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Molecular spectroscopy of ionic and neutral species in the gas phase Cramb, David Thomas 1990

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M O L E C U L A R SPECTROSCOPY OF IONIC AND N E U T R A L SPECIES IN THE GAS PHASE By David Thomas Cramb B. Sc. (Chemistry) University of British Columbia A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1990 © David Thomas Cramb, 1990 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 The University of British Columbia Vancouver, Canada DE-6 (2/88) A b s t r a c t This thesis details the analyses of high resolution visible, infrared, and microwave spectra of gas phase ionic and neutral molecules. The visible and infrared spectra of several ions were measured using velocity modulation spectrometers developed in the present work. In each case the ions were generated in an electric discharge plasma. The microwave spectrum of vinyl iodide, CH2=CHI, has been extensively measured and anal-ysed. Visible Spectroscopy using Velocity Modulation: The (6,1) and (13,6) vibrational bands of the A2Iiu — X2T,+ electronic transition of have been recorded in absorption at Doppler limited resolution. The rotational fine structure was fitted by least squares to standard expressions. The rotational and translational temperatures have been measured and indicate an equilibrium between translational and rotational motion in the He/N 2 plasma. Infrared Spectroscopy using Velocity Modulation: The infrared spectra of H C O + , , HeD + , and N 2 have been observed. Two previously unmeasured lines of the v$ band of H C O + and several previously measured lines of the v<i band of H 3 were used to adjust the spectrometer for maximum sensitivity. A new line in the rotational fine structure of the v = 1 <— 0 band of HeD + was analysed using standard expressions. The rotational fine structure of the (2,5) vibrational band of the A2HU — ^ 2 S+ electronic transition of N 2 has been recorded and analysed in the region 2125 - 2205 cm - 1 . Using the vibra-tional origin, T 2 I5, obtained from this analysis combined with the origins, T 6 ) i and Ti3,6, 11 obtained from the analyses of the visible spectra of , it was possible to determine third order equilibrium vibrational coefficients for both the X2Y,+ and A 2IIU states. Microwave Spectroscopy: The microwave spectrum of vinyl iodide, in its ground and first excited vibrational states, has been measured in the frequency range 20 - 108 GHz. The spectrum contains strong a-type transitions and very weak 6-type transitions; all contain 1 2 7 I quadrupole hyperfine structure, with several large perturbations. A procedure spe-cially devised for analysis of such spectra, which takes advantage of the perturbations, was applied to produce accurate values of constants that are otherwise unobtainable, and have permitted assignment of some 6-type transitions. Also, as a result of this procedure, it was possible to measure both components of the dipole moment with relative ease. The centrifugal distortion constants and inertial defects have been compared with those cal-culated from a published harmonic force field, modified for the out-of-plane vibrations. A partial structure has been obtained. in Table of Contents Abstract 1 1 List of Tables vii List of Figures ix Acknowledgement xi 1 Introduction 1 1.1 Background on the Chemistry and Spectroscopy of Molecular Ions . . . . 3 1.2 A Brief Background of Microwave Spectroscopy . 7 1.3 Introduction to Rotational, Vibrational, and Electronic Spectroscopy . . 9 1.4 Bibliography 14 2 The Visible and Infrared Velocity Modulation Spectrometers 17 2.1 Anatomy of a Discharge 17 2.2 The Technique of Velocity Modulation (as a special case of frequency mod-ulation) 20 2.3 The Visible Velocity Modulation Spectrometer 28 2.4 The Infrared Velocity Modulation Spectrometer 33 2.5 Bibliography 40 3 Observation and Analysis of the Spectra of Molecular Ions using Ve-locity Modulation 42 iv 3.1 Introduction 42 3.2 The Visible Electronic Spectrum of 43 3.2.1 Introduction 43 3.2.2 He / N 2 Plasma Chemistry 45 3.2.3 Theoretical Considerations 47 3.2.4 Least Squares Fitting Procedure 58 3.2.5 Observed Spectra and Analysis 61 3.3 The Infrared Spectra of Molecular Ions 71 3.3.1 Introduction 71 3.3.2 Observation of the Infrared Spectra of HCO+ and 72 3.3.3 Consequences of the Observation of the Infrared Spectrum of HeD + . 78-3.3.4 The Infrared Electronic Spectrum of N^ " 85 3.4 The Future 92 3.5 Bibliography 93 4 The Microwave Spectrum and Dipole Moment of Vinyl Iodide, CH 2 CHI 100 4.1 Introduction 100 4.2 Experimental Procedures 102 4.3 Observed Spectrum and Analysis 106 4.3.1 Theoretical considerations 106 4.3.2 Analysis of the Spectrum 115 4.3.3 Discussion of Derived Constants 128 4.3.4 The Structure of Vinyl Iodide . . . 130 4.4 The Dipole Moment 137 4.5 The Future 142 v 4.6 Bibliography • 144 Appendices 148 A A Reprint of a Report of the Microwave Spectrum of Chlorodifiuo-romethane. 148 B A Reprint of a Report of the Microwave Spectrum of Propargyl Bro-mide. 163 C A Listing of Unassigned Ion Lines in the 18400 cm - 1 Region. 171 vi List of Tables 2.1 The fitted values of parameters from equation 2.18 38 3.1 Observed transitions of the (6,1) and (13,6) bands of the A-X system of 63 3.2 Molecular constants for the (6,1) and (13,6) bands of the A - X system of N+ 66 3.3 Observed transitions of the fundamental vibration of HeD + . 83 3.4 Molecular constants of HeD + 84 3.5 Observed transitions of the (2,5) band of the A - X system of Nj 88 3.6 Molecular constants for the (2,5) band of the A-X system of 89 3.7 Equihbrium molecular constants for the A and X states of NJ. 91 4.1 Measured rotational transitions of Vinyl Iodide 120 4.2 Spectroscopic constants of CH 2=CH 1 2 71 127 4.3 Correlation coefficients 128 4.4 Predicted and observed centrifugal distortion constants of vinyl iodide. . 132 4.5 The harmonic force field of vinyl iodide 133 4.6 Structural parameters of vinyl iodide and related compounds 135 4.7 Principal values of the 1 2 7 I quadrupole coupling tensor 136 4.8 Dipole moment of the vinyl halides 142 C.l Observed transitions in the 18400 cm - 1 region 172 vii List of Figures 1.1 A schematic illustration of the oxygen and nitrogen chemistry of the iono-sphere 4 2.1 The anatomy of a glow discharge 18 2.2 A plot of a Gaussian line-shape and its first and second derivatives 23 2.3 The temporal variation of E and N in an ac glow discharge 25 2.4 The demodulated veloctiy modulated and population modulated ion line-shapes 26 2.5 The visible velocity modulation spectrometer 30 2.6 The infrared velocity modulation spectrometer 34 2.7 The schematic function of a diode laser 35 2.8 The tuning function of a tunable infrared diode laser 35 2.9 A fit to the etalon fringe pattern 39 3.1 The molecular orbitals of 48 3.2 The potential energy curves of .• 49 3.3 Hund's case (a) coupling scheme 50 3.4 Hund's case (b) coupling scheme 51 3.5 A pictorial representation of the A - doubling effect. 56 3.6 Energy levels and transitions of 58 3.7 A depiction of the second difference method of assigning spectra 62 3.8 A portion of the (13,6) band of the A - X system of N j , near 18414 cm '. 65 Vlll 3.9 A Boltzmann plot for the Qn branch of the (13,6) band of the A • X system of N 2 68 3.10 Plots of the infrared spectra observed in a H2/CO discharge 74 3.11 The infrared spectrum observed in a pure H2 discharge 76 3.12 H3 signal in a discharge with various mixtures of He and H 2 78 3.13 The infrared spectrum of HeD + 80 3.14 The R n branch head of the (2,5) band of the A - X system of Nj 87 3.15 The Qn branch head of the (2,5) band of the A - X system of Nj . . . . 90 4.1 The Stark modulated microwave spectrometer 103 4.2 Rotational energy levels of vinyl iodide 117 4.3 A portion of the microwave spectrum of vinyl iodide 118 4.4 The transition 112,9 «- 102,8 of CH 2=CH 1 2 71 129 4.5 The positions of the atoms of vinyl iodide in its principal axis system. . . 137 4.6 A plot of the Stark shift Astark vs. E2 of the \MF\ = 1/2 component of the transition F = 5/2 <— 3/2 of 5i,5 <- 4 M 141 4.7 Stark components of the transition 7ij <— 61,6 • • • 141 ix Acknowledgement There are many people who have enriched my life over the last five years; I thank them all. Some of these people have made major contributions to this work and deserve to be singled out. First of all I thank my boss and friend Dr. Mike Gerry. With his help and encouragement I have learned much about high resolution molecular spectroscopy. I am especially grateful for the latitude he has allowed me in my choice of research topics. There are several other professors which I would also like to acknowledge. Dr. An-thony Merer was always willing to talk matrix elements with me. I also thank him for taking the time to write many reference letters. Dr. Irving Ozier has been great help in the diode laser experiments. His numerous suggestions about electrical pickup, and spectroscopy in general have stimulated me to try many different approaches to solve various problems. I thank Dr. Bill Dalby for always popping into the ion factory to see if I had improved my signal to noise ratio by a factor of 1000. I'm still trying ! The great times had with the Boomers volleyball team I owe to Dr. Chris Orvig. It seems like the high resolution spectroscopy group always pulls in great post docs. I thank Dr. Allan Adam for his friendship and all his help in the first experiments; especially for showing me how to turn an A r + ion laser into a geyser. All I know about the Bloch equations and about blocks in general I owe to the influence of Dr. Wolfgang Jager. See you in Europe ! I thank Dr. Wyn Lewis-Bevan for encouraging me to become computer friendly. I greatly appreciate Dr. Wing Ho for critically reading chapter 2 of this thesis and for many discussions on the subject of plasma chemistry. Without the help of Chris Chan, I doubt that the ion experiments would ever have worked. The number of little black electronics boxes he built for these experiments is immeasurable. x I am probably not alone in considering him an honorary postdoc. I thank Dinie for showing me how to convert the Hellman-Feynman theorem into reality. The Free Radicals, Walt, Ian, Pete and Jim are acknowledged as a source of great times and sore ears. I would especially like to thank Jim for his speedy fingers, Thursday nights, and close friendship. Darryl, Trev, Kenny, and Gord, aka the treefort gang, have provided me with many distractions over the past five years. I thank them in particular for the esoteric times at long beach. With respect to the ion experiment, I thank Drs. Rich Saykally, Mike Radunsky, and Mark Polak for a very informative and warm week spent at Berkeley. Financial help from the Natural Sciences and Engineering Council of Canada in the form of a scholarship and from the University of British Columbia in the form of A Graduate Fellowship are greatfully acknowledged. Without the unquestioning support of my parents, this work would not have been possible. It is to them that this thesis is dedicated. Lastly, I thank Patti. Her patience has no bounds. xi Chapter 1 Introduction Molecular spectroscopy is the branch of chemistry and physics concerned with the absorption and emission of electromagnetic radiation by molecules, ions, and free rad-icals. The electromagnetic spectrum of any of the above species can be thought of as a "finger print" which contains information particular to that species. The first step toward extracting this information is to reduce the large data set (the spectrum) to a smaller data set (the molecular constants) which will accurately reproduce the spectrum. The molecular constants provide insight into the electronic and nuclear structure of the species, and can provide information about the medium in which the species exists. As will be discussed later in this chapter, the energy levels of molecules are usually discussed in three categories, namely rotational (energy, Er), vibrational (energy, Ev), and electronic (energy, Ee) levels, with Er < C Ev < C Ee. Transitions between these levels occur in general (though by no means rigorously) in three spectral regions, which are associated, respectively, with three branches of spectroscopy. 1. Microwave spectroscopy is usually concerned with pure rotational transitions within a particular electronic and vibrational state. It provides information on molecular structure and bonding in that state. The frequency range is roughly 2-600 GHz (0.067 - 20 cm"1). 1 2. Infrared spectroscopy is generally concerned with simultaneous vibrational and ro-tational transitions in a particular electronic state. Thus infrared spectroscopy also provides molecular structure and bonding information. Also, important infor-mation about thermodynamic properties such as heat capacities and dissociation energies can be obtained from an infrared spectrum. The wavenumber range is roughly 30 - 4000 cm"1 (900 - 120,000 GHz). 3. Visible and ultraviolet (UV) spectroscopy is usually concerned with simultaneous changes in electronic, vibrational, and rotational state. The wavenumber region is roughly above 4000 cm - 1 (frequencies > 120,000 GHz)1. Visible-UV spectroscopy can provide all of the previous information, but this time in several electronic states. The work presented in this thesis covers all three frequency ranges, and transitions of all three types have been measured. There have been two basic approaches. Firstly, two "velocity modulation" spectrometers have been developed to measure the spectra of gaseous molecular ions, with the first being used to study the visible spectrum of N 2 , and the second being used to study the infrared spectra of N 2 , HeD + , H C O + , and H3 . The design and function of the spectrometers are presented in Chapter 2. The observation and analysis of the spectra of these molecular ions, presented in Chapter 3, have provided accurate molecular constants and some insight into electric discharge dynamics. Secondly, the microwave spectrum of vinyl iodide has been investigated using a conventional "Stark modulation" technique. The analysis has followed a general theme recently developed in this research group where perturbations in the nuclear electric quadrupole hyperfine structure of microwave spectra are exploited to yield otherwise unobtainable molecular constants. Through this work, which is presented in Chapter 4, it has been possible 1The c m - 1 (wavenumber) units are more commonly used in infrared and visible-UV spectroscopy because the frequency units become quite cumbersome in these regions and also because wavelength standards are historically more accessible. 2 to obtain rotational, centrifugal distortion, and 1 2 7 I quadrupole coupling constants of vinyl iodide, to measure its dipole moment, and to obtain some structural and bonding information. Appendices A and B contain reprints of two further papers, co-authored by the author of this thesis during the course of his Ph. D. studies. Appendix C contains a list of unassigned ion lines measured in the 18500 cm - 1 region. The next two sections of this chapter are presented in order to give the reader an idea of the type of problems which have been solved during the development of the spectroscopic techniques adopted in this thesis. The final section will introduce some of the general formalisms essential for understanding how rotational, vibrational, and electronic spectra arise and will show the connection between them. 1.1 Background on the Chemistry and Spectroscopy of Molecular Ions Molecular spectroscopy has helped to elucidate the role molecular ions play in upper planetary atmospheres, aurorae, comet tails, electric discharges, flames, the interstellar medium, and as reactive intermediates in more conventional chemical systems. Any one of the above topics could fill several volumes of text; therefore, this discussion will be limited to the ions studied in the present work, namely NJ, H C O + , H3 , and HeD +, followed by a brief history of the molecular spectroscopy of gaseous ions. The existence of Nj in the upper atmosphere of Earth is well known [1-1]. The role plays in the chemistry of the ionosphere can be seen from Figure 1.1 [1-1]. In fact, the electronic transition studied in the present work, A2UU — X2T,+, was first observed in the emission spectrum of the aurora [1-2]. One of the vibronic levels (X2Y,+, v = 5) of examined in this thesis is known to participate in the resonant reaction [1-1]: 0+ (2D) +N2 (X1^) —+ 0 (3P) + / V 2 + ( X 2 E g V = 5) (1.1) 3 Figure 1.1: A schematic illustration of the oxygen and nitrogen chemistry of the iono-sphere. The asterisks indicate vibrationally excited or translation ally energetic species. 4 which suggests a potential over abundance of in the Ar2£+,t> = 5 state in the iono-sphere. It is believed that ion-molecule reactions are the most efficient mechanism for pro-ducing interstellar molecules [1-3]. The ion H3 is believed to play a crucial role as a protonator through the reaction: #3+ + X HX+ + H2. (1.2) Molecular ions such as H C O + and HNj, which have been observed in the interstellar medium, are mainly produced through this chemical reaction where X = CO and N 2 , respectively. Although Hj has yet to be observed in the interstellar medium [1-4], its infrared spectrum has recently been identified in the Jovian polar aurora [1-5], [1-6]. Interest in HeH + , the parent isotope of HeD +, was first aroused because of the high abundance of hydrogen and helium in the universe. It seems likely that HeH + is formed in some regions of stellar atmospheres or interstellar clouds [1-7]. It has also been suggested [1-8] that HeH + is responsible for some absorption bands observed in the spectra of a number of early type stars. Clearly the role of molecular spectroscopy in the above discussion is very important. With the use of lasers it has been possible to detect gaseous molecular ions with ever-increasing sensitivity. Recently, laser spectroscopy has been applied directly to detect molecular ions in the atmosphere [1-9], [1-10]. It has also been suggested that laser spectroscopy of ions could be a useful tool in the non-intrusive measurement of electric fields and temperature gradients in plasmas [1-11]. The next few paragraphs contain a brief history of the high resolution spectroscopy of molecular ions. The field has gained momentum over the last ten years: presented here are some milestones in its development. For more detail, there are several excellent and more extensive review articles presently in print, of which references [1-12], [1-13], 5 [1-14], and [1-15] are but a few. In 1971, Herzberg [1-16] published a review of the state of ion spectroscopy. At that time the spectra of about forty molecular ions had been studied using either emission or absorption spectroscopy in the visible-UV region. The microwave spectroscopy of molecular ions made its debut in 1973 with the astro-nomical detection of an unidentified millimeter wave transition in the Orion nebula by Buhl and Snyder [1-17]. The unidentified line (named X-ogen by Buhl and Snyder) was identified as H C O + in 1974 [1-18] from measurements of its rotational spectrum in the laboratory. In 1976, using a fast ion beam, Wing and coworkers [1-19] made the first laboratory measurement of the infrared spectrum of a molecular ion, namely H D + . With Oka's observation [1-20] of the ion by direct absorption in a discharge using a tunable infrared difference frequency laser, another substantial advance in the development of molecular ion spectroscopy was made. A few more molecular ions were observed using this technique, but its general applicability was limited by the overlap of the weak absorptions of the ions with the enormously stronger absorptions of neutral molecules2. Gudeman et al. [1-21] overcame this problem in 1983 with the introduction of velocity modulation spectroscopy. This method exploits the motions of charged particles in the electric fields of discharge plasmas to achieve ion selective detection. It is the one which has been used to measure all the molecular ion spectra presented in this thesis. Several groups are presently using velocity modulation spectroscopy to study some fundamental and important molecular ions, such as H30 +, NH4", and H3 [1-12] for example. Detection of anions such as C2 , CCH~, and NJ [1-12] has also been possible using this technique. 2 In many discharge-type experiments the ratio of ionic to neutral species is ~ j ^ j . Ions are depleted mostly by recombination with electrons and collisions with the vessel walls. 6 The high resolution spectroscopy of cluster ions was ushered in with the detection of the microwave spectrum of ArHj in 1987 by Bogey et al. [1-22]. A lower resolution, but very elegant approach to cluster ion spectroscopy has been developed by Okumura, Yeh and Lee [1-23] in which ion clusters are held in an octopole ion trap and exposed to tunable infrared laser radiation, with their transitions being detected by measuring the intensity of the photodissociation product ion with a quadrupole mass spectrometer. Very recently, the Saykally group has introduced direct infrared laser absorption spec-troscopy in fast ion beams [1-12]. This technique has provided a means with which to measure the infrared spectra of molecular ions at sub-Doppler resolution. 1.2 A Brief Background of Microwave Spectroscopy In 1934 Cleeton and Williams [1-24] presented the first observation of a microwave spectrum. Ironically, it involved the study of the ground state inversion spectrum of ammonia, which is not a pure rotational spectrum. The development of radar during World War II provided new instrumentation with which microwave spectroscopy made large advances. Since then, many improvements in microwave technology have expanded the frequency range and have also given considerably better resolution and sensitivity than were previously available. It is interesting to note that the first laser (or more correctly maser) device developed (in 1954) worked in the microwave region at 23.786 GHz [1-25]. The designers took advantage of the same inversion transition of N H 3 mentioned above. Microwave spectroscopy and the Fourier transform were merged in 1974 in the travel-ing wave pulsed microwave experiments first described by Flygare [1-26]. Subsequently, a series of developments has been made by several other groups. Perhaps the most sig-nificant is that of a standing wave instrument into which the sample gas is supersonically 7 injected [1-27]. These spectrometers have provided the highest resolution and sensitivity now available using microwave spectroscopy. Microwave spectroscopy has been used to detect interstellar neutral and ionic species using radio telescopes. A recent review by Saito [1-28] has revealed several new additions to the list of molecules already observed in the interstellar medium. With the help of laboratory microwave observations, it has been possible for radio astronomers to detect exotic species such as CeH, cyclic C3H, and CCS in the Taurus Molecular Cloud 1 (TMC1) [1-28]. Microwave spectroscopy has also been used extensively in the investigation of the structures and potential functions of van der Waals molecules. An excellent example of this is the study of the ammonia dimer by Nelson et al. [1-29]. Ammonia was once thought to be a hydrogen bond donor, but Nelson et al. have shown that this concept is misleading when used as a predictor of the ammonia dimer orientation determined in their work. The latest studies undertaken in the microwave laboratory at the University of British Columbia have involved both stable and unstable molecules. The unstable molecules, largely ketenes, cyanates, and thiocyanates, were generated at the entrance of the mi-crowave cell and pumped rapidly through it [1-30]. The work led to the development of a computational technique, whereby perturbations in the hyperfine structure of microwave spectra of molecules containing nuclei with large nuclear electric quadrupole moments are used to obtain precise values of some previously unavailable constants [1-30]. This method was essential in the study of vinyl iodide presented in this thesis. 8 1.3 Introduction to Rotational, Vibrational, and Electronic Spectroscopy The oscillating electric field of light interacts with the electric dipole moment of a molecule and under the right conditions can induce transitions between the quantized energy levels of the molecule. Using quantum mechanics, it is possible to model and predict the results of these interactions. The quantized energy levels for any molecule are solutions of the time-independent Schrodinger equation3: H $ = E $ (1.3) where tf is a wave function, which is a function of the electronic and nuclear coordinates, and E and Ti. are the energy and Hamiltonian operator associated with the characteristic of the molecule we would like to measure. This equation can be solved exactly only in very rare instances so approximate methods are used in order to understand molecular spectra. The Born-Oppenheimer approximation [1-31] suggests that since the electrons are much lighter than the nuclei, they move faster and adjust instantaneously to the configuration of the nuclei. As a consequence tf may be factored into an electronic part and a nuclear part: tf = tfe *n (1-4) Furthermore, the nuclear part can be factored further into a rotational part and a vibra-tional part, since the nuclei generally vibrate several hundred times during one rotation. Therefore, the total wavefunction can be written: tf = tfetft,tfr (1.5) 3In this thesis the Hamiltonian operator is represented by a script rl. Vector operators and vectors will be represented in boldface (eg. J). Projections of vectors, quantum numbers and eigenvalues will be in italics (eg. J5and Jz). 9 Since equation 1.5 implies dividing up the Hamiltonian: H = We + Hv + Hr (1.6) it follows that the solution of the time-independent Schrodinger equation gives the total energy, E. E = Ee + Ev + Er (1.7) where usually Ee ^> Ev^> Er. Time-dependent perturbation theory [1-32] is used to describe the interaction of ra-diation with matter producing transitions between the above mentioned energy levels. Consider a transition between two states, \m) and \n). The transition is induced via the interaction operator rij\ Hi = -fi • E(t) (1.8) where, in this treatment n is the molecular electric dipole moment and E(t) is the electric vector of radiation of frequency, v. We will limit our discussion to plane polarized light since all the experiments described in this thesis used it. There are two basic criteria which must be met in order for this interaction to produce a transition between states \m) and |n). The first is that, to first order the energy of the radiation, hv, must equal the energy separation of the two levels [1-33]: AE = En - Em = hv (1.9) where h is Planck's constant. The second is that the transition moment, i?