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UBC Theses and Dissertations

Spectrum of the hydroxyl radical Carlone, Cosmo 1969

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SPECTRUM  OF  THE  HYDROXYL  RADICAL  by COSMO CARLONE B. M.  Sc., U n i v e r s i t y o f Windsor, 1963  Sc., U n i v e r s i t y o f B r i t i s h Columbia, 1965  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY i n the Department of PHYSICS  We accept t h i s t h e s i s as conforming t o the required standard  THE  UNIVERSITY OF BRITISH COLUMBIA March  1969  In p r e s e n t i n g an the  in partia 1 fuIfilment  thesis  of the requirements f o r  advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, Library  I further for  this  s h a l l make i t f r e e l y  agree that  permission  available  I agree  that  f o r r e f e r e n c e and S t u d y .  f o rextensive  copying of this  thesis  s c h o l a r l y p u r p o s e s may be g r a n t e d b y t h e Head o f my D e p a r t m e n t o r  by  h i s representatives.  of  this  written  It i s understood  thes.is f o r f i n a n c i a l  gain  permission.  Department o f  Physics  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  March 25, 1969  Columbia  shall  that  copying or p u b l i c a t i o n  n o t be a l l o w e d w i t h o u t  my  ACKNOWLEDGMENT  I wish t o thank P r o f e s s o r F. W. Dalby f o r suggesting f o r constant  the problem and  supervision.  T h i s work was supported by the N a t i o n a l Research C o u n c i l o f Canada.  ii  ABSTRACT The and  OD  2_  B  2_  +  2^_  +  -) A I  and  C  2  +  E  2  +  A ZT  systems of  were photographed at high r e s o l u t i o n . 2  d i s s o c i a t i o n energy D°(A  £  cm""  1  f  0  H  apparent  ) i s c a l c u l a t e d to be  ± 15) cm' f o r OH and (19263 - 15) l i m i t to D ° ( X T T 3 ) ° 2  The  l  s  d  e  d  u  c  e  d  (188^7  f o r OD. An (35^20 -  1  t o  upper 15)  b e  / 2  -1  OH  2  cm . E v i d e n c e f o r a d i s p e r s i o n hump i n the B( E -1 which i s about 100 cm l a r g e r than the hump i n the  +  ) state 2 + A( 2. )  s t a t e i s presented. The  broadening of the r o t a t i o n a l l i n e s i n s e v e r a l bands  of both systems has  2 the  A(  established  a strong p r e d i s s o c i a t i o n o f  + ) s t a t e near v = 5 i n OH.  2T  predissociated  levels is  IO  - 1 1  The  l i f e t i m e of these  seconds.  A d e f i n i t e iden-  t i f i c a t i o n of the p r e d i s s o c i a t i n g s t a t e has  not been p o s s i b l e . 2 + Newly d i s c o v e r e d v i b r a t i o n a l l e v e l s i n the C( H ) s t a t e have l e d to the f o l l o x ^ i n g c o n s t a n t s , i n cm" , of the 1  OH r a d i c a l i n the C  T  e  D°  to  e  <-o X e  Rotational A(  21  e  2 _ L  =  89500  =  29^18  =  1232.9  =  19.1  +  B - 15  a v a i l a b l e are  2~  <X  e  e  (v=0) % (v=l)  constants and  ) and B(  state  = =  O.078  =  1.09  =  0.88  spin s p l i t t i n g  constants i n  ) s t a t e s , more accurate than  presented.  the  previously  iii TABLE OF CONTENTS PAGE V  LIST OF TABLES LIST OF FIGURES  . . . . .  LIST OF PLATES CHAPTER  vi  .'. . '  v i i 1  I - INTRODUCTION  7  I I - BASIC THEORY OF DIATOMIC MOLECULES. . . . (a)  General t h e o r y  (b)  A p p l i c a t i o n o f the t h e o r y . . . . . .  7 13 . 2 0  I I I - EXPERIMENTAL. . . . . . . . . . . . . .  25  IV - RAW DATA. V - SPIN SPLITTING. . . . . . . . . . . . . .  hQ  VI - ROTATIONAL CONSTANTS. . . .... ...... . . .  56  V I I - DISPERSION HUMPS AND DISSOCIATION ENERGY.  6l  (a) A G(v + i ) o f  A  2  H  6l  +  2 (b) D i s s o c i a t i o n Energy o f (c) Energy l e v e l s  + H  A  2 (d) D i s s o c i a t i o n Energy o f B  state.  + ZZ  state  .  V I I I - VIBRATIONAL CONSTANTS OF  "  72 76  (e) D i s c u s s i o n .  IX - PREDISSOCTATIONS IN  6l 68  A  2  STATES. .  78  STATE. . . .  83  C, B  21  +  (a) Gaydon p r e d i s s o c i a t i o n  83  (b) Strong P r e d i s s o c i a t i o n .  85  (c) R e c o n c i l i a t i o n with t h e o r y  91  I:.  iv  PAGE X - THE  2 _  C  XI - WHAT NOW  APPENDIX  2_  +  -^B  2  L  +  SYSTEM  OH? . . . . . . . . .  98  BIBLIOGRAPHY  102  I - I s o t o p i c constant  105  I I - Computer program I I I - Zero p o i n t Energy. IV - Thermal and Pressure Broadening V - P r e d i s s o c i a t i o n by R o t a t i o n  ...  ,  96  in  2— +  A ^  106 110 I l l 113  s t a t e o f OD  VT - E l e c t r o n i c Isotope S h i f t s  11-+  V  LIST OF TABLES PAGE TABLE 1 - Wavenumbers of the B -> A system  .  2 - Wavenumbers of the C —> A system . . . . . . . .  26 .33  3 - Combination r e l a t i o n s f o r the B s t a t e o f OH . •  3-+  h - Combination r e l a t i o n s f o r the B s t a t e o f OD . .  35  5 - Combination r e l a t i o n s f o r the A s t a t e of OH . .  '37  6 - Combination r e l a t i o n s f o r the v = h l e v e l o f the A s t a t e o f OH . . . . . .  38  7 - Combination r e l a t i o n s f o r the A s t a t e of OD . .  39  8 - Combination r e l a t i o n s f o r the C s t a t e  . . . . .  9 - Band o r i g i n s  If2  10 - S p i n s p l i t t i n g constants  51+  11 - R o t a t i o n a l  59  constants  12 - A G ( v + -£•) o f  A  s t a t e o f OH  .  ,63  13 - A G ( v + i) o f  A  s t a t e o f OD . . . . . . . .  .  fa  Ih - Energy o f the v i b r a t i o n a l l e v e l s  .  69  15 - Wavenumbers o f the (P,o) t r a n s i t i o n o f the C  B  system of OH . . . . . .  97  vi LIST OF FIGURES FIGURE  PAGE  2 —+ x  1 - S t r u c t u r e of a  2 ^- +  z_  2_  2 - C o r r e l a t i o n of A with  2  TT  state of  14-  Mj o f u n i t e d atoms . . . . .  2h  6 - AP(N)  vs. N  7 - t vs  v  in C  in A  A G(8.5)  11 -  A G ( v + i ) vs  vs  curve i n A v  55  i n v = 10 o f A s t a t e o f OD  constants  10 -  53  s t a t e of OH  state  A d l vs (N + i )  9 - Rotational  18  19  OH  5 - Apparatus  8 -  17  M.j o f separated atoms. . . .  3 - C o r r e l a t i o n o f o , with _  transition  v  in A  state  .  58  . . . . .  60 62  s t a t e o f OH . .  in A  state  . . . . . . . . . .  12 - Atomic d a t a and d i s s o c i a t i o n energy  65 71  .  13 - L i m i t i n g curve o f d i s s o c i a t i o n i n the B s t a t e  . . .  75  Ih - Observed bound s t a t e s o f the h y d r o x y l r a d i c a l . . .  82  15 - Gaydon p r e d i s s o c i a t i o n  8*f  16 - P r e d i s s o c i a t i o n s i n the A s t a t e  87  17 - F u l l width a t h a l f maximum i n the (0,10) band of OD 18 - V a r i a t i o n o f the f u l l width due 19 - V a r i a t i o n o f the f u l l width due  . . . . . . . . . .  88  at h a l f maximum to r o t a t i o n  . . . . .  89  a t h a l f maximum to v i b r a t i o n . . . . . 90  vii  LIST OF PLATES PLATE  PAGE I - Three systems o f the h y d r o x y l r a d i c a l I I - The  I I I - The  B—>A  (0,7)  system and  (0,8)  !+5  . transitions  system o f OH IV - The  (0,9)  and  (0,12)  L^.  o f the  B—>A  .  t r a n s i t i o n s of the  .  k6  C—^A  system of OH and OD r e s p e c t i v e l y .  h7  1  CHAPTER I  -  INTRODUCTION  The h y d r o x y l r a d i c a l (OH) i s one o f the more i n t e r e s t i n g molecules i n n a t u r e .  I t i s r e a d i l y formed  r e a c t i o n s where i t s spectrum the temperature  i n combustion  i s o f t e n used to determine  o f a flame (Dieke and Crosswhite, 19-+8).  The OH e m i s s i o n has been d e t e c t e d i n the upper  atmosphere  and i s p r i m a r i l y r e s p o n s i b l e f o r the a i r g l o w ( M e i n e l , 1 9 5 0 ) . R e c e n t l y , the r a d i o frequency t r a n s i t i o n s w i t h i n the two lowest r o t a t i o n a l s t a t e s o f the r a d i c a l have been observed i n a s t r o n o m i c a l sources ( B a r r e t t , 1 9 6 8 ) .  D e t e c t i o n o f the  OH e m i s s i o n has u s u a l l y been accompanied by e x c i t i n g s u r prises.  For example, i t i s almost c e r t a i n that masing  a c t i o n i s r e s p o n s i b l e f o r the r a d i o s i g n a l s o f OH from outer space  and the mechanism f o r the masing a c t i o n i s not  y e t understood.  D e t a i l e d knowledge o f the energy  levels  o f the r a d i c a l , which i s the s u b j e c t o f t h i s t h e s i s , should h e l p to s o l v e the problems encountered with the OH e m i s s i o n . T h i s t h e s i s c o n t a i n s a study o f some o f the e l e c t r o n i c s t a t e s of OH.  A l l o f these s t a t e s have been s t u d i e d  p r e v i o u s l y but new v i b r a t i o n a l l e v e l s and new t r a n s i t i o n s have been observed.  The energy l e v e l diagram o f OH can  now be c o n s t r u c t e d very a c c u r a t e l y up t o 1 0 0 , 0 0 0  cm"  1  2  from the ground s t a t e .  The assignment o f the e l e c t r o n i c  and v i b r a t i o n a l quantum numbers i s unambiguously d e c i d e d by the new t r a n s i t i o n s observed. The e m i s s i o n spectrum o f the r a d i c a l was photographed at h i g h r e s o l u t i o n .  _-> o  sured i s 10  D  times b e t t e r  The assuracy of the wavelengths mea-  A, which i s 10 times and i n some cases 100 than the raw d a t a p r e v i o u s l y  available.  accuracy o f the molecular c o n s t a n t s i n the s t a t e s such as i n t e r n u c l e a r  The  studied,  s e p a r a t i o n and v i b r a t i o n a l f r e q u e n c y ,  has been i n c r e a s e d by a f a c t o r o f 1 0 . One o f the most u s e f u l c o n s t a n t s o f the molecule i s the  d i s s o c i a t i o n energy o f the ground s t a t e .  o f the the  B  2  ^ — *  A £ + • system, Barrow (1956)  state.  calculated  2  d i s s o c i a t i o n energy o f the  excited  From a study  A  2  £  +  s t a t e , the f i r s t  He then determined the d i s s o c i a t i o n energy  o f the ground s t a t e  to be (35^50 1 100) cm"* .  The B Z — >  1  2  +  A ^"*" system of d e u t r o x y l r a d i c a l (OD) has been extended 2  to i n c l u d e t r a n s i t i o n s t o v i b r a t i o n a l l e v e l s near the d i s s o c i a t i o n l i m i t o f the A Z T 2  the e r r o r  +  state.  The estimate o f  o f the d i s s o c i a t i o n energy o f the  AX 2  has been reduced by a f a c t o r o f seven or b e t t e r . same e r r o r  i s transferred  energy of the ground  +  state The  i n c a l c u l a t i n g the d i s s o c i a t i o n  state.  3  The  increase  i n accuracy of the d i s s o c i a t i o n e n e r g i e s  o f the e x c i t e d s t a t e s has d i p o l e - d i p o l e and h i g h e r  made p o s s i b l e the d e t e c t i o n order m u l t i p o l e  i n t e r a c t i o n be-  tween the n e u t r a l hydrogen and oxygen atoms i n the states.  The  of  net e f f e c t of t h i s i n t e r a c t i o n was  be r e p u l s i v e and occurs at an i n t e r n u c l e a r  excited  found to  separation  much l a r g e r than that at which valence f o r c e s are  pre-  dominant. The  h i g h d i s p e r s i o n at which the t r a n s i t i o n s were  photographed r e v e a l e d broad.  that some of the  T h i s e f f e c t was  t r a n s i t i o n s , the  (0,9)  spectral lines  f i r s t observed i n one  2  o f the B E  +  A  2  E  o f the  +  are OD  system,  by Bruce Nodwell i n the summer of 196V,  then an under-  graduate r e s e a r c h  Dalby.  e v e r , d i d not to observe the  student f o r P r o f e s s o r  see the same e f f e c t i n OH, same t r a n s i t i o n i n OH.  The  constructed  emitted  the d e s i r e d t r a n s i t i o n s w i t h h i g h  2  +  2 .—»• A 2T  failed  author subse-  a source of OH which c o n s i s t a n t l y  ?  C Z  how-  i n f a c t , he  quently  l i n e broadening was  He,  seen i n both the B  intensity.  + JL  2 -*A  + £  and  + systems of OH  and  OD.  I t became  evident  2 q u i t e e a r l y t h a t a p r e d i s s o c i a t i o n o c c u r s i n the A s t a t e at h i g h v ' s . ference  The  The  r e s u l t s were r e p o r t e d  at the  + E Con-  of the Canadian A s s o c i a t i o n o f P h y s i c i s t s , h e l d  If  at C a l g a r y , A l b e r t a ,  i n J u n e , 1968.  L a t e r on i n t h e same  y e a r , a paper was d i s c o v e r e d i n the l i t e r a t u r e ( C z a r n y and  F e l e n b o k , 1968) which r e p o r t e d l i n e b r o a d e n i n g i n  the  same (0,9) band o f OD and i n t h e ( 0 , 6 ) ,  (0,8)  bands o f OH.  more comprehensive. d e t e c t e d from  (0,7) and  Our i n v e s t i g a t i o n i s , however, much I n OD, the p r e d i s s o c i a t i o n  was  v = 7 t h r o u g h t o v = 13 and i n OH f r o m  v = 5 t o v = 7.  The sharp appearance o f the t r a n s i t i o n s  i n v o l v i n g v = 6 i n OD and v = h i n OH i s c r u c i a l i n d e c i d i n g where t h e p r e d i s s o c i a t i o n  i s f i r s t noticeable.  dependence o f the p r e d i s s o c i a t i o n quantum number was i n v e s t i g a t e d  The  on t h e r o t a t i o n a l  i n each v i b r a t i o n a l l e v e l .  A l t h o u g h much d a t a has been c o l l e c t e d on the p r e d i s s o c i a t i o n , the  t h e o r e t i c a l e x p l a n a t i o n o f t h e f a c t s needs development. Predissociations  are i n t e r e s t i n g because the i n v e r s e  process, pre-association,  may be a v e r y i m p o r t a n t s t e p i n  the f o r m a t i o n o f m o l e c u l e s .  When two atoms come t o g e t h e r  i n a c o l l i s i o n , they form a " q u a s i - m o l e c u l e " a t t h a t s e p a r a t i o n f o r which v a l e n c e f o r c e s  are large.  The q u a s i -  m o l e c u l e performs one v i b r a t i o n o n l y f o r i t h a s enough energy t o break t h e bond.  I f energy i s l o s t i n t h a t  s h o r t t i m e d u r i n g which t h e v i b r a t i o n l a s t s ( t y p i c a l l y 10"^  seconds) a s t a b l e m o l e c u l e i s formed.  m o l e c u l e can r a d i a t e  The q u a s i - .  t o a lower c l o s e l y l y i n g v i b r a t i o n a l  5 level.  This t r a n s i t i o n l i e s i n the f a r i n f r a - r e d and i s  a slow process,  10 ^ seconds.  The quasi-molecule can  also reach an e x c i t e d s t a t e by p r e - a s s o c i a t i o n r a d i a t e t o the ground s t a t e .  and then  This t r a n s i t i o n l i e s i n the  o p t i o n a l region and i s much f a s t e r ,  10" seconds.  