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The microwave rotational spectrum and the structure of difluorochloromethane McLay, David Boyd 1956

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THE MICROWAVE ROTATIONAL SPECTRUM AND THE STRUCTURE OF D IFLUOROCHLOROMETHANE by DAVID BOYD McLAY A thesis submitted i n partial fulfilment of the requirements for the degree of Doctor of Philosophy i n Physics We accept this thesis as conforming to the standard required from candidates for the degree of Doctor of Philosophy. Members of the Department of Physics. The University of B r i t i s h Columbia April 1956 ABSTRACT The pure rotational spectrum of difluorochloromethane, Freon 22, has "been obtained i n the K-band microwave region with a Stark modulation spec-troscope. Over two hundred spectrum lines, of which the majority are grouped into doublets or quadruplets, have been found. Fifteen doublets and one quad-ruplet correspond i n frequency with previous determinations but the majority of the lines and structures have not previously been recorded. In addition, a definite sestet of lines and two definite t r i p l e t s have been noted. The grouping into multiplets has been made possible by similarities i n the l i n e shape, in the Stark modulation response, and i n the effects of c h i l l i n g the Stark c e l l with dry ice. The latter effect has been the most important factor i n identifying several transitions involving low values of J, the tot a l angular momentum quantum number. The sestet and two quadruplets have been found to be the result of the interaction of the C l 3 ^ quadrupole moment with the electrostatic poten-t i a l at the site of the nucleus. The sestet represents s i x of the possible eight lines for a transition from a J=l rotational level to a J=2 l e v e l . The quadruplets represent two transitions involving only J=3 rotational levels. From these three structures have been obtained the complete solution 35 for the spectrum of the molecule containing CI and the values of the com-35 ponents of the quadrupole coupling constant for the CI nucleus along the principal axes of the angular momentum el l i p s o i d . In a l l , eight multiplets have been correctly identified for the molecule containing C l ^ and the two theories of the rotational levels and of the hyperfine structure for an asymmetric top molecule have been verified. i i From the rotational constants for the molecule containing CI the 37 values for the molecule containing CI can be closely estimated and the rotational spectrum for the latter case has accordingly been predicted with considerable accuracy. By means of the predicted values, five multiplets and 37 one single line have been identified for the molecule containing CI and the theories for the rotational levels and for the hyperfine splittings can be rechecked. From the spectra for the two molecules, five independent rotational constants have been obtained with a precision that compares favour-ably with the precision of other experimenters in the field of microwave spectroscopy. With these five constants and an approximation to the carbon-hydrogen bond length, the structure of the molecule has been calculated with an accuracy much better than that obtained from electron diffraction measurements. 35 The quadrupole coupling constant for CI in Freon 22 has been found to be -71.6 - 0.5 Mc/s, a value which is about 1 Mc/s larger than the value for the molecule in the solid state. The difference between the components of the quadrupole coupling tensor along two axes perpendicular to the carbon-chlorine bond has been found to be rather small in comparison with the value suggested by bond theory. Some comments are offered on the nature of the chemical bond in the light of these electric quadrupole moments for CI3** and the bond lengths for the carbon-chlorine and carbon-fluorine bonds which have been calculated to be 1.7576 - .0093 A and 1.3405 - .0058 A respectively for Freon 22. i i i %xhxtxmi^ of Pritislf (Ealmtthk Faculty of Graduate Studies P R O G R A M M E O F T H E Jflttrai (Bml |L\etmimrtimt fox ttje Jtegm of Jtaxtar of Ifyifostfpljg of DAVID BOYD M c L A Y M.Sc. (McMaster) T U E S D A Y , M A Y 1st, 1956, at 10:00 a.m. I N R O O M 300, P H Y S I C S B U I L D I N G C O M M I T T E E I N C H A R G E D E A N H . F . A N G U S , Chairman G . M . S H R U M T . E . H U L L A . M . C R O O K E R W . A . B R Y C E G . M . V O L K O F F C . A . M C D O W E L L F. A . K A E M P F F E R D . C . CORBETT External Examiner—C. C. COSTAIN, National Research Council THE MICROWAVE ROTATIONAL SPECTRUM AND THE STRUCTURE OF DIFLUOROCHLOROMETHANE ABSTRACT The microwave absorption spectrum of- CHF2C1 has been investigated in the 22 to 27.2 KMc/s and 28.3 to 33.3 KMc/s regions. Measurements were made of the absorption frequencies, the effect of temperature on the line intensities, the hyperfine structure, hfs, of the lines due to the nuclear electric quadrupole moment of chlorine and the Stark modulation of the lines. Eight rotational transitions have been identified for the CHF 2C1 3 5 molecule and six rotational transitions have been identified for CHF 2C1 3 7. These identifications allow the calculation of the inertial ellipsoid for the two molecular species involving CI 3 5 and CI 3 7. From these data the structure of the molecule has been obtained with an accuracy approximately three times better than previous determinations by electron diffraction methods. The hfs. analysis gives —71.6 ± 0.5 Mc/s for the nuclear electric quad-rupole coupling constant for C13B in CHF2C1. This analysis also verifies the first order theory of Bragg and Golden for the hfs. arising from a single quadrupolar nucleus in an asymetric-top molecule. The results for the structure and for the components of the quadrupole coupling dyadic have been analysed from the standpoint of chemical bond theory. PUBLICATIONS Report to Radio Standards Division, N.B.S., Boulder, Colorado, for inclusion in "Supplement to NBS Circular 518" (in preparation). "Nuclear Electric Quadrupole Interaction in the Pure Rotational Spectrum of Chlorodifluoromethane" by Cedric R. Mann and David McLay. Submitted to Can. J. Phys., March, 1956. "The Structure of Difluorochloromethane", in preparation. GRADUATE STUDIES Field of Study: Physics Atomic and Molecular Spectroscopy Quantum Mechanics Nuclear Structure Electromagnetic Theory Magnetism and Dielectrics.... Theory of Relativity Theory of Measurement Advanced Electronics. Chemical Physics Quantum Theory of Radiation.-.. Other Studies: Differential Equations Integral Equations .A. B. McLay ..F. R. Britton - M . W. Johns W. Opechowski W. Opechowski Opechowski ...A. M. Crooker ..W. R. Raudorf 0. Theimer . F. A. Kaempffer ..T. E. Hull ..T. E. Hull ACKNOWLED GMENTS The financial assistance of the National Research Council of Canada i n the form of studentships awarded to the author i n 1951-52 and 1953-54 i s gratefully acknowledged. Grants from the Defence Research Board i n the years up to and including 1952 have made possible the construction and pur-chase of most of the apparatus. The author wishes to express his gratitude to the Physics Department Of the University of B r i t i s h Columbia for accomodation i n the laboratories and for the f a c i l i t i e s of the physics shop and physics library. In partic-ular, he is grateful for the supervision and encouragement of his supervisor, Dr. A. M. Crooker, and for the assistance of the instrument makers and electronic technicians i n the department. Mr. T. R. Hartz has been almost total l y responsible for the con-struction of the accurate microwave frequency standard and Dr. C. R. Mann has designed and constructed the Stark spectrometer. In addition, Dr. Mann has pioneered the study of the spectrum of Freon 22 and has helped the present author by his preliminary analysis of the spectrum. Mr. John Mayhood has kindly made an infrared analysis of the Freon 22 sample to check for impurities. Dr. H. A. Buckmaster, Dr. H. E. D. Scovil and Dr. H. H. Waterman have a l l offered valuable advice on the subject of the microwave and electronic apparatus. The author i s grateful to the Principal and Vice-Principal of Victoria College who have permitted the use of the el e c t r i c a l calculators, the library f a c i l i t i e s and the office spaces belonging to the college. Their aid has made possible the writing of this thesis during the academic year. iv TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS v i LIST OF TABLES v i i CHAPTER I. INTRODUCTION 1 CHAPTER II. THE STARK-MODULATION SPECTROMETER 5 CHAPTER III. ASYMMETRIC ROTOR THEORY 15 CHAPTER IV. SOLUTION OF THE SPECTRA BY ANALYSIS OF THE HYPERFINE STRUCTURE 27 CHAPTER V. THE ACCURATE STRUCTURE OF THE DIFLUORO -CHLOROMETHANE MOLECULE 41 CHAPTER VI. CONCLUSIONS REGARDING THE CHEMICAL BONDS .. 51 APPENDIX I. MICROWAVE SPECTRUM OF DIFLUOROCHLOROMETHANE 6l APPENDIX II. STARK EFFECT MEASUREMENTS 6/, REFERENCES 65 BIBLIOGRAPHY 68 v LIST OF ILLUSTRATIONS FIGURE FACING PAGE 1. Microwave Circuits and Oscillator Tubes ........ 6 2. C.R.O. Display of Frequency Marker 6 3. Stark-Modulation Cell in Dry Ice Box 9 4. Tuned Input to Pre-amplifier 12 5. Expected and Actual C.R.O Displays of Absorption Lines 13 6.' Aspects of the Structure of CHFgCl 16 7. Thermal Distribution of Approximate Energy Levels 24 8. Thermal Distribution of Approximate Energy Levels A*_£ J( J • 1) 24 9. Stark splitting of 5/2 -* 7 / 2 Hyperfine Transition of l o , l - * 2 i , i Line 26 10. Symmetrical Triplet at 32,580 Mc/s 28 vi LIST OF TABLES TABLE FACING PAGE I. Rotational Constants for Assumed Models of CBF2C1 ... 18 II. Hyperf ine Splittings and Relative Intensities for Low J Transitions ., 35 III. Scale Factors for CHFgCl35 37 IV. Scale Factors for CBF2C137 37 35 V. Constants from Q-Branch Transitions of Cffi^Cl . 42 37 VI. Constants from Q-Branch Transitions of CHFgCl . 42 VII. Rotational Constants and Moments of Inertia of CHF 2C1 3 5' 3 7 45 VIII. Nuclear Coordinates of CHF2C1 along Principal Axes in Centre of Mass System 49 IX. Bond Lengths and Angles of CHFgCl 49 X. Structures and Nuclear Electric Quadrupole Resonances of Fluoro- and Chloro-methanes . 53 v i i CHAPTER I INTRODUCTION Aliphatic compounds which contain fluorine and other halogens are very interesting from the chemical standpoint because they exhibit unusual stability in the case of single halogen atoms on carbon atoms adjacent to polyfluoro groups.^" This stability in the fluorochloromethanes has been related to decreases in the carbon-chlorine and carbon-fluorine bond lengths 2 by Brockway on the basis of his electron diffraction data. He has deter-o mined the carbon-chlorine bond lengths to be of the order of 1.77 A for o methane derivatives containing no fluorine atoms, of 1.76 A for monofluoro-o methanes and of 1.74 A for difluoro- and trifluoro- chloromethanes. Sim-ilarly, he has found the carbon-fluorine bond to have a length of the order o o of 1.41 A in monofluoromethanes and of the magnitude of 1.36 A in poly-fluoromethanes. Since his derived bond lengths have a listed deviation of - 0.02 A at best, the apparent trend in the length of the carbon-chlorine bond is questionable and a quantitative measure of the definite trend in the length of the carbon-fluorine bond is not reliable. Recently, the methods of electron diffraction have yielded the more accurate values for the carbon-fluorine bond of 1.357 - 0.017 A in difluoro-methane and of 1.328 - 0.002 A in trifluorochloromethane . They have also given values for the carbon-chlorine bond length to be 1.783 - .003 A in L • • ° 4 methyl chloride* and 1.751 - 0.004 A in trifluorochloromethane . Therefore the substitution of 3 fluorine atoms for 3 hydrogen atoms in methyl chloride causes a shortening of the carbon-chlorine bond length by 0.032 - 0.006, a quite significant effect. Also, the carbon-fluorine bond length in carbon-1 5 ° tetrafluoride has recently been found by electron diffraction^ to be 1.322 A and so the substitution of fluorine atoms for hydrogen atoms and a fluorine atom for a chlorine atom definitely produces a shortening of the carbon-fluorine bond. Unfortunately, electron diffraction results of this accuracy are not available for whole series of fluoromethanes and of fluorochloro-methanes. Although a few bond lengths can be determined with reasonable accuracy 6 7 from rotation-vibration spectra for both symmetric top - and asymmetric top -molecules, very many more results which are quite accurate can be obtained for the same types of molecules i n the vibrational ground-state by the methods of microwave spectroscopy . Townes and Schawlow l i s t the structures 9 determined for five-atom symmetric tops , for symmetric tops of more than five atoms^ and for asymmetric t o p s ^ by microwave spectroscopy. The 12,13 1/ structures of such fluoromethanes as trifluoromethane ' , difluoromethane"^-12,15 and methyl fluoride have been solved by analyses of microwave spectra. The structures of the monochloromethane compounds, methyl c h l o r i d e ^ , 17 18 fluorochloromethane and trifluorochloromethane have also been measured by microwave spectroscopy. Obviously, the results on difluorochloromethane which are presented i n this thesis are necessary to complete the series. Previous measurements on the microwave spectrum of difluorochloro-19 methane have been made by B. P. Dailey and i n this laboratory by Cedric 20 Mann . Dailey* s results comprise eighteen isolated lines, whose frequencies have been measured with a cavity wavemeter only. Mann's results comprise 18 doublets and 1 quadruplet structure i n the 23 to 27 KMc/s region. Of these, 15 doublets and the quadruplet have been verified by the experiments of this writer while one doublet has been rejected as the result of mode discontin-uiti e s . Two very weak doublets found by Mann have not been verified. The preliminary analysis of Mann has indicated that the doublets are the result 3 of unresolved nuclear electric quadrupole interaction splittings and that the quadruplet represents the completely resolved strong components of the hyper-fine structure for the CI3"* nucleus i n a J=10, AJ=0 rotational transition. Moreover the analysis indicates that other J=0 lines may be found i f the range of the spectrometer i s increased from the original range of 23 to 27 KMc/s to a wider range of 20 to 32 KMc/s. This thesis describes how the range of the spectrometer has been improved to cover the 22 to 27.2 KMc/s and 28.3 to 33-3 KMc/s regions and how over two hundred spectrum lines i n the form of one sestet, fifteen quadruplets, two t r i p l e t s and almost one hundred doublets have been measured with precision and i n d e t a i l . Many of the more important lines have only become apparent when the absorption c e l l has been chilled i n a dry ice bath, a new feature of the equipment. The existence of the hyperfine s p l i t t i n g owing to the interaction of the quadrupolar nucleus CI3-* with the electrostatic potential i n the molecule at the site of the nucleus provides more information about chemical bonding. 21 Dailey has derived a simple formula for the nuclear ele c t r i c quadrupole coupling for CI3-* i n molecules involving both ionic bonds and s-p hybrid-22 ization as well as covalent bonds for the chlorine atom. Townes and Schawlow have interpreted the nuclear electric quadrupole coupling i n terms of ionicity, hybridization and double bonding, i n addition to covalent bonding. Meyer and 23 Gutowsky have attempted to correlate the quadrupole coupling constant for 35 CI with the "ehemical s h i f t " for hydrogen and fluorine atoms i n the fluoro-24 chloromethanes and Livingston has commented on the trends i n the quadrupole 35 coupling constant for CI i n the solid and gas states for several fluoro-chloromethanes. In this thesis the quadrupole coupling constant for CI3-* i s calculated as the tensor component along the bond axis. The value so obtained agrees with the value determined i n the solid state and verifies the trends noted by Livingston. u In the case of an asymmetric top there is in general a difference between the components of the quadrupole coupling tensor along two mutually perpendicular axes which are also perpendicular to the bond i n question. 