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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 thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January, 1964. In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Bri t i sh Columbia, I agree that the Library shall, make i t freely available for reference and study. 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 Brit ish Columbia, Vancouver 8, Canada. Date The U n i v e r s i t y of 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 HERBERT FRANCIS SHURVELL B.Sc, Exeter Un i v e r s i t y , 1959 M.Sc, The Uni v e r s i t y of B r i t i s h Columbia, 1962 FRIDAY, MARCH 13, 1964, AT 2:30 P.M. IN ROOM 261, CHEMISTRY BUILDING of COMMITTEE IN CHARGE Chairman: F.H. Soward W.A. Bryce F.W. Dalby K.B. Harvey E.A. Ogryzlo C. Reid R.F. Snider External Examiner: D.F. Eggers J r . Uni v e r s i t y of Washington AN INFRARED STUDY OF SMALL MOLECULES IN INERT MATRICES ABSTRACT Infrared absorption spectra of HC1 and HBr, suspended i n s o l i d argon, krypton and nitrogen, were recorded i n order to obtain information on intermolecular forces. SO2 i n argon and nitrogen, and CO i n argon were also studied. The spectra were observed i n the temperature range from l i q u i d helium temperatures up to the melting point of the matrix. The halogen acids gave more complicated spectra i n the noble gas matrices than i n nitrogen. This has been cor-related with the d i f f e r e n t thermal properties of the matrix materials. Matrix to solute r a t i o s from 100 to 800 to 1 were used and evidence was found for solute-solute 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 solute molecules at the lower r a t i o s . During the warm-up period at the end of an experiment, a d d i t i o n a l peaks appeared i n the spectra. I t i s suggested that these new peaks were due to c l u s t e r s of solute molecules 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 out to e s t i -mate s h i f t s of v i b r a t i o n a l frequencies of the trapped molecules. From these cal c u l a t i o n s i t was concluded that repulsive intermolecular forces play an important part i n determining the magnitude, and d i r e c t i o n of the 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, using a Lennard-Jones' p o t e n t i a l , to determine the e f f e c t of the matrix on the r o t a t i o n a l energy le v e l s of a trapped molecule. Spectra of the clathrate-hydrates of SO2, H2S and krypton were recorded at l i q u i d nitrogen temperatures, and the SO2 hydrate was studied i n the temperature range from t? to 120° K. The spectrum of the water s k e l e t a l v i b r a t i o n s exhibited several i n t e r e s t i n g features. The assignment of the 1600 cm"''- and 2200 cm"! peaks to v 2 and U^+l^w/as confirmed and a new peak at 2410 cm"l was observed. A l a t t i c e mode i n the spectrum of the S02 hydrate was observed.in combination with V$ of SO2. GRADUATE STUDIES F i e l d of Study: Chemistry Topics i n Physical Chemistry Seminar i n Physical Chemistry Quantum Chemistry Chemical Thermodynamics Spectroscopy and Molecular Structure Related Topics D i f f e r e n t i a l Equations Computer Programming Group Th e o r e t i c a l Methods Elementary Quantum Mechanics Unrelated Topics Topics i n Inorganic Chemistry Topics i n Organic Chemistry J.A.R. Coope R.F. Snider J.N. Butler J.A.R. Coope J.N. Butler C. Reid A.N. Bree L.W. Reeves K.B. Harvey S.A. Jennings Charlotte Froese W-,Opechowski W„.Opechowski 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 absorption of some c r y s t a l l i n e inorganic formates. K.B. Harvey, B.A. Morrow and H.F. Shurvell, 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 of some arrangements of solute molecules 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. Shurvell, Can. J.Chem. 42, ( i n press) Infrared absorption of the SO2 clathrate-hydrate. motion of the SO2 molecule. K.B. Harvey, F.R. McCourt and H^F. Shurvell, Can.J. Chem. 42, ( i n press) i i A B S T R A C T I n f r a r e d absorption s p e c t r a of HC1 and HBr, suspended i n s o l i d argon, krypton and n i t r o g e n , were recorded i n order to ob 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 sp e c t r a were observed i n the temperature range from l i q u i d helium temperature up t o the me l t i n g p o i n t of the m a t r i x . The halogen acids gave more complicated s p e c t r a i n the noble gas matrices than i n n i t r o g e n . This 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 ma t r i x m a t e r i a l s . M a t r i x to s o l u t e r a t i o s from 100 to 800 t o 1 were used and evidence 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 so l u t e molecules at the lower r a t i o s . During the warm-up p e r i o d a t the end of an experiment, a d d i t i o n a l peaks appeared i n the spe c t r a . I t i s suggested t h a t these new peaks were due to c l u s t e r s of s o l u t e molecules, produced by d i f f u s i o n of the s o l u t e 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 out t o estimate s h i f t s of v i b r a t i o n a l frequencies of the trapped molecules. From these c a l c u l a t i o n s i t was concluded 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 important p a r t i n determining the magnitude and d i r e c t i o n of the s h i f t s . A f i r s t order 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 de t e r -mine the e f f e c t of the ma t r i x on the r o t a t i o n a l energy l e v e l s of a trapped molecule. i i i 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 interesting features. The assignment of the 1600 cm-'' and 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 v i i i ACKNOWLEDGMENT. I would l i k e to express my g r a t i t u d e t o Dr. K. B. Harvey f o r h i s help and guidance during the course of 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. Snider are a l s o appreciated, and thanks are due to Mr. R. Muehlchen f o r as s i s t a n c e w i t h the c o n s t r u c t i o n and maintenance of the apparatus. F i n a n c i a l a s s i s t a n c e from the S h e l l O i l Company and the N a t i o n a l Research C o u n c i l of Canada i s g r a t e f u l l y acknowledged. i v TABLE OF CONTENTS. Page:. A b s t r a c t i i L i s t of Tables v i L i s t of Figur e s v i i Acknowledgment v i i i CHAPTER I - INTRODUCTION 1-1 P r e l i m i n a r y Remarks 1 1-2 Studies o f Molecular I n t e r a c t i o n s by the M a t r i x I s o l a t i o n Method 1 1-3 Molecular I n t e r a c t i o n s i n the Gas Hydrates L, 1- 4 A Summary of Related Work on the Hydrogen Halides and Carbon Monoxide 5 CHAPTER 2 - EXPERIMENTAL 2- 1 Experimental Methods 8 2-2 D e t a i l s of the Low Temperature C e l l s 11 2-3 D i f f u s i o n i n S o l i d M a t r i c e s 15 2-4 M a t e r i a l s 17 2- 5 The Spectrometers 17 CHAPTER 3 - RESULTS 3- 1 I n f r a r e d Spectra of HC1 i n S o l i d Argon 20 3-2 I n f r a r e d Spectra of HC1 i n S o l i d N itrogen and Krypton 22 3-3 I n f r a r e d Spectra of HBr i n Argon, Krypton and Nitrogen 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 Studies on CO and SO^ 37 3-5 Gas Hydrates 41 Page: CHAPTER 4 - THEORETICAL 4-1 I n t r o d u c t o r y Remarks 45 4-2 S h i f t s of V i b r a t i o n a l Frequencies Due to M a t r i x - S o l u t e I n t e r a c t i o n s 45 4-3 R o t a t i o n of Molecules Trapped i n S o l i d Rare Gases 50 4-4 The Hindered Rotator P o t e n t i a l 51 4-5 C a l c u l a t i o n of Energy Levels of the Hindered Rotator 57 4- 6 S h i f t s Due to Solute-Solute I n t e r a c t i o n s 62 CHAPTER 5 - DISCUSSION 5- 1 C l a s s i f i c a t i o n of Peaks i n the M a t r i x Spectra of HC1 and HBr 64 5-2 I s o l a t e d Solute Molecules 69 5-3 Intermolecular Forces Between Solute and M a t r i x 71 5-4 R o t a t i o n 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 Solute Molecules 86 5-6 M a t r i x I s o l a t i o n Studies of GO and S 0 2 88 5-7 Gas Hydrates 93 5-8 Conclusions 97 Appendix 1 101 Appendix 2 102 B i b l i o g r a p h y 103 v i LIST OF TABLES. Page: 1. I n f r a r e d Absorption of HC1 i n Argon 21 2. I n f r a r e d Absorption of HG1 i n Argon, Krypton and Nitrogen 23 3. I n f r a r e d Absorption of HBr i n Various M a t r i c e s 31 4 . I n f r a r e d Absorption of HBr i n Argon 31 5. I n f r a r e d Absorption of CO i n Argon 37 6. I n f r a r e d Absorption of S O 2 39 7. S k e l e t a l Water Spectrum i n the Gas Hydrates 42 8. Values of Constants i n C a l c u l a t i o n s of M a t r i x S h i f t s 49 9 . F i r s t Order Energies f o r the Hindered Rotator 60 10. Hindered R o t a t i o n a l Energy Levels and Populations 61 11. Values of the Constant i n C a l c u l a t i o n s of Dipole-Dipole I n t e r a c t i o n s 63 12. C l a s s i f i c a t i o n of Peaks i n the Spectra of HC1 and HBr i n Argon 65 13. Force Constants of HBr and HC1 70 14. Band Centres of M a t r i x - I s o l a t e d HC1 and HBr 72 15. V i b r a t i o n a l S h i f t s f o r HC1 i n Various M a t r i c e s 77 16. P r e d i c t e d Spectra of HC1 and HBr i n Argon 82 17. I n t e n s i t i e s of HC1 and HBr Peaks 8 4 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 of HC1 Molecules 87 19. R o t a t i o n a l Energy Levels of S 0 2 91 20. P r o p e r t i e s of Some Gas Hydrates 94 v i i LIST OF FIGURES. Page: F i g . 1 The Apparatus 9 F i g . 2 The Low Temperature C e l l 1 0 F i g . 3 D e t a i l of Window Holder on L i q u i d Helium C e l l 13 F i g . 4 C e l l f o r Studies at L i q u i d N itrogen Temperatures 14 Figs. 5-7 I n f r a r e d Spectra of HC1 i n Argon 24-26 Figs.8,9 I n f r a r e d Spectrum of HC1 i n Nitrogen 27,28 F i g . 1 0 I n f r a r e d Spectrum of S o l i d HC1 29 F i g . 11 I n f r a r e d Spectra of HBr i n Various M a t r i c e s 32 F i g . 12 I n f r a r e d Spectrum of HBr i n Nitrogen 33 Figs.13-15 I n f r a r e d Spectra of HBr i n Argon 3 4 - 3 6 F i g . 16 I n f r a r e d Spectrum of CO i n Argon 4 O F i g . 17 I n f r a r e d Spectra of S O 2 i n Argon and Nitrogen 4 0 F i g . 18 I n f r a r e d Spectrum of S O 2 and Krypton Hydrates 4 3 F i g . 19 I n f r a r e d Spectrum of S O 2 as a S o l i d and a Gas Hydrate 4 3 F i g . 20 Anealed S O 2 Hydrate 4 4 F i g . 21 Co-ordinate System f o r Hindered Rotator C a l c u l a t i o n 53 F i g . 22 Change of 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 66 F i g . 23 F i r s t , Second, T h i r d and Fourth Nearest 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 F i g . 2 4 R e l a t i v e S i z e s of Some Molecules 78 F i g . 25 St r u c t u r e of Type 1 Gas Hydrates 95 1 CHAPTER 1. INTRODUCTION. 1-1 P r e l i m i n a r y Remarks. The bulk of the work f o r t h i s t h e s i s was c a r r i e d out on small molecules i n i n e r t m a t r i c e s . The emphasis throughout has been on the e f f e c t s of environment on the i n f r a r e d s p e c t r a , which n a t u r a l l y leads to a d i s c u s s i o n of i n t e r m o l e c u l a r f o r c e s . I n t h i s l i g h t the work on gas-hydrates becomes d i r e c t l y r e l a t e d t o the ma t r i x work, sin c e we are e f f e c t i v e l y studying small molecules i n a water "matrix". The spectroscopic s t u d i e s of small molecules i n h i g h pressure 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 , which are reviewed i n s e c t i o n 1-4, c o r r e l a t e w i t h the present m a t r i x and gas hydrate work, si n c e i n these environments i n t e r m o l e c u l a r f o r c e s determine the shapes, widths, s h i f t s and s p l i t t i n g of i n f r a r e d bands. The present work attempts t o extend t h i s i n f o r m a t i o n and apply i t to the i n t e r p r e t a t i o n of s p e c t r a of molecules i n ma t r i x and gas hydrate environments. 1-2 Studies of Molecular ..Interactions by the 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 technique i n c o n j u n c t i o n w i t h i n f r a r e d spectroscopy, o f f e r s a unique approach to the problem o f i n t e r a c t i o n s between molecules. The technique c o n s i s t s of d i s p e r s i n g the substance ( s o l u t e ) of 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 at a temperature low enough t o permit s e p a r a t i o n and i s o l a t i o n of s i n g l e s o l u t e molecules. This i s u s u a l l y achieved by condensing gas mixtures on a p l a t e cooled by l i q u i d hydrogen, or l i q u i d helium, as i n the present work. M a t e r i a l s most commonly used f o r matrices are n i t r o g e n and the ra r e gases. 2 Under c o n d i t i o n s of p e r f e c t i s o l a t i o n , the molecule under examination i s subject only t o s o l u t e - m a t r i x i n t e r a c t i o n s . 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 , at very h i g h m a t r i x t o s o l u t e r a t i o s . I n t e r a c t i o n s between s o l u t e molecules become important at low m a t r i x to s o l u t e r a t i o s , and the method can be employed to study i n t e r m o l e c u l a r f o r c e s which manifest themselves i n changes i n the i n f r a r e d spectrum of the i s o l a t e d 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 of very r e a c t i v e species such as f r e e r a d i c a l s , has been wi d e l y used i n recent years f o r the study of small molecules i n a m a t r i x environment. For example, Pimentel et a l ( 1 , 2 , 3 ) have recorded s p e c t r a of s e v e r a l small molecules i n s o l i d n i t r o g e n at 20°K, and M i l l i g a n and co-workers ( 4 , 5 , 6 ) have c a r r i e d out many i n v e s t i g a t i o n s w i t h small molecules 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 the work c a r r i e d out on water by these two groups, both of which reported complex s p e c t r a i n the regions of the three fundamentals of the water molecule. Pimentel ( 2 ) i n t e r p r e t e d the sp e c t r a i n terms of i s o l a t e d monomers, hydrogen-bonded dimers and higher polymers. M i l l i g a n and h i s co-workers ( 4 , 5 ) put forward evidence f o r f r e e r o t a t i o n of the trapped molecules i n the s o l i d m a trix; the l a t t e r view was supported by G l a s e l ( 7 ) on the b a s i s of r e s u l t s from s i m i l a r work. 