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UBC Theses and Dissertations

Vibrations of some aromatic molecules Kydd, Ronald Andrew 1969

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5vo2-  THE V I B R A T I O N S OF SOME A R O M A T I C  MOLECULES  by RONALD ANDREW KYDD B.Sc.(Hons.), U n i v e r s i t y of B r i t i s h  Columbia,  1963  A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T OF THE R E Q U I R E M E N T S FOR THE DEGREE  OF  DOCTOR OF P H I L O S O P H Y in  t h e Department of Chemistry  We  accept  required  this  thesis  as conforming  to the  standard  T H E U N I V E R S I T Y OF B R I T I S H October,  1969  COLUMBIA  In p r e s e n t i n g an the  thesis  advanced degree at Library  I further for  this  shall  the  his  of  this  written  f u l f i l m e n t of  University  of  make i t f r e e l y  agree that  permission  s c h o l a r l y p u r p o s e s may  by  in p a r t i a l  representatives.  be  available for for extensive  g r a n t e d by  gain  permission.  of  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  the  It i s understood  thes.is f o r f i n a n c i a l  Department  British  Columbia  shall  requirements  Columbia,  Head o f my  be  I agree  r e f e r e n c e and c o p y i n g of  that  not  the  that  Study.  this  thesis  Department  copying or  for  or  publication  allowed without  my  ABSTRACT  The thalene-dg, with  infrared  anthracene-h^g  polarized energy  measurements  spectra  With  o f naph-  are reported  parallel  to a l l  of the crystals.  The  e x t e n d d o w n t o 50 cm"'*' a n d a l l l o w a n d many  The l a s e r - e x c i t e d  o f naphthalene-dg  and t h i s  from  t h e new i n f o r m a t i o n  and anthracene-  solution  available  of the assignments  lattice  Raman  d a t a was s u p p l e m e n t e d  r a t i o measurements  a re-evaluation  by de-  and from t h e  from  these  studies  o f the molecular funda-  o f t h e s e t h r e e m o l e c u l e s h a s b e e n made. When t h e l i s t  possible,  attention  out-of-plane  was  directions  crystals  are reported  polarization  tion  radiation  have been a s s i g n e d .  of single  also  mentals  crystals  infrared-active molecular vibrations  vibrations  melt.  optical  of single  and anthracene-d^g  the plane of the incident  three p r i n c i p a l  d^Q  spectra  that  field  o f fundamentals  was d i r e c t e d  interaction  anthracene with  fields.  Transfer  The  as p o s s i b l e  o f these force constants  however,  i t proved  a l lthe observed non-planar  the force  as  a n d t h e assump  c o n s t a n t s s h o u l d be as s m a l l  t o n a p h t h a l e n e was s u c c e s s f u l ; to fit  to the force  o f b e n z e n e was r e c o n s i d e r e d ,  completely supported.  impossible  was a s c o m p l e t e  constants developed  t o be  frequencies of f o r benzene.  An for  in-plane modified  b e n z e n e was  refined  to  three  molecules  The  results  carried  these  out  elsewhere,  particularly order  to  find  by  and  i n the  molecules  molecules,  their  were compared w i t h  calculation presented  and  the  three the  Neto,  certain  how  and  observed  anthracene  perdeuterated  Scrocco  of  and  and  a  v i b r a t i o n s of pyrene  and  and  noted,  ring developed  but  of  similar  Califano  -d-^g  well force fields  and  analogues.  d i f f e r e n c e s were  would t r a n s f e r to r e l a t e d  the  designed  frequencies  results  anthracene-h^g  out  force f i e l d  to naphthalene  f i t simultaneously  all  In  extended  valence  less  modes. for  similar  acenaphthene  were  considered. The h^g,  infrared  pyrene-d^g  sis  on  the  The  data  carried  and  spectra of  by  others  assignments  of  the  fundamental  frequencies  force  tioned and  fields  earlier  and  in this  and  some f a i r l y number and  of  not  of  synthesized from  the  molecules  from the  fairly  complete  calculated frequencies  i n the  planar  fields  fields  of  showed t h a t  region of  they  the  men-  benzene  Comparison of  large discrepancies did arise, located only  The  were c a l c u l a t e d  two  out-of-plane  cyclopentane.  empha-  Raman m e a s u r e m e n t s  l a b o r a t o r y and  these  pyrene-  previously studied.  normal v i b r a t i o n s were p o s s i b l e .  ( f o r acenaphthene)  observed  regions  were s u p p l e m e n t e d by  out  with  crystals  acenaphthene were measured, w i t h  low-frequency  obtained  single  the  although were  few  in  ring stretching  iv  vibrations mentals cated to was  (above  below  that  that  about  1200  energy  the transfer  of  was  cm  possible.  The  fit  to the  most e n c o u r a g i n g , and  force  another i n order to calculate certainly  "*") .  c o n s t a n t s f r o m one  fundaindimolecule  approximate frequencies  T A B L E OF  CONTENTS  CHAPTER I.  PAGE GENERAL INTRODUCTION  1  A.  1  B.  General Outline 1.  Historical  2.  Aim  The  Assignment  of Fundamentals  8  1.  Vibrations  of Molecules. .  8  2.  Symmetry Solution a) b)  3.  Background  1  of Thesis  7  I n f o r m a t i o n from and M e l t S p e c t r a  Symmetry a s s i g n m e n t s spectra Symmetry a s s i g n m e n t s phase band contours  Vapor, 10  from  Raman  from  vapor-  11 12  Symmetry I n f o r m a t i o n from Spectra.  Crystal 14  a) b)  The o r i e n t e d g a s m o d e l . S i n g l e c r y s t a l f l u o r e s c e n c e and phosphorescence . . c) L i m i t a t i o n s o f t h e o r i e n t e d gas model . d) T h e i n t e r a c t i o n o f p l a n e p o l a r i z e d light with a single crystal . . . .  4.  Choosing  Fundamentals  from  Symmetry A s s i g n e d L i n e s . II.  EXPERIMENTAL A.  .  Preparation 1.  Source  .  14 16 20 25  the 28 30  o f Samples of Chemicals  a) N a p h t h a l e n e b) A n t h r a c e n e c) A c e n a p h t h e n e d) P y r e n e . e) S o l v e n t s . v  .  30 30 30 30 31 31 31  vi CHAPTER  PAGE 2.  III.  Growth o f S i n g l e C r y s t a l s  31  B.  S p e c t r o m e t e r s and A c c e s s o r i e s  . . 33  C.  C r y s t a l Data and O p t i c a l P r o p e r t i e s  35  1.  Naphthalene  35  2.  Anthracene  36  3.  Acenaphthene  36  4.  Pyrene .  39  THE VIBRATIONS OF NAPHTHALENE A.  B.  C.  Introduction  B.  . . . . . .  41  1.  C r i t i c a l Review  41  2.  S e l e c t i o n Rules  . 42  Results  46  1.  The Raman S p e c t r a  46  2.  The I n f r a r e d S p e c t r a  . . . . .  53  Assignment o f Fundamentals  61  1.  Lattice Vibrations  61  2.  Raman-active M o l e c u l a r  3.  Infrared-active Molecular  ' I V . THE VIBRATIONS OF ANTHRACENE A.  41  Vibrations. . . .  61  Vibrations . . 65 72  Introduction  72  1.,  C r i t i c a l Review  72  2.  S e l e c t i o n Rules  73  Results  78  vii  CHAPTER  PAGE 1.  Anthracene-h^Q Assignment a) b)  2.  3.  ^  78  Spectra . Assignment  Anthracene-d^g Assignment a) b)  I n f r a r e d Spectra and  78 89 I n f r a r e d Spectra and 99  Spectra Assignment  99 106  Anthracene-d Raman S p e c t r u m a n d Assignment . . . . . .  117  a)  117  1 Q  Spectra  .  b) A s s i g n m e n t V.  123  CALCULATIONS A.  B.  Molecular  128 Vibrations  128  1.  Motion  i n Cartesian Coordinates.  2.  Motion  i n Generalized Coordinates.  3.  Motion  i n Normal Coordinates  4.  Motion  i n Internal  Coordinates  133  5.  Motion  i n Symmetry C o o r d i n a t e s  135  Out-of-Plane  Force  Field  . . . .  129  . . . 131  . . . . . .  132  f o r Aromatic  Molecules  136  1.  137  Benzene a) b)  Symmetry Internal force  force constants valence-coordinate  constants  137  . . . . . . . . . . .  2.  Naphthalene  3.  Anthracene  4.  Discussion of Results  139 143  . . 147 150  v i i i  CHAPTER  PAGE C.  Planar  Force F i e l d  f o rAromatic  Molecules. 1.  The N e t o , S c r o c c o and C a l i f a n o  2.  The D u i n k e r - M i l l s  3.  Refinement o f the Duinker-Mills  4.  Results  5. VI.  VII.  152  Field.  Field  . . 153  . .  of the Refinement.  , 154 Field.  . 155  . . . . , . .165  a) N a p h t h a l e n e - d g b) A n t h r a c e n e - h - ^ Q . c) A n t h r a c e n e - d i o  173 174 175  Conclusions  176  THE V I B R A T I O N S OF P Y R E N E  179  A.  179  Introduction 1.  Critical  Review  2.  Selection Rules.  179 . . . . . .  180  B.  Results  183  C.  C a l c u l a t i o n o f Fundamentals  191  D.  Assignment  195  E.  Conclusion  201  1.  Out-of-Plane Assignment  201  2.  In-plane Assignment  202  THE V I B R A T I O N S OF A C E N A P H T H E N E A.  B.  Introduction 1.  Critical  2.  Selection  Results  . . . . . . . . .  203  .' . 2 0 3 Review Rules.  . . . . . . . 203 .  204 207  ix  CHAPTER  PAGE C.  Calculation  D.  Assignment  221  1.  A^ S p e c i e s  221  2.  B  1  Species  221  3.  B  2  Species  222  4.  A  2  Species  225  E. VIII.  Discussion  CONCLUSION  . .  o f Fundamentals  214  225 227  REFERENCES  233  APPENDIX  240  LIST OF TABLES TABLE  PAGE  1.  C o r r e l a t i o n t a b l e f o r naphthalene  43  2.  The o r i e n t e d - g a s p r e d i c t i o n s o f t h e r e l a t i v e i n t e n s i t i e s o f f r e e - m o l e c u l e Raman l i n e s o f naphthalene i n v a r i o u s c r y s t a l c o n f i g u r a t i o n s . . 45  3.  The o r i e n t e d - g a s p r e d i c t i o n s o f t h e r e l a t i v e i n t e n s i t i e s of the i n f r a r e d active l i n e s of n a p h t h a l e n e a l o n g v a r i o u s c r y s t a l axes. . . . . .  46  4.  The Raman s p e c t r a near t h e e x c i t i n g c r y s t a l s o f naphthalene-dg  50  5.  R e l a t i v e l i n e s t r e n g t h s i n t h e Raman s p e c t r a  6.  of naphthalene-dg above 1 5 0 c m The i n f r a r e d spectrum o f naphthalene-dg  l i n e from  51 57  - 1  7.  The i n f r a r e d energy  spectrum o f n a p h t h a l e n e - h  8.  P l a n a r fundamental v i b r a t i o n s  9.  Non-planar fundamental v i b r a t i o n s Naphthalene-dg  10.  C o r r e l a t i o n t a b l e f o r anthracene  11.  The o r i e n t e d - g a s p r e d i c t i o n s o f t h e r e l a t i v e i n t e n s i t i e s o f t h e f r e e - m o l e c u l e Raman l i n e s o f anthracene i n v a r i o u s c r y s t a l c o n f i g u r a t i o n s . . . 76  12.  The o r i e n t e d - g a s p r e d i c t i o n s o f t h e r e l a t i v e i n t e n s i t i e s of the infrared-active l i n e s of anthracene a l o n g v a r i o u s c r y s t a l axes  77  13.  The i n f r a r e d  85  14.  The a n a l y s i s o f t h e weak i n f r a r e d anthracene-h^g below 6 0 0 c m  15.  The a s s i g n e d i n f r a r e d - a c t i v e anthracene-h^Q  16.  The p o l a r i z e d i n f r a r e d anthracene-d^Q  g  a t low  o f Naphthalene-dg of  . 75  Q  x  lines of  fundamentals o f  spectrum o f  . 69 70  spectrum o f a n t h r a c e n e - h ^ ^ - 1  60  94 98 107  xi TABLE  '  PAGE  17.  A t e n t a t i v e a s s i g n m e n t o f t h e weak l i n e s o f anthracene-d^g  18.  The a s s i g n e d i n f r a r e d - a c t i v e f u n d a m e n t a l s a n t h r a c e n e - d ^ Q . . . . . . . . .  19.  T h e Raman  spectrum  20.  The a s s i g n e d Raman-active anthracene  low-energy . . . . . . . I l l of  of anthracene-d^g fundamentals  118 119  of 125  21.  Out-of-Plane f o r c e c o n s t a n t s f o rbenzene i n symmetry c o o r d i n a t e s . . . . . . . . . . . . . . . 138  22.  R e l a t i o n s h i p between symmetry and i n t e r n a l coordinate force c o n s t a n t s f o rbenzene  140  The o u t - o f - p l a n e f o r c e mdyn A / r a d i a n ^ .  142  23.  24.  25. 26.  27.  •28. 29.  c o n s t a n t s o f benzene, i n  Observed and c a l c u l a t e d of naphthalene-hg  non-planar frequencies  Observed and c a l c u l a t e d of naphthalene-dg  non-planar frequencies  145  146  Observed and c a l c u l a t e d non-planar f r e q u e n c i e s of anthracene-h^g . . . . .  148  Observed and c a l c u l a t e d of anthracene-d^g  non-planar frequencies 149  I n i t i a l and f i n a l force-field .  constants f o r planar  force  . 162  The o b s e r v e d and c a l c u l a t e d p l a n a r f r e q u e n c i e s of benzene, naphthalene and anthracene. . . . . .  166  30.  Correlation  181  31.  The o r i e n t e d - g a s p r e d i c t i o n s o f t h e r e l a t i v e intensities of the infrared active lines of pyrene a l o n g v a r i o u s c r y s t a l axes .  182  The l o w - f r e q u e n c y i n f r a r e d s p e c t r a o f pyrene-h and p y r e n e - d , . . . . . . . . . . . . . .  187  .32.  i n  table  f o rPyrene.  n  xii  TABLE 33.  34.  PAGE Observed and of pyrene  calculated  Observed and of pyrene  calculated  u-fundamentals 196 g-fundamentals 198  35.  Correlation  36.  The o r i e n t e d - g a s p r e d i c t i o n s o f t h e r e l a t i v e i n t e n s i t i e s of the i n f r a r e d - a c t i v e l i n e s of acenaphthene along v a r i o u s c r y s t a l axes  37.  table  f o r acenaphthene  205  The l o w - e n e r g y i n f r a r e d s p e c t r u m o f a s o l u t i o n o f acenaphthene i n benzene and o f ac  section  o f an acenaphthene  38.  Force  39.  The  40.  The  41.  The o u t - o f - p l a n e benzene .  A^  constants  206  an  crystal  f o r acenaphthene  211  calculation.  . .  and  fundamentals of acenaphthene.  . .  a n d B^  fundamentals of acenaphthene.  . . .  symmetry c o o r d i n a t e s  219  .223 224  of 245  LIST OF FIGURES FIGURE  PAGE  1.  The a r o m a t i c m o l e c u l e s s t u d i e d  2.  T y p i c a l appearance o f t y p e A, B, and C c o n t o u r s f o r an asymmetric r o t o r  13  The ab f a c e o f a m o n o c l i n i c c r y s t a l showing the o r i e n t a t i o n o f t h e axes X, Y, Z_ o f t h e indicatrix . .  26  4.  The anthracene u n i t c e l l  37  5.  The acenaphthene u n i t c e l l  38  6.  The pyrene u n i t c e l l  39  7.  The Raman s p e c t r a o b t a i n e d from t h e ac f a c e o f naphthalene-dg  47  8.  The Raman s p e c t r a o b t a i n e d from t h e ab and be'  3.  f a c e s o f naphthalene-dg 9. 10. 11.  Naphthalene-dg  .  i n f r a r e d s p e c t r a above 6 0 0 cm ^.  Naphthalene-dg low-energy c r y s t a l i n f r a r e d spectra Naphthalene-d_ i n benzene s o l u t i o n low-energy i n f r a r e d spectrum  48 . 54 56 56  12.  Naphthalene-hg spectra  13.  Anthracene-h.. _ l o w - f r e q u e n c y i n f r a r e d spectrum; ab f a c e . .  79  14.  Anthracene-h,_ l o w - f r e q u e n c y i n f r a r e d spectrum; be' f a c e . . 7  80  A n t h r a c e n e - h . ^ l o w - f r e q u e n c y i n f r a r e d spectrum; ac f a c e  81  15.  low-energy c r y s t a l i n f r a r e d  9  xiii  . 59  xiv FIGURE  PAGE  16.  Anthracene-h^  17.  Anthracene-d, ab f a c e  0  i n f r a r e d s p e c t r a dDOve 4 0 0 cm  n  low-frequency i n f r a r e d  . . 82  spectrum; 100  18.  Anthracene-d, be' f a c e . .  low-frequency i n f r a r e d  spectrum;  19.  Anthracene-d.^ low-frequency i n f r a r e d ac f a c e  spectrum;  n  101 102  20.  Anthracene-d^Q i n f r a r e d spectrum above 5 0 0 cm ^; ab f a c e 103  21.  Anthracene-d, be' f a c e . .  22.  Anthracene-d ac f a c e  n  i n f r a r e d spectrum above 5 0 0 cm "*";  104  i n f r a r e d spectrum above 5 0 0 cm ; 1  1 Q  105  23.  The l o w - f r e q u e n c y Raman spectrum o f p o l y c r y s t a l l i n e a n t h r a c e n e - d . ^ a t temperatures near t h e melting point 122  24.  Non-planar i n t e r n a l v a l e n c e c o o r d i n a t e s f o r naphthalene . . . . . . . . . . . .. 1 4 4  25.  Non-planar i n t e r n a l v a l e n c e c o o r d i n a t e s f o r anthracene  26.  The p l a n a r i n t e r n a l c o o r d i n a t e s o f benzene. . . . 1 5 8  27.  The p l a n a r i n t e r n a l c o o r d i n a t e s o f n a p h t h a l e n e . . 1 5 9  28.  The p l a n a r i n t e r n a l c o o r d i n a t e s o f anthracene . . 1 6 0  29.  The l o w - f r e q u e n c y i n f r a r e d s p e c t r a o f pyrene-h.^. 1 8 4  30.  The l o w - f r e q u e n c y i n f r a r e d s p e c t r a o f pyrene-d^g. 1 8 6  31.  The i n t e r n a l c o o r d i n a t e s o f pyrene  32.  The i n f r a r e d s p e c t r a o f an ac s e c t i o n o f acenaphthene about 45 m i c r o n s t h i c k  .147  193 20 8  XV  FIGURE 33.  PAGE The l o w - f r e q u e n c y i n f r a r e d s p e c t r u m o f acenaphthene i n benzene s o l u t i o n . . . . . . . . .  34.  The i n t e r n a l  35.  The a r r a n g e m e n t o f atoms u s e d t o d e f i n e an o u t - o f - p l a n e wag  241  The a r r a n g e m e n t o f atoms u s e d torsion  241  36. 37.  coordinates  The o u t - o f - p l a n e benzene  internal  o f acenaphthene.  210  to define  . . . .216  a  coordinates of 242  ACKNOWLEDGMENT  I am e x t r e m e l y g r a t e f u l t o Dr. A. Bree f o r h i s c o n t i n u e d i n t e r e s t and s u p p o r t the c o u r s e o f my graduate  throughout  studies.  I would a l s o l i k e t o e x p r e s s my apprec i a t i o n t o Dr. R.D. S p r a t l e y f o r h i s v a l u a b l e a s s i s t a n c e and t o o t h e r f a c u l t y members and s t u d e n t s f o r many h e l p f u l d i s c u s s i o n s .  CHAPTER I GENERAL INTRODUCTION  A.  General Outline  1.  H i s t o r i c a l Background Much work has been done r e c e n t l y t o determine t h e  fundamental v i b r a t i o n a l f r e q u e n c i e s o f a r o m a t i c m o l e c u l e s . F o r benzene and many o f i t s d e u t e r a t e d d e r i v a t i v e s , t h e two 1 2 monumental s t u d i e s by I n g o l d e t a l .  '  p r o v i d e almost com-  p l e t e a s s i g n m e n t s . Two c o r r e c t i o n s , f i r s t suggested by M a i r and H o r n i g , 3 were c o n f i r m e d by M i l l e r 4 and by B r o d e r s e n and 5 Langseth  and a r e now g e n e r a l l y a c c e p t e d .  of the i n f r a r e d ^  and Raman^'^'  Recent s t u d i e s  s p e c t r a o f naphthalene  have l e d t o a f a i r l y complete u n d e r s t a n d i n g o f t h e fundam e n t a l v i b r a t i o n s o f naphthalene-hg and a somewhat l e s s c e r t a i n assignment f o r naphthalene-dg.  The s i x t y - s i x funda-  m e n t a l modes o f anthracene a r e known w i t h even l e s s c e r t a i n t y , 15-19 d e s p i t e much a c t i v e i n t e r e s t i n i t s i n f r a r e d and 14,20-23 Raman ' spectra. The aim o f most o f t h i s work has been t o p r o v i d e an e x p e r i m e n t a l b a s i s from which c a l c u l a t i o n s can be c a r r i e d 1  2  out t o determine  a f o r c e f i e l d f o r these a r o m a t i c  molecules.  However, t h e most g e n e r a l q u a d r a t i c f o r c e f i e l d c o n t a i n s , e x c e p t f o r v e r y s i m p l e m o l e c u l e s , more f o r c e c o n s t a n t s fundamental f r e q u e n c i e s .  than  Even when t h e problem i s reduced  to i t s s i m p l e s t form by t h e use o f symmetry c o o r d i n a t e s , t h e number o f fundamental v i b r a t i o n s i s n o t s u f f i c i e n t t o d e t e r mine even t h e symmetry f o r c e c o n s t a n t s e x a c t l y , and a p p r o x i mate p o t e n t i a l f u n c t i o n s must be used. Workers i n t h e S o v i e t Union have tended t o use comp l i a n c e m a t r i c e s r a t h e r than f o r c e c o n s t a n t s f o r t h e c a l c u l a t i o n o f fundamental v i b r a t i o n s .  A compliance  matrix i s the  i n v e r s e o f a f o r c e c o n s t a n t m a t r i x and t h e element o f a compliance m a t r i x c o n n e c t i n g any c o o r d i n a t e p a i r has t h e u s e f u l p r o p e r t y t h a t i t i s i n v a r i a n t t o any changes i n d e f i 24  n i t i o n of the other i n t e r n a l c o o r d i n a t e s .  Since force  c o n s t a n t s do n o t have t h i s p r o p e r t y , i t would appear t h a t compliance  c o n s t a n t s a r e more s u i t e d f o r t r a n s f e r r i n g between 24  molecules.  However, C y v i n e t a l .  have r e c e n t l y shown t h a t  i n p r a c t i c e t h e two methods a r e r o u g h l y e q u i v a l e n t , each h a v i n g some d i s a d v a n t a g e s .  I n p a r t i c u l a r , t h e compliance  method r e q u i r e s t h a t a complete s e t o f i n t e r n a l c o o r d i n a t e s be s e t up i n v o l v i n g no r e d u n d a n c i e s ,  and t h i s i s o f t e n  awkward w i t h t h e f a i r l y symmetric a r o m a t i c m o l e c u l e s considered.  t o be  Thus i n t h i s work o n l y t h e f o r c e c o n s t a n t  approach i n which redundant c o o r d i n a t e s a r e more e a s i l y t r e a t e d w i l l be used.  3  Three b a s i c t y p e s o f approximate f o r c e f i e l d may be considered; the c e n t r a l force f i e l d , the valence force f i e l d 25  and t h e U r e y - B r a d l e y  force f i e l d .  The c e n t r a l f o r c e f i e l d  assumes t h a t t h e f o r c e s h o l d i n g atoms i n t h e i r e q u i l i b r i u m p o s i t i o n s e x i s t between every p a i r o f atoms and a c t a l o n g t h e line joining that pair.  When t h e i n t e r n a l c o o r d i n a t e system  i s chosen t o be t h e complete s e t o f i n t e r a t o m i c . d i s t a n c e s , the f o r c e c o n s t a n t m a t r i x i s d i a g o n a l .  This  approximation,  which would be t r u e i f t h e atoms o f a m o l e c u l e were h e l d t o g e t h e r o n l y by i o n i c a t t r a c t i o n s , has met w i t h  little  success. The s i m p l e v a l e n c e f o r c e f i e l d c o n s i d e r s o n l y those f o r c e s i n v o l v e d i n t h e s t r e t c h i n g o r t o r s i o n o f v a l a n c e bonds and t h e bending  o f v a l e n c e a n g l e s ; f o r c e s between non-bonded  atoms a r e n o t c o n s i d e r e d , n o r a r e i n t e r a c t i o n c o n s t a n t s between bonds.  The U r e y - B r a d l e y  f i e l d i s a valence force f i e l d  to which have been added some c e n t r a l f o r c e terms as d i a g o n a l elements. Of g r e a t i n t e r e s t from a c h e m i c a l v i e w p o i n t i s t h e modified valence force f i e l d , since i t describes the forces i n terms o f i n t e r n a l c o - o r d i n a t e s t h a t have c h e m i c a l cance.  signifi-  I n t h i s type o f f i e l d , i n t e r a c t i o n c o n s t a n t s between  some i n t e r n a l c o o r d i n a t e s a r e t a k e n i n t o account; t h i s amounts to c o n s i d e r i n g t h e change i n s t i f f n e s s o f one bond o r angle r e s u l t i n g from t h e d i s t o r t i o n o f o t h e r bonds o r a n g l e s .  The  4 c h o i c e o f which i n t e r a c t i o n c o n s t a n t s t o i n c o r p o r a t e may g u i d e d by c h e m i c a l i n t u i t i o n .  be  I n o r d e r t o p e r m i t the i n -  c l u s i o n o f as many i n t e r a c t i o n c o n s t a n t s as may  be  desirable,  i t i s n e c e s s a r y t o have as much e x p e r i m e n t a l d a t a as p o s s i b l e ; a d d i t i o n a l i n f o r m a t i o n i s p r o v i d e d by the fundamental quencies of i s o t o p i c a l l y s u b s t i t u t e d molecules.  fre-  The  assump-  t i o n t h a t the p o t e n t i a l f u n c t i o n i s unchanged by such  isotopic  s u b s t i t u t i o n i s based on the Born-Oppenheimer s e p a r a b i l i t y of  e l e c t r o n i c and n u c l e a r c o o r d i n a t e s and the assumed harmonic  n a t u r e o f the v i b r a t i o n s . 26  27  M i l l e r and Crawford ' have used b o t h symmetry f a c t o r i z a t i o n and i n f o r m a t i o n from d e u t e r a t e d m o l e c u l e s t o 2 8 29 d i s c u s s , w i t h Wilson's technique, f o r c e f i e l d o f benzene.  '  the complete q u a d r a t i c  The number o f o u t - o f - p l a n e  funda-  mentals known s h o u l d be s u f f i c i e n t t o determine the non26 p l a n a r , symmetrized f o r c e f i e l d e x a c t l y ; approximations 27 were found  t o be n e c e s s a r y f o r the i n - p l a n e problem.  Upon  c a r r y i n g out the c a l c u l a t i o n s , however, they found t h a t i n both cases a m b i g u i t i e s s t i l l e x i s t e d due t o the appearance o f q u a d r a t i c e q u a t i o n s f o r which both r o o t s are p h y s i c a l l y r e a sonable.  W h i f f e n ^ " chose from the a l t e r n a t i v e s e t s o f con-  s t a n t s on the c h e m i c a l b a s i s t h a t the s i m p l e v a l e n c e f i e l d i s most i m p o r t a n t and i n t e r a c t i o n c o n s t a n t s added t o i t s h o u l d be as s m a l l as p o s s i b l e .  5 R e c e n t l y two a l t e r n a t i v e m o d i f i e d v a l e n c e f o r c e f i e l d s have been proposed 31 Scherer  f o r t h e p l a n a r benzene problem.  converted a Urey-Bradley f i e l d t o a modified valence  f i e l d , and by r e f i n i n g o n l y n i n e f o r c e c o n s t a n t s found a v e r y s a t i s f a c t o r y f i t t o t h e f r e q u e n c i e s o f benzene and s e v e r a l o f 32 i t s c h l o r i n a t e d analogues. D u i n k e r and M i l l s made use o f a d d i t i o n a l r e s t r i c t i o n s on t h e f o r c e f i e l d p r o v i d e d by t h e 33 r e c e n t l y observed  C o r i o l i s c o u p l i n g c o n s t a n t s and found  v a l u e s f o r c e r t a i n symmetry f o r c e c o n s t a n t s d i f f e r i n g from those suggested by W h i f f e n " ^ and by Scherer.'*"'"  markedly From  t h e s e f o r c e c o n s t a n t s they developed and r e f i n e d a t h i r t e e n parameter m o d i f i e d v a l e n c e f o r c e f i e l d i n v o l v i n g  interaction  c o n s t a n t s e x p e c t e d t o be s i g n i f i c a n t on t h e b a s i s o f v a r i o u s models (see r e f . 32, p. 4 2 8 ) . S e v e r a l attempts t o t r a n s f e r f o r c e c o n s t a n t s from one a r o m a t i c m o l e c u l e t o another have been made.  Whiffen's  m o d i f i e d v a l e n c e f o r c e f i e l d was a p p l i e d t o naphthalene by 34 35 36 Freeman and Ross and by S c u l l y and W h i f f e n . ' The former a u t h o r s c a r r i e d o u t an i t e r a t i v e r e f i n e m e n t o f t h e f o r c e cons t a n t s t o f i t t h e more c e r t a i n f r e q u e n c i e s o f naphthalene. 37 Scherer t r a n s f e r r e d t o naphthalene an e a r l i e r U r e y - B r a d l e y 38 39 31 field ' o f benzene a l t h o u g h he l a t e r found that a valence f o r c e f i e l d c o u l d reproduce s u b s t i t u t e d benzene f r e q u e n c i e s s i g n i f i c a n t l y b e t t e r than a U r e y - B r a d l e y f i e l d . The o u t - o f 30 plane force constants of Whiffen have a l s o been c a r r i e d _ 40 over t o a n t h r a c e n e .  6  A d i f f e r e n t approach was used by Neto, S c r o c c o and 41 Califano.  Rather than t r a n s f e r a benzene f o r c e f i e l d  to  l a r g e r a r o m a t i c m o l e c u l e s , they assumed the e x i s t e n c e o f an " a r o m a t i c v a l e n c e f o r c e f i e l d " which would s i m u l t a n e o u s l y f i t a number o f s i m p l e a r o m a t i c m o l e c u l e s .  They used t h i s method  to c a l c u l a t e t h e p l a n a r f r e q u e n c i e s o f benzene,  naphthalene  and a n t h r a c e n e , and the f i t w i t h the then a v a i l a b l e d a t a v e r y good (the average e r r o r was  l e s s than 15 cm \  was  although  t h i s v a l u e does depend on the c h o i c e o f e x p e r i m e n t a l a s s i g n ment) . The i n i t i a l f i e l d used i n the benzene p a r t o f t h i s c a l c u l a t i o n 41 was almost i d e n t i c a l t o t h a t found by S c h e r e r 31 and was p r o b a b l y a l s o the r e s u l t o f r e f i n i n g i m p o r t a n t v a l e n c e f o r c e c o n s t a n t s chosen from a U r e y - B r a d l e y One  o f the major d i f f i c u l t i e s  field.  encountered i n e v a l u -  a t i n g a r o m a t i c f o r c e f i e l d s has been l o c a t i n g r e l i a b l e t i o n a l assignments.  vibra-  F o r c e c o n s t a n t c a l c u l a t i o n s depend not  o n l y on p r e c i s e measurements o f the frequency o f a normal mode, b u t a l s o r e q u i r e a knowledge o f e x a c t l y how many fundamentals o f the same symmetry l i e h i g h e r and lower i n energy. In t h i s sense, fewer f r e q u e n c i e s are known d e f i n i t e l y ; when 34 Freeman and Ross  c a r r i e d out t h e i r c a l c u l a t i o n s on naph-  t h a l e n e , they e s t i m a t e d t h a t o n l y t e n o f the t w e n t y - f i v e i n p l a n e fundamental v i b r a t i o n s below 2000 cm ^ s a t i s f i e d requirement.  this  I  7  Many f a c t o r s e n t e r i n t o t h e e x p e r i m e n t a l problem o f a s s i g n i n g t h e fundamental v i b r a t i o n s . the i n f r a r e d , s c o r e s o f c o m b i n a t i o n  F o r example, i n  and o v e r t o n e  frequencies  appear, many w i t h c o n s i d e r a b l e i n t e n s i t y , and l o c a t i n g t h e fundamentals among them i s e x t r e m e l y d i f f i c u l t .  Some o f t h e  problems, though, can be overcome by c a r e f u l t e c h n i q u e , and o t h e r s have d i s a p p e a r e d as t e c h n o l o g i c a l advances have t a k e n place. In much o f t h e p r e v i o u s i n f r a r e d work, a t t e n t i o n was  l i m i t e d t o the r e a d i l y obtained cleavage faces o f the  crystals.  Thus i n c o m p l e t e p o l a r i z a t i o n i n f o r m a t i o n was  o b t a i n e d , and a l t h o u g h these d a t a were supplemented by s o l u t i o n measurements, t h e assignment o f fundamentals was d i f f i c u l t when t h e t r a n s i t i o n d i p o l e was n o t o r i e n t e d near one o f t h e o p t i c a l d i r e c t i o n s of the cleavage face.  I n a d d i t i o n , low  energy m o l e c u l a r v i b r a t i o n s o f t e n f e l l o u t s i d e t h e s p e c t r a l r e g i o n covered by o l d e r i n f r a r e d s p e c t r o m e t e r s , and c o u l d n o t be measured.  Raman s p e c t r a o b t a i n e d b e f o r e t h e advent o f t h e  l a s e r were sometimes u n r e l i a b l e , and p o l a r i z e d Raman s p e c t r a from s i n g l e c r y s t a l s were e x t r e m e l y d i f f i c u l t t o o b t a i n . 2.  Aim o f T h e s i s The work undertaken  i n t o two p a r t s .  f o r t h i s t h e s i s can be d i v i d e d  I n t h e e x p e r i m e n t a l s e c t i o n , complete p o l a r i -  z a t i o n i n f o r m a t i o n about i n f r a r e d l i n e s was o b t a i n e d by measuring t h e s p e c t r a from c r y s t a l f a c e s n o t p r e v i o u s l y  8 studied. the  I n a d d i t i o n , a new s p e c t r o m e t e r was used t o extend  measurements i n t o t h e f a r i n f r a r e d t o l o c a t e a l l t h e  low-energy m o l e c u l a r v i b r a t i o n s .  Raman s p e c t r a were r e c o r d e d  f o r s e v e r a l molecules i n order t o r e s o l v e d o u b t f u l assignments, w i t h emphasis p l a c e d on o b t a i n i n g p o l a r i z e d s p e c t r a from single crystals.  I t was hoped t h a t a l l t h e i n f o r m a t i o n  c o l l e c t e d would p e r m i t more d e f i n i t e assignments t o be made of t h e fundamental v i b r a t i o n s o f s e v e r a l a r o m a t i c m o l e c u l e s . When t h e assignments were as complete as p o s s i b l e , the  f o r c e f i e l d s were c o n s i d e r e d .  Previously  unobserved  fundamentals c o u l d be used t o check t h e a c c u r a c y o f t h e predictions of various force f i e l d s .  I t was hoped t h a t more  c o u l d be l e a r n e d about t h e l e s s - i n t e n s i v e l y s t u d i e d o u t - o f p l a n e f o r c e c o n s t a n t s from t h e new i n f o r m a t i o n about low energy fundamentals.  I n a d d i t i o n , t h e a b i l i t y o f some f o r c e  f i e l d s t o f i t s i m u l t a n e o u s l y t h e f r e q u e n c i e s o f benzene, naphthalene and anthracene was c o n s i d e r e d .  A l s o , two r e l a t e d  b u t l e s s s i m i l a r m o l e c u l e s (pyrene and acenaphthene)  were  s t u d i e d t o see how w e l l t h e f o r c e c o n s t a n t s d e r i v e d f o r t h e f i r s t t h r e e m o l e c u l e s would t r a n s f e r t o o t h e r m o l e c u l e s .  B.  The Assignment o f Fundamentals  1.  V i b r a t i o n s of molecules When a m o l e c u l e e x e c u t e s a fundamental o r normal  v i b r a t i o n , e v e r y atom o f t h e m o l e c u l e v i b r a t e s a t t h e same  9  f r e q u e n c y ; the atoms pass through t h e i r e q u i l i b r i u m  positions  a t t h e same time and r e a c h t h e i r p o s i t i o n s o f maximum d i s placement a t the same t i m e .  The t o t a l number o f normal  v i b r a t i o n s o f a n o n - l i n e a r m o l e c u l e i s 3N-6 number o f atoms.  where N i s the  Each normal v i b r a t i o n has the symmetry o f  10 one o f t h e i r r e d u c i b l e r e p r e s e n t a t i o n s  of the molecular point  group and t h e number o f v i b r a t i o n s b e l o n g i n g t o each r e p r e sentation  can be r e a d i l y d e t e r m i n e d . The f i r s t s t e p i n a s s i g n i n g  fundamentals i s t o l o c a t e  a l l the frequencies a t which the molecule v i b r a t e s .  The f u n -  damentals o f a r o m a t i c m o l e c u l e s l i e i n t h e energy range between 100 cm  and 3200 cm  and some v i b r a t i o n s may be  observed d i r e c t l y i n t h e i n f r a r e d and f a r i n f r a r e d regions.  spectral  I n a d d i t i o n , o t h e r f r e q u e n c i e s may a l s o be found as  i n t e r v a l s i n Raman and e m i s s i o n ( f l u o r e s c e n c e cence) s p e c t r a .  and phosphores-  The second s t e p i n t h e assignment i s t o  i d e n t i f y t h e symmetry t y p e o f each observed v i b r a t i o n .  2.  Symmetry i n f o r m a t i o n melt  from v a p o r , s o l u t i o n and  spectra Some c o n c l u s i o n s about t h e symmetry o f t h e v i b r a -  tions of large m o l e c u l e s — p a r t i c u l a r l y i n f r a r e d o r Raman a c t i v e — c a n spectra  t h o s e modes which a r e  be made by s t u d y i n g t h e i r  i n t h e vapor phase, i n s o l u t i o n o r i n t h e m e l t .  Symmetry assignments from f l u o r e s c e n c e and phosphorescence are more r e a d i l y made from c r y s t a l s p e c t r a of t h e r e l e v a n t section.  and a d i s c u s s i o n  s e l e c t i o n r u l e s w i l l be made i n t h e n e x t  A d i v i s i o n o f t h e v i b r a t i o n s i n t o Raman a c t i v e and  i n f r a r e d a c t i v e modes e f f e c t s an i n i t i a l symmetry  classifi-  c a t i o n , s i n c e t h e s e l e c t i o n r u l e s f o r t h e two p r o c e s s e s a r e  11 different.  Any v i b r a t i o n w h i c h i s i n f r a r e d a c t i v e must b e l o n g  to a representation  o f t h e p o i n t group o f t h e m o l e c u l e which  t r a n s f o r m s l i k e a t r a n s l a t i o n a l o n g t h e x, y_ o r z_ a x i s . Raman a c t i v e v i b r a t i o n s must have t h e symmetry o f one o f t h e representations  w h i c h t r a n s f o r m s l i k e one o f t h e components  of t h e p o l a r i z a b i l i t y t e n s o r ,  a.  I f the molecule contains  a  c e n t e r o f symmetry, as s e v e r a l o f t h e a r o m a t i c compounds s t u d i e d i n t h i s work do, Raman modes a r e gerade w h i l e red-active  infra-  v i b r a t i o n s a r e ungerade. a) Symmetry assignments from Raman s p e c t r a .  Two  t e c h n i q u e s a r e i n use f o r making symmetry assignments from the Raman s p e c t r a o f g a s e s , s o l u t i o n s o r m e l t s .  The f i r s t ,  used t o i d e n t i f y t o t a l l y symmetric v i b r a t i o n s , i s t h e f a m i l i a r 'Raman d e p o l a r i z a t i o n r a t i o  1  measurement.  For the r i g h t -  a n g l e d v i e w i n g arrangement common for.Raman s p e c t r a t h e scattered r a d i a t i o n corresponding t o a non-totally-symmetric v i b r a t i o n has a d e p o l a r i z a t i o n r a t i o  p  0  = 3/4 or  p  depending on whether t h e i n c i d e n t l i g h t i s l i n e a r l y (p.) or natural lines with  =  'I  polarized  ( p ) . The s i g n i f i c a n t r e s u l t i s t h a t a l l  p l e s s than t h e maximum v a l u e must a r i s e from  t o t a l l y symmetric v i b r a t i o n s .  For the c o - a x i a l viewing  d e p o l a r i z a t i o n r a t i o s a r e d e f i n e d by W i l s o n , D e c i u s and C r o s s ( r e f . 29, p. 4 7 ) .  12 arrangement used i n most o f t h i s work the maximum v a l u e o f the d e p o l a r i z a t i o n r a t i o i s 0.75. A l e s s u s e f u l but r a t h e r i n t e r e s t i n g t e c h n i q u e used f o r making symmetry assignments from the Raman s p e c t r a o f 42 r o t a t i n g m o l e c u l e s was r e c e n t l y demonstrated f o r benzene. The a n g u l a r dependence o f the i n t e n s i t y o f Raman s c a t t e r i n g from a l i q u i d  (benzene) e x c i t e d by a Helium-neon  laser  compared w i t h the i n t e n s i t y d i s t r i b u t i o n p r e d i c t e d 42) by P l a c z e k f o r d i f f e r e n t symmetries. agreement  The  was  (see r e f .  excellent  f o r the few v i b r a t i o n s s t u d i e d s e r v e d more t o  demonstrate the method than t o a s s i g n the modes, whose symmetries were a l r e a d y w e l l e s t a b l i s h e d .  This technique  has n o t as y e t come i n t o g e n e r a l u s e , p r o b a b l y because o f b o t h the e x p e r i m e n t a l d i f f i c u l t i e s and the p o s s i b i l i t y o f making assignments from more s t a n d a r d t e c h n i q u e s (e.g. s i n g l e crystal  spectra). b) Symmetry assignments from vapor-phase band  contours.  T r a n s i t i o n s o b s e r v e d i n the i n f r a r e d , Raman o r  e m i s s i o n s p e c t r a o f m o l e c u l e s i n the vapor phase and  attri-  buted t o v i b r a t i o n s are i n f a c t due t o changes i n b o t h the r o t a t i o n a l and v i b r a t i o n a l quantum numbers.  S i n c e the  moments o f i n e r t i a o f a r o m a t i c m o l e c u l e s a r e r e l a t i v e l y  large,  the r o t a t i o n a l s t r u c t u r e cannot be r e s o l v e d , and under normal c o n d i t i o n s the band appears as a s i n g l e l i n e .  Under h i g h e r  r e s o l u t i o n , however, the shape o f the envelope o f t e n can be  13 found and, by comparison w i t h t h e c o n t o u r s p r e d i c t e d f o r d i f f e r e n t symmetries, assignments can be made.  Although the  p r e c i s e shape depends on t h e m o l e c u l a r d i m e n s i o n s , t y p i c a l c o n t o u r s f o r t r a n s i t i o n s p o l a r i z e d a l o n g each o f t h e t h r e e p r i n c i p a l axes o f an asymmetric r o t o r a r e shown i n F i g u r e 2.  B  A  C  F i g u r e 2. T y p i c a l appearance o f t y p e A, B, and C c o n t o u r s f o r an asymmetric r o t o r . A f t e r K i n g ^ 3 , p. 374. A t y p e A band has i t s t r a n s i t i o n moment p a r a l l e l t o t h e p r i n c i p a l a x i s o f s m a l l e s t moment o f i n e r t i a , type B t h e i n t e r mediate moment o f i n e r t i a , and t y p e C bands a r e p o l a r i z e d a l o n g t h e a x i s o f l a r g e s t moment o f i n e r t i a . d i f f i c u l t i e s involved  Despite the  ( p a r t i c u l a r l y i n d i s t i n g u i s h i n g between  type A and t y p e C c o n t o u r s ) symmetries o f some bands o f t h e asymmetric r o t o r naphthalene have been found from t h e v i b r o n i c 44 45 46 6 absorption, ' fluorescence, and i n f r a r e d a b s o r p t i o n spectra.  However, t h i s method i s n o t so u s e f u l f o r a m o l e c u l e  l i k e anthracene which has a much lower vapor p r e s s u r e and a more crowded  spectrum.  14 3.  Symmetry I n f o r m a t i o n  from C r y s t a l  As shown i n the p r e v i o u s  Spectra  s e c t i o n , some i n f o r m a t i o n  about the symmetry of m o l e c u l a r v i b r a t i o n s can be g a i n e d from a study o f the s p e c t r a o f m o l e c u l e s when they are a b l e rotate.  