17 Muller has calculated the difference between two of these components for 35 CI i n fluorocbloromethane and has related the difference to the amount of 25 double-bonding in the carbon-chlorine bond. Goldstein has derived an approximate criterion for the percentage importance of double bonding i n the carbon-chlorine bond for a chlorine atom in a planar molecule such as vinyl chloride. In this thesis, the values of the components along one axis i n the plane of symmetry and perpendicular to the carbon-chlorine bond and along a second axis perpendicular to the plane of symmetry have been derived. The probable percentage importance of double bonding has been calculated and i t is shown that there is some inconsistency between the various theories for the carbon-chlorine bond. The material of this thesis provides then a complete solution for the pure rotational spectra of the difluorochloromethane molecules containing 35 37 both CI J and CI so that the presence of the gas can be detected by any of i t s microwave absorption lines. The internal consistency of the calculations verifies the theory for the rotational energy levels for an asymmetric top. The thorough analysis of the nuclear electric quadrupole s p l i t t i n g verifies the theory for the Interaction of the nuclear electric quadrupole of CI3'* with the electrostatic potential at the site of the nucleus. From the sol-utions for the rotational spectra and for the byperfine splittings, the struc-ture has been determined accurately and data on the nuclear electric quadru-pole coupling tensor has been obtained. The natures of the carbon-chlorine and carbon-fluorine bonds have been discussed in terms of the molecular structure and of the quadrupole coupling tensor. CHAPTER II THE STARK-MODULATION MICROWAVE SPECTROMETER The apparatus comprises an accurate microwave frequency standard con-structed by Mr. T. R. Hartz on the pattern of that designed by Unterburger 26 and Smith , and a Stark-modulation microwave spectrometer b u i l t by C. R. 20 ' 2 7 Mann on the basis of the instrument of McAfee, Hughes and Wilson . Some modifications and improvements have been made by the present author and these are described i n the following pages along with a brief description of the apparatus. The Microwave Frequency Standard The basis of the microwave frequency standard i s a 200 Kc/s crystal-controlled oscillator whose frequency can be varied over a small range by a tuning condenser. The output of the oscillator i s amplified and multiplied to 4800 Kc/s, which signal i s mixed with part of the original 200 Kc/s out-put in a balanced mixer to give a 5 Mc/s signal with an incidental small 200 Kc/s modulation. The 5 Mc/s note and the 10 Mc/s transmission of WWV are picked up simultaneously by the antenna of a radio receiver. The 5 Mc/s note can be tuned so that the beat note of i t s harmonic with WWV i s 1 or 2 cycles. The oscillator i s stable enough so that the beat note does not vary by more than - 5 cycles i n several hours of operation. As a result, the frequency standard i s accurate to one part i n two million at least. The accurate 5 Mc/s signal i s f i l t e r e d and multiplied to 90 Mc/s by conventional frequency multipliers. The 90 Mc/s is divided and part of i t i s amplified by a buffer amplifier and then applied to a 1N26 crystal 5 FIGURE 1 MICROWAVE CIRCUITS AND OSCILLATOR TUP3S FIGURE 2 C . R . O . DISPLAY OF FREQUENCY MARKER 6 multiplier, mounted i n K-band guide as shown i n the centre background of Figure 1 facing this page, by means of a pick up c o i l and coaxial l i n e . The rest of the 90 Mc/s output i s amplified by another buffer amplifier and then multiplied to 270 Mc/s. By means of two voltage amplification stages and one power amplification stage employing an 832A tube and tuned lecher wires i n the plate c i r c u i t , the 270 Mc/s signal i s amplified sufficiently to drive the input resonator of a 2K47 klystron frequency multiplier, shown i n the l e f t background of Figure 1. The output resonator i s tuned to 2970 Mc/s, the eleventh harmonic of 270 Mc/s, and this output i s applied to the 1N26 crystal multiplier by means of a brass coaxial li n e and a sliding stub transformer. The crystal multiplier provides harmonics of 90 Mc/s with a slight 200 Kc/s modulation throughout the K-band region. The harmonics and a small sample of the source frequency for the spectrometer are introduced into the input arms of an H-plane Tee-section i n whose output arm there i s a LN26 crystal detector. The detector output i s introduced by coaxial li n e to the input stage of a Halllcrafters SX-42 receiver which i s continuously tunable between the limits of 0.5 Mc/s and 108 Mc/s. The spectrometer frequency and the nearest 90 Mc/s harmonics beat to give two frequency markers, one from the upper harmonic and one from the lower, whose sum i s 90 Mc/s. The radio receiver detects the beat frequency when i t is tuned to the beat frequency. Since the source frequency varies periodically with a saw-tooth variation, the two frequency markers vary with the source frequency and the radio receiver w i l l only detect a signal when i t i s tuned to a beat frequency i n the range of the variation. The output of the SX-42 receiver i s taken from the second detector, to avoid distortion by the audio-amplifier, and applied to the v e r t i c a l plates of the upper beam of a Cossor double-beam cathode ray oscilloscope whose horizontal sweep is provided by the same saw-tooth voltage that 7 provides the low frequency modulation for the source klystron. Accordingly a deflection in the trace occurs at the point of the sweep for which the receiver i s tuned to the beat frequency between a 90 Mc/s harmonic and the source frequency at that point. The frequency marker can be moved along the trace by varying the SX-42 frequency. The frequency standard has been improved to the extent that sharp markers l i k e that i n Figure 2, facing page 6, can be obtained consistently i f the source klystron i s stable throughout the sweep. The strong centre-marker corresponds to the true beat frequency and the small sidebands, spaced 200 Kc/s apart, are the result of a 200 Kc/s modulation of the 90 Mc/s input-. With such a marker i t i s possible to measure a microwave frequency to an accuracy of about - 0.02 Mc/s, throughout the K-band region. The appropriate 90 Mc/s marker i s identified by means of a cavity wavemeter which measures the source klystron frequency to an accuracy of - 20 Mc/s. In the 22 to 26 KMc/s region a Du Mornay-Budd #4-02 wavemeter has been used and i n the 26 to 34 KMc/s region a Sperry Model 350 wavemeter has been used i n conjunction with a 1N26 crystal detector and galvanometer. Figure 7 of 20 Mann's thesis gives a"block diagram for the frequency standard which s t i l l applies except for the fact that an H-plane Tee-section has replaced the directional coupler. The Microwave Components of the Spectrometer The microwave source oscillator shown in the foreground of Figure 1 i s either a 2K33 klystron for the 22 to 26 KMc/s region or a QK-140 for the 26 to 34 KMc/s region. For greater s t a b i l i t y , the klystron filament voltages are supplied by a storage battery which is mounted in an insulating box because of the large negative cathode potential. The power supply for the klystrons has. been modified so that the control tube is a high voltage NU2C53 tube across which the peak voltage can be as high as 5000 volts. The 8 plate, grid and reflector voltage ranges have been made adjustable by a vari-able series of VR tubes. The supply with these adjustments is capable of supplying to the 2K33 tubes -1800 V for the cathode, -1800 to -1980 V for the grid and -1875 to -2055 V for the reflector. With a change in the series of VR tubes, i t can supply to the QKL40 tubes -2200 V for the cathode, -2200 to -2425 V.for the grid and -2275 to -2500 V for the reflector. The adaptability of the power supply has made possible the extension of the range of the equip-ment from 27 KMc/s to above 33 KMc/s. In a l l , three 2K33 tubes and two QKL40 tubes have been used to cover the range from less than 22 KMc/s to greater than 33 KMc/s. In order to lower the frequency limit of one of the 2K33 tubes from 22.8 KMc/s to less 27 than 22 KMc/s, the tuning set screw has been carefully released and the diameter of the external resonant cavity has been increased by about five per-28 cent • Unfortunately the alteration has not extended the range to 20 KMc/s as hoped but two important quadruplets have been found in the 22 to 23 KMc/s region and so the alteration has been valuable. The K-band waveguide consists largely of RG-66U rectangular copper waveguide with inner dimensions of 0*420 in. x 0.170 in. All Tee-sections, transmission sections, attenuator sections and crystal mount sections consist of this type of guide. Since the Sperry Microline Frequency Meter Model 350 and the QKL40 klystrons have RG-96U input and output guides with inner dimen-sions of 0.280 in. x 0.140 in., the machine shop of the physics department has constructed three taper sections from RG-96U to RG-66U waveguide. The output of the oscillator is attenuated by a flap attenuator and is then divided in an H-plane Tee-section so that almost half the power passes to a calibrated attenuator and. through i t to the Stark-modulation c e l l . The other half passes through another flap attenuator to a second Tee-section in which the power is subdivided. One arm of the Tee introduces the power FIGURE 3 STARK MODULATION CELL IN DRY ICS BOX To face page 9. 9 through a flap attenuator to the cavity frequency meter and subsequent crystal detector. The other arm leads through a flap attenuator to yet another H-plane Tee which is the Tee-section used to mix the source frequency with the 90 Mc/s harmonics and whose output arm is connected to the crystal mixer. The Stark-modulation cell consists of two eight-foot lengths of British X-band waveguide with inner dimensions of 1 in. x 1/2 in. Two taper sections, one for each end, for the transition from RG-66U to this X-band guide have been fabricated by the physics machine shop. One of these and its output connec-tion to a K-band crystal detector mount is shown in the foreground of Figure 3 facing this page. The radiation in the Stark cell is propagated with its E-vector perpendicular to the broad face of the guide just as i t is 29' for the TE^ Q mode in the K-band guide. The Stark-modulation electrode consists of a thin brass septum, about 1/32 in. thick and almost 1 in. wide which runs the length of the guide and is mounted parallel to the broad face in the centre by means of two thin lucite stringers fitted into grooves on 20 the side walls. Figure 1 of Mann's thesis4* shows a cross-section of the Stark-modulation cell. Some changes have been made in order to c h i l l the cell to low temp-eratures without breaking any vacuum seals. The taper sections are connected to short transition sections of X-band guide by flat brass flanges. To the flanges of the transition section are sealed thin mica windows by means of apiezon wax. Lead gaskets about 1/16 in. thick and of the same shape as the flanges have been mounted between the flanges. The flanges are then bolted tightly together by means of steel nuts and bolts so that the lead is com-pressed against the mica. With such an arrangement, the mica windows remain vacuum tight when the cell is chilled to dry ice temperatures. One transition section of X-band guide has a long groove l / l 6 in. wide and about U in. long milled in the centre of one broad face. A brass 10 exhaust chamber has been mounted over this groove and has been sealed vacuum tight to the waveguide with silver solder. The chamber has a copper exhaust tube braized to i t and the copper tube is connected to the glass exhaust line, which leads to the mercury diffusion and o i l pumps, by means of a Kovar copper-to-glass seal. This exhaust section can be safely cycled between room and dry ice temperatures with the absence of leaks. The Stark-modulation voltage is applied to the Stark septum by means of a short lead-in wire in a small Stupakoff seal, one of which is soldered to the centre of the narrow face of each section of guide. This lead-in wire is electrically insulated by the glass bead of the seal and the solder provides a vacuum tight joint which can be cycled between room and dry ice temperatures. The connections between the sections of the Stark-modulation cell and between the cell sections and the transition sections are made by British X-band coupling flanges AP54989and AP54990 which are locked by a lock nut AP54991. These flanges incorporate rubber 0-ring seals which can provide vacuum-tight joints. The special advantages to these couplings is that one of the sections can be removed and the other can be recoupled at both ends to the transition sections, or a long waveguide cell with similar flanges can be substituted easily without disturbing any of the mica windows or connec-tions to the vacuum pumps. The Stark-modulation cell is mounted in a Styrofoam box which can be o f i l l e d with chipped dry ice to reduce the cell temperature to about 200 K. The dry ice can be added to the box while a spectrum line is being observed so that progressive changes in the absorption can be viewed as the cell is chilled. Figure 3, facing page 9, shows the two sections of the Stark cell coupled together and mounted in the styrofoam box for chilling with dry ice. Just outside the box is the coupling to the short transition section which in turn is sealed at the other end by a mica window mounted between two plane brass flanges one of which belongs to the adjacent taper section. In the left foreground can be seen the K-band crystal detector mount and its output coaxial line to the pre-amplifier. The glass vacuum line can be seen at the remote end of the table and the electronic apparatus and control console are in the background. Stark Modulation and Detection The source klystron oscillator has a low frequency saw-tooth voltage applied through a blocking capacitance to its reflector. This modulation, which is variable in frequency and magnitude, causes a saw-tooth variation of several megacycles in the frequency of the oscillator. The same saw-tooth voltage is applied to the X-plates of a Cossor double-beam oscillo-scope so that the sweep of the fluorescent spot can almost be calibrated linearly with the values of the oscillator frequency. The Stark-modulation is a 50 Kc/s square wave which is zero-based and whose magnitude can be varied continuously from about 40 to 400 volts. The magnitude is measured by means of a calibrated Tektronix Cathode Ray Oscilloscope. This provides a Stark-modulation field strength variable from 67 to 670 Volts/cm approximately. The high voltage square wave generator is similar in principle to that of Hedrick3^ but uses two 6L6 power ampli-fiers In place of the VT127 tubes and two 6L6 tubes in place of the RK715B tubes. This part of the equipment has been altered by the present author only to the extent of increasing its output by the use of components with higher ratings and of providing for the calibration of the output. Part of the 50 Kc/s oscillator output is coupled capacitatively to the phase-sensitive detector as a reference signal. If the microwave energy is being absorbed in the cell because of a F I G U R E U To face page 12 rotational absorption transition, then the application of the Stark-modulation will cause a modulation of the absorption by altering the frequency of the absorption for every positive square wave. The resulting 50 Kc/s modulation is detected by the 1N26 crystal detector. A new tuned input stage shown in Figure 4 has been used to match the crystal detector to the pre-amplifier and provide a maximum 50 Kc/s signal across the input of the i n i t i a l tube. The 50 Kc/s pre-amplifier consists of one tube with a tuned plate transformer output and two broadband amplifier stages. Its overall bandwidth at 50 Kc/s is 200 cycles but is reduced to 70 cycles i f the 250 ohm damping resistor is shorted. The pre-amplifier output is matched to a long coaxial cable by a cathode follower. The cable transmits the 50 Kc/s signal to another ampli-fier at the control console whose output is applied to the phase sensitive detector. 20 The phase-sensitive detector described by Mann and shown by him in his Figure 5 is probably not the actual detector used by him. The phase-sensitive detector which belongs to the apparatus is one which is almost 27 identical to that described by McAfee et al ' except that the output of the 6SN7 push-pull double-triode is coupled by a Hammond $42 transformer to an additional 6SJ7 amplifier tube. The output of the amplifier is applied to the lower beam of the Cossor double-beam oscilloscope. The time constant of the detector has three ranges so that a time constant may be selected which gives the best signal to noise ratio without distortion. The property of the phase-sensitive detector is that the outputs for the Stark compon-ents are reversed in sign with respect to the output for the centre line i f the phase of the reference signal is adjusted for maximum output. In this spectroscope, the phase is such that the centre lines point downward and the Stark components point upward on the oscilloscope screen. Figure 5(a) shows the expected S-shaped line for the central component and a single EXPECTED AND ACTUAL C . R . O . D ISPLAYS OF ABSORPTION L I N E S To face page 1 3 . 