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The microwave spectra of propiolamide Little, Gary Bruce 1977

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THE MICROWAVE SPECTRA OF PROPIOLAMIDE by GARY BRUCE LITTLE B.Sc, University of B r i t i s h Columbia, 1975 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Chemistry We accept this thesis as conforming to the required standard THE UNIVERSITY OF June, © Gary Bruce BRITISH COLUMBIA 1977 L i t t l e , 1977 In present ing t h i s thes is in p a r t i a l fu l f i lment o f the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thesis for scho la r ly purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or pub l ica t ion of th is thes is fo r f inanc ia l gain sha l l not be allowed without my wri t ten permission. Department of Chemistry The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date 23 June 1977 i i -ABSTRACT The ground v i b r a t i o n a l state microwave spectra of propiol-amide, HCCCONH^, and two is o t o p i c a l l y - s u b s t i t u t e d species, HCCCOND2 and UCCCOND2, have been assigned in the frequency region 8-40 GHz and the r o t a t i o n a l , centrifugal d i s t o r t i o n and nuclear quadrupole coupling constants have been deter-mined. The spectra for three excited v i b r a t i o n a l states of HCCC0NH2, the i n - and out-of-plane C=C-C bending modes and the nitrogen inversion mode, have also been analyzed; the vi b r a t i o n a l frequencies, as determined by r e l a t i v e intensity measurements, are 273±75 cm"1, >273 cm"1 and 333±75 cm"1, respectively. The molecule has been shown to be es s e n t i a l l y planar with either no barrier to the inversion motion or only a very small one. This result i s based mainly on the small change in the ground state i n e r t i a l defect upon amido-group deuteration (A(HCCCOND9)-A(HCCCOHH2)=-0.0311 amu-A2), the high frequency of the inversion motion, the absence of c-type transitions in the spectra, the s i m i l a r i t y of the d i s t o r t i o n constants i n the ground and f i r s t excited inversion states and the small magnitude of Y • Thus i t is concluded that the planar resonance form of propiolamide, H-C=C-C(0)^H2, is making the only s i g n i f i c a n t contribution to the state of the molecule. Internuclear param-eters of propiolamide have been determined by the substitution method and no anomalies have been found. Stark effect measure-ments have yielded a value of 3.67±0.02 D for the e l e c t r i c - i i i -dipole moment (u =1.08+0.02 D, y =3.51+0.02 D) and i t has been a b -deduced to be directed between the C-C and C=0 bonds at an angle of =11° to the l a t t e r . Spectroscopic Constants of HCCC0NH2 A 11417.938 MHz B 4135.483 MHz C 3032.595 MHz A 0.1816 amu-A2 v 1.85 MHz Aaa y -y 5.79 MHz Abb A c c - i v -TABLE OF CONTENTS CHAPTER PAGE 1. INTRODUCTION 1 1.1 P r o p i o l a m i d e 3 2. BASIC THEORY OF MICROWAVE SPECTROSCOPY 8 2.1 The R i g i d R o t o r 8 2.2 The D i s t o r t a b l e R o t o r 14 2.3 N u c l e a r Q u a d r u p o l e C o u p l i n g 21 2.4 The S t a r k E f f e c t 24 2.5 D e t e r m i n a t i o n o f M o l e c u l a r S t r u c t u r e s . . . . 28 2.6 L i n e a r L e a s t - S q u a r e s F i t t i n g o f Data to S p e c t r o s c o p i c C o n s t a n t s 30 3. EXPERIMENTAL PROCEDURES AND EQUIPMENT 32 3.1 The P r o p i o l a m i d e Samples 32 3.2 The S t a r k - M o d u l a t e d M icrowave S p e c t r o m e t e r . . 32 3.3 Mi c r o w a v e C e l l s and G a s - H a n d l i n g Equipment . . 36 3.4 The S t a r k V o l t a g e M i x e r 37 4. THE MICROWAVE SPECTRA OF PROPIOLAMIDE 39 4.1 A s s i g n m e n t of t h e S p e c t r a 39 4.2 D e t e r m i n a t i o n o f the R o t a t i o n a l , C e n t r i f u g a l D i s t o r t i o n and *^N N u c l e a r Q u a d r u p o l e C o u p l i n g C o n s t a n t s . 45 4.3 V i b r a t i o n a l S a t e l l i t e s — R e l a t i v e I n t e n s i t y Measurements . . . . . . 67 4.4 D e t e r m i n a t i o n o f t h e D i p o l e Moment o f P r o p i o l a m i d e 68 4.4.1 G e n e r a l C o n s i d e r a t i o n s 68 4.4.2 C a l i b r a t i o n o f t h e S t a r k C e l l w i t h C a r b o n y l S u l f i d e 69 - v -CHAPTER PAGE 4.4.3 The S t a r k S h i f t s o f P r o p i o l a m i d e , HCCCONH 2 73 5. THE QUESTION OF PLANARITY OF PROPIOLAMIDE 87 5.1 G e n e r a l C o n s i d e r a t i o n s . 87 5.2 The N a t u r e of t h e I n v e r s i o n M o t i o n 89 5.3 The I n v e r s i o n F r e q u e n c y and t h e ' Q u e s t i o n o f P l a n a r i t y . 93 5.4 The y Component o f t h e D i p o l e Moment and t h e Q u e s t i o n o f P l a n a r i t y 96 14 5.5 N N u c l e a r Q u a d r u p o l e C o u p l i n g C o n s t a n t s and the Q u e s t i o n o f P l a n a r i t y . 98 5.6 The Q u a r t i c C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s and t h e Q u e s t i o n o f P l a n a r i t y 102 5.7 The I n e r t i a l D e f e c t s and t h e Q u e s t i o n o f P l a n a r i t y 106 5.8 C o n c l u s i o n s 114 6. FURTHER DISCUSSION 115 6.1 The M o l e c u l a r S t r u c t u r e o f P r o p i o l a m i d e . . . 115 6.2 The D i r e c t i o n o f t h e D i p o l e Moment i n P r o p i o l a m i d e and i n R e l a t e d M o l e c u l e s . . . . 118 6.3 The C=C-C B e n d i n g F r e q u e n c i e s o f P r o p i o l a m i d e 122 6.4 The A s t r o p h y s i c a l S i g n i f i c a n c e o f P r o p i o l a m i d e 122 6.5 C o n c l u d i n g Remarks 131 BIBLIOGRAPHY 132 - v i -L I S T OF TABLES TABLE P A G E 1.1 The S t r u c t u r e s o f Some Amines and Amides 5 2.1 D e f i n i t i o n o f t h e D i s t o r t i o n and R o t a t i o n a l C o n s t a n t s i n t h e D i s t o r t i o n H a m i l t o n i a n (2.32) 18 2.2 D e f i n i t i o n o f t h e D i s t o r t i o n and R o t a t i o n a l C o n s t a n t s i n Watson's Reduced D i s t o r t i o n H a m i l t o n i a n ( 2 . 3 3 ) . . 19 4.1 HCCCONH 2 T r a n s i t i o n F r e q u e n c i e s - Ground V i b r a t i o n a l S t a t e 7 47 4.2 HCCCONH„ T r a n s i t i o n F r e q u e n c i e s - CEC-C i n - p l a n e -bend V i b r a t i o n a l S t a t e ( v . =1) 50 i n 4.3 HCCC0NH 2 T r a n s i t i o n F r e q u e n c i e s - C=C-C o u t - o f -p l a n e - b e n d V i b r a t i o n a l S t a t e ( v o u t = l ) 52 4.4 HCCCONH T r a n s i t i o n F r e q u e n c i e s - I n v e r s i o n V i b r a t i o n a l S t a t e ( v . =1) 53 mv 4.5 HCCC0ND o T r a n s i t i o n F r e q u e n c i e s - Ground V i b r a t i o n a l S t a t e 2 54 4.6 DCCC0ND„ T r a n s i t i o n F r e q u e n c i e s - Ground V i b r a t i o n a l S t a t e 7 . 5 5 4.7 R o t a t i o n a l and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f HCCC0NH 2 58 4.8 R o t a t i o n a l and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f HCCC0ND 2 and DCCC0ND 2 59 4.9 N u c l e a r Q u a d r u p o l e H y p e r f i n e T r a n s i t i o n s o f HCCC0NH 2 (Ground V i b r a t i o n a l S t a t e ) 60 4.10 N u c l e a r Q u a d r u p o l e H y p e r f i n e T r a n s i t i o n s o f HCCCONH, ( v J =1) 61 2 i n 4.11 N u c l e a r Q u a d r u p o l e H y p e r f i n e T r a n s i t i o n s o f H C C C 0 N H „ (v =1) 62 2 o u t 4.12 N u c l e a r Q u a d r u p o l e H y p e r f i n e T r a n s i t i o n s o f HCCC0NH o ( v . =1) 63 2 m v 4.13 N u c l e a r Q u a d r u p o l e H y p e r f i n e T r a n s i t i o n s o f HCCC0ND 2 (Ground V i b r a t i o n a l S t a t e ) 64 4.14 N u c l e a r Q u a d r u p o l e H y p e r f i n e T r a n s i t i o n s o f DCCC0ND 2 (Ground V i b r a t i o n a l S t a t e ) 65 14 4.15 N N u c l e a r Q u a d r u p o l e C o u p l i n g C o n s t a n t s o f HCCC0NH 2 66 - v i i -TABLE PAGE 4.16 Nuclear Quadrupole Coupling Constants of HCCCOND2 and DCCCOND2 66 4.17 Frequencies of the M =0*-0 Stark Component of the l«-0 Transition of 0 C S 71 4.18 OCS Calibration Graph — Slope and Intercept . . . 71 4.19 Observed frequencies of the |Mj|=<6-*-6, 5*-5 and 4«-4 Stark components of the 6^  ^'^2 4 t r a n s ^ t i o n a n <* of the Mj = 0-<-0 Stark component of the 1^  I ~ ° Q o t r a n s i t i o n of HCCC0NH2 74 2 2 4.20 Slope and Intercept of the v vs. e +e Graph S Cl C cl C for the Mj = Q«-0 Stark Component of the I~®Q Q Transition of HCCC0NH2 79 4.21 Final Iteration "pseudo second-order" Frequencies and (AE 0 ,-AE .)/2 Contributions for the |M | = 6+-6 , 5«-5 and 4«-4 Stark Components of the 6^  ^~^2 A Transition of HCCC0NH2 84 4.22 Final Iteration Slopes and Intercepts of the V vs. z +e Graphs for the |M |=6<-6, 5«-5 S d C SL C J and 4-*-4 Stark Components of the 6^  2~^2 4 Transition of HCCC0NH2 and the Dipole Moment Components Determined by the Iterative Procedures 85 4.23 The E l e c t r i c Dipole Moment of HCCC0NH2 86 5.1 Inversion Frequencies (w-^nv) °f Some Amides and Amines 95 14 5.2 K Quadrupole Coupling Constants ( X c c) °^ Some Amides and Amines 101 5.3 The Distortion Constants of Propiolamide and Related Molecules 105 5.4 I n e r t i a l Defects and their Changes upon Deuteration for Some Amides and Amines 109 5.5 I n e r t i a l Defects of Propiolamide and Other Pr o p i o l y l Molecules 113 - v i i i -TABLE PAGE 6.1 Ground S t a t e Moments o f I n e r t i a f o r HCCC0ND 9 and DCCGOND 2 and t h e A c e t y l e n i c Hydrogen S u b s t i t u t i o n C o o r d i n a t e s 116 6.2 The S t r u c t u r e of P r o p i o l a m i d e and R e l a t e d M o l e c u l e s . . . . . . . . 117 6.3 O b s e r v e d and C a l c u l a t e d (CNDO) D i p o l e Moments and D i r e c t i o n s f o r Some P r o p i o l y l and F o r m y l M o l e c u l e s . . . . . 120 6.4 I n - p l a n e and O u t - o f - p l a n e CSC-C B e n d i n g F r e q u e n c i e s o f Some P r o p i o l y l M o l e c u l e s 123 6.5 O b s e r v e d I n t e r s t e l l a r M o l e c u l e s . . . . . . . . . 124 6.6 A s t r o p h y s i c a l l y - I n t e r e s t i n g T r a n s i t i o n s o f HCCC0NH o . 126 - i x -LIST OF FIGURES FIGURE PAGE , I 3.1 B l o c k D i a g r a m o f t h e S t a r k - M o d u l a t e d S p e c t r o m e t e r ( w i t h BWO s o u r c e ) 33 3.2 The Microwave S p e c t r o m e t e r Vacuum System 37 3.3 C i r c u i t D i a g r a m o f the S t a r k V o l t a g e M i x e r . . . . 38 4.1 A T y p i c a l H y p e r f i n e S p l i t t i n g P a t t e r n f o r P r o p i o l a m i d e 42 4.2 The 6 o ~ 6 9 , T r a n s i t i o n o f P r o p i o l a m i d e i n t h e Ground and v. =1 S t a t e s 44 inv 4.3 F r e q u e n c y o f t h e Mj = 0«-0, J=l«-0 T r a n s i t i o n o f 1 6 0 1 2 C 3 2 S as a F u n c t i o n o f V 2 +V 2 72 dc ac 4.4 F r e q u e n c y o f t h e Mj = 0«-0, 1^ I~®Q Q T r a n s i t i o n o f HCCC0NH 2 as a F u n c t i o n o f t h e Square of t h e E l e c t r i c F i e l d S t r e n g t h . . N 75 4.5 F r e q u e n c y o f t h e | M [ = 6-*-6, 6^ ^~^2 4 T r a n s ^ t : ^ o n °^ HCCC0NH 2 as a F u n c t i o n o f t h e Square o f t h e E l e c t r i c F i e l d S t r e n g t h 76 4 .6 F r e q u e n c y o f t h e |Mj|=5«-5, 6^ ^~^2 4 T r a n s i t i o n of HCCC0NH 2 as a F u n c t i o n o f t h e Square o f t h e E l e c t r i c F i e l d S t r e n g t h 77 4.7 F r e q u e n c y o f t h e |M |»4-*-4t 6^ 2~^2 4 T r a n s i t i o n °f HCCC0NH 2 as a F u n c t i o n o f t h e Squ a r e o f t h e E l e c t r i c F i e l d S t r e n g t h 78 4.8 S e c o n d - o r d e r and E x a c t S t a r k F r e q u e n c i e s . f o r t h e |M |=6«-6, 6 _ - 6 „ . T r a n s i t i o n o f HCCCONH . . . . 81 5.1 The Two Resonance Forms of Amides 88 5.2 The G e n e r a l Form of an I n v e r s i o n P o t e n t i a l . . . . 90 5.3 P o t e n t i a l F u n c t i o n s and E n e r g y L e v e l s f o r (a) a Harmonic O s c i l l a t o r , (b) a S m a l l I n v e r s i o n B a r r i e r , ( c ) a L a r g e I n v e r s i o n B a r r i e r and (d) an I n f i n i t e I n v e r s i o n B a r r i e r . . . . . . . . . . . . . . . . . 92 -x-FIGURE PAGE 6.1 The Structure of Propiolamide 118 6.2 The Direction of the Dipole Moment of Propiolamide . 119 6.3 The Relationship Between the Dipole Moment of a Prop i o l y l Molecule with that of the Corresponding Formyl Molecule 121 - x i -ACKNOWLEDGEMENT The work d e s c r i b e d i n t h i s t h e s i s was c a r r i e d o ut a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a between September 1975 and June 1977 under t h e s u p e r v i s i o n o f Dr. M.C.L. G e r r y . I would l i k e to e x p r e s s my s i n c e r e g r a t i t u d e to Dr. G e r r y f o r h i s e n t h u s -i a s t i c s u p p o r t and f o r o r i g i n a l l y s u g g e s t i n g t h i s t o p i c to me, I would a l s o l i k e to thank t h e U n i v e r s i t y and t h e N a t i o n a l R e s e a r c h C o u n c i l of Canada f o r t h e i r f i n a n c i a l s u p p o r t of t h i s s t u d y i n t h e form o f s c h o l a r s h i p s . I a l s o e x t e n d my a p p r e c i a t i o n t o Z o l Germann o f t h e C h e m i s t r y Department E l e c t r o n i c s Shop f o r k e e p i n g t h e r a t h e r t e m p e r m e n t a l s p e c t r o m e t e r o p e r a b l e , to K a r l H a l l i n f o r h e l p f u l a d v i c e on computer programming and to Bob D a v i s f o r many h o u r s o f i n t e r e s t i n g d i s c u s s i o n . Chapter 1 Introduction The microwave region of the electromagnetic spectrum is generally designated as extending from a frequency of 1 GHz to a frequency of 1000 GHz. In this region, absorption of radiation corresponding to transitions between ro t a t i o n a l levels of a gaseous molecule with a permanent dipole moment is normally detected. The record of molecular absorptions within the 1-1000 GHz frequency range i s called a microwave spectrum and shows rota-t i o n a l transitions not only within the ground v i b r a t i o n a l state of the molecule but also those within excited v i b r a t i o n a l states, provided these states are s u f f i c i e n t l y populated. It i s often possible, as well, to detect transitions attributable to isotopic species present in the sample in natural abundance; the i n t e n s i t i e s of these transitions are d i r e c t l y proportional to the percent abundance. The assignment of a microwave spectrum for a pa r t i c u l a r molecule in a particular v i b r a t i o n a l state yields values for i t s r o t a t i o n a l constants which can then be used to determine the pr i n c i p a l moments of i n e r t i a . Because these moments of i n e r t i a depend on the molecular structure, i t i s possible, by studying enough isotopic species, to determine this structure completely and accurately. It i s also possible to obtain centrifugal d i s t o r t i o n constants d i r e c t l y from the microwave spectrum. These constants arise because of a coupling of the vi b r a t i o n a l and rotational motions of the molecule and, in p r i n c i p l e , can be used in the determination of the force f i e l d and the frequencies of the normal modes of -2-v i b r a t i o n . T h i s a n a l y s i s i s u s u a l l y l i m i t e d to r a t h e r s i m p l e cases (such as t r i a t o m i c m o l e c u l e s ) , however. When the m o l e c u l e b e i n g s t u d i e d c o n t a i n s a n u c l e u s w i t h a s p i n g r e a t e r than o n e - h a l f , f u r t h e r i n f o r m a t i o n i s a v a i l a b l e . In such a c a s e , the observed r o t a t i o n a l t r a n s i t i o n s are s p l i t because of the c o u p l i n g of the n u c l e a r s p i n w i t h the r o t a t i o n a l motion of the m o l e c u l e . I f t h i s s p l i t t i n g can be r e s o l v e d by the s p e c t r o -meter, n u c l e a r quadrupole c o u p l i n g c o n s t a n t s can be o b t a i n e d . These c o n s t a n t s can be r e l a t e d to the e l e c t r o n i c environment i n the immediate v i c i n i t y of the c o u p l i n g n u c l e u s and p r o v i d e a v a l u a b l e i n s i g h t i n t o the n a t u r e of the c h e m i c a l bonds formed by the c o u p l i n g n u c l e u s . The d i p o l e moment o f a m o l e c u l e can a l s o be determined from the microwave spectrum, by measuring r o t a t i o n a l t r a n s i t i o n f r e q u e n c i e s i n the presence of an e l e c t r i c f i e l d ( S t a r k t r a n s i t i o n s ) and o b s e r v i n g how they s h i f t when the f i e l d i s changed. These s h i f t s can be d i r e c t l y r e l a t e d to the components of the e l e c t r i c d i p o l e moment th e r e b y a l l o w i n g them to be determined v e r y a c c u r a t e l y . Microwave s p e c t r a a l s o y i e l d i n f o r m a t i o n r e g a r d i n g any l a r g e -a m p l i t u d e , h i n d e r e d i n t r a m o l e c u l a r m o t i o n s , such as i n t e r n a l r o t a t i o n , i n v e r s i o n and r i n g p u c k e r i n g , which the m o l e c u l e may p o s s e s s . The b a r r i e r s r e s t r i c t i n g t hese motions can u s u a l l y be e a s i l y e s t i m a t e d a f t e r the s p e c t r a l a n a l y s i s i n e x c i t e d s t a t e s has been c a r r i e d out and i n i d e a l cases the exact form of the p o t e n t i a l f u n c t i o n s can be -determined. D e t a i l e d r e v i e w s of microwave s p e c t r o s c o p y and i t s a p p l i c a t i o n s can be found i n s e v e r a l e x c e l l e n t sourcebooks ( 1 ) . -3-1 .1 Propiolamide Propiolamide was f i r s t synthesized in 1920 by Moureu and Bongrand (2) by reacting methyl propynoate with an aqueous solution of ammonia. The amide i s a white s o l i d at room temperature and has a melting point of 61-62°C. Studies of the chemical behaviour of propiolamide have been rather limited; perhaps the most int r i g u i n g behaviour, however, i s the formation of polypropiolamide, (CB~CHgNH)^, by a reaction analagous to the proton-transfer polymerization of acrylamide to 3-Nylon (3,4,5). No s t r u c t u r a l studies of propiolamide i n either the gaseous or condensed phases have been reported in the l i t e r a t u r e . The most interesting geometrical feature to be determined is expected to be the molecular planarity or non-planarity. The Lewis electron-dot picture for propiolamide can be represented by either of the three resonance forms H-C=C-C^ ^ H-C=C=<' H-C = C-C' J)N*-H N-H NN-H 1(a) 1(b) II where a bond represents a pair of electrons. According to simple valence-shell-electron-pair-repulsion (VSEPR) theory, Forms 1(a) and 1(b) are non-planar whereas Form I I i s planar; this difference 2 arises because of the planar arrangement of the three sp -hybridized (3 bond pairs, 0 lone pairs) bonding o r b i t a l s about the amido nitrogen atom in Form I I as opposed to the pyramidal 3 arrangement of the three sp -hybridized (3 bond pairs, 1 lone pair) -4-b o n d i n g o r b i t a l s a b o u t t h e n i t r o g e n atom i n Form 1(a) o r 1 ( b ) . The s t r u c t u r e o f p r o p i o l a m i d e i s depe n d e n t on the r e l a t i v e c o n t r i b u t i o n s o f t h e t h r e e r e s o n a n c e forms to t h e s t a t e of t h e m o l e c u l e and p l a n a r i t y w i l l r e s u l t o n l y i f Form I I i s the o n l y i m p o r t a n t f o r m . The c l a s s i c example of a m o l e c u l e w h i c h e x h i b i t s a p y r a m i d a l a r r a n g e m e n t o f atoms about a t h r e e - c o o r d i n a t e n i t r o g e n atom i s g i v e n by ammonia,„NH^, where the HNH bond a n g l e has been d e t e r m i n e d to be 107.05° ( c l o s e t o the t e t r a h e d r a l a n g l e o f 109.47°) and th e a n g l e between t h e b i s e c t o r o f t h e H(1)NH(2) a n g l e and t h e e x t e n s i o n o f t h e N-H(3) bond ( w h i c h i s d e f i n e d as $) i s $=59° ( 6 ) . T a b l e 1.1 c o n t a i n s a l i s t i n g o f t h e <i>-values o f o t h e r RNH 2-type m o l e c u l e s ( as d e t e r m i n e d by microwave s p e c t r o s c o p i c t e c h n i q u e s ) . A p a r t f r o m t h e a l k y l a m i n e s (CH^Nr!^, C ^ H ^ N H ^ ) , most o f t h e m o l e c u l e s s t u d i e d have been f o u n d to have much s h a l l o w e r p y r a m i d a l c o n f i g -u r a t i o n s about t h e amino (or. amido) n i t r o g e n c e n t e r t h a n does ammonia ($<50°). The l o w e r v a l u e s o f $ f o r t h e s e m o l e c u l e s c a n be i n t e r p r e t e d i n terms o f a p l a n a r R r f l i ^ s t r u c t u r e ( l i k e Form I I of p r o p i o l a m i d e ) c o n t r i b u t i n g s i g n i f i c a n t l y t o t h e o v e r a l l s t a t e o f t h e m o l e c u l e . I n ammonia and a l k y l a m i n e s d e l o c a l i z a t i o n o f the n i t r o g e n l o n e p a i r i s n o t p o s s i b l e and a R=SH 2 s t r u c t u r e c a n n o t e x i s t . A few o f the m o l e c u l e s i n T a b l e 1.1 have 0=0° i n d i c a t i n g t h a t t h e i r n o n - p l a n a r R-NH2 forms a r e o f l i t t l e o r no c o n s e q u e n c e and t h a t o n l y t h e i r p l a n a r R =N " H 2 forms a r e -important: F 2PNH 2, F 2BNH 2 and HCONR^. I n F 2PNH 2 and F 2BNH 2 t h e s t a b l e R=$H2 forms a r i s e b e c a u s e o f s t r o n g . . l o n e - p a i r i n t e r a c t i o n s l e a d i n g to t h e f o r m a t i o n o f a d^-p^ p h o s p h o r u s - n i t r o g e n d o u b l e bond and -5-T a b l e 1.1 The S t r u c t u r e s o f Some Amines and Amides M o l e c u l e * a R e f e r e n c e NH 3 59° 6 CH 3NH 2 52° 7 C0H,.NH- 53° 8 3 5 2 38° 9 p - C 6 H 4 F - N H 2 48° 10 m-C,H.F-NH-6 4 2 36° 11 p-C 5H 4N-NH 2 28° 12 o-Ct.H. N-NH„ 5 4 2 32° 13 m - C c H / N - N H „ 5 4 2 37° 12 2 - C . H „ N 0 - N H „ 4 3 2 I 22° 14 NCNH 2 38° 15 0 2NNH 2 51° 16 H 2CCHNH 2 34° 17 F 2 B N H 2 0° 18 F 2 P N H 2 0° 19 HCONH 2 0° 20 HCSNH 2 p r o b . =0 o 21 FCONH 2 p r o b . =0 o 22 H 2NCONH 2 •I p r o b . ^ o 23 a $ i s t h e a n g l e between t h e b i s e c t o r o f t h e HNH a n g l e and t h e e x t e n s i o n o f t h e N-X bond, where X i s t h e t h i r d atom bonded to N; $=0° f o r a p l a n a r a r r a n g e m e n t a r o u n d t h e n i t r o g en c e n t e r . - 6 -a P^-P^ b o r o n - n i t r o g e n d a t i v e double bond, r e s p e c t i v e l y . The r e s u l t f o r formamide ( H C O N H 2 ) means t h a t the p l a n a r resonance s t r u c t u r e H-<L i s the o n l y i m p o r t a n t form. The formamide s t r u c t u r e i s i n t e r e s t i n g as i t p r o v i d e s e v i d e n c e s u g g e s t i n g t h a t the R - C ( 0 - ) S H 2 resonance form of an amide i s much more s t a b l e than i s the R - C ( 0 ) N H 2 form, a r e s u l t which has been p r e d i c t e d by P a u l i n g ( 2 4 ) . The i m p l i c a t i o n of t h i s i s t h a t the resonance Form I I of p r o p i o l a m i d e i s expected to be the o n l y s t a b l e form and t h a t , t h e r e f o r e , the p r o p i o l a m i d e m o l e c u l e i s p l a n a r . The main o b j e c t i v e of the microwave s p e c t r a l a n a l y s i s of p r o p i o l a m i d e was to determine whether, ( i ) , t h a t the expected r e s u l t h o l d s and the m o l e c u l e i s , i n f a c t , p l a n a r , or ( i i ) , t h a t the m o l e c u l e i s s l i g h t l y n o n - p l a n a r ( l i k e most of the m o l e c u l e s i n Table 1.1) w i t h i t s two amido hydrogen atoms l o c a t e d out of (and on the same s i d e o f ) the H C C C O N p l a n e . I n t e r e s t i n the microwave spectrum of p r o p i o l a m i d e was a l s o aroused by the f a c t t h a t p r o p i o l a m i d e may be p r e s e n t i n i n t e r -s t e l l a r space. More than f o r t y m o l e c u l e s have been i d e n t i f i e d i n i n t e r s t e l l a r gas c l o u d s , most by comparison of t h e i r t e r r e s t r i a l r o t a t i o n a l microwave s p e c t r a w i t h the i n t e r s t e l l a r s p e c t r a d e t e c t e d by r a d i o t e l e s c o p e s ( 2 5 ) . I n c l u d e d i n t h i s t o t a l are s e v e r a l c o n t a i n i n g c a r b on-carbon t r i p l e bonds (methyl a c e t y l e n e , c y a n o a c e t y l e n e , c y a n o t r i a c e t y l e n e and the e t h y n y l r a d i c a l ) and -7-one c o n t a i n i n g t h e amido group ( f o r m a m i d e ) , so t h a t a l l the " p a r t s " needed to s y n t h e s i z e p r o p i o l a m i d e a r e p r e s e n t . A c c u r a t e l y known r o t a t i o n a l s p e c t r a l c o n s t a n t s o f p r o p i o l a m i d e a r e r e q u i r e d by r a d i o a s t r o n o m e r s i f t h e y a r e to s e a r c h f o r i t s i n t e r s t e l l a r t r a n s i t i o n s . In C h a p t e r 2 some o f t h e t h e o r y needed f o r t h e a s s i g n m e n t and a n a l y s i s o f t h e microwave s p e c t r u m o f p r o p i o l a m i d e w i l l be p r e -s e n t e d . C h a p t e r 3 w i l l c o n t a i n d e s c r i p t i o n s o f t h e g a s - h a n d l i n g a p p a r a t u s and t h e microwave s p e c t r o m e t e r . In C h a p t e r 4 t h e o b s e r v e d s p e c t r u m o f p r o p i o l a m i d e w i l l be a n a l y z e d and m o l e c u l a r c o n s t a n t s o b t a i n e d . In C h a p t e r 5 the d e t e r m i n e d c o n s t a n t s w i l l be used to t r y to answer t h e q u e s t i o n o f p l a n a r i t y o f p r o p i o l a m i d e . C h a p t e r 6 w i l l i n c l u d e f u r t h e r d i s c u s s i o n and some c o n c l u d i n g r e m a r k s . -8-Chapter 2 Basic Theory of Microwave Spectroscopy The basic theory needed in the interpretation and analysis of the microwave spectrum of propiolamide w i l l be presented in this chapter. Because propiolamide i s a prolate asymmetric rotor ( i t s two smallest p r i n c i p a l moments of i n e r t i a are nearly equal), the equations derived w i l l be set i n the prolate I R axis represen-tation (26); this i s the conventional choice of microwave spec-troscopists when dealing with prolate top molecules. 