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The microwave spectra and structures of some isocyanates Hocking, William Hiram 1973

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THE MICROWAVE SPECTRA AND STRUCTURES OF SOME ISOCYANATES by W i l l i a m Hiram H o c k i n g B.Sc,  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 , 1969  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  i n the  Department of  Chemistry  We a c c e p t t h i s t h e s i s as c o n f o r m i n g to _ r e q u i r e d standard  —  THE UNIVERSITY OF BRITISH COLUMBIA O c t o b e r , 1973 i  the  In p r e s e n t i n g an a d v a n c e d  this  thesis  degree at  t h e L i b r a r y s h a l l make I f u r t h e r agree for  scholarly  by h i s of  this  written  it  freely  for  that permission for extensive  for  It  financial  gain  of  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  jf  Columbia  l<f?2>  the  requirements  Columbia, reference  copying of  I agree and this  shall  that  not  for  that  study. thesis  by t h e Head o f my D e p a r t m e n t  is understood  permission.  ~J?^  British  available  p u r p o s e s may be g r a n t e d  thesis  fulfilment of  the U n i v e r s i t y of  representatives.  Department  Date  in p a r t i a l  or  copying or p u b l i c a t i o n  be a l l o w e d w i t h o u t my  ii ABSTRACT The microwave spectra and structures of three isocyanate molecules have been studied; they are: chlorine isocyanate (C1NC0), isocyanic acid (HNCO) and cyanogen isocyanate (NCNCO). C1NC0: The microwave spectra of s i x isotopic species of chlorine isocyanate have been measured i n the frequency region 8 - 3 7  GHz.  I t was found that  the rotational energy l e v e l scheme corresponding to each of these spectra was adequately represented by a seven parameter Hamiltonian specific for a well behaved planar molecule.  The parameters, three rotational constants  and four d i s t o r t i o n constants, were determined using a least squares f i t t i n g procedure.  From the rotational constants, the r molecular structure of g  chlorine isocyanate was calculated to be: r(Cl-N) = 1.705 ± 0.005 &  Z_(C1NC) = 118° 50' ± 30'  r(N-C) = 1.225 ± 0.005 A*  Z-(NCO) = 170° 52' ± 30'  r(C-O) = 1.162 ± 0.005 &  Planar, CI and 0 trans  This i s the f i r s t instance i n which an isocyanate molecule has been shown to have a bent NCO chain. Considerable hyperfine structure was also observed i n a l l of the chlorine isocyanate spectra. This was analysed to yield chlorine and nitrogen nuclear quadrupole coupling constants.  These have provided some insight into the  electronic d i s t r i b u t i o n i n the molecule. HNCO: The microwave spectra of s i x isotopic species of isocyanic acid have also been measured i n the frequency region 8 - 3 7  GHz.  The observed (micro-  wave) transitions were analysed together with the available millimeter-wave data (Kewley e t . a l . (150) and Winnewisser (198)) using Watson's general nonr i g i d Hamiltonian.  This analysis yielded rotational constants of s u f f i c i e n t  iii  a c c u r a c y to a l l o w the d e t e r m i n a t i o n of a r e f i n e d  (r ) m o l e c u l a r s  r(H-N) = 0.986 ± 0.015 X  Z.(HNC) = 128° 2' ± 1°  r(N-C) = 1.209 ± 0.005 8  A(NCO) = 180°  structure:  r(C-O) = 1.166 ± 0.005 A* In a d d i t i o n , the b-component o f the d i p o l e moment o f d e u t e r a t e d c y a n i c a c i d was measured.  iso-  The v a l u e o b t a i n e d i s : u, = 1.35 ± 0.10 D. /  b  combined w i t h the p r e v i o u s l y measured ^-component (y  SL  When  = 1.602 ± 0.020 D (153))  i t y i e l d s the t o t a l d i p o l e moment o f DNCO: y = 2.10 ± 0.15 D. NCNCO:  The microwave spectrum o f the n a t u r a l l y most abundant i s o t o p i c  o f cyanogen i s o c y a n a t e has been i n v e s t i g a t e d .  T h i s was found to be c o n s i s -  t e n t w i t h a bent c h a i n s t r u c t u r e r a t h e r t h a n t h e p r e v i o u s l y proposed linear configuration.  species  (18)  A p r e l i m i n a r y m o l e c u l a r s t r u c t u r e was c a l c u l a t e d .  A n a l y s i s o f e x c i t e d v i b r a t i o n a l s t a t e s p e c t r a gave e v i d e n c e f o r s t r o n g q u a s i l i n e a r behavior.  S t a r k measurements y i e l d e d the m o l e c u l a r d i p o l e moment.  iv  TABLE OF CONTENTS CHAPTER  Page  1.  INTRODUCTION  2.  MICROWAVE SPECTROSCOPIC  1 THEORY  6  2.1 The R o t a t i o n a l Energy L e v e l s o f an Asymmetric Top Molecule.  6  2 . 2 N u c l e a r Quadrupole C o u p l i n g .  21  2 . 3 The S t a r k E f f e c t .  26  2 . 4 R o t a t i o n a l C o n s t a n t s , Moments o f I n e r t i a ,  Inertial  D e f e c t and t h e M o l e c u l a r S t r u c t u r e .  3.  4.  31  2 . 5 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 V i b r a t i o n a l Force F i e l d .  42  EXPERIMENTAL  44  3.1 P r e p a r a t i o n of C h l o r i n e I s o c y a n a t e .  44  3.2 Preparation of Isocyanic A c i d .  49  3 . 3 P r e p a r a t i o n o f Cyanogen I s o c y a n a t e .  51  3 . 4 The S t 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 .  54  3 . 5 Double Resonance E x p e r i m e n t s .  58  3 . 6 D i p o l e Moment Measurements.  60  THE MICROWAVE SPECTRUM OF CHLORINE ISOCYANATE  62  4 . 1 Assignment of the Spectrum  63  4 . 2 D e t e r m i n a t i o n of M o l e c u l a r Constants from the Microwave S p e c t r u m .  68  4 . 3 The M o l e c u l a r S t r u c t u r e o f C h l o r i n e I s o c y a n a t e  79  4 . 4 D i s c u s s i o n of t h e N u c l e a r Quadrupole C o u p l i n g Constants.  86  4 . 5 V i b r a t i o n a l Dependence o f the M o l e c u l a r C o n s t a n t s  101  V  CHAPTER  Page 4.6 C a l c u l a t i o n o f 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 and the I n e r t i a l D e f e c t from the M o l e c u l a r F o r c e Field. 4.7 D i s c u s s i o n of the M o l e c u l a r S t r u c t u r e .  5.  106 Ill  THE MICROWAVE SPECTRUM OF ISOCYANIC ACID  118  5.1 Assignment o f the S p e c t r u m .  120  5.2 D e t e r m i n a t i o n of M o l e c u l a r C o n s t a n t s from the Microwave Spectrum. 5.3 The M o l e c u l a r S t r u c t u r e  6.  122 of I s o c y a n i c A c i d .  131  5.4 D i p o l e Moment Measurements; D i s c u s s i o n o f the D i p o l e Moment and the N i t r o g e n N u c l e a r Quadrupole Coupling Constants.  142  5.5 C a l c u l a t i o n o f 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 and the I n e r t i a l D e f e c t from the M o l e c u l a r F o r c e Field.  157  5.6 D i s c u s s i o n of the M o l e c u l a r S t r u c t u r e  165  THE MICROWAVE SPECTRUM OF CYANOGEN ISOCYANATE  174  6.1 Assignment o f t h e S p e c t r u m .  175  6.2 D e t e r m i n a t i o n o f M o l e c u l a r C o n s t a n t s from the Microwave Spectrum. 6.3 The M o l e c u l a r S t r u c t u r e  7.  182 of Cyanogen I s o c y a n a t e .  190  6 . 4 D i p o l e Moment Measurements.  194  6.5 V i b r a t i o n a l Dependence o f the R o t a t i o n a l C o n s t a n t s .  205  6.6 D i s c u s s i o n o f the M o l e c u l a r S t r u c t u r e .  210  MICROWAVE TRANSITION FREQUENCIES OF CHLORINE ISOCYANIC ACID AND CYANOGEN ISOCYANATE BIBLIOGRAPHY  ISOCYANATE,  214 311  vi  LIST OF TABLES TABLE 4.1  Page R o t a t i o n a l C o n s t a n t s 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 of  4.2  3 5  C1  1 4  N  1 2  C  1 6  0 i n the Ground V i b r a t i o n a l S t a t e .  72  R o t a t i o n a l C o n s t a n t s 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 of  CI  N  C  0 i n the Ground V i b r a t i o n a l S t a t e .  4.3  R o t a t i o n a l C o n s t a n t s 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  4.4  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 o f Isocyanate. ... .  4.5  Moments o f I n e r t i a and I n e r t i a l D e f e c t s o f C h l o r i n e Isocyanate.  4.6  C h l o r i n e Isocyanate Atomic Coordinates i n  of C h l o r i n e I s o c y a n a t e .  3 5  C1  1 4  N  1 2  C  1 6  Chlorine  74 76 78 80  the  0 P r i n c i p a l A x i s System.  82  4.7  Molecular Structure  of Chlorine Isocyanate.  84  4.8  N i t r o g e n ai-Coordinate by Double S u b s t i t u t i o n .  4.9  S e l e c t e d C h l o r i n e 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  84  of Chlorine Isocyanate.  87  4.10  T r a n s f o r m a t i o n o f the C h l o r i n e 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 i n t o the C1N Bond A x i s System.  91  4.11  N i t r o g e n Quadrupole C o u p l i n g I n t e r p r e t a t i o n  4.12  CND0/2 C a l c u l a t e d p - O r b i t a l P o p u l a t i o n s on C h l o r i n e and Nitrogen i n Chlorine Isocyanate.  4.13  Comparison of Observed and C a l c u l a t e d N u c l e a r  Townes D a i l e y T h e o r y .  Coupling Constants of  Quadrupole  4.14  C h l o r i n e Isocyanate V i b r a t i o n a l Force F i e l d s .  107  4.15  Fundamental V i b r a t i o n a l F r e q u e n c i e s  108  4.16  C a l c u l a t e d and Observed 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 of C h l o r i n e Isocyanate (  3 5  C1  1 2  I 4  C  97  100  1 4  N  97  0 (G.V.S.).  3 5  C1  u s i n g the  N  1 6  1 2  C  1 6  of C h l o r i n e Isocyanate.  0  G.V.S.)  110  vii  TABLE 4.17  Page C a l c u l a t e d and Observed I n e r t i a l Isocyanate (  4.18  3 5  C1  1 4  N  1 2  C  1 6  0  Defects of  Chlorine  G.V.S.)  110  Comparison o f C h l o r i n e I s o c y a n a t e E l e c t r o n  Diffraction  and Microwave S t r u c t u r e s .  112  4.19  Some " G e n u i n e " CO and NC Double Bond L e n g t h s .  114  4.20  Some NC T r i p l e Bond Lengths and CO 2+ Bond L e n g t h s .  115  4.21  Comparison o f the C h l o r i n e N i t r o g e n Bond L e n g t h s  found  i n a Number o f S m a l l M o l e c u l e s .  115  5.1  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 o f I s o c y a n i c A c i d .  123  5.2  R o t a t i o n a l C o n s t a n t s 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  5.3  of H ^ N ^ C ^ O  u s i n g D i f f e r e n t Methods o f A n a l y s i s .  R o t a t i o n a l C o n s t a n t s 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  of Isocyanic A c i d .  5.4  A R o t a t i o n a l Constants of Isocyanic Microwave and IR d a t a .  5.5  Moments o f I n e r t i a  5.6  K r a i t c h m a n / C o s t a i n S u b s t i t u t i o n P o s i t i o n s o f a l l of  5.7  Molecular Structure Coordinates.  of I s o c y a n i c  Acid:  Atomic  5.8  Molecular Structure  of Isocyanic  Acid:  Geometry.  5.9  Cell Calibration:  5.10  A c i d from Combined  and I n e r t i a l D e f e c t s o f I s o c y a n i c A c i d .  Atoms o f I s o c y a n i c A c i d .  Measurement o f the S t a r k E f f e c t  the J = 0->-l T r a n s i t i o n o f OCS.  the  125 128 133 134 136 139 139  of  146  S t a r k Measurements on Two b-type T r a n s i t i o n s o f D  1 4  N  1 2  C  1 6  0.  147  5.11  Cell Calibration:  Effective  5.12  S t a r k C o e f f i c i e n t s o f Two D  5.13  The b-component of the D i p o l e Moment of D ^ N ^ C ^ O .  5.14  Comparison o f the Observed and C a l c u l a t e d V a l u e s o f D i p o l e Moment o f I s o c y a n i c A c i d .  1 4  Septum-Cell W a l l Spacing.  148  N  148  1 2  C  1 6  0 b-type T r a n s i t i o n s .  152 the  156  viii  TABLE 5.15  Page N i t r o g e n 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 of I s o c y a n i c A c i d and R e l a t e d M o l e c u l e s .  156  5.16  M o l e c u l a r Force F i e l d s of I s o c y a n i c A c i d .  158  5.17  Fundamental V i b r a t i o n a l F r e q u e n c i e s o f I s o c y a n i c A c i d .  159  5.18  Comparison o f C a l c u l a t e d and Observed C e n t r i f u g a l D i s t o r t i o n Constants of I s o c y a n i c A c i d .  5.19  Isocyanic A c i d Molecular Force F i e l d :  5.20  Comparison of C a l c u l a t e d and Observed I s o c y a n i c I n e r t i a l Defects.  5.21  Comparison o f I s o c y a n i c A c i d S t r u c t u r e s .  166  5.22  M o l e c u l a r S t r u c t u r e s o f Some I s o c y a n a t e s .  168  5.23  M o l e c u l a r S t r u c t u r e s o f Some A z i d e s .  170  5.24  M o l e c u l a r S t r u c t u r e s of Some I s o t h i o c y a n a t e s .  170  5.25  Comparison o f Some NH Bond L e n g t h s .  173  6.1  R o t a t i o n a l C o n s t a n t s 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  6.2  6.3  o f Cyanogen I s o c y a n a t e  R.G.F.F.  161 163  Acid  i n the Ground V i b r a t i o n a l S t a t e .  R o t a t i o n a l C o n s t a n t s 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 Cyanogen I s o c y a n a t e i n the F i r s t E x c i t e d V i b r a t i o n a l State.  164  185  187  R o t a t i o n a l C o n s t a n t s 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 Cyanogen I s o c y a n a t e  i n Higher Excited V i b r a t i o n a l States.189  6.4  Cyanogen I s o c y a n a t e Relations.  Constants C a l c u l a t e d Using P o l o ' s  6.5  The Moments o f I n e r t i a and the I n e r t i a l D e f e c t o f Cyanogen I s o c y a n a t e i n the Ground V i b r a t i o n a l S t a t e .  191  6.6  The M o l e c u l a r S t r u c t u r e o f Cyanogen I s o c y a n a t e .  191  6.7  S t a r k Measurements on Cyanogen I s o c y a n a t e .  197  6.8  S t a r k C o e f f i c i e n t s o f F i v e Cyanogen I s o c y a n a t e  6.9  The D i p o l e Moment of Cyanogen I s o c y a n a t e .  189  S t a r k L o b e s . 202 203  ix  TABLE  Page  7.1  Observed T r a n s i t i o n F r e q u e n c i e s of C h l o r i n e N u c l e a r Quadrupole C o u p l i n g A n a l y s i s .  7.2  T r a n s i t i o n Frequencies  7.3  T r a n s i t i o n Frequencies of I s o c y a n i c Quadrupole C o u p l i n g A n a l y s i s .  Acid:  Nuclear  7.4  T r a n s i t i o n Frequencies Distortion Analysis.  of I s o c y a n i c  Acid:  Centrifugal  7.5  T r a n s i t i o n Frequencies  o f Cyanogen  Isocyanate:  of C h l o r i n e  Centrifugal Distortion Analysis.  Centrifugal Distortion Analysis.  Isocyanate:  Isocyanate:  215 283 293 298 305  X  LIST OF FIGURES FIGURE 3.1  Page Schematic I l l u s t r a t i o n of the Vacuum System used i n the Preparation of Chlorine Isocyanate from Silver Cyanate and Chlorine.  48  3.2  Schematic I l l u s t r a t i o n of the Vacuum System used i n the Preparation of Cyanogen Isocyanate.  52  3.3  Schematic I l l u s t r a t i o n of the Spectrometer used i n the Microwave - Microwave Double Resonance Experiments.  59  4.1  I l l u s t r a t i o n of the K  = 2 and 3 Lines of the J = 3+4  a-Type R-Branch Group of C 1 N C 0 (G.V.S.) 3 5  4.2  1 4  1 2  1 6  66  Flow-Chart I l l u s t r a t i n g the Overall Centrifugal Distortion and Nuclear Quadrupole Hyperfine Structure Analysis Scheme.  70  4.3  The Molecular Structure of Chlorine Isocyanate.  85  4.4  I l l u s t r a t i o n of the Various Axis Systems Relevant to the Discussion of the Chlorine Nuclear Quadrupole Coupling Constants.  92  4.5  Vibrational Dependence of the A' Rotational Constant of 3 5  4.6  U  1 2  1 6  102  V  Vibrational Dependence of the B' Rotational Constant of 3 5  4.7  C1 N C 0. C1 N C 0. U  1 2  1 6  103  V  Vibrational Dependence of the C' Rotational Constant of C1 N C 0.  104  Vibrational Dependence of the I n e r t i a l Defect of C1 N C 0.  105  5.1  The Molecular Structure of Isocyanic Acid: I  141  5.2  The Molecular Structure of Isocyanic Acid: I I I  141  5.3  Stark Measurements on the 22~ „„ — 14 12 16 ' D N C 0.  21. „. Transition of '  150  Stark Measurements on the 24„ „, — 14 12 16 °' D N C 0.  23. - Transition of  3 5  4.8  3 5  5.4  U  1 4  1 2  1 2  1 6  V  1 6  24  0 1 > 2 3  151  xi  FIGURE  Page  5.5  The D i p o l e Moment of I s o c y a n i c A c i d .  154  6.1  S c h e m a t i c I l l u s t r a t i o n of the Cyanogen I s o c y a n a t e 6. , — 5. set of T r a n s i t i o n s . 1,6 1,5  178  c  6.2  6.3  Schematic I l l u s t r a t i o n of the Two Microwave - Microwave Double Resonance E x p e r i m e n t s P e r f o r m e d on Cyanogen Isocyanate. P l o t o f t h e F r e q u e n c i e s ( C o r r e c t e d f o r Asymmetry) o f the J = 5+6 a-Type R-Branch T r a n s i t i o n s o f NCNCO ( G . V . S . ) v s . K  2  183  r  6.4  The M o l e c u l a r S t r u c t u r e o f Cyanogen I s o c y a n a t e .  6.5  S t a r k Measurements on t h e 2 of NCNCO ( G . V . S . ) .  —  1 ' ,  '  M  ' 14  200  S t a r k Measurements on the 1 5 . — NCNCO ( G . V . S . ) . ' ^  6.7  The D i p o l e Moments o f Cyanogen I s o c y a n a t e and Cyanogen  n  '  T r a n s i t i o n of  Azide.  V i b r a t i o n a l Dependence o f t h e A NCNCO.  R o t a t i o n a l Constant of  V i b r a t i o n a l Dependence of t h e B NCNCO.  R o t a t i o n a l Constant of  6.10 V i b r a t i o n a l Dependence o f the C NCNCO.  R o t a t i o n a l Constant of  V  6.9  V  V  193  = 0 Transition  6.6  6.8  181  201 204 206 207 208  xii  ACKNOWLEDGEMENTS This dissertation i s an account of work carried out i n the Department of Chemistry at the University of B r i t i s h Columbia under the direction of Dr. M.C.L. Gerry.  It gives me great pleasure to thank Dr. Gerry for his  able supervision and instruction during the course of this research.  I  am further most grateful to him for helping to make my stay at U.B.C. a pleasant one through his continued optimism and encouragement.  I also wish  to acknowledge my colleagues i n the microwave group at U.B.C, especially Mr. C.W. Holt, for many useful discussions and some technical assistance. In addition, I am indebted to Dr. G. Winnewisser for making the millimeter-wave measurements on isocyanic acid, to Dr. R. Green for performing the force f i e l d calculations on isocyanic acid and chlorine i s o cyanate, and to Dr. M. Williams for running the CNDO/2 program on a l l three of the isocyanate molecules studied; to each I express my sincere gratitude. I must also thank Dr. A.J. Merer and Dr. A. Bree for several helpful d i s cussions on v i b r a t i o n a l problems and for the loan of some equipment. I further extend my sincere thanks to the National Research Council of Canada for f i n a n c i a l support during the course of this research. F i n a l l y , I would l i k e to thank Mrs. V.E. Hocking for doing an excellent job of typing this manuscript.  1  CHAPTER 1  INTRODUCTION Microwave S p e c t r o s c o p y may be d e f i n e d as the s t u d y of the a b s o r p t i o n ( o r e m i s s i o n ) o f e l e c t r o m a g n e t i c r a d i a t i o n , by m o l e c u l e s o r atoms,  in  t h a t p a r t o f the spectrum w h i c h f a l l s between r a d i o f r e q u e n c i e s and the infrared.  T h i s r e g i o n i s f r e q u e n t l y more p r e c i s e l y s p e c i f i e d as h a v i n g  a 1 GHz l o w e r boundary and an 800 GHz upper b o u n d a r y .  It  is  further  t r a d i t i o n a l l y b r o k e n down i n t o two s u b r e g i o n s o f r o u g h l y 1 - 4 0  GHz and  40 - 800 GHz w h i c h are c a l l e d , r e s p e c t i v e l y , the microwave r e g i o n and the millimeter-wave r e g i o n . The f i r s t microwave e x p e r i m e n t was r e p o r t e d by C l e e t o n and W i l l i a m s (1)  i n 1934.  o f ammonia.  T h i s was a l i m i t e d i n v e s t i g a t i o n o f the i n v e r s i o n s p e c t r u m No f u r t h e r p r o g r e s s was made u n t i l a f t e r the development o f  s t a b l e t u n a b l e s o u r c e s d u r i n g World War I I .  S i n c e then many a d d i t i o n a l  advances have o c c u r r e d so t h a t the e n t i r e 1 - 800 GHz range i s now a c c e s s i b l e , a l t h o u g h o n l y the 8 - 4 0 available spectrometer.  GHz r e g i o n i s c o v e r e d by a c o m m e r c i a l l y  Measurement a c c u r a c y w i t h c o n v e n t i o n a l microwave  t e c h n i q u e s i s t y p i c a l l y o f the o r d e r o f 1 p a r t i n 10^. A s u r p r i s i n g l y l a r g e number o f q u i t e d i f f e r e n t t y p e s of have been o b s e r v e d i n the m i c r o w a v e / m i l l i m e t e r - w a v e  region.  more e s o t e r i c e x p e r i m e n t s have i n v o l v e d the i n v e s t i g a t i o n of  transitions Some o f  transitions  between A - d o u b l e t s (2) , il-type d o u b l e t s (3) , and a t o m i c s t a t e s i n v e r s i o n problem a l s o belongs i n t h i s c a t e g o r y . t r a n s i t i o n most n a t u r a l l y a s s o c i a t e d w i t h the  the  (4);  the  However the t y p e of  microwave/millimeter-wave  2  r e g i o n i s t h a t between m o l e c u l a r s t a t e s o f d i f f e r e n t r o t a t i o n a l Indeed,  energies.  the term Microwave S p e c t r o s c o p y has come t o be used e s s e n t i a l l y  as a synonym f o r R o t a t i o n a l S p e c t r o s c o p y and i s t r e a t e d as such t h r o u g h out t h i s  thesis.  The g e n e r a l f e a t u r e s  o f the r o t a t i o n a l energy l e v e l p a t t e r n f o r any  g i v e n m o l e c u l e are d e t e r m i n e d l a r g e l y by the masses and the arrangement  of the i n d i v i d u a l atoms w i t h i n t h a t m o l e c u l e .  geometrical Consequently,  p r e c i s e i n f o r m a t i o n about the p h y s i c a l s t r u c t u r e of a m o l e c u l e may be o b t a i n e d , a t l e a s t i n p r i n c i p l e , t h r o u g h a d e t a i l e d e x a m i n a t i o n of microwave s p e c t r u m .  Unfortunately,  a complete s t r u c t u r a l  its  determination  u s u a l l y r e q u i r e s t h a t more t h a n one i s o t o p i c s p e c i e s be s t u d i e d and t h e r e f o r e can become a v e r y time consuming p r o j e c t .  Furthermore,  the n o n r i g i d -  i t y o f r e a l m o l e c u l e s u s u a l l y i n t r o d u c e s an u n c e r t a i n t y i n t o the s t r u c t u r a l parameters w h i c h f a r exceeds the measurement e r r o r  derived  (5,...,10).  T h i s n o n r i g i d i t y i s a l s o r e s p o n s i b l e f o r much o f the c o m p l e x i t y of the t y p i c a l microwave s p e c t r u m .  Many groups o f t r a n s i t i o n s w h i c h would  be i d e n t i c a l l y superimposed f o r a r i g i d m o l e c u l e are s p l i t i n t o complex m u l t i p l e t s by 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 .  In a d d i t i o n , the  pattern  of r o t a t i o n a l l e v e l s f o r each v i b r a t i o n a l s t a t e , under the i n f l u e n c e o f v i b r a t i o n - r o t a t i o n i n t e r a c t i o n , becomes d i s t i n c t l y d i f f e r e n t  from t h a t  of  a l l the o t h e r v i b r a t i o n a l s t a t e s , so t h a t when t h e r e are one o r more low l y i n g excited v i b r a t i o n a l states  the microwave spectrum i s e f f e c t i v e l y  s u p e r p o s i t i o n o f s e v e r a l c l o s e l y r e l a t e d pure r o t a t i o n a l s p e c t r a , one each o f the p o p u l a t e d v i b r a t i o n a l l e v e l s .  a for  The r e s u l t i n g m u l t i p l i c i t y o f  l i k e t r a n s i t i o n s i s o f t e n l o o s e l y r e f e r r e d t o as " f i n e s t r u c t u r e " .  Both  3  the c e n t r i f u g a l d i s t o r t i o n and the v i b r a t i o n - r o t a t i o n i n t e r a c t i o n  effects  are p o t e n t i a l s o u r c e s o f i n f o r m a t i o n on the m o l e c u l a r f o r c e f i e l d  (5,...,10).  One a d d i t i o n a l c o m p l i c a t i o n f r e q u e n t l y e n c o u n t e r e d i n microwave i s n u c l e a r quadrupole h y p e r f i n e s t r u c t u r e .  T h i s o c c u r s whenever at  spectra least  one of the n u c l e i w i t h i n the m o l e c u l e under c o n s i d e r a t i o n has a s p i n a n g u l a r momentum o f g r e a t e r t h a n 1/2.  It  i s produced by a c o u p l i n g o f t h a t n u c l e a r  s p i n t o the t o t a l r o t a t i o n a l a n g u l a r momentum t h r o u g h the i n t e r a c t i o n o f the a s s o c i a t e d n u c l e a r e l e c t r i c q u a d r u p o l e moment w i t h the e x t r a n u c l e a r charges.  A n a l y s i s of such h y p e r f i n e s t r u c t u r e y i e l d s n u c l e a r quadrupole  coupling constants.  These can p r o v i d e c o n s i d e r a b l e i n s i g h t i n t o the  t r o n i c s t r u c t u r e o f the m o l e c u l e .  elec-  The m o l e c u l a r d i p o l e moment i s a s e c o n d ,  complementary, s o u r c e o f i n f o r m a t i o n on the e l e c t r o n i c d i s t r i b u t i o n i n the molecule.  I t may be a c c u r a t e l y d e t e r m i n e d by m e a s u r i n g the e f f e c t o f an  a p p l i e d e l e c t r i c f i e l d on the microwave s p e c t r u m  (5,...,10).  T h i s t h e s i s i s an account o f an i n v e s t i g a t i o n o f the microwave of three isocyanate molecules; s p e c i f i c a l l y , c h l o r i n e isocyanate i s o c y a n i c a c i d (HNCO) and cyanogen i s o c y a n a t e  spectra  (C1NC0),  (NCNCO).  The f i r s t s t u d y , t h a t on c h l o r i n e i s o c y a n a t e , was u n d e r t a k e n p r i m a r i l y t o o b t a i n an a c c u r a t e m o l e c u l a r s t r u c t u r e .  T h i s was of p a r t i c u l a r  interest  because o f the i n t r i g u i n g v a r i a t i o n s i n s t r u c t u r e e x h i b i t e d by the o t h e r i s o c y a n a t e s w h i c h had p r e v i o u s l y been s t u d i e d .  For e x a m p l e , i s o c y a n i c  was known t o have a r o u g h l y 128° HNC a n g l e ( 1 1 ) , m e t h y l i s o c y a n a t e a CNC a n g l e ( 1 2 ) ,  and s i l y l i s o c y a n a t e , a l i n e a r heavy atom c h a i n  F u r t h e r , c h l o r i n e a z i d e , which i s i s o e l e c t r o n i c w i t h c h l o r i n e  acid  140°  (13).  isocyanate,  had been shown to have a d o u b l e b e n t , p l a n a r , s t r u c t u r e w i t h a C1NN a n g l e  4  of 108°40' and a t r a n s a z i d e bend of 8 ° 4 '  (14).  Thus, c h l o r i n e  iso-  c y a n a t e c o u l d c o n c e i v a b l y have been e i t h e r a l i n e a r m o l e c u l e o r a v e r y bent m o l e c u l e and i t  t h e r e f o r e seemed t h a t a d e t a i l e d microwave  s t u d y would be e m i n e n t l y  structural  worthwhile.  A secondary r e a s o n f o r e x a m i n i n g the microwave spectrum o f i s o c y a n a t e was t o d e t e r m i n e the c h l o r i n e and n i t r o g e n n u c l e a r coupling constants.  chlorine  quadrupole  These were o f i n t e r e s t i n t h e i r own r i g h t as a s e n s -  i t i v e probe of the e l e c t r o n i c d i s t r i b u t i o n i n the m o l e c u l e .  However,  it  was a l s o hoped t h a t t h e y m i g h t o f f e r some i n s i g h t i n t o the more c o m p l i c a t e d c h l o r i n e a z i d e q u a d r u p o l e h y p e r f i n e s t r u c t u r e w h i c h had y e t s t i l l i s not)  completely accounted  t o be  (and  for.  The i s o c y a n i c a c i d s t u d y w a s , a t l e a s t i n i t i a l l y , o f somewhat more l i m i t e d scope.  The r o t a t i o n a l s p e c t r a o f b o t h the n a t u r a l l y abundant  d e u t e r i u m s u b s t i t u t e d i s o t o p i c s p e c i e s had p r e v i o u s l y been examined A l s o a r e a s o n a b l y good m o l e c u l a r s t r u c t u r e had been r e p o r t e d ( 1 1 ) .  and (11,15).  One  o b j e c t i v e o f the p r e s e n t s t u d y was t o o b t a i n the r o t a t i o n a l c o n s t a n t s  of  a d d i t i o n a l i s o t o p i c s p e c i e s and t h e r e b y d e t e r m i n e a r e f i n e d m o l e c u l a r structure.  However,  the r e c e n t d i s c o v e r y space ( 1 6 , 1 7 ) !  t h e p r i m a r y i n c e n t i v e f o r r e o p e n i n g t h i s p r o b l e m was (by r a d i o a s t r o n o m y )  of i s o c y a n i c acid i n  interstellar  T h i s d i s c o v e r y meant t h a t almost any a d d i t i o n a l s p e c t r o -  s c o p i c e v i d e n c e w h i c h c o u l d be o b t a i n e d w o u l d be of i n t e r e s t i n The H  1 5  N  1 2  C  1 6  0  and H  1 4  N  1 3  C  1 6  0  itself.  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 were c o n -  s i d e r e d t o be p a r t i c u l a r l y i m p o r t a n t s i n c e i t was thought t h a t e i t h e r  or  b o t h o f t h e s e i s o t o p e s might be p r e s e n t i n the i n t e r s t e l l a r medium i n d e t e c t a b l e amounts.  A c c o r d i n g l y , a t h o r o u g h e x a m i n a t i o n o f the  microwave  5  (and m i l l i m e t e r - w a v e )  spectrum o f HNCO and f i v e of i t s i s o t o p i c a l l y s u b -  s t i t u t e d s p e c i e s was u n d e r t a k e n . The t h i r d p r o j e c t ,  l i k e t h e f i r s t , was p r i m a r i l y d i r e c t e d  obtaining structural information.  Cyanogen i s o c y a n a t e i s  towards  isoelectronic  w i t h b o t h l i n e a r carbon s u b o x i d e and bent cyanogen a z i d e , so t h a t , chlorine isocyanate, o f i t s geometry.  t h e r e was some q u e s t i o n as t o even the main  as w i t h features  I n d e e d , a p r e l i m i n a r y i n f r a r e d s t u d y l e d Mayer(18)  to  propose a l i n e a r c o n f i g u r a t i o n i n the gas phase and a bent one i n the s o l i d phase.  I n the p r e s e n t w o r k , o n l y the n a t u r a l l y most abundant  s p e c i e s was s t u d i e d .  N o n e t h e l e s s t h i s was s u f f i c i e n t t o answer unambig-  u o u s l y the q u e s t i o n " l i n e a r o r b e n t ? " , some s e m i - q u a n t i t a t i v e  isotopic  structural  data.  i n the gas p h a s e , and even y i e l d e d  6  CHAPTER 2 MICROWAVE SPECTROSCOPIC THEORY This chapter i s intended to p r o v i d e a reasonably concise but nonet h e l e s s s u b s t a n t i a l t h e o r e t i c a l framework w i t h i n w h i c h the d e s c r i b e d i n t h i s t h e s i s may be d i s c u s s e d .  The  results  vibrational-rotational  e n e r g e t i c s o f a r e a l m o l e c u l e are c o n s i d e r e d f i r s t .  Two subsequent  s e c t i o n s d e a l w i t h the f i n e s t r u c t u r e t h a t may be i n t r o d u c e d i n t o r o t a t i o n a l spectrum by the p r e s e n c e o f a q u a d r u p o l a r n u c l e u s , o r a p p l i c a t i o n o f an e l e c t r i c f i e l d .  Finally,  T h r o u g h o u t , the emphasis i s on  t h a n on a t t e m p t i n g t o p r o v i d e a comprehensive d i s c u s s i o n o f  2.1  spectro-  and  p r e s e n t i n g e q u a t i o n s t h a t w i l l be o f use i n subsequent c h a p t e r s ,  spectroscopic  the  the r o l e o f microwave  s c o p i c c o n s t a n t s i n the 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 v i b r a t i o n a l force f i e l d s i s discussed.  the  rather  microwave  theory.  The R o t a t i o n a l Energy L e v e l s o f an Asymmetric Top M o l e c u l e S t a r t i n g from a m o l e c u l a r model i n w h i c h the atoms a r e p o i n t masses  moving i n a p o t e n t i a l f i e l d p r o v i d e d by t h e averaged m o t i o n o f the t r o n s , W i l s o n and Howard (19)  elec-  have d e r i v e d the quantum m e c h a n i c a l H a m i l -  tonian for a v i b r a t i n g - r o t a t o r :  H =  /  J  a,3  ua3P a  + 1/2^  P. -  a 3  v\v-\v  /  h P + a a  J  a  I/2V* u^ap ya3 ii"V^ 3 /  J  C  a  r  a,3  + V  h  2.1  k with where  h  a  = 1/2^2  3  ^ " \  6  P  3  y  i  S  +  ^Vc^  i s the o p e r a t o r a s s o c i a t e d w i t h the a component of the  2  A  a  rotational  7 a n g u l a r momentum a l o n g m o l e c u l e f i x e d a x e s , p  i s the o p e r a t o r  associated  w i t h the v i b r a t i o n a l momentum c o n j u g a t e t o the k*"* n o r m a l c o o r d i n a t e Q^, 1  and  i s the o p e r a t o r a s s o c i a t e d w i t h the a component o f the  a n g u l a r momentum a l o n g m o l e c u l e f i x e d axes and i s d e f i n e d by  vibrational (10):  2.1b  P« -^ JkVk -  where the £™  C  are C o r i o l i s c o u p l i n g c o n s t a n t s .  The u  Otp  a r e the  elements  o f the i n v e r s e moment o f i n e r t i a m a t r i x and a r e f u n c t i o n s o f the n o r m a l c o o r d i n a t e s o n l y : p i s the d e t e r m i n a n t of the u „ m a t r i x . ap The S c h r o d i n g e r e q u a t i o n a s s o c i a t e d w i t h the H a m i l t o n i a n cannot be s o l v e d e x a c t l y .  vibrating-rotator  P r o g r e s s can be made, h o w e v e r ,  by s e p a r a t i n g H i n t o a sum of t h r e e t e r m s :  a purely v i b r a t i o n a l  ff° w h i c h i n c l u d e s the l a s t t h r e e terms o f e q u a t i o n 2 . 1 ; a p u r e l y t i o n a l p a r t H° c o n s i s t i n g o f t h o s e p a r t s o f t h e f i r s t term t h a t  part rotaare  d i a g o n a l i n the v i b r a t i o n a l quantum numbers; and f i n a l l y , a p e r t u r b i n g term \H' t h a t i n c l u d e s the second term p l u s the remainder o f the t e r m , w i t h A s m a l l and p o s i t i v e .  first  One can t h e n w r i t e : 2.2a  H = H° +\H' with  H  o  =  o o V + H  2  R  where i t i s p o s s i b l e t o choose w a v e f u n c t i o n s  o f the form  h  such  t h a t the m a t r i x r e p r e s e n t a t i o n o f H° i s d i a g o n a l i n V , b u t n o t d i a g o n a l i n R.  2  necessarily  The m a t r i x r e p r e s e n t a t i o n of H i n terms o f t h e s e same  w a v e f u n c t i o n s on t h e o t h e r hand w i l l have e l e m e n t s o f f - d i a g o n a l i n V o f the o r d e r o f X.  A p p l i c a t i o n o f a Van V l e c k t r a n s f o r m a t i o n (20)  m a t r i x can t h e n be used t o t r a n s f o r m i t  to  this  i n t o a new m a t r i x whose elements  2 o f f - d i a g o n a l i n V a r e reduced t o the o r d e r o f X  or h i g h e r .  With the  n e g l e c t o f t h e s e terms the t r a n s f o r m e d m a t r i x can be f a c t o r e d i n t o  smaller  8 m a t r i c e s , one f o r each v i b r a t i o n a l s t a t e .  The elements o f these  submat-  rices are given by: E  + <vR||vR-> f f  +  y^<vR|^'lv"R"Xv"R"l^'lvR'>  ^  V",R"  E °  v  -  E ° „  v"  where i t i s assumed t h a t E ° - E ° , „ can be approximated b y E ° - E ° „ . RV KV V V D e t a i l e d c o n s i d e r a t i o n o f t h e s e m a t r i x elements i n d i c a t e s t h a t p e r t u r b a t i o n treatment  i s equivalent  this  to r e w r i t i n g the v i b r a t i n g - r o t a t o r  Hamiltonian i n the f o l l o w i n g s i m p l i f i e d form:  H =E + l / 2 V f l . ? P . v  t—J a3 a 3 >  a  + l/4 V  3  where t h e c o e f f i c i e n t s a  n  a3  T _ c.P P P P .  2.3  / J agyo a B y 6 oc,B, ,6 R  Y  and T .  r  apyo  a r e s t r o n g l y dependent on t h e  v i b r a t i o n a l s t a t e t o which E ^ corresponds.  They a r e d e f i n e d b y t h e  following equations:  V + ih S ' K ^ a J ^ X v - ' I\|V> V  V  " <v|u |V'Xv|^|v>}/hV , a y  v v  '  2.3a  " < KJ > 2 E < V | ^ | V ' X V ' l ^ l v X h v ^ , V  V +  ,  V + 2ih£ Kv|y |v«XV|fc V ,  | V > - <v|y |VXV|^|v>}/hv  a e  a Y  where a , 3 , Y take on v a l u e s x . y . z i n c y c l i c o r d e r and h v * *  1  vv  J  v v f  , =E °- E ° . V  V  V I f t h e r o t a t i o n a l a n g u l a r momenta o p e r a t o r s P^ a r e d e f i n e d i n u n i t s of h then t h e a and T „ . have u n i t s o f energy a3 a3y<S 2 n  r i g h t hand s i d e o f e q u a t i o n s 2 . 3 a by h  (one must m u l t i p l y t h e  and t h e r i g h t hand s i d e o f e q u a t i o n  9  2.3b by h^) .  One can t h e n m u l t i p l y e q u a t i o n 2.3 by 10°/h  r o t a t i o n a l e n e r g i e s are measured i n MHz, as w i l l be the if  so t h a t  the  coefficients  t h i s f a c t o r i s a l s o absorbed i n t o t h e i r d e f i n i t i o n s . The second term i n e q u a t i o n 2.3 has e x a c t l y the same form as  r o t a t i o n a l Hamiltonian of a " r i g i d r o t o r " ; i . e . ,  a "molecule" i n which  the atoms a r e p o i n t masses w i t h f i x e d r e l a t i v e p o s i t i o n s .  The t h i r d  term c a n , a t l e a s t i n p a r t , be a s s o c i a t e d w i t h the e f f e c t s o f fugal distortion If  the  centri-  (19).  the l a t t e r i s n e g l e c t e d f o r the moment, t h e n the  remaining  r o t a t i o n a l p a r t o f the H a m i l t o n i a n , denoted H , can be s i m p l i f i e d by means o f an o r t h o g o n a l t r a n s f o r m a t i o n (a r o t a t i o n o f the m o l e c u l e a x i s system w i t h r e s p e c t t o the m o l e c u l a r frame i n t o the p r i n c i p a l i n e r t i a l a x i s system)  H  r  = (d') P x v x  2  + (a') P y v y  2  fixed  so-called  giving:  + (a') P z v z  2.4  2  where the dependence o f the c o e f f i c i e n t s , w h i c h are c a l l e d  rotational  c o n s t a n t s , on v i b r a t i o n a l s t a t e has now been e x p l i c i t l y d e n o t e d . If  any two o f the r o t a t i o n a l c o n s t a n t s i n e q u a t i o n 2.4 are  (a symmetric top)  equal  t h e n the r e s u l t i n g S c h r o d i n g e r e q u a t i o n can be s o l v e d  e x a c t l y t o o b t a i n c l o s e d e x p r e s s i o n s f o r the wave f u n c t i o n s and e i g e n values.  I n the more g e n e r a l asymmetric top case ( a l l  a c l o s e d s o l u t i o n does n o t e x i s t .  It  three a's  i s p o s s i b l e , however,  different)  to express  the asymmetric top wave f u n c t i o n s as a l i n e a r c o m b i n a t i o n o f the rotor functions.  T h e r e f o r e , a m a t r i x r e p r e s e n t a t i o n of the  symmetric  asymmetric  top H a m i l t o n i a n i n terms o f symmetric r o t o r b a s i s f u n c t i o n s can be i  d i a g o n a l i z e d t o g i v e the c o r r e c t asymmetric top " r i g i d r o t o r " Such a r e p r e s e n t a t i o n i s i n i t i a l l y d i a g o n a l i n J ,  energies.  the t o t a l r o t a -  10  t i o n a l a n g u l a r momentum quantum number, because P  2  always commutes w i t h  Each m a t r i x c o r r e s p o n d i n g to a p a r t i c u l a r v a l u e o f J  H .  o f o r d e r 2J+1.  i s square and  F u r t h e r f a c t o r i z a t i o n i s a c h i e v e d by a p p l y i n g a Wang t r a n s -  f o r m a t i o n w h i c h r e d u c e s each J b l o c k i n t u r n t o f o u r s u b m a t r i c e s h a v i n g the symmetries o f the  group ( 2 1 , 2 2 ) .  These a r e then c o n v e n i e n t l y  d i a g o n a l i z e d by the method o f c o n t i n u e d f r a c t i o n s It  i s c o n v e n t i o n a l t o r e l a b e l the x , y , z axes o f the p r i n c i p a l i n e r t i a l  a x i s system (the one i n w h i c h the a (a^)  >(a^) >(a^) -  v  (22).  v  vanish)  as a , b , c ,  such t h a t  There a r e s i x d i f f e r e n t ways o f i d e n t i f y i n g  v  with x,y,z.  D  ap  a,b,c  The most c o n v e n i e n t f o r a near p r o l a t e ( ( a ' ) «(a') ) b v c v  J  c  asymmetric top i s : x -> b , y ->- c , z -> a T h i s i s known as the I rewritten  representation (23).  + Bv p}b  2  where ( a ' ) , ( a ' ) , ( a ' ) a v b v c v v  can t h e n be  as:  H r = Av P a  A , B  E q u a t i o n 2.4  2.5  + Cv P c 2  have been changed t o the more c o n v e n t i o n a l 6  ,C. v  v  The c a l c u l a t i o n o f t h e e i g e n v a l u e s o f a change of v a r i a b l e s . suggested.  i s g r e a t l y f a c i l i t a t e d by  S e v e r a l d i f f e r e n t ways o f d o i n g t h i s have been  One o f t h e most u s e f u l i s t h a t i n t r o d u c e d by Ray ( 2 4 ) .  He  d e f i n e d an asymmetry parameter K b y :  K  =  2B  - A - C v_ _v v v  v  w h i c h v a r i e s from -1 i n the p r o l a t e l i m i t ( B limit  (A^ = B^).  be w r i t t e n  as:  „. 6 ,  2  v  = C^)  t o +1 i n the  oblate  The asymmetric top " r i g i d r o t o r " energy l e v e l s can t h e n  11  E (A ,B ,C ) = 1/2(A + C ) J ( J + 1 ) + 1/2(A - C ) E ( K ) r v ' v v v v v v J  2.7  t  K  where E ( K ) i s e s s e n t i a l l y the energy o f a r i g i d r o t o r w i t h  -1 1 K  rotational  c o n s t a n t s 1, K , and - 1 . The symbol J  K  -1 1 K  p r o v i d e s a u n i q u e l a b e l f o r the r o t a t i o n a l energy  l e v e l s o f an asymmetric top m o l e c u l e ( 2 3 ) . The t o t a l r o t a t i o n a l a n g u l a r momentum quantum number J has a l r e a d y been m e n t i o n e d . v a l u e s 0,1,2, **. -  It  can t a k e on  F o r t h e s p e c i a l case of a symmetric t o p , t h e r e i s a  second good quantum number K,  a s s o c i a t e d w i t h the p r o j e c t i o n o f the  r o t a t i o n a l a n g u l a r momentum a l o n g the symmetry a x i s o f the t o p .  It  total can  t a k e on v a l u e s 0,1,2,"'*,J and t o g e t h e r w i t h J s p e c i f i c a l l y i d e n t i f i e s each symmetric top r o t a t i o n a l energy l e v e l . t o p , the pseudoquantum numbers  and  F i n a l l y , f o r the asymmetric  r e p r e s e n t the v a l u e s o f K a s s o -  c i a t e d w i t h the p a r t i c u l a r energy l e v e l s i n , r e s p e c t i v e l y , t h e  limiting  p r o l a t e and o b l a t e t o p s w h i c h c o r r e l a t e w i t h the asymmetric top  level  under c o n s i d e r a t i o n . A somewhat d i f f e r e n t f o r m u l a t i o n , t h a t i s p a r t i c u l a r l y u s e f u l  if  the m o l e c u l e i s c l o s e to" one of t h e p r o l a t e o r o b l a t e l i m i t i n g c a s e s , i s "  * t h a t due t o Wang ( 2 1 ) . p  _  v " v 2A - B C  by: 2.8  B  V  which v a r i e s  He d e f i n e d an asymmetry p a r a m e t e r b^  V  - C V  from 0 i n the p r o l a t e l i m i t t o -1 i n the o b l a t e l i m i t .  r o t a t i o n a l energy can then be w r i t t e n  The  as:  * A d i f f e r e n t d e f i n i t i o n o f Wang's asymmetry parameter i s more u s e f u l f o r .near o b l a t e asymmetric t o p s , namely: b  O  = (A  V  - B )/(2C V  V  - A V  - B ) V  12  E (A ,B r v v  ,C ) = 1/2(B + C ) J ( J + 1 ) + | A - 1/2(B + C )}E(b ) v v v <v v v ' p J  2.9  t  K  where E(b^)  is effectively  1, ~bp> and b p -  K  the energy o f a r o t o r w i t h r o t a t i o n a l  I n t h e g e n e r a l c a s e , the r e d u c e d e n e r g i e s  +  -1 1  o r E ( b ^ ) ) must be c a l c u l a t e d by m a t r i x d i a g o n a l i z a t i o n . case o f a n e a r p r o l a t e asymmetric t o p , however, e v a l u a t e d by p e r t u r b a t i o n t h e o r y .  The r e s u l t  E(b^)  constants  (either E ( K )  I n the  may be  special  conveniently  is:  E ( b ) = K . + C,b + C „ b + p -1 1 p 2 p 2  2.10  2  where K ^ has been p r e v i o u s l y d e f i n e d and the C.. a r e c o e f f i c i e n t s have been t a b u l a t e d If  (25).  the asymmetry i s v e r y s l i g h t t h e n e q u a t i o n 2.10 may be  a f t e r the second t e r m .  terminated  I n t h i s i n s t a n c e , t h e p a t t e r n o f energy l e v e l s  e s s e n t i a l l y the same as t h a t found i n the p r o l a t e symmetric t o p , t h a t t h e r e a r e now two c l o s e l y spaced l e v e l s f o r each J i n s t e a d of j u s t one.  asymmetry s p l i t t i n g o f  # 0 levels,  f o r a g i v e n b^, d e c r e a s e s  found t h a t the l o w J  terms  levels  The K ^ = 0 l e v e l s n e v e r  i n c r e a s i n g K_^ and i n c r e a s e s w i t h i n c r e a s i n g is generally  = 1  W i t h i n c r e a s i n g asymmetry, h i g h e r  a l s o d e v e l o p t h i s "asymmetry s p l i t t i n g " .  is  except  corresponding to  i n the e x p a n s i o n become i m p o r t a n t and s i m u l t a n e o u s l y h i g h e r  It  that  split;  with  J.  r o t a t i o n a l energy s t a t e s  of  r e a l asymmetric top m o l e c u l e s can be r e a s o n a b l y w e l l accounted f o r  in  terms o f e i t h e r e q u a t i o n 2.7 o r 2 . 9 .  espec-  However,  at h i g h e r J v a l u e s ,  i a l l y i n m o l e c u l e s w i t h one o r more l a r g e r o t a t i o n a l c o n s t a n t s , the of c e n t r i f u g a l d i s t o r t i o n can become q u i t e s i g n i f i c a n t .  It  r e a d i l y t r e a t e d by r e w r i t i n g the r o t a t i o n a l H a m i l t o n i a n a s :  i s most  effect  13  H. = H - EV „ = H + H, R r d where  I?  2.11a  =AP + BP? + C P v a v b v c 2  r  2.11b  2  and d  a,3,Y> .  aByo a 3 Y °  5  T h e , s o l u t i o n of the H i m a t i o n and  problem i s then t a k e n as a z e r o t h o r d e r a p p r o x -  i s t r e a t e d as a ( f i r s t o r d e r )  perturbation.  S i n c e t h e o p e r a t o r s P^ do n o t commute, t h e sum i n e q u a t i o n 2 . 1 1 c has e i g h t y one t e r m s .  However, by symmetry arguments, i t c a n be shown t h a t  o n l y t h e twenty one t o t a l l y symmetric terms w i l l c o n t r i b u t e t o t h e r o t a t i o n a l energy t o f i r s t o r d e r ( 2 6 ) .  F u r t h e r m o r e , many o f t h e c o e f f i c i e n t s  o f t h e s e twenty one terms a r e e q u a l (see d e f i n i t i o n , e q u a t i o n 2.3b) w i t h the r e s u l t t h a t one i s f i n a l l y l e f t w i t h o n l y n i n e d i s t i n c t q u a r t i c c o n stants : T  a a c t a ' aa33 T  =  T  33aa' a3a3 T  =  T  a33a  =  T  3a3a  =  T  3aa3  2 , 1 2  (a,3 = a , b , c and a#3) The v a r i o u s s u r v i v i n g t e r m s , P^P^P P^, o f  may t h e r e f o r e be a r r a n g e d i n t o  n i n e g r o u p s , each w i t h i t s own x c o e f f i c i e n t . A f u r t h e r r e d u c t i o n o f 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 s i x groups o f terms i s a c h i e v e d by c o n s i d e r i n g t h e commutation r u l e s f o r t h e r o t a t i o n a l a n g u l a r momentum o p e r a t o r s .  The a p p r o p r i a t e r e l a t i o n s were f i r s t  by K i v e l s o n and W i l s o n ( 2 6 ) .  They a r e :  (P P + P P )• = 2 ( P PZ+PZP ) + 3P - IP - 2P a 3 3 a a 3 3 a y a 3 Q  2.13  a  where a*3*Y and w i t h a , 3 , Y  t  o  D  e  t a k e n i n c y c l i c o r d e r as a , b , c .  the use o f e q u a t i o n 2.13 i t i s then p o s s i b l e t o e l i m i n a t e t h e T  a3a3 W 3 a (  P  P  ) 2  f r o m t  e  m  S  derived  V  T  h  e  coefficients  T  a  6  a  g  are i  Through  14  those of  2 2 2 2 2 2 2 (P P„+P.P ) and terms i n P , P, and P a r e i n t r o d u c e d . a 8 8 a a b c  These  new q u a d r a t i c terms a r e then absorbed i n t o the " r i g i d r o t o r " p a r t o f r o t a t i o n a l H a m i l t o n i a n w h i c h must now be r e d e f i n e d  H  R  =  + H'  as: 2.14a  d  H'r = A v' P a + B v* Pb + Cv* P c 2  2.14b  2  a,8  T'  =  T  aaaa  aaaa  aa88  aa88  T  and  2  2 7  *d where  the  T  +  a,8 2x  a8a8  *  2.15  6  A'  = A  )  2.16a  B  = B + 1/4(3T - 2T , - 2T , . ) v acac bcbc abab  2.16b  v 1  v  v  + 1/4(3T,  a  = a,b,c  .  bcbc  - 2T . , - 2T  abab  acac  C' = C + 1/4(3T , , - 2 T , , - 2x ) v v abab bcbc acac  2.16c  S i n c e the new r o t a t i o n a l c o n s t a n t s c o n t a i n a 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 n t r i b u t i o n , e f f e c t i v e moments o f i n e r t i a (see s e c t i o n 2.4)  derived  from  them i n c l u d e a n o t h e r a m b i g u i t y i n a d d i t i o n to t h a t a r i s i n g f r o m p u r e l y vibrational  effects.  F o r the s p e c i a l case o f a p l a n a r m o l e c u l e s t i l l can be a c h i e v e d u s i n g the r e l a t i o n s g i v e n below , bcbc  T,  T  cccc  =  T  (27,28):  acac = 0  =  +  \A,  T  further s i m p l i f i c a t i o n  2.17a  + 22C / c l\ \ T . , ., . + c i _T x _ . ^ .+ +( C aaaa „ aabb — I I bbbb A~B" A B W l  u  2.17b  0  i  T  bbcc  =  (f^bbbb  +  (f^aabb  2.17c  15  x aacc = IC I\ T aaaa  +  T  / C \  -  2  T  ^ 2.17d .i/a  aabb  These were o b t a i n e d by a d e t a i l e d c o n s i d e r a t i o n of the K i v e l s o n and W i l s o n e x p r e s s i o n f o r the t a u s  (equation 2.68).  equations 2.15, to r e w r i t e usually  k  H  T  A  A  A  »  A  T  1 / 4  i n terms o f o n l y f o u r independent  bbbb» a a b b T  = haaa[ a P  +  (  C  /  a n c  A  )  4  p  B  )  A  p  T  bbbb[ b  +  T  aabb [ ( 2 C / A B ) P  +  (  C  /  *  C  +  P  They can be u s e d , t o g e t h e r w i t h  T  +  c  +  taus;  abab'  (  C  /  A  )  '  (  ( C / B ) 2 ( P  a c  P  P  b  p 2  c  + P  + P  c a>] ?  c b P  2 )  ] 2.18  4  +  +  T  2  a b  ( P  P  abab[ ( a b 2  P  P  + P  + P  2  b  p 2 )  4  + (C/B)  +  ( C / A )  2  2  (PV+PV)  ( P  b c P  + P  c b>] P  b a>]} P  The e q u i l i b r i u m v a l u e s o f the r o t a t i o n a l c o n s t a n t s s h o u l d be used i n e q u a t i o n s 2.17 and 2 . 1 8 .  In p r a c t i s e , these are very r a r e l y  so i n s t e a d , the 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 used.  (A^, B^,  tV)  available, are  generally  T h i s has been found t o be a v e r y good a p p r o x i m a t i o n f o r w e l l b e -  haved m o l e c u l e s ; i . e .  