„ m , must be non-zero [1-3]: Rnm = JKP ^mdr ± 0 (1.10) where the integral is over all space. Since the field E(t) is defined in a laboratory or space fixed axis system (fixed with respect to the beam of photons) and it is more useful to define fi in terms of a molecule 10 fixed axis system (defined with respect to the positions of the atoms in the molecule), it is necessary to project \l into the molecule fixed system4: V-2 = Y *ZgHg g=a,b,c where \iz is the projection of the dipole moment along the space-fixed Z axis of the photon beam (thus we consider | E(t) | = Ez(t)). §zg is the direction cosine which relates the space fixed Z axis to the a, b, and c principal inertial axes of the molecule. fig is the projection of the molecular dipole moment onto the g principal inertial axis. The right hand side of equation 1.11 can be substituted into equation 1.10 to give, in Dirac bra and ket notation [1-34]: Rnm = {n\ Y $ZoN I m ). (1.12) g=a,b,c If the Born-Oppenheimer approximation holds, Rnm becomes: Rnm — ( K V* \irn\ Y $ZgVg \ (1.13) g=a,b,c Since fig depends on the bond lengths, and hence on the vibrational normal coordi-nates, Qk, it can be expanded as a Taylor series in Qk [1-33]: (1.14) where /z° represents the component of the dipole moment at equilibrium along the molecule fixed g axis, (fg )^o 1S the change of the g component of the dipole moment with respect to the change in the vibrational state \k) with normal coordinate, Qk- Sub-stitution of (1-14) into (1.13) yields: Rnm = ( en |( Vn |( Vn I Y + E Q^) I e - )l Vrn )| Tm ) (1.15) g=a,b,c k vibrations \ 0 4 We consider only one component of \i with respect to the space fixed axis system because we have chosen plane polarized radiation. 11 This is the equation from which most of the selection rules presented in this thesis are obtained. In general, /z° operates on the electronic variables, the Qfc's operate on the normal co-ordinates (vibrations), and the tf^'s operate on the rotational variables. The evaluation of Rnm is slightly different depending on which type of transition one considers. The next three results explain the differences between the three types of molecular spectroscopy from a theoretical point of view: 1. Rotational transitions ( |em) = |e„) and \vm) = \vn) ). Rnm = ( e n |( vn \( rn | E $Zgri°g\em)\vm)\rm) (1.16) g=a,b,c = E ( e « I Ug I em )( vn | vm )( r„ \§Zg | rm ) (1.17)' 9 Thus for Rnm 7^  0 the molecule must possess a permanent dipole moment repre-sented by ( en | fi° | em ) and have non-zero matrix elements ( r„ | <&zg \ rm )• 2. Vibrational transitions (|en) = |em))-Rnm = (en\(vn\(rn\ E E ( Jj7r) Qk I e m )| vm )| r m )(1.18) = E E ( e " I ( | ^ ) I ^  )( Vn\Qk\ Vm )( r„ I $Zg \ Tm > (1.19) The vibrational transition will occur if both ( en | (fg^) 0 I em ) and ( vn \ Qk \ vm ) are non-zero. The direction cosine terms provide the selection rules for the rota-tional fine structure of the vibrational transition. 3. Electronic transitions (|en) ^ |em) ). Rnm is formally the same as for rotational transitions. Rnm = E ( e " I Pi I em ){ Vn \ Vm )( Tn \ §Zg \ rm ) (1.20) 9 12 The term ( en | fi° | em ) is the electronic transition moment, R „ m . The vibrational selection rules depend on the (vn\vm) term, which represents the Franck-Condon overlap factor ( or Franck-Condon overlap integral) [1-34]. Because the two vi-brational states \vn) and \vm) are in different electronic states, the Franck-Condon factor can be non-zero even if vn ^ vm. The magnitude of the Franck-Condon factor depends on the change in the equilibrium positions of the atoms between the two electronic states. The rotational selection rules follow the symmetry properties of | en ) and | em ), which define which component of /x° is active. 13 1.4 Bibliography [1-1] D.G. Torr, in The Photochemistry of Atmospheres, Earth, the Other Planets, and Comets, pp. 164-278, Academic Press, (1985). [1-2] A. Meinel, Astrophys. J. 114, 431 (1953). [1-3] E. Herbst and W. Klemperer, Astrophys. J. 185, 505 (1973). [1-4] T. Oka, Phil. Trans. R. Soc. Lond. A 303, 543 (1981). [1-5] L. Trafton, D.F. Lester, K.L. Thompson, Astrophys. J. 343, L73 (1989). [1-6] P. Drossart, J.-P. Maillard, J. Caldwell, S.J. Kim, J.K.G. Watson, W.A. Majewski, J. Tennyson, S. Miller, S.K. Atreya, J.T. Clark, J.H. White, Jr., and R. Wagener, Nature 340, 539 (1989). [1-7] I. Dabrowski and G. Herzberg, Trans. N.Y. Acad. Sci. 38, 14 (1977). [1-8] T.P. Stecher and J.E. Milligan, Astrophys. J. 136, 1 (1962). [1-9] Topics in Applied Physics Vol 14-' Laser Monitoring of the Atmosphere, E.D. Hinkley, Ed., Springer-Verlag, Berlin (1976). [1-10] Laser Applications in Meteorology and Earth and Atmospheric Remote Sensing, Proc. SPIE, Vol. 1062 (1989). [1-11] M.B. Radunsky and R.J. Saykally, Chem. Phys. Lett. 152, 419 (1988). [1-12] J.V. Coe and R.J. Saykally, in Ion and Cluster Ion Spectroscopy and Structure, J.P. Maier, Ed., Elsevier, (1989). 14 [1-13] T. Amano, Phil. Trans. R. Soc. Lond. A 324, 163 (1988). [1-14] T.J. Sears, J. Chem. Soc. Faraday Trans. 2 83, 111 (1987). [1-15] R.J. Saykally and R.C. Woods, Ann. Rev. Phys. Chem. 32, 403 (1981). [1-16] G. Herzberg, Rev. Chem. Soc. 25, 201 (1971). [1-17] D. Buhl and L. Snyder, Nature 228, 267 (1970). [1-18] R.C. Woods, T.A. Dixon, R.J. Saykally, and P.G. Szanto, Phys. Rev. Lett. 35, 1269 (1975). [1-19] W.H. Wing, G.A. Ruff, W.E. Lamb, and J.J. Spezeski, Phys. Rev. Lett. 36, 1488 (1976). [1-20] T. Oka, Phys. Rev. Lett. 45, 531 (1980). [1-21] CS. Gudeman, M.H. Begemann, J. Pfaff, and R.J. Saykally, Phys. Rev. Lett. 50, 727 (1983). [1-22] M. Bogey, H. Bolvin, C. Demuynck, and J.L. Destombes, Phys. Rev. Lett. 58, 988 (1987). [1-23] M. Okumura, L.I. Yeh, and Y.T. Lee, J. Chem. Phys. 85, 3705 (1985). [1-24] C.E. Cleeton and N.H. Williams, Phys. Rev. 45, 234 (1934). [1-25] J.P. Gordon, H.J. Zeiger, and C.H. Townes, Phys. Rev. 95, 282 (1954). [1-26] W.H. Ekkers and J. Flygare, Rev. Sci. Instrum. 47, 448 (1976). 15 [1-27] S.C. Stinson, Chemical and Engineering News, August 24, 21 (1987). [1-28] S.Saito, Appl. Spectrosc. Rev. 25, 261 (1989-90). [1-29] D.D. Nelson, Jr., G.T. Fraser, and W. Klemperer, Science 238, 1670 (1987). [1-30] M.C.L. Gerry, Can. J. Spectrosc. 34, 77 (1989). [1-31] M. Born and J.R. Oppenheimer, Ann. Physik 84, 457 (1927). [1-32] A. Messiah, Quantum Mechanics, John Wiley and Sons, New York (1958). [1-33] G. Herzberg, Spectra of Diatomic Molecules, Robert E. Krieger Publishing Co., Inc., Malabar, (1989). [1-34] J.M. Hollas, High Resolution Spectroscopy, Butterworth and Co., London, (1982). 16 Chapter 2 The Visible and Infrared Velocity Modulation Spectrometers (Theory and Practice) 2.1 Anatomy of a Discharge A discharge is created when an electric potential between two electrodes induces a cur-rent to flow through a gaseous medium. The various types of discharges are characterized by the measure of current they produce. These are: 1. Townsend discharge, ( IO - 1 0 A < I < IO - 6 A ). 2. Normal glow discharge, ( 10 - 3 A < / < 10_1 A ). 3. Abnormal glow discharge, ( 10_1 A < I < 10 A). 4. Arc discharge, ( 10 A < I ). The glow discharge has been extensively used to create high ion densities in numerous spectroscopic experiments [2-1] and is at the heart of our velocity modulation experiment. It is therefore important to understand the chemistry and physics involved in electric discharge plasmas. The anatomy of a glow discharge is depicted in Figure 2.1 [2-2]. Starting from the cathode, the first region encountered is known as the cathode fall (x = cathode —* a). It is here that electrons are liberated from the cathode by positive ion impact and accelerated by the electric field. The fast moving electrons then enter the negative glow region (x = a —• b). The length of this section is constrained by the mean free path of the electrons 17 Figure 2.1: The anatomy of a glow discharge. X is an arbitrary spatial coordinate. V, E, J e , and J p are the electric potential, field strength, electron current density, and positive ion current density, respectively. For a further description, see text. (a few centimeters in the conditions of a typical velocity modulation discharge). Much ionization takes place here via electron impact with neutral species, thus producing slower secondary electrons. Ion densities as high as 101 4/cm3 can be attained in this part of the discharge [2-3]. The negative glow and positive column of the discharge are separated by the Faraday dark space (x = b —• c). There is little visible emission from this area because the electron energy is too low to excite atoms or molecules. The current in this region is largely a diffusion current [2-2]. The electric field begins to rise again and then becomes constant as we enter the positive column (x = c —• d). Finally, there is a slight voltage drop near the anode which is known as the anode fall region (x = d —+ anode). 18 The positive column covers about 90% of the length of the glow discharge used in our experiment and therefore warrants more detailed discussion. Ions are created here in several ways, namely electron impact, metastable species-molecule (Penning ionization), and ion-molecule reactions: 1. electron impact e~ + A —• A+ + 2e~ (2.1) 2. metastable species-molecule1 A* + B —> B+ A A + e~ (2.2) 3. ion-molecule A+ + B —> C+ + D (2.3) An ion-molecule reaction is usually exothermic and is described by the interaction po-tential [2-4]: v = - £ <«> where a is the polarizability of the molecule, e is the charge of the ion, and r is the distance between the reactants. It then follows that the reaction rate is the Langevin rate [2-4]: i a l 2 kL = 2ne - (2.5) fi is the reduced mass of the reacting pair, ki is ~ 10~9 cm3/sec. It is quite important to note that usually there is no activation energy needed for an ion-molecule reaction to proceed. There are no simple formulae for the rate of the other two ion-generating reactions. 1A metastable species is one in a long-lived (lifetime > 10 3 s) excited electronic state 19 As a result of these reactions in a positive column at 1 Torr pressure, one can expect to create about 1012 ions/cm3 [2-3]. This is smaller than the density in the negative glow region by ~102, but the high electric field found in the positive column is what is essential for velocity modulation. 2.2 The Technique of Velocity Modulation (as a special case of frequency modulation) With a number density of 101 2/cm3 strong electromagnetic radiation absorbers in a path length of 1 m would not be sufficient for a simple, pure absorption experiment to work. This is usually because of the inherent noise in spectrometers. For weak absorptions of electromagnetic radiation passed through a cell of length L filled with an absorbing gas of density N, the transmitted radiation intensity can be estimated by approximating Beer's law as: It{u) = I0(v)[l-1(v)NL] (2.6) where Io(v) is the incident radiation, is the absorption coefficient, and v is the fre-quency of the radiation. If f(u)NL < 0.05, then the absorption could easily be obscured by the inherent noise of the spectrometer. Since we are limited to ion number densities of this order and to a similar path length, it is necessary to use some procedure to recover the absorption signal from the background noise. The technique of velocity modulating the ion signals, developed by Gudeman, Begemann, Pfaff, and Saykally [2-5], is used not only to recover the weak ion absorption signal, but also to ehminate selectively any signal due to the more abundant (xlO4) neutral molecules. Velocity modulation, vm, can be considered a special case of frequency modulation, fm, and since some of the experiments described in this thesis employed frequency modulation, it will be discussed in more depth first. 20 To employ frequency modulation, one must modulate the laser frequency (or any other monochromatic radiation source) at a frequency u;mod, which is large with respect to the scanning rate of the laser frequency. The modulation sweeps the laser periodically from vi - 6u to v\ + 6V. Thus we have the time dependence of the laser frequency described by: v{t) =17+ Sucos(umodt + <f>) (2.7) where F is the mean laser frequency, bv is the modulation amplitude and (f> is the phase of the modulation which is arbitrarily set to zero. Assuming that the intensity of incident radiation does not vary significantly while slowly scanning across an absorption line, the time dependence of IT(V) comes from [2-6]: 7(i/(*)) = 7(F+<Ws(uw<)). (2.8) In the Doppler broadened regime one has Gaussian line-shapes and therefore 7(^ (2)) is approximated by [2-6]: j(v(t)) = exp ln2(u - v0 + 6vcos(umodt))2 (Ai/)' (2.9) which can be substituted into equation 2.6. With some simple algebra we arrive at: In 2(F - vo + 6vcos(u>modt))2 IoW)) ~ h{v{t)) = AI(v(t)) = I0{v(t)) NL exp (A*) 2 (2.10) Here Au is the Doppler half width at half maximum intensity (hwhm) of the Gaussian line profile, and vo is the resonant frequency of the transition. This equation is normalized so that the nonmodulated intensity at the line centre is 1. AI(v(t)) is the signal which 21 a phase synchronous detector (lock-in amplifier) tuned for first harmonic detection will analyse. This is accomplished by electronically subtracting AI(v(t)) during the first half cycle of the modulation from AI(v(t)) during the second half cycle and integrating this difference over the dwell time of the laser scan. If Sv/Av <C 1, this results in a dc output signal from the lock-in amplifier which is the first derivative of the Gaussian intensity profile with respect to the frequency of the laser. The background noise is subtracted out because of its stochastic temporal behaviour. This technique can result in an increase in sensitivity of up to 105. Most lock-in amplifiers also allow for detection at the second harmonic of the modula-tion frequency. The same arguments as for first harmonic detection can be applied except that the lock-in amplifier is now comparing two signals separated in time by one quarter of a modulation cycle. In this case the demodulated signal is the second derivative of the line profile with respect to the laser frequency. A Gaussian profile and its first and second derivatives are shown in Figure 2.2. Velocity modulation exploits the motions of charged particles due to electric fields in plasmas. The ~10 V/cm electric field found in the positive column of a glow discharge induces a drift velocity which can be defined in the low field approximation as [2-7]: vd = Mi E (2.11) where Eis the axial electric field, and Mj is the ionic mobility which is roughly inversely proportional to both pressure and the square root of the mass of the ion. The drift velocity in a positive column is usually 102 — 103 m/sec. If this drift is in the direction of propagation of the radiation any absorption (or emission) will be shifted by: ± SJL = ± « - = ± i o - (2.12) v c where c is the speed of light. The positive or negative Doppler shift depends on whether 22 Intensity A y V finnssinn profile \ S* First derivative \ / (with respect to v) Second derivative \ / (with respect to v) Figure 2.2: A plot of a Gaussian line-shape and its first and second derivatives, v represents frequency. the ions are moving away from or towards the radiation source respectively (the absorp-tion lines are considered to be blue- or red-shifted). Now, if we consider a positive column whose polarity is changing with some frequency LOmoj, any absorption (or emission) line of an ion will be red- or blue-shifted during each half cycle of umoj. Any neutral species will experience no such Doppler shifting of its absorption/emission lines due to the electric field. Assume that the laser frequency v\ is scanned slowly with respect to u>mod, and that there is a transition frequency vq for an ion in a polarity modulated positive column discharge. The intensity of radiation observed by the detector varies as a function of time and laser frequency according to [2-3]: 23 AI{u(t)) = I0LN(t)exp -]n2(ui{t)-v0 + SuG(t)y (2.13) This equation is analogous to the frequency modulation equation (2.10) with the excep-tion of the Nft) term which is the time variation of the ion population in the discharge which will be discussed later. For sinusoidal modulation we choose: G(t) = cos{umodt). (2.14) For the following argument one assumes that the time variation of the electric field, Eft), is a square wave function. Solka et al [2-8] have shown this to be a reasonable assumption. Since the electric field in a positive column is almost independent of current (once the discharge is ignited) Eft) can be represented as shown in Figure 2.3. This figure shows the finite ignition and extinction times of the discharge which depend exponentially (eta,e) on the plasma frequency u>pe [2-9]. The inverse of the plasma frequency is the time, r e, which the electrons take to react to changes in the plasma [2-9]: 1 T, = 9 2 10~8sec (2.15) where n and me are the electron number density and mass respectively. In Figure 2.3 the time domain distance A-B represents the time during which the discharge electric field, Eft), has a constant magnitude. A lock-in amplifier is used to demodulate the first harmonic (If) of the oscillating signal modeled by equation 2.13. It produces a dc signal which is essentially the difference of two Gaussians (hwhm Au) separated from each other by twice their Doppler shift, Su (see Figure 2.4). Since positive and negative ions move in the electric field 180° out of phase, their demodulated profiles are also 180° out of phase. Because neutral species experience no Doppler shift their demodulated signal should always be zero. 24 Figure 2.3: The temporal variation of the electric held, E(x), and ion population, N(x), for one cycle of a polarity modulated discharge. We define x = u>modt. Second harmonic (2f) demodulation exploits the population variation, N(t), of the oscillating discharge. From Figure 2.3 it can be observed that the density of ions oscillates with respect to time. It is perhaps best described starting from the following rate equation for the ions: dN N (2.16) where j is the current density, c is a proportionality constant, and thus aj is the ion production rate, is the rate of depletion due to diffusion to the discharge vessel walls. If one assumes a current density j proportional to sir? (x) where (x = u>moa-t) then [2-8]: 25 Figure 2.4: The demodulated velocity modulated and population modulated line-shapes. 8v is the modulation amplitude and Au is the hwhm of a single (shifted or unshifted) Gaussian profile. xj _ [ 1 + (2awT<ft7/)2 - co52(x) - 2LOmodTdiffsin2(x) ] ^ ^ where nm is some arbitrary normalizing factor and 7^ ,7/ is ~ 10 fis [jdijj ^> T e ) . Consider, once again, Figure 2.3; in the case of If demodulation N(x) — N(x + tt) and therefore there is no dependence of the If line-shape on ion density. Since for 2f demodulation we consider N(x) vs. N(x + f), which are rarely equal, we observe a line-shape dependence on t, i.e. on phase, <f>. As one changes the 2f phase of the lock-in amplifier from <f> to </>+90°, the line-shape changes from a single line to a doublet. This behaviour is rationalized as follows. The single line is due to the finite lifetime of the ion 26 after the extinction of the discharge. This line appears at the zero velocity because the drift velocity of the ions vanishes almost immediately (~10 ns) after the extinction of the discharge [2-8]. The doublet is of course, a result of observing both Doppler shifted components of the ion absorption profile. This doublet is usually distorted in the centre because of the subtraction of the single unshifted line from the doublet by the lock-in amplifier. The result is a line-shape which approximates the second derivative seen in Figure 2.2. If the ion density is changing at twice the modulation frequency (2f) then the density of neutral species must also change at 2f. The difference is that the maximum neutral density occurs 180° out of phase with the maximum ion density. This means that 2f demodulation will also detect neutral species, but the demodulated single line profile will be 180° out of phase with the "Doppler doublet" ion profile. Important experimental work has been done by Gruebele [2-3], Radunsky and Saykally [2-10], Haese, Pan, and Oka [2-11], and Solka et al [2-8], amongst others in order to ex-tract plasma diagnostics from the If and 2f ion line-shapes. A short summary of these is presented here. It can be seen from equation (2.13) that the line profile of a velocity modulated tran-sition contains information on the Doppler shift, Su, and the Doppler width, Au, of the lines due to the ions. These two quantities tell us about the drift velocity, hence ion mobility, and the background temperature in the plasma, respectively. The background temperature, T i r a n s , is extracted from the linewidth with the equation for the Doppler linewidth [2-12]: l n 2 l 2 " i / 0 2N k Tt rans (2.18) c M 27 where Mis the molecular weight, Wis Avogadro's number, k is the Boltzmann constant, u0 is the transition frequency, and c is the speed of light. Often bv and Av are the same order of magnitude and it can be very difficult to sep-arate these two variables. Some authors have had success determining these constants via a least squares fit to the difference of two Gaussian profiles (If line-shape) [2-3],[2-8]. These studies seem to indicate that the Doppler shift is only 0.2 to 0.5 times the hwhm of the transition for molecules heavier than 6 amu. Unfortunately these fits have pro-duced high correlations (~0.99998) between 8v and Av and therefore must be scrutinized carefully [2-3]. The translational temperature of the ions can be defined as: Ttrans — Tneutral "f" Trandom ^neutral (^'^^) where TTand0m is added in because some of the ion drift kinetic energy is converted to random thermal motion via random collisions. It is often observed that Avneutrai < Ai/,on for this reason. 2.3 The Visible Velocity Modulation Spectrometer A diagram of the computer controlled velocity modulation spectrometer used to record the Doppler limited visible absorption spectra of is shown in Figure 2.5. The radiation source was a Coherent CR699-21 ring dye laser, pumped by a Coherent I100-20UV A r + ion laser. For operation in the 17,500 cm - 1 range, rhodamine 6G (R6G) laser dye (Exciton Chemical Corp.) was used, but with the R560 optics in the ring laser to allow operation to the blue of the maximum in the R6G gain curve. Single frequency laser power as high as 600 mW was attained with this configuration. For operation in the 18,500 cm - 1 range, R560 laser dye was used with the same optics. The A r + ion laser pump power was ~6.0 W in each case. A fresh batch of R560, dissolved in ethylene glycol and a 28 trace of methanol, permitted operation of the laser at similar single frequency power to R6G. However, after one day of operation the dye would "die" and produce only ^ of its original power. This problem was alleviated by adding a few drops of concentrated ammonia to the dye mixture, after which, given a few minutes to allow for mixing, the laser power would jump back to its original level. This is believed to be a buffer solution effect. The photochemical decomposition products lower the pH, but the dye works best at high pH. The dye laser output was split into two beams. One beam passed through the dis-charge tube, then through an optical filter/grating combination to separate the back-ground radiation of the discharge from the coherent laser radiation. This beam was then detected by a photodiode, whereas the second beam was sent directly to another photodiode. One signal was electronically subtracted from the other to reduce the broad-band laser amplitude noise. The difference signal was demodulated in two fashions using two Princeton Applied Research 128 lock-in amplifiers. One was set to detect the first harmonic or velocity-modulated signal and the second was set to detect the second har-monic or concentration-modulated signal. Thus it was possible to detect both ionic N* and neutral N 2 absorptions simultaneously. The discharge was driven by a 7-11 kHz sine wave generated by a Wavetek function generator which also sent a T T L reference to both lock-in amplifiers. The sine wave was amplified by a Tecron 7560 power amplifier and stepped up to approximately 2kV peak to peak by either a Triad PR 21 al or P 217 al transformer. The transformers were the factors limiting the applicable discharge frequency. They had been designed to work as step-up transformers (turn ratio ~25 to 1) in the 60 Hz region but by chance are also found to work at higher frequencies [2-13]. However, running the transformers well beyond their specified conditions reduces their lifetime to approximately 160 hours of continuous use. The transformers were air cooled during operation with the use of a 100 cubic feet per minute muffin fan. 29 II Q O t ^ O U t photodiode 2 3* - 90V In B/S I 1 ^ got in 90s out oscillo scope To cup 2 kV T floi In filter photodiode 1 • 3 — • 1-2 o m p grating lock-In 1f 7560 o m p reference Ar + micro vox n computer colibrotion lock-In 2f Figure 2.5: The visible velocity modulation spectrometers with the two discharge cells: I has tantalum cup electrodes mounted in the sidearms of the cell, and II has axially mounted stainless steel tube electrodes and multiple gas inlets. The two standard water-cooled discharge cells used in this spectrometer are depicted in Figure 2.5. The first one was a 1 cm bore and 1 m long water cooled cell with electrodes in the sidearms. These electodes were water-cooled tantalum cups crimped onto tungsten rods. An airtight metal to glass seal was made around the tungsten rod. Tantalum was chosen as the cup material because of its high melting point, 2996 K, and low electron work function, 4.25 eV. The electrode towers were connected to the discharge cell by home-made Cajon-like teflon fittings. This allowed the towers to be removed and the sputtered metal cleaned from their inner surfaces. The positioning of the electrodes meant that the laser beam sampled only the positive column of the glow discharge. 