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An infrared study of small molecules in inert matrices Shurvell, Herbert F. 1964

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AN INFRARED STUDY OF SMALL MOLECULES IN INERT MATRICES by HERBERT F! SHURVELL -  B.Sc. Exeter, 1959, M.Sc. B r i t i s h Columbia, 1962.  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Chemistry  We accept t h i s t h e s i s as conforming t o the required standard  THE UNIVERSITY OF BRITISH COLUMBIA January, 1964.  In presenting this thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall, make i t available for reference and study.  freely  I further agree that per-  mission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives.  It is understood that copying or publi-  cation of this thesis for financial gain shall not be allowed without my written permission.  Department of The University of B r i t i s h Columbia, Vancouver 8, Canada. Date  The U n i v e r s i t y o f B r i t i s h  Columbia  FACULTY OF GRADUATE STUDIES  PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  of  HERBERT FRANCIS SHURVELL  B.Sc, M.Sc,  E x e t e r U n i v e r s i t y , 1959  The U n i v e r s i t y o f B r i t i s h Columbia, 1962  FRIDAY, MARCH 13, 1964, AT 2:30 P.M. IN ROOM 261, CHEMISTRY BUILDING  COMMITTEE IN CHARGE Chairman: F.H. Soward W.A. Bryce F.W. Dalby K.B. Harvey External  E.A. O g r y z l o C. R e i d R.F. S n i d e r  Examiner: D.F. Eggers J r .  University  o f Washington  AN INFRARED STUDY OF SMALL MOLECULES IN INERT MATRICES ABSTRACT  I n f r a r e d a b s o r p t i o n s p e c t r a o f HC1 and HBr, suspended i n s o l i d argon, k r y p t o n and n i t r o g e n , were r e c o r d e d i n order t o o b t a i n i n f o r m a t i o n on i n t e r m o l e c u l a r f o r c e s . SO2 i n argon and n i t r o g e n , and CO i n argon were a l s o s t u d i e d . The s p e c t r a were observed i n the temperature range from l i q u i d h e l i u m temperatures up t o the m e l t i n g p o i n t o f the m a t r i x . The halogen a c i d s gave more c o m p l i c a t e d s p e c t r a i n the noble gas m a t r i c e s than i n n i t r o g e n . T h i s has been c o r r e l a t e d w i t h the d i f f e r e n t thermal p r o p e r t i e s o f the matrix materials. M a t r i x t o s o l u t e r a t i o s from 100 t o 800 t o 1 were used and e v i d e n c e was found f o r s o l u t e s o l u t e i n t e r a c t i o n s , a r i s i n g from incomplete i s o l a t i o n of s o l u t e molecules a t the lower r a t i o s . During the warmup p e r i o d at the end o f an experiment, a d d i t i o n a l peaks appeared i n the s p e c t r a . I t i s suggested that these new peaks were due t o c l u s t e r s o f s o l u t e molecules produced by d i f f u s i o n o f the s o l u t e through the l a t t i c e . S e m i - e m p i r i c a l c a l c u l a t i o n s were c a r r i e d out to e s t i mate s h i f t s o f v i b r a t i o n a l f r e q u e n c i e s o f the trapped molecules. From these c a l c u l a t i o n s i t was concluded that r e p u l s i v e i n t e r m o l e c u l a r f o r c e s p l a y an important p a r t i n d e t e r m i n i n g the magnitude, and d i r e c t i o n o f the s h i f t s . A f i r s t o r d e r p e r t u r b a t i o n c a l c u l a t i o n was made, u s i n g a Lennard-Jones' p o t e n t i a l , t o determine the e f f e c t o f the m a t r i x on the r o t a t i o n a l energy l e v e l s o f a t r a p p e d molecule. S p e c t r a o f the c l a t h r a t e - h y d r a t e s o f SO2, H2S and k r y p t o n were r e c o r d e d at l i q u i d n i t r o g e n temperatures, and the SO2 h y d r a t e was s t u d i e d i n the temperature range from t? to 120° K. The spectrum o f the water s k e l e t a l vibrations exhibited several interesting features. The assignment o f the 1600 cm"'' and 2200 cm"! peaks t o v and U^+l^w/as confirmed and a new peak a t 2410 cm"l was observed. A l a t t i c e mode i n the spectrum o f the S02 hydrate was o b s e r v e d . i n combination w i t h V$ o f SO2. -  2  GRADUATE STUDIES  F i e l d o f Study:  Chemistry  T o p i c s i n P h y s i c a l Chemistry Seminar i n P h y s i c a l Chemistry  J.A.R. Coope R.F. S n i d e r J.N. B u t l e r  Quantum Chemistry  J.A.R. Coope  Chemical Thermodynamics  J.N.  Butler  S p e c t r o s c o p y and M o l e c u l a r Structure  C. R e i d A.N. Bree L.W. Reeves K.B. Harvey  Related Topics D i f f e r e n t i a l Equations Computer Programming  S.A.  Jennings  C h a r l o t t e Froese  Group T h e o r e t i c a l Methods  W-,Opechowski  Elementary Quantum Mechanics  W„.Opechowski  Unrelated Topics T o p i c s i n I n o r g a n i c Chemistry T o p i c s i n O r g a n i c Chemistry  N. B a r t l e t t W.R. Cullen R. Stewart J.P. Kutney  PUBLICATIONS  The i n f r a r e d a b s o r p t i o n o f some c r y s t a l l i n e i n o r g a n i c formates. K.B. Harvey, B.A. Morrow and H.F. S h u r v e l l , Can.J. Chem. 41, 1181 (1963) S t a t i s t i c a l p r o b a b i l i t i e s o f some arrangements o f s o l u t e m o l e c u l e s on s u b s t i t u t i o n a l s i t e s . K.B. Harvey, J.R. Henderson and H.F. S h u r v e l l , Can. J.Chem. 42, ( i n p r e s s ) I n f r a r e d a b s o r p t i o n o f the SO2 c l a t h r a t e - h y d r a t e . motion of the SO2 m o l e c u l e . K.B. Harvey, F.R. McCourt and H^F. S h u r v e l l , Can.J. Chem. 42, ( i n p r e s s )  ii  A B S T R A C T  I n f r a r e d a b s o r p t i o n s p e c t r a o f HC1 and HBr, suspended i n s o l i d a r g o n , k r y p t o n and n i t r o g e n , were r e c o r d e d  i n order t o  o b t a i n i n f o r m a t i o n on i n t e r m o l e c u l a r f o r c e s .  SO2 i n argon and  n i t r o g e n , and CO i n argon were a l s o s t u d i e d .  The s p e c t r a were  o b s e r v e d i n t h e temperature range from l i q u i d h e l i u m  temperature  up t o t h e m e l t i n g p o i n t o f t h e m a t r i x . The h a l o g e n a c i d s gave more c o m p l i c a t e d n o b l e gas m a t r i c e s t h a n i n n i t r o g e n .  spectra i n the  T h i s has been c o r r e l a t e d  w i t h the d i f f e r e n t thermal p r o p e r t i e s of the matrix m a t e r i a l s . M a t r i x t o s o l u t e r a t i o s f r o m 100 t o 800 t o 1 were u s e d and e v i d e n c e was found f o r s o l u t e - s o l u t e i n t e r a c t i o n s a r i s i n g from incomplete i s o l a t i o n o f solute molecules a t the lower r a t i o s . D u r i n g t h e warm-up p e r i o d a t t h e end o f an e x p e r i m e n t , a d d i t i o n a l peaks appeared i n t h e s p e c t r a .  I t i s suggested t h a t t h e s e new  peaks were due t o c l u s t e r s o f s o l u t e m o l e c u l e s ,  produced by  d i f f u s i o n of the solute through the l a t t i c e . Semi-empirical  c a l c u l a t i o n s were c a r r i e d o u t t o e s t i m a t e  s h i f t s of v i b r a t i o n a l frequencies  o f the trapped  molecules.  From t h e s e c a l c u l a t i o n s i t was c o n c l u d e d t h a t r e p u l s i v e i n t e r molecular  f o r c e s p l a y an i m p o r t a n t  part i n determining the  magnitude and d i r e c t i o n o f t h e s h i f t s .  A f i r s t order  perturbation  c a l c u l a t i o n was made, u s i n g a Lennard-Jones' p o t e n t i a l , t o d e t e r mine t h e e f f e c t o f t h e m a t r i x on t h e r o t a t i o n a l energy l e v e l s o f a trapped  molecule.  iii  Spectra of the clathrate-hydrates of S O 2 , H 2 S and krypton were recorded at liquid nitrogen temperatures, and the S O 2 hydrate was studied in the temperature range from 4-° to 120°K. The spectrum of the water skeletal vibrations exhibited several The assignment of the 1600 cm'' and  interesting features. 2200 cm'' peaks to 1?  -  -  z  and  + iS/i  was confirmed and a new  peak at 24.10 cm'' was observed. A lattice mode in the spectrum -  of the S O 2 hydrate was observed in combination with V 3 of S O 2 .  K.B. Harvey  viii  ACKNOWLEDGMENT.  I would l i k e t o e x p r e s s my g r a t i t u d e t o Dr. K. B. Harvey f o r h i s h e l p and guidance d u r i n g t h e c o u r s e o f t h i s work. Many h e l p f u l d i s c u s s i o n s w i t h Dr. R. F. S n i d e r a r e a l s o a p p r e c i a t e d , and thanks a r e due t o Mr. R. Muehlchen f o r a s s i s t a n c e w i t h t h e c o n s t r u c t i o n and maintenance o f t h e apparatus. F i n a n c i a l a s s i s t a n c e from t h e S h e l l O i l Company and t h e N a t i o n a l R e s e a r c h C o u n c i l o f Canada i s g r a t e f u l l y acknowledged.  iv  TABLE OF CONTENTS. Page:. Abstract  i i  L i s t o f Tables  v i  L i s t of Figures Acknowledgment CHAPTER I  -  v i i viii  INTRODUCTION  1-1  P r e l i m i n a r y Remarks  1-2  S t u d i e s o f M o l e c u l a r I n t e r a c t i o n s by t h e  1  M a t r i x I s o l a t i o n Method  1  1-3  M o l e c u l a r I n t e r a c t i o n s i n t h e Gas H y d r a t e s  L,  1- 4  A Summary o f R e l a t e d Work on t h e Hydrogen H a l i d e s and Carbon Monoxide  CHAPTER 2  -  5  EXPERIMENTAL  2- 1  E x p e r i m e n t a l Methods  2-2  D e t a i l s o f t h e Low Temperature C e l l s  11  2-3  Diffusion i n Solid Matrices  15  2-4  Materials  17  2- 5  The Spectrometers  17  CHAPTER 3  -  8  RESULTS  3- 1  I n f r a r e d S p e c t r a o f HC1 i n S o l i d Argon  20  3-2  I n f r a r e d S p e c t r a o f HC1 i n S o l i d N i t r o g e n and K r y p t o n I n f r a r e d S p e c t r a o f HBr i n A r g o n , K r y p t o n  22  and N i t r o g e n M a t r i c e s  30  3-4-  M a t r i x I s o l a t i o n S t u d i e s on CO and SO^  37  3-5  Gas H y d r a t e s  41  3-3  Page: CHAPTER 4  -  THEORETICAL  4-1  I n t r o d u c t o r y Remarks  4-2  S h i f t s of V i b r a t i o n a l Frequencies Matrix-Solute Interactions  4-3  R o t a t i o n of Molecules  45 Due  to 45  Trapped i n S o l i d  Rare Gases  50  4-4  The  51  4-5  C a l c u l a t i o n o f E n e r g y L e v e l s o f the  4- 6 CHAPTER 5  -  5- 1  Hindered Rotator P o t e n t i a l  Hindered Rotator  57  S h i f t s Due  62  to Solute-Solute Interactions  DISCUSSION C l a s s i f i c a t i o n o f Peaks i n the M a t r i x o f HC1  Spectra  64  and HBr  5-2  I s o l a t e d Solute Molecules  5-3  I n t e r m o l e c u l a r F o r c e s Between S o l u t e  69 and  Matrix  71  5-4  Rotation of I s o l a t e d Solute Molecules  80  5-5  I n t e r a c t i o n s Between S o l u t e M o l e c u l e s  86  5-6  M a t r i x I s o l a t i o n S t u d i e s o f GO and S 0  5-7  Gas H y d r a t e s  93  5-8  Conclusions  97  2  88  Appendix 1  101  Appendix 2  102  Bibliography  103  vi  LIST OF  TABLES. Page:  1.  Infrared Absorption  o f HC1  i n Argon  2.  Infrared Absorption Nitrogen  o f HG1  i n Argon, K r y p t o n  3.  Infrared Absorption  o f HBr  i n Various Matrices  31  4.  Infrared Absorption  o f HBr  i n Argon  31  5.  Infrared Absorption  o f CO i n Argon  37  6.  Infrared Absorption  of SO2  39  7.  S k e l e t a l Water Spectrum i n the Gas  8.  V a l u e s o f Constants i n C a l c u l a t i o n s o f M a t r i x S h i f t s  49  9.  F i r s t Order E n e r g i e s f o r the H i n d e r e d R o t a t o r  60  10.  Hindered R o t a t i o n a l Energy Levels  61  11.  V a l u e s o f the Constant i n C a l c u l a t i o n s o f Interactions  12.  21 and 23  Hydrates  42  and P o p u l a t i o n s Dipole-Dipole  C l a s s i f i c a t i o n o f Peaks i n the S p e c t r a o f HC1  63 and  65  i n Argon 13.  F o r c e C o n s t a n t s o f HBr  14.  Band Centres o f M a t r i x - I s o l a t e d HC1  15.  V i b r a t i o n a l S h i f t s f o r HC1  16.  P r e d i c t e d S p e c t r a o f HC1  17.  I n t e n s i t i e s of HC1  18.  C a l c u l a t e d S h i f t s f o r I n t e r a c t i o n Between P a i r s HC1  HBr  and HC1  70 72  i n Various Matrices  and HBr  and HBr  and HBr  77  i n Argon  82 84  Peaks  Molecules  of 87  19.  R o t a t i o n a l Energy Levels  20.  P r o p e r t i e s of Some Gas  of S 0  2  Hydrates  91 94  vii  L I S T OF FIGURES. Page: Fig. 1  The Apparatus  9  Fig. 2  The Low Temperature C e l l  10  Fig. 3  D e t a i l o f Window H o l d e r on L i q u i d H e l i u m C e l l  13  Fig. 4  C e l l f o r Studies at L i q u i d Nitrogen Temperatures  14  F i g s . 5-7  I n f r a r e d S p e c t r a o f HC1 i n Argon  24-26  Figs.8,9  I n f r a r e d Spectrum o f HC1 i n N i t r o g e n  27,28  Fig. 10  I n f r a r e d Spectrum o f S o l i d HC1  29  F i g . 11  I n f r a r e d S p e c t r a o f HBr i n V a r i o u s M a t r i c e s  32  F i g . 12  I n f r a r e d Spectrum o f HBr i n N i t r o g e n  33  Figs.13-15  I n f r a r e d S p e c t r a o f HBr i n Argon  34-36  F i g . 16  I n f r a r e d Spectrum o f CO i n Argon  4O  F i g . 17  I n f r a r e d S p e c t r a o f S O 2 i n Argon and N i t r o g e n  40  F i g . 18  I n f r a r e d Spectrum o f S O 2 and K r y p t o n Hydrates  43  F i g . 19  I n f r a r e d Spectrum o f S O 2 as a S o l i d and a Gas Hydrate  43  F i g . 20  Anealed S O 2 Hydrate  44  F i g . 21  C o - o r d i n a t e System f o r H i n d e r e d R o t a t o r Calculation Change o f Peak I n t e n s i t i e s w i t h D i l u t i o n f o r HC1 and HBr i n Argon  53  F i g . 22 F i g . 23  66  F i r s t , Second, T h i r d and F o u r t h N e a r e s t Neighbour P o s i t i o n s i n a C.C.P. s t r u c t u r e  68  Fig. 24  R e l a t i v e S i z e s o f Some M o l e c u l e s  78  F i g . 25  Structure  95  o f Type 1 Gas H y d r a t e s  1  CHAPTER 1.  1-1  INTRODUCTION.  P r e l i m i n a r y Remarks. The b u l k o f t h e work f o r t h i s t h e s i s was c a r r i e d o u t on s m a l l  molecules i n i n e r t matrices.  The emphasis t h r o u g h o u t has been on  t h e e f f e c t s o f environment on t h e i n f r a r e d s p e c t r a , w h i c h n a t u r a l l y leads to a discussion of intermolecular forces.  I n t h i s l i g h t the  work on g a s - h y d r a t e s becomes d i r e c t l y r e l a t e d t o t h e m a t r i x work, s i n c e we a r e e f f e c t i v e l y s t u d y i n g s m a l l m o l e c u l e s i n a water " m a t r i x " . The  spectroscopic studies of small molecules i n high  gas, l i q u i d , s o l u t i o n and s o l i d s t a t e s , w h i c h a r e r e v i e w e d 1-4,  pressure i n section  c o r r e l a t e w i t h t h e p r e s e n t m a t r i x and gas h y d r a t e work, s i n c e  i n t h e s e environments i n t e r m o l e c u l a r f o r c e s determine t h e shapes, w i d t h s , s h i f t s and s p l i t t i n g o f i n f r a r e d bands.  The p r e s e n t work  attempts t o e x t e n d t h i s i n f o r m a t i o n and a p p l y i t t o t h e i n t e r p r e t a t i o n o f s p e c t r a o f m o l e c u l e s i n m a t r i x and gas h y d r a t e  1-2  environments.  S t u d i e s o f M o l e c u l a r ..Interactions by t h e M a t r i x I s o l a t i o n Method. The m a t r i x i s o l a t i o n t e c h n i q u e  spectroscopy,  i n conjunction with infrared  o f f e r s a unique approach t o t h e problem o f i n t e r a c t i o n s  between m o l e c u l e s .  The t e c h n i q u e  c o n s i s t s o f d i s p e r s i n g t h e substance  ( s o l u t e ) o f i n t e r e s t i n an i n e r t f r o z e n m a t r i x a t a temperature low enough t o p e r m i t  s e p a r a t i o n and i s o l a t i o n o f s i n g l e s o l u t e  T h i s i s u s u a l l y a c h i e v e d by c o n d e n s i n g gas m i x t u r e s  molecules.  on a p l a t e  c o o l e d by l i q u i d hydrogen, o r l i q u i d h e l i u m , as i n t h e p r e s e n t work. M a t e r i a l s most commonly u s e d f o r m a t r i c e s a r e n i t r o g e n and t h e r a r e gases.  2  Under c o n d i t i o n s o f p e r f e c t i s o l a t i o n , t h e m o l e c u l e examination  i s subject only t o solute-matrix interactions.  under Such  i d e a l c o n d i t i o n s occur, w i t h proper d e p o s i t i o n c o n d i t i o n s , a t very high matrix t o solute ratios.  I n t e r a c t i o n s between s o l u t e  molecules  become i m p o r t a n t a t low m a t r i x t o s o l u t e r a t i o s , and t h e method c a n be employed t o s t u d y i n t e r m o l e c u l a r f o r c e s w h i c h m a n i f e s t i n changes i n t h e i n f r a r e d spectrum o f t h e i s o l a t e d  themselves  molecule.  The m a t r i x i s o l a t i o n method, i n i t i a l l y employed f o r t r a p p i n g and r e t e n t i o n o f v e r y r e a c t i v e s p e c i e s such as f r e e r a d i c a l s , has been w i d e l y u s e d i n r e c e n t y e a r s f o r t h e s t u d y o f s m a l l i n a m a t r i x environment.  F o r example, P i m e n t e l e t a l  recorded s p e c t r a o f s e v e r a l small molecules 2 0 ° K , and M i l l i g a n and co-workers  (4,5,6)  i n v e s t i g a t i o n s w i t h s m a l l molecules  molecules  (1,2,3)  have  i n solid nitrogen at  have c a r r i e d o u t many  u s i n g m a t r i x i s o l a t i o n methods.  