t th e r e w as a
t r a d e - o f f , i.e., one could r u n a t high m a g n e tic fie ld s a n d d e te c to r h e liu m
pressures, or o n e co u ld ru n a t lo w e r f ie ld s a n d pressures. Because th e
signal level w as m uch m ore se n sitiv e to th e m a g n e tic fie ld th a n the h e liu m
p ressu re, high pressu res a n d high f ie ld s w e re p r e f e ra b le .
S o m e w h a t d i f f e r i n g d is c h a r g e c o n d itio n s w ere e m ployed f o r the
v a rio u s isotopom ers.
A lm ost all o f th e w o rk in v o lv e d n o rm a l disc h a rg es.
T h e 13C c o n ta i n in g species w ere o b se rv e d c o n c u r r e n tl y w ith H 13C O +,
H 0 13C+, a n d a 3fl 13CO, w h ic h m ad e th e fo llo w in g p ro c e d u re viable: (1)
one d a y r u n th e f a s t flo w l iq u id n itr o g e n cooled d isc h a rg e n eed ed to
observe th e o t h e r species m e n tio n e d a bove, a n d (2) th e n e x t f e w d ay s
ru n slow f lo w d isc h a rg e s w ith no in p u t 13C f o r th e H 13C N spectroscopy.
F or both 13C isotopom ers 20 m T o rr e a ch o f A r a n d H 2 w e re a d d d e d .
For H 1SCN a b o u t 10 m T o rr o f N 2 w as a d d e d , w h e re as f o r H 13C 16N o n ly
5 m T o rr o f 15N 2 w as e m ployed.
D isc h a rg e s f o r both isotopes w ere r u n
109
a t t y p ic a l d is c h a r g e c u r r e n ts o f 500 mA.
F o r th e m a in isotope f a s t f lo w
l iq u i d n i tr o g e n co o lin g was e m p lo y e d , since th e cost o f i n p u t m a te ria ls
w as n o t a f a c to r .
T h e p a r t i a l pressu res w ere 10 m T o rr e a c h f o r C H 4
a n d N 2. F o r th e 16N isotope th e c o n d itio n s w ere s im ila r to th e d o u b le
isotope, i.e., slow flow , w a t e r cooled, w ith an a rg o n b u f f e r a n d a b o u t
5 m T o r r o f 16N 2 a d d e d .
U n f o r t u n a t e l y , low er c u r r e n ts (200-300 m A )
w e re n e e d e d f o r th e 12C c o n ta i n in g species b ecause d is c h a r g e spikes w ere
m o re o f a p ro b le m .
T h is w as th e re s u lt o f e le c tro d e d e te r io r a ti o n .
A tte m p ts
to a ll e v ia t e th e p ro b le m by h a v in g th e e le c tro d e s h o n e d p r o v id e d only
t e m p o r a r y r e lie f .
F o r some w ork w ith 0220 a n d 0380 s a te llite s 1800 volt
a b n o r m a l d is c h a r g e s w ith 8 m T o rr o f A r a n d
0.5 m T o r r each o f N 2 a n d
C H 4 w e re e m ployed. F o r these d is c h a r g e s th e d isc h a rg e m a g n e tic f ie ld
w as n o m in a lly 250 Gauss.
THEORY
T h e p u rp o se o f th is section is to c o n s id e r the c a lc u la tio n o f Bv’s
a n d D v’s f r o m th e o b se rv e d sa te llite f re q u e n c ie s .
O nce th e Bv’s h a v e
been o b t a i n e d , th e y can be used to c a lc u la te Be f ro m th e e q u a tio n :
( 1)
+ E 7 ij(vi+ d i/ 2 ) ( v j+dj /2 ) +
i
>j
E eijk( v i+ d i/ 2 ) ( v j+ dj/2 )( v k+ d k/2 ) + I n i 2.
Bv= Be-
E a i( v i+ d i/2 )
E q u i l i b r i u m s tr u c tu r e s can th e n be c a lc u la te d u sing th e e q u a tio n s:
505379.05
'■(amU * > - B (M Hz)
P>
110
and
I
m Hm C r C H 2+
m Cm N r CN 2+
—
m Hm N ( r CH+ r CN) 2
#
^
mH + mc + mN
C le a rly , i f Be is k n o w n f o r tw o iso to p o m ers an e q u il b r iu m s t r u c t u r e f o r
a tri a to m ic c a n be c a lc u la te d .
If Be is k n o w n fo r f o r m ore t h a n tw o
iso p to p o m ers, th e n th e Be’s c a n be c a lc u la te d f ro m all possible pairs.
In th e lim it o f th e B o r n - O p p e n h e im e r a p p r o x im a tio n , a n d a ssu m in g th a t
th e sum s in E q u a t io n (1) c o n v e rg e to th e "true" Be, th e n th e r e’s sh o u ld
be e q u a l f o r all possible p a ir s .
E q u a t io n (1) is f u n d a m e n t a l to th e w o rk disc u sse d in
th e n e x t th re e c h a p te rs a n d we w ill discuss it in some d e ta il. T h e f ir s t
sum consists o f th re e term s, c o rr e s p o n d in g to v i b r a t io n a l e x c it ia t io n o f
on e o f th e s p e c if ic v ib r a t io n a l modes. T h e r e f o r e , i f we o b serve th e g ro u n d
v i b r a t io n a l s ta te a n d th re e s a te llite s , each w ith e x c it a t i o n in a s e p a ra te
m ode, a n d i f we assum e th e 7 a n d 6 term s a re zero, E q u a t io n (1) red u c e s
to
Bv= Be- E o ,( v i+ d i/2).
i
(4 )
T h is shall be r e f e r r e d to as th e a a p p r o x im a tio n , a n d Be’s c a lc u la te d
f r o m th is e q u a ti o n sh a ll be r e f e r r e d to as a level Be’s. S tr u c tu r e s o b ta in e d
f r o m th e Be’s a n d E q u a tio n s 2 a n d 3 sh a ll be r e f e r r e d to as a level s tru c tu re s .
F o r th e a level w o rk in th is thesis, we will use the 100, 02°0, a n d 001
sa te llite s.
T h is is p r e f e r r e d to th e 0 1 10, since th e 0 ^ 0 has a n in h e r e n t
Ill
7u d e p e n d e n c e . T h e 100, 02°0, a n d 001 will o c c a s io n a lly be r e f e r r e d
to as a level satellites.
I f o n ly th e e’s a r e assum ed to be zero th e n E q u a t io n (1)
r e d u c e s to
Bv= Be-
E ot|(V|+d|/2) + E 7 ij(v i+ d i/2 )( v j+ dj/ 2 )
i
(5)
+ 7 / / / 2-
>j
T h e 7 term s c o rr e s p o n d to d o u b le e x c ita tio n , w h e t h e r tw o q u a n t a in
o ne m ode su c h as the 002 mode, o r c o m b in a tio n s such as th e 101 m ode.
T h is is th e a 7 a p p r o x im a tio n , a n d q u a n titie s c a lc u la t e d f r o m th is e q u a tio n
sh a ll be r e f e r r e d to as a y q u a n titie s .
S a tellites such as th e 200, 101,
llH ), 0 1 11, a n d 002 sh a ll be r e f e r r e d to as a 7 level sa tellites.
T h e e term s in E q u a tio n (1) c o rre sp o n d to trip le
v i b r a t io n a l e x c ita tio n s , such as th e 300, 2 10, l l M m odes. T h e s p e c tr a
o f t r i p ly e x c ite d m odes a re r e f e r r e d to as a 7 e level s a te llite s. T h e fu ll
use o f E q u a t io n (1) is r e f e r r e d to as the a y e a p p r o x i m a t io n , a n d a n y
q u a n ti ti e s c a lc u la te d f r o m the fu ll use o f this e q u a tio n a re a y e q u a n titie s .
It w o u ld be m ost d e s ira b le to be able to o b ta in a y e Be’s,
b u t th e r e a r e d i f f ic u l ti e s . C o n s id e ra b ly m ore d a t a m u st be o b ta in e d
a t e a ch successive a p p ro x im a tio n . T h e g ro u n d v i b r a t io n a l s ta te a n d th re e
e x c ite d v ib r a t io n a l sta te s a re all th a t is n e e d ed to o b t a i n a n a level s tr u c tu r e .
O n e needs seven e x tr a v i b r a t io n a l states to o b t a i n the a y s tr u c tu r e s (six
m ore if no s a te llite s w ith /-type reso n a n c e a re o b served).
e x tr a v i b r a t io n a l sta te s b e y o n d th e a y
th e a 7 e .
A f u r t h e r ten
a p p r o x i m a t io n a r e n e e d ed fo r
While th is c a n be do n e fo r H C N (as sh o w n in b o th C. S. G u d e m a n ’s28
112
thesis a n d in this w ork), it is n o t possible f o r a less a b u n d a n t m olecule
(such as H N C ) or v i b r a t io n a ll y c o ld e r m olecule (such as HCO+). Because
o f th e p r e v io u s ly m e n tio n e d fre e d o m f ro m a c c id e n ta l re s o n a n c e s 28, a n d
b e c au se it is possible to o b ta in a 7 c d a ta , we c a n use th e H C N m olecule
to a d d re s s th e q u e s tio n o f c o n sisten c y o f e q u il ib r i u m s tr u c tu r e s c a lc u la te d
f r o m th e levels o f a p p r o x im a tio n o f E q u a tio n 1.
B e fo re E q u a tio n 1 c a n be used to o b ta in Be, it is
n e c e e s a ry to c a lc u la te Bv f ro m the e x p e rim e n ta l d a ta . All o f th e s a te llite s
f o llo w th e p a tte rn :
v= 2Beff J ' - 4 D eff J ' 3,
(6 )
w h e re J' is th e u p p e r v alue o f J f o r a J —*J +1 tra n s itio n .
F o r the g ro u n d
v ib r a t io n a l s ta te a n d e x c ite d v i b r a t io n a l states, w ith no e x c ita tio n in
th e d e g e n e r a te b e n d in g m ode, Beff = Bv a n d D e(f = Dv. M a tte rs a re , how ever,
c o n s id e r a b ly m ore c o m p lic a te d w h e n th e v2 m ode is e x c ite d .
H c lm in g e r
a n d D e L u c i a 26 h a v e e x a m in e d the th e o r y o f /-type re s o n a n c e a n d /-ty p e
d o u b lin g in c o n s id e ra b le d e ta il, a n d th e i r resu lts will be s u m m a riz e d
in th is section. It can be assum ed by th e r e a d e r , t h a t all m a te r ia l is r e f e re n c e d
f r o m th is source, unless o th e rw is e e x p lic itly stated.
F o r all th e d i f f e r e n t v i b r a t io n a l levels th e m a t r ix ele m en ts
in th e se c u la r d e te r m i n a n t w ill be o f th e type:
< v/|H |v/'>.
F o r v= 1, th e se cu la r d e te r m i n a n t o b ta in e d by u sin g th e m a t r ix ele m en ts
< v,/|H |v,/'> is o f th e form :
113
w ith Wn = q vJ (J + l).
En - e
Wn
Wu
En - C
F o r th is d e te r m i n a n t, v=l a n d l=±l. T h e f o r m u la
f o r th e r o ta t io n a l e n e rg y o f a m olecule, t a k i n g
Iin to a c c o u n t is
E r = Bv [J(J+1)-/2] - D v [J(J+l)-/2]2
(7 )
I f we in s e rt /=±1 in to th is e q u a tio n th e fo llo w in g e q u a tio n is o b ta in e d :
E r± - Bv J(J+1) - Bv + 2D V J(J+1) ± q v J(J+1)
(8 )
- Dv[ J(J+1)2]2 - D v T q v'[ J (J + l )]2.
I g n o rin g the - B v a n d - D v term s (these a re not J d e p e n d e n t a n d c o n tr ib u te
n o th in g to th e r o ta tio n a l fre q u e n c ie s .), th is leads to th e fo llo w in g results:
Beff =
Bv ± q v + 2 D ,
(9 )
and
Deff
= Dv± q v'.
( 10)
T h e r e f o r e , D v can be c a lc u la te d m e re ly by a v e ra g in g th e tw o D e ff’s, a n d
Bv by a v e ra g in g the tw o Beff’s a n d s u b tr a c ti n g tw ice D v.
F o r v= 2, the se cu la r d e te r m i n a n t is giv en as
114
W20
E /> - e
Er o -
W20
e
W20
E*° - 6
W20
w i t h W20=qv/ ( 2 ) 1/ 2 [ J 2(J+ 1)2- 2 J ( J + 1 )] 1/ 2. T h e e n tr ie s in th is d e te r m i n a n t
a ris e f r o m / a n d / ' = - 2 , 0, a n d 2. T h e Wang t r a n s f o r m a t i o n m a tr ix ,
2 -1/2
0
■
2-1/ 2
o
2 " 1/ 2
1
0
0
2-1/ 2
a n d its tra n s p o s e c o n v e r t th is d e te r m i n a n t to
E d° - c
2 1/ aWao
0
2 1/ 2W,n
'20
E r° - 6
0
0
0
E a°- 6
T h e e n e rg y levels r e s u ltin g f ro m this are
E z = E r ° + ( 1 /2 ) 5 - ( l/2 ) { 5 2 + 4 q y2 [J 2( J + 1)2- 2 J ( J + 1)])1/ 2,
( 11)
EAd= E^°,
( 12 )
and
E ^ c= E ^ ° - (1/2)5 + ( l/2 ) { 5 2 + 4qv2 [J2( J + l ) 2- 2 J ( J + l ) ] ) i / 2
( 13)
115
w ith 5=E/10 - E r °. T h e s q u a re roots in E q u a tio n s 8 a n d 10 can be e x p a n d e d
to o b ta in
Ez= Ez° -
q v2/5 [J2(J+ 1)2-2 J(J + 1 )]
( 14)
and
E ^ d= E A° +
q v2/ 5 [J2(J+ 1)2-2J(J+ 1)].
( 15)
F r o m these th e fo llo w in g ex p re ssio n s a re o b tain e d :
Beff (02°0) = Bv + 2 q v2/ 5,
( 16)
D eff (02°0) = D v + q v2/ fi,
( 17)
Beff (022c0) = Bv- 2 q v2/5+ 8 D v,
( 18)
D e„ (022c0) = Dv- q v2/5,
( 19)
Beff (022d0) = Bv + 8 D v,
( 20)
and
( 21)
D eff (022d0) = D v.
T h e se e q u a tio n s also se rv e to e n a b le e s tim a tio n o f q v2/ 5 d i r e c tl y f r o m
th e e x p e r im e n ta l d a ta . C o m b in in g e q u a tio n s 18-21 w ith E q u a tio n 6 a n d
a s su m in g Bv a n d D
, /t
a re th e sam e f o r both 0220 lines, one o b ta in s
v(022d0) ~K022e0)
q / / 6 = -----------4 ( J '3 - J ' )
.
F o r v=3, the fo llo w in g se c u la r d e te r m i n a n t occurs:
( 22)
116
W31
0
0
W3i
E n° - €
Wn
0
0
Wn
E n° - 6
W«
0
0
W3i
V>- €
E*°-
w ith W31 = (3)1/ 2q v/ 2 [J2(J+ 1)2 - 8J(J+1) + 12]i/2,a n d Wu = q vJ (J + l). T h e
e n tr ie s c o rr e s p o n d to / a n d / ' = - 3 , - 1 , 1, a n d 3. T h e Wang ty p e tr a n s f o r m a tio n
m a tr ix
2 - 1/2
0
0
2 - 1/2
0
2 - 1/2
2 - 1/2
0
2 - 1/2
0
0
2 - 1/2
0
-
2 -!/2
2 ' 1/ 2
-
0
a n d its tra n s p o s e c o n v e rt th is d e t e r m i n a n t to
E*° - €
w 31
W31
E n° -W n -e
0
0
0
0
E n ° + Wn - e
w 31
W31
E*° -C
0
T h e f o llo w in g e n e rg y levels result:
0
117
E nd =
E n °+ 5/2 + Wn / 2 - (l/2 ){ [ 5 - W u ]2 + 4WS1*}»/*,
( 23)
=
E * ° - 8/ 2 + Wn / 2 + ( l/2 ){ [ 5 - W n ]2 + 4WJ!2}1/ 2,
(24)
E nc =
E n °+ 8/ 2 - Wu /2 - ( l/2 ){ [ 5 - W 11]J + 4W3!2}1/ 2,
( 25)
E ^ 0 - 5/2 - Wu / 2 + 0 / 2 ) { [ 5 - W u ]2 + 4W3J2}1/ 2.
/2(5/
and
Em =
H e re 5= E.J,0 -
E n °. It sh o u ld be n o te d t h a t this 5 is 2 tim es the 5 f o r
th e v=2 lines. T h e rea so n can be u n d e rs to o d f ro m th e e q u a tio n f o r the
v i b r a t io n a l e n e rg y f ro m A m a t a n d N ie ls o n 31:
( 27)
Ev -
hcE
8
<J8(v„ + gB/2 ) +
E x 8S'(VS + 8s/2 )
( v „-
E
8
Xss(v s + gg/ 2 ) 2 +
+ gs-/2 ) + x,/2.
8S'
T h e f i r s t th r e e term s ca n ce l in c o m p u tin g th e r a tio o f th e fre q u e n c ie s
f o r th e t r a n s it io n s 03s0-*0310 a n d 0 2 ° 0 - >0220, a n d the r e m a in d e r yields
8V =3/8 v =j= 3 2- 1 2/ 2 2- 0 2=2. M a k i32 p ro v id e s e x p e r im e n ta l c o n f i r m a ti o n
2
2
o f th is, o b t a i n in g 5=30.344 c m - 2. Since 5 is a p p r o x im a te ly tw o tim es
g r e a t e r f o r th e v= 3 tra n s itio n s ,
tim es sm a lle r.
q v2/ 5 is, o f course, a p p ro x im a te ly 2
D e L u c ia a n d H e lm in g e r give th e f o llo w in g f o rm u la s f o r
th e 0 3 ld0 states:
®eff = Bv+ q v + 6 q v2/ 5+ 2 D v
( 28)
and
D eff= D v+ q v' + 3 q v2/45.
(29)
118
F o r th e 0 3 lc0 states th e r e s u lts a re
Beff =
Bv - q v + 6 q v2/5 +2 D v
( 30)
D v- q v'+ 3qv2/4S.
( 31)
and
D eff=
No re s u lts w ere given f o r th e 03s0 sta te , b u t th e y can be c a lc u la te d f ro m
e q u a tio n s 21 a n d 23 to be
Beff=
Bv- 6 q v2/5+ 18 D v
(32)
D v- 3qv2/45.
( 33)
and
D eff =
T h is a p p lie s f o r both 033c0 a n d 038d0 states, w hich a r e d e g e n e r a te in
th e lim it o f the th eory.
F o r th e v=4 s a te llite s no d e t e r m i n a n t is listed by D e L u c ia a n d
H e lm in g e r.
M aki a n d L i d e 16, h o w e v e r, p o in t o u t t h a t th e r e a r e tw o d e te r m in a n ts :
Er° - e
W42
0
W42
E*° - e
2 1/ 2W02
0
2 1/ 2W02
Er ° - 6
and
E4 ' €
W42
W42
Er - 6
119
w ith W42= q v[ J 2( J + l ) 2- 1 8 J ( J + l) + 7 2 ] 1/ 2 a n d Woa- ( l / 2 ) ( 6 ) 1/ 2q v [ J 2(J+1)2- 2 J ( J + 1 )] 1/ 2.
U s in g second o r d e r p e r t u r b a t io n th e o ry , the f o llo w in g result
is o b ta in e d f o r th e 04°0 state:
E r = E r °+ 2W022/ ( E 2;° - E / ) .
( 34)
T h is agrees w ith the fo rm u la q u o te d in D e L u c ia a n d H e l m i n g e r 26, a n d
f r o m th is one c a n o b ta in th e expressions (also f o u n d in D e L u c ia a n d
H elm inger):
E r = E r ° - 3 q v2/5 [ J 2( J + l ) 2 -2J(J+ 1)],
(35)
Beff = Bv+ 6 q v2/5,
( 36)
and
D eff = D v+ 3 q v2/5.
( 37)
T h e r e a re no e x p e rim e n ta l results f o r the 0420 a n d 0440 sate llite s, hence
no ex p re ssio n s f o r th em in D e L u c ia a n d H e lm in g e r.26 N e v e rth e le ss, it
is f a i r l y s t r a i g h t f o r w a r d to c a lc u la te them f ro m M aki a n d L id e ’s15 d e te r m i n a n ts
a n d second o r d e r p e r t u r b a t io n th e o ry , a n d th e y will be p re s e n te d here
as a c o n v e n ie n c e f o r f u t u r e e x p e rim e n te rs .
It sh o u ld f i r s t be noted th a t
(16—4 ) /( 4 —0) =3 so E r ° - E ^ 0 = 35. M a k i32 a g a in p ro v id e s e x p e rim e n ta l
p r o o f, m e a s u r in g E ^ - E ^ 0 to be 15.225 c m -1 a n d E r ° - E 4 ° to be 45.675
c m -1. W ith th is in m in d , the f o llo w in g e x p ressions a re o b t a i n e d fo r the
120
0420 state:
E Ac= E a ° +
W422
------- ------ +
E 4° - E r °
2W022
—
E 4° -E z °
( 38)
( 39)
E a = E a o - ( 1 / 3 ) qv2/5 [J 2( J + l ) 2- 1 8 J ( J + l) + 7 2 ] + 3 q v2/5 [J2(J+ 1)2-2J(J+ 1)],
Beff (042c0)=
Bv+ 8 D v,
D eff (042c0)= D v- (8 /3 ) q v2/5 ,
( 40)
( 41)
w 422
E-= E‘0+ TjZ?
E^d= E a ° - ( 1 / 3 ) q V2/S [J2( J + l ) 2-1 8 J ( J + l) + 7 2 ],
( 43)
Beff (042d0)=
( 44)
Bv+ 8 D v+ 6 q v2/8, a n d
D eff (042d0)= D v + (1 /3 ) q v2/5.
( 45)
F o r b o th o f th e (0440) states, th e f o llo w in g e x p re ssio n s a re ob tain e d :
E = E r °+ — — ------ ,
Er» -E /
( 46)
E r = E r °+ (1 /3 ) q v2/5 [J2( J + 1)2- 18 J ( J + 1)+72],
( 47)
Beff = Bv+ 32 D v- 6 q v2/5 ,
( 48)
and
D eff= D v - ( 1 / 3 ) q v2/5.
( 49)
121
E F F E C T IV E C E N T R IF U G A L D IS T O R T IO N C O N S T A N T S
T h e th e o r y o f th e p r e c e d in g se ctio n ha s some f a i r l y in te r e s tin g
c o n seq u e n c e s f o r H C N . A c c o r d in g to M a k i32, 3=15.119 c m -1, a n d q o^ o
is 224 M H z ( th is w o rk or D e L u c ia a n d H e lm in g e r 26), a n d t h e r e f o r e
kH z, a n d D v is also o f th e o r d e r o f 100 kHz.
q v2/5 « 1 0 0
In the l a b o r a to r y sp e c tra ,
w h a t we obse rv e is th e a c tu a l f r e q u e n c y d i v id e d by the h a rm o n ic o f
th e k ly s tro n , i.e, ^actuaj/J'-
"w,..™ -2B.tr 4 >
E q u a tio n 2, w hen d iv id e d by J ' , becom es
(SO)
V J.
T h is leads to th e f o llo w in g u s e fu l rela tio n sh ip s:
»'k.y.tro n (J= 2 ^3 ) =
2 Beff - 36 D ett,
( 51)
>'klystro„(J=3-4) =
2 Beff - 64 D eff,
( 52)
2 Beff - 100 Defr
( 53)
and
"M y.tro„(J=4-5) =
L in e s w ith "norm al" c e n tr if u g a l d is to r tio n , such as the m a in line a n d
such sa te llite s as th e 01*0, 001, o r 100, as well as th e lo w e r 0 2 2c0 w ill
a p p e a r a b o u t 3 M Hz a p a r t a t the k ly s tro n f r e q u e n c y f o r th e J=2-»3 a n d
J=3-*4 t r a n s itio n s a n d a b o u t 4 M H z a p a r t a t the k ly stro n f r e q u e n c y f o r
th e J=3-*4 a n d J=4-*5 tra n s itio n s .
F ig u re s 1-3 show the m ain lin e w ith
3rd, 4 th, a n d 5th h a rm o n ic s , in a d d it io n , th ey show the e f f e c t o f p ro p er
ba selin e sup p re ssio n .
It w as even possible to observe s ix th h a rm o n ic
lines f o r H 1SC N , as show n in F ig u re 4. In F ig u re 5 the J=2-»3 a n d J = 3 —4
122
F ig u re 1-T his s p e c tr u m o f th e
J=2-*3, J= 3 —4, a n d 4-»5 t r a n s it io n s of
th e g r o u n d v i b r a t i o n a l s ta te was o b t a i n e d u n d e r th e fo llo w in g e x p e rim e n ta l
c o n d itio n s : 6 scans, 15 s e c /s c a n , 20 m T o rr a rg o n , 5 m T o rr N 2, 5 m T o rr
C H 4, 300 m A n o r m a l d is c h a rg e , 2400 kH z FM, 30 kH z AM, a n d 1 baseline
su p p re s s io n (800 kH z), f a s t flo w , no sm o o th in g , l iq u id n itr o g e n cooling,
a n d InSb d e te c to r (8 k G a u s s f ie l d a n d 26 T o r r He pressure.)
123
HCN 0 0 0 IB 800kHz
3 .0
J=2-3
J=3-4
J=4-5
-
2. 0
88620.0
8 8 6 2 6 .0
FREQUENCY(MHz)
88632.0
124
F ig u re 2 -T h is is th e sam e d a ta as in F ig u re 1, a n d th e only d i f f e r e n c e
is t h a t o u r b a s e lin e su p p re ssio n is 600 kHz.
125
HCN 0 0 0 IB 600kHz
o
J=2-3
5
J=3-4
J=4-5
0
5
88620.0
8 8 6 2 5 .0
88630.0
FREQUENCY(MHz)
126
F ig u re 3 -T h is is th e sam e d a ta as in F ig u r e 1, a n d th e o n ly d i f f e r e n c e
is t h a t o u r b a s e lin e su p p re ssio n is 480 kHz.
127
HCN 0 0 0 IB 480kHz
3 .0
J=2-3
1.5
J=3-4
J=4-5
.0
1 .5
88620.0
88 625.0
88630.0
FREQUENCY(MHz)
128
F ig u re 4 - U n d e r p r o p e r c irc u m s ta n c e s , it w as possible to observe t r a n s it io n s
o c c u r in g over 500 G H z, as in this sp e c tru m o f th e J = 4 —5 a n d J = 5 —6
tr a n s it io n s o f th e 01 x0 v i b r a t io n a l level o f H 13CN.
T h e e x p e rim e n ta l
c o n d itio n s f o r this o b s e rv a tio n a re 80 scans, 15 s e c /s c a n , 25 m T o rr a rg o n ,
10 m T o r r N 2, no i n p u t 13C, slow flo w , w a te r co o lin g , 500 mA n o rm a l
d is c h a r g e , 1600 k H z FM, 30 k H z AM, 11 p o in t sm o o th , a n d 2 b a selin e
su p p re s s io n s (270 kHz). T h e InSb d e te c to r w as a t 5 k G au ss f ie ld a n d
7 T o r r He pressure.
129
H13CN
v=
0110
2B 270kHz
J=4-5
J=5-6
86300
86305
FREQUENCY(MHz)
86310
130
F ig u re 5 -N o t a ll v i b r a t io n a l states have th e sam e e f f e c ti v e c e n tr if u g a l
d i s to r tio n c o n s ta n ts as th e g ro u n d state, f o r e x a m p le, th e 02°0 state.
T h e J * 2 —3 a n d 3—4 t r a n s itio n s a p p e a r to be 6 M H z a p a r t a t th e k ly s tro n
f r e q u e n c y , as opposed to 3 M Hz d i f f e r e n c e f o r the g ro u n d s ta te tra n s itio n s .
T h e r e a d e r c a n r e a d ily c o n tr a s t this f ig u r e w ith F ig u re s 1-4. E x p e r im e n ta l
c o n d itio n s a r e th e sam e as in F ig u re s 1-3, e x c ep t t h a t we h a v e a v e ra g e d
38 scans a n d used 21 p o in t sm oothing. O u r b a s e lin e s u p p re ssio n is 600
k H z , w h ic h f a v o r s th e J - 3 —4 line.
HCN 02°0 2B 600kHz
J=2-3
J=3-4
89075
89080
FREQUENCY(MHz)
132
F ig u re 6-T he u p p e r tra c e o f th is f ig u r e is th e J = 4 —5 s p e c tr u m o f the
0220 sta te , a n d th e low er tra c e is the th e J = 3 —4 s p e ctru m .
F o r th e 0 2 20
v i b r a t io n a l sta te , the tw o d o u b le ts h a v e d i f f e r e n t e f f e c t i v e c e n tr if u g a l
d i s t o r ti o n co n sta n ts. T h e 022c0 (th e l e f t lines o f b o th sp e c tra ) has a n o rm a l
e f f e c t i v e c e n tr if u g a l d i s to r tio n c o n s ta n t.
T h e J=3-*4 a n d 4 —5 t r a n s itio n s
a p p e a r a p p r o x im a te ly 4 M Hz a p a r t a t the k ly stro n f r e q u e n c y , s im ila r
to th e g r o u n d v i b r a t io n a l state.
T h e 022d0 sta te , ( th e r ig h t lines o f both
s p e c tr a ) h o w e v e r, has a n e f f e c ti v e c e n t r i f u g a l d i s to r tio n c o n s ta n t n e a rly
e q u a l to zero, a n d th e J = 3 —4 a n d 4 —5 t r a n s it io n s o c c u r a t n e a rly the
sam e k ly s tro n f re q u e n c y . T h e e x p e r im e n ta l c o n d itio n s a re th e sam e as
in F ig u re s 1-3, e x c ep t t h a t we h a v e a v e ra g e d 40 scans fo r th e J = 3 —4
a n d 65 scans fo r th e J = 4 —5, a n d we h a v e m u ltip lie d the J = 4 —5 by a f a c to r
o f fiv e .
133
HCN 0 2 20 2B
J=4-5
J=3-4
89030
89035
89040
FREQUENCY(MHz)
134
tr a n s it io n s a r e p r e s e n te d f o r th e 02°0 states, a n d th e r e a d e r can note
t h a t th e r e is c o n s id e r a b ly m o re s e p a r a tio n t h a n f o r th e 000 states. T h e
u p p e r 022d0 line, on th e o th e r h a n d , has a n e f f e c t i v e c e n t r i f u g a l d is to r tio n
c o n s ta n t o f n e a r l y zero, w h ic h m ea n s th a t th e d i f f e r e n t h a rm o n ic s h a v e
a te n d e n c y to "pile up".
All o f th is is i ll u s tr a t e d in F i g u r e 6, w h ic h c o n ta in s
th e 0220 4 th a n d 5th h a rm o n ic lines.
T h is is e s p e c ia lly severe f o r J = 2 —3
t r a n s itio n s , bec au se th e r e is n e a r ly a lw a y s r e s id u a l 4 th h a rm o n ic pow er
fr o m th e k ly stro n . T h e m u lt ip l ie r is so m uch less e f f i c i e n t f o r 5th h a rm o n ic
m u lt ip l ic a t io n t h a t i n te r f e r e n c e f r o m 5th h a r m o n i c t r a n s it io n s is not
so severe. T h e p o w e r r a tio , m e a s u re d by f u ll y m o d u la ti n g th e k ly stro n ,
is a p p r o x i m a t e ly 2 /1 /0 .0 5 fo r th e t h ir d , f o u r t h , a n d f i f t h h a rm o n ic s ,
re s p e c tiv e ly .
When the k ly s tro n was fu lly m o d u la te d w ith a 6th h a rm o n ic
c u t - o f f f il te r , it was n e v e r possible to o b ta in o b s e rv a b le p o w e r a t the
lock-in a m p l if i e r .
STARK EFFECT
T h e 0220 s ta te m e a s u re m e n ts w ere f u r t h e r c o m p lic a te d by two
fa c to rs : th e S ta rk e f f e c t a n d th e n u c le a r q u a d r u p o l e c o u p lin g d u e to
th e I»1 n u c le a r m a g n e tic m o m e n t o f the 14N atom . T h e p o s s ib ility of
S ta rk p e r t u r b a t i o n arise s b ecause th e two 0 2 20 levels a re only s e p a r a te d
by q v2/ 5 [J2(J+ 1)2-2J(J+ 1)]. T h e q u a n t i t y q v2/fi is a p p r o x i m a t e ly 114 k H z
f o r H C N , a n d th e q u a n t i t y [ J 2(J+ 1)2-2 J(J+ 1 )J is 24, 120, 360, a n d 840
f o r J=2, 3, 4, a n d 5, resp e c tiv e ly .
T h e s e p a r a tio n b e tw e e n the levels becom es
2.7 M Hz, 13.6 M Hz, 41.0 M Hz, a n d 95.8 M Hz f o r J=2, 3, 4, a n d 5, respectively.
C le a rly , th e h ig h e r the J ' , th e less p e r t u r b e d th e tr a n s itio n .
F o r all th re e
r e la te d m olecules H C N , H N C , a n d H C O + th e 0220 lin e s w ere w e a k e r
135
a n d b r o a d e r th a n w ould h a v e been exp e cte d f o r u n p e r t u r b e d sp e c tra ,
a lt h o u g h f o r H N C th e p e r t u r b a t io n was not as severe, as will be seen
in th e n e x t c h a p te r. T h e m ost d r a m a ti c e v id e n c e is seen f o r th e J=2-*3,
w h e r e th e f r e q u e n c y o f th e low er t h i r d h a rm o n ic line is d e p e n d e n t on
th e b u f f e r gas e m p lo y e d , as sh o w n in F ig u re 7, w h ic h is a plot o f H C N
0 2 20 t h i r d h a rm o n ic lines in H 2 a n d A r b u f fe r s .
F u r th e r m o r e , s in c e the
d ip o le m a tr ix e le m e n t l/u^l2 is p r o p o rtio n a l to J ' 2- / 2 (see, f o r ex a m p le,
T o w n e s a n d S c h a w lo w 33, p34), the r a tio o f 0220 /0 2 °0 sh o u ld be ( J ' 2 - 4 ) / J ' 2.
T h e r e f o r e , th e ra tio s should be 5 /9, 3 /4, a n d 2 1 /2 5 f o r J=2-»3, 3-*4, a n d
4-*5 tra n s itio n s , resp e c tiv e ly .
F ig u re s 8-10 show t h a t these ra tio s a re
n o t th e o b se rv e d ones, espec ially in F ig u re 8, w h ic h co m p a res th e J=2-»3
tra n s itio n s , a n d in w h ic h it sh o u ld be no ted t h a t we m u ltip lie d th e 0220
s p e c tr u m by fiv e .
F ig u re 8 also serves to illu s tr a te th e e a rlie r m e n tio n e d
"p ilin g up" e f f e c t o f th e lines w ith n e a r-z e ro e f f e c ti v e c e n tr if u g a l d is to r tio n .
In a d d it io n , th e 0 2 20 lines a re c o n s id e r a b ly b r o a d e r , as can also be a s c e r ta in e d
f r o m fig u re s 8-10. T o give th e r e a d e r a f e e lin g f o r how p e r t u r b e d the
v a rio u s h a rm o n ic s a re , T a b le I, w h ic h c o m p a res in te n s ity ratio s a n d line
w id th s f o r th e v a rio u s h a rm o n ic s in both n o rm a l a n d a b n o rm a l d isc h a rg e s ,
h as been in c lu d e d . We h a v e also in c lu d e d the 0 3 ^ a n d 0330 states in
th e table. O n e can note f ro m th is tab le t h a t th e a b n o rm a l a n d n o rm a l
d isc h a rg e s seem to p e r t u r b the 0220 states a b o u t e q u a lly . (T his w ill be
f a r f r o m th e case f o r HCO+.)
What m akes th is all the more i n tr ig u i n g
is t h a t o u r D o p p le r s h if t e x p e rim e n ts on K r D + 34 sh o w e d v e ry little , i f
a n y , e x te r n a l e le c tric f ie ld in the a b n o rm a l d isc h a rg e , as th e re was a
v e ry slig h t negative D o p p le r s h ift.
T h is re s u lt is in a g re e m e n t
136
T a b le I-H C N 02°0 vs 0220 a n d 03*0 vs 0330.
A. N orm al D ischarge
J= 2 —3
J = 3 —4
J= 4-5
Av( 02°0)
0.384
0.516
0.605
Ai/(0220)
1.047
0.924
0.815
I(02°0)/I(0220)
13.
4.
2.5
0.644
0.625
1.450
1.112
A i/^ ^ )
1(03
12.
3.0
B. A b n o rm al D ischarge
J=*2—3
J = 3 —4
J = 4 —5
0.351
0.320
0.390
A v(0220)
0.858
0.547
I(02°0)/I(0220)
3.
2.0
A v^O )
0.380
0.450
Av(0330)
0.828
1.040
1(03
15.
2.5
Av(02°0)
137
F ig u re 7-T he S ta rk e f f e c t p e r t u r b a t io n o f th e J=2-*3 t r a n s it io n o f the
0220 s ta te is d e m o n s tra te d .
E x p e r im e n ta l c o n d ito n s f o r th e s p e c tr u m
r e p r e s e n te d by the solid lin e a r e 35 m T o r r H 2, 3 m T o rr C H 4, a n d 3 m T o r r
N 2. F o r th e d a s h e d line, we h a v e 30 m T o rr A r, 3 m T o rr C H 4, a n d 3 m T o rr
•Nj. T h e f o llo w in g c o n d itio n s w ere com m on to both disc h a rg es: slow flo w ,
w a t e r cooling, 300 m A, 2400 k H z FM, 30 k H z AM, 100 scans, 2 b a selin e
su p p re ssio n s (800 kH z), a n d 21 p o in t smooth.
Please no te t h a t th e d a s h e d
lines a re s h if t e d to g e th e r w ith respect to th e solid lines. T h is d e m o n s tra te s
t h a t the e le c tric f ie ld v a rie s w ith the d isc h a rg e c o n d itio n s.
HCN
v=
0220
J=2-3
S0LD-H2 BUFFER
DASHED-Ar BUFFER
89035
89040
FREQUENCY(MHz)
139
F ig u re 8 -T h e most stro n g ly p e r t u r b e d o f th e 0 2 20 v i b r a t io n a l s ta te t r a n s itio n s
is th e J=2-*3. T h e low er c u rv e is the 02°0 J«2-*3 line, a n d th e u p p e r
c u r v e c o n ta in s the 022c0, J = 2 —3 a n d J = 3 —4 tra n s itio n s a n d th e b le n d
o f th e J=2-*3 a n d J»3-»4 t r a n s itio n s in the 022c0 v i b r a t io n a l state.
E ven
w i t h o u t a c u t o f f the J * 3 —4 o f th e 0 2 2c0 v i b r a t io n a l s ta te line h a s g r e a te r
p e a k in te n s it y th a n th e J « 2 —3. T h e a s y m m e tr y o f this s p e c tr u m occurs
b e c au se o f th e n e a rly zero e f f e c ti v e c e n tr if u g a l d i s to r tio n c o n s ta n t causes
th e m e r g in g o f the u p p e r J = 2 —3 a n d J=3-*4 lines. T h e 02°0 t r a n s it io n
is b o th c o n s id e r a b ly stro n g e r a n d n a rr o w e r th a n the 0220 tra n s itio n s .
E x p e r im e n t a l c o n d itio n s a r e as follows: 15 s e c /s c a n , 20 m T o rr a rg o n ,
5 m T o r r N 2, 5 m T o rr C H 4, 300 mA n o rm a l d isc h a rg e , 2400 k H z FM, 30
k H z AM, 2 b a selin e su p p re ssio n s (800 kHz), f a s t flow , a n d liq u id n itro g e n
cooling. T h e 02°0 s p e c tr u m r e q u ir e d 23 scans, a n d the 0220 s p e c tr u m re q u ir e d
161 scans.
T h e b a r re p re s e n ts 5 M Hz a c tu a l fre q u e n c y . T o f a c i li ta t e
c o m p a r is o n we have m u ltip le d th e 0220 s p e c tru m by a f a c t o r o f 5.
140
HCN 02°0 vs 02*0 J= 2-3 NORMAL DISCHARGE
SCALE 5X
J = 2 -3
J = 3 -4
5 MHz
J = 2 -3
141
F ig u re 9 -T h e J=3-*4 v= 0220 t r a n s it io n s a re also p e tr u r b e d r e la tiv e to the
02°0, J = 3 -> tra n s itio n s , b e in g c o n s id e r a b ly w e a k e r a n d b r o a d e r , as can
be seen in th is fig u r e .
T h e r e a d e r will note th a t th e d i s p a r it y b e tw e e n
th e s p e c tra o f th e tw o v i b r a t io n a l levels is not n e a rly as g r e a t as in the
p r e v io u s fig u r e .
T h e e x p e rim e n ta l c o n d itio n s f o r th is f ig u r e a re 15 s e c /s c a n ,
8 m T o r r a rg o n , 0.5 m T o rr N 2, 0.5 m T o rr C H 4, 1800 volt,
a b n o rm a l d isc h a rg e ,
2400 kH z AM, 30 k H z FM, a n d 2 b a seline s u b tr a c ti o n (600 kH z), 21 p o in t
sm ooth, f a s t flo w , a n d liq u id n itr o g e n cooling.
T h e 02°0 v i b r a t io n a l
sta te s p e c tr u m w as the a v e ra g e o f 31 scans, a n d th e 0220 states w ere o b served
a f t e r 152 scans.
142
HCN 02°0 vs 02*0 J=3-4 ABNORMAL DISCHARGE
5 MHz
143
F ig u re 10-The J * 4 —5 tra n s itio n s o f the 0220 v i b r a t io n a l s ta te a re still
less p e r t u r b e d r e la tiv e to the 02°0 sta te t h a n e ith e r the J*2-»3 or J=3-*4
t ra n s itio n s .
T h e i r p e a k in te n s itie s a re a lm o st 1/2 th e u n p e r t u r b e d sate llite s,
a n d th e y a r e o n ly s lig h tly b ro a d e r, as c a n be noted in th is fig u r e .
Our
e x p e r i m e n t a l c o n d itio n s a re th e sam e as in F ig u re 8, ex c ep t t h a t 122 scans
h a v e b e e n a v e ra g e d f o r the 02°0 t r a n s itio n a n d 142 scans fo r the 0 2 20
t ra n s itio n s .
Both s p e c tra r e q u ir e d 2 b a selin e su ppressions o f 480 k H z
a n d a 21 p o i n t sm ooth. T h e b a r re p re s e n ts 5 M Hz a c tu a l fre q u e n c y .
144
HCN 02°0 vs 0220 J= 4-5 NORMAL DISCHARGE
10 MHz
145
F ig u re 11-The 0330 v i b r a t io n a l sta te , J = 3 —4 t r a n s it io n s a re p e r t u r b e d
r e l a ti v e to th e 02°0. T h e r e a d e r s h o u ld note t h a t th e 0330 lines a r e a
f a c t o r o f IS w e a k e r th a n th e 03*0 v i b r a t io n a l s ta te tra n s itio n s , as well
as b e in g c o n s id e r a b ly b ro a d e r.
T hese s p e c tra w ere m e a s u re d u n d e r the
f o llo w in g c o n d itio n s : 15 s e c /s c a n , 25 m T o rr a rg o n , 5 m T o rr N 2, 5 m T o rr
C H 4, 300 m A , n o r m a l d is c h a rg e , 2400 kH z FM, 30 k H z AM, a n d 3 b a selin e
s u p p re s s io n s (600 kH z), 21 p o in t sm ooth, f a s t flo w , a n d liq u id n itr o g e n
c ooling.
We have a v e ra g e d 34 scans f o r the 03*0 a n d 142 f o r th e 0330,
a n d we h a v e m u ltp lie d th e O S ^ s p e c tr u m by a f a c t o r o f 10. T h e b a r
r e p r e s e n ts 5 M Hz a c tu a l f r e q u e n c y .
146
HCN 03*0 VS 0330 J=3-4 NORMAL DISCHARGE
SCALE 10X
5 MHz
147
F ig u re 12-Even th e J « 4 —5 t r a n s it io n s o f the 03*0 v i b r a t io n a l s ta te a re
q u i t e p e r t u r b e d r e la tiv e to th e 03*0 sta te . T h e e x p e r im e n ta l c o n d itio n s
a r e th e sam e as in th e p re v io u s f ig u r e , e x c ep t t h a t 480 k H z b a s e lin e su ppressions
h a v e been used a n d 140 scans h a v e been a v e ra g e d f o r th e 03*0 s a te llite
a n d 211 s c an s f o r th e 0330 sa te llite .
f re q u e n c y .
T h e b a r re p re s e n ts 5 M Hz a c tu a l
148
HCN 03*0 VS 0330 J=4-5 NORMAL DISCHARGE
5 MHz
149
w i t h w o rk by B lake et a/.35 f o r HOC+. T h e y t r i e d m e a s u r in g th e D o p p le r
s h i f t by re v e rsin g th e lo c a tio n o f th e i r source a n d d e te c to r , a n d cam e
to th e con c lu sio n t h a t t h e i r d i f f u s i o n p u m p w as th e ca u se o f th e rev e rse
D o p p le r s h if t t h a t th e y o b se rv e d . T h e m e a s u re m e n ts in th is la b o r a to r y ,
h o w e v e r, w ere o b ta in e d by r e v e rs in g th e p o la r ity o f th e d is c h a r g e a n d
n o t m oving e ith e r so u rc e o r d e te c to r , a n d a n y e f f e c ts d u e to th e p u m p in g
system can be ru le d out.
We h a v e also obse rv e d th e J = 3 —4 a n d J = 4 —5
t ra n s itio n s o f th e 0330 v i b r a t io n a l sta te , a n d th e y a re s u b s ta n t ia ll y b r o a d e r
a n d w e a k e r t h a n th e 0 3 x0 (see F ig u re s 11 a n d 12). T h e f a c t t h a t th e y
a r e visible a t all, th o u g h , is s o m e w h a t s u rp r is in g , because th e 033c0 a n d
033d0 v i b r a t io n a l sta te s a r e c o m p le te ly d e g e n e r a te a t th e level o f o u r
th eo ry .
A c c o rd in g to M aki a n d L i d e 31 th e c o n s ta n t, p, w h ic h p ro v id e s
th e only d i f f e r e n c e b e tw e e n th e tw o e n e rg y levels is 0.3 kHz. T h e r e f o r e ,
e v e n w ith th e i r m ore e x a c t th e o ry , th e tw o e n e rg y levels a re so closely
spa ce d th a t S ta rk p e r t u r b a t i o n w o u ld be e x p e c te d to e r a d i c a t e th e lines.
W. T. C o n n e r30 has d o n e m ore e x te n s iv e e x p e rim e n ts , a n d he has m odelled
th e S ta rk e f f e c t on a m ic ro sc o p ic e le c tr ic f ie ld c a lc u la te d by H o l t s m a r k 36,
w hose t r e a tm e n t was e x te n d e d by H o o p e r 37.
Q U A D R U P O L E E F F E C T C A L C U L A T IO N S
T h e e f f e c t o f q u a d r u p o l e h y p e r f i n e i n te r a c t io n s on th e sp e ctra
o f the H C N a n d H 13C N iso to p o m ers m u st also be c o n s id e re d . T h e q u a d ru p o le
e f f e c t on lines w ith 1=0 is c a lc u la te d fro m A p p e n d ix II o f T o w n e s a n d
S c h a w lo w 33 to s h i f t th e a p p a r e n t c e n te r f re q u e n c ie s - 2 5 k H z , - 8 kH z,
a n d - 5 kH z fo r J=2-»3, J = 3 —4, a n d
J = 4 —5 t ra n s itio n s , resp e c tiv e ly .
T h ese c a lc u la tio n s w e re c a r r ie d out by c a lc u la tin g th e f r e q u e n c y s h if ts
150
o f e a c h (J,F ) c o m p o n e n t, th e r e la tiv e i n te n s ity f o r e a ch c o m p o n e n t, a n d
th e n t a k i n g a w e ig h te d ave ra g e . T h e reason f o r th e n e t f r e q u e n c y s h i f t
is t h a t th e tw o AF=0 com p o n e n ts, w h ic h c o m p rise a f e w p e rc e n t o f th e
r e l a ti v e in te n s ity , a r e s h if t e d a p p ro x im a te ly 2 M Hz fro m the u n s p lit
lin e f re q u e n c y .
T h is s h i f t leaves th em o u ts id e th e o b s e rv e d lin e p r o file ,
a n d s in c e t h e i r s h i f t is not sym m e tric , the n e t f r e q u e n c y o f th e o b served
line p r o f i l e is slig h tly s h if te d .
M a tte rs a re m ore c o m p lic a te d f o r sa te llite s w ith /-ty p e resonance,
be c au se th e e n e rg y levels m ust be m u ltip lie d by a f a c t o r o f 1 - (3/2) J _1( J + 1)_1
(page 154, T ow nes a n d S c h a w lo w 33), w h ic h c o n s id e r a b ly c h a n g e s the s p littin g
p a tte rn s . T h e 01*0 a n d 03*0 q u a d ru p o le s p littin g s a r e c o n s id e r a b ly re d u c e d
by a p p lic a tio n o f th e I2 term , a n d it is only n e c essa ry to a d d 11 kHz,
6 k H z , a n d 4 kH z to th e J=2-*3, J=3-»4, a n d J = 4 —5 t ra n s itio n s , resp e c tiv e ly .
T h e 0 2 20 sa te llite , on the o th e r h a n d , has a m u ch m ore d i s tin c t q u a d r u p o le
s p littin g p a tte rn .
F ig u re s 13-15 a re stick s p e c tra s h o w in g the s p littin g
p a tt e r n s o f 0 2 20 a n d 02°0 states f o r J=2-»3, J = 3 - ‘4, a n d J=4-»5 tra n s itio n s .
T h e 1-2 lines a re m ore s p re a d out th a n /=0 lines, a n d t h e r e f o r e th e 0 2 20
lines sh o u ld be b r o a d e r th a n the 02°0 ones solely b ecause o f the q u a d r u p o le
e f f e c t.
A s lig h t b it o f e v id e n c e in f a v o r o f th is is p r o v id e d by F ig u re
16, w h ic h c o m p a re s th e 0220 vs 02°0 in the J=4-*5 sta te f o r H l3C 15N,
a n d one can see by c o m p a riso n w ith F ig u re 10, th a t th e line seems so m e w h at
less p e r tu r b e d .
T h e th e 0 2 20 peak in te n s ity is o v e r h a l f the 02°0 peak
i n te n s ity f o r th e H 13C 16N s p e ctru m , w h ile f o r th e H C N s p e c tru m , the
p e a k i n te n s ity o f the 0220 is less th a n h a l f the peak in te n s ity o f th e 02°0.
T h is re s u lt is f a r f ro m d e f i n i t i v e because e x p e r i m e n t a l c o n d itio n s w ere
151
F ig u re 13-A s tic k s p e c tr u m o f a J = 2 —3 t r a n s it io n w ith e Q q = -4 .7 M Hz
(i. e., H C N ) a n d 1=2 is c o m p a r e d to a stic k s p e c tr u m o f a J = 2 —3 tr a n s it io n
w ith e Q q = -4 .7 M H z a n d 1=0. Please note t h a t th e r e a re tw o AF=0 c o m p o n e n ts
o f lesser i n te n s it y t h a t a r e s e p a r a te f o r th e 1=0 (02°0) state. T h e y a re
not s y m m e tr ic w ith respect to th e u n s p lit lin e f re q u e n c y .
Also, no te t h a t
th e 1=2 lines a re sp lit f a r t h e r f r o m the u n s p lit f r e q u e n c y t h a n th e 1=0
lines (e x c e p t f o r th e AF=0 c o m ponents).
152
LINE
HCN 02*0 VS 02°0 QUADRUPOLE SIMULATION J=2-3
48
PERCENT
INTENSITY
UNSPLIT
42
36
30
24
18
12
8
-
1.0
.0
1.0
2.0
FREQUENCY SHIFT (MHz)
153
F ig u re 14-T he s tic k s p e c tr a f o r J = 3 —4 tr a n s it io n s o f 1=2 a n d M ) v i b r a t io n a l
s ta te s a re show n. T h e p a t t e r n is the sam e as in th e p re v io u s f ig u r e , but
all th e lin e s a re c o n s id e r a b ly closer to th e u n s p lit f re q u e n c y , e x c e p t th e
w e a k e r AF=0 lines, w h ic h h a v e been b r o a d e n e d to d is tin g u is h th e m f r o m
tic k m arks.
154
HCN 02*0 VS 02°0 QUADRUPOLE SIMULATION J=3-4
LINE
i
1---- 1
i
i---- r— i---- 1
i
i---- 1---- 1---- i---- 1---- 1---- r— r
48
42
UNSPLIT
i —i
1 SOLID-02s0
.
DASHED-02°0
i
36
PERCENT
INTENSITY
30
24
18
12
6
■* ■ ■ I
-
1.0
*
ill
i I—1! Ii Li— i
.0
i
1
1.0
i
i
i
i
C
2.0
FREQUENCY SHIFT (MHz)
155
F ig u re 15 T h e se s tic k sp e c tra o f J=4-*5 t r a n s itio n s w ith e Q q = -4 .7 M Hz
a re e v e n less s h i f t e d t h a n in the p rev io u s f irg u re s . T h e r e a re , h o w e v e r,
o u t ly i n g A F »0 c o m p o n e n ts f o r the m odel 0220 sp e c tra , as well as th e
m o d el 02°0 s p e ctra.
T h e w e a k e r 4 F » 0 c o m p o n e n ts h a v e been b r o a d e n e d
to d is t i n g u is h th e m f r o m tic k m arks.
156
HCN 02*0 VS 02°0 QUADRUPOLE SIMULATION J=4-5
LINE
—
1---------- 1
T —
i
" T
*T
r
r—
i
i
i
r-—»
i
i
j—
j ---------- —
i
i
i " 1
i
1
1
48
INTENSITY
UNSPLIT
42
i
36
i
i
i
i
i
i
i
«
i
it
ti
ii
ii
-
30
ii
*
24
ii
-
-
18
i
i
»
i
i
•
i
t
ii
ii
ii
i
i
i
i
t
ii
ii
ii
ii
ii
it
ii
n
ii
it
PERCENT
i ii
12
i ii
i ii
—
i ii
i ii
i
i
i
i
i
i
i
i
i
i
i
6
.
______ i______ S—
i—
j ______ 1___ L
-
1.0
ii
ii
ii
ii
ii
ii
ii
ii
ii
ii
ii
______ i---------- 1—
.0
- i...
L l ----------- 1----------1—
1.0
FREQUENCY SHIFT (MHz)
•
a
157
F ig u re 16-T he 02°0 a n d th e 0220 f o r th e J=4-*5 t r a n s it io n o f H 13C 15N
a r e c o m p a re d .
T h e e x p e r im e n ta l c o n d itio n s a r e as follows: 500 m A, slow
flo w , 25 m T o r r A r, 3 m T o rr 16N 2, no in p u t 13C, 2 b a selin e su p p re s s io n s
(480 kH z), 21 p o in t sm o o th 2400 kH z FM, 30 k H z AM, 15 s e c /s c a n , 10
m sec tim e c o n s ta n t, 86 scans f o r th e 02°0 a n d 50 scans f o r th e 0220 state.
T h e sig n a l to noise r a t i o is c o n s id e r a b ly p o o rer t h a n f o r F i g u r e 10, b u t
th e 0 2 20 v i b r a t i o n a l sta te lines a re o f only slig h tly lesser in te n s it y t h a n
th e 02°0 lines.
In F i g u r e 10 (a b n o rm a l d isc h a rg e ), the / d o u b le t lines
a re a lm o st tw ic e as w e a k as th e 02°0. T h e b a r r e p re s e n ts 10 M H z a c tu a l
frequency.
158
H13C15N 02°0
vs
02s0 J=4-5 NORMAL DISCHARGE
10 MHz
159
c o n s id e r a b ly d i f f e r e n t , a n d be c au se th e sig n a l to noise r a t i o w as c o n s id e r a b ly
p o o rer f o r th e H 13C 15N lines th a n f o r th e H C N lines. We d i d n o t, u n f o r t u n a t e l y ,
re a liz e th e im p o r ta n c e o f q u a d r u p o l e s p littin g w h e n we d id th e H C 16N
w o rk , so we d id not look f o r J= 2 —3 tr a n s itio n s f o r th e 0 2 20 state. We
o b se rv e d th e th e J = 3 —4 t r a n s it io n f o r th e 02°0 w i th o u t th e c u t o f f f i l t e r
a n d th e 0 2 20 w ith th e c u t o f f f il te r , so we can o f f e r no l e g itim a te c o m p a ris o n
b e tw e en th e tw o in te n sitie s.
T h e 02°0 J = 3 —4 t r a n s it io n f o r H 13C 15N w as
o v e rla p p e d by th e 01*0, a n d th e r e f o r e we h a v e no c o m p a ris o n f o r this
species e ith e r.
C le a rly , S ta rk e f f e c t d a ta on H C 15N w o u ld be m ost v a lu a b le.
While th e 0220 is b r o a d e n e d m ore t h a n th e /=0 lines, th e r e is less n e t
s h i f t in f re q u e n c y , a n d it is only nec essa ry to a p p ly c o rr e c tio n s o f - 1 0
k H z, - 6 kH z, a n d - 3 k H z f o r th e J = 2 - 3 , 3 - 4 , a n d 4 - 5 t r a n s it io n s , resp e c tiv e ly .
O B S E R V E D F R E Q U E N C IE S AND E R R O R A N A L Y SIS
T a b le II is a c o m p ila tio n o f all th e f re q u e n c ie s o b s e rv e d f o r
all th e isotopes, w ith th e a p p r o p r i a t e c o rre c tio n s f o r th e q u a d r u p o l e e ff e c t.
In o r d e r to p r e s e n t a c o m p le te set o f o u r g r o u p ’s m ic r o w a v e d a ta , we
h a v e also p r e s e n te d G u d e m a n ’s28 results.
We h a v e not, h o w e v e r, in c lu d e d
this d a ta in o u r f it t i n g , b ecause th e r e w e re large e r r o r b a rs f o r some
o f the tr a n s it io n f re q u e n c ie s , su ch as th e H C N 101 v i b r a t i o n a l s a te llite
e rr o r b a rs o f 100 kHz.
T h e r e was also a 1 M Hz u n c e r t a i n t y listed in
th e H 13C N 200 s a te llite f r e q u e n c y a n d a 2 M Hz u n c e r t a i n t y listed in
th e H C 15N 300 s a te llite f r e q u e n c y .
T hese a re alm ost s u rle y m isp rin ts.
We w e re not able, h o w e v e r, to re p r o d u c e his e s tim a te d u n c e r t a i n t i e s o f
57 kH z in th e H 13CN a 7 level Be a n d 59 kH z in th e H C 1BN a y e level
Be u s in g 100 k H z a n d 200 kH z f r e q u e n c y e r r o r bars. B ecause o f these
160
d i f f i c u l t i e s , it was d e c id e d to use o n ly th e p re s e n t d a ta f o r the analysis.
The
Bv’s a n d
D v’s w e re c a lc u la te d a c c o r d in g to th e th e o ry , a n d th e ir
v a lu e s a r e p re s e n te d in T a b le III, a lo n g w ith th e Beff’s, D eff’s, q v’s, a n d
S’s f o r th e sa te llite s w ith v2 e x c ita tio n .
When we h a d th r e e tra n s itio n s ,
i.e., f o r all th e 000 lines, a n d f o r th e H C N 0 1 10, 02°0, a n d 03*0 satellites,
we u s e d least squares. We did not use 01*0 tra n s itio n s , w h ic h w e re o v e rla p p e d
by 02°0 tra n s itio n s . T h e r e a re tw o e x p e r im e n ta l d i f f i c u l t i e s w h ic h should
be m e n tio n e d : (1) th e 11 lc0 line o f
H C 15N w as o b s c u re d by th e 100,
(2) th e 200 a n d 002 sa te llite s o f H 13C 15N w ere se verely b le n d e d .
possible to obse rv e the l l ld0 s ta te w i t h o u t in te r fe re n c e .
It was
T h is m e a n t th a t
i f q u i 0 co u ld be e s tim a te d th a t an a p p r o x im a te v a lu e o f B n i 0 c o u ld be
d e te r m in e d .
T h is was a c co m p lish e d by t a k in g th e d i f f e r e n c e s b e tw e en
q n i 0 a n d q ^ o f o r the o th e r isotopom ers a n d in te r p o la ti n g f o r H C 15N.
It w as possible to see th e 200 peak as a s h o u ld e r on th e 002 p e a k f o r
th e J = 2 —3 f o r H 13C 16N, b u t it was not possible to obse rv e a n y s e p a r a tio n
f o r th e J = 3 —4 p eak s, a n d it was sim p ly assum ed t h a t th e f r e q u e n c y was
th e sam e fo r b o th satellites.
Because o f th e congested n a tu r e o f T a b les II a n d III, e rr o r
lim its w e re not p ro v id e d .
For th e m a in line a n d th e a level sa te llite s
(100, 01*0, 02°0, a n d 001) th e re w ere a t least tw o m e a s u re m e n ts in all
case, a n d these a g re e d to w ith in a t most 30 kH z, 40 kH z, a n d 80 kH z
f o r th e J = 2 —3, J=3-»4, a n d J= 4 —5 tra n s itio n s , resp e c tiv e ly .