30 The second discharge cell was also 1 cm bore by 1 m long and water-cooled, but in this case the electrodes were mounted axially. The electrodes consisted of | inch stainless steel U-shaped tubes through which cooling water was flowed. The electrodes were held in place in a teflon flange by \ inch Swagelok ferrule fittings and were slightly off-centre so that they did not attenuate the laser radiation. The teflon flanges were themselves sealed with O-rings to the electrode towers. Another difference between cells I and II was that cell II used multiple gas inlets so that new reactants were continually being introduced all along the discharge. This is believed to be a very important feature, especially for production of carbon containing ions [2-14]. For both discharge configurations a high voltage was applied to one electrode and the other was kept at ground potential. The current amplitude and waveform were monitored by using an oscilloscope to measure the voltage drop across an 8 Ct resistor placed in series with the discharge. Both cells were pumped out by a Direct-Torr 10 1/s rotary pump. The reactant gases were premixed before introduction into the discharge by simple diffusion in a Swagelok union-cross fitting. All gases were carried to the discharge cells through \ inch Polyflow tubing. One important feature of the gas delivery system was the incorporation of small plugs of glass wool inserted into the Polyflow tubing just prior to the cell. This "trick" prevented discharge arcs back to the regulators and pressure gauge heads. The discharge also had a tendency to arc down the pump line. However, this did not seem to affect ion production significantly. The pressure in the cell was monitored with a two headed Baratron gauge; one head was specified for the 1-10 Torr range and the other for the 0-1 Torr range. Frequency calibration was provided by the system recently developed by Adam et al. [2-15,2-16]. This was based on a 750 MHz Fabry-Perot etalon whose cavity length was servo-locked to the maximum of a transmission fringe of a stabilized HeNe laser. A 31 portion of the ring laser radiation was passed through this etalon. The wavenumbers of the fringes produced by scanning the laser were given to ± 0.02 cm - 1 by a Burleigh WA20-VIS wavemeter which was calibrated against I2 each day, and which was accurate enough to determine the absolute order number of the fringes. The frequencies of the fringes were then just the order numbers multiplied by the free spectral range, and were accurate to about ± 10 MHz (± 0.0003 cm - 1). Repeated measurements were made of several Doppler-limited lines which resulted in an estimated accuracy of ± 0.005 cm - 1 for the most intense lines, S/N > 5, and ± 0.008 cm - 1 for weaker lines, S/N < 5. The measurement of the position of the weaker lines was limited by baseline drift. The spectrometer was controlled by a Micro Vax II computer via the programme BEAMSCAN. This programme directed the computer to scan the laser frequency and collect four data channels of 4096 points each. The data channels were the If and 2f signals, the 750 MHz etalon fringes, and the 150 MHz etalon fringes (which were used to detect possible laser mode hops). Individual scans were limited in range to ~1 cm - 1 to keep the laser locked in the single frequency mode. Individual scans took approximately 10 minutes to complete. The line centres found in both If and 2f data files were calibrated with a graphics cursor routine adapted for velocity modulation data files. Briefly, the line centres of all transitions in a scan were estimated using the cursor routine. This entered the data point numbers of these line centres (1-4096) into a calibration file. The user then enters the frequency and number of a 750 MHz fringe in the scan. The line centre channel numbers were then converted to frequencies. This procedure employed an equation produced by a previous least squares fit of a polynomial (7th order) in channel number to the 750 MHz etalon fringe pattern. 32 2.4 The Infrared Velocity Modulation Spectrometer The infrared velocity modulation spectrometer was very similar to the visible velocity modulation spectrometer as can be seen by comparing Figures 2.5 and 2.6. The main difference was the infrared radiation source, which was a tunable semiconductor diode laser (TDL). A TDL provides the best combination of coverage and resolution in the mid-infrared (300-2800 cm - 1). Because a diode laser is a solid state device, certain problems were inevitable. In order to understand where these problems (which will be discussed later in this section) came from, we will look at the principles of diode laser operation [2-17]. Consider Figure 2.7 (a) through (c) for the following discussion. Commercially made lead salt diode lasers are widely available for application in the mid-infrared. A PbSi_xSex compound is formed into a p-n junction by molecular beam epitaxy. Lasing results from the application of a bias voltage across the p-n junction. Electrons dropping from the n-type conduction band to the p-type valence band emit photons which induce stimulated emission, which in turn is amplified in the planar resonator formed by the cleaved end faces of the small (~.4 mm) lead salt crystal. The energy of the photons is determined by the band gap energy, which has a gain profile of a 50-100 cm - 1 . To tune the laser frequency all the parameters which determine the band gap may be varied. To produce changes in the laser energy greater than ± 200 cm - 1 , one must actually change the composition of the diode. The only safe way to do this is to acquire a new one. Tuning between resonator modes is achieved by altering the diode temperature (10-70 K). Diodes are housed in the cold head of a closed cycle refrigerator which operates just above liquid helium temperature. By altering the cold head temperature one changes both the resonator length, hence changing the free spectral range, and also the refractive 33 I I 9 m h — ^ 1 I LU LLo»«f control I from Micro Vai I Output lo Micro Vo. Figure 2.6: The infrared velocity modulation spectrometer. It contains: Tunable Diode Laser (TDL), Laser Control Module (LCM), Lock-in Amplifier (LIA), InSb Detector (Det.), Optical Isolator (Opt. Isol.), Plasmaloc PL2 Amplifier (PL2), and Spherical Mirrors Ml - M6. The discharge apparatus and TDL unit are situated on separate tables to reduce electrical pickup at the TDL and detector. index of the medium. In this way, it is possible to find resonator modes over a 100 cm - 1 range. The fine scanning of the laser is done by applying a current ramp to the p-n junction (changing the bias voltage with time). This slightly alters the band gap energy as a func-tion of time. Because the resonator length is not synchronously tuned to the maximum in the gain profile, mode hops occur and limit the continuous single mode tunability to ~1 cm - 1 (see Figure 2.7). A typical infrared diode laser will operate at a cw output of 34 (<0 metol bose (b) conduction electrons active n c (c) cavity modes Figure 2.7: The schematic function of a diode laser, (a) The laser construction, (b) Energy level system with a forward voltage applied, (c) The mode spectrum within the gain profile. c m _ 1 _ 2110 -2105 ~ 2100 " continuous tuning range 100 200 300 400 500 Diode current (mA) Figure 2.8: The tuning function of a tunable infrared diode laser. The laser frequency is tuned by changing the diode current. 35 approximately 100 / iW and a maximum single frequency linewidth of 1 MHz (~0.00003 cm - 1). The reader should refer to Figure 2.6 once again for the following discussion. The TDL (Laser Photonics) used for this work provided a 10% spectral coverage in the 2050-2200 cm - 1 region with typical continuous scanning of ~0.75 cm - 1 . Because of the construc-tion of the resonator cavity, the beam was very divergent as it left the laser and therefore needed to be collimated. The first collimating element in the optical path was an off-axis parabolic mirror. From here the beam passed through a beamsplitter (B/S) which was virtually transparent in the mid-infrared and 50/50 in the visible. This beamsplitter allowed us to superimpose a HeNe laser beam (632.8 nm) onto the infrared beam for op-tical alignment purposes. The continual recoUimation of the infrared beam was achieved by inserting spherical focussing mirrors M1-M6 into the optical path. M2 represents a 6 inch ~F/15 mirror which sent the beam off the optical table and across the lab (5 m) to the discharge apparatus. The beam was sent back to the optical table by M4 (6" F/15). It was then passed through a monochromator which selected a single resonator mode. Finally, the beam was focussed onto a liquid nitrogen cooled Optikon InSb detector. The discharge cell was exactly the same as cell II (Fig. 2.5) used in the visible spectrometer. The gas delivery and pumping systems were also unaltered. The amplifier and transformer, however, were changed. We have incorporated the ENI Inc. Plasmaloc PL2 amplifier and RS816T transformer into the discharge system. The PL2 was designed especially for power delivery (up to 1.6 kW) to an ac discharge. With this system, one could impedence-match the discharge and also alter the discharge frequency over the range 25-125 kHz. Our discharge was driven at 25 kHz, which has been observed to be the best frequency for ion production/detection using the PL2 [2-18]. The current and waveform of the discharge were once again examined by monitoring the voltage drop across an 8 fi resistor in series with the discharge. 36 The integration of a solid state laser and an electric discharge plasma was not an easy one. The most serious problem encountered was that of electrical pickup from the discharge by the TDL and the InSb detector. At best, this pickup resulted in a decreased S/N; at worst, the pickup actually frequency modulated the laser at the discharge fre-quency. The result was that the ability to suppress the absorption signal of the neutral molecules was completely lost. The steps taken towards solving the pickup problem were as follows: 1. Physically moving the discharge off the optical table and across the room. 2. Electrically isolating the detector by using alkali batteries for power, and floating the connection between the detector output and the input of the lock-in amplifier. 3. Installing power line noise filters for the lock-in amplifier. 4. Installing an optical isolator between the reference output of the PL2 and the input of the lock-in amplifier. Also installing 16 optical isolators between the Micro Vax II computer and the D/A converter whose analog output is used to scan the TDL. 5. Using graphite insulated Triacs cable instead of the standard coax cable. 6. Employing a certain degree of "Trial and Error", i.e. plugging and unplugging various power bars, oscilloscopes, etc. The combination of all of the above precautions resulted in a 90% reduction of electrical pickup. However, some pernicious ground loops seem to be unavoidable and were a constant source of consternation in this experiment. The wavenumbers of the observed ion transitions were calibrated in the following manner. The laser was scanned by the Micro Vax II computer programme LASERSCAN. It collected one data file which was 2048 points long. For ion scans, the integration time 37 Table 2.1 parameter value1 a 0.328494(97) d b c 0.025(6) 0.0362(25) 1.464(87) Table 2.1: The fitted values of parameters from equation 2.18. 1 Uncertanties in parentheses are one standard deviation in the units of the last significant figure. varied from 5 minutes to 40 minutes over 1 cm - 1 , depending on the apparent strength of the transition to be recorded. Next, a frequency modulated scan of a neutral reference gas (introduced into the vm cell) was taken with the discharge off. The laser was modulated by applying a small sine function (10 mV) to the TDL. Finally, the vm cell was emptied and an etalon was inserted into the optical path between the monochromator and the detector. The scan with the confocal etalon (Spectra Physics) provided interpolation markers between the reference lines and also revealed mode hops and nonlinearity in scanning rate. It was possible to account for nonlinearity in the scanning rate through fitting an oscillatory function of data point number to the fringe pattern. A subroutine of the computer programme, IONFIND, was developed to do this. It was based on a Gauss-Jordan elimination [2-19] and utilized a graphics cursor routine to fix the data to be included in the fit. The fringe pattern was modelled by: where i is the data point number. The fit typically produced constants and uncertainties as shown in Table 2.1. The phase variation in the fringe pattern was the most important feature for our Y = cos( ax + b sin( cx) + d ) (2.20) 38 ~ 0.01 c m - 1 Figure 2.9: A fit to a portion of the etalon fringe pattern.The data are contained in the continuous line. The cross-hatched circles are the fitted pattern described by the constants from Table 2.1. purposes and therefore the zero crossings of the fringe pattern were given ten times the weight of the extrema. Observed and calculated fringe patterns are shown in Figure 2.9. Using IONFIND the line positions were determined to an accuracy of ± 0.002 cm - 1 . This accuracy was limited by the temperature drift (of the refrigerator system) between the three sequential scans. 39 2.5 Bibliography [2-1] T.J. Sears, J. Chem. Soc, Faraday Trans 2 83, 111 (1987). [2-2] M.J. Druyvenstein and F.M. Penning, Rev. Mod. Phys. 12, 87 (1940). [2-3] M.H.W. Gruebele, Ph.D. Thesis, University of California at Berkeley, (1988). [2-4] G. Gioumousis and D.P. Stevenson, J. Chem. Phys. 29, 294 (1958). [2-5] CS. Gudeman, M.H. Begemann, J. Pfaff, and R.J. Saykally, Phys. Rev. Lett. 50, 727 (1983). [2-6] J. Reid and D. Labrie, Appl. Phys. B26, 203 (1981). [2-7] D.G. Samaras, Theory of Ion Flow Dynamics, Dover Publications Inc., New York, (1971). [2-8] H. Solka, W. Zimmerman, D. Reinert, A. Stahn, A. Dax, and W. Urban, Appl. Phys. B48, 235 (1989). [2-9] J.M. Somerville, in Discharge and Plasma Processes, S.C. Haydon Ed., Department of University Extension, The University of New England, Armidale, N.S.W., Australia, (1964). [2-10] M.B. Radunsky and R.J. Saykally, Chem. Phys. Lett. 152, 419 (1988). [2-11] N.N. Haese, F.-S. Pan, and T. Oka, Phys. Rev. Lett. 50, 1575 (1983). 40 [2-12] W. Gordy and R.L. Cook, in Techniques of Chemistry, 3 r d ed., A. Weissberger, ed., Wiley, New York, Vol.XVIII, (1984). [2-13] R.J. Saykally, private communication. [2-14] M.W. Crofton, M.-F. Jagod, B.D. Rehfuss, and T. Oka, J. Chem. Phys. 86, 3755 (1987). [2-15] A.G. Adam, A.J. Merer, D.M. Steunenberg, M.C.L. Gerry, and I. Ozier, Rev. Sci. Instrum. 60, 1003 (1989). [2-16] D.M. Steunenberg, M. Sc. Thesis, University of British Columbia, (1989). [2-17] W. Demtroder, Laser Spectroscopy, Springer-Verlag, Berlin, (1982). [2-18] W.C. Ho, private communication. [2-19] W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes, Cambridge University Press, (1986). 41 Chapter 3 Observation and Analysis of the Spectra of Molecular Ions using Velocity Modulation 3.1 Introduction Laboratory spectroscopy of molecular ions was first achieved in the 1920's, with mea-surements of the optical emission spectra of Nj , C 0 + , and Oj [3-1], [3-2]. With the advent of tunable lasers it has become possible to do higher sensitivity ion spectroscopy using laser induced fluorescence (LIF) and laser absorption techniques. It is important to stress that one of the greatest difficulties with assigning molecular ion spectra ob-served in a glow discharge is that of differentiating the lines of the ions from those of the more abundant (~ 104 x) neutral species. The technique of velocity modulation takes advantage of the drift velocity of the ions induced by their interaction with the small electric fields (~ 10 V/cm) found in the positive column of a glow discharge [3-3]. As was previously stated in Chapter 2, with the correct experimental arrangement, the drift velocity of the ions results in a Doppler-shift of their transition frequencies with respect to the laser frequency. By alternating the polarity of the electric field, Doppler modula-tion of the transitions of the ions is made possible. Neutral species are not accelerated by an electric field and therefore there is no resultant Doppler-shifting of their transition frequencies. In the previous chapter, the form and function of the velocity modulation spectrom-eters was discussed. The present chapter will deal with the observation and analysis of 42 the Doppler-limited electronic and vibrational spectra of some small molecular ions. Section 3.2 describes the analysis of the A 2IIU - A 2 £ + (6,1) and (13,6) bands of N 2 obtained with the visible velocity modulation spectrometer [3-4]. In that section we take a closer look at N£ ion production, especially the mechanism for populating high vibrational levels of the ground electronic state. An estimate of the rotational and translational temperature of N 2 in the He/N 2 plasma is also presented in that section. Section 3.3 describes some infrared velocity modulation laser spectra of H C O + , H 3 , HeD + , and N 2 . The H C O + and H3 spectra were used to "peak up" the spectrometer for work in the infrared and will be considered first. Next, the observation, assignment, and ramifications of the P(4) (v = 1 <—0) transition of HeD + will be discussed. In the final subsection, the -A2IIU - X2H+ (2,5) band of N 2 , observed in the infrared, will be presented. Finally, future possibilities for experiments using the infrared velocity modulation spectrometer will be proposed in Section 3.4. 3.2 The Visible Electronic Spectrum of 3.2.1 Introduction The electronic spectrum of Nj has been the subject of much investigation. Several papers on the A-X, B-X, C-X, and D-A systems have been recently reviewed by Loftus and Krupenie [3-5]. The spectrum of Njj" was identified in 1924 with the study of the B-X system [3-6]. The A2HU state of N£ was first postulated by Childs [3-7] in 1932 as the source of rotational perturbations in the I?2E+ upper state of the First Negative system, B-X. In 1945 Vegard and Kvifte [3-8] observed some of the vibrational bands of the A-X system in the aurora, but misassigned them as members of the Second Positive system of N 2 , C-B. In 1950 Meinel [3-9] observed and assigned the A2Iiu - X2Y,+ auroral 43 emission bands which now bear his name. The first laboratory study of the Meinel system was accomplished by Dalby and Douglas [3-10], who produced the spectrum in a hollow cathode discharge tube containing a mixture of nitrogen and helium. The A-X system has been subsequently studied in several different ways. Moseley and co-workers [3-11] used charge exchange detection to study the (4,0) and (5,0) bands. Benesch et al. [3-12] observed the (0,0), (1,0), (2,0), (3,0), (3,1), (4,1), and (4,2) bands in emission. Miller et al. [3-13] made a more extensive study of the (4,0) band using LIF in a flowing afterglow. They combined their data with data from the Benesch group to produce ground and excited electronic state constants and a set of equilibrium molecular constants. The A2HU state has also been studied indirectly via deperturbation of the rotational structure of the B-X system [3-14], [3-15], [3-16]. Although powerful, the more commonly used techniques of LIF and emission grating spectroscopy are sometimes limited by overlap of the spectra of ions and neutral species. The intensities of the transitions of neutral molecules can be several orders of magni-tude larger than those of ions because of their Franck-Condon factors or their relative abundances. This is the case with several vibrational bands of the A - X system of where neutral N 2 is much more abundant in a He /N 2 discharge than ions and the overlapping bands of whose First Positive (triplet) system are extremely intense. This problem has recently been alleviated in Saykally's laboratory with the use of velocity modulation spectroscopy [3-17], [3-18], [3-19]. Radunsky and Saykally [3-18] have made an extensive study of the (7,3) band of the A - X system and have shown that velocity modulation is almost essential to suppress the First Positive system of neutral N 2 . This section presents the examination of the (6,1) and (13,6) bands of the A-X sys-tem using conditions very similar to those of the previously mentioned study [3-18]. The velocity modulation spectrometer used in this experiment has been previously described in Chapter 2, Section 2.3. A slightly more detailed description and rationalization of the 44 He/N2 plasma chemistry will be presented in the next subsection. 3.2.2 He / N 2 Plasma Chemistry The velocity modulation discharge conditions were, for the (6,1) band, 10 Torr He and 660 mTorr N 2 , with the PR 21 al transformer driven at 11 kHz to produce a current of 312 mA (discharge cell I, Figure 2.3), and for the (13,6) band, 9.05 Torr He and 330 mTorr N 2 , with the P217 al transformer driven at 7 kHz to produce the same discharge current (discharge cell II, Figure 2.3). The ubiquitous N 2 ion could be produced in a He/N 2 glow discharge in three different ways: 1. Ion-molecule reaction He+ + N2 —> N+ + He + N 60% 1.6xl0"9 cm31 sec [3-20] (3.1) —• N2+ + He 40% where He + is produced either via metastable collisions:1 e" + He —• He* + e~ (3-2) He* + He' —> He+ + e" + He 1.5xl0~9 cm3/sec [3-21] or by electron impact:2 e~ + He —> He+ + 2e~ (3.3) 1The rate of production of metastable He* depends on the excitation cross-section which itself is a function of electron energy. The metastable (23S) state of He lies 19.80 eV above the ground state [3-25]. 2The rate of production of He + and from electron impact depends on the ionization cross-section [3-26]. 45 2. Metastable species-molecule (Penning ionization) He* + N2 —• N2+(B) + He + e~ 40% 6.9x10-" cm? j sec [3 - 22] (3.4) —• N2+(X) + He + e~ 60% 3. Electron impact ionization:2 e~ + N2 — • 7V2+ + 2e- (3.5) Since the number densities of electrons and positive ions in a plasma are, by definition, equal [3-23], we could ask the question, "Why not use an electrical discharge through pure N 2 and rely solely on electron impact ionization to produce N 2 ?". If it were possible to produce the same current (~ 0.5 A) as in a pure He discharge, then this question would be valid. This, however, is not the case. Free electrons exchange energy with other particles via collisions. In the case of a molecule, the energy of the electron can be transferred into its electronic or nuclear degrees of freedom. In the first scenario, the molecule could be excited into a metastable or ionic state. In the second scenario, the molecule could be excited into a different translational, rotational, or vibrational state. It so happens that the second outcome is more probable [3-23]. In fact, depending on the excitation cross-section, up to 90 % of the energy of the free electrons can be converted into vibrational excitation in pure H 2 or N 2 plasmas [3-24]. Since the noble gases have only three translational degrees of freedom, it follows that there is a higher probability of a free electron impact induced transition to a metastable or ionic state. This means that a higher degree of ionization is possible in a noble gas discharge than in a molecular gas discharge [3-23]. The preceding was the rationalization for using a He buffer discharge. This ratio-nalization assumed that most was created via the fast ion-molecule and metastable species-molecule reactions. 46 3.2.3 Theoretical Considerations N2 has 13 electrons which occupy the following orbitals in the X2Y,+ ground state: * e i = (agls)2(auls)2(ag2s)2((Tu2s)2(nu2p)4ag2p (3.6) In the first excited electronic state of N2, i42IIu, one electron has moved from the iru2p molecular orbital into the o~g2p orbital: tte. = (aglS)2(auls)2(ag2s)2(au2s)2(iru2p)3(ag2p)2 (3.7) The notation E or II implies that the molecule has either 0 pr 1 unit of resultant orbital angular momentum, respectively. The superscript 2 represents the spin multiplicity of the state (5=§ therefore 25 + 1 = 2). For diatomic molecules with a centre of symmetry, the g or u subscript (gerade or ungerade) refers to whether the angular part of the electronic wavefunction is symmetric (g) or antisymmetric (u) when the coordinates of all the electrons are replaced by their negatives. The + or - superscript indicates that the electronic wave function either remains the same or changes its sign, for reflection in any plane containing the nuclei. The energy levels of the molecular orbitals of N2 X and A states are represented pictorially in Figure 3.1. The potential energy curves for the first five electronic states of N2 are depicted in Figure 3.2 [3-5]. Before going into more detail, we first need to introduce the angular momentum nomenclature which we will use [3-27]. The angular momentum operators which we will use to describe how electronic and nuclear motion influence the energy levels of our system are: 1. L, Lz - electronic orbital angular momentum and its projection onto the internuclear axis, with quantum numbers L and A, respectively. 2. S, Sz - electronic spin angular momentum and its projection onto the internuclear axis, with quantum numbers 5 and E, respectively. 47 MO AO AO 2p 2 ^ 7 T s 2 P « - n f l 2 P y 2 P l 2p, 2p y < ^ " ^ o, 2D. 2p„ 2 P y TTU 2p x , 7TU 2p y o-u 2s 2s = = = 2s - * r r -o-0 2s cru 1s 1s = = r r = = 1s *-4 a B Is Figure 3.1: The -X" 2 £+ and J4 2 I I u molecular orbitals (MO) of built from the atomic orbitals (AO) of two nitrogen atoms. The circled electron moves to the og2pz orbital to make the A 2 JJ U state. 3. R - nuclear rotational angular momentum, with quantum number R. 4. N - total angular momentum excluding spin, with quantum number N. The vector representation of N is N = R + L 5. J, Jz - total angular momentum and its projection onto the internuclear axis, with quantum numbers J and fi. respectively. The vector representation of J is J = R + L + S For open shell diatomics (e.g. Nj) one can imagine various coupling phenomena taking place between the angular momenta. One needs to choose basis functions which 48 \ C 2 £ « ^ " ' Potential Energy 1 (cm" 1) 40000 -30000 ~ \ /n 20000 -A 2 n u -u s / ° 10000 - A ^ r o.e 1.2 1.6 Internuclear distance (A) Figure 3.2: The potential energy curves of the first five electronic states of NJ. Numbers represent vibrational quanta within a particular electronic state. best represent these phenomena. Hund [3-28] suggested four coupling schemes for this purpose which are known as Hund's coupling cases (a - d). To assign the spectra of NJ we need consider only the first two. Hund's case (a) coupling was chosen to represent the molecular wave functions of NJ in the J4 2 I I u state. It implies, that L and S are strongly coupled to the internuclear axis, that L, S, and J all have well defined components along the internuclear axis (see Figure 3.3), and that J is the resultant of the coupling scheme, J = L + R + S (3.8) The projection of J onto the internuclear axis is fi, where, f2 = A + E. The case (a) wave functions can be represented, in the Dirac ket notation, by a product of an electronic 49 J A mm f -* R \ i ^ \ n i i A \ i I L M H-i i A n s ^ - . J s / Figure 3.3: Hund's case (a) coupling scheme. See text for details. orbital part |(L)A), an electronic spin part |5S), a nuclear vibrational part \v), and a nuclear rotational part \JQ,M) [3-27]: tf(a) = |(I)A) |5E) b) |JfiM) (3.9) L is suppressed because it is well defined only in a system with spherical symmetry (i.e. an atom). The vibrational wavefunction \v) is that for an anharmonic oscillator [3-28]. | JQM) is the symmetric top wavefunction [3-27], where M is the projection of J onto the space fixed Z axis. For our study of we did not consider the effect of external electric or magnetic fields on the energy levels of the molecule so we will drop the M term in this discussion. The set of basis functions from equation 3.9 is a useful starting point in many situations because matrix representations of the operators, L2, J 2 , Jz, S 2, and Sz, consist only of diagonal elements. 5 0 Figure 3.4: Hund's case (b) coupling scheme. See text for details. Sometimes it is more useful to start with a case (b) coupling scheme. The difference is that case (b) represents S more strongly coupled to N than to the internuclear axis. The case (b) coupling scheme is as follows (see Figure 3.4) [3-28]: N = R + L (3.10) J = N + S (3.11) Thus in Dirac ket notation we have: *(6) = \v) \NASJ) (3.12) The case (b) basis functions are almost always used to represent 2 £ electronic states [3-27]. For the ground electronic state of , A"2E+, where the eigenvalue of Lz is zero 51 we can ignore the distinction between R and N , so that the coupling representation is quite simple, N = R (3.13) From equation (3.11) we obtain: J = N ± \ (3.14) The Hamiltonian used to model the ground electronic state included just the rotation, centrifugal distortion, and spin-rotation coupling: 7i(2E+) = £ „ N 2 - D „ N 4 + 7 .S-N. (3.15) For a diatomic molecule [3-28]: Bv(r) = -f- (~2)v (cm-1) (3.16) off cfi rl In equation 3.16 h is Planck's constant, c is the speed of light, // is the reduced mass of the molecule, and (^)v is the mean value of ^ i n the vth vibrational level, where r is the internuclear distance. Because a molecule is not rigid, the value of the rotational constant Bv changes as the molecule rotates. One needs to apply a small N dependent correction, Dv, to the rotational energy levels [3-27]. For a diatomic molecule, this correction can be identified with a perturbation treatment of the matrix elements of B(r) in the following manner [3-27]: D v = (v\B(r)W (v'\B(r)\v) ( J U ? ) v, Ev — Ev> where the sum is over all vibrational states within a particular electronic state of the molecule. 