to  Much more i n f o r m a t i o n would be a v a i l a b l e , however,  i f i t were p o s s i b l e t o h o l d a m o l e c u l e f i x e d i n space observe the way  and  i t i n t e r a c t s with plane p o l a r i z e d l i g h t .  The  c l o s e s t approach t o t h i s i d e a l experiment i s t o study s i n g l e c r y s t a l s , i n which the o r i e n t a t i o n s of the m o l e c u l e s i n the u n i t c e l l are known w i t h r e s p e c t t o the c r y s t a l axes.  The  i n t e r p r e t a t i o n o f the s p e c t r a of s i n g l e c r y s t a l s i s u s u a l l y c a r r i e d out under the assumptions o f the o r i e n t e d gas model. a) The  o r i e n t e d gas model.  C r y s t a l s of aromatic  m o l e c u l e s , l i k e those of most o r g a n i c compounds, can c l a s s i f i e d as m o l e c u l a r c r y s t a l s ; t h a t i s , the  be  intermolecular  f o r c e s are much weaker t h a n the i n t r a m o l e c u l a r f o r c e s .  In a 47 48  u s e f u l a p p r o x i m a t i o n , known as the o r i e n t e d gas model,  '  the i n t e r m o l e c u l a r f o r c e s are n e g l e c t e d c r y s t a l i s considered  completely  and  the  t o be a r i g i d l y o r i e n t e d system o f  n o n - i n t e r a c t i n g molecules i n t h e i r e q u i l i b r i u m c r y s t a l l i n e positions.  I n t h i s a p p r o x i m a t i o n each vapor phase band i s  p r e d i c t e d t o produce a s i n g l e l i n e a t e x a c t l y the same f r e quency i n the c r y s t a l spectrum, l i n e s which do not appear i n the f r e e - m o l e c u l e  spectrum are e x p e c t e d t o have zero i n t e n s i t y  15 i n t h e c r y s t a l , and t h e r e l a t i v e i n t e n s i t i e s o f Raman l i n e s and o f i n f r a r e d l i n e s w i l l depend o n l y on t h e o r i e n t a t i o n o f the m o l e c u l e s i n t h e u n i t c e l l w i t h r e s p e c t t o t h e axes a l o n g which t h e i n c i d e n t (and s c a t t e r e d ) r a d i a t i o n i s p o l a r i z e d . P o l a r i z a t i o n r a t i o s f o r infrared absorption.  The  t r a n s i t i o n from v i b r a t i o n a l s t a t e i t o v i b r a t i o n a l s t a t e j w i l l absorb i n f r a r e d r a d i a t i o n o n l y i f t h e r e i s a change i n the e l e c t r i c moment o f t h e m o l e c u l e i n g o i n g from one s t a t e to  the other.  The i n t e n s i t y o f t h e a b s o r p t i o n i s p r o p o r t i o n a l  to  t h e square o f t h e t r a n s i t i o n d i p o l e moment.  For plane-  p o l a r i z e d l i g h t o r i e n t e d a t some angle 8 t o t h e v e c t o r r e p r e s e n t i n g t h e e l e c t r i c moment change t h e i n t e n s i t y o f t h e a b s o r p t i o n w i l l v a r y as c o s ^ e .  I f other molecules i n the  u n i t c e l l are d i f f e r e n t l y o r i e n t e d with respect t o the c r y s t a l axes used, then t h e t o t a l i n t e n s i t y a l o n g each a x i s w i l l be the mean o f t h e c o n t r i b u t i o n s from t h e i n d i v i d u a l  molecules.  I n t e n s i t y d i s t r i b u t i o n f o r Raman s c a t t e r i n g i n t h e c r y s t a l frame.  The d i p o l e moment u_ induced  i n an a n i s o t r o p i c  m o l e c u l e i n an e l e c t r i c f i e l d E i s u —xyz  =  a E =xyz —xyz  where a i s t h e p o l a r i z a b i l i t y t e n s o r .  The s u b s c r i p t s em-  p h a s i z e t h a t t h e above e q u a t i o n i n v o l v e s o n l y t h e m o l e c u l a r a x i s frame, x, y, z.  However, t h e e x p e r i m e n t a l l y a c c e s s i b l e  axes f o r a g i v e n c r y s t a l s e c t i o n a r e n o t x, y, z b u t another o r t h o n o r m a l s e t whose o r i e n t a t i o n i s a p r o p e r t y o f t h e c r y s t a l (see s e c t i o n B . 3 ( d ) o f t h i s  chapter).  16  The i n d u c e d d i p o l e P^bc v e c t o r E_ k a  c  anc  ^  ^he e l e c t r i c  field  i n some c o n v e n i e n t c r y s t a l a x i s s e t a, b, c (not  n e c e s s a r i l y the c r y s t a l l o g r a p h i c axes) are r e l a t e d by a different p o l a r i z a b i l i t y tensor, ^-abc  =abc —abc  I f R i s the m a t r i x d e s c r i b i n g the t r a n s f o r m a t i o n from the m o l e c u l a r t o the c r y s t a l axes, then y  ,  —abc  =  R y = —xyz  and  E , = R E —abc = —xyz  S i n c e x, y, z and a, b, c are both o r t h o n o r m a l b a s e s , the t r a n s p o s e of R e q u a l s the i n v e r s e o f R, and t h e r e f o r e =R  t  y , —abc  = y  —xyz  =  a =xyz =  o r ,'  y  , —abc  =  (R= a=xyz R— )  and hence  a , —abc  =  a .„ =R =R =xyz  fc  R E, t  —abc  E—abc ,  t  The above t r e a t m e n t c o n s i d e r s o n l y one m o l e c u l e i n the u n i t c e l l .  However, p r o v i d e d the symmetry axes t h a t  r e l a t e the m o l e c u l e s i n the u n i t c e l l are c o n t a i n e d i n the o r t h o n o r m a l s e t a, b, c o n l y one m o l e c u l e need be c o n s i d e r e d , s i n c e the Raman s c a t t e r i n g depends o n l y on the square o f the matrix  element. b) S i n g l e C r y s t a l f l u o r e s c e n c e and  phosphorescence.  When an a r o m a t i c m o l e c u l e i n the vapor phase (except a t v e r y low p r e s s u r e s ) , i n s o l u t i o n o r i n a s i n g l e c r y s t a l i s e x c i t e d e l e c t r o n i c a l l y , any energy i n excess o f the ground  vibrational  17 l e v e l of the f i r s t excited  electronic  state i s rapidly  up as heat t o t h e s u r r o u n d i n g m o l e c u l e s .  given  Frequently the  r e m a i n i n g energy w i l l then be l o s t w i t h t h e e m i s s i o n o f a quantum o f t h e a p p r o p r i a t e f r e q u e n c y ; when t h e h i g h e r energy s t a t e i s a s i n g l e t l e v e l , t h e p r o c e s s i s known as f l u o r e s cence; t h e s p i n - f o r b i d d e n t r a n s i t i o n from a t r i p l e t l e v e l i s c a l l e d phosphorescence.  A t low temperature  the highest  energy quanta e m i t t e d a r i s e from t h e t r a n s i t i o n t o t h e ground v i b r a t i o n a l l e v e l o f t h e ground e l e c t r o n i c s t a t e . t r a n s i t i o n s a r e observed  t o v a r i o u s v i b r a t i o n a l l e v e l s o f the  ground s t a t e , and c e r t a i n m o l e c u l a r v i b r a t i o n a l can be found as energy d i f f e r e n c e s Selection  A t J  A  and  The i n state  t o t h e square o f t h e t r a n s i t i o n  , where P =  -AB ^  transitions.  l i n e i n spontaneous e m i s s i o n from  A to state B i s proportional moment u  frequencies  from t h e o r i g i n band.  rules for vibronic  tensity of a vibronic  Other  —  Z: q.r.  1 ^1—1  are eigenfunctions of the Hamiltonian f o r state A  and B, P i s t h e d i p o l e moment o p e r a t o r and t h e i n t e g r a l i s th over a l l space.  The i  l o c a t i o n i s determined  p a r t i c l e has charge q^ and i t s by t h e v e c t o r r ^ .  I n t h e Born-Oppenheimer  a p p r o x i m a t i o n t h e e l e c t r o n i c and n u c l e a r c o o r d i n a t e s a r e i n d e th pendent. Then t h e wave f u n c t i o n f o r t h e i vibrational th product l e v e l of the f e l e c t r o n i c s t a t e can be w r i t t e n as t h e f,i *f * f , i ¥  =  X  18 where ijj^ i s t h e e l e c t r o n i c wave f u n c t i o n f o r t h e e q u i l i b r i u m n u c l e a r c o n f i g u r a t i o n and \  f  • i s t h e v i b r a t i o n a l wave f u n c -  t i o n , depending o n l y on t h e n u c l e a r c o o r d i n a t e s .  Omission  of t h e r o t a t i o n a l wave f u n c t i o n i m p l i e s n e g l e c t o f t h e r o t a t i o n a l i n t e n s i t y d i s t r i b u t i o n w i t h i n each v i b r o n i c band. I f t h e d i p o l e moment, o p e r a t o r P can be separated, i n t o components P  e  f o r t h e e l e c t r o n s and P_ f o r t h e n u c l e i , N  then f o r t h e t r a n s i t i o n from v i b r a t i o n a l l e v e l i o f s t a t e f to v i b r a t i o n a l l e v e l j o f s t a t e Hfi  = # g j  (*fXfil£el Vgj)  g, +  (V<fi'*N  'Vgj)  I f t h e n u c l e a r d i p o l e moment depends o n l y on t h e v i b r a t i o n a l c o o r d i n a t e s then t h e second term w i l l f a c t o r t o g i v e  which equals  zero s i n c e t h e wave f u n c t i o n s f o r d i f f e r e n t  e l e c t r o n i c states are orthogonal. wave f u n c t i o n s ^ f r ^ g  a  r  e  Then i f t h e e l e c t r o n i c  independent o f s m a l l changes i n  n u c l e a r c o o r d i n a t e s t h e f i r s t term f a c t o r s t o g i v e <*f!  l* ) g  (Xfi  I  X  g j  )  Since only dipole-allowed t r a n s i t i o n s are being the f i r s t  term,  considered,  19 will  be n o n - z e r o o n l y  representations which  ^ f i ^ g j ^ the  like  %  x , y_  t h i s simple  and o  r  belong  totally  approximation,  I twill  the emission processes  transitions  non-excited  integral  i n totally fact  motion  theory  Since,  ground  symmetric v i b r a t i o n s interactions  i f the  as  stated  originate  state  from  states  and t o  should  be  between e l e c t r o n i c  was f i r s t  are frequently  discussed  only states  seen. and v i b r a -  a r e n o t i n s i g n i f i c a n t and l i n e s a r i s i n g  involved  among  and X^j c o n t a i n s  (and hence symmetric)  non-totally-symmetric vibrations The  of  considered  to the vibrationless  In tional  the overlap  be non-zero o n l y  symmetric representation.  vibrationally  excited  component  £•  product of the representations  earlier,  has a  d e t e r m i n e s how t h e i n t e n s i t y i s p a r t i t i o n e d  vibrational levels.  direct the  t o which  transforms In  i f the d i r e c t product o f t h e group  from  observed.  by Herzberg and  49 Teller p.  and c a n be found  405). Non-totally  mixing with to  bands a r i s i n g from proportional ground  states.  states  at higher  symmetry t y p e .  ( e . g .see r e f . appear  43,  through  energy which  The i n t e n s i t y o f  such n o n - t o t a l l y  belong vibronic  symmetric v i b r a t i o n s i s  t o t h e i n t e n s i t y o f the t r a n s i t i o n from t h e  to the perturbing  proportional  sources  symmetric v i b r a t i o n s  electronic  the appropriate  i n many  electronic  t o the separation  The l o w e s t e n e r g y  state  and  inversely  between t h e two i n t e r a c t i n g  states  of aromatic molecules a l l  20  involve  IT—TT  t r a n s i t i o n s which are p o l a r i z e d i n t h e m o l e c u l a r  plane.  T h e r e f o r e the symmetry o f the p e r t u r b i n g  vibration i s  g i v e n as the d i r e c t p r o d u c t o f the i r r e d u c i b l e spanned by the i n - p l a n e  t r a n s i t i o n moments.  representations  In naphthalene,  f o r example, the l o w e s t e x c i t e d s i n g l e t s t a t e has symmetry; the o t h e r i n - p l a n e so t h e n o n - t o t a l l y strongly  t r a n s i t i o n has  B  2 u  symmetry and  symmetric v i b r a t i o n s which appear most  i n f l u o r e s c e n c e have symmetry B  2 u  x B^  u  =  I f the t r a n s i t i o n from the f i r s t e x c i t e d  B  3g*  electronic  l e v e l t o the ground s t a t e i s symmetry a l l o w e d and appears s t r o n g l y , t o t a l l y symmetric v i b r a t i o n s dominate the v i b r a t i o n a l s t r u c t u r e ; i f the t r a n s i t i o n appears w e a k l y , t h e n the nont o t a l l y symmetric v i b r a t i o n s a r e more e a s i l y found.  I f the  pure e l e c t r o n i c t r a n s i t i o n i s symmetry f o r b i d d e n then the v i b r o n i c bands r e s u l t i n g from t h e p e r t u r b a t i o n  appear as f a l s e  o r i g i n s , w i t h t o t a l l y symmetric i n t e r v a l s b u i l t upon them. In the e v e n t t h a t the f l u o r e s c e n c e o r phosphorescence  spectra  are o b t a i n e d from s i n g l e c r y s t a l s , the p o l a r i z a t i o n o f the v i b r o n i c band w i t h r e s p e c t t o the c r y s t a l axes can be found and knowing the o r i e n t a t i o n o f the m o l e c u l e s i n the c r y s t a l , the symmetry o f the v i b r a t i o n i n v o l v e d  can be  deduced.  c) L i m i t a t i o n s o f the o r i e n t e d gas model. the o r i e n t e d spectra  Although  gas model i s v e r y u s e f u l i n i n t e r p r e t i n g the  o f s i n g l e c r y s t a l s i t i s o n l y an a p p r o x i m a t i o n , and  e v i d e n c e f o r the f a i l u r e o f the assumptions upon which i t i s  21  based i s o b v i o u s i n a l l s p e c t r a from a r o m a t i c s i n g l e The appearance, w i t h a p p r e c i a b l e i n t e n s i t y , o f  crystals.  fundamentals  which a r e symmetry f o r b i d d e n i n t h e f r e e m o l e c u l e i s n o t p r e d i c t e d by t h e o r i e n t e d gas model, a l t h o u g h t h e f a c t t h a t they do appear i s v e r y u s e f u l i n making f r e q u e n c y F u r t h e r e v i d e n c e o f t h e inadequacy  assignments.  o f t h e o r i e n t e d gas assump-  t i o n i s the general s h i f t i n v i b r a t i o n a l frequency  which  o c c u r s i n g o i n g t o t h e s o l i d s t a t e , and a l s o t h e s p l i t t i n g o f a non-degenerate vapor phase l i n e i n t o two o r more l i n e s i n single crystal spectra.  The i n a b i l i t y o f t h e o r i e n t e d gas  model t o e x p l a i n t h e s e f e a t u r e s i s due, o f c o u r s e , t o t h e f a c t t h a t i t n e g l e c t s t h e i n t e r a c t i o n s between m o l e c u l e s i n the c r y s t a l .  I f , however, t h e i n t e r m o l e c u l a r f o r c e s a r e  s m a l l compared w i t h t h e i n t r a m o l e c u l a r f o r c e s t h e c r y s t a l H a m i l t o n i a n can be b u i l t up as a sum o f f r e e - m o l e c u l e H a m i l t o n i a n s p l u s an i n t e r a c t i o n p o t e n t i a l . I n t h i s case t h e energy  l e v e l s of a c r y s t a l are  g i v e n by t h e e i g e n v a l u e s o f t h e H a m i l t o n i a n H  =  N £ (H k=l K  +  2 &>k  V, ) *  1.1  0  K  th where H^ i s t h e H a m i l t o n i a n f o r t h e k  m o l e c u l e and  is  the i n t e r a c t i o n o p e r a t o r between two o f t h e N m o l e c u l e s i n the c r y s t a l . V  £ k 5 -'ec  ua  The o r i e n t e d gas model corresponds  t o z  e  r  o  -  T  n  e  to setting  wave f u n c t i o n f o r t h e c r y s t a l when  each m o l e c u l e i s i n i t s ground s t a t e i s g i v e n by t h e p r o d u c t  22 of the m o l e c u l a r ground s t a t e wave f u n c t i o n s .  $  G  =  *11*12"  * ' *h,N/h  X  -  2  where h i s the number o f m o l e c u l e s i n each u n i t c e l l . th The z e r o - o r d e r  c r y s t a l wave f u n c t i o n when the p  th mi os l eg ci vu elne oby f the i *ip  t r a n s l a t i o n a l set i s excited to state r =  *11*12 ' ' - * i p ' ' -*h, N/h  There are N such w a v e f u n c t i o n s , a l l e i g e n f u n c t i o n s not o f E I V ^ . considered  The e i g e n f u n c t i o n s  I  -  3  o f EH^ b u t  when the p e r t u r b a t i o n i s  a r e formed as l i n e a r c o m b i n a t i o n s o f the d>. T  and  ip  the c r y s t a l symmetry determines which l i n e a r c o m b i n a t i o n s are appropriate.  The symmetry p r o p e r t i e s o f c r y s t a l s have been 50 summarized by Winston and H a l f o r d and a p p l i e d t o e l e c t r o n i c 51-53 spectra and t o v i b r a t i o n a l s p e c t r a (see, f o r example, the 54 summary by Dows ). The b r i e f o u t l i n e g i v e n here f o l l o w s the 55 54 t r e a t m e n t o f C r a i g and Walmsley and Dows. C r y s t a l symmetry. A l l symmetry o p e r a t i o n s o f a c r y s t a l together  form the f i n i t e space group i n t r o d u c e d 50  Winston and H a l f o r d .  by  They can be d i v i d e d i n t o two sub-  g r o u p s ; the t r a n s l a t i o n o p e r a t i o n s  form one subgroup and the  f a c t o r group a s s o c i a t e d w i t h i t completes the c r y s t a l symmetry operations.  The f a c t o r group, o f t e n c a l l e d the u n i t c e l l  23 group, i s isomorphous w i t h one o f t h e t h i r t y - t w o p o i n t groups possible i n crystals.  I t i s convenient a l s o t o define the  s i t e group, which i s t h e group o f a l l symmetry  operations  a c t i n g t h r o u g h any p o i n t , o r s i t e , i n t h e c r y s t a l ; when t h e s i t e i s chosen t o c o i n c i d e w i t h a m o l e c u l a r  p o s i t i o n i n the  c r y s t a l t h e s i t e group i s a subgroup o f t h e m o l e c u l a r  point  group as w e l l as o f t h e f a c t o r group. The  c r y s t a l Hamiltonian  has t h e f u l l symmetry o f  the f i n i t e space group; i t i s t h e r e f o r e d e s i r a b l e t o choose l i n e a r c o m b i n a t i o n s o f t h e ( J K ^ ( e q u a t i o n 1.3) which have i r r e d u c i b l e symmetry o f t h a t group s i n c e such c o m b i n a t i o n s w i l l n o t have any i n t e r a c t i o n terms c o n n e c t i n g  them.  To form  c o m b i n a t i o n s i r r e d u c i b l e i n t h e t r a n s l a t i o n subgroup t h e b a s i s f u n c t i o n s a r e p r o j e c t e d i n t o t h i s subgroup t o y i e l d ..  -  * *  £  s  i  - - * i p  i k * IT where t h e phase f a c t o r e and t h e v e c t o r r  c o n t a i n s t h e wave v e c t o r k  which d e f i n e s t h e s i t e o f e x c i t a t i o n .  However, t h e above l i n e a r c o m b i n a t i o n s do n o t , i n g e n e r a l , form i r r e d u c i b l e r e p r e s e n t a t i o n s o f t h e f a c t o r group and i t i s o n l y f o r c e r t a i n v a l u e s o f k factorization i s possible.  t h a t f u r t h e r symmetry  The v a l u e o f k o f g r e a t e s t i n t e r e s t  i n o p t i c a l t r a n s i t i o n s i s k = 0 s i n c e c o n s e r v a t i o n o f momentum demands t h a t k = c[ = 0, where c[ i s t h e wave v e c t o r o f t h e i n c i d e n t photon.  In t h i s case,  r  (0) =  &)  h  Z  <}>. . IP  1.5  r  r Linear  c o m b i n a t i o n s o f the above $^(0) can be found w h i c h  b e l o n g t o the i r r e d u c i b l e r e p r e s e n t a t i o n s  o f the f a c t o r  group; the number o f such l i n e a r c o m b i n a t i o n s i s e q u a l t o the number o f m o l e c u l e s i n the u n i t  cell.  The environment about a m o l e c u l e i n a c r y s t a l has, as a r u l e , l e s s symmetry t h a n the m o l e c u l e i t s e l f .  Therefore  when i n t e r a c t i o n s between a m o l e c u l e and i t s s u r r o u n d i n g s are t a k e n i n t o account the m o l e c u l e r e t a i n s o n l y t h o s e symmetry o p e r a t i o n s w h i c h appear i n i t s s i t e group. 29 Cross  have t a b u l a t e d  W i l s o n , D e c i u s and  c o r r e l a t i o n t a b l e s which r e l a t e the  symmetry s p e c i e s o f a group t o t h o s e o f i t s subgroups. correlation tables  f o r s p e c i f i c molecular point  The  groups,  f a c t o r groups and s i t e groups w i l l be i n t r o d u c e d l a t e r as they a r e needed. The r e s u l t s p r e d i c t e d are: Into  (1) a non-degenerate 'h  1  by such a f a c t o r group  analysis  l e v e l i n the vapor phase may  split  l e v e l s i n the c r y s t a l , where h i s the number o f  m o l e c u l e s i n the u n i t c e l l , and mentals and c o m b i n a t i o n s may  (2) i n a c t i v e m o l e c u l a r funda-  appear i n the c r y s t a l s p e c t r a  by  m i x i n g w i t h a c t i v e modes which c o r r e l a t e t o the same symmetry s p e c i e s o f the f a c t o r group.  Together w i t h a s h i f t from the  vapor phase f r e q u e n c y a r i s i n g from the e q u i l i b r i u m f i e l d o f the c r y s t a l l i n e environment, t h e s e two p r e d i c t i o n s  clarify  25 the o b s e r v a t i o n s mentioned e a r l i e r i n r e g a r d t o t h e breakdown o f t h e o r i e n t e d gas model. ^  The i n t e r a c t i o n o f p l a n e p o l a r i z e d l i g h t w i t h a  single crystal.  The p o l a r i z a t i o n p r e d i c t i o n s o f t h e o r i e n t e d  gas model have been d i s c u s s e d w i t h r e f e r e n c e o n l y t o a beam o f l i g h t p o l a r i z e d i n an a r b i t r a r y p l a n e .  In f a c t the d i r -  e c t i o n s o f p o l a r i z a t i o n o f a beam o f l i g h t moving through a c r y s t a l a r e n o t a r b i t r a r y , and some knowledge o f t h e o p t i c a l p r o p e r t i e s o f s i n g l e c r y s t a l s i s r e q u i r e d i n o r d e r t o s e t up the experiments The  and i n t e r p r e t t h e i r  aromatic molecules  results.  c o n s i d e r e d i n t h i s work form  b i a x i a l c r y s t a l s b e l o n g i n g t o the o r t h o r h o m b i c and m o n o c l i n i c systems.  U s u a l l y , a beam o f monochromatic l i g h t i n c i d e n t on  an a n i s o t r o p i c c r y s t a l w i l l be s p l i t by r e f r a c t i o n a t t h e s u r f a c e i n t o two r a y s  (the o r d i n a r y and e x t r a o r d i n a r y r a y s )  which t r a v e l i n d i f f e r e n t d i r e c t i o n s and which have t h e i r e l e c t r i c v e c t o r s p o l a r i z e d i n p l a n e s a t r i g h t a n g l e s t o one another.  A t any p o i n t i n an a n i s o t r o p i c c r y s t a l t h r e e m u t u a l l y  p e r p e n d i c u l a r axes X, Y, Z_ can be c o n s t r u c t e d , t h e s e b e i n g the p r i n c i p a l axes o f a t r i a x i a l e l l i p s o i d c a l l e d t h e indicatrix. determine  The o r i e n t a t i o n and magnitude o f these axes  the o p t i c a l p r o p e r t i e s of the c r y s t a l .  orthorhombic  F o r an  c r y s t a l these t h r e e d i r e c t i o n s c o i n c i d e w i t h t h e  c r y s t a l l o g r a p h i c axes a t a l l wavelengths.  In a monoclinic  system one o f t h e axes i s c o i n c i d e n t w i t h t h e symmetry a x i s  26  (b) o f t h e c r y s t a l b u t t h e o t h e r s can l i e anywhere i n the ac p l a n e and must be l o c a t e d e x p e r i m e n t a l l y ; i n a d d i t i o n t h e position  o f t h e two axes i n t h e ac p l a n e can change w i t h  wavelength. A plane p o l a r i z e d  r a y normal t o a c r y s t a l  surface  which c o n t a i n s two o f t h e i n d i c a t r i x axes w i l l pass  through  the c r y s t a l w i t h o u t r e f r a c t i o n .  This i d e a l s i t u a t i o n i s less  common, p a r t i c u l a r l y f o r m o n o c l i n i c c r y s t a l s , than t h e o r i e n t a t i o n shown i n F i g u r e 3.  C  1  Z  F i g u r e 3. The ab f a c e o f a m o n o c l i n i c c r y s t a l showing the o r i e n t a t i o n o f t h e axes X, Y, "L_ o f t h e i n d i c a t r i x . The a x i s c' i s d e f i n e d t o be normal t o t h e ab p l a n e .  27 In F i g u r e 3 i s shown a c r y s t a l f a c e c o n t a i n i n g o n l y one (X) o f t h e t h r e e p r i n c i p a l axes; t h e o t h e r two axes l i e obliquely polarized  t o the face.  L i g h t t r a v e l l i n g along c  1  and  p a r a l l e l t o b w i l l t r a v e l through t h e c r y s t a l un-  d e v i a t e d , g i v i n g r i s e t o the o r d i n a r y ray.  The d i f f i c u l t y  a r i s e s when l i g h t p r o p a g a t i n g i n t h e same d i r e c t i o n has i t s e l e c t r i c v e c t o r p a r a l l e l t o a; t h i s s i t u a t i o n was  recently  d i s c u s s e d by R o h l e d e r and L u t y ^ who p o i n t e d o u t t h a t t h e a c t u a l p a t h o f such a beam through t h e c r y s t a l was determined by b o t h t h e o r i e n t a t i o n refractive indices  o f Z_ and Y and t h e magnitudes of t h e  i n these d i r e c t i o n s .  In c a l c u l a t i n g the  t h e o r e t i c a l p o l a r i z a t i o n r a t i o s i n the oriented  gas a p p r o x i -  m a t i o n t h e a c t u a l p a t h o f such a r a y (the e x t r a o r d i n a r y r a y ) s h o u l d be d e t e r m i n e d .  U n f o r t u n a t e l y , no i n f o r m a t i o n about t h e  o p t i c a l properties of the c r y s t a l s i n the i n f r a r e d region i s available. the  spectral  Due t o t h e p o s s i b i l i t y o f d i s p e r s i o n  of  i n d i c a t r i x i n m o n o c l i n i c c r y s t a l s and t h e p r o b a b l e changes  i n the r e f r a c t i v e indices no p r e d i c t i o n  o f t h e e f f e c t on t h e p o l a r i z a t i o n r a t i o s i n t h e  i n f r a r e d can be made. the d e v i a t i o n  f o r a l l c r y s t a l s w i t h wavelength,  However, any c o r r e c t i o n  a r i s i n g from  o f t h e e x t r a o r d i n a r y r a y i s e x p e c t e d t o be  s m a l l and need be c o n s i d e r e d o n l y when t h e p o l a r i z a t i o n approaches u n i t y cussed  later).  (see,  ratio  f o r example, t h e case o f pyrene d i s -  28 4.  Choosing Fundamentals from the Symmetry A s s i g n e d L i n e s Once a l l the v i b r a t i o n a l f r e q u e n c i e s o f a m o l e c u l e  have been l o c a t e d and the a s s o c i a t e d v i b r a t i o n c l a s s i f i e d as t o symmetry t y p e the f i n a l s t e p i n making an assignment i s t o choose from a l l the l i n e s t h o s e which c o r r e s p o n d t o normal modes.  I n p r i n c i p l e , i t s h o u l d be p o s s i b l e t o a s s i g n a l l  l i n e s as b e i n g a s s o c i a t e d w i t h e i t h e r a fundamental v i b r a t i o n , an o v e r t o n e o r a c o m b i n a t i o n o f f u n d a m e n t a l s .  In p r a c t i c e ,  the number o f p o s s i b l e c o m b i n a t i o n s and o v e r t o n e s i s u s u a l l y f a r t o o l a r g e and such a complete assignment i s n o t p o s s i b l e e x c e p t a t v e r y low f r e q u e n c y .  C o m b i n a t i o n l i n e s appear by  s t e a l i n g i n t e n s i t y from nearby fundamentals e i t h e r by an intramolecular interaction  (e.g. anharmonic terms i n the  p o t e n t i a l f u n c t i o n ) o r , p a r t i c u l a r l y i n the s o l i d s t a t e , by intermolecular interactions.  The i n t e r a c t i o n s a r e s m a l l so  the s t o l e n i n t e n s i t y w i l l be a p p r e c i a b l e o n l y i f the e n e r g i e s o f the two s t a t e s i n v o l v e d a r e n e a r l y i d e n t i c a l . method o f a s s i g n i n g fundamentals i s the f o l l o w i n g :  Thus the starting  a t low f r e q u e n c y a l l l i n e s a r e a s s i g n e d as fundamentals o r c o m b i n a t i o n s u n t i l the number o f l i n e s a p p e a r i n g makes t h i s impossible.  Then fundamentals a r e chosen on the b a s i s o f  t h e i r s t r e n g t h and i s o l a t i o n from o t h e r s t r o n g l i n e s . o f c o u r s e , p o s s i b l e t h a t a symmetry a l l o w e d fundamental  It i s , may  a c c i d e n t a l l y have no i n t e n s i t y , o r t h a t two normal modes may be a c c i d e n t a l l y d e g e n e r a t e , and thus c a r e may be needed i n  29 a s s i g n i n g the l a s t fundamentals o f a g i v e n symmetry t y p e . The T e l l e r - R e d l i c h p r o d u c t r u l e (see r e f . 1) can be used as a g u i d e t o i n d i c a t e the energy r e g i o n i n w h i c h t o s e a r c h f o r the l a s t one o r two u n a s s i g n e d fundamentals o f a symmetry b l o c k i f i n f o r m a t i o n i s a v a i l a b l e about the f u n d a m e n t a l s o f more than one i s o t o p i c s p e c i e s . relating  the f r e q u e n c i e s o f i s o t o p i c a l l y  Other r u l e s  substituted deriva-  57 58 tives exist,  '  but o n l y i n f r e q u e n t l y i s s u f f i c i e n t  m a t i o n a v a i l a b l e t o make them u s e f u l .  infor-  I t i s occasionally  v a l u a b l e as a check on the f i n a l assignment t o use the fundam e n t a l f r e q u e n c i e s o f the m o l e c u l e t o c a l c u l a t e c e r t a i n thermodynamic f u n c t i o n s (such as the h e a t c a p a c i t y and e n t r o p y ) f o r comparison w i t h e x p e r i m e n t a l l y determined values.  Once a g a i n , however, complete e x p e r i m e n t a l  mation i s o f t e n not a v a i l a b l e .  infor-  CHAPTER I I EXPERIMENTAL  A.  P r e p a r a t i o n o f Samples  1.  Source o f c h e m i c a l s a) Naphthalene.  The naphthalene-hg used was s u p p l i e d  by t h e May and Baker Co., L t d . , E n g l a n d , and was p u r i f i e d by zone r e f i n i n g .  The naphthalene-dg used was c e r t i f i e d 99%  d e u t e r i u m c o n t e n t from t h e S t o h l e r I s o t o p e Chemicals Co., Montreal.  I t was s u b j e c t e d t o 100 passes on t h e z o n e - r e f i n e r ,  d u r i n g which a dark brown i m p u r i t y s e p a r a t e d and t r a v e l l e d t o the bottom o f t h e column. the  Mass s p e c t r o s c o p i c a n a l y s i s o f  r e m a i n i n g sample showed t h a t a p p r o x i m a t e l y 20% o f t h e  m o l e c u l e s c o n t a i n e d one hydrogen atom; i f  c  I Q  D  7  H  I  -*-  S  T  N  E  major i m p u r i t y then t h e f i n a l d e u t e r i u m c o n t e n t . i s i n f a c t about 98%. b) A n t h r a c e n e . e s c i n g anthracene-h^Q  Eastman-Kodak b l u e - v i o l e t  was used a f t e r zone r e f i n i n g .  single c r y s t a l of h i g h l y - p u r i f i e d  fluorA large  a n t h r a c e n e - d ^ ^ was k i n d l y  s u p p l i e d by Dr. D.F. W i l l i a m s o f t h e N a t i o n a l Research C o u n c i l . The monoprotonated  i m p u r i t y was found t o make up about 22%  of t h e sample, c o r r e s p o n d i n g t o a d e u t e r i u m c o n t e n t o f approximately  97.8%.  30  31 c) Acenaphthene. aphthene was  Eastman-Kodak w h i t e - l a b e l acen-  chromatographed 59  c r i b e d by S a n g s t e r  according  t o the method des-  on s i l i c a g e l u s i n g p e t r o l e u m e t h e r  as  an e l u a n t . d) Pyrene.  Eastman-Kodak pyrene-h^g 59  graphed by S a n g s t e r ' s method e t h e r , and was finer.  was.chromato-  u s i n g s i l i c a g e l and p e t r o l e u m  then s u b j e c t e d t o 100 passes on the zone r e -  Pyrene-d^g  was  s u p p l i e d by Merck, Sharp and Dohme o f  M o n t r e a l and was p u r i f i e d by M i s s V. V i l k o s ; the sample was e l u t e d onto a s i l i c a g e l column and developed w i t h p e t r o l e u m e t h e r , and t h e n e l u t e d from the column and  recrystallized  t w i c e i n a 1:4 V/V p e t r o l e u m ether:benzene m i x t u r e . s p e c t r o s c o p i c a n a l y s i s showed s l i g h t l y l e s s than 17% e) S o l v e n t s .  Mass c  ig 9 ^' D  H  F i s h e r s p e c t r o q u a l i t y benzene and  carbon t e t r a c h l o r i d e were used w i t h o u t f u r t h e r p u r i f i c a t i o n , as were Matheson, Coleman and B e l l s p e c t r o - g r a d e normal hydrocarbon s o l v e n t s . 2. Growth o f s i n g l e c r y s t a l s S i n g l e c r y s t a l s were grown i n a l a r g e , g l a s s - w a l l e d Bridgman f u r n a c e by slow s u b l i m a t i o n i n vacuum, from s o l u t i o n , o r , when t h i n c r y s t a l s were adequate, by r a p i d s u b l i m a t i o n i n an i n e r t atmosphere o f carbon d i o x i d e .  The  cleavage  f a c e s o f l a r g e i n g o t s were r e a d i l y l o c a t e d and i d e n t i f i e d by 60 isogyre patterns u s i n g o p t i c a l d a t a summarized by  Winchell  or a v a i l a b l e i n the l i t e r a t u r e .  normal t o a c l e a v a g e p l a n e were needed.  Often sections  The i n t e r s e c t i o n o f  the d e s i r e d f a c e o f t h e c r y s t a l w i t h t h e c l e a v a g e p l a n e was found and t h e c r y s t a l was c u t normal t o t h e c l e a v a g e p l a n e and p a r a l l e l t o t h i s f a c e . was  When such a f a c e was p r e p a r e d i t  p l a c e d on a smooth s u r f a c e i n a d r i l l e d - o u t d i s k o f t h e  required thickness  (0.15  t o 1.0 mm) and h e l d i n p l a c e by  plaster of P a r i s .  When t h e p l a s t e r s e t , t h e u n f i n i s h e d  side  of t h e c r y s t a l was s l o w l y ground w i t h f i n e emery paper. F i n a l p o l i s h i n g was c a r r i e d o u t on a g l a s s p l a t e c o v e r e d w i t h a s o f t t i s s u e paper and dampened w i t h a s u i t a b l e s o l v e n t , e.g.  benzene, a c e t o n e , e t c . When p o l i s h i n g was complete t h e o p t i c a l d i r e c t i o n s  o f t h e s e c t i o n were l o c a t e d w i t h a p o l a r i z i n g m i c r o s c o p e and the sample was p l a c e d on a mount s u i t a b l e f o r t h e Raman o r i n f r a r e d i n s t r u m e n t t o be used.  The t r a n s m i s s i o n e f f i c i e n c y  o f p o l a r i z e d l i g h t through a s p e c t r o m e t e r v a r i e s w i t h wave62 length  and depends on t h e a n g l e between t h e e l e c t r i c  vector  of t h e i n c i d e n t l i g h t and t h e g r a t i n g r u l i n g ; t o e l i m i n a t e t h i s e f f e c t a l l c r y s t a l s e c t i o n s were mounted w i t h  their  o p t i c a l d i r e c t i o n s a t 45° on each s i d e o f t h e v e r t i c a l .  33 B.  S p e c t r o m e t e r s and A c c e s s o r i e s I n f r a r e d s p e c t r a were measured on P e r k i n - E l m e r  model 301 and 421 i n f r a r e d s p e c t r o m e t e r s . was  The model 421  used f o r t h e r e g i o n between 3200 and 400 cm " .  r e g i o n from 700 t o 50 cm  t h e model 301 was used; i t has a  Golay d e t e c t o r , a g l o b a r source and a, h i g h - p r e s s u r e 160 cm  In the  L  f o r e n e r g i e s above 160 cm ^  mercury lamp source  f o r e n e r g i e s below  The r o t a t i o n a l spectrum o f water below 400 cm ^  c o n t a i n s many s t r o n g l i n e s and t h e a i r i n t h e model 301 was c i r c u l a t e d c o n t i n u o u s l y t h r o u g h a d r i e r t o remove t h e water vapor.  The frequency  accuracy  of the spectrometers  was - 1  cm ^ and w i t h t h e p o s s i b l e e r r o r s i n measurement o f t h e l i n e p o s i t i o n t h e f r e q u e n c i e s r e p o r t e d here were p r o b a b l y ate t o w i t h i n * 3 cm  accur-  The s p e c t r a l s l i t w i d t h v a r i e d o v e r  the range o f i n t e r e s t b u t was always l e s s than 4 era ^ and below 400 cm The  was about 1 era \ i n c i d e n t r a d i a t i o n was p o l a r i z e d w i t h P e r k i n -  Elmer g o l d - w i r e g r i d p o l a r i z e r s — o n a s i l v e r bromide subs t r a t e f o r t h e r e g i o n above 300 cm the r e g i o n below 500 cm  and, on p o l y e t h y l e n e f o r  Low frequency  s o l u t i o n measure-  ments were made i n an a d j u s t a b l e p a t h l e n g t h c e l l  (1,5 and  10 mm) f i t t e d w i t h h i g h - d e n s i t y p o l y e t h y l e n e windows. The  Raman s c a t t e r i n g a t r i g h t angles from s i n g l e  c r y s t a l s o f a n t h r a c e n e - d . ^ e x c i t e d by an a r g o n - i o n  l a s e r was  f o c u s e d i n t o a Spex model 1700-11 (3/4 meter, f/6) s p e c t r o -  34 meter/spectrograph.  An RCA1P2 8 p h o t o m u l t i p l i e r a t t h e e x i t  s l i t was a t t a c h e d t o a p h a s e - s e n s i t i v e d e t e c t o r tuned t o t h e frequency  o f a chopper i n t h e l a s e r beam.  The l a s e r , model  300 PV o f t h e Orlando Research C o r p o r a t i o n , F l o r i d a , was operated  a t maximum o u t p u t i n t e n s i t y  4879.9A.  ( n o m i n a l l y 50 mw) a t  D i f f i c u l t i e s were e x p e r i e n c e d  due t o t h e h i g h i n -  t e n s i t y o f t h e e x c i t i n g r a d i a t i o n s c a t t e r e d from i m p e r f e c t i o n s i n t h e c r y s t a l s and t h e i n a b i l i t y o f t h e s p e c t r o m e t e r separate  t h i s l i g h t from t h e Raman-scattered  to  radiation.  A n o t h e r complete s e t o f s p e c t r a o f a n t h r a c e n e - d ^ ^ and a l l o t h e r Raman measurements were made on a Cary 81 Raman s p e c t r o meter equipped w i t h a S p e c t r o p h y s i c s model 125 helium-neon laser.  The o p t i c a l system s e l e c t e d l i g h t s c a t t e r e d c o -  a x i a l l y w i t h t h e e x c i t i n g beam. were e s t i m a t e d  The observed  t o be a c c u r a t e t o t 3 cm  frequencies  \  Raman s p e c t r a o f m o l t e n samples c o n t a i n e d vacuum i n a 6 mm O.D. g l a s s tube were measured. was  under  The tube  i n c l i n e d a t 45° t o t h e v e r t i c a l so t h a t o n l y a s m a l l  amount o f m a t e r i a l was needed.  The lower end had been c l o s e d  and blown i n such a way as t o p r o v i d e a n e a r l y - f l a t  surface  p a r a l l e l t o the c o l l e c t i n g lens of the instrument.  Heating  was  a c h i e v e d by a p p l y i n g a s u i t a b l e v o l t a g e t o chromel  h e a t i n g w i r e wound around t h e tube and h e l d i n p l a c e w i t h Sauereisen  cement.  S m a l l e r s p a c i n g s between t h e w i r e s a t  the upper end p r e v e n t e d  t h e samples from r e f l u x i n g i n t h e  35  tube.  I t was  found  that with molten  in  the tube  of  the spherical lens  heating  i t s t i pcould  be k e p t  anthracene  f o r long  of the spectrometer  periods without  217°C)  within I  mm  appreciably  the lens.  C.  C r y s t a l Data and O p t i c a l P r o p e r t i e s  1.  Naphthalene Crystal  b  (m.p.  data  = 5 . 9 5 , c = 8.68 A ,  2 molecules/unit  cell;  63 U J  6=  m.p.  80.2°C; m o n o c l i n i c  122.1°.  a =  space group P 2 i / a  p e r f e c t cleavage  ab  8.29,  (C^ ); h  plane.  61 Optical ac;  the acute  within  properties.  bisectrix,  a  cosines  from  c and  plane i s  contained  angle. relating  molecular  and c r y s t a l  0.8410  -0.4350  0.3217  -0.4428  -0.2128  0.8709  Y.  0.3102  0.8750  0.3718  z  0.8951  -0.0534  0.4424  -0.0477  0.9756  0.2143  y_ a n d z_ a r e d e f i n e d  according  N  b  £'  =  a* c* X ~ / x,  Z_, i s 9.5°  the obtuse monoclinic Direction  The o p t i c a x i a l  X  axes  t o t h e i n t e r n a t i o n a l conven-  64 tion  with  y_ a n d z_ t h e l o n g  and s h o r t  in-plane  axes r e s p e c t i v e l y ,  36 c' i s the c r y s t a l d i r e c t i o n  normal t o a and b, and a*  c* are the p r i n c i p a l o p t i c a l d i r e c t i o n s  for visible light i n  the ac p l a n e , a* b e i n g the obtuse and c* the acute 2.  and  bisectrix.  Anthracene Crystal  d a t a . m . p . 217°C; m o n o c l i n i c a = 8.561,  b = 6.036, c = 11.163 A, 6 = 124°42'.  Space group  P2 /a 1  ( C ) ; 2 m o l e c u l e s / u n i t c e l l ; P e r f e c t c l e a v a g e ab; a 61 c l e a v a g e ac was never observed i n t h i s work. 6i  secondary  2 h  Optical  data.  The o p t i c  a x i a l p l a n e i s ac w i t h  the acute b i s e c t r i x , Z_, almost p a r a l l e l t o c, and w i t h i n the obtuse m o n o c l i n i c a n g l e .  The  contained  angle Z_ A c  was  found t o be about 2° l e s s than the p r e v i o u s l y r e p o r t e d * ^  7.5°.  The a x i s c' i s normal t o both a and b and the a x i s a' i s normal t o both b and  c.  D i r e c t i o n c o s i n e s r e l a t i n g m o l e c u l a r and c r y s t a l axes ' 0.8059 -0.4960 -0.3234 V  f-1 b c' a' c  =  -0.4347  -0.1248  -0.8919  Z  0.4020  0.8953  -0.3162  z  0.8914  0.0814  -0.4457  -0.1283  0.9989  -0.0759^  The axes are d e f i n e d i n F i g u r e 4. 3.  Acenaphthene  66 C r y s t a l data. m.p. 95°C; orthorhombic a = 8.290, o 2 b = 14.000, c = 7.225 A. The space group i s Pcm2i (C_ ) i n  37  C'  F i g u r e 4. The anthracene u n i t c e l l : (a) the ac f a c e showing the axes a' (normal t o c) and c' Tnormal t o a) and the p r o j e c t i o n o f the anthracene m o l e c u l e . The b a x i s i s normal t o the ac p l a n e ; (b) the ab f a c e o f the anthracene u n i t c e l l .  which a m o l e c u l a r ( & — ) . plane coincide.  