Of p a r t i c u l a r i n t e r e s t i s t h e work c a r r i e d o u t on water b y t h e s e two groups, b o t h o f w h i c h r e p o r t e d complex s p e c t r a i n t h e r e g i o n s o f t h e t h r e e fundamentals o f t h e water m o l e c u l e . (2)  Pimentel  i n t e r p r e t e d t h e s p e c t r a i n terms o f i s o l a t e d monomers, hydrogen-  bonded dimers and h i g h e r polymers. put f o r w a r d evidence the s o l i d matrix;  M i l l i g a n and h i s co-workers ( 4 , 5 )  f o r f r e e r o t a t i o n o f the trapped molecules i n  t h e l a t t e r view was s u p p o r t e d  t h e b a s i s o f r e s u l t s from s i m i l a r work.  b y G l a s e l ( 7 ) on  A disagreement i n i n t e r -  p r e t a t i o n o f r e s u l t s from m a t r i x - i s o l a t i o n s t u d i e s o f ammonia, between P i m e n t e l e t a l and M i l l i g a n e t a l , i s found i n r e f e r e n c e s (3)  and  (6).  .  P r e v i o u s m a t r i x s t u d i e s on HBr and H C 1 were c a r r i e d o u t by Becker and P i m e n t e l  ( 1 ) who r e c o r d e d s u r v e y s p e c t r a under low  3  r e s o l u t i o n o f HBr  and HC1  i s o l a t i o n technique.  i n s o l i d n i t r o g e n as a t e s t o f the  S i n c e t h i s work was  matrix  s t a r t e d , a n o t e by Schoen  e t a l (8) has been p u b l i s h e d , r e p o r t i n g the r o t a t i o n - v i b r a t i o n spectrum o f m a t r i x - i s o l a t e d hydrogen c h l o r i d e . . These workers used h i g h m a t r i x t o s o l u t e r a t i o s and observed a s i m p l e spectrum, w h i c h t h e y i n t e r p r e t e d u s i n g a h i n d e r e d r o t a t o r model. Maki (9) r e p o r t e d i n f r a r e d s p e c t r a o f CO as a s o l i d and i n s o l i d matrices. shoulders  The  s p e c t r a observed were, c o m p l i c a t e d  and peaks due t o i s o t o p i c CO  o n l y by weak  molecules.  Recent work i n t h i s l a b o r a t o r y (10) f o r w a r d e x p l a n a t i o n s based on m o l e c u l a r  indicated that straight-  a s s o c i a t i o n or f r e e r o t a t i o n ,  were inadequate and t h a t a more, d e t a i l e d s t u d y o f i n t e r m o l e c u l a r f o r c e s s h o u l d be c o n s i d e r e d i n the i n t e r p r e t a t i o n of. r e s u l t s a t low m a t r i x t o s o l u t e r a t i o s .  obtained  W i t h t h i s i n mind, and i n view o f  the r e l a t i v e l y s m a l l a t t e n t i o n w h i c h has been g i v e n t o m a t r i x i s o l a t i o n s t u d i e s o f the s i m p l e m o l e c u l e s HC1, i n v e s t i g a t i o n on t h e s e m o l e c u l e s was  HBr  undertaken.  and CO, I t was  a detailed  hoped t h a t  such a s t u d y would p r o v i d e i n f o r m a t i o n w h i c h c o u l d be a p p l i e d t o the i n t e r p r e t a t i o n o f r e s u l t s o b t a i n e d from more complex systems. I n f r a r e d s p e c t r a o f HC1,  HBr and CO i n n i t r o g e n and  m a t r i c e s were r e c o r d e d a t v a r i o u s m a t r i x - t o - s o l u t e r a t i o s . environment was  argon Change i n  a l s o s t u d i e d d u r i n g warming o f the d e p o s i t from  up t o the m e l t i n g p o i n t o f the m a t r i x .  4°K  By a d d i t i o n o f o t h e r s o l u t e  i m p u r i t i e s t o the gas m i x t u r e s , i t was  hoped t o demonstrate the  e x t e n t o f s o l u t e - s o l u t e i n t e r a c t i o n s , and thus s i m p l i f y the  inter-  p r e t a t i o n o f the m a t r i x - s o l u t e s p e c t r a . S e v e r a l t h e o r e t i c a l treatments  (II-I4)  have been c a r r i e d  out  4  on m o l e c u l a r r o t a t i o n i n s o l i d s and h i n d e r e d r o t a t o r models. c e n t r e s and  s o l i d matrices, using various  These c a l c u l a t i o n s p r e d i c t s h i f t s o f band  s p l i t t i n g o f degenerate r o t a t i o n a l l e v e l s .  o f s h i f t s o f v i b r a t i o n a l fundamentals due actions  have been made w i t h some s u c c e s s .  c a l c u l a t i o n s due  to solute-matrix One  T h i s approach was  been t e s t e d s u c c e s s f u l l y by Maki (9)  based on  used more r e c e n t l y  developed an improved t h e o r y .  a quantum m e c h a n i c a l c a l c u l a t i o n , d e r i v e d  inter-  o f the e a r l i e s t  t o K i r k w o o d , Bauer and Magat (15,16) was  simple d i e l e c t r i c theory. P u l l i n ( 1 7 ) , who  Calculations  by  Buckingham ( 1 8 ) ,  in  a u s e f u l formula which  and Ewing and P i m e n t e l  a  has  (19).  A t h i r d approach, based on c l a s s i c a l e l e c t r o s t a t i c f o r c e s , was  used  by L i n e v s k y (20) i n h i s m a t r i x work on l i t h i u m f l u o r i d e . I n Chapter 4 o f t h i s t h e s i s , c a l c u l a t i o n s o f h i n d e r e d r o t a t o r energy l e v e l s f o r the hydrogen h a l i d e s , u s i n g a L e n n a r d - J o n e s p o t e n t i a l are c a r r i e d out.  In a d d i t i o n , intermolecular  1  forces  (6-12) between  solute molecules i n nearest neighbour, next-nearest neighbour, e t c . , p o s i t i o n s are c o n s i d e r e d and  the c o r r e s p o n d i n g v i b r a t i o n a l s h i f t s  calculated.  1-3  Molecular Interactions  i n the Gas  Hydrates.  D i r e c t l y r e l a t e d t o the m a t r i x i s o l a t i o n s t u d i e s point  from the  of view o f m o l e c u l a r i n t e r a c t i o n s i s the p r e s e n t work on  i n f r a r e d spectra  o f gas h y d r a t e s .  The  gas  h y d r a t e s are  the  interesting  compounds because o f t h e i r .unusual c l a t h r a t e , or cage s t r u c t u r e . Von  S t a c k e l b e r g (21) i s r e s p o n s i b l e  o f the  s t r u c t u r e and  properties  f o r much o f our p r e s e n t knowledge  o f the gas  hydrates.  The  compounds  s t u d i e d i n the p r e s e n t work a l l b e l o n g t o the M»6H20 c l a s s w i t h  the  5  s t r u c t u r e d e s i g n a t e d as Type I by Von S t a c k e l b e r g . A p r e l i m i n a r y i n f r a r e d s t u d y on SC^, argon and k r y p t o n was made i n t h i s l a b o r a t o r y by McCourt ( 2 2 ) .  hydrates,  S h i f t s i n frequency o f  c e r t a i n peaks i n t h e s k e l e t a l water spectrum and t h e appearance o f a new peak, n o t p r e s e n t i n t h e spectrum o f i c e , were t h e main f e a t u r e s o b s e r v e d i n t h i s work.  I t was f e l t t h a t a more d e t a i l e d s t u d y might  r e v e a l i n f o r m a t i o n on i n t e r m o l e c u l a r i n t e r a c t i o n s and m o l e c u l a r  motion  i n t h e cage. A comprehensive s t u d y o f S C ^ - h y d r a t e s , u s i n g b o t h n o r m a l and heavy water was u n d e r t a k e n a t l i q u i d n i t r o g e n t e m p e r a t u r e s . o f k r y p t o n and H 2 S h y d r a t e s were a l s o r e c o r d e d .  Spectra  The s k e l e t a l water  v i b r a t i o n s and t h e v i b r a t i o n s o f t h e e n c l a t h r a t e d m o l e c u l e s were examined under h i g h r e s o l u t i o n , u s i n g t h e P e r k i n Elmer 4-21 s p e c t r o meter.  I n one s e r i e s o f experiments w i t h t h e SO?- h y d r a t e , t h e  r e g i o n o f S O 2 was s t u d i e d under h i g h r e s o l u t i o n a t v a r i o u s tempera t u r e s from 4° up t o 120°K u s i n g t h e P e r k i n Elmer 1 1 2 G  1-4  spectrometer.  A Summary o f R e l a t e d Work on t h e Hydrogen H a l i d e s and Carbon Monoxide. I n t e r m o l e c u l a r f o r c e s , as m a n i f e s t e d  i n infrared spectra of  t h e hydrogen h a l i d e s and Carbon monoxide, i n g a s , l i q u i d and s o l i d p h a s e s , have been t h e s u b j e c t o f a g r e a t d e a l o f work i n r e c e n t years.  The appearance o f a Q-branch produced by h i g h p r e s s u r e s o f  f o r e i g n gas i n t h e 1-0 bands o f H C 1 and HBr has been observed by Vodar and h i s co-workers ( 2 3 ) . al  S i m i l a r s t u d i e s were, made by a n k e t R  (24), who s u g g e s t e d t h a t t h e f o r m a t i o n o f a m o l e c u l a r  between t h e h y d r o g e n . h a l i d e  and t h e r a r e - g a s  complex  atoms used as p r e s s u r i z i n g  6  agents o c c u r r e d .  Pressure-induced  s h i f t s o f HG1 caused by n o b l e  gases have been measured by Ben-Reuven e t a l (25) and a t h e o r y d e v e l o p e d w h i c h a c c o u n t s f o r t h e main f e a t u r e s o f t h e o b s e r v e d shifts. Among t h e e a r l i e s t workers i n t h e f i e l d , West and Edwards (15) examined t h e s p e c t r a o f H d i n s o l u t i o n s o f v a r i o u s s o l v e n t s , and i n t e r p r e t e d t h e i r r e s u l t s u s i n g t h e Kirkwood-Bauer-Magat (16) .  formula  R e c e n t l y , Kwok and R o b i n s o n (26) s t u d i e d HC1 i n l i q u i d Xenon  and o b s e r v e d a broad band w i t h two s h o u l d e r s i n t h e r e g i o n o f t h e fundamental.  They a t t r i b u t e t h e i r r e s u l t s t o u n r e s o l v e d P and R  branches combined w i t h s o l v e n t - i n d u c e d 0, Q and S b r a n c h e s .  The  i n f r a r e d s p e c t r a o f HC1 and HBr i n s o l u t i o n i n v a r i o u s I n e r t s o l v e n t s have been r e c o r d e d by Lascomb e t a l (27) who r e p o r t gas t o s o l u t i o n s h i f t s v a r y i n g f r o m -40 t o -142 the s o l v e n t .  cm '', depending on t h e p o l a r i t y o f -  I n s i m i l a r s t u d i e s , o t h e r workers (28,29) c o n c l u d e  f r o m t h e shapes o f t h e a b s o r p t i o n bands t h a t t h e r e i s some degree of r o t a t i o n o f solute  molecules.  A v e r y r e c e n t s t u d y o f t h e o v e r t o n e bands o f pure s o l i d CO and i t s s o l u t i o n i n n i t r o g e n and argon i n t h e gaseous l i q u i d and s o l i d s t a t e s has been made by Vu, Atwood and Vodar ( 3 0 ) . workers concluded  that the anharmonicity  These  c o n s t a n t was v i r t u a l l y  unchanged i n t h e ' l i q u i d and s o l i d s t a t e s , compared w i t h t h e gaseous s t a t e , and t h e observed s m a l l band s h i f t was due o n l y t o t h e change of v i b r a t i o n frequency.  I n s i m i l a r experiments on HC1 and HBr (31)  t h e same w o r k e r s found t h a t t h e a n h a r m o n i c i t y  constant f o r these  molecules decreases c o n s i d e r a b l y i n the s o l i d s t a t e .  The spectrum  o f s o l i d CO has a l s o been r e p o r t e d by Ewing and P i m e n t e l  (19).  7  S t r a i g h t f o r w a r d assignments o f peaks t o t h e fundamentals o f v a r i o u s i s o t o p i c CO m o l e c u l e s were made, and a broad f e a t u r e +70 cm  from  the main peak was a s s i g n e d t o c o m b i n a t i o n s o f t h e v i b r a t i o n a l mode w i t h b o t h r o t a t i o n a l and t r a n s l a t i o n a l l a t t i c e modes. S o l i d HC1 and HBr a t low t e m p e r a t u r e s have been s t u d i e d by H o r n i g and Osberg  (32).  I n the r e g i o n o f the fundamental, sharp  d o u b l e t s were o b s e r v e d w i t h s p l i t t i n g s o f 42 cm"'' f o r HC1 and 34 cm '' f o r HBr.  The gas t o s o l i d s h i f t s were l a r g e , -161 cm '' f o r  HC1 and -137 c m  f o r HBr, and i t was c o n c l u d e d t h a t t h e s e m o l e c u l e s  -  -1  -  form hydrogen-bonded c h a i n s i n t h e i r low temperature c r y s t a l l i n e phases.  I n a l a t t e r paper, H o r n i g and H i e b e r t (33) r e p o r t e d t h e  s p e c t r a o f mixed HC1-DC1 and HBr-DBr c r y s t a l s over t h e e n t i r e c o m p o s i t i o n range.  A t low c o n c e n t r a t i o n s o f DC1 i n HC1 a s i n g l e  peak due t o i s o l a t e d DC1 molecules, was f o u n d .  More complex s p e c t r a  o b s e r v e d f o r h i g h e r DG1 c o n c e n t r a t i o n s were a t t r i b u t e d t o s u p e r p o s i t i o n o f peaks a r i s i n g from hydrogen-bonded c h a i n s o f v a r y i n g length.  8  CHAPTER 2 .  2-1  EXPERIMENTAL.  E x p e r i m e n t a l Methods. The m a t r i x i s o l a t i o n t e c h n i q u e has been d e s c r i b e d by P i m e n t e l  et  a l ( 1 , 3 4 ) , by s e v e r a l a u t h o r s i n t h e book e d i t e d by Bass  B r o i d a ( 3 5 ) , and was o u t l i n e d i n s e c t i o n 1-1  of t h i s  and  thesis.  I n t h e p r e s e n t m a t r i x work, a gaseous m i x t u r e o f a  hydrogen  h a l i d e o r carbon monoxide w i t h argon o r n i t r o g e n , was p r e p a r e d i n a 4 litre  s t o r a g e b u l b s e v e r a l days b e f o r e an experiment.  A convection  c u r r e n t i n t h e gaseous m i x t u r e was produced by h e a t i n g t h e bottom o f the  storage bulb.  T h i s ensured t h o r o u g h m i x i n g o f t h e gases p r i o r t o  deposition. A schematic diagram o f the apparatus i s g i v e n i n F i g . 1 and a diagram o f the low temperature c e l l , i n F i g . 2 .  D u r i n g a r u n , the  m i x t u r e was passed t h r o u g h a d e p o s i t i o n tube i n t o t h e low temperature c e l l where t h e gas stream was a l l o w e d t o impinge on a caesium i o d i d e plate cooled b y - l i q u i d helium. the  A n e e d l e v a l v e was used t o c o n t r o l  d e p o s i t i o n r a t e w h i c h was i n d i c a t e d by t h e p r e s s u r e r e a d i n g o f  a thermocouple gauge.  D e p o s i t i o n was c o n t i n u e d u n t i l a f i l m o f  condensed m a t e r i a l s u i t a b l e f o r i n f r a r e d s t u d y had been produced. T h i s o f t e n r e q u i r e d d e p o s i t i o n t i m e s o f s e v e r a l hours s i n c e t h e m i x t u r e must be d e p o s i t e d s l o w l y t o p r e v e n t temperature r i s e o f the d e p o s i t , w i t h subsequent d i f f u s i o n o f t h e t r a p p e d s p e c i e s . High m a t r i x t o s o l u t e r a t i o s  (^  i s o l a t e d m o l e c u l e s , whereas low r a t i o s  500 : 1) were used t o s t u d y ( \> 100 : 1) were employed /  when i t was d e s i r e d t o observe t h e e f f e c t s o f m o l e c u l a r i n t e r a c t i o n s on t h e i n f r a r e d s p e c t r a .  I n some e x p e r i m e n t s , c o n d i t i o n s such as  fig 1.  THE  APPARATUS  vacuum  helium recovery  i  system  and low  temperature  liquid helium transfer-tube vacuum jacket needle  V 2  ^^  thermocouple gauge ionization gauge Q  liquid nitrogen liquid helium  Csl  window  deposition tube  ?  to pumping system  cell.  10  fig 2 .  THE LOW TEMPERATURE  CELL  .liquid .helium  liquid _ nitrogen  WWA/  to pumping system  Cs I  radiation shield ~  hole to admit infrared beam  deposition window  hole to admit gas from deposition tube  deposition Csl  window  i  tube  11  r a p i d d e p o s i t i o n , o r f o r m a t i o n o f t h e d e p o s i t a t temperatures w e l l above l i q u i d h e l i u m t e m p e r a t u r e s , were u t i l i z e d t o ensure t h a t d i f f u s i o n occurred during deposition.  In addition, several experi-  ments were c a r r i e d o u t i n w h i c h a t h i r d p o l a r m o l e c u l e , SO2 o r CO was added t o t h e gas m i x t u r e . The gas h y d r a t e s t u d i e s were made m o s t l y a t l i q u i d n i t r o g e n t e m p e r a t u r e s i n a low temperature c e l l  (Fig.4).  A few experiments  were c a r r i e d o u t a t l i q u i d h e l i u m temperatures u s i n g t h e same apparatus used f o r t h e m a t r i x i s o l a t i o n work.  M i x t u r e s o f water  vapour and t h e h y d r a t e former were p r e p a r e d by a procedure  similar  to t h a t used i n t h e m a t r i x work, and d e p o s i t e d on a caesium i o d i d e p l a t e cooled by l i q u i d n i t r o g e n .  Short d e p o s i t i o n times, o f the  o r d e r o f seconds, were n e c e s s a r y because i c e absorbs s t r o n g l y i n the  i n f r a r e d , and v e r y t h i n f i l m s were e s s e n t i a l t o produce s a t i s -  factory spectra. When i t was d e s i r e d t o examine t h e s k e l e t a l water v i b r a t i o n s , a m i x t u r e was p r e p a r e d c o n t a i n i n g a s l i g h t excess over t h e s t o i c h i o metric r a t i o o f the hydrate former. was t i e d up as h y d r a t e .  T h i s ensured t h a t a l l t h e water  C o n v e r s e l y , when t h e v i b r a t i o n s o f t h e  e n c l a t h r a t e d m o l e c u l e were s t u d i e d , a s l i g h t excess o f water was used t o e l i m i n a t e t h e f o r m a t i o n o f s o l i d hydrate former.  2-2  D e t a i l s o f t h e Low Temperature C e l l s . The c e l l used f o r t h e m a t r i x i s o l a t i o n s t u d i e s i s o f t h e  Duerig-Mador (36) t y p e and i s i l l u s t r a t e d i n F i g . 2 .  I t consists  e s s e n t i a l l y o f a c e n t r a l l i q u i d h e l i u m c o n t a i n e r surrounded b y a r a d i a t i o n s h i e l d and an o u t e r v e s s e l equipped w i t h o p t i c a l windows  12  o f caesium i o d i d e .  The c e l l i s connected t o a vacuum system o f t h e  conventional type. The l i q u i d h e l i u m c o n t a i n e r i s made o f copper and i s suspended by a s t a i n l e s s s t e e l neck t o m i n i m i z e heat i n f l o w b y c o n d u c t i o n , w h i c h would a c c e l e r a t e t h e e v a p o r a t i o n o f l i q u i d h e l i u m . To improve t h e e f f i c i e n c y o f t h e r a d i a t i o n s h i e l d , i t i s u s u a l l y f i l l e d w i t h a l i q u i d r e f r i g e r a n t s u c h as l i q u i d n i t r o g e n .  A copper  b l o c k a t t h e bottom o f t h e h e l i u m c o n t a i n e r h o l d s a caesium i o d i d e p l a t e on w h i c h t h e d e p o s i t f o r m s .  