52 The spin-rotation coupling constant results from the magnetic moment of the spinning electron interacting with the magnetic field generated by the rotation of the nuclei. The coupling constant 7„ can be evaluated as follows [3-29]: * - £ E ^ <318> where g is the gyromagnetic ratio, ps is the Bohr magneton ( eh/2me ), eo is the permit-tivity of free space, I is the molecular moment of inertia, h = Zeff,ne is the effective nuclear charge, and r e n is the distance of the electron from the nucleus. The sums are over all electrons and all nuclei. The matrix of Ti ( 2 £ * ) is diagonal in the case (b) basis, with eigenvalues: Fi(N) = BVN{N + 1 ) - DVN2(N + l ) 2 + § 7„ (3.19) F2(N) = BVN(N + 1)-DVN2(N + 1)2-^{N + l) (3.20) where the F\ and F2 labels imply J = N + | and J = N - \, respectively. The J4 2IT u state was modeled with a standard R 2 Hamiltonian including spin-orbit coupling, rotation, and lambda doubling appropriate for a case (a) basis [3-30]: Ti(2Uu) = AVLZSZ + Bv(3 - L - S)2 - Dv{3 - L - S)4 + ±ADlV[(J - L - S)2,LZSZ)+ - |(p„ + 2gv)(J+S+ + J_5_) + iqv{Jl + Jl) (3-21) Av is the spin-orbit coupling constant with An,v its centrifugal distortion correction. [(J — L — S)2,LZSZ]+ represents an anticommutator. 53 AV represents the amount of coupling between the magnetic moment of the spinning electron and the magnetic field generated by the orbital motions of the electrons. This coupling splits a 2II state represented in a case (a) basis into two components labeled according to their value of 0 (fi = A + E = § ; \). AV can be evaluated in a similar manner as the spin-rotation coupling constant [3-29]: ^ = r i S £ ^ r (3-22) AQ,V can be formalized by a perturbation treatment analogous to the one used for DV [3-30]: = w i y ( 3 2 3 ) BV and DV in equation 3.21 are again the rotational and centrifugal distortion constants. The terms in pv and qv represent a A - doubling effect, which can perhaps most easily be described in a pictorial way. As a result of the breakdown of the Born-Oppenheimer approximation, valence electrons can become increasingly decoupled from the nuclei as J increases [3-27]. This means that the electronic orbitals may appear to be smeared out as the molecule rotates. In a non-rotating frame the A = 1 and A = -1 components of L in a 7r orbital are degenerate. When the molecule is rotating the degeneracy is lost and we need to take linear combinations of the A components of L because the orbital of 2II~ has a node in the molecular rotation plane and that of 2IT+ does not. This is represented in Figure 3.5. This means that the 2II+ energy levels interact with 2E+ energy levels, thus shifting both the 2L7+ and 2E+ levels. The wave functions representing the 2IL+ and 2Y1~ states are now represented by Wang combinations of the |A = 1) and |A = —1) states respectively. The + or - again implies that the electronic wave function is symmetric or antisymmetric with respect to reflection in the plane of rotation. We follow the e/f 54 convention of Brown et al. [3-31] and designate that for half integral J values e levels have ( - l ) J -2 parity and f levels ( - l ) J + 2 . This means that our case (a) 2 II basis functions can be represented as Wang combinations of the functions found in equation 3.9 [3-27]:3 |2n,,J,e//) = ^ [ |1) |I - |>\J\M) ± | - 1 ) IH) | J-\M)\ \v) (3.24) |2nf,J,e//) = ^  [ |1) | | | ) \ J\M) ± | - 1) | | - | ) \J-\M) ] \v) (3.25) where we have used the shorthand notation: ¥(a) = |2S+1A|n,,J,e//) (3.26) For a 2 n state, the A - doubling parameters can be defined as [3-27]: , ^ ( 2II,v\ \A v L + \2X±,v>) (^,v'\BvL.|2n,v) * = 2 E I ^ W ^ I ' ( 3 , 8 ) Here the sum is over all vibrational levels of all 2S states. L± are ladder operators which increase or decrease A by 1. The representation of ri(2Tiu), from equation 3.21, in a case (a) basis consists of a 2 x 2 matrix connecting the = | and fi = § states for each value of J whose elements are: <2n,,J,e//|ft|2ni,J,e//) 3 There is also an e/f convention for the case (b) functions of a 2 £ + state. These are based on the convention of Brown ei al. [3-31] for half integral J . The ± parity of the case (b) functions depends on the quantum number 7Y. For N = even both Fi and F2 are + parity and vice versa for 7Y = odd. 55 ( a ) ( b ) S u Planes of nuclear rotation Figure 3.5: A pictoral representation of the A - doubhng effect. In (a), the 7r+ orbital is in the plane of nuclear rotation. If this orbital remains stationary when the nuclei rotate by 90°, the orbital takes on the appearance of a au orbital, (b). This leads to an interaction between the 11+ and S u states and a mutual shifting of energies. In (c), the 7T~ orbital is out of the plane of rotation and therefore does not take on the appearance of a cru orbital when the nuclei rotate, (d). Thus there is no interaction and no resultant energy shift. = Tv-\Av + (Bv-\AD,v)z-D^z2 + z-\)T\{Pv + 2qv){J+\) (3-29) (2n§,J,e// \H\ 2nf,J,e//) = Tv + \Av + (Bv + \AD,v)(z-2)-Dv{z2-Zz + Z) (3.30) (2n*,J,e// \H\ 2ni,J,e//) = -VT^~T [ Bv T Uv(J + |) - 2Dv(z - 1) ] (3.31) 56 where Tv is the vibrational origin and z = (J + \)2-When this 2x2 matrix, H, is diagonalized with the eigenfunctions, U, one obtains the energy levels, E: IT H U = E (3.32) One finds that the electronic state is split into 25 + 1 = 2 components which can be identified by values of fL In an inverted 2II state (i.e. A < 0) one can label the Q = | component as F\ and fi = | as F2 (see Figure 3.6). Transitions induced by electric dipole radiation obey the selection rules [3-31]: A J = 0 e <-> / (3.33) A J = ± 1 e'«-> e / «-» / (3.34) The rotational structure of a 2IT u(a)- 2E^" electronic transition forms twelve different types of branches as depicted in Figure 3.6 [3-28]. P(J), Q(J), and R(J) imply A J = -1 , 0, and +1, respectively, with J being that of the lower electronic state. The shorthand notation used to label a transition is: A JFupPerFlowtr ( Jlower ) such that, for example, a (F\ J = 4.5) <— (F2 J = 3.5), A./V = 0 transition is designated: QR12(3.5). The A./V term is included only when AN ^ AJ. The branch indexing follows the standard rules where A./V = -2, -1, 0, 1, and 2 indicates 0 , P, Q, R, and S-form branches, respectively. 57 N- j - * n i (F 2) 4 3 1 3 i\ 2 ^ 1 I • -f • SR N" J " 3 3 f  3 2i 2 f l 1 0 1 l i : 21 22, "021 • • + • f - - f • -f + — • • + f -+ f + • - f - • + f 22 ' n s (F, ) 2 :4| 4 R,i 11 31 3 :2| 2 1* 1 Pi, ^ , 2 °P, 2 . - F, • - F, 2r,+ Figure 3.6: Energy levels involved in the A 2IIU - X2T,+ transition of N 2 • The splitting of the N" levels of the lower state is due to spin-rotation coupling. The splitting between the tt = ~ and tt = | states results from spin-orbit coupling, while the splitting of individual J' levels in the upper state comes from A - doubling. 3.2.4 Least Squares Fitting Procedure The goal of analysing a molecular spectrum is to reduce a large body of data (the transition frequencies) to a smaller number of parameters which appear in the molecular Hamiltonian matrix. Since the number of data can be immense and its reduction intri-cate, one usually employs a least squares fitting computer programme. This programme will iteratively improve upon the estimated values of the parameters. The first step in designing such a programme is to separate the Hamiltonian into two parts, namely-the 58 molecular parameters (e.g. Bv) and their angular momentum operators (e.g. J2): H = X B (3.35) where X is the matrix of parameters and B is the "skeleton" matrix of the associated angular momentum operators. The energy levels of the system are calculated by diago-nalizing the molecular Hamiltonian as in equation (3.32). A computer programme used to do this calculation would produce the eigenfunctions U, eigenvalues E, and the resid-uals AE, which are the observed minus calculated energies for each data point. We can use these residuals to obtain corrections to our estimated values of the parameters, AX, via the Hellman-Feynman theorem, which states [3-32]: dEi t,„,dTi For a given parameter, X„ dEi ri.TrdH [UJ ( f ^ ) U ] „ dXm dXm = Dim (3.37) The rectangular derivatives matrix D, with elements D i m , gives the dependence of the energy levels on changes in the parameters in the following way: AE — D • AX (3.38) Thus the corrections to the parameters are obtained from: AX = (DT W D ) " 1 • D T W • AE (3.39) The corrections, AX are added to the parameters X and the whole process is repeated until the residuals are reduced to a level comparable to the larger of the experimental 59 accuracy of the data or the limit of the model chosen. W is the data weighting matrix and is usually taken to be diagonal. A measure of how well the given model fits the observed data is defined by the stan-dard deviation, a, which is calculated as follows [3-32]: a = (A(E)T W AE n — m (3.40) where n is the number of data points, m is the number of parameters, and thus n — m is the number of degrees of freedom. In order to estimate the precision of the calculated parameters we need to calculate the variance-covariance matrix, © [3-32]: © = a2 [ D r D] - 1 (3.41) The diagonal element, 0;,, is the variance of parameter i (do not confuse this with the variance that is the square of the standard deviation, a2). The standard error of parameter i is just the square root of the variance 0 „ . The off-diagonal elements 0,j are the covariances between parameters i and j [3-32]. A measure of the degree of interdependence between parameters i and j is the corre-lation, dj. The correlation matrix, C, is calculated with the following equation [3-32]: Cij = ^ — — (3.42) where for i = j, Cij = 1 and for i ^ j, -1 < dj < +1. A value of C t J = ± 1 implies that the parameters i and j cannot be determined independently for a given data set and/or model. 60 For all the work presented in this chapter the models chosen were incorporated into an existing least squares programme by way of a subroutine. This subroutine calculated the elements of the skeleton and derivatives matrices and also read the transition frequencies from an input file and entered them into the data matrix used by the least squares programme. 3.2.5 Observed Spectra and Analysis The Doppler-limited spectra of the (6,1) and (13,6) bands of the A 2IIU - X2Y,+ system of N 2 were recorded in the ranges 17700-17500 cm - 1 and 18510-18310 cm - 1 , respectively. An analysis of rotational structure was carried out using energy level expressions previ-ously discussed. It was possible to assign 62 transitions of the A - X (6,1) band of N 2 using a prediction based on the lower state constants of Miller et al. [3-13] and an extrapolation of published upper state constants. Not all the observed lines belonged to the (6,1) band. The A - X (6,1) spectrum was overlapped by both the (2,6) and (1,5) bands of the B-X system of N 2 . Most of the overlapping B-X (2,6) transitions could be identified because they had been previously assigned by Klynning and Pages [3-14]. It was not originally thought that the vibrational temperature of the plasma would be hot enough for the A - X (13,6) band to be observable, but the chance observation of the B-X (2,6) band suggested that the level, X2H+ v = 6, was sufficiently populated for the (13,6) band to be recorded. The position of the band centre of the A-X (13,6) transition was estimated from the equilibrium vibrational constants and vibrational origins calculated by Miller et al. [3-13]. The band centre was found to be ~10 cm - 1 higher than predicted. A rough calculation of the rotational structure was made using constants from the deperturbation by Gottscho et al. [3-16] of the -B 2 £„, v = 2 level (which is nearly coincident with the A2UU, v = 13 level [3-14], [3-15], [3-16]), together 61 4 i a * 1 1 _L • 4 V | m L U ' »| m » | m ^ m\m » | A 2u ~ Avj-Aiv, ~ Av3—Ay2 ~ Aiv4—Av5 Figure 3.7: A depiction of the second difference (A2i/) method of assigning the rotational structure of spectra. One chooses the transitions suspected to be members of a particular branch, *. To a good approximation, these transitions are part of the same branch if the spacing between consecutive pairs of lines is the same plus or minus a correction, A2v. For example, Ar/ 3 ± A2iv = Av4 and Ai/ 2 , respectively. with their ground state constants. It was possible to assign a portion of the observed derivative-like tracings in this region to the (13,6) band using these prediction and the A2iv or second difference method [3-28]. The second difference method is explained in Figure 3.7. Of the 300 derivative-like line-shapes measured in the 18310 - 18510 cm - 1 region, 87 were assigned to the A - X (13,6) band. A typical scan is shown in Figure 3.8. It is possible that the unassigned lines in this region belong to A - X (9,3) and B-X (4,8) bands of Nj . The assigned transitions for both the (6,1) and (13,6) bands are listed in Table 3.1. In each case, the assignments were confirmed using A 2 F " and A 2 F 2 " combination 62 Table 3.1: Observed transitions (cm-1) of the (6,1) and (13,6) bands of the A8II„-A'2E+ system of •ranch (J-)* Biinri luUul k Orach (J-)* Olliniii l n U < u l b (6.1) band J.5 17601.358° -0.023 2.4 17604.879 0.005 3.5 17607.747 0.010 4.5 17609.990* 0.019 6.5 17612.556 -0.001 7.5 17612.903 -0.010 8.5 17612.655 0.008 9.5 17611.755 -0.008 10.5 17610.257 -0.003 14.5 17596.123 0.003 2.5 17672.355c 0.014 5.5 17669.638 0.003 6.5 17667.976 -0.007 B.5 17662.780c 0.013 9.5 17659.384 -0.008 10.5 17655.496 -0.003 2.5 17683.701° -0.013 4.5 17690.130 -0.001 6.5 17694.535 0.005 7.5 17695.961 -0.008 6.5 17696.895 -0.002 9.5 17697.356° 0.045 10.5 17697.188° -0.022 12.5 17695.445 -0.003 15.5 1768B.877 0.004 16.5 17685.639d 0.017 %, 6.5 17586.024d 0.037 4.5 17592.506 -0.002 5.5 17590.940 0.000 6.5 17588.740 -0.003 7.5 17585.930 0.008 9.5 17578.420 0.004 10.5 17573.735 -0.001 17.5 17523.89) -0.002 Q.. 1.5 17663.885 -0.004 3.5 17657.117d 0.017 4.5 17652.971° 0.014 12.5 17601.619 -0.004 13.5 17592.897 -0.004 14.5 17583.660 0.001 19.5 17529.579 0.002 7.5 17667.957d 0.037 8.5 17665.530d -0.028 10.5 17659:305 0.006 11.5 17655.442d 0.045 10.5 17S31.9874 0.021 13.5 17502.859 -0.004 4.5 17576.217 -0.004 11.5 17531.878° 0.0)1 33.3 17313.059 0.002 14.5 17502.744 0.007 16.5 17480.270° -0.011 1.5 17658.916d -0.017 7.5 17612.757 -0.002 11.5 17571.918 0.002 12.5 17560.438 0.008 2.5 17663.855° -0.012 3.5 17660.684° 0.029 5.5 17652.971d 0.062 2.5 17574.429 -0.005 11.5 17486.338 0.005 13.5 17459.977 -0.008 (13.6) band 1.5 18445.937 -0.004 2.5 1*448.908 0.001 3.5 1*451.170 -0.004 5.5 1*453.594° -0.02* 6.5 1*453.797 0.001 7.5 1*453.285 0.003 9.5 18450.182 -0.004 10.5 16447.584 -0.009 12.5 18440.362 -0.004 13.5 1*435.730 0.003 15.5 1*424.418 o.ooe 16. S 1*417.737 0.001 17.5 18410.402° 0.015 18.5 18402.367 0.001 19.5 16393.671 -0.002 20.5 16384.314 0.003 21.5 1(374.291 0.010 22.5 18363.582 -0.004 7.S 18506.238° -0.017 8.5 18502.476 0.006 9.5 1*498.093 0.004 10.5 1*493.114 0.005 12.5 18481.347 0.000 13.5 1*474.558 -0.002 14.5 18467.174 0.007 15.5 18459.160 -0.008 16.5 1*450.545° -0.013 17.5 16441.332 -0.006 19.5 1*421.050° -0.010 20.5 1*409.997 -0.002 21.5 1(398.315 -0.006 22.5 1*366.031 0.004 10.5 1*4*5.379° 0.044 23.5 1*459.135d -0.028 a Branches labelled according to the convention mentioned in this section. b Residuals are observed - calculated wavenumbers. c Weighted at 0.1, and ^ Weighted at 0.01, based on signal-to-noise ratio. 63 Table 3.1: (continued) liter 9 5 1 * 4 1 4 . 2 2 1 * 0 . 0 2 9 *.3 1 6 5 0 6 . 1 9 6 0 . 0 0 5 1 4 5 1 0 3 7 6 . 5 3 7 * 0 . 0 2 5 9.5 10.5 1 * 5 0 2 . 3 9 0 1 * 4 9 7 . 0 9 4 * • 0 . 0 1 0 - 0 . 0 1 7 1 S M 4 » . o e o 0 . 0 0 8 11.5 1 * 4 9 1 . 0 1 0 * - 0 . 0 1 4 4 5 1 6 4 3 6 . 7 M - 0 . 0 0 1 1 3 .5 1 * 4 6 1 . 2 2 2 * - 0 . 0 2 4 5 5 1 6 4 3 4 . 6 6 7 - 0 . 0 0 5 14.5 1 * 4 7 4 . 4 3 1 * - 0 . 0 2 1 6 5 1 6 4 3 1 . 9 5 6 - 0 . 0 0 4 7 5 1 * 4 2 6 . 5 2 4 - 0 . 0 0 5 T . S 1 * 3 9 9 . 7 0 8 - 0 . 0 0 1 • 5 6 6 4 2 4 . 4 1 6 0 . 0 0 2 9.5 1 * 3 6 3 . S 7 5 - 0 . 0 0 6 9 5 1 6 4 1 9 . 6 0 6 - 0 . 0 0 1 1 1 . 5 1 ( 3 6 4 . 6 8 3 * - 0 . 0 2 6 1 0 5 1 6 4 1 4 . 1 1 6 0 . 0 0 4 U . S 1 * 3 4 3 . 1 0 3 0 . 0 0 4 1 1 5 1 6 4 0 7 . 9 3 6 0 . 0 0 3 1 5 . 5 1 * 1 1 8 . 7 6 6 0 . 0 0 8 1 2 5 1 6 4 0 1 . 0 7 0 0 . 0 0 1 1 3 5 1 8 3 9 3 . 5 2 6 0 . 0 0 5 1.5 1 * 4 3 1 . 3 9 4 * - 0 . 0 4 2 1 4 S 1 * 1 6 5 . 2 9 4 - O . O O 5 * .5 1 * 3 9 9 . 6 S 9 C 0 . 0 1 4 1 5 s 1 * 1 7 6 . 3 9 7 0 . 0 0 1 1 0 . 5 1 * 3 8 3 . S 2 0 * 0 . 0 1 7 1 6 5 1 6 1 * 6 . 8 1 * • 0 . 0 0 5 1 1 . 5 1 * 1 7 4 . 3 8 2 * - 0 . 0 1 6 J S 5 1 * 3 3 4 . 0 5 0 - 0 . 0 0 8 U . S 14.5 1 * 3 6 4 . 6 2 2 1 * 3 4 2 . 9 9 7 0 . 0 1 0 0 . 0 0 6 2 5 1 8 5 0 5 . 6 5 4 • 0 . 0 0 2 1 5 . 5 1 * 3 3 1 . 1 6 1 0 . 0 0 1 3 i 1 8 5 0 1 . 7 9 9 0 . 0 0 0 4. 5 1 8 4 9 7 . 3 6 6 0 . 0 1 1 3 . 5 1 * 4 9 1 . 2 6 9 * 0 . 0 1 9 5 5 1 8 4 9 2 . 3 3 5 0 . 0 1 2 4 . S 1 6 4 8 3 . 8 0 2 0 . 0 0 8 6 5 1 8 4 8 6 . 7 0 1 - 0 . 0 0 2 S . S 1 * 4 7 5 . 7 4 1 e - 0 . 0 1 0 7 5 1 6 4 8 0 . 4 9 8 0 . 0 0 6 e 5 1 8 4 7 3 . 6 9 4 0 . 0 0 4 1 6 . 5 1 * 4 0 9 . 2 7 4 0 . 0 0 5 9 5 1 6 4 6 6 . 2 8 7 - 0 . 0 0 9 1 0 5 1 6 4 5 8 . 3 0 5 - 0 . 0 0 2 7 . 5 1 * 1 7 7 . 6 6 2 - O . O 1 0 1 1 5 1 6 4 4 9 . 7 2 0 - 0 . 0 0 3 6 . 5 1 * 3 6 7 . 2 1 1 * - 0 . 0 2 8 1 2 J 1 6 4 4 0 . 5 5 3 ° 0 . 0 1 3 1 0 . 5 1 * 3 4 3 . * 9 9 * - 0 . 0 1 8 64 Figure 3.8: A portion of the (13,6) band of the A - X system of N 2 , near 18414 cm - 1 . It is shown in trace (b) as a velocity modulation (If) scan: lock-in amplifier sensitivity 10 microvolts, time constant 10 s. Note the partially unsuppressed signals of neutral N 2 , which are also given in trace (c), a population modulation (2f) scan with 2.5 millivolts sensitivity and time constant 1 s. Trace (a) gives the fringes of a 750 MHz stabilized etalon (see chapter 2, section 2.3, for discussion of the etalon). differences (which will be discussed in detail in section 3.3.3). The final constants are given in Table 3.2. The Franck-Condon factor for the (6,1) band is small [3-5] and thus the transition was very weak. It therefore was possible to float the constants only for the A2HU state. The constants for A"2E+ v"=l were held fixed at the values of Miller et al. [3-13]. For the excited state, a series of fits was carried out with fixed values of AD,6- The lowest standard deviation of the fit was obtained with AD,6 — ~ 0.000202 cm - 1 , and this value was retained. For the (13,6) band (which was much stronger than the (6,1) band) a 65 Table 3.2: Molecular constants (cm -1) for the (6,1) and (13,6) bands of the A2Tlu - X2T,+ system of . Parameter (6,1) band (13,6) band T 0 17631.4160(17)° 18476.5659(16) Av -74.6004(17) -74.3443(21) B'v 1.620900(23) 1.484333(94) D'v 0.000005579(65) 0.00000597(21) AD<V -0.0002026 0.0006 qv -0.000394(29) -0.000409(33) P v 0.00544(27) 0.01039(27) B'v' 1.90355c 1.80556(10) D'l 0.000005909c 0.00000676(25) 7„ 0.00863c 0.0074486 standard deviation 0.00468 0.00580 "The numbers in parentheses are one standard deviation in units of the last significant digits given. ^Parameter fixed at this value. cParameter fixed at the value obtained by Miller ei al. [3-13]. similar procedure was used, except that the constants for both states could be floated. The constant 76 was obtained in a similar fashion to Ap^ of the (6,1) band. The constant AD,13 was found to have no effect, and was therefore omitted. The value of the ground electronic state rotational constant, B(X2Y,£ ,v = 6) = 1.80556(10) cm - 1 , compares quite well with that found by Gottscho et al. (1.80578(38) cm - 1) [3-16], though the agreement is less good for the distortion constant D6 (0.00000667(25) cm - 1 compared to 0.00000598(28) cm - 1). The constant 76 was held fixed in both studies. Our value for B(A2TLu,v = 13) is lower than that of Klynning and Pages [3-14] by 0.002 cm - 1 , but we believe our value to be more accurate because we observe the A2Hu(v = 13) state directly, whereas Klynning and Pages arrived at their value from a deperturbation 66 of the A2Iiu - -B2E+ interaction where they did not allow for A - doubling in the A2UU state. We see no evidence of perturbations in our spectra for the values of J assigned. This agrees with the work of Gottscho et al. [3-16], where perturbations are seen only near J = 33.5. It is interesting to note that piz ~ 2 x p6. This is not unreasonable. From Equation 3.26 we know that the parameter pv is inversely dependent on the differences in energy of each of the vibronic 2E+ levels and the vibronic A2UU level of interest. From Figure 3.2, we see that the potential minima for all the 2 £ + states of N2" lie above the potential minimum for the A2HU state. For A2ILU ( v = 6 ) all the interacting vibrational levels of the 2E+ state are higher in energy (the closest being ~6000 cm - 1 away) and therefore each difference contributing to pv has the same sign. However, some of the vibrational levels of B2Yi* Ue below the A2UU ( v — 13 ) level. This means that the denominator in Equation 3.26 can have either a positive or a negative contribution to Pis and furthermore the nearest level, f? 2 £+ ( v = 2 ), lies only 750 cm - 1 below A2ILU ( v = 13 ). It is not clear why the same relative change was not observed for qv. In order to probe the dynamical conditions within the plasma, the rotational and translational temperatures were measured. Several Boltzmann plots were made for different rotational branches of both vibra-tional bands. If we assume that the distribution of molecules in the rotational states is thermal, then the intensity of an absorption line is given by [3-28]: 2 cabs v - g y j ' y ; + Lbs = ^ Sj e »Tr where C„&s is a constant which contains the J independent part of the transition moment, Qr is the rotational state sum, Sj is the Honl-London theoretical intensity factor, and the double prime implies parameters of the ground electronic state. From this equation (3.43) 67 In (l/S) vs. J"(J" + 1) 0.0 J"(J" + 1) / 1 0 2 3.3 Figure 3.9: A Boltzmann plot for the Q n branch of the A-X system of N 2 . I is the measured intensity, S is the Honl-London theoretical intensity, and J" represents the total angular momentum quantum number in the ground electronic state. one obtains: l n * A g + i)fc ( 3. 4 4 ) where A = ln(2C£h,u) and may be considered constant since v varies only slightly over a set of transitions within a given branch. The plots of ln(^) versus J"(J" + 1) produced straight lines whose averaged slopes yielded the rotational temperature, Tr. An example of one of these plots is given in Figure 3.9. The plots produced rotational temperatures of 646 ±45 K for the (6,1) band and 608 ±76 K for (13,6). It has been previously noted that the rotational and translational temperatures in the type of positive column discharge plasma described in this thesis should be nearly equal [3-3]. 68 An estimation of the translational temperature has been calculated from the average Doppler-shifts of the ion absorptions. Using equation (2.18), the average peak to trough width gave a translational temperature of 663 ±78 K for the (6,1) band and 663 ±97 K for (13,6). This temperature implies a drift velocity of ~500 m/s. It must be noted that the Doppler-shift and Doppler-width of the lines due to ions are sometimes inseparable quantities with respect to the lineshape. Thus, the standard deviation is probably greater than the calculated value of ~ ±100 K. The lower limit of the translational temperature can be obtained from the Doppler-widths of the lines of the neutral species. The average hwhm (half width at half maximum intensity) of the neutral N 2 transitions yielded a translational temperature of 410 ±41 K for both vibrational levels. The similarity between rotational and translational temperatures is not surprising because it is well known that it takes only a few collisions to thermalize rotational motion in a He/N 2 plasma [3-34]. It is interesting that the rotational temperatures found in the two different velocity modulation cells are nearly equal. This reflects the fact that the rotational temperature is determined by the power put into the plasma and the thermal conductivity of the gas mixture [3-3]. These two conditions were essentially the same for the observations of both the (6,1) and (13,6) bands. No attempt has been made to estimate the vibrational temperature of the plasma. It is clear, however, that the v = 6 vibrational level of the ground electronic state should not be populated appreciably in thermal equilibrium at a temperature of ~650 K. An attempt will now be made to explain how the v > 6 levels become populated. The vibrational excitation of the X2^ state is complex. There are many processes competing both to populate and to quench N 2 molecules in the X2T,+ state. Let us first recall that, because NJ has no electric dipole allowed vibrational transitions and moreover, since the cross-section for collisional vibrational de-excitation depends on the polarizability of N 2 , which is small, it is difficult to de-excite a vibrationally hot N^ 69 molecule [3-35],[3-36]. Now, we will consider vibrational population enhancement as a result of charge trans-fer reactions: He+ + N2 —• Nf(C) + He+ ~ leV —• N?{B) + He + ~ QeV —+ N+(A) + He + ~ 8eV —> N2+(X) + He+ ~9eV Since the C state tends to predissociate and spontaneous emission from the A state is slow with respect to our discharge cycle we might consider only pathways (b) and (d) [3-37], [3-38]. However, recent experiments have shown that the transition rate between the vibrational levels of the A and A' states of Nj can be vastly increased via collisions with He atoms [3-39],[3-40],[3-41],[3-42]. One of the studies reported that, in the 1 - 10 Torr pressure region, the collisional electronic transition X <— A (6,3) ( n ? 6 < - 3 = 1.5 x 10 - n cm3/s) substantially increases the population of the v = 6 level of the ground electronic state of Nj [3-41]. The B and X states may retain the excess energy from the reactions in equations 3.45 (b) and (d) in the form of vibrational excitation. Also we can assume that Nj molecules in the B state radiatively decay to the X state before any vibrational de-excitation occurs. This means that the A^2£+ state should be at least as vibrationally hot as the - 0 2 £ + state, because the Franck-Condon factors for B — X emission indicate Av = ± 1 transitions are most likely [3-5]. The same principle should hold for the Penning ionization processes, He* + N2 '• —> He + iV2+(/3) + e" + ~ leV (a) (3.46) —+ He + N?{X) + e~ + ~ 4eV (b) It is important to note that at least some of the excess energy could be deposited in the translational motion of the electrons released in these reactions. 