Thus  the p r o b a b i l i t y o f molecule formation i s about 10 per y  c o l l i s i o n by p r e - a s s o c i a t i o n , but 1 0 " a lower v i b r a t i o n a l l e v e l .  1 0  by r a d i a t i o n t o .  For OH, the i n t e r e s t i n p r e -  a s s o c i a t i o n i s even greater because of the masing a c t i o n observed i n the OH radio frequency s i g n a l from outer space. 2  +  The C Z state i s very deeply bound and high i n e x c i t a t i o n energy. The properties o f t h i s state have 2  +  been determined from a study of the C JL 2  +  2  +  2  +  —->A JL  system and C JL —> B JL systems The former system has only been r e c e n t l y observed ( M i c h e l , 1957) and the 2  l a t t e r i s reported f o r the f i r s t time.  +  The C JL 2  +  2  state  +  i s not completely understood y e t . The C JL —> A £ system of OH was extended to include t r a n s i t i o n s from a v i b r a t i o n a l l e v e l lower i n energy than the one p r e v i o u s l y thought to be v = 0 ( M i c h e l , 1957). reported f o r the f i r s t time i n OD.  The same system i s The c o r r e c t v i b r a t i o n a l  6 numbering  o f the l e v e l s i n the G £  from the i s o t o p i c r e l a t i o n s . vibrational  The c o n s e q u e n t i a l  deduced new  2 + and r o t a t i o n a l c o n s t a n t s o f the C Z l state  have been determined. structure  s t a t e was  A discussion  2 + o f the C 71 s t a t e  i s also  of the e l e c t r o n i c presented.  7 CHAPTER I I - B a s i c Theory o f Diatomic  Molecules  In t h i s chapter, the g e n e r a l theory of d i a t o m i c molec u l e s i s o u t l i n e d i n p a r t (a) and the a p p l i c a t i o n o f the theory to the d e t e r m i n a t i o n o f the molecular c o n s t a n t s  of  the h y d r o x y l r a d i c a l i s given i n p a r t ( b ) .  (a)  G e n e r a l theory M o l e c u l a r theory i s based  (1928)  approximation  on the Born-Oppenheimer  a c c o r d i n g t o which the t o t a l wave  f u n c t i o n of a molecular system i s the product o f e l e c t r o n i c , v i b r a t i o n a l and r o t a t i o n a l terms.  The  approxi-  mation i s good because the mass o f the e l e c t r o n i s much s m a l l e r than t h a t of the n u c l e u s . I n l i n e a r molecules, the c l a s s i f i c a t i o n o f the t r o n i c terms i s based  on the value of the component A ~$L  of the e l e c t r o n i c angular momentum along the axis  (-'-it  elec-  i s Planck's c o n s t a n t d i v i d e d by  internuclear ).  This i s  p o s s i b l e because there are no torques on the e l e c t r o n i n the d i r e c t i o n o f the i n t e r n u c l e a r a x i s . electronic conserved number. called  The  p r o j e c t i o n o f the  angular momentum along the i n t e r n u c l e a r a x i s i s c l a s s i c a l l y and A  For A TT  = 0> ;  A  1>  2,  ^ ''"  i s t h e r e f o r e a good quantum .. the e l e c t r o n i c s t a t e s are .  Although A i s a good quantum  number o n l y i n the n o n - r o t a t i n g molecule,  i t i s o f t e n found  to be a good quantum number even i n r o t a t i n g to a good  approximation.  molecules  8 The m u l t i p l i c i t y o f the e l e c t r o n i c s t a t e i s d e s i g n a t e d w i t h an upper s c r i p t on the l e f t Viand side and the p r o j e c t i o n of  the t o t a l angular momentum on the i n t e r n u c l e a r a x i s i s  d e s i g n a t e d with a lower i I :y  example  x  The  TTy^  s c r i p t on the r i g h t hand s i d e , f o r  .  e l e c t r o n i c wave f u n c t i o n has a symmetry with r e -  spect t o r e f l e c t i o n at any plane p a s s i n g through the two nuclei.  For A  C  , the p r o j e c t i o n o f the e l e c t r o n i c  angular momentum on the n u c l e a r a x i s i s degeneracy  of these s t a t e s i s t w o - f o l d .  The F o r such degen-  e r a t e s t a t e s , a r e f l e c t i o n o f the e l e c t r o n i c wave f u n c t i o n at  a plane p a s s i n g through the n u c l e i can r e s u l t i n the  same wave f u n c t i o n or i n the other wave f u n c t i o n o f o p p o s i t e sign.  S t a t e s with  have t h e r e f o r e both  symmetries  but i t i s never expressed e x p l i c i t l y because the energy o f both s t a t e s i s the same. different.  A  F o r A — O , the s i t u a t i o n i s  Z^state r e f l e c t s i n t o i t s e l f  p a s s i n g through t h e n u c l e i ,  Z"  where the s u p e r s c r i p t denotes  at any plane  goes i n t o i t s n e g a t i v e , the symmetry with r e s p e c t t o  r e f l e c t i o n a t a plane p a s s i n g through t h e n u c l e i . In of  the Born-Oppenheimer approximation, the e i g e n v a l u e s  the e l e c t r o n i c p a r t of the wave f u n c t i o n depend on the  internuclear separation.  Thus, when the e l e c t r o n i c  terms  are e l i m i n a t e d from the Schroedinger e q u a t i o n f o r the molec u l e , t h e r e remains  a term dependent on the i n t e r n u c l e a r  s e p a r a t i o n , which together w i t h i n t e r n u c l e a r Coulomb  energy  9 can be i n t e r p r e t e d i n the f i e l d is called terms  as the p o t e n t i a l energy of the n u c l e i  o f the e l e c t r o n s .  I f this effective potential  U ( r ) , the Schroedinger  e q u a t i o n f o r the n u c l e a r  reads  j-  (ii-D where J,L  JL1  v*-t-  i s the reduced  the Laplacean  ueo I v = E  mass o f the n u c l e i and  curves  e>  U(r) can be expanded i n a T a y l o r  u(r)  <-Jj- U« f - i : l L ^ S  = c-'K  Expressing putting  z  internuclear  - "M'I.)  N  /(<^M?).  In  distance  series, - a f  V * i n s p h e r i c a l co-ordinates ^  is  Typical  *f, l * f , 1 6 .  are i l l u s t r a t e d i n F i g u r e s  the neighbourhood o f t h e e q u i l i b r i u m •T  V  o p e r a t o r , with r e s p e c t t o the c o - o r d i n a t e s  r e l a t i v e t o the center o f mass o f the n u c l e i . U(r)  v  s  i -  (  h i * / l  ^' i ) L  ;  (Ii-l)  j  and  becomes  2 where  P  i s the square o f the angular momentum o p e r a t o r .  Equation  ( I I - 2 ) d e s c r i b e s the motion o f a v i b - r o t o r .  relative  s i z e s o f the terms i n the expansions  solving  suggest  The  10  which i s the e q u a t i o n of the harmonic o s c i l l a t o r , and , t -± y ~ t/t T , which i s the e q u a t i o n o f a ~ P- ^ r i g i d r o t o r , and then t r e a t i n g the r e s t o f the terms by 7  p e r t u r b a t i o n theory.  The energy v a l u e s i n cm" , are 1  (Herzberg, 1950)  C^(^±)-~LL^X,{^-,i)  Z  =  ±  fx C  where  v  = 0 , 1, 2 ,  J  =0,  U)^n^l)'  i s the v i b r a t i o n a l quantum number.  1, 2 , ..... i s the r o t a t i o n a l quantum number,  and the constants are r e l a t e d t o the shape o f U ( r ) . The  energy values are u s u a l l y grouped d i f f e r e n t l y ,  Jf_, ^ ( u - t - i ) - avxu^-xr-fl-^+i)* Ac  (H-3)  - f B J C J - H ) - p j ^ J - f / j ^ -f- H J ( J t - / _ ) 3  "=  G-(v-)  where i t i s understood  -h FU)  3  >  that B, D, H are f u n c t i o n s o f  Dunham (1932) has s o l v e d ( I I - 2 ) f o r any expanded i n a T a y l o r s e r i e s .  v  .  U ( r ) that can be  For a f i f t e e n term  expansion  of U(r) and w i t h the W e n t z e l - K r a m e r s - B r i l l o u i n p e r t u r b a t i o n method, Dunham found a term i n the e x p r e s s i o n f o r the energy  11  which i s independent  of v  and J  and i s  The s e l e c t i o n r u l e s f o r r a d i a t i o n are obtained i n nonrelativistic  t h e o r y from the non-vanishing  o f the m a t r i x  element o f the e l e c t r i c d i p o l e moment, that i s ,  where of  m  i s the d i p o l e moment.  Since  m  i s the component  a v e c t o r , t h e p a r i t y of the p a r t i c i p a t i n g s t a t e s must be  opposite. have  From the p r o p e r t i e s o f angular momentum we must (Landau and L i f s h i t z , 1 9 6 5 ) .  Z\J - 0 ±\ )  Within  the Born-Oppenheimer approximation, <7\, [ Z ^ - r ^ \JL f Z z , . If  a  r  e  t  n  e  c o - o r d i n a t e s o f the i t h e l e c t r o n ) .  2- i s the d i r e c t i o n o f the i n t e r n u c l e a r a x i s , O  X£  only f o r plane.  <Z |z|2 '> =T O p  p  p- p  Similarly  i A^>tOi  P  p  p  and  p  = p'  only  Cp =- ) .  The theory o f r a d i a t i o n l e s s t r a n s i t i o n s i s n o t as w e l l understood.  ?  by a r e f l e c t i o n through the  '<X lblZ '> for  <"Z (.X | Z >  We have n o t been able t o e x p l a i n the d a t a on  p r e d i s s o c i a t i o n s presented i n Chapter  IX by t h e p r e s e n t  *  f  12  theory.  Since no photon i s exchanged, the p a r t i c i p a t i n g  s t a t e s must have the same p a r i t y and  A .^ ~ & .  It is  assumed t h a t t r a n s i t i o n s from the d i s c r e e t l e v e l s of  a  bound s t a t e to those of an unbound s t a t e are brought about by as  terms i n the H a m i l t o n i a n w i t h the L.S  or J.L  L i f s h i t z , 1965).  (Landau and  r u l e s can be d e r i v e d  same symmetry  J. |  A  < A v ,  (II-5b)  < /\, v r , J , | i - M  J >  z  -4= O  x  Ai Ji >  where 1 r e f e r s t o the bound s t a t e and Kovacs (1958) has d i s c u s s e d  l-O 2 to the unbound s t a t e ,  the m a t r i x elements ( I I - 5 a ) .  are given i n Chapter IX.  o f s i m i l a r symmetry can  i n t e r a c t , but  (1965) s t a t e the o p p o s i t e .  s t a t e s , only  Landau and  the r a d i a t i o n l e s s t r a n s i t i o n i s a strong  10 ^  a strong  seconds or  shorter.  p a r i t y of the  IO  I A, )  and  s t a t e s must be  - 1 1  t i o n s cannot p o s s i b l y a p p l y . how  that'  e f f e c t when the i s o f the  A A the  l i f e t i m e of the p r e d i s s o c i a t e d l e v e l s o f OH Chapter IX to be about  Lifshitz  order  According to Herzberg (1950)  e f f e c t o c c u r s when AS~0  s t a t e s , the  states  Herzberg (1950) a l s o . s t a t e s  l i f e t i m e of the d i s c r e e t l e v e l o f  His  I t i s i n t e r e s t i n g to note  t h a t Herzberg (1950) s t a t e s that f o r 2T  of  selection  from  (II-5a)  results  The  character  seconds, but  °/~  same.  f o r ZT The  i s shown i n the other  Moreover, i t i s not  these statements a r i s e from c o n d i t i o n  I;  (II-5).  condi-  obvious  13  (b)  A p p l i c a t i o n of the theory  to the determination  the molecular c o n s t a n t s o f The  OH.  ground s t a t e of the h y d r o x y l  (the L a t i n l e t t e r  X  serves  of  radicali s  to i d e n t i f y the lowest energy  (T state). Three bound e x c i t e d s t a t e s are known, 2 + 2 + B Y  >  energy). o f the  C ZT  .  A 21 >  (A, B, C l a b e l e x c i t e d s t a t e s i n order o f  A l l measurements i n t h i s t h e s i s come from a study 2_+ 2^_+ 2~.+ 2_ + B 2_ —> A IT and C 2. — > A Z. systems.  From the s e l e c t i o n r u l e s , the p o s s i b l e t r a n s i t i o n s o f 2 v- +  2  a  2_  —?  N  i s the r o t a t i o n a l quantum number,  + -2.  system are as i l l u s t r a t e d i n F i g u r e  angular momentum.  J  1.  i s the t o t a l  The p a r i t y o f the l e v e l s i s deduced  from the f a c t s t h a t t h e s p i n f u n c t i o n i s independent o f i n v e r s i o n , t h a t the symmetry o f the e l e c t r o n i c wave f u n c t i o n i s given by p  inZ  , that the v i b r a t i o n a l wave f u n c t i o n  has no p a r i t y a s s o c i a t e d w i t h i t , and that the p a r i t y o f the r o t a t i o n a l wave f u n c t i o n i s given by the S p h e r i c a l Harmonics. and  I n Figure  1, the R branch f o r which  the P branch f o r which  the Q branch f o r which  A J ~ ~ I are much stronger  A J -O .  5/  =  (j"  +  J"+l  than  The l i n e strengths are  (Herzberg, 1950) (II-6a)  .A J - T - i  ir--v  26  3  J  -  at  *4 Vx  '4 l_  4  7  3  Z  1  +  I-  =  'A  0 +  I  X  III F i g u r e 1.  II!  Ii  S t r u c t u r e of a  SI i l l  ;|  transi tion.  15 (II-6b)  S.  (11-60)  S  _  ,  v  J  where the double prime r e f e r s to the lower The d i r e c t l y observable q u a n t i t i e s tions  R-j_, R , 2  Q]_, Q » 2  as the d i f f e r e n c e stants  p  l * 2'  are the t r a n s i -  Writing  p  state.  these  transitions  between energy l e v e l s , the molecular  can be deduced.  The r e s u l t s are quoted  con-  i n Chapters  V, V I , VTI and VIII" where the c o n s t a n t s are e v a l u a t e d . The  energy  spacing between the l e v e l s w i t h the same  but with r o t a t i o n a l quantum numbers the combination r e l a t i o n It  /^x  N 4- 1  N - 1  and  v  is  f~ C ^ ) -  i s e a s i l y shown that  AaFCH)  -•  ft(N)-PCH)  (-SD't-3f/f  +  -  N  +  ^  ~  Similarly  n + L  -11  upper e l e c t r o n i c •-  "  g i v e s lower e l e c t r o n i c s t a t e  H  1  )  +  -f- (2 j - i ' C i M i - ^ - f - • •  where the s i n g l e prime i n d i c a t e s constants.  0V  (4B'-6  '  (same but w i t h constants.  state  )  The n u m e r i c a l values  o f the combination r e l a t i o n s provide a s t a r t i n g p o i n t  for  16  labelling  the quantum numbers a s s o c i a t e d with the  —In—thl  t h e s i s , the d i s s o c i a t i o n energy  s  ground s t a t e between the in  X ^ N  and  -y^  s t a t e f o r -T —  c o r r e l a t i o n of molecular terms w i t h  atoms and w i t h the  F i g u r e s 2 and  3.  M_,  In the F i g u r e s , {l  i s the  sum  i s the p r o j e c t i o n o f  the i n t e r n u c l e a r a x i s .  o f the magnetic numbers f o r  oxygen and hydrogen atoms s i m u l t a n e o u s l y I n F i g u r e 3»  fluorine  OH  i n Figures  i s the magnetic number of  2 and  The  F i g u r e h- are taken from Dieke and  The  fine structure  I t is- shown i n Chapter VII p o t e n t i a l f u n c t i o n s o f the  dis-  energy values  Crosswhite  in  (19^8).  the shape of the p o t e n t i a l  f u n c t i o n at l a r g e i n t e r n u c l e a r d i s t a n c e s that there B  2  ZT  +  -1 cm  the  3 are taken from Moore ( 1 9 5 2 ) . -  tance are i l l u s t r a t e d i n F i g u r e h.  100  the  p o t e n t i a l w e l l s as a f u n c t i o n o f i n t e r n u c l e a r  R e f e r r i n g to F i g u r e h,  In  i n a weak magnetic  atom i n a weak magnetic f i e l d .  separation The  Mj  the  u n i t e d atom i s i l l u s t r a t e d i n  the t o t a l angular momentum along  field.  ^  s t a t e i s assumed to r e s u l t by d i s s o c i a t i o n i n A  F i g u r e 2,  the  i s the d i f f e r e n c e  CJ  the energy o f the  i - H ( 5). The separated  D  of  energy o f the lowest r o t a t i o n a l l e v e l i n  X ' (1^  The  i s measured.  D°  transition.  i s a hump i n the  s t a t e s which i s about  2 l a r g e r than t h a t i n the  o f these f o r c e s i s unknown but p e r s i v e f o r c e s (London, 1 9 3 7 ) *  A  i s not w e l l known.  + £T  state.  thought t o be due  The  origin  to d i s -  .  O  H  y  O+ H G (Po) + H ( 5) 3  l  cm"  68.0  0  ( R) 3  -f-  H ( s) 5  H PS,) Figure 2. Schematic c o r r e l a t i o n o f the m o l e c u l a r s t a t e s o f OH, including: f i n e s t r u c t u r e , w i t h those of the separated atoms.  fluorine  Mil =  \  o.o  n  OH  % TT l  F i g u r e ''.j*. Schematic c o r r e l a t i o n o f the molecular s t a t e s o f OH, i n c l u d i n g f i n e w i t h those o f the u n i t e d atom. r  structure  Energy  F i g u r e h. C o r r e l a t i o n o f molecular terms w i t h atomic terns, i n c l u d i n g f i n e s t r u c t u r e . The energy v a l u e s are not to s c a l e .  20  Chapter  III  -  2 The  B  Experimental  2 +  + T.  —>  2  A £.  + 21  and the C  2 —^A  + TL  systems  of the h y d r o x y l r a d i c a l are much weaker than the w e l l known 2  +  A T.  2—rr  -  X TT  —^  system.  See P l a t e I .  I t was  a  found t h a t  d i s c h a r g e through water vapour, as t h i s vapour flowed  rapidly  through a hollow cathode produced the d e s i r e d systems of OH quite strongly. a fast  The vacuum system was  designed to achieve  pumping speed o f the water vapour.  water was  kept at  50° C, the vapour was  The source o f then allowed to  enter the vacuum system through a needle v a l v e , and traversing  the d i s c h a r g e area, the vapour was  a l i q u i d nitrogen trap of large area. travelled  a t o t a l d i s t a n c e o f about 2.5  tubes were  cm  i n diameter except f o r  h o l l o w cathode which was length.  0.6  A d i f f u s i o n pump was  cm  collected  The water  kO cm.  after by  vapour  A l l the flow the.aluminum  i n diameter and 2.5  cm  in  used t o br,ing about the f a s t  pumping speed of a l l the gases formed " i n the d i s c h a r g e .  A  schematic diagram o f the apparatus i s shown i n F i g . 5» The pov/er supply used d e l i v e r e d  a maximum c u r r e n t o f  200 m i l l i a m p e r e s and i s the amount o f c u r r e n t u t i l i z e d . I t was was  found t h a t when the aluminum h o l l o w cathode  c l e a n , a b r i g h t r e d glow appeared i n the h o l l o w cathode  area and the graph, was  OH  spectrum, as seen by a manual s p e c t r o -  very strong.  As the d i s c h a r g e was m a i n t a i n e d ,  21  the glow became weaker and the d i s c h a r g e d i s p l a c e d  itself  away from the_hollow cathode.  W i t h i n a.few hours,, the glow  i n the hollow cathode and the  OH  less intense.  spectrum were v e r y much  At the same time, the aluminum became covered  w i t h a rough b l a c k c o a t i n g , presumably t h i s c o a t i n g was size d r i l l  aluminum o x i d e .  When  removed w i t h the h e l p o f a l a t h e and proper  and the hollow cathode put back i n the vacuum  system, a strong spectrum of  OH was  obtained again.  The  weakening of the spectrum due to the appearance o f the c o a t i n g on the hollow cathode l i m i t e d the l e n g t h o f an exposure, which l a s t e d from two The  to f i v e hours.  ..  . P r e l i m i n a r y i n v e s t i g a t i o n s of the spectrum were  done on a H i l g e r medium q u a r t z s p e c t r o g r a p h , from which P l a t e I was made.  Eventually, a Jarrell-Ash  Ebe.rt spectrograph was  used to photograph the r e g i o n s from  o  2500 - 2800 A  3 • h meter  i n f o u r t h order at a d i s p e r s i o n o f  o  O.h  o  and from 3700 - 6500 A i n second order at a d i s o p e r s i o n o f 1 A/mm. I n the v i s i b l e , the s i z e of the p l a t e s A/mm,  o  covered o n l y 500  A  f o r a g i v e n a n g l e . o f the g r a t i n g .  Thus, the f i n a l measurements i n t h i s t h e s i s come from 15 d i f f e r e n t exposures.  -  22 I n photographing the f a r u l t r a - v i o l e t i n f o u r t h o r d e r , a c h l o r i n e l e n s v/as used t o absorb the unwanted r a d i a t i o n o at  3^0  A, which would have otherwise appeared i n 3rd  order. The wavelength  standards on the p l a t e s o r i g i n a t e d i n  an iron-neon hollow cathode.  T y p i c a l l y over 100 w e l l  dis-  t r i b u t e d standard l i n e s were i d e n t i f i e d on each p l a t e . wavelength  The  o f these standards was taken from H.M. C r o s s -  white 's (1967) t a b u l a t i o n .  o For wavelengths  above  U-800 A, Kodak  103 a D  plates  o  were used and below h%00 A, Kodak  103 a 0  p l a t e s were  used. The p l a t e s were r e a d w i t h the a i d o f a Grant with v i s u a l d i s p l a y (Tomkins output.  and F r e d , 1951) and d i g i t a l i z e d  As has a l r e a d y been mentioned,  appeared broad. by measuring  comparator,  some o f the l i n e s  The breadth o f the l i n e s was determined  the observed f u l l width a t h a l f maximum on the  v i s u a l " d i s p l a y o f the l i n e p r o f i l e . " S i n c e d e n s i t y response c a l i b r a t i o n o f the p l a t e s were not made, the measured h a l f widths o f the l i n e s o n l y approximately correspond t o the true half-widths.  N e v e r t h e l e s s , d e f i n i t e c o n c l u s i o n s on the  l i n e breadths could be made, p a r t i c u l a r l y those i n F i g . 16, 17, 18.  illustrated  23  The  UBC  IBM  ?Ohh  computer was  used to f i t . d i s p e r -  s i o n curves to the standard wavelengths and then to i n t e r p o l a t e from these curves the wavelength of the l i n e s o r i g i n a t i n g i n the OH d i s c h a r g e tube.  spectral  The  program  used a l s o c o n v e r t s the a i r wavelengths to wavenumbers, w i t h the a i d of Edlen's formula f o r the change i n the index o f 15°C  r e f r a c t i o n of (dry) a i r at  and 760  mm  Hg  (Coleman  et a l , I960). ( I l l - 1)  n =  1 + 6^-32 . 8 x 1 0 "  8 +  2^9810 1A6 x 1 0  k-1 x  10  8  -  a  -  jfi  J/*  when j j i s the vacuum wavenumber i n cta""^". Appendix I I g i v e s the subroutine t h a t f i t s the e q u a t i o n ( I I I - 2)  y =  B ( l ) + B(2)x  + ... + B (N + l ) x . N  to s e v e r a l experimental p o i n t s ( X i , j/c) The B(N)  o f equation ( I I I - 2)  the r o t a t i o n a l  B  , i = 1,  NDATA.  are not to be confused w i t h  constants.  The  subroutine was  used i n  s e v e r a l circumstances, f o r example i n f i n d i n g the r e l a t i o n s h i p between A G  (v + {) and  e v a l u a t i n g the s p i n s p l i t t i n g are g i v e n i n F i g . 6.  v  i n F i g . 10,  and a l s o i n  constants tf , whose p l o t s  spectrograph  F i g u r e 5.  Schematic  diagram of the  apparatus.  i  25  Chapter  IV  -  Raw Data  The wavenumbers of the s p e c t r a l l i n e s i d e n t i f i e d as t r a n s i t i o n s i n the energy l e v e l s o f OH and OD are g i v e n i n t a b l e s 1 and 2.  Proof o f the i d e n t i f i c a t i o n o f the t r a n s i -  t i o n s i s g i v e n by the combination r e l a t i o n s which are g i v e n i n tables v  3 » ^ , 5 , 6 , 7 , and 8. Table 6 g i v e s proof t h a t the  numbering  i s , the  i n the  AX.  v = .4- i n the  i n both t h e  A—>X  A 2_  s t a t e o f OH i s c o r r e c t ,  that  s t a t e i s the o n l y one observed  system and i n the  B—»A  system.  The  combination r e l a t i o n s f o r t h i s l e v e l as o b t a i n e d from both systems agree with each other, as they s h o u l d . The three systems o f OH and OD are shown on P l a t e I . The major p a r t o f the The  (0,7)  and ( 0 , 8 )  B—A  system i s shown on P l a t e I I .  t r a n s i t i o n s o f the  are shown on P l a t e I I I . The ( 0 , 9 ) i n OH and OD r e s p e c t i v e l y o f the  B-»A  and ( 0 , 1 2 ) C-»A  system o f OH transitions  system are shown  on P l a t e IV. The band o r i g i n s of the bands photographed are g i v e n 2 2_ i n t a b l e 9. .Po  , the band o r i g i n of a  i s the energy d i f f e r e n c e between  J  ='  zl—> and  L transition J  = -§•.  26 H  R  0  *V  Pn  P  l  (1.9) 0 1 2 3 4 5 6 7 8  .  18058.76 18063.57 18064.76 18062.59 18057.54 18050,14 18041.14 18031.72 18021.44  • •• 18063.30 18064.30 18062.00 .18056.80 18049.18 18039.99 . 18030.24 18019.80  •  18038.72 .18024.05 18006.05 17985.60 17963.43 17940.66 17918.62 17899.-87  18023.57 18005.42 17984.79 17962.45 17939.44 17917.25 17898.38  18211.56 18188.80 18159.67 18124.67 18084.20 18038,81 17989.15 17935.88  18188.45 18159.16 18124.02 18083.40 18037.88 17988.08 17934.64  (0,8) 0 1 2 3 4 5 6 7 8 9  18238.46 18242.14 18239.50 .18230.53 : 18215.53 -• 18194.81 18168.94 18138.48 18104.29 18067.22  18239.21 18230.07 18214.90 18194.14 18168.03 18137.45 18103.03 18065.83 (0,7)  0 1 2 3 4 5 6 .7 8  1951.2.3 19512.3 19502.5 19482.8 19453.3 19414.5 19366.2 19309.2 1924 3.1  1  19413.9  19303.9 19236.2 19160.1 19075.2  19308.5  19481.9 19451.5 19411.9 19362.4  19303.1 19235.519158.9  (0,6) 0 1 2 3 4 5 6 7 8  21136.8 21134.4 21119.3 21091.4 21051.0 20998.4 20933.8 20856.6  ' 20997.8 20932.8 20856.1  Table 1. Wavenumbers i n cm~  • 20803.7 20707.4 20600.2  o f OH bands o f the  21103.8 21068.3 21020.4 20960.2 20S8C.1  20802.6 20706.6 20598.8  ^V " A "^ 4  2  +  system.  27 R, (1.6)  21795.2 21788.1 21766.9 21730.6 21679.9 21612.6 -  0 1 2 3 4 5 6  ,. '  .  . ,  •,  21763.2 21726.1 21674.1 . 21607.6 21527.1 2H132.1  .  (0,5) 0 1 2 3 4 5 6  23048.5 23047.2 •  22993.5 - 22944.4 22880.6 22801.3  23016.6  -  (l.S)  0 1 2 3 4 5 6  22922.9 22853.6 22769.6 22671.8 22559.7  23710.6 23701.9 _ . 23G76.8 23633.8 23573.7 23495.4  ; 23676.8 23635.4 23577.2 23409.3 23301.3  •  (1>40 1 2 3 4 5  Table  25S62.40 25832.88 25784.36 25783.92 25716.78 25715.91  f.  •  25838.02 25792.09 25727.77 ' 25727.24 25644.65 25643.88 25542.86 25541.94  Wavenumbers i n cm" o f OH bands o f the B S : - — > A 5 L 1  2  +  2  +  system.  28  * 1 2 3 f  18038.0 18039.9 18040.4  (2.13) .  18026.3 18020.2 . 18014.2 18004.9  '  (1,12) 1 2 3 4 5 6 ' 7 8 9 10  18114.4 18114.4 18111.6 18106.7 18099.6 18090.1 18078.1 18066.0 18051.9 18036.7  " 18077.7 18065.3. 18051.1 18035.9  r  ..  17985.1 17962.1  18099.6 18090.1 18077.7 18062.9 18046.1 18027.1 18006.0  17984.5 17961.1  (0,11) 1 2 3' 4 5 6 7 8 9 10 11 12 13 14 15 16  18267.2 18265.4 18260.0 18251.2 1823S.9 18223.6 18204.8 18183.4 18159.0 18132.2 1810,3.1 18072.2 18039.9 18006.6 17972.8  18182.9 18158.4 18131.5. 18102.3 18071.3 18038.8 18005.4 17971.6  T a b l e l . - Wavenumbers i n cm"  18056.3 18019.2 17979.8  18250.3 18238.1 18221.8 18202.0 18179.0 18152.8 18123.2 18091.0  17896.5 17853.4 17810.1 17767.7  o f OD bands o f the 3 Z. — ^ A  18055.7 17018.3 17978.9"., 17938.0 17895.5 17852.3 17809.0 17766.0  system  29  N 0  1 2 3  if S  6 7  8 9 10 11 12  13 14 15 16  R  2  P  2  F  18814.5 18812.8  18809.0 18801.0  18789.5 ! 18773.1 18753.1 18729.2 18701.7 18670.6 18636.1 18598.2 18557.4 18513.9 18467.9 18419.7  18784 .2 18767 .0 18745 .4 18719 .7 18690 .9 18657.7 18620.9 18580.9 18537.6 18491.4 18442.6 18391.6 18338.0 18284.2 18228.8  I-  t  18670 .2 18635 .2 18597 .4 18556 .4 18512 .9 18466 .8 18418 .2  .  l  18657.1 18620.4 18580.1 18536.7 18490.5 18441.7 18390.5  18337.0 18282.9 18227.4  (0,10) 0  1  2 3  4 5  6 7  8 9 10 11  12 13 14 15 16 17 18 19  20  21  19190.33  19190.-83 19186.56 19177.11 19162.78 19143.89 19120.23 19091.95 19058.99 19021.73 18980.29 18934.83 18885.58 " 18832.78 18776.69 18717.65 18655.96 18592.00 • 18526.45 18459.63  19143 .61 19119 .79 19091 .31 19058 .37 19021 .05 189 79 .53 18934 .07 18884 .67 18831 .82 18775 .59 18716 .43 18654 .70 18590 .62 18525 .07 18458 .20  '"  19174 .34 19158 .89 19138 .69 19113 .57 19083.91 19049.37 19010.33 18966.85 18919.09 18867.26 18811.55 18752.19 18689.43 18623.63 18554.95 18483.96 18410.90 18336.4418109.58  T a b l e 1, . Wavenumbers i n em" o f OD bands o f the B  —>A £  19083.54 19048.92 19009.77 18966.21 18918.38 18866.47 18810.68 . 18751.31"" 18688.41 . 18622.48 18553.80 184S2.60 18409.61 18335.08 18261.35 18185..81 18107.71  system.  30 R  2  P  2  P  l  (0,9) 0  1  2 3 4  5 6  7 8 9 10 11 12 13 14 15 16 17 18 19 20 21  20307.9 20307.4 20300.7 t i 20288.1 20269.4 20244.8 20214.3 20178.2 20136 .2 20135 .7 20088 .0 20088 .4 20034 .8 20035 .3 19976 .7 19976 .1 19912 .5 19S43 .3 19844 .2 19770 .6 19769 .1 19692 .1 19691 .2 19609 .6 19608 .2 19522 .9 19521 .8 19431 .6 19430 .2 19335 .6 19337 .1  20290 .9 20273 .3 20249 .7 20220 .2 20184 .7 20143.6 20096.7 20044.0 19985.8 19922.3 19853.7 19779.5 19700.6 19617.2 19529.6 19437.2 19341.1 19241.6  i-  19033.2 18924.8  20143.3 20096.2 20043.5 19985.1 19921.6 19852.7 19778.5 19699 .8 19616.2 19528.2 19436.1 19339.9 19240.0 19137.3 19031.2 18923.1  (1,9)  1  2 3 4  5 6  7 8 9  Table! .  20852.5 20844.1 20828.9 20807.2 20778.8 20743.9 20702 .5 20702 .1 20654 .4 20654 .2 20600 .0 20599 .4'  Wavenumbers i n cm  20837 .8 20819 .6 20794 .8 20763 .5 20725 .6 20681.4 20630.5 20510.3  o f OD bands o f the B 21 — • > A Z  20681.0 20509.6  system.  (0,8) 21589.6 21588.1 21582.4 21564.0 21541.8 21512.3 21476.4 21432.8  0 1 2 3  4 5 6  7 8  21326.6 21263.4 21194.4 21118.0 21036.4 20948.7 20854.9 20755.3 20650.2 20539.6 20424.1 20303.3  9  10  11  12  13 14 15 16 17 18 19 20 21 22  K  R  21571.7 21525.4 21492.8 21452.1 21405.1 21351.3 21291.0 21224.7 21150.3 ' 21071.3 20985.0 20893.0 20795.3 20692.3  20947.8 20754.1 20648.9 20538.2 20422.5 20301.7  *  20469.0 20349.7  P  19963.6 19775.7  20467.7 20348.2 20224.0 20095.2 19961.9 19774.3  R  P  (1,8) 22135.3 22133.5 22123.4 22105.2 22079.4 22046.2 22005.7 21957.2 21901.3 21837.8  0 1 2 3  4  5  6  7 8  9  10  20795.0 20691.0  (1,7) 22119.0 22098.7 22071.1 '22036.0... 