Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1974_A1 H62_9.pdf [ 22.98MB ]
Metadata
JSON: 831-1.0061099.json
JSON-LD: 831-1.0061099-ld.json
RDF/XML (Pretty): 831-1.0061099-rdf.xml
RDF/JSON: 831-1.0061099-rdf.json
Turtle: 831-1.0061099-turtle.txt
N-Triples: 831-1.0061099-rdf-ntriples.txt
Original Record: 831-1.0061099-source.json
Full Text
831-1.0061099-fulltext.txt
Citation
831-1.0061099.ris

Full Text

THE MICROWAVE SPECTRA AND STRUCTURES OF SOME ISOCYANATES by W i l l i a m Hiram Hocking B . S c , U n i v e r s i t y of B r i t i s h Co lumbia , 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Chemistry We accept t h i s t h e s i s as conforming to the _ r e q u i r e d s tandard — THE UNIVERSITY OF BRITISH COLUMBIA October , 1973 i In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced d e g r e e at t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f The 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 V a n c o u v e r 8, Canada Date ~J?^ jf l<f?2> i i 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 six isotopic species of chlorine isocyanate have been measured in the frequency region 8-37 GHz. It was found that the rotational energy level 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 distortion constants, were determined using a least squares f i t t i n g procedure. From the rotational constants, the r g molecular structure of 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 in which an isocyanate molecule has been shown to have a bent NCO chain. Considerable hyperfine structure was also observed in 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 distribution in the molecule. HNCO: The microwave spectra of six isotopic species of isocyanic acid have also been measured in the frequency region 8-37 GHz. The observed (micro-wave) transitions were analysed together with the available millimeter-wave data (Kewley et.al. (150) and Winnewisser (198)) using Watson's general non-ri g i d Hamiltonian. This analysis yielded rotational constants of sufficient i i i accuracy to a l l ow the de t e rm ina t i on of a r e f i n e d (r ) mo lecu la r s t r u c t u r e : 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° r(C-O) = 1.166 ± 0.005 A* In a d d i t i o n , the b-component of the d i p o l e moment o f deute ra ted i s o -cyan ic a c i d was measured. The va lue obta ined i s : u, = 1.35 ± 0.10 D. When / b combined w i t h the p r e v i o u s l y measured ^-component (y = 1.602 ± 0.020 D (153)) SL i t y i e l d s the t o t a l d i p o l e moment of DNCO: y = 2.10 ± 0.15 D. NCNCO: The microwave spectrum of the n a t u r a l l y most abundant i s o t o p i c spec i es of cyanogen i socyana te has been i n v e s t i g a t e d . Th i s was found to be c o n s i s -t en 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 than the p r e v i o u s l y proposed (18) l i n e a r c o n f i g u r a t i o n . A p r e l i m i n a r y mo lecu 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 spec t r a gave ev idence f o r s t rong q u a s i -l i n e a r behav i o r . S ta rk measurements y i e l d e d the mo lecu la r d i p o l e moment. i v TABLE OF CONTENTS CHAPTER Page 1. INTRODUCTION 1 2 . MICROWAVE SPECTROSCOPIC THEORY 6 2.1 The R o t a t i o n a l Energy Leve l s o f an Asymmetric Top M o l e c u l e . 6 2 .2 Nuc l ea r Quadrupole C o u p l i n g . 21 2 . 3 The S t a rk E f f e c t . 26 2 . 4 R o t a t i o n a l Cons tan t s , Moments o f I n e r t i a , I n e r t i a l Defect and the M o l e c u l a r S t r u c t u r e . 31 2 . 5 C e n t r i f u g a l D i s t o r t i o n Constants and the V i b r a t i o n a l Force F i e l d . 42 3 . 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 socyana te . 44 3 .2 P r e p a r a t i o n of I so cyan i c A c i d . 49 3 .3 P r e p a r a t i o n o f Cyanogen I socyana te . 51 3 .4 The S t a r k Modulated Microwave Spec t rometer . 54 3 .5 Double Resonance Exper iments . 58 3 .6 D i p o l e Moment Measurements. 60 4 . THE MICROWAVE SPECTRUM OF CHLORINE ISOCYANATE 62 4 .1 Assignment of the Spectrum 63 4 . 2 De te rmina t ion of M o l e c u l a r Constants from the Microwave Spectrum. 68 4 . 3 The Mo l e cu l a r S t r u c t u r e o f C h l o r i n e I socyanate 79 4 . 4 D i s c u s s i o n of the Nuc lea r Quadrupole Coup l ing Cons tan ts . 86 4 . 5 V i b r a t i o n a l Dependence of the M o l e c u l a r Constants 101 V CHAPTER Page 4.6 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 Constants and the I n e r t i a l Defect from the M o l e c u l a r Force F i e l d . 106 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 . I l l 5. THE MICROWAVE SPECTRUM OF ISOCYANIC ACID 118 5.1 Assignment of the Spectrum. 120 5.2 De te rmina t ion of M o l e c u l a r Constants from the Microwave Spectrum. 122 5.3 The M o l e c u l a r S t r u c t u r e of I s o c yan 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 of the D i p o l e Moment and the N i t r o g e n Nuc lea r Quadrupole Coup l ing Cons tan ts . 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 Constants and the I n e r t i a l Defect from the M o l e c u l a r Force F i e l d . 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 6. THE MICROWAVE SPECTRUM OF CYANOGEN ISOCYANATE 174 6.1 Assignment o f the Spectrum. 175 6.2 De te rmina t ion o f M o l e c u l a r Constants from the Microwave Spectrum. 182 6.3 The M o l e c u l a r S t r u c t u r e of Cyanogen I socyana te . 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 of the R o t a t i o n a l Cons tan ts . 205 6.6 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 . 210 7. MICROWAVE TRANSITION FREQUENCIES OF CHLORINE ISOCYANATE, ISOCYANIC ACID AND CYANOGEN ISOCYANATE 214 BIBLIOGRAPHY 311 v i LIST OF TABLES TABLE Page 4.1 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 of 3 5 C 1 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 4.2 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 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 . 74 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 Constants of C h l o r i n e I socyana te . 76 4.4 Nuc lear Quadrupole Coup l ing Constants of C h l o r i n e I socyana te . ... . 78 4 .5 Moments o f I n e r t i a and I n e r t i a l De fec t s o f C h l o r i n e I socyana te . 80 4.6 C h l o r i n e Isocyanate Atomic Coord inates i n the 3 5 C 1 1 4 N 1 2 C 1 6 0 P r i n c i p a l A x i s System. 82 4.7 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 socyana te . 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 . 84 4.9 Se l e c t ed C h l o r i n e Nuc l ea r Quadrupole Coup l ing Constants o f C h l o r i n e I socyana te . 87 4.10 T rans fo rmat ion of the C h l o r i n e Nuc lea r Quadrupole Coup l ing Constants i n t o the C1N Bond A x i s System. 91 4.11 N i t r ogen Quadrupole Coup l ing I n t e r p r e t a t i o n u s i n g the Townes D a i l e y Theory. 97 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 N i t r ogen i n C h l o r i n e I socyana te . 97 4.13 Comparison of Observed and C a l c u l a t e d Nuc lea r Quadrupole Coup l ing Constants of 3 5 C 1 1 4 N 1 2 C 1 6 0 ( G . V . S . ) . 100 4.14 C h l o r i n e I socyanate 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 requenc ies of C h l o r i n e I socyana te . 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 Constants of C h l o r i n e Isocyanate ( 3 5 C 1 I 4 N 1 2 C 1 6 0 G.V .S . ) 110 v i i TABLE Page 4.17 C a l c u l a t e d and Observed I n e r t i a l Defec ts of C h l o r i n e I socyanate ( 3 5 C 1 1 4 N 1 2 C 1 6 0 G.V.S . ) 110 4.18 Comparison o f C h l o r i n e Isocyanate 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 . 112 4.19 Some "Genu ine" CO and NC Double Bond Lengths . 114 4.20 Some NC T r i p l e Bond Lengths and CO 2+ Bond Lengths . 115 4.21 Comparison of the C h l o r i n e N i t r o g e n Bond Lengths found i n a Number of Sma l l M o l e c u l e s . 115 5.1 Nuc l ea r Quadrupole Coup l ing Constants of 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 Constants and C e n t r i f u g a l D i s t o r t i o n Constants of H ^ N ^ C ^ O us ing D i f f e r e n t Methods of A n a l y s i s . 125 5.3 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 Constants o f I s o c yan i c A c i d . 128 5.4 A R o t a t i o n a l Constants of I s o c y a n i c A c i d from Combined Microwave and IR d a t a . 133 5.5 Moments of I n e r t i a and I n e r t i a l De fec t s of I s o c y a n i c A c i d . 134 5.6 K ra i t chman/Cos ta in S u b s t i t u t i o n P o s i t i o n s of a l l of the Atoms o f I s o c yan i c A c i d . 136 5.7 M o l e c u l a r S t r u c t u r e of I s o c yan i c A c i d : Atomic C o o r d i n a t e s . 139 5.8 M o l e c u l a r S t r u c t u r e o f I s o c yan i c A c i d : Geometry. 139 5.9 C e l l C a l i b r a t i o n : Measurement of the S ta rk E f f e c t o f the J = 0->-l T r a n s i t i o n of OCS. 146 5.10 S t a rk 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 C e l l C a l i b r a t i o n : E f f e c t i v e Septum-Cel l Wa l l Spac ing . 148 5.12 S ta rk C o e f f i c i e n t s of Two D 1 4 N 1 2 C 1 6 0 b-type T r a n s i t i o n s . 148 5.13 The b-component of the D ipo l e Moment of D ^ N ^ C ^ O . 152 5.14 Comparison of the Observed and C a l c u l a t e d Values of the D ipo l e Moment o f I s o c y a n i c A c i d . 156 v i i i TABLE Page 5.15 N i t r ogen Nuc lear Quadrupole Coup l ing Constants of I so cyan i c A c i d and Re la ted 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 so cyan i c A c i d . 158 5.17 Fundamental V i b r a t i o n a l F requenc ies of I s o c yan i c A c i d . 159 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 I so cyan i c A c i d . 161 5.19 I s o c y a n i c A c i d M o l e c u l a r Force F i e l d : R .G .F .F . 163 5.20 Comparison of C a l c u l a t e d and Observed I so c yan i c A c i d I n e r t i a l D e f e c t s . 164 5.21 Comparison of I s o c yan i c A c i d S t r u c t u r e s . 166 5.22 Mo l e cu l a r S t r u c t u r e s of Some I socyana tes . 168 5.23 M o l e c u l a r S t r u c t u r e s of 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 of Some NH Bond Leng ths . 173 6.1 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 of Cyanogen Isocyanate i n the Ground V i b r a t i o n a l S t a t e . 185 6.2 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 of Cyanogen Isocyanate 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 S t a t e . 187 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 Constants of Cyanogen Isocyanate i n H igher E x c i t e d V i b r a t i o n a l S t a t es .189 6.4 Cyanogen Isocyanate Constants C a l c u l a t e d Us ing P o l o ' s R e l a t i o n s . 189 6.5 The Moments of I n e r t i a and the I n e r t i a l Defec t of Cyanogen Isocyanate 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 of Cyanogen I socyana te . 191 6.7 S ta rk Measurements on Cyanogen I socyana te . 197 6.8 S ta rk C o e f f i c i e n t s of F i v e Cyanogen Isocyanate S tark Lobes. 202 6.9 The D ipo l e Moment of Cyanogen I socyana te . 203 i x TABLE Page 7.1 Observed T r a n s i t i o n F requenc ies of C h l o r i n e I socyana te : Nuc lea r Quadrupole Coup l ing A n a l y s i s . 215 7.2 T r a n s i t i o n Frequenc ies of C h l o r i n e I socyana te : 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 . 283 7.3 T r a n s i t i o n F requenc ies of I s o c yan i c A c i d : Nuc lea r Quadrupole Coup l ing A n a l y s i s . 293 7.4 T r a n s i t i o n Frequenc ies of I s o c yan i c A c i d : 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 . 298 7.5 T r a n s i t i o n Frequenc ies of Cyanogen I socyana te : 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 . 305 X LIST OF FIGURES FIGURE Page 3.1 Schematic Illustration of the Vacuum System used in the Preparation of Chlorine Isocyanate from Silver Cyanate and Chlorine. 48 3.2 Schematic Illustration of the Vacuum System used in the Preparation of Cyanogen Isocyanate. 52 3.3 Schematic Illustration of the Spectrometer used in the Microwave - Microwave Double Resonance Experiments. 59 4.1 Il 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 3 5C1 1 4N 1 2C 1 60 (G.V.S.) 66 4.2 Flow-Chart Illustrating the Overall Centrifugal Distortion and Nuclear Quadrupole Hyperfine Structure Analysis Scheme. 70 4.3 The Molecular Structure of Chlorine Isocyanate. 85 4.4 Illustration 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 5C1 UN 1 2C 1 60. V 102 4.6 Vibrational Dependence of the B' Rotational Constant of 3 5C1 UN 1 2C 1 60. V 103 4.7 Vibrational Dependence of the C' Rotational Constant of 3 5C1 UN 1 2C 1 60. V 104 4.8 Vibrational Dependence of the Inertial Defect of 3 5C1 1 4N 1 2C 1 60. 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~ „„ — 21. „. Transition of 14 12 16 ' ' D N C 0. 150 5.4 Stark Measurements on the 24„ „, — 23. 0- Transition of 14 12 16 °' 2 4 1 > 2 3 D N C 0. 151 x i FIGURE Page 5.5 The D ipo l e Moment of I so cyan i c A c i d . 154 6.1 Schematic I l l u s t r a t i o n of the Cyanogen Isocyanate 6. , — 5. c se t of T r a n s i t i o n s . 178 1,6 1,5 6.2 Schematic I l l u s t r a t i o n of the Two Microwave - Microwave Double Resonance Experiments Performed on Cyanogen I socyana te . 181 6.3 P l o t o f the F requenc ies (Cor rec ted 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 of NCNCO (G.V.S . ) v s . K 2 r 183 6.4 The M o l e c u l a r S t r u c t u r e of Cyanogen I socyana te . 193 6.5 S ta rk Measurements on the 2 — 1 ' , M = 0 T r a n s i t i o n of NCNCO ( G . V . S . ) . ' ' 200 6.6 S t a rk Measurements on the 1 5 n . — 14 T r a n s i t i o n of NCNCO (G .V . S . ) . ' ^ ' 201 6.7 The D ipo l e Moments o f Cyanogen Isocyanate and Cyanogen A z i d e . 204 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 o f NCNCO. V 206 6.9 V i b r a t i o n a l Dependence of the B R o t a t i o n a l Constant of NCNCO. V 207 6.10 V i b r a t i o n a l Dependence of the C R o t a t i o n a l Constant of NCNCO. V 208 x i i ACKNOWLEDGEMENTS This dissertation i s an account of work carried out in the Department of Chemistry at the University of Bri 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 per-forming the force f i e l d calculations on isocyanic acid and chlorine iso-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 dis-cussions on vibrational problems and for the loan of some equipment. I further extend my sincere thanks to the National Research Council of Canada for financial support during the course of this research. Finally, 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 Spectroscopy may be de f i ned as the study of the abso rp t i on (or emiss ion ) of e l e c t romagne t i c r a d i a t i o n , by molecu les or atoms, i n tha t pa r t o f the spectrum which f a l l s between r a d i o f r e q u e n c i e s and the i n f r a r e d . Th i s r eg i on 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 hav ing a 1 GHz lower boundary and an 800 GHz upper boundary. I t i s f u r t h e r t r a d i t i o n a l l y broken down i n t o two subreg ions of rough ly 1 - 4 0 GHz and 40 - 800 GHz which are c a l l e d , r e s p e c t i v e l y , the microwave r eg i on and the mi l l ime te r-wave r e g i o n . The f i r s t microwave experiment was r epo r t ed by C lee ton and W i l l i a m s (1) i n 1934. Th i s was a l i m i t e d i n v e s t i g a t i o n of the i n v e r s i o n spectrum of ammonia. No f u r t h e r p rogress was made u n t i l a f t e r the development o f s t a b l e tunab le sources du r ing World War I I . S ince then many a d d i t i o n a l advances have occur red so tha 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 though on ly the 8 - 4 0 GHz r eg i on i s covered by a commerc ia l l y a v a i l a b l e spec t romete r . Measurement accuracy w i t h conven t i ona l microwave techniques i s t y p i c a l l y o f the order of 1 pa r t i n 10^. A s u r p r i s i n g l y l a r g e number of q u i t e d i f f e r e n t types of t r a n s i t i o n s have been observed i n the microwave/mi l l imeter-wave r e g i o n . Some of the more e s o t e r i c exper iments have i n v o l v e d the i n v e s t i g a t i o n of t r a n s i t i o n s between A-doublets (2) , i l-type doub le t s (3) , and atomic s t a t e s (4 ) ; the i n v e r s i o n problem a l so belongs i n t h i s ca tegory . However the type of 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 microwave/mi l l imeter-wave 2 r e g i o n i s tha t between mo lecu l a r s t a t e s of d i f f e r e n t r o t a t i o n a l e n e r g i e s . Indeed, the term Microwave Spectroscopy has come to 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 Spectroscopy and i s t r ea t ed as such t h rough -out t h i s t h e s i s . The gene ra l f e a tu r e s of 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 ven molecu le are determined l a r g e l y by the masses and the g eom e t r i c a l arrangement of the i n d i v i d u a l atoms w i t h i n tha t mo lecu l e . Consequent ly , 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 molecu le 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 , through a d e t a i l e d examinat ion of i t s microwave spectrum. U n f o r t u n a t e l y , a complete s t r u c t u r a l de t e rm ina t i on u s u a l l y r e q u i r e s tha t more than one i s o t o p i c spec i es be s tud i ed and t h e r e -fo re can become a ve ry t ime consuming p r o j e c t . Fur thermore , the n o n r i g i d -i t y o f r e a l mo lecu les 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 d e r i v e d s t r u c t u r a l parameters which f a r exceeds the measurement e r r o r ( 5 , . . . , 1 0 ) . Th 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 of the complex i t y of the t y p i c a l microwave spectrum. Many groups of t r a n s i t i o n s which would be i d e n t i c a l l y superimposed f o r a r i g i d molecu le 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 p a t t e r n 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 of 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 tha t o f a l l the o the r v i b r a t i o n a l s t a t e s , so tha t when there are one or more low l y i n g e x c i t e d v i b r a t i o n a l s t a t e s the microwave spectrum i s e f f e c t i v e l y a s u p e r p o s i t i o n of 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 f o r each of the popula ted v i b r a t i o n a l l e v e l s . The r e s u l t i n g m u l t i p l i c i t y of l i k e t r a n s i t i o n s i s o f t en l o o s e l y r e f e r r e d to 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 e f f e c t s are p o t e n t i a l sources o f i n f o r m a t i o n on the mo lecu l a r f o r ce f i e l d ( 5 , . . . , 1 0 ) . 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 encountered i n microwave s p e c t r a i s nuc l ea r quadrupole h y p e r f i n e s t r u c t u r e . Th i s occurs whenever at l e a s t one of the n u c l e i w i t h i n the molecu le under c o n s i d e r a t i o n has a s p i n angu la r momentum of g r e a t e r than 1/2. I t i s produced by a coup l i ng o f tha t n u c l e a r s p i n to the t o t a l r o t a t i o n a l angular momentum through the i n t e r a c t i o n of 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 quadrupole 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 coup l i ng c o n s t a n t s . These can p rov ide cons ide r ab l e i n s i g h t i n t o the e l e c -t r o n i c s t r u c t u r e of the mo l e cu l e . The mo lecu l a r d i p o l e moment i s a second, complementary, source of 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 mo lecu le . I t may be a c c u r a t e l y determined by measuring the e f f e c t of an a p p l i e d e l e c t r i c f i e l d on the microwave spectrum ( 5 , . . . , 1 0 ) . Th i s t h e s i s i s an account of an i n v e s t i g a t i o n of the microwave s p e c t r a of th ree i socyana te m o l e c u l e s ; s p e c i f i c a l l y , c h l o r i n e i socyana te (C1NC0), i s o c y a n i c a c i d (HNCO) and cyanogen i socyana te (NCNCO). The f i r s t s t udy , tha t on c h l o r i n e i s o c y a n a t e , was undertaken p r i m a r i l y to o b t a i n an accura te mo lecu l a r s t r u c t u r e . Th i s was of p a r t i c u l a r i n t e r e s t 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 ther i socyana tes which had p r e v i o u s l y been s t u d i e d . For example, i s o c y a n i c a c i d was known to have a rough ly 128° HNC angle (11 ) , methy l i socyana te a 140° CNC angle (12 ) , 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 cha in (13) . 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 i s o c y a n a t e , had been shown to have a double ben t , p l a n a r , s t r u c t u r e w i t h a C1NN angle 4 of 108°40' and a t rans az ide bend of 8 °4 ' (14 ) . Thus, c h l o r i n e i s o -cyanate cou ld conce i vab l y have been e i t h e r a l i n e a r molecu le or a ve ry bent molecu le and i t t h e r e f o r e seemed that a d e t a i l e d microwave s t r u c t u r a l study would be eminent ly wo r thwh i l e . A secondary reason f o r examining the microwave spectrum of c h l o r i n e i socyana te was to determine the c h l o r i n e and n i t r o g e n nuc l ea r quadrupole coup l i ng c o n s t a n t s . These were of 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 mo lecu l e . However, i t was a l so hoped tha t they might o f f e r some i n s i g h t i n t o the more compl i ca ted c h l o r i n e az ide quadrupole h y p e r f i n e s t r u c t u r e which had ye t to be (and s t i l l i s not ) comple te l y accounted f o r . The i s o c y a n i c a c i d s tudy was, 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 of both the n a t u r a l l y abundant and deuter ium s u b s t i t u t e d i s o t o p i c spec i e s had p r e v i o u s l y been examined (11 ,15 ) . A l so a reasonab ly good mo l e cu l a r s t r u c t u r e had been repor ted (11) . One o b j e c t i v e o f the p resent s tudy was to o b t a i n the r o t a t i o n a l constants o f a d d i t i o n a l i s o t o p i c spec i e s and thereby determine a r e f i n e d mo lecu l a r s t r u c t u r e . However, the pr imary i n c e n t i v e f o r reopening t h i s problem was the recent d i s c o v e r y (by radioastronomy) of i s o c y a n i c a c i d i n i n t e r s t e l l a r space (16 ,17 ) ! Th i s d i s c o v e r y meant tha 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 ev idence which cou ld be ob ta ined would be of i n t e r e s t i n i t s e l f . The H 1 5 N 1 2 C 1 6 0 and H 1 4 N 1 3 C 1 6 0 r o t a t i o n a l t r a n s i t i o n f r equenc i e s were c o n -s i d e r e d to be p a r t i c u l a r l y important s i n c e i t was thought tha t e i t h e r or both o f these i so topes might be p resent i n the i n t e r s t e l l a r medium i n de t e c t ab l e amounts. A c c o r d i n g l y , a thorough examinat ion of the microwave 5 (and mi l l imete r-wave ) spectrum of 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 spec i e s was under taken . The t h i r d p r o j e c t , l i k e the f i r s t , was p r i m a r i l y d i r e c t e d towards o b t a i n i n g s t r u c t u r a l i n f o r m a t i o n . Cyanogen i socyana te i s i s o e l e c t r o n i c w i t h both l i n e a r carbon suboxide and bent cyanogen a z i d e , so t h a t , as w i t h c h l o r i n e i s o c y a n a t e , there was some q u e s t i o n as to even the main f e a tu r e s of i t s geometry. Indeed, a p r e l i m i n a r y i n f r a r e d study 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. In the present work, on ly the n a t u r a l l y most abundant i s o t o p i c spec ies was s t u d i e d . Nonethe less t h i s was s u f f i c i e n t to answer unambig-uous ly the q u e s t i o n " l i n e a r or b e n t ? " , i n the gas phase , and even y i e l d e d some s e m i - q u a n t i t a t i v e s t r u c t u r a l d a t a . 6 CHAPTER 2 MICROWAVE SPECTROSCOPIC THEORY Th i s chapter i s in tended to p rov ide a reasonab ly conc i se but none-t 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 which the r e s u l t s 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 v i b r a t i o n a l - r o t a t i o n a l e n e r g e t i c s o f a r e a l molecu le are cons ide red 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 tha t may be i n t r oduced i n t o the r o t a t i o n a l spectrum by the presence o f a quadrupo la r n u c l e u s , o r the a p p l i c a t i o n of an e l e c t r i c f i e l d . F i n a l l y , the r o l e of microwave s p e c t r o -s c o p i c cons tants i n the de t e rm ina t i on of mo l e cu l a r s t r u c t u r e s and v i b r a t i o n a l f o r c e f i e l d s i s d i s c u s s e d . Throughout , the emphasis i s on p r e s e n t i n g equat ions tha t w i l l be of use i n subsequent c h a p t e r s , r a t h e r than on a t tempt ing to p rov ide a comprehensive d i s c u s s i o n of microwave s p e c t r o s c o p i c theory . 2.1 The R o t a t i o n a l Energy Leve l s of an Asymmetric Top Mo lecu le S t a r t i n g from a mo lecu l a r model i n which the atoms are 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 rov ided by the averaged mot ion of the e l e c -t r o n s , W i l son and Howard (19) have de r i v ed the quantum mechan ica l H a m i l -t on i an f o r a v i b r a t i n g - r o t a t o r : H = u aP P. - h P + I/2V* u^p y aii"V^ / J a3 a 3 / J a a / J  Ca a3 r 3 a , 3 a a , 3 + 1/2^ v\v-\vh + V 2.1 k w i t h ha = 1/2^2 ^ " \ 6 P 3 y i S + ^Vc^  2 A a 3 where i s the opera to r a s s o c i a t e d w i t h the a component of the r o t a t i o n a l 7 angular momentum a long molecu le f i x e d axes , p i s the opera to r a s s o c i a t e d w i t h the v i b r a t i o n a l momentum conjugate t o the k*"*1 normal coo rd ina te Q^, and i s the ope ra to r a s s o c i a t e d w i t h the a component of the v i b r a t i o n a l angu lar momentum a long molecu le f i x e d axes and i s de f ined by (10 ) : P« - - ^ C J k V k 2.1b where the £™ 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 are the elements Otp of the i n v e r s e moment of i n e r t i a m a t r i x and are f u n c t i o n s of the normal coo rd ina tes o n l y : p i s the determinant of the u „ m a t r i x . ap The Schrod inger equa t ion a s s o c i a t e d w i t h the v i b r a t i n g - r o t a t o r H a m i l t o n i a n cannot be so l ved e x a c t l y . P rogress can be made, however, by s e p a r a t i n g H i n t o a sum of th ree te rms : a p u r e l y v i b r a t i o n a l p a r t ff° which i n c l u d e s the l a s t th ree terms of equa t ion 2 . 1 ; a p u r e l y r o t a -t i o n a l p a r t H° c o n s i s t i n g o f those p a r t s o f the f i r s t term t h a t a re 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' tha t i n c l u d e s the second term p l u s the remainder o f the f i r s t t e rm, w i t h A s m a l l and p o s i t i v e . One can then w r i t e : H = H° +\H' 2 .2a w i t h Ho = o + H o 2 2 h V R where i t i s p o s s i b l e to choose wave func t ions of the form such tha 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, but not n e c e s s a r i l y d i agona l i n R. 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 these same wave func t ions on the o the r hand w i l l have elements o f f - d i a g o n a l i n V of the o rder o f X. A p p l i c a t i o n o f a Van V l e ck t r a n s f o r m a t i o n (20) to t h i s m a t r i x can then be used to t rans fo rm i t 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 are reduced to the o rde r of X or h i g h e r . W i th the neg l e c t o f these terms the t ransformed m a t r i x can be f a c t o r e d i n t o s m a l l e r 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-r i c e s are g i ven by : E + <vR|f|vR-> + y ^ < v R | ^ ' l v " R " X v " R " l ^ ' l v R ' > ^ E ° - E ° „ V",R" v v " where i t i s assumed tha t E ° - E ° , „ can be approximated by E ° - E ° „ . RV K V V V D e t a i l e d c o n s i d e r a t i o n of these m a t r i x elements i n d i c a t e s tha t t h i s p e r t u r b a t i o n treatment i s equ i v a l en t 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 Ham i l t on i an i n the f o l l o w i n g s i m p l i f i e d fo rm: H = E + l / 2 V f l . ? P . + l/4 V T _ c.P PRP P. 2.3 v t—J a3 a 3 / J agyo a B y 6 a > 3 oc ,B , Y ,6 where the c o e f f i c i e n t s a n and T . r are s t r o n g l y dependent on the a3 apyo v i b r a t i o n a l s t a t e to which E ^ co r responds . They are de f i ned by the f o l l o w i n g e q u a t i o n s : V + ih S ' K ^ a J ^ X v - ' I \ | V > " < v | u a y | V ' X v | ^ | v > } / h V v v , V ' 2 .3a V " <VKJV> + 2E ,<V|^|V 'XV' l ^ l v X h v ^ , V + 2 i h £ , K v | y a e | v « X V | f c | V > - < v | y a Y | V X V | ^ | v > } / h v v v f V where a , 3 , Y take on va lues x . y . z i n c y c l i c order and hv , = E ° - E ° . * * 1 J vv V V V I f the r o t a t i o n a l angu la r momenta ope ra to r s P^ are de f i ned i n u n i t s of h then the a n and T „ . have u n i t s of energy (one must m u l t i p l y the a3 a3y<S 2 r i g h t hand s i d e o f equat ions 2.3a by h and the r i g h t hand s i de of equa t ion 9 2.3b by h^) . One can then m u l t i p l y equa t ion 2.3 by 10°/h so tha t the r o t a t i o n a l energ ies are measured i n MHz, as w i l l be the c o e f f i c i e n t s i f 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 equa t ion 2.3 has e x a c t l y the same form as the r o t a t i o n a l Hami l t on i an of a " r i g i d r o t o r " ; i . e . , a " m o l e c u l e " i n which the atoms are 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 can , at 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 of c e n t r i -f u g a l d i s t o r t i o n (19) . I f the l a t t e r i s neg l e c t ed f o r the moment, then the remain ing r o t a t i o n a l pa r t of 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 of an o r thogona l t r a n s f o r m a t i o n (a r o t a t i o n of the molecu le f i x e d a x i s system w i t h r espec t to the mo lecu l a r frame i n t o the s o - c a l l e d p r i n c i p a l i n e r t i a l a x i s system) g i v i n g : H = (d ' ) P 2 + (a ' ) P 2 + (a ' ) P 2 2.4 r x v x y v y z v z where the dependence of the c o e f f i c i e n t s , which are c a l l e d r o t a t i o n a l 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 denoted. I f any two o f the r o t a t i o n a l cons tants i n equa t ion 2.4 are equa l (a symmetric top) then the r e s u l t i n g Schrod inger equa t ion can be so l ved e x a c t l y to o b t a i n c l o s e d express ions f o r the wave f u n c t i o n s and e i g e n -v a l u e s . In the more gene ra l asymmetric top case ( a l l three a ' s d i f f e r e n t ) a c losed s o l u t i o n does not e x i s t . I t i s p o s s i b l e , however, to express the asymmetric top wave f u n c t i o n s as a l i n e a r combinat ion o f the symmetric r o t o r f u n c t i o n s . 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 asymmetric top Hami l t on i an i n terms of 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 to g i ve the c o r r e c t asymmetric top " r i g i d r o t o r " e n e r g i e s . 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 , the t o t a l r o t a -10 2 t i o n a l angu la r momentum quantum number, because P always commutes w i t h H . Each m a t r i x cor respond ing to a p a r t i c u l a r va lue of J i s square and of o rder 2J+1. Fu r the r f a c t o r i z a t i o n i s achieved by app l y i ng a Wang t r a n s -fo rmat ion which reduces each J b l o c k i n tu rn to f ou r submatr ices hav ing the symmetries of the group (21 ,22 ) . These are then conven i en t l y d i a g o n a l i z e d by the method of cont inued f r a c t i o n s (22 ) . I t i s conven t i ona l t o r e l a b e l the x , y , z axes of 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 which the a D v an i sh ) as a , b , c , such tha t ap ( a^ ) v > ( a ^ ) v > ( a^ ) v - There are s i x d i f f e r e n t ways of i d e n t i f y i n g a , b , c w i t h x , y , z . The most convenient f o r a near p r o l a t e ( ( a ' ) « ( a ' ) ) J c b v c v asymmetric top i s : x -> b, y ->- c , z -> a Th i s i s known as the I r e p r e s e n t a t i o n (23 ) . Equat ion 2.4 can then be r e w r i t t e n a s : H = A P2 + B p} + C P2 2.5 r v a v b v c where (a ' ) , ( a ' ) , ( a ' ) have been changed to the more c o n v e n t i o n a l a v b v c v 6 A , B , C . v v v The c a l c u l a t i o n of the e igenva lues of i s g r e a t l y f a c i l i t a t e d by a change of v a r i a b l e s . S eve ra l d i f f e r e n t ways of doing t h i s have been suggested . One of the most u s e f u l i s t ha t i n t roduced by Ray (24 ) . He de f i ned an asymmetry parameter K by : 2B - A - C v v v „ , K = _ _ 2. 6 v v which v a r i e s from -1 i n the p r o l a t e l i m i t (B v = C^) to +1 i n the ob l a t e l i m i t (A^ = B^). The asymmetric top " r i g i d r o t o r " energy l e v e l s can then be w r i t t e n a s : 11 E (A ,B ,C ) = 1/2(A + C )J(J+1) + 1/2(A - C ) E ( K ) t 2.7 r v ' v v v v v v J K - 1 K 1 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 r o t a t i o n a l constants 1, K , and - 1 . The symbol J p rov ides a unique l a b e l f o r the r o t a t i o n a l energy K - 1 K 1 l e v e l s o f an asymmetric top molecu le ( 2 3 ) . The t o t a l r o t a t i o n a l angu la r momentum quantum number J has a l ready been ment ioned. I t can take on v a l u e s 0,1,2, -**. For the s p e c i a l case of a symmetric t o p , there i s a second good quantum number K, a s soc i a t ed w i t h the p r o j e c t i o n of the t o t a l r o t a t i o n a l angu la r momentum a long the symmetry a x i s o f the t op . I t can take on va lues 0,1,2,"'*,J and toge the 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 . F i n a l l y , f o r the asymmetric t o p , the pseudoquantum numbers and represent the va lues of 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 , the l i m i t i n g p r o l a t e and o b l a t e tops which c o r r e l a t e w i t h the asymmetric top l e v e l 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 , tha t i s p a r t i c u l a r l y u s e f u l i f the molecu le i s c l o se to" one of the p r o l a t e or ob l a t e l i m i t i n g cases , i s " * tha t due to Wang (21). He d e f i n e d an asymmetry parameter b^ b y : _ C v " B v 2.8 p 2A - B - C V V V which v a r i e s from 0 i n the p r o l a t e l i m i t to -1 i n the o b l a t e l i m i t . The r o t a t i o n a l energy can then be w r i t t e n a s : * 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 ob l a t e asymmetric t o p s , namely: b = (A - B )/(2C - A - B ) O V V V V V 12 E (A ,B ,C ) = 1/2(B + C )J(J+1) + |A - 1/2(B + C )}E(b ) t 2.9 r v v v v v < v v v ' p J K - 1 K 1 where E(b^) i s e f f e c t i v e l y the energy o f a r o t o r w i t h r o t a t i o n a l cons tants 1, ~bp> and + bp- In the gene ra l c a se , the reduced energ ies ( e i t h e r E ( K ) 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 . In the s p e c i a l case of a near p r o l a t e asymmetric t o p , however, E(b^) may be c o n v e n i e n t l y eva lua ted by p e r t u r b a t i o n theo r y . The r e s u l t i s : E (b ) = K 2 . + C,b + C„b 2 + 2.10 p -1 1 p 2 p where K ^ has been p r e v i o u s l y de f i ned and the C.. are c o e f f i c i e n t s tha t have been t abu l a t ed (25 ) . I f the asymmetry i s v e r y s l i g h t then equa t ion 2.10 may be te rmina ted a f t e r the second te rm. In t h i s i n s t a n c e , the p a t t e r n of energy l e v e l s i s e s s e n t i a l l y the same as tha t found i n the p r o l a t e symmetric t o p , except tha t there are now two c l o s e l y spaced l e v e l s cor respond ing to = 1 f o r each J i n s t e a d of j u s t one. With i n c r e a s i n g asymmetry, h i ghe r terms i n the expans ion become impor tant and s imu l t aneous l y h i g h e r l e v e l s a l so develop t h i s "asymmetry s p l i t t i n g " . The K ^ = 0 l e v e l s never s p l i t ; asymmetry s p l i t t i n g of # 0 l e v e l s , f o r a g i v en b^, decreases w i t h i n c r e a s i n g K_^ and i n c r ea se s w i t h i n c r e a s i n g J . I t i s g e n e r a l l y found tha t the low 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 molecu les can be reasonab ly w e l l accounted f o r i n terms of e i t h e r equa t ion 2.7 or 2 . 9 . However, at h i ghe r J v a l u e s , e spec -i a l l y i n molecu les w i t h one or 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 e f f e c t 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 . I t i s most 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 Hami l t on i an a s : 13 where and H. = H - E „ = H + H, 2.11a R V r d I? = A P 2 + B P ? + C P 2 2.11b r v a v b v c d aByo a 3 Y ° a , 3 , Y > 5 . T h e , s o l u t i o n of the H problem i s then taken as a z e r o t h order approx -i m a t i o n and i s t r e a t ed as a ( f i r s t order ) p e r t u r b a t i o n . S ince the opera to rs P^ do not commute, the sum i n equa t ion 2.11c has e i g h t y one terms. However, by symmetry arguments, i t can be shown that on l y the 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 to the r o t a -t i o n a l energy to f i r s t o rder (26 ) . Fur thermore , many o f the c o e f f i c i e n t s of these twenty one terms are equa l (see d e f i n i t i o n , equa t ion 2.3b) w i t h the r e s u l t tha t one i s f i n a l l y l e f t w i t h on l y n ine d i s t i n c t q u a r t i c c o n -s t a n t s : T aacta ' Taa33 = T33aa' Ta3a3 = Ta33a = T3a3a = T3aa3 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 te rms , P^P^P P^, of may t h e r e f o r e be arranged i n t o n ine g roups , 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 the d i s t o r t i o n Hami l t on i an t o s i x groups of terms i s achieved by c o n s i d e r i n g the commutation r u l e s f o r the r o t a t i o n a l angu lar momentum o p e r a t o r s . The app rop r i a t e r e l a t i o n s were f i r s t d e r i v e d by K i v e l s o n and W i l son (26) . They a r e : (P P Q + P P )• = 2(P PZ+PZP ) + 3P - IP - 2Pa 2.13 a 3 3 a a 3 3 a y a 3 where a*3*Y and w i t h a,3 ,Y t o D e taken i n c y c l i c o rder as a , b , c . Through the use of equa t ion 2.13 i t i s then p o s s i b l e to e l i m i n a t e the T a 3 a 3 ( W P 3 P a ) 2 t e m S f r o m V T h e c o e f f i c i e n t s T a 6 a g are i 14 2 2 2 2 2 2 2 those of (P P„+P.P ) and terms i n P , P, and P are i n t r o d u c e d . These a 8 8 a a b c new quad ra t i c terms are then absorbed i n t o the " r i g i d r o t o r " pa r t of the r o t a t i o n a l Hami l ton ian which must now be r ede f i ned a s : HR = + H'd 2.14a H' = A ' P 2 + B*P 2 + C*P 2 2.14b *d r v a v b v c 2 7 a,8 where T ' = T aaaa aaaa a,8 = a , b , c Taa88 Taa88 + 2xa8a8 a * 6 2.15 and A' = A + 1/4(3T, . - 2T . , - 2T ) 2.16a v v bcbc abab acac B 1 = B + 1/4(3T - 2T , - 2T , . ) 2.16b v v acac bcbc abab C' = C + 1/4(3T , , - 2T , , - 2x ) 2.16c v v abab bcbc acac S ince the new r o t a t i o n a l cons tan ts c o n t a i n a sma 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 of i n e r t i a (see s e c t i o n 2.4) de r i v ed from them i n c l u d e another ambigu i ty i n a d d i t i o n to tha t a r i s i n g from p u r e l y v i b r a t i o n a l e f f e c t s . For the s p e c i a l case of a p l ana r molecule s t i l l f u r t h e r s i m p l i f i c a t i o n can be ach ieved u s i ng the r e l a t i o n s g i ven below (27 ,28 ) : T, , = T = 0 2.17a bcbc acac T c c c c = + 2 c i _ x _ ^ + ( C l \ l u . 2 .17b \A , A~B" + T + C T . . + / c \ T. , , . aaaa „ 0 aabb I— I bbbb A B W i T bbcc = (f^bbbb + (f^aabb 2.17c 15 x = IC \ T + / C \ 2 T 2.17d aacc T I aaaa - aabb ^ . i / a These were obta ined 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 son e x p r e s s i o n f o r the taus (equat ion 2 .68 ) . They can be used , toge ther w i t h equat ions 2 .15 , to r e w r i t e i n terms of on l y four independent t a u s ; u s u a l l y T A A A A » Tbbbb» T aabb a n c * T a b a b ' Hk = 1 / 4 h a a a [ P a + ( C / A ) 4 p C + ( C / A ) ' ( P a P c + P c ?a>] + T b b b b [ P b + ( C / B ) A p c + ( C / B ) 2 ( P b p 2 c + P c P b 2 ) ] + T aabb [ ( 2 C 4 / A 2 B 2 ) P 4 + (C/B) 2 ( P V + P V ) + ( P a P b + P b p 2 ) + ( C / A ) 2 ( P b P c + P c P b > ] + T a b a b [ 2 ( P a P b + P b P a > ] } 2.18 The e q u i l i b r i u m va lues of the r o t a t i o n a l cons tants shou ld be used i n equat ions 2.17 and 2 .18 . In p r a c t i s e , these are very r a r e l y a v a i l a b l e , 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 cons tants (A^, B^, tV) are g e n e r a l l y used . Th i s has been found to be a ve ry good approx imat ion f o r w e l l b e -haved m o l e c u l e s ; i . e . f o r molecu les t ha t do not have very 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 e f f e c t s . I f i t i s necessary to c a r r y the a n a l y s i s to h i ghe 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 l a r g e o r because h i g h J l e v e l s are b e i n g i n c l u d e d , then 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 gene ra l one d i s cussed below must be used . For the gene ra l asymmetric top i t was long thought that the minimum number of independent f i r s t o rder q u a r t i c constants was s i x . R e c e n t l y , however, Watson has shown that there 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 tha t 16 reduces t h i s number to f i v e (29) . He has a l s o shown tha t no f u r t h e r r e d u c t i o n i s p o s s i b l e (30 ) . There are many d i f f e r e n t se t s of f i v e q u a r t i c cons tants tha t cou ld be used. Only one of the s e v e r a l convenient f o rmu l a t i ons i s reproduced he re : H K = H T + H d 2 - 1 9 a 2 ~ 9 ~ ? H = A P + B PT + C P 2 19b r v a v b v c y *d = V - ^ K ^ a " ¥ l " 2 6 / ( P b - P c > 2 2 ? 9 9 ? 2.19c where v v 6 A - A ' + 16R, 2.20a w i t h and B = B* - 16R , (A , -C ' ) / ( B , -C* ) 2.20b v v 6 v v v v C = C + l e R ^ A ' - B M / ^ B ' - C ' ) 2.20c v v 6 v v v v R, = 1/64Jx' + T ' - 2T* } 2.20d 6 I bbbb cccc bbcc ' A _ = - 1 / 8 | T ' , + T * | 2.21a J i bbbb . c c c c ' A = 3/8|x ' + x ' } - 1 / 4 | T ' + x ' + x ' } 2.21b JK ' bbbb cccc ' « aacc aabb bbcc ' A = - l / 4 J x ' . + T » + T ' } + l/4|x» + x ' + x ' } 2.21c K ( bbbb cccc aaaa ' 1 aacc aabb bbcc ' 6 T = -1/16JT* . - x ' } 2.21d J < bbbb ; c c c c ' Sv = l / 8 x ' ( B ' - A , ) / ( B , - C ' ) + l / 8 x ' ( C ' - A ' ) / ( B ' - C ) K bbbb v v v v cccc v v v v 2.21e + l / 8 j x ' - x ' + x* ( 2 A ' - B ' - C ' ) / ( B , - C ' ) i 1 aacc aabb bbcc v v v v v ' 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 generated s m a l l terms 2 2 2 i n P , P, and P that had to be absorbed i n t o the r o t a t i o n a l c o n s t a n t s , a b c The Hami l ton ians d i s cussed above have been found to g i ve a very good account of the low to medium J r o t a t i o n a l energ ies o f a l a rge number o f molecu les (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 molecu les w i t h l a rge c e n t r i f u g a l d i s t o r t i o n , are c o n s i d e r e d , however, i t can become necessary to extend the r o t a t i o n a l Hami l t on i an to i n c l u d e terms of the s i x t h (and even h ighe r ) power i n the angu la r momentum components. Watson has p o i n t e d out tha t i n genera l there are 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 tha t the n o n - t o t a l l y symmetric q u a r t i c terms neg lec ted i n the f i r s t order treatment are a u t o -m a t i c a l l y absorbed i n t o the s e x t i c (or h ighe r ) terms and, i ndeed , are i n -separab le from them. A convenient form f o r the s e x t i c pa r t o f the r o t a t i o n a l H a m i l t o n i a n , and tha t used i n t h i s work i s : ~ 6 4 2 2 4 6 4 2 2 2.22 + h T P2lP2(pl-P2) + ( P 2 - P 2 ) P 2 | + h | P 4 ( P 2 - P 2 ) + ( P 2 -P 2 ) P 4 } JKT I a b c b c a> K< a b c b c a ' A l though some attempt has been made to r e l a t e the s e x t i c c o e f f i c i e n t s to the cub i c terms i n the v i b r a t i o n a l f o r ce f i e l d (33) i t i s p robab ly bes t to regard them as f i t t i n g parameters . The q u a r t i c c o e f f i c i e n t s on the o the r hand have been used w i t h some success i n the de t e rm ina t i on of quad-r a t i c p o t e n t i a l constants ( 34 ) . The d i s t o r t i o n c o n t r i b u t i o n s to the t o t a l r o t a t i o n a l energy , c o r r e c t to f i r s t o r d e r , may be obta ined by e v a l u a t i n g the e x p e c t a t i o n va lues o f the d i s t o r t i o n Hami l t on i an i n the " r i g i d " asymmetric r o t o r b a s i s f u n c t i o n s . 18 For example, i f the Hami l t on i an g i ven i n equat ions 2.19 i s used then the f i r s t o rder r o t a t i o n a l energy i s (35 ) : E R " E r + E d 2.23a E r = l / 2 ( B v + C v ) J ( J+ l ) + J A v - 1/2(B v + C v ) ( E (b ) 2.23b *d = <^d> = " V 2 ( J + 1 ) 2 " A J K J ( J + 1 ) < P a > " A K< ? a> 2 ' 2 3 c + ( 2 6 J / b p ) J ( J + l ) { E ( b p ) - ( F 2 > [ + 2 ( 6 K / b p ) { E ( b p ) < P 2 > - <P«>} where b i s now g i ven by (C -B )/(2A -B -"c ) and the terms i n P 2 and p v V V V V c 2 ~ P^ were e l i m i n a t e d from the e x p r e s s i o n f o r E^  w i t h the a i d of the f o l l o w i n g r e l a t i o n s ( 26 ,36 ) : <P 2 >= 1/2JCJ+1) - l /2E (b p ) - ( ^ ) { E ( b p ) - <P 2 ) } <P 2 >= 1/2J( J + 1 ) - l /2E (b p ) + ( ^ ) { E ( b p ) - <P 2>} 2.24a 2.24b A s i m i l a r p rocedure , but based i n s t e a d on H'^_ + H1^ ( equat ions 2.14 and 2 .18 ) , may be used to o b t a i n the f i r s t o rder r o t a t i o n a l energy of a w e l l behaved p l ana r mo l e cu 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 equat ions 2 .23 , can p rov ide a convenient s t a r t i n g p o i n t f o r a l e a s t squares a n a l y s i s . I f i t i s necessary to i n c l u d e s e x t i c (and h ighe r ) terms i n the non-r+*t /St/ r i g i d r o t o r Hami l t on i an ( i . e . H„ = H + H, + H + •••) then a s imple f i r s t R r d s v order treatment w i l l i n gene ra l not be comple te l y adequate. Th is i s because the c o n t r i b u t i o n s to the 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 the " 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 of H can be R of s i m i l a r magnitude to the d i agona l s e x t i c elements (35 ) . 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 > 3 + H J K j 2 ( J + 1 ) 2 < P a > + HKJ J ( J + 1 )< Pa> + \(PSa)+ 2h J(-l/b p)J 2(J+l ) 2 J E(b p) - <P 2 ) } 9 A 2 - 2 3 d + 2(-1/VhJKJ(J+1)iE(V<Pa>- <V* 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 essen-t i a l l y "forbidden" and the rest occur with widely varying intensities. Spec-i f i c a l l y , i t can be shown that the probability of a radiation induced trans-i t i o n between two rotational states J„ and J', , i s proportional to K-1 K1 K-1 K1 the following matrix element ( 3 7 ) : K j . K ^ . K j y l J ' . K ^ . K j ^ 2 = ^|<J,K_ 1,K 1|y F|j',K; i,Kj>| 2 2.25 where y„ i s the F component of the molecular dipole moment referred to r space fixed axes (X,Y,Z). Since the y are clearly dependent on the orient-r ation of the molecule in space, i t i s much more convenient to rewrite the above matrix element in 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_ = y 2.26 PF L~i FgHg g 20 where the $_ are the d i r e c t i o n cos ines between the molecu le f i x e d and the Fg space f i x e d a x i s systems. One can then w r i t e : K J . K ^ . K J M J J ' , K ^ , K J > | 2 = J ^ y ^ S ( J . K ^ . K ^ J 1 , K j ) / (2J+1) 2.27 g where the S are c a l l e d l i n e s t r eng ths and are de f ined by : V^-rV^-i^P = S K J ' K- i ' K i» M j l*F g l J ,» KI i» K i ' M j>l 2 2 - 2 7 a F > V M j The summation over and i n equa t ion 2.27a i s necessary to take i n t o account a l l o f the p o s s i b l e t r a n s i t i o n s which i n the absence of an e x t e r n a l f i e l d w i l l be degenerate ; M i s the quantum number f o r the component of the t o t a l angu la r momentum a long some space f i x e d a x i s , and takes on va lues J , J- l ,•••,- J . I t tu rns out tha t the summation over g i n equat ion 2.27 i s redundant because at most on l y one of the three p o s s i b l e l i n e s t r eng ths can be n o n -z e r o . Th i s has prompted a convenient c l a s s i f i c a t i o n of t r a n s i t i o n s as a- types , b-types and c-types a cco rd ing to whether they are a l lowed by a nonzero y^, or y^ r e s p e c t i v e l y . The l i n e s t r eng ths may be r e a d i l y eva lua ted us ing r i g i d r o t o r wave f u n c t i o n s . Ex tens i ve t a b l e s of S ' s have been compi led f o r v a r i o u s va lues g of K (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 be long to a P-branch, the AJ = 0 ones a Q-branch, and.the AJ = +1 ones an R-branch. S i m i l a r s e l e c t i o n 21 r u l e s can be formulated f o r the pseudoquantum numbers and K^. However s i n ce there i s a cons ide r ab l e v a r i a t i o n i n the i n t e n s i t y of the a l lowed 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 to r e f e r d i r e c t l y to one o f the l i n e s t r e n g t h t a b l e s . For an a n a l y s i s o f a mo lecu l a r r o t a t i o n a l spectrum to be complete , 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 tha t may be p r e sen t . Such s t r u c t u r e i s a ve ry common occurrence and i s produced by a coup l i ng of the r o t a t i o n a l angu la r momentum to o ther angu la r momenta i nhe ren t i n the mo lecu le . 