13 positive Stark component i f the modulation voltage i s sufficient to move the Stark component by half the line-width from the central l i n e . This shape also applies i f there are many Stark components with the same s p l i t t i n g from the centre l i n e . In general however, the top peak w i l l be bluered as the compon-ents are spread out. If there are also negative components, they w i l l form peaks on the other side of the central line i n a similar way. Figure 5(b) shows two lines of the type of 5(a) i f the separation between the central lines i s about 1 line-width. Figure 5(c) shows two lines of the type of 5(a) i f the separation between the central lines i s only three quarters of a line width. For comparison two experimental doublets are shown i n Figures 5(d) and 5(e). The doublet of 5(d) i s a characteristic resolved doublet i n the spectrum of difluorochloromethane which probably results from the hyper-fine s p l i t t i n g of a rotational transition with moderately high J. The par t i a l l y resolved doublet of Figure 5(e) consists of the 19/2 *• 19/2 and 23/2 23/2 hyperfine splittings of the 103,7 +-10^ rotational trans-i t i o n i n CHFgCL3^. The frequencies increase from l e f t to right i n a l l the figures. Lastly, i t should be mentioned that the s t a b i l i t y of the spectro-scope has been improved by the elimination of ground loops. The output guide of the source klystron i s insulated from the rest of t he microwave ci r c u i t by the use of a Teflon gasket between i t s flange and the flange of the adjoining waveguide. The two flanges are held together by lucite screws. In a similar way, the crystal detector mount i s insulated from the Stark c e l l . A l l the ground connections are made by solder joints to a thick copper strip, which i s grounded to a water pipe. Also the sheathing on the coaxial cable carrying the reference signal from the 50 Kc/s oscillator to the phase-sensitive detector is discontinued at a point near the input to the detector. Ur With these arrangements, i t has been possible to detect some weak lines and observe the line shape i n each case. The line shape has been very import-ant for identifying a single l i n e of the CBF^Cr^ spectrum. In this thesis the line shapes have been noted for each spectrum l i n e . In some of Mann's 20 figures , such as Figure 2 and Figure 17, the line shape i s not recognizable. The minimum detectable absorption coefficient has been estimated to -6 -1 be 1 x 10 cms for this spectroscope by means of detections of the J=13> K=12 inversion line of ammonia. This i s not very good considering the value -8 -1 27 of 1 x 10 cms for the spectrometer of McAfee et a l • Most of the noise has been shown by experiment to be klystron noise, rather than crystal noise, and so the only solution to the problem is the use of new klystron tubes. Although visual sweeping means a wider bandwidth and less sensitivity, i t provides an experienced operator with a means of detecting a variety of line shapes and intensities. CHAPTER III ASYMMETRIC ROTOR THEORY The classical kinetic energy for any r i g i d rotor can be expressed i n the form 3 1 T = £ ( I ^ 2 • L ^ 2 • I j t ^ 2 ) where I 2 , I3 are the moments of inertia along the three mutually perpend-icular principle axes of the rotor and Uj_, W2, w 3 a r e *^ie components of the angular velocity along the same axes respectively. Since the components of the angular momentum along the same axes are given by P^ = I^ w^  respectively T = + ( f l 2 • Pg 2 • £2 2 ) (1) h h b 2 2 2 2 where p, the tot a l angular momentum, is given by p = p^ • p 2 • P3 . The classical formula for the kinetic energy can be transformed into the quantum mechanical Hamiltonian by the substitution of the angular momen-tum operators P^ for the classi c a l angular momenta p^ where the commutation rules are given by y . " V 7 " "ltex <2) V x - V « s " i f e p y The three principal axes of the moment of inertia e l l i p s o i d are therefore very important for quantum mechanical as well as classical theory. The three axes are usually designated as the a-, b- and c-axes with I a» I*3, I c as the moments of inertia along them respectively. Therefore the Hamiltonian for the rotational energy i s given by Ep0^ where 15 FIGURE 6 To face page 16 16 p A. p ( C p <C H r o t = !a_ * £b * !c_ ( 3 ) 2 I a 2 I b 2I C where the total angular momentum operator P i s given by P 2 = P a 2 • P t 2 • P c 2 . The quantum mechanical theory of the rotational levels has been developed i n terms of these three principal axes, the moments of inertia along them, and the components of the angular momentum operator par a l l e l to them. In addition, the selection rules for the electric dipole transitions between the rotational levels and also the theory of the Stark effect have been derived i n terms of the components of the dipole moment par a l l e l to the principal axes. Moreover, the theory for the nuclear electric quadrupole splittings has been derived i n terms of the components of the nuclear electric quadrupole tensor along the same principal axes. Therefore i t i s important to obtain some approximation to the positions of the principal axes and to the magnitudes of the principal moments of inertia. Approximations to the Structural Parameters of the Freon 22 Molecule The molecule CRFgCl, Freon 22, belongs to the point group G s for which there i s one plane of symmetry, here the HCC1 plane, and no other symmetry element. Two aspects of the approximate structure are presented i n Figures 6(a) and 6(b) facing this page. The approximate bond lengths have been given by Brockway2 on the basis of his electron diffraction results. These are r ^ p = 1.36 * 0.03 A, r c _ c l = 1.73 - 0.03 1 , r F . F _ 2 > 2 4 • 0 > a 4 % and rp_Qi = 2.56 - 0.03 A. The value of TQ_JJ has been assumed to be 1.08 * 0.02 A i n agreement with most determinations for this length i n the halomethanes. Lastly the H-C-Cl angle has been assumed to be 108° * 2°. Four models with different structure parameters, which are a l l with-i n the limits of Brockway1s values, have been assumed and the positions of the principal axes have been calculated for the eight resulting cases, four each for the CI3-* and C I 3 7 isotopes i n CHF2C1. The b-axis i s perpendicular to the HCC1 plane of symmetry i n each case and the a-axis l i e s between the o C-H direction and the C-Cl direction so as to make an angle ©C,about 13.U , with the C-Cl bond axis. The values of o c f o r the eight cases are recorded i n Table I facing page 18. It i s seen that «<decreases by A 1 i f CI 3? i s sub-35 stituted for CI i n each of the four models. This i s a very important fact i n the accurate solution of the molecule. The values of I a , I^ and I c have also been tabulated for a l l the models containing CI3-* and for two of the 37 a -b c models containing CI . It i s evident that the values 1 , 1 and I can be 37 very closely predicted for the model containing CI i f the same values are 35 known accurately for the model containing CI • In addition the values A = n , B = * , C = * and / = 2B - (A • C) , where ti = h 4 i r i a ZTTF 4 i r i c A - c 2ir and h i s Planck's constant, are tabulated for use i n the next section of this chapter. The magnitude and direction of the electric dipole moment has been approximately determined by adding vectorially the bond moments given by 32 -18 Pauling"^ . The result i s a dipole moment of approximately 1.7 x 10 e.s.u. o lying i n the plane of symmetry and at an angle of approximately 7 from the c-axis towards the C-H bond direction. The approximate quadrupole coupling constant for CI3** i n gaseous 35 CHP^Ol has been obtained by choosing a value greater than the value 35 ® 33 -70.50 Mc/s determined for solid CW^Ol at 20 K by Livingston^ and less 35 18 than the value -78.05 Mc/s determined for CI i n gaseous GF3CI Therefore eQq has been assumed to be -75.0 Mc/s for CI3*' i n gaseous CHE^Cl. As a f i r s t approximation, i t has been assumed that the quadrupole coupling tensor i s cylindrically symmetrical with respect to the C-Cl bond. If the C-Cl bond i s chosen as the z-axis and the perpendicular to the plane of TABLE I ROTATIONAL CONSTANTS FOR ASSUMED MODELS OF CHF2C1 Model I Model II Model III Model ] rC - F i n A 1.360 1.390 1.360 1.330 rC-Cl l n A 1.730 1.760 1.730 1.700 rC-H i n A 1.080 1.100 1.080 1.060 rF-F in A 2.240 2.280 2.214 2.186 r F - C l 1 x 1 A 2.560 2.610 2.570 2.510 ^ H-C-Cl 108° 108° 108° 108° CI 3* C I 3 7 CI 3* G l 3 7 C I 3 5 C I 3 7 C I 3 5 C I 3 7 13°22' 13°18« 13°19* 13°15' 13°24.6» 13°20.1« 13°14' 13°11» i f in a.in.u. (A) 2 I b in a.m.u.(A)2 I c in a.m.u.(^)2 51.826 103.147 146.675 51.828 106.39 149.90 53.663 107.350 152.490 53.668 110.644 155.779 . 50.741 104.078 U7.073 50.745 150.28 49.363 99.580 141.025 a* A in Mc/s B in Mc/s C in Mc/s 9754.6 4901.2 3446.7 9754.2 4751.8 3372.5 9420.6 4709.3 3315.2 9419.8 4569.1 3245.2 9963.1 4857.3 3437.3 9962.4 3364.0 10241.3 5076.7 3584.8 (A*C)/2 in Mc/s (A-C)/2 in Mc/s 6600.6 3153.9 6563.4 3190.8 6367.9 3052.7 6332.5 3087.3 6700.2 3262.9 6663.2 3299.2 6913.0 3328.3 --.5388 -.5677 -.5433 -.5712 -.5648 - -.5517 -symmetry (i.e. the b-axis) i s chosen as the y-axis, then the x-axis i s i n the plane of symmetry at right angles to the z-axis. Since q = d^V where V i s Bz2 35 the electrostatic potential at the site of the CI nucleus which results from the external charge distribution and since SJ2? - &v • i 2 ! • = o dx 2 by 2 bz 2 therefore, for cylindrical symmetry, a2? = b'V = -4. bx 2 oy 2 b z 2 and eQV„ = eQ^V = eQQ2? = eQv__ = - 3 7 . 5 Mc/s bx 2 oy 2 ^ Because the b-axis and the y-axis are identical eQV^ = e < ^ y y = * 3 7 . 5 Mc/s. The value of the component of the tensor along the a-axis can be determined 2 2 by the rotation eQV = eQV cos CK. * eQV_ sin 0<L " aa zz xx because i t has been assumed that e<*Vxy = e * V y z = e (3 Vzx = 0 • o With c<= 13.4 , eQV = - 6 9 . 0 Mc/s and because the trace of the tensor i s invariant, sQ^cc = " e t ^ a a " e <3 Vbb = * 3 1 . 5 Mc/s . Theory of the Rotational Energy Levels If there exist an asymmetric rotor, a prolate symmetric rotor and an & c oblate symmetric rotor which have the same moments of in e r t i a I and I , then the asymmetric rotor has energy levels for a given t o t a l angular momen-tum quantum number J which are intermediate between corresponding energy levels of the prolate and oblate symmetric rotors for the same J. For a given total angular momentum quantum number J, the asymmetric rotor has 2 J * l non-degenerate sub-levels E j ^  where - J, J - l , , 0 , . 1-J, - J . A particular level E j -g for the asymmetric rotor (of which I a<l"b<I c ) i±e8 intermediate between the level E T „. for the prolate symmetric rotor ( l b = 1°) and the level E_ _ for the oblate symmetric J»Kc rotor ( l b = I a) i f K + K = J or J • 1. Moreover i f % = K a - K c then E T _ > E T —. , and the asymmetric rotor levels do not cross each other for a given J as I b varies through the range from I a to 1° . This can be . seen from Figure 17 of Herzberg1 s book on infrared and Raman spectra^" The level J*r can be conveniently designated as J„ v for the asymmetric Ra' Rc 3*5 top rotor . The eigenvalues of the rotational energy operator (3) are given by E ( l a , I b , I c ) = • fa2) » ( P c 2 ) (4) r 0 t 21 2L 21 a D c where (?^)» ^ b ^ ' ^ P c 2 ) t b e e i S e n v a l u e s o f t n e operators P^2, 2 and P c , respectively, with respect to the wave function for the asymmetric 2 rotor. Since the eigenvalue of P is given by <P*> = <Pa2> • • <PC2> = t 2 J ( M ) and since equation (4) can be written in the form rot (%*.•> = i 2 {•<\ a>* *4 . a > < p c 2 > } ( 5 ) 4,2 4,2 36 where a = " , b - n and c = " • King, Hainer and Cross 2I a 2 ? 2I C have shown that the rotational energy for the J«£ level can be written i n the form E r o t J.T ( a' b' c) = A * C J ( J * 1) » A " 0 B T T (*) . (6) 2 2 In this formula, j: i s Ray's asymmetry parameter given by Jc - 2b - (a » c) (a - c) which i s -1 for the prolate symmetric rotor (b = c) and *1 for the oblate symmetric rotor (b = a) and E j ^ Of) i s the reduced energy which depends L. 37 only upon J, T and yf • The reduced energy has been calculated for a l l J from 0 to 12, for a l l corresponding T values and for /c from 0 to +1 at intervals of 0.01. Values for / f from 0 to -1 can be obtained by the relation Ej ^ U) = -Ej ^ (-A) • Since the frequency in cycles is more convenient to microwave spectro-scopy than is the energy in ergs, equation (6) can be written in the form . ^ ( A , B , C ) = ^rot J , * C (a,b,c) = A » C J ( J * X ) * A - C E _ _ ( * ) (7) where A = a, B = b, and C = c . h h h The values of A , B , C. and A have been tabulated for the four assumed models of CHFgCl in Table I where the necessary physical constants, Planck's mr constant h, the proton rest mass m , and the ratio of the mass of hydrogen .38 H to the proton rest mass /bp, have been taken from the results of Cohen, Dumond, Layton and Rollett" h = (6.62517 ± 0.00023) x 10~ 2 7 erg sec. mp = (1.67239 - 0.00004) x lO" 2^ gms.. "fynip = 1.000544.6 i TO 19 35 37 The values for the masses of the atoms a , C , F , CI and CI have been copied from the table of the properties of the stable nuclei in Townes and Schawlow*^. mass of H1 = 1.008142 a.m.u. 12 mass of C = 12.003804 a.m.u. mass of F 1^ = 19.004456 a.m.u. mass of Cl"^ = 34.97993 a.m.u. and mass of Cl3 7 = 36.97754 a.m.u. It can be seen from Table I that A •» C ^ 6,500 Mc/s, A - C 35 2 2 3,200 Mc/s and A -0.55 for CHFgCl • These values can then be used to determine the rotational energy levels approximately. For electric dipole transitions, A J = -1 (P-branch), J = 0 (Q-branch) or / \ J - +1 (R-branch). For a Q-branch transition, the frequency of the absorption line i s given by E = EJ/t» " E Therefore i f two Q-branch transitions can be identified, the only unknowns A - C and /f can be determined. However, the identifications of additional 2 Q-branch transitions w i l l only confirm the previous assignments and values of the unknowns. And so a P-branch or an R-branch transition i s needed to completely determine the three unknowns A, B and C. For an R-branch trans-it i o n , the frequency of the absorption lin e i s given by E = (A + C) J(J • 1) • J E j * 1 ) T t ( / 0 - E J j T(X-)J A - C ( 9) 2 where J i s the smaller total angular momentum quantum number of the two levels. The additional selection rules peculiar to the asymmetric top rotor are given by Cross, Hainer and King"^5. For the case i n which the dipole moment i s i n the plane of the a- and c-axes, the selection rules for allowed transitions are £»"C = ^1, -3. In addition, i f the dipole moment l i e s p a r a l l e l to the c-axls, then the parity of the K a pseudoquantum number must change while the parity of the K_ number must be unchanged. The selection rules are then A K Q = *1 and = 0, +2. These are the selection rules 3m C for the c-sub-branches. Since the dipole moment for CHFgCl l i e s within about 7° of being para l l e l to the c-axis, the c-sub-branch transitions should be much more prominent than the a-sub-branch transitions which depend upon a component of the dipole moment paral l e l to the a-axis. Accordingly a l l possible c-sub-branch transitions of the Q-branches and R-branches have been calcu-lated i n the approximate range of the spectrometer with the estimated rotational constants for CBF2CI. It has been found that the only strong R-branch transitions with J < 12 are 1 Q «*• 2^^ ; "*22,1 ' 1, 2„ „ and 2„ ~ «-*• % 0 • Only one of these, 1 -* 2 , is calculated 1,0 2,0 0,2 1,2 ' 0 f l to be in the central part of the range and the others are a l l calculated to li e just outside the upper limit of the range of the spectrometer. Some weak R-branch lines with A T = -3 are also possible but they are less likely to be identified than the stronger transitions with A T = l l . There are, however, many possible Q-branch lines with J < 13 for both A T = *1 and «^>T = *3 in the range of the spectrometer. There should be a simple series of transitions 11^ g "^-^.S » ' 7 7 ' 9 ,-*9. , J 8 8 and 1 -*7. in order of increasing frequency 3,6 4,b 3,5 4,5 3,4 4,4 and with regular spacings of about 3,500 Mc/s. However the presence of other lines and the presence of the same transitions for the CHF? Cl37 molecule make, i t almost impossible to recognize such a series without further information. Dipole Transition Intensities Knowledge of the dipole transition intensities aids in the Identifi-cation of the rotational transitions. The intensity of absorption for the transition n -*-nf is given by Cross> Hainer and King^ to be • • ^ { i - « . < - « ) } . , ( • » ) . ^sn' CC i SLd 2 _ * |Pnsii'I <10> where n represents the lower state J, M, *C , I, F ; n' represents the upper state J', M', *C», I 1, F'j E and E , are the rotational energy levels for the states n and n'; n n' = EnT - En and $ is the transition frequency; N. is the number of molecules per ccj g n is the nuclear spin weight factor of the lower level; and j^ njn'l 2 i s t h e s < l u a r e of the magnitude of the n;n» element in the matrix of the dipole vector ^  . Several simplifications can be made to obtain the relative intens-i t i e s for the rotational transitions of CBFgCl* F i r s t of a l l , experimental measurements are made at almost constant gas pressure so that N i s a const-ant for a l l lines measured at 1 0 microns pressure. Secondly, the molecule has no rotational symmetry so that the wave functions for the asymmetric rotor are neither symmetric nor antisymmetric and the values g^ are the same for a l l states i . Thirdly, -hv" is of the order of 5 x 1 0 " 3 for T ~ 3 0 0 ° K T2F r and 3 0 , 0 0 0 Mc/s so that 1 - exp )\ = h£ . • Fourthly, I . Ter kT n » n may be summed over the Stark components M,Mf i n the absence of a perturbing f i e l d to get the intensity of the central transition. Lastly, i f there i s no external f i e l d , each J , T level i s ( 2 J • l ) - f o l d degenerate so that H e " E l / h T = YL < 2 J • 1 ) exp ( 1 * 0 * 1 i J,r \ B I where E j ^  is measured i n cycles. Then the expression ( 1 0 ) can be simplified to v ^ 2 f-hEj-i) i j , r j J S r oQ * e x p j j ^ f x ( L I N E S T R E N G T H ) J.r: J ' . T ' ( i i ) ( 2 J • 1 ) exp ( i g ^ The values of the factor (Line Strength) j j , ^  have been tab-4 0 ulated by Cross, Hainer and King for a l l allowed transitions involving J values less than 1 3 with k - - 1 . 