Because o f
the nec essity to in c lu d e q u a d r u p o le in te r a c tio n s , it is f e l t t h a t 30 kHz,
40 k H z , a n d 50 kH z e rr o r bars a re n o t u n r e a s o n a b le f o r th e J=2-*3, J = 3 —4,
a n d J=4-»5 t ra n s itio n s o f these satellites.
161
Table II. Observed HCN Frequencies (M H z). a
13c 16n
V
J'
HCN
H 13CN
H C 15N
000
000
000
000
000
1
3
4
5
6
88631.607b
265886.419
354505.453
443116.145
86339.974b
259011.906
345339.863
431659.760
517969.836
86054.974b
258157.002
344200.128
430235.410
251175.216
334891.428
418600.101
100
100
100
1
3
4
88006.644b
264011.523
352005.627
85762.637b
257279.979
343030.728
85455.168b
256357.602
341800.992
249495.462
332651.856
01lc0
01lc0
01lc0
0 1 ld0
01ld0
01ld0
01ld0
0 1 ld0
3
4
5
6
3
4
5
6
265852.732
354460.521
443059.855
258936.096
345238.724
431533.350
517817.976
260224.824=
346956.792
433680.515
520393.902
258134.610
344170.216
430197.790
251112.045
334807.212
418495.025
259406.031
345865.136
432315.935
252325.896
336425.476=
420517.445
001
001
001
1
3
4
88027.290b
264073.245
352087.693
85755.089b
257257.245
343000.344
85475.089b
256417.839
341881.176
249516.786
332680.296
200
200
200
1
3
4
87363.628b
262082.583
349433.775
8 5 168.13b
255495.891
340652.188
84837.561b
254504.796
339330.528
247807.053d
330400.708
l l lc0
l l lc0
1 1ld0
l l ld0
3
4
3
4
264005.124
351997.080
265373.097
353820.351
257227.125
342960.160
258538.425
344708.388
257645.942®
343518.380®
249475.017
332625.512
250714.128
334276.308
101
101
101
1
3
4
87415.210b
262237.313
349639.871
85189.363b
255560.085
340737.528
84887.770b
254655.378
339531.184
247871.379
330486.504
02°0e
02°0®
02°0®
02°0f
1
3
4
5
89087.674b
267243.210
356301.176
445339.400
86747.725b
346944.408
433645.705
86492.06 l b
259458.420
345923.612
022c0
022c0
022d0
022d0
4
5
4
5
356135.456
445152.805
356162.608
445207.565
346782.388
433462.435
346807.736
433513.335
267199.322
356255.609
445303.225
h
252335.304
420502.990
345763.408
432188.200
345787.356
432236.580
336271.168
420324.205
336293.304
420368.595
162
01 lcl
01 lcl
0 1 ld l
0 1 ldl
3
4
3
4
264019.793
352016.884
265364.085
353809.324
257164.086
342876.008
258450.202
344590.568
256375.660
341824.840
257645.895
343518.308
249415.659
332545.828
250627.230
334160.500
002
002
002
1
3
4
87419.372b
262249.686
349656.372
84892.339b
255493.143
340648.216
85167.056b
254667.606
339549.660
247807.106d
330400.708
300
300
300
1
3
4
86701.661b
260096.628
346794.032
253657.653
338201.112
2 1 lc0
2 1 lc0
2 1 ld0
21 ld0
3
4
3
4
262113.036
349474.624
263483.832
351301.640
255476.952
340625.376
256781.094
342366.184
201
201
201
1
3
4
86785.343b
260347.680
347120.428
253810.500
338404.804
12°0
I2°0
12°0
1
3
4
88488.736b
265446.219
353904.136
86193.206b
258563.253
344728.588
l l lcl
l l lcl
11 ld l
11 ldl
3
4
3
4
262203.231
349594.192
263585.013
351436.608
255486.423
340637.912
256795.755
342385.520
102
102
102
1
3
4
86820.087b
260451.873
347259.480
0 3 lc0
0 3 lc0
0 3 lc0
0 3 ld0
0 3 ld0
0 3 lc0
3
4
5
3
4
5
266540.040
355371.680
444190.435
269312.718
359067.788
448809.340
0 330
0330
4
5
356839.652
446040.570
02°1
02°1
02°1
1
3
4
88468.124b
265384.218
353820.984
84201.56b
84282.380b
85918.195b
257735.964
343627.032
84317.437b
253832.505
338433.792
259508.106
345996.756
251668.041
335544.348
262160.766
349532.732
254166.147
338874.304
86149.346b
258429.159
344550.224
85897.304b
257673.819
343543.944
163
01lc2
01 lc2
01 ld2
01ld2
3
4
3
4
262174.623
349556.060
263517.699
351347.076
255382.253
340500.680
256665.939
342211.784
003
003
003
1
3
4
86808.024b
260415.567
347210.924
253719.771
338283.672
14°0
1
88997.850b
04°0
04°0
04°0
1
3
4
89569.166b
268663.347
358166.204
04° 1
1
88933.487b
86342.940b
22°0
1
87871.248b
85325.099b
02°2
02°2
02°2
1
3
4
87844.495b
263513.412
351327.480
85299.225b
06°0
1
90081.339b
87444.692b
84306.308b
86406.730b
87179.898b
261498.780
348617.360
86593.427b
253553.664
338029.376
a F or u n c e r ta in ty estim ates see text.
b M easured by G udem an.
c T he J - 2 —3 tra n s itio n s o f 02°0 a n d 01*0 a re blen d e d
f o r H 13CN, a n d the J - 3 —4 tra n s itio n s o f 02°0 a n d 01*0
a re blen d e d in H 13C 1SN.
d T h e H 13C 15N 200 a n d 002 a re blen d e d (see text).
8 T h e H C 15N 111c0 lines a re obscured by the 100.
f T he H C 1SN 02°0 line is not obscured. We d id not look
f o r it sim ply because o f disc h a rg e d iff ic u ltie s .
164
T a b le III . H C N Bv’s, Dv’s, Beff’s, a n d Deff’s.a
HCN
H 13C N
H C 15N
H 13C 15N
000
000
Bv
Dv
44315.972b*c
87.26c'd
43170.154b>®
83.60®
43027.649bt®
82.06®
41863.943b,c
79.17®
100
100
By
Dy
44003.485
86.93
42881.482
82.53
42727.736
81.64
41583.985
78.21
01*0
01*0
01*0
o ik )
01*0
01*0
01*0
By
Dy
Qy
D efl(c)
B eff(d)
D e«(d)
44422.429
88.77
224.485
44310.362c
87.40c
44534.852®
90.66®
43264.760
85.15
214.833
43157.527
83.96
43372.358
86.34
43129.734
84.08
211.948
43023.924
82.71
43235.877
85.46
41954.440
79.91
202.340
41853.430
79.00
42055.771
80.82
001
001
By
Dy
44013.809
88.99
42877.705
83.17
42737.797
82.82
41587.538
80.82
200
200
By
Dy
43681.984
86.33
42584.129
81.43
42418.896
82.14
41302.573
77.64
11 x0
l l l0
11*0
11 x0
1^0
11*0
11*0
By
Dy
Qy
Befl(c)
D efj(c)
B,fl(cl)
D e«(d)
44116.299
90.16
228.105
44002.421
87.07
44230.538
93.25
42981.806
83.80
218.578
42872.688
83.39
43091.266
84.93
42836.003
42942.523
85.17
41683.682
80.66
206.804
41580.356
79.20
41787.166
82.11
101
101
By
Dv
43707.807
88.211
42594.834
82.61
42444.060
83.21
41313.290
77.39
02°0
02°0
02°0
02°0
ByC
Dy
Beff
D eff
44544.008
92.28
44544.248®
206.28®
43374.026
87.36
43374.238
193.36
43246.235
86.04
43246.437
187.04
42058.841
82.13
42059.026
174.53
0220
0220
02 20
02 20
02 20
0220
0220
0220
By
Dy
Beff(c)
D,ff(c)
Beff(d)
D e(^d)
44519.067
91.54
44519.868
91.75
44519.561
-23.92
114.08f
15.1738
43349.856
86.01
43350.563
86.39
43350.315
-20.36
106.04
14.952
43222.496
88.48
43223.281
89.22
43222.996
-13.25
100.79
15.300
42035.839
81.97
42036.519
81.76
42036.313
-10.92
92.40
15.214
Be«(c)
qvVS
8
21 1.903*
165
01M
OlM
OlM
OlM
OlM
OlM
O l1!
By
Dy
dy
Befl(c)
D e«(c)
BrfKd)
Defi(cl)
44116.684
84.95
224.064
44004.826
84.88
44228.882
85.23
42969.218
85.47
214.392
42862.198
84.28
43076.593
86.62
42836.472
84.47
211.732
42730.783
83.69
42942.518
85.28
41671.492
78.23
202.048
41570.624
74.86
41772.673
81.61
002
002
By
Dy
43709.866
88.18
42583.686
83.10
42446.336
81.08
41302.593
78.27
300
300
By
Dy
43350.948
81.18
42277.737
79.54
21*0
21*0
21*0
21*0
21*0
2^0
21*0
By
Dy
dy
B#fl(c)
D«fl(c)
Befl(d)
D.fl(d)
43801.136
89.55
228.592
43687.021
84.14
43915.601
90.50
42689.529
82.11
84.66
43264.760
84.66
43264.760
84.66
201
201
By
Dv
43392.857
87.61
42303.2228
82.55
12°0
12°0
12°0
12°0
By
Dy
Be«*
D .ff
44244.690
101.67
44244.918
215.68
43097.265
97.265
43097.466
199.78
11M
llll
llll
l l 1!
I I 1!
11M
11M
By
Dy
dy
B.fl(c)
D,fl(c)
Befl(d)
Defl(d)
43817.129
90.14
230.291
43702.164
90.32
43932.455
89.96
42691.572
86.92
217.895
42582.782
95.10
42800.710
78.75
102
102
By
Dy
43410.202
86.46
42306.952
84.89
42959.154
85.78
42959.356
186.78
By
Dy
Qy
Befl(c)
D . h( c)
BefI(d)
Defl(d)
44656.335
93.69
231.106
44425.756°
134.26°
44887.993°
141.21'
0330
0330
0330
0330
By
Dy
B.ff
44605.193
94.07
44606.556
49.97
02° 1
02°1
02° 1
02°1
By
By
B.ff
44234.424
96.00
44234.664
210.00
43074.846
94.50
43075.049
195.96
01*2
0^2
0^2
01*2
01*2
01*2
01*2
By
. Dy
dv
B,h<c)
Defl(c)
D .«(d)
43800.098
89.10
223.811
43697.394
90.21
43921.201
88.00
42671.990
82.80
214.016
42565.154
80.27
43264.760
84.53
003
003
By
Dy
43404.175
90.00
42288.132
83.54
04°0
04°0
04°0
04°0
By
Dyh
44784.794
98.21
44785.516
460.64
43590.119
88.73
43590.793
425.71
02°2
02°2
02°2
02°2
D .f f
B frfd )
Beff
Deff
By
Dy
B ed
D eff
42154.558
84.57
208.244
41946.769
116.42
42363.257
124.04
43474.227
88.54
221.203
43253.609
125.46
43695.865
133.54
03*0
03*0
03*0
03*0
03*0
03*0
03*0
42948.833
87.40
42949.035
188.21
43922.477
95.13
43922.705
211.57
a E r ro r estim ates a re p ro v id e d in text fo r the Bv’s.
b B’s a re in MHz.
c Least squ a re s was used to c a lc u la te B ^ fo r all the isotopom ers,
a n d BeH03i 0, Befl02o0, Befl01i0 fo r the m ain isotopomer.
d D ’s a re in kHz.
e O b ta in e d by e x tr a p o la tin g d i ff e re n c e s betw een q n i o an d
42265.102
90.00
42265.722
376.57
q 01i0 f ro m th e o th e r isotopomers.
f T h e qv2/ 8 ’s a re in kHz. These were ca lc u la te d
f ro m the J=4-*5 lines. See text.
« T h e q u a n t i t y 8 is in c m " 1. We c a lc u la te qv fo r 020
by in te r p o la tio n o f q v o f 01 x0 b e tw een OS1©. F o r th e H C 15N,
we e x tr a p o la te d q02o0 - q 0xto fro m the o ther
isotopes.
hT h e q u a n t i t y 8 is assum ed to have the sam e v alue as f o r the 0220.
168
T h e 7 level s a te llite s (200, 002, 101, I l k ) , 01*10) w ere th e r e s u lt o f tw o
tr i a ls a g re e in g in th e w orst cases to 48 kH z a n d 92 k H z f o r th e J=2-»3
a n d J=3->4.
It is th e r e f o r e rea s o n a b le to assign e r r o r lim its o f 40 kH z
a n d 60 k H z f o r th e J=2-*3 a n d J=3-*4, respectively. B ecause th e 002
a n d 200 o f the H 13C 15N a re b le n d e d , th e u n c e r t a i n t y is s o m e w h a t g rea ter.
B ecause w e c o u ld see a s h o u ld e r f o r th e J=2-»3 tr a n s it io n , 100 k H z seems
a r e a s o n a b le u n c e r t a i n t y f o r them .
F o r the J=3-*4 t r a n s it io n , we could
o b se rv e no s h o u ld e r a n d feel t h a t 250 kH z is a re a s o n a b le e s tim a te o f
the u n certain ty .
T h e a 7 6 level s a te llite s (300, 21l 0, etc.) w e re th e result
o f one t r i a l, a n d th e signal to noise was g e n e ra lly poorer.
R e a s o n a b le
e r r o r lim its a re 90 k H z a n d 120 kHz. T h e 0220 J=3-*4 a n d J=4-»5 lines
w ere th e resu lts o f several tria ls f o r H C N , a n d tw o tria ls f o r all th e o th e r
isotopes.
C o n s e r v a tiv e e r r o r b ars f o r them a re 60 kH z a n d 80 kH z, f o r
th e J=3-»4 a n d J=4-»5 tra n s itio n s , p a r t l y because o f s c a tte r in th e d a ta ,
p a r t l y b ecause o f the u n u s u a l q u a d r u p o l e p a tt e r n , a n d p a r t l y because
o f th e S ta rk e ff e c t.
E r r o r lim its f o r Beff can e s tim a te d by r e a r r a n g i n g e q u a tio n 2
to f o rm
Beff = 2 v / J ' - 4 D effJ ' 2.
( 54)
T h e re s u lt is t h a t u n c e r ta in tie s o f 5 kH z, 7.5 kH z, a n d 15 k H z a re o b ta in e d
f o r a , a 7 , a n d a 7 e s a te llite Bv’s. We t h in k t h a t 25 k H z is a re a s o n a b le
u n c e r t a i n t y f o r the H 13C 15N B002 a n d B200. Because it was n e ccessary
to i n te r p o la te q ^ o fo r H C 16N, a re a s o n a b le u n c e r t a i n t y f o r t h a t Bv is
169
50 kHz.
It is n o t f e l t th e u n c e r t a i n t y sh o u ld be a n y g r e a te r f o r Bv th a n
Beff f o r v 2= l lines, because th e only c o rre c tio n s in v o lv e th e c e n tr if u g a l
d is to r tio n c o n s ta n t, a n d these a re a c c u r a te to 1 kHz.
If e q u a tio n (18)
is c o n s id e re d f o r J=4-*5 t r a n s itio n s o f th e 0 2 20 the re s u lt is
T h u s e rr o r s o f 1 M H z in 0220 f re q u e n c ie s will o n ly ca u se an e r r o r o f
4 kH z in q v2/S . T h e r e f o r e , it seems t h a t it is not neccessary to c o n sider
this a so u rc e o f u n c e r t a i n t y f o r th e 02°0 Bv’s.
C A L C U L A T IO N O F S P E C T R O S C O P I C P A R A M E T E R S
F ro m these
Bv’s we c a lc u la te d Be, th e oij’s, th e T^’s,
a n d th e 7 // f o r e a ch isotopom er, a n d th e c ^ ' s f o r th e m ain isotope a n d
H 13CN. T h is w as a c co m p lish e d by u sing a F O R T R A N p ro g ra m , U N IT Y ,
w h ic h a ccepts in p u t Bv’s a n d v i b r a t io n a l q u a n t u m n u m b e rs, a n d in v e rts
E q u a tio n (1) to solve f o r the spe ctro sc o p ic p a ra m e te rs f r o m th e Bv’s.
A listin g o f the p ro g ra m is in A p p e n d ix 6, a n d here a c u rs o ry a c c o u n t
o f the p r o g r a m ’s f u n c t i o n shall be p rese n ted . G u d e m a n 28 has d o n e so m e th in g
s o m e w h at sim ilar.
He d id not ta k e 7u in to a c c o u n t, h o w e v e r, a n d his
p ro g ra m s w ere d e sig n e d so th a t th ey w ould c a lc u la te a com plete set of
a level p a ra m e te rs , or a c om plete set o f a 7 level p a ra m e te rs , or a com plete
set o f a 7 € level p a ra m e te rs . O u r p ro g ra m is m ore fle x ib le a n d w ill c a lc u la te
p a r a m e te r sets f ro m a p a r tia l c o m p le m e n t o f v i b r a t io n a l s a te llite s at
a giv en level. It is even possible to c a lc u la te some c*7 level p a ra m e te rs
along w ith some a~l€ p a ra m e te rs . (T h is p o in t is o f little m om ent in this
170
T a b le IV. C o e ffic ie n ts of Bv in Be.a
Bv
a
a ,7
a ,7 ,c
000
2.5
6.
10.
100
-0.5
-2 .
-5 .
-4 .
-1 0 .
-2 .
-5 .
0 1 H)
001
-0.5
200
0.375
1.875
11*0
0.5
2.5
101
0.25
1.25
0.25
3.25
02J0
0.75
1.75
OlM
0.50
2.50
002
0.375
1.875
02°0
-0.5
300
-0.313
21*0
-0.375
201
-0.188
12°0
-0.500
11M
-0.250
102
-0.188
03^
-1 .
02° 1
-0.500
0 1 J2
-0.375
003
-0.313
T hese solve th e e q u a tio n Be = £ A-1p)Bv(lj. T he
A -1(i)?s a re c a lc u la te d in the m a n n e r as d e scrib ed in text.
c h a p te r , b u t w ill becom e i m p o r ta n t in th e c h a p te r on H C O +.) In m a t r ix
f o r m E q u a t i o n ( l ) becomes
(56)
Bv = A B n,
w h e r e Bv is a c o lu m n m a tr ix o f th e e x p e r im e n ta l Bv v a lu e s, Bn is a row
m a t r i x o f th e sp e ctroscopic p a ra m e te rs , a n d A is th e c o e f f i c i e n t m a trix .
O u r p r o g r a m notes w h ic h v i b r a t io n a l m odes a r e e x c ite d a n d c a lc u la te s
th e A m a tr ix . T h is m a tr ix is i n v e r te d by a s ta n d a r d F O R T R A N r o u t i n e 38,
y ie ld in g A -1. O nce this m a tr ix is o b ta in e d , one c a lc u la te s the spe ctro sc o p ic
p a r a m e t e r s by using the m a tr ix e q u a tio n
( 57)
M erely c o n s id e r in g Be, th is e q u a tio n leads to
(58)
Be - 12 A x n_1(Bv)n,
n
w h e re th e A l n _1 c o e f f ic ie n ts a re th e f i r s t row in the A _1 m a trix .
a r e d is p la y e d in T a b le IV f o r th e a ,
a 7 , and
a 7 e levels.
T hese
F o r a c om plete
lis tin g o f a set o f A a n d A -1 m a tric e s th e r e a d e r is r e f e r r e d to G u d e m a n ’s28
thesis.
B ecause we used d i f f e r e n t s a te llite s th a n G u d e m a n , his m a tric e s
w ere d i f f e r e n t th a n ours, b u t th e term s should be of s im ila r m a g n itu d e .
A glan c e a t T a b le IV reveals two i n h e r e n t d i f f i c u l t i e s o f o b t a i n in g an
a c c u r a te e q u il ib r i u m s tr u c tu r e a t h ig h e r levels, e sp ec ially the
a7e.
The
173
m ost o b v io u s is th a t h ig h ly e x c ite d v i b r a t io n a l sta te s w ith poor signal
to noise a r e needed, a n d th e i r c o e f f ic i e n t s a re not n e c essa rily sm all, e.g.,
th e 03*0 has a c o e f f ic i e n t o f 1. A m ore su b tle p ro b le m is t h a t th e c o e ff ic ie n ts
o f stro n g sa tellites, su c h as th e 001, in c re a s e g r e a tly f r o m th e a level
a y e level.
to th e
E rro rs in these s a te llite s w ill h a v e on th e o r d e r of
5 or 10 tim es as m uch e f f e c t on the
a 7 e Be’s, as on the a level Be’s.
G u d e m a n 28 c a lc u la te d e rr o r lim its fo r his Be’s by u sin g th e m a tr ix re la tio n s h ip
( 59)
°-p 2 = B a Bv2 ,
w h e re o p 2 is th e m a tr ix o f s q u a re s o f e r r o r lim its o f th e p a ra m e te rs ,
and
o-r
2 is the m a tr ix o f s q u a re s o f th e u n c e r t a i n t ie s in th e in d iv id u a l
DV
Bv values.
T h e B m a tr ix is com posed o f th e s q u a re s o f th e m a tr ix e lem ents
o f the A _1 m a trix .
U s in g this, we c a lc u la te u n c e r t a i n t ie s o f 15 kHz,
40 kH z, a n d 85 kH z, re s p e c tiv e ly f o r B, a t the a , a 7 , a n d
a 7 e lev e ls-
resu lts in ro u g h a g re e m e n t w ith G u d c m a n ’s28. O u r e r r o r e s tim a te s a re
83 k H z a n d 64 kH z f o r th e H C 15N a y a n d H 13C 15N a y level Be’s, because
o f th e p re v io u s ly m e n tio n e d p roblem s, i.e., the 100-11*0 a n d 002-200 b lendin gs.
C e r ta in ly , in view o f the size o f the c o e f f ic i e n t s in T a b le IV, these e rr o r
b a rs do n o t a p p e a r to be all t h a t u n re a s o n a b le . T h e e f f e c t on c a lc u la te d
s tr u c tu r e s shall be d e f e r r e d u n til the p lo ttin g is discussed.
T a b le s V, VI, a n d VII a re c o m p ila tio n s o f th e p a r a m e te r s
a t the a , a y a n d a 7 e levels.
F o r th e a y level we h a v e listed tw o sets
o f c o n s ta n ts, one c a lc u la te d u sing th e 11X0 a n d 0 111 states, a n d the o th e r
u sing th e 12°0 a n d 02°1 states.
T h e most s tr i k in g f e a t u r e o f these T a b les
174
T a b le V. H C N R o ta tio n a l C o n s ta n ts a Level.
HCNa
H 13C N a
H C 15N a
H 13C 15N a
Be
44509.282
43358.772
43213.238
42044.720
«i
312.488
288.671
299.910
276.423
«2
-114.018
-101.942
-109.289
-97.440
«3
302.164
292.448
289.850
279.976
HCNb
H 13C N b
H C 15N b
44509.283
43358.717
43213.259
312.483
288.650
299.905
«2
-114.021
-101.952
-109.276
«s
302.158
292.422
289.862
Be
a T h is work.
b G u d e m a n ’s d a ta .28
175
T able VI. HCN R otational C onstants a y Level
15n
HCN
H 13CN
Bea
44512.238
43361.514
43216.037
Beb
44512.202
43361.503
43216.004
Bec
44512.944
43362.066
43216.781
a ia
313.097
288.558
300.289
« ib
313.246
288.840
300.589
« ic
313.184
288.632
300.571
«2S
-107.314
-95.526
-102.827
«2b
-107.350
-95.536
-102.861
a 2°
-106.316
-94.700
-101.842
a 3a
300.047
290.678
287.912
«3b
299.826
290.406
287.546
«3C
299.771
290.337
287.591
hc
h
13c 15n
42047.403
276.374
-91.269
278.452
176
T a b le VI. (C ontinued).
7„a
-4.449
-4.341
-4.441
7nc
-4.513
-4.303
-4.450
■yi2a
6.364
5.699
6.176
-y b
' 12
6.513
5.961
6.475
7 l2 C
6.506
5.694
6.485
V
6.487
5.801
6.173
■yi3c
6.487
5.785
6.163
7 22a
1.329
1.280
1.270
7 22c
1.589
1.524
1.517
-3.583
-3.103
-3.412
■y23b
-3.804
-3.375
-3.776
723°
-3.808
-3.383
-3.758
W
-0.888
-0.784
-0.806
^33C
-0.900
-0.797
-0.797
-6.235
-6.042
-5.932
a T h e c o n s ta n ts w ere c a lc u la te d using the 11*0 a n d 0 1 11 satellites.
b T h e c o n s ta n ts w ere c a lc u la te d using the 12°0 a n d 02°1 satellites.
c G u d e m a n ’s 28 constants.
-4.271
5.629
5.728
1.210
-2.972
-0.708
-5.751
177
T a b le V II. H C N R o ta tio n a l C o n s ta n ts a y e Level.
HCN*
HCNb
H 13C N a
H C 15N b
Be
44512.245
44512.128
43361.537
43215.858
a,
313.951
313.154
289.352
300.541
a2
-108.177
-107.690
-95.802
-103.318
a3
300.893
299.715
290.986
287.258
7n
-3.868
-4.148
-3.762
-4.036
7 12
6.147
5.995
6.245
6.114
7 is
6.916
5.884
5.346
5.248
7 22
0.778
1.074
0.921
0.974
7 23
-2.974
-3.700
-2.286
-3.971
7 s3
-0.667
-0.893
-0.881
-0.837
178
T a b le V II. (C ontinued).
HCNa
HCNb
H 13C N a
H C 15N b
eu i
-0.113
-0.075
-0.060
-0.049
e U2
-0.065
-0.062
-0.303
-0.179
e ii3
-0.039
0.066
-0.015
-0.027
ei22
0.129
0.100
0.005
0.077
e i2 3
-0.002
0.470
0.014
0.842
e i3 3
-0.135
-0.023
0.185
0.063
e222
0.093
0.055
0.080
0.058
e 223
-0.147
-0.056
-0.260
-0.044
e 233
-0.063
-0.060
-0.046
-0.017
<=333
-0.012
0.014
0.009
0.006
7n
a O u r work.
b G u d e m a n 28.
-6.235
-6.042
179
is th e close a g r e e m e n t b e tw e e n Be ( a 7 ) a n d Be ( a 7 e ) f o r th e H C N a n d
H 13C N isotopom ers. T o f a c i l i t a t e c o m p a ris o n o f o u r results w ith G u d e m a n ’s28
e a r l ie r J=0-»1 d a ta , we also in c lu d e his d a ta in T a b les V, VI, a n d VII.
O u r a level Be’s a n d his a re in o u t s t a n d in g a g re e m e n t (1 kH z) f o r H C N
a n d r e a s o n a b le a g re e m e n t f o r th e o th e r tw o (21 kH z fo r H C 1BN a n d 55
k H z f o r H 13C N ), a n d o u r a 7 f Be is o n ly a b o u t 110 k H z h ig h e r t h a n the
e a r l ie r v a lu e f o r H C N .
On th e o th e r h a n d , ou r a 7 Be’s d i f f e r f r o m the
p re v io u s w o rk by se v era l h u n d r e d k H z f o r all th re e isotopes. P ro b a b ly ,
th is is b e c au se o u r a y level in c lu d e d 7//, a n d G u d e m a n ’s28 d id not.
T h e re
was a n a tt e m p t to o b ta in Be a t th e a y e level f o r th e H C 1BN isotopom er
by c o m b in in g th e r e c e n t resu lts w ith G u d e m a n ’s28 e a rlie r Bv’s. T h e value
o b ta in e d , h o w e v e r, was 43215.6 M Hz, w h ic h was 400 kH z below th e a y
v a lu e a n d o u t o f lin e w ith o u r o th e r results. T h is raises th re e possibilities:
(1) th e r e has been a n e rr o r in th e re c e n t m e a s u re m e n ts , (2) G u d e m a n
has m ad e a n e r r o r in his m e a s u re m e n ts , a n d (3) the spe ctro sc o p ic p a ra m e te rs
a re d e p e n d e n t on th e v i b r a t io n a l states chosen.
It does not seem likely
t h a t th e r e is a n e r r o r in th e re c e n t m ea s u re m e n ts because o u r Be’s fo r
the a y e level a re close to the a 7 level Be’s f o r tw o isotopes. T h is occurs
in s p ite o f th e f a c ts t h a t th e 7 ’s c h a n g e f ro m one level to the n e x t (see
T a b le s VI a n d VII), a n d th e e’s o f te n v a ry both in m a g n itu d e a n d size
b e tw e en th e isotopes (T a b le VII). T h e po ssib ility o f G u d e m a n 28 being
in e r r o r is suggested by th e f a c t th a t his e 123 is 0.842 MHz, a re s u lt th a t
seems r a t h e r larg e f o r a n 6 value.
His e 123 fo r H C N is 0.470 MHz, how e v e r,
a n d his re s u lt f o r Be agrees re a s o n a b ly well w ith o u rs f o r th e m a in isotope.
Some e v id e n c e f o r sa te llite d e p e n d e n c e o f Be can be seen in T a b le VII
180
f o r the a 7 level, w h e re it can be seen t h a t u sin g B 11i0 a n d
B n i! leads
to d i f f e r e n t v a lu e s o f th e spectroscopic c o n s ta n ts o f th e c a lc u la te d a y
sp e c tro sc o p ic c o n s ta n ts t h a n u sing B 12o0 a n d
Bq^.
T h e r e is less c h a n g e
in Be, h o w e v e r , th a n in some o f the a ’s a n d th e a p p r o p r i a t e 7 ’s ( y n
a n d 7 23). A r e a s o n a b ly c o n s is te n t a y e level Be was o b ta in e d by a d d in g
th e d i f f e r e n c e b e tw e e n o u r v a lu e o f Be f o r th e m a in isotope a n d G u d e m a n ’s
v a lu e f o r th e m a in isotope to his v alue f o r th e H C 15N.
S T R U C T U R E C A L C U L A T IO N S
It is possible to use th e r e la tio n s h ip s 26
505379.05
' B.(M H z)
(60>
and
m H m C r CH2+
h
m C m N r CN2+
2-------------------
m Hm N (r CH+ r CN) 2
. ■- — -----------------------m H + mc + mN
( 61)
to m ak e p lots o f r CH vs r CN, a n d use these plots to o b ta in q u a li ta t iv e
i n f o r m a t i o n a b o u t th e c o n sistency o f the v a rio u s levels o f a p p ro x im a tio n .
A d i r e c t p lo t o f r CH vs r CN f o r all o u r d a ta a n d f o r W innew isser, M aki,
a n d J o h n s o n ’s22 a level Be v alue o f DCN is sh o w n in F ig u re 17. All the
H C N c u rv e s a rc n e a rly p a ra lle l, a n d th e re is little i n f o r m a t io n to be o b ta in e d .
E v e n w ith th is c ru d e plot, h o w ever, the a level rCH vs r CN c u rv e s are
c le a rly s e p a r a b le f r o m th e a 7 a n d
a y e level r CH vs r CN cu rv e s, a n d
th e D C N c u r v e has a m a r k e d ly d i f f e r e n t slope f r o m th e H C N curves.
T h is c a n also be d e te r m i n e d a n a ly tic a lly by im p lic it d i f f e r e n t i a t i o n o f
e q u a tio n 61, h o ld in g Be c o n s ta n t, a n d o b t a i n in g the fo llo w in g ex p re ssio n
181
F ig u re 17-T he v a lu e s o f r CH vs r CN, o b t a i n e d f r o m o u r Be’s f o r th e H C N
iso to p o m e rs a n d f r o m th e Be o f D C N f ro m W innew isser et a l a r e p lo tte d
w i t h o u t slope s u b tr a c tio n . N o te how n e a r ly p a ra lle l th e H C N iso to p o m er
c u rv e s are.
N o te also t h a t th e r e is a c le a r d i s t i n c t io n b e tw e e n th e c u rv e s
f o r Ba c a lc u la te d a t th e a level a n d th e c u rv e s f o r Be c a lc u la te d a t the
a 7 o r a 7 6 levels, b u t t h a t th e l a t te r tw o sets o f c u rv e s a re i n d is tin g u is h a b le
on th is scale.
a R e f e r e n c e 22.
rCH (A)
06672
ALPHA LEV/EL
06602
DCN ALPHA
06532
dAMMA
L^VEL
I
l
l
06462
EPSILON LEVEL
1. 1 5 3 0 2
1. 1 5 3 1 4
1. 1 5 3 2 6
1. 1 5 3 3 8
r C N (A)
HCN Re
STRUCTURES
183
f o r th e slope:
d r CH
m Cm Nr CN + m Hm N(r CH +
d r CN
fcn)
m Cm Hr CH + m Hm N(r CH + r CN)
U s in g r CH = 1.065& a n d r CN = 1.153&, we c a lc u la t e slopes o f -5.09, -5.33,
-5.19, a n d -5 .4 4 f o r H C N , H 13C N , H C 15N, a n d H 13C 15N, resp e c tiv e ly ,
a n d a slope o f -3.20 f o r DCN.
T o a llie v ia te th e p ro b le m o f n e a rly e q u a l slopes, M o rin o a n d
N a k a g a w a 39 h a v e d e v e lo p e d a m e th o d o f o r d i n a t e d isp la c e m e n t d esigned
to e x a g g e r a te d i f f e r e n c e s b e tw e e n th e slopes, w h ic h is re a s o n a b ly s t r a i g h t f o r w a r d
to im p le m e n t.
T h e r CN b o n d d is ta n c e is th e abc issa a n d is l e f t u n c h a n g e d .
G iv e n Be a n d a n r CN i n te r v a l ( r CNinitial to r CNfinal), th e values o f r CH a re
c a lc u la te d f r o m E q u a tio n s 56 a n d 57. E q u a tio n 62 is em p lo y e d to e s tim a te
th e a m o u n t o f slope s u b tr a c ti o n desire d . A n o r d in a t e d is p la c e m e n t is
c a lc u la te d f r o m th e ex p re ssio n
(63)
£^r CH/
o rd d is = —
( r CNfinal- r CNinitiai).
a
CN
We c a n n o w c a lc u la te th e r HN' t h a t is p lo tte d by use o f th e e q u a tio n ( lin e a r
t r a n s f o r m a t i o n o f v a ria b le ),
,
...
,
r HN " r HN + o rd d is(
r CN*r CNinitial
---------- ------------).
(64)
CNfinaT CNinitial
G u d e m a n 28 ha d e m p lo y e d th is m e th o d e a rlie r , b u t his plots a re s o m e w h at
d i f f i c u l t to i n te r p r e t, be c au se th e re w as no s t r a i g h t f o r w a r d w ay to re a d
184
r CH f r o m his g rap h s.
In o r d e r to im p ro v e o u r i n te r p r e ta t io n o f th e the
plots, a n e w p r o g ra m , N E W C IN T E R A C (A p p e n d ix 7), h a s b e e n w r i tt e n
on o u r M ic r o V A X c o m p u te r in o r d e r to use th e VWS ( V A X w o r k s ta tio n )
g ra p h ic s to g e n e r a te th e M o rin o - N a k a g a w a 39 plots, to e n a b le in s e r tio n
o f te x t in to th e plots, a n d to p lo t lines o f c o n s ta n t r ^ .
F ig u re 18 is
a plot o f th e sam e d a ta in F ig u r e 17 w ith a slope s u b tr a c ti o n o f -5 .2
(n e a r ly th e slope o f th e
H C 15N species c a lc u la te d fro m E q u a tio n 61).
T h e d o tte d , s lig h tly s la n te d v e rtic a l lines a re th e lines o f actual r CH.
T h e H C N iso to p o m ers a re m u c h m ore c le a rly s e p a r a te d w i t h i n ea ch level
o f a p p r o x i m a t io n , a n d it c a n be seen t h a t th e r e is a la r g e r a re a o f in te rs e c tio n
f o r th e a level a p p r o x i m a t io n th a n th e a 7 -
F ig u re 19 is a n e x p a n sio n
o f th e re g io n o f th e a level in te r s e c tio n a re a , a n d the m ost n o ta b le f e a t u r e
is t h a t th e v a st m a jo r ity o f th e in te rs e c tio n a re a is du e to the H 13C 1BN
line b e in g a p a r t f r o m th e o th e r lines. T h e H 13C 15N m e a s u re m e n ts w ere
r e c h e c k e d , a n d th e r e seem ed to be no e r r o r t h a t w ould h a v e ca u se d a
50 k H z s h i f t in th e a level Be. Also, the sam e d a ta w ere used in the
a 7 level plot, a n d in t h a t case th e r e w as no gross inco n siste n c y .
It is
also in te r e s tin g to no te t h a t the o u tly in g in te rse c tio n o f th e H C N - H C 'N '
p a ir s w as t h a t o f H 13CN a n d H 13C 15N, whose c a lc u la te d slopes only d i f f e r
by 0.11.
In C h a p t e r s V I, f o r H N C , we shall note t h a t b o th o f the singly
s u b s ti tu t e d m olecules, w h ic h give b o n d in te rse c tio n s grossly in c o n s is te n t
w ith th e o t h e r p a irs , h a v e v e ry s im ila r slopes.
We shall also suggest in
C h a p t e r V II, t h a t th e in c o n s is te n c y in th e H C O + bond le n g th s a t the
a level m ay be b ecause th e slopes o f the H 13C O + a n d H C 180 + a re sim ilar.
T h e r e a re , h o w e v e r, tw o c o u n te rp o in ts .
F irs t, the d is c r e p a n c y is a p p r o x im a te ly
185
F ig u re 18-The sam e d a ta as in F ig u re 17 is p lo tte d w ith a slope s u b tr a c ti o n
o f -5.2. T h e r CN v alues can be re a d d ire c tly f ro m th e low er scale, b u t
th e r CH’s a r e r e a d fro m th e s la n tin g d o tte d lines. T h e r CH v a lu e s a re
giv en a t th e top o f the graph.
186
rCH (A)
1. 0 6 7 0
1. 0 6 6 5
1. 0 6 6 0
1. 0 6 5 5
1. 0 6 5 0
1. 0 6 4 5
ALPHA LEVEL
HCN •
GAMMA L E V E L ! / I |
i '
!i
Ie P S I L O N
/
i
!
1
!
I
!I
liEV£L/Li:GilT
11
1. 1 5 3 0 2
i
1
*
1
1. 1 5 3 1 4
• i
1. 1 5 3 2 6
1. 1 5 3 3 8
r C N (A)
HCN R e STRUCTURES
187
F ig u re 19-The r CH vs r CN c u rv e s r e s u ltin g fro m th e Be’s c a lc u la te d at
th e a level a r e p lo tte d a lo n g w ith th e c o rr e s p o n d in g D C N resu lts o f W innew isscr,
M ak i, a n d J o h n s o n .a Please no te t h a t th e c u rv e f o r H 1SC 15N is lies o u tsid e
th e tr i a n g le f o rm e d by th e o th e r curves.
Also no te the D C N c u rv e lies
o u tsid e th e in te r s e c tio n a re a o f th e H C N curves.
a R e f e r e n c e 22.
188
r-CH (A)
1. 0661
1. 0659
1. 0657
1. 0655
ALPHA LEVEL
DCNj
HCN
1. 1 5 3 1 4
1. 1 5 3 1 8
1. 1 5 3 2 2
1. 1 5 3 2 6
rC N (A)
HCN Re
STRUCTURES
189
F ig u re 20-The s tr u c tu r e s re s u ltin g f r o m th e Be’s c a lc u la te d at th e a 7
level a re p lo tte d w ith a slope s u b tr a c ti o n o f -5.2.
P lease note th e c u rv e
f o r th e m ain isotopic species lies o u ts id e th e tr ia n g le f o rm e d by the o th e r
curves.
190
rCH (A)
1. 06S8
1. 0656
1. 0654
1. 065Z
1110
AND
0111
f
i
l
l
HCN.
1. 1 5 3 1 4
1. 1 5 3 1 8
1. 1 5 3 2 2
1. 1 5 3 2 6
rCN (A)
HCN Re GAMMA STRUCTURES
191
F ig u re 21- T h e s tr u c tu r e s fro m Be’s c a lc u la te d a t th e a 7 level u sing Bn i 0
a n d BqjIj a re c o m p a r e d to th e s tr u c tu r e s f r o m Be’s c a lc u la te d a t th e a y
level u sing B 12o0 a n d B ^ o ^
N ote the slight v a r i a ti o n in tria n g le size
b e tw e e n th e tw o series o f curves.
192
rCH (A)
1. 0658
1. 0 656
1. 0654
h
1. 0652
£
n
LIGHT! 1 1 J |0 0 X 1 1
'
'
*
!
HfiAVYl 1 2 0 0 01201
1. 1 5 3 1 4
1. 1 5 3 1 8
1. 1 5 3 2 2
1. 1 5 3 2 6
rCN (A)
HCN Re GAMMA STRUCTURES
193
F ig u re 22- S tr u c tu r e s re s u ltin g fro m the Be’s c a lc u la te d a t th e a 7 c level
a re c o m p a re d to s tr u c tu r e s o b ta in e d fro m Be’s a t th e a 7 level. N ote,
t h a t f o r H C N a n d H 13C N th e cu rv e s re s u ltin g f ro m the tw o levels a re
closely p a ra lle l a n d in te rse c t a t n e a rly th e sam e point.
194
rCH (A)
1 .0 6 6 5
1 .0 6 6 0
1 .0 6 5 5
1 .0 6 5 0
1 .0 6 4 5
THUN-GAMMA
i
l
•
THlicK-EPSliLbN
1. 1 5 3 0 2
1. 1 5 3 1 4
1. 1 5 3 2 6
1. 1 5 3 3 8
rC N (A)
HCN R e
STRUCTURES
195
tw o o r d e r s o f m a g n i tu d e s m a lle r f o r th e H C N case th a n f o r th e o th e r
tw o m olecules. M ore i m p o r ta n t , th e d i f f e r e n c e b e tw e en th e slopes fo r
H C N a n d H C 15N is 0.10, a n d this p a i r is d e f i n i t e l y not a n o u tly in g pair.
T h e o t h e r p o in t to no te f ro m F ig u re 19 is t h a t th e D C N c u rv e (ta k e n
f r o m W innew isser, M a k i, a n d J o h n s o n 22) in te rse c ts th e H C ' N ' c u rv e s
a t h ig h e r r CN a n d lo w e r r CH v a lu e s t h a n those a t w h ic h th e y in te r s e c t
ea ch o th e r , w ith th e e x c e p tio n o f th e H 13CN - H 13C 15N p a ir. As w ill be
seen in C h a p t e r VI, th is re s u lt is s im ila r to H N C , w h e re th e D N C a n d
D 16N C c u r v e s in te rse c t the H N ' C ' c u rv e s o u ts id e th e ra n g e o f all in te rse c tio n s
o f H N C - H N 'C ', e x c e p t th e H N 1SC a n d H 15NC.
F i g u r e 20 is a n e x p a n sio n o f the a 7 level curves,
a n d it ha s a s im ila r p a tt e r n to F ig u re 19. In this case, h o w e v e r, th e HCN
is th e p r i m a r y c o n tr i b u to r to th e i n te r s e c tio n are a .
Because o f th e d i f f i c u l t i e s
in o b t a i n in g B11i0, a n d because B12o0 a n d B02o1 d a ta w ere a v a ila b le fo r
th e m a in isotope a n d th e tw o singly s u b s titu te d species, it was d e c id e d
to c o m p a r e th e Be’s r e s u ltin g f ro m use o f
Bn i0 a n d B01i 1 w ith th e Be.’s
f ro m B12o0 a n d Bq20 j. (Both sets use Bqqq, B100, B01i0, B001, B02o0, B022 q,
a n d B 101, B200, a n d B002.) T h is c o m p a ris o n is sh o w n in F ig u re 21, w h ic h
is a p lo t o f r CH vs r CN c u rv e s, c a lc u la te d f ro m a 7 Be’s. V ery s im ila r
tria n g le s re s u lt in th e tw o in sta n c es, b u t th e r e does seem to be a slight
s h i f t f r o m one set o f d a ta to th e next.
H o w e v er, th e s h if t in th e H C 15N
c u rv e s is a lm o st the sam e as th e s h if t in th e H C N cu rv e s, so it seems
t h a t th e a p p r o x i m a t io n f o r th e 1110 we h a v e used to e s tim a te Bv is a
good one. (T h e r e a d e r is re m in d e d t h a t we o b ta in e d q u i 0 f ° r H C 16N
by i n t e r p o la ti n g th e d i f f e r e n c e s b e tw e en q n t0 a n d Qoihx f ro m th e o th e r
196
isotopom ers.) In F i g u r e 22 th e ot7 level c u rv e s a r e c o m p a r e d to th e a 7 €
curves.
B e fo re d isc u s s in g th is plot, we r e p e a t t h a t th e H C 15N c u rv e was
o b t a i n e d by a d d in g th e d i f f e r e n c e b e tw e e n G u d e m a n ’s28 v a lu e o f Be a n d
o u r v a lu e o f Be f o r H C N to his e a r l ie r v a lu e f o r H C 15N. T h e in te rse c tio n s
f o r th e H C N - H 13C N p a ir o c c u r a t v e ry n e a rly th e sam e v alues f o r r CN
a n d r CH a t b o th th e a 7 a n d a y e levels. T h is le n d s c re d e n c e to th e idea
t h a t t h e r e is a c o n v e rg e n c e f o r th e r 8’s a n d t h a t th e a y level r e’s a re
r e a s o n a b le a p p r o x i m a t io n s o f th e "true" e q u il ib r i u m b o n d dista n c es.
We f u r t h e r n o te t h a t th e H C N a n d H 13CN a y c u rv e s lie a b o v e th e a 7 c
c u rv e s , w h ile th e H C 15N a y c u rv e lies below th e a y e c u rv e .
s u p p o s itio n t h a t if th e
It is a rea so n a b le
m e a s u re m e n ts h a d been e x te n d e d f o r H C 15N,
t h e n th is s it u a ti o n w o u ld h a v e been re v e rs e d a n d th e r e w o u ld be a tria n g le
s im ila r to t h a t a t th e a 7 level.
F ig u re s 23 a n d 24 a re p lots o f th e a a n d
a 7 level c u rv e s w ith e r r o r bars. T h e e a r l ie r e r r o r b a rs o f 15 k H z w ere
a d d e d to th e a level c u rv e s in F ig u re 23.
We h a v e a d d e d th e p r e v io u s ly
c a lc u la te d e r r o r b a rs o f 40 kH z to th e H C N a n d H 13C N c u rv e s, 64 kH z
to th e H x3C 15N, a n d 83 k H z to the H C 15N c u rv e to th e a y level c u rv e s
in F ig u r e 24. In b o th cases the a re a s o f in te r s e c tio n a r e g r e a tly m a g n if ie d
by th e e r r o r ba rs, e s p ec ially a t the a 7 level. A glan c e a t th e r CH scale
on th e to p o f the g r a p h , h o w e v e r, re v e a ls t h a t these e r r o r s do not n e a rly
a c c o u n t f o r th e d i f f e r e n c e s in th e r CH bond d is ta n c e c a lc u la t e d a t the
tw o levels o f a p p ro x im a tio n .
E q u a tio n s 56 a n d 57 c a n also be used to c a lc u la te e q u il ib r i u m
b o n d lengths.
We c a n do th is d ire c tly by sim p ly c a lc u la t in g c u rv e s o f
r cH v s r CN a n d th e i r in te r s e c tio n p o in ts, w h ic h we h a v e do n e in
197
F ig u re 23- Plots o f r CH vs r CN f o r Be’s c a lc u la te d a t the a level a r e c o m p a re d
to plots w ith B = Be± 15 kH z. See te x t f o r e s tim a tio n o f th e e r r o r bars.
Also n o te t h a t th e r CH in te rse c tio n s a r e still d i f f e r e n t t h a n those in th e
a 7 level a p p ro x im a tio n .
198
rCH (A)
1.0661
1. 0659
1.0657
1.0655
H crii
iLIGfjIT IsXPEkl MISNTAX*
!
![
i
s
;
!
i
i
i
ji
i
i
PARKf E R P O r || b A r £
;
1. 1 5 3 1 4
1. 1 5 3 1 8
1. 1 5 3 2 2
1. 1 5 3 2 6
rC N (A)
HCN ALPHA R e STRUCTURES
199
F ig u re 24- Plots o f r CH vs r CN f o r Be’s c a lc u la te d a t th e a 7 level a re c o m p a re d
to plots w i t h B = Be± 43 k H z f o r H C N a n d H 13CN , B=Be ±64 kH z fo r
H 13C 1BC N , a n d B=Be ±83 kH z fo r H C 15CN. See tex t f o r e s tim a tio n o f
th e e r r o r bars.
Also no te t h a t the r CH in te rse c tio n s a re still d i f f e r e n t
f r o m those in th e a level a p p ro x im a tio n .
200
r C H (A)
1. 0 6 5 8
1. 0 6 5 6
1. 0 6 5 4
1. 0 6 5 2
I j l 3 Cl S N
HC1 5 N
Sl i g
f
ht
i
DARk
^ x P E ^ iM £ ;N T A t
ji
e S r OR
1
;1
1
BAttS
rC N (A)
HCN R e GAMMA STRUCTURES
201
T a b le V III E qulibrium Bond L en gth s .
a
a ,7 a
H C N - H 13CN
1.153179
h c n -h c
a ,7 b
a ,7 ,e
1.153189
1.153182
1.153183
1.153180
1.153200
1.153198
1.153253
15n
1.153196
1.153186
1.153184
1.153145
r CN ^)
h cn -h
15n
13 c
h
13 c
n - h c 15n
1.153193
1.153196
h
13 c
n -h
hc
16 n
-h
13c
16n
1.153236
1.153181
13c
15n
1.153204
1.153181
H C N -D C N C
1.153222
a
a ,7 a
a ,7 b
a ,7 ,e
H C N - H 13CN
1.065900
1.065618
1.065660
1.065649
H C N - H C 15N
1.065892
1.065560
1.065572
1.065288
H C N - H 1SC 18N
1.065808
1.065634
H X3 C N -H C 15N
1.065851
1.065609
1.065673
1.065875
H x3 C N - H 13C 15N
1.065592
1.065659
H C 15 N - H 13 C 15N
1.065768
1.065662
H C N -D C N a
1.065654
rCH<^)
a U sin g the 11X0 a n d 0 1 11 satellites
b U s in g the 12°0 a n d 02°1 satellites
c D C N d a ta is f ro m W innewisser, M aki, a n d J o h n s o n .23
T a b le IX. r CN(£) K r a itc h m a n E quilibrium S tru c tu re s
a n d Second M oment r CH( i ) S tru c tu re s
Parent
r CNa
1.153171
HCN
r CH a
r cN a "y
r CN a ? 6
1.153190
1.153202
r cH a ‘y
r cH
HCN
1.065938
1.065608
1.065548
H 13CN
1.065937
1.065607
1.065543
H C 1BN
1.065937
1.065609
1.065553
H 13 C 15N
1.065944
1.065606
DCNa
1.065816
HCNb
1.065693
Parent
H 13CN
r CNa
r CN a ?
1.153191
1.153185
r CH a
r cH a "y
HCN
1.065836
1.065636
H l3CN
1.065831
1.065636
H C 15N
1.065833
1.065637
h
1.065836
1.065636
13 c
DC N
15n
1.065757
T a b le IX . (C o n tin u ed ).
Parent
H C 15N
r CN a
r CN a ‘l'
1.153192
1.153184
r CH a
r CH
HCN
1.065831
1.065637
H 13CN
1.065830
1.065638
H C 15N
1.065826
1.065639
h
1.065830
1.065638
13 c
15n
1.065755
DCN
Parent
H 13C 1SN
r CN a
1.153210
r CH a
r CN
1.153179
r CH a "y
HC N
1.065739
1.065663
H 1SCN
1.065730
1.065665
H C 15N
1.065734
1.065665
h
1.065732
1.065665
13c
DCN
16n
1.065752
a D C N d a ta f ro m W innewisser, M aki, a n d J o h n s o n 22
b F u ll K r a it c h m a n S tru c tu re
204
a p r o g ra m c a lle d B O N D LS4, listed in A p p e n d ix
8.
T h e results a r e p r e s e n te d
in T a b le V III, w h ic h is a c o m p ila tio n o f b o n d le n g th s fo r ea ch level o f
a p p ro x im a tio n .
T h e s e n u m b e rs d i r e c tl y c o rre s p o n d to th e f ig u r e s t h a t
h a v e ju s t b e e n discussed.
th e a level t h a n th e a
7
It can be seen t h a t th e r e is m ore s c a tte r in
level d a ta f o r both r CN a n d r HC, i f one in c lu d e s
the H 13 C N - H 1 sC 15N p a ir.
I f this p a ir is ne g le c te d , h o w e v e r, th e n th e
in te r s e c tio n a re a s a r e ro u g h ly c o m p a ra b le fo r b o th a p p ro x im a tio n s .
T here
is no c le a r c h a n g e in r CN a t a n y level o f a p p ro x im a tio n . (F o r th e a y e
level we o n ly c o n s id e r th e H C N - H 13C N pair.) T h e r HC bond len g th , h o w e v e r,
d e c re a ses by a p p r o x i m a t e ly 2.5 x lO - 4 X w h e n one goes f ro m th e a level
to th e a
7
level. T h e a y e r HC is c o m p a ra b le to th e a y level. A n o th e r
p o in t to no te is t h a t th e r e seems to be a slight in cre ase in r CN a n d d e c re a s e
in r CH w h e n th e
s tr u c tu r e s .
12°0
and
02°1
sa te llite s a re used to c a lc u la te a
7
level
We h a v e also in c lu d e d the H C N -D C N p a ir, a n d we c a n see,
n u m e r ic a lly , t h a t th is in te rs e c tio n occurs a t h ig h e r v alues o f r CN a n d
lo w e r v a lu e s o f r CH t h a n th e in te rse c tio n s o f th e H C ' N ' - H C " N " pairs.
A n o th e r a p p r o a c h to s tr u c tu r e c a lc u la tio n s was d e v e lo p e d by
K r a i t c h m a n 31, w h o pro p o se d th e e q u a tio n
AI
MAM
,
AI = —
tt7z •
M + AM
/i£C 1
( 65)
T h is has t r a d i t i o n a l l y been used to c a lc u la te s u b s titu tio n s tr u c tu r e s in
m olecules f o r w h ic h th e r e is only d a ta in the g ro u n d v i b r a t io n a l state.
F o r e x a m p le, we shall th u s em ploy th e m in C h a p t e r VIII f o r H N N + a n d
H O C+.
We a re , h o w e v e r, a p p ly in g th e e q u a tio n s to e q u il b r iu m d a ta .
205
O u r o r ig in a l p u rp o se in using this m e th o d w as to o b ta in a c o n s is te n t
e q u i l ib r i u m s tr u c tu r e f o r H C O +, as w ill be m e n tio n e d in m ore d e ta il
in a l a t e r c h a p te r.
T h e m eth o d t h a t we use consists o f u sin g e q u a tio n
65 to c a lc u la t e r CN w ith all f o u r H C N isotopom ers as p a r e n t species.
T h e n r CH’s a r e c a lc u la te d fro m E q u a tio n s 60 a n d 61, th e second m o m e n t
c o n d itio n , c o m b in in g th e r CN w ith all f o u r Be’s. T h e r CH’s, t h a t we c a lc u la te ,
a re r e f e r r e d to as second m o m e n t r CH’s, a n d we c all the m eth o d th e K r a it c h m a n
e q u a tio n -s e c o n d m o m e n t m ethod. In T a b le IX th e resu lts o f all th e K r a i t c h m a n
e q u a tio n -s e c o n d m o m e n t s tr u c tu r e s a re given. While th e r e is g r e a t e r co n sisten c y
a m o n g th e f o u r r CN’s c a lc u la te d in this m a n n e r f o r b o th the a a n d a y
levels, th e a v e ra g e bond length is 1.153190 X a t th e a level a n d 1.153185
X a t th e a y level. M a tte rs a re so m e w h a t m ore in te r e s tin g f o r th e second
m o m e n t r HC’s. All the r HC’s c a lc u la te d f r o m a single s u b s ti tu t io n r CN
a g re e to w i t h in
10~5
( i n c l u d in g th e a
a d e c re a s e o f
2
7
X f o r e v e ry s u b s titu tio n s tr u c tu r e a t e v e ry level
e), a n d m a n y agree to w ith in
10~6
X. T h e r e is also
x lO - 4 X going f ro m the a to the a y level, c o n s is te n t w ith
th e d i r e c t in te r s e c tio n d e te r m in a tio n .
o f T a b le IX is th e a
7
e colum n.
Possibly th e most in te r e s tin g a sp ec t
E ven th o u g h one o f th e lines is in v ery
po o r a g re e m e n t w ith th e o th e r two, b o th th e r CN a n d r HC s tr u c tu r e s a re
in f a i r l y r e a s o n a b le a g re e m e n t w ith th e
a y level. T h is leads one to
c o n c lu d e t h a t th e K r a it c h m a n e q u a tio n - second m o m e n t a p p r o a c h gives
a good a p p r o x i m a t io n to the "true"
Be, even if th e d a ta give in c o n s is te n t
s tr u c tu r e s w h e n tr e a te d by the in te r s e c tio n m ethod. T h is p o in t will be
e x p lo re d in m o re d e ta il in C h a p te r VII on H C O +.
T o c o n c lu d e the C h a p te r, we w ill b r ie f ly discuss th e e f f e c t
206
o f d e u t e r i u m s u b s ti tu t io n on s tr u c tu r e c a lc u la tio n .
As was m e n tio n e d
e a r l ie r in th e c h a p te r , in th e lim it o f th e B o r n -O p p e n h e im e r a p p r o x i m a t io n ,
all p a ir s o f iso topom ers should give th e sam e s tr u c tu r e .
It a p p e a r s f r o m
th e c o m b in a tio n o f o u r w o rk a n d t h a t o f W innew isser, M ak i, a n d J o h n s o n 22
t h a t th e B o rn -O p p e n h e im e r a p p ro x im a tio n is n o t v a lid f o r d e u t e r i u m
s u b s titu tio n .
T h is discussion is re s tric te d by th e f a c t t h a t th e r e is lim ite d
e q u i l ib r i u m d a t a f o r D C N 22, a n d none f o r th e o th e r D c o n ta i n in g isotopom ers.
C u r io u s ly e n o u g h , th e s itu a tio n is b e tt e r f o r HNC.
C o m p le te m ic r o w a v e
e q u i l i b r i u m d a t a w ill be p re s e n te d f o r th e D N C a n d D 15N C species in
C h a p t e r V I o f th is thesis. N e v e rth e le ss, a f e w conc lu sio n s c a n be r e a c h e d
fo r HCN.
As c a n be seen g r a p h ic a lly in F ig u re 19 (as has a lr e a d y been
m e n tio n e d ) or n u m e ric a lly in T a b le V III, th e H C N -D C N p a i r i n te r s e c tio n
o c c u rs a t a h ig h e r v a lu e o f r CN’s a n d a low er v a lu e o f r CH th a n th e H C ' N ' H C " N " p a ir inte rse c tio n s.
In a d d it io n , if th e second m o m e n t c o n d itio n
is a p p lie d to D C N f r o m the
f c n ’s
c a lc u la te d f ro m K r a i t c h m a n ’s e q u a tio n s ,
c o n s is te n tly low er r CH’s a re c a lc u la te d t h a n f o r the H C ' N ' species, a
r e s u lt in c om m on w ith HNC.
T his is all d e m o n s tr a te d in T a b le IX.
F in a lly ,
a c o m p le te K r a i t c h m a n e q u ilib r iu m s tr u c tu r e c a n be c a lc u la te d f o r H C N
u s in g th e D C N Be. T h e r CH re s u ltin g is 1.065693
X, w h ic h
is c o n s id e r a b ly
lo w e r t h a n th e 1.065816 X r CH, o b ta in e d f ro m th e second m o m e n t c o n d itio n .
T h is r CH, v alu e, h o w e v e r, is in q u ite good a g re e m e n t w ith th e 1.065654
Xv a lu e
o f r CH f r o m th e H C N -D C N p a ir. T h e co n c lu sio n , w h ic h w ill d r a w n
m o re f ir m l y in C h a p t e r
6,
is th a t s tr u c tu r e c a lc u la tio n s a r e d e p e n d e n t
on w h e t h e r H C ' N ' - H C " N " p a irs or H C ' N ' - D C ' N ' p a ir s a r e used in
th e c a lc u la tio n s .
207
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A. G. M aki, J. Phys. Chem. R e f. D a ta , 3, 221 (1974)
24
F. C. D e L u c ia , J. Mol. Spec. 55, 271 (1976)
25
E. F. P e a rso n , R. A. C resw ell, M. W innew isser a n d G. W innew isser,
Z. N a t u r f o r s c h . 31 a, 1394 (1976).
26 F.
C. D e L u c ia a n d P. A. H e lm in g e r, J. Chem . Phys. 67
27
J. C o lm o n t, J. Mol. Spec. 114, 298 (1985).
4262 (1977).
28
C. S. G u d e m a n , PhD . Thesis. U n iv e rs ity o f W isconsin-M adison 1982.
29
N. D. P iltc h , PhD . T hesis, U n i v e r s i ty o f W isconsin-M adison 1980.
30
W. T. C o n n e r, PhD . T hesis, U n iv e rs ity o f W isconsin-M adison 1988.
31
G. A m a t a n d H. H. N ielson, J. Mol. Spec. 2, 163 (1958).
32
A. M aki, J. Mol. Spec. 38, 508 (1975).
33
C. H. T o w n e s a n d A. L. S chaw low , M ic ro w a v e S p e c tro s c o p y . (D o v e r
P u b lic a tio n s , Inc., N ew Y o rk , 1975).