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 angu lar momenta as w e l l as n u c l e a r s p i n angu la r momenta. S ince most s t a b l e molecu les have ground e l e c t r o n i c s t a t e s , however, on ly 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 nuc leus w i t h s p i n g r e a t e r than 1/2 has an e l e c t r i c quadrupole * moment which 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 ad i en t s produced at tha t nuc leus by the o ther charges i n the mo lecu 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 order of tens of MHz, but v a r i e s g r e a t l y a cco rd ing to the nuc leus and t r a n s i t i o n i n v o l v e d . The complete Ham i l t on i an f o r the i n t e r a c t i o n of a s i n g l e quadrupo lar nuc leus w i t h the mo lecu l a r r o t a t i o n may be w r i t t e n as (39 ) : 2.2 Nuc lea r Quadrupole Coupl ing 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 expe r imen ta l ev idence of a nonzero n u c l e a r e l e c t r i c d i p o l e moment. 22 where the tensor VE_ i s the e l e c t r i c f i e l d g r a d i e n t , at the quadrupolar n u c l e u s , due to the e x t r a n u c l e a r charges and Q_ i s the n u c l e a r quadrupole moment t e n s o r , w i t h components de f ined b y : Q i j = y p ( 3 xi Xj " 6 i j r 2 ) d T 2 - 2 9 a where the i n t e g r a l i s over the n u c l e a r volume and x^ represen ts the X , Y and Z space f i x e d coord ina tes o f a p o i n t i n the n u c l e u s , a t which the charge d e n s i t y i s p. The net e f f e c t of t h i s i n t e r a c t i o n i s a coup l i ng of the r o t a t i o n a l angu lar momentum and the nuc l ea r s p i n angular momentum J . to form a r e s u l t a n t F_ a cco rd ing t o : F = J + I 2.30 2 such tha t ( i n u n i t s o f h ) < F , M F | F 2 | F , M F > = F(F+1) 2.30a where the quantum number F i s r e s t r i c t e d to the v a l u e s : J+I , J+I-l ,•••, | j - l | . I f the coup l i ng i s not too s t r o n g , such tha t J can s t i l l be r e -garded as a good quantum number, then Cas im i r (40) has shown tha t the quadrupole Hami l t on i an may be r e w r i t t e n i n the f o l l o w i n g , more t r a c t a b l e fo rm: Hl = { 2 J ( 2 J - l ) I ( 2 I - l ) } l 3 ( ^ ) 2 + 3 / 2 ^ - I * ' 2 * 2 - 3 1 where eQ i s a measurable n u c l e a r constant c a l l e d the charge weighted e l e c t r i c quadrupole moment, and i s de f i ned b y : eQ = <I ,^ =11 Q z z 11 . M ^ O 2. 31a w h i l e q j i s the ZZ component of the e l e c t r i c f i e l d g r ad i en t tensor averaged over the r o t a t i o n a l s t a t e J , M = J i . e . . —11 23 Q J = O . K ^ . K ^ M ^ J I V ^ I J . K ^ . K ^ M ^ J ) 2.31b 2 2 with V ^ ^ = 3 V/3Z = - ( V E ) ^ . 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 ( 40 ) : EQ " { 2 J ( 2 J - l ) I ( 2 I - l ) } l 3 / 4 C ( C + 1 ) - JCJ+DKI+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. It can be re-written in 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. Specifically: q J = Z ) q g g < J ' K - i ' K i ' M J = J l $ z g l J ' K - r K i ' M j = J > 2 - 3 3 g= a,b,c 2 2 where q =3 V/3g i s essentially independent of rotational state and only gg slightly dependent on vibrational state. There are no cross terms included in equation 2.33 because a l l of the matrix elements of the form (*'Za*2b^ may be shown by a symmetry argument (41,39) to be zero to f i r s t order. The remaining nonzero matrix elements in equation 2.33 may be expressed in terms of the tabulated line strengths (41), or alternatively, the following relation may be used: < J ' K - l ' K l ' M J = J l $ Z g l J ' K - l ' K l ' M J = J > - { ( J + l 2 ( 2 J + 3T } < J >K-1 > K1 l ? g 1 J > K-1 »K1> + (2J+3)"1 2.34 24 One can then w r i t e : qJ = S { ( J + l ) (2J-t-3)}< J»K-1 » K 1 l P gI J » K -1 »K1> 2 ' 3 5 § = a , b , c where the (2J+3) * terms have been e l i m i n a t e d by assuming that the q * s a t i s f y Lap lace s equa t ion , i . e . V 2 V = q + q , . + q = 0 2.36 aa bb ^cc F i n a l l y , w i t h the use of equat ions 2 .24 , 2.35 and 2.36 the f i r s t o rder quadrupole energy of equa t i on 2.32 may be r e w r i t t e n as ( 3 9 , 4 2 ) : 1 = 3C(C+1)-4J(J+1)I(I+1)  hQ 8 I ( 2 I - l ) J ( 2 J - l ) ( J+ l ) ( 2 J+3 ) V J V r a / " ^ ' " a a 2.37 {{3<P2> - J ( J + l ) } X j + ( l /b p )KpJ>-E(b p ) | ( X b b - X c c ) } where the x which are called quadrupole coupling constants are defined b y : X = eQq 2.37a gg gg If there i s more than one quadrupolar nucleus in a molecule then the associated hyperfine structure w i l l usually be very complex. The simplest multiple system (and that encountered in this work) occurs when there are only two quadrupolar nuclei, one of which couples much more strongly than the other. The general theory for this system has been worked out by Bardeen and Townes (43) ; i t i s outlined below. * Th i s i s s t r i c t l y v a l i d on l y i f the charges produc ing the p o t e n t i a l V are e n t i r e l y ou t s ide the nuc leus i . e . have zero p r o b a b i l i t y of o c c u r r i n g i n the nuc l ea r volume. Exper imenta l ev idence suggests tha t i t i s v a l i d to a good approx ima t ion . 25 Let 1^ represent the spin angular momentum of the strongly coupled nucleus, and 1^ that of the weakly coupled nucleus. One can then w r i t e : Ll = 1 + Li 2-38a F = F 1 + I 2 2.38b where the associated quantum numbers and F may take on the values J + I 1 , J + I 1 - l , - - - , | j - I 1 | and F 1 + I 2 , F 1 + I 2 - 1 , - | F 1 - I 2 | r e s p e c t i v e l y . Then i f H i s the quadrupole Hamiltonian f o r nucleus 1 and H that f o r q l Q2 nucleus 2 the f i r s t order perturbation energy i s given by: E Q = < J ' K - l ' K i ' F i ' I 1 ' I 2 ' F ' M F l F F Q 1 + ^ Q 2 | J , K _ 1 , K 1 , F 1 , I 1 , I 2 , F , M F > 2. A closed' expression f o r t h i s f i r s t order energy that i s p a r t i c u l a r l y s u i t a b l e f o r s p e c t r a l analysis has been derived (44): 39 . 3A (A+1)-4I. (I.+l) J(J+1) E = o o 1 1 Q 8 I 1 ( 2 I 1 - l ) J ( 2 J - l ) ( J + l ) ( 2 J + 3 ) j{3<p2)- J ( J + l ) } X a a ( l ) 2.40 + ( 1 /V{< Pa>- E (V}{ Xbb ( 1 ) - X c c ( 1 ) } | J3A X (A^ D-412 (I 2+l) F x ( F ^ l ) } ^  (A 2+1)-4J (J+l) F^ (Fj+1)} + 16I 2(2I 2-1)J(2J-1) (J+l) (2J+3)F 1(2F 1-1)(F 1+1) (2F x+3) X " ° ...xj{ 3<p2>- J ( J + l ) } x a a ( 2 ) + d / b p ) { < P a > - E ( b p ) } { x b b ( 2 ) - xcc(2)}j where ^ = p ^ j - ^ ^ _ i ^ ^ + i ) _ j ( j + i ) 2.40a Al = F(F+1) - I 2 ( I 2 + D - F ^ F ^ l ) 2.40b \ 26 A 2 = ~ J ( J + 1 > " F ^ + D 2.40c In g e n e r a l , t h i s exp ress i on w i l l not be complete ly s u f f i c i e n t f o r such a two nuc leus system because the m a t r i x elements o f f d i agona l i n w i l l u s u a l l y make a s m a l l but s i g n i f i c a n t c o n t r i b u t i o n to the t o t a l quadrupole coup l i ng energy. Th i s can then be e x a c t l y determined on ly 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 the m a t r i x r e p r e s e n t a t i o n of H^. The r e l a t i v e i n t e n s i t i e s o f the quadrupole 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 determined by computing d i p o l e moment m a t r i x elements l i k e those d i s cussed a t the end of 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 rep l a ced by those app rop r i a t e to the 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 example, i n the case o f a s i n g l e c o u p l i n g nuc leus these are O.K^.K^I.F.MpI and | J 1 .K^ ,K* , I , F ' ,MF> . D e t a i l e d c o n s i d e r a t i o n of the t r a n s i t i o n moment, wh ich may be f a c t o r e d i n t o a h y p e r f i n e pa r t and a pure r o t a t i o n a l p a r t , then r e v e a l s tha t 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 F, namely: AF = 0,±1 2.41 A s i m i l a r r u l e a l so a p p l i e s to F^ i n the two n u c l e i case d i s cussed above. S ince there can be 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 these a l lowed h y p e r f i n e components, however, i t i s g e n e r a l l y wor thwh i l e a c t u a l l y t o compute the app rop r i a t e m a t r i x e lements . For the case o f a s i n g l e c o u p l i n g nuc leus t h i s i s not 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 are g e n e r a l , they have been t a b u l a t e d (45 ) . 2.3 The S ta rk E f f e c t In the presence of a un i fo rm e l e c t r i c f i e l d E a molecu le 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 partially 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): where E_ defines the Z direction in space. The associated Stark energies can generally be evaluated to sufficient accuracy using perturbation theory. For asymmetric top molecules, in 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 totally symmetric representation of the rotation group (47). The to t a l rotational energy, correct to second order i n the pertur-bation, may therefore be written as (46): 2.42 g= a,b,c g 2.43 where E° is the unperturbed rotational energy and the second order Stark shifts are given by: 2.43a 28 i n which the summation extends over a l l s t a t e s except J v ; there i s K - 1 K 1 no summation over M' because $ i s d i agona l i n M . S ince the m a t r i x J £g J elements i n equat ion 2.43a can be expressed i n terms of the p r e v i o u s l y i n t roduced l i n e s t r eng ths S , i t i s p o s s i b l e to r e w r i t e the second order S ta rk energ ies i n the f o l l o w i n g more u s e f u l fo rm: r E ( 2 ) l - V' j 2~MJ S g O ^ j . K ^ J - l . K ^ . K p J J K ,K 'MJ \2 J+ l/Z- f J (2J-1) X E o o 2.44 M j S ^ J . K ^ . K ^ J . K ^ . K p ( J+ D 2 -M 2 S ( J . K ^ . K ^ J + l . K ^ . K p J ( J+D X E o _ E o + (J+l) (2J-3) X ~cS ~^ \ ^ JKiK[ J K _ 1 K 1 ( J + 1 ) K _ 1 K ] ; where now the summation over J ' , f o r which on ly the J ' = J , J± l terms are nonzero , has been w r i t t e n o u t . I t shou ld be noted that some n o n t r i v i a l man ipu l a t i on i s r e q u i r e d to get from equat ions 2.27a and 2.43a to equat ion 2.44 (46 ) . The success of the above treatment i s dependent upon the v a l i d i t y of the assumption tha t the S t a rk energ ies are s m a l l compared to the s e p a r -a t i o n of the zero 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 , however, degenerac ies or near degenerac ies 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 encountered. Golden and Wi l son (47) have shown that such cases may be handled by app l y i ng a Van V l e ck t r a n s -fo rmat ion (20) to the m a t r i x r e p r e s e n t a t i o n of HR + Hg. The t ransformed m a t r i x i s then f a c to r ed i n t o submatr ices 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 set o f degenerate or n e a r l y degenerate l e v e l s . The elements connec t ing these submatr ices c o n t r i b u t e to the energy on ly i n the f o u r t h order 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 of the submatr ices g i ves the c o r r e c t S ta rk per turbed r o t a t i o n a l e n e r g i e s . These have a p a r t i c u l a r l y s imp le form f o r the most common s i t u a t i o n i n which the near degeneracy i n v o l v e s on l y a p a i r o f l e v e l s , J and J " „ „ : K - 1 K 1 K - 1 K 1 \ l V M J + ^ " K ^ J \ ( \ l V M J " \>> K«.M 2 | r | 2 E ± . _ ^ L i _ zL±__ ± o - i i J + E \K\ ( 2 < 4 5 where E M and E „ M are computed us ing equa t ion 2 . 4 3 , but K - 1 K 1 J K ^ K ' ^ J the sum i n equa t ion 2.43a (or 2.44) i s on l y over the l e v e l s J ' , , # K - 1 K 1 J v , J " „ v„. The o f f d i agona l elements EE, depend upon the type o f K - 1 K 1 K - 1 K 1 degeneracy be i ng c o n s i d e r e d . The s i m p l e s t case i s tha 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 M2 Z2^2 " j f j + i ) ( 2 J + l ) S g ( J , K _ l f K l S J f K » l f K » ) 2.45a where g w i l l be _a f o r a near p r o l a t e asymmetric t o p , and c f o r a near o b l a t e t o p . Fur thermore , i f the asymmetry s p l i t t i n g i s ve ry s m a l l , o r n i l , then equat ion 2.45 may be s i m p l i f i e d to the f o l l o w i n g approximate e x p r e s s i o n : E - 1/2(E° + E° ) ± « J s * ( J t K K . ; J ,K» K?) K , 1 K 1 K"i^i V J < J + 1 ^ 2 J + 1 ) 8 30 Jv V Jy/-" V " J(J+1) K _ ! K 1 K _ i K i where K i s e i t h e r K_^ or as a p p r o p r i a t e . S ince there can be sma l l asymmetry s p l i t t i n g s i n even q u i t e asym-m e t r i c mo l e cu l e s , i t i s apparent from t h i s l a s t exp re s s i on tha t the s p e c t r a of such molecu les can be expected to con 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 o rder or near f i r s t o rder S ta rk e f f e c t . These are then 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 , which have on ly a second order S t a rk e f f e c t , and hence are 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 ta rk lobes 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 the 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 v e c t o r . I f the two are p a r a l l e l on ly AM^ . = 0 t r a n s i t i o n s which are known as ir-com-ponents are a l l owed ; whereas, f o r the p e r p e n d i c u l a r arrangement on ly the AM_ = ±1 o r a-components are a l l owed . Wi th a conven t i ona l microwave spec t romete r , such as tha t used i n t h i s work , the two f i e l d v e c t o r s are p a r a l l e l and hence on l y the ir-components are observed . The r e l a t i v e i n -t e n s i t i e s of these may be deduced by i n v e s t i g a t i n g the app rop r i a t e d i r e c t i o n cos ine m a t r i x elements (47) and, may be expressed i n the f o l l o w i n g , c l o s e d , comple te l y gene ra l form: I(Mj) = AM2 AJ = 0 AMj = 0 2.47 I(Mj) = B{(J+1) 2 - Mj\ 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 determined 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 of M . There i s an a d d i t i o n a l f a c t o r of 1/2 i n the i n t e n s i t y exp re s s i on f o r the M = 0 -»• 31 Mj = 0 component. Th is a r i s e s because a l l of the l e v e l s w i t h M^> 0 are doubly degenerate . 2.4 R o t a t i o n a l Cons tan t s , Moments of I n e r t i a , I n e r t i a l Defect and the  M o l e c u l a r S t r u c t u r e . The r o t a t i o n a l constants de f i ned by equat ions 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 obscure dependence on the v i b r a t i o n a l s t a t e of the mo lecu l e . Th i s problem 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 authors ( 4 8 , . . . , 5 3 ) . They have shown t h a t , w i t h the assumption of s m a l l v i b r a t i o n a l amp l i tudes , each r o t a t i o n a l constant may be r e w r i t t e n as a converg ing s e r i e s i n the v i b r a t i o n a l quantum numbers. S ince on ly the 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 then has the f o l l o w i n g r e l a t i o n s : A = A - V* a a ( v +d /2) + • • • 2.48a v e s s s s B = B - V a b ( v +d 12) + ••• 2.48b v e _-_> s s s s C = C - y * a C ( v +d /2) + • •• 2.48c v e _-_< s v s s s where A , B and C are 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 are 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 , and v i s the v i b r a t i o n a l r s quantum number o f the s t b normal mode w i t h degeneracy d g . A l though express ions are a v a i l a b l e f o r 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 parameters (51) , s i n c e these c o n t a i n both harmonic and anharmonic p o t e n t i a l constants as w e l l as C o r i o l i s coup l i ng c o n s t a n t s , t h e o r e t i c a l c a l c u l a t i o n of the a ' s i s r a r e l y at tempted. Exper imenta l va lues may be obta ined f o r some of these by s tudy ing the r o t a t i o n a l s p e c t r a of molecu les i n low energy , 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 s t a t e s , 32 By analogy w i t h the r i g i d r o t o r one may de f i ne e f f e c t i v e moments o f i n e r t i a us ing the r e l a t i o n s : IV=-4- I K = - T - iV=-4- 2 . 4 9 3 8ir A ° 8ir B C 8ir C V V V where I V , I? and I V w i l l have u n i t s of a.m.u.S 2 i f the r o t a t i o n a l constants a b c 2 are measured i n MHz and the conve r s ion f a c t o r h/8ir i s taken to be 505390.9 ± 8.0 a.m.u.& MHz (54) . I t then f o l l o w s from equat ions 2.48 t h a t these may be r e l a t e d to e q u i l i b r i u m moments o f i n e r t i a I b y : I V = I e + V * e a ( v +d /2) + • •• (a=a,b,c) 2.50 a a i—J s s s s where /„ 2 e a (on \ , T e , .2 a „ s " V"h-j (V a s 2 ' 5 0 a and I a = - f - ^="4- 1 & = - ^ - 2.50b a 8 i r 2 A B 8TT 2 B C 8 T T 2 C e e e and where i t has been assumed that A » | ^ a 3 ( v +d /2) | e t c . In a d d i t i o n 6 S S S s to the h i ghe r terms i n the v i b r a t i o n a l expans ion , there may a l s o be ve ry s m a l l c o n t r i b u t i o n s to I V from two other sources tha t have not been ex-a p l i c i t l y i n c l u d e d i n equat ion 2 .50 . The f i r s t o f these 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 which a r i s e s when the e f f e c t i v e moments of i n e r t i a are c a l c u l a t e d by r e p l a c i n g the " p u r e " r o t a t i o n a l constants i n equat ion 2.49 •N^  w i t h the more r e a d i l y ob ta ined ( A ' , B ' , C ' ) or ( A , B , C ) ones. The J . V V V V V V second i s due to the e f f e c t s of 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 (55 ) . Both o f these c o n t r i b u t i o n s can u s u a l l y be ignored (56 ) . The e q u i l i b r i u m moments of i n e r t i a i n t roduced i n equat ion 2.50 may 33 be used to de f i ne an e q u i l i b r i u m mo lecu l a r s t r u c t u r e by means of the f o l l o w i n g e x p r e s s i o n s : I 6 = V* m. ( b 2 . + c 2 ) a 1 e i e i x I f = I> . ( a 2 . + c 2 . ) b L^j x e i e i l I 6 = V m . ( a 2 . + b 2 . ) c L^j x e i e i l where a . , b . and c . are the e q u i l i b r i u m coord ina tes of the nuc leus o f ex e i e i ^ t h the i atom of mass nu i n the molecu le f i x e d cen te 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 de f i ned by : V m . a . = 0 V m . b , = 0 v i e i v I e i I i and Em . a .b . = 0 V ' m . a . c , = 0 , l e i e i I ex e i From these l a s t express ions i t i s apparent tha t the C a r t e s i a n coord ina tes (a . , b . , c .) would be changed i f one of the atoms was r ep l aced by i t s e x ' e i ' ex i s o t o p e . Th i s i s due, however, a lmost e n t i r e l y to a s h i f t i n the a x i s system, s i n c e i t has been shown tha t the e q u i l i b r i u m i n t e r n a l coo rd ina tes are e s s e n t i a l l y independent of i s o t o p i c s u b s t i t u t i o n (57) . One cou ld 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 mo lecu l a r s t r u c t u r e by measuring va lues of I f o r a s u f f i c i e n t number of d i f f e r e n t i s o t o p i c s p e c i e s . Un fo r t una 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 to 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 constants not on ly f o r the ground v i b r a t i o n a l s t a t e , but a l s o ' f o r a l l of 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 which each of the normal modes has been s i n g l y e x c i t e d . 2.51a 2.51b 2.51c m. c . = 0 ' l e i 2.52 Y > . b , c . = 0 2.53 4 H x e i e i 3 4 I f a molecule i s p l ana 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 equat ions 2 . 5 1 , and w i t h the c-ax i s pe rpend i cu l a r to the mo lecu la r p l a n e , e e e i t f o l l o w s tha 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 z e r o . S i m i l a r behav io r i s not observed f o r the e f f e c t i v e moments of i n e r t i a de f i ned by equat ions 2 . 4 9 . Th is has l e d to the concept , f i r s t i n t roduced 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 V , d e f i n e d by : A V = I V - if - I V 2 . 5 4 c b a 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 de fec t v a l u e s , A ° , have been e x p e r i m e n t a l l y determined f o r a l a r g e number of s m a l l p l a n a r m o l e c u l e s . They are u s u a l l y p o s i t i v e and t y p i c a l l y o f the order of 10 a .m.u . r (59). A number of t h e o r e t i c a l s t u d i e s have been devoted to the i n e r t i a l de f e c t ( 5 5 , 5 8 , 5 9 , 6 0 ) . Oka and Morino ( 5 5 ) have shown tha t a l though i t i s due l a r g e l y to the v i b r a t i o n a l mot ion of the atoms i n a m o l e c u l e , there may a l s o be ve ry 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 -r o t a t i o n a l i n t e r a c t i o n e f f e c t s so tha t one must w r i t e : A V = A T r T T 3 + A + A 1 2 . 5 5 VIB cent e l e c where _ , ^ i _ c b VIB and J 3 X c  Tl I b I A c e n t " " T a b a b / 4 C ~ + 2 A ~ + 2 B ~ ( 2 , 5 5 B 1 V V V > A , = - (m /m ) 11 g - I g - I e !• 9 SSr e l e c e' p'.< c e c c a 8 a a bKbb> ^ . 3 ^ c T h e A c e n t e x P r e s s i o n i s t h a t a p p r o p r i a t e f o r the case where the e f f e c t i v e mo-ments of i n e r t i a have been c a l c u l a t e d u s i ng A ' , B' and C' r o t a t i o n a l cons t an t s . v v v The new symbols i n t roduced i n the d e f i n i t i o n of A , r epresent the mass e l e c r 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 r o t a t i o n a l P e 35 magnetic moment tensor g a a « S ince the l a t t e r have been measured f o r ve ry few molecu les & e ^ e c va lues can r a r e l y be c a l c u l a t e d . Oka and Morino (59) suggest tha t they may be es t imated 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 -0.005 a.m.u./A2 to each out-of-p lane IT bond i n the mo lecu l e . S ince the i n t r a c t a b l e E ' S appear i n equat ion 2.55a i t would seem at f i r s t tha t the t h e o r e t i c a l c a l c u l a t i o n of the i n e r t i a l de fec t might be h o p e l e s s l y complex. However, as f i r s t po in ted out by D a r l i n g and Dennison (58 ) , the anharmonic c o n t r i b u t i o n s to the e ' s cance l e x a c t l y i n t h i s e q u a t i o n . A gene ra l -exp ress i on 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 subsequent ly obta ined by Oka and Morino (55 ) . I t i s : 2 A VIB * Z - 2 ^ ( V 1 / 2 > Z , 2 M 8 2 , K V 2 + 2 " <4'>2} ~ 7T C t 0 g ( t 0 g - t 0 g f ) 2.56 t IT C \ t / whe re co i s the v i b r a t i o n a l f requency of the s normal mode, the X, , are C o r i o l i s coup l i ng c o n s t a n t s , and the t summation runs on l y over the out-of-p lane v i b r a t i o n s . The r e l a t i o n s d i s cussed i n the p rev ious paragraph have been s u c c e s s -f u l l y used to c a l c u l a t e the i n e r t i a l de f e c t s of a number o f s m a l l molecu les (59, 61 ) . The complex i t y o f such c a l c u l a t i o n s i n c r eases r a p i d l y , however, as l a r g e r molecu les are cons i de r ed . Th i s has prompted Hershbach and L a u r i e (60) to i n v e s t i g a t e v a r i o u s approximate schemes f o r e s t i m a t i n g i n e r t i a l d e f e c t s . One p a r t i c u l a r l y s imple e x p r e s s i o n , which a t t r i b u t e s a l l of 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 de fec t to the lowest f requency in-p lane (bending) v i b r a t i o n to , was found to g i v e s u r p r i s i n g l y good 36 agreement with experiment (usually w i t h i n 20%) . The expression i s : A° £ A V I B « 4 K / U j l 2.57 -1 2 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°" values of nonplanar molecules c a l c u l a t e d using equation 2.54 are t y p i c a l l y of the order of tens of a.m.u.R2, the observation of a small p o s i t i v e i n e r t i a l defect cannot of 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 , there are at l e a s t a few molecules which have small "A°" values but which are d e f i n i t e l y not planar i n t h e i r e q u i l -ibrium configuration ( 62 ,63 ) . I t i s therefore u s u a l l y most d e s i r a b l e to te s t a case of suspected p l a n a r i t y by comparing the observed value of A° with one c a l c u l a t e d assuming a planar s t r u c t u r e , p r e f e r a b l y using equation 2.56. A d d i t i o n a l confirmation may be obtained by determining the v a r i a t i o n of A V with i s o t o p i c s u b s t i t u t i o n . From equation 2.56 i t may be seen that v A f o r a planar molecule should be nearly independent of the atomic masses*. This has been experimentally v e r i f i e d (61 ) . Such i s not the case however f o r a nonplanar molecule where I - 1^ - I £ 0 , and hence "A ", i s strongly mass dependent. Once the question of p l a n a r i t y , or lack of i t , has been decided, the determination of the remaining s t r u c t u r a l features of the molecule may be undertaken. As already i n d i c a t e d only the ground v i b r a t i o n a l state e f f e c t i v e moments of i n e r t i a 1° are normally 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 since t h i s , unlike other s u b s t i t u t i o n s , causes very large changes i n at l e a s t a few of the v i b r a t i o n a l frequencies and hence may produce s i g n i f i c a n t , although u s u a l l y small, changes i n A v. 37 Several d i f f e r e n t procedures have been used to extract s t r u c t u r a l inform-ation from these. One that has seen extensive use i n the past i s simply to define an e f f e c t i v e structure, denoted r , by a set of equations anal-e o ogous to those f o r the equ i l i b r i u m moments: i . e . replace I by I and a a \a ., b ., c .J by la ., b ., c .I i n equations 2 . 5 1 . Then with s u f f i c i e n t 1 e i ' e i ' ei> J I o i o i oi> ^ 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 that the e f f e c t i v e i n t e r n a l coordinates are independent of the atomic masses, an r structure o may be c a l c u l a t e d . There are two serious d e f i c i e n c i e s i n t h i s approach. F i r s t l y , the r Q structure i s not simply r e l a t e d to e i t h e r of the more p h y s i c a l l y meaningful average, <(r)>, or equi l i b r i u m , r , st r u c t u r e s . Secondly, the necessary assump-t i o n that the e f f e c t i v e i n t e r n a l coordinates are independent of i s o t o p i c s u b s t i t u t i o n i s a rather poor approximation. This i s f o r c e f u l l y i l l u s -t r a ted i n the few cases where more than the minimum number of i s o t o p i c species have been studied so that two or more independent r Q structures may be c a l c u l a t e d ( 6 4 ) . These are generally i n rather 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 lengths of up to 0 . 0 1 % have been observed. Such discrepancies, which are frequently r e f e r r e d to as zero-point v i b r a -t i o n a l e f f e c t s , are not s u r p r i s i n g i n view of the averages involved i n the d e f i n i t i o n s of the e f f e c t i v e r o t a t i o n a l constants. They are, however, s u f f i c i e n t l y annoying that the c a l c u l a t i o n of r Q structures has now been l a r g e l y superseded by the semi-empirical approach discussed below. Kraitchman ( 6 5 ) has shown that i f a s i n g l e atom i n a r i g i d molecule i s i s o t o p i c a l l y substituted then i t s coordinates (a, b, c) 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 the unsubstituted species can be expressed d i r e c t l y i n terms of the center of mass p r i n c i p a l moments of 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 exact form of these e x p r e s s i o n s , which are c a l l e d K ra i t chman ' s equa t i ons , depends on the type of molecu le be ing cons ide r ed . For a p l a n a r , asymmetric t op , w i t h the c-ax is pe rpen -d i c u l a r to the mo lecu l a r p l a n e , they a r e : where 2.58a 2.58b 2.59a 2.59b u = (MAm)/(M+Am) 2.59c and 1^ are the cen te r o f mass p r i n c i p a l moments of i n e r t i a of the sub -s t i t u t e d s p e c i e s , I are those 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 of the parent molecu le and Am i s the mass d i f f e r e n c e of the two i so topes (Am = m' - m). These equat ions are a l s o v a l i d f o r r e a l m o l e -cu 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 used . Cos t a i n (64) has shown, however, tha t when 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 are used i n K ra i t chman ' s equat ions the r e s u l t i n g s t r u c t u r e , des ignated r , d i f f e r s s i g n i f i c a n t l y from the p r e v i o u s l y d i s cussed r s t r u c t u r e . He po in ted out tha t f o r d i a tomics the r bond o r s l eng th should be c l o s e r to the e q u i l i b r i u m va lue than the r Q l eng th i s , s p e c i f i c a l l y : r ^ l /2 ( r + r ) w i t h r < r <r 2.60 s e o e s o 39 For p o l y a t o m i c s , a l though there i s not a cor responding s imple r e l a t i o n connect ing the three s t r u c t u r e s , Cos t a i n sugges ted , on the b a s i s of some l i m i t e d expe r imenta l ev idence , tha t the r g s t r u c t u r e shou ld g e n e r a l l y be a good approx imat ion to the r & one. Subsequent work, w i t h a few excep t ions (66 ) , has l a r g e l y supported t h i s t h e s i s , and c e r t a i n l y the r g s t r u c t u r e s have been found to be more c o n s i s t e n t than the r ones (56) . o The most s e r i ous d i f f i c u l t y encountered i n o b t a i n i n g a good r g s t r u c t u r e i s the l o c a t i o n of an atom that i s near a p r i n c i p a l a x i s . I n s p e c t i o n of equat ions 2.58 shows that i f the u n c e r t a i n t y i n A l and AI, i s the l i m i t i n g cl D f a c t o r on the -accuracy to which | a | and |b| may be determined t h e n , the e r r o r i n these coo rd ina tes 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 to the coord ina tes themselves . C o s t a i n has proposed that as a gene ra l r u l e coo rd ina tes s m a l l e r than 0. isX shou ld not be determined by K ra i t chman ' 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 us ing the cen te r of mass or product of i n e r t i a c o n d i t i o n s , i . e . y V a . = 0 e t c . 2.61 ?m.a.b. = 0 e t c . i l l 2.62 S ince the f i r s t moment equa t ion ho lds on l y approx imate ly f o r the r g s t r u c t u r e , i f a coord ina te of the atom i s determined from i t , t h i s coord ina te w i l l d i f f e r from the t rue r va lue by : s . S ( r ) = / , m . r ./m r = a , b, or c 2.63 n l s i n ' ' The va lues of ^ r o ^ r ^ computed f o r molecu les i n which a complete s u b s t i t u -t i o n s t r u c t u r e cou ld be determined i n d i c a t e tha t 6 ( r ) should be l e s s than n 0.0028 f o r an atom as heavy as carbon. A s i m i l a r d i s c u s s i o n i s a p p l i c a b l e 40 to "r " coordinates obtained using the product of i n e r t i a condition. An alternative procedure for locating atoms near to a p r i n c i p a l axis has been proposed by Pierce (67). I t involves a double substitution technique i n which the second differences 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 effects to higher order. Since four i s o -topic species must be studied to 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 discussion the reader i s referred to the o r i g i n a l paper by Pierce (67) and a subsequent one by Pierce and Krisher (68). Consider the non-linear planar molecule WXYZ (c-axis 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 substitution technique. Then a ft ft ft ft suitable set of iso t o p i c species i s WXYZ, WXYZ, W XYZ and W XYZ. The f i r s t molecule i s called 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 rotation from the WXYZ system to the WXYZ system. Also l e t a and b be the coordinates of X i n the WXYZ system. Then i t X X ' can be shown that: AAI = AIV(*WXYZ) - Al (WXYZ) . D D D 2.64 = (k*Cos 29 - k ) a 2 + (2k'CCos6)a__ + k'C2 where x x A I Q ( WXYZ) = I A ( W XYZ) - I ( WXYZ) 2.65a a = a,b ,c AIJWXYZ) = Ia(W*XYZ) - Ia(WXYZ) 2.65b 41 k' = u* Al (*WXYZ) 1 + * ~ a  I (*WXYZ) - I (*WXYZ) SL D - l 2.65c k = y 1 + Al (WXYZ) a I (WXYZ) - I, (WXYZ) cL D -1 and where C = -(b - B)Cos 9 x y = MAm/(M+Am) y' = M'Am/(M'+Am) 2.65d 2.65e 2.66a 2.66b with M = mass of WXYZ, M1 = mass of WXYZ and Am = mass of X - mass of X. 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 c ' s which i s useful when either the a or b - moments of i n -ertia cannot be accurately determined. It i s : AAI = Al ( WXYZ) - Al (WXYZ) c c c = y' (b -B) 2 + (a - A ) 2 _ X X 2.67 The preceding expressions are s t r i c t l y valid only for a rig i d or equilibrium system but seem to yield consistent results when applied to real molecules using ground vibrational state effective moments of inertia (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 inertia. If b^ i s sufficiently large i t may be determined by single substitution; A, B and 8 may be calculated to sufficient accuracy (at least for a f i r s t iteration) using a preliminary, approximate structure. 42 The genera l s u b s t i t u t i o n procedure 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 . Th i s i s because i t g i ves at 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 ing on ly the r e a d i l y 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 of i n e r t i a . I t s most s e r i ous d e f i c i e n c y i s tha 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 b a s i s . There fore a l though the r s t r u c t u r e i s presumed to be a good s approx imat ion to the r £ s t r u c t u r e there i s no t h e o r e t i c a l quarantee tha t t h i s i s so . 2.5 C e n t r i f u g a l D i s t o r t i o n Constants and the V i b r a t i o n a l Force F i e l d . 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 constants i n t r oduced i n s e c t i o n 2.1 are independent of r o t a t i o n a l s t a t e but do depend on the v i b r a t i o n a l s t a t e under c o n s i d e r a t i o n . Th i s i s c l e a r l y ev ident from t h e i r d e f i n i t i o n , equat ion 2 .3b. U n f o r t u n a t e l y , 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 of the d i s t o r t i o n c o n s t a n t s . A c c o r d i n g l y , K i v e l s o n and W i l son (69) have de r i v ed a more convenient approximate r e l a t i o n , i n which the taus are expressed d i r e c t l y i n terms of the mo lecu l a r f o r ce f i e l d . A s m a l l v i b r a t i o n a l amp l i t ude , harmonic f o r c e s , mo lecu l a r model was the s t a r t i n g p o i n t f o r t h i s d e r i v a t i o n . The r e l a t i o n i s : x fl. - -i/2(iei?iei;)-1y'rj%l.(f-1)..rje.l. 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 of 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 t ensor w i t h respec t to the i t b i n t e r n a l c o o r d i n a t e , eva lua ted at e q u i l i b r i u m ; and the (f ^)j>j a r e the elements of the i n ve r se (harmonic) f o r ce constant m a t r i x . I t w i l l be noted tha t the v i b r a t i o n a l dependence of the taus has now d i sappeared . A g a i n , s i n ce 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 necessary to make the a d d i t i o n a l approx-eva lua ted i n such a way tha t the Eckar t c o n d i t i o n s (70) are s a t i s f i e d . K i v e l s o n and W i l son (69) have suggested a reasonably s imple way o f accom-p l i s h i n g t h i s . An a l t e r n a t i v e procedure has been more r e c e n t l y desc r ibed by Po lo (71) . For c a l c u l a t i o n purposes i t i s convenient to rear range s l i g h t l y equa t ion 2.68 to (72 ) : ima t i on of r e p l a c i n g them w i t h I e t c . The d e r i v a t i v e s must be 2.69 where A , A are r o t a t i o n a l constants i n MHz; 1° 1° are e f f e c t i v e p r i n c i p a l o o ' 8 ' y moments of i n e r t i a i n a.m.u./A.2; R = 2 h x l 0 ^ 7 w i t h h i n e rg-sec . Then, i f 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/rad f o r a s t r e t c h and a bend, r e s p e c t i v e l y , and the f o r ce cons tants have u n i t s of mdyne/A*, mdyne-A/rad 2 , and mdyne/rad f o r a s t r e t c h , a bend and a s t re t ch-bend i n t e r -a c t i o n , r e s p e c t i v e l y , the T are 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 Isocyanate C h l o r i n e i s o c y a n a t e , i n n a t u r a l i s o t o p i c abundance, was prepared by the p y r o l y s i s of 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 of 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 laced i n the end of a pyrex tube which was then connected to a vacuum system and pumped on f o r s e v e r a l hou r s . When the pressure had s t a b i l i z e d at l e s s tha t 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 caus ing some of i t to subl ime s l o w l y a long the pyrex tube and i n t o a r e a c t i o n zone. Th i s was a s e c t i o n of the pyrex tube , about 5 inches 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 heated to about 310°C, where the t r i m e r vapor was depo ly-mer i zed . A more o r l e s s constant f l ow o f t r i m e r i n t o the r e a c t i o n zone was mainta ined by s l o w l y i n c r e a s i n g the temperature at the end of the tube from 150°C to 200°C over a p e r i o d o f about e i g h t hou r s . The p y r o l y s i s products were c o l l e c t e d under dynamic vacuum at 77°K. A f t e r comple t ion 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 ap (from -80°C to 77 °K ) , w i t h the midd le p o r t i o n be ing r e t a i n e d f o r s p e c t r o -s c o p i c s tudy . 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 of the sample i n f r a -red s p e c t r a of i t s vapor were r e co rded . The spectrum of the f i r s t d i s t i l l -a te was i d e n t i f i e d as tha t of almost pure carbon d i o x i d e . In subsequent f r a c t i o n s the CC^ bands r a p i d l y decreased i n i n t e n s i t y , wh i l e o the r bands i d e n t i f i e d as be long ing to c h l o r i n e i socyana te appeared w i t h s t e a d i l y 45 i n c r e a s i n g i n t e n s i t y . E v e n t u a l l y , a spectrum was obta ined which agreed almost e x a c t l y w i t h tha t p r e v i o u s l y pub l i shed f o r c h l o r i n e i socyana te (73) . The fo re- run of impure product desc r i bed above c o n s t i t u t e d on ly 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 . A l a rge f r a c t i o n of e s e n t i a l l y pure c h l o r i n e i socyana te (about 2 mis of l i q u i d at -80°C) was then c o l l e c t e d and se t as ide f o r the microwave s t u d i e s . The f i n a l ( sma l l ) f r a c t i o n appa ren t l y conta ined 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 so 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 of the t o t a l product was l o s t du r ing the course of the d i s t i l l a t i o n due to the fo rma t ion of an i n v o l a t i l e s o l i d polymer ( i n the t r a p ) . Th i s p o l y m e r i z a t i o n was appa ren t l y c a t a l y z e d by the presence of i m p u r i t i e s as i t occur red 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 socyana te 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 not i n use samples were s t o r e d at 77°K, at which temperature they were i n d e f i n -a t e l y s t a b l e . 18 A sample of c h l o r i n e i socyana te en r i ched i n 0 was prepared i n the f o l l o w i n g way. Cyanur i c c h l o r i d e (Eastman Organic Chemicals) was f i r s t 18 hydro l ysed w i t h 0 (Bio-Rad L a b o r a t o r i e s ) to produce l a b e l e d c yanu r i c a c i d . Th is was then reac ted w i t h c h l o r i n e gas to produce t r i c h l o r o i s o -c y a n u r i c a c i d . F i n a l l y , 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 depo ly-mer ized u s i ng the p r e v i o u s l y des c r i bed method. The c yanu r i c c h l o r i d e h y d r o l y s i s was accompl ished u s i ng 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 procedure desc r ibed by Gerry (74) . In t h i s case c y a n u r i c c h l o r i d e (.1 gm) was hy ro l y sed i n a s o l u t i o n of sodium hydrox ide 18 (.13 gm) i n H^O (1 ml) en r i ched w i t h 50% 0. The sample was warmed to 85°C f o r about 1/2 hour under a p ressure of 150 t o r r pure n i t r o g e n . A f t e r 46 comple t ion of 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 of the c yanur i c c h l o r i d e , the n i t r o g e n was pumped away (w i th the s o l u t i o n f r ozen at 77°K) and then the water was d i s t i l l e d o f f and c o l l e c t e d . The mix ture of s a l t s l e f t behind (NaCl , sodium cyanurate) was subsequent ly d i s s o l v e d i n a few mis of o r d i n a r y water and set a s i d e . Th i s procedure was repeated f o u r more t imes , i n each case the l a b e l e d water d i s t i l l e d o f f i n the p r e -v i ous run was re-used . 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 ml of concent ra ted 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 of c yanu 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 y i e l d was 0.24 gms (85%). Th is product was then conver ted to 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 the f o l l o w i n g way (75) . C h l o r i n e gas was bubbled through a 0.40 M suspens ion of the c yanu r i c a c i d i n a 1.25 M sodium ace ta te s o l u t i o n whose pH had been i n i t i a l l y ad jus ted to 6.5 by the a d d i t i o n of a l i t t l e d i l u t e a c e t i c a c i d . The temperature was ma in ta ined i n the range 0 ° - 5°C throughout the r e a c t i o n which was te rminated 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 which 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 py ro l y sed as p r e v i o u s l y d e s c r i b e d . A r e spec t ab l e y i e l d of moderate ly pure c h l o r i n e i s o c y a n a t e , 18 about 40% 0 e n r i c h e d , was o b t a i n e d . 15 13 Samples o f c h l o r i n e i socyana te 50% en r i ched i n N and C were p r e -pared 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 of s i l v e r cyanate . Th is was apparen t l y the f i r s t s u c c e s s f u l p r e p a r a t i o n of c h l o r i n e i socyana te by t h i s r e a c t i o n . 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 on l y dimer (76) . R e c e n t l y , however, the s u c c e s s f u l p r e p a r a t i o n of bromine i socyana te from bromine and s i l v e r cyanate u s i ng a procedure very s i m i l a r to tha t desc r ibed here f o r c h l o r i n e i socyana te has been repor ted (77) . 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 ; the f o l l o w i n g one gave the best y i e l d . A m ix tu re of 1/3 gm of f r e s h l y p r e -pared s i l v e r cyanate and 1/2 gm o f f i n e l y powdered s i l i c a was p l a ced i n a t h i n g l a s s tube (8 mm O.D.) and wedged i n p l a ce w i t h two s m a l l p lugs o f g l a s s woo l . Th is tube was then connected at one end to 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 the r end to a vacuum system (see F igu re 3 .1 ) . A f t e r i n i t i a l e vacua t i on at room temperature , the s i l v e r c y a n a t e / s i l i c a m ix tu re was then pumped on f o r s e v e r a l hours w h i l e be ing heated to about 100°C. When a s t a b l e p ressure of l e s s than 1 y had been achieved the s i l v e r cyanate was a l lowed to c o o l to room temperature , the t rap was coo led to 77°K, and the s topcock to the c h l o r i n e sample tube (coo led i n dry 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. Immediately w h i t i s h m a t e r i a l s t a r t e d to c o l l e c t i n the l e f t arm of the t r ap a t the l e v e l of the l i q u i d n i t r o g e n , and s imu l t aneous l y the p ressure on the pump s i d e of the t r ap rose to about 100 u, d e s p i t e the f a c t tha t the whole system was be ing pumped on . A f t e r a few minutes t h i s p ressure s t a r t e d to d e c l i n e , and when i t reached approx imate l y 30 y hea t i ng was aga in a p p l i e d to the s i l v e r cyana te , a t f i r s t g e n t l y , then more s t r o n g l y t i l l a temperature of about 80°C was reached. Throughout the h e a t i n g p e r i o d the p ressure on the pump s i d e of the t r ap f l u c t u a t e d around 20 y . A f t e r 5 to 10 minutes of hea t i ng 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 rap and the p r e p a r a t i o n was s topped . The uncondensable r e a c t i o n products 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 products were separated i n t o three 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 c h l o r i n e and carbon d i o x i d e , an i n t e rmed 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 of 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 of C h l o r i n e Isocyanate from S i l v e r Cyanate and C h l o r i n e . G lass Wool -AgNCO G lass Wool fl D L i q u i d C h l o r i n e (-80°C) To Thermocouple Pressure Gauge t -Trap Sca le 1:2 To Pump Sample — Tube 49 The bes t y i e l d of c h l o r i n e i socyana te obta ined i n t h i s p r e p a r a t i o n was es t imated to be l e s s than 25%. Fur thermore, complete p u r i f i c a t i o n of the c h l o r i n e i socyana te cou ld not be accompl i shed ; at b e s t , on ly 80% p u r i t y , and that on very s m a l l samples , was ach ieved . Gaseous samples of c h l o r i n e i socyana te f o r microwave s p e c t r o s c o p i c s tudy were taken from the vapor above the bu l k l i q u i d sample h e l d at approx -ima te l y -80°C. These samples decomposed and/or po lymer ized i n the meta l c e l l ve ry q u i c k l y at f i r s t , but 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 of the 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 minu tes . P ressures of l e s s than 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 be ing measured us ing 10 - 25 p p r e s s u r e . In a l l of t h i s work the microwave c e l l was coo led w i t h dry i c e enc losed i n po l y s t y r ene boxes . Th i s reduced the l i n e w id ths s l i g h t l y b u t , more impo r t an t , i n c r eased the h a l f - l i f e o f the c h l o r i n e i socyana te samples . 3.2 P r e p a r a t i o n of I so cyan i c A c i d . A sample of 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 obta ined by the vacuum p y r o l y s i s o f c yanur i c a c i d (78) . S ince t h i s r e a c t i o n , u n l i k e tha 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 over a wide range o f exper imenta 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 procedure was used. A few grams of c yanur i c a c i d (Baker Chemical) were p laced i n the end of a pyrex tube which was then evacuated. When a s t a b l e p ressure of l e s s than 1 u had been o b t a i n e d , the c yanu r i c a c i d was heated s t r o n g l y w i t h an a i r-gas 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 products were trapped at 77°K under dynamic vacuum. Subsequent a n a l y s i s by i n f r a r e d spect roscopy (79) revea led tha 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 on l y a s m a l l amount of carbon d i o x i d e i m p u r i t y . P u r i f i c a t i o n was e a s i l y e f f e c t e d by f r a c t i o n a l d i s t i l l a t i o n . 50 An 0 enr i ched sample of i s o c y a n i c a c i d was obta ined by p y r o l y s i s of l a b e l e d c yanu r i c a c i d , which had been prepared us ing the method desc r ibed i n s e c t i o n 3 . 1 . 15 13 I socyan i c a c i d samples 50% enr i ched i n N and C were prepared 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 l a b e l e d sample of s i l v e r cyanate (80) . The exper imenta l procedure used i n t h i s s y n t h e s i s was very s i m i l a r to tha t used i n the analogous c h l o r i n e i socyana te p r e p a r a t i o n ; i ndeed , i t was t h i s s yn thes i s tha t p rov ided 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 cyanate exper iments . The on l y s i g n i f i c a n t d i f f e r e n c e was tha t t h i s r e a c t i o n was c a r r i e d out at room temperature us ing pure s i l v e r cyanate . Respectab le 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 v a r i a b l e amounts of carbon d i o x i d e and hydrogen bromide , were o b t a i n e d . Some p u r i -f i c a t i o n was accompl ished 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 coo led to about -80°C. The i s o t o p i c a l l y en r i ched samples of s i l v e r cyanate used i n the p r e -v i o u s l y desc r ibed exper iments were prepared by the a l k a l i n e permanganate o x i d a t i o n of the cor respond ing sodium cyanide s o l u t i o n , f o l l owed 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 cyanide samples were obta ined from the Isomet Co rpo ra t i on (Oakland, N. J . 07436, U . S . A . ) . A d e t a i l e d account of the o x i d a t i o n r e a c t i o n may be found i n " I n o r g a n i c I s o t o p i c Syntheses " (81 ) . Deuterated samples of i s o c y a n i c a c i d were prepared i n the microwave c e l l by exchange between deuter ium ox ide and normal i s o c y a n i c a c i d . The procedure used was to f i l l the c e l l w i t h about 0.5 t o r r of heavy water f o r about 10 minutes and then pump i t out to a p ressure of l e s s than 1 p. A 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 roduced i n t o the c e l l , and r a p i d deuter ium - hydrogen exchange would occur between the heavy water 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 of the i s o -cyan i c a c i d w i t h the water (78) n e c e s s i t a t e d f requent (about every 5 min . ) replacement of samples. One heavy water 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 to g i ve 20 to 40% d e u t e r a t i o n of 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 to r ed and handled i n much the same way as the c h l o r i n e i socyana te ones. 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 prob lem, and i n the absence of c e l l wa te r , the s p e c t r o s c o p i c samples had to be changed on ly o c c a s i o n a l l y . As b e f o r e , a l l measurements were made w i t h the c e l l coo led i n dry i c e . 