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Studies in high resolution spectroscopy Anderson, Darlene 1986

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STUDIES IN HIGH RESOLUTION SPECTROSCOPY by DARLENE ANDERSON B.Sc. Queen's University 1980 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1986 ® Darlene Anderson, 1986 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at The University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Chemistry The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: October 1986 ABSTRACT The ground state microwave spectra of hypochlorous acid (HOC1), carbonylchlorofluoride (FC1CO), and N-chlorodifluoromethylenimine (CF NCI), have been measured from 8 — 80 GHz and analyzed. The 8Q vibrational band of aminoborane (NH^BH^) near 1223 cm * has been recorded at a resolution of 0.004 cm * and analyzed. HOC1: Rotational constants and quartic centrifugal distortion constants were obtained for the following four isotopic species of hypochlorous acid: D^O^Cl, Q16Q37^^ H ^ O ^ C l and H^O^Cl. The centrifugal distortion constants were combined with vibrational wavenumbers from the literature to determine a valence harmonic force field which was used to calculate an average structure and an estimated equilibrium structure. Effective and full substitution structures have also been evaluated. FC1CO: An extensive set of transitions, to high J and K has been measured a 35 12 37 12 for the two most abundant species, F CI CO and F CI CO, which allowed accurate values for the rotational constants, centrifugal distortion constants and the chlorine nuclear quadrupole coupling constants to be evaluated for each. An 35 13 estimate of the three rotational constants for F CI CO was made from the four transitions measured, as it exists in natural abundance. Harmonic force constants were produced from ab initio calculations and were used in the determination of its harmonic force field. Effective and average structural parameters have been determined. CF 2 NCI: Rotational constants and quartic centrifugal distortion constants have 35 37 been obtained for the two isotopic species CF N CI and CF N CI. The 14 nuclear quadrupole coupling constants of both N and CI have been evaluated. A partial harmonic force field has been determined from the available data. Both effective and average structural parameters have been obtained and indicate that the structure of CF2NC1 is a hybrid of those of CF^NF and CC^NCl. The nuclear quadrupole coupling constants have provided information about the bonding in the molecule. NH 2 BH 2: Rotational constants and centrifugal distortion constants of the upper vibrational state 2v 8 have been determined and have confirmed the assignment of the band. The least squares refinement of the constants has shown an increasing poorness of fit to the higher K transitions which has suggested the a possiblity of Coriolis type perturbations. iii TABLE OF CONTENTS Abstract ii List of Tables vi List of Figures viii Acknowledgements ix 1. Introduction 1 Bibliography 13 2. Theory 15 2.1. The Rotational Hamiltonian 17 2.2. The Vibrational Hamiltonian 25 2.2.1. Selection Rules for Rotational and Vibrational Transitions 27 2.3. Molecular Structures 32 2.4. Harmonic Force Field Calculations 40 2.5. Nuclear Quadrupole Coupling 43 2.6. The Stark Effect: Asymmetric Rotor 47 2.7. Basic Fitting Procedures Used 54 Bibliography 61 3. Experimental Methods 63 3.1. Instrumentation - Microwave Spectra 63 3.1.1. Backward Wave Oscillators 68 3.1.2. Watkins-Johnson Frequency Synthesizer 69 3.1.3. OKI Klystron (30V10) 70 3.2. Instrumentation - Infrared Spectra 72 3.3. Sample Preparation and Handling 78 3.3.1. Hypochlorous Acid: DOC1, and H 1 8 OC1 78 3.3.2. Carbonyl Chlorofluoride, FC1CO 80 3.3.3. N-chlorodifluoromethylenimine, CF 2 NCI 81 3.3.4. Aminoborane, NH 2 BH2 83 Bibliography 90 4. Microwave Spectrum of Hypochlorous Acid 91 4.1. Assignment and Analysis 95 4.2. Effective Structure 100 4.3. Substitution Structure 102 4.4. The Harmonic Force Field 104 4.5. Average Structure 109 4.6. Comments 114 Bibliography 143 iv 5. Microwave Spectrum of Carbonyl Chlorofluoride 145 5.1. Assignment and Analysis 147 5.2. Effective Structure 150 5.3. Harmonic Force Field 152 5.4. Average Structure 155 5.5. Comments 157 Bibliography 178 6. Microwave Spectrum of N-Chlorodifluoromethylenimine 179 6.1. Measurement and Assignment 182 6.2. Analysis of the Microwave Spectrum 185 6.2.1. Nuclear Quadrupole Coupling 185 6.2.2. Rotational and Centrifugal Distortion Constants 190 6.3. Effective Structure 193 6.4. The Harmonic Force Field 195 6.5. Average Structure 199 6.6. Comments on the Bonding in CF 2 NCI 200 6.7. Discussion 207 Bibliography 232 7. The Infrared Spectrum of Aminoborane 233 7.1. Assignment of the Spectrum 236 7.2. Analysis of the Spectrum 240 7.3. Discussion 241 Bibliography • 259 v LIST OF TABLES 2.1 Hamiltonians - I Representation 57 2.2 Matrix Elements - I Representation 58 2.3 Relationship Between Distortion Constants 60 4.1 Representative Sample of Transitions with Resolved Hyperfine Structure of HOC1 119 4.2 Observed Transition Frequencies of HOC1 120 4.3 Spectroscopic Constants of HOC1 122 4.4 Effective and Average Inertial Defects for HOC1 124 4.5 Effective and Substitutions Structures of HOC1 125 4.6 Atomic Coordinates of the Substitution Structure of HOC1, In Its Principal Axis System 126 4.7 Symmetry Coordinates and Geometry of HOC1 Used in the Harmonic Force Field Analysis 127 4.8 Relationship Between Watsons Determinable Rotational Constants and the A and and S Reduction Rotational Constants 128 4.9 Harmonic Force Fields of HOC1 130 4.10 Observed and Calculated Wavenumbers and Centrifugal Distortion Constants of HOC1 131 4.11 Differences Between S Reduction and Determinable Rotational Constants . 134 4.12 The Planar Relations 135 4.13 rabab Values for the Six Isotopic Species of HOC1 136 4.14 Ground State Average Structures of HOC1 137 4.15 Comparison of the Four Structures Determined For HOC1 138 4.16 Comparison of All the Harmonic Force Fields of HOC1 139 4.17 Observed and Calculated Inertial Defects of HOC1 141 5.1 Representative Sample of Transitions with Resolved Hyperfine Structure of F 3 SC1C0 161 5.2 Observed Transition Frequencies of FC1CO 162 5.3 Spectroscopic Constants of FC1CO 166 5.4 Effective and Average Inertial Defects for FC1CO 167 5.5 Comparison of Different Effective Structures Obtained for FC1CO 168 5.6 Symmetry Coordinates and Geometry of FC1CO Used in the Harmonic Force Field Analysis 169 5.7 Harmonic Force Fields of FC1CO 170 5.8 Observed and Calculated Wavenumbers and Centrifugal Distortion Constants of FC1CO , 172 5.9 Effective and Ground State Average Structures of FC1CO 174 6.1 Representative Sample of Transitions of CF 2 N 3 5 CI Showing Both Nitrogen and Chlorine Nuclear Quadrupole Hyperfine Structure 209 6.2 Representative Sample of Transitions with Resolved Hyperfine Structure of CF 2N 3 5C1 ....211 6.3 Observed Transition Frequencies of CF 2 NCI 213 6.4 Spectroscopic Constants of CF 2 NCI 217 6.5 Principal Moments of Inertia and Inertial Defects of the Effective and Average Structures of CF 2 NCI 218 6.6 Effective and Average Structures of CF 2 NCI 219 6.7 Internal Coordinates and Symmetry Coordinates Used in the Final Harmonic Force Field Refinement of CF 2 NCI 220 VI 6.8 Definition of Force Constants Used in Harmonic Force Field of CF, NCI 222 6.9 Harmonic Force Field of CF 2 NCI 223 6.10 Observed and Calculated Wavenumbers and Centrifugal Distortion Constants of CF 2 NCI 224 6.11 Ground State Average Rotational Constants of CF 2 NCI , 225 6.12 Nuclear Quadrupole Coupling Constants of Chlorine in its Principal , Axis System 226 6.13 Observed and Calculated Nuclear Quadrupole Coupling Constants of 1 4 N 227 6.14 Observed and Calculated Nuclear Quadrupole Coupling Constants of 3 5 CI 228 7.1 Vibrational Fundamentals of NH 2 1 1 BH 2 244 7.2 Spectroscopic Constants of NH 2 1 1 BH 2 245 7.3 Assigned Transition Frequencies of the 8g Band of NH 2 BH 2 246 vii LIST OF FIGURES 1.1 Diagram showing the Different Regions of the Earth's Atmosphere 12 3.1 Schematic Diagram of the Microwave Spectrometer and Sample 85 3.2 Schematic Diagram of the Backward Wave Oscillator Microwave Source Circuit 86 3.3 Schematic Diagram of the Klystron Microwave Source Circuit 87 3.4 Schematic Diagram of an Interferometer 88 3.5 Experimental Arrangement for the Production of Gaseous NH 2 BH 2 in a Flow System 89 4.1 The Ground State Average Structure of HOC1 142 5.1 The v3 band of FC1CO 175 5.2 The Ground State Average Structure of FC1CO, in its Principal Inertial Axis System 176 5.3 Three Different Structures Contributing to the Overall Bonding in the C-Cl Bond of FC1CO 177 6.1 Portion of the Microwave Spectrum of CF 2 NCI showing a-type R branch J = 7 —6 transitions 229 6.2 Ground State Average Structure of CF 2 NCI, in its Principal Inertial Axis System 230 6.3 Three Different Structures Contributing to the Overal Bonding in the N-Cl Bond of CF2NC1 231 7.1 The Ka = 4, 5, 6 Q branch lines of the 2v 8 Band of NH 2 BH 2 256 7.2 A Graphic Description of Ground State Combination Differences 257 7.3 Diagram Showing the Vibrational Levels that Could Perturb the 2v 8 Level of NH 2 BH 2 in a Coriolis Type Perturbation 258 viii ACKNOWLEDGEMENTS I would like to thank my supervisor, Mike Gerry for all the encouragement and support he has given me over the past five years. His enthusiasm for microwave spectroscopy and approachability as a teacher and friend will always be appreciated and remembered. I am also very grateful to Wyn Lewis-Bevan and Bob Davis for the many hours of patient help and advice they gave me in analyzing my spectra. ix 1. INTRODUCTION This thesis describes the measurement and analysis of the microwave spectra of the three molecules, hypochlorous acid (HOC1), carbonylchlorofluoride (FC1CO), and N-chlorodifluoromethylenimine (CF NCI), and of the high resolution infrared spectrum of the 8© band of aminoborane (NHgBHg). All of these were studies of the rotational structure of the molecule. Analysis of the microwave spectra determined rotational energy levels of the ground vibrational state only, while analysis of the infrared spectrum gave information about the rotational energy levels of both the ground and the second excited vibrational state. Microwaves are most often used to measure the pure rotational spectrum of the ground vibrational state. However, occasionally they can be used to measure the rotational spectrum of excited vibrational states. This is only possible if the excited vibrational state lies low enough in energy to be sufficiently populated to detect any absorption of microwave radiation. Microwaves have also been used to measure inversion states when the inversion splittings have the same energy as those of microwaves, e.g. ammonia (1). Microwaves can be combined with other forms of radiation to measure the rotational structure of excited electronic or vibrational states in, for example, microwave optical double resonance (MODR) and microwave infrared double resonance (MIDR) experiments. Infrared radiation, on the other hand, is usually used to measure the vibrational structure of a molecule. If the spectrum is taken at low resolution it will only give the approximate frequency of a molecular vibration. However if the resolution is high absorptions between individual rotational levels of the two 1 Introduction / 2 vibrational states will be observed over the entire vibrational band. Careful analysis of these transitions can give information about each state's rotational energy levels plus possible interactions or couplings with different vibrational states and their rotational levels. Transitions are seen in both kinds of spectroscopy because of an interaction of the molecule's dipole moment, ju, with the electric field of the radiation, E(t), as explained in more detail in Chapter 2. The important point to be made about this interaction is that to see a microwave spectrum the molecule must have a permanent dipole moment and to see an infrared spectrum there must be a change in the • dipole moment. The frequency range of microwave radiation covered by the measurements in this work was 8 — 80 GHz. However measurements are being made in other laboratories to frequencies as high as 800 GHz and beyond by using harmonic generators and high frequency sources. This means that the upper frequency range of measurements in microwave spectroscopy overlap the lower frequency limits of measurements being made in far infrared spectroscopy at 10 cm \ (10 cm ^  = 300 GHz). In the work described in this thesis the measurements of any infrared spectra were made within the conventional frequency range of 700-3000 cm"1. All molecules were studied in the gas phase, primarily because the rotational Hamiltonian (section 2.1) used to analyze the spectra describes the motion of molecules that are free to rotate. This can really only occur when the molecules are in the gas phase. In microwave spectroscopy in order to avoid large linewidths caused by pressure broadening or broadening by collisions Introduction / 3 between the molecules, very low pressures are used, e.g. 30 mTorr or less. This leads to very high resolution spectra, that is, approximately one part in 10 . In infrared spectroscopy line widths are not limited as much by pressure broadening but more by the Doppler effect. Consequently higher pressures are usually used in order to get a strong spectrum, e.g. 100—150 mTorr. Measurement of a microwave spectrum provides information about some of the physical properties of a molecule, such as its structure, its dipole moment, nuclear quadrupole coupling and the kind of bonding between the atoms. How this information is obtained from the analysis of the spectrum is described in the next chapter. One very important aspect of an accurately analyzed ground state microwave spectrum is that the rotational constants and centrifugal distortion constants obtained (section 2.1) are often crucial to the success of the analysis of a band in the molecule's high resolution infrared spectrum. A microwave spectrum or a high resolution infrared spectrum is a distinctive fingerprint of a molecule such that the detection of its spectrum will uniquely characterize its existence. This is most important when one is trying to produce unstable and transient molecules that only last for a few minutes or cannot be easily detected in a stationary system. A flow system which provides constant production of the unstable molecule can be easily incorporated into the experimental arrangement and was used in this work for HOC1. As a result of this distinctive spectrum it is possible to detect a molecule in a mixture of gases, as was the case for all the molecules studied in this work. In other words it is not necessary to have a pure sample of the molecule under investigation. Often some of the gases in a mixture will not have a microwave spectrum (no permanent dipole moment) or the gas does not absorb microwave Introduction / 4 radiation in the frequency range being scanned. However interference by transitions of other molecules can sometimes be a problem. Regardless, because it is possible to identify a molecule within a mixture of gases this means molecules such as HOC1 and FC1CO could be detected in the stratosphere using microwave spectroscopy. Reasons for wanting to do this are explained below. The molecules whose spectra were analyzed in this work were studied for a variety of reasons, and these are presented here. Detailed descriptions of the spectroscopic studies carried out on each, prior to this work, are given in the introduction of the chapter that describes the analysis of that molecule. The first two molecules studied, HOC1 and FC1CO are molecules of "stratospheric" interest. Most of the information presented here was taken from references (2 — 5). For the purposes of this discussion it is helpful to know where, in terms of altitude above the surface of the earth, the stratosphere, troposphere, etc. are. Figure 1.1 shows this information. A big concern about "our atmosphere" is of the possible destruction of the ozone layer which protects life on earth against the destructive energy of the sun's rays. It has been suggested that the ozone layer is being destroyed faster than it is being formed because of the introduction of odd-nitrogen and odd-chlorine species into the atmosphere from industrial processes (6). Of particular interest to this discussion are the chlorofluoromethanes, C F 9 G 9 and CFCU. They are released into the atmosphere from aerosal spray Introduction / 5 cans and refrigeration devices. There is no known, significant, tropospheric sink for them and so they are eventually transported to the stratosphere (=20 km above the earth's surface). There they produce atomic chlorine by photodissociation. This initiates the most important ozone destruction cycle attributed to the chlorine family (2): CI + 0 3 *• CIO + 0 2 (1.1) CIO + O('D) — * CI + 0 2 (1.2) 0 3 + 0( 1D) —*- 20 2 (1.3) Reaction (1.3) is the overall reaction where reaction (1.2) is the rate controlling step. 0( 1 D) is produced by the photodissociation of ozone: 0 3 + hv — ^ 0( 1D) + 0 2 (1.4) It is informative to know that 0 Q is also formed by a photodissociation process. o Molecular oxygen photodissociates to form ground state oxygen atoms, 0( 3 P), which then react with more molecular oxygen in a three-body association reaction to form ozone: 0 2 + hv - 20(3P) (1.5) 0( 3P) + 0 2 + M — 0 3 + M (1.6) Eventually the atomic chlorine will react with CH^, CHgO or H0 2 to produce HC1, which is relatively inert. Unfortunately before this happens the Introduction / 6 atomic chlorine will have completed many of its ozone destroying cycles given in reactions (1.1) and (1.2). This cycle can also be halted by the formation of HOC1 and C10N0 2 from CIO (2): CIO + H0 2 >- HOC1 + 0 2 (1.7) CIO + NO. + M — > C10NO_ + M (1.8) Unfortunately these two sinks for CI are photolytically converted back into CI and CIO quite rapidly: HOC1 + hi> — H O + CI (1.9) C10N0 2 + hv —*- CIO + N0 2 (1.10) For HOC1 the rate is believed to be 2.5xl03 c m ' V 1 and for C10N0 2 it is 3 - 3 - 1 8x10 cm s , both of which are significantly larger than the rate at which 3 -3 -1 HC1 is converted into CI (1.5x10 cm s ) (2). This makes HOC1 a less important reservoir species for CI than HC1. As a matter of fact it is believed to drive an ozone destruction cycle (2): CI + 0 3 *• CIO + 0 2 (1.11) CIO + H0 2 —*• HOCl + 0 2 (1.7) OH + 0 3 — » - H0 2 + 0 2 (1.12) HOCl + hv — - CI + OH (1.9) 2 0 3 — 3 0 2 (1.13) Introduction / 7 where reaction (1.13) is the overall reaction. Needless to say information about HOCl is needed and the following two quotes best describe the importance of measuring the microwave spectrum of "The fate of the liberated chlorine atom in the stratosphere is by far the biggest gap in our knowledge. This concerns both the quantitative aspects of the known chemistry and more importantly, the possibility of still unknown gas phase chemistry." (7) "More laboratory work on HOCl is required to determine how important it is in the stratosphere. At the same time, efforts are underway to detect HOCl in the stratosphere using infrared methods." (7) Although the work reported here is on the less abundant isotopic species where a primary goal was to determine an accurate structure, it is heartening to know there is a univeral interest in obtaining more information about the molecule. Although FC1CO is not believed to be as significant a sink for chlorine as HOCl is, it is believed to be produced as an intermediate product in reactions of CFC1 in the stratosphere. The two postulated pathways for its formation are HOCl. (3): Pathway 1: CFCL + O('D) —*- FC1CO + CI (1.14) Pathway 2: CFC13 + hv CI + CFC12 (1.15) CFC12 + i02 — ~ FC1CO (1.16) Introduction / 8 The end products of this cycle are HC1 and HF. Knowledge of the microwave spectrum of FC1CO would be helpful in trying to detect it in the stratosphere to get an idea of its rate of formation (from CFC1 ) and destruction (to HCl and HF). The rotational constants and centrifugal distortion constants obtained from the analysis of the ground state rotational spectrum will also be very useful for any analyses done of its high resolution infrared spectrum. CFgNCl with its unsaturated C = N bond and its N —CI bond is interesting to both the physical chemist, for its structural properties, and the organic chemist for its reactivity. Because it is one of the few molecules having an N —CI bond available for study in the vapour phase, it is interesting and informative to determine its structure for comparison. The molecule is of great interest to the organic chemist because it is a simple imine which has been able to provide routes to novel fluorinated compounds. Some examples of syntheses using CF NCI include: a) The synthesis of oxaziridines via: (8) CF 2 = NC1 + CF 2CFX CF 2 = NCF2CFXC1 (1.17) CF =NCF„CFXC1 + CF OOH CF o00CF„NHCF CFXC1 (1.18) (1.19) X = F, CI, Br Introduction / 9 b) The synthesis of CF NBrCl and CF NBr using CsF: (9) CF 2 = NC1 + Br 2 + CsF — - CF^NBrCl + CFgNBrg (1.20) These are believed to form by the oxidation of the intermediate anion CF„NC1 : The unexpected formation of CF^NB^ in reaction (1.20) requires a substitution of CI by Br. This has been shown to happen when CF^NClBr is reacted with Br 2 in the presence of CsF (9). More details on the chemistry of CF^NCl can be found in papers published by DesMarteau and coworkers who have done a great deal of work with it and similar compounds (10,11,12). A result of these investigations has been to provide the chemist with the opportunity to compare the reactivities of C = N bonds which are affected only by halogen substitution on the N, as well as to compare the reactivity of the N —X bond, where X • = F, CI, and Br. One role of the physical chemist in all this is to provide accurate values for the structural parameters, as well as information about the bonding, so that it can be used. to help explain and even predict the reactivity of these molecules. CF 2 = NC1 + F (1.21) CF3NC1 + *Br 2 CFgNClBr (1.22) The initial interest in BN compounds arose because they are inorganic analogs of organic molecules containing the CC group, where the BN group and CC group are isoelectronic. However the polar nature of the donor-acceptor bond Introduction / 10 between B and N makes these compounds much less stable than the corresponding organic molecules. For example, borane ammonia (NH BH ), the analog of ethane, has a very large dipole moment and is a white crystalline solid which easily decomposes (13). As a result most syntheses with boron and nitrogen usually produce a mixture of many different BN containing compounds. Usually the end products are not simple monomeric molecules but rather a cyclic polymer, e.g. (NH QBH 0) z z n (14—18). This probably led Wiberg to classify the BN system into these three groups of amine boranes (19): 1. Those of empirical composition NH BH o o 2. Aminoboranes, NHgBHg, including cyclic compounds which are then called cycloborazanes 3. Borazines of empirical formula BHNH It was felt that if the simplest olefin NH BH 0 could be isolated and A Z studied a better understanding of the bonding and reactivity of BN compounds would be gained. Therefore one of the most interesting chemical reasons for measuring the spectrum of NHgBHg was to prove that the synthesis had indeed produced the molecule in its monomeric form. Although NH^BH^ has been prepared and spectra measured of it (18,20), the preparative method used in this work and reference (13) was new. Introduction / 11 Immediately following this chapter is one which deals with the theory used to analyze the spectra. It includes an outline of the rotational Hamiltonian and the vibrational Hamiltonian, a description of molecular structure determination, harmonic force field calculations, nuclear quadrupole coupling, the Stark effect and basic fitting procedures. The third chapter describes the experimental aspects of this work; the instrumentation, and sample preparation and handling. The remaining four chapters describe, in detail, the measurement and analysis of the spectrum of each molecule, concluding with a discussion of the results. In all the chapters the reader will find the tables and figures at the end of the chapter in numerical order with the tables first and the figures following. Each chapter has its own bibliography. Introduction / 12 OUR ATMOSPHERE 100k m 50km 20k m Earth's Surface t HETEROSPHERE HOMOSPHERE MESOSPHERE STRATOPAUSE STRATOSPHERE TROPOPAUSE TROPOSPHERE :a-I ) i I , 1 Figure 1.1. Diagram showing the Different Regions of the Earth's Atmosphere BIBLIOGRAPHY 1. W. Gordy and R.L. Cook, Microwave Molecular Spectra, in Technique of Organic Chemistry, Ed. A. Weissberger, Vol. IX, Part II, Interscience Publishers, New York, 1970, Chapter 6, pages 149-154. 2. Ozone in the Free Atmosphere, Editors: R.C. Whitten and S.S. Prasad, Van Nostrand Reinhold Company Inc., New York, 1985. R.C. Whitten and S.S Prasad, Chapter 2, pages 91 and 105-110. 3. CRC Stratospheric Ozone and Man, Editors: F.A. Bower and R.B. Ward, CRC Press Inc, Boca Raton, Florida, 1982 a. J.G. Anderson, Vol 1, Chapter 6, pages 155-193 and b. J.P. Jesson, Vol 2, Chapter 2, pages 29-63. 4. Causes and Effects of Stratospheric Ozone Reduction National Academy Press, Washington, D.C. 1982 (Environmental Studies Board, Commission on Natural Resources National Research Council). 5. Chlorofluorocarbons in the Environment: The Aerosal Controversy, Editors: T.M. Sudgen and T.F. West, Ellis Horwood Ltd, Chichester, England, 1980. 6. M.J. Molina and F.S. Rowland, Nature(London), 249, 810-812 (1974). 7. J.P. Jesson, CRC Stratospheric Ozone and Man, Editors: F.A. Bower and R.B. Ward, CRC Press Inc, Boca Raton, Florida, 1982, Vol 2, Chapter 2, pages 53 and 58. 8. Y.Y. Zheng and D.D. DesMarteau, J Org Chem, 48, 4844-4847 (1983). 9. Y.Y. Zheng, Qui-Chi Mir, B.A. O'Brien, and D.D. DesMarteau, Inorg Chem, 23, 518-519 (1984). 10. Y.Y. Zheng, C.W. Bauknight Jr., and D.D. DesMarteau, J Org Chem, 49, 3590-3595 (1984). 11. A. Sekiya and D.D. DesMarteau, J Org Chem, 46, 1277-1280 (1981). 12. S.C. Chang and D.D. DesMarteau, Inorg Chem, 22, 805-809 (1983). 13. M.C.L. Gerry, W. Lewis-Bevan, A.J. Merer, and N.P.C. Westwood, J Mol Spectrosc, 10, 153-163 (1985). 14. K.W. Boddeker, S.G. Shore, and R.K. Bunting, J Amer Chem Soc, 88, 4396-4401 (1966). 15. D.L. Denton, A.D. Johnson II, C.W. Hickman Jr., R.K. Bunting, and S.G. Shore, Inorg Nucl Chem, 37, 1037-1038 (1975). 16. R. Komm, R.A. Geanangel, and R. Liepins, Inorg Chem, 22, 1684-1686 (1983). 13 / 14 17. P.M. Kuznesof, D.F. Shriver, and F.E. Stafford, J Amer Chem Soc, 90, 2557-2560 (1968). 18. C.T. Kwon and H.A. McGee, Inorg Chem, 9, 2458-2461 (1970). 19. E. Wiberg, Naturwissenschaften, 35, 212-218 (1948). 20. M. Sugie, H. Takeo, and C. Matsumura, Chem Phys Lett, 64, 573-575 (1979) 2. THEORY This chapter gives a brief outline of the rotational and vibrational Hamiltonian, which are both used in the analysis of the spectra studied in this work. The remaining sections deal with the determination of harmonic force fields and molecular structures, nuclear quadrupole coupling, the Stark effect and the basic steps in the analysis of a ground state rotational spectrum. Before looking at the details of these two Hamiltonians it is interesting to » know how and why it is valid, first, to separate electronic and nuclear motions, and then, secondly to separate the molecular motions of translation, vibration and rotation. The Born-Oppenheimer approximation is used to separate nuclear and electronic motions. It says that because the mass of the electron and the nucleus are so different the energies involved with each are also drastically different. As a result neither affect the energy of the other significantly. This approximation is nearly always valid for vibrational and rotational molecular motions as indicated by the fact that any dependence of the molecular structure on the electrons is so small that no observable effect can be detected. Separation of translational energy from vibrational and rotational energy is straightforward because there is no interaction between translational and vibrational or rotational motion. A molecule will vibrate and rotate in exactly the same way regardless of whether it is translating through space. Unfortunately the same is not true for vibrational and rotational motion. A molecule vibrates differently when it is rotating than when it is not. The expression for the kinetic energy of a molecule caused by vibrational and 15 Theory / 16 rotational motions can be divided into three parts: Kinetic = Pure Vibrational + Vibration-Rotation + Pure Rotational Energy Kinetic Energy Interaction K.E. Kinetic Energy Having divided the kinetic energy in the above way it is possible to look at both the vibrational and rotational kinetic energy separately (1), as has been done in the first two sections of this chapter. There is still a term representing a vibration-rotation interaction, however in many situations, as for all the molecules studied here, it is very small and can be neglected. Theory / 17 2.1. THE ROTATIONAL HAMILTONIAN The rotational Hamiltonian H^, for a rigidly rotating body of point masses is: J 2 J 2 J 2 ^ = —— + —2- + (2.1) 21 21 21 x y z 2 2 2 where J , J , J are angular momentum operators, and I , I and I are the x y z x y z principal moments of inertia. For example: I = Em. (y? + z 2 ) (2.2) X l 2 i l ' where x., y., and z. are the cartesian components of the equilibrium position of each particle in a molecule fixed coordinate system. The rigid rotor Hamiltonian is usually expressed slightly differently from that given in equation (2.1). The usual modifications involve relabelling the principal axes with a, b, c, such that the following relationship between the moments of inertia is always true: I < I. < I . Then, rotational constants a b c A, B, C, are defined that relate to the moments of inertia in the following way: A = SJ B = s C = 8 T T 2 I 87r 2 I , 8 T T 2 I a b c This makes the Hamiltonian linear in its constants and easier to deal with mathematically. The rigid rotor Hamiltonian now becomes, in units of frequency: - A J a + B J b + C J c ( 2- 3 ) It is customary to categorize types of molecules according to the following Theory / 18 five relationships between their principal moments of inertia: 1. Linear molecule I =0; 1=1 a b c 2. Spherical top I = L =1 a b c 3. Prolate symmetric top I <I =1 a b c 4. Oblate symmetric top I =1, <I a b c 5. Asymmetric top I <L <I a b c Notice that because I must be the smallest moment of inertia, I, the next largest and so on, there are two different kinds of symmetric tops: the prolate and the oblate. It is possible to designate the x, y, z axes to the a, b, c axes in six different ways, or representations. Each representation indicates how the axes have been designated and whether the labelling has been cyclic in a righthanded (r), or lefthanded (1) sense. For example: r the I labels z t o a , x t o b , y to c the ir" labels z t o b , x to a, y to c the III labels z to c, x to a, y to b r r r The two most commonly used representations are I and III . I is usually used for a prolate type molecule because the "a" axis is associated with the symmetry axis in the prolate symmetric top limit and III is usually used for an oblate type molecule for a similar reason. The representations are usually used in the above way because it leads to the off diagonal matrix elements of the rotational Hamiltonian being smaller than if another representation was used. Nonetheless all representations are equally correct mathematically. a Theory / 19 For symmetric tops, closed form expressions for the rotational energies of a rigid rotor can be found for: H R | J , K , M > = E R | J , K , M > (2.4) For example, E R for a prolate symmetric top is (2): E R = BJ(J+1) + ( A - B ) K 2 (2.5) The symmetric top wavefunctions used are denoted | J , K , M > where J is the quantum number for the total rotational angular momentum and can be zero or any positive integer. K is the projection of the total rotational angular momentum along the symmetry axis of the molecule, in the molecule fixed coordinate system. It can have integral values from — J to J . M is the space fixed component of the total rotational angular momentum, also having integral values from — J to J . However when there is no external electric field it is not possible to determine a value for M (2). For an asymmetric top it is not possible to obtain closed form expressions for the energy levels. They must be determined by generating a matrix with elements of the form: < J ; K ; M , | H R | J , K , M > (2.6) and then diagonalizing it. It turns out that the only non-zero matrix elements are the diagonal Theory / 20 elements: < J,K,M| H R | J,K,M> and the off-diagonal ones: <J,K±2,M| H R | J,K,M>. These elements in the I r representation are (3): <J,K,M| J,K,M> = (I1£)J(J+1) + (A-(2J£))K 2 (2.7) <J,K±2,M| J,K,M> = )-K(K±1 ) ] x (2.8) [J(J+1)-(K±1)(K±2)]} 1 / 2 Comparing equation (2.5) with (2.8) it can be seen that in a symmetric top levels with the same | K| are degenerate and that when the molecule becomes asymmetric this degeneracy is lifted. Before the days of computers, when this theory was developed, various methods were worked out to simplify the diagonalization of this matrix. This has led to a whole host of parameters and methods of diagonalization which today can thoroughly confuse the newcomer as to what is really going on. One must keep in mind that the basic goal is to diagonalize the matrix made up of the elements written down in equations (2.7) and (2.8). The diagonalization of this matrix can be simplified by creating basis functions that belong to one of the symmetry species of the symmetry group of the Hamiltonian. The asymmetric rigid rotor Hamiltonian is symmetric in D , while the symmetric top wavefunctions belong to the continuous two-dimensional rotation group D^. New basis functions that belong to the group are generated from the symmetric top wavefunctions by performing a special unitary transformation on them, using the Wang matrix (4). The new basis functions Theory / 21 created are linear combinations of the symmetric top basis functions. A consequence of having created basis functions that belong to the group is that the Hamiltonian matrix partitions into four submatrices. Each one transforms as one of the symmetry species of the D 0 group: A, B , B, , and z a D B (5). c Since the Hamiltonian matrix has now been factored into smaller matrices it is easier to diagonalize. The resulting eigenvalues are the energies of the rotational levels and the eigenfunctions are linear combinations of the new asymmetric basis functions. These eigenfunctions can then be used to calculate line strengths, Jacobians, etc. Recalling that for a symmetric top the energy levels are labelled using the quantum number K, which is the projection of the angular momentum on the symmetry axis, it should be apparent that this quantum number will no longer be a good one, once there is no symmetry axis. This has led to other ways to label the energy levels. The most unambiguous (and consequently most common) method used is the "K K " scheme, after King, Hainer and Cross (6). a c Here K is the | K| the level would have in the prolate symmetric top limit a and Kfi is the | K| in the oblate symmetric top limit. An older, fairly common method is to use r where r =K — K . This method although less clear is a a c more convenient way to label the asymmetric top wavefunctions, e.g. |J,r,M>. Two parameters seldom used today in the actual diagonalization of the rotational matrix are: the Ray asymmetry parameter, K, (7) where: K = (2.9) Theory / 22 K varies from — 1 to +1 as the molecule varies from a prolate symmetric top to an oblate symmetric top. K is often quoted to give one an idea of how asymmetric a molecule is. The other, the Wang asymmetry parameter, b , (4) P is defined as: bp varies from 0 to -1 as the molecule changes from a prolate symmetric top to an oblate symmetric top. b^ is used in the analysis of the nuclear quadrupole coupling of the molecule (section 2.5). As one knows, molecules are not rigidly rotating bodies but are really masses joined by bonds that stretch and bend as the molecule rotates. At low values of J these distortions caused by centrifugal forces are small and the rigid rotor Hamiltonian does a good job of predicting the transition frequencies. However for higher values of J the distortions of the molecular structure become greater as the molecule is now rotating faster. These changes in the moments of inertia shift the rotational transition frequencies away from those predicted using the rigid rotor Hamiltonian, by a significant amount, sometimes as much as thousands of MHz for asymmetric molecules. To correct this the Hamiltonian is modified by adding a centrifugal distortion term, H N , to the rigid rotor Hamiltonian, H R . The new Hamiltonian, b C-B (2.10) P 2A-B-C H,p — H R + H. D (2.11) Theory / 23 Much work has been done to derive a satisfactory H ^ . One non-rigid rotor Hamiltonian, developed by Kivelson and co-workers, has the form (8,9,10): H _ = A * J 2 + B ' J ? + C ' J 2 + -H-LT' . T a b c 4 a (2.12) where the T ' are called quartic centrifugal distortion constants because the angular momentum terms they describe are raised to the fourth power, and a, |3 can be a, b, c. The rotational constants A', B', C are slightly different from those of the rigid rotor because they now have small contributions from distortion. There are various other forms of (2.12), such as Nielsen's rotational Hamiltonian (11) which uses different linear combinations of the rotational constants and distortion constants, but is entirely equivalent. In all forms of the first rotational Hamiltonians developed to account for centrifugal distortion there are six quartic distortion constants. However in 1966 Watson showed that it is possible to determine, at most, only five quartic asymmetric rotor distortion constants from the analysis of a rotational spectrum, regardless of the centrifugal distortion Hamiltonian being used (12,13). In the same papers he showed how to reduce the number from six to five, by creating new linear combinations of the r's. He developed two different sets of new distortion constants. The first one was the A reduction Hamiltonian. It is relatively simple to use because its matrix elements depend on J, K and M in exactly the same way as those of the asymmetric rigid rotor (Table 2.2). Problems develop when using this reduction when the molecule is only slightly asymmetric. Some of the distortion constants are defined with terms in their Theory / 24 denominators of "B —C", in the I representation, which become very large when the molecule is only slightly asymmetric. This can cause some of the constants to become indeterminate and for there to be large correlations between them. At the worst this will result in a lack of convergence of the least squares refinement. Therefore Watson developed a second reduction called the S reduction, which uses a different linear combination of the distortion constants. It is specifically for use in the analysis of very slightly asymmetric molecules. It is more difficult to diagonalize this Hamiltonian matrix because it is usually pentadiagonal and, at worst can be heptadiagonal, (Table 2.2). The Hamiltonians, both the A reduction and S reduction, are shown in Table 2.1. Again the rotational constants, A, B, C are not exactly the same as those of the rigid rotor but have contributions from centrifugal distortion. As well there are contributions from vibration and to a lesser degree, electron-rotation interactions (14). As a result, the constants include an averaging of the vibrations of the particular vibrational state and vary from one vibrational state to another. For this reason the experimentally determined constants are called effective rotational constants for the particular state, which in microwave spectroscopy is usually the ground state. So far it has been assumed that the five quartic distortion constants can always describe the distortion adequately. For heavier molecules and/or ones that have only had low J transitions measured, this assumption is correct. However as the molecule gets lighter and/or higher values of J are measured the distortion becomes greater and the so called sextic centrifugal distortion constants are required to fit the data properly and accurately predict new line frequencies. These so called "sextics" are higher order corrections to the distortion and Theory / 25 describe angular momentum terms that are raised to the sixth power. These sextic distortion constants have been included in the expressions for the Hamiltonians in Table 2.1 and the matrix elements in Table 2.2. The energies of the rotational levels including distortion are calculated in the same way as for the asymmetric rigid rotor. 