A f t e r s e v e r a l u n s u c c e s s f u l runs  d u r i n g t h e e a r l y p a r t o f t h e p r e s e n t work, t h e window h o l d e r was m o d i f i e d t o improve t h e r m a l c o n t a c t between t h e window and t h e copper block.  A l a r g e r b l o c k was machined (see F i g . 3) w i t h a r e c e s s t o  s u p p o r t t h e caesium i o d i d e p l a t e w h i c h i s t i g h t l y h e l d a g a i n s t t h e b l o c k by means o f a copper g a s k e t s e c u r e d w i t h f o u r copper screws. A l l space between t h e edges o f t h e window, t h e g a s k e t and t h e copper block i s f i l l e d with s i l v e r conductive paint. The c o l d j u n c t i o n o f a g o l d - s i l v e r / g o l d - c o b a l t  thermocouple  i s a t t a c h e d t o t h e copper b l o c k and t h e " h o t " j u n c t i o n i s m a i n t a i n e d at l i q u i d n i t r o g e n temperature.  The E.M.F. from t h i s  thermocouple  i s a m p l i f i e d and r e c o r d e d as a t r a c e on t h e same c h a r t paper as t h e spectrum, thus g i v i n g a r e c o r d o f t h e temperature a t w h i c h t h e spectrum was o b s e r v e d .  No attempt was made t o c a l i b r a t e t h e thermo-  c o u p l e a t p o i n t s between 4 e s t i m a t e d by l i n e a r  0  and 77°K;  i n t e r m e d i a t e t e m p e r a t u r e s were  interpolation.  The l i q u i d h e l i u m c o n t a i n e r w i t h t h e a t t a c h e d window h o l d e r may be t u r n e d t h r o u g h 90° so t h a t t h e caesium i o d i d e p l a t e can f a c e e i t h e r t h e d e p o s i t i o n tube o r t h e windows o f t h e o u t e r v e s s e l .  13  fig  3. DETAIL OF WINDOW HOLDER IN T H E LIQUID HELIUM CELL liquid helium container  gasket  copper block ^  thermocouple leads  protective plate for T.C. junction  this space is filled with silver conductive paint  caesium iodide window  f i g  4 .  CELL FOR  STUDIES AT LIQUID NITROGEN  o ring  TEMPERATURES  liquid nitrogen  leads to heating element cooling coil  caesium iodide deposition plate caesium iodide window  beari ng evacuation tube  deposition tube  15  The c e l l used f o r t h e g a s - h y d r a t e work i s shown i n F i g . 4 . T h i s c e l l r e t a i n s t h e s a l i e n t c h a r a c t e r i s t i c s o f t h e Duerig-Mador c e l l j u s t d e s c r i b e d b u t i s s m a l l e r and has no r a d i a t i o n s h i e l d . Other n o t a b l e f e a t u r e s a r e t h e h e a t i n g and c o o l i n g d e v i c e s by means o f w h i c h t h e temperature may be v a r i e d from 77°K t o w e l l above room t e m p e r a t u r e , as r e q u i r e d . controlled electric  The h e a t i n g i s e f f e c t e d by p a s s i n g a  current through a c o i l of pyrotenax wire.  The  c o o l i n g i s r e g u l a t e d by a f l o w o f c o l d n i t r o g e n gas o r l i q u i d n i t r o g e n t h r o u g h a c o i l e d copper t u b e .  B o t h h e a t i n g and c o o l i n g  c o i l s a r e wound c l o s e t o t h e window h o l d e r .  I t has been found  e x p e d i e n t when w o r k i n g a t 77°K t o keep t h e c e n t r a l tube f i l l e d w i t h l i q u i d n i t r o g e n i n a d d i t i o n t o c i r c u l a t i n g l i q u i d n i t r o g e n through the  cooling  coil.  There i s a l s o a d i f f e r e n c e i n t h e d e v i c e f o r r o t a t i n g t h e window t h r o u g h 90°.  I n the l i q u i d helium c e l l , o n l y the innermost  c o n t a i n e r i s r o t a t e d , by means o f a b e a r i n g l o c a t e d a t t h e neck o f the  container.  I n t h e l i q u i d n i t r o g e n c e l l , both t h e o u t e r v e s s e l  and t h e l i q u i d n i t r o g e n c o n t a i n e r move t h r o u g h 90° on a b e a r i n g s i t u a t e d a t t h e base o f t h e o u t e r v e s s e l . The c o l d j u n c t i o n o f a c o p p e r - c o n s t a n t a n thermocouple i s a t t a c h e d t o t h e bottom o f t h e window h o l d e r and t h e h o t j u n c t i o n i s m a i n t a i n e d a t room t e m p e r a t u r e .  The thermocouple E.M.F. i s o b s e r v e d  by means o f a Leeds and N o r t h r u p m i l l i v o l t p o t e n t i o m e t e r and t h e c o r r e s p o n d i n g temperature o b t a i n e d f r o m t a b l e s .  2-3  Diffusion i n Solid Matrices. I n t h e p r e s e n t s t u d y , some e a r l y m a t r i x experiments and some  16  l a t e r runs i n 'which t h e d e p o s i t was r a p i d l y formed, gave r e s u l t s w h i c h i n d i c a t e d t h a t d i f f u s i o n o f t h e t r a p p e d s p e c i e s had o c c u r r e d during deposition.  The problem o f d i f f u s i o n i n s o l i d m a t r i c e s has  been d i s c u s s e d by P i m e n t e l i n Chapter 4 o f r e f e r e n c e ( 3 5 ) . found t h a t s m a l l m o l e c u l e s d i f f u s e r a p i d l y a t 0.4 - 0.6 melting point of the matrix.  During deposition the f i l m  I t was  of the temper-  a t u r e may r i s e w e l l above t h a t o f t h e c o l d p l a t e i f t h e d e p o s i t i o n rate i s rapid.  T h i s e f f e c t i s s e r i o u s because o f t h e poor t h e r m a l  c o n d u c t i v i t y o f most o f t h e common m a t r i x m a t e r i a l s .  F o r example,  d u r i n g t h e d e p o s i t i o n o f n i t r o g e n a t 4-°K, Fontana (37) observed a temperature r i s e o f a p p r o x i m a t e l y 10°K a t a d e p o s i t i o n r a t e o f 30 cc/min. (S.T.P.)  The d e p o s i t i o n r a t e i n t h i s work d u r i n g a  t y p i c a l two hour r u n was 12.5 c c / m i n . , so one might e x p e c t a maximum temperature r i s e o f 4°K. temperature o f t h e f i l m up t o 0.14  Such a r i s e would b r i n g t h e and 0.11  of the melting point  o f argon and n i t r o g e n r e s p e c t i v e l y , w h i c h s h o u l d be w e l l below t h e temperature a t w h i c h r a p i d d i f f u s i o n s e t s i n . There i s a n o t h e r f a c t o r w h i c h must be c o n s i d e r e d i n a d d i t i o n t o t h e temperature r i s e o f t h e s o l i d m a t r i x f i l m .  I t i s possible  t h a t i n c e r t a i n cases t h e r m a l c o n t a c t d e t e r i o r a t e s between t h e caesium i o d i d e window and t h e window h o l d e r , r e s u l t i n g i n warming o f t h e window and c o n s e q u e n t l y a l s o o f t h e d e p o s i t .  Evidence f o r  t h i s was o b t a i n e d i n e a r l y experiments b e f o r e t h e new window h o l d e r was d e s i g n e d .  I n these e x p e r i m e n t s , e i t h e r no i s o l a t i o n o f t h e  s o l u t e m o l e c u l e was a c h i e v e d , o r peaks were observed w h i c h were n o t n o r m a l l y p r e s e n t a t 4°K, b u t w h i c h had been o b s e r v e d a t h i g h e r t e m p e r a t u r e s d u r i n g warm-up s t u d i e s .  However, w i t h t h e m o d i f i e d  c e l l and u s i n g slow d e p o s i t i o n r a t e s , r e a s o n a b l e i s o l a t i o n was  always  achieved.  2t4  Materials. R e g u l a r grade argon and p r e p u r i f i e d n i t r o g e n f o r m a t r i x work  were o b t a i n e d p u r i f i e d H^S Company. ation.  from Matheson Co. and C P .  Inc.  Anhydrous S 0 £ , HBr  and H C 1 ,  grade CO were a l s o o b t a i n e d from the Matheson  H i g h p u r i t y K r y p t o n was  D 2 O o f 99.8%  s u p p l i e d by A i r R e d u c t i o n C o r p o r -  p u r i t y , supplied.by  G e n e r a l Dynamics  Corporation,  L i q u i d C a r b o n i c D i v i s i o n , and double d i s t i l l e d water were used i n the gas h y d r a t e work.  The  further purification.  r a r e gases and n i t r o g e n were u s e d  without  A l l o t h e r m a t e r i a l s were t r e a t e d by f r e e z i n g  and pumping on the s o l i d t o remove t r a c e s o f non-condensable Mass.spectroscopic  analyses  o f a r g o n , k r y p t o n and n i t r o g e n i n d i c a t e d  an upper l i m i t o f i m p u r i t y f o r argon and n i t r o g e n o f 5-10 m i l l i o n , and 50-60 p.p.m. f o r k r y p t o n .  - 99.8%;  2-5  The  HC1  -  99.0%;  HS 2  parts  per  Minimum p u r i t i e s s t a t e d by  the m a n u f a c t u r e r f o r . t h e o t h e r gases were as f o l l o w s : HBr  gas.  - "99-5%;  SO2  -  99-98%;  and CO - 99.5%.  Spectrometers.  The Per-'kin Elmer 1 1 2 G S p e c t r o m e t e r i s a h i g h r e s o l u t i o n s i n g l e beam, double pass i n s t r u m e n t .  The main f e a t u r e s a r e :  a 60°  P o t a s s i u m bromide f o r e - p r i s m , w h i c h a c t s as a f i l t e r t o e l i m i n a t e the energy o f unwanted o r d e r s , and a 7 5 l i n e s per m i l l i m e t e r e c h e l e t t e g r a t i n g , b l a z e d f o r maximum i n t e n s i t y a t 1 2 jl order.  The  instrument  was  (850  cm~1)  i n the  first  c a l i b r a t e d u s i n g the a c c u r a t e l y known l i n e s  o f the v i b r a t i o n - r o t a t i o n s p e c t r a o f H C 1 ( 3 8 ) ,  HBr  (39), CO ( 4 O ) ,  and  18  other molecules ( A l ) . The o p t i c a l p a t h l e n g t h i n t h e 112  G i n s t r u m e n t i s about  5 metres and a t m o s p h e r i c water and CCU, show s t r o n g a b s o r p t i o n i n t h e neighbourhood  of ^  and b ft-  .  This i n t e r f e r e s s e r i o u s l y with  s p e c t r a r e c o r d e d i n t h e s e r e g i o n s and i t i s v e r y d e s i r a b l e t o remove t h e s e vapours by p a s s i n g a c u r r e n t o f d r y n i t r o g e n gas t h r o u g h t h e i n s t r u m e n t h o u s i n g f o r some time b e f o r e a spectrum i s r e c o r d e d . The P e r k i n Elmer 421  s p e c t r o m e t e r i s a double beam i n s t r u -  ment c a p a b l e o f h i g h r e s o l u t i o n .  The d i s p e r s i o n u n i t  comprises  two g r a t i n g s , each used i n t h e f i r s t o r d e r o n l y . I n t e r f e r e n c e f i l t e r s a r e used t o r e j e c t unwanted o r d e r s o f r a d i a t i o n d i f f r a c t e d by each g r a t i n g ;  t h e s e r e p l a c e t h e customary f o r e - p r i s m .  s t a n d a r d i n s t r u m e n t o p e r a t e s i n t h e range  The  4000 - 650 cm~1, but a  g r a t i n g i n t e r c h a n g e i s a v a i l a b l e which extends t h e a c c e s s i b l e l o n g w a v e l e n g t h r e g i o n out t o 300 cm ''. -  In  an i n f r a r e d s p e c t r o m e t e r , t h e r e s o l u t i o n o b t a i n e d under  g i v e n c o n d i t i o n s depends on t h e f r e q u e n c y i n t e r v a l passed by t h e exit s l i t .  For a p a r t i c u l a r frequency  ~V  0  t h i s i n t e r v a l may be  expressed as:  where:  i s the s p e c t r a l s l i t width.  The s p e c t r a l s l i t w i d t h , w h i c h depends on t h e m e c h a n i c a l . s l i t w i d t h and on t h e o p t i c a l d e s i g n o f t h e i n s t r u m e n t i s a p p r o x i m a t e l y e q u a l to  t h e s e p a r a t i o n o f two l i n e s w h i c h a r e j u s t r e s o l v e d .  f o r m u l a e g i v e n by S i e g l e r (42)  f o r t h e model 112-G  and t a b l e s g i v e n by Roche (43)  f o r t h e model 421  Using  spectrometer, spectrometer,  s p e c t r a l s l i t w i d t h s have been e s t i m a t e d f o r t h e i n s t r u m e n t s e t t i n g s  19  u s e d i n t h e p r e s e n t work and have been i n c l u d e d on t h e s p e c t r a r e p r o d u c e d i n Chapter  3.  20  CHAPTER 3  3-1  RESULTS.  I n f r a r e d S p e c t r a o f HC1 Gas m i x t u r e s  i n S o l i d Argon.  c o n t a i n i n g one p a r t o f HC1  and 800 p a r t s o f argon were d e p o s i t e d a t 4°K.  t o 100, The  200,  500  spectra  obtained  from t h e s e d e p o s i t s are shown i n F i g . 5 and the f r e q u e n c i e s  and  r e l a t i v e i n t e n s i t i e s o f the o b s e r v e d peaks are t a b u l a t e d i n Table I . The  spectrum o f HC1  i n argon a t h i g h m a t r i x t o s o l u t e r a t i o s  c o n s i s t s o f a s t r o n g peak a t 2889 cm '', a peak o f medium -  a t 2853 cm '', and a weak s h o u l d e r a t -  2900  cm ''. -  pond t o those r e p o r t e d by Schoen e t a l ( 8 ) . additional  These peaks c o r r e s -  However, s e v e r a l  f e a t u r e s are o b s e r v e d a t a l l m a t r i x r a t i o s u s e d i n t h i s  work, and a t low r a t i o s c e r t a i n important  intensity  o f t h e s e new  t h a n the t r i o mentioned above.  peaks are more  An i n t e r e s t i n g  feature  o f t h i s d i l u t i o n s t u d y i s the change i n r e l a t i v e i n t e n s i t y o f the peaks i n the spectrum as the m a t r i x t o HC1 100:1  r a t i o i n c r e a s e s from  t o 800:1. I n F i g . 6 a warm-up s t u d y i s d e p i c t e d f o r an argon t o  r a t i o o f 500:1.  Some o f the new  peaks w h i c h appear i n the spectrum  as the temperature r i s e s c o r r e s p o n d  t o c e r t a i n peaks p r e v i o u s l y  o b s e r v e d i n e x p e r i m e n t s conducted a t low m a t r i x t o HC1  ratios.  F u r t h e r m o r e , the peaks w h i c h appear d u r i n g warm-up do not  disappear  or decrease i n i n t e n s i t y on r e c o o l i n g the d e p o s i t t o 4°K. warm-up s t u d i e s i t was s l i t widths  found n e c e s s a r y  m i c r o c r y s t a l s o f the s o l u t e .  During  t o i n c r e a s e the monochromator  as the temperature r o s e because l i g h t s c a t t e r i n g  deposit increased considerably.  HC1  T h i s may  by the  i n d i c a t e the f o r m a t i o n  of  21  TABLE 1.  I n f r a r e d a b s o r p t i o n o f HC1 i n a r g o n a t 4°K. Line i n t e n s i t i e s ( l o g I $ / l ) r e l a t i v e t o the peak a t 2889 cnr*1 •  Frequency • cm"  100:1  1  Argon t o HC1 r a t i o • 200:1' 500:1  800:1  -  2787.5  1.11  .16  2817  1.59  .82  .07  .15  2853  .40  .37  .22  .29  2863  -  .13  .05  .10  .33  .13  .05  2889  1.00  1.00  1.00  2900  sh  sh  2867.5  sh =  shoulder  .07  '  .05 1.00 _  22  To i l l u s t r a t e the e f f e c t o f s o l u t e - s o l u t e i n t e r m o l e c u l a r i n t e r a c t i o n s on the spectrum o f HG1 CO or S O 2 w i t h HC1  i n argon, mixtures  and argon were p r e p a r e d .  f r o m d e p o s i t s o f these m i x t u r e s  The  containing  spectra  are shown i n F i g . 7.  obtained  For  the  HCl/CO/argon m i x t u r e , the i n t e n s i t i e s o f the peaks were changed r e l a t i v e t o the HCl/argon c a s e , but the main f e a t u r e s o f the spectrum were u n a l t e r e d . mixture  s e v e r a l new  Three new  o f one  cm '' -  spectrum.  a v e r y s t r o n g peak a t 2808  em~1,  and a weak peak a t 2829 cm ''. -  I n f r a r e d S p e c t r a o f HC1 At 4-°K  added t o the HCl/argon  f e a t u r e s were o b s e r v e d i n t h e HC1  peaks were f o u n d :  a s h o u l d e r a t 2821  3-2  When S O 2 was  i n S o l i d N i t r o g e n and  the spectrum o f HC1  Krypton.  i n a nitrogen matrix consists  s t r o n g peak w i t h two v e r y weak s a t e l l i t e s  (see F i g . 8 ) .  D u r i n g the warm-up, however, many changes occur i n the spectrum. (See F i g . 9).  S e v e r a l peaks appear and d i s a p p e a r  s o l i d n i t r o g e n sublimes  K.  i d e n t i c a l w i t h t h a t o f s o l i d HC1 o b s e r v e d f r e q u e n c i e s f o r HC1  and  i n - n i t r o g e n i s indeed  a t the same t e m p e r a t u r e .  The  i n n i t r o g e n are compared w i t h t h e  i n argon and k r y p t o n i n Table 2.  S o l i d HC1 2762 cm~1,  deposited at  HC1.  Comparison o f F i g u r e s 9 and 10 i n d i c a t e s  t h a t the f i n a l f o r m o f the spectrum o f HC1  s p e c t r a o f HC1  the  away from t h e window l e a v i n g s o l i d  F i g u r e 10 shows t h e spectrum o f s o l i d HC1 warmed s l o w l y t o 55  before  d e p o s i t e d a t 4-°K  g i v e s a broad band c e n t r e d a t  but as the temperature r i s e s t h i s band r e s o l v e s i n t o  t h r e e peaks a t 2712,  2753 and 2780 cm ''. -  The  changes i n r e l a t i v e  i n t e n s i t y o f the peaks i n the spectrum o f s o l i d HC1  are shown i n F i g . 1 0 .  23  TABLE 2.  I n f r a r e d A b s o r p t i o n o f HC1 i n Argon, K r y p t o n and N i t r o g e n a t 4°K. ( F r e q u e n c i e s i n c m ^ ) . -  Argon 500:1  2787.5 (m)  Krypton 300:1  Nitrogen 200:1  HC1 gas  -  -  -  -  -  2817  (a)  2800 ( s )  2853  (m)  2838 (m)  2863  M  -  2814 (vw)  -  2864 P ( 1 )  -  -  2867.5 M  2854 (w)  2842 (vw)  2889  (vs)  2874 ( v s )  2852 ( v s )  2905 R ( 0 )  2900  sh  2875 (vw)  2925 R ( 1 )  -  I n t h i s and subsequent t a b l e s t h e f o l l o w i n g a b r e v i a t i o n s f o r i n t e n s i t i e s are used:  vs = very strong,  s = s t r o n g , m = medium, w = weak, vw = v e r y weak, and sh = shoulder.  2  4  25  fig  6.  INFRARED SPECTRUM OF HCI  2750  2800  2850  2900  CM"  1  26  fig  7.  INFRARED  2800  SPECTRA  O F H C l IN A R G O N  2850  AT  4°K  2900 CM"  1  27  fig  8.  I N F R A R E D IN  S P E C T R U M  NITROGEN  .  O F ,  HCI  . 1 9 5 : 1  A T  15 ° K  z g  i— GL CC o  CD <  —  i  —  2800  i  2850  C M -  1  fig  9.  INFRARED  2700  S P E C T R U M  O F  2800  HCI  C M "  1  29  •  2700  •  2800  I  C M  30  3-3  I n f r a r e d S p e c t r a o f HBr' i n Argon, K r y p t o n and Matrices. The  Nitrogen  s p e c t r a o f HBr i n a r g o n , k r y p t o n and n i t r o g e n are  compared i n F i g . 