21993.2 21943.1 218S5.3 21820.7 21748.4  11  •  23547.5 2352S.8 23498.9 23462.6 • 23416.6 23362.6 23300.4 23229.6 23150.0 23061.4'  :  23494.8 234 56.3 23409.5 23354,3 23290.3 23219 .5 23139.2 22955.0  (2,7) 23920.5 23915.1 23899.8 23874 .6 23839.4 2379 5.4 23740.8 23676.1  0 1 2 3  4  5  6  7 8  9  -  23903.5 23880.6 2384S.3 23806.8 23755.2 23694.5 23623.3 23543.4 23452.7  Table ' 1. Wavenumbers i n cm"^ o f OD bands of the B 2 l 2  +  —> A Z  syste  32 R-i (1.6) 1 2 3 4 5 6 7 8 9 10  Table  25118.111 25104.84 25082.08 ,25050.25 25009.23 24958.93 24899.35 24830.78 24752.92 24665.88 1  •  25050.04 36008.80 24958.36 24898.76 24829.98 24752.21 24665.28  25103.70 25080.48 25048.04 25006.64 24956.02 24896.26 24827.58 24749^84 24663.10  Wavenumbers i n cm" of. OD bands o f the B 2  25006.32 24955.58 24895.74 24826.84 24749.08 24662.26  —~> A 2  system  33  5  R, OH  0 1 2 3 4 5 6 7 8  37254*59 37259.87 *37257.90 37262.36 •3725S.14 37262.36 37257.90 37259.87 37254.59 37256.22 37250.09 37252.72 37245.67  '-  0 1 2 3 4 5 6 7  •  OE  38428.38 38413.67 38412.78 38396.17 38394.56 38376.47 38374.14 38355.51 38352.38 38334.52 38330.80 38315.47 38310.98 (1,8) 39261.03 39236.44 39235.47 39203.80 39202.15 39163.58 39161.12 39112.84 39062.15 39058.02 (0,12)  37378.7 37381.6 37380.4 37380.4 37378.7 37376.5 37374.2 37369.9 37367.1 37360.9 37357.2  OD 1 2 3 4 5 j> T a b l e 2.  (1,9)  39286.60 39286.60 39284.95 39278.79 39276.00 39262.74 39259.23 39238.83 39234.73 39208.03 39202.94 OD  0 1 2 3 4 5 6 7  37233.78 37219.39 37218.13 37202.20 37200.06 37183.08 37179.98 37162.67 37158.74 37142.49 37137.65 37124.30 37118.57 37111.03 37104.38  38448.89 38454.08 38451.82 38456.09 38453.30 38455.03 38451.82 38451.82 38447.61 38447.61 38442.62 38442.62 38437.24  OH  0 1 2 3 4 5 6  (0,9}  37367.1 37357.2 37444.9 37343.6 37329.2 37327.4 37310.9 37308.8 37290.4 37287.8 37268.3 37264.8 (0,11)  38079.5 38074.8 38073.1 38065.4 38063.4 38052.2 38049.3 38034.3 38030.5 Wavenumbers o f the C *X  38065.4 38052.2 38034.3 38011.5 38009.6 38984.5 37982.2 37953.5 37950.7 /\ ZI"'' system. i  3HOH  v = 1  B*Z"*"  H  1.9  1,4  1.9  1,4  1  £4.49 40.74 56.59 72.01 86.74 100.55 113.00 121.43  24.38 4o.79 56.69 72.13  24.73 40.73 56.56 71.94 86.71 100.50 113.06 121.57  24.38 40.79 56.59 72.03  £  3 4 5  6 7 8  OH  0,8  R  v ^ 0  0,8  0,7  1,6  1,5  24,9 40.8 56.5 72.3 85.6  25.1 41.4 56.7  B 0,6  0,5 F  ^  1 2 3 4  30.58 50.7 7 70.90 90.82 110.73 130.16 149.38 168.32  5 6 7 8  Table 3. B ^ 3  +  30.58 50.70 70.84 90.86 110.62 130.16 149.33 168.40  Combination  s t a t e o f OH.  30.4 51.0 70.9 90.9 110.7 130.0 149.4 168.8  86.8  30.6 51.0 71.0 90.8 110.0 130.1 149.4  30.7 70.6 90.7 111.0 129.5  r e l a t i o n s i n cm""'  f o r the  35 OD N  "  2,7  4-1F  1 2  11.6 19.2 26.3 32.7 40.3 46.3 52.8  P 4 5 6 7  1,12 Ail  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  14.8 24.3 34.1 43.8 53.4 63.0 72.1 80.9 89.8  H  1,9  =r  2  B '2.  2,13 A^F 11.7 19.7 26.2  _:- OD N  v  1  v = 1  -1,11  24.8 34.0 44.0 53.4 62.2 71.5 80.8 89.7 98.6 106.8 114.8 122.3 129.9 135.5 1,8  1,6  1|12  14.71 24.36 34.04 43.61 53.21 62.67 71.78 80.94 89.82  14.8. 24.3 34.1 43.8 53.4 63.0 71.7 80.0 90.0  1>1115.9 24.8 34.0 44.0 53.4 62.2 72.0 81.3 90.0 98.5 107.0 114.9 122.4 129.7 135.3  1,6 14.71 24.36 34.04 43.72 53.05 62.61 71.92 80.91 89.95  1,7  &iF  1 14.7 2 24.5 34.0 3 43.7 4 53.2 5 62.6 6 7 71.6 8 •9. ' .89.7 10 11  14.5 24.6 34.1 43.4 - 53.0 62.6 71.9 80.6 89.4  34.0 42.6 53.1 ' 62.2 72.2 80.9 90.3 106.4  Table 4. Combination B*2" s t a t e o f OD. r  r e l a t i o n s i n cm"'  f o r the  36 OD M  0,11  V.--5 0  0,10  0,9 e  1 2 3 4 5 ' 6 7 8 9 10 11 12 13 14 15 16 17 18  16.9 27.3 38.2 49.2 60.0 70.8 81.5 92.4 102.7 113.0 123.3  H  0,11 A '/\  143.4 153.2 162.7  16.31 27.67 38.43 49.21 59.98 70.87 81.62 92.14 102.64 113.03 123.28 133.40 143.36 153.06 162.74 172.04 181.11 190.01  16.5 27.4 38.3 49.3 60.1 70.7 81.5 - 92.2 102.6 113.0 123.0 133.0 143.6 153.3 162.5 172.4" 181.7 190.0  0,10  0", 9  16.31 27.67 38.43 49.21 60.07 70.86 81.55 92.16 102.67 113.06 123.36 133.36 143.40 153.10 162.65 172.01 181.01 190.00  16.5 27.4 38.4 49.3 60.1 71.0 82.0 92.1 102.8 113.2 123.3  16.3 38.6 49.0 60.2 71.3 81.8 101.9 113.1 123.2 132.9 143.4 153.4 162.6 181.2 189.9 0,8  x  1 16.9 27.3 2 38.2 3 49.2 4 60.0 5 '70 .8 6' 81.5 7 91.9 8 102.7 9 113.0 10 123.4 11 133.3 12 143.4 13 153.1 14 162.6 15 16 17 18 19 Table 4. Coi s t a t e o f OD.  143.4 153.0 163.0 172.1 181.8 190.3 199.0  16.3 38.6 49.0 60.2 71^3 81.8 101.9 113.1 123.2 132.9 143.4 152.8 181.1 190.0 198.5  37 v = 9  OH  C 0,9 1  2 3 4 5 6  7  35.20 57.67 79.28 99.69 117.39 131.92 141.69  —->• A 1  «  B -> A ' . '  9  35.22  57.90 79.62 99.57 117.30 132.14 V  OH  A;'F, C  H 1  2 3 4 5  -•> A  1,8  50.16 82.80 115.22 176.68  6  0,9  1,9  35.20 57.93 79.56 99.58 117.37 131.97 141.62  36.46 57.81 79.16 99.17 116.84 131.53 141.29  -  A^r-  8  A  —  C —> A  B —> A  0,8  1,8  0,8  50.03 82.98 115.17 146.64 •176.70 206.05  51.14 82.80 114.88 146.40 176.71  v x7  V  B->A  B — 3> A  -  0,7  0,6  1  60.8 100.4 140.1 178.8 217.4 254.7 291.0  68.5 114.0 159.1 203.3 247.9 291.1 334.3  7  C  B —> A  N  6  1.9  R  36.11 57.27 79.16 99.44 116.83 131.64  -Ai>7 -  A :  2 3 4 5  A * Z  49.65 82.46 114.85 146.32 176.73 205.65 v  6  -  5  B --> A  F 1,6  69.1 114.1 159.3 203.5' 247.8  Table 5. Combination s t a t e o f OH.  0,5 124.3 223.9 272.6 321.0  1,5 75.2 124.2 224.6 272.4  -  r e l a t i o n s f o r the A  B->A 1.9  34.77 57.52 79.15 99.18 116.92 131.52 141.29  B-V•K  s  A  Ai  h  4.1  4,2  4,3  4,4  80.94  80.7  81.5  81.4  80.5  135.16  134.62  133.7  134.1  134.1  3  189.00  188.23  188.4  188.1  4  241.98  241.50  241.8  242.0  K  1,4  1  80.94  2  Sable 6.  .1.4 '  Combination  4,2  4,3  4,4  80.9  81.1  80.3  81.3  132.8  133.2  133.6  134.7  132.9  187.9  187.1  188.4  188.2  186.7  188.4  242.3  241.9  242.0  241.5  242.9  242\0  state  of. "  r e l a t i o n s f o r the v - 4  OH, as o b t a i n e d from the A Z —^ B*2 - ,  l e v e l o f the A~^2  System and the ;A'~2 —>  y  +  (Tanaka and Koana, 1934). \  _  t  .  F-z.  •  '  '  ,•  r  X ^ f T System  39 OD  -  C --> A 0,12  A c Fi B ~>A 1,12  A4 R  1 \Z 3 4 5 6 7 8  B A 1,12 21.6 36.7 51.5 65.5 79.5 93.5 104.9 116.1  21.5 36.8 51.3 65.4 80.3 92.4  OD  N  A  "2  Ai'F C -> A 0,12 21.5 36.6 51.2 65.6 79.5 92.6  21.6 36.7 51.5 65.5 79.5 93.5 105.6 116.6 v  A'IF>_ B-->A B —> A 0,11 1,11  12  - 11  &i F  &zF  Z  C -> A 0,11  B-> A 1,11  A i' F B--f>A 0,11  A t Fi C-> A 0,11  1 30.3 . 30.3 2 --- -•45.8 45.4 - - 45.1 - -45.8 45.4 63.5 63.4 63.5 3 63.5 63.4 4 - 81.0 81.3 81.2 81.3 81.0 5 98.6 98.4 98.6 98.6 98.4 115.5 6 115.7 116.0 115.7 7 132.2 132.6 132.7 132.6 8 148.2 .148.5 149.0 : 149.0 9 164.1 164.3 165.0 164.5 10 179.2 179.2 179. 7 179.5 193.5 11 1 193.6 193.4 12 206.6 206.7 206.9 206,9 13 219.4 218.8 219.4 219.0 14 229.8 229.7 229.1 229.6 15 •239 .'1 239.2 239 v4 •  OD  U  v  -  A A ^ FT. B ' A 1. 6  -  6  ;  ^  70.37 98.20 98.52 126.03 126.51 153.99 154.68 181.65 181.96 6 7 209.09 209.28 236.25 236.51 8 Table 7. Combination r e l a t i o n s f o r the A s t a t e o f OD. 2 3 4 5  Z  45.1 63.3 80.9 98.6  v - 10  OD  v - 9  OD  AVF  A i Fx N  1 2 3  A  5 6 7 8 9 10 11 12 13 14 15 16 17 18 1920.  0,10  0,10  34.6 31.44 57.7 52.19 72.9S1 80.6 • \ . 93.20 93.57 103.3 113.41 113.86 125.8 133.56 133.85 148.2 153.39 153.58 170.3 172.86 172.93 192.3 191.73 191.90 213.9 210.18 210.37 234.8 228.10 228.22 255.8 245.40 245.63 276.1 261.95 262.19 295.2 277.83 278.02 314.7 292.73 292.99 333.3 306.76 306.82 350.9 319.52 319.62 . 368.0 329.27 339.26 398.4 .350.05 350.49 ...  .  OD • S'-if-L.  0,8 1 2 3 4 5  .6 7  8  0,9  62.7 62,7 86.8 111.1 136.7 .-,161.0 185.4 208.1  v =  8  0,9  0,8  1.8 36.5 62.4 87.3 112.0 136.3 160.9 185.0 208.8 232.6  34.2 57.6 80.6 103.3 125.8 126.2 147.8 148.3 192.4  315.1 333.1 351.3 368.2 384.4 399.0 413.3  F  .At  1,9  1,9  126.2 148.7 170.8 193.1 214.1 235.2 256 • 3 276.2  OD  A'zF,  A;'FI  L  v - 7  A:F 1,7  2,7  39.8 66.7 91.2 93.0 119.3 119.5 144.4 143.9 172.5,.,- .172.1 197.1 197.5 223.3 223.4  9 10 255.3 278.4 11 301.5 12 322.8 13 343.9 344.7 14 15 385.9 16 405.6 405.8 17 424.8 18 443.6 19 460.6 20 AZ Tablei 7. Combination r e l a t i o n s f o r the s t a t e o f OD, o b t a i n e d from the B —>A system. X  hi  OH  v - 0  C  A; 1-7 0,9  D  1 2 3 4 5 6  0.9  26.10 42.97 60.16 76.80 93.55 110.23  24,12 41.01 57.82 74.61 91.26 108.02  V . , ,  ,..  v •= 1  OH  1 2 3 4 5 6 ^  1.8  . .  1.9  25.97 25.69 . 42.35 .'. 42.42 58.94 58.91 75.28 75.36 92.10 108.10 -  - .  ,.. •  -  C A  N ..  .  A;A  ^  1,8 23.92 . 40.53 57.09 73.61 90.10  1.9 23.44 40.52 57.27 73.48 90.23 106.44  •  •i  v - 0  OD  A {A  . A>t7 H  0.11  0,12  0,11  0,12  1 2 3 4 5  14-.-022.7 31.3 40.6 49.8  14.5 23.2 31.6 40.7 49.9  14.0 • 20.9 29.1 39.7 48.3  13; 6" 21.5 30.5 .". 39.7 48.5  Cable 8.  Combination r e l a t i o n s  f o r the C  2  s t a t e , b o t h f o r OH and OD, as o b t a i n e d from the C —5> A system.  H-2  OH  B  —=>  A v\v"  v'.v"  I  0,8  8  18228.3  0,7  8  19502.0  0,6  6  0,5  4  I 4  18050.5  1.6  4  21786.5  21126.6  1,5  4  23702.1  23042.0  1.4  3  25864.9  I  J-i  B  OD  -> A  v\v*»  I  0,11  9  18259.9  1,12  8  18017.0  0,10  10  19184.8  1.11  3  18806.6  0,9  10  20302.4  1,9  6  20849.3.  0,8  10  21584.2  1,8  5  22131.4  2,13  2  18031.6  1.7  5  23558.9  2,7  4  23916.8  1,6  4  25127.6  )H  C  v',v  — A  OD  I 0,9  9  37245.9  1.9  9  38440.5  1,8 1.7 3,7 3,6  8  39277.9  .  H  (Kichelj  (-.TV.-')  C —> A '  v'.v"  I  0,12  8  0,11  8  39278.1 40551.6 42862.6 44450.9  Table 9';', Band o r i g i n s o f the hands photographed. The maximum i n t e n s i t y i s taken a r b i t r a r i l y a t 10; the r e l a t i v e i n t e n s i t y is'estimated by v i s u a l i n s p e c t i o n o f the p l a t e s .  CAPTIOJMS i?0R PLATES  Plate I . _  The three systems o f the h y d r o x y l r a d i c a l (page V f ) . .  Plate I I .  .  .  The B-—>A system o f the h y d r o x y l r a d i c a l (page 4-5) .  j?la.te I I I .  The (0,8)and (0,7) t r a n s i t i o n s o f the  3 — * A system i n OH.  The d i f f u s e  character  o f the (0,7) band shows a p r e d i s s o c i a t i o n of the  A^Z' " s t a t e . 1  In the (0,8) band the  wavelengths o f R ( l ) and P(5) are 5480 and o 5528. A r e s p e c t i v e l y ; in. "'the". CO", 7) band the .wavelengthe o f H ( l ) and P(5) are 5124 and o .... 5179 A r e s p e c t i v e l y ,  t h e two s t r o n g sharp  l i n e s between P{4) and R(7) i n the (0,7) band a r e magnesium l i n e s . Plate IV.  (page %6)  Some bands o f the C—-¥A system a t h i g h  r e s o l u t i o n . . . In the (0,12) band o f OD, the wavelength o f P ( l ) i s 2675 A and o f P(7) i s 2683 A.  (page  hjl  BAND  2 Chapter  V  +  S p i n s p l i t t i n g i n the C _Z  -  A  2  T,  +  2 ,  + ,  B  states.  The s p i n s p l i t t i n g constant # i s c a l c u l a t e d i n t h i s chapter f o r the C, B and A s t a t e s . by Czarny and Felenbok  (1968)  C o n t r a r y to the d e d u c t i o n  t h a t & changes  sign i n the A  s t a t e , evidence i s presented that i t i s p o s i t i v e throughout. The r e l a t i v e  s i z e of Y i n each s t a t e i s d i s c u s s e d . 2  —  2  The l i n e s t r e n g t h s o f the branches o f a have been g i v e n ( I I - 6 ) . P-j_  and  the ?2  ZL  According to these formulas the  R-j_ s p i n components have a g r e a t e r i n t e n s i t y than and R  able at low  2  components, the d i f f e r e n c e being more n o t i c e -  j' . r  T h i s c r i t e r i o n was used t o p i c k the R^ and  components from the R^ and P,j  components i n the (0,9)  band o f the C —» A system of OH, where the i n t e n s i t y o f the P-^ components i s c o n s i s t a n t l y greater than that o f the P components. o f the  See P l a t e IV *.  C—>A  However i n  system o f OH, the P^  t h e ( 1 , 9 ) band  component i s more  i n t e n s e than the" P' 'component except i n P (2) 2  2  and P  (3).  In the B —> A system, the same c o n f l i c t i n g evidence i s found.  I n the (0,8)  and-Felenbok. wavelength  *  (.1968),  t r a n s i t i o n , d i s c u s s e d a l s o by Czarny  the  R branch i n d i c a t e d that the shorter  s p i n component has g r e a t e r i n t e n s i t y .  However,  The R branch i n the C —> A bands r e v e r s e s upon i t s e l f , with t r a n s i t i o n s o f t e n overlapped. Consequently, the i n f o r m a t i o n from the R branch i s not as dependable.  h9  "5  P (2) and  P (5)  have the o p p o s i t e p a t t e r n .  Moreover,  P (6) and  R (4-)  have the longer wavelength  s p i n compon-  ent v i s i b l y p e r t u r b e d , as they are much weaker than t h e o r e t i c a l l y predicted.  Equations  ( I I - 8)  represent poorly  the i n t e n s i t y p a t t e r n observed both i n the C\—>k and B—>A  systems.  F o r t u n a t e l y another way was found  which  determined the sign o f 0 . •  I n the (0,8) band o f the B —3>A  system o f OH, the  Q ^ ( l ) t r a n s i t i o n was found a t the frequency p r e -  weak  d i c t e d by the c a l c u l a t e d value o f X f o r  v = 8, but at  higher frequency than P ( 1 ) .  2  of . A I  +  This implies that i n v = 8 "x. J = \ i s lower i n energy than J = V 2 i n  the N = 1 l e v e l ( F i g . 4-) and hence ^  i s positive.  and Felenbok also observed the same  Q ^ ( l ) transition  Czarny  at h i g h e r frequency then P ( l ) . The  (0,6) and (0,7) t r a n s i t i o n s i n the B — ^ A system  o f OH appeared broad and the s p i n components at low N's could not be r e s o l v e d .  However, at N = 5 , 6, 7 the s p i n  components were r e s o l v e d and the s p l i t t i n g i s comparable t o  *  The assignment o f the s p i n component i n (0,9) band of the C—>A systems t u r n s out t o be the same as that already i n d i c a t e d .  50  t h a t i n ( 0 , 8 ) , implying changed very much.  t h a t the magnitude o f U has not  The nagnitude of ^  in  v = h i s also  l a r g e , as measured from the sharp  (1,*+) t r a n s i t i o n .  M i c h e l (1957)  quotes #  t o be  does n o t g i v e  the r e s o l v e d  in v = 6  - 0 . 0 2 , but he  s p i n components o f the t r a n s i -  t i o n s from which the v a l u e o f o' was c a l c u l a t e d . r e s u l t s indicate that  in v = 6 is ~  %  i n the ( 0 , 5 )  f o r t u n a t e l y , no s p l i t t i n g  0.18 cm"*--. 1  have t o take place  Un-  nor ( 1 , 5 ) t r a n s i -  t i o n s , both o f which are broad, was observed. a change i n the s i g n o f Y  Our .  I f there i s  , which i s u n l i k e l y , i t would  between  v = h  and  v = 6.  From the  pobservation  of the ^ ^ ( l ) t r a n s i t i o n i n  positive i n A  v = 8  Is  and i s probably p o s i t i v e throughout the  as shown i n F i g . 