2.2. ' THE VIBRATIONAL HAMILTONIAN The total vibrational energy of the system is expressed as a sum of the kinetic energy and the potential energy, so the vibrational Hamiltonian, Hy, is written as: Hy = T + V (2.13) where T and V are, respectively, the kinetic energy operator and the potential energy operator. In the simple harmonic oscillator model of vibration, the normal modes, or "vibrations", are considered to be independent and consequently their individual energies can simply be added together to get the total energy. The potential energy operator V is merely a multiplying one so that V equals the classical potential operator V, that is: V = 1 L X k Q k ( 2 - 1 4 ) where the are the normal coordinates and k labels each mode. The X^ are force constants of the normal coordinates and are related to the classical 2 2 frequency of vibration, v j, by: = 4TT (*'cJ)J5- Similarly the kinetic energy Theory / 26 operator T comes from the classical kinetic energy operator T, where T is expressed as: T = \ (2.15) and the are time derivatives of Q^ . However in this case the time derivatives must be replaced by a differential operator so that T becomes: ,2 .2 T = - (2.16) 8ir 9Q£ This leads to the expression for the vibrational wave equation being: 2 2 H^/ = - A _ + { ZXkQ2<// = (2.17) 87T 9Q k where </  is the total wavefunction of the vibrational coordinates and W is the total energy. Because there are no cross terms in the expressions for kinetic and potential energy when using normal coordinates, it is possible to express the wavefunction as a product of wavefunctions, x//^, each of which is a function of only one normal coordinate Q^ , e.g. '/'^ (Q^ )- As a result the total energy becomes a sum of individual energies, W^ , i.e. ^ = rty/k ; w = z w k Each solution to the wave equation in (2.17) gives an eigenfunction which is associated with a quantum number v, giving a (^V), . v labels the vibrational Theory / 27 state and can be any positive integral number. The solution for (4*^)^ is given by: ^ V ) k = N v e x P ( I ^ k Q k ) H v ( ^ k / 2 Q k ) ( 2 - 1 8 ) where N is a numerical normalizing factor, 7, is a constant of the system; A V2 4 7T 7^ = — ^ " ^ c i ^ k a n (* ^ v *S a termite polynomial. The Hermite polynomial 1 is a function of T^Q^ which varies with the value of v; for example H 0 = 1; H,=27*Qk; H 2=4( 7*Q k) 2-2 etc. The eigenvalue, or energy W associated with the. eigenfunction i / / V is: W v = ( v + I ) h " c l ( 2 - 1 9 ) 2.2.1. Selection Rules for Rotational and Vibrational Transitions The selection rules for both a rotational transition and a vibrational transition are determined by considering the interaction of the electric field of the radiation, E, with the dipole moment of the molecule, jtx. Expanding H^(t) in terms of cartesian coordinates gives: H ^ t ) = - # x E x ( t ) - M y E y ( t ) - M z E z ( t ) (2.20) where X, Y, Z are with respect to space fixed coordinates, and E is the magnitude of the electric field. In most experiments the radiation of the electric field is polarized in one direction and is usually labelled the Z direction. This leaves Theory / 28 H ^ t ) = - M z E z ( t ) (2.21) Since is defined with respect to space fixed coordinates, to determine when a molecular transition can occur it must first be linked to the molecule fixed coordinate system. This is done using direction cosines, giving: "z = *Zx«x + *Zy"y + *Zz"z ( 2 " 2 2 ) where $2 X' ^ Zy' ^ Zz a r e direction cosines linking the space fixed Z direction to each molecule fixed coordinate x, y, z. MX, Uy M Z are the components of the permanent dipole moment in the molecule fixed system. Expanding equation (2.22) in a Taylor series expansion gives: *z = z [ ( * i > o * z i + E ( — > o Q k * z i + ( 2- 2 3 ) 9Q k a 2 3 Uz where i = x, y, z. .The zero subscript indicates that the parameter is determined at the equilibrium position. The selection rules are determined by using the total expanded expression for jig in the transition moment integral. This integral is used to evaluate when the intensity of a transition will be non-zero — or "allowed". Because selection rules for both rotational and vibrational transitions are to be determined the wavefunction of interest is \// = *Pv^r> where denotes the vibrational wavefunction and \p ^  is the rotational wavefunction. Ignoring second order and higher terms in equation (2.23) the transition moment integral becomes: Theory / 29 L[<W I (M- ) > + <^'0 ,|Z( r v r 1 1 o Z i 1 v r v r 1 ) Q. 0„ • I ^ > ] (2.24) Expression (2.24) can be separated into the following: 9M, (2.25) . . . x < ^ | <j>zi |^r>] Examining this expression closely the selection rules can be determined. The first part of equation (2.25) indicates that because the wavefunctions are mutually orthogonal must equal for it to be non-zero. This describes a pure rotational transition because ^ v = 0" indicates there has been no change in the vibrational level. Looking at the remaining components in the first part of equation (2.25) in more detail gives the rotational selection rules. Using | J,T,M> to describe the rotational wavefunction 0^ and expanding the integral in terms of x, y, and z gives the expression: A transition occurs when one of the three components of equation (2.26) is non-zero. For this to happen which indicates that for a molecule to have a pure rotational spectrum it must have a permanent dipole moment. Simultaneously the matrix element: <J,'T,'M' | <t>^\ J>T ,M> must be independent of coordinate system, that is be totally symmetric. In the absence of an external Mx<J',r,,M' | 0 Z x | j , r , M > + M y < J \ r ' , M ' | 0 Z y | J,r,M> + M z < J \ r \ M ' |4> Z z|J, r,M> (2.26) Theory / 30 electric field this occurs when: AJ = 0, ±1 and AM = 0. To determine the selection rules for r or K K the D 0 character table must be examined. It a c 2 turns out that both the direction cosines and the asymmetric rotor basis wavefunctions belong to this symmetry group. When x, y, and z have been transformed to the principal axis system, the resulting selection rules for K K a c are: Allowed transitions Type of between K K levels transition a c if M * 0 ee — eo a-type a oo — oe if M^^O ee — oo b-type eo — oe if ee — oe c-type eo — oo where e stands for an even value of K or K and o for an odd value. a c It must be emphasized that a given transition can be allowed by only one component of the dipole moment, either n , ju, or n . Quite logically if it a D c is due to u it is called an a-type transition, to ju, , a b-type transition, etc. a b A transition is also described by the change in J. If A J = +1 it is a R branch line, if AJ = 0 it is a Q branch line and if AJ= —1 it is a P branch line. The second part of equation (2.25) gives the vibrational selection rules. The component ( a n ) indicates that a molecule can absorb infrared radiation d y k ° only when, for a given vibration, there is a change in the dipole moment, i.e. Theory / 31 ( - n ) ^0. Another way of looking at this is to say that M. must be able O 1 to oscillate at the frequency of the vibration. Similar to the rotational selection rules the matrix element < ^ | | ^ v > must also be totally symmetric. When the wavefunctions are considered as simple harmonic a property of the Hermite th polynomials dictates that all the modes except the k state must be identical, th and in the k state itself the vibrational quantum number can change by only one, i.e. Av^=±l. This describes the so called restricted "selection rules" for infrared absorption, where the derivation is dependent on the two assumptions . (1): 1. The molecular vibrations are simple harmonic implying that the normal modes are separable. 2. The higher terms in the Taylor series expansion of the electric dipole moment are negligible. Relaxation of these two assumptions gives the general selection rules and allows for overtones and combination transitions. This means that the wavefunctions are now allowed to contain anharmonicity and will no longer possess the special properties of a Hermite polynomial. Anharmonicity can enter the expression for the wavefunctions in two ways, either as mechanical anharmonicity or as electrical anharmonicity. Mechanical anharmonicity means that the molecular vibrations are no longer simple harmonic, i.e. there is a cubic term in the expression for the potential energy, which means the spacing between the energy levels is no longer equal. This kind of anharmonicity is believed to be the most predominant in allowing for overtones and combination bands. Electrical anharmonicity occurs when it is not valid to assume that the higher terms in the Taylor series expansion of the Theory / 32 electric dipole moment are negligible. For example this means in the expansion 2 of (equation 2.23) there will be a term with in it that can no longer be ignored. The integral associated with this vanishes except when Av^ = 0, ±2. This allows for infrared absorption of two times the fundamental frequency v^, labelled as 2i>. . These are called overtones and involve transitions between the k ground state vibrational level v = 0 with the second excited vibrational state of that mode v = 2. The introduction of anharmonicity, either mechanical or electrical, into the transition moment integrals also allows for the absorption of infrared radiation at frequencies corresponding to the addition of two fundamental vibrations, that is c, =0-»l and v. = 0-*l or v, +v.. These are called k J k j combination bands. 2.3. MOLECULAR STRUCTURES The analysis of a microwave spectrum not only gives the rotational energy diagram of a molecule, but also provides information about its structure. This is because the rotational constants are inversely proportional to the principal moments of inertia which are dependent on the positions of the atoms, as indicated by equation (2.2). Two good discussions on structure determination in the gas phase are given by Robiette (15) and by Gordy and Cook (16). The article by Robiette looks at two methods of determining gas phase molecular structures, namely microwave spectroscopy and electron diffraction, whereas Gordy and Cook deal only with how to calculate structures using information obtained from a microwave spectrum. In this work all structural parameters were determined from microwave spectroscopy for only planar asymmetric tops, so the following Theory / 33 only discusses structure determination from this kind of information. There are four different kinds of structures that can be determined from microwave spectra, although for various reasons it is seldom possible to calculate all four kinds for a given molecule. The most meaningful, and yet most difficult structure to obtain experimentally is the equilibrium, or r , structure. One thinks of this structure as being one in which the molecule is frozen at the bottom of its potential energy curve, and consequently there are no effects from vibration. To the extent that the Born-Oppenheimer approximation is valid, this structure is independent of isotopic substitution. It is the most useful structure from a theoreticians point of view because it is the one obtained from ab initio wavefunction calculations (15). Unfortunately to determine it experimentally for a polyatomic molecule requires information about many vibrational states of many isotopic species. The equilibrium structure is calculated using equilibrium rotational constants. These are obtained by accounting for the effects from vibration. For a diatomic molecule, where there is only one rotational constant, this is expressed as: B e = B v + a(v+l) - 7 ( v + i ) 2 + ... (2.27) where B is the equilibrium rotational constant, and B is the effective rotational e v constant for a given vibrational state v. v labels the vibrational state and can be any positive integral number. a and 7 are constants which give the vibrational dependence of the rotational constant. Two more similar equations, Theory / 34 for A g and C^ , are written for a polyatomic molecule. Since equation (2.27) converges quickly it is sufficiently accurate to keep only those terms linear in v. Doing this yields an expression for each rotational constant of the form: G v = G o - Za^(v k+ ^) (2.28) where G stands for each of the rotational constants A, B, C. v, is the k th vibrational quantum number and d^ is the degeneracy of the k normal mode. Q. The are the vibration rotation constants and are independent of vibrational state. To calculate the equilibrium rotational constants from the ground state rotational constants, equation (2.28) becomes: G e = G o + L4 TT ( 2 - 2 9 ) Q However to calculate all the one needs the rotational constants of all the v=l vibrational states, as well as those of the ground state. Additionally for a planar asymmetric molecule one needs the rotational constants of at least (N —2) different isotopic species in all the above mentioned vibrational states, (where N is the number of atoms in the molecule). For an asymmetric triatomic molecule, where information about only two isotopic species is needed, this involves determining at least sixteen rotational constants! Needless to say an equilibrium structure is not often determined because of the large volume of data that must be collected. As well it is seldom possible to measure the rotational spectrum of all the excited vibrational states using only microwave spectroscopy because the Boltzmann distribution of molecules in the upper states is too small to produce a measurable spectrum. Therefore one must measure an Theory / 35 infrared spectrum of the molecule to get the rotational constants of the higher vibrational states. In determining an equilibrium structure one is trying to obtain bond distances and angles that have had all effects due to vibration, electron-rotation interaction, and centrifugal distortion removed. In other words the molecules would be considered essentially rigid. If the molecule is planar the following relationship should be true, since all the c coordinates of each atom are zero: or (2.30) This indicates that for a planar molecule the moments of inertia are not all independent. For equilibrium rotational constants equation (2.30) should be true. However for other rotational constants, such as those obtained from the analysis of a rotational spectrum or a high resolution vibrational spectrum, there is a small deviation from this relationship, called the inertial defect. It is caused by the fact that the molecule is not rigid. For example, effective rotational constants contain effects from vibration, as well as electron-rotation interactions and centrifugal distortion. The inertial defect, A, is defined as: (2.31) where v indicates the vibrational state the moments of inertia have been Theory / 36 determined for. The inertial defect can also be expressed as a combination of effects due to harmonic vibration, A ., , electron-rotation interactions, A . , and vib elec centrifugal distortion, A , as follows (14): C6T1X A = A ., + A , + A , (2.32) vib elec cent where the harmonic vibrational contribution is usually, by far, the largest. In the discussion on equilibrium structures it was pointed out that it is usually difficult to obtain rotational constants for all the excited v = 1 vibrational states. Consequently one is often faced with having to determine a "good" structure from ground state rotational constants. At present the best possible structure one can obtain from only ground state rotational constants is the average, or r^, structure. Unlike many other structures, it has a well-defined physical meaning. It gives the mean positions of the atoms in the ground vibrational state. An average structure can be calculated for a vibrational state other than the ground state and in this case is v denoted r , where v indicates the vibrational state. The rotational constants z used to determine an average structure in the ground state are calculated from: d k G G = G + L - r£ a, (harmonic) (2.33) z o 2. k Q where the of equation (2.28) have been separated into a harmonic part and an anharmonic part as: G G G = a k (harmonic) + a ^  (anharmonic) (2.34) Theory / 37 Only the harmonic part is used to calculate an average rotational constant Q G = A , B , C . However to get the a, (harmonic)'s it is necessary to know Z Z Z Z -K or be able to calculate the molecule's harmonic force field. Since the inertial defect is caused mainly by effects of harmonic vibration, the inertial defects of average moments of inertia are usually very close to zero. As the average structure still has effects due to anharmonic vibration in it, it is still not isotopically independent. This problem has been dealt with in great detail by Kuchitsu and co-workers (17,18,19). Using the following equation they calculate an estimate of the equilibrium bond distance: (2.35) where r is the average bond length, r is the equilibrium bond length and the Z 6 last two terms account for anharmonicity. "a" is a Morse anharmonicity 2 parameter for the given bond (20), e.g. (O —CI), u is the zero-point mean square vibrational amplitude of the bond and K is the perpendicular amplitude correction 2 for that same bond. Both u and K are calculated from a harmonic force field (21). To date only a correction to the bond lengths has been suggested, but it is felt that these variations are more significant than the variation between equilibrium and average bond angles. To determine a structure from these average rotational constants, the bond lengths and angles are fit to the rotational constants in a least squares fitting routine. The change in bond length caused by isotopic substitution is used to improve the structure by inserting the change, 5r z > into the program as a constant which is tacked onto the value of the parent molecule at the Theory / 38 appropriate time. For example the difference in length between an ^O — 3^C1 bond and an *^0 — 3^C1 bond, 5r (^O — 3^C1 ^O — 3^C1) is calculated using: 5r = | a 5 ( u 2 ) - 5K (2.36) z z 5r e is zero because there should be no change in the equilibrium bond length after isotopic substitution. This procedure often yields a satisfactorily precise structure. Modifying the rotational constants by accounting for electron-rotation interactions and centrifugal distortion will sometimes further improve the structure, (section 4.5). For those situations in which there just is not enough data to calculate average rotational constants (section 2.4), one can calculate what is called an effective, or r , structure for the ground state. This structure is determined using the effective ground state rotational constants determined from the experimental measurements. As this structure is calculated from moments of inertia which have all the above mentioned contributions in them it is only a first approximation. One last structure that can be calculated when enough isotopic substitutions have been made, is the substitution, or r , structure. This ' s structure is determined using equations worked out by Kraitchman (22). In this method, the coordinates of an atom are determined from changes in the moments of inertia caused by isotopic substitution. For a planar asymmetric top, Kraitchman's equations for the two coordinates of the substituted atom, a and Theory / 39 are: 2 I' -I a b (2.37) a s I ' -I a where the I' are the moments of inertia of the substituted molecule and I of g g the unsubstituted, or parent molecule. The parent molecule is usually the one in which all the isotopes in it are the most abundant, n is the reduced mass for the substitution, defined by: where M is the total mass of the parent molecule and Am is the change in mass after isotopic substitution. The position of each atom is obtained by making a substitution at each site. Costain has shown that for a diatomic molecule this structure is a better approximation to r^, over the effective, r^, structure because most of the effects caused by vibration, which are usually similar in each species, are cancelled out when the difference in the moments of inertia is used (23). This has been assumed to be true for polyatomic molecules as well. Unfortunately it is not always possible to calculate a substitution structure because some atoms, such as fluorine, phosphorus and iodine have no stable isotope. Costain has also shown that the substitution method cannot reliably estimate atomic coordinates that are less than 0.15A (24). In either of the above two cases the position of the atom can be determined using the center of mass conditions: Theory / 40 Em. a. = Em.b. = Em.c. = 0 (2.39) i i i i i i or the product of inertia conditions: Em^a^c^ = Em^b^c^ = 0 (2.40) 2.4. ' HARMONIC FORCE FIELD CALCULATIONS In order to calculate a vibrational harmonic force field it is nearly always necessary to have some vibrational wavenumbers for the molecule. They provide direct information about the force constants, because the two are directly related as can be seen in the following matrix equation: where F is the force constant matrix, A is the diagonal matrix containing the squares of the vibrational wavenumbers, G is the inverse of the matrix that T — 1 relates the momentum to the kinetic energy (2T=S G S), and L is the matrix that relates the normal coordinates Q to the internal coordinates rl (R=LQJ. The force constant matrix F, in equation (2.41), that one usually determines is a quadratic force field often referred to as a general valency force field (GVFF). In it the diagonal elements are the principal constants of the bond stretches and angle changes, while the off-diagonal elements are the interaction force constants between each internal coordinate. In general the interaction force constants are smaller than the principal ones and when there are too little data to determine all the force constants some of these are set equal to zero. GFL = LA (2.41) Theory / 41 Unfortunately, for all polyatomic molecules, the vibrational wavenumbers alone do not provide enough information to calculate all the force constants. Consequently additional information must be supplied to determine more of the force constants. This extra information is provided from other experimental data such as: i) vibrational wavenumbers for other isotopes of the molecule, ii) centrifugal distortion constants, iii) Coriolis coupling coefficients, and iv) inertial defects. A problem, often encountered with molecules that contain an H atom is that the experimental wavenumbers themselves actually include a significant amount of anharmonic vibration. Often there is little that can be done about this problem, (section 4.4 and 4.5). In many cases the most convenient additional data to use are the centrifugal distortion constants, since they are readily available from the analysis of the rotational spectrum. A relationship has been derived by Kivelson and Wilson which relates their distortion constants, T'S, to the inverse force constants, as shown below (10): Ta(h6 = e x e e L [ Ja<3] k ( f ~ ' ) k j ' J 7 S * j ( 2 " 4 2 ) a 0 7 5 e — 1 where the I q are the equilibrium principal moments of inertia, the (f are the elements of the inverse harmonic force field matrix and the [ J a ] , are the ap k partial derivatives of the components of the moment of inertia tensor with th respect to the k internal coordinate. They are evaluated at equilibrium: < J « V k = ' T B * ' . ( 2 - 4 3 ) Theory / 42 In practice one seldom has the equilibrium rotational constants, (section 2.3), so effective ground state rotational constants are used. At the same time, the distortion constants determined by today's spectroscopist are almost always those of Watson. Therefore it is necessary to convert Watson's distortion constants to Kivelson and Wilson r's. The necessary information to make up a matrix which will do this conversion for either A or S reduction distortion constants is given in Table 2.3. The force constants are determined by fitting them to the vibrational wavenumbers and centrifugal distortion constants using a least squares fitting routine. Despite the extra information provided by the centrifugal distortion constants it is still not always possible to determine all the force constants. This can occur if it turns out that the symmetry of the molecule is such that there is a large number of force constants in each symmetry block. In these cases one must use assumed values for some of the force constants, obtained for example from theoretical ab initio calculations (section 5.3). If the problem of lack of data is quite severe one sometimes has to resort to determining a simple valency force field, SVFF, where all the off-diagonal force constants are set equal to zero. Another solution is to use the UBS force field (developed by Urey, Bradley and Shimanouchi), where the off-diagonal interaction constants are defined as repulsions between non-bonded atoms. The result is a reduction in the number of force constants to be determined. When considering how much data are available for the least squares refinement, it is important to realize that for a planar molecule not all the centrifugal distortion constants are independent. If there are five experimental distortion constants only four are independent (25). Similarly not all the Theory / 43 vibrational wavenumbers are independent. For the first isotopic species considered all the wavenumbers are independent, however because of the Teller-Redlich product rule wavenumbers of additional isotopic species are not all independent (26). Adding up the number of independent pieces of data gives the maximum number of force constants that can be determined from the data, although it is seldom possible to determine this maximum number. 2.5. NUCLEAR QUADRUPOLE COUPLING Nuclear quadrupole coupling arises from the interaction of a nuclear quadrupole moment with the electric field gradient at that nucleus caused by external charges from the electrons and other nuclei. For this interaction to take place both the nucleus and the electric field must have a non-spherical distribution of charge, nuclear and electronic respectively. If just one of them has a spherically symmetric charge distribution, no interaction can occur. Since atoms with nuclear spins of 0 or 1/2 have a nuclear charge that is spherically symmetric, no nuclear quadrupole coupling is observed for these nuclei. The physical effect of the interaction is that a twisting torque is put on the nucleus which makes it try to align its spin moment along the electric field gradient. As a result the nuclear spin axis precesses about the direction of the resultant field gradient. The precessing nuclear spin moment couples with the molecular rotational angular momentum to split the rotational energy levels to produce nuclear hyperfine structure. Since, in gases, the interaction varies from one rotational state to another, the magnitude of the resulting nuclear quadrupole splitting also varies for each transition seen in a pure rotational spectrum. Theory / 44 Mathematically, the interaction is expressed as: P = 1 + D (2.44) where ^  is the nuclear spin angular momentum, ~3 is the rotational angular momentum, and F is the resulting total net angular momentum. F, J, and I are the quantum numbers associated with "F, ~3, and ^  respectively. F can take rotational level into 21+1 levels. Because the nuclear quadrupole coupling energies are small relative to rotational energies of the asymmetric rotor, the quadrupole Hamiltonian, H„, is solved as a perturbation to the total rotational Hamiltonian, H,p. For most molecules taking the perturbation to first order is more than adequate. Exceptions to this approximation are found for those nuclei with large quadrupole moments, e.g. iodine. First order perturbation energies are obtained from an average of the perturbing Hamiltonian, Hn, over the unperturbed state, so that: where El. is the first order quadrupole energy and 0— are the zeroth order wavefunctions of the rotational Hamiltonian, Hp discussed in section 2.1 (equation 2.11). As a result, even though F is now the total angular momentum, J and I are still basically good quantum numbers. This means the wavefunctions of the hyperfine energy levels can be represented as | F,I,J>. The first order quadrupole Hamiltonian, Hn, for a molecule containing only on values from | J +11 to | J — 11 . This means the interaction has split each E (1 ) Q (2.45) Theory / 45 one quadrupolar nucleus can be expressed as (27,28): HQ = 2 l ( 2 I - e i Q ) q j J ( 2 J - l ) [ 3 ( I * J ) 2 + " l 2 j 2 ] ( 2 - 4 6 ) Since I and J are still being considered good quantum numbers: I.J = F 2 - J 2 - 1 2 ) (2.47) At the same time, only taking the perturbation to first order means that the resulting matrix <F,I,J| H„| F,I,J> is diagonal, and the energy is easily determined to be (27): eQq 7 o EQ = 2 I ( 2 I - 1 ) J ( 2 J - 1 ) [4 C { C + 1 ) " + (2-48) where C = F(F+1) - J(J+1) - 1(1+1) eQ is the charge weighted nuclear quadrupole moment that stays constant for a given nucleus, and reflects its asymmetric charge distribution, q is the electric J field gradient along the space fixed Z axis, that is, when M=J. For an asymmetric rotor in the basis set | J,T,M = J > : 2 q = < J , r , M = J , I — ^ 1 J , r , M = J > (2.49) J 3 Z 2 where V is the electronic potential at the quadrupolar nucleus and Z is in the space fixed system. The overall expression indicates that qj is the average of the second Z derivative of the electronic potential. Since the molecule is rotating when the measurements are being taken it Theory / 46 is necessary to express eQqj with respect to the molecule fixed axis system, as shown in the following equation (27): e Q S j = ( 2 J + 3 ) ( J + D { x a a < j a > + x b b < J b > + * c c < J c > } ( 2 ' 5 0 ) where the x (g = a, b, c) are called the nuclear quadrupole coupling constants and are defined with respect to to the molecule fixed axis system as: *99 " e Q < ^ < 2 ' 5 1 ) 2 2 <J > is the average of J in the asymmetric rotor basis, which is also in the molecule fixed system. Because the charge giving rise to the field gradient is considered to be zero over the total nuclear volume, Laplace's equation holds for the coupling 2 constants; where Laplace's equation is V V = 0 2 2 2 a z v A a^v x a zv (i.e. 2 + 2 2 = ' 3a 3b 3c Therefore: x a a + x b b + x c c = 0 ( 2 - 5 2 ) and there are only two independent constants. Consequently one can only determine two and these usually are: "x " and "\,u~ X "> for an asymmetric aa DO cc molecule being analysed in the I representation. To determine these coupling constants from experimental data the first Theory / 47 order quadrupole energy is sometimes rewritten as (28): E = f (I , J , F) [ 3<J 2> - J(J+1) + rJ L(<Jg> " W(b ) } ] x a (2.53) P where T J = (X. K~ X )/X (I representation), W(b ) is the Wang reduced DD cc aa p energy (29), the Wang asymmetry parameter and f(I,J,F) is Casimir's function, defined by: f(T 7 F) - 0-75 C(C+1) - I(I-H)J(J+1) f l I ' J ' F ) 2(2J + 3)(2J-1 )I (21-1 ) ( 2- 5 4 ) Using equation (2.53) makes fitting of the nuclear quadrupole constants to the experimental data easier because the fitting is to parameters used in the analysis of the rotational spectrum of the unsplit line frequencies. The selection rules for F and I for hyperfine energy transitions are AF = 0, ±1 and AI = 0. The selection rules for J and K K remain the same a c as was given in section 2.2.1, for the rigid asymmetric rotor. 2.6. THE STARK EFFECT: ASYMMETRIC ROTOR In microwave spectroscopy the Stark effect takes place when an external electric field is applied to the rotating molecules. As the dipole moment of each molecule interacts with the external field, the resulting torque perturbs the rotational energy levels. The Stark Hamiltonian, Hg, used to describe this is: Hg = -7I-E = - E ZMg0£g g = a, b, c (2.55) where E is the applied external field, its magnitude is assumed constant (E) and Theory / 48 its direction is usually taken to be the space fixed Z direction. The are the components of the dipole moment in the molecule fixed system and the a re the direction cosines which link the g axes to the space fixed Z axis. Since Hg < < H^ , (the rotational Hamiltonian), one usually uses perturbation theory to calculate the Stark energy Eg. It is usually sufficiently accurate to take the perturbation calculation to only second order so that the Stark energy can be written as: Eg = Eg1 + E | (2.56) 1 2 where Eg and Eg are the first and second order Stark energies, respectively. For linear or symmetric top molecules it is possible to obtain closed form expressions for Eg, but in general, this is not possible for an asymmetric top molecule. As in previous sections the following discussion deals with the Stark effect only as it pertains to the asymmetric rotor. The matrix elements of the perturbation are generated using the asymmetric rigid rotor basis functions |J,T,M>. Again this leads to determining which of the matrix elements <J',r',M' |02g|j,r,M> are non-zero, which will be when the matrix element is totally symmetric. Because 0 ^ in the asymmetric rotor is not totally symmetric this means that for the matrix element to be totally symmetric the two connecting basis functions | J,r,M> and |J',T',M'> cannot be of the same symmetry species. Therefore assuming the energy levels are all non-degenerate, the two connecting basis functions must be two different energy levels. Because the first order Stark effect (at least for a Theory / 49 symmetric top molecule) is between the same two energy levels, there is no first order Stark effect energy for an asymmetric top molecule which has no degenerate energy levels. (If the molecule has degenerate or near degenerate energy levels this is no longer true and a first order Stark effect appears, as will be discussed later). Consequently the perturbation must be taken to second order to determine a Stark energy. This leads to the total energy of the perturbed rotational levels being (30): E R ( J , T , M ) = E ° ( J , T ) + £ E g ( J , r , M ) (2.57) where E R(J,T ,M) is the total rotational energy, E^JjT) is the unperturbed 2 rotational energy, and the last term is the second order Stark energy, Eg. The th expanded expression for the g component is (30): 2 7 J > <J,T,M|0- |J\r',M> 7 E 2 ( J , r , M ) = ^E2 L' | Q 2 9 Q | (2-58) E _ E T where the Ej ^  and Ej' r' are the unperturbed energies of the levels | J,r > and | J,V' > respectively. The summation is only over the primed values of J and T, because there is no non-zero matrix element connecting an energy level to itself. Since the selection rules for J are: A J = 0, +1 equation (2.58) can be expanded to give (30): Theory / 50 Eg(J,r,M) - M 4 J 2 ( 4 J 2 - 1 )' < J , r | 0 z J j - 1 ,r'> E J , r E J - 1 , r ' M 2 s <J.r,\*Zq\J,T',> 2 4 J 2 ( J + 1 ) 2 E ° - E ° . (2.59) ( j + i r - M' 4 ( J + 1 ) ^ ( 2 J + 1 ) ( 2 J + 3 ) <J,r 0 J+1,r'> •2 5 5 1 1 E J , r E J + 1 , r ' Except for very low values of J it is tedious to evaluate the matrix elements in equation (2.59). To simplify the calculations the matrix elements are related to line strengths in the following way: (30) |<J,T, | 0 „ J J - 1 ,T'>| 2 = 4 J X ( J , T ; J - 1 ,T' ) (2.60) g | < J , r | 0 Z g | J , r ' > | 2 = l ^ ^ X g ( j , r ; J , r ' ) | < J , T | « „ | J + 1 , T ' > | 2 = 4 ( J + 1 ) X ( J , T ; J + 1 ,T') where X (J,r ;J+ l,r') is the line strength of the given energy level. These line strengths can be found in extensive tables (31) and are nearly always calculated in asymmetric rotor diagonalization programs. It can be seen from equation (2.58) that if two connecting rotational levels are very close in energy the denominator becomes very small and the second order perturbation treatment breaks down. These near degeneracies can Theory / 51 occur quite frequently in slightly asymmetric top molecules, and it is now necessary to use an "exact" solution for them. The "exact" solution is used only for the perturbation between the two levels that are nearly degenerate. For the remaining levels - which are not nearly degenerate - the regular second order treatment given in equations (2.57) and (2.58) is used to calculate their contributions to the Stark effect. The nearly degenerate level is not included in this summation, instead it is used in an exact solution which involves solving a secular equation of the form: E ( J , r ) En 1 2 En 1 2 E (J',r' ) - e = 0 (2.61) where e is the perturbed energy to be calculated, F^j ^  ^  is the unperturbed energy of the level in question, ^j>r>) is the unperturbed energy of the other nearly degenerate level, E is the magnitude of the applied electric field and u is the matrix element which connects the two interacting, nearly degenerate states. 12 Solving equation (2.61) gives (32): W(JV) + [t-(Jr>--(JV))2 + * 2,,/2 ± 2 ± U 2 } ^ M 1 2 J ~ E, , < < (2.62) where e + is the perturbed energy for the rotational level under consideration |J,T,> and e_ is the perturbed energy for the other level, |J,V,'>. It can be seen from this solution that if the levels are very close in Theory / 52 energy, such that | E° j ^ ^  - E° j, r ? ) | << l-^M^I' ^hen equation (2.62) can be approximated by: E ? T N+ E ? T i > v e ± - U r ) 2 ( J - T > ± E»]2 (2.63) Now the Stark effect looks as though it is first order because the change in energy of the rotational level is linear with the change in applied electric field. Consequently this is referred to as a pseudo first order Stark effect. When the two quantities | E°j ^ j - E ^ j , T i ) | and l ^ j u ^ l a r e comparable magnitude, the full expression in equation (2.62) must be used, in conjunction with equation (2.57) to calculate the Stark energy. However it can happen that two energy levels are actually degenerate, for example, two = ±5 levels in HOCl. This means equation (2.62) reduces to: e± = E ° ( J , T ) ± £ M 1 2 (2.64) meaning that ±£/x 1 2 = Eg (2.65) It turns out that in this situation n a s the same closed form solution as that for a symmetric top, that is : "12 " JTJm <2'6« and the total energy of the two levels is: Theory / 53 In this case, when the degeneracy is real and not accidental, the Stark effect is in fact truly first order. It is possible for the two levels to connect through the asymmetric $ 7 because although they have the same energy they have different symmetries. This is made clear when the asymmetric rotor Hamiltonian is transformed with the Wang matrix, as the two degenerate levels end up in different submatrices. Equation (2.67) also indicates that in the case of a first order Stark effect the electric field causes all degenerate M levels to split. When the rotational energy levels are non-degenerate and a second order Stark effect occurs, only a partial lifting of the M degeneracy occurs, since in this case the 2 energy contains only M terms. In terms of actual transitions between the rotational levels, the selection rules depend on the orientation of the external electric field E with respect to the electric field of the microwave radiation E(t). In most experimental arrangements E is applied so that it is parallel to E(t). In this situation the selection rule for M is AM = 0. If E is applied perpendicular to E(t), AM= + 1. The latter situation is more difficult to achieve experimentally and is seldom used. The selection rules for J and K K remain the same as for the a c asymmetric rotor. For the purposes of measuring a microwave spectrum the Stark effect is used to detect absorption transitions using a method called Stark modulation, (section 3.1) It is also used as a way to check the assignment of a line. In most cases the transition is between two non-degenerate energy levels and the Theory / 54 rotational energy levels only show a second order Stark effect. This means the effect is small and as the external electric field is increased the Stark components (the perturbed lines) shift slowly away from the unperturbed line. For transitions between nearly degenerate energy levels the Stark components move away rapidly from the unperturbed line when the electric field is increased. This is observed because of the pseudo first order Stark effect described in equation (2.63). Again this can help confirm the assignment of a line, because an inspection of the rotational energy level diagram will show when this effect is expected to take place. An important use of the Stark effect is that it can be used to determine a value for the dipole moment, as was done for propiolamide (34) and hypochlorous acid (35). This is possible because the Stark shift is directly 2 dependent on as indicated in equation (2.58). 2.7. BASIC FITTING PROCEDURES USED The measurement of a microwave spectrum is begun by roughly predicting the transition frequencies, in the frequency range under investigation. To do this it is necessary to have an estimate of the rotational constants. If there are no known values for the rotational constants they can be calculated from structural data. In special situations other methods can be used, as described in section 4.1. It is also usually preferable to have estimates of some of the centrifugal distortion constants for the initial prediction. These can be transferred 35 37 from similar molecules (e.g. those of F C1CO for F C1CO) or obtained from a force field calculation if one has been done. Sometimes a few microwave Theory / 55 transitions have already been measured, as was the case for DOC1 and FC1CO, meaning values for the rotational constants were already available. This of course eliminates having to estimate the rotational constants from a structure. The program used in this work to predict line frequencies used Watson's A reduction Hamiltonian and could take distortion constants up to and including sextics. It performed an exact diagonalization of the Hamiltonian matrix to obtain the eigenvectors. These are used to calculate the necessary Jacobians. A Jacobian element is the change in energy with respect to one of the constants and equals the average of the angular momentum term that constant is 2 4 associated with. Two simple examples are: 9E/9A=<J > and 9E/9AT, = <J >. a. K a This allows the constants to be varied to fit the measured transition energies (lines). Initially, estimated values of the molecular constants are used to start the fitting process. Since the values of these Jacobians are not independent of the constants themselves a few iterations of the fitting process are necessary to get a converged refinement. Three iterations are usually enough. After at least two lines have been measured it is possible to do a least-squares fit to the measured data. Two lines allow only one constant to be fit to, or released, three lines allow two constants and so on. Hopefully the measured lines will have been assigned to the correct transition. If they have, the fit will improve the values of the released constants and all the residuals will be small and somewhere around the experimental error. If there has been a misassignment, the error will be larger than expected and sometimes obviously much too large. With only a few pieces of data a misassignment is more difficult to catch because the program will be trying hard to fit the misassigned line(s) to the constants. Kirchhoff has written an informative paper on the Theory / 56 details of fitting data to the constants and also discusses ways of detecting misassigned lines (36). Different kinds of lines give different information. For example in a prolate asymmetric rotor an a-type, K =0 or 1, P or R branch line will give a information about the rotational constants B and C, but very little about A. If it is possible, b-type P or R branch lines must be measured before a reasonable value of A can be determined. However it has been shown that in some special cases it is possible to obtain a value for A with only a-type lines (37). Initially it is not possible to release the distortion constants but as more and more lines of different transition series are measured (and correctly assigned) it is possible to release them. If many lines have been measured, in particular high J and K , and/or the molecule is quite light it will be possible and 3. sometimes necessary to use sextic distortion constants to calculate the rotational energy levels accurately. For molecules that exhibit nuclear quadrupole coupling it is also necessary to have values for the nuclear quadrupole coupling constants. In some cases these can be found in the literature. If not, coupling constants from an electronically and structurally similar molecule can be used to make the initial prediction of the splitting. If absolutely no values are available quadrupole coupling constants can be predicted by ab initio calculations. Once one or two split lines have actually been found and assigned, a least squares fit can be made to the measured split lines to determine better coupling constants, (i.e. an iterative approach is used to obtain the values of the coupling constants). Theory / 57 TABLE 2.1 HAMILTONIANS - f REPRESENTATION* "T = "R + V " HD" ^ = V + HD" A REDUCTION H R = ^ J a + ^ + ^ H f i ' = " A J J 4 " A J K j 2 j a " V a " " ^ " V ^ b - Jc 2 ) + <•£ ~ 4 ) J l ] «£• - + v 6 + * j K j 4 j a + ^ 4 + *A + 2 ^ J J 4 ( J ^ - & + • J R J 2 ^ < ^ " # + ( Jb " J c ) J a }  + *K<Ja(Jb " J c ) + <4> " S REDUCTION 1 3 = A S J 2 + ^ J 2 + C?J^ + d 2 ( j j * 4" - » / * H J K j 4 j a + H K J J 2 < * HK4 * V 4 ( j 2 - + j 2 ) ,2/ A , T4 N ^ u / T6 ^ T6. '2' + h + J!) + h ( J ° + J!) Hp, includes quartic distortion correction terms, FLy, includes sextic distortion correction terms. a Reference (38). J + = J b ± i J c f r o m reference (39). Theory / 58 TABLE 2.2 MATRIX ELEMENTS - I r REPRESENTATION21 A REDUCTION EK K = < J ' K ' M I ^ I J/K,M> = + ( A - ( ^ ) ) K 2 - A A J 2 ( J + D 2 - A J K J ( J + 1 ) K 2 - A R K 4 + $ J J 3 ( J + 1 ) 3 + <t> J 2 ( J + 1 ) 2 K 2 + <l> J ( J + 1 ) K 4 + <J> K 6 EK,K±2 = <J'K±2,M| I^lJ,K,M> = t ( ^ ) - 6 J J ( J + 1 ) - l 0 R { ( K ± 2 ) 2 + K 2} + 0 a J 2 ( J + D 2 + l t f > J K J ( j + 1 ) { (K±2) 2 + K 2} + l 0 K { ( K ± 2 ) 4 + K 4}] x [ { J ( J + 1 ) - K ( K ± 1 ) } { J ( J + 1 ) - ( K ± 1 ) ( K ± 2 ) } ] 1 / 2 S REDUCTION EK,K = < J ' K ' M I J,K,M> = ( I ^ ) J ( J + 1 ) + ( A - ( ^ ) ) K 2 - D a J 2 ( j + l ) 2 - D J K J ( J + 1 ) K 2 - D RK 4 + H a J 3 ( J + l ) 3 + H J R J 2 ( J + 1 ) 2 K 2 + H R J J ( J + 1 ) K 4 + H KK 6 Theory / 59 TABLE 2.2 - continued EK,K+2 = <J,K±2,M| |J,K,M> • h 1 J 2 ( J + D 2 ] 1/2 [ ( ^ ) + d j J f J + l ) + 1 2 j 2x [ { J ( J + D - K(K±1)}{J(J+1) - K(K±1)(K±2)}] EK,K±4 = < J ' K ± 4 ' M I *P\J,K,M> = [ d 2 + h 2 J ( J + l ) ] X [{J(J+1) - K(K±1)} x (J(J+1) - (K±1)(K±2)} x {J(J+1) - (K±2)(K±3)} x (J(J+1) - ( K ± 3 ) ( K ± 4 ) } ] 1 / 2 EK,K±6 = < J' K ±6,M|H S|J,K,M> = h 3 [ { j ( J + l ) - K(K±1)} x {J(J+1) - (K±1)(K±2)} x (J(J+1) - (K±2)(K±3)} x {J(J+1) - (K±3)(K±4)} x {J(J+1) - (K±4)(K±5)} x {J(J+1) - ( K ± 5 ) ( K ± 6 ) } ] 1 / 2 a Reference (40). Theory / 60 TABLE 2.3 RELATIONSHIP BETWEEN DISTORTION CONSTANTS 1. Relationship Between r's and Watson's Quartic Centrifugal Distortion Constants — A Reduction A J 8(rbbbb + Tcccc ) aJK 8VTbbbb rcccc ; 4v raacc Taabb rbbcc; » UK 4vrbbbb cccc raaaa; 4 V aacc aabb bbcc; 5 J = ~T6(Tbbbb " Tcccc ) R = 1-r- (B-A) 1 , (C-A) °K 8Tbbbb(B-C) 8Tcccc(B-C) + I f r ' - r' + r' (2A-B-C), 8 L aacc aabb bbcc (B-C) J 2. Relationship Between Watson's "A Reduction" Distortion Constants and "S Reduction" Distortion Constants D J = A J " 2° 6K DJK= AJK + 3 ° ~ \ DK = AK " 2 A 5K a = 2A-B-C a Reference (42). ^ Reference (41). BIBLIOGRAPHY 1. L.A. Woodward, Introduction to the Theory of Molecular Vibrations and  Vibrational Spectroscopy, Oxford University Press, Ely House, London, 1972. 