and a c r y s t a l l o g r a p h i c ( o — )  mirror  The f o u r m o l e c u l e s i n each u n i t c e l l f a l l  into  two independent s e t s ; m o l e c u l e s I and I I b e l o n g t o one s e t and III  and IV t o the o t h e r . P e r f e c t a£ c l e a v a g e , good ab c l e a v a g e . 67 O p t i c a l data.  the a c u t e b i s e c t r i x , Z = b.  The o p t i c a x i a l p l a n e i s be, w i t h  38 D i r e c t i o n c o s i n e s r e l a t i n g m o l e c u l a r and c r y s t a l axes Molecular type a I  b  =  c  v III  b c  =  0.0000  0.0000  1.0000  0 .0000  1.0000  0.0000  1.0000  0.0000  0.0000  z  -0.8787  0.0000  0.4744  x  O.QOOO  1.0000  0.0000  Z  0.4744  0.0000  0.8787  z  X  The d i r e c t i o n c o s i n e s o f m o l e c u l e s I I and IV can be found by c a r r y i n g o u t t h e o p e r a t i o n c o r r e s p o n d i n g t o a screw r o t a t i o n C^- on t h e d i r e c t i o n c o s i n e s o f I and I I I r e s p e c t i v e l y .  See  F i g u r e 5 f o r t h e d e f i n i t i o n o f m o l e c u l a r axes and numbering.  F i g u r e 5. The acenaphthene u n i t c e l l ; m o l e c u l e s I and I I a r e r e l a t e d by C^/ as a r e m o l e c u l e s I I I and I V .  39  4.  Pyrene 68 Crystal  b = 9.26, c =  data.  cell;  Optical  data.  where c*, t h e acute i n t h e ac plane  optical c  1  150°C; m o n o c l i n i c ,  8.47 A , 3 = 1 0 0 . 2 8 ° .  4 molecules/unit  c  m.p.  direction,  p e r f e c t ab 69  (see Figure  group  axial  P2 /a (C^) • 1  plane  makes an a n g l e 6) a n d a * , t h e  makes an a n g l e  13.65,  cleavage.  The o p t i c  bisectrix,  i s normal t o both  Space  a =  i s be*,  o f 34.3°  third  o f 24.0° w i t h  a.  with  principal The a x i s  a and b.  a' a*  F i g u r e 6. (a) The u n i t c e l l o f t h e p y r e n e c r y s t a l , (b) O r i e n t a t i o n o f m o l e c u l a r a x e s a n d o p t i c a l d i r e c t i o n s i n t h e ac p l a n e .  40  Direction crystal  cosines  relating  the molecular  axes '-0.6428  0.5976  0.4863  0.7466  0.6280  0.2232  0.1736  -0.5000  0.8434  a*  -0.6572  0.7504  0.0961  c*  -0.1084  -0.2089  0.9733  f a  >  b c'  =  N  and  CHAPTER I I I THE V I B R A T I O N S OF N A P H T H A L E N E  Introduction 1.  Critical  review 14  A recent investigation obtained  from  single  crystals  o f t h e Raman  o f naphthalene-hg  a seemingly  secure experimental assignment  fundamental  vibrations,  infrared  spectrum  spectra has l e dt o  o f the gerade  and t h e i n t e r p r e t a t i o n  has been a i d e d by r e c e n t l y  o f t h e crowded  published c a l -  41 culations of the planar fundamentals. The v i b r a t i o n a l s p e c t r a o f naphthalene-dg have been s t u d i e d i n l e s s detail^  8,10,12  assignments  s  the  involved  between t h e e x p e r i m e n t a l  34 3 5 4 1 70 on c a l c u l a t e d f r e q u e n c i e s ' ' ' 7 8 12 ' '  out using mercury-arc  o f naphthalene-dg  excitation  and have  samples i n t h e m e l t o r i n t h e form o f powdered  One a i m o f t h e p r e s e n t w o r k  polarized  single  differences  P r e v i o u s Raman s t u d i e s  have been c a r r i e d  crystals.  veral  and those based  have a r i s e n .  all  e  Raman s p e c t r a ,  crystals  using  has been t o measure  laser  excitation,  of perdeuterated naphthalene  f u n d a m e n t a l modes. 41  from  to assign  the g  42  The complex i n f r a r e d spectrum has been g i v e n v a r i o u s 6 — 10  i n t e r p r e t a t i o n s by d i f f e r e n t a u t h o r s ; t h e assignments have been made, i n g e n e r a l , from band c o n t o u r s i n t h e gas phase, 6 from s o l u t i o n s p e c t r a , o r from p o l a r i z e d 6 ' 8 ' 9 o r even 7  10  unpolarized ' B  2 u  s p e c t r a o f t h e ab f a c e o f s i n g l e  crystals.  bands a r e weak i n t h e ab f a c e and were a s s i g n e d on t h e  b a s i s o f t h e i r i n c r e a s e d r e l a t i v e s t r e n g t h i n t h e vapor o r l i q u i d phases.  Thus a second aim o f t h e p r e s e n t work was t o  r e c o r d t h e p o l a r i z e d i n f r a r e d s p e c t r a from t h e ac f a c e o f naphthalene-dg c r y s t a l s i n an attempt t o more f i r m l y the c - p o l a r i z e d B  2 u  bands.  locate  In a d d i t i o n , the p o l a r i z e d  s p e c t r a o f b o t h t h e ac and t h e ab f a c e s were extended t o low f r e q u e n c y t o v e r i f y t h e e a r l i e r assignments based on u n p o l a r i z e d s p e c t r a " ^ and t o l o c a t e t h e l a t t i c e v i b r a t i o n s .  The  low f r e q u e n c y i n f r a r e d s p e c t r a o f t h e ab and p r e v i o u s l y uns t u d i e d ac f a c e s o f naphthalene-hg were a l s o r u n . 2.  S e l e c t i o n Rules The naphthalene m o l e c u l a r axes were chosen a c c o r 64  ding t o the i n t e r n a t i o n a l convention  (see Chapter I I ) .  A l t h o u g h t h e naphthalene m o l e c u l e may be s l i g h t l y  distorted  0 J  i n the c r y s t a l , i t i s a s u f f i c i e n t l y close approximation t o assume t h a t i t r e t a i n s i t s f u l l D ' symmetry. 2n  The f a c t o r  group i s C ^ and t h e naphthalene m o l e c u l e i s l o c a t e d i n t h e 2  c r y s t a l a t a s i t e h a v i n g C^ symmetry.  43  Table  1.  Correlation  Molecular  table  group  D2h  f o r naphthalene  Site C  N  Bases  9  xx, yy, zz  3  xy_  B  4  xz  B  8  yz  B  group  Factor  i  group  '2h Bases  4  n  I aa, bb,  ig  ab,  2g  be  3g  u B  8 8  Y  B  4  x  B  lu 2u  A  u  *u J  u  b a,  2 c  1  3u  N i s t h e number o f f u n d a m e n t a l s i n t h e f r e e m o l e c u l e and n i s t h e n u m b e r o f l a t t i c e f r e q u e n c i e s h a v i n g k = 0. F a c t o r group symmetry s p e c i e s a r e d i s t i n g u i s h e d by t h e use of lower case symbols.  44  The the  selection  rules  c r y s t a l a r e summarized  state  gives  molecule  states  (Raman a c t i v e )  m o l e c u l e , may m i x w i t h  which  they  factor  state,  symmetry b l o c k  4  6  g '  B  3g'  vibrations  4  the  section  various  which  given  the polarization  i ti s i n t e r a c t i n g .  i n Table  6  B  modes a r e e x p e c t e d  and so below  l u '  1.  The  t h e wave  6  B  2u  a  n  d  4  2 0 0 0 cm B  3u  f  u  n  d  i n each  7 A ,  3  g  a  m  e  n  t  a  in-  B l  g  r  l  appear.  the usual  oriented-gas  assumption  cosines  (Chapter  and c r y s t a l axes determine  of a molecular c r y s t a l faces;  The  projected  the  same a p p r o x i m a t i o n  presented  i n t h e c r y s t a l and  i s made f o r t h e c a s e w h e r e  B.3) t h e d i r e c t i o n  molecular  sities  u'  should In  I,  A  i n the free  zero.  plane 2  with  molecular  inactive  spectrum with  are also  Two CH s t r e t c h i n g  B  b u t because the  An A  u  molecule  modes a n d t h e c r y s t a l d i r e c t i o n i n  analysis  k, e q u a l s  free  and f o r  i n the c r y s t a l , mixing  other u states  are expected  group  vector,  Each  (infrared active)  of the state  number o f l a t t i c e  molecule  and u  appear i n the i n f r a r e d  characteristics The  1.  a t a c e n t e r o f symmetry  does n o t occur.  t h u s may  i n Table  r i s e t o two c r y s t a l s t a t e s ,  sits  between g  f o rthe free  line  i n t h e Raman  the results  (see Chapter II) relating  the relative spectra  are given  from t h e  i n Table  intensities of the infrared-active are listed  i n this thesis  i s based  i n Table  3.  inten-  2.  modes i n  The  on t h e assumption  analysis that  the  45  polarization mixing  Table  ratios  of molecular  2.  a r e n o t so d i s t u r b e d by the c r y s t a l s t a t e s as t o be  The o r i e n t e d - g a s  naphthalene  i n various crystal configurations  0.500  0.036  0.038  ^,, , 0 . 0 0 9  I  of the relative  of free-molecule  I  xx  predictions  intensities  I (A_) y_y_ g  I  reversed.  (A ) 9 CT  of  I (B ) gy_ l g  I (B_ ) xz 2g  I (B. ) y_z_ 3 g  0.011  0.535  0.293  0.078  0.002  0.575  0.036  0.595  0.137  0.586  0.019  0.295  0.053  0.423  zz  (A ) <3  Raman l i n e s  a  1  aa I.. DP  c  I  b  I.  0.139  0.009  0.078  0.000  0.348  0.200  . 0.018  0.035  0.105  0.206  0.011  0.466  0.642  0.000  0.038  0.009  0.627  0.002  : * *0.000 c*c*  0.906  0.002  0.009  0.000  0.175  : * *0.002 a*c*  0.003  0.009  0.767  0.029  DC  a* a*  -  0.176  46  Table 3.  The oriented-gas p r e d i c t i o n s o f the r e l a t i v e i n t e n s i t i e s of the i n f r a r e d naphthalene along v a r i o u s  I  active l i n e s of  c r y s t a l axes  B, (z) lu —  B  0.104  0.189  0.707  0.758  0.045  0.196  0.138  0.766  0.096  0.196  0.003  0.801  0.046  0.952  0.002  2u ^ (  B  (x) 3u — 0  a Z  b  v V  B.  Results  1.  The Raman Spectra The  Raman s p e c t r a are shown.in F i g u r e s 7 and 8 and  the f r e q u e n c i e s l i s t e d i n Tables 4 and 5.  The weaker l i n e s  are b e s t seen i n F i g u r e 8 where the d e t e c t o r s e n s i t i v i t y i s about f i v e times g r e a t e r than i n F i g u r e 7.  The s p e c t r a l  slit  47  (0*0*)  \. 1Ll 1  1  0  1  l  l  I  1  200  i  I  1  1  400  —l  1  i  i  1  1  600  l  1  800  \  i  1  1  1  1 1  1  (c*c*)  «  i  i  ]  1  IOOO  A  '  1  1200  , i  1  /  I4CO  1  I 1 // „ 1  A ]  I A A ,  1600  2200  WAVENUMBER (CM ) -1  F i g u r e 7. The Raman s p e c t r a o b t a i n e d from t h e ac f a c e o f naphthalene-dg. The n o t a t i o n i s d e f i n e d i n T a b l e 4.  w i d t h o f t h e Cary 81 s p e c t r o p h o t o m e t e r v a r i e d o v e r t h e range of o b s e r v a t i o n b u t was n o r m a l l y  l e s s than 5 cm ^ and i n  complex r e g i o n s t h e s p e c t r a were r e p e a t e d w i t h c o n s i d e r a b l y narrower s l i t s .  I t was found t h a t t h e 831 and 838 cm"*" l i n e s ,  which were s e p a r a t e d solution.  -  i n t h e c r y s t a l , c o u l d n o t be r e s o l v e d i n  No attempt was made t o c o r r e c t f o r v a r y i n g d e t e c t o r  48  F i g u r e on f o l l o w i n g page. F i g u r e 8.  The  Raman s p e c t r a o b t a i n e d from the ab  be' f a c e s o f naphthalene-dg. d e f i n e d i n T a b l e 4. approximately  The  and  notation i s  The d e t e c t o r s e n s i t i v i t y i s  f i v e times g r e a t e r than f o r the  s p e c t r a shown i n F i g u r e  7.  WAVENUMBER (CM"')  50 T a b l e 4.  The Raman s p e c t r a  near t h e e x c i t i n g l i n e  from  c r y s t a l s o f naphthalene-dg'f  (a*a*)  (c*c*)  (a*c*)  (aa)  (bb) (c'c')  (ab) (be' ) Symmetry 43 mw 43 mw  49 w  49 s  bg  49 vw 49 ms  a 68 vw 70 ms  70 v s 102 s  102 mw  70 w 102 m  bg  70 vs  102 m  a a  117 mw  g  g  g bg  The two c r y s t a l d i r e c t i o n s w i t h i n p a r e n t h e s e s a t t h e t o p o f each column d e f i n e t h e d i r e c t i o n o f p o l a r i z a t i o n o f t h e i n c i d e n t and s c a t t e r e d r a d i a t i o n r e s p e c t i v e l y .  Table  Av(cm  5.  - 1  )  Relative  p+  162  line  strengths  i n t h e Raman  s p e c t r a o f naphthalene-d„  (a*a*)  (c*c*)  (a*c*)  (aa)  (bb)  —  —  --  —  lh  h h  1  h  348  0.75  410  0.8  494  0.40  43  6  6  547  0.80  h  2  lh  2h  h  l  h  649 697  0.23  761  0.8  4  (c'c')  3  1  h  lh  8  3  1  0  5  58  3  lh  862  0.70 0.20  1 12  35  884  0  967  h h  1175  4  21  2  3  10  Z  6  41  8  8  2g A g  h  3  ig 2g Ag ig  Ag  1  h h  0  0  h  0  0  1274  1317  h 2  0 12  ig B  2  0  1249 0  14  3%  0  0.23  0  4  35  Symmetry  3  14  1214  1295  (be')  17  831 838  1 5 0 cm  —  2h  0 l l  (ab)  h i  2  above  1  h  0  13  h  A  g  Table  Av ( c m  5.  (Continued)  (a*a*)  -  (c*c*)  0.33  3h  100  (bb)  (c'c')  fab)  (be')  9  13  22  100  9  h 22  h  3  20  3  4  6  h  1  1  1428 0.66  5  3  1605  ih  2261  2  0 1  sh  2  5  9  2  3  I  2276  0.39  1  5  2292  0.07  h  5  1  3  8  1  1  1  h  1  2  h  0  2304  t The p =  Symmetry  Ag  Ag  h h  1418 1552  (aa)  h  h  1359 1386  (a*c*)  P  +  +  depolarization polarized.  ratio,  1  p, s h o u l d  have the  v a l u e 0.75  for  n o n -• t o t a l l y  symmetric  3g B A A  A  7  3g-  g g g  modes.  53  sensitivity frequency  i n different  the spectra  under as n e a r l y intensity be'  from the various  i n Table  tetrachloride  several 900 in  5 r u n from  and f o r t h e ac face Depolarization  carbon  o f the spectrum b u t a t each  -  spectra  the  a  molecular  2.  The I n f r a r e d The  operator  they  was  as F i g u r e  definitely  appeared,  and Ag l i n e s  (c c') 1  allowed  from because  or  (c*c*),  through  impossible.  infrared  spectra  2 3 0 0 t o 6 0 0 cm " " o f t h e a b a n d a c f a c e s given  i n benzene and  Spectra  polarized -  relative  i n the region  n o t be d e t e r m i n e d  b e t w e e n B^g l i n e s  The  Even s o , t h e symmetries o f  particularly  i n which  measured  0 t o 100 f o r t h e ab a n d  were measured  solutions.  t o 1 4 0 0 cm "'', c o u l d  distinction  were  independently.  ratios  o f t h e weak l i n e s ,  the only  faces  t h e same c o n d i t i o n s a s p o s s i b l e .  scales  faces,  regions  1  9.  The ab s p e c t r u m  i n the region  from  of naphthalene-dg are  agrees w e l l with  that  g  previously  presented  and i s i n c l u d e d o n l y  p a r i s o n between t h e d i f f e r e n t s c a n was n e g l i g i b l e . the  ab and a c f a c e s  pared with  faces.  The l o w - e n e r g y are given  the solution  Sublimation infrared  as F i g u r e  spectrum  to facilitate  during the  spectra  from  1 0 , a n d may b e  i n benzene g i v e n  com-  as  com-  Figure  7 11.  In a l l spectra  t h e appearance o f bands a p p a r e n t l y  to naphthalene-d^, h^ i s observed. infrared  spectrum o f naphthalene-d  The l i n e s f i  observed  due i n the  a r e summarized i n Table  6.  54  F i g u r e on f o l l o w i n g F i g u r e 9.  page.  Naphthalene-dg i n f r a r e d s p e c t r a above 600 cm  (a) I n c i d e n t l i g h t normal t o the ac f a c e ; s o l i d l i n e c*, broken l i n e // a*; c r y s t a l 0.18 mm  : //  thick.  (b) I n c i d e n t l i g h t normal t o the ab f a c e ; s o l i d l i n e // b, broken l i n e // a; c r y s t a l 0.15 mm t h i c k . 7 s p e c t r a l x n e s due t o i s o t o p i c i m p u r i t i e s w i t h arrows.  In both  a r e marked  55  F i g u r e 10. Naphthalene-dg low-energy c r y s t a l i n f r a r e d s p e c t r a : (a) I n c i d e n t l i g h t normal t o the ac f a c e ; s o l i d l i n e // c*, b r o k e n l i n e / / a * ; c r y s t a l 0.32 mm t h i c k , (b) I n c i d e n t l i g h t normal t o ab f a c e ; s o l i d l i n e //b, broken l i n e / / a ; c r y s t a l 0.45 mm t h i c k below 150 c m ~ l , 0.25 mm t h i c k above 150 c m ~ l .  57  T a b l e 6.  v  The i n f r a r e d spectrum o f n a p h t h a l e n e - d  crystal  Symmetry  63 ms 100 m  -  164 s > \  82 8 v s  u a., u  836 m  178 m ) 193 ms  A  328 ms  B  392 m?  877? s .  3u  879 v s  B  u  906 m  isotopic*  920 ms  isotopic*  l u  400 ms? i 407 v s 447 w 425 s 483 vw 516 vw 538 mw 568 mw  >  S  Symmetry B_ 2u B_ 3u B ? 2u  isotopic? ~ B_ 2u B„ 2u  372 vw  crystal  b  B  351 w  v  g  954 w 964 w 970 vw 1045 vw  R  3u B_ ? i s o t3u opic? B„ 2u B 2 u  isotopic*  1053 vw 1160 vw 1085 1172 m w 1181 mw 1192  0  x  B_ 2u B„ ? 2u B„ 2u B. l2uu BBS, 3u 2u B, B 0  2 u  B„ 2u  vw  1204 mw  ^lu  590 ms  B  2 u  1217 vw  B  62 8 v s  B  3 u  1228 mw  B^  647 s 658 mw  1240 isotopic*  2 u  mw  1249 w  B  1  672 s  B  3 u  1257 ms  B^  738 mw  B  l u  1273 mw  B ^  772 w  isotopic*  1310 mw  'B^  769 w  shoulder  13 41 ms  B  2 u  1393 ms  B  2 u  1416 m  B^  791 s 797 vw 803 w  B  l u  shoulder  1425 mw  B„ 2u  58 T a b l e 6.  (Continued)  'crystal 1439 1452 1542 1550 1562 1570  Symmetry  ms m m  B  mw m m  2u 2u  vcrystal  Symmetry  2250-75  vs  Bl u  2260-90  vs  B 2u  2288  ms  Bl u  7  2u lu 2u  Ref. 7.  The l o w - f r e q u e n c y , p o l a r i z e d  infrared spectra of  the ab and ac f a c e s o f s i n g l e c r y s t a l s o f naphthalene-hg a r e p r e s e n t e d as F i g u r e 12 and t h e r e l e v a n t d a t a a r e summarized as T a b l e  7.  59  F i g u r e 12. Naphthalene-hg low-energy c r y s t a l i n f r a r e d spectrum: (a) I n c i d e n t l i g h t normal t o the ac f a c e ; s o l i d l i n e / / c * , broken l i n e / / a * . (b) I n c i d e n t l i g h t normal t o the ab f a c e ; s o l i d l i n e //b, broken l i n e / / a . F o r b o t h Ta) and (b) the c r y s t a l s were 0.4 mm t h i c k above 150 cm~l and 1.5 mm t h i c k below 150 c m . -1  60 T a b l e 7.  The i n f r a r e d spectrum o f naphthalene-hg a t low energy  Solution*  Crystal 66  ms  100  m  177  vs  19 2  ms  210  m  213  s  359  ms  470  s  480  vs  500  sh  510  vw  554  w  562  572  w  Benzene  595  vvw  614  ms  181  358  473  507?  A s o l u t i o n i n benzene  Assignment  u u B 3u  u Bl u B 3u  B 2u  B 2u  61  C.  Assignment o f Fund ante n t a 1 s  1.  Lattice vibrations Three i n f r a r e d - a c t i v e l a t t i c e v i b r a t i o n s are ex-  p e c t e d , two a ac p l a n e .  u  The  naphthalene-hg  p o l a r i z e d a l o n g b and one b  u  p o l a r i z e d i n the  l i n e s a t 100 cm ( / / b ) and 66 cm "^(//a) i n 1  must c o r r e s p o n d t o the h i g h e s t energy a  and  u  the bu t r a n s l a t i o n a l modes r e s p e c t i v e l y ; the c o r r e s p o n d i n g l i n e s i n naphthalene-dg  l i e a t 100 cm~l and 63 cm ^.  The  l i n e seen a t 53 cm ^ i n the p r o t o n a t e d m o l e c u l e by Harada and 71  Shimanouchi was  and a s s i g n e d as the l o w e s t a  n o t found.  u  Wyncke e t a l . ^ r e p o r t e d an  t r a n s i t i o n a t 54 cm ^ and weak b - p o l a r i z e d 5 7 , 63 and 80 cm  i n naphthalene-hg;  lattice vibration a-polarized l i n e s at 44, 49,  none of t h e s e were  observed. S i x Raman-active l a t t i c e v i b r a t i o n s are e x p e c t e d , t h r e e b e l o n g i n g t o each o f the ag and bg c l a s s e s .  The  lines  a t 4 3 ( b ) , 4 9 ( a ) , 7 0 ( b ) , 7 0 ( a ) , 1 0 2 ( a ) and 117 c m ~ ( b ) 1  g  g  i n the naphthalene-dg  g  g  g  g  spectrum c o r r e s p o n d t o t h e s e v i b r a t i o n s ;  the agreement w i t h the naphthalene-hg  modes r e p o r t e d by  14  S u z u k i , Yokoyama and I t o i s good. 2. Raman-active m o l e c u l a r v i b r a t i o n s E i g h t o f the n i n e e x p e c t e d Ag m o l e c u l a r modes can be r e a d i l y i d e n t i f i e d a t 4 9 4 , 6 9 7 , 8 6 2 , 1 2 9 5 , 1 3 8 6 , 1 5 5 2 ,  62 2 2 7 6 a n d 2 2 9 2 cm ^ f r o m ratios.  their  The a p p r o x i m a t e  strength  location  m e n t a l may b e c a l c u l a t e d  from  and d e p o l a r i z a t i o n  of the remaining  the product rule,  funda-  using the  14 naphthalene-hg 1148,  frequencies reported  1 3 8 0 , 1 4 6 5 , 1579 a n d 3058 c m  CH s t r e t c h i n g  of this  i ssufficiently  ecules of  located  calculation  accurate.  1021, a  second  a t 3 0 5 0 cm mode i s n o t  the estimated  The t h e o r e t i c a l  fre-  value f o r  o f t h e p r o d u c t s o f t h e f r e q u e n c i e s o f t h e two m o l i  s  0.250, w h i c h  requires  t h e r e m a i n i n g A g mode l i e n e a r  spectrum  and i n c l u d i n g  s e c o n d CH s t r e t c h i n g  known, b u t f o ra p r o d u c t r u l e  the r a t i o  - 1  frequency a r b i t r a r i l y  The e x a c t l o c a t i o n  quency  a t 514, 765,  that  t h e unknown  8 0 0 cm ^.  frequency  F r o m t h e Raman  a t 8 3 1 , 838 a n d 884 a r e t h e o n l y p o s s i b l e 45 c h o i c e s f o r t h i s Ag mode. C r a i g and H o l l a s have shown t h a t -1 72 t h e l i n e a t 8 8 4 cm i s due t o a v i b r a t i o n , and McClure 3g found  the lines  that  class.  t h e 8 3 1 cm  1  transition  also  ( T h e i r v a l u e s a r e 8 8 1 a n d 8 2 6 cm  Raman f r e q u e n c i e s o b s e r v e d i n t h i s  Hence t h e l i n e  a t 8 3 8 cm  r e m a i n i n g Ag fundamental  1  rule  ratio  must mark  the presence  papers.) ofthe  i n the deuterated molecule, 12 The  a  confirm-  resulting  i s 0.260.  The t h r e e B be a s s o c i a t e d w i t h  respectively; the  i nearlier  t h e a s s i g n m e n t made b y L u t h e r e t . a l .  product  1  t o t h e B^g  work a r e c o n s i s t e n t l y  few wavenumbers above t h o s e r e p o r t e d  ing  belongs  l  g  fundamentals  the lines  o f naphthalene-dg  a t 3 4 8 , 547 a n d 761 c m  - 1  ,  must which  63  are  the only lines  showing  character i n the entire  spec-  14 trum.  The r e p o r t e d  frequencies f o r naphthalene-hg  7 2 5 a n d 9 3 3 cm "S  390,  the resulting  0.549, compared w i t h t h e t h e o r e t i c a l Only in  t h e Raman lines  observed  B g  fundamentals  the  two h i g h - e n e r g y  under s t r o n g e r  o f naphthalene-dg;  these  a t 4 1 0 a n d 6 4 9 cm ^.  identified correspond to  Comparison w i t h the 14  of the protonated molecule  these must e i t h e r  ratio i s  v a l u e o f 0.531.  2  spectrum  The  rule  two o f t h e f o u r B g modes c a n be  the  2  product  are  indicates  modes h a v e n o t b e e n i d e n t i f i e d ,  be t o o weak t o b e f o u n d  that  and  o r must be  hidden  lines. B^g s y m m e t r y b l o c k i s t h e l e a s t  understood.  45 Craig  and H o l l a s  vibration which  lies  mentals  to resolve  i n this  very 1  these  a n d we  due t o a B^g  t o t h e Ag  find  two l i n e s .  a t 4 9 4 cm The n e x t 72 45 '  fundamental 1  .  We  two  funda-  t o the frequen-  a n d t h e h i g h e s t - e n e r g y B^g  b e l o w t h e CD s t r e t c h i n g  the line  close  b l o c k have been a s s i g n e d  a t 8 3 1 a n d 8 8 4 cm \  mental with  a t 4 9 0 cm  t h e y p l a c e a t 4 9 2 cm  were unable  cies  have shown t h a t one l i n e  funda-  region i s clearly associated  a t 1 6 0 5 cm ^ w h i c h  has never  been a s s i g n e d as  a fundamental before. The p o s i t i o n s o f t h e t w o r e m a i n i n g Bm o d e s b e l o w 2 0 0 0 cm ^ i s u n c e r t a i n . Each o f t h e l i n e s 3g observed 1175,  i n the (c'c')  [or (c*c*)]  crystal  1 2 1 4 , 1 2 4 9 , 1274, 1317 and 1359 c m  - 1  spectrum  a t 967,  c o u l d be due  64  e i t h e r t o a B_  3g  f u n d a m e n t a l , an A„ c o m b i n a t i o n  allowed  9  t h r o u g h the #yy m o l e c u l a r such as CgD^H^.  o p e r a t o r , o r an i m p u r i t y m o l e c u l e  The p o s s i b i l i t y t h a t they are c o m b i n a t i o n s  of o t h e r t h a n Ag symmetry seems v e r y remote.  A l l these  lines  were so weak i n s o l u t i o n t h a t d e p o l a r i z a t i o n r a t i o measurements were not p o s s i b l e . Notably  absent from e i t h e r c r y s t a l o r s o l u t i o n  s p e c t r a are the l i n e s v a r i o u s l y r e p o r t e d as 1 0 2 2 cm mixed c r y s t a l  fluorescence  72  and 1 0 3 0  12  or 1006  7  cm  in -1  i n the  m e l t Raman s p e c t r a e x c i t e d w i t h a mercury lamp; the l i n e a t 1 2 - 1  1330 cm seen o n l y i n the Raman s p e c t r a ; and the l i n e -1 7 12 1 5 7 3 cm seen weakly i n the m e l t Raman s p e c t r a ' but  at  72  a s s i g n e d as a c o m b i n a t i o n  from the f l u o r e s c e n c e  these absences i s i m p o r t a n t  .  Each o f  s i n c e the most r e c e n t c a l c u l a t i o n s  have been r e f i n e d t o f i t fundamentals a s s i g n e d t o these quencies.  The  l i n e a t 1 5 7 3 cm ^ may  c o n v e n i e n t l y be  fre-  replaced  i n the assignment by the p r e v i o u s l y mentioned l i n e a t 1 6 0 5 cm"'". -  I t i s r e c o g n i z e d t h a t a l i n e w h i c h i s Raman a c t i v e  be weak i n f l u o r e s c e n c e , and v i c e v e r s a , r e p o r t e d a t 1 0 2 2 cm ^ may  so t h a t the  mark the presence of a B^g  may  line molecular  fundamental i n t r i n s i c a l l y weak i n the Raman spectrum; however, the i s o l a t e d l i n e a t 967 cm ^ may  a l s o be a contender f o r  t h i s p o s i t i o n i n the assignment and a f i n a l d e c i s i o n cannot be made u n t i l more c o n c l u s i v e e x p e r i m e n t a l available.  The  l o c a t i o n of the r e m a i n i n g  information i s B^g  fundamental  41  below 2000 cm ^ must a l s o remain u n c e r t a i n .  W h i l e we f e e l  t h a t t h e assignment o f a fundamental a t 1330 cm  i s almost  c e r t a i n l y i n c o r r e c t , t h e e x p e r i m e n t a l e v i d e n c e does n o t y e t p e r m i t a c h o i c e t o be made from t h e s e v e r a l l i n e s o b s e r v e d near t h a t energy. Two  CD s t r e t c h i n g f r e q u e n c i e s a r e e x p e c t e d and  the weak l i n e a t 2261 cm  w i t h most o f i t s s t r e n g t h i n t h e  (c'c') and (c*c*) d i r e c t i o n s p r o b a b l y a r i s e s from one o f them.  The o t h e r i s perhaps h i d d e n under t h e s t r o n g and r a t h e r  broad Ag l i n e a t 2276 cm ^. The o n l y f e a t u r e o f t h e Raman spectrum which has n o t y e t been c o n s i d e r e d i s t h e band a t 162 cm \  No gerade  mode o f naphthalene-dg i s e x p e c t e d i n t h i s r e g i o n and t h e l i n e i s p r o b a b l y t h e analogue o f t h e i n f r a r e d - a c t i v e 163  line  ( 3 ) a r i s i n g from t h e presence o f a monoprotonated B  U  i m p u r i t y due t o t h e l i f t i n g o f t h e symmetry r e s t r i c t i o n s , and s t e a l i n g i n t e n s i t y from t h e nearby s t r o n g l a t t i c e modes. A s i m p l e c a l c u l a t i o n on a - n a p h t h a l e n e - d ^ h  with the out-of35 36  p l a n e f o r c e f i e l d t r a n s f e r r e d from S c u l l y and W h i f f e n i n d i c a t e d that the lowest B^ s h i f t o n l y 0.3 cm 3.  u  '  mode o f naphthalene-dg would  i n t h e monoprotonated  molecule.  Infrared-active molecular vibrations A l t h o u g h t h e i n f r a r e d s p e c t r a o f naphthalene-dg  have been t h e s u b j e c t o f even more s t u d y than t h e Raman spec-  66 tra,  many p o i n t s o f d i f f e r e n c e between t h e e x p e r i m e n t a l 6 — 10 assignments s t i l l exist. C a l c u l a t i o n s have been c a r r i e d 34 35 41  out  '  '  i n an attempt t o s e l e c t t h e c o r r e c t s e t from t h e  many proposed fundamentals and t h e v a r i o u s assignments based on t h e s e c a l c u l a t i o n s a r e i n q u i t e good agreement. the  However,  o r i g i n a l e x p e r i m e n t a l assignments were made e i t h e r  ( i ) by  analogy w i t h naphthalene-hg o r ( i i ) by deducing t h e appearance o f t h e c - a x i s spectrum from a comparison o f t h e ab c r y s t a l s p e c t r a w i t h t h e s o l u t i o n spectrum, and i t was  felt  t h a t a more c a r e f u l s t u d y c o u l d improve t h e e x p e r i m e n t a l situation.  I n o r d e r t o complete t h i s more a c c u r a t e assignment,  p a r t i c u l a r l y of the B  2 u  c - p o l a r i z e d modes, t h e p o l a r i z e d  s p e c t r a o f t h e ab f a c e and t h e p r e v i o u s l y u n s t u d i e d ac f a c e have been o b t a i n e d .  I t i s clear  (see F i g u r e s 9 and 10) t h a t  f a r more l i n e s appear i n t h e s p e c t r a t h a n t h e r e a r e f u n d a mentals.  I n o r d e r t o choose from t h e s e many l i n e s , t h e c a l -  c u l a t i o n s were used as a g u i d e t o l o c a t e t h e g e n e r a l r e g i o n i n which t o e x p e c t a fundamental.  Thus t h e r e s u l t i n g a s s i g n -  ment i s n o t s t r i c t l y e x p e r i m e n t a l ; i n v i e w , however, o f t h e apparent a b i l i t y  of the c a l c u l a t i o n s t o f i t a t l e a s t approxi-  m a t e l y t h e f r e q u e n c i e s o f naphthalene-hg and t h e g-modes o f naphthalene-dg  (see T a b l e 8) i t was f e l t t h a t t h e p r e d i c t i o n s  of t h e f o r c e f i e l d c a l c u l a t i o n s s h o u l d n o t be c o m p l e t e l y ignored.  67 The firmly  only A  identified  // b) l i n e  mode o f n a p h t h a l e n e - d g  u  i s associated with  appearing through c r y s t a l  assigned by Chantry e t a l . ^ The  low-energy  polarized  from  t h e 16 6 cm ^ s o l u t i o n  line  a t 1 6 4 cm "*" p a r a l l e l  line  B^  fundamentals  790  cm  - 1  unpolarized  spectra.  clearly  splits  into  10 s h o w a  strong  t o b, c l e a r l y  confirming i t s  molecular fundamental.  The r e m a i n i n g  are firmly  established  a t 4 0 6 , 628 a n d  corresponding energies f o r the lowest  naphthalene-hg  and  their  and t e n t a t i v e l y  . The  in  u  forces  ( 1 9 1 cm "*"  t o a i n t h e ac plane and a weaker  c o m p o n e n t a t 1 7 8 cm ^ p a r a l l e l as a B^  t h e 1 9 3 cm ^  c a n be  spectra presented i n Figure  that  assignment"*"^  which  f o rthe A  (ac p l a n e ) .  u  a r e 1 7 7 cm ( a £ p l a n e ) 1  fundamental  2 1 0 cm ^  I t i s interesting  a n d 1 9 2 cm  1  mode ( / / b)  (// b ) a n d 2 1 3 cm ^  t o note  that  these  splittings  73 agree w e l l magnitude  with  the predictions  of Rich  a n d Dows  both i n  and s i g n . 41 Calculations  mode o f n a p h t h a l e n e - d g line  h a v e p l a c e d t h e h i g h e s t B^ near  1 5 5 0 cm \  has been a s s i g n e d as t h e observed  ring  a n d t h e 1 5 4 0 cm "*" frequency, apparently  7 based  on t h e u n p o l a r i z e d  From t h e ab s p e c t r u m  spectrum  t h e nearby  of Lippincott  line  and O ' R e i l l y .  a t 1 5 6 2 cm ^ i s a l s o  c l e a r l y o f B ^ symmetry, and s i n c e i n t h e ac spectrum i t i s s t r e n g t h , we f e e l i t s h o u l d wh i c h s h o w s c o n s i d e r a b l e B u  3  much more c l e a r l y  polarized  u  t h a n t h e 1 5 4 0 cm ^  transition,  68  t a k e t h e p l a c e o f 15 40 i n t h e assignment. 41  assignments  i n t h e r e g i o n below 2 0 0 0 cm  The r e m a i n i n g B ^ -1  seem e s s e n t i a l l y  c o r r e c t , i f i n f a c t t h e weak l i n e a t 1 0 4 5 cm B^  u  u  i s due t o a  fundamental as r e q u i r e d by t h e c a l c u l a t i o n s . The e x t r e m e l y s t r o n g a b s o r p t i o n i n t h e C-D  stret-  c h i n g r e g i o n has been v a r i o u s l y i n t e r p r e t e d , and as we have been unable t o p e n e t r a t e t h i s r e g i o n i n t h e ac spectrum we can o n l y s u g g e s t t h a t a l l f o u r fundamentals B ) 2 u  (two B^ , two u  l i e i n t h e v e r y s t r o n g band between 2 2 5 0 and 2 2 9 0 cm ^. The B  energy B  2 u  2 u  block i s p o o r l y understood.  r i n g mode i s e x p e c t e d  41  The h i g h e s t  near 1 4 5 0 cm  -1  b u t from  the ab spectrum p r e v i o u s workers have been unable t o l o c a t e any p r o p e r l y , p o l a r i z e d l i n e i n t h i s v i c i n i t y .  I n t h e ac  spectrum, however, i t i s c l e a r t h a t t h e l i n e s a t 1 3 9 3 , 1 4 3 9 and 1 4 5 2 cm  a l l belong t o the B  2 u  c l a s s and, on t h e b a s i s  of s t r e n g t h , t h e l i n e a t 1 4 3 9 cm ^ may r a t h e r a r b i t r a r i l y be a s s o c i a t e d w i t h t h i s mode. 41  been p l a c e d  The n e x t h i g h e s t fundamental has  -1  a t 1 2 9 0 cm  b u t o n l y an e x t r e m e l y weak s h o u l d e r  occurs a t t h a t frequency; the nearest B s t r o n g , w e l l - p o l a r i z e d l i n e a t 1 3 4 1 cm second B  2 u  r i n g mode.  the l i n e a t 1 3 9 3 cm  2 u  l i n e i s t h e medium and t h i s may be t h e  The o n l y a l t e r n a t i v e s appear t o be (too h i g h i n e n e r g y ? ) , t h e l i n e a t  1 2 1 7 cm ^ (very weak) o r t h e l i n e a t 1 1 8 1 cm  (too low i n 41  energy?). and 1 0 8 2 cm  The t h r e e o t h e r B  2 u  l i n e s assigned  a t 5 9 3 , 828  a r e c o n f i r m e d i n t h e ac spectrum, a l t h o u g h t h e  69 T a b l e 8.  P l a n a r fundamental v i b r a t i o n s o f Naphthalene-d  Symmetry  Assigned ( t h i s work)  A  g  B,  lu  B  2 u  2291 2276 1552 1386 1294 862 838 697 494  P r e v i o u s Work Assigned Calculated 2272 2257 1553 1381 1293 866 835 698 493  2295 2260 1542 1370 1288 852 830 695 484  2278  2282  2232  2249  1562  1545  1543  1257  1260  1245  1045 879 738 328  1050 885 734 328  1045 840 749 336  2299  2293  1439 1341 1082 880? 828  2258 — 1290 1082 828 —  2256 1466 1273 1086 837 803  590  593  606  1  70 Table  8.  Symmetry  Table  9.  Symmetry  (Continued)  Assigned ( t h i s work)  Previous Assigned  Work Calculated  2276?  2302  2275  2261  2257  2246  1605  1574  1598  —  1330  1338  967?  1030  1023  884  881  860  831  828  821  494  490  472  Non-planar  fundamental  Assigned ( t h i s work)  vibrations of  Previous Assigned  Naphthalene-d  Work Calculated  —  829  —  648  —  —  511  193  —  185  761  784  751  547  545  528  348  346  316  —  829  812  —  760  754  649  663  665  410  445  429  —  71 T a b l e 9.  Symmetry  B_ 3u  (Continued)  P r e v i o u s Work 35 Assigned Calculated  Assigned ( t h i s work) 791 628  790 628  798 594  402  408  382  166  160  163  m i s s i n g fundamental may  l i e i n the r e g i o n near 880 cm  where  c o n s i d e r a b l e c p o l a r i z e d s t r e n g t h i s seen, r a t h e r than below -1 41 828 cm as suggested by Neto, S c r o c c o and C a l x f a n o . The proposed fundamentals  are summarized i n T a b l e s 8 and  9.  CHAPTER IV THE VIBRATIONS OF ANTHRACENE  A.  Introduction  1.  C r i t i c a l Review S e v e r a l assignments o f the i n f r a r e d - a c t i v e v i b r a -  t i o n s o f anthracene"*"^ "^ and a n t h r a c e n e - d . ^ ^ ' ^ made i n r e c e n t y e a r s .  The assignments were reached by com-  paring the p o l a r i z e d s p e c t r a obtained  from t h e ab f a c e o f  the c r y s t a l w i t h the s o l u t i o n o r pressed-powder B^  u  2 u  spectrum.  t r a n s i t i o n s had t h e i r maximum s t r e n g t h p a r a l l e l t o b  and B B  have been  3 u  t r a n s i t i o n s p a r a l l e l t o a;  the e s s e n t i a l l y c - p o l a r i z e d  t r a n s i t i o n s were e x p e c t e d t o show g r e a t e r  s t r e n g t h i n s o l u t i o n than i n t h e ab s p e c t r a .  relative The  reported  assignments o f t h e i n f r a r e d bands i n t h e r e g i o n above 400 cm "*" have shown good agreement.  However, the s e l e c t i o n  of fundamentals from t h e s e many l i n e s has been r a t h e r more a r b i t r a r y and s e v e r a l p o i n t s o f d i f f e r e n c e have a r i s e n . One aim o f the p r e s e n t work has been t o r e c o r d the s p e c t r a w i t h l i g h t p o l a r i z e d a l o n g t h e c - a x i s t o a s s i g n more f i r m l y t h e B_  bands.  The c - p o l a r i z e d spectrum o f 72  anthracene-h  1 0  has a l r e a d y been r e p o r t e d ;  measurements e x t e n d o n l y down t o 450 cm ments a r e s t i l l u n c e r t a i n .  17 74 ' however, t h e , and some a s s i g n -  F o r a n t h r a c e n e - d ^ t h e p o l a r i z ed 16 17  s p e c t r a from t h e ab f a c e have been r e c o r d e d  '  down t o  about 400 cm "*"; no c - a x i s measurements have been r e p o r t e d and no i n f o r m a t i o n a t a l l i s a v a i l a b l e f o r t h e r e g i o n below 400 cm ^.  Thus a n o t h e r aim o f t h e p r e s e n t work has been t o  extend t h e p o l a r i z e d measurements f o r b o t h c r y s t a l s t o t h e low-energy r e g i o n where agreement between t h e anthracene-h^g 19 40 41 75 observed and c a l c u l a t e d ' ' f r e q u e n c i e s i s poor. The Raman spectrum o f anthracene-h^g has been e x 14 20-23 tensively studied ' and t h e r e c e n t i n v e s t i g a t i o n by 14 S u z u k i , Yokoyama and I t o e x c i t a t i o n has c l a r i f i e d erably.  u s i n g s i n g l e c r y s t a l s and l a s e r the experimental  s i t u a t i o n consid-  An u n p o l a r i z e d Raman spectrum o f an a n t h r a c e n e - d ^ 22  c r y s t a l has been r e p o r t e d  and a n o t h e r aim o f t h i s work  has been t o o b t a i n t h e p o l a r i z e d Raman s p e c t r a o f monoc r y s t a l l i n e anthracene-d^g i n o r d e r t o improve t h e a s s i g n ment o f t h e gerade fundamental v i b r a t i o n s . 2. S e l e c t i o n Rules The anthracene m o l e c u l a r  axes have been chosen  a c c o r d i n g t o t h e recommendations o f t h e J o i n t Commission 64 for  Spectroscopy.  The x - a x i s l i e s normal t o t h e m o l e c u l a r  p l a n e , t h e y_-axis i s t h e l o n g m o l e c u l a r  a x i s and t h e z - a x i s  74 completes the r i g h t - h a n d s e t .  A l t h o u g h the anthracene 65 m o l e c u l e i s v e r y s l i g h t l y b u c k l e d i n the c r y s t a l , i tis a s u f f i c i e n t l y good a p p r o x i m a t i o n t o assume t h a t i t r e t a i n s Y ^- Y  its full  s  mae  r  •  T n e  anthracene m o l e c u l e s i t s a t a  s i t e o f C i symmetry i n the c r y s t a l and the f a c t o r group i s C,,. 2h  The s e l e c t i o n r u l e s f o r the f r e e m o l e c u l e and f o r the  c r y s t a l are summarized i n T a b l e 10.  Each f r e e m o l e c u l e  state  g i v e s r i s e t o two c r y s t a l s t a t e s and, as i n n a p h t h a l e n e , m i x i n g between g (Raman a c t i v e ) and u ( i n f r a r e d a c t i v e ) molecular states i s forbidden. i n the f r e e m o l e c u l e , may  The f i v e A^ s t a t e s , i n a c t i v e  appear i n t h e reduced symmetry o f  the c r y s t a l by m i x i n g w i t h o t h e r u s t a t e s .  In t h i s  event  the p o l a r i z a t i o n c h a r a c t e r i s t i c s o f the t r a n s i t i o n t o the "impure" A  u  s t a t e are those o f the m i x e d - i n component.  The  number o f l a t t i c e modes and the c r y s t a l d i r e c t i o n s i n which they are e x p e c t e d a r e a l s o g i v e n i n T a b l e 10. The r e l a t i v e i n t e n s i t i e s o f a m o l e c u l a r l i n e i n the Raman s p e c t r a o f the v a r i o u s c r y s t a l f a c e s are d e t e r mined i n the u s u a l o r i e n t e d - g a s a p p r o x i m a t i o n from the 65 d i r e c t i o n cosines  r e l a t i n g m o l e c u l a r and c r y s t a l axes and  are g i v e n i n T a b l e 11.  The p r o j e c t e d i n t e n s i t i e s o f the  i n f r a r e d - a c t i v e modes i n the same a p p r o x i m a t i o n are l i s t e d i n T a b l e 12.  75 T a b l e 10.  C o r r e l a t i o n t a b l e f o r anthracene*  M o l e c u l a r group N 12  S i t e group  F a c t o r group 2h Bases  n  aa, bb, c c , ac aa  3  2h Bases  C  x x , y y , z_z  A  4  xy_  6  xz  B ig B2g  11  y_z  B  11  z  B  11  Y_  B 2u  x .  B 3u  ig  bg  ab, be  3g  5  6  lu  a  u  b  u  b  u £  N i s t h e number o f fundamentals i n t h e f r e e m o l e c u l e and n i s t h e number o f l a t t i c e f r e q u e n c i e s w i t h k = 0. F a c t o r group s p e c i e s a r e d i s t i n g u i s h e d by l o w e r case l e t t e r s .  76  Table  11.  The o r i e n t e d - g a s intensities of  predictions of the relative  of the free-molecule  anthracene  i n various  Raman  lines  crystal configurations  I x x (A„) Iyy_ (A ) g  Iz_z (A„) g  Ixy_ (B, ) l g  Ix z (B„ ) Iv_z ( 3Bg ) 2g  0.422  0.061  0.011  0.639  0.272  0.103  0.036  0.000  0.633  0.012  0.601  0.050  0.026  0.545  0.010  0.477  0.065  0.295  I , ab  0.123  0.004  0.083  0.013  0.334  0.233  I, . be'  0.026  0.012  0.080  0.180  0.049  0.529  I  0.631  0.000  0.040  0.021  0.632  0.005  0.000  0.956  0.000  0.064  0.000  0.023  0.013  0.007  0.001  0.759  0.000  0.200  a  I  CT  v  0  v  aa I.. bb I  , ,  ££  a  1  , , a'  I cc I  , a' c  77  Table 1 2 . The o r i e n t e d - g a s p r e d i c t i o n s o f t h e r e l a t i v e i n t e n s i t i e s of the i n f r a r e d - a c t i v e l i n e s of anthracene a l o n g v a r i o u s c r y s t a l axes  a'  0.182  0.008  0.811  a  0.104  0.246  0.650  b  0.795  0.016  0.188  c'  0.100  0.746  0.162  c  0.023  0.976  0.001  78 B.  Results  1.  