70 (a) (b) (c) (d) (3.45) Lastly, it is quite possible that some is made via Penning ionization of N 2 which has been vibrationally excited by electron impact (Eimpact ~10 eV in our discharge) [3-23], and the vibrational distribution of the hot N 2 molecules is transferred to N 2 in the ionization process. It is the author's opinion that this last process is dominant for enhancing the popu-lation high in the vibrational manifold of the electronic states of N 2 . In the future, it may be possible to estimate the vibrational temperature of the He/N 2 plasma from an assignment of the bands of and N 2 overlapping the spectra we have assigned. 3.3 The Infrared Spectra of Molecular Ions 3.3.1 Introduction Section 3.2 of this chapter described the first spectrum of an ion to be recorded at the University of British Columbia using velocity modulation detection, namely the A - X system of N 2 . That study gave us confidence that we could generate and detect molecular ions in the gas phase. A logical extension of velocity modulation in the visible region was to attempt a similar type of experiment in the infrared. The infrared, experiment proved to be quite challenging compared to the visible experiment because of the nature of the lasers involved. As was mentioned in Chapter 2, an infrared diode laser has certain inherent drawbacks because of its solid state construction. It took a great deal of time and thought to overcome these problems. It seemed certain that the major problem was not one of generating ions, but of detecting them. To reiterate from Chapter 2, the ac discharge created substantial elec-tromagnetic fields around itself during operation. The diode laser was affected by these 71 fields. The result of this electrical coupling (either through the air or via power and com-munication cables) was that the diode laser was modulated at the discharge frequency. This meant that signals due to neutral molecules would be detected, at the velocity mod-ulation frequency, with their demodulated signal a first derivative, just like the signals of ions. Thus the ability to discriminate between the signals of ions and neutrals would be lost. The precautions taken to minimize this problem are described in section 2.4 of Chapter 2. 3.3.2 Observation of the Infrared Spectra of HCO+ and . The acquisition of a new InSb detector and a new 2100 cm - 1 laser diode gave us faith that this region would be most fruitful to begin to search for ions. One must always learn to walk first, so H C O + was chosen as a good "peak up" ion. The transitions of H C O + and H 3 reported in this section were used solely for this purpose. All three vibrational bands of HCO+ have been studied previously [3-43], [3-44], [3-45], [3-46], [3-47]. The transition we were interested in was the 1/3 or C-0 stretching fundamental because previous studies [3-46], [3-47] suggested that there should be several lines observable in the 2100 cm - 1 region. The discharge conditions chosen were similar to those used by Gudeman et al. [3-43]. A mixture of ~100 mTorr CO and ~1 Torr H 2 was flowed through the discharge cell described in Chapter 2, section 2.4. To observe the H C O + signal, it was essential to cool the discharge cell with flowing liquid nitrogen. It could be that the by-products of unwanted side reactions, which inhibit H C O + production, were condensed on the walls of the discharge vessel. The peak ion signal was observed with a discharge current and frequency of 180 mA and 25 kHz, respectively. It is believed that H C O + is produced in the positive column of a glow discharge in 72 the following way [3-48]: H2 + e~ — • Ht + 2e~ (a) i f f + # 2 — Hi + H (fe) #3+ + CO — • #C0+ + #2 '(c) H% + CO —» HCO+ + H (<i) Since the proton affinity of CO is higher than that of H 2 , reaction (3.47(c)) is exothermic [3-48]. Figure 3.10 shows the first bona fide infrared-transition of a molecular ion observed with the infrared velocity modulation spectrometer in this laboratory. This previously unmeasured transition is the P(15) line of the v3 = 1<—0 band. The evidence for the assignment of this line was fourfold. Firstly, the measured wavenumber of the transi-tion, (2137.298 cm"1, with respect to a CO calibration spectrum [3-49]) agreed with the wavenumber predicted (2137.2981 cm-1)using the constants of Foster et al. [3-46] to within experimental error (±0.002 cm - 1). Next was the lock-in amplifier phase behaviour (with respect to the discharge phase) of the demodulated signal. Compare Figure 3.10 (a), (b), and (c). The (a) tracing has the demodulated fm signals of both ions and neutral species in the discharge. All the observed transitions in this tracing could be assigned to neutral CO. Tracing (b) is the signal which has been demodulated at the discharge frequency. Here the baseline drift was due to electrical pick up at the laser. Also note that the electrical pick up induced first derivative signals of neutral CO. We also see a suspicious first derivative signal which was not present in scan (a). Tracing (c) is a scan where the pick up has been greatly reduced. The signals due to neutral species have changed phase and look like second derivatives (perhaps the pick up was modulating the laser at half the discharge frequency), but the suspected ion line has maintained its first derivative shape. The discharge chemistry for all three of these scans was exactly the same. The rationalization is as follows. The technique of frequency modulation was not 73 Figure 3.10: The infrared spectrum near 2137 cm - 1 of an H 2 / C 0 discharge.Tracing (a) contains the frequency modulated signal (neutral CO). Tracing (b) contains the velocity modulated signal with discharge induced electrical pick up (HCO + and CO). Tracing (c) is a velocity modulated signal with the pick up greatly reduced. sensitive enough to observe the transition of the ion. However, the more abundant CO transitions could be easily observed. The ion line shows up in tracing (b) because of the increased sensitivity of velocity modulation (vm modulates only the ions; fm modulates ions, neutral species, and the laser noise). The phase change of the signals of CO from tracing (b) and (c) indicate that these signals are pick up induced, whereas the phase stability of the ion line is highly suggestive that this signal was modulated only within the discharge. The third piece of evidence was the greater velocity modulation hne width of the H C O + transition versus those of the CO transitions in scan (b). The indication that the ions had a higher translational temperature than the neutral species is very plausible 74 because of the electric field induced drift velocity of the ions in the positive column. The final confirmation came with the observation and assignment of the R(4) tran-sition of H C O + {vobs = 2198.521 cm"1 vs. u^u = 2198.529 cm"1). The signal of this transition behaved exactly the same as the P(15) transition. The next step in the development of the infrared velocity modulation spectrometer was to employ it in the search for new spectra of molecular ions. Protonated N 2 0 seemed to be very good candidate. The v\ band of protonated N 2 0 had been observed in the 3300 cm - 1 region by Amano [3-50] using a hollow cathode discharge. This ion is isoelectronic with hydrazoic acid, HN3, which is known to have a very strong v2 transition near 2140 cm"1 [3-51], [3-52]. A search for the analogous v2 transition of protonated N 2 0 was made using various combinations of He, H 2 , and N 2 0 with no positive results. The ground state constants of Amano [3-50] did not indicate whether N 2 0 was 0 or N protonated. A microwave study confirmed the constants of Amano but shed no further light on the structure of proto-nated N 2 0 [3-53]. An ab initio prediction of the structure and vibrational frequencies of protonated N 2 0 suggested that the 0 protonated form was about 15 kcal/mol lower in energy [3-54]. This meant that the predicted intensity of the v2 transition of N 2 O H + would be diminished by two orders of magnitude compared with H N 2 0 + , thus making v2 virtually impossible to detect [3-54]. The search for H N 2 0 + was not a complete loss, however, since H3 was serendipitously observed near 2051 cm - 1 . One would indeed ex-pect to make H3 in hydrogen dominated discharges such as those used to search for the infrared spectrum of H N 2 0 + . The infrared spectrum of H 3 was first observed in 1980 by Oka [3-55] and has subse-quently been studied extensively [3-48], [3-56], [3-57], [3-58]. The infrared spectra of D 3 [3-59], [3-60], H2D+ [3-61], [3-62], and D2H+ [3-63], [3-64] also have been exhaustively scrutinized. 75 ~0.1 cm -1 v Figure 3.11: The infrared spectrum observed in a pure H2 discharge. The asterisk in tracing (a) indicates the If (velocity modulated) signal of H3 near 2051.43 cm - 1 . The doublet just below in tracing (b) is a result of both Doppler components present in the 2f (population modulation) scan. Tracing (c) represents the fringe pattern of a ~0.01 cm - 1 free spectral range confocal etalon. The H 3 signal observed in the present work was assigned in the following manner. The wavenumber of a first derivative-like line profile was roughly calibrated against a CO spectrum [3-49] and found to occur at ~2051.43 cm - 1 . This indicated that it was a member of the P branch transitions of the degenerate v2 stretch of H 3 [3-59]. The rather large peak to trough width, 0.018 cm - 1 (3 times that of HCO + ) , implied that this line was generated by a transition of a very light molecule with a high mobility, vd ~1300 m/s. It was possible to calculate the drift velocity for H3 because the large modulation depth, Sf/Au > 1, allowed the two Doppler-shifted components to be completely separated via 2f detection (see Figure 3.11). Also the much narrower absorptions of neutral species (N2O impurities in the cell) are 180° out of phase with the H3 "Doppler-doublet". With 76 the reduced ionic mobility, M 0 , found by Orient [3-65], and the measured drift velocity, it was possible to estimate the axial electric field in our H 2 discharge with the following equation [3-19]: E = 6±JL P 2 7 3 - 1 5 K (3.48) v M0 760 Torr T V ' where P is pressure. Assuming a translational temperature of 500 ±100 K we obtained an electric field strength of 9 ± 2 V/cm in the positive column of the H 3 discharge. Hj is most likely produced via the reactions in equations (3.47(a)) and (3.47(b)). The discharge conditions used to generate the H3 signal shown in Figure 3.11 were, 1.6 Torr H2, with a current of 0.5 A which resulted in the dissipation of 600 Watts in the water-cooled discharge tube. The scan time was ~5 minutes across the 1.2 cm - 1 scan with the lock-in amplifier sensitivity and time constant set to 1 mV and 0.3 s, respectively. Following the arguments proposed in section 3.2, with respect to production enhancement, helium was introduced into a 0.5 Torr H2 discharge to see whether H3 production could be increased. It has been suggested that HeH + production in a He/H2 discharge would lead to an increase in H3 population by way of the following reaction [3-66]: HeH+ + H2 —• He + H+ (3.49) for a low He/H2 mixing ratio. This was not observed. Consider Figure 3.12, which portrays the signal of H3 in a pure H2 discharge, (a), and in several mixtures of He/H2, (b-d). The H 3 signal was substantially diminished upon addition of a 3x fraction of He (no signal was observed with the He/H2 ratio ~ 1). It is possible that even if H3 production was initially enhanced, impurities such as H 2 0 in the commercial grade He gas decreased the H3 population by proton transfer, to make H 3 0 + , for example. The H 3 signal became larger as more He was added, but never reached the original intensity found for the pure H 2 discharge. The diminished signal could have been due, in part, to 77 Figure 3.12: Hj signal resulting from a discharge containing various mixtures of He and H 2 : (a) .5 Torr H 2 . (b) 1.5/.5 Torr He/H 2 ratio, (c) 4.5/.5 Torr He/H 2 ratio, (d) 9.5/.5 He/H 2 ratio. a mobihty reduction in the higher pressure discharge (pHe ~10 Torr). This study led to an interest in the HeH + molecular ion and isotopes thereof. HeH + and HeD + both have vibrational transitions predicted and observed in the spectral region accessible to our spectrometer. The next section presents the results of our study of a He/D 2 discharge plasma. 3.3.3 Consequences of the Observation of the Infrared Spectrum of HeD + . HeH + , the parent isotope of HeD +, was first observed by way of mass spectroscopy in 1925 by Hogness and Ltinn [3-67]. The first spectral measurement of HeH + came much later, when Tolliver, Kyrala, and Wing [3-68] in 1979 reported the observation of five high J P branch transitions of the v = 1«— 0 band and a hot band, v = 2<— 1, using ion-beam 78 laser resonance. Using a similar technique, Carrington et al. [3-69], [3-70] observed the infrared spectra of HeH + and its isotopes near the dissociation limit. Bernath and Amano [3-71] measured transitions using a tunable infrared laser and accurately determined molecular constants for HeH + in the v=0 and u=l states. Blom, Molder, and Filgueira [3-72] employed MOSFET transistors to generate the ac discharge used in their velocity modulation experiment, in which they measured the vibrational fundamental and first hot band of HeH + . Very recently, Crofton, Altman, Haese, and Oka [3-73] reported the observation and analysis of the infrared spectrum of HeH + and its isotopes using velocity modulation. Their study revealed the isotopic dependence of the molecular constants. They also obtained equilibrium constants and isotopically independent parameters, and estimated the dissociation energy, De, to be 16440(22) cm - 1 . Because HeH + and its isotopes are very small and light molecules, they have large rotational constants (HeH+, B ~30 cm - 1 , HeD +, B ~20 cm - 1). This means that the rotational structure of their infrared spectra can be very sparse (~1 line/50 cm - 1). These types of spectra can be very difficult to observe with a diode laser, because of incomplete spectral coverage. As a result of this we were not fortunate enough to observe any HeH+ transitions in the 2100 cm - 1 region. However, we were able to record the previously unmeasured P(4) transition of the v = 1<— 0 band of HeD +. The vibrational spectrum of HeD + was observed in a 25 kHz ac discharge through a mixture of 9.76 Torr He and 0.188 Torr D 2 . The condition for maximum ion production was a discharge current of 400 mA which resulted in a dissipation of 600 Watts in the water-cooled discharge cell. The HeD + spectrum was calibrated against N 20 [3-49], as described in section 2.4 of Chapter 2. The P(4) transition of HeD + is shown in Figure 3.13. 79 H e D + (a) (b) (c) D 3 + DJ ' W ^ O 2134.55334 c m - 1 ~ 0.1 c m - 1 V Figure 3.13: The velocity modulated P(4) transition of the v — 1*— 0 band of HeD +, tracing (a). Tracing (b) and (c) are the N 2 0 spectrum and etalon fringe pattern used to calibrate tracing (a). The molecular ion HeD + was probably generated in our discharge through the reac-tions suggested by Johnsen and Biondi [3-66]. These are: He+ + D2 He + D+ + D (a) He + Dt (6) HeD+ + D (c) (3.50) Dt + He —» HeD+ + D (d) He* + D2 —y HeD+ + D + e~ (3.51) The production of HeD + was very dependent on the partial pressures of He and D 2 . The high He pressure required to generate HeD + seems to agree with the assumption 80 of Johnsen and Biondi [3-66] that (a) dominates reaction (3.50) resulting in large D + production. However, this assumption does not shed any light on the quenching of H 3 mentioned previously in section 3.3.2. The importance of the P(4) v = 1<— 0 transition of HeD + became apparent shortly after recording it. This line has confirmed constants obtained by Crofton et al. [3-73]. In their study they used the standard *E electronic state vibration-rotation Hamiltonian which we will adopt. It is diagonal in a | J, $7 = 0, M) basis with energies: Ev = Tv + BVJ{J+1) - DVJ2{J+1)2 HVJ3{J + 1)3 + LVJ4(J+1)4 (3.52) where Hv and Lv are the sextic and octic centrifugal distortion constants and Tv is the vibrational origin. Tv can be approximated with [3-28]: Tv = To + ue{v + \) - uexe(v+\)2 + ueye(v + \)3 + ... (3.53) where To is the energy of the potential minimum, u>e is the equilibrium harmonic frequency of vibration, i>, and u>exe and uieye are the second and third order equilibrium anharmonic corrections to the potential energy, respectively. The spectrum we have observed was a result of HeD + interacting with electric dipole radiation, thus inducing transitions between the rotational levels of two consecutive vi-brational states in the same electronic state. Thus for a diatomic molecule we have the selection rule A J = ± 1 , i.e. R and P branch transitions [3-28]. In order to obtain reliable constants from the least squares analysis of a spectrum, one must possess at least as many pieces of independent information as parameters to determine, otherwise one risks complete correlation between parameters. There is a simple way to ascertain the amount of independent information available in a set of transitions of a *E molecule. This is to count the number of combination differences [3-28]. 81 Consider the rotational energy levels for any vibrational state of a JE molecule ne-glecting, for now, sextic and octic centrifugal distortion terms. In a two level system, v = 1 and v = 0 say, the transition frequencies have the following dependence on the molecular constants: ETRANSITION = i/o + B 1 ( J ± 1 ) ( ( J ± 1 ) + 1) - D1(J±1)2((J±1) + 1)2 - B0J(J+1) + D0J2(J + 1)2 (3.54) where v0 = Ti — To and + or - indicates R or P branch transitions, respectively. A combination difference is defined as the difference of the measured frequencies of two transitions which share a common level. For example, A2F'(2) = i?(2)-P(2) = 10B1 - 140I?i, (3.55) thus the A2.F'( J) combination differences have no dependence on the ground state con-stants. There are also A 2F"(J) combination differences, which have no dependence on the upper state constants. From equation 3.54 it is clear that to determine B\, Bo, D\, and Do independently one needs four combination differences, two for each vibrational state. Our measured P(4) v = 1<— 0 transition provided the piece of information needed to determine unambiguously the rotational and quartic centrifugal distortion constants for the v = 0 and v = 1 states of HeD +. The assigned frequencies of the v = 1<— 0 band of HeD + are located in Table 3.3. The results of a Hellman-Feynman type least squares analysis of the data are found in Table 3.4. There is a marked improvement in the uncertainty of all the constants which reflects the inclusion of the new information, P(4). Note also that the correlation between D\ and DQ has not changed much as a result of the new datum. In fact, one needs yet another combination difference in order to decouple these two parameters statistically. The sextic and octic centrifugal distortion constants could not be determined 82 Table 3.3: Observed transitions (cm J) of the v = state of HeD + . 1—>0 band in the ground electronic Branch Observed Wavenumber Residual a R(0) 2348.628* -0.002 R(l) 2384.1086 0.002 R(2) 2416.7806 0.001 R(3) 2446.5186 -0.001 R(4) 2473.2026 0.001 R(5) 2496.7036 -0.002 R(6) 2516.9176 -0.001 R(7) 2533.7326 0.000 R(8) 2547.0486 0.000 R(9) 2556.7721 0.002 R(10) 2562.8126 -0.001 P(l) 2269.8126 0.001 P(3) 2181.4326 -0.001 P(4) 2134.017c 0.001 "Residuals are observed - calculated wavenumbers. "Transition measured by Crofton et al. [3-73]. cTransition measured in this work. experimentally, and had to be held fixed to the theoretical values presented by Crofton et al. [3-73] because they produced non-negligible changes in the transition frequencies. As diodes come available we will continue to search for more HeD + and HeH + tran-sitions. Theorists are particularly interested in the breakdown of the Born-Oppenheimer approximation in this simple, light molecule [3-74]. 83 Table 3.4: Molecular constants (cm 1) for the v = 0 —• 1 transition of HeD + in ground electronic state. Parameter This work Crofton et al. vQ 2310.48584(98)6 2310.4859(14) Bx 19.08369(20) 19.08356(51) Di 0.0057564(49) 0.005747(21) Hi 0.00000187c 0.00000187c Lx -0.000000000355c -0.000000000355c B0 20.34920(18) 20.34903(58) D0 0.0058681(64) 0.005847(37) Ho 0.000001266c 0.000001266° L0 -0.000000000345c -0.000000000345° standard deviation 0.0016 0.0019 Coefficients of correlation between the parameters presented in this work Vo 1.000 Bx -0.578 1.000 Dx -0.639 0.917 1.000 Bo -0.328 0.935 0.756 1.000 Do -0.605 0.920 0.998 0.778 "Values found in reference [3-73] *The numbers in parentheses are one standard deviation in units of the last significant digits given. c Parameter held fixed at this value 84 3.3.4 The Infrared Electronic Spectrum of Nj. Velocity modulation spectroscopy has been largely used to examine the vibrational transitions of small molecular cations and anions. Several review papers attest to this [3-3], [3-75], [3-76],[3-77]. There has been only minor application of velocity modulation to study the electronic spectra of molecular ions. The Saykally group have studied the A - X system of N£ and the B - X system of C 0 + [3-17], [3-18], [3-19]; section 3.2 of this chapter has detailed the observation of two more bands of the A - X system of Nj" [3-4]; Das and Farley [3-78] have very recently observed the A2A\ - X2B\ system of B^O 4 -, and Rehfuss et al. [3-79] have analysed three vibrational bands of the A2UU - X2T,g system of C j . The last study is quite interesting in that the A - X system of was observed in the mid-infrared, in the range 2100-3900 cm - 1 , and is the first mid-infrared electronic spectrum to be recorded using velocity modulation. This subsection presents the observation of the A2Tlu - X2Y,+ (2,5) band of near 2150 cm"1. The inspiration for this experiment came from a recent publication by Katayama and Dentamaro [3-42], in which they studied electronic transitions from the A2I1U (v = 3) level to the A'2E+ (v = 6) level of N 2 " induced by inelastic collisions with helium atoms. This process was mentioned earlier in this chapter as a possible means of enhancing X2T,g (v = 6) population. Since electronic transitions induced by electric dipole radiation are governed by similar selection rules to collisionally induced electronic transitions (the difference is that A J « 0 in the collisional scheme [3-42]), it seemed reasonable to expect to observe the infrared electronic spectrum of the A-X system of . If observable, this infrared spectrum could provide useful information for collisional studies, and perhaps furnish clues about any unassigned infrared spectral features found in nitrogen containing discharges. 85 The plausibility of this experiment was evaluated by estimating the absorption inten-sity of the A-X (2,5) transition with respect to the previously observed A-X (6,1) transition with the following equation [3-28]: /nm abs 8TT3 IQ N M T-T~ \Rnr, one Ax (3.56) where Rnm is the electric dipole transition moment between states n and m, and Ax is the path length of the interaction of the radiation with the ions. It was easiest to compare the two bands of interest by taking the ratio of the intensities: 1-2,5 1abs r6,l 1abs R 2,5 -^ 6,1 "2,5 "6,1 (3.57) For our purposes we have assumed IQ'5 = IQ'1 because of the balancing of the higher output power of the visible laser with the higher sensitivity of the InSb infrared detector. We also assumed that the electronic part of the transition moment Rnm did not vary significantly within the A-X transition. Therefore we could approximate Rnm as just the Franck-Condon factor (FCF). Equation 3.57 then becomes: r2,5 1abs 7-6,1 1 abs iVi FCF, 2,5 FCF6A "2,5 "6,1 (3.58) The Franck-Condon factors published by Loftus and Krupenie [3-5] and the measured A - X (6,1) and predicted A - X (2,5) transition frequencies were used to produce the final equation: 7-2,5 1abs 7-6,1 Iabs f x 7.98 (3.59) 86 R„(14.5) R„(16.5) Q 2 2(11-5) v Figure 3.14: The R n branch head of the (2,5) band of the A2H.U - A' 2 £+ system of Nj . tracing (a) is the velocity modulated signal. Tracings (b) and (c) are the N 2 0 reference scan and etalon fringe pattern used to calibrate (a). This equation suggests that one needed only to populate sufficiently the v = 5 level of AT2E+ to produce a spectrum of similar intensity to A - X (6,1). The probability of this was quite high considering that the A"2E+ (v = 6) level had sufficient population to measure the A-X (13,6) in a previous experiment. The band centre of the A 2IIU - AT2E+ (2,5) transition of was predicted using the equilibrium constants of Miller et al. [3-13]. The discharge conditions were initially chosen to be the same as those used to produce the A-X (13,6) band (see section 3.2). The Ru band head of A - X (2,5), observed on the first day of searching, ~2 cm - 1 higher than predicted, is shown in Figure 3.14. The spectrometer used to record the infrared electronic spectrum of N 2 is described 87 Table 3.5: Observed transitions (cm - 1) of the (2,5) band of the A2J1U - A'2E+ system of N+. Branch (J") a Observed Wavenumber Residual 6 Rn 14.5 2188.469 -0.002 16.5 2188.604 -0.007 20.5 2185.368 0.003 ° R 1 2 13.5 2137.066 0.003 Qn 4.5 2151.121° 0.037 5.5 2151.141° 0.045 14.5 2136.933 0.005 Q22 7.5 2203.557 0.006 11.5 2188.701 0.002 15.5 2170.573 -0.002 21.5 2136.905 -0.001 ' P Q 1 2 6.5 2125.283 -0.003 Pn 7.5 2125.216 0.000 P22 3.5 2203.170 -0.002 8.5 2170.726 -0.004 "Branches labelled according to the convention quoted in section 3.2. ^Residuals are observed - calculated wavenumbers. cWeighted at 0.01 based on line blending. in Chapter 2, section 2.4. The discharge conditions were 400 mTorr N2 and 9 Torr of He, with the current set at 625 mA so that 700 Watts were dissipated in the air-cooled discharge tube. The spectrum was recorded in the range 2125-2205 cm - 1 using one laser diode which provided about 10 modes of ~1 cm - 1 width each. Individual scans covering ~1 cm - 1 were collected over a scan time of 5-40 minutes depending on the apparent intensity of the transitions. The transitions were calibrated against N20 [3-49] in the manner described in Chapter 2 section, 2.4, and are accurate to ±0.002 cm - 1 . It was possible to assign 16 transitions of the A - X (2,5) band of Njj" using a prediction 88 Table 3.6: Molecular constants (cm -1) for the (2,5) band of the A2Tlu - X2T,+ system of N 2 +-Parameter This work Previous work ° To 2186.7742(40)6 A2 -74.6319(41) -74.6214(41) B'2 1.69757(18) 1.697305(19) D>2 0.00000615(29) 0.000005830(31) A' -1.00c -1.00(14) Q2 -0.000308c -0.000308(11) P2 0.00487c 0.00487(38) B'l 1.82615(20) 1.825929(70) D'i 0.00000645(32) 0.000006143(60) 75 0.00925(38) 0.0102(21) standard deviation 0.0046 "Parameters for the A7H.U state and A r 2 £ + states found in references [3-16] and [3-13], respec-tively. 