THE MICROWAVE ROTATIONAL SPECTRUM OF METHANE IN THE GROUND VIBRONIC STATE by CRAIG WARD HOLT B.A., Northwestern University, 1963 M.Sc, University of California at Berkeley, 1966 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of Chemistry We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April, 1976 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 representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date I 3 ABSTRACT The microwave rotational spectrum of ground state methane has been observed for the first time. Seven AJ=0 Q-branch transitions have been observed between 7.8 and 20 GHz with peak absorption coefficients < 6 X 10"11 cm-1: these transitions are the weakest ever observed with a Stark-modulated waveguide absorption microwave spectrometer. The spectrometer employed bolometer detectors in a source- noise cancellation scheme. The spectrometer signal was integrated by a signal averager with integration times ranging up to one week. Special experimental techniques are discussed in detail. The bolometer time constant is calculated from hot-wire anemometer heat loss data. The theory required to perform the experiment is presented using the octahedral group 0^ and its rotational subgroup 0 along with the tetrahedral group T^. An understanding of the groups employed by various workers in the field removes many of the contradictions between them. The symmetric top rotational wavefunction parity introduced by Wang is used to obtain the correct total wavefunction parity from the electronic, nuclear spin, vibrational and rotational wavefunctions. The one quartic tensor distortion constant D,p = 132943.41 + .71 Hz, the two sextic constants H4T =-16.9839 +.0076 Hz and H6T = 11.0342 +.0086 Hz, and for the first time the three octic distortion constants L^T = (20.07 +.24) X 10"" Hz, 1 h L.T = (-26.77 +.35) X lO" * Hz and LRT = (-30.0 +1.8) X I0~ Hz iii have been determined using the seven transition frequencies measured here, the J=2 ortho-para splitting known for methane and the two J=7 Q-branch transitions measured earlier in an infra-red laser - microwave double resonance experiment. The above errors are standard deviations given by weighted linear least squares analysis. The estimated absolute errors are also given. Term values are presented which allow the accurate calculation of all ground state splittings of methane up to J=21. iv TABLE OF CONTENTS CHAPTER Page 1. INTRODUCTION 1 2. THEORY OF THE MICROWAVE ROTATIONAL SPECTRUM OF METHANE • 4 2.1 Introduction and Historical Development ... 4 2.2 Symmetry of the Rotational Wavefunctions of Methane 8 2.3 The Rotational Hamiltonian of Methane .... 17 2.3.1 Fourth Degree Tensor Hamiltonian ... 22 2.3.2 Sixth Degree Tensor Hamiltonian ... 23 2.3.3 Eighth Degree Tensor Hamiltonian ... 24 2.3.4 Exact Evaluation of the Tensor Hamiltonian Eigenvalues 26 2.4 Dipole Moment 27 2.5 Selection Rules 29 2.6 Stark Effect 30 2.7 Physical Interpretation 31 2.8 Intensities of Transitions 33 3. EXPERIMENTAL APPARATUS 35 3.1 Introduction 35 3.2 Stark Modulation 36 3.3 Stark Cell 40 3.3.1 X-band 41 3.3.2 Cell above X-band 41 3.4 Frequency Stabilization and Control 43 3.4.1 Microwave Reference Frequency .... 44 3.4.2 Stabilized VHF Reference Oscillator . 44 V CHAPTER Page 3.4.3 Stabilized Microwave Oscillators ... 46 3.4.4 Frequency Determination 47 3.5 Time Averaging 48 3.6 Noise Minimization 55 3.6.1 Stray Pick-up 55 3.6.2 Detector to Preamplifier Impedence Match 56 3.6.3 Minimization of Microwave Oscillator Noise 57 3.6.4 Noise Cancellation 59 3.6.5 Cell Noise 61 3.7 Bolometer Detectors 64 3.7.1 Bolometer Noise 64 3.7.2 Power Saturation 66 3.7.3 Conversion Gain 70 3.7.4 Bolometer Time Constant 74 3.7.5 Bolometer Matching Impedence 76 4. EXPERIMENTAL CONDITIONS AND RESULTS 78 4.1 Introduction 78 4.2 Initial Search 79 4.3 Second Experimental Phase 80 4.4 Final Experimental Phase 88 4.5 Experimental Conditions 90 4.5.1 Line Strengths 96 4.5.2 Sweep Times 96 4.5.3 Stark Fields 97 4.6 Line Identification . 98 vi CHAPTER Page 4.7 Determination of Distortion Constants .... 100 4.8 Influence of Dectic and Higher Order Distortion Constants . 