Anthracene-h-^Q I n f r a r e d S p e c t r a and Assignment a) S p e c t r a . ,  P o l a r i z e d s p e c t r a were r e c o r d e d  l i g h t i n c i d e n t on the ab, b e  1  and ac f a c e s .  The  with  s p e c t r a are  shown i n F i g u r e s 13, 14, and 15, r e s p e c t i v e l y , f o r e n e r g i e s l e s s t h a n 650  cm  0.47  mm  and 0.98  These samples were of t h i c k n e s s respectively.  normal t o the ac  S p e c t r a measured w i t h l i g h t  ( c r y s t a l t h i c k n e s s 0.27  ( c r y s t a l t h i c k n e s s 0.14 g i e s above 400 cm  mm)  The  0.41,  mm)  and b e  1  sections  are shown i n F i g u r e 16 a t e n e r ab s p e c t r a i n t h i s  higher-energy 16 — 18  range were i n good agreement w i t h those a l r e a d y and are not p r e s e n t e d The section was  reported  here.  s l o p i n g base l i n e on the spectrum from the  (most n o t i c e a b l e i n the 1600-1800 cm ^ r e g i o n  be'  //b)  caused p r i n c i p a l l y by the p o l a r i z e r not b e i n g a l i g n e d  e x a c t l y a t 45°  t o the g r a t i n g r u l i n g due  t o the  unfortunate  d i s p o s i t i o n of the o p t i c a l d i r e c t i o n s of the s e c t i o n i n the rather elongated  c r y s t a l sample used; i t was  necessary  to  l i n e up the c r y s t a l l e n g t h w i t h the s l i t f o r maximum t r a n s mission.  The be'  internal strain  s e c t i o n showed e v i d e n c e of ( i . e . , incomplete  considerable  e x t i n c t i o n between c r o s s e d  p o l a r i z e r s ) and the i n t e n s i t i e s of the b - p o l a r i z e d peaks e s p e c i a l l y i n the h i g h e r - e n e r g y Nonreproducible  r e g i o n seem t o be d i s t u r b e d .  f e a t u r e s i n the s p e c t r a were d i s c o u n t e d .  i  100  -  i  1  200  *  —  I  1  300  1  1  400  F i g u r e 13. Anthracene-h low-frequency i n f r a r e d l i n e // b, broken l i n e // a.  1  «  1  500 spectrum; ab f a c e . —  1  1  600 Solid  :  cm-'  r  F i g u r e 14. Anthracene-h,- l o w - f r e q u e n c y i n f r a r e d // b, broken l i n e // c'.  spectrum; b e  1  face.  Solid  line  82  F i g u r e on f o l l o w i n g page. F i g u r e 16.  Anthracene-h^g i n f r a r e d s p e c t r a above  400 c m ; -1  (a) i n c i d e n t l i g h t normal t o the ac  f a c e ; s o l i d l i n e / / c , broken l i n e / / a . 1  (b) i n c i d e n t l i g h t normal t o the be' f a c e ; s o l i d l i n e / / c ' , broken l i n e // b.  Transmission  Transmission  84 There was a sharp drop i n t h e s i g n a l - t o - n o i s e a t t h e extreme  ratio  low-energy end o f t h e spectrum because o f t h e  low i n c i d e n t l i g h t  intensity.  T a b l e 13 l i s t s t h e observed f r e q u e n c i e s o f t h e bands and t h e i r assignments t o g e t h e r w i t h p r e v i o u s a s s i g n ments i n c l u d e d f o r comparison.  The f r e q u e n c i e s e n t e r e d i n t h e  t a b l e were mean f r e q u e n c i e s averaged over s e v e r a l samples and p o l a r i z a t i o n s i n such a way t h a t measurements p a r a l l e l and p e r p e n d i c u l a r t o b were g i v e n e q u a l w e i g h t .  The l i n e p o s i -  t i o n s agreed v e r y w e l l w i t h t h e p r e v i o u s measurements which a r e , a c c o r d i n g l y , o m i t t e d from T a b l e 13. However, n e i t h e r 19 16 IV "~ 1 Chantry e t a l . n o r we c o u l d d e t e c t t h e l i n e ' a t 278 cm Indeed, t h e r e i s l i t t l e agreement between t h e l o w - f r e q u e n c y 17 l i n e s r e p o r t e d by Colombo  and t h o s e i n t h i s t h e s i s ; o u r  d a t a were r e p r o d u c i b l e from sample t o sample and a l o n g t h e same a x i s i n d i f f e r e n t s e c t i o n s . The l o w - f r e q u e n c y s p e c t r a o f a 0.08 M s o l u t i o n o f anthracene i n benzene and o f a s a t u r a t e d s o l u t i o n o f a n t h r a cene i n c y c l o h e x a n e were measured; t h e p a t h l e n g t h was 5 mm. Only two l i n e s a t 233 and 467 cm  were observed w h i l e t h e  presence o f a s t r o n g l i n e a t 180 cm ^ and a weak l i n e a t -1  19  362 cm  as r e p o r t e d by C h a n t r y e t a l .  c o u l d n o t be con-  firmed.  As s o l u t i o n s p e c t r a , o f c o u r s e , p e r m i t a c l e a r  d i s t i n c t i o n t o be made between m o l e c u l a r and l a t t i c e  vibra-  t i o n s , more c o n c e n t r a t e d s o l u t i o n s were r u n i n an attempt  85 Table  v  13.  crystal  63  m  72  w  104 110  l s i  107  w  126  s  166  s  235  s  361  vw  380  w  The  infrared  spectrum  of  anthracene-h  10  A s s i g n m e n t Present work  Ref.  15  R e f . 16  Ref.  b u  m  B  3u  B_  u u  A  a  B  B  T  B_  sh  B  o2 u  456  sh  464  w  469  vs  493  w  B  515  vw  B  536  vw  600  s  B B  o  2u 3u  Bo  il u  B,  o  B  2u  Bo3 u  3u  B  o  B  3u  ?  B  3u 2u  B  3u il u  2u-  B  B  n  B  nl u  o  B  B-  B  o  B.,  B  o  706  ?  B„  730  vs  B  w  3u  lu  B  B  B.  3u  3u' 3u  vw  808  *  ?  689  w  3u  -  B  m  o  7  3u  650  B  3u  e  B  775  3u  lu  431  B  *  l u  o  vw  *  2u B-il u *  B  621  u  B_  3u  sh  m  *  b  423  744  3u  3u ? 2u  B  -5  3u B lu* o3 u  7  B  Bo2 u  lu 2u' 3u  A  B  ' 3u u  A A'u u  . 3u l u  3u 3u  ]  86 Table  v  13.  (Continued)  , , crystal  A s s i g n m e n t Present work  856  m  883  vs s  B  915  ?  l u  B  ?  2u  930 954  s  977  m  998  Ref.  u  o  B  16  Ref.  A u  3u  903  15  A  o3 u  B  Ref.  o  B  B .3 u lu  3u lu  B o3 u  B o3 u  A  A  o  B  3u  Bl u n  B o3 u  B_  3u  B  3u  B  2u  B  2u  B  3u  s  B  2u  1012  vw  B  3u  1068  m  B  2u  B  2u  B  2u  1123  m  B  2u  B  2u  B  2u  1145  s  B  l u  B  l u  1163  s  B  2u  B  2u  1200  sh  B  2u  1219  m  B  2u  B-,l u  1240  m  B o3 u  lu  1270  s  1282  m  Bl u n  B  l u  1297  m  B ,l u  B  l u  1315  s  1345  m  1354  w  1372  vw  B  3u  1392  s  B  2u  1407  vw  B o3 u  1447  s  Bl u  1480  vw  B  3u  1495  m  B  2u  ?  B  l u  B  2u  B-,l u  n  B  u 2u  l u  B  l u  B  2u  B  2u  B  B  l u  B.  B-,l u  lu  lu  B  u 2u  B ,l u  B  l u  B ,l u Bn lu  B  l u  B  2u  B  2u' 3u  B  3u  B  2u  B  2u  B  2u  B  l u  B  l u  B  l u  B  17  87 T a b l e 13. v crystal  1514 1 5 3 3  3  Present work B B  m m s  1635 1654 1 6 9 0  A s s i g n m e n t  m  1561 1571 l o 1 6  (Continued)  m vw 5  1 7 2 3  m  B  u  U  l u  B  l  l u  B  u  2u  B  2u B  l u  B  l u  B  l u  B  l u  B  l u  B  l u  2 u  2 u  vw  B  2670  m  2721 2745  w sh  B  2 u  2793  sh  B  2 u  2806  vw  B  l u  2828 2850 2912 2925 2950 2972 2988  w vw vw m w sh m  B B  B  s h  u  B  2625  010  2u  l u B  sh s  3  B  2 u  1793 1806  m  2u  ?  2 u  l u B B  1 7 8 4  l  l u  B  B  B  B  B  B  m  1739  l  B  2u  u  B  s  R e f . 17  2 u  l  B  2  1713  B  l u  B  Ref. 16  2 u  2u B B  Ref. 15  l u  B  l u  l  B  B B B B B  B  u  B  l u  l u  l u  B  B  l  u  l  u  2 u  l u  l  B B B B B  u  2 u  2 u  l u  2 u  lu  ?  l u  l  u  l  u  B B  l u  ?  2 u  B  l u  B  B B  2 u  3 u  l u  B  l u  l  u  2 u  88 Table 13.  (Continued)  v crystal  3024  ms  3050 3082 3092 3109  vs sh m m  3175 3193  vw  3248  vs sh  Present work  Ref. 15  B,  lu  m e n t Ref. 16  lu  lu' 2u lu 2u B. lu  B  B  B  B  B  lu' 2u 2u B  B  B  Ref.  lu lu 2u  B  B  B  n  lu lu 2u  B  B  m  lu  B  w  B  2u 2u  very strong, shoulder.  A s s i g n  s  strong,  B  m  * d a t a taken from r e f e r e n c e 19.  lu  medium,  B  lu  w  B  weak,  lu  17  89 t o f i r m l y e s t a b l i s h the l o c a t i o n s o f the v e r y low energy m o l e c u l a r modes.  U n f o r t u n a t e l y , anthracene's s o l u b i l i t y i n  the u s e f u l s o l v e n t s proved t o be too low and s m a l l c r y s t a l s formed i n the s o l u t i o n s . b) Assignment. B_3u and f i v e A u B  Of t h e e l e v e n B^ , u  eleven B , 2 u  m o l e c u l a r fundamentals t h r e e B,l u and  six  two  c o r r e s p o n d a p p r o x i m a t e l y t o CH s t r e t c h e s and a r e e x p e c t e d  2 u  near 3000 cm The problem now  r e s o l v e s i t s e l f i n t o one o f s e l e c -  t i n g t h e ungerade fundamentals from the many l i n e s g i v e n i n T a b l e 13.  I n p r i n c i p l e , i t s h o u l d be p o s s i b l e t o account  f o r as c o m b i n a t i o n s a l l l i n e s n o t a s s i g n e d as fundamentals. I n f a c t t h i s proved t o be p o s s i b l e o n l y up t o about 600 cm ^ where the number o f p o s s i b l e c o m b i n a t i o n s became q u i t e l a r g e and i n c o m p l e t e knowledge o f the low f r e q u e n c y (A  u  fundamentals  and some g_-modes) was an a p p r e c i a b l e i n c o n v e n i e n c e .  Above about 600 cm ^ s t r o n g i s o l a t e d l i n e s were u s u a l l y s e l e c t e d as fundamentals; however, a weak l i n e may mark a f u n d a m e n t a l , as must s u r e l y be the case f o r the B^  u  species  of a n t h r a c e n e - d . ^ where, as shown l a t e r , no s t r o n g l i n e s o f the a p p r o p r i a t e p o l a r i z a t i o n were found o v e r a wide energy range. The presence of a weak l i n e n e a r l y degenerate w i t h a s t r o n g one o f a d i f f e r e n t symmetry c r e a t e s a s p e c i a l problem.  S i n c e the two v i b r a t i o n a l s t a t e s may  be mixed by  90 crystal  f o r c e s , the  weak l i n e  acteristics  and  at  represents  744  cm  symmetry w i t h 730  cm  crystal  The  modes i n t o  the  (as  shown i n a  lowest  the  a  B^  solution  The must mark the  the  later  c a s e and  of  the  char-  The  i s probably  character  u  and  to  line  of  line  B^  u  at  of  of  the  these  crystal 13  states  isolated  p o s i t i o n s may the  Classification  at  63  presence The  shift  i n going  spectrum.  of  from  a  Lower case  f o r l a t t i c e modes t o  two  cm  ^ was  of  the  a  lattice  at  u  126  p o l a r i z e d along  only  and  expected  (see  frequencies  symbols  distin-  72  cm  ^;  the  fell  i n a noisy  the  spectrum.  near  cm  i s rather The  of  complex  and  i s given  b-polarized line  ac-polarized line components of  at  110  a B,  cm  at  72  the  10 4 cm  together  molecular  so  Table  latter  weak and  part  at  a and  10)  correspond  line  factor-group  Thus  Raman s p e c t r u m  the  stronger  greatest  molecule.  ment i s somewhat t e n t a t i v e s i n c e  interpretation.  is  intramolecular vibrations.  b-polarized lines  110  of  inter-molecular vibrations i s  mixing  i n Table  line  mode.  region.  s e c t i o n f o r the  line  and  them from  lattice  and  or melt  used here  intra-  frequencies  anthracene-d^Q)  the  such  low-frequency  approximate  guish  symmetry  i t s a s s i g n m e n t becomes ambiguous.  some o f  for  are  mixed  mixed with i t . i)  only  acquires  b to  assign-  cm  was  The  region  following ^ and form  the the  fundamental.  The  u  91  intensity separate the  a l o n g c* i n t h e b e ' s p e c t r u m c-polarized  transition  symmetry o v e r a l l .  u  14 vibration which  (best seen i n  with  that  t h e 72 cm  cm ^ b  near  a t 45 cm  f o ranthracene-h^g, a value  t h e v a l u e o f 4 3 cm  found  (see l a t e r  f o r t h e c o r r e s p o n d i n g mode o f a n t h r a c e n e - d ^ Q .  i s apparent  volve  The l o w e s t b g l a t t i c e  -1  appears  agrees w e l l  section)  63  a t 1 0 7 cm ^  ac s p e c t r a ) which must r e p r e s e n t a combination o f l a t t i c e  modes h a v i n g b  it  i s augmented by t h e  a  t h e 1 0 7 cm u  b  vibration,  u  combination cannot i n -  b u t must i n s t e a d  involve the  l a t t i c e mode, w h i c h w o u l d r e q u i r e an ag f u n d a m e n t a l -1 14 44 cm . Suzuki e t a l . have p l a c e d t h e l o w e s t a u  g  m o d e a t 35 cm "S energy  thus  t h e r e i s a 9 cm ^ m i s m a t c h  f i t f o r t h e 107 b  studies  u  combination.  of anthracene-d-^ located  i n the  H o w e v e r , o u r Raman  the lowest a  g  mode o f t h a t  crystal of  a t 38 cm"''', w h i c h i n d i c a t e s t h a t t h e 35 cm value 14 -1 Suzuki e t a l . may b e 4-5 cm low. I n any event, t h e  position by  Thus  1  of this  the strong The  fundamental  infrared-active  c o m b i n a t i o n may b e  absorption very close line  since  disturbed  toi t .  a t 1 6 6 cm ^ p r o b a b l y m a r k s a B ^ i t has components a l o n g a l l axes  u  molecular a, b and  19 c w i t h maximum s t r e n g t h assigned intensity  this  line  change  as B  from  a l o n g a. 2  u  because  solution  Chantry e t a l .  of the apparently large  to crystal.  H o w e v e r , we  no  evidence of a c-polarized  fundamental  of  the presence  i n t h e weak s o l u t i o n  of this  band  have  below  6 0 0 cm  find nor  spectrum.  92  The p o s s i b i l i t y t h a t t h i s l i n e i s due t o a c o m b i n a t i o n i n v o l v i n g l a t t i c e modes cannot be d e f i n i t e l y r u l e d o u t , and, u n t i l a r e l i a b l e s o l u t i o n spectrum ment as a m o l e c u l a r fundamental  i s available, i t s assign-  must r e l y on i t s r e l a t i v e  i s o l a t i o n and on t h e f a c t t h a t i t appears a l o n g a l l t h r e e crystal  axes. The  l i n e a t 2 3 5 cm ^ was q u i t e s t r o n g w i t h i t s  g r e a t e s t component a l o n g b and was a s s i g n e d as a B ^  funda-  u  mental . In an e f f o r t t o l o c a t e t h e l o w e s t A fundamentals,  molecular  an attempt was made t o a n a l y s e t h e weak l i n e s  a p p e a r i n g i n t h e low-energy weak  u  i n f r a r e d spectrum.  The v e r y  l i n e a t 3 6 1 cm ^ may s a t i s f a c t o r i l y be e x p l a i n e d as  a combination of the 110 B B,l g l i n e . 14  3 u  fundamental  and t h e 2 4 3 cm  -1 The weak B, must then i n v o l v e l u band a t 3 8 0 cm  the same 2 4 3 cm ^ B ^ mode and an A a  e s t i m a t e d t o l i e a t 1 3 7 cm f o r t h e assignment o f an A  u  fundamental a c c o r d i n g l y  Further experimental u  mode a t t h i s energy  evidence  i s provided  by t h e l i n e a t 4 3 1 cm ^, seen o n l y i n c - p o l a r i z a t i o n ,  which 14  may be e x p l a i n e d as t h e c o m b i n a t i o n 1 3 7 ( A ) and 2 9 0 u  The r a t h e r d o u b t f u l s h o u l d e r a t 4 5 6 cm s t r o n g B^ + 290  u  fundamental  ( 2g) fi  •  and a t 4 9 3 cm fundamental  T  h  e  n  e  x  t  (B2g).  (very c l o s e t o t h e  a t 4 6 9 cm "*") may be due t o 1 6 6 ( B ) 3 u  t w o  weak l i n e s appear a t 4 6 4 cm  and a g a i n a r e o v e r l a p p e d by t h e v e r y s t r o n g  a t 4 6 9 cm "S no s i m p l e e x p l a n a t i o n c o u l d be  93 found 600  for either  cm  \  the  planation  as  B^  of  these  line  u  the  lines.  at  515  combination  The  cm of  ^,  n e x t weak  has  110  line  below  a satisfactory  ( 3 )  and  B  U  the  ex-  398  (Ag) 76  line The  known w i t h 536  (Bg )  certainty  line  u  once again  F o u r weak plained  as  presence 423,  464,  the  choice  lines  combinations  of  the  from  493  and  536  of  the  A  any  no  simple  600  cm  one  of  and  1  the  '  explanation.  four  These  been may  ex-  mark  lines  further  from  spectrum.  have not  without  fundamental  u  fluorescence  fundamental.  u  cm  has  below  and  second A  the  77  are  the  at  information  among t h e m i s  not  possible. The is  the  very  only  strong  strong  a-polarized line  c o m p o n e n t a t 464 cm \ B_ f u n d a m e n t a l a t 469 3u The lines  below  1616,  1447,  B^  744  cm  lying 736  cm  u  1314,  fundamentals. m u s t be  cm  very  " * " ( / / b) .  uncertain  since  474  cm  above of  The  strong  1270,  903  cm  1145  one  remaining 1784,  i n a rather to The  and  the  on  and  650  cm  assigned  weak  as  14. B^  lines  at  were chosen  as  u  \ of  The the  2000  cm  line  at  spectrum,  (JL b)  724  determination  of  i t s symmetry  the  a  infrared  at  side of  cm  i t s b  line  the  B^  600  with  fundamental below  complex r e g i o n  strong  very  i t sits  744  - 1  and  \  the  fundamentals.  The  close  at  i s summarized i n Table  1  s e l e c t e d from ^ falls  b e t w e e n 235  which i s accordingly cm ^.  analysis described  600  ii)  absorption  and  b-polarized  is  ^  94  Table  14.  analysis of  The  t h e weak  infrared  a n t h r a c e n e - h •J^Q b e l o w 6 0 0  Observed  lines  361  vw  B  2u  380  w  B  l u  423  sh  B  3u  431  sh  B  2u  456  sh  B  3u  464  w  B  2u  493  w  515  vw  536  vw  cm"  lines  of  1  Assignment  ?  110  (B  137  (A )  + 243  (B  137  (A )  + 290  (B  166  (B_ ) + 2 9 0 3u  (B ) ? 2g  no  (B  + 398  (A ) +  t h u s , t h e 7 4 4 cm  line  3 U  )  u  u  + 243  (B  ) +  1  )  l g  .) +  2  8  4  0  lu B, ? 3u  3 U  )  g  7  3u  component o f t h e B tentatively  3 u  line;  a s s i g n e d as e i t h e r  the B^  u  combination  c a n be 290  (&2q^ 14  +  469  ( 3 )f B  a  g e r a d e modes, and  ^ combination  s  U  o r as an A  i ti s clear  u  involving  fundamental.  t h a t once one i s chosen  t h e o t h e r must be a c o m b i n a t i o n . possible bably  B^  u  combinations  too high  for a ring  a t about  one o f t h e m i s s i n g Two  candidates  as t h e  Presumably 1 7 8 0 cm  mode a n y w a y )  1  remain  fundamental,  t h e r e a r e many (which  so t h a t the  i s proproblem  95 develops  into  near  650  cm  (B^g)  +  since  423  1  one  .  o f d e c i d i n g w h e t h e r any  The  cm  1  only apparent =  (A ) u  the energy  666  f i ti s n o t good and  mental.  Hence i t i s s u g g e s t e d  2 0 0 0 cm  the  423  i s a t 650  1  which  u  to suggest  below  p o s s i b i l i t y i s 2 43  (B-^ )  evidence  cm  cm  1  that  lines  workers  unanimously  621  cm  certainly  there  of  the  as  a t 1533,  intensity pf B ^  i s i n fact  1  spectrum  are those  1 5 - 1 9  Examination  chosen  a combination. available,  since  fall  cm  1  unappealing  t h e r e i s no  i s the  A  second  the eighth B ^  other funda-  u  fundamental  u  . B_  The  fundamentals,  are  the  least  fundamentals  understood.  by  the  previous  998  and  621  cm .  shows t h a t  the  line  at  1392,  along c  1163,  symmetry and  that  i t i s  However, even w i t h the  the problem  with  ^U  t h e i r maximum c o m p o n e n t a l o n g c , The  i s quite  line  1  B n „ fundamentals. —^.u.  iii)  combinations  i s not e a s i l y  a r e more s t r o n g c - p o l a r i z e d  lines  - 1  almost  c-polarized  resolved for  than p o s s i b l e  funda-  mentals . The 998 It  and  cm  and  mentals  600  at way  cm )  below  1345,  of making  this  group  1495,  two  o f them  having B 2 0 0 0 cm  1219,  1123  the choice.  1392,  of B  includes  2  1163,  2  u  ( a t 1495  symmetry. are  1  and  808  t o be cm  If a line  - 1  three lines  and The  600 two  chosen and  1068,  fundamentals.  u  n o t been a s s i g n e d as B  t h a t had  - 1  r e c o g n i z e d as  1690,  that  previously;  fundamentals  a t 1533,  must mark t h e p r e s e n c e  1  i s interesting  1068  not  600  strong lines  2  cm  funda-  u  1  )  were  remaining  from  the  t h e r e i s no  i s cleanly  (1495,  lines clear  c-polarized  96  then  i t represents a transition  mixed w i t h other B and  well  states;  i f a  line  separated i n energy  from  other B  p r o b a b l y marks a appear t h a t and  808  to a state which  the  cm" .  2 u  fundamental. remaining  Certainly  1  Using  the  lines  at  i s cleanly  1345,  most  then i t  approach,  probably  at  c-polarized  lines  2 u  this  fundamentals  has  i t would  l i e at  1219  and  1695  1123  cm  - 1  show c o n s i d e r a b l e h y b r i d c h a r a c t e r . 41 Comparison w i t h the suggests rather  the presence  than  periment 1345  cm  slightly the  a t 1690  bf a B  cm  1  ,  calculations,  so  i s stronger along b s t r o n g e r a l o n g c*  intensity  along c  1  more, f o r example, than  than  i n be' the  line  line  about h a l f  strength i s of Bg  Should B  fundamental,  2 u  it  would  band  as  the  cm  and  i n ac.  a t 1392  1  u  calculations  only  very  at  surprisingly very  It  much  appears  intensity,  character. require  this  however, d e s p i t e i t s p a r t i a l  t h e n become n e c e s s a r y  ex-  line  .  i s o f medium  1  from  Rather  cm  1  This  i s sharply reduced,  that w h i l e the the  a t 1345  a*  a i n ab  cm  data  considered.  than  however,  a t 1345  the r e l e v a n t  s h o u l d be more c a r e f u l l y 1  '  fundamental  2 u  and  75  to explain  line B^  u  the  1690  t o be  a  character, cm  1  a combination.  S i m i l a r s t r o n g l i n e s i n the benzene 78 79 spectrum have been e x p l a i n e d ' as c o m b i n a t i o n s i n v o l v i n g t h e CH o u t - o f - p l a n e b e n d i n g v i b r a t i o n s a n d a n a n a l o g o u s 36  explanation  has  been suggested  quency bands o f naphthalene. exist  f o r anthracene  f o r some o f t h e h i g h I t i s clear  combinations  having B  that 2 u  there  symmetry  frewill overall  97 which of  fall  near the correct  t h e 1690  basis  cm  energy  mode i s c e r t a i n l y  1  assignment  —3u fundamentals  a-polarized The  to  tions  ^ l  a n i e n  a  s  •  The  a t 954,  assignment there  8 8 3 , 7 3 0 , 4 6 9 , 166  different.  v ) CH  stretching  region  line  cm  sities  1  1  Unfortunately  i s dominated  of nearby  by  lines  this  fall  a t 3050  cm  and B £  very strong  sity  the strong  vibraso  sugrepresents  1  symmetry.  U  region line.  The  unpol-  around The  inten-  differences  the transfer  t o t h e weak l i n e s .  "*")  i s strongly  o f f as t h e energy  i n a manner c o n s i s t e n t w i t h  cm  molecule)  i n ac and e s s e n t i a l l y the spectral  .  l o w e s t bands  (isolated  u  - 1  solu-  environment  the line  increase, from  a  ( b e l o w 200  I t has been  fundamentals of B^  i n ab, c - p o l a r i z e d  i n be .  cm  these low-energy  vibrations.  view has been c o n f i r m e d s i n c e  arized  a n d 110  o f t h e two  Further,  the very strong  degenerate  b-polarized  s i x strong  encountered i n attempting to obtain  somewhat  two n e a r l y  t o make  of the s i x  are only  the c o r r e s p o n d i n g v a l u e s i n the gas be  on t h e  o f t h e one r e m a i n i n g  a r e p r o b a b l y p e r t u r b e d by t h e c r y s t a l  1 5  3000  ^  been d e s c r i b e d .  gested '"'"^ t h a t  This  u n (  the molecular character  have a l r e a d y  may  ^  spectrum of the very low-energy  verify  that  Thus  cm  i s automatic since  lines  difficulties  tion  possible.  of the position  B_ f u n d a m e n t a l b e l o w 2000 2u  u  explanation  of experimental evidence alone i t i s impossible  a conclusive  B^  and so s u c h an  choice  of  inten-  between  98 Table  15.  The a s s i g n e d  infrared-active  fundamentals o f  anthracene-h^Q  Symmetry Type  Experimental Present Work f  235  l  g  R  e  Assignment f  >  1  ?  R  e  f  1  8  R  e  f  7  5  Calculated f.41 R e  —  307  490  210  241  650?  743  651  650  627  632  903  907  905  906  922  914  1145  1150  1142  1148  1147  1125  1270  1274  1264  1274  1246  1279  1314  1316  1310  1317  1266  1309  1447  1448  1445  1456  1450  1451  1616  1620  1624  1628  1623  1609  3024?  3022  3028  3008  3051  3030  3050  3049  3050  3020  3062  3079  3 1 0 8?  3110  3100  3040  3073  3082  615  406  —  591  606  —  620  —  808  863  998  999  997  605  1011  1002  1068  1169  1122  1030  1114  1113  1181  1171  600 808?  1163  —  1163  1392  —  1385  1162  1345  1344  —  1495  1398  1537  1350  1387  1409  1533  1462  1680  1438  1457  1441  1533  1720  1524  1534  1542  3050  2972  2990  3045  3040  3026  3093?  3079  3080  3079  3062  3081  110  278  287  —  98  96  166  475  470  392  378  383  469  603  600  581  484  504  730 883 954  72 8 886 957  727 884 954  755  743 916 959  732 892 952^  1345,1695?  *  calculated  i n r e f e r e n c e 40.  —  920  weak c o m b i n a t i o n s and weak fundamentals i s r a t h e r an a r b i t r a r y one b u t on t h e b a s i s o f s t r e n g t h and near-complete p o l a r i z a t i o n , the remaining  fundamentals were chosen a t  3108 (B, l u ) , 3093 (B„2u ) and 3024 c m ~ ( Bl u) . 1  1  A summary o f a l l t h e fundamentals a s s i g n e d i n t h i s work i s made i n T a b l e 15, which a l s o c o n t a i n s experimental 2.  previous  and c a l c u l a t e d a s s i g n m e n t s .  A n t h r a c e n e - d . ^ I n f r a r e d S p e c t r a and Assignment a) S p e c t r a .  P o l a r i z e d s p e c t r a were r e c o r d e d  with  l i g h t i n c i d e n t on t h e ab, bc_' and ac f a c e s ; t h e s p e c t r a a t e n e r g i e s l e s s than 650 cm  1  a r e shown i n F i g u r e s 17, 18 and  19 r e s p e c t i v e l y . F i g u r e s 20, 21 and 22 show t h e s p e c t r a o f the same f a c e s a t e n e r g i e s between 500 and 1900 cm ^. Because o f t h e h i g h e r e x t i n c t i o n c o e f f i c i e n t s a s s o c i a t e d w i t h the CD s t r e t c h i n g v i b r a t i o n s , t h e c r y s t a l s were a l m o s t opaque i n t h e 2260 cm  1  r e g i o n and t h e s p e c t r a are n o t i n c l u d e d .  The ab s p e c t r a f o r t h e h i g h e r - e n e r g y  r e g i o n a r e i n good 16  agreement w i t h those a l r e a d y r e p o r t e d by C a l i f a n o  and, t o  the e x t e n t t h a t t h e ab sample used was r a t h e r t h i c k e r than a s u b l i m a t i o n f l a k e , t h e d a t a shown i n F i g u r e 20 complement his.  On t h e o t h e r hand, t h e r e s o l u t i o n e x h i b i t e d i n t h e 17  s p e c t r a o f Colombo  i s n o t as good and a correspondence  between l i n e s o f h i s s p e c t r a and those i n F i g u r e 20 i s n o t always  obvious.  IOO  200  300  400  500  600cm  F i g u r e 17. Anthracene-^d.. l o w - f r e q u e n c y i n f r a r e d spectrum w i t h i n c i d e n t l i g h t normal t o ab f a c e ; c r y s t a l 0.45 mm t h i c k below 325 c m l , 0.10 mm t h i c k above 325 cm . S o l i d l i n e // b, broken l i n e / / a . Q  -  -1  o  1 0 0  200  300  400  500  6 0 0 cm-'  F i g u r e 19. A n t h r a c e n e - d l o w - f r e q u e n c y i n f r a r e d spectrum w i t h i n c i d e n t l i g h t normal t o ac f a c e ; c r y s t a l 0.95 mm t h i c k below 85 cm" , 0.47 mm t h i c k above 85 cm~^ S o l i d l i n e // a , broken l i n e // c. 1  1  i  600  800  ,  i  IOOO  1  1  I200  1  1  1  1400  r  1600  F i g u r e 20. A n t h r a c e n e - d ^ i n f r a r e d spectrum, 500-1900 c m , normal t o ab f a c e . S o l i d l i n e // b, broken l i n e // a. -1  I800cm~  with incident l i g h t  1  600  800  F i g u r e 21. Anthracene-d normal t o b e f a c e . 1  IOOO  I200  1400  1600  cm"  -1 -, w i t h i n c i d e n t l i g h t i n f r a r e d spectrum, 500-1900 cm"S o l i d l i n e // b, broken l i n e // c . 1  1 Q  BOO  1  106 T a b l e 16 l i s t s the observed band f r e q u e n c i e s and t h e i r assignments based on the o r i e n t e d gas assumption  (see  T a b l e 12) t h a t B^  along  c, and  l i n e s are most i n t e n s e a l o n g b, B  u  a l o n g a.  The mean f r e q u e n c y o f the two  group components was e n t e r e d i n T a b l e 16. s i g n i f i c a n t factor-group s p l i t t i n g  (393, 401), 560  784  (785, 782) cm . 1  (564, 557), 722  factor-  L i n e s t h a t show a  ( w i t h components p a r a l l e l  and p e r p e n d i c u l a r t o b i n p a r e n t h e s e s ) o c c u r a t 102 397  2 u  (724, 720) and  (100, 103), perhaps  That t h e s e are a l l o u t - o f - p l a n e modes  i s c o n s i s t e n t w i t h the s i m i l a r b e h a v i o r o b s e r v e d i n a n t h r a 17 cene-h^g.  I t s h o u l d be noted t h a t Colombo  has  interpreted  the ab spectrum as showing no f a c t o r group s p l i t t i n g s ; i n T a b l e 16 we have a c c o r d i n g l y o m i t t e d Colombo's assignments  of  what we t a k e t o be l e s s i n t e n s e f a c t o r group components. b) Assignment. Of the e l e v e n B ^ , e l e v e n B , s i x B_3u and f i v e A u m o l e c u l a r fundamentals t h r e e B,l u and two 2 u  B  2 u  c o r r e s p o n d t o CD s t r e t c h e s and a r e e x p e c t e d near 2250 cm  The A  u  modes appear p r i n c i p a l l y by s t e a l i n g i n t e n s i t y  intermolecular interactions.  A t low f r e q u e n c i e s an  through  attempt  was made t o a s s i g n a l l the l i n e s , b o t h weak and s t r o n g , i n the hope o f l o c a t i n g the l o w e s t A  u  modes; the low energy  gerade fundamentals used i n making c o m b i n a t i o n s were found i n the c r y s t a l Raman spectrum o f a n t h r a c e n e - d . ^ , which i s d e s c r i b e d i n the n e x t s e c t i o n . beyond 500 cm  1  T h i s a n a l y s i s was not c a r r i e d  because o f a m b i g u i t i e s a r i s i n g from an  1  .  107 T a b l e 16.  The p o l a r i z e d  i n f r a r e d spectrum o f a n t h r a c e n e - d 10  v crystal  A s s i g n m e n t Present  Ref. 16  Ref.  work 60 71 100 102 118 153  m vw ? w s ms m  220 336  s mw  349 363  vw sh  374  w m  393 397 424  vs  435 451  w  s  477  vw vvw  500  w  513 531 548 560 575 601 619  mw vw vw vs vs vw  633 665  w m vw  689  ms  b au ? u b u 3u a u B-, 3u B lu B-, lu n  B  B  3u 3u 2u  ?  2u B, B_3u 3u ? B  B  lu  B  2u  B  3u  B  2u 3u  B  B  B  B  B  B o3u  B  o  3u lu  B  B  ?  3u  ?  2u 2u 3u 2u  Bo  3u B o3u  B o3u B  3u 2u ?  3u 2u B 3u  B  B o3u  B  B  B  Bo  3u  0  B o3u  B o3u  n  lu  B o3u  17  108 Table  16.  (Continued)  v crystal  A s s i g n m e n t Present work  703  ms  B  722  vs  B  755  m  B  784  vs  805  Ref.  2u  16  Ref.  A  u 3u  3u  B-,  3u  B  3u  B-,  3u  B  3u  B o3 u  3u B3u  m  B  3u  824  vs  B  830.  sh  2u B, 3u  860  sh  B,  879  vs  B  l u  lu  892  s  B  3u  B o3 u  904  ms  B  3u  913  s  B  3u  918  w  B  2u  941  m  B  2u  982  ms  B  2u  998  vw  B  3u  1038  w  B  2u  1046  mw  B  3u  106 2  vw  B  2u  1070  vw  B  l u  1120  mw  B  2u  1175  ms  B  2u  1195  vw  B  2u  1210  vw  B  2u  1220  ms  BT  1245  sh  B  1258  vs  B  l u  1298  s  B  2u  1312  ms  B  2u  B  B  l u  B  3u  B  2u  B  2u  B  lu  lu  o3 u  B  ?  B  B  lu  n  3u  7  B  0  B  3u  lu  n  lu B  3u  B  2u  B  3u  B  2u  2u  ?  B o3 u B-,  B  2u  B, lu  B.  ?  lu  lu  B-,  lu  B  B  lu  B-,  lu  B  n  lu  B  n  n  Bn  n  lu  lu  lu  ]  109 Table 16.  v crystal  (Continued)  Present work  1335  s  B  2u  1348  vw  B  lu  1380  ms  1386  ms  1401  s  1406  lu B  3u  B  2u  ms  B  lu  1416  ms  B  2u  1430  m  B  lu  1455  sh  B  2u  1468  ms  B  2u  1493  s  B  2u  1512  mw  B  lu  1530  ms  B  1537  vw  1556  w  1584  s  B  1597  vs  B  1606  vw  1628  m  B  1647  m  B  1670  mw  1749  w  1785  vw  1808  vw  B  1824  ms  B  A s s i g n m e n t Ref. 16  B  2u  B  2u  B  lu  lu  2u B„ ? 2u B lu B. lu  2u  B  2u  lu B-, 3u B  B  2u  3u  2u B-, l B  u  B,l u B  n  2u B, lu  B  B  2u B. lu Blu lu  Ref. 17  B  lu  B  2u  lu  2u Blu B  n  B-, lu  ?  n  B  2u  lu  B  lu  2u  B  2u  110  i n c o m p l e t e knowledge  o f t h e g_ fundamentals and because o f t h e  i n c r e a s e d p r o b a b i l i t y o f f i n d i n g above t h i s energy l i n e s due to i s o t o p i c a l l y substituted  i m p u r i t i e s , such as ^ 4 9 i « c  i ) The low f r e q u e n c y r e g i o n .  D  H  The t h r e e t r a n s l a -  t i o n a l l a t t i c e modes e x p e c t e d , r e f e r r e d t o here and i n T a b l e 16 w i t h lower case symbols, a r e i d e n t i f i e d w i t h t h e two a^j ( p o l a r i z e d a l o n g b) l i n e s a t 7 1 and 1 1 8 cm  1  and t h e b  ( p o l a r i z e d a l o n g a i n t h e ac p l a n e ) l i n e a t 60 cm second b  u  The  l i n e , a t 1 0 0 cm , b e s t seen as a c - p o l a r i z e d 1  u  line  i n t h e ac spectrum, c o u l d be a s s i g n e d as t h e c o m b i n a t i o n o f the b  u  mode a t 60 cm  spectrum a t 38 cm  1  w i t h an ag mode observed i n t h e Raman These f r e q u e n c i e s , as e x p e c t e d , a r e  somewhat l e s s than t h e c o r r e s p o n d i n g v a l u e s found f o r t h e anthracene-h.^ c r y s t a l . The two l i n e s a t 1 0 3 cm plane) and 1 0 0 cm  1  1  ( p o l a r i z e d i n t h e ac  ( p o l a r i z e d a l o n g b) a r e c o n s i d e r e d t o be  the two f a c t o r group components o f what was a B i n the i s o l a t e d molecule.  a t 1 1 0 and 1 0 4 cm ^,  Other m o l e c u l a r fundamentals a r e seen a t 1 5 3 cm cm  - 1  fundamental  These l i n e s a r e c o m p l e t e l y ana-  logous t o t h e p a i r seen i n anthracene-h^Q  220  3 u  1  ( 3 ) and B  U  (B. ) . lu S e v e r a l l o w - f r e q u e n c y l i n e s which appear weakly i n  the i n f r a r e d spectrum o f a n t h r a c e n e - d ^  Q  show mixed symmetry  c h a r a c t e r i s t i c s , i n d i c a t i n g t h e presence o f c r y s t a l - i n d u c e d i n t e r a c t i o n s between modes o f d i f f e r e n t m o l e c u l a r symmetry. L i n e s which showed mixed  and B ^  u  c h a r a c t e r were observed  Ill at  3 4 9 , 3 6 3 , 4 2 4 a n d 4 3 5 cm ^.  was s t o l e n which may  from  the very  dominates  cient  t h e more d i s t a n t  analysis  remembered t h a t tonated  itself  a t 3 9 7 cm  B^  a t 2 2 0 cm  low frequency  i n Table  some o f t h e w e a k  symmetry.  u  17.  lines of  I t s h o u l d be  l i n e s may  be due t o p r o -  impurities.  17.  A tentative lines  Observed  of  assignment  o f t h e weak  B  349  B-,  363  B  3u  374  B  2u  393  B  2u  424  Bo  435  B  l u  451  B  2u  477  B  3u  500  B  2u  lu  n  low-energy  anthracene-d^^  lines  336  Assignment 110  (A )  102  ( B  110  (A )  153  ( B  3u>  153  ( B  3u>  220  (  +  u  228  <v -  2  3u ?  3u  3u  +  )  +  u  261  ( B  261 ( B  2g> 2 g  ?  + 3  )  +  2 2 8 (B  +  261 ( B  2 g  )  + 10?  +  228 ( B  l g  )  + 3?  +  3 8 2 (Ag)  )  +  12  ?  102  1  intensity  u  strong line  was o f B ^  of the remaining  i s suggested  character  u  1  p r o b a b l y be r e l a t i v e l y i n e f f i -  unless the combination  anthracene-d^g  Table  strong B.^ fundamental  t h i s process would  tentative  the B^  t h i s r e g i o n o f the spectrum.  be d e r i v e d from  although  Presumably  B  lu  )  • 3u> ( B  - 7  * The v a l u e s f o r t h e g e r a d e v i b r a t i o n s next section of t h i s thesis.  are taken  from t h e  A  112  I n T a b l e 17 t h e presence o f an A 110 cm  u  fundamental a t  has been p o s t u l a t e d , m a i n l y because o f t h e need f o r  1  such a fundamental t o e x p l a i n t h e medium weak 3 3 6 cm line.  1  B^  u  A l t h o u g h some o f t h e h i g h e r - e n e r g y l i n e s may be caused  by p r o t o n a t e d i m p u r i t i e s , such an e x p l a n a t i o n seems u n l i k e l y f o r t h e 3 3 6 cm  1  l i n e , s i n c e i t l i e s q u i t e f a r above any g  o r u m o l e c u l a r fundamentals o f a n t h r a c e n e - d ^  (see T a b l e 18  o r 2 0 , t o f o l l o w l a t e r ) and t h e i n c r e a s e i n f r e q u e n c y o f the c o r r e s p o n d i n g modes o f t h e monoprotonated m o l e c u l e (the p r i n c i p a l impurity) probably i s not large. t h a t t h e l i n e i s due t o an A b u t near t h e 3 9 7 cm  1  u  fundamental o f anthracene-d^Q,  fundamental any such m o l e c u l a r -  i n a c t i v e mode would be e x p e c t e d t o show B crystal.  I t i s possible  The v e r y weak B^  u  3 u  l i n e a t 3 4 9 cm  mark t h e presence o f t h e second l o w e s t A  u  1  symmetry i n t h e may i n f a c t  fundamental o f  anthracene-d^Q, a l t h o u g h i t l i e s q u i t e f a r below t h e c a l c u 35  l a t e d frequency. A l t h o u g h t h e a n a l y s i s suggested i n T a b l e 17 i s n o t u n i q u e , o t h e r s t r i e d seemed l e s s p l a u s i b l e i n a t l e a s t one r e s p e c t , e.g. t h e p r e d i c t i o n o f an a n t h r a c e n e - d ^  frequency  r a t h e r g r e a t e r than o r v e r y much l e s s than t h e c o r r e s p o n d i n g anthracene-h^ value, or the p r e d i c t i o n of a  fundamental  below 2 5 0 cm \ e t c . I t i s i n t e r e s t i n g t o note t h a t t h e 2 2 0 cm  1  B^  u  fundamental o f anthracene-d^g c o i n c i d e s almost e x a c t l y w i t h the 2 2 1 cm -1 i n t e r v a l o b s e r v e d 77 .i n t h e f l u o r e s c e n c e spectrum  113 of  anthracene-d.^  in a  fluorene matrix.  orescence  interval  was  intensity  from  fluorene lattice  the  ii) expected four to  below  fairly  the  B, —lu  2 0 0 0 cm  879,  1258  cm  lines  1430  fundamental  1406  cm  has  1  mental  certainly by  1406  and  modes. rather  since  cm  strength of the  i s also  1  presence are  of  line  u  included  (see T a b l e  15  protonated molecule). region into  u  While  line.  The  strong  b-polarized  only  B  l u  s  o  anthracene-d^Q  line  lines  n  cm  position line  the  the  i s  1  exaggerated  then  line  suggests  1  l y  50  cm  spectrum from  1220  are the  vibrations  i n - p l a n e bends i s o n l y the  corresponding  above t h i s  1220  i s remarkably to  there  w i t h t h e modes o f  that 1  at  the  s e p a r a t i o n of the CD  at  funda-  I f the  cm  of  intensity;  u  ^.  1200  f o r comparison  r i n g modes and  li®  cm  as  of  trio  symmetry where o n l y t h r e e  approximation, i t i s surprising H  the  three the  a t 1380  above  an  c  of  line  a l s o mark t h e  1386  this  i n ^4 jo  one  the g r e a t e s t B^  at  Only  The  1  been chosen  in  vibration  cm" .  latter  line  fundamentals  made, c o r r e s p o n d i n g  1584  may  forces.  to identify.  at least 1  B, lu  v  flu-  gaining  crystal  i n the assignment,  f o u r fundamentals  f o u r r i n g modes o f B ^  expected  cm  the  fundamental  eight  be  and  arbitrarily  o v e r l a p w i t h the B^  1220  can  From t h e s e  i t p r o b a b l y has  the  The  and  1  u  through  are d i f f i c u l t  medium s t r e n g t h a t 1220  of  the Bj,  assignments  a t 220,  a t 1380,  by  fundamentals.  certain  lines  caused  Presumably  879  cm  i s t h e v e r y weak b a n d a t 1070  1  ,  cm  cm  clear  of  however 1  )  and  1  (the  for  114  this  reason  tatively  the  accepted.  fundamentals ching  one  B^  CD  u  2248 and  as  ratio  of  any  bands.  line  i s  1  ten-  remaining t h e CD  stret-  centered at  spectrum  This  lesser  line  and  2264  i s assigned  i s flanked  s t r e n g t h and  fundamentals  an  attempt  to locate  these  by  as  lines  at  are taken  i n agreement w i t h  a guide.  and  The  u  lines  expected  I f the  -d^Q  fundamentals  B^  which  lines  vibration  Table may  fundamental  complex system the product  of  the  rule  rule  two  as  the  be  16  as  correct,  and  from  then  1  to appear near  s t r o n g a b s o r p t i o n a t 722  cm  then 740 -1  as  both  and  800 20-22  region, are  very intense B  i s assumed t o be  a t 5 6 0 - 5 7 0 cm  product  Figures  corresponding to the 1 Q  have  already assigned for  present i n this by  funda-  calculations  p r o b a b l y l i e b e t w e e n 500  of anthracene-h  by  remaining  value f o r the  are accepted  e x t r e m e l y weak o r h i d d e n I f the  the  b l o c k , the product  I t i s e v i d e n t from  either  the  1  i s 0.182.  unassigned  that  two  i s deferred until  1  region of the  stretching  anthracene-h^Q  .  the  cm  are d i s c u s s e d .  i n the  been used  1  of  a t 1220  , 16,17 workers. In  cm  2 0 0 0 cm  this  2 2 8 3 cm  previous  rule  line  assignment  s t r e t c h i n g mode.  t h e o t h e r CD  mentals  of the  very intense b-polarized  dominates  1  The  below  vibrations A  cm  assignment  or  3 u  650  cm  hidden  B2  U  1  under  the other i s p r e d i c t e d cm  1  and  may  suggested  be by  part Colombo  17  115  and  i n an e a r l y  the  s t r o n g b a n d a t 7 8 4 cm  at  8 2 4 cm  -1  ' as suggested  If, mental very of  work by C a l i f a n o ,  strong  this  earlier,  stealing 1  the final  B^  Since  the available  u  a similar mode n e a r  product 8 4 0 cm  rule  expected,  intense  B ^  u  two o f t h e s e  c-polarized  mark t h e p r e s e n c e fundamentals.  