2. W. Gordy and R.L. Cook, Microwave Molecular Spectra, in Technique of Organic Chemistry, Ed. A. Weissberger, Vol. IX, Part II, Interscience Publishers, New York, 1970, Chapter 6. 3. J.K.G. Watson, in Vibrational Spectra and Structure, a series of advances, Ed. J.R. Durig, Vol. 6, Elsevier, New York, 1977, Chapter 1. 4. S.C. Wang, Phys. Rev., 34, 243-252 (1929). 5. W. Gordy and R.L. Cook, op_. cit., Chapter 7. 6. G.W. King, R.M. Hainer, and P.C. Cross, J Chem Phys, 11, 27-42 (1943). 7. B.S. Ray, Z. Physik, 78, 74-91 (1932). 8. E.B. Wilson Jr., and J.B. Howard, J Chem Phys, 4, 260-268 (1936). 9. D. Kivelson and E.B. Wilson Jr., J Chem Phys, 20, 1575-1579 (1952). 10. D. Kivelson and E.B. Wilson Jr., J Chem Phys, 21, 1229-1236 (1953). 11. H.H. Nielsen, Rev Mod Phys, 23, 90-136 (1951). 12. J.K.G. Watson, J Chem Phys, 45, 1360-1361 (1966). 13. J.K.G. Watson, J Chem Phys, 46, 1935-1949 (1967). 14. T. Oka and Y. Morino, J Mol. Spec, 6, 472-482 (1961). 15. A.G. Robiette, in Molecular Structure by Diffraction Methods a Specialist Periodical Report, Vol. 1, The Chemical Society, London, 1973, Chapter 4. 16. W. Gordy and R.L. Cook, op_. cit, Chapter 13. 17. K. Kuchitsu, J Chem Phys, 49, 4456-4462 (1968). 18. K. Kuchitsu, T. Fukuyama and U. Morino, J Mol Struct, 1, 463-479 (1968). 19. K. Kuchitsu, T. Fukuyama and U. Morino, J Mol Struct, 4, 41-50 (1969). 20. K. Kuchitsu and Y. Morino, Bull Chem Soc. Japan, 38, 805-824 (1965). 21. R. Stolevik, H.M. Seip, and S.J. Cyvin, Chem Phys Lett, 15, 263-265 (1972). 61 / 62 22. J. Kraitchman, Amer J Phys, 21, 17-24 (1953). 23. CC. Costain, J Chem Phys, 29, 864-874 (1958). 24. CC. Costain, Trans Amer Crystallographic Assoc, 2, 157 (1966). 25. J.K.G. Watson, in Vibrational Spectra and Structure, a series of advances, Ed. J.R. Durig, Vol. 6, Elsevier, New York, 1977, Chapter 1, pages 69-73. 26. L.A. Woodward, op_. cit, Chapters 14 and 15. 27. W. Gordy and R.L. Cook, op_. cit., pages 237-251. 28. C Flanagan and L. Pierce, J Chem Phys, 38, 2963-2969 (1963). 29. W. Gordy and R.L. Cook, op^  cit, page 185. 30. W. Gordy and R.L. Cook, op_. cit, pages 303-333. 31. R.H. Schwendeman and V.W. Laurie, Table of Line Strengths for Rotational  Transitions of Asymmetric Rotor Molecules, Pergamon Press, London, 1958. 32. C.H. Townes and A.L. Schawlow, Microwave Spectroscopy, McGraw-Hill Book Company Inc., New York, 1955, pages 248-255. 33. W. Gordy and R.L. Cook, o£. cit, pages 344-347. 34. G.B. Little, The Microwave Spectra of Propiolamide, Master's Thesis, Chemistry, The University of British Columbia, 1977. 35. H.E. Gillis Singbeil, W.D. Anderson, R. Wellington Davis, M.C.L. Gerry, E.A. Cohen, H.M. Pickett, F.J. Lovas, and R.D. Suenram, J Mol Spec, 103, 466-485 (1984). 36. W.H. Kirchhoff, J Mol Spec, 41, 333-380 (1972). 37. H.M. Jemson, W. Lewis-Bevan, N.P.C. Westwood, M.C.L. Gerry, Chem Phys Letters, 108, 496-500 (1984). 38. J.K.G. Watson, op_. cit, pages 34 and 36. 39. J.K.G. Watson, op^  cit, page 16. 40. J.K.G. Watson, op_. cit, pages 42-43. 41. J.K.G. Watson, op^  cit, page 37. 42. J.K.G. Watson, J Chem Phys, 46, 1935-1949 (1967). 3. EXPERIMENTAL METHODS 3.1. INSTRUMENTATION - MICROWAVE SPECTRA The. microwave spectra were measured using a conventional 100 kHz Stark modulated microwave spectrometer which was operated in the frequency range 8 — 80 GHz. The basic components of the spectrometer were a tunable source of microwave radiation, an absorption cell and a detection system. A schematic diagram of the experimental arrangement, spectrometer and sample, is shown in Figure 3.1. The following describes the experimental equipment used to measure the microwave spectra. Three different sources of microwave radiation were used; they are described individually in sections 3.1.1, 3.1.2, and 3.1.3. Independent of the source, the microwaves were passed through commercially made rectangular Stark cells. For the molecules HOCl and FC1CO, these were two Hewlett Packard (HP) X band Stark cells (8425B), approximately one meter in length, that were connected in series. For CF^NCl it was a Custom Microwave X band Stark cell that was approximately three meters long. It conveniently had an inlet port halfway along its length where a crucial pressure gauge was inserted. Each cell had an outer cross sectional dimension of approximately 2.5cm x 1cm. As well, each had a thin copper septum, or voltage plate inserted parallel to the broad faces of the cell. These septa were held in place at the centre of the cell so that when an electric field was applied to them the resulting field inside the cell was as uniform as possible. The walls of the waveguide were insulated from the electric field by teflon runners. 63 Experimental Methods / 64 Brass vacuum ports were connected to each end of the total length of the cells and one of them was connected to a conventional glass vacuum system. The other end was used as an inlet port when it was necessary to flow the gas sample through the cells. Both ends of the total length of the cells were sealed using O-rings and thin sheets of mica. The microwave source was connected to the Stark cells using rectangular pieces of waveguide that can be either solid or flexible, or using a length of insulated microwave cable. A power attenuator was inserted between the source and the cell so that the power could be varied in order to prevent power saturation of strongly absorbing lines. A ferrite isolator was also inserted at the same place to prevent reflected power from going back to the source and interfering with the frequency stabilization system. The absorption of the microwave radiation was Stark modulated using an external electric field. As explained later, this allowed the detector at the far end of the cells to detect the extremely small change in. power that took place when the molecules had absorbed some radiation. The detectors used were only sensitive to power within certain frequency ranges. The different frequency ranges of the microwave spectrum have been divided into "bands" and loosely speaking a given detector usually detects radiation over one band. The various detectors used operated under three different principles of detection. The following chart indicates the detectors used, what kind they were, and over what frequency range they detected radiation. Experimental Methods / 65 Nominal Detector Type Band Freq Range HP H06 X422A Back Diode X 8-12 GHz HP H06 P422A Back Diode P 12-18 GHz HP K422A Point Contact Diode K 18-26.5 GHz HP 11586A Point Contact Diode R 26.5-40 GHz Hughes 47324H-1100 Schottky Barrier Diode M 50-75 GHz To detect lines between 40 — 50 GHz the upper limit of the frequency detection for the R band detector was pushed as far as it could detect past 40 G"Hz and the same was done to the lower limit of the Hughes Schottky barrier diode. The output signal of the detector was then pre-amplified before being sent to a phase sensitive (lock-in) amplifier (Princeton Applied Research, PAR, model 120). From the lock-in amplifier the signal was displayed on an oscilloscope and/or chart recorder. From one of these the frequency of the line was measured. The very last transitions reported in this work, of CF NCI, were measured using a Micro PDP 11/23+ computer. The Watkins-Johnson synthesizer was interrupt driven by the computer which meant that the data was collected in real time, via the lock-in amplifier. The data collection program allowed one to signal average and/or oversample. This meant that the signal to noise ratio and sensitivity of the signal could be improved significantly. Signal averaging was accomplished by collecting data (intensities) from one point (frequency) for several time units and averaging the sum. Oversampling meant that data was collected at given intervals between the pre-set sampling points and then averaged together and put in as the data for a designated sampling point. The final spectrum was then displayed on the terminal and the transition Experimental Methods / 66 frequency was measured by moving the cursor to the centre of the line. The correct Stark voltage had to be determined in set-up scans before the final measurement scan was taken. Stark modulation was used to detect absorption of microwave radiation by the molecules because it removes fluctuations in power from other sources and enhances the signal being looked for. It is necessary to measure a microwave spectrum at low pressures, 10 — 30 microns, as higher pressures cause pressure broadening of the lines and possibly discharging in the cell. At these low pressures the amount of radiation absorbed by the sample molecules is at most, 0.1% of the power that reaches the detector. Indeed it is often one or two orders of magnitude less than this. Other fluctuations in power such as reflections in the cell are usually much larger. To detect only the small change in power by the molecular absorption, a 100 kHz square wave, zero-based voltage is applied to the Stark plates in the cell. This perturbs the molecules as explained in section 2.6. Because the square wave is zero based the field is off for half the cycle and on for the other half. When the field is off the molecules absorb radiation at the zero field or unperturbed frequency, and when the field is on they absorb at slightly shifted frequencies. If the crystal detector is tuned to accept power at only 100 kHz any detected changes in power will be primarily absorption of the radiation by the molecules and power fluctuations at other frequencies will not be detected. The phase sensitive (lock-in) amplifier (PAR model 120) is also tuned to accept only 100 kHz signals. Therefore the detection system is designed to "see" information at only the modulation frequency. In this way it acts as a carrier frequency and since it is fairly high there is a significant reduction in 1/f noise. As a result both the strength Experimental Methods / 67 of the signal and the signal to noise ratio are enhanced by Stark modulation. The Stark voltage was obtained from an Industrial Components Incorporated 100 kHz square wave generator. Its voltage was variable up to a maximum of 2000V. The electric field was applied directly to the Stark plates. Because the plates are parallel to the broad faces this means the applied electric field E, is parallel to the electric field, E(t), of the microwave radiation and therefore the only allowed Stark transitions are those with AM = 0. When the Stark modulated absorption line is displayed on the oscilloscope both the unperturbed and perturbed lines are displayed at the same time, (because the modulation is significantly faster than the sweep rate). The electronics of the lock-in amplifier are such that the zero field line and the Stark components are displayed on opposite sides of the baseline. This makes it easy to adjust the voltage so that all of the Stark component is removed from the zero field line absorption when it is being measured. Experimental Methods / 68 MICROWAVE SOURCES 3.1.1. Backward Wave Oscillators The. first source of microwaves used in this work were backward wave oscillators, BWO's. These can emit radiation over a fairly wide frequency range. In fact one BWO usually covers a microwave "band", as described for the detectors. The BWO's that were available and the frequency ranges they covered were: Watkins-Johnson 2020-2 X Band 8-12 GHz Varian 162Y P Band 12-18 GHz Watkins-Johnson 2062-50 R Band 26.5-40 GHz Higher frequencies were obtained using a Space-Kom DV-1 doubler on R band. This gave frequencies from 54 — 78 GHz. Part way through the measurement period a doubler for X and P band was obtained, Space-Kom model SMD 1427, which allowed for easy measurement of lines at K band frequencies, 18-27 GHz. The output frequency of the BWO was kept stable by mixing it with a harmonic of a stable reference oscillator (HP 8466A). The reference oscillator was at a much lower frequency (240 — 390 MHz) and had be amplified and multiplied before it was mixed with the output frequency of the BWO. The calibrated beat frequency was 20 MHz and it was kept at this by using a phase lock amplifier which was tuned to this frequency. All three were within a negative feedback system which continually adjusted the voltages of the BWO to keep its frequency stable. Figure 3.2 gives a schematic diagram of how the BWO, reference oscillator, and synchronizer were integrated. Experimental Methods / 69 The frequency of the microwaves was given by an electronic counter (HP 5246L), which was integrated into the system. Although it could not measure the frequency of the microwaves directly from the BWO it measured the frequency of the reference oscillator and was internally adjusted to multiply the frequency of the reference oscillator and account for the 20 MHz difference to give a direct reading of the BWO microwave frequency (for the convenience of the user!) The frequency of the BWO was swept using a sweep oscillator (HP 8690) which allowed one to either do a single broad range frequency scan or continuously repeated narrow range frequency scans. It also had a manual control which was used to measure a line by tuning the BWO frequency to the absorption maximum. Most lines could be measured to an accuracy of 50 kHz or better, but some of the weaker lines were estimated to be accurate only to 100 kHz. 3.1.2. Watkins-Johnson Frequency Synthesizer Part way through the data collection a Watkins-Johnson Synthesizer (WJ 1291) became available. It produces microwave frequencies between 8—18 GHz in steps that can be made as small as 10 Hz. Measurements were usually made with frequency increments of 100 or 200 Hz. Frequency selection was greatly improved with the synthesizer. Using the X and P band doubler, (Space-Kom model SMD 1427), which worked beyond its specified frequency of 14 — 27 GHz allowed lines up to 36 GHz to be measured. Experimental Methods / 70 A new X and P band tripler, (Space-Kom model TKa-1) which also worked beyond its specified frequency range of 26.5 — 40 GHz, extended the frequency range to 54 GHz. Because the controls on the synthesizer made it very inconvenient to measure a line on the oscilloscope itself, the absorption signal was also sent to a chart recorder. The exact frequency of the line was then measured from this recording, using frequency markers on the chart. t 3.1.3. OKI Klystron (30V10) It became necessary to measure the weak a-type R branch lines of 18 37 H O CI using a klystron. Since the new system using the Watkins-Johnson Synthesizer only produced frequencies up to 54 GHz (and the lines were between 54 — 55 GHz), the old system using the R band BWO and the appropriate doubler (Space-Kom DV-1) were used initially to try and measure these very weak lines. It eventually became clear that the power output of the BWO (10 — 20 mW) and doubler was too small to detect them. Therefore it was decided that using a klystron, which gave much higher power (110—120 mW) than the BWO, would perhaps allow one to detect these critical a-type lines. This new arrangement was so successful it was used to measure all the lines that fell within its frequency range. A schematic diagram of the experiment using the klystron is shown in Figure 3.3. The source of microwaves was an OKI Klystron, 30V10, which produced microwaves from 27 — 32 GHz. To get the high frequencies that were Experimental Methods / 71 needed the R band doubler was used to double the klystron generated microwaves. To determine the frequency of the microwaves being generated by the klystron, a reference frequency was needed. The Watkins-Johnson Synthesizer was used for this, at one third the frequency of the klystron generated microwaves ( = 9 GHz). These reference microwaves were fed into a harmonic oscillator/mixer (TRG Alpha Industries model X922B) where they were tripled and then mixed with the klystron produced microwaves. The resulting beat frequency was fed into the antenna of a radio receiver (Hammarlund model SP-600) which was calibrated to produce markers, when the beat frequency was 5 MHz. To get a desired frequency one calculated and punched in the corresponding frequency of the reference microwaves and then tuned the klystron, by changing its cavity size, to produce microwaves 5 MHz higher. The appearance of the markers on the oscilloscope indicated that the source and multiplied reference frequencies were exactly 5 MHz apart. To measure a line frequency the output of the crystal detector was put onto the other channel of the oscilloscope. Dual mode display of the oscilloscope was necessary, as one channel displayed the markers while the other gave the absorption line signal. Hopefully the klystron microwave frequency going through the cell was close to the absorption line frequency and the line would appear on the oscilloscope. If it appeared, the reference frequency of the synthesizer was adjusted until the +5 MHz marker was directly under the line. This reference frequency was then read and used to calculate the real line frequency. The formula used was: Experimental Methods / 72 j»(exp) = {[3 x j/(ref)] + 5 } x 2 (3.1) where p(exp) is the real absorption line frequency which was double the klystron generated microwave frequency and p(ref) was the reference frequency put out by the synthesizer which was tripled and mixed with the klystron frequency such that it was 5 MHz lower. If the line did not appear, the frequency of the klystron was changed until it did and the reference frequency was then adjusted accordingly. This particular experimental arrangement is not very good for searching for lines whose locations are poorly known because its sweep range at any one time is very small, approximately 10 MHz, and to shift the frequency of the klystron microwaves was slightly tedious. However for the experiment described above the locations of the lines were fairly well known and therefore it proved to be a very useful system! 3.2. INSTRUMENTATION - INFRARED SPECTRA The infrared spectra were recorded using a Fourier Transform Infrared Interferometer made by BOMEM, Model DA3.002. It can record spectra at a resolution as low as 0.004 cm \ Following is a description of how an interferometer works and the instrumental components that were used in the work described in this thesis. Most of the information in this description is from reference (1). An interferometer measures an infra-red spectrum by measuring an interferogram which is a record of signal intensity versus distance. To get a Experimental Methods / 73 spectrum, defined by spectroscopists as signal intensity versus frequency, a Fourier transform is performed on the interferogram. The Fourier transform is a mathematical function which converts information that is a function of distance, f(6) to information which is a function of frequency, f(u) and vice-versa. Its two forms are shown in equations 3.3 and 3.5. A schematic diagram of a basic interferometer is shown in Figure 3.4. The interferometer works in the following way: A source of light is collimated and directed towards a beamsplitter. An ideal beamsplitter will reflect 50% of the incident light and transmit the remaining 50%. The 50% that is reflected goes to a fixed mirror where it is reflected back to the beamsplitter. At the beamsplitter this reflected light is partially reflected back to the source and partially transmitted to the detector. The 50% that is transmitted goes to a movable mirror where it too is reflected back to the beamsplitter and partially reflected to the detector and partially transmitted to the source. The energy reaching the detector is then a sum of the two beams reflected from the two different mirrors. When the distance from the center of the beamsplitter to the fixed mirror is the same as to the movable mirror the two beams will have travelled the same distance to the detector. This situation is referred to as the ZPD — zero path distance. When the movable mirror is moved, the lengths of the two beams reaching the detector become unequal. This path length difference is called the OPD — optical path difference or the retardation. It is represented by the symbol 5. If the mirror is moved a distance x, then 5 —2x. To understand what intensity the detector sees, a source of light composed of only one frequency is considered. When 5=0 (i.e. at the ZPD), the two light beams reaching the detector will be in phase and interfere constructively meaning Experimental Methods / 74 that they reinforce each other. At this point the intensity of the interferogram, 1(6) will be at a maximum. If the mirror is moved a quarter of a wavelength, ;c=X/4 which means 8 =X/2 then the two wavefronts will be 180° out-of-phase at the detector. They will interfere destructively, cancelling each other and I(5) = I(X/2) = 0. The end result is an interferogram that is an infinitely long cosine wave, represented by: where B(t>) is the intensity of the spectrum as a function of frequency v. In the real situation the source is composed of many frequencies of light, usually a continuum. This means the intensity becomes a sum or integral of all the different frequencies: The interferogram will have a maximum or large spike at 8=0 because at this point wavefronts of all frequencies are in phase. Moving away from the 8=0 position the intensity of the interferogram dies off quickly to a series of lower amplitude oscillations, as waves of different frequencies cancel and reinforce one another. It turns out that the high resolution information is in the wings of the interferogram or where 5 = a maximum. Naturally there is a practical limit to how far a movable mirror can be 1(5) = B(»0cos(2ir5i0 (3.2) 1(8) = f B(i>)cos(2ir5iOd»» (3.3) made to travel. This maximum distance is represented by 8 max and is related to the maximum theoretical resolution by: A, = £ -1 = theoretical limit of resolution (3.4) cm max Experimental Methods / 75 As mentioned, the spectrum B(i>) is obtained by doing a Fourier transform on the interferogram. This is represented mathematically by: B(i>) = / I(5)cos(2ir6iOdS (3.5) One can note that the limits of integration are from —» to +». Since this is not physically possible the real interferogram is convoluted with an apodization function. When no apodization function is applied to the spectrum but rather has only the boxcar trunction applied to it, large negative sidelobes, referred to as "ringing", result. This boxcar truncation is a function which equals + 1 between —8 and +5 and 0 elsewhere. Its Fourier transform is the sine function: (sin x)lx. Unfortunately these large negative side lobes could obscure a weak absorption. Using an apodiztion function minimizes the size of the side lobes, but naturally at a cost, as the resolution of the spectrum is degraded in direct proportion to the reduction in the side lobe intensity. Various apodization functions can be used and the one used in the infrared work described in this thesis is called "HAMMING" and has the functional form: [0.53856 + 0.46144 (cos D)] where D = (optical path difference)/(maximum optical path difference) (2). An important design feature of an FT-IR interferometer is that the movable mirror system be extremely stable. It must be able to stay parallel to itself and to travel at a constant velocity. In the Bomem this is achieved by dynamic alignment of a temperature and frequency stabilized He-Ne laser. Photodetectors in the center of the beam system check that the infrared source light is in phase with the reference frequency. If it is not the fixed mirror is tilted slightly to bring the two beams back into phase. The movable mirror Experimental Methods / 76 travels vertically in this instrument, in comparison with others where it moves horizontally. When actually taking a spectrum it is necessary to have a background, which is then ratioed to the sample spectrum in order to get a spectrum with a flat background. To get spectra with good signal to noise many scans at high resolution are usually taken. It is therefore important that nothing changes between scans, meaning that the following criteria must be met: i) The source must be stable, ii) The optical bench must be stable, iii) The mirror movement must be reproducible, iv) The level of purging must be repeatable. In the experiment described in this thesis, where an infrared band of NH^BHg was measured, the following components were used: 1. A globar light source which emits radiation from 200—10,000 cm"* 2. A potassium chloride beamsplitter which works between 550-4000 cm"1. 3. a) A liquid nitrogen cooled mercury cadmium telluride, MCT detector, which was used for the low resolution scans between 800 — 2800 cm"l It detects from 700 — 4000 cm 1 and is good for weak absorption spectra. b) A liquid helium cooled copper doped germanium detector which detects from 330—1500 cm"^  without a filter. It was used with a cold filter on it that reduced its detection range to 600—1300 cm \ It was used for the high resolution scan between 1050 and 1300 cm"1. 4. A multiple reflection, long path cell with a potassium bromide window. For the measurement of the infrared spectrum of FC1CO at 1 cm 1 resolution between 700 — 2000 cm 1 the globar light source, potassium chloride Experimental Methods / 77 beamsplitter and MCT detector were also used. The only different component was a 20 cm long glass IR cell with cesium iodide windows instead of the multiple reflection long path cell. The data taking and processing were done using a Digital Equipment Corporation, (DEC), PDP 11/23 microcomputer and a Bomem High Speed Vector Processor. The two communicate with each other via a General Purpose Interface Bus, (GPIB). It is the vector processor that actually records the interferogram and performs the Fourier transform on it, with or without an apodization function. The resulting spectrum is then stored on the disks of the computer. Further processing of the data (e.g. calculating transmittance spectra) is done by the computer. The computer is also used to set-up the interferometer for measurement scans, via the vector processor. Experimental Methods / 78 3.3. SAMPLE PREPARATION AND HANDLING 3.3.1. Hypochlorous Acid: DO.C1, and H1 8 OC1 Hypochlorous acidt was prepared by making a slurry of water and yellow mercuric oxide, provided by BDH Chemicals Ltd., England, and then bubbling gaseous chlorine directly into this slurry for approximately 30 seconds. HOC1 is made in this way according to the following reaction: H 20 + 2HgO(s) + 2Cl2(g) »- HgO-HgCl2(s) + 2HOCl(g) (3.6) Immediately after the chlorine was added one could see a reaction taking place because the orange-yellow mercuric oxide started to turn a green-brown colour. Air and other non-condensables were removed by freezing this mixture with liquid nitrogen and then pumping on it. Once the sample had warmed up HOC1 could usually be detected immediately. However leaving it for 15 — 20 minutes improved the yield. The isotopically substituted molecules were made by merely changing the water used. Using deuterium oxide, 99.8% enriched in D (provided by Merck, 18 Sharp and Dohme, Canada Ltd.) produced DOC1 and using H O, 97.5% 1 8 enriched in O (provided by Merck Frosst Canada Inc., MSD ISOTOPES) gave 18 H OC1. In each case when the spectra of these isotopes were measured lines of the normal species, H^OCl could usually be detected, but they were very t In this section references to HOC1 are meant to include all the isotopes that were studied: H(16)0(35)C1, H(16)0(37)C1, D(16)0(35)C1, D(16)0(37)C1, H(18)0(35)C1, and H(18)0(37)C1. Any reference to DOCl and H(18)0C1 is meant to include both isotopes of chlorine, (35)C1 and (37)C1, and unless labelled O is meant to be (16)0. Experimental Methods / 79 weak. Dry ice was wrapped around the Stark cells, using strypfoam troughs, to measure the low J lines, i.e. J=l«-0 and J = 2*-l. This increased the population of molecules in these lower rotational energy levels, which improved the strength of the lines, often signficantly. Cooling with dry ice was not necessary for measuring the higher J lines. Because HOCl is a relatively unstable molecule it was necessary to flow the HOCl through the cell in a continuous stream. For the same reason it usually only lasted 6 — 7 hours in the preparatory vessel, after which time the weak a-type lines became too weak to measure properly. Interference by other molecules or reaction by-products, such as C^O, was never a problem, even though HOCl exists in an equilibrium with Cl^O and water: 2HOC1 C120 + H 20 (3.7) The few times known lines of ClgO were looked for they were not found, although occasionally weak lines whose line shapes and Stark components showed characteristics of a molecule with two chlorine atoms were seen. The microwave spectrum of HOCl in the frequency range under study is very sparse and interference from other lines was seldom a problem. Experimental Methods / 80 3.3.2. Carbonyl Chlorofluoride, FC1CO Carbonyl chlorofluoride was supplied by PCR Research Chemicals Inc., in a small gas cylinder. Since it is a stable gas it was much easier to handle than HOCl. It was more convenient to store a sample of it at room temperature in a glass bulb attached to the vacuum line than to use it directly from the cylinder bottle. To measure its microwave spectrum a small sample from the glass storage bulb was released into the Stark cells, sealed off in them, and the spectrum measured. Because it is a stable gas a flow system was not necessary. The sample appeared to keep quite well in the glass storage bulb for 3 — 4 months. Towards the end of this time the strengths of the FC1CO lines seemed to have decreased somewhat from their original values. The reason for this could be because FC1CO exists in an equilibrium with F^CO and Cl^CO and after a few months the system had probably shifted closer to the thermodynamic equilibrium, where FgCO and C^CO were more abundant. Both FgCO and Cl QCO were found to be present in the sample, although their lines were always z much weaker than those of FC1CO. The spectrum of FC1CO is very rich and consequently interference from other lines, either other transitions of FC1CO itself or transitions of these other two molecules, FgCO and C^CO was often found to be a problem. In most cases it prevented the desired line from being measured accurately and accordingly it was ignored. Nevertheless it was possible to measure enough other lines to determine accurate rotational and centrifugal distortion constants. Cooling with dry ice was not necessary to improve the strength of the Experimental Methods / 81 low J lines. The v 3 band of FC1CO was measured at 1 cm 1 resolution from an infrared spectrum taken between 700 — 2000 cm"1. The sample of FC1CO was obtained by trap to trap distillation of a sample taken from the gas cylinder. The two traps used were liquid nitrogen and dry ice/acetone. Because F^CO was the most volatile (boiling point =— 83°C) it was relatively easy to remove it by pumping off the first vapours released from the dry ice/acetone trap. Because a band of F CO at 774 cm 1 interfered with the i>3 band of FCICO it was important that it was removed. The disappearance of a band of FgCO at 965 cm 1 indicated when the FgCO had been successfully removed. The final spectrum still had some Cl^CO in it but because none of its bands interfered with the Vj band of FCICO this was not a problem. It was much more difficult to separate the C^CO from the FCICO because it is less volatile than FCICO (boiling point of C12C0 = 8.3°C and the boiling point of FC1C0= -44°C). The final spectrum was taken with a cell pressure of 150 mTorr and was the coaddition of thirty scans. 3.3.3. N-chlorodifluoromethylenimine, CF 2 NCI The sample of CFgNCl was kindly prepared and sent to us by Darryl DesMarteau from Clemson University. Two samples of O.lg and 0.2g respectively, were supplied. Each was shipped in a glass bulb and to the best of our knowledge no significant decomposition took place since the spectrum of CF2NC1 was always easily detected. The most impressive example of this was when a sample of approximately 300 microns pressure was used to take a mass Experimental Methods / 82 spectrum to check that it was actually CF^NCl. Despite this amount of sample being at the limits of detection for the mass spectrometer the lines corresponding to CFgNCl came through clearly. Once in the lab it was transferred to another glass storage vessel and stored in liquid nitrogen. When it was being used for an experiment it was warmed to room temperature. In order to let in only small amounts of sample to the microwave cell at one time a series of teflon stopcocks were used to partition the sample before reaching the cell. Three of these were on the storage vessel itself and two others between it and the cell. This reduced the pressure going into the cell from approximately 500 microns to 50 microns. Often during the course of a day the stopcock to the gas itself would not have to be opened because it was possible to use the gas that was stored between the other two. In this way the small sample of gas lasted throughout the entire course of the experiments. Special fluorocarbon grease was used on all greased joints to prevent decomposition of the sample by the grease. Unfortunately it was not so stable once the gas was in the brass cell. Apparently the sample started to decompose immediately. This was concluded after watching the spectrum between 29525 and 29660 MHz. At first only three lines at 29553 MHz (doublet), 29609 MHz ("triplet"), and 29638 MHz (doublet) were observed. Then after a minute or two, new lines at 29541 MHz (singlet) and 29609 MHz appeared. The line at 29609 MHz is assumed because what was observed was a change in the intensity and shape of the line at 29609 MHz. The original lines, assumed to be from CF^NCl did not really diminish in intensity, but the new lines grew to be just as strong as the Experimental Methods / 83 original ones. For this reason a flowing system would have been much better. However because there was so little sample this was not possible. The assignment of the spectrum was probably made slightly more difficult because of these "extra" lines, but luckily it did not actually prevent the assignment or measurement. Needless to say the spectrum was quite rich and there were several lines which could not be measured because of interference. Dry ice was wrapped around the cells to try and slow down the decomposition and to narrow the line widths. 3.3.4. Aminoborane, NH 2 BH 2 Aminoborane was prepared by the carefully controlled thermal decomposition of borane ammonia, NH BH , according to the following reaction: O o NH BH (s) — N H 9 B H 9 ( g ) + NH„BH„(g) + H„(g) (3.8a) 90°C 1 1 6 6 1 NH2BH2(g) + NH 3BH 3(g) + H (g) — N H 9 B H _ ( g ) + H„(g) (3.8b) 400°C Because NH 2BH 2 is an unstable gas its preparation and the measurement of its spectrum are done in a flow system. Figure 3.5 shows the experimental arrangement used. To minimize decomposition of the solid NH BH (a commercial product o o made by Alfa Products) caused by exposure to the air, it was transferred to the heating vessel under nitrogen. It was then uniformly heated to 90°C in an oil bath. When the pressure in the closed preparation system reached approximately 120 microns the system was opened to the pump under very slow pumping Experimental Methods / 84 conditions to maintain this pressure. Constant monitoring of the vapours produced, by doing fast 4 cm 1 resolution scans, revealed that the products from this low heating were: NHgBHg, NH^ and some unknown BN compound, possibly the starting material or diborane, (B H ). To reduce the amount of this Z o unknown BN compound the vapours were passed through a 15 cm long quartz tube heated by a furnace at approximately 400°C. Getting the optimum conditions for maximum production of NHgBHg and minimum production of NHg and the unknown BN compound was no trivial task, but after two to three hours of carefully monitored heating (using fast scans) the yield of NH BH was z z high enough and stable enough to do the high resolution scans. Because the band measured was an overtone and consequently very weak the multiple path reflection IR cell was adjusted to give a long path length of 19.25 m. The 0.004 cm 1 resolution scans were recorded at the stable conditions of: 120 microns sample pressure, 90°C oil bath temperature, and furnace voltage of 45V. Each scan took approximately five minutes and were taken between 1050 and 1300 cm \ In total sixty-five scans were taken and added together to produce the final spectrum. Experimental Methods / 85 Sample Lock in Amplifier Oscilloscope Source of Microwaves Stark Cells to vacuum line ref. Squarewave Generator Detector Pre-Amp Figure 3.1. Schematic Diagram of the Microwave Spectrometer and Sample. Experimental Methods / 86 ' to waveguide At tenuator 5 Isolators Mixer Synchronizer -Directional Coupler Mul iplier ]~Amplifi er Reference Osci l lator Sweep Osci l lator to Lock-in Ampl i f ie r to Frequency Counter Figure 3.2. Schematic Diagram of the Backward Wave Oscillator Microwave Source Circuit. Experimental Methods / 87 Antenna Radio Receiver Harmonic Mixer ® | ' — ® t r ip ler [ x Reference Frequency (Synthesizer) Osc i l l oscope —i Lock in Amp Sweep Box — 4 Direct ional ^ Coupler X | Doubler to waveguide Figure 3.3. Schematic Diagram of the Klystron Microwave Source Circuit. Experimental Methods / 88 Movable Mirror Fixed Mirror f Beamsplitter Sample Detector Light Source Figure 3.4. Schematic Diagram of an Interferometer. Experimental Methods / 89 furnace 1 N H 3 B H 3 ( s ) -t he rmomete r oi l bath Heater Figure 3.5. Experimental Arrangement for the Production of Gaseous NH BH, in a Flow System. BIBLIOGRAPHY W.D. Perkins, J Chem Education ('Topics in Chemical Instrumentation') 63, A5-A10, 1986 Bomem Software User's Guide, Version 3, Revision 1, March 1984, Vanier, Quebec pages 5-217 to 5-227. 90 4. MICROWAVE SPECTRUM OF HYPOCHLOROUS ACID A moderate amount of spectroscopic work has been done on hypochlorous acid, HOCl. In the first study of its microwave spectrum by Lindsey et al (1), the a-type R branch transition 10 , — 0 o 0 was measured for the two normal 35 37 isotopic species and two deuterated species (DO CI and DO CI). This information allowed them to determine rough estimates of the chlorine quadrupole coupling constant x and the structure. A later study, by Mirri et al (2), 3 3 produced measurements of more a-type transitions of the same four isotopic 18 35 species, plus three transitions of D 0 CI. This larger data set meant values for the rotational constants B 0 and C 0 and both chlorine coupling constants X aa 16 35 and were determined for all isotopic species. For H O CI the two distortion constants, A T and A T V were also determined. A measurement of the dipole moment using the Stark effect (3) revealed the interesting information that was large, =1.250, which meant that b-type transitions should be very strong, (if they could be found). A significant improvement in the accuracy of 35 the CI quadrupole coupling constants was made in a Zeeman effect study (4), that also produced molecular g-values, a chlorine nuclear gj factor and magnetic 16 35 anisotropy parameters for H O CI. The vibrational spectrum of this molecule has been measured a number of times. In 1951 Hedberg and Badger (5) measured the gas phase infrared 35 35 spectrum of HO CI and DO CI and calculated a harmonic force field using their data. The matrix isolation infrared spectra of six isotopic species, T T16„35„. Tr16<_.37ri1 „ 1 6 „ 3 5 „ 18„35„, T T18„35„. , T r18„37„. H O CI, H O CI, D O CI, D O CI, H O CI, and H O CI were reported in 1967 by Schwager and Arkell (6). Only the O-Cl stretching frequency was reported for the 3^C1 species because the difference in the 91 Microwave Spectrum of Hypochlorous Acid / 92 frequencies of the other two vibrations between the two chlorine species was too small to measure at low resolution. Their data also allowed them to calculate a harmonic force field. That same year a moderately high resolution gas infrared -1 35 35 spectrum (accurate to 0.05 cm ) of the v ^ band of HO CI and DO CI was recorded and analyzed (7). A few years later the same group measured the v 2 band for HOCl, to the same resolution (8). Years later Sams et al recorded the very high resolution spectrum of both the V\ and v2 bands of HOCl (9,10), producing band centre frequencies accurate to ±0.001 cm \ Very recently Deeley and Mills (11) have recorded the vibration-rotation spectrum of both HOCl and DOC1 to an accuracy of 0.005 cm *. To date seven harmonic force fields are known to have been calculated (5,6,11-15). The variation in the values of the force constants of the earlier calculations is significant - to the point of not knowing which, if any, are reliable. Fortunately later calculations of the force constants agree much better with each other. Various theoretical methods have been used to calculate these force fields. Murrell et al (14) based their determination on calculations of a general potential surface using spectroscopic and thermal properties of the molecule. Botschwina (15) used a variational calculation to construct a potential energy function, with which he was able to estimate both harmonic and anharmonic contributions to the vibrational spectrum. Simultaneous to this work, Deeley and Mills determined a force field by doing a least squares refinement to a data set that included, very accurate values for the vibrational wavenumbers of HOCl and DOC1, the distortion constants of HOCl determined by Gillis et al 35 37 (16), and CI/ CI wavenumber shifts in the fundamentals. The work reported here supplements that done on the normal species by Microwave Spectrum of Hypochlorous Acid / 93 three groups, at: The University of British Columbia (UBC), The Jet Propulsion Lab (JPL), and The National Bureau of Standards (NBS) (16). Interestingly, the work in reference (16) was begun separately by all three groups. This is because a fairly intensive interest in HOCl had arisen due to its role in the stratosphere in reactions between ozone and organochlorine compounds - as explained in more detail in the introductory chapter. The result was an exhaustive study of the microwave spectrum of both normal isotopic species, 35 37 HO CI and HO CI. Measurements were made of previously unobserved b-type transitions and a-type Q branch transitions, and covered various frequency regions in a total range of 8 — 650 GHz (depending on the instrumentation available at each laboratory). Consequently very accurate values for the rotational constants and centrifugal distortion constants were determined for both species. An improved value for the dipole moment was also obtained. The work described in this chapter is of the measurement and analysis of the microwave spectrum of four isotopically substituted species of HOCl: D 1 60 3 5C1, D 1 60 3 7C1, H 1 80 3 5C1, H 1 80 3 7C1. b-type transitions for all isotopic 18 species have been measured for the first time, while for the H OC1 species all the assigned transitions had never been measured before. Consequently this work has produced the first experimentally determined A 0 rotational constant for 18 all the species, and of course for the H OC1 species B 0 and C 0 rotational constants were also determined for the first time. For the deuterated species values for the B 0 and C 0 rotational constants have been greatly improved. Quartic distortion constants were also determined for all the isotopic species and they were used along with those determined for the normal species (16) and the vibrational wavenumbers from the literature to calculate a harmonic force field. Microwave Spectrum of Hypochlorous Acid / 94 This was the first force field determined using centrifugal distortion information. Enough information was also available to determined four different kinds of structures: the effective (r ), the substitution (r ), the ground state average (r ) O S z and an approximate equilibrium (r ). Microwave Spectrum of Hypochlorous Acid / 95 4.1. ASSIGNMENT AND ANALYSIS To start the analysis of the microwave spectrum of each isotopic species it was imperative that the best estimate possible was used for the A 0 rotational constant. This is because the predicted frequencies for any b-type transitions were very dependent on its value. A 0 is very large so the absolute error in its estimate was also large. Unfortunately this meant the predictions of the b-type transition frequencies were very poor (±1000 MHz). Usually preliminary rotational constants are estimated from a structure (section 2.7), however because H (or D) is extremely light it vibrates wildly and there is a lot of vibrational motion in the rotation, which a simple rigid rotor model cannot account for. In this situation A 0 was estimated using a method which accounted for the contribution by harmonic vibration that was incorporated in the rotational constant. Using the harmonic parts of the a's from a preliminary harmonic force field (determined using the distortion constants of reference (16) and the vibrational wavenumbers in the literature) average rotational constants (equation (2.33)) and the average inertial defect, A z (equation (2.31)) were calculated for the normal species (HOCl). The assumption was then made that the variation in between isotopic species was negligible, (this can be confirmed by checking the values listed in Table 4.4). Values for B 0 and C 0 for both deuterated species were available (2), which meant B^ and C^ were easily calculated, leaving as the only unknown in the average inertial defect equation (2.31). A^ was then converted to an effective rotational constant using the a (harmonic)'s from the force field. The distortion constants calculated by the force field were also used as preliminary values in the first refinements. Microwave Spectrum of Hypochlorous Acid / 96 35 Because five transition frequencies were available for DO CI the initial prediction was also a fit to these transitions, where the rotational constants B 0 and C 0 and a distortion constant A T T, were released, (two J = 6-«-5, K = 2 u JK ' a transitions had been measured (2)). The least squares refinement was made to r Watson's A reduction Hamiltonian, in its I representation, given in Table 2.1. 