6 The numbers in parentheses are one standard deviation in the units of the last significant digits given. c Parameter held fixed at the value found in reference [3-13]. based on the upper state constants of Miller et al. [3-13] and the lower state constants of Gottscho et al. [3-16]. It was difficult to measure the transitions near the Qn branch head because of spectral congestion (see Figure 3.15). The wavenumbers of these transitions were therefore not included in the analysis. The assigned transitions are bsted in Table 3.5. Spectroscopic constants for both vibronic states were obtained by a least squares fit to the observed rotational fine structure. The Hamiltonians used were the same as those used in our analysis of the (6,1) and (13,6) bands of the A-X system of (see section 3.2). The final constants are given in Table 3.6. The floated constants are remarkably well determined considering the limited data set. The A - doubling parameters p2 and 89 QM(4.5) QII(5.5) (a) 1 4 N 1 5 N 1 6 0 2151.69440 c m " (b) 0.1 c m " 1 (c) V Figure 3.15: The Q n branch head of the (2,5) band of the v42IIu - A"2E+ system of NJ. tracing (a) is the velocity modulated signal. Tracings (b) and (c) are the N 2 0 reference and etalon fringe pattern used to calibrate (a). 92, and the centrifugal distortion correction to spin-orbit coupling, AD<2, were held fixed at the values of Miller et al. [3-13]. It can be seen from Table 3.6 that our constants agree very well with those previously determined. It was possible to determine third order equihbrium vibration coefficients [3-80] by a least squares analysis of our three vibrational origins (one infrared and two visible) combined with those of Radunsky and Saykally [3-18] and Miller et al. [3-13]. The results of fitting the constants from equation 3.53 to the vibrational origins are presented in Table 3.7. We believe that these constants are the most accurate to date because our larger data set facilitated the determination of the third order anharmonic terms, ueye, for both electronic states. These terms are very important for predicting A - X band centres of N 2 associated with high vibrational quanta. These new data also provide a more definitive check of ab initio calculations of the potential energy curves of the electronic states of [3-81]. 90 Table 3.7: Equilibrium molecular vibration constants (cm :) for the A2UU and X2Y,+ states of Nj . Parameter This work Miller et al. a A2Ylu T e OJeXe 9167.499(16)b 1903.519(10) 15.0470(18) 0.003654(91) 9167.62 1903.45 15.01 UeXe UeVe 2206.991(17) 16.0499(75) -0.04451(89) 2207.27 16.26 standard deviation 0.0068 "Reference [3-13]. ' 'The numbers in parentheses are one standard deviation in units of the last significant digits given. 91 3.4 The Future. The velocity modulation experiments presented in this thesis have been an important first step in the development of ion spectroscopy at the University of British Columbia. Future experiments will involve a variation on the theme by way of isotopic substi-tution, i.e. ( 1 5 N 1 4 N) + . Isotopic substitution induces a dipole moment in a homonuclear diatomic ion because of the difference between the centres of mass and charge. ( 1 5 N 1 4 N) + therefore has both a pure vibrational spectrum and a pure rotational spectrum . In or-der to conserve 1 5 N 1 4 N , the discharge cell will be modified to work with no gas flow. It is therefore very useful to have the A - X (2,5) transition frequencies available for "peaking-up" the new system. We also now have the knowledge that there will be bands of the A-X system of ( 1 5 N 1 4 N) + overlapped with the pure vibrational spectrum. Other interesting molecules such as HeH + , N 0 + , NOj, and OCS + have also been slated for infrared velocity modulation experiments in the near future. 92 3.5 Bibliography [3-1] W. Wein, Ann. Pkysik., 69, 325 (1922). [3-2] W. Wein, Ann. Physik., 81, 994 (1926). [3-3] CS. Gudemann and R.J. Saykally, Annu. Rev. Phys. Chem. 35 387 (1984). [3-4] D.T. Cramb, A. G. Adam, D.M. Steunenberg, A.J. 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In particular, although ac-curate values of the rotational constants B and C can be obtained from them, only an approximate value, at best, can be obtained for A. Usually the problem is overcome by measuring b- or c-type transitions, but these can be difficult to identify when they are very weak. Our group has recently reported a method whereby in certain cases A can be evaluated accurately from a-type R branches alone, using perturbations in nuclear quadrupole hyperfine structure [4-1], [4-2], [4-3]. It has been applied to the molecules BrNCO [4-1] and INCO [4-2], both of which are planar, for which the off-diagonal component Xab of the halogen quadrupole coupling tensor is large. This constant contributes only in high order to the hyperfine structure; the contributions are especially significant in the presence of certain rotational near-degeneracies. Since such near-degeneracies are functions of all three rotational constants, a global fit to all rotational and quadrupole constants (and also centrifugal distortion constants where necessary) can produce accurate values for A, 1a-, b-, and c-type rotational transitions are induced by the interaction of the a, b, or c component of the molecular permanent dipole moment and an oscillating external electric field. 100 as well as for B and C. In the cases of both BrNCO and INCO there was a real problem identifying 6-type transitions, because they were very weak, but by use of this procedure A could be evaluated to within less than 1 MHz, and these transitions could then easily be predicted and assigned. Perhaps the prototype molecule for this procedure is vinyl iodide, CH2=CHI. Surpris-ingly, very little was previously known about its microwave spectrum, apart from some early measurements [4-4], [4-5] of two a-type transitions: 4^ 4 «— 31,3 and 4^3 <— 3i,2- A subsequent analysis by Moloney [4-6], using third-order perturbation theory, produced some reasonable rotational and 1 2 7 I quadrupole constants, including approximate values for AQ (to within 400 MHz) and \ab- Since this was not sufficient for accurate predictions of fe-type transitions, the molecule seemed to be an excellent candidate for application of our method. This chapter presents extensive measurements of the microwave spectrum of vinyl iodide. Since the permanent electric dipole moment component \ia is very large, and the component ^ is small, the spectrum contains strong a-type and very weak 6-type transitions. Section 3.2 contains a description of the experimental apparatus used to record the microwave spectrum of vinyl iodide. The following section, 3 . 3 , details the analysis of rotational transitions in both the ground and first excited vibrational states. The centrifugal distortion constants measured and compared to those calculated from a previously published force field are also found in this section. Since many well resolved Stark components have been observed, both components of the permanent electric dipole moment were measured and are presented in section 4.4. 101 4.2 Experimental Procedures The spectrometer used to record the gas phase microwave spectrum of vinyl iodide in the range 8-108 GHz is shown in Figure 4.1. The radiation source was a Watkins-Johnson 1291 A synthesizer which produced essentially monochromatic light in the range 8-18 GHz with a typical output power of 100 mW. The frequency of the synthesizer was referenced to a crystal and was accurate to 1 part in IO10. Frequencies higher than the 8-18 GHz fundamental were generated with various solid state non-linear devices. These were: 1. Honeywell-SpaceKom 14-27 (doubler) 2. Honeywell-SpaceKom T K a - l (tripler) 3. Millitech FEX-10 Extender (6x) The specified conversion losses for all these multipliers were approximately 10 dB. Multiplication to frequencies 6x the fundamental was produced both by spurious har-monics of the T K a - l (with much higher conversion losses) and by the FEX-10 (which produced considerably more power than the TK a - l ) and measurements were made above 54 GHz by filtering out the lower frequencies with appropriate sized waveguide. Individ-ual multipliers were protected from power damage during operation by attenuating (6-10 dB) the output of the synthesizer. The radiation passed through a 6-ft. Hewlett-Packard X-band Stark cell which was attached to a vacuum line and sealed at both ends by mica windows. The detectors used were diode crystal rectifiers. Because the absorption coefficients in the microwave region are very small, a <~ 10 - 5 cm - 1 , signals are often buried in the noise of the spectrometer. The sources of noise are: 1. Variations in the power output of the source with frequency. 2. Variations in transmission due to reflections in the waveguide. 102 attenuator — i— r ~ multiplier microwave synthesizer Stark cell computer t3jD oscillo-scope buffer amplifier 4 Det square wave generator reference lock-in amplifier pre amplifier Figure 4.1: The Stark modulated microwave spectrometer. 3. Thermal noise in the detector. Thus, as in the ion experiment presented in the previous two chapters, we need a tech-nique with which to recover the signal. The method most commonly used in microwave spectroscopy is Stark modulation. When a static electric field is applied to a molecule with a permanent dipole moment, its quantum mechanical state is changed. The M degeneracy of the rotational energy levels is lifted and the energies of the 2J+1 M sublevels change as a function of the magnitude of the applied field. In our experiment the applied electric field vector is parallel to the electric vector of the radiation. This results in the selection rule A M = 0 for transitions between the M levels [4-7]. If the electric field is turned on and off, at 100 kHz for example, any absorption signal of a rotational transition will also oscillate at 100 103 kHz. This modulated signal can be analysed by a lock-in amplifier which, if the phase is chosen correctly, produces a demodulated Lorentzian line profile. Because the lock-in amplifier is a phase synchronous device, the field-off (absorption lines) and field-on (Stark components) demodulated signals appear 180° out of phase with respect to the baseline. In this experiment, the electric field applied to the molecules resulted from a voltage applied between the waveguide and the septum, which is a flat metal strip placed half way between and parallel to the broad faces of the waveguide (see Figure 4.1). The septum is held in place by teflon strips which also electrically insulate the waveguide from the septum. The modulation is in the form of a 100 kHz zero-based 0-2000 volt square wave potential. The square wave generator also sends a reference to the lock-in amplifier. Stark effect measurements were made by applying a constant voltage (100-1500 V) to the Stark cell, using a Fluke 412B high voltage power supply. Modulation was obtained by applying a small (50 V) 100 kHz square wave voltage on top of the dc voltage. With this arrangement, individual demodulated Stark components appear as two lobes differing in phase by 180°. The lobes represent the frequency of the Stark-shifted transitions during each half cycle of the square wave generator such that one lobe is associated with E j c -f E m and the other with Edc - E m , where E j c and E m are the dc bias voltage and one half of the square wave voltage, respectively. This method was chosen instead of pure ac modulation for two reasons. Firstly, it is very difficult to generate a square wave whose waveform remains undistorted at high voltages. Any irregularities in the wave form results in a broadening of all Stark components. Secondly, it is quite difficult to measure the exact amplitude of a square wave voltage. The amplitude of the small (undistorted) square wave voltage used in this experiment was measured with an oscilloscope. The spacing of the cell was calibrated by doing analogous experiments using OCS and Muenter's accurately measured value of its dipole 104 moment [4-8]. In our spectrometer, the microwave synthesizer was controlled by a Digital (DEC) Micro-PDP 11/23+ microcomputer [4-3]. The computer was interfaced to the synthesizer via a General Purposes Interface Bus (GP-IB IEEE-488 1975 standard) and collected and stored the output of the lock-in amplifier via a 12-bit analog to digital (A/D) converter. The software that controls the spectrometer was written, mostly by Dr. W. Lewis-Bevan and partially by the author, in both high level (FORTRAN-77) and low level (MACRO-11) languages. The menus and general calculations were written in FORTRAN-77, while parts of the graphics routines and data collection routines were written in MACRO-11. The subprogrammes called from the main programme using a menu format included scan, centre, display, and peak. The scan routine was used to collect and store data on the computer. Variables such as step sizes, dwell times, and frequency ranges were input via the scan menu. Each measured line was recorded using sweeps both up and down in frequency and the average of the two was taken to eliminate time constant related frequency shifts. Besides simply scanning frequencies in either direction, the scan routine can signal average and/or over-sample. Signal averaging was done by collecting several data points for each frequency, which were then summed together and stored. Oversampling was slightly different in that it involved stepping the synthesizer in finer increments than those actually stored on disk. An average of up to seven data points could be taken and stored as one data point. The centre routine was used to "peak up" the conditions under which the transitions could be observed. The repeated ramping of the frequency in one direction depended on the centre frequency, sweep width, dwell time, and step size, which were input via the centre menu. This routine was routinely used while adjusting the Stark modulation voltage so that the Stark components and zero field components of transitions were 105 well separated in frequency. The output of the lock-in amplifier was not stored on the computer, but was displayed on an oscilloscope during the operation of this routine. The display routine was used to view the collected data during either the up or down scans on the computer terminal monitor. The peak subprogramme was a variation of the display routine. Transition frequencies were calibrated using the peak routine in which both up and down sweeps are displayed. A graphics cursor subroutine was used to locate the channel numbers of the transitions. These channel numbers were converted to frequencies and then finally the frequencies were averaged over the two sweeps. The accuracy of the line frequency measurements in the present work was limited to ±0.05 MHz by the line widths. The sample of vinyl iodide used in this experiment was purchased from Columbia Organics, and was not purified further. Since it photolyses and polymerizes readily, it was stored in the dark at liquid nitrogen temperature. The spectrum was observed using samples in situ in the microwave cell at room temperature at 10-20 mTorr; in these conditions the sample was stable for about 40 minutes. 4.3 Observed Spectrum and Analysis 4.3.1 Theoretical considerations Vinyl iodide differs from the molecular ions discussed in the previous two chapters in more ways than just charge. Firstly, it is an asymmetric rotor, which means that one needs at least two axes to define the positions of all the atoms with respect to the molecular centre of mass. The coordinates of the atoms in linear and diatomic molecules can be determined, with respect to the centre of mass, using only one axis. Secondly, the iodine nucleus in vinyl iodide has nuclear spin angular momentum quantum number 7 = | and therefore possesses an electric quadrupole moment, Q, which in this case is 106 large. This quadrupole moment interacts with the electric field gradient, V.E, in the molecule, the result of which is a coupling of the nuclear spin angular momentum I, with the rotational2 angular momentum J to produce the total angular momentum F. To analyse the patterns in the microwave spectrum of vinyl iodide, which reflect these two phenomena, it is necessary to use a different Hamiltonian and a set of somewhat different basis functions than those already described in this thesis. The theory needed to explain the rotational spectra of asymmetric rotors, including nuclear quadrupole hyperfine interactions, has been rigorously presented elsewhere [4-7], [4-9], therefore only the formulae pertinent to vinyl iodide will be considered in this section. We have chosen the symmetric top wave functions, introduced in chapter 3, as our starting point and have included nuclear quadrupole coupling [4-7]: F = J + I (4.1) which causes the rotational energy levels to split into the 27-f 1 components, F = J + J, J + I — 1,... | J — I\. Thus, our basis functions took the form [4-7]: $r = \F J K I M F ) (4.2) where K is the projection of J onto the molecular axis of highest symmetry and Mp is the projection of F onto the space fixed Z axis (which is defined by the direction of propagation of the radiation). The Hamiltonians chosen to describe the rotational energy levels of vinyl iodide in the ground electronic state included rotation, quartic centrifugal distortion, and nuclear quadrupole coupling [4-10], [4-11]. These were either: H s = {AJ2a+BJ2 + CJ2}-r{-Dj{32)2 2We now identify J with rotational angular momentum because both L=0 and S=0 and therefore J = R + L+ S = R. 107 or: - D J K l 2 J 2 a - DKJAa + d,J2(J2 + JI) +d2(J4+ + J1)}- { T 2 ( V £ ) • T2(Q)} (4.3) HA = {AJ2 + BJ£ + CJ2} + { - A j(J 2) 2 - A J K J 2 J 2 - AKJ*a - l\6j32 + 8 K J l , J l + J2_}+} -{T2{VE)-T2{Q)} (4.4) The ladder operators J± represent Jt ± i Jc, and Ja, Jb, and Jc are the projection of J onto the a, b, and c molecule fixed inertial axes. These axes are defined by the principal moments of inertia such that, for an asymmetric rotor, Ia < lb < 7C, where [4-7]: atoms Ia = £ m , - ( # + 7?) a^ = abc (4.5) i=i in which, m, and a,/?,7, are the mass and coordinates of atom i. The rotational constants can be identified with the moments of inertia such that [4-7]: A = i k ' B = * k < c = *k- ( i n M H z ) (4-6) The sets of quartic centrifugal distortion constants Dj, DJK, Dx,di, and d2 and A j , AJK, AK, and 6a represent the experimentally determinable linear combinations of the Tap^g distortion constants in what are known as Watson's S (symmetric) and A (asymmetric) reduced Hamiltonians, respectively [4-10]. The parameters represent the change in the moments of inertia with respect to the 3N-6 (N = number of atoms) vibrations in the molecule as follows [4-7]: ^ 3 N - 6 3 N - 6 fij fij Tafi-yS = 0 J j j j Y H TP~JP~ ( 4 J) Ri and Rj are the internal displacement coordinates, ( / _ 1 ) , j is an element of the inverse 108 harmonic force constant matrix, Iaa etc are the diagonal components (Ja, for example) of the moments of inertia tensor, and Iap etc are its off-diagonal components. In the absence of external fields, the matrix elements of Watson's S reduced Hamiltonian excluding quadrupole coupling are [4-10]: ( J K \ H S \ J K ) = \{B + C)J(J + 1) + [A — \{B + C)]K2 - DjJ2(J+l)2 - DJKJ(J + l)K2 - D K K 4 (4.8) ( J K ± 2 | H s | J K ) = {l(B-C) + dyJiJ + 1)} x{[J(J+ 1) - K(K ± 1)][J{J+ 1) - (K ± 1)(K ± 2)]}» (4.9) ( J K ± A \ H S \ J K ) = d2{\J{J + \)-K{K±\)) x[J(J + 1) - (K ± l)(7v ± 2)][J(J + 1) - (K ± 2)(K ± 3)] x[J{J+l)-{K ±3){K ± 4 ) ] } 2 (4.10) The matrix elements of Watson's A reduced Hamiltonian are [4-10]: ( J K \ H A \ J K ) = l(B + C)J(J + l) + [A-\(B + C)]K2 -AjJ2(J + l)2 - AJKJ(J + 1)K2 - A K K 4 (4.11) ( J K ± 2 | HA I J K ) = {\(B-C) - SjJ(J-rl) - \6K[(K±2)2 + K2}} 109 x{[J( J + 1) - K(K ± 1)][J( J + 1) - (K ± 1)(K ± 2)]}» (4.12) T2(VE) • T2(Q) in equations 4.3 and 4.4 represents the scalar product of two second rank tensors, namely the electric field gradient tensor and the halogen nuclear electric quadrupole tensor. Benz, Bauder, and Gunthard [4-12] have published the matrix ele-ments of the quadrupole interaction in a \ JKIFMp) basis. These matrix elements take the form: ( J' K' I F MF | - T2{VE) • T2{Q) \ J K I F M F ) \ ( - V ) M + r \ F ' J'\( ' 2 [ 2 J I J \ -I 0 I x £ ( - l ) J ' - K 7 ( 2 7 + l)(2J' + l ) ( J ' 2 J ) X A K (4.13) It' \ -K> A A' K ) where A J (= J ' — J) and AA' both can take the values 0, ± 1 , and ± 2 . The nuclear electric quadrupole coupling constants, \ Ah' can be defined as follows: X A A ' = 2eQ{K'\\ -T2AK(VE)\\K) (4.14) where e is the charge of an electron. The parentheses contain the elements of a 3-j symbol, while the curly braces contain the elements of a 6-j symbol. For vinyl iodide we can identify the quadrupole coupling constants with respect to their components along the principal inertial axes a, b, and c: XO = Xaa, X±l = ±v/|(Xa6±«Xac) (4.15) X±2 = TftiXbh- Xcc±2ixbc) The parameters which can be obtained from the microwave spectrum of vinyl iodide are Xaa, Xbb — Xcci and Xab- Xac and Xbc a r e z e ro by symmetry, because the molecule is planar. 110 To obtain the energy levels of an asymmetric rotor, the Hamiltonian must be di-agonalized. Since the quadrupole terms are generally much smaller than the combined rotational and centrifugal distortion terms, the traditional approach is to diagonalize the latter part, and treat the quadrupole coupling as a perturbation. The first-order treat-ment of the quadrupole coupling entails including the terms diagonal in F, J , and K, and the terms diagonal in F and J and off-diagonal in K by 2. A Wang transformation is first used to change the basis [4-13]. The new basis is: | J 0 + / F MF ) = | J K = 0 I F MF ) (4.16) | J K+ I F MF ) = ^[ | J K I F MF ) + | J ~K I F MF )} K>0 (4.17) \JK~IFMp) = ^[ | J K I F MF ) - | J -K I F MF )) K > 0 (4.18) This has the effect of taking linear combinations of functions with even K, or odd K, but not mixing even and odd K. The transformed matrix consists of four smaller submatrices, which are now diagonalized to give the energy levels. The notation most commonly used to label the energy levels is: Foi JKa,Kc, where Ka and Kc represent the K quantum number in the prolate symmetric top limit (7a < lb = Ic) and oblate symmetric top limit (Ia = 76 < 7C). The parities of the KaKc representation contain the symmetry of the wave functions designated according to the D 2 symmetry group: 111 D 2 E cs" c b 2 c2 KaKb A 1 1 1 1 eea B a 1 1 -1 -1 eo B b 1 -1 1 -1 oo B c 1 -1 -1 1 oe °e and o represent Ka and Kc be-ing an even or odd integer value. Diagonalization of the asymmetric rotor by the above method has the effect of bringing the terms in Xaa and (xbb — Xcc) on to the diagonal. The first-order treatment thus describes the quadrupole coupling in terms of these two constants [4-7]. The energy levels calculated is this way produce hyperfine patterns in a rotational spectrum which we will call "first order patterns". In some cases the nuclear quadrupole hyperfine structure differs from the first order pattern. This is most likely to happen when the molecule contains an atom whose nucleus has a large quadrupole moment (bromine and iodine are good examples of this), and also when the principal quadrupole axis of the nucleus is at a relatively large angle to the principal inertial axes. For vinyl iodide this angle has been calculated to be 16.0° (see Table 4.2), which is sufficient. Other approaches are necessary to account for the hyperfine structure which is "per-turbed" from the first order pattern. One approach is to use higher order perturbation theory. This technique was used by Moloney [4-6] in his analysis of the hyperfine struc-ture of two rotational transitions of vinyl iodide. An alternative approach is to include all terms from the Hamiltonian either from equation 4.3 or from equation 4.4. This means one must diagonalize a matrix which is diagonal only in F and MF. The microwave spectrum of vinyl iodide contains a large number of perturbations, 112 and so the diagonalization approach was used to analyse it. This is a much more complex method than the first-order treatment, not least because of the large matrices, of the order of (2F+1)(2I+1) for each F. The least squares fitting procedure used was based on the Hellmann-Feynman theorem [4-14] and required so much computer time that the fits were done on the Cray 1-S and X-MP supercomputers of the Atmospheric Environment Service of Canada. The effect of the off-diagonal terms in x<*b, Xaa, Xbb, and \cc ah provided information about constants which would have been unobtainable from a first-order analysis. Therefore, it was important to know which energy levels interact via these effects. To find these levels it is useful to consider the non-vanishing matrix elements of the quadrupole Hamiltonian, HQ = T2(VE) • T2(Q), in the asymmetric rotor basis. These matrix elements have been evaluated by Bragg [4-15] : ( J KaKc I F MF\HQ\J K'aK'c I F MF) = C0eQ{J KaKcMj = J\Vzz\J K'aK'cMj = J) (4.19) ( J KaKc I F MF | HQ | J + 1 K'aK'c I F MF) = C,eQ{J KaKc Mj = J\Vzz\J + l KK Mj = J ) (4.20) ( J KaKc I F Mp | HQ \ J + 2 K'aK'c I F MF) = C2eQ{J KaKcMj = J\Vzz\J + 2K'aK'cMj = J) (4.21) where VZz is the component of the electric field gradient along the space fixed Z axis. In terms of tensor notation, Vzz = ^(^i?) . Co, C\, and C2 are constants, which are functions of 7, J , and F [4-15]. VZz is related to molecule fixed axis system by: Vzz = £ Vgg, $Zg $z9> 9,g' = a,b,c (4.22) 9,9' where we can recall from chapter 1 that, § Z g and $Zg' a r e the direction cosines which relate the Z axis of the space fixed system to the a, 6, and c axes of the molecule fixed 113 system. In general, the energy levels of the asymmetric rotor will interact if both Vgg> and the matrix element (JKaKcMj = J\$Zg$zg'\J'K'aK'cMj = J) are non-zero. Symmetry con-siderations can be used to decide which terms of the matrix elements are non-vanishing. Remember that, following from equations 4.14 and 4.15, Xgg' = zQVgg'- ^ox a n asym-metric rotor the non-zero matrix elements are related to the parities of Ka and Kc as follows: Terms in AKaKc Xaa Xbb Xcc ee <-+ ee, oo <-> oo eo *-+ eo, oe <-> oe Xab eo *-+ oo, ee *-* oe Xac eo <-> oe, ee +-> oo Xbc e o ee) o e 0 0 Thus, for vinyl iodide, "perturbations" of the first-order quadrupole hyperfine struc-ture arise in levels connected either by the Xab term and/or by the Xaa, Xbb, and Xcc terms, all of which have the additional selection rule: AF = 0 (4.23) This effect is particularly important in planar near-prolate molecules like vinyl iodide whose spectrum is dominated by a-type R branch transitions governed by the selection rules: A F = 0, ±1 (4.24) A J = 1 (4.25) AKaKc = ee <-> eo ; 00 <-> oe (4.26) 114 The rotational constant A is not usually available from a first order analysis of this type of transition because the frequencies of the transitions have no dependence on it (essentially it is subtracted out because the value of AK2 is the same in both upper and lower rotational levels). However, the mixing of states through off-diagonal quadrupole matrix elements is dependent on A (and also on B, C and the distortion constants). Therefore, it should be possible to extract the values of these constants through analysing perturbations in the first order quadrupole patterns using the full nuclear quadrupole Hamiltonian. The levels most likely to provide information can be selected from an energy level diagram (see Figure 4.2, for example) using the selection rules previously stated. 