line  strong absorption region  ness  o f t h e samples rule  calculations,  previous authors  575,  below  '  2 0 0 0 cm  1  703  has B  u  A  very  2 2 6 7 cm  1  t w o CD  stretching  must  contained i n  t o reduce  the thick-  and f o rt h e purpose  spectrum,  c a n be chosen  experimental evidence 2  fundamentals  u  1  of  suggested  i s accepted.  previous - 1  a choice t o  17  7 0 3 , 824, 9 8 2 , 1335 a n d 1493 c m  cm  o f 7 4 0 cm  t h e v a l u e o f 2 2 3 8 cm  From t h e c - p o l a r i z e d fundamentals  (efforts  would  2 0 0 0 cm ^.  one o f t h e s e  l e dt o breakage)  16  2  was p r o b a b l y a l s o  this  product  Eleven B  centered a t about  The second  line,men-  1  incomplete.  a p p e a r i n g above  of at least  location  the experimental  s p e c i e s must remain  fundamentals.  funda-  argument  instead  1  41  from t h e  , and i f t h e true  i n f o r m a t i o n does n o t p e r m i t  of the B^ iii)  are  i snot a  1  intensity  made b e t w e e n t h e v a r i o u s a l t e r n a t i v e s ,  assignment  band  and C a l i f a n o .  a t 1 2 2 0 cm  a t 1 2 5 8 cm  then  place  by  Scrocco  m o d e i s m a r k e d b y t h e v e r y w e a k 1 0 7 0 cm  tioned  be  by Neto,  a combination  line  o r i t may b e h i d d e n i n  o r even i n t h e s t r o n g  1  however, t h e l i n e  but rather  16  symmetry.  - 1  .  s i x of the nine immediately a t There  to establish  The s t r o n g l i n e  h a s been no  that  the line at  a t 1 5 9 7 cm  1  116  must correspond and  the  the  line  same d i f f i c u l t y  deciding as  to  on  an  e x i s t s i n the  experimental  a l t e r n a t i v e s f o r one  will  be  delayed  until  i n anthracene-h.^  basis  of  a  the  later  i n choosing between the  strong  line  band  at  1175  cm  list  of  at  1298  cm  1  B2  and  1  cm  1  species  b e t w e e n 1597  and  r i n g modes, and  the  Another  1401  in cm  1  choice  difficulty  c l e a n l y p o l a r i z e d medium-  the  Because of  stronger  but  i t s relative  less isolated  isolation,  t e n t a t i v e l y b e e n c h o s e n and  the  inserted in  the  fundamentals.  U  clarify  cm  .  b a n d has  1  The to  1175  1690  deuterated  chapter.  exists  at  assignment of  the  experimental  a  fundamental at  982  situation in this  cm  helps  1  region  consider-  920  17 Colombo has a s s i g n e d two B 2 f u n d a m e n t a l s a t 903 and —1 16 — 1 cm . Califano h a s n a m e d 9 0 1 cm and N e t o , S c r o c c o  and  Califano  ably.  U  spectra,  41  h a v e c h o s e n 920  i t i s clear that  symmetry, b e l o n g i n g line  at  913  but  i n any  is  clearly  cm  the  41  '  polarized  instead The  line  901  to at  -1  .  cm  the  B^  918  cm  weak, and  From the line  1  ac  i s not  species,  u  1  may  the  and  be  982  cm  of  as  of  be' B2  U  does  B2  the  symmetry  U  assignment  1  preferable.  75  strong  .  the  event i s rather  The pected  1  cm  remaining  between B^  u  line  strength.  800 at  fundamental below and 879  900 cm  1  cm  -1  which  and  2 0 0 0 cm may  be  1  is  hidden  shows u n e x p e c t e d  exin c-  117  —3u choice  ^  u  n  t  ^  a  m  e  n  '  t  :  a  l • s  A  o f the s i xi n f r a r e d - a c t i v e  f°  s  anthracene-d.^ i s automatic.  at  1 0 2 , 1 5 3 , 3 9 7 , 5 6 0 , 722 a n d 784 c m with  product rule predicted  Strong lines  the anthracene-h^g  ratio  anthracene-h^Q,  frequencies.  i s 0.372 w h i c h  i s made  i n Table  a) presented  18, which  and c a l c u l a t e d  Anthracene-d.^  at each nearly  Spectra.  i n Table  also  and  The d e t a i l s  19.  sensitivity  assigned i n this  contains  i n different  t h e same c o n d i t i o n s  benzene and carbon solubility  Assignment  o f t h e Raman s p e c t r a a r e  although  s p e c t r a were measured under as  r a t i o measurements were attempted i n  tetrachloride  solutions  here  a l i n e was c l e a r l y  b u t because the the strongest  lines  s u c c e s s was o b t a i n e d w i t h t h e  i n Chapter  measurements r e p o r t e d  f o r varying  as p o s s i b l e .  Somewhat b e t t e r  described  Raman  regions o f t h e spectrum but  o f a n t h r a c e n e was t o o l o w o n l y  found.  previous ex-  As f o r t h e naphthalene-dg  frequency the various  melt c e l l  The o b s e r v e d  assignments.  Raman S p e c t r u m  Depolarization  were  correlate  compares w e l l w i t h t h e -  m e a s u r e m e n t s , n o a t t e m p t was made t o c o r r e c t detector  observed  0.364.  perimental  3.  were  and these  - 1  A summary o f a l l t h e f u n d a m e n t a l s work  the  out-of-plane fundamentals  of  very w e l l  r  I I and t h e d e p o l a r i z a t i o n  are f o rthe melt. polarized  (p^g  I n many <  K  cases,  0.75) o r  118 Table  18.  The  assigned  infrared-active  fundamentals o f  anthracene-d^Q  Symmetry type  Bl u  B 2u  Present work  Ref.  16  Ref.  41  Ref.  17 R e f .  41 R e f .  7!  220  —  —-  283  199  195  ? ?  (720)  592  592  617  599  822  822  730  825  840  879  881  881  882  861  891  —  981  —  1235  1041  1035  1258  1264  1264  1259  1275  1215  1406?  1389  1389  1400  1380  1357  1584  1583  1583  1515  1582  1603  2248?  2247  2247  2250  2246  2276  2264  2262  2262  2260  2271  2291  2283?  2297  2288  2288  2280  2303  575  580  580  388  588  • 570  703  706  706  562  701  660  824  831  —  830  811  824  879?  901  831  903  840  847  —  920  920  943  1007  1325  1267  1291  982 1175?  1125  1335  1342  1325  1390  1315  1317  1493  1384  1384  1503  1392  1351  1401,1597?1500  1500  1595  1487  1506  2238  2238  2225  2257  2261  2267  2273  2275  2275  2294  2294  102  236  260  93  153  407  403  333  397  563  566  416  560  577  584  571  722  726  690  753  784  790  758  804  — B 3u  Calculated  Experimental  T a b l e 19.  Crystal (cm-1)  The Raman spectrum o f a n t h r a c e n e - d . ^  (aa)  (bb)  Intensity Distribution' (c'c') (ab) ( b e ) 1  (a'a')  (cc) (a'c)  melt (cm" )  Symmetry  1  1  k  k  1  0  4  B  18  3  5  k  2  l  1  ig  B  5  9  3  6  2  3  3  2g  6  382  11  17  35  6  26  9  50  16  415  2  1  9  2  5  1  1  2  488  0  0  0  0  502  4  228  1  261  6  367  601  379 P 407  dp  502  dp  b  3g-  8  5  9  3  4  4  0  0  0  0  0  0  0  Ag?  0  1  k  k  1  B-, ?  1  k  644  k  l  Ik  k  k  0  22  36  6  14  707 P  V  26  80  761  0  k  777  1  l  2h  k  2k  1  1  816  5  6  10  4  9  2  3  20  28  30  12  23  4  20  k  0  k .  5s  B  3  k  l  1  B  886 942 983  c  B  k  c  k  1  1  k  0  2g  770  dp  B-,  3  813  dp  B  7  846 P  lk  0  7  Ag6  709  842  8  t-  2g-  0  k 34  3g  Rig  0  c  659  A„ B "?  7  613 651  364  ?  3g 3g  Agb 3g 0  3g  A ?b rr  1  Table  19.  Crystal (cm-1)  1076  (Continued)  5  (ial  1  h 1  1156 1199  h  1233  (a'a')  (ccl  (i^cT  melt (cm" )  „ . symmetry  1  h  c  1123  1310  Intensity Distribution (bbl (c'c' ) (lb) (be" ")  c  1338  0  h  0  h  0  1  3  2  9  3  3  8  1  0  0  h  h h  1  h  l  0  0  0  h  h  0  0  1153  p  A „  %  h  B  0  h  0  h  0  h  0  100  33  A  1388  p  34  100  83  28  81  18  1402  14  48  19  14  13  5  1419  5  22  7  5  10  2  1485°  0  1  0  h  h  0  1534  11  80  20  14  28  5  8  5  1534  1615  3  4  4  3  4  2  4  4  1610  dp  2259  3  16  5  4  7  1  2  2 2259  p  1  %  2  1  7  2  5  3  2276  h  2287  5  c  1 18  7  5  b  3g  g b  A  H to o  1402 p d  5  3 0  3  2266  g  0  1388  '  A  A  B  g B_ b 3g  A  B  3g  2285 p R e l a t i v e i n t e n s i t y s c a l e s f r o m 0 t o 100 f o r t h e a b a n d b e ' f a c e s , a n d f o r t h e a £ f a c e independently. b T h i s r e s u l t i s s u p p o r t e d by t h e p r e v i o u s f l u o r e s c e n c e a s s i g n m e n t . ' T h i s l i n e i s broad. dThis l i n e i s absent i n the melt spectrum; data entered f o r benzene s o l u t i o n .  7  121 depolarized  (P  o t ) S  £  0.75), a r e p r o d u c i b l e n u m e r i c a l  value  f o r p c o u l d n o t be o b t a i n e d and so t h e l i n e s a r e d e s i g n a t e d o n l y p ( p o l a r i z e d ) o r dp ( d e p o l a r i z e d ) i n T a b l e 19. A comparison o f t h e observed c r y s t a l s p e c t r a w i t h the e x p e c t e d i n t e n s i t i e s , g i v e n i n T a b l e 11, i n d i c a t e s t h a t the p r e d i c t i o n s o f t h e o r i e n t e d - g a s  model cannot p r o p e r l y  account f o r t h e o b s e r v e d s p e c t r a .  The symmetries o f many  of t h e weak l i n e s i n t h e c r y s t a l spectrum c o u l d n o t be a s s i g n e d w i t h c e r t a i n t y a p p a r e n t l y because o f c r y s t a l with adjacent  mixing  s t r o n g e r l i n e s ; as shown i n T a b l e 10, a l l  gerade m o l e c u l a r  modes may mix i n t h e s i t e symmetry o f t h e  molecule i n the c r y s t a l .  Some o f t h e d i f f i c u l t y , however,  may have been caused by s c a t t e r i n g from i m p e r f e c t i o n s i n t h e c r y s t a l or at i t s surface.  The c o a x i a l v i e w i n g  system used  on t h e Cary 81 s p e c t r o p h o t o m e t e r i s p a r t i c u l a r l y s e n s i t i v e t o l i g h t s c a t t e r e d from s u r f a c e  imperfections.  Another source of i n t e n s i t y p e r t u r b a t i o n a v a i l a b l e i n t h e c r y s t a l environment a r i s e s from t h e a r t i f i c i a l s e p a r a t i o n o f i n t r a - and i n t e r m o l e c u l a r m o t i o n s .  The n e g l e c t  of i n t e r a c t i o n s between such modes i s n o t j u s t i f i a b l e f o r a m o l e c u l e as l a r g e as anthracene whose f r e e - m o l e c u l e  funda-  mentals o v e r l a p t h e energy r e g i o n o f t h e l a t t i c e v i b r a t i o n s , as shown i n e a r l i e r s e c t i o n s o f t h i s t h e s i s .  I n F i g u r e 23  i s shown t h e change i n i n t e n s i t y o f t h e two l o w e s t modes o f a n t h r a c e n e - d ,  n  molecular  as a f u n c t i o n o f temperature as t h e  122  63  Frequency  (cm ) - 1  F i g u r e 23. The l o w - f r e q u e n c y Raman spectrum o f . polycrystalline anthracene-d a t temperatures near t h e m e l t i n g p o i n t 1 Q  123 p o l y c r y s t a l l i n e sample nears t h e m e l t i n g p o i n t .  It is  o b v i o u s from t h e s p e c t r a t h a t both l i n e s g a i n i n t e n s i t y i n the c r y s t a l l i n e environment  and t h a t t h e l i n e a t 22 8 cm  1  (room temperature c r y s t a l v a l u e ) g a i n s more than t h e h i g h e r energy mode.  I t i s a l s o i n t e r e s t i n g t o note t h a t t h e f r e -  q u e n c i e s o f t h e l a t t i c e modes and m o l e c u l a r modes decrease 14 as t h e temperature i n c r e a s e s .  S u z u k i , Yokoyama and I t o  have r e p o r t e d f o r anthracene-h-^g  t h a t t h e decrease i n f r e -  quency i n g o i n g from 4°K t o room temperature i s even more marked.  Another i n t e r e s t i n g p o i n t i s t h a t t h e g r o s s i n t e n s i t y  changes shown i n F i g u r e 23 b e g i n even b e f o r e t h e m e l t i n g p o i n t i s reached.  T h i s suggests t h a t a t l e a s t t h e l i b r a -  t i o n a l phonon s t r u c t u r e i s l o s t b e f o r e t h e c r y s t a l  structure  disappears. b) Assignment.  The t h r e e ag l a t t i c e f r e q u e n c i e s  were seen a t 38, 6 8 and 109 cm  1  and comparison w i t h t h e 14  c o r r e s p o n d i n g modes i n anthracene-h^g and 121 cm  1  reported  a t 35, 73,  r e v e a l s t h a t t h e r e i s p r o b a b l y a minor e r r o r i n  the p o s i t i o n o f t h e l o w e s t ag  mode i n one o r both o f t h e  a s s i g n m e n t s , s i n c e an a n t h r a c e n e - d ^ v i b r a t i o n i s n o t expected a t h i g h e r energy than t h e c o r r e s p o n d i n g v i b r a t i o n i n a n t h r a cene-h^g.  Since' t h e energy f i t f o r t h e 100 cm  1  b  u  combin-  a t i o n o f t h e d e u t e r a t e d m o l e c u l e i s b e t t e r than t h e f i t f o r the c o r r e s p o n d i n g c o m b i n a t i o n i n a n t h r a c e n e - h ,  n  (see s e c t i o n  124 B . l ( b ) o f t h x s c h a p t e r ) t h e e r r o r may l i e i n t h e assignment for the protonated molecule.  14  The t h r e e bg l a t t i c e v i b r a t i o n s  were seen a t 43, 63 and 117 cm \ i n good agreement w i t h t h e 14 -1 anthracene-h^Q assignments a t 45, 65 and 125 cm The assignments o f t h e Raman-active m o l e c u l a r f u n damentals o f a n t h r a c e n e - d . ^ a r e l i s t e d i n T a b l e 20.  Since  complete assignments w i t h i n each b l o c k c o u l d n o t be made t h e p o s i t i o n s which t h e fundamentals occupy i n t h e b l o c k were a s s i g n e d e i t h e r by comparison w i t h t h e anthracene-h^g  assign-  ments 14 o r by comparison w i t h t h e c a l c u l a t i o n s . 40 '41 '75 367 and 415 cm  1  The  l i n e s were v e r y weak i n t h e m e l t b u t much  s t r o n g e r i n t h e c r y s t a l spectrum, i n d i c a t i n g t h a t i n t h e s o l i d they had a c q u i r e d c o n s i d e r a b l e Ag c h a r a c t e r by m i x i n g w i t h t h e s t r o n g 3 82 cm  line.  1  B, and B_ fundamentals a r e lg 3g  40 41 e x p e c t e d near t h i s energy The 367 cm  1  '  as w e l l as an Ag fundamental.  l i n e may mark t h e presence o f e i t h e r t h e B ^  fundamental o r t h e c o m b i n a t i o n 153 ( B g ) + 220 ( u  415 cm  1  l i n e appears t o have mixed Ag (382 cm  B l u  ).  g  The  and B^g  c h a r a c t e r i s t i c s i n t h e c r y s t a l , and i s t a k e n as t h e B^g f u n damental.  An Ag fundamental a t 594 cm was observed i n t h e 77 f l u o r e s c e n c e spectrum; the corresponding i n t e r v a l i n the Raman spectrum may be t h e l i n e a t 601 cm 1  A l s o l i s t e d i n T a b l e 20 a r e t h e r e s u l t s o f some force f i e l d calculations  40 41 75 ' ' and t h e a s s i g n e d Raman-active  125 T a b l e 20.  The a s s i g n e d Raman-active fundamentals o f Anthracene  Symmetry Anthracene-d^g Calculated Type assignment ' Ref. 75 Ref s. 40,41 2288 2266 2258 1534 1388 1156 842 709 601 382 B  ig  613? 228  B 2g  761? 644,659? 261  Anthracene-h assignment"^  2295 2264 2263 1587 1435 1335 1188 884 821 744 600 363  2294 2275 2255 1553 1407 1347 1149 848 819 690 634 356  780 592 387 207  774 578 403 220  915  927 787 677 665 485 245  910 801 682 602 510 287  978 904  3056 3027 1557 1481 1402 1261 1163 1007 754 622? 395  243  765 622 290  126 T a b l e 20. Symmetry Type  (Continued) Anthracene-d^^ assignment 2276  Calculated Anthracene-h Ref. 75 R e f s . .40,41 assignment+ 2301 2278 1619 1535  2278 2247 1588 1522  1266 1044  1244 1027  943 816  929 878  960 846  777 , 502  809 479  810 494  956 522?  415  339  361  —  — 1615  — 1233  —  See t e x t f o r d e s c r i p t i o n o f source o f anthracene-h assignments.  3076  — 1630  — — — 1187  —  127 fundamentals o f anthracene-h.^.  The f r e q u e n c i e s l i s t e d f o r  the p r o t o n a t e d m o l e c u l e were t a k e n from S u z u k i , Yokoyama and 14 22 Ito and from T i n g , a l t h o u g h the f i n a l assignment does n o t agree c o m p l e t e l y w i t h e i t h e r o f these a u t h o r s .  The d i f f e r -  ences o c c u r p r i m a r i l y i n t h e Ag and B^^ symmetry b l o c k s and a r i s e to o b t a i n consistency w i t h the p o l a r i z e d fluorescence 77 spectra and w i t h some d e p o l a r i z a t i o n r a t i o s measured f o r a 23 solution and, i n the course o f t h i s work, f o r the m e l t . F o r example, t h e e a r l i e r a u t h o r s have d i s a g r e e d on t h e assignments of t h e i n t e r v a l s 1481 and 1505 cm -1 ; S u z u k i e t a l .14 a s s i g n e d 22 them B^  and Ag, w h i l e T i n g  B^g fundamentals,  c o n s i d e r e d them t o be Ag and  respectively.  I n t h e Raman spectrum o f t h e  m e l t , t h e 1481 cm  1  l i n e was prominant and w e l l p o l a r i z e d  w h i l e t h e 1505 cm  1  l i n e was so weakened t h a t t h e d e p o l a r i z a t i o n  r a t i o c o u l d n o t be measured.  E v i d e n t l y the l a t t e r l i n e i s  i n t r i n s i c a l l y weak and g a i n s s t r e n g t h through c r y s t a l e f f e c t s .  CHAPTER  V  CALCULATIONS  A.  Molecular  In function nuclei  Vibrations  t h e Born-Oppenheimer  representing the restoring  when  they  are displaced  tions  i s independent  tion.  I f the motion  small,  t o a good  and  vibrational  event then  that  potential  approximation wave  which  forces  i n turn  f r e q u e n c i e s o f one m o l e c u l e  calculate  this  method  molecules;  The normal  approximate depends  on t h e degree  i n isotopic  species,  excellent.  128  In the  a r e known,  to find  procedure  and  the  i s t o use the i t s force  to similar  molecules  The r e l i a b i l i t y  of similarity  f o r example,  fre-  of the vibra-  to calculate  frequencies.  rotational  the k i n e t i c  amplitudes  c a n be t r a n s f e r r e d  func-  the vibration i s  c a n be used  and r e l a t i v e  posi-  wave  separable.  determine  known  to  during  on t h e  equilibrium  i n the molecule  of the molecule.  then  acting  the translational,  tions  which  their  functions are also  of vibration  constants  forces  the potential  i n the electronic  o f t h e atoms  the restoring  energy  from  o f changes  the nuclear displacements  quencies  approximation  of  between t h e  the f i t i s  129 1.  Motion i n Cartesian  Coordinates  A system o f N n u c l e i has 3N degrees o f freedom o f which s i x ( o n l y t h e n o n - l i n e a r case i s c o n s i d e r e d )  account  f o r t h e t r a n s l a t i o n s and r o t a t i o n s o f t h e m o l e c u l e as a whole.  I f t h e 3N mass-weighted C a r t e s i a n d i s p l a c e m e n t c o -  o r d i n a t e s {q} a r e i n t r o d u c e d , where q^ =  >/m^  • Axj_,  q2 = y m ^ «Ay^, e t c . t h e n t h e k i n e t i c energy, T, o f t h e m o l e c u l e i s g i v e n by 2 T  =  I  i  V.l  (q )  2  ±  o r , i n m a t r i x n o t a t i o n , where q i s t h e column v e c t o r o f t h e (q), 2 T The  V.la  p o t e n t i a l energy, V, can be expressed  i n the displacement  coordinates  over t h e 3N c o o r d i n a t e s , 2 V =  2 V +  2  n  as a T a y l o r s e r i e s  ( q l , i n which a l l sums a r e  thus:  E ( ? ) ±  The  =  . t. • g_ 2,  q. +  3q. o * i  (^1 i , j 3 .3 E  q  , q.q. + ...v. 2 o ^  } q j  e q u i l i b r i u m c o n f i g u r a t i o n i s a s s o c i a t e d w i t h a minimum i n  the p o t e n t i a l energy s u r f a c e and when i t i s d e f i n e d t o have zero energy t h e f i r s t two terms i n e q u a t i o n  2 drop o u t and,  i f h i g h e r terms a r e n e g l e c t e d , 2 V  =  ) q  i  q  or 2 V =  q.q*. =  f..q.q.  V.3  j q^F %  V.3a  130 The dependence o f t h e p o t e n t i a l energy o n l y on second o r d e r terms i m p l i e s harmonic motions o f t h e atoms; i f t h e d i s placements a r e l a r g e t h i s a p p r o x i m a t i o n i s n o t v a l i d and h i g h e r o r d e r terms b e g i n t o become i m p o r t a n t .  (The appear-  ance o f t h e s e anharmonic terms i n t h e f o r c e f i e l d r e s u l t s i n i n t e r a c t i o n s between harmonic normal modes.) The motions o f t h e system o f n u c l e i a r e governed by Newton's e q u a t i o n s o f m o t i o n , which a r e , i n t h e mass-weighted C a r t e s i a n system and i n L a g r a n g i a n form,  "It all " 4l "  0  -  1 1 = 1 3 N )  v 4  where L, t h e L a g r a n g i a n f u n c t i o n , i s g i v e n by L = T-V. T i s a f u n c t i o n o f t h e q^  Since  and V o f t h e q^, s u b s t i t u t i o n o f  e q u a t i o n s 1 and 3 i n t o 4 g i v e s a s e t o f 3N homogeneous second order d i f f e r e n t i a l equations q'  +  1  One p o s s i b l e  £ f. . q . = 0 j - J J  (i=l,  3N) .  V.5  L  solution i s q^  =  q^ s i n (tj\  +  V.6  6)  o  where q^ i s t h e a m p l i t u d e o f t h e m o t i o n , 6 i s a phase and X i s r e l a t e d t o t h e v i b r a t i o n a l f r e q u e n c y .  factor  Substitution  of e q u a t i o n 6 i n t o 5 g i v e s r i s e t o a s e t o f 3N l i n e a r homogeneous e q u a t i o n s which have n o n - t r i v i a l s o l u t i o n s o n l y i f t h e secular  determinant equals zero, i . e .  131 Six  o f t h e 3N v a l u e s o f X s a t i s f y i n g e q u a t i o n 7 a r e always  found t o be z e r o ; these c o r r e s p o n d  to the three molecular  r o t a t i o n s and t h r e e t r a n s l a t i o n s .  The r e m a i n i n g 3N-6 v a l u e s  o f X a r e r e l a t e d t o t h e normal f r e q u e n c i e s of> v i b r a t i o n , v -1 2 —2 2 ( i n cm ) , by X = 4TT v c ; s u b s t i t u t i o n o f t h e s e v a l u e s o f A  back i n t o e q u a t i o n  q^ v a r i e s w i t h t i m e .  (6) shows how each o f t h e c o o r d i n a t e s The m o t i o n o f t h e n u c l e i  corresponding  to each normal frequency i s known as t h e normal mode o f t h e vibration.  2.  Motion i n g e n e r a l i z e d Coordinates. The normal f r e q u e n c i e s and normal modes o f v i b r a t i o n  are o f c o u r s e independent o f t h e c o o r d i n a t e system used.  The  above s o l u t i o n i n terms o f mass-weighted C a r t e s i a n s i n v o l v e s force constants  which a r e i n c o n v e n i e n t i n two r e s p e c t s ;  s i n c e they cannot be i n t e r p r e t e d i n p h y s i c a l terms they a r e not i m m e d i a t e l y  t r a n s f e r a b l e between m o l e c u l e s , and a l s o o f f -  d i a g o n a l terms a r e n o t a l l z e r o .  I n o r d e r t o d i s c u s s two  c o o r d i n a t e systems, each one o f which e l i m i n a t e s one o f t h e above d i f f i c u l t i e s ,  a completely general, u n s p e c i f i e d co-  o r d i n a t e system w i l l be c o n s i d e r e d f i r s t . Any  s e t o f c o o r d i n a t e s can be r e l a t e d t o a n o t h e r s e t  by a l i n e a r t r a n s f o r m a t i o n U.  In p a r t i c u l a r , the r e l a t i o n  between some s e t {p} and t h e c a r t e s i a n d i s p l a c e m e n t s g i v e n as  {q} i s  132 q = u p In the c o o r d i n a t e s {p} the k i n e t i c energy (from e q u a t i o n l a ) I s g i v e n as 2 T =  j^t^U p  V.8  I f the t r a n s f o r m a t i o n i s o r t h o g o n a l , then U = 2 T  =  3.  1  and  p^  V.9  S i m i l a r l y , from e q u a t i o n 3a, the p o t e n t i a l 2 V =  U  p_ U fc  t  energy i s g i v e n as  F U p  V.10  M o t i o n i n Normal C o o r d i n a t e s The a n a l y s i s o f the v i b r a t i o n a l  problem would be  e x t r e m e l y s i m p l e i f a c o o r d i n a t e system c o u l d be found f o r which a l l c r o s s - t e r m s between c o o r d i n a t e s i n both the  potential  and k i n e t i c energy e x p r e s s i o n s were z e r o ; the mass-weighted C a r t e s i a n s i n t r o d u c e d e a r l i e r have t h i s p r o p e r t y o n l y f o r the k i n e t i c energy. displacement  Such a system can be d e f i n e d ; a  c o o r d i n a t e i n t h i s system d e s c r i b e s  single  the m o t i o n  e x e c u t e d by a l l the atoms when the m o l e c u l e undergoes a normal vibration. are 3N-6  S i n c e t h e r e are 3N-6  fundamental v i b r a t i o n s  of these normal c o o r d i n a t e s .  k i n e t i c and p o t e n t i a l  there  I n t h i s system the  e n e r g i e s are g i v e n by  2 T =  Q  fc  Q  V.ll  133 and  2 V  =  Q^A  Q  V.12  where Q i s a column v e c t o r o f the normal c o o r d i n a t e s _A i s a d i a g o n a l m a t r i x .  The  normal c o o r d i n a t e s can  and be  v i s u a l i z e d i n terms o f the C a r t e s i a n d i s p l a c e m e n t  set; i f  the t r a n s f o r m a t i o n between the two systems i s L,  then  a 4.  =  Motion i n I n t e r n a l  L Q Coordinates  I n the mass-weighted C a r t e s i a n c o o r d i n a t e system used e a r l i e r the elements f ^ j which r e p r e s e n t the e f f e c t a change i n c o o r d i n a t e i has on c o o r d i n a t e j are awkward t o t r a n s f e r from one m o l e c u l e  t o another because they have no  d i r e c t chemical i n t e r p r e t a t i o n .  This disadvantage  overcome by s e t t i n g up the problem i n i n t e r n a l  can  be  coordinates  such as the v a l e n c e c o o r d i n a t e s whose a p p l i c a t i o n was  summar-  80 i z e d by D e c i u s .  These c o o r d i n a t e s measure changes i n bond  l e n g t h s and a n g l e s d u r i n g v i b r a t i o n s and can be  interpreted  c h e m i c a l l y i n terms o f the s t r e n g t h s o f bonds and  their  resistance to d i s t o r t i o n . I n the i n t e r n a l c o o r d i n a t e s {R}, the p o t e n t i a l energy i s g i v e n by 2 V  =  R  fc  F R  V. 13  where the elements o f F are the f o r c e c o n s t a n t s a s s o c i a t e d w i t h the v a r i o u s bond s t r e t c h e s and a n g l e Although  distortions.  F i s d i a g o n a l o n l y i n the s i m p l e s t  approximation,  134 the f o r c e c o n s t a n t s r e l a t e d t o bond s t r e t c h e s and  distor-  t i o n s o f the v a l e n c e a n g l e s s h o u l d be much l a r g e r than i n t e r a c t i o n constants.  I n o r d e r t o determine  the  the k i n e t i c  energy i n the i n t e r n a l c o o r d i n a t e system i t i s n e c e s s a r y  to  f i n d the t r a n s f o r m a t i o n from C a r t e s i a n t o i n t e r n a l c o o r d i n a t e s — t h a t i s , the m a t r i x T i n =  g_  T_ R  V.14  The m a t r i x T i s not r e a d i l y a v a i l a b l e from the molec u l a r geometry, however, and i t i s c o n v e n i e n t t o i n t r o d u c e 2 8 29 the G-matrix elements o f W i l s o n .  '  From the m o l e c u l a r  geometry the m a t r i x B f o r the i n v e r s e t r a n s f o r m a t i o n , R = B q_ can be c a l c u l a t e d . ent d i m e n s i o n s , t o g i v e T.  S i n c e {R} and  V.15  {q} g e n e r a l l y have d i f f e r -  B i s not square and thus cannot be i n v e r t e d  However, B B  i s square and i f the m a t r i x G i s  fc  d e f i n e d as G  =  B B  V. 16  fc  then i t can be shown ( r e f . 29, appendix 7) t h a t the k i n e t i c energy i s g i v e n by 2 T  =  R  G  fc  R  _ 1  V.17  S u b s t i t u t i o n o f the e x p r e s s i o n s f o r T and V i n the  Lagrangian  gives -2 L  =  R  fc  F R  -  R  fc  G  - 1  R  V.18  135 w h i c h , upon s u b s t i t u t i o n i n t o e q u a t i o n 4, g i v e s r i s e t o a set of s e c u l a r equations having n o n - t r i v i a l s o l u t i o n s only if |F Equation  —  A G | _1  = 0  V.19  19 can be m u l t i p l i e d through by G t o g i v e  another  common form |G F - A EI  5.  Motion  i n Symmetry  =0  V.20  Coordinates  The s e c u l a r e q u a t i o n  (19 o r 20) has d i m e n s i o n o f a t  l e a s t 3N-6 and f o r a r o m a t i c m o l e c u l e s  i s quite large; i n  o r d e r t o f a c t o r i t i n t o s m a l l e r b l o c k s symmetry c o o r d i n a t e s are i n t r o d u c e d . combinations  I n t e r n a l symmetry c o o r d i n a t e s a r e l i n e a r  o f t h e i n t e r n a l c o o r d i n a t e s formed by p r o j e c t i n g  one member o f each s y m m e t r i c a l l y e q u i v a l e n t s e t o f i n t e r n a l c o o r d i n a t e s i n t o the p o i n t group o f t h e m o l e c u l e .  Maximum  symmetry f a c t o r i z a t i o n i s thus a c h i e v e d s i n c e no i n t e r a c t i o n terms i n the F o r G m a t r i c e s w i l l occur between two c o o r d i n a t e s o f d i f f e r e n t symmetry.  I f the G F  problem can be  s o l v e d t o g i v e f o r c e c o n s t a n t s i n terms o f t h e v a r i o u s symmetry c o o r d i n a t e s then from the t r a n s f o r m a t i o n between t h e symmetry and i n t e r n a l c o o r d i n a t e s the f o r c e c o n s t a n t s t i v e t o t h e i n t e r n a l c o o r d i n a t e s can be found.  rela-  Unfortunately,  s i n c e t h e r e a r e always more i n t e r n a l f o r c e c o n s t a n t s  than  136  symmetry f o r c e c o n s t a n t s , i t i s not p o s s i b l e t o determine a l l the i n t e r n a l c o n s t a n t s w i t h o u t making s i m p l i f y i n g  B.  Out-of-Plane  Force F i e l d f o r A r o m a t i c  assumptions.  Molecules  The o u t - o f - p l a n e f o r c e f i e l d f o r a r o m a t i c  molecules,  u n l i k e the i n - p l a n e f i e l d , has r e c e i v e d l i t t l e a t t e n t i o n i n recent years.  There are two reasons  t i o n about the non-planar for  for t h i s ; less  informa-  v i b r a t i o n s has been a v a i l a b l e ,  and  those fundamentals which were known, c a l c u l a t i o n s based 30  on the c o n s t a n t s f i r s t suggested i n d i c a t e d t h a t the f i e l d was  by W h i f f e n  f o r benzene  a l r e a d y q u i t e adequate.  r e c e n t l y a v a i l a b l e i n f o r m a t i o n (see Chapter  The  IV) about a n t h r a -  cene, however, shows t h a t i n a t l e a s t one c a s e — t h e  second  40  lowest B  3 u  v i b r a t i o n — t h e force f i e l d predicts  m e n t a l f a r above the observed v a l u e .  a  funda-  As l o n g as t h e r e i s  one such l a r g e d i s c r e p a n c y between the observed  and  calculated  f r e q u e n c i e s , the f o r c e f i e l d cannot be c o n s i d e r e d t o be s e c u r e ; i n an e f f o r t t o improve the f i t the o u t - o f - p l a n e problem has been c o n s i d e r e d a g a i n i n the c o u r s e o f t h i s work.  137 1.  Benzene a) Symmetry f o r c e c o n s t a n t s .  The o u t - o f - p l a n e f o r c e 26  f i e l d o f benzene has been d i s c u s s e d by M i l l e r and Crawford who used W i l s o n ' s t e c h n i q u e t o s o l v e t h e d e t e r m i n e n t a l equation  ( i n t h e form o f e q u a t i o n V.20) f o r t h e f o r c e con-  stants.  Due t o t h e appearance o f q u a d r a t i c e q u a t i o n s  having  two p h y s i c a l l y p o s s i b l e r o o t s t h e s o l u t i o n i n symmetry c o o r d i n a t e s i s n o t unique and c o n v e r t i n g t o i n t e r n a l  valence  c o o r d i n a t e s adds t o t h e u n c e r t a i n t y s i n c e t h e r e a r e t h e n e l e v e n f o r c e c o n s t a n t s t o be e v a l u a t e d from t h e e i g h t symmetry 30 constants.  Whiffen  chose a unique f i e l d from t h e p o s s i b l e  s o l u t i o n s on t h e b a s i s t h a t i n t e r a c t i o n c o n s t a n t s s h o u l d be as s m a l l as p o s s i b l e .  In order t o permit c o n s i d e r a t i o n of  o t h e r f o r c e f i e l d s , the problem i n terms o f symmetry c o o r d i n a t e s was c o n s i d e r e d a g a i n ; t h e f o u r s o l u t i o n s p o s s i b l e are g i v e n i n T a b l e 21.  The d e f i n i t i o n o f the i n t e r n a l , f o r c e  c o n s t a n t s and i n t e r n a l c o o r d i n a t e s i s t h e same as t h a t . u s e d 81 by W h i f f e n ( w i t h t h e t o r s i o n as d e f i n e d by B e l l ), but f o r the purposes o f t h i s work t h e symmetry f o r c e c o n s t a n t 26 n o t a t i o n o f M i l l e r and Crawford  was found more c o n v e n i e n t .  The i n t e r n a l and symmetry c o o r d i n a t e s a r e d e f i n e d i n t h e appendix.  The G-matrix elements f o r benzene a r e a l s o g i v e n  i n t h e appendix, force constants.  a l o n g w i t h t h e d e f i n i t i o n s o f t h e symmetry  138  O u t - o f - P l a n e f o r c e co symmetry  coordinates* °  Force Constant  Value  2  (mdyn A / r a d i a n )  a  .2930  <J>  .3600  n  -.0400  -.1080  6  .0981  .1661  e  .2674  .2186  to  .0277^  9 a  ^407  .0277  .3407  .0785  .3718  .0785  .3718  .2930  .3720  .2930  .3720  Set A  Set B  Set C  Set D  /NSSS  *  The n o t a t i o n f o r t h e ^ g S y m m e t r y f o r c e c o n s t a n t s i s t h a t o f M i l l e r and C r a w f o r d and i s d e f i n e d i n t h e appendix.  139 b) I n t e r n a l v a l e n c e - c o o r d i n a t e f o r c e c o n s t a n t s .  In  order t o t r a n s f e r the f o r c e constants t o other molecules, i t i s necessary  t o e x p r e s s them i n terms o f i n t e r n a l c o o r d i n -  The i n t e r n a l c o o r d i n a t e s y d <\> have been d e f i n e d by 30 35 Whiffen o r S c u l l y and W h i f f e n and a r e a l s o d e f i n e d i n t h e ates.  a n  appendix. Whiffen  The n o t a t i o n f o r t h e f o r c e c o n s t a n t s i s t h a t o f  30  and S c u l l y and W h i f f e n ,  35  and can be deduced from  the f o l l o w i n g p o t e n t i a l f u n c t i o n i n w h i c h t h e s u b s c r i p t s involving  'x' determine  the p o s i t i o n s of the r e l e v a n t i n t e r n a l  c o o r d i n a t e s by l o c a t i n g t h e carbon  atoms i n v o l v e d (see t h e  appendix). 2  V  =  P  E  +  2 Y  X  2  Cc+l  + Q S  +  2  q  P  Z  +  P  2  E  o  m  X  Y  x  +  EY  +  •  cb  +  2  fc  +  x x+l,x+2 T  2 p  EY  m  Z  * x , x 1 *x 3,x 4 m  +  1  o *x,x+1 *x+l,x+2  q  +  - 2 t  Y  o  - 2 t_ p  S Y  +  x  EY  Y  X  2  q  X  m  +  +  2  2 p  p  S  Y  Y ^  X  *x,x+l*x+2,x+3  E  *x,x l +  cb  ,„  ,_  x x+2,x+3 Y  .  I n t h e e q u a t i o n above, each summation i s over a l l p o s s i b l e i n t e r a c t i o n s o f t h e type i n d i c a t e d by t h e s u b s c r i p t s . Care must be t a k e n i n c h o o s i n g t h e s i g n of t h e y<)> i n t e r a c t i o n s s i n c e y' xd>x , x +,lY  Y  x*x+2,x+3  =  / Y < , I 'x x-l,x ' 'x J>x+l,x+2  I = ~ Y ! C  )  Y  -I  T  ,  i  =  -  ' x <fx> - 2 , x - l  Y  T  ^  a n  d  " x*x-3,x-2 ' Y  The r e l a t i o n s h i p between t h e i n t e r n a l and symmetry c o o r d i n a t e s f o r benzene i s g i v e n i n T a b l e 22.  Since there are  140 T a b l e 22.  R e l a t i o n s h i p between symmetry and i n t e r n a l coordinate  force constants  a  1  2  2  1  e  1  •2  2  1  0  1  •1  •1  1  1  1  •1  •1  =  f o r benzene.  /p  k  k  2  3  1-2  6  1  n  2  -k  2  -k  2  -2k -2k -2k  2  1  -  -  -  -1  -1  1  -  -  -  -  -  -  -2  2  -2  P  N  P  Q q  q  o m  q  P  t k =  2/ J3  o t m  141 e l e v e n f o r c e c o n s t a n t s i n i n t e r n a l c o o r d i n a t e s and o n l y e i g h t i n symmetry c o o r d i n a t e s , s o l v i n g f o r t h e i n t e r n a l  constants  r e q u i r e s e i t h e r t h a t t h r e e o f them be f i x e d o r t h a t t h r e e i n t e r n a l r e l a t i o n s h i p s between them be s e t up.  However  t h i s i s done, f o u r s e t s o f i n t e r n a l f o r c e c o n s t a n t s w i l l be produced c o r r e s p o n d i n g t o t h e f o u r s e t s o f symmetry c o n s t a n t s i n T a b l e 21.  W h i f f e n chose s e t A from t h e symmetry c o n s t a n t s  and then s o l v e d f o r t h e f o r c e c o n s t a n t s i n i n t e r n a l c o o r d i n a t e s by s e t t i n g t h e meta and p a r a t o r s i o n i n t e r a c t i o n stants to  ( q and q ) and t h e t o r s i o n - w a g i n t e r a c t i o n m  zero.  reproduce  p  con-  (tp) e q u a l  I n an attempt t o f i n d a f o r c e f i e l d which w i l l t h e anthracene  B^  u  frequencies, several alternative  f o r c e f i e l d s were e v a l u a t e d , based on t h e f o l l o w i n g assumpt i o n s about t h e i n t e r n a l c o o r d i n a t e c o n s t a n t s :  I - assume,  as W h i f f e n d i d , t h a t q '= q„ = t =. 0; I I - assume t h a t q_ = ^m p p ^o -q = q and t h a t t = 0; I I I - assume t h a t p = q = t _ = 0. m rr ir p p hr n  n  The f o u r s e t s o f i n t e r n a l c o n s t a n t s produced from t h e symmetry c o n s t a n t s were found under each assumption, T a b l e 23.  and a r e l i s t e d i n  Each s e t o f f o r c e c o n s t a n t s w i l l , o f course,, r e -  produce t h e f r e q u e n c i e s o f benzene; t h e average e r r o r ( p r o b a b l y a r i s i n g m a i n l y from anharmonic terms i n t h e f o r c e f i e l d ) i s i n each case l e s s than 1.5 cm than 1.0 cm  1  1  f o r CgHg and l e s s  f o r CgDg, o r l e s s than 0.20 p e r c e n t .  The ob-  s e r v e d f r e q u e n c i e s o f benzene were t a k e n from Brodersen Langseth.^  and  Table  23.  Force Constant  The. o u t - o f - p l a n e  Set A  B  force  constants  o o f b e n z e n e , i n mdyn A / r a d i a n  I  Set I I C  A  B  C  D  B  Set I I I C  D  P  3118  3644  .3118  3644  2943  .6077  2338  ,5472  .2930  3457  2930  .3457  Po  0158  0158  .0280  0280  .0071  .1374  0010  ,1194  .0064  ,0064  0186  .0186  0158  ;0421 -.0280  0542  0071  .1637  0110  ,1457  .0064  0327  0186  .0449  P  0187  0187 -.0187  0187  ,0013  .2620  0592  ,2015  0  0  0  0  Q  0589  6455 -.0091  5775  0818  .3262  0931  3375  .0870  6735  0190  .6055  Qo  0196  2737 -.0876  2057  0033  .0456  0146  0343  .0015  2947  0666  .2267  q.•m  0  0  0  0  0033  .0456  0146  ,0343  .0070  0070  0070  .0070  q.  0  0  0  0  .0033  .0456  0146  ,0343  0  0  0  0  t  0160  1967 -.0160  1967  ,0160  ,1967  0160  ,1967  .0160  1967  0160  -.1967  0040  1767 -.0380  1427  0040  .1767  0380  1427  .0040  1767  0380  .1427  0  0  0  0  0  0  0  0  0  p  m  o m  0  0  0  143 2.  Naphthalene The  force  constants 35  Whiffen.  lene-dg.  to naphthalene  Their results  Also listed carried  I I I - A from Table  internal  in  F i g u r e 24.  23;  made by  listed  i n Tables  24  and  25  24  and  are the  25,  naphtharesults  f o r c e c o n s t a n t s e t s I-A,  impossible results  values)  and  of  II-A  constants  ( i . e . frequencies  when t r a n s f e r r e d  to  naphthalene.  f o r the c a l c u l a t i o n  are  shown  f o r c e c o n s t a n t m a t r i x c a n be d e f i n e d , as 34 t h e manner o f Freeman and R o s s , by t h e f o l l o w i n g l i s t .  those  listed  entries nal  f o r naphthalene:  i n Table  i n a matrix  23  and  determined  by  list.  12,12  the  Diagonal  = 14,14  = 1,9  internal  =  a r e t o be  P o  ;  11,12  = 13,14  = 14,21  11,14  = 12,21  = q  = Q; 1,3  ; 1,11  Q  omission  = -1,12  =  -2,13  t o the  i n the  inter-  matrix  1,1  o f many e n t r i e s  = 2,2  = 9,9  = P;  = p ; m  11,13  = -2,11 = 1,21  1,4  = 12,14 = 2,12  =  t. m  = 2,10 = 11,21  = 9,20  from 11,11  O f f - d i a g o n a l elements:  P 2,20  referred  as  c o o r d i n a t e number a s s o c i a t e d  = 1,10  = q ;  are  understood  Their position  elements:  = 21,21  = 9,10  force constants  of force constants  them; symmetry p e r m i t s  the  The  they  c o o r d i n a t e s o f F i g u r e 24.  with  Q  and  The  constants  t ;  Scully  a l l other sets of force  c o o r d i n a t e s used  Force  2,3  i n Tables  23 p r o d u c e d  The  is  are  out with  Table  t h a t have i m a g i n a r y  in  was  out-of-plane  t h e most r e c e n t d a t a on n a p h t h a l e n e  calculations  from  t r a n s f e r o f the benzene  36 '  along with  and  first  1,2 = =  =  p ; p  q ;  = -1,20  m  =  =  144  8 18  17  12  16  13  5  F i g u r e 2 4 . Non-planar i n t e r n a l v a l e n c e c o o r d i n a t e s f o r naphthalene. Numbers l o c a t e d a t atom p o s i t i o n s r e p r e s e n t o u t - o f - p l a n e wags and numbers c e n t e r e d i n bonds r e p r e s e n t t o r s i o n s ; both types o f c o o r d i n a t e s are i d e n t i c a l t o those d e f i n e d by S c u l l y and W h i f f e n . 3 6  Comparison o f the average e r r o r s i n Tables 24 and 25 i n d i c a t e s t h a t a l t h o u g h a l l s e t s o f f o r c e c o n s t a n t s have reproduced  the known f r e q u e n c i e s o f naphthalene  w e l l , set  I I - A and p a r t i c u l a r l y s e t I I I - A g i v e somewhat b e t t e r f i t s t o the observed v a l u e s .  