105 5. CONCLUSIONS 115 APPENDIX A BOLOMETER TIME CONSTANT 119 APPENDIX B THE SYMMETRIC TOP ROTATIONAL WAVEFUNCTION PARITIES 126 BIBLIOGRAPHY 129 vii LIST OF TABLES TABLE Page I Character Table for the Full Molecular Symmetry Group of Methane 11 II Reduction of the Irreducible Representations of 0^ into the Subgroup T^ and the Rotational Subgroup 0 : 12 III Reduction of the Representations and of r g u the Full Rotation-Inversion Group onto T^ .... 14 IV Reduction of the Representations and of r g u the Full Rotation-Inversion Group onto 0^ .... 15 V The Allowed Symmetry Species of the Wavefunctions of Methane in the Ground Vibronic State 18 VI N610B/38B7 Bolometer Conversion Gain 71 VII The Product G-Prf 72 VIII Relative Bolometer Signal Output Power Given by the Product G«Prf 73 IX Predicted Bolometer Behavior with Increased Bias Current 74 X Bolometer Operating Values near 200 ohms 77 XI Experimental Frequencies of X- and P-band AJ=0 Transitions of 12CHit in the Ground Vibronic State together with Predictions based on the Distortion Constants DT, H^T, and HgT of Curl and Tarrago . 82 XII Experimental Conditions 95 XIII Centrifugal Distortion Constants of 12CIU in the Ground State 101 XIV The AJ=0 Transitions of Ground State ^CH* . 103 viii TABLE Page XV Frequency Contributions of the Terms Associated with the Distortion Constants Listed in Table XIII to the Transition Frequency 106 XVI Predicted Transition Frequencies based on the Distortion Constants of Tarrago et al and the Distortion Constants determined here 108 12 XVII Tensor Distortion Energy ET for C1U in the Ground State Ill XVIII Bolometer Heat Dissipation 121 ix LIST OF FIGURES FIGURE Page 3.1 Spectrometer used between 7.8 and 18 GHz with BWO as Source and Single Ended Detection Scheme . 37 3.2 Spectrometer used between 18 and 24 GHz with Klystron Source and Balanced Noise Cancelling Detection Scheme 38 3.3 HP-K15-8400B Microwave Spectroscopy Source Configuration used at X- and P-bands 45 3.4 Improvement in Signal to Noise Ratio Resulting from the Summation of Two Separate Three Day Runs to give a Six Day Run 50 3.5 Frequency Analog Voltage Conditioning Amplifier . 53 3.6 Bolometer Equivalent Circuit given by Cohn ... 76 4.1 512 Sample minus 512 Baseline 51.2 second Scans to give the J=12 E1 -»• J=12 E2 Transition of Ground State 12CR* 83 12 4.2 The J=12 Rotational Energy Levels for CHH ... 84 4.3 512 Sample minus lk 1024 Baseline 51.2 second Scans to give the J=13 E1 -> J=13 E2 Transition of Ground State 12CH-t 85 4.4 1024 Sample minus 1024 Baseline 51.2 second Scans to give the J=14 E2 -»• J=14 E3 Transition of Ground State 12CH-» 86 4.5 512 Sample minus 512 Baseline 51.2 second Scans to give the J=15 E1 + J=15 E2 Transition of Ground State 12GHi» ." 87 X FIGURE Page 4.6 384 Sample minus 384 Baseline 51.2 second Scans to give the J=14 E1 J=14 E2 Transition of Ground State .^CHi, 91 4.7 The J=14 Rotational Energy Levels for .12CHi» ... 92 4.8 3328 Sample minus 3328 Baseline 51.2 second Scans to give the J=16 E2 -»- J=16 E3 Transition LZ of Ground State CHK 93 4.9 3072 Sample minus % 4096 Baseline 51.2 second Scans to give the J=18 E2 •> J=18 E3 Transition of Ground State 12C1U 94 xi ACKNOWLEDGEMENTS The work reported in this thesis was completed in the Department of Chemistry at the University of British Columbia under the patient and able direction of Dr.M.C.L. Gerry. I would like to thank Dr. Gerry for his emphasis on fair-play, his pleasant manner, his optimism (especially throughout the long "initial search period"), his readiness to listen to new ideas, and the large degree of independence allowed all my work. Dr. Irving Ozier is gratefully acknowledged for presenting the problem treated in this thesis as well as for the inexhaustible enthusiasm which he gave to the experiment. The authors of various disciplines cited in the Bibliography are to be credited for the indispensable work they performed laying the foundation upon which this experiment rests. For the use of critical equipment during various stages of the experiment Dr. M. Bloom, Dr. A.V. Bree, Dr. J.E. Eldridge, Dr. J.B. Farmer, Dr. D.C. Frost, Dr. W.N. Hardy, and Dr. C.A. McDowell are given thanks. The many discussions and constant encouragement given by Dr. Walter N. Hardy have been quite useful. I would like to express my gratitude to the University of British Columbia for extending a Graduate Fellowship to me for several years and the National Research Council of Canada for a bursary.