3.3 P r e p a r a t i o n of Cyanogen I socyana te . Cyanogen i socyana te was prepared by the vacuum the rmo l y s i s of s i l v e r cyanate . The procedure 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 of tha t developed by G o t t a r d i (82 ) . About 4 gms of s i l v e r cyanate were p laced i n the end of a pyrex tube which was then connected to a s p e c i a l t rap/sample tube ; t h i s i n t u r n was connected to a vacuum l i n e ( F igure 3 .2 ) . The whole system was then evacuated and pumped on o v e r n i g h t . The next day the t r ap was coo led i n l i q u i d n i t r o g e n and the s i l v e r cyanate was heated w i t h an a i r -gas t o r c h . A f t e r a sho r t warm-up p e r i o d , the s i l v e r cyanate s t a r t e d to undergo a s t r o n g l y exothermic r e a c t i o n , w i t h v i go rous e v o l u t i o n of gas . Hea t ing was 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. W i t h i n a few minutes 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 es idue i n the r e a c t i o n tube , and a l a r g e amount of wh i te s o l i d i n the t r a p . In a d d i t i o n , a c o n -s i d e r a b l e volume of gas had passed through the t rap (presumably N^* 0^ o r CO) and had been pumped away du r i ng the r e a c t i o n . The wh i te s o l i d i n the t rap was subsequent ly determined (by i n f r a r e d 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 of Cyanogen I socyanate . 4 gms AgNCO / Glass Wool •35 cm Trap/Sample Tube To Pump To Thermocouple P ressure Gauge Sca le 1:2 53 spect roscopy ) to be l a r g e l y carbon d i o x i d e a long w i t h a sma 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 imply warming the t rap to about -80 C and then pumping on i t f o r s e v e r a l hours (cyanogen i socyana te has e s s e n t i a l l y zero vapor pressure at t h i s tempera ture ) . Fu r the r warming of the t rap to about -63°C ( ch lo ro form s lush ) gave, a f t e r removal o f the l a s t o f the C ^ , a steady vapor p ressure of about 30 u of cyanogen i socyana te over i t s wh i te s o l i d . No attempt was made to o b t a i n a l a r g e r vapor p ressure over the b u l k sample by s t i l l f u r t h e r warming, because of the r epor ted tendency of cyanogen i socyana te to ve ry r e a d i l y po l ymer ize (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 vapor phase , was. ob ta ined i n the f o l l o w i n g way. Vapor was d i s t i l l e d , over a p e r i o d of e i g h t h o u r s , from the trap/sample tube at -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 at 77°K. The i n f r a r e d c e l l was then s e a l e d , removed from the vacuum l i n e and an i n f r a r e d spectrum was recorded as soon as the c o l d f i n g e r had warmed to room temperature . Th i s spectrum was i n e x c e l l e n t agreement w i t h tha t pub l i shed by Mayer (18) and i d e n t i f i e d as be long ing to cyanogen i s o c y a n a t e . A s e r i e s of s p e c t r a recorded over the next few hours u s i n g the same sample showed a g radua 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 socyana te l i n e s , and s imu l t aneous l y an i n c r ea se i n the s t r e n g t h of a few broad bands subsequent ly ass igned to s o l i d polymer depos i t ed on the c e l l windows. The bu l k sample of cyanogen i socyana te was s to red i n i t s t rap/sample o ^ o tube at 77 K. Spec t ro s cop i c samples were obta ined by warming i t to -63 C; the 20 - 30 u vapor p ressure thus ach ieved be ing more than adequate. Samples decomposed and/or po l ymer ized 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 r ep l aced every 5 - 2 0 minutes . A l l measurements were made at room temperature w i t h sample p ressures of g e n e r a l l y l e s s than 10 u. 3.4 The S ta rk Modulated Microwave Spect rometer . A conven t i ona l 100 kHz S ta rk modulated microwave spectrometer 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 covered was 8 - 3 7 GHz w i t h an average (optimum) measurement accuracy 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 - . i n - 1 0 -1 o f 5x10 cm Two r a t h e r d i f f e r e n t types of microwave r a d i a t i o n sources were used ; 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 (83 ) . The low f requency X- and P-band reg ions were covered w i t h a p a i r of phase s t a b i l -i z e d backward wave o s c i l l a t o r s (Hewlett-Packard H81-8694B and H81-8695A). S ince these sources cou ld be e l e c t r o n i c a l l y tuned over t h e i r e n t i r e f requency range w i t h e x c e l l e n t l ong term s t a b i l i t y , the r e s u l t i n g de t e c to r s i g n a l 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 co rde r (HP 680 ) . The h i g h f requency , 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 over a narrow frequency range (2 - 10 MHz) by app l y i ng a sawtooth v o l t a g e to the k l y s t r o n r e f l e c t o r e l e c t r o d e . Th i s sawtooth was synchron ized w i t h tha t a p p l i e d to the X-p la tes of a Hewlet t-Packard dua l t r a ce o s c i l l o s c o p e (1205A). The a m p l i f i e d de t e c to r output was then used as the Y-vo l tage f o r one of these t r a c e s , thus a l l o w i n g a conven ient d i s p l a y of a sma l l segment of the microwave spectrum. The cen te r f requency of t h i s scan was v a r i e d by manual , mechan i c a l , tun ing 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 generated about 40 - 80 mW of 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 d i s s i -p a t ed , however, by p l a c i n g an a d j u s t a b l e a t t enua to r between the source 5 5 and the microwave c e l l . T y p i c a l l y , measurements were made w i t h on ly 1 - 2 mW of power i n the c e l l i n order to avo id 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 to min imize 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 ressure sample undergoing 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 conven t i ona l microwave c e l l , i s u s u a l l y much l e s s than 0.1% of the t o t a l r each ing the d e t e c t o r . S ince 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 output due to r e f l e c t i o n s i n the c e l l , changes i n source power, e t c . , are g e n e r a l l y much l a r g e r than t h i s , i t i s c l e a r tha t d i r e c t obse r va t i on of microwave t r a n s i t i o n s w i l l g e n e r a l l y be d i f f i c u l t or i m p o s s i b l e . S e ve r a l d i f f e r e n t techn iques have been dev i sed to surmount t h i s d i f f i c u l t y (83 ) . The one most commonly employed, and tha t used e x c l u s i v e l y i n t h i s s t udy , i s S t a rk modu l a t i on . The p r i n c i p l e i n v o l v e d i n S t a rk modu la t ion 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 are i n e f f e c t turned 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 equency , zero based , e l e c t r i c f i e l d as a square wave. In the o f f pa r t o f the c y c l e a l l t r a n s i t i o n s occur at t h e i r normal f r e q u e n c i e s ; i n the on p a r t , they are a l l s h i f t e d as des c r i bed i n s e c t i o n 2 . 3 . S ince sources o f power f l u c t u a t i o n o the r than mo l e cu l a r a b s o r p t i o n are una f f e c t ed by the S t a rk 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 output can be used to d i s c r i m i n a t e aga ins t them. F u r t h e r , the output of the d e t e c t o r now has the modu la t ion f requency as a c a r r i e r f requency 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 no i s e i s a ch i eved . The output of the 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 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 at zero f i e l d and the a b s o r p t i o n w i t h the S ta rk f i e l d on : i . e . the " l i n e s " appear on one s i d e o f the base l i n e , the " S t a r k l o b e s " on the o t h e r . Th is i s g e n e r a l l y 56 a ve ry convenient arrangement, except when i t i s imposs i b l e to ad jus t the ampl i tude o f the square wave to s h i f t a l l S ta rk lobes c l e a r o f the l i n e be ing measured. Two d i f f e r e n t types of de t e c to r s were used to cover the 8 - 3 7 GHz s p e c t r a l r e g i o n . The X- and P-band de tec to r s were f a c t o r y mounted, low-n o i s e , h igh s e n s i t i v i t y , d iodes (Hewlett-Packard H06-X422A and H06-P422A). In the h igh frequency 18 - 37 GHz r e g i o n , s tandard 1N26 c r y s t a l s , hand mounted i n a te rminated tunab le s e c t i o n of K-band waveguide, were used . The output from these de t e c to r s was passed through a p r e - a m p l i f i e r and then fed i n t o a P r i n c e t o n A p p l i e d Research 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 or 121. S t a rk modu la t ion was obta ined by app l y i ng the output from an I ndus -t r i a l Components Incorpora ted 100 kHz square wave generator to a copper septum i n s e r t e d i n the 7 f oo t X-band c e l l . Th i s sheet of copper (0.019 i nches t h i c k ) was h e l d i n the cen te r o f the c e l l p a r a l l e l t o the broad faces of the waveguide and i n s u l a t e d from the narrow ones by a p a i r o f s l o t t e d t e f l o n runne rs . The r e s u l t i n g e l e c t r i c f i e l d was almost e n t i r e l y p e r p e n d i c u l a r to the broad faces of the grounded c e l l . I t s peak to peak ampl i tude cou ld be c o n t i n u o u s l y v a r i e d from 0 to over 4000 V o l t s / c m . T r a n s i t i o n f r equenc i es 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 beat f requency between the source 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 f requency s tandard (83) . These harmonics were generated by m u l t i p l y i n g the 50 MHz output of a Micro-Now Instrument Company Model 101C f requency m u l t i p l i e r cha in w i t h a 1N26 c r y s t a l . They 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 rm ina t ed , t u n a b l e , s e c t i o n of K-band waveguide, connected to the main waveguide l i n e w i t h 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 line 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 . Its 5 MHz fundamental was continuously monitored with a Hewlett-Packard 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 literature 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 (w i th o s c i l l o s c o p e d i s p l a y ) and the f requency read d i r e c t l y from the counte r . 3.5 Double Resonance Exper iments . The b_-type assignments of cyanogen i socyana te 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 per forming two microwave-microwave double resonance exper iments . In both of t he se , an a-type Q-branch l i n e 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 of power w h i l e a h ighe r f requency _b-type l i n e , w i t h which i t shared a common energy l e v e l , was be ing observed . 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 a r e : Observed Pumped Observed Pumped The expe r imenta l set-up used, a l though somewhat u n s o p h i s t i c a t e d , proved to be eminent ly s u c c e s s f u l . ( F igure 3 .3 ) . Pump power s u p p l i e d by the HP phase l ocked source ( s e c t i o n 3.4) was fed d i r e c t l y i n t o the X-band c e l l . S i g n a l power generated by e i t h e r a 20V10 or a 30V10 k l y s t r o n was coupled 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 . Both sources were p ro t e c t ed from r e f l e c t e d power w i t h an app rop r i a t e i s o l a t o r . Pump power was prevented from reach ing 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 hav ing a cut o f f f requency of 14.08 GHz. The procedure f o l l owed was to observe the b-type t r a n s i t i o n us ing normal S ta rk m o d u l a t i o n , and then t r y to de tec t any change i n i t s i n t e n s i t y as the pump frequency was v a r i e d near the resonance f requency of the Q-branch t r a n s i t i o n . 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 e f f e c t 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 (by 15 to 20%) (1) 1 6 n — 15- at 18770.20 MHz U , l b 1 , 1 J 1 5 1 , 1 4 - 1 5 1 , 1 5 at 12102.40 MHz (2) 3 9 1 > 3 8 - 3 8 2 j 3 7 at 3 8 2 , 3 6 - 3 8 2 , 3 7 a t 27905.72 MHz 9191.27 MHz FIGURE 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 Exper iments . Pump Power A t t enua to r o To Power Meter X-Band I s o l a t o r 20 7 db D i r e c t i o n a l Coupler 3 db D i r e c t i o n a l Coupler C e l l K-Band I s o l a t o r T 20 db Cross-Guide D i r e c t i o n a l Coupler . T-f ^ A t t e n u a t o r To Scope Wavemeter T o n -6 . •>- To SP-600 — From Micro-Now 20V10 or 30V10 K l y s t r o n To P r e - A m p l i f i e r K-Band Waveguide Tuning Stub 1N26 C r y s t a l De tec tor 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 resonance. Tuning o f the pump to e i t h e r h igh or low f requency of resonance by more than 1 MHz gave a s t ronger Jb-type s i g n a l , constant over a wide range of pump f r e q u e n c i e s . 3.6 D ipo l e Moment Measurements. D ipo l e moment measurements were made on i s o c y a n i c a c i d and cyanogen i s o c y a n a t e . S ta rk s h i f t s were produced by a p p l y i n g , to the c e l l septum, a l a rge a c c u r a t e l y known DC v o l t a g e , upon which was f l o a t e d a s m a l l AC (100 kHz) modu la t ion f i e l d . . As u s u a l , de t e c to r output 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 . With such a system, each S ta rk component appears as two lobes d i f f e r i n g i n phase by 180°. One lobe i s a s soc i a t ed w i t h an e l e c t r i c f i e l d o f E + E , r J o m' the o ther w i t h a f i e l d of E - E , where E i s the DC b i a s f i e l d and E i s o m o m one h a l f the peak to peak ampl i tude of the square wave. Then, f o r a s t r i c t l y second order S ta rk e f f e c t , l i k e tha t observed i n t h i s work, the average 2 2 f requency of any a s s o c i a t e d p a i r o f lobes i s a l i n e a r f u n c t i o n of E + E^. There are two reasons f o r us ing the above p rocedure , r a t h e r than j u s t AC modu l a t i on . 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 vo l t ages r e s u l t i n g i n a broadening of a l l S t a rk components. Second ly , i t i s d i f f i c u l t to measure a c c u r a t e l y the ampl i tude of the square wave v o l t a g e . Wi th the two f i e l d system and a second order S t a rk e f f e c t , the percent e r r o r i n the s m a l l ( und i s to r t ed ) AC v o l t a g e may be as l a r g e as the percent u n c e r t a i n t y i n the DC vo l t age m u l t i p l i e d by the r a t i o 2 (E /E ) w i thou t becoming the l i m i t i n g f a c t o r on the accuracy of the a m measurements. The source of the DC b i a s p o t e n t i a l was a John F luke Manufac tur ing Co. Model 412B DC power supp ly w i t h an output of 0 to 2100 v o l t s , k i n d l y l e n t to us by Dr . A. J . Merer . Th i s power supply has a s t a t e d c a l i b r a t i o n 61 accuracy of ±0.25% and a r e s e t a b i l i t y of ±0.05%. The modu la t ion f i e l d was produced by the p r e v i o u s l y d i s cussed 100 kHz square wave gene ra to r . I t 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 ta rk vo l t age mixer c o n -s t r u c t e d by C. R. Parent (84) a f t e r a des ign by Muenter (85 ) . 62 CHAPTER 4 THE MICROWAVE SPECTRUM OF CHLORINE ISOCYANATE C h l o r i n e i socyana te was f i r s t prepared i n 1965 by Nachbaur and G o t t a r d i (73) us ing the method desc r i bed i n Chapter 3. I t s chemist ry has been the sub jec t of a number o f more recent 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 ( 8 6 , . . . , 8 9 ) . The i n f r a r e d and Raman s p e c t r a of t h i s molecu le have been ana lysed to y i e l d a v i b r a t i o n a l f o r ce 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 study by Oberhammer (91) p rov ided some i n f o r m a t i o n on the geometry of the molecu le but cou ld not d e f i n i t e l y d i s t i n g u i s h between two a l t e r n a t i v e s t r u c t u r e s . A l l o f these p u b l i c a t i o n s , except the f i r s t , appeared w h i l e the work des c r i bed here 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 of the microwave spectrum of c h l o r i n e i s o -cyanate was undertaken by the author to f u l f i l pa r t o f the requirements o f a B.Sc. degree. 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. T12„16- , 37„114 l l T12 16„ . fc . . . , abundant CI N C 0 and CI N C 0 i s o t o p i c spec i e s were ass igned and measured i n t h a t s tudy . I n the p resent work most of these were r e -measured w i t h a more s e n s i t i v e spect rometer i n order to r e s o l v e t h e i r n i t r o g e n quadrupole coup l i ng h y p e r f i n e s t r u c t u r e . Numerous b-type t r a n s -i t i o n s o f these i s o topes were a l so a s s i gned . In a d d i t i o n , s e v e r a l a r t i -f i c i a l l y en r i ched i s o t o p i c samples were prepared and s t u d i e d so tha t a complete s u b s t i t u t i o n s t r u c t u r e cou ld be o b t a i n e d . A l l t o l d , microwave s p e c t r a were ana lysed f o r s i x i s o t o p i c spec i e s o f c h l o r i n e i s o c y a n a t e ; they a r e : 3 5 C 1 U N 1 2 C 1 6 0 3 5 C 1 1 4 N 1 2 C 1 8 0 3 5 C 1 1 5 N 1 2 C 1 6 0 3 7 C 1 1 4 N 1 2 C 1 6 0 3 5 C 1 1 4 N 1 3 C 1 6 0 3 7 C 1 1 5 N 1 2 C 1 6 0 63 4.1 Assignment of the Spectrum. The r o t a t i o n a l spectrum of c h l o r i n e i socyana te was expected to be tha t o f a near p r o l a t e asymmetric r o t o r . Th i s was deduced by c o n s t r u c t i n g a reasonable mo lecu la r s t r u c t u r e u s i n g the assumed parameters : Z-(NCO) = 180°, r(C-O) = 1.17 A, r(N-C) = 1.20 A, as i n HNCO (11 ) , and r (N-Cl ) = 1.73 &*, Z_(C1NC) = 112°, as i n CIN^ (14) . A r i g i d r o t o r spectrum c a l c u l a t e d 35 1A 12 16 f o r the 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 of t h i s s t r u c t u r e , conta ined a l a r g e number of 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 eg i on of our spec t rometer . Of these , the pseudosymmetric r o t o r a-type R-branch g roups , p r e d i c t e d to occur at V j ^ J + 1 « (J+l)(B+C) « (J+l)(6GHz) and to have near f i r s t o rder S ta rk e f f e c t s (on ly those components f o r which K ^ * 0) , were recogn ized as the most l i k e l y cand idates f o r an e a r l y ass ignment . By c o n -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 , no tab l e on l y f o r t h e i r l a c k of 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 expected to be much more d i f f i c u l t to 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 of the 28 - 32 GHz r eg i on revea led a ve ry r i c h spectrum which 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 . The s t ronges t of these , c o n s i s t i n g of a s i n g l e h igh f i e l d double t at 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 spread out between 30.37 GHz and 30.42 GHz, was 35 1A 12 16 t e n t a t i v e l y ass igned as the J = 4+5 a-type R-branch group of CI N C 0 i n i t s ground v i b r a t i o n a l s t a t e . Three very s i m i l a r but p r o g r e s s i v e l y weaker m u l t i p l e t s o c c u r r i n g at h i ghe r f r equenc ies were presumed to be a s s o c i a t e d w i t h molecu les 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 ep roduc t i on of t h i s whole p a t t e r n , but w i t h a rough ly 1/3 * The terms " low f i e l d " and " h i g h f i e l d " are used to i n d i c a t e the ampl i tude of the S ta rk f i e l d r e q u i r e d to modulate a t r a n s i t i o n and hence make i t d e t e c t a b l e . 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 order S ta rk e f f e c t , h igh f i e l d a second order 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 hype r f i ne s t r u c t u r e , was found n e a r l y 800 MHz to lower f requency . Th i s was e v i d e n t l y the co r respond ing _ c 3 7 ^ 1 4 , 1 2 16 r t . . set of CI N C 0 t r a n s i t i o n s . As a f i r s t t e s t of 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 sought , and found, at the f r equenc i es p r e d i c t e d by : v ( J+l)v^_^/5. The more u sua l procedure f o r de te rmin ing such J va lues by count ing S ta rk lobes cou ld not be used as these were never r e so l ved f o r any of the c h l o r i n e i socyana te t r a n s i t i o n s . Th is was no doubt due at l e a s t i n pa r t to the r e l a t i v e l y s m a l l va lue of the d i p o l e moment, as suggested by the g e n e r a l l y weak abso rp t i on l i n e s . In a d d i t i o n , however, the quad-rupo le 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 ta rk lobe i n t e n s i t i e s , and , more i m p o r t a n t , produced a ve ry complex p a t t e r n i n which there were m u l t i p l e co inc idences of S ta rk lobes from d i f f e r e n t h y p e r f i n e components at v i r t u a l l y a l l v o l t a g e s . From the r e l a t i v e i n t e n s i t i e s and f r equenc ies of the v i b r a t i o n a l s a t e l l i t e s i t was concluded tha t these belonged to e x c i t e d s t a t e s o f the same v i b r a t i o n w i t h a f requency of l e s s than 200 cm ^. Th i s number i s i n good agreement w i t h the Raman measurements of E y s e l and Nachbaur (90) which 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 . The next lowest f requency v i b r a t i o n i s a t 560 cm * and i t s f i r s t e x c i t e d s t a t e shou ld 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 which a few very 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 that cou ld be a t t r i b u t e d to e x c i t e d s t a t e s of or any of the other h ighe r f requency v i b r a t i o n s . P o s s i b l y these are b u r i e d under the much s t ronge r ground, oj^  and 2u),_ 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 . D e f i n i t i v e c o n f i r m a t i o n of the a-type group assignments was achieved by per forming a complete a n a l y s i s of the un ique l y c h a r a c t e r i s t i c h y p e r f i n e 65 s t r u c t u r e of these m u l t i p l e t s . Each group s t a r t e d at i t s low f requency end * w i t h a h i g h f i e l d doublet tha t was c l e a r l y the K ^ — 0 t r a n s i t i o n w i t h p a r t i a l l y r e so l v ed c h l o r i n e quadrupole coup l i ng s t r u c t u r e . To s l i g h t l y h i ghe r f requency a p a i r o f low f i e l d doub le t s was found. S ince the S ta rk components of the lower f requency double t moved to h igh frequency w i t h i n c r e a s i n g f i e l d , and those of the h ighe r f requency d o u b l e t , to low f r equency , these were t e n t a t i v e l y ass igned as the asymmetry s p l i t K = 2 l i n e s , w i t h the doub le t s t r u c t u r e aga in be ing due to c h l o r i n e quadrupole c o u p l i n g . Th is S ta rk component behav io r i s p r e d i c t e d by equa t ion 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 . The d e c i s i o n to a s s i g n these doub le t s as K_j = 2 r a t h e r than = 1 l i n e s was i n i t i a l l y mot i va ted 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 . I t 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 to h i g h e r f requency where a l l of the observed l i n e s cou ld be accounted f o r i n terms of on l y the expected K = 3, 4 and 5 (K ^ J " ) t r a n s i t i o n s . These had no asymmetry s p l i t t i n g but d i d show l a r g e quadrupole h y p e r f i n e s t r u c t u r e which 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 proved to be somewhat more d i f f i c u l t to a s s i g n . These were p r e d i c t e d to be approx imate l y e q u a l l y spaced on e i t h e r s i d e of the a s s o c i a t e d main group, w i t h a t o t a l asymmetry s p l i t t i n g of rough ly ( J+1)(B-C), but because of the d e n s i t y of h i g h e r J unass igned t r a n s i t i o n s s e v e r a l mis-assignments were made i n the course of the e a r l y work. 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 ass ignments , the d i r e c t i o n i n which the S ta rk components moved w i t h i n c r e a s i n g f i e l d and the observed S ince AK ^ = 0 f o r a l l of these pseudosymmetric top t r a n s i t i o n s i t i s f r e q u e n t l y convenient to l a b e l them by j u s t J " , J ' (= J "+1) and K_. For a l l K_j * 0 there are two such t r a n s i t i o n s which may o r may not be degenerate . For K . = 0 there i s on l y one t r a n s i t i o n . 66 FIGURE 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 3 5 C 1 1 4 N 1 2 C 1 6 0 (G.V.S.). r observed c a l c u l a t e d b c observed ca l c u l a t e d V c T c b 1 24310 v(MHz) 1 24315 1 24320 24325 24330 24335 67 quadrupole 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 ea tu res of these _i-type R-branch groups shou ld be emphasized. The f i r s t i s the l a c k of ove r l ap of the m u l t i p l e t s c o r r e s -ponding to 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 . The second i s the e s s e n -t i a l l y complete s e p a r a t i o n of the s t r u c t u r e . The former i n d i c a t e s 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 l a t t e r , s i g n i f i c a n t c e n t r i f u g a l d i s t o r t i o n . Together , 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 e v e n t u a l l y n i t r o g e n quadrupole coup l i ng h y p e r f i n e s t r u c t u r e cou ld be l a r g e l y r e s o l v e d . In c o n t r a s t to t h i s n e a r l y i d e a l c ase , there are numerous examples of 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 of 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 equenc i e s o f the a-type t r a n s i t i o n s , as a l r eady i n d i c a t e d , depend s t r o n g l y on B and C, but conve r se l y are n e a r l y independent of A. Con -sequent l y the a n a l y s i s desc r i bed above produced e x c e l l e n t va lues f o r the former but on ly ve ry rough va lues f o r the l a t t e r . These were i n s u f f i c i e n t f o r the accurate p r e d i c t i o n of the b-type t r a n s i t i o n s whose f r equenc i es are s t rong f u n c t i o n s o f a l l th ree r o t a t i o n a l cons tants and may a l s o have 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 c o n t r i b u t i o n s . The process of 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 ed i ous and i n v o l v e d c o n s i d e r a b l e t r i a l and e r r o r . 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 ass igned i n one b-type s e r i e s , the r e s t of the t r a n s i t i o n s i n tha t s e r i e s cou ld be a c c u r a t e l y p r e d i c t e d . Measurement of these a d d i t i o n a l t r a n s i t i o n s p rov ided conv inc ing proof of the co r r e c tnes s of the i n i t i a l ass ignments . A g a i n , these were always f u r t h e r supported by a comparison of observed and c a l c u l a t e d quadrupole h y p e r f i n e s t r u c t u r e . T r a n s i t i o n s w i t h J v a lues of l e s s than 30 68 were observab le f o r on ly three s e r i e s of b-type P- and R-branches; these were o f the form J Q j J — ( J - D ^ j . p J _ f J _ _ — < J - l > 2 f J _ 2 and J I , J - ^z . j - r The i n t e n s i t i e s of 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 magn i -tude , sugges t ing rough ly comparable va lues f o r the components of the d i p o l e moment a long 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 ta rk lobes were always weak and u n r e s o l v a b l e , no attempt was made to a c c u r a t e l y measure y o and y, . a 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 spec i es had s p e c t r a which were very s i m i l a r to tha 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 these 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 p r e l i m -i n a r y es t imates of the i s o t o p i c mo lecu l a r cons t an t s . Th i s was f o r t u n a t e because the use of on ly 40 - 50% enr i ched 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 spectrum. 4.2 Dete rmina t ion of M o l e c u l a r Constants 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 constants and n u c l e a r quadrupole c o u p l i n g constants were e x t r a c t e d from the microwave spectrum of c h l o r i n e i socyana te through a c i r c u i t o u s procedure i n v o l v i n g suc ces s i v e l e v e l s o f approx imat ion . A more s t r a i g h t f o r w a r d approach cou ld not be used because bo th 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 ana lyses r e q u i r e d va lues f o r the r o t a t i o n a l constants but were a l s o necessary i n order to determine them a c c u r a t e l y . Consequently the f i r s t s tep was always the c a l c u l a t i o n of a t r i a l set 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 app l y i ng the r i g i d r o t o r equat ions to 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 treatment of the c e n t r i f u g a l d i s t o r t i o n i n which each " u n s p l i t - l i n e " t r a n s i t i o n f requency was approximated by an average * Th is i s the h y p o t h e t i c a l f requency which 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 there was no quadrupole h ype r f i ne s t r u c t u r e . 69 of 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 gene ra t i on r o t a t i o n a l constants were i n t u rn used i n a f i r s t a n a l y s i s of the quadrupole h y p e r f i n e pa t t e rns that y i e l d e d , i n a d d i t i o n to f i r s t gene ra t ion quadrupole coup l i ng c o n s t a n t s , a much improved s e r i e s of " 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 to a new round i n the process o f r e f inement . S ince the quadrupole energ ies were on ly a s l o w l y v a r y i n g f u n c t i o n of the r o t a t i o n a l cons tants the " u n s p l i t - l i n e " f r equenc 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 norma 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 from those obta ined i n the f i r s t c y c l e . A l though three 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 ea tu res o f 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 were always the same. A f i r s t o rde r p e r t u r b a t i o n treatment was used . The r e q u i r e d angular momentum m a t r i x elements and reduced ene rg i es ( E (b p ) ) were computed a long w i t h a se t of r i g i d r o t o r f r equenc i es ( v r ) us ing the most r e c e n t l y ob ta ined r o t a t i o n a l cons t an t s . A l e a s t squares f i t was then made to the d i f f e r e n c e s v , - v obs r where w a s the hes t a v a i l a b l e se t of observed " 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 bo th the d i s t o r t i o n constants and 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 . The l a t t e r were a l lowed to have l i n e a r v a r i a t i o n s i n on ly the r i g i d r o t o r c o n t r i b u t i o n (Av^) to 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 incremented r o t a t i o n a l constants cent r 6 were subsequent ly used to 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 , f r e q u e n c i e s . Th is procedure gave s t a b l e r e s u l t s ( i n c l u d i n g agreement obs of used and c a l c u l a t e d r o t a t i o n a l cons tan ts ) on the second or t h i r d c y c l e , when the observed f r equenc i es conta ined s u f f i c i e n t i n f o r m a t i o n to determine a l l of the i n c l u d e d parameters . The important f e a tu r e s of the o v e r a l l a n a l y s i s scheme have been i l l u s -t r a t e d w i t h a f l ow char t i n F i gu re 4.2. 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 Nuc lear Quadrupole Hyper f ine S t r u c t u r e A n a l y s i s Scheme. T r i a l R o t a t i o n a l Constants T r i a l " U n s p l i t - L i n e " Frequenc ies -input f o r the f i r s t run of the f i r s t 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 i npu t f o r the f i r s t 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 CENTRIFUGAL DISTORTION PROGRAM on l y t i l l -no f u r t h e r change Improved R o t a t i o n a l Constants c o l l e c t on l y the f i n a l se 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 i npu t f o r the f i r s t run of subsequent d i s t o r t i o n ana lyses S t ab l e Re f ined R o t a t i o n a l Constants Quadrupole S p l i t t i n g s NUCLEAR QUADRUPOLE HYPERFINE STRUCTURE PROGRAM c o l l e c t on ly the f i n a l se t o f Coup l ing Constants Improved " U n s p l i t - L i n e " T r a n s i t i o n Frequenc ies " c o l l e c t f i n a l se t i npu t f o r subsequent c e n t r i f u g a l d i s t o r t i o n ana lyses 71 S ince c h l o r i n e i socyana te was expected to be a p l ana r m o l e c u l e , i t was thought tha t the Hami l t on i an d e f i n e d by equa t ion 2.18 might be adequate f o r a 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 . In a f i r s t treatment the e q u i l -i b r i u m r o t a t i o n a l constants appear ing i n t h i s exp re s s i on were r ep l a ced w i t h the bes t a v a i l a b l e e f f e c t i v e ones ; i . e . those used to c a l c u l a t e the angular momentum m a t r i x elements e t c . The scheme was then 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 . ) da ta s e t . Least squares f i t s were made on three groups o f t r a n s i t i o n s namely: J = 0 - 20 , J = 0 - 25 , and J = 0 - 30. The r e s u l t s are compared i n Table 4 . 1 . I t w i l l be noted tha t the l a r g e s t set o f t r a n s i t i o n s gave apparen t l y w e l l determined va lues f o r a l l seven constants and the s m a l l e s t s e t , good va lues f o r on l y s i x , w i t h x , , i n d e t e r m i n a t e . 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 s i x abab ' parameters , 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 to be ve ry s l i g h t and, i n every case , s m a l l e r than the exper imenta l e r r o r . Th i s suggested tha t h i g h e r o rde r e f f e c t s were o f minor importance i n a l l o f the observed t r a n s i t i o n s and c e r t a i n l y tha t no sys temat i c e r r o r would be i n t roduced i n t o any of the de r i ved c o n s t a n t s , w i t h the p o s s i b l e excep t i on of T a k a b > by i n -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 f i t . A v a r i a t i o n of the above procedure was a l s o cons idered i n which 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 equa t ion 2.18) were r ep l aced w i t h ground s t a t e va lues o f A and B and a va lue of C ad jus ted to make the i n e r t i a l de fec t z e r o . The r e s u l t s of 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 14 12 16 t r a n s i t i o n s of CI N C 0 G . V . S . , are a l so g i v en i n Table 4 . 1 . The r o t a t i o n a l constants and two of the d i s t o r t i o n cons tants agree w e l l w i t h those of the p rev ious c a l c u l a t i o n (on the same d a t a ) , but the o thers do n o t ; i ndeed , ^ 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 ou t s i de the exper imenta l e r r o r . Th is must be regarded as an anomalous behav io r s i n c e 72 TABLE 4.1 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 of 35 1A 12 16 C l N C 0 i n the Ground V i b r a t i o n a l S t a t e . I I ' Number of T r a n s i t i o n s A' o B» o C» o aaaa bbbb ' aabb abab J = 0 - 20 41 51576.246 + 0 . 0 8 6 c 3130.5904 ± 0.0066 2945.1781 ± 0.0066 -59.204 ± 0.083 -0.01092 + 0.00018 0.6824 ± 0.0186 (-0.0012 ± 0.0173) J = 0 - 25 47 51576.181 ± 0.068 3130.5858 ± 0.0041 2945.1768 ± 0.0041 -59.148 ± 0.049 -0.01077 ± 0.00003 0.6878 ± 0.0031 (-0.0061 ± 0.0027) I I I ' IV Number o f T r a n s i t i o n s A ' o B' o c o aaaa bbbb ' aabb abab J = 0 - 30 52 51576.213 ± 0.065 3130.5875 ± 0.0029 2945.1709 ± 0.0027 -59.139 ± 0.047 -0.010752 ± 0.000025 0.6923 ± 0.0008 -0.0101 ± 0.0006 J = 0 - 30 52 51576.219 ± 0.065 3130.5913 ± 0.0029 2945.1663 ± 0.0027 -59.141 ± 0.048 -0.010748 ± 0.000025 0.6992 ± 0.0008 -0.0175 ± 0.0006 In the r e l a t i o n s reduc ing the number of determinab le d i s t o r t i o n cons tants to f o u r , the r o t a t i o n a l cons tants used were A ' , B' and C ' . o o o In the r e l a t i o n s reduc ing the number of determinab le d i s t o r t i o n cons tan ts to f o u r , the r o t a t i o n a l cons tants 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 ther p l ana r molecu les the r e s u l t s of these two a n a l y s i s schemes have been found to be i n agreement (93) . I t i s not c l e a r which 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 comple te 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 tha t i t would be p r e f e r a b l e not to 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 end, an attempt was made to use the gene ra l 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 Hami l t on i an d e f i n e d by equat ions 2 .19 , 2.20 and 2 .21 . Again the 35 1A 12 16 C l N C 0 G.V.S . t r a n s i t i o n s were taken as t e s t d a t a . Watson has sugges t -ed tha t t h i s i s p robab ly the bes t approach f o r t r e a t i n g p l ana r molecu les w i t h l a r g e d i s t o r t i o n e f f e c t s (30) . In t h i s case , however, on ly fou r of the d i s t o r t i o n constants were w e l l de te rmined ; the f i f t h , 6 , was i n d e t e r -K mina te . F u r t h e r , there were very l a rge 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) connect ing 6.. w i t h B and C and A T w i t h A T T , . Th i s i s to be con t r a s t ed ° K o o J JK w i t h the two p rev ious f i t s where a l l of the parameters were w e l l determined and u n c o r r e l a t e d . The r e s u l t s o f these three schemes are compared i n Table 4 . 2 . The Watson constants g i ven i n columns I I I A and IVA were c a l -c u l a t e d from the tau cons tants of ana lyses I I I and IV (Table 4.1) r e s p e c -t i v e l y w i t h the a i d of equat ions 2 .17 , 2.20 and 2 .21 . The e x c e l l e n t agreement of a l l but the <5 va lues 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 rder Watson constants g i ven i n column V of Table 4.2 were used i n the f u l l m a t r i x scheme to c a l c u l a t e " e x a c t l y " the f r equenc i es 35 1A 12 16 of a l l of the observed t r a n s i t i o n s of C l N C 0 G .V .S . As expec ted , most o f these " e x a c t " f r equenc ies were found to be i d e n t i c a l to t h e i r co r r e spond ing , 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 f requency . However, s m a l l 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 of the b_-type t r a n s i t i o n s be long ing to the s e r i e s J — (J-l) _ F o r t u n a t e l y , when these were accounted f o r us ing the procedure desc r i bed i n Chapter 6 , the new va lues of 74 3. 3. TABLE 4.2 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 of 3 5 C 1 U 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 . V I I I A b IVA° J = 0 -• 30 J = 0 - 30 J = 0 - 30 Number of T r a n s i t i o n s 52 52 52 A o 51576.184 + 0 . 0 6 8 d 51576.213 51576.219 B o 3130.6603 + 0.0094 3130.6721 3130.6750 C o 2945.1026 + 0.0123 2945.0867 2945.0828 A J 0.001979 + 0.000006 0.001976 0.001975 A JK -0.27697 + 0.00025 -0.27711 -0.27715 A K 15.057 + 0.012 15.060 15.060 6 J 0.0003569 + 0.0000007 0.0003560 0.0003558 6 K (0.00392 + 0.00483) 0.01032 0.01186 Measured i n MHz. b Computed from the r e s u l t s o f a n a l y s i s I I I (Table 4 . 1 ) . ° Computed from the r e s u l t s o f a n a l y s i s IV (Table 4 . 1 ) . ^ Standard e r r o r s . 75 the determinab le mo lecu l a r constants 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 obta ined i n the f i r s t o rder t reatment . 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 cons idered f u r t h e r . Table 4.3 con ta ins 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 constants of a l l of the i s o t o p i c spec i es o f c h l o r i n e i socyana te s t u d i e d . These were determined us ing the f i r s t of the three 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 tha t i t seemed somewhat a r t i f i c i a l ; 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 care must be taken i n i n t e r p r e t i n g the r e s u l t s i n Table 4 . 3 . I t i s c l e a r , f o r a s t a r t , tha t the d i s t o r t i o n ana lyses have y i e l d e d accura te r o t a t i o n a l cons tants which can be used f o r the de te rm ina t i on of the mo lec -u l a r s t r u c t u r e (94) . The s i g n i f i c a n c e of the d i s t o r t i o n cons tants i s l e s s c l e a r . The v a r i a t i o n s noted above suggest tha t the ^ va lues are s u s -p e c t , and t ha t a complete se t o f p h y s i c a l l y mean ingfu l d i s t o r t i o n cons tants can p robab ly be obta ined on l y through a f u l l f i v e parameter f i t u s i ng a d d i t i o n a l b ranches . 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 -ab le i n the f requency range o f our spectrometer to 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 ana lyses were i n i t i a l l y based on the presump-t i o n tha t the f i r s t o rder exp re s s i on g i ven i n equa t ion 2.40 represented a good approx imat ion to the t rue quadrupole e n e r g i e s . L i n e a r l e a s t squares f i t s were made to a l l w e l l r e so l ved quadrupole s p l i t t i n g s of the measured t r a n s i t i o n s up to J = 30. The v a l i d i t y of the approach was then t e s t ed by us ing the computed f i r s t o rder coup l i ng constants i n the f u l l m a t r i x scheme to 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 . In every case , the elements o f f - d i a g o n a l i n J and were found to g i ve n e g l i g i b l e c o n t r i b u t i o n s to 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 order t rea tment . The f i n a l v a lues o f the c h l o r i n e and n i t r o g e n nuc l ea r quadrupole c o u p l i n g constants 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 C o n s t a n t s 3 of C h l o r i n e I socyanate . 3 5 C 1 1 4 N 1 2 C 1 6 0 (G.V.S . ) 3 7 C 1 1 V 2 C 1 6 0 (G.V.S . ) Number of T r a n s i t i o n s A ' o B' o c o aaaa Lbbbb aabb abab 52 51576.213 ± 0 . 0 6 5 C 3130.5876 ± 0.0029 2945.1709 ± 0.0027 -59.139 ± 0.047 -0.010752 ± 0.000025 0.69230 ± 0.00080 -0.01009 ± 0.00058 47 51256.447 ± 0.065 3057.5962 ± 0.0028 2879.4646 ± 0.0027 -58.428 ± 0.047 -0.010272 ± 0.000023 0.67184 ± 0.00098 -0.00926 ± 0.00078 3 5 0 1 1 4 12 18„ , „ T T „ x CI N C 0 (G.V.S . ) 3 5 C 1 1 5 N 1 2 C 1 6 0 (G.V.S . ) Number o f T r a n s i t i o n s A ' o B' o c o aaaa bbbb aabb abab 47 50689.754 ± 0.074 2957.2339 ± 0.0031 2788.5436 ± 0.0029 -57.524 ± 0.056 -0.009569 ± 0.000025 0.64604 ± 0.00092 -0.00982 ± 0.00068 27 49090.359 ± 0.052 3130.6330 ± 0.0026 2936.5686 ± 0.0022 -53.151 ± 0.039 -0.010610 ± 0.000029 0.65900 ± 0.00078 -0.01003 ± 0.00052 77 TABLE 4.3 cont inued 3 7 C 1 1 5 N 1 2 C 1 6 0 (G.V.S . ) 3 5 C 1 1 4 N 1 3 C 1 6 0 (G.V.S . ) Number o f T r a n s i t i o n s A ' o B' o c o aaaa • T bbbb aabb ' abab 18 48771.584 ± 0.055 3057.5618 ± 0.0023 2871.0664 ± 0.0038 -52.454 ± 0.029 -0.010133 ± 0.000025 0.6414 ± 0.0025 -0.0111 ± 0.0021 22 51513.460 ± 0.059 3107.0181 ± 0.0028 2924.0943 ±0.0030 -59.263 ± 0.040 -0.010437 ± 0.000029 0.6904 ± 0.0014 -0.0107 ± 0.0010 3 5 C 1 1 V 2 C 1 6 0 ( v 5 = 1) 3 5 C 1 1 4 N 1 2 C 1 6 0 ( v 5 = 2) Number o f T r a n s i t i o n s 43 23 A* 53261.08 ± 0.11 55137.02 ± 0.33 v B' 3147.3629 ± 0.0045 3163.210 ± 0.018 v C f 2953.7724 ± 0.0048 2961.743 ± 0.038 v x -70.308 ± 0.078 -84.24 ± 0.26 aaaa -0.011159 ± 0.000037 -0.01217 ± 0.00060 boob T 0.7572 ± 0.0021 0.760 ± 0.077 aabb T , , -0.0242 ± 0.0017 (0.027 ± 0.071) abab Measured i n MHz. The e f f e c t i v e r o t a t i o n a l cons tants f o r the app rop r i a t e v i b r a t i o n a l s t a t e 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 . 78 TABLE 4.4 Nuc lear Quadrupole Coup l ing Constants of C h l o r i n e I socyana te . 3 5 C 1 1 4 N 1 2 C 1 6 0 (G.V.S . ) 3 7 C 1 1 4 N 1 2 C 1 6 0 (G.V.S . ) X ( l ) b ' -71.133 ± 0 . 0 6 3 3 -56.611 ± 0.074 A a a X b b ( D - X C ( D -42.594 ± 0.035 -33.147 ± 0.044 X (2) 3.989 ± 0.044 4.135 ± 0.052 aa X,, (2) - x (2) 1.963 ± 0.021 1.998 ± 0.023 bo cc 3 5 C 1 1 4 N 1 2 C 1 8 0 (G.V.S . ) 3 5 C 1 1 4 N 1 3 C 1 6 0 (G.V.S . ) aa X ( D -69.824 ± 0.088 -70.570 ± 0.132 X b b ( l ) - X C C ( D -43.813 ± 0.052 -42.381 ± 0.050 X a a ( 2 ) 4.025 ± 0.054 4.132 + 0.072 del X b b ( 2 ) - X c c ( 2 ) 2.000 ± 0.030 2.037 ± 0.028 3 5 C 1 1 4 N 1 2 C 1 6 0 ( v 5 = 1) 3 5 C 1 1 4 N 1 2 C 1 6 0 ( v 5 - 2) x (1) -71.39 ± 0.10 -70.99 ± 0.24 A a a X u v C D - X C D -43.06 ± 0.08 -43.52 ± 0.17 bb cc X (2) 4.12 ± 0.07 3.78 + 0.12 aa Xu^(2) - X (2) 2.10 ± 0.05 2.10 ± 0.12 A bb cc 3 5 C 1 : 1 5 N 1 2 C 1 6 0 (G.V.S . ) 3 7 C 1 1 5 N 1 2 C 1 6 0 (G.V.S . ) X (1) -71.252 ± 0.075 -56.873 ± 0.116 3 3 . X u u d ) - X (1) -42.673 ± 0.042 -33.092 ± 0.062 ob cc i Measured i n MHz; + o r - one s tandard e r r o r . b C h l o r i n e i s nuc leus 1; n i t r o g e n i s nuc leus 2. 79 are g i ven i n Table 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 I socyanate . 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 de fec t of a l l of the i s o t o p i c spec ies of c h l o r i n e i socyana te s t u d i e d are presented i n Table 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 g i ven i n Table 4.3 by means of equat ions 2.49 and 2 .54. 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 de f e c t s are a l l seen to be s m a l l p o s i t i v e numbers which change very 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 . Th i s i s conv inc ing ev idence tha t the molecu le i s p l ana 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 ) . Fu r the r support f o r t h i s premise i s ob ta ined by c a l c u l a t i n g the f requency of the lowest f requency in-p lane v i b r a t i o n (to^) 35 1A 12 16 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 de f ec t of C l N C 0 w i t h the a i d of equa t ion 2 .57 . The va lue obta ined i s to = 185 cm * i n good agreement w i t h the f r equenc i e s measured i n the 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 Kra i tchman s u b s t i t u t i o n p o s i t i o n s of the four atoms i n c h l o r i n e i socyana te 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 of 35 1A 12 16 i n e r t i a i n Table 4.5 us ing equat ions 2 .58. In t h i s , the C l N C 0 i s o t o p i c spec i e s was taken to be the parent m o l e c u l e , and hence a l l of the coord ina tes are measured w i t h respec t to i t s cente 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 ince on l y the abso lu te va lues of the coo rd i na t e s are d i r e c t l y ob ta ined i n the s u b s t i t u t i o n p rocedure , i t was a l so necessary to appea l to the cente r o f mass and product of i n e r t i a c o n d i t i o n s i n order to determine t h e i r r e l a t i v e s igns (by i n s p e c t i o n ) . The r e s u l t s are c o l l e c t e d as s t r u c t u r e I i n Table 4 . 6 . I t w i l l be noted that the n i t r o g e n a-coord inate i s imag ina ry . Th i s d i s q u i e t i n g f ea tu re i s not unique to c h l o r i n e , i s o c y a n a t e . Indeed, i t has been found that the a p p l i c a t i o n of 80 TABLE 4.5 Moments o f I n e r t i a 3 and I n e r t i a l D e f e c t s 3 o f C h l o r i n e I socyanate . 3 5 C 1 1 4 N 1 2 C 1 6 0 (G.V.S. ) 3 7 C 1 1 4 N 1 2 C 1 6 0 (G.V.S. ) 3 5 C 1 1 4 N 1 2 C 1 8 0 (G.V.S . ) 1° 9.798915 9.860046 9.970277 cl 1° 161.43643 165.29027 170.89987 1° 171.59986 175.51558 181.23830 c . o 0.36452 0.36526 0.36815 3 5 C 1 1 4 N 1 3 C 1 6 0 (G.V.S . ) 3 5 C 1 1 5 N 1 2 C 1 6 0 (G.V.S . ) 3 7 C 1 1 5 N 1 2 C 1 6 0 (G.V.S) 1 ° 9.810851 10.295115 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 C 1 1 4 N 1 2 C 1 6 0 ( v 5 - 1) 3 5 C 1 1 4 N 1 2 C 1 6 0 ( v 5 - 2) 1^ 9.488935 9.166090 a 160.57599 159.7715 I V 171.10015 170.6397 c A V 1.03523 1.7021 3 Measured i n a . m . u . A 2 . 81 K ra i t chman ' s equa t i ons , us ing ground s t a t e moments of i n e r t i a , to the d e t e r -m ina t i on of ve ry s m a l l coord ina tes g e n e r a l l y g i ves q u i t e i n a c c u r a t e , and o c c a s i o n a l l y imag ina ry , r e s u l t s (68 ,56 ) . Herschbach and L a u r i e (95) have shown that t h i s behav io r i s due, at l e a s t i n p a r t , to 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 mo lecu l a r s t r u c t u r e ( i . e . to zero p o i n t v i b r a -t i o n a l e f f e c t s ) . With 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 c o n t r i -bu t i ons are a much s m a l l e r percentage of the t o t a l A I ° ' s , these e r r o r s are a co r r e spond ing l y reduced. None the less , 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 tandard e r r o r s g i v en i n Table 4 . 6 , which 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 to 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 de te rmin ing the n i t r o g e n a-coord inate i s by a p p l i c a t i o n of the cente r o f mass c o n d i t i o n (__]m.a. = 0 ) . Th i s i s i a l s o t rue f o r the carbon b-coord inate ( V , m . b , = 0) which i s seen to be — • V i i l s m a l l e r than the 0.15 °v tha t Cos t a i n (64) has e m p i r i c a l l y suggested shou ld be a lower bound on the s i z e of coo rd ina tes 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 cen te r of mass determined a^ and b^ are a l s o presented i n Table 4 . 6 , as pa r t o f s t r u c t u r e I I . Here the o ther coo rd ina tes were aga in taken to have t h e i r s u b s t i t u t i o n v a l u e s . I t w i l l be noted that the new va lue f o r the c a r -bon b-coord inate 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 rev ious one, which had a l r eady been regarded as suspect and can now be d i s c o u n t e d . Of the remain ing s u b s t i t u t i o n determined coo rd ina tes the s m a l l e s t , and hence most u n c e r t a i n , i s b „ , which at 0.17945 A i u s t s a t i s f i e s C o s t a i n ' s C l J c r i t e r i o n of a c c e p t a b i l i t y (0.15 X). As a check on t h i s v a l u e , the product o f i n e r t i a c o n d i t i o n (X]m^ a^ b^  = 0) was used a long w i t h the cen te r of mass r e l a t i o n (]Cm4D-t = ^ t o re-determine the carbon and c h l o r i n e b-coo rd ina t e s . 