ROVIBRATIONAL ANALYSIS ON ASYMMETRIC TOP MOLECULES IN VIBRATIONALLY EXCITED STATES BY HIGH-RESOLUTION FTIR SPECTROSCOPY GOH KER LIANG, M.Sc.,Dip.Ed A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY NATIONAL UNIVERSITY OF SINGAPORE 2003 ii ACKNOWLEDGEMENTS Thanks to Professor Ong Phee Poh who was my supervisor since 1996 during my honours year, who has given me precious ideas, guidance, great support and encouragement throughout Dr Tan Tuck Lee Augustine, my co-supervisor for his guidance, help and efforts, and his resourcefulness, with which without his help, I would never get through Dr Wang Weifeng for his research directions and materials Mr Teo Hoon Hwee for his great reliable help in setting up of the experiments as well as his encouragement I am also in debt to Soek Fong, and my family Finally, National University of Singapore for providing me an excellent research environment iii PUBLICATIONS High-Resolution FTIR Spectrum of the ν5 Band of HCOOD, K L Goh, P P Ong, T L Tan, H H Teo, and W F Wang, Journal of Molecular Spectroscopy 191, 343347 (1998) Analysis of High-Resolution FTIR Spectrum of the ν6 Band of H13COOH, P P Ong, K L Goh, and H H Teo, Journal of Molecular Spectroscopy 194, 203-205 (1999) FTIR Spectrum of the ν4 Band of DCOOD, T L Tan, K L Goh, P P Ong, and H Teo, Journal of Molecular Spectroscopy 195, 324-327 (1999) H Improved Rovibrational Constants for the ν3 Infrared Band of HCOOD, K L Goh, P P Ong, H H Teo, and T L Tan, Journal of Molecular Spectroscopy 197, 322323 (1999) Rovibrational Constants for the ν6 and 2ν9 Bands of HCOOD by Fourier Transform Infrared Spectroscopy, T L Tan, K L Goh, P P Ong, and H H Teo, Journal of Molecular Spectroscopy 198, 110-114 (1999) Rovibrational Analysis of ν2 and 2ν5 Bands of DCOOH by High Resolution FTIR Spectroscopy, T L Tan, K L Goh, P P Ong, and H H Teo, Journal of Molecular Spectroscopy 198, 387-392 (1999) High-resolution Fourier transform infrared spectroscopy and analysis of the ν12 fundamental band of ethylend-d4, T L Tan, K L Goh, P P Ong, and H H Teo, Chemical Physics Letters 315, 82-86 (1999) The ν3 Band of DCOOH, K L Goh, P P Ong, and T L Tan, Spectrochimica Acta Part A 55, 2601-2614 (1999) High resolutoin FTIR spectrum of the ν1 band of DCOOD, K L Goh, P P Ong, H H Teo, and T L Tan, Spectrochimica Acta Part A 56, 991-1001 (2000) 10 High-resolution FTIR Spectroscopy of the ν11 and ν2+ν7 bands of ethylene-d4, K L Goh, T L Tan, P P Ong, and H H Teo, Molecular Physics 98, 583-588 (2000) 11 The Coriolis Interaction between the ν9 and ν7 Fundamental Bands of Methylene Fluoride-d2, K L Goh, T L Tan, P P Ong, and H H Teo, Journal of Molecular Spectroscopy 201, 310-313 (2000) 12 High-resolution FTIR spectroscopy of the ν6 fundamental of methylene fluoride-d2, K L Goh, T L Tan, P P Ong, and H H Teo, Chemical Physics Letters 323, 361364 (2000) 13 Analysis of the Coriolis Interactions between ν6 and ν8 Bands of HCOOH, T L Tan, K L Goh, P P Ong, and H H Teo, Journal of Molecular Spectroscopy 202, 194206 (2000) 14 High-Resolution FTIR Spectrum of the ν9 Band of Ethylene-D4 (C2D4), T L Tan, K L Goh, P P Ong, and H H Teo, Journal of Molecular Spectroscopy 202, 249252 (2000) 15 Analysis of the coriolis interacion of the ν12 band with 2ν10 of cis-d2-ethylene by high-resolution Fourier transform infrared spectroscopy, K L Goh, T L Tan, P P Ong, and H H Teo, Chemical Physics Letters 325, 584-588 (2000) 16 High-resolution FTIR spectroscopy of the Coriolis interacting ν3 and ν9 fundamentals of methylene fluoride-d2, K L Goh, T L Tan, P P Ong, K H Chaw, and H H Teo, Molecular Physics 98, 1343-1346 (2000) 17 High-Resolution Fourier Transform Infrared Spectroscopy of the ν12 Fundamental Band of Ethylene (C2H4), T L Tan, S Y Lau, P P Ong, K L Goh, and H H Teo, Journal of Molecular Spectroscopy 203, 310-313 (2000) 18 Analysis of the ν12 Band of Ethylene-13C2 by High Resolution FTIR Spectroscopy, T L Tan, K L Goh, P P Ong, and H H Teo, Journal of Molecular Spectroscopy 207, 189-192 (2001) iv PURPOSE OF THIS STUDY AND SUMMARY Spectral analyses to obtain spectroscopic as well as coupling constants have been made in order to fit the vibrational-rotational energy levels and study the vibrationalrotational structure of some gaseous asymmetric top molecules The present study focuses on isotopic variants of formic acid, i.e, DCOOH, DCOOD, HCOOD, and H13 COOH, the extensively studied variants of ethylene, i.e, C2D4, cis-ethylene-d2, as well as that of methylene fluoride-d2, i.e., CD2F2, all of which fall into the major category of asymmetric top molecules Rotationally resolved spectra with a spectral resolution of 0.004 cm-1 collected using the Bomem DA3.002 High-resolution Fourier transform spectrometer have been fitted to the well established Watson’s Hamiltonian including rovibrational coupling terms in order to derive precise upper state spectroscopic constants This thesis consists of 13 chapters Chapters to are dedicated to the working principles of fourier transform spectroscopy, a brief description of the experiment setup and the spectrometer, the theory based on Watson’s Hamiltonian, including vibrational coupling terms, as well as the nonlinear least-squares fit algorithm Chapters to reports the detailed measurements and analyses of the high-resolution infrared spectra of formic acid, i.e the ν5, ν3, ν6, and 2ν9 bands of HCOOD, ν2, and ν3 bands of DCOOH, ν4, and ν1 of DCOOD, as well as the ν6 fundamental of H13COOH v Chapters and 10 describes the works on ethylene, i.e the ν12, ν11, and ν9 bands of C2D4, the ν12 bands of cis-ethylene-d2 and ethylene-13C2 Chapters 11 and 12 focuses on the analyses of Methylene fluoride-d2 (CD2F2), i.e on the ν6, ν9, ν3, and ν7 fundamental bands of this molecule A Conclusion and future research proposal are discussed in Chapter 13 CONTENTS ACKNOWLEDGEMENTS ii PUBLICATIONS iii PURPOSE OF THIS STUDY CHAPTER FOURIER TRANSFORM SPECTROSCOPY 1.1 1.2 1.3 1.4 1.5 Michelson Interferometer (pg 1) Fourier Transform Spectroscopy (pg 2) Apodization and Resolution (pg 3) Sampling (pg 4) Advantages of Fourier Transform Spectroscopy (pg 5) CHAPTER THE BOMEM DA3.002 FT SPECTROMETER 2.1 2.2 2.3 2.4 2.5 Introduction (pg 7) Dynamic Alignment (pg 7) Optical Configuration and the Laser Source (pg 7) The PCDA3INT and PCDA Software (pg 8) Apodization (pg 9) CHAPTER VIBRATIONAL-ROTATIONAL STRUCTURE OF ASYMMETRIC TOP MOLECULES 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 Introduction (pg 12) The Semirigid Molecule (pg 12) The Complete Vibration-Rotation Hamiltonian (pg 13) Expansion of Hamiltonian (pg 14) Transformation of Hamiltonian Using The Contact Transform Method (pg 15) Rotational Constants (pg 16) Quartic and Sextic Centrifugal Terms (pg 16) Vibrational Dependence of Rotational Hamiltonian (pg 17) Coriolis Interactions (pg 17) Third-Rank Resonances (pg 17) Reduction of Hamiltonian (pg 18) The Wang Transformation (pg 21) Selection Rules (pg23) CHAPTER LEAST-SQUARES REFINEMENT OF MOLECULAR PARAMETERS (pg 27) iv CHAPTER HIGH RESOLUTION FTIR SPECTRA OF THE ν6, 2ν9, ν5, AND ν3 BANDS OF HCOOD 5.1 5.2 5.3 5.4 5.5 Introduction (pg 30) Experimental Details (pg 30) Analysis of the ν6, and 2ν9 Dyad (pg 33) The ν5 Band (pg 49) Improved