0 , - 0 . 5 , 0 , + 0 . 5 , and •l.O. For k = - 0 . 5 , the relative line strengths for the 1 Q ^ 2 ^ ^  transition: the 8 3 ^* 8 ^ 5 transition; the 9^tS •> 9 ^ , 6 transition; the 1 0 3 , 7 l G ^ r a n s i t l o n ; and the I I 3 g •> 1 1 4 , 8 "transition are 1 . 5 0 , 2 . 8 2 , 3 . 5 3 , 4 . 5 4 and 5 . 9 2 respect-ively. But a transition at frequency 3 0 , 0 0 0 Mc/s i s approximately 1 . 3 times as strong as a transition at 2 6 , 5 0 0 Mc/s because of the y" factor. This FIGURE 7 0 10 20 30 40 J FIGURE 8 To face page 24. l a t t e r factor combined with the relative line strength factor means that the series 8- c - * 8 , _ : : 11 0 - 11. rt which are i n order of decreasing itJ 4,5 J»° 4,8 frequency with spacings of about 3,500 Mc/s, should exhibit almost identical intensities i f the exp ( J> c ) factor i s neglected, kT Since the reduced energy E j <g (A) varies from +ve to -ve values, an intermediate rotational energy level for J-^ i s , from equation (6), < E J,*>inter»d.~<4-S J ( J * l j ( 1 2> With A » C r>^, 6,500 Mc/s for CHF.Cl, exp<" h^ ^ ) J( J • 1) I13 2 A \ kT J 1.0 for J = 1 and only down to 0.87 for J * 11. However, for J - 25 the factor i s of the order of 0.5 and for J = 40, the factor has decreased to 0.2. This Boltzmann factor i s competing with the lin e strength factor and so there should be a maximum intensity for J levels of the order of 20. Since each level with quantum number J has an M-degeneracy of 2'J * 1, the product (2J • 1) exp 1 2 v ' > should give approximately I kT J the relative thermal distribution of levels. In Figure 7 facing this page, o the factor i s plotted with A - C = 6,500 Mc/s for both T = 300 K (room temperature) and T = 200 K (dry ice temperature). It is seen that o M-degenerate levels with Jr-»22 have the greatest population at 300 E o but that levels with J/^18 have the greatest population at 200 K. The o strongest transitions w i l l probably occur at 300 K.for values of J near o 22 and at 200 E for values of J near 18. If the c e l l temperature i s reduced from 300° E (room temperature) Q to approximately 200 E (dry ice temperature) then the intensities of a l l rotational transitions are enhanced by the factor 3/2 owing to the factor 1/T and by a factor depending upon the relative decrease i n the denominator of expression (11). The denominator may be approximated by J L kT J since the intermediate level for the (2J • 1) M-degenerate levels of rotational state i s given by expression (12). The value inside the summation sign o o is plotted against J i n Figure 8 for both T = 300 K and T = 200 K. Approximately, the value of the summation i s the area under the curve. It i s o evident that the area under the curve at 200 K i s less than half that at 300° K. Therefore the denominator of expression ( U ) i s reduced to half the previous value at most when the c e l l i s chilled to dry ice temperature and the intensities are enhanced by a factor of at least 2 through the con-tribution of this factor. The overall enhancement factor Is 3/2 x 2 = 3, at least, for low J transitions. There i s also a change i n the factor exp \ -h A • C J(J • 1) I o ^ o 2 kT J when the c e l l temperature i s reduced from 300 K to 200 K. But the effect i s negligible for transitions involving J values less than 5 and so these transitions should show an overall enhancement figure of 3 for the absorp-tion Intensity. For values of J *>* 15, the overall enhancement factor is only down to 2.7 but for values of J*w27 the factor i s down to 2 and for values of J~»37, the factor i s only 1.5* Therefore the decrease i n c e l l temperature not only provides better sensitivity but also provides some discrimination between high and low J , transitions. When the c e l l i s chilled to dry ice temperatures, a double line near 2A,800 Mc/s can be recognized as part of a sestet of lines. Furthermore, three important quadruplets which are not evident at room temperatures can be detected. (These have proved to be Q-branch transitions for GW*pT?^ and so are very important for the solution of the molecular structure). The intensity of a widely spaced quadruplet shows an increase by a factor of 3 when the c e l l i s chilled and several other quadruplets exhibit FIGURE 9 STARK S P L I T T I N G OF 5/zS/Z HJPERFINE TRANSITION OF 10>1 +-Zlfl L I N E To f a c e page 26. enhancement figures of 2. In several cases, part of an apparent complex structure has exhibited an increase, while some other part has exhibited no increase or even a decrease. By this type of observation an apparent multi-plet may be demonstrated to be an accidental coincidence of absorption lines. The Stark Effect The theory for the Stark Effect of an asymmetric rotor i s given by Golden and Wilson^*". They show that i n the case where the ele c t r i c vector of the radiation i s parallel to the e l e c t r i c f i e l d , there w i l l be ( J • 1) com-ponents for an R-branch transition where J i s the quantum number of the lower level and there w i l l be J components for a Q-branch transition as long as neither of the rotational levels i s accidentally degenerate. For high J values, therefore, there w i l l be so many components that separation w i l l be impossible. However, the 1Q transition should show two Stark components and other low J transitions should manifest a marked dependence on the Stark-modulation voltage. Stark s p l i t t i n g has been found for only one line i n the entire spectrum and that line has been the strong line of the sestet at 24,800 Mc/s. Figure 9 facing this page shows the strong central line at l e f t and the weak Stark component under the frequency marker. The separation i s about 2.1 Mc/s with an applied modulation f i e l d of 330 V/cm. No attempt has been made i n the thesis to analyse the Stark effect. Some experimental results on Stark s p l i t t i n g and Stark broadening are presented i n Appendix II. The strongest lin e of the quadruplet with broad spacing and large temperature enhancement factor i s very sensitive to the applied Stark voltage and exhibits considerable distortion of the lin e shape as the Stark-modulation voltage increases. It i s probable that this quadruplet, as well as the sestet, is a transition involving low J values since i t s Stark effect is almost resolvable. It i s also noted that a l l members of a multiplet show the same dependence upon the Stark-modulation voltage. CHAPTER TV SOLUTION OF THE SPECTRA BY ANALYSIS OF THE HYPERFINE STRUCTURE qc 37 The microwave spectra of the molecules CBF2C1 and CBF2C1 i n their natural abundances have been obtained i n the regions 22.0 to 27.2 KMc/s and 28.3 to 33.2 KMc/s with the Stark-modulation spectrometer described i n Chapter II. The spectra have been measured both with the absorption c e l l o at room temperature ( —-300 K) and with the c e l l at dry ice temperature o (~200 K). Approximately 250 absorption lines have been detected with the c e l l at dry ice temperatures. Some of these have not been detected at room temperature i n spite of prior knowledge of their frequencies determined from the measurements at dry ice temperature. For instance, only two lines of the sestet at 24,800 Mc/s are evident at room temperatures. To ensure that no line i s purely the result of a reflection i n the waveguide or a mode dis-continuity of the source klystron, the gas i s pumped out of the c e l l u n t i l the absorption line disappears and then new gas i s slowly admitted u n t i l the absorption re-appears. The relative intensity (estimated by the signal to noise rati o ) , the line width, the dependence upon gas pressure and the dependence upon the Stark-modulation voltage have a l l been measured along with the exact frequency for each of the lines at both room and dry ice temperatures. The frequency, line width, optimum gas pressure, optimum Stark-modulation, estimated relative intensity and temperature enhancement factor are tabulated for each line i n Appendix I. Even a cursory look at the table reveals that the lines are grouped into doublets or multiplets with the exception of 17 apparently 27 SYMMETRICAL TRIPLET AT 32,580 Mc/s 28 single lines. There are 1 sestet, 14 quadruplets consisting of 2 doublets each, 2 t r i p l e t s resembling the components of a quadruplet, 2 symmetrical t r i p l e t s and 2 possible quadruplets with peculiar li n e shapes. Most of the spectrum lines can be detected most easily at a pressure of 10 microns of mercury and with a Stark-modulation f i e l d of 330 Volts/cm. Also most of these lines show the type of line shape shown i n either Figure 5(d) or Figure 5(e). There are however a t r i p l e t and a singlet at 25,100 Mc/s, a quadruplet at 27,200 Mc/s, a singlet at 32,400 Mc/s, a symmet-r i c a l t r i p l e t at 32,600 Mc/s and a very close doublet at 33,050 Mc/s which a l l exhibit the same characteristics. They exhibit a maximum signal-to-noise ratio i f the gas pressure i s 100 microns and i f the Stark-modulation f i e l d i s 110 Volts/cm. Under these conditions, their line widths are about three times that of other lines and also they have a trough-like shape with the Stark components apparently spread out. The strong, symmetrical t r i p l e t at 32,600 Mc/s i s reproduced i n Figure 10, facing this page. The spacings between the components are about 5*3 Mc/s. As yet no explanation has been advanced for these broad lines. They certainly depend on the presence of the gas from the Freon 22 bottle. The gas i s a commercial sample, supplied by Matheson Company, but an infrared analysis of the sample by John Mayhood of the physics department of the University of B r i t i s h Columbia has revealed only the vibrational bands characteristic of CBFgCl. There appear to be eleven quadruplets a l l detected at a gas pressure of 10 microns and with a Stark-modulation f i e l d of 330 Volts/cm which consist of two doublets spaced by several megacycles. In some cases the doublets themselves are barely resolvable i f the spacings between the components are megacycle or less. Most of these quadruplets manifest a considerable improvement i n the signal-to-noise ratio when the c e l l i s chilled to dry ice temperature. A l l the four components of this type of quadruplet have approximately the same signal-to-nolse ratio. In addition, the set of three lines at 2 5 , 6 3 0 Mc/s and the set of three broadly spaced lines at 2 9 , 3 0 0 Mc/s each exhibit the characteristics of the components of quadruplets similar to the eleven, definite quadruplets. It w i l l be demonstrated i n this chapter that four of the quadruplets and both of the incomplete quadruplets can be 35 assigned as Q-branch transitions of CHF 2 C 1 sad that four other quadruplets 37 can be assigned as Q-branch transitions of CW^Ol by means of analyse® of the nuclear electric quadrupole splittings for CI 3* and C I 3 7 respectively. The most interesting lines are the weak singlet at 2 4 , 4 0 0 Mc/s; the sestet at 2 4 , 8 0 0 Mc/s; the very weak, widely-spaced quadruplet at 2 8 , 7 0 0 Mc/s and the widely-spaced quadruplet at 3 0 , 4 0 0 Mc/s. The singlet and at least half the lines of each of these multiplets cannot be detected at room temper-atures. Each member of a multiplet shows the same pressure and Stark-modula-tion dependence as the other members. The optimum Stark-modulation f i e l d for the singlet and the members of the sestet i s 1 7 7 Volts/cm, a value peculiar to these seven lines. The strong lin e of the sestet shows Stark s p l i t t i n g (as portrayed i n Figure 9 facing page 26) while the singlet and the other members of the sestet show a marked distortion as the Stark-modulation f i e l d i s increased from 1 7 7 Volts/cm. Both quadruplets also exhibit distortion as the Stark-modulation voltage i s increased from the optimum value. There i s a large variation i n the signal-to-noise ratios of the widely spaced compon-ents of each multiplet. The characteristics exhibited by these lines are those of transitions involving low J values. It appears very l i k e l y that the sestet represents the rotational transition 1 Q 1 2 1 1 » with i t s hyperfine 35 structure, for CRF-jCl^. If this assignment i s correct, then i t i s possible to identify the weak singlet at 2 4 , 4 0 0 Mc/s as the strongest hyperfine trans-i t i o n for the 1 Q ^ * * 2-J_ I M U L ' F C I P L E ' T belonging to CHFgCl 3 7 by means of a careful comparison of the rotational constants l i s t e d for the models of CHF 2C1 3^ and C r E ^ C l 3 7 i n Table.I. An analysis of the hyperfine structure i s needed to confirm the assignment, however, because the data on the Stark s p l i t t i n g i s so meagre. In principal, i t i s possible to identify a series of Q-branch trans-itions spaced by about 3500 Mc/s and showing similar signal-to-noise ratios. However, the unfortunate gap i n the spectrum from 27.2 to 23.3 KMc/s, the presence of transitions for both CHF2C135 and CHFgCl^7, and the lack of accurate knowledge about any of the three rotational constants make unambig-uous assignments very d i f f i c u l t . For instance, the quadruplet at 26,400 Mc/s can.be either the I I 3 g - * l l ^ g transition, the 1 0 ^ 7 - » 1 0 ^ 7 transition or the 9^ 6 "*^4 6 transition f ° r CHF-jOl5-* with the appropriate choice of rotational parameters A, B and C. Fortunately the nuclear electric quadru-20 pole s p l i t t i n g can be used to identify the transitions and Mann has demon-strated that the estimated hyperfine s p l i t t i n g for the 103,7 * 10^ 7 trans-35 i t i o n i n CHFgCl agrees very well with the structure of the quadruplet at 26,400 Mc/s. The assignment is not t o t a l l y trustworthy because the struc-tures for the 9 0 • -»9. , and 11_ <, -*11, a transitions are very similar jfO 4,0 j,o 4,0 and d i f f e r mainly i n the magnitude of the sp l i t t i n g , which depends on the 35 assumed value of eQq for CI i n Freon 22. The calculation of the nuclear electric quadrupole s p l i t t i n g i s therefore essential for positive identification of the Q-branch transitions, i f not for the only strong R-branch transition 1Q ^ ~*2± ]_ • * n the follow-ing section, the l g ^ "*"2^ ^ transition i s unambiguously identified by i t s hyperfine structure and from the splittings i n this known multiplet, accurate values of eQV^ and eQV^ can be obtained. These values can be used i n turn to estimate the hyperfine structures of Q-branch transitions. By this method 35 the 3 2 1 •* 33 and 3 2 2 •» 3^ Q rotational transitions for CHFgCl*^ have been identified for the f i r s t time. From these two, a l l the Q-branch trans-35 itions of CHFgCl can be predicted with great accuracy and the correspond-ing transitions for CHFgCl3''' can be estimated with f a i r accuracy. Theory of the Nuclear Electric Quadrupole Interaction The nuclear electric quadrupole of a nucleus which has a nuclear spin I >^ £ interacts with the electrostatic potential at the site of the nucleus to give 2 1 + 1 hyperfine levels for a given rotational level Sx . The hyperfine levels may be designated by the quantum number F where F takes on the values J+I, J+I-l, | j - l | . Two theories have been given for the interaction of the nuclear electric quadrupolar nucleus with the electrostatic potential in an asymmet-L2. r i c top. According to the theory of Bragg , the interaction energy for the J«£,I,F level can be written i n the form 2J where S a, S b, and S c are the lin e strengths tabulated i n Cross, Hainer and K ing 4 0 for the a-, b- and c-sub-branches, respectively, of the Q-branch rotational transitions for the molecule; where eQV&a, eQV^, and ©Qv"cc are the components along the a-, b- and c-axes, respectively of the quadrupole coupling dyadic O Q VE; and where f ( l , J,F) i s Casimir's function given by W T J F A - fo(C + 1) - 1(1 • 1) J( J + 1) ' ' ' 21(21 - 1 ) ( 2 J - 1)(2J • 3) with C = F(F • 1) - 1(1 • 1) - J( J • 1) . The theory of Bragg i s useful at low J-values for which the line strengths can be quickly ascertained from the tables. However at high J values, there are so many possible Q-branch transitions that the calculation becomes laborious. The worst fault of the theory is that i t makes use of tables calculated for A -values of -1.0, -0.5, 0, +0.5 and +1.0 only. Interpolation i n the tables by graphical meth-ods i s very uncertain because the peak line strength often l i e s between the limits A - - 1 . 