82 35 14 12 16 TABLE 4.6 C h l o r i n e Isocyanate Atomic Coord inates i n the CI N C 0 P r i n c i p a l A x i s System. Coord ina te ' i r I I I d . a c i -1.40678 + 0.000046 -1.40678 + 0.00004 -1.40678 + 0.00004 *N imaginary 0.04747 + 0.00013 0.04747 + 0.00013 a c 1.11192 + 0.00009 1.11192 + 0.00009 1.11192 + 0.00009 a o 2.19981 + 0.00003 2.19981 + 0.00003 2.19981 + 0.00003 b c i 0.17945 + 0.00003 0.17945 + 0.00003 0.18047 + 0.00002 b N -0.71001 + 0.00001 -0.71001 + 0.00001 -0.71001 + 0.00001 b c -0.11022 + 0.00008 -0.10133 + 0.00009 -0.10431 + 0.00007 b o 0.30529 + 0.00002 0.30529 + 0.00002 0.30529 + 0.00002 m i a i 0.0 0.0 m.b. l l -0.10671 0.0 0.0 y ^ m . a . b . •V i i i l >,m.a. . i i l x 9.82176s 0.09008 161.4743f 9.799198 0.0 161.4743f 9.81939* 3 Measured i n A*. S u b s t i t u t i o n p a^ and b^ from cente r of 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^ from cen te r of mass, b ,^ and i n e r t i a , 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° ( exp t . ) = 161.43643 a.m.u.X 2 . S Compare w i t h 1° ( exp t . ) = 9.7989145 a.m.u.R 2. cl b p o s i t i o n s (K ra i t chman 's e q u a t i o n s ) . ^ ^ from cen te r of ma s, b ,^ and b ^ from cente r o f mass and product o f 83 A l l of the o the r coord ina tes were determined by s u b s t i t u t i o n , except |^ which was c a l c u l a t e d from the cen te r o f mass c o n d i t i o n ( i . e . the same as i n I I ) . The r e s u l t s are a l s o presented i n Table 4 . 6 , as s t r u c t u r e I I I ; The changes i n the b ^ and b^ coord ina tes on going from I I to I I I are 0.00102 1 and 0.00298 1 r e s p e c t i v e l y . A l though much l a r g e r than the c a l -cu l a t ed s tandard e r r o r s these d i f f e r e n c e s would nonethe less 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 of the gene ra l s u b s t i t u t i o n procedure . The mo lecu l a r geometr ies tha t may be c a l c u l a t e d from the atomic p o s i -t i o n s ob ta ined i n ana lyses I I and I I I are presented i n Tab le 4 . 7 . Of the two s t r u c t u r e s , I I i s to 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 the b e t t e r r ep roduc t i on of 1 ° . In any case , one can not reasonab ly expect tha t e i t h e r shou ld 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 tha t the d i f f e r e n c e s between them would be s i g n i f i c a n t . There fore an average of the two s t r u c t u r e s was computed and i s a l s o presented i n Tab le 4 . 7 , as s t r u c t u r e IV. In F igu re 4.3 the mo lecu l a r geometry of c h l o r i n e i socyana te i s i l l u s -t r a t e d w i t h a s c a l e d rawing . In 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 procedure o f P i e r c e and K r i s h e r (67,68) was used 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 ng the n i t r o g e n a-coord ina te . S ince the p r e v i o u s l y obta ined cente r o f mass a^ j va lue was thought to be q u i t e a c c u r a t e , the experiment was rega rded , from the b e g i n n i n g , more as a t e s t of t h i s seldom used sem i-emp i r i c a l technique than 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 spec ies used a r e : 3 5 C 1 1 4 N 1 2 C 1 6 0 3 7 C 1 U N 1 2 C 1 6 0 3 5 C 1 1 5 N 1 2 C 1 6 0 3 7 C 1 1 5 N 1 2 C 1 6 0 3 5 1 4 1 2 1 6 3 7 1 4 1 2 1 6 w i t h C l N C 0 taken to be the " p r i n c i p a l framework" and C l N C 0 the "secondary framework" so tha t the new a^ coord ina te would be d i r e c t l y comparable to the cente r o f mass v a l u e . The necessary 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 I socyana te . I I C I I I d I V e r ( C l - N ) a 1.70469 1.70523 1.705 ± 0 . 0 0 5 f r(N-C) 1.22619 1.22471 1.226 ± 0.005 r(C-O) 1.16140 1.16244 . 1.162 ± 0.005 A(C1NC) 118° 47 ' 118° 53 ' 118° 50* ± 30 ' z.(NCO) b 170° 44» 171° 0 ' 170° 52 ' ± 30 ' A l l d i s t a n c e s are i n A*. C l and 0 are t r a n s . Computed from I I i n Table 4 . 6 . Computed from I I I i n Table 4 . 6 . Average of I I . and I I I . Es t imated 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 parameters . TABLE 4.8 N i t r o g e n a-Coordinate 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 1 a N (C0M) = 0.04747 A FIGURE 4.3 The Molecular Structure of Chlorine Isocyanate. 86 37 1A 12 16 s p e c i f i c a l l y , the coord ina tes (A,B) of the cen te r of mass of C l N C 0 i n the cen te 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) of 35 1A 12 16 C l N C 0 and a l s o the angle (9) between the p r i n c i p a l a x i s systems of these 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 are g i v en i n Table 4 .8 a long w i t h two double s u b s t i t u t i o n va lues f o r a^. The f i r s t was obta ined from second d i f f e r e n c e s of I^'s (equat ion 2 . 6 4 ) , the second from i ° ' s (equat ion 2 . 6 7 ) ; the d i f f e r e n c e between them i s 0.00388 °v. The reasons 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 repancy are 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 to the a^ va lue obta ined us ing the cen te r of mass c o n d i t i o n , i t would seem to be the b e t t e r of 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 of 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 of v i b r a t i o n a l e f f e c t s w i t h the AAI. (or AA I ) c b a e x p r e s s i o n than 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 tha t f o r the second d i f f e r e n c e s technique to 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 (0.03 A* o r more ) , w i t h respec t to tha t of the pr imary one, a long the d i r e c t i o n i n q u e s t i o n . Th is c r i t e r i o n i s c l e a r l y s a t i s f i e d i n the present case , which cou ld t h e r e f o r e be regarded 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 de t e rm ina t i on o f b £ , f o r example, would be r a t h e r tenuous. 4.4 D i s c u s s i o n of the Nuc lea r Quadrupole Coup l ing Cons tan t s . In the preced ing s e c t i o n i t was shown tha t c h l o r i n e i socyana te i s almost c e r t a i n l y a p l a n a r mo l e cu l e . Th is deduc t ion i s c o n s i s t e n t w i t h the observed c h l o r i n e nuc l ea r 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 c h l o r i n e nuc l ea r quadrupole coup l i ng cons tants of the three i s o t o p i c spec i e s expected to 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 of 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 systems, w i t h respec t to the mo lecu l a r f rame, are presented i n Table 4 . 9 . 87 TABLE 4.9 Se l ec ted C h l o r i n e Nuc lea r Quadrupole Coupl ing C o n s t a n t s 3 of C h l o r i n e I socyanate . 3 5 C 1 1 4 N 1 2 C 1 6 0 3 5 C 1 U N 1 2 C 1 8 0 3 7 C 1 U N 1 2 C 1 6 0 X -71.133 ± 0.063° -69.824 ± 0.088 -56.611 ± 0.074 aa X b b 14.270 ± 0.036 13.006 ± 0.051 11.732 ± 0.043 X 56.863 ± 0.036 56.819 ± 0.051 44.879 ± 0.043 A c c X ( 3 5 C 1 1 4 N 1 2 C 1 6 0 ) / X ( 3 7 C 1 1 4 N 1 2 C 1 6 0 ) = 1.2565 ± 0.0020 3.3. 33 X b b ( 3 5 C l 1 4 N 1 2 C 1 6 0 ) / x b b ( 3 7 C l 1 4 N 1 2 C 1 6 0 ) = 1.2163 ± 0.0054 X ( 3 5 C 1 1 4 N 1 2 C 1 6 0 ) / X ( 3 7 C 1 1 4 N 1 2 C 1 6 0 ) = 1.2670 ± 0.0015 cc A c c Q ( 3 5 C 1 ) / Q ( 3 7 C 1 ) = 1.26878 ± 0 .00015 d 0 Measured i n MHz. k Ground v i b r a t i o n a l s t a t e v a l u e s , c Standard e r r o r s . d From Gordy and Cook (128) . 88 35 The two C l spec i e s are seen to have n e a r l y equa l x c c v a l u e s , but s i g -n i f i c a n t l y d i f f e r e n t Xiv and x v a l u e s . Fur thermore , the r a t i o bb A a a ' 35 37 X ( C l ) / x ( C l ) i s i n agreement w i t h the r a t i o o f the quadrupole act aa ° M r moments of the two c h l o r i n e i so topes on l y f o r a = c. E v i d e n t l y the p r i n -c i p a l i n e r t i a l a x i s systems of the v a r i o u s i s o topes are r e l a t e d by a s imp le r o t a t i o n about a common _c-ax is ; as expected f o r a p l ana r s t r u c t u r e . A comple te ly r i g o r o u s i n t e r p r e t a t i o n of nuc l e a r quadrupole coup l i ng constants would be ext remely d i f f i c u l t because of the complex dependence o f the 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 . Cons ide rab le progress can be made, however, u s i n g a very approximate treatment f i r s t i n t roduced by Townes and D a i l e y (96) and l a t e r m o d i f i e d and extended by many others (97) . In i t s s i m p l e s t form t h i s theory a t t r i b u t e s the f i e l d g r a d i e n t s e n t i r e l y to the p-e lec t rons i n the va lence s h e l l o f the atom which con ta ins the coup l i ng n u c l e u s ; a l l o ther charges are i g n o r e d . I f x , y and z de f i ne a C a r t e s i a n a x i s system on t h i s nuc leus t h e n : X = (n - 1/2(n + n ))eQq i n = -(U ) eQq i n 4 .1a xx x y z n n l O p xx X M n l O X = (n - l/2(n + n ))eQq = -(U ) eQq i n 4.1b yy y x z x ^ n l O p yy x ^ n l O X = (n - l/2 (n + n ))eQq i n = -(U ) eQq 4.1c zz z x y ^ n n l O p zz x n n l O where n , n and n are the occupa t ion numbers of the va lence s h e l l p - o r b i t a l s x y z and q. n ig i s the f i e l d g r ad i en t o f an atomic p-e l e c t ron i n the n t b (va lence) 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 long the r e fe rence a x i s . The " a t o m i c " coup l i ng cons tants eQq_^g have been e x p e r i m e n t a l l y determined f o r most common quadrupo la r n u c l e i . I f the c o u p l i n g atom has a fo rma l p o s i t i v e or nega t i ve charge , equat ion 4.1 should be m o d i f i e d to account f o r the reduced or i n c reased s c r een ing of 89 the valence shell p-electrons. For a fractional positive charge c + the recommended (98) form i s : X = -(1 + c E)(U ) eQq , r t gg P gg y 4 n l O 4.2 For a fractional negative charge c i t i s : "gg • - (V«"< 1W ( l + <="«> 4.3 where e is a semi-empirical "screening constant".' Townes and Schawlow (99) have calculated e values for a number of different atoms from the variation of q with ionic state. nnlO The p-orbital populations may be related to the electronic structure of the molecule using either the Valence Bond (100) or the LCAO-MO (101) formalism. The latter approach i s the one taken here. In order to apply the Townes Dailey theory to the chlorine quadrupole coupling of this 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 clearly be achieved by a simple clockwise rotation of 9 about the c^-axis. It then follows that i f x i s the quad-z a —-rupole tensor in the i n e r t i a l axis system and x is the quadrupole tensor in the bond axis system one has: X B = R _ 1 X R 4.4 where R = Cos9 -Sin9 0 za za S i n e ' Cose 0 za za 0 0 1 B X = B B X X zz xz B B X x xz 0 0 0 0 yy 4.4a 4.4b 9 0 and X = 'aa xab Cab Xbb 0 X. 4.4c cc B B and the off-diagonal elements y > X t. > X > X are a l l zero because the ac ab xy zy axis perpendicular to the plane i s , by symmetry, a p r i n c i p a l axis of the quadrupole coupling tensor (101). A general solution of equation 4.4 for the diagonal tensor elements i n the bond axis system gives expressions con-taining the unknown Y r. as w e l l as the known Y . If> however, the C1N ab Aaa bond axis i s also a p r i n c i p a l axis of the quadrupole coupling tensor then X x z i s zero and these relations may be s i m p l i f i e d to the following ones by eliminating x ab' B 2 2 2 ? X v v = (X Sin 9 - XvvCos 9 )/(Sin 9 - Cos 9 ) xx aa za bb za za za 4.5a zz = (x Cos29 - Xi,iSin 29 )/(Cos 29 - Sin 29 ) aa za bb za za za 4.5b B Xyy X c c 4.5c Since the C1N bond has indeed been found to approximate closely a p r i n c i p a l axis of the chlorine nuclear quadrupole coupling tensor i n several related molecules (102), such was assumed to be the case here too, and the 35 14 12 16 Cl N C 0 (G.V.S.) data were substituted into equations 4.5 to obtain B 35 values for x ( C l ) . The results are presented i n Table 4.10: the r e l a t i v e aa orientations of the various axis systems are i l l u s t r a t e d i n Figure 4.4. B 35 The computed X z z ( Cl) at -122.2 MHz i s of the same magnitude as 35 ' ~ e^310^ ~ ""109.7 MHz; thus implying that the C1N a bond i s nearly co-valent. This i s consistent with the e s s e n t i a l l y equal chlorine and nitrogen 91 TABLE 4.10 Trans fo rmat ion of the C h l o r i n e Nuc lear Quadrupole Coup l ing Constants i n t o the C1N Bond A x i s System. 35 1A 12 16 A. C l N C 0 (G.V.S . ) constants t ransformed from the i n e r t i a l a x i s system to the bond a x i s system us ing equat ions 4 . 5 . S t r u c t u r e I I S t r u c t u r e I I I Y B 65.311 65.500 xx XB 56.864 56.864 yy XB -122.174 -122.363 A z z 0 31° 27 ' 31° 29 ' za B. 3 5 C 1 1 4 N 1 2 C 1 6 0 (G.V.S . ) and 3 5 C 1 1 4 N 1 2 C I 8 0 (G.V.S . ) da ta used to f i n d the p r i n c i p a l axes of the c h l o r i n e quadrupole coup l i ng t e n s o r . S t r u c t u r e I I S t r u c t u r e I I I X x ' x ' 53.731 68.723 x y V 56.864 56.864 X z * z ' -110.594 -125.586 8 • aa 30 ' 28' 9 , z a 29° 20 ' 31° 58 ' B X x x 53.658 68.707 B 56.864 56.864 B X z z -110.444 -125.571 Measured i n MHz. z i s a long the C1N bond, y i s p e r p e n d i c u l a r to the mo lecu la r p l a n e . x ' , y ' , z ' p r i n c i p a l a x i s system of 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 to the p l a n e , z ' i s n e a r l y p a r a l l e l to the C1N bond. 92 FIGURE 4.4 I l l u s t r a t i o n of the Var ious A x i s Systems Relevant to the D i s c u s s i o n of the C h l o r i n e Nuc lear Quadrupole Coup l ing Cons tan 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 of C l N C O (G.V.S . ) w i t h o r i g i n at cen te r o f mass of t h i s i s o t o p e . ( 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 of 3 5 C l 1 4 N l 2 c 1 8 0 (G.V.S . ) w i t h o r i g i n of cente r of mass of t h i s i s o t o p e . ( x , y , z ) = C1N Bond a x i s sys tem. ( 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 quadrupole coup l i ng t ensor 16 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 . The angles 9 , and 9 , have been exaggerated f o r c l a r i t y . 93 e l e c t r o n e g a t i v i t i e s (103) . Now any double bond cha rac te r (IT ) i n the C1N bond must be of the d a t i v e type from c h l o r i n e to n i t r o g e n and would the re fo re B 35 35 tend to decrease |x__( Cl) | r e l a t i v e to l e P ^ ^ n C Cl) | . On the o ther hand, B 35 the e f f e c t of i o n i c cha ra c t e r ( i ) i n the cr bond i s to i n c r ea se |Y ( C l ) I a ' zz 1 when the p o s i t i v e po le i s on c h l o r i n e . To o b t a i n a q u a n t i t a t i v e es t imate of these opposed e f f e c t s i t i s necessary to make two a d d i t i o n a l assumpt ions , namely: (1) tha t o r b i t a l ove r l ap may be ignored i n n o r m a l i z i n g the mo lecu l a r o r b i t a l s and (2) tha t the a bonding c h l o r i n e atomic o r b i t a l i s a pure p^ o r b i t a l , r a t h e r than an sp h y b r i d . Taken toge ther these shou ld be a f a i r l y good approx imat ion (104) . The popu l a t i ons of the va lence s h e l l c h l o r i n e p - o r b i t a l s may then be w r i t t e n down a s : n = 2 n = 2 - IT n = 1 - i 4 .6 x y c z a S u b s t i t u t i o n o f these express ions a long w i t h E = 0 . 1 5 (99) and the app rop r i a t e c o u p l i n g cons tants i n t o equat ions 4.2 y i e l d s i ^ = 0 . 1 1 2 (11%) and TTc = 0.050 (5%), a not unreasonable r e s u l t . A ve ry s i m i l a r a n a l y s i s , by Cook and Gerry (14 ) , on the i s o e l e c t r o n i c c h l o r i n e az ide molecu le gave i = 12% and ir = 8%. a c These f i g u r e s must be viewed w i t h c a u t i o n , however, because of the approx -imat ions i nhe ren t i n the Townes D a i l e y t h e o r y , and because of 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 > to the co r r e c tness of the assump-J act t i o n tha t the ClN bond i s 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 ad i en t t enso r . In p r i n c i p l e i t shou ld be p o s s i b l e to use the i s o t o p i c data to determine B * 35 un ique l y the x a a • I f x' r ep resen ts the C l quadrupole coup l i ng tensor o f an i s o t o p i c a l l y s u b s t i t u t e d spec ies of c h l o r i n e i s o c y a n a t e , whose a ' - a x i s * To a very good approx imat ion 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 of the f i e l d g r ad i en t t e n s o r , w i t h respec t to the mo lecu l a r f rame, w i l l be independ -ent of i s o t o p i c s u b s t i t u t i o n (101) . 94 makes an angle 6 , ( p o s i t i v e f o r c l ockw i se r o t a t i o n a+a') w i t h the a—axis aa — — — o f C l N C 0 (G.V.S . ) , i t f o l l o w s t h a t : where R and x were de f i ned e a r l i e r and: X* = *aa X a b 0  X a b *bb ° x' A c c 4.7a Equat ion 4.7 may be so l ved f o r x i_ (or xV) i n terms of on l y the known x ab A ab J aa and X^ a» d i a g o n a l i z a t i o n of x_ (or x_') then y i e l d s the p r i n c i p a l va lues o f the quadrupole coup l i ng t e n s o r . 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 system i s t r i v i a l . 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 taken to 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 Table 4 .10 . They are seen to be c r i t i c a l l y dependent on the va lue of 8 , ; i ndeed , a change i n t h i s aa angle of on l y 2' on go ing from s t r u c t u r e I I to I I I produces a 15 MHz v a r i a t i o n 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 . I t i s g r a t i f y i n g to see tha t these two se t s of r e s u l t s b racke t those obta ined i n the p reced ing a n a l y s i s . S ince i t was necessary to use the product o f i n e r t i a r e l a t i o n ( X / m i a i b i = )^ t o determine the angle 6 , i t i s more c o n s i s t e n t to use s t r u c t u r e I I I r a t h e r aa than s t r u c t u r e I I , i n t h i s c a l c u l a t i o n . An attempt was a l s o made to i n t e r p r e t the n i t r o g e n quadrupole c o u p l i n g i n terms of the Townes D a i l e y t heo r y . S ince the n i t r o g e n atom was expected to have a fo rma l nega t i ve charge , equat ions 4 . 3 , r a the r than 4 . 2 , were used i n t h i s a n a l y s i s . U n f o r t u n a t e l y there i s some u n c e r t a i n t y as to what va lue should be ass igned to the " a t o m i c " n i t r o g e n coup l i ng constant appear ing i n these 14 e x p r e s s i o n s . In t h i s case , eQ^io^ N) was taken to be -10 MHz as suggested 95 by Gordy and Cook (105) . A v a lue of 0.30 was used f o r the s c reen ing c o n -s t a n t e (99) . The n e a r l y 120° C1NC bond angle s t r o n g l y suggests tha t i t would be appro-p r i a t e to regard the n i t r o g e n atomic o r b i t a l s tha t are p a r t i c i p a t i n g i n bond 2 fo rmat ion as e s s e n t i a l l y pure sp h y b r i d s . I f the x - a x i s i s de f ined to be the b i s e c t o r of the C1NC ang l e , and the y-ax i s i s chosen to be p e r p e n d i c u l a r to the mo lecu l a r frame these are conven i en t l y w r i t t e n a s : Hybr id Number o f Des igna t i on E l e c t r o n s lone p a i r n^„ 4 .8a S **x if>2 = JT/3 ( j ) g +N/I76<j>_ +>/T72<J>_ NC o bond n ^ 4.8b X z * 3 =Jl73<!> s +N/l76<J>p -JT/2t NCI a bond n ^ 4 .8c X z ^4 = <J>p ou t-of-p lane n_ 4.8d y TT bond IT Fur thermore , 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 to make the f o l l o w i n g i d e n t i f i c a t i o n s : X X X ( U n > * * b b < U N > X Z Z ( 1 4 N ) « X A A ( U N ) X Y Y ( U N ) = X C C ( 1 4 N ) 4.9 Th i s avo ids any h i g h l y tenuous coo rd ina te t r a n s f o r m a t i o n s . Here , u n l i k e the c h l o r i n e case , there i s no obv ious cho ice f o r an i n-p l ane 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 the i s o t o p i c v a r i a t i o n s of the c o u p l i n g cons tan ts are n e g l i g i b l e . From equat ions 4.8 the n i t r o g e n p - o r b i t a l popu l a t i ons may be r e w r i t t e n a s : n x = 2 / 3 n L P + 1 / 6 n N C + 1 / 6 n N C l 4 ' 1 0 a n = n 4.10b y TT 96 n z = 1 / 2 n N C + 1 / 2 n N C l 4 ' 1 0 c S ince even w i t h set equa l to 1.1 (the va lue obta ined 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 three unknowns and on ly two independent coup l i ng c o n s t a n t s , i t i s c l e a r tha t one a d d i t i o n a l assumption 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 , the " l o n e p a i r " o r b i t a l was presumed to be comp le te l y nonbonding and f i l l e d , i . e . n^p = 2. S o l u t i o n of equat ions 4.3 u s i n g the 35 14 12 16 C l N C 0 (G.V.S . ) c oup l i ng constants then gave the r e s u l t s c o l l e c t e d i n column I of Table 4 . 1 1 . The l a r g e nega t i ve fo rma 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 are comple te ly unreasonab le . Th is l eads to the c o n c l u s i o n t ha t e i t h e r the s i m p l i f i e d v e r s i o n o f the Townes D a i l e y theory used here i s inadequate , or tha t the assumption of a comple te l y nonbonding lone p a i r on n i t r o g e n i s i n c o r r e c t . To i n v e s t i g a t e the l a t t e r p o s s i b i l i t y n NC W a S e s t i m a t e a from the e l e c t r o n e g a t i v i t i e s of carbon and n i t r o g e n and it^p was a l lowed to v a r y . The s i m p l e s t r e l a t i o n connec t ion i o n i c cha 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 tha t p o s t u l a t e d by Gordy (106) : ' i = |*(A) - * ( B ) | / 2 , f o r |Z(A) - X(B)|<2 4.11 With *(N) = 3.00 and Z(C) = 2.50 (103) t h i s g i ves i^(NC) = 0.25 and hence n N C <1.25. S ince the carbon atom here i s a l so a t tached to 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 tha t t h i s over es t imates the i o n i c cha rac te 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 the r e fo r e performed three t imes w i t h n „ _ v a r i e d from 1.0 • NC 35 14 12 16 to 1.2; aga in the C l N C 0 (G.V.S . ) c oup l i ng cons tants were used . The r e s u l t s are a l so c o l l e c t e d i n Table 4 . 1 1 . The t o t a l nega t i ve charge on i n i t r o g e n i s seen to be a s e n s i t i v e f u n c t i o n of the cho ice of n , the i n -IN Kj d i v i d u a l popu l a t i ons l e s s s o . I f i t i s assumed tha t c shou ld be l e s s th an TABLE 4.11 N i t r ogen Quadrupole Coupl ing I n t e r p r e t a t i o n us ing the Townes D a i l e y Theory. I I I I I I IV n L P 2a 1.60 1.69 1.78 n TT 1.94 1.55 1.64 1.73 "NC 1.45 1 .00a 1 .10 a 1 . 2 0 a n N C l 1 .10b 1.10 b i . i o b i . i o b n X 1.76 1.41 1.49 1.57 n y 1.94 1.55 1.64 1.73 n z 1.28 1.05 1.10 1.15 n s 1.50 1.23 1.30 1.36 c 1.49 0.25 0.53 0.81 a Assumed. b C a l c u l a t e d from c h l o r i n e quadrupole c o u p l i n g . TABLE 4.12 CND0/2 C a l c u l a t e d p - O r b i t a l Popu l a t i ons on C h l o r i n e and N i t r o g e n i n C h l o r i n e I socyana te . C h l o r i n e (IA) C h l o r i n e (BA) N i t r ogen (IA) n x n 1.7235 1.9934 1.1051 1.9356 0.0064 1.9920 1.9934 0.8365 1.9356 0.0064 1.2776 1.4501 1.0120 1.4831 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 3 5 C 1 1 4 N 1 2 C 1 6 0 (G .V . S . ) . BA = C1N Bond a x i s system. 98 0.5 electrons (107) t h i s a n alysis i n d i c a t e s a nearly covalent NC bond. The smallish (<2) values can be r a t i o n a l i z e d only by p o s t u l a t i n g some par-t i c i p a t i o n of i j ^ i n an in-plane IT NCO bond. The out-of-plane IT NCO bond apparently has considerable nitrogen lone p a i r character. The r e l a t i v e pop-ul a t i o n s n T T 1>n are consistent with the more favorable overlap of tfi. and LP TT R 4 the out-of-plane carbon p - o r b i t a l , as compared to the overlap of \J> and the in-plane carbon p - o r b i t a l ; indeed 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 not l a r g e r . A q u a l i t a t i v e l y reasonable p i c t u r e of the bonding at nitrogen has thus emerged. In t h i s , the NC and NCI a bonds are nearly covalent, w h i l s t the and \JJ^  nitrogen o r b i t a l s both p a r t i c i p a t e i n a TT system that presumably runs the length of the NCO chain. The out-of-plane p - o r b i t a l s on each of nitrogen, oxygen and carbon may be used to construct three molecular o r b i t a l s , two of which w i l l be doubly occupied with very unequally shared e l e c t r o n s . A s i m i l a r scheme would apply to the in-plane ir system. However, because of the many assumptions and approximations that were made i n constructing t h i s model i t would be naive to attach any qu a n t i t a t i v e s i g n i f i c a n c e to the numbers i n Table 4.11. Semi-empirical SCF-M0-CND0 theory has been previously employed i n con-j u n c t i o n with the Townes Dailey theory to c a l c u l a t e nuclear quadrupole coupling constants (108). Good agreement of cal c u l a t e d and observed values has generally been obtained f o r halogen n u c l e i ; rather poorer agreement, f o r nitrogen n u c l e i . Such c a l c u l a t i o n s were performed on chlorine isocyanate by Dr. M. L. Williams (109) and kindl y communicated to the author. In t h i s instance the desired p - o r b i t a l populations were computed using the Santry and Segal (110) parameterization of the SCF-M0-CND0/2 method. The atomic o r b i t a l basis set included s-, p- and d - o r b i t a l s on c h l o r i n e , but only s-99 and p - o r b i t a l s on ca rbon , oxygen and n i t r o g e n . Two d i f f e r e n t a x i s systems were c o n s i d e r e d , namely: (1) the p r i n c i p a l i n e r t i a l a x i s system, .and (2) the C1N bond a x i s system. The computed p - o r b i t a l popu l a t i ons are presented i n Table 4 . 1 2 . The c o u p l i n g constants which may be c a l c u l a t e d from them us ing equat ions 4.3 are compared i n Table 4.13 w i t h the expe r imenta l ones. The c a l c u l a t e d and "obse r ved " c h l o r i n e n u c l e a r quadrupole coup l i ng c o n -s t a n t s are seen to be i n reasonable agreement. Th i s i s so f o r both 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 system. The l a t t e r r e s u l t s p rov ide f u r t h e r ev idence tha t the C1N bond i s indeed at l e a s t approx imate ly 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 ad i en t t e n s o r . The CNDO/2 c a l c u l a t i o n a l so suppor ts the assumption made e a r l i e r tha t 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 rma t ion of a a bond to n i t r o g e n i s e s s e n t i a l l y pure " p " . Both the " f i l l e d " 3s and "empty" 3d c h l o r i n e atomic o r b i t a l s are found to p l a y on ly a v e r y minor r o l e i n the o v e r a l l (CNDO/2) bonding scheme. Th i s apparent 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 socyana te bonding i s c o n s i s t e n t w i t h cu r r en t t h e o r i e s on the f a c t o r s a f f e c t i n g the importance o f d - o r b i t a l s i n mo lecu l a r bonding (111,112) . In the case of 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 , the CNDO/2 c a l c u l a t i o n has y i e l d e d x and x v a lues which are i n good agreement w i t h exper iment , but a l s o a x D b va lue which i s l e s s than h a l f the observed one. S t i l l , the r e s u l t s are q u i t e r e spec t ab l e when compared w i t h o ther n i t r o g e n quadrupole 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 gns have f r e q u e n t l y been encountered (110) . I t i s perhaps more i l l u m i n a t i n g to look at the n i t r o g e n p - o r b i t a l pop -u l a t i o n s r a t h e r than the c o u p l i n g c o n s t a n t s . The CNDO/2 numbers are rough ly comparable to those l i s t e d i n column I I of Table 4 . 1 1 , and s i g n i f i c a n t l y 100 TABLE 4.13 Comparison of Observed and C a l c u l a t e d Nuc lea r Quadrupole Coup l ing C o n s t a n t s 3 of 3 5 C 1 1 4 N 1 2 C 1 6 0 (G .V . S . ) . Exper imenta l CNDO/2 % D i f f e r e n c e * a a ( C 1 ) -71.133 -82.59 16.1 W C 1 ) 14.270 19.10 33.8 x c c (c i ) 56.863 63.49 11.6 * a a ( N ) 3.989 3.294 17.4 X b B ( N ) -1.013 -0.465 54.1 X C C ( N ) -2.976 -3.053 2.6 Ca l cu l a t ed (A , I I ) ° CND0/2 b % D i f f e r e n c e d X B (C l ) 65.31 63.26 3.1 xx X B (C l ) 56.86 63.49 11.7 yy X B Z ( C 1 ) -122.17 -126.76 3.8 ° Measured i n MHz. b C a l c u l a t e d from the o r b i t a l popu l a t i ons i n Table 4 .12 . c C a l c u l a t e d from the expe r imen ta l v a l u e s , assuming the C1N bond to 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 ad i en t t e n s o r . d % d i f f e r e n c e = ( (xn„ ( exp t . ) - x„„ (CNDO/2) ) / x _ ( exp t . ) ) x l 0 0 . i 101 d i f f e r e n t from those i n column I. They thus support our c o n t e n t i o n of 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 in-p lane TT bonding system of c h l o r i n e i s o c y a n a t e . 4.5 V i b r a t i o n a l Dependence of the M o l e c u l a r Cons tan ts . 35 14 12 16 The r o t a t i o n a l constants of the C l N C 0 i s o t o p i c spec i es of c h l o r i n e i socyana te 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 lowest f requency i n-p l ane v i b r a t i o n i n F i gu r e s 4 . 5 , 4.6 and 4 . 7 . The near 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 , at l e a s t w i t h respec 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 c o n -s t a n t s i s c o n s i s t e n t w i t h the s imple theory (equat ions 2 .48 ) . I n c l u s i o n of q u a d r a t i c terms i n the v i b r a t i o n a l expans ion would presumably comple te l y account f o r the r e l a t i v e l y s m a l l d e v i a t i o n s from l i n e a r behav io r seen he re . However, s i n c e the 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 (90 ) , and the b a r r i e r to 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 angle of bend , i s a lmost 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 to be expected tha t at l a r g e va lues 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 at which the molecu le can v i b r a t e through the l i n e a r c o n f i g u r a t i o n . As t h i s 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 i n c r ease d r a m a t i c a l l y u n t i l i t becomes a bending v i b r a t i o n f requency of the l i n e a r mo lecu l e . None-t h e l e s s , the l i m i t e d expe r imen ta l ev idence suggests t h a t f o r the lowest 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 , the r o t a t i o n a l cons tants are w e l l behaved. Hence, the s u b s t i t u t i o n s t r u c t u r e determined i n s e c t i o n 4.3 shou ld represent the e q u i l i b r i u m one to a good app rox ima t i on . 35 14 12 16 In F i gu re 4.8 the i n e r t i a l de fec t of the C l N C 0 i s o t o p i c spec i es has a l s o been p l o t t e d as a f u n c t i o n of v^. The e s s e n t i a l l y exact s t r a i g h t l i n e observed i s i n agreement w i t h the Oka and Mor ino e x p r e s s i o n f o r the v i b r a t i o n a l dependence of the i n e r t i a l de fec t ( equat ion 2 .56 ) . S ince the 102 103 FIGURE 4.6 V i b r a t i o n a l Dependence of the B' R o t a t i o n a l Constant o f 3 5 C 1 1 4 N 1 2 C 1 6 0 . 3120 + 0 T 1 (v 5 + 1/2) T 2 104 FIGURE 4.7 V i b r a t i o n a l Dependence of the C' Rotational Constant of 3 5 C 1 1 4 N 1 2 C 1 6 0 . ( v 5 + 1/2) 105 106 i n t e r c e p t of t h i s l i n e i s approx imate ly zero i t seems tha t the c o n t r i b u t i o n s to A° from the o the 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 . There fore one might reasonab ly expect tha t the s imple Hershbach and L a u r i e e x p r e s s i o n A° ~ 4K/co^ should g i ve a r e spec t ab l e r e s u l t ; t h i s has a l r eady been shown to 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 cons tants of c h l o r i n e i socyana te behave r a t h e r 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 . Two, x, , , , and x , are J ' bbbb aabb n e a r l y the same i n a l l three s t a t e s s t u d i e d , wh i l e x i n c r eases r a p i d l y 3-3.33. w i t h v,.; the f o u r t h , T a b a b > w a s w e l l determined f o r o n l y the ground s t a t e . A s i m i l a r phenomenon has been observed f o r o the r q u a s i - l i n e a r molecu les (113) . Johns (114) has managed to account q u a n t i t a t i v e l y f o r the i n c r ea se i n x aaaa f o r s e v e r a l of these u s i ng as a bending p o t e n t i a l a harmonic o s c i l l a t o r per tu rbed w i t h a L o r e n t z i a n b a r r i e r ( to l i n e a r i t y ) . H i s a n a l y s i s a l s o i n d i c a t e d tha t as the energy i n the bending v i b r a t i o n approaches the amount necessary to 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 ease i n x shou ld aaaa become d rama t i c . S ince the v a r i a t i o n s of A and x observed here are v aaaa rough ly l i n e a r over the low va lues of v r , a r a t h e r h i g h b a r r i e r to l i n e a r i t y i s expected f o r c h l o r i n e i s o c y a n a t e . 4.6 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 Constants and the I n e r t i a l  Defect from the M o l e c u l a r Force F i e l d . The i n f r a r e d and Raman spec ta o f c h l o r i n e i socyana te have been i n v e s t i -gated by E yse l and Nachbaur (90) . These authors ob ta ined a complete a s s i g n -ment of a l l s i x fundamental v i b r a t i o n s and a l s o performed a normal coord ina te f o r c e constant a n a l y s i s . T h e i r r e s u l t s have been reproduced i n Tables 4.14 * A c t u a l l y three f o r c e f i e l d s were de te rmined ; one f o r each of three d i f f e r e n t s t r u c t u r a l models . ' The model which corresponds to the f o r ce f i e l d g iven i n Table 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 determined 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 F i e l d s Force C o n s t a n t 3 E .N .F .F . 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 ) b 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 . 0 0 0 C 0.0512 f (NC0:C lN) 0.369 0.6053 f(NCO:NC) 0.000° 0.0000° f(NCO:CO) 0.000° 0.0000° f(C1NC:NC0) -0.188 0.0303 3 S t r e t c h i n g f o r c e cons tan ts are i n mdyne/X, bends are i n mdyne 'R/rad , bend-s t r e t ch i n t e r a c t i o n s are i n mdyne/rad. b Value depends on cho i ce of cor respond ing G m a t r i x element (Ggg) whose d e f i n i t i o n con ta ins an a r b i t r a r y s c a l e f a c t o r . Choice o f G ^ and hence f^^ does not a f f e c t the 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 , d i s -t o r t i o n cons tan ts are independent of fgg-Set equa l to 0 i n i t i a l l y . 108 TABLE 4.15 Fundamental V i b r a t i o n a l F requenc ies of C h l o r i n e I socyana te . a Fundamental Frequency D e s c r i p t i o n oj^  2215 NCO asymmetric s t r e t c h OJ2 1309 NCO symmetric s t r e t c h OJ3 708 NCO bend ( in-p lane ) to, 608 b C1N s t r e t c h 4 oi 5 199 (157 ) c C1NC bend ( in-p lane ) o)g 559 out-of-p lane bend Measured i n cm ; gas phase i n f r a r e d f requency un l e s s o therw ise i n d i c a t e d . L i q u i d phase Raman measurement, does not appear i n gas phase IR. The f i r s t number i s the Raman, s o l i d phase, f r equency ; the second, the gas phase i n f r a r e d f requency . 109 and 4 . 1 5 . The fo r ce f i e l d was cons t ruc ted us ing an approximate method p r e v i o u s l y desc r i bed by Becher and Mattes (115) . S ince t h i s procedure has r e c e n t l y come under severe c r i t i c i s m (116) i t i s of some i n t e r e s t to t e s t the E y se l and Nachbaur f o r c e f i e l d ( E .N .F . F . ) aga ins t independent d a t a . 35 14 12 16 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 cons tan ts of C l N C 0 (G.V.S . ) were c a l c u l a t e d from the E .N .F .F . w i t h the a i d of the K i v e l s o n W i l son theory o u t l i n e d i n s e c t i o n 2 . 5 . The c a l c u l a t e d cons tan ts are compared w i t h the observed ones i n Table 4 . 1 6 ; the agreement i s r a t h e r poo r . Th i s i s presum-a b l y , a t l e a s t to some e x t e n t , a r e f l e c t i o n on the method of Becher and Ma t t e s . In a d d i t i o n , however, there i s some u n c e r t a i n t y as to what f requency should be ass igned to to,.. Th i s i s e s p e c i a l l y important i n the present 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 cons tan t s are p a r t i c u l a r l y s e n s i t i v e t o the s m a l l d i a g o n a l (bending) f o r c e c o n s t a n t s . E y s e l and Nachbaur found to,. = 199 cm * i n the s o l i d s t a t e and OJ,. = 175 cm * i n the l i q u i d s t a t e ; they used the former 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 . In the course of the present work the f a r i n f r a r e d gas phase spectrum of c h l o r i n e i socyana te was i n v e s t i g a t e d . Only one band was found . I t had a PR contour w i t h a cente r f requency o f 157 cm 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 reproduce the microwave da t a i t i s c l e a r l y p r e f e r a b l e to use the gas phase va lue of to,.. A second f o r c e f i e l d (R .G .F .F . ) has on l y r e c e n t l y been obta ined f o r c h l o r i n e i socyana te by Dr . R. Green (117) . I t i s based on the s t r u c t u r e repor ted here and the v i b r a t i o n a l f r equenc i e s and assignments of E y s e l and Nachbaur, except tha t to,, was taken to be 157 cm * r a t h e r than 199 cm ^. The approx imat ions used i n t h i s case , i n o rder to o b t a i n a s o l u t i o n of the 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 , are e s s e n t i a l l y those desc r i bed 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 Constants of C h l o r i n e Isocyanate ( C l N C 0 G.V.S . ) D i s t o r t i o n Constant Observed Value C a l c u l a t e d from E .N .F .F . C a l c u l a t e d from R.G.F .F , aaaa l bbbb aabb abab -59.139 -0.01075 0.6923 -0.0101 -26.22 -0.00866 0.3943 -0.01144 -45.04 -0.01260 0.6706 -0.01287 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 procedure 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 Defec ts of C h l o r i n e Isocyanate ( 3 5 C 1 U N 1 2 C 1 6 0 G . V . S . ) . C a l c u l a t i o n VIB cent A VIB + A c e n t E .N .F . F . R .G.F .F . 0.2606 0.3265 0.0008 0.0009 0.2614 0.3274 0.3645 0.3645 3 Measured i n a . i n .u . 8 2 . I l l f o r the s o - c a l l e d Hybr id O r b i t a l Force F i e l d Mode l . However, some of the d e t a i l s of the c a l c u l a t i o n procedure are q u i t e n o v e l . A complete account of these w i l l appear s h o r t l y . The R .G.F .F . and the d i s t o r t i o n cons tan ts which i t y i e l d s have a l s o been g iven i n Tables 4.14 and 4.16 r e s p e c t i v e l y . The agreement between the c a l c u l a t e d and observed d i s t o r t i o n cons tants i s now q u i t e r e s p e c t a b l e . F i n a l l y , both f o r ce f i e l d s were sub jec ted to 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 . Equa t ion 2.56 was used to determine the v i b r a t i o n a l c o n t r i b u t i o n ; equat ion 2 .55b, 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 t r i b u t i o n . The e l e c t r o n i c p a r t , which i s p robab l y s m a l l and nega t i ve (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 cons tants were computed w i t h the a i d of a program w r i t t e n by Schachtschne ider (119) . The r e s u l t s are compared i n Tab le 4.17 w i t h the observed 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 noted t ha t the R .G .F .F . has g i v en c o n s i d e r a b l y b e t t e r agreement w i t h experiment than the E .N .F . F . However, there i s e v i d e n t l y s t i l l some room f o r improvement i n even the fo rmer . 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 spectrum of c h l o r i n e i socyana te has r e c e n t l y been i n v e s t i g a t e d by Oberhammer (91 ) . I t was found tha t the observed spectrum cou ld be reproduced 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 models . In one, the NCO cha in was b e n t , i n the o ther i t was l i n e a r . The bent NCO cha in s t r u c t u r e was then proposed to be the c o r r e c t one on the b a s i s of a number of secondary c o n s i d e r a t i o n s . However, a d e f i n -i t i v e cho i ce between the two cou ld not be made. 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 Table 4 .18 . The agreement i s q u i t e good. In Table 4.19 a number of "genu ine " CO and NC double bond l eng ths have 112 TABLE 4.18 Comparison of C h l o r i n e Isocyanate 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 . I n t e r n a l Coord inate Microwave E l e c t r o n D i f f r a c t i o n r (C l-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* ± 30 ' 118° 12' ± 36 ' Z.(NCO) 170° 52 ' ± 30 ' 170° ± 2° 6' Bond l eng ths are measured i n A*. 113 been p resen ted . I t w i l l be noted that these are a l l s i g n i f i c a n t l y l onger than the cor respond ing c h l o r i n e i socyana te i n t e m u c l e a r d i s t a n c e s . In f a c t , the i socyana te 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 and double NC bond i n l e n g t h ; w h i l e the i socyana te CO d i s t ance i s v i r t u a l l y i d e n t i c a l t o tha t found i n the OCX molecu les (X = 0 , S, S e ) , a l l of which have a d e l o c a l i z e d TT system ( i . e . 2+ bond order (120) ) , and i s on l y s l i g h t l y l onger than the carbon monoxide " t r i p l e " bond (121) . No doubt the shor tness of the c h l o r i n e i socyana te NC and CO bonds r e l a t i v e to those i n Tab le 4.19 may be p a r t l y a t t r i b u t e d to an i n c r ea se i n a bond s t r e n g t h a s s o c i a t e d w i t h 2 * the change i n the carbon atom h y b r i d i z a t i o n from sp to sp , However, the 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 of the NCO TT system. Th i s has p r e v i o u s l y been proposed i n connec t ion w i t h o ther i socyana tes (123 ,124 ) . For c h l o r i n e i socyana te i t has a l r eady been shown ( s e c t i o n 4.4) t ha t the n i t r o g e n n u c l e a r quadrupole coup l i ng i s c o n s i s t e n t w i t h rough ly comparable i n-p l ane (weaker) and out-of-p lane ( s t ronger ) TT bonding at n i t r o g e n . The Valence Bond (125) approach p rov ides an a l t e r n a t i v e , perhaps c l e a r e r , p i c t u r e of how the c h l o r i n e i socyana te NC and CO bonds may a t t a i n g r e a t e r than double bond c h a r a c t e r . Only th ree o f the many p o s s i b l e resonance forms are l i k e l y to be major c o n t r i b u t o r s to the composite wave func t i on ; these a r e : C l C l \ C l N = C 0 " \ + ,N C=0 + _:N C = 0 41 411 4 I I I * Coulson (122) has shown that the a bond ove r l ap 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 decreases w i t h an i n c r ease 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 tha t a bond s t r e n g t h v a r i e s a s : s p > s p >sp > s or p. Such a t rend i s c l e a r l y observed f o r the CH bonds and i s r e f l e c t e d i n t h e i r l e n g t h s . 114 TABLE 4.19 Some "Genuine" CO and NC Double Bond Lengths. Molecule Formula r(C-O) Reference Formaldehyde H 2CO 1.204 (129) Formamide NH2CHO 1.193 (129) Formic A c i d HCOOH 1.202 (129) Aceta ldehyde CH3CHO 1.216 (129) A c e t y l C h l o r i d e CH 3C0C1 1.192 (129) T y p i c a l CO double bond l e n g t h = 1.20 A- (?) c f . r(C-O) = 1.162 °v i n c h l o r i n e i s o c y a n a t e . Mo lecu le Formula r(C-N) Reference N-Methyl Methy len imine CHINCH, 1.30 (130) Formaldoxime 1.3.4- T h i a d i a z o l e 1 .2 .5- Oxad iazo le N e i t h e r of these are " p u r e " double NC bonds s i n ce both molecu les have been shown to have a s m a l l degree of a r o m a t i c i t y . " P u r e " double NC bonds seem to 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) have , by i n t e r p o l a t i n g between the NC s i n g l e and double bond l e n g t h s , come up w i t h a v a l ue of 1.28 A* f o r the NC " p u r e " double 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 . H0NCH 2 1.276 (131) NCHSCHN 1.302* (132) CHNONCH 1.300* (133) 115 TABLE 4.20 Some NC T r i p l e Bond Lengths and CO 2+ Bond Lengths . Mo lecu le r ( N - C ) 3 Molecu le r ( C - O ) 3 CH3CN 1.157 OCO 1.162 b CF 3CN 1.153 OCS 1.160 HCN 1.153 OCSe 1.159 FCN 1.159 CO 1.128 C1CN 1.160 BrCN 1.160 Measured i n A*. Taken from Gordy and Cook (129) , except CO Taken from Herzberg (135) . TABLE 4.21 Comparison of the C h l o r i n e N i t r o g e n Bond Lengths found i n a Number of Sma l l M o l e c u l e s . Mo lecu le r ( C l - N ) a Angles Reference C1NC0 1. 705 + 0.005 Z_(C1NC) = 118° 50 ' C1NNN 1. 745 + 0.005 /1(C1NN) = 108° 40 ' (14) H 2NC1 1. 748 + o . o o o i b ^-(HNCl) = 103° 41 ' ; i_ (HNH) = 107° (102) HNC1 2 1. 760 + ? Z.(C1NC1) ^ 106°; Z.(HNC1) ^ 103° (136) Me 2 NCl 1. 770 + 0.02 Z.(MeNCl) = 107°; /.(MeNMe) = 108° (137) MeNC l 2 1. 740 + 0.02 :^(C1NC1) = 108°; /.(MeNCl) = 109° (137) NC1 3 1. 759 + 0.002 (102) N0C1 1. 975 + 0.005 Z.(0NC1) = 113° 20 ' (138) N0 2C1 1. 840 + 0.002 /l(ONCl) = 114° 42 ' (139) Measured i n X . Measurement e r r o r . 116 Then, i f 411 and 4 I I I are of s i m i l a r importance to 4 1 , a bond order of 2+ i s to be expected f o r both of the two m u l t i p l e bonds (126) . I t i s i n t e r e s t -i n g to compare t h i s s i t u a t i o n w i t h tha t found f o r i s o e l e c t r o n i c c h l o r i n e az ide where the form equ i v a l en t to 411 i s l i k e l y to be of minor importance . Here the dominant resonance forms are probab ly 4 1 ' and 4 I I I ' (14 ) : C l C l \ C l N ^ = N N \ .N N = N + + " ;N N = N + " + 41V 4 1 1 ' 4 I I I ' Th i s i s supported by the obse r va t i on t ha t the t e r m i n a l NN d i s t ance i s s h o r t e r than the 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 (14 ) ) . A l s o , the C1NX (X = C, N) angle i s l a r g e r i n the i socyana te (118° 50 ' ) than i n the az ide (108° 4 0 ' ) . The c h l o r i n e n u c l e a r quadrupole coup l i ng o f c h l o r i n e i socyana te 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 cha r a c t e r (5%) i n the C1N bond. A l i k e l y resonance form showing such double bond cha rac t e r i s : +C1 \ - d c 4IV I t i s noteworthy tha t t h i s form i s a l s o compat ib le w i t h the bend found i n the NCO cha in (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 az ide which has been shown to have an 8 ° 4 ' ( t rans ) az ide bend as w e l l as 8% C1N double bond cha r a c t e r (14 ) . Aga in bo th e f f e c t s may be a t t r i b u t e d to a s m a l l c o n -t r i b u t i o n from one resonance fo rm, namely: + C 1 ^ N Nv 4 1 V X 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 both the i socyana te and the az ide but i s e v i d e n t l y not important f o r e i t h e r , p robab ly because of nonbonding r e p u l s i o n of the c h l o r i n e and oxygen (or n i t r ogen ) e l e c t r o n systems at the two ends of the mo lecu l e . A CNDO/2 c a l c u l a t i o n performed by Oberhammer (91) p r e d i c t e d tha t c h l o r i n e i socyana te should have a t r ans bend at carbon of approx imate ly 7 ° . The C1N bond l eng ths found i n a number of d i f f e r e n t s m a l l molecu les have been c o l l e c t e d i n Table 4 . 2 1 . Two of t he se , namely those i n N0C1 and N 0 2 C 1 , are anomalously l o n g . In both cases , c h l o r i n e has bonded to a s t a b l e p a r a -magnet ic 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 long C1N bond (84 ,127) . A l l of the remain ing bond l eng ths i n Table 4.21 are of s i m i l a r magnitude and are c l o s e to the sum of 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 (1.73 °v). The s h o r t e s t one i s t ha t r epor ted here f o r c h l o r i n e i s o c y a n a t e . S ince c h l o r i n e i socyana te 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 tha t t h i s i s due l a r g e l y to 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 cha r a c t e r are apparen t l y of l e s s e r importance o r c a n c e l . 