11, and t h e observed f r e q u e n c i e s t a b u l a t e d i n Table 3.  The  r a t i o of 320:1  spectrum of HBr i n k r y p t o n a t a m a t r i x t o s o l u t e i s seen t o be v e r y s i m i l a r t o t h a t o f HBr i n argon  a t a r a t i o o f 500:1.  The main d i f f e r e n c e i s a s h i f t o f the whole  spectrum t o l o w e r wave numbers i n t h e k r y p t o n m a t r i x .  In s o l i d  n i t r o g e n , a s i m p l e spectrum c o n s i s t i n g o f one main peak w i t h t h r e e v e r y weak s u b s i d i a r i e s i s observed.  The  s u b s i d i a r y peaks  i n c r e a s e i n i n t e n s i t y d u r i n g warm-up (see F i g . 1 2 ) , i n a s i m i l a r t o t h a t observed f o r HC1  way  i n nitrogen.  A d i l u t i o n s t u d y o f HBr i n argon a t m a t r i x r a t i o s o f 300 and 500 t o 1 was shown i n F i g . 13.  100,  c a r r i e d o u t , and the r e s u l t i n g s p e c t r a are  The  f r e q u e n c i e s , w i t h i n t e n s i t i e s a t the  v a r i o u s argon t o HBr r a t i o s , are g i v e n i n Table 4«  A variation  i n t h e number and r e l a t i v e i n t e n s i t i e s o f peaks w i t h d i l u t i o n i s evident i n t h i s s e r i e s of  experiments.  A t y p i c a l warm-up s t u d y i s i l l u s t r a t e d by F i g . 14,  where  v a r i a t i o n s i n the spectrum o f HBr i n argon a t a m a t r i x t o s o l u t e r a t i o o f 300:1  are shown.  New  peaks w h i c h appear d u r i n g warm-up  do not d i s a p p e a r on r e c o o l i n g t o 4°K.,  and f u r t h e r d e p o s i t a t t h i s  t e m p e r a t u r e adds o n l y t o the i n t e n s i t y o f the peaks o r i g i n a l l y observed at molecules HC1.  S p e c t r a o f HBr, p e r t u r b e d by o t h e r s o l u t e  i n an argon m a t r i x , were r e c o r d e d as i n t h e work w i t h  These s p e c t r a are r e p r o d u c e d i n F i g . 15.  o f t h e HBr  The main f e a t u r e s  spectrum remain unchanged, but when GO i s p r e s e n t a  new,  31 v e r y s t r o n g peak i s o b s e r v e d a t 2520 cm ' and w i t h SO2, t h r e e new -  peaks a r e f o u n d a t 2484, 2517 and 2524 cm ''. -  TABLE 3. I n f r a r e d a b s o r p t i o n o f HBr i n v a r i o u s m a t r i c e s a t 4°K. ( F r e q u e n c i e s i n c m ^ ) . -  Ar (505:1)  K r (320:1)  N (l75:1)  HBr ( g a s )  2  2465 w  -  -  -  2496 m  2491  s  2493 vw  2550 m  2531 s  2506 vw  2558 vw  2541 w  2569 s  2551 vs  2542 p(1) -  . 2535w  2575 R(0)  2545 vs -  2575 sh  2591 R ( D  TABLE 4 I n f r a r e d a b s o r p t i o n o f HBr i n argon a t 4°K. L i n e ( l o g I / l ) r e l a t i v e t o t h e peak a t 2569 cm 1.  intensities  -  0  Frequency cm-1  110:1  Argon t o HBr r a t i o 215:1 300:1 "  2465  -  1.60  .50  .21  2496  1.24  1.15  .98  .71  2550  .41  .36  .40  .36  2558  .18  .09  .20  .14  2569  1.00  1.00  1.00  1.00  2575  sh  sh  sh  sh  505:1  INFRARED  2500  S P E C T R A  OF  H B r  2550  IN  VARIOUS  C M  H  12.  fig  INFRARED IN  S P E C T R U M  O F  H B r  NITROGEN  2500  2550  CM""'  34  fig  13. INFRARED  SPECTRUM  OF  HBr  IN  ARGON  AT  4°K  II  2450  2500  2550  CM"  1  35  fig  14.  36  jig  15.  INFRARED SHOWING  SPECTRA  OF  HBr  IN  ARGON  T H E E F F E C T OF OTHER  2500  AT 4°K  SOLUTES  2550  37  3-4  M a t r i x I s o l a t i o n S t u d i e s on CO and SO^. The spectrum o f CO i n argon ( F i g . 16) c o n s i s t s o f one very-  s t r o n g peak a t 2138.5 cm '', w i t h a peak o f medium i n t e n s i t y a t -  2152 c m .  Three v e r y weak s a t e l l i t e s were a l s o observed  on t h e low  f r e q u e n c y s i d e o f the main peak when v e r y t h i c k d e p o s i t s were examined. No changes i n t h e spectrum o f CO were observed when some CO  molecules  were r e p l a c e d by HC1 o r HBr.  I n t h e overtone r e g i o n o f CO, one weak  peak a t 4253 cm '' was found.  The observed  -  frequencies together with  r e s u l t s o b t a i n e d by o t h e r workers f o r b o t h s o l i d and m a t r i x i s o l a t e d CO a r e i n c l u d e d i n Table 5.  TABLE 5.  I n f r a r e d A b s o r p t i o n o f CO i n Argon a t 4°K, Compared w i t h R e s u l t s o f Other Workers. ( F r e q u e n c i e s i n cm '') -  T h i s Work CO/Ar a t 4°K.  4253  w  2152  m  M a k i (9) CO/Ar a t 20°K.  -  4253.5  2148.0 21^,2 • l^.  2138.5 vs  Ewing and P i m e n t e l (19) S o l i d CO a t 20°K.  —  2137.2  2138.1  2115  vw  -  2112.3  2091  w  -  2092.2 2088.4  2065  38  I n f r a r e d s p e c t r a i n t h e r e g i o n s o f t h e symmetric and antisymmetric  s t r e t c h i n g fundamentals ( V ; and ~])^ ) o f S O 2 i n  argon and n i t r o g e n m a t r i c e s a r e p r e s e n t e d  i n F i g . 17.  A  signi-  f i c a n t d i f f e r e n c e between t h e spectrum o f S O 2 i n t h e two m a t r i c e s i s observed.  I n a r g o n , b o t h t h e ~V, and V  s t r o n g d o u b l e t w i t h a weak s a t e l l i t e .  3  bands c o n s i s t o f a  I n n i t r o g e n , however,  o n l y one s t r o n g peak i s found i n each r e g i o n , a g a i n w i t h a weak satellite.  The d o u b l e t s c o a l e s c e i n t o a s i n g l e peak d u r i n g  warm-up. I n Table 6 t h e observed f r e q u e n c i e s a r e l i s t e d f o r gaseous SO2,  solid  S O 2 , S O 2 i n argon and n i t r o g e n m a t r i c e s and S 0 2 i n t h e  gas h y d r a t e .  39  TABLE 6.  I n f r a r e d A b s o r p t i o n o f SCvj ( f r e q u e n c i e s i n cm ''), -  SO2 Gas r e f e r e n c e (44)  518  Solid 80°K  Hydrate 80°K  521  s  528  sh  521  1151  H44.5 vs  v  I n Nitrogen 4°K  -  1035 II4I.8 m  s  I n Argon 4©K  -  1140.0 v  1148.8 s  1147.3 s  1145.0 u  1152.1 s  1152.6 s  1334.3 u  1334.8 w  1342.5 vs  1351.4 vs  1346.7 s h  1349  1355.6 v s  1351.8 vs  1305.5 s 1312.0 vs 1325.0 vs  1362  1326  w  1336  sh  sh  4-1  3-5  Gas H y d r a t e s . The s k e l e t a l water spectrum o f SC>2 and k r y p t o n h y d r a t e s i s  compared w i t h t h e spectrum o f i c e i n F i g . 18.  The c o r r e s p o n d i n g  f r e q u e n c i e s , w h i c h a r e t a b u l a t e d i n T a b l e 7, a r e t h e averages o f s e v e r a l runs.  Due t o t h e u n c e r t a i n t y i n l o c a t i n g t h e maxima o f  t h e s e broad bands, the. f r e q u e n c i e s i n Table 7 a r e a c c u r a t e o n l y t o _ 10 cm '. I n s p i t e o f t h i s however, F i g . 18 c l e a r l y shows _-i  s h i f t s o f t h e peaks a t 820 and 1600 cm" i n t h e spectrum o f i c e t o 780 and I64O cm '' i n t h e SO2 h y d r a t e , and a new peak a t -  2420 cm '' i n t h e k r y p t o n and SOg h y d r a t e s i s , a l s o e v i d e n t . -  The  frequencies a s s o c i a t e d w i t h the S O 2 molecule  h y d r a t e and t h e s o l i d a r e compared i n F i g . 19d i f f e r e n c e s a r e found f o r each o f t h e t h r e e The  V 3 r e g i o n o f SOg d u r i n g a n experiment  i n the  Significant  fundamentals. i n which S O 2 hydrate  was formed a t 80°K c o o l e d t o 4°K and rewarmed t o 120°K, i s p r e s e n t e d i n F i g . 20.  The c e n t r a l peak a t 1340 cm  i s seen t o  have two s h o u l d e r s a t 120°K, one o f w h i c h i s n o t p r e s e n t a t 4°K.  42  TABLE 7.  S k e l e t a l Water Spectrum i n t h e Gas Hydrates a t 8G°K ( f r e q u e n c i e s i n cm ''). -  Ice  S0 .6H 0  Kr.6H 0  H S.6H 0  820 s  780 s  820 s  815 s  1600 m  1640 m  1610 m  1620 m  2220  2220 •w2410 vw  2210 2420 w  2190 VI  3230 vs  3260 vs  3230 vs  2  2  2  2  2  -  _  Assignment  4-3  fig  fig  18.  19.  44  f i g 2 0 .  _i  1300  \  i  1  1310  1320  1330  FREQUENCY (cm ) -1  1—  1340  45  CHAPTER A.  4-1  THEORETICAL.  I n t r o d u c t o r y Remarks. The c a l c u l a t i o n s d e s c r i b e d i n t h i s c h a p t e r f a l l i n t o t h r e e  categories: (i)  C a l c u l a t i o n o f s h i f t s o f v i b r a t i o n a l f r e q u e n c y due t o i n t e r a c t i o n s between s o l u t e  (ii)  Calculations  of perturbation  l e v e l s of i s o l a t e d solute (iii)  and m a t r i x .  energies f o r r o t a t i o n a l  molecules.  C a l c u l a t i o n o f s h i f t s o f v i b r a t i o n a l f r e q u e n c y due t o m u t u a l i n t e r a c t i o n s between p a i r s o f s o l u t e molecules i n nearest neighbour, next nearest neighbour, e t c . , s i t e s i n the l a t t i c e .  The f o r m u l a e and r e s u l t s developed i n t h i s c h a p t e r w i l l be applied  4-2  i n Chapter 5 t o t h e i n t e r p r e t a t i o n o f t h e observed  spectra.  S h i f t s o f V i b r a t i o n a l F r e q u e n c i e s Due t o M a t r i x - S o l u t e Interactions. The energy o f i n t e r a c t i o n between a s o l u t e m o l e c u l e and t h e  s u r r o u n d i n g m a t r i x i s made up o f t h e sum o f t h r e e terms  0  =  (45):  0 (ind) + 0 (dis) + 0 (es)  (l)  A f o u r t h t e r m s h o u l d be added t o Eq. ( l ) t o t a k e account o f r e p u l sive forces.  However, t h i s e f f e c t w i l l be t r e a t e d  empirically  later. The i n d u c t i o n  energy 0 ( i n d ) may be e s t i m a t e d from t h e  energy o f i n t e r a c t i o n between t h e permanent charge d i s t r i b u t i o n o f one m o l e c u l e and t h e moments i n d u c e d i n t h e o t h e r .  The term 0 ( d i s )  46  i s the London d i s p e r s i o n energy and represents the i n t e r a c t i o n between the two induced charge d i s t r i b u t i o n s .  The t h i r d term,  0 (es) i s the purely e l e c t r o s t a t i c i n t e r a c t i o n energy between the permanent charge d i s t r i b u t i o n s .  The e l e c t r o s t a t i c energy i s zero  f o r the rare gas matrices, but i s non-zero f o r nitrogen which has an e l e c t r i c quadrupole moment. The i n d u c t i o n p o t e n t i a l i n the case of the nitrogen or rare gas matrices i s given by (45): 0 (ind) = -pi  oL (icos 6  1  G •+• \)/[ 6  (2)  r  . where: 0(5 i s the p o l a r i z a b i l i t y of the matrix atom, /4a. i s the dipole moment of the solute molecule, -r i s the i n t e r n u c l e a r distance i n the s o l i d rare gas, and Q i s the angle between the z a x i s (chosen as a cube a x i s ) and the axis of the dipole (the molecular a x i s ) . By considering the average i n t e r a c t i o n , the angular part of Eq. (2) gives a c o n t r i b u t i o n of +2 regardless of the o r i e n t a t i o n of the solute molecule.  The rare gases c r y s t a l l i z e with the cubic  close-packed structure (46), and the Lennard-Jones' sum f o r an inverse s i x t h power p o t e n t i a l f o r t h i s l a t t i c e i s 14.45  (47).  This sum gives the e f f e c t i v e number of nearest neighbours, and takes account of i n t e r a c t i o n s between the i s o l a t e d solute molecule and the rare gas atoms or nitrogen molecules i n the whole l a t t i c e . Hence Eq. (2) becomes:  0 (ind) = -14.45 JUJ QCj, T  6  which gives r i s e t o a frequency s h i f t given by:  (3)  47  A V  -14.45  (ind) =  AC"l) r  where:  For  t  f  oCb  =  C,  (4)  ^ Of*)  he  /I (f^a.) i s t h e change i n t h e square o f t h e d i p o l e moment between t h e ground and f i r s t e x c i t e d v i b r a t i o n a l states. t h e n i t r o g e n m a t r i x , t h e r e w i l l be a d d i t i o n a l terms i n  the p o t e n t i a l i n v o l v i n g t h e e l e c t r i c quadrupole o f t h e n i t r o g e n molecule;  however, t h e c o n t r i b u t i o n  from t h e s e terms w i l l be much  s m a l l e r t h a n Eq. (4) and t h e y c a n be n e g l e c t e d . An approximate e x p r e s s i o n f o r t h e d i s p e r s i o n  energy i s  g i v e n b y (45):  0 (dis) =  where:  (  (5)  •)  C^a. and 0^4 a r e t h e p o l a r i z a b i l i t i e s o f t h e s o l u t e m o l e c u l e and m a t r i x atom o r m o l e c u l e , and E a n d E are a p p r o x i m a t e l y e q u a l t o t h e i r r e s p e c t i v e i o n i z a t i o n energies. a  Eq.  (8) may be used t o e s t i m a t e t h e d i s p e r s i o n  f e  contribution  to the s h i f t i n v i b r a t i o n a l frequency o f a solute molecule, i n the f o l l o w i n g way.  B o t h t h e p o l a r i z a b i l i t y and t h e i o n i z a t i o n  potential  o f t h e s o l u t e m o l e c u l e change d u r i n g a v i b r a t i o n a l t r a n s i t i o n .  /(dis)  = -  \f*}°-  (6)  C  a  0 (dis) =  where;  ^  Thus:  _ '/  (7)  =  t h e double prime denotes t h e ground v i b r a t i o n a l s t a t e and t h e s i n g l e prime t h e f i r s t e x c i t e d v i b r a t i o n a l state. The c o n s t a n t 02.= 3° 4 ^6 /iT <  6  48  Subtracting Eq. (7) from Eq. (6) we get:  </>—</> -  -  O^a  Ci  Ot-a.  Ea.  tig.  (8)  ¥e again introduce a f a c t o r of I 4 . 4 5 t o account f o r the i n t e r a c t i o n of the solute molecule w i t h the e n t i r e matrix.  The  d i s p e r s i o n c o n t r i b u t i o n t o the s h i f t of v i b r a t i o n a l frequency i s given by: " c " E«  (9)  +£(>  In the case of the nitrogen matrix the e l e c t r o s t a t i c term c o n s i s t s of a dipole-quadrupole i n t e r a c t i o n given by ( 4 5 ) :  cos & O£os & -l)  -25>n<9«Sw6b  2  a  where:  b  COSC^f^- tfb) (10)  i s the quadrupole moment of N , i s the dipole moment of the solute molecule, 9<^, 9 t , 0 , 0b, are the polar angles associated w i t h the dipole (HC1 or HBr) and the quadrupole ( N ) , and v i s the nearest neighbour distance i n the s o l i d matrix. 2  a  2  The average of the angular terms i n Eq. (10) i s zero; however, i n the case of n i t r o g e n , the symmetry of the s u b s t i t u t i o n a l s i t e i s not s p h e r i c a l and the e l e c t r o s t a t i c i n t e r a c t i o n .is not expected t o vanish. 0(es)  An estimate of the order of magnitude of  may be obtained by assuming maximum i n t e r a c t i o n which leads  to a value of ~^//^  P  e r  nitrogen molecule regardless of the  49 (20).  o r i e n t a t i o n o f t h e s o l u t e molecule  N i t r o g e n below 35°K  s t r u c t u r e (4-8), and t h e  c r y s t a l l i z e s i n a cubic close-packed  Lennard-Jones' sum f o r an i n v e r s e f o u r t h power p o t e n t i a l i n t h i s l a t t i c e i s 25.34 (47).  E q . (10) now becomes:  and t h e s h i f t i n v i b r a t i o n a l f r e q u e n c y o f t h e ' s o l u t e , i s g i v e n b y :  _  fiV (es)  l ™  0  / ^ *  Q  t>  =  A/^a  (12)  where: A / ^ a . i s t h e change i n d i p o l e moment between t h e ground ana f i r s t e x c i t e d v i b r a t i o n a l s t a t e s . I n Table 8, t h e c o n s t a n t s i n Eqs.  (4)> (9) and (12) a r e  e v a l u a t e d f o r argon, k r y p t o n and n i t r o g e n m a t r i c e s , u s i n g t h e v a l u e s o f p o l a r i z a b i l i t y , i n t e r n u c l e a r d i s t a n c e , e t c . , f r o m Appendix I . TABLE 8. V a l u e s o f Constants  Formula  i n Calculations of Matrix S h i f t s .  AV(fod)  A V (dis)  f \ Cl  Expression f o r the c o n s t a n t Units o f C  14.. 45  oC  h  [  Oi'd Ea.  Ay(es) -C  z  21.68 E i , oC b  17.00 0.4  -3 J  -2 esu  cm +  -2 -1 cm e s u  -;l  Ar  3.76 x 10  1.42 x 10  -  Kr  3.95  x 10  1.32 x 10  -  N  3.17  x 10  1.18  2  Apcu  he  cm  x 10  5.03  -  x 10  50 4-3  Rotation of Molecules Trapped i n S o l i d Rare Gases. Schoen et a l (8) assumed that the solute molecule was  confined i n a f i e l d o f c y l i n d r i c a l symmetry.  The p o t e n t i a l b a r r i e r  to r o t a t i o n was taken as C1(1-COS 9) where  i s the b a r r i e r height  2  and 6 the angle between the molecular axis and the c y l i n d e r a x i s . Using t h i s model f o r HC1 i n argon, these workers p r e d i c t e d a three l i n e spectrum corresponding t o R(0), P(1) and R*(1), where R*(1) i s due to a blend of t r a n s i t i o n s o f the hindered r o t a t o r . The p o t e n t i a l f u n c t i o n used by Schoen et a l i s e s s e n t i a l l y that used by Pauling ( I 4 ) ;  V (1-cos 2 9 ) ^ f o r a diatomic molecule  rotating i n a cylindrical well. Armstrong (12) i n v e s t i g a t e d the e f f e c t of e l e c t r o s t a t i c i n t e r a c t i o n s on the r o t a t i o n a l energy l e v e l s o f an i s o l a t e d solute molecule trapped i n a rare gas l a t t i c e at low temperatures.  He  concluded that these i n t e r a c t i o n s produce no e f f e c t on the r o t a t i o n a l energy l e v e l s of the solute molecule, and h i s expression f o r the i n t e r a c t i o n energy i s very s i m i l a r t o the sum of Eqs. (6) and (8) of the previous s e c t i o n .  Armstrong also considered dipole-dipole  i n t e r a c t i o n s between the solute molecules.  For a diatomic molecule  i n a s o l i d rare-gas h i s r e s u l t s i n d i c a t e t h a t a s l i g h t mixing o f r o t a t i o n a l states occurs, the J = 2 l e v e l being the f i r s t l e v e l t o be s p l i t . More r e c e n t l y Flygare (11) presented a theory d e a l i n g w i t h the same problem.  