2.1 The Rigid Rotor The Hamiltonian for a r i g i d , rotating molecule i s well known (27) and i s given by H - AP 2 + BP 2 +CP2 2.1 r a b c where a,b,c are labels for the p r i n c i p a l i n e r t i a l axes (axes with respect to which the i n e r t i a tensor i s diagonal) and P 8 (g=a,b,c) represents the operator for the component of angular momentum about the g axis in units of h/2ir. A, B and C are called the rotational constants of the molecule and are given by A.- h B = h C = h 2.2 8TT2I 8TT2I^ 8TT2I a b c where I i s the moment of i n e r t i a about the g axis. By convention, the three p r i n c i p a l i n e r t i a l axes are labe l l e d in such a way that A>B>C (or I < I , _ < I ) . a b c' A symmetric top molecule i s one with at least one C symmetry -9-a x i s (n>2); such a molecule has two e q u i v a l e n t p r i n c i p a l i n e r t i a l axes p e r p e n d i c u l a r to the symmetry a x i s and hence two of the three r o t a t i o n a l constants are the same. For a symmetric top, i t can 2 2 2 2 2 be shown that P (P = ^ a + ^ b + I > c * s fc^e operator f o r the square of the t o t a l r o t a t i o n a l angular momentum), P (the operator f o r the angular momentum about the molecular symmetry a x i s ) and P^(the operator f o r the angular momentum about a s p a c e - f i x e d a x i s Z) a l l commute ( 2 8 ) ; thus the symmetric top r o t a t i o n a l wave f u n c t i o n s can be represented by the eigenket | JKM > with P 2|jKM a> = J(J+ 1 ) ( h / 2 i r ) 2 | JKMj> 2.3a P |JKM > » K(h/2n)|JKM > 2.3b Z J J P Z|JKM J> = M J(h/2ir) | JKMj> 2.3c where J = 0 , 1,2,3,... 2.4a K = 0, + l , ± 2 , . . . ,.±J 2.4b Mj= 0 , ± 1 ,±2, +J : 2.4c are the r o t a t i o n a l quantum numbers. For a p r o l a t e symmetric top molecule A>B=C, and the molecular symmetry a x i s (the z a x i s ) i s l a b e l l e d as the a i n e r t i a l a x i s . Thus the p r o l a t e top Hamiltonian i s given by H = AP 2 + B ( P 2 + P 2) - AP 2 + B ( P 2 - P 2) 2.5 r a b c a a and i s di a g o n a l i n the |JKM^> b a s i s ; hence the exact r i g i d r o t o r energy of a p a r t i c u l a r |JKM^> l e v e l of a p r o l a t e symmetric top i s E - <JKM |H |JKM > = BJ(J+1) + (A-B)K 2 2.6 IT J IT J 2 Because of the energy dependence on K there are only J+l d i s t i n c t -10-K - l e v e l s f o r e a c h J - l e v e l ; a l s o , t h e r e i s no e n e r g y dependence on Kj i n t h e a b s e n c e o f an a p p l i e d e x t e r n a l f i e l d . The s y m m e t r i c top w a v e f u n c t i o n s , |JKM >, c a n be d e t e r m i n e d e x p l i c i t l y f r o m a s o l u t i o n of t h e r o t a t i o n a l S c h r o d i n g e r e q u a t i o n ( 2 9 ) . The s o l u t i o n g i v e s the r e s u l t t h a t | J KM T>-N T V M ( s i n 9/2)l K" Mjl(cos 9 / 2) I K + M J 1 F ( s i n 2 6 / 2 ) e i K ( J > e ± M J X 2.7 J JKMj where N i s a n o r m a l i z a t i o n f a c t o r , F ( s i n 2 0 / 2 ) i s a h y p e r -JKMj g e o m e t r i c s e r i e s and 8 , <j), x a r e E u l e r ' s a n g l e s ( 3 0 ) . The c o n c e p t o f a d i r e c t i o n c o s i n e w i l l now be i n t r o d u c e d as i t w i l l be needed l a t e r when d i s c u s s i n g t r a n s i t i o n p r o b a b i l i t i e s and t h e S t a r k e f f e c t . D i r e c t i o n c o s i n e s a r e d e s i g n a t e d by and r e p r e s e n t t h e c o s i n e of t h e a n g l e between a s p a c e - f i x e d a x i s F and a m o l e c u l e - f i x e d a x i s g. T h i s a n g l e depends on t h e r o t a t i o n a l s t a t e o f t h e m o l e c u l e ; hence t h e m a t r i x e l e m e n t s o f t h e d i r e c t i o n c o s i n e s i n t h e s y m m e t r i c top b a s i s , <JKM | $ |j'K',M '>, a r e n e e ded. J c g J T hese e l e m e n t s can be w r i t t e n as (31) and s i n c e t h e w a v e f u n c t i o n s o f t h e s y m m e t r i c t o p , 2.7, a r e known, the i n t e g r a l s on t h e r i g h t o f e q . 2.8 can be e v a l u a t e d i n a s t r a i g h t f o r w a r d manner ( 3 1 ) ; t h e r e s u l t s a r e a v a i l a b l e i n t a b l e s ( 3 2 ) . When a m o l e c u l e has t h r e e u n e q u a l moments of i n e r t i a i t i s c a l l e d an a s y m m e t r i c t o p . B e c a u s e o f t h e asymmetry, t h e r i g i d r o t o r H a m i l t o n i a n m a t r i x f o r t h e a s y m m e t r i c r o t o r i n t h e s y m m e t r i c r o t o r w a v e f u n c t i o n b a s i s i s n o t d i a g o n a l and K i s no l o n g e r a good -11-quantum number. A l t h o u g h K r e t a i n s no p h y s i c a l meaning f o r t h e a s y m m e t r i c r o t o r , i t i s r e t a i n e d as a l a b e l f o r t h e e n e r g y l e v e l s : a l e v e l i s d e s i g n a t e d as J T , „ ( o r J ; T = K - K ) v/here K i s ° K , K T p o p p * o the v a l u e K would have f o r t h e l i m i t i n g p r o l a t e c a s e (where B=C) i and K q i s t h e v a l u e K would have f o r t h e l i m i t i n g o b l a t e c a s e (where A=B) . T h e r e a r e 2J+1 d i s t i n c t T - l e v e l s f o r each J - l e v e l . The d e g r e e o f asymmetry o f a m o l e c u l e i s commonly i n d i c a t e d by two p a r a m e t e r s , t h e Ray asymmetry p a r a m e t e r (ic) and t h e Wang asymmetry p a r a m e t e r (bp) where K = 2B-A-C b = C-B 2.9 A-C P 2A-B-C C l e a r l y , tc r a n g e s from a v a l u e o f -1 f o r a p r o l a t e s y m m e t r i c top to +1 f o r an o b l a t e s y m m e t r i c top and b^ r a n g e s from 0 f o r a p r o l a t e s y m m e t r i c top t o -1 f o r an o b l a t e s y m m e t r i c t o p . In terms o f t h e s e asymmetry p a r a m e t e r s t h e r i g i d r o t o r H a m i l t o n i a n can be w r i t t e n as (33) H r = { ( A + C ) / 2 } P 2 + { ( A - C ) / 2 } H ( 1 , K , - 1 ) 2.10a o r H f = { ( B + C ) / 2 } P 2 + {A-(B+C)/2}H(1,-b ,b ) 2.10b where H ( 1 , K , - 1 ) = P 2 + K P ? - P 2 2.11a a b e H ( l , - b ,b ) = P 2 - b P . 2 + b P 2 2.11b p ' p a p b p c O n l y H ( l , - b ,bp) and t h e H a m i l t o n i a n , 2.10b, w i l l be d i s c u s s e d h e r e as i t i s t h e e i g e n v a l u e s and e i g e n v e c t o r s of H ( l , - b p , b ) w h i c h -12-have been used here in f i t t i n g data to spectroscopic constants. The matrix elements of H ( 1,-rb^ ,b^) in the symmetric top basis are readily available (34) and diagonalization of the matrix yields the wavefunction for each asymmetric rotor l e v e l as a lin e a r combin-ation of the symmetric rotor wavefunctions and also yields W (b ), the Wang reduced energy, for each l e v e l . The t o t a l J T P rotational r i g i d rotor energy of a part i c u l a r J ^ - l e v e l i s then E = {(B+C)/2}J(J+1) + {A-(B+C)/2}WT (b ) 2.12 R T P Transitions between the rotational energy levels can be . : induced by microwave electromagnetic radiation (35). The prob-a b i l i t y (or intensity) or a radiation-induced t r a n s i t i o n (36) between two rotational states | Jif.M > and | J ' T ' M '> i s proportional to the squared matrix element |<JTM J J J I J ' T ' M '>| 2 = Z I ';uJ|<JTMT|*_ | J ' x ' M / > | 2 2.13 J J g F g J J ? g J where y is the component of the dipole moment along the g i n e r t i a l 8 axis and _y_ i s the t o t a l molecular dipole moment with components along the space-fixed F=X,Y,Z axes given by ^F * * V g 2-14 Thus the selection rules governing a microwave rot a t i o n a l t r a n s i t i o n can be obtained by requiring that the integral on the right of 2.13 be t o t a l l y symmetric. This integral can be written as the product of three others (as in eq. 2.8): -13-< J T M |4 |J'T'M '> - <J|<S> | J ' X J T | $ | J ' T ' X J M J * |J'M •> 2.15 J r g J r g r g J r g J and from t a b l e s o f d i r e c t i o n c o s i n e m a t r i x e l e m e n t s i t i s f o u n d t h a t t h e f i r s t t erm on t h e r i g h t o f 2.15 i s t o t a l l y s y m m e t r i c ( n o n - z e r o ) when AJ=0,±1 (F=X,Y,Z; g=a,b,c) 2.16 S i m i l a r l y , t h e t h i r d term on t h e r i g h t of 2.15 i s n o n - z e r o when AMj=0 (F=Z; g=a,b,c) 2.17a AM - ± 1 (F=X,Y; g = a,b,c) 2.17b The r e m a i n i n g term, < J T | $ | J ' T ' > , i s more d i f f i c u l t to e v a l u a t e . However, i t has been shown to be n o n v a n i s h i n g f o r t h e f o l l o w i n g t y p e s of t r a n s i t i o n s (37) : ee«--*eo -, i g = a oo-*-->-oe ' B } g=b (F=X,Y,Z) 2.18 eo^+oe ee^+oe -, oo-»-->-eo & where ee, oe e t c . r e f e r to t h e e v e n n e s s o r o d d n e s s o f K and K . ' p o Thus the s e l e c t i o n r u l e s f o r a t r a n s i t i o n between two asym-m e t r i c r o t o r e n e r g y l e v e l s a r e g i v e n by 2.16, 2.17 and 2.18. The s e l e c t i o n r u l e s i n v o l v i n g , 2.17, become i m p o r t a n t when an e x t e r n a l f i e l d i s a p p l i e d to t h e s y s t e m w h i c h l i f t s t h e M^-degen-e r a c y o f e a c h o f t h e r o t a t i o n a l l e v e l s . T r a n s i t i o n s w h i c h a r e a l l o w e d when g=a a r e c a l l e d " g - t y p e " t r a n s i t i o n s ; f o r example, t h e t r a n s i t i o n 2. 9 - 2 n „ i s a c - t y p e t r a n s i t i o n ( o e ^ + e e ) . A - 1 4 -n e c e s s a r y c o n d i t i o n f o r the o b s e r v a t i o n of a g - t y p e t r a n s i t i o n i s t h a t u be n o n - z e r o . A t r a n s i t i o n w i t h A J = 0 , A J = + 1 o r AJ=-1 g i s c a l l e d a Q-, R- o r P - b r a n c h t r a n s i t i o n , r e s p e c t i v e l y . I t i s c o n v e n i e n t to d e f i n e a q u a n t i t y , X, c a l l e d t h e l i n e s t r e n g t h , as 2 X ( J T ; J ' T ' ) = Z | < J T M T | $ „ | J ' T ' M *>| 2 . 1 9 g F . M j » V 8 where J^-^J^., i s a g - t y p e t r a n s i t i o n . W i t h t h i s d e f i n i t i o n , eq. 2 . 1 3 can be w r i t t e n as 2 7 | < J T M J ' T ' M '>| = u X ( J T ; J ' T ' ) 2 . 2 0 ( 2 J + 1 ) so t h a t i t i s a p p a r e n t t h a t the l i n e s t r e n g t h of a t r a n s i t i o n g i v e s a good i n d i c a t i o n o f i t s i n t e n s i t y o r r e l a t i v e i n t e n s i t y . V a l u e s o f l i n e s t r e n g t h s o f a s y m m e t r i c r o t o r t r a n s i t i o n s a r e r e a d i l y a v a i l a b l e i n t a b l e s ( 3 8 ) o r can be e v a l u a t e d f r o m t h e known a s y m m e t r i c t o p r i g i d r o t o r w a v e f u n c t i o n s . 2 . 2 The D i s t o r t a b l e R o t o r The H a m i l t o n i a n c o n s i d e r e d i n the p r e v i o u s s e c t i o n i s c a l l e d t h e r i g i d r o t o r H a m i l t o n i a n s i n c e i t s d e r i v a t i o n assumes t h a t t h e bond l e n g t h s and a n g l e s o f t h e m o l e c u l e do n o t change as t h e m o l e c u l e r o t a t e s . I t i s a p p l i c a b l e f o r t h e a c c u r a t e p r e d i c t i o n o f l o w - J t r a n s i t i o n f r e q u e n c i e s o n l y , however, b e c a u s e as J i n c r e a s e s t h e m o l e c u l e r o t a t e s more q u i c k l y and c e n t r i f u g a l f o r c e s w i l l t e n d to d i s t o r t t h e m o l e c u l a r geometry t h e r e b y p e r t u r b i n g t h e r o t a t i o n a l e n e r g y l e v e l s . I n o r d e r to a c c o u n t f o r t h i s e f f e c t , a c e n t r i --15-fugal d i s t o r t i o n Hamiltonian, H^, must be added to the r i g i d rotor Hamiltonian, H , so that the t o t a l Hamiltonian becomes H = H + H, 2.21 r d By use of 2.21, the rotational t r a n s i t i o n frequencies for a l l i J-values may be accurately predicted. The centrifugal d i s t o r t i o n contribution to the t o t a l energy of a l e v e l is usually much smaller than the r i g i d rotor contribution; thus i t may be deter-mined by conventional perturbation-theory techniques. The c l a s s i c a l Hamiltonian for a vibrating and rotating molecule, assuming harmonic v i b r a t i o n a l potential functions, is given by (39) : H = I Z ( I " 1 ) ^ P R + I £ G P p + I Z f^R^R. 2.22 2 a,B ccB a 3 2 i f i xj x j 2 i , j 1 J 1 3 where a,B=x,y,z (molecule-fixed axes), (I ^ ) a ^ a r e t n e elements of the inverse moment of i n e r t i a tensor, G.. are elements of the i j Wilson G-matrix which depend on the molecular geometry, R^  are the internal displacement coordinates (3N-6 of them, where N i s the number of atoms in the molecule), p^ are the conjugate mom-enta to the R. and f.. are the molecular force constants (40). l i j The f i r s t term on the right of 2.22 represents the rotational energy of the system, the second term represents the vi b r a t i o n a l k i n e t i c energy and the third term represents the v i b r a t i o n a l potential energy, V. In order to consider the centrifugal d i s t o r t i o n e f f e c t s , i t is convenient to consider the molecule as being in i t s equilibrium configuration (that i s , not v i b r a t i n g ) . Under these conditions -16-th e f o l l o w i n g c o n d i t i o n s h o l d : 3H = 0 8R i i=l,2,...,3N-6 2.23 P ± = 0 so that the f o l l o w i n g 3N-6 simultaneous equations h o l d : j. I 3 ( 1 W P PR + 3V - 0 i=l,2,...,3N-6 2.24 2 a,6 3R t a p 3R ± which, i n e f f e c t , are equating the c e n t r i f u g a l f o r c e s with the r e s t o r i n g f o r c e s . The q u a n t i t y (I * ) a g can be approximated by a T a y l o r s e r i e s -1 e expansion about i t s e q u i l i b r i u m value of (T : where < 1 _ 1 > a e ) = { 8 ( I _ 1 > a 0 / 3 R i } e 2 ' 2 6 S u b s t i t u t i n g (I * ) a g from equation 2.25 i n t o equations 2.24 and s o l v i n g the 3N-6 l i n e a r equations f o r R gives R. - *1 I Z ( f " 1 ) , . ( i " 1 ) ( ^ P PQ 2.27 J 2 i a,B j i a 3 a — 1 t h where (f ) . . i s the i i element of the i n v e r s e of the f o r c e j i constant m a t r i x . Equations 2.25 and 2.27 can then be used to put the Ha m i l t o n i a n , 2.22, i n t o the form H = 1 Z ( I - 1 ) E Q P P„+ 1 S T „ ~P P„P P. 2.28 2 a,B a B a B 4 o ,B,Y.« ^ a with the c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s , x, def i n e d as -17-W • - i . E . ^ " ^ a ^ ^ ' ^ i j ^ " 1 ^ ^ 2 ' 2 9 The f i r s t term on the right of 2.28 represents the usual r i g i d rotor energy and the second term represents the centrifugal d i s t o r t i o n energy. Within the approximations given, the rotational constants and the d i s t o r t i o n constants are independent of the v i b r a t i o n a l coordinates. Actually, this i s not the case as these constants have been experimentally shown to depend on the vi b r a t i o n a l state of the molecule. Thus the p r i n c i p a l moments of i n e r t i a and d i s t -ortion constants obtained from a spectrum are actually those averaged over the part i c u l a r v i b r a t i o n a l state under consideration and are ef f e c t i v e constants. The Hamiltonian for the distortable rotor, 2.28, can be written in the p r i n c i p a l axis system (x,y,z) as H ' = H' + H I r d H' = A'P 2 + B'P2 + C'P2 2.30 r z x y HI = h 4 Z T 0 pP P DP P x d R . oc8Y<S a 3 Y <S where A' = h/8ir 2I z etc. and angular momentum i s in units of h/2tr. Clearly, the d i s t o r t i o n Hamiltonian contains 81 terms, and is very unwleldly indeed. Fortunately, i t is possible to reduce this number to six by treating the molecule to f i r s t - o r d e r (41) with E d = < H d > = < j T l H d ' j T > 2 , 3 1 and by appealing to the commutation rules for the P (42). By doing t h i s , the following expression for the Hamiltonian i s obtained: -18-H = H + H. r d H - A " P 2 + B " P 2 + C " P 2 2.32 r z x y Hj - 1 Z T ' Q O P 2 P O d T a > 6 aaBB a B w i t h t h e r o t a t i o n a l c o n s t a n t s and d i s t o r t i o n c o n s t a n t s as d e f i n e d i n T a b l e 2.1. T a b l e 2.1 D e f i n i t i o n o f t h e D i s t o r t i o n and R o t a t i o n a l C o n s t a n t s i n t h e D i s t o r t i o n H a m i l t o n i a n (2.32) T' xxxx zz ( h / 2 i r ) 4 x xxxx T ' x x z z ( h / 2 T T ) 4 ( T + 2T x x z z x z x z y y y y 8 ( h / 2 T T ) 4 T yyyy T' xxyy ( h / 2 7 T ) 4 ( T + 2T xxyy xyxy z z z z - ( h / 2 i T ) 4 T v z z z z T' y y z z ( h / 2 i r )4 ( T + 2T y y z z y z y z A' + { ( h / 2 i r ) 4 / 4 } ( 3 T xyxy - 2x - 2T ) x z x z y z y z B" = B * + { ( h / 2 T T ) 4 / 4 } ( 3 T y z y z - 2x - 2T ) xyxy x z x z C" = C' + { ( h / 2 T T ) 4 / 4 } ( 3 T x z x z - 2T - 2T ) xyxy y z y z The problem'wTftl "the appTicatfi'on o f t h i s H a m i l t o n i a n i s t h a t i t c o n t a i n s s i x q u a r t i c d i s t o r t i o n c o n s t a n t s whereas t h e maximum number t h a t can be o b t a i n e d f r o m e x p e r i m e n t a l d a t a i s f i v e ( 4 3 ) . To c i r c u m v e n t t h i s p r o b l e m , Watson has d e v e l o p e d a u n i t a r y t r a n s -f o r m a t i o n w h i c h c o n v e r t s t h i s H a m i l t o n i a n to an e q u i v a l e n t ' r e d u c e d ' H a m i l t o n i a n w h i c h c o n t a i n s o n l y f i v e q u a r t i c d i s t o r t i o n c o n s t a n t s ( 4 4 ) . -19-Watson's H a m i l t o n i a n i s 2 2 2 H - AP + BP + CP r z x y 2 33 H d - - i J p 4 - i J K p 2 p r A K p * - 2 { J p 2 < P x - P y ) - 6 K { p 2 Z < ^ - p y > + < ^ - P y ) P ' } where x , y , z a r e t h e p r i n c i p a l i n e r t i a l a x e s , A, B and C a r e Watson's e f f e c t i v e r o t a t i o n a l c o n s t a n t s , A J f A K > A J K » 6^, 6 R a r e t h e q u a r t i c d i s t o r t i o n c o n s t a n t s and a n g u l a r momentum i s i n u n i t s o f h/2ir. The e f f e c t i v e r o t a t i o n a l and d i s t o r t i o n c o n s t a n t s a r e d e f i n e d i n T a b l e 2.2. T a b l e 2.2 D e f i n i t i o n o f t h e D i s t o r t i o n and R o t a t i o n a l C o n s t a n t s i n Watson's Reduced D i s t o r t i o n H a m i l t o n i a n (2.33) A = - ( T ' +T' )/8 J xxxx y y y y ' a « - 3 < T ; „ X + T ; w , / 8 - ( t ; y 2 2 + T x x z z + T . x y y ) / 4 6 j = - ( T x x x x - T ; y y y > / 1 6 V T x x x x ( B " - - A M ) / ^ B " - C » ) + T y y y y ( C » - A » ) / 8 ( B » - C » ) + {T' - T ' +T' ( 2 A , , - B , , - C " ) / ( B " - C " ) } / 8 y y z z x x z z xxyy A'=A" + 16R, o B=B"-16R 6(A"-C")/(B"-C") C=C"+16R 6(A , ,-B")/ (B"-C") R, = (h/2Tr) 4'{'T +x - 2 ( T +2T )}/64 6 xxxx y y y y x xyy xyxy -20-Watson has a l s o expanded t h e d i s t o r t i o n H a m i l t o n i a n t o i n c l u d e s e x t i c terms ( 4 5 ) . The s e x t i c d i s t o r t i o n H a m i l t o n i a n i s g i v e n by s e x t i c = p 6 + H p 4 p 2 + 1 I P 2 P 4 + H P 6 + 2 h T P 4 ( P 2 - P 2 ) d J J K z K J z K z J v x y + h T t , P 2 { P 2 ( P 2 - P 2 ) + ( P 2 - P 2 ) P 2 } 2.34 JK z x y x y z + h 1 , { P 4 ( P 2 - P 2 ) + ( P 2 - P 2 ) P 4 } K z x y x y z where H , H T t,, H T , H , h T , h T „ and h a r e t h e s e x t i c d i s t o r t i o n c o n s t a n t s . The i n c l u s i o n o f t h i s H a m i l t o n i a n w i t h t h e one g i v e n by 2.33 i s n e c e s s a r y when i n v e s t i g a t i n g t r a n s i t i o n s o f l i g h t m o l e c u l e s and v e r y - h i g h - J t r a n s i t i o n s o f a l l m o l e c u l e s ; f o r t h e s e c a s e s the c e n t r i f u g a l d i s t o r t i o n e f f e c t s a r e v e r y l a r g e . By c o n s i d e r i n g t h e c e n t r i f u g a l d i s t o r t i o n e f f e c t s to be a p e r t u r b a t i o n o f t h e r i g i d r o t o r , t h e f i r s t - o r d e r . d i s t o r t i o n e n e r g y can be f o u n d by e v a l u a t i n g < H ^ > i n t h e r i g i d a s y m m e t r i c r o t o r b a s i s . T h i s e n e r g y can be e x p r e s s e d i n the I a x i s r e p r e s e n t a t i o n as (46) : E d = - A J J 2 ( J + l ) 2 - A J K J ( J + l ) < P 2 > - A K < P 4 > + ( 2 6 T / b )J(J+1){W_ (b )-<P 2>} 2.35 J p J ^ p a + ( 2 6 K / b p ) { W j T ( b p ) < E 2 > - < P 4 > } where b i s t h e Wang asymmetry p a r a m e t e r ( s e e eq. 2 . 9 ) , W (b ) P T P i s the Wang r e d u c e d e n e r g y and <P > i s t h e a v e r a g e o f P i n the a a r i g i d a s y m m e t r i c r o t o r b a s i s . The l a t t e r q u a n t i t i e s a r e o b t a i n e d f r o m t h e d i a g o n a l i z a t i o n o f H ( l , - b p , , b p ) ( s e e eq. 2.11b). Thus the t o t a l e n e r g y o f a r o t a t i o n a l l e v e l , t o f i r s t - o r d e r , i s t h e sum o f t h e d i s t o r t i o n e n e r g y , 2.35, and the r i g i d r o t o r e n e r g y , 2.12. H i g h e r o r d e r c o n t r i b u t i o n s a r e g e n e r a l l y v e r y s m a l l . -21-2.3 Nuclear Quadrupole Coupling When a molecule contains a nucleus that has a spin greater than 1=1/2, the molecular e l e c t r i c f i e l d gradient interacts with the e l e c t r i c quadrupole moment of the nucleus. This interaction causes each rotational l e v e l to be s p l i t into several hyperfine levels and introduces hyperfine structure into each observed rotational t r a n s i t i o n . This nuclear quadrupole hyperfine structure provides information about the chemical bonding in the molecule. Before considering the quadrupole Hamiltonian, the wave-functions for the rotating coupled system w i l l be introduced. The nuclear spin wavefunctions of the coupling atom can be denoted by |lMj>. The square of the t o t a l nuclear spin angular momentum, 2 I , and the component of the spin along an external Z-axis, I , are both quantized so that where M^=I,I-1,...,-I. The effect of the molecular quadrupole interaction i s to couple the nuclear spin angular momentum 1^  with the rotational angular momentum to form a resultant, t o t a l angular momentum 1? : I.2|lM > = 1(1+1) (h/2-rr)2 | IM][> IZ|IM];> = M].(h/2Tr) |IMI> 2.36 F « I + J 2.37 Thus the appropriate wavefunctions for this coupled system are FM > where F2|FMp> - F(F+1) (h/2 - r r ) 2 | FMp> Fz|FMp> = M F(h/2TT) |FMF> 2.38 -22-In a f i r s t - o r d e r t r e a t m e n t ( w h i c h i s s u f f i c i e n t i n most c a s e s ) J and I a r e s t i l l good quantum numbers so t h a t t h e new quantum numbers a r e g i v e n by F=J+I, J + I - l | J - I | 2.39 M F=F,F-1,...,-F and t h e h y p e r f i n e e n e r g y l e v e l s o f a m o l e c u l e can be r e p r e s e n t e d by t h e more c o n v e n i e n t e i g e n k e t | j I F > . The q u a d r u p o l e H a m i l t o n i a n f o r a s y s t e m c o n t a i n i n g one c o u p l i n g n u c l e u s can be w r i t t e n as (47) : H - e Q q J { 3 ( F 2 - J 2 - I 2 ) 2 / 4 + 3 ( F 2 - J 2 - I 2 ) / 4 - I2J2} 2.40 Q 2 1 ( 2 1 - 1 ) J ( 2 J - 1 ) = = - -where eQ, t h e c h a r g e - w e i g h t e d n u c l e a r q u a d r u p o l e moment, i s a c o n s t a n t r e f l e c t i n g t h e a s y m m e t r i c c h a r g e d i s t r i b u t i o n i n t h e c o u p l i n g n u c l e u s (48) and q^ i s t h e a v e r a g e o f t h e s e c o n d Z - d e r i v a t i v e o f t h e e l e c t r o n i c p o t e n t i a l , V , a t t h e n u c l e u s o v e r t h e s t a t e | J T M J = J > : q3 = < J T M J = J | 8 2 V / 3 Z 2 | J T M J = J > 2 . 4 1 The e n e r g i e s o f the h y p e r f i n e l e v e l s may be e a s i l y c a l c u l a t e d f r o m t h e H a m i l t o n i a n , 2.40, s i n c e i t i s d i a g o n a l i n t h e | j I F > b a s i s . The h y p e r f i n e e n e r g y o f a |JIF> l e v e l i s g i v e n by E - 1 e Q q J { 3 C ( C + l ) / 4 - 1 ( 1 + 1 ) J ( J + 1 ) } 2.42 4 2 1 ( 2 1 - 1 ) J ( 2 J - 1 ) where C - F ( F + 1 ) - J ( J + 1 ) - I ( I + 1 ) 2.43 -23-The q u a n t i t y eQq i s dependent on t h e r o t a t i o n a l s t a t e of t h e m o l e c u l e ( s e e eq. 2.41) and, by making use o f t h e r e l a t i o n s h i p ZZ , gg Zg Zg 6 » 6 where V , = 8 2V/3g3g' e t c . may be w r i t t e n , to f i r s t - o r d e r , as ( 4 9 ) : S S eQ<ij = 2 { X a a < P a > + X b b < P b > + X c c < P c > } 2 * 4 5 - (2J+3)(J+1) where x =eQ<8 2V/8g 2> (g=a,b,c) a r e the n u c l e a r q u a d r u p o l e c o u p l i n g SS 2 2 c o n s t a n t s and <P > i s t h e a v e r a g e o f P i n t h e r i g i d a s y m m e t r i c g S r o t o r b a s i s . S i n c e L a p l a c e ' s e q u a t i o n h o l d s f o r t h e c o u p l i n g c o n s t a n t s , X + Xuu + X = 0 2.46 A a a A b b A c c and so t h e r e a r e o n l y two i n d e p e n d e n t c o n s t a n t s ; hence i t i s c u s t o m a r y to quo t e x a n ^ n=(Xki,~X )/X when d i s c u s s i n g c o u p l i n g Si SL. D D C C 3. «1 c o n s t a n t s . In terms o f t h e s e two i n d e p e n d e n t p a r a m e t e r s , t h e q u a d r u p o l e e n e r g y c an be w r i t t e n , to f i r s t - o r d e r , as (50) E ^ = f ( I J F ) ( 3 < P 2 > - J ( J + l ) + n { < P 2 > - W - ( b n ) } / b >X n a 2.47 Q J ( J + 1 ) a a J t p p aa where f ( I J F ) i s C a s i m i r ' s f u n c t i o n d e f i n e d by f ( I J F ) = 0. 