0 and A - + 1 . 0 . A more recent paper by Bragg and Golden^ allows a much more con-venient calculation of the nuclear electric quadrupole interaction energy. Their results lead to WQ = 1 f(l,J,F) eQV a a-/j(J + 1 ) • E U ) - 1 ) Mil] Q J ( J •> 1 ) L I J { J J • 1 ) - E(/r ) • (/t - 1 ) • eQV cc If A i s known, the values of E(/f ) and ffiM*,) c a n D e obtained very o A accurately by interpolation i n the tables for E(/f) of Townes and Schawlow37. The selection rules for transitions between hyperfine levels are A F - 0 , - 1 . The intensities of the hyperfine structure components and the values for Casimir's function are l i s t e d for J ^ I O i n Townes and Schawlow^. Since the nuclear spin I = 3 / 2 *"or both CI3** and C I 3 7 , the hyperfine struc-tures are very similar for the two isotopes. It can be seen from the tables that there are four strong components/\F = A J for i f I - 3 / 2 . There-fore,, for Q-branch transitions, with A J = 0 , the four strong components are those for which A F - 0 . Equation (L4) can be modified to give the hyper-fine transition energy A WQ for the cases A J - 0 , A F = 0 . AWQ = (WQ)J,-T«,F " <WQ)J,T,F = ' 1 f(l , J,F)feQV A A / A E ( > t ) " DAW*)] J(J • 1 ) L L *A J + e Q v b b | 2 A ^ i l } ( 1 5 ) cc | - A E ( X ) •> ( / - D^?|^ L>jJ where ^ E ( ^ ) = E j ~ , ( ^ ) - E J T(>(-) and / \ * E ( y f ) = >_AE(^) Equation ( 1 5 ) may be written b r i e f l y i n the form /\WQ = f ( l , J , F ) j-(J,T,I,/f ) (16) where *J*( J,T, I, J[) i s a scale factor which depends on the nuclear spin I, the rotational level J-£ and the asymmetry parameter^ but not on the F quantum number. From the nature of the function f ( l , J,F) for I = 3/2» i t can be seen that the resulting quadruplet consists of two doublets with equal spacing. One doublet consists of the J - 3/ 2 —> J - 3/2 transition and the J * 3/2 J * 3/2 transition and the other consists of the J - -g- J - •§• and the J + J + transitions. As J increases, the scale factor de-creases so that the spacings between the components of the quadruplet become smaller. At values of J ^ I S , approximately, the internal spacing of each doublet becomes so small that the doublets are no longer resolvable. As a consequence, the quadruplet appears as two lines, separated by several mega-cycles. Figure 5(d) indicates such an unresolved quadruplet while Figure 5(e) shows one of the doublets of a resolved quadruplet. This explanation for the doublets and quadruplets has been advanced by Mann i n his thesis. In this thesis, the explanation of Mann is verified completely and the one assignment made by him has been made unambiguous by the abundance of data here presented. Rotational Transition Assignments If the formula (13) i s applied to the l Q j l and 2^^ levels, the results are that (Wrt), v = -f(3/2,l,F) eQV where F = 5, 3 and 1 i n turn 9 iO,lJ J J a a 2 2 2 and that (W_)„ „ = f (3/2,2,F) eQV,. where F = 7, 5, 3 and 1 i n Q Z l f l , l . DD 2 2 2 2 turn. With the estimated values eQV & a = -69.0 Mc/s and eQV = +37.5 Mc/s, which have been calculated on page 18, the hyperfine structure for the 1Q ^ 2^ ^  I^11© c a n determined completely. The selection rules <AF = 0, ^ 1 and the relative intensities within the multiplet are given by 13 Townes and Schawlow . Almost perfect agreement i n spacing and i n relative intensity i s found between the lines of the experimental sestet at 24,800 Mc/s and the six hyperfine transitions given by A F = 0, +1 for the l o , l ~ * 2 l , l rotational absorption l i n e . Evidently the A F = -1 transitions are too weak for detection since even the 1/2—> 3/ 2 hyperfine transition has been detected with only a 2:1 signal-to-noise ratio. If the formula (13) i s applied to determine the hyperfine structure of the 1. , 2 0 , and Q -* 2 2 o rotational transitions, quite different results are obtained i n which the strong l i n e of the sestet has the third lowest hyperfine s p l i t t i n g /\WN instead of the fourth largest as found experimentally. The estimated Q structures for the 2 ->2 and for the 2 -»3, 0 rotational trans-1,1 2,1 X, <c itions also show no agreement with the experimental sestet. And so i t can be concluded definitely that the sestet represents the hyperfine structure of the 1Q T_—>-2T_ ]_ rotational transition. The application of formula (14) gives exactly the same results for the hyperfine structure for the 1Q I ~ * 2 I J_ line since the exp l i c i t solu-t i o n s 3 6 for E(/^ ) are ( /( - 1) for the I Q ^ level and 4 ^  for the 2^ 1 l e v e l . The respective values of ^E(Xr) are then +1 and +4« Formula (14) reduces to -f( 3/2,l,F) eQV a a for the lQfl level and to +f(3/2,2,F) eQV b b for the 21 1 l e v el» which are the values determined from formula (13). Formula (14) for these levels and for a l l rotational levels with J less than 5 gives an 36 exact formula for WQ because of the explicit formulae for the reduced energy whereas formula (13) involves interpolation i n the li n e strength tables even for J levels of 2. Now that the hyperfine structure of the 1() l " * 2 i l ^ n e n a s been identified, i t i s possible to calculate accurately the two values eQV and £L£L eQV^b from the five independent separations between the experimental lines. The values which satisfy the five independent equations for the separations are ©QV a a = -65.0 - 0.2 Mc/s and eQV b b = +35.2 - 0.3 Mc/s. The maximum TABLE II HYPERFINE SPLITTINGS AND RELATIVE INTENSITIES FOR LOW J TRANSITIONS Rotational Transition Centre Frequency Mc/s Hyperfine A W Q in Mc/s Transition Experi- Calcu-F - F» mental* lated# Rel.Intensity Experi- Theor-mental etical V2 ••3/2 -16.28 -16.25 0.09 0.083 V2 -5/2 - 9.48 - 9.55 0.11 0.090 ^,1 "*21,1 24,818.15 V 2 • -V2 - 7.38 - 7.45 0.11 0.083 5/2 - 7/2 - 0.78 - 0.74 0.35 0.400 3/2 - 5/2 • 6.72 • 6.71 0.22 0.210 3/2 -3/2 •13.02 •13.00 0.11 0.107 3/2 ->3/2 - -16.92 0.0 0.143 32,1 -*33,1 29,294.60 9/2 -9/2 - 7.1 - 7.06 0.3 0.333 5/2 -5/2 • 4.3 • • 4.24 0.3 0.191 7/2 - 7/2 •14.1 •14.12 . 0.4 0.225 3/2 -3/2 -16.1 -16.13 . 0.11 0.143 32,2 ^hfO 30,405.47 9/2 -9/2 - 6.7 - 6.73 0.44 0.333 5/2 -5/2 • 3.9 • 4.03 0.20 0.191 7/2 - 7/2 +13.4. •13.42 0.17 0.255 * Accurate to - 0.05 Mc/s at best. # Using eQVaa = -65.0 Mc/s, > e« Vbb = •35.2 Mc/s, and /f = -0.597520 • To face page 35 errors are the result of the possible experimental errors of -0.05 Mc/s i n each strong lin e and of *0«10 i n each weak line of the multiplet. These errors are due primarily to uncertain lin e shapes for the weak lines. The derived values, e Q v a a = -65.0 Mc/s and eQV^ = -35.2 Mc/s have been used to calculate the hyperfine splittings of the structure's com-ponents from the central rotational frequency. These calculated values are presented along with the experimental splittings i n Table II facing this page. Also the theoretical relative intensities are compared with the ex-perimental relative intensities which have been estimated from the signal-to- noise ratios. Since the experimental frequencies are accurate to *0.05 Mc/s at best and since the signal-to-noise ratios are accurate to approximately -20$ at best, the•agreement i s excellent for the frequency splittings and good for the relative intensities. The hyperfine structure for a l l the possible J = 3 Q-branch trans-itions has been calculated with eQV a a = -65.0 Mc/s, eQV^ = -35.2 Mc/s and /{ = -0.55 by both formula (13) and formula (15). The calculated structures for the 3 2 2 "* ^ 3 g rotational level shows close agreement i n the frequency splittings and approximate agreement in the relative intensities with the experimental multiplet at 30,400 Mc/s. Moreover, the three strongest trans-itions of the calculated hyperfine structure for the 32,1 ** 33 j_ lin e show very good agreement i n frequency splittings with the three experimentally determined lines at 29,300 Mc/s. The experimental centre frequencies for the 32,2 "*"33,0 rotational transition and for the 3 2 ^ "* 33 ^ rotational trans-i t i o n can now be obtained from any two lines of each multiplet by the use of formula (16). Since the central frequencies of Q-branch transitions depend on only two unknownsj A - C and ^  , these values may be calculated from two experimental lines by substituting i n equation (8) and by interpolating i n 37 the tables for E(/f ) . The resulting values are ^ = -0.59752 and A - C = 3,363.54 Mc/s. The hyperfine splittings can now be recalculated with this accurate value ofyf . The calculated and experimental frequency-splittings are tabulated i n Table I I along with the theoretical and exper-imental relative intensities. The agreement for the frequency splittings i s excellent except i n the case of the weak 5/2 -* 5/2 hyperfine transition of the 3_ „ 3 0 « li n e . This agreement guarantees the correctness of the assignments since the error i s greater than the possible experimental error in only one case out of seven hyperfine transitions. Now that the value of /f" i s known accurately and the two lines have been identified directly, i t i s possible to use the. hyperfine splittings for the 32 i * " * ^ 1 a n < * ^2,2"*33,0 to"8113^!0118 *° solve for eQv*aa and eQV^ as unknowns i n formula (15). The results are eQV = - 6 4 . 8 2 - 0.25 Mc/s and eQV^ = +35.1 * 1.5 Mc/s, which are well within the limits of the experiment/-a l values determined from the lo , l ""^  *~L,1 transition. The latte r are accordingly accepted as the correct results since their possible errors are smaller. The centre frequency of any rotational transition can now be obtained from equation (8) with the known values of and A - C . As well, the hyperfine structure for any Q-branch line can be accurately predicted from formula (16). The simultaneous application of these two c r i t e r i a makes the assignment completely certain. Five more Q-branch transitions have been identified for the molecule CHF^Cl by their central frequencies and by their hyperfine structures. These are the 5_ _ 5 , - ; 5~ , -» 5o 0 ; < C f j J,J <s»4 Jf£ ^2,k~* ^ 3,A '* 9 3 , 6 " ~ * 9 4 , 6 ; and l O ^ ^ - ^ l O ^ 7 transitions. The hyperfine scale factor ^ " ( J J T J I ^ ) of formula (16) has been calculated for these structures by the method of Bragg and Golden i n equation (15) with the accurate value / f = -0.59752 and the respective experimental values have been determined from the experimental splittings. The centre frequencies of the SCALE FACTORS FOR HYPERFINE SPLITTING OF Q-BRANCH TRANSITIONS TABLE III SCALE FACTORS FOR CHFgCl35 in Mc/s Rotational Centre Experimental Calculated Transition Frequency Method Method Mc/s of Bragg of Bragg# & Golden* 32,1 "*33,1 29,294.60 -84.8 * 0.4 -84.8 -84.7 32,2 "*33,0 30,405.47 -80.3 - 0.3 -80.6 -81.1 52,3"*53,3 25,629.4 -38.4 - 0.8 -37.5 mm 52,4~*53,2 32,635.20 -28.8 - 0.3 -28.3 -27.6 62,4 "* 63,4 22,550.33 -27.9 - 0.3 -27.8 -26.6 93,6 ^  9 4, 6 31,193.00 -20.9 - 0.3 -20.4 -18.1 1 03,7- > 1 04,7 26,441.94 -17.5 * 0.3 -17.2 -14.3 Lng eQVaa = -•65.0 Mc/s, eQV-j^  = +35.2 Mc/s, and A = -0.597520. # Using ^ ~ -0.6 . TABLE IV SCALE FACTORS FOR CBFgCl 3 7 "If in Mc/s Rotational Transition Centre Frequency Mc/s Experimental Calculated, by Method of Bragg & Golden0 4-2,2 +h92 28,689.4 -41.0 - 0.8 -41.8 62,4 "*63,4 23,708.00 -22.0 - 0.3 -21.9 93,6 33,169.79 -16.1 i 0.3 -16.0 1 03,7 *1°4,7 28,699.67 -13.6 * 0.4 -13.6 u3,8 * U4,8 23,729.82 -11.3 * 0.4 -11.4 eQ vaa = "51-23 Mc/s, eQVbb = +27.74 Mc/s, and /( = -0.622078 To face page 37 seven Q-branch transitions for CHFgCl 3* are tabulated i n Table III, facing this page, along with the experimental and calculated values for the hyper-fine s p l i t t i n g scale factor J / ^ I j / f ) . T n e agreement between the exper-imental values and the values calculated from equation (15) are very good, except i n the case of the 5o o **• 5o o transition for which there are only the three experimental components and near which there i s a disturbing doublet. In each of the cases for J ^ 5, the calculated value i s slig h t l y less than the experimental value. The theory of Bragg , as expressed i n equation ( 1 3 ) , has been used to calculate the scale factor *3~ for the transitions 32,1 "^^J,! * 3 2 , 2 ^ 3 3 , 0 ' 62,4^S,4 J 9 3 , 6 - * 9 4 , 6 ' « * 1 0 3 , 7 * 1 0 4 , 7 ' G r a p h i c a l interpolation has been used i n order to get the line strengths for /f\= -0.6, approximately, from the line strength tables of Cross, Hainer and King . The values calculated from equation (13) are tabulated i n Table III also. The agreement i s f a i r for the J = 3 transitions but the formula ( 1 5 ) , based on the theory of Bragg and Golden 4 4, gives better agreement with experiment. As J increases, the value of calculated from equation (13) exhibits an increase i n the % deviation from both the experimental value and from the value from equation ( 1 5 ) . Therefore, i t can be concluded that the method of Bragg and Golden i s much more valuable than the earlier approach of Bragg i n calculating the hyperfine s p l i t t i n g of Q-branch transitions. Possibly the formula (13) w i l l yield more accurate results when the line strength tables have been expanded to give values of /f" at intervals of 0.01. The formula (15) w i l l s t i l l be superior however because there are so many Q-branch transitions for high J values but only one A E ( ^ ) and one d A E ( / r ) for ax a given transition. 37 The Hyperfine Structure for Transitions i n CHFgCl-" The ratio of the nuclear electric quadrupole moments for CI3-* and C I 3 7 is given by Livingston 2 4" to be (eQq) C I 3 5 = 1.2688. Since the a- and (eQq) C I 3 7 c-axes of CHFgCl3''' d i f f e r by approximately 4' only from the a- and c-axes of CHJV^Cl3*', the component of the quadrupole coupling tensor along any axis i n on 35 CHF 2 C1 should be the component along the same axis i n CHFgCl divided by 1.2688. Therefore eQV a a = -51.23 Mc/s, eQV"bb = +27.74 Mc/s and eQV c c = +23.49 Mc/s for the' molecule containing C I 3 7 . From Table I, i t can be seen that increases numerically by approx-imately 0.029 and that A - G increases by approximately 36 Mc/s when C I 3 7 i s substituted for CI 3- 5 i n Freon 22. This gives /f = -0.627 and A - C = 3,400 Mc/s for CHF.Cl 3 7. With these values, the very weak widely-2 2 spaced quadruplet at 28,690 Mc/s can be tentatively identified as the 4 2 2 43 2 "transition. This structure has been only f u l l y detected at dry ice temperature and only i t s strongest component can be seen at room temper-ature. Also a quadruplet with close spacings at 28,700 Mc/s, which has been detected only at dry ice temperatures, can be identified as the 103^7-^10^ 7 transition. Similarly a quadruplet at 23,700 Mc/s can be identified as the 62^-* 6 3 ^ transition; a quadruplet at 33,170 Mc/s can be identified as the 9 3 ^ — » 9 ^ 6 transition; and a very closely-spaced and relatively strong quadruplet at 23,730 Mc/s can be identified as the 113,3 - 1^4,8 trans-i t i o n . The approximate calculation of the hyperfine structure for /{= -0.627 indicates that the assignments are correct. The values of A - C and J{ can now be obtained accurately from any two centre frequencies by means of equation (8) and interpolations for E(^") 37 i n the accurate tables of Turner et a l . The centre frequencies of the transitions can be obtained from the,hyperfine structure by using formula (16) with the experimental scale factor. I f the 9o t ->9, • and J,o 4,0 10 — » 1 0 . „ transition centre frequencies are used i n the calculation, the 3,7 4, I results are A* = - 0 . 6 2 2 1 0 and A - C = 3 , ^ 0 0 . 7 Mc/s for CHF,C137. These 2 * values satisfy the other assignments and so the analysis i s correct. The scale factors are now calculated accurately for the five Q-branch transitions i n CHE^Cl 3 7 by means of equation (15) and the experimental scale factors are calculated from equation (16) and the experimental splittings. The calculated and experimental values for along with the central frequen-cies for the five quadruplets are recorded i n Table IV, facing page 3 7 . The agreement i s excellent, except i n the case of the 4 2 2"* > 43 2 ' * ' r a n s i ' ' ' i o n °^ which two of the components are barely detectable. Strangely, the agreement 37 between experimental and calculated values i s better i n the case of CHF2C1 than i n the case of CHFgCl"'-'. This can hardly be the result of the slight rotation of the a- and c-axes by 4' and may be just the result of chance experimental errors. At any rate, the theory of Bragg and Golden i s verified for these Q-branch transitions to a high degree of accuracy up to J values of 11. With the accurate knowledge of A - C and /c and with an approxima-~ " R " 3 5 , tion to A • C , obtained from the A + C value of CW^Ol (determined from the 1Q ] _ - * 2 - ^ transition) by noting that A • C i n Table I decreases by approximately 36 Mc/s for C I 3 7 substitution i n CBF 2 C 1 3 5 , i t i s possible to identify the weak singlet at 2 4 , 3 8 4 . 