This author agrees w i t h Armstrong t h a t the  t V (1-cos 26) = 2V  sin e 2  =  C (1-COS 9) 1  2  51  dipole-induced  dipole term does not e f f e c t the r o t a t i o n a l energy,  but goes on to show that higher m u l t i - p o l a r i n t e r a c t i o n s can be responsible f o r the r o t a t i o n a l perturbations experienced by the solute molecules. A l l the above authors ignore exchange i n t e r a c t i o n s a r i s i n g from overlap of e l e c t r o n i c charge d i s t r i b u t i o n s of the solute molecule and surrounding matrix atoms.  The r e p u l s i v e exchange  forces would give r i s e to a "blue" s h i f t of the v i b r a t i o n a l frequency, whereas a "red" s h i f t i s u s u a l l y observed.  However, i t  i s possible that the e f f e c t of the r e p u l s i v e i n t e r a c t i o n s i s undetected because the a t t r a c t i v e e l e c t r o s t a t i c forces give r i s e to a large "red" s h i f t of the v i b r a t i o n a l frequency. The f o l l o w i n g c a l c u l a t i o n s are based on the assumption that the i s o l a t e d solute molecule experiences r e p u l s i v e forces i n a d d i t i o n to a t t r a c t i v e forces which perturb the r o t a t i o n a l energy levels.  4-4  The Hindered Rotator P o t e n t i a l . In t h i s section a p o t e n t i a l w i l l be developed f o r the case  of a hydrogen h a l i d e molecule surrounded by twelve nearest neighbour matrix atoms.  The model used f o r the c a l c u l a t i o n assumes that the  hydrogen h a l i d e molecule rotates about i t s centre of mass which i s taken to be at the nucleus of the halogen atom."!" We also assume that the molecular centre of mass i s on a l a t t i c e p o i n t , which i s not s t r i c t l y t r u e .  In f a c t , the centre of volume of the molecule  t The a c t u a l C.O.M. of HG1 i s 0.035A from the chlorine nucleus; t h i s may be compared with the Internuclear distance i n HG1 1.275A.  52  • w i l l more p r o b a b l y be on a l a t t i c e p o i n t .  However, i t may be  shown (4-9) t h a t r e g a r d l e s s o f t h e c h o i c e o f o r i g i n , t h e a n g u l a r dependence o f t h e p o t e n t i a l w i l l be t h e same. A u s e f u l m a t h e m a t i c a l form f o r an i n t e r a c t i o n p o t e n t i a l which includes  repulsive  and a t t r a c t i v e f o r c e s  i s the Lennard-  Jones' (6-12) p o t e n t i a l (50)z  V(r)  =  €  (U)  (  where: Tyi i s t h e i n t e r n u c l e a r d i s t a n c e o f t h e i n t e r a c t i n g atoms, -Co i s t h e i n t e r n u c l e a r d i s t a n c e a t w h i c h t h e p o t e n t i a l i s a minimum, and <£<? i s t h e depth o f t h e p o t e n t i a l minimum. Eq.  (14) may be r e w r i t t e n a s :  Ver) = V T -  -VoTyi  0  where:  •t=l 2,.-,/2. J  and VC =  Vo = €<>  (15)  l^ofo^  The m a t r i x - h a l o g e n i n t e r a c t i o n s w i l l be d i f f e r e n t from t h e m a t r i x hydrogen i n t e r a c t i o n s , and V  0  and V' w i l l n o t be t h e same f o r t h e 0  two c a s e s . The c o - o r d i n a t e system u s e d i n t h e f o l l o w i n g c a l c u l a t i o n i s i l l u s t r a t e d i n F i g . 2 1 . The d i s t a n c e  T j i between t h e n u c l e u s o f  the h a l o g e n atom and each o f t h e t w e l v e n e a r e s t n e i g h b o u r m a t r i x atoms i s e q u a l t o t h e i n t e r n u c l e a r and  distance i n the s o l i d r a r e gas,  e q u a t i o n (15) g i v e s : V ( r ) = 12 V where:  r - ' - -12 V</ r - 6 2  c  r i s the i n t e r n u c l e a r  (16)  d i s t a n c e i n t h e s o l i d r a r e gas.  53  fig  21.  CO-ORDINATE HINDERED  SYSTEM  ROTATOR  U S E D  FOR  POTENTIAL  T H E  54  Thus, the h a l o g e n - m a t r i x  i n t e r a c t i o n s g i v e r i s e t o an a n g l e -  independent term i n t h e p o t e n t i a l w h i c h we w i l l c a l l V . For t h e h y d r o g e n - m a t r i x  i n t e r a c t i o n s t h e p o t e n t i a l has an  a n g u l a r dependence, s i n c e t h e i n t e r n u c l e a r d i s t a n c e s 7*j i  depend on  6 and 0 (see F i g . 2 l ) . The T|£ may be e v a l u a t e d u s i n g t h e  formula  o f a n a l y t i c a l geometry:  TU-  J(x.-*y*(y--yy*fy-P  w h i c h l e a d s t o e x p r e s s i o n s o f the  r , i = r / |  where:  4  t  ^  ( 1 7 )  form:  f(ej)  ~  (is)  d i s the i n t e r n u c l e a r d i s t a n c e i n the s o l u t e molecule and -f (erf) i s a f u n c t i o n o f 9 and 0.  A t y p i c a l Y\l  r,  + ^  z  = rj\  ^-  s:  +  +  ~ ^ (sinQ Si"* -Cos ©)  2  F u t u r e c a l c u l a t i o n s w i l l be s i m p l i f i e d i f we n e g l e c t d / r  2, o  to  compared  1. T h i s i s a poor a p p r o x i m a t i o n s i n c e d / r * f o r HC1 i n argon  i s 0.111. to  2  ( 1 9 )  The square r o o t may be expanded by t h e b i n o m i a l theorem  give: (20)  55  Again we neglect terms i n d V S and higher powers.  By t h i s  R  procedure the y, ' are found to be: t  yz plane  V ( \ ± CCOS& ± C $'» 6> 6<>S <j> )  xz plane  7- £ / ± £ COS 6  xy plane  y  where:  ±  ± Ct\»6CO$p  C  0 St" 4)  ± CSl*6  (21) \  2r  On s u b s t i t u t i n g the values of  "f,' i n t o Eq. (15) we get twelve L  terms of the form: (22)  where:  x = c-f(efi)  Expanding the inverse t w e l f t h and inverse s i x t h power terms by the binomial theorem gives:  L  2»  -  1  (23)  I t i s necessary to take the inverse t w e l f t h power expansion up to the s i x t h power of x because the binomial c o e f i c i e n t s are l a r g e , and ( ^ / r )  n  does not decrease r a p i d l y enough w i t h n.  However, f o r  the inverse s i x t h power expansion, only the terms up to the f o u r t h power of x are important.  56  When the twelve expressions f o r x are s u b s t i t u t e d i n Eq.23, and a f t e r much s i m p l i f i c a t i o n , the expression f o r V(00) becomes:  V (e f) = v. + V + i/j Cose sin e + VV sin+e cos*d> sm 0 z  ^^  z  2  + V$ Si» e 6  COS 0 S'm <fi l  z  •where:  • VI  2  0  (\7.+$*  -\l\Joy-  Mi  -  V  =Cf/i + /8»Vor-  3  with  = 12V T - - '  + H-j8  Vo-F -(i^  2  682.5. dVr^-  ^ =  1547  In Eq. (24),  +  +4-5 +4-*$)  U  oC = 78 dVr A=  6  T-  / 2  o~ = 21 ' T=  dVr  Vox'  6  6  2  63 d % * -  d%« w i l l give r i s e t o a constant p e r t u r b a t i o n which  a f f e c t s a l l r o t a t i o n a l energy l e v e l s e q u a l l y and thus w i l l not e f f e c t the r o t a t i o n a l s t r u c t u r e of the spectrum of the solute molecule. Hence the angle dependent p o t e n t i a l V (60) may be w r i t t e n :  V(e<p) - V3 cos©sin^e + (\4  s'm^e + V sm e) 6  s  Cos'tp s'tfy  (25)  The p o t e n t i a l given by Eq. (25)^may be considered as a p e r t u r b a t i o n and may be used to c a l c u l a t e c o r r e c t i o n s t o the energy l e v e l s of the hindered r o t a t o r . 1" I t has been p o i n t e d o u t (49) t h a t the p o t e n t i a l , Eq.24, does n o t have the symmetry o f the o c t a h e d r a l s i t e , due t o the i n c l u s i o n o f s i x t h power terms. A l t h o u g h t h i s i s i n c o n s i s t a n t w i t h the treatments o f p r e v i o u s workers (11,13) the r e s u l t s are expected t o be q u a l i t a t i v e l y correct.  57 4-5  C a l c u l a t i o n of Energy Levels of the Hindered Rotator. From p e r t u r b a t i o n theory (51), the f i r s t order energies  f o r a degenerate l e v e l E  are the roots of a secular determinant.  y  The number of rows and columns of the determinant i s 2 J + 1, the degeneracy o f the l e v e l E  CO  v  Such a determinant may be w r i t t e n :  ( 1  V i< Z  (26)  Vol!  - E  0>  w i t h v ^ = <<n/ v where V i s the p e r t u r b a t i o n and tyi , f-A normalized orthogonal wave functions belonging t o the unperturbed degenerate l e v e l E * . The corrected energy l e v e l s are given by: a r e  c  E  ;  (27)  7M  In the case of a diatomic molecule, the normalized s p h e r i c a l j are the zero order r o t a t i o n a l wave f u n c t i o n s . The f i r s t order c o r r e c t i o n s are given by: 0  J = 1  .0)  (28)  (V„ - E,„)  V  IS =  V 31  0  (29)  58  V  where:  =  U  with  < Y * \ \ / < * 4 » l  M;, M^=  J = 2  )  V  V,,  V  (30)  Y^>  1, 0, -1  V,  Vi3  i a >  (V  I  4-  W>  E  0  (31)  32  V«r  5  (32)  where;  with  M;,  =  2, 1, 0, - 1 , -2.  A l l o f f diagonal terms i n Eqs. (2.9) and (31) vanish because they a l l involve i n t e g r a l s of the form: .TT  exp + i n 0 d 0 ' = O  (n = a r e a l non-zero i n t e g e r )  J o  A f u r t h e r s i m p l i f i c a t i o n r e s u l t s from the property  — + ^ Yj** ° 1s  a) i) i tn io  E  E  *^^ ^ ^  t h a t Eqs  t  £"!, = < Y ! E  |v<«^iY!>  Z,I  E  II)  2,0  <Yr|vt-e^/ y ° >  29  and  31  give:  59  The n o r m a l i z e d s p h e r i c a l harmonics  f o r J = 0, 1 and 2,  are ( 5 1 ) :  Y Y;  o  (  —  The  )  *  Sine  \/o  Y  4-F  (  ° -  3  A  \ x  COS 0  Y  <r<?5 0  (if?) * ^ ° ' s  fine -e  -0  e  and t h e p e r t u r b i n g p o t e n t i a l V (9 0)  from E q . (25)  (i) were s u b s t i t u t e d i n t o t h e e x p r e s s i o n s f o r E the r e s u l t i n g i n t e g r a l s e v a l u a t e d . standard i n t e g r a l s  T(W)  . . from E q s . (33) and  Use was made o f t a b l e s o f  (52) i n t h e e v a l u a t i o n o f t h e E  T M  .  The f i r s t o r d e r e n e r g i e s were found t o be i d e n t i c a l f o r the J = 0 and J = 1 l e v e l s , but s m a l l s p l i t t i n g s o f t h e J = 2 l e v e l s were f o u n d .  N u m e r i c a l r e s u l t s were o b t a i n e d u s i n g  v a l u e s f o r t h e c o n s t a n t s T" and d . f  accepted  - 3-83 A f o r s o l i d argon (4-5),  d = 1.275 A f o r HG1 (38) and d = 1.4.20 A f o r HBr ( 3 9 ) . The r e s u l t s are t a b u l a t e d i n Table 9. To c a l c u l a t e t h e r o t a t i o n a l energy l e v e l s f o r HG1 and HBr, v a l u e s must be a s s i g n e d t o t h e c o n s t a n t s K, and  o f Table 9.  Reasonable f i r s t o r d e r c o r r e c t i o n s t o t h e r o t a t i o n a l e n e r g y l e v e l s are o b t a i n e d by g i v i n g 7 " / _  t h e v a l u e 0.85 and 6  Q  t h e v a l u e 10cm""''.  60 TABLE 9. F i r s t Order Energies f o r the Hindered Rotator.  E'(J,M)  HC1  (J,M)  HBr  (00) 12.7K,- 0.62K  (1,0)  21.8K,- 0.95 K  2  x  (1,+ 1) (2,0)  9.50K,- 0.44K*  16.4K, - 0.68K  (2,± 1)  U.8K,- 0.73K  25.5K,- 1.13K  (2,+ 2)  12.2K,-  where  o K, = V,  2  20.9K,-  0.59K2.  0.91K  2  t  t  and K = 2  Using these a r b i t r a r y values the constants K, and K were found to be 1.4-2 cm ^ and 3.77 cm'' r e s p e c t i v e l y . -  -  %  The f i r s t  order energies were c a l c u l a t e d , and are l i s t e d i n column two of Table 10. Since we are only i n t e r e s t e d i n energy d i f f e r e n c e s , E*(0,0)  i s set equal t o zero, and the other f i r s t order energies  are given r e l a t i v e t o  E'(0,0).  The unperturbed r o t a t i o n a l  energies f o r the ground v i b r a t i o n a l state are given by: E'J  where:  =  B"J(J+1)  -D"J(J+1)  (35)  B " and D " are the r o t a t i o n a l constants f o r the ground vibrational state,  and have been tabulated i n references (38) and (39) f o r HC1 and HBr r e s p e c t i v e l y .  The hindered r o t a t i o n a l l e v e l s are l i s t e d i n  column three of Table 10 and the l a s t three columns give the r e l a t i v e populations of the energy l e v e l s at 5°, 1 0 ° and 20°K  61  using the formula: N(J,M) where:  =  N(0,0)  g exp - E(«T,M)/kT  (36)  N(J,M) i s t h e number o f m o l e c u l e s i n t h e l e v e l (J,M), N(0,0) i s a r b i t r a r i l y s e t e q u a l t o one ; g i s t h e degeneracy o f t h e l e v e l ; k, t h e Boltzmann c o n s t a n t , and T, t h e a b s o l u t e temperature. 1  I t s h o u l d be n o t e d t h a t t h e r e s u l t s o f t h e above c a l c u l a t i o n are o n l y q u a l i t a t i v e i n n a t u r e , owing t o the•many assumptions and approximations  made. TABLE 10.  H i n d e r e d R o t a t i o n a l E n e r g y L e v e l s and P o p u l a t i o n s f o r HC1 and HBr i n Argon. (a) HG1 level J,M  0. 0 1,0 1, +1 2,0 2, +1 2,+2  1 s t Order Energy E ( J , M ) cm-1 7  0.0 0.0 0.0 -3.8 +2.6 -0.6  Corrected Energy L e v e l cm-1  0.0 20.9 20.9 58.8 65.2 62.0  Relative Population 5°K 10°K 2QOK  1 .002 .004 -  1 .05 .10 -  1  .22 .44 .01 .02 .02  (b) HBr Level J,M 0. 0 1,0 1, ±1 2,0 2, ±1 2,+2  1 s t Order Energy E'(J,M) c u r l 0.0 0.0 0.0 -6.6 +4.6 -1.1  C o r r e c t e d Energy L e v e l cm -1  0.0 16.7 .16.7 43.6 54-8 49.1  Relative Population 5°K 10°K 20OK 1 1 1 0.008 0.09 0.016 0.18 0.001 0.002 0.002  0.30 0.61 0.03 0.06 0.06  62  4-6  S h i f t s Due to Solute-Solute I n t e r a c t i o n s . In t h i s s e c t i o n , i n t e r a c t i o n s between solute molecules i n  nearest neighbour, next nearest neighbour, e t c . s i t e s w i l l be considered. The p o t e n t i a l energy of i n t e r a c t i o n between two i d e a l dipoles i s given by ( 4 5 ) :  - 2 c o s e c o s e -Sino b  a  a  Sme Cos (<j> -<f>*)(37) b  b  At low temperatures, where <j> i s greater than kT, the dipoles ab  are assumed t o be aligned t o give maximum a t t r a c t i o n . 0  b  = 0  and Q = 6 b  That i s ,  ; Eq. (37) then becomes:  a  The maximum value of Eq. (38) i s obtained when Q= 0, hence A>  = _  Mb  ( 3 9 )  The s h i f t i n v i b r a t i o n a l frequency f o r the case of i n t e r a c t i o n between l i k e dipoles i s then given by:  (40) &b where: /[ (jj}) i s the change i n the square of the dipole moment during a t r a n s i t i o n from the ground state t o the f i r s t excited v i b r a t i o n a l s t a t e .  63  For the case of i n t e r a c t i o n between u n l i k e d i p o l e s :  Values of the constant C. i n Eqs. (40) 4  i n Table 11 f o r various values of Tab  and (4I)  are tabulated  encountered i n the cubic  l a t t i c e s of argon, krypton and nitrogen, assuming that the dipoles are trapped on s u b s t i t u t i o n a l s i t e s i n the l a t t i c e . Other terms i n the i n t e r a c t i o n energy between p a i r s of dipoles could be included. sion forces.  These a r i s e from i n d u c t i o n and d i s p e r -  However, the intermolecular p o t e n t i a l s due to these  e f f e c t s both involve the inverse s i x t h power of the intermolecular distance, and even f o r the case of contiguous solute molecules, the c o n t r i b u t i o n to the s h i f t of v i b r a t i o n a l frequency i s n e g l i g i b l e . TABLE ,11. Values of the constant of 10^7  r  ab  Argon  esu  i n Eq.(40) i n u n i t s - 2  cm . -3  Krypton  Nitrogen  17.92  15.27  15.85  J2v  6.34  5.40  5.60  /3r  3.45  2.94  3.05  2.24  1.91  1.98  64 CHAPTER 5.  5-1  DISCUSSION.  C l a s s i f i c a t i o n of Peaks i n the Matrix Spectra of HC1 HBr.  and  The observed peaks i n the matrix spectra can be c l a s s i f i e d according to t h e i r behaviour under various conditions. examination  of the spectra of HC1  (Figs. 5-7)  Closer  and HBr (Figs. 13-15)  reveals that the observed peaks f a l l i n t o four groups: (i)  Peaks which are present at a l l matrix to solute r a t i o s , whose i n t e n s i t i e s r e l a t i v e to other peaks i n the spectrum increase w i t h d i l u t i o n .  (ii)  Peaks which are present at low matrix to solute r a t i o s whose i n t e n s i t i e s r e l a t i v e to group ( i ) decrease with d i l u t i o n .  (iii)  Peaks which appear during warm-up s t u d i e s .  (iv)  Peaks which are only present when other solutes are included i n the mixtures.  D i v i s i o n of peaks i n the spectra of HC1 and HBr among the f i r s t three categories i s made i n Table  12.  The behaviour with d i l u t i o n of the four most important peaks i n the spectra of HBr and HG1 i n argon, i s i l l u s t r a t e d g r a p h i c a l l y i n F i g . 22.  In the case of HBr, i t i s seen t h a t ,  r e l a t i v e to the peak at 2569 cm '', the i n t e n s i t y of the peak at -  2550 cm"'' remains constant, while those at 2496 and 2465 cm'' -  decrease w i t h d i l u t i o n .  A s i m i l a r s i t u a t i o n i s found f o r HC1 where  the i n t e n s i t y of the peak at 2853 cm'' -  2889 cm'' -  r e l a t i v e to the peak at  remains constant, while those at 2817 and 2787.5  cm'' -  65  TABLE 12. C l a s s i f i c a t i o n of Observed Peaks i n the Spectra of HC1 and HBr i n argon.  Group ( i )  Group ( i i )  Group ( i i i )  2749* 2761* . 2787  2787  2817 2853 HC1  2863 2867 2889 2900 sh  2426* 24362450* 24.65 2496  HBr 2550  2558 2569 2575 sh  "These peaks were only observed during warm-up and were not  !:  p r e v i o u s l y included i n Table 1.  fig  22.  C H A N G E WITH  i \0O  loo  O F  P E A K  INTENSITY  DILUTION  i 100 ,  200  i  i  30O  *tOO  matrix  to  joo  koo  matrix  to  i  500  solute  SOO  solute  i 60O  i too  i $00  ratio  600  ratio  ,700  0OO  67  decrease r a p i d l y on d i l u t i o n . I t seems reasonable to assume that peaks i n the f i r s t category are due to i s o l a t e d HC1 or HBr molecules.  These peaks would be the  only ones observed i n studies of very d i l u t e mixtures c a r e f u l l y deposited to minimize the p o s s i b i l i t y of d i f f u s i o n of solute molecules. I t i s suggested that i n t e r a c t i o n s between p a i r s of solute molecules i n contiguous and other adjacent s i t e s , as i l l u s t r a t e d i n F i g . 