7«  state  v = 8,  t i o n r e l a t i o n s f o r the  A  In order t o make the combina-  s t a t e from the C — ^ A  and , B — > A  systems agree with each o t h e r , the longer frequency components of the with the state  F^  CH>A  t r a n s i t i o n s had t o be  levels.  If has the same s i g n i n the  as i t does i n the  A  P (N) - P (N) 1  2  is plotted i n Fig. 6 of the  C-?A  = (tf'-o" ) 7  f o r the ( 0 , 9 ) ,  system o f OH.  C  state.  The. r e l a t i o n s h i p (V - 1)  associated  (Herzberg, 1950) N - -§• (1,9)  (2f'+»") and ( 1 , 8 )  bands  By s i m i l a r p l o t s , the ft 's  51  of most v i b r a t i o n a l l e v e l s were o b t a i n e d . OD i n the are  C—?A  The d a t a  from  system i s l e s s accurate because the l i n e s  broad. The  spin s p l i t t i n g  from t h e combination  constant can a l s o be c a l c u l a t e d  r e l a t i o n s , that i s ,  (Herzberg, 1 9 5 0 )  (V - 2) g i v e s v e r y accurate values o f %  Equation  i n the  C s t a t e because i t i s l a r g e i n t h a t state^ and r e a s o n a b l y accurate v a l u e s o f  i n the A s t a t e .  A l l the measured s p i n s p l i t t i n g  constants are g i v e n  i n table 1 0 . The v a r i a t i o n o f the s p i n - s p l i t t i n g constant i s shown in F i g . 7.  The minimum at h i g h  v's i s r e a l as i s obvious  from t h e d i f f e r e n t s l o p e s o f equation (V - 1) f o r the ( 1 , 8 ) and  ( 1 , 9 ) bands o f F i g . 6 .  According  the major c o n t r i b u t i o n t o the" s p i n s p l i t t i n g i n a a r i s e s from the non-vanishing  (1929)  to Van V l e c k 2  ] T state  magnetic moment o f the e l e c t -  r o n i c angular momentum due t o r o t a t i o n a l d i s t o r t i o n . s p l i t t i n g i s p r o p o r t i o n a l to r o t a t i o n a l constant and jJ  B/^^  where  B  This  i s the  i s the energy s e p a r a t i o n t o the  2-n-  nearest  |( s t a t e .  The experimental d a t a at low  out Van V l e c k ' s theory, s i n c e  v's bears  52  fr (v = o, OP) # Cv = 0 , OH)  ~  fr (v = 0 , OD) (v "= 0 , OH)  B  (QD)  _  B(OH) Perhaps a more  X  quantitative  0.55  0.13 =  0.57  °-23  ~  :  =  o_6 1.09  —  0.53  =  a p p l i c a t i o n o f Van V l e c k ' s  theory can e x p l a i n , not o n l y the minimum observed but a l s o the r e l a t i v e s i z e s o f the ft i n the states.  For example, i n the  crease l i n e a r l y up to range,  of  decreases  value decreases by o n l y ear l y by  6$;  4-5$.  v = 5 by  A s t a t e , the by  25$.  A, B, and C, v a l u e s de-  30$ ( F i g . 9 ) ; i n the same  I n the  l i n e a r l y i n going from  i n the same range,  B  i n F i g . 7>  7$  C  s t a t e , the  v = 0  to  decreases  B  v = 3 non-lin-  53  State C  Y  OE  "  3 2 1 0  a — 0.88 1.09 '  State C .. . - .  OD_  O  0.6  _  b  C-^A  B-t A  B->A  9 0.18 0.20 8 0.16 0.16 7 c ft 6 — — 5 0.19 4  A  v  A  0.11 0.10 0.08 0.09  12 11 10 9 8. 7 6  o;ii A - >X  A->X 3 2 1 0  B  1 0  Table -a. b. c.  d. e. f.  0.1$ 0.19 . 0.20 0.21 * ' 0.22 '  0  4  0.08 *  s  ;  < 0.03 < 0.03  Spin s p l i t t i n g s  B  1 0  <0.05 <0.05  c o n s t a n t s , i n cm  M i c h e l ' s - value i s 0.67. •-• ~ ' - - - •'• M i c h e l ' s value i s 0.87. The l i n e s o f the (0,6j and (0,7; bands a r e broad and the s p i n components c o u l d not be r e s o l v e d a t low ri. iiT - 5,6,7 the s p l i t t i n g s observed were comparable to those i n the (0,8; band, i n d i c a t i n g t h a t Z i n v - b and 7 i s comparable i n magnitude to that i n v - 8 . See Fig. 1. These are c a l c u l a t e d from the data o f Dieke and Crosswhite (1948) C a l c u l a t e d from the data o f uura and I-Iinomiya (1943) C a l c u l a t e d from the data o f Ishaq (1937) j  /(cm" ) 1  F i g u r e 7. S p i n s p l i t t i n g constant i n A " _ T The f i r s t f o u r p o i n t s i n the OH curve are taken from Dieke and Crosswhite (1948). For v = 6,7 i n OH, X i s estimated from a few t r a n s i t i o n s o n l y . In OD, f o r v - O l s taken from Ishaq (1937) and f o r v - l from Oura and; Kinomiya (1943) a  v  v(0H)  "T"  0  i  0  z  3  i  4  5  6  5  4  S  i  8  7 i  9  v  i  8 (OO) i  9 l s  10 II 1213  56  Chapter  VI  -  R o t a t i o n a l Constants i n the 2_  The ship  r o t a t i o n a l constants  (vi - i )  fr  -  u  +  Aji-; r  — r r — —  Usually  fr  and  H  they are not i n c l u d e d  i n the e q u a t i o n .  of e q u a t i o n (VI - 1 ) ,  without the  2  -  ~ C D -fr 2 J L il) i- (- £ & + 3 4 tf )(N 4- f J +1 a H (N ^ x)  i s positive.  (N + i-)  states.  are found from the r e l a t i o n -  fr  —±~L—~ 3  p  1950)  (Herzberg,  A  if  2 2__+  +  i n F i g . 8 f o r the  I t was found t h a t even at low  v = 10  fr  are so s m a l l  that  The l e f t hand  side  , i s plotted l e v e l of x  (N + -"»-) values  A X 2  o f OD.  +  the c o r r e c t i o n  due to the fr could not be n o t i c e d i n the F i g u r e . C  against  For the  s t a t e where tf i s v e r y l a r g e , i t v/as found t h a t the  c o r r e c t i o n i s demantatory i n order curves obtained.  t o make any sense o f the  F i g . 8 shows the n e c e s s i t y o f a three 2  expansion of the r o t a t i o n a l energy i n o f OD  s i n c e the l a s t  the s t r a i g h t l i n e .  v = 10  s i x points deviate  of  term +  A z_  considerably  from  57  (VI  - 2)  F (N)  =  BN(N+0 -  D'N\NI-')%H  N (N+l) 3  3  The r o t a t i o n a l c o n s t a n t s o f the A, B, and C s t a t e s are g i v e n i n t a b l e 11 and are p l o t t e d i n F i g . 9. Assuming that f o r the  then  B  Testing  a  =  4-. 24-7  cm"  1  G  state,  and 0<f  0.078  =  the i s o t o p i c r e l a t i o n s i n the  C  14?^-- 4 4 ^ - - o- s-3+- j The agreement i s e x c e l l e n t . ^  e  =  2.04-8  A.  The  B-  cm" . 1  state,  O. s a ?  value o f  OH g i v e s  59 OH D  Stats v  B  3 2  a  1  4.146 4.213  0  B =4'3'47 c  r~ e  B  OD E " '  «Q= 0.078 cm .  era"*' ;  2.048 A  ;  "•  Bp(OD) 2.25 _ 0.534 B^(OH) " 4.213  ;p~  9 8 7 6 5  5.888 8.342 10.09 11.44 12.53 13.51 14.222 15.287 16.129 16.916  8.63 30 4.94 3.41 2.65 2.26 2.00 2.06'2.06 2.03 • . 2.04  1  H  .  2.91 0.929  0  D  2.25  0.2 0.2  4.119 5.086  3 2  0  C  B  r  1 0  4  State Y  c  15 B  2 1 0  1.947 2.445 2.745  13 12 11 10  2.44 3.682 4.566 5.239 5.781 6.276 6.658 7.046 8.068 8.393 8.714 9.037  9  "8 7 6 3 2 1  A  (  -  0.529  0  1.89 0.448 0.16 0.250 0.12  4.27 1.33 1.04 0.848 0.778 0". 613 0.644 0.55 0.55 0.54 0.55  12.2 0.74' 0.30 0.22  Table I I . R o t a t i o n a l c o n s t a n t s , i n cm ; the D v a l u e s are m u l t i p l i e d by 10"** and the H v a l u e s by -IO*" . a. b. c.  M i c h e l ' s v a l u e i s 3.96. M i c h e l ' s v a l u e i s 4.12* __ 3 y From a study o f the A -X'*— > X"il system, t h i s value . i s 13.494. \ / d. Che r o t a t i o n a l c o n s t a n t s i n the A \ state f o r 0,1,2,3 , i n OH and OD, are taken from Barrow (1956) 5  y T  60  39  00  20  &± — A «  »  —  _ i  >  i  F i g u r e 9.  Rotational  constants i n the A2.  values are  m u l t i p l i e d by  10  and  H "by —-10  state. •  The  D  61  Chapter  VII  -  D i s p e r s i o n Humps i n the 2 -r-. + B  <T  A  H  and  S t a t e s and the D i s s o c i a t i o n  Energy o f OH 2 (a)  V i b r a t i o n a l Quanta o f  + 21  A  The v i b r a t i o n a l quanta were c a l c u l a t e d by talcing comb i n a t i o n d i f f e r e n c e s between corresponding l i n e s o f two bands having (VII -  _R*<v,*00 - (W  1):  1950):  the same upper s t a t e / that i s , (Herzberg, ( N  ]  ~  Pv'v/' (N) -  P v v - C  N)  Greater accuracy was o b t a i n e d by adding t o the combination differences c a t e s the  ( B// v  B  —  Bw"  )  N (N + 1 ) , where  B  value as obtained from the combination  t i o n s , and p l o t t i n g the r e s u l t i n g v a l u e a g a i n s t A t y p i c a l p l o t i s shown i n F i g . 1 0 , where o b t a i n e d from the  C—?A  system.  are g i v e n i n t a b l e s 12 and 1 3 ,  indirela-  N (N + 1 ) .  AG(&$)  is  The v i b r a t i o n a l quanta  together w i t h t h e i r e x p e r i -  mental v a l u e s . 2 (b)  D i s s o c i a t i o n Energy o f In F i g . 1 1 , 2 +  the A( 71  AG  A (  + Zl  ).  the e x p e r i m e n t a l values A ^ ( v  + -g-) f o r  ) s t a t e of OH and OD are p l o t t e d a g a i n s t v.  (v + i )  =  G (v + 1)  -  G(v).  F i g u r e 10. A p l o t o f equation ( V t l - l ) f o r the (1,9) and (1,8) bands o f the C—>A system, thus g i v i n g - 5 ( 8 . 5 ) o f the A * E s t a t e . +  63 v  ASfv-f-jy) experimental  AG(experimental; -AG(calculatedJ ' : : II :  .  :  b  i  2  3 4 5  6 7  8 9  0.1 -0.2 0.3 0.0 -0.7 0.8 -0.1 -0.1 0.1 287.7  2988.6^ 2793.0^ 2593.5 ^ 2385.5 °~ 2162.4± 0.4 1915.6 ± 0 . 3 1624.8 t 0.2 1273.8i0.2 8 3 7 . 6 ± 0.2  b  6  5^  '  i-  0.1 -0.3 0.4 0.1 0.3 -0.7 -0.2 0.0 0.0 288.8  h  e  0.1 -0.1 00.1 0.1. -0.5 -0.3 -0.50.2 0.0 297.9 b  9.9422 9.9454 9.9773 v - i n t e r c e p t 18843  Table T2-. a. b. ^  0  1 2 3  4 5  6  i) (A Z" 'j e  q  t  18854  f o r OH.  Taken from i jjarrow Calculated AG. d c 3084.08 -189.316 -4.07045 0.941340 -0.176504  18844  (1956)  3083.71 -188.311 -4.79355 1.14394 -0.202176 0.C0114100  e 3086.28 -196.559 3.06261 -2.09695 0.451410 -0.0619602 0.00233706  D°(cm"'j  6h  A G ( experimental J - A G ( c a l c a l a t e d ) M  AG(v~|) experimental  ,„ c  0  1 2 3 4 5 6  7  8 9 10 11 12 13  5  6  0.0 . 0.1 0.1 0.0 -0.3 -0.3 00.2 0.0 0.2 1900.9 1901.0 1901.6 1791.9 17S2.0 1792.6 1678.6 1678.7 1678.9 0.0 -0.1 -0.1 0.2 0.2 . 0.3 -0.7 0.3 -0.7 0.7 0.8 0.6 -0v2 -0.1 -0.1 0.0 -0.2 -0.2 0.0 , 0.1 0.1 117.7 117.3 1 2 0 . 4  2214.6 °2111.5 °~ 2007.5 °-  b b  b  1588.3± 0.5 1 4 2 7 . 9 t 0.5 1281.5 t O . 3 1 1 1 7 . 4 t 0.3 924.8 10.2 699.8 ± 0 . 3 433.9 ± 0 . 5  b  13.832 13.831 13.845 192^0  Sable 1^. D ( A Z ) c  a. b.  +  -99.9520 -1.77224 0.3058S7 -0.0369535  -.1  19264  f o r OD.  Taken from Barrow (1956) Calculated. AG. d c  $ 0 2264.60 1 2 3 4 5 6  a  19260  v  2265.00 -100.229 -1.61107 0.272176 -0.0340381 -0.0000890593  e 2266.46 -104.192 1.24785 -0.551900 0.0782618 -0.00735406 0.000179802  65  Figure  11.  A  "and OD.  aiv+!) va v f o r the A*_.  +  s t a t e o f OH  Thevarea under each curve from v -  0 to the v- i n t e r c e p t i s D~(A  X* ) .  66  The  a r e a under a curve from  i s t h e d i s s o c i a t i o n energy was  o b t a i n e d by f i t t i n g  v = 0 D°  t o the  of that  v - intercept  state.*  The  area  polynomials  and performing the i n t e g r a t i o n .  The  r e s u l t s of the i n t e •  gration  are g i v e n i n t a b l e s 3 and h f o r  When the A 6 ( v  JL.  5>  M =  6.  + •§•) were i n c r e a s e d by adding to each t h e i r  experimental values,  D°'was i n c r e a s e d by no more than 3  i n each i n t e g r a t i o n .  S i m i l a r l y , w i t h the AG(v  creased by the experimental e r r o r , than  3 cm  blishing  1  D°  i n each i n t e g r a t i o n . . (A  2  curves of F i g . 11, point.  The  £  +  )  a r i s e s from  each de-  D° decreased by no  less  The major e r r o r i n e s t a the e x t r a p o l a t i o n  beyond the l a s t observed  polynomial f i t t i n g  +  cm"  of the  experimental  and the i n t e g r a t i o n were done  by computer, and double p r e c i s i o n was used to remove round2 + off errors. A l l the D° (A ) v a l u e s i n t a b l e s 3 and 4. - i converge t o a value w i t h a spread o f _ / cm i n OH and  *  A d e t a i l e d c a l c u l a t i o n i s g i v e n i n p a r t ( d ) , where the same c a l c u l a t i o n f o r 3 p o i n t s i s done by hand and checked by computer.  +  I t was found that with M< e q u a t i o n (2) gave poor r e p r o d u c t i o n of the experimental A& . With M>6, the l e a s t squares d e v i a t i o n d i d not change s i g n i f i c a n t l y and the c a l c u l a t e d A C curve behaved p e c u l i a r l y at low v's.  67  -  3 cm  energy  i n OD.  Moreover, the v a l u e s o f the d i s s o c i a t i o n  D ° ( X |TJ/ ) f o r OH as o b t a i n e d from the OH d a t a X  a  and OD d a t a are i n e x c e l l e n t  agreement  (following section).  Assuming t h a t the p o t e n t i a l curve o f the A X. haves " n o r m a l l y " beyond the l a s t observed  s t a t e be-  vibrational level,  the accuracy of the e x t r a p o l a t i o n o f the OH curve i s 10 cm"*^ or b e t t e r , and o f t h e OD curve i t i s 5 cm""''" or b e t t e r . judge cm  -1•  a c o n s e r v a t i v e e r r o r on  D ° (A }T  We  ) o f OH t o be - 15  68 (c)  Energy l e v e l s i n OH and OD To f a c i l i t a t e d i s c u s s i o n ,  the energy-of-the  l e v e l s i n OH and OD are g i v e n i n t a b l e v = 0  of  cm" ). is  a  p ' (1)  The  1  X ( '7IVa.)  of  o  f  0  H  i  lh.  t r a n s i t i o n o f the  A-^X  A X. 2  o f OH i s then  +  system of OH  The d i s s o c i a t i o n  1  limit of  J = 1-g- l e v e l  The  taken as 0.0 ( a l l u n i t s i n  s  32 r +0.6 (Dieke and Crosswhite, 1 9 ^ 3 ) . l  vibrational  51287.6 - 15, from t a b l e l>f.  Taking the d i s s o c i a t i o n l i m i t o f  2  +  A 2 1  o f OH and OD t o be  2 coincident, i s 3202 +.6. 1  OD i s of  The  32528.5  P, (1) t r a n s i t i o n . o f the  A L  A-> X  o f OD system o f  (Ishaq, 1937) and the J = i£ l e v e l o f v = 0  XT7y o f OD a  a  The  the v = 0 l e v e l o f  from t a b l e d ,  +  i s - 503.9.  difference  i n energy o f the v = 0 l e v e l s o f OH and  1T^/ )  OD i n the X (X  X  s t a t e comes from the d i f f e r e n t  vibra-  t i o n a l f r e q u e n c i e s o f the two molecules and from the zero point  correction  calculated ent  to be  (Dunham, 1 9 3 2 ) . ^98.1  The t o t a l d i f f e r e n c e i s  (Appendix I I I ) .  agreement w i t h the experimental value  This i s i n e x c e l l (503.9  — 15)•  The minima of the p o t e n t i a l curves o f OH and OD are n o t expected t o c o i n c i d e  because  ^Bunker•(1968) c a l c u l a t e s of *  5 ^ 10  of e l e c t r o n i c isotope s h i f t s .  these s h i f t s to be o f the order - •  cm" . * 1  Appendix VI t r e a t s e l e c t r o n i c i s o t o p e s h i f t s i n g r e a t e r detail.  69  OH State  v  I X*TJ>A,  OD Energy  Calculated  4 5 6 7 8 9  Si?  0 1  0 1  C.^E "  • -3 4 5 6 7 - 8 9 10 11 12 13  .  -503.9  35419.9  32024.6 34239.2 36350.7 -" 3 8 3 5 8 . 