34
H. E. W arner, W. T. C o n n e r, a n d R. C. Woods, J. Chem.
Phys. 81, 5413 (1984).
35
G. A. B lake, P. H e lm in g e r, E. H crbst, a n d F. C. D e L u c ia ,
Ap. J. 264, L69 (1983).
36
J. H o ltsm a rk , A nn. P h y sik , 58, 577 (1919).
37
C. F. H o o p e r Jr.,
38
M. L. Jam es, G. M. S m ith, a n d J. C. W olford,
A p p lie d N u m e ric a l M ethods f o r D ig ita l C o m p u ta tio n w ith
F O R T R A N . ( I n t e r n a ti o n a l T e x tb o o k C o m p a n y ,
S c ra n to n , P e n n s y lv a n ia , 1967).
39
Y. M orino a n d T. N a k a g a w a , J. Mol. Spec. 26, 496(1968).
Phys. Rev. 165, 215 (1967).
210
IN T R O D U C T IO N
T h e r e has been c o n s id e ra b ly less e x p e r im e n ta l w o rk on
H N C t h a n H C N . T h e m olecule was f ir s t o b se rv e d by M illig a n a n d J a c o x 1
in 1963, w h e n th e y o b se rv e d i n f r a r e d e m ission o f p h o to ly sis p ro d u c ts
o f C H 3 N 3 in a n A r m a t r ix a t 4 K. T h e a s sig n m m e n t w as c o n f i r m e d w hen
th e sam e b a n d s w ere o b se rv e d in p h o to ly sis o f H C N in A r a n d N 2 m atric e s
a t 14 K . 2 S n y d e r a n d B u h l 3 -4 f ir s t o b se rv e d the J = 0 —1 p u r e r o ta t io n a l
tr a n s it io n as r a d i o em ission f ro m i n te r s t e ll a r clouds. S u b s e q u e n t r a d io
a s tr o n o m ic a l w ork by S ny d e r, Hollis, a n d B u h l 5 o b ta in e d the n itro g e n
q u a d r u p o l e c o u p lin g c o n s ta n t f o r th e m a in isotope. T h e isotopom ers
H N 13 C , 6 D N C ,
7
a n d H 15NC
a f t e r l a b o r a to r y d e te c tio n .
8
w ere o b se rv e d in the in te r s t e ll a r m edium
In a la te r i n te r s te lla r e x p e rim e n t, F r e r k in g
et al. 9, o b ta in e d a d i f f e r e n t v a lu e f o r th e H N C q u a d r u p o l e c o u p lin g
c o n s ta n t f o r th e m ain isotope th a n S n y d e r, Hollis, a n d B u h l .5 T h e y also
o b ta in e d the f i r s t d e te r m i n a ti o n o f the q u a d r u p o l e c o u p lin g c o n s ta n t
o f th e H N 13C isotopom er.
B la c k m a n et al.10 a tte m p te d to o b se rv e H N C
w ith a c o n v e n tio n a l S ta rk s p e c tro m e te r in e q u il ib r i u m w ith H C N a t room
te m p e r a tu r e , b u t w e re not successful.
A r r in g t o n a n d O g r y z lo 11 f ir s t observed
th e m olecule te r r e s t r i a ll y in th e gas phase by o b se rv in g th e C-H s tre tc h
in a d is c h a r g e o f N 2 a n d C 2 H 4. T h e r e w ere th e n th re e m ic ro w a v e o b se rv a tio n s
o f g r o u n d v i b r a t io n a l sta te tra n s itio n s , m ore or less sim u lta n e o u sly . Saykally
et a / . 12 in th is la b o r a to r y obse rv e d th e J = 0 — 1 tr a n s it it o n o f H N C in a
D.C. glow d is c h a r g e using v a rio u s m ix tu re s , c o n ta i n in g H 2, (C N )2, (C H )2,
a n d N 2. B la c k m a n et a / . 13 o b served J = 0 —1 t r a n s itio n s f o r H N C , H N 13 C,
a n d D N C in e q u i l ib r i u m w ith H C N or D C N a t 1000 K. C resw ell et al.1*
211
o b se rv e d th e J ^ - ^ l a n d J = l- * 2 t r a n s itio n s fo r H N C , H N 1SC, a n d D N C
by a d d in g C H 3Br o r the a p p r o p r i a t e iso topic f o r m o f C H 3I to a c tiv e nitro g e n .
L a te r th e y e x te n d e d th e ir w o r k to in c lu d e all e ig h t isotopom ers o f H N C
a n d H C N , as m e n tio n e d in th e p re v io u s c h a p t e r . 16 A n d e r s o n 16 was able
to o b se rv e th e tw o s tr e tc h in g sa te llite s f o r th e m a in isotope. G u d e m a n 17
obse rv e d tw o c a n d id a te s f o r th e v 2= 2 b e n d in g m ode, b u t was u n a b le to
d e f i n i t i v e l y assign the tra n s itio n .
C resw ell a n d R o b i e t t e 18 used a c a lc u la te d
a n h a r m o n ic f o rc e fie ld to e s tim a te th e e q u il ib r i u m geom etry. T h e re
have also b e e n a n u m b e r o f ab initio th e o r e tic a l c a lc u la tio n s o f th e e q u ilib r iu m
s t r u c t u r e . 19" 26
T h e r e w ere several e x c e lle n t rea so n s f o r s tu d y i n g HNC. D e te rm in a tio n
o f th e e q u il ib r i u m s tr u c tu r e w o u ld p r o v id e a test f o r th e th e o re tic a l c a lc u la tio n s.
A n o th e r rea so n we u n d e r to o k this p ro je c t was to d e te r m in e th e c o n sisten cy
o f s tr u c tu r e s d e te r m in e d f r o m the d i f f e r e n t isotopic pairs.
As th e r e a d e r
has seen in C h a p t e r V, H C N gave e x tre m e ly c o n s is te n t s tr u c tu r e s fo r
all isotopic p a irs a t all levels o f a p p ro x im a tio n .
G u d e m a n 17 h a d , h o w e v e r,
o b se rv e d in c o n siste n c ie s in th e s tr u c tu r e s f o r H C O + , on the o r d e r of
0 .0 0 2
Xf o r
rco and
0 .0 1
Xf o r
r CH.
T hese w ill be discussed in m ore
d e ta il in C h a p t e r VII. It was hoped t h a t a test on a n o th e r 14-electron
m olecule m ig h t p ro v id e some in sig h t in to th e H C O + problem .
We also
w a n te d to in v e s tig a te the e f f e c t o f d e u te r iu m s u b s titu tio n on m ole c u la r
s tru c tu re s .
T h e o b v io u s cho ic e w ould h a v e been D C N , but, u n f o r t u n a te ly ,
we h a d no k ly s tro n , w h ic h o p e ra te d a t th e DCN f re q u e n c ie s , a n d we
d id h a v e one t h a t o p e ra te d a t D N C fre q u e n c ie s . T h e q u a n t i t y q v2/ 5 is
c o n s id e r a b ly d i f f e r e n t in H N C , th a n in H C N o r H C O +. T h e r e f o r e , it
212
w as o f i n te r e s t to us to o b se rv e th e
0 2 20
lines a n d to d e te r m in e how th e
S ta rk e f f e c t c o m p a re d to th e S ta rk e f f e c t o f H C N a n d H C O +. F in a lly ,
H N C is is o e le c tro n ic w ith H O C + , a n d both m olecules h a v e low f r e q u e n c y
b e n d in g m odes. T h e r e f o r e , we hop e d to use H N C to p r o v id e in sig h t in to
u n d e r s t a n d i n g th is i m p o r ta n t a n d closely r e la te d ion.
E X P E R IM E N T A L
T hese e x p e rim e n ts w e re c a r r ie d o u t in tw o d i f f e r e n t tim e
in te rv a ls .
T h e old d is c h a r g e se tu p , as m e n tio n e d in H a e se ’s 26 thesis, was
used to o b serve th e J = 0 — 1 t ra n s itio n s . G u d e m a n ’s 16 phase lock loop a n d
th e H u g h e s d io d e d e te c to r w ere also em p lo y e d f o r these m ea surem ents.
All th e d isc h a rg e s in v o lv e d w ere n o rm a l d isc h a rg e s , w ith ty p ic a l c u r r e n ts
on th e o r d e r o f 500 mA.
F o r th e m ain isotope we used f a s t flo w , liq u id
n itro g e n cooling, A r b u f f e r s , 5 m T o r r C H 4 a n d N 2. F o r th e h y d ro g e n
c o n ta i n in g isotopom ers we em p lo y e d slow flo w , w a te r cooling, A r b u f f e r ,
a n d 2 m T o rr e a ch o f th e iso to p ic a lly e n ric h e d m e th a n e or nitro g e n .
For
D N C we used slow flo w , 35 m T o rr D 2, 30 m T o rr Ar, a n d 5 m T o rr each
o f C H 4 a n d N 2, w h ile f o r D 15N C we used less
w ith the sam e c o n d itio n s .
15 N 2,
b u t o th e rw is e ra n
We d id not do a n y w o rk w ith D N 13C a n d D 15 N 13 C,
b ecause we h a d no k ly s tro n t h a t co u ld rea c h th e n e cessary f re q u e n c ie s .
O u r w o rk w ith th e h ig h e r J t r a n s itio n s was d o n e w ith th e new
d is c h a r g e s e tu p a n d the liq u id h e liu m cooled InSb d e te c to r. T h e new
e x p e rim e n ts w e re do n e c o n c u r r e n tl y w ith those on H C N , d e s c rib e d in
th e p re v io u s c h a p te r , a n d the c o n d itio n s f o r each isotopom er w ere the
sam e as f o r th e c o r r e s p o n d in g H C N species, e.g., o u r w o rk on H N 13C
was d o n e u n d e r th e sam e c o n d itio n s as o u r w o rk on H 13 CN.
We a tte m p te d
213
to o b se rv e H N C in a n a b n o rm a l d isc h a rg e , b u t w ere u n successful.
THEORY
T h e re la tio n s h ip s b e tw e e n Beff a n d Bv a r e th e sam e as f o r H C N ,
a n d we r e f e r the r e a d e r to C h a p t e r V f o r d e ta ils.
O B S E R V E D S A T E L L IT E S .
T a b le I is a c o m p ila tio n o f th e f r e q u e n c ie s o f th e H c o n ta in in g
lines, a n d T a b le II is a s im ila r c o m p ila tio n f o r th e d e u te r a t e d lines.
The
v i b r a t io n a l s a te llite s m a r k e d w ith a n a "c" w ere o r g in a lly o b se rv e d by
A n d e r s o n . 8 T h e lin e s o b se rv e d o rig in a lly by P e a rso n et a / . 15 w e re d e n o te d
w ith a "b". We h a v e re m e a s u r e d th e m all, h o w e v e r, because th e new phase
lock system , d e s ig n e d b y C. S. G u d e m a n , 17 w as e x p e c te d to im p ro v e th e
f r e q u e n c y a c c u ra c y .
F o r th e ea ch o f th e H c o n ta i n in g species, the Beff’s,
D eff’s, Bv’s a n d Dv’s, w e re c a lc u la te d a n d a re p r e s e n te d in T a b le III. We
h a v e also em p lo y e d th e
0 2 20
d a ta f o r th e m a in isotope to c a lc u la te a
5 o f 9.72 c m -1, s lig h tly in d is a g r e e m e n t w ith th e 9.4 ± 0.2 c m - 1 v alue
o f M aki a n d Sams . 27 L east s q u a re s w as em p lo y e d to c a lc u la te Beff a n d
D eff o f sa te llite s f o r w h ic h we m e a s u re d th re e tra n s itio n s .
T h e D v fo r
th e 02°0 w as c a lc u la te d by e x t r a p o la t in g D v fo r the 000 a n d 01 !0 fo r
th e isotopom ers w h e r e th e r e w as no 0220 d a ta .
T h is D v was th e n s u b tr a c te d
f r o m th e D eff to give a n e s tim a te fo r q v2 /5, w h ic h w as th e n used to c a lc u la te
Bv f r o m Beff. F o r th e m ain isotope th e d i f f e r e n c e b e tw e e n the scaled
02°0 Bv a n d the one c a lc u la te d f ro m the 0220 d a ta w as 7 kH z, re s u ltin g
in a 3 k H z d i f f e r e n c e in th e Be c a lc u la tio n s .
F or the sake o f consisten c y ,
the scaled Bv w as u sed f o r the bond len g th c a lc u la tio n s .
F or the D c o n ta in in g
species, we used th e D 000's o f P earson et al.14 f o r th e 000, 100, a n d 001
214
sta te s, since no h ig h e r J tra n s itio n s w e re o bserved.
we assu m e d t h a t D v w as 3 kH z h ig h er.
F o r th e 02°0 s ta te
It w as n o t nec essa ry to c o n c e rn
ou rse lv e s w ith q v2/ 5 because
vj
=
o- i
(1)
= 2Beff - 4D eff ,
a n d re c a llin g e q u a tio n s 13-14 o f th e th e H C N c h a p te r
(2 )
Befl(02o0) = Bv + 2 q v2/S
and
(3 )
D eff(02°0) = D v + q v2/S ,
we c a n see th is leads r e a d ily to
v3=0^
(4 )
= 2BV - 4 D V .
T h e Bv’s f o r th e D c o n ta i n in g species a r e d is p la y e d in T a b le IV. Sam ple
s p e c tr a f o r th e J = 0 —*1 t r a n s it io n f o r th e 000 o f D N C a n d fo r th e J = 2 —3,
3 —4, a n d 4 —5 o f H 15N C a re show n in F ig u re s 1 a n d 2. T a b le V c o n ta in s
th e a level c o n s ta n ts f o r the H N C iso to p o m ers a n d the a
7
partial level
c o n s ta n ts f o r H N C , w h ile T a b le VI c o n ta in s th e a level c o n s ta n ts f o r
th e D N C isotopom ers.
T h e se arc h f o r th e sa te llite s w as g u id e d by th e o r e tic a l c a lc u la tio n s
o f H e n n ig , K r a e m e r , a n d D ie r c k s e n 19 ( h e n c e f o r t h r e f e r r e d to as H K D ),
a n d in T a b le VII we p re s e n t o u r e x p e r i m e n t a l a ’s, th e ir c a lc u la te d a ’s,
215
T a b le I. O bserved H N C F requ en cies (M H z).a
V
r
000
1
000
3
4
5
000
000
HNC
H 15NC
H N 13C
H 15N 13C
90663.579
271981.131
362630.336
453270.025
88865.708b
266587.884
355439.748
87090.842b
261263.592
348341.064
85258.895b
255768.108
341014.312
100
1
100
3
4
90064.994°
270185.433
360236.100
88300.895
264893.484
353180.560
86523.157
259560.519
346070.284
84723.737
254162.355
338872.772
3
4
5
3
4
5
271924.257
362554.660
453175.020
273869.672
365145.336
456415.025
266472.264
355285.756
261220.227
348283.308
255668.424
340881.540
268352.184
357791.724
263018.592
350680.468
257402.313
343192.688
001
1
001
001
3
4
89993.224°
269969.985
359948.720
88213.735°
264631.953
352831.780
86458.295
259365.931
345810.796
84644.839
253926.090
338558.368
02°0
1
02°0
3
4
5
273980.109
365252.952
456480.240
268404.246
357822.812
87724.978
263136.390
350803.492
85833.111
257463.369
343242.544
3
4
5
3
4
5
273644.661
364847.260
456040.535
273678.942
364935.408
456217.300
100
0 1 lc 0
0 1 lc 0
0 1 lc 0
0 1 ld 0
0 1 ld 0
0 1 ld 0
02°0
02°0
0 2 2c0
0 2 2° 0
0 2 2c0
0 2 2d0
0 2 2d0
0 2 2d0
216
T a b le I. O bserved H NC Frequencies (C on tin u ed )
V
J'
HNC
200
1
89447.792
101
1
101
3
4
89397.734
268183.638
357566.996
101
002
1
002
002
3
4
89321.393'
267954.447
357261.236
102
1
88724.376
0 3 lc0
0 3 lc0
0 3 ld0
0 3 ld0
3
4
3
4
272988.879
363959.524
276957.897
369249.264
003
1
88649.316
004
1
87979.042
H 15NC
a E r r o r e s tim a tes o f fre q u e n c y in text.
b F irs t observed by P earson et al.16
c F irst observed by A n d e r s o n . 16
H N 13C
257468.118
343280.284
H 15 N 13C
T a b le II. O bserved DNC F req u en cies (M H z).a
v
J'
DN C
D 15NC
000
1
76305.725b
75286.783b
100
1
75704.532
74712.737
02°0
1
77190.106
76115.598
001
1
75828.423
74817.293
a E r ro r estim ates o f fre q u e n c y in text.
b F irs t observed by Pearson et al.15
218
T a b le III. H N C Bv’s, Dv’s, B eff’s, and Deff’s .a
v
HNC
H 15NC
H N 13C
H 15 N 13C
By
Dy
45331.986fa,c
99.72c*d
44433.046b>c
96.18C
43545.606b>'
92.94'
42629.598b
87.78'
By
Dv
45032.696'
99.48c
44150.642'
95.91'
43621.759'
92.93'
42362.051'
92.40'
0 1 x0
By
Dv
Qy
B.«(c)
D.fi(c)
Befl(d)
Defl{d)
45484.477
102.48
324.385
45322.480c
98.36c
45646.882c
106.60c
43264.760
97.25
313.404
44413.747
94.61
44727.162
99.89
43688.090
95.16
299.822
43538.364
92.22
43838.198
98.11
42757.419
89.68
289.081
42612.962
86.54
42902.056
92.82
001
001
By
Dy
44996.812'
100.54'
44107.061'
96.49'
43229.334'
93.26'
42322.593'
87.45'
02°0
02°0
02°0
02°0
By
Dy
Befr
D.ff
45671.271
112.63
45672.016'
480.89'
44741.331
98.39
44741.998
442.107
43862.693
97.54
43863.293
401.74
42916.737
91.58
42917.304
374.58
02 20
02*0
0220
0220
0220
0220
0220
02 20
By
Dy
B.fl(c)
Defl(c)
Befl(d)
D.q(d)
qvV 5
45608.347
101.69
45609.203
101.00
45608.385
-266.88
368.260*
9.72f
002
002
By
Dy
44996.807'
100.54'
03*0
03*0
03*0
03 x0
03*0
03*0
03*0
By
Dy
Qy
B,ff(c)'
D efl(c)
Befl(d )'
De«(d)
45833.184
93.69
330.923
45502.261
228.75
46164.107
247.64
000
000
100
100
01*0
0 ^ 0
01*0
0 ^ 0
01*0
01*0
8
42913.047
94.10
a E r ro r e stim ates a re p ro v id e d in text fo r the Bv’s.
219
b B’s a r e in MHz.
c L e a s t sq u ares was used to c a lc u la te Be{f a n d D eff
d D ’s a r e in kHz.
6
T h e q v2 / 5 ’s a re in kHz. These w ere c a lc u la te d
f r o m the J=4-*5 lines. See text.
f T h e q u a n t i t y b is in c m -1. We c a lc u la te qv f o r 020
by in te r p o la tio n o f q v o f 0 1 x0 betw een 03*0.
T a b le IV . O bserved D N C Bv’s (M H z).
v
DNC
D 15NC
000
38153.003
37643.526
100
37582.406
37356.504
02 °0
38595.197
38057.938
001
37914.352
37408.782
221
T a b le V. H N C S pectroscopic P a r a m e te r s (MHz).
a level a
HNC
H 15NC
H N 13C
H 15 N 13C
Be
45479.572
44583.099
43687.120
42773.303
«1
299.290
282.405
283.843
267.545
«2
-169.646
-154.114
-158.544
-143.570
«3
335.172
325.985
316.272
307.005
®7partial
HNC
Be
45484.002
«1
300.064
a 2
-163.880
«3
335.223
7 13
1.552
7 22
1.449
7 3s
-0.365
7n
-15.748
222
a C a lc u la te d w ith B000, B 100, B 02 o0, a n d Bo^.
k C a lc u la te d w ith Bqqq, B 100, Bq^Iq, Bqqj, B101, Bq20 o» ®0 2 *o* an<l ®oo2 *
223
T a b le VI. DNC Spectroscopic P a ra m e te rs(M H z )
DN C
D 15NC
Be
38201.530
37697.203
ax
300.597
287.023
a
2
-221.097
-207.026
a
3
238.651
234.745
224
F ig u re 1-This f ig u r e is th e J = 0 —1 tr a n s it io n o f th e g r o u n d v i b r a t io n a l
sta te o f D N C a t 76305.725 MHz. T h e e x p e r im e n ta l c o n d itio n s a re as
follow s: slow flo w , w a te r cooling, 500 mA d isc h a rg e , 35 m T o r r D 2, 5 m T o rr
C H 4, 5 m T o rr N 2, 12 scans, 2 b a seline supp re ssio n s (800 kH z), 800 k H z
FM, 100 k H z AM, 11 p o in t sm o o th in g , a n d 10 juvolt f u ll scale lock-in
s e n s itiv ity .
225
DNC 0 0 0 2B 800kHz
J=0-1
76300
76305
FREQUENCY(MHz)
226
F ig u re 2-T his f i g u r e show s the J * 2 —3, 3—4, a n d 4 —5 tr a n s it io n s f o r the
g r o u n d v i b r a t io n a l s ta te o f H 1SN C in a sin g le scan.
T he experim ental
c o n d itio n s a re as follow s: slow flo w w a te r cooling, 300 m A d is c h a rg e ,
20 m T o rr A r, 5 m T o r r C H 4, 2 m T o rr
16 N 2,
10 scans, 1 b a selin e su p p re ssio n
(800 kH z), 2400 k H z FM, 30 k H z AM, 11 p o in t s m o o th in g , 10 juvolt fu ll
scale lock-in s e n s itiv ity , a n d InSb d e te c to r a t
p ressu re.
8
k G a u ss a n d 26 T o r r h e liu m
227
H1SNC 0 0 0 IB 800kHz
J=3-4
J=2-3
J=4-5
88860
88865
KLYSTRON FREQUENCY(MHz)
228
Table V II. Observed vs. HKDa Scaled a Values.
HNC
a 2
a.
a exp
a HKD
a e x p /a HKD
299.290
-169.646
335.172
323
-123
320
0.927
1.381
1.047
a exp
a HKD
a e x p /a HKD
282.405
-154.114
325.985
-111
a exp
a HKD
283.843
-158.544
316.272
306
-115
302
H 15NC
ai
«2
a.
305
312
0.926
1.388
1.045
H N 13C
«1
a 5
a,
a e x p / a HKD
0.928
1.379
1.047
H 18 N 13C
a exp
ai
a.
a HKD
a e x p /a HKD
267.545
-143.570
307.005
288
-104
294
a exp
a HKD
300.597
-221.097
238.651
324
-1 6 4
223
0.928
1.348
1.070
HKD
a e x p / a HKD
308
-1 5 4
0.931
1.345
1.067
0.929
1.380
1.044
DNC
a,
a5
a.
® ex p / a HKD
D 15N C
a exp
al
«S
a,
a R e f e re n c e 19.
287.023
-207.206
234.745
a
220
229
a n d th e a exp/ a HKD ratios. T h e r e a d e r c a n see t h a t th e r e is r e m a r k a b l e
c o n sisten c y in th ese r a tio s f ro m isotope to isotope even b e tw e e n H a n d
D c o n ta i n in g species, e specially f o r the
04
m ode. T h e ra tio s f o r th e a x
c o n s ta n t o n ly v a r y f ro m 0.927 to 0.931, a v a r i a ti o n o f less t h a n 0.5 per
cent. T h e r e is s o m e w h a t m ore v a r i a ti o n in th e a
2
a n d a 3 ratio s, espec ially
going f r o m H N ' C ' isotopom ers to D N ' C ' isotopom ers.
Even in these
cases, th e m a x im u m v a r i a ti o n in th e otexp/a HKD ra tio s w as o n ly a b o u t
3 p e r cent.
E R R O R A N A L Y S IS
Because th e 14N q u a d r u p o le c o u p lin g c o n s ta n t is 0.28 M H z f o r
H N C 9, as opposed to - 4.7 M Hz f o r H C N , th e q u a d r u p o l e h y p e r f i n e e f f e c t
is re d u c e d by a f a c t o r o f 15 f ro m H C N , a n d need not be c o n s id e r e d as
a so u rc e o f u n c e r t a i n t y in o u r m e a s u re m e n ts .
R e a s o n a b le e r r o r estim a tes
fo r th e J = 0 —1 tr a n s itio n s a re 5 kH z f o r th e g r o u n d s ta te lines a n d 20
k H z f o r v i b r a t i o n a l satellites. O u r J=0-»1 m e a s u re m e n ts w ere i n v a r i a b l y
based on f o u r tria ls.
F or th e J = 2 —3 tra n s itio n s , we e s tim a te u n c e r ta in tie s
o f 20 k H z f o r th e 000 lines a n d 50 kH z f o r th e v i b r a t io n a l satellites.
T hese w ere b ased on tw o trials.
F o r th e J=3-*4 tra n s itio n s , it is f e lt th a t
40 k H z a n d 80 k H z a re rea so n a b le e rr o r e s tim a te s fo r th e 000 lines a n d
f o r th e v i b r a t io n a l sa te llite s, resp e c tiv e ly .
We o n ly o b se rv e d J=4-*5 f o r
th e g r o u n d v i b r a t io n a l sta te , a n d th e 01*0, 02°0, a n d 0220 sa tellites. O u r
u n c e r t a i n t ie s a r e 60 kH z fo r th e g r o u n d v i b r a t io n a l s ta te a n d 100 kH z
f o r th e satellites.
T h e u n c e r t a i n t y in the Beff’s is a p p r o x im a te ly 1 /(2 J ') tim es
th e u n c e r t a i n t y in th e f re q u e n c ie s . (See C h a p t e r V f o r details.)
U sing
230
th is as a ro u g h g u id e , we e s tim a te u n c e r t a i n t i e s o f 2 kH z in Bqoq a n d
5 k H z in B 100 a n d B001. It is f e lt t h a t
6
k H z is a re a s o n a b le u n c e r t a i n t y
in Beff f o r the 02°0 state. T h e r e is, h o w e v e r, no 0 2 20 d a ta f o r th e s u b s titu te d
isotopom ers, a n d it is fe lt th is c o n tr i b u te s a n o th e r 10 kH z u n c e r t a i n t y
to th e B 0 2 20 v a lu e f o r th e H N C iso to p o m ers, so a re a s o n a b le u n c e r t a i n t y
is 16 kH z. T h is leads to a n u n c e r t a i n t y o f 12 k H z in th e a level Be’s,
i f we use th e sam e a p p ro a c h as th e p re v io u s c h a p te r. (We m u ltip ly a
m a t r ix o f th e sq u a re s o f th e m a t r ix e le m e n ts o f A - 1 by the s q u a re s o f
th e u n c e r t a i n t ie s in the Bv v a lu e s to o b t a i n th e s q u a re o f th e u n c e r t a i n t y
o f Be. T h e A m a t r ix rela te s th e Bv’s to Be a n d th e a ’s.)
A S S IG N M E N T O F S T R E T C H I N G S A T E L L I T E S
T h e o b s e rv a tio n o f the s tr e tc h i n g sa te llite s was c o n sisten tly
s t r a i g h t f o r w a r d f o r all th e isotopes, i.e., th e r e w ere no i n t e r f e r i n g lines,
a n d as p o in te d o u t above the H K D 19 scaling w o rk e d q u ite well.
A n d e r s o n 13
t h o u g h t he h a d seen the 001 line o f H 15N C a t 88213 MHz, b u t he ra n
out of
16 N 2
a n d was u n a b le to c o n f i r m his o b s e rv a tio n or assignm ent.
T h is led r e a d i ly to ou r d e te c tio n o f th is tr a n s it io n a t 88213.7 MHz.
It
sh o u ld also be p o in te d o u t t h a t th e high res o lu tio n i n f r a r e d w o rk o f M aki
a n d S am s 27 a n d the v e ry rec e n t F o u r ie r t r a n s f o r m i n f r a r e d w ork o f B u r k h o ld e r
el a / . 28 o b ta in e d B 100 a n d B001 v alues in e x t r a o r d i n a r i l y good a g re e m e n t
w ith o u rs fo r th e H N C a n d D N C isotopom ers, as c a n be seen in T a b le
VIII.
O u r h ig h e r f r e q u e n c y w o rk c o n f i r m s A n d e r s o n ’s 15 a ssig n m en ts
f o r th e
100, 0 0 1
, and
002
sa te llite s o f th e m a in isotope a n d ena b le s us
to c a lc u la te Bv a n d D v f o r ea ch o f them .
We h a v e also observed th e J = 0 —1,
2 —3, a n d 3—4, t r a n s itio n s o f the 101 s a te llite , as well as th e J = 0 — 1
T ab le V III. In fra r ed B V alues vs Microwave B V a lu es (M H z).
HNC
b v IR
B vIRb
D
a yjX
wave
000
45332.037
45332.022
44531.984
100
45032.731
45032.670
45032.696
01*0
45486.157
45484.473
45484.477
02°0
45674.028
45671.259
02*0
45611.444
45608.347
44996.833
44996.807
Q v IR &
dvIR
^vfiw av*
328.4
324.375
324.365
001
01*0
DNC
000
38152.991
38153.003
100
37852.446
37852.406
a R e f e re n c e 27.
b R e f e re n c e 28.
232
t r a n s it io n s o f th e 200, 102, 003, a n d 004 s a te llite s f o r th e m a in isotope.
O u r w o r k on th e 101 s a te llite has led to a c o n f l i c t w ith th e i n f r a r e d
w o r k o f W inter a n d Jo n e s29, w ho sta te a v a lu e o f 44656(3) M H z f o r Bv
f r o m w h a t th e y c la im is the 101-001 b a n d sytem . T h is is in s h a r p d is a g r e e m e n t
w i t h o u r v a lu e o f 44699 M Hz fo r B101, b u t in f a i r l y good a g re e m e n t w ith
o u r v a lu e o f 44660 M H z f o r B002. T h e se c o m p a ris o n s lead us to c o n c lu d e
th e y m isa ssig n e d th e ba n d .
tw o f re q u e n c ie s .
No o th e r lines w e re f o u n d in b e tw e e n the
T h a t we h a v e m ade the c o rr e c t a s sig n m e n t is based
on these pieces o f evidence: ( 1 ) the lines we c la im a re th e
tim es s tr o n g e r th a n those we c la im a re th e
101,
t h a t th e 001 is 4 tim es as s tro n g as the 100, a n d
o f 1.552 M H z a n d -0.365 M H z f o r
7
1S a n d
002
a re f o u r
c o n s is te n t w ith th e f a c t
(2) we o b ta in th e v a lu e s
7 2 3 * resp e c tiv e ly .
R e v e r s in g
th e a s s ig n m e n t leads to v a lu e s o f -36.62 M Hz a n d 18.72 M Hz, w h ic h a re
c le a rly not co rre c t. T h is c a n be d e m o n s tr a te d by u sing th e e q u a tio n
Bv = Be - E
oti (v j+ d j/ 2 ) + E
7
ij ( v i+di/ 2 )(vj+ dj/ 2 ).
( 5)
F r o m th is e q u a tio n it can be sh o w n th a t
? 1 3 “ B v(000) ~ B v(100)
B v(00l) + B v(101)
( 6)
and
7 33 - 1 /2 ( B v (ooo) ~ 2B v(100) + B y^oojj),
( 7)
a n d these e q u a tio n s lead d i r e c tl y to the a b o v e 7 values. T h is a ssig n m e n t
is f u r t h e r s u p p o rte d by o u r o b s e rv a tio n o f th e J = 0 —1 t r a n s it io n s o f the
233
102, 003, a n d 004 s a te llite s
A S S IG N M E N T O F B E N D IN G S A T E L L IT E S
T h e a ssig n m e n t o f th e 01 x0 s a te llite s w a s n o t d i f f i c u l t , a n d
was a c h ie v e d f o r a ll f o u r isotopom ers. M aki a n d S am s 27 p r o v id e d good
Bv a n d q v v a lu e s f o r th e m a in isotope.
F o r th e o t h e r isotopic species
th e use o f H K D 19 sc alin g w o rk e d well f o r the a 2, as s h o w n in T a b le
VII, a n d e x t r a o r d i n a r i l y well in p r e d ic tin g q 0 ito» as c a n
seen *n T a b le
IX. T h e m ore re c e n t w o rk o f B u r k h o ld e r et al . 28 is in e x tr e m e ly good
a g re e m e n t w ith as ours. T h e o b s e rv a tio n o f th e b e n d in g 02°0 satellites,
h o w e v e r, w as f a r f r o m tr i v ia l , because th e re w ere i n t e r f e r i n g lines to
deal w ith f o r all th e isotopic species.
G u d e m a n 16 h a d o b s e rv e d two
c a n d id a te s f o r th e J = 0 —1 line (91341.92 M H z a n d 91347.88 MHz). We
h a v e o b se rv e d 3rd, 4th, a n d 5th h a rm o n ic s f o r this line a n d c o n f i r m one
of his c a n d id a te s , th e line a t 91341.92 MHz.
We h a v e also o b se rv e d 3rd,
4th, a n d 5th h a r m o n ic lines o f th e 02 20, a n d th e J = 2 —3 a n d 3 —4 tra n s itio n s
o f the 03*0 f o r th e m ain isotope.
A tte m p ts to observe th e 0330 a n d 04°0
w ere n o t suc ce ssfu l. Both th e 02°0 a n d 0220 se arches w e re g u id e d by
th e i n f r a r e d w o rk o f M aki an d Sam s27. While ou r Bv’s a r e only in m o d e ra te ly
good a g re e m e n t w ith th e irs (T a b le V III) by c o m p a ris o n to th e ex c elle n t
100
a g re e m e n t m e n tio n e d b e fo re , th e ir w o rk w as still i n s tr u m e n ta l in
the d e te c tio n o f these b e n d in g satellites.
F o r th e H N 1SC a n d H 15 N 13C,
we o b se rv e d p a ir s o f c a n d id a te s f o r th e 02°0, J = 0 —1 lin e s, b u t w ere a b le
to use th e h ig h e r h a rm o n ic d a ta to u n a m b ig u o u s ly assign th e lines.
235
F o r D N C we h a d th r e e c a n d id a te s f o r th e 02°0 (77190.106 M Hz, 77198.022
M H z, a n d 77204.626 M Hz) a n d tw o f o r th e D 15N C (76099.374 M H z a n d
76115.598 MHz). O n ly th e 77190 a n d 76115 lines, h o w e v e r, gave a 2’s w h ic h
sc ale d c o n s is te n tly w ith H K D 14. Also, w h e n e q u il ib r i u m s tr u c tu r e s w ere
c a lc u la te d f o r th e D N C - D 16N C p a ir w ith each possible set o f c a n d id a te s
o n ly these tw o gave a rea s o n a b le s tr u c tu r e .
All o f th is is sh o w n in T a b les
X a n d XI.
F o r th e H 15N C m a tte r s w ere c o n s id e ra b ly m ore c o m p lic a te d .
We o b se rv e d a co m p le x p a t t e r n o f closely spaced lines a t th e J = 0 —*1 f r e q u e n c y
( F ig u r e 3), a n d w ere n e v e r a ble to assign a J=0-*1. T h e r e w ere th re e
lines in t h i r d h a rm o n ic ra n g e a n d f o u r in the f o u r t h h a rm o n ic region.
Because o f c e n t r i f u g a l d is to r tio n , we w e re able to n a r r o w th e a s sig n m e n t
to tw o p a ir s (268416.3 M H z a n d 357849.2 M Hz) a n d (268404.2 M H z a n d
357822.8 MHz). T w o pieces o f d a ta w ere used to assign th e tra n s itio n .
To begin w ith , we c a lc u la te d Be a ssu m in g each p a ir w as c o rre c t, a n d
th e n used K r a i t c h m a n ’s e q u a ti o n s 30 (see th e p re v io u s c h a p te r) to c a lc u la te
r CN’s, a n d second m o m e n t c o n d itio n s to c a lc u la te r N H ’s. T h e re s u lts are
sh o w n in T a b le X II, w h ic h will be discussed in m ore d e ta il in th e section
on s tr u c tu r e c a lc u la tio n .
F o r now th e p o in t we wish to co n v e y is t h a t
th e use o f th e 268404.2 M H z /3 5 7 8 2 2 M hz p a ir shows gives s tr u c tu r e s
o f e x t r a o r d i n a r y c o n sisten c y , w h ile th e 268416.3 M H z/357849.2 M H z p a ir
does not.
As a f u r t h e r test, we c a n c a lc u la te 5 by e s tim a tin g q v 2/ 8 as
m e n tio n e d a b o v e , a n d u sing th e q v a lu e s f ro m the 01 *0 sa te llite .
When
we do this, we o b ta in a 5 v a lu e o f 9.7 c m - 1 f o r H 15 NC, in c o n tr a s t to
9.7 c m - 1,9.6 c m -1, a n d 9.7 c m - 1 f o r H N C , H N 18 C, a n d H 15 N 13C re s p e c tiv e ly ,
236
F ig u re 3 -T h is illu s tr a te s th e d i f f i c u l t i e s we h a d in m e a s u rin g the J = 0 — 1
02°0 t r a n s it io n .
T h e e x p e r im e n ta l c o n d itio n s a r e as follows: slow flo w ,
w a t e r cooling, 300 m A d isc h a rg e , 20 m T o r r A r, 5 m T o r r C H 4, 2 m T o rr
2 N 2,
40 scans, 2 b a s e lin e su p p re ssio n s (800 kH z), 800 k H z FM, 100 k H z
AM, 11 p o in t sm o o th , a n d 10 j i v olt fu ll scale lo ck -in s e n sitiv ity .
237
H ^ jC
89480
v=O g0Q
89485
search
j
= 0 _
89490
FREQUENCY(MHz)
238
Table X. H K Da S caling for DNC and D 1SNC 02°0 C andidates.
D N C(M H z)
a 2 (exp)
a 2 (H K D )
a 2 ( e x p ) / a 2(H K D )
77190.106b
-221.095
-164.
1.348
77198.022
-223.074
-164.
1.360
77204.626
-224.725
-164.
1.370
D 15 NC(M Hz)
a 2 (exp)
a 2(H K D )
a 2( e x p ) / a 2(H K D )
76099.374
-203.148
-154.
1.319
76115.598b
-207.204
-1 5 4 .
1.345
a R e f e re n c e 19.
b C o rrec t v alues in boldface.
T a b le XI. D N C -D 16NC Bond D istances U sing 02°0 C a n d id a te s.
D 15NC
rC N ( X)
rN H ( X)
77190.106
76099.374
1.165616
1.004882
77198.022
76099.374
1.164344
1.008907
77204.626
76099.374
1.163279
1.012265
77190.106a
76115.598
1.168310
0.996578
77198.022
76115.598
1.167045
1.000602
77204.626
76115.598
1.165987
1.003960
DNC
C o rrec t choice in boldface.
240
T a b le X II. K r a it c h m a n E quilibrium Structures rCN(^)
and Second Moment rNH(&).
T r u e 02°0a
False 02°0b
1.168565
1.168636
HNC
0.996313
0.995921
H 15N C
0.996340
0.995954
H N 13C
0.996276
0.995873
H 15 N 13C
0.996303
0.995884
DNC
0.995788
0.995569
D 15N C
0.995764
0.995538
H 15N C p a r e n t r CN
1.168567
1.168587
HNC
0.996302
0.996191
H 15N C
0.996328
0.996236
H N 13C
0.996265
0.996151
H 15 N 13C
0.996291
0.996173
DNC
0.995782
0.995720
D 15N C
0.995757
0.995693
H N C p a r e n t r CN
Second m o m e n t r CH’s
Second m o m e n t r CH’s
241
T r u e 02°0
F a lse 02°0
1.168568
1.168568
HNC
0.996297
0.996297
H 15NC
0.996322
0.996344
H N 13C
0.996259
0.996259
H 15 N 13C
0.996285
0.996285
DNC
0.995779
0.995779
D 15N C
0.995754
0.995754
T r u e 02°0
False 02°0
1.168570
1.168523
HNC
0.996285
0.996545
H 15NC
0.996311
0.996603
13c
0.996248
0.996514
0.996273
0.996551
DNC
0.995773
0.995918
D 15N C
0.995748
0.995898
H N 13C p a r e n t r CN
Second m o m e n t r CH’s
H 15 N 13C p a r e n t r CN
Second m om ent r CH’s
h n
h
15 n
13c
242
a F o r these c a lc u la tio n s , we are assu m in g th e J = 2 —3 tr a n s it io n
o f th e H 15N C is 268404.246 M Hz a n d th e J = 3 —4 tr a n s it io n is
357822.812 MHz.
b For these c a lc u la tio n s , we are assu m in g the J=2-»3 t r a n s it io n
o f the H 15N C is 268404.222 M Hz a n d th e J = 3 —4 tr a n s it io n is
357849.192 MHz.
243
w h ile on t h e o th e r h a n d , th e false p a i r gives a 5 v a lu e o f 12.7 c m -1, w h ic h
is c le a rly o u t o f line.
STARK EFFECT
O n e o f th e m ost in te r e s tin g asp ec ts o f o u r w o rk on H N C was the
o b s e rv a tio n o f th e 0220 satellites.
F ro m ou r o b s e rv a tio n s o f th e J=4 -*5
sta te , we h a v e d e te r m in e d th a t q v2/ 5 is 0.368 M H z f o r H N C as opposed
to 0.1 M H z f o r H C N . We re m in d th e r e a d e r o f th e f o r m u la re la tin g q v2/3
to th e J=4-*5 tr a n s it io n f re q u e n c ie s (C h a p te r V)
q v2/5 «
i'(022d) -v (0 2 2c)
W
, or
•
480
( 8)
Because o f th is large v a lu e o f q v2 /5, the 0220 lines a r e c o n s id e ra b ly f a r t h e r
a p a r t , a t t h e k ly stro n f re q u e n c y , a n d c o n s id e r a b ly less p e r tu r b e d th a n
t h e i r H C N c o u n te r p a r ts .
It was s im p le r to look f o r each o f the 0220
t r a n s it io n s s e p a r a te ly , b ecause the lines w ere 12, 22, a n d 33 M Hz a p a r t
a t the k ly s tr o n f r e q u e n c y f o r th e 3rd, 4 th, a n d 5th h a rm o n ics, respectively.
F ig u re s 4-6 p ro v id e a c o m p a rs io n b e tw e e n th e /=0 a n d 1=2 sa te llite s f o r
th e v a rio u s ha rm o n ics. T h e 0220 lines w ere c o n s id e ra b ly less p e r t u r b e d
w i t h r e g a r d to th e 02°0 lines a t all th e h a rm o n ic s th a n in H C N o r HCO+.
We re m in d th e r e a d e r t h a t in C h a p t e r V, it was s ta te d th a t the l/u^l2 w ere
p r o p o r t io n a l to J '
2
- /2, a n d the th e o r e tic a l 02 20/0 2 °0 in te n s ity ra tio s
w e re 5 /9 , 3 /4 , a n d 2 1 /2 5 f o r th e J=2-*3, J=3-*4, a n d J=4-*5 tra n s itio n s ,
re s p e c tiv e ly .
A glance a t F ig u re s 3-5, w ill reveal th a t th e obse rv e d ra tio s
a r e not s ig n i f ic a n tl y low er th a n these.
It can also be seen th a t the 0220
a r e o n ly s lig h tly b r o a d e r th a n the 02°0 lines.
It is c le a r th a t S ta rk p e r t u r b a t io n
244
F ig u re 4-T his f ig u r e is a c o m p a ris o n o f the J=2-»3 o f 02°0 tra n s itio n
a n d th e J=2-»3 o f 022c0 tra n s itio n . T h e e x p e rim e n ta l c o n d itio n s a re as
follow s: f a s t flo w , liq u id n itr o g e n cooling, 300 mA n o rm a l d isc h a rg e ,
a p p r o x i m a t e ly 100 scans f o r both lines, 20 m T o rr A r, 5 m T o r r C H 4, 5
m T o r r N 2, 2 b a selin e su p p re ssio n s (800 kHz), 2400 kH z FM, 100 k H z AM,
31 p o in t sm ooth, 20 /uvolt fu ll scale lock-in s e n sitiv ity .
245
HNC 02°0 vs 0220 J=2-3
5 MHz
246
F ig u re 5 -T h is f ig u r e p ro v id e s a c o m p a ris o n f o r th e J = 3 —4 lin e s o f 02°0
a n d 0 2 2c0. T h e e x p e r im e n ta l c o n d itio n s a re th e sam e as F ig u re 4, e x c e p t
t h a t we h a v e u sed 2 b a selin e su p p re ssio n s o f 600 kH z. a n d we h a v e used
th e
10
jmvolt sc ale on the lock-in.
247
HNC 02°0 vs 0220 J=3-4
5 MHz
248
Figure
6
-T h is plot is a c om parison o f the J>4-»5 t r a n s itio n s f o r 02°0 a n d
02 2 0. T h e e x p e rim e n ta l c o n d itio n s are the sam e as in the prev io u s two
fig u re s, ex c ep t t h a t we h a v e used 480 kH z b a selin e s u b tr a c tio n , ISO scans
fo r b o th lines, a n d
2
juv scale on th e lock-in a m p lif ie r .
HNC 02°0 vs 0220 J=4-5
02°0
5 MHz
250
is a s ig n i f ic a n tl y less p r o m i n e n t e f f e c t in H N C , t h a n in H C N or, as we
shall see in C h a p t e r V II, in H C O +.
S T R U C T U R E C A L C U L A T IO N S
H a v in g o b ta in e d th e Be values, we now c a lc u la te e q u ilib r iu m
s tru c tu re s .
We h a v e less d a ta th a n f o r H C N a n d H C O +, a n d c a n only
c a r r y o u t a level c a lc u la tio n s .
H o w e v er, in one v e ry i m p o r ta n t respect
we h a v e m ore d a ta f o r H N C t h a n f o r th e o th e r m olecules.
We have com plete
m ic ro w a v e e q u il ib r i u m Be v a lu e s f o r tw o d e u te r a t e d species.
F or this
m olecule we w ill be a ble to e x p lo re the e f f e c t o f th e s u b s ti tu t io n o f d e u te r iu m
f o r h y d ro g e n on c a lc u la te d e q u il ib r i u m geom etry. F ig u re 7 is a M o rin o -N a k a g a w a
p lo t 31 (or C h a p t e r V) s h o w in g all th e in te rse c tio n s, w h ile F ig u re
8
is
an e x p a n d e d v iew s h o w in g ju s t th e m ain a re a o f in te rest. F ig u re s 9 a n d
10 show th e e f f e c t o f a d d in g 25 kH z e rr o r b ars (these a re tw ic e th e e s tim a te d
e rr o r ba rs) to th e Be’s f o r th e H c o n ta in in g isotopom ers.
As c a n be seen
f ro m these f ig u re s , the e rr o r b a rs h a v e little e f f e c t on the size o f the
in te r s e c tio n are a s.
It w o u ld h a v e been d e s ira b le to a d d th e D N C a n d
D 1BNC c u rv e s to F ig u re s 9 a n d 10, b u t o u r c o m p u te r p r o g ra m w as not
set up to h a n d le so m a n y c u rv e s in one figure.
T h e r e a d e r c a n see t h a t H 16N C a n d H N 1SC c u rv e s h a v e a n in te rse c tio n
grossly d i f f e r e n t f r o m th e r e m a in in g p a irs o f H c o n ta i n in g species.
A
p a r t i a l e x p la n a ti o n o f th is c a n be m ad e by using the e q u a tio n f o r th e
slope o f r NH vs r NC ( p re v io u s c h a p te r w ith s u ita b le m o d if ic a tio n f o r H N C)
(9 )
d r NH _
d f CN
m C m N r CN +
m Nm H r NH +
m Hm c ( r NH + r CN)
m Hm c ( r NH + r CN)
251
F ig u re 7 -T h is f i g u r e is a M o rin o - N a k a g a w a 22 plot o f a level e q u il ib r i u m
s tr u c tu r e s o f H N C s h o w in g the e n tir e ra n g e o f in te rse c tio n . T h e plots
w ere m a d e w ith a slope s u b tr a c tio n o f - 5.7.
252
rHN (A)
0 .9 9 5 2
0 .9 9 1 2
JHNC
DNC
1. 1 6 8 4 0
1. 1 6 8 8 0
1. 1 6 9 2 0
1. 1 6 9 6 0
rC N (A)
HNC R e STRUCTURES
253
F ig u re
8 -T h is
is F ig u re 7 b lo w n up to show only th e m a in ra n g e o f in te rse c tio n .
N o te th e r a t h e r s t r i k i n g sy m m e try o f th e tria n g le s.
254
rHN (A)
0. 9 9 7 2 0. 9 9 6 7 0. 9 9 6 2 0. 9 9 5 7 0. 9 9 5 2 0. 9 9 4 7
E(NC
HN
16842
16854
16866
16878
r C N (A)
HNC Re STRUCTURES
255
F ig u re 9 -T h is is a plot o f th e c u rv e s in F ig u re 7 w ith e r r o r b a rs o f 25
kHz added.
P lease no te th e in te r s e c tio n a re a s a re n o t g r e a tly e n la r g e d
by th e e r r o r bars.
256
rNH (A)
0.9952
0.9 9 1 2
h
I-S n c
i I
H1 5 ^ | 1 3 c
1. 1 6 8 4 0
1. 1 6 8 8 0
1. 1 6 9 2 0
1. 1 6 9 6 0
rC N (A)
HNC R e STRUCTURES
257
F ig u re 10-T his is a plot o f th e c u rv e s in F ig u re
kHz added.
8
w ith e rr o r b a rs o f 25
258
rNH (A)
0 .9 9 7 2 0 .9 9 6 7 0 .9 9 6 2 0 .9 9 5 7 0 .9 9 5 2 0 .9 9 4 7
HN0
UGHT
e x per im en ta l
HEAVY
1. 1 6 8 4 2
1. 1 6 8 5 4
1. 1 6 8 6 6
1. 1 6 8 7 8
rC N (A)
HNC R e STRUCTURES
259
T a b le X III. E q u ilib riu m Bond L e n g th s r CN(
Pair
r CN(
X)
a n d r NH(
r NH< *)
H N C - H 15NC
1.168724
0.995498
H N C - H N 13C
1.168325
0.997642
H N C - H 1 SN 13C
1.168545
0.996443
H 15 N C - H N 13C
1.169784
0.989331
H 15 N C -H 15 N 13C
1.168346
0.997597
h n
1.168718
0.995475
D N C - D 15NC
1.168310
0.996578
H N C -D N C
1.168782
0.995119
H N C - D 15NC
1.168801
0.995003
H 1SN C -D N C
1.168776
0.995138
H 15 N C -D 1SNC
1.168793
0.995038
h n
1.168755
0.995202
H N 13 C - D 1SNC
1.168772
0.995106
H i5N i3 c -D N C
1.168751
0.995217
H l 5 N 13 C - D 15NC
1.168766
0.995126
13c
13 c
-h
16 n
13c
-d n c
X).
260
T a b le X IV . E qu ilib riu m Bond L e n g th s r CN(
P a ir
X) a n d
t cn (
rnh(
H N 'C '- D N 'C '
1.1688
0.9951
H N 'C '- H N " C "
1.1685
0.9964
D N 'C '- D N " C "
1.1681
0.9976
C and R a
1.1689
0.9940
a R e f e re n c e 18.
r NH(
X).
261
T a b le XV. T h e o r e t i c a l .a n d E x p e rim e n ta l r e’s.
r CN(
r NH(
Exp. ( H N C - H N 13 C)a
1.1685
0.9964
Exp. (H N C -D N C ) a
1.1688
0.9951
CRb
1.1689
0.9940
HKDC
1.1719
0.9979
P e a rso n el al.d
1.1696
0.995
T a y l o r el al.e
1.168
0.995
D y k s tr a a n d S e c re stf
1.1722
0.9943
B o tsc h w in a a n d Scbald*
1.1676
0.998
L a id ig e t a/.(C I)h
1.182
0.997
L a id ig et al.{SC F )h
1.159
0.986
D e F re e s et al>
1.1747
0.9948
aT h is w ork.
b R e f e r e n c e 18.
c R e f e r e n c e 19.
d R e f e r e n c e 20.
e R e f e r e n c e 21.
f R e f e r e n c e 22.
s R e f e r e n c e 23.
h R e f e r e n c e 24.
‘ R e f e r e n c e 25.
262
U sing r CN = 1.168
Xa n d
r ^ j = 0.996
Xwe
ca lc u la te slopes o f -5.53, -5.73,
-5.68, a n d -5.90 f o r H N C , H 15 NC, H N 13 C, a n d H 15 N 13 C, respectively,
so t h a t th e tw o singly s u b s titu te d species h a v e n e a rly e q u a l slopes. T h u s
a sm all c h a n g e in th e e x p e rim e n ta l v alue o f one o f the Be’s causes the
p o in t o f in te rse c tio n to move a long way.
As we shall see in C h a p te r
VII, th e re a re sim ila r inconsistencies in the a level H C O + stru c tu re s ,
a n d we th in k the s im ila r slopes of the tw o singly s u b s titu te d species m ig h t
be a possible e x p la n a tio n th e r e too.
T h e r e a d e r c a n also observe fro m F ig u re s 7 a n d
8
th a t the
H N ' C ' - H N " C " p a ir in te rse c tio n s oc c u r a t h ig h e r r HN’s a n d low er r CN’s
th a n th e H N ' C ' - D N ' C ' p a i r in tersectio n s, a n d also th a t th e H N ' C ' cu rv e s
f o r m a n "hour-glass" p a t t e r n w ith th e H N C - H 16 N 13C in te rse c tio n the c e n te r
o f the hour-glass. In T a b le X III, we have p rese n ted all th e e q u ilib r iu m
b o n d len g th s c a lc u la te d f ro m the p a i r intersections. O ne can see th a t
th e H N ' C ' - D N ' C ' p a ir in te rse c tio n s yield bond d ista n c es o f 1.1688 X
f o r r CN a n d 0.9951
Xf o r
r NH. These a rc in good a g re e m e n t w ith Creswell
a n d R o b ie tte ’s 18 c a lc u la te d values o f 1.1689(2)
Xa n d
0.9940(8)
Xfro m
the a n h a rm o n ic fo rc e fie ld . T h e H N C - H 16 N 13C p a ir (th e a v e ra g e v alue
o f th e in te rse c tio n o f the H N 'C '- H N " C " pairs) gives a n r CN o f 1.1685
Xa n d
a n r NH o f 0.9964
X, c o n s id e ra b ly
less in a g re e m e n t w ith C resw ell
a n d R o b ie tte . 18 T h e D N C - D 15NC p a ir gives a s tr u c tu r e o f 1.1683
r CN a n d 0.9966
Xfo r
Xf o r
r NH, e v e n less in a g re e m e n t w ith R e f e re n c e 18 th a n
the H N C - H 15 N 13C pair. M oreover, it should be p o in te d o u t th a t the H N C - H 15NC
p a ir gave th e best a g re e m e n t w ith Creswell a n d R o b i e tt e 18 o f th e H only
pairs. T h e r e f o r e , it is h ig h ly possible the D N C -D 1BN 13C m icrow ave p a ir
263
c o u ld be y e t f a r t h e r a w a y fro m th e ir values.
I f we assum e th e sam e
r e la ti o n s h ip b e tw e e n the D N C -D 15NC a n d D N C - D 15 N 1SC p a irs, as exists
f o r th e c o rr e s p o n d in g H c o n ta in in g pairs, th e n th e D N C - D 1BN 13C p a i r
in te r s e c tio n is p r e d ic te d to occur a t a p p r o x im a te ly a n r CN o f 1.1681 X
a n d a n r NH o f 0.9976
X.
In T a b le X IV , we h a v e s u m m a riz e d th e results
e n u m e r a t e d in th is p a r a g r a p h , a n d th e r e a d e r c a n no te a g a in th e c u rio u s
re s u lt o f th e H N ' C ' - H N ' ' C " p a ir s tr u c tu r e s b e in g i n te r m e d ia t e b e tw e e n
th e D N ' C ' - D N " C " p a ir s tru c tu re s a n d th e H N ' C ' - D N ' C ' p a ir s tr u c tu r e s .
In T a b le X V , we c o m p a re our e x p e rim e n ta l re s u lts to th e th e o r e tic a l
values.
r NH
We see t h a t th e c a lc u la tio n s all te n d to be w i t h in
0 .0 0 2
Xo f
the
values, w h e re a s th e r e is c o n s id e ra b ly m ore d i f f e r e n c e b e tw e e n the
th e o r e tic a l a n d e x p e rim e n ta l r CN’s.
T a b le X II is a c le a r d e m o n s tra tio n o f th e p o w e r o f the K r a it c h m a n second m o m e n t m ethod. T h e fiv e p a ir in te r s e c tio n s ( n e g le c tin g th e o u tly in g
H 15 N C - H N 13C p a ir ) h a d 0.0004
Xin co n siste n c y
in r CN a n d
in r NH. T h e in co n s is te n c ie s in r CN a re re d u c e d to 0.000003
m a x im u m in c o n s is te n c y in r HN is
0 .0 0 0 1
X,
0 .0 0 2
X in co n siste n c y
X, a n d
th e
i f we r e s tr ic t the c o m p a ris o n
to only th e H c o n ta i n in g isotopom ers (only th e " T rue 02°0" colum n).
T h e r e is also v e ry s a tis fy in g a g re e m e n t b e tw e e n th e 1.16857
r CN’
Xv a lu e
of
c a lc u la te d f ro m th e K r a itc h m a n - s e c o n d m o m e n t m eth o d , a n d th e
1.16854
Xo f
r CN, c a lc u la te d fro m the in te rs e c tio n o f the H N C - H 16 N 13C
p a i r (w e re m in d the r e a d e r th a t this in te r s e c tio n is th e c e n te r o f th e
hour-glass). T h e second m om ent r HN v a lu e o f 0.9963
the H N C - H 16 N 13C in te rse c tio n v alue o f 0.9964
X.
Xagrees
well w ith
T h e rea l a d v a n ta g e
o f th e K r a it c h m a n - s e c o n d m om ent m eth o d becom es c le a r by g la n c in g
264
a t th e section o f T a b le X II w h e r e H N C is th e p a r e n t species. T h i s r CN
w as c a lc u la te d w i t h o u t u sin g th e d o u b ly s u b s ti tu t e d iso to p o m er d a ta .
E v e n th o u g h th e Be c u rv e s f o r H N C , H 16 N C , a n d H N 13C gave v e ry in c o n s is te n t
in te rse c tio n s , th e use o f th e K r a itc h m a n - s e c o n d m o m e n t m e th o d gave
a good e q u il ib r i u m g e o m e try u sing ju st those th r e e pairs. T h e r e f o r e ,
we can use th e m e th o d w ith H C O + a n d o b t a i n a n a level e q u i l i b r i u m
s tr u c tu r e f o r t h a t m olecule (w h ic h we shall do in C h a p t e r VII).
It is
also c le a r t h a t Be o f D N 13C a n d e specially D 15 N 13C a re n e c c e s s a ry to
o b ta in a n a c c u r a te D N C - D N 'C ' e q u il ib r i u m s tr u c tu r e .
T h e r e f o r e , we
h a v e in c lu d e d T a b le X V I, w h ic h lists c a lc u la tio n s o f th e J = 0 —►
1 t r a n s it io n s
o f th e 100, 02°0, a n d 001 sate llite s, o b ta in e d by scalin g H K D 19. We also
no te f r o m T a b le X II, t h a t i f th e second m o m e n t c o n d itio n is a p p lie d
to D N ' C ' isotopom ers, a lo n g w ith th e r CN’s c a lc u la te d f r o m th e H N ' C '
isotopom ers, we c a lc u la te r HN’s o f 0.9958 X. T h is resu lt is i n te r m e d ia t e
be tw e e n th e H N ' C ' - D N ' C ' a n d H N ' C ' - H N " C " r CH values.
F in a lly ,
we c a n c a lc u la te c o m p le te K r a i t c h m a n e q u il ib r i u m s tr u c tu r e s f o r H N C
a n d H N l 5 C, a n d we o b t a i n a v a lu e o f r NH= .995178 X w ith H N C as th e
p a r e n t a n d r NH= .995104 X w ith H 15N C as th e p a re n t.
T h e se re s u lts a r e
s im ila r to the d i r e c t in te r s e c tio n o f th e H N ' C ' - D N ' C ' pairs.
T o s u m m a riz e
e v e r y th in g , th e r e a re 3 w ays o f a p p ly in g K r a i t c h m a n ’s e q u a ti o n s to o u r
d a ta .
T h e f ir s t is to c a lc u la te second m o m e n t r CH’s f ro m th e o t h e r H N ' C '
species, w h ic h w ill yield a n r CH e q u a l to th e H N ' C ' - H N " C " p a i r in te rse c tio n
value. T h e second is to c a lc u la te second m o m e n t r CH’s f r o m th e D N ' C '
isotopom ers, w h ic h w ill y ie ld a n r CH i n te r m e d ia t e in v a lu e b e tw e e n th e
H N ' C ' - H N " C " p a ir in te r s e c tio n s a n d th e H N ' C ' - D N ' C ' p a i r in te rse c tio n s .
265
T h e t h i r d is to m ak e f u ll use o f K r a i t c h m a n ’s e q u a tio n s , a n d th is results
in a n r CH e q u a l to th e H N ' C ' - D N ' C ' p a i r in te r s e c tio n value.
We w ish to c o n c lu d e th is c h a p te r w i t h a f e w r e m a r k s a b o u t
HOC+.
We h a v e d e f i n i t e l y m e a s u re d a n a level e q u il ib r i u m s tr u c tu r e
f o r H N C , w h ic h also has a sh allow b e n d in g p o te n tia l.