The most n o t i c e a b l e d i f f e r e n c e s  between f o r c e c o n s t a n t s I I - A and I I I - A , and s e t I-A  (which  35  i s the s e t chosen by S c u l l y and W h i f f e n  ) i s that set  I-A  has a s m a l l e r d i a g o n a l e n t r y f o r the t o r s i o n f o r c e c o n s t a n t and a l a r g e r i n t e r a c t i o n c o n s t a n t between para-hydrogen-wags. I t i s perhaps worthy o f note t h a t i n g e n e r a l the o f f - d i a g o n a l f o r c e c o n s t a n t s are s m a l l e r f o r s e t s I I and I I I than f o r s e t I  (except where the s e t I c o n s t a n t s were f i x e d a t z e r o ) .  145 T a b l e 24.  Observed and c a l c u l a t e d n o n - p l a n a r f r e q u e n c i e s of Naphthalene-h„  Observed Symmetry  A  o  2g  3u  Average error  Calculated I-A II-A  III-A  1022  980  978  978  807  864  863  863  594  613  632  638  212  207  161  198  206  933  920  933  937  938  725  704  724  732  734  390  365  363  381  386  980  971  989  983  982  878  881  900  889  885  786  770  754  752  750  467  485  471  474  474  957  962  972  961  958  782  759  777  770  768  475  445  439  445  445  181  177  182  177  175  u  ig  B  S c u l l y and F r e q . Whiffen35  14.3 cm  1  15.8 cm  1  11.4 cm  1  10.6 cm  1  146 T a b l e 25.  Observed and c a l c u l a t e d n o n - p l a n a r f r e q u e n c i e s of Naphthalene-d  R  Observed Symmetry  A  S c u l l y and Whiffen35  I-A  II-A  III-A  —  829  814  813  813  —  648  685  677  675  —  511  520  538  543  193  185  144  178  187  761  751  756  756  757  547  528  543  548  549  348  316  318  335  340  —  812  825  826  827  —  754  739  742  742  649  665  668  653  649  410  429  424  425  425  791  798  797  792  790  628  594  607  604  602  402  382  382  384  384  166  163  168  164  162  Freq.  u  ig  2g  3u  Average error  Calculated  16.8 cm  1  17.1  cm  1  9.6  -1 cm  8.5 cm  1  147  3.  Anthracene The  force  first  constants  to  transfer  of  anthracene  the  was  benzene  carried  out-of-plane  out  by  Evans  i n Tables  26  and  and  40 Scully.  Their  along  with  the  d^g.  Also  listed  calculations  results  most  III-A  from  the  calculation  recent  Table are  listed  data  i n Tables  carried  and  are  26  out  with  23.  The  and  30  anthracene  and  27  results  force  are  the  constant  internal  illustrated  23  on  sets  coordinates  i n Figure  25.  The  29  27,  anthraceneof  I-A, used  the  matrix  abbreviated  can form  be  written, with  used  for  force  16  F i g u r e 25. Non-planar i n t e r n a l valence coordinates anthracene; d e f i n i t i o n s as i n F i g u r e 24.  constant  II-A,  respect  f o r naphthalene  as:  to  Figure Diagonal  for  25,  in  148 Table  26.  Observed  and  calculated  Anthracene-h,  non-planar frequencies  n  Observed Symmetry  A u  B  i  ig  B  o  2a  Freq.  — — • — —  Evans and Scully40  II-A  III-A  982  980  980  876  881  874  872  826  696  706  708  552  500  504  505  137  137  104  131  138  915  936  952  949  948  739  755  751  750  466  419  437  440  243  235  243  237  234  978  960  984  981  980  904  909  935  915  909  871  868  866  866  —  754  753  750  747  617  571  598  606  290  321  245  290  299  954  952  972  958  954  883  892  894  896  896  730  732  736  743  745  469  504  437  444  444  166?  383  350  373  378  96  96  94  93  — —  —  110 Average Average  I-A  966  765  3u  Calculated  error*(a) error*(b)  28 . 7 13 . 0  1 cm cm"1  -1 33 .0 27.1 cm 20 .2 12.1 cm"-'-  1 cm" 27.6 cm" 1 1 2 . 2  1 cm .cm" 1  A v e r a g e e r r o r (a) w a s c a l c u l a t e d i n c l u d i n g t h e o b s e r v e d f r e q u e n c y a t 166 c m ~ l ; a v e r a g e e r r o r (b) w a s calculated by o m i t t i n g t h a t f r e q u e n c y .  of  149 T a b l e 27.  Observed and c a l c u l a t e d n o n ^ p l a n a r f r e q u e n c i e s of  Anthracene-d.^  Observed Symmetry Freq,  A  u  Evans and Scully 4 0  — — — —  ig  3u  III-A  859  818  818  818  787  710  708  656 481 124  627 455 94  708 628 459  774 578  120  775 584  773 580  772 579  403 220  370 228  387 222  390 220  910  821  822  823  801  782  782  781  682  691  681  678  602  679  657  649  510  491  514  522  261  287  219  263  273  784 722  819 729  798 727  791 727  560 397 153? 102  556  557 380  562 382  788 726 564  307 91  330 89  — — — 228  B 2g  II-A  620 460 126  109  B  Calculated I-A  — — — — —  Average e r r o r * ( a ) Average e r r o r * ( b )  416 337 90  381 336 88  28 . 7 cm"1 29. 0 c m 26 . 4 cm"1 29 . 1 cm"1 13 .0 cm" 1 13. 4 cm~l 7 . 6 cm 1 9 . 9 crn 1 -x  -  -  Average e r r o r (a) was c a l c u l a t e d i n c l u d i n g the observed f r e q u e n c y a t 153 cm~ ; average e r r o r (b) was c a l c u l a t e d by omitting that frequency. x  150 elements:  1,1 = 2,2 = 9,9 = 11,11 = P; 15,15 = 16,16  = 19,19 = 29,29 = Q; 2,3 = 9,11 p ; m  1,4 = 2,12  -1,28 9,30  4.  = 11,12  O f f - d i a g o n a l elements:  = p ;  = 9,10  Q  1,3 = 1,12  = 11,13 = p ;  = 11,28 = -11,27 = 9,27 = -2,17  18,18  1,2 = 1,11  = 2,11 = 9,12  = =  = 12,13  = -2,15  = 2,16  =  = t ; 2,28 = -1,16  = 1,29  =  p  1,15  =  = t . m  D i s c u s s i o n of R e s u l t s T h i s study o f the o u t - o f - p l a n e f o r c e f i e l d o f benzene,  naphthalene and anthracene was undertaken i n an e f f o r t t o f i n d a s e t o f f o r c e c o n s t a n t s which would r e p r o d u c e , w i t h i n r e a s o n a b l e l i m i t s , the observed f r e q u e n c i e s o f the t h r e e m o l e c u l e s , i n c l u d i n g the second l o w e s t  frequency of anthracene.  This  e f f o r t was n o t s u c c e s s f u l ; i n T a b l e s 26 and 27 i t can be seen t h a t none o f the s e t s o f f o r c e c o n s t a n t s used c o u l d account f o r the  low energy o f t h a t anthracene v i b r a t i o n .  There a r e t h r e e  possible explanations f o r t h i s discrepancy:  (1) the observed  assignment may  be i n c o r r e c t ;  (2) a s i m p l e f o r c e f i e l d  which  w i l l f i t a l l n o n - p l a n a r f r e q u e n c i e s o f the t h r e e m o l e c u l e s e x i s t s but was n o t found; (3) the f o r c e f i e l d o f anthracene i s s u f f i c i e n t l y d i f f e r e n t so t h a t t r a n s f e r o f f o r c e c o n s t a n t s from benzene and naphthalene cannot be s u c c e s s f u l . The second p o s s i b i l i t y i s l e a s t l i k e l y ,  s i n c e many  f o r c e f i e l d s were t r i e d w i t h o u t s u c c e s s , and a l t h o u g h o t h e r f o r c e f i e l d s based on d i f f e r e n t r e l a t i o n s h i p s between benzene's  151 i n t e r n a l f o r c e c o n s t a n t s do e x i s t , i t i s f e l t t h a t t h e most p h y s i c a l l y r e a s o n a b l e p o s s i b i l i t i e s were c o n s i d e r e d .  In  a d d i t i o n t o the d i r e c t t r a n s f e r o f f o r c e c o n s t a n t s , a p e r t u r 82 b a t i o n program the  which a d j u s t s the f o r c e c o n s t a n t s t o f i t a l l  observed f r e q u e n c i e s was used on some o f the b e t t e r  In each c a s e , however, i t was the  166-153 cm  1  fields.  found t o be i m p o s s i b l e t o f i t  p a i r i n anthracene and a n t h r a c e n e - d . ^ w i t h  a f o r c e f i e l d t h a t would reproduce the observed f r e q u e n c i e s of  the o t h e r m o l e c u l e s . The f i r s t e x p l a n a t i o n r e q u i r e s t h a t the 166-153 cm  1  p a i r a r i s e from c o m b i n a t i o n s i n v o l v i n g l a t t i c e modes and a l s o r e q u i r e s t h a t an a c c i d e n t a l l y i n a c t i v e B^ l o c a t e d some 200 cm values.  1  u  fundamental  be  h i g h e r i n energy than the a s s i g n e d  Since a l l other B.j f u n d a m e n t a l s — i n other molecules u  as w e l l as a n t h r a c e n e — a r e marked by s t r o n g i n f r a r e d absorpt i o n bands, the o c c u r r e n c e o f one w i t h l i t t l e o r no i n t e n s i t y seems somewhat u n l i k e l y , and i n the absence o f any  firm  e x p e r i m e n t a l e v i d e n c e t o the c o n t r a r y the assignment as g i v e n must be a c c e p t e d as c o r r e c t .  Thus i t appears t h a t the f o r c e  f i e l d f o r anthracene m u s t . d i f f e r s u f f i c i e n t l y from t h a t f o r benzene and naphthalene so t h a t no s i n g l e v a l e n c e f o r c e f i e l d can reproduce a l l the observed f r e q u e n c i e s . S i n c e o n l y s e t A o f the f o u r p o s s i b l e s e t s o f symmetry f o r c e c o n s t a n t s f o r benzene produced i n t e r n a l c o n s t a n t s which would t r a n s f e r t o n a p h t h a l e n e , i t i s c l e a r t h a t W h i f f e n ' s 30 . c h o i c e o f symmetry c o n s t a n t s i s c o r r e c t . I t appears,  152 however, t h a t a f o r c e f i e l d  (e.g. I I - A o r I I I - A ) i n v o l v i n g  s m a l l e r p a r a - i n t e r a c t i o n terms l e a d s t o somewhat more a c c u r ate  r e s u l t s than t h e i n t e r n a l f i e l d chosen by W h i f f e n .  C.  P l a n a r Force F i e l d f o r Aromatic Molecules The p l a n a r f o r c e f i e l d o f a r o m a t i c m o l e c u l e s has  been t h e s u b j e c t o f much d i s c u s s i o n i n r e c e n t y e a r s .  The  f i r s t s i g n i f i c a n t c a l c u l a t i o n s were c a r r i e d o u t u s i n g a modif i e d valence force f i e l d ; ^ ' ' ^ ' ^ 2  4  37_39  modified Urey-Bradley f i e l d s , 31 f i e l d s when S c h e r e r  emphasis t h e n s h i f t e d t o  5  33  '  returning t o valence  showed t h a t such a f i e l d was  signifi-  c a n t l y more s u c c e s s f u l than a U r e y - B r a d l e y f i e l d i n f i t t i n g the f r e q u e n c i e s o f some c h l o r i n a t e d benzenes. 41 Neto, S c r o c c o and C a l i f a n o  Since then,  have d e v e l o p e d a m o d i f i e d .  valence force f i e l d designed t o f i t simultaneously the p l a n a r f r e q u e n c i e s o f benzene, naphthalene and anthracene and t h e i r d e u t e r a t e d analogues. In and C a l i f a n o  t h i s c h a p t e r t h e p r e d i c t i o n s o f t h e Neto, S c r o c c o 41 (NSC) f i e l d  w i l l be compared w i t h t h e e x p e r i -  m e n t a l assignments i n Chapters I I I and IV f o r naphthalene 32 and a n t h r a c e n e . for  In addition, a f i e l d  recently  developed  benzene w i l l be extended t o naphthalene and anthracene  and a comparison o f t h e p r e d i c t i o n s o f t h e two f i e l d s w i l l be made.  153 1.  The N e t o , S c r o c c o and C a l i f a n o F i e l d The NSC f i e l d f o r a r o m a t i c m o l e c u l e s was developed  i n t h e f o l l o w i n g manner. was  F i r s t , a simplified force f i e l d  found f o r benzene a l o n e , u s i n g t h e minimum number o f  force constants compatible w i t h a reasonable f i t t o the 3  observed  frequencies.  A l t h o u g h t h e source o f t h e i n i t i a l  benzene f o r c e c o n s t a n t s was n o t s p e c i f i e d , t h e v e r y c l o s e agreement w i t h t h e c o n s t a n t s found by S c l i e r e r t h a t t h e s t a r t i n g p o i n t was a U r e y - B r a d l e y  3 1  indicates  field.  benzene f i e l d was then extended t o naphthalene  This  and t o a n t h r a -  cene s e p a r a t e l y , r e f i n i n g t h e f o r c e c o n s t a n t s t o f i t observed f r e q u e n c i e s which t h e a u t h o r s c o n s i d e r e d t o be s e c u r e . s h o u l d be p o i n t e d o u t , however, t h a t t h e e x p e r i m e n t a l  It fre-  q u e n c i e s a c c e p t e d by N e t o , S c r o c c o and C a l i f a n o f o r naphthal e n e and anthracene  were t a k e n , i n g e n e r a l , from assignments 34 35 83  based on p r e v i o u s c a l c u l a t i o n s .  '  for  a l l f r e q u e n c i e s which had  each m o l e c u l e was completed,  '  When t h e r e f i n e m e n t  p r e v i o u s l y been o m i t t e d as u n c e r t a i n were r e c o n s i d e r e d ; i f t h e c a l c u l a t i o n s i n d i c a t e d a c h o i c e c o u l d be made between t h e c o n f l i c t i n g e x p e r i m e n t a l assignments,  t h a t v a l u e assumed t o  be c o r r e c t was e n t e r e d i n t h e l i s t o f secure f r e q u e n c i e s f o r the f i n a l s t e p o f t h e r e f i n e m e n t . T h i s f i n a l s t e p was t o r e f i n e a s i n g l e f o r c e f i e l d for  a l l the molecules  simultaneously.  Force  constants  which r e f e r r e d t o i n t e r n a l c o o r d i n a t e s o f t h e same type i n  154 each of t h e t h r e e m o l e c u l e s were c o l l e c t e d t o g e t h e r i n t o  one  term, p r o v i d e d the t h r e e s e p a r a t e r e f i n e m e n t s i n d i c a t e d they were o f n e a r l y the same magnitude. c o n t a i n i n g o n l y 34 independent  T h i s produced  a  field  f o r c e c o n s t a n t s , which  was  r e f i n e d t o f i t a l l the f r e q u e n c i e s a s s i g n e d i n the p r e v i o u s step.  One  u n u s u a l f e a t u r e o f t h i s f o r c e f i e l d i s t h a t an  i n t e r n a l c o o r d i n a t e which has a seemingly i d e n t i c a l e n v i r o n ment i n two o f the m o l e c u l e s not uncommonly has a q u i t e d i f f e r e n t f o r c e c o n s t a n t i n each m o l e c u l e .  This i s , of  c o u r s e , a r e s u l t o f the i n i t i a l r e f i n e m e n t o f each f o r c e 4  f i e l d separately.  Another p o i n t worthy o f mention i s t h a t  e i g h t o f the 34 f o r c e c o n s t a n t s r e f e r t o o n l y one One  molecule.  consequence o f t h i s i s t h a t t h e s e c o n s t a n t s may  a d j u s t e d by t h e • r e f i n e m e n t procedure  be  t o v a l u e s f a r removed  from p h y s i c a l r e a l i t y i n o r d e r t o compensate f o r o t h e r def i c i e n c i e s i n the f o r c e f i e l d . The r e s u l t s o f the N e t o , S c r o c c o and C a l i f a n o c a l c u l a t i o n are t a b u l a t e d i n S e c t i o n . C - 3 o f t h i s c h a p t e r , where they a r e compared w i t h the f r e q u e n c i e s p r e d i c t e d by a s i m i l a r calculation  ( d e s c r i b e d i n the n e x t s e c t i o n ) , and  d i s c u s s i o n w i l l be postponed 2.  until  further  then.  The D u i n k e r - M i l l s F i e l d S h o r t l y a f t e r Neto, S c r o c c o and C a l i f a n o developed 32  t h e i r g e n e r a l f o r c e f i e l d , D u i n k e r and M i l l s new p l a n a r v a l e n c e f i e l d f o r benzene.  presented a  They had found t h a t  155 the p r e v i o u s l y p u b l i s h e d did  not give accurate  force f i e l d s f o r that molecule 33  values  o f the r e c e n t l y o b s e r v e d  C o r i o l i s coupling constants. do n o t p r o v i d e  31 39 84 ' '  Although the C o r i o l i s  constants  s u f f i c i e n t i n f o r m a t i o n t o determine a unique  f i e l d f o r benzene, a m o d i f i e d  v a l e n c e f i e l d was d e v e l o p e d ,  i n v o l v i n g the f o l l o w i n g i n t e r a c t i o n constants:  (1) a l l i n t e r 85  a c t i o n c o n s t a n t s p r e d i c t e d by t h e M i l l s ' h y b r i d o r b i t a l model t o be s i g n i f i c a n t ( s t r e t c h - b e n d i n t e r a c t i o n s ) were i n c l u d e d ; * type i n t e r a c t i o n c o n s t a n t 37 ' 39 between CC (2) a "Kekule" s t r e t c h e s was i n c l u d e d ;  (3) i n t e r a c t i o n s between CH  wags and between CCC a n g l e bending c o o r d i n a t e s  were  in-plane included;  these a r e p r e d i c t e d on t h e b a s i s o f L i n n e t ' s o r b i t a l - f o l l o w i n g 86 arguments  t o be s i g n i f i c a n t ;  (4) i t was a l s o found n e c e s s a r y  to include i n t e r a c t i o n constants bending  between meta and p a r a CH  coordinates. A thirteen-parameter  i n t e r a c t i o n constants  f i e l d i n c l u d i n g t h e above  was r e f i n e d by D u i n k e r and M i l l s , and  they found i t p o s s i b l e t o o b t a i n s i m u l t a n e o u s l y a good f i t 5 both t o t h e observed f r e q u e n c i e s o f benzene and t o t h e 33 C o r i o l i s coupling constants.  I t was t h i s s u c c e s s t h a t  prompted us t o attempt t o e x t e n d t h i s f i e l d t o naphthalene and 3.  anthracene. Refinement o f t h e D u i n k e r - M i l l s F i e l d The f o r c e c o n s t a n t s  o f the D u i n k e r - M i l l s benzene  f i e l d were t r a n s f e r r e d t o naphthalene and anthracene w i t h as  156 few  changes as  possible.  was  multiplied  by  the  force constants  where  f and  tively  and  a factor  r are A  and  The  would  the  CC  stretching  related  to the  f i t a curve  force constant  x were g i v e n  the  of  force  bond the  and  values  constant  l e n g t h so  form  f =  bond  length  1170  and  that  Ae respec-  3.65  res~  8 7 pectively was  as  chosen  triple  CC  suggested  s i n c e the bonds of  w e l l when x = Mills  value  3.65  by  This  force constants  aliphatic and  f o r the  Steele.  A  =  stretching  f o r the  for single,  systems  1239.  form  f i t such  To  constant  double  a curve  reproduce  curve  the  and  quite  Duinker-  of benzene  i t  was  87 found  t o be  b e t w e e n CC involved are  necessary  i s a ring-junction  in different by  The and  CC  bond  r,  CCC  internal  anthracene  angle  bends by  These i n t e r n a l benzene  x is  to  constants  coordinates two  coordinates  force constant is  used  determined  by  f o r benzene,  i n Figures R,  CH  naphtha-  26-28, i n which  bond s t r e t c h e s  i n - p l a n e h y d r o g e n wags  motion of  i t s equilibrium position  ( o u t - o f - p l a n e ) , and g i v e n by  The  R j , X..  i n the  the  by  by  can  a x i s s e t a t each atom.  atom from  number  Scherer.  designated  coordinates  internal  f a c t o r whose v a l u e 37  illustrated  a and  Interaction  be d e f i n e d w i t h r e f e r e n c e 30 i n the manner o f W h i f f e n by s e t t i n g up a l o c a l th  Cartesian carbon  the  coordinates  are  s t r e t c h e s are  1170.  set equal  a weighting by  of  =  b o n d , o r when t h e  r i n g s were  the manner suggested  lene  set A  s t r e t c h e s when one  21 m u l t i p l i e d in  to  to  j  radial,  the  the mutually perpendicular d i r e c t i o n th a n d IK . T h e j h y d r o g e n atom i s a t t a c h e d  157 th to the j  carbon atom and i t s m o t i o n i s d e s c r i b e d i n a s i m i -  l a r manner by r . , x. and u.. 3  3  3  The i n t e r n a l c o o r d i n a t e s i n . t h e s e C a r t e s i a n a x i s s e t s a r e g i v e n by: R. = - (R. + R.,,) -3 2 3 3+1 r .=  3  a. = "3 where R  Q  U..,) 3+1  r . - R. 3  -3  6. = ~  - ^1 (u. 2 3  r  3  - (u. - U.) + ^ o 4R 3  J  Q  /T 2R  o  /T, - - R. - , ) - —1 (U. (R. 4R +1  11  1  1  3  Q  i ( R . -2R. + R._,_,) + -=— 3-1 3 3+1 . 2 R o  i s t h e CC bond l e n g t h and r  3  Q  + 2U. +U ^  (U. , - U.^,) 3-1 3 + 1,  t h e CH bond l e n g t h .  The l i s t which f o l l o w s each diagram g i v e s t h e f o r c e constants  ( u n r e l a t e d by m o l e c u l a r symmetry) used t o c a l c u l a t e  the f u n d a m e n t a l s .  The a b b r e v i a t e d nomenclature i s s i m i l a r t o 34  t h a t o f Freeman and Ross  and t o t h a t used e a r l i e r i n t h i s  c h a p t e r f o r t h e o u t - o f - p l a n e f o r c e f i e l d , e x c e p t t h a t where p r e v i o u s l y the l i s t contained the value of the force constant, i n t h i s case i t c o n t a i n s o n l y t h e f o r c e c o n s t a n t number. i n i t i a l and f i n a l v a l u e s o f t h e f o r c e c o n s t a n t s a r e l i s t e d a f t e r F i g u r e s 26-28 i n T a b l e 28.  The  158  0,  Figure  Entries  26.  elements:  Off-diagonal ]  R  l  R  l 6  a  3  l  =  R  planar  i n the benzene  Diagonal  1 0 ; a _«  The  elements:  = 11; & &  2  ±  l 2 a  =  = - 1 3 R  B  j  R  1 6  =  '  ^ l 2 0  -  a  2  =  coordinates  force constant R  i  1*  =  R  j 2  = 12;  2  internal  R  r  =  3 _3  ~ ^ l  ]  a  i  i  r  7 ;  =  i  R  3  = -13;  3  6  R  1 8  '  R  l ^ l  benzene  matrix  2*  =  of  ^1^1  =  =  8 ;  R  3 _B ]  =  _ R  4  i 4 R  =  9 ;  r  = -14;  1^2  =  1 9  l  =  r  ar 1  '  ±  3  ^' =  =  15;  159  1 ^7  .R"  7 •  Q  r R \ ~  s  ci  R  . R  a  '  a  ~R.  r  r a  a  7  a. 6  R-  a  6^  J  „  i 4 ^ R .  R:  4  5  !  F i g u r e 27. The p l a n a r i n t e r n a l c o o r d i n a t e s o f naphthalene. E n t r i e s i n t h e naphthalene f o r c e c o n s t a n t m a t r i x Diagonal elements: 1.040 R a _ a ]  1  l l R l l  0.870  = 1; r  ^ = r r 2  = 5; 3 _3 = 3 8  1 1  ]  1  2  r r 1  B  R  = 10;  3  l 3 3  =  1 3 ;  10 l0 a  =  18; R 8 1  3  R  1  = a a 2  1 4 6  =  ll 10 a  1  =  a  l  1 6 ?  R  4  r  = 2;  2  R  R 1  =  R  2  M  =  *  1  2  R  l  =  10 9 a  a  =  2 2  =  1 7 ;  3  r  1 5 ;  l 2 a  = -R\ L8-, = -R-,3, = R 2 82 0 1 1 2 lfl  2  = a a  i io  = 0^0^= a  3  R 2  0 9 6  R  4 4 R  =  = 3; a a  2  9  = 4;  9  = 6.  2  O f f - d i a g o n a l elements:  = 1.083 R  RJRJ,  M  9  M  9  =  7 ;  1 0  a  R  =  R  R  a  =  8 ;  R  1 4 R  = 11; 8 6  1 3  l l _ p  1 3  1  =  R  2 2 a  l 10 a  =  e  =  R  2 3 a  2  a  _  9 ;  = ~3 3  2  l 2 =  =  = R  3  =  10 f  2 l a  3  a  =  = 19; R-,l 3 44 = -"R1 03 4 = R 8, = ~ "4 2 v  P  in  P A  4  P  1 2  ;  160 ~ 11 2 R  "  3  2  0  " 1 11 "  ;  R  R-jRg = " R j R g  R  = R- 5 R  R  ~ 2 6  =  R  2  /3  2 11 "  R  R  =  R  4 11 ~ " 1 5 "  R  R  2 7  •  R  R  R  =  0  a  l l  a  l l  28.  R  2 4  a  l 12  R  a  •e B  3  l  l  1  R  =  a  R  =  The p l a n a r  5  R 5  1  a  6 12 R  a  =  4  ;  a  i  r  r  13 13 a  8 ;  12 15 a  =  R  a  1 4 R  9  a  =  l l  R  R  =  = 13; 8 ^ 4 = -e 8 9  =  R  l 2 a  =  i  elements:  =  R  2 2 a  =  L-  internal  R  =  r  =  5  2*2 ;  i 2 R  R  1 0  3  =  =  a  ~ 3  =  =  B  R  r  1  1  l ;  r  B  = 14; =  R  2 ;  2 2 6  =  3  R  =  =  =  i  a  =  B  0  l 2 3  ;  a  =  l  a  3  a  =  R  1 5  anthracene  7  2  l l  6  4 4 R  a  1 ( J  Vl4  R  3  2 3  =  =  =  R  5 5  3  ;  R  ' l  R  88  R  9  2®2  ;  B  =  2  a  =  = a a  1  =  " 2 3  =  =  l5 12  «  i  a  6  R  1  1  9 9  12 13  R  of  matrix  2 2  R  r  1 14  ;  1 2 9  9 9  r  1 1 R  9  ll 14  4 15 a  ~ !'  5 12 a  coordinates  force constant  0.885  = 1 '*  12 12  Off-diagonal R  -J  elements:  a  "  R  »Sa  i n the anthracene  =  1  R  ^<  Figure  1  2  ~ " 1 7  R  r  R.e  —I  1.139  *  3  1 6  £'  A  =  3  r  >  Diagonal  3  £s  8  "i  Entries  ,  R  a  1  r  2  ==  =  ;  = 15;  1 0  =  161  V l O  =  Vll  =  6  1 3  R  1 6  R  4 13  6  ;  R  1 4 l l  " 9 20 3  3  =  R  a  R  R  13 12  1 8 ;  3  a  B  l l" R  =  1 7  R  B  R  R  =  R  R  l 2 a  3  3  R  2 5  '*  ~ 1 14  =  2 4 = - 2 15  " 1 13  =  0.50  R  =  =  R  1 12  =  a  = ~ 1 4  R  R  1  R  =  B  R  ~ 2 6  =  =  9 5  R  R  3  6  =  a  9 13 R  4 5 R  a  6  =  R  R  3 2  B  2  R  0  R  R  1  9  ~ 1 5  ?  " 4 6  =  =  " 9 12 =  =  -*9 6  =  =  " 2 l  =  R  =  ;  =  R  " 4 12 R  R  =  x 21.  The o b s e r v e d  frequencies t o which  constants have been r e f i n e d in  parentheses  i n Table  in  t h e f o l l o w i n g manner:  the i n i t i a l  force  (these are-the ones n o t e n c l o s e d  29, which  follows  later)  were  chosen  (1) f o r b e n z e n e , a l l a s s i g n m e n t s 5  made b y B r o d e r s e n a n d L a n g s e t h tain  assignments  those  listed  were used;  i n Table  (2) t h e m o r e  8 f o r naphthalene-dg  frequencies f o r naphthalene-hg  f o r which  cer-  and  there i s gen-  6-9 14 e r a l agreement ' were used. The p r o p o s e d a s s i g n m e n t o f a B 2 r i n g m o d e n e a r 1 7 0 0 cm i n naphthalene-hg has n o t been 1  U  accepted, in  this  since  region  i t has been suggested  36  that the strong  a r e due t o c o m b i n a t i o n s a n d s i n c e  calculations  34 35 37 4 1 70 ' ' ' ' have unanimously  fundamental  s o m e 150 cm  controversial used  2 u  the previous  placed  this  (3) t h e l e s s  T a b l e s 1 5 , 18 a n d 20 w e r e  Arguments s i m i l a r  block of naphthalene  modes o f t h i s for  lower i n energy;  f r e q u e n c i e s from  f o r anthracene.  the B  1  bands  resulted  t o those involved f o r  i n the highest ring  s y m m e t r y b e i n g p l a c e d a t 1 5 3 3 a n d 1 4 9 3 cm  t h e p r o t o n a t e d and d e u t e r a t e d anthracenes  1  respectively.  162  Table  28.  Initial  and f i n a l  force  constants for  planar  force-field*  + Type  Initial  Value  Final  Value  RR  1  7.015  7.040  rr  2  5.125  5.061  oca  3  1.097  1.103  aa  4  0.731  0.711  aa  5  0.731  0.814  B B  6  1.034  1.020  RR  7  0.531  0.650  8  -0.531  -0.609  9  0.531  0.295  10  0.000  0.034  11  -0.097  -0.097  12  0.028  0.028  13  0.022  0.015  14  0.032  0.032  a.r.  15  -0.014  -0.014  a .R.  16  0.441  0.602  17  0.000  -0.323  18  -0.063  -0.063  .R.  19  -0.364  -0.315  3  20  0.000  -0.027  21  0.531  0.090  o m RRp R R  m aa r r  o 6 B  m  3  a.  B  J 3 R R  *  Number  3 R j  D+2 I.R.  o  U n i t s a r e mdyn/A f o r s t r e t c h i n g c o n g t a n t s , mdyn/radian f o r s t r e t c h - b e n d i n t e r a c t i o n s and mdyn A / r a d i a n f o r bending constants. o,m,p i m p l y i n t e r a c t i o n s b e t w e e n c o o r d i n a t e s o r t h o , m e t a a n d p a r a t o one a n o t h e r ; t h e s u b s c r i p t ' j ' s p e c i f i e s t h e c a r b o n atom w h i c h i d e n t i f i e s t h e c o o r d i n a t e ( s e e t e x t ) .  163 The  adjustment of  the  force constants  was  carried 82' 88  out w i t h and  a program  modified  puting  t o meet the  system  quently select  an  (FPERT) w r i t t e n by  those  model  observed  to give and  IBM  360/67)•  interaction  are most s e n s i t i v e constants  requirements  ( i n i t i a l l y an  IBM  and  The  to refine  '  available  com-  subse-  i s designed  to which  these  least  the  the  program  and  the the  squares  frequencies.  were g i v e n z e r o w e i g h t and a w e i g h t of V\ , ,. observed  of  7044 c o m p u t e r and  constants  a weighted  calculated  Schachtschneider  to  frequencies diagonal  f i t between  Uncertain  the  frequencies  known f r e q u e n c i e s were  given  3  The  thirteen  non-zero  force constants  used  by  32 Duinker  and  Mills  s t a n t s when t h e anthracene. arose  because  junction force  f i e l d was of  three  the  extra constants  angle  Duinker  Mills  (force constants  o r t h o , meta and  (numbers 4 and  split  8 and  Steele.  Two  single  Kekule  into  9 ) , one  three  stretch  interactions.  non-zero  force constant  entered  into  constant  21)  previously  the  mentioned.  inter-ring  CC  the  The  refinement  stretching  5) ring  more constant  separate  f o r each of  CC  was  para  7,  was  conand  bends were d e f i n e d a t each 87  w e r e n e e d e d when t h e and  to eighteen  t r a n s f e r r e d to naphthalene  i n t h e manner d e s c r i b e d by  constants  u s e d by terms  Two  f o r benzene gave r i s e  the final (force  constant  164 I n a d d i t i o n t o t h e non-zero f o r c e  constants,  s e v e r a l o t h e r i n t e r a c t i o n s which were thought t o be p o s s i b l y i m p o r t a n t were d e f i n e d b u t g i v e n i n i t i a l f o r c e c o n s t a n t s o f zero.  Three o f these f o r c e c o n s t a n t s  (numbers 10, 17 and  20) were found t o a f f e c t t h e f r e q u e n c i e s entered  appreciably  and were  i n t o the refinement. I t i s , o f c o u r s e , v e r y dangerous t o form  about t h e p h y s i c a l meaning o f t h e f o r c e c o n s t a n t s modified  conclusions i n such a  f o r c e f i e l d , where so many i n t e r a c t i o n c o n s t a n t s  have been n e g l e c t e d .  Thus, w h i l e t h e f a c t t h a t f o r c e con-  s t a n t s 9 and 21 d e c r e a s e c o n s i d e r a b l y  during the refinement  may i m p l y t h a t l o n g range i n t e r a c t i o n s between CC s t r e t c h e s 32 37 are l e s s i m p o r t a n t t h a n p r e v i o u s l y t h o u g h t ,  '  i t may  e q u a l l y i m p l y t h a t some d e f i c i e n c y e x i s t s e l s e w h e r e i n t h e f o r c e f i e l d and f o r c e c o n s t a n t s t o compensate f o r i t .  9 and 21 a r e b e i n g  adjusted  The v a l u e o f t h i s c a l c u l a t i o n l i e s  not i n i t s p h y s i c a l s i g n i f i c a n c e , b u t r a t h e r i n t h e f a c t t h a t i t p e r m i t s an e s t i m a t e work t o be made.  of the accuracy o f the previous  Since the s t a r t i n g p o i n t i n t h i s c a l c u l a t i o n  was q u i t e d i f f e r e n t from t h a t f o r t h e NSC f i e l d , t h e a s s i g n ments which were made i n t h a t work can be checked  against  the p r e d i c t i o n s o f t h i s . f i e l d . I t i s , however, i n t e r e s t i n g t o compare t h e i n i t i a l and  f i n a l force constants  constants  listed  i n T a b l e 28.  The f i r s t s i x  appear on t h e d i a g o n a l o f t h e F - m a t r i x and f i v e o f  165  t h e s e remain w i t h i n t h r e e p e r c e n t o f t h e i r i n i t i a l v a l u e s ; the of  o t h e r , number 5 , i n c r e a s e d by o n l y e l e v e n p e r c e n t .  Five  t h e f i f t e e n i n t e r a c t i o n c o n s t a n t s remained unchanged, and  o n l y f o u r o f them (numbers 9, 1 6 , 17 and 21) were a d j u s t e d t o v a l u e s v e r y f a r removed from t h e i r i n i t i a l v a l u e s .  Evidently  the  D u i n k e r - M i l l s f i e l d f o r benzene i s q u i t e w e l l s u i t e d  for  t r a n s f e r r i n g t o n a p h t h a l e n e and a n t h r a c e n e . D u r i n g t h e p r e l i m i n a r y s t a g e s o f t h i s work two s e t s 34  of  f o r c e , c o n s t a n t s p u b l i s h e d f o r naphthalene  35  '  were t r a n s -  f e r r e d t o anthracene and s e v e r a l attempts were made t o c a r r y o u t a r e f i n e m e n t s i m i l a r t o t h a t d e s c r i b e d above f o r t h e D u i n k e r - M i l l s benzene f i e l d .  F o r b o t h f i e l d s many o f t h e  f i n a l f o r c e c o n s t a n t s were found t o be q u i t e d i f f e r e n t from the  i n i t i a l ones; sometimes, i n f a c t , t h e f i n a l f o r c e  was u n r e c o g n i z a b l e .  field  I t was, t h e r e f o r e , e n c o u r a g i n g t o f i n d  t h a t t h e D u i n k e r and M i l l s benzene f i e l d needed so l i t t l e r e f i n e m e n t t o f i t t h e n a p h t h a l e n e and anthracene f r e q u e n c i e s . 4.  R e s u l t s o f t h e Refinement The observed f r e q u e n c i e s t o which t h e r e f i n e m e n t  was made and t h e r e s u l t s o f t h e c a l c u l a t i o n a r e l i s t e d i n Table 2 9 .  A l s o i n c l u d e d i n T a b l e 29 a r e t h e observed and 41  c a l c u l a t e d f r e q u e n c i e s from t h e NSC c a l c u l a t i o n .  The  average e r r o r w i t h t h e newly-developed f i e l d i n t h e f i t t o the  1 1 9 observed f r e q u e n c i e s was 1.50 p e r c e n t o r 1 4 . 8 cm . 1  166 Table  29.  The o b s e r v e d  and c a l c u l a t e d p l a n a r  benzene, naphthalene  and  frequencies  of  anthracene*  41 T h i s work Observed Calculated C  6 6 H  A  3073  3075  3063  3073  993 1350  979 1356  993 1346  993 1350  3056  3040  3046  3056  1599  1581  1602  1599  1178  1167  1165  1178  606  611  601  606  3057  3074  3043  3057  1010  1015  1007  1010  1309  1290  1316  1309  1146  1149  1173  1152  3064  3041  3056  3064  1482  1476  1482  1482  1037  1028  1026  1037  2303  2287  2279  2303  945  931  946  945  1059  1054  1058  1059  2274  2257  2268  2274  1558  1551  1159  1558  869  840  836  869  579  583  580  579  Bl u  2285  2288  2266  2285  970  965  957  970  B2u  1282  1269  1287  1282  824  826  848  824  ^2g :  2g  Bl u B 2u El u  C  Neto,, S c r o c c o & C a l i f a n o Calculated Observed  6 6 D  '2g  E 2g  167 Table  29  (Continued)  This Observed  J  C  lu  work Calculated  Neto, Scrocco Calculated  &  Califano Observed  2288  2259  2272  2288  1333  1307  1339  1333  814  812  793  814  3058  3065  3085  3055  3040  3038  3025  1579  1610  1577  1579  1465  1464  1445  1460  1380  1418  1368  1379  1148  1160  1173  1144  1021  1018  1013  1025  765  716  767  763  514  482  504  512  3063  3064  3065  3042  3020  3029  1596  1608  1597  1595  1390  1388  1379  1389  1297  1258  1265  1129  1125  1125  800  795  810  359  369  362  3064  3084  3056  3039  3037  3029  1521  1529  1509  1382  1357  1361  1241  1186  1209  1174  1136  1144  1008  1020  1007  1008  622  637  628  618  10 8 H  Bl u  1125 359  B2u 1509  41  168 Table  29.  (Continued)  This Observed  B  10  D  3g  work Calculated  Neto, Scrocco Calculated  & Califano Observed  3062  3062  3055  2980  3042  3019  2980  1636  1644  1625  1624  1446  1445  1442  1436  1240  1236  1253  1240  1168  1150  1117  1099  953  950  938  936  509  518  488  506  2281  2295  2272  2256  2260  2257  1552  1586  1542  1553  1386  1443  .1370  1381  1294  1251  1288  1293  862  856  852  866  838  824  830  835  697  660  695  698  494  463  484  493  2279  2282  2278  2266  2249  2232  (1562)  1570  1543  1545  1257  1260  1245  1260  (1045)  1058  1045  1050  879  863  840  885  738  741  749  734  328  326  336  328  2280  2293  2299  2254  2256  2258  (1439)  1466  1466  (1341)  1346  1273  8  A,  Bl u  B2u  1290  41  169 T a b l e 29.  (Continued)  T h i s work Observed Calculated  B 3g  1082 (880?)  1102 840  1086 837  828 590  834 610  803 606  593  (2276?)  2276  2275  2302  (2261) 1605  2263 1620 1334 1029  2246 1598 1338 1023  2257 1574  884 831  877 825  494  501  860 821 472  3056  3064 3052  3085 3053  3027  3039  3037  1557  1563  1584  1561  1481 1402  1494 1390  1476 1398  1481 1403  1261  1308  12 40  1261  1163 1007 754 (622?) 395  1167 999 713  1169 1007  1165  3108 3050  3063 3053  3053  3024 1616  3042 1612  3019 1616  — (967?)  C  N e t o , S c r o c c o & C a l i f a n o 41 Calculated Observed 1082 828  T  1330 1030 881 828 490  14 10 H  Bl u  643 362  :  735 658 369  3063  3088  — —  1007 745 652  — 3100 3049 3022 1620  170 Table  29.  (Continued)  T h i s work Observed Calculated  Neto,Scrocco & Calculated  Califano Observed  1447  1436  1446  1448  1314  1318  1341  1316  1270  1282  1277  1274  1145  1145  1123  1150  903  925  921  907  657  647  651  227  214  244  3064  3085  3079  3050  3039  3037  3048  1533  1559  1532  1533  (1495)  1510  1441  1462  (1392)  1397  1394  1398  (1345)  1344  1377  1346  (1163)  1207  1169  1169  (1068)  1147  1127  1125  992  1007  999  745  812  —  600  597  609  615  3066  3063  3063  3045  3042  3019  3006  1630  1632  1612  1631  1558  1563  1596  1387  1389  1291  1273  1184  1206  1106  1093  956  912  912  —  522  531  517  522  —  398  388  400  (650?) 235 (3093?)  998 (808?)  — — 1187  —  —  — — 1188  41  171 T a b l e 29.  (Continued) 41 T h i s work Observed Calculated  (2288) (2266) (2258) 1534  — 1388 1156  —  Neto,Scrocco & Calxfano Calculated Observed  2280 2269 2254 1542  2294 2275  1438  1407 1347 1149  1366 1158  2255 1553  — — — — — — — — — — —  709  841 832 672  —  617  848 819 690 634  382  349  356  2283  2278  2280  2264  2270  2271  2288 2262  2248  2263  2246  2247  1584  1585 1354  1582 1380  1268 1050  1275 1041  1583 1389 1264  (879)  879 825  (565?)  626 211  861 825 617 199  (842)  (1406?) 1258  —  220  — 881 822 592  2294  2275  1493  2280 2254 1542  2257 1487  (1401)  1466  1392  2238 1500 1384  (1335)  1316  1315  1325  2267 2238  172 Table  29.  (Continued)  T h i s work Observed Calculated  Neto,Scrocco Calculated  &  Califano Observed  1199  1267  —  (982)  948  943  920  (879?)  835  840  831  824  830  811  --  703  662  701  706  575  574  588  580  2277  2278  2264  2247  1615  1588  1526  1522  1238  1244  1043  1027  943  931  960  816  868  846  777  804  810  502  506  . 494  (415)  370  361  1175?)  2276)  —  1615  —  1233  The o b s e r v e d f r e q u e n c i e s e n c l o s e d i n p a r e n t h e s e s zero weight i n the force constant refinement.  — — —  were  given  173 In t h e e a r l i e r w o r k  t h e f o r c e c o n s t a n t s were r e f i n e d t o  4 1  d i f f e r e n t f r e q u e n c i e s and, as i n d i c a t e d i n C h a p t e r s I I I and IV, a few o f them a r e a l m o s t c e r t a i n l y i n c o r r e c t and some others are d o u b t f u l . is difficult  Thus comparison o f t h e average e r r o r s  t o i n t e r p r e t ; however, t h e average d i f f e r e n c e  between t h e observed  and c a l c u l a t e d f r e q u e n c i e s o f Neto e t a l .  i s 13.1 cm The  r e s u l t s o f t h e two c a l c u l a t i o n s a r e , i n g e n e r a l ,  q u i t e s i m i l a r ; t h e r e a r e some d i f f e r e n c e s , however, and t h e s e w i l l now be c o n s i d e r e d and a comparison w i t h t h e e x p e r i m e n t a l assignments from Chapters I I I and IV f o r n a p h t h a l e n e - d g , anthracene-h.^  and anthracene-d^^  a) Naphthalene-dg.  w i l l be made.  There i s l i t t l e cause f o r  comment i n t h e Ag and 3 g b l o c k s s i n c e t h e t o t a l l y symmetric B  modes a r e e x p e r i m e n t a l l y secure and both c a l c u l a t i o n s a r e i n f a i r l y good agreement about t h e B  3 a  frequencies.  The NSC  f i e l d was, however, somewhat more s u c c e s s f u l i n f i t t i n g t h e r i n g modes i n t h e Ag b l o c k . v a l u e o f 1570 cm  u  block the c a l c u l a t e d  s u p p o r t s t h e e x p e r i m e n t a l assignment i n  1  which t h e 1562 cm  In the B^  l i n e r e p l a c e s t h e .1545 cm  1  1  line pre-  7 41 v i o u s l y assigned.  '  T h i s c a l c u l a t i o n a l s o p r e d i c t s a funda-  m e n t a l i n t h i s b l o c k i n t h e r e g i o n o f v e r y weak a b s o r p t i o n near 1050 cm  and thus g i v e s added w e i g h t t o t h e c o n c l u s i o n  p r e v i o u s l y made **' 1  the i n f r a r e d .  41  t h a t t h i s mode i s i n t r i n s i c a l l y weak i n  I n t h e B^^ b l o c k t h e assignment o f a funda-  174  mental  near  indicate  1 4 5 0 cm  that  fundamental tively lines  t h e 1 4 5 2 cm  i n Chapter  assigned line a r e o n l y 13 cm  not p a r t i c u l a r l y choice w i l l  l i n e mentioned  1  as a  I I Ishould replace  a t 1 4 3 9 cm  S i n c e t h e two  i n only a small  i s very  interesting  t h e n e x t mode a t 1 3 4 1 cm  possible  the rather  a p a r t , however, t h i s  1  calculations  tenta-  observed  conclusion i s  c o m p e l l i n g and i n any event  result  It of  i s s u p p o r t e d , and b o t h  1  an  incorrect  error.  t o note  that  the  assignment  i n p l a c e o f t h e 1 2 9 0 cm  1  1  line  41 previously  suggested  calculation  has been s t r o n g l y  (calculated  frequency  f r e q u e n c y was g i v e n z e r o w e i g h t The o n l y o t h e r p o i n t the  observed  line  second  lowest fundamental  lowest  as p r e v i o u s l y  1  may  i n this  known  a b o u t t h e Ag and  supported,  be a s s o c i a t e d w i t h t h e block rather  blocks;  f o r the B^  i s interesting  experimental  procedure.  block i s that  both  than  and both  fields  agree  o f t h e unknown f u n d a m e n t a l s .  agreement i s found species  i n the  this  the  third  Once a g a i n t h e r e i s l i t t l e  frequencies quite well,  mate l o c a t i o n  ^) e v e n t h o u g h  suggested.  b) A n t h r a c e n e - h . ^ . discuss  1 3 4 6 cm  i n the refinement  of interest  a t 8 2 8 cm  s u p p o r t e d by t h e  assignment  u  modes.  i n several  The B  respects.  of a fundamental  a l t h o u g h once a g a i n t h i s  to  predict the  on t h e a p p r o x i T h e same 2  u  sort  of  symmetry  First,  a t 1 4 9 5 cm  t h e new 1  i s  f r e q u e n c y was g i v e n  zero  175 weight i n the refinement.  The danger o f making assignments  from c a l c u l a t e d f r e q u e n c i e s i s a l s o c l e a r l y i l l u s t r a t e d i n this block.  