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 of ammonia, between Pimentel et a l and M i l l i g a n et a l , i s found i n references ( 3 ) and ( 6 ) . . Previous 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 out by Becker and Pimentel ( 1 ) who recorded survey s p e c t r a under low 3 r e s o l u t i o n of HBr and HC1 i n s o l i d n i t r o g e n as a t e s t of the m a t r i x i s o l a t i o n technique. Since t h i s work was s t a r t e d , a note by Schoen et a l (8) has been published, 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 of m a t r i x - i s o l a t e d hydrogen chloride.. These workers used h i g h m a t r i x to s o l u t e r a t i o s and observed a simple spectrum, which they i n t e r p r e t e d u s i n g a hindered r o t a t o r model. Maki (9) reported i n f r a r e d s p e c t r a of CO as a s o l i d and i n s o l i d m a trices. The s p e c t r a observed were, complicated only by weak shoulders and peaks due to i s o t o p i c CO molecules. Recent work i n t h i s l a b o r a t o r y (10) i n d i c a t e d t h a t s t r a i g h t -forward explanations based on molecular 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 study of i n t e r m o l e c u l a r f o r c e s should be considered 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 obtained at low m a t r i x to s o l u t e r a t i o s . With t h i s i n mind, and i n view of the r e l a t i v e l y s m a ll a t t e n t i o n which has been given to m a t r i x i s o l a t i o n s t u d i e s of the simple molecules HC1, HBr and CO, a d e t a i l e d i n v e s t i g a t i o n on these molecules was undertaken. I t was hoped t h a t such a study would provide i n f o r m a t i o n which could be a p p l i e d to the i n t e r p r e t a t i o n of r e s u l t s obtained from more complex systems. I n f r a r e d s p e c t r a of HC1, HBr and CO i n n i t r o g e n and argon matrices were recorded at various m a t r i x - t o - s o l u t e r a t i o s . Change i n environment was a l s o s t u d i e d during warming of the deposit from 4°K up to the m e l t i n g p o i n t of the matrix. By a d d i t i o n of other s o l u t e i m p u r i t i e s to the gas mixtures, i t was hoped to demonstrate the extent of 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 i n t e r -p r e t a t i o n of 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 ( I I - I 4 ) have been c a r r i e d out 4 on molecular r o t a t i o n i n s o l i d s and s o l i d m a t r i c e s , u s i n g various hindered r o t a t o r models. 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 of band centres and s p l i t t i n g of degenerate r o t a t i o n a l l e v e l s . C a l c u l a t i o n s of s h i f t s of v i b r a t i o n a l fundamentals due to s o l u t e - m a t r i x i n t e r -a c t i o n s have been made w i t h some success. One of the e a r l i e s t c a l c u l a t i o n s due t o Kirkwood, Bauer and Magat (15,16) was based on a simple d i e l e c t r i c theory. This approach was used more r e c e n t l y by P u l l i n (17), who developed an improved theory. Buckingham (18), i n a quantum mechanical c a l c u l a t i o n , d e r i v e d a u s e f u l formula which has been t e s t e d s u c c e s s f u l l y by Maki (9) and Ewing and Pimentel (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 Linevsky (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 . In Chapter 4 of t h i s t h e s i s , c a l c u l a t i o n s of hindered 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 Lennard-Jones 1 (6-12) 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 , i n t e r m o l e c u l a r f o r c e s between so l u t e molecules i n nearest neighbour, next-nearest neighbour, e t c . , p o s i t i o n s are considered and the corresponding v i b r a t i o n a l s h i f t s c a l c u l a t e d . 1-3 Molecular I n t e r a c t i o n s i n the Gas Hydrates. D i r e c t l y r e l a t e d to the m a t r i x i s o l a t i o n s t u d i e s from the p o i n t of view of molecular i n t e r a c t i o n s i s the present work on the i n f r a r e d s p e c t r a of gas hydrates. The gas hydrates are i n t e r e s t i n g compounds because of 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 Stackelberg (21) i s r e s p o n s i b l e f o r much of our present knowledge of the s t r u c t u r e and p r o p e r t i e s of the gas hydrates. The compounds st u d i e d i n the present work a l l belong 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 designated as Type I by Von Stac 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 study on SC^, argon and krypton hydrates, was made i n t h i s l a b o r a t o r y by McCourt ( 2 2 ) . S h i f t s i n frequency of c e r t a i n peaks i n the s k e l e t a l water spectrum and the appearance of a new peak, not present i n the spectrum of i c e , were the main f e a t u r e s observed 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 study 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 molecular motion i n the cage. A comprehensive study of SC^-hydrates, u s i n g both normal and heavy water was undertaken at l i q u i d n i t r o g e n temperatures. Spectra of krypton and H 2 S hydrates were al s o recorded. The s k e l e t a l water v i b r a t i o n s and the v i b r a t i o n s of the e n c l a t h r a t e d molecules were examined under hig h r e s o l u t i o n , u s i n g the P e r k i n Elmer 4-21 s p e c t r o -meter. In one s e r i e s of experiments w i t h the SO?- hydrate, the r e g i o n of S O 2 was s t u d i e d under hig h r e s o l u t i o n at various temper-atures from 4° up to 120°K us i n g the P e r k i n Elmer 1 1 2 G spectrometer. 1-4 A Summary of Related Work on the Hydrogen Halides and Carbon Monoxide. Intermolecular f o r c e s , as manifested i n i n f r a r e d s p e c t r a of the hydrogen h a l i d e s and Carbon monoxide, i n gas, l i q u i d and s o l i d phases, have been the subject of a great deal of work i n recent years. The appearance of a Q-branch produced by high pressures of f o r e i g n gas i n the 1-0 bands of H C 1 and HBr has been observed by Vodar and h i s co-workers ( 2 3 ) . S i m i l a r s t u d i e s were, made by Rank et a l (24), who suggested t h a t the formation of a molecular complex between the hydrogen.halide and the rare-gas atoms used as p r e s s u r i z i n g 6 agents occurred. Pressure-induced s h i f t s of HG1 caused by noble gases have been measured by Ben-Reuven et a l (25) and a theory developed which accounts f o r the main features of the observed s h i f t s . Among the e a r l i e s t workers i n the f i e l d , West and Edwards (15) examined the sp e c t r a of H d i n s o l u t i o n s of various 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 the Kirkwood-Bauer-Magat formula (16) . Recently, Kwok and Robinson (26) s t u d i e d HC1 i n l i q u i d Xenon and observed a broad band w i t h two shoulders i n the r e g i o n of the 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 unresolved P and R branches combined w i t h solvent-induced 0, Q and S branches. The i n f r a r e d s p e c t r a of HC1 and HBr i n s o l u t i o n i n various I n e r t solvents have been recorded by Lascomb et 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 from -40 t o -142 cm-'', depending on the p o l a r i t y of the s o l v e n t . I n s i m i l a r s t u d i e s , other workers (28,29) conclude from the shapes of the absorption bands t h a t there i s some degree of r o t a t i o n of s o l u t e molecules. A very recent study of the overtone bands of 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 the 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 (30). These workers concluded t h a t the anharmonicity constant 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 the gaseous s t a t e , and the observed small band s h i f t was due only t o the change of v i b r a t i o n frequency. In s i m i l a r experiments on HC1 and HBr (31) the same workers found t h a t the anharmonicity 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 of s o l i d CO has a l s o been reported by Ewing and Pimentel (19). 7 St r a i g h t f o r w a r d assignments of peaks to the fundamentals of various i s o t o p i c CO molecules were made, and a broad f e a t u r e +70 cm from the main peak was assigned to combinations of the v i b r a t i o n a l mode w i t h both 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 at low temperatures have been s t u d i e d by Hornig and Osberg (32). I n the r e g i o n o f the fundamental, sharp doublets were observed w i t h s p l i t t i n g s of 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 cm - 1 f o r HBr, and i t was concluded t h a t these molecules form hydrogen-bonded chains 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, Hornig and Hiebert (33) reported the spe c t r a of mixed HC1-DC1 and HBr-DBr c r y s t a l s over the e n t i r e composition range. At low concentrations of 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 found. More complex spe c t r a observed f o r higher DG1 concentrations were a t t r i b u t e d to super-p o s i t i o n of peaks a r i s i n g from hydrogen-bonded chains of va r y i n g l e n g t h . 8 CHAPTER 2 . EXPERIMENTAL. 2-1 Experimental Methods. The m a t r i x i s o l a t i o n technique has been described by Pimentel et a l (1,34), by s e v e r a l authors i n the book e d i t e d by Bass and B r o i d a (35), 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 t h e s i s . I n the present m a t r i x work, a gaseous mixture of a hydrogen h a l i d e or carbon monoxide w i t h argon or n i t r o g e n , was prepared i n a 4 l i t r e storage bulb s e v e r a l days before an experiment. A convection c u r r e n t i n the gaseous mixture was produced by heating the bottom of the storage bulb. This ensured thorough mixing of the gases p r i o r to d e p o s i t i o n . A schematic diagram of the apparatus i s given i n F i g . 1 and a diagram of the low temperature c e l l , i n F i g . 2 . During a run, the mixture was passed through a d e p o s i t i o n tube i n t o the low temperature c e l l where the gas stream was allowed to impinge on a caesium i o d i d e p l a t e cooled b y - l i q u i d helium. A needle valve was used to c o n t r o l the d e p o s i t i o n r a t e which was i n d i c a t e d by the pressure reading of a thermocouple gauge. D e p o s i t i o n was continued u n t i l a f i l m of 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 study had been produced. This o f t e n r e q u i r e d d e p o s i t i o n times of s e v e r a l hours since the mixture must be deposited s l o w l y t o prevent temperature r i s e of the d e p o s i t , w i t h subsequent d i f f u s i o n of the trapped 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 ( ^ 500 : 1) were used to study i s o l a t e d molecules, whereas low r a t i o s (/\> 100 : 1) were employed when i t was d e s i r e d to observe the e f f e c t s of molecular i n t e r a c t i o n s on the i n f r a r e d s p e c t r a . In some experiments, c o n d i t i o n s such as fig 1. THE APPARATUS vacuum system and low temperature cell. helium i recovery liquid nitrogen liquid helium Csl window liquid helium transfer--tube vacuum jacket needle V 2 ^ ^ deposition tube thermocouple gauge ionization gauge Q to pumping ? system 10 fig 2 . THE LOW TEMPERATURE CELL liquid _ nitrogen radiation shield ~ hole to admit infrared beam .liquid .helium to pumping system WWA/ Cs I deposition window hole to admit gas from deposition tube deposition tube Csl window i 11 r a p i d d e p o s i t i o n , or formation of the deposit at temperatures w e l l above l i q u i d helium temperatures, were u t i l i z e d to ensure t h a t d i f f u s i o n occurred during d e p o s i t i o n . I n a d d i t i o n , s e v e r a l e x p e r i -ments were c a r r i e d out i n which a t h i r d p o l a r molecule, SO2 or CO was added to the gas mixture. The gas hydrate s t u d i e s were made mostly at l i q u i d n i t r o g e n temperatures i n a low temperature c e l l ( F i g . 4 ) . A few experiments were c a r r i e d out at l i q u i d helium temperatures u s i n g the same apparatus used f o r the ma t r i x i s o l a t i o n work. Mixtures of water vapour and the hydrate former were prepared by a procedure s i m i l a r to t h a t used i n the m a t r i x work, and deposited 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, of the order of seconds, were necessary 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 very t h i n f i l m s were e s s e n t i a l to produce s a t i s -f a c t o r y s p e c t r a . When i t was d e s i r e d to examine the s k e l e t a l water v i b r a t i o n s , a mixture was prepared c o n t a i n i n g a s l i g h t excess over the s t o i c h i o -m etric r a t i o of the hydrate former. This ensured t h a t a l l the water was t i e d up as hydrate. Conversely, when the v i b r a t i o n s of the en c l a t h r a t e d molecule were s t u d i e d , a s l i g h t excess of water was used to e l i m i n a t e the formation of s o l i d hydrate former. 2-2 D e t a i l s of the Low Temperature C e l l s . The c e l l used f o r the ma t r i x i s o l a t i o n s t u d i e s i s of the Duerig-Mador (36) type and i s i l l u s t r a t e d i n Fig.2. I t c o n s i s t s e s s e n t i a l l y of a c e n t r a l l i q u i d helium container surrounded by a r a d i a t i o n s h i e l d and an outer v e s s e l equipped w i t h o p t i c a l windows 12 of caesium i o d i d e . The c e l l i s connected to a vacuum system of the conventional type. The l i q u i d helium container i s made of copper and i s suspended by a s t a i n l e s s s t e e l neck to minimize heat i n f l o w by conduction, which would a c c e l e r a t e the evaporation of l i q u i d helium. To improve the e f f i c i e n c y of the 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 such as l i q u i d n i t r o g e n . A copper block at the bottom of the helium container holds a caesium i o d i d e p l a t e on which the deposit forms. 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 during the e a r l y p a r t of the present work, the window holder was modifie d to improve thermal contact between the window and the copper bl o c k . A l a r g e r block was machined (see F i g . 