7 5C(C+1)-!(!+!) J(J-t-l) 2.48 2 ( 2 J + 3 ) ( 2 J - 1 ) 1 ( 2 1 - 1 ) E q u a t i o n 2.47 p r o v e s e x t r e m e l y u s e f u l when f i t t i n g e x p e r i m e n t a l 2 d a t a to t h e c o u p l i n g c o n s t a n t s s i n c e t h e v a l u e s o f < I > a > a n a W (b ) a r e r e a d i l y d e t e r m i n a b l e f r o m t h e d i a g o n a l i z a t i o n o f t h e Wang r e d u c e d e n e r g y m a t r i x . -24-The s e l e c t i o n r u l e s f o r q u a d r u p o l e e n e r g y l e v e l h y p e r f i n e t r a n s i t i o n s a r e t h e f o l l o w i n g (51) : AF=0,±1 2.49 AI=0 along with the ones previously discussed for J and T. 2.4 The S t a r k E f f e c t When a r o t a t i n g m o l e c u l e i s p l a c e d i n an e l e c t r i c f i e l d t h e r e i s an i n t e r a c t i o n between i t s d i p o l e moment and t h i s f i e l d . The e n e r g y o f t h e i n t e r a c t i o n i s o b t a i n e d f r o m the S t a r k H a m i l t o n i a n (52) : H = -e Z y 4_ " 2.50 g g Z g whetre y i s t h e component o f t h e e l e c t r i c d i p o l e moment a l o n g t h e g a x i s , $„ i s a d i r e c t i o n c o s i n e and e i s t h e m a g n i t u d e o f t h e g e l e c t r i c f i e l d w h i c h i s a p p l i e d a l o n g t h e s p a c e - f i x e d Z - a x i s . The e f f e c t o f t h e i n t e r a c t i o n i s to l i f t t h e ( 2 J + l ) - f o l d M -d e g e n e r a c y o f e a c h r o t a t i o n a l l e v e l . C o n v e n t i o n a l f i r s t - and s e c o n d - o r d e r p e r t u r b a t i o n t h e o r y c an be u s e d to d e t e r m i n e t h e S t a r k e n e r g i e s o f t h e M - l e v e l s . F o r l i n e a r and p r o l a t e s y m m e t r i c top m o l e c u l e s y^=y c=0 so t h a t t h e S t a r k H a m i l t o n i a n i s s i m p l y H e - - ^ a * Z a 2 ' 5 1 and c l o s e d e x p r e s s i o n s f o r t h e e n e r g i e s i n t e r m s - o f e, y and t h e r o t a t i o n a l quantum numbers can be o b t a i n e d (53) . One r e s u l t w i l l be p r e s e n t e d h e r e f o r l a t e r r e f e r e n c e . The f r e q u e n c y s h i f t f r o m -25-V Q , t h e z e r o - f i e l d l i n e f r e q u e n c y , o f t h e J=l<-0, M=0«-0 S t a r k t r a n s i t i o n o f a l i n e a r m o l e c u l e i s g i v e n by Av - 0.1352 y 2 e 2 2.52 v o where a c o n v e r s i o n f a c t o r has been i n c o r p o r a t e d so t h a t Av i s i n u n i t s o f MHz when y i s i n Debyes, e i s i n v o l t s / c m and V q i s i n MHz Fo r a s y m m e t r i c top m o l e c u l e s t h e S t a r k e n e r g y o f a |jxMj> l e v e l i s g i v e n by t h e e x p r e s s i o n (54) : J x g ( J 2 - H j ) z J < J T 1 » 8 r 1 J - I . T ' > | + M2 z | < J T | » 8 8 | J T ' > 4 J 2 ( 4 J 2 - 1 ) T ' E° -E° . 4 J 2 ( J + 1 ) 2 T * ' E°T -E° T T T —1 T T 2 . 2 ( J + l ) 2 - M 2 j. | < J T | * | J + l . T ' H 4 ( J + 1 ) 2 ( 2 J + 1 ) ( 2 J + 3 ) T ' E° - E j + , T X ' 2 2 g where E° i s t h e r o t a t i o n a l e n e r g y o f t h e |JT> l e v e l a t z e r o f i e l d . T T h i s r e s u l t f o l l o w s f r o m a p u r e l y s e c o n d - o r d e r p e r t u r b a t i o n t h e o r y a n a l y s i s ; t h e r e a r e no f i r s t - o r d e r c o n t r i b u t i o n s to t h e e n e r g y . 2 t h e m a t r i x e l e m e n t s |<JT|$ | J ' T ' > | i n e q . 2.54 can be e x p r e s s e d ^8 i n terms o f t h e l i n e s t r e n g t h s , A ( J x ; J ' x ' ) , w h i c h were d e f i n e d by eq. 2.19, as f o l l o w s (55) : | < J T | * z | J + l , T • > | 2 - 4 ( J + l ) X g ( J x ; J + l , x ' ) 2 <|J<JT|* I J T • > I = 4 J ( J + 1 ) X ( J x ; J x ' ) 2.54 8 2J+1 8 | < J T | $ Z g | J - 1 , T ' > | 2 - 4J X g ( J x ; J - l , x ' ) S u b s t i t u t i o n o f t h e s e e x p r e s s i o n s i n t o eq. 2.53 g i v e s t h e f o l l o w -i n g u s e f u l e x p r e s s i o n f o r t h e ( s e c o n d - o r d e r ) S t a r k e n e r g y : X -26-z ( J 2 - M 2 ) z X g ( J x ; J - l , x ' ) + M 2 E X g ( J x ; J x ' ) 8 J ( 4 J 2 - 1 ) T ' E° - E ° _ 1 t J ( J + 1 ) ( 2 J + 1 ) T ' E° -E° ( J + l ) 2 - M 2 z X g ( J x ; J + l , x ' ) x' „o „o ( J + l ) ( 2 J + 1 ) ( 2 J + 3 ) E" - E " X X ' 2.55 2 2 „ v g 2 2 y e = Z K° y e 8 g J x M J 8 where K 8 d e n o t e s t h e c o n s t a n t w i t h i n t h e s q u a r e b r a c k e t s . As J M _ X J n o t e d i n S e c t i o n 2.1, t h e l i n e s t r e n g t h s a r e commonly o b t a i n e d from t a b l e s w h i c h a r e a v a i l a b l e (30) o r c a l c u l a t e d e x a c t l y f r o m the e i g e n v e c t o r s o f the r i g i d r o t o r H a m i l t o n i a n m a t r i x . E q u a t i o n 2.55 i s v a l i d o n l y when t h e r e a r e no n e a r - d e g e n e r a t e l e v e l s w h i c h a r e c o n n e c t e d t o t h e |jx> l e v e l under c o n s i d e r a t i o n . ( L e v e l s a r e s a i d t o be c o n n e c t e d i f t h e t r a n s i t i o n between them i s a l l o w e d ) . I f t h e r e i s s u c h a n e a r - d e g e n e r a c y t h e d e n o m i n a t o r s on t h e r i g h t - h a n d s i d e o f eq. 2.53 w i l l be v e r y s m a l l c a u s i n g t h e s e c o n d - o r d e r p e r t u r b a t i o n t h e o r y t o f a i l ; h e nce a d i f f e r e n t method o f c a l c u l a t i n g t h e S t a r k s h i f t s must be u s e d . T h i s o t h e r method o f c a l c u l a t i o n makes use of t h e t h e o r y f i r s t d e v e l o p e d by Van V l e c k ( 5 6 ) . By use o f a s p e c i a l t r a n s f o r m a t i o n t h e S t a r k e n e r g y m a t r i x c a n be r e d u c e d to a number of s m a l l e r s u b -m a t r i c e s e a c h o f w h i c h i s a s s o c i a t e d w i t h a group o f d e g e n e r a t e o r n e a r - d e g e n e r a t e l e v e l s . The m a t r i x e l e m e n t s between t h e s e s u b -m a t r i c e s can be n e g l e c t e d up to f o u r t h o r d e r i n e n e r g y t h u s a l l o w -i n g e ach s u b m a t r i x to be t r e a t e d i n d e p e n d e n t l y . The d i a g o n a l e l e m e n t s o f t h e s u b m a t r i c e s a r e t h e e n e r g i e s o f t h e p a r t i c u l a r M j - l e v e l u n d e r c o n s i d e r a t i o n f o r each a s y m m e t r i c r o t o r l e v e l |jx> c a l c u l a t e d by e v a l u a t i n g t h e s e c o n d - o r d e r p e r t u r b a t i o n sums i n eq. 2.55, b u t w i t h t h e sums n o t i n c l u d i n g t h e n e a r --27-degenerate l e v e l s . If there is a pair of near-degenerate l e v e l s , the 2x2 submatrix formed w i l l have off-diagonal elements, e|£|, the squares of which are given by e2U|2 = | < J T M |H | J'T ' M j>| 2 2.56 which in the often-encountered case of a Q-branch near-degeneracy is just e 2 I ^ I 2 = M2 |<JT | * _ I J T ' > 1 2 y 2 e 2 2.57 4J Z(J+1)* In order to obtain the exact Stark energies of the l e v e l s , each of the submatrices is diagonalized. For the 2x2 case, direct diagonalization yields the Stark energies of the two levels as E + = E x+E 2 ± {(E 1-E 2) 2/4 + e2U|2}1/2 2.58 2 where Ej and E 2 are the diagonal elements of the matrix. The selection rules governing Stark transitions are given by eq. 2.17. For this study, however, the Stark f i e l d was applied p a r a l l e l to the e l e c t r i c vector of the microwaves so that only the AMj=0 transitions were observed. The i n t e n s i t i e s of these trans-i t i o n s are proportional to the squared matrix element |<JM |$ |j'M > J L g J and are given by (57) : 2 Intensity <* M AJ=0 2 2 2 , 5 9 Intensity « {(J+l) -M^ } AJ=±1 Thus the Stark contour of a Q-branch t r a n s i t i o n i s di f f e r e n t from that of a P- or R-branch t r a n s i t i o n . This fact aids in the i n i t i a l assignment of a spectrum as does the number of Stark transitions (or -28-" l o b e s " ) . F o r J-«-J t r a n s i t i o n s J l o b e s s h o u l d be s e e n and f o r J+l«-J t r a n s i t i o n s J + l l o b e s s h o u l d be p r e s e n t . The main use o f S t a r k e f f e c t measurements i s i n the d e t e r m -i n a t i o n o f v e r y a c c u r a t e e l e c t r i c d i p o l e moments. T h i s i s p o s s i b l e 2 2 b e c a u s e of t h e d i r e c t d e p e n d ences o f t h e S t a r k s h i f t s on y a , y^ 2 and y as i n d i c a t e d by e q . 2.55. 2.5 D e t e r m i n a t i o n o f M o l e c u l a r S t r u c t u r e s The s t r u c t u r e of a m o l e c u l e may be deduced from a knowledge of t h e c o o r d i n a t e s o f a l l of i t s atoms i n t h e i n e r t i a l a x i s s y s t e m . The most c h e m i c a l l y m e a n i n g f u l c o o r d i n a t e s a r e t h e e q u i l i b r i u m c o o r d i n a t e s ( t h o s e w i t h t h e m o l e c u l e i n t h e h y p o t h e t i c a l v i b r a t i o n -l e s s s t a t e v = - l / 2 ) and t h e y a r e r e l a t e d to t h e m o l e c u l a r p r i n c i p a l moments o f i n e r t i a by I* = E m ^ U * ) 2 + ( c * ) 2 } 2.60 i e e e where m^ and ( a ^ , b ^ , c ^ ) a r e t h e mass and e q u i l i b r i u m c o o r d i n a t e s o f t h e i * " * 1 atom. U n f o r t u n a t e l y , t h e moments o f i n e r t i a a r e d e p e n d e n t on t h e v i b r a t i o n a l s t a t e o f t h e m o l e c u l e (58) and t h o s e c a l c u l a t e d f r o m the g r o u n d (v=0) s t a t e r o t a t i o n a l c o n s t a n t s by 1° - h 2.61 a 8"FA" o a r e n o t t h e same as t h o s e i n eq. 2.60. R a t h e r , t h e y r e f l e c t the a v e r a g e s o f t h e s q u a r e s o f t h e c o o r d i n a t e s i n t h e ground v i b r a t i o n a l s t a t e by -29-= £ m.{<a> +<c.> } i o i o 2.62 2 6 2 and <aj> H ( a j . Thus unless the vi b r a t i o n a l dependences of i o > i the moments of i n e r t i a can be completely determined, which is unlikely for polyatomic molecules, i t is not possible to deter-ge mine the I and the equilibrium atomic coordinates and alternative g procedures must be used to develop a meaningful structure. Several methods of calcu l a t i o n of atomic coordinates, each d i f f e r i n g in their treatment of the vi b r a t i o n a l problem, have been used to determine molecular structures from their ground state r o t a t i o n a l constants. Of these, i t i s the substitution method which w i l l be discussed here. This method was f i r s t developed by Kraitchman (59) and involves the calcu l a t i o n of the p r i n c i p a l axis coordinates of a part i c u l a r atom in a molecule in terms of the changes of the moments of i n e r t i a of the molecule resulting from an isotopic substitution of that atom. For a planar asymmetric molecule Kraitchman's equations give the coordinates of the substituted atom as H / 2 ^b-V^a-V b "^a-V^b -V 2.63 1/2 where the primed and unprimed moments of i n e r t i a refer to the iso-t o p i c a l l y substituted and the parent molecule, respectively, and y = MAm M+Am 2.64 -30-where M i s the mass of the paren t m o l e c u l e and Am i s the d i f f e r -ence i n the i s o t o p i c masses of the s u b s t i t u t e d atom. Kraitchman's e q u a t i o n s have been used e x t e n s i v e l y f o r the d e t e r m i n a t i o n of the s t r u c t u r e s of m o l e c u l e s and have been shown to g i v e c o o r d i n a t e s which are v e r y c l o s e to the e q u i l i b r i u m v a l u e s (60) . T h e i r main drawback appears to be t h a t they cannot be used a c c u r a t e l y to l o c a t e atoms near the c e n t r e of mass of a mol e c u l e or near the i n e r t i a l axes (60) . The c o o r d i n a t e s of such atoms, however, may be determined by use of the cent r e - o f - m a s s c o n d i t i o n s E m.a. «= £ m.b. = I m,c, = 0 2.65 . i i . 1 1 . i i i l l or the second moment c o n d i t i o n s - E m.a.b. = - Z m.b.c. = - I m.a.c. = 0 2.66 i i i . i i i . i l l i i i These c o n d i t i o n s are a c t u a l l y met by the e q u i l i b r i u m c o o r d i n a t e s o n l y but have been shown to be v e r y n e a r l y s a t i s f i e d by the s u b s t i t u t i o n c o o r d i n a t e s ( 6 0 ) . 2.6 L i n e a r L e a s t - S q u a r e s F i t t i n g of Data to S p e c t r o s c o p i c C o n s t a n t s O f t e n i t i s n e c e s s a r y to f i t e x p e r i m e n t a l d a t a to a l i n e a r e q u a t i o n of the form n y = £ a . x . 2.67 j - 1 j 3 where y i s the dependent v a r i a b l e , the x^ are the independent v a r i a b l e s and the a. are the n l i n e a r c o e f f i c i e n t s to be determined; J t h i s was done here by a l i n e a r l e a s t - s q u a r e s f i t t i n g p r o c e d u r e . -31-The l e a s t - s q u a r e s p r o c e d u r e (61) i n v o l v e s t h e m i n i m i z a t i o n o f t h e q u a n t i t y N 2 S = Z {y - Z a x } 2.68 i — i i 2 where t h e i n d e x i l a b e l s t h e p a r t i c u l a r x 's s e t by t h e i e x p e r i -ment and t h e measured o u t p u t v a r i a b l e , y. N i s t h e t o t a l number o f d a t a p o i n t s . To m i n i m i z e S, one s e t s 3S/9a^=0 f o r e a c h k so t h a t 2Z { y ± - Z a . x ^ J x f c i " 0 k = l , 2 , . . . , n 2.69 i j 2 2 o r Z y i x k i " Z(Z x ^ i x k i ) a j k = l , 2 , . . . , n 2.70 In m a t r i x n o t a t i o n , t h e n e q u a t i o n s o f 2.70 may be w r i t t e n as P = XA 2.71 g i v i n g t h e s o l u t i o n v e c t o r , A, as A = X _ 1 P 2.72 -1 The m a t r i x X i s c a l l e d t h e v a r i a n c e - c o v a r i a n c e m a t r i x . 2 The v a r i a n c e o f t h e f i t , a , i s g i v e n by a 2 - _ J ^ _ Z (y - Z a x ) 2 2.73 N-n i j 2 2 where t h e a r e t h o s e d e t e r m i n e d f rom 2.72. The v a r i a n c e s o f 2 - 1 -1 t h e a^ a r e g i v e n by a X ^ where X ^ * s the a p p r o p r i a t e d i a g o n a l e l e m e n t of X ; the s t a n d a r d d e v i a t i o n s a r e g i v e n by the s q u a r e r o o t s o f t h e v a r i a n c e s . ( -32-Chapter 3 E x p e r i m e n t a l P r o c e d u r e s and Equipment 3.1 The P r o p i o l a m i d e Samples The sample of p r o p i o l a m i d e , HCCCONH^, used i n the a n a l y s e s was o b t a i n e d from T e r r a - M a r i n e B i o - R e s e a r c h and was p u r i f i e d by vacuum s u b l i m a t i o n . I t i s a s o l i d a t room temperature and has a m e l t i n g p o i n t o f 61-62°C. Two d e u t e r a t e d s p e c i e s of p r o p i o l a m i d e were s t u d i e d , HCCCOND2 and DCCCOND2; they were p r e p a r e d by a s t a n d a r d D2O exchange r e a c t i o n (62) w i t h HCCCONR^. A s m a l l amount of HCCCONR^ was d i s s o l v e d i n a l a r g e excess of 99% D^O and the s o l u t i o n was a l l o w e d to s i t f o r 24 hours b e f o r e the excess water was ev a p o r a t e d o f f under vacuum. More D2O was then added to the d r i e d sample and a l l o w e d to exchange f o r a f u r t h e r 24 hours b e f o r e b e i n g e v a p o r a t e d o f f . The r e s u l t i n g p r o p i o l a m i d e sample was an a p p r o x i m a t e l y 50-50 m i x t u r e of HCCC0ND2 and DCCC0ND2. 3.2 The S t a r k - M o d u l a t e d Microwave Spectrometer The s p e c t r o m e t e r used i n these experiments was a St a r k - m o d u l a t e d microwave s p e c t r o m e t e r of the type f i r s t d e s c r i b e d by Hughes and W i l s o n i n 1947 (63) and c u r r e n t l y i n widespr e a d use by microwave s p e c t r o s c o p i s t s . F i g u r e 3.1 shows a b l o c k diagram of the s p e c t r o -meter. Two d i f f e r e n t s o u r c e s of microwaves were used i n t h i s s t u d y . One was a phase s t a b i l i z e d H e w l e t t - P a c k a r d 8400B microwave spec-t r o s c o p y s o u r c e composed of a HP H81-8690A sweep o s c i l l a t o r , a HP 8709A s y n c h r o n i z e r and a HP 8466A r e f e r e n c e o s c i l l a t o r t o g e t h e r - 3 3 -R e c o r d e r o r b s c i l l o s e o p e p h a s e - s e n s i t i v e d e t e c t o r a m p l i f i e r p r e a m p l i f i e r i s o l a t o r a t t e n u a t o r d e t e c t o r BWO s o u r c e S t a r k c e l l m i x e r square-wave g e n e r a t o r s y n c h r o n -izer F i g u r e 3.1 B l o c k Diagram o f t h e S t a r k - M o d u l a t e d S p e c t r o m e t e r ( w i t h BWO s o u r c e ) -34-w i t h HP H81-8694B X-band (8-12.5 GHz), HP H81-8695A P-band ( 1 2 . 5 -18 GHz) and HP 8697A R-band (26.5-40 GHz) p h a s e - s t a b i l i z e d b a c k -ward wave o s c i l l a t o r s (BWO'.s). The f r e q u e n c y o f t h e microwaves was a u t o m a t i c a l l y r e c o r d e d and d i s p l a y e d w i t h a HP 5246L e l e c t r o n i c c o u n t e r . The o t h e r s o u r c e used was an OKI 30V10 r e f l e x k l y s t r o n ( f r e q u e n c y r a n g e 28-32 GHz) w h i c h was powered by a S p e r r y M i c r o l i n e M o del 62A1 k l y s t r o n power s u p p l y . The microwave power was d e t e c t e d i n t h e X-band and P-band r e g i o n s by HP H06-X422A and HP H06-P422A back d i o d e d e t e c t o r s , r e s p e c t i v e l y . In t h e R-band r e g i o n , a HP 11586A p o i n t c o n t a c t d i o d e was u s e d . R o t a t i o n a l t r a n s i t i o n s were d e t e c t e d by a p p l y i n g a 100 kHz square-wave m o d u l a t i o n f i e l d a c r o s s the c e l l - w a v e g u i d e and a p p l y -i n g t h e d e t e c t e d s i g n a l t h r o u g h a p r e a m p l i f i e r to a P r i n c e t o n A p p l i e d R e s e a r c h Model 120 p h a s e - s e n s i t i v e l o c k - i n a m p l i f i e r f o r r a d i o f r e q u e n c y d e t e c t i o n . The a d v a n t a g e i n u s i n g t h i s S t a r k m o d u l a t i o n i s t h a t t h e h i g h f r e q u e n c y square-wave e l e c t r i c f i e l d m o d u l a t e s t h e f r e q u e n c i e s of t r a n s i t i o n s b u t does n o t m o d u l a t e d e t e c t o r n o i s e o r n o i s e c a u s e d by r e f l e c t i o n s i n t h e c e l l . Thus t h e s i g n a l - t o - n o i s e r a t i o i s e x c e l l e n t when u s i n g S t a r k m o d u l a t i o n . B e c a u s e p h a s e - s e n s i t i v e d e t e c t i o n was u s e d , and one t i p o f t h e square-wave was a t z e r o -f i e l d , t h e s i g n a l o b s e r v e d on the o s c i l l o s c o p e or c h a r t showed b o t h t h e z e r o - f i e l d a b s o r p t i o n l i n e and the S t a r k components, w i t h t h e l a t t e r i n v e r t e d a t t h e b a s e l i n e . T h i s was v e r y h e l p f u l i n the i d e n t i f i c a t i o n o f s p e c t r a l l i n e s . The m o d u l a t i o n was a p p l i e d t o t h e c e l l by c o n n e c t i n g t h e -35-o u t p u t o f an I n d u s t r i a l Components I n c o r p o r a t e d 100 kHz s q u a r e -wave g e n e r a t o r (0-2000 v o l t s p e a k - t o - p e a k ) to a S t a r k septum made of c o p p e r h e l d p a r a l l e l to t h e b r o a d w aveguide f a c e o f t h e c e l l by s l o t t e d T e f l o n i n s u l a t o r s . The septum was f i t t e d i n the e x a c t c e n t e r of t h e c e l l t o e n s u r e a u n i f o r m e l e c t r i c f i e l d . Two d i f f e r -e n t gas c e l l s were u s e d i n t h i s s t u d y : a 0.5 i n . x 1 i n . x 10 f t . X-band c e l l and a 1.5 i n . x 2 i n . x 10 f t . S-band c e l l . To measure the microwave f r e q u e n c y when u s i n g t h e BWO s o u r c e , t h e microwave sweep o s c i l l a t o r was p h a s e - l o c k e d to a h a r m o n i c o f the r e f e r e n c e o s c i l l a t o r w i t h t h e s y n c h r o n i z e r . The c o r r e c t h a r m o n i c was c h o s e n by c o m p a r i n g t h e c o u n t e r r e a d o u t w i t h a r o u g h l y c a l i b r a t e d s c a l e on t h e sweep o s c i l l a t o r . The o u t p u t o f t h e sweep o s c i l l a t o r c o u l d be made to t r i g g e r HP 8429A f r e q u e n c y m a r k e r s on a HP 680 s t r i p c h a r t r e c o r d e r t o e n a b l e r o u g h f r e q u e n c y measurements to be made. F o r p r e c i s e measurements, manual sweeps were c a r r i e d o u t and t h e f r e q u e n c y was t a k e n d i r e c t l y f r o m t h e c o u n t e r . When th e k l y s t r o n was u s e d , r o u g h f r e q u e n c y measurements were made w i t h an o n - l i n e c a v i t y wavemeter. P r e c i s e f r e q u e n c y measurements were made by a d j u s t i n g t h e f r e q u e n c y o f a m u l t i p l e o f t h e HP r e f e r e n c e o s c i l l a t o r ( a s measured by t h e c o u n t e r and s u b s e q u e n t l y o f f s e t i n t e r n a l l y by 20 MHz) to t h a t i n d i c a t e d by t h e wavemeter and t h e n m i x i n g t h e o s c i l l a t o r o u t p u t w i t h t h e k l y s t r o n m i crowave power w i t h a 1N26 c r y s t a l d i o d e . The d i f f e r e n c e i n t h e two f r e q u e n c i e s ( t h e b e a t f r e q u e n c y ) was t h e n d e t e c t e d by a Hammarlund SP-600 r a d i o r e c e i v e r t u n e d to a b e a t f r e q u e n c y o f 20 MHz, t h e o u t p u t o f w h i c h was c o n n e c t e d t o t h e y - p l a t e s o f t h e s e c o n d beam o f a d u a l -beam o s c i l l o s c o p e . An a c c u r a t e t r a n s i t i o n f r e q u e n c y was s u b --36-s e q u e n t l y measured by t u n i n g t h e f r e q u e n c y o f t h e m u l t i p l e of t h e r e f e r e n c e o s c i l l a t o r ;to t h e p o i n t where t h e marker from t h e r a d i o r e c e i v e r o u t p u t was a l i g n e d w i t h t h e l i n e d i s p l a y e d on t h e f i r s t ' beam o f t h e s c o p e . I n o r d e r to remove t i m e - c o n s t a n t e f f e c t s t h i s p r o c e d u r e was r e p e a t e d by s c a n n i n g t h e f r e q u e n c y i n t h e o p p o s i t e d i r e c t i o n and t h e a v e r a g e o f the, two c o u n t e r r e a d i n g s gave t h e t r a n s i t i o n f r e q u e n c y d i r e c t l y . M easured l i n e s had an e s t i m a t e d a c c u r a c y o f b e t t e r t h a n ±100 kHz. The p r e c i s i o n o f t h e i n s t r u m e n t was c h e c k e d p e r i o d i c a l l y a g a i n s t t h e c u r r e n t l y a c c e p t e d f r e q u e n c y o f t h e 3«-2 t r a n s i t i o n o f 16 12 32 0 C S ( 6 4 ) . I n a l l i n s t a n c e s t h e measurement was w i t h i n 50 kHz o f t h i s v a l u e . 3.3 M i c r o w a v e C e l l s and G a s - H a n d l i n g Equipment Two d i f f e r e n t m icrowave c e l l s were used i n t h i s s t u d y -- an X-band c e l l and an S-band c e l l . E a ch c e l l had windows c o n s t r u c t e d o f t h i n s h e e t s o f m i c a and a g l a s s gas I n l e t , p o r t was c o n n e c t e d to e a c h end. The c e l l d i m e n s i o n s and d e s c r i p t i o n o f t h e S t a r k septum were g i v e n i n t h e p r e v i o u s s e c t i o n . The c e l l s were c o n n e c t e d v i a the gas i n l e t p o r t s to a c o n -v e n t i o n a l vacuum s y s t e m to w h i c h t h e b u l b s c o n t a i n i n g t h e p r o p i o l -amide samples c o u l d be a t t a c h e d . The a r r a n g e m e n t was s u c h t h a t i t was p o s s i b l e t o f l o w c o n t i n u o u s l y t h e s u b l i m e d p r o p i o l a m i d e i n t h r o u g h one o f t h e gas p o r t s and out t h r o u g h t h e o t h e r u s i n g a r o t a r y pump ( s e e F i g u r e 3 . 2 ) . T h i s f l o w i n g p r o c e d u r e was u s e d t o p r e v e n t d e c o m p o s i t i o n o f t h e sample w i t h i n t h e c e l l and gave p r e s s u r e s o f 10-20 m i l l i t o r r as measured by a t h e r m o c o u p l e vacuum gauge. A l l measurements were c a r r i e d out w i t h the c e l l a t room -37-t e m p e r a t u r e , te To Pump Sample i S t a r k c e l l Ml I.. F i g u r e 3.2 The M i c r o w a v e S p e c t r o m e t e r Vacuum System ( t h e a r r o w s i n d i c a t e t h e sample f l o w ) 3.4 The S t a r k V o l t a g e M i x e r F o r a c c u r a t e S t a r k e f f e c t measurements, the e l e c t r i c f i e l d i n t h e c e l l was c r e a t e d by a p p l y i n g a l a r g e DC b i a s p o t e n t i a l to the S t a r k septum and f l o a t i n g on top o f t h i s a much s m a l l e r 100 kHz square-wave m o d u l a t i o n v o l t a g e . A S t a r k v o l t a g e m i x e r , b a s e d on a d e s i g n by Muenter ( 6 5 ) , was used to a c c o m p l i s h t h i s ; t h e c i r c u i t d i a g r a m i s shown i n F i g u r e 3.3. The s o u r c e o f t h e DC v o l t a g e was a J o hn F l u k e Mfg. Co. Model 412B DC power s u p p l y w i t h a c a l i b r a t i o n a c c u r a c y o f ± 0 . 