Rovibrational Constants for the ν3 Band (pg 58) CHAPTER ANALYSIS OF FTIR SPECTRA OF THE ν2, AND ν3 BANDS OF DCOOH 6.1 6.2 6.3 6.4 Introduction (pg 63) Experimental Details (pg 63) Analysis of the ν2 Band (pg 65) Analysis of the ν3 Band (pg 78) CHAPTER FTIR SPECTRA OF THE ν4, AND ν1 BANDS OF DCOOD 7.1 7.2 7.3 7.4 Introduction (pg 84) Experimental Details (pg 85) The ν4 Band (pg 87) The Weak ν1 Band (pg 93) CHAPTER ANALYSIS OF THE HIGH-RESOLUTION FTIR SPECTRUM OF THE ν6 BAND OF H13COOH 18.1 18.2 18.3 Introduction (pg 99) Experimental Details (pg 99) Analysis (pg 100) CHAPTER THE HIGH-RESOLUTION FTIR SPECTRA OF THE ν12, ν11, AND ν9 BANDS OF ETHYLENE-d4 (C2D4) 9.1 9.2 9.3 9.4 9.5 9.6 The ν12 Band – Introduction (pg 108) Experiment Details of ν12 (pg 109) The ν12 Band – Results and Analysis (pg 110) The ν11 Band – Introduction (pg 119) Experimental Details of ν11 (pg 121) The ν11 Band – Analysis and Results (pg 122) 9.7 9.8 The ν9 Band – Introduction and Experiment (pg 131) Assignment, Analysis and Discussion of ν9 (pg 133) CHAPTER 10 ANALYSIS OF THE CORIOLIS INTERACTIONS OF THE ν12 BAND WITH 2ν10 OF cis-d2-Ethylene, AND THE ν12 BAND OF Ethylene-13C BY HIGH-RESOLUTION FTIR SPECTROSCOPY 10.1 10.2 10.3 10.4 Introduction (pg 143) Experiment (pg 144) Analysis and Results (pg 145) The ν12 Band of Ethylene-13C (pg 153) CHAPTER 11 ANALYSIS OF THE CORIOLIS INTERACTIONS BETWEEN THE ν7, ν9, AND ν3 BANDS OF METHYLENE FLUORIDE-d2 (CD2F2) 11.1 11.2 11.3 11.4 11.5 The ν7, and ν9 Bands – Introduction (pg 158) Experimental Details (pg 160) Analysis of the Bands, Results, and Discussion (pg 161) The Coriolis Interaction between the ν9, and ν3 Bands (pg 171) Observations on the ν8, and ν2 Bands of CD2F2 (pg 179) CHAPTER 12 HIGH RESOLUTION FTIR SPECTROSCOPY OF THE ν6 FUNDAMENTAL OF METHYLENE FLUORIDE-d2 12.1 12.2 Introduction and Experimental Details (pg 186) Analysis and Results (pg 187) CHAPTER 13 CONCLUSION 13.1 13.2 Conclusion (pg 194) Proposal for Future Research – High Resolution Experimental Studies on Reactive Molecules (pg 195) REFERENCES (pg 197) CHAPTER - FOURIER TRANSFORM SPECTROSCOPY 1.1 Michelson Interferometer The underlying principle of Fourier transform spectroscopy is the Michelson interferometer In Fig 1.1, a schematic diagram of the Michelson interferometer is shown Moving mirror Fixed mirror Source Beamsplitter To detector Fig 1.1 A schematic diagram of the Michelson interferometer The source beam is divided into two by the beamsplitter positioned at an angle of 45o from the incidence One ray goes to the fixed mirror and the other goes to the moving mirror After reflection by the mirrors they are recombined and enter the detector Patterns of interference are produced by the optical path difference in the two beams Zero path difference is obtained when the two mirrors are at equidistance from the beamsplitter The source in our case is the Globar for the mid- and near-infrared spectral region 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 ... (1999) Rovibrational Analysis of ν2 and 2ν5 Bands of DCOOH by High Resolution FTIR Spectroscopy, T L Tan, K L Goh, P P Ong, and H H Teo, Journal of Molecular Spectroscopy 198, 387-392 (1999) High- resolution. .. PUBLICATIONS High- Resolution FTIR Spectrum of the ν5 Band of HCOOD, K L Goh, P P Ong, T L Tan, H H Teo, and W F Wang, Journal of Molecular Spectroscopy 191, 343347 (1998) Analysis of High- Resolution FTIR. .. CHAPTER ANALYSIS OF THE HIGH- RESOLUTION FTIR SPECTRUM OF THE ν6 BAND OF H13COOH 18.1 18.2 18.3 Introduction (pg 99) Experimental Details (pg 99) Analysis (pg 100) CHAPTER THE HIGH- RESOLUTION FTIR