7 Mc/s as a part of the l o , l " " * 2 l , l multiplet for CHFgCl 3 7. Since the 5 / 2 7 / 2 hyperfine transition of the multiplet i s almost twice as strong as any other, this singlet i s identified as the strong hyperfine transition. The experimental evidence on the opti-mum Stark-modulation f i e l d and on the Stark-modulation distortion verifies this assignment. Also the single line was surrounded on both sides by a disturbed line shape indicating the presence of weaker components. The central line frequency can now be obtained by subtracting the hyperfine splitting'for this component. The value of the s p l i t t i n g i s the -0.74- Mc/s for the CHFgCl3'5 spectrum divided by 1.2688 since the hyperfine s p l i t t i n g for this rotational transition i s independent o f . The result Is 37 24,385.3 Mc/s for the centre frequency of the l n , 2 , , line of CHF.C1 . From this R-branch transition frequency and any two Q-branch transition frequencies, the rotational constants A, B and C can be completely deter-mined for this molecule. Therefore the analysis of the hyperfine structure has made possible the calculation of the structure of the molecule, which i s recorded i n the next chapter. Fortunately, the R-branch transition fre-quency can be verified by a relation between the moments of in e r t i a for the 35 37 two molecules CBF2C1 and C H F g C l . And so six definite rotational trans-37 itions for the molecules containing CI as well as eight definite rotation-35 al transitions for the molecule containing CI have been identified by means of the hyperfine structure analysis. CHAPTER V THE ACCURATE STRUCTURE OF THE DIFLUOROCHLOROMETHANE MOLECULE Since the centre frequency of an R-branch transition has been found for each of the molecules CHFgCl 3^ and CBFgCl 3 7, i t i s possible to calculate the rotational constants A, B and C for each molecule by using equation (9) and the values of A - C and determined from the Q-branch transitions. 2 However, the calculation of the molecular structure depends upon the accuracy of the small differences between pairs of rotational constants, one of each pair from the CHFgCl-3** molecule and the other from the CBFgCl-57 molecule. It becomes very important to obtain accurate values for the rota-tional constants by reducing experimental errors with many determinations and by accounting for centrifugal distortion. The experimental frequency for the l g j_ "*2^ centre line of CHFgCl^S should be accurate to -0.05 Mc/s since it. has been calculated from six different components. The same line for CHFgCl 3 7 i s accurate to only -0.1 Mc/s, however, since there i s only one weak hyperfine component. The centrifugal distortion of the J = 1 and J = 2 levels should be negligble. Since E(/f) for the 1 Q ^ level i s ^  - 1 and since for the 2.^  ^  level i t i s 4/f, equation (9) becomes 24,818.15 - 0.05 Mc/s = 2(A • C) • A - C ( 3 ^ + 1) (17) 2 and 24,385.3 * 0.1 Mc/s = 2(A« • C ) • A1 - C* (3/-« v 1) (18) 2 where the A, B, C and yf belong to the CHE^cr3*5 molecule and the A1, B», C andX 1 belong to the CHF 2 C1 3 7 molecule. Accurate values of A - C (3^- + 1) and A' - C1 ( 3 ^ ' +1) are therefore essential. 41 ROTATIONAL CONSTANTS FROM PAIRS OF Q-BRANCH TRANSITIONS TABLE V CONSTANTS FROM Q-BRANCH TRANSITIONS OF CHF-Cl' Q-Branch Transition Pairs * A - C 2 i n Mc/s (3/T+ 1) A - C 2 i n Mc/s 4 H * i n Mc/s 103,7-IO4,7 -0.597536 * '000004 3,363.26 * 0.03 -2,665.747 * 0.022 -2,009.669 * 0.007 52,4^ 53,2 -0.597520 * .000002 3,363.48 * 0.01 -2,665.760 * 0.024 -2,009.747 * 0.009 52,3 "* 53,3 52,4~* 5 3, 2 -0.597524 * .000007 3,363.48 * 0.04 -2,665.800 * 0.068 -2,009.760 * 0.022 3 2 , l - 3 3 , i 32,2",'33,o -0.597519 - .000015 3,363.540 * 0.006 -2,665.80 * 0.15 -2,009.779 ± 0.055 Extrapolated Values -0.597520 * .000002 3,363.54 * 0.01 TABLE VI -2,665.78 * 0.02 -2,009.77 * 0.02 CONSTANTS FROM Q-BRANCH TRANSITIONS OF CHFgCl 3 7 Q-Branch Transition Pairs A»-C« 2 i n Mc/s (3 / f- '+ 1) A»* C i n Mc/s i n Mc/s 1:L3,8"*i:LA,8 i o 3 ; 7 - < 7 -0.622105 - .000004 3,400.631 * 0.040 -2,946.018 * 0.018 -2,115.550 - 0.011 93,6-* 94,6 -0.622097 * .000003 3,400.704 * 0.030 -2,945.999 ± 0.011 -2,115.568 * 0.011 Best Values -0.622078 * .000010 3,400.98 * 0.04 -2,946.03 - 0.02 -2,115.67 i 0.02 To face page 42 Since L A - C = B - A • C (19) A 2 2 and X ' AJ_z_Cl = B' - A' • C (20) 2 2 the accurate values of A - C A and A' - C1 ' are also essential. 2 2 ^ Accurate Rotational Constants Values of A - C and can be obtained from any pair of Q-branch 2 37 transitions from interpolation i n the accurate tables for E ( ^ ) . However, both of these parameters vary because of centrifugal distortion as J i n -creases. Therefore the best method of calculating the parameters i s to select a pair of Q-branch transitions with equal or nearly equal J values. 2 c i 35 For this reason, the values yf* and A - C have been calculated for CBF, 1 2 from the pairs 3 2 > 1 - 3 3 > 1 and 32j2-* 3^Q J 5 2 > 4 - 5 3 f 2 and 52,3-* 53,3 J 52,4"* 53,2. 62,4~*63,4 5 L A S T L Y ' 9 3 , 6 — 9 4 , 6 and IO- 10, n . In each case the interpolation has been done by f i n i t e differences so that the experimental errors i n the central lines of the rotational transitions are the only errors. The values of ^ , A - C , (3^ + 1) A - C and A - C are tabula-ted i n Table V, facing this page, for the various pairs of Q-branch trans-itions. In each case, the experimental errors have been calculated and inserted. It can be seen that the numerical value of /f" increases monoton-i c a l l y and that the value of A - C decreases monotonically as J increases. Therefore the numerical values of (3 A; • 1) A - C and > A - C show a 1 2 ' 2 much smaller relative variation since part of the increase i n the numerical value of ^ i s caused, by the decrease i n the value of A - C . Also part of the error i n A - C i s the result of the error i n the determination of /(" 2 and this part cancels the error i n n for the product /r A - C since an i n -x 2 crease i n the numerical value of causes a decrease i n the value for A ? C and vice versa. The best values, extrapolated to low J, are 2 A = -0.597520 - .000002 •A - C = 3,363.54 * 0.01 Mc/s 2 (3>f • 1) A - C = 2,665.78 * 0.02 Mc/s ' 2 ^ A - C = 2,009.77 - 0.02 Mc/s. When these values are substituted i n equations (17) and (19), the rotational constants can be determined to be A = 10,234.52 - .03 Mc/s B = 4,861.21 * .04 Mc/s . C = 3,507.44 - .03 Mc/s for CHF^Cl3*. The moments of inertia can be obtained from these constants, 38 • the physical constants of Cohen, Dumond, Layton and Rollett and the atomic masses l i s t e d by Townes and Schawlow39 which are recorded on page 20 of this thesis. The resulting moments of inertia are I a = 49.39557 - .00013 a.m.u.(A) I b = 103.99468 ± .00086 a.m.u.(A)2 I c = 144.13361 ± .000125 a.m.u.(I)2. In each case the errors have been analysed thoroughly at every step. However the possible errors of the physical constants of Cohen et a l . have not been included because they contribute exactly the same error, between the limits of -0.0063 %, to each rotational constant of either the CHF2C13* or the CHF 2C1 3 7 molecule. The values ^  ', A1 - C , (3/f * • 1) A' - C and /r • A* - C along ~2 2 » 2 . with the possible experimental errors are tabulated i n Table VI, facing 37 page 42, for the pairs of rotational transitions for CHFgCl , 9 3 ^ •» 9^  £ and 1 0 3 > 7 * 1 0 4 > 7 J 1 0 3 > 7 - > 1 0 4 j 7 and l L ^ g - l l ^ g . The U2f2 * A3f2 line i s not used because of the larger experimental error i n i t s hyperfine structure and the 62,4"* ^ 3,4 ^ n e * s n o ^ u s e ( * because there Is no other accurate Q-branch transition with a J value of 4, 5 or 6. The values of (3/^' +1) A* - C and ' A' - C show a smaller % deviation than either or A1 - Cf because an increase in i s p a r t i a l l y cancelled by a decrease in A1 - C . The same sort of trend that appears i n Table V i s 2 apparent i n Table VI. As J increases, /{ and >f ' increase numerically while A - C and A' - C1 decrease. Since there are no accurate Q-branch trans-2 2 f i t ions with low J i n CBF0C1 , the accurate values for A' - C , /( ', * 2 (3/f' * 1) A' - C and > 1 A1 - C must be obtained by extrapolation with 2 N 2 the results of Table V as a guide. The values obtained by careful extra-37 polation for Freon 22 containing Cl~^ are /f- ' = -0.622078 - .000010 A' - C = 3,400.98 - .04 Mc/s 2 (3/f ' • 1) A' - C = 2,946.03 - .02 Mc/s 2 A' - C - 2,115.67 - .02 Mc/s . " 2 These values give good agreement with the 4 0 o ~+ 4o o and 6 0 , -* 6, . «c,.c ^ , 4 .2,4 centre frequencies. When these accurate values are substituted i n equations (18) and (20), the rotational constants for CBFgCl can be obtained. These are A' = 10,233.82 * .07 Mc/s B' = 4,717.17 - .05 Mc/s C = 3,431.86 - .07 Mc/s . From these rotational constants, the moments of in e r t i a for the CHF^Cl 3 7 molecule along i t s own principal axes, the a'-, b'- and c'-axes, have been 38 calculated with the use of the physical constants of Cohen et a l . and the 39 atomic masses l i s t e d by Townes and Schawlow . These moments of inertia are labelled and calculated to be ( I ' ) a ' = 49.39895 - .00034 a.m.u.(A)2 ( I , ) b * = 107.17019 - .00115 a.m.u.(A)2 TABLE VII ROTATIONAL CONSTANTS AND MOMENTS OF INERTIA OF CRFgCl 35,37 CBF2C1 Rotational Constants in Mc/s A = 10,234.52 ± 0.03 B = 4,861.21 * 0.04 C = 3,507.44 * 0.03 35 Moments* of Inertia in a.m.u. (A) 2 along a-, b- and c-axes I a = 49.39557 * .00013 I b =103.99468 ± .00086 I c =144.13361 - .00125 Rotational Constants in Mc/s A' = 10,233.82 * 0.07 B» = 4,717.17 * 0.05 C» = 3,431.86 - 0.07 CBF2C1 37 Moments*of Inertia in a.m.u. (a) 2 Along a A, b-, c-axes Along a-, b-, c-axes I , a ' = 49.39895 ± .00034 .b' I 1 = 107.17019 * .00115 I , c ' = 147.30787 * .00300 I' a = 49.39897 - .00034 I' D = 107.17019 * .00115 I»c = 147.3072 ± .0030 38 * Using the physical constants of Cohen et al. : a = 6.62517 - 0.00023 x I O - 2 7 erg sec. .-24 nip = 1.67239 - 0.00004 x 10 gms. mH/mp = 1.0005446 To face page 45. ( l ' ) c ' = 147.30787 * .00300 a.m.u.(i)2 . Since the b-axis and the b'-axis are identical and since the a 1- and c'-axes are rotated by only 4' with respect to the a- and c-axes, the moments of inertia for CHF^Cl 3 7 along the a-, b- and c-axes can be determined by a rotation of the moments of inertia ellipsoid by 4', and these are I ' a = 49.39897 * .00034 a.m.u.(A)2 I ' b = 107.17019 * .00115 a.m.u.(A)2 o 2 I ' c = 147.3072 * .0030 a.m.u. (A) . The small change because of the rotation of the axes i s considerably less than the experimental error i n each case so that a small error i n the angle of rotation i s insignificant. A l l the experimental rotational constants for the Freon 22 molecules containing both 01^5 and C I 3 7 are tabulated i n Table VII, facing this page. The experimental accuracies of the constants i n most cases are better than the experimental accuracies l i s t e d for the determinations of the same 14 17 constants l i s t e d for the sli g h t l y asymmetric rotors CHjFg , CB^FCl , and 46 CHgCLj • The good degree of accuracy has been obtained through the use of many experimental lines, the accurate analyses of the hyperfine structures, 37 the accuracy of the tables of Turner et a l . , the careful extrapolation to low J values and the calculation of the experimental errors of each step i n the analysis. Very few writers l i s t their experimental errors i n either the rotational constants or i n the.resulting structural parameters. Calculation of the Bond Lengths and Angles The molecule CBFgCl involves six independent structural parameters, which are the C-H, C-F, C-Cl bond lengths and the F-C-F, F-C-Cl and H-C-Cl bond angles. In principle, these can be calculated i f there are six inde-pendent rotational constants. Unfortunately i n this analysis, only five independent rotational constants can be obtained and one of the parameters must be assumed. Since the C-H bond length has been calculated to be 1.098 A i n CHF 3 1 3, 1.092 % i n CH^ 1^, 1.073 - 0.005 A i n CHjFCl 1?', and 1.068 - 0.005 A i n CHgCLg*6, an approximation of 1.08 - .02 A should be justi f i e d for CHFgCl. The atomic masses of CI 3*, C 1 2, H*- and F 1 9 can be represented by m^ , n^, nig and m^  respectively and their coordinates along the a-, b- and c-axes i n the centre of mass system for CBF^Cl 3* can be represented by (a^,0,c^), (a2,0,c 2), (a 3,0,c 3) and (a^,*b^,c^) respectively. The conditions that the centre of mass be at the origin i s given by m l a l * ^2*2 * m3 a3 * 2 m 4 a 4 = 0 (21) and m l c l * ^2^2 * m3 c3 * 2m^c^ = 0 (22) The equations for the moments of inertia along the a-, b- and c-axes are, respectively, * ^z8^ * m 3 a 3 2 * 2m^(a^2 • b^ 2) • = I c (23) m l c l 2 * ^2* 4 * 2m^(c^2 + b^ 2) = I a (24) and * c l 2 ) * m 2 v a 2 2 * °2^ * • c3 2) * 2m^(a^2 • c^ 2) = I b(25) 2 a c b Immediately i t can be seen that 4ni^b^ = 1 + 1 - 1 where 2b^ i s the separation between the fluorine atoms at (a^,^b^,c^). Accordingly the fluorine-fluorine distance can be obtained without any approximations to the C-H bond length. The condition that the a-axis is the principal axis for the least moment of inertia (and that the c-axis i s the principal axis for the greatest moment of inertia) i s given by m l a l c l * m2 a2 c2 * n^a^c^ * 2m^a^ci^  = 0 (26) It i s assumed that the substitution of the C I 3 7 isotope for the Cl35 isotope does not appreciably affect the bond distances or angles. It w i l l , however, cause a shift of the centre of mass i n the plane of symmetry toward 37 A y v the CI by an amount A a along the a-axis and an amount A c along the c-axis. The mass of the C I 3 7 isotope can be represented by (m^ + A m) and i t s coord-inates i n the centre of mass system for CHF0 are (a^ - A a , 0 , c x - ^ c ) . Similarly the coordinates for mg, m^ , and m^  are (ag - A a,0,c 2 - Ac), (a^ - Aa,0 , 0 3 -Zlc) and (a^ - A a,*b^, c^ - Ac) respectively. The conditions that the centre of mass be at (Aa,0, Ac) are (n^ *Am)(ai -Aa) • ^2^&Z - Aa) + 1113(33 -Aa) • 2m^(a^ -Aa) = 0 (27) (mx +Am)(cj_ -Ac) + mgfcg -Ac) + 113(03 -Ac) + 2m^(c^ -Ac) = 0 (28) Now from (27) and (21) Aa - f^m a-i mj_ +Z\m • 1112 + 103 + 2m^  and from (28) and (22) Ac = Am cj_ m-^  +^ \m + mg * 103 + 2m^  Therefore Aa. = ka^ and Ac - kc 1 where k = 0.0227005 can be determined from the isotopic masses li s t e d on page 20. 37 The equations for the moments of inertia of CHFgCl^ along the a-, b- and c-axes are, respectively, (m 1+«m)(a 1-ka 1) 2*m2(a 2-ka 1) 2*m3(a3-ka 1) 2+2m^(a^-ka 1) 2+2m^b^ 2 = I ' c (29) 2 2 2 2 2 (m1+flm)(c]_-kc]_) +1112(02-kcx) +1113(03-kcj_) •2m^(cijk-kcT_) +2m^ b^  = I* (30) (mj+dm) j(a 1-ka 1) 2+(c 1-kc 1 ) 2 j+m2|(a 2-ka 1) 2+(c 2-kc 1 ) 2 j -+m 3|(a 3-ka 1) 2+(c3-kc 1) 2|+2m^(a 4-ka 1) 2+(c 4-kc 1) 2^ = I» b (31) When equation (31) i s subtracted from the sum of equation (29) and equation (30), the result i s 4 m ^ 2 = l ' a + i « c - l « b . But ^ b ^ 2 is also equal to l a + 1° - I b and so only five of the six values l a , I*3, 1°, a b c I 1 , I* , and I 1 are independent. However the equality offers an excel-lent check upon the assignments, particularly of the ^/Z -*7/2 hyperfine component of the 1Q ±^ -*2J_ 1 transition i n CHFgCl 3 7, and also a check of the experimental accuracy. Since I a + I c - I b = 89.53450 - .00224 a.m.u.(A)2 and I , a + I ' C - I» b = 89.5360 - .0045 a.m.u.