37 For DO CI only three transition frequencies were available so the initial refinement was to only B 0 and C 0. A prediction of the nuclear quadrupole splitting by the chlorine was made using the values reported in reference (4). Even though a relatively good estimate had been made for the value of A 0, the only real solution to determining a good value for it was to find and correctly assign a b-type transition. Luckily the search problems were greatly simplified for two reasons: (1) The spectrum was very sparse. (2) The b-type (K =l*-0) lines were very strong, (especially compared to the a-type lines), a Measurement of the microwave spectrum of the two normal species had confirmed the prediction that the b-type lines should be strong. This previous experience had also shown that in order to get a strong, steady supply of HOCl that allowed for easy detection of it a flow system was necessary. Consequently when a huge line, with a large unresolved Stark lobe was found it was relatively easy to make an assignment, as it could only be one of three or four b-type K =l*-0 transitions. The broad Stark lobe was caused by a the fact that the b-type lines found in this frequency range were ones of fairly high J (J=12 and 13). 35 The first b-type line found for DO CI was assigned a transition, put into a refinement where A 0 was released and a new prediction of the spectrum Microwave Spectrum of Hypochlorous Acid / 97 made. This initial assignment was confirmed when the new refinement predicted the location of two more K =l«-0 b-type lines extremely well. a To get the best possible prediction for the location of the K = 2 *-1 b-type a transitions, all three measured b-type lines were put into a new refinement. This new prediction was sufficiently accurate that two K =2«-l lines were found a and assigned quite easily. With two different series of b-type lines now measured, Aj and A-^  were released in a refinement. A subsequent refinement where 5 T was released improved the standard deviation of the fit. J Now with a fairly accurate prediction of the spectrum two very weak a-type Q branch transitions were measured. A remeasurement of the a-type R branch transitions reported in the literature was also made. The new lines meant there was enough data to release 8j^. An attempt was made to determine some sextic distortion constants but there was not enough data. When the Watkins Johnson synthesizer arrived the available frequency range increased which allowed more a-type Q branch lines and b-type lines to be measured. 37 The spectrum of DO CI was assigned and analyzed in a similar manner. Because DOC1 is only a very slightly asymmetric prolate rotor (*c = — 0.996), problems arose in determining good values for some of the distortion constants, caused by large correlations between some of the constants, using the A reduction Hamiltonian. Therefore, as for the normal species, the S 37 reduction Hamiltonian was used in the final refinements. For DO CI a value for D^ could not be determined because it was almost perfectly correlated to 35 D . Consequently it was fixed at the value determined for it for DO CI. JK. Because DOC1 is a relatively light molecule whose rotation contains a fair Microwave Spectrum of Hypochlorous Acid / 98 amount of distortion, caused largely by the "H" atom, sextic distortion constants predict the spectrum significantly more accurately. However, since no sextic distortion constants could be determined from the data, values for them had to be transferred from the normal species, and subsequently constrained in the fits. For Hj the values were transferred directly from the corresponding chlorine species. For H J ^ J and H^ scaled down values of HOCl were used, as determined by using the ratio of the D 's calculated by the harmonic force field. This was necessary because these two distortion constants vary significantly on substitution of H by D. Values for the other sextic distortion constants were considered too small to be needed in the model. The refined and fixed rotational constants and centrifugal distortion constants for each species are given in Table 4.3. Table 4.2 lists the unsplit line frequencies measured for each isotopic species. A new least squares refinement to the chlorine quadrupole coupling constants was done because different series of transitions were now available which would provide more information about the quadrupole coupling. The most important new lines measured were the low J b-type P branch lines which have a great deal of information about X ^ - * c c- A representative sample of the frequencies of the split lines used to calculate the chlorine quadrupole coupling 16 35 constants for D O CI is given in Table 4.1 and the newly refined values are in Table 4.3. 18 Measurement of the spectra of the two H OC1 isotopic species was very similar to that of the deuterated species. The major difference was that the spectra were weaker, and much fewer transitions could be measured, hence fewer Microwave Spectrum of Hypochlorous Acid / 99 distortion constants were determined. Since no previous measurements of the microwave spectrum of either of these two species had been made, preliminary values for B 0 and C 0 had to be estimated from a structure. The same program which fits a structure to the rotational constants was used to do this. When ridiculously large uncertainties are given to the rotational constants, (preliminary values used were those of the corresponding normal species), this causes the program to calculate values for the rotational constants that are consistent with the structure given. The structure used was that of Mirri et al (2). A more detailed description of the program is given in Section 4.2. Using the estimates determined from this program for B 0 and C 0, a value for A 0 was estimated in the same way as for the deuterated species (using the preliminary force field). A prediction of the spectrum was made using the estimated rotational constants and the values of the quartic distortion constants that were determined by the force field. The hyperfine splitting was predicted using the chlorine quadrupole coupling constants of the 16 appropriate normal species (H OC1). To start the measurement of these spectra it was necessary to find the low a-type R branch lines; J=l-«-0 and J = 2-«-l, to determine refined values for B 0 and C 0. This was easily done for the 3^C1 species, but for H 1 80 3^C1 detection problems caused by the weakness of the spectrum were encountered. The experimental arrangement described in section 3.1.3 had to be used to measure the J=2«-l a-type R branch transitions. Then b-type transitions were found and assigned in a similar manner to that described for the deuterated species. Unfortunately no K = 2 •*-1 b-type transitions or a-type Q branch Microwave Spectrum of Hypochlorous Acid / 100 transitions could be found, with the result that values for and 6^ could not be determined. Since these were the two that could not be well determined in the analysis of the other isotopic species using the A reduction Hamiltonian no 18 problems of this type arose in the analysis of the H OC1 spectra. Nonetheless to be consistent the S reduction Hamiltonian was used for the final refinements, was constrained to a value scaled down from that of the corresponding 16 H OC1 by the ratio obtained for the calculated values from the harmonic force i field. The sextic distortion constants and were constrained to the corresponding H^OCl values. The refined and fixed constants for H^OCl are given in Table 4.3. Because substitution at by leads to a much smaller change in the inertial axis system relative to that of the normal species, than substitution 16 at H does, the chlorine quadrupole coupling constants of H QC1 were sufficiently accurate to analyze the spectrum. Too few transitions were measured for the 18 H OC1 species to make a refinement to the chlorine quadrupole coupling constants worthwhile. 4.2. EFFECTIVE STRUCTURE Enough isotopic data has been collected for HOCl to determine its complete structure. The effective inertial defects for all the isotopic species are given in Table 4.4. All are small and positive which indicates the molecule is o 2 planar, as HOCl has to be. However the difference of 0.021 uA between the deuterated species and the other four indicated that problems would be encountered in the structure determination. Microwave Spectrum of Hypochlorous Acid / 101 The structure Fitting program used, for all the work described in this thesis, performs a least squares fit of the structure to all three moments of inertia, despite the fact that for a planar molecule only two are independent. Appropriate Jacobians are determined which allow the structural parameters to be changed to fit the information given by the rotational constants. How much the parameters vary to fit to a given rotational constant depends on the weight given to the constant. A high weight influences the values determined for the structural parameters more than a low one. Rather than a weight the program requires an uncertainty be given each rotational constant. The weight is related to the uncertainty as: _2 weight °< (uncertainty) (4.1) For the determination of the effective structure of HOCl the somewhat arbitrary uncertainties given the rotational constants were: 1% for B 0 and C 0 and 2% for A 0. The relative magnitudes of these uncertainties reflect how accurately each constant had been determined. The structure of HOCl is completely described by the three structural parameters, r(0—H), r(0 —CI) and <(H0C1). The values obtained for each parameter are listed in Table 4.5. Since there were twelve independent rotational constants from the six isotopic species it was initially assumed there would be no problem in determining the structure. However as is evident from the results presented in Table 4.5, the determined effective structure has a large uncertainty associated with it. This uncertainty can be partially explained by the inherently ambiguous physical meaning of effective rotational constants. They contain an undefined Microwave Spectrum of Hypochlorous Acid / 102 combination of effects from vibration, centrifugal distortion, etc., and therefore will never be able to reproduce a 'good' structure. For HOCl any structure fitting problems will be amplified by the presence of the O —H bond. This is because substitution of H by D causes a significantly large change in the structure. This occurs because the relative change in mass is large (50%). Use of Kuchitsu's equation (2.36) showed that the change in O —H bond length after substitution by D was approximately an order of magnitude bigger than for other isotopic substitutions. (This is quite common). Although it is not possible to calculate a change in the <(H0C1) after D substitution, it too is expected to be quite large. The vibrational levels will shift considerably changing the average positions of the atoms and the HOCl angle. Unknown effects from centrifugal distortion will also affect the angle. The poor results for the effective structure and the large difference between the effective inertial defect of the deuterated species and the hydrogen species indicated quite convincingly that an attempt should be made to account for the change in structure caused by substitution by D. This was done in the determination of the average structure, (described in section 4.5), where it was felt to be more worthwhile. 4.3. SUBSTITUTION STRUCTURE Because rotational constants had been determined for a set of isotopic species where all the atoms had been substituted, it was possible to calculate a full substitution structure. This proved to be quite useful when deciding how reliable the effective structure was. Microwave Spectrum of Hypochlorous Acid / 103 The coordinates for each atom of the substitution structure were calculated using Kraitchman's equations (section 2.3, equation (2.37)). These are presented in Table 4.6. Inspection of this table shows that the b-coordinate of the CI atom, b(Cl), is extremely small, putting it almost on the a-axis. The b-coordinate of the O atom, b(O), is also quite small and as a result neither could be reliably determined using Kraitchman's equations (17). One problem with Kraitchman's equations is that only the absolute value of the coordinate is determined. If this value is small it is then often unclear as to whether it is positive or negative. In order to determine the signs and more reliable values of the b-coordinates for chlorine and oxygen, the first moment, second moment and product of inertia equations were used. They are given below, specifically for HOCl: First Moment: m T I b „ + m„b„ + m-.b-,. = 0 (4.2a) rl 11 U U CI CI 2 2 2 Second Moment: mTJbTT + m~b„ + m„.b„. = I (4.2b) xl rl U U CI CI a Product of Inertia: "^^H^H + mO aO^O + mCl aCl' : )Cl = ^ (4.2c) Table 4.6 gives the three sets of values calculated for b(O) and b(Cl). (There are three different combinations of two equations from these three equations). It can be seen that all the values calculated are consistent with those calculated for them using Kraitchman's equations. The results from using the first moment and product of inertia equations, (method 2) were taken to be the most reliable because the second moment equation involves the principal moment of inertia, I . By definition I will contain unknown contributions from a a Microwave Spectrum of Hypochlorous Acid / 104 vibrations etc, that might become (undesirably) incorporated into the structure. However it was decided that because the values calculated for b(0) and b(Cl) using the above three methods agreed so well with those calculated using Kraitchman's equations that it would be most consistent to use the coordinates calculated from Kraitchman's equations for the final substitution structure calculation, given in Table 4.5. The signs of b(O) and b(Cl) were confirmed in the following way. When b(O) was made positive the resulting value for b(Cl) was ridiculously large and still positive. Having all b-coordinates positive does not make sense physically as a molecule would not lie entirely to one side of one of its principal inertial axes. A negative sign for b(O) led to b(Cl) being small and positive, and this makes sense physically. The next section describes the determination of the harmonic force field which produced harmonic parts of the a's used to calculate an average structure. However, to determine a force field a good estimate of the structure is needed. Because the uncertainty in the determined effective structure was so large the question arose as to whether this structure was accurate enough. The excellent agreement of it with the substitution structure led to the conclusion that it was. 4.4. THE HARMONIC FORCE FIELD HOCl is a simple three atom molecule with C g symmetry. All its vibrations are in the A' symmetry group. Determination of its symmetry coordinates was straightforward as each could be directly related to the three internal coordinates: Ar(O-H), Ar(O-O) and A < (HOCl). The symmetry Microwave Spectrum of Hypochlorous Acid / 105 coordinates and geometry used in the force field calculation are given in Table 4.7. A definition of the six force constants is also given in this table. The input data for the vibrational wavenumbers was an interesting, but carefully selected set of values from the literature. The two important criteria were that the data should be consistent and that they include the most accurately determined numbers. Therefore the v ^ and v 2 wavenumbers used for 16 35 16 37 H O CI and H O CI were those from the very high resolution gas IR work ' 16 35 of Sams and coworkers (9,10). The values for v \ and t>2 of D 0 CI were 1835 1835 those reported by Hedberg and Badger (5). For H O CI and D O CI the only values for v ^ and v 2 were those from the matrix infrared work. These wavenumbers were converted to "gas" IR values by applying the difference in gas and matrix IR frequencies from the corresponding "^0 species to them. For 16 37 18 37 D O CI and H O CI there were no values at all for v y and v 2. For the v 3 vibration there was almost a full set of matrix IR wavenumbers and only a few low resolution gas IR wavenumbers. Therefore the matrix IR values were used for v 3. Comparision of gas and matrix IR values for v 3 showed that there was only a few wavenumbers difference. The quartic centrifugal distortion constants determined in the analysis of each species' microwave spectrum (reference (16) and table 4.3) were also used as input data for the force field refinement. Values used as preliminary force constants to start the refinements were reasonable estimates made from the existing force fields. These values were then refined in a least squares fitting program which fits them to those vibrational wavenumbers and centrifugal distortion constants that have been included as input. It is a flexible program which takes any combination of Microwave Spectrum of Hypochlorous Acid / 106 wavenumbers and distortion constants available from any of a molecule's isotopic species. Similar to the structure fitting program the experimental data must be weighted. The weighting given a piece of data usually reflects how accurately it has been determined. Again the weighting is given as a somewhat arbitrary -2 uncertainty, where the weighting is proportional to the (uncertainty) . It turns out with this program that in order to make the program use the information provided by the wavenumbers the distortion constants must be given a larger percentage uncertainty than the wavenumbers. The uncertainties used in the final refinement will be given later as the values used varied throughout the analysis, as explained below. With all this input data - distortion constants and wavenumbers from six isotopic species - a good force field should have been easy to determine. However once again the large amount of anharmonicity present caused problems. The steps taken to obtain the best and most meaningful force field are described below. At first the uncertainty given each piece of data was varied in a realistic way to take into account how accurately the number had been determined. With no significant improvement from this procedure the observed vibrational wavenumbers v ^ , v 2 , f 3 were converted into estimated harmonic vibrational wavenumbers, a>, , CJ 2 , (*) 3 . This was done using the vibrational wavenumbers, v (calc), and harmonic vibrational wavenumbers, cj(calc), calculated by Botschwina (15). The difference between his two calculated numbers was applied to the observed vibrational wavenumbers, i>(exp), to get an estimated harmonic vibrational wavenumber, to (est), using the following equation: Microwave Spectrum of Hypochlorous Acid / 1 0 7 cj(est) = j>(exp) + {o)(calc)-i> (calc)} (4.3) Theoretically these harmonic vibrational wavenumbers have all anharmonic contributions removed from them which should make it easier for a harmonic force field to predict accurate values for them. Again there was no real improvement. Nevertheless it was interesting to learn that the anharmonic contribution to Vy was = 2 0 0 cm \ This unencouraging result led to doing a refinement which fit to Watson's determinable distortion constants: T , T , , , , , T , r ., and T n , rather than aaaa bbbb cccc 1 2 ' Watson's S reduction distortion constants. Determinable distortion constants and rotational constants are just a different linear combination of distortion constants and rotational constants which are independent of the reduction Hamiltonian used. In other words the same value is calculated for a determinable constant, regardless of the Hamiltonian used. The relationship between the two is given in Table 4.8. The vibrational data used for this refinement were the estimated harmonic vibrational wavenumbers. Once again there was no noticeable improvement. Since attempts to account for anharmonicity were apparently fruitless, the final force field was calculated using unaltered experimental wavenumbers and S reduction distortion constants. In these final refinements, the wavenumbers were given an uncertainty of 1%, while the distortion constants Dj and d^ were given uncertainties of 5%, and D J J ^ and Dj^ 1 0 % . was weighted out of the fit for all of the isotopic species because it was too poorly determined. This conclusion was made after calculating how well the following planarity condition Microwave Spectrum of Hypochlorous Acid / 108 for the quartic distortion constants held (18): 4C 0D J-(B 0 -C 0)D J K+2(2A 0 +B 0 +C 0)d 1-4(4A 0 +B 0 -3C 0)d 2 = 0 (4.4) For H O . CI the value calculated was 42.3 MHz. This non-zero value is caused by indeterminable contributions to the constants from vibration effects. Since d^ was the most poorly determined constant it seemed reasonable to accredit most of the error to the last term containing d^. The determined force field with all the force constants released is given in Table 4.9, under Fit I. It can be seen from Fit I in Table 4.9, that the two smallest force constants ^ 2 and f] 3 were not determined. This was most likely because f, 2 and ^ 3 are interaction force constants related to a high frequency vibration. Information about these constants comes primarily from the vibrational wavenumbers themselves and apparently there was not enough information available to determine them. Centrifugal distortion constants usually contain information mainly about force constants that describe lower frequency vibrations. Consequently a second refinement was done where ^ 2 and f, 3 were constrained to the values calculated by Botschwina (15). The results of this refinement are also presented in Table 4.9, under Fit II. Fit II with f, 2 and fj 3 constrained was taken to be the most reliable force field because ^ 2 and 3 were indeterminate. Therefore it was output from Fit II that was used in all further calculations. Table 4.10 shows how well the final force field predicts the vibrational wavenumbers and centrifugal distortion constants. The larger percentage error in the prediction of the frequency of the O —H stretching vibration was considered Microwave Spectrum of Hypochlorous Acid / 109 acceptable because this normal mode is the most likely to deviate from being well described by a harmonic potential function. For the distortion constants there was no way of knowing how the anharmonicity affected them, so the degree of accuracy in the force field prediction of them was gauged only by how accurately they were determined in the analysis of the rotational spectrum. 4.5. AVERAGE STRUCTURE The average rotational constants were calculated using the a (harmonic) 's produced by the harmonic force field, Fit II, and equation (2.33). The structure fitting program, described in section 4.2, was used to determine the average structure. The same percentage uncertainties as given to the effective rotational constants were given to the average rotational constants in all the refinements discussed below. Since an isotopic substitution had been made at each atomic site it. was possible to release all three structural parameters. The initial average structure determined was definitely an improvement over the effective structure. However it was felt that a more accurate structure could be determined if the change in O —H bond length on substitution by D was accounted for and the rotational constants had the contributions from electron-rotation interactions and centrifugal distortion effects removed. The steps taken to do this will be described below as concisely as possible. 18 Initially the change in O —H bond length after substitution by D (and O 37 and CI) was accounted for by using equation (2.36), developed by Kuchitsu (19). The values for the Morse anharmonicity parameter - "a" - were taken from reference (20), which contains a list of the "a" values (a3) for a number Microwave Spectrum of Hypochlorous Acid / 110 of diatomic molecules. The value of "a" for the O —H bond was taken directly 0 -1 from the paper as 2.305A while the value for the O-Cl bond had to be averaged from the values given for and Clg. This gave a(0 — CI) as ° -1 2 2.092A . 8(u ) and 5K were calculated from the values given by the force field 2 for u and K. The structure fitting program is written to accept the change in bond length, Sr^, upon isotopic substitution, so it was an easy matter to include the 8rz's in the refinement. This made yet another improvement in the precision of the structure. As mentioned 6r^ for O—D was an order of magnitude larger than for most other isotopic substitutions. Because 8rz(0—D) was so large it was felt that actually refining to this change might improve the accuracy. The subroutine that defines the structural parameters was modified and 8r (O —D) z was released as a fitting parameter. There was too little data to determine an accurate value for it; however it was encouraging to observe that 8rz(0 —D) determined by the program was essentially the same as that calculated using Kuchitsu's equation (2.36). 8r (O-D) = -0.0028(19)A; 5r (O-D) z reiineci z calc 0 -0.0024A. In a similar way the structural parameter subroutine was modified to fit to the change in <(DOCl), 8a z < The resulting refinement using this parameter was not as accurate as the previous one, but the standard deviation was still better than when only the three structural parameters were released. To ensure that every possible contribution to the rotational constants preventing an accurate determination of the structure was removed, the contribution from the electron-rotation interactions was accounted for using the following expression developed by Oka and Morino (21). Microwave Spectrum of Hypochlorous Acid / 111 AG = - ^ g G G G 0 G = A, B, C (4.5) where g G G is the molecular g-value for that principal axis; m and M are the mass of an electron and a proton, respectively. This change in rotational constant is added to the average rotational constant to get the modified one, (minus electron-rotation interactions), which has been given the symbol, G z g: G = G + AG (4.6) ze z The only molecular g-values available for HOCl were those determined by 16 35 Suzuki and Guarnieri (4) for H O CI. Consequently it was assumed that the g-values were isotopically invariant. Although not strictly true, the assumption was valid in this situation because the isotopic variation in g-values was less than the uncertainty in the rotational constants. Using the G 's in a structure ze refinement produced a small improvement in the accuracy. As a last step in the structure determination it was decided to remove the contributions to the rotational constants from centrifugal distortion. This decision was made when it was noticed that the difference between the observed and calculated values (from the structure refinements) for B 0 and C 0 was very 18 35 18 37 similar for each pair of chlorine species, (e.g. H O CI and H O CI). This indicated a non-random error in the calculated rotational constants, that could have been caused by centrifugal distortion. The large difference between the determinable rotational constants and the S reduction rotational constants for B 0 and C 0 was yet another indication. These differences are given in Table 4.11. This large difference can arise when the A rotational constant is very large. It Microwave Spectrum of Hypochlorous Acid / 112 only occurs to the B 0 and C 0 rotational constants because their determinable rotational constants are defined using a term that is proportional to the square of the A rotational constant (22). The determinable rotational constants are related to Kivelson and Wilson rotational constants (equation (2.12)), in the following way: D .KW _ ^ bbcc A" = A - iT D KW B = - \r (4.7) aacc D „ K W aabb D D D KW KW KW where A , B , C are determinable rotational constants and A , B , C are Kivelson and Wilson rotational constants. The method used to convert S reduction rotational constants to rigid rotor rotational constants (i.e. rotational constants with contributions from centrifugal distortion removed) was quite long and complicated. Only a bare outline will be explained here: Step 1: Watson's determinable rotational constants were converted to Kivelson and Wilson rotational constants using equations (4.7). A^, B^, C"^  were calculated from S reduction output using the equations given in Table 4.8. r \ , , T ' . . , T ' were taken from the output of the harmonic force field, bbcc aabb aacc Step 2: ?" a D a b was calculated for each isotopic species. This can be done in a variety of complicated ways. Here the easiest and most convenient method was deemed to be sufficiently accurate. The expression used was (22,23): T , , = \{r 1 - r ,, - T - r u u ) (4.8) abab 1 aabb aacc bbcc Microwave Spectrum of Hypochlorous Acid / 113 The expression for r 1 is given in Table 4.8, and r r , r,, were J. c l c l D D 3.3.CC D O C C calculated using the planar relations given in Table 4.12. All constants used in these calculations were those from the S reduction refinement. The values calculated for T ^  ^ are given in Table 4.13 where it can be seen that the 18 T ak &k values for the two H OC1 species are drastically different. Since no values for DT. or d 0 were determined for these two species it was decided that it would be more accurate to use the r , , values calculated for the abab 16 corresponding H OC1 species. Step 3: Kivelson and Wilson rotational constants were converted to true R R R\ effective (rigid rotor) rotational constants, (A , B , C ), using the following equations: A R = A K W + l/2r h h abab R KW B = B + 1 / 2'abab ( 4- 9 ) C R = C K W - 3/4r h h abab After this calculation was complete it was necessary to account for harmonic vibration and electron rotation interactions. These rotational constants were given the symbol &zer a n ^ were used to determine the three final average structures presented in Table 4.14. The difference between the three structures is the number and kind of parameters released, and is described earlier in this section with regard to the change in the structure caused by substitution of H Microwave Spectrum of Hypochlorous Acid / 114 by D. It can be seen that Fit 2 has the lowest standard deviation and therefore it was taken to represent the r^ structure in Table 4.15 where all four structures determined in this study are given for comparison. The last structural parameters calculated were estimates of the equilibrium 2 bond lengths, r , calculated using equation (2.35): = r^ — 3/2au +K. The 2 values for u and K were taken directly from the force field. No value could be calculated for the r angle so it was taken to be the r value. These e z estimated values are also in Table 4.15. The final average structure is shown in Figure 4.1. 4.6. COMMENTS The measurement of b-type lines has led to the determination of much 35 improved values for the quadrupole coupling constants for both the CI and 37 CI deuterated species. The previously determined values are given along with the most recently determined ones for comparison, in Table 4.3. Since HOCl is a planar molecule a good measure of the accuracy of the constants can be 35 37 determined by how well the ratio x ( (. ^ agrees with the theoretical value obtained when this ratio is taken for the quadrupole moments of the nuclei. The experimental value of 1.2732 is in excellent agreement with the theoretical value of 1.2688. An interesting conclusion can be drawn from the value of X • The 3 3 a-inertial axis is very close to lying along the O — CI bond, the angle between them, 8 , is 2.26°. It is usually assumed that the bond containing the za chlorine atom is the principal axis of the quadrupole coupling tensor. This has Microwave Spectrum of Hypochlorous Acid / 115 been shown to be true for chloroketene (24) and was assumed to be true for HOCl as well. A value for Y > X and X can be calculated from Y , zz xx yy ~aa X^, and x c c by rotating the axes using a transformation matrix. The details of this are explained in section 6.6. x for HOCl was determined to be zz — 122.2 MHz. This is larger than the value for the chlorine atom, (x a t ) , of zz — 109.7 MHz (25). For most molecules bonding causes |x | to drop because of the increased screening of the nucleus. However the increase in x for zz HOC! can be explained by the fact that the chlorine is bonded to a more electronegative atom than itself, oxygen. The oxygen will draw electrons away from the 3p bonding orbital of chlorine thereby reducing the screening around the chlorine. Using Townes-Dailey theory the amount of ir character in the O — CI bond was calculated from X x x and Xy y (equation(6.9)) and turned out to be 1.6%. This theory is explained in detail in section 6.6, in the discussion of the bonding in CF NCI. Knowing x and ir a value for the amount of ionic character, i, in the O —CI bond was calculated. There are three structures having different forms of bonding that can contribute to the value of X z z of HOCl. One is of normal covalent bonding, the second is an ionic form and the last is a double bond structure. (See Figure 6.3 for an example of these three types of at structures). Since Xzz(HOCl) > X (CI) the ionic form should have the CI as the positive pole. In this case it is valid to ignore any contributions from sp hybridization at CI and screening of the nucleus caused by a changed charge distribution because chlorine is less electronegative than oxygen (26). When these two approximations have been made the expression to calculate the amount of ionic character in the O —CI bond becomes: Microwave Spectrum of Hypochlorous Acid / 116 (l-i-7T)(xl t) + i(2xlfc) + TTdxf) (4.10) Y Z Z " ' ~ " Z Z ' ' "zz' ""zz' Substituting in for all the known variables gave a value of 12.2% for i, the ionic character. This made the amount of covalent character in the O —CI bond 86.2%. As already mentioned, eight force fields have been determined for this molecule. To be able to compare them all, the force constants of each are given in Table 4.16. The one reported here and the one calculated by Deeley and Mills (11) have both been determined using comparable size experimental data sets. It can be seen that they too had difficulty determining f, 2 and -f, 3 . It is interesting to see that the value determined by them for f, 2 is so large. Their value for f 1 3 , like ours is not determined, but agrees with ours, within the error limits given. Although all the force constants for the harmonic force field of HOCl could not be determined from this data, there are many reasons why the one quoted in Table 4.9, under Fit II, is believed to be a reliable force field. One reason is that the force field accurately predicts the ground state inertial defect, A0, for each isotope very well. This was determined using the equation (21): ^vib + ^cent + ^elec (4.11) where A ., is the contribution from the harmonic force field, A , is a vib cent centrifugal distortion contribution to account for small distortion corrections to the observed effective rotational constants and A . is the electronic contribution. elec Table 4.17 has the calculated values for all these contributions plus the Microwave Spectrum of Hypochlorous Acid / 117 experimentally observed A 0. It can be seen that the A 0 (obs) is in excellent agreement with A 0 (calc), such that even the shift in A 0 for the deuterated species has been well reproduced. A second indication that the force field is reliable is that the values predicted for d^ agree very well with the measured ones in both magnitude and sign. Recall that even though values for dg were determined for four of the six isotopic species none of them were used as input data for the force field determination. Lastly it is encouraging to note that the four values released in both Fit I and Fit II are in excellent agreement. This indicates that even though 2 and ^ 3 could not be determined in Fit I the values calculated are good estimates. A last point that needs to made about the determined force field is that because it was calculated using unaltered experimental numbers the force constants determined cannot be true values for a purely harmonic force field. There is a lot of anharmonicity in the potential function for HOCl so any force constants determined with only experimental numbers have to be degraded somewhat by it. With this in mind it is interesting to see that Botschwina's force constants are = 10% larger (anharmonicity usually decreases vibrational amplitudes) - but then they were determined using theoretically calculated harmonic vibrational wavenumbers, a>! In order to determine a significantly more reliable force field than presently available it would be necessary to have information about the anharmonicity from vibrational overtones or combinations, plus other types of Microwave Spectrum of Hypochlorous Acid / 118 experimental data (e.g. Coriolis coupling constants). The ideal situation would be to measure the rotational spectra of all the first excited vibrational levels (v = 1) and therefore be able to determine the a's for all these levels. Then anharmonicity could be properly accounted for. Microwave Spectrum of Hypochlorous Acid / 119 TABLE 4.1 Representative Sample of Transitions with Resolved Hyperfine Structure of HOCl Transition Frequency (uncertainty) (MHz) Obs-Calce splits (MHz) D 1 60 3 5C1 lo 1 uo o 2.5 1.5 0.5 1.5 1.5 1.5 27979.925(20) 27949.540(20) 28004.160(20) 0.026 0.000 -0.030 '1 2 -1 1 1 3.5 - 2.5 55328.404(30) 1.5 - 0.5 55335.784(30) 2.5 - 1.5 55297.990(30) 1.5 - 1.5 55309.180(30) 2.5 - 2.5 55312.870(30) 0.5 - 0.5 55351.360(30) -0.003 0.011 -0.058 -0.001 0.049 0.001 '1 8 J 0 9 7.5 - 8.5 54603.274(20) 8.5 - 9.5 54602.842(20) 6.5 - 7.5 54602.440(20) 9.5 - 10.5 54601.960(20) 0.006 0.008 -0.032 0.018 9, 9-10, o 1 o 10.5 - 11.5 23961.718(20) 8.5 - 9.5 23962.746(20) 9.5 - 10.5 23962.258(40) 7.5 - 8.5 23962.258(40) 0.030 -0.004 0.112 -0.138 12 1 1 i 12 1 1 2 13.5 - 13.5 48556.638(40) 10.5 - 10.5 48556.638(40) 12.5 - 12.5 48557.496(40) 11.5 - 11.5 48557.496(40) -0.072 0.026 -0.026 0.072 Observed frequency minus the frequency calculated using the fitted spectroscopic constants. Microwave Spectrum of Hypochlorous Acid / 120 TABLE 4.2 Observed Transition Frequencies (in MHz), with Hyperfine Structure Removed of HOCl Transition Frequency Obs-Calc Weight D i U0° JCl 1 0 1 • 0 0 0 27973.824 -0.018 1.0000 2 0 2 - 1 0 1 55946.175 -0.058 1.0000 2 1 2 - 1 i 1 55321.001 0.070 1.0000 2 1 1 - 1 i 0 56567.202 0.029 1.0000 6 2 4 - 5 2 3 167815.110? -0.013 1.0000 6 2 5 - 5 2 4 167783.180 0.002 1.0000 8 1 7 - 8 1 8 22423.594 . 0.066 1.0000 8 1 8 - 9 0 9 54602.573 0.001 1.0000 9 1 9 • 10 0 1 0 23962.195 -0.006 1.0000 9 1 8 - 9 1 9 . 