T h e r e f o r e , it seems
lik e ly t h a t a d e f i n i t e e q u il ib r i u m s t r u c t u r e c a n be m e a s u r e d f o r this
ion.
B e rry a n d H a r m o n y 32 h a v e sent us a m a n u s c r ip t w ith a n e s tim a te
o f th e e q u il ib r i u m g e o m e try o f H O C +. We w ill say m ore a b o u t this in
th e n e x t c h a p te r.
T h e v alues th ey give a re
r o c = 1.1570(5) X. a n d r HO=0.975(2)
X. W hile we d o not k n o w how a c c u r a te these v a lu e s re a lly a re , we can
a t lea st use th em to e s tim a te th e slopes o f th e Be curves.
I f we a p p ly
these v a lu e s to e q u a tio n 9, we o b ta in slopes o f -5.97, -6.34, - 6.15, a n d
-6 .5 4 f o r th e Be c u rv e s o f H O C +, H 18 O C +, H 0 13 C +, a n d H 18 0
13 C+,
resp e c tiv e ly .
I f o u r "sim ilar slope” e x p la n a ti o n is c o rre c t, th e n Be c u rv e s f o r the m ain
iso to p e a n d th e tw o singly s u b s titu te d isotopom ers s h o u ld not f o rm a
larg e tr ia n g le , since th e slopes a re re a s o n a b ly d i f f e r e n t .
If th is e x p la n a tio n
is in c o r r e c t, a n d a large t r ia n g le results, th e n a p p lic a tio n o f th e K r a itc h m a n - s e c o n d
m o m e n t m e th o d sh o u ld give a re lia b le re.
266
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D. E. M illgan a n d M E. Jaco x , J. Chem . Phys. 47, 278 (1967).
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L. E. S n y d e r a n d D. B uhl, Bull. Am. A stro. Soc. 3, 388 (1971).
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L. E. S n y d e r a n d D. B uhl, A nn. N Y A cad. Sci. 194, 17 (1972).
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L. E. S n y d e r, J. M. H ollis, a n d D. B uhl, Ap. J. 215, L87 (1977).
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R. D. B row n, P. D. G o d f r e y , J. W. V. Storey, a n d F. O. C la rk ,
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R. L. Snell a n d A. Wooten, Ap. J. 216, LI 11 (1977).
R. D. B row n, P. D. G o d f r e y , H. I. G u n n , G. L. B lackm an, a n d
S to re y
Mon. N ot. R. A str. Soc. 180, 87P (1977).
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J. W.
M. A. F r e r k i n g , W. D. L a n g c r, a n d R. W. Wilson, Ap. J. 232,
L65 (1979).
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G. L. B la c k m a n , R. D. B row n, P. D. G o d f r e y , a n d H. I. G u n n ,
C hem Phys. L ett. 93, 716 (1975).
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C. A. A r r in g to n a n d E. A. O gryzlo, J. Chem . Phys. 63, 3670 (1975).
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R. J. S a y k a lly , P. G. Szanto, T. G. A n d e rs o n , a n d R. C. Woods,
Ap. J. L ett. 204, L143(1976).
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G. L. B la c k m a n , R. D. B row n, P. D. G o d f r e y , a n d H. L. G u n n ,
N a t u r e 261, 395 (1976).
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R. A. C resw ell, E. F. P e arson, M. W innew isser a n d G. W innew isser,
Z. N a tu r f o r s c h . 31 a, 221 (1976).
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E. F. P e a rso n , R. A. Cresw ell, M. W innew isser a n d G. W innew isser,
Z. N a t u r f o r s c h . 31 a, 1394 (1976).
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T. A. A n d e rs o n , , PhD . Thesis. U n iv e r s ity o f W isconsin-M adison 1976.
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C. S. G u d e m a n , PhD . Thesis. U n i v e r s i ty o f W isconsin-M adison 1982.
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R. A. C re sw e ll a n d A. G. R o b ie tte , Mol. Phys. 58, 869 (1978).
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P. H e n n ig , W. P. K r a e m e r , a n d G. H. F. D ie rc k se n , M P I /P A E
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M uiichen, 1977).
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P. K. P e a rs o n , H. F. S c h a e fe r , a n d U. W ahlgren, J. C hem . Phys.
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P. R. T a y lo r, G. B. B acskay, N. S. H ush, a n d A. C. H u rle y ,
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C. E. D y k s t r a a n d D. Secrest, J. Chem . Phys. 75, 3967 (1981).
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P. B o ts c h w in a a n d P. S ebald, J. Mol. Spec. 100, 1 (1983).
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W. D. L a id ig , Y. Y a m a g u c h i, a n d H. F. S c h a e fe r III, J. Chem . Phys.
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N. N. H aese, PhD . Thesis. U n i v e r s i ty o f W isconsin-M adison 1981.
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A. G. M aki a n d R. L. Sams, J. Chem . Phys. 75, 4178 (1981).
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Y. M o rin o a n d T. N a k a g a w a , J. Mol. Spec. 26, 496(1968).
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R. J. B e rry a n d M. D. H a r m o n y , p r iv a t e c o m m u n ic a tio n .
CHAPTER VII.
T H E E Q U I L IB R I U M S T R U C T U R E O F HCO+.
269
IN T R O D U C T IO N
T h e J = 0 —*■1 tr a n s it io n o f H C O + a r o u n d 89.189 G H z was
f ir s t o b se rv e d by S n y d e r a n d B u h l 1 in th e i n te r s te lla r m e d iu m in 1970.
T h e y w ere u n c e r t a i n o f its i d e n tity , h o w e v e r, a n d r e f e r r e d to it as X -o g e n . 1
T h a t year, K l e m p e r e r 2 p roposed t h a t th e c a r r ie r w as in f a c t H C O +. In
1975, Woods et al.3 d e m o n s tr a te d th is to be th e case by o b s e rv in g the
tr a n s it io n in a DC glow d isc h a rg e o f CO a n d H 2. In 1981, Woods et al.*
r e p o r te d o b s e rv a tio n s o f J = 0 —►
1 t r a n s itio n s f o r H 13 C O +, H C 18 0 +, DCO+,
D 13 CO+, a n d D C lsO +, u sing He as a b u f f e r gas w ith sm all a m o u n ts o f
CO a n d H 2. In th e sam e y e a r, Bogey et a l 3 used a n R F d isc h a rg e to e x te n d
th e H C O + m e a s u re m e n ts to J = 2 —3, th e H 13C O + a n d H C 18 0 + m e a su rem e n ts
to J = l-* 2 , a n d th e D C O +, D 13 C O +, a n d D C 18 0 + iso to p o m er m e a su rem e n ts
to J=3-*4. At a b o u t th e sam e tim e, Sastcy et al.6 m e a s u re d f re q u e n c ie s
up to J=4-*5 f o r H C O + a n d J= 5 — 6 f o r DCO+.
Van den Heuvel and D ynam us7
used a hollow c a th o d e d isc h a rg e a n d f a r i n f r a r e d laser to observe t r a n s itio n s
1 2 f o r H C O +. G u d e m a n 8 used a D C glow d is c h a r g e an d
up to J= 1 1 —►
p h a se locked k ly s tr o n to obse rv e J=0-*1 t r a n s itio n s f o r th e 100, 02°0,
a n d 001 sa te llite s f o r H C O +, H 13C O +, a n d H C lsO + a n d to o b ta in the
f ir s t e q u il ib r i u m s t r u c t u r e o f a m o le c u la r ion.
tr a n s itio n s f o r th e
002
He also m e a s u re d J=0-»1
v i b r a t io n a l s ta te o f the m ain isotope a n d the g ro u n d
v ib r a t io n a l s ta te o f H 13 C 18 0 + .
G u d e m a n et al.9 e x te n d e d th e w o rk to
th e i n f r a r e d , u s in g ve lo c ity m o d u la tio n to see th e
band.
A m a n o 10
used a d i f f e r e n c e f r e q u e n c y laser a n d d is c h a r g e m o d u la tio n to see the
sam e b a n d a n d o b t a i n im p ro v e d co n sta n ts.
D e L u c ia et a l.11 d e v e lo p e d
th e e x te n d e d n e g a tiv e glow d isc h a rg e , a n d P lu m m e r et a l.n used it to
270
o b se rv e th e J=2->3 t r a n s it io n s o f H C 17 0 + a n d H C lsO + in n a t u r a l a b u n d a n c e .
T h e v3 b a n d w as o b s e rv e d by F o s te r et a l.13, w ho used a h ollow c a th o d e
a n d c o n v e n tio n a l s o u rc e f r e q u e n c y m o d u la tio n , a n d D a v ie s et a l.u , w ho
used v e lo c ity m o d u la tio n .
F o s te r a n d M c K e ll a r 15 d e te c te d th e v3 b a n d
o f D C O + u s in g d is c h a r g e m o d u la tio n . T h e b e n d in g m ode w as o b served
by D a v ie s a n d R o t h w e l l 16 u sing v e lo c ity m o d u la tio n a n d K a w a g u c h i
et a l.17 u sin g m a g n e tic f ie ld m o d u la tio n .
K a w a g u c h i et a l.13 o b s e rv e d th e
E m p lo y in g th e sam e te c h n iq u e ,
b a n d o f DCO+.
E a r li e r th is year,
B lake et a l.19 e m p lo y e d f a r i n f r a r e d laser s id e b a n d sp e ctro sc o p y to observe
h ig h J p u re r o t a t i o n a l t r a n s it io n s o f H C O + in th e g ro u n d v i b r a t io n a l
s ta te a n d th e 01*0 sta te .
C a z z o li 20 h a s r e c e n tly o b ta in e d m e a s u re m e n ts
o f the 01 x0, 100, a n d 001 v ib r a t io n a l states fo r H C O + f o r th e J= 1—
*2 a n d
J=2-»3 f r e q u e n c ie s , a n d he has r e p o r te d o b s e rv a tio n s o f th e 001 a n d 01 x0
s a te llite s f o r DCO+.
G u d e m a n ’s 8 w o r k w as n o te w o r th y f o r b e in g th e f ir s t d e te r m i n a ti o n
o f th e e q u i l i b r i u m s t r u c t u r e f o r a m o le c u la r ion. T h e r e was, how e v e r,
a r a t h e r larg e d i s c r e p a n c y b e tw e e n s tr u c tu r e s c a lc u la te d f r o m the th re e
p a ir s o f isotopes. T h e r c o b o n d len g th s v a rie d by a p p r o x i m a t e ly 0.002
Xf r o m
X.
one p a ir to a n o th e r , a n d th e r CH’s v a rie d by a p p r o x im a te ly
O n th e o t h e r h a n d , his a level r CN’s v a rie d by 0.00006
a n d his a level r CH’s v a rie d by 0.000320
X.
Xf o r
0 .0 1
HCN,
T h e o r ig in a l p u rp o se o f o u r
w o rk w as to e x te n d G u d e m a n ’s 8 w o rk to h ig h e r J t r a n s it io n s a n d to H 13 C 18 0 + .
It was h o ped t h a t m o re a c c u r a te Be v a lu e s a n d d a ta on a n o th e r isotope
w o u ld p r o v id e i n s ig h t in to th e p ro b le m o f the H C O + e q u il ib r i u m s tr u c tu r e .
L a te r , it w as r e a liz e d t h a t the a b n o rm a l d isc h a rg e a n d im p ro v e d d e te c to r
271
c o n d itio n s w o u ld resu lt in th e o b s e rv a tio n o f h i g h e r o r d e r sa tellites.
T h e o b s e rv a tio n o f these sa te llite s w o u ld re s u lt in Be’s w ith a h ig h e r
o r d e r t r e a t m e n t o f th e v i b r a t io n - r o t a ti o n in te r a c tio n .
T h e o b s e rv a tio n
o f th e 04°0 s a te llite w o u ld be e s p e c ia lly d e s ir a b le to test G u d e m a n ’s 8
su g g e stio n o f a c c id e n ta l re s o n a n c e b e tw e e n th e 04°0 a n d 100 v i b r a t io n a l
levels.
E X P E R IM E N T A L
T h e s p e c tro m e te r se tu p w as th e sam e as f o r H C N a n d th e h ig h e r
h a r m o n i c lines o f H N C , i.e., we used V a r ia n k ly stro n s to d r iv e th e M illitec h
m u lt ip l ie r to p r o d u c e 3rd, 4 th, a n d 5th h a rm o n ic s , we used th e sam e phase
lock loop, a n d we f i t th e d a ta in th e sam e m an n e r.
T h e sam e d is c h a r g e
cell w as e m p lo y e d as in the e x p e r im e n ts ju s t m e n tio n e d . T h e p r e d o m i n a n t
d i f f e r e n c e w as in the m eans o f p r o d u c in g the sam ple.
F o r v i r t u a ll y all
o f th e w o r k in th is c h a p te r we em p lo y e d f a s t flo w liq u id n itr o g e n cooling
w ith a b o u t
8
m T o rr o f a rg o n a n d 0.2 m T o rr e a ch o f H 2 a n d th e p r o p e r
iso topic f o rm s o f CO a n d a b n o rm a l d isc h a rg e s a r o u n d 1800 V. It was
f o u n d t h a t th e signal o f th e m a i n lin e d id not v a ry s ig n i f ic a n tl y b e tw e e n
0.2 m T o r r a n d 0.5 m T o rr o f r e a c ti v e gases. T h e sig n a l s tr e n g th w as d im in is h e d
a t lo w e r r e a c tiv e gas pressu res a n d a t h ig h e r re a c tiv e gas pressures. T h e
H C O + s ig n a ls te n d e d to in c re a s e lin e a r ly w ith a rg o n p ressu re.
th e d is c h a r g e s te n d e d to be u n s ta b le a b o v e
8
m T o rr.
U n fo rtu n a tely ,
In o r d e r to o b serve
th e 0 2 2 0, J=3->4 tra n s itio n s , it w as n e cessary to em p lo y n o r m a l d isc h a rg e s
w ith 20 m T o r r A rg o n a n d 0.5 m T o r r o f th e r e a c tiv e gases. Since
w as not a v a ila b le , it was nec essa ry to use
lines.
13 C H 4
and
18 0 2
13 C 180
to see th e H 13 C 18 0 +
Work w ith the m ain isotope, h o w e v e r, d e m o n s tr a te d t h a t th is re s u lte d
272
in sig n a l r e d u c t io n o f a b o u t a f a c t o r o f 4 f r o m C O a n d H 2. T h a t a n d
th e f a c t t h a t th e M illite c h m u ltip lie r d id not w o rk as w ell a t th e low er
f re q u e n c ie s se v e re ly lim ite d o u r w o rk on the d o u b ly s u b s ti tu t e d isotopic
species.
As has been m e n tio n e d in e a r l ie r c h a p te rs , d u r i n g the course
o f th is w o rk we d isc o v e re d t h a t s ig n a ls c o u ld be in c r e a s e d by a f a c t o r
o f ten by r u n n i n g th e d e te c to r a t h ig h e r m a g n e tic fie ld s , (9 k G auss f o r
t h ir d h a rm o n ic s o f th e k ly s tro n a n d 11 k G a u ss f o r h ig h e r harm o n ics),
a n d h ig h e r h e liu m p re s s u re (26 T o rr).
Both o f th e 13C isotopom ers w ere
o r ig in a lly o b s e rv e d u n d e r th e i n f e r i o r d e te c to r c o n d itio n s , b u t the H 13 C O +
lines w ere r e e x a m in e d u n d e r th e new c o n d itio n s.
A n a tt e m p t to see H C O +
in slow flo w w as u n s u c c e s s fu l, a n d a n a tt e m p t to see th e ion in f a s t flo w
w ith no i n p u t CO w as suc ce ssfu l, b u t th e g r o u n d s ta te signal was d im in is h e d
by a f a c t o r o f
10,
so no a tte m p ts to observe sa te llite s in this m a n n e r w ere
m ade.
THEORY
T h e r e la ti o n s h ip b e tw e en Beff a n d Bv is th e sam e as fo r H C N ,
a n d we r e f e r th e r e a d e r to C h a p t e r V fo r d e ta ils o f th e th e o ry o f /-type
d o u b lin g a n d /-ty p e reso n a n c e , w h ic h is e sse n tia l to th e e n s u in g analysis.
OBSERVED SPECTRA.
T h e most d r a m a t i c im p a c t o f th e a b n o r m a l d is c h a r g e was on
o u r w o rk w ith H C O +. T h e i n te n s ity o f the g r o u n d s ta te v ib r a tio n a l lines
was a u g m e n te d by a f a c t o r o f
20,
a n d becam e c o m p a r a b le to th e in te n s ity
o f H C N g r o u n d v i b r a t io n a l s ta te lines in a n o r m a l d is c h a r g e a n d c o n s id e r a b ly
g r e a te r t h a n th e i n te n s ity o f H N C g r o u n d sta te v i b r a t io n a l lines (see
F ig u re 1). T h e c o m b in a tio n o f th is a n d o u r im p r o v e d m eth o d o f d e te c to r
273
o p e r a tio n r e s u lte d in r o u ti n e sig n a l to noise o f 500 to 1 on a single scan.
W hat m a d e th is e v e n m ore s a ti s f y i n g w as t h a t th e results w ere o b ta in e d
w ith o n ly 0.2 m T o r r ea ch o f CO a n d H 2, th u s m a k in g o b s e rv a tio n o f
s u b s titu te d iso to p ic f o rm s a v ia b le e x p e rim e n t.
As d r a m a t i c as these e f f e c ts w e re on the g r o u n d state
v i b r a t io n a l lines, th e m ost i m p o r ta n t a sp ec t w as th e ir e n h a n c e m e n t o f
th e v i b r a t io n a l s a te llite in te n sitie s.
It was possible to observe th e 001
a n d 02°0 J=2-*3 a n d J=3-»4 t r a n s it io n s w ith a sig n a l to noise ra tio o f
2 on a single scan.
We h a v e d e te c te d th e 0 1 M, 02 2 0, 03*0, 0330, a n d 04°0
s a te llite s f o r th e f ir s t tim e f o r H C O +, H 13 C O +, a n d H C 18 0 +. In a d d it io n ,
o u r o b s e rv a tio n o f th e J=2-*3 a n d 3-*4 tr a n s itio n s o f th e 002 v i b r a t io n a l
s ta te c o n f i r m e d G u d e m a n ’s 8 te n a t iv e a s sig n m e n t o f th e tra n s itio n a t 88007.9
MHz. T h is c o n c lu sio n w as f u r t h e r b u ttre ss e d by o u r o b s e rv a tio n o f th e
002 v i b r a t io n a l s ta te t r a n s itio n s o f H lsC O + a n d H C 18 0 + . T h e o b se rv e d
f r e q u e n c ie s a r e d isp la y e d in T a b le I, a lo n g w ith G u d e m a n ’s 8 f re q u e n c ie s ,
a n d in T a b le II, th e
D eff’s, Bv’s, D v’s, q v2 / 5 ’s, a n d 5’s c a lc u la te d f r o m
th e m a r e p re s e n te d . G u d e m a n ’s f re q u e n c ie s a re listed, so t h a t th e r e w ill
be a c o m p le te list o f all th e H C O + d a t a o b ta in e d by o u r re se a rc h gro u p .
We d id not, h o w e v e r, in c lu d e this d a t a in o u r a n a ly s is, because his u n c e r t a i n t ie s
w ere a p p r o x i m a t e ly 100 k H z f o r se v e ra l o f th e tra n sitio n s.
T h e reason
his u n c e r t a i n t ie s w e re so la rg e was t h a t he was u sing a n o rm a l d is c h a rg e ,
a n d his signal to noise r a tio w as c o n s id e r a b ly p o o re r th a n ours.
F u r th e r m o r e ,
th is re q u ir e s g r e a t e r c o n s u m p tio n o f e x p e n siv e r a r e isotopes a n d th u s
th e m e a s u r e m e n ts c o u ld not be r e p e a te d too m a n y times. We o b ta in e d
Beff a n d D eff f r o m a least s q u a re s f i t f o r th e th e g r o u n d states
274
F ig u re 1-The J»2-»3 a n d J=*3-*4 tra n s itio n s o f th e g ro u n d v i b r a t io n a l
sta te s o f H N C , H C O + , a n d H C N a re c o m p a red . T h e
a re as fo llo w s f o r H N C a n d HCN:
6
e x p e r im e n ta l c o n d itio n s
scans, 15 s e c /s c a n , 20 m T o rr a rg o n ,
5 m T o r r N 2, 5 m T o rr C H 4, 300 m A n orm al d isc h a rg e , f a s t flow , 2400
k H z FM , 30 k H z AM, a n d 1 baseline s u p p re ssio n (600 kHz), no sm o o th in g ,
l i q u i d n itr o g e n cooling, a n d InSb d e te c to r (5 k G a u ss f ie ld a n d 10 T o r r
He p ressure).
8
F o r H C O +, the c o n d itio n s are as follows:
8
scans, 15 se c /sc a n ,
m T o r r a rg o n , 0.2 m T o rr CO a n d H 2, 1800 volt a b n o rm a l d isc h a rg e ,
f a s t f lo w , l iq u id n itr o g e n cooling, 250 G auss d is c h a r g e fie ld , 2400 kH z
FM , 30 k H z AM, 1 b a seline su ppression (600 kH z), no sm o o th in g , a n d
InSb d e te c to r (5 k G au ss f ie ld a n d 10 T o rr He pressure).
HCO+ and HCN
a re on the sam e scale, th e H N C scale ha s been m u ltip le d 50 tim es.
Please
n o te th e 600 k H z b a selin e su ppression is the p r o p e r one fo r the 4 th h a rm o n ic
o f th e k ly s tr o n , a n d t h e r e f o r e , th e J=2-*3 tr a n s it io n s w ill be a p p e a r d isto rte d .
275
HCO\HCN, and HNC 0 0 0 IB 6 0 0 kHz
276
T a b le I. O bserved H C O + F req u en cies (M H z ).8
V
J
000
1
000
3
4
5
000
000
hc
18 o +
H C O+
H 13 CO+
89188.541b
267557.616
356734.304
445903.060
86754.279b
260255.360
346998.316
433733.710
85162.222b
255479.412
340630.688
425774.685
H 13C 180 +
82666.776b
247993.419
330649.488
100
1
100
3
4
88480.748b
265434.234
353903.444
86095.985b
258280.509
344365.262
84489.022b
253461.372
337940.412
3
4
5
3
4
5
267418.552
356548.676
445670.715
268688.874
358242.392
447787.635
260089.026
346776.440
433456.340
261301.968
348393.700
435477.655
255367.245
340481.024
247855.020
330465.180
256528.169
342028.775
248959.422
331937.484
001
1
001
3
4
88599.475b
265790.166
354377.576
86183.517b
258542.790
344715.092
84609.789b
253822.008
338420.908
85489.022b
256451.961
341918.344
427369.480
100
0 1 lc 0
0 1 lc 0
0 1 lc 0
0 1 ld 0
0 1 ld 0
0 1 ld 0
001
02°0
1
02°0
3
4
5
89535.625b
268589.232
358098.516
447590.215
87063.788b
261174.795
348213.912
433645.705
4
5
4
5
357996.104
447479.510
358019.104
447524.950
348112.644
435126.065
348133.844
435168.780
3
4
3
4
265568.730
354082.112
266908.524
355868.632
258320.112
344417.788
259576.869
346093.860
253660.072
338204.432
254861.394
339806.552
002
1
002
002
3
4
88007.936b
264015.465
352011.520
256823.160
342422.068
253660.059
338204.540
0 3 lc0
03lc0
0 3 lc0
0 3 ld0
0 3 ld0
3
4
5
3
4
267798.585
357051.000
446291.590
270396.936
360515.016
260386.749
347169.136
255742.647
340978.040
262868.034
350477.096
258115.332
344141.384
02°0
02°0
0 2 2c0
0 2 2c0
0 2 2d0
0 2 2d0
01 lc l
01 lc l
01 ld l
0 1 ld l
427264.160
427300.520
277
0 3ld0
5
450620.710
0330
0330
4
5
358537.860
448163.455
348583.336
435720.480
342334.552
427909.340
04°0
04°0
3
4
269625.738
359456.338
262100.334
349425.192
257427.210
343199.500
a F o r e r r o r e stim ates see text.
b G u d e m a n ’s 8 fre q u e n c ie s.
278
T a b le II. H C O + Bv’s, Dy’S, B(jf s, a n d Deff’s.
V
HCO+
H 13C 0 +
hc
18o +
000
000
Dv
44594.416a-b*c
82.00d
43377.308
78.64
42581.270
76.04
100
100
Bv
Dv
44240.464
79.27
43048.158
78.12
42244.862
74.23
01*0
01*0
01*0
01*0
01*0
01*0
0^0
ByC
Dy
Qv
Befl(c)
D.ff(c)
B.fl(d)
D.«(d)
44676.970
84.43
211.727
44571.271
83.98
44783.008
84.88
43450.524
79.68
202.156
43349.596
79.27
43551.772
80.09
42659.160
76.59
193.438
42562.595
77.11
42756.031
76.07
001
001
By
Dy
44299.857
83.14
43091.852
77.03
42305.024
75.32
02°0
02°0
02°0
02°0
ByC
Dy
B«ff
D .ff
44767.973
88.17
44768.163
182.83
43532.032
81.79
43532.210
170.96
42744.678
81.93
42744.830
157.68
0 220
0 220
0220
0220
0220
02 20
0220
0220
By
Dy
44751.636
87.77
44752.289
86.78
44752.197
-5.94
94.66
16.159
43516.023
81.06
43516.700
81.86
43516.468
-8.19
89.17
15.641
42729.841
81.43"
42730.488
81.43
42730.336
5.68
75.75
16.845
o o o o o o o
By
Dy
Qv
B#£f(c)
D efl(c)
B.«(d)
D efl(d)
43374.456
84.49
223.281
44262.986
85.07
44486.265
83.92
42969.218
78.89
209.391
43054.803
80.60
43264.203
77.19
42378.044
78.61
200.176
42278.116
80.07
42478.287
77.14
By
Dv
44004.040
81.25
42805.276
78.67
42278.102
79.21
002
002
By
B.«(c)
D«a(c)
Befl(d)
Def^d)
Qy / 5
5 *
h
13c 18o +
41333.587
75.04
41402.389
74.07
184.099
41310.486
73.03
41494.589
75.11
03*0
03*0
03x0
03x0
03 x0
03 x0
03*0
By
Dv
Qy
Bef|(c)g
De«(c)
Be«(d)
D ,«(d)
44851.409
88.74
216.565
44635.312
123.04
45068.443
127.07
43606.274
85.49
206.807
43399.912
117.82
43813.527
121.57
42823.077
80.55
197.742
42625.728
108.53
43021.213
110.64
0330
0330
0330
0330
By
Dv
Beff
44817.558
85.58
44818.809
49.28
43573.250
82.48
43574.462
48.28
'42792.217
78.20
42793.392
49.17
04°0
04°0
04°0
04°0
By
Dvh
Beff
44944.204
101.66
44944.798
398.62
43689.556
94.44
43690.126
374.29
42909.971
91.02
42910.446
328.39
D.ff
a E r r o r e stim ates a re p ro v id e d in tex t f o r th e Bv’s.
b B’s a re in MHz.
c Be{r a n d D eff f r o m least squares.
d D’s a re in kHz.
e We w ere u n a b le to observe th e J=3-»4 tra n sitio n s. We
m ake th e a ssu m p tio n th a t Dv is the sam e as fo r the 02°0
state.
fThe q u a n t i t y qv2/5 is in kHz. These were c a lc u la te d
fro m th e J - 4 —5 lines.
* 5 is in c m -1. qv f o r 0220
o b ta in e d by in te rp o la tio n o f q v o f 01*0
a n d 03s0.
h T h e q u a n ti ty , 5, is assum ed to have the sam e value as f o r th e 0220.
280
(ex c e p t H 13C 180 +) a n d f o r the sa te llite s f o r w h ic h we h a d th r e e tra n s itio n s .
U n lik e H C N a n d H N C , we did not h a v e p ro b le m s w ith b le n d in g or i n t e r f e r i n g
lines ( w ith th e possible e x c e p tio n o f o u r se a rc h f o r th e 11X0 satellite).
We w e re u n a b le to observe the J=3-*4 t r a n s it io n s o f th e 0220 sta te o f
H C 180 + a n d w e re f o rc e d to assum e t h a t its D v w as th e sam e as t h a t f o r
th e 02°0. B ecause we w e re a ble to observe th e J = 4 —5 tr a n s itio n s , we
d id o b t a i n q v2/$ f r o m th e J=4-*5 f re q u e n c ie s by use o f th e e q u a tio n ,
HO22d0) - v(022c0)
q */ 8 ----------------------
.
(i)
4 ( J '3- J ' )
T h is e q u a ti o n w as o b ta in e d by c o m b in in g th e f o r m u la s in C h a p t e r V
f o r Beff a n d D efr in term s o f Bv an d D v, a n d a s su m in g th e e q u a li ty o f
Bv(022c0) a n d Bv(022d0) a n d the e q u a lity o f Dv(022c0) a n d D v(022d0). F or
f u r t h e r d e ta ils th e r e a d e r is r e f e rr e d to C h a p t e r V. A tte m p ts to observe
th e 200, 101, a n d 1110 s a te llite s w ere unsu c ce ssfu l.
Because o f th e pro b le m s
m e n tio n e d in th e E x p e r im e n ta l section, we w e re only a ble to o b serve
th e g ro u n d v i b r a t io n a l sta te a n d th e 01 x0 v i b r a t io n a l sta te o f H 13C 180 + .
We d id o b serve c a n d id a te s f o r the l l ld0 s a te llite o f the m a in isotopic
species a t 266637.66 M Hz a n d 355509.92 MHz, a n d possible J= 3 —4 lines
f o r th e 11 lc0 a t 353710.16 MHz an d 353728.16 MHz.
No lines, h o w e v e r,
w ere seen a t the J=2-*3 fre q u e n c y .
E F F E C T IV E C E N T R F IG U A L D IS T O R T IO N C O N S T A N T S
A n in te r e s tin g a sp ec t o f this w ork was th e s im ila r ity b e tw e en H C O +
a n d H C N in e f f e c ti v e c e n tr if u g a l d is to r tio n p a tt e r n s , a n d th e c o n tr a s t
b e tw e e n these tw o a n d HN C. F or v ib r a tio n a l s ta te s w ith n o rm a l c e n tr if u g a l
281
d is t o r ti o n , t h e r e is little to choose f r o m b e tw e e n th e three, a lt h o u g h H N C
has a s lig h tly la r g e r c e n tr if u g a l d i s to r tio n c o n s ta n t.
T h is c a n be o b s e rv e d
in F i g u r e 1. B ecause q v2/ 5 is a p p r o x im a te ly 100 k H z fo r H C N (see C h a p t e r
V, T a b le III) a n d H C O + a n d 375 kH z (see C h a p t e r VI, T a b le III) f o r
H N C , m a tte r s a r e c o n s id e r a b ly d i f f e r e n t f o r such satellites as th e 02°0
a n d th e 0220. F o r H N C th e J=2-»3 a n d 3-*4 t r a n s itio n s a re 13 M H z a p a r t
a t th e k ly s tr o n f r e q u e n c y , a n d we h a v e no scan w ith both lines, since
o u r u s u a l s c a n n in g ra n g e was 15 M Hz a t th e k ly s tro n fre q u e n c y .
The
s im i la r i t y o f H C N a n d H C O + a r e sh o w n in F ig u re 2, w h ic h is a p lo t
a t th e k ly s tr o n f r e q u e n c y sh o w in g the J=2-»3 a n d J= 3 —4 tr a n s it io n s o f
th e 02°0 state. T h e H N C 022d0 lines h a d a s u b s ta n tia l n e g a tiv e e f f e c t i v e
c e n t r i f u g a l d i s to r tio n , a n d it w as not possible to see both H N C 0 2 20 lines
f o r a single h a rm o n ic o f th e k ly stro n on th e sam e scan.
F ig u re 3 show s
th e H C O + J=3-»4 a n d J=4-»5 0220 t ra n s itio n s , a n d F ig u re 4 show s th e
c o rr e s p o n d in g tr a n s itio n s f o r H C N . T h e r e a d e r c a n note th a t f o r b o th
m olecules th e low er 0 2 2c0 sta te has a n o rm a l c e n tr if u g a l d i s t o r ti o n c o n s ta n t
a n d th e u p p e r 022d0 has an e f f e c ti v e c e n tr if u g a l d is to r tio n c o n s ta n t o f
n e a r l y zero. T a b le III is a d isp la y o f e f f e c ti v e c e n tr if u g a l d is t o r ti o n
c o n s ta n ts f o r H C O +, H C N , a n d HN C.
F o r all th e v i b r a tio n a l levels w ith
u n u s u a l c e n t r i f u g a l d is to r tio n , the d i f f e r e n c e b e tw e e n D eff a n d D v is
r o u g h ly c o m p a r a b le f o r H C O + a n d H C N , a n d c o n s id e r a b ly g r e a t e r f o r
HN C.
RELATIVE VIBRATIONAL INTENSITIES
A m a jo r c o n c e rn o f G u d e m a n ’s8 w h e n r e p o r tin g
th e o b s e rv a tio n o f the 002 J = 0 —*■1 r o ta tio n a l tr a n s it io n was t h a t it w as
282
F ig u re 2- F o r H C N a n d H C O + th e e f f e c ti v e c e n tr if u g a l d is t o r ti o n c o n s ta n ts
o f th e 02°0 s a te llite a r e q u ite c o m p a ra b le , as c a n be seen in this fig u re .
E x p e r im e n t a l c o n d itio n s a re the sam e as in F ig u re 1, e x c ep t t h a t th e
d e te c to r is a t 9 k G a u ss f ie ld a n d 26 T o r r He pressure. T h e s p e c tr a r e q u i r e d
18 sc an s f o r th e H C O + a n d 20 scans f o r th e H C N .
283
HCO+ and HCN 02°0 2B 6 0 0 kHz
J=3-4
HCN
J= 2 -3
J=3-4
HCO
284
F ig u re 3 -H e re we show th e J=3-*4 (lo w er tra c e ) a n d J = 4 —5 tr a n s it io n s
( u p p e r tra c e ) o f H C O + in a n o r m a l disc h a rg e.
T h e 022c J=4-*5 is a p p r o x im a te ly
4 M H z lo w e r in k ly s tr o n f r e q u e n c y th a n th e 022c J=3-»4, m e a n in g t h a t
it ha s a n o r m a l c e n t r i f u g a l d i s t o r ti o n c o n sta n t. O n th e o t h e r h a n d , the
J=3-*4 a n d J=4-*5 0 2 2d0 t r a n s it io n s o c c u r a t n e a rly th e sam e k ly s tro n
f r e q u e n c y , m e a n in g a n e a r ly z e ro e f f e c ti v e c e n t r i f u g a l d i s t o r ti o n c o n s ta n t.
E x p e r im e n t a l c o n d itio n s c o m m o n to b o th tra c e s a re as follow s: 15 s e c /s c a n ,
20 m T o r r a rg o n , 0.5 m T o rr H 2, 0.5 m T o rr CO, 300 mA n o r m a l d is c h a rg e ,
2400 k H z FM, 30 k H z AM, a n d 3 b a selin e su p pressions, f a s t flo w , 31
p o in t s m o o th in g , l iq u id n itr o g e n cooling, a n d InSb d e te c to r (8 k G a u ss
f i e l d a n d 26 T o r r He p ressure). T h e d i f f e r e n c e s a re th a t we h a v e a v e ra g e d
295 scans a n d used b a selin e su p p re ssio n s o f 600 kH z f o r th e J = 3 —4 a n d
a v e r a g e d 265 scans a n d used b a s e lin e su p p re ssio n s o f 480 k H z f o r th e
J=4-*5.
Also, we h a v e m u ltp lie d the J = 4 —5 tra c e by a f a c t o r o f fiv e .
HCO + 0 2 20 NORMAL DISCHARGE
SCALE 5X
J=4-5
J=3-4
89495
89505
KLYSTRON FREQUENCY (MHz)
286
F ig u re 4 -T h e e f f e c t i v e c e n t r i f u g a l d i s to r tio n c o n s ta n ts a r e s im ila r f o r
H C O + a n d H C N , as c a n be seen in this d is p la y o f the J = 3 —4 a n d J=4-»5
tr a n s itio n s o f th e 0 2 20 s ta te o f HC N . T h e e x p e r i m e n t a l c o n d itio n s c om m on
to b o th tra c e s in th is f i g u r e a re 15 s e c /s c a n , 20 m T o rr a rg o n , 5 m T o rr
N 2, 5 m T o rr C H 4, 300 m A n o rm a l d isc h a rg e , 2400 k H z FM, 30 k H z AM,
a n d 2 b a s e lin e su p p re ssio n s, f a s t flow , no s m o o th in g , l iq u id n itr o g e n
c ooling, a n d InSb d e te c to r (8 k G a u ss f ie ld a n d 26 T o r r He pressure).
T h e d i f f e r e n c e s a re t h a t we h a v e a v e ra g e d 40 scans a n d used b a selin e
su p p re ssio n s o f
600 k H z f o r th e J=3-*4 a n d a v e ra g e d 65 scans a n d used
b a seline su p p re s s io n s o f 480 k H z f o r the J = 4 —5. Also, we h a v e m u ltp lie d
th e J=4-»5 tra c e
by a f a c t o r o f five.
HCN 0220 2B
J=4-5
J=3-4
89030
89035
89040
FREQUENCY(MHz)
288
Table III. E ffectiv e C entrifugal D istortion C onstants (kH z).
H C O+
HCN
HNC
000
82.00
87.26
99.72
02°0
182.68
206.28
480.89
022c0
87.77
91.75
101.00
022d0
-5.94
-23.92
-266.88
0 3lc0
123.04
134.29
228.75
03ld0
127.07
141.39
247.64
038d0
49.28
49.97
04°0
398.62
460.04
V
289
o n ly d o w n by a f a c t o r o f 4 f r o m th e 001 s a te llite , w h ile th e 001 s a te llite
w as d o w n by a f a c t o r o f 25 f r o m th e g r o u n d v i b r a t io n a l state. In o u r
a b n o r m a l d isc h a rg e s , h o w e v e r, th e v ib r a t io n a l e x c ita tio n follow s a m ore
e x a g g e r a te d p a tt e r n .
T h e 002 v i b r a t io n a l s a te llite is 5 tim es w e a k e r t h a n
th e 001, w h ic h in t u r n is 250 tim es w e a k e r t h a n th e g r o u n d v i b r a t io n a l
state.
R a tio s f o r th e i n te n s ity o f th e g r o u n d v ib r a t io n a l s ta te to those
o f th e s a te llite s a re p r e s e n te d in T a b le IV. O n e no tic e s f ro m th is ta b le
t h a t a c o n s is te n t p a t t e r n em erges f o r th e v 2 ,v s , a n d ^2- l ,s satellites.
T h e f i r s t e x c ita tio n in to e it h e r o f these m odes e n ta ils a large ( e ith e r
50 or 250) d r o p o f f in signal, b u t s u b s e q u e n t e x c ita tio n s result in only
f i v e f o l d re d u c tio n .
F ro m G u d e m a n ’s8 results f o r th e 002 it a p p e a rs t h a t
th e r e is a s im ila r r e d u c t io n o f 5 in i n te n s ity u p o n s e c o n d a ry e x c ita tio n
o f th e v3 m ode f o r s a te llite s in th e n o rm a l d isc h a rg e . I f such a p a tt e r n
oc c u rs, th e r e is little p r o f i t in lo o k in g f o r sa te llite s in the n o rm a l d isc h a rg e .
While th e i n te n s ity o f th e 02°0 a n d 001 v i b r a t io n a l sa te llite s a re w e a k e r
w ith re s p e c t to th e m a in line, th e f a c t o r o f 20 in cre ase o f the m ain lin e
sig n a l in going to th e a b n o r m a l d is c h a r g e m ore t h a n overcom es this.
S u b s e q u e n t sig n a ls all d r o p o f f by th e sam e f a c t o r o f 4 or 5 per in c r e m e n t
o f v, so th e sig n a l s tr e n g th s a r e a lw a y s g r e a t e r in th e a b n o rm a l d isc h a rg e .
Since we w ere u n a b le to obse rv e th e 200, 1110, a n d 101 sa tellites, it seem s
lik e ly t h a t th e sig n a l s tr e n g th s a re d i m in is h e d by a f a c t o r g r e a te r th a n
5 f o r sa te llite s s e c o n d a r ily e x c ite d in th e v x m ode.
It is th u s possible
t h a t th e n o r m a l d is c h a r g e w o u ld o f f e r th e best c h a n c e o f o b s e rv in g them .
O u r f a i l u r e s to o b serve th e 101 a n d 11*0 r o ta tio n a l tra n s itio n s a re e s p e c ia lly
in te r e s t in g in th is re g a rd . T h e 002 a n d 0 1 11 s a te llite s w ere 1250 tim es
T a b le IV . R e la tiv e I n te n s itie s o f H C O + S a te llite s .
I 0 / I v(A b n o rm a l)
V
100
1000
01*0
50
250
001
01
ll
I 0 / I v(Nor
114
25
1250
02°0
250
28
0 2 20
2750b
84c
002
1250
92
03*0
1250
0330
3750b
04°0
6000
a R e fe re n c e
8.
b O nly tru e f o r th e J=4-*5 tra n s itio n .
c C o m b in in g o u r 0 2 °0 /0 2 20 ra tio w ith G u d e m a n ’s8 000/02°0 ratio.
291
F ig u re 5 -T h e w e a k e s t n o n - p e r tu rb e d s a te llite w as in th e 04°0 v i b r a t io n a l
sta te .
E x p e r im e n t a l c o n d itio n s a re as follows:
cooling, 0.2 m T o rr H 2 a n d CO,
8
f a s t flo w , l iq u i d n itro g e n ,
m T o rr a rg o n , 1900 volt a b n o rm a l d isc h a rg e ,
250 G a u ss d is c h a r g e m a g n e tic fie ld , 2400 kH z FM, 30 k H z AM, 2 b a selin e
s u p p re s s io n s (800 kH z), 21 p o in t sm ooth, 139 scans, a n d InSb d e te c to r
(9 k G a u ss f ie ld a n d 26 T o r r He pressure).
292
HCO+ v = 0 4 °0 J = 2 - 3
269610
269630
FREQUENCY (MHz)
293
w e a k e r t h a n th e m ain line, a n d th e 100 tr a n s it io n w as 4 tim es w e a k e r
t h a n th e 001. T h e r e f o r e , if th e v x in te n s itie s w ere c o n s is te n t w ith all
th e o th e rs , th e
11*0
and
101
w e a k e r th a n th e m ain line.
sa te llite s sh o u ld h a v e been o n ly 6000 tim es
We w ere a ble to see th e 04°0, J=2-»3 t r a n s itio n ,
w h ic h w a s 6000 tim es w e a k e r th a n th e m ain line, w ith a sig n a l to noise
o f a p p r o x i m a t e ly 10 (see F ig u re 5). In a d d it io n , if 16 f o ld r e d u c tio n
is a ssu m e d f o r th e
200
sa te llite w ith respect to the
002
s a te llite , it should
h a v e b e e n observable.
STARK EFFECT
T h e p o ssib ility o f S ta rk p e r t u r b a t io n o f H C O + was raise d by C a z z o li20,
w h o o b s e rv e d p e r t u r b a t io n o f th e 01 x0 tra n s itio n s .
H is e f f e c t i v e c e n tr if u g a l
d i s t o r ti o n c o n s ta n ts w ere 78 k H z a n d 93 kH z, re s p e c tiv e ly , fo r th e 01 lc0
a n d 0 1 ld s ta te s f r o m th e J= 1—►2 a n d J=2-»3 t r a n s it io n s . 20 A t th e tim e
we s t a r t e d th e H C O + we d id not h a v e a f r e q u e n c y d o u b le r. T h e r e f o r e ,
it w as im possible f o r us to observe th e J = l —2 tr a n s itio n .
O u r f ir s t e v id e n c e
o f S ta r k p e r t u r b a t io n in v o lv e d the 0220 a n d 0 3 30 sta te s, w h ic h w e re m ore
m ore p e r t u r b e d in H C O + th a n in HC N .
It w as n e v e r possible to observe
th e J=2-»3 t r a n s itio n s o f th e 02 20, in e ith e r n o rm a l or a b n o rm a l d ischarges.
As m e n tio n e d e a rlie r, a line, the 04°0 sa te llite , a b o u t 25 tim es w e a k e r
th a n th e
o f ten.
02°0
r o ta tio n a l tr a n s it io n , was obse rv e d w ith a sig n a l to noise
A rea so n a b le u p p e r lim it f o r the 0220 s a te llite i n te n s ity is th u s
a b o u t 1/80 o f the 02°0 in te n s ity .
We also f o u n d it im possible to observe
th e J=3-»4 tr a n s it io n in th e a b n o rm a l d isc h a rg e , b u t w ere a b le to obse rv e
it in a n o r m a l d ischarge.
Its in te n s ity was, h o w e v e r, d o w n by a f a c t o r
o f 7.5 f r o m the 02°0 in te n s ity .
C o m p a riso n s b e tw e e n th e 02°0 a n d 0220
294
a n d b e tw e e n t h e 0 3 ^ a n d 03s0 a re p re s e n te d in T a b le V, alo n g w ith th e
c o rr e s p o n d in g H C N i n te n s it y ratios. F ig u re s 6-9 a r e c o m p a riso n s b e tw e e n
th e n o n p e r t u r b e d sa te llite s a n d th e p e r tu r b e d s a te llite s in n o rm a l a n d
a b n o r m a l d isc h a rg e s .
As m e n tio n e d in C h a p t e r V, W. T. C o n n e r 21 has
m a d e m o re e x te n s iv e m e a s u re m e n ts o f the S ta rk e f f e c t a n d has p roposed
a m odel b a sed on th e H o lts m a rk field.
L a te r , w h e n a C u sto m M ic ro w a v e d o u b le r w as a v a ila b le , th e J = l- » 2
tr a n s it io n o f th e 0 1 vi br a t i ona l s ta te was sought.
w ith re s p e c t to th e m a in lin e line, a n d over
200
It was se v e re ly b r o a d e n e d
tim es w e a k e r, as show n
in F i g u r e 10. F i g u r e 11, on th e o th e r h a n d , f o r th e J=2-*3 t ra n s itio n ,
show s th e
0 1 x0
v i b r a t i o n a l s a te llite h a v in g the sam e lin e s h a p e as th e g r o u n d
s ta te a n d b e in g o n ly 50 tim es w eaker. T h is e x p e rim e n t s h o u ld be e x te n d e d
to H C N , b u t th e r e w ill be d if f ic u l ti e s . O u r d o u b le r, a t best, puts out
1/3 th e p o w e r o f th e t h i r d h a rm o n ic o f th e M illitec h m u ltip lie r.
In a d d itio n ,
w e lose a f a c t o r o f 3 in th e a b s o rp tio n c o e f f ic i e n t going fro m a J = 2 —3
t r a n s it io n to a J = l- * 2 tra n s itio n .
T h e H C N signals in a n a b n o rm a l d isc h a rg e
a r e c o n s id e r a b l y p o o re r t h a n those f o r HC O+, a n d m o re o v e r, th e q u a d r u p o l e
h y p e r f i n e e f f e c t w ill be a c o m plication.
ERROR AN AL YSI S
T h e H C O + g r o u n d s ta te lines had e x tre m e ly high sig n a l to noise
ra tio s, a n d o u r f i t s f o r th e m w ere q u ite con sisten t, o f te n a g re e in g to
3 k H z f o r i n d e p e n d e n t tria ls. T h e r e has, h o w e v e r, been no a tt e m p t to
c o rr e c t f o r th e D o p p le r s h if t. O u r w ork on K r D + has show n th is to be
a p p r o x i m a t e ly a 25 k H z c o rr e c tio n f o r K r D + in th e a b n o rm a l d isc h a rg e
(see also A p p e n d i x l ) . 22 As m e n tio n e d in C h a p t e r V, both Blake et al , 23
295
T a b le V -H C O + 02°0 vs 0 2 20 and 03*0 vs 0 3 30.
A. N o rm al D ischarge
Av(02°0)
J = 2 —3
J - 3 —4
J=*4—5
0.660
0.664
0.885
1.090
1.291
7.5 (4)»
3 (2.5)*
Av(02 2 0)
I(02°0)/I(02 20)
(13)*
B. A b n o rm a l D ischarge
Av(02°Q)
J-2 -3
J - 3 —4
J-4 -5
0.360
0.394
0.457
Av(0220)
I(02°0)/I(02 20)
1.055
(3)*
10. (2.0)*
Av(03x0)
0.480
0.550
Av(0330)
1.080
0.920
10. (15.)*
3. (2.5)*
a H C N r a tio s in parentheses.
296
F ig u re
6 -The
0220 s a te llite t r a n s itio n s a re q u i te p e r t u r b e d c o m p a r e d to
th e 02°0 tra n s itio n s , as c a n be o b se rv e d in th is s p e c tr u m o f th e J = 3 —4
t r a n s itio n .
E x p e r im e n t a l c o n d itio n s a re as follow s: f a s t flo w , l i q u i d n itro g e n ,
c ooling, 0.5 m T o rr H 2 a n d CO, 20 m T o rr a rg o n , 300 m A n o r m a l d is c h a rg e ,
2400 k H z FM , 30 k H z AM, 3 b a selin e su p p re s s io n s (600 kH z), 21 p o in t
sm ooth, a n d InSb d e te c to r (9 k G au ss f ie ld a n d 26 T o r r He p ressure).
T h e 02°0 s a te llite r e q u i r e d 32 scans, a n d th e 0220 r e q u i r e d 240 scans.
P lease n o te t h a t we h a v e m u ltp lie d th e 022c0 scale by a f a c t o r o f
6
.
HCO* 02°0 vs 02*0 J=3-4 NORMAL DISCHARGE
SCALE 6X
02 0
5MHz
02°0
298
F ig u re 7-E ven the J = 4 —5 t r a n s it io n s o f th e 0220 s ta te a re p e rtu r b e d .
E x p e r im e n ta l c o n d itio n s a re as follow s:
0.2 m T o r r H 2 a n d CO,
8
f a s t flo w , l iq u id n itro g e n , cooling,
m T o rr a rg o n , 1900 volt a b n o r m a l d isc h a rg e ,
250 G auss d is c h a r g e m a g n e tic f ie ld , 2400 k H z FM, 30 k H z AM, 3 b a selin e
su p p re ssio n s (480 k H z), 21 p o in t sm ooth, a n d InSb d e te c to r (9 kG auss
f ie ld a n d 26 T o r r H e pressure). T h e 02°0 s a te llite r e q u i r e d 17 scans,
a n d th e 0220 r e q u i r e d 271 scans. T h e b a r re p re s e n ts 10 M H z a c tu a l f re q u e n c y .
In th is c o m p a ris o n o f sp e c tra , we h a v e m u ltip lie d th e scale o f th e 0220
s p e c tr u m by a f a c t o r o f
10.
299
HCO+ 0 2 °0 vs 0 2 20 J = 4 -5 ABNORMAL
SCALE 10X
10 MHz
300
F ig u re
8
-T h e J®3-*4 t r a n s it io n s o f th e 0 3 ^ v ib r a tio n a l sta te a r e c o m p a re d
to th e J=3-*4 t r a n s it io n s o f th e 0 3 x0 v i b r a t io n a l state, w ith th e fo llo w in g
e x p e r i m e n t a l c o n d itio n s :
H 2 a n d CO,
8
f a s t flo w , liq u id n itro g e n cooling, 0.2 m T o rr
m T o r r a rg o n , 1900 volt a b n o rm a l d isc h a rg e , 250 G a u ss
d is c h a r g e m a g n e tic f ie ld , 2400 kH z FM, 30 kH z AM, 3 b a selin e supp re ssio n s
(600 kH z), 21 p o in t sm ooth, a n d InSb d e te c to r (9 k G a u ss f ie ld a n d 26
T o r r H e pressure). T h e 0 3 x0 s a te llite r e q u i r e d 36 scans, a n d th e 0 2 20
r e q u i r e d 185 scans. T h e b a r re p re s e n ts 5 M Hz a c tu a l f re q u e n c y .
scale o f th e 03s0 h a s been m u ltip le d by a f a c t o r o f 10.
The
301
HCO* 0 ^ 0 vs OJ’O J=3-4 ABNORMAL DISCHARGE
SCALE 10X
302
F ig u re 9 -T h e J = 4 —5 t r a n s it io n s o f th e 0330 v i b r a t io n a l sta te a re c o m p a r e d
to th e J=4-*5 tr a n s it io n s o f th e 03*0 v i b r a t io n a l sta te , w ith th e sam e e x p e rim e n ta l
c o n d it io n s as in F i g u r e
kH z.
8,
e x c ep t t h a t th e b a s e lin e su p p re ssio n w as 480
T h e 03*0 lin e r e q u i r e d 113 scans, a n d th e 0330 r e q u i r e d 184 scans.
T h e b a r re p r e s e n ts 5 M Hz a c tu a l f r e q u e n c y .
f o r th is c o m p a r is o n o f s p e ctra.
T h e r e is no scale m u lt ip l ic a t io n
303
HCO* 03*0 vs 03*0 J=4-5 ABNORMAL DISCHARGE
304
F ig u re 10-The J=2->3 t r a n s it io n is a p p r o x i m a t e ly 50 tim es w e a k e r f o r
th e 01*0 v i b r a t i o n a l s ta te t h a n f o r th e g r o u n d v i b r a t io n a l state. It does,
h o w e v e r, h a v e a s im ila r lineshape. T h e
e x p e r i m e n t a l c o n d itio n s a re
f a s t flo w , l iq u id n itr o g e n cooling, 1800 volt a b n o r m a l d is c h a rg e ,
A r, 0.2 m T o rr CO a n d H 2,
1
8
m T o rr
baseline s u p p re s s io n (800 k H z), 2400 k H z
FM , 30 k H z AM, 11 p o in t sm ooth. T h e g r o u n d sta te tr a n s it io n w as o b se rv e d
o n a 50 jav scale a n d r e q u i r e d 12 scans a t 15 se c /sc a n .
T h e 0 1 x0 was
d o n e on a 5ju,v scale a n d r e q u i r e d 27 scans. T h e 0 1 x0 scan has been m u ltip lie d
by a f a c t o r o f 40.
305
HCO+ 000 vs 0 1 ^ J = 2 -3 2B 80 0 kHz
SCALE 40X
3MHz
306
F ig u re 11-T he J=1 —2 tr a n s it io n o f the 01*0 s ta te is c o n s id e r a b ly m ore
S ta rk p e r t u r b e d r e la tiv e to th e g ro u n d v i b r a t io n a l s ta te t h a n th e J - 2 —3
t r a n s it io n o f th e 01*0 state. T h e u p p e r c u rv e in this f ig u r e is th e 01*0
s p e c tru m , w h ic h has been m a g n if ie d 200 times. T h e e x p e r i m e n t a l c o n d itio n s
a re th e sam e as in F ig u re 10, e x c e p t t h a t we h a v e used 2 b a s e lin e supp re ssio n s
o f 1200 kH z. T h e g ro u n d s ta te lin e r e q u i r e d 10 scans, a n d th e 01 *0 s a te llite
r e q u i r e d 80 scans.
307
HCO+ 0 0 0 vs 0 1 l 0 J = l- 2
SCALE 200X
2B 1 2 0 0 kHz
308
a n d w e 22 o b s e rv e d re v e rs e D o p p le r s h ifts, in H O C + a n d K.rD+ resp e c tiv e ly .
T h e r e p r o b a b ly is a sm all rev erse D o p p le r s h if t in o u r d isc h a rg e f o r H C O +,
b u t u n t i l f u r t h e r te s tin g is done, we c a n not be c e rta in .
F o r th is reason,
we w ill assign e r r o r b a rs o f 30 kH z, 40 kH z, a n d 50 k H z to th e g ro u n d
sta te J=2-*3, J=3-»4, a n d J = 4 —5 tra n s itio n s .
We also assign these e rr o r
b a rs to th e 02°0 v i b r a t io n a l s ta te tra n s itio n .
T h e r e w as m ore s c a tte r in
th e d a ta , b u t we h a d se v era l tim es the n u m b e r o f tria ls fo r this s a te llite
as f o r a n y o th e r, b o th b ecause we could c o n s is te n tly o b ta in sig n a l to
noise o f tw o on a single scan, a n d because th e f r e q u e n c y w as close to
th e 0220 a n d 0330 v i b r a t io n a l sa te llite fre q u e n c ie s .
T hese f a c to r s m ade
it a u s e fu l lin e to use f o r tu n in g up the s p e c tro m e te r, a n d re s u lte d in
a la rg e n u m b e r o f m ea su rem e n ts.
F or the 100 a n d 001 satellites, th e re
w e re a t least tw o tria ls fo r each h a rm o n ic .
F or the J=2-*3 a n d J=3-»4
th e r e w e re a p p r o x i m a t e ly 40 a n d 60 kH z d i f f e r e n c e s b e tw een tria ls, a n d
it is f e l t t h a t 50 k H z a n d 70 k H z a re re a s o n a b le u n c e r t a i n t ie s f o r the
J=2-*3 a n d 3-»4 tra n s itio n s .
F or the 002, 03*0, a n d 04°0 s a te llite s th e re
w e re tw o tria ls f o r e a c h h a rm o n ic .
While the sig n a l to noise r a tio was
less, th e r e was n o t n o tic e a b ly lesser c o n sistency b e tw e e n th e fits, a n d
it seem s r e a s o n a b le to a p p ly th e sam e e r r o r b ars to these tra n s itio n s .
T h e 01*0 f i t s w ere m ore c o n s is te n t, a g re e in g to 30 kH z, 50 kH z, a n d 90
k H z f o r th e J=2-*3, J = 3 —4, a n d J = 4 —5 tra n s itio n s , resp e c tiv e ly . T h e
J=2-»3 lines, h o w e v e r, a r e s o m e w h a t S ta rk p e r t u r b e d (see F ig u re s 10 a n d
11). We w ill t h e r e f o r e assign u n c e r t a i n t y e stim a tes o f 50, 70 , a n d 90
k H z to th e J= 2 —3, J=3-*4, a n d J = 4 —5 tr a n s itio n s , respectively. T h e 0 1 X1
s a te llite s g a v e as c o n s is te n t f r e q u e n c ie s as th e 002, 03*0, a n d 04°0 states.
309
T h e y w e re , h o w e v e r , as S ta r k p e r t u r b e d as th e 01 x0, a n d we shall assign
u n c e r t a i n t i e s o f 70 a n d 90 k H z to th e J=2-»3
a n d J=3-*4 tr a n s itio n s ,
re s p e c tiv e ly .
E s tim a tio n o f th e u n c e r t a i n t y o f th e 0220 a n d 0330 f re q u e n c ie s
is a m u c h m o re d i f f i c u l t task , be c au se these s a te llite s a r e v e ry stro n g ly
S ta rk p e r t u r b e d . T h e d i s c r e p a n c y b e tw e e n th e tria ls w as s o m e w h a t worse
(96 k H z f o r th e J=3-*4 a n d 135 k H z f o r th e J=4-»5), a n d we assign e rr o r
b a rs o f 90 k H z a n d 120 kHz.
F o r H 13 C O + , we w ere a b le to o b ta in only
one t r i a l f o r th e J= 3 —4 0 2 20 tra n s itio n s , a n d f o r H C O + we o b ta in e d tw o
tria ls. T h e r e w e re 80 kH z a n d 180 k H z d i f f e r e n c e s b e tw e e n th e results
o f th e tw o tria ls f o r th e 022c0 a n d 0 2 2d0 t ra n s itio n s , re s p e c tiv e ly .
o f th e p ro b le m in o b t a i n in g a c o n s is te n t f r e q u e n c y f o r th e
0 2 2d0
Part
state
is t h a t its e f f e c t i v e c e n tr if u g a l d i s to r tio n c o n s ta n t, giv en by th e e q u a tio n
(see C h a p t e r V)
D eff (02 2d0) = D v - q v2 /5 ,
(2)
is n e a r ly ze ro f o r H C O +. T h is m ea n s t h a t the J=4-*5 tr a n s it io n w ill a p p e a r
a t a p p r o x i m a t e ly th e sam e k ly s tr o n f r e q u e n c y as th e J = 3 —4 tra n s itio n
(like H C N ).
T h is is show n g r a p h ic a lly in F ig u re 3, w h ic h is a co m p a riso n
o f th e J=3-»4 a n d J=4-»5 tr a n s itio n s o f th e 0220 v i b r a t io n a l s ta te lines
in a n o r m a l d is c h a rg e . T h e sig n a l to noise is poor f o r th e J=4-*5 tra n s itio n s ,
b u t th e
0 2 2c0
and
0 2 2d0
c o m p o n e n ts a re e q u a l in i n te n s ity a n d line shape.
T h e J=3-*4, 022d0 t r a n s it io n is s o m e w h a t b r o a d e r a n d less in te n se th a n
th e J=3-»4, 0 2 2c0 tr a n s it io n (See T a b le II f o r v a lu e s o f q v2 /5 , D v’s, a n d
310
D eff’s). T h e rea so n f o r th is is t h a t th e c u t o f f f i l t e r t h a t we em p lo y e d
to o b s e rv e th e J=3-*4 t r a n s it io n p e r m i tt e d some r a d i a t i o n f r o m th e f i f t h
h a rm o n ic o f th e k ly s tr o n to pass th ro u g h . T h is m e a n t t h a t we also o b served
th e J=4-*5 tr a n s it io n o f 02 2 d0, w h ic h w as a t n e a r ly th e sam e k ly s tro n
f r e q u e n c y as th e J=3-*4 tra n s itio n . T h e 5th h a rm o n ic c u t o f f f i l t e r w ould
only p e r m i t 5 th a n d
6
th h a rm o n ic s o f th e k ly s tr o n th ro u g h , a n d as m e n tio n e d
in C h a p t e r V, we w e re n e v e r a b le to o b ta in o b s e rv a b le p o w e r f r o m the
six th h a r m o n ic , e v e n w ith a six th h a rm o n ic c u t o f f filte r .