4.3.2 Analysis of the Spectrum A series of a-type R branch transitions was predicted using the values of Bo and Co of Morgan and Goldstein [4-5], and the values of AQ and the 1 2 7 I quadrupole constants from Moloney's analysis [4-6] as input data for our programme. An initial search for low J lines was fruitful, and several KA = 0 and 1 lines were assigned by comparison of their predicted and observed frequencies. The rotational transitions were resolved to up to ten components due to 1 2 7 I quadrupole coupling, and much of the hyperfine structure was perturbed from a first-order pattern. Refinement of the spectroscopic constants was then begun, following the same pro-cedure as that used for BrNCO [4-1] and INCO [4-2]. This involved the global fitting programme, which did a simultaneous least-squares fit to the rotational, distortion, and 1 2 7 I quadrupole coupling constants, including the off-diagonal term Xab- The values ob-tained were then used to predict and assign further transitions in the frequency range of the spectrometer, and the procedure was repeated several times. Each refinement produced a decrease in the uncertainty of AQ, even though at this 115 point the only measured transitions were a-type R branches. The rotational energy diagram for vinyl iodide is given in Figure 4.2; on it are in-dicated some of the closest near degeneracies responsible for quadrupole perturbations. Those giving rise to perturbations of low J transitions (J < 10) are between KA = 0 and 1 levels. Good examples are 8o,s — 7i,6 and IQJ — 61,5 and the transitions 8o,s 7rj,7 a n ( ^ ?i,6 *~ 61,5 are indeed strongly perturbed. Inclusion in the fit of all a-type transitions with 3 < J < 10 and KA = 0 and 1 (examples in Table 4.1) gave a value for A0 with an uncertainty of ± 3 MHz; all the quadrupole constants were well determined, as were three centrifugal distortion constants. In order to improve the accuracy of AQ further, it was necessary to find some b-type transitions. They were, however, very weak, and difficult to identify among the strong a-types with large quadrupole splittings. However, the search regions had been considerably narrowed by our earlier fits, and it was at this point relatively easy to find two such transitions, namely 12o,i2 «— l l i . n and 13o,i3 *— 12i,i2, within 2 MHz of the predicted frequencies. Their identities were confirmed by their relatively low intensities, their high field Stark effects3 and especially their quadrupole splitting patterns. One such transition, 12o,i2 *— H i,ii, is shown in Figure 4.3, which also includes the a-type transition 5i,4 «— 41,3. The difference in the intensities reflects the relative magnitudes of Ha and fib- The resulting fit allowed AQ to be refined to within ±0.04 MHz. The next step in the analysis was to determine all the quartic distortion constants by measuring further transitions. Normally for a planar molecule such as vinyl iodide this is done by measuring 6-type transitions between levels with KA = 1 and 2, to augment those between levels with KA — 0 and 1, and thus separate the A-reduction [4-10] distortion constant A K from the rotational constant A. For vinyl iodide, however, such transitions, though sought, were too weak to measure, and instead further perturbations, between 3A detailed description of the Stark effect will be presented in section 4.4. 116 5 — X CD 0>_ 5 2 K CD cn c\j oj OO <X<> lO t V I O CM IV to o-cgni CM K a> 1 — — 2 00 m to in •o *> i s (vj tn — cu O — ro e u -ro o CM o O o co o o ID o o o to -°o° o O I O O CD 1~ O O i n o o "3-O O to ZH9 / A9d3N3 i o o o o "I o Figure 4.2: Rotational energy levels of CH 2 =CH 1 2 7 I . Several important near-degeneracies are shown. Those between KA — 0 and 1 levels with J < 10 were used to determine A from a-type R branches alone. Those between KA = 1 and 2 levels were used to separate AQ and DK • 117 T — r ¥ • 0 1 9' state 32174.00 MHz 1 -25 MHz-Figure 4.3: Comparison of the a-type transition 5i,4 <— 4i i 3 and the 6-type transition 12o,i2 *— lli.n- The relative intensities of the ground state lines reflect the relative magnitudes of the dipole moment components /x0 and Hb- Transitions of the molecules in the lowest excited vibrational state (91) are also indicated. Values of F are given in Table 4.1. levels with Ka = 1 and 2, were used following the method used for INCO [4-2]. In vinyl iodide a very near degeneracy, between the levels 13i,i3 and 112,9, whose unsplit energies are within 264 MHz, was particularly important (see Figure 4.2). The required perturbations were observed in the transitions 112,9 «— 102,8 and 13i,i3 <— 1 2 U 2 . The frequencies of the F = 27/2 «- 25/2 and 25/2 <- 23/2 components were shifted by ~10 MHz when compared with those calculated with the first order quadrupole effect. This is shown in Figure 4.4. It is interesting that in this case it is perturbations in a-type transitions that were used to evaluate AK, in contrast to the perturbations in fe-type transitions used for INCO [4-2]. The resulting measurements were included in a global fit, this time to all rotational, quadrupole, and quartic distortion constants. A 118 separation of A^- from AQ was indeed obtained. After a few more a-type transitions had been measured, the final fit was carried out. Unfortunately, when it was done using Watson's A-reduced Hamiltonian, large correlations were introduced between Bo, Co and SK, because AQ Bo ~ Co (K ~ -0.9923, where K = 2B^JC [4-16]). Since these are the circumstances in which the A reduction breaks down, the S reduction was used instead [4-10]. No attempt was made to measure a-type lines with KA > 2, which were badly overlapped among the various quadrupole components and vibrational states. The final constants are in Table 4.2. The measured ground vibronic state transitions are in Table 4.1, along with the residuals calculated with Xab omitted and Xab included. Close inspection of this table reveals that almost every transition is at least slightly perturbed from the Xab — 0 quadrupole pattern. The magnitude of the shifting of energy levels due to this effect ranges from ~22 MHz to ~0.05 MHz. Of course the lines whose frequencies have the greatest shift contain the most information, but the large number of slightly perturbed lines were also of assistance in improving the precision of the constants determined. Many strong vibrational satellite transitions were observed throughout the spectrum. The strongest ones were presumably due to molecules in the first excited state of the lowest wavenumber mode, the 91 state, at 309 cm"1 [3-16], [3-17] (see Figure 4.3). The quadrupole structure of some transitions was resolved, and was used to make assignments. Four transitions were measured; they were chosen with reference to energy level diagram (Figure 4.2) to give the maximum probability of obtaining all rotational and quadrupole constants. The measurements are also in Table 4.1, and the derived constants are in Table 4.2. Table 4.3 shows that the constants are essentially uncorrelated. 119 TABLE 4.1 Measured r o t a t i o n a l t r a n s i t i o n s ( i n MHz) of V i n y l Iodide T r a n s i t i o n N o r m a l i s e d 1 Observed R e s i d u a l s 2 F' - F" Weight Frequency Without X»* With The ground v i b r a t i o n a l s t a t e 4 i • 7 / 2 -5/2 " 9 /2 -3/2 -1 1/2 -1 3/2 -3 5/2 3/2 7 / 2 1/2 9 / 2 11/2 i 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 2 4 8 6 9 . 2 8 2 4 8 7 7 . 4 6 2 4 8 8 8 . 3 7 2 4 9 1 7 . 7 9 2 4 9 1 9 . 6 4 2 4 9 4 2 . 2 9 0 . 1 3 0 . 0 8 0 . 3 8 - 0 . 0 0 0 . 7 2 0 . 7 5 0 . 0 3 0 . 0 7 0 . 0 5 0 . 0 0 - 0 . 0 2 0 . 0 2 4 o « 5/2 -7/2 -9/2 -1 3/2 -1 1/2 -3 3/2 5/2 7 / 2 11/2 9/2 0 * 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 2 5 2 3 1 . 3 2 2 5 2 4 2 . 6 2 2 5 2 8 0 . 6 4 2 5 3 0 6 . 6 0 2 5 3 1 8 . 4 0 - 0 . 8 6 - 1 . 3 1 -1 . 2 3 0 . 0 3 - 0 . 0 7 0 . 0 4 . 0 . 0 0 - 0 . 0 2 0 . 0 0 0 . 0 3 4 , * 7/2 -5/2 -9/2 -1 1/2 -3/2 -1 3/2 -3 " 5/2 3/2 7/2 9/2 1/2 11/2 i *1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 2 5 6 4 1 . 3 2 2 5 6 5 0 . 6 1 2 5 6 5 7 . 4 4 2 5 6 8 5 . 9 5 2 5 6 8 8 . 9 0 2 5 7 0 9 . 4 1 0 . 0 5 0 . 2 1 - 0 . 0 1 0 . 0 5 0 . 0 3 0 . 1 8 - 0 . 0 1 - 0 . 0 2 0 . 0 4 0 . 0 1 - 0 . 0 3 - 0 . 0 1 5 , s 9/2 -7/2 -1 1/2 -5/2 -1 3/2 -1 5/2 -4 7/2 5/2 9/2 3/2 11/2 1 3 / 2 i * 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 31 1 1 5 . 5 3 31 1 1 6 . 4 4 3 1 1 3 1 . 0 9 3 1 1 4 0 . 0 9 3 1 1 5 1 . 3 4 3 1 1 6 0 . 0 6 - 0 . 0 1 - 0 . 0 3 0 . 1 0 - 0 . 0 6 0 . 1 3 0 . 1 9 - 0 . 0 2 - 0 . 0 3 0 . 0 4 - 0 . 0 5 - 0 . 0 4 0 . 0 2 5 o 5 7/2 -9/2 -5/2 -1 1/2 -1 5/2 -1 3/2 -4 5/2 7/2 3/2 9/2 1 3 / 2 1 1/2 0 * 1 . 0 0 0 1 .000 1 . 0 0 0 1 . 0 0 0 1 .000 1 . 0 0 0 3 1 5 8 1 . 3 8 3 1 5 9 1 . 2 9 3 1 5 9 5 . 9 5 3 1 6 1 3 . 5 9 3 1 6 2 4 . 2 3 3 1 6 3 0 . 8 6 1 . 5 5 3 . 1 2 0 . 2 3 2 . 8 5 0 . 0 4 - 0 . 1 7 - 0 . 0 2 - 0 . 0 0 0 . 0 0 0 . 0 4 0 . 0 2 0 . 0 1 5 , , 1 3/2 -9/2 -7/2 -1 1/2 -5/2 -4 1 3 / 2 7/2 5/2 9/2 3/2 1 3 i . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 .000 1 . 0 0 0 3 1 8 7 1 . 7 7 3 2 0 7 8 . 2 7 3 2 0 7 9 . 9 5 3 2 0 9 1 . 9 8 3 2 1 0 2 . 1 6 - 0 . 6 9 0 . 1 7 0 . 3 1 0 . 0 2 - 0 . 0 3 - 0 . 0 4 - 0 . 0 2 - 0 . 0 3 0 . 0 3 - 0 . 0 4 120 Table 4 . 1 (continued) T r a n s i t i o n Normalised Observed R e s i d u a l s F' F" Weight Frequency Without With X-t 1 3 / 2 -1 5 / 2 -9 / 2 -7 / 2 -5/2 -1 1 / 2 1 3 / 2 9/2 7 / 2 5/2 • • • • * ooooo ooooo ooooo 3 2 1 1 0 . 8 5 3 2 1 2 0 . 3 0 3 2 1 7 3 . 9 9 3 2 2 2 7 . 1 5 3 2 2 4 5 . 5 2 0 . 0 7 0 . 3 6 0 . 7 6 0 . 3 6 - 0 . 8 4 0 . 0 1 0 . 0 1 - 0 . 0 3 - 0 . 0 0 - 0 . 0 6 12 o 12 2 1 / 2 -1 9 / 2 -2 3 / 2 -2 9 / 2 -2 5 / 2 -2 7 / 2 -- 11 1 9 / 2 1 7 / 2 2 1 / 2 2 7 / 2 2 3 / 2 2 5 / 2 1 1 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 3 2 2 3 2 . 6 9 3 2 2 3 3 . 0 2 3 2 2 3 5 . 4 0 3 2 2 3 7 . 2 0 3 2 2 3 9 . 4 3 3 2 2 4 1 . 7 6 0 . 6 6 0 . 8 3 0 . 2 7 0 . 0 3 0 . 3 9 0 . 9 2 0 . 0 0 - 0 . 0 6 - 0 . 0 0 0 . 0 6 0 . 0 0 0 . 0 3 6 1 « 9/2 -1 1/2 -13/2 -7/2 - ' 1 5 / 2 -1 7 / 2 -5 7/2 9/2 11/2 5/2 13/2 15/2 1 5 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 3 7 3 5 1 . 4 2 3 7 3 5 2 . 6 0 3 7 3 6 4 . 5 8 3 7 3 6 6 . 6 6 3 7 3 7 8 . 3 9 3 7 3 8 1 . 8 8 - 0 . 0 1 - 0 . 0 1 0 . 0 5 0 . 0 0 0 . 1 0 0 . 0 7 - 0 . 0 0 - 0 . 0 0 0 . 0 3 0 . 0 1 0 . 01 - 0 . 0 0 6 0 s 9/2 -1 1/2 -7 / 2 -13/2 -1 7 / 2 -15/2 -5 7/2 9/2 5/2 1 1 / 2 15/2 13/2 0 5 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 3 7 9 0 8 . 7 0 3 7 9 1 4 . 7 0 3 7 9 1 9 . 0 0 3 7 9 2 9 . 8 0 3 7 9 3 8 . 5 1 3 7 9 4 3 . 2 1 - 0 . 5 9 - 0 . 7 4 - 0 . 4 8 - 0 . 7 5 0 . 0 4 - 0 . 2 4 0 . 0 5 - 0 . 0 0 ' 0 . 0 0 0 . 0 2 0 . 0 2 0 . 0 9 6 1 5 1 3 / 2 -7/2 -1 5 / 2 -17/2 -5 1 1/2 5/2 13/2 15/2 1 • . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 3 8 5 1 7 . 4 5 3 8 5 2 0 . 3 0 3 8 5 3 0 . 3 6 3 8 5 3 4 . 9 5 0 . 1 0 0 . 0 1 0 . 1 3 0 . 8 4 0 . 0 3 0 . 0 2 - 0 . 0 0 - 0 . 0 1 13 0 13 2 1 / 2 -2 3 / 2 -2 7 / 2 -2 9 / 2 -- 12 1 9 / 2 2 1 / 2 2 5 / 2 2 7 / 2 1 1 ' . 0 0 0 1 .000 1 . 000 . 0 0 0 3 9 5 4 4 . 0 1 3 9 5 4 4 . 7 5 3 9 5 5 1 . 2 0 3 9 5 5 2 . 5 4 0 . 8 3 0 . 7 4 0 . 4 8 0 . 7 2 - 0 . 0 1 0 . 0 0 - 0 . 0 1 0 . 0 0 7 , 7 1 1 / 2 -1 3 / 2 -9/2 -1 5 / 2 -1 7 / 2 -6 9/2 1 1/2 7/2 1 3 / 2 1 5 / 2 1 c . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 4 3 5 8 2 . 6 1 4 3 5 8 4 . 3 5 4 3 5 9 3 . 0 9 4 3 5 9 3 . 6 2 4 3 6 0 3 . 5 7 - 0 . 0 2 - 0 . 0 6 - 0 . 0 3 - 0 . 0 5 0 . 0 5 - 0 . 0 1 - 0 . 0 5 - 0 . 0 2 - 0 . 0 5 0 . 0 0 121 Table 4.1 (continued) T r a n s i t i o n Normalised Observed R e s i d u a l s F' - F" Weight Frequency Without Xo* With Xok 19/2 - 17/2 1.000 43604.87 0.01 -0.02 7 O 7 11/2 -13/2 -9/2 -15/2 -19/2 -17/2 -9/2 1 1/2 7/2 13/2 17/2 15/2 6 0 ' l . O O O 1.000 1.000 1.000 1.000 1.000 44226.60 44233.79 44235.51 44244.67 44250.16 44253.10 -0.76 -0.29 -0.96 -0.26 0.06 -0.77 - 0 . 0 ' -0.04 -0.00 0.03 0.05 0.07 7 , , 13/2 -11/2 -9/2 -15/2 -17/2 -19/2 -11/2 9/2 7/2 13/2 15/2 17/2 6 i B 1.000 1.000 1.000 1 .000 1 .000 1 .000 44935.26 44936.02 44938.51 44939.15 44948.62 44954.85 5.33 7.53 0.02 0.72 0.96 5.58 0.03 -0.01 0.03 0.00 0.01 0.00 8 , , 13/2 -15/2 -11/2 -17/2 -19/2 -21/2 -1 1/2 13/2 9/2 15/2 17/2 19/2 7 1 7 1.000 1.000 1.000 1 .000 1 .000 1.000 49810.91 49812.61 49818.53 . 49820.16 49827.55 49827.89 -0.09 -0.05 -0.07 -0.03 0.01 0.01 -0.07 -0.04 -0.06 -0.03 -0.01 -0.01 8 o . 13/2 -11/2 -15/2 -17/2 -1 1/2 9/2 13/2 15/2 7 0 ? 1.000 1 .000 1 .000 1.000 50537.24 50540.27 50545.52 50553.50 -5.36 -7.59 -0.80 -1.01 0.00 -0.00 0.00 0.01 8 2 7 15/2 -17/2 -13/2 -19/2 -11/2 -21/2 -13/2 15/2 11/2 17/2 9/2 19/2 7 2 * 1.000 1.000 1.000 1.000 1.000 1.000 50584.01 50587.63 50588.30 50596.55 50602.50 50607.37 0.07 0.12 -0.03 0.15 -0.02 0.06 0.05 0.05 -0.03 0.07 -0.02 0.00 e 2 t 15/2 -17/2 -13/2 -19/2 -11/2 -21/2 -13/2 15/2 11/2 17/2 9/2 19/2 7 2 *1.000 1.000 1.000 1.000 1.000 1.000 50630.91 50634.49 50635.20 50643.33 50649.25 50654.13 0.02 0.01 -0.01 0.02 -0.03 0.04 0.01 -0.01 -0.01 -0.02 -0.03 0.00 122 Table 4.1 (continued) Transition Normalised Observed Residuals F' - F" Weight Frequency Without J C* With X* 8 , 7 - 7 i < 13/2 - 11/2 1.000 51335.14 - 1 3 . 3 4 - 0 . 0 0 15/2 - 13/2 1.000 51340.40 - 9 . 6 8 - 0 . 0 0 21/2 - 19/2 1.000 51352.47 - 1 1 . 8 1 -0 .01 19/2 - 17/2 1.000 51361.82 -1 .90 - 0 . 0 2 9 1 , - 8 , I - 0 . 0 4 15/2 - 13/2 1.000 56036.97 - 0 . 0 7 17/2 - 15/2 1.000 56036 .77 - 0 . 0 4 - 0 . 0 2 13/2 - 11/2 1.000 56042.74 - 0 . 0 4 - 0 . 0 3 19/2 - 17/2 1.000 56044.74 0 .00 0.01 9 0 9 - 8 o s 17/2 - 15/2 1.000 56854.10 1.36 -o.oc 15/2 - 13/2 1 .000 56859.36 9.62 0.00 19/2 - 17/2 1.000 56860.98 1 .84 0 .00 23 /2 - 21/2 1.000 56661.67 0.04 0.03 13/2 - 11/2 1.000 56867.06 13.27 - 0 . 0 2 21/2 - 19/2 1 .000 56876.00 11 .82 0.01 9 , , - 8 , 7 15/2 - 13/2 1.000 57768.16 2.00 - 0 . 0 6 17/2 - 15/2 1 .000 57769.22 1.51 - 0 . 0 4 13/2 - 11/2 1 .000 57771.54 - 0 . 0 8 - 0 . 0 5 19/2 - 17/2 1.000 57773.37 0.18 - 0 . 0 2 21/2 - 19/2 1 .000 57778.83 0.33 - 0 . 0 2 23/2 - 21/2 1 .000 57781.10 2.56 -0 .01 1 0 O I O ~ 9 o » 17/2 - 15/2 1.000 63149.20 -1 .61 0.00 15/2 - 13/2 1 .000 63151.96 -2 .11 0.01 19/2 - 17/2 1.000 63153.04 - 0 . 2 3 . 0.03 21/2 - 19/2 1.000 63156.06 - 0 . 3 6 0.02 23/2 - 21/2 1.000 63159.90 -2 .51 0.05 25/2 - 23/2 1.000 63160.57 0.04 0.03 10 2 » * 9 2 , 19/2 - 17/2 1.000 63230 .05 - 0 . 6 2 0.04 21/2 - 19/2 1.000 63232.47 - 1 . 4 6 - 0 . 0 2 23 /2 - 21/2 1.000 63237.76 -1 .76 0.02 15/2 - 13/2 1.000 63240.07 - 0 . 0 8 - 0 . 0 7 25/2 - 23 /2 1.000 63243.19 -1 .21 0.01 11 j » - 10 j 25/2 - 23/2 1 .000 69659.56 - 2 1 . 7 9 - 0 . 0 0 23 /2 - 21 /2 1.000 69667.54 - 9 . 3 7 0.03 21/2 - 19/2 1.000 69670.79 - 3 . 1 4 0.01 19/2 - 17/2 1.000 69674.60 - 0 . 0 2 - 0 . 0 3 123 Table 4 . 1 (continued) Transit ion Normalised Observed Residuals F' - F" Weight Frequency Without x«* With x«* - 11 - 11 - 12 1 7 / 2 - 1 5 / 2 12 , i i 2 3 / 2 - 2 1 / 2 2 1 / 2 - 1 9 / 2 2 5 / 2 2 3 / 2 19/2 - 1 7 / 2 2 7 / 2 - 2 5 / 2 2 9 / 2 2 7 / 2 12 , 1 0 -2 9 / 2 - 2 7 / 2 2 1 / 2 - 1 9 / 2 2 3 / 2 - 2 1 / 2 19/2 - 17/2 2 5 / 2 - 2 3 / 2 2 7 / 2 — 2 5 / 2 13. , 1 3 -2 7 / 2 - 2 5 / 2 2 1 / 2 - 1 9 / 2 31/2 - 2 9 / 2 2 9 / 2 - 2 7 / 2 2 3 / 2 - 2 1 / 2 2 5 / 2 — 2 3 / 2 13 , 1 2 -2 7 / 2 - 2 5 / 2 2 1 / 2 - 19/2 2 9 / 2 - 2 7 / 2 3 1 / 2 — 2 9 / 2 13 2 1 1 -2 7 / 2 2 5 / 2 2 1 / 2 - 19/2 2 9 / 2 - 2 7 / 2 3 1 / 2 — 2 9 / 2 14 , i 2 -2 9 / 2 - 2 7 / 2 2 3 / 2 2 1 / 2 3 1 / 2 - 2 9 / 2 3 3 / 2 — 3 1 / 2 15 2 i « -3 1 / 2 - 2 9 / 2 2 5 / 2 - 2 3 / 2 3 3 / 2 - 3 1 / 2 1 . 0 0 0 i o 12 2 t 12 - 13 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 6 9 6 8 0 . 7 6 7 5 8 7 0 . 4 3 7 5 8 7 0 . 7 1 7 5 8 7 3 . 1 6 7 5 8 7 5 . 9 0 7 5 8 7 6 . 8 7 7 5 8 7 9 . 3 8 7 6 0 1 0 . 4 2 7 6 0 2 9 . 7 4 7 6 0 3 2 . 2 8 7 6 0 3 4 . 6 3 7 6 0 4 0 . 8 3 7 6 0 5 6 . 7 5 8 0 8 9 7 . 9 4 8 0 9 2 6 . 5 0 8 0 9 2 7 . 1 3 8 0 9 2 7 . 6 1 8 0 9 3 0 . 3 2 8 0 9 4 3 . 9 4 8 2 1 9 0 . 1 4 8 2 1 9 1 . 9 7 8 2 1 9 3 . 2 3 8 2 1 9 5 . 0 2 8 2 3 9 2 . 3 6 8 2 3 9 3 . 7 7 8 2 3 9 5 . 4 2 8 2 3 9 6 . 9 9 8 8 7 5 7 . 6 2 8 8 7 5 8 . 5 0 8 8 7 6 0 . 1 3 8 8 7 6 1 . 2 4 9 4 8 1 9 . 0 7 94819.92 9 4 6 2 1 . 3 5 - 0 . 0 0 0 . 0 6 - 0 . 0 5 0 . 1 4 0 . 0 7 0 . 1 2 0 . 1 6 • 2 7 . 6 2 - 0 . 0 2 2 . 6 0 - 0 . 0 0 6 . 6 9 2 0 . 9 7 • 2 7 . 1 3 3 . 1 2 0 . 0 4 0 . 0 1 9 . 3 8 21 . 8 2 0 . 0 7 - 0 . 01 0 . 0 4 0 . 0 2 0 . 1 5 - 0 . 0 2 0 . 1 9 0 . 1 6 0 . 0 9 0 . 0 1 0 . 0 6 0 . 0 5 0 . 0 1 - 0 . 0 2 0 . 0 3 - 0 . 0 0 0 . 0 2 - 0 . 0 5 0 . 0 4 0 . 0 8 - 0 . 0 0 0 . 0 7 0 . 0 1 - 0 . 0 3 - 0 . 0 1 - 0 . 0 0 0 . 0 0 0 . 0 0 • 0 . 0 2 •0 . 02 0 . 0 3 0 . 0 1 •0.01 0 . 0 2 0 . 0 3 • 0 . 0 0 • 0 . 0 0 - 0 .01 - 0 . 0 0 •0.01 - 0 . 01 0 . 0 0 0 . 0 4 0 . 0 1 •0.01 • 0 . 0 2 0 . 0 0 - 0 . 01 0 . 0 1 124 Table 4 . 1 (continued) Transit ion Normalised Observed Residuals F' F" Weight Frequency Without x* With x«* 3 5 / 2 - 3 3 / 2 : 1 . 0 0 0 9 4 8 2 2 . 4 1 0 . 0 6 0 . 0 5 15 , i> - 14 3 1 3 3 1 / 2 - 2 9 / 2 1 . 0 0 0 9 5 1 2 8 . 5 1 0 . 0 4 0 . 0 2 2 5 / 2 - 2 3 / 2 1 . 0 0 0 9 5 1 2 8 . 9 4 - 0 . 0 5 - 0 . 0 4 3 3 / 2 - 3 1 / 2 1 . 0 0 0 9 5 1 3 0 . 6 9 0 . 0 6 0 . 0 1 3 5 / 2 - 3 3 / 2 1 . 0 0 0 9 5 1 3 1 . 5 2 0 .1 1 0 . 0 4 16 2 i s " 15 3 1 • 3 3 / 2 - 3 1 / 2 1 . 0 0 0 1 0 1 1 3 0 . 8 0 - 0 . 0 4 - 0 . 0 4 2 7 / 2 - 2 5 / 2 1 . 0 0 0 1 0 1 1 3 1 . 3 7 - 0 . 0 7 - 0 . 0 6 3 5 / 2 - 3 3 / 2 1 . 0 0 0 1 0 1 1 3 2 . 7 7 - 0 . 0 3 r 0 . 0 4 3 7 / 2 - 3 5 / 2 1 . 0 0 0 1 0 1 1 3 3 . 5 5 - 0 . 0 3 - 0 . 0 5 17 , i s - 16 2 1 5 3 7 / 2 - 3 5 / 2 1 . 0 0 0 1 0 7 4 4 2 . 4 7 0 . 0 4 0 . 0 3 3 9 / 2 - 3 7 / 2 1 . 0 0 0 1 0 7 4 4 3 . 0 9 0 . 0 6 0 . 0 4 The 9 1 vibrational state 7 , 7 6 1 c 1 9/2 - 1 7 / 2 1 . 0 0 0 4 3 5 5 3 . 8 1 0 . 0 6 - 0 . 0 4 17/2 - 1 5/2 1 . 0 0 0 4 3 5 5 2 . 5 6 0 . 14 0 . 0 3 13/2 - 1 1/2 1 . 0 0 0 4 3 5 3 3 . 2 5 0 . 0 0 - 0 . 0 3 1 1 / 2 9/2 1 . 0 0 0 4 3 5 3 1 . 5 2 0 . 0 7 0 . 0 3 7 , c 6 1 5 1 9 / 2 - 1 7 / 2 1 . 0 0 0 4 4 9 1 4 . 1 8 4 . 4 7 0 . 0 2 17/2 - 1 5 / 2 1 . 0 0 0 4 4 9 0 8 . 8 0 0 . 7 3 - 0 . 0 0 15/2 - 1 3/2 1 . 0 0 0 4 4 8 9 9 . 3 4 0 . 4 8 - 0 . 0 4 9/2 7/2 1 . 0 0 0 4 4 8 9 8 . 9 6 0 . 0 0 0 . 0 2 8 o « - 7 0 7 2 1 / 2 - 1 9 / 2 1 . 0 0 0 5 0 5 0 5 . 8 8 0 . 0 0 - 0 . 0 4 1 9 / 2 - 1 7 / 2 1 . 0 0 0 5 0 5 0 4 . 4 0 - 4 . 4 1 0 . 0 2 17/2 - 1 5 / 2 1 . 0 0 0 5 0 5 0 1 . 4 8 - 0 . 7 5 0 . 0 4 1 5 / 2 - 1 3 / 2 1 . 0 0 0 5 0 4 9 3 . 4 8 - 0 . 5 6 0 . 0 4 1 1 / 2 - 9/2 1 . 0 0 0 5 0489 . 81 - 5 . 7 9 - 0 . 0 1 1 3 / 2 - 1 1 / 2 1 . 0 0 0 5 0466 . 21 - 4 . 1 1 - 0 . 0 1 125 Taole 4.1 (continued) Transit ion Normalised Observed Residuals F' F" Height Frequency Without x*t> With Xot 8 , 7 19/2 21/2 15/2 13/2 17/2 19/2 13/2 11/2 1.000 1.000 1.000 1.000 51316.69 51307.96 51296.22 51291.47 -1.77 -11.07 -8.63 •11.80 -0.01 0.00 -0.01 0.01 1 Measurements were weighted according to 1/c 1, where o is the uncertainty in the measurements. Unit weight corresponded to an uncertainty of 0.05 MHz. 2 Observed frequency minus the frequency calculated using the constants in Table 4.2. 126 Table 4.2: Spectroscopic constants of CH.2=CH 1 2 7I. Ground state Parameter Present work Ref. [4-6] Ref. [4-20] 91 state Rotational constants/MHz A 52697.108(60)° 53300.(400) 52696.108(35) 52976.7(85) B 3258.7759(11) 3258.72(3) 3258.789(4) C 3066.6190(11) 3066.66(3) 3066.618(7) 3256.3662(17) 3062.5668(21) Centrifugal distortion constants/kHz Dj 1.0369(13) DJK -25.20(12) DK 1224.(16) ^ -0.0766(25) d2 -0.00792(54) 1.11(10) -23.7(153) -0.09(5) 1.03696 -25.20b 12246 -0.-7666 -0.007926 1 2 7 I quadrupole coupling constants/MHz Xaa -1655.17(19) -1654.3(10) Xbb~Xcc I Xab I •116.31(24) 755.72(23) -116.7(15) 710.(25) Inertial defect ( amu A 2 ) A 0.1274 0.231 -1654.62(23) -115.98(25) 755.32(392) 0.1278 -1656.6(20) -127.9(44) 752.8(13) 0.2812 "In the present work, numbers in parentheses are one standard deviation in units of the last significant figures. *Distortion constants of the 9 1 state were held fixed at the values obtained for the ground vibrational state. 127 Table 4.3: Correlation coefficients. A 0 1.000 Bo 0.583 1.000 C0 -0.445 -0.823 1.000 Dj -0.387 0.187 0.089 1.000 DJK 0.596 -0.003 0.155 -0.668 1.000 DK 0.843 0.604 -0.518 -0.200 -0.279 1.000 di -0.103 -0.775 0.831 -0.129 0.251 -0.248 1.000 d2 -0.057 0.029 -0.150 -0.228 0.005 0.033 -0.239 1.000 Xaa -0.002 0.052 -0.138 -0.063 -0.035 -0.128 -0.073 0.019 1.000 Xbb~Xcc 0.030 0.073 -0.130 -0.047 -0.015 -0.070 -0.073 0.010 0.566 1.000 Xab 0.008 0.010 -0.023 -0.092 0.080 0.044 -0.070 0.047 0.109 0.070 1.000 4.3.3 Discussion of Derived Constants It can be seen from the results in Table 4.2 that this work has provided another excel-lent example of how perturbations in nuclear quadrupole hyperfine structure can be used to evaluate rotational and distortion constants which might otherwise be unavailable. For vinyl iodide A was evaluated to within ± 3 MHz using a-type rotational transitions with J <10 and Ka = 0 and 1. This is not so spectacular a result as was found for INCO [4-2], where the uncertainty in A obtained by the same means was ±0.5 MHz, because in CH2CHI the accidentally nearly degenerate levels of the correct type were both fewer in number and not so close in energy. Since, however, it predicted 6-type transitions to within 2 MHz, and these could then be easily identified from their quadrupole splitting patterns, the application has certainly been successful. As with INCO, it has been possible to evaluate centrifugal distortion constants using quadrupole perturbations. In this case these have been DK and maybe 0*2, obtained from perturbations of nearly degenerate levels having Ka = 1 and 2 (see Figure 4.4). For vinyl iodide the perturbed transitions were a-type R branches, rather than 6-type transitions 128 10 MHz 69700.00 MHz (I) <«) di") (Q) (W Figure 4.4: The transition 112,9 «— 102,8 of CH2=CH127I, with associated energy levels, (a) The energy levels; (i) hypothetical unsplit rotational energies; (ii) quadrupole energies as derived from first order theory; (iii) 1 2 7I quadrupole energy levels as derived from the exact Hamiltonian, showing the "exact" transition of (b). (b) The observed transitions compared to the calculated first order and exact Hamiltonian patterns. used for INCO. Again, the uncertainty in DK is rather larger in this case because really only one near degeneracy was involved. However the two levels involved, 13i,i3 and 112,9, are so close together (264 MHz) that the uncertainty is less than it might otherwise be. Although the determinacy of <f2 perhaps depends somewhat on this near degeneracy it really results from the measurement of several a-type R branch transitions with KA = 2 [4-19], which could not be done for INCO [4-2]. Comparison of the present results with those of Moloney [4-6] (Table 4.2) indicates 129 that we have obtained a great improvement in the accuracy of the constants, as well as the first measurement of the centrifugal distortion constants. Moloney's values are re-markably good however, considering the small amount of data he had to work with. Two years after the work presented in this chapter had been published [4-3], Hayashi, Ikeda, and Imagusa [4-20] reported the repetition of the analysis of the microwave spectrum of normal vinyl iodide. They also have analysed the microwave spectra of several isotopic species. The constants they have obtained for the parent isotopomer of vinyl iodide agree quite well with ours (see Table 4.2) with the exception of AQ. This is because they have not measured transitions which allow the separation of AQ and DK- Although they did measure 10 6-type transitions compared with our 2, our constants are all more precise, reflecting our larger data base. 4.3.4 The Structure of Vinyl Iodide The inertial defect, A, is an important parameter used for testing the planarity of a molecule: J A = 7° - 7° - 7° (4.27) A would normally be zero for a planar molecule in its equilibrium configuration. However, A is usually a small positive number, mostly because of in-plane vibrational effects, but also because of out-of-plane vibrational effects and electronic and centrifugal effects [4-21]. The inertial defect of vinyl iodide in its ground vibrational and electronic state, given in Table 4.2, is a small positive number, consistent with a planar structure. The value obtained is at variance with 0.24 amu A 2 , obtained by Moloney [4-6] and reflects the improved accuracy of AQ. An attempt to account for A assuming that it arises chiefly 130 from the lowest frequency in-plane vibration, u>9, using the simple equation [4-22]: (4.28) where K = g£j, gives u9 = 524 cm - 1 , considerably different from the measured value of 309 cm - 1 [4-17], [4-18]. This situation, which also arises for other vinyl halides [4-23], is probably due to the presence of other low frequency modes. It would be more fruitful to account for A using a full harmonic force field. The harmonic force field calculations employed the following matrix equation [4-24]: G F L = L A (4.29) where F is the force constant matrix, A is the diagonal matrix containing the squares of the vibrational wave numbers, G is the inverse of the matrix that relates conjugate momentum to kinetic energy (2T = RT G _ 1 R), and L is the matrix which relates the normal coordinates Q to the internal coordinates R (R = L Q). The diagonal elements in F are the principal force constants of the bond stretches and angle changes, while the off-diagonal elements are the interaction force constants between each internal coordinate. It can be seen from equation 4.7 that the centrifugal distortion constants are related to the harmonic force field, and in favorable cases can be used to refine it. The normal modes of vinyl iodide transform as 9A'-f-3A" in the point group Cs; since the molecule is planar, only the in-plane (A') force constants contribute to the distortion constants. An attempt was made to account for the observed values using the modified valence force field of Elst et al. [4-18]; the results are in Table 4.4. Very reasonable agreement has been obtained for all the constants although one, d2, disagrees by a factor of ~2.3. Because of the disagreement, and because, in fact, the published force field was approximate, attempts were made to refine the A' force constants with a least squares fit including distortion constants as new information. The published in-plane symmetry coordinates were used 131 Table 4.4: Predicted and observed centrifu-gal distortion constants (in kHz) of vinyl io-dide. Predicted a Observed Dj Dm DK d2 1.080 -24.57 1.037 -25.20 1095. 1224. -0.095 -0.0033 -0.0766 -0.00792 "Predictions are from the harmonic force field of Ref. [4-18]. [4-18] and the diagonal force constants and several off-diagonal constants (notably those involving C-I stretches and Z( I - C - X ) bends) were released one or two at a time in the fits. No significant improvement in the force field could conclusively be made in this way, and the attempts were abandoned. The ground state inertial defect was also calculated from the harmonic force field, via the harmonic parts of the vibration-rotation a constants[4-25]. The a constant gives the vibrational dependence of the rotational constant in the following way [4-7]: where G stands for each of the rotational constants A, B, and C. Vk and dk are the vibrational quantum number and degeneracy of the kth normal mode, respectively. To determine A for vinyl iodide in this way both the A' and A" force constants were re-quired. Although the known A' constants were adequate for this [4-18], we were required to reevaluate the out-of-plane constants because our out-of-plane coordinates [4-26] are different from those of Elst et al. [4-18], and the latter, in any case, have been shown to (4.30) 132 Table 4.5: The harmonic force field of vinyl iodide. Geometry: as in Ref. [4-18] A' block: symmetry coordinates and force field as in Ref. [4-18]. A" block: Symmetry coordinates: Sio — A 7 (CHI)a Su = A 7 (CH 2)a 5i2 = A r a Force constants (mdyn A rad-2) 7*io,io 0.349 7*io,ii 0.010 0.297 7^10,12 -0.015 7*12,12 0.110 7*11,12 -0.030 Observed (Ref. [4-18]) and calculated wave numbers and Coriolis coupling coefficients. Obs. Calc. |Obs.