f o r m o l e c u l e s t h a t do n o t have v e r y l a r g e c e n t r i -  fugal distortion effects.  If  i t i s n e c e s s a r y t o c a r r y the a n a l y s i s  h i g h e r o r d e r , however, e i t h e r because the d i s t o r t i o n i s i n h e r e n t l y  to large  o r because h i g h J l e v e l s a r e b e i n g i n c l u d e d , t h e n t h i s f o r m u l a t i o n i s i n s u f f i c i e n t and the more g e n e r a l one d i s c u s s e d below must be u s e d . F o r the g e n e r a l asymmetric top i t was l o n g thought t h a t the minimum number o f independent f i r s t o r d e r q u a r t i c c o n s t a n t s was s i x .  Recently,  however, Watson has shown t h a t t h e r e i s an a d d i t i o n a l r e l a t i o n s h i p  that  16  reduces t h i s number to f i v e reduction i s possible  (29).  He has a l s o shown t h a t no f u r t h e r  (30).  There a r e many d i f f e r e n t s e t s o f f i v e q u a r t i c c o n s t a n t s t h a t c o u l d be u s e d .  Only one o f the s e v e r a l c o n v e n i e n t f o r m u l a t i o n s i s  reproduced  here: H  H  K  =  T  H  +  = A P r v a  *d = V  H  2  d  2  ~ 9 ~ + B PT + C P v b v c - ^ K ^ a 2  where  ?  and  " ¥  l  2 ?  "  2 6  P  P  9 9 ?  2.19c  A - A ' + 16R, v v 6  2.20a  B = B* - 1 6 R , ( A - C ' ) / ( B - C * ) v v 6 v v v v  2.20b  C = C + leR^A'-BM/^B'-C') v v 6 v v v v  2.20c  R, = 1/64Jx' + T' - 2T* } 6 I bbbb cccc bbcc'  2.20d  A_ = -1/8|T'  2.21a  J  ,  ,  + T*  i bbbb  |  . cccc'  (  6  T  1  = -1/16JT*  J K  a  /( b- c>  A = -l/4Jx' . + T» + T' } + l/4|x» K bbbb cccc aaaa' aacc  v  9  y  A = 3/8|x' + x' } - 1/4|T' + x' + x' } JK ' bbbb cccc' « aacc aabb bbcc'  S  1  2 19b  ,  with  -  .  - x'  < bbbb  + x' aabb  + x' } bbcc'  }  2.21d  ,  + l/8jx' - x' + x* (2A'-B'-C')/(B -C')i aacc aabb bbcc v v v v v ' ,  1  2.21c  ;cccc'  = l/8x' (B'-A )/(B -C') + l/8x' (C'-A')/(B'-C) bbbb v v v v cccc v v v v ,  2.21b  2.21e  17  I t w i l l be noted t h a t , as b e f o r e , the r e d u c t i o n has g e n e r a t e d s m a l l terms 2 2 2 i n P a , P,b and P c t h a t had t o be absorbed i n t o the r o t a t i o n a l  constants,  The H a m i l t o n i a n s d i s c u s s e d above have been found t o g i v e a v e r y good account o f t h e l o w t o medium J r o t a t i o n a l e n e r g i e s o f a l a r g e number o f molecules  (31).  When h i g h J s t a t e s , e s p e c i a l l y i n m o l e c u l e s w i t h  c e n t r i f u g a l d i s t o r t i o n , a r e c o n s i d e r e d , however, i t can become  large  necessary  t o e x t e n d t h e r o t a t i o n a l H a m i l t o n i a n t o i n c l u d e terms o f t h e s i x t h (and even h i g h e r )  power i n t h e a n g u l a r momentum components.  Watson has p o i n t e d  out t h a t i n g e n e r a l t h e r e a r e seven l i n e a r l y independent s e x t i c c e n t r i f u g a l d i s t o r t i o n constants  (32).  He has a l s o shown t h a t the n o n - t o t a l l y  symmetric q u a r t i c terms n e g l e c t e d i n t h e f i r s t o r d e r t r e a t m e n t m a t i c a l l y absorbed i n t o t h e s e x t i c ( o r h i g h e r ) s e p a r a b l e from them.  are a u t o -  terms a n d , i n d e e d , a r e i n -  A c o n v e n i e n t form f o r t h e s e x t i c p a r t o f t h e r o t a t i o n a l  H a m i l t o n i a n , and t h a t used i n t h i s work i s : ~  6  42  24  6  4 2 2 2.22  + h P lP (pl-P ) JKT I a b c 2  T  2  2  + (P -P )P | + h |P (P -P ) b c a> K< a b c 2  2  2  4  A l t h o u g h some attempt has been made t o r e l a t e  2  2  + (P -P )P } b c a' 2  2  4  the s e x t i c c o e f f i c i e n t s to  the c u b i c terms i n t h e v i b r a t i o n a l f o r c e f i e l d (33) i t i s p r o b a b l y b e s t t o r e g a r d them as f i t t i n g p a r a m e t e r s .  The q u a r t i c c o e f f i c i e n t s on the  o t h e r hand have been used w i t h some s u c c e s s i n t h e d e t e r m i n a t i o n o f q u a d r a t i c p o t e n t i a l constants ( 3 4 ) . The d i s t o r t i o n c o n t r i b u t i o n s t o t h e t o t a l r o t a t i o n a l e n e r g y ,  correct  t o f i r s t o r d e r , may be o b t a i n e d by e v a l u a t i n g the e x p e c t a t i o n v a l u e s o f the d i s t o r t i o n H a m i l t o n i a n i n t h e " r i g i d " asymmetric r o t o r b a s i s  functions.  18  For example, i f t h e H a m i l t o n i a n g i v e n i n e q u a t i o n s 2.19 i s used then t h e f i r s t o r d e r r o t a t i o n a l energy i s ( 3 5 ) : E  R "  E  E  r  +  E  d  = l/2(B  r  *d  =  <^d>  =  v  2.23a + C )J(J+l) + JA v  "V  2 ( J + 1 ) 2  + (26 /b )J(J l){E(b ) J  p  +  p  "  A  JK  v  - 1/2(B  J ( J + 1 )  v  + C )(E(b )  2.23b  v  < a > " K< a> P  A  ?  2  '  2  3  c  - ( F > [ + 2 ( 6 / b ) { E ( b ) < P > - <P«>} 2  K  p  2  p  where b i s now g i v e n b y (C -B ) / ( 2 A -B -"c ) and t h e terms i n P and p v V V V V c 2 ~ P^ were e l i m i n a t e d from t h e e x p r e s s i o n f o r E^ w i t h t h e a i d o f t h e 2  following relations  (26,36):  <P >= 2  1/2JCJ+1) - l / 2 E ( b ) - ( ^ ) { E ( b )  - <P )}  2.24a  <P >=  1/2J(J ) - l/2E(b ) + ( ^ ) { E ( b )  - <P >}  2.24b  2  p  +1  2  p  p  2  p  A s i m i l a r p r o c e d u r e , b u t b a s e d i n s t e a d o n H'^_ + H ^ ( e q u a t i o n s 2.14 1  and 2 . 1 8 ) , may be used t o o b t a i n t h e f i r s t o r d e r r o t a t i o n a l energy o f a w e l l behaved p l a n a r m o l e c u l e .  The r e s u l t i n g e x p r e s s i o n s , l i k e  equations  2 . 2 3 , can p r o v i d e a c o n v e n i e n t s t a r t i n g p o i n t f o r a l e a s t squares If  i t i s necessary  t o i n c l u d e s e x t i c (and h i g h e r ) r+*t  r i g i d r o t o r H a m i l t o n i a n ( i . e . H„ = H R  terms i n t h e n o n -  /St/  + H, + H r  analysis.  d  s  + •••) then a s i m p l e  first  v  o r d e r t r e a t m e n t w i l l i n g e n e r a l n o t be c o m p l e t e l y adequate.  T h i s i s because  the c o n t r i b u t i o n s t o t h e r o t a t i o n a l energy from the o f f - d i a g o n a l  elements  i n t h e " r i g i d " asymmetric r o t o r b a s i s m a t r i x r e p r e s e n t a t i o n o f H  c a n be  of s i m i l a r magnitude t o t h e d i a g o n a l s e x t i c elements  R  ( 3 5 ) . A method f o r  19  handling such "higher order" effects w i l l be discussed later (see Chapter 6). The f i r s t order sextic distortion energy i s given by:  E  s " <*s> - H j J  3 ( J + 1  S  H  JK  j 2 ( J + 1 ) 2  < a> P  2  a  J  (- V JK 1/  3 +  +  H  KJ  J ( J + 1 )  < a> P  2h (-l/b )J (J+l) J (b ) - <P )}  + \(P )+ +2  >  h  2  p  J(J+1)  E  2  p  9  A  2  i V a>- <V* E(  <P  -  2 3 d  The molecular rotational energy states which have just been considered on a theoretical basis can be experimentally investigated by inducing transitions between them with, for example, microwave radiation.  Of the  great multitude of potential radiation induced transitions most are essent i a l l y "forbidden" and the rest occur with widely varying i n t e n s i t i e s .  Spec-  i f i c a l l y , i t can be shown that the probability of a radiation induced transi t i o n between two rotational states J„ K  and J ' ,  -1 1 K  K  , i s proportional to  -1 1 K  the following matrix element ( 3 7 ) : Kj.K^.KjylJ'.K^.Kj^  2  = ^|<J,K_ ,K |y |j',K; ,Kj>| 1  1  F  2  i  2.25  where y„ r i s the F component of the molecular dipole moment referred to space fixed axes (X,Y,Z).  Since the y are clearly dependent on the orientr  ation of the molecule i n space, i t i s much more convenient to rewrite the above matrix element i n terms of the components of the dipole moment referred to the molecule fixed axes (y ). This can be accomplished using g the following relationship: y_ yg 2.26 F L~i Fg g =  P  H  20  where the $_ a r e the d i r e c t i o n c o s i n e s between the m o l e c u l e f i x e d and the Fg space f i x e d a x i s s y s t e m s . K J . K ^ . K J M J J '  , K ^ , K J > |  One can then w r i t e : (J.K^.K^J  = J ^ y ^ S  2  , K j ) / (2J+1)  1  2.27  g where the S  a r e c a l l e d l i n e s t r e n g t h s and a r e d e f i n e d b y :  V^-rV^-i^P  F  The summation o v e r  K ' -i' i» jl*F l » Ii» i' j>l J  S  =  K  K  M  J,  K  K  M  2  2  g  -  2 7 a  >V j  and  M  i n equation 2.27a i s necessary to take i n t o  account a l l o f t h e p o s s i b l e t r a n s i t i o n s w h i c h i n t h e absence o f an e x t e r n a l f i e l d w i l l be d e g e n e r a t e ; M  i s the quantum number f o r the component o f  the t o t a l a n g u l a r momentum a l o n g some space f i x e d a x i s , and t a k e s on values It  J,J-l,•••,-J. t u r n s out t h a t the summation over g i n e q u a t i o n 2.27 i s  redundant  because at most o n l y one o f the t h r e e p o s s i b l e l i n e s t r e n g t h s can be n o n zero.  T h i s has prompted a c o n v e n i e n t c l a s s i f i c a t i o n o f t r a n s i t i o n s as  a - t y p e s , b-types and c - t y p e s a c c o r d i n g t o whether they are a l l o w e d by a nonzero y^,  o r y^  respectively.  The l i n e s t r e n g t h s may be r e a d i l y e v a l u a t e d u s i n g r i g i d r o t o r wave functions. of  K  E x t e n s i v e t a b l e s o f S ' s have been c o m p i l e d f o r v a r i o u s g  values  (38). There i s a r i g o r o u s s e l e c t i o n r u l e f o r J ,  namely:  AJ = 0,±1  2.28  The AJ = -1 t r a n s i t i o n s are s a i d to b e l o n g t o a P - b r a n c h , the AJ = 0 ones a Q-branch, a n d . t h e AJ = +1 ones an R-branch.  Similar  selection  21  r u l e s can be f o r m u l a t e d f o r the pseudoquantum numbers  and K^.  s i n c e t h e r e i s a c o n s i d e r a b l e v a r i a t i o n i n the i n t e n s i t y o f the  However allowed  t r a n s i t i o n s , i t i s g e n e r a l l y more p r o f i t a b l e t o r e f e r d i r e c t l y t o one o f the l i n e s t r e n g t h t a b l e s . 2.2  N u c l e a r Quadrupole C o u p l i n g F o r an a n a l y s i s o f a m o l e c u l a r r o t a t i o n a l spectrum t o be c o m p l e t e ,  i t must account f o r any h y p e r f i n e s t r u c t u r e t h a t may be p r e s e n t .  Such  s t r u c t u r e i s a v e r y common o c c u r r e n c e and i s produced by a c o u p l i n g o f  the  r o t a t i o n a l a n g u l a r momentum to o t h e r a n g u l a r momenta i n h e r e n t i n the m o l e c u l e . These may i n c l u d e e l e c t r o n s p i n and o r b i t a l a n g u l a r momenta as w e l l as n u c l e a r s p i n a n g u l a r momenta.  S i n c e most s t a b l e m o l e c u l e s have  ground  e l e c t r o n i c s t a t e s , however, o n l y the l a t t e r i s g e n e r a l l y of i n t e r e s t  to  the microwave s p e c t r o s c o p i s t . Any n u c l e u s w i t h s p i n g r e a t e r t h a n 1/2 has an e l e c t r i c q u a d r u p o l e * moment  w h i c h may i n t e r a c t w i t h the e l e c t r i c f i e l d g r a d i e n t s produced at  t h a t n u c l e u s by the o t h e r charges i n the m o l e c u l e .  The r e s u l t i n g h y p e r -  f i n e s t r u c t u r e i s t y p i c a l l y of the o r d e r o f t e n s o f MHz, b u t v a r i e s  greatly  a c c o r d i n g t o the n u c l e u s and t r a n s i t i o n i n v o l v e d . The complete H a m i l t o n i a n f o r the i n t e r a c t i o n o f a s i n g l e q u a d r u p o l a r n u c l e u s w i t h the m o l e c u l a r r o t a t i o n may be w r i t t e n as  (39): 2.29  x,y,z  The e l e c t r i c monopole moment i s j u s t the n u c l e a r charge eZ. There i s no e x p e r i m e n t a l e v i d e n c e of a n o n z e r o n u c l e a r e l e c t r i c d i p o l e moment.  22  where t h e t e n s o r VE_ i s t h e e l e c t r i c f i e l d g r a d i e n t , a t t h e q u a d r u p o l a r n u c l e u s , due t o the e x t r a n u c l e a r charges and Q_ i s t h e n u c l e a r q u a d r u p o l e moment t e n s o r , w i t h components d e f i n e d b y :  Q  ij  =  y  p(3x  i j " X  i j  6  r  2  )  d  T  2  -  2 9 a  where t h e i n t e g r a l i s o v e r t h e n u c l e a r volume and x^ r e p r e s e n t s t h e X , Y and Z space f i x e d c o o r d i n a t e s o f a p o i n t i n t h e n u c l e u s , a t w h i c h t h e charge d e n s i t y i s p. The n e t e f f e c t o f t h i s i n t e r a c t i o n i s a c o u p l i n g o f t h e r o t a t i o n a l a n g u l a r momentum  and t h e n u c l e a r s p i n a n g u l a r momentum J . t o form a  r e s u l t a n t F_ a c c o r d i n g t o : F =J + I  2.30 2  such that ( i n u n i t s o f h ) < F , M | F | F , M > = F(F+1) F  2  2.30a  F  where t h e quantum number F i s r e s t r i c t e d t o t h e v a l u e s : J + I , J + I - l , • • • , |j-l|.  I f t h e c o u p l i n g i s n o t too s t r o n g , such t h a t J can s t i l l be r e -  garded as a good quantum number, t h e n C a s i m i r (40) has shown t h a t t h e q u a d r u p o l e H a m i l t o n i a n may be r e w r i t t e n i n t h e f o l l o w i n g , more  tractable  form:  l  H  =  {2J(2J-l)I(2I-l)}l  3 (  ^  ) 2  +  3  /  2  ^  -  I*' * 2  2  -  3  1  where eQ i s a measurable n u c l e a r c o n s t a n t c a l l e d t h e charge w e i g h t e d e l e c t r i c q u a d r u p o l e moment, and i s d e f i n e d b y : eQ = <I ,^=11 Q  z z  11 . M ^ O  2. 31a  w h i l e q j i s t h e ZZ component o f t h e e l e c t r i c f i e l d g r a d i e n t t e n s o r over the r o t a t i o n a l s t a t e J  —11  ,M=J i.e.  .  averaged  23  = O.K^.K^M^JIV^IJ.K^.K^M^J)  Q J  2  2.31b  2  with V ^ ^ = 3 V/3Z  = -(VE)^.  The eigenvalues of the operator enclosed  in brackets i n equation 2.31 are then readily determined and the following expression i s obtained for the f i r s t order quadrupole energy ( 4 0 ) : E  Q " {2J(2J-l)I(2I-l)}l  - JCJ+DKI+1)}  3 / 4 C ( C + 1 )  2  -32  with C = F(F+1) - J(J+1) - 1(1+1)  2.32a  This i s not a suitable expression for the calculation of quadrupole energies, however, because the f i e l d gradient q^ i s referred to the space fixed Z-axis, and i s therefore a function of rotational state.  I t can be re-  written i n terms of molecule fixed (principal i n e r t i a l axis) f i e l d gradients using the previously introduced direction cosines. S p e c i f i c a l l y : q  J  =  Z ) gg ' -i' i' J l z l ' -r i' j q  < J  K  = J  M  K  $  g  J  K  K  M  = J >  -  2  33  g=  a,b,c where q  gg  =3  2 2 V/3g i s essentially independent of rotational state and only  s l i g h t l y dependent on vibrational state.  There are no cross terms included  i n equation 2.33 because a l l of the matrix elements of the form (*' *2b^ Za  may be shown by a symmetry argument (41,39)  to be zero to f i r s t order.  The remaining nonzero matrix elements i n equation 2.33 may be expressed i n terms of the tabulated l i n e strengths (41), or alternatively, the following relation may be used: < ' - l ' l ' J = l Z g l ' - l ' l ' J > - { (J l (2J 3T} J  K  K  M  J  $  J  K  K  M  = J  2  +  <J  +  + (2J+3)"  1  >-1 1 K  >K  l ?  g  1 J >K  -1 » 1> K  2.34  24  One can then w r i t e :  J  q  =  S { ( J + l ) (2J-t-3)}< » -1 » 1 l g I » - 1 » 1> § a,b,c J  K  K  P  J  K  K  2  '  3  5  =  where t h e (2J+3) * terms have been e l i m i n a t e d by assuming t h a t t h e q  *  s a t i s f y Laplace s equation , i . e . V V =q 2  aa  + q,. + q bb  ^cc  =0  2.36  F i n a l l y , w i t h t h e use o f e q u a t i o n s 2 . 2 4 , 2 . 3 5 and 2.36 t h e f i r s t  order  q u a d r u p o l e energy o f e q u a t i o n 2.32 may be r e w r i t t e n as ( 3 9 , 4 2 ) : h  1 Q  =  3C(C+1)-4J(J+1)I(I+1) 8 I ( 2 I - l ) J ( 2 J - l ) ( J + l ) ( 2 J + 3 ) {{3<P V V a > - J"( J^+'l ") }a a 2  J  +  (l/b )KpJ>-E(b )|( p  where the x  p  X b b  r  -  X j  /  X c c  2.37  )}  which are c a l l e d quadrupole coupling constants are defined  by:  X = eQq gg gg  2.37a  I f there i s more than one quadrupolar nucleus i n a molecule associated hyperfine structure w i l l usually be very complex. multiple system (and that encountered  then the  The simplest  i n t h i s work) occurs when there are  only two quadrupolar n u c l e i , one of which couples much more strongly than the other.  The general theory for t h i s system has been worked out by  Bardeen and Townes (43) ; i t i s outlined below.  *  T h i s i s s t r i c t l y v a l i d o n l y i f t h e charges p r o d u c i n g t h e p o t e n t i a l V are e n t i r e l y o u t s i d e t h e n u c l e u s i . e . have z e r o p r o b a b i l i t y of o c c u r r i n g i n t h e n u c l e a r volume. E x p e r i m e n t a l e v i d e n c e s u g g e s t s t h a t i t i s v a l i d t o a good a p p r o x i m a t i o n .  25  L e t 1^ nucleus,  represent  and  1^  Ll  the s p i n a n g u l a r momentum of the s t r o n g l y  t h a t of the weakly c o u p l e d n u c l e u s .  1  + I  where the a s s o c i a t e d  E  Q  2  1  1  Q  1  J  K  K  F  order p e r t u r b a t i o n  I 1  '  I  ' ' Fl F  2  =  M  F F  Q  1  +  1  +  1  order  1  1  by:  1  2  2. 39  F  energy t h a t i s p a r t i c u l a r l y  been d e r i v e d  (1/  j{ <p2)- J ( 3  V{< a>- V}{ bb P  E(  X  (1)  X  2  - cc X  J3A ( A ^ D - 4 1 2 ( I + l ) F ( F ^ l ) } ^  (44):  J +  ( 1 )  l)}  X a a  (l)  }|  2.40  (A +1)-4J (J+l) F^ (Fj+1)}  x  2  1 6 I ( 2 I - 1 ) J ( 2 J - 1 ) (J+l) ( 2 J + 3 ) F ( 2 F - 1 ) ( F + 1 ) (2F +3) 2  2  1  ...xj{ <p2>- J 3  where  that f o r 2  ^Q |J,K_ ,K ,F ,I ,I ,F,M >  for this f i r s t  ( A + 1 ) - 4 I . (I.+l) J(J+1) o o 1 1 8I (2I -l)J(2J-l)(J+l)(2J+3)  energy i s g i v e n  2  Then  3A  1  +  values  2  Q  s u i t a b l e f o r s p e c t r a l a n a l y s i s has  .  2  i s the quadrupole H a m i l t o n i a n f o r n u c l e u s 1 and H  A closed' e x p r e s s i o n  E  take on the  l  < ' -l' i' i'  =  F may  and  F + I , F + I - 1 , - | F - I | respectively.  1  n u c l e u s 2 the f i r s t  -38a 2.38b  2  quantum numbers  1  q  then w r i t e :  2  J + I , J + I - l , - - - , | j - I | and if H  can  = 1 + Li  F = F  1  One  coupled  ^  A  =  l  p^j-^^  ( J  +l)}x  a a  _ i^^+i)  = F(F+1) - I ( I + D 2  2  (2) +  1  1  X  x  "°  d / b ) { < P > - E ( b ) } { x ( 2 ) - x (2)}j  _ j(j+i)  - F^F^l)  p  a  p  b b  cc  2.40a  2.40b  \  26  A  2  ~ (  =  J  J + 1  >  " F ^ + D  2.40c  I n g e n e r a l , t h i s e x p r e s s i o n w i l l n o t be c o m p l e t e l y s u f f i c i e n t f o r such a two n u c l e u s system because t h e m a t r i x elements o f f d i a g o n a l i n  will  u s u a l l y make a s m a l l b u t s i g n i f i c a n t c o n t r i b u t i o n t o t h e t o t a l  quadrupole  coupling energy.  T h i s can then be e x a c t l y d e t e r m i n e d o n l y by d i a g o n a l i z i n g  the v a r i o u s F^ b l o c k s i n t h e m a t r i x r e p r e s e n t a t i o n o f H^. The r e l a t i v e  i n t e n s i t i e s o f t h e q u a d r u p o l e s p l i t components o f a  r o t a t i o n a l t r a n s i t i o n may be d e t e r m i n e d by computing d i p o l e moment m a t r i x elements l i k e t h o s e d i s c u s s e d a t the end o f s e c t i o n 2 . 1 . Now, however, the pure r o t a t i o n a l wave f u n c t i o n s N^JJK^.KJJ and | j ' , K ^ , K j > must be r e p l a c e d by t h o s e a p p r o p r i a t e t o t h e p a r t i c u l a r h y p e r f i n e s t a t e s ; f o r e x a m p l e , i n t h e case o f a s i n g l e c o u p l i n g n u c l e u s t h e s e a r e O . K ^ . K ^ I . F . M p I and | J  1  . K ^ ,K* , I , F ' ,M > . D e t a i l e d c o n s i d e r a t i o n o f F  the t r a n s i t i o n moment, w h i c h may be f a c t o r e d i n t o a h y p e r f i n e p a r t and a pure r o t a t i o n a l p a r t , t h e n r e v e a l s  that there i s a rigorous  selection  r u l e f o r F, n a m e l y : AF = 0,±1  2.41  A s i m i l a r r u l e a l s o a p p l i e s t o F^ i n t h e two n u c l e i case d i s c u s s e d above. S i n c e t h e r e c a n be c o n s i d e r a b l e v a r i a t i o n i n t h e i n t e n s i t y o f t h e s e a l l o w e d h y p e r f i n e components, however,  i t i s generally  a c t u a l l y t o compute t h e a p p r o p r i a t e m a t r i x e l e m e n t s .  worthwhile F o r t h e case o f  a s i n g l e c o u p l i n g n u c l e u s t h i s i s n o t d i f f i c u l t and f u r t h e r , s i n c e the r e s u l t s a r e g e n e r a l , they have been t a b u l a t e d ( 4 5 ) . 2.3  The S t a r k E f f e c t In the presence o f a u n i f o r m e l e c t r i c  f i e l d E a molecule w i t h a  27  dipole moment _M experiences a torque which tends to align the moment axis along the f i e l d direction.  This interaction, which i s known as the Stark  effect, perturbs the rotational energies of the molecule and at least p a r t i a l l y l i f t s their (2J+l)-fold spatial degeneracy. The rotational Hamiltonian for the perturbed molecules may be written as the sum of the zero f i e l d Hamiltonian and the following Stark Hamiltonian (46): 2.42 g= a,b,c where E_ defines the Z direction i n space.  The associated Stark energies  can generally be evaluated to sufficient accuracy using perturbation theory. For asymmetric top molecules, i n the absence of approximate symmetric rotor or accidental degeneracies, there i s no f i r s t order Stark effect. This follows from the fact that none of the direction cosines, $_g' belong to the t o t a l l y symmetric representation of the rotation group  (47).  The t o t a l rotational energy, correct to second order i n the perturbation, may therefore be written as (46): 2.43 g where E°  i s the unperturbed rotational energy and the second order  Stark shifts are given by: 2.43a  28  i n w h i c h the summation extends o v e r a l l s t a t e s except J  v K  no summation o v e r M' because $ J  i s diagonal i n M .  £g  -1 1  ; there  is  K  S i n c e the m a t r i x  J  elements i n e q u a t i o n 2.43a can be e x p r e s s e d i n terms o f the p r e v i o u s l y i n t r o d u c e d l i n e s t r e n g t h s S , i t i s p o s s i b l e to r e w r i t e the second o r d e r S t a r k e n e r g i e s i n the f o l l o w i n g more u s e f u l f o r m :  rE  ( 2 )  l J K J  ,K ' J M  -  V'  \2J+l/Z-f  j2  ~ J  SgO^j.K^J-l.K^.Kp  M  J(2J-1)  X  o  E  o  2.44 M  j  S^J.K^.K^J.K^.Kp  J(J+D  X  E  o  _ o J  2  +  E  \ ^  (J+D -M  S  2  (J+l) (2J-3)  ~cS  X  Ki [  n o n z e r o , has been w r i t t e n o u t .  ~^ J K  K  where now the summation o v e r J ' ,  (J.K^.K^J+l.K^.Kp  _  K 1  f o r w h i c h o n l y the J ' It  ( J + 1 ) 1  K_ K]; 1  = J , J ± l terms  are  s h o u l d be n o t e d t h a t some n o n t r i v i a l  m a n i p u l a t i o n i s r e q u i r e d t o get from e q u a t i o n s 2.27a and 2.43a t o e q u a t i o n 2.44  (46). The s u c c e s s of the above t r e a t m e n t i s dependent upon the v a l i d i t y of  the a s s u m p t i o n t h a t the S t a r k e n e r g i e s are s m a l l compared t o the a t i o n o f the z e r o f i e l d r o t a t i o n a l s t a t e s .  A l l too f r e q u e n t l y ,  separhowever,  d e g e n e r a c i e s o r n e a r d e g e n e r a c i e s i n v o l v i n g l e v e l s connected by nonzero d i p o l e moment m a t r i x elements are e n c o u n t e r e d .  Golden and W i l s o n  have shown t h a t such cases may be h a n d l e d by a p p l y i n g a Van V l e c k f o r m a t i o n (20)  t o the m a t r i x r e p r e s e n t a t i o n of H  R  + Hg.  (47) trans-  The t r a n s f o r m e d  m a t r i x i s then f a c t o r e d i n t o s u b m a t r i c e s each a s s o c i a t e d w i t h a p a r t i c u l a r  29  s e t o f degenerate o r n e a r l y degenerate l e v e l s .  The elements c o n n e c t i n g  these s u b m a t r i c e s c o n t r i b u t e t o the energy o n l y i n the f o u r t h o r d e r and may be n e g l e c t e d .  Hence, d i a g o n a l i z a t i o n o f t h e s u b m a t r i c e s g i v e s t h e  correct Stark perturbed r o t a t i o n a l energies.  These have a p a r t i c u l a r l y  s i m p l e form f o r t h e most common s i t u a t i o n i n w h i c h t h e near involves only a p a i r of l e v e l s , J  and J " „ K  \ E ±  l  J  M  V  . _ ^ L i  where E  ^ " K ^ J  +  -1 1 K  l  V  K  J  M  „ :  - 1  K  1  " \>> K«.M - ii  o  ±  2  |  r  |  2  J E \K\ +  (  2 < 4 5  and E „ a r e computed u s i n g e q u a t i o n 2 . 4 3 , b u t K^K'^J  M K  K  \ ( \  zL±__  _  -1 1  degeneracy  M  J  the sum i n e q u a t i o n 2.43a ( o r 2.44) i s o n l y o v e r the l e v e l s J ' , J  , J " „ „. -1 1 - 1 1 v  K  v  K  K  , #  -1 1 The o f f d i a g o n a l elements EE, depend upon t h e type o f K  K  K  degeneracy b e i n g c o n s i d e r e d .  The s i m p l e s t case i s t h a t o f an asymmetry  s p l i t d o u b l e t , (see s e c t i o n 2.1) f o r w h i c h : 2 ,2 2 £  M  " jfj i)  Z^ 2  2  +  ( 2 J +  l)  S (J,K_ K g  l f  l S  J K» K») f  2.45a  l f  where g w i l l be _a f o r a n e a r p r o l a t e asymmetric t o p , and c f o r a n e a r oblate top.  F u r t h e r m o r e , i f t h e asymmetry s p l i t t i n g i s v e r y s m a l l , o r n i l ,  then e q u a t i o n 2.45 may be s i m p l i f i e d t o t h e f o l l o w i n g a p p r o x i m a t e e x p r e s s i o n :  E  - 1/2(E° K  ,1 1 K  + E°  ) ± «  "i^i V <  K  J  J  J+1  ^  2J+1  )  s*(J K t  8  K.;J,K» K?)  30  J  V  v  K  Jy/-" V "  _! 1  K  K  J(J+1)  _i i K  where K i s e i t h e r K_^ o r  as  appropriate.  S i n c e t h e r e can be s m a l l asymmetry s p l i t t i n g s i n even q u i t e m e t r i c m o l e c u l e s , i t i s apparent  from t h i s l a s t e x p r e s s i o n t h a t  asymthe  s p e c t r a o f such m o l e c u l e s can be e x p e c t e d to c o n t a i n a s i g n i f i c a n t number of t r a n s i t i o n s w i t h a f i r s t order or near f i r s t order Stark e f f e c t .  These  are t h e n c l e a r l y d i s c e r n i b l e from the r e s t of the t r a n s i t i o n s , w h i c h have o n l y a second o r d e r S t a r k e f f e c t ,  and hence a r e e a s i l y a s s i g n e d , even when  the i n d i v i d u a l S t a r k l o b e s cannot be r e s o l v e d . The s e l e c t i o n r u l e s f o r  depend on the r e l a t i v e  o r i e n t a t i o n s of  a p p l i e d e l e c t r i c f i e l d and the microwave r a d i a t i o n e l e c t r i c f i e l d If  vector.  the two a r e p a r a l l e l o n l y AM^. = 0 t r a n s i t i o n s w h i c h a r e known as ir-com-  ponents are a l l o w e d ; w h e r e a s , AM_  the  f o r the p e r p e n d i c u l a r arrangement  = ±1 o r a-components are a l l o w e d .  With a conventional  only  microwave  s p e c t r o m e t e r , such as t h a t used i n t h i s w o r k , the two f i e l d v e c t o r s p a r a l l e l and hence o n l y the ir-components a r e o b s e r v e d .  completely general  are  The r e l a t i v e  t e n s i t i e s o f t h e s e may be deduced by i n v e s t i g a t i n g the a p p r o p r i a t e c o s i n e m a t r i x elements  the  (47) a n d , may be e x p r e s s e d i n the f o l l o w i n g ,  in-  direction closed,  form:  I(Mj)  = AM  I(Mj)  = B { ( J + 1 ) - Mj\  AJ = 0  2  AMj = 0 2  2.47  AJ = ±1  where J i s the s m a l l e r of the two J ' s i n v o l v e d , and A , B are d e t e r m i n e d by the s t r e n g t h of the u n s p l i t l i n e and are independent o f M .  There i s  a d d i t i o n a l f a c t o r o f 1/2 i n the i n t e n s i t y e x p r e s s i o n f o r the M  = 0 -»•  an  31  Mj = 0 component. are d o u b l y 2.4  T h i s a r i s e s because a l l of the l e v e l s w i t h M^> 0  degenerate.  R o t a t i o n a l C o n s t a n t s , Moments o f I n e r t i a , Molecular  Inertial  Defect  and the  Structure.  The r o t a t i o n a l c o n s t a n t s d e f i n e d by e q u a t i o n s 2.3 c l e a r l y have a s i g n i f i c a n t i f somewhat o b s c u r e dependence on the v i b r a t i o n a l s t a t e o f molecule.  T h i s p r o b l e m has been s t u d i e d i n some d e t a i l by s e v e r a l  (48,...,53).  the  authors  They have shown t h a t , w i t h the a s s u m p t i o n of s m a l l v i b r a t i o n a l  a m p l i t u d e s , each r o t a t i o n a l c o n s t a n t may be r e w r i t t e n as a c o n v e r g i n g i n the v i b r a t i o n a l quantum numbers.  series  S i n c e o n l y t h e l i n e a r terms need  u s u a l l y be r e t a i n e d one t h e n has the f o l l o w i n g r e l a t i o n s : A = A - V* v e s B  v  =B  e  a ( v +d /2) + • • • s s s  2.48a  a  - V a ( v +d 12) + ••• _-_> s s s s  2.48b  b  C = C - y * a ( v +d /2) + • •• v e _-_< s s s s  2.48c  C  v  where A , B and C a r e e q u i l i b r i u m r o t a t i o n a l c o n s t a n t s , the a ' s e e e ^ v i b r a t i o n - r o t a t i o n i n t e r a c t i o n parameters,  t b  n o r m a l mode w i t h degeneracy  A l t h o u g h e x p r e s s i o n s are a v a i l a b l e a c t i o n parameters  i s the  vibrational  s  r  quantum number o f the s  and v  are  d . g  f o r the v i b r a t i o n - r o t a t i o n  inter-  (51) , s i n c e t h e s e c o n t a i n b o t h harmonic and anharmonic  p o t e n t i a l c o n s t a n t s as w e l l as C o r i o l i s c o u p l i n g c o n s t a n t s , c a l c u l a t i o n of the a ' s  is rarely  attempted.  theoretical  E x p e r i m e n t a l v a l u e s may be  o b t a i n e d f o r some o f t h e s e by s t u d y i n g the r o t a t i o n a l s p e c t r a o f m o l e c u l e s i n low e n e r g y ,  and hence s i g n i f i c a n t l y p o p u l a t e d , e x c i t e d v i b r a t i o n a l  states,  32  By analogy w i t h the r i g i d r o t o r one may d e f i n e e f f e c t i v e moments o f i n e r t i a using the r e l a t i o n s :  I =-4-  =-4-  iV  V  8ir A  3  where I , a  b  °  V  I? and I  V  I K = - T 8ir B V  V  c  w i l l have u n i t s o f  8ir C  C  a.m.u.S  V  i f t h e r o t a t i o n a l constants  2  2  are measured i n MHz and t h e c o n v e r s i o n f a c t o r h/8ir 505390.9 ± 8 . 0 a.m.u.&  MHz ( 5 4 ) .  i s t a k e n t o be  I t then f o l l o w s from e q u a t i o n s 2 . 4 8  t h a t t h e s e may be r e l a t e d t o e q u i l i b r i u m moments o f i n e r t i a I I = I + V * e ( v +d /2) + • •• ( a = a , b , c ) a a i—J s s s s V  where  e  2.49  e  by:  a  /„ 2 a (on \ , e( , . 2 a s " V"h-j V s  2.50  „  T  a  2  '  5  0  a  and I  a = - f -  a  8ir A 2  ^="4-  e  2  8TT C  C  e  2.50b  =-^-  1 &  8TT B  B  2  e  and where i t has been assumed t h a t A » | ^ a ( v +d /2) | e t c . 6 S S S s 3  In addition  t o t h e h i g h e r terms i n t h e v i b r a t i o n a l e x p a n s i o n , t h e r e may a l s o be v e r y small contributions to I  V  a  from two o t h e r s o u r c e s t h a t have n o t been e x -  p l i c i t l y included i n equation 2.50.  The f i r s t o f t h e s e i s a c e n t r i f u g a l  d i s t o r t i o n term w h i c h a r i s e s when t h e e f f e c t i v e moments o f i n e r t i a a r e c a l c u l a t e d by r e p l a c i n g t h e " p u r e " r o t a t i o n a l c o n s t a n t s i n e q u a t i o n 2.49 •N^  w i t h t h e more r e a d i l y o b t a i n e d ( A ' , B ' , C ' ) o r ( A , B , C ) o n e s . J  .  V  V  V  V  V  V  The  second i s due t o t h e e f f e c t s o f e l e c t r o n i c - r o t a t i o n a l i n t e r a c t i o n ( 5 5 ) . B o t h o f t h e s e c o n t r i b u t i o n s can u s u a l l y be i g n o r e d ( 5 6 ) . The e q u i l i b r i u m moments o f i n e r t i a i n t r o d u c e d i n e q u a t i o n 2.50 may  33  be used t o d e f i n e an e q u i l i b r i u m m o l e c u l a r s t r u c t u r e by means o f  the  following expressions: I  2.51a  I bf = I > . x( a e.i + c e.i) L^j  2.51b  I  2.51c  a  =  V* m.1( be i.  )  6  2  x  + c  2  2  ei  2  l  6  c  =V .(a . + L^j x ei l 2  m  b .) ei 2  where a . , b . and c . a r e the e q u i l i b r i u m c o o r d i n a t e s o f the n u c l e u s o f ex ei ei ^ th the i  atom o f mass nu i n the m o l e c u l e f i x e d c e n t e r o f mass p r i n c i p a l  i n e r t i a l a x i s system d e f i n e d b y : Vm.a . = 0 v i ei  Vm.b , = 0 vi I e i  E, ml. a e .bi  V'm.a .c , = 0 I ex e i  I  and  . = 0  ei  m. c . = 0 ' l ei ,c . = 0 x ei ei  Y>.b 4H  2.52 2.53  From t h e s e l a s t e x p r e s s i o n s i t i s apparent t h a t the C a r t e s i a n c o o r d i n a t e s (a . , b . , c .) w o u l d be changed i f one o f the atoms was r e p l a c e d by ex' ei' ex isotope.  its  T h i s i s due, however, a l m o s t e n t i r e l y t o a s h i f t i n the a x i s  s y s t e m , s i n c e i t has been shown t h a t the e q u i l i b r i u m i n t e r n a l c o o r d i n a t e s a r e e s s e n t i a l l y independent o f i s o t o p i c s u b s t i t u t i o n ( 5 7 ) .  One c o u l d  t h e r e f o r e , i n p r i n c i p l e , o b t a i n an e q u i l i b r i u m m o l e c u l a r s t r u c t u r e by measuring values of I  f o r a s u f f i c i e n t number o f d i f f e r e n t i s o t o p i c s p e c i e s .  U n f o r t u n a t e l y i t i s u s u a l l y i m p o s s i b l e t o e x t r a c t e q u i l i b r i u m moments o f i n e r t i a from the r o t a t i o n a l spectrum as t h i s r e q u i r e s the measurement of r o t a t i o n a l c o n s t a n t s n o t o n l y f o r the ground v i b r a t i o n a l s t a t e , b u t a l s o ' f o r a l l o f the 3N-6  e x c i t e d v i b r a t i o n a l s t a t e s i n w h i c h each o f the n o r m a l  modes has been s i n g l y e x c i t e d .  34  If  a m o l e c u l e i s p l a n a r i n i t s e q u i l i b r i u m c o n f i g u r a t i o n , then from  equations 2 . 5 1 ,  and w i t h the c - a x i s p e r p e n d i c u l a r to the m o l e c u l a r e  it  e  plane,  e  f o l l o w s t h a t the q u a n t i t y 1^ - I  - I  i s i d e n t i c a l l y zero.  Similar  b e h a v i o r i s n o t o b s e r v e d f o r the e f f e c t i v e moments o f i n e r t i a d e f i n e d by e q u a t i o n s 2 . 4 9 . T h i s has l e d t o the c o n c e p t , f i r s t i n t r o d u c e d by D a r l i n g and Dennison ( 5 8 ) , o f an i n e r t i a l d e f e c t , A , d e f i n e d b y : A = I - if - I c b a V  V  V  2.54  V  Ground v i b r a t i o n a l s t a t e i n e r t i a l d e f e c t v a l u e s , A ° , have been e x p e r i m e n t a l l y d e t e r m i n e d f o r a l a r g e number o f s m a l l p l a n a r m o l e c u l e s . p o s i t i v e and t y p i c a l l y o f the o r d e r o f 10  a.m.u. r  They a r e  (59).  A number o f t h e o r e t i c a l s t u d i e s have been d e v o t e d t o t h e defect  Oka and M o r i n o ( 5 5 )  (55,58,59,60).  usually  inertial  have shown t h a t a l t h o u g h i t  is  due l a r g e l y t o t h e v i b r a t i o n a l m o t i o n o f t h e atoms i n a m o l e c u l e , t h e r e may a l s o be v e r y s m a l l c o n t r i b u t i o n s from c e n t r i f u g a l d i s t o r t i o n and e l e c t r o n i c rotational interaction effects A where  = A + A + A VIB cent elec  V  TrTT3  ,^i_c  J3  X  cent " " abab/4 T  1  and  h  e  b  l  T  c  C~  +  V  2A~ V  I  b  I  2B~( V>  +  2  A, = - (m /m ) 11 g - I g - I e !• elec e' p'.< c c c a aa b bb> e  T  2.55  1  _  VIB  A  so t h a t one must w r i t e :  A  cent  e  x  P  r  e  s  s  i  o  n  i  s  t  h  a  t  8  9  a p p r o p r i a t e f o r the c a s e where the v  v  The new symbols i n t r o d u c e d i n the d e f i n i t i o n o f A ,  5  5  B  SSr  ^.3^c  K  ments o f i n e r t i a have been c a l c u l a t e d u s i n g A ' , B'  ,  effective  and C' r o t a t i o n a l  mo-  constants.  v represent  the mass  elec of the p r o t o n , m , and the e l e c t r o n , m , and the components of the P e r  rotational  35  m a g n e t i c moment t e n s o r g «  S i n c e t h e l a t t e r have been measured f o r v e r y  a a  few m o l e c u l e s & ^ e  values  e c  can r a r e l y be c a l c u l a t e d .  Oka and M o r i n o (59)  s u g g e s t t h a t they may be e s t i m a t e d by a s s i g n i n g a c o n t r i b u t i o n o f - 0 . 0 0 5 a.m.u./A  2  t o each o u t - o f - p l a n e IT bond i n t h e m o l e c u l e .  Since the i n t r a c t a b l e first  E ' S appear i n e q u a t i o n 2 . 5 5 a i t would seem a t  t h a t t h e t h e o r e t i c a l c a l c u l a t i o n o f t h e i n e r t i a l d e f e c t might be  h o p e l e s s l y complex. (58),  However,  as f i r s t p o i n t e d o u t by D a r l i n g and Dennison  t h e anharmonic c o n t r i b u t i o n s t o t h e e ' s c a n c e l e x a c t l y i n t h i s  equation.  A g e n e r a l - e x p r e s s i o n s u i t a b l e f o r c a l c u l a t i o n of A „ ' v a l u e s V JLiS  was s u b s e q u e n t l y o b t a i n e d by Oka and M o r i n o ( 5 5 ) . 2 A  VIB *  Z-2^ V (  ~  1  /  2  >Z  7T C  ,  2  M 8  2  t0 (t0 -t0 g  g  g f  ,KV  2 +  )  It i s :  2  " <4'> } 2  2.56  t  IT C \  t /  whe r e co i s t h e v i b r a t i o n a l f r e q u e n c y o f t h e s  n o r m a l mode, t h e X,  ,  are C o r i o l i s c o u p l i n g c o n s t a n t s , and t h e t summation runs o n l y o v e r t h e out-of-plane v i b r a t i o n s . The r e l a t i o n s d i s c u s s e d i n the p r e v i o u s p a r a g r a p h have been s u c c e s s f u l l y used t o c a l c u l a t e t h e i n e r t i a l d e f e c t s o f a number o f s m a l l m o l e c u l e s (59, 6 1 ) .  The c o m p l e x i t y o f such c a l c u l a t i o n s i n c r e a s e s r a p i d l y ,  as l a r g e r m o l e c u l e s a r e c o n s i d e r e d . Laurie  however,  T h i s has prompted Hershbach and  (60) t o i n v e s t i g a t e v a r i o u s a p p r o x i m a t e schemes f o r e s t i m a t i n g  i n e r t i a l defects.  One p a r t i c u l a r l y s i m p l e e x p r e s s i o n , w h i c h  a l l of t h e ground v i b r a t i o n a l s t a t e i n e r t i a l d e f e c t in-plane  (bending)  attributes  to the lowest  frequency  v i b r a t i o n to , was found t o g i v e s u r p r i s i n g l y good  36  agreement w i t h experiment  A° £  A  V I B  «  4K/  (usually w i t h i n 20%).  The  expression i s : 2.57  U j l  2  -1 where QJ^, assumed to be nondegenerate, i s measured i n cm  and K = h/8ir  = 16.858 a.m.u.A^cm Although  " A ° " v a l u e s of nonplanar  molecules  calculated using  equation  2.54 are t y p i c a l l y o f the o r d e r o f tens o f a.m.u.R2, the o b s e r v a t i o n o f a s m a l l p o s i t i v e i n e r t i a l d e f e c t cannot o f i t s e l f be taken as a d e f i n i t i v e proof of p l a n a r i t y .  In f a c t , t h e r e are at l e a s t a few m o l e c u l e s  which  have s m a l l " A ° " v a l u e s but which are d e f i n i t e l y not p l a n a r i n t h e i r ibrium configuration (62,63).  I t i s t h e r e f o r e u s u a l l y most d e s i r a b l e t o  t e s t a case of s u s p e c t e d p l a n a r i t y by comparing the observed w i t h one 2.56. of A  V  equil-  value of  c a l c u l a t e d assuming a p l a n a r s t r u c t u r e , p r e f e r a b l y u s i n g  A d d i t i o n a l c o n f i r m a t i o n may with isotopic substitution.  be o b t a i n e d by d e t e r m i n i n g From e q u a t i o n 2.56  i t may  A°  equation  the v a r i a t i o n be seen t h a t  v A  f o r a planar molecule  s h o u l d be n e a r l y independent o f the atomic masses*.  T h i s has been e x p e r i m e n t a l l y v e r i f i e d f o r a nonplanar  m o l e c u l e where I  (61).  - 1^ - I  Such i s not the case however £ 0,  and hence "A ", i s s t r o n g l y  mass dependent. Once the q u e s t i o n of p l a n a r i t y , o r l a c k of i t , has been d e c i d e d , d e t e r m i n a t i o n o f the remaining undertaken.  s t r u c t u r a l f e a t u r e s o f the m o l e c u l e  may  the be  As a l r e a d y i n d i c a t e d o n l y the ground v i b r a t i o n a l s t a t e  e f f e c t i v e moments of i n e r t i a 1° are n o r m a l l y a v a i l a b l e f o r t h i s purpose. * The s u b s t i t u t i o n of deuterium f o r hydrogen must be regarded as a s p e c i a l case s i n c e t h i s , u n l i k e o t h e r s u b s t i t u t i o n s , causes v e r y l a r g e changes i n at l e a s t a few o f the v i b r a t i o n a l f r e q u e n c i e s and hence may produce s i g n i f i c a n t , a l t h o u g h u s u a l l y s m a l l , changes i n A . v  37  S e v e r a l d i f f e r e n t p r o c e d u r e s have been used to e x t r a c t s t r u c t u r a l a t i o n from these.  One t h a t has seen e x t e n s i v e  use i n the p a s t  inform-  i s simply  to d e f i n e an e f f e c t i v e s t r u c t u r e , denoted r , by a s e t o f e q u a t i o n s  anal-  e o I by I and a a Then w i t h s u f f i c i e n t  ogous to those f o r the e q u i l i b r i u m moments: i . e . r e p l a c e \a ., b ., c .J by la ., b ., c .I i n e q u a t i o n s 2 . 5 1 . 1 e i ' e i ' ei> I oi oi oi> ^ J  i s o t o p i c s u b s t i t u t i o n , and the a d d i t i o n a l assumption t h a t the e f f e c t i v e i n t e r n a l coordinates  a r e independent o f the atomic masses, an r o  structure  may be c a l c u l a t e d . There a r e two s e r i o u s d e f i c i e n c i e s i n t h i s approach. s t r u c t u r e i s n o t simply  Firstly,  the r  Q  r e l a t e d to e i t h e r o f t h e more p h y s i c a l l y m e a n i n g f u l  average, <(r)>, o r e q u i l i b r i u m , r , s t r u c t u r e s . t i o n that the e f f e c t i v e i n t e r n a l coordinates s u b s t i t u t i o n i s a r a t h e r poor a p p r o x i m a t i o n .  S e c o n d l y , t h e n e c e s s a r y assumpa r e independent o f i s o t o p i c This i s f o r c e f u l l y  illus-  t r a t e d i n the few cases where more than the minimum number o f i s o t o p i c s p e c i e s have been s t u d i e d  so t h a t two o r more independent r  Q  structures  may be c a l c u l a t e d ( 6 4 ) . These a r e g e n e r a l l y i n r a t h e r poor agreement, and v a r i a t i o n s i n e f f e c t i v e bond l e n g t h s  o f up t o 0 . 0 1 % have been o b s e r v e d .  Such d i s c r e p a n c i e s , w h i c h a r e f r e q u e n t l y r e f e r r e d to as z e r o - p o i n t  vibra-  t i o n a l e f f e c t s , a r e n o t s u r p r i s i n g i n v i e w o f t h e averages i n v o l v e d i n t h e d e f i n i t i o n s o f the e f f e c t i v e r o t a t i o n a l constants. s u f f i c i e n t l y annoying t h a t  the c a l c u l a t i o n o f r  l a r g e l y superseded by t h e s e m i - e m p i r i c a l Kraitchman  Q  They a r e , however,  s t r u c t u r e s has now been  approach d i s c u s s e d  ( 6 5 ) has shown t h a t i f a s i n g l e atom i n a r i g i d  i s i s o t o p i c a l l y s u b s t i t u t e d then i t s c o o r d i n a t e s  expressed d i r e c t l y  i n terms o f the c e n t e r  molecule  ( a , b, c) i n the c e n t e r  o f mass p r i n c i p a l i n e r t i a l a x i s system o f the u n s u b s t i t u t e d be  below.  s p e c i e s can  o f mass p r i n c i p a l moments o f  38  i n e r t i a of the two i s o t o p i c s p e c i e s .  The e x a c t form o f these e x p r e s s i o n s ,  w h i c h are c a l l e d K r a i t c h m a n ' s e q u a t i o n s , depends on the type of m o l e c u l e being considered.  F o r a p l a n a r , asymmetric t o p , w i t h the c - a x i s p e r p e n -  d i c u l a r t o the m o l e c u l a r p l a n e , they  are:  2.58a  2.58b  where  2.59a 2.59b u = (MAm)/(M+Am)  2.59c  and 1^ are the c e n t e r o f mass p r i n c i p a l moments o f i n e r t i a o f the s u b stituted species, I  are t h o s e of the u n s u b s t i t u t e d s p e c i e s , M i s  the  t o t a l mass o f the p a r e n t m o l e c u l e and Am i s the mass d i f f e r e n c e of two i s o t o p e s (Am = m' - m).  the  These e q u a t i o n s a r e a l s o v a l i d f o r r e a l m o l e -  c u l e s i f e q u i l i b r i u m moments o f i n e r t i a are u s e d . C o s t a i n (64) has shown, however,  t h a t when ground v i b r a t i o n a l  e f f e c t i v e moments o f i n e r t i a are used i n K r a i t c h m a n ' s e q u a t i o n s r e s u l t i n g s t r u c t u r e , designated r discussed r  o  structure.  the  , d i f f e r s s i g n i f i c a n t l y from the  He p o i n t e d out t h a t r  f o r d i a t o m i c s the r  l e n g t h s h o u l d be c l o s e r t o the e q u i l i b r i u m v a l u e t h a n the r  Q  state  s  previously bond  length i s ,  specifically: r  s  ^ l/2(r  e  + r ) o  with  r <r <r e s o  2.60  39  For p o l y a t o m i c s , a l t h o u g h t h e r e i s not a c o r r e s p o n d i n g s i m p l e r e l a t i o n c o n n e c t i n g the t h r e e s t r u c t u r e s , C o s t a i n s u g g e s t e d , on the b a s i s of some l i m i t e d e x p e r i m e n t a l e v i d e n c e , t h a t the r a good a p p r o x i m a t i o n t o the r  &  one.  g  s t r u c t u r e s h o u l d g e n e r a l l y be  Subsequent w o r k , w i t h a few e x c e p t i o n s  ( 6 6 ) , has l a r g e l y s u p p o r t e d t h i s t h e s i s , and c e r t a i n l y the r have been found t o be more c o n s i s t e n t t h a n the r  ones  g  structures  (56).  o The most s e r i o u s d i f f i c u l t y e n c o u n t e r e d i n o b t a i n i n g a good r i s the l o c a t i o n o f an atom t h a t i s n e a r a p r i n c i p a l a x i s . e q u a t i o n s 2.58 shows t h a t i f the u n c e r t a i n t y i n A l  structure  g  I n s p e c t i o n of  and AI,  i s the l i m i t i n g D  cl  f a c t o r on the -accuracy t o w h i c h | a | and | b | may be d e t e r m i n e d t h e n ,  the  e r r o r i n t h e s e c o o r d i n a t e s w i l l be i n v e r s e l y p r o p o r t i o n a l t o the c o o r d i n a t e s themselves. t h a n 0. isX  C o s t a i n has p r o p o s e d t h a t as a g e n e r a l r u l e c o o r d i n a t e s s m a l l e r s h o u l d not be d e t e r m i n e d by K r a i t c h m a n ' s e q u a t i o n s .  They c a n ,  however, be a c c u r a t e l y measured u s i n g t h e c e n t e r o f mass o r p r o d u c t of inertia conditions,  i.e.  yVa.  =  0  etc.  ?  m.a.b. = 0 i l l  2.61  etc.  2.62  S i n c e the f i r s t moment e q u a t i o n h o l d s o n l y a p p r o x i m a t e l y f o r the r if  a c o o r d i n a t e o f the  value by: s  n  structure,  atom i s d e t e r m i n e d from i t , t h i s c o o r d i n a t e w i l l  d i f f e r from the t r u e r S(r  g  .  ) = / , m . r ./m l si n  r = a , b, or c ' '  2.63  The v a l u e s o f ^ r o ^ r ^ computed f o r m o l e c u l e s i n w h i c h a complete s u b s t i t u t i o n s t r u c t u r e c o u l d be d e t e r m i n e d i n d i c a t e t h a t 6 ( r  ) s h o u l d be l e s s  than  n  0.0028  f o r an atom as heavy as c a r b o n .  A similar discussion is  applicable  40  to " r " coordinates obtained using the product of i n e r t i a c o n d i t i o n . An a l t e r n a t i v e procedure f o r l o c a t i n g atoms near to a p r i n c i p a l axis has been proposed by P i e r c e (67). I t involves a double s u b s t i t u t i o n technique i n which the second d i f f e r e n c e s of moments of i n e r t i a are employed i n order to reduce v i b r a t i o n a l e f f e c t s to higher order.  Since four i s o -  t o p i c species must be studied t o locate one atom, and very accurate moments of i n e r t i a are required, t h i s procedure has not been widely used. The appropriate equations are merely presented here.  For a more complete  d i s c u s s i o n the reader i s r e f e r r e d t o the o r i g i n a l paper by P i e r c e (67) and a subsequent one by P i e r c e and K r i s h e r (68). Consider the n o n - l i n e a r planar molecule WXYZ ( c - a x i s perpendicular to plane).  Assume that the a-coordinate of X i s very small and that i t  i s to be determined using the double s u b s t i t u t i o n technique. Then a ft ft ft ft  s u i t a b l e set of i s o t o p i c species i s WXYZ, WXYZ, W XYZ and W XYZ.  The  f i r s t molecule i s c a l l e d the " p r i n c i p a l framework", the second one, the "secondary framework". Let A,B be, the coordinates of the center of mass ft of WXYZ i n the center of mass p r i n c i p a l i n e r t i a l axis system of WXYZ and ft  l e t 9 be the angle of r o t a t i o n from the WXYZ system to the  WXYZ system.  Also l e t a and b be the coordinates o f X i n the WXYZ system. X  X  Then i t  '  can be shown t h a t : AAI = AI (*WXYZ) - A l (WXYZ) . V  D  D  D  2.64 = (k*Cos 9 - k ) a + (2k'CCos6)a__ + k'C x x 2  where  2  2  A I ( WXYZ) = I ( W XYZ) - I ( WXYZ) Q  2.65a  A  a = a,b ,c AIJWXYZ) = I (W*XYZ) - I (WXYZ) a  a  2.65b  41  k' = u*  Al (*WXYZ) a * ~ I (*WXYZ) - I (*WXYZ)  1 +  SL  k = y1  +  -l  2.65c  D  Al (WXYZ) a I (WXYZ) - I, (WXYZ)  -1  2.65d  D  cL  and  C = -(bx - B)Cos 9  2.65e  where  y = MAm/(M+Am)  2.66a  y' = M'Am/(M'+Am)  2.66b  with M = mass of WXYZ, M = mass of WXYZ and Am = mass of X - mass of X. 1  A similar relation connecting AAI and b i s suitable for the case where a x X i s very close to the _i-axis.  