Complete r e l i a n c e on t h e c a l c u l a t i o n s would  r e s u l t i n t h e replacement o f t h e e x p e r i m e n t a l l y a s s i g n e d l i n e a t 1068 cm  1  w i t h t h e l i n e p r e v i o u s l y mentioned (see'  Chapter IV) a t 1219 cm \  s i n c e then the f i t w i t h the h i g h -  energy c a l c u l a t e d f r e q u e n c i e s i s e x c e l l e n t .  However, t h e  41 earlier calculations of the B  2 u  have suggested y e t a n o t h e r assignment  b l o c k , and by c h o o s i n g t h e e x p e r i m e n t a l v a l u e s  p r o p e r l y a good f i t was o b t a i n e d (see T a b l e 2 9 ) .  Since the  two f i e l d s s u p p o r t d i f f e r e n t assignments t h e c h o i c e o f t h e p r o p e r s e t o f fundamentals from t h e c a l c u l a t i o n s cannot be made, and, i n g e n e r a l ,  g r e a t c a r e must be t a k e n i n comparing  o b s e r v e d and c a l c u l a t e d fundamentals when s e v e r a l c l o s e - • l y i n g f r e q u e n c i e s a r e p r e d i c t e d and t h e r e a r e many observed l i n e s w h i c h can be f i t t e d t o them.  A n o t h e r p o i n t worthy o f 41 note i s t h a t t h e p r e v i o u s c a l c u l a t i o n was r e f i n e d t o a fundamental a t 146 2 cm where i n f a c t o n l y a v e r y weak band 16 i s seen a t t h a t energy i n s o l u t i o n and no l i n e a t a l l i s 16 — 18 1  found t h e r e i n t h e c r y s t a l ;  as p r e v i o u s l y mentioned,  this  l i n e has been r e p l a c e d i n t h e assignment by t h e s t r o n g cp o l a r i z e d l i n e a t 1495 cm . 1  c) A n t h r a c e n e - d . ^ .  Very l i t t l e new i n f o r m a t i o n  can be g a i n e d from t h e c a l c u l a t e d f r e q u e n c i e s i n t h e Ag, B^g or B^  u  blocks.  Both f i e l d s agree f a i r l y w e l l i n t h e i r p r e -  176 dictions is  that  work  of these  fundamentals,  the calculations  favor B^  r i n g mode r a t h e r  tively  suggested  41  o f 1 3 8 0 cm  t h a n t h e 1 4 0 6 cm  i n Chapter  IV.  of interest  out i n the course o f this  t h e previous assignment  second  u  carried  and t h e o n l y p o i n t  f o r the  line  1  Three p o i n t s  -1  tenta-  f o r considera-  4 tion of  arise  a fundamental  symmetry) a  i n the B  line  that  2  block.  u  a t 1 3 8 4 cm  First, (this  1  line  c a n c o n v e n i e n t l y be c o r r e c t e d  a t 1 4 0 1 cm  t h e 1 1 7 5 cm  1  Secondly, assignment  i n Chapter  I V may b e c o r r e c t ,  native  assignment  a t 1 2 9 8 cm  the fact  that  i s i n fact  rather  as suggested  than  cm  mental  exist  i n the force  i s not surprising,  constants 5.  i t s value i n anthracene-h^,  frequencies differ  deficiency  b y 94 cm  field.  1  field.  unable  more  than  while the experi-  i s p r o b a b l y d u e t o some  That such  of course, since  a deficiency s o many  does  interaction  have been n e g l e c t e d .  Conclusions i)  by  the alter-  t h e p e r t u r b a t i o n p r o g r a m was  17  from  sug-  b y t h e NSC  move t h e h i g h e s t r i n g mode i n a n t h r a c e n e - d ^ g  of  indicate  r i n g mode  to  1  o f B_ 3u  by t h e assignment  of the fourth  1  assignment  these calculations  gested  Thirdly,  the incorrect  Duinker  good  Very  little  and M i l l s  refinement of the basic  f o r benzene  and anthracene.  derived  i s necessary t o achieve a  f i tt o most o f t h e p l a n a r observed  thalene  field  The average  f r e q u e n c i e s o f naph-  error  i n the f i t tothe  177 f r e q u e n c i e s t o which the r e f i n e m e n t was made was However, some e v i d e n c e  of inadequacies  14.8  cm . -1  i n the r e s u l t i n g  f i e l d does e x i s t ; t h i s i s not s u r p r i s i n g s i n c e o n l y 21 f o r c e c o n s t a n t s were r e f i n e d i n the attempt t o f i t the 184 f r e q u e n c i e s o f the s i x m o l e c u l e s  planar  studied.  i i ) Although, as shown i n C h a p t e r s I I I and IV, the 41 NSC  field  was  r e f i n e d t o some i n c o r r e c t a s s i g n e d  frequen-  c i e s , i t s p r e d i c t i o n s are i n g e n e r a l q u i t e accurate.  Compari-  41 son o f t h e i r  observed  average e r r o r o f 13.1 assignments,  and c a l c u l a t e d f r e q u e n c i e s g i v e s an  cm "*"; however, because o f the i n c o r r e c t  t h i s i s somewhat m i s l e a d i n g as the average e r r o r  i n the f i t t o the c o r r e c t e d observed g r e a t e r (about 14 cm  1  f r e q u e n c i e s i s somewhat  ) .  I t i s i n t e r e s t i n g t o compare the agreement o f the 41 calculated frequencies  w i t h e x p e r i m e n t a l assignments t o  which the f o r c e c o n s t a n t s were not r e f i n e d .  In p a r t i c u l a r ,  Neto e t a l . d i d not r e f i n e t o any d a t a i n the Ag and  B^g  v i b r a t i o n a l s p e c i e s o f a n t h r a c e n e - d ^ g , and the agreement o f t h e i r c a l c u l a t i o n s w i t h the c e r t a i n e x p e r i m e n t a l for  those b l o c k s  e r r o r = 21.5 refine.  (see Table 20) i s not as good  frequencies (average  cm "*") as f o r the f r e q u e n c i e s t o w h i c h they d i d  T h i s i s not s u r p r i s i n g , p r i n c i p a l l y because i t  would be expected  t h a t the r e f i n e m e n t procedure would mask  any d e f e c t s i n the n e c e s s a r i l y approximate f o r c e f i e l d ; c r i t i c i s m i s e q u a l l y t r u e , o f c o u r s e , f o r the f o r c e r e f i n e d i n t h i s work.  this  field  NSC  178 iii)  The c a l c u l a t i o n s performed i n t h i s work a r e  v a l u a b l e i n t h a t they g i v e some i n d i c a t i o n o f t h e r e l i a b i l i t y of t h e p r e d i c t i o n s o f t h e p r e v i o u s work.  In general, the  f r e q u e n c i e s g e n e r a t e d by t h e two f o r c e f i e l d s were v e r y s i m i l a r and t h i s r e s u l t g i v e s added w e i g h t t o many o f t h e assignments made by N e t o , S c r o c c o calculations.  and C a l i f a n o from t h e i r  However, i n r e g i o n s where s e v e r a l fundamentals  of t h e same symmetry a r e e x p e c t e d t o f a l l c l o s e t o g e t h e r and where t h e e x p e r i m e n t a l  s i t u a t i o n i s u n c l e a r , t h e danger o f  using the c a l c u l a t i o n s t o support was p o i n t e d o u t .  a p a r t i c u l a r assignment  The b e s t example o f t h i s i s i n t h e a n t h r a -  cene-h^Q and - d ^ B Q  2 u  symmetry s p e c i e s where each f o r c e  f i e l d s u g g e s t s a d i f f e r e n t assignment.  CHAPTER V I THE VIBRATIONS OF PYRENE A.  Introduction  1.  C r i t i c a l Review Two v i b r a t i o n a l assignments o f pyrene have been 89  reported recently.  Mecke and K l e e  measured t h e i n f r a r e d  spectrum o f t h e ab f a c e and, by comparison w i t h t h e s o l u t i o n and vapor phase s p e c t r a , attempted t o deduce t h e appearance of  t h e s p e c t r a a l o n g a l l c r y s t a l axes.  The s o l u t i o n Raman  spectrum was a l s o r e c o r d e d and some assignments were made from t h e d e p o l a r i z a t i o n r a t i o measurements. 90 Abbondanza the  C a l i f a n o and  have proposed a f a i r l y complete assignment o f  i n f r a r e d - a c t i v e ungerade v i b r a t i o n s o f b o t h pyrene-h^Q  and -d^Q from t h e i r p o l a r i z e d measurements o f t h e ab and ac c r y s t a l faces. 400 cm  1  However, t h e i r s p e c t r a extended o n l y down t o  and one aim o f t h i s work has been t o c o n t i n u e t h e  p o l a r i z e d measurements t o about 50 cm low energy m o l e c u l a r fundamentals.  1  t o locate a l l the  Knowledge o f t h e s e low-  energy modes i s i m p o r t a n t s i n c e i t e n a b l e s t h e e x i s t e n c e o f c o m b i n a t i o n s a t h i g h e r e n e r g i e s t o be r e c o g n i z e d . A new assignment o f t h e fundamental v i b r a t i o n s has been p r o p o s e d , based on t h e new low f r e q u e n c y i n f r a r e d i n f o r m a t i o n and t h e 179  180 r e s u l t s o f a study c a r r i e d out i n t h i s l a b o r a t o r y  91  of the  l a s e r - e x c i t e d Raman s p e c t r a from s i n g l e c r y s t a l s o f p y r e n e . Another aim o f t h e p r e s e n t work was t o c a l c u l a t e the  fundamental f r e q u e n c i e s o f pyrene.  The i n - p l a n e f o r c e  c o n s t a n t s were t r a n s f e r r e d from t h e s i m p l i f i e d f o r c e  field  developed f o r benzene, naphthalene and anthracene as desc r i b e d i n Chapter V;  t h e o u t - o f - p l a n e f o r c e c o n s t a n t s were  a l s o t a k e n from Chapter V.  The c r y s t a l s t r u c t u r e o f pyrene  does n o t p e r m i t a c l e a r d i s t i n c t i o n t o be made between and B  3 u  modes and i n t h e r e g i o n below 1000 cm  1  where funda-  mentals o f both species are expected the c a l c u l a t e d frequenc i e s a r e v a l u a b l e as a g u i d e t o d i f f e r e n t i a t e between them. A normal c o o r d i n a t e a n a l y s i s o f pyrene has a l s o been c a r r i e d 91 out i n t h i s l a b o r a t o r y using force constants transferred 41 from t h e p l a n a r f i e l d d e s c r i b e d by Neto e t a l . and t h e o u t 36 o f - p l a n e f i e l d used f o r n a p h t h a l e n e , the 2.  and a comparison o f  two s e t s o f c a l c u l a t e d f r e q u e n c i e s was made. S e l e c t i o n Rules The pyrene m o l e c u l a r axes have been chosen t o c o n 64  form t o t h e i n t e r n a t i o n a l c o n v e n t i o n F i g u r e 5.  . and a r e shown i n  S i n c e t h e pyrene m o l e c u l e does n o t s i t a t a s p e c i a l  p o s i t i o n i n t h e u n i t c e l l , a l l f r e e - m o l e c u l e s t a t e s can mix i n the c r y s t a l .  Each m o l e c u l a r s t a t e g i v e s r i s e t o f o u r  c r y s t a l s t a t e s w i t h k = 0 and t h e s e l e c t i o n r u l e s f o r t h e  181 f r e e m o l e c u l e and the c r y s t a l are summarized i n T a b l e 30. I n the i n f r a r e d spectrum o f the f r e e m o l e c u l e , three  and two B  CH s t r e t c h e s are e x p e c t e d so t h a t  2 u  below 2000 cm "nine B, , t e n B_ and seven B_ lu' 2u 3u s h o u l d appear.  fundamentals  I n the c r y s t a l the spectrum may  be more com-  p l e x due t o the presence o f m o l e c u l e - f o r b i d d e n bands appeari n g because o f the absence of s i t e symmetry. I n the u s u a l o r i e n t e d - g a s a p p r o x i m a t i o n the r e l a t i v e i n t e n s i t y of a b s o r p t i o n a l o n g v a r i o u s c r y s t a l axes can be determined from the d i r e c t i o n c o s i n e s r e l a t i n g m o l e c u l a r and c r y s t a l axes; a summary o f the r e s u l t s i s g i v e n i n T a b l e 31. T a b l e 30,  C o r r e l a t i o n t a b l e f o r Pyrene*  Molecular D  N 13 5 4 12 7 12 12 7 *  group  S i t e group Cl  2h  Factor C  Bases  2h  Bases  x x , y_y_, zz  A  g  u  A  ^ *  group  lg lu  B  B  ™  B  2g 2u  TL  B  ^  B  3g  £  B  3u  a a  g  u  b  n  aa, bb, c c , ac  6  b  5  ab, be  6  a, b  4  g  N i s the number o f m o l e c u l a r fundamentals and n i s the number of l a t t i c e f r e q u e n c i e s , assuming k=0. F a c t o r group symmetry s p e c i e s are d i s t i n g u i s h e d by lower case l e t t e r s .  182  T a b l e 31  t  The  o r i e n t e d -gas p r e d i c t i o n s o f t h e r e l a t i v e  i n t e n s i t i e s of the i n f r a r e d a c t i v e l i n e s o f pyrene a l o n g v a r i o u s  c r y s t a l axes *  lu  *  3u  a*  0.010  0.562  0.433  a  0.237  0.357  0.413  b  0 .050  0.394  0.557  g'  0.711  0.250  0.030  c*  0.937  0.046  0.011  The axes a*, c* and c  1  are d e f i n e d i n Chapter I I .  183 B.  Results The  low f r e q u e n c y i n f r a r e d s p e c t r a o f pyrene-h^g  are shown i n F i g u r e 29 f o r t h e ab and ac s e c t i o n s and f o r a s o l u t i o n i n benzene.  I n F i g u r e 30 a r e shown t h e s p e c t r a o f  an ab s e c t i o n o f pyrene-d^g and o f a s o l u t i o n o f p y r e n e - d ^ g i n benzene.  Because t h e s u p p l y o f p y r e n e - d ^ g was l i m i t e d ,  s i n g l e c r y s t a l s l a r g e enough t o p r e p a r e a£ s e c t i o n s c o u l d n o t be grown and some symmetry assignments f o r t h i s m o l e c u l e ( p a r t i c u l a r l y i n the B^ pyrene-h^Q.  s p e c i e s ) were made by analogy w i t h  u  The s o l u t i o n s p e c t r a were e s p e c i a l l y v a l u a b l e  s i n c e i n a d d i t i o n t o d i f f e r e n t i a t i n g between m o l e c u l a r and l a t t i c e modes t h e y a i d e d i n t h e i d e n t i f i c a t i o n o f m o l e c u l a r modes a p p e a r i n g o n l y t h r o u g h c r y s t a l f o r c e s .  The s p e c t r a  were r e c o r d e d a t h i g h e r f r e q u e n c i e s b u t a r e n o t p r e s e n t e d s i n c e good agreement was found w i t h t h e r e s u l t s a l r e a d y pub90 l i s h e d by C a l i f a n o and Abbondanza.  Only two s i g n i f i c a n t  d i f f e r e n c e s were n o t e d ; i n t h e ac spectrum o f p y r e n e - h ^ g , b o t h t h e l i n e a t 1002 cm cm  1  and an i n t e n s e s h o u l d e r a t 1585  1  were found t o be c* p o l a r i z e d .  r e p o r t e d t h a t t h e 1002 cm f i n d t h e 1585 cm  1  1  C a l i f a n o and Abbondanza  l i n e was d e p o l a r i z e d and d i d n o t  shoulder.  The l i n e s which appear i n t h e low-energy  infrared  s p e c t r a o f pyrene-h-^g and pyrene-d^g a r e summarized, a l o n g w i t h t h e i r assignment, i n T a b l e 32.  The f o l l o w i n g d i s c u s s i o n  i s based on p y r e n e - h ^ g ; t h e assignments o f t h e c o r r e s p o n d i n g l i n e s o f pyrene-d^g a r e r e a d i l y deduced from T a b l e 32.  184  F i g u r e on f o l l o w i n g ure 29.  page.  The l o w - f r e q u e n c y i n f r a r e d s p e c t r a o f  pyrene-h^Q.  Upper, 0.30 mm t h i c k ab  f u l l l i n e // b, b r o k e n l i n e // a. mm t h i c k ac s e c t i o n ; l i n e // a*.  section;  M i d d l e , 0 30  f u l l l i n e // c*, b r o k e n  Lower, s o l u t i o n i n benzene.  185  LOSSIUUSUDJi.  %  T  I  100  I  I  200  I  1  300  1  ,  -,  400  .  500  .  Wavenumber (cm." ) 1  F i g u r e 30. Low-frequency i n f r a r e d s p e c t r a o f p y r e n e - d . Upper, 0.40 mm t h i c k ab s e c t i o n ; f u l l l i n e // b, broken l i n e // a. Lower) s o l u t i o n i n benzene. 1 Q  187 T a b l e 32.  The l o w - f r e q u e n c y i n f r a r e d s p e c t r a o f pyrene-h and p y r e n e - d ,  Pyrene 1 0 S o l u t i o n //b //a  n  Pyrene-d^o  _ h  / / a * //£*  Solution  //b  //a  V  70? 71? 89  89  102 124 219 319 350  99  123  105 129  105 129  220  158 217  158 217  258  258 320  349  349 392  349 392  105 114 201  452  453  484  482  485  485  495  494  493  525  538 570  536 573 585  115  105 122  203  147? 200  b  B  3u 3u  240  A ? u  349 392  323  324 355  324 351  493  2u B,l u B  432 449  430  431 448  461  462 472  460  B  lu  B  2u  500  520  au ? b u u u a  396  406 453  Symmetry  3u  497 509  505  520  518  520  565  566  570  B. 3u  596  600  3u  524 537  537  571  572  585  586  537  586  188 The  i n t e n s e l i n e s i n the pyrene-h^g s o l u t i o n  spectrum a t 124, 219, 350, 484, 495 and 538 c m as m o l e c u l a r fundamentals. 495 cm  1  marks a  B^  u  were t a k e n  s t r o n g c* p o l a r i z e d l i n e a t  fundamental and the two l o w e s t energy  l i n e s a t 124 and 219 cm modes.  The  -1  As observed  must a r i s e from o u t - o f - p l a n e  1  f o r naphthalene  and a n t h r a c e n e ,  B  3 u  these  l i n e s are e s p e c i a l l y i n t e n s e and show a f a c t o r - g r o u p  s p l i t t i n g i n the c r y s t a l .  A t h i r d l i n e which has t h e s e c h a r o -1 a c t e r i s t i c s appears i n s o l u t i o n a t 484 cm and i s a c c o r d i n g l y a s s i g n e d B^  symmetry.  349 and 537 c m t a k e n as B  2 u  -1  The  s t r o n g a and b p o l a r i z e d l i n e s a t  t h a t show no s p l i t t i n g i n the c r y s t a l  fundamentals.  are  These assignments are i n agreement 90  with Califano's c r i t e r i o n , 92 structure data,  deduced from o l d e r c r y s t a l  t h a t f o r an ab s e c t i o n B ^  what s t r o n g e r a l o n g b w i t h B  2 u  modes are some-  modes n e a r l y d e p o l a r i z e d but  s l i g h t l y s t r o n g e r a l o n g a. 68 The more r e c e n t c r y s t a l s t r u c t u r e d e t e r m i n a t i o n shows t h a t the p o l a r i z a t i o n r a t i o s u s u a l manner, s h o u l d be 1.35 both g r e a t e r than u n i t y . the o b s e r v a t i o n t h a t B  2 u  for B ^  ( k / ) c a l c u l a t e d i n the R  a  and 1.10  for B  2 u  modes,  There i s thus a d i s c r e p a n c y between modes are s l i g h t l y s t r o n g e r a l o n g a  i n ab and the p r e d i c t i o n s o f the o r i e n t e d - g a s model, u s i n g the l a t e s t c r y s t a l d a t a .  The  above v a l u e s , however, are  s i m p l y the r a t i o s o f the squared d i r e c t i o n c o s i n e s t a k e n w i t h r e s p e c t t o a and b.  F o r l i g h t p a s s i n g down c  1  i n c i d e n t on  an  189  ab  s e c t i o n , the  on  through the  b p o l a r i z e d beam sample a l o n g  (the e x t r a o r d i n a r y by  an  I.)  angle For  £.  this axis  ray)  (The  the  has  b e e n n o t e d by  1  may  deviate  situation  the  from c  0.5°  ratio  Luty ^  Using  visible the  indeed,  the  extraordinary  Refractive  indices  (y)  were m e a s u r e d by  light  and  vector  along  a and  the be  ratios  of  (10)  1.59  use  values.  of data  red r e s u l t s .  The  3,  plane Chapter  be  evaluated  This correction suggested  £ was  i s within  found  with  2°  the  insertion  of r e f e r e n c e  ratios  56  of  c.  light  electric  of  this  yielded 1.57  still  cause f o r t h i s  ultraviolet  c'  i m m e r s i o n methods i n  f o r B_ modes and 3u  The  ac  have a l s o  1.66  The  taken i n v i s i b l e strong  £.  light,  ray  and  T h e s e c o r r e c t i o n s move t h e  experimental the  1.76  b respectively.  i n t o equation  polarization * modes.  f o u n d t o be  continues  d e v i a t i o n i s from  t o w a r d s c;  information  should  who  5  f o r p y r e n e and  yellow  i n the  1  i s shown i n F i g u r e  R o h l e d e r and £.  ray)  a p o l a r i z e d beam  frame r o t a t e d a b o u t b t h r o u g h  a method f o r m e a s u r i n g 8.6  c' w h i l e  case the p o l a r i z a t i o n  for  t o be  (the o r d i n a r y  new  for  B  further  2u n  from  discrepancy  must  to i n t e r p r e t i n f r a -  absorption  systems  are  93 long-axis sion  polarized  i s t o make y * c  indicatrix  should  fundamentals are w o u l d be A small  expected shift  be  and the very  so  the  effect  largest.  On  different  in this  direction  t o make t h e p o l a r i z a t i o n  ratio  1  the  i n the  t h e most i n t e n s e , and t o bend from c  o f anomalous  the  other  f o r B_  8°)  hand,  the  i n f r a r e d where extraordinary  in a direction (7 o r  disper-  B ray  away f r o m  w o u l d be  modes change  3 u  c.  sufficient from  190 g r e a t e r than u n i t y t o l e s s t h a n u n i t y i n agreement w i t h t h e experimental r e s u l t s . The l e s s i n t e n s e bands i n t h e i n f r a r e d s p e c t r a a r e g i v e n the f o l l o w i n g i n t e r p r e t a t i o n . 453, 406, 258 and 158 cm  The bands a t 585, 500,  which appear o n l y i n t h e c r y s t a l  1  91 s p e c t r a mark A ,  B  g  3 g  /  A  g/ 2g B  a n d  A  u m o l e c u l a r fundamentals  r e s p e c t i v e l y , which i n the low s i t e symmetry can appear through c r y s t a l f o r c e s .  A  u  and g modes, f o r b i d d e n i n t h e  f r e e - m o l e c u l e spectrum, g i v e r i s e t o f o u r components  (k=0),  t r a n s i t i o n s t o two o f which a r e f o r m a l l y i n f r a r e d a c t i v e i n the c r y s t a l  (see T a b l e 3 0 ) .  The i n t e n s i t y o f t h e s e i n d u c e d  bands i s d e r i v e d from o t h e r s t r o n g bands nearby. c u l a r , t h e bands a t 158 and 258 cm  1  In p a r t i -  p r o b a b l y appear by m i x i n g  w i t h l a t t i c e modes, much as t h e low-energy Raman-active molec u l a r modes o f anthracene-d^Q from t h e l a t t i c e  were shown t o g a i n i n t e n s i t y  (see Chapter I V ) . W h i l e some o f t h e s e weak  bands a t t r i b u t e d above t o g  fundamentals have a l t e r n a t i v e  e x p l a n a t i o n s as c o m b i n a t i o n s , t h i s i s n o t t r u e f o r the bands a t 406 and 500 cm  1  and, f u r t h e r , i t s h o u l d be p o i n t e d o u t  (see a l s o T a b l e 32) t h a t t h e m o l e c u l e - f o r b i d d e n l i n e s i n d u c e d i n t h e i n f r a r e d spectrum o f pyrene-d^^ c r y s t a l c o r r e s p o n d e x a c t l y t o t h o s e observed i n pyrene-h^^. Among the r e m a i n i n g weak low-energy l i n e s i n t h e pyrene-h^g i n f r a r e d spectrum t h e c o m b i n a t i o n a t 39,2 cm -1  191 i s most i m p o r t a n t , s i n c e t h e energy f i t shows t h a t t h e f u n damentals a t 126 cm  1  (mean o f o b s e r v e d components) and  263 cm -1 (seen i n t h e Raman spectrum 91 ) a r e i n v o l v e d . the  26 3 cm  1  i n t e r v a l i s shown t o be o f  Thus  symmetry, a f a c t  which i s n o t c l e a r from t h e Raman e v i d e n c e a l o n e . The weak l i n e s a t 525 and 572 cm the  A  u  p r o b a b l y mark  c o m b i n a t i o n s 126 (B_ ) + 406 (A„) and 228 (B.. ) + 349 (B„ ) 3u g lg 2u  respectively. the  1  No energy match can be found t o account f o r  l i n e a t 320 cm  and so i t i s t e n t a t i v e l y a s s i g n e d as an  1  fundamental. L i n e s i n t h e spectrum o f pyrene-d^^ which have n o t  been i n d i r e c t l y c o n s i d e r e d i n t h e above d i s c u s s i o n appear a t 448, 497 and 505 cm  1  and a r e assumed t o be caused by t h e  p r e s e n c e o f i s o t o p i c i m p u r i t y m o l e c u l e s which do n o t have f u l l D„,  symmetry.  C.  C a l c u l a t i o n o f Fundamentals A normal c o o r d i n a t e a n a l y s i s was c a r r i e d o u t f o r  pyrene u s i n g p l a n a r f o r c e c o n s t a n t s t r a n s f e r r e d from t h e f i e l d 32 developed i n Chapter V from t h e D u i n k e r - M i l l s benzene to  field  f i t s i m u l t a n e o u s l y benzene, naphthalene and a n t h r a c e n e .  The CC s t r e t c h i n g c o n s t a n t s were made p r o p o r t i o n a l t o t h e bond l e n g t h by f i t t i n g them t o t h e curve f = Ae  described  192  i n Chapter V. Two s e t s o f o u t - o f - p l a n e f o r c e c o n s t a n t s were t r i e d ; they were t a k e n from t h e benzene f o r c e f i e l d s d e s i g nated I I - A and I I I - A i n C h a p t e r V. The i n t e r n a l c o o r d i n a t e s a r e d e f i n e d i n F i g u r e 31 where CC bond s t r e t c h e s ( d e s i g n a t e d as R ) , CH bond s t r e t c h e s ( r ) , CCC a n g l e bends ( a ) , and i n - p l a n e hydrogen wags (8) a r e shown.  The CC bond t o r s i o n s (<f>) and t h e o u t - o f - p l a n e wags  (y) a r e numbered i n t h e same way as t h e R and t h e a r e s p e c t i v e l y and a r e n o t shown on t h e diagram. The l i s t f o l l o w i n g F i g u r e 31 g i v e s t h e f o r c e cons t a n t s u n r e l a t e d by m o l e c u l a r symmetry i n an a b b r e v i a t e d nomenclature s i m i l a r t o t h a t used e a r l i e r .  The c o n s t a n t s  are named w i t h r e f e r e n c e t o t h e i n t e r n a l c o o r d i n a t e s and t h e u n i t s a r e mdyn/A  f o r s t r e t c h i n g c o n s t a n t s , mdyn/radian f o r 2  o  s t r e t c h bend i n t e r a c t i o n s and mdyn A / r a d i a n  f o r bending  constants. In-plane force constants: 1.081 R  1 9  R  R R 2  2  = 1.161  1.103; i  (a a 3  ^= r  a_a_ = a . a . =  3 3 3  + a a 4  4 4 4  +  3  5  = -0.609;  R  R R 4  ^=  4  = 5.061;  0.712;  1  3  R  = 1.068  Ri5  Yl = 1 5  °2°2  =  = 0.814; a~-.a~-. = a .a . 5 5 23 23 24 24 = 0.746; 3 ^ - B B = 6363 = 1.020.  R ^  R 2  0.934 R^R-^ =  = 1.068  a a c  c  0  2  O f f - d i a g o n a l terms: R R  = 0.680  R3R3  = 7.040; r  1 9  D i a g o n a l terms:  = R  R 1  1  4  = 0.295; r r 2  = 1 Q  R  2  3 4 = 0-650; R  = 0.034;  R R. 1  =  13  = a a 2  3  =  0  193  F i g u r e 31.  The  i n t e r n a l c o o r d i n a t e s of pyrene.  194  a  4 6 a  -6 3 3  =  6 7 a  =  a  =  a  2  12  15 4 a  =  R  a  -0.323; 3 a 2  B  1 1  B  1 15 R  e  =  3  R  A long-range  2 2  6  - 1 18  =  a  a  R  R  =  6  ' ^  0 9 7  =  R  a  a  6 0 2 ;  3  a  R  =  a  B  2 18 R  R  e  " 2 13  =  6  R  Kekule-type  R  =  e  3 16  B  R  g  =  3 4 a  " 2 1 = 3 4 = " 3 3  =  R  = R, ,-ou = 15 3  a  =  3  =  4 6 a  -°-  =  6  R  = -0.014;  3  2 4  R  " 3 19  =  =  = a r  2  3 3  _ 3  e  = R.a, 46  30 b  ~ l 22  =  ®l 2  =  = R a,  °'  =  i iO  _ 6  2  30 %  19 24  =  2  = a r  = R a.  2. 30  15 24  R  -°-  =  = -0.015;  = -&2 l  3  " i 14  =  =  a  = R„a  2 20  15 23  4 24  1 0  = R~a  = R,a~  1 1  R  3 23  a  = 0.028; 3 3  4  R,a, R  a  =  _  ^*063;  3 1 5 ;  - '  =  0  0 2 7  -  i n t e r a c t i o n c o n s t a n t between RR  s t r e t c h e s was a l s o i n c l u d e d and i s b e s t d e s c r i b e d t h u s :  any  i n t e r a c t i o n between CC s t r e t c h i n g c o o r d i n a t e s when one o r b o t h bonds were n o t on t h e p e r i m e t e r o r when t h e two bonds were i n d i f f e r e n t r i n g s was g i v e n a f o r c e c o n s t a n t o f 0.090, m u l t i p l i e d by a w e i g h t i n g f a c t o r found i n a manner a l r e a d y d e s 37 cribed. Out-of-plane Y  3 3 Y  =  Y  ^lS^lS  4 4 Y  force constants:  =  Y  15 15 Y  *19*19  =  °'  =  °-  =  0 8 7  0.006;  Y L  -0.006; *  1 5  *i9  *3*5 CJ> Y 3  4  Y  = Y Y  3  2  <J><|, 1  2  *4*15  =  =  -<r> Y 3  3  2  2  = Y  4  = ( f r ^= $ * 2  = 0.00.2; ^ ^ =  1 5  =  ^ 1 6  =  <f> Y 4  5  *3*3'  =  =  = Y Y  2  = Y Y  1 5  *1*1 *2*2  2 9 3 ;  Y^Y^  *4*4  =  Y Y  =  2  = 2  =  -  O f f - d i a g o n a l terms: y y ±  D i a g o n a l terms:  =  1 5  = Y3Y4 = Y Y  1 7  1 ?  4  Y  2 6  4> <f» 2  3  =Y Y 1 ?  =  = Y Y  5  4  <f> <f> 3  = Y  5  4  3  °-  0 0 7 ;  = t> Y _(  4  4  1  *1 2 Y  =  - ( ) )  = -0.016.  1 1 Y  =  *2 3 Y  =  =Y Y =  1 6  J 7  3  =  15  4> * 3  _cf,  Y  = Y Y  1 5  <t> *  =  = <()<|)3 = c ^ c j , ^ = ( f r ^ g = 1  1 5  =  ; L 9  2 2 Y  4 >  =  1  5  =  1 3  *  1  2 5  8  =  195 The c a l c u l a t i o n s were c a r r i e d out on an IBM 360/67 computer u s i n g a somewhat m o d i f i e d v e r s i o n o f a program 88 (VSEC) w r i t t e n by S c h a c h t s c h n e i d e r summarized i n T a b l e s 33 and 34.  • and the r e s u l t s a r e  A l s o included i n Tables  33 and 34 a r e the r e s u l t s o f a s i m i l a r c a l c u l a t i o n c a r r i e d 91 out i n t h i s l a b o r a t o r y u s i n g f o r c e c o n s t a n t s from d i f f e r e n t 35 41 sources.  '  The two s e t s o f c a l c u l a t e d f r e q u e n c i e s a r e  compared w i t h the new assignment o f t h e fundamentals t o be d e s c r i b e d i n the n e x t s e c t i o n . D.  Assignment The assignment o f the Raman-active m o l e c u l a r  fundamentals g i v e n i n T a b l e 34 was t a k e n from t h e r e c e n t 91 laser-Raman s t u d y o f pyrene c r y s t a l s and s o l u t i o n s .  The  i n f r a r e d - a c t i v e m o l e c u l a r fundamentals were a s s i g n e d a t low energy from t h e s p e c t r a p r e s e n t e d i n t h i s c h a p t e r and a t h i g h e r energy from the s p e c t r a p u b l i s h e d by C a l i f a n o and 90 Abbondanza, a l t h o u g h even a t h i g h e r energy the assignment proposed here does not agree c o m p l e t e l y w i t h the one g i v e n 90 i n t h a t paper.  The two c o r r e c t i o n s noted e a r l i e r i n the  ac s p e c t r a were t a k e n i n t o account i n making t h i s  assignment.  T a b l e 3 3 . Observed and c a l c u l a t e d u-fundamentals o f pyrene  Pyrene-h-LQ Observed Ref. 90 T h i s work  Calculated T h i s work R e f . 9 1  Pyrene-d Observed Calculated Ref. 90 T h i s work T h i s work Ref. 9 1 1 Q  965  942  803  789  906  897  731  736  648  660  582  592  320?  410  391  367  344  188  163  179  161  151  165  3098  3098  3064  3081  2294  2294  2279  2292  3080  3080  3052  3029  2278  2278  2270  2247  3040  3040  3051  3020  2256  2256  2265  2241  1517  1585  1569  1613  1523  1570?  1549  1588  1468  1468  1487  1432  1427  1427  1442  1392  1449  1449  1393  1418  1366  1366  1248  1314  1417  1242  1238  1255  1302  1188?  1047  1026  1242  1095  1089  1074  1188  841  983  954  1094  1064  1020  982  841  821?  829  814  810  767  821  755  753  711  683  651  659  626  502  503  465  468  1064 495  820?  493  462  461  Table  33.  (Continued)  Ref.  B 2u  B 3u  Pyrene-h 10 Observed This 90 T h i s work  Pyrene-d^Q Calculated work R e f . 91  Ref.  Observed 90 This  work  This  Calculated work R e f . 91  3028  3028  3057  3073  2242  2242  2288  2289  2989  2989?  3040  3049  2211  2211  2257  2264  1599  1599  1692  1607  1561  1561  1668  1564  1432  1487?  1608  1472  1338  1461?  1576  1425  1310  1432  1489  1397  1276  1338  1454  1382  1272  1310  1370  1384  1037  1276  1209  1271  1204  1272  1190  1172  996  1037  1039  1016  1184  1184  1179  1169  973  945  954  911  1002  1085?  1127  1145  945  903  842  833  962  963  982  954  789  762  815  828  820  537  567  506  762  519  545  489  540  349  344  355  521  324  320  330  963  963  988  957  804  804  817  798  845  845  825  816  745  745  704  703  748  748  767  753  603  598  620  638  710  710  703  717  571  568  576  568  487  484  484  483  432  431  436  428  447  219  206  195  202  189  178  126  112  113  119  105  105  H  ^  198 Table 34.  Observed and c a l c u l a t e d g-fundamentals o f pyrene  Pyrene-hio Observed Calculated Ref.91 T h i s work Ref. 91  Pyrene-dio Observed Calculated Ref. 91 T h i s work Ref. 91  3101 3060  3064 3057  3081 3073  2302 2292  2289  2294  2278  3029  3052  3021  2273  2270  2287 2242  1628  1669  1656  1619  1641  1644  1554  1614  1567  1504  1597  1517  1407  1500  1407  1388  1462  1358  1354  1337  1300  1275  1270  1263  1242  1220  1232  1164  1146  1162  1143  1152  1142  875  860  841  1066  1069  1058  833  830  820  807  805  737  752  752  703  592  5.74  607  564  550  579  406  402  393  399  392  383  907  899  744  739  819  811  650  653  507  512  458  262  251  237  463 224  988  963  820  808  966 788  947 764  796 752  768 754  765  755  600  600  583  579  506  489  475  469  424  414  267  272  251  254  228  263  205  235  199  T a b l e 34.  (Continued)  Pyrene-hio Observed Calculated Ref.91 T h i s work Ref. 91 B  3g  Pyrene-dio Observed Calculated Ref. 91 T h i s work Ref. 91  3048? 3016?  3051 3040  3049 3028  2273? 2252  2268  2265  2258  2245  1593  1603  1601  1582  1586  1590  1568?  1509  1509  1433?  1477  1451  1411  1383  1373?  1319  1313  1382  1357  1239  1212  1198  1230  1220  1064  1036  1163  1160  939  904  1110  1135  1077  833  839  835  739  741  694  690  695  647  503  492  496  466  449  455  457  442  425  437  427  411  200  For the B^  u  s p e c i e s , the frequency  820 cm  been i n c l u d e d i n the pyrene-h^Q s e t and 755 cm pyrene-d^Q s e t .  The  820  cm  has  1  i n the  1  l i n e , w h i c h appears i n the  ac  spectrum as a s h o u l d e r t o the v e r y s t r o n g l i n e a t 845 cm  \  1  has g r e a t e r s t r e n g t h i n c* t h a n i n a* p o l a r i z a t i o n and i s a c c o r d i n g l y a s s i g n e d as a B^  and not a B fundamental, i n 89 -1 agreement w i t h Mecke and K l e e . The l i n e a t 755 cm i s . not u  2 u  a component of the s t r o n g e r 762 cm  1  l i n e s i n c e no  factor-  group s p l i t t i n g s h o u l d appear i n the ac spectrum. a d d i t i o n t o the B^  s p e c i e s i s the l i n e a t 1585  u  The  cm  i n the  1  p r o t o n a t e d m o l e c u l e which r e p l a c e s the l i n e a s s i g n e d C a l i f a n o 90 a t 1517 cm -1 The most o b v i o u s change i n the modes o f B  other  by  2 u  sym-  metry f o l l o w s from the r e c o g n i t i o n o f a fundamental near 350 cm  The  t e n fundamentals below 2000 cm  may  1  f i e d r a t h e r c r u d e l y as f i v e r i n g modes, t h r e e CH wags and two s k e l e t a l d e f o r m a t i o n s .  Although  be c l a s s i -  in-plane  some m i x i n g  w i t h the CH i n - p l a n e wags must o c c u r , a t l e a s t f o u r of. the f i v e r i n g modes s h o u l d show a r e l a t i v e l y s m a l l drop i n f r e quency upon d e u t e r a t i o n and so the band a t 1487  cm  1  has  been t a k e n t o mark a fundamental i n pyrene-h^g, and 1461 i n p l a c e of 996  cm  minor, i n v o l v i n g ,  1  i n pyrene-d^g.  1  1  cm  1  the c h o i c e o f  i n s t e a d o f the weak  l i n e and the prominent l i n e a t 762 cm  a band a t 789  1  o t h e r changes are  f o r the d e u t e r a t e d m o l e c u l e ,  the f a i r l y i n t e n s e l i n e a t 903 cm 973 cm  The  cm  not observed i n t h i s work.  1  i n p l a c e of The  theoretical  201  v a l u e o f 5.52 maining B  p l a c e s the r e -  fundamental o f pyrene-h^g near 1100  2 u  t h a t i t may 10 85  f o r the p r o d u c t r u l e r a t i o now  cm ^ so  be t e n t a t i v e l y i d e n t i f i e d w i t h the weak l i n e a t  cm . -1  With the new o f the B  low-energy i n f o r m a t i o n the assignment  fundamentals i s now  3 u  complete.  The  experimental  v a l u e o f 2.74  f o r the p r o d u c t r u l e r a t i o i s v e r y c l o s e t o  the expected  2.76.  E.  Conclusion  1.  Out-of-Plane  Assignment  The c a l c u l a t i o n o f the o u t - o f - p l a n e fundamentals has now  been c a r r i e d out w i t h t h r e e s l i g h t l y d i f f e r e n t f o r c e  fields.  In the course o f t h i s work, two s e t s o f f o r c e con-  s t a n t s were t r a n s f e r r e d from benzene ( s e t s I I - A and I I I - A o f Chapter V ) .  The r e s u l t s were v e r y good f o r b o t h f i e l d s  and  o n l y the f r e q u e n c i e s c a l c u l a t e d w i t h s e t I I I - A c o n s t a n t s p r e s e n t e d i n Tables 33 and 34.  S i n c e the o u t - o f - p l a n e  are  field  used i n r e f e r e n c e 91 was made up w i t h f o r c e c o n s t a n t s d e r i v e d f o r b e n z e n e ^ ' ^ i n a s i m i l a r manner i t i s not t h a t the f r e q u e n c i e s c a l c u l a t e d  surprising  (see T a b l e s 33 and 34)  are  a l s o v e r y c l o s e t o the observed v a l u e s , and, i n f a c t , t h e r e  202  was l i t t l e t o choose between t h e t h r e e s e t s o f c a l c u l a t e d results.  The average e r r o r i n t h e f i t t o t h e c e r t a i n f u n d a -  mentals was i n each case about 15 cm . 1  2.  I n - p l a n e Assignment W h i l e agreement between t h e observed fundamentals  and e i t h e r s e t o f c a l c u l a t e d f r e q u e n c i e s was q u i t e good, i n s p e c t i o n o f T a b l e s 33 and 34 shows t h a t t h e f i e l d d e r i v e d 32 from t h e D u i n k e r and M i l l s benzene f i e l d (see Chapter V) was n o t i c e a b l y b e t t e r f o r t h e fundamentals below about 1100 cm -1 and t h e Neto, S c r o c c o and C a l i f a n o f i e l d 41 '91 was a p p r e c i a b l y b e t t e r above t h a t energy. the  former f i e l d was l e a s t s u c c e s s f u l i n f i t t i n g t h e h i g h e s t -  energy B  0  r i n g modes and a l s o p r e d i c t e d A  h i g h e r than t h e e x p e r i m e n t a l v a l u e s . to  As f o r a n t h r a c e n e ,  modes c o n s i d e r a b l y  Both f i e l d s were unable  f i t t h e CH i n - p l a n e bending f r e q u e n c i e s o f t h e B^  u  species  of pyrene-d^g and t h i s may be due t o t h e presence i n t h i s r e g i o n o f a fundamental i n t r i n s i c a l l y  weak i n t h e i n f r a r e d .  As p o i n t e d o u t i n Chapters I I I and IV an analogous e x i s t s i n t h e B,  situation  s p e c i e s o f naphthalene-d„ and a n t h r a c e n e - d ,  n  CHAPTER V I I THE VIBRATIONS OF ACENAPHTHENE  Introduction 1.  Critical  Review  Polarized  i n f r a r e d s p e c t r a o f acenaphthene  single  c r y s t a l s a t e n e r g i e s above 400 cm -1 have been r e p o r t e d 94'95 96 97 and a comparison w i t h o l d e r Raman d a t a ' has l e d t o a 94 f a i r l y complete assignment o f t h e fundamental v i b r a t i o n s . Some d i f f i c u l t i e s s t i l l e x i s t , however; f o r example, t h e i n t e r p r e t a t i o n o f t h e f l u o r e s c e n c e and phosphorescence 98 99 spectra ' has r e q u i r e d m o l e c u l a r fundamentals t o be l o c a t e d -1 -1 98 99 near 220 cm and near 416 cm ' and t h e s e have n o t been 94 r e c o g n i z e d i n t h e l a t e s t assignment.  One aim o f t h e p r e -  s e n t work has been t o e x t e n d t h e i n f r a r e d s o l u t i o n and s i n g l e c r y s t a l measurements t o low energy t o a s s i g n more f i r m l y t h e low f r e q u e n c y fundamentals.  L a s e r Raman s t u d i e s on s i n g l e  c r y s t a l s o f acenaphthene were b e i n g c a r r i e d o u t i n t h i s l a b o r a t o r y s i m u l t a n e o u s l y w i t h t h i s work"*^ and a comparison of t h e i n f r a r e d s p e c t r a w i t h t h e more complete Raman d a t a p e r m i t t e d a more s e c u r e assignment o f t h e m o l e c u l a r fundam e n t a l s t o be made. 203  In a d d i t i o n , t h e f r e q u e n c i e s o f t h e normal modes of acenaphthene were c a l c u l a t e d w i t h f o r c e c o n s t a n t s t r a n s f e r r e d from o t h e r m o l e c u l e s .  The c a l c u l a t e d and a s s i g n e d  f r e q u e n c i e s were compared i n an attempt t o a s s e s s t h e t r a n s f e r a b i l i t y of the force  2.  fields.  S e l e c t i o n Rules The acenaphthene m o l e c u l a r axes have been chosen 64  t o conform w i t h t h e i n t e r n a t i o n a l c o n v e n t i o n f i n e d i n F i g u r e 4.  and a r e de-  S i n c e t h e acenaphthene m o l e c u l e does n o t  c o n t a i n a c e n t e r o f symmetry, Raman and i n f r a r e d  spectra  supplement each o t h e r ; t h e s e l e c t i o n r u l e s f o r t h e f r e e m o l e c u l e and f o r t h e c r y s t a l a r e summarized  i n T a b l e 35.  Because t h e r e a r e f o u r m o l e c u l e s i n t h e u n i t c e l l , each  line  i n t h e spectrum o f t h e f r e e m o l e c u l e i s e x p e c t e d t o s p l i t i n t o f o u r components i n t h e c r y s t a l a l t h o u g h comparison w i t h the  s p e c t r a o f n a p h t h a l e n e , anthracene and pyrene s u g g e s t s  t h a t o n l y f o r t h e o u t - o f - p l a n e modes w i l l t h e s p l i t t i n g be appreciable.  The A  2  states are i n f r a r e d i n a c t i v e i n the free  m o l e c u l e b u t can appear i n t h e Raman spectrum and a l s o , by mixing with B  2  s t a t e s , i n t h e i n f r a r e d spectrum o f t h e c r y s t a l .  Four CH s t r e t c h i n g v i b r a t i o n s a r e e x p e c t e d i n each o f t h e A-, and B~ m o l e c u l a r symmetry b l o c k s , and one CH s t r e t c h i n  \  each o f t h e A  2  and B^ b l o c k s .  205  T a b l e 35.  N  C o r r e l a t i o n t a b l e f o r acenaphthene*  M o l e c u l a r group '2v Bases  S i t e group  F a c t o r group C, '2v Bases n  20  x x , y y , z z ; z_ A-|_  11  xz ; x  10  xy_  a  2  19  y_z_ ; y  b  2  B.  a  A'  l  b^  £' fL .' bb/ 3  a;  ££  ac  ab b; be  N i s t h e number o f fundamentals i n t h e f r e e m o l e c u l e and n i s t h e number o f l a t t i c e f r e q u e n c i e s , assuming k = 0. F a c t o r group symmetry s p e c i e s a r e d i s t i n g u i s h e d here and e l s e w h e r e i n t h e t e x t by l o w e r case l e t t e r s .  