23, account f o r the peaks which decrease i n i n t e n s i t y w i t h d i l u t i o n . P r o b a b i l i t i e s f o r f i n d i n g such p a i r s at various matrix to solute r a t i o s have been c a l c u l a t e d (53) assuming a random d i s t r i b u t i o n of solute molecules on s u b s t i t u t i o n a l s i t e s i n a cubic close-packed crystal. For the peaks which only appear during warm-up, a s i m i l a r explanation i s offered.  In t h i s case, however, i n t e r a c t i o n s  between more than two solute molecules are suggested.  Such  i n t e r a c t i o n s are expected to be important during warm-up, since d i f f u s i o n of the trapped molecules would enable t r i p l e and l a r g e r c l u s t e r s to be formed.  At temperatures close t o the melting point  of the m a t r i x , peaks appear i n the region of s o l i d HG1 or HBr. From the work of Hornig and h i s co-workers (54-,55,56), i t i s reasonable to assume that these peaks are due to hydrogen-bonded chains of varying length. In many cases i t was possible to resolve peaks i n the spectrum of HG1 i n t o doublets due to the HCl35 and HCl^? i s o t o p i c molecules.  I t i s perhaps s i g n i f i c a n t that c e r t a i n other peaks i n  the same spectrum remained unresolved under the same conditions of high r e s o l u t i o n .  These peaks were u s u a l l y broader than the  68  fig  23.  CLOSE  - P A C K E D - C U B I C  S T R U C T U R E  showing  first, second , third  nearest  neighbour  (a)  o  i  j  J-—O-T—>—O O  v  &  fourth  positions  (b)  0  —O  (0  (d)  69 resolvable ones and often corresponded to the group ( i ) peaks. However, the problem of s c a t t e r i n g w i t h the consequent l o s s of r e s o l u t i o n makes t h i s l a t t e r c l a s s i f i c a t i o n u n c e r t a i n .  5-2  I s o l a t e d Solute Molecules. The observed i n f r a r e d spectra of HC1 and HBr i n s o l i d  matrices, i n d i c a t e that the s t a t i s t i c a l l y predicted i s o l a t i o n of solute molecules (57) was never achieved under the experimented conditions employed i n t h i s work.  However, i s o l a t i o n approaching  the s t a t i s t i c a l values was u s u a l l y obtained when high matrix to solute r a t i o s were used. The three peaks which are assigned to HC1 molecules i s o l a t e d i n argon are; the very strong peak at 2889 cm '', the -  shoulder at 2900 cm'' and the peak of medium i n t e n s i t y at 2853 -  cm~^.  These three peaks make up a v i b r a t i o n - r o t a t i o n band centred a t 2871 cm'' which i s s h i f t e d by -13.5 cm"'' from the gas phase. -  A s i m i l a r s i t u a t i o n holds f o r HBr i n argon where the observed frequencies are: 2550, 2569 and 2575 cm''. The corresponding band -  centre i s at 2559.5 cm  , which represents a s h i f t from the gas  phase of +1 cm''. -  In a d i s c u s s i o n of the behaviour of i s o l a t e d solute molecules i n i n e r t matrices i t i s necessary to consider several e f f e c t s which, f o r the purpose of i n t e r p r e t i n g the observed i n f r a r e d spectra, w i l l be considered separately under the headings of v i b r a t i o n and r o t a t i o n . I n the f i r s t case, we examine the causes and e f f e c t s of perturbations of the v i b r a t i o n a l p o t e n t i a l f u n c t i o n of the molecule.  Under the  second heading, we consider the hindered r o t a t i o n of the i s o l a t e d  70  solute molecule. One could circumvent the problem of the observed gas-matrix s h i f t of the v i b r a t i o n - r o t a t i o n band centre by invoking a change i n the force constant of the solute molecule. (54)  Hornig and Osberg  estimated that the force constant of HC1 decreases from  4.81 md/A i n the gas to 4.31 md/A i n the s o l i d s t a t e .  A smaller  change i s expected going from gas to matrix, and f o r HC1 i n argon the c a l c u l a t e d value i s 4.73 md/A.  However, f o r HBr i n argon, a  s l i g h t increase i n the force constant i s necessary t o account f o r the observed frequency s h i f t .  Force constants f o r HBr and HC1 i n  various matrices are compared i n Table 13 using the expression: f ( m a t r i x ) = f (gas) ["V^^riag)"]  L y(gas)  2  J  TABLE 13. Force constants of HBr and HC1 i n various matrices.  Force Constant (md/A) State  HBr  HC1  gas  3.85  4.81  solid  3.45  4.31  argon matrix  3.85  4.77  krypton matrix  3.'SO  4.72  nitrogen matrix  3.75  4.64  71  One might also consider the anharmonicity  of the v i b r a t i o n  of the solute molecule i n a d i s c u s s i o n of the s h i f t of the v i b r a t i o n a l frequency.  An increase i n the anharmonicity  constant  6J«Xe -would r e s u l t i n a s h i f t to lower wave numbers, i n agreement w i t h experiment.  However, Vodar et a l (31) note that OJ^Xe f o r  HC1 or HBr decreases considerably i n the s o l i d state and as a r e s u l t , the change of We i s l a r g e r than the observed s h i f t .  It is  not p o s s i b l e , however, to discuss changes i n the anharmonicity  of  a matrix i s o l a t e d solute molecule without knowledge of frequency s h i f t s of overtone bands.  The i n t e n s i t y of the overtones of  HC1  and HBr were too weak to be observed i n the matrix work, because of the small amounts of m a t e r i a l i n the deposits studied. In the event that changes of force constants or anharmonic i t i e s could account f o r the observed v i b r a t i o n a l s h i f t s i n a consistant way,  the question of the o r i g i n of these e f f e c t s would  s t i l l remain unanswered.  A f a r more s a t i s f a c t o r y approach i s to  consider the perturbing forces which could e f f e c t the p o t e n t i a l f u n c t i o n of the solute molecule.  5-3  Intermolecular Forces Between Solute and Matrix. In s e c t i o n 4-2 we considered i n d u c t i o n , d i s p e r s i o n and  e l e c t r o s t a t i c e f f e c t s , a l l of which give r i s e to a "red" s h i f t of the v i b r a t i o n a l frequency.  To these three a t t r a c t i v e i n t e r -  actions we must add the r e p u l s i v e forces which produce a s h i f t i n the opposite d i r e c t i o n .  Repulsive forces are u s u a l l y ignored  (11, 12, 20), but Maki and Decius (58), van der Elsken (59) and Bryant and T u r r e l l (60) considered these forces i n t h e i r i n t e r -  72 p r e t a t i o n of spectra of ions i s o l a t e d i n a l k a l i h a l i d e l a t t i c e s . The observed s h i f t s of band centres f o r matrix i s o l a t e d HC1 and HBr, which are tabulated i n Table 14, can be expressed as a sum of four terms: AV Cobs) - AVCind)  +- AV(d*s) ±Av(es)  +Av(-rep)  ^  ( A V (es) being zero f o r the rare gases.)  TABLE 14.  Observed Band Centres of M a t r i x - I s o l a t e d HC1 and HBr.  Molecule  Gas Phase  I n Argon  I n Krypton  HC1 band centre* shift  2884-. 5 -  2871 -13.5  2856 -28.5  HBr band centre shift  2558.5 -  2559-5 +1  254-1 -17.5  ---mean value f o r H C l  I n Nitrogen 2833 -51.5 2525.5 -33  and HC1 .  3 5  37  ¥e w i l l now consider s h i f t s of the band centre of HC1 i n the various matrices.  The f i r s t term i n Eq. (42) i s given by Eq.4:  Av (ind)  = - C, A(H-l)  Values of the constant C have been tabulated i n Table 8, so t o (  evaluate  AV (ind) we need a value f o r the change i n the square of  the dipole moment during the v i b r a t i o n a l t r a n s i t i o n .  Benedict et  a l (61) have given a dipole moment f u n c t i o n f o r HC1:  a  + ^.(r-re)  + Mx(-r-r<,f+ ...  (43)  73  where:  M = M , = M = 0  2  1 .085 Debye 0.880 D/A 0.082 D/A 2  Values o f dyu/dr f o r the c r y s t a l l i n e hydrogen h a l i d e s have been reported by F r i e d r i c h and Person (62) and f o r HC1, djU/dr = 2.12 D/A. Neglecting the quadratic term i n Eq. (43), we obtain an A( )  expression f o r  /U,*-/U  = M *[ (  2 0  where:  l  r  Y  l  - r ^ -  to-r.)  1  ] + 2MoM,(^-r )  1  (44)  0  To and 7", are the i n t e r n u c l e a r distances i n HC1 f o r the ground and f i r s t e x c i t e d v i b r a t i o n a l s t a t e s , and f i s the e q u i l i b r i u m i n t e r n u c l e a r distance. e  For HC1 gas T = 1.275 A and ~T = 1.284 A from reference (38). e  0  To obtain an estimate of AC/* ) i n the matrix, we use the observed 1  s p l i t t i n g of the R(0) and P(1) peaks t o c a l c u l a t e *r, , assuming: V R(O) - V P ( 0 where:  = 4 8,  (45)  B, i s the r o t a t i o n a l constant f o r the f i r s t e x c i t e d vibrational state.  This i s a poor approximation s i n c e : V R(0) - V P ( D where:  =  2(B + B ) 0  (46)  (  B i s the r o t a t i o n a l constant f o r the ground s t a t e , 0  and probably also changes i n the matrix.  However, using Eq.(45)  we can obtain an order of magnitude f o r the i n d u c t i o n s h i f t . The observed value of V R(0) - V ^ O ) was 36 cm'' f o r HC1 i n both argon -  and krypton, and 38 cm"! i n the nitrogen matrix. -  Now y  t  i s given  by: T,  =  I  h  '  ^)  73a  In a p r i v a t e communication from D. F. Eggers J r . , i t was p o i n t e d out t h a t i n the above c a l c u l a t i o n ,  A V  Yi - T »  —^e  approximation  ( i . e . when  ).  However, the approach used  (58) g i v e s a non zero v a l u e f o r A V  by Maki and D e c i u s approximation.  ( i n d ) v a n i s h e s i n the harmonic  These workers f o l l o w the treatment  ( i n d ) i n any  adopted  i n chapter  4-2 as f a r as Eq. ( 3 ) .  (j>(ind)  Jul  _  =  Then, t o e s t i m a t e the e f f e c t upon the v i b r a t i o n a l f r e q u e n c i e s ^Xa. r e p l a c e d by square  \  (.^M /^Q  }o  a  ^  •  I  n  t  h  i  s  c  a  s  e  t  n  e  is  change i n the  o f the d i p o l e moment between the ground and f i r s t  excited  vibra-  t i o n a l s t a t e s i s g i v e n by:  (42 a)  where:  ^  }  denotes a quantum mechanical  mean v a l u e .  U s i n g the harmonic o s c i l l a t o r wave f u n c t i o n s we f i n d :  <Qf>-<a:> = -pfcs where: By  ~lS  0  i s t h e gas phase v i b r a t i o n a l frequency  substitution  o f E q . (42b) and E q .  s h i f t o f v i b r a t i o n a l frequency  A V  (ind)  =  (42a) i n t o E q . ( 3 ) , the  i s g i v e n by:  _  I^M  1  C  J, V°  where:  C, ,  i n cm~l.  i s the v a l u e i n Table 8.  (42c)  73b  (42d)  we  F i n a l l y , the v i b r a t i o n a l  AVf'  n c  O  and AV(WcL)  f i n d f o r HC1:  s h i f t s were found t o be:  =  - 1  '  5  c m - 1  — -1.2 c m  f o r  -1  A r and Kr, for N . 2  I t i s seen t h a t these s h i f t s are an o r d e r of magnitude l e s s those c a l c u l a t e d i n the anharmonic a p p r o x i m a t i o n . would appear  two  treatments  t o supplement each o t h e r , and i n s p i t e o f the i n a c c u r a c y o f  the p r e s e n t c a l c u l a t i o n , most important term. of HC1  The  than  i t seems t h a t the anharmonic c o n t r i b u t i o n i s the  I t i s u n f o r t u n a t e t h a t no d a t a on the overtone bands  i n the m a t r i x i s a v a i l a b l e at t h i s time s i n c e t h i s would g i v e  v a l u a b l e i n f o r m a t i o n on the a n h a r m o n i c i t y of the p o t e n t i a l  function.  74  where: h i s Planck's constant, c i s the v e l o c i t y of l i g h t and m the reduced mass f o r HC1. Hence T, = 1.38 A i n the rare gas matrices and 77 = 1.35 A i n nitrogen. and r j i n t o Eq. (44) together  S u b s t i t u t i n g the values of T , T e  0  w i t h a value f o r M, of 1.8 D/A f o r HC1 i n the matrix, we f i n d A (jji ) = 4 . 2 x 10 3'7 1  -  e s u  2  A (jU ) = 2 . 6 x 10~3'7 f  c m  l  o  r  f  2  QT  jjCl i n argon or krypton and  jjCl i n n i t r o g e n . Wow, using the  r e s u l t s of Table 8, we may c a l c u l a t e the s h i f t s due t o the i n d u c t i o n forces: A U (ind) = -16 cm'' i n argon -  l\ j) (ind) = -17 cm 1  i n krypton  -  A V (ind) =  -8 cm'' i n n i t r o g e n . -  The second term i n Eq. (42) can be evaluated i f we can estimate the change i n c<ei and E i n Eq. C'T)  :  a  1  c  E >  where:  " r"  1  E.  E'i'+E,  two primes denote the ground state and one prime the f i r s t e x c i t e d v i b r a t i o n a l s t a t e .  The i o n i z a t i o n p o t e n t i a l s E (, f o r argon, krypton and nitrogen are 126,475 cm , 112,359 cm -1  -1  and 125,104 cm , r e s p e c t i v e l y (63). -1  The i o n i z a t i o n p o t e n t i a l of HC1 i n the ground state E i s 111,311 a  cm"' (63) and the d i f f e r e n c e between the ground and f i r s t e x c i t e d -  v i b r a t i o n a l s t a t e i s taken as the v i b r a t i o n a l frequency i n the matrix.  Hence E i s 108,440 cm a  -1  i n argon, 108,455 cm ' i n krypton -  and 108,478 cm'' i n n i t r o g e n . -  To estimate the change i n p o l a r i z a b i l i t y , we expand ex. i n  75  terms of the change i n i n t e r n u c l e a r distance ( T — T  =  d  Q  4- <tfi ( Y" — r ) e  E  }:  + *•-  (48)  Values of c<i f o r various molecules have been estimated by Stansbury et a l (64) from i n t e n s i t y measurements of Raman spectra. Taking c<o as 2.63 A  For HG1 the value was 1.0 A . 2  3  (65) and  oC, as 1.0 A i n Eq. (48) we get <*a = 2.74 A f o r HC1 i n argon 2  3  and krypton matrices, and c< = 2.70 A i n n i t r o g e n . Using these 3  a  values, together w i t h E „ , E  a  , and E^, the s h i f t s due t o the  d i s p e r s i o n forces were c a l c u l a t e d : AV  ( d i s ) = -48 cm'' f o r argon,  AV  ( d i s ) = -49 cm'' f o r krypton,  A V  ( d i s ) = -18 cm'' f o r n i t r o g e n .  -  -  -  Thus, the s h i f t s due t o d i s p e r s i o n forces are l a r g e r than those due to i n d u c t i o n f o r c e s , i n agreement w i t h the work of Ben Reuven et a l (66). These workers used an approach s i m i l a r t o the present one, t o c a l c u l a t e pressure-induced s h i f t s of HC1 l i n e s due to noble gases. In the case of HC1 i n n i t r o g e n , there i s a c o n t r i b u t i o n from the t h i r d term i n Eq. (42). The expression f o r A V (es) was given by Eq. (jl) J  AV(es)  = - Q  Aft*  Using Eq. (43) the change i n dipole moment of HG1 during a vibrational transition i s :  Ay-  = M, (r.-n  )  76  Using the same values of r  a  and r, as before, Eq. (4.9)  gives  A ft- =0.11 D f o r HC1 i n n i t r o g e n , and the corresponding s h i f t Al>(es) =  -56 cm''. -  The r e s u l t s of the above c a l c u l a t i o n s f o r HG1 i n argon, krypton and n i t r o g e n matrices are l i s t e d i n Table 15 together w i t h the observed gas-matrix s h i f t s .  Although the accuracy of  these c a l c u l a t i o n s i s undoubtedly questionable, they do c o n s i s t e n t l y p r e d i c t a greater "red" s h i f t than was observed.  Thus, i t  i s reasonable t o assume that r e p u l s i v e forces contribute t o the overall shift. Since r e p u l s i v e forces a r i s e from overlap of charge clouds, i t i s i n s t r u c t i v e to compare the r e l a t i v e s i z e s of HC1, argon, krypton and n i t r o g e n .  This i s done i n F i g . 2L,, where i t i s seen  that the HC1 molecule i s l a r g e r than a s u b s t i t u t i o n a l s i t e i n any of the three matrices.  On s p a t i a l grounds one would expect the  r e p u l s i v e i n t e r a c t i o n to increase i n the order krypton, n i t r o g e n , argon, but from Table 15 the apparent order obtained by s u b t r a c t i n g A V (obs) from A V (calc) i s n i t r o g e n , krypton, argon.  The  explanation f o r t h i s may w e l l l i e i n the value taken f o r r, , the i n t e r n u c l e a r distance i n the e x c i t e d v i b r a t i o n a l s t a t e .  The  value estimated f o r t h i s q u a n t i t y was very approximate, and a smaller value of r , would r e s u l t i n smaller values of A V (ind) and £ U  (disp).  Thus the c o n t r i b u t i o n from the r e p u l s i v e forces  f o r HC1 i n nitrogen could be between the values f o r the argon and krypton matrices. I t should be emphasised that the numerical r e s u l t s of t h i s s e c t i o n are orders of magnitude only, since many assumptions and  77  TABLE 15.  V i b r a t i o n a l S h i f t s i n cm''  f o r HG1 i n Various Matrices.  -  Matrix  V (  t o t a l  observed.  )  AV  ( s) calc.  zlv(ind) calc.  ^V(disp) calc. -48  e  Ar  -13.5  -  -16  Kr  -28.5  -  -17  N  -51.5  -56  -8  2  '  -49 -18  79  approximations were made i n the c a l c u l a t i o n s . Calculations of the gas-matrix s h i f t s f o r HBr could be c a r r i e d out i n the same way as f o r HC1. This has not been done here because the value of r , c a l c u l a t e d from the observed s p l i t t i n g between R(0) and P(1) peaks i s not reasonable.- However, an idea of the magnitudes of the s h i f t s r e l a t i v e t o those c a l c u l a t e d f o r HC1 can be obtained by comparing the dipole moments, p o l a r i z a b i l i t i e s and i o n i z a t i o n p o t e n t i a l s of HC1 and H^r, l i s t e d i n Appendix 2. The dipole moment of HBr i s smaller than that o f HG1, which suggests a smaller dipole d e r i v a t i v e .  The value of d-f^/^y  quoted by F r i e d r i c h and Person (62) f o r s o l i d HBr was 1.72 D/A compared w i t h 2.12 D/A f o r s o l i d HC1. A s i m i l a r gas-matrix change i n r, i s expected f o r HBr as f o r HC1. Thus, the value of A C  i  n Eq. (44) i s expected t o be smaller f o r HBr than f o r  HC1, hence the value of  £V  (ind) f o r HBr w i l l be smaller.  