(A)2, the agreement i s well within the limits of the experimental error. The distance between the fluorine atoms i s therefore 2b^ where 2b 4 = 2.170538 - .000028 1 i n CBF 2C1 3 5 and " 2b^ = 2.170566 ± .000056 A i n CBFgCl 3 7 . The agreement i s extraordinarily good and the measured value of the fluorine-fluorine distance may be taken as the intermediate value 2.17054-6 - .000030 A. From equations (23) and (29), a solution for a-^  can be obtained for the chlorine atom i n a, 2 (1 - k) = I ' c - I c . The result i s a. = 1.27499 o A m ' * 0.00086 A and this value is independent of the assumption for the C-H bond length. The possible error i s the result of the possible experimental error i n I ' 0 - I c . Similarly from equations (24) and (30), c, 2 (1 - k) = I , a - I a . This gives c. = -0.04174 - .0029 A for the 1 Am 1 chlorine atom. The possible error is entirely the result of experimental error and i s independent of the possible error i n a^ or i n the C-H bond length. With the calculated values of a^, c^ and b^ the equations (21), (22), (23), (24) and (25) can be reduced to fiv e equations i n the six un-knowns a 2, &y a^, c 2, C 3 , and c^. If a value i s assumed for a^ (the co-ordinate of hydrogen along the a-axis), then the corresponding values of ag and a can be calculated from equations (21) and (23). If a value i s 4 assumed for c 3 (the coordinate of hydrogen along the c-axis), then the corresponding values of c 2 and c^ can be calculated from equations (22) and (24). Since the C-H bond length i s assumed to be 1.080 * .020 A , the only acceptable solutions are those for which equation (26) i s satisfied and for 2 2 ® 2 which ( a 3 - ag) • ( c 3 - c 2) = (1.080 * .020 A) . A whole series of values for a^ and c^ have been assumed so that the two conditions above are satisfied. The possible range for the assumed values contributes to the to t a l possible error i n the coordinates ag, a^, c 2 and c^. The calculated values for the coordinates of CI 3*, C 1 2, H 1 and F 1 9 along the a-, b- and c-axes of CHF2C13* with the centre of mass at the TABLE VIII NUCLEAR COORDINATES OF CBFgCl ALONG PRINCIPAL AXES AND IN CENTRE OF MASS SYSTEM FOR CHFgCl 35 Nucleus CI 35 CI ,12 37 CJ H1 F 1 9 J.9 Atomic Mass* in a.m.u. 34.97993 36.97754 12.003804 1.008142 19.004456 Calculated Coordinates i n A along a-axis b-axis c-axis 1.27570 *.00040 -0.4274 £ .0081 -0.500 * .020 -1.02578 ± .00167 +1.085273 - .000015 -1.085273 - .000015 -0.04446 * .00174 •0.3896 ± .0028 •1.470 * .010 -0.12118 - .00080 Reference 39. TABLE IX BOND LENGTHS AND ANGLES OF CBF^Cl Bond Length Microwave Electron i n A Spectroscopy Diffraction^ C-H 1.083 - 0.015 (Assumed) C-Cl 1.7576 * 0.0093 1.73 * 0.03 C-F 1.3405 - 0.0058 1.36 * 0.03 Cl-F 2.5456 * 0.0020 2.56 * 0.03 F-F 2.170546 * .000030 2.24 * 0.04 Bond Angle H-C-Cl 108.2° * 1.8° Cl-C-F 109.8° ± 0.5° 110.5° * 1° F-C-F 108.1° * 0.6° 110.5° - 1° # reference 2. To face page 49. origin are l i s t e d i n Table VIII, facing this page. The carbon-hydrogen distance has been assumed to 1.080 - .020 A and the possible error result-ing from this assumption has been incorporated along with the experimental error i n the total possible error for each coordinate. In some cases, notably the C-coordinate of CI3'', the satisfaction of the condition posed by equation (26) eliminates some of the possible error. About half the possible error i n each of the coordinates a^, a^, C g , and c^ is due to the uncertain-ty i n the carbon-hydrogen bond length. Therefore a determination of the 35 rotational constants and moments of inertia for CDFgCl-"' would probably allow more accurate estimates for a^ and c^ from which in turn more accurate values of the other coordinates could be obtained. The bond lengths and angles can easily be obtained from the coordin-ates of the atoms with respect to the centre of mass. The fluorine-fluorine separation, r ^ j , , has already been calculated as 2.170546 - .000030 A . This value is significantly less than the distance 2.24 - .04 A obtained 2 by Brockway from electron diffraction. The carbon-fluorine bond length, r c _ F , i s 1.3405 - .0058 A which i s lower than Brockway's 1.36 - .03 A . The resulting angle F-C-F is 108.1? - 0.6°, a value definitely less than the tetrahedral angle of 109° 28'. The large angular error of -0.6° i s largely the result of the uncertainty in the hydrogen bond length so that a more accurate estimate of would lead to a more precise value of angle F-C-F, which i s important for bond theory. The fluorine-chlorine distance, r F - C l ' 3 1 1 ( 1 t h e c a r 1 aon-chlorine bond length are calculated to be 2.5456 ± .0020 A and 1.7576 * .0093 A . The former value agrees with the 2.56 - .03 A of Brockway but the value for r„ „ corrects the low value o-ci 1.73 s 0.03 A calculated from electron diffraction data. .The angle F-C-Cl i s calculated to be 109.8° - 0.5° so that the angle is slightly but not significantly larger than the tetrahedral angle. The angle H-C-Cl which is consistent with the values for the coordinates i s 108.2° * 1.8° of which the error largely depends upon the range for r c _ H . The bond lengths and angles which have been determined i n this present investigation have been tabulated i n Table IX, facing page 49, along with the values determined from electron diffraction by Brockway. Quadrupole Coupling Constant for C l 3 ^ i n Freon 22 The components of the nuclear electric quadrupole coupling tensor 35 for CI i n Freon 22 along the a- and b-axes have been determined to be eQV a a = -65.0 - 0.2 Mc/s and eQVbl) = +35.2 * 0.3 Mc/s, respectively. Since the errors i n two components are almost independent, the component along the c-axis w i l l be +29.8 * 0.5 Mc/s. 3 5 In order to obtain the quadrupole coupling constant eQq for C l ^ i n the molecule, i t i s assumed that the C-Cl bond i s a principal axis, the z-axis, of the quadrupole coupling dyadic. Another principal axis, the x-axis, w i l l be perpendicular to the z-axis but also i n the plane of symmetry. The third principal axis, the y-axis, w i l l be perpendicular to the plane of symmetry and w i l l be equivalent to the b-axis. Therefore eQV = +35.2 Mc/s. yy The components eQv" and eQV" can be obtained from a rotation about XX zz the b-axis through an angle «< equal to the angle between the C-Cl bond (the z-axis) and the a-axis, by the method described on page 18 of this thesis. eQV a a = eQV z z cos2«< + eQV.^ sin2<=< eQV c c = eQV z z sin2<< • eQV^ cos 2-* The value calculated from the experimentally determined coordin-ates of C I 3 5 and C 1 2 along the principal axes i s 14.3°- 0.2°. This and the experimental values for eQv^ and eQV c c y i e l d the values ©QV^ = +36.4 -0.8 Mc/s and eQV z z = -71.6 - 0.5 Mc/s which i s equivalent to eQq for CI 35 i n gaseous Freon 22. This value agrees very well with the value -70.50 Mc/s 33 determined for solid Freon 22 at 20° K by Livingston • CHAPTER VI CONCLUSIONS REGARDING THE CHEMICAL BONDS The nature of the carbon-chlorine and carbon-fluorine bond lengths i n the halomethanes is a subject of considerable interest since the bonding mechanisms used i n these compounds probably contribute to the bond character 2 in a l l halogenated organic substances. Brockway has attempted to explain the changes i n the carbon-fluorine bond by a varying amount of double bond in character. Pauling has also commented on the decreases i n the carbon-chlorine and carbon-fluorine bond lengths i n the fluorochloromethanes. He has suggested that chlorine has only half the a b i l i t y of fluorine to form double bonds. Neither Brockway nor Pauling has been able to make quantita-tive conclusions of any r e l i a b i l i t y because of the relatively large exper-• o imental errors, of -0.02 A at least, i n the bond lengths obtained from measurements of electron diffraction. Pauling has estimated that a carbon-fluorine bond achieves about 10 % double bond character i f at least one other fluorine atom is attached to the same carbon atom and that a carbon-chlorine bond aquires about 5% double bond character i f at least one fluorine atom i s attached to the same carbon atom. Experimental results on the "chemical s h i f t " of the nuclear magnetic resonances of protons and fluorine nuclei have been correlated with the changes i n the carbon-hydrogen, carbon-fluorine and carbon-chlorine bonds by 23 Meyer and Gutowsky . They have deduced that an increasing "chemical s h i f t " tig for hydrogen reflects an increase i n the ionic character of the C-H bond but that an increasing "chemical s h i f t " 6™ for fluorine i s related to an 51 increase i n the covalent character and a decrease i n the ionic nature of the C-F bond. Therefore the increases i n $ H from CH^ X to CBgXg and from CHgXg to CHX^  have been explained by the increasing ionic character of the C-H bond produced by the inductive mechanism H - C - X . Similarly the sig-nificant increases i n i g from CEL^ F,, to CHgClg, from CHgClg to CHgBrg, from CHF0 to CHC1_, and from CHC1- to CHBr^ have been interpreted as increases i n 3 3 3 3 the ionic character of the C-H bond resulting from competition from two X" X* • " •» resonating double bond structures of the form H - C = X and H - C X , H E for which the order of importance is F >Cl>Br. These explanations are con-sistent with the experimentally-measured increases i n from CH^F to CHgFg, from CHgFg to CBF^ and from CHF^ to CF^ since an increasing number of fluorine atoms and a decreasing number of hydrogen atoms results i n a competition among the fluorine atoms for the electrons of the remaining hyd-rogen atoms. However the increase i n from CF^Cl to CFgClg and from CF^Cl^ to CFCl^ seems to be inconsistent with the previous interpretation since a carbon-fluorine bond should exhibit an increasing ionic nature as the number of chlorine atoms increases by virtue of the double bonding of the chlorine through structures of the form F~ C = CI* . Additional information on the nature of the carbon-chlorine and possibly of the carbon-fluorine bonds i s given by the magnitude of the nuclear electric quadrupole coupling constant for chlorine i n the chloromethanes. The interpretation of the coupling constant i s complicated by the fact that i t depends upon the Ionic character of the bond involving chlorine, upon the amount of double bonding, and upon the amount of 3s hybridization with the dominating 3p bond-forming electron of chlorine. The quadrupole coupling constant depends primarily upon the number of unpaired 3p electrons i n chlor-ine so that ionization of the form I Cl~ should reduce the coupling constant - * 21 and ionization of the form F CI should increase the coupling constant , TABLE X Molecule STRUCTURES AND NUCLEAR ELECTRIC QUADRUPOLE RESONANCES OF FLUORO- AND CHLORO- METHANES C-Cl i n i Angle F-C-F Angle F-C-Cl Angle Cl-C-Cl CH3F c d CHF--CF 4 CF 3C1 9 CHF2C1 CHgFCl1 CHjC^ CHgClg1 c "•3 i CHGL C-F i n A 1.385 1.358 * .001 1.332 1.322 1.328 - .002 eQq for CI -Gas 108°14' ± 6' 108°48« 109°28« 1.751 - .004. 108.6° i 0.4° 110.3° - 0.5° 1.3405 -.0058 1.7576 ±.0093 108.1° ± 0.6° 109.8° * 0.5° CC1, 1.378 - .006 1.759 - .003 1.781 1.7724 -.0005 1.767 (1.783-.003)* 1.755 - .005 110°1» - 2» 111°47» - 1' 110°24' 109°28» i n Mc/s Solid at 20°K -78.05"1 -71.6 - 0.5 -77.58 .m -70.50 m n -70.46 - 1.0 -67.60 k m -74.740 - -68.40 h m -78.4 - 2.0 -72.47 -76.98 -81.851 m m a. Reference 12. b. Reference 14• c. Reference 13. d. Reference 5. e. Reference 4. f. Reference 17. g. Reference 16. h. Reference 46. i . Reference 2. j . Reference 18. k. Reference 49. m. Reference 33. n. Reference 50. since CI has a reduced deficiency and CI has an increased deficiency of 3p electrons. 22 Townes and Schawlow have calculated that the contribution to the quadrupole coupling constant of the form CI* i s given by - 2 i ^ ( l •t ) eQHj^Q where eQo^Q * s the quadrupole coupling constant for a single 3p^- orbital electronj i + is the fractional importance of the ionic form Cl*jand £. , equal to 0.1$ for chlorine, i s an ionization term. If the fractional import-ance of the ionic form C l " i s i _ , then the contribution of i t to the coupling constant i s i _ x 0 x ©Oo^^g since the ion has no unbalanced 3p electrons. Townes and Dailey have calculated that 3s3p hybridization i n the chlorine bonding orbital of the covalent bond in IC1 reduces the number of 22 unbalanced 3p v electrons by 18% while Townes and Schawlow estimate that 15% 3s3p hybridization i s a reasonable assumption for the chlorine bonding orbital in a covalent bond to an atom, such as carbon, which is electro-positive with respect to chlorine by more than 0.25 units. The contribution of a covalent bond with 15% 3s3p hybridization to the quadrupole coupling constant i s therefore -0.85eQq^Q • If the fractional importance of the single covalent bond is (1 - i - i _ - f) where f is the fractional import-ance of a double bond involving a 3p<rr unbalanced electron for chlorine, then the contribution of the covalent part of the bond to the coupling constant is ( e C & ) c o v a i e n t = ~ H " " f ) x 0.85eQq 3 1 0 (32) The ionic form C~C1* i s not l i k e l y to occur i n the chloromethanes since Cl i s more elctronegative than 0. and so equation (32) becomes ^ c o v a l e n t = "U " i . " *> * O.SSeQq^ . For chlorine i n chloromethanes, double bonding involves a 3Pip orbital. Such an orbital, which is perpendicular to the bond axis, does not contribute as much to the quadrupole coupling constant as a 3 p 7 orbital, which i s parallel to the bond axis. It does contribute something, however, 22 and Townes and Schawlow have deduced the contributions to eQVzz, ©QV^ and eQVyy of a 3Py orbital where the y-axis is perpendicular to the plane of symmetry and the z-axis is parallel to the bond. If there is a 3pv bond, there will be an excess of one 3p x electron in a 3pw orbit in the x direct-ion. Therefore the contribution to eQV^ is + f y ( l * OeQo^io ax& t n e c o n'" tributions to eQVzz and eQVyy are both ~ 2 * y ( l * ^ ^ Q ^ i o w h e r e f y i s t n e fractional importance of the 3Py bonding orbital. 1 • £ is equal to 1.15 for an extra 3p electron in chlorine. Similarly i f a 3p x bonding orbital occurs, the contribution to eQVyy will be * f x ( l * t) eQ (l3io a n d *° both eQVzz and to eQV^ will be -£*x(l * OeQq 3 1 0 where f = f y • f x . Since the single covalent bond is almost symmetrical about the bond axis, the contributions to the coupling dyadic along the x- and y-axes are each equal to H K e Q 0 c o v a i e n 4 j • ^be contributions to the components of the quadrupole coupling dyadic may be summed as eQq = eQVzz = - ( i f x 1.15 • (1 - i _ - f) x O.85} eQq 3 1 0 = -(0.85 - 0.85 i . - 0.28 f) eQq 3 1 Q (33) eQV^ = ( f y - £f x) x 1.15eQq310 + £(l - i _ - f) x 0.85eQq31Q (34) eQV^ = ( f x - £fy) x 1.15eQq310 • £(1 - i . - f) x 0.85eQq310 (35) Equation (33) shows that i f the fractional importance of the double bonding increases at the expense of the ionic bond then the quadrupole coupling constant will show a small increase. If the fractional importance of the double bond increases at the expense of the single covalent bond, however, the quadrupole coupling will show a substantial decrease. Moreover eQvxx " eQ vyy = ( fy " fx) x ©Qq3io ^ ^be measure of the p y electron deficiency is given by f - f x = 2 eQvxx " eQ vyv . (36) 3.45 eQci 3io 25 Goldstein's criterion for the Py electron deficiency in vinyl chloride is a considerably larger value, in fact 3.45 x ( f y - f x ) . Goldstein's 2 criterion i s very close numerically to the value f obtained from Dean's I V relation 3f = eQ vxx ~ eQ vyy , cited by Muller and used by him to 2 - f eQY z z estimate the double bond character i n the carbon-chlorine bond of CHgFCl, for which the 3p v orbital i s presumably dominant. Muller 1s value for the fractional importance of the double bond in CH^FCl i s 6.6 * 2 %, i n agree-ment with the estimate of 5% by Pauling. If double bonding Is the result of the resonant form F C = Cl*, then CHF2CI and CF3CI should involve a greater fractional importance for the double bond. For CF^Cl, ©QV^ = e ^ y y ^ r o m rotational symmetry and Dean's method of finding f becomes meaningless. Either the relation (36) or Gold-stein's criterion have meaning, however, because they involve the d i f f e r -ences between the contribution of the 3Py and 3p x bonding orbitals. In the case of rotational symmetry C 3 there i s no difference and f = f_ . It i s X jr possible that the fractional importance of the double bonding, f = f x +• fy , is of the order of 10$. If the criterion of equation (36) i s applied to the experimental values for CHFgCl as calculated i n the previous chapter, the value of f y - i x l i e s between 0.1% and 1.2% where eQq^Q = -109.6 Mc/s for chlorine . If Goldstein's criterion i s applied, the 3p v electron deficiency l i e s between the limits of 0.1% and 2.1% . It i s possible then that fractional importance of the 3p x bond i s about 4% i f the fractional importance of the 3py bond i s 5%. This gives a value for f of 9%. This estimate may now be used i n explaining some bond lengths and quadrupole coupling constants i n fluoro-chloromethanes. The carbon-fluorine and carbon-chlorine bond lengths are tabulated along with the angles F-C-F, F-C-Cl and Cl-C-Cl i n Table X, facing page 53 for the fluoromethanes, the monochlorofluoromethanes and the chloromethanes. In addition the nuclear electric quadrupole resonance for Cl i s tabulated for the chloromethanes both i n the gas state ( i f known) and i n the solid state at 20° K. It can be seen from the tables that the substitution of a fluorine atom for a hydrogen atom i n either a fluoromethane or a fluoro-chloromethane produces a decrease of the order of 0.02 A i n the carbon-fluorine bond. The explanation for this i s the double bonding resonance form F~ C = F* . Such a resonant form should decrease the mutual repulsion between the fluorine atoms and so i t i s not surprising to see the F-C-F angle less than the tetrahedral angle. The substitution of chlorine for hydrogen i n the chloromethanes produces a small decrease of the order of 0.01 A i n the carbon-chlorine bond. This can be explained by the double bonding resonance form C l " C = C l * with the power of chlorine to form double bonds only half that of fluorine. The fact that the Cl-C-Cl angle decreases to the tetrahedral angle for CC1, as chlorine i s substituted for hydrogen suggests that the mutual repulsion between the chlorine ions i s stronger than any attraction resulting from double bonding. The substitution of a chlorine atom for a hydrogen atom i n the fluoromethanes produces an average shortening i n the carbon-fluorine bond of o approximately 0.01 A . This shortening