In addition there i s a third relation  involving I ' which i s useful when either the a or b - moments of i n s  c  e r t i a cannot be accurately determined. AAI c = A lc( WXYZ) - A lc(WXYZ)  It i s : 2.67  = y' (b - B ) + (a - A ) 2  _ X  2  X  The preceding expressions are s t r i c t l y v a l i d only for a r i g i d or equilibrium system but seem to y i e l d consistent results when applied to real molecules using ground v i b r a t i o n a l state effective moments of i n e r t i a (68).  Solution of either equation 2.64 or 2.67 for a^ requires a prior  knowledge of b^, B and A (or 8) as well as the moments of i n e r t i a . I f b^ i s s u f f i c i e n t l y large i t may be determined by single substitution; A, B and 8 may be calculated to s u f f i c i e n t accuracy (at least for a f i r s t iteration) using a preliminary, approximate structure.  42  The g e n e r a l s u b s t i t u t i o n p r o c e d u r e i s now the most w i d e l y used method f o r e x t r a c t i n g s t r u c t u r a l i n f o r m a t i o n from microwave d a t a .  This i s  because  i t g i v e s a t l e a s t i n t e r n a l l y c o n s i s t e n t r e s u l t s u s i n g o n l y the  readily  measured ground v i b r a t i o n a l s t a t e e f f e c t i v e moments o f i n e r t i a .  Its  most  s e r i o u s d e f i c i e n c y i s t h a t i t does not have a r e a l l y sound t h e o r e t i c a l basis.  T h e r e f o r e a l t h o u g h the r  s t r u c t u r e i s presumed t o be a good s  a p p r o x i m a t i o n t o the r this is 2.5  £  s t r u c t u r e t h e r e i s no t h e o r e t i c a l q u a r a n t e e  that  so.  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 the V i b r a t i o n a l F o r c e  Field.  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 i n t r o d u c e d i n  section  2.1 are independent o f r o t a t i o n a l s t a t e b u t do depend on the s t a t e under c o n s i d e r a t i o n . equation 2.3b.  T h i s i s c l e a r l y e v i d e n t from t h e i r  Unfortunately,  definition,  t h i s e x p r e s s i o n i s not s u i t a b l e f o r a  t h e o r e t i c a l c a l c u l a t i o n o f the d i s t o r t i o n c o n s t a n t s . and W i l s o n  vibrational  Accordingly, Kivelson  (69) have d e r i v e d a more c o n v e n i e n t approximate r e l a t i o n ,  in  w h i c h the taus a r e e x p r e s s e d d i r e c t l y i n terms o f the m o l e c u l a r f o r c e A s m a l l v i b r a t i o n a l a m p l i t u d e , harmonic f o r c e s , m o l e c u l a r model was starting point for this derivation.  field.  the  The r e l a t i o n i s :  x . - -i/2(i i?i i;)- y'rj%l.(f- )..rj .l. e  fl  e  1  1  e  where the 1^ are e q u i l i b r i u m p r i n c i p a l moments o f i n e r t i a ; the  |j  are p a r t i a l d e r i v a t i v e s  of the components o f the moment of i n e r t i a  w i t h r e s p e c t t o the i  i n t e r n a l c o o r d i n a t e , evaluated at  and the (f matrix.  ^)j>j  a  r  e  t  b  the elements of the i n v e r s e  (harmonic)  tensor  equilibrium; force  constant  I t w i l l be n o t e d t h a t the v i b r a t i o n a l dependence o f the t a u s has  now d i s a p p e a r e d .  A g a i n , s i n c e the e q u i l i b r i u m moments of i n e r t i a  are  A3  r a r e l y a v a i l a b l e i t i s g e n e r a l l y n e c e s s a r y t o make the a d d i t i o n a l approxi m a t i o n o f r e p l a c i n g them w i t h I  etc.  e v a l u a t e d i n such a way t h a t the E c k a r t  The  derivatives  c o n d i t i o n s (70)  must be are s a t i s f i e d .  K i v e l s o n and W i l s o n (69) have s u g g e s t e d a r e a s o n a b l y s i m p l e way o f accomplishing this. by P o l o  An a l t e r n a t i v e p r o c e d u r e has been more r e c e n t l y  described  (71).  For c a l c u l a t i o n purposes i t i s convenient to rearrange s l i g h t l y e q u a t i o n 2.68 t o  (72):  2.69 where A , A a r e r o t a t i o n a l c o n s t a n t s i n MHz; 1 ° 1° are e f f e c t i v e o o ' 8' y moments o f i n e r t i a i n a.m.u./A. ; R = 2 h x l 0 ^ 2  7  with h i n erg-sec.  principal  Then,  if  the d e r i v a t i v e s have u n i t s o f a . m . u . A and a . m . u . A / r a d f o r a s t r e t c h and a b e n d , r e s p e c t i v e l y , and the f o r c e c o n s t a n t s have u n i t s o f mdyne/A*, m d y n e - A / r a d , and mdyne/rad f o r a s t r e t c h , a bend and a s t r e t c h - b e n d i n t e r 2  a c t i o n , r e s p e c t i v e l y , the T  a r e i n MHz.  44  CHAPTER 3  EXPERIMENTAL 3.1  P r e p a r a t i o n of C h l o r i n e I s o c y a n a t e Chlorine isocyanate,  i n n a t u r a l i s o t o p i c abundance, was p r e p a r e d by  the p y r o l y s i s o f t r i c h l o r o i s o c y a n u r i c a c i d a f t e r the method o f Nachbaur and G o t t a r d i  (73).  About 5 gms. o f commercial t r i c h l o r o i s o c y a n u r i c a c i d (Baker  Chemical)  were p l a c e d i n the end o f a p y r e x tube w h i c h was then c o n n e c t e d t o a vacuum system and pumped on f o r s e v e r a l h o u r s . at l e s s that some of i t  When the p r e s s u r e had s t a b i l i z e d  1 u, the t r i c h l o r o i s o c y a n u r i c a c i d was warmed to 150°C c a u s i n g  t o s u b l i m e s l o w l y a l o n g the p y r e x tube and i n t o a r e a c t i o n z o n e .  T h i s was a s e c t i o n o f the p y r e x t u b e , about 5 i n c h e s l o n g , s t u f f e d w i t h g l a s s w o o l , and h e a t e d to about 310°C, where the t r i m e r v a p o r was d e p o l y merized.  A more o r l e s s c o n s t a n t f l o w o f t r i m e r i n t o the r e a c t i o n zone  was m a i n t a i n e d by s l o w l y i n c r e a s i n g the temperature at the end o f the from 150°C t o 200°C o v e r a p e r i o d o f about e i g h t h o u r s . p r o d u c t s were c o l l e c t e d under dynamic vacuum a t 77°K.  tube  The p y r o l y s i s A f t e r completion of  the r e a c t i o n they were f r a c t i o n a l l y d i s t i l l e d from the c o l l e c t i o n t r a p (from -80°C t o 7 7 ° K ) , w i t h the m i d d l e p o r t i o n b e i n g r e t a i n e d f o r s p e c t r o scopic study. As a p r e l i m i n a r y check on the i d e n t i t y and p u r i t y o f the sample red s p e c t r a o f i t s v a p o r were r e c o r d e d .  The spectrum of the f i r s t  a t e was i d e n t i f i e d as t h a t o f almost pure c a r b o n d i o x i d e .  In  infra-  distill-  subsequent  f r a c t i o n s the CC^ bands r a p i d l y d e c r e a s e d i n i n t e n s i t y , w h i l e o t h e r bands i d e n t i f i e d as b e l o n g i n g t o c h l o r i n e i s o c y a n a t e appeared w i t h  steadily  45  increasing intensity.  Eventually,  a spectrum was o b t a i n e d w h i c h  agreed  almost e x a c t l y w i t h t h a t p r e v i o u s l y p u b l i s h e d f o r c h l o r i n e i s o c y a n a t e  (73).  The f o r e - r u n o f impure p r o d u c t d e s c r i b e d above c o n s t i t u t e d o n l y a s m a l l f r a c t i o n of the t o t a l and was d i s c a r d e d . e s e n t i a l l y pure c h l o r i n e i s o c y a n a t e  A large f r a c t i o n of  (about 2 mis of l i q u i d a t -80°C) was  then c o l l e c t e d and s e t a s i d e f o r the microwave s t u d i e s .  The f i n a l  (small)  f r a c t i o n a p p a r e n t l y c o n t a i n e d some l e s s v o l a t i l e u n i d e n t i f i e d i m p u r i t i e s and was a l s o d i s c a r d e d . A s i g n i f i c a n t p o r t i o n o f the t o t a l p r o d u c t was l o s t d u r i n g the  course  o f the d i s t i l l a t i o n due t o the f o r m a t i o n o f an i n v o l a t i l e s o l i d polymer ( i n the t r a p ) .  T h i s p o l y m e r i z a t i o n was a p p a r e n t l y c a t a l y z e d by the  presence  o f i m p u r i t i e s as i t o c c u r r e d much more s l o w l y i n the p u r i f i e d c h l o r i n e i s o c y a n a t e sample under s i m i l a r c o n d i t i o n s ( i . e .  at -80°C).  When n o t  in  use samples were s t o r e d at 77°K, at w h i c h t e m p e r a t u r e they were i n d e f i n ately  stable. 18 A sample o f c h l o r i n e i s o c y a n a t e e n r i c h e d i n  f o l l o w i n g way.  0 was p r e p a r e d i n  C y a n u r i c c h l o r i d e (Eastman O r g a n i c C h e m i c a l s ) was  the  first  18 hydrolysed with acid.  0 (Bio-Rad L a b o r a t o r i e s )  t o produce l a b e l e d  cyanuric  T h i s was then r e a c t e d w i t h c h l o r i n e gas t o produce t r i c h l o r o i s o -  cyanuric acid.  Finally,  the l a b e l e d t r i c h l o r o i s o c y a n u r i c a c i d was d e p o l y -  m e r i z e d u s i n g the p r e v i o u s l y d e s c r i b e d method. The c y a n u r i c c h l o r i d e h y d r o l y s i s was a c c o m p l i s h e d u s i n g a s l i g h t l y m o d i f i e d v e r s i o n of a p r o c e d u r e d e s c r i b e d by G e r r y c y a n u r i c c h l o r i d e (.1  (74) .  In t h i s  case  gm) was h y r o l y s e d i n a s o l u t i o n o f sodium h y d r o x i d e 18  (.13 gm) i n H^O (1 ml)  e n r i c h e d w i t h 50%  0.  The sample was warmed  85°C f o r about 1/2 hour under a p r e s s u r e o f 150 t o r r pure n i t r o g e n .  to After  46 c o m p l e t i o n o f the r e a c t i o n , as i n d i c a t e d by complete d i s s o l u t i o n o f  the  c y a n u r i c c h l o r i d e , the n i t r o g e n was pumped away ( w i t h the s o l u t i o n f r o z e n at 77°K) and then the w a t e r was d i s t i l l e d o f f and c o l l e c t e d .  The m i x t u r e  of s a l t s l e f t b e h i n d ( N a C l , sodium c y a n u r a t e ) was s u b s e q u e n t l y i n a few mis of o r d i n a r y w a t e r and s e t a s i d e .  dissolved  T h i s p r o c e d u r e was  repeated  f o u r more t i m e s , i n each case the l a b e l e d w a t e r d i s t i l l e d o f f i n the p r e v i o u s run was r e - u s e d .  The s a l t s o l u t i o n s were then combined and a c i d -  i f i e d w i t h about 1 m l o f c o n c e n t r a t e d h y d r o c h l o r i c a c i d .  The r e s u l t i n g  p r e c i p i t a t e o f c y a n u r i c a c i d was f i l t e r e d , washed and d r i e d ; the t o t a l  yield  was 0.24 gms ( 8 5 % ) . T h i s p r o d u c t was then c o n v e r t e d t o t r i c h l o r o i s o c y a n u r i c a c i d i n f o l l o w i n g way ( 7 5 ) .  the  C h l o r i n e gas was b u b b l e d t h r o u g h a 0.40 M s u s p e n s i o n  o f the c y a n u r i c a c i d i n a 1.25 M sodium a c e t a t e s o l u t i o n whose pH had been i n i t i a l l y a d j u s t e d t o 6.5 by the a d d i t i o n o f a l i t t l e d i l u t e a c e t i c  acid.  The t e m p e r a t u r e was m a i n t a i n e d i n the range 0 ° - 5°C throughout the  reaction  w h i c h was t e r m i n a t e d when the pH reached 2.  The l a b e l e d t r i c h l o r o i s o c y a n -  u r i c a c i d w h i c h p r e c i p i t a t e d was i s o l a t e d , d r i e d , and p y r o l y s e d as p r e v i o u s l y described.  A r e s p e c t a b l e y i e l d o f m o d e r a t e l y pure c h l o r i n e  18 about 40% 0 e n r i c h e d , was o b t a i n e d . Samples o f c h l o r i n e i s o c y a n a t e 50% e n r i c h e d i n  15  isocyanate,  13  N and  C were p r e -  p a r e d by the d i r e c t r e a c t i o n o f gaseous c h l o r i n e w i t h an a p p r o p r i a t e l y l a b e l e d sample o f s i l v e r c y a n a t e .  T h i s was a p p a r e n t l y the f i r s t  p r e p a r a t i o n o f c h l o r i n e i s o c y a n a t e by t h i s r e a c t i o n .  successful  A much e a r l i e r  attempt  under q u i t e d i f f e r e n t r e a c t i o n c o n d i t i o n s r e p o r t e d l y produced o n l y dimer (76).  Recently,  however,  the s u c c e s s f u l p r e p a r a t i o n o f bromine  isocyanate  from bromine and s i l v e r c y a n a t e u s i n g a p r o c e d u r e v e r y s i m i l a r t o d e s c r i b e d h e r e f o r c h l o r i n e i s o c y a n a t e has been r e p o r t e d  (77).  that  47  Many d i f f e r e n t m o d i f i c a t i o n s o f t h i s p r e p a r a t i o n were t r i e d ; f o l l o w i n g one gave the b e s t y i e l d .  the  A m i x t u r e of 1/3 gm o f f r e s h l y p r e -  p a r e d s i l v e r c y a n a t e and 1/2 gm o f f i n e l y powdered s i l i c a was p l a c e d i n a t h i n g l a s s tube (8 mm O.D.) glass wool.  and wedged i n p l a c e w i t h two s m a l l p l u g s o f  T h i s tube was then c o n n e c t e d at one end t o a sample tube  c o n t a i n i n g pure c h l o r i n e , and at the o t h e r end t o a vacuum system Figure 3.1).  A f t e r i n i t i a l e v a c u a t i o n a t room t e m p e r a t u r e , t h e  (see  silver  c y a n a t e / s i l i c a m i x t u r e was t h e n pumped on f o r s e v e r a l h o u r s w h i l e b e i n g h e a t e d t o about 100°C.  When a s t a b l e p r e s s u r e o f l e s s than 1 y had been  a c h i e v e d the s i l v e r c y a n a t e was a l l o w e d t o c o o l t o room t e m p e r a t u r e ,  the  t r a p was c o o l e d t o 77°K, and t h e s t o p c o c k t o the c h l o r i n e sample tube ( c o o l e d i n d r y i c e t r i c h l o r o e t h y l e n e s l u s h , about -80°C) was opened. I m m e d i a t e l y w h i t i s h m a t e r i a l s t a r t e d t o c o l l e c t i n the l e f t arm o f  the  t r a p a t t h e l e v e l o f t h e l i q u i d n i t r o g e n , and s i m u l t a n e o u s l y the p r e s s u r e on the pump s i d e of the t r a p r o s e t o about 100 u , d e s p i t e the f a c t the whole system was b e i n g pumped o n .  that  A f t e r a few m i n u t e s t h i s p r e s s u r e  s t a r t e d t o d e c l i n e , and when i t reached a p p r o x i m a t e l y 30 y h e a t i n g was a g a i n a p p l i e d t o the s i l v e r c y a n a t e , a t f i r s t g e n t l y , t h e n more s t r o n g l y t i l l a t e m p e r a t u r e o f about 80°C was r e a c h e d .  Throughout the h e a t i n g  p e r i o d the p r e s s u r e on the pump s i d e o f the t r a p f l u c t u a t e d around 20 y . A f t e r 5 to 10 m i n u t e s o f h e a t i n g the g r e e n i s h t i n g e o f c h l o r i n e became c l e a r l y v i s i b l e i n the t r a p and the p r e p a r a t i o n was s t o p p e d . The uncondensable r e a c t i o n p r o d u c t s were presumably n i t r o g e n , oxygen and/or carbon monoxide.  The condensable r e a c t i o n p r o d u c t s were s e p a r a t e d  i n t o t h r e e f r a c t i o n s : a v o l a t i l e f r a c t i o n c o n s i s t i n g l a r g e l y of  chlorine  and carbon d i o x i d e , an i n t e r m e d i a t e f r a c t i o n of c h l o r i n e i s o c y a n a t e , and a l e s s v o l a t i l e f r a c t i o n o f one o r more u n i d e n t i f i e d compounds.  FIGURE 3.1  Schematic I l l u s t r a t i o n of the Vacuum System used i n the P r e p a r a t i o n o f C h l o r i n e I s o c y a n a t e from S i l v e r Cyanate and C h l o r i n e .  Glass Wool  To Thermocouple P r e s s u r e Gauge  To Pump  t  -AgNCO Glass Wool  -Trap fl  D Sample — Tube  Liquid Chlorine (-80°C)  Scale  1:2  49 The b e s t y i e l d of c h l o r i n e i s o c y a n a t e o b t a i n e d i n t h i s was e s t i m a t e d t o be l e s s than 2 5 % .  preparation  F u r t h e r m o r e , complete p u r i f i c a t i o n o f  the c h l o r i n e i s o c y a n a t e c o u l d n o t be a c c o m p l i s h e d ; at b e s t , o n l y 80% p u r i t y , and t h a t on v e r y s m a l l s a m p l e s , was a c h i e v e d . Gaseous samples o f c h l o r i n e i s o c y a n a t e f o r microwave s p e c t r o s c o p i c s t u d y were t a k e n from the v a p o r above the b u l k l i q u i d sample h e l d a t a p p r o x i m a t e l y -80°C.  These samples decomposed and/or p o l y m e r i z e d i n t h e m e t a l  c e l l v e r y q u i c k l y at f i r s t , b u t more s l o w l y a f t e r some c o n d i t i o n i n g o f c e l l , and e v e n t u a l l y w i t h a h a l f - l i f e o f about 10 m i n u t e s .  the  Pressures of  l e s s t h a n 10 u were used f o r most measurements, w i t h an o c c a s i o n a l weak l i n e b e i n g measured u s i n g 10 - 25 p p r e s s u r e . I n a l l o f t h i s work the microwave c e l l was c o o l e d w i t h d r y i c e e n c l o s e d i n polystyrene boxes.  T h i s reduced the l i n e w i d t h s s l i g h t l y b u t , more  i m p o r t a n t , i n c r e a s e d the h a l f - l i f e o f the c h l o r i n e i s o c y a n a t e s a m p l e s . 3.2  P r e p a r a t i o n of I s o c y a n i c  Acid.  A sample o f i s o c y a n i c a c i d i n n a t u r a l i s o t o p i c abundance was o b t a i n e d by the vacuum p y r o l y s i s o f c y a n u r i c a c i d ( 7 8 ) .  Since t h i s r e a c t i o n , u n l i k e  t h a t f o r c h l o r i n e i s o c y a n a t e , can be s u c c e s s f u l l y performed o v e r a wide range o f e x p e r i m e n t a l c o n d i t i o n s , the f o l l o w i n g r a t h e r crude p r o c e d u r e was used.  A few grams o f c y a n u r i c a c i d (Baker Chemical) were p l a c e d i n the end  o f a p y r e x tube w h i c h was t h e n e v a c u a t e d .  When a s t a b l e p r e s s u r e o f  less  t h a n 1 u had been o b t a i n e d , the c y a n u r i c a c i d was h e a t e d s t r o n g l y w i t h an a i r - g a s t o r c h and the r e s u l t i n g p y r o l y s i s p r o d u c t s were t r a p p e d at 77°K under dynamic vacuum.  Subsequent a n a l y s i s by i n f r a r e d s p e c t r o s c o p y  (79)  r e v e a l e d t h a t a good y i e l d of i s o c y a n i c a c i d had been o b t a i n e d , w i t h o n l y a s m a l l amount of c a r b o n d i o x i d e i m p u r i t y . by f r a c t i o n a l d i s t i l l a t i o n .  P u r i f i c a t i o n was e a s i l y  effected  50  An  0 e n r i c h e d sample o f i s o c y a n i c a c i d was o b t a i n e d by p y r o l y s i s  of l a b e l e d c y a n u r i c a c i d , w h i c h had been p r e p a r e d u s i n g the method described i n section 3.1. 15 Isocyanic  a c i d samples 50% e n r i c h e d i n  N and  13 C were p r e p a r e d by  the d i r e c t r e a c t i o n of hydrogen bromide gas w i t h an a p p r o p r i a t e l y sample of s i l v e r cyanate ( 8 0 ) .  labeled  The e x p e r i m e n t a l p r o c e d u r e used i n t h i s  s y n t h e s i s was v e r y s i m i l a r t o t h a t used i n the analogous c h l o r i n e  isocyanate  p r e p a r a t i o n ; i n d e e d , i t was t h i s s y n t h e s i s t h a t p r o v i d e d the i n s p i r a t i o n f o r the c h l o r i n e / s i l v e r c y a n a t e e x p e r i m e n t s .  The o n l y s i g n i f i c a n t  difference  was t h a t t h i s r e a c t i o n was c a r r i e d out at room t e m p e r a t u r e u s i n g pure cyanate.  Respectable y i e l d s of i s o c y a n i c a c i d , contaminated w i t h  amounts o f c a r b o n d i o x i d e and hydrogen b r o m i d e , were o b t a i n e d .  silver  variable  Some p u r i -  f i c a t i o n was a c c o m p l i s h e d by pumping away the most v o l a t i l e f r a c t i o n w i t h the sample tube c o o l e d to about -80°C. The i s o t o p i c a l l y e n r i c h e d samples o f s i l v e r c y a n a t e used i n the p r e v i o u s l y d e s c r i b e d e x p e r i m e n t s were p r e p a r e d by the a l k a l i n e  permanganate  o x i d a t i o n of the c o r r e s p o n d i n g sodium c y a n i d e s o l u t i o n , f o l l o w e d by p r e c i p i t a t i o n of the s i l v e r s a l t .  The l a b e l e d sodium c y a n i d e samples were  o b t a i n e d from the Isomet C o r p o r a t i o n ( O a k l a n d , N . J .  07436, U . S . A . ) .  d e t a i l e d account o f the o x i d a t i o n r e a c t i o n may be found i n I s o t o p i c Syntheses"  A  "Inorganic  (81).  D e u t e r a t e d samples o f i s o c y a n i c a c i d were p r e p a r e d i n the microwave c e l l by exchange between d e u t e r i u m o x i d e and n o r m a l i s o c y a n i c a c i d . p r o c e d u r e used was t o f i l l  The  the c e l l w i t h about 0.5 t o r r of heavy w a t e r f o r  about 10 m i n u t e s and t h e n pump i t out t o a p r e s s u r e o f l e s s than 1 p. s m a l l sample of i s o c y a n i c a c i d (<10 u) was then i n t r o d u c e d i n t o the  A  cell,  and r a p i d d e u t e r i u m - hydrogen exchange would o c c u r between the heavy w a t e r  51  adsorbed on the c e l l w a l l s and the a c i d .  Subsequent r e a c t i o n o f the  c y a n i c a c i d w i t h the w a t e r (78) n e c e s s i t a t e d f r e q u e n t replacement o f s a m p l e s .  iso-  (about e v e r y 5 m i n . )  One heavy w a t e r c e l l c o n d i t i o n i n g , however,  was  u s u a l l y s u f f i c i e n t t o g i v e 20 to 40% d e u t e r a t i o n o f s e v e r a l i s o c y a n i c a c i d samples. The i s o c y a n i c a c i d samples were s t o r e d and h a n d l e d i n much the same way as the c h l o r i n e i s o c y a n a t e o n e s .  P o l y m e r i z a t i o n was, however, a l e s s  s e r i o u s p r o b l e m , and i n the absence of c e l l w a t e r , had t o be changed o n l y o c c a s i o n a l l y .  the s p e c t r o s c o p i c samples  As b e f o r e , a l l measurements were made  w i t h the c e l l c o o l e d i n d r y i c e . 3.3  P r e p a r a t i o n o f Cyanogen  Isocyanate.  Cyanogen i s o c y a n a t e was p r e p a r e d by the vacuum t h e r m o l y s i s o f cyanate.  silver  The p r o c e d u r e used was a s l i g h t l y m o d i f i e d v e r s i o n o f t h a t  by G o t t a r d i ( 8 2 ) .  developed  About 4 gms o f s i l v e r c y a n a t e were p l a c e d i n the end o f  a p y r e x tube w h i c h was then connected t o a s p e c i a l t r a p / s a m p l e t u b e ; i n t u r n was connected t o a vacuum l i n e ( F i g u r e 3 . 2 ) . then e v a c u a t e d and pumped on o v e r n i g h t .  this  The whole system was  The n e x t day the t r a p was c o o l e d  i n l i q u i d n i t r o g e n and the s i l v e r c y a n a t e was h e a t e d w i t h an a i r - g a s t o r c h . A f t e r a s h o r t warm-up p e r i o d , the s i l v e r c y a n a t e s t a r t e d t o undergo a s t r o n g l y e x o t h e r m i c r e a c t i o n , w i t h v i g o r o u s e v o l u t i o n of g a s . d i s c o n t i n u e d as soon as the r e a c t i o n was w e l l under way.  H e a t i n g was  W i t h i n a few  m i n u t e s the r e a c t i o n was f i n i s h e d , l e a v i n g a b l a c k r e s i d u e i n the t u b e , and a l a r g e amount o f w h i t e s o l i d i n the t r a p . s i d e r a b l e volume o f gas had passed t h r o u g h the t r a p  reaction  In a d d i t i o n , a c o n (presumably N^* 0^ o r  CO) and had been pumped away d u r i n g the r e a c t i o n . The w h i t e s o l i d i n the t r a p was s u b s e q u e n t l y d e t e r m i n e d (by  infrared  FIGURE 3.2  Schematic I l l u s t r a t i o n of the Vacuum System used i n the P r e p a r a t i o n o f Cyanogen I s o c y a n a t e .  4 gms AgNCO / Glass Wool  To Pump  •35 cm  To Thermocouple P r e s s u r e Gauge  Trap/Sample Tube  Scale  1:2  53  spectroscopy)  t o be l a r g e l y carbon d i o x i d e a l o n g w i t h a s m a l l e r amount of  cyanogen i s o c y a n a t e .  The carbon d i o x i d e was removed by s i m p l y warming the  t r a p t o about -80 C and then pumping on i t  f o r s e v e r a l hours  i s o c y a n a t e has e s s e n t i a l l y z e r o v a p o r p r e s s u r e a t t h i s  (cyanogen  temperature).  F u r t h e r warming o f the t r a p t o about -63°C ( c h l o r o f o r m s l u s h ) g a v e , removal o f the l a s t o f the C ^ ,  after  a s t e a d y v a p o r p r e s s u r e o f about 30 u o f  cyanogen i s o c y a n a t e o v e r i t s w h i t e s o l i d .  No attempt was made t o o b t a i n a  l a r g e r v a p o r p r e s s u r e over the b u l k sample by s t i l l f u r t h e r w a r m i n g , because of the r e p o r t e d tendency of cyanogen i s o c y a n a t e to v e r y r e a d i l y p o l y m e r i z e (18). An i n f r a r e d spectrum of the p u r i f i e d cyanogen i s o c y a n a t e , i n i t s p h a s e , was. o b t a i n e d i n the f o l l o w i n g way.  vapor  Vapor was d i s t i l l e d , o v e r a  p e r i o d of e i g h t h o u r s , from the t r a p / s a m p l e tube a t -63°C i n t o a g l a s s i n f r a r e d c e l l whose c o l d f i n g e r was a t 77°K.  The i n f r a r e d c e l l was t h e n  s e a l e d , removed from the vacuum l i n e and an i n f r a r e d s p e c t r u m was r e c o r d e d as soon as the c o l d f i n g e r had warmed t o room t e m p e r a t u r e .  T h i s spectrum  was i n e x c e l l e n t agreement w i t h t h a t p u b l i s h e d by Mayer (18) as b e l o n g i n g t o cyanogen i s o c y a n a t e .  and i d e n t i f i e d  A s e r i e s of s p e c t r a r e c o r d e d over  the n e x t few h o u r s u s i n g the same sample showed a g r a d u a l d e c l i n e i n the i n t e n s i t y o f the cyanogen i s o c y a n a t e l i n e s , and s i m u l t a n e o u s l y an i n c r e a s e i n the s t r e n g t h o f a few b r o a d bands s u b s e q u e n t l y a s s i g n e d to s o l i d p o l y m e r d e p o s i t e d on the c e l l windows. The b u l k sample of cyanogen i s o c y a n a t e was s t o r e d i n i t s  trap/sample  o ^ tube at 77 K. S p e c t r o s c o p i c samples were o b t a i n e d by warming i t  o t o -63 C;  the 20 - 30 u v a p o r p r e s s u r e thus a c h i e v e d b e i n g more than a d e q u a t e .  Samples  decomposed and/or p o l y m e r i z e d s l o w l y i n the microwave c e l l and were t h e r e f o r e  54  u s u a l l y replaced every 5 - 2 0  minutes.  A l l measurements were made a t room  t e m p e r a t u r e w i t h sample p r e s s u r e s o f g e n e r a l l y l e s s than 10 u. 3.4  The S t a r k Modulated Microwave  Spectrometer.  A c o n v e n t i o n a l 100 kHz S t a r k modulated microwave s p e c t r o m e t e r was used f o r t h i s work.  The s p e c t r a l r e g i o n c o v e r e d was 8 - 3 7  GHz w i t h an average  (optimum) measurement a c c u r a c y o f ±0.05 MHz, and an u l t i m a t e s e n s i t i v i t y - . -10 -1 o f 5x10 cm i n  Two r a t h e r d i f f e r e n t t y p e s o f microwave r a d i a t i o n s o u r c e s were u s e d ; namely backward wave o s c i l l a t o r s and r e f l e x k l y s t r o n s ( 8 3 ) .  The l o w  f r e q u e n c y X- and P-band r e g i o n s were c o v e r e d w i t h a p a i r o f phase  stabil-  i z e d backward wave o s c i l l a t o r s ( H e w l e t t - P a c k a r d H81-8694B and H81-8695A). S i n c e t h e s e s o u r c e s c o u l d be e l e c t r o n i c a l l y tuned o v e r t h e i r e n t i r e range w i t h e x c e l l e n t l o n g term s t a b i l i t y , the r e s u l t i n g d e t e c t o r was g e n e r a l l y d i s p l a y e d on a s t r i p c h a r t r e c o r d e r frequency,  (HP 6 8 0 ) .  frequency  signal  The h i g h  18 - 37 GHz, r e g i o n was spanned u s i n g OKI 20V10, 24V10, 30V10,  35V10, and 35V11 k l y s t r o n s .  These were e l e c t r o n i c a l l y scanned o v e r a  narrow f r e q u e n c y range (2 - 10 MHz) by a p p l y i n g a s a w t o o t h v o l t a g e t o the klystron reflector electrode.  T h i s sawtooth was s y n c h r o n i z e d w i t h  that  a p p l i e d t o the X - p l a t e s o f a H e w l e t t - P a c k a r d d u a l t r a c e o s c i l l o s c o p e (1205A).  The a m p l i f i e d d e t e c t o r o u t p u t was t h e n used as the Y - v o l t a g e  f o r one o f t h e s e t r a c e s , thus a l l o w i n g a c o n v e n i e n t d i s p l a y o f a s m a l l segment o f t h e microwave s p e c t r u m .  The c e n t e r f r e q u e n c y o f t h i s scan was  v a r i e d by m a n u a l , m e c h a n i c a l , t u n i n g o f the k l y s t r o n c a v i t y . The backward wave o s c i l l a t o r s g e n e r a t e d about 40 - 80 mW o f power, the k l y s t r o n s anywhere from 200 to 600 mW.  Most o f t h i s power was  dissi-  p a t e d , however, by p l a c i n g an a d j u s t a b l e a t t e n u a t o r between the s o u r c e  55  and the microwave c e l l .  T y p i c a l l y , measurements were made w i t h o n l y  1-2  mW of power i n the c e l l i n o r d e r to a v o i d s a t u r a t i o n of the observed t r a n s i t i o n s and t o m i n i m i z e r e f l e c t i o n s . The amount o f r a d i a t i o n absorbed by a low p r e s s u r e sample u n d e r g o i n g a p a r t i c u l a r r o t a t i o n a l t r a n s i t i o n i n a c o n v e n t i o n a l microwave  cell,is  u s u a l l y much l e s s t h a n 0 . 1 % o f the t o t a l r e a c h i n g the d e t e c t o r .  Since f r e -  quency dependent v a r i a t i o n s i n the d e t e c t o r o u t p u t due t o r e f l e c t i o n s the c e l l ,  in  changes i n s o u r c e power, e t c . , are g e n e r a l l y much l a r g e r t h a n t h i s ,  i t i s c l e a r t h a t d i r e c t o b s e r v a t i o n o f microwave t r a n s i t i o n s w i l l be d i f f i c u l t o r i m p o s s i b l e .  generally  S e v e r a l d i f f e r e n t t e c h n i q u e s have been d e v i s e d  t o surmount t h i s d i f f i c u l t y ( 8 3 ) .  The one most commonly e m p l o y e d , and t h a t  used e x c l u s i v e l y i n t h i s s t u d y , i s S t a r k m o d u l a t i o n . The p r i n c i p l e i n v o l v e d i n S t a r k m o d u l a t i o n i s r e a l l y q u i t e s i m p l e : the r o t a t i o n a l l i n e s a r e i n e f f e c t t u r n e d on and o f f by a p p l i c a t i o n of a h i g h f r e q u e n c y , z e r o b a s e d , e l e c t r i c f i e l d as a square wave.  I n the o f f  p a r t o f the c y c l e a l l t r a n s i t i o n s o c c u r a t t h e i r n o r m a l f r e q u e n c i e s ; the on p a r t ,  they a r e a l l s h i f t e d as d e s c r i b e d i n s e c t i o n 2 . 3 .  in  Since sources  o f power f l u c t u a t i o n o t h e r than m o l e c u l a r a b s o r p t i o n are u n a f f e c t e d by the S t a r k f i e l d , phase s e n s i t i v e a m p l i f i c a t i o n of the d e t e c t o r o u t p u t can be used t o d i s c r i m i n a t e a g a i n s t them.  F u r t h e r , the o u t p u t of the d e t e c t o r now  has the m o d u l a t i o n f r e q u e n c y as a c a r r i e r f r e q u e n c y and hence a s i g n i f i c a n t r e d u c t i o n i n i t s 1/f n o i s e i s  achieved.  The o u t p u t o f the phase s e n s i t i v e  (lock-in)  a m p l i f i e r when d i s p l a y e d  on the o s c i l l o s c o p e appears as the d i f f e r e n c e between the a b s o r p t i o n a t z e r o f i e l d and the a b s o r p t i o n w i t h the S t a r k f i e l d o n : i . e . one s i d e o f the base l i n e ,  the " l i n e s " appear on  the " S t a r k l o b e s " on the o t h e r .  This i s  generally  56  a v e r y c o n v e n i e n t arrangement,  e x c e p t when i t i s i m p o s s i b l e t o a d j u s t  a m p l i t u d e o f the square wave t o s h i f t a l l S t a r k l o b e s c l e a r o f the  the  line  b e i n g measured. Two d i f f e r e n t t y p e s o f d e t e c t o r s were used t o c o v e r the 8 - 3 7 spectral region.  GHz  The X- and P-band d e t e c t o r s were f a c t o r y mounted, low-  n o i s e , high s e n s i t i v i t y , diodes (Hewlett-Packard  H06-X422A and H06-P422A).  I n the h i g h f r e q u e n c y 18 - 37 GHz r e g i o n , s t a n d a r d 1N26 c r y s t a l s ,  hand  mounted i n a t e r m i n a t e d t u n a b l e s e c t i o n o f K-band w a v e g u i d e , were u s e d . The o u t p u t from t h e s e d e t e c t o r s was passed t h r o u g h a p r e - a m p l i f i e r and then f e d i n t o 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 phase s e n s i t i v e l o c k - i n a m p l i f i e r , Model 120 o r 121. S t a r k m o d u l a t i o n was o b t a i n e d by a p p l y i n g the o u t p u t from 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 square wave g e n e r a t o r t o a copper  septum i n s e r t e d i n the 7 f o o t X-band c e l l .  T h i s sheet o f copper  (0.019  i n c h e s t h i c k ) was h e l d i n the c e n t e r o f the c e l l p a r a l l e l t o the b r o a d f a c e s o f the waveguide s l o t t e d t e f l o n runners.  and i n s u l a t e d from the narrow ones by a p a i r o f The r e s u l t i n g e l e c t r i c f i e l d was a l m o s t  p e r p e n d i c u l a r t o the b r o a d f a c e s o f the grounded c e l l .  Its  entirely  peak t o peak  a m p l i t u d e c o u l d be c o n t i n u o u s l y v a r i e d from 0 t o o v e r 4000 V o l t s / c m . T r a n s i t i o n f r e q u e n c i e s were measured i n the k l y s t r o n r e g i o n by d e t e c t i n g the b e a t f r e q u e n c y between the s o u r c e r a d i a t i o n and a harmonic of a c r y s t a l c o n t r o l l e d frequency standard (83).  These harmonics were  g e n e r a t e d by m u l t i p l y i n g the 50 MHz o u t p u t o f a Micro-Now  Instrument  Company Model 101C f r e q u e n c y m u l t i p l i e r c h a i n w i t h a 1N26 c r y s t a l . were then mixed w i t h the k l y s t r o n r a d i a t i o n i n a t e r m i n a t e d , s e c t i o n o f K-band w a v e g u i d e ,  They  tunable,  connected to the main waveguide l i n e  with  57  a 20 db cross-guide directional coupler.  The resulting beat frequencies  were detected with the same 1N26 crystal and measured with a Hammarlund Model SP-600 calibrated communications receiver. The output of the receiver was displayed on the second trace of the dual trace oscilloscope as one or more sharp "marker pips". Transitions were then measured by tuning the receiver u n t i l one of these "pips" lined up with the absorption displayed on the other trace, and the beat frequency was read directly off the calibrated receiver scale. Beat frequencies from about 5 to 55 MHz could be detected with this system.  Their signed frequency when added to that  of the associated harmonic gave the true l i n e frequency.  Exactly which  harmonic was producing the particular beat observed was readily determined by making a preliminary rough (to within 20 MHz) frequency measurement with a calibrated cavity wavemeter (83). The Micro-Now frequency generator was found to have excellent long term s t a b i l i t y . Hewlett-Packard  I t s 5 MHz fundamental was continuously monitored with a electronic counter (Model 5246L) and maintained, with  occasional minor adjustments, at exactly 5.000000 MHz.  As a further check  on the accuracy of the frequency measurements, known transitions were occasionally measured; agreement with the l i t e r a t u r e value to within 0.05 MHz was always obtained. In X- and P- band operation the source frequency was continuously monitored with an HP5246L counter.  The output of this counter could be  used to trigger an HP8429A frequency marker system which then produced calibration marks on the chart paper spectral display at intervals of 0.1, 1, 10, 100 and 1000 MHz as desired.  Alternatively the source could be  manually swept to the center frequency of the transition being measured  58  (with oscilloscope display) 3.5  Double Resonance  and the f r e q u e n c y read d i r e c t l y from the  counter.  Experiments.  The b_-type assignments o f cyanogen i s o c y a n a t e i n i t s ground v i b r a t i o n a l s t a t e were c o n c l u s i v e l y v e r i f i e d by p e r f o r m i n g two d o u b l e resonance e x p e r i m e n t s .  microwave-microwave  In b o t h o f t h e s e , an a-type Q-branch  line  o c c u r r i n g i n the X-band r e g i o n was pumped w i t h up to 50 mW o f power w h i l e a h i g h e r f r e q u e n c y _b-type l i n e , w i t h w h i c h i t s h a r e d a common energy was b e i n g o b s e r v e d . (1)  16  U  1 5  (2)  n  —  , lb  1,14-  3 9 3 8  The p a i r s of t r a n s i t i o n s s t u d i e d  1  >  3  8  15-  1, 1  1 5  1,15  - 3 8  2,36 -  J  3 8  2  j  3  7  2,37  are:  at  18770.20 MHz  Observed  at  12102.40 MHz  Pumped  at  27905.72 MHz  Observed  a t  level,  9191.27 MHz  Pumped  The e x p e r i m e n t a l s e t - u p u s e d , a l t h o u g h somewhat u n s o p h i s t i c a t e d , proved t o be e m i n e n t l y s u c c e s s f u l . ( F i g u r e 3 . 3 ) . phase l o c k e d s o u r c e ( s e c t i o n 3.4)  Pump power s u p p l i e d by the HP  was f e d d i r e c t l y i n t o the X-band  S i g n a l power g e n e r a t e d by e i t h e r a 20V10 o r a 30V10 k l y s t r o n was i n t o the main waveguide  l i n e w i t h a 3 db d i r e c t i o n a l c o u p l e r .  cell.  coupled  Both s o u r c e s  were p r o t e c t e d from r e f l e c t e d power w i t h an a p p r o p r i a t e i s o l a t o r .  Pump  power was p r e v e n t e d f r o m r e a c h i n g the d e t e c t o r by the use o f a K-band d e t e c t o r mount h a v i n g a c u t o f f f r e q u e n c y o f 14.08 GHz. The p r o c e d u r e f o l l o w e d was t o observe the b-type t r a n s i t i o n u s i n g n o r m a l S t a r k m o d u l a t i o n , and t h e n t r y t o d e t e c t any change i n i t s as the pump f r e q u e n c y was v a r i e d near the resonance f r e q u e n c y of Q-branch t r a n s i t i o n .  intensity the  In both cases a s m a l l but c l e a r l y d i s c e r n i b l e  was d e t e c t e d : the b_-type t r a n s i t i o n had a reduced i n t e n s i t y  effect  (by 15 t o 20%)  FIGURE 3.3  Schematic Resonance  I l l u s t r a t i o n of the Spectrometer Experiments.  used i n the Microwave - Microwave  Double  Pump Power  Attenuator  o  To Power Meter  To  Pre-Amplifier  3 db Directional Coupler  X-Band Isolator  Cell  K-Band Waveguide Tuning Stub  20 db D i r e c t i o n a l Coupler 7  K-Band T  20 db Cross-Guide D i r e c t i o n a l Coupler.  ^Attenuator  T-f  T o n -  To Scope Wavemeter  Isolator  6.  •>- To SP-600 — From Micro-Now  20V10 o r 30V10 K l y s t r o n  1N26 Crystal Detector  60  when the a-type t r a n s i t i o n was e x a c t l y i n r e s o n a n c e .  Tuning o f the pump t o  e i t h e r h i g h o r low f r e q u e n c y of resonance by more than 1 MHz gave a s t r o n g e r Jb-type s i g n a l , c o n s t a n t over a wide range o f pump f r e q u e n c i e s . 3.6  D i p o l e Moment Measurements. D i p o l e moment measurements were made on i s o c y a n i c a c i d and cyanogen  isocyanate.  S t a r k s h i f t s were produced by a p p l y i n g , t o the c e l l septum, a  l a r g e a c c u r a t e l y known DC v o l t a g e , upon w h i c h was f l o a t e d a s m a l l AC (100 kHz) m o d u l a t i o n f i e l d . . As u s u a l , d e t e c t o r o u t p u t was a m p l i f i e d w i t h a phase s e n s i t i v e l o c k - i n a m p l i f i e r . W i t h such a s y s t e m , each S t a r k component appears as two l o b e s d i f f e r i n g i n phase by 180°. r  J  One l o b e i s a s s o c i a t e d w i t h an e l e c t r i c f i e l d o f E + E , o m'  the o t h e r w i t h a f i e l d o f E  o  - E , where E m  o  i s the DC b i a s f i e l d and E  one h a l f the peak t o peak a m p l i t u d e o f the square wave. second o r d e r S t a r k e f f e c t ,  m  is  Then, f o r a s t r i c t l y  l i k e t h a t o b s e r v e d i n t h i s w o r k , the average 2  f r e q u e n c y o f any a s s o c i a t e d p a i r o f l o b e s i s a l i n e a r f u n c t i o n of E  2 + E^.  There are two r e a s o n s f o r u s i n g the above p r o c e d u r e , r a t h e r than j u s t AC m o d u l a t i o n .  F i r s t l y , the square wave waveform becomes q u i t e d i s t o r t e d  a t h i g h v o l t a g e s r e s u l t i n g i n a b r o a d e n i n g of a l l S t a r k components. S e c o n d l y , i t i s d i f f i c u l t t o measure a c c u r a t e l y the a m p l i t u d e of the wave v o l t a g e .  W i t h the two f i e l d system and a second o r d e r S t a r k  the p e r c e n t e r r o r i n the s m a l l ( u n d i s t o r t e d )  AC v o l t a g e may be as  as the p e r c e n t u n c e r t a i n t y i n the DC v o l t a g e m u l t i p l i e d by the  2  square  effect, large  ratio  (E /E ) w i t h o u t becoming the l i m i t i n g f a c t o r on t h e a c c u r a c y o f a m measurements.  the  The s o u r c e o f the DC b i a s p o t e n t i a l was a John F l u k e M a n u f a c t u r i n g Co. Model 412B DC power s u p p l y w i t h an o u t p u t of 0 to 2100 v o l t s , k i n d l y l e n t t o us by D r . A. J . M e r e r .  T h i s power s u p p l y has a s t a t e d c a l i b r a t i o n  61  a c c u r a c y o f ±0.25% and a r e s e t a b i l i t y o f ±0.05%.  The m o d u l a t i o n f i e l d  was produced by the p r e v i o u s l y d i s c u s s e d 100 kHz square wave g e n e r a t o r . It  was f l o a t e d on the DC b i a s p o t e n t i a l w i t h a S t a r k v o l t a g e m i x e r c o n -  s t r u c t e d by C. R. P a r e n t  (84)  a f t e r a d e s i g n by Muenter  (85).  62  CHAPTER 4  THE MICROWAVE SPECTRUM OF CHLORINE ISOCYANATE C h l o r i n e i s o c y a n a t e was f i r s t p r e p a r e d i n 1965 by Nachbaur and G o t t a r d i (73) u s i n g the method d e s c r i b e d i n Chapter 3.  Its  c h e m i s t r y has been the  s u b j e c t of a number o f more r e c e n t i n v e s t i g a t i o n s by G o t t a r d i and Henn (86,...,89).  The i n f r a r e d and Raman s p e c t r a o f t h i s m o l e c u l e have been  analysed to y i e l d a v i b r a t i o n a l force f i e l d (90).  An e l e c t r o n d i f f r a c t i o n  s t u d y by Oberhammer (91) p r o v i d e d some i n f o r m a t i o n on the geometry o f m o l e c u l e b u t c o u l d n o t d e f i n i t e l y d i s t i n g u i s h between two structures.  the  alternative  A l l o f t h e s e p u b l i c a t i o n s , e x c e p t the f i r s t ,  appeared w h i l e  the work d e s c r i b e d h e r e was i n p r o g r e s s . A p r e l i m i n a r y i n v e s t i g a t i o n o f the microwave spectrum o f c h l o r i n e c y a n a t e was u n d e r t a k e n by the a u t h o r t o f u l f i l p a r t o f the o f a B.Sc.  degree.  iso-  requirements  Only a few a-type R-branch t r a n s i t i o n s o f the n a t u r a l l y  , , \ 35„..U. 12„16, 37„ 14 12 16„ . . . . , abundant CI N C 0 and CI N C 0 i s o t o p i c s p e c i e s were a s s i g n e d T  1  and measured i n t h a t s t u d y .  llT  fc  I n the p r e s e n t work most of t h e s e were r e -  measured w i t h a more s e n s i t i v e s p e c t r o m e t e r i n o r d e r t o r e s o l v e n i t r o g e n quadrupole c o u p l i n g h y p e r f i n e s t r u c t u r e . i t i o n s o f t h e s e i s o t o p e s were a l s o a s s i g n e d .  their  Numerous b-type t r a n s -  In a d d i t i o n , several  arti-  f i c i a l l y e n r i c h e d i s o t o p i c samples were p r e p a r e d and s t u d i e d so t h a t a complete s u b s t i t u t i o n s t r u c t u r e c o u l d be o b t a i n e d .  A l l told,  s p e c t r a were a n a l y s e d f o r s i x i s o t o p i c s p e c i e s o f c h l o r i n e they  microwave  isocyanate;  are: 3 5  C1 N  3 7  C1  U  1 4  N  1 2  1 2  C C  1 6  0  3 5  C1  1 4  N  1 2  C  1 8  0  3 5  C1  1 5  N  1 2  C  1 6  0  1 6  0  3 5  C1  1 4  N  1 3  C  1 6  0  3 7  C1  1 5  N  1 2  C  1 6  0  63  4.1  Assignment o f the  Spectrum.  The r o t a t i o n a l spectrum o f c h l o r i n e i s o c y a n a t e was e x p e c t e d t o be t h a t o f a n e a r p r o l a t e asymmetric r o t o r .  T h i s was deduced by c o n s t r u c t i n g  a r e a s o n a b l e m o l e c u l a r s t r u c t u r e u s i n g the assumed p a r a m e t e r s : 180°,  r(C-O) = 1.17 A , r(N-C) = 1.20 A , as i n HNCO ( 1 1 ) ,  1.73 &*, Z_(C1NC) = 112°, 35 f o r the  as i n CIN^ ( 1 4 ) .  Z-(NCO) =  and r ( N - C l ) =  A r i g i d r o t o r spectrum  calculated  1A 12 16 CI  N  C  0 i s o t o p i c s p e c i e s , w i t h the a i d o f t h i s  structure,  c o n t a i n e d a l a r g e number o f t r a n s i t i o n s i n the o p e r a t i o n a l r e g i o n o f o u r spectrometer.  Of t h e s e , the pseudosymmetric r o t o r a-type R-branch g r o u p s ,  p r e d i c t e d to occur at  Vj^  f i r s t order Stark e f f e c t s  J + 1  « (J+l)(B+C) «  (J+l)(6GHz) and t o have n e a r  ( o n l y t h o s e components f o r w h i c h K ^ * 0) , were  r e c o g n i z e d as the most l i k e l y c a n d i d a t e s f o r an e a r l y a s s i g n m e n t . t r a s t the w i d e l y s c a t t e r e d b-type R- and P-branch t r a n s i t i o n s ,  By c o n -  notable  o n l y f o r t h e i r l a c k o f p a r t i c u l a r l y d i s t i n g u i s h i n g c h a r a c t e r i s t i c s , were e x p e c t e d to be much more d i f f i c u l t t o a s s i g n . A p r e l i m i n a r y i n v e s t i g a t i o n o f the 28 - 32 GHz r e g i o n r e v e a l e d a v e r y r i c h spectrum w h i c h i n c l u d e d s e v e r a l complex m u l t i p l e t s . these,  c o n s i s t i n g of a s i n g l e high f i e l d  The s t r o n g e s t  of  d o u b l e t a t 30.37 GHz and a s e r i e s  o f low f i e l d t r a n s i t i o n s s p r e a d out between 30.37 GHz and 30.42 GHz, was 35 tentatively  a s s i g n e d as the J = 4+5 a-type R-branch group of  i n i t s ground v i b r a t i o n a l s t a t e .  Three v e r y s i m i l a r b u t  1A 12 16 CI  N  C  0  progressively  weaker m u l t i p l e t s o c c u r r i n g at h i g h e r f r e q u e n c i e s were presumed t o be associated w i t h molecules i n e x c i t e d v i b r a t i o n a l s t a t e s .  An e s s e n t i a l l y  complete r e p r o d u c t i o n of t h i s whole p a t t e r n , but w i t h a r o u g h l y  1/3  * The terms " l o w f i e l d " and " h i g h f i e l d " are used t o i n d i c a t e the a m p l i t u d e o f the S t a r k f i e l d r e q u i r e d t o modulate a t r a n s i t i o n and hence make i t detectable. G e n e r a l l y , low f i e l d i m p l i e s a f i r s t o r d e r S t a r k e f f e c t , h i g h f i e l d a second o r d e r e f f e c t .  64 r e d u c t i o n i n i n t e n s i t y and a s l i g h t l y a l t e r e d h y p e r f i n e s t r u c t u r e , was found n e a r l y 800 MHz t o lower f r e q u e n c y .  T h i s was e v i d e n t l y the c o r r e s p o n d i n g  _ 3 7 ^ 1 4 , 1 2 16 . . s e t of CI N C 0 t r a n s i t i o n s . c  rt  As a f i r s t t e s t o f these t e n t a t i v e  assignments the r e l a t e d J = 3+4  and J = 5->6 groups were s o u g h t , and f o u n d , a t the f r e q u e n c i e s p r e d i c t e d b y : v  (J+l)v^_^/5.  The more u s u a l p r o c e d u r e f o r d e t e r m i n i n g such J  values  by c o u n t i n g S t a r k l o b e s c o u l d not be used as t h e s e were n e v e r r e s o l v e d any o f the c h l o r i n e i s o c y a n a t e i n p a r t t o the r e l a t i v e l y  transitions.  T h i s was no doubt due a t  s m a l l v a l u e o f the d i p o l e moment, as  by the g e n e r a l l y weak a b s o r p t i o n l i n e s .  I n a d d i t i o n , however,  for least  suggested the 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 reduced the l i n e and S t a r k l o b e i n t e n s i t i e s , a n d , more i m p o r t a n t , produced a v e r y complex p a t t e r n i n w h i c h t h e r e were m u l t i p l e c o i n c i d e n c e s o f S t a r k l o b e s from d i f f e r e n t h y p e r f i n e components at all  virtually  voltages. From the r e l a t i v e  i n t e n s i t i e s and f r e q u e n c i e s o f the  vibrational  s a t e l l i t e s i t was c o n c l u d e d t h a t t h e s e b e l o n g e d t o e x c i t e d s t a t e s o f same v i b r a t i o n w i t h a f r e q u e n c y of l e s s t h a n 200 cm ^.  T h i s number i s  good agreement w i t h the Raman measurements of E y s e l and Nachbaur  (90)  gave to^ = 199 cm ^ i n the s o l i d and u),. = 175 cm * i n the l i q u i d . lowest frequency v i b r a t i o n i s  the in which  The n e x t  a t 560 cm * and i t s f i r s t e x c i t e d  state  s h o u l d t h e r e f o r e have about the same p o p u l a t i o n as 3co^, f o r w h i c h a few v e r y weak l i n e s were measured.  No r o t a t i o n a l t r a n s i t i o n s were observed  t h a t c o u l d be a t t r i b u t e d t o e x c i t e d s t a t e s o f frequency v i b r a t i o n s .  o r any of the o t h e r  higher  P o s s i b l y t h e s e are b u r i e d under the much s t r o n g e r  g r o u n d , oj^ and 2u),_ v i b r a t i o n a l s t a t e  transitions.  D e f i n i t i v e c o n f i r m a t i o n o f the a-type group assignments was by p e r f o r m i n g a complete a n a l y s i s o f the u n i q u e l y c h a r a c t e r i s t i c  achieved hyperfine  65  s t r u c t u r e of t h e s e m u l t i p l e t s .  