2 5 % and a r e s e t t a b i l i t y o f ± 0 . 0 5 % . The AC m o d u l a t i o n was p r o v i d e d by -38-the Industrial Components Inc. square-wave generator described in Section 3.2. Figure 3.3 C i r c u i t Diagram of the Stark Voltage Mixer - 3 9 -C h a p t e r 4 The M i c r o w a v e S p e c t r a o f P r o p i o l a m i d e 4.1 A s s i g n m e n t o f t h e S p e c t r a In o r d e r to b e g i n t h e a s s i g n m e n t o f t h e s p e c t r u m o f t h e i s o -12 12 12 16 1A t o p i c a l l y most abundant s p e c i e s o f p r o p i o l a m i d e , H C C C 0 NR^, a p r e d i c t i o n of t h e r i g i d r o t o r t r a n s i t i o n f r e q u e n c i e s was made u s i n g v a l u e s o f t h e r o t a t i o n a l c o n s t a n t s e s t i m a t e d by as s u m i n g a m o l e c u l a r s t r u c t u r e b a s e d on t h e s t r u c t u r e s o f two r e l a t e d 14 m o l e c u l e s , p r o p y n a l (66) and formamide ( 2 0 ) . S i n c e t h e N n u c l e u s has a s p i n «I#1, q u a d r u p o l e h y p e r f i n e s p l i t t i n g o f some o f t h e r o t a t i o n a l t r a n s i t i o n s was o b s e r v e d . The m a g n i t u d e s o f t h e s e s p l i t t i n g s were p r e d i c t e d u s i n g c o u p l i n g c o n s t a n t s w h i c h were e s t i m a t e d by n o t i n g t h a t , v / i t h r e s p e c t to t h e -C(0)NH2 amido g r o u p , t h e a and b i n e r t i a l axes o f p r o p i o l a m i d e were e x p e c t e d to be v e r y n e a r l y p a r a l l e l to t h e b and a a x e s , r e s p e c t i v e l y , of form a m i d e , so t h a t x a a ( p r o p i o l a m i d e ) ( f o r m a m i d e ) and X ^ ^ ( p r o p i o l a m i d e ) = X a a ( ^ o r m a m i ^ e ) • Bond moment c a l c u l a t i o n s s i m i l a r t o t h o s e made f o r formamide (108) i n d i c a t e d t h a t t h e b component o f t h e d i p o l e moment would be l a r g e r t h a n t h e a comp-o n e n t , so t h a t t h e s p e c t r u m was e x p e c t e d to have s t r o n g b - t y p e and weaker a - t y p e t r a n s i t i o n s . The i n i t i a l s p e c t r a l p r e d i c t i o n i n d i c a t e d t h a t t h e v e r y s t r o n g Q - b r a n c h , b - t y p e s e r i e s o f l i n e s o f t h e t y p e j - j * " ^ j £ would', be p r e s e n t w i t h i n the f r e q u e n c y r a n g e s a v a i l a b l e (8-18 GHz, 26.5-40 GHz) and t h a t t h e s e l i n e s would e x h i b i t v e r y s m a l l h y p e r -f i n e s p l i t t i n g s . The o b s e r v e d s p e c t r u m d i d show s e v e r a l s u c h l i n e s i d e n t i f i e d as Q- b r a n c h e s by t h e i r c h a r a c t e r i s t i c S t a r k c o n t o u r s . -40-The number of Stark lobes could be estimated for some of these l i n e s , giving an indication of the J-value involved in the trans-i t i o n . Several possible assignment combinations of the lines were then f i t to the rotational constants (see next section for the f i t t i n g procedures). The correct assignment was i d e n t i f i e d by i t s low f i t deviation (==5 MHz) and gave values for (A-C)/2 and the Ray asymmetry parameter K (67) ; other Q-branch lines were subsequently predicted, found and assigned, with the magnitude of the hyperfine s p l i t t i n g s often the important c r i t e r i o n of proper assignment. Since only (A-C)/2 and K can be determined from a f i t of Q-branch t r a n s i t i o n frequencies, a P- or R-branch l i n e had to be assigned in order to determine the three rotational constants independently and to allow for a complete spectral assignment. 2 The tack taken was to assume an i n e r t i a l defect of A=0.25 amu-A ( A = I c - I a - I b ) , a quantity similar to that found for HCCCOF (68) and HCCCOOH (69), and to calculate, using the information obtained from the Q-branch assignment, values for A, B and C. A search was then made for the 1^  \~®Q Q i i n e i n t n e appropriate frequency region re s u l t i n g in the discovery of the l i n e at 14450 MHz, showing the expected single Stark component and three hyperfine components. After the assignment of the 1^  \~®Q Q t r a n s i t i o n , another f i t to the rotational constants and prediction of the spectral frequen-cies was made. However, i t was d i f f i c u l t to match these predictions with l i n e s in the spectrum because the high centrifugal d i s t o r t i o n corrections of the Q-branch transitions were straining the f i t . (A f i t to the d i s t o r t i o n constants could not be made because at least three P- or R-branch t r a n s i t i o n frequencies are needed for -41-t h e a n a l y s i s ) . To remove t h i s s t r a i n t h e c e n t r i f u g a l d i s t o r t i o n c o r r e c t i o n s were a p p r o x i m a t e d by t h o s e o b s e r v e d f o r t h e same t r a n s i t i o n s i n p r o p i o l y l f l u o r i d e (68) ( w h i c h i s i n e r t i a l l y s i m i l a r t o p r o p i o l a m i d e ) and were s u b t r a c t e d f r o m t h e o b s e r v e d p r o p i o l a m i d e l i n e f r e q u e n c i e s . These c o r r e c t e d f r e q u e n c i e s and the l-.+'O-^ f r e q u e n c y were t h e n r e f i t t o t h e r o t a t i o n a l c o n s t a n t s 1,1 lyj and, a f u r t h e r s p e c t r a l p r e d i c t i o n was made. T h i s p r e d i c t i o n t u r n e d o u t to be v e r y u s e f u l f o r t h e a s s i g n m e n t o f s e v e r a l o t h e r l o w - J R - b r a n c h l i n e s ( w h i c h had v e r y s m a l l c e n t r i f u g a l d i s t o r t i o n c o r r e c t i o n s ) . When more t h a n two R - b r a n c h e s had been a s s i g n e d , a f i t to t h e r o t a t i o n a l and t h e q u a r t i c c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s u s i n g t h e a c t u a l l i n e f r e q u e n c i e s c o u l d be c a r r i e d o u t ; t h i s f i t a l l o w e d t h e p r e d i c t i o n and a s s i g n m e n t o f t h e r e m a i n d e r o f t h e s p e c t r u m up t o J=30. The r e l a t i v e i n t e n s i t i e s o f the. a l l o w e d h y p e r f i n e components f o r e a c h r o t a t i o n a l t r a n s i t i o n were c a l c u l a t e d f r o m t a b l e s (70) and i n d i c a t e d t h a t o n l y t h r e e o f t h e components would be d e t e c t -a b l e : f o r Q - b r a n c h e s , t h e t h r e e AF=0 components, o r , f o r R - b r a n c h e s , t h e t h r e e AF=+1 components. I n t h e few c a s e s where a l l t h r e e components were r e s o l v e d by t h e s p e c t r o m e t e r , a s t r a i g h t f o r w a r d a s s i g n m e n t u s i n g r e l a t i v e i n t e n s i t i e s was made based on t h e i n i t i a l p r e d i c t i o n o f h y p e r f i n e s p l i t t i n g s m e n t i o n e d above. However, when o n l y two h y p e r f i n e l i n e s were o b s e r v a b l e b e c a u s e o f an i n a b i l i t y to r e s o l v e t h e n e a r l y c o i n c i d e n t F=J+l«-F=J+l and F=J-l«-F=J-l components f o r Q - b r a n c h e s , o r t h e F=J+2«-F=J+l and F=J«-F=J-1 components f o r R - b r a n c h e s , t h e f r e q u e n c y o f t h e s t r o n g e r l i n e was a s s i g n e d as t h e o v e r l a p p e d l i n e s . T h i s was done s i n c e -42-t h e combined r e l a t i v e i n t e n s i t y o f t h e two n e a r - d e g e n e r a t e compon-e n t s was a l w a y s g r e a t e r t h a n t h e r e l a t i v e i n t e n s i t y o f t h e r e m a i n i n g component. A t y p i c a l h y p e r f i n e s p l i t t i n g p a t t e r n i s shown i n F i g u r e 4.1. F i g u r e 4.1 A T y p i c a l H y p e r f i n e S p l i t t i n g P a t t e r n f o r P r o p i o l a m i d e P r o p i o l a m i d e was e x p e c t e d t o have o n l y t h r e e l o w - l y i n g e x c i t e d v i b r a t i o n a l s t a t e s — t h e CEC-C i n - p l a n e and o u t - o f - p l a n e b e n d i n g modes as i n p r o p i o l y l f l u o r i d e ( 6 8 ) , p r o p i o l y l c h l o r i d e (71) and p r o p y n a l (72) and t h e a m i d o - h y d r o g e n i n v e r s i o n mode as i n formamide ( 2 0 , 7 3 ) . The r o t a t i o n a l t r a n s i t i o n s w i t h i n t h e s e e x c i t e d s t a t e s were e x p e c t e d to be s t r o n g enough to be d e t e c t a b l e i n t h e p r o p i o l a m i d e s p e c t r u m and so s e a r c h e s were made f o r them. The r o t a t i o n a l t r a n s i t i o n s w i t h i n t h e C=C-C i n - p l a n e and o u t - o f - p l a n e b e n d i n g s t a t e s ( v ^ n = i a n Q ^ u t ^ * r e s P e c t l v e x y ) were q u i t e e a s i l y a s s i g n e d once t h e gr o u n d s t a t e s p e c t r u m had been s o l v e d . The r o t a t i o n a l c o n s t a n t s o f p r o p i o l a m i d e w i t h i n t h e s e -43-excited states were estimated by noting the changes in the rot a t i o n a l constants between the ground and these excited states for the i n e r t i a l l y similar p r o p i o l y l f l u o r i d e , making similar changes to the ground state constants of propiolamide, and then predicting the spectra. These predictions were quite good and assignments were made by methods similar to those used for tine ground state assignment. The magnitude of the hyperfine structure often served as confirmation of the assignments. The assignment of the ro t a t i o n a l spectrum within the inversion state (v, =1) was more d i f f i c u l t because of the low i n t e n s i t i e s inv of the t r a n s i t i o n s . A Q-branch assignment was made after a persistent search came up with a host of unassigned Q-branch tr a n s i t i o n frequencies. The key to the correct assignment turned out to be the discovery of the 600«-6„, t r a n s i t i o n which was 3,3 2,4 i d e n t i f i e d by i t s marked s i m i l a r i t y to the corresponding ground state l i n e , having no hyperfine structure and showing four resolvable Stark components (see Figure 4.2). The assignment of R-branch transitions was even mo r e " d i f f i c u l t ; as in the ground state analysis, an i n e r t i a l defect for the inversion state v/as estimated (based on results found for formamide (20)) and used with the values of (A-C)/2 and K obtained from the Q-branch f i t to determine values for A, B and C. The res u l t i n g spectral prediction eventually led to the discovery of only a few weak R-branch transitions which were p o s i t i v e l y i d e n t i f i e d by the magnitudes of their hyperfine structure and their Stark character-i s t i c s . The assignment of the v i b r a t i o n a l mode to the three sets of -44-63,3~ 62,4 Ground State 500 v / c i 30 MHz sweep 63,3~ 62,4 Inversion State 500 v/cm 30 MHz sweep Figure 4.2 The 6^ ^ ~^2 4 T r a n s i t i o n o f Propiolamide in the Ground and v, =1 States inv excited state r o t a t i o n a l transitions discussed above was v e r i f i e d after the spectral analyses were completed by comparing the changes in the rotational constants and i n e r t i a l defects between the ground and excited v i b r a t i o n a l states with those observed in the similar molecules, p r o p i o l y l f l u o r i d e (68) and formamide (20). No anomalies were found. The microwave spectra of two deuterated species of propiol-amide, HCCCOND2 and DCCC0ND2, were also investigated. The quad-rupolar deuterium nuclei (1=1) had no observable effects on the spectra and rotational and hyperfine t r a n s i t i o n assignments were made by a procedure similar to that used for the HCCC0NH2 assign-ments. Because of the crowded nature of the HCCC0ND2/DCCC0ND2 spectrum, however, attempts to assign the spectra of deuterated propiolamide in excited v i b r a t i o n a l states were not carried out. -4 5-4.2 D e t e r m i n a t i o n o f t h e R o t a t i o n a l , C e n t r i f u g a l D i s t o r t i o n and 14 N N u c l e a r Q u a d r u p o l e C o u p l i n g C o n s t a n t s The r o t a t i o n a l t r a n s i t i o n s o f p r o p i o l a m i d e and i t s d e u t e r a t e d d e r i v a t i v e s were p e r t u r b e d by the p r e s e n c e o f h y p e r f i n e s t r u c t u r e 14 c a u s e d by t h e q u a d r u p o l a r N . n u c l e u s . T h i s f e a t u r e was v e r y u s e f u l i n t h e a s s i g n m e n t o f t h e s p e c t r a , as was i n d i c a t e d i n t h e p r e v i o u s s e c t i o n , b u t i t c o m p l i c a t e d t h e m a t h e m a t i c a l a n a l y s i s . T h i s was b e c a u s e t h e computer program used to f i t a s s i g n e d t r a n s -i t i o n s to r o t a t i o n a l and c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s took ' u n s p l i t ' f r e q u e n c i e s ( t h e f r e q u e n c i e s i n the l i m i t , o f z e r o n i t r o g e n n u c l e a r q u a d r u p o l e moment) as t h e d a t a i n p u t . But t h e q u a d r u p o l e c o u p l i n g c o n s t a n t s needed to f i n d t h e s e u n s p l i t f r e q u e n c i e s were d e t e r m i n e d by f i t t i n g t h e h y p e r f i n e t r a n s i t i o n f r e q u e n c i e s u s i n g t h e f i r s t - o r d e r e x p r e s s i o n f o r t h e q u a d r u p o l e e n e r g y l e v e l s , eq. 2.47, and f o r t h i s t h e c o r r e c t r o t a t i o n a l c o n s t a n t s had to be known i n  a d v a n c e . Hence t h e p r o c e d u r e i n v o l v e d i n d e t e r m i n i n g t h e r o t a t i o n a l , d i s t o r t i o n and c o u p l i n g c o n s t a n t s v/as an i t e r a t i v e one. P r e l i m i n a r y u n s p l i t t r a n s i t i o n f r e q u e n c i e s were e s t i m a t e d by t a k i n g s i m p l e a v e r a g e s o f t h e h y p e r f i n e t r a n s i t i o n f r e q u e n c i e s o f e a c h r o t a t i o n a l t r a n s i t i o n ; t h e s e were t h e n f i t to t h e r o t a t i o n a l and d i s t o r t i o n c o n s t a n t s . The r o t a t i o n a l c o n s t a n t s so o b t a i n e d were t h e n u s e d i n the f i t t o t h e c o u p l i n g c o n s t a n t s w h i c h a l l o w e d new u n s p l i t f r e q u e n c i e s t o be d e t e r m i n e d . These 'new' f r e q u e n c i e s were t h e n r e f i t and t h e i m p r o v e d r o t a t i o n a l c o n s t a n t s o b t a i n e d were used to f i t a g a i n to t h e c o u p l i n g c o n s t a n t s ( w h i c h t h e n y i e l d e d b e t t e r u n s p l i t f r e q u e n c i e s ) . T h i s p r o c e d u r e was r e p e a t e d u n t i l t h e c o n s t a n t s o b t a i n e d c o n v e r g e d to c o n s t a n t v a l u e s . B e c a u s e o f t h e 14 s m a l l q u a d r u p o l e s p l i t t i n g s c a u s e d by t h e N n u c l e u s i n p r o p i o l --46-amide, two i t e r a t i o n s were s u f f i c i e n t f o r c o n v e r g e n c e . L i n e a r l e a s t - s q u a r e s f i t s o f o b s e r v e d t r a n s i t i o n f r e q u e n c i e s to s p e c t r a l c o n s t a n t s and the d i a g o n a l i z a t i o n o f t h e m a t r i c e s were c a r r i e d o u t by an IBM 370/168 computer u s i n g d o u b l e p r e c i s i o n (16 d i g i t ) a r i t h m e t i c t h r o u g h o u t . The f i t t i n g p r o c e d u r e s used were as o u t l i n e d i n S e c t i o n 2.6 and t h e m a t r i x d i a g o n a l i z a t i o n r o u t i n e s were b a s e d on t h e J a c o b i (74) o r H o u s e h o l d e r (75) methods. In t h e a n a l y s e s f o r t h e c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s , i n p u t v a l u e s o f t h e r o t a t i o n a l c o n s t a n t s were f i r s t u sed to c a l c u -l a t e r i g i d r o t o r t r a n s i t i o n f r e q u e n c i e s , V f , u s i n g eq. 2.12. The d i f f e r e n c e s between t h e o b s e r v e d and r i g i d r o t o r f r e q u e n c i e s , V o b s ~ V r ' w e r e t h e n f i t t o changes i n t h e r o t a t i o n a l c o n s t a n t s and to the d i s t o r t i o n c o n s t a n t s . The c o n s t a n t s o b t a i n e d were t h e n u s e d to c a l c u l a t e f i r s t s - o r d e r t r a n s i t i o n f r e q u e n c i e s , V f ^ r s t * by u s i n g eq.2.35 and e q . 2.12. The e x a c t t r a n s i t i o n f r e q u e n c i e s , V , were s u b s e q u e n t l y e x a c t c a l c u l a t e d by d i r e c t d i a g o n a l i z a t i o n o f t h e f u l l H a m i l t o n i a n , 2.33. The d i f f e r e n c e s , v - v , . , r e p r e s e n t e d h i g h e r o r d e r c o n t r i -62C £L C C I 1 1 S t b u t i o n s and were v e r y s m a l l . To c o m p l e t e t h e a n a l y s i s p r o p e r l y t h e s e h i g h e r - o r d e r c o n t r i b u t i o n s were s u b t r a c t e d f r o m V , and t h e obs r e s u l t i n g "pseudo f i r s t - o r d e r " f r e q u e n c i e s v , - (v - \ ) , . ^) ° ^ obs x e x a c t f i r s t ' were f i t to t h e r o t a t i o n a l and d i s t o r t i o n c o n s t a n t s u s i n g t h e r i g i d r o t o r and f i r s t - o r d e r d i s t o r t i o n e n e r g y e x p r e s s i o n s ( e q . 2.35 and e q . 2 . 1 2 ) . The c o n s t a n t s o b t a i n e d from t h i s f i t were t h e n u s e d to c a l c u l a t e new h i g h e r - o r d e r c o n t r i b u t i o n s to be s u b t r a c t e d f r o m V o b s * T h i s p r o c e d u r e was r e p e a t e d u n t i l t h e h i g h e r - o r d e r c o n t r i -b u t i o n s s t a b i l i z e d ; two i t e r a t i o n s were s u f f i c i e n t f o r t h e p r o p i o l --47-amide a n a l y s e s . The f i n a l c a l c u l a t e d t r a n s i t i o n f r e q u e n c i e s , V c a l c ' w e r e d e t e r m i n e d by a d d i n g t h e d e t e r m i n e d h i g h e r - o r d e r c o n t r i b u t i o n s to t h e f i r s t - o r d e r t r a n s i t i o n f r e q u e n c i e s o b t a i n e d i n t h e f i n a l i t e r a t i o n . The a s s i g n e d t r a n s i t i o n s and t h e i r o b s e r v e d and c a l c u l a t e d f r e q u e n c i e s f o r HCCCONH^ i n t h e ground and t h r e e e x c i t e d v i b r a t i o n a l s t a t e s and f o r HCCCOND 2 and DCCCOND 2 i n t h e i r g round s t a t e s a r e l i s t e d i n T a b l e s 4.1-4.6. The c a l c u l a t e d r o t a t i o n a l and q u a r t i c c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s f o r t h e s i x a s s i g n e d s p e c t r a a r e f o u n d i n T a b l e s 4.7-4.8. T a b l e 4.1 HCCCONH 2 T r a n s i t i o n F r e q u e n c i e s (MHz) Ground V i b r a t i o n a l S t a t e T r a n s i t i o n O b s e r v e d C a l c u l a t e d ^ c Q u a r t i c H i g h e r o r d e r F r e q u e n c y F r e q u e n c y Term Term *i,i-°o.o 14450.56 14450.52 -0.01 0.00 3 -3 J 3 , l 2,2 39237.96 39237.91 -0.64 0.00 3 -3 J l , 2 J 0 , 3 11637.14 11637.18 -0.47 0.00 3 -2 J 0 , 3 1,2 14752.88 14752.91 0.07 0.00 4 -4 3,1 *2,2 37929.99 37930.04 -1.43 0.00 4 - 4 4 1 , 3 *0,4 14676.43 14676.44 -0.83 0.00 4 1 , 4 " 3 0 , 3 31283.53 31283.56 -0.22 0.00 5 -5 3,2 2,3 36659.35 36659.45 -2.51 0.00 5 2 , 4 " 5 1 , 5 32136.59 32136.66 -2.27 0.00 5 3 , 2 ~ 4 3 , 1 36320.21 36320.26 -2.26 0.00 5 -4 2,3 2,2 37590.80 37590.85 -1.17 0.00 -48-T a b l e 4.1 ( c o n t i n u e d ) 3 b e c T r a n s i t i o n O b s e r v e d C a l c u l a t e d Q u a r t i c H i g h e r O r d e r F r e q u e n c y F r e q u e n c y Term Term S1.5"«l.« 32649.23 5 -4 1,4 1,3 38005.77 5 2 , 4 ~ 4 2 , 3 35581.91 5 0 , 5 ~ 4 0 , 4 33827.73 5 0 , 5 " 4 1 , 4 30126. 17 6 3 , 3 " 6 2 , 4 34912.04 6 2 , 5 _ 6 1 , 6 35663.59 6 l , 5 - 5 2 , 4 29365.56 6 1 . 6 - 5 1 , 5 38962.40 7 3 , 4 ~ 7 2 , 5 32931.40 7 1 , 6 ~ 7 0 , 7 30361.04 7 l , 6 - 6 2 , 5 38926.28 8 3 , 5 ~ 8 2 , 6 31104.35 8 1 , 7 " 8 0 , 8 37162.06 8 2 , 6 ~ 7 3 , 5 29950.25 8 2 , 7 - 7 3 , 4 11966.83 9 3 , 7 " 8 4 , 4 10238.03 9 3 , 6 ~ 9 2 , 7 29865.57 9 -9 *2,7 y l , 8 28382.79 1 0 3 , 7 - 1 0 2 , 8 29605.88 1 0 2 , 8 - 1 0 1 , 9 33834.68 1 0 3 , 8 - 9 4 , 5 16606.81 1 0 2 , 9 - 9 3 , 6 16208.89 32649.23 -0.12 0.00 38005.68 -0.49 0.00 35581.89 -0.92 0.00 33827.80 -0.03 0.00 30126.22 0.20 0.00 34912.07 -3.82 0.00 35663.57 -3.20 0.00 29365.60 0.64 0.00 38962.40 -0.17 0.00 32931.49 -5.34 0.00 30361.11 -2.45 0.00 38926.14 0.86 0.00 31104.35 -7.00 0.00 37162.04 -3.23 0.00 29950.26 x 2.70 0.00 11966.73 5.21 0.00 10238.05 6.27 0.00 29865.55 -8.70 0.00 28382.79 -5.58 0.00 29605.97 -10.37 0.00 33834.73 -6.73 0.00 16606.82 9.09 0.00 16208.86 9.57 0.00 -49-T a b l e 4.1 ( c o n t i n u e d ) T r a n s i t i o n O b s e r v e d 3 C a l c u l a t e d Q u a r t i c ° H i g h e r o r d e r F r e q u e n c y F r e q u e n c y Term Term 1 1 3 , 8 _ 1 1 2 , 9 ^ 30622.01 30621. 93 -11. 95 0.00 12 -12 i Z 3 , 9 ^ 2 , 1 0 33107.84 33107. 83 -13. 40 0.00 1 3 4 , 9 - 1 2 5 , 8 33197.62 33197. 54 17. 36 0.00 1 4 4 , 10"* 1 43, 11 39036.56 39036. 59 - -27. 17 0.00 1 4 4 , 1 1 _ 1 3 5 , 8 32001.19 32001. 12 24. 24 0.00 1 5 5 , 1 0 _ 1 4 6 , 9 29375.22 29375. 27 27. 53 0.00 15 -15 i 3 4 , l l J3,12 39497.15 39497. 10 -28. 88 0.00 l 6 5 , U 2 - 1 5 6 , 9 33922.73 33922. 67 35. 52 0.00 1 7 7 , l f 1 6 8 , 8 8761.25 8761. 37 35. 16 -0.01 1 7 7 , 1 0 ' 1 6 8 , 9 8838.24 8838. 28 35. 01 -0.01 1 7 6 , 1 1 _ 1 6 7 , 1 0 26960.00 26959. 99 40. 00 0.00 1 8 7 , 1 2 ~ 1 7 8 , 9 16818.39 16818. 44 44. 97 -0.01 1 8 7 , 1 1 ~ 1 7 8 , 1 0 16988.77 16988. 71 44. 72 -0.01 1 8 6 , 1 2 _ 1 7 7 , 1 1 36109.85 36109. 82 48. 95 0.01 l 8 6 , 1 3 ~ 1 7 7 , 1 0 34006.97 34006. 96 49. 72 0.01 2 ° 1 1 , 9 ~ 1 9 1 2 , 8 -33832.14 -33832. 14 14. 97 -0.09 20 -19 Z 8,12 ^9,11 15878.66 15878. 67 60. 33 -0.02 2 0 7 , 1 4 - 1 9 8 , 1 1 33279.73 33279. 72 67. 04 0.00 2 0 7 , 1 3 - 1 9 8 , 1 2 33993.82 33993. 79 66. 56 0.00 2 0 8 , 1 3 _ 1 9 9 , 1 0 15828.33 15828. 38 60. 45 -0.02 22 -21 ^ 1 2 , 1 0 A 1 3 , 9 -34794.40 -34794 . 30 24. 10 -0.15 22 -21 ^ 9 , 1 4 Z i 1 0 , l l 14830.91 14831. 00 79. 03 -0.04 22 -21 9,13 Z i 1 0 , 1 2 ; 14845.36 14845. 36 78. 98 -0.04 -50-T a b l e 4.1 ( c o n t i n u e d ) T r a n s i t i o n O b s e r v e d 3 C a l c u l a t e d b Q u a r t i c 0 H i g h e r o r d e r C F r e q u e n c y F r e q u e n c y Term Term 22 -21 z z 8 , 1 4 A9,13 32494. 16 32494.15 87. 50 0.00 23 -22 Z J 1 2 , 1 2 ^ 1 3 , 9 -27159. 47 -27159.39 43. 00 -0.16 24 -23 ^ 1 3 , 1 2 Z J 1 4 , 9 -35751. 27 -35751.24 35. 67 -0.22 2 4 9 , 1 5 ~ 2 3 1 0 , 1 4 31258. 09 31258.02 112. 05 -0.01 24 -23 ^ 1 0 , 1 5 J l l , 1 2 13844. 22 13844.25 100. 97 -0.07 25 -24 " l 3 , 1 3 ^ 1 4 , 1 0 -28104. 66 -28104.63 57. 98 -0.24 2 6 1 4 , 1 3 ~ 2 5 1 5 , 1 0 -36703. 29 -36703.21 49. 93 -0.32 2 7 1 0 , 1 8 " 2 6 1 1 , 1 5 38426. 94 38426.94 162. 02 -0.01 2 7 1 3 , 1 5 ~ 2 6 1 4 , 1 2 -12657. 33 -12657.40 106. 55 -0.26 2 7 1 4 , 1 4 " 2 6 1 5 , 1 1 -29045. 50 -29045.61 75. 94 -0.34 2 8 1 5 , 1 4 ~ 2 7 1 6 , 1 1 -37650.25 -37650.36 67. 15 -0.45 2 9 1 1 , 1 9 ~ 2 8 1 2 , 1 6 37327. 91 37327.96 198. 17 -0.03 T a b l e 4.2 HCCC0NH 2 T r a n s i t i o n F r e q u e n c i e s (MHz) CHC-C i n - p l a n e - b e n d V i b r a t i o n a l S t a t e < V i n = 1 > T r a n s i t i o n Ob s e r v e d F r e q u e n c y b e c C a l c u l a t e d Q u a r t i c H i g h e r o r d e r F r e q u e n c y Term Term 4 1 , 4 ~ 3 0 , 3 4 -4 *1,3 *0,4 5 -5 J2,4 J l , 5 5 -5 J3,2 D2t3 31186.87 14682.06 31896.67 35964.33 31186.88 14682.03 31896.72 35964.30 •0.20 •0.77 -1.98 •1.80 0.00 0. 00 0.00 0.00 -51-T a b l e 4.2 ( c o n t i n u e d ) T r a n s i t i o n O b s e r v e d 3 C a l c u l a t e d * 5 Q u a r t i c H i g h e r o r d e r F r e q u e n c y F r e q u e n c y Term Term 5 0 , 5 " 4 1 , 4 30304.08 30304. 11 0.17 0.00 6 2 , 5 " 6 1 , 6 35473.60 35473.50 -2.83 0.00 6 3 , 3 " 6 2 , 4 34185.83 34185.83 -3.01 0.00 6 0 , 6 ~ 5 1 , 5 37508.33 37508.26 0.15 0.00 7 3 , 4 _ 7 2 , 5 32202.77 32202.86 -4.42 0.00 7 l , 6 - 7 0 , 7 30608.79 30608.84 -2.26 s 0.00 8 1 , 7 _ 8 0 , 8 37452.19 37452.21 -2.97 0.00 8 3 , 5 " 8 2 , 6 30422.57 30422.56 -5.97 0.00 8 2 , 6 " 7 3 , 5 31019.59 31019.62 1.86 0.00 9 -9 3,6 *2,7 29291.07 29291 .08 -7.59 0.00 9 2 , 7 _ 9 1 , 8 28602.90 28602.92 -5.16 0.00 1 0 3 , 7 - 1 0 2 , 8 29199.35 29199.40 -9.19 0.00 U 4 , 7 - 1 0 5 , 6 14870.90 14870.89 5.73 0.00 1 1 3 , 8 _ 1 1 2 , 9 30437.09 30437.04 -10.74 0.00 12 -12 3,9 2,10 33187.24 33187.17 -12.20 0.00 1 3 4 , 9 - 1 2 5 , 8 35187.73 35187.76 12.58 0.00 13 -13 3,10 2,11 37513.27 37513.24 -13.61 0.00 1 4 4 , 1 1 - 1 3 5 , 8 33222.60 33222.58 19.75 0. 00 14 -14 i H 4 , 1 0 i 4 3 , l l 38386.43 38386.39 -23.84 0.00 15 -15 3 4 , 1 1 i J 3 , 1 2 39185.81 39185.89 -25.64 0.00 -52-T a b l e 4.3 HCCC0NH 2 T r a n s i t i o n F r e q u e n c i e s (MHz) C = C-C o u t - o f - p l a n e - b e n d V i b r a t i o n a l S t a t e (v =1) ou t T r a n s i t i o n O b s e r v e d 3 C a l c u l a t e d 1 3 Q u a r t i c 0 H i g h e r o r d e r F r e q u e n c y F r e q u e n c y Term Term 4 -4 3,1 ^2,2 38491.29 38491 .30 -1.56 0.00 4 -4 *1,3 *0,4 14782.04 14782 .10 -0.90 0.00 4 1 , 4 ~ 3 0 , 3 31462.35 31462 .37 -0.29 0.00 5 -5 33,2 3 2 , 3 37227.44 37227 .36 -2.70 0.00 5 2 , 4 ~ 5 1 , 5 32475.66 32475 .71 -2.46 0.00 5 0 , 5 ~ 4 1 , 4 30153.90 30153 .94 0.10 0.00 6 2 , 5 _ 6 1 , 6 36006.92 36006 .90 -3.49 0.00 6 3 , 3 _ 6 2 , 4 35480.95 35481 .04 -4.10 0.00 6 0 , 6 _ 5 1 , 5 37419.21 37419 . 