3) w i t h a recess to support the caesium i o d i d e p l a t e which i s t i g h t l y h e l d against the block by means of a copper gasket secured w i t h four copper screws. A l l space between the edges of the window, the gasket and the copper block i s f i l l e d w i t h s i l v e r conductive p a i n t . The c o l d j u n c t i o n of a g o l d - s i l v e r / g o l d - c o b a l t thermocouple i s attached to the copper block and the "hot" j u n c t i o n i s maintained 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 recorded as a t r a c e on the same chart paper as the spectrum, thus g i v i n g a re c o r d of the temperature a t which the spectrum was observed. No attempt was made to c a l i b r a t e the thermo-couple at p o i n t s between 4 0 and 77°K; intermediate temperatures were estimated by l i n e a r i n t e r p o l a t i o n . The l i q u i d helium container w i t h the attached window holder may be turned through 90° so tha t the caesium i o d i d e p l a t e can face e i t h e r the d e p o s i t i o n tube or the windows of the outer v e s s e l . 13 fig 3. DETAIL OF WINDOW HOLDER IN THE LIQUID HELIUM CELL liquid helium container copper b lock gasket ^ thermo-couple 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 TEMPERATURES o ring cooling coil caesium iodide deposition plate caesium iodide window liquid nitrogen leads to heating element beari ng evacuation tube deposition tube 15 The c e l l used f o r the gas-hydrate work i s shown i n F i g . 4 . This c e l l r e t a i n s the s a l i e n t c h a r a c t e r i s t i c s of the Duerig-Mador c e l l j u s t described but i s smaller and has no r a d i a t i o n s h i e l d . Other notable f e a t u r e s are the heating and c o o l i n g devices by means of which the temperature may be v a r i e d from 77°K to w e l l above room temperature, as r e q u i r e d . The heating i s e f f e c t e d by passing a c o n t r o l l e d e l e c t r i c c u r r e n t through a c o i l of pyrotenax wi r e . The c o o l i n g i s r e g u l a t e d by a flow of c o l d n i t r o g e n gas or l i q u i d n i t r o g e n through a c o i l e d copper tube. Both heating and c o o l i n g c o i l s are wound c l o s e to the window holder. I t has been found expedient when working at 77°K to keep the 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 c o o l i n g c o i l . There i s a l s o a d i f f e r e n c e i n the device f o r r o t a t i n g the window through 90°. I n the l i q u i d helium c e l l , o n l y the innermost container i s r o t a t e d , by means of a bearing l o c a t e d at the neck of the c o n t a i n e r . I n the l i q u i d n i t r o g e n c e l l , both the outer v e s s e l and the l i q u i d n i t r o g e n container move through 90° on a bearing s i t u a t e d at the base of the outer v e s s e l . The c o l d j u n c t i o n of a copper-constantan thermocouple i s attached to the bottom of the window holder and the hot j u n c t i o n i s maintained at room temperature. The thermocouple E.M.F. i s observed by means of a Leeds and Northrup m i l l i v o l t potentiometer and the corresponding temperature obtained from t a b l e s . 2-3 D i f f u s i o n i n S o l i d M a t r i c e s . In the present study, 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 the deposit was r a p i d l y formed, gave r e s u l t s which i n d i c a t e d t h a t d i f f u s i o n of the trapped species had occurred during d e p o s i t i o n . The problem of d i f f u s i o n i n s o l i d matrices has been discussed by Pimentel i n Chapter 4 of reference (35). I t was found t h a t small molecules d i f f u s e r a p i d l y at 0.4 - 0.6 of the m e l t i n g p o i n t of the matrix. During d e p o s i t i o n the f i l m temper-ature may r i s e w e l l above that of the c o l d p l a t e i f the d e p o s i t i o n r a t e i s r a p i d . This e f f e c t i s serious because of the poor thermal c o n d u c t i v i t y of most of the common m a t r i x m a t e r i a l s . For example, during the d e p o s i t i o n of n i t r o g e n at 4-°K, Fontana (37) observed a temperature r i s e of approximately 10°K at a d e p o s i t i o n r a t e of 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 during a t y p i c a l two hour run was 12.5 cc/min., so one might expect a maximum temperature r i s e of 4°K. Such a r i s e would b r i n g the temperature of the f i l m up t o 0.14 and 0.11 of the m e l t i n g po i n t of argon and n i t r o g e n r e s p e c t i v e l y , which should be w e l l below the temperature at which r a p i d d i f f u s i o n s e t s i n . There i s another f a c t o r which must be considered i n a d d i t i o n t o the temperature r i s e of the s o l i d m a t r i x f i l m . I t i s p o s s i b l e that i n c e r t a i n cases thermal contact d e t e r i o r a t e s between the caesium i o d i d e window and the window h o l d e r , r e s u l t i n g i n warming of the window and consequently a l s o of the de p o s i t . Evidence f o r t h i s was obtained i n e a r l y experiments before the new window holder was designed. I n these experiments, e i t h e r no i s o l a t i o n of the so l u t e molecule was achieved, or peaks were observed which were not normally present at 4°K, but which had been observed a t higher temperatures during warm-up s t u d i e s . However, w i t h the modif 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 , reasonable i s o l a t i o n was always achieved. 2t4 M a t e r i a l s . Regular 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 obtained from Matheson Co. Inc. Anhydrous S 0 £ , HBr and H C 1 , p u r i f i e d H^S and C P . grade CO were a l s o obtained from the Matheson Company. High p u r i t y Krypton was s u p p l i e d by A i r Reduction Corpor-a t i o n . D 2 O of 99.8% p u r i t y , supplied.by General Dynamics Corporation, L i q u i d Carbonic 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 hydrate work. The r a r e gases and n i t r o g e n were used without f u r t h e r p u r i f i c a t i o n . A l l other 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 to remove t r a c e s of non-condensable gas. Mass.spectroscopic analyses of argon, krypton 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 of i m p u r i t y f o r argon and n i t r o g e n of 5 - 1 0 p a r t s per m i l l i o n , and 50-60 p.p.m. f o r krypton. Minimum p u r i t i e s s t a t e d by the manufacturer f o r . t h e other gases were as f o l l o w s : S O 2 - 99-98%; HBr - 99.8%; H C 1 - 9 9 . 0 % ; H 2S - "99-5%; and CO - 99.5%. 2 - 5 The Spectrometers. The Per-'kin Elmer 1 1 2 G Spectrometer i s a high r e s o l u t i o n s i n g l e beam, double pass instrument. The main fea t u r e s a r e : a 60° Potassium bromide f o r e - p r i s m , which acts as a f i l t e r to e l i m i n a t e the energy of unwanted orders, 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 at 1 2 jl ( 8 5 0 cm~1) i n the f i r s t order. The instrument was 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 of 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 of H C 1 ( 3 8 ) , HBr (39), CO ( 4 O ) , and 18 other molecules ( A l ) . The o p t i c a l path l e n g t h i n the 112 G instrument i s about 5 metres and atmospheric water and CCU, show strong absorption i n the 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 w i t h s p e c t r a recorded i n these regions and i t i s very d e s i r a b l e t o remove these vapours by passing a cu r r e n t of dry n i t r o g e n gas through the instrument housing f o r some time before a spectrum i s recorded. The P e r k i n Elmer 421 spectrometer i s a double beam i n s t r u -ment capable of 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 the f i r s t order only. I n t e r f e r e n c e f i l t e r s are used to r e j e c t unwanted orders of 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 ; these r e p l a c e the customary f o r e - p r i s m . The standard instrument operates i n the range 4000 - 650 cm~1, but a g r a t i n g interchange i s a v a i l a b l e which extends the a c c e s s i b l e l o n g wavelength r e g i o n out t o 300 cm-''. In an i n f r a r e d spectrometer, the r e s o l u t i o n obtained under given c o n d i t i o n s depends on the frequency i n t e r v a l passed by the e x i t s l i t . For a p a r t i c u l a r frequency ~V0 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 width, which depends on the m e c h a n i c a l . s l i t width and on the o p t i c a l design of the instrument i s approximately equal to the s e p a r a t i o n of two l i n e s which are j u s t r e s o l v e d . Using formulae given by S i e g l e r (42) f o r the model 112-G spectrometer, and t a b l e s given by Roche (43) f o r the model 421 spectrometer, s p e c t r a l s l i t widths have been estimated f o r the instrument s e t t i n g s 19 used i n the present work and have been i n c l u d e d on the s p e c t r a reproduced i n Chapter 3. 20 CHAPTER 3 RESULTS. 3-1 I n f r a r e d Spectra of HC1 i n S o l i d Argon. Gas mixtures c o n t a i n i n g one p a r t of HC1 to 100, 200, 500 and 800 p a r t s of argon were deposited at 4°K. The s p e c t r a obtained from these deposits are shown i n F i g . 5 and the frequencies and r e l a t i v e i n t e n s i t i e s of the observed peaks are t a b u l a t e d i n Table I . The spectrum of HC1 i n argon at h i g h m a t r i x to s o l u t e r a t i o s c o n s i s t s of a strong peak at 2889 cm-'', a peak of medium i n t e n s i t y at 2853 cm-'', and a weak shoulder at 2 9 0 0 cm-''. These peaks c o r r e s -pond to those reported by Schoen et a l (8). However, s e v e r a l a d d i t i o n a l f e a t u r e s are observed at a l l m a t r i x r a t i o s used i n t h i s work, and at low r a t i o s c e r t a i n of these new peaks are more important than the t r i o mentioned above. An i n t e r e s t i n g f e a t u r e of t h i s d i l u t i o n study i s the change i n r e l a t i v e i n t e n s i t y of the peaks i n the spectrum as the m a t r i x to HC1 r a t i o i n c r e a s e s from 100:1 to 800:1. In F i g . 6 a warm-up study i s depicted f o r an argon t o HC1 r a t i o of 500:1. Some of the new peaks which appear i n the spectrum as the temperature r i s e s correspond to c e r t a i n peaks p r e v i o u s l y observed i n experiments conducted at low m a t r i x to HC1 r a t i o s . Furthermore, the peaks which appear during 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 deposit to 4°K. During warm-up s t u d i e s i t was found necessary to increase the monochromator s l i t widths as the temperature rose because l i g h t s c a t t e r i n g by the deposit i n c r e a s e d c o n s i d e r a b l y . This may i n d i c a t e the formation of m i c r o c r y s t a l s of the s o l u t e . 21 TABLE 1. I n f r a r e d absorption of HC1 i n argon at 4°K. Li n e i n t e n s i t i e s ( l o g I $ / l ) r e l a t i v e to the peak at 2889 cnr*1 • Frequency • Argon t o HC1 r a t i o cm"1 100:1 • 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 2867.5 .33 .13 .05 ' .05 2889 1.00 1.00 1.00 1.00 2900 sh sh .07 _ sh = shoulder 22 To i l l u s t r a t e 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 m o l e c u l a r i n t e r a c t i o n s on the spectrum of HG1 i n argon, mixtures c o n t a i n i n g CO or S O 2 w i t h HC1 and argon were prepared. The s p e c t r a obtained from deposits of these mixtures are shown i n F i g . 7. For the HCl/CO/argon mixture, the i n t e n s i t i e s of the peaks were changed r e l a t i v e to the HCl/argon case, but the main fea t u r e s of the spectrum were u n a l t e r e d . When S O 2 was added to the HCl/argon mixture s e v e r a l new features were observed i n the HC1 spectrum. Three new peaks were found: a very strong peak at 2808 em~1, a shoulder at 2821 cm-'' and a weak peak at 2829 cm-''. 3-2 I n f r a r e d Spectra of HC1 i n S o l i d Nitrogen and Krypton. At 4-°K the spectrum of HC1 i n a n i t r o g e n m a t r i x c o n s i s t s of one strong peak w i t h two very weak s a t e l l i t e s (see F i g . 8 ) . During the warm-up, however, many changes occur i n the spectrum. (See F i g . 9). Several peaks appear and disappear before the s o l i d n i t r o g e n sublimes away from the window l e a v i n g s o l i d HC1. Figure 10 shows the spectrum of s o l i d HC1 deposited at and warmed s l o w l y to 55 K. Comparison of Figures 9 and 10 i n d i c a t e s t h a t the f i n a l form of the spectrum of HC1 i n - n i t r o g e n i s indeed i d e n t i c a l w i t h t h a t of s o l i d HC1 at the same temperature. The observed frequencies f o r HC1 i n n i t r o g e n are compared w i t h the s p e c t r a of HC1 i n argon and krypton i n Table 2. S o l i d HC1 deposited at 4-°K gives a broad band centred at 2762 cm~1, 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 three peaks at 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 of the peaks i n the spectrum of s o l i d HC1 are shown i n Fig.10. 23 TABLE 2. I n f r a r e d Absorption of HC1 i n Argon, Krypton and Nitrogen at 4°K. (Frequencies i n cm -^). Argon Krypton Nitrogen HC1 500:1 300:1 200:1 gas 2787.5 (m) - - -2817 (a) 2800 (s) - -2853 (m) 2838 (m) 2814 (vw) 2864 P(1) 2863 M - - -2867.5 M 2854 (w) 2842 (vw) -2889 (vs) 2874 (vs) 2852 (vs) 2905 R(0) 2900 sh - 2875 (vw) 2925 R ( 1 ) In t h i s and subsequent t a b l e s the 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 s t r o n g , s = str o n g , m = medium, w = weak, vw = very weak, and sh = shoulder. 2 4 f i g 6 . 25 INFRARED SPECTRUM OF HCI 2 7 5 0 2 8 0 0 2 8 5 0 2 9 0 0 CM"1 26 f i g 7. I N F R A R E D S P E C T R A O F H C l IN A R G O N A T 4°K 2800 2850 2900 CM" 1 27 z g i— GL CC o CD < f i g 8 . I N F R A R E D S P E C T R U M O F , H C I IN N I T R O G E N . . 1 9 5 : 1 A T 15 ° K — i — 2 8 0 0 i 2 8 5 0 C M - 1 f i g 9 . I N F R A R E D S P E C T R U M O F H C I 2 7 0 0 2 8 0 0 C M " 1 29 • • I 2 7 0 0 2 8 0 0 C M 30 3-3 I n f r a r e d Spectra of HBr' i n Argon, Krypton and Nitrogen M a t r i c e s . The s p e c t r a of HBr i n argon, krypton and n i t r o g e n are compared i n F i g . 11, and the observed frequencies t a b u l a t e d i n Table 3. The spectrum of HBr i n krypton at a m a t r i x t o s o l u t e r a t i o of 320:1 i s seen to be very s i m i l a r to t h a t of HBr i n argon at a r a t i o of 500:1. The main d i f f e r e n c e i s a s h i f t of the whole spectrum t o lower wave numbers i n the krypton m a t r i x . I n s o l i d n i t r o g e n , a simple spectrum c o n s i s t i n g of one main peak w i t h three very 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 increase i n i n t e n s i t y during warm-up (see F i g . 12), i n a way s i m i l a r t o t h a t observed f o r HC1 i n n i t r o g e n . A d i l u t i o n study of HBr i n argon at m a t r i x r a t i o s of 100, 300 and 500 t o 1 was c a r r i e d out, and the r e s u l t i n g s p e c t r a are shown i n F i g . 