28026.131 -0.030 1.0000 10 1 9 - 10 1 1 0 34249.676 -0.014 1.0000 11 1 1 0 - 11 1 1 1 41093.508 -0.031 1.0000 12 0 1 2 - 11 1 1 1 38109.690 -0.017 LOOOO 12 1 1 1 - 12 1 1 2 48557.067 0.023 1.0000 13 0 1 3 - 12 1 1 2 69523.520 0.013 1.0000 28 2 2 7 - 29 1 2 8 9186.160 -0.035 1.0000 30 1 2 9 - 29 2 2 8 27435.144 -0.068 1.0000 31 1 3 0 - 30 2 2 9 64291.160 0.033 1.0000 7C1 1 0 1 - 0 O O 27473.340 -0.024 1.0000 2 0 2 - 1 0 1 54945.357 -0.003 1.0000 2 2 - 1 1 1 54342.197 0.082 1.0000 2 1 - 1 1 0 55544.236 -0.064 1.0000 8 8 - 9 0 9 59707.578 -0.015 1.0000 9 8 - 9 1 9 27035.611 0.017 1.0000 9 9 - 10 0 1 0 29657.574 0.028 1.0000 10 9 - 10 1 1 O 33039.262 0.032 1.0000 11 1 0 - 11 1 1 1 39641.242 -0.066 1.0000 12 1 1 - 12 1 1 2 46841.232 0.026 1.0000 12 0 1 2 - 11 1 1 1 31210.264 0.017 1.0000 13 0 1 3 - 12 1 1 2 62011.440 -0.006 1.0000 27 2 2 6 - 28 1 2 7 64454.440 -0.027 1.0000 28 2 2 7 - 29 1 2 8 28851.108 0.037 1.0000 31 1 3 0 - 30 2 2 9 43052.270 0.011 1.0000 Microwave Spectrum of Hypochlorous Acid / 121 TABLE 4.2 - continued Transition Frequency Obs-Calca Weight 1 0 1 - 0 0 0 27805.247 0.008 1.0000 2 1 2 - 1 1 1 55263.220 0.000 1.0000 2 1 1 - 1 1 0 55947.587 -0.000 1.0000 2 0 2 - 1 0 1 55609.770 -0.004 1.0000 17 1 1 7 - 18 0 1 8 68322.600 -0.004 1.0000 18 1 1 8 - 19 0 1 9 37637.265 0.007 1.0000 21 0 2 1 - 20 1 2 0 24147.195 0.007 1.0000 22 0 2 2 - 21 1 2 1 55240.130 -0.003 1.0000 7C1 1 0 1 - 0 0 0 27284.065 -0.004 1.0000 2 1 2 - 1 1 1 54233.520 -0.001 1.0000 2 0 2 - 1 0 1 54567.450 0.003 1.0000 2 1 1 - 1 1 0 54892.660 -0.000 1.0000 18 1 1 8 - 19 0 1 9 48797.487 -0.029 1.0000 19 1 1 9 - 20 0 2 0 18600.430 0.073 1.0000 21 0 2 1 - 20 1 2 0 11728.616 0.053 1.0000 22 0 2 2 - 21 1 2 1 42186.315 -0.001 1.0000 23 0 2 3 - 22 1 2 2 72769.860 -0.007 1.0000 Observed frequency minus the frequency calculated using the fitted spectoscopic constants. Mirri et al, reference (2). Microwave Spectrum of Hypochlorous Acid / 122 TABLE 4.3 Spectroscopic Constants of HOCl Parameter D 1 60 3 5C1 D 1 60 3 7C1 H 1 80 3 5C1 H 1 80 3 7C1 Rotational Constants (MHz) A 0 331338.764(114)a 331311.616(141) 608205.795(323) 608187.493(1710) B 0 14298.5405(78) 14037.2853(75) 14073.7664(45) 13806.8723(243) C 0 13675.3910(78) 13436.1650(76) 13731.5653(43) 13477.2884(230) Centrifugal Distortion Constants (KHz) D J 22.2427(330) 21.4794(224) 23.1623(657) 23.0493(3270) D J K 774.94(153) 751.77(56) 1130.36(286) 1123.96(1536) D K 39682.6(863) 39700.b 126750.b 126850.b d l -0.91411(330) -0.87254(427) -0.54770(775) -0.45406(3501) d2 -10.288(366)xl0"2 -9.335(462)xl0"2 -5.6xl0"2 b -4.7X10"2 b z -5 b -5 b -5 b -5 b H I -2.4x10 -1.8x10 -2.4x10 -1.8x10 0 H K J 0.3b b 0.3b b 0.7b b 0.65b b H K 21.5 21.5 125.0 128.0 hlorine Quadrupole Coupling Constants (MHz) X 0 0 -121.438(47)C -95.712(75)° e e aa -121.54(8)d -95.61(15)d X b b ~ x -3.251(85)C cc , -2.220(15)C e e -3.36(26)d -2.37(47)d 62.344(85)C 48.966(114)° e e C C 62.45(17)d 48.99(31)d Microwave Spectrum of Hypochlorous Acid / 123 Numbers in parentheses are one standard deviation in units of the last significant figures. Constrained as described in text. Values obtained in present work. Values from reference (2). ^ Constrained to corresponding values of H OC1. Microwave Spectrum of Hypochlorous Acid / 124 TABLE 4.4 Effective and Average Inertial Defects for HOCl Inertial Defects (uA ) Species Effective A 0 Average A Average A zer H 1 60 3 5C1 H 1 60 3 7C1 D 1 60 3 5C1 D 1 60 3 7C1 H 1 80 3 5C1 H 1 80 3 7C1 0.06392 0.06394 0.08530 0.08533 0.06396 0.06417 0.002758 0.002774 0.002335 0.002348 0.002577 0.002794 0.001202 0.001340 0.000854 0.000752 0.000349 0.000704 Definition of the Inertial Defects Effective A 0 = Jc " !B ~ XA Average A z = I* - I* - I* Average (corrected) A = 1^, — iff — I * e r b zer C B A Microwave Spectrum of Hypochlorous Acid / 125 TABLE 4.5 Effective and Substitution Structures of HOCl a b Parameter Effective Substitution r(O-H) 0.964±0.075A 0.962 + 0.005A r(O-Cl) 1.695 + 0.027A 1.693±0.003A , <(HOCl) 102.7+15.8° 102.4 + 0.3° Si k Standard deviation of the fit is 14.4 MHz. Errors estimated from adequacies of the r method. s Microwave Spectrum of Hypochlorous Acid / 126 TABLE 4.6 Atomic Coordinates of the Substitution Structure of HOCl, In Its Principal Axis System a and b Coordinates of Each Atom Determined Using Kraitchman's Equations s s Atom a g (A) b g (A) H -1.377 0.867000 0 -1.133 ±0.063110 CI 0.558 ±0.003992 Comparison of Results from Three Methods Used to Calculate b(O) and b(Cl) Method b(O) b(Cl) 1 -0.06375A 0.004161A 2 -0.06254A 0.003608A 3 -0.06395A 0.002294A Method 1: First and Second Moments of Inertia Method 2: First Moment and Product of Inertia Method 3: Second Moment and Product of Inertia Microwave Spectrum of Hypochlorous Acid / 127 TABLE 4.7 Symmetry Coordinates and Geometry of HOCl Used in the Harmonic Force Field Analysis Symmetry Coordinates, Internal Coordinates and Geometry S, = R, = Ar(O-H) = 0.964A 5 2 = R3 = A < (HOCl) = 103° 5 3 = R2 = Ar(O-Cl) = 1.695A Definition of the Force Constants A' r(O-H) <(HOCl) r(O-Cl) r(O-H) f, i . f 1 2 f, 3 <(HOCl) f 2 2 f 2 3 r(O-Cl) f 3 3 From effective structure calculation (Table 4.5). Microwave Spectrum of Hypochlorous Acid / 128 TABLE 4.8 Relationship Between Watson's Determinable Rotational Constants and the A Reduction Rotational Constants A ° = A A + 2Aj B D = B A + 2Aj + A J K - 25j - 2 5 R C D = C A + 2Aj + A J R + 25j + 2 5 R raaaa = " 4 ( A J + A J K + V Tbbbb = ~ 4 ( A J + 2*J> r = -4(A T " 26 ) cccc J J T 1 4 ^ 3 ^ J + ^JK^ raaaa + Tbbbb + Tcccc r 2 = -4(B R + C R+A R)A J - 2(B R+C R)A J K + 4(B R-C R)(5j + o R) = A K W r ' + B K W r ' + C K W r ' h h bbcc aacc aabb where TL — T CC + 2r„ „ ffgg ffgg fgfg a References (23) and (27). A^, B^, C^ are determinable rotational constants. A R, B R, C R are rigid rotor rotational constants. A A A A , B , C are A reduction rotational constants. Microwave Spectrum of Hypochlorous Acid / 129 TABLE 4.8 - continued Relationship Between Watson's Determinable Rotational Constants and the S Reduction Rotational Constants A D = A S + 2Dj + 6d 2 B D = B S + 2Dj + D J R + 2d 1 + 4d 2 C D = C S + 2Dj + D J R - 2d 1 + 4d 2 'aaaa = " 4 ( D J + °JK + D K } rbbbb = " 4 ( D J " 2 d l - 2 ( V Tcccc = ~ 4 ( D J + 2 d l " 2 d 2 } T l = " 4 ( 3 D J + D J K + ^ r 2 = -4(B R+C R+A R)D J - 2(B R+C R)D J K - 4(B R-C R)d 1 - 24A Rd 2 a References (23) and (27). A^, B^ C^ are determinable rotational constants. A R, B R, C R are rigid rotor rotational constants. S S S A , B , C are S reduction rotational constants. Microwave Spectrum of Hypochlorous Acid / 130 TABLE 4.9 Harmonic Force Fields of HOCl Force Constant Fit I Fit II Value Value Species A' f, , 7.375(50)b 7.363(48) f, 2 0.14(10) 0.031° f, 3 -0.15(19) -0.145° f 2 2 0.796(8) 0.795(5) f 2 3 0.414(56) 0.422(19) f 3 3 3.674(31) 3.678(22) " 0 Units of mdyn/A for stretching constants, mdyn A/rad for bending constants, and mdyn/rad for stretch-bend interactions Numbers in parentheses are one standard deviation in units of the last significant figures. Fixed at these values determined by Botschwina (15). Microwave Spectrum of Hypochlorous Acid / 131 TABLE 4.10 Observed and Calculated Wavenumbers and Centrifugal Distortion Constants of HOCl H 1 60 3 5C1 obsa calc'3 obs-calc H 1 60 3 7C1 obsa calcb obs-calc Wavenumbers (cm ) v j 3609.481 v2 1238.621 v 3 729.002 3631.70 1240.77 728.18 -22.22 -2.15 0.82 3609.481 1238.121 723.002 3631.70 1240.32 721.82 -22.22 -2.20 1.18 Centrifugal Distortion Constants (kHz) A J 26.888 27.139 -0.251 25.973 26.213 -0.240 A J K 1251.42 1182.36 69.06 1215.81 1149.25 66.56 A K 130198.9 119836.7 10362.2 130289.7 119823.8 10465.9 5 J -0.635 -0.594 -0.041 -0.600 -0.564 -0.036 5 K -0.056 -0.035 -0.021 -0.048 -0.033 -0.015 Observed distortion constants are from this work. Calculated values were obtained from the harmonic force field given in Table 4.9. 1 Reference (9,10)- high resolution gas infrared 2 Reference (6) - matrix infrared Microwave Spectrum of Hypochlorous Acid / 132 TABLE 4.10 - continued D 1 60 3 5C1 D 1 60 3 7C1 v obsa calc^ obs-calc obsa calc^ obs-calc Wavenumbers (cm ^) i», 2674.003 2645.25 28.75 - 2645.25 v2 911.003 907.22 3.78 - 906.79 3 728.002 723.74 4.26 - 717.11 Centrifugal Distortion Constants (kHz) 22.243 22.569 -0.326 21.480 21.787 -0.307 A J K 774.96 744.68 30.28 751.77 721.00 30.77 A K 39682.6 37903.1 1779.5 - 37894.4 5 J -0.915 -0.896 -0.019 -0.873 -0.850 -0.023 5 K -0.103 -0.089 -0.014 -0.093 -0.081 -0.012 Observed distortion constants are from this work. Calculated values were obtained from the harmonic force field given in Table 4.9. 2 Reference (6) - matrix infrared 3 Reference (5) - gas infrared Microwave Spectrum of Hypochlorous Acid / 133 TABLE 4.10 - continued H 1 80 3 5C1 obsa calcb obs-calc H 1 80 3 7C1 obsa calcb obs-calc Wavenumbers (cm *) v, 3577.90" 3619.55 -41.65 - 3619.55 v 2 1237.00* 1237.24 -0.24 - 1236.77 v3 701.002 700.39 0.61 695.002 693.80 1.20 Centrifugal Distortion Constants (kHz) Aj 23.162 23.717 -0.555 23.049 22.848 0.201 ATT. 1130.36 1071.76 58.60 1123.96 1039.86 84.10 AR - 116671.4 - 116662.9 5j -0.548 -0.486 -0.062 -0.454 -0.459 0.005 5 R - -0.027 - -0.026 a b Observed distortion constants are from this work. Calculated values were obtained from the harmonic force field given in Table 4.9. Reference (6) - matrix infrared Matrix infrared values from reference (6) were converted to gas infrared values by applying the difference between observed gas and matrix values from the corresponding 1 6 O species. Microwave Spectrum of Hypochlorous Acid / 134 TABLE 4.11 Differences Between S Reduction and Determinable Rotational Constants (in MHz) For D 1 60 3 5C1, D 1 60 3 7C1, H 1 8Q 3 5C1, and H 1 80 3 ?C1 Species Constant Determinable S Reduction Difference Constant Constant D 1 60 3 5C1 A B C 331338.808 14299.358 13676.212 331338.764 14298.541 13675.391 0.044 0.817 0.821 D 1 60 3 7C1 A B C 331311.640 14038.077 13436.960 331311.598 14037.285 13436.165 0.042 0.792 0.795 H 1 80 3 5C1 A B C 608209.461 14074.942 13732.743 608209.415 14073.766 13731.565 0.046 1.176 1.178 H 1 80 3 7C1 A B C 608191.149 13808.041 13478.459 608191.103 13806.872 13477.288 0.046 1.169 1.171 Microwave Spectrum of Hypochlorous Acid / 135 TABLE 4.12 The Planar Relations T = r, , = 0 acac bcbc A 2 B 2 r_ Taaaa _ rbbbb r c c c c •  'aabb = 2 L " A 4 " B4 c 4 A 2 C 2 r raaaa _ Tbbbb r c c c c 'aacc = 2 L A4 " B4 c 4 B 2 C 2 r_ Taaaa Tbbbb T c c c c -• Tbbcc ~ 4 4 4 g^  ^ Information from reference (25) For a planar molecule in the "ab" plane. Microwave Spectrum of Hypochlorous Acid / 136 TABLE 4.13 7"abab Values for the Six Isotopic Species of HOCl Species r ^ ^(MHz) H 1 60 3 5C1 -1.6410 H 1 60 3 ?C1 -1.5453 D 1 60 3 5C1 -1.2607 D 1 60 3 7C1 -1.2525 H 1 80 3 5C1 -1.976la H 1 80 3 7C1 -0.6752a These values appeared to be poorly determined so the values for the corresponding 1 6 O species were used instead. Microwave Spectrum of Hypochlorous Acid / 137 TABLE 4.14 Ground State Average Structures of HOCl Parameter Pit I Fit II Fit III r(O-H) r(O-Cl) <(HOCl) 6r (O-D) z 5 a (DOC1) z 0.9731(44)A 1.6974(15)A 102.45(87)° s.d. 0.76 0.9732(23)A 1.6974(07)A 102.45(42)° -0.0028(19)A 0.35 0.9725(56)A 1.6975(18)A 102.3(14)° 0.08(69)° 0.47 Numbers in parentheses are one standard deviation in units of the last significant figures. Standard Deviation of the fit in MHz. Microwave Spectrum of Hypochlorous Acid / 138 T A B L E 4.15 Comparison of the Four Structures Determined for HOCl Parameter Effective Substitution Average Equilibrium r r r r o s z e r(O-H) (A) r(O-Cl) (A) <(H0C1) (°) 0.964(75) 1.695(27) 103.(16) 0.962(5)b 1.693(3) 102.4(3) 0.9732(23)a 1.6974(07) 102.45(42) 0.9636(25)b 1.6908(10) Numbers in parentheses are one standard deviation in units of the last significant figures. Numbers in parentheses are estimated uncertainties in units of the last significant figures. Microwave Spectrum of Hypochlorous Acid / 139 TABLE 4.16 Comparison of All the Harmonic Force Fields* of HOCl August 1986 Force Hedberg1 Schwager2 Ogilvie3 Namasivayam4 Constant et al et al et al f, , 7.35 7.104 7.317 7.276 f, 2 - - -0.100 0.011 f, 3 - - - -0.018 f 2 2 0.77 0.775 0.790 0.769 f 2 3 0.45 0.677 0.384 0.161 f 3 3 3.86 3.980 3.620 3.542 Force Botschwina5 Murrell6 Deeley7 This Constant et al et al Work f, , 8.196 7.9305 7.377(364)" 7.36(48) f, 2 0.031 -0.1264 0.439(117) 0.031C f, 3 -0.145 0.0 0.112(315) -0.145C f 2 2 0.8396 0.8815 0.8423(256) 0.795(5) f 2 3 0.638 0.9007 0.543(104) 0.422(19) f 3 3 4.208 4.5039 3.787(118) 3.678(22) Units of mdyn/A for stretching constants, mdyn A/radz for bending constants, and mdyn/rad for stretch-bend interactions Numbers in parentheses are one standard deviation in units of the last significant figures. Kept constrained at the values determined by Botschwina (15). Microwave Spectrum of Hypochlorous Acid / 140 1 Reference (5). 2 Reference (6). 3 Reference (12). a Reference (13). 5 Reference (15). 6 Reference (14). 7 Reference (11). Microwave Spectrum of Hypochlorous Acid / 141 TABLE 4.17 * 2 Observed and Calculated Inertial Defects (uA ) of HOCl Isotopic Observed Calculated Values Species Value ( A o ) Avib Acent *elec H 1 60 3 5C1 H 1 60 3 7C1 D 1 60 3 5C1 D 1 60 3 7C1 H 1 80 3 5C1 H 1 80 3 7C1 0.06392 0.061162 0.004684 0.000069 0.065915 0.06394 0.061166 0.004568 0.000065 0.065799 0.08530 0.082965 0.004116 0.000324 0.087405 0.08533 0.082982 0.004239 0.000319 0.087540 0.06396 0.061383 0.005274 0.000053 0.066829 0.06417 0.061376 0.005274 0.000048 0.066698 Microwave Spectrum of Hypochlorous Acid / 142 Figure 4.1. The Ground State Average Structure of HOCl, in its Principal Inertial Axis System. BIBLIOGRAPHY 1. D.C. Lindsey, D.G. Lister and D.J. Millen, Chem Commun, 950-951 (1969). 2. A.M. Mirri, F. Scappini, and G. Cazzoli, J Mol Spectrosc, 38, 218-227 (1971). 3. D.G. Lister and D.J. Millen, Trans Faraday Soc, 67, 601-604, (1971). 4. M. Suzuki and A. Guarnieri, Z Naturforsch, 30A, 497-505 (1975). 5. K. Hedberg and R.M. Badger, J Chem Phys, 19, 508 (1951). 6. I. Schwager and A. Arkell, J Amer Chem Soc, 89, 6006-6008 (1967). 7. R.A. Ashby, J Mol Spectrosc, 23, 439-447 (1967). 8. R.A. Ashby, J Mol Spectrosc, 40, 639-640 (1971). 9. J.S. Wells, R.L. Sams, and W.J. Lafferty, J Mol Spectrosc, 77, 349-364 (1979). 10. R.L. Sams, and W.B. Olson, J Mol Spectrosc, 84, 113-123 (1980). 11. CM. Deeley and I.M. Mills, J Mol Spectrosc, 114, 368-376 (1985). 12. J.F. Ogilvie, Can J Spectrosc, 19, 171-177 (1974). 13. R. Namasivayam and S. Mayilavelan, Z Naturforsch, 34A, 716-720 (1979). 14. J.N. Murrell, S. Carter, I.M. Mills, and M.F. Guest, Mol Phys, 37, 1199-1222 (1979). 15. P. Botschwina, Chem Phys, 40, 33-44 (1979). 16. H.E. Gillis Singbeil, W.D. Anderson, R.W. Davis, M.C.L. Gerry, E.A. Cohen, H.M. Pickett, F.J. Lovas and R.D. Suenram, J Mol Spectrosc, 103, 466-485 (1984). 17. C.C. Costain, Trans Amer Crystallographic Assoc, 2, 157 (1966) r 18. J.K.G. Watson, in Vibrational Spectra and Structure, a series of advances, Ed. J.R. Durig, Vol. 6, Elsevier, New York, 1977, Chapter 1, page 73. 19. K. Kuchitsu, J Chem Phys, 49, 4456-4462 (1968); K. Kuchitsu, T. Fukuyama and Y. Morino, J Mol Struct, 4, 41-50 (1969) 20. K. Kuchitsu and Y. Morino, Bull Chem Soc Japan, 38, 805-824 (1965). 21. T. Oka and Y. Morino, J Mol Spectrosc, 6, 472-482, (1961) 143 / 144 22. D. Kivelson and E.B. Wilson Jr, J Chem Phys, 21, 1229-1236 U953). 23. J.K.G. Watson, J Chem Phys, 46, 1935-1949 (1967). 24. M.C.L. Gerry, W. Lewis-Bevan, and N.P.C. Westwood, J Chem Phys, 79, 4655-4663 (1983) 25. W. Gordy and R.L. Cook, Microwave Molecular Spectra, in Technique of Organic Chemistry, Ed. A. Weissburger, Vol IX, Part II, Interscience Publishers, New York, 1970, page 224. 26. W. Gordy and R.L. Cook, op_. cit., chapter 14, page 583. 27. J.K.G. Watson, in Vibrational Spectra and Structure, a series of advances, Ed. J.R. Durig, Vol. 6, Elsevier, New York, 1977, Chapter 1, pages 40-41. 5. MICROWAVE SPECTRUM OF CARBONYL CHLOROFLUORIDE The first measurements of microwave transitions of carbonyl chlorofluoride, FC1CO, were carried out by Mirri et al (1) in 1962. For F C1CO twenty-two transitions which included both a- and b-type P and Q branch lines were measured. Using an incorrect model of the rotational Hamiltonian (pre Watson era), the three rotational constants and six quartic centrifugal distortion constants 37 were reported. For F C1CO eleven transitions were measured and included the • 3 5 same variety of lines as those measured for F C1CO. However interestingly, only the three rotational constants and the two nuclear quadrupole coupling 37 constants of CI were obtained. The data also allowed them to make an estimate of the structure. Later the dipole moment was measured in a Stark effect study of three low J transitions (2). A Zeeman effect study allowed Scappini et al (3) to determine the chlorine quadrupole coupling constants for 35 F C1CO plus its chlorine nuclear gj factor, molecular g-values and the magnetic susceptibility anisotropies. Its electronic spectrum has also been measured (4). The first and only reported vibrational spectrum was taken in 1952 by Nielsen et al (5). It was taken in the gas phase at low resolution (4 cm )^ for 35 the F C1CO species only. Recently a structural study of FC1CO was carried out by Oberhammer who measured its electron diffraction intensities (6). These and the two sets of rotational constants were used to determine a reliable estimate of the average structure. Previous ab initio calculations of the structure (7) agreed very well with his results. In order to calculate this structure a harmonic force field was also determined. Only the diagonal force constants could be obtained; the off-diagonal ones were transferred from the harmonic force field of FC1CS. 145 Microwave Spectrum of Carbonyl Chlorofluoride / 146 Because FCICO may be an important intermediate in reactions taking place in the stratosphere between ozone and organochlorine compounds (see introductory chapter for more details), the need to monitor or detect its rotational spectrum may arise. Should this occur, the constants available, in particular the centrifugal distortion constants, are not adequate to make reliable predictions of the spectrum to high J and K , or to high microwave frequencies (e.g. a 600 — 800 GHz). The ground state rotational constants and centrifugal distortion constants are also very important and necessary for the analysis of the vibrational bands of its high resolution infrared spectrum. The work reported here was undertaken to remedy this situation. The 35 12 37 12 microwave spectra of the three isotopic species: F CI CO, F CI CO and 35 13 F CI CO have been measured as they exist in natural abundance and analyzed using Watson's A reduction Hamiltonian (8). For F 3 5C1 1 2C0 and F 3 7C1 1 2C0 transitions were measured to very high J and K . Collaboration with Dr. Colin a Marsden (University of Melbourne) has led to the determination of a reliable harmonic force field that is unique to FCICO. Because the only harmonic force field available for FCICO used force constants of another molecule he determined a set of force constants using ab initio calculations that were specifically for FCICO. These values were used to start the least squares refinement of the harmonic force field. Some values were subsequently refined, while others had to be kept fixed at the values calculated by the ab initio methods. In an attempt to determine a chlorine isotope shift in the vibrational wavenumbers, the v 3 band, which is the C — CI stretching vibration, has been remeasured. And, finally two of the five structural parameters of both an effective and average structure have been determined. Microwave Spectrum of Carbonyl Chlorofluoride / 147 5.1. ASSIGNMENT AND ANALYSIS The measurement and analysis of the spectra of the two normal species was quite straightforward. Values for the rotational constants of each were available from reference (1), and these were used to do an initial prediction of the spectrum. The twenty-two lines measured by Mirri et al, plus seven measured by Dr. Robert Davis (9) were included in the refinement/predictions of 35 F C1CO. However those transitions from reference (1) that could not be remeasured were later removed because they had not been measured as accurately as those in this study. A prediction of the nuclear quadrupole splitting by chlorine was made using the coupling constants reported by Scappini 37 35 and Guarnieri (3). For the CI species, values of the F C1CO coupling constants scaled by the ratio of the two atomic quadrupole moments were used. Because FC1CO is a fairly heavy molecule consisting of atoms all of comparable mass a rigid rotor Hamiltonian predicts the transition frequencies quite well, with the low J transitions being predicted almost exactly. Its centrifugal distortion constants are very small, (compare those in Table 5.3 for FC1CO with those in Table 4.3 for HOCl). Therefore to be able to determine accurate values for the distortion constants it was necessary to measure and assign transitions up to as high J and K as possible. This also meant 3. measuring at least four to five transitions within a series before an improvement was observed in the accuracy of the determined distortion constants. The least squares refinements were made to Watson's A reduction Hamiltonian in its I r representation, given in Table 2.1. Being a very asymmetric molecule, 0c=-0.60), it is ideally suited for analysis using the A reduction. Microwave Spectrum of Carbonyl Chlorofluoride / 148 The first measurements were of low J transitions between 27 — 38 GHz. These included lines that had previously been measured plus some new ones. The usual iterative procedure to measure and predict increasingly higher J and K transitions was used to measure and assign as many transitions as possible a between 8 — 80 GHz. Transitions up to J = 38 and K = 19 were measured for a 35 37 the CI species, and up to J = 31 and K =10 for the CI species. a Most problems encountered while measuring these two spectra were caused by the richness of the microwave spectrum in this frequency region. Occasionally a wrong assignment was made but it was quickly spotted because it had a much larger residual (obs-calc) than any of the other transitions (10). Often it was not possible to measure a transition's frequency because of interference from other lines, either of FCICO itself, or of F CO and CI CO. A thermal equilibrium exists between these three molecules so that any sample of FCICO will contain some of the other two. However any lines observed of the other two, F^CO and C^CO, were weak so they were probably present in low concentrations. A second problem encountered in the measurement of the spectra was an inability to modulate some of the lines completely. The voltage required to do so was too high for the square-wave generator to produce. Therefore no measurement could be made for such a transition. These were not major problems because the spectrum was rich enough that in the end many a- and b-type transitions of both R and Q branches were measured for both species. The unsplit line frequencies can be found in Table 5.2, and the determined rotational constants and centrifugal distortion constants are given in Table 5.3. Microwave Spectrum of Carbonyl Chlorofluoride / 149 Besides being rich, the spectrum of FC1CO was quite strong, especially the a-type lines (ju = 1.03D). This allowed for the exciting measurement of four a "forbidden" (by rigid rotor selection rules) transitions where AK = 2. They were a the four a-type Q branch transitions: l l a 8 — 1 1 2 9 , 10a 7 — 102 a , 1 2 3 1 0 — 1 2 1 1 1 ; 3 5 and 1 1 3 9 - 1 1 1 1 0 , of F C1CO. These strong a-type transitions also suggested that it might be possible to measure some transitions of the ^ 3C (3^C1) species - as it existed in natural 12 abundance. This meant the transitions of the corresponding C species had to be strong enough that they could still be detected if they were two orders of 13 magnitude weaker, since the natural abundance of C is 1.1%. The transitions chosen for this search were the J= 7, 8, and 9 a-type R branch transitions with K =0 and 1. a 35 13 A prediction of the spectrum of F CI CO was made using rotational constants estimated by the structure fitting program (section 4.2) and centrifugal 35 12 distortion constants transferred from F CI CO. The search and assignment of 35 13 the F CI CO transitions was a bit difficult. Possible lines were found but it was not obvious if they were from the correct isotopic species. Since these particular a-type R branch transitions showed no resolvable quadrupole splitting, assignments could not be confirmed from an observed hyperfine splitting. In the end the four assignments were made by confirming that the intensity, frequency and Stark lobes of each were consistent with the prediction and known 35 12 information about the corresponding F CI CO transition. For example, the 35 12 8o 8 — 7o 7 transition of F CI CO has a Stark effect which perturbs the transitions to lower frequencies, which is unusual for a transition of this high J. Therefore when a line was found at the approximate frequency predicted for the Microwave Spectrum of Carbonyl Chlorofluoride / 150 35 13 8o 8 — 7 transition of F CI CO, with a reasonable intensity (^l/lOOth that 35 12 of the F CI CO line) and with Stark components which moved to lower frequency, these three factors together confirmed the assignment. Modulation voltage and line shape were the other two clues used for line assignments. Since only four transitions could be confidently assigned only values for the three rotational constants were determined; the distortion constants had to be 35 12 constrained to those of F CI CO. They are given in Table 5.3 along with those' of the two normal species. The four unsplit line frequencies are given in Table 5.2. Because so many more transitions had been measured, many of which showed hyperfine splitting by chlorine, a least squares refinement was made to the split line frequencies of the two most abundant species to determine the chlorine quadrupole coupling constants of each. A representative sample of the 35 split line frequencies used in the CI refinement is given in Table 5.1, and the nuclear quadrupole coupling constants that were determined are given in Table 5.3. It can be seen that there was not a significant improvement in the 35 accuracy of the determined CI constants, despite the significant increase in the 37 amount of data. This is not the case for F C1CO as the previously reported values appear to be wrong. 5.2. EFFECTIVE STRUCTURE The effective inertial defects for FCICO, given in Table 5.4, are all small and positive. This confirms that the molecule is planar. As such it has five independent structural parameters. They were chosen to be the three bond lengths: r(C-Cl), r(C-F), and r(C = 0), and the two angles: <(OCCl) and Microwave Spectrum of Carbonyl Chlorofluoride / 151 <(OCF). The amount of structural information available was limited and it was not anticipated that all five parameters could be determined from the data. From the rotational constants of the three isotopic species there were only six independent rotational constants. At the same time isotopic substitutions had not been made at all atomic sites, (it is impossible at F). Since only two of the four atoms had had isotopic substitutions made no substitution structural parameters were calculated. The structure fitting program used is described in section 4.2, and the uncertainty given each rotational constant was 1%. The initial values used in the structure refinements, were the average structural parameters determined by Oberhammer from the combination of electron diffraction and microwave data (6). It turned out that only two structural parameters could be determined from the data. It was decided that the two most useful parameters to release for refinement were the C —F and C — CI bond lengths. The reasons for this decision were: (i) The C = 0 bond length, because it was a double bond, would vary the least between an r 0 and r^ structure, and between different molecules, (as confirmed by structural data given in reference (11)). (ii) It was more difficult to determine accurate values for the bond angles. A comparison is made in Table 5.5 of four fits where different combinations of two parameters were released. This shows, for fits with similar overall standard deviations, what the variation and accuracy in a determined parameter was. The chosen effective structure is given in Table 5.9. The next two sections describe the work done to determine a reliable harmonic force field and two parameters of an average structure. Microwave Spectrum of Carbonyl Chlorofluoride / 152 5.3. HARMONIC FORCE FIELD FC1CO has C g symmetry; its normal modes transform as 5A' + A". The lone vibration in the A" symmetry group is the out-of-plane bend. The symmetry coordinates and geometry used in the analysis of the harmonic force field are given in Table 5.6. The table also includes a definition of the force constants. Input data used to determine the force field were the six vibrational 35 wavenumbers of F C1CO and the ten quartic centrifugal distortion constants of 35 37 F C1CO and F C1CO. The least squares refinement program used is described in section 4.4. The uncertainty given the wavenumbers was 1% and the uncertainty assigned to most of the distortion constants was 5%. Because they 37 were determined less accurately A A„, 6 T, and 6,, of F C1CO were given an uncertainty of 10%. With sixteen force constants to be determined and only fourteen pieces of independent data an attempt was made to obtain more, by trying to observe the chlorine shift of some of the wavenumbers. To this end, the infrared spectrum from 650 — 2000 cm ^ was taken on the Bomem interferometer, (described in section 3.2), at a resolution of 1 cm \ No definitive chlorine shift was observed, even for the t>3 vibration - the C — CI stretch - where one was most likely to be seen. What was observed for the i>3 band was interesting and is shown in Figure 5.1. It is an a-type band which shows P and R branch lobes with three central Q branch spikes. It was anticipated that there would be two central Q 35 37 branches showing an intensity ratio of 3:1, arising from the CI and CI species respectively. The three branches observed can only be explained as being Microwave Spectrum of Carbonyl Chlorofluoride / 153 transitions from hot bands interfering with the v = Oj*-l transitions. It is not improbable that hot bands could be present because the lowest lying vibration is at 415 cm \ No confirmed assignments could be made, however it was assumed that the strongest central branch at 764.2 cm 1 was the band centre 35 for the CI species. This value is somewhat different from that reported by Nielson et al (5) for this band (776 cm *) and the new one was used instead, in the harmonic force field refinement. The first force constants used as preliminary values in the force field refinement were appropriate values transferred from the force fields determined for F CO and C19C0 by Carpenter and Rimmer (12). In the first refinement Z Z all six diagonal force constants were released. This immediately determined a value for f 6 6 which predicted the value of the out-of-plane vibration frequency. Since it was totally independent from the others it was kept constrained at this value for the remainder of the analysis. Unfortunately the values of the fixed off-diagonal force constants were sufficiently wrong that the refinement did not converge. Because FCICO is a very asymmetric molecule it was thought that perhaps the off-diagonal constants played a significant role in the description of the force field. The Jacobians of the vibrational wavenumbers and centrifugal distortion constants were inspected to determine which off-diagonal force constants contributed most to the data. The decision to release some combination of the following force constants: f2«, f3 « , f35, and f„ 5 was made knowing the sensitivity of the constants to the data and that centrifugal distortion constants contain information mainly about low frequency vibrations. However even when the maximum number of off-diagonal force constants were released (when more than two off-diagonal force constants were released the fit diverged), the Microwave Spectrum of Carbonyl Chlorofluoride / 154 refinement still would not converge - no matter what combination of two was used. The second set of preliminary force constants used were those of Oberhammer (6) who had fixed the off-diagonal force constants at the values determined for FC1CS. He had been able to determine only the diagonal force constants. This, at last, was an initial force field which would converge using our input data, when the diagonal force constants and two off-diagonal ones were released. However this was still felt to be an unsatisfactory description of a harmonic force field for FC1CO. In the end, the force constants were predicted in four sets of ab initio calculations (13) done by Dr. Colin Marsden (University of Melbourne). Part of the aim behind this part of the study was to determine which was the most cost-effective method to theoretically predict harmonic force constants. The four sets, labelled A, B, C, and D varied in the basis set used to describe the atoms. All sets used double-zeta s, p basis sets for the atoms and the variation was in whether a polarization function was included. Set A contained no polarization functions, while set B had polarization functions on every atom. Set C contained polarization functions on CI only and set D on C only. The polarization functions allow greater freedom to the motion of the electrons in the valence shell, consequently allowing an atom to become polarized. This makes it possible to predict better values for the force constants. All four sets of force constants produced force fields which would converge. As expected set B with polarization functions on all the atoms produced the best results. However set D with polarization functions only on C produced Microwave Spectrum of Carbonyl Chlorofluoride / 155 comparable results and was judged to be the cost-effective choice. All four sets of force constants are given in Table 5.7, along with the force field determined from the least squares refinement. The stretch-stretch interaction force constants were scaled by a factor of 0.85 from the theoretically calculated value because the Hartree-Fock method f usually overestimates them (14). This is caused by an incorrect description of the bond dissociation (13). The diagonal stretching force constants are also usually overestimated but since they were refined it was not necessary to scale them down. However it can be observed from the values of the force constants in Table 5.7 that the fitted diagonal stretching force constants are almost exactly 0.85 the theoretically calculated values. A number of refinements was done with different combinations of off-diagonal force constants released, and variations in the total number of force constants released. The maximum number of force constants that could be determined at one time was seven. The force field chosen to be the most reliable is given in Table 5.7 and was the one with the off-diagonal force constants f 3 a and ffl 5 released. It was chosen because it had the lowest overall standard deviation, both off-diagonal force constants (being relatively large) were determined, and it predicted the wavenumbers and distortion constants very well, as shown in Table 5.8. 5.4. AVERAGE STRUCTURE The a (harmonic) 's produced from the output of the harmonic force field were used to determine the ground state average rotational constants. These Microwave Spectrum of Carbonyl Chlorofluoride / 156 were used to calculate two parameters of an average structure using the structure fitting program described in section 4.2. The same uncertainties were assigned to the rotational constants as for the effective structure. Even though a significantly better structure was determined using the average rotational constants it was still only possible to determine two parameters. As for HOCl the refinement of the structure was improved by calculating the §rz's, (using equation (2.36)), which account for slight changes in bond length caused by isotopic substitution. The "a" values were obtained from 2 reference (15) and the 5u and 8K were calculated from the output of the harmonic force field. 35 Because molecular g-values were available for F C1CO (3) the average rotational constants were further corrected by accounting for contributions from electron-rotation interactions using equations (4.5) and (4.6). The valid assumption was made that the difference in the molecular g-values for the other two isotopic species was negiglible, so that the molecular g-values for the 35 F C1CO species were used for all three. There was only a slight improvement using these, which indicated that electron-rotation interactions contributed very little to the rotational constants of FC1CO. The final results for the average structure are presented in Table 5.9 and the structure is shown in Figure 5.2. The structure was sufficiently well determined that it was not felt necessary to make corrections to the rotational constants for centrifugal distortion' contributions. Two sets of average inertial defects for each isotopic species are given in Table 5.4. One set was calculated using rotational constants that has only had the harmonic contributions removed, A , while the other set has also had Microwave Spectrum of Carbonyl Chlorofluoride / 157 electronic contributions removed, A . It can be seen by comparing the effective ze inertial defects, A0 to the average inertial defect Az that the 'inertial defect' is mostly caused by contributions from harmonic vibration. There is a difference of two orders of magnitude between A0 and A^, whereas the difference between the two different average inertial defects, A and A is negligible in comparison. z ze 5.5. COMMENTS It can be seen from a comparison of the previous sets of rotational constants and those reported here, in Table 5.3 that a significant improvement has been made in their accuracy and it is the first time rotational constants 35 13 have been determined for F CI CO. Centrifugal distortion constants from Watson's rotational Hamiltonian have been determined for both normal species for the first time. It has been shown that the procedure where six distortion constants are determined contains an indeterminacy and should not be used for fitting purposes (8). With these accurate rotational and centrifugal distortion constants it is now possible to make accurate predictions of the ground state rotational spectrum to fairly high J (J=40). These constants will also be extremely useful in the analysis of the rotational structure of a high resolution infrared spectrum. The accuracy of the chlorine quadrupole coupling constants has also 35 37 improved slightly. The agreement of the ratio of X c c( C1)/XC(,( CI) for the molecules, which was 1.2588, is in good agreement with the theoretical ratio for the two nuclei of 1.2688. Having values of the chlorine nuclear quadrupole coupling constants it is Microwave Spectrum of Carbonyl Chlorofluoride / 158 interesting to calculate a value for the amount of TT back bonding and the ionic character, i, in the C — CI bond, using Townes Dailey theory, TT was calculated from the difference in Y and Y as they give an indication of the lack of Axx Ayy ' s cylindrical symmetry of the field around the C — CI bond. X > X and x were xx yy zz determined by rotating the principal inertial axes to the principal axis system of the quadrupole coupling tensor. The assumption was made that the C —CI bond is one of the principal axes (16). See section 6.6 for more details. The angle between the a-principal inertial axis and the C —CI bond, which is taken to be the z axis of the quadrupole coupling tensor, 6 , is 4.6°. This means the za quadrupole coupling constants changed very little after the transformation. Using equation (6.9) 7T was calculated to be 10.5%. Because x of FC1CO (-73.9 MHz) was less than x of the chlorine ~zz zz at atom (-109.7 MHz), x , (unlike for HOCl and CFQNC1), the ionic form of ZZ Z FC1CO will be one where the chlorine is the negative pole, Figure 5.3b. For this reason, and because chlorine is more electronegative than carbon by more 2 than 0.30 (17), the s character, ag, in the sp hybrid orbital bonding at chlorine and the screening, e, • of the nucleus by the changed charge distribution should 2 be accounted for. For chlorine both ag and e are usually taken to be 0.15 (17). With these two parameters included the expression for the nuclear quadrupole constant X z z for the molecule, which is a contribution of the three forms shown in Figure 5.3, becomes (17): The first term is the contribution to X z z from the covalent bonding, the second term from the ionic form and the third term accounts for the TT back + 0 + (5.1) Microwave Spectrum of Carbonyl Chlorofluoride / 159 bonding by chlorine. Solving this for i gives i= 15.2%, which makes the amount of covalent character in the C —CI bond 74.3%. This work has finally produced a harmonic force field that is unique to FC1CO and does not use off-diagonal force constants transferred from force fields of other molecules. It should be noted however that the theoretically predicted force constants are for a truly harmonic force field. The vibrational wavenumbers and distortion constants used as input data in the least squares refinement of the force field are slightly contaminated by anharmonicity. This will influence the values determined for the force constants somewhat, but for this molecule is not believed to be much. An idea of the discrepancy can be obtained by comparing the vibrational wavenumbers and centrifugal distortion constants predicted by the theoretically calculated force constants with those predicted by the fitted force constants, given in Table 5.8. An interesting observation made of these predicted values was that the 37 fitted force field predicts the v 3 vibration frequency of F C1CO to be 762.4 cm \ This coincides almost exactly with the frequency of the second largest Q branch spike found in this band. This strongly suggests that it is the 37 band centre for v 3 of F C1CO (again assuming the Q branch is at the band centre, as is often the case. See Chapter 7 for the analysis of an a-type band for which this is not true). It would seem that the intensity ratio was not as 37 expected because the v3 band of F C1CO was overlapped by a hot band of 35 F C1CO. This hot band transition could be from the first excited state of v 5 at 415 cm'l The third, weakest, Q branch would then be the corresponding 37 hot band of F C1CO. Microwave Spectrum of Carbonyl Chlorofluoride / 160 The two average structural parameters determined in this work agree very well with the electron diffraction values (6). The accuracy of the two bond lengths, r z(C — CI) and r (C —F) has apparently improved a great deal, but because the remaining three parameters had to be constrained this effect may not be totally real. It is unfortunate that only two structural parameters could be determined from the data, but this was probably a result of the fact that only two isotopic substitutions had been made. Microwave Spectrum of Carbonyl Chlorofluoride / 161 TABLE 5.1 Representative Sample of Transitions with Resolved Hyperfine Structure of F 3 5 C1CO Transition F' . F" Frequency (uncertainty) (MHz) Obs-Calc splits (MHz) F 3 5C1C0 3 2 2 2 2 ! 1.5 - 0.5 26824.980(30) 4.5 - 3.5 26811.750(20) 2.5 - 1.5 26806.570(20) 3.5 - 2.5 26793.550(20) 0.098 -0.074 -0.031 0.007 *2 3 -4 1 4 4.5 - 4.5 30693.640(20) 3.5 - 3.5 30691.560(20) 5.5 - 5.5 30687.760(20) 2.5 - 2.5 30685.710(20) 0.017 -0.009 -0.006 -0.002 8 3 5 -8 2 6 8.5 - 8.5 27648.890(20) 7.5 - 7.5 27648.450(20) 9.5 - 9.5 27646.340(20) 6.5 - 6.5 27645.900(20) -0.015 0.003 -0.003 0.015 3 7 9.5 - 9.5 53860.260(40) 8.5 - 8.5 53859.740(40) 10.5 - 10.5 53856.940(40) 7.5 - 7.5 53856.420(40) -0.003 0.007 -0.007 0.003 10 4 7 10 2 8 10.5 - 10.5 65505.580(40) 9.5 - 9.5 65504.820(40) 11.5 - 11.5 65500.440(40) 8.5 - 8.5 65499.700(40) 0.005 -0.014 0.004 0.005 Observed frequency minus the frequency calculated using the fitted spectroscopic constants. Microwave Spectrum of Carbonyl Chlorofluoride / 162 TABLE 5.2 Observed Transition Frequencies (in MHz), with Hyperfine Structure Removed, of FC1CO Transition Frequency Obs-Calc Weight F°"C1 CO 1 1 1 " 0 0 0 15479.040 -0.001 1.0000 1 0 1 " 0 0 0 8935.620 0.010 1.0000 2 0 2 " 1 0 1 17600.320 0.009 1.0000 2 1 2 " 1 1 1 16233.000 0.006 1.0000 3 2 1 " 2 2 0 27844.345 . 