14 '!0.03 0.00 7 3 , 4 " 7 2 , 5 33488.21 33488 .25 -5.72 0.00 7 1 , 6 " 6 2 , 5 38801.91 38801 .92 0.59 0.00 8 1 , 7 ~ 8 0 , 8 37306.81 37306 .81 -3.66 0.00 8 3 , 5 ~ 8 2 , 6 31629.61 31629 .58 -7.49 0.00 9 -9 *3,6 *2,7 30337.94 30337 .95 -9.33 0.00 9 -9 *2,7 y l , 8 28500.43 28500 .46 -6.12 0.00 1 0 3 , 7 - 1 0 2 , 8 30006.71 30006 .64 -11.16 0.00 1 0 2 , 8 - 1 0 1 , 9 33917.95 33917 .92 -7.46 0.00 1 1 3 , 8 ~ 1 1 2 , 9 30936.89 30936 .80 -12.92 0.00 U 3 , 8 - 1 0 4 , 7 37286.63 37286 .63 8.43 0.00 13 -13 3,10 J 2 , 11 37274.76 37274 .75 -12.27 0.00 1 4 4 , 1 0 " 1 4 3 , 1 1 39621.59 39621 .57 -29.27 0.00 15 -15 J 4 , l l i 3 3 , 1 2 39943.63 39943 .71 -31.32 0.00 -53-Table 4.4 HCCCONH2 Transition Frequencies (MHz) Inversion Vibrational State < vinv = 1> Transition Observed 3 Calculated* 5 c Quartic c Higher order Frequency Frequency Term Term 41,4 _ 30,3 31266.02 31266.03 -0.23 0.00 5 -5 J3,2 J2,3 36579.73 36579.66 -2.45 0.00 5 -4 31,5 0,4 36335.73 36335.73 -0.37 0.00 5 -4 ^0,5 *1,4 30117.52 30117.51 0.16 0.00 63,3~ 62,4 34839.15 34839.26 -3.74 0.00 62,5~ 61,6 35562.43 35562.41 -3.12 0.00 61,5" 52,4 29358.85 29358.85 0.59 0.00 11,6"70,7 30254.99 30255.10 -2.36 0.00 71,6 _ 62,5 38908.35 38908.35 0.78 0.00 81,7" 80,8 37032.88 37032.85 -3.07 0.00 1 02,8- 1 01,9 33711.50 33711 .46 -6.60 0.00 1 03,7- 1 02,8 29534.88 29534.84 -10.27 0.00 1 13,8 - 1 12,9 30537.14 30537.11 -11.84 0.00 13 -13 i J4,9 J3,10 39911.47 39911 .46 -24.56 0.00 1 44,10*" 1 43,11 38949.16 38949.15 -26.91 0.00 15 -15 J 4 , l l 3,12 39392.10 39392.15 -28.63 0.00 -54-T a b l e 4.5 HCCCOND 2 T r a n s i t i o n F r e q u e n c i e s (MHz) Ground V i b r a t i o n a l S t a t e T r a n s i t i o n O b s e r v e d 3 C a l c u l a t e d Q u a r t i c 0 H i g h e r o r d e r 0 F r e q u e n c y F r e q u e n c y Term Term 4 -4 H 2 , 2 *1,3 17164 .32 17164 .37 -0.93 0.00 5 3 , 3 " 5 2 , 4 35318 .46 35318 .35 -2.47 0.00 5 3 , 2 ~ 5 2 , 3 31438 .59 31438 .67 -2.10 0.00 5 1 , 5 " 4 0 , 4 33810 .15 33810 .18 -0.23 0.00 6 2 , 4 ~ 6 1 , 5 17874 .20 17874 .13 -2.19 0.00 6 3 , 4 ~ 6 2 , 5 36409 .84 36409 .81 -3.79 0.00 6 1 , 6 " 5 0 , 5 38740 .08 38739 .97 -0.28 0.00 6 0 , 6 ~ 5 0 , 5 37634 .13 37634 .21 -0.02 0.00 6 1 , 6 - 5 1 , 5 36897 . 14 36897 .11 -0.04 0.00 6 0 , 6 " 5 1 , 5 35791 .33 35791 .36 0.22 0.00 7 3 , 4 " 7 2 , 5 27816 .77 27816 .84 -4.42 0.00 8 1 , 7 " 8 0 , 8 36441 .77 36441 .75 -3.32 0.00 9 -9 *2,7 y l , 8 28021 .69 28021 .83 -4.95 0.00 1 0 2 , 8 - 1 0 1 , 9 33933 .26 33933 .29 -6.24 0.00 1 0 4 , 6 - 1 0 3 , 7 39508 .88 39508 .83 -12.72 0.00 U 3 , 8 ~ 1 1 2 , 9 28456 .62 28456 .69 -9 .74 0.00 n 4 , 7 - 1 1 3 , 8 36981 .70 36981 .61 -15.20 0.00 12 -12 3,9 2,10 32085 .47 32085 .43 -11.13 0.00 12 -12 4,8 A^3,9 34993 .16 34993 .28 -17.48 0.00 13 -13 J 3 , 1 0 i J 2 , l l 37232 .89 37232 .82 -12.73 0.00 13 -13 1 J 4 , 9 i J 3 , 1 0 34042 .27 34042 .29 -19.42 0.00 15 -15 ^4,11 ^3,12 36657 .26 36657 .24 -22.35 0.00 -55-Table 4.5 (continued) Transition Observed 3 Calculated Quartic C Higher order 0 Frequency Frequency Term Term 1 ? 6 , 12" 1 67,9 33897 .30 33897. 22 34. 66 0.00 1 ? 6 , 11- 1 67,10 36048 .17 36048. 20 33. 85 0. 00 1 9 4 , 16~ 1 85,13 37919 .49 37919. 51 42. 26 0. 00 1 9 7 , 13 _ 1 88,10 34645 .31 34645. 309 47. 32 0. 00 1 9 7 , 12~ 1 88,11 35457 .00 35456. 95 46. 83 0. 00 2 1 8 , -20 14 z u 9 , l l 35110 .97 35111. 04 62. 65 0. 00 2 3 9 , -22 15 10,12 35487 .75 35487. 83 80. 87 -0. 01 2 3 9 , -22 14 10,13 35585 .95 35585. 94 80.72 -0. 01 2 3 5 , 21~ 2 46,18 35628 .30 35628 . 29 80. 64 -0. 02 2 510 , 16 - 2 411,13 35851 .69 35851. 77 102. 18 -0. 02 2 510 ,15~2411,14 35884 .22 35884 . 15 102. 11 -0. 02 2 711 ,17 _ 2 612,14 36227 .58 36227 . 54 126. 80 -0. 04 2 711 ,16~ 2 612, 15 36237 .98 36237. 97 126. 77 -0. 04 Table 4.6 DCCC0ND2 Transition Frequencies (MHz) Ground Vibrational State Transition Observed Frequency Calculated* 5 Quartic° Higher order c Frequency Term Term 4 -4 ^1,3 40,4 4 -4 3,2 2,3 4 -4 3,1 ^2,2 13067.89 35700.97 34319.55 13067.89 35701.08 34319.57 -0.67 -1.03 -0.85 0.00 0.00 0.00 -56-Table A.6 (continued) £L D C C Transition Observed Calculated Quartic Higher order Frequency Frequency Term Term 5 -5 1.4 ^0,5 16722 .33 5 -5 ^2,3 31,4 17603 .88 5 -5 33,2 D2,3 33218 .58 5 -4 D l , 5 ^0,4 32488 .58 62,5 _ 61,6 31919 .03 62,4 _ 61,5 17924 . 68 60,6 _ 51,5 33186 .95 73,5~ 72,6 38265 .37 70,7- 6l,6 39339 .04 71,6 _ 62,5 34255 .66 81,7~ 80,8 32853 .93 83,6 - 82,7 39975 .81 83,5" 82,6 28270 .61 91,8~ 90,9 39117 .61 9 -9 3,6 2,7 27086 .23 1 02,8- 1 01,9 29824 .86 1 03,7- 1 02,8 26724 .37 U 3 , 8 - 1 1 2 , 9 27453 .94 U3,8- 1 04,7 32563 .72 13 -13 J3,10 J 2 , l l 32820 .89 13 -13 4,9 J3,10 36401 .08 16722.32 -1.04 0.00 17603.86 -1.39 0.00 33218.49 -1.73 0.00 32488.65 -0.29 0.00 31918.99 -2.54 0.00 17924.64 -2.06 0.00 33186.96 0.15 0.00 38265.38 -4.79 0.00 39338.96 0.08 0.00 34255.66 0.62 0.00 32853.99 -2.62 0.00 39975.84 -6.43 0.00 28270.64 -5.40 0.00 39117.62 -3.44 0.00 27086.18 -6.83 0.00 29824.78 -5.49 0.00 26724.37 -8.25 0.00 27453.96 -9.61 0.00 32563.73 6.45 0.00 32820.84 -12.10 0.00 36401.00 -19.62 0.00 -57-T a b l e 4.6 ( c o n t i n u e d ) T r a n s i t i o n O b s e r v e d 3 C a l c u l a t e d Q u a r t i c 0 H i g h e r o r d e r 0 F r e q u e n c y F r e q u e n c y Term Term 1 4 3 , i r U 2 , 12 37517 .74 37517 .75 -1=3. 35 0. 00 11 35352 .59 35352 .63 -21. 73 0. 00 1 54,11- 1 5 3 , 12 35496 .97 35497 .03 -23. 39 0. 00 H y p o t h e t i c a l u n s p l i t f r e q u e n c y w i t h h y p e r f i n e s t r u c t u r e removed. F r e q u e n c y c a l c u l a t e d u s i n g t h e r o t a t i o n a l and c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s i n T a b l e s 4.7 and 4.8. Q u a r t i c term i s c a l c u l a t e d f i r s t - o r d e r c o n t r i b u t i o n o f t h e q u a r t i c d i s t o r t i o n terms to t h e t r a n s i t i o n f r e q u e n c y . H i g h e r o r d e r term i s t h e c o n t r i b u t i o n o f terms o f f - d i a g o n a l i n t h e r i g i d a s y m m e t r i c r o t o r a p p r o x i m a t i o n . The v a l i d i t y o f t h e q u a r t i c model used f o r t h e c e n t r i f u g a l d i s t o r t i o n a n a l y s e s was c h e c k e d by r e p e a t i n g t h e a n a l y s e s but i n c l u d i n g Watson's s e x t i c H a m i l t o n i a n , 2.34, i n t h e f u l l H a m i l t o n i a n . The s e x t i c c o n s t a n t s t h a t were so c a l c u l a t e d were a l l i n d e t e r m i n a b l e i n d i c a t i n g t h a t t h e q u a r t i c model was s u f f i c i e n t f o r d e s c r i b i n g t h e s p e c t r a o f p r o p i o l a m i d e . The q u a d r u p o l e c o u p l i n g c o n s t a n t s o f p r o p i o l a m i d e were d e t e r -mined by c a r r y i n g o u t a l i n e a r l e a s t - s q u a r e s f i t o f t h e o b s e r v e d h y p e r f i n e t r a n s i t i o n s p l i t t i n g s to x a n t * H u s i n g e q. 2.47. The 3.8L 2 q u a n t i t i e s < P a > a n a Wj ( b p ) needed i n eq. 2.47 were o b t a i n e d from the d i a g o n a l i z a t i o n o f t h e r i g i d r o t o r H a m i l t o n i a n m a t r i x . In t h e c o u p l i n g c o n s t a n t a n a l y s e s f o r HCCCOND, and DCCCOND, the e f f e c t s -58-T a b l e 4.7 R o t a t i o n a l and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f HCCCONH 2 a V i b r a t i o n a l S t a t e Ground v. =1 i n A (MHz) 11417.938 ± 0.005 11306.856 ± 0.009 B (MHz) 4135.483 ± 0.002 4153.947 ± 0.003 C (MHz) 3032.595 ± 0.002 3036.029 ± 0.004 A j (kHz) 0.580 ± 0.008 0.586 ± 0.021 A J K ( k H z ) 21.09 ± 0.06 19.33 ± 0.16 A K (kHz) -10.03 ± 0.03 -16.98 ± 0.46 6 j (kHz) 0.194 ± 0.006 0.187 ± 0.012 6 K (kHz) 11.76 ± 0.01 11.08 ± 0.23 A*5 (amu-A 2) 0.1816 ± 0.0001 0.1015 ± 0.0002 No. o f t r a n s i t i o n s 70 24 S t d . dev. o f f i t (MHz) 0.06 0.06 V i b r a t i o n a l S t a t e v = 1 out v, =1 i n v A (MHz) 11537.970 ± 0.016 11397.294 ± 0.020 B (MHz) 4146.317 ± 0.005 4131.114 ± 0.013 C (MHz) 3041.814 ± 0.005 3032.370 ± 0.010 A j (kHz) 0.836 ± 0.036 0.639 ± 0.164 A,j K(kHz) 22.78 ± 0.24 20.66 ± 0.43 A R (kHz) -10.82 ± 1.54 -10.09 ± 2.63 6j (kHz) 0.232 ± 0.015 0.175 ± 0.028 6 K (kHz) 12.32 ± 0.35 12.13 ± 0.56 A (amu-A ) 0.4563 ± 0.0003 -0.0154 ± 0.0004 No. o f t r a n s i t i o n s 22 16 S t d . dev. o f f i t (MHz) 0.06 0.07 Quoted u n c e r t a i n t i e s a r e one s t a n d a r d d e v i a t i o n . A=I - I -I =(1/C - 1/A - l / B ) h / 8 i r 2 and i s c a l c u l a t e d u s i n g t h e c a b „ c o n v e r s i o n f a c t o r h / 8 i r 2 = 505379.045 MHz-amu-A . -59-Table 4.8 Rotational and Centrifugal Distortion Constants of HCCCOND2 and DCCCOND^ HCCCOND„ DCCCOND A (MHz) 10267.745 ± 0.009 10264.225 ± 0.014 B (MHz) 3979.454 ± 0.004 3672.302 + 0.005 C (MHz) 2865.486 ± 0.003 2702.349 ± 0.005 Aj (kHz) 0.463 ± 0.014 0.484 ± 0.031 A J K(kHz) 17.80 ± 0.13 17.19 ± 0.14 A R (kHz) -8.74 ± 0.22 -12.94 ± 1.20 &j (kHz) 0.256 + 0.005 0.159 ± 0.008 6 R (kHz) 8.87 ± 0.15 9.47 ± 0.19 A*3 (amu-A2) 0.1505 ± 0.0003 0.1586 ± 0.0004 of transitions 35 27 Std. dev. of f i t (MHz) 0.07 0.06 a Quoted uncertainties are one standard deviation. b A=I - I - I =(1/C - 1/A - l/B)h/8ir 2and i s calculated using the c a b n conversion factor h/8tr 2 = 505379 .045 MHz-amu-A . of the quadrupolar deuterium nuclei could be neglected since the nuclear quadrupole moment of deuterium is extremely small ( 7 6 ) . The assigned hyperfine transitions and their observed and calculated s h i f t s from the unsplit l i n e frequencies for the six spectra investigated are l i s t e d in Tables 4.9-4.14. The calc-14 ulated N nuclear quadrupole coupling constants are found in Tables 4.15-4.16. -60-T a b l e 4.9 N u c l e a r Q u a d r u p o l e H y p e r f i n e T r a n s i t i o n s o f HCCC0NH o (Ground V i b r a t i o n a l S t a t e ) 3 T r a n s i t i o n F' F" O b s e r v e d Q u a d r u p o l e C o r r e c t i o n F r e q u e n c y O b s e r v e d C a l c u l a t e d h.rVo 0-1 14449.59 -0.97 -0.98 2-1 14450.45 -0.11 -0.10 1-1 14451.07 0.51 0.49 3 -3 J l , 2 J 0 , 3 3-3 11636. 10 -1.04 -1.04 4-4 11637.50 0.36 0.35 2-2 11637.96 0.82 0.83 4 -4 1,3 0,4 4-4 14675.30 -1.13 -1.11 5-5 14676.85 0.42 0.40 3-3 14677.23 0.80 0.79 5 -5 2,4 3 1 , 5 5-5 32135.66 -0.93 -0.92 6-6, 4-4' 32137.08 0.49 0.48 6 2 , 5 ' 6 1 , 6 6-6 35662.68 -0.91 -0.88 7-7 } 5-5 1 35664.07 0.48 0.46 6 1 , 5 " 5 2 , 4 6-5 29365.20 -0.36 -0.36 7-6 } 5-4' 29365.76 0.20 0.19 7 1 , 6 ~ 7 0 , 7 7-7 30359.89 -1.15 -1.18 8-8, 6-6* 30361.64 0.60 0 i 6 0 8 1 , 7 _ 8 0 , 8 8-8 37160.96 -1.10 -1.11 9-9 } 7-7 ; 37162.63 0.57 0.57 -61-T a b l e 4.9 ( c o n t i n u e d ) T r a n s i t i o n F' F" O b s e r v e d Q u a d r u p o l e C o r r e c t i o n ^ F r e q u e n c y O b s e r v e d C a l c u l a t e d 8 2 , 7 ~ 7 3 , 4 7-6' 11966.50 -0.33 -0.34 8-7 11967.47 0.64 0.67 1 0 2 , 8 - 1 0 1 , 9 10-10 33833 .92 -0.76 -0.75 11-11, 9-9 ' 33835.06 0.38 0.38 1 0 2 , 9 - 9 3 , 6 11-10, 9-8 ' 16208.42 -0.47 -0.48 10-9 16209.83 0.94 0.94 T a b l e 4.10 N u c l e a r Q u a d r u p o l e H y p e r f i n e T r a n s i t i o n s of HCCC0NH„ ( v , = l ) a 2 i n T r a n s i t i o n F» p" O b s e r v e d Q u a d r u p o l e C o r r e c t i o n ^ F r e q u e n c y O b s e r v e d C a l c u l a t e d 4 -4 *l,3 ^0,4 4-4 14680.94 -1 .12 -1.12 5-5 14682.49 0.43 0.41 3-3 14682.86 0.80 0.80 4 1 , 4 ~ 3 0 , 3 5-4 } 3-2 ' 31186.61 -0.26 -0.25 4-3 31187.37 0.50 0.49 5 -5 2,4 ^1,5 5-5 31895.80 -0.87 -0.90 6-6, 4-4' 31897.13 0.46 0.48 6 2 , 5 ~ 6 1 , 6 6-6 35472.68 -0.92 -0.87 5-5' 35474.02 0.42 0.45 -62-T a b l e 4.10 ( c o n t i n u e d ) T r a n s i t i o n F' F" O b s e r v e d Q u a d r u p o l e C o r r e c t i o n ^ F r e q u e n c y O b s e r v e d C a l c u l a t e d 7 1 , 6 " 7 0 , 7 7-7 30607.58 -1.21 -1.18 8-8,' 6-6' 30609.41 0.62 0.61 8 2 , 6 " 7 3 , 5 8-7 31019.19 -0.40 -0.43 9-8 } 7-6' 31019.80 0.21 0.21 8 1 , 7 " 8 0 , 8 8-8 37451 .07 -1.12 -1.10 9-9 } 7-7' 37452.77 0.58 0.57 9 -9 *2,7 *1,8 9-9 28602.24 -0.66 -0.68 10-10, 8-8 ' 28603.23 0.33 0.35 T a b l e 4.11 N u c l e a r Q u a d r u p o l e H y p e r f i n e HCCC0NH o (v =1) 2 o u t T r a n s i t i o n s a o f T r a n s i t i o n F* F" O b s e r v e d Q u a d r u p o l e C o r r e c t i o n ^ F r e q u e n c y Ob s e r v e d C a l c u l a t e d 4 -4 4 1 , 3 0,4 4-4 14780.95 -1.09 -1 .10 5-5 14782.48 0.44 G0440 3-3 14782.78 0.74 0.78 5 -5 ^2,4 D l , 5 5-5 32474.69 -0.97 -0.94 6-6, 4-4' 32476. 17 0.51 0.50 6 2 , 5 " 6 1 , 6 6-6 36006.04 -0.88 -0.89 7" 7} 5-5' 36007.38 0.46 0.47 -63-T a b l e 4.11 ( c o n t i n u e d ) T r a n s i t i o n F * F " O b s e r v e d Q u a d r u p o l e C o r r e c t i o n F r e q u e n c y O b s e r v e d C a l c u l a t e d 8 1 , 7 " 8 0 , 8 8-8 37305.68 -1.13 -1.09 9-9 } 37307.39 0.58 0.56 9 -9 *2,7 *1,8 9-9 28499.85 -0.58 -0.65 10-10, 8-8 ' 28500.73 0. 30 0.33 1 0 2 , 8 - 1 0 1 , 9 10-10 33917.21 -0.74 -0.73 11-11-, 9-9 ' 33918.33 0.38 0.37 T a b l e 4.12 N u c l e a r Q u a d r u p o l e H y p e r f i n e HCCC0NH 2 ( v ± -1) T r a n s i t i o n s a o f T r a n s i t i o n F' F" O b s e r v e d Q u a d r u p o l e C o r r e c t i o n F r e q u e n c y O b s e r v e d C a l c u l a t e d 5 1 , 5 " 4 0 , 4 6-5 } 4-3' 36335.58 -0.15 -0.18 5-4 36336.06 0.33 0.36 6 2 , 5 - 6 l , 6 6-6 35561.57 -0.86 -0.84 7" 7} 5 - 5 ; 35562.87 0.44 0.43 6 1 , 5 " 5 2 , 4 6-5 29358.50 -0.35 -0.33 7-6 } 5-4 ' 29539.04 0.19 0.18 7 1 , 6 _ 7 0 , 7 7-7 30253.85 -1.14 -1.11 8§8, 6-6' 30255.59 0.60 0.57 -64-T a b l e 4.12 ( c o n t i n u e d ) T r a n s i t i o n F* F" O b s e r v e d Q u a d r u p o l e C o r r e c t i o n ^ F r e q u e n c y O b s e r v e d C a l c u l a t e d 8 1 7" 80 8 8 - 8 37031.85 -1.03 -1.04 9~ 9} 37033.39 0.51 0.54 1 0 2 8 - 1 0 l 9 10-10 33710.81 -0.69 -0.71 I^g1} 33711.85 0.35 0.36 T a b l e 4.13 N u c l e a r Q u a d r u p o l e H y p e r f i n e T r a n s i t i o n s o f HCCC0ND 2 (Ground V i b r a t i o n a l S t a t e ) 3 T r a n s i t i o n F* F" O b s e r v e d Q u a d r u p o l e C o r r e c t i o n b F r e q u e n c y O b s e r v e d C a l c u l a t e d 8,. -,-8„ _ 8-8 36440.69 -1>.08 -1.07 1 , / U , o 9" 9} 36442.32 0.55 0.55 9„ ,-9, Q 9-9 28021 .05 -0.64 --0.67 2.7 1, a 28022.02 0.33 0.35 o — o 1 0 o Q - 1 0 . _ 10-10 33932.55 -0.71 -0.68 2.8 1,9 33933.62 0.36 0.34 1 3 3 1 0 " 1 3 2 n 13*13 37232.45 -0.44 -0.45 12-12* 37233.11 0.22 0.23 -65-Table 4.14 Nuclear Quadrupole Hyperfine Transitions of DCCCOND- (Ground Vibrational S t a t e ) 3 Transition Observed Frequency Quadrupole Observed Correction ^ Calculated 4 -4 ^1,3 *0,4 4-4 13066.78 -1.11 -1.10 3-3 ' 13068.49 0.60 0.59 5 1 , 4 _ 5 0 , 5 5-5 16721.18 -1.15 -1.17 6-6, 4—4 16722.94 0.61 0.62 6 2 , 5 ~ 6 1 , 6 6-6 31918.16 -0.87 -0.87 5-5 1 31919.50 0.47 0.45 8 1 , 7 " 8 0 , 8 8-8 32852.78 -1.15 -1.12 9-9 } 7-7 J 32854.51 0.58 0.57 Transition frequencies and quadrupole corrections are in MHz. Frequency s h i f t of hyperfine t r a n s i t i o n from hypothetical unsplit t r a n s i t i o n frequency calculated from the constants in Tables 4.15 and 4.16. P a r t i a l l y resolved quadrupole corrections were calc-ulated by averaging the frequency s h i f t s of the components contributing to the unresolved t r a n s i t i o n . -66-T a b l e 4.15 1 4 N N u c l e a r Q u a d r u p o l e C o u p l i n g C o n s t a n t s o f HCCCONH 2 a V i b r a t i o n a l S t a t e Ground v. =1 i n X a a (MHz) 1.85 ± 0.14 1.58 ± 0.34 Xbb ' X c c (MHz) 5.79 ± 0.07 5.84 ± 0.11 n 3.13 ± 0.24 3.70 ± 0.80 V i b r a t i o n a l S t a t e v -1 out v, =1 i n v X a a ( M H z > 2.52 ± 0.75 1.91 ± 0.47 X b b ~ X c c (MHz) 5.63 ± 0.20 5.46 ± 0.13 n " 2.23 ± 0.67 2.86 ± 0.71 T a b l e 4.16 1 4 N N u c l e a r Q u a d r u p o l e C o u p l i n g C o n s t a n t s o f HCCC0ND 2 and DCCC0ND 2 a HCCC0ND 2 DCCC0ND 2 X a a ( M H z ) 16.11 ± 4 . 8 6 1.66 ± 2.01 Xbb " X c c (MHO 4.92 ± 0.22 5.81 ± 0.37 n 0.31 ± 0.09 3.50 ± 4.24 Quoted u n c e r t a i n t i e s a r e one s t a n d a r d d e v i a t i o n . -67-4.3 V i b r a t i o n a l S a t e l l i t e s — R e l a t i v e I n t e n s i t y Measurements In o r d e r to d e t e r m i n e the e n e r g y s e p a r a t i o n o f t h e g r o u n d 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 o f e a c h o f t h e t h r e e low-f r e q u e n c y v i b r a t i o n a l modes o b s e r v e d f o r t h e n o r m a l s p e c i e s o f p r o p i o l a m i d e , r e l a t i v e i n t e n s i t y measurements were c a r r i e d o u t . S i n c e t h e r e a r e no e q u i v a l e n t atoms i n p r o p i o l a m i d e , the v a r i o u s v i b r a t i o n a l l e v e l s a r e p o p u l a t e d a c c o r d i n g to t h e B o l t z m a n n f a c t o r (77) and t h e v=l-v=0 s e p a r a t i o n f o r a p a r t i c u l a r v i b r a t i o n ( g i v e n by co ..) can be a p p r o x i m a t e d by where k i s B o l t z m a n n ' s c o n s t a n t , T i s t h e a b s o l u t e t e m p e r a t u r e of t h e gas sample and I i s t h e r a t i o o f t h e i n t e n s i t y o f a r o t a t i o n a l t r a n s i t i o n i n t h e v = l s t a t e t o i t s i n t e n s i t y i n t h e v=0 g r o u n d s t a t e . B e c a u s e o f power f l u c t u a t i o n s f r o m the backward-wave o s c i l l a t o r s o u r c e , m e a n i n g f u l measurements c o u l d be o b t a i n e d o n l y when t h e two t r a n s i t i o n s t o be compared were a few Mega-h e r t z a p a r t . The 4^  3~ AQ 4 t r a n s i t i o n s f o r t h e g round and t h e v ^ n = l C5C-C i n - p l a n e - b e n d e x c i t e d v i b r a t i o n a l s t a t e s met t h i s c r i t e r i o n and a v a l u e o f io^ n=273±75 cm * was e s t i m a t e d (1=0.27, T = 2 9 8 ° K ) . F o r t h e d e t e r m i n a t i o n of t h e i n v e r s i o n v i b r a t i o n a l f r e q u e n c y t h e 5 Q 4 t r a n s i t i o n s were u s e d g i v i n g w i n v = 3 3 3 ± 7 5 (1=0.20, T = 2 9 8 ° K ) . A c o n v e n i e n t t r a n s i t i o n w i t h i n the v =1 C=C-C o u t - o f - p l a n e - b e n d e x c i t e d v i b r a t i o n a l s t a t e was n o t f o u n d ; however, r o t a t i o n a l t r a n s i t i o n s w i t h i n t h i s e x c i t e d s t a t e were g e n e r a l l y s l i g h t l y weaker t h a n t h o s e w i t h i n th e v. =1 e x c i t e d ; v i b = - k T£nI 4.1 o u t s t a t e i n d i c a t i n g t h a t to out i s s l i g h t l y l a r g e r t h a n to i n * -68-4.4 Determination of the Dipole Moment of Propiolamide 4.4.1 General Considerations The y g and y^ components of the dipole moment of propiol-amide are both non-zero since both a- and b-type transitions were observed in the microwave spectrum. The third component, y c, is either zero or non-zero depending on whether or not the molecule is planar (a planar molecule l i e s e n t i r e l y in the ab plane). How-ever, for reasons set forth in Section 5.4, the contributions of y c to the Stark s h i f t s of the |M^|-components of the rotational transitions that were investigated can be neglected even i f is non-zero; thus in the dipole moment analysis only y g and y^ were considered. As was indicated in Section 3.4, Stark s h i f t s were induced by applying a large, accurately known DC voltage to the Stark c e l l septum and f l o a t i n g on top of this a r e l a t i v e l y small 100 kHz AC square-wave modulation voltage using the Stark voltage mixer. Using phase-sensitive detection with this double-field system, each Stark component appears as two lobes on the oscilloscope face. One lobe (+) i s associated with a f i e l d of e, +e and dc ac the other lobe (-), which is 180° out-of-phase, with a f i e l d of e, -e where e , i s the f i e l d r esulting from the applied DC dc ac dc & potential, V^ c, and £ a c is the f i e l d resulting from one-half the peak-to-peak modulation voltage, V . The f i e l d was applied 3 C p a r a l l e l to the e l e c t r i c vector of the microwave radiation; thus the Stark effect selection rule was AM =0. Assuming a purely second-order Stark s h i f t (eq. 2.55), the average frequency of the ( + ) and (-) lobes for a given ±M «-±M -69-component of an a s y m m e t r i c r o t o r J ^ J ^ i r o t a t i o n a l t r a n s i t i o n c a n be w r i t t e n as v - v + I ( K 8 , - K f , _. ) y 2 ( e 2 + e 2 ) 4 . 2 s o J T M j j ' , M j / H g dc a c 7 where V q i s t h e z e r o - f i e l d l i n e f r e q u e n c y ; t h e dependence o f t h e S t a r k s h i f t on t h e components o f t h e d i p o l e moment i s c l e a r . I n t h e e x p e r i m e n t s , e was f i x e d a t t h e minimum v a l u e s t i l l 3. C p r o d u c i n g f u l l m o d u l a t i o n o f t h e (+) and (-) l o b e s (V =35v) and d i f f e r e n t S t a r k s h i f t s were i n d u c e d by c h a n g i n g t h e DC f i e l d by v a r y i n g V ^ c (V^ c=100-»"1000) . No a t t e m p t was made to c a l i b r a t e a c c u r a t e l y t h e m o d u l a t i o n v o l t a g e s i n c e under t h e c o n d i t i o n s o f 2 2 t h e e x p e r i m e n t s e , >>e and so t h e u n c e r t a i n t y of t h e sum Q C cl C 2 2 E ^ c + e a c ( r e q u i r e d i n 4 . 2 ) i s n o t a f f e c t e d by a l a r g e r e l a t i v e u n c e r t a i n t y i n £ a c « The d o u b l e - f i e l d t e c h n i q u e u s e d to p r o d u c e S t a r k s h i f t s a l l o w s f o r v e r y a c c u r a t e f r e q u e n c y measurements o f t h e S t a r k l o b e s . T h i s i s b e c a u s e V i s n o r m a l l y k e p t so s m a l l t h a t the ac waveform from, t h e square-wave g e n e r a t o r i s u n d i s t o r t e d r e s u l t i n g i n v e r y n a r r o w a b s o r p t i o n l i n e s . 4 . 4 . 2 C a l i b r a t i o n o f t h e S t a r k C e l l w i t h C a r b o n y l S u l f i d e I n o r d e r to d e t e r m i n e t h e p r e c i s e m a g n i t u d e of t h e e l e c t r i c f i e l d i n t h e S t a r k c e l l b o t h t h e a p p l i e d v o l t a g e and t h e septum s p a c i n g must be a c c u r a t e l y known, To d e t e r m i n e t h e septum s p a c i n g i t i s common p r a c t i c e to c a l i b r a t e t h e c e l l by o b s e r v i n g S t a r k s h i f t s o f a m o l e c u l e w i t h an a c c u r a t e l y known d i p o l e moment, These S t a r k s h i f t s a l l o w t h e c a l c u l a t i o n o f an e f f e c t i v e septum s p a c i n g , a s p a c i n g w h i c h t a k e s i n t o a c c o u n t t h e f i e l d inhomogen--70-e i t i e s i n the c e l l ; b e c a u s e o f t h i s f e a t u r e , t h e e f f e c t i v e s p a c i n g i s p r e f e r a b l e t o t h e a b s o l u t e s p a c i n g w h i c h would be o b t a i n e d by a d i r e c t p h y s i c a l measurement. The m o l e c u l e c h o s e n f o r t h e c a l i b r a t i o n was c a r b o n y l s u l f i d e , X 6 12 32 0 C S. T h i s gas was c h o s e n b e c a u s e i t i s i n e x p e n s i v e , a b s o r b s microwave r a d i a t i o n v e r y s t r o n g l y , has u s e f u l t r a n s i t i o n s w i t h i n t h e f r e q u e n c y r a n g e s o f t h e s p e c t r o m e t e r and has an a c c u r a t e l y known d i p o l e moment of 0.71521+0.00020 D ( 6 5 ) . In t h i s s t u d y , f r e q u e n c y measurements were made on t h e s i n g l e M =0«-0 S t a r k component o f t h e J=l-«-0 t r a n s i t i o n of the l i n e a r j 0 C S m o l e c u l e ; t h e S t a r k s h i f t o f t h i s t r a n s i t i o n , c o r r e c t to s e c o n d o r d e r , i s g i v e n by eq. 2.52 w i t h H ^ u ^ g b e i n g t h e d i p o l e moment of c a r b o n y l s u l f i d e m e n t i o n e d a b o v e . The e l e c t r i c f i e l d i n t h e S t a r k c e l l can be r e l a t e d to t h e e f f e c t i v e septum s p a c i n g , d, by e=V/d 4.3 where V. i s t h e a p p l i e d v o l t a g e ; t h e a v e r a g e f r e q u e n c y o f t h e (+) and (-) S t a r k l o b e s can t h e n be w r i t t e n as v = v + 0.1352 y 2 _(v5 +V 2 ) 4.4 s o = ^OCS dc ac d v o where VQ i s t h e z e r o - f i e l d f r e q u e n c y o f t h e J = l*-0 t r a n s i t i o n . - 2 2 Thus a p l o t o f V as a f u n c t i o n o f V, +V ;should g i v e a s a C 3 c - 2 - 1 2 s t r a i g h t l i n e w i t h a s l o p e , m o c s » o f 0.1352d V D ^OCS a n d a n i n t e r c e p t o f V q ; t h e septum s p a c i n g can t h e n be d e t e r m i n e d as "°- 1 3 5 2 ^ o c s V o m 0 C S 1/2 4.5 -71-The o b s e r v e d f r e q u e n c y and v o l t a g e d a t a f o r t h e Mj = 0+-0 component a r e l i s t e d i n T a b l e 4.17 and p l o t t e d i n F i g u r e 4.3. As e x p e c t e d , t h e r e l a t i o n s h i p i s l i n e a r and a l e a s t - s q u a r e s f i t of t h e d a t a t o e q u a t i o n 4.4 gave t h e r e s u l t s shown i n T a b l e 4.18. T a b l e 4.17 F r e q u e n c i e s o f t h e Mj = 0+-0 S t a r k Component of t h e 1+-0 T r a n s i t i o n o f 1 6 0 1 2 C 3 2 S 2 2 2 -4 VT + VL (v ) x l O 4 dc ac v < ,s 1.04 12163.230 4.04 12164.015 9.04 12165.315 16.04 12167.115 25.04 12169.465 36.04 12172.320 49.04 12175.685 64.04 12179.590 81.04 12184.000 100.04 12188.925 3 F r e q u e n c i e s a r e a v e r a g e s o f t h e (+) and (-) l o b e s i n MHz. T a b l e 4.18 OCS C a l i b r a t i o n Graph — S l o p e and I n t e r c e p t m o c s = s l o p e ( 2 . 