13. The frequencie s, w i t h i n t e n s i t i e s at the various argon to HBr r a t i o s , are given i n Table 4« A v a r i a t i o n i n the number and r e l a t i v e i n t e n s i t i e s of 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 study 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 of HBr i n argon at a m a t r i x to s o l u t e r a t i o of 300:1 are shown. New peaks which appear during warm-up do not disappear on r e c o o l i n g to 4°K., and f u r t h e r deposit at t h i s temperature adds only to the i n t e n s i t y of the peaks o r i g i n a l l y observed at Spectra of HBr, perturbed by other s o l u t e molecules i n an argon m a t r i x , were recorded as i n the work w i t h HC1. These s p e c t r a are reproduced i n F i g . 15. The main f e a t u r e s of the HBr spectrum remain unchanged, but when GO i s present a new, 31 very strong peak i s observed a t 2520 cm -' and w i t h SO2, three new peaks are found at 2484, 2517 and 2524 cm-''. TABLE 3. I n f r a r e d absorption of HBr i n various matrices at 4°K. (Frequencies i n cm -^). Ar (505:1) Kr (320:1) N 2(l75:1) HBr (gas) 2465 w - -2496 m 2491 s 2493 vw -2550 m 2531 s 2506 vw 2542 p(1) 2558 vw 2541 w . 2535 w -2569 s 2551 vs 2545 vs 2575 R(0) 2575 sh - 2591 R ( D TABLE 4 I n f r a r e d absorption of HBr i n argon at 4°K. Line i n t e n s i t i e s ( l o g I 0 / l ) r e l a t i v e to the peak at 2569 cm-1. Frequency Argon to HBr r a t i o cm-1 110:1 215:1 300:1 " 505:1 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 I N F R A R E D S P E C T R A O F H B r IN V A R I O U S 2 5 0 0 2 5 5 0 C M H f i g 1 2 . I N F R A R E D S P E C T R U M O F H B r IN N I T R O G E N 2 5 0 0 2 5 5 0 C M " " ' 34 f i g 1 3 . I N F R A R E D S P E C T R U M O F H B r IN A R G O N A T 4°K II 2 4 5 0 2 5 0 0 2 5 5 0 C M " 1 35 f i g 1 4 . 36 j i g 15 . INFRARED SPECTRA OF HBr IN ARGON AT 4°K SHOWING THE EFFECT OF OTHER SOLUTES 2500 2550 37 3-4 M a t r i x I s o l a t i o n Studies on CO and SO^. The spectrum of CO i n argon ( F i g . 16) c o n s i s t s of one very-strong peak at 2138.5 cm-'', w i t h a peak of medium i n t e n s i t y at 2152 c m . Three very weak s a t e l l i t e s were a l s o observed on the low frequency side of the main peak when very t h i c k deposits were examined. No changes i n the spectrum of CO were observed when some CO molecules were replaced by HC1 or HBr. I n the overtone r e g i o n of CO, one weak peak at 4253 cm-'' was found. The observed frequencies together w i t h r e s u l t s obtained by other workers f o r both s o l i d and matri x i s o l a t e d CO are in c l u d e d i n Table 5. TABLE 5. I n f r a r e d Absorption of CO i n Argon at 4°K, Compared w i t h Results of Other Workers. (Frequencies i n cm-'') This Work Maki (9) Ewing and Pimentel (19) CO/Ar at 4°K. CO/Ar at 20°K. S o l i d CO at 20°K. 4253 w - 4253.5 2152 m 2148.0 21^ ,2 • l^. — 2138.5 vs 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 the regions of the symmetric and antisymmetric s t r e t c h i n g fundamentals ( V; and ~])^ ) of S O 2 i n argon and n i t r o g e n matrices are presented i n F i g . 17. A s i g n i -f i c a n t d i f f e r e n c e between the spectrum of S O 2 i n the two matrices i s observed. In argon, both the ~V, and V 3 bands c o n s i s t of a strong doublet w i t h a weak s a t e l l i t e . I n n i t r o g e n , however, only one strong peak i s found i n each r e g i o n , again w i t h a weak s a t e l l i t e . The doublets coalesce i n t o a s i n g l e peak during warm-up. In Table 6 the observed frequencies are l i s t e d f o r gaseous S O 2 , s o l i d S O 2 , S O 2 i n argon and n i t r o g e n matrices and S 0 2 i n the gas hydrate. 39 TABLE 6. I n f r a r e d Absorption of SCvj (frequencies i n cm-''), SO2 Gas S o l i d Hydrate In Argon I n Nitrogen reference (44) 80°K 80°K 4©K 4°K 518 521 s 521 s -528 sh - -1035 v -II4I.8 m - 1140.0 v 1151 H44.5 vs 1148.8 s 1147.3 s 1145.0 u 1152.1 s 1152.6 s 1305.5 s 1312.0 vs 1325.0 vs 1326 w 1336 sh 1334.3 u 1334.8 w 1342.5 vs 1351.4 vs 1346.7 sh 1349 sh 1355.6 vs 1351.8 vs 1362 4-1 3-5 Gas Hydrates. The s k e l e t a l water spectrum of SC>2 and krypton hydrates i s compared w i t h the spectrum of i c e i n F i g . 18. The corresponding frequencies, which are t a b u l a t e d i n Table 7, are the averages of s e v e r a l runs. Due to the u n c e r t a i n t y i n l o c a t i n g the maxima o f these broad bands, the. frequencies i n Table 7 are accurate only t o _ 10 cm '. I n s p i t e of t h i s however, F i g . 18 c l e a r l y shows _ - i s h i f t s of the peaks at 820 and 1600 cm" i n the spectrum of i c e t o 780 and I64O cm-'' i n the SO2 hydrate, and a new peak at 2420 cm-'' i n the krypton and SOg hydrates i s , a l s o evident. The frequencies a s s o c i a t e d w i t h the S O 2 molecule i n the hydrate and the s o l i d are compared i n F i g . 19- S i g n i f i c a n t d i f f e r e n c e s are found f o r each of the three fundamentals. The V 3 r e g i o n of SOg during an experiment i n which S O 2 hydrate was formed at 80°K cooled to 4°K and rewarmed to 120°K, i s presented i n F i g . 20. The c e n t r a l peak at 1340 cm i s seen t o have two shoulders at 120°K, one of which i s not present at 4°K. 42 TABLE 7. S k e l e t a l Water Spectrum i n the Gas Hydrates at 8G°K (frequencies i n cm-''). Ice S0 2.6H 20 Kr . 6 H 20 H 2S.6H 20 Assignment 820 s 780 s 820 s 815 s 1600 m 1640 m 1610 m 1620 m 2220 2220 •w- 2210 2190 VI 2410 vw 2420 w -3230 vs 3230 vs 3260 vs _ 4-3 f i g 1 8 . f i g 1 9 . 44 f i g 2 0 . _ i \ i 1 1— 1300 1310 1320 1330 1340 FREQUENCY (cm - 1) 45 CHAPTER A. THEORETICAL. 4-1 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 described i n t h i s chapter f a l l i n t o three c a t e g o r i e s : ( i ) C a l c u l a t i o n of s h i f t s of v i b r a t i o n a l frequency due to i n t e r a c t i o n s between so l u t e and ma t r i x . ( i i ) C a l c u l a t i o n s of p e r t u r b a t i o n energies f o r r o t a t i o n a l l e v e l s of i s o l a t e d s o l u t e molecules. ( i i i ) C a l c u l a t i o n of s h i f t s of v i b r a t i o n a l frequency due to mutual i n t e r a c t i o n s between p a i r s of 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 formulae and r e s u l t s developed i n t h i s chapter w i l l be a p p l i e d i n Chapter 5 to the i n t e r p r e t a t i o n of the observed sp e c t r a . 4-2 S h i f t s of V i b r a t i o n a l Frequencies Due to M a t r i x - S o l u t e I n t e r a c t i o n s . The energy of i n t e r a c t i o n between a s o l u t e molecule and the surrounding m a t r i x i s made up of the sum of three terms (45): 0 = 0 (ind) + 0 ( d i s ) + 0 (es) ( l ) A f o u r t h term should be added to Eq. ( l ) t o take account of r e p u l -s i v e f o r c e s . However, t h i s e f f e c t w i l l be t r e a t e d e m p i r i c a l l y l a t e r . The i n d u c t i o n energy 0 (ind) may be estimated from the energy of i n t e r a c t i o n between the permanent charge d i s t r i b u t i o n of one molecule and the moments induced i n the other. The term 0 ( d i s ) 4 6 i s the London dispersion energy and represents the interaction 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 interaction energy between the permanent charge d i s t r i b u t i o n s . The el e c t r o s t a t i c energy i s zero for 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 induction potential i n the case of the nitrogen or rare gas matrices i s given by (45): 0 (ind) = -pi oL6 (icos1 G •+• \)/[r6 (2) . 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 internuclear distance i n the s o l i d rare gas, and Q i s the angle between the z axis (chosen as a cube axis) 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 contribution of +2 regardless of the orientation 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 for an inverse s i x t h power potential for t h i s l a t t i c e i s 14.45 (47). This sum gives the effective number of nearest neighbours, and takes account of interactions between the isola 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, (3) T 6 which gives r i s e to a frequency s h i f t given by: 47 A V (ind) = -14.45 AC"l) oCb = C, ^ O f * ) (4) r t f h e where: /I (f^a.) i s the change i n the square of the d i p o l e moment 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 s . For the n i t r o g e n m a t r i x , there 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 the e l e c t r i c quadrupole of the n i t r o g e n molecule; however, the c o n t r i b u t i o n from these terms w i l l be much smaller than Eq. (4) and they can be neglected. An approximate expression f o r the d i s p e r s i o n energy i s given by (45): 0 ( d i s ) = ( • ) (5) where: C^a. and 0^4 are the p o l a r i z a b i l i t i e s of the sol u t e molecule and m a t r i x atom or molecule, and E a a n d E f e are approximately equal to 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. Eq. (8) may be used to estimate the d i s p e r s i o n c o n t r i b u t i o n to the s h i f t i n v i b r a t i o n a l frequency of a sol u t e molecule, i n the f o l l o w i n g way. Both the p o l a r i z a b i l i t y and the i o n i z a t i o n p o t e n t i a l of the s o l u t e molecule change during a v i b r a t i o n a l t r a n s i t i o n . Thus: / ( d i s ) = - C\f*}°- (6) a _ '/ 0 (dis) = ^ = (7) where; the double prime denotes the ground v i b r a t i o n a l s t a t e and the s i n g l e 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 constant 02.= 3° <4 ^ 6 /iT6 4 8 Subtracting Eq. (7) from Eq. (6) we get: </>—</> - - Ci O^a Ea. Ot-a. tig. ( 8 ) ¥e again introduce a factor of I 4 . 4 5 to account for the inter a c t i o n of the solute molecule with the entire matrix. The dispersion contribution to the s h i f t of v i b r a t i o n a l frequency i s given by: E« +£(> " c " (9) In the case of the nitrogen matrix the e l e c t r o s t a t i c term consists of a dipole-quadrupole interaction given by ( 4 5 ) : cos &aO£os2&b-l) -25>n<9«Sw6b COSC^f^- tfb) (10) where: i s the quadrupole moment of N 2, i s the dipole moment of the solute molecule, 9<^ , 9t, 0 a, 0b, are the polar angles associated with the dipole (HC1 or HBr) and the quadrupole (N 2), and v i s the nearest neighbour distance i n the s o l i d matrix. The average of the angular terms i n Eq. (10) i s zero; however, i n the case of nitrogen, the symmetry of the substitutional s i t e i s not spherical and the el e c t r o s t a t i c interaction .is not expected to vanish. An estimate of the order of magnitude of 0(es) may be obtained by assuming maximum interaction which leads to a value of ~^//^ P e r nitrogen molecule regardless of the 49 o r i e n t a t i o n of the s o l u t e molecule (20). Nitrogen below 35°K c r y s t a l l i z e s i n a cubic close-packed s t r u c t u r e (4-8), and the Lennard-Jones' sum f o r an in 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). Eq. (10) now becomes: and the s h i f t i n v i b r a t i o n a l frequency of the'solute, i s given by: fiV(es)- _ l ™ 0 / ^ * Qt> = A/^a (12) where: A / ^ a.is the change i n d i p o l e moment between the 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 . In Table 8, the constants i n Eqs. (4)> (9) and (12) are evaluated f o r argon, krypton and n i t r o g e n m a t r i c e s , u s i n g the values of 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 . , from Appendix I . TABLE 8. Values of Constants i n C a l c u l a t i o n s of M a t r i x S h i f t s . Formula AV(fod) - A V (dis) f \ Oi'd Ea. Cl[ Ay(es) --Cz Apcu Expression f o r 14.. 45 oCh 21.68 E i , oC b 17.00 0.4 the constant he U n i t s of C -3 -2 cm J esu cm-;l+ -2 -1 cm esu Ar 3.76 x 10 1.42 x 10 -Kr 3.95 x 10 1.32 x 10 -N 2 3.17 x 10 1.18 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 of c y l i n d r i c a l symmetry. The potential barrier to rotation was taken as C1(1-COS29) where i s the barrier height and 6 the angle between the molecular axis and the cylinder axis. Using this model for HC1 i n argon, these workers predicted a three l i n e spectrum corresponding to R(0), P(1) and R*(1), where R*(1) i s due to a blend of transitions of the hindered rotator. The potential function 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 29)^ for a diatomic molecule rotating i n a c y l i n d r i c a l w e l l . Armstrong (12) investigated the effect of e l e c t r o s t a t i c interactions on the r o t a t i o n a l energy levels of an isolat e d solute molecule trapped i n a rare gas l a t t i c e at low temperatures. He concluded that these interactions produce no effect on the r o t a t i o n a l energy levels of the solute molecule, and his expression for the interaction energy i s very si m i l a r to the sum of Eqs. (6) and (8) of the previous section. Armstrong also considered dipole-dipole interactions between the solute molecules. For a diatomic molecule i n a s o l i d rare-gas his results indicate that a s l i g h t mixing of rot 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 to be s p l i t . More recently Flygare (11) presented a theory dealing with the same problem. This author agrees with Armstrong that the t V (1-cos 26) = 2V s i n 2 e = C1(1-COS29) 51 dipole-induced dipole term does not effect the r o t a t i o n a l energy, but goes on to show that higher multi-polar interactions can be responsible for 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 interactions a r i s i n g from overlap of electronic charge distributions of the solute molecule and surrounding matrix atoms. The repulsive 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 usually observed. However, i t i s possible that the effect of the repulsive interactions i s undetected because the attractive 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 following calculations are based on the assumption that the i s o l a t e d solute molecule experiences repulsive forces i n addition to attractive forces which perturb the r o t a t i o n a l energy l e v e l s . 