0.030 1.0000 3 2 2 " 3 1 3 . 27159.050 -0.026 1.0000 3 2 2 " 2 2 1 26806.600 0.067 1.0000 3 1 3 " 2 0 2 29368.240 -0.012 1.0000 3 1 2 " 2 1 1 29078.080 -0.034 1.0000 4 3 2 _ 4 2 3 37647.870 -0.040 1.0000 4 2 3 _ 4 1 4 30689.900 -0.014 1.0000 4 3 1 _ 3 3 0 36375.950 -0.057 1.0000 4 1 3 " 3 1 2 38383.870 -0.004 1.0000 4 0 4 _ 3 0 3 33386.970 0.035 1.0000 6 1 5 " 6 1 6 32250.545 -0.029 1.0000 6 3 3 _ 6 2 4 29663.110 0.069 1.0000 7 4 4 _ 6 4 3 63792.050 0.062 1.0000 7 4 3 _ 6 4 2 64068.320 -0.078 1.0000 7 3 4 " 6 3 3 66169.440 0.015 1.0000 7 3 4 _ 7 2 5 27961.260 0.050 1.0000 7 2 6 • 6 1 5 68633.130 0.001 1.0000 7 1 7 _ 6 0 6 55242.170 -0.028 1.0000 7 0 7 _ 6 1 6 54300.290 -0.037 1.0000 7 0 7 " 6 0 6 54932.620 -0.051 1.0000 8 3 5 " 7 3 4 76742.070 0.004 1.0000 8 3 6 _ 7 3 5 72250.710 -0.019 1.0000 8 4 4 _ 7 4 3 73818.030 -0.051 1.0000 8 4 5 " 7 4 4 73102.685 -0.008 1.0000 8 5 3 _ 7 5 2 72848.530 -0.064 1.0000 8 5 4 " 7 5 3 72807.950 0.072 1.0000 8 7 2 " 7 7 1 72329.370 0.108 1.0000 8 7 1 " 7 7 0 72329.370 0.094 1.0000 8 1 8 " 7 0 7 62288.860 0.091 1.0000 8 1 7 " 7 1 6 70550.590 -0.004 1.0000 8 3 5 " 8 2 6 27647.420 0.029 1.0000 8 0 8 ' 7 0 7 62142.605 -0.075 1.0000 Microwave Spectrum of Carbonyl Chlorofluoride / 163 TABLE 5.2 - continued Transition Frequency Obs-Calca Weight 9 3 6 " 9 2 7 29272.630 0.031 1.0000 9 1 9 _ 8 0 8 69458.660 -0.001 1.0000 9 2 7 " 8 3 6 67327.580 -0.011 1.0000 9 4 6 " 9 3 7 53858.370 -0.022 1.0000 9 0 9 " 8 O 8 69391.550 0.006 1.0000 10 .4 7 " 10 2 8 65502.670 -0.033 1.0000 10 4 6 " 10 3 7 37933.690 -0.008 1.0000 11 3 9 " 11 1 1 0 64499.180 -0.018 1.0000 11 4 8 _ 11 2 9 65417.470 -0.050 1.0000 11 3 8 " 11 3 9 33422.625 -0.012 1.0000 11 4 7 " 11 3 8 36437.020 0.129 1.0000 12 3 1 0 " 12 1 1 1 70895.720, 0.019 1.0000 12 4 8 " 12 4 9 17116.990 0.028 1.0000 14 6 8 " 13 7 7 38099.280 -0.038 1.0000 14 4 1 0 " 14 4 1 1 36190.000 -0.011 1.0000 15 6 9 " 15 5 1 O 63695.480, -0.028 1.0000 15 5 1 0 " 15 5 1 1 17747.140 -0.020 1.0000 15 7 8 " 14 8 7 30849.070 0.169 0.0004 15 7 9 " 14 8 6 30573.420 -0.122 1.0000 16 5 1 1 " 16 5 1 2 26900.760, -0.020 1.0000 18 6 1 2 " 18 6 1 3 17809.820 -0.034 1.0000 19 6 1 3 " 19 6 1 4 27199.195 -0.008 1.0000 20 8 1 3 " 19 9 1 O 66584.635 0.025 1.0000 20 8 1 2 " 19 9 1 1 68079.560 0.017 1.0000 21 9 1 3 _ 20 1 O 1 O 59886.270 0.076 1.0000 21 9 1 2 " 20 1 O 1 1 60189.615 0.002 1.0000 21 6 1 5 " 21 5 1 S 64364.565 -0.019 1.0000 21 7 1 4 " 21 6 1 5 61751.420, -0.015 1.0000 21 7 1 4 " 21 7 1 5 17439.750 0.010 1.0000 22 9 1 4 " 21 1 O 1 1 70773.045 -0.054 1.0000 22 9 1 3 " 21 1 O 1 2 71453.900 0.102 1.0000 22 7 1 5 " 22 7 1 6 26888.595 0.021 1.0000 23 1 0 1 4 " 22 1 1 1 1 63924.440 -0.129 0.0004 24 8 1 6 " 24 7 1 7 70916.320, -0.052 1.0000 24 8 1 6 " 24 8 1 7 16749.610 0.034 1.0000 25 1 1 1 5 " 24 1 2 1 2 67937.410 -0.076 1.0000 25 8 1 7 " 25 7 1 8 68900.980 0.032 1.0000 26 8 1 8 " 26 7 1 9 70120.260, -0.015 1.0000 27 9 1 8 " 27 9 1 9 15834.110 0.011 1.0000 27 8 1 9 " 27 7 2 O 74857.210 0.041 1.0000 29 9 2 0 " 29 9 2 1 36806.435 0.065 1.0000 Microwave Spectrum of Carbonyl Chlorofluoride / 164 TABLE 5.2 - continued Transition Frequency Obs-Calc Weight 30 , 0 2 0 - 30 1 0 2 1 14772.000 0.022 1.0000 32 , 6 1 7 - 31 1 7 1 4 56749.370 -0.021 1.0000 32 , O 2 2 - 32 1 0 2 3 35169.025 -0.033 1.0000 33 , 1 2 2 - 33 1 1 2 3 13627.190 -0.015 1.0000 33 , 6 1 7 - 32 1 7 1 6 67045.190 0.021 1.0000 34 , 7 1 8 • 33 1 8 1 5 60797.290 0.145 1.0000 35 , 8 1 8 - 34 1 9 1 5 54648.950 -0.038 1.0000 35 , 1 2 4 - 35 1 1 2 5 33205.165 -0.146 1.0000 35 , 7 1 8 - 34 1 8 1 7 71093.450 -0.095 1.0000 38 ! 2 2 6 - 38 1 2 2 7 31013.395 0.090 1.0000 2 co 1 1 1 - 0 0 0 15402.620 -0.057 1.0000 2 O 2 - 1 0 1 17160.590 -0.041 1.0000 7 1 7 - 6 0 6 54190.470 0.007 1.0000 7 2 6 - 6 2 5 59103.525 0.089 1.0000 7 4 3 - 6 4 2 62236.450 -0.016 1.0000 7 2 5 - 6 2 4 65977.810 -0.028 0.0100 7 O 7 - 6 0 6 53812.200 0.028 ' 1.0000 7 3 4 - 6 3 3 64100.000 -0.037 1.0000 7 2 6 - 6 1 5 68005.450 0.038 1.0000 8 4 5 - 7 4 4 71070.950 -0.009 1.0000 8 3 5 - 7 3 4 74323.960 -0.021 1.0000 8 3 6 - 7 3 5 70375.660 -0.008 1.0000 8 2 6 - 7 2 5 75042.400 . -0.028 1.0000 8 5 4 - 8 4 5 66084.155 -0.037 1.0000 9 0 9 - 8 1 8 67767.540 -0.034 1.0000 9 3 6 - 9 3 7 13845.480 0.006 1.0000 9 5 5 - 9 4 6 65843.340 -0.058 1.0000 9 5 4 - 9 4 5 63860.910 0.044 1.0000 10 1 1 O - 9 O 9 75108.180 0.022 1.0000 10 S 6 - 10 4 7 65779.170 -0.045 1.0000 10 5 5 - 10 4 6 61657.060 0.033 1.0000 10 4 7 - 10 3 8 56252.855 -0.096 1.0000 11 4 8 - 11 3 9 59160.065 0.117 1.0000 11 3 8 - 11 2 9 37389.255 0.074 1.0000 11 3 9 - 11 2 1 0 62599.740 -0.001 1.0000 Microwave Spectrum of Carbonyl Chlorofluoride / 165 TABLE 5.2 - continued Transition Frequency Obs-Calc Weight 11 4 7 - 11 3 8 37430.090 0.072 1.0000 11 5 6 - 11 4 7 58530.040 0.065 1.0000 12 4 9 - 12 3 1 0 62957.540 -0.024 1.0000 12 5 8 - 12 4 9 66865.365 -0.008 1.0000 12 4 8 - 12 4 9 14396.930 0.045 1.0000 13 5 9 - 13 4 1 0 68371.370 -0.056 1.0000 13 4 1 0 - 13 3 1 1 67613.400 -0.002 1.0000 13 6 7 - 13 5 8 74965.760 0.131 1.0000 14 6 8 - 14 5 9 71555.250 -0.106 1.0000 17 6 1 1 - 17 5 1 2 58022.115 -0.064 1.0000 18 6 1 2 • 18 5 1 3 54914.800 0.011 1.0000 18 6 1 2 - 18 6 1 3 13584.310 . -0.053 1.0000 19 6 1 3 - 19 5 1 4 53963.990 -0.005 1.0000 20 7 1 3 - 20 6 1 4 69323.900 0.002 1.0000 21 7 1 4 - 21 7 1 5 12615.000 0.011 1.0000 25 8 1 7 - 25 7 1 8 71588.130 0.019 1.0000 26 8 1 8 - 26 7 1 9 70088.900 -0.002 1.0000 28 9 1 9 - 28 9 2 0 16796.910 0.023 1.0000 31 1 0 2 1 - 31 1 0 2 2 14957.300 -0.015 1.0000 3CO 7 0 7 - 6 0 6 54839.000 -0.008 1.0000 8 0 8 - 7 0 7 62035.660 0.017 1.0000 9 0 9 • 8 0 8 69271.200 -0.008 1.0000 9 1 9 - 8 1 8 69191.220 -0.001 1.0000 Observed frequency minus the frequency calculated using the fitted spectroscopic constants. Measured by R.W. Davis, reference (9). Microwave Spectrum of Carbonyl Chlorofluoride / 166 TABLE 5.3 Spectroscopic Constants of FCICO F 3 5C1 1 2C0 F 3 7C1 1 2C0 F 3 5C1 1 3C0 This Work Ref (3) This Work Ref (1) This Work Rotational Constants (MHz) A 0 11830.3447(26)a 11830.35(3) 11830.2626(77) 11829.42(5) 11828.48(19) B 0 5286.9105(9) 5286.93(3) 5128.3015(41) 5127.73(5) 5275.35(16) C 0 3648.7056(8) 3648.69(3) 3572.4228(39) 3572.54(5) 3642.248(11; Centrifugal Distortion Constants (kHz) Aj 1.5234(25) 1.4255(292) 1.52b A T T. 6.2604(182) A R 4.614(17) 6.0222(436) 4.654(171) 6.26b 4.61b 5j 0.49354(169) 0.45475(376) 0.49b Sv 6.2008(265) hj 1.27(26)xl0° 6.0700(607) 1.2xl06 b 6.2b 1.3xl06 b Chlorine Nuclear Quadrupole Coupling Constants (MHz) X -73.125(36) -73.04(2) 3 3 -57.538(69) -58.0(5) X b b-X c c 16.497(80) 16.38(4) 12.56(12) 1.3(7) X c c 28.31(12) 28.33(3) 22.49(19) 28.4(7) Numbers in parentheses are one standard deviation in units of the last significant figures. These constants were held fixed at these values. Microwave Spectrum of Carbonyl Chlorofluoride / 167 TABLE 5.4 Effective and Average Inertial Defects for FC1CO • 2 Inertial Defects (uA ) Species Effective Average Average A 0 A A u z ze F CI CO 0.1996 37 19 F CI CO 0.2005 F 3 5C1 1 3C0 0.2290 0.00207 -0.00146 0.00204 -0.00154 0.03137 0.0277 Definition of the Inertial Defects Effective A 0 = 1° - Ig - l£ Average A = if, — if. — lz. 6 z C B A Average (corrected) A = iff — iff — I Microwave Spectrum of Carbonyl Chlorofluoride / 168 TABLE 5.5 Comparison of Different Effective Structures Obtained for FCICO Parameter Initial Value Fit 1 Fit 2 Fit 3 Fit 4 r(C-Cl)A r(C-F)A r(C = 0)A <(OCF)° <(OCCl)° s.d. 1.725 1.334 1.173 123.7 127.5 1.72338(75) 1.33200(85) 3.513 123.628(65) 128.66(27) 3.522 1.72358(79) 1.1705(10) 3.515 1.33057(87) 123.844(67) 3.514 Reference (6). Numbers in parentheses are one standard deviation in units of the last significant figures. Standard Deviation of the fit in MHz. Microwave Spectrum of Carbonyl Chlorofluoride / 169 TABLE 5.6 Symmetry Coordinates and Geometry of FC1CO Used in the Harmonic Force Field Analysis Symmetry Coordinates, Internal Coordinates and Geometry : S, = Ar(C = 0) = 1.173A 5 2 = Ar(C-F) = 1.334A 5 3 = Ar(C-Cl) = 1.724A Sfl = A<(OCF) = 123.7° S 5 = A<(OCCl) = 127.5° Definition of the Force Constants A' r(C = 0) r(C-F) r(C-Cl <(OCF) <(OCCl) r(C = 0) fi 1 f 1 3 f 1 4 fis r(C-F) f 2 2 f 2 3 f 2 4 f 2 5 r(C.-Cl) f 3 3 f 3 4 fa 5 <(OCF) f n n f«5 <(OCCl) f 5 5 A" <(oop)b < (oop) These are the "MW + ED" values in Table VI of reference (6). (oop) = out-of-plane bend. The definition of this coordinate is that of Hoy, Mills and Strey, Mol Phys, 24, 1265-1290 (1972). Microwave Spectrum of Carbonyl Chlorofluoride / 170 TABLE 5.7 Harmonic Force Fields'1 of FCICO n b e Parameter ab initio Values Fit B C D Species A' f l 1 16.676 . 16.858 16.731 16.600 14.38(10)d f 1 2 1.086 1.256 1.099 1.233 1.0686 f l 3 0.775 0.882 0.883 0.861 0.7506 f l « 0.669 0.634 0.661 0.644 0.6346 f l 5 0.524 0.471 0.517 0.467 0.4716 f2 2 7.625 6.406 7.630 6.325 5.78(11) f 2 3 0.581 0.663 0.608 0.630 0.5646 f2 n 0.015 0.035 0.030 0.024 0.0356 f 2 5 -0.739 -0.670 -0.724 -0.655 -0.6706 f 3 3 4.330 • 4.205 4.208 3.980 3.634(49) f 3 A -0.774 -0.701 -0.743 -0.698 -0.669(18) f 3 5 -0.170 -0.171 -0.147 -0.188 -0.1716 f« fl 2.775 2.746 2.746 2.787 2.615(69) 1.364 1.322 1.333 1.374 1.262(74) f 5 5 2.347 2.268 2.313 2.326 2.038(13) Species A" f s 6 f f f f 0.725 Units of mdyn/A for stretching constants, mdyn A/rad for bending constants, and mdyn/rad for stretch-bend interactions These values are obtained by the various methods outlined in the text. These were obtained by fitting to the experimental data. Microwave Spectrum of Carbonyl Chlorofluoride / 171 Numbers in parentheses are one standard deviation in units of the last significant figures. Constrained to the values of set B. Stretch-stretch interaction constants were constrained to 85% of the values in set B. Not calculated theoretically. The value from the fit gives an exact calculation of v 6 . Microwave Spectrum of Carbonyl Chlorofluoride / 172 TABLE 5.8 Observed and Calculated Wavenumbers and Centrifugal Distortion Constants of FC1CO 3^  3 7 F C1CO F C1CO obsa calc^ obs-calc obsa calc^ obs-calc Wavenumbers (cm 1868.0 1867.97 0.03 — 1867.95 Vl 1095.0 1095.00 0.00 - 1094.80 V2 764.2 764.03 0.17 762.2° 762.37 Vn 501.0 500.76 0.24 — 494.33 "5 415.0 413.84 1.16 — 411.52 667.0 667.13 -0.13 — 666.80 rifugal Distortion Constants i (kHz) * J 1.523 1.526 -0.003 1.425 1.444 -0.019 A J K 6.260 6.250 0.010 6.022 6.039 -0.017 A K 4.614 4.553 0.061 4.654 4.842 -0.188 5 J 0.493 0.487 0.006 0.455 0.453 0.002 8 K 6.201 6.008 0.193 6.070 5.815 0.255 Observed wavenumbers, except v 3, are from reference (5). All other observed values are from this work. k These calculated values were obtained from the force constant fit in Table 5.6. Not included in the fit. Microwave Spectrum of Carbonyl Chlorofluoride / 173 TABLE 5.8 - continued 35 d Calculated Wavenumbers and Centrifugal Distortion Constants of F C1CO ab initio values A B C D Wavenumbers (cm ) V\ 2031 2024 2032 2008 u2 1257 1169 1253 1165 u3 811 808 809 797 Vn 539 529 535 521 V5 442 434 438 440 v 6 e e e e Centrifugal Distortion Constants (kHz) A 1.31 1.36 1.34 1.41 J A J R 5.32 5.54 5.34 5.26 A„ 4.14 4.46 4.07 4.79 K. 6j 0.42 0.44 0.43 0.45 6,, 5.21 5.42 5.30 5.35 Calculated from the corresponding force fields in Table 5.7. Not calculated theoretically. Microwave Spectrum of Carbonyl Chlorofluoride / 174 TABLE 5.9 Effective and Ground State Average Structures of FCICO Parameter Electron Effective Average Diffraction3, (r 0) (r ) r(C-Cl) r(C-F) r(C = 0) <(0CC1) <(OCF) 1.725(2)Ab 1.334(3)1 1.173(2)1 127.5(3)° 123.7(2)° 1.7234(8)1 1.3320(9)1 1.173A 127.5°° 123.7°° 1.72433(6)Ab 1.33428(7)1 O p 1.173A 127.5°° 123.7°° Reference (6). Numbers in parentheses are one standard deviation in units of the last significant figures. Held fixed at the electron diffraction values. Figure 5.1. The v2 band of FCICO at 1.0 cm resolution. Microwave Spectrum of Carbonyl Chlorofluoride / 176 Microwave Spectrum of Carbonyl Chlorofluoride / 177 F a. —CI covalent bonding 0 CI" ionic bonding F F " c. ix back bonding Figure 5.3. Three Different Structures Contributing to the Overall Bonding the C-Cl Bond of FCICO. BIBLIOGRAPHY 1. A.M. Mirri, A. Guarnieri, P. Favero and G. Zuliani, Nuovo Cimento, 25, 265-273 (1962). 2. A.M. Mirri and A. Guarnieri, Atti Accad Naz Lincei, CI Sci Fis Mat Nat Rend, XL, 837-842 (1966). 3. F. Scappini and A. Guarnieri, Z Naturforsch, 31A, 369-373 (1976). 4. I. Zanon, G. Giacometti, and D. Picciol, Spectrochim Acta, 19, 301-306 (1963) 5. A.H. Nielsen, T.G. Burke, P.J. Woltz, and E.A. Jones, J Chem Phys, 20, 596-604 (1952). 6. H. Oberhammer, J Chem Phys, 73, 4310-4313 (1980). 7. H. Oberhammer and J.E. Boggs, J Mol Struct, 55, 283-294 (1979). 8. J.K.G. Watson, J Chem Phys, 45, 1360-1361 (1966); J.K.G. Watson, J Chem Phys, 46, 1935-1949 (1967); J.K.G. Watson, in Vibrational Spectra and Structure, a series of advances, Ed. J.R. Durig, Vol 6, Elsevier, New York, 1977, Chapter 1. 9. R.W. Davis, private communication. 10. W.H. Kirchh'off, J Mol Spectrosc, 41, 333-380 (1972). 11. H.D. Harmony, V.W. Laurie, R.L. Kuczkowski, R.H. Schwendeman, D.A. Ramsay, F.J. Lovas, W.J. Lafferty and A.G. Maki, J Phys Chem Ref Data, 8, 619-721 (1979). 12. J.H. Carpenter and D.F. Rimmer, J Chem Soc, Faraday Trans II, 74, 466-479 (1978). 13. W.D. Anderson, M.C.L. Gerry and C.J. Marsden, J Mol Spectrosc, 114, 70-83 (1985) 14. C.J. Marsden, unpublished results. 15. K. Kuchitsu and Y. Morino, Bull Chem Soc Japan, 38, 805-824 (1965). 16. M.C.L. Gerry, W. Lewis-Bevan and N.P.C. Westwood, J Chem Phys, 79, 4655-4663 (1983). 17. W. Gordy and R.L. Cook, Microwave Molecular Spectra, in Technique of Organic Chemistry, Ed. A. Weissberger, Vol. IX, Part II, Interscience Publishers, New York, 1970, chapter 14. 178 6. MICROWAVE SPECTRUM OF N-CHLORODIFLUOROMETHYLENIMINE All of the previous spectroscopic studies of N-chlorodifluoromethylenimine, CF^NCl, have been done at low resolution. This is primarily because they were carried out to characterize it. It was first made in 1970 by Young, Anderson and Fox (1), by the thermolysis of NN-dichlorodifluorochloromethylamine, CFgClNClg. This dechlorination reaction goes as follows: CF0C1NC10 1 0 0^ 0 01 CF =NC1 + Cl„ (6.1) 2 2 4 hrs 2 2 CF C1NC1Q is prepared from cyanogen chloride and chlorine monofluoride: C1CN + 2C1F —^U- CF2C1NC12 (>90%) (6.2) To prove that they had made it, Young et al took a mass spectrum, 1 9 F NMR spectrum and an infrared spectrum. At approximately the same time, Hirschmann, Simon and Young (2) measured a wider range of the infrared spectrum at accuracies between 1 — 3 cm \ They found only seven of the nine fundamentals and so had to estimate the position of the missing two from combination band data. More recently (1984), O'Brien et al (3) have measured the Raman spectrum and remeasured the infrared spectrum. This enabled them to make a reassignment of the two previously unobserved fundamentals. Structural studies have been carried out for the two trihalogen methylenimines, CF NF and CC19NC1. This work is described here because it is useful for comparison purposes and some of the results from these studies were used to help analyze the spectra of CFgNCl. For CF 2NF a fairly detailed analysis of the microwave spectrum was made by Christen (4), such that he 179 Microwave Spectrum of N-Chlorodifluoromethylenimine / 180 was able to determine nuclear quadrupole coupling constants for the nitrogen. These microwave data were combined with medium resolution infrared spectra, Raman spectra, electron diffraction data and ab initio calculations to determine a reliable structure and a harmonic force field (5). Similar work has been done on CClgNCl, except that a measurement of the microwave spectrum has not yet been done because of the four nuclear quadrupolar atoms. Infrared and Raman spectra were measured years ago by Burke and Mitchell (6). Recently an electron diffraction study allowed Christen and Kalcher (7) to determine its structure, and a more detailed investigation of the vibrational spectrum has yielded a harmonic force field (8). In the present study similar results were obtained, where the primary achievement was the detection and measurement of the microwave spectrum of OK Q7 the two naturally occuring isotopes of CF NCI: CF N CI and CF N CI. From Z Z z this measurement accurate values for the rotational constants, quartic centrifugal distortion constants and nuclear quadrupole coupling constants for both chlorine 14 and nitrogen ( N) were determined. The quadrupole coupling constants yielded important and interesting information about the bonding in the C = N —CI group. The centrifugal distortion constants were combined with the existing vibrational data to determine a very reasonable estimate of the harmonic force field. Information about the harmonic contributions to the vibration allowed average rotational constants to be calculated which in turn gave a structural parameter of the ground state average structure. With so little isotopic data it was possible to determine only one of the seven structural parameters. This was Microwave Spectrum of N-Chlorodifluoromethylenimine / 181 chosen to be the C = N —CI angle, because in the other two similar molecules, CF 2NF and CC1 NCI, the C = N-X angle varies from 107.9° in CF 2NF (5) to 117.1° in CC12NC1 (7). Obtaining a value for this angle gave further information about the bonding, in particular the degree and kind of hybridization at nitrogen. Microwave Spectrum of N-Chlorodifluoromethylenimine / 182 6.1. MEASUREMENT AND ASSIGNMENT Although no previous microwave or structural data were available in the literature, by simple bonding theory CF^NCl was expected to be a planar molecule with C g symmetry, which would probably have both a- and b-type transitions. Preliminary rotational constants were calculated from an estimated structure. This was done using two methods. The first was to use appropriate bond lengths and angles from similar molecules, which included C1NCO, C1N , H2C = NH, COF 2 and C^CFg. The second was to use the structural parameters of the CF group which had been determined for CF NF and those of the Z Z C = N —CI group of CClgNCl. Not surprisingly, the rotational constants calculated by the latter estimate of the structure produced a better prediction of the spectrum. It predicted the location of the a-type R branch J=7*-6 lines to within 400 MHz and the splittings between each asymmetry pair, the a-type R branch series and most b-type series to better than 5%. To start a search it was also necessary to have a prediction of the hyperfine pattern. Initially the splitting which would result from nitrogen nuclear quadrupolar coupling was assumed to be negligible. Again estimated values, this time of the chlorine nuclear quadrupole coupling constants, had to be used for the initial prediction of the quadrupole splitting. Those of C1NCO were chosen (9,10) because it is electronically and structurally similar to CFgNCl, (each contain the C = N —CI group). They turned out to be relatively good estimates. It was important for assignment purposes that reliable values of the coupling constants be available to predict the hyperfine pattern because the Microwave Spectrum of N-Chlorodifluoromethylenimine / 183 observed splitting of the lines was a crucial factor in their assignment. This was especially true when there were other lines nearby or actually interfering. The next section describes the fitting and determination of the quadrupole coupling constants in more detail. To assign the spectrum of a molecule which is expected to have a-type lines, the easiest method is to find the characteristic a-type R branch groups. These are spaced (B + C)(J+1) apart. The usual characteristic features are that they occur as clusters of lines such that the transitions from the higher K & lines, e.g. 7a -64 , 73 -63 usually appear at very low modulation voltages, that is 20 —40V. At this time very little else is present. Then as the voltage is increased the K & = 0 line appears somewhere near the center of this cluster and the 1 lines appear on either side. Another feature often observed in these a-type R branch clusters is that the two lines from near degenerate K & asymmetry pairs exhibit Stark lobes which move towards each other in frequency (and eventually cross). This can be seen in Figure 6.1 and is very often used to make the first line assignments. This effect is caused by the two energy levels of the asymmetry pairs being very close together. As a result an exact solution of the determinant given in equation (2.62) is necessary to determine the Stark energy. The search was started by scanning the frequency range 27 — 36 GHz at three diffferent voltages — 40V, 100V and 400V. This was done to try and pick out a-type R branch clusters where the K = 0 and K = 1 lines were not a a present at 40V but had appeared by 400V. It took a great deal of searching to actually locate some a-type R branch transitions because the K asymmetry a. pairs were not as close together as initially expected. Microwave Spectrum of N-Chlorodifluoromethylenimine / 184 During this time a search was made for b-type Q branch lines between 12 — 18 GHz. This frequency range was chosen because this is where the low J transitions were predicted to occur and a rigid rotor model predicts the frequencies of low J transitions more accurately (since they are shifted less by centrifugal distortion). Eventually, after careful scrutiny, some lines on a broad band scan taken a 100V were noticed that could be from 3, 4 and 5 of the J=7-*-6 a-type R branch transition. This portion of the spectrum is shown in Figure 6.1. Tentative confirmation of these lines, (73 5 -63 a , 73 4 -63 3 , 7ft 4 -6a 3 3 "64 2) w a s made when the two K =4 lines of the J = 8*-7 transition were a found. This assignment was made in an interesting way. At the approximate location of where these two lines, 8 4 5 -7fl fl and 8a 4 -7a 3 , were predicted to occur a distinctive triplet was present. At first this caused some consternation, until it was realized that the triplet was most likely an overlap of the two lines, which are split by chlorine coupling. The four most convincing lines were put into a refinement which fit to the rotational constants B and C, and the distortion constant Aj, of Watson's A reduction rotational Hamiltonian. (See Section 2.7 for fitting procedures and Table 2.1 for the equation of the Hamiltonian). It converged tolerably well and accurately predicted the frequencies of more a-type R branch lines - since only B and C are determined from this type of transition. In order to get a value for the rotational constant A and to be able to predict more b-type lines it was necessary to include some b-type lines. Two tentative b-type Q branch lines were included in a fit which turned out to be reliable enough to predict Microwave Spectrum of N-Chlorodifluoromethylenimine / 185 accurately the location of more. The usual bootstrapping procedure was then used to assign and fit lines of increasingly higher J and K . a 37 The spectrum of the CI species was measured and analysed in the same way. First the a-type R branch lines were found and assigned. These were followed by measurement of b-type R and Q branch lines. The line 37 assignments for the CI species were easily confirmed by noticing that 35 corresponding lines to the CI species had approximately one third the intensity, t (caused by the ratio of the natural abundance of the two), and the corresponding a-type R branch lines were lower in frequency. 6.2. ANALYSIS OF THE MICROWAVE SPECTRUM 6.2.1. Nuclear Quadrupole Coupling CFgNCl has two naturally occurring isotopes, C F g^N^Cl and CFg^N^Cl, each of which contain two nuclei which could cause splitting of the rotational levels into hyperfine levels. They are, chlorine-35 or chlorine-37, each with spin If =3/2 and nitrogen-14 with spin I 2=l- The coupling of the nitrogen nuclear quadrupole moment with the rotational angular momentum is approximately an order of magnitude smaller than that of chlorine. As a result hyperfine splitting by the nitrogen was, at first, not expected to be large enough to be seen. Therefore in the initial approach to the analysis of the spectrum it was assumed that any splitting seen was caused only by chlorine. It was important for assignment purposes that the prediction of the hyperfine structure (by chlorine) was correct. Microwave Spectrum of N-Chlorodifluoromethylenimine / 186 Since there were no values available for the quadrupole coupling constants of CF^NCl it was necessary to determine reliable ones from the first lines measured showing quadrupole splitting. In the first few refinements the two b-type Q branch transitions had to be included so that X ^ - X c c could be determined. This was a slightly risky procedure because the assignment of these two transitions had not yet been confirmed. Because there were only two of them the least squares fit could appear reasonable, despite their being misassigned. Fortunately further analysis confirmed the assignment to be correct so no problems arose from this. Once enough accurately measured quadrupole split lines, of both a- and b-type, had been measured the error of the refinement dropped to within the experimental error. The quadrupole constants determined from this fit were then used to predict the hyperfine splitting of the rotational levels, which was used for the remainder of the analysis. 37 The quadrupole coupling constants used for splitting by CI were taken 35 to be 0.78 (the ratio of the two atomic quadrupole moments) that of the CI values, and proved to predict the splitting satisfactorily. As the analysis of the spectrum continued, it became increasingly clear that splitting caused by the nitrogen nucleus was affecting how accurately the fits could determine the constants. During the course of measuring the lines an extra dip or two was noticed on a few of the lines. Therefore a prediction of the nitrogen splitting was made, again using constants from C1NCO, this time those determined for the nitrogen quadrupole coupling. These were: x — 4.0 and X^u - X — 2.0. These produced a 3 3 DD CC predicted splitting pattern of "weak-strong-weak-strong" (increasing frequency); Microwave Spectrum of N-Chlorodifluoromethylenimine / 187 caused by the fact that two of the three nitrogen split lines are nearly always split by less than 0.15 MHz, while the third one splits by a measurable amount (>0.30 MHz). When the nitrogen splitting was carefully measured the hyperfine pattern observed was "strong-weak-strong-weak". This indicated that the value for X^p - X £ C was negative. When the values determined for the nitrogen quadrupole coupling in CFgNF were used (for which X ^ - X c c is negative), a more accurate prediction of the hyperfine pattern was obtained. The carefully measured lines which showed nitrogen splitting were put into a refinement which fit to both the nitrogen and chlorine splitting. The refinement program used was written for the situation where the coupling by one nucleus is much stronger than the other, and where first order theory can be applied. It assumed the following coupling scheme: J + I, = F, (6.3a) F, + I 2 = F (6.3b) Here I, is the nuclear spin of the chlorine which couples quite strongly to the rotational angular momentum J. The spin of the nitrogen, I 2, is then taken as a perturbation to the resulting F, to produce the final F. This total perturbation to the rotation can still be well approximated by a first order perturbation energy E Q which can be represented by: EQ=<J,KaKc,F1,I1,I2,F,MF|HQ + H ^ J . K K ^ F , ,1, ,I2 F,MF> (6.4) 1 2 where H Q is the quadrupole Hamiltonian for the chlorine and H Q for the nitrogen. Hocking and Gerry (10) have developed a closed form expression to Microwave Spectrum of N-Chlorodifluoromethylenimine / 188 evaluate E~ as given below: . 3A 0 (A 0 +1)~4I , ( I , +1 ) J ( J+1 ) 0 E ! = [ { 3 J 2 - J ( J + 1)} X__(D Q 81 ,.(21,-1 )J(2J-1)(J+1 )(2J+3) 3 a a + d / b p ) { j 2 - E ( b p ) } { x b b ( D " X c c d ) } ] (6.5) 3A,(A,+1)-4I 2(l 2+1)F,(F,+1) + { } x ... 161 2(21 2-1)J(2J-1)(J+1)(2J+3) 3A 2(A 2+1)-4J(J+1)F,(F,+1) x { } x ... F,(2F,-1)(F|+1)(2F,+3) x [ { 3 j 2 j ( j + l ) } X a a ( 2 ) + ( l / b p ) { j 2 - E ( b p ) } ( x b b ( 2 ) - x c c ( 2 ) } ] where A 0 = F,(F,+1) - I,(I,+1) - J(J+1) A, = F(F+1) - I 2 ( I 2 + 1 ) - F,(F,+1) A 2 = I , ( I , + 1 ) - J(J+1) - F,(F, + 1) It is this expression which is used in the least squares refinement program to determine the two sets of quadrupole coupling constants. For all well measured transitions the elements off-diagonal in J and F, were found to give negligible contributions to the calculated splittings. This was determined by comparing the splittings calculated by the first order fitting program with those calculated by a prediction program which used a full matrix diagonalization Microwave Spectrum of N-Chlorodifluoromethylenimine / 189 scheme. A representative sample of the transition frequencies used in the fits to 35 both sets of coupling constants for CF^N CI are given in Table 6.1, along with the values it determined for all the nuclear quadrupole coupling constants. It can be seen that for the chlorine-35 species all four constants are determined fairly well, especially considering only six transitions were used. However for the chlorine-37 species only X ^ - X c c for the nitrogen was determined with any degree of accuracy. X for the nitrogen was not determined at all, even though aa there were four transitions included in the fit. The reason for this difference is 35 believed to be because, for CFgN CI, two of the transitions included in the fit showed more resolution of the nitrogen splitting than the other four, that is two sets of quartets. The other four transitions included were measured as two sets of triplets; where each triplet was caused by the overlap of two doublets. The two transitions which were "fully" resolved gave much more information about the quadrupole coupling than the others which were not. Unfortunately for 37 CFgN CI only transitions showing 'triplets' or overlapping doublets were 37 measured, with the consequent reduction in accuracy of the CI refinement. To determine better quadrupole coupling constants for chlorine all the lines showing splitting by chlorine were put into a least squares fit. Those with resolvable nitrogen splitting were also included, after the splitting by the nitrogen had been accounted for. A sample representation of these transition frequencies are listed in Table 6.2. Table 6.4 has the chlorine nuclear quadrupole coupling constants determined from this refinement. Microwave Spectrum of N-Chlorodifluoromethylenimine / 190 6.2.2. Rotational and Centrifugal Distortion Constants The rotational constants and centrifugal distortion constants were determined by fitting the unsplit line frequencies to Watson's A reduction r rotational Hamiltonian, I representation, which is given in Table 2.1. They were accurately determined using the usual iterative approach of assigning low J and low K lines first. Then as the accuracy of the refinement improved higher a. J and K lines were assigned. In the first refinements it was possible to a release only A, B, C and A T because only a-type R branch lines and low K j a b-type lines were included. After some b-type lines between K = 2-*-1 were a measured A R was released, but unfortunately there was still too little information to determine it accurately. It was only after some b-type K = 3«-2 lines were a measured and included in the fit that A R became determined. At the same 37 time 5 R was released and determined. The analysis of the CI spectrum 35 proceeded in a similar manner. Because the CI constants were available the 37 preliminary estimates of the constants for CI were very good and the locations of its lines were well predicted from the start. Throughout these two analyses the fits were never remarkable in their apparent accuracy, but always predicted the location of new, unmeasured lines exactly. By the time all the lines that needed to be measured between 8 — 54 GHz had been measured this problem still existed. The residuals on many of the lines were unacceptably high, that is 0.2 — 0.5 MHz. This magnitude of difference between the observed and calculated frequency is almost enough to suspect a misassignment. Yet there was absolute confidence that the lines in each spectrum had been correctly assigned. Microwave Spectrum of N-Chlorodifluoromethylenimine / 191 Various causes for this problem were suggested and the following describes the solutions used to remedy the situation. One possible cause was poor line measurement caused by a too high sample pressure. When the pressure of a sample is too high it is not possible to get the resolution necessary to see the splitting of the lines. The lines had been initially measured at a slightly too high pressure because there was so little sample, and it was necessary to make sure the spectrum was at least roughly measured and assigned before it was all used up. Remeasurement of most of the lines at a lower sample pressure led to the observation of splitting of some lines which previously had been measured unresolved. Naturally when this occurs the accuracy of the unsplit line measurement improves. A second solution was to realize that the splitting of many of the lines by nuclear quadrupole coupling (by both nitrogen and chlorine) was large enough to increase the line width to the point of making a good, accurate measurement of the frequency impossible. Yet at the same time the splitting was still too small for each component to become resolved and be measured independently. Accordingly a weighting scheme was developed and applied to the lines to account for this problem. This scheme also took into account problems caused by interference and an inability to modulate the lines properly. A weight of 1.00 corresponded to a measurement uncertainty of 0.03 MHz. A lower weight corresponded, roughly, to a measurement uncertainty of (1/weight) x 0.03 MHz. Despite being a somewhat arbitrary weighting scheme it established a self consistent method of weighting the lines. The weighting scheme is given below: Weight Microwave Spectrum of N-Chlorodifluoromethylenimine / 192 Quality of Line 1.00 0.10 Accurate: Good: 0.01 Fair: 0.0001 Poor: .000001 Bad: includes a quartet, well spaced doublets with narrow internal splitting, a narrow singlet and no interference. includes a doublet with internal splitting >0.3 MHz and <0.6 MHz, (and therefore is not well spaced but rather is blended), and a singlet with a spread of >0.3 MHz and <0.4 MHz. includes same as those with a weighting of 0.10, but now have a poor shape or their modulation is dubious. Singlets have a spread of >0.4 MHz and <0.6 MHz. includes quartets or doublets with interference so only half the quartet or doublet could be measured, and singlets with a spread of >0.6 MHz and <0.8 MHz includes a singlet with a spread >0.8 MHz. A refinement made with the transitions weighted according to this scheme improved the accuracy of the constants slightly. However it was noticed that some of the residuals on lines that were supposed to be either well resolved or had narrow line widths were still quite large. On further investigation these were discovered to be ones with possible interference or modulation problems, so -12 they were weighted out of the fit completely, using a weight of 10 . This, finally, produced an acceptably accurate fit. Table 6.4 gives the final, most accurate set of rotational constants and centrifugal distortion constants determined for each isotopic species. It also gives the final nuclear quadrupole coupling constants determined for chlorine and nitrogen. The unsplit line frequencies are given in Table 6.3. Microwave Spectrum of N-Chlorodifluoromethylenimine / 193 6.3. EFFECTIVE STRUCTURE The ground state principal moments of inertia and the inertial defects for the two isotopes of CF NCI are given in Table 6.5. Both inertial defects are small positive numbers and are remarkably similar which confirms that the ground state of the molecule is planar. The molecular structure is described by seven non-redundant parameters which were chosen to be: the four bond lengths, r(C = N), r(N-Cl), r(C-F t) and r(C-F ), and the three angles, <(CNC1), <(NCF ) and <(NCF ). With only c t c four pieces of independent data from the two sets of rotational constants, determination of a full structure of any kind would be impossible. At best, determination of two to three parameters of a crude ground state effective structure and possibly an average structure was hoped for. Initial refinements to a ground state effective structure indicated that only two parameters could be fit to at one time, as releasing three parameters made it impossible for the refinement to converge. Therefore which two of the seven parameters should be determined had to be decided on. After looking at the • structures of the two similar molecules CFgNF and CC^NCl, it was easy to see that determining the C = N —CI angle would be the most informative. The value for the C = N —X angle (X = F or CI) varies by almost 10° between these two other molecules. It would be interesting to know what it was for CF^NCl, a hybrid molecule of the other two. Since two parameters could be determined from the data another one had to be chosen and it was taken to be the N —CI bond length. The reasons for this choice are: (i) this bond length tends to vary more between different molecules than the other five, and (ii) a combination of Microwave Spectrum of N-Chlorodifluoromethylenimine / 194 the quadrupole information determined from the analysis of the microwave spectrum and structural values for both the C = N — CI angle and N —CI bond length would yield the most information about the kind of bonding taking place in the C = N —CI group of this molecule. Unfortunately, it turned out that when these • two parameters were released in the structure refinement program (described in section 4.2) both could not be determined at the same time because they were perfectly correlated. This was caused by the chlorine atom being very close to the 'a'-principal inertial axis (Figure 6.2). This was also indicated by the A rotational constant of CF 2N CI being slightly larger than it was for CFgN CI. Therefore only the C = N —CI angle was released in the fit. Because the estimated structural parameters do not predict the rotational constants exactly, it was not possible to get a very accurate value for the C = N —CI angle. The least Squares refinement had to try and fit all the error (in the structure) into the one parameter released. This is why the error on the determined C = N — CI angle is so large, for both the effective and average structure. Since most of the error in the estimated structure results in a poor value for the A rotational constant, a fit was done where the A rotational constant was weighted out of the fit completely. The other two constants were given equal weights. This gave a fit with a lower standard deviation, but did not indicate that it was more reliable. In order to get an idea of how the C = N — CI angle would vary with change in length of the N —CI bond a range of lengths, (three from other molecules (7,9,11)), was put in the fit and constrained to those values. For Microwave Spectrum of N-Chlorodifluoromethylenimine / 195 these fits the A rotational constant was put back in with the same weight as B and C. The results of this procedure are given in Table 6.6, for both the effective and average structures. It is interesting to see that the longer N —CI bond lengths of 1.745A and 1.788A gave the fits with the lowest standard deviations, whereas the N —CI bond length of 1.683A from a more similar molecule, CCl^NCl, gave the least accurate value. As a result the structure with the longer N —CI bond length is the favoured one. The centrifugal distortion constants determined from the analysis of the microwave spectrum plus existing vibrational data meant there was enough data available to determine a harmonic force field. The results from it were used to calculate average rotational constants to use in an average structure refinement, which indicated the best N —CI bond length. The above was done and is described in the next two sections. 6.4. THE HARMONIC FORCE FIELD The harmonic force field was determined by using the recently determined centrifugal distortion constants as additional information to the existing vibrational data. The normal modes of CF0NC1 transform as 7A' + 2A" in C . The 2 s non-redundant symmetry coordinates chosen are given in Table 6.7 in terms of the internal displacement coordinates. In the A' symmetry block, the symmetry coordinates were chosen to equal the displacement of an internal coordinate. To determine appropriate symmetry coordinates for the A" block it was necessary to check that the transposed B matrix (symmetrized) described an out-of-plane bend (of the CF^ group) and a torsion. Since there is often ambiguity in defining out-of-plane coordinates Table 6.7 also contains the non zero components of their Microwave Spectrum of N-Chlorodifluoromethylenimine / 196 B matrix. In the preliminary force field refinements the geometrical parameters used were those transferred from CF NF and CC1 NCI where r(N-Cl) was 1.683A and <C = N —CI was 117.1°. To be self consistent, after the best ground state average structure was determined these two parameters were changed to those given in Table 6.7. The vibrational data used was that reported by O'Brien et al (3). Except for the values for the i>7 and vg vibrations (in the A' and A" symmetry group respectively) these values were identical to those reported by Hirschmann et al (2). In the early paper by Hirschmann the v 7 and v 9 vibrations were not observed and had to be estimated from combination band data. O'Brien et al had recently assigned new frequency values to these two vibrations, but were reported to be two overlapping bands. Therefore in the first few refinements these two vibrations were weighted out of the fit (with the ridiculously high uncertainty of 9999.0 cm"1). Later, when they were included in the fit they were given uncertainties of 5% and 10% respectively. The remainder of the vibrations were included with assigned uncertainties of 1%. There were no 37 vibrational data available for the CI isotope. All the centrifugal distortion constants except 5 R were assigned percentage uncertainties of 2%. 