5959+0 . 0 0 0 5 ) x l 0 "5 MHz/v 2 V q = I n t e r c e p t 12162 .960+0.003 MHz Quoted u n c e r t a i n t i e s a r e one s t a n d a r d d e v i a t i o n . - 7 2 --73-The v a l u e d e t e r m i n e d f o r t h e i n t e r c e p t i s i n e x c e l l e n t agreement w i t h t h e c u r r e n t l y a c c e p t e d z e r o - f i e l d f r e q u e n c y o f 12162.97 MHz f o r t h e J = l-<-0 t r a n s i t i o n (64) . The e f f e c t i v e septum s p a c i n g as c a l c u l a t e d from eq-4.5 i s d = 0.4680 ± 0.0010 cm. 4.4.3 The S t a r k S h i f t s o f P r o p i o l a m i d e , HCCC0NH 2 Two r o t a t i o n a l t r a n s i t i o n s were u s e d i n t h e d e t e r m i n a t i o n o f t h e d i p o l e moment of p r o p i o l a m i d e : t h e 6^ 2~^2 4 a n c * *1 1~^0 0 t r a n s i t i o n s . F o r t h e f o r m e r , t h e s h i f t s o f t h e |M |=6«-6, 5+5 and 4«-4 S t a r k t r a n s i t i o n s were measured and f o r t h e l a t t e r , t h e s h i f t of t h e s i n g l e Mj = 0«-0 S t a r k t r a n s i t i o n was m easured. No s p l i t t i n g o f t h e S t a r k l o b e s due to h y p e r f i n e e f f e c t s was o b s e r v e d . The d a t a were o b t a i n e d as o u t l i n e d i n S e c t i o n 4.4.1 and a r e l i s t e d i n T a b l e 4.19. The a p p l i e d f i e l d s were c a l c u l a t e d f r o m t h e a p p l i e d v o l t a g e s by u s i n g t h e e f f e c t i v e septum s p a c i n g c a l c u l a t e d i n t h e p r e v i o u s s e c t i o n and a p p l y i n g eq. 4.3. A c c o r d i n g to eq. 4.2, i_f t h e S t a r k s h i f t s a r e p u r e l y s e c o n d -2 2 o r d e r , t h e n p l o t s o f v as a f u n c t i o n o f e, +e s h o u l d y i e l d s Q c a c 2 2 s t r a i g h t l i n e s w i t h s l o p e s d e p e n d i n g on u and u,; t h e p l o t s f o r Si D t h e f o u r t r a n s i t i o n s c o n s i d e r e d h e r e a r e shown i n F i g u r e s 4.4-4.7. F o r t h e Mj = 0-<-0 component o f t h e 1^ I~®Q Q t r a n s i t i o n t h e p l o t i s , i n d e e d , l i n e a r . A l e a s t - s q u a r e s f i t o f t h e measured d a t a to eq. 4.2 gave t h e v a l u e s f o r t h e s l o p e and i n t e r c e p t shown i n T a b l e 4.20. F o r t h i s t r a n s i t i o n , t h e s l o p e , m^, i s g i v e n by m_ - 7 . 9 5 5 6 x l 0 - 6 u 2 + 7 . 5 0 7 7 x l 0 ~ 6 y 2 4.6 0 a b -The c o r r e s p o n d i n g p l o t s f o r t h e t h r e e d i f f e r e n t j M j — •J -74-T a b l e 4.19 O b s e r v e d f r e q u e n c i e s 3 of t h e JMj|=6*6, 5*5 and 4*4 S t a r k components o f t h e 6^ _-6„ . t r a n s i t i o n and of ,3 2,4 th e Mj = 0«-0 S t a r k component of t h e 1. .-0Q Q t r a n s i t i o n of HCCC0NH 2 V S e 2 +e 2 ( v 2 / c m 2 x l O - 5 ) |MT|=6*6 Cl C <1 C J ( 6 3 , 3 " 6 2 , 4 ) |M |-5*5 | lij | =4*4 1.8822 34922.28 34918.59 34915.71 4.1651 34934.14 34926.68 34920.27 7.3611 34949.36 34937.05 34926.30 11.4702 34966.72 34949. 17 34933 . 34 16.4925 34985.20 34962.48 34941.72 22.4279 35004.40 34976.35 34950.11 29.2764 34991.05 34959.01 V 2 2 2 2 - S S Z, + E (v /cm x l O •) dc ac <1i.r°o,o> M =0*0 0.1701 14451.76 0.5125 14454.99 1.0832 14461.11 1 .8822 14469.03 2.9095 14479.47 4. 1651 14492.37 5.6489 14507.46 F r e q u e n c i e s a r e a v e r a g e s o f t h e (+) and (-) l o b e s i n MHz. -75-14510 r £j + e 2 (v 2/cm 2 xlO 5) dc ac Figure 4.4 Frequency of the M^  = 0-«-0, 1^  i~^o 0 ^ r a n s ^ t : ^ O I : 1 of HCCC0NH2 as a Function of the Square of the E l e c t r i c F i e l d Strength -76-o f HCCCONH- as a F u n c t i o n o f t h e S q u a r e o f t h e E l e c t r i c F i e l d S t r e n g t h -77-34910 1 1 1 1 1 1 L_ 5 10 15 20 25 30 2 2 2 2 - 5 z, +e (vif/cm xlO J) dc ac Figure 4.6 Frequency of the |Mj|=5«-5, 6^  3~^2 4 Transition of HCCCONH2 as a Function of the Square of the E l e c t r i c F i e l d Strength -78-of HCCCONH- as a F u n c t i o n o f t h e Square o f t h e E l e c t r i c F i e l d S t r e n g t h -79-2 2 T a b l e 4.20 S l o p e and I n t e r c e p t o f t h e v v s . e, +£ Graph S Cl C cl C f o r t h e M J = 0-«-0 S t a r k Component o f t h e i j J - O Q q T r a n s i t i o n o f H C C C O N H ^ 3 m Q - S l o p e (MHz/v 2/cm 2) ( 1 . 0 1 8 ± 0 . 0 0 2 ) x l 0 ~ 4 V q - I n t e r c e p t (MHz) 14449.93+0.07 Quoted u n c e r t a i n t i e s a r e one s t a n d a r d d e v i a t i o n . components o f t h e 6„ n-6„ , t r a n s i t i o n a r e d e f i n i t e l y n o t l i n e a r , however. The r e a s o n f o r t h e n o n - l i n e a r i t y i s t h e breakdown of t h e s e c o n d - o r d e r e x p r e s s i o n f o r t h e S t a r k e n e r g y b e c a u s e of a n e a r - d e g e n e r a c y o f t h e 6^ 3 and 6^ ^ l e v e l s ; t h e s e l e v e l s a r e c o n n e c t e d by u and a r e s e p a r a t e d by o n l y 618.96 MHz. I n o r d e r t o a c c o u n t f o r t h e c u r v a t u r e o f t h e p l o t s , i t i s n e c e s s a r y to c a l c u l a t e the e x a c t S t a r k e n e r g i e s f o r t h e s e l e v e l s . The e x a c t e n e r g i e s o f t h e 6^ ^ a n < * 6^ ^ l e v e l s can be d e t e r m i n e d by d i a g o n a l i z i n g t h e 2x2 s u b m a t r i x t h e y f o r m a f t e r the a p p l i c a t i o n o f t h e Van V l e c k t r a n s f o r m a t i o n to t h e s y s t e m , {see S e c t i o n 2 . 4 ) . A c c o r d i n g t o e q s . 2.57 and 2.58 t h e s e e n e r g i e s a r e g i v e n by E ^ J +E*J J M M , 1/2 2 3,3 3,4 where e2lel2 = E 2 H J X a ( 6 3 , 3 ; 6 3 , 4 ) ^a 4.8 546 -80-i s the square of the o f f - d i a g o n a l element and and E^ ^ & '3,3 b3,4 r e p r e s e n t second-order S t a r k e n e r g i e s but w i t h o u t the p e r t u r b a t i o n sum i n c l u d i n g the n e a r - d e g e n e r a t e l e v e l . The + s t a t e i n 4.7 r e f e r s to 6„ „ and the - s t a t e to 6_ . . 3,3 3,4 I n terms of E ^ J , E^J and I £ I2, the second-order energy 63,3 63,4 of the 6„ 0 l e v e l and of the 6- . l e v e l can be w r i t t e n as 3,3 3,4 E 2 n d - E M J + e ' l E l 2 3,3 3,3 E o _ Eo 6 3 3 6 3 4 - & - e2Ul2 ' E° -E° 63,3 63,4 where E° and E? are the z e r o - f i e l d e n e r g i e s of the r o t a t i o n a l 63,3 63,4 l e v e l s . F i g u r e 4.8 i n d i c a t e s the r e l a t i v e magnitudes of the second-o r d e r and e x a c t S t a r k s h i f t s f o r the 6_ ,-6_ . t r a n s i t i o n . The 3,3 2,4 q u a n t i t i e s AE and AE„ , are d e f i n e d by 63CcLCC *L W CL AE = E + -E" = 2{(E^J - E ^ J ) 2/4 + e2U(2}1/2 e x a c t e x a c t e x a c t 6_ _ 6- . 1 1 3,3 3,4 AE„ . - E 2 n d - E 2 n d - 2 _ _ £ l i i i i _ 2nd 6„ , 6_ . LJ2-1  3,3 3,4 £ o £ o 63,3 63,4 I t i s c l e a r from eqs. 4.7 and 4.9 t h a t the d i f f e r e n c e between the e x a c t S t a r k energy and the second-order S t a r k energy i s the same f o r the 6|:.^  and the 6^ A l e v e l s but i s o p p o s i t e i n s i g n . There-f o r e , the d i f f e r e n c e between the e x a c t (observed) 6_ o~6 9 /. S t a r k t r a n s i t i o n f r e q u e n c y and the f r e q u e n c y p r e d i c t e d by the second-order p e r t u r b a t i o n t h e o r y I s g i v e n by (AE„ ,-AE ».)/ 2, -81-^^2nd ^ E e x a c t ^ ^ 3,3" 618.96 zero-f i e l d l i n e f r eq. '2.4-observed (exact) Stark f req. \ exac t •74 .0 •63,4 exact hAE exact E63,4 2nd hAE 2nd "pseudo second-order" Stark frequency E|2,4 a n d E&2 4 exact 2nd FIELD OFF FIELD ON Figure 4.8 Second-order and Exact Stark Frequencies for the |M |=6«-6, 6 3 3 - 6 2 4 .Transition of HCCCONH2 (in MHz) (with e 2=2.25xl0*£v 2/cm 2, y2=1.16 D2 y2=12.33,D?) cl D -82-as indicated in the figure. In order to carry out the dipole moment analysis i t was necessary to convert a l l the observed frequencies to "pseudo second-order" frequencies by adding to them the amount (A^2nd~ AE )/2. The analysis could then proceed using the conven-exact ti o n a l second-order Stark effect expressions. The "pseudo second-order" frequencies for the Stark tran-s i t i o n s of propiolamide and the components of the dipole moment were determined by an i t e r a t i v e procedure since the value of 2 y needed to calculate AE„ , and AE „ was, of course, not p a 2nd exact ' ' known in advance. 2 In the procedure, y was i n i t i a l l y estimated to be 1 Debye and the frequency difference (AE_ ,-AE )/2 for the particular 4-T\CL 6 X a C L M -component being considered was calculated. This difference 2 (which depends on e ) was then used to calculate a f i r s t estimate of the "pseudo second-order" frequencies of the (+) and (-) lobes and their average (v ). These averages were then f i t to eq. 4.2 s and a slope of m^  (n=6,5,4 for the |Mj|=6-<-6, 5-<-5 and 4*-4 Stark components, respectively) was obtained. The second-order dependence 2 2 of the slope on y^ and y^ i s given by m2 = 7.0060xl0 - 5y 2 - 1.8586xl0~ 6y 2 • 6 a b or mc - 4.8692xl0~ 5y 2 - 1.5181x10"%? 4.11 5 a b or m. • 3 .1210xl0" 5y 2 - 1 . 2398xl0 - 6y 2 4 a b E E 2 and is calculated by evaluating E (K? -K6, )y in eq. 4.2. g b 3 , 3 , M J b 2 , 4 , M J g The appropriate equation for the M^-component being considered -83-was then used together with the equation for the slope of the graph for the Mj = 0-«-0 Stark component of the 1^  I~®Q Q t r a n s i t i o n , 2 2 2 eq. 4.6, to solve for y and y., : the new value of y so obtained M ' • a b a allowed new frequency differences to be calculated which led to new^'-pseudd' second-order" frequencies and to a newer, better 2 2 determination of y a (and y^). This procedure was repeated u n t i l the change in the slopes between two successive i t e r a t i o n s was less than the standard error in the slope. The "pseudo second-order" Stark frequencies determined in the f i n a l i t e r a t i o n s of the |Mj|=6-«-6, 5-«-5 and 4-*-4 analyses are presented in Table 4.21 together with the calculated (AE_ ,-AE ,.)/2 J /.XXO. 6 X 3 C c 2 2 contributions. The new plots of V vs. e, +£ are shown in s dc ac Figures 4.5-4.7 and are l i n e a r , as expected. The slopes and intercepts, as determined by least-squares f i t s to eq. 4.2, are found in Table 4.22: the values of y and y, determined in the a b f i n a l i t e r a t i o n are also included in this table. The values of the intercepts are a l l very close to the expected value of 34912.04 ± 0.10 MHz, the measured z e r o - f i e l d frequency of the 6, 0-6„ , t r a n s i t i o n . 3,3 2,4 Since the values of y and y, determined in the three i t e r -a o ative procedures were not s t a t i s t i c a l l y d i f f e r e n t they were simply averaged to obtain the f i n a l dipole moment results found in Table 4.23. The quantity y ^ is the t o t a l dipole moment in 2 2 2 the ab plane (^JaD = ^ a + l J ^ ) a n c* represents the t o t a l molecular dipole moment i f propiolamide i s planar. Only the absolute values of the dipole moment and i t s components can be determined since the second-order Stark effect depends on the squares of the y^. -84-T a b l e 4.21 F i n a l I t e r a t i o n "pseudo s e c o n d - o r d e r " F r e q u e n c i e s and (AE„ ,-AE .)/2 C o n t r i b u t i o n s f o r the |M |= z.T\& 6 X 3 C t J 6*6, 5*5 and 4*4 S t a r k Components of t h e 6^ 2~^2 4 T r a n s i t i o n o f HCCC0NH o 2 b + £ ac | M j | - 6*6 | M j | -c 5*5 |M 4*4 1. 8822 34922 .69 (0.41) 34918 .80 (0. 21) 34915. 79 (0. 08) 4. 1651 34935 .97 (1.83) 34927 .61 (0. 93) 34920. 66 (0. 39) 7. 3611 34954 .58 (5.22) 34939 .75 (2 . 70) 34927. 47 ( 1 . 17) 11 . 4702 34978 .30 (11 .58) 34955 .27 (6 . 10) 34936. 03 (2. 69) 16. 4925 35007 .03 (14.83) 34974 .20 ( 1 1 . 72) 34946. 99 (5 . 27) 22. 4279 35041 .12 (36.72) 34996 .43 (20. 08) 34959. 32 ( 9 . 21) 29. 2764 -— 35022 .69 (31. 64) 34973. 81 (14. 80) "Pseudo s e c o n d - o r d e r " f r e q u e n c i e s a r e t h e a v e r a g e s o f t h e (+) and (-) l o b e s i n MHz. b 2, 2 l n - 5 v /cm x l O F r e q u e n c i e s i n b r a c k e t s a r e the (AE„ ,-AE ,.)/2 c o n t r i b u t i o n s -85-Table 4.22 Fi n a l Iteration Slopes and Intercepts of the — 2 2 v vs. e, 4-e Graphs for the | M | =6«-6, 5*-5 S Q C SL C >J and 4*4 Stark Components of the 6^  ^~^2 4 Transition of HCCCONH2 and the Dipole Moment Components Determined by the Iterative Procedures M J =6*6 J Mj|=5*5 mn= Slope (MHz/v2/cm2) V q= Intercept (MHz) lM a l (D) l " b l (D) (5.762+0.009)xl0 34912.02±0.12 1.07+0.02 3.51+0.02 3.67±0.02 -5 (3.783+0.006)xl0 34911.80±0.09 1.08±0.02 3.51+0.02 3.67+0.02 -5 Mj|=4*4 m = Slope n (MHz/v2/cm2) (2. 118±0.004)xl0 - 5 V q= Intercept (MHz) 34911.84+0.07 IM.I (D) 1.08+0.01 • l - b l (D) 3.51±0.01 K b ' (D) C 3.67+0.01 Quoted uncertainties are one standard deviation. b See text for the method of calc u l a t i o n of the dipole moment components. c 2 2 2 u . =u +u, . ab a b -86-T a b l e 4.23 The E l e c t r i c D i p o l e Moment o f HCCCONH |u | - 1.08 ± 0.02 Debyes |vibl = 3.51 ± 0.02 Debyes |y , | » 3.67 ± 0.02 Debyes Quoted u n c e r t a i n t i e s a r e one s t a n d a r d d e v i a t i o n . b 2 2^ 2 ^ a b ^ a ^ b -87-Chapter 5 The Question of Planarity of Propiolamide The purpose of this chapter i s to interpret the results of the analysis of the microwave spectra of propiolamide in terms of the molecular planarity or non-planarity. The question of planarity w i l l be shown to be closely tied to the nature of the potential function describing the inversion motion of the amido group hydrogen atoms. The i n e r t i a l defect and i t s change with amido-group deuteration, the inversion frequency, the yi^ comp-14 onent of the dipole moment, the N nuclear quadrupole coupling constants and the centrifugal d i s t o r t i o n constants a l l provide information regarding the form of this p o t e n t i a l . The inform-ation that they provide w i l l be presented below. 5.1 General Considerations The microwave spectra of the p r o p i o l y l molecules where X=H (66,72), X=F (68) and X=C1 (78) indicate that each of these molecules is planar, a result which i s as expected from elementary bonding theories (such as VSEPR theory). Thus the HCCCNO skeleton of propiolamide can be considered as being planar and the question of planarity of the entire molecule becomes the same as the question of planarity of the -C(0)NH2 amido group. The question can be answered by determining whether or not the the two amido hydrogen atoms are in the OCN plane. X -88-Amides such as propiolamide are generally considered to resonate between the two canonical forms of Figure 5.1 with a resonance energy of 21 kcal/mole (24). Form I exhibits 3 es s e n t i a l l y sp hybridization and a pyramidal geometry about the nitrogen center (as in ammonia) and the two hydrogens are positioned out of the OCN plane. Form II exhibits e s s e n t i a l l y 2 sp hybridization and a planar geometry about the nitrogen because of the involvement of the nitrogen lone pair in the formation of a double bond to the adjacent carbon atom. Thus the amido group of propiolamide may be planar or non-planar depending on the r e l a t i v e contributions of Forms I and II (with R = H-C=G). Intermediate structures w i l l have a shallow pyramidal structure about the nitrogen atom with the two amido hydrogen atoms positioned on the same side of the HCCCNO plane. A third canonical form i s also possible for propiolamide, E-C-C—C , but i t i s highly unlikely that this form contributes X N H 2 to the state of the molecule since the two carbon-carbon bond lengths in other pr o p i o l y l molecules have been shown to have no double bond character (66,72,68,78,120). R-Cf 0 H N-H II ,0 Figure 5.1 The Two Resonance Forms of Amides -89-In contrast to amides, amines (R-NH2) are usually expected to have only small ir-type nitrogen lone pair interactions with 3 the R group resulting in non-planar amino groups with nearly-sp hybridization about the nitrogen atoms; in some amines, however, stronger interactions are possible which can lead to planar 2 configurations and sp hybridization about the nitrogens (as in BF 2NH 2 (18) and PF 2NH 2 (19) ). The structure of several amines and amides was given e a r l i e r in Table 1.1. The average positions of the amido-group hydrogen atoms in the ground v i b r a t i o n a l state r e l a t i v e to the HCCCNO plane are required in order to decide which is the more abundant canonical form of propiolamide; these positions are closely tied to the nature of the potential function describing the out-of-plane inversion motion of the amido-group hydrogen atoms. The features of such a potential w i l l be discussed in the following section. 5.2 The Nature of the Inversion Motion An inversion i s a large amplitude, hindered intramolecular motion which exists when a molecule has two equivalent stable configurations not related by a simple molecular rotation. These equivalent configurations are each associated with a potential energy well and the two wells are separated by a potential barrier which hinders the intraconversion. For the case of an amide, the inversion motion is the "wagging" of the two amido hydrogen atoms across the OCN plane. The most general form of an amido-group (or amino group) inversion potential i s shown in Figure 5.2. The inversion barrier -90-'2 Figure 5.2 The General Form of an Inversion Potential i s centered about the planar configuration ($=0°; see Table 1.1 for the d e f i n i t i o n of $) and the two wells correspond to the two hydrogens being above and below the OCN plane, respectively. Since the ground v i b r a t i o n a l l e v e l (0 ) i s positioned below the maximum of the central b a r r i e r , the average positions of the hydrogens are out of the plane. The double-minimum form shown can be approximated by any one of several mathematical functions (79) . The v i b r a t i o n a l eigenfunctions for this potential must be either symmetric or antisymmetric with respect to the inversion (80) and i f ip and if>D denote the wavefunctions for the same l e v e l L K in the l e f t and right well, respectively, then they can be written as H,_ = ( 1 / 2 ) % ( ^ L - >J,R) 5. lb 5.1a -91-where the + and - labels refer to symmetric and asymmetric wave-functions. The energy separation of the two lowest inversion levels ( 0 + and 0 ) depends on the size of the central barrier and i s called the inversion frequency. The changes in the potential energy function as a central inversion barrier i s introduced to a harmonic o s c i l l a t o r potential are shown in Figure 5.3. The harmonic o s c i l l a t o r potential (a) has evenly spaced v i b r a t i o n a l levels but as a small barrier i s introduced, adjacent levels begin to move together in pairs (as shown) u n t i l in the high barrier case (c) near-degenerate pairs + + of levels below the barrier maximum are found (0~,1~ etc. ) . In the presence of an i n f i n i t e b a r r i e r , case (d), the paired levels become degenerate. Thus the effect of increasing the size of the inversion barrier is to reduce the magnitude of the inversion frequency u n t i l , in the case of an extremely high b a r r i e r , i t becomes zero. C l a s s i c a l l y , the presence of a central barrier above the lower v i b r a t i o n a l levels (as in case (c)) precludes the p o s s i b i l i t y of inversion. However, quantum-mechanical tunnelling through the barrier can occur. This can be seen from the time-dependent form of the inversion wave function, ¥(t) (81) : n t ) - d/2)l5(V + ^ 0 . e 2 i r i V t ) e 2 T T i E 0 + t / h 5.2 Here is the energy of the 0 + l e v e l and hv is the 0+-0 energy separation and i t is assumed that the molecule is i n i t i a l l y in the l e f t potential well (this can be seen by setting t=0). When t = l/(2v), f = i | ) g^IEo+t/h g o t j i a t t n e m o i e c u l e has moved over to -92-(c) (d) Figure 5.3 Potential Functions and Energy Levels for (a) a Harmonic O s c i l l a t o r , (b) a Small Inversion Barrier, (c) a Large Inversion Barrier and (d) an I n f i n i t e Inversion Barrier -93-t h e r i g h t - h a n d p o t e n t i a l w e l l — t h a t i s , i n v e r s i o n has o c c u r r e d . The t i m e t a k e n f o r a c o m p l e t e c y c l e i s 2{1/(2v)}=1/v so t h a t t h e i n v e r s i o n f r e q u e n c y i s V. Thus, a s p e c t r o s c o p i c l i n e s h o u l d be o b s e r v e d a t t h i s f r e q u e n c y . F o r t h e v e r y h i g h b a r r i e r c a s e ( d ) , however, t h e i n v e r s i o n i s e x t r e m e l y slow (as has been p r e d i c t e d f o r AsH^ (82) ) and on t h e microwave tim e s c a l e t h e m o l e c u l e can be c o n s i d e r e d n o t to i n v e r t . The p l a n a r i t y o r n o n - p l a n a r i t y o f p r o p i o l a m i d e can be d e t e r -mined from a knowledge o f the form o f t h e p o t e n t i a l d e s c r i b i n g t h e a m i d o - h y d r o g e n i n v e r s i o n m o t i o n . I f t h e r e i s no i n v e r s i o n b a r r i e r o r o n l y a s m a l l b a r r i e r w h i c h m a x i m i z e s below t h e f i r s t i n v e r s i o n l e v e l (0 +) t h e n t h e ground s t a t e a v e r a g e p o s i t i o n s o f the amido h y d r o g e n atoms a r e i n t h e OCN p l a n e and the m o l e c u l e i s p l a n a r . However, i f t h e ground s t a t e l e v e l i s below t h e b a r r i e r maximum, t h e n the a v e r a g e p o s i t i o n s o f the h y d r o g e n s a r e o u t o f t h e p l a n e and t h e m o l e c u l e i s n o n - p l a n a r . The microwave s p e c t r u m p r o v i d e s much i n f o r m a t i o n c o n c e r n i n g the n a t u r e o f t h e i n v e r s i o n p o t e n t i a l . I n t h e f o l l o w i n g s e c t i o n s d i s c u s s i o n s o f t h e s p e c t r a l c o n s t a n t s o f p r o p i o l a m i d e as t h e y r e l a t e to t h e f o r m o f t h e p o t e n t i a l w i l l be p r e s e n t e d . 5.3 The I n v e r s i o n F r e q u e n c y and the Q u e s t i o n o f P l a n a r i t y As i n d i c a t e d i n the p r e v i o u s s e c t i o n , the m a g n i t u d e o f the amido- o r amino-group i n v e r s i o n f r e q u e n c y d e c r e a s e s as t h e h e i g h t of t h e i n v e r s i o n b a r r i e r i n c r e a s e s . Thus n o n - p l a n a r g r o u p s a r e a s s o c i a t e d w i t h h i g h e r i n v e r s i o n b a r r i e r s and much l o w e r i n v e r s i o n f r e q u e n c i e s t h a n a r e p l a n a r g r o u p s . -94-Th e inversion frequencies of several amides and amines have been determined from their microwave spectra by r e l a t i v e intensity measurements similar to those outlined in Section 4.3 for propiol-amide; these are l i s t e d in Table 5.1. As expected, the frequen-cies determined for the molecules with non-planar amido- or amino groups ($ non-zero) are a l l considerably lower than those found for the molecules with planar groups <»#-0 ). The inversion frequencies for the molecules with $^0° are usually so small that a J^-^-J^i t r a n s i t i o n in the 0 + state is separated by only a few Megahertz from the same t r a n s i t i o n in the 0 state; thus doublets of near-equal intensity are observed in the microwave spectra. Furthermore, in the case of cyanamide, the 0+-0 vi b r a t i o n a l l e v e l separation is small enough that non-rigid rotor behaviour caused by inversion-rotation interactions i s also observed (15,83). The spectrum of propiolamide showed neither the t r a n s i t i o n doubling nor the anomalous non-rigid rotor behaviour. The inversion frequency which was determined from r e l a t i v e intensity measurements (see Section 4.3) i s 333 ± 75 cm *; this i s quite close to that found for the planar formamide molecule and is cl e a r l y much larger than any of the frequencies found for the non-planar amines in Table 5.1. It is l i k e l y , therefore, that the inversion barrier of propiolamide is either non-existent or is very small and that the molecule i s planar. Another, a l b e i t u n likely, p o s s i b i l i t y , however, i s that the barrier i s extremely high (case (d) of Fig . 