T h e re s u lt
is t h a t th e J=4->5 lines will n o t be a f f e c t e d by th e J= 5 — 6 tra n s itio n .
T h e r e a d e r is r e f e r r e d to C h a p te r V f o r a discussion o f the th e o ry .
Because
o f th e po o r sig n a l to noise, th e S ta rk p e r t u r b a t i o n , the s c a tte r in th e d a ta
w ith m ore t h a n one t r i a l, a n d the pro b le m w ith th e zero e f f e c ti v e c e n tr if u g a l
d i s t o r ti o n c o n s ta n ts, 200 kH z is p r o b a b ly not an u n re a s o n a b le u n c e r t a i n t y
lim it f o r the J=3-»4 tra n s itio n s . T h e s it u a ti o n w as m ore f a v o r a b le f o r
the J=4-*5 tr a n s it io n , because th e re is less S ta rk p e r t u r b a t io n , a n d less
p ro b le m w ith zero e f f e c t i v e c e n tr if u g a l d i s to r tio n c o n s ta n t. T h e r e was,
h o w e v e r, c o n s id e r a b ly less source pow er, th e lines w ere still se verely
p e r t u r b e d , a n d th e D o p p le r s h if t will be g re a te r.
It seems rea s o n a b le
to assign 250 k H z e r r o r b ars to these tra n s itio n s .
E r r o r e s tim a te s o f the Bv’s follow a lo n g th e lines o f C h a p t e r V.
F o r sa te llite s w ith no /-type reso n a n c e , th e u n c e r t a i n t y in Bv is a p p ro x im a te ly
1/2J' th e u n c e r t a i n t y in v. Because we a r e o b se rv in g m ore th a n one state,
th e t r u e u n c e r t a i n t y o f th e Befr w ill be s o m e w h a t less th a n th is a m o u n t.
T h is also holds f o r th e 02°0, 01 *0, a n d 0 1 11 states. It is t h e r e f o r e , rea so n a b le
to assign 5 k H z e r r o r b a rs f o r the g r o u n d sta te Bv’s, a n d
8
k H z f o r the
311
u p p e r s ta te Bv’s. F o r Bv o f th e 0220 sta te s w e assign a n u n c e r t a i n t y o f
30 kHz.
A f u r t h e r e s tim a te o f th e a c c u r a c y o f o u r re s u lts can
be o b t a i n e d by c o m p a r in g o u r resu lts w ith th e lit e r a tu r e .
T a b le VI is
a c o m p a r is o n o f o u r w o rk w ith o th e r m ic ro w a v e d a ta . T h e r e is good
a g re e m e n t f o r th e g r o u n d v ib r a t io n a l s ta te o f th e m a in isotopic species.
Sastry et al .6 o b served f re q u e n c ie s o f 267557.619(010) M H z, 356734.288(050)
MHz, a n d 445902.996(050) M Hz fo r th e J = 2 - 3 , J = 3 - 4 , a n d J=4->5 tra n sitio n s.
These a r e in e x c elle n t a g re e m e n t w ith o u r v a lu e s o f 267557.616(030) MHz,
356734.304(040) MHz, a n d 445903.060(050) M H z f o r th e sa m e tra n s itio n s .
O u r v a lu e o f 255479.412(30) M Hz f o r th e J=2-*3 tr a n s it io n o f H C 18 0 +
is in good a g re e m e n t w ith th e v a lu e o f 255479.389(20) M Hz o b ta in e d
by P lu m m e r et a / . 12 C a z z o lli 20 m e a s u re d a f r e q u e n c y o f 265434.256 MHz
f o r th e J=2-*3 tr a n s it io n o f th e 100 v i b r a t io n a l sta te o f H C O +. T h is
agrees w ell w ith th e 265434.234(50) M Hz v a lu e t h a t we h a v e o b ta in e d .
O u r a g re e m e n t was so m e w h a t p o o re r, b u t still rea so n a b le , f o r the J=2-*3
t r a n s it io n s o f th e 0 1 lc0, 0 1 ld0, a n d 001 states. C a z z o lli 20 o b ta in e d values
o f 267418.644 MHz, 268688.942 MHz, a n d 265790.223 M Hz, in c o n tr a s t
to o u r v a lu e s o f 267418.552(50) M Hz, 268688.874(50) M Hz, a n d 265790.166(50)
MHz.
We o b ta in e d his re s u lts by w a y o f a p r iv a t e c o m m u n ic a tio n , a n d
u n c e r t a i n t y e s tim a tes w ere not p ro v id e d .
o nly 7 k H z o u tsid e o f o u r e r r o r lim its.
H is 001 f r e q u e n c y is, how ever,
A s su m in g his u n c e r t a i n t y is c o m p a ra b le
to o u rs, th e a g re e m e n t is reaso n a b le . T h e d is a g r e e m e n t b e tw e e n o u r w ork
a n d his is s lig h tly la r g e r f o r th e 01 x0 satellites: 90 k H z f o r th e 0 1 lc0,
a n d 70 k H z f o r the 0 1 ld0. I f his u n c e r t a i n t ie s w ere c o m p a r a b le to ours,
312
this w o u ld a c c o u n t f o r th e d if f e r e n c e .
F u r t h e r m o r e , th e r e a d e r sh o u ld
k eep in m in d th a t th e J = l- » 2 t r a n s itio n is s tr o n g ly S ta rk p e r t u r b e d (see
F ig u re s 10 a n d 11) a n d th e J=2-*3 slig h tly p e r t u r b e d .
Thus, d iffe re n c es
in th e c o n d itio n s o f th e d isc h a rg es in the tw o l a b o r a to r ie s w ould cause
d i f f e r e n c e s in m e a s u re d fre q u e n c ie s.
In T a b le V II, we c o m p a re o u r results
f o r B 0 1 i0, q 0 iio» Bioo> an(* B i o l t 0 those f r o m th e IR w o rk , w ith w h ic h
th e y a re in re a s o n a b le a g re e m e n t.
C A L C U L A T IO N O F S P E C T R O S C O P I C P A R A M E T E R S
In T a b le s VIII a n d
IX , the s p e ctro sc o p ic c o n s ta n ts
c a lc u la te d f r o m th e Bv’s a re listed.
F or th e a level Be c a lc u la tio n s we
used th e 000, 100, 02°0, a n d 001 v ib r a tio n a l s ta t e Bv’s. As m e n tio n e d
in C h a p te rs V a n d VI, H e n n ig , K ra e m e r , a n d D i e r c k s e n 24 (H K D ) h a v e
p e r f o r m e d a series o f ab initio c a lc u la tio n s on th e 14-electron m olecules
t h a t we have used to g u id e o u r searches f o r th e
1 0 0 , 0 1 10 , 0 2 ° 0
, and
001
satellites. In T a b le X we h a v e c o m p a re d o u r a ’s a n d q 0 xio’s w ith th e irs,
a n d we h a v e in c lu d e d th e c o rre s p o n d in g H C N iso to p o m er r a t i o in p a re n th ese s.
T h e co n sisten c y o f th e sc alin g fa c to rs f r o m o n e isotopic f o rm to a n o th e r
is q u ite good, e specially f o r th e q values. T h e H C 18 0 + a
2
a n d the
o f th e m a in isotopic species h a v e s lig h tly o u t ly i n g e x p / H K D ratio s.
We
ca n see, how ever, f r o m th e H C N v alues t h a t th e d is c r e p a n c ie s in the
H C O + e x p / H K D a re not c o n s id e ra b ly g r e a t e r t h a n th e H C N ratio s. F o r
all th e 0£7partial level Be c a lc u la tio n s we e m p lo y e d (in a d d i t i o n to th e
Bv’s a lr e a d y used a t th e a level) the 01*0, 0 1 M, a n d 002 v i b r a t io n a l sta te
Bv’s. Because we w ere u n a b le to observe th e 200, 11*0, a n d 101 s a te llite s,
it w as im possible to c o m p le te ly solve e q u a tio n
1
even a t th e a y level
T ab le V I. O ur F requ en cies vs. L iteratu re F requ en cies.
this w ork
lit e r a tu r e
HC O + 000 J - 2 - 3
267557.616(030)
267557.619(010)a
H C O+ 000 J - 3 —4
356734.304(040)
356734.288(050)“
HCO+ 000 J - 4 - 5
445903.060(050)
445902.996(050)“
H C 180 + 000 J - 2 - 3
255479.412(030)
255479.389(020)b
H C O+ 01lc0 J - 2 - 3
267418.552(050)
267418.644c
H C O+ 01ld0 J - 2 - 3
268688.874(050)
268688.942c
HCO+ 100 J - 2 - 3
265434.234(050)
265434.256°
H C O+ 001 J - 2 - 3
265790.166(050)
265790.223°
tra n s itio n
a R e fe re n c e
6.
b R e fe re n c e 12.
c R e fe re n c e 20.
314
T a b le V II. I n f r a r e d B Values vs Microwave B V alues f o r H C O + S a te llite s.
Boio(MHz)
IR a
IR b
IR C
/uwave
44677.5
44677.29
44676.980
44676.970
q 010 (MHz)
211.95
211.383
211.778
211.727
D 010 (kHz)
86.9
84.60
84.43
84.43
D 100 (kHz)
B 100 (MHz)
Dioo(kHz)
a R e f e re n c e 14.
b R e f e re n c e 17.
c R e f e re n c e 19.
d R e f e re n c e 10.
e R e fe re n c e 13.
IR d
/uwave
44240.34
44240.464
80.3
79.27
IR«
juwave
44299.90
44299.857
83.0
83.14
T ab le V III. H C O + R o ta tio n a l C o n sta n ts a L evel.
H C O +a
H 13C O +a
H C lsO +a
B.
44831.884
43607.170
42805.901
a,
353.948
329.154
336.410
a,
-86.779
-77.360
-81.704
294.555
285.460
276.248
H C O +b
H 13 C O +b
H C 180 +b
B.
44831.872
43607.175
42805.813
Oti
353.894
329.147
336.304
a,
-86.773
-77.377
-81.700
a.
294.530
285.381
276.216
T his work.
G u d e m a n ’s d a t a .28
T a b le IX . H C O + R o ta tio n a l C on stan ts ot7partial L evel.
HC O +
Be
ax
a2
a3
7 22
04°0*
03 ^
7 23
44827.376
353.931
-91.074
285.342
-0.304
-7.994
44827.681
353.931
-90.515
285.342
0.001
-7.994
733
~ 0 -6 1 3
"°-613
e 222
7n
0.071
-4.097
0.020
-4.097
43603.874
329.238
-80.516
278.341
-0.301
-5.797
-0.627
0.072
-4.003
43604.045
329.238
-80.202
278.341
-0.130
-5.797
-0.627
0.044
-4.003
42800.862
336.347
-87.706
270.366
-1.543
-4.912
-0.503
0.198
-4.064
42801.082
336.347
-87.301
278.366
-1.323
-4.912
-0.503
0.162
-4.064
.
H 13CO+
Be
ai
Otj
7j2
"^23
7 S3
e 222
7u
hc
18 o +
Be
ai
a2
«»
7 2j
7 23
7 33
6 222
7u
For both sets we used the 000, 100, 01*0, 001, 02°0, 02°0,
01 xl, a n d 002 satellites. F or the results in this c olum n, the 04°0
state was included.
In this case, we used the 03*0 s a te llite an d not the 04°0
satellite.
T a b le X. O bserved vs. H K D a S ca led a and q o i^ V a lu es
HC O+
ai
a 2
a3
Qo^o
ex p /H K D
exp
HKD
353.948
-86.779
294.555
211.727
321
273
196.3
(1.170)b
1.315 (1.140)
1.079 (1.049)
1.079 (1.093)
exp
HKD
ex p /H K D
329.154
-77.360
285.460
202.156
294
-59
265
187.5
exp
HKD
336.410
-81.704
276.248
193.438
301
-6 3
257
179.4
exp
HKD
ex p /H K D
184.099
170.6
1.079 (1.094)
-66
1 .1 0 2
H 13 CO+
«2
«3
Qoi^)
1.120
1.311
1.077
1.078
(1.178)
(1.133)
(1.052)
(1.093)
H C lsO +
«i
a 2
«3
Qo^o
h
ex p /H K D
1.118
1.297
1.074
1.078
(1.171)
(1.127)
(1.050)
(1.094)
13c 18 o +
Qo^o
a R e f e re n c e 24.
b C o r re s p o n d in g HCN isotopom er ratio in parentheses.
318
f o r Be. T h e o b s e rv a tio n o f th e 0 3 x0 a n d 04°0 r o ta t io n a l t r a n s it io n s p e rm itte d
i n d e p e n d e n t d e te r m i n a ti o n s o f e222. As n o te d in C h a p te r V, o u r p ro g ra m
p e r m i tt e d d e t e r m i n a ti o n o f some
7
level a n d / o r € level p a ra m e te rs , i f
a c o m p le te set o f d a t a w as n o t a v a ila b le .
T h is a p p r o x i m a t io n shall be
r e f e r r e d to as th e a 7 p artial a p p ro x im a tio n .
In a d d it io n , we used B 0 Si 0
f o r one set o f oi7partial level Be c a lc u la tio n s , a n d B04 o0 f o r a n o th e r set.
When it is d e s ire d to r e f e r to a s p e c if ic c a lc u la tio n , we shall use th e term s
a 7 partiai(04°0) level a n d a 7 partiai(0310) level. T h e c o e f f ic i e n t s o f th e v i b r a tio n a l
sta te s in Be a re d is p la y e d in T a b le XI. T h e Be v a lu e is slig h tly m ore
d e p e n d e n t on th e
0 1 x0
s ta te t h a n on th e g ro u n d sta te , a n d th e v e ry u n c e r ta in
B 0 2 20 has a larg e c o e f f i c i e n t in b o th cases (1.75 f o r the
a n d 1.25 f o r th e a 7 partia,(04°0)).
We e s tim a te th e u n c e r t a i n t y in Be, u sin g th e sam e m eth o d
as in C h a p t e r V. T h is consists o f e m p lo y in g th e m a tr ix re la tio n s h ip ,
T h e a r r a y a B^2 is th e m a tr ix o f th e s q u a re o f th e u n c e r t a i n t ie s o f the
Bv v alu e, a p
2
is th e a r r a y o f the s q u a re s o f th e u n c e r t a i n t ie s o f th e spectroscopic
p a ra m e te rs , a n d B is th e m a tr ix o b ta in e d by s q u a r i n g all th e ele m en ts
o f A -1. U sing th e u n c e r t a i n t ie s in the Bv’s a n d th is m a tr ix e q u a tio n ,
we o b ta in e rr o r b a rs o f 14 k H z f o r th e a level Be’s a n d 55 k H z f o r the
a 7 partial level Be’s.
P O S S I B I L I T Y O F 100-04°0 R E S O N A N C E
B e fo re c o n s id e r a tio n o f th e e q u il ib r i u m s tr u c tu r e , we s h o u ld deal
T a b le X I. C o e ffic ie n ts o f B v in B e.a
Bv
a
a , p a r t i a l 7(03*0)
a ,p a r t i a l 7(04°0)
000
2.5
5.875
5.250
100
-0.5
01*0
-0.5
-0.5
-6.5
-5.5
001
-0.5
-1.75
-1.75
02°0
-0.5
2.25
1.25
0220
1.75
1.25
OlM
0.375
0.375
002
0.500
0.500
03*0
04°0
-1.00
-0.25
a T hese solve the e q u a tio n Be » ZZ A - 1{i)Bv(i)* T he
A " 1^
a re c a lc u la te d in the m a n n e r e x p la in e d in C h a p te r V.
320
w i t h th e p o s s ib ilty o f th e
100
v i b r a t io n a l level o f one or m ore isotopic
fo rm s b e in g p e r t u r b e d by th e 04°0 v i b r a t io n a l level. T h e p o s s ib ility o f
re s o n a n c e b e tw e e n these s ta te s h a d been suggested by G u d e m a n 8 as a
possible ca u se o f the in c o n s is te n c y in th e s tr u c tu r e s o b ta in e d f r o m th e
th re e d i f f e r e n t p a irs o f iso topic species. We begin by r e c a llin g th e f u n d a m e n t a l
e q u a tio n r e l a ti n g th e Bv’s to Be,
Bv= Be- E a l(v ,+ d ,/ 2 ) + E
7
ij( v i+ d i/ 2 )(vj+ d j / 2 ) +
(I)
£ijkcijk(vi+di/2Xvj+dj/2Kvk+dk/2) + 7///a.
If we ig n o re all o t h e r a ’s,
7
’s, a n d e’s, th is e q u a tio n re d u c e s to th e fo llo w in g
5 e q u a tio n s f o r the g r o u n d v i b r a t io n a l s ta te a n d th e f ir s t f o u r m odes
w ith e x c it a t i o n in th e b e n d in g mode:
® 000 -
®e - a 2 + ^22'
®0110 - ®e
2 a 2 + 4 "^22 + ^H’
( 2)
( 3)
® 02°0 = ®e - 3 a 2 + 9 7 2 2 1
( 4)
B os^ = Be _ 4 a 2 + ,6 ^22 +711,
( 5)
Bq40o - Be
( 6)
5 a 2 + 2 5 722-
S t r a i g h t f o r w a r d s u b tr a c ti o n o f B0 Si 0 f r o m B 04 o0, B02 o0 f r o m B0 s i0, etc.,
321
a n d c o m b in a tio n s o f th e d i f f e r e n c e s e v e n tu a lly leads to
( 7)
®04 °o= 2B 0 3 i 0 - 2B 0 3 i 0 + B000.
U s in g th e Bv’s in T a b le II f o r th e 000, 0110, a n d 0 3 ^ states, we c a lc u la te
B04o0’s o f 44943.302 M Hz, 43688.810 M Hz, a n d 42909.106 M Hz f o r HCO+,
H 13 CO +, a n d H C lsO +, resp e c tiv e ly . T h e e x p e r im e n ta l values f o r these
s a te llite s a re 44944.204 M Hz, 43689.556 M Hz, a n d 42909.971 M Hz, a n d
th e d i f f e r e n c e s b e tw e e n th e e x p e r im e n ta l a n d c a lc u la te d values a re 0.902
M H z, 0.746 M Hz, a n d 0.865 M Hz, respectively. C le a rly , th e 04°0 v i b r a t io n a l
s ta te is n o t s e v ere ly p e r t u r b e d , a n d th u s, the
100
sta te is not se v ere ly
p e r t u r b e d by it.
E Q U IL IB R IU M ST R U C T U R E S
O n e o f o u r m a jo r goals in u n d e r t a k in g this p ro je c t was to
a tt e m p t e ith e r r e d u c e th e large in co n siste n c y in G u d e m a n ’s 8 r e values,
or to a t least u n d e r s t a n d w h y th e in co n siste n c y w as so large.
We have
d e f i n i t e l y a c c o m p lis h e d the f i r s t goal, the lo w e rin g o f th e p a ir in te r s e c tio n
in c o n s is te n c y w ith th e use o f th e a
7
partial level m eth o d .
F ig u re 12 is
a M o r i n o - N a k a g a w a 25 p lo t s h o w in g the in te rs e c tio n s o f th e a level a n d
a 7 part;ai(040) pairs.
T h e r e is a tre m e n d o u s r e d u c t io n in the size o f the
in te r s e c tio n tria n g le s going f r o m c a lc u la tio n s a t th e a level to th e a
7
partiai
level. T h is r e d u c t io n is c o n s id e r a b ly m ore t h a n th e c o r r e s p o n d in g r e d u c tio n
f o r H C N in th e size o f th e in te r s e c tio n a re a going f r o m the a level to
th e a y level. T h e se re s u lts a re e specially in te r e s tin g in lig h t o f th e fa c ts
t h a t th e o b se rv e d a y level c o n s ta n ts a n d e 222
322
Figure 12- T h e r CH vs r CN c u rv e s c a lc u la te d f r o m th e a level Ba’s ( th in
lines) a r e p lo tte d a lo n g w i t h th e c u rv e s f r o m th e a 7 partiai level B ,’s c a lc u la te d
using B 04 o0 ( h e a v y lines).
N ote th e large d i s p a r it y in tria n g le sizes.
323
rCH (A)
1. 1107
1. 1007
p Xr t i Al
1. 0907
gsammA
1. 0807
le
hco*
ALPHA LEVEL
1. 10200
1 .1 0 4 0 0
1. 1 0 6 0 0
1. 1 0 8 0 0
rCO (A)
HCO+ R e STRUCTURES
324
F ig u re 13- T h e p lots o f r CH vs r c o fo r the a 7 parti*i(04oO) ,evel Be’s ( t h *n
lines) a n d th e aTparttaiCO^O) level Be’s ( h e a v y lines) a r e q u ite s im ila r,
b u t th e y a r e slig h tly d i f f e r e n t .
325
rCH (A)
1. 0979
1. 0969
1. 0959
MA 1 0 4 0 6
HC0+
I P A R f r i A l g a H m a 031
1. 1 0 4 5 6
1. 1 0 4 7 2
1. 1 0 4 8 8
1. 1 0 5 0 4
rCO (A)
HCO+ Re STRUCTURES
326
F ig u re 14- T h e r CH vs r c o c u rv e s c a lc u la te d f r o m the a level Be’s a re
p l o tt e d a lo n g w ith c u rv e s f o r Be ± 14 kHz. See th e te x t f o r c a lc u la tio n
o f th e e r r o r bars. T h e r e a d e r c a n o b se rv e th e re is no s ig n i f ic a n t in c re a s e
in t r i a n g le size; in f a c t on th is scale th e e r r o r lim it c u rv e s a r e n o t resolved
f r o m th e m a in curves.
327
rCH (A)
1. 1107
1. 1007
1. 0 907
1. 0B07
Al p h a
level
error
bars
hc*o +
1 . 10200
1. 1 0 4 0 0
1. 1 0 6 0 0
1. 1 0 8 0 0
rCO (A)
HCO+ R e STRUCTURES
328
F ig u re 15- T h e plots o f r CH vs r c o f o r th e a 7 partiai(04°0) level Be’s ( th i n
lines) a n d f o r Be ± 55 k H z a re p r e s e n te d in th is fig u r e . See te x t fo r
c a lc u la t io n o f th e e r r o r bars.
N ote th e r c 0 scale is 1/12 th e scale o f the
p re v io u s f ig u r e , a n d the r CH scale is 1/10 the scale o f F ig u re 14.
329
rCH (A)
PARTIAL GAMMA 040
6co+
1. 1 0 4 5 6
1. 104 72
1. 1048B
1. 1 0 5 0 4
rCO (A)
HCO+ R e STRUCTURES
330
v a ry c o n s id e r a b ly betw een th e iso to p ic species, a n d t h a t th e u n c e r t a i n
Bv’s f o r th e 0220 sta te h a v e larg e c o e f f ic i e n t s f o r Be. T h e r e is even c o n s id e r a b le
c h a n g e in e 222 c a lc u la te d f ro m in c lu s io n o f e it h e r th e 03*0 or 04°0 states.
It can be re c a lle d fro m C h a p t e r V, t h a t c a lc u la te d s tr u c tu r e s e x h ib ite d
some d e p e n d e n c e on the choice o f v i b r a t io n a l sta te s selected. Because
o f th is, we also c a r r ie d o u t ot7 partial c a lc u la tio n s in c lu d in g the 03*0 sta te ,
a n d we c o m p a r e th e s tr u c tu r e s o b ta in e d f r o m th e tw o m eth o d s in F ig u re
13. T h e r e is a slig h t d i f f e r e n c e in th e size o f th e tria n g le s (the 0 3 x0
is s o m e w h a t la rg e r), a n d th e re is a d e f i n i t e d i f f e r e n c e in th e s tr u c tu r e s
o b ta in e d f r o m th e two a
7
partial level c a lc u la tio n s .
A glance at th e scales
o f F ig u re s 12 a n d 13 reveals t h a t th e r c 0 scale o f F ig u re 12 is a p p r o x im a te ly
12 tim es t h a t o f F ig u re 13, a n d th e r CH scale is a p p ro x im a te ly 10 tim es
g r e a te r in F ig u r e 12. T h e c o n c lu sio n is t h a t w h ile th e a
7 p a rtia l(0 4 ° 0 )
a n d otTpartjaiCOS1©) give so m e w h a t d i f f e r e n t s tr u c tu r e s , th e d i f f e r e n c e
is c o n s id e r a b ly less th a n b e tw e e n th e a a n d th e a 7 partiai(0400) levels.
F ig u re s 14 a n d 15 are plots o f th e a a n d ot7Partiai(04°0) level c u rv e s w ith
e r r o r b a rs o f 13 a n d 55 kH z, resp e c tiv e ly . T h e r e a d e r c a n note t h a t the
e r r o r b a rs in c re a s e th e size o f th e of7partia| in te r s e c tio n tria n g le .
A glance
a t the scales, h o w e v e r, reveals t h a t th e in te r s e c tio n a re is still c o n s id e r a b ly
sm a lle r th a n f o r th e a level plots. T h e a level plots a re n o t n o tic e a b ly
c h a n g e d by th e in clu sio n o f th e 13 k H z e r r o r bars.
Because H C O + is a p o sitiv e ion, th e to ta l m o le c u la r w e ig h t is one
e le c tro n mass less th a n th e sum o f th e H, C, a n d O a to m ic masses. In
a d d it io n , we do not know e x a c tly how to ta k e th is m issing mass in to
a c co u n t.
P ro p e r t r e a tm e n t w o u ld in v o lv e a d e ta i le d a n a ly s is o f th e b r e a k d o w n
331
o f th e B o r n -O p p e n h e im e r a p p r o x im a tio n , a n d we h a v e r e s tric te d ourselves
to a m uch m ore s im p lis tic a p p ro a c h , w ith th e p r im a r y goal o f e s tim a tin g
th e m a g n itu d e o f th e e f f e c t.
F ig u re s 16 a n d 17 a r e
plots o f r CH vs r c o
c a lc u la te d f r o m th e a a n d ot7partjai(04o0) le v e * B*’s» along w ith plots f o r
th e e le c tro n m ass rem o v e d fro m the H a to m , f ro m th e C a to m , a n d f ro m
e a c h o f the atom s (i.e. ea ch a to m ic m ass ha s one t h ir d th e e le c tro n mass
rem oved). T h e d a ta w ith th e c o rr e c tio n on the O a to m was not in c lu d e d ,
because it is v e ry s im ila r to th e d a ta w i t h th e C a to m a n d o u r c o m p u te r
m em o ry was n o t s u f f i c e n t to h a n d le th e n u m b e r of plots r e q u ir e d .
The
a level c u rv e s a r e s h if t e d , the most by rem o v a l o f th e e le c tro n f r o m the
H atom , th e n e x t most by one t h ir d rem o v a l f ro m all the atom s, a n d the
least by rem o v a l f ro m the C atom .
A t th is level, how e v e r, it is d i f f i c u l t
to d e te c t a n y c h a n g e in th e size o f th e tria n g le s.
At the a 7 partiai level,
th e tria n g le s fa ll in th e sam e o r d e r as th e a level. T h e r e a re d e f i n i t e
in cre ase s in th e size o f th e in te rse c tio n tria n g le s f o r the cases w h e re
all th e e le c tro n mass is rem o v e d fro m one ato m , w ith a la rg e r in cre ase
be in g fo r rem o v a l f r o m th e H atom .
R e m o v a l o f 1/3 the e le c tro n mass
fr o m all th e atom s does not s ig n i f ic a n tl y in cre ase th e tria n g le size, a lth o u g h
it does c re a te a la rg e r s h if t in all the c u rv e s th a n rem oval fro m th e C
o r th e O atom .
We can also n u m e r ic a lly c a lc u la te b o n d len g th s f o r the
Be’s. T a b le X II d isp la y s the bond d ista n c e s c a lc u la te d f ro m
th e in te rse c tio n s
o f th e th re e isotopom ers a t th e a level, b o th w ith ou r d a ta a n d G u d e m a n ’s8,
a n d the tw o a
7
partial level c a lc u la tio n s .
With a glance a t this tab le , one
can see n u m e r ic a lly w h a t w as o b se rv e d g r a p h ic a lly in F ig u re s 11 a n d
332
F ig u re 16- T h e r CH vs r CN c u rv e s f o r th e Be’s c a lc u la te d a t th e a level
a r e p lo tte d w ith th e n o r m a l iso topic masses a n d w ith c o rr e c tio n s f o r th e
mass o f th e e le c tro n .
T h e t h i n series o f c u rv e s lab e lle d A a r e th e u n c o rr e c te d
masses. T h e B c u rv e s a r e those w ith th e e le c tro n mass re m o v e d f ro m
th e h y d r o g e n atom . T h e C c u rv e s a re f o r one t h ir d o f a n e le c tro n mass
re m o v e d f r o m e a c h o f the n u clei.
T h e D cu rv e s a re c o m p u te d by s u b tr a c ti n g
th e e le c tr o n mass f r o m the C nucleus.
n o tic a b ly d i f f e r e n t in size.
N ote t h a t the tria n g le s a re not
333
rCH (A)
1. 1107
1. 1007
1. 0 907
1. 1 0 2 0 0
1. 1 0 4 0 0
1. 1 0 6 0 0
1. 0807
1. 1 0 8 0 0
rCO (A)
HCO+ Re ALPHA LEVEL
334
F ig u re 17- T h e r CH vs r CN c u rv e s f o r th e Be a t th e
(04°0) a p p r o x im a tio n
a r e p lo tte d w ith th e n o rm a l isotopic masses a n d w ith c o r r e c tio n s f o r th e
m ass o f th e ele c tro n . T h e lig h t series o f lines lab e lle d A a r e those f o r
th e u n c o r r e c te d a to m ic masses. T h e B lines a re c a lc u la te d w i t h th e e le c tro n
m ass re m o v e d f r o m th e h y d r o g e n ato m . T h e C lines a r e f o r on e t h i r d
o f a n e le c tr o n m ass re m o v e d f r o m ea ch o f the nuclei. T h e D lin e s a r e
those f o r w h ic h th e e n ti r e e le c tro n m ass was s u b tr a c te d f r o m th e C nucleus.
N o te th e la rg e s t tria n g le s a r e f o r th e s tr u c tu r e s w h e re th e w hole m ass
o f th e e le c tr o n w as re m o v e d f r o m one atom .
Also, no te th e d i f f e r e n c e
in scale b e tw e e n F ig u re s 12 a n d 13. T h e v a r a t io n in th e r c o is 5 tim es
g r e a t e r in F ig u re 12, a n d th e v a r i a t i o n in the r CH c o o r d i n a te is a p p r o x im a te ly
4 tim es g r e a t e r in F ig u re 12.
335
r C H (A)
1. 1009
1. 0959
1. 1 0 4 4 0
1. 1 0 4 8 0
1. 1 0 5 2 0
1. 1 0 5 6 0
rCO (A) C
HCO+ Re PARTIAL GAMMA
336
T a b le X II. H C O + E xp erim en tal E quilibrium S tru ctu res.
a le v e la
H C O + -H 13 CO+
H C 0 + - H C 18 0 +
H 13C 0 +- H C 180 +
rc o
1.105035
1.104343
1.106330
0.001987
1CH
1.095405
1.098918
1.088492
0.010426
H C O + -H 13 CO +
H C 0 + - H C 180 +
H 13C 0 + - H C 180 +
V
rc o
1.105008
1.104291
1.106350
0.002059
CH
1.095540
1.099179
1.088378
0.010801
H C 0 + - H C 18 0 +
H 13C 0 + - H C 180 +
V
a lev e l 0
« 7 partial(0 3 li0 )
H C O + -H 13 C O +
rco
1.104774
1.104763
1.104795
0.000032
r CH
1.097042
1.097093
1.096933
0.000160
H C O + -H 13C O +
H C 0 + - H C 180 +
H 13C 0 +- H C 180 +
V
rc o
1.104737
1.104732
1.104746
0.000014
CH
1.097255
1.097280
1.097205
0.000075
“ ■ypartial(04°0)
a G u d e m a n ’s 8 results.
b T h e q u a n ti ty 5r is th e a bsolute value o f th e d i f f e r e n c e
betw een the most d is p a ra te bond lengths.
c T h is work.
337
T ab le X III. H C O + S tru ctu res C orrected fo r E lectron M ass.
no mass c o rre c tio n
H C O + -H 13 CO+
Tl CO
nn
1.104737
1.097255
r CH
H C 0 + - H C 180 +
1.104732
1.097280
e le c tro n mass only o f f h y d ro g en
H C O + -H 13 CO+
H C O + -H C 180 +
rco
1.104715
1.104790
r CH
1.097818
1.097433
H 13 C O + -H C 18 0 +
1.104746
1.097205
h
13c
0.000014
0.000075
o + - h c 18o +
1.104572
1.098579
V
0.000218
0.001146
1/3 ele c tro n mass o f f all atom s
H C O + -H 13 CO +
H C O + -H C lsO+
1.104731
1.104748
r co
1.097469
1.097377
r CH
H 13C 0 + - H C 18 0 +
1.104697
1.097648
V
0.000051
0.000271
ele c tro n mass only o f f C
H C O + -H 13 CO+
rc 0
1.104724
r CH
1.097369
H C O + -H C 180 +
1.104765
1.097160
H 13C 0 + - H C l 8 0 +
1.104646
1.097783
V
0.000119
0.000623
e le c tro n mass only o f f O
H C O + -H 13 CO+
rco
1.104753
r CH
1.097218
H C O + -H C 180 +
1.104689
1.097538
h
V
0.000183
0.000954
H C O +-H C 180 +
0.000101
0.000370
H 13C 0 + - H C 18 0 +
0.000300
0.001995
13c
o + - h c 18 o +
1.104872
1.096584
A reraajib
r CO
r CH
h c o + - h 13 c o +
0.000038
0.000600
a T h e q u a n tity fir is the ab so lu te v alue o f the d i f f e r e n c e be tw e en the
most d is p a r a te bond lengths o f d i f f e r e n t p airs w ith in the same
electron mass co rre c tio n .
b T h e q u a n ti ty
is the absolute value o f the d i f f e r e n c e
o f the most d is p a r a te bond lengths for a p a r t i c u l a r
p a ir am ong the d i f f e r e n t e le c tro n mass corrections.
338
12. F o r the t t 7 partiai(04o0) level bond lengths, th e r e is consistency to 10'
f o r th e r c o a n d
0 .0 0 0 0 1
Xf o r
5
X
th e r CH. T h e consistency is slightly poo rer f o r
th e otTpurtiaKOS1©) s tr u c tu r e , 3x10
“6
X f o r r c o a n d 0.00016X fo r r CH. T h e re
a r e also slight d i f f e r e n c e s b e tw een th e 04°0 a n d 03x0 a 7 partiai stru c tu re s ,
a b o u t 4xlO_B Xfo r r c o a n d
0 .0 0 0 0 2
Xf o r
r HC.
T able X III is a c o m p ila tio n f o r the a T p ^ u i ^ o O ) ,
w ith v a rio u s c o m b in a tio n s o f ele c tro n mass rem oval. We have in clu d e d th e
3P w h ic h is th e v a r ia tio n o f the pairs, a n d th e
v a r i a ti o n betw een c o rre c tio n s fo r a single pair.
th e
6 r’s
w hich is the
T h e r e a d e r can see fro m
w h a t was observed g r a p h ic a lly in F ig u re 13, t h a t rem oval o f one
t h i r d the ele c tro n mass fro m all th e atom s does n o t increase the ran g e o f
in te rse c tio n n e a rly as m u ch as rem o v in g th e e le c tro n mass fro m a single
atom .
By g lan c in g a t th e v alues f o r AMmBM a n d c o m p a rin g th em to 5r’s, we
c an see th a t a t the a
7
partiai level th e re is g r e a te r inconsistency in th e
s tr u c tu r e s c a lc u la te d w ith d i f f e r e n t fo rm s o f ele c tro n mass c o rre c tio n , th a n
th e re is in th e s tr u c tu r e s c a lc u la te d by d i f f e r e n t isotopic pairs.
It can also
be observed th a t the o u tly in g H 1SC 0 +-H C 18 0 + p a ir is a f f e c te d the most by
e le c tro n mass rem oval.
T h e re is c o n sid e rab le in co nsistency b e tw een the bond
len g th s c a lc u la te d a t th e a level; they d i f f e r by
0.002
Xfor
th e r c o .
0 .0 1
Xfor
the r CH
and
T h is s itu a tio n is v ery s im ila r to HN C, a n d in T a b le
X IV we c o m pare the bond lengths f ro m the th re e isotopic p a irs o f H C O + to
th e
bond
len g th s f r o m
th e
th re e
a nalogous
H N C - H N 13C, H N C - H 15 NC, a n d H 16 N C -H N 13C.
p a irs
of
isotopic species:
We h a v e also inclu d e d the
H C N pairs, in o rd e r t h a t the r e a d e r can view the m uch g re a te r consistency
339
T a b le X IV . C om parison o f C on sisten cy A m ong a L evel S tru ctu res.
HCO+
H C O + -H 13 CO+
H C O + -H C 18 0 +
H 13 C 0 + - H C 180 +
r co
1.105008
1.104291
1.106350
0.002059
r CH
1.095405
1.099179
1.088378
0.010801
H N C - H 15NC
H N C - H N 13C
H N 1SC - H 15NC
r CN
1.168724
1.168325
1.169784
0.001459
r CH
0.995498
0.997642
0.989331
0.008311
H C N - H 13C N
H C N -H C 15N
H 13 C N -H C 16N
Sr
r CN
1.153179
1.153180
1.153193
0.000014
r CH
1.065900
1.065892
1.065851
0.000049
HNC
HCN
a T h e q u a n ti ty 5r is th e absolute value o f the d i f f e r e n c e betw een the
tw o most d is p a r a te bond lengths.
340
b e tw e e n th e p a ir s f o r th is m olecule. T h e d i f f e r e n c e b e tw e e n r x x f o r
th e H C O + - H 13 C O + p a ir a n d th e H C 0 +- H C 180 +
p a ir is .0007
X, n o t
q u ite
tw ic e as la rg e as th e 0.0004 X d i f f e r e n c e b e tw e e n th e H N C - H N 13C a n d
H N C - H 15N C pairs.
Xf o r
T h e d i f f e r e n c e s b e tw e e n th e r ^ ’s is 0.0044
Xf o r
th e H C O + p a irs, a n d 0.0022
th e H N C pairs. As we h a v e n o te d in
C h a p te r VI, th e H N 13 C - H 15N C p a ir te n d s to lie o u tsid e th e ra n g e o f in te rse c tio n s
o f th e o t h e r H c o n ta i n in g isotopom ers, a t a h ig h e r r NC a n d low er r CH.
T h is is also t r u e f o r th e H C O + m olecule, as in all cases b o n d d ista n c e s
f r o m th e H C O + - H 13 C O + a n d H C 0 +- H C 18 0 + p a irs a re closer to each o th e r
th a n th ey a r e to th e H 13 C O +- H C 18 0 +. T h is even holds tru e a t th e a 7 pBrtiai
level. T h e r CN’s f o r th e o u tly in g p a ir o f th e H N C m olecule a r e a p p ro x im a te ly
0.0010
Xa n d
0.0014
Xh ig h e r
th a n f o r th e H N C - H 16N C a n d H N C - H N 13C
pa irs, resp e c tiv e ly . T h e c o rr e s p o n d in g d i f f e r e n c e s f o r the r c o ’s in H C O +
a re 0.0013
Xa n d
0 .0 0 2 0
X.
T h e r NH’s a re a p p r o x im a te ly
0.006
Xa n d
0.007
X low er f o r th e o u tly in g p a ir o f singly s u b s ti tu t e d species th a n f o r th e
o th e r pairs.
0.011 X.
In HC O+, the c o r r e s p o n d in g d i f f e r e n c e s a re 0.007
T h e im p o r t o f all th is is th a t even th o u g h th e
a level
Xa n d
d a ta a p p e a rs
to be grossly in c o n s is te n t w ith respect to th e Qt7 partial level, the in co n siste n c y
is n o t t h a t m u ch g r e a t e r th a n f o r HNC.
It sh o u ld also be no ted th a t
the a v e ra g e v a lu e o f r c o f o r th e H C O + - H 13C O + a n d H C O + -H C 18 0 + p a irs
is 1.104650
X, in
rea so n a b le a g re e m e n t w ith the 1.104739
level a p p ro x im a tio n .
T h is s h i f t o f 0.0001
Xf o r
Xf r o m
the a 7 partial(04°0)
H C O + is not o b ta in e d
fo r H C N , in t h a t case th e re is no a p p re c ia b le c h a n g e b e tw e e n th e r CN’s
o f th e a level a n d th e a y level. T h e a v e ra g e r HC b e tw e e n th e sam e p a irs
is 1.097359
Xa t
th e a level, as opposed to the aTpartiaiC ^O ) o f 1.097068
341
Xa n d
th e ot7partial(04°0) v a lu e o f 1.097267
X.
I f one e x a m in e s T a b le VIII
o f C h a p t e r V, one disc o v e rs t h a t the a v e ra g e v a lu e o f th e a level r CH
in te rse c tio n s in H C N is 1.0658
in te rse c tio n s is 1.0656
X, a
Xa n d
th e a v e ra g e v a lu e o f th e a~f level
d e c re a s e o f
s tr u c tu r e s o f H C O + is 1.09716
the a level (See T a b le XII).
Xf o r
0 .0 0 0 2
X.
T h e a v e ra g e o f th e a
r CH, a d e c re a s e o f
0 .0 0 0 2
7
partiai
Xfro m
In th is re g a rd th e n , H C O + is q u ite sim ila r
to H C N . T h e c o n c lu sio n o f th is section is t h a t if we c o n s id e r the H C 180 +
- H 13 C O + as a n o u tly in g p a ir , th e n th e a level does not p r o v id e a n u n re a s o n a b le
s tr u c tu r e . T h e best s tr u c tu r e fro m the in te rs e c tio n s o f c u rv e s is o b ta in e d
by a v e r a g in g th e s tr u c tu r e s f r o m the o th e r tw o isotope pairs.
A possible e x p la n a tio n f o r the s im ila r ity b e tw een H C O +
a n d H N C can be o b ta in e d i f one a d a p ts e q u a tio n (58) o f C h a p t e r V fo r
a g e n e ra l H X Y l in e a r tria to m ic :
( 8)
d r XH
d r XY
_
m X m Yr XY +
m X m Hr XH +
m Hm Y ( r XH + f X y )
m Hm Y (r XH + r XY)
As m e n tio n e d in C h a p t e r VI, slopes o f -5.52, -5.68, -5.72, a n d -5 .9 0 result
fo r th e H N C , H N 13 C, H 16 NC, a n d H 15 N 13C isotopom ers.
va lu e s o f 1.1047
X fo r
r c o a n d 1.0972
Xf o r
I f we use the
r CH, th e n slopes o f -5.07,
-5.31, -5.23, a n d -5 .5 0 a re o b ta in e d f o r th e H C O + , H 13 CO+, H C 18 0 + ,
a n d H 13 C 180 + species. In both cases the slopes f o r the two singly s u b s titu te d
species a re n e a rly e q u a l, a n d t h e r e fo r e , slig h t e r r o r s in Be w ill m a g n if y
e rro rs in the in te rse c tio n . F o r H C N on the o th e r h a n d we c a lc u la te slopes
o f -5 .0 9 , -5.33, -5.19, a n d -5 .4 4 fo r H C N , H 13 C N , H C 16N , a n d H 13C 1 BN.
Since th e tw o singly s u b s titu te d p a irs h a v e slopes t h a t a re m ore d i f f e r e n t ,
342
th e s tr u c tu r e d e te r m i n a ti o n can be e x p e c te d to be m ore a c c u r a te w h e n
these tw o iso to p ic fo rm s a re used together.
I f w e use K r a i t c h m a n ’s e q u a tio n s a n d th e second m o m e n t c o n d itio n s
to c a lc u la te r e f r o m th e a 7 partiaj s tr u c tu r e s ( r e f e r to C h a p te r V f o r deta ils),
th e n e x c e lle n t a g re e m e n t w ith th e i n te r s e c tio n m eth o d is o b ta in e d .
T h is
c a n be o b s e rv e d in T a b le X V . T h e v a lu e o f r c o f ro m K r a i t c h m a n ’s e q u a tio n
f o r the a 7 partial(04°0) is 1.104735
w i t h th e v a lu e o f 1.104738
in te rse c tio n s .
X, in
X, o b ta in e d
X.
f r o m th e
a v e ra g e s o f the p a ir
T h e r e is only a s lig h tly g r e a t e r d i s c r e p a n c y f o r r CH, the
seco nd m o m e n t r CH be in g 1.097261
1.097248
e x t r a o r d i n a r i l y good a g re e m e n t
X, a n d
th e in te rs e c tio n a v e ra g e being
We h a v e e s se n tia lly th e sam e r e s u lt fo r the ot7partiai(0310)
case, o b t a i n i n g a r c o o f 1.104772
X, c o m p a re d
to th e 1.104778
Xa v e ra g e
o f th e p a ir s o f i n te r s e c tin g isotopes. O u r a v e ra g e fo r the in te rse c tio n
r CH’s w as 1.097024
X, a n d
ou r second m o m e n t a v e ra g e was 1.097056
X.
T h e c o n c lu sio n is t h a t the K r a it c h m a n e q u a ti o n - s e c o n d m om ent c o n d itio n
m e th o d gives e x c e lle n t a g re e m e n t w ith p a ir in te r s e c tio n d a ta w hen the
l a t te r gives c o n s is te n t s tr u c tu r e s f r o m d i f f e r e n t isotope pairs.
O f c o n s id e r a b ly m ore im p o r ta n c e is the a p p lic a tio n o f K r a i t c h m a n ’s
e q u a tio n a n d th e second m o m e n t c o n d itio n f o r th e a level Be’s. T hese
resu lt in a n r c o o f 1.104815
a g re e m e n t w ith th e a
7
Xa n d
a n a v e ra g e r CH o f 1.096531
partial s tru c tu re s .
X, in
A glan c e a t T a b le X V will show
t h a t th e v a r i a t i o n in r CH, c a lc u la te d f r o m th e th re e isotopom ers, is
X, c o n s id e r a b ly
^partial le v e l
m ore th a n th e
re a s o n a b le
10"6 X v a r i a ti o n
1 0 -4
f o r th e r CH’s f r o m th e
c a lc u la tio n s , b u t also c o n s id e r a b ly less t h a n th e
10"2 Xv a ria tio n
b e tw e e n th e r CH’s c a lc u la te d f r o m th e p a ir in te rse c tio n s. It is a b s o lu te ly
343
c le a r t h a t th e c o m b in a tio n o f K r a i t c h m a n e q u a tio n s a n d th e second m o m e n t
c o n d it io n is th e p r o p e r w a y to d e te r m in e e q u ilib r iu m g e o m etries w h e n
th e r e a r e gross in c o n siste n c ie s in th e s tr u c tu r e s o b ta in e d f ro m th e sim ple
in te r s e c tio n m e th o d u sing d i f f e r e n t isotopic pairs.
R e c a llin g th e s tr u c tu r e in c o n siste n c ie s we h a d u sing the p a ir
i n te r s e c ti o n m e th o d f o r th e e le c tro n mass c o rre c tio n s, th e logical t h in g
to do is a p p ly th e K r a itc h m a n - s e c o n d m o m e n t c o n d itio n m eth o d to th is
pro b le m . T h e resu lts a re p re s e n te d in T a b le X V I. T w o in te r e s tin g p o in ts
to note: ( 1 ) th e r e is v i r t u a ll y no c h a n g e in r CN, reg a rd le ss o f th e lo c a tio n
o f e le c tr o n m ass rem o v a l, a n d ( 2 ) th e re a re slig h t cha n g es in r CH d e p e n d in g
on w h ic h a to m h a s th e e le c tro n mass rem oved.
I f all the e le c tro n mass
is re m o v e d f r o m th e H atom , th e r CH’s in c re a s e 0.0005
r e d u c e d to
0 .0 0 0 2
T h e r e is o n ly a
X, i f
1 0 -4
th e C or th e N atom .
X.
T h e s h i f t is
1/3 th e e lc tro n mass is rem oved fro m ea ch atom .
Xs h i f t
i f th e e le c tro n m ass is rem oved fro m e it h e r
We th u s see a c o n s id e ra b le r e d u c tio n in u n c e r t a i n t y
d u e to th e e le c tro n mass c o rr e c tio n , f r o m 0.0003
r c o b o n d d is ta n c e a n d f ro m 0.001995
Xto
0.0005
Xto
Xin
0 .0 0 0 0 0 1
Xin
th e
the r CH bond d ista n c e.
Table XV. rc o (&) Kraitchm an Equilibrium Structures
and Second Moment rCH(X) Structures.
a
«TWi.i(04°0)
« 7 partiBl(03iO)
‘ CO
1.104815
1.104735
1.104772
r CH(HCO+)
1.096519
1.097261
1.097055
r CH ( H 13 C O +)
1.096566
1.097262
1.097056
r CH ( H C 180 )
1.096436
1.097261
1.097054
T able X V I. rC0(X) K raitchm an Equilibrium Structures
and Second Moment rCH(X) Structures for Electron Mass
Corrections.11
No correction®
r co
r CH(HCO+)
r CH ( H 13 C O + )
r CH ( H C lsO + )
1.104735
1.097261
1.097262
1.097261
H a to m c o rre c te d
rco
r CH(HCO+)
r CH ( H 13C O + )
r CH ( H C 180 + )
1.104736
1.097713
1.097708
1.097722
All atom s c o rre c te d
r co
r CH(HCO+)
r CH ( H 13C O + )
r CH ( H C 180 + )
1.104735
1.097445
1.097444
1.097447
C a to m c o rre c te d
r co
r CH(HCO+)
r CH (H « C O + )
r CH ( H C 180 + )
1.104736
1.097312
1.097310
1.097317
O a to m c o rre c te d
rco
r CH(HCO+)
r CH ( H 13 CO+ )
r CH ( H C 180 + )
1.104736
1.097306
1.097309
1.097298
“ "^partial (04°0).
346
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348
C H A P T E R VIII.
T H E S U B S T IT U T IO N S T R U C T U R E S O F H N N + A N D HOC+.
349
IN T R O D U C T IO N
U n l i k e th e series HC O+, H C N , a n d H N C , we w ere only a b le to
o b se rv e th e O l1!) s a te llite s f o r H N N + a n d no s a te llite s f o r H O C +. T h e r e f o r e ,
we w e re o n ly a b le to o b ta in s u b s titu tio n s tr u c tu r e s f o r these m olecules,
as opposed to e q u il ib r i u m s tr u c tu r e s f o r th e others.
In view o f th e h isto ry
o f H N N + , it is s o m e w h a t s u rp r is in g t h a t we co u ld do no b e tt e r f o r this
ion. T h e J = 0 —►
1 t r a n s it io n was f i r s t o b s e rv e d in th e in te r s t e ll a r m e d iu m
by T u r n e r 1, a n d G re e n et al.2 c a rr ie d o u t a SC F c a lc u la tio n o f th e g e o m e try
a n d h y p e r f i n e c o n s ta n t a n d c o n c lu d e d t h a t H N N + was in d ee d a r e a s o n a b le
assig n m en t.
Im p ro v e d a stro n o m ic a l o b s e rv a tio n s by T h a d d e u s a n d T u r n e r 3
re s u lte d in a re s o lu tio n o f th e h y p e r f i n e s t r u c t u r e an d d e te r m i n a ti o n
o f th e q u a d r u p o l e c o u p lin g c o n stant. S h o rtly t h e r e a f t e r in o u r la b o r a to r y ,
S a y k a lly et al.4 o b se rv e d th e J= 0 —•1 tr a n s it io n in a DC glow d isc h a rg e
c o n ta i n in g H 2 a n d N 2, a n d A nd e rso n et a l.6 o b se rv e d the c o rr e s p o n d in g
t r a n s it io n f o r D N N + in a s im ila r d isc h a rg e w ith d e u te r iu m .
T h is d isc o v e ry
m a d e possible th e in te r s te lla r d e te c tio n o f D N N + by S n y d e r et al.6 L a te r,
S z a n to et a l.7 o b se rv e d the J = 0 —
*1 t r a n s itio n s o f H N N + , H 15 N N + , H 15 N 15 N +,
D N N + , D 1 BN N +, a n d D 15 N 16 N +, a n d r e p o r te d a s u b s titu tio n s tr u c tu r e .
T h is p a p e r h a d a m ism ea su rem e n t o f the H 15 N N + f r e q u e n c y , as w as p o in te d
o u t by G u d e m a n 8, w ho observed the J = 0 —►
1 t ra n s itio n s o f all f o u r H c o n ta in in g
isotopom ers.
T h is o b s e rv a tio n p e rm itte d L in k e et al.9 to o b serve H 16 N N +
a n d H N 15 N + in th e in te r s te lla r m edium . S a s try et a l.10 o b se rv e d tra n s itio n s
u p to J=4-*5 f o r th e m ain isotope a n d J=5-*6 f o r DN N +.
V an den Heuvel
a n d D y m a n u s 11 m e a s u re d th e J= 11 —
*12 tr a n s it io n w ith th e f a r i n f r a r e d
s id e b a n d s p e c tr o m e te r , m e n tio n e d in th e p re v io u s c h a p te r.
Since then,
350
t h e e x p e r i m e n t a l w o rk on H N N + a n d D N N + has been p r im a r i ly in th e
i n f r a r e d , s t a r t i n g w i t h G u d e m a n et a l , 12 r e p o r tin g o b s e rv a tio n s o f th e
Vj b a n d w ith th e c olor c e n te r laser a n d ve lo c ity m o d u la tio n .
F o s te r a n d
M c K e l l a r 13 o b s e rv e d th e v3 b a n d s o f H N N + a n d D N N + in th e sam e e x p e rim e n t
as DC O+. N e s b itt et a t.14 used ve lo c ity m o d u la tio n a n d a d i f f e r e n c e f r e q u e n c y
la s e r to see th e Vj f u n d a m e n ta l a n d th e v x-v 2 hot b a n d o f DN N+.
T h is
m a d e possible th e d e te c tio n o f the v2 f u n d a m e n ta l b a n d o f H N N + by
S e a rs . 16 He s u b s e q u e n tly m ea su red th e v2 f u n d a m e n t a l o f D N N + . 16 O w ru ts k y
et a l.17 m e a s u re d h ig h J t ra n s itio n s in th e Vj b a n d a n d th e Vx~v2 h o t b a n d
f o r b o th H N N + a n d D N N + , a n d c o m b in e d th is d a ta w ith e a rlie r w o rk
to o b ta in a n e q u il ib r i u m s tr u c tu r e fo r H N N + .
R e c e n tly , Cazzoli et a l.ls
m e a s u r e d eq Q f o r th e in n e r N atom , as well as th e o u t e r N atom , in a n
a b n o r m a l d is c h a r g e . O u r w ork was in sp ire d by tw o fa c to rs : (1) th e e r r o r
in th e e a r l ie r p a p e r f o r th e H 16 N N + isotope m ade us r e a liz e t h a t th e re
c o u ld be d i f f i c u l t i e s w ith the d e u te r iu m isotopes as well (in d e e d th e re
w e re , as w ill be m e n tio n e d late r) a n d in a n y case th e phase lock loop
w o u ld yield m ore a c c u r a te m ea su rem e n ts, a n d ( 2 ) the i n f r a r e d spe ctro sc o p y
h a d c o n s id e r a b ly n a r r o w e d the se arc h ran g e fo r v i b r a t io n a l s a te llite tra n s itio n s ,
a n d it was h o p e d t h a t e q u il ib r i u m s tr u c tu r e s c o u ld be o b ta in e d .
In th is
c h a p te r we w ill p re s e n t o b s e rv a tio n s o f th e J=0-»1 t r a n s it io n fo r D N N +,
D 15 N N +, a n d D N 1 BN +, the J= 2 —3 tr a n s itio n s f o r th e 01 x0 (in c o lla b o ra tio n
w ith W. T. C o n n e r ), a n d th e J= 2 —3, J=3-*4, a n d J=4-*5 t r a n s itio n s f o r
H N N + . (also in c o lla b o ra tio n w ith W. T. C onner).
T h e r e h a s been c o n s id e ra b le th e o r e tic a l 19*3S a n d mass
s p e c tr o m e tr ic w o rk on H O C + . 3 4 ’ 41 T h e f ir s t d e f i n i t i v e d e te c tio n o f th e
351
ion, h o w e v e r, w as G u d e m a n a n d Woods ’42 o b s e rv a tio n o f th e J = 0 —►
I t r a n s itio n s
f o r H O C +, H 18 O C +, a n d H 0 13 C + in 1982. S u b s e q u e n tly Woods et a / . 43
h a v e r e p o r t e d a t e n a t i v e o b s e rv a tio n o f H O C + in th e i n te r s t e ll a r m ed iu m .
B lake et al.44 e x te n d e d th e m e a s u re m e n ts o f th e m a in isotope to the J= 3 —4
t r a n s it io n , u sin g th e e x te n d e d n e g a tiv e glow c ite d in th e p re v io u s c h a p t e r .45
Bogey et al.4e h a v e r e p o r te d o b s e rv a tio n o f tra n s itio n s f ro m J = l-» 2 to
j =4
-* 5
f o r DOC+.
O n ly this ye a r has H O C + been o b se rv e d in th e i n f r a r e d ;
N a k a n a g a a n d A m a n o 4 7 d e te c te d the v x f u n d a m e n t a l b a n d . In this c h a p te r
we w ill r e p o r t m e a s u re m e n ts o f the J=2-*3 a n d 3-*4 t r a n s itio n s fo r H O C +,
H 18O C +, a n d H 0 1SC +, as well as the J=2-»3 t r a n s it io n f o r H 18 0
13 C+.
We w e re in s p ir e d to do th is rese a rc h , by th e d e sire to o b ta in e x a c t Bqqo’s
f o r th e H 0 1 SC +, H 18 0 1SC+, a n d e specially H 18 OC+, w h e re th e J= 0— 1
t r a n s i t i o n co u ld o n ly be o b served by s p littin g th e i n t e r f e r i n g
0
" —l~ (v= 2 )
a 3/7 C lsO lin e a t 86116.26 M H z .8
E X P E R IM E N T A L
T h e H N N + a n d D N N + m e a s u re m e n ts w ere c a r r ie d o u t in a b n o rm a l
d is c h a r g e s w ith 0.2 m T o rr o f H 2 or D 2 a n d
8
m T o rr o f a rg o n f o r the
a b n o r m a l d isc h a rg e s a n d 0.5 m T o rr ea ch o f r e a c tiv e gases w ith a b o u t
20 m T o r r a rg o n f o r th e n o rm a l d is c h a r g e s — m ore or less s im ila r to H C O +.
A b n o r m a l d is c h a r g e voltages w ere a r o u n d 1800 volts, a n d n o rm a l d isc h a rg e s
w e re r u n a t ty p ic a l c u r r e n ts o f 500 mA. F o r th e D N N + m e a s u re m e n ts
we used th e H u g h e s S c h o ttk y d io d e d e te c to r , a n d f o r the H N N + m e a s u re m e n ts
we used th e InSb d e te c to r w ith 5 k G au ss m a g n e tic f ie ld a n d 7 T o r r h e liu m
p re s s u re ( a b o u t 1.7 K).
We d id not h a v e a k ly s tro n t h a t w o rk e d at 73
G H z , a n d t h e r e f o r e we were u n a b le to o b serve th e D 15 N 15 N+ species.
352
A n u n s u c c e s s fu l a tt e m p t to see H N N + w as m a d e in a slow flo w disc h a rg e.
T h e H O C + lin e s w e re o b s e rv e d c o n c u r r e n tl y w ith th e c o rr e s p o n d in g
H C O + lines.
T h e r e f o r e , s im ila r a b n o rm a l d isc h a rg e c o n d itio n s w e re used
as in th e p r e v io u s c h a p te r , i. e., 0.2 m T o rr each o f the p r o p e r isotopic
fo rm s o f CO a n d H 2,
8
m T o r r a rg o n , f a s t flo w , liq u id n itr o g e n cooling,
InSb d e te c to r , etc. It w as f o u n d t h a t a lth o u g h use o f C H 4 a n d 0
2
as
r e a c tiv e gases re s u lte d in f o u r f o l d r e d u c tio n o f signal f o r H C O +, th e
use o f these gases d id not r e s u lt in r e d u c e d signal s tr e n g th f o r H O C+,
so
13 C H 4
and
18 0 2
and
18 0 2
w e re used f o r th e H x8 O x3 C + s e arc h , a n d we used C H 4
f o r th e H 18 O C + w ork.
Because th e m u ltip lie r d id not w ork
well a t th e lo w e r f re q u e n c ie s , we d id n o t a tt e m p t to f in d th e J=3-»4 t r a n s itio n
fo r th e H 18 0 1 SC + species.
We d id not use n o rm a l d isc h a rg e s f o r HO C+
a n d its isotopom ers.
n 2h
+
o b se r v a t io n s a nd su b st it u t io n st r u c t u r e
O u r H N N + g ro u n d v i b r a t io n a l s ta te lines w ere e sse n tia lly
c o m p a r a b le in in te n s it y to H C O + lines, a n d we even o b ta in e d the sam e
o r d e r o f im p r o v e m e n t going f ro m the n o rm a l to the a b n o rm a l d is c h a r g e
fo r th e 000 ( a p p r o x i m a te l y a f a c t o r o f 20). N e v e rth e le ss, th e 000 to 01 x0
r a tio is a b o u t 120 in a n a b n o rm a l d is c h a rg e , as c o m p a re d to 50 fo r HC O+,
as c a n be seen in F ig u re s 1 a n d 2, w h ic h a re c o m p a riso n s o f th e sp e ctra
of th e tw o sta te s, w ith th e
0 1 x0
H N N + a n d 40 tim es f o r HCO+.