8 -40259.4 42051.6 43730.4 45288.7 46716.6 47998.1 49115.5 50040-3 50740.1 51174.0  dissociation limit 0 1 2  —  0  •  51287.6±15  68300.3 68847.2 69205.1  dissociation limit  88261.3 89456.0  69212.3  88114.9  •  91731.0  Calculated  Table]^.  .  68406.1 69065.8  2 3  0 1 2  32440.6 35429.2 38222.2 40815.7 4 3 2 0 1 ..2 45363.6 47279.2 48904.0 50177.8 51015.4  .Calculated  1  0  dissociation limit  Calculated  B V +  Enerey  v  0.0  0  0 1 2  . .,  dissociation limit  117679  Energy v a l u e s ( c m " ) o f the v i b r a t i o n a l l e v e l s . The d i s s o c i a t i o n l i m i t : ; o f . the A s t a t e c a l c u l a t e d from the A G ' s -of that s t a t e . 5he d i s s o c i a t i o n l i m i c o f the X, B, C, s t a t e s i s deduced from atomic d a t a . 1  70  The 0  energy s e p a r a t i o n s  0 (*D) - 0 C^IJ.) and 0 (' S) -  are w e l l known (Moore, 1 9 5 2 ) . ( F i g . 12)  (*D)  culated d i s s o c i a t i o n l i m i t of (B  ">~ ) , i s 69212.3 +  2  35^19.9 + 1 5 .  0 ('s)  a  "PV^  H (*S), i . e . OH  i 15 and that o f 0 (?? ) + H ( S) i s a  x  The d i s s o c i a t i o n l i m i t  r a d i c a l i s t h e d i f f e r e n c e between X  +  The c a l -  and the d i s s o c i a t i o n l i m i t  D° o f the h y d r o x y l  J = 1.5 i n v = 0 0 ( B^) 3  +  of  H (*"S) which  is  (35^19.9 - 15)  +  A s l i g h t l y b e t t e r value could be o b t a i n e d i f the e l e c t r o n i s o t o p e s h i f t i n the ground s t a t e were known. D° ( A 5jV of OD could then be used e x c l u s i v e l y .  cm" .'*' 1  71  F i g u r e 12. A t o m i c d a t a u s e d to c a l c u l a t e i)°iX TT). the v i b r a t i o n a l l e v e l s o b s e r v e d i n OH a r e a l s o shown. x  72  (d)  Dissoeiation For  the B  2 - + Energy o f B L State state,  the experimental v i b r a t i o n a l  f o r OH, A G ( 0 . 5 )  are, 5^.9  cm"  1  =  659.7  and A G ( 1 . 5 )  =  cm"  quanta  and f o r 0D,AG(0.5)  1  357.9 cm" . 1  F o r a three term  e x p a n t i o n o f the v i b r a t i o n a l energy, that i s  then  Using t h e i s o t o p i c r e l a t i o n s , one must s o l v e  659.7  = co. - a uvx<» -+ 3 » 3 s*  y.  €  5^.9 357.9  The  =  OJ. ~ e  4jA^e X <  3  solution i s = " 976.5  cm"  109.3  cm"  U^X^ = tu^cj Also,  e  = - 20.99 cm"  To f i n d  1  1  1  AG~°%s)= 119.7 cm" AG°\i4  to  + U'25*p' <-C^ <j  the v  solve  d XT  intercept  2 52.2 cm'  1  1  o f the A G ( v ) curve, one needs  73  1^ =  which g i v e s  2.512.  2  e The  d i s s o c i a t i o n energy  D  o f the  +  B X  state  i s then  2 It i s d i f f i c u l t  t o assess the e r r o r ,  since  the  +  B XL  state  i s very shallow and the i s o t o p e r e l a t i o n s were invoked. Predissociation  by r o t a t i o n has been r e p o r t e d by Felenbok  2 (1963) f o r the  B  + IL  s t a t e o f OH, who determined the d i s s o -  c i a t i o n energy o f the  B  state  g i v e s c o n v i n c i n g evidence that l e v e l o f the  v = 0  state.  drop i n i n t e n s i t y f o r the N = 8  We have seen  N = 15 i s the l a s t  A^G-  rotational  He d i d not see the same sudden v = 1  N = 9  l e v e l and assumed  v = 1  in  t h i s i s the l a s t r o t a t i o n a l l e v e l ,  of d i s s o c i a t i o n g i v e s an apparent This  Felenbok  -1  i s the l a s t r o t a t i o n a l l e v e l i n v = 1  more l e v e l s . that  1315 c m .  to be  D  that  as he saw no and assuming  the l i m i t i n g curve  (B ^_  ) =  1360 cm  .  value agrees extremely w e l l with that obtained by the (v) method. The  l i m i t i n g curve o f d i s s o c i a t i o n has been redrawn i n  F i g . 13 w i t h the energy measured from the v = 0 of the X ( a T H % ) s t a t e o f OH. *  Predissociation J  ^  .J  by r o t a t i o n i s a consequence o f the term h •  / I f J  :<M.<iyr<  T h i s procedure has the advantage \  ) i n e q u a t i o n ( I I - 2 ) . Herzberg (1950) d i s c u s s e s p r e d i s s o c i a t i o n by r o t a t i o n and the l i m i t i n g curve o f d i s s o c i a t i o n i n great d e t a i l .  ****  ' t  r  6  7* 1  v = 0  t h a t the e r r o r i n e s t a b l i s h i n g the to the minimum o f the Felenbok's d a t a from our d a t a ,  B 2U-  s t a t e i s absent.  F (15) i n v = 0 F (9)  in v = 1  i n v = 0 i s c a l c u l a t e d to be v = 1  i s c a l c u l a t e d to be  is  69265 cm. . 1  1  i s 3^7  cm" . 1  1312.7 cm"  F (16) F (10) i n  o f the 1  B  + JL  s t a t e i s found  A lower l i m i t , from F i g . 13...  For comparison, from t a b l e lh, the d i s s o -  c i a t i o n l i m i t o f the t  and  1  and  1  cm" .  2  (69212  From  hl7 cm" .  . The d i s s o c i a t i o n l i m i t 69323  relative  i s . 1165.2 .cm"  2  from Fig.13 to be  level  B 2_  + s t a t e i s c a l c u l a t e d t o be  15) cm" , from t h e A G v s 1  v curves o f F i g . 11.  76  (e)  Discussion The d i s s o c i a t i o n e n e r g i e s  (A E  ) o f OH and OD  from the areas under the curves o f F i g . 11  as c a l c u l a t e d predict  D°  the d i s s o c i s t i o n energy  D°  (X ^"^3/  x  (35*+20 t 15) cm" .  be  1  The d i s s o c i a t i o n l i m i t of the (69212 - 15)  l a r l y deduced t o be X ( ^TT'J/x )  o  f  *  0 H  2  B  2  X.  state i s s i m i -  +  cm  -1 i s 69323  o f B( X  error  do not reduce t h i s value to the deduced  )  cm  and our estimates o f  t h i s d i s c r e p a n c y i s n o t due to e r r o r s  value.  can f u r t h e r  be seen  v = 2  i n the  zL  B  s t a t e of OD i s  to the deduced d i s s o c i a t i o n l i m i t , o f the  + 2". ) s t a t e  which l i e s polation  N = 9  and we have seen  159 cm"  1  N = 0.  above  or d i s p e r s i o n  Either  Since  -«r- +  v = 13 i n A ( 2_  ) s t a t e o f OD i s o n l y  2  +  from the expected d i s s o c i a t i o n l i m i t o f A ( 2-  and v = 9 i n OH i s 272 cm" Z.  level,  the e x t r a -  -1 11^ cm  v = 2  humps are, causing the d i s -  2 crepancy.  i n this  of the curves o f F i g . 11 does not f o l l o w the  dashed p o r t i o n s ,  (A  That  2 v~ +  from t a b l e 14, where  2  in  D i r e c t c a l c u l a t i o n o f the d i s s o c i a t i o n  +  extremely c l o s e  v = 0  above  limit  B(  ) °f OH t o  1  from the same l i m i t , and D °  ) o f OH and OD both p r e d i c t  D ° (X  2  to such a good agreement, we cannot b e l i e v e  TTs/^  ) o f OH  the f i r s t  )  7  alternative.  I t i s quite  possible  7  t h a t the d i s p e r s i o n hump  2 + 1 B ( Z- ) s t a t e i s about 1 0 0 cm 2 + i n the A ( ZL ) s t a t e . *  i n the  l a r g e r than  that  We have no way of knowing how l a r g e the hump i n the 2 + A ( EL ) s t a t e i s . of the AG  A  Assuming that  the d i s s o c i a t i o n energy  s t a t e i s g i v e n c o r r e c t l y by the area under the  curves o f F i g . 1 1 , an upper bound to the d i s s o c i a t i o n  energy of the ground s t a t e o f  OH i s  ( 3 5 ^ + 2 0  -  1 ^ )  cm"* . The 1  true d i s s o c i a t i o n energy i s l e s s by an amount e q u a l t o the 2  h e i g h t o f the d i s p e r s i o n hump o f the The  +  A ( 2 1 ) state.  slope o f the l i m i t i n g curve o f d i s s o c i a t i o n p r e -  d i e t s the maximum v a l u e o f the hump i n the B £_  o f OH  o  s t a t e a t an i n t e r n u c l e a r d i s t a n c e  of  3.8 A.  Kolos and Wolniex^icz ( 1 9 6 5 ) have c a l c u l a t e d a d i s p e r s i o n hump o f h e i g h t 1 0 5 cm" a t t = H - . 7 5 & i n the 'TTo state of E. 1  0  78  Chapter  VIII  2  and  B( 51 ) 2  +  In the i n v e s t i g a t i o n o f the  C  state, a vibrational v = 0 by M i c h e l  l e v e l was found below the one l a b e l l e d (1957).  I n t h i s s e c t i o n , proof i s g i v e n through the i s o -  t o p i c r e l a t i o n s that the given h e r e , i s c o r r e c t that the (a)  +  V i b r a t i o n a l c o n s t a n t s o f C( 2L )  -  v  numbering i n the  C  s t a t e as  and that M i c h e l a c t u a l l y observed  ( 1 , 8 ) , ( 1 , 7 ) , ( 1 , 6 ) , (3,7)  and ( 3 , 6 )  transitions of  C ~ ^ A system o f OH. V i b r a t i o n a l Constants o f the  C  state.  The measured A C ( 0 . 5 ) o f OH i s 119H-.7 cm" . 1  measured 4 ^ ( 1 . 5 ) C O ^ = 1232.9 cm"  + 4 0 ( 2 . 5 ) = 2275 cm" .  With these v a l u e s  1  1  and U i X e  e  19.1 cm" .  =  Michel  1  Using the i s o -  t o p i c r e l a t i o n s i t i s s t r a i g h t forward to c a l c u l a t e both f o r OH and OD and the Dunham z e r o p o i n t (Appendix I I I ) .  S i n c e the  1H-, i t i s found that  *  corrections,  v = 0 energy are known, t a b l e  the energy o f the minimum o f the  p o t e n t i a l i s (-87650 - 15) cm" f o r OD.  G(0)  1  The agreement i s q u i t e  f o r OH and (87668 t 15)  cm"  good. *  Because o f e l e c t r o n i c i s o t o n i c s h i f t s , the two minima are not expected to have the same energy.  79  The next  2-.  r u l e s beyond the  B  s t a t e allowed by the V/igner-Witmer £  2  state i s  +  from the c o n f i g u r a t i o n  0 ( l s  3  0 ( P ) + H(^P), a r i s i n g 3  2 s * ' 2 p '  -  f  +  " )  s o c i a t i o n l i m i t of t h i s s t a t e l i e s  The  H(gp).  cm"  8 2 2 5 9  1  dis-  above the  d i s s o c i a t i o n l i m i t o f the ground s t a t e of OH (Moore,  1 9 5 2 ) .  Since terms o f l i k e s p e c i e s cannot cross and t a k i n g the d i s s o c i a t i o n energy of the ground/\given i n Chapter V I I ,  (C X1 ) 2  D°  =  +  (29H-18  ~  2 T to  f o r the  e  cm" , 1  8 7 6 5 0  (  8  9  5  1  +  C  s t a t e of OH i s o b t a i n e d by adding and Yoo  G ( 0 )  0  cm" .  1 5 )  0  )  of the ground s t a t e .  T  cm" . 1  The e l e c t r o n i c energy l e v e l o f OH i n c l u d i n g , the s t a t e i s given i n F i g . Ih.  9  5  6  )  Michel  ,  (  1  9  5  7  )  .  C  The i d e n t i f i c a t i o n o f the C  s t a t e w i t h atomic s t a t e s has always been debated 1  =  e  (Barrow,  There i s now no doubt about the  T^  2 v-+ value o f the  C state.  Z  Some  2 Wignerj-Witmer  r u l e s beyond. B 2l  i n g from the  0 (  l 3 * 2 s * 2 p  4  )  +  s t a t e s allowed by the  +  3  2  are 0 ( P). + H( P)_ a r i s 0 ( ' D )  H ( 2 p ) ,  + H( S) a r i s i n g a  from 0 0 . 8 * 2 8 * 2 ? * ) + H(2s ) , 0 ( ' D ) + H ( P ) from o a s 2 s * 2 p ) + H ( 2 p . ) , 0 ( ' s ) + H(' S) from 0 C L s * 2 s * 2 p ) + Hfes ) , and + + _ possibly 0 + H or 0 + H . The energy o f these s t a t e s x  3  1  above  v  =  0  of X 4  (  a  T T ^ )  +  4  o f OH i s  II7678 -  1 5 ,  1 3 3 5 ^ 6  1  1 5 ,  80  1335*+6 t l 5 , 133227 - 1 5 , cm  1  respectively.  133267 - UO and 13898^ - 1 6 0  The e l e c t i o n a f f i n i t y of oxygen i s  (1.V65 1 0.005) ev (Branscomb e t a l . 1958) and t h a t o f Hydrogen i s (0.77 — 0 . 0 2 ) ev Michel correlated  the  (Weisner and Armstrong, 196*f).  C  state with  0 " +.H .  This  +  may be so, but because o f the n o n - c r o s s i n g r u l e , the d i s s o c i a t i o n l i m i t o f the It i s interesting curve f o r the the  C  state  i s 0 (~P) + H( :P).  to note that A G  o f the  = 19900  but  D°  (b)  V i b r a t i o n a X U o n s t a n t s o f the  has a l r e a d y been given as  ™ * (29^18 ~ 15)  cm" . 1  B state.  B s t a t e Is very s h a l l o w , i n f a c t only two l e v e l s  have been seen i n OH and isotopic relations  3 i n OD.  tfith  the help o f the  and using a l l the observed v i b r a t i o n a l  quanta o f the B s t a t e , (d),  The d i s s o c i a t i o n  G s t a t e by l i n e a r e x t r a p o l a t i o n i s  .D =T53^7  The  v  C s t a t e has p o s i t i v e c u r v a t u r e , r a t h e r than  usual negative curvature of F i g . 11.  limit  (v + •§-) vs  i t has been found i n Chapter V I I -  that  Oi x e  e  =  9^6.5  =  109.3  cm"  1  = - 20.99 cm"  1  81  Although these constants reproduce e x a c t l y , they p r e d i c t , 2 7 2 . 2 cm" . 1  69318 cm" , 1  the observed A G  (v +  f o r example, A G ( 1 . 5 ) f o r OH t o be  The energy of the  v = 2 l e v e l of OH would be  which very l i k e l y does not e x i s t ( t a b l e  Ih)  .  In view o f t h i s awk.-zard s i t u a t i o n , the meaning of the v i b r a t i o n a l constants of the  C state  i s not very c l e a r .  82  F i g u r e 14.  observed  bound s t a t e s of the h y d r o x y l  radical.  83  Chapter  IX  -  A Strong P r e d i s s o c i a t i o n state  (a)  i n the A in-  o f OH  Gaydon P r e d i s s o c i a t i o n  2 _ + A weak p r e d i s s o c i a t i o n i n the first  A  Z_  s t a t e o f OH  d e t e c t e d by Gaydon and Wolfhard ( 1 9 5 1 ) .  gators found that i n the  A—>X  was  These i n v e s t i -  system, the i n t e n s i t y o f  2 v = 1 l e v e l of  the t r a n s i t i o n s o r i g i n a t i n g i n the  become abnormally weak beginning at j'= 22-g-. the  A ~C  They found  same weakening o f i n t e n s i t y f o r a l l the l e v e l s i n  v = 2. the  +  Char ton and Gaydon (1958) have l a t e r found  that  v = 3 l e v e l s i s a l s o a f f e c t e d by the weak p r e d i s s o c i a -  tion.  N a e g e l i and Palmer (1967) have found that a l l the  l e v e l s beyond  J = 29-2- i n the  by the p r e d i s s o c i a t i o n t o o . have also  studied  v = 0  l e v e l are a f f e c t e d  N a e g e l i and Palmer (1968)  the p r e d i s s o c i a t i o n i n OD.  d i s s o c i a t i o n at low  This  pre-  v ' s , h e n c e f o r t h r e f e r r e d to as "v/eak  p r e d i s s o c i a t i o n " or " G a y d o n - p r e d i s s o c i a t i o n " i s characterized' by the f a c t that  the l e v e l s with  more than those with  J = N -  Gaydon proposed the t h e o r y that state i s responsible i s shown i n  Figure  J = N + i  are a f f e c t e d  To e x p l a i n t h i s f a c t a slightly attractive  f o r the p r e d i s s o c i a t i o n . 15.  This  A  theory  Because of the s t r i c t  84-  Figure  1$.  Gaydon P r e d i s s o c i a t i o n  s e l e c t i o n r u l e s A J = 0 and the p a r i t y must be same, the o n l y way that the F-j_ l e v e l can be_ p r e d i s s o c i a t e d more than 2 - the F l e v e l i s that the 2L i s repulsive. 2 _ + A 2.  o f OH i s  -6 0.99 x 10" seconds (Bennett and Dalby, 196k). 2 ._ +  Since the  The l i f e t i m e o f the  v = 0 l e v e l of  Gaydon p r e d i s s o c i a t i o n i n the through s m a l l  A 2_  s t a t e was d e t e c t e d  i n t e n s i t y changes, the l i f e t i m e o f the  v = 1,2,3 l e v e l s cannot be too much d i f f e r e n t from 10" seconds.  