The d i s p e r s i o n s h i f t depends on the p o l a r i z a b i l i t y and i o n i z a t i o n p o t e n t i a l i n the ground and f i r s t e x c i t e d v i b r a t i o n a l states  Eq. (12).  I n Appendix 2, the i o n i z a t i o n p o t e n t i a l of  HBr i s seen t o be l e s s than that o f HC1, while the p o l a r i z a b i l i t y i s considerably l a r g e r f o r HBr than f o r HC1. I t i s expected, t h e r e f o r e , that  &~0 ( d i s ) f o r HBr i n the matrix w i l l be l a r g e r  than the values f o r HC1. The o v e r a l l a t t r a c t i v e e f f e c t s compared w i t h HC1 may w e l l be s i m i l a r or perhaps l a r g e r for.HBr. On s p a t i a l grounds, one would expect the r e p u l s i v e forces t o be greater i n HBr than i n HC1, since the HBr molecule i s l a r g e r  80 than HC1  (see F i g . 24.).  Repulsive forces u s u a l l y give r i s e to  an upward s h i f t of v i b r a t i o n a l frequency, thus an increase i n r e p u l s i v e i n t e r a c t i o n could account f o r the smaller "red" s h i f t s observed f o r HBr i n the matrix compared to the HG1  5-4-  case.  Rotation of I s o l a t e d Solute Molecules. There i s considerable evidence i n the l i t e r a t u r e supporting  free or n e a r l y free r o t a t i o n of small molecules i n i n e r t matrices. In the present study, groups of absorption peaks i n the spectra of HC1 and HBr i n argon, krypton and nitrogen matrices, are assigned to v i b r a t i o n - r o t a t i o n bands.  However, s e v e r a l features must be  explained before the issue i s f i n a l l y s e t t l e d . The f i r s t problem i s the observed s p l i t t i n g of the R(0)  and  P(1) peaks i n the matrix spectra of HC1 and HBr, which gives r i s e to r o t a t i o n a l constants smaller than the gas phase values.  No,  t h e o r e t i c a l treatment to date has predicted a change of V R(0) -1>P(1) i n the matrix.  However, very r e c e n t l y , Gebbie and  S'tone (67) measured widths,and s h i f t s of pure r o t a t i o n l i n e s of HC1 perturbed by rare gases and found that the only l i n e f o r which there was any measurable s h i f t was the J(0-1) l i n e . ponds to R(0) of the v i b r a t i o n - r o t a t i o n spectrum.  This c o r r e s A perturbation  which a f f e c t s R(0) more than P(1) could account f o r the observed change i n 4B^ i f both s h i f t s were to the "red".  Ben-Reuven et a l  (66) report "red" s h i f t s of v i b r a t i o n - r o t a t i o n l i n e s of  HG1  perturbed by.noble gases, except R(0) i n argon and krypton which  t A c t u a l l y , the separation of R(0) and P(1) i s B-j and BQ may change i n the matrix.  2(B-|+B ), 0  and both  81 i s s h i f t e d t o the "blue".  These workers also note that f o r low J  numbers the s h i f t s of corresponding l i n e s are greater i n the P branch than i n the R branch.  I n other words, the observed s p l i t t i n g  between R(0) and P(1) i s increased by a d d i t i o n of noble gases, contrary t o the observations f o r HC1 i n s o l i d rare gases. An i n t e r e s t i n g feature of the spectrum of HC1 i n n i t r o g e n was the small change i n the separations between R(1), R(0) and P(1),  going from gas to matrix.  On t h i s basis i t would appear .  that the HC1 molecule experiences l e s s p e r t u r b a t i o n of i t s r o t a t i o n a l l e v e l s i n n i t r o g e n than i n the rare gas matrices, i n s p i t e of the greater s h i f t of the band centre.  This could be due  to smaller r e p u l s i v e forces i n the n i t r o g e n matrix, i n agreement w i t h the c a l c u l a t i o n s of the previous s e c t i o n . The p e r t u r b a t i o n treatment of the previous chapter p r e d i c t s a s p l i t t i n g of the R(1) peak of HC1 or HBr i n t o three components. The c a l c u l a t e d frequencies are l i s t e d i n Table 16 f o r these molecules i n argon. J = + 1 and  For these c a l c u l a t i o n s the s e l e c t i o n r u l e s  M = 0,+ 1 apply, and no v i o l a t i o n s of these  s e l e c t i o n r u l e s are p r e d i c t e d by f i r s t order p e r t u r b a t i o n theory (69).  The frequencies of the allowed t r a n s i t i o n s are given by: V R° (0) =  V 'R(0) + E'(1,0)  VR°  VJR(1)+  (1) =  o  E'(2,0) - E'(1,0)  1^R (1)=  ^ R 0 ) + E'(2,±1) - E ' U , ^ )  Vv°  (1) =  I ^ P ( 1 ) - E'(1,0)  VTC  (1) =  VJR(0+  ±  where:  E'(2,±2) - E (l,±l) y  E'(0,0) has been a r b i t r a r i l y set equal t o zero. The Vo are the gas phase frequencies corrected f o r the s h i f t of the band centre i n the matrix. The s u p e r s c r i p t on the symbol V R (0) r e f e r s to the value of the quantum number M, of the lower l e v e l . M  82  TABLE 16. P r e d i c t e d Spectrum of HC1 and HBr i n Argon, Compared With Observed and Gas Phase Spectrum.  (a)  HC1 Frequencies i n cm ^  Peak  Calculated  Observed  Gas Phase  P°  (D  2850.5  2853  2864  R°  (0)  2891.5  2889  2905  R°  (D  2907.5  2900 .  2925  R  (D  2914 2911  ±1  (b)  HBr Frequencies i n cm'' -  Peak  Calculated  Observed  Gas Phase  P°  (D  2543  2550  2542  R°  (0)  2576  2569  2575  R°  (D  2585  2575  2591  R  (D  2596.5 2591  ±1  83  S p l i t t i n g of the R(1)  peak was not observed i n e i t h e r the  present work or the work of Schoen et a l (8).  Previous  hindered  r o t a t i o n a l c a l c u l a t i o n s (8, 12, 13, 14-) also predicted a s p l i t t i n g of the R(1) peak.  Thus, i t appears t h a t a theory i s needed which  w i l l p r e d i c t perturbations of a l l r o t a t i o n a l energy l e v e l s of the solute molecule, but which does not remove the degeneracy of these levels. I t has been suggested (69)  that I n an octahedral f i e l d  w i t h a b a r r i e r height of about 10 cm (E  =0.0  cm'') of HG1 would be perturbed considerably more than -  the J = 1 l e v e l (E t h i s (69)  , the J = 0 l e v e l  = 20.9  cm 1). -  The p h y s i c a l i n t e r p r e t a t i o n of  i s that a molecule i n the J = 0 l e v e l does not r o t a t e ,  but executes o s c i l l a t i o n s about some mean p o s i t i o n , whereas a molecule i n the J = 1 l e v e l can undergo more or l e s s free r o t a t i o n . Such a model would p r e d i c t a spectrum i n agreement with the observed spectrum. A second major problem i s the observed r e l a t i v e i n t e n s i t i e s i n the matrix spectra.  In Table 17, the observed i n t e n s i t y r a t i o s  of the R(0) and P(1) peaks of HC1 and HBr i n various matrices, are compared w i t h c a l c u l a t e d r a t i o s at several temperatures.  A simple  explanation f o r the observed i n t e n s i t i e s i s that the temperature of the deposit during the recording of the spectrum may not have been 4°K, but i n f a c t , s e v e r a l degrees higher. thermal c o n d u c t i v i t y of the s o l i d rare gases (70)  The very poor could enable a  thermal gradient to be e s t a b l i s h e d i n the deposit, w i t h the surface l a y e r s at, a higher temperature than the l a y e r s near the caesium  84.  iodide p l a t e .  This idea i s supported by the i n t e n s i t y r a t i o s f o r  HC1 and HBr i n nitrogen which are much c l o s e r t o the 5°K f i g u r e (see Table 17). The thermal c o n d u c t i v i t y of nitrogen (71) i s 2.5 times that of argon and 7 times that of krypton at 5°K, thus the warming of the deposit by the i n c i d e n t r a d i a t i o n should be l e s s important i n the nitrogen matrix.  Further evidence f o r the  warming of the rare gas deposits was provided by the warm-up study of HC1 i n nitrogen (see F i g . 12). At 15°K the i n t e n s i t y of P(1) r e l a t i v e to R(0) was the same as that observed f o r HG1 i n the rare gas matrices at the lowest temperature, when the thermocouple recorded 4°K. TABLE 17. I n t e n s i t i e s of the P(1) peak of HC1 and HBr R e l a t i v e t o R(0) = 100, i n Various Matrices. (a)  HC1  Matrix Ar Kr N  30 30  4  2  (b)  Observed 4°K---  5°K  Calculated 10OK  20OK  0.6 0.6 0.6  15 15 15  66 66 66  5°K  Calculated 10°K  20°K  2.4 2.4 2.4  27 27  HBr  Matrix  Observed 4°K*  Ar Kr N  35 3  2  40  27  91 91 91  I t i s believed that i n the noble gas matrices the temperature was several degrees above 4°K. See t e x t f o r d i s c u s s i o n of t h i s point.  if  85  One f u r t h e r i n t e n s i t y anomaly i s found i n the spectra of HBr and HC1 i n the rare gas matrices.  The shoulder on the high  frequency side of R(0), which i s assigned t o R(1), i s much weaker than the P(1) peak.  The i n t e n s i t i e s of these peaks should be  comparable since they both o r i g i n a t e from the J = 1 l e v e l . In f a c t , i n the gas phase, R(1) i s somewhat stronger than P(1), due to the d i f f e r e n c e i n absorption frequencies and t r a n s i t i o n moments f o r these two l i n e s .  The energy absorbed during a  t r a n s i t i o n from the mth t o the nth energy l e v e l i s given by (68):  d.E where:  =  K  (51)  NL V,  K i s a constant, Nm i s the population of the mth l e v e l , V mn i s the absorption frequency, and | yU n | i s the t r a n s i t i o n moment. w  From Eq. (53.) the r a t i o of the i n t e n s i t i e s of R(1) and P(1) i s :  (52)  In the gas phase  IR(1)/IP(1)  i s found t o be 1.5 f o r HG1 and 1.3  f o r HBr, while i n the matrix, the r a t i o i s of the order of 0.3. The explanation may be that the R(1) peak i n the matrix i s close to the r e l a t i v e l y broad R(0) peak and some of the R(1) i n t e n s i t y i s included i n t h i s very strong peak.  However, i t seems doubtful  that t h i s could account f o r the f a c t o r of f i v e between the gas and matrix i n t e n s i t i e s .  86  5-5  I n t e r a c t i o n s Between Solute Molecules. I t i s suggested that i n t e r a c t i o n s between non-isolated  solute molecules give r i s e t o the peaks c l a s s i f i e d i n s e c t i o n 5-1 i n t o groups i i , i i i and i v . Such p a i r s , t r i p l e c l u s t e r s , e t c . , could be formed by d i f f u s i o n of solute molecules i n the l a t t i c e . The thermal c o n d u c t i v i t y of the s o l i d rare gases i s very small (70), and i t i s quite p o s s i b l e that the new l a y e r s of deposit are not cooled t o 4°K r a p i d l y enough t o prevent d i f f u s i o n e n t i r e l y .  This  i s supported by experiments i n which a mixture was deposited at the normal r a t e , and very r a p i d l y , and the r e s u l t i n g spectra compared.  I n the case of r a p i d deposit, a d d i t i o n a l peaks were  observed, many of which were only observed during warm-up of the slowly deposited mixture. S t a t i s t i c a l l y (53), the most probable p a i r of solute molecules i s the t h i r d nearest neighbour p a i r (see F i g . 23). However, when d i f f u s i o n occurs, the nearest neighbour p a i r ( i . e . the dimer) i s e n e r g e t i c a l l y more favourable.  S h i f t s of  v i b r a t i o n a l frequencies due t o d i p o l e - d i p o l e i n t e r a c t i o n between p a i r s of solute molecules may be c a l c u l a t e d using the values of A(jA  ) f o r HG1 estimated i n s e c t i o n 5-2, and Eq. (AO) developed  I n s e c t i o n 4-6:  AV  =  -C  M) 2  4  r  The s h i f t s c a l c u l a t e d from t h i s equation are added t o the matrix s h i f t s from Table 14, and the r e s u l t s compared w i t h the observed spectra i n Table 18.  87  TABLE 18. Calculated S h i f t s * i n cm'' f o r Interactions Between P a i r s of HC1 Molecules. -  Ar calc.  obs.  Kr calc.  obs.  N calc.  obs.  r  -89  -67.5  -88.5  -84.5  -92.5  -  r  -4.0  -  -51  -  -67  -  VJr  -28  -21.5  -41  -30.5  -59.5  2  -23  -17  -36.5  -  -56.5  Internuclear Distance  ft  r  2  -42.5  -  *These s h i f t s include the matrix s h i f t s from Table 14.  In the case of i n t e r a c t i o n s between solute molecules i n s i t e s other than nearest neighbour s i t e s , the observed s h i f t s w i l l be l e s s than predicted i n Table 18, because screening by the matrix atoms w i l l tend to reduce the intermolecular f o r c e s .  With  t h i s i n mind, the agreement between observed and c a l c u l a t e d s h i f t s i n Table 18 i s remarkably good.  I t i s also s i g n i f i c a n t that i n  the case of HC1 i n n i t r o g e n , no peak i s found near 2790 cm'', the -  predicted frequency f o r HC1 molecules i n nearest neighbour s i t e s i n t h i s matrix.  The only observed peak corresponds to the s t a t i s -  t i c a l l y favourable second nearest neighbour p a i r .  These obser-  vations are compatible w i t h the higher thermal c o n d u c t i v i t y and smaller heat of sublimation (see Appendix 1) of nitrogen at 4°K compared w i t h the rare gases, since i f d i f f u s i o n i s minimized a s t a t i s t i c a l d i s t r i b u t i o n of solute molecules i n the l a t t i c e would  88  be  expected. Peaks at frequencies lower than the "nearest neighbour"  frequency must be due t o i n t e r a c t i o n s between three or more solute molecules.  Many of these peaks are found only during  warm-up (see F i g s . 6 and 14) and the others are only found at low matrix t o solute r a t i o s (see F i g s . 5 and 13). The e f f e c t of s o l u t e - s o l u t e i n t e r a c t i o n was also demons t r a t e d i n experiments where other solute molecules were added to the gas mixtures.  Several new features were introduced i n t o  the spectra of HG1 and HBr (see F i g s . 7 and 15), which can be explained q u a l i t a t i v e l y on the basis of d i p o l e - d i p o l e i n t e r a c t i o n s between the hydrogen h a l i d e and the other solute molecule.  5-6  M a t r i x I s o l a t i o n Studies of GO and S O 2 . The observed spectra of CO and S O 2 i n the matrix are  simpler than the HC1 or HBr spectra.  I n the case of S O 2 , the  large dimensions of the molecule compared t o argon or nitrogen (see F i g . 24.) make r o t a t i o n very u n l i k e l y .  S h i f t s of band  centres from the gas phase are s u r p r i s i n g l y small f o r these molecules.  I n the case of SOg, t h i s could be due t o the  balancing of r e p u l s i v e and a t t r a c t i v e f o r c e s , w i t h a small net e f f e c t , as was found f o r HBr i n argon.  CO, on the other hand,  has a very small dipole moment and a smaller p o l a r i z a b i l i t y than the hydrogen h a l i d e s , thus i n t e r a c t i o n s w i t h the matrix are expected t o be l e s s . On s p a t i a l grounds, CO should be able t o r o t a t e i n an  89 argon matrix.  Nevertheless, i t i s d i f f i c u l t t o c o r r e l a t e the  observed matrix spectrum w i t h the gas phase v i b r a t i o n - r o t a t i o n spectrum.  I t i s i n t e r e s t i n g t o note that a c a l c u l a t i o n by  Ewing (72) predicts a Q branch i n the v i b r a t i o n - h i n d e r e d r o t a t i o n spectrum of l i q u i d CO.  I f Ewing's theory could be c a r r i e d over  i n t o the present matrix s i t u a t i o n , the very strong peak at 2138.5 cm~1 could be assigned t o an unresolved t r i p l e t due to the P ( 1 ) , Q(0) and R(0) t r a n s i t i o n s . assigned t o R(1).  The peak at 2152 cm 1 would then be -  However, i t i s very doubtful t h a t such an  explanation could be c o r r e c t .  The r o t a t i o n a l constant f o r CO i s  about 2 cm-1 (40) and the expected separation of P(1) and Q(0) or Q(0) and R(0) would be approximately 4 cm 1 . -  The 112 G  spectrometer should be capable of r e s o l v i n g these peaks, whereas the 2138.5'cm 'peak was unresolved.  Furthermore, no v i o l a t i o n  -  of the A J = ± 1 s e l e c t i o n r u l e i s expected i n the matrix environment ( 6 9 ) . The very weak peaks at 2115 and 2091 cm'' are undoubtedly -  due to i s o t o p i c CO molecules (19)-  I n the spectrum of CO  perturbed by HC1 (see F i g . 17'), i f we assign the peak at 2065 cm ^ -  to CO molecules i n t e r a c t i n g w i t h HC1 molecules i n nearest  neighbour  s i t e s , then the change i n dipole moment of CO during a v i b r a t i o n a l t r a n s i t i o n may be c a l c u l a t e d from Eq.  (41)s.  AV  which i s of the same order of magnitude as that estimated f o r HC1 i n the matrix i n section 5-3. In the gas phase spectrum of SO2 the band centres are at  90  1151.4 cm 1 and 1361.8 cm~1 f o r \ ) and V3 r e s p e c t i v e l y (44). _  [  The s h i f t s i n the nitrogen matrix f o r ~)) and V were + 1.2 cm""1 3  {  and -10 cm-1, and i n argon, -1.7 cm-1 and -8.3 cm~1 r e s p e c t i v e l y . These s h i f t s are small compared w i t h the g a s - s o l i d s h i f t s of -1  1  - 8 cm  -  and -46 cm  f o r these bands.  I t may be noted also that  the g a s - s o l i d s h i f t s are much smaller f o r SO2 than f o r HC1 or HBr, because there i s no hydrogen bonding i n s o l i d SO2. Rotation of the S 0 molecule i s u n l i k e l y on s p a t i a l grounds, 2  and the appearance of the matrix spectrum supports t h i s conclusion. The SO2 molecule has r o t a t i o n a l constants: B = 0.34 cm 1 and G = 0.29 cm -  -1  (73).  A = 2.03 cm~1,  I t i s therefore a n e a r l y  p r o l a t e symmetric top w i t h asymmetry parameter  K = -0.94-  Using  the formulae given i n reference (68) the lower r o t a t i o n a l l e v e l s were c a l c u l a t e d and are tabulated i n Table 19 together w i t h r e l a t i v e populations at 5°, 10°, and 20°K. At 5 K, a l l l e v e l s up to 3-f  are appreciably  and at 10°K, higher l e v e l s w i l l also be important.  