000
and
0 1 x0
signal b e in g m a g n if ie d
100
tim es f o r
A possible c o m p lic a tio n is t h a t the H N N +
v i b r a t io n a l states will h a v e d i f f e r e n t q u a d r u p o l e s p littin g
p a tte rn s , b e c au se /=1 f o r th e 01*0 sta te (see C h a p te r V f o r details).
The
H N N + 01 x0 lin e does a p p e a r s o m e w h a t b r o a d e r th a n the H N N + g ro u n d
353
v i b r a t i o n a l state.
F o r th is reason, w e h a v e d o n e a s im u la tio n o f th e q u a d ru p o lc
e f f e c t f o r b o th th e
000
and
01*0
sta te s, a n d we h a v e p re s e n te d th e results
in F ig u re 3. T h e r e a d e r c a n observe t h a t th e 01 *0 (solid lines) a r e slig h tly
m o re s p r e a d o u t t h a n th e g ro u n d v i b r a t io n a l state lines (d ash e d lines).
T h is s lig h t b it o f b ro a d e n in g will n o t, h o w e v e r, ca u se a f a c t o r o f tw o
r e d u c t io n in th e 01*0 sig n a l re la tiv e to th e g r o u n d state signal.
O u r a tte m p ts
to o b serve o th e r sa te llite s o f H N N + (100, 001, a n d 02°0) w ere not successful
in e i t h e r n o r m a l or a b n o rm a l disc h a rg es.
It s h o u ld be e m p h a s iz e d th a t
this w o rk w as d o n e b e fo re it was re a liz e d th a t t h r o t tl in g th e p ressure
on th e d e te c to r a n d ra is in g the m a g n e tic fie ld could c o n s id e ra b ly e n h a n c e
signals.
T h e r e f o r e , it seem s to us t h a t m ore w ork is nec essa ry b e fo re
it can be s ta te d t h a t th e s tr e tc h in g s a te llite s a re not d e te c ta b le .
We d id
d e te c t th e 100, 001, a n d 02°0 s a te llite s o f H 13 C O +, how e v e r, u n d e r the
sam e c o n d itio n s t h a t f a i l e d f o r H N N +, a n d in light o f F ig u re s 1,2, and
3, it seem s a le g itim a te con c lu sio n t h a t H N N + is v i b r a t io n a ll y c o ld e r
t h a n HCO+.
T a b l e I is a p re s e n ta tio n o f H N N + 000 a n d 01*0 f re q u e n c ie s ,
a lo n g w ith a c o m p a ris o n w ith th e re s u lts o f S a stry et al.Q, a n d th e r e a d e r
can see t h a t o u r a g re e m e n t is f a i r l y rea s o n a b le f o r th e J=2-«3 tra n s itio n ,
a n d e x tr e m e ly good f o r th e J=3-»4 t r a n s itio n .
It sh o u ld be a d d e d th a t
th e y q u o te e rr o r lim its o f 250 kH z f o r th e J*»4-*5, a n d we a r e well w ith in
these. We have also c o rr e c te d f o r u n re s o lv e d h y p e r f i n e q u a d r u p o l e s tr u c tu r e
in th e m a n n e r d iscussed in C h a p te r V on HC N . We d id not have th e
c u t o f f f i l t e r w hen this w ork w as d o n e , so the a m o u n t o f f o u r t h h a rm o n ic
po w e r v a r i e d w ith the k ly stro n f r e q u e n c y , a n d we w e re a b le to observe
354
th e J=3-*4 o f th e 0 1 lc0 line, b u t n o t th e 0 1 ld0. In o r d e r to o b t a i n Bv
f o r th e u p p e r s ta te we assu m e d t h a t D upper w as 2 k H z h ig h e r t h a n D lower,
w h ic h is a p p r o x im a te ly tru e f o r H C N a n d H C O +. In T a b le II, we p re s e n t
a c o m p a ris o n o f o u r results w ith th e i n f r a r e d d a ta a n d we c a n see re a s o n a b ly
good a g re e m e n t f o r th e B 000 ’s. O u r a g re e m e n t f o r B 0 1 i 0 a n d q 0iio 1S b e tte r
w ith S e a rs 15 t h a n w ith O w ru ts k y et a l.17. T h e reason f o r th is b ecause
S e a rs 15 o b s e rv e d th e f u n d a m e n t a l a n d O w ru ts k y et a l.17 o b s e rv e d th e
h o t b a n d . F o r the D N N + d a ta we p re s e n t T a b le III, w h ic h show s th e f re q u e n c ie s
o f the h y p e r f i n e co m p o n e n ts, th e c a lc u la te d u n s p lit f re q u e n c ie s , e q Q ’s,
a n d cN’s.
O u r u n c e r t a i n t y e s tim a tes f o r th e H N N + lines a re c o m p lic a te d
by th e f a c t t h a t b o th the 14N q u a d r u p o le h y p e r f i n e e f f e c t a n d th e D o p p le r
e f f e c t m ust be c o n sid e red . T h e r e f o r e , we assign u n c e r t a i n t ie s o f 50,
70, a n d 90 k H z f o r the J=2-*3, J=3-*4, a n d J = 4 —5 t r a n s it io n s o f th e g ro u n d
sta te , e v e n t h o u g h o u r p rec isio n is m uch g r e a te r (a s t a n d a r d d e v ia t io n
o f 9 k H z f o r 4 trials).
F o r th e J=2-*3 t r a n s itio n s o f th e 0 1 J0 we a v e ra g e d
4 tria ls each w ith a s ta n d a r d d e v ia tio n o f 39 kHz. T h e r e f o r e , it seems
t h a t 80 kH z is a re a s o n a b le u n c e r t a i n t y e stim ate.
F o r th e J=3-*4 t r a n s itio n
t h a t we w ere a ble to observe we ha d 3 tria ls w ith a s t a n d a r d d e v ia t io n
o f 60 kH z, a n d we assign a n e r r o r b a r o f 100 k H z to th is tra n s itio n .
F o r the N 2 D + lines th e signal to noise ra tio s w ere h ig h , a n d o u r fits w ere
e x tr e m e ly c o n s is te n t,
8
kH z b e in g th e m a x im u m s t a n d a r d d e v ia tio n .
We will a d d 10 kH z to th e u n c e r t a i n t y b ecause no a tt e m p t w a s m ade
to c o rre c t f o r the D o p p le r e f f e c t.
We also no te th a t A n d e r s o n ’s 5 results
o f 77107.86*0.09 M Hz f o r the F=1 —1 c o m p o n e n t a n d 77109.61*0.08 M Hz
355
F ig u re 1-T his f ig u r e is the c o m p a riso n o f J = 2 —3 t r a n s it io n s o f th e g ro u n d
v i b r a t i o n a l s ta te o f H N N + a n d th e 01 *0 v i b r a t io n a l state. T h e e x p e r im e n ta l
c o n d itio n s a re as follows: f a s t flow , liq u id n itr o g e n cooling, 1800 volt
a b n o r m a l d is c h a rg e ,
8
m T o rr A r, 0.2 m T o rr H 2 a n d N 2, 2 b a selin e supp re ssio n s
(800 k H z), 2400 k H z FM, 100 kH z AM, a n d 21 p o in t sm ooth. T h e 000
t r a n s it io n was o b s e rv e d on a 50 juv lock-in scale a n d r e q u i r e d
12
scans
a t 15 s e c /s c a n . T h e 01*0 was do n e on a 2 juvolt scale, r e q u i r e d 130 scans
a t 15 s e c /s c a n a n d has been m u ltip le d by a f u r t h e r f a c t o r o f 4 to f a c i li ta t e
c o m p a riso n .
T h e b a r in the g r a p h co rre sp o n d s to a n a b s o lu te f r e q u e n c y
in c r e m e n t o f 3 MHz.
356
HNN* 000 vs OlH)
SCALE 100X
357
F ig u re 2 -T h is f ig u r e is th e c o m p a ris o n o f J » 2 —3 t r a n s it io n s o f th e g ro u n d
v i b r a t i o n a l s ta te o f H C O + a n d th e OHO v ib r a t io n a l state. T h e e x p e r im e n ta l
c o n d it io n s a r e as follow s: fa s t flo w , l iq u id n itr o g e n cooling, 1800 volt
a b n o r m a l d is c h a r g e ,
8
m T o rr A r, 0.2 m T o r r H 2 a n d CO, 2 b a selin e supp re ssio n s
(800 k H z), 2400 k H z FM, 100 k H z AM, 21 p o in t sm ooth. T h e 000 tr a n s it io n
was o b s e rv e d on a 30 juv lock-in scale a n d r e q u ir e d 12 scans a t 15 se c /sc a n .
T h e 01*0 w as d o n e on a 5 juvolt scale, r e q u i r e d 27 scans a t 15 s e c /s c a n ,
a n d has b e e n m u ltip le d by a f u r t h e r f a c t o r o f 4 to f a c i l i t a t e com p a riso n .
T h e b a r in th e g r a p h c o rre s p o n d s to a n a b so lu te f r e q u e n c y in c r e m e n t
o f 3 MHz.
358
HCO* 000 vs 01*0
3MHz
359
F ig u re 3 -T h is f ig u r e is a stic k s p e c tr u m o f th e q u a d r u p o l e s p littin g p a tte rn s
o f th e 000 (d a s h e d lines) a n d OlK) s ta te s (solid lines).
th e
01*0
w ill be s o m e w h a t b r o a d e r t h a n the
000.
Please no te t h a t
360
HNN+ QUADRUPOLE SIMULATION 000 VS 01*0
48
|
|
|
I
I
"
I
" " T
I
'
DASHED LINES 000
36 .
SOLID LINES 01l 0
"
T
" T " -
1—
I
I
I
I
"
" I"
I'
42
j
UNSPLIT
30
24
PERCENT
LINE
INTENSITY
I1
12
18
6
■
I
-.20
.0
i
! ■_ _ _ i I I I
I_ _ _ i_ _ _ i_ _ _ i- - - -
.20
FREQUENCY SHIFT (MHz)
l
T a b le I. O bserved H N N + F re q u en cie s (M H z).
v
y
‘'fit
‘'c o r r
‘'SHH D*
ooo
3
279511.720
279511.752
27951 1.701
000
4
372672.500
372672.511
372672.497
000
5
465824.860
465824.865
465824.947
01 lc0
3
279374.616
279374.627
01 lc0
4
372489.524
372489.529
0 1 ld0
3
280904.116
280904.127
R e f e r e n c e 10.
362
T a b le II. I n f r a r e d B V alues vs M icrowave B V alues fo r 000 andO ^ O .
HNN+
B000 (M Hz)
Dooo(kHz)
IR a
IR b
IR C
/mwave
46589.217
46586.85
46586.069d
46586.871
87.71
93.23
46990.57
B0 1 i 0 (M H z)
46689.973'
87.67
46691.33
q 0 1 i 0 (MHz)
254.4
251.73
254.95
D 0 1 i 0 (kH z)
84.5
86.31
90.1
DNN+
B000 (MHz)
IR f
IR«
IR C
juwave
38554.9
38554.7
38554.7
38554.757
a R e f e r e n c e 12.
b R e f e r e n c e 15. T hese c o n s ta n ts w e re f r o m th e f u n d a m e n ta l b a n d .
c R e f e r e n c e 17.
d B 000 a n d D 000 w ere f r o m th e v x f u n d a m e n ta l band.
e B 0 1 i 0, D 0 1 i 0, a n d q 0iio a re f ro m th e hot band.
f R e f e r e n c e 14.
s R e f e r e n c e 16.
364
f o r th e F = l-> 2 c o m p o n e n t a g re e a re in r e a s o n a b ly good a g re e m e n t w ith
o u r v a lu e s o f 77107.815(18) M H z a n d 77109.568 MHz(18), resp e c tiv e ly .
O u r v0 o f 77109.271(18) M H z does not a g re e well w ith th e 77109.191(50)
M H z p r e d i c te d f r o m th e c o n s ta n ts o f S a stry et al. 9, b u t th e i r c a lc u la te d
v a lu e f o r th e J = l- * 2 tr a n s it io n is 174 k H z low er th a n th e ir e x p e r im e n ta l
v a lu e , so we fee l f a i r l y c o n f i d e n t o f o u r resu lt. In T a b le IV, we p rese n t
all th e Bqoq v a lu e s f o r th e e ig h t H N N + isotopom ers a lo n g w ith th e results
o f S za n to et a l.7 T h e H N N + v a lu e w as c a lc u la te d d ir e c tly f ro m o u r e x p e rim e n ta l
d a ta , th e v a lu e s f o r th e o t h e r H c o n ta i n in g isotopom ers w e re o b ta in e d
by u s in g G u d e m a n ’s 8 rest f r e q u e n c ie s a n d scaling th e c e n t r i f u g a l d is to r tio n
c o n s ta n ts, th e D N N + , D 15 N N +, a n d D N 1 EN + v a lu e s w ere o b ta in e d f r o m
o u r J = 0 —*1 f r e q u e n c ie s a n d th e Dqoq’s o f S a stry et al.9, alo n g w ith a p p r o p r i a t e
scaling. T h e r e a d e r can see t h a t th e r e w as also a m is m c a s u re m e n t fo r
th e D 15 N N + species in th e e a r lie r w o rk by Szanto et al.7. In T a b le V,
we p re s e n t a c o m p le te set o f s u b s titu tio n s tr u c tu r e s , a n d we c a n note
th e r a t h e r s tr i k in g c o n sisten c y w ith in b o th th e set o f H c o n ta i n in g isotopom ers
a n d th e set o f D c o n ta i n in g isotopom ers, a n d the s h a rp d i f f e r e n c e s be tw e en
th e v a lu e s o f th e tw o sets. S u b s titu tio n s tr u c tu r e s f o r H N N +, H C N , H N C ,
H C O +, a n d th e i r d e u te r iu m a n a lo g s a re p re s e n te d in T a b le V I, so th e
r e a d e r c a n o b serve t h a t th e r e a re e x tre m e ly c o n s is te n t d i f f e r e n c e s b e tw e en
th e s u b s ti tu t io n s tr u c tu r e s o f H N N + , H C O +, a n d H C N , a n d t h e i r d e u te r iu m
a n alogs, w h ile th e H N C -D N C s tr u c tu r e s b e h a v e s o m e w h a t d i f f e r e n t l y .
H O C + O B S E R V A T IO N S AND S U B S T I T U T I O N S T R U C T U R E
U n f o r t u n a t e l y , we do n o t h a v e e n o u g h d a ta on H O C + to in c lu d e
it in th e a b o v e tab le , as it w ould be most in te r e s tin g to see if H O C + b e h a v e d
T a b le IV . H N N + B 000 V alu es.
Iso to p o m er
B o o o (M H z)
p
a
D Sean to
HNN+
46586.871
46586.70
H 15 N N +
45603.038
H N 15 N+
45132.080
45130.53
H 15N 15N +
44132.192
44132.06
DNN+
38554.757
38554.67
D 15 N N +
38009.274
d n
37380.528
15 n
+
D 1 SN 1SN+
R e f e r e n c e 7.
37379.60
36817.76
366
T a b le V. H N N + S u b s titu tio n S tru c tu re s .
Parent
r N H; ( * )
HNN+
1.095050
1.031649
H 1 BN N +
1.095046
1.031614
h n
15 n +
1.095045
1.031581
15 n 15 n +
1.095041
1.031544
DNN+
1.094751
1.031772
D 15 N N +
1.094754
1.031734
D N 1 BN+
1.094755
1.031702
d
1.094758
1.031663
h
16 n 1 bn +
T a b le V I . H X X vs D X X S u b s titu tio n S tru ctu r es.
P a re n t
fnn (^)
W *)
HNN+
1.095050
1.031649
DNN+
1.094751
1.031772
At
0.000296
-0.000123
H C O+
1.07215
1.092921
DCO+
1.06923
1.093107
A
0.000292
-0.000186
HCN
1.155272
1.063139
DCN
1.154996
1.063249
At
0.000276
HNC
1.171888
0.986151
DN C
1.171515
0.986140
A
0.000373
0.000011
t
t
-
0.000110
368
as m u c h lik e H N C as H N N + b e h a v es lik e H C N a n d HCO+.
F igure 4
is a sam ple s p e c tr u m c o n ta i n in g th e J=2-*3 a n d 3-*4 o f H 18 O C +, a n d
in F ig u re 5 we c o m p a re this s p e c tr u m to th e c o rr e s p o n d in g one f o r H C lsO +,
a n d we see t h a t th e H C O + /H O C + i n te n s ity r a tio a p p e a r s to be a b o u t
40 in o u r d is c h a r g e w ith C H 4 a n d 0
2
as r e a c tiv e gases a n d 160 w ith H 2
a n d CO. B ecause th e d ip o le m o m e n t o f H O C + is 2.8 D ebye, a n d th e H C O +
d ip o le m o m e n t is 4.0 D e b y e 28, th e c o n c e n t r a t io n r a t i o w ill be one h a l f
th e in te n s ity ratio . (T h e in te n s it y o f a p u r e r o ta t io n a l t r a n s it io n is p r o p o rtio n a l
to ju,2). T h is m ea n s t h a t th e [H C O + ]/[H O C + ] r a t i o a p p e a r s to be 20 in
a C H 4 and 0
2
d isc h a rg e a n d 80 in a d isc h a rg e w ith H 2 a n d a n d CO, as
c o m p a re d to a m in im u m o f 330 in th e in te r s t e ll a r m e d iu m . 43 In T a b le
V II, we h a v e r e p o r te d th e t r a n s itio n s we w ere a b le to observe, alo n g w ith
Bv f o r all th e H c o n ta i n in g isotopom ers, a n d D v f o r all e x c e p t th e d o u b le
isotope.
F o r th e d o u b le isotope, we a ssum ed t h a t th e d is p la c e m e n t o f
D v fro m the m a in isotopic species w as tw o tim es t h a t b e tw e e n th e m ain
isotope a n d th e a v e ra g e o f th e singly s u b s ti tu t e d species; th is p ro c e d u re
w as only 1 kH z in e r r o r f o r HN C. T h e r e f o r e , th is is a t least a rea so n a b le
guess, b u t a 1 k H z e r r o r in D v w ill ca u se a n 18 k H z e r r o r in Bv, since
Bv = ( ^ = 2 - 3 +
IQ 8 D v)/6-
(
1)
O u r e s tim a te d e r r o r b a rs f o r the J=2-*3 tr a n s it io n s a re 50 kH z, a p p ro x im a te ly
20 k H z f o r m e a s u re m e n t p rec isio n a n d 30 k H z f o r the D o p p le r s h ift.
T h e se are f o r 3 trials.
F or th e d o u b le isotope, we a v e ra g e d tw o tria ls,
w hose d i f f e r e n c e was 45 kH z, a n d we assign a n u n c e r t a i n t y o f 60 kH z
369
F ig u re 4 -T h is f ig u r e c o n ta in s th e J=2->3 a n d J = 3 —4 t r a n s it io n s o f H 18O C +.
T h e e x p e r im e n ta l c o n d itio n s a re as follow s: f a s t flo w , l iq u id n itr o g e n
c ooling, 1800 volt a b n o r m a l d is c h a rg e ,
18 0
8
m T o rr A r, 0.2 m T o r r C H 4 a n d
2, 2 b a seline su p p re ssio n s (600 kH z), 2 4 00kH z FM , 30 k H z AM, 21
p o in t sm ooth. T h is o b s e rv a tio n r e q u i r e d 251 scans a t 15 s e c o n d s /s c a n .
370
H18OC+ 2B 600kHz
J=3-4
J=2-3
86605
KLYSTRON FREQUENCY(MHz)
371
F ig u re 5 -T h is f i g u r e is th e c o m p a ris o n o f J=2-*3 tr a n s it io n H C lsO + a n d
H 18 0 +C. T h e e x p e r i m e n t a l c o n d itio n s a re th e sam e as in th e p re v io u s
f i g u r e e x c e p t w e h a v e used a 800 k H z b a selin e sup p re ssio n . T h e H C lsO +
w as a v e ra g e d f o r 10 scans, a n d th e H 18 O C + w as m u lt ip l ie d by 40 times.
T h e b a r in th e g r a p h c o rre s p o n d s to a n a b s o lu te f r e q u e n c y in c r e m e n t
o f 3 MHz.
HC18<7
vs
h18o c + a b n o rm a l d is c h a rg e
SCALE 40X
3MHz
FREQUENCY(MHz)
373
T a b le V II. O b served H O C + F req u en c ies a n d C o n s ta n ts (M H z).
HOC+
H 18OC+
H O X3 C+
J=2-*3
268451.049
259824.117
257247.768
J= 3 -4
357921.656
346020.024
342985.012
44743.943
43305.969
42876.559
^000
D ooo(kH z)
116.75
108.32
107.25
H 180
13 C+
248459.964
41411.773
374
f o r th is tr a n s it io n .
F o r th e J = 3 —4 tra n s itio n s , we h a d tw o tr ia ls th a t
a g re e d to 48 k H z , a n d we assign 70 k H z e r r o r b a rs to these tra n s itio n s .
O u r J = 2 —3 f r e q u e n c y o f 268451.049(50) M H z is in re a s o n a b ly good
a g re e m e n t w i t h th e 268451.094 M Hz r e p o r te d by B lake et al.44, b u t o u r
v a lu e o f 357921.656(70) M Hz is in r a t h e r poor a g re e m e n t w ith th e ir v alue
o f 357921.987 M Hz. T h is d is c r e p a n c y c a n be resolved by n o tin g th a t
if one ta k e s t h e i r v alues fo r th e J = 1—*2 a n d J = 2 —3, one c a lc u la te s a Bv
o f 44743.944 M Hz, a Dv o f 116.35 kH z, a n d a J = 3 - 4 f r e q u e n c y o f 357921.756
M Hz, all o f w h ic h a re in re a s o n a b le a g re e m e n t w ith o u r v alues o f 44744.943
M H z f o r Bv, 116.75 kH z fo r D v, a n d 357921.656(70) M Hz f o r J = 3 - 4 .
F u r th e r m o r e , th e i r J= 1—»2 a n d 2 —3 t r a n s it io n s p r e d i c t a J = 0 —1 f r e q u e n c y
o f 89487.422 M Hz, a n d o u r J = 2 - 3 a n d 3 - 4 p r e d i c t a J = 0 - 1 o f 89487.420
M Hz, both in o u ts ta n d in g a g re e m e n t w ith G u d e m a n ’s 8 ’42 v a lu e o f 89487.414
MHz. O n th e o t h e r h a n d , th e ir J = 2 —3 a n d 3—4 p r e d ic t a f r e q u e n c y o f
89487.356 M H z, in m uch p o o rer a g re e m e n t w ith th e J = 0 — 1 d a ta .
It is
re a s o n a b le to c o n c lu d e th a t th e y slig h tly m is m e a s u re d th e J = 3 —4 tra n s itio n .
In T a b le V III we h a v e re p o rte d the a v a ila b le s u b s titu tio n s tr u c tu r e s o f
HO C+, a n d c o m p a r e d them to HN C. T h e r e a d e r can note th e re is f o u r
tim es as la rg e a d isc re p a n c y b e tw e e n th e rx x v alues b e tw e e n th e m ain
isotope (as p a r e n t species) a n d th e d o u b ly s u b s titu te d isotope o f HO C+
as th e r e is f o r H N N + by c o m p a ris o n w ith T a b le V. It c a n also be noted,
ho w ever, t h a t th is is the case f o r the D c o n ta i n in g isotopom ers o f HN C,
in w h ic h it w as neccessary to c o m b in e o u r d a ta w ith th a t o f P earson
et a / . 48 a n d use th e ir Dqqq values, b u t not the case fo r th e H c o n ta in in g
isotopom ers o f H N C , w here we c o u ld use only o u r ow n d a ta (see C h a p te r
375
VI on H N C f o r f u r t h e r d etails).
it is u n c e r t a i n t y in th e
All o f th is leads us to c o n c lu d e t h a t
o f H 18 0
13 C +
t h a t is th e ca u se o f th e d isc re p a n c y .
A m e a s u r e m e n t o f th e J=3-*4 tr a n s it io n f o r H 180
be d e s ira b le .
13 C +
w o u ld a s su re d ly
E v e n m ore v a lu a b le w o u ld be m e a s u r e m e n ts f o r th e D 0 13 C+,
D 18 O C +, a n d D 18 0
18 C +
isotopom ers.
We h a v e , t h e r e f o r e , in T a b le IX ,
in c lu d e d p r e d ic tio n s f o r th e D 18 O C + a n d D 0 13 C+ species u sin g th e s u b s titu tio n
s tr u c tu r e f o r th e m a in isotope, th e Bqqq v a lu e fo r D O C + f r o m B ogey 46
et al., a n d K r a i t c h m a n ’s 49 e q u a tio n ,
Al =
M SM
M+ SMJ
( 2)
We h a v e also in c lu d e d in T a b le IX th e a n a lo g o u s resu lts f o r H N C , along
w ith th e e x p e r i m e n t a l v alues to illu s tr a te t h a t th is m e th o d gives re a so n a b ly
a c c u r a te p r e d ic tio n s in these k n o w n cases, a lth o u g h th e r e is s o m e w h a t
m ore c o n s is te n c y f o r the D N C iso topom ers th a n th e H O C + ones. We have
in c lu d e d a p r e d i c ti o n f o r the D 180
13 C +
f ro m o u r H 18 0
13 C +,
w o rk w ith
th e c a v e a t t h a t a b e tte r p r e d ic tio n w ill a lm o st s u re ly com e f r o m the D 18 OC+
a n d D 0 13 C+ results.
S T R U C T U R E C O M P A R IS O N
We c o n c lu d e this c h a p te r by c o m p a r in g e q u il ib r i u m ,
s u b s titu tio n , a n d r 0 geo m e trie s f o r th e 14-electron m olecules t h a t we have
s tu d ie d in th is thesis.
I f th e r e is no e x c ite d v i b r a t io n a l s ta te d a ta , two
t r a d i t i o n a l a p p ro a c h e s to c a lc u la tin g m o le c u la r s tr u c tu r e s a re th e r 0 a p p ro a c h
T a b le V I I I . H O C + and H N C S u b s titu tio n S tru ctu res.*
P arent
r oc(^-)
r OH(^)
HOC+
1.159486
0.964093*
H 18 OC+
1.159461
ho
13 c +
1.159466
15 o 13 c +
1.159444
h
HNC
1.171888
0.986151
H 1 SN C +
1.171884
0.986154
H N 13 C+
1.171882
0.985967
H 1SN 13 C+
1.171878
0.985955
DNC
1.171516
0.986140
D 15 N C +
1.171493
0.986144
D N 13C +
1.171478
0.986009
1.171457
0.985995
d
15 n 13 c
+
aB000 f o r D O C + f r o m Bogey et a l . 46
bB000 f o r D N 13C a n d D 15 N 13 C + f ro m P earson et al.id
377
Table IX. Predicted DOC+ and DNC R otational Constants from
K raitchm an’s Equation.a-b
Isotopom er
Parent
Booo(Pr e d )
do
13 c +
DO C+
36638.2
D 18 O C +
DO C+
37349.1
D 18 0
H 18 0
35769.0
13 C +
13 C +
B000 (exper)
H 0 13 C+
DOC+
42871.3
42876.559
H 18O C +
DO C+
43312.4
43305.969
DO C+
HOC+
38201.4
38193.197
D 15 N C +
DNC
37644.6
37643.526
d n
DNC
36680.7
36684.003
D 15 N 13 C +
36157.4
36155.521
h
13c +
15 n 13 c
+
aB000 fo r D O C + f r o m Bogey et a / . 46
bB000 fo r D N 13C a n d D 15 N 13C + f ro m P earson et a / . 48
378
a n d th e s u b s titu tio n s tr u c tu r e m eth o d in v o lv in g K r a i t c h m a n ’s e q u a ti o n s .49
T h e r 0 a p p r o x im a tio n , consists o f u sin g th e e q u a tio n s
( 3)
Bv= Be-
E ai(Vi+di/2) + E 7 ij(v i+ di/2 )( v j+dj/2 )
i
>j
£ cijk( v i+ di/ 2 )(vj+ dj/ 2 )(vk+ dk/ 2 ) +
ijk
7
+
///2,
505379.05
I «(amU X > - B.(M Hz) •
(4>
and
I
-
m Hm C r CH2+
e~
m C m Nr CN2+
m Hm N (r CH-|' r C N )2
mH + m c + mN
a n d j u s t assu m in g t h a t all th e a ’s,
B000’s d ire c tly .
7
’s, a n d c’s a re zero, i.e., u sin g the
F ig u re s 6-11 a re plots o f r ^ vs rXY c a lc u la te d f r o m B 000
f o r H N N + , D N N + , HC O+, H O C+, H C N , a n d HN C.
T h e r e a d e r sh o u ld
n o te t h a t ea ch set o f th e r 0 plots has a c o n sisten t "hour-glass" p a tt e r n
o f 5 in te rse c tio n s a n d a n e x tre m e ly d is p a r a te in te r s e c tio n o f th e tw o
sin g ly s u b s titu te d isotopom ers. In a c c u ra c ie s in th e r o ta t io n a l c o n s ta n t
d a t a a re im m e d ia te ly rec o g n iza b le as d e f o r m a t io n s o f th e s y m m e tr y o f
these k in d s o f p a tte rn s .
T h e best a v e ra g e o f th e r 0’s com es f r o m the
p a i r c o n sistin g o f th e m a in isotopic species a n d th e d o u b ly s u b s ti tu t e d
iso to p ic species (the c e n te r o f the hourglass). T h e r e f o r e , we w ill use
th e in te r s e c tio n o f th is p a ir to c a lc u la te r 0 f o r th e 14-electron m olecules.
379
F ig u re
o f 5.2.
6 -T h is
f ig u r e is th e r 0 plot o f H N N + , w ith a slope s u b tr a c tio n
380
1 .0 5 7 1
1. 0 9 2 0 0
rNH (A)
1.0471
1. 0 9 4 0 0
1 .0371
1.0 271
1.0 9 6 0 0
1.0171
1.09800
rN N (A)
HNN+ RO STRUCTURES
381
F ig u re 7 -T h is is th e r 0 p lo t o f D N N + w ith a slope s u b tr a c ti o n o f 3.2.
Please n o te t h a t th e r e c u r r i n g "hour glass" p a tte rn .
Also note t h a t th e
in te r s e c tio n s a r e a t d i f f e r e n t r NN’s a n d r NH’s t h a n those in the p re v io u s
fig u r e .
382
rND (A)
1 . 0406
1 . 0306
09400
1 . 0206
1. 0 9 8 0 0
1 . 0106
10200
1 . 0006
1. 1 0 6 0 0
rN N (A)
DNN+ RO STRUCTURES
383
F ig u re
o f 5.2.
8
-In th is f ig u r e we d isp la y th e r 0 p lo t o f H C N w i t h a slope s u b tr a c tio n
384
rCH (A)
1. 0 8 0 9
1. 0 7 0 9
1. 0 6 0 9
1. 0 5 0 9
CN
1. 1 5 3 0 0
1. 1 5 5 0 0
1. 1 5 7 0 0
1. 1 5 9 0 0
rC N (A)
HCN R 0 STRUCTURES
385
F ig u re 9 -T h e r 0 p lo t o f H C O + is v e ry s im ila r to the r 0 plots o f H N N +
a n d H C N . T h e slope s u b tr a c tio n is 5.2.
386
rCH (A)
1. 1 1 6 4
1. 1 0 6 4
1. 1 0 6 0 0
1. 0 9 6 4
1. 1 0 8 0 0
1. 0 8 6 4
1 . 11000
1. 0 7 6 4
1 . 11200
rCO (A)
HCO+ RO STRUCTURES
387
F ig u re 10-T his f ig u r e is th e r 0 plot o f H N C w ith a slope s u b tr a c tio n o f
5.7. P lease n o te h o w t h a t the a re a o f in te r e s e c tio n is c o n s id e r a b ly g r e a te r
t h a n th e a re a s o f i n te r s e c tio n in th e p re v io u s fig u re s.
388
rCH (A)
0 .9 9 4 1
0.9 8 4 1
0.9 7 4 1
0.9 6 4 1
0 .9541
HNC?
DNC
1. 1 7 1 0 0
1. 1 7 3 0 0
1. 1 7 5 0 0
1. 1 7 7 0 0
rC N (A)
HNC RO STRUCTURES
389
F ig u re 11-T his f ig u r e is the r 0 plot o f H O C + w ith a slope s u b tr a c ti o n
o f 5.7. P lease n o te h o w t h a t th e a re a o f in te r e s e c tio n is c o n s id e r a b ly
g r e a t e r t h a n th e a re a o f in te rs e c tio n o f th e H N C plot. H o w e v er, th e
c u rv e s f o r th e isotopes f o r m th e sam e p a t t e r n as in th e p re v io u s f ig u re s .
390
rOH (A)
0.9869
0.9769
0.9669
0.9569
0.9469
DOC+
1. 1 5 6 0 0
1. 1 5 8 0 0
1. 1 6 0 0 0
1. 1 6 2 0 0
rCO (A)
HOC+ RO STRUCTURES
391
T ab le X. H X Y C om parison o f re, rs, and r0.
rxy(^)
r Hx(^)
H OC+ r ea
H OC+ r ,
H OC+ r 0
r,-re
r0 - r e
r0- r ,
1.1570
1.1594
1.1596
0.0024
0.0026
0.975
0.9649
0.9631
-0.0101
-0.0119
-0.0018
HNN+ r,b
HNN+ r,
HNN+ r0
r§- r e
r0- r a
r0- r ,
1.0927
1.0947
1.0950
0.0023
0.0003
1.0335
1.0317
1.0406
-0.0018
0.0071
0.0089
HCO+ r e
HCO+ r,
HCO+ r 0
r,-re
r0 - r ,
r0- r ,
1.1047
1.1072
1.1070
0.0025
0.0023
-0.0002
1.0972
1.0929
1.1032
-0.0043
0.0060
0.0103
HCN r ,
HCN r,
HCN r 0
r,-re
r0- r e
r0- r ,
1.1532
1.1553
1.1552
0.0019
0.0020
-0.0001
1.0656
1.0631
1.0704
-0.0025
0.0048
0.0073
HNC re
H N C r„
HNC r0
r,-r,
r0- r e
r0- r B
1.1684
1.1718
1.1716
0.0034
0.0032
-0.0002
0.9964
0.9861
0.9912
-0.0103
-0.0052
0.0051
a R e fe re n c e 50.
a R e fe re n c e 17.
0 .0 0 0 2
0 .0 0 2 0
392
We h a v e r e c e n tly re c e iv e d a m a n u s c r ip t f r o m B e rry a n d H a r m o n y 50
d e s c r ib in g a m e th o d f o r sc alin g r 0 d a t a to o b ta in good a p p ro x im a tio n s
to r e s tr u c tu r e s , u sin g m odel f o rc e f ie l d c a lc u la tio n s to c o rr e c t f o r c h a n g es
in z e ro - p o in t e n e rg y u p o n lig h t a to m s u b s titu tio n , a n d th e y h a v e c a lc u la te d
e q u i l i b r i u m v a lu e s o f r OH= 0.975*0.002 X a n d r o c = 1.1570*0.0005 X fo r
H O C+.
We e m p lo y these r e e s tim a te s f o r H O C +, th e v alues o f O w ru ts k y
et al . 16 f o r th e H N N + r e’s, a n d o u r o w n r e v alues f o r th e o t h e r m olecules
in T a b le X , w h ic h co m p a res th e r 0 s tr u c tu r e s , th e r g s tr u c tu r e s , a n d th e
r e s tr u c tu r e s .
O u r H C O+ e q u il ib r i u m s tr u c tu r e is th e a v e ra g e o f th e ot7partiai(04o0)
p a irs , o u r H C N r e s tr u c tu r e is the a v e ra g e o f th e a 7 p a i r in te rse c tio n s ,
a n d o u r H N C is th e a v e ra g e o f th e in te r s e c tio n o f all th e p a irs, e x c ep t
th e H N 1SC - H 15N C p a ir (see C h a p t e r VI).
T h e r e a r e se v era l s a lie n t f e a t u r e s to note f ro m T a b le X. T h e most
s tr i k in g is t h a t th e r e is v i r t u a ll y no d i f f e r e n c e b e tw e e n th e r 0 a n d r g
v a lu e s o f r XY f o r a n y o f th e m olecules.
T h is m ea n s t h a t u sing K r a i t c h m a n ’s
e q u a tio n s re s u lts in no im p r o v e m e n t o v e r u sing th e r 0 s tr u c tu r e s f o r c a lc u la tin g
th e r XY’s (as long as th e r 0 s tr u c tu r e is o b ta in e d f ro m th e o p tim u m isotope
pa ir). T h e o t h e r p o in t to note f o r th e r XY’s is t h a t th e d i f f e r e n c e b e tw e en
th e s u b s ti tu t io n (or r 0) values a n d th e e q u il b r iu m v a lu e is v i r t u a ll y c o n s ta n t
f o r all th e m olecules, e x c ep t f o r H N C , w h e re it is so m e w h a t grea ter.
I f th is is t r u e f o r a n y iso e le ctro n ic set o f X ’s a n d Y ’s, th e n a series o f
e q u i l i b r i u m rXY’s c o u ld be e s tim a te d by f i n d i n g r e f o r one m em b e r o f
th e set, a n d r 0 f o r th e rest. T h e r HX’s b e h a v e a lik e f o r the " stiff" m olecules,
H C N , H C O + , a n d H N N + . T h e d i f f e r e n c e b e tw e e n th e r 0 v a lu e o f r HX
a n d th e e q u i l i b r i u m v a lu e o f r ^
is r e la tiv e ly large a n d po sitiv e, w hile
393
t h a n th e d i f f e r e n c e b e tw e e n th e r g v a lu e a n d th e r e is r e la tiv e ly sm all
a n d n e g a tiv e . T h is m ea n s t h a t th e r 0 a p p r o x i m a t io n c o n s id e ra b ly o v e re s tim a te s
th e b o n d len g th s f o r these m olecules, a n d th e rs a p p r o x im a tio n slig h tly
u n d e r e s tim a te s them . M a tte rs a r e s o m e w h a t d i f f e r e n t f o r H N C. In th is
case th e r 0 a p p r o x i m a t io n u n d e r e s t im a t e s th e r ^
by a p p ro x im a te ly th e
sam e a m o u n t t h a t it o v e re s tim a te s th e b o n d le n g th s o f H C N , H C O +, a n d
H N N + . T h e a p p lic a tio n o f K r a i t c h m a n ’s 49 e q u a tio n s i.e., the r a m eth o d ,
d r iv e s th e c a lc u la te d v a lu e o f r ^ d o w n even f u r t h e r , a n d a n even worse
a p p r o x i m a t io n to r e resu lts th a n t h a t f o r th e r 0 m ethod.
In th e case o f
H O C + , th e r e is c o n s id e r a b le u n d e r e s tim a tio n o f th e r HX b o n d len g th by
th e r 0 m e th o d , a n d a p p r o x i m a t e ly th e sam e u n d e re s tim a tio n by the s u b s titu tio n
m eth o d . T h e s ig n if ic a n c e o f the H O C + c o m p a riso n s, how ever, m ust be
te m p e re d by th e f a c t th e a c c u r a c y o f th e r e e s tim a te s be in g used is not
r e a lly k n o w n .
It seem s t h a t K r a i t c h m a n ’s 49 e q u a tio n s , will give re a s o n a b le
a p p r o x i m a t io n s to r ^ e q u il ib r i u m bond len g th s only if th e r 0 m eth o d
i n it ia l ly o v e re s tim a te s them .
T h e m eth o d s t h a t we h a v e m e n tio n e d , th e r 0 a n d th e r,, a re not
th e o n ly m eth o d s a v a ila b le in th e l i t e r a t u r e f o r e s tim a tin g re f ro m r 0
d a ta .
W atson 51 pro p o se d a m eth o d , w h ic h in v o lv e d c a lc u la tin g th e Ir
f o r e a ch iso to p o m er, f ro m th e fo llo w in g e q u a tio n
Ir = 21. - I 0.
( 6)
T h e q u a n t i t y I 8 w as the m o m e n t o f in e r t ia c a lc u la te d f r o m a c om plete
s u b s ti tu t io n s tr u c tu r e , a n d I 0 w as th e m o m e n t o f in e rtia f ro m the r 0 s tr u c tu r e .
394
We t r i e d th is m e th o d , b u t th e s tr u c tu r e s o b ta in e d w e re n o t s ig n i f ic a n tl y
b e tte r t h a n th e r B s tr u c tu r e s .
T h is d id not s u rp rise us, bec au se W atson 51
h a d s a id in his p a p e r t h a t he d id n o t ex p e ct th e m e th o d to w o rk f o r H
c o n ta i n in g m olecules.
H a r m o n y 52 su b s e q u e n tly p ro p o se d a n o t h e r m eth o d ,
w h ic h in v o lv e d c a lc u la t in g IP f o r th e m a in iso topic species in th e sam e
m a n n e r as th e W atson 51 m ethod.
was Is/ I 0 f o r th e m a in isotope.
T h is w ould p r o d u c e a c o n s ta n t p w h ic h
T h e m om ent o f in e r t ia f o r th e o t h e r iso topom ers
w o u ld be giv en by I H= plo- N o th in g w as said in th e p a p e r a b o u t w h e th e r
o r n o t th e m e th o d w o u ld w ork f o r H c o n ta in in g m o le c u le s .52 We trie d
th is m e th o d as well, a n d no b e tt e r results w ere o b ta in e d w ith th is m eth o d
t h a n w ith e it h e r th e s u b s ti tu t io n s tr u c tu r e or W atson’s 51 m eth o d .
Berry
a n d H a r m o n y 50 c la im t h e i r new m eth o d is a p p lic a b le to H - c o n ta in in g
m olecules.
We h a v e n o t h a d a c h a n c e to test it, h o w e v e r, a n d c a n m ake
n o e s tim a te o f its a c c u r a c y .
395
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A P P E N D IX 1.
T H E M ICRO W A VE D E T E C T IO N O F K r D +
399
The lowest rotational transition of several isotopic forms of KrD+a)
Hugh E Warner, William T. Conner, and R. Claude Woods
Dtparrm tn t o fChtm iary, Unmmity o f Wisconsin. Madison. Wisconsin 1 3 7 0 6
(Received 14 August 1984; accepted 6 September 1984)
H i e / » 0-1 absorption line o fK rD 4" has been observed for ail six stable krypton isotopes in a dc
glow discharge in K r-D , mixtures. For " K r D 4- the quadrupole coupling constant
[ e Q q — 549.1(3) MHz] and nuclear magnetic coupling constant [Cv *■ — 0.022(2) MHz] were
determined. By combining the new microwave data for K tD * with very precise published
Dunham constants for K i H * f r o m Johns’ high resolution infrared spectral data, the mass
independent Dunham parem eten Cfpi, 4 pi, and 4 y were deduced. Precise Doppler shift
measurements indicated a small drift velocity in the magnetic held enhanced, abnormal discharge
in the direction opposite to that naively expected from the electrode polarity.
L INTRODUCTION
Microwave spectroscopy has by now been succeaafally
applied to several molecular ions as dienitacd in a recent
review article.1A recent addition to the list of ions studied by
the technique waa A rD 4-, which Bowman s t a L 1 were aide to
observe for three argon isotopes (*°Ar, 33Ar, and MAr) in
natural abundance. Johns3 has made extensive new measure­
ments of the high resolution infrared spectrum of A tH 4-,
which he combined with earlier high resolution infrared data
of Brault and Davis,4 Haese and Oka,3 and the microwave
measurements* on A rD 4* to obtain an extensive set o f Dun­
ham coefficients Y u and mass independent Dunham param­
eter! U u , A j f , * a d d % for the A rH * ion. In the same paper
Johns3 also reposted extensive measurements on the high
resolution Fourier transform infrared spectrum of the 1-0
and 2-1 bands o f K rH 4’ for five krypton isotopes. This was
again analyzed in terms o f an extensive set o f Dnnham coef­
ficients Y u (or U u ), but despite the large number of krypton
isotopes studied none o f the d w parameters could be de­
duced. The U u parameters o f Johns3 made possible a very
dose frequency prediction for the microwave spectrum of
K rD 4- and prompted us to search for i t Theoretical CEPA
calculations from Rosmus and co-workers indicated com­
parable, large dipole moments for K rH 4* (1.944 D|* and
A rH 4* (2129 D)7 and thus suggested the microwave spec­
trum o fK rD 4* would be conveniently strong. T h e 0-1
transition has been observed and precisely measured for the
six stable krypton isotopes in the vicinity of 251 GHz. (The
similar transitions for K rH 4' are beyond the current fre­
quency range o f our microwave spectrometer.) By combin­
ing our microwave data on K tD 4- with the infrared data3 on
K rH 4, we have been able to obtain values for d o , a n d d j^ ,
which compare well with the corresponding parameters for
A rH 4*. The analogous parameters in another diatomic ion,
CO4*, were recently determined by Bogey t t a i .* from mea­
surements of the microwave spectrum in numerous vibra­
tional states and isotopic forma. Our microwave data on
*Thii woftwaimpportcd by th>Ninond Science FeHirvlanofi'iStrucTOrmi
rv p iiM y Program, the Wisconsin Alumni Raunreh Foundation, and
tha Donon oTthe Petroteum Heaaarch Fund, admtnuured by the Amarican Chemical Soaecy.
J .C !w m .P tiy s .a i(1 2 ).P ll, 15 Dec. 1984
K tD 4- includes the a K r form, which exhibits a large hyperfine splitting and permits the first determination o f the hyperfine coupling constants t q Q and C s f o r t h i s i o n .
IL EXPERIMENTAL
The micr owave spectrometer used in this stork is the
same one used in earlier studies of HOC4'* end H jD 4*l0. The
dc glow discharge tube is 10 cm in diameter and 300 cm o f it,
including one of tha electrodes, is in the microwave radiation
path. Liquid nitrogen cooling of this cell waa employed
throughout this work. A solenoid magnet capable o f provid­
ing an axial field o f 300 O was used to enhance the micro­
wave abeorption o f the io ta as suggested by the work of DeLuria i t a i . " Radiation was obtained from the third
harmonic o f an 84 G Hz Varian klystron in a Millitech
triplet. An Advanced K inetics InSh detector operated at 1.7
K with the crystal in a 5 kG magnetic field was used to detect
the u in iw tw wave radiation. The tone burst13 source mo­
dulation scheme of Pickett was employed, and the klystron
was phase locked to a harmonic of a frequency synthesizer
that was digitally swept by a computer. All spectra were fit
by nonlinear least squares to a sum-of-Lorentzians model
line shape to extract precise center frequencies. Prior to be­
ginning microwave searching, the production o f K rD 4" was
investigated with a quadrupole mats spectrometer system
attached to the discharge tube. We found that K r-D j mix­
tures were preferable to A r-K r-D 2 mixtures, but the pro­
portions o f D} arid K r were not so critical as those of
and
A r in the work o f Bowman «r a/.,2 where the D] concentra­
tion had to be kept very low. This is reasonable since the
greater proton affinity of K r mitigates the loss of XD4through D 4" transfer to Dr Mixtures of about 1 mTorr D ,
and 9-14 mTorr K r were used in the microwave work, in a
nwHinm fast flow system' pumped by a throttled difflision
pump. Moet of the measurements were carried out in the
magnetic field enhanced, abnormal discharge mode with a
discharge voltage near 1500 V and a few milliamps current.
The *4K rD 4' species was, however, also readily observed in
normal zero field glow discharges with currents o f 200-500
mA, with a loss o f only a factor o f about 2-4 in intensity. The
frequency standard was compared to NBS station WWVB
and a small correction of seven parts in 10* (—2 kHz) was
obtained and applied to all measured frequencies.
0021-9606/84/24541344X02.10
® 1984 Amancwi Institute of Phytic*
5413
400
Comar. and Woods: Rotational transMensolKrO*
5414
TABLE L Fraqsaacy at "KrD* Unalaaa 231 545.0 MHz in MHx for difNormal ffimharai
Phn polarity*
M aas polarity*
0313
0306
0310
0321 .
0324
------ OS2T
03247*
030&
Abnormal discharpt
Minas polarity*
0340
0347
0342
0343
0343*
0317*
•Tha polarity grisn is that of tha ab en d s a
* fl >1IW» if Iha iwllililad Irtm
• A im rn <*«h* •*» pobridae ia the adreal d U q n M
FREQUENCY/3
to to tha
NL MASURCMCMTB
FREQUENCY/3
§4000.0
FREQUENCY/3
FIG. l .t a a a a t b q a a B c r b D '.A ld l t a i a a i d a a a ir i l la ik
normal f)04i i1laihnr|t ia ■ imsnrrin laid at 300 O. Tha rood liaa is tba
ll|ia i« lf ll rtnll iftT sra-t" lOOOdiplll paints, aad tha daahad lias ia tha
toad modalllaa ahapa. Tha modalartna pattata la that aipaaad fertha
law bam modabdca atow a. (a) Tha stress "K iP * liaa. 14 ■Tarr Kr
aad I mTott IV (b) Tha pareally hlmdart a KiD~ sad "K rD " (P - 9/2
- 9/ 3) maaadoaa. I aToar Kr aad I aToar O f Tha nlanaa iaaaaiqr of
tha tao faatuaa waa eoaanaaaad ia tha Uoa shape nodal to a vataa of 3.00
baaadoa Ilia uaa il| sqaal lman|T alanatanraa and rt>aIrnnaa dlrscnon oodaa matrix a te a o a . (cf Tha naakrit lina obaarmd. ’•KrD*’. with 14
mTorr Kr tad 1mTcrr Dp Th* MjnxUtxxsss ratio shown m s obcsrosd
After aboot 1/2 hofagMiavwmgimg.
TheB(nai-to-oaaia ratio is some typical K rD * spectra
and tha quality o f tba line shape t o that aoold be obtained
a n illustrated in R g. 1. Tha strong " K rD * line shown in
R g. 1(a) waa observed aad fit several times each in the mag­
netic Arid enhnnced discharge (with a single polarity) and in
the normal zaro field glow for both discharge polarities. The
ranter frequency data thos obtained is collected in Table I.
Each o f the three data sets is eeen to be internally ronsistrtit
and significantly differen t from the other sets. The Doppler
shift dne to ion drift velocity in the normal discharge ia seen
to be small and of the expectad sign, and the two polarities
can be averaged to obtain the rest frequency. The abnormal
discharge m a lt ascends this value by 26 kHz, end a negative
correction o f this magnitude has accordingly been applied to
the frequencies for all other isotopic forms, which were ob­
served only in the magnetic field (abnormal mode). The most
interesting result in Table I is the sign o f tha Doppler shift in
the abnorm al mode, which is exactly opposite to what would
be predicted from the direction of current flow. Blake «i a i . 13
also observed a backward Doppler shift in their abnormal
glow observations oo H OC*, but attributed it to gas flow in
the ceil. Such an explanation is not available in the present
work since the direction of microwave propagation and the
direction and speed of gas flow were the same for all the
esperimsnta shown in Table L The observed Doppler shift
appears to indicate a small negative electric field, i.e* one
pointing from cathode to anode, in the region where the ions
are being observed. Some author* have suggested soch a
small negative field in the negative glow region o f glow dis­
charges.14
The only other complication in the frequency measure­
ments waa the accidental partial Mending o f the “ K rD * line
and the F m 9/2-*9/2 hyperfine component of “ K rD *
shown in R g 1(b). At the pressure used for that spectrum
(—9 mTorr) sufficient separation was obtained so that the
frequency accuracy ofthe two lines was not much degraded.
The weakest transition observed, that o f 71K rD *, is shown
in R g 1(c), and the line shape fit can be seen to be still adequate for a very good frequency determination. Several independent spectra were fit for each line and the final averaged*
J. Chem. Phy*.. Vol. at. No. 12. Pi 1. 15 Oocomoor 1964
401
Warner. Conner, and Woods: Rotational transitions of KrO"
TA H I B n 0 . . . - . . 4 .»H
“ Kr
•*Kr
Vf - T2 " T 2- )/
( "
t
-
t
)
(*bl
“ Kr
■Kr
” Kr
f— p.—w^ . ft—■— h m t n p , A— (I. M U .|
Obaenred
Calculated
O-C
231 408.(83(13)
231 343.317(10)
231 383.608(20)
231 408899
231 343.304
-0 0 1 4
4-0013
231 613317
231 688287
231 838347
231 996008
4-0.008
-o.ooa
4-aoto
-a o io
231 388268(20)
..........................
231 689.066(201
231613.823(20)
231688379(13)
231 838337(23)
231991998(23)
corrected frequencies are shown in Table n , along with a
hyperflne removed frequency for “ K rD + .
tain revised molecular parameters. The basic Dunham for­
m ula" for the rovibrational energies
IV. ANALYSIS AND DISCUSSION
+
As a first step in treating the data o f Table II the three
° K r D '* hyperflne components were employed in the contact of the
Hamiltonian
fn*(i)+cw
i-j
♦
in
to obtain the coupling constants * Q q and C H, shown in Table
HI, and the unperturbed center frequency v„. With only
three components available there is no redundancy in this
determination, but the precision of the measurements is ade­
quate to reiiably obtain ail three values. In Table m the same
two coupling constants for the isoelectronic D 7*Br and
D*‘Br molecules are given for comparison along with values
for the nuclear magnetic dipole moments (p) and electric
quadrupole moments (0 ) o f the relevant nuclei. Although
the e Q q values are clearly more precise than the Q values, as
evidenced by the comparison o f the two bromine isotopes, it
can be inferred that the field gradient parameter q is rather
similar in K rD * and DBr, indicating very similar electronic
structure. The magnetic coupling constant C v for t , KrD'*
is negative as would be expected17 for a nucleus with a nega­
tive magnetic moment like “ Kr. The magnitude c S C „ is
even smaller in u KrD'*' (relative to DBr) than would be ex­
pected from the relative sizes o f the nuclear magnetic mo­
ments.
There remain in Table II six rotational frequencies to be
combined with the Dunham constant data o f Johns1 to ob­
rOrlMHz)
C.IMHz)
Q (bama)
H(ouclaar ma(Batoas|
“ KrD*(or“ Kr)
349.1(31*
-O022(2r
4-<X270(13r
-0.970 66913)*
D*'Br (or *'Bf)
443.363(1031*
4-0138(12)*
+Q.2wr
4-2370 360(4r
(2)
is used along with the formula1*-11
giving the Dunham coefficients in terms of mass indepen­
dent parameters. The reduced mass ^ in Eq. (3) is according
to Watson1*:
M - M .A f» /(M .
(4)
where C is the charge number o f the species (1 for K tD *).
Johns1 " ” «■* all 4 's were zero and obtained U u for
k i m 10,20.01,11,21,02,12,03, and 04. O f these only If01,
U n , If,,, C/in, *°d If,, have any nonnegiigible contribution
to t h e / ■■0-1 frequencies for K tD * . These five were used to
predict the microwave transition frequencies with resultant
values systematically cxcrrriing the actual observed frequen­
cies by about 9 MHz, just as Bowman
.* found in the
ArD'* case. This is due to th e d “i coefficient, and in addi­
tion there is a small systematic trend in the variation of ob­
served minus predicted frequency with krypton mass num­
ber. The latter effect will be ascribed to d ie d $ f coefficient.
The other d coefficients are expected to make a negligible
contribution to these variations with krypton isotope and
hydrogen isotope. In particular Sastry t t a l . a have found the
Y „ scales very accurately as
in the N aH -N aD pair.
Consequently all the other four Dunham coefficients If,,,
tt at
TABLE m . Hypartna coupling comtana and nuclear moman a for “ KrD* and D*‘Br and D^Br.
Qoaadty
+
D"Br(or ™Br)
330.648(741*
4-0148(91*
4-0293*
4-2.106 399(41*
‘This work.
"Reference IS.
0Reference 16.
j. Cham. Phys.. Vol. 81. No. 12, P t 1.19 Oaeambar 1984
Wamar, Conrw. and Woods: Rotational transitions of KrD*
5416
TABLE IV. H u Doaham cradlriaita and aqmKbrinm bond »««««-<—for
KrH4 aad m
a a p a a i with ArH". Uu in uma of (MHz)
fm m ?"* . d Mis tHmanainalaaa
Qaaadty
Vataa
Thaory
KiH*
_.v«
V.
(Oariaaaa
lU l + a a,d 8 /J# .l
4ST
4£
r-lAl
AxH*
d ir
dS
a* ,
rflA l
• I d h w n l.
‘T taw e* .
'Radm aer 6
—7937.021(731*
36390(23)*
- 113331(17)*
ai2IS2(lSr
250 23r03(30r
230222.644113)*
0.682(70|P
a 1213(40)*
230214364(300)*
1.4211911(7)“
I.4l9(3r
a9 i(io r
0.1244(37)*
306 279J43(34r
13503726(1)“
1356*
001 ( '? “ ) 2 - * - 305 379 MHz A2 amu
!
— H I . ..1 1 — 11— U -
terms)]
,3 >
was
used
(7)
used by Bogey t t a l .* for CO4". The errors in r , shown in
Table IV merely reflect the experimental precision in U o l ,
not model errors o r error in the conversion factor. The re­
sults for the r , ’s are also compared very successftilly to the
CEPA values ofRosmua and co-workers.4,7The r , o fK rH 4
exceeds that of HBr (1.4145 A11) by 0.0067 A and r , of
ArH 4, exceeds that o f H Q (1.2746 A11) by 0.0058 A.
‘C d o M t n M l .
*IUnsaaos7.
rSMtha to t conoaraint «nr m r J°.
U 7 l, U m and U a were hekl B u d a t the values derived by
Johns.1These are shown inTsble IV converted to MHz units
(c « 2.997 924 58X 1010 H z/cm -1). Atomic masses were
taken from Mathews and R io,21 and m , —0.000 348 J80 3
amn was employed. The equation
^ [v •
Table IV and the residuals with the experimental values are
displayed in Table II, where it may be seen the latter are
essentially random and of a magnitude consistent with the
estimated measurement errors.
Finally the U m Dunham coefficient can be used to cal­
culate the Bom-Oppenheimer equilibrium bond distance. In
T able IV this has been done for K rH 4 , and also for compari­
son purposes the same computation was made for A rH 4
uihig this U m of Johns.1 The calculation was marie with the
u i m simple relation
with
linear least squares to find
U n { l + m ^ a x / M o ) and
[ibe intercept and
slope a plot o f left-hand side vs (Af*,)-1]. Finally Johns
value o f
moat be reinterpreted as
at
*■0 l o iM B[ i +xr^“ ^Srl»
(®)
J
and the values for <70„ A ”,, and 3 S ' can be found from the
three linear equations. These are also given in Table IV
where they are compared to the similar results for ArH 4’A rD 4-. The tw o d parameters are very pleasingly consistent
between the two ions, indicating they have been well deter­
mined in each case. The a i m in the values o f U 0 l a n d d "
come mostly from the value of the infrared T a , coefficient,
but am correlated so that the microwave value of U 0 )
(1 + m .d ft/M o Jis given correctly. The error i n d j f comes
entirely from the measurement errors in the microwave tran­
sitions. The frequencies computed from the parameters in
‘R. C Woods, in M oitnlar I<mr. Sim.-tmm.vff, Stm am . a tti CStmiarf,
adtad by T. A. Millar sad V. E. Boodybay INonb-HoOaad. Ajmtodaa.
19S3lp.ll.
T r r iviwiihs n r t nw aaiu n H w it iw ir r n«i mis r nm n
Phya. 79, 2093119131.
>1. W. C io tas. J. MoL Spaonoao. 106, 124119S4L
*1. W. BnahaadS. P. Daria. Phya. Scr. 25,268(1982).
’N.HaaaaaadT.OkaltobapabUahad).
—"
‘
■ — 1064(19801.
> . Roauaa, Thsor. CUn. AcaSL 339(1979).
*M- Bopy. C. Daeaayack. sad J. L. Daaaoabaa, J. d am . Phya. 79.4704
(19U).
*C.1 (M m a s a d A C Woods. Phya. Rav. Lao. 48.1344(1982).
"H. E Wamar. W. T. Coonw. R. t t PanaichL aad R. C. Woods, J. d m .
Phya. I t 2314(1914*.
"F. C DaLada. & Harbaa, O. M. Phuaaur. sad O. BMu. J. d m Phys.
76.2312 (1963).
” H. M. Ptefcact. AppL Opt. 19,2743 (1910).
aQ. A. Btaka P. Halaaaaar, & Hsrbat. aad F. C DaLuraa, Astmphya. J.
264. L69( 1983).
I4J. O. rulikia Gamomi Caadanan TStory and Eigtimriag AppUcaxxxa
(Dorar. Naw York. 1938), pp. 213-213.
“F. C. DaLada. P. Hetaaaav.aad W. Ooady. Phya. Ra*. A 3 ,1S49( 1971).
'•T ata o fbatata. 7th ad. (WDay. taw York. 1978).
ITCH .Tow aaaaadA 1.5ct awlow.Jft'»wMa iaSipae«»«aewy(Doiiar.taw
York. 1973), pp. 216-217.
» j. L. Doahaaa. Phya. Rav. 4L 72111932).
'*1. K. O. Waaoa. J. MoL Spactraao. 80.411 (1980).
"A .R M . Rosa.R. S. Ea* and H.KildatOpt. Common. 12.43311974|.
"P. A Boakar. J. MoL Spaeooao. (6 36711971L
“ K. V. L. N. Sassy, E. Harbat, aad F. C DeLuda. J. dam . Phya. 75,4733
I19IIL
°C W. Mathawaaad K- N. Rao, MobcuIarSptcmucopr Madam Ataarch
(Acadaaau taw York. 1972).