5 5  206  The r e l a t i v e i n t e n s i t i e s o f i n f r a r e d - a c t i v e mentals  i n the v a r i o u s c r y s t a l d i r e c t i o n s  may  be  i n the u s u a l o r i e n t e d gas a p p r o x i m a t i o n , from the  funda-  calculated, direction  c o s i n e s r e l a t i n g m o l e c u l a r and c r y s t a l axes, and a r e summarized i n Table 36.  Table 36.  The o r i e n t e d - g a s p r e d i c t i o n s o f the i n t e n s i t i e s o f the i n f r a r e d - a c t i v e  relative l i n e s of  acenaphthene a l o n g v a r i o u s c r y s t a l axes  B (y) 2  1.00  0.63  0.00  I.  0.00  0.00  1.00  I  0.63  1.00  0.00  I  a b c  207  B.  Results The  p o l a r i z e d i n f r a r e d s p e c t r a o f an ac s e c t i o n o f  acenaphthene a r e p r e s e n t e d  i n F i g u r e 32 and t h e o b s e r v e d  f r e q u e n c i e s a t low energy a r e l i s t e d w i t h t h e i r assignments i n T a b l e 37.  The assignments were based, as u s u a l , on t h e  assumption t h a t c r y s t a l f o r c e s would n o t mix t h e m o l e c u l a r states s u f f i c i e n t l y t o reverse p o l a r i z a t i o n r a t i o s .  The  s p e c t r a a t h i g h e r e n e r g i e s agreed w e l l w i t h both p r e v i o u s 94 95 results  '  and so t h e assignments i n T a b l e 37 were n o t  c a r r i e d p a s t 650 cm \  A t e n e r g i e s l e s s than 200 cm  \  however, where t h e s p e c t r a o v e r l a p w i t h those o f Wyncke e t al.,^  t h e r e i s disagreement i n t h a t t h e c r y s t a l axes a and  c appear t o have been r e v e r s e d i n t h a t work.  This a s s e r t i o n  i s based n o t o n l y on t h e e x c e l l e n t agreement o f o u r r e s u l t s 94 95 w i t h those o f Colombo and o f Nefedov and F i a l k o v s k a y a where they o v e r l a p , b u t a l s o on t h e i r c o n s i s t e n c y w i t h t h e r e s u l t s o f t h e laser-Raman s t u d i e s . A l s o i n c l u d e d i n T a b l e 37 a r e t h e l i n e s observed i n t h e i n f r a r e d spectrum o f acenaphthene i n benzene a t low energy.  The spectrum i s p r e s e n t e d  as F i g u r e 33.  The  measurements extend o n l y up t o about 580 cm ^ where t h e s o l v e n t began t o absorb s t r o n g l y .  T h i s spectrum was e s p e c i a l l y  u s e f u l i n t h a t i t (a) demonstrates t h a t a l l l i n e s above 150 cm  represented molecular  and n o t l a t t i c e modes and (b) d i s -  t i n g u i s h e s f a c t o r - g r o u p components from n e a r l y degenerate molecular v i b r a t i o n s .  208  F i g u r e on f o l l o w i n g page. F i g u r e 32.  The i n f r a r e d s p e c t r a o f an ac s e c t i o n  o f acenaphthene about 45 m i c r o n s t h i c k . s p e c t r a near 1000 cm 0.25 mm  1  thick crystal.  line //c.  The  are a l s o shown f o r a F u l l l i n e //a, dotted  209  UOISSIUUSUDJ^ %  UOISSIUUSUDJ|_ %  i  A  ( i n  • i  l ^ —  200  k  lUkJi 300  400  w a v e n u m b e r  (cm  500 -  1  )  F i g u r e 33. The l o w - f r e q u e n c y i n f r a r e d spectrum o f acenaphthene i n benzene The peak a t 225 cm * was remeasured u s i n g a d i l u t e s o l u t i o n . -  solution.  211  T a b l e 37.  The low-energy i n f r a r e d spectrum o f a s o l u t i o n o f acenaphthene i n benzene and o f an ac  section  o f an acenaphthene c r y s t a l  Solution  Assignment  //a 54  b  70  b  71  a  88 99  a  b  102  a  167 174 m  190  l l l l l l  B  l  B  l  19 8 225 225 vs  234 252  414 ms  414  415  A  l  460 467  460  B  l  A  l  B  2 l  442 m 471 vw 460 w 500 w 540 m 546 m  pi  540 553 632  538 549  B  A  A  a  l l  See, f o r example, r e f e r e n c e 94 and t h e Raman s p e c t r a i n r e f e r e n c e 100.  212 The s o l u t i o n spectrum c l e a r l y shows t h a t t h e l o w e s t - e n e r g y m o l e c u l a r v i b r a t i o n s a r e a t 174 and 225 cm ^. These a r e a s s o c i a t e d w i t h t h e c r y s t a l , l e v e l s a t 167, 190 and 19 8 cm  1  and a t 225, 234 and 252 c m  - 1  respectively.  The  p o l a r i z a t i o n r a t i o , found by summing the c o n t r i b u t i o n s i n each p o l a r i z a t i o n , f a v o r s a  assignment i n b o t h c a s e s .  The o b s e r v a t i o n t h a t t h e means o f t h e e n e r g i e s o f the c r y s t a l l e v e l s a r e g r e a t e r than t h e s o l u t i o n v a l u e s may be a t t r i b u t e d t o m i x i n g o f c r y s t a l and l a t t i c e s t a t e s , a phenomenon which has a l r e a d y been observed i n the Raman spectrum o f a n t h r a cene-d^Q  (see C h a p t e r I V ) . The n e x t two l i n e s i n the i n f r a r e d spectrum appear  a t 414 and 442 cm ^ i n s o l u t i o n , and a r e a s s i g n e d as A^ and B  m o l e c u l a r fundamentals r e s p e c t i v e l y . The l a t t e r a s s i g n 94 -1 ment was made by Colombo; the l i n e a t 415 cm was n o t 2  i n c l u d e d i n h i s l i s t o f fundamentals a l t h o u g h i t s symmetry assignment i s c l e a r from the ac spectrum; i t i s o b v i o u s l y n e i t h e r an o v e r t o n e nor a c o m b i n a t i o n o f two l o w e r energy fundamentals. The i n t e r p r e t a t i o n o f t h e v a r i o u s s p e c t r a near 460 cm  i s c o m p l i c a t e d . The i n f r a r e d s o l u t i o n spectrum  demonstrates the presence o f two m o l e c u l a r l e v e l s and t h e 94 absence o f any b - p o l a r i z e d a b s o r p t i o n l e v e l s can o n l y have A^ o r B^ symmetry.  shows t h a t t h e s e Using the i n f r a r e d  and Raman"^^ s o l u t i o n .data f o r the lower-energy fundamentals  213  a s i g n i f i c a n t energy mis-match f o r a l l p o s s i b l e c o m b i n a t i o n s i s found so t h a t t h e presence o f two fundamentals i s i n d i cated.  The o v e r a l l  intensity  r a t i o i n the infrared  spectrum c l e a r l y demonstrates t h e presence o f an mental.  crystal funda-  On t h e o t h e r hand, t h e Raman s p e c t r a ^ i n d i c a t e t h e 1  presence o f a  molecular  mode whose b^ c r y s t a l  was seen i n t h a t work a t 469 cm ^.  component  The a^ c r y s t a l  component  of t h i s B^ mode must be a s s o c i a t e d w i t h t h e l i n e observed i n the i n f r a r e d  a t 460 cm  These o b s e r v a t i o n s  with the p r e d i c t i o n s of the oriented-gas  are consistent  model t h a t a B^  mode o f t h e f r e e m o l e c u l e s h o u l d have i t s a^ c r y s t a l compone n t most i n t e n s e i n t h e i n f r a r e d  spectrum and i t s b^ compon-  e n t most i n t e n s e i n t h e Raman spectrum. t h i s B^ m o l e c u l a r  The b^ component o f  mode can a l s o be a c t i v e  i n the infrared  and may be adding t o t h e a - p o l a r i z e d i n t e n s i t y a l r e a d y a s s o c i a t e d w i t h an A^ fundamental. A^ fundamental does n o t e x h i b i t the " o u t - o f - p l a n e " results  a t 46 7 cm  1  That t h e " i n - p l a n e "  factor-group  splitting  while  B^ fundamental does i s c o n s i s t e n t w i t h t h e  observed e a r l i e r f o r n a p h t h a l e n e , anthracene and  pyrene. 9 4 95 The two e a r l i e r s t u d i e s ' have d i f f e r e d  i n the  assignment o f t h e s t r o n g b u t n e a r l y d e p o l a r i z e d band a t 1369 -1 cm  94 . Colombo : a s s i g n e d ;  i t as a B^ fundamental and Nefedov  and F i a l k o v s k a y a ^ as an A^ fundamental.  The Raman s p e c t r a ^  have shown t h a t t h i s l i n e i s c l e a r l y a s s o c i a t e d w i t h an A^  1  214  fundamental  and t h i s  assignment  i s included  summary o f m o l e c u l a r f u n d a m e n t a l s .  Other  i n the later  reversals of  94 Colombo's assignments spectra"*" cm  line  and  and which  0 0  marks  which were c l e a r  are o f importance here  the presence  1 3 5 8 cm ^ i n t e r v a l s  (iii)  the lines  from  o f an A  2  mode,  are associated with  a t 8 0 6 a n d 8 4 2 cm  1  t h e Raman  a r e ( i ) t h e 746 ( i i ) B  2  two d i s t i n c t  molecular will  molecular levels.  fundamentals  b e made  following  the  normal  C.  Calculation  of  B  2  the force  field  of the calculation of  o f acenaphthene  out a normal  c o n s t a n t s must be t r a n s f e r r e d t h e acenaphthene  symmetry  species  almost e x c l u s i v e l y . frequencies two  information  Fundamentals  n o t known, i n o r d e r t o c a r r y  Although  t h e above  of the  vibrations.  Since  force  b u t a r e due  A new a s s i g n m e n t  incorporating a discussion  modes a n d  are notfactor-group 94  c o m p o n e n t s o f t h e same m o l e c u l a r f u n d a m e n t a l to  t h e 765  molecule  involve  planar  i s , of course,  coordinate analysis  from o t h e r molecules. i s not planar,  internal coordinates  Two. c a l c u l a t i o n s  o f the fundamental  i n t h e s e symmetry b l o c k s were c a r r i e d  different  sets  of force  t h e A^ a n d  out,  using  constants f o rthe naphthalene  215  s e c t i o n o f the acenaphthene m o l e c u l e .  C a l c u l a t i o n 1 used  the f o r c e c o n s t a n t s r e f i n e d from the D u i n k e r - M i l l s benzene 32 field i n Chapter V; c a l c u l a t i o n 2 used c o n s t a n t s t r a n s 41 f e r r e d from the Neto, S c r o c c o and C a l i f a n o f i e l d . essentially aliphatic — C H — C H — 2  2  the f o r c e c o n s t a n t s f o r the A and B  2  2  and  fragment o f acenaphthene as w e l l as f o r the A-^  symmetry s p e c i e s were d e r i v e d from a f i e l d used t o  d e s c r i b e the normal modes o f c y c l o p e n t a n e . O n l y c u l a t i o n of the e s s e n t i a l l y o u t - o f - p l a n e A was  c a r r i e d out.  naphthalene  The  2  the  Whiffen.  i n t e r n a l c o o r d i n a t e s were d e f i n e d as i n F i g u r e  In t h i s f i g u r e CC bond s t r e t c h e s ( d e s i g n a t e d by R) ,  CH bond s t r e t c h e s (r) and angle bends ( a )  are shown.  bond t o r s i o n s (<}>) and o u t - o f - p l a n e bends ( y )  The  CC  are not shown  i n F i g u r e 34 but were numbered i n the same way a  cal-  and B-^ f r e q u e n c i e s  s e c t i o n o f the acenaphthene m o l e c u l e was 35  The  one  source o f the f o r c e c o n s t a n t s f o r the  o u t - o f - p l a n e f i e l d o f S c u l l y and  34.  F o r the  as the R and  respectively. The  l i s t which f o l l o w s d e f i n e s the f o r c e c o n s t a n t  m a t r i x by g i v i n g the number o f the f o r c e c o n s t a n t a s s o c i a t e d w i t h each m a t r i x element.  The n u m e r i c a l v a l u e s o f the  s t a n t s are g i v e n i n Table 38.  con-  The CC s t r e t c h i n g f o r c e con-  s t a n t s used f o r the c a l c u l a t i o n c a r r i e d out w i t h the p l a n a r c o n s t a n t s t a k e n from Chapter V ( C a l c . 1) were made t o f i t —xr the c u r v e f = Ae where r i s the bond l e n g t h and x and A  216  F i g u r e 34.  The i n t e r n a l c o o r d i n a t e s o f acenaphthene  217  were d e f i n e d e a r l i e r  (Chapter V ) .  For the c a l c u l a t i o n 41  c a r r i e d o u t w i t h t h e Neto, S c r o c c o and C a l i f a n o  field  ( C a l c . 2) t h e CC s t r e t c h i n g constants' were i n t e r p o l a t e d from a p l o t o f t h e CC f o r c e c o n s t a n t s quoted t h e r e a g a i n s t t h e c o r r e s p o n d i n g bond l e n g t h s .  To reduce t h e o r d e r o f t h e  m a t r i c e s t o be h a n d l e d , t h e a n g l e bending c o o r d i n a t e s o u t 41 s i d e t h e naphthalene r i n g of  and r e - d e f i n e d as i n - p l a n e wags  t h e CH bonds.  Diagonal elements:  R  1/ 2 2  =  R  =  2 ;  R  =  3 ?  r  2 3 = 9; r ^ r ^ = 10; a ^ a ^ = 11; o^o^ = ^2 3  a  10 10  5 ;  R  R  =  6 ;  R  R  R  R  =  8 ;  a  1 9  a  =  a  13 13 a  = 15; a  1 9  '  =21  1  2  3  ;  a  ]  a  2  l l l l a  = a  1  *3*3  =  *4*4  =  R  =  R  9 10 R  =  R  4 11 R  2 10 4 10 26; R R = R R R  =  R  X  R R 2  9  R  R  =  4  2  =  2  3  = R R  12 13  a  a  2 5  14 14 a  =  16 16  a  a  =  =  1  4  2 2  r  a  ;  r  4 4 a  =  1  =  17 17  a  a  = ^  = 16; 0 ^  4 ;  2 ?  =  = 17; 6363 =  ^lO^lO  =  *11*11  =  =  2  0  *12*12  ;  =  '  O f f - d i a g o n a l elements: 4 5  2 5  =  =  =  x  *2*2  =  MM  R  r  R  _ Y Y _ Y Y _ Y Y. _ Y Y _Y Y _ iq. 2 2 3 3 4 4 11 11 14 14 *'  1 1  Ml  =  4 4  R  l l  r  a  IP. Y-Y  R  7 ;  r  a  R  =  13 13  3 3  R  10 10  =  12 12  R  R  R  11 11  i i  R  3 1 ;  4  =  ;  1()  2  a  l 10 R  ^ 2 R  10 11 R  =  1 9 3 5 = 27; R ^  R  = R R  5  R  R  =  R  1 X  a  =  R  R  23  =  =  R  2 3 R  R  =  a  R  R  3 4 R  =  =  R  2 4  R  R  1 10 R  =  '  2 2  =  1 1 1 3 1 1 "' 4 9 = R R = 28; R ^ g = R R R  R  =  3  10 10 R  R  '* 1 3  =  a  R  R  =  25  R  R  =  g  = 29; R ^ g =  4 4  =  - R  3  2 g = R  13 4 R  =  a  R  R 2  10 ll R  =  " x =30; R R = R  7  g  R  7  =  9  12  218  a  13 ll  a  3 3  R  R  =  =  a  3 2 ;  2 2 R  ll 10  a  =  R  a  3 2 R  =  =  3 3 ;  3 5 ;  a  14 4 R  16 l  a  R  =  3 4 = " 1 2 " 2 2 " 3 3 a R = 38; a ^ R ^ = a R 6  R  B  1 9  R  =  6  4  =  1 3  a  y Y  =  a i  a  = a  1 ( J  a  a  3  ?  = 46;  l Y l l  1 4 Y  =  Y  2 14 Y  49; <J, -cf Y 3  a  2 l r  ~ l l a  3  R  lYl  R  =  a  3 2 r  a  =  8  a  =  Y l  =  3 11 Y  Y  Y l  =  =  3 3 6  a  4  4 3 r  =  5 3 ;  " 13 3  =  a  - 3 10 6  3  = "* Y  l o Y l  R  e  =  5 6  '  a  =  l l  a  R  18 10 R  =  3 7  1 2  a  R  2  a  2  =  a  2 l  3  1 1  =  3  2 3  R  =  a  R  = Y Y  4  2  R  =  3  4  = * 2  9 10  =  a  l2 4 R  =  1  3  Y  0  1 0  3  R  =  4 3 ;  4  4  =-Y Y 3  1 4  = 41;  1 2  l 2 = Y r  5 4 ;  =  2 2  B  3 1  3  R  =  =  a  Y  = -* Y 2:  e  =  - 1 11 R  =  1 4  =  = 47;  U  ^ V l O  3 i B  1 1  4  2  a  =  = Y T  14  = -*iY  n  r  -Ms  =  a  =  4  = - 0 ^ 2 = 51; 6 ^  1 4 = 2 10 R  3  = a  1 4  *3*4  =  =  19 12 = a a =a a  a  n  =  R  2  3  = 50; B 3  B  =  a  3  M 3  =  4  5 5 ;  R  4  a  = * Y  R  4 3  19 21 19 25 = Y Y = Y Y = Y Y  4 2 ;  *1*2  1 4  3 6 ;  a  = a a  2  3  =  ' 17 12 = 39;  =  = Y Y  1 4  4 8 ;  2  a  3 4 ;  = 40;  1 3  a  2  = -*  =  Y  a  ~ 21 25 = 45; Y  =  Y l Y 3  =  1 ( J  = <f> Y = * Y  4  - 2 11 B  3  2 5  21 22 25 26 r r = 44; r r 2  =  1 3  a a a  R  =  3  :  = = 52;.  219  Table 38.  Number  F o r c e c o n s t a n t s f o r acenaphthene  Value* Calc. 1 Calc. 2  1  7.814  2  Number  calculation  Value* Calc. 1 Calc. 2  24  -0.609  -0.316  6.266  6.85 5.86  25  -0.030  3  8.518  7.20  26  0.030  -0.176 0.158  4  6 .477  6.00  27  5 6 7  7.000  6.25  -0.160  7.040  6.43  28 29  0.295 -0.030 0.030  0.156  4.560 4.239 5.061  4.66 4.43  0.030  0.000  8 9 10 11 12 13 14 15 16 17 18 19  5.05 4 .56  0.711 1.103 0.711 0.814  0.934 0.934 0.619 0.920 0 .833 0 .666 1.00 1.02  1.020 1.020  20  0 .317 0 .057  21  0 .029  22 23  30 31 32 33 34 35 36 37 38 39 40 41 42 43 44  0.342  0. 064 0.602  0.397  0.351 0.000 0.602  0.397 0.397 0.279 0.174  0.000 0.315  0.174 0. 351 0. 263  -0.097 0.000  -0.045 0.111  -0. 016 -0. 124 0.020 0.068  0.650  0.750  45  0. 016  0.030  0.457  46  0. 013  220  Table 38.  Number  (Continued)  Value* Calc. 1 Calc. 2  Number  Value* Calc. 1 Calc. 2  47  -0.024  52  0.015  0.000  48  -0.019  53  -0.014  0.000  49  -0.019  54  -0.323  0.000  50  -0.021  55  -0.063  0.000  56  -0.027  0.000  51  0.028  0.000  The s o u r c e s from which t h e two s e t s o f f o r c e c o n s t a n t s were d e r i v e d a r e d e s c r i b e d i n t h e t e x t . The u n i t s t h r o u g h o u t are mdyn/A f o r s t r e t c h i n g c o n s t a n t s mdyn/radian f o r s t r e t c h bend i n t e r a c t i o n s and mdyn A / r a d i a n f o r bending constants. 6  2  221  D.  Assignment  1.  A j Species In the i n f r a r e d  spectrum t h e s t r o n g l i n e s a p p e a r i n g  a t 415, 467, 551, 632, 1170, 1251, 1418, 1446, 1500 and 1602 cm  were a s s i g n e d as f u n d a m e n t a l s . S t r o n g i n f r a r e d 94 -1 l i n e s have been r e p o r t e d a t 2838, 2925 and 3055 cm , t h e 1  l a t t e r h a v i n g t h e appearance o f a near degeneracy. Raman e x p e r i m e n t s and 1369 cm  1  1 0 0  The  have added 806, 1001, 1042, 1172, 1221  intervals to this l i s t of t o t a l l y  symmetric 94  modes and t h e r e m a i n i n g A^ fundamental has been l o c a t e d at 1593 cm \  an assignment which i s i n agreement w i t h t h e  r e s u l t s of the c a l c u l a t i o n s ,  b o t h o f which p r e d i c t two h i g h  energy r i n g modes. 2.  B i Species The s t r o n g l i n e s a t 186, 234, 463, 539, 743, 775,  835 and 890 cm  1  i n the i n f r a r e d  B^ fundamentals.  spectrum must c o r r e s p o n d t o  The v a l u e s quoted here a r e t h e means o f  f a c t o r - g r o u p components;  f o r example, 463 cm  1  i s t h e mean  of t h e a^ and b^ components observed i n t h e i n f r a r e d a t 460 cm  1  and a second b^ component seen a t 469 cm  Raman s p e c t r u m . 900 cm  1 0 0  The f o u r i n t e n s e l i n e s between  spectrum 1  i n the  700 and  a r e n o t f a c t o r - g r o u p components s i n c e t h e y a l l 94 appear i n t h e s o l u t i o n spectrum. The two r e m a i n i n g funda1  222 mentals may be r e p r e s e n t e d by t h e weaker c - p o l a r i z e d a t 903 and 935 era \  lines  I f t h e s e l a t t e r assignments a r e  c o r r e c t then t h e f o r c e f i e l d on which t h e c a l c u l a t i o n o f these e s s e n t i a l l y o u t - o f - p l a n e fundamentals was based must be d e f i c i e n t , s i n c e t h e c a l c u l a t e d v a l u e s a r e n e a r l y 200 cm higher.  3.  B  2  Species 94 95 The b - p o l a r i z e d i n f r a r e d spectrum  '  indicates  t h a t t h e l i n e s a t 446, 500, 647, 1015, 1093, 1209, 1275, 1429, 1500, 1618, 2920, 3038 and 3068 cm" characteristics.  Additional B  2  1  have B  fundamentals  2  symmetry  identified ^ 1  from t h e Raman spectrum o c c u r a t 765, 1097, 1153, 1358 and 1474 cm  The one remaining, fundamental i s p r e d i c t e d by  C a l c u l a t i o n 1 t o l i e j u s t above 500 cm 2 t o l i e j u s t below 500 cm  and by C a l c u l a t i o n  1  (see T a b l e 39) b u t cannot be  1  l o c a t e d i n e i t h e r t h e i n f r a r e d o r R a m a n ^ spectrum. 1  The assignments a r e summarized  i n T a b l e s 39 and 40  along with the r e s u l t s of the force constant c a l c u l a t i o n s . In t h e column headed ' C a l c . l  1  are the f r e q u e n c i e s c a l c u l a t e d  by u s i n g f o r t h e naphthalene s e c t i o n o f t h e acenaphthene m o l e c u l e t h o s e f o r c e c o n s t a n t s r e f i n e d from t h e D u i n k e r and 32 M i l l s benzene f i e l d (see T a b l e 2 8 ) . I n t h e column headed ' C a l c . 2' t h e f o r c e c o n s t a n t s f o r t h a t p a r t o f t h e m o l e c u l e 41 were t a k e n from t h e Neto, S c r o c c o and C a l i f a n o f i e l d .  1  T a b l e 39.  The A, and B„ fundamentals o f acenaphthene A, symmetry  B  2  symmetry  94 Calc. 1  Calc. 2  Experiment  Colombo  Calc. 1  Calc. 2  Experiment  Colombo  430 513 586  439 496 592  459 465 552  436 501 521  432 479  446 500  446 500  631  643 762  415 467 551 632  630  680  498 646  647  851  796  765  1046  1047 1114  1015 1093  1189  1153 1209 1275  818 1003 1014 1092 1210 1266 1364 1466 1506 1543 1656 1690 2911 3041 3054 3065 a c  1000  806 1001  1019 1083  1042  1000 1042  1170  1145  1178 1217  1209 1237  1221 1251  1176 1254  1293 1330  1234  1349 1420  1369 1426 1450 1500  1310 1416  1390 1473  1435 1502  1529 1625  1598 1605 2838 2925 3015 3050  1705 2903 3040 3054 3064  1360 1441 1533 1600 1673 2900 3019 3048 3079  1449 1533 1649 1659 2909 3020 3049 3080  1593 1605 2838 2926 3055 3061  a  a  T h i s v a l u e i s t h e mean o f t h e o b s e r v e d f a c t o r - g r o u p T a k e n from Nefedov and F i a l k o v s k a y a . 9 5  1288  components.  1358 1429 1474 1500 1618 2920 3018 3038 3068 b  b  647 1015 1093 1150  b  b  c  b  c  b  b  1209 1275 1442 1500 1595 1770 1792 2840 2920 3038 3068  T a k e n from Colombo.  224 T a b l e 40.  The A  2  and  2 symmetry C a l c u l a t e d Experiment  fundamentals o f acenaphthene  A  176 271 460  173 252  635 . 819  617 746  999 1048 1055 1226 2877  94 Colombo  615 760  872 1352 1938?  l symmetry 94 C a l c u l a t e d Experiment Colombo B  179 229 478  186 234 463  536 731  539 743  816 910 1018 1087  775 835 890  1159 2870  a  a  a  a  a  745 784 835 940 1365 1445  2943  T h i s v a l u e i s the mean o f t h e o b s e r v e d f a c t o r - g r o u p components.  2940  225  4.  A_2 S p e c i e s The A  fundamentals a r e i n a c t i v e i n t h e i n f r a r e d  2  spectrum o f t h e f r e e m o l e c u l e and t h e assignments g i v e n i n Table 40 a r e c a r r i e d o v e r d i r e c t l y from the Raman r e s u l t s .  E.  Discussion Comparison o f t h e observed and c a l c u l a t e d f r e q u e n -  c i e s i n T a b l e s 39 and 40 i n d i c a t e s t h a t t h e s y n t h e s i s o f a f o r c e f i e l d f o r acenaphthene  from t h e f o r c e c o n s t a n t s o f  naphthalene and o f c y c l o p e n t a n e has been r e a s o n a b l y s u c c e s s ful.  I t s h o u l d n o t be f o r g o t t e n , however, t h a t some r e l i a n c e  was p l a c e d on t h e r e s u l t s o f t h e c a l c u l a t i o n s i n making t h e assignment o f 1593 as t h e second  r i n g mode and, perhaps  more i m p o r t a n t , t h e assignment o f a f i n a l B  2  mode near 500  cm . 1  The two c a l c u l a t i o n s c a r r i e d o u t f o r t h e A^ and B s p e c i e s show t h a t w h i l e t h e f i e l d r e f i n e d f o r benzene, naphthalene and anthracene i n Chapter V was s l i g h t l y more s u c c e s s f u l f o r the low f r e q u e n c i e s , t h e Neto, S c r o c c o and 41 Califano f i e l d For  t h e B^ and A  was b e t t e r a b l e t o f i t t h e r i n g modes. 2  v i b r a t i o n s a comparison w i t h t h e observed  frequencies i s l e s s h e l p f u l , since the experimental a s s i g n -  2  226  ments are n o t complete.  I t appears, however, t h a t the c a l -  c u l a t i o n has p l a c e d t h e h i g h e r - e n e r g y modes t o o h i g h , perhaps i n d i c a t i n g t h a t the o u t - o f - p l a n e bending f o r c e c o n s t a n t s used were t o o l a r g e . In g e n e r a l , however, t h e r e s u l t s o f the f o r c e cons t a n t c a l c u l a t i o n s were r e a s o n a b l y e n c o u r a g i n g . of  The t r a n s f e r  f o r c e c o n s t a n t s between s i m i l a r m o l e c u l e s o r even s i m i l a r  s e c t i o n s o f m o l e c u l e s seems t o be j u s t i f i e d , a t l e a s t f o r the  purposes o f u s i n g the c a l c u l a t e d f r e q u e n c i e s as a g u i d e  to l o c a t e t h e m o l e c u l a r fundamentals.  CHAPTER V I I I CONCLUSION  The s p e c t r o s c o p y o f a r o m a t i c m o l e c u l e s and t h e study o f t h e f o r c e f i e l d s o f t h e s e m o l e c u l e s a r e areas o f r a p i d l y growing i n t e r e s t .  With t h e a i d o f new s p e c t r o -  meters and w i t h t e c h n i q u e s d e s i g n e d t o produce t h e maximum amount o f p o l a r i z a t i o n i n f o r m a t i o n from t h e Raman and i n f r a red  s p e c t r a o f m o l e c u l a r c r y s t a l s i t has been p o s s i b l e t o  r e - e v a l u a t e e x i s t i n g assignments o f t h e fundamental  vibra-  t i o n s o f t h e two s i m p l e s t p o l y a c e n e s , naphthalene and anthracene.  While the e x t r a p o l a r i z a t i o n i n f o r m a t i o n obtained  from s i n g l e c r y s t a l f a c e s which a r e l e s s e a s i l y o b t a i n e d and t h e r e f o r e n o t n o r m a l l y s t u d i e d c o n f i r m e d t h e l o c a t i o n o f many h i g h e r - f r e q u e n c y fundamentals, s e v e r a l misassignments a l s o noted.  I n a d d i t i o n , many l o w - f r e q u e n c y  were  fundamentals  were l o c a t e d as p o l a r i z e d f a r - i n f r a r e d s p e c t r a o f n a p h t h a l e n e dg, a n t h r a c e n e - h . ^ and anthracene-d^Q were o b t a i n e d f o r t h e f i r s t time.  A l s o s t u d i e d f o r t h e f i r s t time were t h e l a s e r -  e x c i t e d p o l a r i z e d Raman s p e c t r a o f naphthalene-dg and anthracene-d.^. When t h e e x p e r i m e n t a l assignments were as complete as p o s s i b l e , a t t e n t i o n was d i r e c t e d to t h e f o r c e f i e l d s . 227  The  228 o u t - o f - p l a n e f i e l d o f benzene was c o m p l e t e l y r e c o n s i d e r e d , and w h i l e t r a n s f e r o f f o r c e c o n s t a n t s t o naphthalene showed 30 t h a t t h e b a s i c assumption made by W h i f f e n  that a l l i n t e r -  a c t i o n c o n s t a n t s s h o u l d be as s m a l l as p o s s i b l e was comp l e t e l y s u p p o r t e d , i t was a l s o found t h a t minor changes i n the  benzene f i e l d c o u l d s l i g h t l y improve t h e f i t t o t h e  observed f r e q u e n c i e s o f n a p h t h a l e n e . are  Whether t h e s e changes  m e a n i n g f u l o r n o t cannot be d e t e r m i n e d s o l e l y from t h e  o b s e r v e d f r e q u e n c i e s , s i n c e t h e improvement i s s m a l l ; a more s e n s i t i v e t e s t might be t h e form o f t h e normal modes p r e d i c t e d by each benzene f i e l d , b u t u n t i l some way o f r e l a t i n g t h e motion o f t h e atoms t o some p h y s i c a l o b s e r v a b l e i s developed for  (e.g. a r e l i a b l e method o f c a l c u l a t i n g  each normal mode), any r e a l d i s t i n c t i o n between t h e o u t -  o f - p l a n e f i e l d s remains i m p o s s i b l e . of  intensities  Such a r e l i a b l e method  c a l c u l a t i n g i n t e n s i t i e s would a l s o be v e r y h e l p f u l i n  l o c a t i n g t h e o u t - o f - p l a n e fundamentals o f a n t h r a c e n e , where one l a r g e d i s c r e p a n c y e x i s t s  ( f o r t h e second-lowest B^  v i b r a t i o n ) between t h e o b s e r v e d and c a l c u l a t e d the  p o s s i b i l i t y t h a t t h e 166 cm  1  line  u  frequencies;  (anthracene-h^^ v a l u e )  a r i s e s from l a t t i c e e f f e c t s and t h a t t h e second l o w e s t B ^ fundamental i s weak and absent from t h e i n f r a r e d  u  spectrum  c o u l d be t e s t e d more f u l l y . An i n - p l a n e f o r c e f i e l d d e v e l o p e d by D u i n k e r and 32 Mills  f o r benzene was t r a n s f e r r e d t o naphthalene and  229 anthracene  and r e f i n e d t o f i t s i m u l t a n e o u s l y t h e observed  f r e q u e n c i e s o f a l l t h r e e m o l e c u l e s and t h e i r t h r e e p e r d e u t e r a t e d analogues.  The r e s u l t s were compared w i t h those o f a  s i m i l a r c a l c u l a t i o n c a r r i e d o u t by Neto, S c r o c c o and C a l i f a n o 41 (NSC).  A l t h o u g h t h e l a t t e r f i e l d gave a s l i g h t l y b e t t e r  f i t t o t h e observed f r e q u e n c i e s (the average e r r o r i n t h i s work was about 14.8 cm ; t h e NSC r e s u l t s were about 1 cm 1  1  b e t t e r ) t h i s i s perhaps n o t s u r p r i s i n g i n view o f t h e l a r g e r number o f f o r c e c o n s t a n t s r e f i n e d i n t h e NSC c a l c u l a t i o n (34 c o n s t a n t s compared w i t h 21 c o n s t a n t s f o r t h e f i e l d cribed i n this  des-  thesis).  The p l a n a r f o r c e f i e l d p r e s e n t e d i n t h i s t h e s i s has at  l e a s t two p o i n t s t o recommend i t .  First,  t h e f o r c e con-  s t a n t s r e f i n e d t o f i t a l l s i x m o l e c u l e s a r e remarkably c l o s e to  t h e o r i g i n a l benzene c o n s t a n t s proposed  by D u i n k e r and  Mills.  I n p a r t i c u l a r , t h e carbon-carbon s t r e t c h i n g c o n s t a n t o was r e f i n e d t o 7.040-mdyn/A, a v a l u e v e r y near t h e o r i g i n a l o D u i n k e r - M i l l s v a l u e and a l s o much c l o s e r t o t h e 7.43 mdyn/A 87 expected  f o r a normal a r o m a t i c bond l e n g t h than t h e v a l u e o 41 of 6.43 mdyn/A found by Neto e t a l . A second advantage o f t h e g e n e r a l f i e l d d e s c r i b e d here i s that i t c o n t a i n s no f o r c e c o n s t a n t s which a r e unique 41 to one molecule..  The NSC f o r c e f i e l d  c o n t a i n s e i g h t such  c o n s t a n t s and we f e e l t h i s i s dangerous because o f t h e p o s s i b i l i t y t h a t such c o n s t a n t s w i l l be r e f i n e d t o v a l u e s f a r removed from p h y s i c a l r e a l i t y i n o r d e r t o compensate f o r  230 other d e f i c i e n c i e s i n the f i e l d . The r e s u l t s o f t h e normal c o o r d i n a t e a n a l y s i s c a r r i e d o u t i n t h e c o u r s e o f t h i s work gave a d d i t i o n a l supp o r t t o many assignments which were made i n t h e e a r l i e r work 41 (NSC  ) on t h e b a s i s o f c a l c u l a t i o n s , b u t which we f e l t were  not e x p e r i m e n t a l l y c e r t a i n .  However, s e v e r a l assignments  made i n t h a t work, p a r t i c u l a r l y i n t h e i n - p l a n e B of  2 u  species  a n t h r a c e n e , were n o t s u p p o r t e d ( i n f a c t a new assignment  was suggested by o u r c a l c u l a t i o n s ) and we f e e l t h a t a t t h i s time no f i r m c o n c l u s i o n s about such assignments s h o u l d be made. As f o r t h e o u t - o f - p l a n e f r e q u e n c i e s , a r e l i a b l e method o f c a l c u l a t i n g t h e i n t e n s i t y o f v i b r a t i o n s would be e x t r e m e l y valuable. In o r d e r t o f i n d o u t how w e l l f o r c e f i e l d s developed f o r benzene, naphthalene and anthracene would t r a n s f e r t o r e l a t e d b u t l e s s s i m i l a r m o l e c u l e s , t h e v i b r a t i o n s o f pyrene and acenaphthene were c o n s i d e r e d . The i n f r a r e d s p e c t r a o f these m o l e c u l e s were measured ( w i t h emphasis on t h e p r e v i o u s l y u n s t u d i e d low-energy r e g i o n ) and, by u s i n g Raman d a t a o b t a i n e d by o t h e r s i n t h i s l a b o r a t o r y of  9 1  '  1 0 0  f a i r l y complete assignments  t h e normal v i b r a t i o n s were p o s s i b l e .  C a l c u l a t i o n of the  m o l e c u l a r fundamentals w i t h p l a n a r f o r c e c o n s t a n t s from t h e two f i e l d s mentioned e a r l i e r and o u t - o f - p l a n e c o n s t a n t s o r i g i n a t i n g i n t h e benzene f i e l d  (Chapter V and r e f e r e n c e 30)  showed t h a t i t was i n d e e d p o s s i b l e t o t r a n s f e r t h e f o r c e c o n -  231  stants  quite  successfully  to these  relatively  dissimilar  molecules. Although  the  planar  field  derived  from  the  Duinker-  32 Mills the  benzene  field  lower-energy  was  slightly  fundamentals  more  (below  successful  about  1000  in  fitting  cm  of  41 pyrene  and  better  at  those  acenaphthene, fitting  of  the  t h e NSC  field  was  higher-energy ring  significantly  modes,  particularly  symmetry. 34 Freeman  tion  of  similar the  the to  stant  that  to  one  of  argument w i l l  the  of  be  towards  be  shows  while  v a l e n c e , the  B2  expected that U  such  vibrations  f o r pyrene  the  send  a  of  the  the  vibration;  detailed that  Kekule since the  to  this  abnormally  low.  force of  con-  molecule  their  i t s three  resistance  with  force  compatible with  t o be a  problem  i t is basically  ring  2 u  of  Although  two  are p a r t i c u l a r l y  important f o r the  acenaphthene,  a B  a  attributed  field,  structures.  calcula-  calculations  have  presented here,  ordinary  argument  They  in their  naphthalene  i n the  in their  i t i s undergoing  of  us  of  deformations which  distorts  deformation might  similar  field.  absence,  n o t be  Kekule' s t r u c t u r e s quirements  type  the  reported  fundamentals  i t s Kekule  when n a p h t h a l e n e structures,  have  e n c o u n t e r e d by  controlling  toward  Ross  planar  Duinker-Mills  difficulty  and  Kekule  retype  constant should  anthracene  the  A also  and  structures  cannot  232 f  be r e a d i l y i d e n t i f i e d w i t h one p a r t i c u l a r p l a n a r symmetry class. 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E l e k t r o c h e m . 65_, 138 (1961); A. Bree and V.V.B. V i l k o s , J . Chem. Phys. 40, 3125 (1964).  239 94.  L. Colombo, J . Chem. Phys. 3_9, 1942 (1963).  95.  O.V. Nefedov and O.V. F i a l k o v s k a y a , Opt. S p e k t r o s k . 2 0 , 1016  (1966) [Opt. S p e c t r o s c . 20, 445 ( 1 9 6 6 ) ] .  96.  H. L u t h e r and C. R e i c h e l , Z. P h y s i k . Chem. 195, 103 (1960)  97.  J . P . M a t h i e u , M. E c o l l a n and J.F. E c o l l a n , J . Chim. Phys. 5_0, 250 (1954) .  98.  L. P e s t e i l , J . Chim. Phys. 58, 204 (1961).  99.  V . I . M i k h a i l e n k o and P.A. T e p l y a k o v , 48  Opt. S p e k t r o s k . 22,  (1967) [Opt. S p e c t r o s c . 22, 24 (1967)].  100.  A. B r e e , R.A. Kydd and T.N. M i s r a , t o be p u b l i s h e d .  101.  F.H. Kruse and D.W.  S c o t t , J . M o l . S p e c t r y . 20, 276 (1966)  A P P E N D I X  241 A.  D e f i n i t i o n of O u t - o f - P l a n e  1.  Out-of-plane  wag  Internal  Coordinates  (Y) a t atom 1  a  F i g u r e 25. The arrangement of atoms used t o d e f i n e an o u t - o f - p l a n e wag. The p o s i t i v e d i r e c t i o n of the x - a x i s i s up out of the p l a n e of the paper. The  out-of-plane  deformation  a t atom 1 i s d e f i n e d  as y  ±  =  (X  2  - X )/a ±  +  (X  3  - X )/b  + (X  ±  where a, b and c are the bond l e n g t h s and the X's pendicular displacements  F i g u r e 36. The a torsion. The  4  -  are the  X-^/c per-  o f the atoms.  arrangement of atoms used t o d e f i n e  t w i s t i n g of the bond between atoms 1 and 2 i s  d e s c r i b e d by the c o o r d i n a t e <J> which i s d e f i n e d  as  <f>  = lr2  k  7 3  { ( x  i  - 4 / x  )  a  ~ < i ~ x  x  ) / - < b  3  B.  C a l c u l a t i o n of the O u t - o f - P l a n e  1.  Out-of-plane  x  " 5 / x  2  )  d  +  (X  2  Force Constants  ~  x  6  )  /  e  }  of Benzene  I n t e r n a l C o o r d i n a t e s o f Benzene  8  11  4  F i g u r e 37. The o u t - o f - p l a n e i n t e r n a l c o o r d i n a t e s o f benzene  The o u t - o f - p l a n e i n t e r n a l c o o r d i n a t e s o f benzene are shown i n F i g u r e 37.  The numbers a t the.atom p o s i t i o n s r e p r e -  s e n t o u t - o f - p l a n e wags and the numbers c e n t e r e d i n the carbon-carbon 2.  bonds r e p r e s e n t t o r s i o n s about those bonds.  Method o f C a l c u l a t i n g the Elements o f F from G and  the  Frequencies From e q u a t i o n s 13 and 17 of Chapter V, t h a t i s 2 V  =  R  fc  F R  V.13  243  and  2 T =  R  cf  fc  R  1  V.17  and from t h e t r a n s f o r m a t i o n from i n t e r n a l c o o r d i n a t e s t o normal c o o r d i n a t e s , R = A Q we g e t  2  and  v  =  1  Q ^Z t  2 T = Q  fc  A  1  .Q  A  G  _ 1  2  A Q  3  From t h e above two e q u a t i o n s and from e q u a t i o n s 11 and 12 o f Chapter V, 2 T =  Q  t  Q  2 V =  Q  fc  A Q  t i t i s e a s i l y seen t h a t  A  and  A  V.12  -1  G fc  V . l l  A = E  F A =  4  A .  5  where A i s t h e d i a g o n a l m a t r i x o f t h e e i g e n v a l u e s o f t h e GF secular equation.  Using the p r o p e r t i e s o f matrices t h a t  T r ( B C) = T r ( C B) and t h a t Det(B C)= Det (C B ) , where Tr(B) means t h e t r a c e o f t h e m a t r i x B, and Det(B) means t h e d e t e r m i n a n t o f B, we g e t , from e q u a t i o n s 4 and 5, Tr(A  - 1  G F A)  =  T r ( G F)  =  Tr(A)  and a l s o , Det(A  - 1  G F A) =  Det(G F) = Det(A)  6  244 which are the e q u a t i o n s used i n t h i s t h e s i s t o f i n d  the  elements o f the o u t - o f - p l a n e f o r c e c o n s t a n t m a t r i x , F, f o r benzene.  The elements o f G are r e a d i l y c a l c u l a t e d from the  m o l e c u l a r geometry, by the method o u t l i n e d i n r e f . 29,  and  the r e l a t i o n s h i p between the fundamental f r e q u e n c i e s , v , i n wave numbers, and the elements,  A, o f the d i a g o n a l m a t r i x A  is: \  3.  Out-of-plane  =  4TT2  V C 2  2  Symmetry C o o r d i n a t e s and  Fundamental  F r e q u e n c i e s o f Benzene . Symmetry c o o r d i n a t e s are l i n e a r combinations  o f the  i n t e r n a l c o o r d i n a t e s chosen so as t o t r a n s f o r m l i k e the i r r e d u c i b l e r e p r e s e n t a t i o n s o f the p o i n t group o f the  molecule.  The symmetry c o o r d i n a t e s are d e f i n e d i n Table 41, which a l s o 5 c o n t a i n s the f r e q u e n c i e s  a s s o c i a t e d w i t h each o u t - o f - p l a n e  symmetry s p e c i e s o f benzene.  Table 41. The o u t - o f - p l a n e symmetry c o o r d i n a t e s o f benzene  Symmetry coordinate  Internal , coordinates  Symmetry type A2u  1  1+2+3+4+5+6  2  1-2+3-4+5-6  3  7-8+9-10+11-12  £ 5  S  \  7-9+10-12  E  6  -2+3-5+6  7  -7+2(8)-9-10+2(11)-12  9  C  6 6 H  C  6 6 D  Values o f Aa C  6 6 H  C  6 6 D  673  496  0.2668  0.1449  990  829  0.5774  0.4048  707  599  0.2944  0.2114  967  787  0.5509  0.3648  398  345  0.0933  0.0701  846  600  0.4216  0 .2566  ' -2 (D+2+3-2 (4)+5+6 L  8  ^  (cm-1 )  Frequencies  2u  >  J  >  1-3-4+6 -1-2(2)-3+4+2(5)+6  >  10  7+8-10-11  11  7-8-2 (9)-10+11+2(12)  5  J  A i s defined i n the text the l i n e a r combinations  a r e t o be m u l t i p l i e d by a n o r m a l i z i n g f a c t o r .  to cn  246 and F- M a t r i c e s f o r t h e O u t - o f - p l a n e Benzene Problem a)  —2u  block.  C  6 6 H  C  0.4933  0.9150  G  6°6  F  a  b) B, b l o c k , -ig 6 6  2.0381  1.5786  6 6 1.6164  1.5786  4.6173  0.6407  C  H  C  c) E_ —2u b l o c k ,  G  'x  y  0  °1  y  z  0  0  0  0  X  y  ,o  0  y  z  .  f o r CgHg x = 1. 6293 , y = - l . 7940, D  6  x = 1.2075, y = -0. 9505, z = 1 0  e  °1  0  0  0  a  foF 0  0  D  0.6407 2.3680  247 d) —El q  block.  n  0  z  o  0  X  0  z  z  0  y  0  0  z  0  'x  G  =  where, f o r C H g  6  v  x = 1.0678, 6 = 1.4237, z = 1.2329 and f o r  C D, x = 0.6460, y = 0.8613 z = 0.7459.  The symmetry c o -  r  ordinates S  R  and S g form a degenerate p a i r , as do symmetry  c o o r d i n a t e s S-^Q and S ^ , and t h e two c o o r d i n a t e s i n each p a i r have been chosen t o be o r t h o g o n a l . p a i r s o f symmetry c o o r d i n a t e s S ,  In a d d i t i o n , the  and S  R  P  , S^g have  been chosen so t h a t t h e sum o f t h e F - m a t r i x e l e m e n t s , f^^•, c o n n e c t i n g them i s z e r o . f  10,10 =  f  ll,ll'  f  8,10  F  =  f  I t can be shown t h a t f g g = f ^ , Q  9,ll  *  T  h  S  t h e  F  0  8,8  =  u  0  0  :  8,10  i s  0  0  0 :  m a t r i x  8,10  f8,8 8,10  ~  f8,10  10,10 0  0 f10,10j  The redundancy r e l a t i o n s i n t h i s b l o c k a r e : S  10 ~  k S  8  =  0  a n d  S  l l  kSg = 0  where k = J3  The F - m a t r i x can t h e n be s i m p l i f i e d by making t h e s u b s t i t u tions S  1 Q  =  kSg  and  S.^ = k S  q  248 to give • F  =  /  2 f  8,8  +  2 k f  8,10  +  k  f  10,10  0 The  f  8,8  +  2 k f  8,10  +  k  f  2 10,10  rows c o r r e s p o n d i n g t o symmetry c o o r d i n a t e s S ^ Q  and S ^ ^ can t h e n be o m i t t e d from the G - m a t r i x , 29 d e s c r i b e d by W i l s o n , Decius and Cross  i n the manner  (page 140 e t seq.)  to  give G  0  = v.  where the v a l u e s o f x are g i v e n above. 2 sum  f  g + k f g io 2  g  +  k  f  F  10  10  l s  c a  H ^ $i e  F o r convenience  the  so we have  0  = 0  The u n i t s f o r the o u t - o f - p l a n e f o r c e c o n s t a n t s are mdyn A/radian'  1  

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