118 CHAPTER 5 THE MICROWAVE SPECTRUM OF ISOCYANIC ACID Isocyanic acid i s a reactive, easily polymerized, compound that has played a prominent role in organic chemistry for many years. It i s readily prepared either by the direct reaction of a hydrogen halide gas with silver cyanate or by the thermal decomposition of a number of organic compounds (e.g. cyanuric acid, urea, cyamelide). Its physical properties were f i r s t characterized by Linhard (140). A review of isocyanate chemistry has recently been published by Ozaki (141). An early study of the ultraviolet absorption spectrum of isocyanic acid vapor by Woo and Lin (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 liquid and interpreted i t as showing that the molecule existed i n the keto form (HNCO) rather than the enol form (HOCN). This was subsequent-ly verified by Eyster, G i l l e t t e and Brockway (123) in an electron di 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 iso-cyanic acid was performed by Herzberg and Reid (H. and R.) (144) who reported a complete assignment of a l l six fundamental vibrations as well as a slightly improved molecular geometry. A vibrational force f i e l d , based on the data of H. and R., was published shortly thereafter by Orville 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 ce f i e l d s , based on the da ta o f A . and W., have now been pub l i shed f o r i s o c y a n i c a c i d (147,148) ; they are not i n agreement. The pure r o t a t i o n a l spectrum of i s o c y a n i c a c i d has been the sub jec t of s e v e r a l i n v e s t i g a t i o n s . The e a r l i e s t microwave measurements were made by Jones e t . a l . (11) on the 1Q ^ — OQ Q t r a n s i t i o n o f the H ^ N ^ C ^ O , 14„T12„16„ , T T15„12 16„ . . ' . „ - . , D N C 0 and H N C O i s o t o p i c s p e c i e s . These gave accura te va lues o f B Q + C q . Subsequent r e s o l u t i o n of the h y p e r f i n e s t r u c t u r e of t h i s same t r a n s i t i o n ( H ^ N ^ C ^ O spec i es ) pe rmi t t ed the d e t e r m i n a t i o n o f y (^^N), aa w h i l e S ta rk measurements y i e l d e d va lues of u f o r the ground and two e x c i t e d v i b r a t i o n a l s t a t e s (149) . More r e c e n t l y , Kewley e t . a l . (150) measured a number of _i-type R-branch mm-wave t r a n s i t i o n s be l ong ing to the H ^ N ^ C ^ O and D ^ N ^ C ^ O i s o t o p i c s p e c i e s , from which accura te v a l ues of B and C r r > O O but on l y rough va lues of A q were e x t r a c t e d . A c o n v e n t i o n a l f a r i n f r a r e d study o f the pure r o t a t i o n a l spectrum of these same two i s o t o p e s , by Krakow e t . a l . (151) , produced s l i g h t l y r e f i n e d A q v a l u e s . Both the mm-wave and the i n f r a r e d work i n d i c a t e d that i s o c y a n i c a c i d has ext remely 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 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 (152) has d i s cussed t h i s phenomenon i n terms of a s imple n o n r i g i d r o t o r model . F i n a l l y , White and Cook (153) have shown tha t the a-component of 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 of r o t a t i o n a l s t a t e . The i n i t i a l o b j e c t i v e of the present study was s imp l y to measure a few a^-type R-branch t r a n s i t i o n s of the carbon-13, n i t r o g e n - 1 5 , and oxygen-18 s u b s t i t u t e d spec i es of i s o c y a n i c a c i d . These were expected to g i ve an i m -proved mo lecu la r s t r u c t u r e , but were a l s o of i n t e r e s t i n t h e i r own r i g h t ( to the a s t r o p h y s i c i s t ) . I t was soon d i s c o v e r e d , however, tha t many a d d i t i o n -a l t r a n s i t i o n s were obse r vab l e . These i n c l u d e d a-type Q-branch t r a n s i t i o n s 120 of the type — j and _b-type R- and P-branch t r a n s i t i o n s of the type JQ J — ( J - l ) ^ From the h y p e r f i n e s t r u c t u r e of the fo rmer , a va lue was obta ined f o r the n i t rogen-14 quadrupole c o u p l i n g asymmetry parameter , w h i l e the l a t t e r pe rmi t t ed a much improved de t e rm ina t i on of the A r o t a -o t i o n a l c o n s t a n t s . In a d d i t i o n , the S ta rk 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 approximate va lue f o r y^. In a l l , s i x i s o t o p i c spec i e s were s t u d i e d , namely: H 1 4 N 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 H U 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 0 A l l of the microwave measurements and the a n a l y s i s were by the au tho r . The mm-wave measurements were made by Dr . G. Winnewisser us ing i s o t o p i c samples s u p p l i e d by the au thor . 5.1 Assignment o f the Spectrum The bes 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 (11) were used to p r e d i c t the f requency of the 1Q ^ — OQ Q t r a n s i t i o n f o r each of the new i s o t o p i c s p e c i e s . A l l o ther t r a n s i t i o n s were expected to l i e i n the mm-wave r e g i o n . In each c a se , a s t r ong a b s o r p t i o n was found near the p r e d i c t e d 14 f requency . Fo 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 rov ided c o n c l u s i v e v e r i f i c a t i o n of the ass ignment. A re-examinat ion of t h i s t r a n s i t i o n i n the s p e c t r a of the p r e v i o u s l y s t u d i e d i so topes s u r p r i s i n g l y r evea l ed the u n s p l i t - l i n e f requency p u b l i s h e d f o r D 1 4 N 1 2 C 1 6 0 to be i n e r r o r by over 1 MHz (11) . There can be l i t t l e doubt tha t the f requency g i ven here i s the c o r r e c t one s i n ce i t i s i n agreement w i t h the mm-wave da t a (150) . The d i s c o v e r y o f the a-type Q-branch t r a n s i t i o n s of i s o c y a n i c a c i d was, to 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 socyana te such t r a n s i t i o n s were 121 found to be unobservably 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 are i n h e r e n t l y s m a l l (38 ) . In the case of HNCO, however, the l a r g e r a-component of the d i p o l e moment makes them weakly obse r vab l e . By comparison the a-type R-branch t r a n s i t i o n s are at l e a s t an order of magnitude s t r o n g e r . The f i r s t i n d i c a t i o n of the e x i s t e n c e of the i s o c y a n i c a c i d Q-branch l i n e s came when a s e r i e s of w i d e l y spaced weak doub le t s was found i n the spectrum of H ^ N ^ C ^ O . Once the i d e n t i t y o f the 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 to a f a i r l y good app rox ima t i on : v_{J> = 1/2J(J+1)(B - C ) 5.1 Q o o and hence { j + 1 } _ { j } _ ( J + 1 ) ^ _ ^ 5 > 2 Subsequent, f u r t h e r i n v e s t i g a t i o n of the s p e c t r a o f the o ther i so topes y i e l d e d the cor respond ing s e r i e s f o r each. The b-type t r a n s i t i o n s of H^ 4 N^ 2 C^O were a l s o e x p e r i m e n t a l l y l o c a t ed w e l l be fo re any thought had been g i ven to the p o s s i b i l i t y tha t such t r a n s -i t i o n s might be obse r vab l e . They showed up as three ve ry w i d e l y spaced s t rong l i n e s , broadened s l i g h t l y by unreso l ved quadrupole h y p e r f i n e s t r u c -t u r e . S ince the e x i s t i n g da ta were s u f f i c i e n t t o g i ve on ly a rough es t imate of t h e i r J v a l u e s , the assignment process 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 of these 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 desc r ibed i n the next s e c t i o n , on l y one reasonable assignment would g i ve a good frequency p r e d i c t i o n f o r the t h i r d . F u r t h e r , t h i s same assignment was the on ly one which would g i v e an acceptab le l e a s t .squares f i t when a l l three t r a n s i t i o n s were i n c l u d e d . Hence there i s but l i t t l e doubt t ha t i t i s the c o r r e c t one. A s i m i l a r procedure was used to a s s i g n the b_-type t r a n s i t i o n s of the other i s o t o p e s , w i t h the excep t i on of the H ^ N ^ C ^ O spec i es f o r which on ly 122 two l i n e s were a v a i l a b l e . These were ass igned so tha t the r e s u l t i n g H ^ N ^ C ^ O i n e r t i a l de f ec t was i n agreement w i t h the A° va lues obta ined TT14„712 16„ „14„13„16 r t , 14 12 18„ _ . . . . c . f o r H N C O , H N C O and H N C O . Fu r t he r v e r i f i c a t i o n of the b-type assignments through 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 search through the microwave r eg ion turned up on l y a few a d d i t i o n a l i s o c y a n i c a c i d a b s o r p t i o n s . These were t e n t a t i v e l y ass igned 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 De te rmina t ion of M o l e c u l a r Constants from the Microwave Spectrum. The c e n t r i f u g a l d i s t o r t i o n and nuc l ea r quadrupole c o u p l i n g ana lyses were separated us ing b a s i c a l l y the same scheme as was fo l l owed f o r c h l o r i n e i s o c y a n a t e . Th is was a l e s s compl i ca ted process i n t h i s case , however, because of 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 . For the ^ N i s o t o p i c spec i e s there was .of course 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 -quencies cou ld 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 S ince N has a r a t h e r s m a l l quadrupole moment, the f i r s t o rder e x p r e s s i o n g i ven i n equa t ion 2.37 adequate ly represents the t rue quadrupole energ ies of i s o c y a n i c a c i d . Least squares f i t s were made u s i ng t h i s r e l a t i o n 14 to a l l observed quadrupole s p l i t t i n g s f o r each N i s o t o p i c s p e c i e s . The r e s u l t s have been c o l l e c t e d i n Table 5 . 1 . Many of the abso rp t i ons due to the DNCO i s o t o p i c spec i es appeared to be s l i g h t l y broadened compared to the cor respond ing HNCO a b s o r p t i o n s . Th is behav io r was a t t r i b u t e d to ve ry weak deuter ium n u c l e a r quadrupole coup l i ng e f f e c t s . R e s o l u t i o n of such very 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 conven t i ona l spec t romete 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 gene ra l Watson Hami l t on i an (equat ions 2.19 and 2 .22 ) . A f i r s t o rder treatment was aga in used (equat ions 2 .23 ) , w i t h l i n e a r v a r i a t i o n s of the r o t a t i o n a l cons tants 123 TABLE 5.1 Nuc lear Quadrupole Coup l ing Constants of I socyan i c A c i d . H U N 1 2 C 1 6 0 H 1 4 N 1 3 C 1 6 0 X a a X a a 2.045 ± 0.038° 2.067 ± 0.020 v,.. - x 1 . H 2 ± 0.025 1.103 + 0.010 A bb A c c H 1 4 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 X , , - x 1 . H 9 ± 0.011 1.031 ± 0.016 bb cc Measured i n MHz. D Standard e r r o r s . i 124 a l l owed . No attempt was made to use the s imp l e r four parameter exp re s s i on (equat ion 2.18) s p e c i f i c f o r a w e l l behaved p l ana r molecu le s i n ce i t was known from prev ious work (150,151) tha t i s o c y a n i c a c i d had ext remely 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 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 . A l though i t was recogn ized from the s t a r t tha t the a v a i l a b l e t r a n s -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 to determine a complete set of f i v e q u a r t i c d i s t o r t i o n cons t an t s , an attempt was nonethe less made to f i t the H ^ N ^ C ^ O da ta to the q u a r t i c Hami l t on i an (equat ion 2 . 1 9 ) ; bo th A and 1 were found to be comple te l y i nde t e rm ina t e . E l i m i n a t i o n of these two parameters pe rmi t t ed a more r e a l i s t i c de t e rm ina t i on of the remain ing ones , but w i thout s i g n i f i c a n t l y reduc ing the r a t h e r l a rge s tandard d e v i a t i o n of the f i t (SDFIT). E v i d e n t l y h ighe r order terms were impor t an t . With A and Sv a l r eady shown to be unobta inab le i t was unreasonable to i n c l u d e e i t h e r Hj, o r h^. Of the remain ing s e x t i c parameters H^j was found to be the most impo r t an 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 dramat ic improvement i n the SDFIT. H j , H ^ and h j were found to be on 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 nde t e rm ina t e . The r e s u l t s of these d i f f e r e n t ana lyses are presented i n Table 5 . 2 ; the H^ 4 N^ 3 C^O t r a n s i t i o n s were chosen as t e s t da ta because they were the l a r g e s t se t o f f r equenc ies a v a i l a b l e . S i m i l a r f i t s were made to the " u n s p l i t - l i n e " t r a n s i t i o n f r equenc i es o f the o the r i s o t o p i c s p e c i e s , except D ^ N ^ C ^ O . For some spec i es the e x t r a s e x t i c cons tants H , H and h were i n d e t e r m i n a t e , f o r o thers 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 of o b t a i n i n g c o n s i s t e n t se t s o f r o t a t i o n a l cons tants ( f o r s t r u c t u r a l purposes) a l l spec i es were e v e n t u a l l y f i t t e d to the same t runca ted Hami l t on i an (A , A , 6 and H ) . These J JK J KJ r e s u l t s are presented i n Table 5 .3 . Th i s was not a comple te ly s a t i s f y i n g approach but was a l so appa ren t l y the bes t tha t cou ld be done w i t h the 125 Si 3. 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 of H ^ N ^ C ^ O us ing D i f f e r e n t Methods of A n a l y s i s . I I SDFIT No. T rans . ~* A o ~* B o ~* C o A j X 1 0 3 A J K X 1 0 1 6 T x l 0 5 0.734 42 . 910446.7 ± 7 . 2 d 11071.349 ± 0.017 10910.601 ± 0.018 3.120 ± 0.050 8.028 ± 0.033 7.19 ± 0.38 0.219 42 910477.6 ± 2.7 11071.439 ± 0.007 10910.691 ± 0.007 3.354 ± 0.019 8.639 ± 0.033 7.25 ± 0.11 6.86 ± 0.36 I I I IV SDFIT 0.208 0.208 No. T rans . 42 42 ~* A o 910463.9 + 6.8 910470.1 + 4.3 ~* B o 11071.455 + 0.010 11071.451 + 0.009 ~* C o 10910.706 + 0.010 10910.703 + 0.009 A j X 1 0 3 3.509 + 0.074 3.471 + 0.057 A J K X L ( ) 1 8.623 + 0.033 8.610 + 0.034 6 j X 1 0 5 7.29 + 0.11 7.29 + 0.11 H j x l 0 7 0.46 + 0.21 H J K X 1 ° 5 -1.11 + 0.50 " K J - 1 0 ' 6.70 + 0.35 6.71 + 0.35 126 TABLE 5.2 cont inued V VI SDFIT 0.209 0.214 No. T rans . 42 42 ~* A o 910460.7 ± 8.6 910467.5 + 15.5 ~* B o 11071.454 ± 0.010 11071.453 + 0.013 ~* C o 10910.703 ± 0.009 10910.703 + 0.013 A j X 1 0 3 3.482 ± 0.066 3.481 + 0.109 A J K X 1 Q 1 8.625 ± 0.033 8.613 + 0.044 6 j X 1 0 5 7.81 ± 0.29 7.38 + 0.71 H X 1 0 7 J 0.045 + 1.17 H J K X 1 ° 5 -0.832 + 2.36 6.72 ± 0.35 6.70 + 0.36 9 h x X 1 0 8.15 ± 3.99 1.48 + 11.0 V I I SDFIT No. Trans. A o B V 1 0 A J K X 1 ° ] 6 j X 1 0 5 K K 0.688 42 850669.4 ± 23814.4 11065.7 ± 12.2 10916.4 ± 12.2 3.70 ± 0.34 8.01 ± 0.04 7.37 ± 0.37 -2.86 ± 6.10 -59750. ± 23804. 127 TABLE 5.2 cont inued Large C o r r e l a t i o n s (|p|>0.9) A n a l y s i s I : p(B - C) = 0.95 A n a l y s i s I I : p(B - C) = 0 . 9 7 ; p ( A J R - H^) = 0.95 A n a l y s i s I I I : p(A - A ) = - 0 . 9 0 ; p(A - Hj ) = - 0 . 9 3 ; p(B - C) = 0 . 9 9 ; p (A j - Hj) = 0 . 9 7 ; p ( A J R - H R J ) = 0.96 A n a l y s i s IV : p(B - C) = 0 . 9 8 ; p ( A T - H ) = - 0 . 9 5 ; p(A - H ) = 0.94 J JK JK. KJ A n a l y s i s V : p(A - Aj ) = - 0 . 9 2 ; p(A - hj) = - 0 . 9 6 ; p(B - C) = 0 . 9 8 ; p (A j - h j ) = 0 . 9 6 ; p ( A J K - H R J ) = 0 . 9 6 ; p (f i j - h j ) = 0.93 A n a l y s i s VI : p (B - C) = 0 . 9 5 ; p(C - A T V ) = 0 . 9 0 ; p(<5T - h_) = 0.99 JK J J A n a l y s i s V I I : p(A - A ) = 1.00; p(B - C) = - 1 . 0 0 ; p(B - O = 1.00; p(C - Sv) = -1 .00 Measured i n MHz. SDFIT = Standard D e v i a t i o n of the F i t . No. T rans . = Number of t r a n s i t i o n s used i n the a n a l y s i s . Standard e r r o r s . 128 TABLE 5.3 R o t a t i o n a l C o n s t a n t s 3 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 3 of I socyan i c A c i d . H U N 1 2 C 1 6 0 15 12 16„ H N C O SDFIT No. Trans. ~* A o ~ A B o ~* C o A x l O 3 •J A J K X 1 ( ) 1 6 T x l 0 5 x lO" 0.373 34 912673.6 + 4 . 7 b 11070.932 ± 0.015 10910.500 ± 0.015 3.198 ± 0.035 8.311 ± 0.057 7.28 ± 0.19 2.44 ± 0.36 0.147 20 903147.5 ± 4.4 10737.790 ±' 0.012 10585.425 ± 0.012 3.114 ± 0.034 9.434 ± 0.084 6.297 ± 0.076 8.67 ± 0.89 H U N 1 3 C 1 6 0 H 1 4 N 1 2 C 1 8 0 SDFIT No. Trans . ~* A o ~* B o ~* C o Aj-xlO 3 A J K X 1 Q 1 6 J X 1 0 5  H K J X 1 ° 3 0.219 42 910477.6 ± 2.7 11071.439 ± 0.007 10910.691 ± 0.007 3.354 ± 0.019 : 8.639 ± 0.033 7.26 ± 0.11 6.86 ± 0.36 0.257 28 912601.8 ± 4.1 10470.857 ± 0.010 10327.204 ± 0.011 3.018 ± 0.024 7.659 ± 0.052 6.10 ± 0.12 6.28 ± 0.70 129 TABLE 5.3 cont inued D 1 4 N 1 2 C 1 6 0 D 1 5 N 1 2 C 1 6 0 SDFIT No. Trans. ~* A o ~* B o ~* C„ A j X 1 0 A J K X 1 Q 1 S j X l O 4 x l O " 0.326 35 510973.0 ± 1.0 10313.711 ± 0.011 10079.674 ± 0.012 3.432 ± 0.038 -2.291 ± 0.029 2.041 ± 0.053 -5.04 ± 0.12 10044.575 ± 0.050 9819.435 ± 0.050 Measured i n MHz. Standard e r r o r s . Es t imated measurement e r r o r s . 130 a v a i l a b l e f r e q u e n c i e s . The a d d i t i o n a l t r a n s i t i o n s which would have p e r -m i t t e d a more thorough treatment f a l l i n the f a r i n f r a r e d and were t h e r e -fo re i n a c c e s s i b l e . In the case of the doubly s u b s t i t u t e d s p e c i e s , D ^ N ^ C ^ O , i n s u f f i c i e n t t r a n s i t i o n s were a v a i l a b l e to a l l ow 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 order to o b t a i n r o t a t i o n a l constants f o r t h i s s p e c i e s , the measured f r equenc ies 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 to be the same as f o r the cor respond ing t r a n s i t i o n s of D ^ N ^ C ^ O , then the r i g i d r o t o r energy express ions were a p p l i e d to the c o r r e c t e d f r e q u e n c i e s , i . e . v { 1 o , i - ° o , o } = B + c 5 - 3 3 1 1 ( 1 ( v n { J » = 1/2J(J+1)(B - C) 5.4 ii c o r r The r e s u l t s have a l so been c o l l e c t e d i n Table 5 .3 . The r o t a t i o n a l constants presented i n Tab les 5.2 and 5.3 have been s t a r r e d to i n d i c a t e tha t they are not the t rue Watson constants one might n a i v e l y expect the above a n a l y s i s to y i e l d . In f a c t , they c o n t a i n s i g n i f i -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 . By c o n s i d e r i n g the type of t r a n s -i t i o n s used i n the l e a s t squares f i t s , and bea r ing i n mind tha t the molecu le i s ve ry n e a r l y a symmetric t o p , i t i s not d i f f i c u l t to show t h a t : A ^ A - A„ + + ••• 5.5a B* ^ 'B - 26 + • • • 5.5b K. C ^ C + 2<5__ + • • • 5.5c K. Cos t a i n and Kro to (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 az ide and a l s o concluded that t h e i r e f f e c t i v e A c o n -s t an t s were r e a l l y A - T)v (Dv — A ) . They apparen t l y cons idered 6 to be i n s i g n i f i c a n t ; such i s not l i k e l y to be the case he re . S ince i t was the e f f e c t i v e r o t a t i o n a l cons tants A Q , B q and C Q that 131 were used to compute the c o e f f i c i e n t s of the parameters i n both the quad-rupo le 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 conce i vab le tha 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 cou ld i n t r oduce a s y s t ema t i c e r r o r i n t o the f i n a l va lues of the de r i ved cons t an t s . Th is would seem to be u n l i k e l y , however, because both ana lyses were found to g i ve unchanged r e s u l t s when the inpu t va lues of the r o t a t i o n a l constants 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 though the SDFITs i n Tab le 5.3 are acceptab le there i s s t i l l some room f o r improvement. Rather l a r g e expe r imen ta l u n c e r t a i n t i e s (+.25 MHz to ±.50 MHz) i n some of the e a r l y mm-wave measurements on H^ 4 N^ 2 C^O and D ^ N ^ C ^ O p a r t i a l l y account f o r the e x t r a l a rge SDFITs observed f o r these two s p e c i e s . In a d d i t i o n many of the t r a n s i t i o n s of a l l spec i es p robab ly have s m a l l f i r s t o rder f requency c o n t r i b u t i o n s from terms not 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) . I t i s expected tha t the p resent 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 . Ge r r y , G. Winnewisser and g W.H.H.) to i n c l u d e P e t c . te rms, as necessa r y , i n order to o b t a i n more accura te f requency 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 source of model e r r o r i s h i ghe r order 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 constants i n Table 5.3 were used J JK. J KJ i n the f u l l m a t r i x scheme to p r e d i c t the f r equenc i e s o f a l l the observed t r a n s i t i o n s . In every case , exact agreement w i t h the c a l c u l a t e d f i r s t o rder f r equenc i es 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 so cyan i c A c i d . The moments of 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 de t e rm ina t i on are p r e f e r a b l y de f i ned 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 then 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 . 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 determined e f f e c t i v e r o t a t i o n a l cons tants 132 A , B and C c o n t a i n s i g n i f i c a n t 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 . The o o o a r t i f i c i a l i n c o r p o r a t i o n of A,, and &„ i n t o A , B and C was d i s cussed i n r K K o o o s e c t i o n 5 .2 . In a d d i t i o n , i t w i l l be r e c a l l e d tha t the t rue Watson constants themselves c o n t a i n d i s t o r t i o n terms. These are norma l l y i n s i g n i f i c a n t but i n t h i s case , because of the ext remely 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 rev ious i n v e s t i g a t i o n of the pure r o t a t i o n a l f a r i n f r a r e d spectrum of i s o c y a n i c a c i d by Krakow, Lord and Neely (151) has y i e l d e d va lues f o r the D R (=A K) and IL^ d i s t o r t i o n cons tants of H 1 4 N 1 2 C 1 6 0 and D 1 4 N 1 2 C 1 6 0 . ~* These numbers were used to conver t the A cons tan ts ob ta ined here f o r these o two i so topes i n t o A q c o n s t a n t s , a f t e r equat ion 5 .5a . F u r t h e r , s i n ce i t seemed 15 13 18 u n l i k e l y tha t 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^, u14..12„16_ . . . „ * T * * „15„12_16_ _14 M13„16 n the H N C O va lues 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 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 Table 5 .4 ; the a s s o c -i a t e d moments of i n e r t i a , i n Tab le 5 .5 . U n f o r t u n a t e l y a s i m i l a r procedure cou ld not be a p p l i e d to the B q and C q cons tan ts due to the l a c k o f e x p e r i -mental v a lues f o r 6 . Consequent ly there was no a l t e r n a t i v e but to d e f i n e K moments of i n e r t i a i n terms of them. These have a l s o been c o l l e c t e d i n Table 5 .5 . A l though A i s enormous a s i m i l a r l a r g e va lue of $ i s not to be K K expec ted . For cyanogen i socyana te (Chapter 6 ) , wh ich 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 . The c e n t r i f u g a l d i s t o r t i o n terms K K i nhe ren t i n the Watson r o t a t i o n a l cons tan ts should be co r r e spond ing l y s m a l l . R ega rd l e s s , s i n c e on l y d i f f e r e n c e s of moments of i n e r t i a were used i n the mo lecu la 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 atomic coo rd ina t e s was m in im ized . The l a r g e s t such d i s c r e p a n c i e s are l i k e l y to be a s soc i a t ed w i t h the hydrogen p o s i t i o n 133 TABLE 5.A A R o t a t i o n a l Constants o f I so cyan i c A c i d from Combined Microwave and IR Data A* o H 1 4 N 1 2 C 1 6 0 917664.6 + 4 0 0 . c 4 9 9 1 . d D 1 4 N 1 2 C 1 6 0 513674.0 + 200. 2 7 0 1 . d H 1 5 N 1 2 C 1 6 0 908138.5 + 400. 4 9 9 1 . 6 H 1 4 N 1 3 C 1 6 0 915468.6 + 400. 4 9 9 1 . e H 1 4 N 1 2 C 1 8 0 917592.8 + 400. 4 9 9 1 . 6 Measured i n MHz. b ~* C a l c u l a t e d from A va l ues i n Tab le 5.3 (see t e x t ) , o Es t imated e r r o r s . d From i n f r a r e d work of Krakow, Lord and Neely (151) . e Assumed. 134 TABLE 5.5 Moments of I n e r t i a and I n e r t i a l Defec ts o f I so cyan i c A c i d . H 1 4 N 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° a 0.55074° 0.55651 0.55206 45.650258° 47.066566 45.648167 c 46.321516° 47.744035 46.320705 A° 0.12052 0.12096 0.12048 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 0 1° a 0.55078 0.98387 $ 48.266431 49.001848 50.31481 i ° c 48.937825 50.139608 51.46843 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 constants i n Tab le 5 .4 . C a l c u l a t e d from r o t a t i o n a l cons tants i n Table 5 .3 . 135 as deuter ium 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 dramat i c change i n 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 of the heavy atom s u b s t i t u t i o n s . However, even f o r hydrogen, c a l c u l a t i o n s based on the f o r ce f i e l d s d i s -cussed i n s e c t i o n 5.5 i n d i c a t e tha 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 de fec t s of f i v e i s o t o p i c spec ies of i s o c y a n i c a c i d have a l s o been presented i n Table 5 .5 . These are a l l seen to be s m a l l p o s i t i v e numbers, f ou r of which are e s s e n t i a l l y e q u a l ; the f i f t h , which i s the on l y one be long ing to a deutera ted s p e c i e s , i s s l i g h t l y l a r g e r . The sma l l magn 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 p rov ide c o n v i n c i n g p roo f t ha t the molecu le i s p l a n a r . In s e c t i o n 5.5 i t has been shown tha 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 ana r model . The K ra i t chman/Cos ta in s u b s t i t u t i o n p o s i t i o n s of a l l o f the atoms of i s o c y a n i c a c i d i n the cen te 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 " molecu le ) were c a l c u l a t e d from the moments of i n -e r t i a i n Tab le 5.5 us ing equat ions 2 .58 . The r e s u l t s have been presented i n Tab le 5 .6 . E v i d e n t l y , the a-ax is i s n e a r l y co- in c i den t w i t h the NCO cha in and the carbon atom i s ve ry c l o s e t o the cen te r of mass. Hence, the s i n g l e s u b s t i t u t i o n determined va lues of a^,, b^, b ,^ and b^ must be regarded w i t h cons ide r ab l e s c e p t i c i s m . The imaginary r e s u l t obta ined f o r the carbon a-coord inate may be a t t r i b u t e d to the dominat ion o f zero p o i n t v i b r a t i o n a l e f f e c t s over a very sma l l A I^ ; j u s t as was observed f o r the n i t r o g e n a-coord ina te of c h l o r i n e i s o c y a n a t e . A r e l i a b l e va lue of a was obta ined by t a k i n g the o the r a-coord inates to have t h e i r s u b s t i t u t i o n va lues and then i n v o k i n g the cen te r of mass c o n -d i t i o n ( ^ m ^ a _ = 0) • F i r s t , however, i t was necessary to determine the r e l a t i v e s igns of these o ther c o o r d i n a t e s . U n l i k e the c h l o r i n e i socyana te 136 TABLE 5.6 Kra i t chman/Cos ta in S u b s t i t u t i o n P o s i t i o n s 3 of a l l of the Atoms of I socyan i c A c i d . Coord inate Coord inate 1.83736 ± 0.00003° l b„l 0.68793 ± 0.00036° M 1.20552 ± 0.00004 I V 0.07820 ± 0.00232 l-cl imaginary 0.03670 ± 0.00472 1.16882 ± 0.00002 l bol 0.00487 ± 0.01927 Measured i n 7A. C a l c u l a t e d from s tandard e r r o r s a s s o c i a t e d w i t h B c o n s t a n t s . C a l c u l a t e d from es t imated 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 on l y measurement u n c e r t a i n t i e s , i . e . do not take 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 cou ld not be done s imp ly by i n s p e c t i o n . Ra ther , the s i m i l a r magnitudes o f |a^| and j | made the a l t e r n a t i v e cyanate s t r u c t u r e a d i s -t i n c t p o s s i b i l i t y . With t h i s assumption a was c a l c u l a t e d to be ±0.30549. Now, s i n c e any coord ina te l a r g e r than 0.15 X shou ld be a c c u r a t e l y d e t e r -minab le by s i n g l e s u b s t i t u t i o n the cyanate s t r u c t u r e cou ld be s a f e l y e l i m -i n a t e d . Th is o f course was not s u r p r i s i n g s i n ce a l l of the p r e v i o u s l y repor ted ev idence (142,143,123,144,11) had c l e a r l y po in ted to an i socyana te s t r u c t u r e . For such a c o n f i g u r a t i o n the cen te r of mass c o n d i t i o n y i e l d s a ve ry s m a l l va lue f o r a , c o n s i s t e n t w i t h the imaginary r e s u l t obta ined from Kra i t chman ' s equa t i ons . The de t e rm ina t i on of accura te v a l ues f o r the s m a l l b-coord ina tes o f n i t r o g e n , oxygen and carbon proved to 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 cente r o f mass and product o f i n e r t i a c o n d i t i o n s : y V b . , = 0 5.6a 1 1 1 V m . a . b . = 0 5.6b i-l 1 1 x i A t h i r d i s r e q u i r e d . In the f i r s t i n s t ance t h i s was taken to be the l i n e a r -i t y o f the NCO c h a i n , conven i en t l y formula ted a s : % ~ V / ( a o - ac> = ( b c " V ' ^ c - V 5 - 6 c S o l u t i o n of equat ions 5 .6 , u s ing s u b s t i t u t i o n va lues f o r a^, a^, a Q and b^ and the cen te r of mass va lue f o r a p , 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 i n Table 5.7 as s t r u c t u r e I. Now, the s u b s t i t u t i o n method i s based on the premise tha t zero 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 through the use of d i f f e r e n c e s o f moments of i n e r t i a . I f such i s e x a c t l y the case , t h e n : 138 A I ° = A l 6 5.7 a a and hence f o r a p l ana r m o l e c u l e : A I ° - A I ° - A I ° = A(A° ) = 0 5.8 c b a Equat ion 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 both c h l o r i n e i socyana te and i s o c y a n i c a c i d ; i . e . the change i n the i n e r t i a l de fec t i s ve ry s m a l l . However, i t i s not w e l l s a t i s f i e d when hydrogen i s r ep l aced w i t h deuter ium 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 . * Th is l a s t r e s u l t i m p l i e s tha 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 to incomplete c a n c e l l a t i o n of v i b r a t i o n a l e f f e c t s , i s l a r g e . An i n d i c a t i o n of j u s t how l a r g e may be obta ined by r e p l a c i n g A I ° i n equa t ion Si 2.58b w i t h A I ° - A I ° and then r e c a l c u l a t i n g b^. Th i s has been done and the 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 ) i n which a l l of the jt-coord ina tes were taken to be the same as i n s t r u c t u r e I, w h i l e the three remain ing b-coord inates were determined w i t h the a i d of equat ions 5 .6 . The s t r u c t u r e I I atomic coo rd ina tes are a l s o g i ven i n Table 5 .7 . I t w i l l be noted t h a t , a l though b i n c r eases q u i t e s u b s t a n t i a l l y (by 0.0260 X) on going n. from s t r u c t u r e I to I I , the o the r three b-coord inates show on l y minor changes. S ince c h l o r i n e i socyana te has been shown to have a s m a l l bend at c a rbon , the assumption o f a l i n e a r NCO cha in i n i s o c y a n i c a c i d i s c l e a r l y r a t h e r tenuous. An attempt was t h e r e f o r e made to o b t a i n an independent d e t e r m i n -a t i o n of the n i t r o g e n b-coord ina te u s i ng the double s u b s t i t u t i o n technique of P i e r c e and K r i s h e r (68) . The fou r i s o t o p i c spec i es used were H 1 4 N 1 2 C ^ 0 , D 1 4 N 1 2 C 1 6 0 , H 1 5 N 1 2 C 1 6 0 and D 1 5 N 1 2 C 1 6 0 where the f i r s t of these was taken to be the " p r i n c i p a l framework" and the second, the "secondary framework". Only the AAI e x p r e s s i o n (equat ion 2.67) was cons idered because I ° ( D ^ N ^ 2 C ^ 0 ) c a * 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 M o l e c u l a r S t r u c t u r e of I socyan i c A c i d : Atomic C o o r d i n a t e s 3 . I b I I b I I I b -1.83736 -1.83736 -1.83736 -1.20552 -1.20552 -1.20552 3 c 0.00312 0.00312 0.00312 a o 1.16882 1.16882 1.16882 b H 0.68793 0.71393 0.68793 b N -0.05521 -0.05729 -0.07670 b c -0.01778 -0.01845 0.03331 b o 0.01832 0.01902 -0.00118 3 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 of procedure used t o o b t a i n these three s t r u c t u r e s . TABLE 5.8 M o l e c u l a r S t r u c t u r e of I s o c yan i c A c i d : Geometry. I b I I b I I I b r ( H - N ) a 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' Bond l eng ths measured i n A. C a l c u l a t e d from cor respond ing se t of atomic coo rd ina tes i n Table 5.7. 140 was u n a v a i l a b l e ( a l so the I va lues of the o ther i so topes have l a rge u n -c e r t a i n t i e s ) . The coord ina tes of the cente r of mass o f D ^ N ^ C ^ O i n the COMPIAS o f H 1 4 N 1 2 C 1 6 0 were computed us ing s t r u c t u r e I to be : A = -0.04201 & and B = 0.01573 A*. S u b s t i t u t i o n of these numbers a long w i t h AAI° = c -0.093697 a .m.u .X 2 and a^ = -1.20552 X i n t o the second d i f f e r e n c e s equa t ion y i e l d e d a va lue of 0.0767 ± 0.020 A* f o r b^. The l a r g e e r r o r e s t i m a t e , wh ich 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 vea l s tha t t h i s technique has u n f o r t u n a t e l y not produced the accura te r e s u l t hoped f o r . 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 ve ry s m a l l . Second ly , the moments of i n e r t i a from which i t was c a l c u l a t e d are not p a r t i c u l a r l y accura te ( c f . c h l o r i n e i s o c y a n a t e ) . 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 o c o n t r i b u t i o n s to AAI p rov ide an a d d i t i o n a l unknown f a c t o r . These d i f f i -c 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 tha t a necessary 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 double s u b s t i t u t i o n technique i s a s h i f t i n the cen te r o f mass of the "secondary framework" w i t h r espec t t o the COMPIAS of the "p r ima ry framework" , a long the 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 on l y 0.0157 R. The e x c e l l e n t agreement of the s i n g l e and double s u b s t i t u t i o n va lues f o r b^ i s i n t r i g u i n g . However, both numbers have such l a r g e u n c e r t a i n t i e s tha t they cannot be regarded 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 va lue obta ined assuming a l i n e a r NCO c h a i n . Converse ly there i s no hard p h y s i c a l ev idence a v a i l a b l e to i n d i c a t e tha t the NCO cha in 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 . A c c o r d i n g l y a t h i r d s t r u c t u r e was determined u s i ng the double s u b s t i t u t i o n va lue f o r b^. In t h i s the b^ , and bg coord ina tes were aga in c a l c u l a t e d w i t h the a i d of the c en t e r o f mass and product o f i n e r t i a r e l a t i o n s (equat ions 5.6a and 5 .6b ) , wh i l e the r e s t -0.5 142 of the coord ina tes were taken to be the same as i n s t r u c t u r e I. The r e s u l t s have been c o l l e c t e d i n Tab le 5.7 as s t r u c t u r e I I I . The atomic coord ina tes i n Table 5.7 have been converted i n t o bond l engths and angles which are presented i n Table 5 .8 . S t r u c t u r e s I and I I I are i l l u s t r a t e d w i t h s c a l e drawings i n F igures 5.1 and 5.2 r e s p e c t i v e l y . Comparison of the three s t r u c t u r e s i n Table 5.8 r e vea l s tha t t h i s work has y i e l d e d accura te va lues 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 d i s t a n c e s . 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 de te rm ina t i on of the NH bond l eng th has c l e a r l y not been ach i eved ; a l s o the u n c e r t a i n t y i n the two angles i s s t r o n g l y dependent on whether, or not the assumption of a l i n e a r NCO cha in i s c o r r e c t . These l a s t two p o i n t s are d i s cussed i n more d e t a i l i n s e c t i o n 5 .6 . 5.4 D ipo l e Moment Measurements; D i s c u s s i o n of the D ipo l e Moment and the  N i t r o g e n Nuc lea r Quadrupole Coup l ing Cons tan ts . 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 of the atoms that make up i s o c y a n i c a c i d , and t h e i r geome t r i c a l arrangement, i t may be reasoned tha t t h i s molecu le shou ld have non-zero d i p o l e moment components a long i t s a- and b-p r i ' n c i pa l i n e r t i a l axes . Th i s has o f course been shown to be t rue through the obse r va t i on of both a- and b-type t r a n s i t i o n s . On the o the r hand, the ^-component of the d i p o l e moment must be zero because the c^-axis i s p e r p e n d i c u l a r to the p lane of symmetry of the mo lecu l e . The a-component of 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 White and Cook (153) . These authors found tha t y has a 3. 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 ^. They were unable to o b t a i n a va lue f o r y^> however, due to the n e g l i g i b l e dependence of the S ta rk 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 of the d i p o l e moment. In t h i s work a number of b-type t r a n s i t i o n s have been repor ted f o r i s o c y a n i c a c i d . These have a S ta rk e f f e c t which i s a s t rong f u n c t i o n o f but which i s n e a r l y independent of 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 requency range of our spect rometer are o f r a t h e r h i g h J , hence r e s o l u t i o n of t h e i r i n d i v i d u a l S ta rk components was i m p o s s i b l e . I t t u rns o u t , however, tha t i n each case the s t ronges t and most r a p i d of these S ta rk components move out n e a r l y together 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 , but s t i l l s u r p r i s i n g l y symmetric aggregate S ta rk l o b e . A c c o r d i n g l y , an attempt was made to deduce an approx -imate va lue of from the f i e l d dependence of these composite l o b e s . I t shou ld be po in ted out tha t the low J b-type t r a n s i t i o n s , f o r which i n d i v i d u a l S ta rk components w i l l be r e s o l v a b l e , l i e a t ve ry h i g h f requency and w i l l have ve ry s m a l l S t a rk c o e f f i c i e n t s . Consequently a s tudy of t h e i r S t a rk e f f e c t i s l i k e l y to be both d i f f i c u l t and u n p r o f i t a b l e ( i . e . i t would not g i v e a s i g n i f i c a n t l y b e t t e r va lue f o r than tha t r epor ted h e r e ) . S t a rk 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 , 2 2 2 1 1 , 2 1 2 4 0 , 2 4 2 3 1 , 2 3 These were chosen i n p re fe rence to the a v a i l a b l e H^ 4N^" 2C^O b-types f o r two impor tant reasons . F i r s t l y , t h e i r composite S ta rk lobes are f a s t e r and l e s s broadened (fewer components) than those o f the H ^ N ^ C ^ O t r a n s i t i o n s . I Second ly , the l i n e s t r eng ths r e q u i r e d f o r computat ion of asymmetric r o t o r S ta rk energ ies have been t abu l a t ed on l y up to J = 35 ; the H ^ N ^ C ^ O b-types i n v o l v e J v a lues g r e a t e r than 35 . Two d i f f e r e n t microwave c e l l s were used i n the course of t h i s work. 144 P r e l i m i n a r y measurements were made on the 22^ ^ — 21^ ^ t r a n s i t i o n u s i ng the 7 foo t X-band c e l l d e s c r i bed i n Chapter 3. However, s i n ce 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 centered a l l S ta rk lobes were a d d i t i o n a l l y broadened. 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) became a v a i l a b l e the experiment was repeated us ing the 24^ ^ — 23^ 23 t r a n s i t i o n . The two se ts of 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 ta rk e f f e c t of the J = 0-»-l t r a n s i t i o n o f c a rbony l s u l f i d e (OCS). Th i s procedure has the dua l advantage 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 measur ing the d i s t a n c e between the septum and the c e l l w a l l , and a l s o averag ing out any f i e l d inhomogene i t i es . The e l e c t r i c f i e l d induced f requency 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 to second o r d e r , i s g i ven by (156 ) : AvS = (8/15) (0.50344) 2p 2£" 2/v 5.9 where V q = 12162.97 MHz i s the zero f i e l d f requency of the t r a n s i t i o n , y i s the d i p o l e moment of 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 i n Vo l t s/cm and 0.50344 MHz•(Debye-Volts/cm) ' i s a convers ion f a c t o r (157) . I t then f o l l o w s tha t i f a DC b i a s p o t e n t i a l of V ( Vo l t s ) and an AC modu-o l a t i o n f i e l d w i t h a h a l f - a m p l i t u d e of V m ( Vo l t s ) (see s e c t i o n 3.5) are a p p l i e d to the c e l l septum the average f requency s h i f t A\J w i l l be g i ven b y : 2\ /, \2 Av£> = ( 8 / 1 5 ) ( 0 . 5 0 3 4 4 ) 2 ^ | - ) (V 2 + V 2 ) ? 7 5.10 = C(V + V ) o m where E = 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 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 shou ld t h e r e f o r e g i ve a v 0->l o m " s t r a i g h t l i n e w i t h s lope C and i n t e r c e p t V q . From C and Muenter ' s (158) va lue f o r the d i p o l e moment of OCS (y = 0.71521 ± 0.00020 D) 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 da ta f o r the two c e l l s have been c o l l e c t e d _ 2 2 i n Table 5 .9 . In both c a s e s , a p l o t of VQ+I v s • V Q + v m 8 a v e a very good s t r a i g h t l i n e as expec ted . A l e a s t squares f i t t i n g procedure was then used to o b t a i n the r e s u l t s which have been c o l l e c t e d i n Table 5 .11 . The ag ree -ment of the i n t e r c e p t s w i t h the p u b l i s h e d va lue of V q (159) i s e x c e l l e n t . Equat ion 2.44 was used to o b t a i n exp ress ions f o r the second order S t a rk energ ies o f the fou r r o t a t i o n a l s t a t e s of D ^ N ^ C ^ O i n v o l v e d i n the two t r a n s i t i o n s s t u d i e d . The r e q u i r e d l i n e s t r eng ths were ex t r a c t ed from the NBS Tables (160) us ing 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 = -0.95 ( K o f D ^ N ^ C ^ O i s -0 .999070 ) . The-energy denominators were obta ined i n two d i f f e r e n t ways. The l a r g e ones were c a l c u l a t e d to s u f f i c i e n t accuracy us ing the r i g i d r o t o r approx imat ion and the r o t a t i o n a l constants i n Table 5 .3 . The two s m a l l denominators which correspond to the two observed t r a n s i t i o n f r equenc i es dominate the S ta rk energy e x p r e s s i o n s . For these the exact energ ies ( f r equenc ies ) were used . S ince none of the fou r s t a t e s i s c o n -nected by a nonzero d i p o l e moment m a t r i x element to any other nearby s t a t e , there was no f i r s t order or pseudo f i r s t o rder S t a rk e f f e c t to c o n s i d e r . The energy express ions were then used i n c o n j u n c t i o n w i t h the 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) to o b t a i n r e l a t i o n s f o r the average frequency s h i f t s o f the S ta rk components. These a r e : Moo M — 91 M = f y 2 ( -9 .49011x l0~ 6 + 18 .1238x l0~ 9 M 2 ) 0,22 J 1,21 J 1 ° J 5.11a + u 2 (-0 .00230x10 6 + 0.11645x10 V ) \ (l/ r 2) (V 2 + V 2 ) (0.50344) 2 a J J - -c o m M 2 4 M — ?3 M = ^ ( 1 2 . 2 0 4 1 2 x 1 0 6 ~ 2 2 . 4 2 5 5 x l 0 " 9 M 2 ) ^ 0 , 2 4 , M J Z J 1 , 2 3 ' M J I b J + u 2 ( - 0 . 0 0 1 8 0 x l 0 ~ 6 + 0 .07025x l0 " 9 M 2 ) | ( l / r 2)(V? + vf) (0 .50344) 2 5.11b c o m 146 TABLE 5.9 C e l l C a l i b r a t i o n : Measurement of the S ta rk E f f e c t o f the J = O+l T r a n s i t i o n of OCS. m C e l l v a o 1 Frequency 0 ( v ) V m C e l l V o 2 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 ta rk Measurements on Two b-type T r a n s i t i o n s of D 1 4 N 1 2 C 1 6 0 22 — 21 0,22 1,21 ( C e 1 1 X> 24 — 23 40,24 1,23 ( C e 1 1 2 ) v a m v a 0 Frequency* 3 (v) V m V o 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 C e l l C a l i b r a t i o n : E f f e c t i v e Septum-Cel l Wa l l Spac ing . C e l l 1 C e l l 2 S l o p e a x l 0 5 2.62458 ± 0.00082 2.56822 ± 0.00094 I n t e r cep t d 12162.973 ± 0.003 0.46541 ± 0.00020 12162.982 ± 0.005 0.47048 ± 0.00022 a _ 2 2 2 Slope o f the v v s . V q + V"m s t r a i g h t l i n e graph i n MHz/Volts . b _ 2 2 I n t e r c ep t of the v v s . V q + V s t r a i g h t l i n e graph i n MHz; c f . v = 12162.97. o Standard e r r o r . E f f e c t i v e septum-ce l l w a l l spac ing i n cm. 95% conf idence l i m i t . TABLE 5.12 S ta rk C o e f f i c i e n t s of Two D 1 4 N 1 2 C 1 6 0 b-type T r a n s i t i o n s , 2 2 0 , 2 2 - 2 1 l , 2 1 ( C e 1 1 X ) 2 4 0 , 2 4 23j_ 2 3 ( C e l l 2) S l o p e a x l 0 5 I n t e r cep t -1.9338 ± 0.0061 -26074.30 ± 0 . 0 4 d 2.3610 ± 0.0099 19619.48 ± 0 . 0 5 d •26074.49 ± 0.10 19619.58 ± 0.10 S lope of the v v s . + s t r a i g h t l i n e graph i n MHz/Vo l t s^ . — 2 2 I n t e r cep t of the v v s . V + V s t r a i g h t l i n e graph i n MHz. O m o r Observed zero f i e l d t r a n s i t i o n f requency i n MHz. Standard e r r o r s . Es t imated e r r o r s . I 149 where Av i s in MHz i f u , u, are in Debyes, r is in cm, and V , V are in 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 in Table 5.10. _ 2 2 For both transitions i t was found that a plot of v vs. V + V gave a rather o m 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 lines. The numbers are presented in Table 5.12. I t w i l l be noted that for both transitions, the intercept i s in good agreement with the observed zero f i e l d frequency. Two sets of values were then cal-culated by assuming that the peak maxima of the composite Stark lobes corres-ponded 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 in Table 5.13. Since for both transitions the relative intensities of the various M com-2 ponents decrease with Mj and the separation between components increases 2 with Mj. i t seems probable that the maximum in 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 in the number of components, this maximum should occur at a slightly 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 total 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 2 + V 2 ) x l O ~ 5 ( v o l t s 2 ) o m 152 TABLE 5 .13 The b-coraponent of the D ipo l e Moment of D U N 1 2 C 1 6 o . 22 — 21 0 , 2 2 1,21 2 4 0 , 2 4 ~ 2 3 1 , 2 3 M J K M , ) " y b (Debyes ) b K M j ) (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 of the v a r i o u s Mj S ta rk 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 of the aggregate S t a rk lobe corresponds to v a r i o u s va lues of M . 153 of a mo lecu 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 cou ld have any one of four d i f f e r e n t d i r e c t i o n s , cor respond ing to the four 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 gns f o r y and u, . Now, i t i s known that the NCO r a d i c a l has a moderate ly a b 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 ca rbon ) . T h e r e f o r e , i t seems reasonable tha t the d i p o l e moment of i s o c y a n i c a c i d should p o i n t roughly from n i t r o g e n to hydrogen when the p o s i t i v e d i r e c t i o n i s taken i n the sense - - * • + . In terms of "bond moments", a s m a l l NCO component (0 -*• N +) adds to a l a r g e r NH component (N ->• H + ) to g i v e a s t i l l l a r g e r t o t a l moment, which w i l l make a s l i g h t l y s m a l l e r angle w i t h the a-ax is than does the NH bond; t h i s i s observed when the s igns of y and y, are taken to be as i n d i -a b cated i n F i g u r e 5 .5 . A l though H ^ N ^ C ^ O and D ^ N ^ C ^ O should 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 nonethe less d i f f e r s l i g h t l y due to a r o t a t i o n (by 1° 29 ' ) of the p r i n c i p a l i n e r t i a l a x i s system on go ing from one i so tope to the o t h e r . 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 determined D ^ 4 N ^ 2 C ^ 0 components y and y, were t ransformed i n t o new com-a b ponents y 1 and y ' measured w i t h r espec t to the H^^N^C^O p r i n c i p a l i n e r t i a l a b a x i s system. S t r u c t u r e I was assumed to be the c o r r e c t s t r u c t u r e f o r t h i s purpose , and the s i gns of the components were taken to be as i n d i c a t e d i n F igu re 5 .5 . The r e s u l t s are compared i n Table 5.14 w i t h va lues of y ' 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 ng the CNDO/2 formal i sm and s t r u c t u r e I. The s i gns o f the CNDO/2 p r e d i c t e d components are seen to support our p rev ious deduc t i ons . F u r t h e r , there i s even good agreement i n the magnitude of the c a l c u l a t e d and "obse r ved " numbers. An es t imate o f the i o n i c cha rac t e r i n the NH bond of i s o c y a n i c a c i d 154 FIGURE 5.5 The D ipo l e Moment of I socyan i c A c i d . b(A) H j u = -1.57 D 155 may be obta ined from the measured d i p o l e moment us ing the f o l l o w i n g s imple r e l a t i o n : \ = 5 - 1 2 where 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 (0.975x10 cm). The r e s u l t ob ta ined i s i = 0.441 (or 44 .1% ) . 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 cha rac t e r 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 of hydrogen and n i t r o g e n w i t h the a i d of equa t ion 4 . 1 1 . I f X(R) and Z(N) are taken to be 2.15 and 3.00 (103) r e s p e c t i v e l y , t h i s r e l a t i o n y i e l d s i = 0.425 (or 42.5%) i n e x c e l l e n t agreement w i t h the d i p o l e moment r e s u l t . However, s i n ce both procedures have been g e n e r a l l y found to be poor approx imat ions when a p p l i e d to p o l y -atomic m o l e c u l e s , t h i s agreement must be regarded 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 quadrupole c o u p l i n g cons tan ts of i s o c y a n i c a c i d and a number o f r e l a t e d molecu les are compared i n Table 5 .15 . I t w i l l be noted tha t these are c o n s i s t e n t w i t h the proposed i socyana te (HNCO) r a t h e r than the a l t e r n a t e p o s s i b l e cyanide (HOCN) c o n f i g u r a t i o n f o r t h i s mo l e cu l e . In 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 nega t i v e X c c > i n c o n t r a s t to the cyan ides f o r wh ich x c c i s p o s i t i v e . I n a d d i t i o n , both the i socyana tes 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 cyanides i s t y p i c a l l y n e g a t i v e . 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 c i d a l so gave va lues f o r the n i t r o g e n atomic p - o r b i t a l p o p u l a t i o n s . These were * I t has been i m p l i c i t l y assumed here tha t on ly 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 of the Observed and C a l c u l a t e d Values of the D ipo l e Moment of I socyan i c A c i d . Observed (DNCO)b Observed (HNCO)C C a l c u l a t e d " a -1.567 -1.575 -1.404 1.391 1.600 IJLI 2.095 2.129 a A l l components measured w i t h respec t to p r i n c i p a l i n e r t i a l a x i s system of H* 4 N* 2 C*" D 0 i n Debyes. ° E x p e r i m e n t a l l y determined D * 4 N * 2 C ^ 0 components (u = -1.602 D, 1 4 X 2 1 6 ^ u, = 1.35 D) t ransformed i n t o H N C O i n e r t i a l a x i s system. 