J. Cham. Phya.. Vol. 81. No. 12. PL 1.15 OeeemCer 1984
403
A P P E N D IX 2.
T H E D E T E C T IO N O F T H E l n - l 10 T R A N S IT IO N O F H 2 D+.
404
Laboratory detection of the 1i<r*-1u submillimeter wave transition
of the H2D+ iona)
Hugh E W amer, William T. Conner, Rudolph H. Petrmichl, and R. Claude W oods
Department o fChemistry, Unioersity o f Wisconsin. Madison, Wisconsin 53706
(Received 7 June 1984; accepted 19 June 1984)
In the interstellar medium H,* is one o f the most abun­
dant ions and also one o f the most fundamental to the chem­
istry.' The high resolution infrared spectrum of H,* was
obtained by Oka2 several years ago, but because the dipole
moment vanishes by symmetry, there is no pure rotational
spectrum and Hs+ is not a candidate for radio astronomy. As
pointed out by Dalgamo er a/.3 though, its isotopic variant
H2D * has a substantial dipole moment (0.6 D) in its center of
mass system, and thus it does have a sparse pure rotational
spectrum. Only a few
transitions across the/T-type doub­
lets fall within the range below 1000 G Hz that is at all acces­
sible to microwave techniques. O f these the 110»—1M is the
strongest and also the one o f greatest astrophysical interest
because it involves the lowest rotational levels, those that are
populated at low interstellar temperatures. In fact, these two
levels are the lowest ones that exist in the stack with proton
spin statistical weight 3 so the 1,, level will have substantial
population at even the lowest temperatures in the interstellar
environment The H jD * ion itself is of great importance in
the interstellar medium because the reaction
HD + Hj*—H iD ^ + H j
(1)
is understood to be responsible for the dramatic fractiona­
tion of deuterium into molecular ions like DCO* and
D N N *.' The reverse reaction o f Eq. (1) is greatly inhibited
by zero point vibrational effects. Recently Amano and Wat­
son4 have observed the v, band of H ,D +, and Oka and co­
workers9 have observed the v, band. We were greatly assist­
ed in this work by having access to the frequency prediction
of 372 383 ± 106 MHz for the transition of interest that
comes from the spectra and analysis o f Amano and Watson.4
We were also fortunate to have been provided an estimate of
372 681 MHz based on corrected a b i n i t i o results in March,
1981 by Porter.6
We have observed the 1,0- l ,, transition ofH 2D * in the
same 10 cm diam glow discharge tube system used earlier for
H OC*.7 The fourth harmonic of a 93 GHz klystron was
generated in a Millitech harmonic generator, and detection
was by crystal o f InSb in a 5 kG magnetic field at 1.7 K. A
solenoid magnet was added to provide an axial magnetic
field of 300 G in the discharge according to the scheme of
DeLuda e t a i .* and a modified hollow cylinder cathode (8
cm diam by 20 cm long) was placed just inside the magnet.
Discharge voltage was 1900 V, the current was 20-40 mA,
and liquid nitrogen cooling was always used. Mixtures of 8
mTorr A r and 0.3 to 3 mTorr total H2 plus D} in a 2/1 ratio
were used in a fast flow system. Mixtures without argon were
not usable because of discharge instabilities. The observed
signal disappeared when either H} o r D} flow was cut off,
and when the H2/D 2 ratio was changed from 2/1 to 1/2 the
signal intensity decreased by a factor of two as expected for a
molecule with one D atom and two H atoms. The observed
2 6 1 4
J . C h e m . P h y s . 8 1 ( 6 1 .1
S e p te m b e r 1 9 6 4
line was visibly quite broad, as would be expected for a very
light ion, and the variation of signal strength with discharge
voltage was typical of that observed for ions. The signal-tonoise ratio that was obtained was never better than about 6
or 7 to 1 with a few minutes of signal averaging, but the line
was very reproducibly observed on every one of 23 attempts.
We have obtained a frequency of 372 421.380 MHz by
averaging the results of nonlinear least squares fits on 13
independent sets o f spectral data. The 93% confidence limit
is ;± 0.023 MHz based on the Student-; distribution and the
observed sample standard deviation for the 13 trials, but the
uncertainty must be increased to ± 0.100 MHz to allow for
possible systematic errors including Doppler shift due to ion
drift and gas flow and small admixture of anomalous disper­
sion into the absorption line shape. In the experiments the
direction of microwave propagation was the same as that of
the gas flow and opposite to that of the drift velocity. None of
these three directions could be conveniently reversed, so no
measurement of Doppler shift was attempted. Previous
workers,6*10however, have observed that Doppler shifts are
particularly small for this kind of abnormal discharge in a
magnetic field. The actual observed frequency is well within
the range predicted by Amano and Watson,4 and the pre­
viously mentioned prediction of Porter6 must also be consid­
ered to have been very successful The present precise fre­
quency for one transition can o f course be merged with the
infrared data to obtain an improved set of molecular con­
stants. Even greater refinement will be passible if one or
more additional rotational transitions can be detected.
After this work was completed we learned that this
same transition, in very similar conditions, and at about the
same time was also observed by M. Bogey, G Bemuynck, M.
Denis, J. L. Destombes, and B. Lemoine [Astron. Astrophys. (to be published)].
“This work wnsupportedby the NuioulScienceFoundation'sStructural
o^m iuiy Program, the Wisconsin Alumni Poundslion, aad tbs Donors
of tbs Petroleum Research Fuad, admiaiiaand by tht AnMncan Chemi­
cal Sodccy.
'R. Clauds Woods, in Molecular/txsr SpKtmmxipr,Stmctun, aW Chtmistry, edited by T. A. Miller and V. E Boodybey, (North-Holland, Am­
sterdam, 1983), p. 11. This review article contains an overview of the role
ofH D * in tbe interstellar chemistry and provides many references to the
original aatnnsosnicalliteraiure.
*T. Oka, Phya. Rev. Leo. 45.331 (1980).
’A. Dalgarno, E Herhet, S. Novick, aad W. Klemperer, Aattopbys. J. 113,
L13L(1973).
*T. Amano and J. K. O. Watson, 3. Chcffl. Phys. (to be published).
*T. Oka (private communication).
*R. N. Porter (private communication).
’C S. Oodemaa and R G Woods, Phys. Rev. Leu. 45. 1344(1982).
'F. G DeLuda, E Herhst, O. M. Plummer, and O. A. Blake, J. Chest.
Phya. 78.2312 (1983).
*W. G Bowman, E Herhst, and F. G DeLuda, 1. Chan. Phys. 77,4261
(1982).
>0O. A. Blake, P. Hehninger, E Herhst, and F. G DeLuda, Astrophys. I.
264, L69( 1983).
0 0 2 1 - 9 6 0 6 /8 4 /1 7 2 5 1 4 4 )1 $ 0 .2 .1 0
O
1 9 8 4 A m e r ic a n
I n s t i tu t e o t P h y s ic s
APPENDIX 3.
PR O G R A M D O U B PI.FO R .
P R O G R A M D O U B P I.F O R
i m p lic it real* 16 (a-h,o-z)
d im e n sio n a( 2 ,2 ),c( 2 ,2 ),z( 2 ,2 ),ct( 2 , 2 ),res( 2 , 2 ),anew res( 2 , 2 ),
lzt(2,2),zfin(2,2),w (40),zm at(40)
a g l= l.
ag2=2.0023
a m u b - 1.3996108
C
C T H E I N P U T P A R A M T E R S A R E R E A D IN T H E O R D E R A, B, D,
P,
C H, GN , GP, A N D
C GQ. T H E I N P U T IS F R E E FO R M A T .
C
read(20,*)an,b,d,A P R ,h,A G N ,agp,A G Q
w rite(10,1065)an,b,d,h,A P R ,A G N ,agp,A G Q
1065
f o rm a t(3 x ,’a is e q u a l to ’,3x,fT7.8,’c m - r / 3 x , ’b is equal to
13x,f 17.8,’a n d d is e q u a l’,f 10.7,’a n d h is e q u a l’,f l0 .6 /3 X ,
2’a n d th e lam b d a d o u b lin g p a ra m e te r is’,f 17.8/2x,’G N
3p a ra m e te r is’.f 13.7/’GP IS \F 1 3 .7 /’GQ IS’,F13.7)
an=an*29979.2458
do 1 0 i 2 j = l , 1 0
IN V A R -4 * (I2 J - 1)
sj=qfloat(i2j)-0.5
sj0=sj+0.5
sjl2=(sj+0.5)**2.
a f a c = a m u b * h /( 2 .*s j*(s j + 1 .))
DO 11 I P A R -1 ,2
IN T E R M -2 * I P A R
C
C T H E Z E R O F IE L D M A T R IX ELE M E N T S A R E C A L C U L A T E D
F O R B O T H P A R IT IE S
C 1 C O R R E S P O N D S T O T H E O M E G A - 1/2 A N D 2 T O O M E G A - 3 /2
C
A P F A C -(2.*Q F L O A T (IP A R ))-3.
a( 1,1 )-an/2.+b*((sj**2.)+s j-(7./4.))
1-d*((sj 12**2.)+(3.*sj 12)+1.)
IF (12J .EQ. l ) A ( l ,l ) - 0 .0
a( 1,2)—(b+apr/4.-(2.*d*s j 12))*qsqrt(s j*(s j + 1.)-(3./4.))
IF (12J .EQ. 1)A(1,2)=0.0
a(2,2)—an/2.+ b*(sj 12)-d*((sj 12**2.)+(3.*s j 12))
l+ (Q F L O A T (I2J)*A P F A C *( A P R /2.))
a( 2 ,l ) = a ( l , 2 )
B T = a (l,l)+ a (2 ,2 )
C T a=(a( 1,1 )*a(2,2))-(a( 1,2)**2.)
C
C T H E E IG E N V A L U E S A R E C A L C U L A T E D F O R BOTH P A R IT IE S
C
W up-(BT+QSQRT(BT**2.-4.*CT a))/2.
w (IN V A R + IN T E R M -1 )=wup
W lower=(BT-QSQRT(BT**2.-4.*CT a))/2.
407
w (IN V A R + IN T E R M )= w low er
IF (i2J .EQ. 1)C2C1=0.
IF (i2J .EQ. l)G O T O 22
C 2 C 1=(a( 1,1 )-W low er)/a( 1,2)
22
A R C 1=(C2C 1**2.)+1.
C (2 ,1)-(1 ./A R C 1)**0.5
C (2,2)= C (2,1)*C2C I
IF (i2 J .EQ. 1)C (2,2)-1.
IF (i2 J .EQ. l)C (2 ,l)-0 .
c ( l,l) - c ( 2 ,2 )
c ( l ,2 ) - c ( 2 ,l )
c t( l,l) - c ( 2 ,2 )
c t( 2 ,l) - c ( l,2 )
ct(2,2)=c(2,2)
c t ( l ,2 ) - c ( l ,2 )
c a ll m u lt(a ,c ,re s)
c all m u lt(c t,re s,a n e w re s)
do 1492 ic k -1 ,2
do 1493 jc k -1 ,2
w rite (1 0 ,1 4 9 4 )sj,ic k ,jc k ,a n e w re s(ick ,jc k )
1494
f o rm a t( l lx .’f o r j - \ f 5 .2 ,/ 3 x ,’fo r i a n d j\2 i3
1,’o u r e n e rg y m at is \f l9 .8 )
1493
c o n tin u e
1492
c o n tin u e
w rite ( 10,1066)a( 1,1 ),a( I ,2 ),a(2,2),w up,w low er,c(2,1),c(2,2)
1066
fo rm a t(3 x ,’th e m a trix elem en ts < 3/2|3/2> ,
l< 3 /2 |l/2 > ,a n d < l/ 2 |l /2 > a re as fo llo w s,/3 f2 0 .8 /3 x ,,th e en erg y
2 e ig e n v lau e s a re ’/2 f2 0 .8 /3 x ,’an d th e tra n s o rm a tio n c o e ffic ie n ts
3 a re ’/ 2 f 15.8)
C
C T H E ZE E M A N M A T R IX ELE M E N TS A R E C A L C U L A T E D
C
z(2,2)«afac*(agl-0.5*ag2)+ (A P F A C *((afac*sj0)*agp))
1-2.* A G N*S J 12* A F AC
z( 1,2 ) - a f ac*(ag2-( A PFA C * A G Q ))*qsqrt(sj 12-1.)
z (2 ,l) - z ( l,2 )
z( 1,1 )-3.*afac*(agl+ 0.5*ag2)-2.*A G N *SJ 12* A F AC
ca ll m u lt(z,c,res)
ca ll m u lt(c t,re s ,z fin )
do 1496 ic k -1 ,2
do 1497 jc k -1 ,2
w rite (1 0 ,1 4 9 8 )ic k ,jc k ,z (ic k ,jc k ),z fin (ic k ,jc k )
1498
1497
1496
11
10
fo rm a t(3 x ,’f o r i a n d j ’,2i3,’o u r zeem an m a trix is’,2 f 19.8)
c o n tin u e
c o n tin u e
z m a t(IN V A R + IN T E R M -1 )= zf in( 1,1)
z m a t(IN V A R + IN T E R M )» z f in(2,2)
C O N T IN U E
c o n tin u e
W R ITE( 10,23)
23
F O R M A T (2 X ,’F O R T H E O M E G A -1/2 CASE WE H A V E
CALCULATED TH E
1 FO L L O W IN G T R A N S IT IO N F R E Q U E N C IE S ’/3 X ,’T H E
IN F O R M A T IO N IS G IV E N
2 IN T H E O R D E R JLO W ER JU P P E R N U (-) N U (+ )’)
do 20 Ij-2 ,3 6 ,4
tra n s= w (ij+ 4 )-w (ij)
tra n s l= w (ij+ 6 )-w (ij+ 2 )
S J= (IJ)/4 .
SJ1-S J+ 1.
w rite ( 10,21 )SJ,SJ 1,tra n s I .tra n s
21
fo rm a t( 1x ,2 F 5.2,2 F 17.8)
20
c o n tin u e
W RITE( 10,230)
230
F O R M A T (2 X ,’FO R T H E O M E G A -3 /2 CASE WE H A V E
CALCULATED TH E
1 FO L L O W IN G T R A N S IT IO N F R E Q U E N C IE S 7 3 X ,’T H E
IN F O R M A T IO N IS G IV E N
2 IN T H E O R D E R JLO W ER JU P P E R N U ’)
do 208 Ij=2,36,4
tra n s= w (i j+ 3)-w (i j - 1)
tra n s 1=w (i j+5)-w (i j+ 1 )
S J - (I J )/4 .
SJ1-S J+ 1.
w rite ( 10,218)S J,SJ 1,tra n s 1, tra n s
218
fo rm a t(lx ,2 F 5 .2 ,2 F 1 7 .8 )
208
c o n tin u e
w rite ( 10,330)
330
fo rm a t(2 x ,’N ow we w ill p r in t th e zeem an e ffe c ts f o r the
om ega
1= 1 /2 s ta te ’)
do 331 ij-2 ,3 6 ,4
a j- q f lo a t( ij) /4 .
a jl- a j+ 1 .
w rite ( 10,335)a j,a j 1
335
f o r m a t( lx ,’F O R T H E J - ’,F7.3,’T O ’,F7.3,’T R A N S IT IO N S 7 2 X ,
I ’M LO W E R ’,2 X ,’M U P P E R ’,2 X ,’D E L N U -P A R ’,2X ,’D EL N U +
P A R ’,2X ,
2’R E L A T IV E IN T E N S IT Y ’)
su m n p -0 .0
su m p p -0 .0
su m in t-0 .0
D O 3310 I J 2 —ij,IJ,4
A IJ2 = Q F L O A T (IJ2 )/4 .
A IJ2 1 -A IJ2 + 1 .
te rm l= A IJ 2 * z m a t(ij)
term 2= (A I J 2 + 1.)*zm at(i j+4)
te rm 3 -a IJ2 * z m a t(ij+ 2 )
term 4 = (A IJ2 + l.)* zm a t(ij+ 6 )
sp litn p = 2 .0 * (te rm 2 -term 1)
A IN T = ( A J 1+ A IJ2 + 1.)*( A J 1+ A IJ2)
splitp p = 2 .0 * (term 4 -term 3 )
s u m in t-s u m in t+ a in t
s u m n p -s u m n p + (a in t* s p litn p )
su m p p » su m p p + (a in t* sp litp p )
w rite (1 0 ,3 3 3 )a IJ2 ,A IJ2 1 ,sp litn p ,sp litp p ,A IN T
333
fo rm at(2 x ,F 7 .3 ,2 X ,F 7 .3 ,2 X ,F 10.6,2X ,F 10 .6 ,2 X ,F 8 .3 ).
3310
c o n tin u e
a v e n p -s u m n p /s u m in t
a v e p p -s u m p p /s u m in t
w rite (1 0 ,3 3 4 )a v e n p ,av e p p
334
f o r m a t( lx ,’wc h av e a w eig h ted a v e ra g e f o r th e s p littin g s ’/
1’- p a r ity ’,f 13.7,’+ p a r ity ’,f 13.7)
331
c o n tin u e
stop
end
s u b ro u tin e m u lt(a l,a 2 ,a 3 )
im p lic it real* 16 (a-h.o-z)
d im e n sio n aI(2,2),a2(2,2),a3(2,2)
do 2 i-1 ,2
do 3 j-1 ,2
a3 (i,j)-0 .0
3
c o n tin u e
2
c o n tin u e
do 10 i-1 ,2
do 20 k -1 ,2
d o 30 j —1,2
a 3 (i,k )-a 3 (i,k )+ a 1(i,j)*a2(j,k)
30
c o n tin u e
20
c o n tin u e
10
c o n tin u e
re tu rn
en d
A P P E N D IX 4.
P R O G R A M SIM U L A T E .FO R .
im p lic it real*16 (a-h,o-z)
IN T E G E R V D _ ID ,W D _ ID 1,w d _ id ,V D _ I D 2
d im en sio n az(2,2),c(2,2),z(2,2),ct(2,2),res(2,2),anew res(2,2),
lzt(2,2),zfin(2,2),w (4),zm at(4),X Z (20),Y Z (20)
d im e n sio n a(50,2),anofld(2,2)
c h a ra c te r* 1 ian s,id isty p e
D IM E N SIO N X ( 1000),shape( 1000),
1 y n o fld (1 0 0 0 ),y 1(1000),
2 y2(1000),y(1000)
a g l= l.
ag2=2.0023
a m u b - 1.3996108
read (20,*)an,b,d,A P R ,h,A G N ,agp,A G Q
w rite(1 0,1065)an,b,d,h,A P R ,A G N ,agp,A G Q
1065
fo rm a t(3 x ,’a is e q u a l to \3 x ,f 17.8,’c m - l’/3 x ,’b is e q u a l to ’,
13x,f 17.8,’a n d d is e q u a l’,f 10.7,’a n d h is e q u a l’,f!0 .6 /3 X ,
2’a n d th e lam b d a d o u b lin g p a ra m e te r is’,f 17.8/2x,’G N
3 p a ra m e te r is’,f 13.7/’G P IS’,F 1 3 .7 /’G Q IS’,F13.7)
an»an*29979.2458
W RITE(*,*)’W HAT IS LOW ER J?’
R EA D (*,*)SJ
im ax= (nint(4.*sj))+ 2
im a x o 2 -im a x /2
im m a x o 2 1= im ax 0 2 + 1
w rite(*,*) ’ N u m b er o f baselines ’
read(*,*) nbase
W RITE(*,*) ’ O n th e k ly stro n : f r e q /p o in t, HWHM, FM (all
M H z)’
read(*,*) fin c ,h w h m ,fm
W RITE(*,*)’W HAT H A R M O N IC O F T H E K L Y S T R O N ?’
R E A D (*,*)A H A R M FA C
d o 6 ia p -1 ,2
a p fa c » (2 .* q flo at(ia p )-3 .)
d o 11 izz-1,1000
x (iz z )-0 .0
y(izz)=0.0
y l(izz)= 0 .0
y2(izz)=0.0
11
c o n tin u e
a p fa c - q flo a t( ia p )
do 10 i2 JA = 0 ,l
IT E R -(2*I2JA )+ 1
A I2J= F L O A T (I2JA )
I2 J -2
IF (SJ .EQ. 0.5 )I2J=1
sj0=sj+0.5
sjl2=(sj+0.5)**2.
afac= am u b * h /(2 .* sj* (sj+ l.))
C
IN T E R M = 2*IP A R
C
A P FA C =(2.*Q FL O A T (IPA R ))-3.
az( 1,1 )=an/2.+b*((sj**2.)+sj-(7./4.))
1-d*((s j 12**2.)+( 3 *sj 12)+1.)
IF (12J .EQ. l)A z (l,l)= 0 .0
az( 1,2)—(b+ apr/4.-(2.*d*sj 12 ))*qsqrt(sj*(sj+ 1.)-(3./4.))
IF (I2J .EQ. l)A z(l,2)= 0.0
a z (2 ,2 )-a n /2 .+ b * (s j 12)-d*((sj 12**2.)+(3.*sj 12))
1+(SJO* A PF AC*( A P R /2 .))
a z (2 ,l)- a z ( l,2 )
B T -a z (l,l)+ a z (2 ,2 )
C T a -(a z ( 1,1 )*az(2,2))-(az( 1,2)**2.)
W up-(B T +Q SQ R T(B T**2.-4.*C Ta))/2.
w (IT E R )-w u p
W Iow er-(B T-Q SQ R T(B T**2.-4.*C T a))/2.
w (IT E R + 1)-w lo w e r
IF (i2J .EQ. l)C 2 C l-0 .
IF (i2J .EQ. l)G O TO 22
C 2 C 1-(a z ( 1,1)-W lowcr )/a z ( 1,2)
22
A R C 1*»(C2C 1**2.)+1.
C (2 ,1)-(1 ./A R C 1)**0.5
C (2 ,2 )-C (2 ,1)*C2C 1
IF (i2J .EQ. 1)C(2,2)-1.
IF (i2J .EQ. l)C (2 ,l)-0 .
c (l,l)- c ( 2 ,2 )
c ( l ,2 ) - c ( 2 ,l )
c t( l,l) -c ( 2 ,2 )
c t( 2 ,l)- c ( l,2 )
ct(2,2)-c(2,2)
c t ( l ,2 ) - c ( l ,2 )
call m ult(az,c,res)
call m u lt(ct,res,an ew res)
do 1492 ic k -1 ,2
do 1493 jc k -1 ,2
w ritc ( 10,14 9 4 )sj,ick ,jck ,an ew res(ick ,jck )
1494
fo rm a t(l lx .’fo r j - ’,f5 .2 ,/3 x ,’f o r i an d j\2 i3
1,’o u r e n erg y m at is \f l9 .8 )
1493
c o n tin u e
1492
c o n tin u e
w rite (1 0 ,1 0 6 6 )a z (l,l),a z (l,2 ),a z (2 ,2 ),w u p ,w lo w e r,c (2 ,l),c (2 ,2 )
1066
fo rm a t(3 x ,’th e m a trix elem ents < 3/2|3/2> ,
l< 3 /2 |l/2 > ,a n d < l/2 |l/2 > a rc as fo llo w s 7 3 f2 0 .8 /3 x ,’th e en erg y
2 eig en v lau es a re 7 2 f2 0 .8 /3 x ,’a n d th e tra n s o rm a tio n c o e ffic ie n ts
3 a re 7 2 f 15.8)
z(2,2)-afac*(agl-0.5*ag2)+ (A P F A C *((afac*sj0)*agp))
1-2.*AGN*SJ12*AFAC
z( 1,2 ) - a f ac*(ag2-( A PFA C * A G Q ))*qsqrt(sj 12-1.)
z (2 ,l)-z (l,2 )
z( 1,1 )-3 .* a f ac*(agl+0.5*ag2)-2.*A G N *SJ 12*A FA C
call m ult(z,c,res)
c all m u lt(c t,re s,z fin )
413
do 1496 ic k = l,2
do 1497 jc k = l,2
w rite ( 10,14 9 8 )ic k ,jck ,z (ic k ,jck ),z f in (ic k ,jc k )
1498
1497
1496
c
10
fo rm a t(3 x ,’f o r i a n d j\2 i3 ,’o u r zeem an m a trix is’,2 fl9 .8 )
c o n tin u e
c o n tin u e
z m a t(IT E R )= z f in ( 1,1)
z m a t(IT E R + 1)= zfin(2,2)
freq0= w (4)-w (2)
SJ=SJ+1.
c o n tin u e
S J-S J-2 .
W RITE( 10,330)
fo rm a t(2 x ,’N ow we w ill p r in t th e zeem an e ff e c ts fo r th e
330
om ega
1= 1 /2 s ta te ’)
aj=SJ
a jl- a j+ 1 .
AIJ2=4.*SJ
AIJ2S=2.*SJ
IJ* N IN T (A IJ2 )
IJ2A = N IN T (A IJ2S )
IN T =2*IJ2A +4
w rite (1 0 ,3 3 5 )a j,a jl
335
f o r m a t( lx ,’F O R T H E J= ’,F7.3,’T O ’,F 7 .3 ,T R A N S IT IO N S V 2 X ,
I ’M LO W E R ’,2X ,’M U P P E R ’,2X ,’D E L N U -P A R ’,2 X ,’D EL N U +
P A R ’,2X ,
2’R E L A T IV E IN T E N S IT Y ’)
sum int= 0.0
DO 3310 IJ2 IN = l,Im a x o 2
IJ2= (4*IJ2IN )-IN T
A IJ2 = Q F L O A T (IJ2 )/4 .
A IJ21=A IJ2+1.
term l= A IJ2 * z m a t(2 )
term 2= ( AI J 2 + 1.)*zm at(4)
sp litn p = (te rm 2 -te rm 1)
iv a r= im a x o 2 + ij2 in
a (iv a r,l)= s p litn p
a (ij2 in ,l)= -s p litn p
c
X M A X = SPL IT N P* 100
C
X M IN =SPL IT N P*100
TS=2.*SPLITN P
A IN T =( A J 1+ A IJ2 + 1.)*( A J 1+A IJ2)
a (iv a r,2 )= a in t
a (ij2 in ,2 )= a in t
c
A IN T -A IN T /1 0 0 .
c
Y M A X = aint
c
YMIN=0.01
c
C A LL U M O V E (X M IN ,Y M IN )
c
C A LL U D R A W (X M A X ,Y M A X )
su m in t= su m in t+ a in t
su m n p = su m n p + (a in t* sp litn p )
w rite ( 1 0,333)aIJ2,A IJ21,sp litn p ,A IN T ,T S
333
f o rm at(2x,F 7.3,2X ,F 7.3,2X ,F 10.6,2X ,F 10.6,2X ,F8.3)
3310
c o n tin u e
c
a n o fld ( l,l)= 0 .
c
a n o fld (l,2 )= 2 .* su m in t
a v e n p = s u m n p /s u m in t
a v e p p = su m p p /su m in t
w rite(1 0 ,3 3 4 )av en p ,av ep p
334
f o r m a t( lx ,’we h a v e a w e ig h te d a v e ra g e fo r th e s p littin g s ’/
1’- p a r ity ’,f 13.7,’+ p a r ity ’.f 13.7)
331
c o n tin u e
c now a d d u p a ll th e lin e sh ap e fu n c tio n s, th e re a re im ax lines,
c each is c e n te re d a t a (l,l) w ith in te n s ity a(i,2)
M A X S H P -1000
fcen = M A X S H P /2 .* fin c
do 30 k= l,M A X S H P
fre q = fin c * k
C M U L T IP L Y BY 0.001 T O SC A LE DOWN V A LU E S
sh ap e(k )= 0 .0 0 1*hw hm *( 1./( ( f re q -f cen)**2.+h whm**2.)
1 -.5 /((f re q -f c e n -f m)**2.+h whm**2.)
2 -.5/((freq-fcen+ fm )**2.+ hw hm **2.))
30 c o n tin u e
x m in —500.*FIN C
xm ax= 500.*finc
do 50 k -1 ,1 0 0 0
x (k )= x m in + f in c * (k -1)
x (k )= x (k )/a h a rm fa c
50 c o n tin u e
do 60 1=1,im ax
c i s t a r t - f i r s t p o in t in y a rr a y to a d d th e lin e shape fu n c tio n shape(k)
ista rt= n in t(M A X S H P /2 -(a (l,l)-X M IN )/fin c )
do 70 k » l,1 0 0 0
k s= ista rt+ k -l
IF (K S .L T .l) G O TO 70
IF(KS.GT.IOOO) G O T O 70
c
y n o fld (k )= a n o fld (l,2 )* sh a p e (k s)+ y n o fld (k )
y(k)= a(l,2)*shape(ks)+ Y (K )
70 c o n tin u e
60 c o n tin u e
c
c E n d o f calc loop
c
c2
w rite(*,*) ’W hat d evice a re you using?’
c
w r i t e ( V ) ’ VT-241
E n te r A ’
c
w rite(*,*) ’ LN 03
E n te r B’
c
w rite(*,*) ’ O th e r T ek E n te r D’
c
w rite(*,*) ’ H P p lo t E n te r F ’
415
c
r e a d (*,1) ians
cl
f o rm a t( a l)
c
w rite(*,*) ian s
c
if(ia n s.e q .’A ’) th e n
c
c a ll uslD G G
c
O P E N (U N IT = 8 8 ,F IL E = ’$D A T A D IS K :[T E M P L A T E ]V T 241.C O N F IG ’,
c
, R E A D O N L Y ,S T A T U S = ’O L D ’)
c
C A L L U C O N FG (88.)
cc
else if(ia n s.e q .’B’) then
cc
c a ll uslL N 3
CC
O P E N (U N IT = 8 8 ,F IL E = ’$U SER D ISK :[40R C W .W T C ]LN 03.C O N FIG \
cc
, R E A D O N L Y ,S T A T U S -’O L D ’)
cc
C A L L U C O N FG (88.)
c
else if(ia n s.e q .’D ’) th en
c
call u slT E K
c
else if(ia n s.e q .’F ’) th en
c
w r i te ( V ) ’H P p lo tte r selected.’
c
c a ll uslH EW
cC
c a ll upset(4houtp,53.0)
cC
c a ll u p set(4 h w rit,5 4 .0 )
c
else
c
w rite(*,*) ’E rro r in e n try ; e n te r A th ro u g h F to select d e v ic e .’
c
go to 2
c
en d if
c
H O P E N (U N IT = l 1,F IL E = ’$ D A T A D IS K :[T E M P L A T E ]T P L F N T .F N T ’,R E A D O N L Y ,
c
, A C C E S S -’D IR E C T ’, S T A T U S -’O L D ’)
C***
C A L L U C O N FG (3.0)
C
c
CALL U STA RT
C DRAW G R A P H H E R E
c
C A L L U S E T (’P E R C E N T U N IT S ’)
c
C A L L U V W PR T (0.0,100.0,0.0,100.0)
c
c
c
c
IF(IA N S.E Q .’B’) T H E N
C A LL U S E T (’SIM U ’)
C A LL U F O N T (’D R O M ’)
E N D IF
c
c
c
call u p rin t(0 .,9 5 .,’mu=
C A LL U P R N T 1(X M U .’R E A L ’)
C A LL U P R N T 1(’ J u p p e r*
X JU P = JU P
C A L L U P R N T l(X ju p ,’in te ’)
C A L L U P R N T H ’ q* * 2 /d elta=
C A L L U P R N T l(q sQ o v d e l,’re a l’)
call u p r n tl ( ’ Nbase=>
base= nbase
c
c
c
c
c
call u p r n tl(b a s e ,’in te ’)
c
c a ll u p r n t l f c h a rg e c
c h a rg e -ic h a rg e
c
call u p r n tl( c h a r g e ,’in te ’)
c
c a ll u p rn tl(* n ran g e, step=
c
C A L L UM O VE(0.,91.)
c
call u p r n tl(d e n s m in ,’e x p o ’)
c
c a ll u p rn tl(d e n s m a x ,’e x p o ’)
c
C A L L U P R N T l(d e n s in c ,’ex p o ’)
c
c a ll u p r n t l ( ’ D isch arg e ty p e c
IF (ID IS T Y P E .E Q .’N ’) G O T O 221
c
C A L L U P R N T 1(’A
c
G O T O 222
c 221 C A L L U P R N T 1(’N
c 222 C O N T IN U E
c
C A L L U P R N T I f F in e c
C A L L U P R N T 1( fin e ,’re a l’)
c
C A L L U P R N T 1(* H W H M c
C A L L U P R N T l(h w h m ,’re a l’)
c
C A L L U P R N T 1(’ F M c
C A L L U P R N T l(f m ,’re a l’)
c
call u p rn tl(* E s te p s z s te p -n s te p
c
call u p r n tl(z s te p ,’in te ’)
c
C A L L UVW PRT(0.,100.,0.,91.)
c
C A L L U P SE T (’X L A B E L ’,’K ly stro n freq (M H z), fro m 1-doub
c e n te r
c
c a ll u p set(’y la b e l\’R e la tiv e In te n sity
c
C A L L U S E T (’X B O T H ’)
c
C A L L U S E T (’Y B O T H ’)
c
C A L L U S E T (’OW N SCA LE’)
c
c v a ry th e d e n sity a n d d isp la y as a c a rto o n
c N ow do th e b aselin e su p p ressio n s
c
if(n b a se .g e .l) th en
n f m = n in t( fm /f in c )
is p e c - 1000-(2*nf m *nbase)
io n e-1
w rite ( 12,10691 )ispec,ione
10691 fo rm a t(2 I6 )
do 80 k - l,n b a s e
do 85 j-1 ,1 0 0 0
y i(j)-y (j)
85
y 2 (j)-y n o fld (j)
c o n tin u e
do 90 j-l+ k * n fm ,1 0 0 0 -k * n fm
y( j) - y 1(j)-(y 1 (j- n f m )+y 1(j+ n f m ))/2.
y n o f ld( j) - y 2(j)-(y 2( j- n f m )+y 2( j+ n f m ))/2.
w ri te( 12,1069)x( j),y (j)
1069 f o r m a t( lx ,2 f 15.8)
90 c o n tin u e
80 c o n tin u e
do 95 j= l,n b a s e * n fm
y(j)=o.o
y(1000-j)=0.0
yn o fld (j)= 0 .0
y n o f ld( 1000-j)=0.0
95 c o n tin u e
e n d if
C SET M IN A N D M AX Y V A L U E S
if( ic a rt.e q .l) th e n
Y M IN -Y n o f ld( 1)
Y M A X -y n o f ld( 1)
c iy m ax is a rr a y su b sc rip t v a lu e f o r larg e st y v alu e
iy m a x -1
D O 100 1-2,1000
if(y n o fld (i).lt.y m in ) y m in - y n o fld ( i)
IF (y n o fld (I).G T .Y M A X ) th en
Y M A X -y n o fld (I)
iy m a x -i
en d i f
100 C O N T IN U E
c
c
C A L L U W IN D O (X M IN ,X M A X ,Y M IN ,Y M A X )
C A L L U A X IS(X M IN ,X M A X ,Y M IN ,Y M A X )
c p lo t th e no f ie ld lin e shape
c
call u set(’m a g e n ta ’)
c
call u lin e (x ,y n o fld ,1000.0)
c d if f e r e n t color fo r w ith fie ld cases
c
C A L L U S E T (’G R E E N ’)
e n d if
c m a g n ify the w ith fie ld lin e sh ap es if necessary
if((iscale.eq .0 ).an d .(y (iy m ax ).lt.y m ax /6 .)) th en
isc a le-1
d e n s c a le -d e n s ity
c
c a ll u set(’g a p p e d ’)
en d i f
if(is c a le .e q .l) th en
do klm -1 ,1 0 0 0
y(k lm )-y (k lm )* 5 .
e n d do
en d if
c plot th e lin e w ith fie ld
c
C A L L U L IN E (X ,Y ,1000.0)
2000 c o n tin u e
c c
i f (isc a le .e q .l) then
c
c
c
c
c
c
c
6
c a ll uw indo(0.,100.,0.,100.)
c a ll u p rin t(2 .,9 5 .,’Y *5 f o r n .ge.
c a ll u p rn tl(d e n s c a le ,’e x p o ’)
c a ll u p rin t(2 .,90.,’M a g n ifie d lin e s g a p p e d
e n d if
IF(IA N S.N E .’B’) C A L L U P A U S E
CALL UEND
c o n tin u e
STO P
END
s u b ro u tin e m u lt(a l,a 2 ,a 3 )
im p lic it real*16 (a-h,o-z)
d im e n sio n a 1(2,2),a2(2,2),a3(2,2)
do 2 i—1,2
do 3 j-1 ,2
a3(i,j)=0.0
3
c o n tin u e
2
c o n tin u e
do 10 i-1 ,2
do 20 k = l,2
do 30 j-1 ,2
a3 (i,k )= a3 (i,k )+ a 1(i,j)*a2(j,k)
30
c o n tin u e
20
c o n tin u e
10
c o n tin u e
r e tu r n
end
A P P E N D IX 5.
P R O G R A M S O L E V E L .FO R .
420
C
PROGRAM
N E W SO LEV EL.FO R
CALCULATES
ENERGY
LEV ELS,
T R A N S IT IO N
F R E Q U E N C IE S ,
C
AND
T R A N S F O R M A T IO N C O E F F IC IE N T S F O R T R IP L E T SIGM A
M O L E C U L E S. T H E H A M IL T O N IA N C U SED IS T H A T O F
B O G E Y ,E T AL.() T H IS IS T H E CA SE B H A M IL T O N IA N .
IM P L IC IT R E A L * 16 (A -H .O -Z )
D IM E N SIO N W(0:13,0:13)
COM M ON W
C F IR S T T H E IN P U T P A R A M E T E R S A R E R E A D IN
R E A D (20,*)B E,A LA M ,A G A M ,D E,D LA M ,D G A M
W RITE( 10,1 )B E,A L AM, A G A M .D E ,D L A M ,D G AM
1
F O R M A T (lX ,7 X ,’IN P U T PA R A M T E R S A R E AS
F O L L O WS’/1 X ,’B V ’,10X ,F 17.6/
H 11X ,’LA M BDA V ’,5X ,F 17.6/1X ,’GAM M A V’,6X ,F 17.6/1 X .’D V ’, 10 X ,F 17.6/
21 X ,’D LA M BD A V ’,4 X ,F 17.6/1 X .’DGAM M A V ’,5X ,F 1 7 .6 //)
C T H E E N E R G Y L E V E L S IN T H IS P R O G R A M A R E E X PR E S SE D
IN T E R M S O F W (J,N)
C
DO 3 J -0 ,1 3
DO 2 N -0 ,1 3
W (J,N )-0.0
2
C O N T IN U E
3
C O N T IN U E
a ju n -(2 .* a la m /3 .)-a g a m
W (0,1)«2.*(BE-A LA M )- A G A M -4.*(D E+(2.*D G A M ))-(8.*D LA M /3.)+a ju n
W RITE( 10,4) W(0,1)
4
F O R M A T (21X ,’ J - 0 ’/ ’ N - l A N D T H E E N E R G Y L E V E L
IS’,/F 1 5 .5 //)
DO 7 J -1 ,1 3
A J -Q F L O A T (J )
A J1 -A J+ 1 .
A JSQ «A J**2.
A J1S Q -A J1**2.
A JM 1-A J-1.
A J2 -A J+ 2 .
A JM 1SQ «AJM 1**2.
A J2SQ -A J2**2.
A S-(2.*A J)+1.
W( J, J)-(B E + (2.*D L A M /3.)-D G A M )* A J* A J 1-(DE* A JSQ* A J 1SQ)+a ju n
A L A M T E R M l-A L A M + (D L A M * A JM lS Q /3 .)
A L A M T E R M 2«A L A M + (D L A M *A J2SQ /3.)
A L A M T E R M 3 -A L AM +(D L AM*( A JSQ +A J + 1.))
H A 11 -(B E *A J*A JM1 )-(D E* A JS Q *A JM lS Q )-((2* A J* AL A M T E R M 1) / AS)+
1(AGAM * A J)+(D G A M * A J* A JM1 SQ)+ a ju n
H A 22-(B E *A J 1*A J2)-(D E *A J 1SQ*A J2SQ)-((2.*A J 1* A L A M T E R M 2)/A S)1(AGA M * A J 1M D G A M * A J 1* A J2SQ )+ a ju n
A 12=»(( A J* A J 1)**0.5)*2.* A L A M T E R M 3/A S
B T -A 11+ A 22
C T »( A 11 * A22)-( A 12**2.)
W (J,J+ 1)«(B T+Q SQ R T(B T**2.-4*C T))/2.
W( J, J - 1)-(B T-Q S Q R T (B T **2.-4*C T ))/2.
W R ITE( 10,5) J, J - 1,J ,J + 1, W( J, J - 1),W (J,J),W (J,J+1)
5
F O R M A T (21X ,’J » ’,I 3 ,/’ F O R N = \3 I3 ,2 X ,/
1’ T H E E N E R G Y L E V E L S A R E R E S P E C T IV E L Y \/3 F 1 5 .5 )
C 2 C 1- ( A 11 - W( J, J - 1 ))/A 12
A R C 1-(C 2 C 1**2.)+1•
C 1-(1 ./A R C 1)**0.5
C 2-C 1*C 2C 1
W R ITE( 10,6) A 11, A 22, A 12,C 1,C2
6
F O R M A T (lX ,’ T H E H A M IL T O N IA N M A T R IX ELEM EN TS
IN T H E O R D E R
1(J-1|J-1),(J+1|J+1),(J-1|J+1) A R E ’/3 F 1 5 .5 /’
THE
T R A N S F O R M A T IO N
2C O E F F IC IE N T S W HICH C O N N E C T T O T H E E N E R G Y
L E V E L S A R E 7 2 F 1 5 .9 //)
7C O N T IN U E
W R ITE(10,8)
8
F O R M A T (lX ,’
T H E T R A N S IT IT O N F R E Q U E N C IE S AS
FOLLOW S W ITH
1 F O R M A T ’, / ’ JL O W E R ,N L O W E R ,JU P P E R ,N U P P E R ’)
D O 9 N -0 ,1 2
N P -N + 1
J-N + l
JP -N
C A L L F R E Q (J,N ,JP ,N P )
JP -N + 1
C A L L F R E Q (J,N ,JP ,N P )
J P -N + 2
IF (JP .EQ. 14)GO T O 25
C A L L F R E Q (J,N ,JP ,N P )
J-N
JP -N
IF (N .EQ. 0 .AN D. J .EQ. 0)G O T O 25
C A L L F R E Q (J,N ,JP ,N P )
JP -N + 1
IF (N .EQ. 0 .AN D. J .EQ. 0)G O T O 25
C A L L F R E Q (J,N ,JP ,N P )
9
C O N T IN U E
D O 11 N -1 ,1 2
N P -N + 1
J-N -l
JP -N
FR E Q A -W (JP ,N P )-W (J,N )
W R ITE( 10,10) J,N ,JP ,N P ,F R E Q A
10
FO R M A T ( 1X ,4I5,F 15.3)
11
C O N T IN U E
STO P
END
S U B R O U T IN E F R E Q (J,N ,JP ,N P )
IM P L IC IT R E A L * 16 (A -H ,0 -Z )
D IM E N S IO N W(0:13,0:13)
CO M M O N W
FR E Q B »W (JP,N P)-W (J,N )
W R ITE( 10,12)J,N ,JP ,N P ,F R E Q B
F O R M A T ( 1X ,4I5,F 15.3)
RETURN
EN D
A P P E N D IX 6.
P R O G R A M U N IT Y .F O R .
424
IM P L IC IT R E A L * 16 (A -H .O -Z )
D IM E N S IO N A (23,23),B (23),X (23),A IN V (23,23),
1V I(23),V J(23),V K (23),V L (23),IP (21),X I( 15), A AM H ( 15),A A M N ( 15),
2A A M C( 15)
c h a ra c te r NA M E(21)*7
D A T A N A M E /’B E V A L P H A 1V A L P H A 2V A L P H A 3V G A M M A 11’,
’G A M M A 12’,
H 1’G A M M A 13’,’G A M M A22’,’G A M M A23’,’G A M M A33’,’EPS 111’,’E P S l 12’,
2’EPS 113’,’EPS 122’,’EPS 123’,’EPS 133’,’EPS222’,’EPS223’,’E P S 2 3 3 \
3’EPS333’,’G A M M A LL’/
C O M M O N /K IR K /A A M H ,A A M N ,A A M C ,S T A R T ,S T E P ,T O L E R ,X I
C O M M O N /B A R R IE /D IS P .N L IN E S
C O M M O N /K IK O /A W IN ,B W IN ,Y L W IN ,Y W IN
C F IR S T T H E D A T A IS R E A D IN W ITH T H E IN IT IA L GU ESS
FO R RHEAVYATOM C H E A V Y A T O M (A G O O D G U ESS IS 1.1),T H E IN C R EM EN T (.00001
IS A G O O D V A L U E )
CTHE
TOLERATED
ERROR
W HEN
BE
IS
B A C K -C A L C U L A T E D (.00001 A G A IN W ORKS
C W EL L),A N D T H E N U M B E R O F SETS O F F R E Q U E N C IE S
READ (20,*)A W IN ,BW IN ,Y LW IN ,Y W IN
R E A D (20,*)S T A R T ,S T E P ,T O L E R ,D IS P ,N L IN E S
B E G T O L E R -T O L E R
D O 1111 IR -l.N L IN E S
C T H E N E X T C A R D IS T H E N U M B ER O F L IN E S IN T H E F IR S T
SET
R E A D (20,1)N
1
F O R M A T (I2)
C
N E X T T H E T H R E E A T O M IC MASS N U M BER S A R E IN P U T
IN T H E O R D E R
CM ASS H2.M ASS IN N E R H E A V Y ATOM ,M ASS O U T E R H E A V Y
A T O M .(N O T E ,T H E Y A R E
C C A L L E D M H H ,M N ,A N D M C,BECA U SE TH IS P A R T O F T H E
P R O G R A M WAS W R IT T E N
C IN 1983 W HEN I WAS W O R K IN G O N H N C)
R E A D (20,*)A A M H (IR ),A A M N (IR ),A A M C (IR )
D O 6 1-1,4
IP (I ) -I
6
C O N T IN U E
IN D E X -5
DO 1096 I-1 ,N
C
T H E N E X T N C A R D S R E A D IN T H E B V A L U E A N D T H E
V IB R A T IO N A L Q U A N T U M
CNUM BERS
IN
ORDER
V L IG H T
A TO M
S T R E T C H ,V B E N D .V H E A V Y A TO M S T R E T C H , A N D
C V L D O U B L IN G . SO 1 22 1 W OU LD BE E N T E R E D AS BE 1. 2. 1. 2.
A LSO N O T E
425
C T H E V IB R A T IO N A L Q U A N T U M N U B E R S A R E R E A L .
R E A D (20,*)B (I), V I(I), V J (I), V K (I), V L (I)
W R ITE( 10,2599)B (I),V I(I),V J(I),V K (I),V L (I)
2599 F O R M A T ( 1X ,F 15.8.4F6.3)
C
T H E P U R P O S E O F T H E B U L K O F T H IS P R O G R A M IS T O
CALCULATE TH E
C A P P R O P R IA T E M A T R IX A O F T H E E Q U A T IO N A X -B W H ER E
B IS T H E C O L U M N
C M A T R IX O F T H E BV’S ,X IS T H E C O L U M N M A T R IX O F
BE, A L P H A 1,G A M M A 1,ETC .
C T H E N E X T F O U R S T A T E M E N T S SE T U P T H E A P P R O P R IA T E
ROWS F O R B E ,A N D T H E
C T H R E E A L PH A S. I AM A SSU M IN G T H E Y W ILL ALW AYS BE
CALCULATED.
A (I,1 )-1 .0
A (I,2)=-V I(I)-.5
A (I,3 )-V J (I)-1 .
A (I,4 )-V K (I)-.5
1096
C O N T IN U E
C
IF O N L Y T H E A L P H A L E V E L IS D E S IR E D T H E P R O G R A M
SK IPS T O T H E
C S IM U L T A N E O U S
E Q U A T IO N
S O L V IN G
S U B R O U T IN E
L A SSO L .A N D B E ,A N D T H E T H R E E
C A L PH A S A R E C A L C U L A T E D
IF (N .EQ. 4)G O T O 15
IN D E X N -IN D E X
C T H E N E S T E D DO LO O PS D E T E R M IN E IF G A M M A 11 IS
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX . IN D E X N IS T H E
ROW IN D E X . IT IS
C S T E PPE D U P O N E IF IT IS D E S IR E D T O C A L C U L A T E T H E
A P P R O P R IA T E C O N S T A N T ,
C A N D N O T IN C R E M E N T E D IF T H IS IS N O T D E S IR E D . ALSO
T H E A R R A Y IP IS SET
C SE T U P T O P R IN T T H E A P P R O P R IA T E NAM ES.
D O 50 I-1 ,N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O T O 50
IF (V I(I) .LE. 1.0)GO T O 50
DO 51 J - l . N
A (J,IN D E X )= A (J,2)**2.
IF (J .EQ. N )IP (IN D E X )= 5
IF (J .EQ. N )IN D E X -IN D E X + 1
51
C O N T IN U E
50
C O N T IN U E
C T H E N E S T E D DO LO OPS D E T E R M IN E IF GAM M A 12 IS
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
DO 52 1=1,N
426
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O T O 52
IF (V I(I) .EQ. 0.0)GO T O 52
IF (V J(I) .EQ. 0.0)GO T O 52
DO 53 J -1 ,N
A (J,IN D E X )-A (J,2 )* A (J,3 )
IF (J .EQ. N )IP (IN D E X )-6
IF (J .EQ. N )IN D E X -IN D E X + 1
53
C O N T IN U E
52
C O N T IN U E
C T H E N E ST E D DO LO O PS D E T E R M IN E
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
D O 54 I-1 ,N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O T O 54
IF (V I(I) .EQ. 0.0)GO T O 54
IF (V K (I) .EQ. 0.0)GO T O 54
DO 55 J -1 ,N
A (J,IN D E X )-A (J,2 )* A (J,4 )
IF (J .EQ. N )IP (IN D E X )-7
IF (J .EQ. N )IN D E X -IN D E X + 1
55
C O N T IN U E
54
C O N T IN U E
C T H E N E ST E D DO LO O PS D E T E R M IN E
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
IT E S T -0
D O 56 I-1 .N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O T O 56
IF (V J(I) .LE. 1.0)GO T O 56
IF (V J(I) .GE. 2.0)GO T O 57
IP R IM E -I
DO 58 J -1 ,N
IF (J .EQ. IP R IM E )G O T O 58
IF (V J(J) .EQ. 0.)GO T O 58
IF (V J(J) .EQ. l.)IT E S T -l
IF (V J(J) .GT. 2.)IT E ST -1
58
C O N T IN U E
IF (IT E S T .EQ. 0)G O T O 56
57
D O 59 K - l .N
A (K ,IN D E X )-A (K ,3)**2.
IF (K .EQ. N )IP (IN D E X )= 8
IF (K .EQ. N )IN D E X -IN D E X + 1
59
C O N T IN U E
56
C O N T IN U E
IN D E X N -IN D E X
IF
GAM M A 13
IS
IF
G A M M A22
IS
427
C T H E N E ST E D DO LO O PS D E T E R M IN E IF GAM M A23 IS
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
D O 60 I=1,N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O T O 60
IF (V K (I) .EQ. 0.0)GO T O 60
IF (V J(I) .EQ. 0.0)GO T O 60
D O 61 J - l . N
A (J,IN D E X )= A (J,3)*A (J,4)
IF (J .EQ. N )IP (IN D E X )-9
IF (J .EQ. N )IN D E X » IN D E X + 1
61
C O N T IN U E
60
C O N T IN U E
C T H E N E ST E D D O LO O PS D E T E R M IN E IF GAM M A33 IS
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
D O 62 I-1 ,N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O T O 62
IF (V K (I) .LE. 1.0)GO T O 62
D O 63 J -1 ,N
A (J,IN D E X )-A (J,4 )* * 2 .
IF (J .EQ. N )IP (IN D E X )-10
IF (J .EQ. N )IN D E X -IN D E X + 1
63
C O N T IN U E
62
C O N T IN U E
C T H E N E ST E D D O LO OPS D E T E R M IN E IF EPSILO N111 IS
D E S IR E D .A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
D O 66 I - I .N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O T O 66
IF (V I(I) .LE. 2.0)GO T O 66
DO 67 J -1 .N
A (J,IN D E X )-A (J,2 )* A (J,2 )* A (J,2 )
IF (J .EQ. N )IP (IN D E X )-1 1
IF (J .EQ. N )IN D E X -IN D E X + 1
67
C O N T IN U E
66
C O N T IN U E
C T H E N E ST E D DO LO OPS D E T E R M IN E IF E PSILO N 112 IS
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
DO 68 I-1 ,N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O T O 68
IF (V I(I) .LE. 1.0)GO T O 68
428
IF (V J(I) .EQ. 0.)GO T O 68
DO 69 J -1 ,N
A (J,IN D E X )—A (J,2)*A (J,3)*A (J,2)
IF (J .EQ. N )IP (IN D E X )-1 2
IF (J .EQ. N )IN D E X »IN D E X + 1
69
C O N T IN U E
68
C O N T IN U E
C T H E N E ST E D DO LO OPS D E T E R M IN E IF EPSILO N 113 IS
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
DO 70 I - l . N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O T O 70
IF (V I(I) .LE. 1.0)GO TO 70
IF (V K (I) .EQ. 0.0)GO T O 70
DO 71 J«1,N
A (J,IN D E X )—A (J,2)*A (J,4)*A (J,2)
IF (J .EQ. N )IP (IN D E X )-13
IF (J .EQ. N )IN D E X -IN D E X + 1
71
C O N T IN U E
70
C O N T IN U E
C T H E N E ST E D DO LO OPS D E T E R M IN E IF EPSILO N 122 IS
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
IT E S T -0
DO 72 I-1 ,N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O T O 72
IF (V J(I) .LE. 1.0)GO T O 72
IF (V I(I) .EQ. 0.0)GO TO 72
IF (V J(I) .GT. 2.0)GO T O 73
IP R IM E -I
DO 74 J -1 ,N
IF (J .EQ. IP R IM E )G O T O 74
IF (V J(J) .EQ. 0.)GO T O 74
IF ((V J(J) .EQ. l.).A N D .(V I(J) .GT. 0.))IT E ST -1
IF (V J(J) .GT. 2.)IT E S T -1
74
C O N T IN U E
IF (IT E S T .EQ. 0)G O TO 72
73
D O 75 K -1 .N
A (K ,IN D E X )—A (K ,3)*A (K ,2)*A (K ,3)
IF (K .EQ. N )IP (IN D E X )-14
IF (K .EQ. N )IN D E X -IN D E X + 1
75
C O N T IN U E
72
C O N T IN U E
C T H E N E ST E D DO LO OPS D E T E R M IN E IF EPSILO N 123 IS
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
429
IN D E X N = IN D E X
D O 170 I-1 .N
ID IF F -IN D E X -IN D E X N
I F (ID IF F .EQ. l)G O TO 170
IF (V I(I) .EQ. 0.0)GO T O 170
IF (V J(I) .EQ. 0.0)GO T O 170
IF (V K (I) .EQ. 0.0)GO T O 170
D O 171 J -1 ,N
A (J,IN D E X )—A (J,3)*A (J,4)*A (J,2)
IF (J .EQ. N )IP (IN D E X )-15
IF (J .EQ. N )IN D E X -IN D E X + 1
171 C O N T IN U E
170 C O N T IN U E
C T H E N E S T E D D O LO OPS D E T E R M IN E IF
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
D O 700 I - l .N
ID IF F -IN D E X -IN D E X N
I F (ID IF F .EQ. l)G O T O 700
IF (V K (I) .LE. 1.0)GO T O 700
IF (V I(I) .EQ. 0.0)GO T O 700
D O 710 J -1 ,N
A (J,IN D E X )-A (J,4 )* A (J,4 )* A (J,2 )
IF (J .EQ. N )IP (IN D E X )-16
IF (J .EQ. N )IN D E X -IN D E X + 1
710 C O N T IN U E
700 C O N T IN U E
C T H E N E S T E D DO LO OPS D E T E R M IN E IF
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
IT E S T -0
D O 76 I-1 .N
ID IF F -IN D E X -IN D E X N
I F (ID IF F .EQ. l)G O T O 76
IF (V J(I) .LE. 2.0)GO T O 76
IF (V J(I) .EQ. 3.0)GO T O 77
IF (V J(I) .GT. 4.0)GO T O 77
IP R IM E -I
D O 770 I C - l.N
IF (IC .EQ. IP R IM E )G O T O 770
IF (V J(IC ) .EQ. 0.)GO T O 770
IF (V J(IC ) .EQ. 6.)GO T O 77
IF (V J(IC ) .EQ. 3.)GO T O 77
IF (V J(IC ) .EQ. 2.)IC P»IC
D O 771 I C T - l.N
IF (IC T .EQ. IC P)G O T O 771
IF (V J(IC ) .EQ. l.)G O T O 77
771 C O N T IN U E
EPSILO N 133 IS
EPSILO N 222
IS
430
770
C O N T IN U E
D O 78 J -1 ,N
IF (J .EQ. IPR IM E )G O T O 78
IF (V J(J) .EQ. 6.)IT E ST -1
78
C O N T IN U E
IF (IT E S T .EQ. 0)GO TO 76
77
D O 79 K = 1,N
A (K ,IN D E X )-A (K ,3 )* A (K ,3 )* A (K ,3 )
IF (K .EQ. N )IP (IN D E X )-1 7
IF (K .EQ. N )IN D E X * IN D E X + 1
79
C O N T IN U E
76
C O N T IN U E
C T H E N E S T E D DO LOOPS D E T E R M IN E IF E PSILO N 223
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
IT E S T -0
D O 82 I-1 .N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. I)G O T O 82
IF (V J(I) .LE. 1.0)GO TO 82
IF (V K (I) .EQ. 0.0)GO T O 82
IF (V J(I) .GT. 2.0)GO TO 83
IP R IM E -I
D O 84 J - l . N
IF (J .EQ. IPR IM E )G O T O 84
IF (V J(J) .EQ. 0.)GO T O 84
IF ((V J(J) .EQ. l.).A N D .(V K (J) .GT. 0.))IT E S T -1
IF (V J(J) .GT. 2.)IT E ST -1
84
C O N T IN U E
IF (IT E S T .EQ. 0)GO TO 82
83
D O 85 K -1 ,N
A (K ,IN D E X )-A (K ,3 )* A (K ,4 )* A (K ,3 )
IF (K .EQ. N )IP (IN D E X )-18
IF (K .EQ. N )IN D E X -IN D E X + 1
85
C O N T IN U E
82
C O N T IN U E
C T H E N E ST E D DO LO OPS D E T E R M IN E IF E PSILO N 233
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
DO 90 I - l .N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O T O 90
IF (V K (I) .LE. 1.0)GO TO
IF (V J(I) .EQ. 0.0)GO TO 9D O 91 J -1 ,N
A (J,IN D E X )—A(J,4)*A f 4)*A(J,3)
IF (J .EQ. N )IP (IN D E X 19
IF (J .EQ. N )IN D E X -I. n OEX+1
IS
IS
91
C O N T IN U E
90
C O N T IN U E
C T H E N E ST E D DO LO OPS D E T E R M IN E IF EPSILO N 333 IS
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
D O 86 I-1 .N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O T O 86
IF (V K (I) .LE. 2.0)GO T O 86
D O 87 J -1 .N
A (J,IN D E X )-A (J,4 )* A (J,4 )* A (J,4 )
IF (J .EQ. N )IP (IN D E X )-2 0
IF (J .EQ. N )IN D E X -IN D E X + 1
87
C O N T IN U E
86
C O N T IN U E
C T H E N E ST E D DO LO OPS D E T E R M IN E IF G A M M A LL IS
D E S IR E D ,A N D C A L C U L A T E
C T H E A P P R O P R IA T E ROW IN T H E M A T R IX
IN D E X N -IN D E X
DO 64 I-1 .N
ID IF F -IN D E X -IN D E X N
IF (ID IF F .EQ. l)G O TO 64
IF (V L (I) .EQ. 0.0)G O T O 64
D O 65 J - l . N
A (J,IN D E X )-V L (J)**2.