Each group s t a r t e d a t i t s low f r e q u e n c y end  * w i t h a h i g h f i e l d d o u b l e t t h a t was c l e a r l y the K ^ — 0  transition with  p a r t i a l l y r e s o l v e d c h l o r i n e quadrupole c o u p l i n g s t r u c t u r e . h i g h e r f r e q u e n c y a p a i r o f low f i e l d d o u b l e t s was f o u n d .  To s l i g h t l y S i n c e the S t a r k  components o f the l o w e r f r e q u e n c y d o u b l e t moved t o h i g h f r e q u e n c y w i t h increasing f i e l d ,  and t h o s e o f the h i g h e r f r e q u e n c y d o u b l e t , t o low f r e q u e n c y ,  t h e s e were t e n t a t i v e l y a s s i g n e d as the asymmetry s p l i t K  = 2 l i n e s , with  the d o u b l e t s t r u c t u r e a g a i n b e i n g due t o c h l o r i n e q u a d r u p o l e c o u p l i n g . T h i s S t a r k component b e h a v i o r i s p r e d i c t e d by e q u a t i o n 2.45 f o r any p a i r o f asymmetry s p l i t t r a n s i t i o n s . K_j = 2 r a t h e r t h a n  The d e c i s i o n to a s s i g n t h e s e d o u b l e t s as  = 1 l i n e s was i n i t i a l l y m o t i v a t e d by the p r e d i c t i o n ,  based on the assumed s t r u c t u r e , of a much l a r g e r asymmetry s p l i t t i n g f o r the l a t t e r .  It  was q u i c k l y v e r i f i e d by c o n t i n u i n g the a n a l y s i s t o h i g h e r  f r e q u e n c y where a l l of the observed l i n e s c o u l d be a c c o u n t e d f o r i n terms o f o n l y the e x p e c t e d K  = 3, 4 and 5 (K ^ J " )  transitions.  no asymmetry s p l i t t i n g b u t d i d show l a r g e q u a d r u p o l e h y p e r f i n e  These had structure  w h i c h unambiguously f i n g e r p r i n t e d them. The K j = 1 t r a n s i t i o n s p r o v e d t o be somewhat more d i f f i c u l t t o a s s i g n . These were p r e d i c t e d t o be a p p r o x i m a t e l y e q u a l l y spaced on e i t h e r s i d e o f the a s s o c i a t e d main g r o u p , w i t h a t o t a l asymmetry s p l i t t i n g o f r o u g h l y (J+1)(B-C), b u t because o f the d e n s i t y of h i g h e r J  unassigned t r a n s i t i o n s  s e v e r a l m i s - a s s i g n m e n t s were made i n the c o u r s e o f the e a r l y w o r k .  As  b e f o r e , i n u l t i m a t e l y making the c o r r e c t a s s i g n m e n t s , the d i r e c t i o n i n w h i c h the S t a r k components moved w i t h i n c r e a s i n g f i e l d and the o b s e r v e d S i n c e AK ^ = 0 f o r a l l of t h e s e pseudosymmetric top t r a n s i t i o n s i t  is  f r e q u e n t l y c o n v e n i e n t t o l a b e l them by j u s t J " , J ' ( = J " + 1 ) and K_.  For  a l l K_j  * 0 t h e r e are two such t r a n s i t i o n s w h i c h may o r may n o t be  degenerate.  F o r K . = 0 t h e r e i s o n l y one t r a n s i t i o n .  66 FIGURE 4.1  Illustration  of the K  a-Type R-Branch Group of  = 2 and 3 L i n e s of the J = 3+4 3 5  C1  1 4  N  1 2  C  1 6  0  (G.V.S.).  r  observed  calculated  b  c  T c  1  v(MHz)  1  24310  1  24320  24315  observed  V c  calculated  24325  24330  24335  b  67 q u a d r u p o l e h y p e r f i n e s t r u c t u r e were i n v a l u a b l e . Two f o r t u i t o u s f e a t u r e s o f these _i-type R-branch groups s h o u l d be emphasized.  The f i r s t i s the l a c k o f o v e r l a p o f the m u l t i p l e t s  ponding t o the d i f f e r e n t v i b r a t i o n a l s t a t e s . t i a l l y complete s e p a r a t i o n o f the  The second i s the e s s e n -  structure.  The former  l a r g e v i b r a t i o n - r o t a t i o n i n t e r a c t i o n a s s o c i a t e d w i t h u)^, the significant centrifugal distortion.  corres-  indicates latter,  T o g e t h e r , they produced a p a t t e r n  of n i c e l y spaced out r o t a t i o n a l t r a n s i t i o n s whose c h l o r i n e and  eventually  n i t r o g e n q u a d r u p o l e c o u p l i n g h y p e r f i n e s t r u c t u r e c o u l d be l a r g e l y  resolved.  I n c o n t r a s t t o t h i s n e a r l y i d e a l c a s e , t h e r e are numerous examples o f s i m i l a r near p r o l a t e asymmetric r o t o r s where such d i s t o r t i o n e f f e c t s  are  much s m a l l e r , r e s u l t i n g i n a c o l l a p s e o f the a-type m u l t i p l e t s i n t o an u n r e s o l v a b l e mess  (92).  The f r e q u e n c i e s o f t h e a-type t r a n s i t i o n s , as a l r e a d y i n d i c a t e d , depend s t r o n g l y on B and C, b u t c o n v e r s e l y are n e a r l y independent o f A . s e q u e n t l y the a n a l y s i s d e s c r i b e d above produced e x c e l l e n t v a l u e s f o r m e r b u t o n l y v e r y rough v a l u e s f o r the l a t t e r .  Confor  the  These were i n s u f f i c i e n t  f o r the a c c u r a t e p r e d i c t i o n o f the b-type t r a n s i t i o n s whose  frequencies  a r e s t r o n g f u n c t i o n s o f a l l t h r e e r o t a t i o n a l c o n s t a n t s and may a l s o have large centrifugal d i s t o r t i o n contributions.  The p r o c e s s o f a s s i g n i n g the  b-type t r a n s i t i o n s was t h e r e f o r e q u i t e t e d i o u s and i n v o l v e d t r i a l and e r r o r .  considerable  However, once a few t r a n s i t i o n s had been c o r r e c t l y  assigned  i n one b-type s e r i e s , the r e s t o f the t r a n s i t i o n s i n t h a t s e r i e s c o u l d be accurately predicted.  Measurement of these a d d i t i o n a l t r a n s i t i o n s  c o n v i n c i n g p r o o f of the c o r r e c t n e s s of the i n i t i a l a s s i g n m e n t s .  Again,  these were always f u r t h e r s u p p o r t e d by a comparison o f observed and quadrupole h y p e r f i n e s t r u c t u r e .  provided  calculated  T r a n s i t i o n s w i t h J v a l u e s o f l e s s than 30  68  were o b s e r v a b l e f o r o n l y t h r e e s e r i e s o f b-type P- and R-branches; were o f the form J  Q  j  J  —  (J-D^j.p  J_  f J  __ —  <J-l>  2 f J  _  2  these  and  I , J - ^z.j-r  J  The i n t e n s i t i e s o f the a- and b-type t r a n s i t i o n s were of s i m i l a r m a g n i t u d e , s u g g e s t i n g r o u g h l y comparable v a l u e s f o r the components of the d i p o l e moment a l o n g the a- and _b-axes.  S i n c e , as p r e v i o u s l y n o t e d , the S t a r k l o b e s  were always weak and u n r e s o l v a b l e , no attempt was made t o a c c u r a t e l y y  a o  measure  and y, . b The i s o t o p i c a l l y s u b s t i t u t e d s p e c i e s had s p e c t r a w h i c h were v e r y s i m i l a r  t o t h a t o f n a t u r a l l y abundant c h l o r i n e i s o c y a n a t e .  The a n a l y s i s o f  s p e c t r a was g r e a t l y s i m p l i f i e d by the a v a i l a b i l i t y o f r e s p e c t a b l e i n a r y e s t i m a t e s o f the i s o t o p i c m o l e c u l a r c o n s t a n t s .  T h i s was  these  prelim-  fortunate  because the use of o n l y 40 - 50% e n r i c h e d samples r e s u l t e d i n r a t h e r weak l i n e s i n a more c l u t t e r e d s p e c t r u m . 4.2  D e t e r m i n a t i o n o f M o l e c u l a r C o n s t a n t s from the Microwave  Spectrum.  R o t a t i o n a l c o n s t a n t s , 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 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 were e x t r a c t e d from the microwave  spectrum  of c h l o r i n e isocyanate through a c i r c u i t o u s procedure i n v o l v i n g s u c c e s s i v e l e v e l s of approximation.  A more s t r a i g h t f o r w a r d approach c o u l d n o t be used  because b o t h the h y p e r f i n e s t r u c t u r e and the 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 r e q u i r e d v a l u e s f o r the r o t a t i o n a l c o n s t a n t s but were a l s o n e c e s s a r y o r d e r t o determine them a c c u r a t e l y .  in  C o n s e q u e n t l y the f i r s t s t e p was always  the c a l c u l a t i o n o f a t r i a l s e t of r o t a t i o n a l c o n s t a n t s , u s u a l l y by a p p l y i n g the r i g i d r o t o r e q u a t i o n s t o a few s e l e c t t r a n s i t i o n s .  These were then  r e f i n e d i n a p r e l i m i n a r y t r e a t m e n t o f the c e n t r i f u g a l d i s t o r t i o n i n w h i c h each " u n s p l i t - l i n e " t r a n s i t i o n f r e q u e n c y  was approximated by an average  * T h i s i s the h y p o t h e t i c a l f r e q u e n c y w h i c h the pure r o t a t i o n a l t r a n s i t i o n would have i f t h e r e was no q u a d r u p o l e h y p e r f i n e s t r u c t u r e .  69 o f i t s h y p e r f i n e component f r e q u e n c i e s .  The r e s u l t i n g second g e n e r a t i o n  r o t a t i o n a l c o n s t a n t s were i n t u r n used i n a f i r s t a n a l y s i s of the q u a d r u p o l e h y p e r f i n e p a t t e r n s that y i e l d e d , i n a d d i t i o n to f i r s t generation quadrupole c o u p l i n g c o n s t a n t s , a much improved s e r i e s o f " u n s p l i t - l i n e " t r a n s i t i o n f r e q u e n c i e s , and hence l e d t o a new round i n the p r o c e s s o f  refinement.  S i n c e the q u a d r u p o l e e n e r g i e s were o n l y a s l o w l y v a r y i n g f u n c t i o n o f  the  r o t a t i o n a l c o n s t a n t s the " u n s p l i t - l i n e " f r e q u e n c i e s c a l c u l a t e d i n the second h y p e r f i n e s t r u c t u r e a n a l y s i s were n o r m a l l y i n s i g n i f i c a n t l y d i f f e r e n t t h o s e o b t a i n e d i n the f i r s t  from  cycle.  A l t h o u g h t h r e e d i f f e r e n t m o d i f i c a t i o n s were c o n s i d e r e d , the b a s i c f e a t u r e s o f 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 i s were always t h e same. f i r s t o r d e r p e r t u r b a t i o n t r e a t m e n t was u s e d .  A  The r e q u i r e d a n g u l a r momentum  m a t r i x elements and reduced e n e r g i e s ( E ( b ) ) were computed a l o n g w i t h a s e t p  of r i g i d r o t o r frequencies constants.  ( ) v  r  u s i n g the most r e c e n t l y o b t a i n e d r o t a t i o n a l  A l e a s t squares f i t was t h e n made t o t h e d i f f e r e n c e s v ,  - v  obs where  w  a  s  r  the h e s t a v a i l a b l e s e t o f o b s e r v e d " u n s p l i t - l i n e " f r e q u e n c i e s .  The parameters i n t h i s f i t were b o t h the d i s t o r t i o n c o n s t a n t s and the effective rotational constants.  The l a t t e r were a l l o w e d t o have l i n e a r  v a r i a t i o n s i n o n l y the r i g i d r o t o r c o n t r i b u t i o n (Av^) t o the c a l c u l a t e d d i f f e r e n c e s (v ^ + Av ) . The r e s u l t i n g i n c r e m e n t e d r o t a t i o n a l c o n s t a n t s cent r 6  were s u b s e q u e n t l y used t o i n i t i a t e a new d i s t o r t i o n a n a l y s i s on the unchanged v , frequencies. obs  T h i s p r o c e d u r e gave s t a b l e r e s u l t s ( i n c l u d i n g  of used and c a l c u l a t e d r o t a t i o n a l c o n s t a n t s )  agreement  on the second o r t h i r d c y c l e ,  when the o b s e r v e d f r e q u e n c i e s c o n t a i n e d s u f f i c i e n t i n f o r m a t i o n t o d e t e r m i n e a l l o f the i n c l u d e d p a r a m e t e r s . The i m p o r t a n t f e a t u r e s o f the o v e r a l l a n a l y s i s scheme have been trated w i t h a flow chart i n Figure  4.2.  illus-  70 FIGURE 4.2  Flow-Chart I l l u s t r a t i n g the O v e r a l l C e n t r i f u g a l D i s t o r t i o n and N u c l e a r Quadrupole H y p e r f i n e S t r u c t u r e A n a l y s i s Scheme.  Trial Rotational Constants  Trial "Unsplit-Line" Frequencies  -input f o r the f i r s t r u n of the f i r s t centrifugal distortion analysis  i n p u t f o r the f i r s t centrifugal distortion analysis  CENTRIFUGAL DISTORTION PROGRAM only t i l l no f u r t h e r change Improved R o t a t i o n a l  i n p u t f o r the f i r s t run of subsequent d i s t o r t i o n analyses  Constants  Stable Refined R o t a t i o n a l Constants  NUCLEAR QUADRUPOLE HYPERFINE STRUCTURE PROGRAM  Improved " U n s p l i t - L i n e " T r a n s i t i o n Frequencies " i n p u t f o r subsequent centrifugal distortion analyses  c o l l e c t o n l y the f i n a l s e t of D i s t o r t i o n Constants and R o t a t i o n a l Constants  Quadrupole Splittings  c o l l e c t o n l y the f i n a l set of Coupling Constants  collect final  set  71  S i n c e c h l o r i n e i s o c y a n a t e was e x p e c t e d t o be a p l a n a r m o l e c u l e , was thought t h a t the H a m i l t o n i a n d e f i n e d by e q u a t i o n 2.18 m i g h t be for a centrifugal distortion analysis.  I n a f i r s t t r e a t m e n t the  it  adequate  equil-  i b r i u m r o t a t i o n a l c o n s t a n t s a p p e a r i n g i n t h i s e x p r e s s i o n were r e p l a c e d w i t h the b e s t a v a i l a b l e e f f e c t i v e o n e s ; i . e .  t h o s e used t o c a l c u l a t e  the  a n g u l a r momentum m a t r i x elements e t c .  The scheme was t h e n t e s t e d on the  " ^ C l ^ N ^ C ^ O ground v i b r a t i o n a l s t a t e  (G.V.S.) data set.  f i t s were made on t h r e e groups o f t r a n s i t i o n s n a m e l y : J = 0 - 2 5 , and J = 0 - 3 0 .  Least squares  J = 0 - 20,  The r e s u l t s are compared i n T a b l e 4 . 1 .  It  will  be n o t e d t h a t the l a r g e s t s e t o f t r a n s i t i o n s gave a p p a r e n t l y w e l l d e t e r m i n e d v a l u e s f o r a l l seven c o n s t a n t s and the s m a l l e s t s e t , good v a l u e s f o r o n l y s i x , with x , , indeterminate. abab  N e v e r t h e l e s s , the v a r i a t i o n i n the f i r s t '  six  p a r a m e t e r s , e s p e c i a l l y the r o t a t i o n a l c o n s t a n t s , i s seen t o be v e r y s l i g h t and, i n e v e r y c a s e , s m a l l e r t h a n the e x p e r i m e n t a l e r r o r .  This suggested  t h a t h i g h e r o r d e r e f f e c t s were o f m i n o r i m p o r t a n c e i n a l l o f the o b s e r v e d t r a n s i t i o n s and c e r t a i n l y t h a t no s y s t e m a t i c e r r o r would be i n t r o d u c e d i n t o any of the d e r i v e d c o n s t a n t s , w i t h the p o s s i b l e e x c e p t i o n of c l u d i n g the J = 20 - 30 t r a n s i t i o n s i n the  T  a  k b > by i n a  fit.  A v a r i a t i o n of the above p r o c e d u r e was a l s o c o n s i d e r e d i n w h i c h the e q u i l i b r i u m r o t a t i o n a l constants  ( i n e q u a t i o n 2.18) were r e p l a c e d w i t h  ground s t a t e v a l u e s o f A and B and a v a l u e o f C a d j u s t e d t o make the defect zero.  inertial  The r e s u l t s o f t h i s a n a l y s i s , a p p l i e d to the J = 0 - 30 35  t r a n s i t i o n s of  14 12 16 CI  N  C  0 G . V . S . , are a l s o g i v e n i n Table 4 . 1 .  The  r o t a t i o n a l c o n s t a n t s and two o f the d i s t o r t i o n c o n s t a n t s agree w e l l w i t h those o f the p r e v i o u s c a l c u l a t i o n (on the same d a t a ) , b u t the o t h e r s do n o t ; indeed,  ^ i s d i f f e r e n t by a f a c t o r o f n e a r l y two, w e l l o u t s i d e t h e  experimental e r r o r .  T h i s must be r e g a r d e d as an anomalous b e h a v i o r  since  72 TABLE 4.1  R o t a t i o n a l C o n s t a n t s ^ 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 of 35 1A 12 16 Cl  N  C  0 i n the Ground V i b r a t i o n a l  State. II'  Number o f Transitions  J = 0 - 20  J = 0 - 25  41  47  A' o  51576.246 + 0 . 0 8 6  B»  3130.5904 ± 0.0066  3130.5858 ± 0.0041  2945.1781 ± 0.0066  2945.1768 ± 0.0041  o  C»  o aaaa  bbbb ' aabb abab  c  -59.204 ± 0.083 -0.01092 + 0.00018 0.6824 ± 0.0186 (-0.0012 ± 0.0173)  III'  51576.181 ± 0.068  -59.148 ± 0.049 -0.01077 ± 0.00003 0.6878 ± 0.0031 (-0.0061 ± 0.0027)  IV  J = 0 - 30  J = 0 - 30  52  52  A' o  51576.213 ± 0.065  51576.219 ± 0.065  B'  3130.5875 ± 0.0029  3130.5913 ± 0.0029  2945.1709 ± 0.0027  2945.1663 ± 0.0027  Number o f Transitions  o  c o aaaa bbbb ' aabb abab  -59.139 ± 0.047  -59.141 ± 0.048  -0.010752 ± 0.000025  -0.010748 ± 0.000025  0.6923 ± 0.0008  0.6992 ± 0.0008  -0.0101 ± 0.0006  -0.0175 ± 0.0006  I n the r e l a t i o n s r e d u c i n g the number of d e t e r m i n a b l e d i s t o r t i o n  constants  t o f o u r , the r o t a t i o n a l c o n s t a n t s used were A ' , B' and C ' . o o o In the r e l a t i o n s r e d u c i n g the number of d e t e r m i n a b l e d i s t o r t i o n c o n s t a n t s t o f o u r , the r o t a t i o n a l c o n s t a n t s used were A ' , B' and C = 1/(1/A' + 1 / B ' ) . o o o o Standard e r r o r s . Measured i n MHz.  73  f o r a number of o t h e r p l a n a r m o l e c u l e s the r e s u l t s o f t h e s e two schemes have been found t o be i n agreement  (93).  It  analysis  i s not c l e a r w h i c h i s  the b e t t e r h e r e ; c e r t a i n l y n e i t h e r i s l i k e l y to be c o m p l e t e l y c o r r e c t ,  and  t h e r e f o r e the i m p l i c a t i o n i s t h a t i t would be p r e f e r a b l e n o t t o employ the p l a n a r i t y r e l a t i o n s at a l l . To t h i s e n d , an attempt was made t o use the g e n e r a l q u a r t i c d i s t o r t i o n H a m i l t o n i a n d e f i n e d by e q u a t i o n s 2 . 1 9 , 2.20 and 2 . 2 1 . 35  centrifugal A g a i n the  1A 12 16 Cl  N  C  0 G . V . S . t r a n s i t i o n s were t a k e n as t e s t d a t a .  Watson has s u g g e s t -  ed t h a t t h i s i s p r o b a b l y the b e s t approach f o r t r e a t i n g p l a n a r m o l e c u l e s with large d i s t o r t i o n effects  (30).  I n t h i s c a s e , however, o n l y f o u r o f  the d i s t o r t i o n c o n s t a n t s were w e l l d e t e r m i n e d ; the f i f t h , 6 , was i n d e t e r K  minate. F u r t h e r , t h e r e were v e r y l a r g e c o r r e l a t i o n c o e f f i c i e n t s (>0.95) c o n n e c t i n g 6.. w i t h B and C and A w i t h A , . T h i s i s t o be c o n t r a s t e d ° K o o J JK T  TT  w i t h the two p r e v i o u s f i t s where a l l of the parameters were w e l l d e t e r m i n e d and u n c o r r e l a t e d . Table 4 . 2 .  The r e s u l t s o f t h e s e t h r e e schemes a r e compared i n  The Watson c o n s t a n t s g i v e n i n columns I I I A and IVA were  c u l a t e d from the t a u c o n s t a n t s o f a n a l y s e s I I I  and IV  t i v e l y w i t h the a i d o f e q u a t i o n s 2 . 1 7 , 2.20 and 2 . 2 1 .  (Table 4.1)  cal-  respec-  The e x c e l l e n t  agreement o f a l l but the <5 v a l u e s i s most g r a t i f y i n g . F i n a l l y , the f i r s t o r d e r Watson c o n s t a n t s g i v e n i n column V of T a b l e were used i n the f u l l m a t r i x scheme t o c a l c u l a t e " e x a c t l y " the 35 o f a l l o f the o b s e r v e d t r a n s i t i o n s o f  4.2  frequencies  1A 12 16 Cl  N  C  0 G.V.S.  As e x p e c t e d ,  most o f t h e s e " e x a c t " f r e q u e n c i e s were found t o be i d e n t i c a l t o corresponding, p r e v i o u s l y c a l c u l a t e d , f i r s t order frequency.  their  However,  small  d i s c r e p a n c i e s (<lMHz) were n o t i c e d i n the case o f the b_-type t r a n s i t i o n s b e l o n g i n g t o the s e r i e s J  —  (J-l)  _  F o r t u n a t e l y , when t h e s e were  accounted f o r u s i n g the p r o c e d u r e d e s c r i b e d i n Chapter 6 , the new v a l u e s o f  74  3.  TABLE 4.2  3.  R o t a t i o n a l Constants 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 of C 1 N C '0 i n the Ground V i b r a t i o n a l S t a t e . 3 5  U  1 2  1 6  IIIA  V  A B  o  o C  o  A  J  A  JK  A  K  6  J  6  K  Measured  J = 0 - 30  J = 0 -• 30  Number of Transitions  52  52  52  +  0.068  d  51576.213  51576.219  3130.6603  +  0.0094  3130.6721  3130.6750  2945.1026  +  0.0123  2945.0867  2945.0828  0.001979  +  0.000006  0.001976  0.001975  -0.27697  +  0.00025  -0.27711  -0.27715  15.057  +  0.012  15.060  15.060  0.0003569  +  0.0000007  0.0003560  0.0003558  (0.00392  +  0.00483)  0.01032  0.01186  i n MHz. of a n a l y s i s  III  ° Computed from the r e s u l t s  of a n a l y s i s  IV  ^ Standard  J = 0 - 30  51576.184  Computed from the r e s u l t s  b  IVA°  b  errors.  (Table (Table  4.1). 4.1).  75 the d e t e r m i n a b l e m o l e c u l a r c o n s t a n t s d i f f e r e d i n s i g n i f i c a n t l y from those o b t a i n e d i n the f i r s t o r d e r t r e a t m e n t .  A c c o r d i n g l y , such " o f f - d i a g o n a l "  c o n t r i b u t i o n s were not c o n s i d e r e d f u r t h e r . T a b l e 4.3 c o n t a i n s the 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 a l l of the i s o t o p i c s p e c i e s o f c h l o r i n e i s o c y a n a t e s t u d i e d .  These were  d e t e r m i n e d u s i n g the f i r s t o f the t h r e e a n a l y s i s schemes d i s c u s s e d .  The  second scheme was r e j e c t e d l a r g e l y on the grounds t h a t i t seemed somewhat artificial;  the t h i r d , because the e x t r a parameter was not r e q u i r e d .  Some c a r e must be t a k e n i n i n t e r p r e t i n g the r e s u l t s i n T a b l e 4 . 3 . It  i s c l e a r , f o r a s t a r t , t h a t the d i s t o r t i o n a n a l y s e s have y i e l d e d  accurate  r o t a t i o n a l c o n s t a n t s w h i c h can be used f o r the d e t e r m i n a t i o n of the m o l e c u l a r s t r u c t u r e (94). clear.  The s i g n i f i c a n c e o f the d i s t o r t i o n c o n s t a n t s i s  The v a r i a t i o n s n o t e d above suggest t h a t the  less  ^ values are s u s -  p e c t , and t h a t a complete s e t o f p h y s i c a l l y m e a n i n g f u l d i s t o r t i o n c o n s t a n t s can p r o b a b l y be o b t a i n e d o n l y t h r o u g h a f u l l f i v e parameter f i t u s i n g a d d i t i o n a l branches.  U n f o r t u n a t e l y , i n s u f f i c i e n t t r a n s i t i o n s were o b s e r v -  a b l e i n the f r e q u e n c y range o f our s p e c t r o m e t e r t o a l l o w such a f i t . The h y p e r f i n e s t r u c t u r e a n a l y s e s were i n i t i a l l y based on the presumpt i o n t h a t the f i r s t o r d e r e x p r e s s i o n g i v e n i n e q u a t i o n 2.40 r e p r e s e n t e d a good a p p r o x i m a t i o n t o the t r u e q u a d r u p o l e e n e r g i e s .  Linear least  squares  f i t s were made t o a l l w e l l r e s o l v e d q u a d r u p o l e s p l i t t i n g s of t h e measured t r a n s i t i o n s up t o J = 3 0 .  The v a l i d i t y o f the approach was t h e n t e s t e d by  u s i n g the computed f i r s t o r d e r c o u p l i n g c o n s t a n t s i n the f u l l m a t r i x scheme t o p r e d i c t the h y p e r f i n e p a t t e r n s . i n J and  I n e v e r y c a s e , the elements o f f - d i a g o n a l  were found t o g i v e n e g l i g i b l e c o n t r i b u t i o n s t o the c a l c u l a t e d  s p l i t t i n g s , thus j u s t i f y i n g the use of a f i r s t o r d e r t r e a t m e n t .  The  final  v a l u e s o f the c h l o r i n e and 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 c o u p l i n g c o n s t a n t s  76  TABLE 4 . 3  R o t a t i o n a l Constants and C e n t r i f u g a l D i s t o r t i o n of Chlorine Isocyanate.  3 5  C1  1 4  N  1 2  C  1 6  0  (G.V.S.)  3 7  C1 V C 1  2  1 6  Constants  0  (G.V.S.)  Number o f Transitions  52  A'  51576.213 ± 0 . 0 6 5  B'  3130.5876 ± 0.0029  3057.5962 ± 0.0028  2945.1709 ± 0.0027  2879.4646 ± 0.0027  -59.139 ± 0.047  - 5 8 . 4 2 8 ± 0.047  o o  c o aaaa L  bbbb aabb abab  47 51256.447 ± 0.065  C  -0.010752 ± 0.000025  0.67184 ± 0.00098  -0.01009 ± 0.00058  -0.00926 ± 0.00078  0 1  Number o f Transitions  -0.010272 ± 0.000023  0.69230 ± 0.00080  3 5 1 4 12 18„ , „ „ CI N C 0 ( G . V . S . ) TT  x  47  3 5  C1  1 5  N  1 2  C  1 6  0  (G.V.S.)  27  A'  50689.754 ± 0.074  49090.359 ± 0.052  B'  2957.2339 ± 0.0031  3130.6330 ± 0.0026  2788.5436 ± 0.0029  2936.5686 ± 0.0022  -57.524 ± 0.056  -53.151 ± 0.039  o  o  c o aaaa bbbb aabb abab  -0.009569 ± 0.000025  3  -0.010610 ± 0.000029  0.64604 ± 0.00092  0.65900 ± 0.00078  -0.00982 ± 0.00068  -0.01003 ± 0.00052  77  TABLE 4 . 3 c o n t i n u e d  3 7  C1  1 5  N  1 2  Number o f Transitions A'  o  B'  o  c  aaaa o  •  T  bbbb  0  (G.V.S.)  3 5  C1  1 4  N  1 3  C  1 6  0  (G.V.S.)  22  48771.584 ± 0.055  51513.460 ± 0.059  3057.5618 ± 0.0023  3107.0181 ± 0.0028  2871.0664 ± 0.0038  2924.0943 ±0.0030  -52.454 ± 0.029  - 5 9 . 2 6 3 ± 0.040  -0.010133 ± 0.000025  ' abab  3 5  Transitions  1 6  18  aabb  Number o f  C  -0.010437 ± 0.000029  0.6414 ± 0.0025  0.6904 ± 0.0014  -0.0111 ± 0.0021  -0.0107 ± 0.0010  C1 V C 1  2  1 6  0  (v  5  = 1)  43  3 5  C1  1 4  N  1 2  C  1 6  0 (v  5  = 2)  23  A* v  53261.08 ± 0.11  B' v  3147.3629 ± 0.0045  3163.210 ± 0 . 0 1 8  C v  2953.7724 ± 0.0048  2961.743 ± 0.038  x  - 7 0 . 3 0 8 ± 0.078  -84.24 ± 0.26  -0.011159 ± 0.000037  -0.01217 ± 0.00060  f  T  aaaa boob  aabb T , , abab  0.7572 ± 0.0021 -0.0242 ± 0.0017  55137.02 ± 0 . 3 3  0.760 ± 0.077 (0.027 ± 0.071)  Measured i n MHz. The 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 f o r t h e a p p r o p r i a t e v i b r a t i o n a l were used i n the p l a n a r i t y r e l a t i o n s . Standard e r r o r s .  state  78 TABLE 4 . 4  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  3 5  X A  (l) '  C1  N  1 4  1 2  C  1 6  0  (G.V.S.)  -71.133 ± 0 . 0 6 3  b  of C h l o r i n e  3 7  C1  1 4  N  1 2  C  Isocyanate.  1 6  0  (G.V.S.)  -56.611 ± 0.074  3  aa  X  b b  X  (D  - X (D C  -42.594 ± 0.035  -33.147 ± 0.044  3.989 ± 0.044  4.135 ± 0.052  1.963 ± 0.021  1.998 ± 0.023  (2)  aa X,, (2) - x (2) bo cc  3 5  X  aa  X  b b  (D (l)  - X  C C  (D  C1  N  1 4  1 2  C  1 8  0  (G.V.S.)  3 5  C1  1 4  N  1 3  C  1 6  0  (G.V.S.)  -69.824 ± 0.088  -70.570 ± 0.132  - 4 3 . 8 1 3 ± 0.052  -42.381 ± 0.050  4.025 ± 0.054  4.132 + 0.072  2.000 ± 0.030  2.037 ± 0.028  X (2) a a  del  X (2) b b  - X (2) c c  3 5  (1)  x  aa Xbb u v C D - Xc c C D A  X  C1  1 4  N  1 2  C  1 6  0  (v  = 1)  5  3 5  C1  1 4  N  1 2  C  1 6  0  (v  5  -71.39 ± 0.10  - 7 0 . 9 9 ± 0.24  -43.06 ± 0.08  -43.52 ± 0.17  4 . 1 2 ± 0.07  3.78 + 0.12  2.10 ± 0.05  2.10 ± 0.12  (2)  - 2)  aa Xu^(2) A  bb  - X  (2)  cc  3 5  X  (1)  C1:  1 5  N  1 2  C  1 6  0  (G.V.S.)  3 7  C1  1 5  N  1 2  C  1 6  0  (G.V.S.)  - 7 1 . 2 5 2 ± 0.075  - 5 6 . 8 7 3 ± 0.116  - 4 2 . 6 7 3 ± 0.042  -33.092 ± 0.062  33.  Xuud) ob  - X (1) cc  i  Measured i n MHz; + o r - one s t a n d a r d b  Chlorine i s nucleus  error.  1; n i t r o g e n i s n u c l e u s 2.  79  are g i v e n i n T a b l e 4 . 4 . 4.3  The M o l e c u l a r S t r u c t u r e  of C h l o r i n e  Isocyanate.  The p r i n c i p a l moments of i n e r t i a and the i n e r t i a l d e f e c t  o f a l l of  the  i s o t o p i c s p e c i e s o f c h l o r i n e i s o c y a n a t e s t u d i e d are p r e s e n t e d i n T a b l e 4 . 5 . These were c a l c u l a t e d from the e f f e c t i v e  r o t a t i o n a l constants given  in  T a b l e 4 . 3 by means o f e q u a t i o n s 2.49 and 2 . 5 4 . The ground v i b r a t i o n a l s t a t e i n e r t i a l d e f e c t s are a l l seen t o be s m a l l p o s i t i v e numbers w h i c h change v e r y l i t t l e w i t h i s o t o p i c s u b s t i t u t i o n .  This  i s c o n v i n c i n g e v i d e n c e t h a t the m o l e c u l e i s p l a n a r i n i t s e q u i l i b r i u m c o n f i g u r a t i o n (see s e c t i o n 2 . 4 ) .  Further support f o r t h i s premise i s  obtained  by c a l c u l a t i n g the f r e q u e n c y of the l o w e s t f r e q u e n c y i n - p l a n e v i b r a t i o n 35 from the observed ground v i b r a t i o n a l s t a t e i n e r t i a l d e f e c t o f w i t h the a i d o f e q u a t i o n 2 . 5 7 .  The v a l u e o b t a i n e d i s to  (to^)  1A 12 16 Cl  N  C  = 185 cm * i n good  agreement w i t h t h e f r e q u e n c i e s measured i n t h e Raman spectrum (to^ = to^ = 199 cm * i n the s o l i d and 174 cm * i n the l i q u i d )  (90).  The K r a i t c h m a n s u b s t i t u t i o n p o s i t i o n s o f the f o u r atoms i n c h l o r i n e i s o c y a n a t e were c a l c u l a t e d from the ground v i b r a t i o n a l s t a t e moments o f 35 i n e r t i a i n T a b l e 4.5 u s i n g e q u a t i o n s 2 . 5 8 .  I n t h i s , the  1A 12 16 Cl  N  C  0  i s o t o p i c s p e c i e s was t a k e n t o be the p a r e n t m o l e c u l e , and hence a l l of  the  c o o r d i n a t e s are measured w i t h r e s p e c t t o i t s c e n t e r o f mass p r i n c i p a l i n e r t i a l a x i s system.  S i n c e only the absolute values of the  coordinates  are d i r e c t l y o b t a i n e d i n the s u b s t i t u t i o n p r o c e d u r e , i t was a l s o  necessary  t o a p p e a l t o the c e n t e r o f mass and p r o d u c t of i n e r t i a c o n d i t i o n s i n o r d e r to determine t h e i r r e l a t i v e  s i g n s (by i n s p e c t i o n ) .  c o l l e c t e d as s t r u c t u r e I i n T a b l e 4 . 6 . a-coordinate  i s imaginary.  chlorine, isocyanate.  Indeed,  The r e s u l t s  are  I t w i l l be n o t e d t h a t the n i t r o g e n  This d i s q u i e t i n g feature  0  i s not u n i q u e  to  i t has been found t h a t the a p p l i c a t i o n o f  80 TABLE 4 . 5  3 5  Moments o f I n e r t i a  C1  1 4  N  1°  1 2  C  1 6  0 (G.V.S.)  and I n e r t i a l D e f e c t s  3  3 7  C1  1 4  N  9.798915  cl  1 2  C  1 6  0  (G.V.S.)  3  of Chlorine  3 5  C1  1 4  1 2  N  9.860046  C  1 8  Isocyanate.  0  (G.V.S.)  9.970277  1°  161.43643  165.29027  170.89987  1° c .o  171.59986  175.51558  181.23830  0.36452  0.36526  0.36815  3 5  C1  1 4  N  1°  1 3  C  1 6  0  (G.V.S.)  3 5  C1  1 5  9.810851  N  1 2  C  1 6  0  (G.V.S.)  10.295115  3 7  C1  1 5  N  1 2  C  1 6  0  10.362405  d  I_  162.66107  161.43409  165.29213  1°  172.83673  172.10253  176.02898  A°  0.36481  0.37333  0.37445  3 5  C1  1 4  N  1^a  I  V  A  3  c  1 2  C  1 6  0  (v  5  9.488935  - 1)  3 5  C1  1 4  N  1 2  C  1 6  0  9.166090  160.57599  159.7715  171.10015  170.6397  1.03523  1.7021  V  Measured i n  (v  a.m.u.A . 2  (G.V.S)  5  - 2)  81 K r a i t c h m a n ' s e q u a t i o n s , u s i n g ground s t a t e moments o f i n e r t i a , t o the d e t e r m i n a t i o n of very s m a l l coordinates g e n e r a l l y gives q u i t e i n a c c u r a t e ,  and  occasionally imaginary, r e s u l t s (68,56).  have  Herschbach and L a u r i e  (95)  shown t h a t t h i s b e h a v i o r i s d u e , at l e a s t i n p a r t , t o s l i g h t i s o t o p i c v a r i a t i o n s i n the average m o l e c u l a r s t r u c t u r e ( i . e . tional effects).  t o zero p o i n t v i b r a -  W i t h l a r g e r c o o r d i n a t e s , where the v i b r a t i o n a l  contri-  b u t i o n s are a much s m a l l e r p e r c e n t a g e o f the t o t a l A I ° ' s , t h e s e e r r o r s  are  a correspondingly reduced.  N o n e t h e l e s s , they may s t i l l be s i g n i f i c a n t l y  g r e a t e r than the measurement e r r o r , and hence the s t a n d a r d e r r o r s g i v e n i n T a b l e 4 . 6 , w h i c h were c a l c u l a t e d assuming the s u b s t i t u t i o n method t o be e x a c t , have no r e a l s i g n i f i c a n c e . C l e a r l y the p r e f e r r e d method f o r d e t e r m i n i n g the n i t r o g e n  a-coordinate  i s by a p p l i c a t i o n of the c e n t e r o f mass c o n d i t i o n (__]m.a. = 0 ) . a l s o t r u e f o r the c a r b o n b - c o o r d i n a t e —  This  is  i ( V , m . b , = 0) w h i c h i s seen t o be • V i i l  s m a l l e r than the 0.15 °v t h a t C o s t a i n (64) has e m p i r i c a l l y suggested s h o u l d be a l o w e r bound on the s i z e o f c o o r d i n a t e s c a l c u l a t e d by s i n g l e s u b s t i t u t i o n . The c e n t e r o f mass d e t e r m i n e d a^ and b^ are a l s o p r e s e n t e d i n T a b l e 4 . 6 , as part of s t r u c t u r e II.  Here the o t h e r c o o r d i n a t e s were a g a i n t a k e n t o have  their substitution values.  I t w i l l be n o t e d t h a t the new v a l u e f o r the  car-  bon b - c o o r d i n a t e d i f f e r s s i g n i f i c a n t l y (by 0.00889 A) from the p r e v i o u s o n e , w h i c h had a l r e a d y been r e g a r d e d as s u s p e c t and can now be d i s c o u n t e d . Of the r e m a i n i n g s u b s t i t u t i o n d e t e r m i n e d c o o r d i n a t e s the s m a l l e s t , and hence most u n c e r t a i n , i s b „ , w h i c h a t 0.17945 A i u s t s a t i s f i e s Cl c r i t e r i o n of a c c e p t a b i l i t y of i n e r t i a condition r e l a t i o n (]C 4 -t m  D  =  ^  (0.15 X).  (X]^a^b^ = m  t o  Costain's  J  As a check on t h i s v a l u e , the p r o d u c t  0) was used a l o n g w i t h the c e n t e r o f mass  r e - d e t e r m i n e the carbon and c h l o r i n e b - c o o r d i n a t e s .  82  TABLE 4.6  C h l o r i n e Isocyanate Atomic Coordinates i n the P r i n c i p a l A x i s System.  Coordinate' a  a  c  a  o  b  ci N  b  c  b  o  m  0.00004  6  imaginary  *N  b  +  l  i  -1.40678  +  0.00004  -1.40678  +  0.00004  0.04747  +  0.00013  0.04747  +  0.00013  0.00009  1.11192  +  0.00009  1.11192  +  0.00009  2.19981  +  0.00003  2.19981  +  0.00003  2.19981  +  0.00003  0.17945  +  0.00003  0.17945  +  0.00003  0.18047  +  0.00002  -0.71001  +  0.00001  -0.71001  +  0.00001  -0.71001  +  0.00001  -0.11022  +  0.00008  -0.10133  +  0.00009  -0.10431  +  0.00007  0.30529  +  0.00002  0.30529  +  0.00002  0.30529  +  0.00002  -0.10671  y^m.a.b. •V i i i l .  0.0  0.0  0.0  0.0  0.09008  0.0 161.4743  161.4743  f  f  i  9.82176  x  d .  +  a  >,m.a.  III  1.11192  i i  m.b. l l  14 12 16  CI N C 0  ir -1.40678  ci  35  s  9.81939*  9.79919  3  Measured i n A*.  b  S u b s t i t u t i o n pp o s i t i o n s ( K r a i t c h m a n ' s  8  equations).  a^ and b^ from c e n t e r o f mass c o n d i t i o n s , r e s t by s u b s t i t u t i o n (as I ) ^ a^ a^ from from c ce ennt et er r oof fmma as s s, , b^, b^, and and b ^ from c e n t e r o f mass and p r o d u c t o f inertia,  r e s t by s u b s t i t u t i o n .  Standard e r r o r s .  ^ Compare w i t h 1 ° ( e x p t . ) = 161.43643 a . m . u . X . 2  S  Compare w i t h 1 ° ( e x p t . ) = 9.7989145 a.m.u.R . 2  cl  83  A l l o f the o t h e r c o o r d i n a t e s were d e t e r m i n e d by s u b s t i t u t i o n , e x c e p t w h i c h was c a l c u l a t e d from the c e n t e r o f mass c o n d i t i o n ( i . e . i n II).  the same as  The r e s u l t s a r e a l s o p r e s e n t e d i n T a b l e 4 . 6 , as s t r u c t u r e  The changes i n the b ^  and b^ c o o r d i n a t e s on g o i n g from I I  0.00102 1 and 0.00298 1 r e s p e c t i v e l y .  |^  to III  III; are  A l t h o u g h much l a r g e r t h a n the  cal-  c u l a t e d s t a n d a r d e r r o r s t h e s e d i f f e r e n c e s would n o n e t h e l e s s appear to be r e p r e s e n t a t i v e o f the l i m i t a t i o n s o f the g e n e r a l s u b s t i t u t i o n p r o c e d u r e . The m o l e c u l a r g e o m e t r i e s t h a t may be c a l c u l a t e d from the a t o m i c p o s i t i o n s obtained i n analyses II two s t r u c t u r e s , I I  and I I I  are presented i n Table 4 . 7 .  Of the  i s t o be perhaps s l i g h t l y p r e f e r r e d because i t g i v e s  b e t t e r r e p r o d u c t i o n of 1 °  .  I n any c a s e , one can n o t r e a s o n a b l y e x p e c t  e i t h e r s h o u l d so c l o s e l y approximate the e q u i l i b r i u m s t r u c t u r e t h a t d i f f e r e n c e s between them w o u l d be s i g n i f i c a n t .  that  the  T h e r e f o r e an average o f  two s t r u c t u r e s was computed and i s a l s o p r e s e n t e d i n T a b l e 4 . 7 , as IV.  the  the  structure  I n F i g u r e 4 . 3 the m o l e c u l a r geometry o f c h l o r i n e i s o c y a n a t e i s  illus-  trated with a scale drawing. I n a f i n a l s t r u c t u r a l i n v e s t i g a t i o n the double s u b s t i t u t i o n p r o c e d u r e o f P i e r c e and K r i s h e r (67,68) was u s e d as an a l t e r n a t i v e method f o r d e t e r m i n i n g the n i t r o g e n a - c o o r d i n a t e .  S i n c e the p r e v i o u s l y o b t a i n e d c e n t e r o f mass  a^j v a l u e was thought t o be q u i t e a c c u r a t e ,  the e x p e r i m e n t was r e g a r d e d , from  the b e g i n n i n g , more as a t e s t o f t h i s seldom used s e m i - e m p i r i c a l t e c h n i q u e t h a n as a way of o b t a i n i n g an improved n i t r o g e n p o s i t i o n .  The i s o t o p i c  s p e c i e s used a r e : 3 5  with  C1  1 4  N  1 2  C  1 6  0  3 7  C1 N U  1 2  C  1 6  0  3 5  C1  1 5  N  1 2  C  1 6  0  3 7  C1  1 5  N  1 2  C  1 6  0  35141216 37141216 C l N C 0 t a k e n t o be the " p r i n c i p a l framework" and Cl N C 0  the " s e c o n d a r y framework" so t h a t the new a^ c o o r d i n a t e would be d i r e c t l y comparable t o the c e n t e r o f mass v a l u e .  The n e c e s s a r y a d d i t i o n a l d a t a ,  84  TABLE 4 . 7  M o l e c u l a r S t r u c t u r e of C h l o r i n e  II r(Cl-N)  Isocyanate.  III  C  IV  d  e  1.70469  1.70523  1.705 ± 0 . 0 0 5  r(N-C)  1.22619  1.22471  1.226 ± 0.005  r(C-O)  1.16140  1.16244  A(C1NC)  118° 4 7 '  118° 5 3 '  118° 50* ± 3 0 '  z.(NCO)  170°  171°  170° 5 2 ' ± 3 0 '  a  b  44»  0'  .  f  1.162 ± 0.005  A l l d i s t a n c e s are i n A*. C l and 0 a r e  trans.  Computed from I I Computed f r o m I I I Average of I I . a n d  i n Table  4.6.  i n Table 4 . 6 . III.  E s t i m a t e d p o s s i b l e d e v i a t i o n from e q u i l i b r i u m s t r u c t u r e  TABLE 4 . 8  N i t r o g e n a - C o o r d i n a t e by Double S u b s t i t u t i o n . A = -0.03558 A B = 0.00454 A 0 = 9' a ^ C A A l " ) = 0.04609 &" a ^ C A A l " ) = 0.04221 a (C0M) N  1  = 0.04747 A  parameters.  FIGURE 4.3  The Molecular Structure of Chlorine Isocyanate.  86  37 specifically,  the c o o r d i n a t e s (A,B)  o f the c e n t e r of mass o f  1A 12 Cl  N  16 C  0  i n the c e n t e r of mass p r i n c i p a l i n e r t i a l a x i s system (COMPIAS) o f  35  1A 12 Cl  N  16 C  0 and a l s o the a n g l e (9)  between the p r i n c i p a l a x i s systems o f  t h e s e two s p e c i e s , were computed w i t h the a i d of s t r u c t u r e I I .  These  g i v e n i n T a b l e 4 . 8 a l o n g w i t h two double s u b s t i t u t i o n v a l u e s f o r a^. f i r s t was o b t a i n e d from second d i f f e r e n c e s o f I^'s second from i ° ' s  (equation 2.64),  are The  the  ( e q u a t i o n 2 . 6 7 ) ; the d i f f e r e n c e between them i s 0.00388 °v.  The r e a s o n s f o r t h i s a t l e a s t m a r g i n a l l y s i g n i f i c a n t d i s c r e p a n c y a r e u n c l e a r . However, s i n c e the 1^ r e s u l t i s n e a r l y i d e n t i c a l t o the a^ v a l u e o b t a i n e d u s i n g the c e n t e r o f mass c o n d i t i o n , i t would seem t o be the b e t t e r o f  the  two. P o s s i b l y t h i s i s i n d i c a t i v e o f a g e n e r a l b e h a v i o r ; i . e . more n e a r l y complete c a n c e l l a t i o n o f v i b r a t i o n a l e f f e c t s w i t h the AAI. ( o r A A I ) b a c  e x p r e s s i o n t h a n w i t h the A A I  c  one.  P i e r c e and K r i s h e r have emphasized t h a t f o r the second d i f f e r e n c e s t e c h n i q u e t o be s u c c e s s f u l - t h e COMPIAS of the secondary framework must be s i g n i f i c a n t l y s h i f t e d ( 0 . 0 3 A* o r m o r e ) , w i t h r e s p e c t to t h a t o f the p r i m a r y o n e , a l o n g the d i r e c t i o n i n q u e s t i o n .  This c r i t e r i o n i s c l e a r l y  satisfied  i n the p r e s e n t c a s e , w h i c h c o u l d t h e r e f o r e be r e g a r d e d as a n e a r l y i d e a l one. By c o n t r a s t , a s i m i l a r d e t e r m i n a t i o n o f b , £  f o r e x a m p l e , would be r a t h e r  tenuous. 4.4  D i s c u s s i o n o f the 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 . I n the p r e c e d i n g s e c t i o n i t was shown t h a t c h l o r i n e i s o c y a n a t e i s  c e r t a i n l y a planar molecule.  almost  T h i s d e d u c t i o n i s c o n s i s t e n t w i t h the o b s e r v e d  c h l o r i n e nuclear quadrupole c o u p l i n g .  The ground v i b r a t i o n a l s t a t e  chlorine  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 the t h r e e i s o t o p i c s p e c i e s e x p e c t e d t o show the l a r g e s t v a r i a t i o n i n the o r i e n t a t i o n o f t h e i r p r i n c i p a l i n e r t i a l a x i s s y s t e m s , w i t h r e s p e c t t o the m o l e c u l a r f r a m e , a r e p r e s e n t e d i n T a b l e 4 . 9 .  87  TABLE 4.9  S e l e c t e d C h l o r i n e 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 Chlorine Isocyanate.  C1  3 5  X  0  1 6  C1 N  3 5  U  1 2  C  1 8  0  ( 3.3. b b  cc  3 5  C1  (  3 5  Cl  (  3 5  C1  1 4  1 4  1 4  1 2  C  1 6  0  13.006 ± 0.051  11.732 ± 0.043  5 6 . 8 6 3 ± 0.036  56.819 ± 0.051  44.879 ± 0.043  1 2  1 2  N  C  C  1 2  1 6  1 6  C  0)/  1 6  0)/  (  X  33  0)/x  3 5  X A  b b  cc  ( (  3 7  3 7  3 7  C1 Cl  1 4  1 4  C1  N  N  1 4  1 2  1 2  N  C  C  1 2  3 7  0  Measured i n MHz. k Ground v i b r a t i o n a l s t a t e c Standard  U  14.270 ± 0.036  N  N  C1 N  -56.611 ± 0.074  1 6  C  0)  = 1.2565 ± 0.0020  0)  = 1.2163 ± 0.0054  0)  = 1.2670 ± 0.0015  1 6  1 6  Q ( C 1 ) / Q ( C 1 ) = 1.26878 ± 0 . 0 0 0 1 5  d  3 7  cc  X X  C  1 2  of  - 6 9 . 8 2 4 ± 0.088  b b  X A  N  - 7 1 . 1 3 3 ± 0.063°  X aa X  1 4  3  values,  errors.  From Gordy and Cook  (128).  d  88  The two  35  C l s p e c i e s a r e seen t o have n e a r l y e q u a l x  n i f i c a n t l y d i f f e r e n t Xiv and x X act (  35  C l ) / xaa (  37  bb  A  values.  c  c  v a l u e s , but  F u r t h e r m o r e , the  aa  sig-  ratio  '  C l ) i s i n agreement w i t h the r a t i o o f the Mq u a d r urp o l e °  moments o f the two c h l o r i n e i s o t o p e s o n l y f o r a = c.  Evidently  the  prin-  c i p a l i n e r t i a l a x i s systems o f the v a r i o u s i s o t o p e s a r e r e l a t e d by a s i m p l e r o t a t i o n about a common _ c - a x i s ; as e x p e c t e d f o r a p l a n a r s t r u c t u r e . A completely r i g o r o u s i n t e r p r e t a t i o n of 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 would be e x t r e m e l y d i f f i c u l t because of the complex dependence o f t h e f i e l d g r a d i e n t s (<1  )  o n  a l l of the e x t r a n u c l e a r charges.  Considerable  p r o g r e s s can be made, however, u s i n g a v e r y a p p r o x i m a t e t r e a t m e n t i n t r o d u c e d by Townes and D a i l e y many o t h e r s ( 9 7 ) .  (96)  first  and l a t e r m o d i f i e d and extended by  I n i t s s i m p l e s t form t h i s t h e o r y a t t r i b u t e s t h e  field  g r a d i e n t s e n t i r e l y t o the p - e l e c t r o n s i n the v a l e n c e s h e l l o f the atom w h i c h c o n t a i n s the c o u p l i n g n u c l e u s ; a l l o t h e r charges a r e i g n o r e d .  If  x , y and  z d e f i n e a C a r t e s i a n a x i s system on t h i s n u c l e u s t h e n : X = (n - 1/2(n + n ))eQq = -(U ) eQq xx x y z nlO p xx nlO i n  n  X  yy  X  zz  = (n = (n  y z  - l/2(n - l/2(n  X M  4.1a  i n  x  + n ))eQq = -(U ) eQq z ^nlO p yy ^ n l O  4.1b  x  + n ))eQq = -(U ) eQq y ^ nlO p zz nlO  4.1c  x  i n  x  n  i n  x n  where n , n and n a r e the o c c u p a t i o n numbers o f the v a l e n c e s h e l l x y z and q . i g i s the f i e l d g r a d i e n t o f an a t o m i c p - e l e c t r o n i n the n n  t b  p-orbitals  (valence)  s h e l l , w i t h the symmetry a x i s o f the p - o r b i t a l a l o n g the r e f e r e n c e  axis.  The " a t o m i c " c o u p l i n g c o n s t a n t s eQq_^g have been e x p e r i m e n t a l l y d e t e r m i n e d f o r most common q u a d r u p o l a r n u c l e i . If  the c o u p l i n g atom has a f o r m a l p o s i t i v e o r n e g a t i v e c h a r g e ,  equation  4.1 s h o u l d be m o d i f i e d t o account f o r the reduced o r i n c r e a s e d s c r e e n i n g o f  89 the valence s h e l l p-electrons. recommended (98)  For a f r a c t i o n a l p o s i t i v e charge c  +  the  form i s :  X = -(1 + c E ) ( U ) eQq , gg P gg n l O  For a f r a c t i o n a l negative charge c  "gg • - V«" W (  <1  (l +  4.2  rt  y 4  i t is:  <="«>  4.3  where e i s a semi-empirical "screening constant".' Townes and Schawlow  (99)  have calculated e values f o r a number of d i f f e r e n t atoms from the v a r i a t i o n of q with i o n i c state. nlO n  The p - o r b i t a l populations may be related to the e l e c t r o n i c structure of the molecule using either the Valence Bond (100) or the LCAO-MO (101) formalism.  The l a t t e r approach i s the one taken here.  In order to apply the Townes Dailey theory to the chlorine  quadrupole  coupling of t h i s molecule, i t i s convenient to have the f i e l d gradients measured with respect to a bond axis system defined by the C1N bond (z) and a perpendicular to the plane (y), rather than the i n e r t i a l axis system. The desired transformation may c l e a r l y be achieved by a simple clockwise rotation of 9 about the c^-axis. za  I t then follows that i f x i s the quad—-  rupole tensor i n the i n e r t i a l axis system and x  i s the quadrupole  tensor  i n the bond axis system one has: X  B  = R  _ 1 X  4.4  R  where Cos9 R =  Sine  0  za za  -Sin9 '  Cose  0  za za  0 0  1  B X =  B X zz B X xz 0  B X xz B  x  0  0 0 yy  4.4a 4.4b  90  and  X=  'aa  x  ab  ab  X  bb  C  0  4.4c  X.  cc  and the o f f - d i a g o n a l elements y  ac  B B > X t. > X > X are a l l zero because the ab xy zy  a x i s perpendicular to the plane i s , by symmetry, a p r i n c i p a l a x i s of the quadrupole coupling tensor (101).  A general s o l u t i o n of equation 4.4 f o r  the diagonal tensor elements i n the bond a x i s system gives expressions cont a i n i n g the unknown Y r. as w e l l as the known Y ab aa  . If> however, the C1N  A  bond a x i s i s a l s o a p r i n c i p a l a x i s of the quadrupole  coupling tensor then  X i s zero and these r e l a t i o n s may be s i m p l i f i e d to the f o l l o w i n g ones by eliminating x ab' x z  B  2  2  2  ?  Xxx = (X aaS i n 9za - XvvCos 9 )/(Sin 9 - Cos 9 ) bb za za za vv  zz  X  B yy  = (x  X  aa  Cos 9 2  za  - Xi,iSin 9 )/(Cos 9 - Sin 9 ) bb za za za 2  2  2  4.5a  4.5b  4.5c  cc  Since the C1N bond has indeed been found to approximate c l o s e l y a p r i n c i p a l a x i s of the c h l o r i n e nuclear quadrupole molecules 35  coupling tensor i n s e v e r a l r e l a t e d  (102), such was assumed to be the case here too, and the  14 12 16 Cl  N  C  0 (G.V.S.) data were s u b s t i t u t e d i n t o equations 4.5 to obtain  B 35 values f o r x ( C l ) . The r e s u l t s are presented i n Table 4.10: the r e l a t i v e aa o r i e n t a t i o n s of the various a x i s systems are i l l u s t r a t e d i n Figure 4.4. B 35 The computed X ( zz  35 ~ ^310^ e  valent.  Cl) at -122.2 MHz i s of the same magnitude as '  ~ ""109.7 MHz; thus implying that the C1N a bond i s n e a r l y coThis i s consistent w i t h the e s s e n t i a l l y equal c h l o r i n e and n i t r o g e n  91  TABLE 4 . 1 0  T r a n s f o r m a t i o n o f the C h l o r i n e N u c l e a r Quadrupole C o u p l i n g Constants  A.  i n t o the C1N Bond A x i s System.  35  1A 12 16 C l N C 0 ( G . V . S . ) c o n s t a n t s t r a n s f o r m e d from the i n e r t i a l system t o the bond a x i s system u s i n g e q u a t i o n s 4 . 5 .  Structure II Y xx B  B  X  X A  yy zz B  0 B.  za  Structure  65.311  65.500  56.864  56.864  -122.174  -122.363  31° 2 7 '  31° 2 9 '  axis  III  C 1 N C 0 ( G . V . S . ) and C 1 N C 0 ( G . V . S . ) d a t a used t o f i n d the p r i n c i p a l axes o f t h e c h l o r i n e q u a d r u p o l e c o u p l i n g t e n s o r .  3 5  1 4  1 2  1 6  X  x'x'  yV  x  X  z*z'  8  aa 9 ,  X  X  3 5  •  z a B xx B B zz  1 4  1 2  Structure  II  I 8  Structure  53.731  68.723  56.864  56.864  -110.594  -125.586  30'  III  28'  29° 2 0 '  31° 5 8 '  53.658  68.707  56.864  56.864  -110.444  -125.571  Measured i n MHz. z i s a l o n g t h e C1N b o n d , y i s p e r p e n d i c u l a r t o t h e m o l e c u l a r p l a n e . x ' , y ' , z ' p r i n c i p a l a x i s system o f c h l o r i n e f i e l d g r a d i e n t . t e n s o r , y ' i s p e r p e n d i c u l a r t o t h e p l a n e , z ' i s n e a r l y p a r a l l e l t o the C1N bond.  92  FIGURE 4.4  I l l u s t r a t i o n o f the V a r i o u s A x i s Systems R e l e v a n t t o the  D i s c u s s i o n o f the C h l o r i n e 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 .  ( a , b , c ) = P r i n c i p a l i n e r t i a l a x i s system o f Cl N o r i g i n a t c e n t e r o f mass of t h i s i s o t o p e .  C O  ( a ' , b ' , c ' ) = P r i n c i p a l i n e r t i a l a x i s system o f C l N c o r i g i n o f c e n t e r o f mass of t h i s i s o t o p e . 3 5  1 4  l 2  1 8  (G.V.S.) 0  (G.V.S.)  with with  ( x , y , z ) = C1N Bond a x i s s y s t e m . ( x ' , y ' , z ' ) = P r i n c i p a l a x i s system o f c h l o r i n e q u a d r u p o l e c o u p l i n g t e n s o r 16  The a n g l e s 9  18  as c a l c u l a t e d from 0/ 0 i s o t o p e s h i f t . , and 9 , have been e x a g g e r a t e d f o r c l a r i t y .  93  electronegativities  (103).  bond must be o f the d a t i v e tend t o d e c r e a s e  Now any double bond c h a r a c t e r  (IT ) i n the C1N  t y p e from c h l o r i n e t o n i t r o g e n and would  B 35 |x__( Cl) | r e l a t i v e  to l e P ^ ^ n C  35 Cl) | .  therefore  On the o t h e r h a n d , B  the e f f e c t  of i o n i c c h a r a c t e r  (i  ) i n the cr bond i s t o i n c r e a s e  when the p o s i t i v e p o l e i s on c h l o r i n e .  namely:  (1)  Cl)I  i t i s necessary  To o b t a i n a q u a n t i t a t i v e  1  estimate  t o make two a d d i t i o n a l a s s u m p t i o n s ,  t h a t the a b o n d i n g c h l o r i n e a t o m i c o r b i t a l i s a pure p^  r a t h e r than an sp h y b r i d .  good a p p r o x i m a t i o n ( 1 0 4 ) .  Taken t o g e t h e r t h e s e s h o u l d be a f a i r l y  The p o p u l a t i o n s o f the v a l e n c e  p - o r b i t a l s may t h e n be w r i t t e n down a s : n = 2 n = 2 - IT x y c  n  z  shell  = 1 - i  S u b s t i t u t i o n of these e x p r e s s i o n s along w i t h E = 0 . 1 5  (99)  a not unreasonable r e s u l t .  chlorine 4.6  a  and the  c o u p l i n g c o n s t a n t s i n t o e q u a t i o n s 4.2 y i e l d s i ^ = 0 . 1 1 2 (11%) (5%),  (  t h a t o r b i t a l o v e r l a p may be i g n o r e d i n n o r m a l i z i n g the m o l e c u l a r  o r b i t a l s and (2) orbital,  |Y ' zz  a  o f t h e s e opposed e f f e c t s  35  appropriate  and TT = 0 . 0 5 0 c  A v e r y s i m i l a r a n a l y s i s , by Cook and G e r r y  ( 1 4 ) , on t h e i s o e l e c t r o n i c c h l o r i n e a z i d e m o l e c u l e gave i  = 12% and ir  = 8%. c  a  These f i g u r e s must be viewed w i t h c a u t i o n , however, because o f t h e a p p r o x i m a t i o n s i n h e r e n t i n the Townes D a i l e y t h e o r y , and because o f the extreme s e n s i t i v i t y of the c a l c u l a t e d c o n s t a n t s , y > t o the c o r r e c t n e s s o f the assumpact J  t i o n t h a t the C l N bond i s a p r i n c i p a l a x i s o f the c h l o r i n e f i e l d  gradient  tensor. In p r i n c i p l e i t u n i q u e l y the x  B * a a  •  s h o u l d be p o s s i b l e t o use the i s o t o p i c d a t a t o I f x'  represents  the  35  determine  C l quadrupole c o u p l i n g tensor of  an i s o t o p i c a l l y s u b s t i t u t e d s p e c i e s of c h l o r i n e i s o c y a n a t e , whose  a'-axis  * To a v e r y good a p p r o x i m a t i o n the o r i e n t a t i o n o f the p r i n c i p a l axes o f the f i e l d g r a d i e n t t e n s o r , w i t h r e s p e c t t o the m o l e c u l a r f r a m e , w i l l be i n d e p e n d ent of i s o t o p i c s u b s t i t u t i o n ( 1 0 1 ) .  94  makes an a n g l e 6 , ( p o s i t i v e f o r c l o c k w i s e r o t a t i o n a+a') w i t h the a—axis aa —— —  of  Cl  N  C  0 (G.V.S.), i t follows  that:  where R and x were d e f i n e d e a r l i e r a n d : *aa X* =  X  X  ab  ab  0  *bb  4.7a  °  x' A  cc  E q u a t i o n 4.7 may be s o l v e d f o r x i_ (or xV) ab and X^ » a  A  d i a g o n a l i z a t i o n o f x_ (or x_')  the q u a d r u p o l e c o u p l i n g t e n s o r . system i s t r i v i a l .  i n terms of o n l y the known x  ab  aa  J  then y i e l d s the p r i n c i p a l v a l u e s  A f i n a l t r a n s f o r m a t i o n i n t o the bond a x i s  The r e s u l t s of t h i s a n a l y s i s , w i t h " ^ C l ^ N ^ C ^ O t a k e n  t o be the s u b s t i t u t e d s p e c i e s , are c o l l e c t e d i n T a b l e 4 . 1 0 . t o be c r i t i c a l l y dependent on the v a l u e o f 8  aa  a n g l e o f o n l y 2' on g o i n g from s t r u c t u r e I I i n the c a l c u l a t e d c o u p l i n g c o n s t a n t s .  It  They a r e  to III  produces a 15 MHz v a r i a t i o n  i s g r a t i f y i n g t o see t h a t  these  two s e t s o f r e s u l t s b r a c k e t t h o s e o b t a i n e d i n the p r e c e d i n g a n a l y s i s . m  d e t e r m i n e the a n g l e 6  aa  seen  , ; i n d e e d , a change i n t h i s  i t was n e c e s s a r y t o use the p r o d u c t o f i n e r t i a r e l a t i o n ( X / i i i  than s t r u c t u r e I I ,  of  a  b  , i t i s more c o n s i s t e n t t o use s t r u c t u r e I I I  =  ^)  Since t o  rather  in this calculation.  An attempt was a l s o made t o i n t e r p r e t the n i t r o g e n q u a d r u p o l e c o u p l i n g i n terms of the Townes D a i l e y t h e o r y .  S i n c e the n i t r o g e n atom was e x p e c t e d  t o have a f o r m a l n e g a t i v e c h a r g e , e q u a t i o n s 4 . 3 , r a t h e r than 4 . 2 , were used in this analysis.  U n f o r t u n a t e l y t h e r e i s some u n c e r t a i n t y as t o what v a l u e  s h o u l d be a s s i g n e d t o the " a t o m i c " n i t r o g e n c o u p l i n g c o n s t a n t a p p e a r i n g i n expressions.  I n t h i s c a s e , eQ^io^  14  these  N) was t a k e n t o be -10 MHz as suggested  95  by Gordy and Cook ( 1 0 5 ) . stant e  A v a l u e of 0.30 was used f o r the s c r e e n i n g  con-  (99).  The n e a r l y  120°  C1NC bond a n g l e s t r o n g l y s u g g e s t s t h a t i t would be appro-  p r i a t e t o r e g a r d the n i t r o g e n a t o m i c o r b i t a l s t h a t a r e p a r t i c i p a t i n g i n bond 2 f o r m a t i o n as e s s e n t i a l l y pure sp  hybrids.  If  the x - a x i s i s d e f i n e d t o be  the b i s e c t o r o f the C1NC a n g l e , and the y - a x i s i s chosen t o be p e r p e n d i c u l a r t o the m o l e c u l a r frame t h e s e a r e c o n v e n i e n t l y w r i t t e n Hybrid Designation  2  + /T72<J>_  + /I76<j>_  g  >  N  X  *  3  =Jl73<!>  Number o f Electrons  lone p a i r  n^„  4.8a  NC o bond  n^  4.8b  NCI a bond  n ^  4.8c  out-of-plane TT bond  n_  4.8d  **x  S  if> = J T / 3 ( j )  as:  + /l76<J>  s  N  z  -JT/2t  p  z  X  ^4 = <J> y p  IT  F u r t h e r m o r e , s i n c e the b - p r i n c i p a l i n e r t i a l a x i s a l s o n e a r l y b i s e c t s the C1NC angle i t  i s p o s s i b l e t o make t h e f o l l o w i n g i d e n t i f i c a t i o n s :  XXX  ( U n  > *  *bb<  U N  >  X  Z Z  (  1 4  N) « X  ( N) U  A A  X  ( N) = X U  Y Y  T h i s a v o i d s any h i g h l y tenuous c o o r d i n a t e t r a n s f o r m a t i o n s .  C C  (  1 4  4.9  N)  Here, u n l i k e  the  c h l o r i n e c a s e , t h e r e i s no o b v i o u s c h o i c e f o r an i n - p l a n e p r i n c i p a l f i e l d g r a d i e n t a x i s , and t h e i s o t o p i c v a r i a t i o n s o f t h e c o u p l i n g c o n s t a n t s  are  negligible. From e q u a t i o n s 4.8 t h e n i t r o g e n p - o r b i t a l p o p u l a t i o n s may be  rewritten  as: n  x  n  =  2 / 3 n  = n y  TT  LP  +  1 / 6 n  NC  +  1 / 6 n  NCl  4  '  1  0  a  4.10b  96  n  z  =  1 / 2 n  NC  +  1 / 2 n  NCl  '  4  1  0  c  S i n c e even w i t h  s e t e q u a l t o 1.1 (the v a l u e o b t a i n e d from the c h l o r i n e  quadrupole a n a l y s i s )  there are s t i l l  t h r e e unknowns and o n l y two independent  c o u p l i n g c o n s t a n t s , i t i s c l e a r t h a t one a d d i t i o n a l a s s u m p t i o n i s r e q u i r e d . In the f i r s t i n s t a n c e , t h e " l o n e p a i r " o r b i t a l was presumed t o be c o m p l e t e l y nonbonding and f i l l e d , 35  i . e . n^p = 2.  S o l u t i o n of equations 4.3 u s i n g the  14 12 16 Cl  N  C  0 ( G . V . S . ) c o u p l i n g c o n s t a n t s then gave t h e r e s u l t s c o l l e c t e d i n  column I o f T a b l e 4 . 1 1 .  The l a r g e n e g a t i v e f o r m a l charge on n i t r o g e n and  the s t r o n g l y i o n i c NC bond a r e c o m p l e t e l y u n r e a s o n a b l e .  This leads to the  c o n c l u s i o n t h a t e i t h e r t h e s i m p l i f i e d v e r s i o n o f t h e Townes D a i l e y  theory  used h e r e i s i n a d e q u a t e , o r t h a t t h e a s s u m p t i o n o f a c o m p l e t e l y nonbonding l o n e p a i r on n i t r o g e n i s i n c o r r e c t . n  NC  W  a  S  e  s  t  i  m  a  t  e  a  To i n v e s t i g a t e t h e l a t t e r p o s s i b i l i t y  from the e l e c t r o n e g a t i v i t i e s o f c a r b o n and n i t r o g e n and  it^p was a l l o w e d t o v a r y . The s i m p l e s t r e l a t i o n c o n n e c t i o n i o n i c c h a r a c t e r and e l e c t r o n e g a t i v i t y  (X) i s t h a t p o s t u l a t e d by Gordy 'i  = |*(A) - * ( B ) | / 2 ,  (106):  for  |Z(A) - X(B)|<2  4.11  W i t h * ( N ) = 3.00 and Z ( C ) = 2.50 (103) t h i s g i v e s i^(NC) = 0.25 and hence n  N C  <1.25.  S i n c e t h e carbon atom h e r e i s a l s o a t t a c h e d t o a s t r o n g l y  e l e c t r o n e g a t i v e oxygen atom (X(0)  = 3.50) i t seems l i k e l y t h a t t h i s  over  e s t i m a t e s the i o n i c c h a r a c t e r o f the NC bond i n c h l o r i n e i s o c y a n a t e .  The  c a l c u l a t i o n was t h e r e f o r e performed t h r e e t i m e s w i t h n „ _ v a r i e d from 1.0  to 1.2; again the  35  •  Cl  14 12 16 N  C  NC 0 (G.V.S.)  c o u p l i n g c o n s t a n t s were u s e d .  r e s u l t s are a l s o c o l l e c t e d i n Table 4 . 1 1 . i  The t o t a l n e g a t i v e charge on  n i t r o g e n i s seen t o be a s e n s i t i v e f u n c t i o n o f the c h o i c e o f n  The  , the i n IN Kj  dividual populations less so.  If  i t i s assumed t h a t c  s h o u l d be l e s s t h  an  TABLE 4.11  N i t r o g e n Quadrupole C o u p l i n g I n t e r p r e t a t i o n D a i l e y Theory.  I n  LP  n  TT  "NC n  NCl  n n n n c  X  y z s  II  III  IV  1.60  1.69  1.78  1.94  1.55  1.64  1.73  1.45  1.00  a  1.10  1.10  b  i.io  2  a  1.10  b  1.49  1.57  1.94  1.55  1.64  1.73  1.28  1.05  1.10  1.15  1.50  1.23  1.30  1.36  1.49  0.25  0.53  0.81  b  C a l c u l a t e d from c h l o r i n e q u a d r u p o l e c o u p l i n g .  n  a  b  CND0/2 C a l c u l a t e d p - O r b i t a l P o p u l a t i o n s on C h l o r i n e and N i t r o g e n i n Chlorine Isocyanate.  C h l o r i n e (IA)  x  i.io  b  1.41  Assumed.  n  1.20  a  1.76  a  TABLE 4.12  u s i n g the Townes  C h l o r i n e (BA)  Nitrogen  (IA)  1.7235  1.9920  1.2776  1.9934  1.9934  1.4501  1.1051  0.8365  1.0120  1.9356  1.9356  1.4831  0.0064  0.0064  0.2229  IA = P r i n c i p a l i n e r t i a l a x i s system of  BA = C1N Bond a x i s s y s t e m .  3 5  C1  1 4  N  1 2  C  1 6  0  (G.V.S.).  98  0.5 e l e c t r o n s (107) t h i s a n a l y s i s i n d i c a t e s a n e a r l y c o v a l e n t NC bond. smallish  (<2)  v a l u e s can be r a t i o n a l i z e d o n l y by p o s t u l a t i n g some p a r -  t i c i p a t i o n o f i j ^ i n an i n - p l a n e IT NCO bond.  The o u t - o f - p l a n e IT NCO bond  a p p a r e n t l y has c o n s i d e r a b l e n i t r o g e n l o n e p a i r c h a r a c t e r . ulations n  T T 1  >n  LP  The  The r e l a t i v e pop-  a r e c o n s i s t e n t w i t h t h e more f a v o r a b l e o v e r l a p o ftfi.and TT  4  R  the o u t - o f - p l a n e c a r b o n p - o r b i t a l , as compared t o t h e o v e r l a p o f \J> and t h e in-plane carbon p - o r b i t a l ; indeed not  i t i s s u r p r i s i n g that the d i f f e r e n c e i s  larger. A q u a l i t a t i v e l y r e a s o n a b l e p i c t u r e o f t h e b o n d i n g a t n i t r o g e n has thus  emerged.  I n t h i s , t h e NC and NCI a bonds a r e n e a r l y c o v a l e n t , w h i l s t t h e  and \JJ^ n i t r o g e n o r b i t a l s b o t h p a r t i c i p a t e i n a TT system t h a t presumably runs t h e l e n g t h o f t h e NCO c h a i n .  The o u t - o f - p l a n e p - o r b i t a l s on each o f  n i t r o g e n , oxygen and carbon may be used t o c o n s t r u c t t h r e e m o l e c u l a r two  o f w h i c h w i l l be d o u b l y  occupied with very unequally  A s i m i l a r scheme would a p p l y t o the i n - p l a n e ir system. the many assumptions and a p p r o x i m a t i o n s  orbitals,  shared e l e c t r o n s . However, because o f  t h a t were made i n c o n s t r u c t i n g t h i s  model i t would be n a i v e t o a t t a c h any q u a n t i t a t i v e s i g n i f i c a n c e t o the numbers i n T a b l e 4.11. Semi-empirical  SCF-M0-CND0 t h e o r y has been p r e v i o u s l y employed i n c o n -  j u n c t i o n w i t h the Townes D a i l e y t h e o r y constants  (108).  Good agreement o f c a l c u l a t e d and observed  g e n e r a l l y been o b t a i n e d f o r halogen nitrogen nuclei.  to c a l c u l a t e n u c l e a r quadrupole c o u p l i n g  n u c l e i ; rather poorer  v a l u e s has  agreement, f o r  Such c a l c u l a t i o n s were performed on c h l o r i n e i s o c y a n a t e  by Dr. M. L. W i l l i a m s  (109) and k i n d l y communicated t o the a u t h o r .  In t h i s  i n s t a n c e the d e s i r e d p - o r b i t a l p o p u l a t i o n s were computed u s i n g t h e S a n t r y and  Segal  (110) p a r a m e t e r i z a t i o n o f the SCF-M0-CND0/2 method.  The atomic  o r b i t a l b a s i s s e t i n c l u d e d s - , p- and d - o r b i t a l s on c h l o r i n e , but o n l y s-  99  and p - o r b i t a l s on c a r b o n , oxygen and n i t r o g e n . were c o n s i d e r e d , n a m e l y :  (1)  the C1N bond a x i s s y s t e m . i n Table 4 . 1 2 .  Two d i f f e r e n t a x i s systems  the p r i n c i p a l i n e r t i a l a x i s s y s t e m , . a n d  (2)  The computed p - o r b i t a l p o p u l a t i o n s are p r e s e n t e d  The c o u p l i n g c o n s t a n t s w h i c h may be c a l c u l a t e d from them  u s i n g e q u a t i o n s 4 . 3 a r e compared i n T a b l e 4 . 1 3 w i t h the e x p e r i m e n t a l o n e s . The c a l c u l a t e d and " o b s e r v e d " c h l o r i n e 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 seen t o be i n r e a s o n a b l e agreement.  T h i s i s so f o r b o t h the  p r i n c i p a l i n e r t i a l a x i s system and the bond a x i s s y s t e m .  The l a t t e r  results  p r o v i d e f u r t h e r e v i d e n c e t h a t the C1N bond i s i n d e e d a t l e a s t a p p r o x i m a t e l y a p r i n c i p a l a x i s of the c h l o r i n e f i e l d g r a d i e n t  tensor.  The CNDO/2 c a l c u l a t i o n a l s o s u p p o r t s the a s s u m p t i o n made e a r l i e r  that  the c h l o r i n e h y b r i d o r b i t a l i n v o l v e d i n f o r m a t i o n o f a a bond t o n i t r o g e n i s e s s e n t i a l l y pure " p " .  B o t h the " f i l l e d " 3s and "empty" 3d c h l o r i n e a t o m i c  o r b i t a l s a r e found t o p l a y o n l y a v e r y m i n o r r o l e i n the o v e r a l l (CNDO/2) b o n d i n g scheme.  T h i s a p p a r e n t l a c k of s i g n i f i c a n t c h l o r i n e d - o r b i t a l p a r - ,  t i c i p a t i o n i n the c h l o r i n e i s o c y a n a t e b o n d i n g i s c o n s i s t e n t w i t h  current  t h e o r i e s on t h e f a c t o r s a f f e c t i n g t h e i m p o r t a n c e o f d - o r b i t a l s i n m o l e c u l a r bonding (111,112). I n the case o f the 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 c o u p l i n g , the CNDO/2 c a l c u l a t i o n has y i e l d e d x experiment, but a l s o a x Still,  D b  and x  v a l u e s w h i c h a r e i n good agreement  with  v a l u e w h i c h i s l e s s t h a n h a l f the o b s e r v e d one.  the r e s u l t s a r e q u i t e r e s p e c t a b l e when compared w i t h o t h e r n i t r o g e n  q u a d r u p o l e c a l c u l a t i o n s where even i n c o r r e c t s i g n s have f r e q u e n t l y been encountered It  (110).  i s perhaps more i l l u m i n a t i n g t o l o o k at the n i t r o g e n p - o r b i t a l p o p -  u l a t i o n s r a t h e r t h a n the c o u p l i n g c o n s t a n t s . comparable t o those l i s t e d i n column I I  The CNDO/2 numbers are r o u g h l y  of T a b l e 4 . 1 1 , and s i g n i f i c a n t l y  100  TABLE 4 . 1 3  Comparison of Observed and C a l c u l a t e d N u c l e a r Coupling Constants  3  of  3 5  Experimental  C1  1 4  N  1 2  C  1 6  0  Quadrupole  (G.V.S.).  CNDO/2  % Difference  -71.133  -82.59  16.1  WC1)  14.270  19.10  33.8  x (ci)  56.863  63.49  11.6  *aa  ( C 1 )  c c  *aa  ( N )  3.989  3.294  17.4  X B  ( N )  -1.013  -0.465  54.1  -2.976  -3.053  2.6  b  X (N) C C  Calculated(A,II)°  CND0/2  b  % Difference  Xxx ( C l )  65.31  63.26  3.1  X  (Cl)  56.86  63.49  11.7  X (C1)  -122.17  -126.76  3.8  B  B  d  yy B  Z  ° Measured i n MHz. b  c  d  C a l c u l a t e d from t h e o r b i t a l p o p u l a t i o n s i n T a b l e 4 . 1 2 . C a l c u l a t e d from the e x p e r i m e n t a l v a l u e s , assuming t h e C1N bond t o be a p r i n c i p a l a x i s of the c h l o r i n e f i e l d g r a d i e n t t e n s o r . % d i f f e r e n c e = ( (x „ ( e x p t . ) - x„„ (CNDO/2) ) / x _ ( e x p t . ) ) x l 0 0 . n  i  101  d i f f e r e n t from those i n column I.  They thus s u p p o r t our c o n t e n t i o n o f p a r -  t i c i p a t i o n by the n i t r o g e n " l o n e - p a i r " o r b i t a l i n the i n - p l a n e TT b o n d i n g s y s t e m of c h l o r i n e 4.5  isocyanate.  V i b r a t i o n a l Dependence o f the M o l e c u l a r 35 The r o t a t i o n a l c o n s t a n t s of the  Constants.  14 12 16 Cl  N  C  0 i s o t o p i c species of  chlorine  i s o c y a n a t e have been p l o t t e d as a f u n c t i o n of the v i b r a t i o n a l quantum number (v,.)  o f the l o w e s t f r e q u e n c y i n - p l a n e v i b r a t i o n i n F i g u r e s 4 . 5 , 4 . 6 and 4 . 7 .  The n e a r s t r a i g h t l i n e s observed i n d i c a t e t h a t , a t l e a s t w i t h r e s p e c t  to  t h i s one v i b r a t i o n , the low v v i b r a t i o n a l dependence of the r o t a t i o n a l s t a n t s i s c o n s i s t e n t w i t h the s i m p l e t h e o r y  (equations  2.48).  q u a d r a t i c terms i n the v i b r a t i o n a l e x p a n s i o n would presumably account f o r the r e l a t i v e l y  con-  I n c l u s i o n of completely  s m a l l d e v i a t i o n s from l i n e a r b e h a v i o r seen h e r e .  However, s i n c e t h e u),. v i b r a t i o n i s e s s e n t i a l l y a C1NC bend ( 9 0 ) ,  and the  b a r r i e r t o l i n e a r i t y o f the NCO c h a i n , because o f the s m a l l a n g l e o f b e n d , i s a l m o s t c e r t a i n l y w e l l below the ground v i b r a t i o n a l s t a t e , i t i s t o be e x p e c t e d t h a t at l a r g e v a l u e s o f v<. a p o i n t w i l l e v e n t u a l l y be reached w h i c h the m o l e c u l e can v i b r a t e  t h r o u g h the l i n e a r c o n f i g u r a t i o n .  s i t u a t i o n i s approached the A  r o t a t i o n a l constant w i l l increase  at  As t h i s dramatically  u n t i l i t becomes a b e n d i n g v i b r a t i o n f r e q u e n c y o f the l i n e a r m o l e c u l e . t h e l e s s , the l i m i t e d experimental evidence suggests t h a t f o r the v i b r a t i o n a l s t a t e s , i n p a r t i c u l a r the ground s t a t e , are w e l l behaved.  None-  lowest  the r o t a t i o n a l  Hence, the s u b s t i t u t i o n s t r u c t u r e d e t e r m i n e d i n  constants section  4 . 3 s h o u l d r e p r e s e n t the e q u i l i b r i u m one t o a good a p p r o x i m a t i o n . 35 I n F i g u r e 4 . 8 the i n e r t i a l d e f e c t of the has a l s o been p l o t t e d as a f u n c t i o n o f v^.  14 12 16 Cl  N  C  0 isotopic  The e s s e n t i a l l y e x a c t  straight  l i n e o b s e r v e d i s i n agreement w i t h t h e Oka and M o r i n o e x p r e s s i o n f o r v i b r a t i o n a l dependence of the i n e r t i a l d e f e c t  (equation 2.56).  species  Since  the the  102  103  FIGURE 4.6  V i b r a t i o n a l Dependence of the B' 3 5  3120 + 0  C1  1 4  N  1 2  C  1 6  R o t a t i o n a l Constant  0.  T 1  T  2  (v + 1/2) 5  of  104  FIGURE 4.7  V i b r a t i o n a l Dependence o f the C' R o t a t i o n a l 3 5  C1  1 4  N  1 2  C  1 6  0.  (v  5  + 1/2)  Constant o f  105  106  i n t e r c e p t o f t h i s l i n e i s a p p r o x i m a t e l y z e r o i t seems t h a t t h e t o A° from the o t h e r f i v e v i b r a t i o n s must n e a r l y c a n c e l .  contributions  Therefore  might r e a s o n a b l y e x p e c t t h a t t h e s i m p l e Hershbach and L a u r i e  one  expression  A° ~ 4K/co^ s h o u l d g i v e a r e s p e c t a b l e r e s u l t ; t h i s has a l r e a d y been shown t o be the  case.  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 of c h l o r i n e i s o c y a n a t e behave d i f f e r e n t l y as a f u n c t i o n of v i b r a t i o n a l s t a t e . J  n e a r l y the same i n a l l t h r e e s t a t e s w i t h v,.;  the f o u r t h ,  T  a b a b  >  w  a  s  Two, x, , , , and x , ' bbbb aabb  studied, while x  3-3.33.  increases  rather are  rapidly  w e l l d e t e r m i n e d f o r o n l y t h e ground s t a t e .  A s i m i l a r phenomenon has been observed f o r o t h e r q u a s i - l i n e a r m o l e c u l e s Johns (114) has managed t o account q u a n t i t a t i v e l y  (113).  f o r the i n c r e a s e i n x aaaa  f o r s e v e r a l o f t h e s e u s i n g as a b e n d i n g p o t e n t i a l a harmonic o s c i l l a t o r perturbed with a Lorentzian b a r r i e r  (to l i n e a r i t y ) .  His analysis  also  i n d i c a t e d t h a t as the energy i n the b e n d i n g v i b r a t i o n approaches the n e c e s s a r y t o surmount the b a r r i e r c l a s s i c a l l y the i n c r e a s e i n x  amount should  aaaa become d r a m a t i c .  S i n c e the v a r i a t i o n s o f A v  r o u g h l y l i n e a r o v e r the low v a l u e s o f v , r  i s expected f o r c h l o r i n e 4.6  and x  observed here  are  aaaa  a rather high b a r r i e r to  linearity  isocyanate.  C a l c u l a t i o n of 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 and the D e f e c t from the M o l e c u l a r F o r c e  Inertial  Field.  The i n f r a r e d and Raman s p e c t a o f c h l o r i n e i s o c y a n a t e have been i n v e s t i g a t e d by E y s e l and Nachbaur  (90).  These a u t h o r s o b t a i n e d a complete a s s i g n -  ment o f a l l s i x f u n d a m e n t a l v i b r a t i o n s and a l s o performed a n o r m a l  coordinate  force constant a n a l y s i s . T h e i r r e s u l t s have been r e p r o d u c e d i n T a b l e s 4.14 * A c t u a l l y t h r e e f o r c e f i e l d s were d e t e r m i n e d ; one f o r each of t h r e e d i f f e r e n t s t r u c t u r a l m o d e l s . ' The model w h i c h c o r r e s p o n d s t o the f o r c e f i e l d g i v e n i n T a b l e 4.14 i s i n f a i r l y good agreement w i t h the s t r u c t u r e d e t e r m i n e d i n t h i s work.  107  TABLE 4.14  C h l o r i n e Isocyanate V i b r a t i o n a l Force  Force C o n s t a n t  3  b  R.G.F.F.  f(C1N)  2.818  3.026  f (NC)  13.228  13.462  f (CO)  13.297  13.462  f(C1NC)  0.501  0.3604  f(NCO)  0.967  0.9243  f(l)  0.398  0.6513  f(C1N:CN)  0.17  0.0000°  f(C1N:C0)  0.10  0.0000°  f(CN:CO)  1.19  1.023  f(C1NC:C1N)  0.101  0.1513  f(CINCrNC)  0.146  0.6731  f(C1NC:C0)  0.000  f(NC0:ClN)  0.369  0.6053  f(NCO:NC)  0.000°  0.0000°  f(NCO:CO)  0.000°  0.0000°  b  f(C1NC:NC0)  3  E.N.F.F.  Fields  C  -0.188  0.0512  0.0303  S t r e t c h i n g f o r c e c o n s t a n t s a r e i n mdyne/X, bends a r e i n mdyne'R/rad , b e n d - s t r e t c h i n t e r a c t i o n s a r e i n mdyne/rad. V a l u e depends on c h o i c e o f c o r r e s p o n d i n g G m a t r i x element d e f i n i t i o n c o n t a i n s an a r b i t r a r y s c a l e f a c t o r .  (Ggg) whose  C h o i c e o f G ^ and  hence f^^ does n o t a f f e c t t h e C o r i o l i s c o u p l i n g c o n s t a n t s , a l s o , t o r t i o n c o n s t a n t s a r e independent o f f g g Set e q u a l t o 0 i n i t i a l l y .  dis-  108  TABLE 4.15  Fundamental V i b r a t i o n a l F r e q u e n c i e s of C h l o r i n e  Fundamental  Frequency a  Isocyanate.  Description  oj^  2215  NCO asymmetric  OJ  1309  NCO symmetric s t r e t c h  OJ  708  to,  608  oi  199(157)  2  3  4 5  o)g  Measured i n cm indicated.  559  stretch  NCO bend ( i n - p l a n e ) C1N s t r e t c h  b  c  C1NC bend  (in-plane)  o u t - o f - p l a n e bend  ; gas phase i n f r a r e d f r e q u e n c y u n l e s s  otherwise  L i q u i d phase Raman measurement, does n o t appear i n gas phase  IR.  The f i r s t number i s the Raman, s o l i d p h a s e , f r e q u e n c y ; the s e c o n d , the gas phase i n f r a r e d f r e q u e n c y .  109  and 4 . 1 5 .  The f o r c e f i e l d was c o n s t r u c t e d u s i n g an a p p r o x i m a t e method  p r e v i o u s l y d e s c r i b e d by Becher and M a t t e s  (115).  S i n c e t h i s p r o c e d u r e has  r e c e n t l y come under s e v e r e c r i t i c i s m (116) i t i s o f some i n t e r e s t t o t e s t the E y s e l and Nachbaur f o r c e f i e l d ( E . N . F . F . )  a g a i n s t independent d a t a . 35  A c c o r d i n g l y , the c e n t r i f u g a l d i s t o r t i o n constants of  14 12 16 Cl  N  C  0 (G.V.S.)  were c a l c u l a t e d from t h e E . N . F . F . w i t h t h e a i d o f t h e K i v e l s o n W i l s o n outlined i n section 2.5.  theory  The c a l c u l a t e d c o n s t a n t s a r e compared w i t h t h e  o b s e r v e d ones i n T a b l e 4 . 1 6 ; t h e agreement i s r a t h e r p o o r .  This i s presum-  a b l y , a t l e a s t t o some e x t e n t , a r e f l e c t i o n on t h e method o f Becher and Mattes. I n a d d i t i o n , however, t h e r e i s some u n c e r t a i n t y as t o what f r e q u e n c y s h o u l d be a s s i g n e d t o to,..  T h i s i s e s p e c i a l l y i m p o r t a n t i n t h e p r e s e n t case  s i n c e the c e n t r i f u g a l d i s t o r t i o n constants are p a r t i c u l a r l y s e n s i t i v e to t h e s m a l l d i a g o n a l (bending)  force constants.  E y s e l and Nachbaur found  to,. = 199 cm * i n t h e s o l i d s t a t e and OJ,. = 175 cm * i n t h e l i q u i d s t a t e ; used t h e f o r m e r i n t h e i r f o r c e f i e l d c a l c u l a t i o n .  they  In the course of the  p r e s e n t work t h e f a r i n f r a r e d gas phase s p e c t r u m o f c h l o r i n e i s o c y a n a t e was investigated.  Only one band was f o u n d .  f r e q u e n c y o f 157 cm  I t had a PR c o n t o u r w i t h a c e n t e r  For the purpose of c o n s t r u c t i n g a f o r c e f i e l d which  w i l l r e p r o d u c e t h e microwave d a t a i t i s c l e a r l y p r e f e r a b l e t o use t h e gas phase v a l u e o f to,.. A second f o r c e f i e l d ( R . G . F . F . ) has o n l y r e c e n t l y been o b t a i n e d f o r c h l o r i n e i s o c y a n a t e by D r . R. Green ( 1 1 7 ) .  It  i s based on t h e s t r u c t u r e  r e p o r t e d h e r e and t h e v i b r a t i o n a l f r e q u e n c i e s and a s s i g n m e n t s o f E y s e l and N a c h b a u r , e x c e p t t h a t to,, was t a k e n t o be 157 cm * r a t h e r t h a n 199 cm ^.  The  a p p r o x i m a t i o n s used i n t h i s c a s e , i n o r d e r t o o b t a i n a s o l u t i o n o f t h e v i b r a t i o n a l s e c u l a r e q u a t i o n , a r e e s s e n t i a l l y t h o s e d e s c r i b e d by M i l l s (118)  110  TABLE 4.16  C a l c u l a t e d and Observed 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 Chlorine Isocyanate (  Distortion Constant  -59.139  bbbb aabb  C  0 G.V.S.)  Calculated from R . G . F . F ,  -26.22  -45.04  -0.01075  -0.00866  -0.01260  0.6923  0.3943  0.6706  -0.01144  -0.01287  -0.0101  abab  N  Calculated from E . N . F . F .  Observed Value  aaaa l  Cl  Measured i n MHz. C a l c u l a t e d from the measured spectrum u s i n g 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 i s p r o c e d u r e I (see t e x t : s e c t i o n 4 . 2 ) .  TABLE 4.17  C a l c u l a t e d and Observed I n e r t i a l Isocyanate (  Calculation  3  VIB  3 5  C1 N U  1 2  C  1 6  0  cent  Defects  of Chlorine  G.V.S.).  A  VIB  +  A  cent  E.N.F.F.  0.2606  0.0008  0.2614  0.3645  R.G.F.F.  0.3265  0.0009  0.3274  0.3645  Measured i n  a.in.u.8 . 2  Ill  f o r the s o - c a l l e d H y b r i d O r b i t a l F o r c e F i e l d M o d e l . d e t a i l s o f the c a l c u l a t i o n p r o c e d u r e are q u i t e n o v e l . of t h e s e w i l l appear s h o r t l y .  However, some of  the  A complete account  The R . G . F . F . and the d i s t o r t i o n c o n s t a n t s  w h i c h i t y i e l d s have a l s o been g i v e n i n T a b l e s 4.14 and 4.16  respectively.  The agreement between the c a l c u l a t e d and o b s e r v e d d i s t o r t i o n c o n s t a n t s  is  now q u i t e r e s p e c t a b l e . F i n a l l y , b o t h f o r c e f i e l d s were s u b j e c t e d t o one a d d i t i o n a l t e s t , namely a c a l c u l a t i o n of the i n e r t i a l d e f e c t .  E q u a t i o n 2.56 was used t o d e t e r m i n e  the v i b r a t i o n a l c o n t r i b u t i o n ; e q u a t i o n 2 . 5 5 b , the c e n t r i f u g a l d i s t o r t i o n contribution.  The e l e c t r o n i c p a r t , w h i c h i s p r o b a b l y s m a l l and n e g a t i v e  (see s e c t i o n 2 . 4 ) , was i g n o r e d .  The r e q u i r e d C o r i o l i s c o u p l i n g c o n s t a n t s  were computed w i t h the a i d of a program w r i t t e n by S c h a c h t s c h n e i d e r  (119).  The r e s u l t s a r e compared i n T a b l e 4.17 w i t h the o b s e r v e d i n e r t i a l d e f e c t . A g a i n , i t w i l l be n o t e d t h a t t h e R . G . F . F . has g i v e n c o n s i d e r a b l y b e t t e r agreement w i t h e x p e r i m e n t t h a n the E . N . F . F .  However, t h e r e i s  evidently  s t i l l some room f o r improvement i n even the f o r m e r . 4.7  D i s c u s s i o n of the M o l e c u l a r S t r u c t u r e . The gas phase e l e c t r o n d i f f r a c t i o n s p e c t r u m o f c h l o r i n e i s o c y a n a t e has  r e c e n t l y been i n v e s t i g a t e d by Oberhammer ( 9 1 ) .  I t was found t h a t the o b s e r v e d  spectrum c o u l d be r e p r o d u c e d e q u a l l y w e l l s t a r t i n g from e i t h e r o f two d i f f e r ent s t r u c t u r a l m o d e l s . linear.  I n o n e , the NCO c h a i n was b e n t , i n the o t h e r i t  The bent NCO c h a i n s t r u c t u r e was t h e n p r o p o s e d t o be the  one on the b a s i s of a number of s e c o n d a r y c o n s i d e r a t i o n s . i t i v e c h o i c e between the two c o u l d n o t be made.  was  correct  However, a d e f i n -  Oberhammer s p r e f e r r e d ?  (bent) s t r u c t u r e has been compared w i t h our " b e s t " s t r u c t u r e i n T a b l e 4 . 1 8 . The agreement i s q u i t e good. I n T a b l e 4 . 1 9 a number of " g e n u i n e " CO and NC double bond l e n g t h s have  112  TABLE 4 . 1 8  Internal  Comparison o f C h l o r i n e I s o c y a n a t e E l e c t r o n D i f f r a c t i o n and Microwave S t r u c t u r e s .  Coordinate  Microwave  Electron Diffraction  r(Cl-N)  1.705 ± 0.005  1.700 ± 0.002  r(N-C)  1.225 ± 0.005  1.227 ± 0.005  r(C-O)  1.162 ± 0.005  1.156 ± 0.006  /.(CINC)  118° 50* ± 3 0 '  118° 12' ± 3 6 '  Z.(NCO)  170° 5 2 ' ± 3 0 '  170° ± 2 ° 6'  Bond l e n g t h s a r e measured i n A*.  113  been p r e s e n t e d .  It  w i l l be n o t e d t h a t these are a l l s i g n i f i c a n t l y  longer  than the c o r r e s p o n d i n g c h l o r i n e i s o c y a n a t e i n t e m u c l e a r d i s t a n c e s . the i s o c y a n a t e NC bond i s n e a r l y h a l f way between a " p u r e " t r i p l e double NC bond i n l e n g t h ; w h i l e the i s o c y a n a t e CO d i s t a n c e i s i d e n t i c a l t o t h a t found i n the OCX m o l e c u l e s (X = 0 , S, S e ) , have a d e l o c a l i z e d TT system ( i . e .  In  fact,  and  virtually a l l of which  2+ bond o r d e r ( 1 2 0 ) ) , and i s o n l y s l i g h t l y  l o n g e r t h a n t h e carbon monoxide " t r i p l e " bond ( 1 2 1 ) . of the c h l o r i n e i s o c y a n a t e NC and CO bonds r e l a t i v e  No doubt the  shortness  t o those i n T a b l e 4.19  may be p a r t l y a t t r i b u t e d t o an i n c r e a s e i n a bond s t r e n g t h a s s o c i a t e d  2 t h e change i n the c a r b o n atom h y b r i d i z a t i o n from sp  with  * t o sp ,  However,  dominant f a c t o r i s l i k e l y to be a d e r e a l i z a t i o n o f the NCO TT s y s t e m . has p r e v i o u s l y been p r o p o s e d i n c o n n e c t i o n w i t h o t h e r i s o c y a n a t e s  the This  (123,124).  F o r c h l o r i n e i s o c y a n a t e i t has a l r e a d y been shown ( s e c t i o n 4 . 4 )  that  n i t r o g e n n u c l e a r quadrupole c o u p l i n g i s c o n s i s t e n t w i t h roughly  comparable  i n - p l a n e (weaker) and o u t - o f - p l a n e The V a l e n c e Bond (125)  (stronger)  TT bonding a t n i t r o g e n .  approach p r o v i d e s an a l t e r n a t i v e ,  perhaps  p i c t u r e o f how t h e c h l o r i n e i s o c y a n a t e NC and CO bonds may a t t a i n t h a n d o u b l e bond c h a r a c t e r .  the  clearer,  greater  O n l y t h r e e o f t h e many p o s s i b l e r e s o n a n c e  forms  are l i k e l y t o be major c o n t r i b u t o r s t o the composite w a v e f u n c t i o n ; t h e s e Cl  \  ,N  Cl  C=0 41  N = C  0"  Cl \  _:N  +  411  C=  0  are:  +  4III  * C o u l s o n (122) has shown t h a t the a bond o v e r l a p i n t e g r a l i s maximum f o r sp h y b r i d i z a t i o n , and d e c r e a s e s w i t h an i n c r e a s e i n e i t h e r s o r p c h a r a c t e r . 2 3 From t h i s i t may be i n f e r r e d t h a t a bond s t r e n g t h v a r i e s a s : s p > s p > s p > s o r p. Such a t r e n d i s c l e a r l y o b s e r v e d f o r the CH bonds and i s r e f l e c t e d in their lengths.  114  TABLE 4.19 Some "Genuine" CO and NC Double Bond Lengths. Molecule  Formula  r(C-O)  Formaldehyde  H CO  1.204  (129)  Formamide  NH CHO  1.193  (129)  Formic A c i d  HCOOH  1.202  (129)  Acetaldehyde  CH CHO  1.216  (129)  Acetyl  CH C0C1  1.192  (129)  Chloride  2  2  3  3  T y p i c a l CO d o u b l e bond l e n g t h = 1.20 A (?) i n chlorine isocyanate. -  Molecule  cf.  Reference  r(C-O) = 1.162 °v  Formula  r(C-N)  N-Methyl M e t h y l e n i m i n e  CHINCH,  1.30  (130)  Formaldoxime  H0NCH  1.276  (131)  1.3.4- T h i a d i a z o l e  NCHSCHN  1.302*  (132)  1.2.5- Oxadiazole  CHNONCH  1.300*  (133)  2  Reference  N e i t h e r o f t h e s e a r e " p u r e " d o u b l e NC bonds s i n c e b o t h m o l e c u l e s have been shown t o have a s m a l l degree of a r o m a t i c i t y . "Pure" double NC bonds seem t o be r e a l l y q u i t e r a r e . Cox and J e f f r e y (134) h a v e , by i n t e r p o l a t i n g between the NC s i n g l e and d o u b l e bond l e n g t h s , come up w i t h a v a l u e o f 1.28 A* f o r the NC " p u r e " d o u b l e bond l e n g t h , c f . r(N-C) = 1.225 A* i n c h l o r i n e i s o c y a n a t e .  115  TABLE 4 . 2 0  Some NC T r i p l e Bond Lengths and CO 2+ Bond L e n g t h s .  Molecule  r(N-C)  3  Molecule  r(C-O)  CH CN  1.157  OCO  1.162  CF CN  1.153  OCS  1.160  HCN  1.153  OCSe  1.159  FCN  1.159  CO  1.128  C1CN  1.160  BrCN  1.160  3  3  Measured i n A*.  b  Taken from Gordy and Cook ( 1 2 9 ) , e x c e p t CO  Taken from H e r z b e r g  TABLE 4.21  (135).  Comparison o f the C h l o r i n e N i t r o g e n Bond L e n g t h s i n a Number o f S m a l l M o l e c u l e s .  Molecule  3  r(Cl-N)  Angles  a  found  Reference  C1NC0  1. 705 + 0.005  Z_(C1NC) = 118° 5 0 '  C1NNN  1. 745 + 0.005  /1(C1NN) = 108°  40'  (14)  H NC1  1. 748 + o . o o o i  ^-(HNCl) = 103°  4 1 ' ; i_ (HNH) = 107°  (102)  HNC1  1. 760 + ?  Z.(C1NC1)  ^ 106°; Z.(HNC1)  Me NCl  1. 770 + 0.02  Z.(MeNCl)  = 107°; /.(MeNMe) = 108°  MeNCl  1. 740 + 0.02  2  2  2  NC1  3  2  b  :  ^(C1NC1) = 108°; /.(MeNCl)  1. 759 + 0.002  ^ 103°  = 109°  (136) (137) (137) (102)  N0C1  1. 975 + 0.005  Z.(0NC1) = 113°  20'  (138)  N0 C1  1. 840 + 0.002  /l(ONCl) = 114° 4 2 '  (139)  2  Measured i n X . Measurement  error.  116  Then, i f 411 and 4 I I I a r e o f s i m i l a r i m p o r t a n c e t o 4 1 , a bond o r d e r o f 2+ i s t o be e x p e c t e d f o r b o t h of t h e two m u l t i p l e bonds ( 1 2 6 ) .  It i s interest-  i n g t o compare t h i s s i t u a t i o n w i t h t h a t found f o r i s o e l e c t r o n i c  chlorine  a z i d e where t h e form e q u i v a l e n t t o 411 i s l i k e l y t o be o f m i n o r i m p o r t a n c e . Here t h e dominant resonance forms a r e p r o b a b l y 4 1 ' and 4 I I I ' ( 1 4 ) : Cl \  .N  Cl  N = N + "  N^=N + +  41V  Cl  N "  \  ;N  411'  N  =  N  + 4III'  T h i s i s s u p p o r t e d by t h e o b s e r v a t i o n t h a t t h e t e r m i n a l NN d i s t a n c e i s s h o r t e r than t h e c e n t r a l one (1.133 A" and 1.252 A* r e s p e c t i v e l y C1NX (X = C , N) a n g l e i s l a r g e r i n t h e i s o c y a n a t e  (14)).  A l s o , the  (118° 5 0 ' ) t h a n i n t h e  a z i d e (108° 4 0 ' ) . The c h l o r i n e 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 o f c h l o r i n e i s o c y a n a t e was i n t e r p r e t e d e a r l i e r as i n d i c a t i n g a s m a l l degree o f double bond (5%)  i n t h e C1N b o n d .  character  A l i k e l y resonance form showing s u c h d o u b l e bond  character i s : +  C1  \ - d c  4IV  I t i s n o t e w o r t h y t h a t t h i s form i s a l s o c o m p a t i b l e w i t h t h e bend found i n t h e NCO c h a i n ( 9 ° 8 ' ) .  A s i m i l a r s i t u a t i o n p r e v a i l s f o r c h l o r i n e azide which  has been shown t o have an 8 ° 4 ' ( t r a n s ) a z i d e bend as w e l l as 8% C1N double bond c h a r a c t e r  (14).  A g a i n b o t h e f f e c t s may be a t t r i b u t e d t o a s m a l l c o n -  t r i b u t i o n from one resonance f o r m , +  namely:  C1 ^ N  Nv X  41V N  117  A c i s s t r u c t u r e i s p o s s i b l e f o r b o t h the i s o c y a n a t e and the a z i d e but  is  e v i d e n t l y not i m p o r t a n t f o r e i t h e r , p r o b a b l y because o f nonbonding r e p u l s i o n o f the c h l o r i n e and oxygen (or n i t r o g e n ) o f the m o l e c u l e .  e l e c t r o n systems at the two ends  A CNDO/2 c a l c u l a t i o n performed by Oberhammer (91)  t h a t c h l o r i n e i s o c y a n a t e s h o u l d have a t r a n s bend at carbon o f  predicted  approximately  7°. The C1N bond l e n g t h s found i n a number o f d i f f e r e n t s m a l l m o l e c u l e s have been c o l l e c t e d i n T a b l e 4 . 2 1 . are anomalously l o n g .  Two o f t h e s e , namely t h o s e i n N0C1 and N 0 C 1 , 2  I n b o t h c a s e s , c h l o r i n e has bonded t o a s t a b l e  para-  m a g n e t i c s p e c i e s , g i v i n g r i s e t o a p o o r l y l o c a l i z e d , weak, and a p p r o p r i a t e l y l o n g C1N bond ( 8 4 , 1 2 7 ) .  A l l of the r e m a i n i n g bond l e n g t h s i n T a b l e 4.21  are  o f s i m i l a r magnitude and are c l o s e t o the sum o f the c h l o r i n e and n i t r o g e n s i n g l e bond r a d i i ( 1 . 7 3 °v). chlorine isocyanate.  The s h o r t e s t one i s t h a t r e p o r t e d h e r e f o r  S i n c e c h l o r i n e i s o c y a n a t e a l s o has the l a r g e s t C1NX  a n g l e , i t seems l i k e l y t h a t t h i s i s due l a r g e l y t o the h y b r i d i z a t i o n e f f e c t mentioned e a r l i e r .  Other p o t e n t i a l f a c t o r s , such as TT o r i o n i c  are apparently of l e s s e r importance or c a n c e l .  character  118  CHAPTER 5 THE MICROWAVE SPECTRUM OF ISOCYANIC ACID Isocyanic acid i s a reactive, easily polymerized, compound that has played a prominent role i n organic chemistry for many years.  I t i s readily  prepared either by the direct reaction of a hydrogen halide gas with s i l v e r cyanate or by the thermal decomposition of a number of organic compounds (e.g. cyanuric acid, urea, cyamelide). characterized by Linhard (140).  Its physical properties were f i r s t  A review of isocyanate chemistry has  recently been published by Ozaki (141). An early study of the u l t r a v i o l e t absorption spectrum of isocyanic acid vapor by Woo and L i n (142) revealed only diffuse absorption bands similar to those produced by various other molecules known to contain an NH bond. At about the same time Goubeau (143) recorded the Raman spectrum of the l i q u i d and interpreted i t as showing that the molecule existed i n the keto form (HNCO) rather than the enol form (HOCN). This was subsequently v e r i f i e d by Eyster, G i l l e t t e and Brockway (123) i n an electron d i f f r a c tion study which also yielded an approximate molecular structure.  The  f i r s t thorough investigation of the vibration-rotation spectrum of i s o cyanic acid was performed by Herzberg and Reid (H. and R.) (144) who reported a complete assignment of a l l s i x fundamental vibrations as well as a s l i g h t l y improved molecular geometry. A vibrational force f i e l d , based on the data of H. and R., was published shortly thereafter by O r v i l l e Thomas (124). Recently, Ashby and Werner (A. and W.)  (145) re-investigated the infrared  spectrum of H^N^C^O and proposed an alternative assignment for the three low frequency fundamentals.  These authors have also recorded and analysed  119  the v i b r a t i o n - r o t a t i o n spectrum of D ^ N ^ C ^ O  (146).  Two new v i b r a t i o n a l  f o r c e f i e l d s , based on the d a t a o f A . and W., have now been p u b l i s h e d f o r i s o c y a n i c acid (147,148);  they are n o t i n  agreement.  The pure r o t a t i o n a l spectrum o f i s o c y a n i c a c i d has been the of s e v e r a l i n v e s t i g a t i o n s . by Jones e t . a l . D B  (11)  Q  T  TT  + C  q  .  The e a r l i e s t microwave measurements were made  on the 1Q ^ —  14„ 12„16„ , 15„12 16„ N C 0 and H N C O  OQ Q t r a n s i t i o n o f the  H^N^C^O,  . . ' . „ - . , isotopic species. These gave a c c u r a t e v a l u e s  Subsequent r e s o l u t i o n o f the h y p e r f i n e s t r u c t u r e of t h i s  transition (H^N^C^O  species)  p e r m i t t e d the d e t e r m i n a t i o n o f y  w h i l e S t a r k measurements y i e l d e d v a l u e s v i b r a t i o n a l states  (149).  of u  D^N^C^O  aa  same (^^N),  More r e c e n t l y , Kewley e t . a l .  (150) measured a H^N^C^O  i s o t o p i c s p e c i e s , from w h i c h a c c u r a t e v a l u e s of B r  b u t o n l y rough v a l u e s o f A  r  and C O  > q  were e x t r a c t e d .  of  f o r the ground and two e x c i t e d  number o f _i-type R-branch mm-wave t r a n s i t i o n s b e l o n g i n g t o the and  subject  A conventional far  O  infrared  s t u d y o f the pure r o t a t i o n a l spectrum o f t h e s e same two i s o t o p e s , by Krakow et.al.  ( 1 5 1 ) , produced s l i g h t l y r e f i n e d A  q  values.  B o t h the mm-wave and  the i n f r a r e d work i n d i c a t e d t h a t i s o c y a n i c a c i d has e x t r e m e l y l a r g e f u g a l d i s t o r t i o n a s s o c i a t e d w i t h r o t a t i o n about i t s a - a x i s .  Neely  centri(152)  has d i s c u s s e d t h i s phenomenon i n terms of a s i m p l e n o n r i g i d r o t o r m o d e l . F i n a l l y , White and Cook (153)  have shown t h a t the a-component o f the d i p o l e  moment i s a s l o w l y v a r y i n g f u n c t i o n o f r o t a t i o n a l The i n i t i a l o b j e c t i v e  state.  o f the p r e s e n t s t u d y was s i m p l y t o measure a few  a^-type R-branch t r a n s i t i o n s o f the c a r b o n - 1 3 , n i t r o g e n - 1 5 , and oxygen-18 s u b s t i t u t e d species of i s o c y a n i c a c i d .  These were e x p e c t e d t o g i v e an i m -  proved m o l e c u l a r s t r u c t u r e , but were a l s o o f i n t e r e s t ( t o the a s t r o p h y s i c i s t ) .  i n t h e i r own r i g h t  I t was soon d i s c o v e r e d , however,  a l t r a n s i t i o n s were o b s e r v a b l e .  t h a t many a d d i t i o n -  These i n c l u d e d a-type Q-branch  transitions  120  of the t y p e  —  type J Q J —  and _b-type R- and P-branch t r a n s i t i o n s o f  j  (J-l)^  the  From the h y p e r f i n e s t r u c t u r e o f the f o r m e r , a v a l u e  was o b t a i n e d f o r the n i t r o g e n - 1 4 q u a d r u p o l e c o u p l i n g asymmetry  parameter,  w h i l e the l a t t e r p e r m i t t e d a much improved d e t e r m i n a t i o n of the A  rotao  t i o n a l constants.  I n a d d i t i o n , the S t a r k components o f the b-type t r a n s -  i t i o n s of D ^ N ^ C ^ O  y i e l d e d an a p p r o x i m a t e v a l u e f o r y^.  In a l l , s i x  i s o t o p i c s p e c i e s were s t u d i e d , namely: H  1 4  N  H N U  C  1 2  1 2  C  1 6  0  H  1 5  N  1 2  C  1 6  0  H  1 4  N  1 3  C  1 6  0  1 8  0  D  1 4  N  1 2  C  1 6  0  D  1 5  N  1 2  C  1 6  0  A l l of the microwave measurements  and the a n a l y s i s were by the a u t h o r .  mm-wave measurements were made by D r . G. W i n n e w i s s e r s u p p l i e d by the 5.1  u s i n g i s o t o p i c samples  author.  Assignment o f the  Spectrum  The b e s t a v a i l a b l e i s o c y a n i c a c i d s t r u c t u r a l parameters t o p r e d i c t the f r e q u e n c y o f the 1Q ^ — isotopic species. region.  The  (11) were u s e d  OQ Q t r a n s i t i o n f o r each of the new  A l l o t h e r t r a n s i t i o n s were e x p e c t e d t o l i e i n the mm-wave  I n each c a s e , a s t r o n g a b s o r p t i o n was found n e a r the p r e d i c t e d 14  frequency.  F o r the  N i s o t o p i c s p e c i e s , i t s unique n u c l e a r  quadrupole  h y p e r f i n e s t r u c t u r e p r o v i d e d c o n c l u s i v e v e r i f i c a t i o n o f the a s s i g n m e n t . r e - e x a m i n a t i o n o f t h i s t r a n s i t i o n i n the s p e c t r a o f the p r e v i o u s l y  A  studied  i s o t o p e s s u r p r i s i n g l y r e v e a l e d the u n s p l i t - l i n e f r e q u e n c y p u b l i s h e d f o r D  1 4  N  1 2  C  1 6  0  t o be i n e r r o r by over 1 MHz ( 1 1 ) .  There can be l i t t l e doubt  the f r e q u e n c y g i v e n h e r e i s the c o r r e c t one s i n c e i t i s i n agreement the mm-wave d a t a  that  with  (150).  The d i s c o v e r y o f t h e a-type Q-branch t r a n s i t i o n s o f i s o c y a n i c a c i d w a s , t o some e x t e n t , f o r t u i t o u s .  For c h l o r i n e i s o c y a n a t e such t r a n s i t i o n s were  121  found t o be u n o b s e r v a b l y weak; t h e i r t r a n s i t i o n p r o b a b i l i t i e s a r e i n h e r e n t l y small (38).  I n the case o f HNCO, however,  t h e l a r g e r a-component o f t h e  d i p o l e moment makes them w e a k l y o b s e r v a b l e .  By comparison the a-type  R-branch t r a n s i t i o n s a r e a t l e a s t an o r d e r o f magnitude s t r o n g e r . f i r s t i n d i c a t i o n o f the e x i s t e n c e o f t h e i s o c y a n i c a c i d  The  Q-branch l i n e s came  when a s e r i e s o f w i d e l y spaced weak d o u b l e t s was found i n t h e spectrum o f H^N^C^O.  Once t h e i d e n t i t y o f t h e s e r i e s was r e c o g n i z e d , i n d i v i d u a l  assignments were s t r a i g h t f o r w a r d s i n c e t o a f a i r l y good a p p r o x i m a t i o n : v_{J> = 1/2J(J+1)(B - C ) Q o o and hence  {  Subsequent,  j  +  1  }  _  {  j  }  _  (  J  +  1  ^  )  5.1 _ ^  f u r t h e r i n v e s t i g a t i o n o f the s p e c t r a o f t h e o t h e r  5  >  2  isotopes  y i e l d e d the corresponding s e r i e s f o r each. The b-type t r a n s i t i o n s o f H ^ N ^ C ^ O were a l s o e x p e r i m e n t a l l y 4  2  located  w e l l b e f o r e any thought had been g i v e n t o t h e p o s s i b i l i t y t h a t such t r a n s i t i o n s might be o b s e r v a b l e .  