14 12 16 C E x p e r i m e n t a l l y determined H N C O component f o r K_, = 1 l e v e l s (153) . TABLE 5.15 N i t r ogen Nuc lea r Quadrupole Coup l ing Constants of I so cyan i c A c i d and Re la ted M o l e c u l e s . Mo lecu le X a a x bb X c c Reference H U N 1 2 C 1 6 0 (obs) 2.045 -0.466 -1.578 H 1 4 N 1 2 C 1 6 0 ( ca l c ) 2.845 . -0.571 -2.273 (109) 3 5 C 1 1 4 N 1 2 C 1 6 0 3.99 -1.01 -2.97 1 2 C H 3 1 4 N 1 2 C 1 6 0 2.86 (12) H 1 4 N 1 2 C 3 2 S 1.2 (149) 1 2 C H 3 1 4 N 1 2 C 3 2 S 1.90 (12) 3 2 S ( 1 2 C 1 4 N ) 2 -1.51 0.30 1.21 (162) 1 2 C H 3 1 2 C 1 4 N -4 .20 2.10 2.10 (163) H 1 2 C 1 4 N -4.58 2.29 2.29 (164) 1 2 C H 3 3 2 S 1 2 C 1 4 N -3 .13 2.19 0.94 (12) Measured i n MHz. 157 converted i n t o n i t r o g e n n u c l e a r quadrupole c o u p l i n g constants w i t h the a i d of the Townes D a i l e y Theory, as desc r ibed i n s e c t i o n 4.4 (equat ion 4.3). The r e s u l t s are a l s o presented i n Table 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 though the agreement w i t h the observed constants i s not o u t -s t a n d i n g , i t i s c e r t a i n l y acceptab le i n view of the l i m i t a t i o n s of the theory 14 and the u n c e r t a i n t y i n the magnitude of eQl2io^ ^ " 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 Constants and the I n e r t i a l  Defect from the M o l e c u l a r Force F i e l d . I t was noted i n the i n t r o d u c t i o n to t h i s chapter tha t three d i f f e r e n t 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 ass ignments , have been p u b l i s h e d f o r i s o c y a n i c a c i d . These have been reproduced i n Table 5.16. The f i r s t , tha 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 of Herzberg and Re id (144) on the s i n g l e i s o t o p e H 1 4 N ^ 2 C ^ O . I t was found to g i v e a poor p r e d i c t i o n o f the D 1 4 N ^ 2 C ^ O fundamental v i b r a t i o n f r equenc ies and was t he r e fo r e not cons idered f u r t h e r . The o the r two f o r c e f i e l d s are both based on the more complete da ta o f Ashby and Werner (145,146). I n t h e s e , W a r r i a r e t . a l . (147) used the observed 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 . (148) used the " u n -p e r t u r b e d " f r e q u e n c i e s ; i . e . those 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 c o u p l i n g . The l a t t e r approach would seem to be the c o r r e c t one, but f o r t u n -a t e l y the two se t s of f r equenc ies do not d i f f e r g r e a t l y . I t i s not c l e a r how Wa r r i a r e t . a l . managed to c a l c u l a t e 32 f o r c e cons tan ts from 12 observed f r e q u e n c i e s . In a d d i t i o n , both groups gave a l l f o r ce cons tants i n u n i t s of mdyne/X but d i d not s p e c i f y how they had s ca l ed t h e i r bending d i s p l a c e -ment coo rd ina tes to achieve t h i s r e s u l t . S e ve r a l a l t e r n a t i v e p o s s i b i l i t i e s were c o n s i d e r e d ; tha t i n d i c a t e d i n Table 5.16 gave the bes t r e p r o d u c t i o n 158 TABLE 5 .16 Molecular Force F i e l d s of Isocyanic Acid. Force O r v i l l e Thomas^ c Warriar e t . a l . Orel e t . a l . a Constant HNCO HNCO DNCO HNCO/DNCO fR 6 . 9 6 . 9 0 5 0 6 . 9 6 0 0 7.031 f r l f r 2 1 4 . 0 1 4 . 2 9 0 0 1 4 . 5 5 0 0 11 .791 1 5 . 0 1 4 . 7 1 0 0 1 4 . 2 2 0 0 1 7 . 9 0 4 s 0 . 5 8 0 . 3 0 1 0 0 . 0 4 0 0 0 . 1 9 9 f R r 2 0 . 0 6 0 . 3 4 9 0 0 . 0 6 0 0 f r l r 2 1.32 1 .2400 1 .3840 2 . 1 9 4 f a 0 . 3 3 0 . 2 3 1 2 0 . 2 4 8 4 0 . 1 8 4 f e 0 . 4 8 0 . 6 6 8 0 0 .5447 0 . 8 1 2 fRa 0 . 0 2 0 . 0 0 9 0 0 . 0 3 4 0 f R9 - 0 . 0 2 - 0 . 0 3 1 0 - 0 . 0 0 5 0 f r l a 0 . 1 7 0 . 1 3 9 0 0 . 1 5 8 0 f r 2 a 0 . 1 0 0 . 0 7 9 0 0 . 0 9 1 0 \° 0 .04 0 . 0 2 5 0 - 0 . 0 4 2 0 0 . 1 0 0 %. 0 . 0 2 0 . 0 1 4 0 - 0 . 0 2 4 0 0 . 0 9 9 0 . 0 9 0 . 0 6 5 0 - 0 . 0 3 1 0 0 . 1 2 9 0 . 4 2 1 4 0 . 4 5 9 3 a In mdynes/R; R = NH, rl = NC, r 2 = CO, a =/LHNC, 9 = Z.NC0 (in-plane) 6 =Z.NC0 (out-of-plane). Bending displacement coordinates defined as: RAa and r 2A9. C Bending displacement coordinates presumed to be: ^ /Rr^Act, ^jr^v^Q and A 6 J r 1 r 2 -159 TABLE 5.17 Fundamental V i b r a t i o n a l F requenc ies of I socyan i c A c i d H. and R. b A. and W. C Fundamental D e s c r i p t i o n HNCO HNCO DNCO "1 3531 2634.9 HN s t r e t c h ^2 2274 2235 NCO asymmetric s t r e t c h "3 1327 1310 NCO symmetric s t r e t c h W4 798 ' 777. 1(761 • 5 ) d 460(468.5) HNC bend ( in-p lane) u 5 572 659. 8(642 .8) 766.8(758.3) NCO bend ( in-p lane ) u 6 670 577. 5(610 .1) 602.9 out-of-p lane bend " Measured i n cm A . b Taken from Herzberg and Re id (144) . Taken from Ashby and Werner (145,146) . d Numbers not i n b r a cke t s are the observed band o r i g i n f r e q u e n c i e s ; numbers i n b racke t s are " unpe r tu rbed " 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 ce f i e l d s of both War r i a r e t . a l . and O re l e t . a l . were used to 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 constants of 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 son theory ( s e c t i o n 2.5) and the p l a n a r i t y r e l a t i o n s (equat ions 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 constants i n Table 5 .18. The o v e r a l l agreement i s r a t h e r poor . The most s e r i o u s d i s c repancy occurs f o r the A d i s t o r t i o n 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 spec ies both of the c a l c u l a t e d va lues are o f oppos i t e s i g n to the observed one. Th i s does not come as a complete s u r p r i s e , however, s i n ce Neely (152) has p r e v i o u s l y suggested that A shou ld be ext remely s e n s i t i v e to the s t re tch-bend i n t e r a c t i o n constants i n the mo l e cu l a r f o r ce 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 f o r c e f i e l d s i s p a r t i c u l a r l y o u t s t a n d i n g . A c c o r d i n g l y , Dr . R. Green (117) has r e cons ide red the i s o c y a n i c a c i d f o r ce f i e l d problem us i ng h i s p r e v i o u s l y mentioned method ( s e c t i o n 4 . 6 ) . Th is c a l c u l a t i o n was a l so based on the v i b r a t i o n a l f r equenc i e s ( co r rec ted ) and assignments o f Ashby and Werner; except tha t the co^  and to^ . assignments of the H^^N^^C^O spec i es were r e v e r s e d . The H 1 4 N 1 2 C ^ O assignments are now c o n s i s t e n t w i t h those of D ^ N ^ C ^ O and a l s o C1NC0. Th is change does not i n any way a f f e c t the C o r i o l i s coup l i ng 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 of observed band o r i g i n f r equenc i e s to g i v e " unpe r tu rbed " f r e q u e n c i e s ) . However, i t shou ld be po in t ed out tha t there i s apparen t l y s t i l l some cons ide r ab l e doubt as to the importance of such i n t e r a c t i o n s (165) . Consequent ly n e i t h e r the " unpe r tu rbed " f r equenc i es nor even the ass ignments , 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 regarded as f i n a l y e t . In any case , on ly the numbers g i ven i n Table 5.17 are p r e s e n t l y a v a i l a b l e , so they were used . 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 I socyan i c A c i d . 3 H U N 1 2 C 1 6 0 Constant Observed W . F . F . b 0 . F . F . C R . G . F . F . d A j X 1 0 3 3.198 3.606 3.785 3.366 A J K X 1 Q 1 8.311 -4.482 -11.005 9.179 A K x l 0 - 3 5 .096 6 2.902 3.371 3.982 6 j X 1 0 5 7.277 10.459 13.883 5.847 6 K X 1 Q 1 4.832 _14. T12 16 r t D N C 0 5.971 5.520 Constant Observed W.F.F . O .F . F . R .G .F .F . A j X 1 0 3 3.432 3.676 4.131 3.153 A J K X 1 Q 1 -2.291 -9.240 -12.874 -2.793 A K x l 0 " 3 2 . 7 5 8 e 1.146 1.156 1.415 6 x l O 4 2.042 2.577 3.188 1.959 v i ( ) 1 4.161 4.969 4.727 a 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 of Wa r r i a r e t . a l . (147) . C C a l c u l a t e d from the f o r c e f i e l d of O r e l e t . a l . (148) . 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 (117) . 6 From the f a r i n f r a r e d da ta of Krakow e t . a l . (151) . 1 6 2 The f o r c e f i e l d determined by Green (R .G .F .F . ) has been presented i n Table 5 .19. Here the H 1 4 N 1 2 C 1 6 0 and D 1 4 N 1 2 C 1 6 0 problems were t r ea t ed s e p a r a t e l y . The near equ iva lence of the two r e s u l t i n g se ts of numbers i s r e a s s u r i n g . The d i s t o r t i o n constants which they y i e l d are aga in compared w i t h the observed ones i n Table 4 .18 . I t w i l l be noted t ha t the o v e r a l l agreement i s much improved now. In p a r t i c u l a r , the c a l c u l a t e d A va lues J K are not on l y of the r i g h t s i g n but a l s o , app rox ima te l y , the r i g h t magnitude. Only f o r the A constant are the d i s c r e p a n c i e s between the observed and c a l -ls. 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 tha t these are due ma in ly to the i nhe ren 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 son theory (114) r a t h e r than to any se r i ous d e f i c i e n c y i n the R .G.F .F . Desp i te the apparent s u p e r i o r i t y of the R .G .F .F . over both the Wa r r i a r and O re l f o r ce f i e l d s a l l th ree were a l so used to c a l c u l a t e the i n e r t i a l de f e c t s of H * 4 N * 2 C ^ O and D*" 4 N^ 2 C* D 0. The procedure f o l l owed was e s s e n t i a l l y the same as tha t desc r ibed i n s e c t i o n 4 . 6 ; i . e . A I T T t > was c a l c u l a t e d w i t h the a i d of equa t ion 2 .56 , A was es t imated by s u b s t i t u t i n g the c a l c u l a t e d d i s t o r t i o n constants i n t o equat ions 5 .5 , 2.20 and 2 .16 , and ^ e ^_ e c w & s i g n o r e d . The r e s u l t s have been c o l l e c t e d i n Table 5 .20. In each case , the sum A T r T n + A ^ (= A , ) i s i n r e spec t ab l e agreement w i t h the observed i n e r -VIB cent c a l c v t i a l d e f e c t . Th is 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) a s s e r t i o n tha t the i n e r t i a l de f ec t i s no rma l l y on 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 mo lec -u l a r f o r ce f i e l d . However, i t w i l l be noted tha t a l though the d i f f e r e n c e s are s l i g h t the R .G.F .F . has aga in g i ven the bes t agreement w i t h exper iment . The remain ing d i s c r e p a n c i e s between A° and A ^ (R .G .F .F . ) p robab ly cannot be a t t r i b u t e d to &e-^ec s i n c e the l a t t e r i s l i k e l y to be s m a l l and nega t i v e (59) . I t i s perhaps s i g n i f i c a n t tha t the agreement i s s l i g h t l y b e t t e r f o r D ^ 4 N 1 2 C ^ O than H * 4 N * 2 C ^ 0 ; the C o r i o l i s coup l i ng i s more important i n the 163 TABLE 5.19 I socyan i c A c i d M o l e c u l a r Force F i e l d : R .G .F .F . Force Constant 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 b f (HN:C0) 0 .0000 b o.oooob f(NC:CO) 1.4299 1.5270 f(HN:HNC) 0.3436 0.3486 f(HN:NCO) o.oooob o.oooob f(NC:HNC) 0.7318 0.7331 f(NC:NCO) o.oooob o.oooob f(CO:HNC) 0.0715 0.0763 f(CO:NCO) 0 .0000 b o.oooob f(HNC:NCO) -0.1047 -0.1003 S t r e t c h i n g f o r c e constants are i n mdyne/X, bends are i n mdyne-X/rad , bend-s t r e t ch i n t e r a c t i o n s are i n mdyne/rad. Set equa l to 0 i n i t i a l l y . TABLE 5.20 Comparison of C a l c u l a t e d and Observed I socyan i c A c i d I n e r t i a l D e f e c t s . H 1 4 N 1 2 C 1 6 0 C a l c u l a t i o n A VIB A cent A VIB + A c e n t 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 D U N 1 2 C 1 6 0 0.1101 0.1205 C a l c u l a t i o n \ l B A cent A VIB + A c e n t A° W.F.F. ' 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 l a t t e r . F i n a l l y , i t i s now c l e a r tha t the observed i n c r ea se i n A° on going from H * 4 N * 2 C ^ O to D ^ N ^ C ^ O i s e n t i r e l y compat ib le w i t h a p l a n a r s t r u c t u r e f o r i s o c y a n i c a c i d . 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 . The mo l e cu l a r s t r u c t u r e determined f o r i s o c y a n i c a c i d i n t h i s work i s compared i n Tab le 5.21 w i t h the r e s u l t s o f two p rev ious s t r u c t u r a l i n v e s t i -g a t i o n s . 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 of E y s t e r e t . a l . (123) i s seen to have y i e l d e d on ly approximate es t imates of the NC and CO bond l e n g t h s , a f t e r the remain ing parameters had been g i ven assumed v a l u e s . The m i c r o -wave " r 11 s t r u c t u r e obta ined by Jones e t . a l . (11) i s a cons ide r ab l e improve -ment on the e l e c t r o n d i f f r a c t i o n one. In f a c t , i t i s n e a r l y as good as the " r 11 s t r u c t u r e ob ta ined he re . The present study 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 , but has not 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 nhe ren 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 hydrogen/ deuter ium 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 . I t h a s , however, more c l e a r l y demonstrated the e x i s t e n c e of such 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 of a bend i n the NCO c h a i n . In l i g h t of t h i s , the s m a l l e r r o r es t imates g i v en by Jones e t . a l . f o r the HNC angle and the NH bond l e n g t h are seen to 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 of i s o t o p i c d a t a , i t was s t i l l imposs i b l e to prove r i g o r o u s l y whether o r not the NCO cha in i n i s o c y a n i c a c i d was l i n e a r or ben t . A s i m i l a r s i t u a t i o n e x i s t s w i t h regards to the s t r u c t u r e s of 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 the r t e chn ique , such as e l e c t r o n d i f f r a c t i o n , i s capable o f 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 chemica l grounds , the s t r u c t u r e w i t h the l i n e a r heavy atom cha in must be the p r e f e r r e d one. Resonance forms l i k e those drawn p r e v i o u s l y ( s e c t i o n 4.7) 166 TABLE 5.21 Comparison o f I socyan i c A c i d S t r u c t u r e s . E y s t e r e t . a l . Jones e t . a l . Th is Work° ( e l e c t r o n d i f f r a c t i o n ) " r " " r " o s r(N-H) ( 1 . 0 1 ) b 0.987 ± 0.01 0.986 ± 0. 0 1 5 d r(N-C) 1.19 ± 0.03 1.207 ± 0.01 1.209 ± 0. 0 0 5 d r(C-O) 1.19 ± 0.03 1.171 ± 0.01 1.166 ± 0. 0 0 5 d Z.(HNC) (125 ° ) b 128° 5' ± 30 ' 128° 2' + ^o e z_(NCO) (180 ° ) b ( 180 ° ) b ( 180 ° ) b 3 Bond l eng ths measured i n A*. b Assumed. ° Th i s i s an average of s t r u c t u r e s I and I I (Table 5 .8 ) . d Es t imated 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 " but 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 es t imate i f the assumption of a l i n e a r NCO cha in i s i n c o r r e c t . 167 to e x p l a i n the observed bends i n c h l o r i n e i socyana te and c h l o r i n e az ide are not p o s s i b l e f o r the a c i d s . The NC and CO bond l engths i n i s o c y a n i c a c i d are very s i m i l a r to the d i s t a n c e s repor ted e a r l i e r f o r the cor respond ing c h l o r i n e i socyana te bonds. Consequent ly , i t would appear tha 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 system. In terms o f the Valence Bond approach, three resonance forms are aga in l i k e l y to be the dominant c o n t r i b u t o r s to the composite wave-* f u n c t i o n (123) . These a r e : H \ H N = C 0~ H X 51 511 5 I I I S ince hydrogen has a much lower 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 .15 , X(C1) = 3.00) (103) i t i s to be expected tha t form 511 w i l l be s t a b i l i z e d w i t h respec t to the equ i v a l en t c h l o r i n e i socyana te form (411) . F u r t h e r -more, 5 I I I shou ld be d e s t a b i l i z e d r e l a t i v e to 4 I I I . Both o f these deduc-t i o n s are c o n s i s t e n t w i t h the observed i n c r ease i n the XNC angle (X = H, C l ) on going from c h l o r i n e i socyana te to i s o c y a n i c a c i d ; l i k e w i s e , the s l i g h t decrease i n the NC bond i e n g t h and the s l i g h t i n c r ease i n the CO bond l eng th (see Table 5 .22 ) . Th is t rend i s cont inued when hydrogen i s rep laced w i t h the even more s t r o n g l y e l e c t r o n dona t ing methy l group (166) . 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 methy l i socyana te i s a l so g i ven i n Table 5 .22. I t w i l l be noted tha t the XNC angle (X = Methy l ) has widened to 140" (f rom 128 f o r X = H) w h i l e s imu l t aneous l y the NC bond has shortened and the CO one lengthened to the p o i n t where r(N-C) i s now sma l l e r than * The i o n i c form H+NC0 i s a l s o important but i s not r e l e v a n t to the present d i s c u s s i o n . 168 TABLE 5.22 M o l e c u l a r S t r u c tu r e s of Some I socyana tes . I socyanate r(X-N) r(N-C) r(C-O) /L(XNC) A(NCO) Method C1NC0 1.705 1.225 1.162 118° 50 ' 170° 52 ' MW HNCOb 0.975 1.209 1.166 128° 36 ' 180° c MW (0.997) (1.209) (1.166) (127° 29 ' ) (180° C ) MW CH3NCO 1.450 1.168 1.202 140° 16' 180° c ED (167) CH3NCO 1.44 1.207° 1.171° 140° 180° c MW (12) SiH 3NCO 1.699 1.150 1.179 180° 180° MW (13) SiH 3NCO 1.703 1.216 1.164 151° 42 ' 180° c ED (173) GeH3NCO 1.831 1.190 1.182 141° 18' 180° c ED (172) GeH3NCO 1 . 8 1 c 1 .19 C 1.18° 143° 180° c MW (174) PF 2NCO 1.683 1.256 1.168 130° 36 ' 180° c ED (171) S iF 3 NCO 1.648 1.190 1.168 160° 42* 180° c ED (173) S iC l 3 NCO 1.646 1.219 1.139 138° 180° c ED (175) SlMe 3NCO 1.76 1.20 1.18 150° 180° c ED (176) SiMe 3NCO 1.69 1 .15 C 1.18° 180° 180° MW (177) a Bond l eng ths are measured i n ?v. b F i r s t se t of numbers was obta ined us ing A I ° and LI° t o l o c a t e the hydrogen; second se t A I ° and A I ° used to l o c a t e H (see t e x t , s e c t i o n 5 .3 ) . b e r Assumed. ^ MW = Microwave; 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 app rop r i a t e resonance forms are (167) : Me Me \ Me N = C (T \ ,N C = 0 + _:N C ^ = 0 5 1 ' 511 ' 5 I I I * where 511 ' i s of much g r e a t e r importance than 5 I I I 1 . The s t r u c t u r e s o f a few az ide and i s o t h i o c y a n a t e molecu les have been c o l l e c t e d i n Tables 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 tha t these a l s o e x h i b i t t r ends s i m i l a r to t ha t d e s c r i b e d above. For the az ides t h i s may be a t t r i b u t e d to a d e s t a b i l i z a t i o n of 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 of X (X = C l , H, Me) : X \ X - N ^ = N N X \ X N N = N + + - N N w = N + + 5 1 " 511 " 5 I I I " where 5 1 1 " i s of s l i g h t impor tance . For the i s o t h i o c y a n a t e s the t rend i s a r e f l e c t i o n o f the combined e f f e c t of 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 5 I I I " ' (X = H, Me) : X \ X NEEEEC S X \ .N C=S + ~ J N r . = s + 5 1 " * 511"* 5 I I I " ' The obse r va t i on tha t each o f the az ides has a s m a l l e r XNY angle than the cor respond ing i socyana te (Y = N and C r e s p e c t i v e l y ) i s c o n s i s t e n t w i t h the sugges t ion tha t form 511" i s unimportant (168) . On the o ther hand, the s m a l l i n c r ea se i n the XNC angle on going from an i socyana te to the c o r r e s -ponding 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 to r a t i o n a l i z e ; e s p e c i a l l y s i n ce the NC bond l engths are i n the oppos i t e sense ( i . e . l onger f o r the i s o t h i o -cyana te ) . P a r t i c i p a t i o n o f the s u l f u r d - o r b i t a l s i n the NCS TT bonding i s 170 TABLE 5.23 M o l e c u l a r S t r u c t u r e s of Some A z i d e s . Az ide r (N x -N 2 ) r (N 2 -N 3 ) A ( XN X N 2 ) A ( N 1 N 2 N 3 ) Method C1N 3 1.745 1.252 1.133 108° 40 ' 171° 56 ' M W (14) H N 3 b 0.975 1.237 1.133 114° 8' 180° c M W (178) (1.004) (1.237) (1.133) (111° 57V) 180° C M W CH 3 N 3 1.468 1.216 1.130 116° 46» 180° c ED (167) C H 3 N 3 1.46 1 .24 C 1 .13 C 117° 180° c M W (179) S i H 3 N 3 <180° M W (180) GeH 3 N 3 1,845 1.250 1.140 119° 180° C ED (172) NCN 3 1.312 1.252 1.133° 120° 13 ' 180° C M W (154) a Bond l engths are measured i n A*. F i r s t se t of numbers ob ta ined u s i ng A l and A l to l o c a t e H; Si D second se t A l , and A l used to l o c a t e H. b c Assumed. TABLE 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 . XNCS r(X-N) r(N-C) r(C-S) A(XNC) Z.(NCS) Method HNCS a (0.989) (1.216) (1.560) (135°) ( 180 ° ) b MW (150) CH3NCS 1.479 1. 192 1.597 141° 3 5 ' 180° b ED (167) CH3NCS 1.45 1.216 b 1.561 b 147° 30 ' 180° b MW (12) SiH 3NCS 1.714 1.211 1.560 b 180° 180° MW (170) SiH 3NCS 163° 38 ' ED (171) PF 2NCS 1.686 1.221 1.553 140° 30 ' 180° b ED (171) Hydrogen s u b s t i t u t i o n p o s i t i o n determined us ing AI^ and A l ^ . Assumed. 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 quadrupole c o u p l i n g constants of HNCO, HNNN and HNCS p rov ide a d d i t i o n a l support 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 cha in i n a l l three m o l e c u l e s , a comparison o f x va lues i s v a l i d . These a r e : 3 3 X (HN ) = 4.65 ± 0.25 MHz (NH n i t r ogen ) (169) 3 3 -J X (HNCO) = 2.045 ± 0.038 MHz 3.3. X (HNCS) = 1.2 ± 0.2 MHz (149) aa 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) tha t acco rd ing to the s i m p l e s t v e r s i o n of the Townes D a i l e y theory x i s g i ven b y : 3 3 X = -U e Q q o i n ( U N ) = 10U MHz 5.13 A a a p x n 2 1 0 p r a r a * a Then s i n ce U i s c l e a r l y g r e a t e s t f o r resonance forms of type I I I and l e a s t P a f o r forms of type I I i t i s to be expected tha t HNCS which e v i d e n t l y has the 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 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 , to the extent to which the r e l a t i v e s i z e s of the three HNY angles q u a n t i t a t i v e l y r e f l e c t the importance of the v a r i o u s resonance fo rms , x 3 3 (HNCO) shou ld be c l o s e r to x (HNCS) than to x (HN„). Both deduc t ions aa aa J are i n agreement w i t h exper iment . 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 Tab les 5 .22 , 5.23 and 5.24. These were not mentioned i n the p rev ious d i s c u s s i o n because they are a l l thought to i n -vo l ve some degree of dir - pit bonding (between N and S i , Ge or P) . On the one hand, such bonding appa ren t l y p l ays a major r o l e i n de te rmin ing the s t r u c t u r e s of s i l y l i socyana te (74) and s i l y l i s o t h i o c y a n a t e (170) , both 172 of which have been shown to 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 . to have a l i n e a r SiNCX cha in ) . On the o ther hand, i t i s p robab ly of r e l a t i v e l y m ino r , but not i n s i g n i f i -c an t , importance i n the phosphorus and germanium compounds (171,172) . Th is t rend e v i d e n t l y cont inues across the p e r i o d i c t a b l e to c h l o r i n e (171 ) ; r e c a l l tha t c h l o r i n e i socyana te has been " f o u n d " to have e s s e n t i a l l y no drr - p-rr bonding ( 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 Tables 5.22 and 5.23 f o r both 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 . In the f i r s t one the hydrogen sub -s t i t u t i o n p o s i t i o n was determined from A I ° and A I ° ; i n the second ( i n a b b r a c k e t s ) , from A I ° and A I ° (see t e x t , s e c t i o n 5 .3 ) . The s i n g l e i s o t h i o -c yan i c a c i d s t r u c t u r e (Table 5.24) was obta ined u s i n g A I ° and A I ° t o l o c a t e the hydrogen ( 5 . 1 4 ) . For t h i s molecule the a l t e r n a t e approach was not p o s s i b l e , because A I ° was known on l y ve ry app rox ima te l y . C l e a r l y a comparison of the NH bond l engths i n these a c ids w i l l be v a l i d on ly i f the same method has been used to determine a l l of them. N e c e s s a r i l y , t h i s means the numbers i n b r a c k e t s . These are seen to decrease g r a d u a l l y w i t h i n c r e a s i n g HNX ang le . I t w i l l be r e c a l l e d tha t the C1N bond l engths e x h i b i t e d a s i m i l a r b e h a v i o 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 ea se i n a bond s t r e n g t h accompanying an i n c r ea se i n the s-charac te r of the n i t r o g e n atomic 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 fo rmat ion t o hydrogen (or c h l o r i n e ) . A com-p a r i s o n of the NH bond l eng ths found i n a number of s m a l l molecules i s presented i n Tab le 5 .25 . * I t i s i n t e r e s t i n g tha 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 these molecu les (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 very low frequency bending v i b r a t i o n (173) . 173 TABLE 5.25 Comparison of Some NH Bond Lengths. Molecule r(N-H) a Angles NH 3 b 1.014 A(HNH) = 107° 3' NHF 2 b 1.026 A(FNF) = 102° 5 4 ' ; A(HNF) = 99° 48 ' NH 2Cl b 1.017 Z.(HNC1) = ' 103° 4 1 ' ; Z.(HNH) = 107° MeNH2 1.011 A(HNH) = 105° 52 ' ; Z-(CNH) = 112° 18* Me 2NH b 1.022 Z.(CNC) = 112° 12' ; Z.(CNH) = 108° 48 ' PYRROLEb . 0.996 Z-(CNC) = 109.8°; planar HNCO 0.975(0.992) L. (HNC) = 128° 50'(127° 29 ' ) HN3 0.975(1.004) Z-(HNN) = 114° 8'(111° 57 ' ) HNCS (0.989) /L (HNC) = (135°) Measured i n X. Taken from Gordy and Cook (129) . 174 CHAPTER 6 THE MICROWAVE SPECTRUM OF CYANOGEN ISOCYANATE The e x i s t e n c e of a gaseous compound w i t h the fo rmula C2N2O was f i r s t p o s t u l a t e d by Okamoto and S h i r a i (181) du r ing t h e i r i n v e s t i g a t i o n of the hardening of s t e e l w i t h " c i t y gas " i n the presence of cyan ide . L a t e r Basco (182) , u s i ng the f l a s h p h o t o l y s i s t e chn ique , d i s cove red a t r a n s i e n t spec i es X among the products ob ta ined when cyanogen r a d i c a l s were reac ted w i t h mo lecu l a r oxygen. He surmised tha t X cou ld be any one of three s p e c i e s , namely: NCOCN, NCNCO o r NCOOCN. In 1970 Mayer (18) a g i t a t e d a m ix tu re of s i l v e r cyanate and cyanogen c h l o r i d e i n a sea led tube f o r two weeks and thereby ob ta ined 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 po l ymer i c substance wh i ch , when heated to above 150°C, depolymer ized i n t o gaseous monomer. The monomer was subsequent ly i d e n t i f i e d by mass spect rometry as 0 2 ^ 0 . Fu r the r i n v e s t i g a t i o n of t h i s system revea led tha t the p o l y m e r i z a t i o n process was l a r g e l y r e v e r s i b l e , and tha t , a l though the e q u i l i b r i u m was f a r on the polymer s i d e at room temperature , some monomer p e r s i s t e d f o r s e v e r a l hours i n r a p i d l y coo led samples ; a l s o , tha t monomer trapped as a wh i te 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 po l ymer -i z e d r a p i d l y . On the b a s i s o f a l i m i t e d study of the chemis t ry of the monomer, Mayer suggested tha t i t was the i socyana te (NCNCO) r a t h e r than the d i cyano-ox ide (NCOCN). Th i s c o n c l u s i o n was then supported by an a n a l y s i s o f the i n f r a r e d spectrum which was i n t e r p r e t e d as i n d i c a t i n g tha t the molecu le had a l i n e a r s t r u c t u r e i n the gas phase but a bent one i n the s o l i d phase. In a d d i t i o n , Mayer specu la ted tha t the spec i e s X . d i s cove red by Basco was p robab ly a l s o cyanogen i s o c y a n a t e . 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 thermal decompos i t ion products of s i l v e r cyanate which he i d e n t i -f i e d through mass spect rometry and i n f r a r e d spec t roscopy as be ing i d e n t i c a l to tha 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 . Desp i t e the f a c t tha t G o t t a r d i ' s p r e p a r a t i o n of NCNCO g i v e s a much s m a l l e r y i e l d than M a y e r ' s , i t was the one tha t was used to o b t a i n the samples r e q u i r e d f o r the microwave study desc r ibed here because i t i s a l so much the e a s i e r to pe r fo rm. Only the n a t u r a l l y most abundant i s o t o p i c spec i es ( ^ N ^ C ^ N ^ C ^ O ) was i n v e s t i g a t e d , a l though samples a r t i f i c i a l l y en r i ched w i t h n i t r o g e n - 1 5 , carbon-13 o r oxygen-18 shou ld not be d i f f i c u l t to p r epa r e , and w i l l hope -f u l l y be s t u d i e d at some f u t u r e da te . 6.1 Assignment of the Spectrum. A rough probable spectrum was p r e d i c t e d us ing the f o l l o w i n g reasonable s t r u c t u r a l model : a l i n e a r molecu le w i th r(N-C) = 1.218 X ( a l l three) and r(C-O) = 1.165 A* (bond l eng ths as i n c h l o r i n e i s o c y a n a t e ) . S i n g l e t r a n s i t i o n s , each hav ing on l y a second o rde r S ta rk e f f e c t , were them expected a t : v = 2B(J+1) . f o r J->J+1 6.1 W i t h B = 2.4 GHz A p r e l i m i n a r y examinat ion of the spectrum revea led tha t the assumption of a l i n e a r mo lecu le was i n c o r r e c t . Very complex groups o f s t rong low f i e l d abso rp t i on l i n e s were found at i n t e r v a l s o f rough ly 5.3 GHz. These were soon recogn ized as t y p i c a l a-type R-branch t r a n s i t i o n s (J-hJ+1, AK_^  = 0) of a near p r o l a t e asymmetric r o t o r ; i . e . a bent mo l e cu l e . I t was then s t r a i g h t f o r w a r d to a s s i g n J v a lues to each group s i n c e : v « (B+C)(J+1) « (5.3GHz)( J+l ) 6.2 group 176 A d d i t i o n a l confirmation of group assignments was r e a d i l y obtained by counting the number of Stark lobes associated with each of a few selected strong t r a n s i t i o n s (46). During the course of the i n i t i a l s o r t i n g out process, i t became quite apparent that there were f a r more absorption l i n e s i n each group than could be accounted f o r i n terms of j u s t the ground v i b r a t i o n a l s t a t e . Evidently t r a n s i t i o n s were also being observed between r o t a t i o n a l states of molecules i n a s i g n i f i c a n t number of d i f f e r e n t excited v i b r a t i o n a l s t a t e s . The K_^ = 1 t r a n s i t i o n s were the f i r s t l i n e s to be i n d i v i d u a l l y assigned. These occur as p a i r s of small sub-groups roughly equally spaced on e i t h e r side of each main group. They were i d e n t i f i e d by t h e i r p o s i t i o n i n the spectrum and by 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 (see c h l o r i n e isocyanate, se c t i o n 4.1). The strongest component of each sub-group was immediately assigned as the appropriate ground v i b r a t i o n a l state t r a n s i t i o n . The remaining four to seven prog r e s s i v e l y weaker l i n e s spaced out to higher frequency, at i n t e r v a l s of roughly 20 MHz,were then t e n t a t i v e l y assigned as the same t r a n s i t i o n i n excited v i b r a t i o n a l states attained by successive e x c i t a t i o n of the lowest frequency v i b r a t i o n ; i . e . v =0, 1, 2, 3, • • • and {v^ = 0}^ except i * £, where % designates the lowest frequency v i b r a t i o n . From the r e l a t i v e i n t e n s i t i e s of corresponding r o t a t i o n a l t r a n s i t i o n s i n the ground and f i r s t excited v i b r a t i o n a l state was estimated to be 144 ± 40 cm \ In a d d i t i o n , a few weak t r a n s i t i o n s were observed close to each ground state l i n e . These probably belong to excited v i b r a t i o n a l states i n which one of the higher .frequency v i b r a t i o n s has been * s i n g l y excited. They were not considered f u r t h e r . One such K . = 1 sub-* The lowest frequency i n f r a r e d absorption reported by Mayer l i e s at 365 cm the next at 455 cm 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 gu re 6 . 1 . The d e t a i l e d a n a l y s i s of the main groups proved to be c o n s i d e r a b l y more t ed ious because of s i g n i f i c a n t ove r l app ing of the se t s of t r a n s i t i o n s 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 . the f o r t u i t o u s l y b e t t e r behav io r o f c h l o r i n e i s o c y a n a t e ) . I n d i v i d u a l t r a n s i t i o n s be long ing to one v i b r a t i o n a l s t a t e were found to occur at p r o g r e s s i v e l y h i ghe r f r e -quencies w i t h i n c r e a s i n g K ^, w h i l e se ts of t r a n s i t i o n s a s s o c i a t e d w i t h 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 so observed to s h i f t to h ighe r f r equenc i es w i t h i n c r e a s i n g v . Consequent ly , each main group was i n i t i a l l y t a c k l e d at i t s low f requency 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 immediate ly by an a t t a ck on the h i g h e r K_^ l i n e s of t h i s same v i b r a t i o n a l s t a t e . Next the t r a n s i t i o n s be long ing to 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 were c o n s i d e r e d , aga in s t a r t i n g w i t h the K_^ = 0 l i n e , and so on . 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 s t r i c t l y second order S t a rk e f f e c t ; a l l o f the h i ghe r K ^ main group t r a n s i t i o n s have a f i r s t o rde r S ta rk e f f e c t . Most of the = 2 t r a n s i t i o n s were found to have a s m a l l asymmetry s p l i t t i n g . Th is and the r e s u l t i n g c h a r a c t e r -i s t i c S t a rk component behav io r ( a g a i n , see c h l o r i n e i s o c y a n a t e , s e c t i o n 4.1) g r e a t l y f a c i l i t a t e d t h e i r ass ignment . T r a n s i t i o n s between r o t a t i o n a l s t a t e s w i t h K_j va lues g r ea t e r than 2 d i d not 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 tu 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 to s o r t ou t . S e ve r a l a c c i d e n t a l co inc idences of t r a n s i t i o n s be long ing to 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 f u r t h e r compl i ca ted 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 i n the a n a l y s i s o f these complex g roups . The r e a d i l y ass igned = 0 , 1, and 2 t r a n s i t i o n s were f i t to a t runca ted Watson Hami l t on i an c o n t a i n i n g r ^ j r > n the minimum number of r e q u i r e d terms ( u s u a l l y j u s t A, B, C, A ^ , A J K > v H K j / ^ * FIGURE 6.1 Schematic I l l u s t r a t i o n of the Cyanogen Isocyanate 6. , — 5, _ se t of T r a n s i t i o n s , 1,6 1,5 31480 31500 31520 31540 31560 v (MHz) V 1 v * = 2 V 6 V 5 V 4 V 3 G.V.S . 179 T h i s , i n t u r n , gave moderate ly good p r e d i c t i o n s f o r the f r equenc i e s of the h ighe r K_^ a-type t r a n s i t i o n s . These were then e a s i l y l o c a t ed and s u c c e s s -i v e l y added to the l e a s t squares f i t . In t h i s way, a l l of the s t ronge r l i n e s be long ing to the a^-type R-branch groups were e v e n t u a l l y g i ven r e a s o n -able ass ignments . A search f o r b-type t r a n s i t i o n s was then under taken. 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 throughout the spectrum i t was c l e a r tha t such t r a n s i t i o n s had to be p r e sen t . They belong to the tx^o s e r i e s : J Q J — ( J-l )^ J _ J and J j — ( J - l )2 j _ 2 * P r e d i c t i o n s were made us ing the da ta e x t r a c t e d from the p reced ing a n a l y s e s , but these were q u i t e i n -accura te because the b-type f r equenc i es are a l l s t r o n g l y dependent on A whereas the a-type R-branch f r equenc i es are n e a r l y independent of A. F o r -t u n a t e l y , the r e l a t i v e spac ings of the l i n e s i n both b-type s e r i e s are e s s e n t i a l l y independent of A and cou ld t h e r e f o r e be p r e d i c t e d reasonab ly w e l l . A c c o r d i n g l y , assignments were made u s i ng a t r i a l and e r r o r p rocedure . A l i k e l y l o o k i n g cand idate f o r the f i r s t s e r i e s would be chosen from one of the l e s s c l u t t e r e d r eg ions of 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 of t h i s same s e r i e s , at the f r equenc ies 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 ass igned 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 co r r e c tness of the a s s i g n -ment was e a s i l y checked. Once the f i r s t s e r i e s had been c o r r e c t l y s o r t e d out a s i m i l a r procedure would be a p p l i e d to the second s e r i e s . The former y i e l d s an accura te va lue f o r on ly 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 ; i . e . A = A - A . The l a t t e r then permi ts the separate de te rm ina t i on 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 owed by those of 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 to 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 s t a t e (v = 2 ) . A c o n s i s t e n t set of assignments cou ld not be found. Th is was not d i s c o n c e r t i n g , however, s i n c e the l i n e s sought a f t e r were expected to be very weak. 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 absorp t ions were not s t r o n g ; c e r t a i n l y they were much weaker than the cor respond ing j i-type R-branch l i n e s . From the l a t t e r obse r va t i on i t was concluded tha t u was s i g n i f i c a n t l y l a r g e r than u . cl D S ince the a-component of the d i p o l e moment was apparen t l y r a t h e r l a r g e , a search was a l so made f o r the i n h e r e n t l y weak a-type Q-branch t r a n s i t i o n s be long ing to the two s e r i e s : J 1 1 — J . and J „ _ — J Wi th the a i d o f what were by now very good f requency 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 abso rp t i ons 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 observed 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 these were ve ry weak, no attempt was made to extend the coverage to h ighe 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 . The a n a l y s i s scheme desc r i bed above l e d to appa ren t l y reasonable 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 of the weaker, abso rp t ions observed i n the f requency range 8 - 3 7 GHz. None-t h e l e s s , because the assignment process had been based to a l a r g e extent on the i n t e r n a l cons i s t ency 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 f i t s , i t seemed d e s i r a b l e to 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 double resonance exper iments were at tempted. 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 gu re 6 . 2 . The exper imenta l d e t a i l s were des c r i bed i n s e c t i o n 3 .5 . Both exper iments 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 ass ignments . Then, by i n f e r e n c e , s i n ce 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 scheme comple te l y p a r a l l e l e d the ground s t a t e one, i t too must be e s s e n t i a l l y c o r r e c t . 181 FIGURE 6.2 Schematic I l l u s t r a t i o n of the Two Microwave - Microwave Double Resonance Experiments Performed on Cyanogen I socyanate . 16 0,16 observe (v = 18770.20 MHz) 15 1,14 pump (v = 12102.40 MHz) 15 1,15 39 1,38 observe (v = 27905.72 MHz) T 38 2,36 pump (v = 9191.27 MHz) 38 2,37 E R ( 1 6 Q 1 6 ) = 719.973 GHz E R ( 1 5 1 u ) = 713.305 GHz E D ( 1 5 . .,) = 701.203 GHz K. 1, 1 J E R ( 3 9 1 3 8 ) = 4 2 3 7 . 5 0 1 GHz E r , ( 3 8 0 -,) = 4218.787 GHz K Z , j o E R ( 3 8 2 3 ? ) = 4209.596 GHZ 182 Many of the measured cyanogen i socyana te abso rp t ions were observed to be r a t h e r b road . A few of 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 idths at h a l f he igh t of over 1 MHz. C l e a r l y both e f f e c t s may be a t t r i b u t e d to the presence of unreso l ved 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 nuc l ea r quadrupole c o u p l i n g : The two n i t rogen-14 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 to 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 expe r imenta 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 h i ghe r r e s o l u t i o n i t should be p o s s i b l e to s p l i t some of the broadest 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 determine the n i t r o g e n nuc l ea r quadrupole c o u p l i n g c o n s t a n t s . 6.2 De te rmina t ion of M o l e c u l a r Constants from the Microwave Spectrum. Dur ing the p r e l i m i n a r y stages o f t h i s work i t became q u i t e apparent tha t cyanogen i socyana te 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 . In p a r t i c u l a r , a p l o t of the f r equenc i e s ( co r rec ted f o r asymmetry) o f the J = 5-»-6 a-type 2 R-branch, 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 v s . K_^ (reproduced i n * F igu re 6.3) gave a smooth curve r a t h e r than the expected s t r a i g h t l i n e . Th is i n d i c a t e s tha 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 to the t o t a l r o t a t i o n a l e n e r g i e s . Consequent ly , a l though a p l ana r s t r u c t u r e seemed to be a reasonable s u p p o s i t i o n , no attempt was made to f i t the spectrum to a f ou r tau Hami l t on i an ( i . e . equa t ion 2 .18 ) . Ra the r , the more gene ra l fo rma l i sm of Watson was used. 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 , terms were cons i de r ed . A thorough treatment was a p p l i e d to both 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 . For the h ighe 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 near 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 shou ld g i ve a ve ry good s t r a i g h t l i n e , at l e a s t f o r l o w i s h J . Th i s i s the observed behav io 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 Frequenc ies (Cor rec ted f o r Asymmetry) of the a-Type R-Branch T r a n s i t i o n s of NCNCO (G.V.S. ) v s . K 2 . 31770 +- 1 1 1 . r 0 5 i 10 15 20 25 184 to use a much s i m p l i f i e d procedure . The former a n a l y s i s i s d i s cussed immediate ly be low, the l a t t e r , toward the end of t h i s s e c t i o n . To beg in w i t h a s t r i c t l y f i r s t o rder t rea tment , i n p r i n c i p l e i d e n t i c a l to tha t desc r i bed i n s e c t i o n 4 . 2 , was at tempted. In t h i s case , the ze ro th o rder H a m i l t o n i a n was H 3 as de f i ned by equa t ion 2 .19b, and the p e r t u r -b a t i o n Hami l t on i an was H, + H as de f i ned by equat ions 2.19c and 2 .22 . d s • M The f i r s t o rder d i s t o r t i o n energ ies were then g i ven by equat ions 2.23c and 2 .23d. As b e f o r e , l e a s t squares f i t s were made to the d i f f e r e n c e s v ^ " v r where v i s a r i g i d r o t o r f requency c a l c u l a t e d us ing t r i a l r o t a t i o n a l c o n -s t an t s and v ^ i s t n e co r respond ing observed f requency . A g a i n , 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 cons tants were a l l o w e d . I t was immediate ly d i s cove red tha t there 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 to permi t the de t e rm ina t i on 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 . By a process of e l i m i n a t i o n ( l i k e tha 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 ac id ) the i nde te rmina te s e x t i c cons tants were i d e n t i f i e d and then removed from the f i t ; a l l f i v e q u a r t i c constants were r e q u i r e d . Once an a p p r o p r i a t e , t r u n -c a t e d , v e r s i o n of the Hami l t on i an had been a r r i v e d a t , the l e a s t squares f i t was repeated once more, u s i n g the most recent v a l ues of the r o t a t i o n a l c o n s t a n t s , to ensure tha t a s t a b l e s o l u t i o n had been found. The end r e s u l t o f such a f i r s t order a n a l y s i s , c a r r i e d out on the ground v i b r a t i o n a l s t a t e spectrum of cyanogen i s o c y a n a t e , i s presented i n Table 6 . 1 . Next the d e r i v e d f i r s t order constants were used i n the f u l l m a t r i x scheme to r e - c a l c u l a t e the f r equenc i e s of 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 cor respond ing " e x a c t " and f i r s t order f r equenc i es were found to be i d e n t i c a l . However, f o r t r a n s i t i o n s be long ing to the two s e r i e s J ^ j ^ — ( J - l ) 2 j _ 2 a n c * J 2 J 2 — J2 J 1 s m a H d i s c r e p a n c i e s were observed. E v i d e n t l y , 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 185 TABLE 6.1 R o t a t i o n a l C o n s t a n t s 3 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 3 of Cyanogen Isocyanate i n the Ground V i b r a t i o n a l S t a t e . F i r s t Order Exact SDFIT No. Trans. A J x l ° A J K X 1 ° 3 -1 A K x l O 6 x l O 4 6 R x l 0 2 H j x l 0 8 h j X 1 0 9 0.096 61 74358.668 ± 2699.0365 ± 2597.8656 ± 1.0815 ± -5.2702 ± 8.6249 ± 2.0580 ± 2.7517 ± -1.5978 ± -1.962 ± 2.590 ± 0.081 0.0034 0.0031 0.0117 0.0071 0.0038 0.0118 0.0736 0.0325 0.193 0.324 0.096 61 74358.690 ± 2699.0367 ± 2597.8663 ± 1.0904 ± -5.2713 ± 8.6254 ± 2.0694 ± 2.6929 ± -1.6024 ± -0.0535 ± 1.026 ± 0.081 0.0033 0.0031 0.0116 0.0071 0.0038 0.0117 0.0732 0.0323 0.192 0.322 Large C o r r e l a t i o n s (|p >0.9) p (A j - A J K ) = 0 .908 ; p ( A J K - H^) = 0 .927 ; p(&3 - 6 R ) = -0.968 p(6j - hj) = 0 .986 ; p ( 6 K - h j ) -0.930 Measured i n MHz. Standard D e v i a t i o n of the F i t . Number of t r a n s i t i o n s used i n the a n a l y s i s . Standard e r r o r s . 186 of 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 not 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 us ing an i t e r a t i v e procedure f i r s t suggested by P i e r c e et a l . (183) and subsequent ly f u r t h e r developed by Helminger et a l . (34 ,184 ) . In t h i s , the d i f f e r e n c e between the c a l c u l a t e d f i r s t o rder and " e x a c t " f r equenc ies ( V f ^ r s t a n ^ v e x a c t r e s p e c t i v e l y ) of a g i ven t r a n s i t i o n i s taken to 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 to the cor respond ing observed f requency . The c o r r e c t e d observed f r e q u e n c i e s , v ^ g ' j a r e then re-ana lysed us ing the f i r s t o rder theo ry . That i s , w i t h the d i s t o r t i o n energ ies c a l c u l a t e d from equat ions 2.23c and 2 .23d , a l e a s t squares f i t i s made to the d i f f e r e n c e s c o r r , v , - v where: obs r c o r r , -v r i v , = v , - (v - v r , . ) 6.3 obs obs exact f i r s t The r e s u l t i n g new constants are then i n t u r n used to r e - c a l c u l a t e the v e x a c t and the c y c l e i s r epea ted . The v f . ._ are always taken to be the most recent X. X ITS L set o f f i r s t o rder f r e q u e n c i e s . 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 -menta l adjustments of the i npu t r o t a t i o n a l c o n s t a n t s . For cyanogen i s o -cyanate s t a b l e r e s u l t s were obta ined a f t e r two i t e r a t i o n s . The f i n a l se t 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 constants i s compared w i t h the c o r r e s -ponding se t o f f i r s t o rder constants i n Tab le 6 . 1 . I t w i l l be noted tha t 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 r o t a t i o n a l constants and most o f the d i s t o r t i o n cons t an t s . C l e a r l y , i n the f i r s t o rde r t reatment 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 h j and H 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 Table 6 . 2 . For 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 on l y a few 187 TABLE 6.2 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 C o n s t a n t s 3 of Cyanogen Isocyanate 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 S t a t e . F i r s t Order Exact SDFIT No. T r ans . ' A, B 1 V 1 0 A J K X 1 ° ] -1 A K x l 0 Sj-xlO 4 6 K x l 0 2 H j X 1 0 8 0.134 35 82777.563 ± 2704.3294 ± 2599.7717 ± 1.2457 ± -6.7709 ± 15.0445 ± 2.0952 ± 7.6053 ± -3.0256 ± -1.536 ± 0.160 0.0060 0.0058 0.0189 0.0129 0.0079 0.0100 0.1361 0.0554 0.333 0.126 35 82777.808 ± 2704.3222 ± 2599.7778 ± 1.2401 ± -6.7712 ± 15.0581 ± 2.1701 ± 7.1198 ± -3.0275 ± . 0.642 ± 0.150 0.0057 0.0055 0.0177 0.0121 0.0074 0.0094 0.1273 0.0520 0.312 Large C o r r e l a t i o n s (|p[>0.9) p ( A J " A J K } = ° ' 9 0 1 ; p ( A J K " H K J ) = ° ' 9 4 9 ; p ( < S J _ V = - ° ' 9 7 8 Measured i n MHz. Standard D e v i a t i o n of the F i t . Number of t r a n s i t i o n s used i n the a n a l y s i s . Standard e r r o r s . 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 d i s t o r t i o n ana lyses 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 scope. They y i e l d e d accura te va lues 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 , but on l y ve ry approximate va lues of A. The l a t t e r was to be expected of course due to the l a ck 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 cons tants were A , A J JK and H . S ince none of the observed t r a n s i t i o n s were of the type pre-v i o u s l y found to 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 order treatment was used i n each case . The r e s u l t s have been c o l l e c t e d i n Table 6 . 3 . A few a d d i t i o n a l very weak a b s o r p t i o n s , not r epor ted he re , were t e n t a t i v e l y a t t r i b u t e d to s t i l l h i ghe 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 . No attempt was made to determine mo lecu l a r constants from these measurements because o f the tenuous nature of the ass ignments . I t shou ld be po in t ed out tha t one of the s e x t i c c o n s t a n t s , namely H , K neg l e c t ed 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 ana l y se s , i s not l i k e l y to be comple te ly i n s i g n i f i c a n t . Ra ther , i t was i n sepa r ab l e from the A and A cons tan ts because o f an i n s u f f i c i e n c y of d i f f e r e n t types o f t r a n s i t i o n s . The a d d i t i o n a l b-type t r a n s i t i o n s which are r e q u i r e d t o d e t e r -mine IL^ l i e i n the mm-wave r e g i o n . The net r e s u l t of t h i s i s tha t the numbers r epo r t ed here f o r A and hv are not e x a c t l y c o r r e c t . They are i n IX ~* * f a c t r e a l l y va lues of the e f f e c t i v e constants A and A where: A* — A - 4Hj, + • • • 6 . 4a * AT, s A„ - 51^ + ••• 6.4b An es t imate of H may be obta ined by doing a very s imple c a l c u l a t i o n f i r s t suggested by Po lo (165) . Th i s author has proposed tha t f o r q u a s i -l i n e a r molecu les the r o t a t i o n about the l e a s t moment of i n e r t i a w i l l be so s t r o n g l y coupled to the bending v i b r a t i o n s tha t i t i s probab ly best 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 Constants o f Cyanogen Isocyanate i n H igher 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 = 2) T h i r d (v = 3) SDFIT 0.127 0.083 No. T rans . 