5.3) and that the observed v i b r a t i o n a l frequency actually corresponds to the l~*-0~ t r a n s i t i o n ; i f this -95-i s t h e c a s e p r o p i o l a m i d e can be c o n s i d e r e d to be n o n - i n v e r t i n g and n o n - p l a n a r . T a b l e 5.1 I n v e r s i o n F r e q u e n c i e s ( w ^ n v ) of Some Amides and Amines M o l e c u l e u. (cm ) i n v $ a R e f e r e n c e n i t r a m i d e <10 51° 16 cyanamide 15 38° 15 v i n y l a m i n e 65 34° 17 a n i l i n e 43 38° 9 m - f l u o r o a n i l i n e 50 36° 11 2 - a m i n o p y r i d i n e 135 32° 13 3 - a m i n o p y r i d i n e 50 37° 12 4 - a m i n o p y r i d i n e 100 28° 12 formamide 295+10 0° 20,73 t h i o f o r m a m i d e 393±40 0° 21 p r o p i o l a m i d e 333±75 THIS WORK $ i s t h e a n g l e between t h e b i s e c t o r o f t h e HNH a n g l e and t h e e x t e n s i o n o f t h e N-X bond, where X i s t h e t h i r d atom bonded to N; i f t h e XNH„ a r r a n g e m e n t i s c o p l a n a r , t h e n $=0 . - 9 6 -5.4 The Component of t h e D i p o l e Moment and t h e Q u e s t i o n o f  P l a n a r i t y F u r t h e r i n d i c a t i o n s of t h e form o f t h e i n v e r s i o n p o t e n t i a l o f p r o p i o l a m i d e c an be p r o v i d e d by the m a g n i t u d e of t h e y^ comp-onent o f t h e d i p o l e moment. I f i s z e r o , t h e n t h e m o l e c u l e must n e c e s s a r i l y be p l a n a r , l y i n g e n t i r e l y i n the ab p l a n e , h a v i n g a s m a l l o r v a n i s h i n g i n v e r s i o n b a r r i e r . I f y £ i s n o n - z e r o , however, t h e n t h e m o l e c u l e must be n o n - p l a n a r , h a v i n g a h i g h i n v e r s i o n b a r r i e r . U n f o r t u n a t e l y , t h e r e a r e d i f f i c u l t i e s i n d e t e r m i n i n g from t h e u s u a l S t a r k e f f e c t measurements b e c a u s e o f the f a c t t h a t y c i s a n t i s y m m e t r i c w i t h r e s p e c t to the i n v e r s i o n m o t i o n (84) — t h a t i s , y c -*• -y upon i n v e r s i o n . The a p p r o p r i a t e s e l e c t i o n r u l e s i n v o l v i n g y c ~ c o n n e c t e d t r a n s i t i o n s when i s a c t i v e l y i n v e r t i n g a r e d e t e r m i n e d by r e q u i r i n g t h a t where i , j l a b e l i n v e r s i o n s t a t e s , be t o t a l l y s y m m e t r i c ( 8 4 ) . S i n c e i s a n t i s y m m e t r i c w i t h r e s p e c t to t h e i n v e r s i o n , the v^ and V j i n v e r s i o n l e v e l s must be of o p p o s i t e s y m m e t r i e s i n o r d e r t h a t <v^ | y^ | v^ >' be n o n v a n i s h i n g ; t h u s the v i b r a t i o n a l s e l e c t i o n r u l e becomes + «-+_ ± -V ± 5.4 The < ( J x ) i | $ F c | ( J ' T * ) J > term g i v e s r i s e to t h e o r d i n a r y c - t y p e s e l e c t i o n r u l e s (ee++oe, oo+->eo) e x c e p t t h a t now t h e c o n n e c t e d - 9 7 -r o t a t i o n a l l e v e l s a r e i n d i f f e r e n t i n v e r s i o n s t a t e s . (Note t h a t u and u, a r e b o t h s y m m e t r i c w i t h r e s p e c t to the i n v e r s i o n so a b t h a t t h e v i b r a t i o n a l s e l e c t i o n r u l e s a r e ±+~»-± and o r d i n a r y a- and b - t y p e t r a n s i t i o n s i n d i s t i n c t i n v e r s i o n s t a t e s a r e o b s e r v e d ) . The c o n t r i b u t i o n s o f to t h e S t a r k s h i f t o f an M j - l e v e l i n t h e ground ( 0 + ) v i b r a t i o n a l s t a t e , ( J T M J ) + , i s t h e n g i v e n by t h e q u a n t i t y (compare w i t h eq. 2.53) E | < ( J T M ) | $ | ( J ' T ' M ) > | 2 |<O +|U |O->| 2 E 2 ( J ' T ' M , ) — — — - C S , ; > E ( J T ) + E ( J ' T ' ) _ where t h e ( J ' T ' M J ) a r e S t a r k l e v e l s ' i n the 0 i n v e r s i o n s t a t e . T h i s q u a n t i t y i s z e r o i f p r o p i o l a m i d e i s p l a n a r s i n c e t h e n U c=0. U n f o r t u n a t e l y , even i f U £ i s n o n - z e r o t h i s q u a n t i t y c an be t a k e n as b e i n g e f f e c t i v e l y z e r o s i n c e t h e d e n o m i n a t o r s E ° J T J - E ° J , T , ^ ( t h e e n e r g y d i f f e r e n c e s o f t h e z e r o - f i e l d r o t a t i o n a l l e v e l s ) a r e a l l t r e m e n d o u s l y l a r g e , b e i n g a p p r o x i m a t e l y e q u a l to t h e p r o p i o l -amide i n v e r s i o n f r e q u e n c y o f 333 cm * ( w h i c h i s =10,000 G i g a h e r t z ) . Thus u c c a n n o t be d e t e r m i n e d from, a ^ s t a n d a r d S t a r k s h i f t a n a l y s i s when su c h a h i g h i n v e r s i o n f r e q u e n c y i s p r e s e n t . As n o t e d i n the p r e v i o u s s e c t i o n , however, t h e r e i s a (remote) p o s s i b i l i t y t h a t t h e b a r r i e r to i n v e r s i o n i n p r o p i o l a m i d e i s e x t r e m e l y h i g h and t h a t t h e 333 cm * f r e q u e n c y c o r r e s p o n d s n o t - + + + to t h e 0 «-0 t r a n s i t i o n but r a t h e r to t h e l~-*-0~ t r a n s i t i o n . F o r t h i s c a s e t h e m o l e c u l e would n o t i n v e r t , c - t y p e t r a n s i t i o n s w i t h i n t h e d e g e n e r a t e ground v i b r a t i o n a l s t a t e (0~) would be p r e s e n t i n the s p e c t r u m and t h e c o n t r i b u t i o n to t h e S t a r k s h i f t c o u l d n o t be n e g l e c t e d i n t h e d i p o l e moment a n a l y s i s . In a d d i t i o n , i t i s -98-r e a s o n a b l e to assume, f o r t h i s e x t r e m e l y h i g h b a r r i e r c a s e , t h a t the amido h y d r o g e n atoms would be p o s i t i o n e d w e l l o ut of t h e p l a n e formed by t h e o t h e r atoms so t h a t U c would be o f s i m i l a r m a g n i t u d e to t h e 1.09 D e s t i m a t e d f o r a n i l i n e (85) (where <J>=38° and t h e i n v e r s i o n b a r r i e r i s o n l y m o d e r a t e l y h i g h ) . Thus the c - t y p e t r a n s i t i o n s would be o f s i m i l a r i n t e n s i t y to t h e a - t y p e t r a n s i t i o n s o b s e r v e d f o r p r o p i o l a m i d e and would be s t r o n g enough to be d e t e c t a b l e i n t h e microwave s p e c t r u m . The f a c t t h a t no s u c h t r a n s i t i o n s were o b s e r v e d i s v e r y s t r o n g e v i d e n c e t h a t the e x t r e m e l y h i g h b a r r i e r c a s e can be e l i m i n a t e d as a p o s s i b l e form o f t h e i n v e r s i o n p o t e n t i a l o f p r o p i o l a m i d e . 14 5.5 N N u c l e a r Q u a d r u p o l e C o u p l i n g C o n s t a n t s and t h e Q u e s t i o n  o f P l a n a r i t y N u c l e a r q u a d r u p o l e c o u p l i n g c o n s t a n t s a r e a measure o f t h e e l e c t r o n i c asymmetry i n t h e v i c i n i t y o f t h e c o u p l i n g n u c l e u s ; hence t h e y can p r o v i d e v a l u a b l e i n f o r m a t i o n r e g a r d i n g c h a r g e d i s t r i b u t i o n s and t h e n a t u r e o f t h e bonds formed by t h e c o u p l i n g atom ( 8 6 ) . The r e l a t i o n s h i p s between e l e c t r o n i c p r o p e r t i e s and th e c o u p l i n g c o n s t a n t s were d e v e l o p e d by Townes and D a i l e y (87) and i n v o l v e many s i m p l i f y i n g but j u s t i f i a b l e a s s u m p t i o n s . A c c o r d -i n g to t h e t h e o r y , t h e c o u p l i n g c o n s t a n t s c an be a t t r i b u t e d e n t i r e l y to t h e u n e q u a l o c c u p a t i o n o f p - o r b i t a l s i n t h e v a l e n c e s h e l l o f t h e c o u p l i n g n u c l e u s and a r e g i v e n by X g g = eQ<3 2V/3g 2> = eQ E E N ^ . q ^ (g=x,y,z) 5.6 1 k (k=x,y,z) -99-where i s the o r b i t a l c o e f f i c i e n t of the atomic o r b i t a l in the i t b molecular o r b i t a l , N^ is the electron population of the i * " * 1 molecular o r b i t a l and is the contribution to 3 2V/3g 2 from an electron in the p. o r b i t a l . k Equation 5.6 can be written more conveniently as X = Z N.{n .-%(n ,+n .)}eQq.T ( c y c l i c ) 5.7 Azz . l z i xx y i J 2 t t i where n j c ^ = aj l-j t 1 S t n e P^-orbital electron population of the i molecular o r b i t a l and q^ is the e l e c t r i c f i e l d gradient along the z-axis caused by an electron in a nitrogen 2p^ or 2p^ o r b i t a l . The value of eQq^, the atomic coupling constant, cannot be measured 14 d i r e c t l y from atomic experiments since N has a spherically sym-2 2 1 1 1 metric Is 2s 2p^2p^2pz ground state; however, an estimated value of -10 MHz i s commonly used in coupling constant analyses (88). Equation 5.7 shows the direct relationship between the quadrupole coupling constants and the p - o r b i t a l populations. Unfortunately, i t i s usually not possible to determine the values of the coupling constants along the axes of the p-orbitals (X >X >X ) from the microwave spectrum but only their comp-x x y y 2s Z onents along the p r i n c i p a l i n e r t i a l axes ( X a a > X ^ b * X c c ) • However, in the case of propiolamide and other RNH^-type molecules where the RN skeletons are coplanar and the two hydrogen atoms are on the same side of the RN plane or in the plane, the i n e r t i a l c axis i s p a r a l l e l or very nearly p a r a l l e l to the d i r e c t i o n of the p - o r b i t a l containing the nitrogen lone pair of electrons (89). Defining this d i r e c t i o n as the di r e c t i o n of the z-axis, one has then that y ~x A c c z z Assuming the a-orbitals of the nitrogen atom of these types -100-of molecules to be idealized sp hybrids (90) and the lone-pair T T-orbital to be the p c o r b i t a l , the following expression for X ( =X ) can be obtained from eq. 5.7 : A c c A z z X c c - (a - lb -|c}eQq N 5.8 Here a, b and c are the populations of the lone-pair o r b i t a l , the C-N a - o r b i t a l and the N-H a - o r b i t a l s , respectively. The problem in solving eq. 5.8, however, i s that eQq^ i s not accurately known and that there are three unknowns to be deter-mined from only one observable. Thus eq. 5.8 can only be used q u a l i t a t i v e l y to investigate the bonding in propiolamide and similar molecules. The quadrupole coupling constants of propiolamide and other amides and amines where x ~X a r e given in Table 5.2. If the CC z z C-N and N-H a - o r b i t a l populations (b and c) of these molecules are considered to be r e l a t i v e l y constant i t i s possible to compare their coupling constants with respect to the de l o c a l i z a t i o n of the nitrogen lone pair. Equation 5.8 indicates that i f b and c are fixed, then a large absolute value for X c c w i l l result i f a, the lone-pair o r b i t a l population, is large. Since a large lone-pair o r b i t a l population is indicative of a non-planar amido- or amino-group geometry (Form I of Fig. 5.1) i t is possible to associate very large absolute values of x c c with non-planar structures ($^6°) and smaller values with planar structures ( $ = 0 ° ) . The results in Table 5.2 bear this out; the non-planar molecules ( $ ^ 0 ° ) each have a |x | which is moderately larger than those -101-14 Table 5.2 N Quadrupole Coupling Cons tants (X ) of Some A c c Amides and Amines 3 Molecule X c c (MHz) *b Reference HCCCONH2 -3.82 ± 0.08 THIS WORK HC0NH2 -3.85 ± 0.02 0° 91 F 2 P N H 2 S -3.45 ± 0.25 0° 19 H 2NCONH 2 -4.04 ± 0.04 prob. \0° 23 H 2CCHNH 2 -4.13 ± 0.20 34° 17 NCNH2 -4.90 38° 15 C1NH 2 -5.3 68° 93 Except f o r F 2 PNH 2 > these molecules are a l l such that X =X (see A c c z z t e x t ) ; f o r F 2 P N H 2 » Xbb i s given s i n c e the lo n e -p a i r d i r e c t i o n i n the molecule i s i n the d i r e c t i o n of the b i n e r t i a l a x i s and so Xi_x.~X bb zz $ i s the angle between the b i s e c t o r of the HNH angle and the extension of the X-N bond, where X i s the t h i r d atom bonded to N; $=0 f o r a planar XNH 2 arrangement. of the planar molecules ($=0°). The value f o r propiolamide of |X C C I =3.82 MHz f i t s r i g h t i n with the small values found f o r the l a t t e r group i n d i c a t i n g that propiolamide probably has a planar amido group and t h a t , t h e r e f o r e , the e n t i r e molecule i s p l a n a r . It should be noted that t h i s a n a l y s i s h a r d l y provides c o n c l u s i v e evidence of the p l a n a r i t y of propiolamide. Coupling constant analyses tend to be very s e n s i t i v e to a x i s o r i e n t a t i o n s , -102-molecular o r b i t a l descriptions of the bonding and o r b i t a l pop-ulations. However, though the simplifying assumptions concerning these factors here may not be e n t i r e l y v a l i d , the analysis is nevertheless consistent with planarity. 5.6 The Quartic Centrifugal Distortion Constants and the  Question of Planarity Further evidence as to the structure and the form of the inversion potential of propiolamide i s provided by a comparison of the magnitudes of the quartic centrifugal d i s t o r t i o n constants for the ground v i b r a t i o n a l state with those found for the f i r s t excited inversion state. In the theoretical treatment of centrifugal d i s t o r t i o n presented in Section 2.2, i t was assumed, for s i m p l i c i t y , that the 3N-6 v i b r a t i o n a l modes of the asymmetric rotor being con-sidered are a l l harmonic. This assumption led to the determ-ination of a r e l a t i v e l y simple expression defining the d i s t o r t i o n constants, eq. 2.29, which was independent of the v i b r a t i o n a l state of the rotor. For the purposes of this discussion, however a more general expression defining the d i s t o r t i o n constants w i l l be considered. This expression gives the centrifugal d i s t o r t i o n constants in a p a r t i c u l a r v i b r a t i o n a l state, | v>= | v. > | v„> • .* • | v_ as (94) T a8Y<$ • > y 2 5.9 where the Q are the 3N-6 normal coordinates of vib r a t i o n and -103-a < 0 t 3 ) = o l 0/dQ etc. r a3 r For a molecule where a l l the Iv > are harmonic o s c i l l a t o r 1 r wavefunctions, the perturbation sum in 5.9 i s independent of the v i b r a t i o n a l state, being given by 2 v I<v j Q j v•>I , , i n L i r 1 r' r ' » 5.10 v \v' E -E , 2A r r v v r r r 2 2 2 th where X =4ir c w and OJ is the wavenumber of the r vibration, r r r Thus the T^^g a r e also independent of the |vf> and the expression for the d i s t o r t i o n constants of the harmonically o s c i l l a t i n g molecule i s a ( c c 3 ) a ( Y 6 ) T a 6 y 6 - -1 2 _ r r 1 5.11 2 r Te Te Te_e A I I„I I . r a B y o and i s actually the same as eq. 2.29 except that i t i s written in terms of the normal coordinates rather than the internal displacement coordinates. Although eq. 5.11 is s t r i c t l y v a l i d only for an idealized molecule with 3N-6 harmonic v i b r a t i o n a l modes, i t is expected to hold approximately for the vibrations of real molecules as well, provided none of the vibrations are too anharmonic. For the extreme case where one of the v i b r a t i o n a l modes of the molecule i s a large-amplitude, very anharmonic motion which i s described by a double-minimum potential (such as an inversion or a ring-puckering motion) and the other 3N-7 modes are approximately harmonic, the v i b r a t i o n a l independence of the d i s t o r t i o n constants is shattered. This i s because the perturbation term involving the large-amplitude motion (say an -104-inversion) , v kv' inv ' inv e 5.12 E -E , v v inv inv inv i s dependent on the inversion state, v ^ n v - Creswell and M i l l s (95) have analyzed this case for the trimethylene oxide (TMO) molecule where the inversion i s a ring-puckering motion. Using the known form of the double-minimum puckering potential of TMO, they that, t h e o r e t i c a l l y , this anomalous dependence can lead to a z i g -zagging v a r i a t i o n of Watson's quartic centrifugal d i s t o r t i o n constants as well. Such variations were, indeed, experimentally observed for the d i s t o r t i o n constants of TMO. Although the puckering barrier of the TMO potential i s very small, maximizing well below the v=0 l e v e l , the effects on the d i s t o r t i o n constants are great; for example, the A constant was found to be six times larger in the v = l puckering state than in the v = 0 ground state. Thus the changes in the d i s t o r t i o n constants between the v=0 and v=l states of a pa r t i c u l a r v i b r a t i o n can provide a good indicati o n of whether or not that vibration has a non-zero potential barrier or whether i t is described by a single-minimum harmonic or slightly-anharmonic potential. The d i s t o r t i o n constants of propiolamide in the ground and f i r s t excited inversion state (see Table 4.7) are given in Table 5.3. Clearly, none of the d i s t o r t i o n constants in the v ^ n v = l state are appreciably d i f f e r e n t from their counterparts in the v=0 ground state. showed that 6 exhibits a zig-zagging dependence on v. and inv inv -105-This i s a strong piece of evidence that the potential function describing the inversion motion of propiolamide is not highly anharmonic, that i t has a single minimum, and that, therefore, propiolamide i s planar. Similar small variations of the d i s t o r t i o n constants between the ground and f i r s t excited inversion states have been observed for the formamide molecule (20), which i s planar. Further evidence of the planarity of propiolamide is provided by the s i m i l a r i t y of i t s d i s t o r t i o n constants to those of the i n e r t i a l l y similar molecules HCCCOF and HCCCOOH (see Table 5.3). Table 5.3 The Distortion Constants of Propiolamide and Related Molecules HCCC0NH2 HCCCOF (68) HCCCOOH (69) v=0 v. =1 inv v=0 v=0 A J 0.58010.008 0.63910.164 0. 54910. 073 0.53810. 015 AJK 21 .0910.06 20.6610.43 22 .4310. 014 21.3210. 10 AK -10.0310.03 -10.0912.63 -10 .5210. 087 -7.71510. 045 6 J 0. 19410.006 0. 17510.028 0. 18010. 004 0.16110. 004 6K 11.7610.01 12. 1310.56 12 .4410. 09 12.1910. 13 Distortion constants are in kHz. -106-5.7 The I n e r t i a l Defects and the Question of Planarity By far the most important available evidence needed in proving the planarity or non-planarity of propiolamide i s pro-vided by the molecular i n e r t i a l defect and the change in the defect upon amido-group deuteration. The i n e r t i a l defect for a planar or near-planar molecule, A, is defined as A = I - I - I, 5.13 c a b and for a r i g i d rotor the i n e r t i a l defect i s related to c^, the c-coordinate of the i t b atom, by A = -2 Z m,c2 5.14 r i i t 111 where m^  i s the mass of the i atom and the r subscript indicates the assumption of r i g i d i t y . For a r i g i d planar molecule, a l l the c^ (the out-of-plane coordinates) are zero so that Ar=0 and for a r i g i d non-planar molecule i t is clear from eq. 5.14 that Ar<0. Thus i f molecules were r i g i d i t would be an easy task to determine planarity once the rotational constants had been ob-tained from the microwave spectrum. But, of course, molecules are not r i g i d even in their ground v i b r a t i o n a l states. Because of these v i b r a t i o n a l e f f e c t s , eq. 5.14 i s not s t r i c t l y v a l i d for rea l molecules and a v i b r a t i o n a l correction term, A V, must be included, so that the observed i n e r t i a l defect, A, is given by A « -2 Z m.c2 + A V = A + A V 5.15 i 1 1 Ab i n i t i o calculations of ground state i n e r t i a l defects have -107-been presented by Oka and Morino (96) and Herschbach and Laurie (97). The l a t t e r authors have shown that the i n e r t i a l defect of a planar molecule (where A=AV) can be written as the sum of two parts: A V - A(i) + A(o) 5.16 where A(i) is a positive contribution and A(o) is a negative contribution to A V from the i n - and out-of-plane molecular vib-rations, respectively; the lowest frequency vibrations contribute the most to A V. The sign of the t o t a l i n e r t i a l defect for a planar molecule depends on the r e l a t i v e magnitudes of the two contributions, but is usually a small positive quantity. How-ever, there are special cases where this is not so. Herschbach and Laurie have shown that the negative magnitude of the A(o) contribution is generally larger for lower out-of-plane frequencies and that i f a planar molecule has one or two out-of-plane v i b -r a t i o n a l modes of very low frequency, then the t o t a l defect may be negative. This has been observed for halogenated styrenes (98,99) and for benzoic acid derivatives (100,101) where there are low-frequency torsional motions and for HCOND2 (20,73) where a low-frequency inversion motion is present. Equation 5.16 can also be used to approximate the v i b r a t i o n a l contributions to the t o t a l i n e r t i a l defects of near-planar molecules. Consider a near-planar amide or amine of the general type R-NH2 where the R-N skeleton i s coplanar. Here the R-N group i s usually much heavier than the mass of the two hydrogens so that to a good approximation i t can be considered as lying in the ab plane (as i t would exactly i f the molecule were planar -108-with the two hydrogen atoms i n , rather than above, the R-N plane). Thus, for the purpose of calculating the vi b r a t i o n a l contribution to the to t a l i n e r t i a l defect, such a molecule can be considered to be planar, with A(i) and A(o) retaining their o r i g i n a l s i g n i f -icance. In such a treatment, the inversion vibration i s consid-ered as an out-of-plane motion. The t o t a l i n e r t i a l defect of a near-planar molecule i s , then, given by A - -2 I m.c? + A(i) + A(o) 5.17 ^ l i and i s usually expected to be negative. However, i f A(i)+A(o) is large enough, A could be po s i t i v e . The ground state i n e r t i a l defect of propiolamide is compared with those of other planar or near-planar RNH^-type molecules in Table 5.4. Clearly, the defects vary considerably from molecule to molecule but are found to be positive for planar amides and amines and negative for near-planar ones, as i s usually expected. The fact that propiolamide has a positive i n e r t i a l defect, how-ever, cannot be used as conclusive evidence of planarity. There remains the p o s s i b i l i t y that the amido hydrogens are s l i g h t l y above the HCCCON plane and that the negative A f contribution to A i s more than counterbalanced by a positive v i b r a t i o n a l cont-ri b u t i o n , A V, a r i s i n g from the eighteen fundamental modes of propiolamide, resulting in a net positive t o t a l defect. A more useful quantity to consider in order to decide the planarity or non-planarity of propiolamide is the change in the i n e r t i a l defect upon amido-group deuteration. For planar or near-planar amides (and amines) there are two major contributions -109-Table 5.4 I n e r t i a l Defects and their Changes upon Deuteration a b for Some Amides and Amines ' Molecule A(R-NH^) A(R-ND2> S h i f t 0 $ d Ref. Propiolamide 0. 1816 0. 1505 -0. 0311 THIS WORK Fo rmamide 0. 0065 -0. 0214 -0. 0279 0° 20 Thioformamide 0. 0508 0. 0288 -0. 0220 0° 21 Difluoroaminoborane 0. 152 0. 141 -0. 011 0° 18 Nitramide -0. 438 -0. 8781 -0. 4401 51° 16 Aniline -0. 4119 -0. 8124 -0. 4005 38° 9,121 p - F l u o r o a n i l i n e -0. 4524 -0. 9602 -0. 5078 48° 10,121 p-Chloroaniline -0. 4287 -0. 8268 -0. 3981 ^0° 121 m-Fluoroaniline -0. 3531 -0. 6933 -0. 3402 36° 11 2-Aminopyr id ine -0. 259 -0. 511 -0. 252 32° 13 3-Aminopyr id ine -0. 3890 -0. 7615 -0. 3725 37° 12 4-Aminopyridine -0. 2507 -0. 4786 -0. 227,9 28° 12 2-Amino pyr iniidine -0. 149 -0. 519 -0. 370 22° 14 I n e r t i a l Defects and Shifts are in amu-A . These molecules are of the type RNH^ where the RN group i s coplanar and the two hydrogens are either in the RN plane or on the same side of i t ; molecules where the hydrogens are above the RN plane are called "near-planar" (see text). C Shift = A(R-ND2) - A(R-NH2). d $ i s the angle between the bisector of the HNH angle and the extension of the N-X bond, where X i s the third atom bonded to N; $=o for a planar XNH„ arrangement. -110-to this change: (1) upon deuteration the inversion frequency drops markedly (73) thereby increasing the negative magnitude of A(o) (97) and v making A smaller. (2) upon deuteration the amido-group hydrogen atoms are replaced by twice-as-massive deuterium atoms so that the change in the A r contribution to A can be approximated to be (14) A r(RND 2) - A r(RNH 2) = - 8 C 2 - (-4c2) = -4c 2 5.18 where c 1 7 i s approximately the distance of the hydrogen atoms from the plane of the other atoms. Contributions (1) and (2) are both negative so that the change in the i n e r t i a l defect is also negative. The t o t a l change is given by A(RND„) - A(RNH-) = -4c 2 + {AV(RND_) - A V(RNH„)} 5.19 2 2 h Z Z which, for a planar molecule, s i m p l i f i e s to A(RND2) - A(RNH2) - A V(RND £) - A V(RNH 2) 5.20 Thus the change i s usually smaller for a planar molecule than for a near-planar molecule. Table 5.4 shows the changes in the i n e r t i a l defect upon amido-group deuteration for propiolamide and other planar or near-planar amides and amines. As expected, the near-planar molecules a l l exhibit larger changes than do the planar molecules. The change observed for propiolamide is very similar to those of the planar species but, unfortunately, i t i s not - I l l -possible to determine exactly what part of this s h i f t , i f any, 2 i s attributable to a (non-planar) -4c„ contribution. An upper l i l i m i t for the c-coordinate of the amido-group hydrogen atoms in v v propiolamide can be determined by assuming that A (RND^J-A (RNH^) 2 is zero and that the entire change i s attributable to - 4 c ; the c a l c u l a t i o n gives c =0.088 A. This is c l e a r l y an u n r e a l i s t i c r l V V assumption, however, in view of the fact that A (RND2)-A (RNH^) 2 2 ranges from -0.011 amu-A for difluoroaminoborane to -0.028 amu-A for formamide. The propiolamide i n e r t i a l defect change is so similar to that observed for the related formamide molecule that i t is l i k e l y that most or a l l of i t is due to a change in A V meaning that c T I is either zero or very small. Thus propiolamide, i f not perfectly planar in the ground v i b r a t i o n a l state, i s ce r t a i n l y very nearly planar, and the inversion barrier is either zero or very small. The inversion state dependence of the i n e r t i a l defect is also helpful in determining whether or not a barrier exists in the inversion potential. Gwinn e_t. a_l. (102) have shown that the e f f e c t i v e r otational constants in a particular inversion state can be written as a power series in the even powers of Q. , the inv' normal coordinate for the inversion: 2 4 <A> = a + a.