They showed up as t h r e e v e r y w i d e l y  spaced  s t r o n g l i n e s , broadened s l i g h t l y by u n r e s o l v e d q u a d r u p o l e h y p e r f i n e ture.  struc-  S i n c e t h e e x i s t i n g d a t a were s u f f i c i e n t t o g i v e o n l y a rough e s t i m a t e  o f t h e i r J v a l u e s , t h e assignment p r o c e s s i n v o l v e d some t r i a l and e r r o r . However,  i t was found t h a t , when any two o f t h e s e t r a n s i t i o n s were i n c l u d e d  i n the 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 i s described i n the next s e c t i o n , only one r e a s o n a b l e assignment would g i v e a good f r e q u e n c y p r e d i c t i o n f o r t h e third.  Further,  t h i s same assignment was t h e o n l y one w h i c h would g i v e an  a c c e p t a b l e l e a s t .squares f i t when a l l t h r e e t r a n s i t i o n s were i n c l u d e d .  Hence  t h e r e i s b u t l i t t l e doubt t h a t i t i s the c o r r e c t o n e . A s i m i l a r p r o c e d u r e was used t o a s s i g n t h e b_-type t r a n s i t i o n s o f the o t h e r i s o t o p e s , w i t h the e x c e p t i o n o f t h e H ^ N ^ C ^ O s p e c i e s f o r w h i c h o n l y  122  two l i n e s were a v a i l a b l e .  These were a s s i g n e d so t h a t the r e s u l t i n g  H ^ N ^ C ^ O i n e r t i a l d e f e c t was i n agreement w i t h the A° v a l u e s 14„ 12 16„ for H N C O , TT  7  „14„13„16 H N C O  rt  , 14 12 18„ and H N C O .  obtained  _ ... . F u r t h e r v e r i f i c a t i o n of c  . the  b-type assignments t h r o u g h measurement of a d d i t i o n a l mm-wave t r a n s i t i o n s would c l e a r l y be d e s i r a b l e . A complete s e a r c h t h r o u g h the microwave r e g i o n t u r n e d up o n l y a few additional isocyanic acid absorptions.  These were t e n t a t i v e l y a s s i g n e d as  e x c i t e d v i b r a t i o n a l s t a t e b_-type t r a n s i t i o n s . 5.2  D e t e r m i n a t i o n o f M o l e c u l a r C o n s t a n t s from the Microwave S p e c t r u m . The c e n t r i f u g a l d i s t o r t i o n and 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 a n a l y s e s  were s e p a r a t e d u s i n g b a s i c a l l y the same scheme as was f o l l o w e d f o r c h l o r i n e isocyanate.  T h i s was a l e s s c o m p l i c a t e d p r o c e s s i n t h i s c a s e ,  because o f the much s i m p l e r h y p e r f i n e s t r u c t u r e . there was.of  however,  F o r the ^ N i s o t o p i c s p e c i e s  c o u r s e no h y p e r f i n e s t r u c t u r e and the observed t r a n s i t i o n f r e -  q u e n c i e s c o u l d be used d i r e c t l y i n the 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 i s . 14 Since  N has a r a t h e r s m a l l q u a d r u p o l e moment, the f i r s t o r d e r  e x p r e s s i o n g i v e n i n e q u a t i o n 2.37 a d e q u a t e l y r e p r e s e n t s the t r u e q u a d r u p o l e energies of i s o c y a n i c a c i d .  L e a s t squares f i t s were made u s i n g t h i s  relation  14 t o a l l o b s e r v e d q u a d r u p o l e s p l i t t i n g s f o r each r e s u l t s have been c o l l e c t e d i n T a b l e 5 . 1 .  N isotopic species.  The  Many of the a b s o r p t i o n s due t o  the DNCO i s o t o p i c s p e c i e s appeared t o be s l i g h t l y broadened compared t o the c o r r e s p o n d i n g HNCO a b s o r p t i o n s .  T h i s b e h a v i o r was a t t r i b u t e d t o v e r y  weak d e u t e r i u m 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 e f f e c t s .  R e s o l u t i o n of such v e r y  s m a l l s p l i t t i n g s was not p o s s i b l e w i t h our c o n v e n t i o n a l s p e c t r o m e t e r . The 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 i s was based on the g e n e r a l Watson H a m i l t o n i a n ( e q u a t i o n s 2.19 and 2 . 2 2 ) .  A f i r s t o r d e r t r e a t m e n t was  again  used ( e q u a t i o n s 2 . 2 3 ) , w i t h l i n e a r v a r i a t i o n s o f the r o t a t i o n a l c o n s t a n t s  123  TABLE 5.1  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  H N U  X  aa  v,.. - x bb cc A  A  aa  X,,  bb  - x  cc  1 6  0  H  1 4  N  1 3  C  1 6  0  2.067 ± 0.020  1.H2  1.103 + 0.010  1 4  ± 0.025  N  1 2  C  1 8  0  D  1 4  N  1 2  C  1 6  0  2.040 ± 0.020  2.012 ± 0.028  1.H9  1.031 ± 0.016  Measured i n MHz. D  C  2.045 ± 0.038°  H  X  1 2  of Isocyanic  Standard e r r o r s .  i  ± 0.011  Acid.  124  allowed.  No attempt was made t o use the s i m p l e r f o u r parameter e x p r e s s i o n  ( e q u a t i o n 2.18)  s p e c i f i c f o r a w e l l behaved p l a n a r m o l e c u l e s i n c e i t  was  known from p r e v i o u s work (150,151) t h a t i s o c y a n i c a c i d had e x t r e m e l y c e n t r i f u g a l d i s t o r t i o n a s s o c i a t e d w i t h r o t a t i o n about i t s  large  a-axis.  A l t h o u g h i t was r e c o g n i z e d from the s t a r t t h a t the a v a i l a b l e  trans-  i t i o n s were almost c e r t a i n l y i n s u f f i c i e n t t o d e t e r m i n e a complete s e t  of  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 , an attempt was n o n e t h e l e s s made t o  fit  the H ^ N ^ C ^ O d a t a to the q u a r t i c H a m i l t o n i a n ( e q u a t i o n 2 . 1 9 ) ; b o t h A were found t o be c o m p l e t e l y i n d e t e r m i n a t e .  and  1  E l i m i n a t i o n o f t h e s e two  parameters p e r m i t t e d a more r e a l i s t i c d e t e r m i n a t i o n o f the r e m a i n i n g o n e s , b u t w i t h o u t s i g n i f i c a n t l y r e d u c i n g the r a t h e r l a r g e s t a n d a r d d e v i a t i o n of the f i t  S  v  (SDFIT).  E v i d e n t l y h i g h e r o r d e r terms were i m p o r t a n t .  With A  and  a l r e a d y shown t o be u n o b t a i n a b l e i t was u n r e a s o n a b l e t o i n c l u d e e i t h e r  Hj, o r h^.  Of the r e m a i n i n g s e x t i c parameters H^j was found t o be the most  i m p o r t a n t ; i t s i n c l u s i o n i n the f i t gave a r a t h e r d r a m a t i c improvement the SDFIT.  Hj, H ^  in  and h j were found t o be o n l y m a r g i n a l l y s i g n i f i c a n t ,  hj^. was i n d e t e r m i n a t e .  The r e s u l t s o f t h e s e d i f f e r e n t a n a l y s e s are p r e s e n t e d  i n T a b l e 5 . 2 ; the H ^ N ^ C ^ O t r a n s i t i o n s were chosen as t e s t d a t a because 4  3  t h e y were the l a r g e s t s e t o f f r e q u e n c i e s  available.  S i m i l a r f i t s were made t o the " u n s p l i t l 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 the o t h e r i s o t o p i c s p e c i e s , e x c e p t D ^ N ^ C ^ O .  F o r some s p e c i e s  the  e x t r a s e x t i c constants H , H and h were i n d e t e r m i n a t e , f o r o t h e r s one o r • J JK. J more was m a r g i n a l l y s i g n i f i c a n t .  In the hope o f o b t a i n i n g c o n s i s t e n t  sets  o f r o t a t i o n a l c o n s t a n t s ( f o r s t r u c t u r a l p u r p o s e s ) a l l s p e c i e s were e v e n t u a l l y f i t t e d t o the same t r u n c a t e d H a m i l t o n i a n (A , A , 6 and H ) . J JK J KJ r e s u l t s are p r e s e n t e d i n T a b l e 5 . 3 .  These  T h i s was not a c o m p l e t e l y s a t i s f y i n g  approach b u t was a l s o a p p a r e n t l y the b e s t t h a t c o u l d be done w i t h  the  125  3.  Si  TABLE 5.2  R o t a t i o n a l Constants  and C e n t r i f u g a l D i s t o r t i o n  Constants  o f H ^ N ^ C ^ O u s i n g D i f f e r e n t Methods o f A n a l y s i s . II 0.734  SDFIT No. T r a n s . ~* A o ~* B o ~* C o A 10 j X  A  J K  X  1  3  0  6 xl0  1  5  T  0.219 42  42 . 910446.7 ± 7 . 2  d  910477.6 ± 2.7  11071.349 ± 0 . 0 1 7  11071.439 ± 0.007  10910.601 ± 0 . 0 1 8  10910.691 ± 0.007  3.120 ± 0.050  3.354 ± 0.019  8.028 ± 0.033  8.639 ± 0.033  7.19 ± 0 . 3 8  7.25 ± 0.11 6.86 ± 0.36  III SDFIT  0.208  No.  Trans. ~* A ~ *o B ~ *o C o A 10 3  j X  A  J K  6 H j  H  j X  X  L  (  10  xl0  J K  X  " K J -  )  1  1  5  7  °  1  0  IV 0.208  42  42  910463.9  +  6.8  910470.1  +  4.3  11071.455  +  0.010  11071.451  +  0.009  10910.706  +  0.010  10910.703  +  0.009  3.509  +  0.074  3.471  +  0.057  8.623  +  0.033  8.610  +  0.034  7.29  +  0.11  7.29  +  0.11  0.46  +  0.21 -1.11  +  0.50  +  0.35  5  '  6.70  +  0.35  6.71  126  TABLE 5.2  continued  V SDFIT No.  Trans. ~* A ~ *o B ~ *o C  A  6  j X  o  10  j X  J K  A  X  1  3  Q  10  X  h 10  42  910460.7 ± 8.6  910467.5 + 15.5  11071.454 ± 0.010  11071.453 + 0.013  10910.703 ± 0.009  10910.703 + 0.013  3.482 ± 0.066  3.481 + 0.109  8.625 ± 0.033  8.613 + 0.044  7.81 ± 0.29  7.38 + 0.71 0.045 + 1.17  °  1  -0.832 + 2.36  5  9  6.72 ± 0.35  6.70 + 0.36  8.15 ± 3.99  1.48 + 11.0  x X  VII SDFIT No.  Trans.  0.688 42 850669.4 ± 23814.4  A B  o  11065.7 ± 12.2 10916.4 ± 1 2 . 2  V A  J K  6  j X  K K  3.70 ± 0.34  1 0  X  1  10  °  ]  5  0.214  42  7  X  J K  1  5  H 10 J H  0.209  VI  8.01 ± 0 . 0 4 7.37 ± 0 . 3 7 -2.86 ± 6.10 -59750. ± 23804.  127  TABLE 5.2  continued  Large C o r r e l a t i o n s Analysis I A n a l y s i s II Analysis III  (|p|>0.9)  : p(B - C) = 0.95 : p(B - C) = 0 . 9 7 ; p ( A  = 0.97; p ( A  : p(B - C) = 0 . 9 8 ; p ( A  T  p(Aj - hj)  = 0.96; p ( A  = 0.96  R J  - H  ) = - 0 . 9 5 ; p(A JK  = - 0 . 9 2 ; p(A - hj)  A n a l y s i s V : p(A - A j )  = - 0 . 9 3 ; p(B - C) = 0 . 9 9 ;  - H )  J R  J  A n a l y s i s VI  = 0.95  : p(A - A ) = - 0 . 9 0 ; p(A - H j ) p ( A j - Hj)  A n a l y s i s IV  - H^)  J R  J K  JK.  = - 0 . 9 6 ; p(B - C) = 0 . 9 8 ;  - H ) R J  : p (B - C) = 0 . 9 5 ; p(C - A ) T V  = 0 . 9 6 ; p (fij - h j )  = 0 . 9 0 ; p(<5 - h_)  JK A n a l y s i s VII  T  J  : p(A - A ) = 1 . 0 0 ; p(B - C) = - 1 . 0 0 ; p(B - O p(C - S ) v  = -1.00  Measured i n MHz. SDFIT = S t a n d a r d D e v i a t i o n o f the  Fit.  No. T r a n s . = Number o f t r a n s i t i o n s used i n the Standard  - H ) = 0.94 KJ  errors.  analysis.  = 0.93  = 0.99  J = 1.00;  128  TABLE 5.3  Rotational Constants of I s o c y a n i c A c i d .  H N U  SDFIT  ~A  B  o ~* C o 3  •J A  J K  X  1  (  )  6 xl0  6 J  H  1  X10  K J  X  1  3  Q  1  5  °  b  3  903147.5 ± 4.4  10585.425 ± 0.012  3.198 ± 0.035  3.114 ± 0.034  8.311 ± 0.057  9.434 ± 0.084  7.28 ± 0 . 1 9  6.297 ± 0.076  2.44 ± 0.36  8.67 ± 0 . 8 9  1 3  C  1 6  0  0.219  No. T r a n s . ~* A o ~* B o ~* C o  X  20  10910.500 ± 0.015  1  SDFIT  0.147  10737.790 ±' 0 . 0 1 2  U  J K  15 12 16„ H N C O  0  11070.932 ± 0.015  H N  A  1 6  912673.6 + 4 . 7  xlO"  Aj-xlO  C  34  5  T  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  0.373  No. T r a n s . ~* A o  A xlO  1 2  3  H  1 4  N  1 2  C  1 8  0  0.257  42  28  910477.6 ± 2.7  912601.8 ± 4.1  11071.439 ± 0.007  10470.857 ± 0 . 0 1 0  10910.691 ± 0.007  10327.204 ± 0.011  3.354 ± 0 . 0 1 9 : 8.639 ± 0.033  3.018 ± 0.024 7.659 ± 0.052  7.26 ± 0.11  6.10 ± 0.12  6.86 ± 0.36  6.28 ± 0 . 7 0  3  129  TABLE 5.3  continued  D SDFIT No. T r a n s . ~* A o ~* B o ~* C„ j X  J K  X  1  SjXlO  N  1 2  C  1 6  0  Q  1  4  xlO"  1 5  N  1 2  C  1 6  0  35 510973.0 ± 1.0 10313.711 ± 0.011  10044.575 ± 0.050  10079.674 ± 0.012  9819.435 ± 0.050  -2.291 ± 0.029 2.041 ± 0.053 - 5 . 0 4 ± 0.12  Measured i n MHz. Standard e r r o r s . E s t i m a t e d measurement  D  0.326  3.432 ± 0.038  A 10 A  1 4  errors.  130  available  frequencies.  The a d d i t i o n a l t r a n s i t i o n s w h i c h would have p e r -  m i t t e d a more thorough t r e a t m e n t fore  f a l l i n t h e f a r i n f r a r e d and were t h e r e -  inaccessible. I n the case o f t h e d o u b l y s u b s t i t u t e d s p e c i e s , D ^ N ^ C ^ O ,  t r a n s i t i o n s were a v a i l a b l e  insufficient  t o a l l o w even such a l i m i t e d d i s t o r t i o n a n a l y s i s .  Hence, i n o r d e r t o o b t a i n r o t a t i o n a l c o n s t a n t s f o r t h i s s p e c i e s , t h e measured f r e q u e n c i e s were f i r s t c o r r e c t e d f o r c e n t r i f u g a l d i s t o r t i o n , assuming i t t o be t h e same as f o r t h e c o r r e s p o n d i n g t r a n s i t i o n s o f D ^ N ^ C ^ O ,  then t h e  r i g i d r o t o r energy e x p r e s s i o n s were a p p l i e d t o the c o r r e c t e d f r e q u e n c i e s , v  3 1 1 ( 1  {  1  o , i - ° o , o  }  =  B  +  c  5  (v {J» = 1/2J(J+1)(B - C) ii corr  -  i.e.  3  5.4  n  The r e s u l t s have a l s o been c o l l e c t e d i n T a b l e 5 . 3 . The r o t a t i o n a l c o n s t a n t s p r e s e n t e d i n T a b l e s 5.2 and 5.3 have been s t a r r e d t o i n d i c a t e t h a t they a r e n o t t h e t r u e Watson c o n s t a n t s one might n a i v e l y e x p e c t t h e above a n a l y s i s t o y i e l d . cant c e n t r i f u g a l d i s t o r t i o n c o n t r i b u t i o n s . i t i o n s used i n t h e l e a s t squares f i t s ,  In f a c t ,  they c o n t a i n  By c o n s i d e r i n g the t y p e o f t r a n s -  and b e a r i n g i n mind t h a t t h e m o l e c u l e  i s v e r y n e a r l y a symmetric t o p , i t i s n o t d i f f i c u l t t o show A  ^ A - A„ +  that:  + •••  5.5a  + • ••  5.5b  ^ C + 2<5__ + • • •  5.5c  B* ^ 'B - 26 C  signifi-  K.  K. C o s t a i n and K r o t o (154) have performed a s i m i l a r 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 i s f o r cyanogen a z i d e and a l s o c o n c l u d e d t h a t t h e i r e f f e c t i v e A c o n s t a n t s were r e a l l y A - T) (D — A ) . v  v  They a p p a r e n t l y c o n s i d e r e d 6  t o be  i n s i g n i f i c a n t ; such i s n o t l i k e l y t o be t h e case h e r e . S i n c e i t was the e f f e c t i v e  r o t a t i o n a l constants A , B Q  q  and C  Q  that  131  were used t o compute the c o e f f i c i e n t s o f the parameters i n b o t h the q u a d r u p o l e and 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 , i t i s c o n c e i v a b l e t h a t  these  d i s t o r t i o n c o n t r i b u t i o n s c o u l d i n t r o d u c e a s y s t e m a t i c e r r o r i n t o the v a l u e s o f the d e r i v e d c o n s t a n t s .  final  T h i s would seem t o be u n l i k e l y , however,  because b o t h a n a l y s e s were found t o g i v e unchanged r e s u l t s when the i n p u t v a l u e s of the r o t a t i o n a l c o n s t a n t s were v a r i e d by l a r g e amounts; A by thousands o f MHz, B and C by MHz. A l t h o u g h the SDFITs i n T a b l e 5.3 are a c c e p t a b l e t h e r e i s s t i l l some room f o r improvement.  Rather l a r g e experimental u n c e r t a i n t i e s  (+.25 MHz t o  ±.50 MHz) i n some o f the e a r l y mm-wave measurements on H ^ N ^ C ^ O and 4  D^N^C^O  2  p a r t i a l l y account f o r the e x t r a l a r g e SDFITs o b s e r v e d f o r  two s p e c i e s .  these  I n a d d i t i o n many o f the t r a n s i t i o n s o f a l l s p e c i e s p r o b a b l y  have s m a l l f i r s t o r d e r f r e q u e n c y c o n t r i b u t i o n s from terms n o t i n c l u d e d i n 2 6  the l e a s t squares f i t s ; e . g . L j ^ j ? ?  z  (155).  It  i s expected that the present  a n a l y s i s w i l l e v e n t u a l l y be extended (by M . C . L . G e r r y , G. W i n n e w i s s e r  g  W.H.H.) t o i n c l u d e P  etc.  and  t e r m s , as n e c e s s a r y , i n o r d e r t o o b t a i n more  a c c u r a t e f r e q u e n c y p r e d i c t i o n s o f f u r t h e r (mm-wave) t r a n s i t i o n s .  An a l t e r -  n a t i v e p o s s i b l e s o u r c e o f model e r r o r i s h i g h e r o r d e r c o n t r i b u t i o n s from A , A , 6 and H . To check on t h i s , the c o n s t a n t s i n T a b l e 5.3 were used J JK. J KJ i n the f u l l m a t r i x scheme t o p r e d i c t the f r e q u e n c i e s o f a l l the o b s e r v e d transitions.  I n e v e r y c a s e , e x a c t agreement w i t h the c a l c u l a t e d f i r s t  order  f r e q u e n c i e s was o b t a i n e d . 5.3  The M o l e c u l a r S t r u c t u r e o f I s o c y a n i c  Acid.  The moments o f i n e r t i a r e q u i r e d f o r a s t r u c t u r a l d e t e r m i n a t i o n a r e p r e f e r a b l y d e f i n e d i n terms of the pure r o t a t i o n a l c o n s t a n t s .  At l e a s t  any d i s c r e p a n c i e s can be d e f i n i t e l y a t t r i b u t e d t o v i b r a t i o n a l e f f e c t s .  then For  i s o c y a n i c a c i d the e x p e r i m e n t a l l y d e t e r m i n e d 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  132  A , B and C o o o  contain s i g n i f i c a n t centrifugal d i s t o r t i o n contributions.  a r t i f i c i a l i n c o r p o r a t i o n o f A,, and &„ i n t o A , B K K o  and C was d i s c u s s e d i n o o  r  section 5.2.  The  I n a d d i t i o n , i t w i l l be r e c a l l e d t h a t the t r u e Watson c o n s t a n t s  themselves c o n t a i n d i s t o r t i o n t e r m s .  These a r e n o r m a l l y i n s i g n i f i c a n t b u t  i n t h i s c a s e , because o f the e x t r e m e l y l a r g e c e n t r i f u g a l d i s t o r t i o n ,  they  cannot be so e a s i l y d i s m i s s e d . A p r e v i o u s i n v e s t i g a t i o n o f the pure r o t a t i o n a l f a r i n f r a r e d spectrum o f i s o c y a n i c a c i d by Krakow, L o r d and N e e l y the D  R  (=A ) K  (151) has y i e l d e d v a l u e s  and IL^ d i s t o r t i o n c o n s t a n t s o f H  1 4  N  1 2  C  1 6  0 and D  1 4  N  1 2  C  1 6  for 0.  ~* These numbers were used t o c o n v e r t the A  constants obtained here f o r  these  o two i s o t o p e s i n t o A  q  constants, a f t e r equation 5.5a.  Further, since i t  seemed  15 13 18 u n l i k e l y that N, C or 0 s u b s t i t u t i o n would g r e a t l y a f f e c t A^ o r H^, 14..12„16_ . . . „ * T* * „15„12_16_ _ 1 4 1 3 „ 1 6 the H N C O v a l u e s were a l s o used to c o r r e c t A f o r H N C O , H N C O u  M  o  and H ^ N ^ C ^ O .  The r e s u l t s have been c o l l e c t e d i n T a b l e 5 . 4 ;  i a t e d moments o f i n e r t i a , i n T a b l e 5 . 5 . c o u l d n o t be a p p l i e d to the B mental values f o r 6 . K  q  and C  q  '  the a s s o c -  Unfortunately a s i m i l a r procedure  c o n s t a n t s due t o the l a c k o f  experi-  C o n s e q u e n t l y t h e r e was no a l t e r n a t i v e b u t t o d e f i n e  moments of i n e r t i a i n terms o f them.  These have a l s o been c o l l e c t e d  in  Table 5.5. A l t h o u g h A i s enormous a s i m i l a r l a r g e v a l u e o f $ i s n o t t o be K K e x p e c t e d . F o r cyanogen i s o c y a n a t e (Chapter 6 ) , w h i c h i s a l s o a near p r o l a t e  asymmetric t o p , the r a t i o A^/6 i s ~ 3 0 0 0 . K K  The c e n t r i f u g a l d i s t o r t i o n terms  i n h e r e n t i n the Watson r o t a t i o n a l c o n s t a n t s s h o u l d be c o r r e s p o n d i n g l y s m a l l . R e g a r d l e s s , s i n c e o n l y d i f f e r e n c e s o f moments o f i n e r t i a were used i n the m o l e c u l a r s t r u c t u r e c a l c u l a t i o n s (below) the f i n a l d i s t o r t i o n c o n t r i b u t i o n to the e r r o r i n the computed a t o m i c c o o r d i n a t e s was m i n i m i z e d .  The l a r g e s t  such d i s c r e p a n c i e s a r e l i k e l y t o be a s s o c i a t e d w i t h the hydrogen p o s i t i o n  n  133  TABLE 5.A  A R o t a t i o n a l Constants Microwave and IR D a t a  o f I s o c y a n i c A c i d from Combined  A* o  b  H  1 4  N  1 2  C  1 6  0  917664.6  +  400.  4991.  d  D  1 4  N  1 2  C  1 6  0  513674.0  +  200.  2701.  d  H  1 5  N  1 2  C  1 6  0  908138.5  +  400.  4991.  6  H  1 4  N  1 3  C  1 6  0  915468.6  +  400.  4991.  e  H  1 4  N  1 2  C  1 8  0  917592.8  +  400.  4991.  6  c  Measured i n MHz.  ~* C a l c u l a t e d from A v a l u e s i n T a b l e 5.3 o  (see  text),  Estimated e r r o r s . d  e  From i n f r a r e d work o f Krakow, L o r d and N e e l y Assumed.  (151).  134  TABLE 5.5  Moments o f I n e r t i a  H  c  N  1 2  C  1 6  0  H  1 5  N  1 2  C  1 6  0  of Isocyanic  H  1 4  N  1 3  C  Acid.  1 6  0  0.55074°  0.55651  0.55206  45.650258°  47.066566  45.648167  46.321516°  47.744035  46.320705  0.12096  0.12048  1° a  1 4  and I n e r t i a l D e f e c t s  0.12052  A°  H  1 4  N  1 2  C  1 8  0  D  1 4  N  1 2  C  1 6  0  D  1 5  N  1 2  C  1 6  1° a  0.55078  0.98387  $  48.266431  49.001848  50.31481  i°  48.937825  50.139608  51.46843  c A°  0.12062  0.15388  Measured i n a.m.u.7A . C a l c u l a t e d from r o t a t i o n a l c o n s t a n t s i n T a b l e 5 . 4 . C a l c u l a t e d from r o t a t i o n a l c o n s t a n t s i n T a b l e 5 . 3 .  0  135  as d e u t e r i u m s u b s t i t u t i o n produces a c o n s i d e r a b l y more d r a m a t i c change  in  the c e n t r i f u g a l d i s t o r t i o n than do any o f the heavy atom s u b s t i t u t i o n s . However,  even f o r h y d r o g e n , c a l c u l a t i o n s based on the f o r c e f i e l d s  cussed i n s e c t i o n 5.5  dis-  i n d i c a t e t h a t the " d i s t o r t i o n e r r o r " i s n e g l i g i b l e .  The i n e r t i a l d e f e c t s o f f i v e i s o t o p i c s p e c i e s of i s o c y a n i c a c i d have a l s o been p r e s e n t e d i n T a b l e 5 . 5 .  These are a l l seen t o be s m a l l p o s i t i v e  numbers, f o u r o f w h i c h are e s s e n t i a l l y e q u a l ; the f i f t h , w h i c h i s the o n l y one b e l o n g i n g t o a d e u t e r a t e d s p e c i e s , i s s l i g h t l y l a r g e r .  The s m a l l m a g n i -  tude o f A° and i t s l a c k of v a r i a t i o n on heavy atom i s o t o p i c s u b s t i t u t i o n provide c o n v i n c i n g proof t h a t the molecule i s p l a n a r .  I n s e c t i o n 5.5  it  has been shown t h a t the i n c r e a s e i n A° on d e u t e r a t i o n can l a r g e l y be accounted f o r i n terms o f a p l a n a r m o d e l . The K r a i t c h m a n / C o s t a i n s u b s t i t u t i o n p o s i t i o n s o f a l l o f the atoms of i s o c y a n i c a c i d i n the c e n t e r o f mass p r i n c i p a l i n e r t i a l a x i s system of H ^ N ^ C . ^ O (the " p a r e n t " m o l e c u l e ) were c a l c u l a t e d from the moments o f i n e r t i a i n T a b l e 5.5 u s i n g e q u a t i o n s 2 . 5 8 . i n Table 5.6.  Evidently,  The r e s u l t s have been p r e s e n t e d  the a - a x i s i s n e a r l y c o - i n c i d e n t w i t h the NCO c h a i n  and t h e c a r b o n atom i s v e r y c l o s e t o t h e c e n t e r o f mass. H e n c e , the  single  s u b s t i t u t i o n d e t e r m i n e d v a l u e s of a^,, b^, b^, and b^ must be r e g a r d e d  with  considerable scepticism.  The i m a g i n a r y r e s u l t o b t a i n e d f o r the  a - c o o r d i n a t e may be a t t r i b u t e d t o the d o m i n a t i o n o f zero p o i n t  carbon vibrational  e f f e c t s o v e r a v e r y s m a l l A I ^ ; j u s t as was o b s e r v e d f o r the n i t r o g e n acoordinate of c h l o r i n e  isocyanate.  A r e l i a b l e value of a  was o b t a i n e d by t a k i n g the o t h e r  t o have t h e i r s u b s t i t u t i o n v a l u e s dition ( ^ ^ _ m  relative  a  =  0) •  a-coordinates  and t h e n i n v o k i n g the c e n t e r of mass c o n -  F i r s t , however,  i t was n e c e s s a r y  s i g n s of these o t h e r c o o r d i n a t e s .  to determine  U n l i k e the c h l o r i n e  the  isocyanate  136  TABLE 5.6  Kraitchman/Costain S u b s t i t u t i o n P o s i t i o n s Atoms o f I s o c y a n i c A c i d .  Coordinate  M  3  o f a l l o f the  Coordinate  1.83736 ± 0.00003°  l „l  0.68793 ± 0.00036°  1.20552 ± 0.00004  IV  0.07820 ± 0.00232  b  imaginary  l-cl  1.16882 ± 0.00002  0.03670 ± 0.00472  l ol b  0.00487 ± 0.01927  Measured i n 7A. C a l c u l a t e d from s t a n d a r d e r r o r s a s s o c i a t e d w i t h B  constants.  C a l c u l a t e d from e s t i m a t e d e r r o r s i n A c o n s t a n t s . Q  I n d i c a t e o n l y measurement u n c e r t a i n t i e s , i . e . do n o t t a k e i n t o account v i b r 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 e f f e c t s .  137  case t h i s c o u l d n o t be done s i m p l y by i n s p e c t i o n . magnitudes o f  | a ^ | and j  tinct possibility.  | made the a l t e r n a t i v e  With t h i s assumption a  Rather,  the s i m i l a r  cyanate s t r u c t u r e a d i s -  was c a l c u l a t e d t o be ±0.30549.  Now, s i n c e any c o o r d i n a t e l a r g e r than 0.15 X s h o u l d be a c c u r a t e l y  deter-  m i n a b l e by s i n g l e s u b s t i t u t i o n the c y a n a t e s t r u c t u r e c o u l d be s a f e l y inated.  T h i s o f c o u r s e was n o t s u r p r i s i n g s i n c e a l l o f the  reported evidence structure.  elim-  previously  ( 1 4 2 , 1 4 3 , 1 2 3 , 1 4 4 , 1 1 ) had c l e a r l y p o i n t e d t o an  isocyanate  F o r such a c o n f i g u r a t i o n the c e n t e r o f mass c o n d i t i o n y i e l d s a  v e r y s m a l l v a l u e f o r a , c o n s i s t e n t w i t h the i m a g i n a r y r e s u l t o b t a i n e d from Kraitchman's  equations.  The d e t e r m i n a t i o n o f a c c u r a t e v a l u e s f o r the s m a l l b - c o o r d i n a t e s  of  n i t r o g e n , oxygen and c a r b o n proved t o be a c o n s i d e r a b l y more d i f f i c u l t problem.  Only two u s e f u l r e l a t i o n s are d i r e c t l y a v a i l a b l e , namely  the  c e n t e r o f mass and p r o d u c t o f i n e r t i a c o n d i t i o n s : = 0  yVb., 1  1  Vm.a.b.  i-l  5.6a  1  1  = 0  5.6b  x  1  i A third i s required.  I n the f i r s t i n s t a n c e t h i s was t a k e n t o be the  i t y o f the NCO c h a i n , c o n v e n i e n t l y f o r m u l a t e d  %  ~V  / ( a  o - c> = a  ( b  as:  c" V ' ^ c - V  5  S o l u t i o n of equations 5.6, using s u b s t i t u t i o n values and the c e n t e r o f mass v a l u e f o r a , p  T a b l e 5.7 as s t r u c t u r e  linear-  f o r a ^ , a^,  a  -  Q  6 c  and b^  then y i e l d e d the r e s u l t s c o l l e c t e d  in  I.  Now, the s u b s t i t u t i o n method i s based on the premise t h a t z e r o p o i n t v i b r a t i o n a l e f f e c t s may be e l i m i n a t e d t h r o u g h the use o f d i f f e r e n c e s moments o f i n e r t i a .  If  such i s e x a c t l y the c a s e ,  then:  of  138  AI°  a  = Al  5.7  6  a  and hence f o r a p l a n a r m o l e c u l e : A I ° - A I ° - A I ° = A(A°) c b a  =0  5.8  E q u a t i o n 5.8 i s w e l l s a t i s f i e d f o r heavy atom i s o t o p i c s u b s t i t u t i o n s i n b o t h c h l o r i n e i s o c y a n a t e and i s o c y a n i c a c i d ; i . e . defect i s very small.  the change i n the  inertial  However, i t i s n o t w e l l s a t i s f i e d when hydrogen i s  replaced w i t h deuterium i n i s o c y a n i c a c i d ; h e r e , A(A°)  = 0.03336 a . m . u . X . 2  * T h i s l a s t r e s u l t i m p l i e s t h a t the u n c e r t a i n t y  i n the hydrogen s u b s t i t u t i o n  p o s i t i o n , due t o i n c o m p l e t e c a n c e l l a t i o n o f v i b r a t i o n a l e f f e c t s , i s An i n d i c a t i o n of j u s t how l a r g e may be o b t a i n e d by r e p l a c i n g A I °  large.  i n equation  Si  2.58b w i t h A I ° - A I °  and t h e n r e c a l c u l a t i n g b^.  r e s u l t i n c o r p o r a t e d i n t o a second s t r u c t u r e ( I I )  T h i s has been done and the i n w h i c h a l l of the jt-  c o o r d i n a t e s were t a k e n t o be the same as i n s t r u c t u r e I,  w h i l e the  three  r e m a i n i n g b - c o o r d i n a t e s were d e t e r m i n e d w i t h the a i d of e q u a t i o n s 5 . 6 . structure II  atomic c o o r d i n a t e s are a l s o g i v e n i n Table 5 . 7 .  noted t h a t , although b  The  I t w i l l be  i n c r e a s e s q u i t e s u b s t a n t i a l l y (by 0.0260 X) on g o i n g n.  from s t r u c t u r e I t o I I ,  the o t h e r t h r e e b - c o o r d i n a t e s show o n l y m i n o r changes.  S i n c e c h l o r i n e i s o c y a n a t e has been shown t o have a s m a l l bend a t c a r b o n , the a s s u m p t i o n o f a l i n e a r NCO c h a i n i n i s o c y a n i c a c i d i s c l e a r l y tenuous.  rather  An attempt was t h e r e f o r e made t o o b t a i n an independent d e t e r m i n -  a t i o n o f the n i t r o g e n b - c o o r d i n a t e u s i n g the d o u b l e s u b s t i t u t i o n t e c h n i q u e of P i e r c e and K r i s h e r ( 6 8 ) . D  1 4  N  1 2  C  1 6  0, H  1 5  N  1 2  C  1 6  0  and D  The f o u r i s o t o p i c s p e c i e s used were H 1 5  N  1 2  C  1 6  1 4  N  1 2  C^0,  0 where the f i r s t o f t h e s e was taken t o  be the " p r i n c i p a l framework" and the s e c o n d , the " s e c o n d a r y f r a m e w o r k " . Only the AAI e x p r e s s i o n ( e q u a t i o n 2.67) was c o n s i d e r e d because I ° ( D ^ N ^ C ^ 0 ) c a 2  * P o s s i b l e d e v i a t i o n from e q u i l i b r i u m v a l u e .  139  TABLE 5.7  Molecular  S t r u c t u r e of Isocyanic  I  3  a  3  3  III  b  b  -1.83736  -1.83736  -1.20552  -1.20552  -1.20552  0.00312  0.00312  0.00312  1.16882  1.16882  1.16882  0.68793  0.71393  0.68793  -0.05521  -0.05729  -0.07670  c  -0.01778  -0.01845  0.03331  o  0.01832  0.01902  -0.00118  c o H  b  N  b  II  Atomic C o o r d i n a t e s .  -1.83736  b  b  b  Acid:  Measured i n X . See t e x t ( s e c t i o n 5.3) f o r e x p l a n a t i o n o f p r o c e d u r e used t o o b t a i n these three s t r u c t u r e s .  TABLE 5.8  Molecular  Structure of Isocyanic  I r(H-N)  b  II  A c i d : Geometry.  b  III  b  0.97544  0.99700  0.99191  r(N-C)  1.20922  1.20926  1.21364  r(C-O)  1.16626  1.16630  1.16621  Z-(HNC)  128° 36'  127° 29'  124° 22'  ^(NCO)  (180°)  (180°)  173° 6'  a  Bond l e n g t h s measured i n A . C a l c u l a t e d from c o r r e s p o n d i n g s e t o f a t o m i c c o o r d i n a t e s i n T a b l e 5.7.  140  was u n a v a i l a b l e certainties) . COMPIAS o f H  1 4  ( a l s o the I  v a l u e s o f the o t h e r i s o t o p e s have l a r g e u n -  The c o o r d i n a t e s o f the c e n t e r o f mass o f D ^ N ^ C ^ O N  1 2  C  1 6  0 were computed u s i n g s t r u c t u r e I  and B = 0.01573 A*. -0.093697 a . m . u . X  t o b e : A = -0.04201 &  S u b s t i t u t i o n of these numbers a l o n g w i t h AAI° = c  2  i n the  and a^ = -1.20552 X i n t o the second d i f f e r e n c e s  y i e l d e d a v a l u e o f 0.0767 ± 0.020 A* f o r b^.  equation  The l a r g e e r r o r e s t i m a t e , w h i c h  o  was c a l c u l a t e d from the u n c e r t a i n t y i n AAI^ a l o n e , r e v e a l s  that t h i s  has u n f o r t u n a t e l y not produced the a c c u r a t e r e s u l t hoped f o r .  technique  The reasons  o f o r t h i s f a i l u r e are c l e a r .  F i r s t l y , AAI  c  i s very small.  Secondly,  moments o f i n e r t i a from w h i c h i t was c a l c u l a t e d a r e n o t p a r t i c u l a r l y (cf.  chlorine isocyanate).  c o n t r i b u t i o n s t o AAI  o c  the accurate  P o s s i b l e v i b r a t i o n a l or c e n t r i f u g a l d i s t o r t i o n  p r o v i d e an a d d i t i o n a l unknown f a c t o r .  These  diffi-  c u l t i e s are c o n s i s t e n t w i t h P i e r c e and K r i s h e r ' s a s s e r t i o n t h a t a n e c e s s a r y c o n d i t i o n f o r the s u c c e s s f u l a p p l i c a t i o n of the d o u b l e s u b s t i t u t i o n t e c h n i q u e i s a s h i f t i n the c e n t e r o f mass of the " s e c o n d a r y framework" w i t h r e s p e c t t o the COMPIAS o f the " p r i m a r y f r a m e w o r k " , a l o n g t h e d i r e c t i o n i n q u e s t i o n , by more than .03 X ; here the s h i f t i s o n l y 0.0157 R. The e x c e l l e n t agreement o f the s i n g l e and d o u b l e s u b s t i t u t i o n v a l u e s f o r b^ i s i n t r i g u i n g .  However, b o t h numbers have such l a r g e  uncertainties  t h a t they cannot be r e g a r d e d as s i g n i f i c a n t l y d i f f e r e n t from the v a l u e o b t a i n e d assuming a l i n e a r NCO c h a i n .  C o n v e r s e l y t h e r e i s no h a r d p h y s i c a l  e v i d e n c e a v a i l a b l e t o i n d i c a t e t h a t t h e NCO c h a i n i s e x a c t l y l i n e a r i n the e q u i l i b r i u m c o n f i g u r a t i o n of i s o c y a n i c a c i d .  Accordingly a t h i r d structure  was determined u s i n g the d o u b l e s u b s t i t u t i o n v a l u e f o r b^.  I n t h i s the b^,  and bg c o o r d i n a t e s were a g a i n c a l c u l a t e d w i t h the a i d o f the c e n t e r o f mass and p r o d u c t o f i n e r t i a r e l a t i o n s  ( e q u a t i o n s 5.6a and 5 . 6 b ) , w h i l e the  rest  -0.5  142 o f the c o o r d i n a t e s were t a k e n t o be the same as i n s t r u c t u r e I. have been c o l l e c t e d i n T a b l e 5.7 as s t r u c t u r e  The r e s u l t s  III.  The a t o m i c c o o r d i n a t e s i n T a b l e 5.7 have been c o n v e r t e d i n t o bond l e n g t h s and a n g l e s w h i c h a r e p r e s e n t e d i n T a b l e 5 . 8 .  S t r u c t u r e s I and I I I  i l l u s t r a t e d w i t h s c a l e drawings i n F i g u r e s 5.1 and 5.2  are  respectively.  Comparison o f the t h r e e s t r u c t u r e s i n T a b l e 5.8 r e v e a l s  t h a t t h i s work  has y i e l d e d a c c u r a t e v a l u e s f o r the i s o c y a n i c a c i d NC and CO i n t e r n u c l e a r distances.  U n f o r t u n a t e l y , a s i m i l a r r e f i n e d d e t e r m i n a t i o n o f the NH bond  l e n g t h has c l e a r l y n o t been a c h i e v e d ; a l s o the u n c e r t a i n t y i n the two a n g l e s i s s t r o n g l y dependent on whether, o r n o t the assumption of a l i n e a r NCO c h a i n is correct.  These l a s t two p o i n t s are d i s c u s s e d i n more d e t a i l i n s e c t i o n  5.6. 5.4  D i p o l e Moment Measurements; D i s c u s s i o n o f the D i p o l e Moment and the N i t r o g e n 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 . On the b a s i s o f the r e l a t i v e e l e c t r o n e g a t i v i t i e s o f the atoms t h a t make  up i s o c y a n i c a c i d , and t h e i r g e o m e t r i c a l arrangement, i t may be reasoned t h a t t h i s m o l e c u l e s h o u l d have non-zero d i p o l e moment components a l o n g a- and b - p r i ' n c i p a l i n e r t i a l a x e s .  its  T h i s has o f c o u r s e been shown t o be t r u e  t h r o u g h the o b s e r v a t i o n o f b o t h a- and b-type t r a n s i t i o n s .  On the o t h e r  hand, the ^-component o f the d i p o l e moment must be z e r o because the c^-axis i s p e r p e n d i c u l a r t o the p l a n e o f symmetry of the m o l e c u l e . The a-component o f the i s o c y a n i c a c i d d i p o l e moment has been p r e v i o u s l y i n v e s t i g a t e d by W h i t e and Cook ( 1 5 3 ) .  These a u t h o r s found t h a t y  s m a l l but s i g n i f i c a n t and r a t h e r p e r p l e x i n g v a r i a t i o n w i t h K ^.  3.  has a  They were  u n a b l e t o o b t a i n a v a l u e f o r y^> however, due t o the n e g l i g i b l e dependence o f the S t a r k e f f e c t o f the then a v a i l a b l e  (a-type) t r a n s i t i o n s on t h i s  143  component o f the d i p o l e moment. I n t h i s work a number o f b-type t r a n s i t i o n s have been r e p o r t e d f o r isocyanic acid.  These have a S t a r k e f f e c t w h i c h i s a s t r o n g f u n c t i o n o f  b u t w h i c h i s n e a r l y independent o f u^.  U n f o r t u n a t e l y , a l l o f the b-type  t r a n s i t i o n s o c c u r r i n g i n the f r e q u e n c y range o f o u r s p e c t r o m e t e r a r e o f r a t h e r h i g h J , hence r e s o l u t i o n o f t h e i r i n d i v i d u a l S t a r k components was impossible.  It  t u r n s o u t , however,  t h a t i n each case the s t r o n g e s t and  most r a p i d o f t h e s e S t a r k components move out n e a r l y t o g e t h e r w i t h i n c r e a s i n g f i e l d r e s u l t i n g i n a s i n g l e , r a t h e r b r o a d , b u t s t i l l s u r p r i s i n g l y symmetric aggregate S t a r k l o b e . imate v a l u e o f  A c c o r d i n g l y , an attempt was made t o deduce an a p p r o x -  from the f i e l d dependence o f t h e s e c o m p o s i t e l o b e s .  It  s h o u l d be p o i n t e d out t h a t the low J b-type t r a n s i t i o n s , f o r w h i c h i n d i v i d u a l S t a r k components w i l l be r e s o l v a b l e , l i e a t v e r y h i g h f r e q u e n c y and w i l l have v e r y s m a l l S t a r k c o e f f i c i e n t s .  C o n s e q u e n t l y a s t u d y of t h e i r  e f f e c t i s l i k e l y t o be b o t h d i f f i c u l t and u n p r o f i t a b l e ( i . e . give a s i g n i f i c a n t l y better value f o r  Stark  i t would n o t  than that reported h e r e ) .  S t a r k measurements were made on two D ^ N ^ C ^ O b-type t r a n s i t i o n s : 2 2  0,22  2 1  1,21  2 4  0,24  2 3  1,23  These were chosen i n p r e f e r e n c e t o the a v a i l a b l e H^ N^" C^O b-types 4  important reasons.  2  f o r two  F i r s t l y , t h e i r c o m p o s i t e S t a r k l o b e s a r e f a s t e r and  l e s s broadened (fewer components)  than t h o s e o f the H ^ N ^ C ^ O  transitions.  I  S e c o n d l y , the l i n e s t r e n g t h s r e q u i r e d f o r c o m p u t a t i o n o f asymmetric r o t o r S t a r k e n e r g i e s have been t a b u l a t e d o n l y up t o J = 3 5 ; the H ^ N ^ C ^ O  b-types  i n v o l v e J v a l u e s g r e a t e r than 3 5 . Two d i f f e r e n t microwave c e l l s were used i n the c o u r s e o f t h i s w o r k .  144  P r e l i m i n a r y measurements were made on the 22^ ^  —  the 7 f o o t X-band c e l l d e s c r i b e d i n Chapter 3.  21^ ^  However,  t r a n s i t i o n using s i n c e the septum  i n t h i s c e l l was s l i g h t l y d i s t o r t e d and not e x a c t l y c e n t e r e d a l l S t a r k were a d d i t i o n a l l y b r o a d e n e d . became a v a i l a b l e transition.  lobes  T h e r e f o r e , when a b e t t e r c e l l (10 f o o t , X-band)  the experiment was r e p e a t e d u s i n g the 24^ ^  The two s e t s o f r e s u l t s are i n good agreement.  —  Both c e l l s  were c a l i b r a t e d i n the u s u a l way by measuring the S t a r k e f f e c t t r a n s i t i o n o f c a r b o n y l s u l f i d e (OCS).  23^ 23  of the J = 0-»-l  T h i s p r o c e d u r e has the d u a l  of e l i m i n a t i n g the n e c e s s i t y of p h y s i c a l l y m e a s u r i n g the d i s t a n c e  advantage between  the septum and t h e c e l l w a l l , and a l s o a v e r a g i n g out any f i e l d i n h o m o g e n e i t i e s . The e l e c t r i c f i e l d i n d u c e d f r e q u e n c y s h i f t i n the J = 0^-1 t r a n s i t i o n of OCS, c o r r e c t t o second o r d e r , i s g i v e n by Av  where V  q  S  (156):  = (8/15) (0.50344) p £" /v 2  2  5.9  2  = 12162.97 MHz i s the z e r o f i e l d f r e q u e n c y o f the t r a n s i t i o n , y i s  the d i p o l e moment o f OCS i n Debyes, E i s the e l e c t r i c f i e l d s t r e n g t h V o l t s / c m and 0.50344 MHz•(Debye-Volts/cm) It  ' i s a conversion factor  t h e n f o l l o w s t h a t i f a DC b i a s p o t e n t i a l o f V  in  (157).  ( V o l t s ) and an AC moduo  l a t i o n f i e l d w i t h a half-amplitude of V  m  (Volts)  (see s e c t i o n 3.5)  are  a p p l i e d t o the c e l l septum the average f r e q u e n c y s h i f t A\J w i l l be g i v e n b y : Av£> = ( 8 / 1 5 ) ( 0 . 5 0 3 4 4 ) 2\ ^ |/,- ) \2 ( V 2  = C(V where E  ?  2  + V ) 2  5.10  7  + V ) o m  = V / r , E = V / r and r i s an e f f e c t i v e d i s t a n c e from the septum o c m m c c 2 2 t o the c e l l w a l l . A p l o t of v „ , v s . V + V s h o u l d t h e r e f o r e g i v e a o  v  0->l  o  m  s t r a i g h t l i n e w i t h s l o p e C and i n t e r c e p t V . q  "  From C and M u e n t e r ' s  v a l u e f o r the d i p o l e moment of OCS (y = 0.71521 ± 0.00020 D)  (158)  may then  145  be c a l c u l a t e d .  The c a l i b r a t i o n d a t a f o r the two c e l l s have been _  i n Table 5 . 9 .  In both cases, a p l o t of  s t r a i g h t l i n e as e x p e c t e d .  2  VQ+I  v s  •  V  +  collected  2 8  v  Q  m  a v e  a  v e r y good  A l e a s t squares f i t t i n g p r o c e d u r e was then used  to o b t a i n t h e r e s u l t s w h i c h have been c o l l e c t e d i n T a b l e 5 . 1 1 . ment o f t h e i n t e r c e p t s w i t h t h e p u b l i s h e d v a l u e o f V  q  The a g r e e -  (159) i s e x c e l l e n t .  E q u a t i o n 2.44 was used t o o b t a i n e x p r e s s i o n s f o r t h e second o r d e r energies of the four r o t a t i o n a l states of D ^ N ^ C ^ O transitions studied. NBS T a b l e s  Stark  i n v o l v e d i n t h e two  The r e q u i r e d l i n e s t r e n g t h s were e x t r a c t e d from t h e  (160) u s i n g l i n e a r i n t e r p o l a t i o n between K = - 1 . 0 and K = - 0 . 9 5  (K of D ^ N ^ C ^ O  i s -0.999070).  two d i f f e r e n t ways.  The-energy denominators were o b t a i n e d i n  The l a r g e ones were c a l c u l a t e d t o s u f f i c i e n t  accuracy  u s i n g t h e r i g i d r o t o r a p p r o x i m a t i o n and t h e r o t a t i o n a l c o n s t a n t s i n T a b l e 5 . 3 . The two s m a l l denominators w h i c h c o r r e s p o n d t o t h e two observed f r e q u e n c i e s dominate t h e S t a r k energy e x p r e s s i o n s . energies  (frequencies)  were u s e d .  transition  For these the exact  S i n c e none o f t h e f o u r s t a t e s i s c o n -  n e c t e d by a n o n z e r o d i p o l e moment m a t r i x element t o any o t h e r nearby t h e r e was no f i r s t o r d e r o r pseudo f i r s t o r d e r S t a r k e f f e c t  state,  to c o n s i d e r .  The energy e x p r e s s i o n s were then used i n c o n j u n c t i o n w i t h t h e s e l e c t i o n r u l e AMj = 0 (see s e c t i o n 2.3) t o o b t a i n r e l a t i o n s f o r t h e average s h i f t s o f t h e S t a r k components. Moo  M — 0,22 J  91 M 1,21 J  + u (-0.00230x10 a 2  M 4 2  =  These a r e :  fy (-9.49011xl0~ ° 2  M  2  J  r  — ?3 M =^(12.20412x10 ^0,24 J 1,23' J I Z J  9  V )J \ J ( l / -) ( V-  M  , M  + 18.1238xl0~ M )  6  1  + 0.11645x10  6  frequency  2  2  c o  + V ) (0.50344) m 2  5.11a 2  ~ 22.4255xl0" M )  6  9  b  2  J  5.11b  + u ( - 0 . 0 0 1 8 0 x l 0 ~ + 0.07025xl0" M )|(l/r )(V? + vf)(0.50344) c o m 2  6  9  2  2  2  146  TABLE 5.9  C e l l C a l i b r a t i o n : Measurement J = O+l T r a n s i t i o n of OCS.  o f the S t a r k E f f e c t o f the  Cell 1 m  v  a  o  Cell 2  Frequency (v)  V m  V  0  o  Frequency  10  50  12163.04  10  100  12163.64  10  100  12163.23  10  200  12164.01  10  200  12164.03  10  300  12165.29  10  300  12165.33  10  400  12167.09  10  400  12167.18  10  500  12169.40  10  360  12166.38  10  550  12170.75  10  450  12168.30  10  600  12172.23  10  500  12169.54  10  650  12173.83  10  550  12170.91  10  700  12175.57  10  600  12172.42  10  750  12177.46  10  700  12175.85  10  800  12179.43  10  800  12179.77  10  850  12181.55  10  900  12184.23  10  900  12183.79  10  950  12186.15  10  1000  12188.65  Measured i n V o l t s . Measured i n MHz.  (>  147  TABLE 5.10  S t a r k Measurements on Two b-type T r a n s i t i o n s of D  22 — 21 0,22 1,21 v  a  m  v  a  0  (  C  e  1  24 — 23 1,23 0,24  >  1X  Frequency* (v) 3  4  V m  V  o  1 4  (  N C 0  C  1 2  e  1  1 6  1 2  )  Frequency  20  200  -26075.14  10  100  19619.80  20  300  -26076.07  10  200  19620.46  20  400  -26077.40  10  300  19621.66  20  500  -26079.04  15  400  19623.26  20  600  -26081.18  30  400  19623.34  20  700  -26083.80  25  500  19625.34  20  800  -26086.81  25  600  19627.80  20  900  -26090.00  25  700  19631.02  20  1000  -26093.67  25  800  19634.48  20  1100  -26097.65  25  900  19638.62  25  1000  19643.26  Measured i n V o l t s . Measured i n MHz.  148  TABLE 5.11  Slope xl0 a  Cell Calibration:  5  Intercept  b  Septum-Cell W a l l Spacing.  Cell 1  Cell 2  2.62458 ± 0.00082  2.56822 ± 0.00094  12162.973 ± 0.003  d  a  Effective  12162.982 ± 0.005  0.46541 ± 0.00020  0.47048 ± 0.00022  _ 2 2 2 S l o p e o f the v v s . V + V" s t r a i g h t l i n e graph i n M H z / V o l t s . q  m  _  I n t e r c e p t o f the v v s . V c f . v = 12162.97. o Standard e r r o r . Effective  2 q  + V  2  s t r a i g h t l i n e graph i n MHz;  s e p t u m - c e l l w a l l s p a c i n g i n cm.  95% c o n f i d e n c e l i m i t .  TABLE 5.12  S t a r k C o e f f i c i e n t s o f Two D  2  Slope xl0 a  2  5  0,22-  2  1  l,21  ( C e 1 1  •26074.49 ± 0.10  S l o p e o f the v v s .  N  X )  1 2  C  1 6  0 b-type T r a n s i t i o n s ,  2 4  0,24  - 1 . 9 3 3 8 ± 0.0061 -26074.30 ± 0 . 0 4  Intercept  1 4  +  d  23j_  19619.48 ± 0 . 0 5 19619.58 ± 0.10  s t r a i g h t l i n e graph i n M H z / V o l t s ^ .  O  m  o  Observed z e r o f i e l d t r a n s i t i o n f r e q u e n c y i n MHz. errors.  Estimated e r r o r s .  I  (Cell  2.3610 ± 0.0099  — 2 2 I n t e r c e p t o f the v v s . V + V s t r a i g h t l i n e graph i n MHz.  Standard  2 3  r  d  2)  149  where Av i s i n MHz i f u , u, are i n Debyes, r i s i n cm, and V , V are i n a' b c o m }  Volts.  The relative intensities of the various components are given by  equation 2.47. The D^N^C^O Stark measurements have been collected i n Table 5.10. 2 2 For both transitions i t was found that a plot of _v vs. Vo + Vm gave a rather  good straight l i n e , as expected; see Figures 5.3 and 5.4. A least squares f i t t i n g procedure was used to obtain "best values" for the slope and intercept of each of these l i n e s .  The numbers are presented i n Table 5.12. I t w i l l be  noted that for both transitions, the intercept i s i n good agreement with the observed zero f i e l d frequency.  Two sets of  values were then c a l -  culated by assuming that the peak maxima of the composite Stark lobes corresponded to various values of M^. from 0 to 10. Here, the a-component of the dipole moment was taken to be 1.602 D, the value reported by White and Cook (153) for K_^ = 1 levels.  The results have been collected i n Table 5.13.  Since for both transitions the relative intensities of the various M com2  ponents decrease with Mj and the separation between components increases 2  with Mj. i t seems probable that the maximum i n each of the aggregate Stark lobes w i l l correspond to a lowish value of M ; say M « 5. Also, because of the increase i n the number of components, this maximum should occur at a s l i g h t l y larger value of M^. for the 24Q ^ — 23^ 23 transition than for the  22Q 22 —  21  j  21  O N E  5  a S  observed.  Thus the b_-component of the dipole  moment of D^N^C^O has been determined to be 1.35 ± 0.10 D. Then with the a-component taken to be  1.602 ± 0.020  D, the t o t a l dipole moment i s  u = 2.10 ± 0.15 D. To this accuracy the variations with K_^ observed by White and Cook are unimportant. Stark effect measurements yield only the magnitude of the components  150  151  (V + V )xlO~ o m 2  2  5  (volts ) 2  152  TABLE 5 . 1 3  22 0,22 M  J  The b-coraponent o f the D i p o l e Moment o f  —  21 1,21  KM,)"  2 4  y  b  (Debyes)  0,24 ~  D N U  2  3  1 2  C  1 6  1 , 2 3  KMj)  b  o.  (Debyes)  0  242  1.3194  0  288  1.2998  1  483  1.3207  1  575  1.3012  2  480  1.3245  2  572  1.3048  3  475  1.3310  3  567  1.3108  4  468  1.3402  4  560  1.3194  5  459  1.3524  5  551  1.3308  6  448  1.3677  6  540  1.3450  7  435  1.3865  7  526  1.3625  8  420  1.4091  8  512  1.3835  9  403  1.4361  9  495  1.4086  10  384  1.4682  10  475  1.4383  R e l a t i v e i n t e n s i t i e s o f the v a r i o u s M j S t a r k components. ^ b_-component of the d i p o l e moment c a l c u l a t e d assuming the peak maximum o f the a g g r e g a t e S t a r k l o b e c o r r e s p o n d s t o v a r i o u s v a l u e s o f M .  153  o f a m o l e c u l a r d i p o l e moment.  Hence, at t h i s p o i n t i n the d i s c u s s i o n ,  the  d i p o l e moment of i s o c y a n i c a c i d c o u l d have any one o f f o u r d i f f e r e n t d i r e c t i o n s , c o r r e s p o n d i n g t o the f o u r d i f f e r e n t p o s s i b l e p a i r s of s i g n s for y  a  and u, . b  Now, i t i s known t h a t the NCO r a d i c a l has a m o d e r a t e l y  s m a l l d i p o l e moment (y = 0.641 D)  (161).  F u r t h e r , hydrogen i s s i g n i f i c a n t l y  l e s s e l e c t r o n e g a t i v e than n i t r o g e n (or oxygen, or carbon).  