15 12 A 90431.5 ± 3 5 9 0 . l b V 117342.8 ± 4718.5 B 2708.320 + 0.014 V 2711.191 ± 0.012 C 2601.244 ± 0.017 V 2601.659 ± 0.012 A j X 1 0 3 0.931 ± 0.180 1.333 ± 0.189 A_ x l O 1 -9.149 ± 0.029 JK -13.361 ± 0.052 R ^ x l O 3 -6.82 ± 0.17 -19.20 + 0.50 Large C o r r e l a t i o n s (|p|>0.9) v £ 2: p ( A J K - H R J ) = 0 .977 ; v £ = 3: p(A JK " HKJ> = ° ' 9 8 6 a. Measured i n MHz. D S tandard e r r o r s . TABLE 6.4 Cyanogen Isocyanate C o n s t a n t s 3 C a l c u l a t e d Us ing P o l o ' s R e l a t i o n s . Ca lcu lated^ 5 Observed c Cor rec ted A 88.25 86.254 K 87.824 Ev 0.314 K \ - \ 9008.5 8419.2 A 74358.690 o 74359.946 Measured i n MHz. C a l c u l a t e d u s i n g equat ions 6 . 5 . Observed constants co r r e c t ed us ing equat ions 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 p o t e n t i a l f o r the v i b r a t i o n a l mot ions ; j u s t as i s done f o r d i a tomic molecu les (185) . I t f o l l o w s t h a t , i f i s the v i b r a t i o n by which the molecu le can achieve the l i n e a r c o n -f i g u r a t i o n , and a l l o the r degrees o f freedom are n e g l e c t e d , then i n the harmonic approx imat ion (165) : A si 4A3/CLV 6 .5a Js. O D - A Q — bA^/o^ + 60A3 )/to2 j 6 .5c For cyanogen i s o c y a n a t e , i f i t i s assumed tha t co, = co. = 144 cm * and A D IL Q i s taken to be 74358.6 MHz then one ob t a i n s the r e s u l t s g i ven i n Table 6 .4 . The c a l c u l a t e d A^ and A^ - A q va lues are seen to be i n ve ry good agreement w i t h the expe r imen ta l numbers. However, i n v iew of the l a r g e u n c e r t a i n t y i n o)^  and the approximate na ture o f the c a l c u l a t i o n t h i s must be regarded as f o r t u i t o u s . S t i l l , i t seems reasonable to assume tha t the c a l c u l a t e d H va lue i s o f s i m i l a r accuracy . A c c o r d i n g l y t h i s number has been used to convert the e x p e r i m e n t a l l y determined A q and va lues i n t o h o p e f u l l y more accura te r e s u l t s . The c o r r e c t i o n s , a l though s m a l l , are not i n s i g n i f i c a n t . I t i s l i k e l y tha t H^ i s much l a r g e r than any of the o the r 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 , j u s t as A i s much l a r g e r than any of the q u a r t i c d i s -K t o r t i o n c o n s t a n t s . Hence, the o ther neg l e c t ed s e x t i c d i s t o r t i o n cons tants have p robab l y not produced a s i m i l a r b i a s s i n g of any of the r o t a t i o n a l cons t an t s . 6.3 The M o l e c u l a r S t r u c t u r e of Cyanogen I socyana te . The moments of i n e r t i a and the i n e r t i a l de f ec t of cyanogen i socyana te i n i t s ground v i b r a t i o n a l s t a t e are presented i n Table 6 . 5 . 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 ana r e q u i l i b r i u m s t r u c t u r e . A l though 191 TABLE 6.5 The Moments of I n e r t i a and the I n e r t i a l Defect o f Cyanogen Isocyanate 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 Mo l e cu l a r S t r u c t u r e of Cyanogen I socyana te . Assumed C a l c u l a t e d 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 ana r molecu les t y p i c a l l y have i n e r t i a l de fec t s of the order of 0.1 a.m.u.A^ (59 ,61 ) , l a r g e r v a l u e s , s i m i l a r to that r epor ted here f o r NCNCO, are not unknown. For example, s u l f u r d i c y a n i d e , which has been c l e a r l y shown to be a p l ana r m o l e c u l e , has an i n e r t i a l de fec t of 0.4869 a .m.u . X 2 i n i t s ground v i b r a t i o n a l s t a t e (162) . Such an o v e r s i z e d A ° i s of course to be expected whenever the molecu le i n ques t i on has a low frequency i n-p l ane bending v i b r a t i o n . In the present case , 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 (equat ion 2 .57 ) , y i e l d s an es t imate f o r OJ^  of 136 cm Th i s i s i n e x c e l l e n t agreement w i t h the -1 * va lue 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 support f o r the p l ana r s t r u c t u r e hypo thes i s i s p rov ided by the complete absence of any c^type t r a n s i t i o n s i n the observed spectrum. How-eve r , these t r a n s i t i o n s would a l s o be unobservab ly weak f o r a s l i g h t l y n o n -p l ana r molecu le w i t h an a p p r o p r i a t e l y s m a l l y c » Thus, a l though the p r e s e n t l y a v a i l a b l e ev idence s t r o n g l y suggests tha t cyanogen i socyana te i s a p l ana r m o l e c u l e , a d e f i n i t i v e p roof must await the study of f u r t h e r i s o t o p i c s p e c i e s . In the i n t r o d u c t i o n to t h i s chapter i t was mentioned tha t Mayer s t r o n g l y favored the i socyana te (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 cyanate (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 of "cyanogen i s o c y a n a t e " . The present microwave study suppor ts t h i s c o n t e n t i o n : I f the molecu le was r e a l l y the cyanate , and p l a n a r , then i t would have symmetry and hence e i t h e r a- or b-type t r a n s i t i o n s , but not b o t h . A complete de t e rm ina t i on of the mo lecu 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 throughout tha t the lowest f requency v i b r a t i o n i s i n f a c t an i n-p l ane bending v i b r a t i o n ; s p e c i f i c a l l y , the one tha t i n v o l v e s l a r g e l y a deformat ion of the CNC angle (see p rev ious s e c t i o n ) . FIGURE 6 . 4 The Mo lecu l a r S t r u c tu r e of Cyanogen I socyanate . 194 s i b l e w i thout a d d i t i o n a l i s o t o p i c d a t a . In f a c t , on l y two u s e f u l p i eces of 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° (1° = 1° + I.° + A° ) . a b c a b Hence at most on 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 then on ly a f t e r a l l of the remain ing ones have been g i ven assumed v a l u e s . The two parameters which are l i k e l y to be the most d i f f i c u l t to es t imate a c c u r -a t e l y are the nomina l l y s i n g l e NC-NCO bond l eng th and the CNC ang le . A c c o r d i n g l y these were chosen as the two a l lowed v a r i a b l e s . A s o l u t i o n of the moment of i n e r t i a equat ions was then obta ined a f t e r the f o l l o w i n g assumptions had been made: (1) a p l ana r m o l e c u l e , (2) l i n e a r NCN and NCO c h a i n s , (3) cyanide and i socyana te bond l eng ths the same as i n cyanogen az ide (154) and c h l o r i n e i socyana te r e s p e c t i v e l y (44 ) . S ince a l l th ree of the assumed i n t e r n u c l e a r d i s t a n c e s are a s s o c i a t e d w i t h m u l t i p l e bonds , i t i s l i k e l y tha t the numbers used here are good approx imat ions to the t rue NCNCO bond l e n g t h s . The assumption of l i n e a r NCN and NCO cha ins i s not so e a s i l y j u s t i f i e d because bends at carbon of over 5° are w e l l known f o r both cyanides (162) and i socyana tes (44) . Th i s g i ves r i s e to 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 parameters , e s p e c i a l l y the CNC ang le . The r e s u l t s have been c o l l e c t e d i n Table 6 . 6 . The mo l e cu 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 ipo l e Moment Measurements. The measurement of the d i p o l e moment of cyanogen i socyana te was under -taken w i t h the p r i o r knowledge tha t there were nonzero components of u a long at l e a s t the a- and b - p r i n c i p a l i n e r t i a l axes . T h i s was c l e a r l y e v i -dent through the o b s e r v a t i o n of both a- and b_-type t r a n s i t i o n s . The c_-component of the d i p o l e moment was presumed to be z e r o . For a t r u l y p l a n a r molecu le must be i d e n t i c a l l y zero by symmetry. At w o r s t , NCNCO can be on l y s l i g h t l y nonp l ana r , i n which case u^.would be nonzero but ve ry s m a l l . 195 The i n d i v i d u a l S ta rk components of the low J a-type R-branch t r a n s -i t i o n s were found to be e a s i l y r e s o l v a b l e . U n f o r t u n a t e l y a l l of these have f i e l d induced frequency s h i f t s which are s t r o n g l y dependent on u 3. but which are n e a r l y independent of u^. Hence, they were s u i t a b l e on l y f o r the de t e rm ina t i on of the former component. S t a rk measurements were made on f o u r such l o b e s , namely: 2 0 , 2 - V l ' M J = 1 1 2 1 , 2 - 1 1 , 1 ' M J = ° 21,1 - ^ . O ' M J " 0 30,3 - 20,2> M J - 0 These were s e l e c t e d from amongst the many a v a i l a b l e s i m i l a r a-type lobes 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 : (1) they e x h i b i t a l a r g e , s t r i c t l y second o r d e r , S t a rk e f f e c t , (2) they occur i n a convenient r e g i o n o f the spectrum (X- and P-band) and (3) they are not i n t e r f e r e d w i t h by any o the r abso rp t i ons over the range of f i e l d s used. Then, i n order to o b t a i n a good va lue f o r i t was necessary a l so to measure the S t a rk e f f e c t o f a b-type t r a n s i t i o n . As w i t h i s o c y a n i c a c i d , none of 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 requency range of our spect rometer had r e s o l v a b l e S ta rk components and consequent ly there was no a l t e r n a t i v e but to make use of an aggregate l o b e . A g a i n , i t was found tha t f o r t r a n s i t i o n s be long ing to the s e r i e s JQ J — ( J - l ) ^ j j t n e s t r onges t and f a s t e s t o f the i n d i v i d u a l S ta rk components move out n e a r l y together 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 spec t ab l e l o o k i n g aggregate l o b e s . Seve ra l d i f f e r e n t t r a n s i t i o n s were cons idered be fo re the 15Q — 14^ ^ one was s e l e c t e d as the bes t c and ida te . Th is t r a n s i t i o n , of a l l the a v a i l a b l e b-types , not on ly has the l a r g e s t S ta rk e f f e c t but a l s o one of the sharpest aggregate l o b e s . The l a t t e r i s due to 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 of the Mj dependence of the i n d i v i d u a l S t a r k components. 196 In the gene ra l exp re s s i on f o r the frequency s h i f t of these components (equat ion 6 .6e ) , the M dependent u term i s of s i m i l a r magnitude but oppos i t e s i g n to the M^ dependent y^ te rm. At f i e l d s of up to s e v e r a l thousand Vo l ts/cm t h i s aggregate lobe i s a c t u a l l y narrower than the i n d i -v i d u a l quadrupole broadened S ta rk components of some of the low J a-type R-branch t r a n s i t i o n s . Express ions f o r the average f requency s h i f t s of the v a r i o u s S ta rk com-ponents , c o r r e c t to second o r d e r , were obta ined us ing the procedure des c r i bed i n s e c t i o n 5 .4 . These a r e : [Av ] 9 + 1 , + 1 = F (£ ) J23 .374x l0 _ 6 y 2 + 1 . 5 8 4 1 x l 0 " 6 y 2 [ 6 .6a U + 1 = F( f f ) | .374x10 y + 1. 1x1  V [ Z 0 , 2 , " i V l ' 3 b [Av] = F(£')]23.599xlC" 6 2 1 1 " ~ 6 2 Z 1 , 2 ' U -v~6_ 2 , n , . - 6 2 6.6b 2 , , 0 — 1 . . , 0 =  HE){23.599xl<f\£ - 1.1771xlO" bMjJ 1, i. 1,1 [ A v ] 2 q x Q « F ^ ^ S . l S S x l O " 6 ^ 2 + 0 . 2 6 7 4 x l 0 _ 6 u 2 } 6.6c 1,1 1,0 ' [Av]_ n , n = F(£){-4.7945xl0"" 6y 2 - 0.2066x10 6 y 2 } 6.6d J 0 , 3 5 0 , 2 , U a D [Av] . , = F(E)|(-0.02751xl0-6 + 0 . 2 9 0 6 9 x l 0 _ 8 M 2 ) y 2 0,15 J 1,14 J J a + ( 1 7 . 4 8 6 x l 0 - 6 - 9 . 8 4 0 0 x l 0 - 8 M 2 ) y 2 } - 6.6e J b ' w h e r e 7(E) = ( 0 . 5 0 3 4 4 ) 2 ( V 2 + V 2 ) / r 2 6.7 o m c and the Av are measured i n MHz i f V , V are i n v o l t s , r i s i n cm and y , o ' m ' c a ' y^ are i n Debyes. The cyanogen i socyana te S ta rk measurements have been c o l l e c t e d i n Tab le 6 . 7 . These were made e n t i r e l y i n c e l l 1. For each l o b e , a p l o t of - 2 2 v v s . V Q + v m w a s found to g i v e the expected s t r a i g h t l i n e ; two such p l o t s * The OCS c a l i b r a t i o n da ta and the c a l c u l a t e d e f f e c t i v e sep tum-ce l l w a l l spac ing (r^) were g i ven p r e v i o u s l y ( s e c t i o n 5 .4 ) . 197 TABLE 6.7 S ta rk Measurements on Cyanogen I socyanate . 2 — 1 0,2 A o , r M j = ±1 2 1 , 2 M J = 0 v a m v a o Frequency^ (v) V m V o Frequency (v) 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 i , o , M j = 0 V m V o Frequency ("v) V m V o Frequency (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 10708.30 198 TABLE 6.7 cont inued 3 — 2 0,3 0 , 2 ' M J = 0 1 5 0 , 1 5 - 1 4 1 , 1 4 ' M J V m V o Frequency (v) V m V o Frequency 15 260 15887.89 20 200 12794.73 12.5 300 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 V o l t s . Measured i n MHz. 199 have been reproduced i n F igu res 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 to o b t a i n " bes t v a l u e s " f o r the s lope and i n t e r c e p t of each of these l i n e s . The numbers are presented i n Table 6 . 8 . I t w i l l be noted that 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 f requency . F i f t e e n p a i r s o f u and y, va lues were c a l c u l a t e d from the measured a b S ta rk c o e f f i c i e n t s (Table 6.8) by assuming tha t the peak maximum i n the aggregate S ta rk lobe corresponded to each of the p o s s i b l e M v a l u e s . A l e a s t squares f i t t i n g procedure was used f o r t h i s purpose , w i t h the b-type S ta rk c o e f f i c i e n t s c a l ed by a f a c t o r of 50 to make i t of s i m i l a r magnitude to the ^-type ones. Such " w e i g h t i n g " was necessary to take f u l l advantage o f the a c c u r a t e l y de te rmined , but s m a l l , b-type S ta rk c o e f f i c i e n t . The r e s u l t s have been c o l l e c t e d i n Table 6 . 9 . The cho ice of i s much l e s s c r i t i c a l here than i t was f o r i s o c y a n i c a c i d . A va lue g r ea t e r than 10 i s comple te l y unreasonab le , and a l l va lues l e s s than 10 g i v e ve ry 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 very l i k e l y . Thus the d i p o l e moment of cyanogen i socyana te has been c a l c u l a t e d to 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 es t imates represent ou t s i de l i m i t s of e r r o r . The d i p o l e moment of cyanogen az ide has r e c e n t l y been repor ted (154, 186) . Th i s molecu le has a ve 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 of these two molecu les i s of some i n t e r e s t . Th i s has been done i n F i gu re 6 . 7 . The indicated^y^\ d i r e c t i o n s are of course 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 2 + V 2 ) x l 0 ~ 5 ( v o l t s 2 ) o m 202 TABLE 6.8 S ta rk C o e f f i c i e n t s of F i v e Cyanogen Isocyanate S ta rk Lobes. 2 0 , 2 ~ V l ' MJ = ± l 1,2 ^ l ' M J = ° ( S l o p e a ) x l 0 4 I n t e r cep t c 1.6914 ± 0.0022 10593.721 ± 0 . 0 2 9 d 10593.65 ± 0 . 2 0 e 1.7041 ± 0.0040 10494.958 ± 0.035 10494.80 ± 0.20 3 0 , 3 - 2 0 , 2 ' M J = ° ( S lope )x lO I n t e r c ep t 1.6849 ± 0.0066 10696.999 ± 0.058 10697.08 ± 0.20 -0.35560 ± 0.00028 15890.343 ± 0.016 15890.18 ± 0.20 15 — 14 M ^0,15 ^ 1 , 1 4 ' J ( S lope )x lO I n t e r c ep t 4.3499 ± 0.0060 12794.511 ± 0.011 12794.58 ± 0.10 Slope of the v v s . V Q + v m s t r a i g h t l i n e graph i n MHz/Volts . b 2 2 I n t e r cep t of the v v s . V + V s t r a i g h t l i n e graph i n MHz. o m Observed zero f i e l d t r a n s i t i o n frequency i n MHz. d Standard e r r o r s . e Es t imated e r r o r s . 203 TABLE 6.9 The D ipo l e Moment of Cyanogen I socyanate . K M / y (Debyes) cl y^ (Debyes) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 112.5 224 221 216 209 200 189 176 161 144 125 104 81 56 29 2.4881 2.4881 2.4881 2.4881 2.4881 2.4881 2.4881 2.4881 2.4881 2.4881 2.4881 2.4880 2.4878 2.4868 ± 0.0030 ± 0.0030 ± 0.0030 ± 0.0030 + 0.0030 ± 0.0030 ± 0.0030 ± 0.0030 ± 0.0030 ± 0.0030 ± 0.0030 ± 0.0031 ± 0.0032 ± 0.0056 0.4715 ± 0.0007 0.4718 ± 0.0007 0.4725 ± 0.0007 0.4737 ± 0.0008 0.4756 ± 0.0008 0.4783 ± 0.0008 0.4820 ± 0.0009 0.4872 ± 0.0010 0.4945 ± 0.0011 0.5053 ± 0.0013 0.5226 ± 0.0016 0.5537 ± 0.0022 0.6253 ± 0.0035 0.9950 ± 0.0152 imaginary Value of M T to which the peak maximum of the 15„ , r — 14, J 0,15 1,14 aggregate S ta rk lobe i s assumed to cor respond . b R e l a t i v e i n t e n s i t i e s of the v a r i o u s S ta rk components of the 15_ , r — 14, , . t r a n s i t i o n . 0,15 1,14 Standard e r r o r s . 204 205 (3 to 4 D) , p o s i t i v e i n the sense N + c"1" (187,188) . Isocyanate and az ide cha ins may be expected to show r a t h e r s m a l l e r group moments (109,186) . The magnitude of the NC-NCO bond moment (189) and the c e n t r a l n i t r o g e n h y b r i d i z a t i o n ( lone p a i r ) moment (188) are even l e s s c e r t a i n but n e i t h e r i s l i k e l y to be a dominant f a c t o r . Thus, one might reasonably expect t h a t , f o r both m o l e c u l e s , the t o t a l d i p o l e moment would roughly p a r a l l e l the NCN cha in w i t h the nega t i ve end " o n " the cyanide n i t r o g e n . Th is c o n d i t i o n i s most c l o s e l y approximated when the component d i r e c t i o n s are taken to be those suggested i n F igure 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 molecu le cou ld e a s i l y accommodate a " p o s i t i v e " _b-component. The i n c r ease i n u on going from NCNCO to NCN can be r a t i o n a l i z e d a JJ i n terms of the r e l a t i v e d i r e c t i o n s of the i socyana te and az ide group moments. The former i s p robab l y p o s i t i v e i n the sense 0 N + and hence l a r g e l y opposes the cyanide 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 tha t the oppos i t e s i t u a t i o n p e r t a i n s . A number of CNDO/2 c a l c u l a t i o n s i n d i c a t e tha t such shou ld be the case (186 ,109) , as do the observed d i p o l e moments of 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 = 0.847 D) a a (190) . I t f o l l o w s then that the d i p o l e moment of cyanogen az ide shou ld be l a r g e r than tha t of cyanogen i s o c y a n a t e , as observed. A CNDO/2 c a l c u l a t i o n was attempted f o r cyanogen i socyana te (109) , but u n f o r t u n a t e l y i t f a i l e d to converge. 6.5 V i b r a t i o n a l Dependence of the R o t a t i o n a l Cons tan t s . The r o t a t i o n a l cons tants of cyanogen i socyana te have been p l o t t e d as a f u n c t i o n of v^ + 1/2 i n F igu res 6 . 8 , 6.9 and 6 .10 . The s t r a i g h t l i n e s expected on the b a s i s o f the s imple theory (equat ions 2.48) are not observed. In f a c t , two of the p l o t s (A_r and C^) do not even g i ve smooth cu r ves . The 206 FIGURE 6.8 V i b r a t i o n a l Dependence of 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 " • r 0 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 of NCNCO. 2601. v (MHz) 2600H 2599-j 2598 H 2597 © © © T 3 © ( v A + 1/2) 209 apparent sudden upswing i n the F igure 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 o f i n a c cu ra t e A va lues f o r v„ = 2, 3 (the e r r o r bars are ±1 v £ ' s tandard e r r o r ) . To the ex ten t to which i t i s r e a l , t h i s dramat i c i n c r e a s e i n d i c a t e s tha t the top o f the b a r r i e r to l i n e a r i t y i s be ing 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 so suggests that the molecule i s undergoing a marked change i n b e h a v i o r . I r r e g u l a r v i b r a t i o n a l dependence of r o t a t i o n a l constants near the top of a v i b r a -t i o n a l b a r r i e r has been observed be fo re (191) . F i n a l l y , the l a r g e CNC angle (140°) and the l o w i s h to0 f requency ( ~ 1 4 0 cm *) are both c o n s i s t e n t w i t h cyanogen i socyana te hav ing a r a t h e r low b a r r i e r to l i n e a r i t y . The dependence o f the A v r o t a t i o n a l constant and the (k^) d i s -t o r t i o n constant on the bending v i b r a t i o n a l quantum number v^ has been thorough ly 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 molecu les (114) . I t has been shown that the e x p e r i m e n t a l l y observed behav io r can be approx -ima te l y reproduced u s i ng a s imple model i n which the bending v i b r a t i o n i s cons idered to be a two d imens iona l i s o t o p i c o s c i l l a t o r per tu rbed by a s u i t a b l e hump (192,193) . A s i m i l a r approach shou ld be a p p l i c a b l e t o cyanogen i socyana te and h o p e f u l l y would y i e l d a good es t imate of i t s b a r r i e r to l i n e a r i t y . F i r s t , however, i t would be necessary to o b t a i n r e f i n e d expe r imenta l A and AT„ v a lues f o r the v„ = 2 , 3 and h i ghe r e x c i t e d v K 1 v i b r a t i o n a l s t a t e s . Th i s would e n t a i l the measurement of a d d i t i o n a l , ve ry 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 spectrometer than tha t used i n the present work. An i n v e s t i g a t i o n of the mm-wave r eg i on of the spectrum would p robab ly a l s o be ve ry h e l p f u l . * The behav io r of A as a f u n c t i o n of v, f o r q u a s i - l i n e a r molecu les was v b n d i s cussed p r e v i o u s l y ( s e c t i o n 4 . 5 ) . 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 S t r u c t u r e . The three i s o e l e c t r o n i c molecu les carbon subox ide , cyanogen az ide and cyanogen i socyana te show an i n t e r e s t i n g v a r i a t i o n i n mo lecu l a r s t r u c t u r e . 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 the Valence Bond f o rma l i sm . Carbon suboxide has been shown to be a l i n e a r molecu le i n i t s ground v i b r a t i o n a l s t a t e (194) . Th i s i s not s u r p r i s i n g s i n c e the two resonance forms which are l i k e l y to be of g r ea t e s t importance are (195) : o = c = c = c = o  +g==r. c.=c. o~ 61 611 The shor t CC and CO d i s t ances (1.289 % and 1.163'A* r e s p e c t i v e l y ) are c o n -s i s t e n t w i t h 611 be ing of s i m i l a r importance to 61 . Other forms such a s : 0. .0 X R ^ X : C = C = 0 6 I I I 6IV which cou ld l e a d to a bent s t r u c t u r e are l e s s r easonab le . A s i m i l a r approach, a p p l i e d to cyanogen a z i d e , i n d i c a t e s tha t t h i s mo l e cu l e , u n l i k e C^C^' cou ld not accommodate a l i n e a r c o n f i g u r a t i o n : A l l o f i t s l i k e l y resonance forms are ben t ! These a r e : x y- - N v y x y \ ^ + >^ / + x - / + 61* 611 ' 6 I I I ' * A c t u a l l y , a recent e l e c t r o n d i f f r a c t i o n study (196) has i n d i c a t e d tha 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 sma l l "hump" at the l i n e a r c o n f i g u r a t i o n . 211 F u r t h e r , l i n e a r forms such a s : N C i = N - — - N = N N C = N N = N + + - + + 6IV' 6 V v i o l a t e P au l i ngs adjacent charge r u l e (197) and hence must be of minor importance . Cyanogen az ide does of course have a bent s t r u c t u r e . Th i s 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 the p rev ious s e c t i o n ( F igure 6 . 7 ) . The bond l eng ths and angles may be found i n Table 5 .23 . These i n d i c a t e tha t the above p i c t u r e i s b a s i c a l l y sound. Any tendency of the CNN angle to open beyond the observed 120° due to s m a l l c o n t r i b u t i o n s from 6IV ' and 6V' i s appa ren 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 socyana te i s l e s s e a s i l y p r e d i c t e d . Two of the three most l i k e l y resonance forms are l i n e a r , the t h i r d i s bent (18 ) . These a r e : N = = C N : F = C 0 N-rr-C: N C = 0 ^ C , C ' + - - + \ A> X N ^ 6 1 " 611 " 6 I I I " A d d i t i o n a l forms which are probab ly o f l e s s e r importance 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 to the cases of C^O,, and NCN^, the q u e s t i o n " l i n e a r or ben t ? " cou ld not be answered w i t h any conf idence p r i o r to an exper imenta l i n v e s t i g a t i o n . Indeed, on the b a s i s of a p r e l i m i n a r y i n f r a r e d study Mayer (18) m i s t aken 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 phase ) , 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 of the 212 dominance of resonance forms 6 1 " and 6 1 1 " . The present work has of course shown that cyanogen i socyana te i s a bent mo lecu l e . However, the l a r g e CNC angle (140°) and the s t rong q u a s i - l i n e a r behav io r both i n d i c a t e that 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 611 " as w e l l as form 6 I I I " which i s p robab ly 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 ances have been determined to be 1.312 ± 0.02 ft and 1.283 ± ? ft, r e s p e c t i v e l y . The l a t t e r number i s some what u n c e r t a i n due to the many assumptions tha t were made i n the course o f i t s c a l c u l a t i o n . None the l ess , there can be no doubt tha t t h i s (nomina l l y s i n g l e ) bond i s remarkably s h o r t i n both 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 of a s t r o n g l y d e l o c a l i z e d TT system. A l l o f the p r e s e n t l y a v a i l a b l e chemica l (18,82) and s p e c t r o s c o p i c ev idence 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 on l y the i socyana te c o n f i g -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 yan ide s t r u c t u r e (NCOCN) i s apparen t l y l e s s s t a b l e . Th 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 oppos 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 analogue C2N2S. A r easonab 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 i s aga in p rov ided by the Va lence Bond approach. The s t r u c t u r e of s u l f u r d i c yan ide has been determined by P i e r c e e t . a l . (162) . The SC i n t e r n u c l e a r d i s t ance here (1.701 ± 0.002 ft) was found to be s i g n i f i c a n t l y s m a l l e r than t ha t of a " no rma l " SC s i n g l e bond (1.80 ft). Th i s was a t t r i b u t e d to 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 resonance forms l i k e 6 1 1 " ' as w e l l as form 6 1 " ' which i s p robab ly the c h i e f one: 61"' s 611"' 213 I t was f u r t h e r shown tha t the n i t r o g e n nuc l ea r quadrupole coup l i ng was c o n s i s t e n t w i t h as much as 25% double bond cha rac t e r i n the CN bond. Now f o r the oxygen d i c y a n i d e , resonance forms equ i v a l en t to 6 1 1 ' " would be much l e s s favored because of the g r ea 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 .50 , J (S ) = 2.50) (103) . Thus C ^ O has g r ea t e r resonance s t a b i l -i z a t i o n p o s s i b i l i t i e s i n the i socyana te than i n the d i c yan ide 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 not 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 the d i c yan ide ( (CN ) 0 S ) . 214 CHAPTER 7 MICROWAVE TRANSITION FREQUENCIES OF CHLORINE ISOCYANATE, ISOCYANIC ACID AND CYANOGEN ISOCYANATE Th i s chapter con ta ins the measured microwave t r a n s i t i o n f r equenc i e s upon which the e n t i r e t h e s i s i s based . In Table 7.1 the observed t r a n s i t i o n f r equenc i es of c h l o r i n e i socyana te have been ca t a logued . Each h y p e r f i n e component has been u n i q u e l y des ignated by s p e c i f y i n g the F^  and F quantum numbers of both the upper s t a t e (denoted w i t h a s i n g l e prime) and the lower s t a t e (denoted w i t h a double p r ime ) . Only the s t r onges 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 which 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 equenc i e s which were e x t r a c t e d from the da t a i n Table 7.1 have been c o l l e c t e d i n Table 7 .2 . Tables 7.3 and 7.4 c o n t a i n the i s o c y a n i c a c i d f r e q u e n c i e s ; they have been o rgan ized i n e s s e n t i a l l y the same way as the two p r e v i o u s , c h l o r i n e i s o -cyanate , t a b l e s . I t w i l l be noted t ha t f o r the i s o c y a n i c a c i d a-type Q-branch t r a n s i t i o n s the s t r onges t h y p e r f i n e components correspond to AF = 0. F i n a l l y , Table 7.5 con ta ins the observed cyanogen i socyana te t r a n s i t i o n f r equenc i e s (hyper f ine s t r u c t u r e u n r e s o l v e d ) . 215 TABLE 7.1 Observed T r a n s i t i o n Frequenc ies of C h l o r i n e I socyanate : Quadrupole Coup l ing A n a l y s i s . Nuc lear 1 II II •rt Observed Observed C a l c u l a t e d F l r F l r Frequency C o r r e c t i o n C o r r e c t i o n 3 5 C 1 U N 1 2 c 1 6 o Ground V i b r a t i o n a l S ta te 3 1 , 3 - 2 1 , 2 2.5 1.5 1.5 1.5 17945.84° -4.16° - 4 . 1 7 d 2.5 1.5 1.5 0.5 17945.84 -4.16 -4.17 2.5 3.5 1.5 2.5 17946.15 -3.85 -3.89 2.5 2.5 1.5 2.5 17946.80 -3.20 -3.23 2.5 2.5 1.5 1.5 17946.80 -3.20 -3.23 3.5 2.5 2.5 1.5 17947.52 -2.48 -2.55 3.5 4 .5 2.5 3.5 17947.52 -2.48 -2.43 3.5 3.5 2.5 2.5 17948.08 -1.92 -1.90 1.5 0.5 0.5 0.5 17949.90 -0.10 -0.08 1.5 0.5 0.5 1.5 17949.90 -0.10 -0.08 1.5 2.5 0.5 1.5 17950.59 0.59 0.56 4.5 3.5 3.5 3.5 17951.03 1.03 0.95 1.5 1.5 0.5 1.5 17951.38 1.38 1.35 1.5 1.5 0.5 0.5 17951.38 1.38 1.35 4.5 3.5 3.5 2.5 17951.98 1.98 2.01 4.5 5.5 3.5 4 .5 17951.98 1.98 2.04 4.5 4 .5 3.5 3.5 17952.42 2.42 2.44 4.5 4.5 3.5 4 .5 17953.28 3.28 3.26 3 — 0,3 2 1 , 2 4.5 4.5 3.5 3.5 * 2.15 4.5 5.5 ' 3.5 4.5 -30020.49* 1.75 1.75 4.5 3.5 3.5 2.5 -30020.49* 1.75 1.72 1.5 1.5 0.5 1.5 -30021.47* 0.77 0.67 1.5 1.5 0.5 0.5 -30021.47* 0.77 0.67 1.5 2.5 0.5 1.5 -30022.34 -0.10 -0.12 3.5 3.5 2.5 2.5 -1.34 3.5 4.5 2.5 3.5 -30024.13 -1.89 -1.87 3.5 2.5 2.5 1.5 -30024.13 . -1.89 -1.99 2.5 2.5 1.5 2.5 -3.06 2.5 2.5 1.5 1.5 -3.06 2.5 3.5 1.5 2.5 -30025.99 -3.75 -3.72 * Overlapped by 5. — 4 3 5 1,4 C 1 1 4 N 1 2 C 1 6 0 F i r s t E x . V i b . S t . 4 0 . 4 ~ J 0 , 3 3.5 2.5 2.5 1.5 24295.55 -1.61 -1.63 3.5 4.5 2.5 3.5 24295.55 -1.61 -1.63 2.5 3.5 1.5 2.5 24295.55 -1.61 -1.59 2.5 1.5 1.5 0.5 -1.41 3.5 3.5 2.5 2.5 -1.33 2.5 2.5 1.5 1.5 -1.32 4.5 5.5 3.5 4.5 24297.68 0.52 0.45 4.5 3.5 3.5 2.5 24297.68 0.52 0.46 216 1 F l i F I I F l M F Observed Frequency Observed C o r r e c t i o n C a l c u l a t e C o r r e c t i o 5.5 6.5 4.5 5.5 24297.68 0.52 0.52 5.5 4.5 4.5 3.5 24297.68 0.52 0.56 5.5 5.5 4.5 4.5 24297.68 0.52 0.59 4.5 4.5 3.5 3.5 24297.68 0.52 0.65 - 3 1 , 3 3.5 2.5 2.5 1.5 23930.27 -2.27 -2.25 3.5 4.5 2.5 3.5 23930.27 -2.27 -2.23 3.5 3.5 2.5 2.5 23930.67 -1.87 -1.84 4.5 3.5 3.5 2.5 23931.86 -0.68 -0.68 4.5 5.5 3.5 4.5 23931.86 -0.68 -0.67 2.5 3.5 1.5 2.5 23932.16 -0.38 -0.44 4.5 4.5 3.5 3.5 23932.16 -0.38 -0.36 2.5 1.5 1.5 0.5 23932.16 -0.38 -0.31 2.5 2.5 1.5 1.5 23932.50 -0.04 -0.07 5.5 6.5 4.5 5.5 23933.72 1.18 1.15 5.5 4.5 4.5 3.5 23933.72 1.18 1.16 5.5 5.5 4.5 . \ 4.5 23933.99 1.45 1.34 3.5 2.5 2.5 1.5 24673.36 -1.29 -1.29 3.5 4.5 2.5 3.5 24673.36 -1.29 -1.27 3.5 3.5 2.5 2.5 24673.67 -0.98 -1.02 4.5 3.5 3.5 2.5 24673.67 -0.98 -0.97 4.5 5.5 3.5 4.5 24673.67 -0.98 -0.96 4.5 4.5 3.5 3.5 24673.91 -0.74 -0.75 2.5 3.5 1.5 2.5 24675.17 0.52 0.52 2.5 1.5 1.5 0.5 24675.17 0.52 0.56 2.5 2.5 1.5 . 1.5 24675.48 0.83 0.76 5.5 4.5 4.5 3.5 24675.48 0.83 0.84 5.5 6.5 4.5 5.5 24675.48 0.83 0.84 5.5 5.5 4.5 4.5 24675.68 1.03 1.00 4 2 , 3 — 3 2,2 4.5 3.5 3.5 2.5 24306.34 -4.70 -4.74 4.5 5.5 3.5 4.5 24306.34 -4.70 -4.64 4.5 4.5 3.5 3.5 24306.79 -4.25 -4.22 3.5 2.5 2.5 1.5 24308.84 -2.20 -2.24 3.5 4.5 2.5 3.5 24308.84 -2.20 -2.13 3.5 3.5 2.5 2.5 24309.34 -1.70 -1.75 5.5 4.5 4.5 3.5 . 24313.43* 2.39 2.35 5.5 6.5 4.5 5.5 24313.43* 2.39 2.44 5.5 5.5 4.5 4.5 24314.08* 3.04 2.95 2.5 1.5 1.5 0.5 4.80 2.5 3.5 1.5 2.5 24316.01 4.97 4.98 2.5 2.5 1.5 1.5 24316.48 5.44 5.41 * Overlapped by 4 3 , 2 " " 3 3 , 1 and 4 2 > 2 — 3 2 > 1 o f 3 5 C 1 1 4 N 1 2 C 1 6 0 G.V.S . 217 1 F, i F I I F I I F Observed Observed Calculated 1 1 Frequency Correction Correction 42,2 - 3 2 , I 4.5 3.5 3.5 2.5 24311.67 -4.65 -4.71 4.5 5.5 3.5 4.5 24311.67 -4.65 -4.62 4.5 4.5 3.5 3.5 24312.20+ -4.12 -4.20 3.5 2.5 2.5 1.5 24314.08* -2.24 -2.23 3.5 4.5 2.5 3.5 24314.08* -2.24 -2.11 3.5 3.5 2.5 2.5 24314.63 -1.69 -1.73 5.5 4.5 4.5 3.5 24318.68 2.36 2.33 5.5 6.5 4.5 5.5 24318.68 2.36 2.43 5.5 5.5 4.5 4.5 24319.29 2.97 2.93 2.5 1.5 1.5 0.5 4.77 2.5 3.5 1.5 2.5 24321.25+ 4.93 4.96 2.5 2.5 1.5 1.5 24321.66+ 5.34 5.38 * Overlapped + Overlapped b * 42,3 h ? 43,2 ~ 3 2 , 2 3 5 C 1 1 4 N 1 2 C 1 6 0 G.V.S. 43,2 ~ 3 3 , 1 4 3 , 1 - 3 3 , 0 4.5 3.5 3.5 2.5 24312.55 -11.10 -11.25 4.5 5.5 3.5 4.5 • 24312.55 -11.10 -11.02 4.5 4.5 3.5 3.5 24313.43* -10.22 -10.33 3.5 2.5 2.5 1.5 24320.95+ -2.70 -3.02 3.5 4.5 2.5 3.5 24320.95+ -2.70 -2.77 3.5 3.5 2.5 2.5 24321.25+ -2.40 -2.28 5.5 4.5 4.5 3.5 24328.39 4.74 4.59 5.5 6.5 4.5 5.5 24328.39 4.74 4.85 5.5 5.5 4.5 4.5 24329.55 5.90 5.92 2.5 1.5 1.5 0.5 13.16 12.58 2.5 3.5 1.5 2.5 24336.81 13.16 13.21 2.5 2.5 1.5 1.5 24337.50 13.85 13.83 * Overlapped + Overlapped b * 42,3 ^ 42,2 32,2 - 3 2 , 1 3 5 C 1 1 4 N 1 2 C 1 6 0 G.V.S. ~ 3 1 , 3 4.5 4.5 3.5 3.5 1.21 4.5 3.5 3.5 2.5 ; -23674.01 0.99 1.03 4.5 5.5 3.5 4.5 -23674.01 0.99 1.01 5.5 5.5 4.5 4.5 -23674.72 0.28 0.31 5.5 4.5 4.5 3.5 -23674.72 0.28 0.28 5.5 6.5 4.5 5.5 -23674.72 0.28 0.24 3.5 3.5 2.5 2.5 -1.16 3.5 4.5 2.5 3.5 -23676.55 -1.55 -1.46 3.5 2.5 2.5 1.5 -23676.55 -1.55 -1.46 2.5 2.5 1.5 1.5 -2.00 2.5 1.5 1.5 0.5 -2.09 2.5 3.5 1.5 2.5 -23677.25 -2.25 -2.27 218 1 i •rt I I II Observed Observed C a l c u l a t e F i r F l r F r e q u e n c y C o r r e c t i o n C o r r e c t i c 5 0 , 5 - *0,« 4.5 5.5 3.5 4.5 30366.30 -0.88 -0.92 4.5 3.5 3.5 2.5 30366.30 -0.88 -0.89 3.5 4.5 2.5 3.5 30366.30 -0.88 -0.87 3.5 2.5 2.5 1.5 30366.30 -0.88 -0.77 4.5 4.5 3.5 3.5 30366.30 -0.88 -0.76 3.5 3.5 2.5 2.5 30366.30 -0.88 -0.74 5.5 6.5 4.5 5.5 30367.55 0.37 0.30 5.5 4.5 4.5 3.5 30367.55 0.37 0.32 6.5 7.5 5.5 6.5 30367.55 0.37 0.37 6.5 5.5 5.5 4.5 30367.55 0.37 0.40 6.5 6.5 5.5 5.5 30367.55 0.37 0.42 5.5 5.5 4.5 4.5 30367.55 0.37 0.42 5 1 , 5 -4.5 5.5 3.5 4 .5 29913.08 -1.30 -1.35 4.5 3.5 3.5 2.5 29913.08 -1.30 -1.33 4.5 4.5 3.5 3.5 29913.08 -1 .30 -1.12 3.5 4.5 2.5 3.5 29913.97 -0.41 -0.45 3.5 2.5 2.5 1.5 29913.97 -0.41 -0.35 3.5 3.5 2.5 2.5 29913.97 -0.41 -0.25 5.5 6.5 4.5 5.5 29914.23 -0.15 -0.19 5.5 4.5 ' 4 .5 3.5 29914.23 -0.15 -0.17 5.5 5.5 4.5 4.5 29914.23 -0.15 0.00 6.5 7.5 5.5 6.5 29915.14 0.76 0.73 6.5 5.5 5.5 4.5 29915.14 0.76 0.76 6.5 6.5 5.5 5.5 29915.14 0.76 0.85 4 1 , 3 4.5 5.5 3.5 4.5 30841.13 -0.83 -0.81 4.5 3.5 3.5 2.5 30841.13 -0.83 -0.81 4.5 4 .5 3.5 3.5 30841.13 -0.83 -0.67 5.5 6.5 4.5 5.5 30841.58 -0.38 -0.39 5.5 4.5 4.5 3.5 30841.58 -0.38 -0.39 5.5 5.5 4.5 4.5 30841.58 -0.38 -0.26 3.5 4.5 2.5 3.5 30842.02 0.06 0.09 3.5 2.5 2.5 1.5 30842.02 0.06 0.13 3.5 3.5 2.5 2.5 30842.02 0.06 0.22 6.5 7.5 5.5 6.5 30842.53 0.57 0.52 6.5 5.5 5.5 4.5 30842.53 0.57 0.53 6.5 6.5 5.5 5.5 30842.53 0.57 0.61 5 2 , 4 -4 2,3 5.5 4.5 4.5 3.5 30385.57 -2.19 -2.16 5.5 6.5 4.5 5.5 30385.57 -2.19 -2.13 5.5 5.5 4.5 4.5 30385.89 -1.87 -1.85 4.5 3.5 3.5 2.5 30386.15 -1.61 -1.65 4.5 5.5 3.5 4.5 30386.15 -1.61 -1.61 219 F ' F ' p" p" Observed Observed Calculated L 1 Frequency Correction Correction 4.5 4.5 3.5 3.5 30386.45 -1.31 -1.33 6.5 5.5 5.5 4.5 30389.18 1.42 1.41 6.5 7.5 5.5 6.5 30389.18 1.42 1.43 6.5 6.5 5.5 5.5 30389.62 1.86 1.72 3.5 2.5 2.5 1.5 30389.62 1.86 1.92 3.5 4.5 2.5 3.5 30389.62 1.86 1.95 3.5 3.5 2.5 2.5 30390.00 2.24 2.24 L 52,3 ~ ~ 2,2 5.5 4.5 4.5 3.5 30396.21 -2.13 -2.13 5.5 6.5 4.5 5.5 30396.21 -2.13 -2.10 5.5 5.5 4.5 4.5 30396.69 -1.65 -1.82 4.5 3.5 3.5 2.5 30396.69 -1.65 -1.62 4.5 5.5 3.5 4.5 30396.69 -1.65 -1.59 4.5 4.5 3.5 3.5 30397.01 -1.33 -1.31 6.5 5.5 5.5 4.5 30399.78* 1.44 1.38 6.5 7.5 5.5 6.5 30399.78* 1.44 1.41 6.5 6.5 5.5 5.5 30400.08* 1.74 1.69 3.5 2.5 2.5 1.5 30400.33* 1.99 1.89 3.5 4.5 2.5 3.5 30400.33* 1.99 1.92 3.5 3.5 2.5 2.5 30400.61* 2.27 2.21 Overlapped by 53,3 ~~ "*3,2 3 5 C 1 1 4 N 1 2 C 1 6 0 G.V.S. 53,3 43,2 5 — 4 3,2 H3.1 5.5 4.5 4.5 3.5 30399.33 -5.35 -5.29 5.5 6.5 4.5 5.5 30399.33 -5.35 -5.18 5.5 5.5 4.5 4.5 30400.08* -4.60 -4.70 4.5 3.5 3.5 2.5 30402.18 -2.50 -2.60 4.5 5.5 3.5 4.5 30402.18 -2.50 -2.48 4.5 4.5 3.5 3.5 30402.61 -2.07 -2.04 6.5 5.5 5.5 4.5 30407.43 2.75 2.67 6.5 7.5 5.5 6.5 30407.43 2.75 2.78 6.5 6.5 5.5 5.5 30408.07 3.39 3.36 3.5 2.5 2.5 1.5 5.31 3.5 4.5 2.5 3.5 30410.18 5.50 5.50 3.5 3.5 2.5 2.5 30410.72 6.04 5.99 : Overlapped by 52,3 42,2 3 5 C 1 1 4 N 1 2 C 1 6 0 G.V.S. 44,1 \ o 5.5 4.5 4.5 3.5 30413.87 -9.55 -9.68 5.5 6.5 4.5 5.5 30413.87 -9.55 -9.47 5.5 5.5 4.5 4.5 30414.72 -8.70 -8,70 4.5 3.5 3.5 2.5 30419.62 -3.80 -3.96 4.5 5.5 3.5 4.5 30419.62 -3.80 -3.71 220 1 ' n ti Observed Observed Calculated F F F 1 1 Frequency Correction Correction 4.5 4.5 3.5 3.5 30420.41 -3.01 -3.05 6.5 5.5 5.5 4.5 30427.98 4.56 4.45 6.5 7.5 5.5 6.5 30427.98 4.56 4.67 6.5 6.5 5.5 5.5 30429.12 5.70 5.66 3.5 2.5 2.5 1.5 10.06 3.5 4.5 2.5 3.5 30433.92 10.50 10.49 3.5 3.5 2.5 2.5 30434.64 11.22 11.26 5 ° , 5 ~ -5.5 4.5 4.5 3.5 -17238.55 2.03 2.03 5.5 5.5 4.5 4.5 -17238.55 2.03 1.99 5.5 6.5 4.5 5.5 -17238.55 2.03 1.98 4.5 4.5 3.5 3.5 -17240.70 -0.12 -0.09 4.5 3.5 3.5 2.5 -17240.70 -0.12 -0 .10 4.5 5.5 3.5 4.5 -17240.70 -0.12 -0.16 6.5 5.5 5.5 4.5 -17241.15 -0.57 -0.48 6.5 7.5 5.5 6.5 -17241.15 -0.57 -0.54 6.5 6.5 5.5 5.5 -17241.15 -0.57 -0.61 3.5 2.5 2.5 1.5 -17243.25 -2.67 -2.55 3.5 3.5 2.5 2.5 -17243.25 -2.67 -2.67 3.5 4.5 2.5 3.5 -17243.25 -2.67 -2.70 6 — 5 0,6 5.5 6.5 4.5 5.5 36433.65 -0.59 -0.60 5.5 4.5 4.5 3.5 36433.65 -0.59 -0.57 4.5 5.5 3.5 4.5 36433.65 -0.59 -0.54 5.5 5.5 4.5 4.5 36433.65 -0.59 -0.51 4.5 3.5 3.5 2.5 36433.65 -0.59 -0.48 4.5 4.5 3.5 3.5 36433.65 -0.59 -0.46 6.5 7.5 5.5 6.5 36434.52 0.28 0.21 6.5 5.5 5.5 4.5 36434.52 0.28 0.23 7.5 8.5 6.5 7.5 36434.52 0.28 0.28 7.5 6.5 6.5 5.5 36434.52 0.28 0.31 7.5 7.5 6.5 6.5 36434.52 0.28 0.32 6 — 5 „ 1,6 1,5 5.5 6.5 4.5 5.5 35894.68 -0.88 -0.89 5.5 4.5 4.5 3.5 35894.68 -0.88 -0.86 5.5 5.5 4.5 4.5 35894.68 -0.88 -0.75 4.5 5.5 3.5 4 .5 : 35895.20 -0.36 -0.37 4.5 3.5 3.5 2.5 35895.20 -0.36 -0.30 4.5 4.5 3.5 3.5 35895.20 ' -0.36 -0.25 6.5 7.5 5.5 6.5 35895.58 0.02 -0.03 6.5 5.5 5.5 4.5 35895.58 0.02 -0.01 6.5 6.5 5.5 5.5 35895.58 0.02 0.09 7.5 8.5 6.5 7.5 35896.09 0.53 0.51 7.5 6.5 6.5 5.5 35896.09 0.53 0.53 7.5 7.5 6.5 6.5 35896.09 0.53 0.58 221 1 F F I I F F Observed Observed Ca lcu la te *1 Frequency C o r r e c t i o n Co r r e c t i c 6 1 , 5 -• 5.5 6.5 4.5 5.5 37007.69 -0.54 -0.55 5.5 4.5 4.5 3.5 37007.69 -0.54 -0.53 5.5 5.5 4.5 4.5 37007.69 -0.54 -0.45 6.5 7.5 5.5 6.5 37008.16 -0.07 -0.18 6.5 5.5 5.5 4.5 37008.16 -0.07 -0.17 6.5 6.5 5.5 5.5 37008.16 -0.07 -0 .10 4.5 5.5 3.5 4.5 37008.16 -0.07 -0.02 4.5 3.5 3.5 2.5 37008.16 -0.07 0.01 4.5 4.5 3.5 3.5 37008.16 -0.07 0.06 7.5 8.5 6.5 7.5 37008.63 0.40 0.35 7.5 6.5 6.5 5.5 37008.63 0.40 0.36 7.5 7.5 6.5 6.5 37008.63 0.40 0.41 6 2 , 5 - 5 2 , 4 5.5 6.5 4.5 5.5 36462.75 -1.03 -1.13 6.5 5.5 5.5 4.5 36462.75 -1.03 -1.13 5.5 4.5 4.5 3.5 36462.75 -1.03 -1.13 6.5 7.5 5.5 6.5 36462.75 -1.03 -1.12 6.5 6.5 5.5 5.5 36462.75 -1.03 -0.93 5.5 5.5 4.5 4.5 36462.75 -1.03 -0.93 4.5 5.5 3.5 4.5 36464.77 0.99 0.91 7.5 6.5 6.5 5.5 36464.77 0.99 0.92 4.5 3.5 3.5 2.5 36464.77 0.99 0.92 7.5 8.5 6.5 7.5 36464.77 0.99 0.93 7.5 7.5 6.5 6.5 36464.77 0.99 1.09 4.5 4.5 3.5 3.5 36464.77 0.99 1.10 6 2 , 4 - 5 2 , 3 5.5 4.5 4.5 3.5 36481.46 -1.00 -1.11 6.5 5.5 5.5 4.5 36481.46 -1.00 -1.09 5.5 6.5 4 .5 5.5 36481.46 -1.00 -1 .10 6.5 7.5 5.5 6.5 36481.46 -1.00 -1.08 5.5 5.5 4.5 4.5 36481.46 -1.00 -0.91 6.5 6.5 5.5 5.5 36481.46 -1.00 -0.90 4.5 5.5 3.5 4.5 36483.41* 0.95 0.88 4.5 3.5 3.5 2.5 36483.41* 0^95 0.89 7.5 6.5 6.5 5.5 36483.41* 0.95 0.89 7.5 8.5 6.5 7.5 . 36483.41* 0.95 0.90 4.5 4.5 3.5 3.5 36483.41* 0.95 1.07 7.5 7.5 6.5 6.5 36483.41* 0.95 1.07 * Overlapped by 6 3 , 4 - 5 3 , 3 G.V.S . S , 4 - 5 3 , 3 6 3 , 3 ~ 5 3 , 2 6.5 5.5 5.5 4.5 36483.41* -2.44 -2.85 6.5 7.5 5.5 6.5 36483.41* -2.44 -2.80 6.5 6.5 5.5 5.5 36483.41* -2.44 -2.48 222 Observed Observed C a l c u l a t e d *1 t h F Frequency C o r r e c t i o n C o r r e c t i o n 5.5 4.5 4.5 3.5 36484.19 -1.66 -1.86 5.5 6.5 4.5 5.5 36484.19 -1.66 -1.80 5.5 5.5 4.5 4.5 36484.19 -1.66 -1.49 7.5 6.5 6.5 5.5 36487.71 1.86 1.70 7.5 8.5 6.5 7.5 36487.71 1.86 1.75 7.5 7.5 6.5 6.5 36487.71 1.86 2.10 4.5 3.5 3.5 2.5 36488.68 2.83 2.69 4.5 5.5 3.5 4.5 36488.68 2.83 2.76 4.5 4.5 3.5 3.5 36488.68 2.83 3.09 * Overlapped by 6 2 , 4 - - 5 2 , 3 3 5 C 1 U N 1 2 C 1 6 0 G.V.S . u 4 , 3 J 4 , 2 6 4 , 2 - 5 4 . 1 6.5 5.5 .  5.5 5.5 4.5 . 36502.77 -5.19 -5.28 6.5 7.5 5.5 6.5 36502.77 -5.19 -5.18 6.5 6.5 5.5 5.5 36503.25 -4.71 -4.66 5.5 4.5 4.5 3.5 36505.15 -2.81 -2.88 5.5 6.5 4.5 5.5 * 36505.15 -2.81 -2.76 5.5 5.5 4.5 4.5 36505.60 -2.36 -2.27 7.5 6.5 6.5 5.5 36510.89 2.93 2.81 7.5 8.5 6.5 7.5 36510.89 2.93 2.91 7.5 7.5 6.5 6.5 36511.51 3.55 3.51 4.5 3.5 3.5 2.5 36513.38 5.42 5.18 4.5 5.5 3.5 4.5 36513.38 5.42 5.35 4.5 4.5 3.5 3.5 36513.89 5.93 5.89 6 5 , 2 - \i 5 5 , 0 6.5 5.5 5.5 4.5 36528.76 -8.28 -8.41 6.5 7.5 5.5 6.5 36528.76 -8.28 -8.24 6.5 6.5 5.5 5.5 36529.58 -7.46 -7.46 5.5 4.5 4 .5 3.5 36532.98 -4.06 -4.19 5.5 6.5 4.5 5.5 36532.98 -4.06 -3.99 5.5 5.5 4.5 4.5 36533.80 -3.24 -3.28 7.5 6.5 6.5 5.5 36541.34 4.30 4.24 7.5 8.5 6.5 7.5 36541.34 4.30 4.40 7.5 7.5 6.5 6.5 36542.38 5.34 5.33 4.5 3.5 3.5 2.5 36545.68 8.64 8.39 4.5 5.5 3.5 4 .5 36545.68 . 8.64 8.69 4.5 4.5 3.5 3.5 36546.52 9.48 9.48 6 0 , 6 ~~ 5 i , s 6.5 5.5 5.5 4.5 -10718.54 2.38 2.43 6.5 7.5 5.5 6.5 -10718.54 2.38 . 2.38 6.5 6.5 5.5 5.5 -10718.54 2.38 2.28 5.5 4 .5 4.5 3.5 -10720.31 0.61 0.65 5.5 6.5 4.5 5.5 -10720.31 0.61 0.59 223 1 F, i F II F it F Observed Observed Calculated 1 1 Frequency Correction Correction 5.5 5.5 4.5 4.5 -10720.31 0.61 0.53 7.5 6.5 6.5 5.5 -10721.89 -0.97 -0.93 7.5 8.5 6.5 7.5 -10721.89 -0.97 -0.98 7.5 7.5 6.5 6.5 -10721.89 -0.97 -1.14 4.5 3.5 3.5 2.5 -10723.68 -2.76 -2.68 4.5 5.5 3.5 4.5 -10723.68 -2.76 -2.79 4.5 4.5 3.5 3.5 -10723.68 -2.76 -2.89 9 — 0,9 81,8 7.5 7.5 6.5 6.5 9318.03 -2.87 -2.92 7.5 8.5 6.5 7.5 9318.30 -2.60 -2.69 7.5 6.5 6.5 5.5 9318.30 -2.60 -2.63 10.5 10.5 9.5 9.5 9319.02 -1.88 -1.82 10.5 11.5 9.5 10.5 9319.29 -1.61 -1.57 10.5 9.5 9.5 8.5 9319.29 -1.61 -1.53 8.5 8.5 7.5 7.5 9322.14 1.24 1.31 8.5 9.5 7.5 8.5 9322.43 1.53 1.54 8.5 7.5 7.5 6.5 9322.43 1.53 1.59 9.5 9.5 8.5 8.5 9323.32 2.42 2.42 9.5 10.5 8.5 9.5 9323.61 2.71 2.65 9.5 8.5 8.5 7.5 9323.61 2.71 2.69 1 0 o , i o - _ 9 i . 9 8.5 8.5 7.5 7.5 16148.28 -2.87 -2.88 8.5 9.5 7.5 8.5 16148.55 -2.60 -2.63 8.5 7.5 7.5 6.5 16148.55 -2.60 -2.57 11.5 11.5 10.5 10.5 16149.21 -1.94 -1.92 11.5 12.5 10.5 11.5 16149.50 -1.65 -1.65 11.5 10.5 10.5 9.5 16149.50 -1.65 -1.62 9.5 9.5 8.5 8.5 16152.58 1.43 1.43 9.5 10.5 8.5 9.5 16152.82 1.67 1.67 9.5 8.5 8.5 7.5 16152.82 1.67 1.71 10.5 10.5 9.5 9.5 16153.59 2.44 2.40 10.5 11.5 9.5 10.5 16153.83 2.68 2.64 10.5 9.5 9.5 8.5 16153.83 2.68 2.68 n o , n - - 1 0 1 ,10 9.5 9.5 8.5 8.5 23046.77 -2.82 -2.83 9.5 10.5 8.5 9.5 23047.08 -2.51 -2.57 9.5 8.5 8.5 7.5 23047,08 -2.51 -2.52 12.5 12.5 11.5 11.5 23047.59 -2.00 -1.97 12.5 13.5 11.5 12.5 23047.89 -1.70 -1.70 12.5 11.5 11.5 10.5 23047.89 -1.70 -1.67 10.5 10.5 9.5 9.5 23051.05 1.46 1.50 10.5 11.5 9.5 10.5 23051.37 1.78 1.75 10.5 9.5 9.5 8.5 23051.37 1.78 1.79 11.5 11.5 10.5 10.5 23051.93 2.34 2.36 11.5 12.5 10.5 11.5 23052.22 2.63 2.61 11.5 10.5 10.5 9.5 23052.22 2.63 2.65 224 1 F, i F I I F I I F Observed Observed C a l c u l a t e d 1 1 Frequency C o r r e c t i o n C o r r e c t i o n 12 0,12 ,11 10.5 10.5 9.5 9.5 30008.85 -2.77 -2.76 10.5 11.5 9.5 10.5 30009.14 -2.48 -2.50 10.5 9.5 9.5 8.5 30009.14 -2.48 -2.46 13.5 13.5 12.5 12.5 30009.59 ' -2.03 -2.00 13.5 14.5 12.5 13.5 30009.89 -1.73 -1.73 13.5 12.5 12.5 11.5 30009.89 -1.73 -1.70 11.5 11.5 10.5 10.5 30013.14 1.52 1.55 11.5 12.5 10.5 11.5 30013.43 1.81 1.81 11.5 10.5 10.5 9.5 30013.43 1.81 1.84 12.5 12.5 11.5 11.5 30013.94 2.32 2.31 12.5 13.5 11.5 12.5 30014.20 2.58 2.57 12.5 11.5 11.5 10.5 30014.20 2.58 2.60 1 3 0 , 1 3 ~ 1 2 1 . 11.5 11.5 10.5 10.5 37029.70 -2.70 -2 .70 11.5 12.5 10.5 11.5 37030.00 -2 .40 -2.43 11.5 10.5 10.5 9.5 37030.00 -2 .40 -2 .39 14.5 14.5 13.5 13.5 37030.37 -2.03 -2.02 14.5 15.5 13.5 14.5 37030.66 -1.74 -1.74 14.5 13.5 13.5 12.5 37030.66 -1.74 -1.71 12.5 12.5 11.5 11.5 37033.96 1.56 1.57 12.5 13.5 11.5 12.5 37034.25 1.85 1.83 12.5 11.5 11.5 10.5 37034.25 1.85 1.87 13.5 13.5 12.5 12.5 37034.67 2.27 2.26 13.5 14.5 12.5 13.5 37034.96 2.56 2.52 13.5 12.5 12.5 11.5 37034.96 2.56 2.55 1 6 1 , 1 5 14 16.5 15.5 15.5 14.5 -36019.39 2.55 2.59 16.5 17.5 15.5 16.5 -36019.39 2.55 2.56 16.5 16.5 15.5 15.5 -36019.86 2.08 2.26 15.5 16.5 14.5 15.5 -36019.86 2.08 2.07 15.5 14.5 14.5 13.5 -36019.86 2.08 2.07 15.5 15.5 14.5 14.5 -36020.19 1.75 1.77 17.5 16.5 16.5 15.5 -36023.83 -1.89 -1.89 17.5 18.5 16.5 17.5 -36023.83 -1.89 -1.91 17.5 17.5 16.5 16.5 -36024.33 -2.39 -2.20 14.5 13.5 13.5 12.5 -36024.33 -2.39 -2.40 14.5 15.5 13.5 14.5 -36024.33 -2.39 -2.42 14.5 14.5 13.5 13.5 -36024.64 -2.71 " l , 1 6 - 15 17.5 16.5 16.5 15.5 -28460.08 2.60 2.61 17.5 18.5 16.5 17.5 -28460.08 2.60 2.58 17.5 17.5 16.5 16.5 -28460.51 2.17 2.26 16.5 17.5 15.5 16.5 -28460.51 2.17 2.13 16.5 15.5 15.5 14.5 -28460.51 2.17 2.12 16.5. 16.5 15.5 15.5 -28460.89 1.79 1.81 225 t F l i F II F l n F Observed Frequency Observed C o r r e c t i o n C a l c u l a t e d C o r r e c t i o n 18.5 17.5 17.5 16.5 -28464.62 -1.94 -1.93 18.5 19.5 17.5 18.5 -28464.62 -1.94 -1.95 18.5 18.5 17.5 17.5 -28465.05 -2.37 -2.25 15.5 14.5 14.5 13.5 -28465.05 -2.37 -2.41 15.5 16.5 14.5 15.5 -28465.05 -2.37 -2.44 15.5 15.5 14.5 14.5 -28465.42 -2.74 -2.73 1 8 1 , 1 7 ~ 1 7 2 ,16 18.5 17.5 17.5 16.5 -20821.90 2.61 2.62 18.5 19.5 17.5 18.5 -20821.90 2.61 2.60 18.5 18.5 17.5 17.5 -20822.30 2.21 2.43 17.5 16.5 16.5 15.5 -20822.30 2.21 2.16 17.5 18.5 16.5 17.5 -20822.30 2.21 2.01 17.5 17.5 16.5 16.5 -20822.70 1.81 1.85 19.5 18.5 18.5 17.5 -20826.49 -1.98 -1.97 19.5 20.5 18.5 19.5 -20826.49 -1.98 -1.99 19.5 19.5 18.5 18.5 -20826.89 -2.38 -2.29 16.5 15.5 15.5 14.5 -20826.89 -2.38 -2.42 16.5 17.5 15.5 16.5 -20826.89 -2.38 -2.44 16.5 16.5 15.5 15.5 -20827.29 -2.78 -2.74 ~ 1 8 2 .17 19.5 18.5 18.5 17.5 -13106.31 2.62 2.62 19.5 20.5 18.5 19.5 -13106.31 2.62 2.60 19.5 19.5 18.5 18.5 2.44 18.5 17.5 17.5 16.5 -13106.70 2.23 2.20 18.5 19.5 17.5 18.5 2.04 18.5 18.5 17.5 17.5 -13107.08 1.85 1.87 20.5 19.5 19.5 18.5 -13110.92 -1.99 -1.99 20.5 21.5 19.5 20.5 -13110.92 -1.99 -2.01 20.5 20.5 19.5 19.5 -13111.30 -2.37 -2.32 17.5 16.5 16.5 15.5 -13111.30 -2.37 -2.42 17.5 18.5 16.5 17.5 -13111.30 -2.37 -2.44 17.5 17.5 16.5 16.5 -13111.70 -2.77 -2.74 22 1,21 ~ 2 1 2 ,20 20.5 20.5 19.5 19.5 10482.70 -2.70 -2.73 20.5 21.5 19.5 20.5 10483.03 -2.37 -2.43 20.5 19.5 19.5 18.5 : 10483.03 -2.37 -2.41 23.5 23.5 22.5 22.5 ! 10483.03 -2.37 -2.37 23.5 24.5 22.5 23.5 10483.37 -2.03 -2.06 23.5 22.5 22.5 21.5 10483.37 -2.03 -2.04 21.5 21.5 20.5 20.5 10487.30 1.90 1.93 21.5 20.5 20.5 19.5 10487.63 2.23 2.25 21.5 22.5 20.5 21.5 1 10487.63 2.23 2.25 22.5 22.5 21.5 21.5 10487.63 2.23 2.27 22.5 23.5 21.5 22.5 10488.02 2.62 2.60 22.5 21.5 21.5 20.5 10488.02 2.62 2.62 226 1 F l i F I I F l I I F Observed Frequency Observed C o r r e c t i o n C a l c u l a t e d C o r r e c t i o n 2 3 1 ? 2 2 — 22 2 ,21 21.5 21.5 20.5 20.5 18490.24 -2.71 -2.72 21.5 22.5 20.5 21.5 18490.54 -2.41 -2.41 21.5 20.5 20.5 19.5 18490.54 -2.41 -2.40 24.5 24.5 23.5 23.5 18490.54 -2.41 -2.38 24.5 25.5 23.5 24.5 18490.93 -2.02 -2.06 24.5 23.5 23.5 22.5 18490.93 -2.02 -2.05 22.5 22.5 21.5 21.5 18494.81 1.86 1.93 22.5 21.5 21.5 20.5 18495.18 2.23 2.26 22.5 23.5 21.5 22.5 18495.18 2.23 2.26 23.5 23.5 22.5 22.5 18495.18 2.23 2.27 23.5 24.5 22.5 23.5 18495.58 2.63 2.59 23.5 22.5 22.5 21.5 18495.58 2.63 2.61 24 1,23 — 23 J 2 ,22 22.5 22.5 21.5 21.5 26565.53 -2.70 -2.71 22.5 23.5 21.5 22.5 26565.85 -2.38 -2 .40 22.5 21.5 21.5 20.5 26565.85 -2.38 -2.38 25.5 25.5 24.5 24.5 26565.85 -2.38 -2.38 25.5 26.5 24.5 25.5 26566.18 -2.05 -2.07 25.5 24.5 24.5 23.5 26566.18 -2.05 -2.05 23.5 23.5 22.5 22.5 26570.15 1.92 1.94 24.5 24.5 23.5 23.5 26570.49 2.26 2.26 23.5 24.5 22.5 23.5 26570.49 2.26 2.26 23.5 22.5 22.5 21.5 26570.49 2.26 2.27 24.5 25.5 23.5 24.5 26570.83 2.60 2.58 24.5 23.5 23.5 22.5 26570.83 2.60 2.60 2 5 1 , 2 4 - 2 4 2 ,23 23.5 23.5 22.5 22.5 34706.26 -2.68 -2.70 23.5 24.5 22.5 23.5 34706.57 -2.37 -2.39 26.5 26.5 25.5 25.5 34706.57 -2.37 -2.38 23.5 22.5 22.5 21.5 34706.57 -2.37 -2.37 26.5 27.5 25.5 26.5 34706.90 -2.04 -2.07 26.5 25.5 25.5 24.5 34706.90 -2.04 -2.05 24.5 24.5 23.5 23.5 34710.85 1.91 1.94 25.5 25.5 24.5 24.5 34711.17 2.23 2.25 24.5 25.5 23.5 24.5 34711.17 2.23 2.26 24.5 23.5 23.5 22.5 34711.17 2.23 2.27 25.5 26.5 24.5 25.5 34711.52 2.58 2.57 25.5 24.5 24.5 23.5 34711.52 2.58 2.58 2 4 1 , 2 4 — 23 2 ,21 22.5 22.5 21.5 21.5 -35022.93 4.87 4.89 25.5 25.5 24.5 24.5 -35023.47 4.33 4.41 22.5 23.5 21.5 22.5 -35023.47 4.33 4.30 22.5 21.5 21.5 20.5 -35023.47 4.33 4.28 25.5 26.5 24.5 25.5 -35024.00 3.80 3.82 25.5 24.5 24.5 23.5 -35024.00 3.80 3.80 227 1 T? i V I I •p I I V Observed Observed C a l c u l a t e d *1 *1 r Frequency C o r r e c t i o n C o r r e c t i o n 23.5 23.5 22.5 22.5 -35031.39 -3.59 -3.60 24.5 24.5 23.5 23.5 -35031.93 -4.13 -4.07 23.5 24.5 22.5 23.5 -35031.93 -4.13 -4.19 23.5 22.5 22.5 21.5 -35031.93 -4.13 -4.20 24.5 25.5 23.5 24.5 -35032.50 -4.70 -4.66 24.5 23.5 23.5 22.5 -35032.50 -4.70 -4.68 2 5 1 , 2 5 - 2 4 2 ,22 23.5 23.5 22.5 22.5 -32531.74 4.96 4.98 26.5 26.5 25.5 25.5 -32532.24 4.46 4.51 23.5 24.5 22.5 23.5 -32532.24 4.46 4.39 23.5 22.5 22.5 21.5 -32532.24 4.46 4.37 26.5 27.5 25.5 26.5 -32532.79 3.91 3.91 26.5 25.5 25.5 24.5 -32532.79 3.91 3.89 24.5 24.5 23.5 23.5 -32540.43 -3.73 -3.68 25.5 25.5 24.5 24.5 -32540.97 -4.27 -4.15 24.5 25.5 23.5 24.5 -32540.97 -4.27 -4.29 24.5 23.5 23.5 22.5 -32540.97 -4.27 -4.30 25.5 26.5 24.5 25.5 -32541.49 -4.79 -4.75 25.5 24.5 24.5 23.5 -32541.49 -4.79 -4.78 2 6 1 , 2 6 ~ 2 5 2 ,23 24.5 24.5 23.5 23.5 -30274.54 5.04 5.09 27.5 27.5 26.5 26.5 -30275.03 4.55 4.62 24.5 25.5 23.5 24.5 -30275.03 4.55 4.48 24.5 23.5 23.5 22.5 -30275.03 4.55 4.45 27.5 28.5 26.5 27.5 -30275.59 3.99 4.01 27.5 26.5 26.5 25.5 -30275.59 3.99 3.99 25.5 25.5 24.5 24.5 -30283.39 -3.81 -3.77 26.5 26.5 25.5 25.5 -30283.92 -4.34 -4.24 25.5 26.5 24.5 25.5 -30283.92 -4.34 -4.39 25.5 24.5 24.5 23.5 -30283.92 -4.34 -4.40 26.5 27.5 25.5 26.5 -30284.47 -4.89 -4.85 26.5 25.5 25.5 24.5 -30284.47 -4.89 -4.87 2 7 1 , 2 7 — 2 6 2 ,24 25.5 25.5 24.5 24.5 -28258.39 5.16 5.19 28.5 28.5 27.5 27.5 -28258.82 4.73 4.73 25.5 26.5 24.5 25.5 -28259.02 4.53 4.57 25.5 24.5 24.5 23.5 -28259.02 4.53 4.53 28.5 29.5 27.5 28.5 -28259.43 4.12 4.10 28.5 27.5 27.5 26.5 -28259.43 4.12 4.08 26.5 26.5 25.5 25.5 -28267.40 -3.85 -3.87 27.5 27.5 26.5 26.5 -28267.88 -4.33 -4.32 26.5 27.5 25.5 26.5 -28268.04 -4.49 -4.49 26.5 25.5 25.5 24.5 -28268.04 -4.49 -4.51 27.5 28.5 26.5 27.5 -28268.50 -4.95 -4.95 27.5 26.5 26.5 25.5 -28268.50 -4.95 -4.97 228 T i T? n T? I I Observed Observed C a l c u l a t e d F l r . F l r Frequency C o r r e c t i o n C o r r e c t i o n 2 8 1 , 2 8 - 2 7 2 ,25 26.5 26.5 25.5 25.5 -26489.81 5.25 5.29 29.5 29.5 28.5 28.5 -26490.36 4.70 4.83 26.5 27.5 25.5 26.5 -26490.36 4.70 4.66 26.5 25.5 25.5 24.5 -26490.36 4.70 4.63 29.5 30.5 28.5 29.5 -26490.88 4.18 4.20 29.5 28.5 28.5 27.5 -26490.88 4.18 4.18 27.5 27.5 26.5 26.5 -26499.00 -3.94 -3.96 28.5 28.5 27.5 27.5 -26499.56 -4.50 -4.41 27.5 28.5 26.5 27.5 -26499.56 -4 .50 -4.60 27.5 26.5 26.5 25.5 -26499.56 -4 .50 -4.61 28.5 29.5 27.5 28.5 -26500.10 -5.04 -5.05 28.5 27.5 27.5 26.5 -26500.10 -5.04 -5.07 29 1,29 ~ 2 8 2 , 2 6 27.5 27.5 26.5 26.5 -24974.93 5.37 5.39 30.5 30.5 29.5 29.5 -24975.36 4.94 4.94 27.5 28.5 26.5 27.5 -24975.59 4.71 4.75 27.5 26.5 26.5 25.5 -24975.59 4.71 4.73 30.5 31.5 29.5 30.5 -24976.00 4.30 4.30 30.5 29.5 29.5 28.5 -24976.00 4.30 4.28 28.5 28.5 27.5 27.5 -24984.34 -4.04 -4.06 29.5 29.5 28.5 28.5 -24984.80 -4.50 -4.51 28.5 29.5 27.5 28.5 -24984.99 4.69 -4.70 28.5 27.5 27.5 26.5 -24984.99 -4.69 -4.72 29.5 30.5 28.5 29.5 -24985.44 -5.14 -5.15 29.5 28.5 28.5 27.5 -24985.44 -5.14 -5.17 3 0 1 , 3 0 - 2 9 2 ,27 28.5 28.5 27.5 27.5 -23719.17 5.45 5.50 31.5 31.5 30.5 30.5 -23719.59 5.03 5.05 28.5 29.5 27.5 28.5 -23719.83 4.79 4.85 28.5 27.5 27.5 26.5 -23719.83 4.79 4.82 31.5 32.5 30.5 31.5 -23720.24 4.38 4.39 31.5 30.5 30.5 29.5 -23720.24 4.38 4.37 29.5 29.5 28.5 28.5 -23728.75 -4.13 -4.15 30.5 30.5 29.5 29.5 -23729.19 -4.57 -4.60 29.5 30.5 28.5 29.5 -23729.39 -4.77 -4.80 29.5 28.5 28.5 27.5^ -23729.39 -4.77 -4.82 30.5 31.5 29.5 3 0 . 