4-4 The Hindered Rotator Potential. In t h i s section a potential w i l l be developed for the case of a hydrogen halide molecule surrounded by twelve nearest neighbour matrix atoms. The model used for the calculation assumes that the hydrogen halide 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 point, which i s not s t r i c t l y true. In f a c t , the centre of volume of the molecule t The actual 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 probably 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 of the choice of o r i g i n , the angular dependence of the p o t e n t i a l w i l l be the same. A u s e f u l mathematical 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 i n c l u d e s r e p u l s i v e and a t t r a c t i v e forces 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 the i n t e r n u c l e a r d i s t ance of the i n t e r a c t i n g atoms, -Co i s the i n t e r n u c l e a r distance at which the p o t e n t i a l i s a minimum, and <£<? i s the depth of the p o t e n t i a l minimum. Eq. (14) may be r e w r i t t e n as: Ver) = V 0 T - - V o T y i •t=lJ2,.-,/2. (15) where: Vo = €<> and VC = l^ofo^ The matrix-halogen 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 the m a t r i x -hydrogen i n t e r a c t i o n s , and V 0 and V '0 w i l l not be the same f o r the two cases. The co-ordinate system used i n the 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 . 21. The distance T j i between the nucleus of the halogen atom and each of the twelve nearest neighbour m a t r i x atoms i s equal t o the i n t e r n u c l e a r distance i n the s o l i d r a r e gas, and equation (15) g i v e s : V ( r ) = 12 V c r - ' 2 - -12 V</ r - 6 (16) where: 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 r a r e gas. 53 f i g 2 1 . C O - O R D I N A T E S Y S T E M U S E D F O R T H E H I N D E R E D R O T A T O R P O T E N T I A L 54 Thus, the halogen-matrix i n t e r a c t i o n s give r i s e to an angle-independent term i n the p o t e n t i a l which we w i l l c a l l V . For the hydrogen-matrix i n t e r a c t i o n s the p o t e n t i a l has an angular dependence, since the i n t e r n u c l e a r distances 7*j i depend on 6 and 0 (see F i g . 2 l ) . The T|£ may be evaluated u s i n g the formula of a n a l y t i c a l geometry: T U - J ( x . - * y * ( y - - y y * f y - P z ( 1 7 ) which leads t o expressions of the form: r , i = r / | + ^ t ^ f(ej) ~ (is) where: d i s the i n t e r n u c l e a r distance i n the s o l u t e molecule and -f (erf) i s a f u n c t i o n of 9 and 0. A t y p i c a l Y\l ^-s: r , 4 = rj\ + + ~ ^ (sinQ Si"* -Cos ©) ( 1 9 ) 2 Future 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 neglect d / r 2 compared 2, o to 1. This i s a poor approximation s i n c e d / r * f o r HC1 i n argon i s 0.111. The square root may be expanded by the binomial theorem to g i v e : (20) 55 Again we neglect terms i n d V R S and higher powers. By t h i s procedure the y, t' are found to be: yz plane V ( \ ± CCOS& ± C $'» 6> 6<>S <j> ) xz plane 7- £ / ± £ COS 6 ± C 0 St" 4) (21) xy plane y ± Ct\»6CO$p ± CSl*6 \ where: (22) 2 r On substituting the values of "f,'L into Eq. (15) we get twelve terms of the form: where: x = c-f(efi) Expanding the inverse twelfth 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 twelfth power expansion up to the s i x t h power of x because the binomial coeficients are large, and ( ^ / r ) n does not decrease rap i d l y enough with n. However, for the inverse s i x t h power expansion, only the terms up to the fourth power of x are important. 56 When the twelve expressions for x are substituted i n Eq.23, and after 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. + V2 + i/j Cose sinze + VV sin+e cos*d> smz0 ^ ^ + V$ Si»6e COSl0 S'mz<fi •where: • VI = 12V0 T - - ' 2 -\l\Joy-6 Mi - (\7.+$* + H-j8 Vo-FU-(i^ +4-5 +4-*$) Vox'6 V3 = C f / i + / 8 » V o r - / 2 T-6 with oC = 78 dVr 2- o~ = 21 d V r 2 A = 682.5. dVr^- ' T= 63 d % * -^ = 1547 d % « In Eq. (24), + w i l l give r i s e to a constant perturbation which affects a l l r o t a t i o n a l energy levels equally and thus w i l l not effect the r o t a t i o n a l structure of the spectrum of the solute molecule. Hence the angle dependent potential V (60) may be written: V(e<p) - V3 cos©sin^e + (\4 s'm^e + Vssm6e) Cos'tp s'tfy (25) The potential given by Eq. (25)^may be considered as a perturbation and may be used to calculate corrections to the energy levels of the hindered rotator. 1" I t has been pointed out (49) that the p o t e n t i a l , Eq.24, does not have the symmetry of the octahedral s i t e , due to the i n c l u s i o n of s i x t h power terms. Although t h i s i s inconsistant with the treatments of previous workers (11,13) the r e s u l t s are expected to be q u a l i t a t i v e l y c o r r e c t . 57 4-5 Calculation of Energy Levels of the Hindered Rotator. From perturbation theory (51), the f i r s t order energies for a degenerate l e v e l E y are the roots of a secular determinant. The number of rows and columns of the determinant i s 2 J + 1, the degeneracy of the l e v e l E Such a determinant may be written: CO V Zi< v ( 1 Vol! - E 0> (26) with v ^ = <<n- / v where V i s the perturbation and tyi , f-A a r e normalized orthogonal wave functions belong-ing to the unperturbed degenerate l e v e l E c* ; . The corrected energy levels are given by: E 7 M (27) In the case of a diatomic molecule, the normalized spherical j are the zero order r o t a t i o n a l wave functions. The f i r s t order corrections are given by: .0 ) 0 (28) J = 1 (V„ - E,„) V IS V 31 = 0 (29) 58 where: VU = < Y * l \ \ / < * 4 » I Y^> with M;, M^= 1, 0, -1 (30) J = 2 ) V i a > V i 3 V , 4-( V EW> V , , V 32 V«r5 0 (31) where; with M;, = 2, 1, 0, -1, -2. A l l off diagonal terms i n Eqs. (2.9) and (31) vanish because they (32) a l l involve integrals of the form: .TT exp + i n 0 d 0 ' = O (n = a r e a l non-zero integer) J o A further s i m p l i f i c a t i o n results from the property a) E i) i tn E ito E Z , I II) 2,0 E — + ^ Yj** 1 s ° t h a t Eqs* ^29^and ^ 31^give: £"!, = < Y ! | v < « ^ i Y ! > < Y r | v t - e ^ / y ° > 59 The normalized s p h e r i c a l harmonics f o r J = 0, 1 and 2, are (51): Sine A Y o — ( 4-F ) * Y; \/o ( 3 \ x COS 0 Y <r<?5 0 fine -e Y ° - (if?) * ^ ° s ' e -0 The and the p e r t u r b i n g p o t e n t i a l V (9 0) from Eq. (25) (i) . . were s u b s t i t u t e d i n t o the expressions f o r E T ( W ) from Eqs. (33) and the r e s u l t i n g i n t e g r a l s evaluated. Use was made of t a b l e s of standard i n t e g r a l s (52) i n the e v a l u a t i o n of the E T M . The f i r s t order energies were found to 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 small s p l i t t i n g s of the J = 2 l e v e l s were found. Numerical r e s u l t s were obtained u s i n g accepted values f o r the constants T" and d . f - 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 (39). 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 the r o t a t i o n a l energy l e v e l s f o r HG1 and HBr, values must be assigned t o the constants K, and of Table 9. Reasonable f i r s t order c o r r e c t i o n s to the r o t a t i o n a l energy l e v e l s are obtained by g i v i n g 7 " / _ the value 0.85 and 6Q the value 10cm""''. 60 TABLE 9. F i r s t Order Energies for the Hindered Rotator. ( J , M ) HC1 E ' ( J , M ) HBr (00) (1,0) 12.7K,- 0.62K2 21.8K,- 0.95 K x (1,+ 1) (2,0) 9.50K,- 0.44K* 16.4K, - 0.68K2 (2,± 1) U.8K,- 0.73K2 25.5K,- 1.13Kt (2,+ 2) 12.2K,- 0 . 59K2 . 20.9K,- 0.91Kt where K, = V, o 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-'' respectively. The f i r s t order energies were calculated, and are l i s t e d i n column two of Table 10. Since we are only interested i n energy differences, E*(0 ,0) i s set equal to zero, and the other f i r s t order energies are given r e l a t i v e to E ' ( 0 , 0 ) . The unperturbed r o t a t i o n a l energies for the ground v i b r a t i o n a l state are given by: E ' J = B " J( J + 1 ) - D " J ( J + 1 ) (35) where: B " and D " are the r o t a t i o n a l constants for the ground v i b r a t i o n a l state, and have been tabulated i n references (38) and (39) for HC1 and HBr respectively. The hindered r o t a t i o n a l levels 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 levels at 5°, 1 0 ° and 20°K 61 u s i n g the formula: N(J,M) = N(0,0) g exp - E(«T,M)/kT (36) where: N(J,M) i s the number of molecules i n the 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 equal to one ; g i s the degeneracy of the l e v e l ; 1 k, the Boltzmann constant, and T, the absolute temperature. I t should be noted t h a t the r e s u l t s of the above c a l c u l a t i o n are only q u a l i t a t i v e i n nature, owing to the•many assumptions and approximations made. TABLE 10. Hindered R o t a t i o n a l Energy Levels and Populations f o r HC1 and HBr i n Argon. (a) HG1 level 1st Order Energy Corrected Energy R e l a t i v e P o p u l a t i o n J,M E 7(J,M) cm-1 L e v e l cm-1 5°K 10°K 2QOK 0. 0 0.0 0.0 1 1 1 1,0 0.0 20.9 .002 .05 .22 1, +1 0.0 20.9 .004 .10 .44 2,0 -3.8 58.8 - - .01 2, +1 +2.6 65.2 - - .02 2,+2 -0.6 62.0 - - .02 (b) HBr L e v e l 1st Order Energy Corrected Energy R e l a t i v e P o p u l a t i o n J,M E'(J,M) c u r l L e v e l cm - 1 5°K 10°K 20OK 0. 0 0.0 0.0 1 1 1 -1,0 0.0 16.7 0.008 0.09 0.30 1, ±1 0.0 .16.7 0.016 0.18 0.61 2,0 -6.6 43.6 - 0.001 0.03 2, ±1 +4.6 54-8 - 0.002 0.06 2,+2 -1.1 49.1 - 0.002 0.06 6 2 4 - 6 Shifts Due to Solute-Solute Interactions. In t h i s section, interactions between solute molecules i n nearest neighbour, next nearest neighbour, etc. s i t e s w i l l be considered. The potential energy of interaction between two id e a l dipoles i s given by ( 4 5 ) : -2cose acos eb-Sinoa Smeb Cos (<j>b-<f>*) (37) At low temperatures, where <j>ab i s greater than kT, the dipoles are assumed to be aligned to give maximum attr a c t i o n . That i s , 0b = 0 and Qb = 6 a ; Eq. (37) then becomes: 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 for the case of inte r a c t i o n between l i k e dipoles i s then given by: &b (40) 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 to the f i r s t excited v i b r a t i o n a l state. 63 For the case of interaction between unlike dipoles: Values of the constant C. i n Eqs. (40) and (4I) are tabulated 4 i n Table 11 for various values of Tab 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 substi 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 interaction energy between pairs of dipoles could be included. These arise from induction and disper-sion forces. However, the intermolecular potentials due to these effects both involve the inverse s i x t h power of the intermolecular distance, and even for the case of contiguous solute molecules, the contribution 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 i n Eq.(40) i n units of 10^7 e s u - 2 cm - 3. r ab Argon Krypton Nitrogen J2v / 3 r 17.92 6.34 3.45 2.24 15.27 5.40 2.94 1.91 15.85 5.60 3.05 1.98 64 CHAPTER 5. DISCUSSION. 5-1 C l a s s i f i c a t i o n of Peaks i n the Matrix Spectra of HC1 and HBr. 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. Closer examination of the spectra of HC1 (Figs. 5-7) and HBr (Figs. 13-15) reveals that the observed peaks f a l l into 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 with d i l u t i o n . ( i i ) Peaks which are present at low matrix to solute ra 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 . ( i i i ) Peaks which appear during warm-up studies. (iv) Peaks which are only present when other solutes are included i n the mixtures. Di 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 graphically i n F i g . 22. In the case of HBr, i t i s seen that, 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 with d i l u t i o n . A similar s i t u a t i o n i s found for HC1 where the i n t e n s i t y of the peak at 2853 cm-'' r e l a t i v e to the peak at 2889 cm-'' 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 ) HC1 2749* 2761* . 2787 2787 2817 2853 2863 2867 2889 2900 sh HBr 2426* 2436-2450* 24.65 2496 2550 2558 2569 2575 sh !:"These peaks were only observed during warm-up and were not previously included i n Table 1. f i g 2 2 . C H A N G E O F P E A K I N T E N S I T Y W I T H D I L U T I O N i i i i i i i i \0O 100 , 30O *tOO 500 60O too $00 m a t r i x t o s o l u t e r a t i o loo 200 joo koo SOO 600 ,700 0OO m a t r i x t o s o l u t e r a t i o 67 decrease rap 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 isola 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 interactions between pairs 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 for the peaks which decrease i n i n t e n s i t y with d i l u t i o n . P r o b a b i l i t i e s for finding such pairs at various matrix to solute ratios have been calculated (53) assuming a random d i s t r i b u t i o n of solute molecules on substitutional s i t e s i n a cubic close-packed c r y s t a l . For the peaks which only appear during warm-up, a similar explanation i s offered. In t h i s case, however, interactions between more than two solute molecules are suggested. Such interactions 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 larger clusters to be formed. At temperatures close to the melting point of the matrix, peaks appear i n the region of s o l i d HG1 or HBr. From the work of Hornig and his 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 into doublets due to the HCl35 and HCl^? isotopic molecules. I t i s perhaps s i g n i f i c a n t that certain other peaks i n the same spectrum remained unresolved under the same conditions of high resolution. These peaks were usually broader than the 68 f i g 2 3 . C L O S E - P A C K E D - C U B I C S T R U C T U R E s h o w i n g f i r s t , s e c o n d , t h i r d & f o u r t h n e a r e s t n e i g h b o u r p o s i t i o n s (a) (b) o i j J-—O-T—>—O O v—O 0 (0 (d) 69 resolvable ones and often corresponded to the group ( i ) peaks. However, the problem of scattering with the consequent loss of resolution 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 uncertain. 