IF (J .EQ. N )IP (IN D E X )-2 1
IF (J .EQ. N )IN D E X » IN D E X + 1
65
C O N T IN U E
64
C O N T IN U E
15
C O N T IN U E
M -N
C
H E R E T H E B E,A LPH A S,G A M M A S,A N D EPSILO N S A R E
CALCULATED
C A L L LA SSO L(N ,N P 1,A ,B ,A B ,M ,X ,R ,IFL A G )
DO 49 IT -1 ,N
W RITE( 10,1494)N A M E (IP (IT )),X (IT )
1494 FO R M A T ( 1X ,A 7,F 15.8)
C (IT )-X (IT )
49
C O N T IN U E
C T H E N E X T S T A T E M E N T SETS U P A N A R R A Y O F T H E BE’S
X I(IR )-C (1 )
C
T H E PU R PO SE O F T H IS SEG M EN T IS TO C A L C U L A T E T H E
IN V E R S E O F T H E
C
C O E F F IC IE N T M A T R IX
D O 1999 I Z - l .N
B (IZ )-0.0
1999 C O N T IN U E
DO 2001 IM -1.N
B(IM )-1.0
C A L L L A SSO L (N ,N P 1,A ,B ,A B ,M ,X ,R ,IFL A G )
D O 30 I J - l . N
A IN V (IJ,IM )-X (IJ)
B(IM)=0.0
30
C O N T IN U E
2001 C O N T IN U E
C
H E R E WE T A K E T H E IN V E R S E A N D BA CK C A L C U L A T E
TH E B VALUES
C
AS A C H E C K O N T H E SO L U T IO N S
C A L L L A SSO L (N ,N P 1,A IN V ,C ,A B ,M ,X ,R ,IF L A G ,N P 1)
D O 27 IX -1 ,N
W R ITE( 10,1492)X (IX )
1492 F O R M A T ( 1X ,F 15.8)
27
C O N T IN U E
W R ITE( 10,2066)
2066 F O R M A T ( 1X /T H E C O E E F F IC IE N T M A T R IX IS’)
D O 304 IC -1 ,N
W R ITE( 10,306)( A (IC ,JC ), J C - 1,N)
306 FO R M A T (< N > F8.3)
304 C O N T IN U E
W R ITE( 10,2067)
2067 F O R M A T ( 1X .’ITS IN V E R S E IS’)
D O 305 IC -1 ,N
W R ITE( 10,307)( A IN V (IC , JC ), J C - 1,N )
307 FO R M A T (< N > F8.3)
305 C O N T IN U E
996 C O N T IN U E
1111 C O N T IN U E
W R ITE( 10,99999)
99999 F O R M A T (lX ,’I AM O U T O F DO L O O P ’)
C N E X T WE G O T O T H E S U B R O U T IN E BO ND LS W H ER E T H E
D IF F E R E R IN G BE’S A R E
C USED TO CA LCU LA TE BOND LEN G TH S
C A L L BO N D LS( X I,R C N O U T ,R C H O U T )
C
C A L L G R A P H IC
STO P
EN D
S U B R O U T IN E L A SSO L (N ,N P 1,A ,B ,A B ,M ,X ,R ,IFL A G )
IM P L IC IT R E A L * 16 (A -H ,0 -Z )
D IM E N S IO N A (23,23),B(23),X (23),A B (23,24)
N P 1-N + 1
N M 1-N -1
D O 3 I-1 ,N
ROWMAX-O.O
D O 1 J - 1 ,N
1
IF (A B S(A (I,J)) .GT. R O W M A X )R O W M A X -A B S(A (I,J))
IF(R O W M A X .EQ. 0)G O T O 14
SC A L E - 1./R O W M A X
D O 2 J -1 .N
2
A B (I,J)-A (I,J)*S C A L E
3
A B (I,N P 1)-B (I)*SC A L E
D O 9 K=1,NM 1
B IG -0.0
D O 4 I - K ,N
T E M PB -A B S(A B (I,K ))
IF (B IG .G E .TEM PB )G O T O 4
B IG -T E M P B
ID X P IV -I
4
C O N T IN U E
IF(BIG .EQ.O )GO T O 14
IF (ID X P IV .E Q .K )G O T O 6
D O 5 I-K ,N P 1
T E M P I-A B (K ,I)
A B (K ,I)-A B (ID X P IV ,I)
5
A B (ID X P IV ,I)-T E M P I
6
K P 1 -K + 1
D O 8 I-K P 1 ,N
Q U O T -A B (I,K )/A B (K ,K )
DO 7 J-K P 1 .N P 1
7
A B (I,J)-A B (I,J)-Q U O T * A B (K ,J)
8
C O N T IN U E
9
C O N T IN U E
IF(A B(N,N ).EQ.O.)GO T O 14
X (N )-A B (N ,N P 1)/A B (N ,N )
D O 11 IB -2 ,N
I-N P 1 -IB
IP 1-I+ 1
SU M -0.0
D O 10 J« IP 1 ,N
10
S U M -SU M + A B (I,J)*X (J)
11
X (I)-( A B (I,N P 1)-SU M )/A B (I,I)
R -0 .0
D O 13 I-1 ,N
S U M R -0.0
D O 12 J -1 .N
12
S U M R -S U M R + A (I,J)*X (J)
13
IF (SU M R .G T. B (I))R -S U M R
C
W R ITE(10,16)R
C16
F O R M A T ( 1X ,’T H E R V A L U E IS \F 15.8)
IF L A G -1
RETURN
14
IF L A G -2
RETURN
END
S U B R O U T IN E B O N D L S (X I,R C N O U T ,R C H O U T )
IM P L IC IT R E A L * 16 (A -H .O -Z )
C O M M O N /B IL L /R H N
C O M M O N /B R E T T /X T E S T .Y T E S T
C O M M O N /R O L F /X ,Y
C O M M O N /K IR K /A A M H ,A A M N ,A A M C ,S T A R T ,S T E P ,T O L E R
C O M M O N /B A R R IE /D IS P .N L IN E S
D IM E N S IO N X I( 15),A A M H ( 15),AAM N( 15),AAM C( 15)
C
T O L E R * 100 *T O L E R
W R ITE( 10,673)
673 F O R M A T (lX ,’I AM IN BO ND LS’)
D O 70 I-1 ,N L IN E S
B E =X I(I)
A M H -A A M H (I)
A M N -A A M N (I)
A M C -A A M C (I)
DO 80 J -1 .N L IN E S
IF (J .LE. I)G O T O 80
B E 2 -X I(J)
A M H 2 -A A M H (J)
A M N 2-A A M N (J)
A M C 2-A A M C (J)
IF (A M H .EQ. A M H 2)G O T O 11111
11111 IF (A M N 2 .EQ. A M N )G O T O 11112
IF (A M N 2 .NE. A M N )G O T O 222
11112 IF (AM C2 .EQ. AM C)G O TO 80
222 W R ITE(10,82)B E,A M H ,A M N ,A M C,BE2,A M H 2,A M N 2,A M C 2
82
F O R M A T (IX ,’IN IT IA L IN P U T ’/4F 1 5 .8 /4 F 1 5 .8 )
R C N -S T A R T
I
C A L L R C (R C N ,B E,A M H ,A M N ,A M C )
Y l-R H N
C A L L R C (R C N ,B E2,A M H 2,A M N 2,A M C 2)
Y A 1 -R H N
X l- R C N
R C N -R C N + S T E P
C A L L R C (R C N ,B E,A M H ,A M N ,A M C )
X 2 -R C N
Y 2 -R H N
C A L L R C (X 2,B E2,A M H 2,A M N 2,A M C 2)
Y A 2 -R H N
C A L L T E S T (X 1,X2,Y 1,Y 2,Y A 1,YA2)
CALL
TO L (X TEST ,Y TEST.B E,A M H ,A M N ,A M C ,B E2,A M H 2,A M N 2,A M C 2)
IF (X -T O L E R )2 5 ,2 5 ,2 1
25
IF (Y -T O L E R )2 6 ,2 6 ,2 1
21
R C N -X T E S T
GO T O 1
26
W R ITE( 10,40)X T E S T , Y T EST
40
F O R M A T ( 1X .’O U R F IN A L R E SU L T S A R E ’/2F 15.8)
80
C O N T IN U E
70
C O N T IN U E
RETURN
END
S U B R O U T IN E T E S T (X 1,X 2,Y 1,Y 2 ,Y A 1,Y A 2)
IM P L IC IT R E A L * 16 (A -H .O -Z )
C O M M O N /B R E T T /X T E S T ,Y T E S T
435
SLO PE=(Y 2-Y 1)/(X 2 -X 1)
C E P T -Y l-(X l* S L O P E )
S L 0 P E 2 * ( Y A2-Y A 1)/(X 2 -X 1)
C E P T 2 -Y A 1-(X 1*SLOPE2)
X T E S T *(C E P T -C E P T 2)/(S L O P E 2-S L O P E )
Y T E ST = (SL O P E *X T E ST )+C E PT
RETURN
END
S U B R O U T IN E
T O L (X T E S T , Y TEST,B E, A M H ,A M N ,A M C,jb£2,A M H 2,A M N 2,A M C 2)
IM P L IC IT R E A L *16 (A -H ,0 -Z )
C O M M O N /R O L F /X ,Y
R E A L * 16 M OM ,A M H ,AM N,A M C,A M H 2,AM N 2,AM C2,M OM 2
H M O M «((X TEST+Y TEST)**2.0)*(A M H *A M C)+((A M H *A M N )*(Y TEST**2.0))
M OM -M O M +(A M N *A M C)*(X TEST**2.0)
B T EST-(A M H +A M N +A M C )*505379.05/M O M
M O M 2-((X TEST+Y TEST)**2.0)*(A M H 2*A M C 2)
M O M 2-M O M 2+((A M H 2*A M N 2)*(Y TEST**2.0))
M O M 2-M O M 2+(A M N 2*A M C2)*(X TEST**2.0)
BTEST2«(A M H 2+A M N 2+A M C2)*505379.05/M O M 2
X -A B S(B T E S T -B E )
Y - ABS(BTEST2-BE2)
X -1 0 * X
Y -1 0 * Y
RETURN
END
S U B R O U T IN E R C (R C N ,B E,A M H ,A M N ,A M C )
IM P L IC IT R E A L * 16 (A -H ,0 -Z )
C O M M O N /B IL L /R H N
R E A L * 16 IN ,M I,A M H ,A M N ,A M C
B -(2.0*A M C *R C N )/(A M N +A M C )
IN -5 0 5 3 7 9 .0 5 /B E
M I-IN *(A M H +A M N +A M C )
TO P-((A M C*A M N )+(A M H *A M C ))*(R C N **2.0)
A «(TO P-M I)/((A M H *A M N )+(A M H *A M C ))
R H N —B+SQRT((B**2.0)-(4.0*A))
R H N -R H N /2 .0
RETURN
END
A P P E N D IX 7.
P R O G R A M N E W C IN T E R A C .FO R .
437
cP R O G A M C IN T E R A C WAS D E SIG N E D T O DRAW R C H VS R C N
PLO TS
FO R NAKAGAW AC M O R IN O PLO TS O N VMS G R A PH IC S.T H IS P R O G R A M O N LY
W ORKS
O N T H E V A X S T A T IO N .
IM P L IC IT R E a l * 8 (A -H .O -Z )
IN T E G E R V D ID,W D I D l,w d id,V D ID2
C H A R A C T E R * 1 IT IT L E ,IF S A M E ,IF S A M E 1,IFS AM E2
C H A R A C T E R * 6 S T R IN G
C H A R A C T E R *7 S T R IN G 2,S U P E R S C R IP T
C H A R A C T E R *20 F IL E N A M E ,A T E X T ,O U T P U T _ F IL E
C H A R A C T E R * 12 A L A B E L
C H A R A C T E R *40 title ,X _ T I T L E ,Y _ T I T L E
L O G IC A L F IR S T _ T IM E
R E A L * 8 M H,M N,M C
D IM EN SIO N BE( 16),M H( 16),M N( 16),MC( 16),AL( 16)
C O M M O N /B IL L /R H N
in c lu d e ’ra y 2 ::sy s$ lib ra ry :u ise n try ’
in c lu d e ’r a y 2 ::sy s$ lib ra ry :u isu srd e f’
in c lu d e ’r a y 2 ::sys$library:uism sg’
IN C L U D E ’R A Y 2::S Y S$L IB R A R Y :H C U ISD E F’
C
IN C L U D E ’(U IS E N T R Y )’
C
IN C L U D E ’(U IS U S R D E F )’
C
IN C L U D E ’(UISM SG )’
C
IN C L U D E ’(H C U IS D E F )’
cT H E SE F U N C T IO N S X B A R A N D Y B A R SC A LE T H E A C T U A L X ,
LE. R H E A V Y -A T O M -H E A V Y
C A T O M A N D D ISPL A C E D Y.I.E. H Y D R O G E N -H E A V Y ATOM
BO ND
L E N G T H S T O A P L A IN B O U N D E D
CBY T H E PO IN T S (0,0) A N D (1,1). T H IS SC A L IN G IS
N E C E SSA R Y ,B E C A U SE T H E UIS
C S U B R O U T IN E S A R E S IN G L E P R E C IS IO N A N D A L L MY
BO N D L E N G T H S A R E D O U B LE PR E C ISIO N
x b a r(x )» (x -s ta rt)/a m a r
y b a r(y )-(y -y s ta rt)/(y s to p -y s ta rt)
C T H E L O G IC A L V A R IA B L E F IR S T _ T IM E IS IN IT IA L L Y
D E F IN E D T O BE T R U E ,L A T E R
C IT WILL BE FA LSE W HEN IT IS D E S IR E D TO
R U N A G A IN . N E X T , T H E O P E R A T O R IS
C G IV E N C H O IC ES O F W H ET H ER T O R U N
IN T E R A C T IV E L Y O R W ITH A N IN P U T F IL E .
C O N E CA N ALSO D E C ID E W H E T H E R O R N O T A T IT L E IS
D E SIR E D .
C IT SH O U L D F U R T H E R BE N O T E D T H A T A L L C H A R A C T E R
V A R IA B L E S N E E D O N LY
C T H E A P P R O P R IA T E L E T T E R V A L U E S .IT IS N E V E R
N E C E SSA R Y T O USE A PO STR O PH ES.
438
x car= . 0 2 d 0
y c a r - .0 2 d 0
IF S A M E l-’N ’
IFSA M E2=’N*
F IR S T _ T IM E = .T R U E .
C
C
C
C
1
w rite (* *)’
W OULD Y O U P R E F E R T O E N T E R D A T A
IN T E R A C IV E L Y (Y ) O R
1 U SE A N E X IS T IN G D A T A F IL E (N )’
R E A D (u n it« * ,F M T « ’(A )’)IIN T E R A C
if(IIN T E R A C .eq. ’Y ’ .OR. IIN T E R A C .eq. ’y ’)go to 3
IF (F IR S T _ T IM E )G O T O 2
C IF O N E IS R U N N IN G A G A IN ,O N E M AY USE T H E SAM E O R A
D IF F E R E N T IN P U T F IL E .
W RITE(*,*)’ W OU LD Y O U L IK E A NEW IN P U T F IL E ? ’
R E A D (u n it-* ,F M T -’(A )’)INEW
IF (INEW .EQ. ’N ’ .O R. INEW .EQ. ’n ’)G O TO 4
2
W RITE(*,*)’ W HAT IS T H E N A M E O F Y O U R IN P U T F IL E ?’
C IF O N E WISHES T O U SE A P R E P A R E D IN P U T F IL E T H ESE
STATEM ENTS ENABLE TH E
C U S E R T O D O T H IS .O N E N E E D M E R E L Y E N T E R T H E F IL E
N A M E. N O A P O ST R O P H E S A R E
C N E E D E D .IT IS,O F C O U R S E ,N E C E S S A R Y TO M A K E S U R E T H E
F IL E N A M E IS LESS T H A A N
C 20C H A R A C T E R S
LONG.
A
SA M PLE
IN P U T
F IL E
IS
M E N T IO N E D F O R T H E U SER S
C C O N V IE N C E .
C
8
C
1.1529 1.1535 0.0005 0.0005
C
5.2
C
44509.234 1.0 12.0 14.0 1.0
C
43358.693 1.0 13.0 14.0 1.0
C
43213.186 1.0 12.0 15.0 1.0
C
42044.733 1.0 13.0 15.0 1.0
C
44512.022 1.0 12.0 14.0 2.0
C
43361.432 1.0 13.0 14.0 2.0
C
43215.857 1.0 12.0 15.0 2.0
C
42047.173 1.0 13.0 15.0 2.0
c
re a d (u n it-* ,F M T » ’(A 20)’)file n a m e
o p e n ( u n it- 2 0 ,f ile » file a a m e ,s ta tu s « ’o ld ’)
3
C O N T IN U E
4
C O N T IN U E
C
C
C
IF (.N O T .F IR S T T IM E )G O T O 5
w rite (V )’
W OULD Y O U L IK E A T IT L E F O R Y O U R
G R A P H 7Y O R N ’
R E A D (u n it« * ,F M T ■’( A)’)IT IT L E
GO TO 7
5
W R IT E (*, 6 )IT IT L E
6
F O R M A T (3 X ,’IT IT L E IS C U R R E N T L Y ’,3 X ,A 1 /’ DO Y O U
WISH T O C H A N G E ?’)
R E A D (u n it-* ,F M T -’(A )’)IC H A N G E
IF (IC H A N G E .EQ. ’N ’ .OR. IC H A N G E .EQ. ’n ’)GO T O 7
W R IT E (V )’ W HAT IS T H E NEW V A L U E O F IT IT L E ?’
R E A D (u n it-* ,F M T -’(A )’) IT IT L E
7
C O N T IN U E
if(IT IT L E .cq. ’N ’ .OR. IT IT L E .cq. ’n ’)go to 8
IF (.N O T .F IR S T _ T IM E )th e n
W R ITE(*,*)’ W OULD Y O U L IK E T O K E E P T H E SAME
T IT L E ? ’
R E A D (u n it« * ,F M T ■’( A)’)IFS AME
IF (IFS A M E .EQ. ’Y* .OR. IFSAM E .EQ. ’y ’)GO T O 8
e n d if
W R IT E (*,*)’ PL E A SE E N T E R Y O U R T IT L E ’
re a d (U N IT -* ,F M T -’(A 40)’)title
8
c o n tin u e
C
C
C
C
C IF IT IS D E C ID E D N O T TO R U N IN T E R A C T IV E L Y ,O N E R EA D S
T H E D A TA FRO M
C A N IN P U T F IL E .
IF (IIN T E R A C .EQ. ’Y ’ .OR. IIN T E R A C .EQ. ’y’)GO TO 9
IF(IN E W .EQ. ’N ’ .OR. INEW .EQ. ’n ’)G O TO 9
re a d ( 2 0 ,*)nplots
R E A D (2 0 ,* )S T A R T ,S T o P ,A IN T ,ap rin t
read(20,*)S L O PE 2
CA
FEW
CO M M ENTS
ABOUT
T H IS
D A TA
ARE
IN
O R D E R .N P L O T S IS T H E N U M BER O F LIN ES
C Y O U WISH T O DRAW . S T A R T A N D STO P A R E T H E IN IT IA L
A N D F IN A L R H E A V Y ATOM C H E A V Y A T O M D ISTA N C ES.IT IS IM P O R T A N T T H A T T H E Y BE
E N T E R E D IN T H E O R D E R
C S T A R T S T O P .A IN T
IS T H E IN T E R V A L O F C O N ST A N T
R H H E A V Y A TO M BO N D D ISTA N C E
C L IN E S ,I.E . D O T T E D LIN ES. A P R IN T IS T H E IN T E R V A L A T
W H ICH T H E A C T U A L D ISTA N C E
CIS P R IN T E D O N T O P O F T H E G R A P H . SLO PE2 IS T H E SLO PE
O F T H E U N D IS P L A C E D
C L IN E . C
9
C O N T IN U E
i f (IIN T E R A C .eq. ’N ’ .OR. IIN T E R A C .eq. ’n ’)go to 10
C IF IT IS D E C ID E D
T O R U N IN T E R A C T IV E L Y ,O N E R E A D S
T H E D A T A FR O M
C T H E T E R M IN A L .
W RITE(*,*)’ HOW M A N Y L IN E S A R E T O BE D R A W N ?’
read(*,*)N PL O T S
W RITE(*,*)’ W HAT A R E T H E LOW ER A N D U P P E R R C N
V A T T T F ^ ?’
* e a d (V )S T A R T ,S T O P
W RITE(*,*)’ A T W HAT IN T E R V A L SH O U L D L IN E S O F
CO N STA N T RCH
1 BE D R A W N ?’
rea d (V )A IN T
W RITE(*,*)’ A T W HAT IN T E R V A L S H O U L D T H E L IN E S O F
CO NSTAN T RCH
1 BE P R IN T E D ? ’
read (* ,* )A P R IN T
W RITE(*,*)’ W HAT IS T H E SLO PE O F T H E N O N -D ISPL A C E D
L IN E ?’
10
read(*,*)SLOPE2
C O N T IN U E
IF (IN EW .EQ. ’N ’ .OR. INEW .EQ. ’n ’)G O T O 14
C
C
C
C
DO 13 K A S -l,n p lo ts
IF (IIN T E R A C .EQ. ’Y* .OR. IIN T E R A C .EQ. ’y’)GO T O 11
R E A D (2 0,*)be(kas),m h(kas),m n(kas),m c(kas),al(kas)
C T H IS M A K ES IT POSSIBLE TO SIM PLY E N T E R T H E ISO TO PE
N U M B ER S,I.E . 1. 12.
C14. F O R T H E M A IN ISO TO PE O F H C N .F O R E X A M PL E . IF O N E
WISHES T O USE D IF F E R E N T
C A T O M IC W EIG H TS,H E C A N SIM PLY E N T E R T H E M A L TEL L S
T H E C O M P U T E R HOW WIDE
C T O D R A W T H E L IN E F O R A G IV E N ISO TO PE. IT SH O U L D
ALSO BE N O T E D T H A T M N R E F E R S
C T O T H E H E A V Y A TO M W HICH IS B O N D ED T O T H E
H Y D R O G E N ,A N D MC R E F E R S T O T H E
C H E A V Y A TO M A T T H E E N D O F T H E M O LE C U L E,SO F O R HCN.
O N E M U ST BE C A R E F U L TO
C E N T E R T H E ATOM IC W EIGHTS IN T H A T O R D E R ,I.E . F O R HCN
M N W O U LD E Q U A L 12.
C A N D M C 14.
i f (m h(kas).eq. l.)m h (k a s ) -l.00782519d0
i f (m h(kas).eq. 2.)m h(kas)=2.01410222d0
if (m n(kas).eq. 14.)m n(kas)=14.00307439d0
if (m c(kas).eq. 14.)m c(kas)=14.00307439d0
i f (m n(kas).eq. 13.)mn(kas)=>13.0033544d0
i f (m c(kas).eq. 13.)m c(kas)=13.0033544d0
if (m n(kas).eq. 15.)m n(kas)-15.0001077d0
11
i f (m c(kas).eq. 15.)m c(kas)-15.0001077d0
i f (m n(kas).eq. 16.)m n(kas)*15.99491502d0
i f (m c(kas).eq. 1 6 .)m c(k as)-l 5.99491502d0
i f (m n(kas).eq. 18.)m n(kas)«l 7.99916002d0
i f (m c(kas).eq. 18.)m c(kas)=l 7.99916002d0
C O N T IN U E
IF (IIN T E R A C .EQ. ’N ’ .OR. IIN T E R A C .EQ. ’n ’)G O T O 12
W R IT E (V )’ W RITE BE,M H,M N,M C, T H E L IN E W ID TH ’
R E A D (*,*)be(kas),m h(kas),m n(kas),m c(kas),al(kas)
i f (m h(kas).eq. l.)m h (k a s ) - 1.00782519d0
i f (m h(kas).eq. 2.)m h(kas)-2.01410222d0
i f (m n(kas).eq. 14.)m n(kas)-14.00307439d0
i f (m c(kas).eq. 14.)m c(kas)-14.00307439d0
i f (m n(kas).eq. 13.)m n(kas)=13.0033544d0
i f (m c(kas).eq. I3.)m c(k as)-I3 .0 0 3 3 5 4 4 d 0
i f (m n(kas).eq. 1 5 .)m n (k as)-l 5.0001077d0
i f (m c(kas).eq. 1 5 ,)m c(k as)-l 5.0001077d0
i f (m n(kas).eq. 1 6 .)m n (k as)-l 5.99491502d0
i f (m c(kas).eq. 1 6 .)m c(k as)-l 5.99491502d0
i f (ran(kas).eq. 18.)m n(kas)«l 7.99916002d0
i f (m c(kas).eq. 1 8 .)m c(k as)-l 7.99916002d0
C O N T IN U E
C O N T IN U E
C O N T IN U E
12
13
14
C
C
C
C
C
C W H E T H E R O R N O T O N E R U N S IN T E R A C T IV E L Y H E CA N
CH A N G E TH E VALUES OF TH E
C IN P U T P A R A M E T E R S FO R R U N S A F T E R T H E F IR S T TIM E.
T H IS SE G M E N T O F T H E PR O G R A M
CSETS T H IS
U P .F IR S T
THE
IN P U T
PA R A M E T E R S
ARE
W R IT T E N O U T . IF T H E U SER DOES
C N O T WISH T O C H A N G E T H E M H E C A N SIM PLY E N T E R A Y
A N D T H E Y W ILL R E M A IN T H E
CSAM E. N E X T T H E C O M PU T E R WILL P R O M P T H IM J F HE
WISHES T O C H A N G E A P A R A M E T E R
C A N D IF H E DO ES ASK H IM FO R T H E NEW V A L U E .A W ORD
A B O U T C H A N G IN G NPLO TS.
C IF IT IS M A D E SM A L LER T H A N O N L Y T H E F IR S T X LIN ES
A R E W R IT T E N IF IT IS
C M A D E L A R G E R , T H E N T H E U S E R WILL BE A SK E D TO
S U P P L Y BE,M H ,M N ,M C ,A N D LIN E W ID T H
CD A T A F O R T H E NEW LINES.
IF (F IR S T TIM E )G O T O 29
W R IT E (*,15)N PL O T S,ST A R T ,ST O P, A IN T ,A P R IN T ,S L O P E 2
15
F O R M A T (3X ,’T H E V A L U E S F O R T H E FO LLO W IN G
P R O P E R T IE S
1A RE AS FO LLOW S’
1 /’ N P L O T S’,15/’ S T A R T \F 1 5 .8 /’ STO P’,lx ,F 1 5 .8 /
2’ A IN T ’, 1x ,F 15.8/’ A P R IN T ’,F 1 4 .8 /
2 / ’ SLO PE2’,F 1 4 .8 /
3’ IF Y O U WISH T H E M A L L U N C H A N G E D T Y P E
3Y O T H ER W ISE T Y P E SOM E O T H E R L E T T E R ’)
R E A D (u n it= * ,F M T =’( A)’)IF N O N E
IF (IF N O N E .EQ. ’Y’ .OR. IF N O N E .EQ. ’y ’)G O T O 29
W R ITE(*,16)N PLO TS
16
F O R M A T (3X ,’N P L O T S IS’,15,’W OU LD Y O U L IK E TO
C H A N G E IT ?’)
REA D (unit«=*,FM T»’(A )’)IF C H A N G E
IF (IF C H A N G E .EQ. ’N* .O R. IF C H A N G E .EQ. ’n ’)GO T O 18
W RITE(*,*)’ W HAT IS Y O U R NEW V A L U E O F N P L O T S’
R E A D (*,*)N PLO TSN EW
IF (N PLO TSN EW .LE. N P L O T S )T H E N
N PLO TS=N PLO TSN EW
GO T O 18
E N D IF
N P 1-N PL O T S+ 1
DO 17 K A S -N P 1,N P L O T S N E W
W RITE(*,*)’ W R ITE BE,M H ,M N,M C, T H E L IN E W ID TH’
R E A D (* ,*)be(kas),m h(kas),m n(kas),m c(kas),al(kas)
if (m h(kas).eq. I.)m h(kas)»1.00782519d0
if (m h(kas).eq. 2 .)m h (k as)-2 .0 I4 1 0 2 2 2 d 0
if (m n(kas).eq. 14.)m n(kas)»14.00307439d0
if (m c(kas).eq. 14.)m c(kas)=14.00307439d0
if (m n(kas).eq. 13.)m n(kas)»13.0033544d0
if (m c(kas).eq. 13.)m c(kas)=13.0033544d0
if (m n(kas).eq. 1 5 .)m n (k a s)-l 5.0001077d0
i f (m c(kas).eq. 15.)m c(kas)-15.0001077d0
if (m n(kas).eq. 1 6 .)m n (k a s)-l 5.99491502d0
if (m c(kas).eq. 16.)m c(kas)=15.99491502d0
if (m n(kas).eq. 18.)m n(kas)»l 7.99916002d0
if (m c(kas).eq. 1 8 .)m c(k as)-l 7.99916002d0
17
C O N T IN U E
N P L O T S -N P L O T S N E W
18
C O N T IN U E
W RITE(*, 19)ST A R T
19
F O R M A T (3X ,’S T A R T IS’, F l 5.8,5X ,’W OULD Y O U L IK E TO
C H A N G E IT ?’)
R E A D (u n it= * ,F M T » ’(A )’)IF C H A N G E 2
IF (IF C H A N G E 2 .EQ. ’N ’ .OR. IF C H A N G E 2 .EQ. ’n ’)GO T O 20
W RITE(*,*)’ W HAT IS Y O U R NEW V A L U E O F S T A R T ?’
R E AD(*,*)ST A R T
20
C O N T IN U E
W R ITE(*,2 1 )STO P
21
F O R M A T (3X ,’STO P IS’,F 1 5.8,5X ,’W O U LD Y O U L IK E TO
C H A N G E IT ?’)
R E A D (u n it= * ,F M T » ’(A )’)IF C H A N G E 3
IF (IF C H A N G E 3 .EQ. ’N ’ .OR. IF C H A N G E 3 .EQ. ’n ’)G O T O 22
W R IT E (V )’ W HAT IS Y O U R NEW V A L U E O F STO P?’
R E A D (* * )S T O P
22
C O N T IN U E
W R IT E (*,23)A IN T
23
F O R M A T (3X ,’T H E IN T E R V A L O F C O N ST A N T Y L IN E S
IS* F I 5 8 /
’ r W OULD Y O U L IK E TO C H A N G E IT ?’)
R E A D (u n it-* ,F M T - ’(A)*)IFCH A N G E 4
IF (IF C H A N G E 4 .EQ. ’N ’ .OR. IF C H A N G E 4 .EQ. ’n ’)G O T O 24
W RITE(*,*)’ W HAT IS Y O U R IN T E R V A L O F P R IN T E D
L IN E S ?’
R E A D (V )A IN T
24
C O N T IN U E
W R IT E (*,25)A PR IN T
25
F O R M A T (3 X ,’T H E IN T E R V A L O F P R IN T E D Y L IN E S
V A L U E S ’JF 15.8/
1’ W OU LD Y O U L IK E TO C H A N G E IT ?’)
R E A D (u n it-* ,F M T -’(A )’)IF C H A N G E 5
IF (IF C H A N G E 5 .EQ. ’N ’ .OR. IF C H A N G E 5 .EQ. ’n ’)G O T O 26
W RITE(*,*)’ W HAT IS Y O U R IN T E R V A L O F P R IN T E D Y
VA LUES’
R E A D (*,*)A P R IN T
26
C O N T IN U E
W RITE(*,27)SLO PE2
27
F O R M A T (3 X ,’SLO PE2 IS’,F15.8,’W O U LD Y O U L IK E T O
C H A N G E IT ?’)
R E A D (u n it-* ,F M T -’(A )’)IF C H A N G E 7
IF (IF C H A N G E 7 .EQ. ’N ’ .OR. IF C H A N G E 7 .EQ. ’n ’)GO T O 28
W RITE(* *)’ W HAT IS Y O U R NEW V A L U E O F SL O PE 2?’
R E A D (*,*)SLO PE2
28
C O N T IN U E
29
C O N T IN U E
C
C
C
C
IF (F IR S T _ T IM E )G O TO 34
CA LSO O N E C A N C H A N G E E X IS T IN G LIN ES. T H E C O M P U T E R
LISTS T H E L IN E IN D E X ,A N D
C T H E B E,M H ,M N ,M C,A N D L IN E W ID TH. IF T H E U S E R IS
SA T S IF IE D H E C A N SIM PLY
C E N T E R Y A N D N O N E O F T H IS D A T A IS A F F E C T E D . IF H E
WISHES T O C H A N G E SO M E TH IN G
CHE
ENTERS
THE
L IN E
IN D E X .A N D
THE
CO M PUTER
PR O M PTS H IM T O T Y P E A NEW L IN E .
C IT IS ,U N F O R T U N A T E L Y N E C E SSA R Y T O R E T Y P E T H E
W HOLE L IN E T O M A K E A SIN G LE
CCHANGE.
W RITE(* *)’ H E R E IS T H E L IST O F BE,M H ,M N ,M C ,A N D L IN E
W ID TH ’
D O 31 K A S = l,n p lo ts
W R ITE(*,30)K A S,B E(K A S),M H (K A S),M N (K A S),M C (K A S),A L (K A S)
30
FO R M A T ( 1X ,I2,2x,F 9.3,2x,3(F 11.8,2x)F5.3)
31
C O N T IN U E
W RITE(*,*)’ IF Y O U WISH T O K E E P T H E SAME BES,MASSES,
1 0 R L IN E W IDTHS E N T E R Y’
R E A D (u n it« * ,F M T = ’(A )’)IF N O T
IF (IF N O T .EQ. ’Y ’ .OR. IF N O T .EQ. ’y ’)GO T O 34
32
W RITE(*,*)’ E N T E R T H E IN D E X O F T H E L IN E Y O U WISH
CHANGED’
R E A D (*,*)K A S
W R ITE(*,33)K A S,B E(K A S),M H (K A S),M N (K A S),M C (K A S),A L (K A S)
33
F O R M A T (3X ,’T H E O L D V A L U E S F O R KA S E Q U A L
T O ’,13,’A R E ’/
V ’ BE’,F9.3,2x,’M H ’,F l 1.8,2x,’M N ’,F l 1.8,2x,’MC’,F l 1.8,2x
2,’A L ’,F 5.3/
2’ E N T E R Y O U R NEW V A L U E S(N O T E ,A S ALW AYS Y O U
NEED M ERELY EN TER
3 / T H E N E A R E S T R E A L W HOLE N U M BER F O R MASS
V A L U E S)’)
R E A D (*,*)B E (kas),M H (kas),M N (kas),M C (kas),A L (kas)
if (m h(kas).eq. l.)m h (k a s ) - 1.00782519d0
i f (m h(kas).eq. 2.)m h(kas)-2.01410222d0
if (m n(kas).eq. 14.)m n(kas)»14.00307439d0
if (m c(kas).eq. 14.)m c(kas)-14.00307439d0
if (m n(kas).eq. 13.)m n(kas)-13.0033544d0
if (m c(kas).eq. 13.)m c(kas)-13.0033544d0
i f (m n(kas).eq. 1 5 .)m n (k a s)-l 5.0001077d0
if (m c(kas).eq. 1 5 .)m c(k as)-l 5.0001077d0
if (m n(kas).eq. 1 6 .)m n (k a s)-l 5.99491502d0
i f (m c(kas).eq. 1 6 .)m c(k as)-l 5.99491502d0
if (m n(kas).eq. 1 8 .)m n (k a s)-l 7.99916002d0
if (m c(kas).eq. 1 8 .)m c(k as)-l 7.99916002d0
c O N E C A N C H A N G E AS M A N Y L IN E S AS H E D ESIR ES
T Y P E *,’ W OULD Y O U L IK E T O C H A N G E O T H E R L IN E S ?’
R E A D (u n it-* ,F M T -’(A )’)IC H A N G E
.SP1
IF (IC H A N G E .EQ. ’Y ’ .O R. IC H A N G E .EQ. ’y’)GO T O 32
34
C O N T IN U E
A M A R -S T O P -S T A R T
C
C
C
C
cT H IS P A R T O F T H E P R O G R A M C A L C U L A T E S T H E Y PO IN TS
O N T H E G R A P H FR O M
c T H E IN P U T X C O O R D IN A T E S . T H E H E A V Y -A T O M D IST A N C E
IS C O N S ID E R E D T O BE T H E
C T H E X C O O R D IN A T E .IT S V A L U E C A N BE D IR E C T L Y R E A D
F R O M T H E A BCISSA .TH E Y IS
C D IS P L A C E D .B U T ITS A C T U A L V A L U E C A N
BE R E A D
D IR E C T L Y F R O M T H E T O P O F T H E
C G R A P H .T H E D O T T E D L IN E S A R E LIN ES O F C O N ST A N T
R H _ H E A V Y A T O M T H E LOWEST
CPO SSIB LE V A L U E O F Y IS C H O SE N TO BE Y S T A R T ,A N D T H E
H IG H E S T IS Y STO P
C T H IS IS D O N E BY C A L C U L A T IN G Y (S T A R T ) A N D Y (ST O P)FO R
A L L T H E LIN ES
w rite(* ,* )’how m any lines a re w a n te d f o r th e b o u n d a rie s? ’
r e a d ( u n it- * ,f m t- ’(I)’)IB O U N
D O 35 K A S -l.IB O U N
c a ll rc(start,b e(k as),m h (k as),m n (k as),m c(k as))
a y s ta r t- r h n
a y s to p - r h n
i f (k as .eq. l)y s ta rt= a y s ta rt
i f (k as .eq. l)y sto p = a y sto p
i f ( a y s ta rt .It. y s ta rt)y s ta rt« a y s ta rt
i f (ay sto p .gt. y stop)ystop= aystop
c
y s to p - y s ta r t+ 0 . 0 0 2
ste p « (a m a r ) / 1 OOO.dO
d isp « slo p e 2 *(am ar)
c
c a ll rc(stop,be(kas),m h(kas),m n(kas),m c(kas))
a y s to p « rh n + d isp
a y s ta r t- rh n + d is p
i f ( a y s ta rt .It. y s ta r t) y s ta r t- a y s ta r t
i f (ay sto p .gt. y stop)ystop= aystop
c
35
c o n tin u e
C
C
C
C
C IN T H IS P A R T O F T H E P R O G R A M T H E WINDOW AN D
D ISPL A Y A R E SE T UP. N O T E ,T H E
C D IS P L A Y B O U N D A R IE S O F (-.2,-.2)A N D (1.2,1.2)A R E A R B IT A R Y
A N D T H E U S E R CA N
C E A SIL Y C H A N G E TH ESE IF H E SO D ESIR ES. T H IS SIM PLY IS
D O N E T O G IV E A M A R G IN
C F O R T IT L E S . ALSO X C A R A N D Y C A R W HICH I SET E A R L Y IN
T H E P R O G R A M TO BE .02
C C A N BE C H A N G E D .T H E Y A R E U SED TO D E T E R M IN E T H E
R E L A T IV E SIZ E O F T H E O U T C P U T T IT L E S A N D T E X T . MY V A L U E S,H O W E V E R ,G IV E G O O D
R E S U L T S .T H E (0,0) A N D
C( 1,1 )B O U N D A R IE S O F T H E P L O T A R E T H E R E S U L T OF
S C A L IN G A LL T H E X A N D Y
446
C P O IN T S A N D N O T EA SILY C H A N G E D .
T X C A R = (2.0d0*X C A R )
T Y C A R -(2.0d0*Y C A R )
vd id -u is $ c re a te display(-0.2,-0.2,1.2,1.2,13.0,18.0)
w d id 1-u is S c re a te w in d o w (v d id ,’sys$ w o rk s ta tio n ’,’p lo ts’)
call uis$plot(vd__id, 0 ,0 .,0 ., 1 .,0 .)
call uis$plot(vd__id, 0 ,l .,0 ., 1 ., 1 .)
call uis$pl©t( vd__id, 0 , 1 ., 1 .,0 ., 1 .)
call u is$ p lo t( v d _ i d , 0 ,0 ., 1 .,0 .,0 .)
if ( ititlc .eq. *N’ .OR. ititle .eq. ’n ’)go to 38
C
ONE
F IR S T
ENTERS
THE
G RAPH
T IT L E
IT
IS
A U T O M A T IC A L L Y C E N T E R E D ON
C T H E M ID P P O IN T O F T H E X -A X IS. O N E USES T H E C U R SO R TO
PLA C E IT W H ER E HE
C L IK E S O N T H E Y -A X IS.T H E FO LLO W IN G ALSO H O LD S T R U E
F O R T H E LOW ER A N D U P P E R
CT IT L E S.
call uisS set f o n t(v d _ id ,2 ,8 ,’m y _ f o n t _ l 2’)
call u is $ s e t_ c h a r _ s iz e (v d id , 2 , 8 „ tx c a r,ty c a r)
T Y P E V P O S IT O N T H E C U R S O R W HERE Y O U W OULD L IK E
T H E T IT L E ’
PA U SE
H ST A T U S -U IS S G E T P O IN T E R
K -IN D E X (T IT L E ,’ ’)-l
IF (K .LE. 0) K -4 0
P O S IT IO N (V D
ID,W D
ID 1,R E T X ,R E T Y )
C A LL
U ISSM EA SU R E T E X T (V D ID , 8 ,% D E SC R (T IT L E (:K )),F__
2W ID TH T IT L E ,F H E IG H T T IT L E )
C A LL U IS $T E X T (vd id , 8 ,% D E SC R (T IT L E (:K )),
1
0 .5 -F _ W ID T H _ T IT L E /2 .,R E T Y )
C
IF (.N O T .F IR S T _ T IM E )th e n
C T H E SE C O N D TIM E A R O U N D ,O N E C A N O P T T O K E E P T H E
SAME T IT L E S O R TO C H A N G E
C T H E M AS D ESIR ED .
W R IT E (V )’ W OULD Y O U L IK E TO K E E P T H E SAME
LOW ER T IT L E ? ’
R E A D (u n it-* ,F M T -’( A )’)IFSA M E 1
e n d if
IF (IFSA M E 1 .EQ. ’Y’ .OR. IFSA M E 1 .EQ. ’y ’)GO T O 36
T Y P E * ’W HAT IS Y O U R LOW ER T IT L E ?’
R E A D (U N IT «*, F M T - ’(A 40)’)X T IT L E
36
T Y P E *,’PO SIT O N T H E C U R S O R W HERE Y O U W OULD L IK E
T H E LOW ER T IT L E ’
PA U SE
H ST A T U S -U IS S G E T P O IN T E R _ P O S IT IO N (V D _ _ ID ,W D _ ID 1,R E T X ,R E T Y )
call u is $ s e t_ fo n t(v d _ id ,3 ,9 ,’m y _ f o n t _ 1 4 ’)
call u is $ s e t_ c h a r size( v d id ,3 ,9 „ T x c a r.ty c a r)
447
K 1= IN D E X (X T IT L E ,’ > 1
IF(K 1 .LE. 0) K l - 4 0
C A LL
U IS $ M E A S U R E _ T E X T ( V D _ ID ,9 ,% D E S C R (X _ T IT L E (:K 1) ) ,F _
2W ID TH X T I T L E ,F _ H E I G H T _ X T IT L E )
C A L L U IS $T E X T ( v d _ id ,9 ,% D E S C R (X _ T IT L E (:K 1)),
1
0.5-F__W ID TH _X _T IT L E /2 .,R E T Y )
IF (.N O T .F IR S T _ T IM E )th e n
W RITE(*,*)’ W OU LD Y O U L IK E T O K E E P T H E SAME
U P P E R T IT L E ? ’
R E A D (u n i t-* ,F M T - ’( A )’)IFSA M E2
e n d if
IF (IFSA M E2 .EQ. ’Y ’ .O R. IFSA M E2 .EQ. ’y’)GO T O 37
T Y P E * ’W HAT IS Y O U R U P P E R T IT L E ? ’
R E A D (u n it-* ,F M T -’(A 40)’)Y T IT L E
37
T Y P E * ’PO SIT O N T H E C U R S O R W H ER E Y O U W OU LD L IK E
T H E U P P E R T IT L E ’
PA U SE
H ST A T U S -U IS S G E T P O IN T E R P O S IT IO N (V D ID,W D
c a ll uisS set fo n t(v d id ,4,10,’m y f o n t 13’)
c a ll u is $ s e t_ c h a r _ s iz e ( v d _ id ,4 ,10 „ T x c a r.ty c a r)
K 2 -IN D E X (Y T IT L E ,’ ’)-l
IF (K 2 .LE. 0) K 2 -4 0
ID 1,R E T X ,R E T Y )
CA LL
UISSM E A S U R E _ T E X T ( V D _ ID , 10,% D ESCR( Y _ T IT L E (:K 2 ) ) ,F _
2W ID TH Y _ T IT L E ,F H E IG H T _ Y _ T IT L E )
C A L L U IS $ T E X T (v d _ id ,1 0 ,% D E S C R (Y _ T IT L E (:K 2 )),
1
0.5-F__W ID TH__Y_T IT L E /2 .,R E T Y )
38
C O N T IN U E
C
C
C
C
C T H IS P A R T O F T H E P R O G R A M DRAW S L IN E S O F C O N ST A N T
X AS D A SH E D LIN ES,
do 40 j t e s t - 1 ,1001,100
R C N -S T A R T +(jte sT -1 .)*STEP
if (jte st .eq. l)go to 39
i f (jte st .eq. 1001)go to 40
39
c a ll uisS set lin e _ s ty le (v d id,0,5,’f f f 0 f f f 0 ’x)
call u is $ p lo t(v d _ id ,5 ,x b a r(rc n ),y b a r(y s ta rt),x b a r(rc n ),
1 y b a r(y sto p ))
40
c o n tin u e
C
C
C
C
C T H IS P A R T O F T H E P R O G R A M P R IN T S T H E R C N V A LU ES
SU C H T H A T T H E Y A R E P R O P E R L Y
C C E N T E R D O N T H E C O R R E C T D A SH ED LINES,
do 42 j w te s t- 2 0 1,801,200
R C N -S T A R T +(jw te sT -1 .)*STEP
e n c o d e (7 ,4 1,strin g 2 )rc n
41
fo rm a t(f7 .5 )
c a ll u isS set fo n t(v d id ,0,4,’m y f o n t 12’)
c a ll u is $ s e t_ c h a r _ s iz c (v d _ id ,0 ,4 „ x c a r ,y c a r )
c
c a ll u is$ s e t_ c h a r_ s p a c in g (v d _ id ,0 ,4 ,x s p a c e ,y s p a c e )
te x p o s -rc n
c a ll u is $ te x t(v d _ id ,4 ,s trin g 2 ,x b a r(te x p o s )-3 .* x c a r,y b a r(y s ta rt))
42
c o n tin u e
C
C
C
C
C T H IS DO L O O P A C T U A L L Y PLO TS T H E LIN ES
DO 44 K A S -l,n p lo ts
C alL R C (start,b e(k as),m h (k as),m n (k as),m c(k as))
C alL U ISSSET L IN E W ID TH (V D ID ,0,7,al(kas))
C F IR S T A N IN IT IA L X P O IN T IS G IV E N ,A N D A N IN IT IA L Y
P O IN T IS C A L C U L A T E D
CBY T H E S U B R O U T IN E RC
y l-rh n
r c n - s ta r t
D O 43 J-1,1001
S IT -J
s it 2 - s i t + l .d 0
R C N -S T A R T + (S IT -1.)*STEP
R C N 2 -S T A R T + (S IT 2 -1.dO)*STEP
C alL R C (R C N 2,be(kas),m h(kas),m n(kas),m c(kas))
Y 1 2 -R H N
Y 1 2 -Y 12+(D ISP*(SIT2- I.d0)/1 OOO.dO)
C T H E N T H E WE E N T E R T H E LO O P W HERE T H E SE C O N D Y IS
C A L C U L A T E D .T H E N T H E X
C
VALUES
ARE
SC A LED
AS
X B A R (X )-X A C T U A L -X S T A R T /X S T O P -X S T A R T . T H E Y PO IN TS
C A R E SC A L E D IN T H E SAME WAY. T H E R E F O R E ,IN W ORLD
C O O R D IN A T E S E V E R Y T H IN G
CIS P L O T T E D BETW EEN 0. A N D 1. A T T H E E N D O F T H E LOOP
T H E SEC O N D PO IN T
CIS D E F IN E D AS T H E F IR S T P O IN T IN T H E N E X T SEG M EN T.
T H U S 1000 SEG M EN TS A R E
CPLOTTED.
IF (Y B A R (Y I) .LT. 0.)GO T O 430
IF (Y B A R (Y 12) .GT. l.)G O T O 430
c a ll u is $ p lo t(v d _ id ,7 ,x b a r(rc n ),y b a r(y 1),x b a r(rc n 2 ),y b a r(y 12))
430 y l « y l2
43
C O N T IN U E
44
C O N T IN U E
C
449
C
C
c
a d if f = s to p -s ta rt
s lo p e - d is p /a d if f
i f (slope .eq. 0 .0 )slope - 1 .
arslo p e= 1 ,0 d 0 /slo p e
y d iff= y s to p -y s ta rt
C
H E R E T H E LIN ES O F C O N S T A N T Y A R E P R IN T E D AS
D O T T E D L IN E S
DO 48 JI«1,101
S j- J I
s j l - s j - 1.
X S T A R T A *ST A R T + ((Sj 1)* A R SL O PE * A IN T )
x s to p A » x s ta rtA + (a rs lo p e * y d iff)
i f (x s ta rtA .gt. stop)go to 48
i f (x sto p A .gt. stop)go to 48
C alL U ISSSET L IN E W ID TH (V D ID ,0,6,1.)
ca ll u is $ s e t_ J in e _ s ty le ( v d id,0,6,’A A A A A A A A ’x)
c a ll u is $ p lo t(v d _ id , 6 ,x b a r(x s ta rtA ),y b a r(y s ta rt),x b a r(x s to p A ),
1 y b a r(y sto p ))
y a c t« y s ta rt-((s j 1 )* ain t)
C AS M E N T IO N E D E A R L IE R A P R IN T IS T H E IN T E R V A L A T
W HICH O N E S WISHES T O P R IN T
C T H E A C T U A L Y V A LU E S. A N D A IN T IS T H E IN T E R V A L A T
W HICH T H E D O T T E D L IN E S
C A R E D R A W N . T H E R A T IO A P R IN T /A IN T M UST BE AN
IN T E G E R .
in d a » ( a p r in t/a in t)
do 47 jip lo t* l,1 0 1 ,in d a
C T H IS D O L O O P P R IN T S T H E A C T U A L Y V A L U E S
i f (jip lo t .ne. ji)go to 47
e n c o d e(6 ,4 5 ,strin g )y a c t
45
fo rm a t(f6 .4 )
x P L O T A -x sT O P A
ca ll uisS set fo n t(v d id,0,7,’m y__font__l 2’)
ca ll uisS set c h a r size(v d id ,0 ,7 „ x c a r,y c a r)
x p lo tte st* x b a r(x sto p a )-3 .0 * x c a r
x p lo tte s t 2 “ x p lo tte st+ 6 .0 *x car
if(x p lo tte s t2 .gt. l.)go to 46
if(x p lo tte s t .ge. 0.)call u is $ te x t(v d _ id ,7 ,s trin g ,x p lo tte s t
1 ,y b a r(y sto p )+ 2 .0 *ycar)
46
c a ll u isS set lin e sty le (v d id ,0 ,3 .’A A A A A A A A ’x)
47
c o n tin u e
48
C O N T IN U E
C
C
C
C
ty p e* ,’ W OULD Y O U L IK E T O IN S E R T T E X T IN T H E
450
G R A PH ?’
R E A D (u n it= * ,F M T » ’(A )’)IT E X T
IF (IT E X T .EQ. ’N ’ .OR. IT E X T .EQ. ’n’)G O T O 50
49
T Y P E *,’ W R ITE T H E D E S IR E D T E X T ’
R E A D (U N IT **,FM T =’( A 20)’) A T E X T
T Y P E *,’PO S IT IO N T H E C U R S O R W H ER E Y O U W OULD L IK E
T O P U T IT ’
PA U SE
H S T A T U S « U IS $ G E T _ P O IN T E R _ P O S IT IO N (V D _ ID ,W D _ ID l,A R E T X ,A R E T Y )
A X C A R -1 .5 d 0 * X C A R
A Y C A R - 1.5dO*YCAR
c a ll uisS set f o nt( v d id ,0 , 1 0,’m y _ f o n t 3’)
c a ll u is $ s e t_ c h a r _ s iz e ( v d id ,0 ,1 0 „A x c ar,A y c a r)
call u is$ te x t(v d id , 10, A T E X T ,A R E T X ,A R E T Y )
T Y P E *,’ W O U LD Y O U L IK E T O C O N T IN U E ?’
R E A D (u n it-* ,F M T -’(A )’)IC O N A
IF (IC O N A .EQ. ’Y ’ .OR. IC O N A .EQ. ’y ’)GO T O 49
50
T Y P E *,’ W O U LD Y O U L IK E A T IT L E F O R Y O U R L IN E S?’
R E A D (u n it-* ,F M T -’(A )’)IL IN E S
IF (IL IN E S .EQ. ’N ’ .OR. IL IN E S .EQ. ’n ’)G O T O 53
51
T Y P E *,’ W R ITE T H E D E S IR E D T IT L E ’
R E A D (* ,F M T -’( A 12)’)A L A BEL
T Y P E *,’ PO S IT IO N T H E C U R S O R W H ER E Y O U W OULD
L IK E T O P U T IT ’
PA U SE
HST A T U S « U IS $ G E T P O IN T E R PO SIT IO N ( V D ID,W D ID 1,R E T X ,R E T Y)
c a ll uisS set fo n t(v d id,0,9,’m y _ f o n t _ 4 ’)
c a ll u is $ s e t_ c h a r _ s iz e ( v d id ,0 ,9 „ x c a r,y c a r)
c a ll u is$ te x t(v d _ id ,9 ,A L A B E L ,R E T X ,R E T Y )
T Y P E *,’ W OU LD Y O U L IK E S U P E R S C R IP T S ?’
R E A D (u n it-* ,F M T -’(A )’)IS U P E R
IF (IS U P E R .EQ. ’N ’ .OR. IS U P E R .EQ. ’n ’)G O T O 52
T Y P E * ’P R IN T Y O U R S U P E R S C R IP T . IF Y O U O N L Y W ANT
T O S U P E R S C R IP T
1 T H E T H IR D A T O M L E A V E O N E SPA C E B L A N K ’
Y S U P E R « R E T Y + (Y C A R /4 .)
X S U P E R -R E T X + X C A R
R E A D (* ,F M T -’(A 7)’)S U P E R S C R IP T
c a ll u is$ te x t(v d _ _ id ,9,S U P E R S C R IP T ,X S U P E R ,Y S U P E R )
52
T Y P E *,’ W O U LD Y O U L IK E T O C O N T IN U E ?’
R E A D (u n it-* ,F M T « ’(A )’)IC O N
IF d C O N .EQ. ’Y ’ .O R. IC O N .EQ. ’y ’)G O T O 51
53
W R ITE(*,*)’ W OULD Y O U L IK E T O W RITE T H IS PL O T TO
A D IS K F IL E ?’
R E A D (u n it» * ,F M T » ’(A )’)ID IS K F IL E
if ( id is k f ile .eq. ’n ’ .OR. id is k file .eq. ’N ’)G O TO 530
T Y P E *,’ W HA T W OULD L IK E TO C A L L Y O U R O U T P U T
F IL E ? ’
o
o
o
o
rea d (u n it« * ,F M T = ’(A 20)’)O U T P U T F IL E
ST A T U S= H C U IS$W R IT E D ISPL A Y (V D ID ,O U T P U T F IL E )
530
id is k filc = ’N ’
C alL U IS $ D E L E T E _ W IN D O W (w d _ id l)
C alL U IS $ D E L E T E _ D IS P L A Y (v d id)
W RITE(* *)' W OULD Y O U L IK E T O R U N A G A IN ?’
r e a d ( u n it-* ,F M T - ’(A )’)IR U N
F IR S T T IM E -.F ALSE.
IF (IR U N .EQ.’Y ’ .OR. IR U N .EQ. ’y ’)GO T O 1
END
S U B R O U T IN E R C (R C N ,be,m h,m n,m c)
C T H IS S U B R O U T IN E C A L C U L A T E S R H N FR O M R C N A N D BE
IM P L IC IT R E a l * 8 (A -H ,0 -Z )
C O M M O N /B IL L /R H N
R E a l * 8 IN ,M I,m h,m n,m c
B -(2.0d0*m c*R C N )/(m n+ m c)
IN -5 0 5 3 7 9 .0 5 d 0 /b e
M I-IN *(m h+ m n+ m c)
TO P-((m c*m n)+(m h*m c))*(R C N **2.0dO )
A -(T O P -M I)/((m h*m n)+ (m h*m c))
R H N —B+D SQRT((B**2.0d0)-(4.0d0*A ))
R H N « R H N /2 .0 d 0
RETURN
END
A P P E N D I X 8.
P R O G R A M B O N D LS4.FO R.
453
30
82
1
25
21
26
40
IM P L IC IT R E A L * 16 (A -H ,0 -Z )
C O M M O N /B IL L /R H N
C O M M O N /B R E T T /X T E S T , Y T E ST
C O M M O N /R O L F /X ,Y
D IM EN SIO N ABE( 10),AM H( 10),AM N( 10),AMC( 10)
R E A L * 16 M H,M N,M C,M H2,M N2,M C2
R E A D (20,*)N L IN E S
DO 30 I-1 ,N L IN E S
R E A D (20,*)A B E (I),A M H (I),A M N (I),A M C (I)
C O N T IN U E
R E A D (20,*)ST A R T ,S T E P
R E A D (20,*)T O L E R
B E G T O L E R -T O L E R
DO 6 6 I -l.N L IN E S
DO 65 J-1 ,N L IN E S
T O L E R -B E G T O L E R
IF (I .LE. J) G O T O 65
B E -A B E (I)
M H -A M H (I)
M N -A M N (I)
M C -A M C (I)
B E 2-A B E (J)
M H 2-A M H (J)
M N 2-A M N (J)
M C 2-A M C (J)
W RITE( 10,82)BE,M H,M N ,M C,BE2,M H 2,M N2,M C2
FO R M A T ( IX ,’IN IT IA L IN P U T ’/4F 15.8/4F 15.8)
R C N -S T A R T
C A L L R C (R C N ,B E,M H ,M N ,M C )
Y l- R H N
C A L L RC (R C N ,B E2,M H 2,M N 2,M C 2)
Y A 1 -R H N
X l- R C N
R C N -R C N + S T E P
C A L L RC (R C N ,B E,M H ,M N ,M C )
X 2 -R C N
Y 2 -R H N
C A LL RC (X 2,BE2,M H 2,M N 2,M C2)
Y A 2 -R H N
C A L L T E S T (X 1,X 2 ,Y 1,Y 2 ,Y A 1,YA2)
C A LL TO L(X TEST,Y TEST,B E,M H ,M N ,M C ,B E2,M H 2,M N 2,M C 2)
T O L E R - 100000.0*TO LER
Z -X -T O L E R
Z 2 -Y -T O L E R
IF (X -T O L E R )25,25,2l
IF(Y -T O L E R )26,26,21
R C N -X T E S T
GO T O 1
W RITE( 10,40)X T E S T , Y TEST
FO R M A T ( 1X .’O U R F IN A L A N SW ER’,2F15.8)
65 C O N T IN U E
6 6 C O I'JT IN U E
END
S U B R O U T IN E RC (R CN ,BE,M H ,M N ,M C)
IM P L IC IT R E A L * 16 (A -H .O -Z )
C O M M O N /B IL L /R H N
R E A L * 16 IN ,M I,M H ,M N,M C
B«(2.0*M C*R CN )/(M N +M C )
IN -5 0 5 3 7 9 .0 5 /B E
M I=IN*(M H+M N+M C)
TO P-((M C *M N )+(M H *M C ))*(R CN **2.0)
A -(TO P-M I)/((M H *M N )+(M H *M C ))
R H N —B+QSQRT((B**2.0)-(4.0*A))
R H N -R H N /2 .0
RETURN
END
S U B R O U T IN E T E S T (X 1,X 2,Y 1,Y 2,Y A 1,YA2)
IM P L IC IT R E A L * 16 (A -H .O -Z )
C O M M O N /B R E T T /X T E S T ,Y T E S T
S L O P E -( Y 2 -Y 1)/(X 2 -X 1)
C E P T - Y 1- (X 1*SLO PE)
SL O PE 2«(Y A2-Y A 1)/(X 2 -X 1)
C E P T 2 -Y A 1-(X I *SLO PE2)
X T E S T -(C E P T -C E P T 2)/(S L O P E 2-S L O P E )
Y T E S T -(S L O P E *X T E S T )+ C E P T
RETURN
END
S U B R O U T IN E
T O L (X T E S T , Y TEST,BE,M H,M N,M C,BE2,M H2,M N 2,M C2)
IM P L IC IT R E A L * 16 (A -H .O -Z )
C O M M O N /R O L F /X .Y
R E A L * 16 M OM ,M H,M N,M C,M H2,M N2,M C2,M OM 2
M O M -((X TEST+Y TEST)**2.0)*(M H *M C)+((M H *M N )*(Y TEST**2.0))
M OM =M OM +(M N*M C)*(XTEST**2.0)
BTEST-(M H +M N +M C )*505379.05/M O M
M O M 2-((X TEST+Y TEST)**2.0)*(M H 2*M C2)
M OM 2-M OM 2+((M H2*M N2)*(YTEST**2.0))
- M OM 2=M OM 2+(M N2*M C2)*(XTEST**2.0)
BTEST2»(M H 2+M N 2+M C2)*505379.05/M O M 2
X -A B S(B T E S T -B E )
Y -A B S(B T E ST 2-B E )
X -100000.0*X
Y - l 00000.0* Y
RETURN
END
title
o f th e s is
i*:____The M i c r o w a v e
S p e c tr o sc o p y
of
Ion s
and
Other Transient Species in DC Glow and Extended Negative
Glew Discharges_________________________________________
MAJOR PROFESSOR
R. Claude Woods________________________
MAJOR
Chendatry______________________________ ________
m in o r
Physics________________________________________
NAME
Hugh Edward Warner
p l a c e an d d a t e o f b i r t h
Exeter> New Hampshire Feb, 29>1956
COLLEGES AND UNIVERSITIES: TEARS ATTENDED AND DEGREES _______________
Wake * Forest University, BS, 1978
Attended 1974-1978____________________________________
University of Wiscenain-Madisen, 1978-1988 Ph.D.
MEMBERSHIPS IN LEARNED OR HONORARY SOCIETIES
p u b lic a tio n s
"The lowest rotational transition of several
isetepic feras ©f KrD+" Hugh E. Warner, Williaa T. Conner,
and R. Claude Weeds, J. Che*«Phys. *81, 5413(198*0.
"Laboratory Detection of the
submillimeter wave
transition of the HgD* ion", Hugh E. Warner, Williaa T.
Conner, Rudolph H. Petraichl, and R. Claude Weeds, J. Chea.
Phys. 81, 2514 (1981).
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