5 ; -23729.86 -5.24 -5.25 30.5 29.5 29.5 28.5 -23729.86 -5.24 -5.27 229 1 p ' p " p " Observed Observed Calculated 1 1 Frequency Correction Correction 3 5 C 1 1 4 N 1 2 C 1 8 0 Ground V i b r a t i o n a l State 3 — 2 1,3 1,2 2.5 1.5 1.5 1.5 16981.05 -4.11 -4.16 2.5 1.5 1.5 0.5 16981.05 -4.11 -4.16 2.5 3.5 1.5 2.5 16981.33 -3.83 -3.87 2.5 2.5 1.5 2.5 16981.97 -3.22 -3.21 2.5 2.5 1.5 1.5 16981.97 -3.22 -3.21 3.5 2.5 2.5 1.5 16982.70 -2.46 -2.50 3.5 4.5 2.5 3.5 16982.70 -2.46 -2.38 3.5 3.5 2.5 2.5 16983.28 -1.88 -1.85 1.5 0,5 0.5 1.5 16985.00* -0.16 -0.14 1.5 0.5 0.5 0.5 16985.00* -0.16 -0.14 1.5 2.5 0.5 1.5 16985.68 0.52 0.50 1.5 1.5 0.5 1.5 16986.49 1.33 1.29 1.5 1.5 0.5 0.5 16986.49 1.33 1.29 4.5 3.5 3.5 2.5 16987.11 1.95 1.98 4.5 5.5 3.5 4.5 16987.11 1.95 2.02 4.5 4.5 3.5 3.5 16987.57 2.41 2.41 * Very weak — tenuous 30,3 _ 2 I , 2 4.5 4.5 3.5 3.5 -30313.52 2.09 2.05 4.5 5.5 3.5 4.5 -30313.97 1.64 1.66 4.5 3.5 3.5 2.5 -30313.97 1.64 1.62 1.5 1.5 0.5 1.5 -30315.14 0.47 0.44 1.5 1.5 0.5 0.5 -30315.14 0.47 0.44 1.5 2.5 0.5 1.5 -30315.89 -0.28 -0.36 1.5 0.5 0.5 0.5 -30316.65 -1.04 -0.99 3.5 3.5 2.5 2.5 -30316.65 -1.04 -1.13 3.5 4.5 2.5 3.5 -30317.34 -1.73 -1.67 3.5 2.5 2.5 1.5 -30317.34 -1.73 -1.79 2.5 2.5 1.5 1.5 -30318.50 -2.89 -3.00 2.5 3.5 1.5 2.5 -30319.42 -3.81 -3.66 2.5 1.5 1.5 1.5 -30319.42 -3.81 -3.94 2.5 1.5 1.5 0.5 -30319.42 -3.81 -3.94 3.5 2.5 2.5 1.5: 22643.86 -2.17 -2.24 3.5 4.5 2.5 3.5 22643.86 -2.17 -2.21 3.5 3.5 2.5 2.5 22643.86 -2.17 -1.82 4.5 3.5 3.5 2.5 22645.53 -0.50 -0.66 4.5 5.5 3.5 4.5 22645.53 -0.50 -0.65 2.5 3.5 1.5 2.5' 22645.53 -0.50 -0.46 4.5 4.5 3.5 3.5 22645.53 -0.50 -0.34 2.5 1.5 1.5 0.5 22645.53 -0.50 -0.32 2.5 2.5 1.5 1.5 -0.08 5.5 6.5 4.5 5.5 22647.19 1.16 1.13 5.5 4.5 4.5 3.5 22647.19 1. 16 1.15 5.5 5.5 4.5 4.5 22647.19 1.16 1.33 230 ' F ' " p" Observed Observed C a l c u l a t e d I 1 Frequency C o r r e c t i o n C o r r e c t i o n 4 1 , 3 3 1 , 2 3.5 2.5 2.5 1.5 23320.58 -0.98 -1.25 3.5 4.5 2.5 3.5 23320.58 -0.98 -1.22 3.5 3.5 2.5 2.5 23320.58 -0.98 -0.98 4.5 3.5 3.5 2.5 23320.58 -0.98 -0.96 4.5 5.5 3.5 4.5 23320.58 -0.98 -0.95 4.5 4 .5 3.5 3.5 23320.58 -0.98 -0.74 2.5 3.5 1.5 2.5 23322.39 0.83 0.53 2.5 1.5 1.5 0.5 23322.39 0.83 0.57 2.5 2.5 1.5 1.5 23322.39 0.83 0.77 5.5 4.5 4.5 3.5 23322.39 0.83 0.81 5.5 6.5 4.5 5.5 23322.39 0.83 0.82 5.5 5.5 4.5 4.5 23322.39 0.83 0.98 4 2,3 3 2 , 2 4.5 3. 5 3.5 2.5 22986.04 -4.58 -4.66 4.5 5.5 3.5 4.5 22986.04 -4.58 -4.56 4.5 4.5 3.5 3.5 22986.50 -4.12 -4.14 3.5 2.5 2.5 1.5 22988.49 -2.13 -2.21 3.5 4.5 2.5 3.5 22988.49 -2.13 -2.10 3.5 3.5 2.5 2.5 22988.97 -1.65 -1.71 5.5 4.5 4.5 3.5 22992.94* 2.32 2.30 5.5 6.5 4.5 5.5 22992.94* 2.32 2.40 5.5 5.5 4 .5 4 .5 22993.43* 2.81 2.91 2.5 3.5 1.5 2.5 4.89 2.5 1.5 1.5 0.5 4.70 2.5 2.5 1.5 1.5 5.32 * Overlapped b y 4 2 , 2 — 3 J 2 , l 3 5 C 1 1 4 N 1 2 C 1 8 0 G.V.S . 4 2 , 2 4.5 3.5 3.5 2.5 22990.50 -4.58 -4.64 4.5 5.5 3.5 4.5 22990.50 -4.58 -4.54 4.5 4.5 3.5 3.5 22991.26* -3.82 -4.12 3.5 2.5 2.5 1.5 22992.94+ -2.14 -2.19 3.5 4.5 2.5 3.5 22992.94+ -2.14 -2.08 3.5 3.5 2.5 2.5 22993.43+ -1.65 -1.70 5.5 4.5 4.5 3.5 22997.43 2.35 2.29 5.5 6.5 4.5 5.5 22997.43 2.35 2.38 5.5 5.5 4.5 4.5 22997.97 2.89 2.89 2.5 1.5 1.5 0.5 22999.62* 4.54 4.69 2.5 3.5 1.5 2.5 22999.62* 4.54 4.87 2.5 2.5 1.5 1.5 5.29 * Overlapped + Overlapped b * 4 3 , 2 b * 4 2 , 3 - 3 3 , 1 3 2 , 2 3 5 C 1 1 4 N 1 2 C 1 8 0 G.V.S . 231 ' F ' F " " Observed Observed Calculated 1 1 Frequency Correction Correction 4 — 3 3,2 3,1 43,1 33,0 4.5 3.5 3.5 2.5 22991.26* -11.12 -11.07 4.5 5.5 3.5 4.5 22991.26* -11.12 -10.83 4.5 4.5 3.5 3.5 22992.25 -10.13 -10.14 3.5 2.5 2.5 1.5 22999.62* -2.76 -2.98 3.5 4.5 2.5 3.5 22999.62* -2.76 -2.73 3.5 3.5 2.5 2.5 22999.62* -2.76 -2.24 5.5 4.5 4.5 3.5 23007.00 4.62 4.50 5.5 6.5 4.5 5.5 23007.00 4.62 4.76 5.5 5.5 4.5 4.5 23008.22 5.84 5.83 2.5 1.5 1.5 0.5 12.34 2.5 3.5 1.5 2.5 23015.42 13.04 12.98 2.5 2.5 1.5 1.5 23016.24 13.86 13.61 * Overlapped by 4 2,2 - 3 2 , 1 3 5 C 1 1 4 N 1 2 C 1 8 0 G.V.S. ~ 4 0 , 4 4.5 5.5 3.5 4.5 28718.26 -0.84 -0.91 4.5 3.5 3.5 2.5 28718.26 -0.84 -0.88 3.5 4.5 2.5 3.5 28718.26 -0.84 -0.86 3.5 2.5 2.5 1.5 28718.26 -0.84 -0.76 4.5 4.5 3.5 3.5 28718.26 -0.84 -0.75 3.5 3.5 2.5 2.5 28718.26 -0.84 -0.73 5.5 6.5 4.5 5.5 28719.43 0.33 0.30 5.5 4.5 4.5 3.5 28719.43 0.33 0.32 6.5 7.5 5.5 6.5 28719.43 0.33 0.36 6.5 5.5 5.5 4.5 28719.43 0.33 0.40 6.5 6.5 5.5 5.5 28719.43 0.33 0.41 5.5 5.5 4.5 4.5 28719.43 0.33 0.41 51,5 4.5 5.5 3.5 4.5 28305.30 -1.34 -1.34 4.5 3.5 3.5 2.5 28305.30 -1.34 -1.32 4.5 4.5 3.5 3.5 28305.30 -1.34 -1.11 3.5 4.5 2.5 3.5 28306.45 -0.19 -0.46 3.5 2.5 2.5 1.5 28306.45 -0.19 -0.36 3.5 3.5 2.5 2.5 28306.45 -0.19 -0.25 5.5 6.5 4.5 5.5 28306.45 -0.19 -0.18 5.5 4.5 4.5 3.5 28306.45 -0.19 -0.17 5.5 5.5 4.5 4.5 28306.45 -0.19 0.00 6.5 7.5 5.5 6.5 28307.36 0.72 0.72 6.5 5.5 5.5 4.5 28307.36 0.72 0.75 6.5 6.5 5.5 5.5 28307.36 0.72 0.84 5 M - 4 1 , 3 4.5 5.5 3.5 4.5 29149.80 -0.76 -0.79 4.5 3.5 3.5 2.5 29149.80 -0.76 -0.78 232 1 F l i F II F l 11 F Observed Frequency Observed C o r r e c t i o n C a l c u l a t i Cor rec t i c 4.5 4.5 3.5 3.5 29149.80 -0.76 -0.64 5.5 6.5 4.5 5.5 29150.23 -0.33 -0.39 5.5 4.5 4 .5 3.5 29150.23 -0.33 -0.39 5.5 5.5 4 .5 4.5 29150.23 -0.33 -0.26 3.5 4.5 2.5 3.5 29150.63 0.07 0.09 3.5 2.5 2.5 1.5 29150.63 0.07 0.14 3.5 3.5 2.5 2.5 29150.63 0.07 0.23 6.5 7.5 5.5 6.5 29151.10 0.54 0.51 6.5 5.5 5.5 4.5 29151.10 0.54 0.51 6.5 6.5 5.5 5.5 29151.10 0.54 0.60 — 4 2,3 5.5 4.5 4.5 3.5 28735.42 -2.05 -2.12 5.5 6.5 4.5 5.5 28735.42 -2.05 -2.09 5.5 5.5 4.5 4.5 28735.92 -1.55 -1.81 4.5 3.5 3.5 2.5 28735.92 -1.55 -1.62 4.5 5.5 3.5 4 .5 28735.92 -1.55 -1.58 4.5 4.5 3.5 3.5 -1.30 6.5 5.5 5.5 4.5 28738.86 1.39 1.38 6.5 7.5 5.5 6.5 28738.86 1.39 , 1.41 6.5 6.5 5.5 5.5 28739.35 1.88 1.69 3.5 2.5 2.5 1.5 28739.35 1.88 1.89 3.5 4.5 2.5 3.5 28739.35 1.88 1.92 3.5 3.5 2.5 2.5 2.21 5 2 , 3 ~ - A ^2,2 5.5 4.5 4 .5 3.5 28744.32 -2.07 -2.09 5.5 6.5 4 .5 5.5 28744.32 -2.07 -2.06 5.5 5.5 4.5 4.5 28744.68 -1.71 -1.78 4.5 3.5 3.5 2.5 28744.68 -1.71 -1.60 4.5 5.5 3.5 4.5 28744.68 -1.71 -1.56 4.5 4.5 3.5 3.5 28745.06 i -1.33 -1.28 6.5 5.5 5.5 4.5 28747.91* 1.52 1.36 6.5 7.5 5.5 6.5 28747.91* 1.52 1.39 6.5 6.5 5.5 5.5 28748.26* 1.87 1.67 3.5 2.5 2.5 1.5 28748.26* 1.87 1.86 3.5 4.5 2.5 3.5 28748.26* 1.87 1.89 3.5 3.5 2.5 2.5 28748.58* 2.19 2.18 * Overlapped by 5 3 , 3 — 4 3,2 3 5 C 1 1 4 N 1 2 C 1 8 0 G .V . .S. Note : Hype r f i ne s t r u c t u r e of 5 — 4 5 J 2 , 4 4 2 , 3 ' °2 ,3 — 4 35 2,2 J C1 1 4 N 1 2 C 1 8 0 G.V.S . not c l e a r l y r e s o l v e d 5 3 , 3 4 3 , 2 5 3 , 2 ~ 4 3 , 1 5.5 4.5 4.5 3.5 5.5 6.5 4.5 5.5 28747.91* 28747.91* -5.14 -5.14 -5.20 -5.09 233 Observed Observed C a l c u l a t e d Frequency C o r r e c t i o n C o r r e c t i o n 5.5 5.5 4 .5 4.5 28748.26 -4.79 -4.61 5.5 5.5 4.5 4.5 28748.58 -4.47 -4.61 4.5 3.5 3.5 2.5 28750.80+ -2.25 -2.57 4.5 5.5 3.5 4.5 28750.80+ -2.25 -2.44 4.5 4.5 3.5 3.5 28750.80+ -2.25 -2.00 6.5 5.5 5.5 4.5 28755.81 2.76 2.62 6.5 7.5 5.5 6.5 28755.81 2.76 2.73 6.5 6.5 5.5 5.5 28756.33 3.28 3.31 3.5 2.5 2.5 1.5 28758.70+ 5.65 5.21 3.5 4.5 2.5 3.5 28758.70+ 5.65 5.40 3.5 3.5 2.5 2.5 28758.70 5.65 5.90 * Overlapped by 5„ - 4 2 , 2 3 5 C 1 1 4 N 1 2 C 1 8 0 G.V .S . + Weak broad " l i n e " w i t h a " h i n t " o f s p l i t t i n g . \,2~ 5.5 4.5 4 .5 3.5 28761.36 -9.35 -9.52 5.5 6.5 4.5 5.5 28761.36 -9.35 -9.31 5.5 5.5 4.5 4.5 28762.07 -8.64 -8.53 4.5 3.5 3.5 2.5 28767.01 -3.70 -3.90 4.5 5.5 3.5 4 .5 28767.01 -3.70 -3.65 4 .5 4.5 3.5 3.5 28767.77 -2.94 -2.99 6.5 5.5 5.5 4 .5 28775.23 .4.52 4.37 6.5 7.5 5.5 6.5 28775.23 4.52 4.58 6.5 6.5 5.5 5.5 28776.34 5.63 5.58 3.5 2.5 2.5 1.5 28780.91 10.20 9.88 3.5 4 .5 2.5 3.5 28780.91 10.20 10.30 3.5 3.5 2.5 2.5 28781.82 11.11 11.08 5 0 , 5 -5.5 4.5 4.5 3.5 -18247.85 2.11 2.14 5.5 5.5 4 .5 4.5 -18247.85 2.11 2.11 5.5 6.5 4.5 5.5 -18247.85 2.11 2.10 4 .5 4.5 3.5 3.5 -18249.97 -0.01 -0.02 4.5 3.5 3.5 2.5 -18249.97 -0.01 -0.03 4.5 5.5 3.5 4.5 -18249.97 -0.01 -0.09 6.5 5.5 5.5 4.5 -18250.61 -0.65 -0.56 6.5 7.5 5.5 6.5 -18250.61 -0.65 -0.61 6.5 6.5 5.5 5.5 -18250.61 -0.65 -0.69 3.5 2.5 2.5 1.5 -18252.73 -2.77 -2.68 3.5 3.5 2.5 2.5 -18252.73 -2.77 -2.80 3.5 4.5 2.5 3.5 -18252.73 -2.77 -2.83 6 0 , 6 ~ 5 0 , 5 5.5 6.5 4.5 5.5 34456.88 -0 .60 -0.59 5.5 4 .5 4.5 3.5 34456.88 -0.60 -0.56 4.5 5.5 3.5 4.5 34456.88 -0.60 -0.53 5.5 5.5 4 .5 4.5 34456.88 -0.60 -0.50 4.5 3.5 3.5 2.5 34456.88 -0 .60 -0.47 234 p p' F " Observed Observed C a l c u l a t e d 1 1 Frequency C o r r e c t i o n C o r r e c t i o n 4.5 4.5 3.5 3.5 34456.88 -0.60 -0.46 6.5 7.5 5.5 6.5 34457.80 0.32 0.21 6.5 5.5 5.5 4.5 34457.80 0.32 0.23 6.5 6.5 5.5 5.5 34457.80 0.32 0.28 7.5 8.5 6.5 7.5 34457.80 0.32 0.28 7.5 6.5 6.5 5.5 34457.80 0.32 0.30 7.5 7.5 6.5 6.5 34457.80 0.32 0.31 6 1 , 6 5.5 6.5 4 .5 5.5 33965.60 -0.87 -0.88 5.5 4.5 4 .5 3.5 33965.60 -0.87 -0.85 5.5 5.5 4.5 4.5 33965.60 -0.87 -0.74 4.5 5.5 3.5 4.5 33966.19 -0.28 -0.37 4.5 3.5 3.5 2.5 33966.19 -0.28 -0.30 4.5 4.5 3.5 3.5 33966.19 -0.28 -0.25 6.5 7.5 5.5 6.5 33966.46 -0.01 -0.02 6.5 5.5 5.5 4.5 33966.46 -0.01 -0.00 6.5 6.5 5.5 5.5 33966.46 -0.01 0.09 7.5 8.5 6.5 7.5 33967.03 0.56 0.50 7.5 6.5 6.5 5.5 33967.03 0.56 0.52 7.5 7.5 6.5 6.5 . 33967.03 0.56 0.57 6 1 , 5 5.5 6.5 4.5 5.5 34978.36 -0.53 -0.53 5.5 4.5 4.5 3.5 34978.36 -0.53 -0.52 5.5 5.5 4.5 4 .5 34978.36 -0.53 -0.44 6.5 7.5 5.5 6.5 34978.80 -0.09 -0.18 6.5 5.5 5.5 4 .5 34978.80 -0.09 -0.17 6.5 6.5 5.5 5.5 34978.80 -0.09 -0.10 4.5 5.5 3.5 4 .5 34978.80 -0.09 -0.02 4.5 3.5 3.5 2.5 34978.80 -0.09 0.02 4.5 4.5 3.5 3.5 34978.80 -0.09 0.07 7.5 8.5 6.5 7.5 34979.26 0.37 0.34 7.5 6.5 6.5 5.5 34979.26 0.37 0.35 7.5 7.5 6.5 6.5 34979.26 0.37 0.40 6 2 , 5 5.5 4.5 4.5 3.5 34482.55 -1.04 -1.12 6.5 5.5 5.5 4.5 : 34482.55 -1.04 -1.11 5.5 6.5 4.5 5.5 : 34482.55 -1.04 -1.11 6.5 7.5 5.5 6.5 34482.55 -1.04 -1.10 6.5 6.5 5.5 5.5 34482.55 -1.04 -0.91 5.5 5.5 4.5 4.5 34482.55 -1.04 -0.91 4.5 5.5 3.5 4.5 ! 34484.54 0.95 0.90 7.5 6.5 6.5 5.5 ! 34484.54 0.95 0.90 4.5 3.5 3.5 2.5 34484.54 0.95 0.90 7.5 8.5 6.5 7.5 34484.54 0.95 0.91 7.5 7.5 6.5 6.5 34484.54 0.95 1.08 4.5 4.5 3.5 3.5 34484.54 0.95 1.09 235 1 T ? i 11 II r» Observed Observed C a l c u l a t e d F i r F l r Frequency C o r r e c t i o n C o r r e c t i o n 5 2 , 3 5.5 4.5 4.5 3.5 34498.38 -1.01 -1.09 5.5 6.5 4.5 5.5 34498.38 -1.01 -1.08 6.5 5.5 5.5 4.5 34498.38 -1.01 -1.07 6.5 7.5 5.5 6.5 34498.38 -1.01 -1.07 5.5 5.5 4.5 4.5 34498.38 -1.01 -0.89 6.5 6.5 5.5 5.5 34498.38 -1.01 -0.88 4.5 5.5 3.5 4.5 34500.30 0.91 0.87 4.5 3.5 3.5 2.5 34500.30 0.91 0.87 7.5 6.5 6.5 5.5 34500.30 0.91 0.88 7.5 8.5 6.5 7.5 34500.30 0.91 0.88 4.5 4.5 3.5 3:5 34500.30 0.91 1.05 7.5 7.5 6.5 6.5 34500.30 0.91 1.05 S,4 5 3 , 3 6 3 , 3 5 3 , 2 6.5 5.5 5.5 4.5 34501.23 -2.57 -2.80 6.5 7.5 5.5 6.5 34501.23 -2.57 -2.76 6.5 6.5 5.5 5.5 34501.23 -2.57 -2.43 5.5 4.5 4.5 3.5 34502.14 -1.66 -1.83 5.5 6.5 4 .5 5.5 34502.14 -1.66 -1.77 5.5 5.5 4.5 4.5 34502.14 -1.66 -1.45 7.5 6.5 6.5 5.5 34505.60 1.80 1.67 7.5 8.5 6.5 7.5 34505.60 1.80 1.72 7.5 7.5 6.5 6.5 34505.60 1.80 2.07 4.5 3.5 3.5 2.5 34506.60 2.80 2.64 4.5 5.5 3.5 4.5 34506.60 2.80 2.71 4.5 4.5 3.5 3.5 34506.60 2.80 3.04 - V 6.5 5.5 5.5 4.5 34519.65 -5.11 -5.20 6.5 7.5 5.5 6.5 34519.65 -5.11 -5.09 6.5 6.5 5.5 5.5 34520.19 -4.57 -4.57 5.5 4.5 4.5 3.5 34522.02 -2.74 -2.84 5.5 6.5 4.5 5.5 34522.02 -2.74 -2.72 5.5 5.5 4.5 4.5 34522.53 -2.23 -2.22 7.5 6.5 6.5 5.5 34527.56 2.80 2.76 7.5 8.5 6.5 7.5 34527.56 2.80 2.86 7.5 7.5 6.5 6.5 34528.20 3.44 3.46 4.5 3.5 3.5 2.5 34529.98 5.22 5.09 4.5 5.5 3.5 4.5 34529.98 5.22 5.26 4.5 4.5 3.5 3.5 34530.58 5.82 5.79 6 5 . 2 - 5 5 , 1 ~ 5 5 , 0 6.5 5.5 5.5 4.5 34543.99 -8.16 -8.27 6.5 7.5 5.5 6.5 34543.99 -8.16 -8.10 236 f? M Observed Observed Ca l cu l a te F l r F l r Frequency C o r r e c t i o n C o r r e c t i c 6.5 6.5 5.5 5.5 34544.85 -7.30 -7.32 5.5 4.5 4.5 3.5 34548.19 -3.96 -4.13 5.5 6.5 4.5 5.5 34548.19 -3.96 -3.93 5.5 5.5 4.5 4.5 34549.02 -3.13 -3.21 7.5 6.5 6.5 5.5 34556.36 4.21 4.15 7.5 8.5 6.5 7.5 34556.36 4.21 4.32 7.5 . 7.5 6.5 6.5 34557.42 5.27 5.25 4.5 3.5 3.5 2.5 34560.59 8.44 8.23 4.5 5.5 3.5 4.5 34560.59 8.44 8.53 4.5 4.5 3.5 3.5 34561.45 9.30 9.33 60,6 " ~ 5 1 . 5 6.5 5.5 5.5 4.5 -12096.75 2.46 2.54 6.5 7.5 5.5 6.5 -12096.75 2.46 2.48 6.5 6.5 5.5 5.5 -12096.75 2.46 2.39 5.5 4.5 4.5 3.5 -12098.57 0.64 0.73 5.5 6.5 4.5 5.5 -12098.57 0.64 0.66 5.5 5.5 4.5 4.5 -12098,57 0.64 0.59 7.5 6.5 6.5 5.5 -12100.28 -1.07 -1.01 7.5 8.5 6.5 7.5 -12100.28 -1.07 -1.06 7.5 7.5 6.5 6.5 -12100.28 -1.07 -1.22 4.5 3.5 3.5 2.5 -12102.12 -2.91 -2.79 4.5 5.5 3.5 4.5 -12102.12 -2.91 -2.90 4.5 4.5 3.5 3.5 -12102.12 -2.91 -3.00 1 0 o , i o - 9 1 , 9 8.5 8.5 7.5 7.5 13230.96 -2.98 -2.98 8.5 9.5 7.5 8.5 13231.24 -2.70 -2.73 8.5 7.5 7.5 6.5 13231.24 -2.70 -2.67 11.5 11.5 10.5 10.5 13231.91 -2.03 -2.00 11.5 12.5 10.5 11.5 13232.19 -1.75 -1.73 11.5 10.5 10.5 9.5 13232.19 -1.75 -1.69 9.5 9.5 8.5 8.5 13235.41 1.47 1.50 9.5 10.5 8.5 9.5 13235.68 1.74 1.74 9.5 8.5 8.5 7.5 13235.68 1.74 1.79 10.5 10.5 9.5 9.5 13236.47 2.53 2.49 10.5 11.5 9.5 10.5 13236.72 2.78 2.74 10.5 9.5 9.5 8.5 13236.72 2.78 2.78 U 0,11 - 1 0 i , 10 9.5 9.5 8.5 8.5 19731.70 -2.93 -2.93 9.5 10.5 8.5 9.5 19731.99 -2.64 -2.67 9.5 8.5 8.5 7.5 19731.99 -2.64 -2.62 12.5 12.5 11.5 11.5 19732.55 -2.08 -2.06 12.5 13.5 11.5 12.5 19732.82 -1.81 -1.78 12.5 11.5 11.5 10.5 19732.82 -1.81 -1.75 10.5 10.5 9.5 9.5 19736.20 1.57 1.58 10.5 11.5 9.5 10.5 19736.47 1.84 1.83 10.5 9.5 9.5 8.5 19736.47 1.84 1.87 237 0 1 F l F I I F l I I F Observed Frequency Observed C o r r e c t i o n C a l c u l a t e d C o r r e c t i o n 11.5 11.5 10.5 10.5 19737.07 2.44 2.45 11.5 12.5 10.5 11.5 19737.40 2.77 2.71 11.5 10.5 10.5 9.5 . 19737.40 2.75 13 0,13 ~ 1 2 1 ,12 11.5 11.5 10.5 10.5 32908.57 -2.82 -2.81 11.5 12.5 10.5 11.5 32908.86 -2.53 -2.53 11.5 10.5 10.5 9.5 32908.86 -2.53 -2.50 14.5 14.5 13.5 13.5 32909.27 -2.12 -2.11 14.5 15.5 13.5 14.5 32909.55 -1.84 -1.82 14.5 13.5 13.5 12.5 32909.55 -1.84 -1.80 12.5 12.5 11.5 11.5 32913.03 1.64 1.65 12.5 13.5 11.5 12.5 32913.33 1.94 1.92 12.5 11.5 11.5 10.5 32913.33 1.94 1.95 13.5 13.5 12.5 12.5 32913.78 2.39 2.36 13.5 14.5 12.5 13.5 32914.07 2.68 2.63 13.5 12.5 12.5 11.5 32914.07 2.68 2.66 1 7 1 , 1 6 - 1 6 2 ,15 17.5 16.5 16.5 15.5 -33126.86 2.70 2.70 17.5 18.5 16.5 17.5 -33126.86 2.70 2.67 17.5 17.5 16.5 16.5 -33126.86 2.70 2.51 16.5 15.5 15.5 14.5 -33127.33 2.23 2.20 16.5 17.5 15.5 16.5 2.05 16.5 16.5 15.5 15.5 1.89 18.5 17.5 17.5 16.5 -33131.60 -2.04 -2.01 18.5 19.5 17.5 18.5 -33131.60 -2.04 -2.03 18.5 18.5 17.5 17.5 -33132.08 -2.52 -2.33 15.5 14.5 14.5 13.5 -33132.08 -2.52 -2.50 15.5 16.5 14.5 15.5 -33132.08 -2.52 -2.53 15.5 15.5 14.5 14.5 -2.82 1 8 1 , 1 7 ~ 1 7 2 ,16 18.5 17.5 17.5 16.5 -25955.15 2.71 2.71 18.5 19.5 17.5 18.5 -25955.15 2.71 2.69 18.5 18.5 17.5 17.5 -25955.15 2.71 2.52 17.5 16.5 16.5 15.5 -25955.60 2.26 2.24 17.5 18.5 16.5 17.5 2.09 17.5 17.5 16.5 16.5 -25955.97 1.89 1.92 19.5 18.5 18.5 17.5 -25959.90 -2.04 -2.04 19.5 20.5 18.5 19.5 -25959.90 -2.04 -2.06 19.5 19.5 18.5 18.5 -25960.32 -2.46 -2.37 16.5 15.5 15.5 14.5 -25960.32 -2.46 -2.51 16.5 17.5 15.5 16.5 -25960.32 -2.46 -2.53 16.5 16.5 15.5 15.5 -25960.75 -2.89 -2.83 1 9 1 , 1 8 - 1 8 2 ,17 19.5 18.5 18.5 17.5 -18711.98 2.71 2.72 19.5 20.5 18.5 19.5 -18711.98 2.71 2.70 238 1 F, i F II F, II F Observed Observed C a l c u l a t e d 1 1 Frequency C o r r e c t i o n C o r r e c t i o n 19.5 19.5 18.5 18.5 -18712.38 2.31 2.32 18.5 19.5 17.5 18.5 -18712.38 2.31 2.32 18.5 17.5 17.5 16.5 -18712.38 2.31 2.28 18.5 18.5 17.5 17.5 -18712.78 1.91 1.95 20.5 19.5 19.5 18.5 -18716.73 -2.04 -2.07 20.5 21.5 19.5 20.5 •-18716.73 -2.04 -2.09 20.5 20.5 19.5 19.5 -18717.16 -2.47 -2.40 17.5 16.5 16.5 15.5 -18717.16 -2.47 -2.51 17.5 18.5 16.5 17.5 -18717.16 -2.47 -2.53 17.5 17.5 16.5 16.5 -18717.62 -2.93 -2.84 2 ° 1 ,19 - 1 9 0 ,18 20.5 19.5 / '19.5 18.5 -11398.82 2.69 2.72 20.5 21.5 19.5 20.5 -11398.82 2.69 2.70 20.5 20.5 19.5 19.5 -11399.21 2.30 2.35 19.5 20.5 18.5 19.5 -11399.21 2.30 2.32 19.5 18.5 18.5 17.5 -11399.21 2.30 2.30 19.5 19.5 18.5 18.5 -11399.57 1.94 1.97 21.5 20.5 20.5 19.5 -11403.61 -2 .10 -2.09 21.5 22.5 20.5 21.5 -11403.61 -2 .10 -2.11 21.5 21.5 20.5 20.5 -11403.98 -2.47 -2.42 18.5 17.5 17.5 16.5 -11403.98 -2.47 -2.51 18.5 19.5 17.5 18.5 -11403.98 -2.47 -2.53 18.5 18.5 17.5 17.5 -11404.35 -2.84 -2.84 23 1,22 — 22 2 ,21 21.5 21.5 20.5 20.5 10940.31 -2.80 -2.82 21.5 22.5 20.5 21.5 10940.63 -2.48 -2.51 21.5 20.5 20.5 19.5 10940.63 -2.48 -2.49 24.5 24.5 23.5 23.5 10940.63 -2.48 -2.46 24.5 25.5 23.5 24.5 10940.97 -2.14 -2.15 24.5 23.5 23 .5 22.5 10940.97 -2.14 -2.13 22.5 22.5 21.5 21.5 10945.09 1.98 2.01 22.5 23.5 21.5 22.5 10945.44 2.33 2.34 22.5 21.5 21.5 20.5 10945.44 2.33 2.35 23.5 23.5 22.5 22.5 10945.44 2.33 2.36 23.5 24.5 22.5 23.5 10945.82 2.71 2.69 23.5 22.5 22.5 21.5 10945.82 2.71 2.70 2 4 1 , 2 4 ~ 2 3 2 ,21 22.5 22.5 21.5 21.5 -37135.38 4.87 4.89 25.5 25.5 24.5 24.5 -37135.88 4.37 4.41 22.5 23.5 21.5 22.5 -37135.88 4.37 4.32 22.5 21.5 21.5 20.5 -37135.88 4.37 4.29 25.5 26.5 24.5 25.5 -37136.43 3.82 3.83 25.5 24.5 24.5 23.5 -37136.43 3.82 3.81 23.5 23.5 22.5 22.5 -37143.86 -3.61 -3.61 24.5 24.5 23.5 23.5 -37144.43 -4.18 -4.09 23.5 24.5 22.5 23.5 -37144.43 -4.18 -4.19 239 Observed Observed C a l c u l a t e d Frequency C o r r e c t i o n C o r r e c t i o n 23.5 22.5 22.5 21.5 -37144.43 -4.18 -4.21 24.5 25.5 23.5 24.5 -37144.97 -4.72 -4.67 24.5 23.5 23.5 22.5 -37144.97 -4.72 -4.69 2 4 1 , 2 3 — 23 2. ,22 22.5 22.5 21.5 21.5 18517.93 -2.79 -2.81 22.5 23.5 21.5 22.5 18518.27 -2.45 -2.49 22.5 21.5 21.5 20.5 18518.27 -2.45 -2.48 25.5 25.5 24.5 24.5 18518.27 -2.45 -2.47 25.5 26.5 24.5 25.5 18518.62 -2.10 -2.15 25.5 24.5 24.5 23.5 18518.62 -2.10 -2.14 23.5 23.5 22.5 22.5 18522.68 1.96 2.02 23.5 22.5 22.5 21.5 18523.02 2.30 2.35 23.5 24.5 22.5 23.5 18523.02 2.30 2.35 24.5 24.5 23.5 23.5 18523.02 2.30 2.35 24.5 25.5 23.5 24.5 18523.40 2.68 2.68 24.5 23.5 23.5 22.5 18523.40 2.68 2.69 2 5 1 , 2 5 - " 2 , 22 23.5 23.5 22.5 22.5 -34577.95 5.04 4.99 26.5 26.5 25.5 25.5 -34578.52 4.47 4.51 23.5 24.5 22.5 23.5 -34578.52 4.47 4.40 23.5 22.5 22.5 21.5 -34578.52 4.47 4.38 26.5 27.5 25.5 26.5 -34579.07 3.92 3.92 26.5 25.5 25.5 24.5 -34579.07 3.92 3.90 24.5 24.5 23.5 23.5 -34586.72 -3.73 -3.70 25.5 25.5 24.5 24.5 -34587.27 -4.28 -4.17 24.5 25.5 23.5 24.5 -34587.27 -4.28 -4.29 24.5 23.5 23.5 22.5 -34587.27 -4.28 -4.31 25.5 26.5 24.5 25.5 -34587.82 -4.83 -4.76 25.5 24.5 24.5 23.5 -34587.82 -4.83 -4.78 2 5 1 , 2 4 ~ 2 4 2 , 23 23.5 23.5 22.5 22.5 26156.95 -2.83 -2.80 23.5 24.5 22.5 23.5 26157.31 -2.47 -2.48 26.5 26.5 25.5 25.5 26157.31 -2.47 -2.47 23.5 22.5 22.5 21.5 26157.31 -2.47 -2.46 26.5 27.5 25.5 26.5 26157.65 -2.13 -2.15 26.5 25.5 25.5 24.5 26157.65 -2.13 -2.14 24.5 24.5 23.5 23.5 26161.77 1.99 2.02 25.5 25.5 24.5 24.5 26162.12 2.34 2.34 24.5 25.5 23.5 24.5 26162.12 2.34 2.35 24.5 23.5 23.5 22.5 26162.12 2.34 2.35 25.5 26.5 24.5 25.5 26162.48 2.70 2.67 25.5 24.5 24.5 23.5 26162.48 2.70 2.68 2 6 1 , 2 6 23 24.5 24.5 23.5 23.5 -32226.77 5.11 5.09 27.5 27.5 26.5 26.5 -32227.34 4.54 4.62 240 F l i F II • F l II F Observed Frequency Observed C o r r e c t i o n C a l c u l a t e d C o r r e c t i o n 24.5 25.5 23.5 24.5 -32227.34 4.54 4.49 24.5 23.5 23.5 22.5 -32227.34 4.54 4.47 27.5 28.5 26.5 27.5 -32227.89 3.99 4.02 27.5 26.5 26.5 25.5 -32227.89 3.99 4.00 25.5 25.5 24.5 24.5 -32235.70 -3.82 -3.79 26.5 26.5 25.5 25.5 -32236.26 -4.38 -4.25 25.5 26.5 24.5 25.5 -32236.26 -4.38 -4.39 25.5 24.5 24.5 23.5 -32236.26 -4.38 -4.41 26.5 27.5 25.5 26.5 -32236.77 -4.89 -4.86 26.5 25.5 25.5 24.5 -32236.77 -4.89 -4.88 ~ 2 5 2 ,24 ••• 24.5 24.5 23.5 23.5 33855.46 -2.77 -2.78 27.5 27.5 26.5 26.5 33855.76 -2.47 -2.47 24.5 25.5 23.5 24.5 33855.76 -2.47 -2.46 24.5 23.5 23.5 22.5 33855.76 -2.47 -2.45 27.5 28.5 26.5 27.5 33856.12 -2.11 -2.15 27.5 26.5 26.5 25.5 33856.12 -2.11 -2.14 25.5 25.5 24.5 24.5 33860.20 1.97 2.02 26.5 26.5 25.5 25.5 33860.56 2.33 2.33 25.5 26.5 24.5 25.5 33860.56 2.33 2.34 25.5 24.5 24.5 23.5 33860.56 2.33 2.35 26.5 27.5 25.5 26.5 33860.90 2.67 2.65 26.5 25.5 25.5 24.5 33860.90 2.67 2.67 2 7 1 , 2 7 - 2 6 2 ,24 25.5 25.5 24.5 24.5 -30088.31 5.17 5.19 28.5 28.5 27.5 27.5 -30088.85 4.63 4.72 25.5 26.5 24.5 25.5 -30088.85 4.63 4.58 25.5 24.5 24.5 23.5 -30088.85 4.63 4.55 28.5 29.5 27.5 28.5 -30089.40 4.08 4.11 28.5 27.5 27.5 26.5 -30089.40 4.08 4.09 26.5 26.5 25.5 25.5 -30097.38 -3.90 -3.88 27.5 27.5 26.5 26.5 -30097.90 -4.42 -4.34 26.5 27.5 25.5 26.5 -30097.90 -4.42 -4.50 26.5 25.5 25.5 24.5 -30097.90 -4.42 -4.51 27.5 28.5 26.5 27.5 -30098.43 -4.95 -4.96 27.5 26.5 26.5 25.5 -30098.43 -4.95 -4.98 2 8 1 , 2 8 ~ 2 7 2 ,25 26.5 26.5 25.5 25.5 -28168.65 5.28 5.29 29.5 29.5 28.5 28.5 -28169 .10 4.83 4.83 26.5 27.5 25.5 26.5 -28169.28 4.65 4.67 26.5 25.5 25.5 24.5 -28169.28 4.65 4.64 29.5 30.5 28.5 29.5 -28169.74 4.19 4.21 29.5 28.5 28.5 27.5 -28169.74 4.19 4.19 27.5 27.5 26.5 26.5 -28177.89 -3.96 -3.97 28.5 28.5 27.5 27.5 -28178.35 -4.42 -4.43 27.5 28.5 26.5 27.5 -28178.52 -4.59 -4 .60 241 Observed Frequency Observed C o r r e c t i o n C a l c u l a t e d C o r r e c t i o n 27.5 28.5 28.5 26.5 29.5 27.5 26.5 27.5 27.5 25.5 28.5 26.5 -28178.52 -28178.99 -28178.99 -4.59 -5.06 -5.06 -4.62 -5.05 -5.08 30 1,30 29 2,27 28.5 28.5 27.5 27.5 -25008.53 5.48 31.5 31.5 30.5 30.5 -25008.96 5.05 28.5 29.5 27.5 28.5 -25009.21 4.80 28.5 27.5 27.5 26.5 -25009.21 4.80 31.5 32.5 30.5 31.5 -25009.60 4.41 31.5 30.5 30.5 29.5 -25009.60 4.41 29.5 29.5 28.5 28.5 -25018.16 -4.15 30.5 30.5 29.5 29.5 -25018.62 -4.61 29.5 30.5 28.5 29.5 -25018.82 -4.81 29.5 28.5 28.5 27.5 -25018.82 -4.81 30.5 31.5 29.5 30.5 -25019.25 -5.24 30.5 29.5 29.5 28.5 -25019.25 -5.24 5.50 5.05 4.85 4.83 4.40 4.38 -4.15 -4.60 -4.81 -4.82 -5.26 -5.28 C l N C O Ground V i b r a t i o n a l S t a t e 3 1 . 3 2 1 , 2 2.5 1.5 1.5 1.5 17541.56* -3.36 -3 .40 2.5 1.5 1.5 0.5 17541.56* -3.36 -3.40 2.5 3.5 1.5 2.5 17541.85* -3.07 -3.11 2.5 2.5 1.5 2.5 17542.47* -2.45 -2.44 2.5 2.5 1.5 1.5 17542.47* -2.45 -2.44 3.5 2.5 2.5 1.5 17542.83 -2.09 -2 .10 3.5 4.5 2.5 3.5 17543.00 -1.92 -1.98 3.5 3.5 2.5 2.5 17543.43 -1.49 -1.43 1.5 0.5 0.5 1.5 17544.72* -0.20 -0.23 1.5 0.5 0.5 0.5 17544.72* -0.20 -0.23 1.5 2.5 0.5 1.5 17545.38 0.46 0.43 1.5 1.5 0.5 0.5 1.24 1.5 1.5 0.5 1.5 1.24 4.5 3.5 3.5 2.5 17546.44 1.52 1.56 4.5 5.5 3.5 4.5 17546.44 1.52 1.59 4.5 4.5 3.5 3.5 17546.91 1.99 2.00 * Very weak; tenuous at b e s t . 242 p' F* F" F" Observed Observed C a l c u l a t e d —i 1 Frequency C o r r e c t i o n C o r r e c t i o n 4 — 3 0,4 J0,3 3.5 2.5 2.5 1.5 23741.39 -1.35 -1.32 3.5 4.5 2.5 3.5 23741.39 -1.35 -1.32 2.5 3.5 1.5 2.5 23741.39 -1.35 -1.29 2.5 1.5 1.5 0.5 23741.39 -1.35 -1.11 3.5 3.5 2.5 2.5 23741.39 -1.35 -1.01 2.5 2.5 1.5 1.5 23741.39 -1.35 -1.01 4.5 5.5 3.5 4.5 23743.19 0.45 0.34 4.5 3.5 3.5 2.5 23743.19 0.45 0.35 5.5 6.5 4.5 5.5 23743.19 0.45 0.41 5.5 4.5 4.5 3.5 23743.19 0.45 0.45 5.5 5.5 4.5 4.5 23743.19 0.45 0.48 4.5 4.5 3.5 3.5 23743.19 0.45 0.55 3.5 2.5 2.5 1.5 23390.59 -1.82 -1.82 3.5 4.5 2.5 3.5 23390.59 -1.82 -1.79 3.5 3.5 2.5 2.5 23391.01 -1.40 -1.39 4.5 3.5 3.5 2.5 23391.86 -0.55 -0.57 4.5 5.5 3.5 4.5 23391.86 -0.55 -0.56 2.5 3.5 1.5 2.5 23392.16 -0.25 -0.37 4.5 4.5 3.5 3.5 23392.16 -0.25 -0.24 2.5 1.5 1.5 0.5 23392.16 -0.25 -0.24 2.5 2.5 1.5 1.5 23392.44* 0.03 0.01 5.5 6.5 . 4.5 5.5 23393.31 0.90 0.90 5.5 4.5 4.5 3.5 23393.31 0.90 0.91 5.5 5.5 4.5 4.5 23393.57* 1.16 1.10 \ 3 3.5 2.5 2.5 1.5 24104.24 -1.06 -1.06 3.5 4.5 2.5 3.5 24104.24 -1.06 -1.04 4.5 3.5 3.5 2.5 24104.52 -0.78 -0.79 3.5 3.5 2.5 2.5 24104.52 -0.78 -0.78 4.5 5.5 3.5 4.5 24104.52 -0.78 -0.77 4.5 4.5 3.5 3.5 24104.75* -0.55 -0.56 2.5 3.5 1.5 2.5 24105.66 0.36 0.39 2.5 1.5 1.5 0.5 24105.66 0.36 0.43 2.5 2.5 1.5 1.5 24105.97 0.67 0.64 5.5 4.5 4.5 3.5 24105.97 0.67 0.66 5.5 6.5 4.5 5.5 24105.97 0.67 0.66 5.5 5.5 4.5 4.5 24106.15* 0.85 0.83 * Very weak; tenuous 243 F* F' F" F" Observed Observed C a l c u l a t e d - i . 1 Frequency C o r r e c t i o n C o r r e c t i o n 4 2 , 3 3 2 . 2 4.5 3.5 3.5 2.5 23752.33 -3.77 -3.83 4.5 5.5 3.5 4.5 23752.33 -3.77 -3.73 4.5 4.5 3.5 3.5 23752.82 -3.28 -3.29 3.5 2.5 2.5 1.5 23754.32 -1.78 -1.84 3.5 4.5 2.5 3.5 23754.32 -1.78 -1.72 3.5 3.5 2.5 2.5 23754.84 -1.26 -1.33 5.5 4.5 4.5 3.5 23757.96 1.86 1.81 5.5 6.5 4.5 5.5 23757.96 1.86 1.91 5.5 5.5 4.5 4.5 23758.50 2.40 2.44 2.5 1.5 1.5 0.5 3.76 2.5 3.5 1.5 2.5 23760.06* 3.96 3.94 2.5 2.5 1.5 1.5 23760.42* 4.32 4.38 * Weak, p o o r l y r e s o l v e d , Overlapped by 4 . „ — " 3 3 , 1 3 7 C 1 1 4 N 1 2 C 1 6 0 G.V.S 4„ „ — 3 2,2 2,1. 4.5 3.5 3.5 2.5 23757.23 -3.71 -3.81 4.5 5.5 3.5 4 .5 23757.23 -3.71 -3.71 4.5 4 .5 3.5 3.5 23757.64 -3 .30 -3.27 3.5 2.5 2.5 1.5 23759.24* -1 .70 -1.82 3.5 4 .5 2.5 3.5 23759.24* -1 .70 -1.71 3.5 3.5 2.5 2.5 23759.60* -1.34 -1.32 5.5 4 .5 4 .5 3.5 23762.79 1.85 1.80 5.5 6.5 4.5 5.5 23762.79 1.85 1.90 5.5 5.5 4.5 4.5 23763.36 2.42 2.43 2.5 1.5 1.5 0.5 23764.83 3.89 3.74 2.5 3.5 1.5 2.5 23764.83 3.89 3.93 2.5 2.5 1.5 1.5 23765.34 4.40 4.36 * Over lapped by 4 3 ) 2 - 3 3 j l 3 7 ^ 1 2 ^ 6 , 4 3 , 2 3 3 , 1 4 — 3 3,1 ^3.0 4.5 3.5 3.5 2.5 23759.24* -9.06 -9.06 4.5 5.5 3.5 4.5 23759.61* -8 .69 -8.82 23760.06+ -8.24 4.5 4.5 3.5 3.5 23760.42+ -7.88 -8.11 3.5 2.5 2.5 1.5 23766.06 -2.24 -2.50 3.5 4.5 2.5 3.5 23766.06 -2.24 -2.23 3.5 3.5 2.5 2.5 23766.53 -1.77 -1.73 5.5 4.5 4.5 3.5 23771.99 3.69 3.53 5.5 6.5 4.5 . 5.5 23771.99 3.69 3.80 244 1 F, i F II F it F Observed Observed C a l c u l a t e d 1 1 Frequency C o r r e c t i o n C o r r e c t i o n 5.5 5.5 4.5 4.5 23773.27 4.97 4.90 2.5 1.5 1.5 0.5 9.85 2.5 3.5 1.5 2.5 23778.78 10.48 10.50 2.5 2.5 1.5 1.5 11.14 * Overlapped by 4„ . ^ >/-+ Overlapped by. 4„ „ Z. , j — 3 2,2 3 7 C 1 U N 1 2 C 1 6 0 G.V.S . ~ 3 1 , 3 4.5 4.5 3.5 3.5 -24000.01 0.84 0.94 4.5 3.5 3.5 2.5 -24000.01 0.84 0.73 4.5 5.5 3.5 4.5 -24000.01 0.84 0.72 5.5 5.5 4 .5 4.5 -24000.60 0.25 0.30 5.5 4.5 4.5 3.5 -24000.60 0.25 0.25 5.5 6.5 4.5 5.5 -24000.60 0.25 0.22 3.5 3.5 2.5 2.5 -0.89 3.5 4.5 2.5 3.5 -24002.04 -1.19 -1.21 3.5 2.5 2.5 1.5 -24002.04 -1.21 2.5 2.5 1.5 1.5 -1.46 2.5 1.5 1.5 0.5 -1.57 2.5 3.5 1.5 2.5 -24002.54 -1.69 -1.75 5 0 , 5 - 4 0 , 4 4.5 5.5 3.5 4 .5 29673.83 -0.62 -0.75 4.5 3.5 3.5 2.5 29673.83 -0.62 -0.72 3.5 4.5 2.5 3,5 29673.83 -0.62 -0.71 3.5 2.5 2.5 1.5 29673.83 -0.62 -0 .60 4.5 4.5 3.5 3.5 29673.83 -0.62 -0.58 3.5 3.5 2.5 2.5 29673.83 -0.62 -0.57 5.5 6.5 4.5 5.5 29674.75 0.30 0.23 5.5 4.5 4.5 3.5 29674.75 0.30 0.26 6.5 7.5 5.5 6.5 29674.75 0.30 0.29 6.5 . 5 .5 5.5 4.5 29674.75 0.30 0.32 6.5 6.5 5.5 5.5 29674.75 0.30 0.34 5.5 5.5 4.5 4 .5 ; 29674.75 0.30 0.35 5 1 , 5 -*!.«• 4.5 5.5 3.5 4 . 5 : 29238.17 -1.14 -1.09 4.5 3.5 3.5 2.5 29238.17 -1.14 -1.07 4.5 4.5 3.5 3.5 -0.85 3.5 4.5 2.5 3.5 -0.37 3.5 2.5 2.5 1.5 -0.27 5.5 6.5 4.5 5.5 29239.14 -0.17 -0.17 245 f If 17 it Observed Observed C a l c u l a t e d F l r F l r Frequency C o r r e c t i o n C o r r e c t i o n 3.5 3.5 2.5 2.5 29239.14 -0.17 -0.17 5.5 4.5 4.5 3.5 29239.14 -0.17 -0.15 5.5 5.5 4.5 4.5 0.02 6.5 7.5 5.5 6.5 29239.93 0.62 0.57 6.5 5.5 5.5 4.5 29239.93 0.62 0.60 6.5 6.5 5.5 5.5 29239.93 0.62 0.69 - \ 3 4.5 5.5 3.5 4.5 30129.65 -0.65 -0.67 4.5 3.5 3.5 2.5 30129.65 " -0.65 -0.66 4.5 4.5 3.5 3.5 30129.65 -0.65 -0.51 5.5 6.5 4.5 5.5 30130.01 -0.29 -0.32 5.5 4.5 4.5 3.5 30130.01 -0.29 -0.32 5.5 5.5 4.5 4.5 30130.01 -0.29 -0.19 3.5 4.5 2.5 3.5 30130.38 0.08 0.05 3.5 2.5 2.5 1.5 30130.38 0.08 0.10 3.5 3.5 2.5 2.5 30130.38 0.08 0.19 6.5 7.5 5.5 6.5 30130.75 0.45 0.41 6.5 5.5 5.5 4.5 30130.75 0.45 0.42 6.5 6.5 5.5 5.5 30130.75 . 0.45 0.50 V — 4 2,3 5.5 4.5 4.5 3.5 29692.34 -1.75 -1.75 5.5 6.5 4.5 5.5 29692.34 -1.75 -1.71 5.5 5.5 4.5 4.5 29692.76 -1.33 -1.42 4.5 3.5 3.5 2.5 29692.76 -1.33 -1.34 4.5 5.5 3.5 4.5 29692.76 -1.30 -1 .30 4.5 4.5 3.5 3.5 29693.16 -0.90 -1.01 6.5 5.5 5.5 4.5 29695.23 1.17 1.09 6.5 7.5 5.5 6.5 29695.23 1.17 1.12 6.5 6.5 5.5 5.5 29695.62 1.56 1.41 3.5 2.5 2.5 1.5 29695.62 1.56 1.50 3.5 4.5 2.5 3.5 29695.62 1.56 1.54 3.5 3.5 2.5 2.5 1.83 5 2 , 3 4 2 , 2 5.5 4.5 4.5 3.5 29702.27 -1.71 -1.72 5.5 6.5 4.5 5.5 29702.27 -1.71 -1.69 5.5 5.5 4.5 4.5 29702.63 -1.35 -1.40 4.5 3.5 3.5 2.5 29702.63 -1.35 -1.32 4.5 5.5 3.5 4.5 29702.63 -1.35 -1.28 4.5 4.5 3.5 3.5 29702.99 -0.99 -0.99 6.5 5.5 5.5 4.5 29705.07 1.09 1.08 6.5 7.5 5.5 6.5 29705.07 1.09 1.11 246 1 F l t F I I F l I I F Observed ' Frequency Observed C o r r e c t i o n Ca lcu la te Co r rec t i c 6.5 6.5 5.5 5.5 29705.42 1.44 1.40 3.5 2.5 2.5 1.5 29705.42 1.44 1.48 3.5 4.5 2.5 3.5 29705.42 1.44 1.51 3.5 3.5 2.5 2.5 1.81 5 3 , 3 — 4 3,2 5 3 , 2 5.5 4.5 4.5 3.5 29706.28 -4.20 -4.27 5.5 6.5 4 .5 5.5 29706.28 -4.20 -4.16 5.5 5.5 4.5 4.5 29706.81 -3.67 -3.66 4.5 3.5 3.5 2.5 29708.56 1.92 -2.13 4.5 5.5 3.5 4.5 29708.56 1.92 -2.01 4.5 4.5 3.5 3.5 29708.56 1.92 -1.55 6.5 5.5 5.5 4.5 29712.62 2.14 2.07 6.5 7.5 5.5 6.5 29712.62 2.14 2.17 6.5 6.5 5.5 5.5 29713.23 2.75 2.77 3.5 2.5 2.5 1.5 4.16 3.5 4.5 2.5 3.5 29715.13 4.65 4.36 3.5 3.5 2.5 2.5 29715.13 4.65 4.87 5 4 ,2 5 4 , 1 5.5 4.5 4.5 3.5 29721.17 -7.64 -7.81 5.5 6.5 4 .5 5.5 29721.17 -7.64 -7.59 5.5 5.5 4.5 4.5 29722.03 -6 .78 -6.79 4.5 3.5 3.5 2.5 29725.74 -3.07 -3.25 4.5 5.5 3.5 4.5 29725.74 -3.07 -3.00 4.5 4.5 3.5 3.5 29726.59 -2.22 -2.31 6.5 5.5 5.5 4.5 29732.38 3.57 3.43 6.5 7.5 . 5.5 6.5 29732.38 3.57 3.65 6.5 6.5 5.5 5.5 29733.46 4.65 4.69 3.5 2.5 2.5 1.5 29737.08 8.27 7.87 3.5 4.5 2.5 3.5 29737.08 8.27 8.31 3.5 3.5 2.5 2.5 29737.90 9.09 9.12 5 0 , 5 5.5 4 .5 4.5 3.5 -17717.30 1.53 1.55 5.5 5.5 4.5 4.5 -17717.30 1.53 1.53 5.5 6.5 4.5 5.5 -17717.30 1.53 1.51 4.5 4.5 3.5 3.5 -17718.93 -0.10 -0.09 4.5 3.5 3.5 2.5 -17718.93 -0 .10 -0.11 4.5 5.5 3.5 4.5 -17718.93 -0.10 -0.16 6.5 5.5 5.5 4.5 -17719.24 -0.41 -0.34 6.5 7.5 5.5 6.5 -17719.24 -0.41 -0.39 6.5 6.5 5.5 5.5 -17719.24 -0.41 -0.46 3.5 2.5 2.5 1.5 -17720.90 -2.07 -1.94 3.5 3.5 2.5 2.5 -17720.90 -2.07 -2.05 3.5 4.5 2.5 3.5 -17720.90 -2.07 -2.09 247 1 F l i F ti F l ii F Observed Frequency Observed C o r r e c t i o n Calcu late Cor rec t i e 6 0 , 6 5.5 6.5 4.5 5.5 35603.00 -0.42 -0.49 5.5 4.5 4.5 3.5 35603.00 -0.42 -0.46 4.5 5.5 3.5 4.5 35603.00 -0.42 -0.44 5.5 5.5 4.5 4.5 35603.00 -0.42 -0.39 4.5 3.5 3.5 2.5 35603.00 -0.42 -0.37 4.5 4.5 3.5 3.5 35603.00 -0.42 -0.36 6.5 7.5 5.5 6.5 35603.63 0.21 0.16 6.5 5.5 5.5 4.5 35603.63 0.21 0.18 7.5 8.5 6.5 7.5 35603.63 0.21 0.22 6.5 6.5 5.5 5.5 35603.63 0.21 0.24 7.5 6.5 6.5 5.5 35603.63 0.21 0.25 7.5 7.5 6.5 6.5 35603.63 0.21 0.25 5.5 6.5 4 .5 5.5 35084.91 -0.62 -0.72 5.5 4.5 4.5 3.5 35084.91 -0.62 -0.69 5.5 5.5 4 .5 4 .5 35084.91 -0.62 -0.57 4.5 5.5 3.5 4.5 35085.41 -0.12 -0.30 4.5 3.5 3.5 2.5 35085.41 -0.12 -0.23 4.5 4.5 3.5 3.5 35085.41 -0.12 -0.18 6.5 7.5 5.5 6.5 35085.41 -0.12 -0.03 6.5 5.5 5.5 4.5 35085.41 -0.12 -0.01 6.5 6.5 5.5 5.5 35085.41 -0.12 0.09 7.5 8.5 6.5 7.5 35085.94 0.41 0.40 7.5 6.5 6.5 5.5 35085.94 0.41 0.42 7.5 7.5 6.5 6.5 35085.94 0.41 0.47 ~ V 5.5 6.5 4.5 5.5 36154.05 -0.47 -0.45 5.5 4.5 4.5 3.5 36154.05 -0.47 -0.43 5.5 5.5 4 .5 4.5 36154.05 -0.47 -0.35 6.5 7.5 5.5 6.5 36154.45 -0.07 -0.15 6.5 5.5 5.5 4.5 36154.45 -0.07 -0.14 6.5 6.5 5.5 5.5 36154.45 -0.07 -0.06 4.5 5.5 3.5 4.5 36154.45 -0.07 -0.03 4.5 3.5 3.5 2.5 36154.45 -0.07 0.00 4.5 4.5 3.5 3.5 36154.45 -0.07 0.06 7.5 8.5 6.5 7.5 36154.85 0.33 0.28 7.5 6.5 6.5 5.5 36154.85 0.33 0.29 7.5 7.5 6.5 6.5 36154.85 0.33 0.34 6 2 , 5 _ s 2 . « 5.5 4.5 4.5 3.5 35630.59 -0.86 -0.92 6.5 5.5 5.5 4 .5 35630.59 -0.86 -0.91 5.5 6.5 4 .5 5.5 35630.59 -0.86 -0.91 6.5 7.5 5.5 6.5 35630.59 -0.86 -0.90 6.5 6.5 5.5 5.5 35630.59 -0.86 -0.71 5.5 5.5 4.5 4.5 35630.59 -0.86 -0.71 248 1 F, i F I I F 11 F Observed Observed Ca lcu la te 1 1 Frequency C o r r e c t i o n Co r rec t i c 4.5 5.5 3.5 4.5 35632.21 0.76 0.71 7.5 6.5 6.5 5.5 35632.21 0.76 0.72 4.5 3.5 3.5 2.5 35632.21 0.76 0.72 4 . 5 ' 3.5 3.5 2.5 35632.21 0.76 0.72 7.5 8.5 6.5 7.5 35632.21 0.76 0.72 7.5 7.5 6.5 6.5 35632.21 0.76 0.90 4.5 4.5 3.5 3.5 35632.21 0.76 0.91 ~ 5 2 , 3 5.5 4.5 4 .5 3.5 35648.00 -0.83 -0.90 5.5 6.5 4 .5 5.5 35648.00 -0.83 -0.89 6.5 5.5 5.5 4.5 35648.00 -0.83 -0.89 6.5 7.5 5.5 6.5 35648.00 -0.83 -0.88 5.5 5.5 4.5 4.5 35648.00 -0.83 -0.70 6.5 6.5 5.5 5.5 35648.00 -0.83 -0.69 4.5 5.5 3.5 4 .5 35649.57 0.74 0.69 4.5 3.5 3.5 2.5 35649.57 0.74 0.69 7.5 6.5 6.5 5.5 35649.57 0.74 0.70 7.5 8.5 6.5 7.5 35649.57 0.74 0.71 7.5 7.5 6.5 6.5 35649.57 0.74 0.88 4.5 4.5 3.5 3.5 35649.57 0.74 0.88 6 3 , 4 5 3 , 3 6 3 , 3 _ 5 3 , 2 6.5 5.5 5.5 4 .5 35650.55 -2.13 -2.31 6.5 7.5 5.5 6.5 35650.55 -2.13 -2.26 6.5 6.5 5.5 5.5 35650.55 -2.13 -1.92 5.5 4.5 4.5 3.5 35651.41 -1.27 -1.51 5.5 6.5 4.5 5.5 35651.41 -1.27 -1.46 5.5 5.5 4.5 4.5 35651.41 -1.27 -1.13 7.5 6.5 6.5 5.5 35654.10 1.42 1.32 7.5 8.5 6.5 7.5 35654.10 1.42 1.37 7.5 7.5 6.5 6.5 35654.10 1.42 1.73 4.5 3.5 3.5 2.5 35654.98 2.30 2.11 4.5 5.5 3.5 4.5 35654.98 2.30 2.18 4.5 4.5 3.5 3.5 35654.98 2.30 2.52 6 4 , 3 6 4 , 2 - V 6.5 5.5 5.5 4.5 35670.20 -4.19 -4.27 6.5 7.5 5.5 6.5 35670.20 -4.19 -4.16 6.5 6.5 5.5 5.5 35670.78 -3.61 -3.62 5.5 4.5 4.5 3.5 35672.08 -2.31 -2.36 5.5 6.5 4 .5 5.5 35672.08 -2.31 -2.23 5.5 5.5 4.5 4.5 35672.68 -1.71 -1.72 7.5 6.5 6.5 5.5 35676.61 2.22 2.17 7.5 8.5 6.5 7.5 35676.61 2.22 2.28 7.5 7.5 6.5 6.5 35677.32 2.93 2.90 4.5 3.5 3.5 2.5 35678.64 4.25 4.05 4.5 5.5 3.5 4.5 35678.64 4.25 4.23 249 1 F l i F II F l II F Observed Frequency Observed C o r r e c t i o n Ca lcu la te Co r rec t i c 4.5 4.5 3.5 3.5 35679.22 4.83 4.79 ~ 5 5 ; l 6 5 , 1 " _ 5 5 , 0 6.5 5.5 5.5 4.5 35696.15 -6.60 -6.79 6.5 7.5 5.5 6.5 35696.15 -6.60 -6.61 6.5 6.5 5.5 5.5 35696.98 -5.77 -5.80 5.5 4.5 4 .5 3.5 35699.44 -3.31 -3.44 5.5 6.5 4.5 5.5 35699.44 -3.31 -3.22 5.5 5.5 4.5 4.5 35700.34 -2.41 -2.48 7.5 6.5 6.5 5.5 35706.06 3.31 3.27 7.5 8.5 6.5 7.5 35706.06 3.31 3.44 7.5 7.5 6.5 6.5 35707.17 4.42 4.40 4.5 3.5 3.5 2.5 6.83 6.56 4.5 5.5 3.5 4 .5 35709.58 6.83 6.87 4.5 4.5 3.5 3.5 35710.43 7.68 7.70 6 0 , 6 " 6.5 5.5 5.5 4.5 -11353.05 1.82 1.89 6.5 7.5 5.5 6.5 -11353.05 1.82 1.83 6.5 6.5 5.5 5.5 -11353.05 1.82 1.74 5.5 4.5 4 .5 3.5 -11354.40 0.47 0.50 5.5 6.5 4.5 5.5 -11354.40 0.47 0.44 5.5 5.5 4.5 4.5 -11354.40 . 0.47 0.38 7.5 6.5 6.5 5.5 -11355.65 -0.79 -0.69 7.5 8.5 6.5 7.5 -11355.65 -0.78 -0.74 7.5 7.5 6.5 6.5 -11355.65 -0.78 -0.90 4.5 3.5 3.5 2.5 -11357.00 -2.13 -2.04 4.5 5.5 3.5 4.5 -11357.00 -2.13 -2.16 4.5 4.5 3.5 3.5 -11357.00 -2.13 -2.25 9 0,9 7.5 7.5 6.5 6.5 8201.15 -2.15 -2.31 7.5 8.5 6.5 7.5 8201.15 -2.15 -2.08 7.5 6.5 6.5 5.5 8201.15 -2.15 -2.01 10.5 10.5 9.5 9.5 8202.00 -1.30 -1.45 10.5 11.5 9.5 10.5 8202.00 -1.30 -1.20 10.5 9.5 9.5 8.5 8202.00 -1.30 -1.16 8.5 8.5 7.5 7.5 8204.40 1.10 0.98 8.5 9.5 7.5 8.5 8204.40 1.10 1.20 8.5 7.5 7.5 6.5 8204.40 1.10 1.25 9.5 9.5 8.5 8.5 8205.40 2.10 1.84 9.5 10.5 8.5 9.5 8205.40 2.10 2.07 9.5 8.5 8.5 7.5 8205.40 2.10 2.12 1 0 0 , 1 0 8.5 8.5 7.5 7.5 14865.28 -2.28 -2.28 8.5 9.5 7.5 8.5 14865.55 -2.01 -2.03 250 1 V t ti p I I Observed Observed C a l c u l a t e d *1 i/ . *1 Frequency C o r r e c t i o n C o r r e c t i o n 8.5 7.5 7.5 6.5 14865.55 -2.01 -1.97 11.5 11.5 10.5 10.5 14866.02 -1.54 -1.53 11.5 12.5 10.5 11.5 14866.29 -1.27 -1.26 11.5 10.5 ' 10.5 9.5 14866.29 -1.27 -1.23 9.5 9.5 8.5 8.5 14868.61 1.05 1.07 9.5 10.5 8.5 9.5 14868.87 1.31 1.31 10.5 10.5 9.5 9.5 14869.40 1.84 1.82 10.5 11.5 9.5 10.5 14869.67 2.11 2.07 10.5 9.5 9.5 8.5 14869.67 2.11 2.11 U 0 , 1 1 - 1 0 1 9.5 9.5 8.5 8.5 21595.80 -2.23 -2.24 9.5 10.5 8.5 9.5 21596.05 -1.98 -1.98 9.5 8.5 8.5 7.5 21596.05 -1.98 -1.93 12.5 12.5 11.5 11.5 21596.46 -1.57 -1.58 12.5 13.5 11.5 12.5 21596.76 -1.27 -1.30 12.5 11.5 11.5 10.5 21596.76 -1.27 -1.30 10.5 10.5 9.5 9.5 21599.11 1.08 1.13 10.5 11.5 9.5 10.5 21599.41 1.38 1.38 10.5 9.5 9.5 8.5 21599.41 1.38 1.42 11.5 11 .5 10.5 10.5 21599.81 1.78 1.79 11.5 12.5 10.5 11.5 21600.12 2.09 2.05 11.5 10.5 10.5 9.5 21600.12 2.09 2.09 1 2 0 , 1 2 - U l 10.5 10.5 9.5 9.5 28388.33 -2.22 -2.20 10.5 11.5 9.5 10.5 28388.62 -1.93 -1.93 10.5 9.5 9.5 8.5 28388.62 -1.93 -1.89 13.5 13.5 12.5 12.5 28388.96 -1.59 -1.60 13.5 14.5 12.5 13.5 28389.24 -1.33 -1.33 13.5 12.5 12.5 11.5 28389.24 -1.33 -1.30 11.5 11.5 10.5 10.5 28391.71 1.16 1.16 11.5 12.5 10.5 11.5 28391.98 1.43 1.42 11.5 10.5 10.5 9.5 28391.98 1.43 1.46 12.5 12.5 11.5 11.5 28392.32 1.77 1.76 12.5 13.5 11.5 12.5 28392.59 2.04 2.02 12.5 11.5 11.5 10.5 28392.59 2.04 2.05 13 J 0 , 1 3 ~ 1 2 1 ,12 11.5 11.5 10.5 10.5 35238.31 -2.13 -2.15 11.5 12.5 10.5 11.5 35238.63 -1.81 -1.88 11.5 10.5 10.5 9.5 35238.63 -1.81 -1.84 14.5 14.5 13.5 13.5 35238.63 -1.81 -1.62 14.5 15.5 13.5 14.5 35239.10 -1.34 -1.34 14.5 13.5 13.5 12.5 35239.10 -1.34 -1.31 12.5 12.5 11.5 11.5 35241.59 1.15 1.18 12.5 13.5 11.5 12.5 35241.98 1.54 1.45 12.5 11.5 11.5 10.5 35241.98 1.54 1.48 13.5 13.5 12.5 12.5 35241.98 1.54 1.72 251 1 17 i •p I I V I I 17 Observed Observed C a l c u l a t e d bl £ F l r Frequency C o r r e c t i o n C o r r e c t i o n 13.5 14.5 12.5 13.5 35242.47 2.03 1.99 13.5 12.5 12.5 11.5 35242.47 2.03 2.02 1 ? 1 , 1 6 ~ I 6 2 , 15 17.5 16.5 16.5 15.5 -30598.95 2.05 2.05 17.5 18.5 16.5 17.5 -30598.95 2.05 2.03 17.5 17.5 16.5 16.5 -30599.32 1.68 1.69 16.5 17.5 15.5 16.5 -30599.32 1.68 1.69 16.5 15.5 15.5 14.5 -30599.32 1.68 1.68 16.5 16.5 15.5 15.5 -30599.68 1.32 1.35 18.5 17.5 17.5 16.5 -30602.47 -1.47 -1.47 18.5 19.5 17.5 18.5 -30602.47 -1.47 -1.49 18.5 18.5 17.5 17.5 -30602.85 -1.85 -1.80 15.5 14.5 14.5 13.5 -30602.85 -1.85 -1.84 15.5 16.5 14.5 15.5 -30602.85 -1.85 -1.87 15.5 15.5 14.5 14.5 -30603.17 -2.17 -2.17 1 8 1 , 1 7 16 18.5 17.5 17.5 16.5 -23158.77 2.05 2.06 18.5 19.5 17.5 18.5 -23158.77 2.05 2.04 18.5 18.5 17.5 17.5 -23159.12 1.70 1.71 17.5 18.5 16.5 17.5 -23159.12 1.70 1.71 17.5 16.5 16.5 15.5 -23159.12 1.70 1.71 17.5 17.5 16.5 16.5 -23159.47 1.35 1.38 19.5 18.5 18.5 17.5 -23162.32 -1 .50 -1 .50 19.5 20.5 18.5 19.5 -23162.32 -1.50 -1.52 19.5 19.5 18.5 18.5 -23162.67 -1.85 -1.83 16.5 15.5 15.5 14.5 -23162.67 -1.85 -1.85 16.5 17.5 15.5 16.5 -23162.67 -1.85 -1.87 16.5 16.5 15.5 15.5 -23163.02 -2.20 -2.18 1 9 1 , 1 8 17 19.5 18.5 18.5 17.5 -15643.73 2.05 2.07 19..5 20.5 18.5 19.5 -15643.73 2.05 2.05 18.5 17.5 17.5 16.5 -15644.05 1.73 1.73 18.5 19.5 17.5 18.5 -15644.05 1.73 1.73 19.5 19.5 18.5 18.5 -15644.05 1.73 1.72 18.5 18.5 17.5 17.5 -15644.39 1.39 1.40 20.5 19.5 19.5 18.5 -15647.31 -1.53 -1.52 20.5 21.5 19.5 20 .5 -15647.31 -1.53 -1.54 20.5 20.5 19.5 19.5 -15647.64 -1.86 -1.85 17.5 16.5 16.5 15.5 -15647.64 -1.86 -1.85 17.5 18.5 16.5 17.5 -15647.64 -1.86 -1.87 17.5 17.5 16.5 .16.5 -15647.99 -2.21 -2.19 23 Z J 1 , 2 2 — 22 21 21.5 21.5 20.5 20.5 15128.47 -2.15 -2.18 24.5 24.5 23.5 23.5 15128.77 -1.85 -1.90 252 1 r ti 11 T? Observed Observed C a l c u l a t e d F l F F l F Frequency C o r r e c t i o n C o r r e c t i o n 21.5 22.5 20.5 21.5 15128.77 -1.85 -1.85 21.5 20.5 20.5 19.5 15128.77 -1.85 -1.84 24.5 25.5 23.5 24.5 15129.05 -1.57 -1.58 24.5 23.5 23.5 22.5 15129.05 -1.57 -1.57 22.5 22.5 21.5 21.5 15132.06 1.44 1.45 23.5 23.5 22.5 22.5 15132.38 1.76 1.72 22.5 23.5 21.5 ' 22.5 15132.38 1.76 1.78 22.5 21. 5 21.5 20.5 15132.38 1.76 1.79 23.5 24.5 22.5 23.5 15132.69 2.07 2.04 23.5 22.5 22.5 21.5 15132.69 2.07 2.06 24 — 23„ ,22 1,23 2 22.5 22.5 21.5 21.5 22992.46 -2.15 -2.17 25.5 25.5 24.5 24.5 22992.75 -1.86 -1.91 22.5 23.5 21.5 22.5 22992.75 -1.86 -1.85 22.5 21.5 21.5 20.5 22992.75 -1.86 -1.83 25.5 26.5 24.5 25.5 22993.05 -1.56 -1.58 25.5 24.5 24.5 23.5 22993.05 -1.56 -1.57 23.5 23.5 22.5 22.5 22996.04 1.43 1.46 24.5 24.5 23.5 23.5 22996.37 1.76 1.71 23.5 24.5 22.5 23.5 22996.37 1.76 1.78 23.5 22.5 22.5 21.5 22996.37 1.76 1.79 24.5 25.5 23.5 24.5 22996.68 2.07 2.04 24.5 23.5 23.5 22.5 22996.68 2.07 2.05 2 5 1 , 2 4 2 4 2 , 2 3 23.5 23.5 22.5 22.5 30920.24 -2.14 26.5 26.5 25.5 25.5 30920.52 -1.86 23.5 24.5 22.5 23.5 30920.52 -1.86 23.5 22.5 22.5 21.5 30920.52 -1.86 26.5 27.5 25.5 26.5 30290.92 -1.56 26.5 25.5 25.5 24.5 30920.82 -1.56 24.5 24.5 23.5 23.5 30923.82 1.44 25.5 25.5 24.5 24.5 30924.13 1.75 24.5 25.5 23.5 24.5 30924.13 1.75 24.5 23.5 23.5 22.5 30924.13 1.75 25.5 26.5 24.5 25.5 30924.44 2.06 25.5 24.5 24.5 23.5 30924.44 2.06 2 6 1 ? 2 6 ~ 2 5 2 ,23 24.5 24.5 23.5 23.5 -31165.96 3.99 27.5 27.5 26.5 26.5 -31166.30 3.65 24.5 25.5 23.5 24.5 -31166.54 3.41 24.5 23.5 23.5 22.5 -31166.54 . 3.41 27.5 28.5 26.5 27.5 -31166.90 3.05 27.5 26.5 26.5 25.5 -31166.90 3.05 25.5 25.5 24.5 24.5 -31172.81 -2.86 26.5 26.5 25.5 25.5 -31173.13 -3.18 25.5 26.5 24.5 25.5 -31173.38 -3.43 25.5 24.5 24.5 23.5 -31173.38 -3.43 -2.16 -1.91 -1.83 -1.82 -1.59 -1.57 1.46 1.70 1.78 1.80 2.03 2.04 4.02 3.66 3.40 3.37 3.03 3.01 -2.80 -3.16 -3.43 -3.44 253 1 i If f f Observed Observed C a l c u l a t e d F l r . F l r Frequency C o r r e c t i o n C o r r e c t i o n 26.5 27.5 25.5 26.5 -31173.73 -3.78 -3.78 26.5 25.5 25.5 24.5 -31173.73 -3.78 -3.81 2 7 1 , 2 7 - 2 6 2 , 2 4 25.5 25.5 24.5 24.5 -29088.68 4.08 4.10 28.5 28.5 27.5 27.5 -29089.02 3.74 3.74 25.5 26.5 24.5 25.5 -29089.30 3.46 3.46 25.5 24.5 24.5 23.5 -29089.30 3.46 3.44 28.5 29.5 27.5 28.5 -29089.65 3.11 3.11 28.5 27.5 27.5 26.5 -29089.65 3.11 3.08 26.5 26.5 25.5 25.5 -29095.63 . -2.87 -2.87 27.5 27.5 26.5 26.5 -29096.02 -3.26 -3.22 26.5 27.5 25.5 26.5 -29096.28 -3.52 -3.51 26.5 25.5 25.5 24.5 -29096.28 -3.52 -3.53 27.5 28.5 26.5 27.5 -29096.62 -3.86 -3.86 27.5 26.5 26.5 25.5 -29096.62 -3.86 -3.88 2 8 1 , 2 8 - 2 7 2 ,25 26.5 26.5 25.5 25.5 -27246.40 4.14 4.18 29.5 29.5 28.5 28.5 -27246.73 3.81 3.83 26.5 27.5 25.5 26.5 -27247.02 3.52 3.53 26.5 25.5 25.5 24.5 -27247.02 3.52 3.51 29.5 30.5 28.5 29.5 -27247.37 3.17 3.18 29.5 28.5 28.5 27.5 -27247.37 3.17 3.16 27.5 27.5 26.5 26.5 -27253.48 -2.94 -2.94 28.5 28.5 27.5 27.5 -27253.82 -3.28 -3.29 27.5 28.5 26.5 27.5 -27254.12 -3.58 -3.59 27.5 26.5 26.5 25.5 -27254.12 -3.58 -3.61 28.5 29.5 27.5 28.5 -27254.46 -3.92 -3.94 28.5 27.5 27.5 26.5 -27254.46 -3.92 -3.96 29 1,29 - 2 8 2 ,26 27.5 27.5 26.5 26.5 -25644.90 4.23 4.26 30.5 30.5 29.5 29.5 -25645.24 3.89 3.91 27.5 28.5 26.5 27.5 -25645.55 3.58 3.60 27.5 26.5 26.5 25.5 -25645.55 3.58 3.58 30.5 31.5 29.5 30.5 -25645.87 3.26 3.25 30.5 29.5 29.5 28.5 -25645.87 3.26 3.23 28.5 28.5 27.5 27.5 -25652.14 -3.01 -3 .00 29.5 29.5 28.5 28.5 -25652.48 -3.35 -3.35 28.5 29.5 27.5 28.5 -25652.79 -3.66 -3.67 28.5 27.5 27.5 26.5 -25652.79 -3.66 -3.69 29.5 30.5 28.5 29.5 -25653.14 -4.01 -4.02 29.5 28.5 28.5 27.5 -25653.14 -4.01 -4.04 3 0 1 , 3 0 — 29 2 ,27 28.5 28.5 27.5 27.5 -24289.74 4.33 4.34 31.5 31.5 30.5 30.5 -24290.09 3.98 4.00 28.5 27.5 27.5 26.5 -24290.40 3.67 3.64 254 " p" Observed Observed C a l c u l a t e d 1 Frequency C o r r e c t i o n C o r r e c t i o n 2 8 . 5 2 9 . 5 2 7 . 5 2 8 . 5 - 2 4 2 9 0 . 4 0 3 .67 3 .67 3 1 . 5 3 0 . 5 3 0 . 5 2 9 . 5 - 2 4 2 9 0 . 7 5 3 .32 3 .30 3 1 . 5 3 2 . 5 3 0 . 5 3 1 . 5 - 2 4 2 9 0 . 7 5 3 .32 3 .32 2 9 . 5 2 9 . 5 2 8 . 5 2 8 . 5 - 2 4 2 9 7 . 1 5 - 3 . 0 8 - 3 . 0 7 3 0 . 5 3 0 . 5 2 9 . 5 2 9 . 5 - 2 4 2 9 7 . 6 4 * - 3 . 5 7 - 3 . 4 1 2 9 . 5 3 0 . 5 2 8 . 5 2 9 . 5 - 2 4 2 9 7 . 6 4 * - 3 . 5 7 - 3 . 7 5 2 9 . 5 2 8 . 5 2 8 . 5 2 7 . 5 - 2 4 2 9 7 . 6 4 * - 3 . 5 7 - 3 . 7 7 3 0 . 5 3 1 . 5 2 9 . 5 3 0 . 5 - 2 4 2 9 8 . 1 5 - 4 . 0 8 - 4 . 0 9 3 0 . 5 2 9 . 5 2 9 . 5 2 8 . 5 - 2 4 2 9 8 . 1 5 - 4 . 0 8 -4 .11 * Overlapped by u n i d e n t i f i e d t r a n s i t i o n 3 5 C 1 1 4 N 1 2 c 1 6 o F i r s t E x c i t e d V i b r a t i o n a l S ta te ~ 3 0 , 3 3 .5 2 .5 2 .5 1.5 2 4 3 9 6 . 6 3 - 1 . 5 7 - 1 . 6 4 3 .5 4 . 5 2 .5 3 .5 2 4 3 9 6 . 6 3 - 1 . 5 7 - 1 . 6 4 2 .5 3 .5 1.5 2 .5 2 4 3 9 6 . 6 3 - 1 . 5 7 - 1 . 6 0 2 .5 1.5 1.5 0 . 5 2 4 3 9 6 . 6 3 - 1 . 5 7 - 1 . 4 2 3 .5 3 .5 2 .5 2 .5 2 4 3 9 6 . 6 3 - 1 . 5 7 - 1 . 3 3 2 .5 2 .5 1.5 1.5 2 4 3 9 6 . 6 3 - 1 . 5 7 - 1 . 3 2 4 . 5 5 .5 3 .5 4 . 5 2 4 3 9 8 . 7 3 0 . 5 3 0 . 4 5 4 . 5 3 .5 3 .5 2 .5 2 4 3 9 8 . 7 3 0 . 5 3 0 . 4 6 5 .5 6 .5 4 . 5 5 .5 2 4 3 9 8 . 7 3 0 . 5 3 0 . 5 3 5 .5 4 . 5 4 . 5 3 .5 2 4 3 9 8 . 7 3 0 . 5 3 0 .57 5 .5 5 .5 4 . 5 4 . 5 2 4 3 9 8 . 7 3 0 . 5 3 0 . 6 0 4 . 5 4 . 5 3 .5 3 .5 2 4 3 9 8 . 7 3 0 . 5 3 0 . 6 6 3 .5 2 .5 2 .5 1.5 2 4 0 1 5 . 4 8 - 2 . 2 7 - 2 . 2 7 3 .5 4 . 5 2 .5 3 .5 2 4 0 1 5 . 4 8 - 2 . 2 7 - 2 . 2 4 3 .5 3 .5 2 .5 2 .5 2 4 0 1 5 . 9 5 - 1 . 8 0 - 1 . 8 4 4 . 5 3 .5 3 .5 2 .5 2 4 0 1 7 . 0 6 . - 0 . 6 9 - 0 . 6 8 4 . 5 5 .5 3 .5 4 . 5 2 4 0 1 7 . 0 6 - 0 . 6 9 - 0 . 6 7 2 .5 3 .5 1.5 2 .5 - 0 . 4 5 4 . 5 4 . 5 3 .5 3 .5 - 0 . 3 5 2 . 5 1.5 1.5 0 . 5 -0 .31 2 .5 2 .5 1.5 1.5 - 0 . 0 6 5 .5 6 .5 4 . 5 5.5 2 4 0 1 8 . 9 1 1.16 1.15 5 .5 4 . 5 4 . 5 3 .5 2 4 0 1 8 . 9 1 1.16 1.16 5 .5 5.5 4 . 5 4 . 5 1.36 « 1 , 3 -3 .5 2 .5 2 .5 1.5 2 4 7 9 1 . 2 4 - 1 . 2 7 - 1 . 3 0 3 .5 4 . 5 2 .5 3 .5 2 4 7 9 1 . 2 4 - 1 . 2 7 - 1 . 2 7 3 .5 3 .5 2 .5 2 .5 2 4 7 9 1 . 4 9 - 1 . 0 2 - 1 . 0 2 4 . 5 3 .5 3 .5 2 .5 2 4 7 9 1 . 4 9 - 1 . 0 2 - 0 . 9 8 255 J ' Observed Observed C a l c u l a t e d l Frequency C o r r e c t i o n C o r r e c t i o n 4.5 5.5 3.5 4.5 24791.49 -1.02 -0.96 4.5 4.5 3.5 3.5 24791.85 -0.66 -0.75 2.5 3.5 1.5 2.5 24793.03 0.52 0.52 2.5 1.5 1.5 0.5 24793.03 0.52 0.56 2.5 2.5 1.5 1.5 24793.35 0.84 0.77 5.5 4.5 4.5 3.5 24793.35 0.84 0.84 5.5 6.5 4 .5 5.5 24793.35 0.84 0.84 5.5 5.5 4.5 4.5 24793.53 1.02 1.01 4 — 3 2.3 2,2 4.5 3.5 3.5 2.5 24408.30 -4.70 -4.76 4.5 5.5 3.5 4.5 24408.30 -4.70 -4.67 4.5 4.5 3.5 3.5 24408.75 -4.25 -4.23 3.5 2.5 2.5 1.5 24410.80 -2.20 -2.26 3.5 4.5 2.5 3.5 24410.80 -2.20 -2.14 3.5 3.5 2.5 2.5 24411.26 -1.74 -1.75 5.5 4.5 4.5 3.5 24415.44* 2.44 2.35 5.5 6.5 4 .5 5.5 24415.44* 2.44 2.45 5.5 5.5 4.5 4.5 24416.00* 3.00 2.98 2.5 1.5 1.5 0.5 4.81 2.5 3.5 1.5 2.5 5.00 2.5 2.5 1.5 1.5 5.44 * Overlapped by 4 3,2 - 3 3 , 1 3 5 C 1 1 4 N 1 2 C 1 6 0 1st E x . V i b . S t . 4 .5 3.5 3.5 2.5 24413.92 -4.62 -4.74 4.5 5.5 3.5 4.5 24413.92 -4.62 -4.65 4.5 4.5 3.5 3.5 24414.37 -4.17 -4.21 3.5 2.5 2.5 1.5 24416.41* -2.13 -2.24 3.5 4.5 2.5 3.5 24416.41* -2.13 -2.13 3.5 3.5 2.5 2-5 * -1.74 5.5 4 .5 4.5 3.5 24420.92 2.38 2.33 5.5 6.5 4.5 5.5 24420.92 2.38 2.43 5 .5 . 5.5 4.5 4.5 24421.45 2.91 2.96 2.5 1.5 1.5 0.5 24423.71+ 5.17 4.78 2.5 3.5 1.5 2.5 24423.71+ 5.17 4.97 2.5 2.5 1.5 1.5 24423.71+ 5.17 5.41 * Pa r t of p o o r l y r e so l v ed m u l t i p l e t + Overlapped by 4„ _ ~ 3 3 , 1 3 5 C 1 1 4 N 1 2 C 1 6 0 1st E x . V i b . S t . 4 — 3,2 " 3 3 , 1 - 3 J 3 , 0 4.5 3.5 3.5 2.5 24415.44* -10.89 -11.31 4.5 5.5 3.5 4 .5 24415.44* -10.89 -11.07 4.5 4.5 3.5 3.5 24416.00* -10.33 -10.35 3.5 2.5 2.5 1.5 24423.71+ -2.62 -3.05 3.5 4.5 2.5 3.5 24423.71+ -2.62 -2.79 256 t i it II Observed Observed C a l c u l a t e d F l r F l r Frequency C o r r e c t i o n C o r r e c t i o n 3.5 3.5 2.5 2.5 24423.71+ -2.62 -2.28 5.5 4.5 4.5 3.5 24431.07 4.74 4.59 5.5 6.5 4.5 5.5 24431.07 4.74 4.86 5.5 5.5 4.5 4.5 24432.32 5.99 5.97 2.5 1.5 1.5 0.5 12.61 2.5 3.5 1.5 2.5 13.27 2.5 2.5 1.5 1.5 13.91 * Overlapped + Overlapped ^ 4 2 , 3 ^ 4 2 , 2 — 3 2,2 ~ 3 2 , 1 3 5 C 1 1 4 N 1 2 C 1 6 0 1st E x . V i b . S t . V 4.5 4.5 3.5 3.5 -25217.94 1.10 1.23 4.5 3.5 3.5 2.5 -25217.94 1.10 1.04 4.5 5.5 3.5 4.5 -25217.94 1.10. 1.03 5.5 5.5 4.5 4.5 -25218.75 0.29 0.30 5.5 4.5 4.5 3.5 -25218.75 0.29 0.28 5.5 6.5 4.5 5.5 -25218.75 0.29 0.24 3.5 3.5 2.5 2.5 -1.16 3.5 2.5 2.5 1.5 -25220.55 -1.51 -1.46 3.5 4.5 2.5 3.5 -25220.55 -1.51 -1.46 2.5 2.5 1.5 1.5 -2.02 2.5 1.5 1.5 0.5 -2.11 2.5 3.5 1.5 2.5 -25221.36 -2.32 -2.30 5 0 , 5 4.5 5.5 3.5 4.5 30492.53 -0.81 -0.93 4.5 3.5 3.5 2.5 30492.53 -0.81 -0.90 3.5 4.5 2.5 3.5 30492.53 -0.81 -0.88 3.5 2.5 2.5 1.5 30492.53 -0.81 -0.77 4.5 4.5 3.5 3.5 30492.53 -0.81 -0.77 3.5 3.5 2.5 2.5 30492.53 -0.81 -0.74 5.5 6.5 4.5 5.5 30493.69 0.35 0.30 5.5 4.5 4.5 3.5 30493.69 0.35 0.32 6.5 7.5 5.5 6.5 30493.69 0.35 0.37 6.5 5.5 5.5 4 .5 30493.69 0.35 0.41 6.5 6.5 5.5 5.5 30493.69 0.35 0.42 5.5 5.5 4.5 4.5 30493.69 0.35 0.42 4.5 5.5 3.5 4.5 30019.65 -1.23 -1.36 4.5 3.5 3.5 2.5 30019.65 -1.23 -1.34 4.5 4.5 3.5 3.5 30019.65 -1.23 -1.12 3.5 4.5 2.5 3.5 30020.49* -0.39 -0.46 3.5 2.5 2.5 1.5 30020.49* -0.39 -0.36 3.5 3.5 2.5 2.5 30020.49* -0.39 -0.25 5.5 6.5 4.5 5.5 30020.49* -0.39 -0.19 5.5 4.5 4.5 3.5 30020.49* -0.39 -0.17 257 1 F, F II F, II F Observed Observed C a l c u l a t i 1 1 Frequency C o r r e c t i o n Co r r e c t i ( 5.5 5.5 4.5 4.5 0.00 6.5 7.5 5.5 6.5 30021.57* 0.69 0.74 6.5 5.5 5.5 4.5 30021.57* 0.69 0.76 6.5 6.5 5.5 5.5 30021.57* 0.69 0.85 * Overlapped by 3Q ^ - 2 1 , 2 3 5CI 1 4N 1 2C 1 6O G.V.S . V 4.5 5.5 3.5 4.5 30988.40 -0.81 -0.82 4.5 3.5 3.5 2.5 30988.40 -0.81 -0.81 4.5 4 .5 3.5 3.5 30988.40 -0.81 -0.67 5.5 6.5 4.5