5-2 Isolated Solute Molecules. The observed infrared spectra of HC1 and HBr i n s o l i d matrices, indicate 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 usually obtained when high matrix to solute ratios were used. The three peaks which are assigned to HC1 molecules iso 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 vibration-rotation band centred at 2871 cm-'' which i s shifted by -13.5 cm"'' from the gas phase. A similar s i t u a t i o n holds for 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 discussion of the behaviour of isola t e d solute molecules i n i n e r t matrices i t i s necessary to consider several effects which, for the purpose of interpreting the observed infrared spectra, w i l l be considered separately under the headings of vibrat i o n and rotation. In the f i r s t case, we examine the causes and effects of perturbations of the v i b r a t i o n a l potential function of the molecule. Under the second heading, we consider the hindered rotation of the is 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 vibration-rotation band centre by invoking a change i n the force constant of the solute molecule. Hornig and Osberg (54) 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 state. A smaller change i s expected going from gas to matrix, and for HC1 i n argon the calculated value i s 4.73 md/A. However, for HBr i n argon, a sl i g h t increase i n the force constant i s necessary to account for the observed frequency s h i f t . Force constants for HBr and HC1 i n various matrices are compared i n Table 13 using the expression: f(matrix) = f (gas) ["V^^riag)"] 2 L y(gas) 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 s o l i d 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 vibration of the solute molecule i n a discussion of the s h i f t of the vibra-t i o n a l frequency. An increase i n the anharmonicity constant 6J«Xe -would resu l t i n a s h i f t to lower wave numbers, i n agreement with experiment. However, Vodar et a l (31) note that OJ^Xe for 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 larger than the observed s h i f t . I t i s not possible, 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 material i n the deposits studied. In the event that changes of force constants or anharmoni-c i t i e s could account for 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 effects would s t i l l remain unanswered. A fa r more satisfactory approach i s to consider the perturbing forces which could effect the potential function of the solute molecule. 5-3 Intermolecular Forces Between Solute and Matrix. In section 4-2 we considered induction, dispersion and e l e c t r o s t a t i c effects, 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 repulsive forces which produce a s h i f t i n the opposite direction. Repulsive forces are usually 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 pretation of spectra of ions isola t e d i n a l k a l i halide l a t t i c e s . The observed s h i f t s of band centres for 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 for the rare gases.) TABLE 14. Observed Band Centres of Matrix-Isolated HC1 and HBr. Molecule Gas Phase In Argon In Krypton In Nitrogen HC1 band centre* 2884-. 5 2871 2856 2833 s h i f t - -13.5 -28.5 -51.5 HBr band centre 2558.5 2559-5 254-1 2525.5 s h i f t - +1 -17.5 -33 ---mean value for H C l 3 5 and HC1 3 7. ¥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 to evaluate AV (ind) we need a value for the change i n the square of the dipole moment during the vi 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 function for HC1: a + ^.(r-re) + Mx(-r-r<,f+ ... (43) 73 where: M 0 = 1 .085 Debye M , = 0.880 D/A M 2 = 0.082 D/A2 Values of dyu/dr for the c r y s t a l l i n e hydrogen halides have been reported by Fr i e d r i c h and Person (62) and for HC1, djU/dr = 2.12 D/A. Neglecting the quadratic term i n Eq. (43), we obtain an expression for A ( r l ) /U,*-/U02 = M * [ ( Y l - r ^ 1 - to-r.)1 ] + 2 M o M , ( ^ - r 0 ) (44) where: To and 7", are the internuclear distances i n HC1 for the ground and f i r s t excited v i b r a t i o n a l states, and fe i s the equilibrium internuclear distance. For HC1 gas Te = 1.275 A and ~T0 = 1.284 A from reference (38). To obtain an estimate of AC/*1) i n the matrix, we use the observed s p l i t t i n g of the R(0) and P(1) peaks to calculate *r, , assuming: V R(O) - V P ( 0 = 4 8, (45) where: B, i s the r o t a t i o n a l constant for the f i r s t excited v i b r a t i o n a l state. This i s a poor approximation since: V R(0) -VP (D = 2(B 0 + B () (46) where: B0 i s the ro t a t i o n a l constant for the ground state, and probably also changes i n the matrix. However, using Eq.(45) we can obtain an order of magnitude for the induction s h i f t . The observed value of V R(0) - V ^ O ) was 36 cm-'' for HC1 i n both argon and krypton, and 38 cm-"! i n the nitrogen matrix. Now yt i s given by: T, = I h ' ^) 73a In a private communication from D. F. Eggers J r . , i t was pointed out that i n the above c a l c u l a t i o n , A V (ind) vanishes i n the harmonic approximation ( i . e . when Yi - T » —^e ). However, the approach used by Maki and Decius (58) gives a non zero value f o r A V (ind) i n any approximation. These workers follow the treatment adopted i n chapter 4-2 as f a r as Eq. (3). (j>(ind) = _ Jul Then, to estimate the e f f e c t upon the v i b r a t i o n a l frequencies ^Xa. i s replaced by \ (.^Ma/^Q }o ^ • I n t h i s c a s e t n e change i n the square of the dipole moment between the ground and f i r s t excited v i b r a -t i o n a l states i s given by: (42 a) where: ^ } denotes a quantum mechanical mean value. Using the harmonic o s c i l l a t o r wave functions we f i n d : <Qf>-<a:> = -pfcs where: ~lS0 i s the gas phase v i b r a t i o n a l frequency i n cm~l. By s u b s t i t u t i o n of Eq. (42b) and Eq. (42a) into Eq. (3), the s h i f t of v i b r a t i o n a l frequency i s given by: A V (ind) = _ I^M1 C J, where: C, , i s the value i n Table 8. V° (42c) 73b (42d) we f i n d f o r HC1: F i n a l l y , the v i b r a t i o n a l s h i f t s were found to be: A V f ' n c O = - 1' 5 c m - 1 f o r Ar and Kr, and AV(WcL) — -1.2 cm - 1 f o r N 2. I t i s seen that these s h i f t s are an order of magnitude l e s s than those c a l c u l a t e d i n the anharmonic approximation. The two treatments would appear to supplement each other, and i n s p i t e of the inaccuracy of the present c a l c u l a t i o n , i t seems that the anharmonic contribution i s the most important term. I t i s unfortunate that no data on the overtone bands of HC1 i n the matrix i s a v a i l a b l e at t h i s time since t h i s would give valuable information on the anharmonicity 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 for HC1. Hence T, = 1.38 A i n the rare gas matrices and 77 = 1.35 A i n nitrogen. Substituting the values of Te , T0 and r j into Eq. (44) together with a value for M, of 1.8 D/A for HC1 i n the matrix, we f i n d A (jji1) = 4.2 x 10-3'7 e s u 2 c m 2 fQT jjCl i n argon or krypton and A (jU l) = 2 .6 x 10~3'7 f o r jjCl i n nitrogen. Wow, using the results of Table 8, we may calculate the s h i f t s due to the induction 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 nitrogen. The second term i n Eq. (42) can be evaluated i f we can estimate the change i n c<ei and Ea i n Eq. C'T) : 1 c1 " r " E > E . E'i'+E, where: two primes denote the ground state and one prime the f i r s t excited v i b r a t i o n a l state. The i o n i z a t i o n potentials E (, for argon, krypton and nitrogen are 126,475 cm - 1, 112,359 cm - 1 and 125,104 cm - 1, respectively (63). The i o n i z a t i o n potential of HC1 i n the ground state E a i s 111,311 cm-"' (63) and the difference between the ground and f i r s t excited v i b r a t i o n a l state i s taken as the v i b r a t i o n a l frequency i n the matrix. Hence E a i s 108,440 cm - 1 i n argon, 108,455 cm-' i n krypton and 108,478 cm-'' i n nitrogen. 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 internuclear distance ( T — TE }: = dQ 4- <tfi ( Y" — re) + * • - (48) Values of c<i for 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. For HG1 the value was 1.0 A 2. Taking c<o as 2.63 A 3 (65) and oC, as 1.0 A 2 i n Eq. (48) we get <*a = 2.74 A 3 for HC1 i n argon and krypton matrices, and c<a = 2.70 A 3 i n nitrogen. Using these values, together with E„ , E a , and E^, the s h i f t s due to the dispersion forces were calculated: A V (dis) = -48 cm-'' for argon, A V (dis) = -49 cm-'' for krypton, A V (dis) = -18 cm-'' for nitrogen. Thus, the s h i f t s due to dispersion forces are larger than those due to induction forces, i n agreement with the work of Ben Reuven et a l (66). These workers used an approach sim i l a r to the present one, to calculate 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 nitrogen, there i s a contribution from the t h i r d term i n Eq. (42). The expression for 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 vib r a t i o n a l t r a n s i t i o n i s : Ay- = M, (r.-n ) 76 Using the same values of ra and r, as before, Eq. (4.9) gives A ft- =0.11 D for HC1 i n nitrogen, and the corresponding s h i f t A l>(es) = -56 cm-''. The results of the above calculations for HG1 i n argon, -krypton and nitrogen matrices are l i s t e d i n Table 15 together with the observed gas-matrix s h i f t s . Although the accuracy of these calculations i s undoubtedly questionable, they do consist-ently predict a greater "red" s h i f t than was observed. Thus, i t i s reasonable to assume that repulsive forces contribute to the over a l l s h i f t . Since repulsive forces arise 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 sizes of HC1, argon, krypton and nitrogen. This i s done i n Fig. 2L,, where i t i s seen that the HC1 molecule i s larger than a substitutional s i t e i n any of the three matrices. On s p a t i a l grounds one would expect the repulsive i n t e r a c t i o n to increase i n the order krypton, nitrogen, argon, but from Table 15 the apparent order obtained by subtracting A V (obs) from A V (calc) i s nitrogen, krypton, argon. The explanation f o r t h i s may well l i e i n the value taken for r, , the internuclear distance i n the excited v i b r a t i o n a l state. The value estimated for t h i s quantity 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 contribution from the repulsive forces for HC1 i n nitrogen could be between the values for the argon and krypton matrices. I t should be emphasised that the numerical results of th i s section are orders of magnitude only, since many assumptions and 77 TABLE 15. Vibrational Shifts i n cm-'' for HG1 i n Various Matrices. Matrix V ( t o t a l ) AV ( es) z l v(ind) ^ V ( d i s p ) observed. calc. calc. calc. Ar -13.5 - -16 -48 Kr -28.5 - -17 ' -49 N 2 -51.5 -56 -8 -18 79 approximations were made i n the calculations. Calculations of the gas-matrix s h i f t s for HBr could be carried out i n the same way as for HC1. This has not been done here because the value of r, calculated 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 to those calculated for 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 io n i z a t i o n potentials 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 of HG1, which suggests a smaller dipole derivative. The value of d-f^/^y quoted by F r i e d r i c h and Person (62) for s o l i d HBr was 1.72 D/A compared with 2.12 D/A for s o l i d HC1. A similar gas-matrix change i n r, i s expected for HBr as for HC1. Thus, the value of A C i n Eq. (44) i s expected to be smaller for HBr than for HC1, hence the value of £V (ind) for HBr w i l l be smaller. The dispersion s h i f t depends on the p o l a r i z a b i l i t y and ion i z a t i o n potential i n the ground and f i r s t excited v i b r a t i o n a l states Eq. (12). In Appendix 2, the ion i z a t i o n potential of HBr i s seen to be less than that of HC1, while the p o l a r i z a b i l i t y i s considerably larger for HBr than for HC1. I t i s expected, therefore, that &~0 (dis) for HBr i n the matrix w i l l be larger than the values for HC1. The ove r a l l attractive effects compared with HC1 may well be similar or perhaps larger for.HBr. On s p a t i a l grounds, one would expect the repulsive forces to be greater i n HBr than i n HC1, since the HBr molecule i s larger 80 than HC1 (see Fig. 24.). Repulsive forces usually 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 repulsive interaction could account f o r the smaller "red" s h i f t s observed for HBr i n the matrix compared to the HG1 case. 5-4- Rotation of Isolated Solute Molecules. There i s considerable evidence i n the l i t e r a t u r e supporting free or nearly free rotation 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 vibration-rotation bands. However, several 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 recently, Gebbie and S'tone (67) measured widths,and s h i f t s of pure rotation l i n e s of HC1 perturbed by rare gases and found that the only l i n e for which there was any measurable s h i f t was the J(0-1) l i n e . This corres-ponds to R(0) of the vibration-rotation spectrum. A perturbation which affects R(0) more than P(1) could account for 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 vibration-rotation l i n e s of HG1 perturbed by.noble gases, except R(0) i n argon and krypton which t Actually, the separation of R(0) and P(1) i s 2 ( B - | + B 0 ) , and both B-j and BQ may change i n the matrix. 81 i s shifted to 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. In other words, the observed s p l i t t i n g between R(0) and P(1) i s increased by addition of noble gases, contrary to the observations for HC1 i n s o l i d rare gases. An interesting feature of the spectrum of HC1 i n nitrogen 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 less perturbation of i t s r o t a t i o n a l levels i n nitrogen than i n the rare gas matrices, i n spite of the greater s h i f t of the band centre. This could be due to smaller repulsive forces i n the nitrogen matrix, i n agreement with the calculations of the previous section. The perturbation treatment of the previous chapter predicts a s p l i t t i n g of the R(1) peak of HC1 or HBr into three components. The calculated frequencies are l i s t e d i n Table 16 for these molecules i n argon. For these calculations the selection rules J = + 1 and M = 0,+ 1 apply, and no violations of these selection rules are predicted by f i r s t order perturbation theory (69). The frequencies of the allowed transitions are given by: V R° (0) = Vo'R(0) + E'(1,0) V R ° (1) = VJR(1)+ 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) = V J R (0+ E'(2,±2) - Ey(l,±l) where: E'(0,0) has been a r b i t r a r i l y set equal to zero. The Vo are the gas phase frequencies corrected for the s h i f t of the band centre i n the matrix. The superscript on the symbol V R M(0) refers to the value of the quantum number M, of the lower l e v e l . 