Therefore,  it  seems r e a s o n a b l e t h a t the d i p o l e moment o f i s o c y a n i c a c i d s h o u l d p o i n t r o u g h l y from n i t r o g e n t o hydrogen when the p o s i t i v e d i r e c t i o n i s t a k e n i n the sense - - * • + .  I n terms o f "bond moments", a s m a l l NCO component (0 -*• N ) +  adds t o a l a r g e r NH component (N ->• H ) +  t o g i v e a s t i l l l a r g e r t o t a l moment,  w h i c h w i l l make a s l i g h t l y s m a l l e r a n g l e w i t h the a - a x i s t h a n does the NH b o n d ; t h i s i s o b s e r v e d when the s i g n s o f y cated i n F i g u r e  and y, a  5.5.  A l t h o u g h H ^ N ^ C ^ O and D ^ N ^ C ^ O  a r e t a k e n t o be as  b  s h o u l d have e s s e n t i a l l y the same  t o t a l d i p o l e moment, t h e i r i n d i v i d u a l components w i l l n o n e t h e l e s s s l i g h t l y due t o a r o t a t i o n (by 1° 2 9 ' ) on g o i n g from one i s o t o p e t o the o t h e r . d e t e r m i n e d D ^ N ^ C ^ 0 components y 4  ponents y  1  a  2  differ  of the p r i n c i p a l i n e r t i a l a x i s system A c c o r d i n g l y the e x p e r i m e n t a l l y  and y, were t r a n s f o r m e d i n t o new com-  a b and y ' measured w i t h r e s p e c t t o the H ^ ^ N ^ C ^ O p r i n c i p a l i n e r t i a l  a x i s system.  b  S t r u c t u r e I was assumed t o be the c o r r e c t s t r u c t u r e f o r  p u r p o s e , and the s i g n s o f the components were t a k e n t o be as i n d i c a t e d Figure 5.5.  indi-  The r e s u l t s are compared i n T a b l e 5.14 w i t h v a l u e s o f y '  this in and  Si  y^ c a l c u l a t e d by W i l l i a m s  (109) u s i n g the CNDO/2 f o r m a l i s m and s t r u c t u r e  I.  The s i g n s o f the CNDO/2 p r e d i c t e d components a r e seen t o s u p p o r t our p r e v i o u s deductions.  F u r t h e r , t h e r e i s even good agreement i n the magnitude o f  the  c a l c u l a t e d and " o b s e r v e d " numbers. An e s t i m a t e o f the i o n i c c h a r a c t e r i n the NH bond o f i s o c y a n i c  acid  154  FIGURE 5.5  The D i p o l e Moment of I s o c y a n i c  Acid.  b(A) j  H  u  = -1.57 D  155  may be o b t a i n e d from the measured d i p o l e moment u s i n g the f o l l o w i n g s i m p l e relation:  \ where  -  5  =  1  2  i s the p r o j e c t i o n o f the d i p o l e moment on the NH bond  (2.074x10  esu-cm), e i s the e l e c t r o n charge (4.8209x10  esu)  and  —8 r^jjj i s the NH bond l e n g t h ( 0 . 9 7 5 x 1 0 i  = 0.441 (or 4 4 . 1 % ) .  cm).  The r e s u l t o b t a i n e d i s  A l t e r n a t i v e l y one may c a l c u l a t e the i o n i c  character  i n the NH bond from the e l e c t r o n e g a t i v i t i e s o f hydrogen and n i t r o g e n w i t h the a i d o f e q u a t i o n 4 . 1 1 . (103) r e s p e c t i v e l y ,  I f X(R)  and Z(N)  a r e t a k e n t o be 2.15 and 3.00  this relation yields i  agreement w i t h the d i p o l e moment r e s u l t .  = 0.425 (or 42.5%) i n e x c e l l e n t However, s i n c e b o t h p r o c e d u r e s  have been g e n e r a l l y found t o be p o o r a p p r o x i m a t i o n s when a p p l i e d t o p o l y a t o m i c m o l e c u l e s , t h i s agreement must be r e g a r d e d as f o r t u i t o u s . The 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 c o u p l i n g c o n s t a n t s o f i s o c y a n i c and a number o f r e l a t e d m o l e c u l e s are compared i n T a b l e 5 . 1 5 . n o t e d t h a t t h e s e are c o n s i s t e n t w i t h the proposed i s o c y a n a t e than the a l t e r n a t e p o s s i b l e c y a n i d e  acid  I t w i l l be (HNCO)  rather  (HOCN) c o n f i g u r a t i o n f o r t h i s m o l e c u l e .  I n the f i r s t p l a c e , i s o c y a n i c a c i d , l i k e c h l o r i n e i s o c y a n a t e , has a n e g a t i v e X  c  c  >  i n c o n t r a s t t o the c y a n i d e s f o r w h i c h  x  c  c  is positive.  In a d d i t i o n ,  b o t h the i s o c y a n a t e s and the i s o t h i o c y a n a t e s a l l have a p o s i t i v e x whereas the x  o f the c y a n i d e s i s t y p i c a l l y  negative.  The CNDO/2 c a l c u l a t i o n performed by W i l l i a m s  (109) on i s o c y a n i c  a l s o gave v a l u e s f o r the n i t r o g e n a t o m i c p - o r b i t a l p o p u l a t i o n s . * It  >  acid  These were  has been i m p l i c i t l y assumed h e r e t h a t o n l y the NH bond moment makes a  s i g n i f i c a n t c o n t r i b u t i o n to u  NH  .  156  TABLE 5.14  Comparison o f the Observed and C a l c u l a t e d V a l u e s o f the D i p o l e Moment o f I s o c y a n i c A c i d . Observed (DNCO) -1.567  "a  IJLI  a  Observed (HNCO)  b  C  Calculated  -1.575  -1.404  1.391  1.600  2.095  2.129  A l l components measured w i t h r e s p e c t t o p r i n c i p a l i n e r t i a l a x i s system of H * N * C * " 0 i n Debyes. 4  2  D  ° E x p e r i m e n t a l l y d e t e r m i n e d D * N * C ^ 0 components (u = - 1 . 6 0 2 D, 14X216 ^ u, = 1.35 D) t r a n s f o r m e d i n t o H N C O i n e r t i a l a x i s s y s t e m . 14 12 16 4  C  2  E x p e r i m e n t a l l y determined H N C O  TABLE 5.15  U  C  1 2  X  1 6  (calc)  2.845  . -0.571  -2.273  0  3.99  1 6  0  3 5  C1  1 4  N  1 2  C  1 2  CH N  1 2  CH  3 2  S(  1 2  CH  H 1 2  1 2  1 2  3  1 4  C  CH  1 2  1 4  3  3 2  C  1 6  0  C  N) 1 4  3 2  S  2  N  N 3 2  S  1 2  -1.01  C  1 4  N  Measured i n MHz.  Reference  (109)  (12)  2.86  (149) (12)  1.90  (153).  Isocyanic  -2.97  1.2  S  1 2  1 4  1 6  C  1 2  N  C  1 2  3  C  cc  -1.578  C  1 4  X  -0.466  1 2  H  bb  2.045  N  N  x  (obs)  1 4  1 4  aa  0  H  3  = 1 levels  N i t r o g e n 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 o f A c i d and R e l a t e d M o l e c u l e s .  Molecule H N  component f o r K_,  -1.51  0.30  1.21  (162)  -4.20  2.10  2.10  (163)  -4.58  2.29  2.29  (164)  -3.13  2.19  0.94  (12)  157  c o n v e r t e d i n t 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 c o u p l i n g c o n s t a n t s w i t h the  aid  o f the Townes D a i l e y T h e o r y , as d e s c r i b e d i n s e c t i o n 4.4 ( e q u a t i o n 4.3). The r e s u l t s are a l s o p r e s e n t e d i n T a b l e 5.15.  A g a i n , as w i t h c h l o r i n e  i s o c y a n a t e , a l t h o u g h the agreement w i t h the observed c o n s t a n t s i s n o t o u t s t a n d i n g , i t i s c e r t a i n l y a c c e p t a b l e i n v i e w o f the l i m i t a t i o n s o f the  theory  14 and the u n c e r t a i n t y i n the magnitude o f Ql2io^ e  5.5  ^"  C a l c u l a t i o n o f 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 and the  Inertial  D e f e c t from the M o l e c u l a r F o r c e F i e l d . I t was n o t e d i n the i n t r o d u c t i o n t o t h i s c h a p t e r t h a t t h r e e  different  harmonic f i e l d s , based on two d i f f e r e n t v i b r a t i o n a l a s s i g n m e n t s , have been published for isocyanic acid. The f i r s t ,  These have been reproduced i n T a b l e 5.16.  t h a t p u b l i s h e d by O r v i l l e Thomas (124), i s a s s o c i a t e d w i t h  the  e a r l y measurements o f H e r z b e r g and R e i d (144) on the s i n g l e i s o t o p e H N^ C^O. 1 4  I t was found t o g i v e a p o o r p r e d i c t i o n o f the  2  D N^ C^O 1 4  2  f u n d a m e n t a l v i b r a t i o n f r e q u e n c i e s and was t h e r e f o r e n o t c o n s i d e r e d f u r t h e r . The o t h e r two f o r c e f i e l d s a r e b o t h based on the more complete d a t a o f Ashby and Werner (145,146).  I n these, Warriar e t . a l .  o b s e r v e d band o r i g i n f r e q u e n c i e s , w h i l e O r e l e t . a l . perturbed" frequencies; i.e. coupling.  (147) used the  (148) used the " u n -  t h o s e c o r r e c t e d f o r the e f f e c t s o f C o r i o l i s  The l a t t e r approach w o u l d seem t o be the c o r r e c t o n e , b u t f o r t u n -  a t e l y the two s e t s o f f r e q u e n c i e s do n o t d i f f e r g r e a t l y .  I t i s not  clear  how W a r r i a r e t . a l . managed t o c a l c u l a t e 32 f o r c e c o n s t a n t s from 12 observed frequencies.  I n a d d i t i o n , b o t h groups gave a l l f o r c e c o n s t a n t s i n u n i t s  of mdyne/X b u t d i d not s p e c i f y how they had s c a l e d t h e i r b e n d i n g d i s p l a c e ment c o o r d i n a t e s t o a c h i e v e t h i s r e s u l t .  Several alternative p o s s i b i l i t i e s  were c o n s i d e r e d ; t h a t i n d i c a t e d i n T a b l e 5.16 gave the b e s t r e p r o d u c t i o n  158  TABLE 5 . 1 6  Orville  Force Constant  f  Molecular  f l  r  2  f  s f  Rr  f r  f f  f  f  l 2  c  Orel  et.al.  et.al.  HNCO  HNCO  DNCO  HNCO/DNCO  6.9  6.9050  6.9600  7.031  14.0  14.2900  14.5500  11.791  15.0  14.7100  14.2200  17.904  0.58  0.3010  0.0400  0.199  0.06  0.3490  0.0600  1.32  1.2400  1.3840  2.194  0.33  0.2312  0.2484  0.184  0.48  0.6680  0.5447  0.812  0.02  0.0090  0.0340  -0.02  -0.0310  -0.0050  0.17  0.1390  0.1580  0.10  0.0790  0.0910  0.04  0.0250  -0.0420  0.100  0.02  0.0140  -0.0240  0.099  0.09  0.0650  -0.0310  0.129  0.4214  0.4593  r  e Ra  R9  f f  Warriar  Acid.  2  a  r  Thomas^  a  R r  Force F i e l d s o f Isocyanic  l  a  r a 2  \°  %.  a  I n mdynes/R; 6 =Z.NC0  R = NH, r  l  = NC, r  = CO, a =/LHNC, 9 = Z.NC0 ( i n - p l a n e )  (out-of-plane).  Bending d i s p l a c e m e n t c o o r d i n a t e s C  2  d e f i n e d a s : RAa and r A 9 . 2  Bending d i s p l a c e m e n t c o o r d i n a t e s presumed t o be: ^/Rr^Act, ^jr^v^Q A6Jr r 1  2  and  159  TABLE 5.17  Fundamental  "1 ^2 "3 W  Fundamental V i b r a t i o n a l F r e q u e n c i e s o f I s o c y a n i c H. and R. HNCO  5  u  6  HNCO  DNCO  Description  HN s t r e t c h  2274  2235  NCO asymmetric  1327  1310  NCO symmetric  460(468.5)  HNC bend  (in-plane) (in-plane)  stretch stretch  798  ' 777. 1(761 • 5 )  572  659. 8(642 .8)  766.8(758.3)  NCO bend  670  577. 5(610 .1)  602.9  o u t - o f - p l a n e bend  A  d  .  Taken from H e r z b e r g and R e i d Taken from Ashby and Werner  d  C  2634.9  " Measured i n cm b  W.  3531  4  u  A. and  b  Acid  (144). (145,146).  Numbers n o t i n b r a c k e t s a r e t h e o b s e r v e d band o r i g i n f r e q u e n c i e s ; numbers i n b r a c k e t s are " u n p e r t u r b e d " f r e q u e n c i e s .  160 of f r e q u e n c i e s . The f o r c e f i e l d s o f b o t h W a r r i a r e t . a l . and O r e l e t . a l . were used t o c a l c u l a t e 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 o f H ^ N ^ C ^ O and D ^ N ^ C ^ O w i t h the a i d of the K i v e l s o n W i l s o n t h e o r y ( s e c t i o n 2.5) the p l a n a r i t y r e l a t i o n s  (equations 2.17).  The r e s u l t s are compared w i t h  the e x p e r i m e n t a l l y observed c o n s t a n t s i n T a b l e 5 . 1 8 . i s rather poor.  and  The o v e r a l l  The most s e r i o u s d i s c r e p a n c y o c c u r s f o r the A  agreement distortion  JK  c o n s t a n t ; f o r the H ^ N ^ C ^ O i s o t o p i c s p e c i e s b o t h o f the c a l c u l a t e d v a l u e s are o f o p p o s i t e s i g n t o the o b s e r v e d one. complete s u r p r i s e , however, s i n c e N e e l y that A  T h i s does not come as a  (152) has p r e v i o u s l y s u g g e s t e d  s h o u l d be e x t r e m e l y s e n s i t i v e t o the s t r e t c h - b e n d i n t e r a c t i o n  c o n s t a n t s i n the m o l e c u l a r f o r c e f i e l d .  E v i d e n t l y n e i t h e r o f the above  force f i e l d s i s p a r t i c u l a r l y outstanding. A c c o r d i n g l y , D r . R. Green (117) has r e c o n s i d e r e d t h e i s o c y a n i c a c i d f o r c e f i e l d p r o b l e m u s i n g h i s p r e v i o u s l y mentioned method ( s e c t i o n T h i s c a l c u l a t i o n was a l s o based on the v i b r a t i o n a l f r e q u e n c i e s  4.6).  (corrected)  and a s s i g n m e n t s o f Ashby and W e r n e r ; e x c e p t t h a t the co^ and to^. a s s i g n m e n t s o f the H^^N^^C^O s p e c i e s were r e v e r s e d . now c o n s i s t e n t w i t h t h o s e o f D ^ N ^ C ^ O  The H  1 4  N  1 2  C ^ O assignments  and a l s o C1NC0.  are  T h i s change does  n o t i n any way a f f e c t the C o r i o l i s c o u p l i n g c a l c u l a t i o n of Ashby and Werner (the c o r r e c t i o n o f o b s e r v e d band o r i g i n f r e q u e n c i e s t o g i v e " u n p e r t u r b e d " frequencies).  However, i t s h o u l d be p o i n t e d out t h a t t h e r e i s  apparently  s t i l l some c o n s i d e r a b l e doubt as t o the importance o f such i n t e r a c t i o n s (165).  C o n s e q u e n t l y n e i t h e r the " u n p e r t u r b e d " f r e q u e n c i e s n o r even the  a s s i g n m e n t s , e s p e c i a l l y f o r the H ^ N ^ C ^ O s p e c i e s , can be r e g a r d e d as f i n a l yet.  I n any c a s e , o n l y the numbers g i v e n i n T a b l e 5.17 are p r e s e n t l y  a v a i l a b l e , so they were u s e d .  161  TABLE 5.18  Comparison of C a l c u l a t e d and Observed C e n t r i f u g a l D i s t o r t i o n Constants of Isocyanic A c i d . 3  H N U  Constant A 10  3  j X  J K  A  X  1  Q  1  A xl0K  6  K  6  10  j X  X  1  Q  3  Observed  C  1 6  0  W.F.F.  0.F.F.  b  C  R.G.F.F.  3.198  3.606  3.785  3.366  8.311  -4.482  -11.005  9.179  2.902  3.371  3.982  10.459  13.883  5.847  4.832  5.971  5.520  5.096  6  7.277  5  1 2  1  _14. 12 1 6 D N C 0 T  Constant A A  j X  J K  10 X  1  3  Q  1  A xl0"  3  K  6 xlO  4  vi()1 a  Observed  rt  W.F.F.  O.F.F.  3.432  3.676  4.131  3.153  -2.291  -9.240  -12.874  -2.793  1.146  1.156  1.415  2.577  3.188  1.959  4.161  4.969  4.727  2.758 2.042  e  Measured i n MHz.  b  C a l c u l a t e d from the f o r c e f i e l d o f W a r r i a r e t . a l .  C  C a l c u l a t e d f r o m t h e f o r c e f i e l d of O r e l e t . a l .  d  C a l c u l a t e d from the f o r c e f i e l d of Green  6  From t h e f a r i n f r a r e d d a t a o f Krakow e t . a l .  (147).  (148).  (117). (151).  R.G.F.F.  d  162  The f o r c e f i e l d d e t e r m i n e d by Green ( R . G . F . F . ) has been p r e s e n t e d Table 5.19.  Here the H  separately.  The n e a r e q u i v a l e n c e of the two r e s u l t i n g s e t s of numbers i s  reassuring.  The d i s t o r t i o n c o n s t a n t s w h i c h they y i e l d are a g a i n compared  1 4  N  1 2  C  1 6  0 and D  w i t h the observed ones i n T a b l e 4 . 1 8 . agreement i s much improved now.  1 4  N  1 2  C  1 6  0 problems were  in  treated  I t w i l l be n o t e d t h a t the  overall  I n p a r t i c u l a r , the c a l c u l a t e d A  values  JK  a r e not o n l y o f the r i g h t s i g n b u t a l s o , a p p r o x i m a t e l y , the r i g h t m a g n i t u d e . Only f o r the A  ls.  c o n s t a n t are the d i s c r e p a n c i e s between the o b s e r v e d and c a l -  c u l a t e d numbers s t i l l r a t h e r l a r g e .  F u r t h e r , i t i s l i k e l y that these  due m a i n l y t o the i n h e r e n t l i m i t a t i o n s o f the K i v e l s o n W i l s o n t h e o r y  are (114)  r a t h e r t h a n t o any s e r i o u s d e f i c i e n c y i n the R . G . F . F . D e s p i t e the apparent s u p e r i o r i t y of the R . G . F . F . o v e r b o t h the W a r r i a r and O r e l f o r c e f i e l d s a l l t h r e e were a l s o used t o c a l c u l a t e the i n e r t i a l d e f e c t s o f H * N * C ^ O and D * " N ^ C * 0 . 4  2  4  2  D  The p r o c e d u r e f o l l o w e d was  the same as t h a t d e s c r i b e d i n s e c t i o n 4 . 6 ; i . e . a i d of equation 2.56, A  A  I T T t >  was c a l c u l a t e d w i t h  was e s t i m a t e d by s u b s t i t u t i n g the  the  calculated  d i s t o r t i o n c o n s t a n t s i n t o e q u a t i o n s 5 . 5 , 2.20 and 2 . 1 6 , and ^ ^ _ e  The r e s u l t s have been c o l l e c t e d i n T a b l e 5 . 2 0 .  essentially  ec  w  &  s  ignored.  I n each c a s e , the sum  A + A ^ (= A , ) i s i n r e s p e c t a b l e agreement w i t h the o b s e r v e d i n e r VIB cent calc T r T n  v  t i a l defect.  T h i s i s c o n s i s t e n t w i t h Oka and M o r i n o ' s (59)  assertion that  the i n e r t i a l d e f e c t i s n o r m a l l y o n l y a s l o w l y v a r y i n g f u n c t i o n of the m o l e c ular force f i e l d .  However, i t w i l l be n o t e d t h a t a l t h o u g h the  differences  a r e s l i g h t the R . G . F . F . has a g a i n g i v e n the b e s t agreement w i t h e x p e r i m e n t . The r e m a i n i n g d i s c r e p a n c i e s between A° and A be a t t r i b u t e d t o & -^ e  (59).  It  D^ N C^O 4  1 2  ec  ^  ( R . G . F . F . ) p r o b a b l y cannot  s i n c e the l a t t e r i s l i k e l y t o be s m a l l and n e g a t i v e  i s perhaps s i g n i f i c a n t t h a t the agreement i s s l i g h t l y b e t t e r than H * N * C ^ 0 ; 4  2  the C o r i o l i s c o u p l i n g i s more i m p o r t a n t i n  for the  163  TABLE 5.19  Isocyanic  Force  Constant  A c i d M o l e c u l a r Force F i e l d : R . G . F . F .  HNCO  DNCO  f (HN)  6.8727  6.9729  f(NC)  14.6352  14.6622  f(CO)  14.6352  14.6622  f(HNC)  0.2632  0.2546  f(NCO)  1.0808  1.0778  fC±)  0.6620  0.6500  f(HN:NC)  0.0000°  0.0000  f(HN:C0)  0.0000  o.oooo  f(NC:CO)  1.4299  1.5270  f(HN:HNC)  0.3436  0.3486  f(HN:NCO)  o.oooo  o.oooo  f(NC:HNC)  0.7318  0.7331  f(NC:NCO)  o.oooo  o.oooo  f(CO:HNC)  0.0715  0.0763  f(CO:NCO)  0.0000  f(HNC:NCO)  b  b  b  -0.1047  b  b  b  b  b  o.oooo  b  -0.1003  S t r e t c h i n g f o r c e c o n s t a n t s are i n mdyne/X, bends a r e i n mdyne-X/rad , b e n d - s t r e t c h i n t e r a c t i o n s a r e i n mdyne/rad. Set e q u a l t o 0 i n i t i a l l y .  TABLE 5.20  Comparison o f C a l c u l a t e d and Observed I s o c y a n i c A c i d Defects.  H Calculation  A  1 4  N  1 2  C  1 6  0  A  VIB  Inertial  A  cent  VIB  +  A  cent  A°  W.F.F.  0.0919  0.0058  0.0977  0.1205  O.F.F.  0.1006  0.0070  0.1076  0.1205  R.G.F.F.  0.1027  0.0074  0.1101  0.1205  D N U  Calculation W.F.F.  \lB '  1 2  C  1 6  A cent  0 A  VIB  +  A  cent  A°  0.1317  0.0069  0.1386  0.1539  O.F.F.  0.1375  0.0074  0.1449  0.1539  R.G.F.F.  0.1423  0.0082  0.1505  0.1539  Measured i n a.m.u.7A .  165  latter.  F i n a l l y , i t i s now c l e a r t h a t the o b s e r v e d i n c r e a s e i n A° on g o i n g  from H * N * C ^ O t o D ^ N ^ C ^ O i s e n t i r e l y c o m p a t i b l e w i t h a p l a n a r 4  2  structure  for isocyanic acid. 5.6  D i s c u s s i o n o f the M o l e c u l a r  Structure.  The m o l e c u l a r s t r u c t u r e d e t e r m i n e d f o r i s o c y a n i c a c i d i n t h i s work  is  compared i n T a b l e 5.21 w i t h t h e r e s u l t s o f two p r e v i o u s s t r u c t u r a l i n v e s t i gations.  The e a r l y e l e c t r o n d i f f r a c t i o n work o f E y s t e r e t . a l .  (123)  is  seen t o have y i e l d e d o n l y a p p r o x i m a t e e s t i m a t e s of the NC and CO bond l e n g t h s , a f t e r the r e m a i n i n g p a r a m e t e r s had been g i v e n assumed v a l u e s . wave " r  11  s t r u c t u r e o b t a i n e d by Jones e t . a l .  ment on the e l e c t r o n d i f f r a c t i o n one. the " r  11  structure obtained here.  (11)  The m i c r o -  i s a considerable improve-  I n f a c t , i t i s n e a r l y as good as  The p r e s e n t s t u d y has y i e l d e d r e f i n e d  NC and CO bond l e n g t h s , b u t has n o t s i g n i f i c a n t l y improved the NH d i s t a n c e . The l a t t e r i s due t o the i n h e r e n t u n c e r t a i n t y a s s o c i a t e d w i t h h y d r o g e n / deuterium s u b s t i t u t i o n zero p o i n t v i b r a t i o n a l e f f e c t s .  It  h a s , however,  more c l e a r l y demonstrated the e x i s t e n c e of s u c h d i f f i c u l t i e s , i n c l u d i n g the p o s s i b i l i t y o f a bend i n the NCO c h a i n .  I n l i g h t of t h i s , the s m a l l e r r o r  e s t i m a t e s g i v e n by Jones e t . a l . f o r the HNC a n g l e and the NH bond l e n g t h a r e seen t o be o p t i m i s t i c . I t was shown i n s e c t i o n 5.3 t h a t , even w i t h an abundance o f i s o t o p i c d a t a , i t was s t i l l i m p o s s i b l e t o p r o v e r i g o r o u s l y whether o r not the NCO c h a i n i n i s o c y a n i c a c i d was l i n e a r o r b e n t .  A similar situation exists  w i t h r e g a r d s t o the s t r u c t u r e s o f h y d r a z o i c a c i d and i s o t h i o c y a n i c a c i d . F u r t h e r , i t i s d o u b t f u l i f any o t h e r t e c h n i q u e , such as e l e c t r o n d i f f r a c t i o n , i s capable of p h y s i c a l l y r e s o l v i n g t h i s q u e s t i o n .  However, on p u r e l y  c h e m i c a l g r o u n d s , the s t r u c t u r e w i t h the l i n e a r heavy atom c h a i n must be the p r e f e r r e d one.  Resonance forms l i k e t h o s e drawn p r e v i o u s l y ( s e c t i o n  4.7)  166  TABLE 5.21  r(N-H)  Comparison o f I s o c y a n i c A c i d S t r u c t u r e s .  Eyster e t . a l .  Jones e t . a l .  (electron diffraction)  "r " o  (1.01)  b  "r  s  "  0.987 ± 0.01  0.986 ± 0 . 0 1 5  d  r(N-C)  1.19 ± 0 . 0 3  1.207 ± 0.01  1.209 ± 0. 0 0 5  d  r(C-O)  1.19 ± 0 . 0 3  1.171 ± 0.01  1.166 ± 0. 0 0 5  d  128°  Z.(HNC)  (125°)  b  128°  z_(NCO)  (180°)  b  (180°)  3  Bond l e n g t h s measured i n A*.  b  Assumed.  ° T h i s i s an average of s t r u c t u r e s I d  T h i s Work°  and I I  5' ± 3 0 '  (180°)  b  (Table  ^o e 2' + b  5.8).  E s t i m a t e d maximum p o s s i b l e d e v i a t i o n from e q u i l i b r i u m v a l u e . Same as " d " b u t q u a l i f i e d w i t h a p r o v i s i o n f o r a much l a r g e r e r r o r e s t i m a t e i f the a s s u m p t i o n o f a l i n e a r NCO c h a i n i s i n c o r r e c t .  167  t o e x p l a i n t h e o b s e r v e d bends i n c h l o r i n e i s o c y a n a t e and c h l o r i n e a z i d e are n o t p o s s i b l e f o r t h e a c i d s . The NC and CO bond l e n g t h s i n i s o c y a n i c a c i d a r e v e r y s i m i l a r t o t h e d i s t a n c e s reported e a r l i e r f o r the corresponding c h l o r i n e isocyanate bonds. C o n s e q u e n t l y , i t would appear t h a t i s o c y a n i c a c i d a l s o has a d e l o c a l i z e d NCO TT s y s t e m .  I n terms o f t h e V a l e n c e Bond a p p r o a c h , t h r e e resonance forms  are a g a i n l i k e l y t o be t h e dominant c o n t r i b u t o r s t o t h e c o m p o s i t e wavefunction  *  H  (123).  These a r e :  \  H 51  N = C  0~  H  X  511  5III  S i n c e hydrogen has a much l o w e r e l e c t r o n e g a t i v i t y than c h l o r i n e (X(H) = 2 . 1 5 , X(C1)  = 3.00) (103) i t i s t o be e x p e c t e d t h a t form 511 w i l l be s t a b i l i z e d  w i t h r e s p e c t t o t h e e q u i v a l e n t c h l o r i n e i s o c y a n a t e form ( 4 1 1 ) . more, 5 I I I s h o u l d be d e s t a b i l i z e d r e l a t i v e t o 4 I I I .  Further-  Both o f t h e s e d e d u c -  t i o n s a r e c o n s i s t e n t w i t h t h e observed i n c r e a s e i n t h e XNC a n g l e (X = H, C l ) on g o i n g from c h l o r i n e i s o c y a n a t e t o i s o c y a n i c a c i d ; l i k e w i s e , t h e s l i g h t d e c r e a s e i n t h e NC bond i e n g t h and t h e s l i g h t i n c r e a s e i n t h e CO bond l e n g t h (see T a b l e 5 . 2 2 ) .  T h i s t r e n d i s c o n t i n u e d when hydrogen i s r e p l a c e d w i t h  the even more s t r o n g l y e l e c t r o n d o n a t i n g m e t h y l group ( 1 6 6 ) .  The e l e c t r o n  d i f f r a c t i o n determined s t r u c t u r e of methyl isocyanate i s a l s o given i n Table 5.22.  I t w i l l be n o t e d t h a t t h e XNC a n g l e (X = M e t h y l )  has widened  t o 140" (f rom 128 f o r X = H) w h i l e s i m u l t a n e o u s l y t h e NC bond has s h o r t e n e d and t h e CO one l e n g t h e n e d t o t h e p o i n t where r(N-C) i s now s m a l l e r  * The i o n i c form H NC0 discussion. +  i s also important but i s not relevant  than  t o the p r e s e n t  168  TABLE 5.22  M o l e c u l a r S t r u c t u r e s o f Some  Isocyanate  r(X-N)  r(N-C)  r(C-O)  /L(XNC)  A(NCO)  C1NC0  1.705  1.225  1.162  118° 5 0 '  170° 5 2 '  HNCO  0.975  1.209  1.166  128° 3 6 '  180°  (0.997)  (1.209)  (1.166)  CH NCO  1.450  1.168  1.202  140°  CH NCO  1.44  1.207°  1.171°  140°  180°  SiH NCO  1.699  1.150  1.179  180°  180°  SiH NCO  1.703  1.216  1.164  151° 4 2 '  180°  GeH NCO  1.831  1.190  1.182  141°  180°  GeH NCO  1.81  1.19  C  1.18°  143°  180°  PF NCO  1.683  1.256  1.168  130° 3 6 '  180°  SiF NCO  1.648  1.190  1.168  160° 42*  180°  SiCl NCO  1.646  1.219  1.139  138°  180°  SlMe NCO  1.76  1.20  1.18  150°  180°  SiMe NCO  1.69  1.15  1.18°  180°  180°  b  3  3  3  3  3  3  2  3  3  3  3  a  b  r  c  C  Isocyanates.  (127°  29') 16'  18'  (180°  Method  c  MW MW  )  MW  180° c  ED  (167)  MW  (12)  MW  (13)  ED  (173)  ED  (172)  MW  (174)  ED  (171)  ED  (173)  ED  (175)  ED  (176)  MW  (177)  C  c  c c c c c c c  Bond l e n g t h s a r e measured i n ?v. F i r s t s e t o f numbers was o b t a i n e d u s i n g A I ° and LI° t o l o c a t e t h e h y d r o g e n ; second s e t A I ° and A I ° used t o l o c a t e H (see t e x t , s e c t i o n 5 . 3 ) . b e Assumed.  ^ MW = M i c r o w a v e ; ED = E l e c t r o n d i f f r a c t i o n .  169 r(C-O).  The a p p r o p r i a t e resonance forms a r e ( 1 6 7 ) : Me  \  Me ,N  N = C  C = 0  Me  (T  +  51'  \ _:N  C^=0  511'  5III*  where 5 1 1 ' i s o f much g r e a t e r i m p o r t a n c e t h a n  5III . 1  The s t r u c t u r e s o f a few a z i d e and i s o t h i o c y a n a t e m o l e c u l e s have been c o l l e c t e d i n T a b l e s 5.23 and 5.24 r e s p e c t i v e l y .  I t i s i n t e r e s t i n g to note  t h a t t h e s e a l s o e x h i b i t t r e n d s s i m i l a r t o t h a t d e s c r i b e d above.  For the  a z i d e s t h i s may be a t t r i b u t e d t o a d e s t a b i l i z a t i o n o f resonance form 5 I I I " w i t h i n c r e a s i n g e l e c t r o n r e l e a s i n g a b i l i t y o f X (X = C l , H , M e ) : X  \ X  N  N = N  X  +  -N^=N + +  51"  X  \  N  N  511"  where 5 1 1 " i s o f s l i g h t i m p o r t a n c e . r e f l e c t i o n o f t h e combined e f f e c t 5III"'  N -  +  w = N  5III"  F o r the i s o t h i o c y a n a t e s  the trend i s a  o f a s t a b i l i z e d 5 1 1 " ' and a d e s t a b i l i z e d  (X = H , M e ) : X  \  X .N  C=S 51"*  NEEEEC  S  +  ~  X  \ JN  511"*  r . = s  +  5III"'  The o b s e r v a t i o n t h a t each o f t h e a z i d e s has a s m a l l e r XNY a n g l e t h a n t h e corresponding isocyanate  (Y = N and C r e s p e c t i v e l y )  s u g g e s t i o n t h a t form 5 1 1 " i s u n i m p o r t a n t  (168).  i s c o n s i s t e n t w i t h the  On t h e o t h e r h a n d , t h e  s m a l l i n c r e a s e i n t h e XNC a n g l e on g o i n g from an i s o c y a n a t e  to the c o r r e s -  p o n d i n g i s o t h i o c y a n a t e i s more d i f f i c u l t t o r a t i o n a l i z e ; e s p e c i a l l y  since  the NC bond l e n g t h s a r e i n t h e o p p o s i t e sense ( i . e . l o n g e r f o r t h e i s o t h i o cyanate).  P a r t i c i p a t i o n o f t h e s u l f u r d - o r b i t a l s i n the NCS TT b o n d i n g i s  170  TABLE 5.23  Molecular Structures  Azide C1N HN  b  3  CH N 3  CH N 3  3  3  SiH N 3  GeH N 3  NCN  r(N -N )  r(N -N )  A(XN N )  1.745  1.252  1.133  108° 4 0 '  171° 5 6 '  MW  (14)  0.975  1.237  1.133  114° 8'  180°  c  MW  (178)  (1.004)  (1.237)  (1.133)  (111° 5 7 V )  180°  C  1.468  1.216  1.130  116° 46»  180°  c  1.46  1.24  1.13  117°  180°  c  x  3  o f Some A z i d e s .  2  2  C  3  C  3  2  A ( N  1 2 3 N  N  )  <180°  3  3  X  Method  MW  ED  (167)  MW  (179)  MW  (180)  1,845  1.250  1.140  119°  180°  C  ED  (172)  1.312  1.252  1.133°  120° 1 3 '  180°  C  MW  (154)  Bond l e n g t h s a r e measured i n A*.  a  F i r s t s e t o f numbers o b t a i n e d u s i n g A l  and A l Si  second s e t A l , and A l used t o l o c a t e H. b c Assumed.  TABLE 5.24 XNCS  Molecular Structures  o f Some  r(X-N)  r(N-C)  r(C-S)  (0.989)  (1.216)  (1.560)  CH NCS  1.479  1. 192  1.597  CH NCS  1.45  1.216  SiH NCS  1.714  1.211  HNCS  a  3  3  3  b  A(XNC) (135°)  Z.(NCS) b  MW  (150)  141° 3 5 '  180°  b  ED  (167)  b  MW  (12)  MW  (170)  ED  (171)  ED  (171)  147° 3 0 '  180°  1.560  b  180°  180°  163° 3 8 ' 1.686  1.221  1.553  140° 3 0 '  180°  b  Hydrogen s u b s t i t u t i o n p o s i t i o n d e t e r m i n e d u s i n g AI^ and A l ^ . Assumed.  Method  (180°)  b  3  2  Isothiocyanates.  1.561  SiH NCS PF NCS  t o l o c a t e H; D  171  p o s s i b l y a f a c t o r i n t h i s apparent  anomaly.  The 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 c o u p l i n g c o n s t a n t s o f HNCO, HNNN and HNCS p r o v i d e a d d i t i o n a l s u p p o r t f o r the above p i c t u r e .  Because  the  a-axis  i s n e a r l y c o i n c i d e n t w i t h the heavy atom c h a i n i n a l l t h r e e m o l e c u l e s , a comparison o f x  values i s v a l i d .  These  are:  3 3  X X X  3 3 3.3.  aa  (HN ) = 4.65 ± 0.25 MHz (NH n i t r o g e n )  (169)  -J  (HNCO) = 2.045 ± 0.038 MHz (HNCS) = 1.2 ± 0.2 MHz (149)  Now i t w i l l be r e c a l l e d ( s e c t i o n 4.4) o f the Townes D a i l e y t h e o r y x  t h a t a c c o r d i n g t o the s i m p l e s t v e r s i o n  i s given by: 3 3  X = -U e Q q ( N) aa p 210 a A  x n  o i n  U  r  = 10U p r  a  MHz  5.13  *a Then s i n c e U P  a  i s c l e a r l y g r e a t e s t f o r resonance forms o f t y p e I I I  f o r forms o f t y p e I I  and l e a s t  i t i s t o be e x p e c t e d t h a t HNCS w h i c h e v i d e n t l y has  l a r g e s t c o n t r i b u t i o n from the l a t t e r w i l l have the s m a l l e s t x  the  w h i l e HN_ aa  o  w i t h the l a r g e s t c o n t r i b u t i o n from the former w i l l have the l a r g e s t x 3 3  F u r t h e r , t o the e x t e n t t o w h i c h the r e l a t i v e s i z e s o f the t h r e e HNY a n g l e s q u a n t i t a t i v e l y r e f l e c t the i m p o r t a n c e of the v a r i o u s resonance f o r m s , x 3 3  (HNCO) s h o u l d be c l o s e r t o x  (HNCS) t h a n t o x aa  a r e i n agreement w i t h e x p e r i m e n t .  (HN„). aa  Both deductions  J  A number o f s i l i c o n , germanium and phosphorus c o n t a i n i n g compounds have a l s o been i n c l u d e d i n T a b l e s 5 . 2 2 , 5.23 and 5 . 2 4 .  These were n o t  mentioned i n the p r e v i o u s d i s c u s s i o n because they a r e a l l thought t o i n v o l v e some degree o f dir - pit b o n d i n g (between N and S i , Ge or P) .  On the  one h a n d , such b o n d i n g a p p a r e n t l y p l a y s a major r o l e i n d e t e r m i n i n g the structures of s i l y l isocyanate  (74)  and s i l y l i s o t h i o c y a n a t e  (170),  both  172  o f w h i c h have been shown t o e x h i b i t a symmetric top r o t a t i o n a l spectrum  * i n t h e i r ground v i b r a t i o n a l s t a t e  (i.e.  t o have a l i n e a r SiNCX c h a i n )  On the o t h e r h a n d , i t i s p r o b a b l y of r e l a t i v e l y m i n o r , but not  .  insignifi-  c a n t , i m p o r t a n c e i n the phosphorus and germanium compounds ( 1 7 1 , 1 7 2 ) . t r e n d e v i d e n t l y c o n t i n u e s a c r o s s the p e r i o d i c t a b l e t o c h l o r i n e  This  (171);  r e c a l l t h a t c h l o r i n e i s o c y a n a t e has been " f o u n d " t o have e s s e n t i a l l y no drr - p-rr b o n d i n g ( s e c t i o n  4.4).  Two d i f f e r e n t s t r u c t u r e s have been quoted i n T a b l e s 5.22 and 5.23 b o t h i s o c y a n i c a c i d and h y d r a z o i c a c i d .  I n the f i r s t one the hydrogen s u b -  s t i t u t i o n p o s i t i o n was d e t e r m i n e d from A I ° a b r a c k e t s ) , from A I °  and A I °  l o c a t e the hydrogen ( 5 . 1 4 ) .  and A I ° ;  i n the second  (in  b  (see t e x t , s e c t i o n 5 . 3 ) .  c y a n i c a c i d s t r u c t u r e ( T a b l e 5.24)  The s i n g l e  was o b t a i n e d u s i n g A I °  isothio-  and A I °  to  F o r t h i s m o l e c u l e the a l t e r n a t e approach was  n o t p o s s i b l e , because A I ° was known o n l y v e r y a p p r o x i m a t e l y .  Clearly a  comparison of the NH bond l e n g t h s i n t h e s e a c i d s w i l l be v a l i d o n l y i f same method has been used t o d e t e r m i n e a l l of them. the numbers i n b r a c k e t s . HNX a n g l e . behavior.  for  the  N e c e s s a r i l y , t h i s means  These are seen t o d e c r e a s e g r a d u a l l y w i t h i n c r e a s i n g  I t w i l l be r e c a l l e d t h a t the C1N bond l e n g t h s e x h i b i t e d a s i m i l a r A g a i n , t h i s may be a t t r i b u t e d t o an i n c r e a s e i n a bond s t r e n g t h  accompanying an i n c r e a s e i n the s - c h a r a c t e r  of the n i t r o g e n a t o m i c h y b r i d  o r b i t a l i n v o l v e d i n a bond f o r m a t i o n t o hydrogen ( o r c h l o r i n e ) .  A com-  p a r i s o n o f the NH bond l e n g t h s found i n a number o f s m a l l m o l e c u l e s  is  presented i n Table 5.25.  * I t i s i n t e r e s t i n g t h a t the e l e c t r o n d i f f r a c t i o n s p e c t r a of t h e s e m o l e c u l e s (see a l s o Me^SiNCO) are a l l c o n s i s t e n t w i t h bent heavy atom c h a i n s ; i n each case t h i s i s almost c e r t a i n l y an a r t i f a c t o f a v e r y low f r e q u e n c y bending v i b r a t i o n (173).  173  TABLE 5.25  Comparison o f Some NH Bond  Molecule  r(N-H)  Lengths.  Angles  a  1.014  A(HNH) = 107°  3'  1.026  A(FNF) = 102°  5 4 ' ; A(HNF) = 99°  1.017  Z.(HNC1) ='  1.011  A(HNH) = 105°  5 2 ' ; Z-(CNH) = 112°  18*  1.022  Z.(CNC) = 112°  1 2 ' ; Z.(CNH) = 108°  48'  0.996  Z-(CNC) = 1 0 9 . 8 ° ;  HNCO  0.975(0.992)  L. (HNC) = 128° 5 0 ' ( 1 2 7 ° 2 9 ' )  HN3  0.975(1.004)  Z-(HNN) = 114°  NH  b 3  NHF  b 2  NH Cl  b  2  MeNH  2  Me NH  b  2  PYRROLE  b  .  HNCS  (0.989)  4 1 ' ; Z.(HNH) = = 107°  (129).  planar  8'(111°  /L (HNC) = (135°)  Measured i n X. Taken from Gordy and Cook  103°  48'  57')  174  CHAPTER 6  THE MICROWAVE SPECTRUM OF CYANOGEN ISOCYANATE The e x i s t e n c e o f a gaseous compound w i t h the f o r m u l a C2N2O was p o s t u l a t e d by Okamoto and S h i r a i  (181)  first  d u r i n g t h e i r i n v e s t i g a t i o n of  h a r d e n i n g of s t e e l w i t h " c i t y g a s " i n the p r e s e n c e of c y a n i d e .  the  Later  Basco ( 1 8 2 ) , u s i n g the f l a s h p h o t o l y s i s t e c h n i q u e , d i s c o v e r e d a t r a n s i e n t s p e c i e s X among t h e p r o d u c t s o b t a i n e d when cyanogen r a d i c a l s were w i t h molecular oxygen.  reacted  He s u r m i s e d t h a t X c o u l d be any one o f t h r e e  namely: NCOCN, NCNCO o r NCOOCN.  In  1970 Mayer  (18)  species,  a g i t a t e d a mixture of  s i l v e r c y a n a t e and cyanogen c h l o r i d e i n a s e a l e d tube f o r two weeks and t h e r e b y o b t a i n e d a n e a r l y q u a n t i t a t i v e y i e l d of a p o l y m e r i c  substance  w h i c h , when h e a t e d t o above 150°C, d e p o l y m e r i z e d i n t o gaseous monomer. The monomer was s u b s e q u e n t l y i d e n t i f i e d by mass s p e c t r o m e t r y as 0 2 ^ 0 . F u r t h e r i n v e s t i g a t i o n o f t h i s system r e v e a l e d t h a t the p o l y m e r i z a t i o n p r o c e s s was l a r g e l y r e v e r s i b l e , and t h a t , a l t h o u g h the e q u i l i b r i u m was on the polymer s i d e a t room t e m p e r a t u r e ,  some monomer p e r s i s t e d f o r  far  several  hours i n r a p i d l y c o o l e d s a m p l e s ; a l s o , t h a t monomer t r a p p e d as a w h i t e s o l i d below -63°C d i d not p o l y m e r i z e , w h i l e the l i q u i d at -40°C p o l y m e r ized rapidly.  On the b a s i s o f a l i m i t e d s t u d y o f the c h e m i s t r y o f  monomer, Mayer s u g g e s t e d t h a t i t was the i s o c y a n a t e the d i c y a n o - o x i d e (NCOCN).  (NCNCO) r a t h e r  the than  T h i s c o n c l u s i o n was then s u p p o r t e d by an  a n a l y s i s o f the i n f r a r e d spectrum w h i c h was i n t e r p r e t e d as i n d i c a t i n g t h a t the m o l e c u l e had a l i n e a r s t r u c t u r e i n the gas phase b u t a bent one i n the s o l i d p h a s e .  In a d d i t i o n , Mayer s p e c u l a t e d t h a t the s p e c i e s X .  d i s c o v e r e d by Basco was p r o b a b l y a l s o cyanogen  isocyanate.  175  S t i l l more r e c e n t l y , G o t t a r d i (82)  i s o l a t e d a compound from the  gaseous t h e r m a l d e c o m p o s i t i o n p r o d u c t s o f s i l v e r c y a n a t e w h i c h he  identi-  f i e d t h r o u g h mass s p e c t r o m e t r y and i n f r a r e d s p e c t r o s c o p y as b e i n g  identical  t o t h a t c h a r a c t e r i z e d by Mayer as cyanogen i s o c y a n a t e .  Despite the  t h a t G o t t a r d i ' s p r e p a r a t i o n o f NCNCO g i v e s a much s m a l l e r y i e l d  fact  than  M a y e r ' s , i t was the one t h a t was used t o o b t a i n the samples r e q u i r e d the microwave s t u d y d e s c r i b e d h e r e because i t perform.  for  i s a l s o much the e a s i e r  Only the n a t u r a l l y most abundant i s o t o p i c s p e c i e s  to  (^N^C^N^C^O)  was i n v e s t i g a t e d , a l t h o u g h samples a r t i f i c i a l l y e n r i c h e d w i t h n i t r o g e n - 1 5 , carbon-13 o r oxygen-18 s h o u l d n o t be d i f f i c u l t t o p r e p a r e , and w i l l h o p e f u l l y be s t u d i e d at some f u t u r e 6.1  Assignment of the  date.  Spectrum.  A rough p r o b a b l e s p e c t r u m was p r e d i c t e d u s i n g the f o l l o w i n g s t r u c t u r a l model:  a l i n e a r m o l e c u l e w i t h r(N-C) = 1.218 X ( a l l  reasonable three)  and r(C-O) = 1.165 A* (bond l e n g t h s as i n c h l o r i n e i s o c y a n a t e ) .  Single  t r a n s i t i o n s , each h a v i n g o n l y a second o r d e r S t a r k e f f e c t , were them e x p e c t e d at: v = 2B(J+1) W  i  t  h  .for  J->J+1  6.1  B = 2.4 GHz  A p r e l i m i n a r y e x a m i n a t i o n of the spectrum r e v e a l e d t h a t the a s s u m p t i o n of a l i n e a r m o l e c u l e was i n c o r r e c t .  Very complex groups o f s t r o n g low f i e l d  a b s o r p t i o n l i n e s were found at i n t e r v a l s o f r o u g h l y 5.3 GHz. soon r e c o g n i z e d as t y p i c a l a-type R-branch t r a n s i t i o n s of a n e a r p r o l a t e asymmetric r o t o r ; i . e .  (J-hJ+1, AK_^  a bent m o l e c u l e .  s t r a i g h t f o r w a r d t o a s s i g n J v a l u e s t o each group s i n c e : v « (B+C)(J+1) « ( 5 . 3 G H z ) ( J + l ) group  These were  I t was  = 0) then 6.2  176  Additional  c o n f i r m a t i o n o f group assignments was  c o u n t i n g the  number o f S t a r k l o b e s a s s o c i a t e d  apparent t h a t be  course o f the  initial  w i t h each of a few  s o r t i n g out  p r o c e s s , i t became  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 s were a l s o b e i n g observed between r o t a t i o n a l s t a t e s a s i g n i f i c a n t number o f d i f f e r e n t e x c i t e d The  K_^  = 1 t r a n s i t i o n s were the  These o c c u r as p a i r s s i d e of  section  by  4.1).  a s s i g n e d as  They were i d e n t i f i e d by  the  the  t o seven p r o g r e s s i v e l y  {v^  the  = 0}^  transitions  i n the  e s t i m a t e d to be  v i b r a t i o n a l states  chlorine  ± 40  cm  first  \  i n which one  excited  immediately  attained =0,  of  line. the  a few  the  isocyanate,  1,  lowest  The  to  higher assigned  by  successive  2,  3,  •••  frequency  rotational  v i b r a t i o n a l state  In a d d i t i o n ,  either  transition.  r e l a t i v e i n t e n s i t i e s of corresponding  to each ground s t a t e  v i b r a t i o n a l states  spaced on  r o u g h l y 20 MHz,were then t e n t a t i v e l y  ground and  144  of m o l e c u l e s  i n d i v i d u a l l y assigned.  weaker l i n e s spaced out  except i * £, where % d e s i g n a t e s the  From the  observed c l o s e  (see  lowest f r e q u e n c y v i b r a t i o n ; i . e . v  vibration.  Evidently  their position in  a p p r o p r i a t e ground v i b r a t i o n a l s t a t e  same t r a n s i t i o n i n e x c i t e d  e x c i t a t i o n of and  quite  states.  s t r o n g e s t component of each sub-group was  f r e q u e n c y , a t i n t e r v a l s of as  l i n e s to be  t h e i r c h a r a c t e r i s t i c Stark e f f e c t The  remaining four  first  vibrational  of s m a l l sub-groups r o u g h l y e q u a l l y  each main group.  spectrum and  selected  t h e r e were f a r more a b s o r p t i o n l i n e s i n each group than c o u l d  accounted f o r i n terms o f j u s t the  in  by  (46).  strong t r a n s i t i o n s D u r i n g the  r e a d i l y obtained  was  weak t r a n s i t i o n s were  These p r o b a b l y b e l o n g to  h i g h e r .frequency v i b r a t i o n s  excited has  been  * singly excited.  * The 365  They were not  lowest frequency i n f r a r e d cm  the  next at 455  cm  considered further.  One  such K  . =  a b s o r p t i o n r e p o r t e d by Mayer l i e s  at  1  sub-  177  group p a t t e r n has been i l l u s t r a t e d i n F i g u r e 6 . 1 . The d e t a i l e d a n a l y s i s of the main groups proved t o be c o n s i d e r a b l y more t e d i o u s because of s i g n i f i c a n t o v e r l a p p i n g of the s e t s o f a s s o c i a t e d w i t h the v a r i o u s v i b r a t i o n a l s t a t e s ( c f . better behavior of chlorine isocyanate).  transitions  the f o r t u i t o u s l y  Individual t r a n s i t i o n s belonging  t o one v i b r a t i o n a l s t a t e were found t o o c c u r a t p r o g r e s s i v e l y h i g h e r  fre-  q u e n c i e s w i t h i n c r e a s i n g K ^, w h i l e s e t s o f t r a n s i t i o n s a s s o c i a t e d  with  d i f f e r e n t v i b r a t i o n a l s t a t e s were a l s o o b s e r v e d t o s h i f t t o h i g h e r  frequencies  with increasing v .  C o n s e q u e n t l y , each main group was i n i t i a l l y  tackled  at i t s low f r e q u e n c y end s t a r t i n g w i t h the K ^ = 0 l i n e of the ground v i b r a t i o n a l s t a t e , f o l l o w e d i m m e d i a t e l y by an a t t a c k on the h i g h e r K_^  lines  o f t h i s same v i b r a t i o n a l s t a t e .  first  Next the t r a n s i t i o n s b e l o n g i n g t o the  e x c i t e d v i b r a t i o n a l s t a t e were c o n s i d e r e d , a g a i n s t a r t i n g w i t h t h e K_^ = 0 l i n e , and so o n .  The K_^ = 0 l i n e s were e a s i l y i d e n t i f i e d by t h e i r  second o r d e r S t a r k e f f e c t ;  a l l o f the h i g h e r K ^ main group  have a f i r s t o r d e r S t a r k e f f e c t .  Most o f the  found t o have a s m a l l asymmetry s p l i t t i n g . i s t i c S t a r k component b e h a v i o r  s t a t e s w i t h K_j  values greater  transitions  = 2 t r a n s i t i o n s were  T h i s and the r e s u l t i n g  ( a g a i n , see c h l o r i n e i s o c y a n a t e ,  g r e a t l y f a c i l i t a t e d t h e i r assignment.  strictly  character-  section  4.1)  T r a n s i t i o n s between r o t a t i o n a l  t h a n 2 d i d n o t e x h i b i t any such u n i q u e l y  i d e n t i f y i n g f e a t u r e s and were a c c o r d i n g l y r a t h e r d i f f i c u l t t o s o r t S e v e r a l a c c i d e n t a l c o i n c i d e n c e s of t r a n s i t i o n s b e l o n g i n g t o  out.  different  v i b r a t i o n a l s t a t e s f u r t h e r complicated t h i s confused p i c t u r e . C e n t r i f u g a l d i s t o r t i o n l e a s t squares f i t s were an i n v a l u a b l e a i d the a n a l y s i s o f t h e s e complex g r o u p s .  The r e a d i l y a s s i g n e d  =0,  in 1,  and 2 t r a n s i t i o n s were f i t t o a t r u n c a t e d Watson H a m i l t o n i a n c o n t a i n i n g the minimum number of r e q u i r e d terms  r^j  r > n  ( u s u a l l y j u s t A , B,  C, A ^ , A  J K >  v j/^* H  K  FIGURE 6.1  31480  Schematic I l l u s t r a t i o n of the Cyanogen I s o c y a n a t e  31500  31520  6. , — 5, _ s e t o f T r a n s i t i o n s , 1,6  1,5  31540  v  31560  (MHz)  V V  V V v  V  G.V.S.  1  *=  2  3  4  5  6  179  T h i s , i n t u r n , gave m o d e r a t e l y good p r e d i c t i o n s f o r the f r e q u e n c i e s of h i g h e r K_^ a-type t r a n s i t i o n s .  the  These were then e a s i l y l o c a t e d and s u c c e s s -  i v e l y added t o the l e a s t squares f i t .  I n t h i s way, a l l o f the  stronger  l i n e s b e l o n g i n g t o the a^-type R-branch groups were e v e n t u a l l y g i v e n r e a s o n able assignments. A s e a r c h f o r b-type t r a n s i t i o n s was then u n d e r t a k e n . From the d e n s i t y o f h i g h f i e l d a b s o r p t i o n l i n e s s c a t t e r e d t h r o u g h o u t t h e spectrum i t was c l e a r t h a t such t r a n s i t i o n s had t o be p r e s e n t . JQ J —  ( J - l ) ^ J _ J and J j  —  (J-l)2 j_2*  They b e l o n g t o the tx^o s e r i e s : P r e d i c t i o n s were made u s i n g  the d a t a e x t r a c t e d from the p r e c e d i n g a n a l y s e s , but t h e s e were q u i t e i n a c c u r a t e because the b-type f r e q u e n c i e s are a l l s t r o n g l y dependent on A whereas the a-type R-branch f r e q u e n c i e s are n e a r l y independent of A. tunately,  the r e l a t i v e s p a c i n g s of the l i n e s i n b o t h b-type s e r i e s  For-  are  e s s e n t i a l l y independent o f A and c o u l d t h e r e f o r e be p r e d i c t e d r e a s o n a b l y well.  A c c o r d i n g l y , assignments were made u s i n g a t r i a l and e r r o r p r o c e d u r e .  A l i k e l y l o o k i n g c a n d i d a t e f o r the f i r s t s e r i e s would be chosen from one o f the l e s s c l u t t e r e d r e g i o n s o f the spectrum and v a r i o u s p o s s i b l e a s s i g n ments t r i e d .  Then by l o o k i n g f o r a d d i t i o n a l b-types o f t h i s same s e r i e s ,  at the f r e q u e n c i e s p r e d i c t e d w i t h the t e n t a t i v e l y a s s i g n e d one i n c l u d e d i n the c e n t r i f u g a l d i s t o r t i o n l e a s t squares f i t , the c o r r e c t n e s s o f the a s s i g n ment was e a s i l y c h e c k e d .  Once t h e f i r s t s e r i e s had been c o r r e c t l y  out a s i m i l a r p r o c e d u r e would be a p p l i e d t o the second s e r i e s .  sorted  The former  y i e l d s an a c c u r a t e v a l u e f o r o n l y an e f f e c t i v e A r o t a t i o n a l c o n s t a n t ; A  = A - A .  i.e.  The l a t t e r then p e r m i t s the s e p a r a t e d e t e r m i n a t i o n of A and A .  The ground v i b r a t i o n a l s t a t e b-types were measured f i r s t , f o l l o w e d by those o f the f i r s t e x c i t e d v i b r a t i o n a l s t a t e .  F i n a l l y , an attempt was made  t o l o c a t e a few f i r s t s e r i e s b_-types f o r the second e x c i t e d v i b r a t i o n a l  180  state  (v  = 2).  A c o n s i s t e n t s e t of assignments c o u l d not be f o u n d .  was n o t d i s c o n c e r t i n g , however, t o be v e r y weak.  This  s i n c e the l i n e s sought a f t e r were e x p e c t e d  The ground and f i r s t e x c i t e d v i b r a t i o n a l s t a t e b-type  a b s o r p t i o n s were not s t r o n g ; c e r t a i n l y c o r r e s p o n d i n g j i - t y p e R-branch l i n e s . concluded that u  they were much weaker than the From the l a t t e r o b s e r v a t i o n i t  was  was s i g n i f i c a n t l y l a r g e r t h a n u . D  cl  S i n c e the a-component of the d i p o l e moment was a p p a r e n t l y r a t h e r a s e a r c h was a l s o made f o r the i n h e r e n t l y weak a-type Q-branch b e l o n g i n g t o the two s e r i e s :  J  1  1  —  J.  and J „  _ —  large,  transitions  J  With  the a i d o f what were by now v e r y good f r e q u e n c y p r e d i c t i o n s , the d e s i r e d ground v i b r a t i o n a l s t a t e a b s o r p t i o n s were e a s i l y l o c a t e d .  A few such t r a n s -  i t i o n s were a l s o o b s e r v e d f o r the f i r s t e x c i t e d v i b r a t i o n a l s t a t e .  However,  as t h e s e were v e r y weak, no attempt was made t o extend the coverage t o h i g h e r excited vibrational  states.  