5 R was given an uncertainty of 4% because it was the most poorly determined constant. The _2 weights were proportional to the (uncertainty) . Preliminary estimates of the force constants were made by transferring appropriate values determined for the force fields of CFgNF (5) and CC12NC1 (8). For CF NF twenty-one of the thirty-one possible force constants were reported. Microwave Spectrum of N-Chlorodifluoromethylenimine / 197 This force field was determined from a great deal of input data that included results from infrared, Raman and microwave spectra, electron diffraction and ab initio calculations. Consequently it seems reasonable that enough data were used to determine a reliable force field of this many force constants. On the other hand, for CCl^NCl values for all thirty-one force constants were reported. This does not seem feasible since the only input data were from infrared and Raman spectra. Therefore only force constants which were subsequently refined were transferred from the CClgNCl force field. These were the diagonal force constants f 2 2 and f 5 5 , (the N —CI stretch and the C = N — CI bend respectively), and the off-diagonal force constant f 2 5. See Table 6.8 for a complete description of the force constants. The first step in the determination of the force field was to release the seven diagonal force constants of the A' symmetry group. Often these are released first because they are usually an order of magnitude larger than the off-diagonal force constants and can be determined more easily. Surprisingly the refinement would not converge, even though this seemed a reasonable number of constants to release given the amount of input data. Apparently some of the off-diagonal force constants played a fairly large role in the description of the force field. To determine which ones these might be the transposed Jacobians for the wavenumbers and distortion constants were examined to see which force constants produced large values. The off-diagonal force constants which produced large values the most often were chosen to be the ones released in the force field refinements. However it now became necessary to constrain some diagonal force constants. These tended to be the ones describing the higher frequency vibrations because the centrifugal distortion constants have less information about Microwave Spectrum of N-Chlorodifluoromethylenimine / 198 them. It was also felt that the diagonal constants of the A" block should be released. Therefore many force field refinements were done releasing different combinations of force constants. At the same time by varying the number of force constants in a fit the number that could be evaluated at any one time was determined. This maximum number turned out to be nine, which seems reasonable given that there were seventeen pieces of independent data (eight independent centrifugal distortion constants and nine vibrational wavenumbers). It also transpired that f 3 and f 4 a, the diagonal force constants describing the two C — F stretches were indeterminate and were left at the values for CF^NF. In one instance, a force constant, f 6 7, had to be left constrained because it was too highly correlated with another, f 7 7. Partway through the analysis it was observed that the force field was sufficiently reliable to predict the frequency of the v 7 vibration to within 3 cm 1 of that assigned to it by O'Brien et al in 1984. Consequently it and v 9 were put into the fit by giving them realistic uncertainties. The final force field is given in Table 6.9. It was chosen because all its constants were determined, it had no large correlations and it predicted the observed vibrational wavenumbers and centrifugal distortion constants pleasingly well, as can be seen in Table 6.10. The reliability of this harmonic force field was further confirmed by the fact that it predicted the inertial defect very well, shown in Table 6.5. Microwave Spectrum of N-Chlorodifluoromethylenimine / 199 6.5. AVERAGE STRUCTURE The average rotational constants were calculated using the a, . 's harmonic produced by the harmonic force field and equation (2.33). They are given in Table 6.11. The principal moments of inertia and the inertial defect of the average rotational constants are given with those for the effective rotational constants in Table 6.5. Similar to the effective structure four different fixed values for the N —CI bond length were used to see how the C = N — CI angle would vary. The results are presented in Table 6.6 where it can be seen that an N —CI bond length of 0 1.745A gave the fit with the lowest standard deviation. The bond lengths chosen indicated that the accuracy of the refinement went through a minimum somewhere near a structure with an N —CI bond length of 1.745A. Therefore this was the chosen structure for any further calculations and is shown in Figure 6.2. The results do not really give a great deal of definitive information about the structure because only one parameter was determined. Nevertheless the value determined for the C = N —CI angle has been taken to be approximately correct and used to make some suggestions about the bonding at the nitrogen. Despite the fact that the accuracy of the value determined for the C = N —CI angle must be viewed with reserve it is encouraging to note that it lies between the two values determined for CF^NF and CC12NC1 (107.9° and 117.1° respectively). Microwave Spectrum of N-Chlorodifluoromethylenimine / 200 6.6. COMMENTS ON THE BONDING IN C F 2 NCL Information about the bonding in the C = N-C1 group can be obtained from the nuclear quadrupole coupling constants of nitrogen and chlorine. This is done by relating the field gradients (x's) to the population of the p-electrons in the valence shell of the atom with the quadrupolar nucleus. This is an approximate treatment of the situation first introduced by Townes and Dailey (12). One form of the theory is expressed as: n + n X„„ « ~ " OeQq„ i n (6.6a) y z 2 n X + n z 2 n X + n y 2 X y y = - ( ^ - 2 - ^ " V^mo (6'6b) X z z - - £ 4 - ^ " n z ) e Q q n 1 ( ) (6.6c) where x, y and z have been defined as an axis system on the quadrupolar nucleus. n x, n^ and are the populations of the electrons in the corresponding valence p-orbitals, and eQ°ln^Q is the field gradient of an atomic p-electron in the n t b (valence) shell. In order to derive meaningful information about the nitrogen-chlorine bond from the experimentally determined nuclear quadrupole coupling constants it was necessary to transform the constants to the principal axis system of. the quadrupole coupling (as opposed to being in the principal inertial axis system). This is done using the following transformation equation: where is the quadrupole tensor in the principal axis system of the Microwave Spectrum of N-Chlorodifluoromethylenimine / 2 0 1 quadrupole coupling (and therefore will have no off-diagonal elements), x is the quadrupole tensor in the principal inertial axis system and for a planar near symmetric prolate molecule is given by: X a a Xab 0 Xab xbb 0 0 0 C C and R is the transformation matrix given by: R cosd — sin0 0 za za sin# C O S 0 0 za za 0 0 1 where 8 is the angle between the z-axis and the a-axis. When v , is za & ab eliminated the following simple relations exist between the coupling constants in the two axis systems: X = (X cos 20 - X u u S i n 2 0 )/(cos2 8 - sin2 8 ) zz aa za bb za za za X = (X s i n 2 0 - Xuucos20 )/(sin2 8 - cos2 8 ) Axx aa za bb za za za yy C C (6.8a) (6.8b) (6.8c) where y is taken to be the out-of-plane axis. These equations were used to convert the nuclear quadrupole coupling constants in the principal inertial axis Microwave Spectrum of N-Chlorodifluoromethylenimine / 202 system to those in the assumed principal quadrupole coupling axis system. The calculated values are given in Table 6.12. The axis system chosen will be discussed below. Information about the bonding given by the chlorine quadrupole coupling constants will be discussed first. For chlorine, bonding is usually assumed to be with an electron in a pure p-orbital. For this reason a principal axis of the quadrupole coupling has often been found to be along the bond with the CI atom (13). This was assumed to be the case for CF NCI, so that the N —CI bond was taken to be the z-axis, and y perpendicular to the plane of the molecule. In order to calculate x > X and X it was necessary to determine xx' yy zz J 9 To do this a structure was needed and this was taken to be the average za structure with the N-Cl bond length = 1.745A, (given in Table 6.6). This gave a value of 29.08° for 8 , which in turn gave the value of —111.7 MHz za at for x • This is very close to the value (x ) for the chlorine atom of ZZ z z — 109.7 MHz. As a result it was assumed initially that there would be very little ionic character to the bond. Because the value was slightly larger than at X the form of the ionic bonding was taken to be with the chlorine on the ZZ positive pole, as shown in Figure 6.3b. This will tend to increase X z z relative to its atomic value. However if there is any ir bonding in the N —CI bond, it will be of the dative type from chlorine to nitrogen and will tend to decrease X . These two structures, plus the covalent a bond structure will all influence zz r the value of X > and are used to calculate the amount of ionic character in the zz a bond between nitrogen and chlorine. Figure 6.3 illustrates the three contributing structures. The amount of ir character is calculated from x — X , b xx yy as this indicates how far from cylindrical symmetry the populations of the Microwave Spectrum of N-Chlorodifluoromethylenimine / 203 electrons are around the a bond. This lack of cylindrical symmetry is caused by T T back bonding by the chlorine in one of the planes. The expression used is: (14,15) * = ( X x x " x y y } (6.9) 3 / 2 ( e Q q n l 0 ) This gave a value of 9.3% for the 7r character. The expression used to calculate the amount of ionic character, (i), in the a bond is: (16) X = (l-i-7T)(xat) + i(2xat) + 7r(*xat) (6.10) zz zz zz zz Substituting in for all the known variables gave a value of 6.5% for the percentage ionic character. The amount of covalent bonding is (1 — i —ir) which turned out to be 84.2%. It must be pointed out that in these calculations any contributions from sp hybridization at CI and screening of the nucleus caused by a changed charge distribution, were ignored. This is usually a valid approximation when the chlorine has approximately the same electronegativity as the atom it is bonded to, which in CFgNCl is nitrogen (16). The bonding at the nitrogen is somewhat more complicated. The first problem that arises is the question of what the principal axis system of the nitrogen quadrupole coupling is. It is not as straightforward for nitrogen as it was for the chlorine because instead of a pure p-orbital covalent bond, simple bonding theory predicts the use of sp2 hybrid orbitals. Somewhat arbitrarily the z-axis was chosen to be the bisector of the C = N —CI angle. This turned out to be very close to the b-axis, by only 4.9°. Therefore the following Microwave Spectrum of N-Chlorodifluoromethylenimine / 204 approximations were made: X — X r . , X — X and x — X • y was again zz u D xx aa yy cc taken to be the out-of-plane axis. Because the C = N —CI angle was determined to be 112° it was initially supposed that this suggested sp3 hybridization at the nitrogen. Using the axis system described above, this gave the four hybrid orbitals as: #1 = hl> + Wm + pz px (6.11) * 2 = + pz px * 3 = W 8 - ^ + /Wpy * • = * ^ S - * % Z - ^ p y Using these equations the electron populations n^, n^ and were determined in terms of the orbital populations, n, , n 2, n 3 and n 4. When these were used in equations (6.6) to calculate the nuclear quadrupole coupling constants the theoretical result of x = 0 was obtained, and this was not zz observed experimentally. This suggested that perhaps the wrong kind of hybrid orbital bonding system had been chosen. Therefore the calculations were repeated using sp 2 hybrid orbitals, (same axis system). To account for the fact that the C = N —CI angle was not 120°, as is predicted by a pure sp2 hybrid orbital the normalized valence orbitals were determined using the following equations suggested by Gordy and Cook (17): Microwave Spectrum of N-Chlorodifluoromethylenimine / 205 ¥, = / ( 1 - 2 a g ) ^ s - v/(2aj)i// p z (6.12) a py 2 where a g represents the amount of s character in the nitrogen a bonding orbitals. It was calculated from (17): 2 = cos e s cos 6 - 1 where 6 is the measured bond angle. For CF2NCI this was taken to be 112°. The resulting values calculated for the nuclear quadrupole coupling constants although not in very good agreement were at least closer to the experimentally observed values. They are listed in Table 6.13 for comparison with the 14 experimental values. In all calculations the N atomic constant eQ° 1 2io w a s taken to be -10 MHz (17). In the above approach to this problem to calculate the n , n and n x y z electron populations the populations in all four orbitals, (the lone pair, the two a bonds N —CI and C = N, and the TT bond) were assumed and these assumed values are given in Table 6.13. The n , n , and n values were then used to 0 x y z calculate the quadrupole coupling constants. Another approach is to use the Microwave Spectrum of N-Chlorodifluoromethylenimine / 206 experimentally determined coupling constants to calculate these values. However because there are only two independent coupling constants and four unknown electron populations, n, , n 2, n 3, and n a (associated with each orbital) two of the orbital populations must be assumed. Because the sp3 hybrid orbitals will give X z z = 0 independent of electron population, it was felt that this calculation would only be useful for the sp2 hybrid orbitals. It was possible that the poor values for the coupling constants were a result of bad approximations for the n , n and n populations, x y z r In the sp 2 hybrid orbital scheme the n 2 and n 3 electron populations were assumed. n 2 was associated with the C —N bond and set equal to 1.1 after Hocking, Williams and Gerry (9), and n 3 was associated with the N —CI bond and set equal to 1.065 - the sum of the covalent bond plus ionic bond character. Using equations (6.6) and solving for n, and n„ gave n, = 1.884 (associated with the lone pair) and n„ = 1.330 (associated with the 7T bond). These seem to be reasonable results for these populations. The resulting values for n , n , and n are given in Table 6.13 under the experimental column. It x y z can be seen that they are in tolerable agreement with the values calculated by ab initio, that is they agree in the ordering of the size of each population. They are also considerablely different from the assumed values used to calculate the quadrupole coupling constants. A better prediction of the orbital populations was obtained using ab initio methods. For this a Gaussian 70 computer program with an STO-3G basis set was used. The structure used was the r structure with r(N —CI) = 1.745A. z The electron populations it determined for the nitrogen are also given in Table 6.13, along with the resulting calculated quadrupole coupling constants. Microwave Spectrum of N-Chlorodifluoromethylenimine / 207 From this orbital population prediction values for x > X.u a n a X of aa DD cc chlorine were also calculated, using equation (6.6) (since the electron populations of all the atoms were determined in the principal axis system). These results are given in Table 6.14 and it can "be seen that the calculated values are in good agreement with the experimentally determined ones. 6.7. DISCUSSION The results of this study seem to suggest quite strongly that to a good approximation CFgNCl can be described as a hybrid of the two molecules CFgNF and CC1-NC1. This was made evident at the beginning of the analysis when the transferred structural parameters predicted the rotational constants so well. The results of the structural refinements added more credibility to this description by determining the C = N — CI angle to be halfway between that determined for the other two. It is interesting to see that for CFgNCl a somewhat longer N —CI bond length (than in CCLNC1) is indicated. Nonetheless it turns out that c* o this longer bond length of 1.745A is much closer to the sum of the two atomic O 0 radii, of 1.73A, given by Pauling (18) for nitrogen and chlorine, than is 1.683A (in CC12NC1). Since the molecule is planar the ratio of the coupling constants 35 37 X c c( Cl)/\ ( CI) should be the ratio of the quadrupole moments of the nuclei (1.2688). The value obtained is 1.289 + 0.024 which is in fair agreement. In the harmonic force field refinement a choice of which force constant should be transferred for the C=N stretching vibration had to be made. From an inspection of each of the vibration frequencies for the C = N stretch, the Microwave Spectrum of N-Chlorodifluoromethylenimine / 208 preferred choice was from CF NF because the value of the two frequencies were much closer. p(C = N stretch) for CF^NF is 1740 cm"1, and for CF2NC1 is 1728 cm"1, while for CCl^NCl it is 1571 cm"1. For the same reason it was best to choose the r(C=N) bond length from CF 2NF. From the ab initio calculations of the electron populations it was interesting to observe that the calculated out-of-plane p-orbital electron population for chlorine was 1.98. This indicates virtually no (=2%) 7T back bonding by the chlorine; which is in slight disagreement with the value of 9.3% calculated earlier. However since the theory is quite simple and crude there is little cause for concern. Microwave Spectrum of N-Chlorodifluoromethylenimine / 209 TABLE 6.1 Representative Sample of Transition Frequencies (MHz) of CFgN CI Showing Both Nitrogen and Chlorine Nuclear Quadrupole Hyperfine Structure Transition F,' F' - F'2' F" Observed Obs Calc Frequency Splitting Splitting 4.5 4.5 - 3.5 3.5 28653.929 -1.423 -1.428 4.5 5.5 • 3.5 4.5 28654.255 -1.097 -1.129 4.5 3.5 • 3.5 2.5 28654.382 -0.970 -1.010 5.5 5.5 -• 4.5 4.5 28654.874 -0.478 -0.490 3.5 3.5 • 2.5 2.5 28654.874 -0.478 -0.480 5.5 6.5 -• 4.5 5.5 28655.240 -0.112 -0.150 3.5 4.5 • 2.5 3.5 28655.240 -0.112 -0.120 5.5 4.5 -• 4.5 3.5 28655.240 -0.112 -0.030 3.5 2.5 -• 2.5 1.5 28655.240 -0.112 0.010 6.5 6.5 • • 5.5 5.5 28655.684 0.332 0.429 6.5 7.5 • • 5.5 6.5 28656.303 0.951 0.899 6.5 5.5 • • 5.5 4.5 28656.303 0.951 1.001 4.5 3.5 • • 4.5 3.5 14839.067 -3.758 -3.805 4.5 5.5 • • 4.5 5.5 14839.067 -3.758 -3.681 4.5 4.5 • • 4.5 4.5 14839.691 -3.134 -3.137 7.5 6.5 • • 7.5 6.5 14840.365 -2.460 -2.470 7.5 8.5 • • 7.5 8.5 14840.365 -2.460 -2.392 7.5 7.5 • • 7.5 7.5 14840.977 -1.848 -1.810 5.5 4.5 • • 5.5 4.5 14844.701 1.876 1.778 5.5 6.5 • • 5.5 6.5 14844.701 1.876 1.873 5.5 5.5 • • 5.5 5.5 14845.293 2.468 2.388 6.5 5.5 • 6.5 5.5 14845.976 3.151 3.094 6.5 7.5 • • 6.5 7.5 14845.976 3.151 3.177 6.5 6.5 • • 6.5 6.5 14846.471 3.646 3.710 5.5 4.5 • • 5.5 4.5 33624.599 -3.909 -3.953 5.5 6.5 • 5.5 6.5 33624.599 -3.909 -3.896 5.5 5.5 • 5.5 5.5 33624.946 -3.562 -3.587 8.5 7.5 • - 8.5 7.5 33625.711- -2.797 -2.683 8.5 9.5 • 8.5 9.5 33625.711 -2.797 -2.645 8.5 8.5 • • 8.5 8.5 33626.100 -2.408 -2.321 6.5 5.5 - 6.5 5.5 33630.772 2.264 2.249 6.5 7.5 • 6.5 7.5 33630.772 2.264 2.295 6.5 6.5 - 6.5 6.5 33631.071 2.563 2.591 Microwave Spectrum of N-Chlorodifluoromethylenimine / 210 TABLE 6.1 - continued Transition Ff F' - F'2' F" Observed Obs Calc Frequency Splitting Splitting (MHz) (MHz) (MHz) 7.5 6.5 - 7.5 6.5 33632.158 3.650 3.511 7.5 8.5 - 7.5 8.5 33632.158 3.650 3.551 7.5 7.5 - 7.5 7.5 33632.455 3.947 3.855 Nuclear Quadrupole Coupling Constants (MHz) CF 2N 3 5C1 CF 2N 3 7C1 Chlorine x -69.8+1.9 -59.9+17.1 aa X,,- X -25.86±0.29 -17.7±1.3 bb cc Nitrogen x 3.42 + 0.61 7.2±11.1 X u u- X -2.822±0.087 -2.67 + 0.43 bb cc Microwave Spectrum of N-Chlorodifiuoromethylenimine / 211 TABLE 6.2 Representative Sample of Transitions with Resolved Hyperfine Structure of CF NCI (Chlorine Only) z Transition F' - F" Frequency Obs —Calc a (uncertainty) splits (MHz) (MHz) 3 ^ CF 2N CI 6,6 -5 , 5 5.5 - 4.5 26141.859(50) 0.023 4.5 - 3.5 26142.498(30) 0.063 6.5 - 5.5 26142.498(30) -0.077 7.5 - 6.5 26143.165(30) -0.009 6 3 f t - 5 3 3 6.5 - 5.5 27773.668(30) -0.035 5.5 - 4.5 27774.633(30) -0.055 7.5 - 6.5 27778.237(30) 0.063 4.5 - 3.5 27779.185(30) 0.027 8 5 f l-7 5 3 6.5 - 5.5 37008.250(30) -0.065 9.5 - 8.5 37007.240(30) 0.004 7.5 - 6.5 37003.110(30) -0.009 8.5 - 7.5 37002.110(30) 0.070 7 0 7 -6 , 6 5.5 - 4.5 26332.903(30) 0.063 6.5 - 5.5 26333.245(30) -0.023 8.5 - 7.5 26333.587(30) 0.009 7.5 - 6.5 26333.958(30) -0.048 6,6 - 5 0 5 7.5 - 6.5 32087.123(30) -0.022 4.5 - 3.5 32086.600(30) 0.009 6.5 - 5.5 32085.885(30) -0.003 5.5 - 4.5 32085.350(30) 0.016 6,5 - 6 0 6 4.5 - 4.5 14839.283(50) 0.011 7.5 - 7.5 14840.572(30) -0.021 5.5 - 5.5 14844.904(30) 0.045 6.5 - 6.5 14846.145(30) -0.035 Microwave Spectrum of N-Chlorodifluoromethylenimine / 212 TABLE 6.2 - continued Transition F' - F" Frequency Obs —Calc (uncertainty) splits (MHz) (MHz) 12,,,—12 0 1 2 10.5 - 10.5 35598.275(30) -0.021 13.5 - 13.5 35599.016(30) 0.074 11.5 - 11.5 35603.600(30) -0.046 12.5 - 12.5 35604.286(30) -0.007 2^ 5 -7, 6 5.5 - 5.5 22773.449(50) -0.019 8.5 - 8.5 22773.782(50) . -0.033 6.5 - 6.5 22775.223(50) 0.048 7.5 - 7.5 22775.527(50) 0.004 14 2, 2 -14, , 3 12.5 - 12.5 29520.736(30) -0.018 15.5 - 15.5 29521.076(30) 0.020 13.5 - 13.5 29523.601(30) -0.057 14.5 - 14.5 29524.015(30) 0.055 Observed frequency minus the frequency calculated using the fitted spectroscopic constants. Microwave Spectrum of N-Chlorodifluoromethylenimine / 213 TABLE 6.3 Observed Transition Frequencies (in MHz), with Hyperfine Structure Removed, of CF2NC1 Transition Frequency Obs-Calc Weight CF 2N CI 5 2 4 " 5 1 S 30451.090 -0.013 1.0000 5 1 5 " 4 0 4 28655.352b 0.043 1.0000 5 0 5 " 4 1 4 15878.683 -0.157 0.0000 6 2 5 " 6 i 6 31912.724 0.037 1.0000 6 2 4 _ 5 2 3 28221.114 -0.019 1.0000 6 3 4 _ 5 3 3 27776.362 0.033 0.0100 6 3 3 " 5 3 2 27801.612 0.007 1.0000 6 0 6 _ 5 0 5 27070.136 -0.069 0.1000 6 1 5 " 6 0 e 14842.825 0.019 1.0000 6 1 6 " 5 0 5 32086.353 0.197 0.0000 6 1 6 • 5 1 5 26142.639 -0.010 0.0001 6 0 6 _ 5 1 5 21126.519 -0.179 0.0000 6 2 5 _ 5 2 4 27604.312 0.079 1.0000 7 2 5 _ 7 1 6 22774.530 0.103 0.1000 7 2 6 " 7 1 7 33628.508 -0.017 1.0000 7 0 7 " 6 0 6 31349.563 0.009 1.0000 7 1 6 " 6 1 5 33674.168 -0.051 0.0100 7 3 5 " 6 3 4 32427.661 0.018 0.1000 7 1 7 " 6 0 6 35458.518 -0.000 0.0100 7 3 4 _ 6- 3 3 32484.106 -0.043 0.1000 7 0 7 _ 6 1 6 26333.520 -0.084 1.0000 8 2 6 _ 8 1 7 22453.480 0.040 1.0000 8 2 7 " 7 2 6 36691.501 0.051 1.0000 8 2 6 _ 7 2 5 38046.288 -0.111 0.0100 8 3 5 " 7 3 4 37195.515 -0.066 1.0000 8 4 5 " 7 4 4 37043.765 -0.012 1.0000 8 1 1 7 " 7 1 6 38367.494 0.109 0.0000 8 8 " 7 1 7 34721.401 -0.076 0.0100 8 1 7 " 8 0 8 19976.286 -0.295 0.0000 8 0 8 " 7 1 7 31449.265 -0.046 0.0000 8 4 4 " 7 4 3 37046.785 -0.032 1.0000 8 1 8 " 7 0 7 38830.436 -0.005 1.0000 8 5 4 " 7 5 3 37005.110 0.040 1.0000 8 0 8 7 0 7 35558.237 -0.038 0.1000 8 5 3 " 7 5 2 37005.110 0.003 1.0000 9 1 9 • 8 1 8 38979.500 -0.169 0.0001 Microwave Spectrum of N-Chlorodifluoromethylenimine / 214 TABLE 6.3 - continued Transition Frequency Obs-Calc Weight 9 1 8 • 8 1 7 43004.901 -0.007 0.0100 9 2 7 • 8 2 6 43011.526 -0.141 0.0000 9 O 9 • 8 1 8 36440.291 0.058 0.0000 9 1 8 • 9 0 9 23268.840 -0.250 0.0000 9 3 6 8 3 5 41944.025 0.053 1.0000 9 0 9 - 8 0 8 39712.477 0.078 0.0001 9 1 8 • 8 2 7 24110.673 -0.152 0.0000 10 3 7 • 10 2 8 40096.710 0.026 0.0000 10 2 8 • 10 1 9 22866.509 0.031 1.0000 10 O 1 0 ' • 9 1 9. 41291.635 -0.051 0.0001 10 1 9 - 9 2 8 30485.896 0.058 0.0000 10 1 9 • 10 0 1 0 27013.492 -0.242 0.0000 11 2 9 ' - 11 1 1 0 23732.212 0.026 1.0000 11 1 1 1 • 10 0 1 0 49365.369 -0.056 0.1000 11 1 1 0 ' - 10 2 9 36871.356 0.023 0.0000 12 3 9 - 12 2 1 O 37386.480 -0.038 1.0000 12 O 1 2 - 11 1 1 1 50594.400, -0.083 0.1000 12 1 1 1 - 12 0 1 2 35601.320 -0.021 1.0000 12 1 1 2 - 11 0 1 1 53077.076 -0.071 0.1000 13 5 9 - 14 4 1 0 14483.459 0.011 1.0000 13 2 1 2 - 13 1 1 3 49032.787 -0.131 0.1000 13 3 1 0 - 13 2 1 1 36124.976 -0.039 1.0000 13 1 1 2 - 13 0 1 3 40273.163 0.510 0.0000 13 2 1 1 - 13 1 1 2 27028.881 -0.052 0.1000 13 2 1 1 - 12 3 1 0 27416.442, -0.088 0.1000 14 2 1 2 - 14 1 1 3 29522.368 0.013 1.0000 14 2 1 2 - 13 3 1 1 34622.747 . -0.246 0.0000 14 3 1 1 - 14 2 1 2 35076.982 -0.006 1.0000 15 3 1 2 - 15 2 1 3 34352.147, -0.008 1.0000 15 2 1 3 - 15 1 1 4 32590.239 0.018 1.0000 16 3 1 3 - 16 2 1 4 34048.222 0.023 1.0000 16 2 1 4 - 16 1 1 5 36209.480 0.009 0.0100 17 7 1 1 - 18 6 1 2 32150.286 -0.002 1.0000 17 3 1 4 - 17 2 1 5 34246.825 -0.115 1.0000 17 3 1 4 - 16 4 1 3 27392.030 -0.369 0.0000 18 3 1 5 - 18 2 1 6 35013.589 0.012 1.0000 18 3 1 5 - 17 4 1 4 34869.318 0.088 0.1000 19 2 1 7 - 19 1 1 8 49738.644 -0.159 0.0000 19 3 1 6 - 19 2 1 7 36397.027 -0.043 1.0000 20 3 1 7 - 20 2 1 8 38429.509 0.046 1.0000 20 4 1 6 - 20 3 1 7 48027.496 0.047 1.0000 Microwave Spectrum of N-Chlorodifluoromethylenimine / 215 TABLE 6.3 - continued Transition Frequency Obs-Calc Weight CF N CI 5 i 5 " 4 0 4 28281.947 0.155 0.0000 6 2 a " 6 1 5 23621.750 0.142 1.0000 6 2 5 " 5 2 4 26899.581 0.055 1.0000 6 2 a • 5 2 3 27454.955, 0.001 1.0000 6 1 6 " 5 O 5 31641.394 -0.035 1.0000 6 0 6 " • 5 0 S 26418.375 -0.023 0.0000 6 0 6 " 5 1 5 20290.538 -0.211 0.0000 7 2 5 ' 7 1 6 23033.086 -0.129 0.0000 7 2 5 ' 6 2 4 32200.603 0.040 1.0000 7 3 5 _ 6 3 4 31583.592 -0.001 1.0000 7 3 a " 6 3 3 31631.352 -0.068 1.0000 7 0 7 " 6 O 6 30609.268 0.028 0.0001 7 1 7 " 6 1 6 29714.189 -0.024 0.0001 7 1 6 6 1 5 32788.940 -0.016 0.0001 7 0 7 " 6 1 6 25386.166 -0.043 0.0000 7 2 6 6 2 5 31340.966 -0.080 1.0000 8 2 7 8 1 8 35326.000 -0.145 1.0000 8 2 6 • 8 1 7 22657.707 -0.033 1.0000 8 0 S 7 O 7 34732.721 0.033 0.0001 8 1 8 • 7 1 7 33895.487 0.170 0.0000 8 1 8 7 0 7 38223.368 0.047 1.0000 8 0 8 7 1 7 30404.644 -0.040 0.0000 8 1 7 7 1 6 37369.099 0.024 0.0100 8 2 6 • 7 2 5 36993.607, 0.007 0.0100 9 1 8 9 O 9 22473.297 0.072 1.0000 9 0 9 • 8 1 8 35311.351 0.035 0.0001 10 3 7 - 10 2 8 40754.324 0.041 0.1000 10 0 1 0 • 9 1 9 40088.319 0.199 0.0000 10 2 8 • 10 1 9 22854.693 0.012 1.0000 10 1 9 - 9 2 8 28665.904 -0.023 0.1000 11 1 1 1 • 10 O 1 O 48439.057 -0.486 0.0000 11 1 1 0 - 10 2 9 34899.338 -0.082 0.1000 12 3 9 - 12 2 1 O 38120.798 -0.054 1.0000 12 1 1 2 - 11 O 1 1 52032.491 0.025 0.0000 12 0 1 2 - 11 1 1 1 49254.618 0.002 1.0000 12 2 1 1 - 11 2 1 O 53220.156 -0.094 0.0000 13 3 1 1 - 13 2 1 2 50195.851 0.057 1.0000 13 3 1 0 - 13 2 1 1 36839.012 -0.088 0.0000 13 0 1 3 - 12 1 1 2 53669.541 0.065 1.0000 13 1 1 2 - 13 O 1 3 38691.460 -0.128 0.1000 Microwave Spectrum of N-Chlorodifluoromethylenimine / 216 TABLE 6.3 - continued Transition Frequency Obs-Calc Weight 13 2 1 1 - 13 1 1 2 26400.138 0.026 1.0000 13 2 1 1 - 12 3 1 0 24682.904 0.010 0.1000 14 3 1 1 - 14 2 t 2 35718.300 -0.017 1.0000 14 1 1 3 - 13 2 1 2 53231.433 -0.094 0.1000 14 2 1 2 - 14 1 1 3 28612.738 -0.017 1.0000 14 2 1 2 - 13 3 1 1 31648.477 -0.011 0.1000 15 3 1 2 - 15 2 1 3 34862.596 0.130 0.0000 15 2 1 3 - 15 1 1 4 31372.363 -0.018 1.0000 15 2 1 3 - 14 3 1 2 38755.237, -0.449 0.0000 15 1 1 4 - 15 0 1 5 48070.442 0.017 1.0000 16 3 1 3 - 16 2 1 4 34367.037, -0.012 1.0000 16 2 1 4 - 16 1 1 5 34668.546 0.013 1.0000 16 1 1 5 - 16 0 1 6 52807.612 -0.150 0.0000 17 3 1 4 - 16 4 1 3 23695.250 0.031 0.0000 17 3 1 4 - 17 2 1 5 34314.413 -0.040 1.0000 17 2 1 5 - 16 3 1 4 53188.238 -0.031 1.0000 17 2 1 5 - 17 1 1 6 38465.531 -0.137 0.0000 18 3 1 5 - 17 4 1 4 30821.306 0.009 1.0000 18 3 1 5 - 18 2 1 6 34772.247 0.028 1.0000 19 3 1 6 - 18 4 1 5 38251.635 -0.037 0.0000 19 2 1 7 - 19 1 1 8 47301.586 0.560 0.0000 20 4 1 6 - 20 3 1 7 49341.578 0.010 1.0000 20 3 1 7 - 20 2 1 8 37415.402 -0.098 0.0000 Observed frequency minus the frequency calculated using the fitted spectroscopic constants. Transitions showing resolvable hyperfine structure by nitrogen. Microwave Spectrum of N-Chlorodifluoromethylenimine / 217 TABLE 6.4 Spectroscopic Constants of CF NCI CF 2N 3 5C1 CF 2N 3 7C1 Rotational Constants (MHz) A 0 11260.8730(48)a 11260.8818(88) B 0 2542.2000(12) 2470.9258(15) C 0 2072.4246(11) 2024.8091(16) Centrifugal Distortion Constants (kHz) Aj 0.3584(57) 0.3667(37) AT„ 3.939(30) 3.813(54) Av 8.05(12) 8.16(96) 5 j 0.0690(15) 0.0623(14) 5^ 2.546(83) 2.474(60) Chlorine and Nitrogen Nuclear Quadrupole Coupling Constants (MHz) Chlorine Nitrogen aa cc aa cc Xbb" X cc cc -70.33(41) -26.02(15) 48.17(85) 3.42(61) -2.822(86) -0.30(63) -54.73(67) -20.02(18) 37.37(56) 7.2(11.1) -2.67(43) b Numbers in parentheses are one standard deviation in units of the last significant figures. Not evaluated because X is indeterminate. Microwave Spectrum of N-Chlorodifluoromethylenimine / 218 TABLE 6.5 Principal Moments of Inertia and Inertial Defects (uA2) Of the Effective and Average Structures of CF2NC1 Parameter CF 2N CI 3 7 CF 2N CI Effective Structure I a L 44.879206(19) 198.79594(10) 243.85883(13) 44.879171(70) 204.53024(13) 249.59343(20) 0.18368(25) 0.18398(40) Average Structure I a L 44.9518984 198.987165 243.939110 44.9513035 204.724696 249.675675 A (calc) o 0.000046 0.183634 -0.000325 0.184305 Calculated using the rotational constants of Table 6.4 using the conversion factor 505379.045 uA 2 From the harmonic force field refinement. Microwave Spectrum of N-Chlorodifluoromethylenimine / 219 TABLE 6.6 Effective and Average Structures of CF^NCl Variation of Bond Angle, C = N —Cl,with Change in Bond Length, N-Cl Values of Structural Parameters Kept Fixed in all Refinements a r(C = N) 1.273A <N--C-F c 127.2° r(C-F ) rCC-F') 1.300A 1.300A <N-• C " F t 119.8° Effective ( ro } Average <r*> Bond Length from r(N-Cl) b (A) <C=N-C1 (°) , c s.d. <C=N-C1 (°) s.d. CCl 2NCl d 1.683 115.7±19.4 6.7 115.8±12.4 4.3 C1NC06 1.705 114.3±15.1 5.3 114.4 + 8.2 2.9 Cl N 3 f 1.745 111.9±7.2 2.6 112.0±0.4 0.14 1.788 109.5±3.1 1.2 109.6 + 8.1 3.1 b From reference (5) Kept fixed in the refinement ^ Standard Deviation of refinement (MHz) Reference (7) e £ Reference (9) Reference (11) Microwave Spectrum of N-Chlorodifluoromethylenimine / 220 TABLE 6.7 Internal Coordinates and Symmetry Coordinates Used in the Final Harmonic Force Field Refinement of CF-NC1 Internal Coordinates and Geometry A' block r, = r(C = N) = 1.273A :b r 2 = r(N-Cl) = 1.745A r 3 = r(C-F ) = 1.300A rfl = r(C-F) = 1.300A a,, = <(CNC1) = 112.0° 0, = <(NCFc) = 127.2° j32 = <(NCF) = 119.8° A" block 7 = CF 2 out-of-plane bend (oop) T = torsion angle Symmetry A' block Coordinates S, = Ar, 5 2 = Ar 2 5 3 = Ar 3 Sfl = Ar, 5 5 = Aa, 5 6 = A0, 5 7 = A/3 2 A" block S 8 = A 7 S 9 = A T Microwave Spectrum of N-Chlorodifluoromethylenimine / 221 TABLE 6.7 - continued c ° -1 B Matrix Elements of the Out-of-Plane Coordinates (A ) C N CI 5 8 2.0500 -0.7399 0.0000 5 9 -0.7289 1.6166 -0.9441 From reference (5) unless determined in this work. Determined in this work as an average structure. All values given are out-of-plane components, as all other components are zero. F F, c t -0.6832 -0.6269 0.6832 -0.6269 Microwave Spectrum of N-Chlorodifluoromethylenimine / 222 TABLE 6.8 Definition of Force Constants Used in Harmonic Force Field of CF2NC1 A' r(C = N) r(N-Cl) r(C-FJ r(C-F ) <(CNC1) <(NCFc) <(NCF ) r(C = N) f,, f 1 2 ft 3 f, a f 1 s fi 6 fi 7 r(N-Cl) f 2 2 f 2 3 f 2 4 f 2 5 f 2 6 f 2 7 r(C-F c) f 3 3 f3« f 3 5 f 3 6 f 3 7 r(C-F t) f 4 4 f 4 5 f 4 6 f 4 7 <(CNC1) f 5 5 f 5 6 f 5 7 <(NCFc) f 6 6 f 6 7 <(NCFt) f 7 7 A" CF^ oop tors CF 2 oop f 8 f 8 9 tors f 3 9 Microwave Spectrum of N-Chlorodifluoromethylenimine / 223 TABLE 6.9 Harmonic Force Field a of CF2NC1 Parameter Value Parameter Value Species A' f i i f l 2 f l 3 f l 4 f l 5 f l 6 f l 7 2^ 2 f 2 3 f2 4 f 2 5 f 2 6 f 2 7 f 3 3 8.69(36) 0.0 0.0 0.0 0.0 0.367C 0.367C 4.21(33) 0.0 0.0 1.22(15) 0.0 0.0 7.53C r3 4 f 3 5 f 3 6 hi f4 4 fa 5 f 4 6 f4 7 f 5 5 f 5 6 f 5 7 f 6 6 f 6 7 f 7 7 0.773 0.0 -0.01C -0.765C 7.49C 0.0 -0.765C -0.01C 1.441(37) 0.377(42) 0.0 2.560(100) 1.374c 2.513(60) Species A" l8 8 la 9 0.551(23) 0.007C lg g 0.207(66) Units are mdyn/A for stretching constants, mdyn A/radz for bending constants, and mdyn/rad for stretch-bend interactions Numbers in parentheses are one standard deviation in units of the last significant figures. Force constants without numbers in parentheses were kept constrained in the refinement. Values transferred from harmonic force field of CF QNF (5). Microwave Spectrum of N-Chlorodifluoromethylenimine / 224 TABLE 6.10 Observed and Calculated Wavenumbers and Centrifugal Distortion Constants of CF NCI CF 2N 3 5C1 CF N 3 7C1 obsa calc^ obs-calc obsS calc'3 obs-calc Wavenumbers (cm ^) 1728.0 1732.0 -4.0 - 1731.9 v2 1322.0 1359.0 -37.0 - 1359.0 "3 981.0 977.5 3.5 - 976.3 "4 771.0 769.7 1.2 - 767.0 V5 598.0 594.2 3.8 - 594.0 Vs 465.0 467.5 -2.5 - 463.1 v7 228.0 230.5 -2.5 - 228.4 658.0 658.0 0.0 - 658.0 v9 234.0 234.0 0.0 — 233.2 Centrifugal Distortion Constants (kHz) A J 0.358 0.376 -0.017 0.367 0.360 0.007 A J K 3.939 3.952 0.013 3.813 3.820 0.007 A K 8.05 8.094 0.044 8.16 8.242 -0.082 6 J 0.069 0.067 0.002 0.062 0.063 -0.001 5 K 2.546 2.545 -0.001 2.474 2.457 -0.017 a Observed wavenumbers are from reference (3). Observed distortion constants are from this work. Calculated values were obtained from the harmonic force field given in Table 6.9. Microwave Spectrum of N-Chlorodifluoromethylenimine / 225 TABLE 6.11 Ground State Average Rotational Constants of CF NCI (MHz) CF 2N 3 5C1 CF N 3 7C1 A 11242.6630 11242.8118 z B 2539.7570 2468.5788 z C 2071.7426 2024.1421 Microwave Spectrum of N-Chlorodifluoromethylenimine / 226 TABLE 6.12 Nuclear Quadrupole Coupling Constants of Chlorine in its Principal Axis System (MHz) (For axis system chosen see discussion, section 6.6) Parameter Value X 111.72 zz X 63.54 xx X 48.18 yy d 29.08° za Microwave Spectrum of N-Chlorodifluoromethylenimine / 227 TABLE 6.13 Observed and Calculated Nuclear Quadrupole Coupling Constants of 1 4 N (MHz) in CF2NC1 (using Townes Dailey Theory and Three Different Methods of Calculating the Orbital Populations) Parameter Experimental Calculated Ab Initio sp 2 hybrid orbitals xx yy zz 3.42 -0.30 -3.12 1.082 1.330£ 1.519 a a 4.66 -1.39 -3.27 2.08 3.32 -5.40 0.856 1.260 1.385 1.082 1.000 1.582 Calculated using sp2 hybrid orbital wavefunctions and experimentally determined quadrupole coupling constants, as described in the text. Microwave Spectrum of N-Chlorodifluoromethylenimine / 228 TABLE 6.14 Observed and Calculated Nuclear Quadrupole Coupling Constants of 3 5 CI (MHz) in CF NCI (Using Gaussian 70, STO-3G in the principal inertial axis system) Parameter Experimental Calculated -70.33 22.15 48.17 -61.44 15.37 46.06 Microwave Spectrum of N-Chlorodifluoromethylenimine / 229 Figure 6.1. Portion of the Microwave Spectrum of CF2NC1 Showing a-type R branch J = 7<-6 transitions. Microwave Spectrum of N-Chlorodifluoromethylenimine / 230 Figure 6.2. Ground State Average Structure of CF2NC1, in its Principal Inertial Axis System with r(N-Cl)= 1.745A. Microwave Spectrum of N-Chlorodifluoromethylenimine / 231 covalent bonding ionic bonding TI back bonding Figure 6.3. Three Different Structures Contributing to the Overall Bonding in the N-Cl Bond of CF2NC1. BIBLIOGRAPHY 1. D.E. Young, L.R. Anderson, and W.B. Fox, J Chem Soc, Chem Comm, 395 (1970) 2. R.P. Hirschmann, H.L. Simon, and D.E. Young, Spectrochimica Acta, 27A, 421-424 (1970) 3. B.A. O'Brien, J.S. Thrasher, C.W. Bauknight Jr., M.L. Robin, and D.D. DesMarteau, J Amer Chem Soc, 106, 4266-4267 (1984) 4. D. Christen, J Mol Struct, 79, 221-226 (1982) 5. D. Christen, H. Oberhammer, R.M. Hammaker, S.C. Chang and D.D. DesMarteau, J Amer Chem Soc, 104, 6186-6190 (1982) 6. J.M. Burke, and R.W. Mitchell, Spectrochimica Acta, 28A, 1649-1654 (1972) 7. D. Christen and K. Kalcher, J Mol Struct, 97, 143-146 (1983) 8. E. Nachbaur and A. Popitsch, J Mol Spectrosc, 102, 174-183 (1983) 9. W.H. Hocking, M.L. Williams, and M.C.L. Gerry, J Mol Spectrosc, 58, 250-260 (1975) 10. W.H. Hocking and M.C.L. Gerry, J Mol Spectrosc, 42, 547-566 (1972) 11. R.L. Cook and M.C.L. Gerry, J Chem Phys, 53, 2525-2528 (1970) 12. C.H. Townes and B.P. Dailey, J Chem Phys, 17, 782-796 (1949); C.H. Townes and B.P. Dailey, J Chem Phys, 20, 35-40 (1952); C.H. Townes and B.P. Dailey, J Chem Phys, 23, 118-123 (1955). 13. M.C.L. Gerry, W. Lewis-Bevan, and N.P.C. Westwood, J Chem Phys, 79, 4655-4663 (1983) 14. R. Bersohn, J Chem Phys, 22, 2078-2083 (1954) 15. J.H. Goldstein, J Chem Phys, 24, 106-109 (1956) 16. W. Gordy and R.L. Cook, Microwave Molecular Spectra, in Technique of Organic Chemistry, Ed. A. Weissberger, Vol. IX, Part II, Interscience Publishers, New York, 1970, Chapter 14, page 583 17. Gordy and Cook, op_. cit, pages 601-602, and-607. 18. L. Pauling, The Chemical Bond, Cornell University Press, Ithaca, New York, 1960. 232 7. THE INFRARED SPECTRUM OF AMINOBORANE ANALYSIS OF THE ROTATIONAL STRUCTURE IN THE 8g BAND As a small piece of work in an extensive study being done at the University of British Columbia (UBC), of the infrared spectrum of aminoborane, NHgBHg, the 8*, band at 1223 cm"1 was analyzed. To date theoretical studies (1-6) done on this molecule far outnumber the spectroscopic studies. Its interest as a subject of theoretical and spectroscopic attention lies in its B —N bond, and the fact that it is one of the simplest species containing one. Because of the donor-acceptor type of bonding present it should be very polar. Questions of how polar, what model should be used to describe both its a and TT character, how planar is it, etc., have been addressed. Some of this interest grows from the B = N bond being isoelectronic with the C = C bond, which makes NH BH an inorganic analogue of ethylene. Z Z Experimental observation has been limited because of the difficulty involved in synthesizing it. At room temperature it is a very unstable gas which readily polymerizes. Nonetheless some successful syntheses and spectroscopic work have been done of it. The possibility of its existence was first suggested in 1948 by Wiberg (7). He proposed that it was an intermediate in the formation of borazine (HNBH)^, which is made from diborane and ammonia. Since then it has been detected by mass spectrometry and thermogravimetric methods to be present in the vapour over ammonia borane (NH BH ) (8,9). It has been made from the pyrolysis of (HgNBHg^ (10) a n d from the rf discharge of borazine (11). It was from this later experiment that the only experimental vibrational wavenumbers, previous to 233 The Infrared Spectrum of Aminoborane / 234 the work done at UBC, have been reported. Kwon and McGee trapped out the NH BH in its solid phase, in which state they measured its infrared spectrum, z z at low resolution. MNDO calculations by Dewar and McKee (12) also produced a set of vibrational wavenumbers. Gas phase spectroscopy was first done by Sugie et al when they measured its microwave spectrum (13,14). They prepared it in a flow system where at 500°C they pyrolysed a mixture of ammonia and diborane. The preparative method in this work was similar, but involved the controlled thermolysis of ammonia borane (NHgBHg) instead, as described in Chapter 3 and reference (15). Using this same preparative technique Westwood and Werstiuk (16) have recently measured its Hel photoelectron spectrum. At UBC, each active band of its infrared spectrum is being systematically recorded and analyzed at high resolution (0.004 — 0.008 cm 1 in the range 450 — 3500 cm ^). Many of the fundamental bands exhibit strong perturbations in their rotational structure. Those at lower wavenumbers show perturbations caused by Coriolis interactions while those at higher wavenumbers are also involved in Fermi resonance type perturbations. In some instances lines from infrared inactive bands have been observed because of intensity borrowing caused by the perturbations (17). Similarly bands predicted to be infrared active are missing. The band studied in this work was initially thought to be the v 5 BHg symmetric bend (15). Upon assigning the vB NH^ wag at 612 cm 1 the band was reassigned to be the overtone of v 8. The work done here confirms this assignment. Subsequent work has confirmed the assignment of v n at The Infrared Spectrum of Aminoborane / 235 1122.2 cm \ but no direct evidence for i>5, predicted to be at 1145 cm \ has yet been found. The work described here is the analysis of the rotational structure of the overtone of u 8. The band was sufficiently strong to assign lines up to J = 25 and K = 10, plus obtain good values of the rotational constants and quartic a centrifugal distortion constants for the upper state. Unfortunately the intensity ran out when things were possibly getting interesting ... The Infrared Spectrum of Aminoborane / 236 7.1. ASSIGNMENT OF THE SPECTRUM Aminoborane is a planar, asymmetric prolate rotor with Cg^ . symmetry. Its normal modes transform as 5A, + A 2 + 2B, + 4A 2, where all but the torsion of A 2 symmetry are predicted to be infrared active. The band assignments of the fundamentals, to date, are given in Table 7.1. In the inertial axis system, v 8 transforms as B, symmetry and gives rise to c-type transitions. However all overtones, by the direct product rule, are totally symmetric, which in the case of NHgBHg are a-type bands. The characteristic feature of an a-type band, of a prolate nearly symmetric rotor, is a sharp spike at the band centre caused by coincident Q branch transitions, with coincident R and P branch lines for each K to either side. This occurs a because the rotational constants in the ground state are often very similar to those in the excited state. An initial quick inspection of the 8§ band of NHgBHg revealed no sharp spike in the centre. Instead there were easily identified Q branch lines moving to lower frequency (Figure 7.1), with no absorption at all at the band centre. This indicated that the rotational constants of the upper state, especially A since it governs how quickly the Q branch transitions move away from the band centre, were significantly different from those of the ground state. They allowed for the initial assignments of the spectrum, once the K associated with each a cluster was properly identified. This was done using information provided by nuclear spin statistics and predictions using combination differences. • Intensities of lines are affected by nuclear spin statistics when there is at least one pair of identical particles. When these two identical particles are The Infrared Spectrum of Aminoborane / 237 protons, which have a nuclear spin of i the total molecular wavefunction, \p, must be antisymmetric to exchange of these two identical nuclei. NH BH has two pairs of identical protons which means 1// must be symmetric to their exchange. In NHgB^ this exchange is achieved with a rotation of T T about the symmetry axis which is also the principal a-inertial axis. The wavefunction \|/ is often represented by: = $ (7.1) r r e v r r r n s where i// , \b , \p and \b are' the electronic, vibrational, rotational and nuclear e v r ns -spin wavefunctions respectively. For the 8Q band of N^BHg both and xj/^ are symmetric because it is in its ground electronic state, and both the ground and upper state of the 8Q vibration are totally symmetric. The variations in intensity seen in the spectrum are caused by the symmetries of even and odd Ka's in the rotational wavefunction and the symmetries of the nuclear spin wavefunctions. From group theory \p with even values of K are symmetric to r a a TT rotation about the a-symmetry axis while odd values are antisymmetric. Coupling of the four protons produce ten symmetric nuclear spin wavefunctions, ^ > and six antisymmetric. Because the total molecular wavefunction must be symmetric there are ten nuclear spin wavefunctions associated with an even K a while there are only six associated with an odd one. Therefore the ratio of even K 's to odd K 's is 10:6. a a Figure 7.1 shows three clusters of Q branch lines, each having different overall intensities, which could be labelled as medium, weak and strong. For the The Infrared Spectrum of Aminoborane / 238 reasons explained above even K & values were associated with the medium and strong clusters. The exact assignment was determined using combination differences of the ground state levels. Because most upper state levels of a transition (unless at the low end of a series) are associated with three ground state levels to produce P, Q and R branch transitions, the energy difference between the ground state levels can be calculated and used to predict, the differences in frequency of P, Q and R branch transitions which all have the same upper state. Both A,F and A2F combination differences were used to assign new transitions. A, means there is a change in | J | = 1 between the two ground state rotational levels and A 2 means there is a change of | J| =2; F represents the term value, in this case (J,K). Figure 7.2 explains this concept diagramatically. Accurate predictions of the energies of the ground state levels could be made because the analysis of the v 8 band had produced an excellent set of ground state rotational and centrifugal distortion constants from ground state combination differences, in that band (17). They are sufficiently accurate that if a correct assignment had been made the combination difference method predicted the frequency of another line with the same upper state level to within + 0.003 cm \ If the difference was greater than this, then the orginal line was misassigned. This method showed that the initial assignment of K =2 to the a cluster at 1219 cm 1 was wrong, but that rather these were K =4 Q branch a transitions. This assignment was confirmed by using combination differences to verify that the cluster at 1217 cm 1 was from ^ = 5 transitions and the one at 1214 cm 1 from K =6 transitions. Assignment of each K series out to higher The Infrared Spectrum of Aminoborane / 239 J was made by knowing that the change in spacing from one J to the next was similar. The assignments of most series were extended in this way and were checked using combination differences. The lines from the K = 4, 5 and 6 transitions were put into a least a squares refinement program to produce an initial set of rotational constants for the upper state. The least squares refinement was made to Watson's A reduction Hamiltonian, in its I representation, given in Table 2.1. Each transition was given a weight which was proportional to its (uncertainty) and indicated how accurately it could be measured. To start the refinement the rotational and centrifugal distortion constants of the ground state were used as preliminary upper state values. The refined set of upper state constants were then used in a predictor program to predict the frequencies of other unassigned transitions. Although the predictions were only accurate to +0.01 cm 1 this was accurate enough to suggest the correct frequency for a transition. These tentative assignments were then confirmed and checked using ground state combination differences. This method was most useful for the lower K = 0, 1, a 2 and 3 lines which either had no Q branch transitions or for which the cluster was so weak it was not readily identifiable. A later prediction of the spectrum using a more accurate set of excited state rotational and centrifugal distortion constants was accurate to +0.003 cm 1 up to J=20, and so was used to make the last assignments of a few of the K series. The Infrared Spectrum of Aminoborane / 240 7.2. ANALYSIS OF THE SPECTRUM It was noticed during the course of the analysis that although combination differences confirmed the line assignments the residuals on the higher K lines of a 7, 8 and 9 were generally quite large. The residuals on the K = 7 lines were a ==+0.002 cm"1, on the K =8 lines =-0.003 cm"1, and =-0.02 cm"1 on the ' a K a=9 lines. Unfortunately these residuals did not always show consistent trends around the values listed above. For example, the residuals on the K & = 8 lines switched from being negative to positive. Despite this occasional lack of consistency it was felt that perhaps the poorness of the fits of the higher K a transitions was caused by a weak perturbation. This was postulated as a reason because it was known that perturbations of some of the lines had been seen in the 8<J band, although to which K lines was not known. It was also known that most of the bands were affected by perturbations to some degree because there were so many fundamental vibrations near each other in frequency (energy). A plot of log Ap(the residual) versus log [J'(J'+1) — K'(K'— 1)] was made for K =8 and 9 to see if a straight line having a slope equal to the a. order (first, second, third) of a Coriolis type perturbation resulted. The results were meaningless as neither plot was a sloping straight line. The conclusion was that if there is a perturbation it is very small. Unfortunately intensity of the lines ran out at K =9 for the P and R branch transitions and K =10 for a a the Q branch. Assignment of higher K lines would have helped confirm and a. check this possibility of a perturbation. Figure 7.3 shows why it is reasonable that the 2v 8 band could be involved in a Coriolis type perturbation. The combination band of (vB + v ^ 2) which would occur at 1354 cm 1 is of symmetry A 2 (B 1xB 2). For Coriolis The Infrared Spectrum of Aminoborane / 241 coupling to occur between the two vibrational levels the symmetry of the coupled levels must be the same as the symmetry of a rotation. The symmetry of 2v 8 coupled with (i> 8 + v, 2) is A 2 and this is the same as the symmetry of a rotation about the z axis, or a-inertial axis. Since 1354 cm 1 is 131 cm 1 above the band centre of 2v 8 the perturbation could be expected to be quite small. However the important criteria on the size of a perturbation would be how different the A rotational constant is between the two coupling vibrational levels, as this constant governs how rapidly the rotational levels move away from the band centre. Similarly, the combination band (v6+vs) at 1442 cm ^ could perturb 2v B . The final set of rotational and centrifugal distortion constants was obtained by removing all the K = 7, 8, 9 and 10 transitions from the fit. All blended, a _2 broad or weak lines were weighted according to their (uncertainty) . The constants of the ground state were fixed at the most recent and accurate values available, (from the analysis of the uB band (17)). The values determined for the constants of the upper state - 8Q , are given in Table 7.2. For comparison purposes those of level one, 80, and the most accurate ground state constants, to date, are also included in the table. The complete list of assigned transitions is given in Table 7.3. 