The Gaydon p r e d i s s o c i a t i o n i s thus weak.  85  In summary, the c h a r a c t e r i s t i c s o f the Gaydon p r e d i s s o c i a t i o n are the f o l l o w i n g : (1)  i t sets i n near  v = 2 i n OH  (2)  one o f the s p i n components i s e f f e c t e d more than the o t h e r  (3)  (b)  I t i s weak  Strong  Predissociation  Regarding the p r e d i s s o c i a t i o n at h i g h  v's r e p o r t e d  i n t h i s work, i t was d e t e c t e d through broadening o f the rotational transitions. maximum i s  0.6 c m . -1  The "average" f u l l width at h a l f From the Heisenberg r e l a t i o n  AE-At  *  i  the average l i f e t i m e of the p r e d i s s o c i a t e d -11 10  seconds.  l e v e l s i s -P**  The p r e d i s s o c i a t i o n a t h i g h  v's  i s thus  strong. Plate of the  B —> A  l i t shows the system of OH.  (0,8) and  (0,7) t r a n s i t i o n s  S i n c e these t r a n s i t i o n s b e g i n  i n the same upper s t a t e , the p r e d i s s o c i a t i o n occurs i n the lower s t a t e .  The l i n e broadening cannot be due to thermal  broadening, S t a r k broadening, nor c o l l i s s i o n a l  broadening  because some of the OH l i n e s appear sharp and o t h e r s do n o t .  86  The  molecular  The  broadening due  Appendix  IL,  l i n e s i d e n t i f i e d also  to these e f f e c t s i s c a l c u l a t e d  found that  the  v a r i a t i o n i n h a l f - w i d t h i s very-  d i f f e r e n t from band to band. the  at h i g h  N.  The  refers R  and  transitions  l8.  The  summarized i n  dots r e f e r  d o t t e d l i n e s were o b t a i n e d by  In c o n t r a s t  to the  components... are .equally maximum-  a v i b r a t i o n a l state  subtracting  unresolved  b l a c k dots  c i r c l e s . - to  to s p i n  small dots to s p i n - r e s o l v e d  s p i n s p l i t t i n g from the  band.  are broad at f i r s t , then sharp,  P t r a n s i t i o n s , the  large  sharp  (0,9)  In each of these F i g u r e s , the  transitions.  components, the  ( 0 , 1 1 ) bands  and  become very  These r e s u l t s are  to an unresolved  The  (0,8)  very o p p o s i t e i s true i n the  then broad a g a i n .  F i g . 17  In the  t r a n s i t i o n s b e g i n broad, but  In ( 0 , 1 0 ) , the and  in  V.  . I t was  of OD,  appeared sharp.  unresolved  components.' the  both  spin  with'our experimental  h a l f - w i d t h of the is plotted  calculated  transitions.  Gaydon p r e d i s s o c i a t i o n , affected,  error.  r o t at i o n a l l e v e l s w i t h i n  i n F i g . 19.  d i s s o c i a t i o n becomes d e t e c t a b l e between  The  s t r o n g pre-  v = 6 and  7 in  OD,  2  +  -1 which i s about 13,500 cm"  above the minimum of the  F i g . 1 9 s h o u l d be  taken f o r i t s q u a l i t a t i v e  state.  The  A  2!  features  87 F i g u r e l 6 , some e l e c t r i c p o t e n t i a l c u r v e s o f t h e O H . m o l e c u l e . A new p r e d i s s o c i a t i o n h a s been o b s e r v e d somewhere betweera v^-4.and . The l o t t e d iypo the t i c a l . .  0 (  f  S ) +  O C ' D J  3  1  (A)  +  2  S )  H ^ S )  ( P) + H( S)  0  r  H (  2  if-  Figure 17. V a r i a t i o n o f the f u l l w i d t h a t h a l f maximum o f the r o t a t i o n a l l e v e l s o f v - 10 . o f A^Z"*" i n CD. The l i n e a r e x t r a p o l a t i o n a t low E v a l u e s was o b t a i n e d by s u b t r a c t i n g the c a l c u l a t e d s p i n d o u b l i n g from the u n r e s o l v e d P and R t r a n s i t i o n s .  half width  H  : 1  ~——~  i  0  1  0  1  1  1  1  1  5  1  1  1  1  10  !  -i  1  4-r—-H  15  1  —!  —{  j  20  j  T>  N  half width (cm" )  Figure 18. V a r i a t i o n o f the f u l l ' width a t h a l f maximum o f the r o t a t i o n a l l e v e l s o f the predi'ssooiated v i b r a t i o n a l s t a t e s o f CD. 'ilhe dashed p a r t s o f the. curves were obtained, from the unre» s o l v e d components hy s u b t r a c t i n g from the width the c a l c u l a t e d spin s p l i t t i n g .  1  2  -  J.  v=9  v=8  -i——+-  0  H  1  1  ' j I '-  I 1 1  1  -J—  1 0  0  1 ,  H  1—•—H  — » — - — <  15  1  1  1  1  *  2 0  H  CO  F i g u r e . 1 9 . The maximum f u l l , w i d t h a t half.maximum o f the r o t a t i o n a l l e v e l s w i t h i n a band. The; p r e d i s s o c i a t i o n s e t s i n a t about 13500 cm" above the miminum o f t h e A*H" " s t a t e . Caarny and Felenbok (1968) have observed t h a t v = 8 i n OH i s a l s o p r e d i s s o c i a t e d . 1  P  :  half width (cm") 1  OD  A  OH  i—L  1-41-2100-8 0-6 0-4 02  instrument width 6 1  OD OH  V-  4 1  \ i  1 ro  v  .1  \ -P>  7 1 5 1 •  8 1 1. cn  9 1 ... 1  0)  6 1  1 -si  V  ' p ,  7 1 1  00  'f  8  1 <°.  1  1 ro  'P 9 1  1 1  0 00 M.  Ca-  91  only.  Since the d a t a f o r OD bands comes f o r 20 t r a n s i t i o n s  i n each band and that since  of OH from 7 t r a n s i t i o n s o n l y , and  the h a l f breadth i s s t r o n g l y dependent on  N, the  two curves would probably l o o k more a l i k e i f more  transi-  t i o n s had been seen i n OH. The  observed f a c t s r e g a r d i n g  the strong  predissociation  can be summarized as f o l l o w s : (1)  i t i s strong  (2)  i t becomes d e t e c t a b l e  (3)  the p r e d i s s o c i a t i o n shows d e f i n i t e dependence on  .-  between  v = 6 and 7 i n OD  the r o t a t i o n (h)  within  the accuracy o f the experimental e r r o r ,  both s p i n components are e q u a l l y (c)  broad.  R e c o n c i l i a t i o n with theory Present theory pertaining  to p r e d i s s o c i a t i o n s  can be  summarized as f o l l o w s (1)  According t o the Wigner-V/itmer r u l e s when  H ( S) combine, the r e s u l t i n g s t a t e s  (2)  are  3 0 (- P) and  X*TT, ^ "IT,  On the b a s i s of s e l e c t i o n r u l e s f o r p r e d i s s o c i a t i o n ,  interaction  between  l e a d s to weak e f f e c t .  A  2  ]E  +  and e i t h e r o f  ^ 7T^  2 .  ^ZL  92  (3)  Kovacs (1958) has  turbations.  c a l c u l a t e d m a t r i x elements f o r per21  Between  h i s c a l c u l a t i o n s show no (U-)  The  states  J dependence.  extent of p r e d i s s o c i a t i o n depends on the  between the wave f u n c t i o n s bound s t a t e . tional.state  The and  In a p p l y i n g can  overlap t o the  of the r e p u l s i v e  i s very s e n s i t i v e to the  the  vibra-  e f f e c t of r o t a t i o n .  strong  TJ,  ^ 2, ,  p r e d i s s o c i a t i o n observed  at  /.",.„,.^.J-J.-.."-  high v's.  Interaction  it  overlap  s t a t e and  these r e s u l t s , none o f the  account f o r the  effects.  and  I f the  between Z~ 2' TT comes from  and  0 ( D)  i s bound as shown i n F i g . 1 6 .  occurs i n two  the A  s u f f i c i e n t l y c l o s e to the  x  l e a d s to s t r o n g 2 + H ( S ) , perhaps  Predissociation TT  steps, f i r s t t o the  I t i s a l s o p o s s i b l e that  TT ^  2  TT  and  then  then t o the  JL"  ground s t a t e comes  s t a t e near  v = 5 at hi?rh  v's  2-rr  that p r e d i s s o c i a t i o n takes place state.  F i g . 17 and  pends on the  l8  through the  show t h a t the  quantum number  N.  what f e a t u r e s  observed.  o f F i g . 18  are  || ground  predissociation  If a  TT  d i s s o c i a t i n g s t a t e , a l i n e a r dependence on Such an e f f e c t i s not  X  i s the  pre-  J i s expected.  Moreover i t i s not  caused by  de-  the e f f e c t o f  known  93  r o t a t i o n on the amount o f o v e r l a p .  2 Gaydon's theory that the  c —  2~  i s responsible f o r  the p r e d i s s o c i a t i o n a t low  v's i s a p p e a l i n g . Conceiv2 a b l y h i s theory h o l d s when the 2L i s r e p u l s i v e and r  2— + A 2=  cuts the  curve near  2^ same  Z.  'X, < ^  could then c u t  The  A L.  v = 5 at  again near  causing the s t r o n g p r e d i s s o c i a t i o n . and H a r r i s (1963) have  p o t e n t i a l curves f o r OH.  2  E  near  v = 3  ^Z""  cutting  and ^Tf near  v  calculated  Z- y  They f i n d t h a t  TT are a l l r e p u l s i v e w i t h  v = 2,  .  2— +  Recently Michels  4  n, > t  v = 2 at  A  - 4*.  2  L X  +  and near  9*f  -not In summary, we have^been  able to decide which  state  i s r e s p o n s i b l e f o r the s t r o n g p r e d i s s o c i a t i o n at h i g h v's 2 ^_ + i n the  A  2_  s t a t e , nor i f both p r e d i s s o c i a t i o n s observed  i n the  A s t a t e are cuased by the same s t a t e .  M i c h e l ( 1 9 5 7 ) observed a sudden decrease i n i n t e n s i t y 2 — + 2 — + i n the ( 1 , 8 ) at N = 9  band of the  1.  system b e g i n n i n g  We  agree w i t h h i s f i n d i n g s f o r  C —> A system and found the same e f f e c t i n the B~>  system. mained —  ->A  and suggested that a p r e d i s s o c i a t i o n of the A  s t a t e o c c u r s near v = 8 . the  C  A  However, the same sudden i n t e n s i t y decrease r e i n the C —> A system when the bands were photographed  — o n - a .much-faster instrument than the h i g h r e s o l u t i o n . s p e c t r o g r a p h , but many h i g h e r r o t a t i o n a l l e v e l s i n the B—9-A system.  appeared  Thus the i n t e n s i t y drop i s due to  the C s t a t e r a t h e r than the A s t a t e .  Moreover  s i t y d i s t r i b u t i o n depends v e r y much on the way from water. M i c h e l ( 1 9 5 7 )  the i n t e n OH i s formed  a l s o formed OH from water.  We  thus recommend c a u t i o n i n the i n t e r p r e t a t i o n o f these i n t e n sity  anomalities. R e f e r r i n g t o the ( 0 , 8 )  Rn(^)  band o f OH shown i n P l a t e Il£>  or the longer wavelength component of R(h) i s weaker  95 V  than i t should be, R ( 3 ) , R(5)  and  by comparison to the components of  R(6); R (5) 1  appears f u z z y .  a l s o shows the abnormal i n t e n s i t y but of P(*+)  and  P(5). are q u i t e normal.  We  P (6)  the two  1  also  components  are unable to  e x p l a i n these s m a l l p e r t u r b a t i o n s , except that they due  to the upper, or B s t a t e .  are  96  2 Chapter  X  -  The  2 The C  +  C Yl 2  "~> B  21  +  2  +  ~~> B 2-  System  + K,  System has never been observed  p r e v i o u s l y , but i t s t r a n s i t i o n s can be p r e d i c t e d from t a b l e 1*+. was  In f a c t the (0,0)  found and the f r e q u e n c i e s . a r e  exactly  t r a n s i t i o n o f the  C~>B  g i v e n on t a b l e 15.  It  i s easy to v e r i f y from combination r e l a t i o n s that assignment i s c o r r e c t .  The  (0,0)  band o f OH, although  about 10 times weaker than the (0,6) system,  band o f the B—>A  appears i n a c l e a n r e g i o n and was  i d e n t i f i e d from i t s s t r u c t u r e .  the  quickly  The heads o f other bands  p r e d i c t e d by t a b l e lh have been observed.  Even the  band o f the OD system has been found at i t s p r e d i c t e d quency.  There i s thus no doubt about the v  the C s t a t e and about the p o s i t i o n o f the energy l e v e l  diagram.  (1,1) fre-  numbering i n C  s t a t e i n the  97  H 0 1 2 3 4 5  1 2 3 4  R,  H,  19865.75 19871.20 19870.89 19876.51 19675.56 19879.70 19876.51 19881.96 19878.94  25.96 42.12 59.45 76.49  25.63 41.17 58.03 74.71  P  P  t  ^  19845.24 19834.39""" 19820.25 19818.48 19805.47 19804.23"+ 19789.43 19786.31  31.36 50.95 52.41 71.04 71.33 90.27 90.20  2 ' 4*  A hydrogen l i n e occurs a t the p r e d i c t e d value o f the o t h e r P (2) component. The l i n e ouoted i s probably P , (2) .  +  This  l i n e blends  -Table 1 5 .  with an i r o n  of OH. The ( 0 , 0 )  standard  band o f the C 2T a  line.  ^ B  a  Z  +  system  93  Chapter  XI  -  What now  OH?  T h i s chapter d i s c u s s e s problems which have a r i s e n the r e s e a r c h on the OH molecule The  and which are not r e s o l v e d .  exact s i z e o f the d i s p e r s i o n hum^in the A s t a t e  should be measured.  T h i s can be done by d e t e c t i n g p r e -  d i s s o c i a t i o n by r o t a t i o n i n the  A  s t a t e of OD.  With  j u s t s l i g h t l y more e x t e n s i v e d a t a than t h a t presented it  from  i s very p o s s i b l e t o see t h i s e f f e c t .  g i v e n i n Appendix V.  here,  The d e t a i l s are  The same r e s u l t can be o b t a i n e d the-  o r e t i c a l l y s i n c e the i n t e r a c t i o n s are very w e l l known and e x i s t i n g computer c a l c u l a t i o n o f atomic wave f u n c t i o n s are r e a s o n a b l y good. The d e t a i l s of the p r e d i s s o c i a t i o n s d e s c r i b e d i n Chapter The  IX  a l s o have t o be e x p l a i n e d by theory.  e x c i t a t i o n o f the OH molecule  i s peculiar.  The  i n t e n s i t y of the t r a n s i t i o n s i n the B—-5»A system f a l l s t o v a r y s m a l l , v a l u e s beyond temperature  of the OH molecules  below room temperature. observed  N, = 8 (Fig.III*),. .The c a l c u l a t e d i n the B s t a t e i s w e l l  Excitation of  N y  8  have been  i n the B —> A system on a f a s t e r instrument  the 3.4- meter s p e c t r o g r a p h . have found  Czarny  and Felenbok  the same i n t e n s i t y d i s t r i b u t i o n .  than  (1968)  I n the  99  (0,6)  band o f the B - ^ A  system, they found t h a t the r o t a -  t i o n a l temperature i s 130° K at low N.  The temperature i n the ( 0 , 0 )  N  and 3 5 0 ° K a t h i g h  t r a n s i t i o n o f the A—-> X (1958)  system has been measured by C a r r i n g t o n and B r o i d a who o b t a i n e d N  T = 6 6 9 ° K at low N  and by M e i n e l  (I967)  and 2 0 8 0 0 ° K a t h i g h N. C—*A  and T =  who found T =  276O  610° K  K at h i g h  0  at low N  The i n t e n s i t y d i s t r i b u t i o n i n the  system ( p l a t e I V ) seems to' be q u a l i t a t i v e l y the same.  In each of these cases the OH was produced from H 0 2  and the  p e c u l i a r i n t e n s i t y d i s t r i b u t i o n may be a r e s u l t of the mode of f o r m a t i o n of OH.  Although no q u a n t i t a t i v e r e s u l t s f o r OD  e x i s t , from p l a t e I V , the G—? A system o f OD h a s - q u a l i t a t i v e l y the same p e c u l i a r i n t e n s i t y p a t t e r n .  