populated, Thus, the  r o t a t i o n - v i b r a t i o n bands even at 5°K would be very complex, c o n s i s t i n g of several groups of unresolved l i n e s .  The simple  appearance of the spectrum of S 0 i n argon and nitrogen 2  matrices, t h e r e f o r e , i n d i c a t e s that r o t a t i o n of the trapped molecule does not occur. I t i s i n t e r e s t i n g t o note that i n the argon matrix both the 1// and 2/3 bands c o n s i s t of strong doublets, while i n n i t r o g e n , the main feature i n each of these bands i s a s i n g l e strong peak.  One might put forward an explanation analogous t o  i n v e r s i o n doubling (74) based on the f o l l o w i n g argument.  91  TABLE 19. R o t a t i o n a l Energy Levels of the S0  J  0  cirri  T  0.00  o  1-  2  Molecule.  Populations R e l a t i v e to 0  o  5°K  10°K  20°K  1  1  1  O.64  .84  .91  .96  2.32  .51  .72  .84  1,  2.37  .51  .71  .84  2- 1  1.63  .63  .79  .89  2- i  3.55  .36  .60  .78  2  3.70  .35  .59  -77  2,  8.75  -08  .28  .52  2  J>  9.03  . 07  3- 1  3.77  .34  -58  .76  3-Z  5.34  -21  .46  .68  3-1  5.65  .20  .44  .67  10.63  .05  .21  .46  3,  10.65  .05  .21  .46  31  19.22  .004  .06  .25  3  19.21  .004  .06  .25  1  3  1  0  0  0  3  . 27  . 52  92 Assuming that the SO2 molecule i s prevented from r o t a t i n g by the surrounding matrix atoms, then the molecule can only execute v i b r a t i o n s i n an e q u i l i b r i u m p o s i t i o n i n the c a v i t y . I f the sulphur atom passes between the oxygen atoms t o an equivalent p o s i t i o n on the other s i d e , an i n v e r t e d c o n f i g u r a t i o n i s obtained. This s i t u a t i o n could not occur i n the free molecule because the equivalent p o s i t i o n could be obtained by a simple r o t a t i o n .  The  two e q u i l i b r i u m p o s i t i o n s may be described mathematically by a double minimum p o t e n t i a l , which gives r i s e to a doubling o f the v i b r a t i o n a l energy l e v e l s o f the molecule (74-)•  This phenomenon  has been observed f o r the ammonia molecule i n the gas phase, and more r e c e n t l y i t has been suggested that i n v e r s i o n doubling may occur.in s o l i d phosphine  (75).  The s p l i t t i n g i n the ground state i s very s m a l l , but as the energy l e v e l s approach the b a r r i e r height the separation increases r a p i d l y (74). V/  Thus, i f the observed s p l i t t i n g s f o r  and V3 of SO2 are due to the type o f i n v e r s i o n doubling  described above, then the s p l i t t i n g s f o r the overtones 2Vi and 2Vj  should be much l a r g e r . A l s o , i t i s expected that the bending  mode y  x  should e x h i b i t greater s p l i t t i n g (74).  Unfortunately,  i t was not p o s s i b l e to study these bands i n the present work because the overtones are too weak, and the region o f the bending mode was i n a c c e s s i b l e . Arguments against the above explanation are:  the absence  of doubling i n nitrogen, and the l a r g e reduced mass o f SO2, which would be expected t o l i m i t the s p l i t t i n g s t o very small values, unless the b a r r i e r t o i n v e r s i o n was low (74)-  I n view of t h i s ,  93  the observed s p l i t t i n g s of 4.8  cm~1  f o r V,  and 4.2  cm  -  f o r 2^3  would appear to be too large to a r i s e from i n v e r s i o n doubling. Another explanation.involving m u l t i p l e trapping s i t e s could be considered.  Harvey and O g i l v i e (76)  i n t h e i r work on  formaldehyde i n an argon matrix, suggested t h a t the  formaldehyde  molecule could be trapped i n a s u b s t i t u t i o n a l s i t e , or i n l a r g e r holes i n which two or three argon atoms were displaced.  Applying  t h i s suggestion to the SC^/argon spectrum, one can account f o r the doublets observed f o r the  5-7  and  bands.  Gas Hydrates. The hydrates studied i n the present work have the compo-  s i t i o n M'6H20 and have been c l a s s i f i e d as type I hydrates by von Stackelberg (21).  In these compounds the hydrate former M  i s trapped i n hydrogen bonded cages of water molecules.  The  structure of the type I gas hydrates has been worked out by von Stackelberg (21), P a u l i n g and Marsh (77) and Claussen (78), and i s i l l u s t r a t e d i n F i g . 25. Two types of cages are formed i n the type I hydrates, pentagonal dodecahedra e n c l o s i n g n e a r l y s p h e r i c a l c a v i t i e s of diameter 5.1  A, and tetraxa*decahedra enclosing s l i g h t l y oblate  c a v i t i e s of diameter 5.8 A (79).  These c a v i t i e s should be large  enough t o allow r o t a t i o n of small molecules, and X-ray d i f f r a c t i o n data (21,77) f o r SO2, H2S and CI 2 could be i n t e r p r e t e d as i n d i c a t i n g free r o t a t i o n of these molecules i n the cages. The p h y s i c a l p r o p e r t i e s of some of these compounds are l i s t e d i n Table  20.  94 TABLE 20. P r o p e r t i e s of Some Gas Hydrates.  M  M.P. of M  d i s s , press, atm. at 0°C  decomp. temp. °C at latm.  Ar  -190  Kr  -152  14-5  -27.8  Xe  -107  1.5  - 3.4  - 34  0.33  9.6  HS  - 60  0.96  0.35  so  - 10  0.39  7.0  ci  2  2  2  -42.8  105  Discussion of the spectra of the gas hydrates can be considered i n two p a r t s .  The spectrum of the s k e l e t a l water  v i b r a t i o n s , and the spectrum of the hydrate former (where i t exists). The s k e l e t a l water spectrum has several points of i n t e r e s t . In the S 0 hydrate, the l i b r a t i o n a l frequency of H 0 i s s h i f t e d 2  2  by -40 cm '', while the peak a t 1600 cm'' i n i c e i s s h i f t e d i n -  -  the opposite d i r e c t i o n by 40 cm '', confirming i t s assignment t o -  rather than 2  , as has been suggested (80). The peak at  2230 cm'' i n i c e , u s u a l l y assigned t o -  1? + x  , has almost the  same frequency i n the hydrate, i n agreement with the above conclusion. A new feature i n the s k e l e t a l water spectrum at 2410 cm'' -  i s observed i n a l l the hydrates studied i n t h i s work.  This may  95  fig  25.  S T R U C T U R E  A  portion  oxygen  of  OF  the  atoms  the  G A S  HYDRATES  hydrogen-bond  framework,  are  tetrakaidecahedra  The  TYPE  at and  arrangement gas  denote  hydrate centres  of  the  corners  of  dodecahedra .  the  crystal. of  I  dodecahedra The  cavities.  open  in  circles  96  be a second component of the combination band  V  x  + VR  . The s h i f t  of the l i b r a t i o r i a l frequency i n the S 0 hydrate precludes the p o s s i 2  b i l i t y that the new peak i s an overtone of  •  The S 0 peaks i n the hydrate are generally broader than i n 2  the s o l i d (see F i g . 19) which may be due t o unresolved r o t a t i o n a l structure or intermolecular f o r c e s .  The s p l i t t i n g of peaks observed  i n s o l i d S 0 i s not found i n the hydrate, since the S 0 molecules 2  2  are i s o l a t e d i n t h i s environment and c r y s t a l e f f e c t s (81) are The weak peak at 1035 cm"' i s assigned t o 2 24 . This  absent.  -  overtone peak was not reported i n previous work on s o l i d S 0  2  (82,83). An anealed deposit of SO^ hydrate was studied over the temperature range 4°-120°K.  I n F i g . 20, the J/J  peak was seen t o  have two shoulders at 120°K spaced at 6.5 cm"' above and below -  the p r i n c i p a l peak at 134-2.5 cm ''. -  The i n t e n s i t y of the low  frequency shoulder decreases as the temperature i s lowered.  This  observation i s explained by a sum and differences of the V j fundamental w i t h a r o t a t o r y  or t r a n s l a t o r y l a t t i c e mode, the decrease  i n i n t e n s i t y of the difference peak w i t h lowering of the temperature would r e s u l t from depopulation of the upper l e v e l i n the ground s t a t e . I t might be i n t e r e s t i n g t o examine the spectrum of the SO?hydroquinone c l a t h r a t e compound (84) since the c a v i t y s i z e i s much smaller (79) than i n the case of the hydrate, and motion of the S 0  2  molecule would be even more r e s t r i c t e d than i t appears t o be i n the S0  2  hydrate.  97  5-8  Conclusions. I t i s concluded that hydrogen h a l i d e molecules i s o l a t e d  i n s o l i d rare gases and nitrogen are able t o execute hindered rotations.  At the same time, the v i b r a t i o n a l p o t e n t i a l f u n c t i o n  of the solute molecule i s perturbed by i n t e r a c t i o n s w i t h the surrounding matrix.  I t has been possible to c o r r e l a t e the s h i f t  of the v i b r a t i o n a l frequency w i t h various intermolecular forces and i t was found that the r e p u l s i v e forces play an important r o l e i n determining the magnitude and d i r e c t i o n of.the s h i f t . Thus, the main features of the matrix spectra of HC1 and HBr may be i n t e r p r e t e d as a v i b r a t i o n - r o t a t i o n band.  Other peaks  i n the observed spectra are a t t r i b u t e d t o mutual i n t e r a c t i o n s between c l u s t e r s of solute molecules i n contiguous and other . neighbouring s i t e s .  At the lowest temperatures, only i s o l a t e d  solute molecules and p a i r s of solute molecules are present i n s i g n i f i c a n t concentrations. Arguments against r o t a t i o n of i s o l a t e d hydrogen h a l i d e molecules may be r a t i o n a l i z e d .  I n the spectra of HC1 and HBr i n  s o l i d argon, three of the peaks observed were assigned to R(0), R(1) and P(1), but at 4°K only the R(0) should have an observable intensity.  The explanation i s probably that the argon matrix  warms s l i g h t l y during the recording of the spectrum, due to poor thermal c o n d u c t i v i t y of s o l i d argon.  The temperature r i s e allows  the J = 1 l e v e l t o become appreciably populated, and thus the R(1) and P(1) t r a n s i t i o n s are observed.  In nitrogen, the R(0) peak  predominates and i t may be concluded that the temperature i n t h i s  98  matrix remains near 4°K.  This i s reasonable because s o l i d nitrogen  has a higher thermal c o n d u c t i v i t y than s o l i d argon.  A second  argument against r o t a t i o n i s the f a i l u r e t o observe changes i n r e l a t i v e i n t e n s i t y of peaks i n the spectra of HC1 and HBr i n argon, as the temperature r i s e s during warm-up.  The explanation  f o r t h i s may be that d i f f u s i o n sets i n r a p i d l y enough t o reduce the concentration of i s o l a t e d solute molecules before the changes i n the v i b r a t i o n - r o t a t i o n band are observed.  This i s supported  by the warm-up studies on HBr and HG1 i n n i t r o g e n , where the R(1) and P(1) peaks do increase i n i n t e n s i t y r e l a t i v e t o R(0) i n the e a r l y part of the warm-up.  The i n t e n s i t i e s of R(2) and P(2) are  n e g l i g i b l e below 20°K and are therefore not observed. I t would be i n t e r e s t i n g t o observe the spectra of DC1 and DBr under the same conditions as i n t h i s work, since the bond lengths, force constants and dipole moments are the same as f o r HC1 and HBr, t o a good approximation  (85,86).  The expected  v i b r a t i o n a l s h i f t s should be the same f o r the heavy hydrogen halides as f o r the '•rio.r.mal h a l i d e s .  The v i b r a t i o n - r o t a t i o n l i n e s ,  on the other hand, should be c l o s e r together since the r o t a t i o n a l constants are smaller.  There i s also the p o s s i b i l i t y that the R(2)  and P(2) t r a n s i t i o n s could be observed during the e a r l y part of a warm-up study.  Thus, the matrix spectra of DC1 and DBr could  provide supporting evidence f o r the i n t e r p r e t a t i o n given i n t h i s t h e s i s of the observed spectra of HG1 and HBr. I t i s also p o s s i b l e that f u r t h e r information could be obtained on the causes of the reduced separation of the R(0) and P(1) peaks.  99  Problems a r i s i n g from d i f f u s i o n of solute molecules during deposition can be reduced by using d i l u t e mixtures and forming the deposits slowly.  The problem of warming of the sample by the  i n c i d e n t r a d i a t i o n could be eliminated by arranging the spectrometer o p t i c s so that the i n f r a r e d beam i s dispersed before passing through the sample.  By t h i s means, the t o t a l i n t e n s i t y of the  r a d i a t i o n f a l l i n g on the deposit w i l l be a f r a c t i o n of i t s value i n t h i s work. The observed spectra of CO i n argon i s g e n e r a l l y i n good agreement w i t h previous work.  However, a d i f f e r e n t i n t e r p r e t a t i o n  i n v o l v i n g r o t a t i o n of the CO molecule i s put forward.  A new peak  i n the CO spectrum when HC1 was added t o the gas mixtures i s explained on the basis of a d i p o l e - d i p o l e i n t e r a c t i o n between CO and HC1 molecules i n nearest neighbour s i t e s . An i n t e r e s t i n g d i f f e r e n c e i n the spectrum of SO2 i n argon and nitrogen matrices was found.  I n the argon matrix both the  1/| and 2/3 bands c o n s i s t of strong doublets, while i n nitrogen the main feature of each band i s a s i n g l e strong peak.  The s h i f t s  from the gas phase i n both cases were s m a l l , from which i t i s concluded that r e p u l s i v e and a t t r a c t i v e forces are n e a r l y balanced. Two possible explanations f o r the doubling i n the SO^argon spectrum have been suggested.  The f i r s t was based on a type of i n v e r s i o n  doubling, a r i s i n g from r e s t r i c t i o n of r o t a t i o n a l freedom of the trapped molecule.  The second explanation involved m u l t i p l e trapping  s i t e s i n s o l i d argon i n which the SO2 molecule replaces one or two argon atoms.  I t would be u s e f u l t o be able t o observe the bending  100  mode V i o f SO2 i n the two matrices. There i s a small upward s h i f t o f v i b r a t i o n a l frequency (+3 cm'') going from gaseous t o -  s o l i d SC>)j so one would expect l i t t l e or no s h i f t i n the matrix. I t would be i n t e r e s t i n g t o see i f s p l i t t i n g of the i/^ peak i n the  argon m a t r i x occurs. The magnitude of the s p l i t t i n g might  give some i n d i c a t i o n of the o r i g i n of the e f f e c t since, i f i n v e r s i o n doubling occurs, the bending mode i s expected t o show the  greatest s p l i t t i n g ( 7 4 ) .  Further work w i t h SO2 i n various  matrices might provide a d d i t i o n a l information on intermolecular forces and r e s t r i c t i o n of r o t a t i o n . The work on the gas hydrates has provided confirmation of the assignment of the ,1',600 cm'' peak i n the spectrum o f i c e , -  to the bending mode l/  x  . A new peak i n the s k e l e t a l water  spectrum has been observed which may be a second component of the combination mode Vz + IS*. the  . Evidence f o r r e s t r i c t e d motion of  SO2 molecule i n the hydrate was found from v a r i a t i o n s w i t h  temperature o f the spectrum.  Further studies on the gas hydrates  by i n f r a r e d spectroscopic methods are contemplated t o study the motion of molecules i n the cages, and t o i n v e s t i g a t e the o r i g i n of the new peak i n the water spectrum.  101  APPENDIX 1. P h y s i c a l Properties of Matrix M a t e r i a l s .  Properties  Ar  Kr  N  References  2  melting point  °K  83.9  116.6  63.3  (61)  b o i l i n g point  °K  87.5  120.3  77.4  (61)  cal/mole  284  392  85.3  heat of v a p o r i z a t i o n cal/mole  1555  2162.  667  heat of f u s i o n  thermal c o n d u c t i v i t y at  5°K  20  7  50  m i l l i w a t t s / c m °K  10°K  40  15  26  at 20°K  15  10  -4  at  c e l l constant i n t e r n u c l e a r distance  polarizability  (r)  10 ^  cm  2  ionization potential  5.43  5.71  5.64  A  3.83  4.04  3.99  1.63  2.36  1.76*  15.68  13.93  3  e.v.  * mean p o l a r i z a b i l i t y •where: oC  A  t  oC — y (o<,-h o( + c<j z  >^3  a r e  15.51  )  "three p r i n c i p a l  components of the p o l a r i z a b i l i t y  tensor.  (87)  (88)  (68)  (69)  (45)  (47)  (63) (61)  102  APPENDIX 2. P r o p e r t i e s of Some Diatomic  Property  Units  melting point  °K  b o i l i n g point  °K  R(0)  (gas)  cm  ., (gas)  cm  ionization potential  -1  e.v.  dipole moment polarizability*  -1  D 10~  24  cm  3  molecular dimensions A i n t e r n u c l e a r distance ( r ) A  -"mean p o l a r i z a b i l i t y  Molecules.  HG1  HBr  161 189.5  184.5  66  206  83  2884.5  2558.5  2143  (41)  2905  2575  2147  (41)  13.8  13.2  CO  References  U.1  1.085  0.78  0.112  2.63  3.61  1.95  4-27  4.57  3.73  3.60  3.90  2.80  1.42  1.13  1.275  (61)  (61) (89)(44)(90) (63)  (91)  (38) (39) (40)  103  BIBLIOGRAPHY 1.  E.D. Becker and G.G. Pimentel, J . Chem. Phys. 25j. 224 (1956).  2.  M. Van T h i e l , E.D. Becker and G.C. Pimentel, I b i d . , 27, 95, 486 (1957).  3.  G.C. Pimentel, M.O. Bulanin and M. Van T h i e l , I b i d . , 3_6, 500 (1962).  4.  E. Catalano and D.E. M i l l i g a n , I b i d . , 20, 45 (1959).  5.  R.L. Redington and D.E. 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