82 TABLE 16. Predicted Spectrum of HC1 and HBr i n Argon, Compared With Observed and Gas Phase Spectrum. (a) HC1 Peak Calculated Frequencies i n cm ^ Observed Gas Phase P° (D 2850.5 2853 2864 R° (0) 2891.5 2889 2905 R° (D R ± 1 (D 2907.5 2914 2911 2900 . 2925 (b) HBr Peak Calculated Frequencies i n cm-'' Observed Gas Phase P° (D 2543 2550 2542 R° (0) 2576 2569 2575 R° (D R ± 1 (D 2585 2596.5 2591 2575 2591 83 S p l i t t i n g of the R(1) peak was not observed i n either the present work or the work of Schoen et a l (8). Previous hindered r o t a t i o n a l calculations (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 that a theory i s needed which w i l l predict 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 l e v e l s . I t has been suggested (69) that In an octahedral f i e l d with a barrier height of about 10 cm , the J = 0 l e v e l (E =0.0 cm-'') of HG1 would be perturbed considerably more than the J = 1 l e v e l (E = 20.9 cm -1). The physical interpretation of t h i s (69) i s that a molecule i n the J = 0 l e v e l does not rotate, but executes o s c i l l a t i o n s about some mean position, whereas a molecule i n the J = 1 l e v e l can undergo more or less free rotation. Such a model would predict 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 ratios of the R(0) and P(1) peaks of HC1 and HBr i n various matrices, are compared with calculated ratios at several temperatures. A simple explanation for 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 , several degrees higher. The very poor thermal conductivity of the s o l i d rare gases (70) could enable a thermal gradient to be established i n the deposit, with the surface layers at, a higher temperature than the layers near the caesium 84. iodide plate. This idea i s supported by the i n t e n s i t y ratios for HC1 and HBr i n nitrogen which are much closer to the 5°K figure (see Table 17). The thermal conductivity 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 incident radiation should be less important i n the nitrogen matrix. Further evidence for the warming of the rare gas deposits was provided by the warm-up study of HC1 i n nitrogen (see Fig. 12). At 15°K the in 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 for HG1 i n the rare gas matrices at the lowest temperature, when the thermocouple recorded 4°K. TABLE 17. Intensities of the P(1) peak of HC1 and HBr Relative to R(0) = 100, i n Various Matrices. (a) HC1 Observed Calculated Matrix 4°K--- 5°K 1 0 O K 2 0 O K Ar 30 0.6 15 66 Kr 30 0.6 15 66 N 2 4 0.6 15 66 (b) HBr Observed Calculated Matrix 4°K* 5°K 10°K 20°K Ar 40 2.4 2 7 91 Kr 35 2.4 27 91 N 2 3 2.4 27 91 i fIt i s believed that i n the noble gas matrices the temperature was several degrees above 4°K. See text for discussion of t h i s point. 85 One further 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 to 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 originate 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 difference i n absorption frequencies and t r a n s i t i o n moments for 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 to the nth energy l e v e l i s given by (68): where: 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 w n | i s the t r a n s i t i o n moment. 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) In the gas phase IR(1 ) / I P ( 1 ) i s found to be 1.5 for HG1 and 1.3 for 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 for the factor of f i v e between the gas and matrix i n t e n s i t i e s . d.E = K NL V, (51) i s : (52) 86 5-5 Interactions Between Solute Molecules. I t i s suggested that interactions between non-isolated solute molecules give r i s e to the peaks c l a s s i f i e d i n section 5-1 into groups i i , i i i and i v . Such pairs, t r i p l e c l u s t e r s , etc., 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 conductivity of the s o l i d rare gases i s very small (70), and i t i s quite possible that the new layers of deposit are not cooled to 4°K rapidly enough to 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 rate, and very ra p i d l y , and the re s u l t i n g spectra compared. In the case of rapid deposit, additional 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 pair of solute molecules i s the t h i r d nearest neighbour pair (see F i g . 23). However, when di f f u s i o n occurs, the nearest neighbour pair ( i . e . the dimer) i s energetically more favourable. Shifts of vi b r a t i o n a l frequencies due to dipole-dipole interaction between pairs of solute molecules may be calculated using the values of A(jA ) for HG1 estimated i n section 5-2, and Eq. (AO) developed In section 4-6: The s h i f t s calculated from t h i s equation are added to the matrix s h i f t s from Table 14, and the results compared with the observed spectra i n Table 18. AV = -C 4 Mr2) 87 TABLE 18. Calculated S h i f t s * i n cm-'' for Interactions Between Pairs of HC1 Molecules. Internuclear Distance Ar calc. obs. Kr calc. obs. N 2 calc. obs. r -89 -67.5 -88.5 -84.5 -92.5 -ft r -4.0 - -51 - -67 -V J r -28 -21.5 -41 -30.5 -59.5 -42.5 2 r -23 -17 -36.5 - -56.5 -*These s h i f t s include the matrix s h i f t s from Table 14. In the case of interactions between solute molecules i n si 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 less than predicted i n Table 18, because screening by the matrix atoms w i l l tend to reduce the intermolecular forces. With t h i s i n mind, the agreement between observed and calculated 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 nitrogen, no peak i s found near 2790 cm-'', the predicted frequency for 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 pai r . These obser-vations are compatible with the higher thermal conductivity and smaller heat of sublimation (see Appendix 1) of nitrogen at 4°K compared with the rare gases, since i f di 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 to interactions between three or more solute molecules. Many of these peaks are found only during warm-up (see Figs. 6 and 14) and the others are only found at low matrix to solute r a t i o s (see Figs. 5 and 13). The effect of solute-solute interaction was also demon-strated i n experiments where other solute molecules were added to the gas mixtures. Several new features were introduced into the spectra of HG1 and HBr (see Figs. 7 and 15), which can be explained q u a l i t a t i v e l y on the basis of dipole-dipole interactions between the hydrogen halide and the other solute molecule. 5 -6 Matrix 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. In the case of S O 2 , the large dimensions of the molecule compared to argon or nitrogen (see Fig. 24.) make rotation very u n l i k e l y . Shifts of band centres from the gas phase are surprisingly small for these molecules. In the case of SOg, t h i s could be due to the balancing of repulsive and attractive forces, with a small net eff e c t , as was found for 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 halides, thus interactions with the matrix are expected to be l e s s . On s p a t i a l grounds, CO should be able to rotate i n an 89 argon matrix. Nevertheless, i t i s d i f f i c u l t to correlate the observed matrix spectrum with the gas phase vibration-rotation spectrum. I t i s inter e s t i n g to note that a calculation by Ewing (72) predicts a Q branch i n the vibration-hindered rotation spectrum of l i q u i d CO. I f Ewing's theory could be carried over into the present matrix s i t u a t i o n , the very strong peak at 2138.5 cm~1 could be assigned to 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 . The peak at 2152 cm-1 would then be assigned to R(1). However, i t i s very doubtful that such an explanation could be correct. The ro t a t i o n a l constant for 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 resolving 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 selection rule i s expected i n the matrix environment ( 6 9 ) . The very weak peaks at 2115 and 2091 cm-'' are undoubtedly due to isotopic CO molecules (19)- In the spectrum of CO perturbed by HC1 (see Fig. 17'), i f we assign the peak at 2065 cm-^ to CO molecules interacting with 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 calculated from Eq. (41)s. of magnitude as that estimated for HC1 i n the matrix i n section 5-3. In the gas phase spectrum of SO2 the band centres are at AV which i s of the same order 90 1151.4 cm_1 and 1361.8 cm~1 for \ ) [ and V3 respectively (44). The s h i f t s i n the nitrogen matrix for ~)){ and V3 were + 1.2 cm""1 and -10 cm-1, and i n argon, -1.7 cm-1 and -8.3 cm~1 respectively. These s h i f t s are small compared with the gas-solid s h i f t s of 1 -1 -8 cm- and -46 cm for these bands. I t may be noted also that the gas-solid s h i f t s are much smaller for SO2 than for HC1 or HBr, because there i s no hydrogen bonding i n s o l i d SO2. Rotation of the S0 2 molecule i s u n l i k e l y on s p a t i a l grounds, and the appearance of the matrix spectrum supports t h i s conclusion. The SO2 molecule has ro t a t i o n a l constants: A = 2.03 cm~1, B = 0.34 cm-1 and G = 0 .29 cm - 1 (73). I t i s therefore a nearly prolate symmetric top with 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 levels were calculated and are tabulated i n Table 19 together with r e l a t i v e populations at 5°, 10°, and 20°K. At 5 K, a l l levels up to 3-f are appreciably populated, and at 10°K, higher levels w i l l also be important. Thus, the rotation-vibration bands even at 5°K would be very complex, consisting of several groups of unresolved l i n e s . The simple appearance of the spectrum of S0 2 i n argon and nitrogen matrices, therefore, indicates that rotation of the trapped molecule does not occur. I t i s interesting to note that i n the argon matrix both the 1// and 2/3 bands consist of strong doublets, while i n nitrogen, the main feature i n each of these bands i s a single strong peak. One might put forward an explanation analogous to inversion doubling (74) based on the following argument. 91 TABLE 19. Rotational Energy Levels of the S0 2 Molecule. J T cirri Populations Relative to 0 o 5°K 10°K 20°K 0 o 0.00 1 1 1 1- 1 O.64 .84 .91 .96 1 0 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 0 3.70 .35 .59 -77 2, 8.75 -08 .28 .52 2 J > 9.03 . 07 . 27 . 52 3- 1 3.77 .34 -58 .76 3-Z 5.34 -21 .46 .68 3-1 5.65 .20 .44 .67 3 0 10.63 .05 .21 .46 3, 10.65 .05 .21 .46 31 19.22 .004 .06 .25 3 3 19.21 .004 .06 .25 92 Assuming that the SO2 molecule i s prevented from rotating by the surrounding matrix atoms, then the molecule can only execute vibrations i n an equilibrium position i n the cavity. I f the sulphur atom passes between the oxygen atoms to an equivalent position on the other side, an inverted configuration i s obtained. This s i t u a t i o n could not occur i n the free molecule because the equivalent position could be obtained by a simple rotation. The two equilibrium positions may be described mathematically by a double minimum po t e n t i a l , which gives r i s e to a doubling of the vi b r a t i o n a l energy l e v e l s of the molecule (74-)• This phenomenon has been observed for the ammonia molecule i n the gas phase, and more recently i t has been suggested that inversion 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 small, but as the energy levels approach the barrier height the separation increases r a p i d l y (74). Thus, i f the observed s p l i t t i n g s for V/ and V3 of SO2 are due to the type of inversion doubling described above, then the s p l i t t i n g s for the overtones 2Vi and 2Vj should be much larger. Also, i t i s expected that the bending mode yx should exhibit greater s p l i t t i n g (74). Unfortunately, i t was not possible to study these bands i n the present work because the overtones are too weak, and the region of the bending mode was inaccessible. Arguments against the above explanation are: the absence of doubling i n nitrogen, and the large reduced mass of SO2, which would be expected to l i m i t the s p l i t t i n g s to very small values, unless the barrier to inversion was low (74)- In view of t h i s , 93 the observed s p l i t t i n g s of 4 .8 cm~1 for V, and 4 .2 cm- for 2^ 3 would appear to be too large to arise from inversion doubling. Another explanation.involving multiple trapping s i t e s could be considered. Harvey and Ogilvie (76) i n t h e i r work on formaldehyde i n an argon matrix, suggested that the formaldehyde molecule could be trapped i n a substit u t i o n a l s i t e , or i n larger 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 for the doublets observed for the and bands. 5-7 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), Pauling and Marsh (77) and Claussen (78), and i s i l l u s t r a t e d i n Fig. 25. Two types of cages are formed i n the type I hydrates, pentagonal dodecahedra enclosing nearly spherical 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 cavities should be large enough to allow rotation of small molecules, and X-ray d i f f r a c t i o n data (21,77) for SO2, H2S and CI 2 could be interpreted as i n d i -cating free rotation of these molecules i n the cages. The physical properties of some of these compounds are l i s t e d i n Table 20. 94 TABLE 20. Properties of Some Gas Hydrates. M M.P. of M diss , press, atm. at 0°C decomp. temp. °C at latm. Ar -190 105 -42.8 Kr -152 14-5 -27.8 Xe -107 1.5 - 3.4 c i 2 - 34 0.33 9.6 H2S - 60 0.96 0.35 so2 - 10 0.39 7.0 Discussion of the spectra of the gas hydrates can be considered i n two parts. The spectrum of the sk e l e t a l water vibrations, and the spectrum of the hydrate former (where i t e x i s t s ) . The sk e l e t a l water spectrum has several points of int e r e s t . In the S0 2 hydrate, the l i b r a t i o n a l frequency of H20 i s shifted by -40 cm-'', while the peak at 1600 cm-'' i n ice i s shifted i n the opposite dire c t i o n by 40 cm-'', confirming i t s assignment to rather than 2 , as has been suggested (80). The peak at 2230 cm-'' i n i c e , usually assigned to 1?x + , has almost the same frequency i n the hydrate, i n agreement with the above con-clusion. 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 f i g 2 5 . S T R U C T U R E O F T Y P E I G A S H Y D R A T E S A p o r t i o n o f t h e h y d r o g e n - b o n d f r a m e w o r k , o x y g e n a t o m s a r e a t t h e c o r n e r s o f t e t r a k a i d e c a h e d r a a n d d o d e c a h e d r a . The a r r a n g e m e n t o f t h e d o d e c a h e d r a i n t h e g a s h y d r a t e c r y s t a l . T h e o p e n c i r c l e s d e n o t e c e n t r e s o f c a v i t i e s . 