I n the B — ? A  system o f OD, the i n t e n s i t y drop i s n o t n o t i c e a b l e  until  N = 20. Many c l o s e l y spaced l i n e s without any obvious s t r u c t u r e o o have been observed-between  -39°° A and *+100 A.  trum i s d i f f e r e n t f o r the H 0 2  conceivable  and D 0 2  The s p e c - "  sources.  It is  that these are t r a n s i t i o n s from the h i g h e r  v i b r a t i o n a l l e v e l s o f the C s t a t e to the B s t a t e . emitter o f these l i n e s i s at present unknown.  The  100  The  apparatus d e s c r i b e d i n Chapter I I I with E^O  as  source should y i e l d a r i c h spectrum of OH i n the vacuum ultra-violet.  By l o o k i n g  at F i g * 14 one cannot h e l p but  f e e l t h a t there are other deeply bound s t a t e s of OH h i g h e r i n energy than the C s t a t e . w i l l c e r t a i n l y appear and the C —>X  In any case, the C -> A system  (the t a i l end of i t i s r e p o r t e d here)  system w i l l probably be observed too (Felenbok  and Cz arny, 1964-) . One  of the reasons f o r undertaking t h i s p r o j e c t  to observe the  H2O  .  near I n f r a - r e d .  have not seen i t .  was  I t s spectrum i s p r e d i c t e d to occur i n We  have i n v e s t i g a t e d up to 6500 A and  I t i s v e r y strange that the hollow  cathode, which supposedly b r i n g s out spectrum of i o n s , f a i l e d to b r i n g out the 0H  +  spectrum.  We have observed  o the and  doubly i o n i z e d oxygen l i n e s at 3 7 5 9 . 871  379+* 697  o A, 3757.239 A,  A, whose e x c i t a t i o n energy i s 36.5  0 I I I ' l i n e s * were-also seen. 1  ev. Other  We don't'understand why  h i g h l y e x c i t e d l i n e s from 0 I I I were observed, but 0H whose e x c i t a t i o n energy ^  15  ev. were not observed.  a d i f f e r e n t source should be used to d e t e c t  H 0 . +  2  these +  lines Perhap  101  In  the B"~^A  and C  A  systems, the l i f e t i m e o f the  lower l e v e l s has been s*ftown to be  10  1  1  seconds, which  -is much s h o r t e r than that of the upper s t a t e . inversion, naturally build  -Population  one o f the c o n d i t i o n s f o r l a s i n g a c t i o n , o c c u r s i n these systems.  a chemical  OH  laser.  I t would be i n t e r e s t i n g  to  102 BIBLIOGRAPHY B a r r e t t , A. H. Barrow, R. F.  1967.  Science.  1956.  l ^ Z , 881.  Ark. f u r F y s i k , 1 1 , 196M-.  Bennett, R. G. and Dal by, F. w.  281.  J . Chem. Phys.  kO, 1914-. Born, M. and Oppenheiraer, R. Branscomb, L. M. e t a l . 1958.  1927.  Ann. d. P h y s i k , $k,  Phys. Rev.  Ill,  4-57  504-  Bunker, R. R. 1968. J o u r . Mol. Spec. 28, 4-22. C a r r i n g t o n , T. and B r o i d a , H. P. 1958. J o u r . Mol. Spec.  2, Charton, M.  273.  and Gaydon, A. G. 1958. (London) A 24-5, 84-.  Proc. Roy.  Soc.  Coleman, C. D. e t a l . " i 9 6 0 "Table o f Wavenumbers" V o l . I . U.S. Dept. of Commerce. N a t i o n a l Bureau of Standards. Crosswhite, H. M. 1967 "F Unpublished.  - N  Czarny, J . and Felenbok, P. 14-1.  1968.  Q  Dieke, G. H.  Dunham, J . L. Felenbok, P.  e  Hollow Cathode Standards". Ann.  Astrophys.  31,  and Crosswhite, H. M. 194-8. "The u l t r a - v i o l e t bands of OH - Fundamental Data", Bumblebee s e r i e s , r e p o r t #37, Nov. 194-8. 1932. 1963.  Phys. Rev. kl, Ann.  Astrophys. 5 ,  Felenbok, P. and Czarny, J .  27,  721.  1964-.  Ann.  393. Astrophys.  2kk.  Gaydon, A. G. and W o l f h a r d , H. G. Soc. A 208, 6 3 .  1951.  Proc.  Roy.  1  Herzberg, G. Ishaq, M. K o l o s , W.  3  1 9 5 0 . " S p e c t r a o f Diatomic M o l e c u l e s " , Van Nostrand Co., I n c .  1  9  3  7  .  P r o c . Roy. Soc.  and W o l n i e w i c z , L. i±a,  Kovacs, I .  0  2  ^  1958.  -  2  1  0  .  J o u r . Chem. Phys.  1 9 6 5 * 9  A 159. 1  .  Can. J . Phys. 3  6  , 3  0  9  .  Landau, L. D. and L i f s h i t z , E . M. 1 9 6 5 . "Quantum Mechanics n o n - r e l a t l v i s t i c Theory", Pergamon P r e s s . London, F.  1  9  3  7 9  .  M e i n e l , A. B.  1  5  Meinel-, H.  1  9  6  7  M i c h e l , A.  1  9  5  7  Trans . 0  F a r . Soc. 8  .  Astrophys. J .  .  Z. N a t u r f o r s c h , 2  .  .  I l l , 5  Z. N a t u r f o r s c h .  M i c h e l s , H. H. and H a r r i s , F. E . 1 9 6 8 . Chem. V o l . I I s, 2 1 .  2 1  2  5  5  .  a  , 9  7  7  .  a  , 8  8  7  .  I n t . J . Quant.  Moore, C. E . 1 9 5 2 . "Atomic Energy L e v e l s " V o l . I , .. . C i r c u l a r M-67, U. S. Dept. o f Commerce, N a t i o n a l Bureau o f S t a n d a r d s . N a e g e l i , D. W.  and Palmer, H. B.  21,  I 9 6 7 .  J . Mol. Spec.  kh.  Oura, H. and Ninomiya, M. 1 9 ^ 3 . P r o c . Phys. Math. Soc. Japan, 2 £ , 3 5 5 . Palmer, H. B. and N a e g e l i , D. W.  1 9 6 8 . J . Mol. Spec. 2 8 ,  M-17.  Stone, J . M.  " R a d i a t i o n and O p t i c s " , McGraw H i l l Book Co., I n c . , 260.  I 9 6 3 .  Tanaka, T. and Koana, Z. 1 9 3 ^ . P r o c . Phys. Math. Soc. Japan, 1 6 , 3 6 5 .  Tomkins, F. S. and F r e d , M. Van V l e c k , J . H.  1929.  1951.  Phys. Rev.  J . Opt. Soc. Amer. 3^,  h67.  Weisner, J . D. and Armstrong, B. H. 1964-. Phys. Soc. (London) 8 ^ , Wigner, E . and Wltmer, E . E .  1928.  Proc. 31.  Z. Phys. £ 1 ,  859.  io5  Appendix  The  I  -  The i s o t o p i c  isotopic  constant jy  constant  i s d e f i n e d by  V JJL" where JX. i s the reduced OD.  From  mass o f  Herzberg- (1950)y  /C°  OH  ••  =  q.9^3376  =  1.789H03  =  0.728008  =  - 0.529996  =  0.3858^1  "Thus  />  3  and •  i s that o f • -•  106  Appendix  II  -  A program f o r l e a s t - s q u a r e s p o l y n o m i a l approximation.  Suppose that through the s e t o f p o i n t s ( X ^ y ; ) , 0 , ^ .a 7!,  C =  y--  b  6  one wants to f i t the polynomial  1  b>x  t  + b,  -t- - ; - •  under t h e c o n d i t i o n o f l e a s t square e r r o r  Let .-.  ^  ;  bo +  u? b, + • •• • • +•  E,  * • I- y . ^ ' x  b  TO  = (iry) 0  » t  The  h's can now be solved by Cramer's r u l e .  the b  are r e p l a c e d by  meters are The  N  I n the program  B (k + 1), the number o f p a r a -  and the number o f data p o i n t s are N D  a c t u a l program used, and given i n the f o l l o w i n g  was taken from the L i b r a r y o f Programs,  ATA. pages,  UBC Computing  Centre  107  The parameters t h a t best r e p r e s e n t the A & ( v q u a n t i t i e s i n the  B s t a t e (Chapter V I I ) were c a l c u l a t e d  by hand and by computer. The v a r i a b l e s  X  and  The r e s u l t s were the same. Y  appear i n the main program  T h e i r DIMENSION i n the main program i s NDATA. "CALL  POLYFT  +  (X, Y, N,  The  usual  NDATA)" i n the main program  w i l l i n t r o d u c e c o m p i l a t i o n and e x e c u t i o n of the subroutine.  108 FORTRAN ISN  SOURCE STATEMENT 0 1 2 3 4 5 6  7 10  11 12 13 14 15 16 17 21 22 24 25 26 27 30 31 32 33 35 36 37 42 43 44 45 46 51 52 53 54 55 56 61 62 x  SOURCE L I S T  64 65 66 67 70 71  * $I8FTC. PGLYFT SUBROUTINE PGLYFT { X , Y , N , N D AT A ) DIMENSION X(NOATA),Y(NDATA) * DIMENSION A ( 1 0 , 1 0 ) , V(20),. V Y ( l l ) , B ( 1 0 ) DIMENSION E P ( 5 0 0 ) * COMMON /COEFF /B * * COMMON/RMSE/E C PRINT 323, N i NDATA * 323 FORMAT(1H-» 6X » 4HN = ,13, 5 X , 8HNDATA = , 13/) * C BEGIN CALCULATION OF POLYNOMIAL COEFFICIENTS * C * C N IS THE POLYNOMIAL DEGREE * C NDATA I S THE NO. OF DATA POINTS N P i = N+l * NP2=N+2 N2l=2*N+l E = 0. * DO 100 1=1,NP2 V(I)=0. * 100 VY(I)=0. DO 106 I=NP2,N21 * 106 V(I)=0. * DO 105 1=1,NDATA VY(l)=VY(l)+Y( I ) * VY(NP2)=VY(NP2)+Y(I)*Y(I ) * XX=X(I ) * DO 101 J=2,NP1 * V(J)=V(J)+XX * VY{J)=VY(J)+XX*Y(I) * 101 XX = X X * X U ) * DO 105 J=NP2,N2l * V(.J)=V( J ) + XX 105 x x = x x * x m ; V { 1 ) =NDATA * ABOVE BUILT UP V,NOW BUILD UP A C * DO 102 K - l . N P l DO 102 L = l ,K -- -- * * KSL1=K-L+1 * 102 A(L,KSL1)=V(K) * DO 103 K=NP2,N21 * LS=N21-K+i * DO 103 L=1,LS KLNP1=K+L-NP1 * NP2L=NP2-L * 103 A(KLNP1,NP2L)=V(K) * DO 104 K=1,NP1 * 104 A(K,NP2)=VY(K) WE NOW SOLVE A MATRIX A OF N+l ROWS AND NP2 COLUMNS * C DO 399 I = 1, N * IP1=I+1 DO 399 J = I P I , N P I * * G = A ( J , I ) / A ( 1,1) DO 399 K = I P I , NP2 A(J,K) = A(J,K) - A(I,K)*Q * 399  *  102 FORTRAN ISN  "  SOURCE  75 76 * 77 * ICO * 101 102 * 103 * 302 1C5 * 301 107 110 * 398 112 * 113 * 114 115 * 116 * 117 * 120 * 95 122 * 123 33 3 * C - • • * C * C 125 126 133 * 310 134 * . 135 * 136 340 137 140 141 *  NO  MESSAGES  FOR  SOURCE  LIST  POLYFT  STATEMENT  B(NPl)=A(NPl NP2)/A{NPl,NP1 ) DO 3 0 1 1 = 2 , N P l J=NP2-I JPl=J+l B(J)=A(J,NP2) DO 3 0 2 K = J P I , N P 1 B(J)=B(J)-B(K)*A(J,K) B ( J ) =B ( J ) / A ( J , J )' DO 3 9 8 I = I , N P l E = E + B(I)*VY{I) E=VY(NP2)-E ESUM = 0. DO 3 3 3 K = 1 , N D A T A TS = B ( l ) DO 9 5 N.M = 2 , N P l ML = MM-1 TS = T S + B(MM)*X(K)**(ML) EP(K) = (Y(K)-TS) * (Y(K)-TS) ESUM = ESUM + E P ( K ) f  •  ;  END  CALCULATION  CF  POLYNOMIAL  ASSEMBLY  "•"  ERROR  =  -  ;  COEFFICIENTS^  NPl=N+l P R I N T 3 1 0 , ( K , B ( K ) , K - 1 » NP 1 ) FORMAT ( 7 X , 2 H B ( 1 1 , 2 H ) = F 1 2 . 5 ) XN = N D A T A E =. S Q R T ( E S U M / X N ) P R I N T 3't0,E FORMAT(IHO, ICX,24HLEAST SQUARES RETURN END  ABOVE  •  "  -  ,F12.5)  -  -  110  Appendix  III -  Zero p o i n t Energy.  Knowledge o f CO^ and G ( 0 ) c a n he determined  f o r a molecule means t h a t since  G (0)  ^  ~"2  -  ^±*e  T~  The minimum o f a p o t e n t i a l curve can then he determined. The f o l l o w i n g t a b l e g i v e s these v a l u e s f o r s e v e r a l e l e c tronic  s t a t e s o f OH and OD. State  -  OH  OD  X JX  1846.9  3.14  1349.4 2.58  A  1566.5 " 8.58  1140.7 1.60  611.7 -0.99  447.0 * -0.50*  X  c  r  3  On the.bottom l i n e i s g i v e n the Dunham z e r o p o i n t c o r r e c t i o n term y. 0 0  *  '_  Y  c  o  6e  f  , ,o^tOy  ° (  e  ^ e  UB<- i l T B j  From i s o t o p i c r e l a t i o n s .  <A>^  -f  Ill  Appendix  IV  -  Thermal broadening and Pressure broading of S p e c t r a l Lines.  Some s p e c t r a l l i n e s i n the spectrum observed t o be broad.  of OH and OD were  The i n c r e a s e d breadth i s not due t o  thermal broadening nor pressure broadening because t i o n s from the same upper  s t a t e were observed to be broad  ( i n OH, the (l,*f) and ( 1 , 9 )  and sharp  sharp, but ( 1 , 5 )  and ( 1 , 6 )  are b r o a d ) .  t r a n s i t i o n s are N e v e r t h e l e s s , the  c l a s s i c a l l i n e breadth due t o temperature can be c a l c u l a t e d .  transi-  According t o Stone  and p r e s s u r e  (1963) " R a d i a t i o n  and O p t i c s " , the h a l f width o f a s p e c t r a l l i n e i s g i v e n by  A where  C0  0  i s the frequency of the t r a n s i t i o n = 3 x IO  c  i s the speed o f l i g h t  k  i s Boltzmann's constant  T  i s the temperature £S 3 3 0 ° K  M  i s the mass of the molecule  r  =  I  A  1 0  cm/sec  .-16  x 10  erg/deg  112 o For (M  X  ^00  =  /-)  2 x 1.7 x 10  =  A,  =  fied  hydrogen  gm),  2.5  This i s only a factor dissociation.  and f o r m o l e c u l a r  x 10  1 0  / sec.  of 10 l e s s than that due  In f a c t , several  H  2  to p r e -  l i n e s were i d e n t i -  and they are a l l sharp. From  Stone, the h a l f width of a s p e c t r a l l i n e  due  to p r e s s u r e broadening i s  x where  D  B S J W  i s the diameter of the molecule and  pressure.  The maximum p r e s s u r e i s t h a t of  which i s 95 mm  Hg.  Taking  is =  D  a4o  ~. l v  / 5« t  P  H0 2  i s the at 50°  C  rn , then f o r H,  cy  ,  Thus c o l l i s i o n s i n " t h e c l a s s i c a l sense' do not c o n t r i b u t e at. a l l to the h a l f width.  As long as the e f f e c t i v e d i a k  meter of the molecule are h o t  important.  i s l e s s than  10  &  A, c o l l i s i o n s  113  Appendix  V  -  P r e d i s s o c i a t i o n by R o t a t i o n i n the A  H  "state o f OD The magnitude o f the d i s p e r s i o n hump i n the A s t a t e could  be determined  observed i n the  A  i f p r e d i s s o c i a t i o n by r o t a t i o n were E.  v = 13 l e v e l i s llh is  5 ^ - 8 cm" , 1  cm  N = 12 i n v = 12,  transition).  v = 10 i s  N = 17 i n v = 1 1 ,  1  that,  N = 20 i n v = 10  The N = 18 l e v e l has been seen i n  t r a n s i t i o n ) and N = 21 i n v = 10 ( 0 , I t i s thus q u i t e p o s s i b l e  t i o n by r o t a t i o n can be d e t e c t e d i n the  the t h e s i s .  cm"  are bound i n v = 1 3 ,  that 2  OD with l i t t l e  2172  From the B,\ i t i s expected  N = 8 levels  N = 2k i n v = 9. (0,11  .  From t a b l e 1H-, the  from the expected l i m i t , v = 12 1  excluding r o t a t i o n ,  v = 11  -1  v = 11 i s 128W cm" ,  and v = 9 i s 3290 cm  and  s t a t e o f OD.  modification  A ]T  10  predissocia+  state of  of the technique d e s c r i b e d  in  llh  Appendix  VI  -  E l e c t r o n i c isotope e f f e c t 2  The  accuracy of the d i s s o c i a t i o n energy of the A  +  H  s t a t e o f OH and OD, as presented i n t h i s t h e s i s i s j u s t outside  the range o f d e t e c t i n g e l e c t r o n i c i s o t o p e  shifts.  T h i s e f f e c t a r i s e s from the d i f f e r e n c e i n the shape o f the p o t e n t i a l w e l l f o r two molecules, o f d i f f e r e n t i s o t o p e , e.g.  OH and OD..  Imagining  the molecule, t o be n e i t h e r  v i b r a t i n g nor r o t a t i n g , the e l e c t r o n i c motion i s s t i l l present s i n c e the molecule trons.  i s h e l d together by the e l e c -  The e l e c t r o n s i n t u r n drag the n u c l e i behind them.  Because the center o f mass i s d i f f e r e n t f o r OH and OD, the energy  t o "keep the molecule  t i a l i s d i f f e r e n t f o r OH and OD.  a t minimum" o f the potenMathematically,  this  e f f e c t i s due t o the breakdown o f the Born-Oppenheimer approximation. isotope  Bunker (1968) has c a l c u l a t e d e l e c t r o n i c  s h i f t s i n s e v e r a l molecules  o f the order o f w i t h experiment  5^10  cm" . 1  and they are t y p i c a l l y  The agreement of h i s theory  i s not bad.  For OH, Bunker's formula p r e d i c t s that OH p o t e n t i a l w e l l s are deeper -  than the OD p o t e n t i a l w e l l s by 6 . ? ,  0.7 and ^ . 5 0 cm"  1  51.1,  i n the X, A, B & d C s t a t e s r e s p e c t i v e l y . n  115  E x p e r i m e n t a l l y , we (  -  3«6  +  15)  cm"  1  have obtained f o r the X and  (5*8  +  15)  A states  em  and  respectively.  

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