<Q, > + a„<Q; > + ... v. o 1 inv v. 2 ^xnv v. inv xnv xnv _ _ «J • mm X (similar for B and C) where the a are constants and the averages are over the inversion state v. . The e f f e c t i v e i n e r t i a l defect in the state v. is inv xnv defined in terms of these rotational constants bv: -112-<A> . = {h/(8ir 2) }{1/<C> - 1/<A> - 1/<B> } 5.22 inv inv inv inv and by expanding 1/<B> etc. using the binomial theorem, the inv defect can be written as <A> - 6 + 6,<Q2 > 5.23 v. o 1 inv inv where the smaller higher-order terms have been neglected for the purposes of this discussion and 6 q and 6^ are constants. If the inversion motion of propiolamide i s described by a 2 harmonic potential, then <Q. > w i l l be a linear function of xnv v i n v (103). However, i f a small barrier at the planar position 2 is perturbing the harmonic potential, then <Q^ n v > w i l l show a zig-zagging v a r i a t i o n with v i b r a t i o n a l quantum number ( 1 0 3 ) . This behaviour arises because such a perturbation strongly interacts with the even harmonic levels to remove some of the non-zero probability density at the planar position and place i t at larger values of Q^ n v» b u t bas only a small effect on the odd levels because they have nodes at the planar position. Since the r o t a t i o n a l constants and the i n e r t i a l defect depend d i r e c t l y 2 on < Q j _ n v > they w i l l also exhibit either the smooth or zig-zagging v a r i a t i o n with v, , depending on whether or not the barrier i s xnv ° present. The "zig-zag test" has been used successfully in several microwave studies to determine the presence or absence of a potential barrier (14,98,99,102,104). The i n e r t i a l defect in the ground and f i r s t excited inversion state of propiolamide were given in Table 4.7. Since the rotational spectrum in the v. =2 state was too weak to be assigned, a third xnv & ' defect is not available and i t i s not possible to say d i r e c t l y whether or not the i n e r t i a l defect has a zig-zag dependence on -113-Table 5.5 I n e r t i a l Defects of Propiolamide and Other Pr o p i o l y l Molecules <A> , v. mv HCCCONH2 0.2801b <A> _ v = 0 HCCCOF 0.2723 < A > n v = 0 HCCCOOH 0.2452 a . .2 in amu-A . b Calculated assuming a linear v a r i a t i o n of A with v. (see text) ° mv v. . However, i f the i n e r t i a l defect i s assumed to vary l i n e a r l y mv ' with v. , i t is possible to calculate easily what the defect of mv the molecule would be in the hypothetical "inversionless" ground state v. --h (this i s the state at the bottom of the inversion inv potential well(s) -- the equilibrium stat e ) . Using the determined values of <A> „ and <A> , given in Table 4.7, this calc-v. =0 v. = 1 ° inv inv 2 ulation gives <A> , =0.2801 amu-A . If the var i a t i o n of v, =-*5 inv <A> with v. i s , indeed, l i n e a r , this "inversionless" defect v. mv inv should be very similar to the ground state defect found for the i n e r t i a l l y similar HCCCOF and HCCCOOH molecules where, of course, the inversion vibration i s not present. On the other hand, i f <A> has a zig-zag dependence on v. , the calculated value inv of <A> , is incorrect and should be substantially d i f f e r e n t v . =--i mv from the defects of HCCCOF and HCCCOOH, The ground state i n e r t i a l defects of pr o p i o l y l fluoride and pro p i o l i c acid are compared with the calculated value of <A> inv -114-in Table 5.5. As can be seen, the defects agree reasonably well and thus i t appears that <A> varies l i n e a r l y (or at least inv smoothly) with v j j _ n v » This i s additional strong evidence that the inversion barrier is very small or zero and that propiolamide i s planar. 5.8 Conclus ions The magnitudes of the inversion frequency, coupling constants, centrifugal d i s t o r t i o n constants and the i n e r t i a l defects of propiolamide are a l l consistent with the conclusion that propiol-amide i s e s s e n t i a l l y a planar molecule and that the barrier to inversion i s either zero or only very small; thus the resonance structure II of Figure 4.1 is the dominant canonical form of propiolamide. However, without a knowledge of the frequencies of the inversion overtone and hot bands (which l i e in the f a r -infrared) there i s not enough v i b r a t i o n a l data available to determine the exact form of the inversion potential function and a categorical statement of planarity cannot be made. It i s l i k e l y , though, that the inversion potential of p r o p i o l -amide i s very similar to that determined for the planar formamide molecule by a recent microwave and fa r - i n f r a r e d study (20) and that i t i s somewhat anharmonic but has n_o b a r r i e r . These two 14 molecules have remarkably similar N quadrupole coupling constants, dipole moments, inversion frequencies and i n e r t i a l defect s h i f t s upon deuteration and so there is no reason to suspect that their inversion potentials are r a d i c a l l y d i f f e r e n t . -115-Chapter 6 Further Discussion 6.1 The Molecular Structure of Propiolamide Assuming propiolamide to be a planar molecule, there remain sixteen atomic coordinates to be determined in order to describe the molecular structure — that i s , the a- and b-coordinates of each of the eight atoms. These coordinates describe a t o t a l of thirteen independent geometrical parameters: seven bond lengths and six bond angles. The structure of propiolamide was determined by the sub-s t i t u t i o n method (see Section 2.5). In order to determine the structure from the limited isotopic data available, several of these parameters had to be assumed in the analysis. The C-H and C=C bond lengths were taken to be the same as in propynal (66) and the C=0 bond length, the OCN bond angle and the parameters about the nitrogen atom were taken to be the same as those in formamide (20); the acetylenic chain was assumed to be l i n e a r , as found for pro p i o l y l chloride (71). The substitution coordinates of the acetylenic hydrogen atom in the DCCCOND^ p r i n c i p a l axis system were obtained by applying Kraitchman's equations for a planar r i g i d molecule, eqs. 2.63, to the DCCC0ND2/HCCC0ND2 isotopic pair; the p r i n c i p a l moments of i n e r t i a of these molecules (as determined from the ground state rotational constants by applying eq. 2.61) and the coordinates determined are shown in Table 6.1. Unfortunately, the b-coord--116-Table 6.1 Ground State Moments of Inertia for HCCCOND2 and DCCCOND2 and the Acetylenic Hydrogen Substitution Coordinates Moment of Inertia HCCCOND, DCCCOND, 49.22009 126.99718 176.36772 49.23694 137.61914 187.01472 Coordinates of acetylenic hydrogen in the DCCC0ND2 p r i n c i p a l axis system: b I - 3.23 A - 0.12 A a 2 In units of amu-A ; calculated using the conversion factor BI, = h/(8ir 2) = 505379.045 MHz-amu-A2 . D inate obtained was very small and i s probably very inaccurate (60) With these coordinates and the assumed structural parameters, only two independent geometrical features remained to be deter-mined: the C-C bond length and the CCO angle (the other unassumed angle, <CCN, is related to <CC0 and the assumed <0CN by <CCN = 360° - <CC0 - <OCN). These two parameters were calculated by applying the two center-of-mass conditions Z m. a . i 1 1 0 Z m.b. = 0 i 1 1 6.1 and the second moment condition E m . a . b . = 0 i l x l 6.2 The derived and assumed bond lengths and angles of propiol--117-Table 6.2 The Structure of Propiolamide and Related Molecules (Bond Lengths in Angstroms) HCCCONH2 HCCCOF3 HCCC0Cl b HCCCH0C r(H-C) ft 1.055 1.055* 1.057±0.004 1.055+0.001 r(CSC) ft 1 .209 1.209* 1.207* 1.209±0.001 r(C-C) 1 .47 + 0.02 1.454 1.423+0.012 1.445±0.001 r(C=0) * 1.219 1.181* 1.210±0.012 1.21510.001 r(C-N) ft 1 .352 r(N-H) 1 .002* <(HCC) o* 180 o * o * o 180 180 180.0+0.2 <(CCC) o* 180 180°* 179.810.4° 178.4+0.2° <(CCO) 122.3+2° 127.21° 126.1+0.4° 123.810.2° <(OCN) o* 124.7° <(CNH c) d o* 118.5 <(CNH t) d o* 120.0 3 Ref. 68 b Ref. 71 \ C Ref. 66 * Assumed. d H is the c amido-group hydrogen atom closest to the oxygen; H is the amido-group hydrogen atom farthest from the oxygen. amide are shown in Table 6.2 along with the st r u c t u r a l features of some similar molecules. As can be seen, the calculated C-C bond length and CCO angl e are not determined very accurately but are of reasonable magnitudes in l i g h t of the results shown for the other p r o p i o l y l molecules. The determined structure i s represented p i c t o r a l l y in Figure 6.1. -118-6.2 The Direction of the Dipole Moment in Propiolamide and  in Related Molecules The Stark effect measurements for an asymmetric rotor such as propiolamide do not yi e l d any information about the signs (that i s , the directions) of the components of the dipole moment. However, the directions can usually be deduced by arguments based on atom el e c t r o n e g a t i v i t i e s and/or theoretical calculations. Assuming propiolamide to be planar, the out-of-plane component of the dipole moment, , i s zero and the t o t a l molecular dipole moment i s positioned in the molecular ab plane. Figure 6.1 shows the positions of the a and b i n e r t i a l axes in HCCCONH^. Since the oxygen atom i s the most electronegative atom in propiolamide i t i s expected that there is a buildup of electron density at -119-th i s end of the molecule. Because of this buildup i t is very probable that the t o t a l e l e c t r i c dipole moment vector l i e s nearly p a r a l l e l to the C-O bond. Thus u a and are most l i k e l y directed along the positive a and b axes, respectively, as shown in Figure 6.2 (in this discussion, the dipole moment vectors point to the negative end of the dipole), so that the t o t a l dipole moment, p, makes an angle of 72.9° to the a axis and 11° to the C-O bond. Figure 6.2 The Direction of the Dipole Moment of Propiolamide (the dipole moment vectors point to the negative end of the dipole) To confirm that this i s the correct orientation of the dipole moment in propiolamide, complete-neglect-of-differential-overlap (CNDO) calculations were carried out using a computer program written by Pople and Dobash (105). CNDO molecular-o r b i t a l theory and i t s application to the calculation of the magnitudes and directions of molecular dipole moments has been discussed by Pople and Beveridge (106). The result of the calc--120-ulation for propiolamide, given in Table 6.3, shows that the CNDO dipole moment dire c t i o n is in almost exact agreement with that presented in Figure 6.2. CNDO dipole moment calculations for other p r o p i o l y l molecules and their formyl analogs have also been included in Table 6.3. As can be seen, the theoretical predictions of dipole moment magnitudes and directions are generally quite close to the observed r e s u l t s . Table 6.3 Observed and Calculated (CNDO) Dipole Moments and Directions for Some Pr o p i o l y l and Formyl Molecules OBSERVED CNDO a y <yC0 a u <yC0b Ref . HCCC(0)NH2 3 .67+0.02 +11.1° 3.86 + 9.1° THIS WORK HCCC(0)0H 1 .59±0.03 +2.8° 1. 20 -5.4° 69 HCCC(0)F 2 .98+0.02 -43.5° 2.82 -44.8° 68 HC(0)NH2 3 .71+0.06 +16.9° 3.67 +16.3° 20,108 HC(0)0H 1 .42+0.01 +15.5° 0.89 +35.6° 109 HC(0)F 1 .99+0.03 -37.0° 1.91 -44.2° 110 in Debyes. <yC0 i s the angle between the dipole moment vector and the C-0 bond; positive angles indicate that y points between the C-0 and the R-C bonds (R=HCC or H) and negative angles indicate that y points between the C-0 and the C-X bonds (X=NH ,0H or F). From the results presented in Table 6.3 i t can be seen that -121-t h e e f f e c t o f s u b s t i t u t i n g t h e R=H atom o f a R-C(0)X m o l e c u l e (X=NH o,0H o r F) w i t h t h e R=HCC e t h y n y l group i s to r o t a t e t h e d i r e c t i o n of t h e d i p o l e moment c l o c k w i s e , towards t h e d i r e c t i o n of t h e C-X bond (a c l o c k w i s e r o t a t i o n i s the v e c t o r sweep t h r o u g h the C-0, t h e n the C-X and f i n a l l y t h e R-C d i r e c t i o n s ) . The d i p o l e moment o f t h e p r o p i o l y l m o l e c u l e can be r e p r e s e n t e d i n terms o f t h a t o f t h e c o r r e s p o n d i n g f o r m y l m o l e c u l e and t h e bond moments, y_(H-C) and y „ ( H C C - C ) , a s : jj(HCCCOX) = jj(HCOX) + {y (HCC-C) - iLg(H-C)} 6.3 T h i s e q u a l i t y i s r e p r e s e n t e d s c h e m a t i c a l l y i n F i g u r e 6.3. In o r d e r to a c c o u n t f o r t h e o b s e r v e d r o t a t i o n s o f t h e d i p o l e moments, {y.,(HCC-C) - y „ ( H - C ) } must be d i r e c t e d as shown i n the f i g u r e so t h a t |£ (HCC-C) | > |_y (H-C) | . T h i s i s as e x p e c t e d s i n c e the { y B ( H C C - C ) - y B ( H - C ) } R y(HCCCOX) F i g u r e 6.3 The R e l a t i o n s h i p Between the D i p o l e Moment of a P r o p i o l y l M o l e c u l e w i t h t h a t of t h e C o r r e s p o n d i n g F o r m y l M o l e c u l e ( i t i s assumed t h a t |_y (HCC-C) | > |y (H-C)|) -122-ethynyl group is more polarizable than the hydrogen atom because of the presence of extensive ir-bonding. Equation 6.3 also predicts that since |_y_B (HCC-C) | > | jig (H-C) | the dipole moment of a p r o p i o l y l molecule should be larger than that for i t s formyl analog. This is observed experimentally for HCCCOOH/HCOOH and HCCCOF/HCOF but not for HCCCONH2/HCONH2. The uncertainty in the measurement of the dipole moment of formamide i s r e l a t i v e l y large, however, and this 'anomalous' result may not be r e a l . 6.3 The C5C-C Bending Frequencies of Propiolamide The C=C-C in-plane and out-of-plane bending frequencies (v=l-*-0) determined for propiolamide (see Section 4.3) are com-pared with those found for other p r o p i o l y l molecules in Table 6.4. As can be seen, the frequencies are generally quite d i f f e r e n t from molecule to molecule but for each molecule the out-of-plane v i b r a t i o n a l mode i s of a higher frequency than i s the in-plane mode. 6.4 The As trophysical Significance of Propiolamide The space between the stars of our Galaxy i s not empty. Approximately 10% of the mass of the Milky Way i s present in the form of i n t e r s t e l l a r gas and dust p a r t i c l e s , with the dust accounting for about 1% of the mass of the i n t e r s t e l l a r matter (25), The composition of the dust i s unknown; however, the gas is known to be comprised mostly of atomic hydrogen. In addition to the hydrogen, more than forty molecules, some of them rather complex, -123-Table 6.4 In-plane and Out-of-plane C=C-C Bending Frequencies of Some Prop i o l y l Molecules in-plane mode out-of-plane mode Method Ref . HCCCONH2 273175 >273 microwave THIS WOR] HCCCHO 150±15 230±10 microwave 72 206 260 u l t r a v i o l e t 111 200±10 280+10 infrared 111 HCCCOF 188±25 218125 microwave 68 189 229 Raman (li q u i d ) 112 HCCCOC1 167 227 Raman (liquid) 113 in cm have been discovered in the i n t e r s t e l l a r gas, a l l but four since 1968 (25). A complete l i s t of these molecules (to June 1977) is found in Table 6.5. As can be seen, several fundamental mol-ecules of b i o l o g i c a l interest have been found: water, ammonia, formaldehyde, etc. The presence of these and more complex organic species indicates that there may be an i n t e r s t e l l a r biochemistry. The fact that molecules containing carbon-carbon t r i p l e bonds (the ethynyl r a d i c a l (114), methylacetylene (115), cyanoacetylene and cyanotriacetylene (117)) and the amido group (formamide (118)) have been found i s a good indication that propiolamide i s present as well in i n t e r s t e l l a r space. Information about i n t e r s t e l l a r molecules i s transmitted to -124-Table 6.5 Observed I n t e r s t e l l a r Molecules H 2 hydrogen NH3 ammonia OH hydroxyl H2CO formaldehyde SiO s i l i c o n monoxide HNCO isocyanic acid SiS s i l i c o n s u l f i d e H2CS thioformaldehyde NS nitrogen s u l f i d e H2CNH methanimine SO sulfur monoxide NCNH cyanamide CH methylidyne HCOOH formic acid CH+ methylidyne ion HC3N cyanoacetylene CN cyanogen H 2C 20 ketene CO carbon monoxide CH30H methanol CS carbon monosulfide CH3CN cyanomethane H20 water HCONH2 formamide N 2H + protonated nitrogen CH3NH2 methylamine H2S hydrogen s u l f i d e CH 3C 2H methyl acetylene so 2 sulfur dioxide HCOCH3 acetaldehyde CCH ethynyl H2CCHCN v i n y l cyanide HCN hydrogen cyanide HCOOCH3 methyl formate HNC hydrogen isocyanide (CH 3) 20 dimethyl ether HCO+ formyl ion C 2H 50H ethanol HCO formyl H(C 2) 3CN cyanotriacetylene OCS carbonyl s u l f i d e C 3H 5CN ethyl cyanide Si From reference 92 (in part). -125-astronomers through their spectra (usually emission), which are received on Earth by extremely sensitive telescopes. The i n t e r -s t e l l a r spectra are subsequently i d e n t i f i e d and assigned by detailed comparison with existing t e r r e s t r i a l spectra. Most i n t e r s t e l l a r molecules have been i d e n t i f i e d by a comparison involving their radio-microwave ro tat ional spectra. This is because radio-microwave frequencies can be measured to such a high precision (better than 1 part in 10^) that the i d e n t i f i c a t i o n of only one t r a n s i t i o n i s usually s u f f i c i e n t to confirm the presence of the molecule (119). Also, i t i s usually not possible to obtain the infrared v i b r a t i o n a l spectra or the u l t r a v i o l e t electronic spectra of i n t e r s t e l l a r molecules with telescopes located on the surface of the Earth since infrared and u l t r a -v i o l e t radiation are strongly attenuated by the atmosphere. At this time, several radio-microwave lines have been detected in several sources which have not yet been assigned. While most of these may be attributable to highly reactive radicals whose t e r r e s t r i a l microwave spectra would be very d i f f i c u l t to obtain, some are undoubtedly attributable to previously unstudied stable molecules, such as propiolamide, whose spectra are readily obtain-able. The predicted frequencies and standard deviations of some transitions of propiolamide unmeasured in this study, but which should be of interest in radioastronomy, are given in Table 6.6. Both a- and b-type transitions up to a maximum of J=13 and of frequency = 100 GHz are included. With these frequencies, as well as the observed ones given in Chapter 4, searches for i n t e r s t e l l a r transitions of propiolamide are now possible. -126-Table 6.6 Astrophysically-Interesting Transitions of HCCCONH2a Transition Calculated unsplit frequency + quadrupole s h i f t s Line strength + r e l a t i v e intensity of hyperfine components ^.O"1!, 1 F=2 - F=2 F=2 - F=l F=l - F=2 F=l - F=l F=l - F=0 F=0 - F=l 1102.84 0.29 -0.30 -0.86 -1.45 0.03 1.42 0.002 1 .50 0.42 0.14 0.14 0.08 0.11 0.11 1 o , i - ° o , o F=2 - F=l F=l - F=l F=0 - F=l 7168.08 -0.09 0.46 -0.92 0.003 1.00 0.56 0.33 0.11 11,0 _ 10,1 F=2 - F=2 F=2 - F=l F-l F=2 F=l - F=l F=l - F=0 F=0 - F=l 8385 .29 0.28 -0.27 -0.86 -1.42 -0.03 1.45 0.004 1. 50 0.42 0.14 0.14 0.08 0.11 0.11 -127-Table 6.6 (continued) Transition Calculated unsplit frequency + quadrupole s h i f t s Line strength + r e l a t i v e intensity of hyperfine components 2 -2 1,1 0,2 F = 3 - F=3 F=2 - F=2 F=l - F=l 9604.04 0.30 -1 .05 1 .05 0.005 2.33 0.42 0.23 0.15 2 -1 1,2 10,1 F=3 - F=2 F=2 - F-2 F=2 - F=l F=l - F== 1 F=l - F=0 20515.67 -0.18 ,1.05 0.49 -1.42 -0.03 0.010 1 .50 0.47 0.08 0.25 0.08 0.11 2 -1 0,2 1,1 F=3 - F=2 F = 2 - F=2 F=2 - F=l F=l - F=l F=l - F=0 6937.69 -0.06 0.66 0.07 -1. 05 0.42 0.003 0.60 0.47 0.08 0.25 0.08 0.11 3 -2 0,3 0,2 F=4 - F=3 F=3 - F=2 F=2 - F=l 21048.44 -0.07 0.14 0.00 0.009 2.97 0.43 0.30 0.20 -128-Table 6.6 (continued) Transition Calculated unsplit frequency + quadrupole s h i f t s Line strength + r e l a t i v e intensity of hyperfine components 3 -2 J l , 3 1,2 3 -2 1,2 Z l , l F=4 - F=3 F=3 - F=2 F=2 - F=l 19780.78 2,3081 .58 -0.03 0.15 -0.22 0.009 0.009 2.66 2.66 0.43 0.30 0.20 3 -2 1,3 0,2 F=4 - F=3 F=3 - F=2 F=2 - F=l 26076.31 -0.21 0.54 -0.32 0.013 2.07 0.43 0.30 0.20 4 -3 ^0,4 J l , 3 F=5 - F=4 F=4 - F=3 F=3 - F=2 22554.12 0.05 -0.23 0.26 0.009 2.20 0.41 0.31 0.24 5 -5 °1,4 30,5 F=6 - F=6 F=5 - F=5 F=4 - F=4 18854.32 0.45 -1.17 0.78 0.016 3.26 0.38 0.31 0.26 5 -4 1,5 ^0,4 F=6 - F=5 F=5 - F=4 F=4 - F=3 36350.81 -0.17 0.39 -0.22 0.018 3.53 0.39 0.32 0.26 -129-Table 6.6 (continued) 1 Calculated Line strength Transition unsplit frequency a + r e l a t i v e intensity + quadrupole s h i f t s of hyperfine components 6. ,-6 n , 24149.89 0.020 3.14 1,50,6 F=7 - F=7 0.48 0.38 F«6 - F=6 -1.20 0.32 F=5 - F-5 0.76 0.27 6 A ,-5. c 37352.37 0.015 4.23 U , D 1 , 5 61 6 - 5 Q 5 41485.42 0.019 4.43 F=7 - F=6 -0.13 0.39 F=6 - F=5 0.28 0.32 F=5 - F=4 -0.15 0.27 71,7~ 60,6 46814.21 0.021 5.40 F=8 - F=7 -0.09 0.38 F=7 - F=6 0.19 0.33 F=6 - F=5 -0.09 0.28 7 Q 7 - 6 l 6 44228.58 0.018 5.29 1 2 l , l l " U l , 1 0 82511.26 0.045 11 .57 1 3 0 ^ 1 3 - 1 2 0 > 1 2 81909.09 0.100 12.83 1 31,13" 1 21 12 81884.67 .0.100 12.83 1 3 1 12" 1 21 11 88391.52 0.061 12.57 -130-T a b l e 6.6 ( c o n t i n u e d ) T r a n s i t i o n C a l c u l a t e d u n s p l i t f r e q u e n c y + q u a d r u p o l e s h i f t s a a L i n e s t r e n g t h + r e l a t i v e i n t e n s i t y o f h y p e r f i n e components 13 -1 2 J 1 , 1 3 0,12 81936.62 0. 101 11.40 13 -12 0,13 1,12 81857.14 0. 100 11.42 1 4 0 , 1 4 ~ 1 3 0 , 1 3 87966.41 0. 130 13.84 1 4 1 , 1 4 ~ 1 3 1 , 1 3 87953.32 0. 130 13.84 1 4 1 , 1 3 " 1 3 1 , 1 2 94320.82 0. 081 13.54 1 4 0 , 1 4 ~ 1 3 1 ,13 87938.88 0. 130 12.44 1 5 0 , 1 5 ~ 1 4 0 , 1 4 94026.66 0. 165 14.83 1 5 1 , 1 5 ~ 1 4 1 , 1 4 94019.73 0. 165 14.83 1 5 0 , 1 5 ~ 1 4 1 , 1 4 94034.18 0. 166 13.45 1 5 1 , 1 5 ~ 1 4 0 , 1 4 94012.22 0. 165 13.45 T r a n s i t i o n s f r e q u e n c i e s a r e i n MHz; a i s t h e s t a n d a r d d e v i a t i o n o f t h e u n s p l i t l i n e f r e q u e n c y . -131-6.5 Concluding Remarks In summary, several pieces of information were available from the microwave spectra of propiolamide which were important in deducing the molecular planarity or non-planarity. These were: (1) No c-type transitions were observed. (2) The inversion frequency was large. (3) The coupling constant |xccl w a s small. (4) The centrifugal d i s t o r t i o n constants in the ground and f i r s t excited inversion state were s i m i l a r . (5) The apparently near-linear v a r i a t i o n of the i n e r t i a l defect with the inversion quantum number, v. . inv (6) The small change in the ground state i n e r t i a l defect upon amido-group deuteration. These observations were shown to be consistent with the conclusion that the barrier to the amido-group hydrogen inversion motion i s zero, although the presence of a very small barrier could not be e n t i r e l y ruled out. As explained in Chapter 5, this led to the conclusion that the propiolamide molecule is planar or e s s e n t i a l l y planar in the ground v i b r a t i o n a l state. The study reported here is only the second detailed gas-phase str u c t u r a l analysis of a carboxylic amide that has been reported (formamide being the other) and helps to s o l i d i f y the R-C(O) NH^-*--* R-C(O)N"H„ resonance picture f i r s t developed by Pauling in the 1930's. Obviously, however, more such microwave studies are warranted in order to check that other amides are planar or e s s e n t i a l l y planar and that this picture i s a general one. Amides which might give easily observable microwave spectra are acet-amide (CH_C0NH„), acrylamide (H„CCHC0NH o) and benzamide (C„H cC0NH o). -132-Bibliography 1. a) W. Gordy, W.V. Smith and R.F. Trambarulo, Microwave Spec- troscopy , John Wiley and Sons, Inc., New York, 1953. b) M.W.P. Strandberg, Microwave Spectroscopy, Methuen, London, 1954. c) C.H. Townes and A.L. Schawlow, Microwave Spectroscopy, McGraw-Hill Book Co., New York, 1955. d) T.M. Sugden and C.N. 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