96 be a second component of the combination band Vx + 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 S0 2 hydrate precludes the possi-b i l i t y that the new peak i s an overtone of • The S0 2 peaks i n the hydrate are generally broader than i n the s o l i d (see F i g . 19) which may be due to unresolved ro t a t i o n a l structure or intermolecular forces. The s p l i t t i n g of peaks observed i n s o l i d S0 2 i s not found i n the hydrate, since the S0 2 molecules are isola t e d i n t h i s environment and c r y s t a l effects (81) are absent. The weak peak at 1035 cm-"' i s assigned to 2 24 . This overtone peak was not reported i n previous work on s o l i d S0 2 (82,83). An anealed deposit of SO^ hydrate was studied over the temperature range 4°-120°K. In Fig. 20, the J/J peak was seen to 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 funda-mental with a rotatory or translatory 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 with lowering of the temper-ature would res u l t from depopulation of the upper l e v e l i n the ground state. I t might be i n t e r e s t i n g to examine the spectrum of the SO?-hydroquinone clathrate compound (84) since the cavity size i s much smaller (79) than i n the case of the hydrate, and motion of the S0 2 molecule would be even more r e s t r i c t e d than i t appears to be i n the S0 2 hydrate. 97 5-8 Conclusions. I t i s concluded that hydrogen halide molecules isola t e d i n s o l i d rare gases and nitrogen are able to execute hindered rotations. At the same time, the vi b r a t i o n a l potential function of the solute molecule i s perturbed by interactions with the surrounding matrix. I t has been possible to correlate the s h i f t of the v i b r a t i o n a l frequency with various intermolecular forces and i t was found that the repulsive forces play an important role i n determining the magnitude and direc 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 interpreted as a vibration-rotation band. Other peaks i n the observed spectra are attributed to mutual interactions between clusters of solute molecules i n contiguous and other . neighbouring s i t e s . At the lowest temperatures, only isol a t e d solute molecules and pairs of solute molecules are present i n si g n i f i c a n t concentrations. Arguments against rotation of isolat e d hydrogen halide molecules may be ra t i o n a l i z e d . In 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 i n t e n s i t y . 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 conductivity of s o l i d argon. The temperature r i s e allows the J = 1 l e v e l to become appreciably populated, and thus the R(1) and P(1) transitions 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 conductivity than s o l i d argon. A second argument against rotation i s the f a i l u r e to 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 for this may be that d i f f u s i o n sets i n rapidly enough to reduce the concentration of iso l a t e d solute molecules before the changes i n the vibration-rotation band are observed. This i s supported by the warm-up studies on HBr and HG1 i n nitrogen, 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 to R(0) i n the early part of the warm-up. The i n t e n s i t i e s of R(2) and P(2) are negligible below 20°K and are therefore not observed. I t would be interesting to observe the spectra of DC1 and DBr under the same conditions as i n this work, since the bond lengths, force constants and dipole moments are the same as for HC1 and HBr, to 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 for the heavy hydrogen halides as for the '•rio.r.mal halides. The vibration-rotation l i n e s , on the other hand, should be closer together since the rot 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) tr a n s i t i o n s could be observed during the early part of a warm-up study. Thus, the matrix spectra of DC1 and DBr could provide supporting evidence for the interpretation given i n th i s thesis of the observed spectra of HG1 and HBr. I t i s also possible that further 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 incident radiation could be eliminated by arranging the spectro-meter optics so that the infrared beam i s dispersed before passing through the sample. By th i s means, the t o t a l i n t e n s i t y of the radiation 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 generally i n good agreement with previous work. However, a different interpretation involving 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 to the gas mixtures i s explained on the basis of a dipole-dipole interaction between CO and HC1 molecules i n nearest neighbour s i t e s . An in t e r e s t i n g difference i n the spectrum of SO2 i n argon and nitrogen matrices was found. In the argon matrix both the 1/| and 2/3 bands consist of strong doublets, while i n nitrogen the main feature of each band i s a single strong peak. The s h i f t s from the gas phase i n both cases were small, from which i t i s concluded that repulsive and att r a c t i v e forces are nearly balanced. Two possible explanations for the doubling i n the SO^argon spectrum have been suggested. The f i r s t was based on a type of inversion doubling, a r i s i n g from r e s t r i c t i o n of rot a t i o n a l freedom of the trapped molecule. The second explanation involved multiple 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 useful to be able to observe the bending 1 0 0 mode V i of SO2 i n the two matrices. There i s a small upward s h i f t of vi b r a t i o n a l frequency (+3 cm-'') going from gaseous to 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 inter e s t i n g to see i f s p l i t t i n g of the i/^ peak i n the argon matrix occurs. The magnitude of the s p l i t t i n g might give some indication of the o r i g i n of the effect since, i f inversion doubling occurs, the bending mode i s expected to show the greatest s p l i t t i n g (74). Further work with SO2 i n various matrices might provide additional information on intermolecular forces and r e s t r i c t i o n of rotation. The work on the gas hydrates has provided confirmation of the assignment of the ,1',600 cm-'' peak i n the spectrum of 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*. . Evidence for r e s t r i c t e d motion of the SO2 molecule i n the hydrate was found from variations with temperature of the spectrum. Further studies on the gas hydrates by infrared spectroscopic methods are contemplated to study the motion of molecules i n the cages, and to investigate the o r i g i n of the new peak i n the water spectrum. 101 APPENDIX 1. Physical Properties of Matrix Materials. Properties Ar Kr N 2 References melting point °K b o i l i n g point °K heat of fusion cal/mole heat of vaporization cal/mole 83.9 116.6 63.3 87.5 120.3 77.4 284 392 85.3 1555 2162. 667 (61) (61) (87) (88) thermal conductivity at 5°K milliwatts/cm °K at 10°K at 20°K 20 7 50 40 15 26 15 10 -4 (68) (69) c e l l constant A internuclear distance (r) A 5.43 5.71 5.64 3.83 4.04 3.99 (45) (47) p o l a r i z a b i l i t y 102^ cm 3 i o n i z a t i o n potential e.v. 1.63 2.36 1.76* 15.68 13.93 15.51 (63) (61) * mean p o l a r i z a b i l i t y oC — y (o<,-h o(z + c<j ) •where: oCt > ^ 3 a r e "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. 102 APPENDIX 2. Properties of Some Diatomic Molecules. Property Units HG1 HBr CO References melting point °K b o i l i n g point °K 161 184.5 66 189.5 206 83 (61) (gas) cm-1 R(0) ., (gas) cm-1 2884.5 2558.5 2143 2905 2575 2147 (41) (41) i o n i z a t i o n potential e.v. dipole moment D p o l a r i z a b i l i t y * 10~ 2 4 cm3 13.8 13.2 U.1 1.085 0.78 0.112 2.63 3.61 1.95 (61) (89)(44)(90) (63) molecular dimensions A 4-27 4.57 3.73 3.60 3.90 2.80 (91) internuclear distance (r ) A 1.275 1.42 1.13 (38) (39) (40) -"mean p o l a r i z a b i l i t y 103 BIBLIOGRAPHY 1. E.D. Becker and G.G. Pimentel, J . Chem. Phys. 25j. 224 (1956). 2. M. Van Thi 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 Thiel, 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. M i l l i g a n , I b i d . , 3J_., 2162 (1962); Ib i d . , 22, 1276 (1963). 6. D.E. M i l l i g a n , R.M. Hexter and K. Dressier, I b i d . , 3JZ, 1009 (1961.). 7. J.A. Glasel, I b i d . , 21, 252 (i960). 8. L.J. Schoen, D.E. Mann, C. Knobler and D. White, I b i d . , 22? H46, (1962). 9. A. Maki, I b i d . , 21, 931 (1961). 10. H.F. Shurvell, M.Sc. Thesis, U.B.C. (1962). 11. W. H. Flygare,.J. Chem. Phys. 3_9_, 2263 (1963). 12. R.L. Armstrong, I b i d . , 36, 2429 (1962). 13. A.F. Devonshire, Proc. Roy. Soc. (London) A 153. 601 (1963). 14. L. Pauling, Phys. Rev. 36, 430 (1930). 15. W. West and R. T. Edwards, J. Chem. Phys. 5_, 14 (1937). 16. E. Bauer and M. Magat, J . Phys. rad. 9_, 319 (1938); Physica, 5_, 718 (1938). 17. A.D.E. P u l l i n , Spectrochimica Acta, 11, 125 (1958). 18. A.D. Buckingham, Proc. Roy. Soc. (London), A 248, 169 (1958). 19- G.E. Ewing and G.C. Pimentel, J. Chem. Phys. 3J>, 925 (1961). 20. M.J. Linevsky, I b i d . , 24, 507 (1961). 21. M. von Stackelberg et a l , Z. Electrochem. $8, 25, 4O, 99, IO4, 162 (1954). 22. F. McCourt, B.Sc. Thesis, U.B.C. (1962). 104 23. G.C. T u r r e l l , H. Vu and B. Vodar, J. Chem. Phys. 21, 315 (1960). 24. D.H. Rank, B.S. Rao and T.A. Wiggins, I b i d . , 3_7, 2511 (1962). 25. A. Ben-Reuven, S. Kimel, M.A. Hirshfeld and J.A. Jaf f e , I b i d . , 3_5_, 955 (1961). 26. J . Kwok and G.W. Robinson, I b i d . , 3J>, 3137 (1962). 27. J . Lascombe, P.V. Huong and M.L. Josien, Bull.. Soc. Chim., France, 1175 (1959). 28. M.O. Bulanin and N.D. Orlova, Optika i Spectroskopiya, 4, 569, (1958). 29. N.J. Jones and N. Sheppard, Trans. Far. Soc. 5j6, 625 (1960). 30. H. Vu, M.R. Atwood and B. Vodar, J. Chem. Phys., 3_8, 2671 (1963)-31. H. Vu, M.R. Atwood and B. Vodar, Intern. Symp. Mol. Struct. Specty. Tokyo, Japan (1962). 32. D.F. Hornig and W.E. Osberg, J. Chem. Phys. 23, 662 (1955). 33. D.F. Hornig and G.L. Hiebert, I b i d . , 2£, 752 (1957). 34- E. Whittle, D.A. Dows, and G.C. Pimentel, I b i d . , 22, 1943 (1954). 35- A.M. Bass and H.P. Broida, "Formation and Trapping of Free Radicals", Academic Press, N.Y. (1960). 36. . W.H. Duerig and I.L. Mador, Rev. S c i . Instr. 23_, 421 (1952). 37. B.J. Fontana, J. Appl. Phys. 29_, 668 (1958). 38. E.K. P l y l e r and E.D. Tidwell, 2 . Electrochem. 64, 717 (1960). 39. E.K. P l y l e r , J. Res. Natl. Bur. Stand., 64A. 377 (i960). 40. E,K. P l y l e r , J. Opt. Soc. Am., 45_, 102 (1955). 41. "Tables of Wave Numbers for the Calibration of Infrared Spectrometers", Butterworths, London (1961). 42. E.H. Siegler, Engineering report no. 563, Perkin-Elmer Corpn., Norwalk (1959). 43. J.M. Roche, Engineering report no. 601, Perkin-Elmer Corpn., Norwalk (1962). 44- R.D. Shelton, A.H. Nielsen and W.H. Fletcher, J . Chem. Phys. 21, 2178 (1953). 105 4-5. J.O. Hirschfelder, CF. Curtiss and R.B. B i r d , "Molecular Theory of Gases and Liquids", John Wiley & Sons, New York (1954). 4-6. R.G. Wyckoff, "Crystal Structures", Interscience Publishers, New York (1948), Vol. 1. 47. J.E. Lennard-Jones and A.E. Ingham, Proc. Roy. Soc. A 107, 636 (1925). 48. L.H. Bolz, M.E. Boyd, F.A. Mauer and H.S. Pieser, Acta Cryst. 12, 247 (1959). 49- R.F. Snider - Private Communication. 50. K.S. P i t z e r , "Quantum Chemistry", Prentice-Hall, Englewood C l i f f s , N.J. (1953). 51. L. Pauling and E.B. Wilson, J r . , "Introduction to Quantum Mechanics", McGraw-Hill, New York (1935). 52. G. P e t i t Bois, "Tables of Indefinite Integrals", Dover, New York, (1961). 53. K.B. Harvey, J.R. Henderson and H.F. Shurvell, Can. J. Chem. 4-2. (1964). 54- D.F. Hornig and-W.E. Osberg, J. Chem. Phys. 23, 662 (1955). 55. D.F. Hornig and G.L. Hiebert, I b i d . , 27, 752 (1957). 56. G.L. Hiebert and D.F. Hornig, I b i d . , 28, 316 (1958). 57. R.E. Behringer, I b i d . , 29_, 537 (1958). 58. A. Maki and J.G. Decius, Ibid. , 3J_, 772 (1959). 59. J . van der Elsken, Ph.D. Thesis, University of Amsterdam (1959). 60. J . L Bryant and G.C. T u r r e l l , J . Chem. Phys. 3_7, 1069 (1962). 61. W.S. Benedict, R. Herman, G.E. Moore and S. Silverman, Ibid. , 26, 1671 (1957). 62. H.B. F r i e d r i c h and W.B. Person, J. Chem. Phys. 3J2, 811 (1963). 63. "Handbook of Chemistry", 44th Ed. (1962-63), Chemical Rubber Publishing Co., Cleveland, Ohio. 64. E.J. Stansbury, M.F. Crawford and H.L. Welsh, Can. J. Phys. 3J., 954 (1953). 106 65. "Landolt-Bornstein Tables", Springer-Verlag, B e r l i n 1950, Vol. 1. 66. A. Ben-Reuven, S. Kimel, M.A. Hirshfeld and J.H. J a f f e , J. Chem. Phys. 21, 955 (1961). 67. H.A. Gebbie and N.W.B. Stone, Proc. Phys. Soc. 82, 309 (1963). 68. G.M. Barrow, "Introduction to Molecular Spectroscopy", McGraw-H i l l , New York (1962). 69. J.A.R. Coope - Private Communication. 70. G.K. White and S.B. Woods, P h i l May 3_, 785 (1958). 71. H.M. Roder, Cryogenics 2, 302 (1962). 72. G.E. Ewing, J. Chem. Phys. 27, 2250 (1962). 73. M.H. Sirv e t z , I b i d . , 19_, 938 (1951). 74. G. Herzberg, "Infrared and Raman Spectra", Van Nostrand, Princeton, N.J., (1945). 75. A.H. Hardin and K.B. Harvey, Can. J. Chem. 42,, 84 (1964). 76. K.B. Harvey and J.F. O g i l v i e , I b i d . , AO, 85 (1962). 77. L. Pauling and R.E. Marsh, Proc. Nat. Acad. S c i . , 2_8, 112 (1952), 78. TS.F. Claussen, J . Chem. Phys. 19_, 259, 662, 1425 (1951). 79. J.H. van der Waals and J.C. Platteeuw, "Advances i n Chemical Physics", Interscience, New York (1959), v o l . 2, p.1. 80. D.F. Hornig, H.F. White and F.P. Reding, Spectrochimica Acta 12, 338 (1958). 81. W. Vedder and D.F. Hornig, "Advances i n Spectroscopy", Interscience, New York (1961), Vol. 2, p.189. 82. P.A. Giguere and M. Falk, Can. J. Chem. 3J., 1833 (1956). 83. R.N. Wiener and E.R. Nixon, J . Chem. Phys. 25_, 175 (1956). 84. D.E. Pa l i n and H.M. Powell, J . Chem. Soc. 208, (1947). 85. E.B. Wilson, J.C. Decius and P.C. Cross, "Molecular Vibrations", McGraw-Hill, New York (1955). 86. G. Herzberg, "Spectra of Diatomic Molecules", Van Nostrand, Princeton, N.J. (1950). 107 87. P. Flubacher, A.J. Leadbetter and J.A. Morrison, Proc. Phys. Soc. 78, 1449 (1961). 88. R.H. Beaumont, H. Ghihara and J.A. Morrison, I b i d . , 7.8, 14-62 (1962). 89. R.P. B e l l and I.E. Coop, Trans. Faraday Soc. 3Jt, 1209 (1938). 90. C.A. Burrus, J. Chem. Phys. 28, 427 (1958). 91. L. Pauling, "The Nature of the Chemical Bond", Cornell, Ithaca, N.Y. (1960). 

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