The a n a l y s i s scheme d e s c r i b e d above l e d t o a p p a r e n t l y r e a s o n a b l e a s s i g n ments f o r v i r t u a l l y a l l o f the s t r o n g e r , as w e l l as a l a r g e p r o p o r t i o n o f the w e a k e r ,  a b s o r p t i o n s o b s e r v e d i n t h e f r e q u e n c y range 8 - 3 7  GHz.  None-  t h e l e s s , because the assignment p r o c e s s had been based t o a l a r g e e x t e n t on the i n t e r n a l c o n s i s t e n c y o f the c e n t r i f u g a l d i s t o r t i o n l e a s t squares  fits,  i t seemed d e s i r a b l e t o o b t a i n a d d i t i o n a l independent c o n f i r m a t i o n of  the  e n t i r e scheme.  A c c o r d i n g l y , two d o u b l e resonance e x p e r i m e n t s were a t t e m p t e d .  They have been s c h e m a t i c a l l y i l l u s t r a t e d i n F i g u r e 6 . 2 . d e t a i l s were d e s c r i b e d i n s e c t i o n 3 . 5 .  The e x p e r i m e n t a l  B o t h e x p e r i m e n t s were s u c c e s s f u l  and hence c o n c l u s i v e l y v e r i f i e d the ground v i b r a t i o n a l s t a t e Then, by i n f e r e n c e , s i n c e the f i r s t e x c i t e d v i b r a t i o n a l s t a t e scheme c o m p l e t e l y p a r a l l e l e d the ground s t a t e o n e , i t correct.  assignments. analysis  t o o must be  essentially  181  FIGURE 6.2  S c h e m a t i c I l l u s t r a t i o n of the Two Microwave - Microwave Double Resonance E x p e r i m e n t s Performed on Cyanogen I s o c y a n a t e .  39  1,38  observe 16  (v = 27905.72 MHz)  0,16  observe (v = 18770.20 MHz) 15  1,14  T  38  2,36  pump  (v = 12102.40 MHz)  pump  (v = 9191.27 MHz)  15 1,15  E (16 R  E (15 R  D  = 719.973 GHz  )  = 713.305 GHz  .,)  = 701.203 GHz  1 6  1  u  E (15. K.  )  Q  1, 1 J  38  E  E  R  ( 3 9  1 38  r,(38 K  E (38 R  0  =  4 2  3 7 . 5 0 1 GHz  -,)  = 4218.787 GHz  )  = 4209.596 GHZ  Z , jo 2  )  2,37  3 ?  182  Many of the measured cyanogen i s o c y a n a t e a b s o r p t i o n s were o b s e r v e d be r a t h e r b r o a d .  to  A few o f the a^-type R-branch t r a n s i t i o n s had n o t i c e a b l y  asymmetric l i n e shapes w i t h f u l l w i d t h s at h a l f h e i g h t o f o v e r 1 MHz. C l e a r l y b o t h e f f e c t s may be a t t r i b u t e d t o the presence o f  unresolved  m u l t i p l e t s t r u c t u r e produced by 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 c o u p l i n g :  The  two n i t r o g e n - 1 4 n u c l e i cause each r o t a t i o n a l t r a n s i t i o n t o s p l i t i n t o a number o f c l o s e l y spaced components w h i c h , under the e x p e r i m e n t a l c o n d i t i o n s used h e r e , are c o l l i s i o n broadened i n t o an aggregate a b s o r p t i o n .  With  s l i g h t l y higher resolution i t  the  s h o u l d be p o s s i b l e t o s p l i t some o f  b r o a d e s t l i n e s i n t o t h e i r h y p e r f i n e components and hence d e t e r m i n e  the  n i t r o g e n 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 . 6.2  D e t e r m i n a t i o n o f M o l e c u l a r C o n s t a n t s from the Microwave  Spectrum.  D u r i n g the p r e l i m i n a r y s t a g e s o f t h i s work i t became q u i t e t h a t cyanogen i s o c y a n a t e had l a r g e c e n t r i f u g a l d i s t o r t i o n . a p l o t o f the f r e q u e n c i e s  (corrected  R-branch, ground v i b r a t i o n a l s t a t e , F i g u r e 6.3)  f o r asymmetry)  In  apparent  particular,  o f the J = 5-»-6 a-type 2  t r a n s i t i o n s v s . K_^  (reproduced  gave a smooth c u r v e r a t h e r than the e x p e c t e d s t r a i g h t  T h i s i n d i c a t e s t h a t terms i n P^ make a s i g n i f i c a n t c o n t r i b u t i o n t o t o t a l rotational energies.  in  *  line. the  Consequently, although a planar s t r u c t u r e  seemed  t o be a r e a s o n a b l e s u p p o s i t i o n , no attempt was made t o f i t the spectrum t o a four tau Hamiltonian ( i . e . f o r m a l i s m o f Watson was u s e d . terms were c o n s i d e r e d .  equation 2.18).  Rather,  the more  general  C o n t r i b u t i o n s from s e x t i c , as w e l l as q u a r t i c ,  A thorough t r e a t m e n t was a p p l i e d t o b o t h the ground  and f i r s t e x c i t e d v i b r a t i o n a l s t a t e s p e c t r a .  F o r the h i g h e r e x c i t e d v i b -  r a t i o n a l s t a t e s , where fewer t r a n s i t i o n s were a v a i l a b l e , i t was  necessary  * For a n e a r p r o l a t e asymmetric t o p , w i t h moderate c e n t r i f u g a l d i s t o r t i o n , such a p l o t s h o u l d g i v e a v e r y good s t r a i g h t l i n e , a t l e a s t f o r l o w i s h J . T h i s i s the observed b e h a v i o r f o r c h l o r i n e i s o c y a n a t e .  183  FIGURE 6.3  P l o t of the F r e q u e n c i e s  ( C o r r e c t e d f o r Asymmetry) o f  a-Type R-Branch T r a n s i t i o n s o f NCNCO ( G . V . S . ) v s . K  31770 +0  1 5  i  1  1  10  15  .  20  2  the .  r  25  184  t o use a much s i m p l i f i e d p r o c e d u r e . i m m e d i a t e l y b e l o w , the l a t t e r ,  The former a n a l y s i s i s  discussed  toward the end of t h i s s e c t i o n .  To b e g i n w i t h a s t r i c t l y f i r s t o r d e r t r e a t m e n t , i n p r i n c i p l e t o t h a t d e s c r i b e d i n s e c t i o n 4 . 2 , was a t t e m p t e d . o r d e r H a m i l t o n i a n was H  3  identical  I n t h i s c a s e , the z e r o t h  as d e f i n e d by e q u a t i o n 2 . 1 9 b , and t h e p e r t u r -  b a t i o n H a m i l t o n i a n was H, + H d  as d e f i n e d by e q u a t i o n s 2.19c and 2 . 2 2 . s  •  M  The 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 i e s were then g i v e n by e q u a t i o n s 2.23c and 2.23d.  As b e f o r e , l e a s t squares f i t s were made t o the d i f f e r e n c e s v ^  "  where v  i s a r i g i d r o t o r frequency c a l c u l a t e d using t r i a l r o t a t i o n a l  con-  s t a n t s and v ^  is  corresponding observed frequency.  t n e  v a r i a t i o n s o f the r o t a t i o n a l c o n s t a n t s were a l l o w e d .  It  Again, was  d i s c o v e r e d t h a t t h e r e were i n s u f f i c i e n t t r a n s i t i o n s a v a i l a b l e  linear  immediately to permit  the d e t e r m i n a t i o n of a l l of the q u a r t i c and s e x t i c c o n s t a n t s . of e l i m i n a t i o n ( l i k e  v  By a p r o c e s s  t h a t d e s c r i b e d i n s e c t i o n 5.2 f o r i s o c y a n i c a c i d )  the  i n d e t e r m i n a t e s e x t i c c o n s t a n t s were i d e n t i f i e d and then removed from the fit;  a l l f i v e q u a r t i c c o n s t a n t s were r e q u i r e d .  Once an a p p r o p r i a t e ,  c a t e d , v e r s i o n o f the H a m i l t o n i a n had been a r r i v e d a t ,  the l e a s t  f i t was r e p e a t e d once m o r e , u s i n g t h e most r e c e n t v a l u e s o f the c o n s t a n t s , t o ensure t h a t a s t a b l e s o l u t i o n had been f o u n d . o f such a f i r s t o r d e r a n a l y s i s ,  trun-  squares rotational  The end r e s u l t  c a r r i e d out on t h e ground v i b r a t i o n a l  state  spectrum of cyanogen i s o c y a n a t e , i s p r e s e n t e d i n T a b l e 6 . 1 . Next the d e r i v e d f i r s t o r d e r c o n s t a n t s were used i n the f u l l m a t r i x scheme t o r e - c a l c u l a t e t h e f r e q u e n c i e s o f a l l of the observed t r a n s i t i o n s . In most i n s t a n c e s , the c o r r e s p o n d i n g " e x a c t " and f i r s t o r d e r were found t o be i d e n t i c a l . series ^ j J  observed.  ^ —  (J-l)  Evidently,  2  j _  However, 2  a n c  *  J  2  J  frequencies  f o r t r a n s i t i o n s b e l o n g i n g t o the two  2 —  J  2  J  1  s  m  a  H  d i s c r e p a n c i e s were  f o r these t r a n s i t i o n s , the o f f - d i a g o n a l c o n t r i b u t i o n s  r  185  TABLE 6.1  R o t a t i o n a l C o n s t a n t s 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 of Cyanogen I s o c y a n a t e i n the Ground V i b r a t i o n a l S t a t e . 3  First SDFIT No.  J  A  A  JK  l  A xlO K  6 xl0 R  h  xl0 j X  61  61  74358.668 ± 0.081  74358.690 ± 0.081  2699.0365 ± 0.0034  2699.0367 ± 0.0033  2597.8656 ± 0.0031  2597.8663 ± 0.0031  1.0815 ± 0.0117  1.0904 ± 0.0116  - 5 . 2 7 0 2 ± 0.0071  - 5 . 2 7 1 3 ± 0.0071  8.6249 ± 0.0038  8.6254 ± 0.0038  2.0580 ± 0.0118  2.0694 ± 0.0117  2.7517 ± 0.0736  2.6929 ± 0.0732  -1.5978 ± 0.0325  -1.6024 ± 0.0323  ° -1 3  6 xlO  H j  0.096  ° X 1  10  Exact  0.096  Trans.  x  Order  4  2  8  - 1 . 9 6 2 ± 0.193  -0.0535 ± 0.192  9  2.590 ± 0.324  1.026 ± 0.322  Large C o r r e l a t i o n s p(Aj - A ) J K  p(6j  (|p  >0.9)  = 0.908; p ( A  - hj) = 0 . 9 8 6 ; p ( 6  K  J K  - H^)  - hj)  = 0 . 9 2 7 ; p(&  3  -0.930  Measured i n MHz. S t a n d a r d D e v i a t i o n of the  Fit.  Number o f t r a n s i t i o n s used i n the Standard e r r o r s .  3  analysis.  - 6 ) R  = -0.968  186  o f the q u a r t i c  (and 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 , i n the r i g i d  asymmetric  r o t o r b a s i s , were n o t i n s i g n i f i c a n t . These " h i g h e r o r d e r " e f f e c t s were accounted f o r u s i n g an p r o c e d u r e f i r s t suggested by P i e r c e et a l . d e v e l o p e d by H e l m i n g e r e t a l .  (34,184).  (183)  and s u b s e q u e n t l y  In t h i s , the d i f f e r e n c e  the c a l c u l a t e d f i r s t o r d e r and " e x a c t " f r e q u e n c i e s respectively)  iterative  ( f^ V  r s t  a n  ^  v  further between  e x  act  of a g i v e n t r a n s i t i o n i s t a k e n t o be the " h i g h e r o r d e r "  c e n t r i f u g a l d i s t o r t i o n c o n t r i b u t i o n t o the c o r r e s p o n d i n g observed The c o r r e c t e d o b s e r v e d f r e q u e n c i e s , v ^ g ' j f i r s t order theory.  t h e n r e - a n a l y s e d u s i n g the  a r e  That i s , w i t h the d i s t o r t i o n e n e r g i e s c a l c u l a t e d  e q u a t i o n s 2.23c and 2 . 2 3 d , a l e a s t squares f i t i s made t o the corr , v , - v where: obs r  corr v, = v , obs  frequency.  , - (v  obs  - v , r  exact  differences  r i 6.3  -v .)  first  The r e s u l t i n g new c o n s t a n t s are t h e n i n t u r n used t o r e - c a l c u l a t e and the c y c l e i s r e p e a t e d .  The v . f  from  the  v  ._ are always t a k e n t o be the most  e  x  a  c  t  recent  X. X ITS L  set of f i r s t order frequencies.  The v  r  are c o n t i n u o u s l y r e f i n e d by i n c r e -  m e n t a l a d j u s t m e n t s of the i n p u t r o t a t i o n a l c o n s t a n t s .  F o r cyanogen  c y a n a t e s t a b l e r e s u l t s were o b t a i n e d a f t e r two i t e r a t i o n s .  The f i n a l  o f r e f i n e d ground v i b r a t i o n a l s t a t e c o n s t a n t s i s compared w i t h the ponding s e t o f f i r s t o r d e r c o n s t a n t s i n T a b l e 6 . 1 .  treatment and H  set  corres-  I t w i l l be n o t e d  the o f f - d i a g o n a l c o r r e c t i o n s have had a n e g l i g i b l e e f f e c t on the c o n s t a n t s and most o f the d i s t o r t i o n c o n s t a n t s .  iso-  that  rotational  C l e a r l y , i n the f i r s t  order  the " h i g h e r o r d e r " e f f e c t s have been l a r g e l y absorbed i n t o the  hj  terms. J  The f i r s t e x c i t e d v i b r a t i o n a l s t a t e a n a l y s i s p a r a l l e l e d the ground s t a t e one.  The r e s u l t s have been c o l l e c t e d i n T a b l e  6.2.  F o r the second and t h i r 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 , where o n l y a few  187  TABLE 6.2  R o t a t i o n a l Constants  of Cyanogen I s o c y a n a t e i n the F i r s t  First  Excited Vibrational  Order  Exact 0.126  35  35  A,  82777.563 ± 0.160  82777.808 ± 0.150  B  2704.3294 ± 0.0060  2704.3222 ± 0.0057  2599.7717 ± 0.0058  2599.7778 ± 0.0055  1.2457 ± 0.0189  1.2401 ± 0.0177  -6.7709 ± 0.0129  -6.7712 ± 0.0121  15.0445 ± 0.0079  15.0581 ± 0.0074  2.0952 ± 0.0100  2.1701 ± 0.0094  7.6053 ± 0.1361  7.1198 ± 0.1273  -3.0256 ± 0.0554  -3.0275 ± 0.0520  No.  A  Constants  0.134  SDFIT  V  and C e n t r i f u g a l D i s t o r t i o n  Trans.'  1  JK  1  0  X 1  °  ]  -1  A xl0 K  Sj-xlO  4  6 xl0  2  K  H 10  - 1 . 5 3 6 ± 0.333  8  j X  Large C o r r e l a t i o n s p  (  A  J  " JK A  }  =  .  0.642 ± 0.312  (|p[>0.9) °'  9 0 1 ;  p ( A  JK  " KJ H  )  =  °'  9 4 9 ;  Measured i n MHz. S t a n d a r d D e v i a t i o n o f the  Fit.  Number o f t r a n s i t i o n s used i n the Standard e r r o r s .  analysis.  p ( < S  J  _  V  =  -°'  9 7 8  3  State.  188  a-type R-branch t r a n s i t i o n s were a v a i l a b l e ,  the c e n t r i f u g a l  a n a l y s e s were n e c e s s a r i l y r a t h e r l i m i t e d i n s c o p e .  They y i e l d e d  v a l u e s f o r the B and C r o t a t i o n a l c o n s t a n t s , b u t o n l y v e r y v a l u e s o f A.  distortion accurate  approximate  The l a t t e r was to be e x p e c t e d o f course due t o the l a c k of  any b-type t r a n s i t i o n s .  The i n c l u d e d d i s t o r t i o n c o n s t a n t s were A , A JK  J  and H  .  S i n c e none o f the observed t r a n s i t i o n s were of the type p r e -  v i o u s l y found t o have s i g n i f i c a n t o f f - d i a g o n a l c o n t r i b u t i o n s , a f i r s t t r e a t m e n t was used i n each c a s e . 6.3.  order  The r e s u l t s have been c o l l e c t e d i n T a b l e  A few a d d i t i o n a l v e r y weak a b s o r p t i o n s , n o t r e p o r t e d h e r e , were  tentatively  a t t r i b u t e d to s t i l l higher e x c i t e d v i b r a t i o n a l s t a t e s .  attempt was made t o d e t e r m i n e m o l e c u l a r c o n s t a n t s from t h e s e  No  measurements  because o f the tenuous n a t u r e of the a s s i g n m e n t s . It  s h o u l d be p o i n t e d out t h a t one o f the s e x t i c c o n s t a n t s , namely H , K  n e g l e c t e d i n the ground and f i r s t e x c i t e d v i b r a t i o n a l s t a t e a n a l y s e s , n o t l i k e l y t o be c o m p l e t e l y i n s i g n i f i c a n t . t h e A and A  Rather,  is  i t was i n s e p a r a b l e  from  c o n s t a n t s because o f an i n s u f f i c i e n c y o f d i f f e r e n t t y p e s o f  transitions.  The a d d i t i o n a l b-type t r a n s i t i o n s w h i c h are r e q u i r e d t o  mine IL^ l i e i n the mm-wave r e g i o n . numbers r e p o r t e d here f o r A and h  v  The net r e s u l t of t h i s i s t h a t are n o t e x a c t l y c o r r e c t .  deter-  the  They a r e  in  IX ~* f a c t r e a l l y v a*l u e s of the e f f e c t i v e A s A A„ - - 4Hj, 5 1 ^++ •••• A*, — •• T  An e s t i m a t e o f H f i r s t s u g g e s t e d by P o l o  constants A  * and A  where:  6.4b 6 . 4a  may be o b t a i n e d by d o i n g a v e r y s i m p l e c a l c u l a t i o n (165).  T h i s a u t h o r has proposed t h a t f o r q u a s i -  l i n e a r m o l e c u l e s the r o t a t i o n about the l e a s t moment o f i n e r t i a w i l l be so s t r o n g l y c o u p l e d t o the b e n d i n g v i b r a t i o n s t h a t i t i s p r o b a b l y b e s t  to  189  TABLE 6.3  R o t a t i o n a l Constants 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 Cyanogen I s o c y a n a t e i n H i g h e r E x c i t e d V i b r a t i o n a l S t a t e s .  Second (v SDFIT  B  C  V  j X  10  15  12  1  2711.191 ± 0.012  2601.244 ± 0.017  2601.659 ± 0.012  0.931 ± 0 . 1 8 0  1.333 ± 0.189  - 9 . 1 4 9 ± 0.029  -13.361 ± 0.052  - 6 . 8 2 ± 0.17  -19.20 + 0.50  3  Large C o r r e l a t i o n s v  a. D  £  2: p ( A  J K  117342.8 ± 4718.5  b  2708.320 + 0.014  3  A_ x l O JK R^xlO  = 3)  0.083  90431.5 ± 3 5 9 0 . l  V  V  A  T h i r d (v  0.127  No. T r a n s . A  = 2)  of  (|p|>0.9)  - H ) R J  = 0.977; v  £  = 3 : p(A  JK " KJ> = ° ' H  9 8 6  Measured i n MHz. Standard e r r o r s .  TABLE 6.4  Cyanogen I s o c y a n a t e C o n s t a n t s  . Calculated^ A K E K \ - \ v  A  5  88.25  3  Calculated Using P o l o ' s  Observed 86.254  Corrected  Relations c  87.824  0.314 9008.5  o  8419.2 74358.690  74359.946  Measured i n MHz. Calculated using equations 6 . 5 . Observed c o n s t a n t s c o r r e c t e d u s i n g e q u a t i o n s 6.4 and the c a l c u l a t e d H,  190  t h i n k o f the r o t a t i o n as c r e a t i n g an e f f e c t i v e motions; j u s t if  as i s done f o r d i a t o m i c m o l e c u l e s  p o t e n t i a l f o r the (185).  It  vibrational  follows  that,  i s the v i b r a t i o n by w h i c h the m o l e c u l e can a c h i e v e t h e l i n e a r c o n -  f i g u r a t i o n , and a l l o t h e r degrees o f freedom are n e g l e c t e d , t h e n i n harmonic a p p r o x i m a t i o n A  (165):  si 4A /CLV  6.5a  3  Js.  O  - A  Q  the  D  — bA^/o^ + 60A /to 3  F o r cyanogen i s o c y a n a t e , i f i t  )  2  6.5c  j  i s assumed t h a t co, = co. = 144 cm * and A D  IL  Q  i s t a k e n t o be 74358.6 MHz then one o b t a i n s the r e s u l t s g i v e n i n T a b l e The c a l c u l a t e d A^ and A^ - A  values  q  w i t h t h e e x p e r i m e n t a l numbers.  a r e seen t o be i n v e r y good agreement  However,  i n view of the l a r g e  uncertainty  i n o)^ and t h e a p p r o x i m a t e n a t u r e o f the c a l c u l a t i o n t h i s must be as f o r t u i t o u s . H  Still,  it  seems r e a s o n a b l e t o assume t h a t t h e  value i s of s i m i l a r accuracy.  It  results.  regarded  calculated  A c c o r d i n g l y t h i s number has been used t o  convert the e x p e r i m e n t a l l y determined A accurate  6.4.  q  and  v a l u e s i n t o h o p e f u l l y more  The c o r r e c t i o n s , a l t h o u g h s m a l l , a r e n o t i n s i g n i f i c a n t .  i s l i k e l y t h a t H^ i s much l a r g e r than any o f the o t h e r s e x t i c  t o r t i o n c o n s t a n t s , j u s t as A  dis-  i s much l a r g e r than any of the q u a r t i c d i s K  tortion constants.  H e n c e , the o t h e r n e g l e c t e d s e x t i c d i s t o r t i o n  have p r o b a b l y n o t p r o d u c e d a s i m i l a r b i a s s i n g o f any o f the  constants  rotational  constants. 6.3  The M o l e c u l a r S t r u c t u r e  o f Cyanogen  Isocyanate.  The moments o f i n e r t i a and the i n e r t i a l d e f e c t o f cyanogen i n i t s ground v i b r a t i o n a l s t a t e are p r e s e n t e d i n T a b l e 6 . 5 .  isocyanate  The s m a l l  p o s i t i v e A° i s c o n s i s t e n t w i t h a p l a n a r e q u i l i b r i u m s t r u c t u r e .  Although  191  TABLE 6.5  The Moments o f I n e r t i a and the I n e r t i a l D e f e c t o f Cyanogen I s o c y a n a t e i n the Ground V i b r a t i o n a l S t a t e . 1° = 6.7966622 a 1° = 187.24862 D  1° = 194.54077 c A° = 0.49548  a  Measured i n a . m . u . A ^ .  TABLE 6.6  The M o l e c u l a r S t r u c t u r e of Cyanogen I s o c y a n a t e .  Assumed  Calculated  r(N-CNCO) = 1.164 X  r(NC-NCO) = 1.283 X  r(NCN-CO) = 1.218 A  Z-(CNC) = 140°  r(NCNC-O) = 1.165 A Z.(NCN) = 180° A(NCO) = 180°  192 p l a n a r m o l e c u l e s t y p i c a l l y have i n e r t i a l d e f e c t s o f the o r d e r of 0.1  a.m.u.A^  ( 5 9 , 6 1 ) , l a r g e r v a l u e s , s i m i l a r t o t h a t r e p o r t e d here f o r NCNCO, are n o t unknown.  F o r example, s u l f u r d i c y a n i d e , w h i c h has been c l e a r l y shown t o  be a p l a n a r m o l e c u l e , has an i n e r t i a l d e f e c t o f 0.4869 a . m . u . X ground v i b r a t i o n a l s t a t e  (162).  in  its  Such an o v e r s i z e d A ° i s o f c o u r s e t o be  e x p e c t e d whenever the m o l e c u l e i n q u e s t i o n has a low f r e q u e n c y bending v i b r a t i o n .  2  in-plane  In the p r e s e n t c a s e , the observed A ° , i n c o n j u n c t i o n  w i t h the approximate Herschbach and L a u r i e e x p r e s s i o n ( e q u a t i o n 2 . 5 7 ) , an e s t i m a t e f o r OJ^ o f 136 cm  yields  T h i s i s i n e x c e l l e n t agreement w i t h the -1 *  v a l u e p r e v i o u s l y deduced from r e l a t i v e i n t e n s i t y measurements  (144 ± 40 cm  ).  A d d i t i o n a l s u p p o r t f o r the p l a n a r s t r u c t u r e h y p o t h e s i s i s p r o v i d e d by the complete absence o f any c^type t r a n s i t i o n s i n the observed s p e c t r u m .  How-  e v e r , t h e s e t r a n s i t i o n s would a l s o be u n o b s e r v a b l y weak f o r a s l i g h t l y n o n p l a n a r m o l e c u l e w i t h an a p p r o p r i a t e l y s m a l l y »  T h u s , a l t h o u g h the p r e s e n t l y  c  a v a i l a b l e e v i d e n c e s t r o n g l y s u g g e s t s t h a t cyanogen i s o c y a n a t e i s a p l a n a r m o l e c u l e , a d e f i n i t i v e p r o o f must a w a i t the s t u d y o f f u r t h e r i s o t o p i c species. I n the i n t r o d u c t i o n t o t h i s c h a p t e r i t was mentioned t h a t Mayer s t r o n g l y f a v o r e d the i s o c y a n a t e  (NCNCO) r a t h e r than the a l t e r n a t i v e p o s s i b l e c y a n a t e  (NCOCN) c o n f i g u r a t i o n f o r the s t r u c t u r e o f "cyanogen i s o c y a n a t e " . p r e s e n t microwave s t u d y s u p p o r t s t h i s c o n t e n t i o n : the c y a n a t e ,  and p l a n a r , t h e n i t would have  If  The  the m o l e c u l e was  symmetry and hence  really  either  a- o r b-type t r a n s i t i o n s , b u t n o t b o t h . A complete d e t e r m i n a t i o n of the m o l e c u l a r s t r u c t u r e i s c l e a r l y impos-  * I t has been assumed t h r o u g h o u t t h a t the l o w e s t f r e q u e n c y v i b r a t i o n i s i n f a c t an i n - p l a n e b e n d i n g v i b r a t i o n ; s p e c i f i c a l l y , the one t h a t i n v o l v e s l a r g e l y a d e f o r m a t i o n o f the CNC a n g l e (see p r e v i o u s s e c t i o n ) .  FIGURE 6 . 4  The M o l e c u l a r S t r u c t u r e of Cyanogen I s o c y a n a t e .  194  s i b l e without a d d i t i o n a l i s o t o p i c data.  I n f a c t , o n l y two u s e f u l p i e c e s  o f i n f o r m a t i o n are c u r r e n t l y a v a i l a b l e , namely 1° and 1 ° a  b  (1° = 1° + I.° + A ° ) . c  a  b  Hence at most o n l y two s t r u c t u r a l parameters may be c a l c u l a t e d , and t h e n o n l y a f t e r a l l o f the r e m a i n i n g ones have been g i v e n assumed v a l u e s .  The  two p a r a m e t e r s w h i c h a r e l i k e l y t o be t h e most d i f f i c u l t t o e s t i m a t e  accur-  a t e l y are the n o m i n a l l y s i n g l e NC-NCO bond l e n g t h and the CNC a n g l e . A c c o r d i n g l y t h e s e were chosen as the two a l l o w e d v a r i a b l e s .  A solution  o f the moment of i n e r t i a e q u a t i o n s was then o b t a i n e d a f t e r the f o l l o w i n g assumptions had been made: chains,  (3)  (1)  a p l a n a r m o l e c u l e , (2)  l i n e a r NCN and NCO  c y a n i d e and i s o c y a n a t e bond l e n g t h s the same as i n cyanogen  a z i d e (154) and c h l o r i n e i s o c y a n a t e r e s p e c t i v e l y  (44).  Since a l l three of  the assumed i n t e r n u c l e a r d i s t a n c e s a r e a s s o c i a t e d w i t h m u l t i p l e b o n d s , i s l i k e l y t h a t t h e numbers used h e r e are good a p p r o x i m a t i o n s t o the NCNCO bond l e n g t h s .  it  true  The a s s u m p t i o n o f l i n e a r NCN and NCO c h a i n s i s n o t so  e a s i l y j u s t i f i e d because bends a t c a r b o n o f over 5 ° a r e w e l l known f o r b o t h cyanides  (162)  and i s o c y a n a t e s  (44).  T h i s g i v e s r i s e t o an a d d i t i o n a l u n -  c e r t a i n t y i n the c a l c u l a t e d p a r a m e t e r s , e s p e c i a l l y the CNC a n g l e .  The  r e s u l t s have been c o l l e c t e d i n T a b l e 6 . 6 .  The m o l e c u l a r s t r u c t u r e has been  i l l u s t r a t e d w i t h a s c a l e drawing i n F i g u r e  6.4.  6.4  D i p o l e Moment Measurements. The measurement o f the d i p o l e moment of cyanogen i s o c y a n a t e was u n d e r -  t a k e n w i t h the p r i o r knowledge t h a t t h e r e were nonzero components o f u a l o n g a t l e a s t t h e a- and b - p r i n c i p a l i n e r t i a l a x e s .  T h i s was c l e a r l y  dent t h r o u g h the o b s e r v a t i o n of b o t h a- and b_-type t r a n s i t i o n s . component o f the d i p o l e moment was presumed to be z e r o . molecule  must be i d e n t i c a l l y z e r o by symmetry.  evi-  The c_-  For a t r u l y planar  At w o r s t , NCNCO can be  o n l y s l i g h t l y n o n p l a n a r , i n w h i c h case u^.would be nonzero b u t v e r y  small.  195  The i n d i v i d u a l S t a r k components of the low J a-type R-branch i t i o n s were found t o be e a s i l y  resolvable.  Unfortunately  a l l of  transthese  have f i e l d i n d u c e d f r e q u e n c y s h i f t s w h i c h a r e s t r o n g l y dependent on u 3.  b u t w h i c h a r e n e a r l y independent o f u^.  Hence, they were s u i t a b l e  f o r the d e t e r m i n a t i o n o f t h e former component. made on f o u r such l o b e s , 2  2  0 , 2 1,1 -  Vl'  M  J  S t a r k measurements were  namely: =  1 1  ^ . O ' J " M  only  1,2- 1,1' J  2  0  1  3  0,3 -  M  2  0,2>  M  = °  J -  0  These were s e l e c t e d from amongst t h e many a v a i l a b l e s i m i l a r a-type l o b e s on the b a s i s o f the f o l l o w i n g c r i t e r i a : second o r d e r , S t a r k e f f e c t ,  ( 1 ) they e x h i b i t a l a r g e ,  (2) they occur i n a convenient  strictly  region of  the  s p e c t r u m (X- and P-band) and ( 3 ) t h e y a r e n o t i n t e r f e r e d w i t h by any o t h e r a b s o r p t i o n s o v e r the range o f f i e l d s u s e d . T h e n , i n o r d e r t o o b t a i n a good v a l u e f o r measure the S t a r k e f f e c t  i t was n e c e s s a r y a l s o  o f a b-type t r a n s i t i o n .  to  As w i t h i s o c y a n i c a c i d ,  none o f the b-type t r a n s i t i o n s o c c u r r i n g i n the f r e q u e n c y range o f o u r s p e c t r o m e t e r had r e s o l v a b l e S t a r k  components and c o n s e q u e n t l y t h e r e was no  a l t e r n a t i v e b u t t o make use o f an a g g r e g a t e l o b e . f o r t r a n s i t i o n s b e l o n g i n g t o t h e s e r i e s JQ J — and f a s t e s t o f the i n d i v i d u a l S t a r k  A g a i n , i t was found t h a t  (J-l)^ j  j  t  n  e  components move out n e a r l y  w i t h i n c r e a s i n g e l e c t r i c f i e l d g i v i n g r i s e to q u i t e r e s p e c t a b l e aggregate l o b e s . 15Q  —  14^ ^  Several d i f f e r e n t  together looking  t r a n s i t i o n s were c o n s i d e r e d b e f o r e  one was s e l e c t e d as the b e s t c a n d i d a t e .  of a l l the a v a i l a b l e b - t y p e s ,  strongest  This t r a n s i t i o n ,  not o n l y has the l a r g e s t S t a r k e f f e c t  a l s o one of the s h a r p e s t a g g r e g a t e l o b e s .  the  but  The l a t t e r i s due t o a f o r t u i t o u s  p a r t i a l c a n c e l l a t i o n o f the M j dependence o f the i n d i v i d u a l S t a r k  components.  196  In the g e n e r a l e x p r e s s i o n f o r the f r e q u e n c y s h i f t of these (equation 6.6e),  the M  dependent u  components  term i s o f s i m i l a r magnitude but  o p p o s i t e s i g n t o the M^ dependent y^ t e r m .  A t f i e l d s o f up t o  thousand V o l t s / c m t h i s aggregate l o b e i s a c t u a l l y narrower  several  than the  v i d u a l q u a d r u p o l e broadened S t a r k components o f some of the low J R-branch  indi-  a-type  transitions.  E x p r e s s i o n s f o r the average f r e q u e n c y s h i f t s of the v a r i o u s S t a r k comp o n e n t s , c o r r e c t t o second o r d e r , were o b t a i n e d u s i n g the p r o c e d u r e i n s e c t i o n 5.4. [ A v ]U 9  Z  [Av]  2 Z  [Av]  These  ,  i  _ 6  HE)  =  q  6  1,0' ,  e  r  0,3  5  0,15  J  6  0,2  , U  1  -  " ~ MjJ 1.1771xlO" 1  6  b  ,  1,14  2  2  J  = F(E)|(-0.02751xl0  6.6b  2  _ 6  2  o  6.6c  2  - 0.2066x10 y 6  }  2  + 0.29069xl0 M )y  -6  _ 8  + V )/r 2  m  - 6  - 9.8400xl0 M )y } - 8  2  J  2  b'  2  c  o'  m  are i n v o l t s , r  v vs.  These were made e n t i r e l y i n c e l l 1.  2 V  Q  2 +  v  m  w a s  2  '  c  2  a  - 6.6e 6.7  i s i n cm and y , a'  The cyanogen i s o c y a n a t e S t a r k measurements have been c o l l e c t e d Table 6.7.  6.6d  D  J  and the Av are measured i n MHz i f V , V y^ are i n Debyes.  n  a  7(E) = ( 0 . 5 0 3 4 4 ) ( V  e  6.6a  2  b  2  = F(£){-4.7945xl0"" y  n  + (17.486xl0 h  2  6  3  -v~6_ 2 , ,.-6 2 « F ^ ^ S . l S S x l O " ^ + 0.2674xl0 u }  Q  x  n  [Av].  w  6  ++ 11.5841x10 . 5 8 4 1 x l 0 " y V[ [  2  U  1,1  J  == FF(( £ f f))J|2 3 ..337744xx1 l00 yy  ++1 1  , , 0 — 1 . . , 0 = F(£')]23.599xlC" {23.599xl<f\£ 1,1 11, , 2i. '  2  [Av]_  are:  , Vl'  + 1  0,2 "  described  in  F o r each l o b e , a p l o t o f  found t o g i v e the e x p e c t e d s t r a i g h t l i n e ;  * The OCS c a l i b r a t i o n d a t a and the c a l c u l a t e d e f f e c t i v e s p a c i n g (r^) were g i v e n p r e v i o u s l y ( s e c t i o n 5 . 4 ) .  two such p l o t s  septum-cell w a l l  197  TABLE 6.7 2  S t a r k Measurements on Cyanogen I s o c y a n a t e . —  1  0,2  v  a  A  v  a  M  j  = ±1  2  o,r Frequency^  (v)  1,2  M  V  V  J  =  0  Frequency  m  o  15  100  10595.42  10  50  10495.40  10  130  10596.73  10  100  10496.76  10  160  10598.11  10  150  10498.75  10  ' 230  10602.60  10  180  10500.47  10  260  10605.14  10  220  10503.24  10  290  10607.90  10  250  10505.60  10  320  10611.02  10  280  10508.31  9  350  10614.45  10  310  10511.45  10  380  10618.19  10  340  10514.55  10  410  10622.18  10  370  10518.36  10  440  10626.54  10  400  10522.25  10  470  10631.08  10  500  10636.03  2  1,1  —  1  m  i,o  ,  M  j  o  = 0  V m  V  10  100  10698.74  10  290  10711.05  10  150  10700.87  10  320  10714.22  10  200  10703.77  10  360  10719.00  10  230  10705.95  10  400  10723.98  10  260  10708.30  Frequency o  ("v)  (v)  V  m  V  Frequency o  (v)  198  TABLE 6.7 3 V m  continued  0,3  —  2  0,2'  V  15  o 260  12.5  M  J  = 0  Frequency  1  (v)  V m  5  0,15V  1 4  1,14'  M  J  Frequency  15887.89  20  o 200  300  15887.15  20  300  12794.93  12.5  350  15885.99  20  400  12795.24  10  400  15884.64  20  500  12795.60  10  450  15883.11  20  600  12796.07  10  500  15881.44  20  700  12796.62  12.5  550  15879.59  20  800  12797.26  12.5  600  15877.52  20  900  12797.99  12.5  650  15875.37  20  1000  12798.84  12.5  700  15872.90  20  1100  12799.77  12.5  750  15870.32  20  1200  12800.80  12.5  790  15868.25  20  1300  12801.87  12.5  830  15865.87  20  1400  12803.03  12.5  870  15863.42  20  1500  12804.31  12.5  910  15860.87  20  1600  12805.63  12.5  950  15858.24  20  1700  12807.06  12.5  990  15855.44  20  1800  12808.66  12.5  1030  15852.60  20  1900  12810.21  Measured i n  Volts.  Measured i n MHz.  12794.73  199  have been r e p r o d u c e d i n F i g u r e s 6.5 and 6 . 6 .  A l e a s t squares f i t t i n g p r o -  cedure was used t o o b t a i n " b e s t v a l u e s " f o r the s l o p e and i n t e r c e p t o f each of t h e s e l i n e s .  The numbers are p r e s e n t e d i n T a b l e 6 . 8 .  I t w i l l be n o t e d  t h a t f o r a l l f i v e t r a n s i t i o n s the i n t e r c e p t i s i n good agreement w i t h the zero f i e l d frequency. F i f t e e n p a i r s of u  a  and y,  b  S t a r k c o e f f i c i e n t s ( T a b l e 6.8)  v a l u e s were c a l c u l a t e d from the measured  by assuming t h a t the peak maximum i n t h e  a g g r e g a t e S t a r k l o b e c o r r e s p o n d e d t o each o f the p o s s i b l e M  values.  A  l e a s t squares f i t t i n g p r o c e d u r e was used f o r t h i s p u r p o s e , w i t h the b-type S t a r k c o e f f i c i e n t s c a l e d by a f a c t o r of 50 t o make i t of s i m i l a r magnitude t o the ^ - t y p e o n e s .  Such " w e i g h t i n g " was n e c e s s a r y t o take f u l l  advantage  o f the a c c u r a t e l y d e t e r m i n e d , but s m a l l , b-type S t a r k c o e f f i c i e n t . r e s u l t s have been c o l l e c t e d i n T a b l e 6 . 9 .  The c h o i c e o f  c r i t i c a l h e r e t h a n i t was f o r i s o c y a n i c a c i d .  The  i s much l e s s  A v a l u e g r e a t e r than 10 i s  c o m p l e t e l y u n r e a s o n a b l e , and a l l v a l u e s l e s s t h a n 10 g i v e v e r y s i m i l a r answers.  A g a i n , a l o w i s h v a l u e , say Mj. ^ 4 , seems v e r y l i k e l y .  Thus the  d i p o l e moment of cyanogen i s o c y a n a t e has been c a l c u l a t e d t o b e : y = 2.488 ± 0.010 D y, = 0.476 ± 0.020 D a b y = 2.533 ± 0.011 D where the e r r o r e s t i m a t e s r e p r e s e n t o u t s i d e l i m i t s of e r r o r . The d i p o l e moment o f cyanogen a z i d e has r e c e n t l y been r e p o r t e d ( 1 5 4 , 186).  T h i s m o l e c u l e has a v e r y s i m i l a r s t r u c t u r e t o , and i s i s o e l e c t r o n i c  w i t h , cyanogen i s o c y a n a t e .  Hence, a comparison of the d i p o l e moments o f  t h e s e two m o l e c u l e s i s of some i n t e r e s t .  T h i s has been done i n F i g u r e 6 . 7 .  The i n d i c a t e d ^ y ^ \ d i r e c t i o n s are o f c o u r s e s p e c u l a t i v e ; they were a r r i v e d at i n the f o l l o w i n g way.  Cyanides t y p i c a l l y have l a r g e d i p o l e moments  200  201  (V + V ) x l 0 ~ o m 2  2  5  (volts ) 2  202  TABLE 6.8  S t a r k C o e f f i c i e n t s o f F i v e Cyanogen I s o c y a n a t e S t a r k  2  (Slope )xl0 a  ~ Vl' J M  0,2  =  ±l  1.6914 ± 0.0022  4  10593.721 ± 0 . 0 2 9  Intercept c  10593.65 ± 0 . 2 0  0,3 -  2  0,2' J = °  10697.08 ± 0.20  15890.18 ± 0 . 2 0  14 M ^1,14' J  12794.511 ± 0.011 12794.58 ± 0.10  b  Intercept  Q  +  v  m  of the v v s . V  s t r a i g h t l i n e graph i n M H z / V o l t s .  2 2 + V s t r a i g h t l i n e g r a p h i n MHz. o m  Observed z e r o f i e l d t r a n s i t i o n f r e q u e n c y i n MHz. d  Standard  e  Estimated  errors. errors.  M  -0.35560 ± 0.00028  4.3499 ± 0.0060  V  °  10494.80 ± 0 . 2 0  e  15890.343 ± 0.016  (Slope)xlO  S l o p e o f the v v s .  =  10696.999 ± 0.058  15 — ^0,15  Intercept  J  10494.958 ± 0.035  d  1.6849 ± 0.0066  Intercept  M  1.7041 ± 0.0040  3  (Slope)xlO  ^ l '  1,2  Lobes.  203  TABLE 6.9  The D i p o l e Moment of Cyanogen  K M /  y  cl  y^  (Debyes)  (Debyes)  0  112.5  2.4881 ± 0.0030  0.4715 ± 0.0007  1  224  2.4881 ± 0.0030  0.4718 ± 0.0007  2  221  2.4881 ± 0.0030  0.4725 ± 0.0007  3  216  2.4881 ± 0.0030  0.4737 ± 0.0008  4  209  2.4881 + 0.0030  0.4756 ± 0.0008  5  200  2.4881 ± 0.0030  0.4783 ± 0.0008  6  189  2.4881 ± 0.0030  0.4820 ± 0.0009  7  176  2.4881 ± 0.0030  0.4872 ± 0.0010  8  161  2.4881 ± 0.0030  0.4945 ± 0.0011  9  144  2.4881 ± 0.0030  0.5053 ± 0.0013  10  125  2.4881 ± 0.0030  0.5226 ± 0.0016  11  104  2.4880 ± 0.0031  0.5537 ± 0.0022  12  81  2.4878 ± 0.0032  0.6253 ± 0.0035  13  56  2.4868 ± 0.0056  0.9950 ± 0.0152  14  29  Value of M  T  J  imaginary  t o w h i c h the peak maximum o f the 15„  aggregate S t a r k l o b e i s assumed t o  b  Isocyanate.  correspond.  ,  r  0,15  —  R e l a t i v e i n t e n s i t i e s o f the v a r i o u s S t a r k components o f 15_ , — 14, , . t r a n s i t i o n . 0,15 1,14 Standard e r r o r s . r  14,  1,14  the  204  205  (3 t o 4 D ) , p o s i t i v e i n the sense N  + c"" ( 1 8 7 , 1 8 8 ) . 1  I s o c y a n a t e and a z i d e  c h a i n s may be e x p e c t e d t o show r a t h e r s m a l l e r group moments The magnitude o f the NC-NCO bond moment (189) h y b r i d i z a t i o n (lone p a i r )  moment (188)  i s l i k e l y t o be a dominant f a c t o r .  (109,186).  and the c e n t r a l  nitrogen  are even l e s s c e r t a i n b u t  neither  T h u s , one might r e a s o n a b l y e x p e c t  that,  f o r b o t h m o l e c u l e s , the t o t a l d i p o l e moment would r o u g h l y p a r a l l e l the NCN c h a i n w i t h the n e g a t i v e end " o n " the c y a n i d e n i t r o g e n .  This condition i s  most c l o s e l y a p p r o x i m a t e d when the component d i r e c t i o n s are t a k e n t o be those s u g g e s t e d i n F i g u r e 6 . 7 .  The u  d i r e c t i o n s seem f a i r l y c e r t a i n ,  the  u^, l e s s s o ; i n f a c t , e i t h e r m o l e c u l e c o u l d e a s i l y accommodate a " p o s i t i v e " _b-component. The i n c r e a s e i n u  a  on g o i n g from NCNCO to NCN can be r a t i o n a l i z e d JJ  i n terms o f the r e l a t i v e moments.  d i r e c t i o n s o f the i s o c y a n a t e and a z i d e group  The f o r m e r i s p r o b a b l y p o s i t i v e i n t h e sense 0  N  and hence  +  l a r g e l y opposes the c y a n i d e moment w h i l e f o r the l a t t e r i t i s l i k e l y the o p p o s i t e s i t u a t i o n p e r t a i n s .  A number o f CNDO/2 c a l c u l a t i o n s  that  indicate  t h a t such s h o u l d be the case ( 1 8 6 , 1 0 9 ) , as do the observed d i p o l e moments o f i s o c y a n i c a c i d (u  = 1.592 D)  (149)  and h y d r a z o i c a c i d (p  a (190).  It  = 0.847 D) a  f o l l o w s then t h a t the d i p o l e moment o f cyanogen a z i d e s h o u l d be  l a r g e r t h a n t h a t o f cyanogen i s o c y a n a t e ,  as o b s e r v e d .  A CNDO/2 c a l c u l a t i o n was attempted f o r cyanogen i s o c y a n a t e unfortunately i t 6.5  f a i l e d to  (109),  but  converge.  V i b r a t i o n a l Dependence o f the R o t a t i o n a l  Constants.  The r o t a t i o n a l c o n s t a n t s o f cyanogen i s o c y a n a t e have been p l o t t e d as a f u n c t i o n o f v^ + 1/2 i n F i g u r e s 6 . 8 , 6.9 and 6 . 1 0 .  The s t r a i g h t  e x p e c t e d on the b a s i s o f the s i m p l e t h e o r y  2.48)  In f a c t ,  two o f the p l o t s  (equations  lines  are not o b s e r v e d .  (A_ and C^) do n o t even g i v e smooth c u r v e s . r  The  206 FIGURE 6.8  V i b r a t i o n a l Dependence o f the A  R o t a t i o n a l Constant of NCNCO.  110000  A v (MHz) 100000 -  90000H  © 80000 4  ©  70000  T" 3 (v  A  + 1/2)  207  FIGURE 6.9 Vibrational Dependence of the B Rotational Constant of NCNCO.  © 2710-  B v  (MHz)  2706-1  ©  2702 H  © 2698 " • 0  r 1  T  3 (v  A  + 1/2)  208  FIGURE 6.10  V i b r a t i o n a l Dependence of the  R o t a t i o n a l Constant o f NCNCO.  © © 2601.  v (MHz) 2600H  ©  2599-j  2598 H  ©  2597  T  3  (v  A  + 1/2)  209  apparent sudden upswing i n the F i g u r e 6.8 p l o t at v^ = 2 may be p a r t i a l l y an a r t i f a c t  of inaccurate A  standard e r r o r ) .  v a l u e s f o r v„ = 2, 3 (the e r r o r b a r s are ±1  v  £  '  To t h e e x t e n t t o w h i c h i t i s r e a l , t h i s d r a m a t i c  increase  i n d i c a t e s t h a t the top o f the b a r r i e r t o l i n e a r i t y i s b e i n g r a p i d l y * ~ approached. The d i s c o n t i n u i t y i n the C p l o t at v = 2 a l s o s u g g e s t s t h a t the m o l e c u l e i s u n d e r g o i n g a marked change i n b e h a v i o r .  Irregular  v i b r a t i o n a l dependence o f r o t a t i o n a l c o n s t a n t s n e a r the top o f a v i b r a t i o n a l b a r r i e r has been observed b e f o r e angle  (140°) and the l o w i s h to  (191).  frequency  0  Finally,  (~140  cm *)  are b o t h c o n s i s t e n t  w i t h cyanogen i s o c y a n a t e h a v i n g a r a t h e r low b a r r i e r t o The dependence o f the A  the l a r g e CNC  linearity.  r o t a t i o n a l c o n s t a n t and the  v  (k^) d i s -  t o r t i o n c o n s t a n t on the b e n d i n g v i b r a t i o n a l quantum number v^ has been t h o r o u g h l y i n v e s t i g a t e d f o r a number o f " b e n t " t r i a t o m i c m o l e c u l e s It  (114).  has been shown t h a t the e x p e r i m e n t a l l y observed b e h a v i o r can be a p p r o x -  i m a t e l y r e p r o d u c e d u s i n g a s i m p l e model i n w h i c h the b e n d i n g v i b r a t i o n  is  c o n s i d e r e d t o be a two d i m e n s i o n a l i s o t o p i c o s c i l l a t o r p e r t u r b e d by a s u i t a b l e hump ( 1 9 2 , 1 9 3 ) .  A s i m i l a r approach s h o u l d be a p p l i c a b l e  cyanogen i s o c y a n a t e and h o p e f u l l y would y i e l d a good e s t i m a t e o f b a r r i e r to l i n e a r i t y .  F i r s t , however,  refined experimental A v vibrational states.  and A „ v a l u e s T  i t would be n e c e s s a r y  to its  to o b t a i n  f o r the v„ = 2 , 3 and h i g h e r e x c i t e d  K  1  T h i s w o u l d e n t a i l the measurement o f a d d i t i o n a l , v e r y  weak, b-type t r a n s i t i o n s and would r e q u i r e a more s e n s i t i v e t h a n t h a t used i n the p r e s e n t work.  spectrometer  An i n v e s t i g a t i o n of the mm-wave r e g i o n  o f the spectrum would p r o b a b l y a l s o be v e r y h e l p f u l . * The b e h a v i o r o f A  v  as a f u n c t i o n of v,  discussed previously  (section  4.5).  b  f o r q u a s i - l i n e a r m o l e c u l e s was n  210  6.6  D i s c u s s i o n o f the M o l e c u l a r  Structure.  The t h r e e i s o e l e c t r o n i c m o l e c u l e s carbon s u b o x i d e , cyanogen a z i d e and cyanogen i s o c y a n a t e show an i n t e r e s t i n g v a r i a t i o n i n m o l e c u l a r  structure.  The observed d i f f e r e n c e s can be r e a d i l y accounted f o r i n terms o f t h e V a l e n c e Bond f o r m a l i s m . Carbon s u b o x i d e has been shown t o be a l i n e a r m o l e c u l e i n i t s ground vibrational state  (194).  T h i s i s n o t s u r p r i s i n g s i n c e t h e two resonance  forms w h i c h a r e l i k e l y t o be o f g r e a t e s t o=  c = c  =  i m p o r t a n c e a r e (195) : g==r.  c = o  c.=c.  +  61  o~  611  The s h o r t CC and CO d i s t a n c e s  (1.289 % and 1.163'A* r e s p e c t i v e l y )  are con-  s i s t e n t w i t h 611 b e i n g o f s i m i l a r i m p o r t a n c e t o 6 1 . O t h e r forms such a s : .0  0. X  R  X :  ^  6III  C = C = 0 6IV  w h i c h c o u l d l e a d t o a bent s t r u c t u r e a r e l e s s  reasonable.  A s i m i l a r a p p r o a c h , a p p l i e d t o cyanogen a z i d e , i n d i c a t e s t h a t  this  m o l e c u l e , u n l i k e C^C^' c o u l d n o t accommodate a l i n e a r c o n f i g u r a t i o n : o f i t s l i k e l y resonance forms a r e b e n t !  x  y-  \ ^ + 61*  These a r e :  y  - v N  ^> / + 611'  x  x-/+  All  y  6III'  * A c t u a l l y , a r e c e n t e l e c t r o n d i f f r a c t i o n s t u d y (196) has i n d i c a t e d t h a t the OJ^ (bending v i b r a t i o n ) p o t e n t i a l may have a s m a l l "hump" a t t h e linear configuration.  211  Further,  l i n e a r forms such a s :  N  Ci=N-—-N=N  +  N  +  C=  -  6IV'  N=  +  N  6 V  v i o l a t e Paulings adjacent importance.  N  +  charge r u l e  (197) and hence must be o f m i n o r  Cyanogen a z i d e does o f course have a bent s t r u c t u r e .  This  was i l l u s t r a t e d w i t h a s c a l e drawing i n t h e p r e v i o u s s e c t i o n ( F i g u r e 6 . 7 ) . The bond l e n g t h s and a n g l e s may be found i n T a b l e 5 . 2 3 . These t h a t t h e above p i c t u r e i s b a s i c a l l y s o u n d .  indicate  Any tendency o f t h e CNN a n g l e  t o open beyond t h e observed 120° due t o s m a l l c o n t r i b u t i o n s from 6 I V ' and 6V' i s a p p a r e n t l y c a n c e l l e d by a l a r g e r c o n t r i b u t i o n from 6 I I I . 1  The s t r u c t u r e o f cyanogen i s o c y a n a t e  i s less easily predicted.  Two o f  the t h r e e most l i k e l y resonance forms a r e l i n e a r , t h e t h i r d i s bent ( 1 8 ) . These a r e : N==C  N F=C + :  0 -  N-rr-C: -  N +  C = 0  ^C  ,C' A>  \ X  61"  N ^  611"  6III"  A d d i t i o n a l forms w h i c h a r e p r o b a b l y o f l e s s e r i m p o r t a n c e i n c l u d e :  +X  X  X A  6IV"  6V"  C l e a r l y , f o r NCNCO, i n c o n t r a s t t o t h e cases o f C^O,, and NCN^, t h e q u e s t i o n " l i n e a r or bent?"  c o u l d n o t be answered w i t h any c o n f i d e n c e p r i o r t o an  experimental i n v e s t i g a t i o n . s t u d y Mayer  I n d e e d , on t h e b a s i s o f a p r e l i m i n a r y  infrared  (18) m i s t a k e n l y proposed a l i n e a r c o n f i g u r a t i o n f o r NCNCO ( i n  the gas p h a s e ) ,  and then r a t i o n a l i z e d t h i s " o b s e r v a t i o n " i n terms o f t h e  212  dominance of resonance forms 6 1 " and 6 1 1 " .  The p r e s e n t work has o f  shown t h a t cyanogen i s o c y a n a t e i s a bent m o l e c u l e . angle  However,  course  t h e l a r g e CNC  (140°) and the s t r o n g q u a s i - l i n e a r b e h a v i o r b o t h i n d i c a t e t h a t  there  are s u b s t a n t i a l c o n t r i b u t i o n s from forms 6 1 " and 6 1 1 " as w e l l as form 6 I I I " which i s probably the c h i e f  one.  The NC-N^ and NC-NCO i n t e r n u c l e a r d i s t a n c e s have been d e t e r m i n e d be 1.312 ± 0.02 ft and 1.283 ± ? ft, r e s p e c t i v e l y .  to  The l a t t e r number i s some  what u n c e r t a i n due t o the many assumptions t h a t were made i n t h e c o u r s e o f its  calculation.  single)  Nonetheless,  t h e r e can be no doubt t h a t t h i s  (nominally  bond i s r e m a r k a b l y s h o r t i n b o t h m o l e c u l e s ; t h i s i s a f u r t h e r i n -  d i c a t i o n o f a s t r o n g l y d e l o c a l i z e d TT s y s t e m . A l l o f the p r e s e n t l y a v a i l a b l e  c h e m i c a l (18,82)  and s p e c t r o s c o p i c  e v i d e n c e i s c o n s i s t e n t w i t h 0 2 ^ 0 e x i s t i n g i n o n l y the i s o c y a n a t e u r a t i o n (NCNCO).  The a l t e r n a t e p o s s i b l e d i c y a n i d e s t r u c t u r e  apparently less s t a b l e .  (NCOCN)  is  T h i s i s at l e a s t s u p e r f i c i a l l y s u r p r i s i n g s i n c e  e x a c t l y the o p p o s i t e s i t u a t i o n p r e v a i l s f o r the w e l l known s u l f u r C2N2S.  config-  analogue  A r e a s o n a b l e , p a r t i a l , e x p l a n a t i o n of t h i s apparent anomaly  is  a g a i n p r o v i d e d by the V a l e n c e Bond a p p r o a c h . The s t r u c t u r e o f s u l f u r d i c y a n i d e has been d e t e r m i n e d by P i e r c e (162).  et.al.  The SC i n t e r n u c l e a r d i s t a n c e h e r e (1.701 ± 0.002 ft) was found t o  be s i g n i f i c a n t l y s m a l l e r than t h a t o f a " n o r m a l " SC s i n g l e bond ( 1 . 8 0  ft).  T h i s was a t t r i b u t e d t o s u b s t a n t i a l c o n t r i b u t i o n s from r e s o n a n c e forms  like  611"'  as w e l l as form 6 1 " ' w h i c h i s p r o b a b l y the c h i e f  61"'  s  611"'  one:  213  I t was f u r t h e r shown t h a t the 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 c o u p l i n g was c o n s i s t e n t w i t h as much as 25% double bond c h a r a c t e r i n t h e CN b o n d .  Now  f o r the oxygen d i c y a n i d e , resonance forms e q u i v a l e n t t o 6 1 1 ' " would be much l e s s f a v o r e d because o f t h e g r e a t e r e l e c t r o n e g a t i v i t y o f oxygen (Z(0) = 3 . 5 0 , J ( S )  = 2.50) ( 1 0 3 ) .  Thus C ^ O has g r e a t e r resonance  stabil-  i z a t i o n p o s s i b i l i t i e s i n t h e i s o c y a n a t e t h a n i n the d i c y a n i d e c o n f i g u r a t i o n . I t i s l e s s c l e a r why C2N2S does n o t e x i s t as the i s o t h i o c y a n a t e (NCNCS) as w e l l as t h e d i c y a n i d e  ((CN) S). 0  214  CHAPTER 7 MICROWAVE TRANSITION FREQUENCIES OF CHLORINE ISOCYANATE, ISOCYANIC ACID AND CYANOGEN ISOCYANATE T h i s c h a p t e r c o n t a i n s the measured microwave t r a n s i t i o n f r e q u e n c i e s upon w h i c h the e n t i r e t h e s i s i s b a s e d .  I n T a b l e 7.1 the 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 o f c h l o r i n e i s o c y a n a t e have been c a t a l o g u e d .  Each h y p e r f i n e  component has been u n i q u e l y d e s i g n a t e d by s p e c i f y i n g the F^ and F quantum numbers of b o t h the upper s t a t e state  (denoted w i t h a s i n g l e prime)  (denoted w i t h a double p r i m e ) .  and the  lower  Only the s t r o n g e s t such components  have been c o n s i d e r e d ; g e n e r a l l y , t h i s means the components f o r w h i c h AF^ = +1 and AF = +1.  The " u n s p l i t l i n e " t r a n s i t i o n f r e