7.3. DISCUSSION One of the most important results of this work has been to confirm the assignment of this band as being the overtone of the v8 vibration. The confirmation has been made in a number of ways. The Infrared Spectrum of Aminoborane / 242 One has been to observe the trend in the rotational constants from the ground state to the second vibrational level. The difference in the A rotational constant from the ground state to the first vibrational level is 0.154 cm \ and from the first vibrational level to the second is 0.111 cm 1. A similar decreasing trend is seen in the B rotational constant while the C rotational constant increases. Because the refined values of the constants compare so well with those of the 8 0 band and ground state, this, in essence, confirms the assignment and confirms the band as a vibration of NHgBHg. A second indication that this is the 8Q band was that the goodness of the fit started to deteriorate at the same K value (=7) for both bands (8<J a. and 8Q ). This meant that for both bands the accurate upper state rotational and centrifugal distortion constants were obtained by using transitions with K &<6. For the analysis of this band the intensity ran out before an unambiguous observation of a perturbation could be made. However for the 8 0 band, being a very strong band, it was possible to assign lines up to K =16 a and observe many examples of perturbed rotational levels (17). The observation of the 8Q band at all can be argued as feasible because the fundamental is so strong, one of the strongest in the entire spectrum. In general the 8Q band was quite sparse. This can be noted by the fact that only 585 transitions were assigned, yet nearly all the strong lines were accounted for. A more usual number, for a fundamental, is 1000—1500. To lower frequency there was evidence of interference from the b-type v, ( band at 1122.2 cm \ Interference from lines of ammonia was also a minor problem at lower frequencies. An interesting observation was that despite the sparseness of the spectrum many (=50) of the transitions of this band (8Q) overlapped. In The Infrared Spectrum of Aminoborane / 243 all cases of interference the transitions were either given a low weight or weighted out of the fit entirely, depending on how the interference affected the resolution of the line. Despite the fact that there were lines of ammonia present in the scan, they could not be used to calibrate the spectrum because all well measured, absolute frequencies reported in the literature for ammonia were saturated on the scan. Therefore an estimate of the absolute uncertainty of the frequency measurement was made by comparing the difference in the band centre frequency determined in this analysis for the 8§ band [1223.57677(32) cm"1] with the addition of the centre frequencies determined for the 80 and 8 2 bands [612.19866(21) + 611.38053(22) = 1223.57919(86) cm"1]. All frequencies used in the analysis of these latter two bands were calibrated. The difference is 0.0024 cm 1, which compares well with previously made calibrations. The relative uncertainty is estimated to be 0.0005 cm 1 which is confirmed by the standard deviation of the fit being 0.00054 cm 1. The Infrared Spectrum of Aminoborane / 244 TABLE 7.1 Vibrational Fundamentals of N H „ 1 1 B H 9 (cm"1) - August 1986 Gas Phasea Solid MNDOC Type of Motion A, V 1 3451 3333 3416 NH symm. str. v2 2495 2445 2530 BH symm. str. v3 16171 1613 1663 NH 2 symm. bend v* 1337.4742 1342 1345 BN stretch 1145 1130 1192 BH 2 symm. bend A 2 v6 830 - 789 Torsion B-, 10053 962 936 BH 2 wag 612.1987" - 621 NH 2 wag B 2 v9 3533.85 3460 3399 NH anti. str. V 1 0 2564s 2525 2583 BH anti. str. " 1 1 1122.27 1105 1061 NH 2 rock Vy 2 742 738 704 BH 2 rock k Work being done at the University of British Columbia, Vancouver. Reference (11). 0 Reference (12). 1 Analysis in progress 2 Reference (15) 3 Analysis in progress u Reference (17) 5 Analysis on hold 6 Reference (18) 7 Analysis in progress - Michael Lyne - Judith Barry - Dinie Steunenberg The Infrared Spectrum of Aminoborane / 245 TABLE 7.2 Spectroscopic Constants of NH 2 BH 2 of the 8Q , 8 0 and Ground State Vibrational Levels 8*, Band 8 0 Band' Ground State Rotational Constants (cm A 4.345235(28)b 4.456312(56) 4.6105692(82) B 0.9094725(18) 0.9127845(20) 0.9168971(20) C 0.76474868(95) 0.7640361(16) 0.7631374(22) ifugal 5 Distortion Constants (10 cm ) A J 0.15515(23) 0.15372(16) 0.15420(20) A J K 1.6613(85) 1.2836(88) 0.9872(30) A K -11.70(20) -6.75(37) 8.6920(84) 5 J 0.02812(11) 0.027779(86) 0.028560(29) 5 K -0.0464(89) 0.1203(68) 1.0164(19) H J K 0.000082(18) -0.0000177(94) 0.0000070(32) H K -0.0181(36) -0.0091(66) 0.000594(30) Band Centre 1223.57677(11) 612.19866(21) From reference (17). Numbers in parentheses are one standard deviation in units of the last significant figures. The Infrared Spectrum of Aminoborane / 246 TABLE 7.3 Assigned Transition Frequencies (in cm"1) of the 81 Band at 1223.6 cm"1 of the Infrared Spectrum of N H „ B H 0 Transition Frequency Obs-Calca Weight 2 2 1 - 2 2 0 1222 .50812 0 . 0 0 0 1 0 0 .09766 2 2 0 - 2 2 1 1222 .51763 0 .0004 4 0 .01000 3 2 2 - 3 2 1 1222 .47162 - 0 . 0 0 0 0 4 1 .ooooo 3 2 1 - 3 2 2 1222 .51763 0 .00017 0. .01000 4 2 3 - 4 2 2 1222 .40080 - 0 . 0 0 0 8 6 0 .00010 4 2 2 - 4 2 3 1222 .53865 0 .00001 1 .ooooo 5 2 4 - 5 2 3 . 1222 .27976 - 0 . 0 0 0 4 3 0 .01000 5 2 3 - 5 2 4 ' 1222 .59840 0 .00044 0 .00010 3 3 1 - 3 3 0 1221 .19551 0.O0OO3 1 .ooooo 4 3 1 - 4 3 2 1221 .17159 - 0 . 0 0 0 4 2 1 .ooooo 5 3 3 - 5 3 2 = 1221 .13927 0 .00077 0 .09766 4 4 1 - 4 4 0 1219 .36927 0 .00035 1 .ooooo 5 4 1 - 5 4 2 1219 .33840 0 .00006 1 .ooooo 6 4 3 - 6 4 2 1219 .30147 0 .00011 1 .ooooo 7 4 3 - 7 4 4 1219 .25820 - 0 . 0 0 0 1 5 1 .ooooo 8 4 5 - 8 4 4 1219 .20809 0 .00049 1 .ooooo 9 4 6 - 9 4 5 1219 . 15 129 0 .00128 o .09766 5 5 1 - 5 5 0 1217 .04813 - 0 . 0 0 0 0 5 1 .ooooo 6 5 1 - 6 5 2 1217 .01101 0 .00020 1 .ooooo 7 5 3 - 7 5 2 12 1G .96690 - 0 . 0 0 0 1 5 1 .ooooo 8 5 3 - 8 5 4 1216 .91573 - 0 . 0 0 1 0 9 1 .ooooo 9 5 5 - 9 5 4 1216 .85985 - 0 . 0 0 0 1 4 0 .09766 10 5 5 - 10 5 6 1216 .79635 - 0 . 0 0 0 2 6 0 .09766 6 6 1 - 6 e 0 12 14 . 25279 0 . 0 0 0 3 0 1 .00000 7 6 1 - 7 6 2 1214 .20771 - 0 . 0 0 0 2 3 1 .ooooo 8 6 3 - 8 6 2 1214 . 15724 0 .00036 1 .ooooo 9 6 3 - 9 6 4 1214 .09940 0 .00017 1 .ooooo 10 6 5 - 10 6 4 1214 .03485 - 0 . 0 0 0 0 6 1 .ooooo 1 1 6 5 - 1 1 6 6 1213 .96415 0 .00029 1 .ooooo 12 6 7 - 12 6 6 1213 .88650 0 .00052 0 .09766 13 6 7 - 13 6 8 1213 .80172 0 .00052 0 .09766 7 7 1 - 7 7 0 1211. .00361 -0 .00041 0 .0 8 7 1 - 8 7 2 1210. .95185 0 .00002 0 .0 9 7 3 - 9 7 2 1210. 89339 0 .00043 0 .0 10 7 3 -• 10 7 4 1210. .82830 0 .00094 0 .0 1 1 7 5 - 1 1 7 4 1210, .75561 0 .00065 0 .0 12 7 5 -• 12 7 e 1210. .67585 0 .00015 0 .O 13 7 7 -• 13 7 e 12 10. .59094 0 .00143 0 .0 14 7 7 -• 14 7 8 12 10. .49750 0 .00119 0 .0 15 7 9 -• 15 7 8 1210. .39698 0 .00096 0 .0 8 8 1 -• 8 8 0 1207 . . 32686 -O.00O4O 0 .0 9 8 2 -• 9 8 1 1207 . 26664 - 0 . 0 0 0 2 4 0 .0 10 8 2 -• 10 8 3 1207 . 20048 0 .00084 0 .0 1 1 8 4 -• 1 1 8 3 1207 . 12765 0 .00215 0 .0 12 8 4 -• 12 8 5 1207 . 04730 0 . 0 0 2 9 0 o. .0 9 9 1 -• 9 9 0 1203 . 24627 - 0 . 0 0 1 8 3 0 .0 10 9 1 -- 10 9 2 1203 . 17694 - 0 . 0 0 1 9 9 0 .o 1 1 9 3 -- 1 1 9 2 1203 . 10060 - 0 . 0 0 2 1 0 0 .0 12 9 3 -• 12 9 4 1203 . 01786 -0 .00151 0 .0 13 9 5 -- 13 9 4 1202 . 92595 - 0 . 0 0 2 9 5 0. .0 14 9 5 -- 14 9 6 1202 . 82795 - 0 . 0 0 3 2 8 0 .0 10 10 1 -- 10 10 O 1 198 . 86332 0 .07044 o .0 1 1 10 2 -- 1 1 10 1 1 198. 79200 0 .07775 0 .0 12 10 2 • - 12 10 3 1 198 . 70753 0 .07918 0 .0 13 10 4 • - 13 10 3 1 198. 62432 0 . 0 8 9 1 9 0 .0 14 10 4 • - 14 10 5 1 198 . 52053 0 .08597 0, .0 The Infrared Spectrum of Aminoborane / 247 TABLE 7.3 - continued Transition Frequency Obs-Calc Weight 15 10 6 - 15 10 5 1 198 . 41171 0 .08511 0 . 0 16 10 6 - 16 10 7 1 198 . 28963 0 .07842 0 . 0 1 0 1 - 2 0 2 1220. 21599 0 .00035 0 . 01000 2 0 2 - 3 0 3 1218 . 53874 0 .00037 1. 00000 3 0 3 - 4 0 4 1216. 87035 0 .00041 0 . 01000 4 0 4 - 5 O 5 1215 . 21579 0 .00067 1. 00000 5 0 5 - 6 0 6 1213 . 57832 0 .00032 1. 00000 6 0 6 - 7 0 7 1211. 96122 - 0 . 0 0 0 1 0 1. 00000 7 0 7 - 8 0 8 1210. 36627 0 .00028 1. 00000 8 O 8 - 9 0 9 1208 . 79068 - 0 . 0 0 0 1 4 1. 00000 9 O 9 - 10 0 10 1207 . 23301 0 .00008 1. ooooo 10 0 10 - 1 1 0 1 1 1205. 68847 - 0 . 0 0 0 0 4 1. 00000 1 1 0 1 1 - 12 0 12 1204 . 15377 0 .00002 1. ooooo 12 0 12 - 13 0 13 ^ 1202. 62550 0 .00001 1. ooooo 13 0 13 - 14 0 14 1201 . 10156 0 .00004 1. ooooo 14 0 14 - 15 0 15 1 199 . 58047 - 0 . 0 0 0 0 3 1. ooooo 15 O 15 - 16 0 16 1 198 . 06157 - 0 . 0 0 0 1 9 1. ooooo 16 0 16 - 17 0 17 1 196 . 545 18 0 .00012 1. ooooo 17 0 17 - 18 0 18 1 195 . 03047 0 .00003 1. ooooo 18 0 18 - 19 o 19 1 193 . 51814 0 . 0 0 0 1 0 1. ooooo 19 0 19 - 20 0 20 1 192 . .00872 0 . 0 0 0 7 0 o . 01000 20 0 20 - 21 0 21 1 190. 5009 1 0 .00032 0 . 09766 21 0 21 - 22 0 22 1 188 . 99575 - 0 . 0 0 0 1 5 0 . 01000 22 0 22 - 23 0 23 1 187 . .49459 0 .00051 0 . 01000 23 0 23 - 24 o 24 1 185 .  99648 0 .00124 0 . 01000 24 0 24 - 25 0 25 1 184 . .50098 0 .00152 0 . 01000 25 o 25 - 26 0 26 1 183 . 00745 0 .00063 o . 01000 26 0 26 -• 27 0 27 1181. .51849 0 .001 15 1. ooooo 27 0 27 -• 28 0 28 1 180, 03196 0 .00088 1. ooooo 28 0 28 -• 29 0 29 1 178. .54984 0 .00178 0. .01000 2 1 1 -• 3 1 2 1218 .01584 - 0 . 0 0 0 2 9 0. .00010 2 1 2 - 3 1 3 1218 .50482 0 . 0 0 0 7 0 0. .01000 3 1 2 -• 4 1 3 1216 .23530 - 0 . 0 0 0 0 7 1. .ooooo 3 1 3 -• 4 1 4 1216 .90342 - 0 . 0 0 0 0 9 1. .ooooo 4 1 3 -- 5 1 4 1214 .45022 0 .00032 1 .ooooo 4 1 4 : • 5 1 5 1215 .30645 0 .00021 1 .ooooo 5 1 4 -- 6 1 5 1212 .66205 0 .00043 1 .ooooo 5 1 5 -- 6 1 6 1213 .71 137 - 0 . 0 0 1 8 8 1 .ooooo 6 1 5 - 7 1 6 1210 .87289 0.OOO16 0 .09766 6 1 6 -- 7 1 7 1212 .12608 0 .00071 1 .ooooo 7 1 6 • - 8 1 7 1209 .08549 - 0 . 0 0 0 2 8 1 .ooooo 7 1 7 -- 8 1 8 1210 .54239 - 0 . 0 0 0 8 4 1 .ooooo 8 1 7 -- 9 1 8 1207 .30389 0 .00028 1 .ooooo 8 1 8 • - 9 1 9 1208 .96725 - 0 . 0 0 0 0 2 1 .ooooo 9 1 8 • - 10 1 9 1205 .52960 0 . 0 0 0 1 0 1 .ooooo 9 1 9 • - 10 1 10 1207 .39779 0 .00006 1 .ooooo 10 1 9 • - 1 1 1 10 1203 .767 14 0 .00025 1 .ooooo 10 1 10 • - 1 1 1 1 1 1205 .83503 0 .00034 0 .01000 1 1 1 10 • - 12 1 1 1 1202 .01901 -0 .00031 1 .ooooo 1 1 1 1 1 • - 12 1 12 1204 .27813 0 .00007 1 .ooooo 12 1 1 1 - 13 1 12 1200 .29036 0 .00031 1 .ooooo 12 1 12 • - 13 1 13 1202 . 72662 - 0 . 0 0 1 0 3 0 .09766 13 1 12 - 14 1 13 1 198 .58241 0 .00079 1 .ooooo 13 1 13 - 14 1 14 1201 .18314 - 0 . 0 0 0 0 4 1 .ooooo 14 1 13 - 15 1 14 1 196 .89544 0 . 0 0 0 0 0 1 .ooooo 14 1 14 - 15 1 15 1 199 .64429 - 0 . 0 0 0 0 3 1 .ooooo 15 1 14 - 16 1 15 1 195 . 23217 0 .00082 1 .ooooo 15 1 15 - 16 1 16 1 198 .11060 - 0 . 0 0 0 1 3 1 .ooooo 16 1 15 - 17 1 16 1 193 .58792 0 .0003 1 1 .ooooo 16 1 16 - 17 1 17 1 196 .58171 - 0 . 0 0 0 3 9 1 .ooooo The Infrared Spectrum of Aminoborane / 248 TABLE 7.3 - continued Transition Frequency Obs-Calc Weight 17 1 16 - 18 1 17 1191 .96146 0.OO031 1 . ooooo 17 1 17 - 18 1 18 1 195 .05789 - 0 . 0 0 0 2 1 1 . ooooo 18 1 17 - 19 1 18 1 190 .34884 0 . 0 0 0 7 0 1 . ooooo 18 1 18 - 19 1 19 1 193 .53816 - 0 . 0 0 0 3 2 0 . 09766 19 1 18 - 20 1 19 1 188 .74553 0 .00076 1 . OOOOO 19 1 19 - 20 1 20 1 192 .02077 -O .00224 0 . 09766 20 1 19 - 21 1 20 1 187 .14802 0 . 0 0 0 3 0 0 . 01000 20 1 20 - 21 1 21 1 190 .51209 0 . 0 0 0 6 0 1 . ooooo 21 1 20 - 22 1 21 1 185 .55503 0 .00052 0. OO010 21 1 21 - 22 1 22 1 189 .00470 0 .00093 0. .09766 22 1 21 - 23 1 22 1 183 .96385 0.O0032 0. 01000 22 1 22 - 23 1 23 1 187 .49459 - 0 . 0 0 5 1 4 0. .01000 23 1 22 - 24 1 23 1 182 .374 14 0 .00026 0. .00010 23 1 23 - 24 1 24 1 185 .99648 - 0 . 0 0 2 8 0 0. 01000 24 1 23 - 25 1 24 1 180 .78447 - 0 . 0 0 0 6 9 0. 01000 24 1 24 - 25 1 25 1 184 .50098 - 0 . 0 0 1 3 6 0 , .01000 25 1 24 - 26 1 25 1 179 .19554 - 0 . 0 0 1 7 8 0. .00010 25 1 25 - 26 1 26 1 183 .00745 -0 .00141 0. .01000 2 2 0 - 3 2 1 1217 .452 14 - 0 . 0 0 1 9 0 0. 01000 2 2 1 - 3 2 2 1217 .46614 - 0 . 0 0 6 8 7 0. .00010 3 2 1 - 4 2 2 1215 .73152 -0 .00001 1.  ooooo 3 2 2 - 4 2 3 1215 .77968 0 .00036 1. ooooo 4 2 2 - 5 2 3 12 13 .98286 - 0 . 0 0 4 4 5 0. .01000 4 2 3 - 5 2 4 1214 .08333 0 .00015 0 09766 5 2 3 - 6 2 4 1212 . 2 1842 0 .00014 1. ooooo 5 2 4 - 6 2 5 1212 . 38590 0 .00036 1. ooooo 6 2 4 - 7 2 5 12 10 .42295 0 .00021 1. ooooo 6 2 5 - 7 2 6 1210 .68767 0 .00033 1. ooooo 7 2 5 - 8 2 6 1208 .60126 0 .00036 1. ooooo 7 2 6 - 8 2 7 1208 .98967 0 . 0 0 0 1 0 1. ooooo 8 2 6 - 9 2 7 1206 . 75555 0 .00043 1. ooooo 8 2 7 - 9 2 8 1207. .29336 0 .00017 1. ooooo 9 2 7 - 10 2 8 1204 . .88939 - - 0 . 0 0 0 1 9 1.  ooooo 9 2 8 - 10 2 9 1205 . .59916 0 .00001 1.  ooooo 10 2 8 - 1 1 2 9 1203 . .00991 0 .00043 1. ooooo 10 2 9 - 1 1 2 10 1203. 90827 - 0 . 0 0 0 1 0 1. ooooo 1 1 2 9 - 12 2 10 1201 . .11980 -0 .00041 1. ooooo 1 1 2 10 - 12 2 1 1 1202 . 22049 -0 .00121 0. .01000 12 2 10 - 13 2 1 1 1 199 . 22661 - 0 . 0 0 0 0 8 1. ooooo 12 2 1 1 - 13 2 12 1200. 53987 - 0 . 0 0 0 0 4 0. .01000 13 2 1 1 - 14 2 12 1 197 . 33293 - 0 . 0 0 0 2 0 1 .ooooo 13 2 12 - 14 2 13 1 198 . 86331 - 0 . 0 0 0 3 7 0 .01000 14 2 12 - 15 2 13 1 195 . 44268 - 0 . 0 0 0 4 6 1 .ooooo 14 2 13 - 15 2 14 1 197 . 19334 -0 .00021 1 .ooooo 15 2 13 - 16 2 14 1 193 . 55972 - 0 . 0 0 0 2 1 1 .ooooo 15 2 14 - 16 2 15 1 195 . 53109 0 .00117 0 .00010 16 2 14 - 17 2 15 1191. .68662 O.00005 1 .ooooo 16 2 15 - 17 2 16 1 193 . 87309 0 .00002 1 .ooooo 17 2 15 - 18 2 16 1 189. 82602 - 0 . 0 0 0 0 5 1 .ooooo 17 2 16 - 18 2 17 1 192 . 22326 0 .00016 1 .ooooo 18 2 16 - 19 2 17 1 187 . 98294 O.00151 0 .01000 18 2 17 - 19 2 18 1 190. 58029 0 .00032 0 .01000 19 2 17 - 20 2 18 1 186 . 15683 0 .00134 0 .01000 20 2 18 - 21 2 19 1 184 . 35123 0 .00057 1 .ooooo 20 2 19 - 21 2 20 1 187 . 31373 O.OOO16 1 .ooooo 21 2 19 - 22 2 20 1 182 . 56935 0 .00082 1 .ooooo 21 2 20 - 22 2 21 1 185 . 69002 0 . 0 0 0 3 0 1 .ooooo 22 2 20 - 23 2 21 1 180. 80962 0 .00003 1 .ooooo 22 2 21 - 23 2 22 1 184 . 07172 0 .00012 1 .00000 23 2 21 - 24 2 22 1 179 . 07339 0 .00047 0 .01000 The Infrared Spectrum of Aminoborane / 249 TABLE 7.3 - continued Transition Frequency Obs-Calc Weight 23 2 22 - 24 2 23 1 182 . 45869 - 0 . .00015 1 . ooooo 24 2 22 - 25 2 23 1 177 . 35571 - 0 .00052 1 . ooooo 24 2 23 - 25 2 24 1 180. 85095 - 0 .00007 1 . ooooo 25 2 23 - 26 2 24 1 175. 65567 -o .00050 0 . 00010 25 2 24 - 26 2 25 1 179. 24606 - 0 .00171 0 . 01000 26 2 24 - 27 2 25 1 173 . 96749 -0 . .00138 0 . 00010 26 2 25 - 27 2 26 1 177 . 65760 0. .00886 0 . 00010 3 3 1 - 4 3 2 1214. 46686 - 0 . .00056 0 . 00010 4 3 1 - 5 3 2 1212 . 75680 0 .00102 1 . ooooo 5 3 3 - 6 3 4 1211. 03516 - 0 . .00464 0 . 09766 6 3 3 - 7 3 4 1209 . 30191 - 0 . .00037 1 . ooooo 7 3 4 - 8 3 5 1207 . 55621 - 0 . .00052 1 . ooooo 7 3 5 - 8 3 6 1207 . 58012 0. .00049 0 . 09766 8 3 5 - 9 3 6 1205 . 79100 - 0 . .00501 0 . 01000 8 3 6 - 9 3 7 1205. 83503 - 0 . 00284 0 . 01000 9 3 6 - 10 3 7 1204 . 01765 - 0 . 00010 1 . ooooo 9 3 7 - 10 3 8 1204 . 08365 - 0 . 00536 0 . 0 10 3 7 - 1 1 3 8 1202 . 22049 0 . 001 1 5 1 . ooooo 10 3 8 - 1 1 3 9 1202 . 33359 - 0 . 00026 1 . ooooo 1 1 3 8 - 12 3 9 1200. 39776 - 0 . 00042 1 . ooooo 1 1 3 9 - 12 3 10 1200. 57294 - 0 . 00037 1 . ooooo 12 3 9 - 13 3 10 1 198 . 55146 -o. 00050 1 . ooooo 12 3 10 - 13 3 1 1 1198. 80794 -o. 00054 1 . ooooo 13 3 10 - 14 3 1 1 1 196 . 67850 -o. 00062 0. 09766 13 3 1 1 - 14 3 12 1 197 . 04024 - 0 . 00026 0 . 01000 14 3 1 1 - 15 3 12 1 194 . 77867 -o. 00065 0. 01000 14 3 12 - 15 3 13 1 195 . 27089 0 . 00029 1. ooooo 15 3 12 - 16 3 13 1 192 . 85326 - 0 . 00057 1. ooooo 15 3 13 - 16 3 14 1 193 . 49901 - 0 . 00098 1. ,ooooo 16 3 13 - 17 3 14 1 190. 90498 -o. 00062 1. ooooo 16 3 14 - 17 3 15 1191. .72960 - 0 . 00024 0. 01000 17 3 14 - 18 3 15 1 188 . .93863 -o. 00043 0. 010O0 17 3 15 - 18 3 16 1 189 .96097 - - 0 . 00031 0 . ,09766 18 3 15 - 19 3 16 1 186 . .96015 o. 00070 0. 01000 18 3 16 - 19 3 17 1 188 . .19536 0 . 00001 1. ooooo 19 3 16 - 20 3 17 1 184 .97172 -o. 00054 1.  ooooo 19 3 17 - 20 3 18 1 186 .43252 - 0 . 00046 1. ,ooooo 20 3 17 - 21 3 18 1 182 .98273 0 . 0001 3 0 . .09766 20 3 18 - 21 3 19 1 184 .66986 - 0 . 005 14 0 .00010 21 3 18 - 22 3 19 1 180 .99422 - 0 . 00077 1. ooooo 21 3 19 - 22 3 20 1 182 .92137 - 0 . 0007 1 1 .ooooo 22 3 19 - 23 3 20 1 179 .01294 - 0 . 00040 0 .00010 22 3 20 - 23 3 21 1181 .17439 - 0 . .00036 0 .00010 23 3 20 - 24 3 2 1 1 177 .041 19 0. . 00012 0 .01000 23 3 21 - 24 3 22 1 179 .43155 - 0 . .00184 0 .01000 4 4 1 - 5 4 2 1210 .96154 0. ,00083 1 .ooooo 5 4 1 - 6 4 2 1209 .24573 0 .00036 1 .ooooo 6 4 3 - 7 4 4 1207 .52240 0 .00020 1 .ooooo 7 4 3 - 8 4 4 1205 .79101 0 .00077 0 .01000 8 4 5 - 9 4 6 1204 .05022 - 0 .00041 1 .ooooo 9 4 5 - 10 4 6 1202 .30031 0 .00107 1 .ooooo 10 4 7 - 1 1 4 8 1200 .53987 - 0 .00376 0 .01000 1 1 4 7 - 12 4 8 1 198 .76750 0 .00028 1 .ooooo 1 1 4 8 - 12 4 9 1 198 .77679 0 .00048 1 .ooooo 12 4 8 - 13 4 9 1 196 .98375 o .00013 1 .ooooo 12 4 9 - 13 4 10 1 197 .00005 0 .00037 1 .00000 13 4 9 - 14 4 10 1 195 .18721 0 .00O50 o .01ooo 13 4 10 - 14 4 1 1 1 195 .21475 0 .00096 0 .01000 14 4 10 - 15 4 1 1 1 193 .37596 0 .00094 1 .00000 14 4 1 1 - 15 4 12 1 193 .41913 0 .00031 1 .ooooo The Infrared Spectrum of Aminoborane / 250 TABLE 7.3 - continued 3. Transition Frequency Obs-Calc Weight 15 4 1 1 - 16 4 12 1191. 54735 0.00055 1 .ooooo 15 4 12 - 16 4 13 1191. 61550 0.00036 1 .ooooo 16 4 12 - 17 4 13 1 189 . 70061 0.00057 0 .01000 16 4 13 - 17 4 14 1 189. 80381 0.0005S 1 .ooooo 17 4 13 - 18 4 14 1 187 . 83321 0.00066 1 .ooooo 17 4 14 - 18 4 15 1 187 . 98294 -0.00088 0 .01000 18 4 14 - 19 4 15 1 185 . 94190 -0.00015 1 .ooooo 18 4 15 - 19 4 16 1 186 . 15683 -0.00084 0 .01000 19 4 15 - 20 4 16 1 184 . 02677 0.00034 1 .ooooo 19 4 16 - 20 4 17 1 184 . 32733 0.00158 1 .ooooo 20 4 16 - 21 4 17 1 182 . 08454 0.00048 0 .09766 20 4 17 - 21 4 18 1 182 . 491 18 0.00208 0 .09766 21 4 17 - 22 4 18 1 180. 11414 -0.00002 1 .00000 21 4 18 - 22 4 19 1 180. 65061 0.00176 1 .ooooo 22 4 18 - 23 4 19 1 178 . 1 1709 -0.00010 1 .ooooo 22 4 19 - 23 4 20 1 178 . 80943 0.00327 0 .01000 5 5 1 - 6 5 2 1206 . 96070 0.00009 1 .ooooo 6 5 1 - 7 5 2 1205 . 23929 -0.00025 0 .09766 7 5 3 - 8 5 4 1203. 51 143 0.00047 1 .ooooo 8 5 3 - 9 5 4 1201 . 77456 -0.00004 1 .ooooo 9 5 5 - 10 5 6 1200. 03021 -0.00005 1. .ooooo 10 5 5 - 1 1 5 6 1 198 . 27742 -0.00013 1 ooooo 1 1 5 7 - 12 5 8 1 196. 51642 -0.00011 1 .ooooo 12 5 7 - 13 5 8 1 194 . 74587 -0.00026 1, .ooooo 13 5 9 - 14 5 10 1 192 . 96656 -0.00110 1 .ooooo 14 5 9 - 15 5 10 1191. 17790 0.00033 1. . ooooo 15 5 1 1 - 16 5 12 1 189. 37809 -0.00353 1. ooooo 16 5 1 1 - 17 5 12 1 187 . .56813 -0.00023 0. 00010 17 5 13 - 18 5 14 1 185 . 75620 -0.00048 0. 00010 18 5 13 - 19 5 14 1 183 . 9 1323 -0.00045 0. 00010 18 5 14 - 19 5 15 1 183 92807 -0.00119 0. 00010 19 5 14 - 20 5 15 1 182 . 06557 -0.00167 0. 01000 6 6 1 - 7 6 2 1202 48664 0.00030 0. 01000 7 6 1 - 8 6 2 1200. . 75885 -0.00008 1. ooooo 8 6 3 - 9 6 4 1 199 . .02479 0.00058 1. ooooo 9 6 3 - 10 6 4 1 197 . .28204 O.00003 1. ooooo 10 6 5 - 1 1 6 6 1 195 .53109 -0.00107 0. 00010 1 1 6 5 - 12 6 6 1 193 77447 -0.00001 1. ooooo 12 6 7 - 13 6 8 1 192 .00873 -0.00005 0. 01000 13 6 7 - 14 6 8 1 190 . 23540 0.00054 1. ooooo 14 6 9 - 15 6 10 1 188 .45276 0.00020 0. 09766 15 6 9 - 16 6 10 1 186 .66201 0.00049 1. ooooo 16 6 1 1 - 17 6 12 1 184 .86237 0.00055 1. ooooo 17 6 1 1 - 18 6 12 1 183 .05310 0.00048 1. ooooo 18 6 13 - 19 6 14 1 181 . 23457 -0.00025 1. .ooooo 19 6 13 - 20 6 14 1 179 .40679 0.00077 1 .ooooo 20 6 15 - 2 1 6 16 1 177 .'56847 -0.00128 1 .ooooo 2 1 6 15 - 22 6 16 1 175 .71933 0.OOO18 1 .ooooo 22 6 17 - 23 6 18 1 173 .85883 -0.00606 0 .0 23 6 17 - 24 6 18 117 1 .98877 0.00009 0 o 25 6 19 - 26 6 20 1 168 .22518 0.01504 0 .0 7 7 1 - 8 7 2 1 197 .55651 -0.00377 0 .0 8 7 1 - 9 7 2 1 195 .82556 -0.00045 0 .0 9 7 3 - 10 7 4 1 194 .08506 0.00055 0 .0 10 7 3 - 1 1 7 4 1 192 .33552 -0.OOO12 0 .0 1 1 7 5 - 12 7 6 1 190 .58030 0.00101 0 .0 12 7 5 - 13 7 6 1 188 .81652 0.00119 0 .0 13 7 7 - 14 7 8 1 187 .04498 0.00135 0 .0 14 7 7 - 15 7 8 1 185 .26605 0.00202 0 .0 15 7 9 - 16 7 10 1 183 .47831 0.00190 0 .0 The Infrared Spectrum of Aminoborane / 251 TABLE 7.3 - continued Transition Frequency Obs-Caka Weight 16 7 9 - 17 7 10 1181 .68276 0 .00217 0 .0 17 7 11 - 18 7 12 1 179 .87885 0 .00241 0 .0 18 7 11 - 19 7 12 1 178 .06724 0 .00349 0 .0 19 7 13 - 20 7 14 1 176 .24585 0 .00344 0 .0 20 7 13 - 21 7 14 1 174 .4 1495 0 .00283 0 .0 21 7 15 - 22 7 16 1 172 .57576 0 .00284 0 .0 22 7 15 - 23 7 16 1 170 .72523 0 .00103 0 .0 23 7 17 - 24 7 18 1 168 .86970 0 .00324 0 .0 24 7 17 - 25 7 18 1 167 .00022 0 .00198 0 .0 8 8 1 - 9 8 2 1 192 .20726 0 .00018 0 .0 9 8 2 - 10 8 3 1 190 .46518 - 0 . 0 0 0 2 5 0 .0 10 8 2 - 1 1 8 3 1 188 .71754 0 .00101 0 .o 1 1 8 4 - 12 8 5 1 186 .96016 - 0 . 0 0 0 1 2 0 .0 12 8 4 - 13 8 5 1 185 .19919 0 .00258 0 .0 13 8 6 - 14 8 7 1 183 .42964 0 .00422 0 .0 14 8 6 - 15 8 7 1181 .65194 0 .00534 0. .0 15 8 8 - 16 8 9 1 179 .86623 0 .00618 0 .0 16 8 8 - 17 8 9 1 178 .07413 0 .00846 0 .0 17 8 10 - 18 8 1 1 1 176 .27344 0 . 0 1 0 1 0 0. .0 18 8 10 - 19 8 1 1 1 174 .46294 0 .00999 0. .0 19 8 12 - 20 8 13 1 172 . 64688 0 .01251 0. .0 20 8 12 - 21 8 13 1 170. .82094 0 .01346 0 . 0 21 8 14 - 22 8 15 1 168 .98633 0 .01419 0. 0 22 8 14 - 23 8 15 1 167 . 14261 0 . 0 1 4 4 0 0. 0 13 9 5 - 14 9 6 1 179 . 40680 -0 .00341 0 . 0 14 9 5 - 15 9 6 1 177 . 62719 - 0 . 0 0 3 7 4 0 . 0 15 9 7 - 16 9 8 1 175. .84 120 - 0 . 0 0 2 8 6 0. 0 16 9 7 - 17 9 8 1 174 , .04586 - 0 . 0 0 3 6 5 0 . 0 18 9 9 - 19 9 10 1 170. ,43111 - 0 . 0 0 5 9 9 0 . 0 19 9 1 1 - 20 9 12 1 168 .61 185 - 0 . 0 0 7 2 0 0. 0 20 9 1 1 - 2 1 9 12 1 166 . ,77581 - 0 . 0 1 7 1 9 0 . 0 3 0 3 - 2 0 2 1228 . .56403 - 0 . 0 0 0 1 5 0 . 09766 4 O 4 - 3 0 3 1230 19503 0 .00004 1. ooooo 5 0 5 - 4 0 4 1231 . .80422 0 .00017 1. ooooo 6 0 6 - 5 0 5 1233 . .3897 1 0 .00053 1. . ooooo 7 0 7 - 6 0 6 1234 .95000 0 .00019 1. .ooooo 8 0 8 - 7 0 7 1236 .48743 -O .00005 1 ooooo 9 0 9 - 8 0 8 1238 . 00585 0 .00008 1. .ooooo 10 0 10 - 9 0 9 1239 .50990 0 .00007 1 .ooooo 1 1 0 1 1 - 10 0 10 1241 .00505 - 0 . 0 0 0 3 3 1 .ooooo 12 O 12 - 1 1 0 1 1 1242 .49764 -0 .00001 1 .ooooo 13 0 13 - 12 0 12 1243 . .99029 - 0 . 0 0 0 4 2 1 .ooooo 14 0 14 - 13 0 13 1245 .48691 - O . 0 0 0 3 3 1 .ooooo 15 0 15 - 14 0 14 1246 .98880 0 . 0 0 0 1 0 1 .ooooo 16 0 16 - 15 0 15 1248 .49565 0.OOOOO 1 .ooooo 17 0 17 - 16 0 16 1250 .00794 - 0 . 0 0 0 1 3 1 .ooooo 18 o 18 - 17 0 17 125 1 .52531 - 0 . 0 0 0 3 5 .1 .ooooo 19 0 19 - 18 0 18 1253 .04798 -0.OOOOO 1 .ooooo 20 0 20 - 19 0 19 1254 .57455 - 0 . 0 0 0 0 2 1 .ooooo 21 0 21 - 20 0 20 1256 .10486 - 0 . 0 0 0 1 5 1 .ooooo 22 0 22 - 21 0 21 1257 .63872 - 0 . 0 0 0 1 9 0 .01000 23 0 23 - 22 0 22 1259 .17586 - 0 . 0 0 0 1 0 1 .ooooo 24 0 24 - 23 0 23 1260 .71622 0 .00033 0 .09766 25 0 25 - 24 0 24 1262 .25334 - 0 . 0 0 5 1 6 0 .0 26 0 26 - 25 o 25 1263 .80226 - 0 . 0 0 1 3 4 0 .09766 27 0 27 - 26 0 26 1265 .35024 - 0 . 0 0 0 8 0 0 .09766 28 0 28 - 27 0 27 1266 .90063 -O .00008 1 .ooooo 29 0 29 - 28 0 28 1268 .45145 - 0 . 0 0 1 0 6 1 .ooooo 30 o 30 - 29 0 29 1270 .00649 0.OOO16 1 .ooooo 2 1 1 - 1 1 0 1226 .7974 1 0.OOO14 0 .OOO10 The Infrared Spectrum of Aminoborane / 252 TABLE 7.3 - continued Transition Frequency Obs-Calc Weight 2 1 2 - 1 1 1 1226 51713 0 . 0 0 0 3 0 0 . 0 0 0 1 0 3 1 2 - 2 1 1 1228 52233 0 .00214 0 . 0 3 1 3 -• 2 1 2 1228 1 1423 0 .00109 0 . 0 4 1 3 -- 3 1 2 1230 22887 - 0 . 0 0 0 3 9 1 .OOOOO 4 1 4 -• 3 1 3 1229 70508 0 . 0 0 0 1 0 1.ooooo 5 1 4 -- 4 1 3 1231 92392 0 .00069 1.ooooo 5 1 5 -- 4 1 4 1231 29184 0 .00024 1.ooooo 6 1 5 -- 5 1 4 1233 60026 - 0 . 0 0 0 4 5 1.ooooo 6 1 6 -- 5 1 5 1232 87278 0 .0003 1 1.ooooo 7 1 6 -• 6 1 5 1235 26016 - 0 . 0 0 0 0 2 1.ooooo 7 1 7 -- 6 1 6 1234 44730 0 .00004 1.ooooo 8 1 7 -- 7 1 6 1236 90013 0 .00018 1.ooooo 8 1 8 -- 7 1 7 1236 01680 0 .00089 0 . 0 1 0 0 0 9 1 8 -- 8 1 7 1238 51827 0 .00013 1.ooooo 9 1 9 -- 8 1 8 1237 57853 - 0 . 0 0 0 0 3 1.ooooo 10 1 9 -- 9 1 8 1240 1 1328 0 .00054 1.ooooo 10 1 10 -- 9 1 9 1239 13546 - 0 . 0 0 0 1 0 1.ooooo 1 1 1 10 -- 10 1 9 124 1 68148 - 0 . 0 0 0 2 5 1.ooooo 1 1 1 1 1 -• 10 1 10 1240 68712 - 0 . 0 0 0 3 3 1.ooooo 12 1 1 1 -- 1 1 1 10 1243 22321 -0 .00O06 1.ooooo 12 1 12 -- 1 1 1 1 1 1242 23466 - 0 . 0 0 0 2 4 1.ooooo 13 1 12 -- 12 1 1 1 1244 73584 - 0 . 0 0 0 2 6 1.ooooo 13 1 13 -- 12 1 12 1243 77850 - 0 . 0 0 0 1 6 1.ooooo 14 1 13 -• 13 1 12 1246 22032 0 .00044 1.ooooo 14 1 14 -- 13 1 13 1245 31949 - 0 . 0 0 0 0 2 1.ooooo 15 1 14 -- 14 1 13 1247 67597 0 .00022 1.ooooo 15 1 15 -• 14 1 14 1246 85801 -O .00023 1.ooooo 16 1 15 -- 15 1 14 1249 10674 0 .00019 1.ooooo 16 1 16 -• 15 1 15 1248 39543 - 0 . 0 0 0 1 6 1.ooooo 17 1 16 -- 16 1 15 1250 51713 0 .00035 1.ooooo 17 1 17 - 16 1 16 1249 93235 0 .00012 1.ooooo 18 1 17 -- 17 1 16 1251 90954 - 0 . 0 0 2 6 2 0 . 0 1 0 0 0 18 1 18 - 17 1 17 1251 46845 -O .00028 1.ooooo 19 1 18 -• 18 1 17 1253 29881 -0 .00001 1.ooooo 19 1 19 -• 18 1 18 1253 00578 0 .00017 1.ooooo 20 1 19 -- 19 1 18 1254 68295 0 .00056 1.ooooo 20 1 20 -- 19 1 19 1254 543 16 - 0 . 0 0 0 1 0 1.ooooo 21 1 20 -- 20 1 19 1256 06813 0 .00072 0 . 0 1 0 0 0 21 1 21 -• 20 1 20 1256 08210 0 . 0 0 0 1 0 0.01OOO 22 1 21 -- 21 1 20 1257 45701 -0.OOOOO 0 . 0 1 0 0 0 22 1 22 -- 21 1 21 1257 62231 0 .00021 1.ooooo 23 1 22 -- 22 1 21 1258 85288 - 0 . 0 0 0 0 9 0 . 0 1 0 0 0 23 1 23 - 22 1 22 1259 16485 0 .00111 O.01000 24 1 23 -- 23 1 22 1260 25579 - 0 . 0 0 0 2 3 0 . 0 1 0 0 0 24 1 24 -- 23 1 23 1260 70764 0 . 0 0 0 6 0 0 .00010 25 1 24 -- 24 1 23 1261 66175 - 0 . 0 0 4 3 7 0 . 0 1 0 0 0 25 1 25 -• 24 1 24 1262 25334 0 .00122 0 . 0 3 2 1 -- 2 2 0 1227 55276 0 . 0 0 0 3 0 1.ooooo 3 2 2 -- 2 2 1 1227 53532 0 .00051 1.ooooo 4 2 2 -- 3 2 1 1229 23178 0 . 0 0 0 8 0 0 . 0 1 0 0 0 4 2 3 -- 3 2 2 1229 18830 0 .00071 1.ooooo 5 2 3 -- 4 2 2 1230 91681 0 .00038 1.ooooo 5 2 4 -- 4 2 3 1230 83146 -O .00007 1.ooooo 6 2 4 -- 5 2 3 1232 60955 - 0 . 0 0 0 7 7 1.ooooo 6 2 5 • - 5 2 4 1232 46647 0 .00048 0 . 0 1 0 0 0 7 2 5 -- 6 2 4 1234 31116 - 0 . 0 0 1 3 5 0 .01000 7 2 6 -- 6 2 5 1234 09075 0 .00036 1.ooooo 8 2 6 -- 7 2 5 1236 01680 - 0 . 0 0 4 0 2 0 . 0 1 0 0 0 8 2 7 -- 7 2 6 1235 70433 0 .00014 1.ooooo 9 2 7 - 8 2 6 1237 73065 - 0 . 0 0 0 3 3 1.ooooo The Infrared Spectrum of Aminoborane / 253 TABLE 7.3 - continued Transition Frequency Obs-Calc Weight 9 2 8 - 8 2 7 1237 . 30685 -o .00006 1 . ooooo 10 2 8 - 9 2 7 1239 . 43697 -o .00016 1 . ooooo 10 2 9 - 9 2 8 1238 . 89796 -o .00021 1 . ooooo 1 1 2 9 - 10 2 8 1241 . 13280 0 .00001 1 . ooooo 1 1 2 10 - 10 2 9 1240. 47778 0 00012 1 . ooooo 12 2 10 - 1 1 2 9 1242 . 81 172 -o .00017 0 . 01000 12 2 1 1 - 1 1 2 10 1242 . 04550 0 .00030 1. ooooo 13 2 1 1 - 12 2 10 1244 . 46939 -o. .00001 1. ooooo 13 2 12 - 12 2 1 1 1243 . 601 14 0. .00041 0. .01000 14 2 12 - 13 2 1 1 1246 . 10138 -o .00016 1. ooooo 14 2 13 - 13 2 12 1245 . 14431 - 0 . 00002 1. ooooo 15 2 13 - 14 2 12 1247 . 70546 - 0 . 00013 1. ooooo 15 2 14 - 14 2 13 1246 . 67628 o 00002 1. ooooo 16 2 14 - 15 2 13 1249. 27948 -o. 0OO06 1. ooooo 16 2 15 - 15 2 14 1248 . 19686 - 0 . . 00005 1. ooooo 17 2 15 - 16 2 14 1250. 82195 0. 00012 1. ooooo 17 2 16 - 16 2 15 1249. 70642 -o. 00043 1. ooooo 18 2 16 - 17 2 15 1252 . 33126 0 . 00015 1. ooooo 18 2 17 - 17 2 16 1251 . 20675 -o. 00005 1. ooooo 19 2 17 - 18 2 16 1253 . 80640 0 . 00013 0. 01000 19 2 18 - 18 2 17 1252 . 697 1 1 -o. 00048 1. ooooo 20 2 18 - 19 2 17 1255 . 24677 0 . 00020 1. ooooo 20 2 19 - 19 2 18 1254 . 18022 0 . 00006 1. ooooo 21 2 19 - 20 2 18 1256 . .65199 0 . 00005 1. ooooo 21 2 20 - 20 2 19 1255 . 65592 0 . 0004 1 1. ooooo 22 2 20 - 21 2 19 1258 . .02209 - 0 00128 0. .01000 22 2 21 - 2 1 2 20 1257 . .12471 0. 00005 1. ooooo 23 2 21 - 22 2 20 1259 36100 -o. 00227 1 .ooooo 23 2 22 - 22 2 21 1258 .58870 0 . 00010 1 .ooooo 24 2 22 - 23 2 21 1260 .6757 1 0 . 00002 1 .ooooo 24 2 23 - 23 2 22 1260 .04808 -o. 00023 1 .ooooo 25 2 23 - 24 2 22 1261 . 96543 -o. 0007 2 0 .00010 25 2 24 - 24 2 23 1261 .50421 -o. 00045 1 .ooooo 26 2 24 - 25 2 23 1263 .23931 - 0 . 00183 0 .01000 26 2 25 - 25 2 24 1262 .95765 -o. 00080 1 .ooooo 4 3 1 - 3 3 0 1227 .90002 -o. 00005 0 .09766 5 3 3 - 4 3 2 1229 .55566 0. 00092 1 .ooooo 6 3 3 - 5 3 2 1231 .20633 -o. 00386 1 .ooooo 7 3 4 - 6 3 3 1232 .86184 -o. 00020 1 .ooooo 7 3 5 - 6 3 4 1232 .85121 -o. 00029 1 .ooooo 8 3 5 - 7 3 4 1234 .51307 -o. 00023 1 .ooooo 8 3 6 - 7 3 5 1234 .49155 -o. .00093 1 .ooooo 9 3 6 - 8 3 5 1236 .16514 -o. 00022 1 .ooooo 9 3 7 - 8 3 6 1236 .12723 -o. 00055 1 .ooooo 10 3 7 - 9 3 6 1237 .81954 -o. .00023 1 .ooooo 10 3 8 - 9 3 7 1237 .75647 -o 00015 1 .ooooo 1 1 3 8 - 10 3 7 1239 .47814 0. .00002 1 .ooooo 1 1 3 9 - 10 3 8 1239 .37767 -o 00036 1 .ooooo 12 3 9 - 1 1 3 8 124 1 .14234 0 .00055 0 .09766 12 3 10 - 1 1 3 9 1240 .99069 - 0 . 00029 1 .ooooo 13 3 10 - 12 3 9 1242 .81 173 o .00007 0 .01000 13 3 1 1 - 12 3 10 1242 .59359 -o .00076 1 .ooooo 14 3 1 1 - 13 3 10 1244 .48693 -o .00067 1 .ooooo 14 3 12 - 13 3 1 1 1244 .18635 -o .00069 1 .ooooo 15 3 12 - 14 3 1 1 1246 .16736 -o .00071 1 .ooooo 15 3 13 - 14 3 12 1245 .7677 1 - 0 .00028 1 .ooooo 16 3 13 - 15 3 12 1247 .84891 - 0 .00084 1 .ooooo 16 3 14 - 15 3 13 1247 .33573 - 0 .00051 1 .ooooo 17 3 14 - 16 3 13 1249 .52698 -o .00064 1 .ooooo 17 3 15 - 16 3 14 1248 .88980 - 0 .00113 1 .ooooo The Infrared Spectrum of Aminoborane / 254 TABLE 7.3 - continued Transition Frequency Obs-Calc Weight 18 3 15 - 17 3 14 1251 . 19425 - 0 . 0 0 1 1 3 0 . 0 1 0 0 0 18 3 16 - 17 3 15 1250. 43089 - 0 . 0 0 0 5 1 1.ooooo 19 3 16 - 18 3 15 1252 . 84590 - 0 . 0 0 0 3 4 1.ooooo 19 3 17 - 18 3 16 1251 . 95647 - 0 . 0 0 0 6 5 O.09766 20 3 17 - 19 3 16 1254 . 47348 - 0 . 0 0 0 3 0 0 . 0 20 3 18 - 19 3 17 1253 . 46753 - 0 . 0 0 0 2 5 1.OOOOO 5 4 1 - 4 4 0 1227 . 74651 - 0 . 0 0 0 0 4 1.OOOOO 6 4 3 - 5 4 2 1229 . 39435 0 .00003 1.ooooo 7 4 3 - 6 4 2 1231 . 03715 - 0 . 0 0 0 3 5 1.ooooo 8 4 5 - 7 4 4 1232 . 67576 0 .00006 1.ooooo 9 4 5 - 8 4 4 1234 . 31116 0 . 0 0 0 6 0 0 . 0 1 0 0 0 10 4 7 - 9 4 6 1235 . 93973 0 .00104 1.ooooo 1 1 4 7 - 10 4 6 1237 . 56440 - 0 . 0 0 3 4 5 0 . 0 1 0 0 0 1 1 4 8 - 10 4 7 1237 . 56440 0 .00114 0 . 0 1 0 0 0 12 4 8 - 1 1 4 7 1239. . 19213 0 .00059 1.ooooo 12 4 9 - 1 1 4 8 1239 . . 18367 0 .00064 1.ooooo 13 4 9 - 12 4 8 1240. 81242 - 0 . 0 0 0 2 3 1.ooooo 13 4 10 - 12 4 9 1240. . 79788 0 .00017 1.ooooo 14 4 10 - 13 4 9 1242 . 43176 - 0 . 0 0 0 1 8 1.ooooo 14 4 1 1 - 13 4 10 1242 . 40718 0 .00028 1.ooooo 15 4 1 1 - 14 4 10 1244 . 05040 0 . 0 0 0 1 0 1.ooooo 15 4 12 - 14 4 1 1 1244 . 01096 0 . 0 0 0 9 0 1.ooooo 16 4 12 - 15 4 1 1 1245 . 66948 0 .00063 1.ooooo 16 4 13 - 15 4 12 1245. .60752 0 .00103 1.ooooo 17 4 13 - 16 4 12 1247 . . 28932 0 .00049 1.ooooo 17 4 14 - 16 4 13 1247 . . 19593 0 .00058 1.ooooo 18 4 14 - 17 4 13 1248 . .9114 1 -0.OOO15 1.ooooo 18 4 15 - 17 4 14 1248 . .77693 0 .00126 1.ooooo 19 4 15 - 18 4 14 1250 53853 0 .00025 1.ooooo 19 4 16 - 18 4 15 1250. . 34784 0 .00145 1.ooooo 20 4 16 - 19 4 15 1252 . .16988 0 .00004 1.ooooo 20 4 17 - 19 4 16 1251 . .90954 0 .00318 0 . 0 1 0 0 0 21 4 17 - 20 4 16 1253 . .80640 0 .00001 0 . 0 1 0 0 0 2 1 4 18 - 20 4 17 1253 . .45617 0 .00179 1.ooooo 22 4 18 - 21 4 17 1255 . .44680 -0.OOO15 1.ooooo 22 4 19 - 21 4 18 1254 . .99214 0 .00284 1.ooooo 6 5 1 - 5 5 0 1227 . .09853 0 .00015 1.ooooo 7 5 3 - 6 5 2 1228 .73787 - 0 . 0 0 0 4 5 1.ooooo 8 5 3 - 7 5 2 1230 .37304 0 . OO01 3 1.ooooo 9 5 5 - 8 5 4 1232 .00171 -0 .00051 1.ooooo 10 5 5 - 9 5 4 1233 .62578 - 0 . 0 0 0 5 7 1.ooooo 1 1 5 7 - 10 5 6 1235 . 24459 - 0 . 0 0 0 6 3 1.ooooo 12 5 7 - 1 1 5 6 1236 .85882 - O . 0 0 0 4 0 1.ooooo 13 5 9 - 12 5 8 1238 . . 46810 0 .00047 1.ooooo 14 5 9 - 13 5 8 1240 .07097 - 0 . 0 0 1 1 0 1.ooooo 15 5 1 1 - 14 5 10 124 1 .66956 0 .00013 1.ooooo 16 5 1 1 - 15 5 10 1243 .26284 - 0 . 0 0 2 8 7 1.ooooo 17 5 13 - 16 5 12 1244 .84989 - 0 . 0 0 0 2 4 0 .09766 18 5 13 - 17 5 12 1246 .44086 - O . 0 0 0 7 0 0 .09766 18 5 14 - 17 5 13 1246 .43085 - 0 . 0 0 1 3 5 0 .09766 19 5 14 - 18 5 13 1248 .02160 - 0 . 0 0 1 9 9 0 .09766 19 5 15 - 18 5 14 1248 .00735 - 0 . 0 0 1 0 8 0 .09766 7 6 1 - 6 6 0 1225 .97373 - 0 . 0 0 0 3 6 0 .01000 8 6 3 - 7 6 2 1227 .60587 - 0 . 0 0 0 0 2 1.ooooo 9 6 3 - 8 6 2 1229 .23178 - 0 0 0 0 1 1 0 .01000 10 6 5 - 9 6 4 1230 .85233 0 . 0 0 0 2 0 0 .01000 1 1 6 5 - 10 6 4 1232 .46647 - 0 . 0 0 0 1 5 0 .01000 12 6 7 - 1 1 6 6 1234 .07546 O.00009 1.ooooo 13 6 7 - 12 6 6 1235 .67901 0 .00061 1.ooooo 14 6 9 - 13 6 8 1237 . 27580 0 .00012 1.ooooo The Infrared Spectrum of Aminoborane / 255 TABLE 7.3 - continued Transition Frequency Obs-Calc Weight 1 5 6 9 - 1 4 6 8 1 2 3 8 . 8 6 7 3 9 0 . 0 0 0 1 2 1 . ooooo 1 6 6 1 1 - 1 5 6 1 0 1 2 4 0 . 4 5 3 1 2 0 . 0 0 0 1 1 1 . ooooo 1 7 6 1 1 - 16 6 1 0 1 2 4 2 . 0 3 3 2 6 0 . 0 0 0 0 6 1 . ooooo 1 8 6 1 3 - 17 6 1 2 1 2 4 3 . 6 0 1 1 3 - 0 . 0 0 6 0 6 0 . 0 1 0 0 0 1 9 6 1 3 - 1 8 6 1 2 1 2 4 5 . 1 7 5 8 4 - 0 . 0 0 0 3 3 1 . ooooo 2 0 6 1 5 - 1 9 6 14 1 2 4 6 . 7 3 8 2 3 0 . . 0 0 0 3 4 1 . ooooo 2 1 6 1 5 - 2 0 6 14 1 2 4 8 . 2 9 4 3 3 - 0 . . 0 0 1 9 6 1 . ooooo 2 2 6 17 - 2 1 6 16 1 2 4 9 . 8 4 4 5 2 - 0 . . 0 0 0 0 2 0 . 0 1 0 0 0 8 7 1 - 7 7 0 1 2 2 4 . 3 9 6 3 7 0 . . 0 0 0 8 0 0 . 0 9 7 3 - 8 7 2 1 2 2 6 . 0 1 4 6 0 -o. . 0 0 4 1 7 0 . 0 1 0 7 3 - 9 7 2 1 2 2 7 . 6 3 6 3 2 0 0 0 0 5 1 0 . 0 1 1 7 5 - 1 0 7 4 1 2 2 9 . 2 4 3 6 4 - 0 . 0 0 3 0 3 0 . 0 1 2 7 5 - 1 1 7 4 1 2 3 0 . 8 5 2 3 3 0 . 0 0 0 9 6 0 . 0 1 3 7 7 - 1 2 7 6 1 2 3 2 . 4 5 1 2 6 0 . 0 0 1 3 8 0 . 0 14 7 7 - 1 3 7 6 1 2 3 4 . 0 4 4 1 5 0 . 0 0 1 9 5 0 . 0 1 5 7 9 - 1 4 7 8 1 2 3 5 . 6 3 0 3 4 0 . 0 0 2 0 4 0 . 0 1 6 7 9 - 1 5 7 8 1 2 3 7 . 2 1 0 9 7 0 . . 0 0 2 8 1 0 . 0 1 7 7 1 1 - 1 6 7 1 0 1 2 3 8 . 7 8 4 2 1 0 . 0 0 2 4 7 0 . 0 1 8 7 1 1 - 1 7 7 1 0 1 2 4 0 . 3 5 1 7 7 0 . . 0 0 2 7 5 0 . o 1 9 7 1 3 - 18 7 1 2 1 2 4 1 . . 9 1 3 2 3 0 . . 0 0 3 2 9 0 . 0 2 0 7 1 3 - 1 9 7 1 2 1 2 4 3 . . 4 6 6 8 2 o . 0 0 2 3 0 0 . 0 2 1 7 1 5 - 2 0 7 1 4 1 2 4 5 . . 0 1 5 6 8 0 . . 0 0 3 11 0 . 0 2 2 7 1 5 - 2 1 7 14 1 2 4 6 . 5 5 6 4 1 0 . . 0 0 2 1 1 0 . 0 2 3 7 17 - 2 2 7 16 1 2 4 8 . 0 9 1 8 1 0 . 0 0 2 5 9 0 . 0 2 4 7 17 - 2 3 7 16 1 2 4 9 . 6 1 9 4 7 0 0 0 1 4 0 0 . 0 2 5 7 1 9 - 2 4 7 18 1 2 5 1 . 1 3 9 4 8 0 . 0 O 0 O 8 0 . 0 o 8 1 - 8 8 0 1 2 2 2 . 3 8 6 2 7 - 0 . 0 0 0 7 8 0 . 0 1 0 8 2 - 9 8 1 1 2 2 4 . 0 0 1 2 1 0 . 0 0 0 1 2 0 . 0 1 1 8 4 - 1 0 8 3 1 2 2 5 . 6 1 0 3 9 0 . 0 0 1 7 8 0 . 0 1 2 8 4 - 1 1 8 3 1 2 2 7 . 2 1 2 7 4 0 . . 0 0 3 1 3 0 . 0 1 3 8 6 - 1 2 8 5 1 2 2 8 . 8 0 7 7 9 0 . 0 0 3 7 2 0 . 0 14 8 6 - 1 3 8 5 1 2 3 0 . 3 9 6 7 5 0 . 0 0 4 7 9 0 . . 0 1 5 8 8 - 14 8 7 1 2 3 1 . 9 7 9 6 8 0 . . 0 0 6 4 1 0 . . 0 1 6 8 8 - 1 5 8 7 1 2 3 3 . 5 5 5 6 9 0 . 0 0 7 7 4 0 . 0 17 8 1 0 - 1 6 8 9 1 2 3 5 . 1 2 4 3 4 0 . 0 0 8 3 6 0 . 0 18. 8 1 0 - 17 8 9 1 2 3 6 . 6 8 7 8 7 0 . 0 1 0 5 6 0 . 0 1 9 8 1 2 - 1 8 8 1 1 1 2 3 8 . 2 4 3 4 7 0 . 0 1 1 5 7 0 . 0 2 0 8 1 2 - 1 9 8 1 1 1 2 3 9 . 7 9 3 0 4 0 . 0 1 3 3 3 0 . 0 2 1 8 14 - 2 0 8 1 3 1 2 4 1 . 3 3 5 0 1 0 . 0 1 4 3 2 0 . 0 2 2 8 14 - 2 1 8 1 3 1 2 4 2 . 8 6 9 3 2 0 . 0 1 4 5 4 0 . 0 1 2 9 3 - 1 1 9 2 1 2 2 3 . 1 7 5 1 0 -o . 0 0 0 6 8 0 . 0 1 3 9 5 - 1 2 9 4 1 2 2 4 . 7 6 4 6 9 - 0 . 0 0 1 6 0 0 . 0 1 4 9 5 - 1 3 9 4 1 2 2 6 . 3 4 7 3 0 - 0 . 0 0 2 6 2 0 . 0 1 5 9 7 - 1 4 9 6 1 2 2 7 . 9 4 7 7 5 0 . 0 2 1 1 3 0 . 0 1 6 9 7 - 1 5 9 6 1 2 2 9 . 4 9 1 4 9 - 0 . 0 0 4 9 0 0 . 0 1 7 9 9 - 1 6 9 8 1 2 3 1 . 0 4 9 5 2 -o . 0 0 9 6 5 0 . 0 1 8 9 9 - 17 9 8 1 2 3 2 . 6 0 9 5 5 - 0 . 0 0 5 3 8 0 . 0 1 9 9 1 1 - 1 8 9 1 0 1 2 3 4 . 1 5 6 2 8 - 0 . 0 0 7 3 4 o . 0 2 0 9 1 1 - 1 9 9 1 0 1 2 3 5 . 6 9 0 0 5 - 0 . 0 1 5 1 6 0 . 0 Observed frequency minus the frequency calculated using the fitted spectroscopic constants. The Infrared Spectrum of Aminoborane / 256 The Infrared Spectrum of Aminoborane / 257 Excited State J u common 3 ^ upper ft state Ground State Figure 7.2. A Graphic Description of Ground State Combination Differences. (Asymmetry in the K stack is taken to be zero). The Infrared Spectrum of Aminoborane / 258 A, 1223 c m ' 1354 cm 1442 cm-B, B, 612 cm" 742 cm - i 830 cm-Ground Vibrational State Figure 7.3. Diagram Showing the Vibrational Levels that Could Perturb the 2vB Level of NH 2BH 2 in a Coriolis Type Perturbation. An arrow indicates which two levels might perturb each other. The letters give the symmetry of the level. BIBLIOGRAPHY 1. R. Hoffman, J Chem Phys, 40, 2474-2480 (1964). 2. D.R. Armstrong, B.J. Duke and P.G. Perkins, J Chem Soc(A), 2566-2572 (1969). 3. O. Gropen and H.M. Seip, Chem Phys Lett, 25, 206-208 (1974). 4. J.D. Dill, P.v.R. Schleyer, and J.A. Pople, J Amer Chem Soc, 97, 3402-3409 (1975). 5. T. Fjeldberg, G. Gundersen, T. Jonvik, H.M. Seip, and S. SaebcS, Acta Chem Scand A, 34, 547-565 (1980). 6. B. Maouche and J. Gayoso, Int J Quantum Chem, 23, 891-904 (1983). 7. E. Wiberg, Naturwissenschaften, 35, 212-218 (1948). 8. P.M. Kuznesof, D.F. Schniver, and F.E. Stafford, J Amer Chem Soc, 90, 2557-2560 (1968). 9. M.G. Hu, R.A. Geanangel and W.W. Wendlandt, Thermochim Acta, 23, 249-255 (1978). 10. K.W. Boddeker, S.G. Shore, and R.K. Bunting, J Amer Chem Soc, 88 4396-4401 (1966). 11. C.T. Kwon and H.A. McGee, Inorg Chem, 9, 2458-2461 (1970). 12. M.J.S. Dewar and M.L. McKee, J Mol Struct, 68, 105-115 (1980). 13. M. Sugie, H. Takeo, and C. Matsumura, Chem Phys Lett, 64, 573-575 (1979). 14. M. Sugie, K. Kawashima, H. Takeo, and C. Matsumura, Koen Yoshishu-Bunshi Kozo Sogo Toronkai, 168-169 (1979). 15. M.C.L. Gerry, W. Lewis-Bevan, A.J. Merer, and N.P.C. Westwood, J Mol Spectrosc, 110, 153-163 (1985). 16. N.P.C. Westwood and N.H. Werstiuk, J Amer Chem Soc, 108, 891-894 (1986). 17. D. Steunenberg, The Infrared Spectrum of Gaseous Aminoborane; Rotational  Structure in the 8p Band, BSc Thesis, The University of British Columbia, Vancouver, 1986. 18. D. Cramb, The Infrared Spectrum of Gaseous Aminoborane; Rotational  Structure in the 10o Band, BSc Thesis, The University of British Columbia, Vancouver, 1985. 259 

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