i s similar to that produced i n the • carbon-chlorine bond by a chlorine for a hydrogen substitution and i t suggests that the F" C = C l * mechanism i s responsible. The substitution of a fluorine atom for a hydrogen atom in methyl chloride produces a de-o crease of 0.022 A i n the carbon-chlorine distance and this also suggests the double bonding mechanism F" C = C l * with a strength about twice that of the C l " C = C l * mechanism. The substitution of a fluorine atom for a hyd-rogen atom i n the resulting monofluoromonochloromethane changes the carbon-chlorine bond by a negligible amount but produces the very large decrease of o _ + .037 A i n the carbon-fluorine bond length. This suggests that the F C = F resonance form i s of more importance than the F~ C = C l * form. The substitution of another fluorine atom for the hydrogen atom in the difluoro-chloromethane produces a significant shortening in the carbon-fluorine distance of .013 A and a possible shortening of .007 A in the carbon-chlorine distance. The conclusion from these facts is that the fractional importance of the chlorine double bond in CF^Cl is not twice that of the double bond in CHgFCl because of the competing fluorine double bond. The values for the nuclear electric quadrupole coupling constant of chlorine in the fluorochloromethanes, both in the gaseous and in the solid state at 20° K, confirm the previous analysis. If the double bonding is increased at the expense of the ionic bonding, then eQq should show a small increase numerically. The numerical value increases fromj-70.5 Mc/s|in gaseous CRgFCl to|-71.6 Mc/s|in gaseous CBF2C1 and fromJ-71.6 Mc/s|to j-78.05 Mc/s|in gaseous CF^Cl. The corresponding changes in the solids are from j-67.60 Mc/sjto J-70.50 Mc/sjto J-77.58 Mc/sj. Livingston 2 4 has noted that the % deviation of the solid state value from the gas value increases as the number of hydrogen atoms in the molecule increases. The deviation is -0.6% for CF3CI, -1.5% for CHFgCl, -4.1% for GHgFGl, -7.6% for CHgCL, and -8.5% for Cfi^Cl. Since the importance of the ionic C* Cl" bond should 21 increase in the same order from CF^Cl to CH^Cl, i t may be postulated that the lower values for the solid state are the result of crystal structures involving stronger ionic bonds. The explanations offered in this chapter account qualitatively for most of the changes in the bond lengths and angles and in the values of eQq 35 for chlorine from molecule to molecule in the series of fluoro- and chloro-methanes. Some of the measured changes seem to be rather erratic so that more precise measurements are required. Accurate solutions for the struc-tures of CHFC12, CF2C12 and CFCI3 should aid in the interpretation of chem-ical bonding in the fluoro- and chloro-methanes. As yet there is no simple explanation for the relatively large values of eQq for C l - ^ i n gaseous CHjCl and gaseous CHgCLj, since i _ i n equation (36) for the C CI" ionic form should' be relatively large i n these two molecules. Nor i s there any simple explanation for the measurements of Meyer and Gutowsky23 on Op for the series CF^Cl, CFgClgand CFCl^. Evidently, the theories for the carbon-chlorine and carbon-fluorine bonds are not yet adequate. It should be noted that one disadvantage to the method of microwave g spectroscopy i n determining the structure i s that the effective moments of inertia involve the averages of the squares of the bond lengths rather than the squares of the average bond lengths. The average of the square of the bond length differs slightly from the square of the average bond length. Moreover, the average bond length i s generally not equal to the equilibrium bond length for the zero-point vibration and the latter depends to some extent upon the isotopic constitution. However, Myers and Gwinn4^ have calculated the r.m. s. separations of the two chlorine atoms in methylene chloride for the various isotopic forms involving CI3-', C I 3 7 , H^  and D 2 and o 37 have shown that the separation changes by only O.OOO4 A at most i f CI is substituted for CI3''. Such a difference between the root mean square values of the C-Cl3'' and the C - C l 3 7 bond lengths should not contribute appreciably to the rather large experimental error i n the C-Cl and C-F bond lengths determined for difluorochloromethane i n this thesis. The difference w i l l , however, contribute appreciably to the error i n the r.m.s. separation of the fluorine atoms so that the error of 0.00003 A calculated i n this thesis for the separation in difluorochloromethane i s actually much less than the possible error resulting from the isotopic substitution and the zero-point vibrations. APPENDIX I MICROWAVE SPECTRUM OF DIFLUOROCHLOROMETHANE In the following tables, the optimum Stark-modulation voltage i s 330 V/cm, the optimum gas pressure i s 10 microns of mercury and the line shape i s that of one of the lines i n Figure 5(d) unless otherwise stated. The relative intensity i s based on the signal-to-noise ratio measurement at dry ice temperature and the temperature enhancement factor i s the ratio of the intensity at dry ice temperature to the intensity at 300° K. The symbol >1 is used i f i t has been impossible to detect the li n e at 300° K and a dash i s employed i f no measurement has been made on the line at 300° K. Characteristics for Opt. Conditions Frequency Intensity Temp. Factor Line width i n Mc/s i n Mc/s Comments 22025.43 22025.70 22028.10 22028.38 22409*5 22411*5 22545.9 22547.5 22552.9 22554.5 23334.0 23335.4 23704.6 23705,8 23710.0 23711.4 23728.2 23728.6 23731.0 23731.4 23837.6 23838.7 24234.3 24235.4 8 8 8 8 6 6 3 3 3 3 20 20 0.2) 0.2 ) C Barely ( Resolved 2.5 2.5 2 2 6 6 6 6 1.3 1.3 0.8 0.8 0.6 0.6 0.6 0.6 1.0 1.0 0.7 0.7 0.7 0.7 Trough-shape Trough-shape 10 10 10 10 2 2 1.5 1.5 0.5 0.5 0.7 0.7. 59 60 Characteristics for Optimum Conditions Frequency Intensity Temp. Factor Line Widt i n Mc/s in Mc/s 2 4 3 H . 0 2.5 - 0.8 24317.S • 2.5 - 0.3 24384.7 2 - 0.5 24516.6 2.2 - 0.8 24513.2 2.5 - 0.8 24523.9 2 - 0.5 24525.1 2 - 0.5 24801.9 2 > 1 0.6-) 24308.7 2.5 > 1 0.6 24810.8 2.5 >1 0 . 6 \ 24817.4 8 3 0 . 9 / 24824.9 5 2 0 . 7 24831.2 2.5 > 1 0 . 6 J 24918.3 3 1.5 0.3 24918.9 3 1.5 0.3 24924.0 3 1.5 0.3 "l 24924.4 3 1.5 0.3 > 24925.8 6 1.5 0.5 .24926.7 6 1.5 0.5 24993.7 4 1.3 0.8 24995.5 3 1.3 0.8 25126.4 2 > 1 0 . 7 1 25129.0 6 3 0.7 > 25131.4 2 > 1 0 . 7 25146.6 6 3 0.7 ) 25621.1 10 3.3 0 . 7 25622.4 10 3.3 0.7 25625.6 5 2 0.7 25632.7 3 1.5 0.7 25635.3 3 1.5 0.7 25729.6 2 > 1 1.2 25736.3 2 > 1 1.2 25737.2 2 > 1 1.2 25740.6 3 1.5 0.3 25741.5 3 1.5 0.3 25753.0 6 1.5 1.0 25755.2 6 1.5 1.0 257c96.4 20 1.3 0 . 9 25798.1 20 1.3 0 . 9 25863.6 20 1.3 0 . 9 25865.0 20 1.3 0 . 9 25894.3 3 2 0 . 7 25897.8 3 2 0.7 26439.4 8 2 0.41 26440.0 8 2 0.4 J 26443.3 8 2 0 . 4 \ 26444.4 8 2 0.4 i 26469.8 8 1.6 0 . 9 \ 26471.6 8 1.6 0.9 ) 26476.4 3 1.5 0.8 26479.5 1.5 > 1 0.8 Comments llOV/cm, Reversed shape n 11 177V/cm, Stark ;distortion 177V/cm, Stark distortion n ti n 11 " , Stark s p l i t t i n g " , Stark distortion /Barely (_Resolved Trough-shape < Broader at 200°K llOV/cm Broader at Dry Ice Trough-shape Uncertain shape n fOverlapping <• Doublet ( Overlapping I Doublet /Double \.Trough Trough-shape Trough-shape 61 Characteristics for Optimum Conditions Frequency Intensity Temp. Factor Line Width i n Mc/s in Mc/s 26585-8 8 1.6 0.9 26587.7 8 1.6 0.9 26690.9 6 1.5 0.6 26691.9 6 1.5 0.6 26823.1 3 0.6 0.9 26825.1 3 0.6 0.9 26831.6 2.5 >1 0.8 26834.9 2.5 >1 0.8 26976.0 2 >1 0.8 26979.0 2 >1 0.8 27044.3 3 1 0.7 27046.4 3 1 0.7 27203.4 2 >1 0.8 27206.3 2 >1 0.8 27221.5 5 2 1.4 "A 27227.5 5 2 1.4 > 27234.7 5 2 1.4 ( 27240.5 5 2 1.4; Region from 27,280 - 28,300 Mc/s not 28333.0 4 - 0.5 \ 28333.4 4 - 0.5 J 28336.2 4 - 0.5 > 28336.4 4 - 0.5 J 28624.0 15 1.5 1.0 28626.8 15 1.5 1.0 28681.8 1.5 >1 ? \ 28685.5 2.5 1.6 0.7 V 28692.6 1.5 > 1 ? J 28695.6 2 ;>i ? / 28697.7 3.5 «»i 0.5 \ 28698.2 3.5 » i 0.5 J 28701.1 3.5 />i 0.5 X 28701.6 3.5 M. 0.5 i 28715.4 5 2 1.4 28720.5 5 2 1.4 28745-3 3 1.5 0.9 28748.7 3 1.5 0.9 29055.0 2.5 1.6 0.7 29056.2 2.5 1.6 0.7 29061.4 2.5 1.6 0.7 29062.8 1.5 71 0.7 29065.8 2.5 1.2 0.7 29068.9 2.5 1.2 0.7 29120.0 5 1.6 0.8 29121.2 5 1.6 0.8 29215.7 20 1.3 0.8 29217.4 20 1.3 0.8 29236.2 1.5 1 ? 29245.1 3 1.2 0.7 29247.8 3 1.2 0.7 29287.5 3 2 0.9 29298.9 3 2 0.9 Comments Trough-shape n 11 it CTriangular Troughs I 100 u gas. pressure [ HOV/cm investigated. / Barely t Resolved < Barely 1 Resolved Line shapes uncertain Other peculiar lines Stark distortion { Overlapping Doublet ( Overlapping \ Doublet Trough-shape it tt tt Reversed shape Reversed shape tt tt n n Uncertain shape Trough-shape tt Characteristics for Optimum Conditions Frequency Intensity Temp. Factor Line Width i n Mc/s in Mc/s 29308.7 4 » 1 0.9 29384.3 8 1 0.8 29385.5 8 1 0.8 29466.1 4 2.7 0.7 29467.0 4 2.7 0.7 29473.0 4 2.7 0.7 29473.9 4 2.7 0.7 29605.1 1.5 < 1 ? 29606.9 6 1.5 0.8 29609.1 1.5 * 1 • 29610.5 6 1.5 0.8 29612.2 1.5 <1 7 29874.5 2.5 1 0.8 29875.6 2.5 1 0.8 29931.8 3 2.5 0.9 29938.8 3 2.5 0.9 29955.6 2 1.7 0.9 30007.8 2.5 0.6 0.9 30009.0 2.5 0.6 0.9 30240.0 6 2 0.8 30244.7 6 2 0.8 30258.0 4 0.8 0.9 30259.4 4 0.8 0.9 30262.8 1.5 >1 ? 30271.9 2.5 >1 r 1.4 30272.5 2.5 >1 t 30276.7 2.5 >1 n.4 30277.2 2.5 >1 I 30389.4 2 7 1 0.7 30398.8 8 3 1.0 30409.4 3.5 » 1 0.7 30418.9 3 2 0.7 30522.6 2.5 >1 1.5 30526.6 2.5 >1 1.5 30544.5 2 >1 1.5 30548.7 1.5 >1 1.5 30551.2 2.5 >1 0.7 30552.2 2.5 >1 0.7 30555.8 6 1.2 0.7 30556.8 6 1.2 0.7 30558.4 2.5 >1 0.7 30559.4 2.5 71 0.7 30728.6 3 0.7 0.8 30730.2 3 0.7 0.8 30893.0 3 1.5 0.7 30894.0 3 1.5 0.7 30996.8 2 <1 0.8 31000.0 2 <1 0.8 31182.8 4 1.3 0.9 31183.9 4 1.3 0.9 31186.1 4 1.3 0.9 31187.2 4 1.3 0.9 V Comments Trough-shape Stark distortion Reversed shape Stark distortion Reversed shape Uncertain shape } Trough-shape Trough-shape Uncertain shape C Barely \ Resolved f Barely 1 Resolved Stak distortion 154V/cm / Trough-shape I HOV/cm / Trough-shape I HOV/cm /Reversed shape \llOV/cm /Reversed shape \llOV/cm Uncertain shape Uncertain shape ^Double Peak ^Double Peak 63 Characteristics for Optimum Conditions Frequency Intensity Temp. Factor Line Width i n Mc/s in Mc/s 31194.9 5 2 0.7 1 31195.8 5 2 0.7 p 31200.1 3 1.5 0.7 31201.0 3 1.5 0.7 J 31226.2 5 1 2.0 31232.5 3 1 2.0 31282.2 6 1.5 0.8 31233.4 6 1.5 0.8 31429.2 6 . 2 0.7 31430.4 6 2 0.7 31432.7 6 2 0.7 31433.7 6 2 0.7 31460*1 1.5 1 ? 31868.2 1.5 <T1 31870.4 2 <1 ? 31875.2 6 1.5 1.0 31379.3 6 1.5 1.0 31885.5 2 1 0.8 31888.1 2 1 0.8 31995.8 3 - • 0.8 31997.0 3 - 0.3 32024.6 12 1.2 0.8 32026.0 12 1.2 0.8 32064.6 8 2 0.8 32067.1 8 2 0.8 32166.5 2 - 0.5 32167.3 2 - 0.5 32174.3 3 2 0.8 32177.0 3 2 0.8 32181.3 3 0.6 32182.6 3 - 0.6 32208.3 24 1.5 0.7 32210.3 24 1.5 0.7 32250.1 3 1.5 0.7 32252.7 3 1.5 0.7 32406.5 8 2 2.0 32510.9 8 2 1.0 32513.6 8 2 1.0 32576.4 10 2 1 .61 32581.6 15 1.5 1.6 V 32587.0 10 2 1.6 J 32630.4 8 2 0.8 32632.4 8 . 2 0.8 32637.6 8 2 0.8 32639.6 8 2 0.8 32764.9 3 » 1 0.7 32767.9 3 » 1 0.7 32823.5 2 >1 0.7 32825.0 2 < 1 ? 32885.7 2.5 1 1.0 32887.2 3 1 1.0 32891.3 2 1 1.0 Comments Poor klystron mode f Reversed shape (llOv/cm, 100 microns ^Distorted Doublet ^Distorted Doublet Uncertain shape Uncertain shape Uncertain shape Stark distortion Stark distortion Uncertain shape Trough, llOV/cm, 100 microns fTrough-shape ] llOV/cm V100 microns Reversed shape it it n Uncertain shape Uncertain shape 11 it 1? Frequency i n Mc/s Characteristics for Optimum Conditions Intensity Temp. Factor Line Width i n Mc/s Comments 32892.8 2 1 1.0 33016.2 10 1 0.7 33017.6 10 1 0.7 33047.2 15 1.5 1.0 33048.0 15 1.5 1.0 33053.4 3 ^ 1 0.7 33054.5 3 <1 0.7 33167.4 3 1.5 0.4 33168.1 3 1.5 0.4 33171.4 3 1.5 0.4 33172.1 ' 3 1.5 0.4 33199.7 2 - 1.0 33201.5 2 - 1.0 } Uncertain shape ( Double \ Trough f Barely \ Resolved {Barely Resolved Uncertain shape n APPENDIX II STARK EFFECT MEASUREMENTS Stark Splitting of 5/2 -» 7/2 Hyperfine Transition of 1 Q ^ -+2-^ Stark Modulation Displacement of Stark i n Volts/cm Component i n Mc/s 300 330 405 480 - , +1.9 •1.0, +2.1 - , +2.9 •3.4, +4.2 Stark Spli t t i n g of 9/2 ->9/2 Hyperfine Transition of 3 2 >2 "^^3,0 Stark Modulation i n Volts/cm Width of Envelope of Stark Components in Mc/s 75 95 110 125 155 175 250 330 0.4 0.5 0.9 1.2 1.5 1.7 1.7 1.7 REFERENCES 1. Haszeldine, R.N. and Sharpe, A.G., Fluorine and Its Compounds. London, Methuen, 1951, pp. 76-79. 2. Brockway, L.O., J.Phys.Chem. 41, 185 (1937). 3. Hamilton, W.C. and Hedberg, K., J.Am.Chem.Soc. 74, 5529 (1952). 4. Bartell, L.S. and Brockway, L.O.. J.Chem.Phys. 23, i860 (1955). 5. Brockway, L.O., cited i n Meyer, L.H. and Gutowsky, H.S., J.Phys.Chem. 57, 481 (1953). 6. Herzberg, G., Infrared and Raman Spectra of Polyatomic Molecules. New York, Van Nostrand, 1951, pp. 438-440. 7. Ibid., p. 489. 8. Kraitchman, J., Am.J.Phys. 21,17 (1953). 9. Townes, CH. and Schawlow, A.L., Microwave Spectroscopy. New York, McGraw-H i l l , 1955, p. 55. 10. Ibid., pp. 56-59. 11. Ibid.. pp. 110-114. 12. Gilliam, O.R., Edwards, H.D. and Gordy, W., Phys.Rev. 75, 1014 (1949). 13. Ghosh, S.N., Trambarulo, R. and Gordy, W., J.Chem.Phys. 20, 605 (1952) 14. Lide, D.R.,Jr., J.Am.Chem.Soc. 74, 3548 (1952). 15. King, W.C. and Gordy, W., Phys.Rev. 93, 407 (1954). 16. Miller, S.L., Aamodt, L.C., Dousmanis, G., Townes, CH., and Kraitchman, J., J.Chem.Phys. 20, 1112 (1952). 17. Muller, N., J.Am.Chem.Soc. 75, 860 (1953). 18. Coles, D.K. and Hughes, R.H., Phys.Rev. 76, 858(L) (1949). 19. Kisliuk, P. and Townes, CH., Molecular Microwave Spectra Tables. N.B.S. Circular 518, U.S.A., National Bureau of Standards, 1952, p. 13. 20. Mann, C.R., Ph.D. Thesis, University of B r i t i s h Columbia, 1952. 21. Dailey, B.P., J.Phys.Chem. 57, 490 (1953). 65 22. Townes and Schawlow, Chapter 9* 23. Meyer, L.H. and Gutowsky, H.S., J.Phys.Chem. 57, 481 (1953). 2A. Livingston, R., J.Phys.Chem. 57, 496 (1953). 25. Goldstein, J.H., J.Chem.Phys. 24, 106 (1956). 26. TJnterburger, R.R. and Smith, W.V., Rev.Sci.Instr. 19, 580 (1948). 27. McAfee, K.B.,Jr., Hughes, R.H., and Wilson, E.B.,Jr., Rev.Sci.Instr. 20, 821 (1949). 28. Sharbaugh, A.H., Rev.Sci.Instr. 21, 120 (1950). 29. Townes and Schawlow, p. 382. 30. Hedrick, L.C., Rev.Sci.Instr. 20, 781 (1949). 31. Slater, J.C. and Frank, N.H., Mechanics. New York, McGraw-Hill, 1947, p.101 32. Pauling, L., The Nature of the Chemical Bond. Ithaca, N.Y., Cornell University, 1948, p. 68. 33. Livingston, R., J.Chem.Phys. 19, 1434(L) (1951). 34. Herzberg, p. 45. 35. Report on Notation for the Spectra of Polyatomic Molecules, J.Chem.Phys. 23, 1991 (1955). 36. King, G.W., Hainer, R.M., and Cross, P.C., J.Chem.Phys. 11, 27 (1943). 37. Turner, T.E., Hicks, B.L., and Rietwiesner, G., B a l l i s t i c s Research Laboratory Report No. 878. Aberdeen, Md., 1953, reproduced i n Townes and Schawlow, Appendix IV. 38. Cohen, E.R., Dumond, J.W.M., Layton, T.W., and Rollett, J.S., Rev.Mod.Phys. 27, 363 (1955). 39. Townes and Schawlow, Appendix VII. 40. Cross, P.C., Hainer, R.M. and King, G.W., J.Chem.Phys. 12, 210 (1944). 41. Golden, S. and Wilson, E.B.,Jr., J.Chem.Phys. 16, 669 (1948). 42. Bragg, J.K., Phys.Rev. 74, 533 (1948). 43. Townes and Schawlow, p. 134* 44. Bragg, J.K. and Golden, S., Phys.Rev. 75, 735 (1949). 45. Townes and Schawlow, Appendix I. 46. Myers, R.J. and Gwinn, W.D., J.Chem.Phys. 20, 1420 (1952). 67 47. Pauling, pp. 235-237. 48. Townes, CH. and Dailey, B.P., J.Chem.Phys. 17, 782 (1949). 49. White, R.L., Ph.D. thesis, Columbia University, 1954, cited i n Townes and Schawlow, Appendix VI. 50..Livingston, R., J.Chem.Phys. 20, 1170 (1952). BIBLIOGRAPHY Bak, Borge, Elementary Introduction to Molecular Spectra, Amsterdam, North Holland,-1954. Coulson, C.A., Valence, London, Oxford, 1952. Debye, P., Polar Molecules, New York, Dover, (copyright, 1929). Feenberg, E. and Pake, G.E., Notes on the Quantum Theory of Angular Momentum, Cambridge, Mass., Addison-Wesley, 1953. Gordy, W., Smith, W.V. and Trambarulo, R.F., Microwave Spectroscopy, New York,, John Wiley, 1953. Haszeldine, R.N. and Sharpe, A.G., Fluorine and Its Compounds. London, Methuen, 1951. Herzberg, G., Molecular Spectra and Molecular Structure. II. Infrared and  Raman Spectra of Polyatomic Molecules, New York, Van Nostrand, 1945. Kisliuk, P. and Townes, C.H., Molecular Microwave Spectra Tables, 1952, Washington, D.C., National Bureau of Standards Circular 518. Massachusetts Institute of Technology Radiation Laboratory Series, New York, McGraw H i l l , Vol.11. Montgomery, C.G. (ed.), Techniques of Microwave Measurements, 1947. Vol.15. Torrey, H.C. and Whitmer, C. A. (ed.), Crystal Rectifier, 1948. Vol.18. Valley, G.E. and Wallman, H. (ed.), Vacuum Tube Amplifiers. 1948. Miner, R.W. (ed.), "Microwave Spectroscopy", Annals of the New York Academy  of Sciences, vol.55, pp 743-966, 1952. Pauling, L., The Nature of the Chemical Bond. Ithaca, N.Y., Cornell University Press, 2nd ed., 1948. Slater, J.C. and Frank, N.H., Mechanics, New York, McGraw-Hill, 1947. Strandberg, M.W.P., Microwave Spectroscopy. New York, John Wiley, 1953. Townes, CH. and Schawlow, A.L., Microwave Spectroscopy. New York, McGraw-H i l l , 1955. 68 

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