| Calc. 0.31 -0.31 0.41 0.38 0.39 -0.49 "These are the parameters of Hoy, Mills, and Strey (Ref. [4-27]). In the present case the 5-matrix elements are, with the atoms labeled as in Ref. [4-18]: c2 7 H4 # 5 776 1.8634 -0.6559 -0.4180 -0.7896 0.0000 0.0000 Sn 0.6557 -2.2386 0.0000 0.0000 0.7839 0.7990 Si 2 0.4658 0.0150 0.5637 -1.0650 -1.0560 1.0764 be incorrect [4-27]. The available data were vibrational wave numbers and Coriolis cou-pling coefficients4 [4-17], [4-18]; since, however, our programme will not fit to off-diagonal Coriolis coupling coefficients, we were forced to make trial and error calculations repro-ducing the wave numbers, letting the Coriolis coupling coefficients follow. The results are in Table 4.5. Fortunately, the resulting force field is nearly diagonal, consistent with those of other vinyl hah des [4-29], [4-30], [4-31], and very reasonable values of the Coriolis coupling coefficients were calculated. We have clearly obtained a very useful approximate 4The Coriolis coupling coefficients, £ ° t , are a measure of the interaction of a pair of normal coordi-nates, r,s, induced by rotation about one of the axes, a = a, b, or c [4-28] uio 948 948 (7,10 vn 910 907 C?,ii 1/12 539 534 Cs.12 133 force field; in any case overall a constants and the inertial defects are rather insensitive to slight variations in the out-of-plane constants. The ground state inertial defect calculated from the force field is 0.1328 amu A 2 , this time in good agreement with the observed value. The inertial defect of the 91 excited vibrational state has also been calculated from the force field, as 0.2548 amu A . This is in excellent agreement with the measured value for the apparent lowest excited vibrational state, thus confirming the assignment. Because the spectrum has been measured for only one isotopic species, only a little structural information can be obtained. Ground state average (rz) [4-32] values for the C-I bond length and ICC bond angle have been estimated, with all other structural parameters fixed at the rav values of vinyl bromide [4-3.1]. This is justified because the fixed parameters hardly vary in the other vinyl halides. To do this, harmonic parts of the Q constants obtained from the force field were subtracted from the experimental rotational constants. A least squares fit was then made to the corresponding moments of inertia; the resulting parameters are in Table 4.6. They are reasonable in comparison with those of related molecules, and the sum of the covalent radii [4-33], and are in excellent agreement'with the substitution (r„) values found more recently by Hayashi, Ikeda, and Inagusa [4-20]. The relative positions of the atoms in the principal inertial axis system are in Figure 4.5. The 1 2 7 I quadrupole tensor was diagonalized; the principal values are in Table 4.7. The angle between the ^-principal axis and o-inertial axis, found from the diagonalization process, is 16.0°. This is slightly higher than 15.2° ± 0.7° obtained by Moloney [4-6], but is nevertheless within ~ 1° of the angle between the C-I bond and the a axis (15.65°). Within the limits of the accuracy of the structural determination this difference is probably not significant, and the maximum electron density can be taken to be along the C-I internuclear axis. 134 Table 4.6: Structural parameters of vinyl iodide and re-lated compounds. Molecule r(C-X)/A Z(XCC)/deg CH 2CHI 2.081(6)° 123.2(3)° CH 2 CHI 6 2.084(1) 122.97(7) CH 2 CHBr c 1.880(7) 122.8(3) CH 2 CHCl d 1.726(5) 122.3(5) C H 2 C H F e 1.347(9) 120.8(3) CH 3 I e 3.132(1) C F 3 C F 2 I e 2.142(40) 113.4(16) CI 2 CI 2 e 2.106(5) 127.9(5) HCCI 1.988 ... CH 3 CIO e 2,217(9) 111.8(9) CH 3 CH 2 I e 2.139(10) 112.2(5) "Ground state average (r,)values; see the text. 'Ground state substitution (r,) values from Ref. [4-20]. eRef. [4-31]. ''Ref. [4-40]. eRef. [4-41]. The three most predominant canonical forms of vinyl iodide are probably: v / c + - c c — c / = \ / ^ / \ H H H H H H ( I ) ( II ) ( I" ) Assuming that partially filled bp orbitals are primarily responsible for the electric field gradient around the I nucleus, one can relate the elements of the quadrupole tensor to the 135 Table 4.7: Principal values of the 1 2 7 I quadrupole coupling tensor. ~x7z -1871.5(12)° MHz X x x 985.70(67) MHz Xyy 885.75(46) MHz "Numbers in parenthese are one standard deviation in units of the last significant figure given. number or fractional number of electrons in their orbitals using the equations of Townes and Dailey [4-7]: Xgg = eQqg = ~(Up)geQqn,m g = x,y,z (4.31) {Up)x = \(ny + n z ) - n x (UP)y = \{nz + n x ) - n y (Up), = \(nx + ny)-nz (4.32) where nx, n y, and nz are the number of electrons in the px, py, and pz orbitals, and qnim is the electric field gradient coupling constant for a single atom. The difference 2^x^Qgiyy^ is a measure of the 7r character of the C-I bond (i.e., the contribution of form III) [4-34]; this is ~3% (Moloney [4-6] obtained 2%). The ionic character, i, is obtained from [4-7]: Xz, = eQqi[(l-i) + 2i(l + e)] (4.33) where (1 + e) accounts for the decreased screening effect at the I nucleus by the electrons in form II. e « 0.15 for the halogens [4-9]. The contribution of form II was calculated as 17% (as compared with 23% for vinyl chloride). The covalent character is thus ~ 80%. 136 b \ /Q 1/ / * i.o H "1 °x / V1.0 \ -2.0V X H H Figure 4.5: The positions of the atoms of vinyl iodide in its principal axis system; coordi-nates are given in angstroms. At the right the most likely direction of the dipole moment is given. 4.4 The Dipole Moment Because many resolved Stark components were observed, it has been possible to measure the dipole moment. Although many dipole moments have been obtained by microwave spectroscopy this was a nontrivial problem for vinyl iodide for two reasons: (i) Since the spectrum showed large, often perturbed quadrupole structure, care had to be taken to ensure that the derived values were not distorted by the perturbations, and 137 (ii) Since m <C pa most Stark shifts could be expected to be largely independent of fib, and further care had to be taken to measure components where this was not the case. Fortunately, both difficulties could be overcome, and well-determined values for both /z0 and fib have been obtained. The formalism used to explain the effects of an applied electric field on the microwave spectrum of an asymmetric rotor has been extensively treated in the textbook of Gordy and Cook [4-7]. Most of the formulae used in this discussion have been extracted from that reference. The Hamiltonian used to explain the microwave Stark spectrum of any molecule is: Hstark = - / i - E (4.34) where n is the permanent electric dipole moment of the molecule, defined in terms of the molecule fixed axis system, and E is the external electric field which is assumed in the present case to be constant in magnitude and to be oriented along the space fixed Z axis. Therefore, Hstark can be rewritten: Hstark = -E Yl N*zg (4-35) g=a,b,c where the $zg terms are the direction cosines. In the weak field case, the energies due to the Stark effect are much smaller than the nuclear quadrupole hyperfine splittings and thus can be treated with second order perturbation theory. The spatial degeneracy of the basis functions (Equation 4.2) is removed and the energy levels split into 2F+1 MF components. The shifted energies of these are given by [4-7]: [Lg '\JKaKcMF - HgE p p (4.36) JI F l ^JXaKcIF - Ev i F , where the energies in the denominator are those of the MF degenerate lines and can be 138 extracted from our global least squares program. The sum is over all states which are connected by the direction cosine $zg- We have used the formula for the Stark energies for the situation where the Stark splitting is small with respect to the hyperfine splitting presented by Gordy and Cook [4-35]. This was based on their evaluation of the direction cosine matrix elements from equation 4.36. If the fia component of the dipole moment dominates equation 4.36 and the molecule is a near prolate rotor, then the strongest Stark interaction is between the two components of the asymmetry-split levels. Consider Figure 4.2, in particular the 5i,5 <— 4^4 and 5i ,4 <— 4 i ) 3 transitions. When an external electric field is applied the F components of levels 5it5 and 5i ,4 interact as do those of 4 i 4 and 4i , 3 . The result is that the interacting levels are pushed away from each other as a function of increasing field. It follows from equation 4.36 that the closer the zero field levels are to each other, the faster they shift. This means that the Stark effect causes all the Mp components of the 5i,5 <— 4 l t 4 transition to move to higher frequency and all those of 5^4 <— 4 i ) 3 to move to lower frequency (with respect to the zero field transition frequency). This phenomena helped us to assign the microwave Stark spectrum of vinyl iodide as will be seen shortly. To determine the dipole moment of vinyl iodide the following procedure was used. Initially a value for \ia was obtained using the |Mp | = 1/2 and 3/2 components of transition F = 5/2 +— 3/2 of 5^5 <— 4 i j 4 . This choice was governed by several factors. The closest levels to these two which might cause quadrupole perturbations are 7o,7 and 6o,6, respectively (Figure 4.2); since, however, the perturbations require A F = 0, and F ^ 5/2 or 3/2 for J = 7 or 6, respectively, there could be no perturbations from this source. The next nearest perturbing levels are 5o,s and 4o,4, both of which are over 48 GHz away from 5i ,4 and 4 i ) 3 , respectively, and their effect on the Stark shifts is negligible. The actual measured Stark shifts could thus be accounted for using the weak field approximation derived assuming no perturbations. A plot of Stark shift Avstark vs. E2 gave a straight 139 line and a good first estimate of fia — 1.30 D (see Figure 4.6). To confirm that fib had no effect on this measurement, and that there was no effect due to perturbations, the determination was repeated using the corresponding Stark components of 5i,4 *— 4^3, with the same result. The component fib was obtained using the transition 7ij *— 61,6- For this, the lower frequency component of an a-type K doublet, the Stark effect is usually dominated by the a-type near degeneracies 7^6 — 71,7 and 6i ) 5 — 6i ,6, with the result that the Stark components move to higher frequencies. For vinyl iodide several components actually move to lower frequency (Figure 4.7). The energy level diagram shows that, fortuitously, both these levels have 6-type near degeneracies (80,8 — 7\,i a n d 6i,6 — 7o,7) in the cor-rect arrangement to counteract the a interaction, making this an excellent candidate for measuring fib-An estimate of fib was obtained by making Stark measurements using components \MF\ = 7/2 and 1/2 of F = 9/2 «- 7/2 of 71<7 <- 61,6. These two are shown in Figure 4.7. The choice of components was governed by the same considerations as for 5i,5 +— 4 1 4 . Initially the effect of fia was calculated, and subtracted off the measured frequencies. A plot of the differences against E2 again gave a straight line, and fib was estimated, again using the weak field equation [4-35]. Any effects of perturbations on the components of 7i,6 and 61,5 arising from their near degeneracies with 80,8 and 7o,7 were found to be negligible. This was done by extracting the coefficients of all the functions contributing to the eigenfunctions of these levels from our global fitting programme. Finally, a simple simultaneous least squares fit was made of all measured Stark shifts (19 measurements) to fia and fib- The results are in Table 4.8. The relative magnitudes of the a and b components of the dipole moment are con-sistent with the observed relative intensities of the a- and 6-type transitions. The total dipole moment, 1.312 D, is a little larger than 1.17 D, predicted by Abraham and Hudson 140 (MHz) 3 — 2 — 1 — I ' l l I I I I I I - . , . . 1 2 3 4 5 6 7 8 9 10 E 2/'0 3 (V/cm) Figure 4.6: A plot of the Stark shift Astark vs. E2 of the \Mp\ = 1/2 component of the transition F = 5/2 <— 3/2 of 5i i5 <— 4i,4. zero field/U3593.09 MHz MOMHzH f Figure 4.7: Stark components of the transition 7i,7 «— 6i,6, displayed using a dc voltage of 900 V, with an ac voltage of ±25 V. Two Stark components having the two values of \MF\ for F" = 7/2 are indicated; these were used to evaluate fib. Note that \MF\ = 1/2 moves to low frequency, while \Mpj = 7/2 moves to high frequency. The frequency of the unsplit line is indicated. 141 Table 4.8: Dipole moment of the vinyl halides (in Debye units). 0.2468(6) 0.629(30) r1 total CH 2 CHP CH 2 CHF C CH2CHC1 CH 2 CHBr / 1.288(5)6 1.280(6) 1.42(2)d 1.311(5) 1.427(10) 1.45e 1.42 "This work. *In this work, numbers in parentheses are one standard deviation in units of the last significant figures. cRef. [4-38. dRef. [4-40. eRef. [4-42. >Ref. 4-36. [4-36]. Their calculation also suggested that the dipole moment of vinyl iodide should be substantially smaller than that of ethyl iodide. This is indeed the case, for the latter is 1.75 D, [4-37]. A similar trend is found for vinyl and ethyl fluorides, with dipole moments 1.43 and 1.96 D, respectively [4-37], [4-39]. The total dipole moment of vinyl iodide is compared with those of other vinyl halides in Table 4.8. The relative magnitudes are consistent with the smaller electronegativity of iodine. The angle between the dipole moment and the a-inertial axis is 11°, making it probably almost parallel to the C-I bond, with the negative end towards I. This is shown in Figure 4.5; it is consistent with the direction of the dipole moment of vinyl fluoride, which was also obtained from a microwave study [4-26]. 4.5 The Future Recently, the technique of using the full quadrupole Hamiltonian to analyse the mi-crowave spectra of molecules has come to the fore. The analyses of the spectra of molecules such as cyclopropyl bromide [4-43], propargyl bromide [4-44], and isopropyl - 142 iodide [4-45] have all been simplified using this technique. Experiments done with pulsed microwave spectrometers produce spectra with higher resolution than those obtained with conventional Stark spectrometers. This was the case with CF 2CFC1 [4-46] where even though the quadrupole moment of the chlorine nucleus is smaller than that of either a bromine or an iodine nucleus, the higher precision of the line measurements meant that a full quadrupole Hamiltonian analysis was needed in order to produce residuals (observed - calculated line frequencies) which were comparable to the experimental error. Presently, a pulsed microwave spectrometer is under construction in our laboratory. Analyses of the spectra of molecules containing Cl, Br, or I atoms will very likely employ the full quadrupole Hamiltonian to produce residuals limited by experimental error and not by choice of model. 143 4.6 Bibliography [4-1] H.M. Jemson, W. Lewis-Bevan, N.P.C. Westwood, and M.C.L. Gerry, J. Mol. Spectrosc. 118, 481 (1986). [4-2] H.M. Jemson, W. Lewis-Bevan, N.P.C. Westwood, and M.C.L. Gerry, J. Mol. Spectrosc. 119, 22 (1986). [4-3] D.T. Cramb, M.C.L. Gerry, and W. Lewis-Bevan, J. Chem Phys. 88, 3497 (1988). 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Rao, ed., Academic Press, New York, (1976). [4-15] J.K. Bragg, Phys. Rev. 74, 533 (1948). [4-16] B.S. Ray, Z. Physik 78, 74 (1983). [4-17] R. Elst and A. Oskam, J. Mol. Spectrosc. 40, 84 (1971). [4-18] R. Elst, W. Rogge, and A. Oskam, Rec. Trav. Chim. Pays. Bas 92, 427 (1973). [4-19] G. Winnewisser, J. Chem. Phys. 56, 2944 (1972). [4-20] M. Hayashi, C. Ikeda, and T. Inagusa, J. Mol. Spectrosc. 139, 299 (1990). [4-21] T. Oka and Y. Morino, J. Mol. Spectrosc. 6, 472 (1961). [4-22] V.W. Laurie and D.R. Herschbach, J. Chem. Phys. 40, 3142 (1964). [4-23] M.C.L. Gerry, Can. J. Chem. 49, 255 (1971). [4-24] L.A. Woodward, Introduction to the Theory of Molecular Vibrations and Vibrational Spectroscopy, Oxford University Press, London, (1972). 145 [4-25] T. Oka and Y. Morino, J. Mol. Spectrosc. 6, 472 (1961). [4-26] D. de Kerckhove Varent, Ann. Soc. Sci. Bruxelles 84, 277 (1970). [4-27] A.R. Hoy, LM. Mills, and G. Strey, Mol. Phys. 24, 1265 (1972). [4-28] G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand, New York, (1945). [4-29] P.A.G. Huisman, F.C. Mijlhoff, and G.H. Renes, J. Mol. Struct. 51, 191 (1979). 4-30] P.A.G. Huisman and F.C. Mijlhoff, J. Mol. Struct. 54, 145 (1979). 4-31] P.A.G. Huisman and F.C. Mijlhoff, J. Mol. Struct. 57, 83 (1979). 4-32] A.G. Robiette, in Molecular Spectroscopy by Diffraction Methods, a Specialist Periodical Report, Vol. 1, pp. 160-197, The Chemical Society, London (1973). 4-33] L. Pauling, The Nature of the Chemical Bond, 3 r d Ed., Cornell University, Ithaca, (1960). 4-34] J.H. Goldstein, J. Chem. Phys. 24, 106 (1956). 4-35] W. Gordy and R.L. Cook, op^ dt, equation 10.95. 4-36] R.J. Abraham and E. Hudson, J. Comput. Chem. 6, 562 (1984). 4-37] T. Kasuja and T. Oka, J. Phys. Soc. Jpn. 15, 2961 (1960). [4-38] A.M. Mirri, A. Guarnieri, and P.G. Favero, II. Nuovo Cimento 19, 1189 (1961). 146 [4-39] J. Kraitchman and E.P. Dailey, J. Chem. Phys. 23, 184 (1955). [4-40] D. Kivelson, E.E. Wilson, and D.R. Lide, J. Chem. Phys. 32, 1 (1960). [4-41] J.H. Collomon, E. Hirota, K. Kuchitsu, W.J. Lafferty, A.G. Maki, and CS. Pote, in Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Group II, Vol. 7, edited by K.-H. Hellwege, Springer, Heidelberg, (1976). [4-42] J.A.C. Hugill, I.E. Coop, and L.E. Sutton, Trans. Faraday Soc. 34, 1518 (1938). [4-43] H. Li, M. Sc. Thesis, The University of British Columbia, (1989). [4-44] P.K.J. Duffy, C. Hwang, D.T. Cramb, W. Lewis-Bevan, and M.C.L. Gerry, J. Mol. Spectrosc. 127, 549 (1988). [4-45] J. Gripp and H. Dreizler, Z. Naturforsch. 45a, 715 (1990). [4-46] K.W. Hillig II, E.R. Bittner, R.L. Kuczkowski, W. Lewis-Bevan, and M.C.L. Gerry, J. Mol. Spectrosc. 132, 369 (1988). 147 Appendix A A Reprint (with permission) of a Report of the Microwave Spectrum of Chlorodifluoromethane. 148 Journal of Molecular Structure, 190 (1988) 387-400 Elsevier Science Publishers B.V., Amsterdam — Printed in The Netherlands 387 THE MICROWAVE SPECTRUM, HARMONIC FORCE FIELD AND STRUCTURE OFCHLORODD7LUOROMETHANE,CHF2C1*** D.T. C R A M B , Y . BOS, H . M . J E M S O N " * and M.C .L . G E R R Y Department of Chemistry, The University of British Columbia, 2036 Main Mall, Vancouver, British Columbia V6T1Y6 (Canada) C J . M A R S D E N Department of Inorganic Chemistry, University of Melbourne, Parkville, Victoria 3052 (Australia) (Received 25 Apri l 1988) A B S T R A C T Rotational spectra of four isotopic species of cUorodifluoromethane, C H F 2 3 5 C 1 , C H F 2 3 7 C 1 , CDF 2 3 S C1 and CDF 2 3 7 C1, have been extensively measured, and have been analysed for rotational constants, centrifugal distortion constants and chlorine nuclear quadrupole coupling constants. The distortion constants have been combined with vibrational wavenumbers from the literature and with ab initio force constants calculated in the present work to refine the harmonic force field. Ground state effective (r0), substitution (r,) and ground state average (r,) structures have been evaluated for the molecule. I N T R O D U C T I O N Chlorodifluoromethane (CHF2C1, CFC 22) is rapidly becoming a replace-ment for CFC 11 and CFC 12 in refrigerators and air conditioners, because the latter are believed to be potential causes of stratospheric ozone depletion [1 ]. It is however, unclear that CHF2C1 is not also itself active in the destruction of ozone. It has been detected in the lower stratosphere [2], and has also been suggested as a tracer for Arctic haze [3]. Some means of monitoring it are its infrared [2] and possibly its microwave spectra. In order to understand these spectra properly highly accurate rotational and centrifugal distortion con-stants are needed. The spectrum of chlorodifluoromethane has been studied previously in the •Dedicated to the memory of Professor Walter Gordy. **Work supported by the Natural Sciences and Engineering Research Council of Canada. •"Present address: Science and Technology Division, Sci -Med New Zealand Limited, 60-66 France Street, South Newton, P.O. Box 68-232, Auckland, New Zealand. 0022-2860/88/$03.50 © 1988 Elsevier Science Publishers B.V. 149 388 microwave region by McLay and Mann [4], and by Beeson et al. [5]. Some isotopic data were obtained, though none for any deuterated species, and a partial structure was calculated. No attempt was made to account for centrif-ugal distortion. The infrared spectrum of CHF2C1 in liquid Ar was reported by McLaughlin et al. [6 ], and, most recently, the gas phase spectrum at moderate resolution was published by Magill et al. [7]. The latter obtained a harmonic force field from vibrational data and ab initio calculations. In the present paper we present extensive measurements of the microwave spectra of four isotopic species of chlorodifluoromethane (CHF236C1, CHF237C1, CDF236C1 and CDF237C1). They have been analysed to produce accurate rota-tional and centrifugal distortion constants and Cl nuclear quadrupole coupling constants. We also present a new estimate of the harmonic force field, obtained by combining our centrifugal distortion constants, results of a new ab initio calculation, and vibrational wavenumbers from the literature. It has been used to estimate the harmonic contributions to the vibration-rotation a-constants and the ground state average (rx) structure of the molecule. Ground state ef-fective (r0) and substitution (rB) structures are also presented. EXPERIMENTAL METHODS The samples of both normal and deuterated chlorodifluoromethane used in this work were kindly provided by W.F. Murphy, and were used without further purification. The spectra were measured in a conventional 100 kHz Stark mod-ulated spectrometer with 6 and 10 ft. X-band cells. The fundamental power was provided initially by a Hewlett-Packard 8400C Microwave Spectroscopy Source (8-40 GHz) and later by a Watkihs-Johnson 1291A Synthesizer (8-18 GHz) a strolled by a Digital Micro-PDP 11/23+ Computer, which was also used for data collection and analysis [8]. Where necessary the synthesizer frequency was multiplied by Honeywell-SpaceKom 14-27 and TK a-l multi-pliers, to provide a total frequency range of 8-60 GHz. The data were collected with the samples held at both room and dry ice temperatures. OBSERVED SPECTRA AND ANALYSIS A conventional bootstrap procedure was used to assign the spectra of each isotope. For the normal species the rotational and Cl quadrupole constants of McLay and Mann [4 ] were used to predict some previously unmeasured tran-sitions. Several were easily found and were included in a new fit, this time to rotational, distortion and chlorine quadrupole constants, which in turn were used for further predictions, leading to assignments, which were then included in the fit. This procedure was repeated several times. Several of the transitions in ref. 4 were remeasured; good agreement was obtained. In all 32 and 30 tran-150 TABLE 1 Observed rotational frequencies (in M H z ) , with hyperfine structure removed Transition Frequency Deviation* CHF^Cl l ) o - 0 o o 15095.938b 0.015 2 i i - 1 o I 24818.354b 0.019 3 3 o " 3 2 2 30405.675 0.058 3 3 i - 3 2 1 29294.778b 0.001 3 1 2 - 2 o 2 35288.224b 0.052 4 3 2 - 4 2 2 27906.008b -0.042 4 2 2 " 4 j 4 28300.928 -0.028 5 3 3 - 5 2 3 25629.461" -0.072 5 l 4 ~ 4 2 2 29058.735 -0.032 6 2 4 - 5 3 2 27716.971 0.020 6 1 5 _ 5 2 3 36234.590 -0.034 ' 2 5 - 6 3 3 38633.603 0.019 7 1 6 - 6 2 4 41455.901 -0.038 8 4 s - 8 3 5 35210.198 0.032 8 2 7 - 7 3 6 28324.068 -0.078 8 3 6 - ' 4 ] 32757.984 -0.048 9 4 6 - 9 j ( 31198.256 0.048 9 3 6 - 3 4 4 44823.177 -0.031 10 3 7 - 9 4 6 56845.069 -0.014 10 4 7 " 9 6 6 32346.369 -0.006 11 5 7 -10 6 6 29470.283 0.057 12 6 8 "II 6 6 38685.320 0.038 13 6 g -12 7 g 35087.663 0.005 14 5 10-14 4 1 0 28334.881 0.014 15 7 9 -14 g 7 40573.111 0.029 15 8 8 "14 9 6 27225.015 0.050 18 6 13-18 6 !3 28625.576 0.010 19 7 1 3 " 19 g 13 52283.420 0.049 20,2 9 -1913 7 21171.526 0.000 20 7 14-20 g 14 44326.082 -0.001 21 12 9 "20 13 7 30242.668 -0.013 22 7 16-22 g ie 27667.375 -0.016 23 8 16"23 7 !g 53184.274 -0.046 24 g n-24 7 17 43892.894 -0.007 2515 10-24 ie s 28037.855 -0.055 25 B 18"25 7 is 34549.035 -0.006 26 8 19-26 7 19 25797.495 0.035 2717 n-26i8 9 20616.326 0.032 2817 12-27 ig io 29608.865 0.013 3019 12-2920 10 22202.228 -0.009 CHF231Cl 1 1 0 - 0 0 0 14950.940 -0.033 2 2 1 - 111 35418.510 0.028 2 2 0 " 1 1 0 34332.780 0.047 151 390 T A B L E 1 (continued) Transition Frequency Deviation* CHF237Cl 3 2 i - 3 1 3 23417.650 0.022 3 i j - 2 0 2 34525.480 0.010 4 3 2 - 4 2 2 28689.190 0.027 4 3 , - 4 2 3 31550.870 0.038 5 s 2 - 5 2 4 32889.380 -0.008 5 1 4 - 4 2 2 27651.350 -0.055 6 , . - 5 2 3 34937.010 -0.021 8 4 6 - 8 3 6 36843.600 -0.073 9 4 e - 9 3 6 33169.880 0.006 10 4 7 -10 3 7 28699.760 -0.021 13 6 7 -12 7 6 30621.820 -0.058 14 5 10 -14 4 ,0 31976.040 -0.023 16 a 9 -15 9 7 30524.830 0.026 18 6 13 "18 6 13 33826.570 0.032 19 6 14 -19 6 ,4 26586.930 0.054 20 7 u -20 6 ,4 50789.150 0.019 20 6 15 -20 5 15 19806.750 0.050 2112 10 -20 13 8 22240.805 -0.010 22 7 1 6 -22 e 16 34480.900 -0.030 23)3 io -2214 B 26833.300 0.018 24 13 i 2 - 2 3 1 4 10 35700.090 -0.015 24 M „ - 2 3 1 5 g 22619.480 0.026 24 , i 8 -24 6 ,e 19265.070 -0.044 26 15 l 2 - 2 5 1 6 10 27205.020 0.023 26 s 19 -26 7 19 34145.710 -0.053 2716 11 -26 17 g 23009.900 0.054 28 16 13 _ 27]7 u 31796.790 0.015 29 17 13 -28 i s 11 27589.816 -0.047 30 18 13 -2919 11 23408.720 -0.033 30 9 22 -30 8 22 33017.170 0.031 CDF23b CI 1 . 0 - 0 o 0 14554.150 0.038 2 2 0 - 1 1 0 33119.010 -0.037 3 2 2 - 3 1 2 13433.520 -0.014 3 3 0 - 3 2 2 28539.898 0.057 3 ] 2 - 2 0 2 34239.470 0.048 4 2 2 - 4 1 4 26359.240 -0.043 4 3 , - 4 2 3 29176.480 -0.008 5 4 2 - 5 3 2 38826.730 -0.051 5 3 2 - 5 2 4 30556.390 0.067 5 4 1 - 5 3 3 39408.650 0.010 5 2 3 " 5 , 5 31774.570 -0.028 5 1 4 - 4 2 2 29230.260 -0.072 6 3 3 - 6 2 6 33127.570 -0.041 6 1 5 - 5 2 3 36446.220 0.027 7 4 4 - 7 3 4 36044.020 0.077 7 3 4 - 7 2 6 37372.660 0.047 152 391 T A B L E 1 (continued) Transition Frequency Deviation* CDF^Cl 8 4 S - 8 3 6 33298.110 -0.003 9 4 6 - 9 3 8 29627.850 -0.040 10 2 9 - 9 3 7 38030.490 -0.027 11 6 7 -10 e 6 31876.940 -0.031 11 6 6 -10 8 4 32816.130 -0.062 12 g g -12 4 e 38284.210 -0.012 12 6 7 "II 7 6 28748.100 0.049 13 g g -13 4 9 33088.710 0.023 13 g g -12 7 g 37896.180 0.021 14 6 1 0 - 1 4 4 1 0 27341.110 -0.007 15 8 7 -14 9 6 31313.550 -0.030 17 g 12-17 g 12 34856.500 0.012 18 g 13-18 6 13 27969.940 0.033 19 11 8 - 18l2 6 30693.070 0.005 21 7 15~21 g i5 35184.480 -0.079 22 7 ig-22 g ig 27430.170 0.035 2314 9 -2215 7 30192.110 -0.008 24i5 i o ~ 2 3 i 6 8 27102.300 0.077 25 8 18~25 7 1 8 34320.780 0.018 25 16 10-24 ie 8 35927.180 -0.016 27n io-26]g s 29739.920 0.036 28n 12~2718 io 38554.230 0.035 29 9 21*29 g 21 32517.990 -0.004 29 ie ii-2819 9 35458.360 -0.009 30 19 12-29 2 0 io 32379.140 -0.070 CDF^Cl 2 2 1 - 1 1 1 34021.770 0.034 2 2 0 " 1 1 0 33016.840 0.059 3 3 1 - 3 2 1 - 28160.720 -0.062 3 1 2 - 2 o 2 33504.940 0.016 4 3 1 - 4 2 3 29615.680 0.020 4 3 2 - 4 2 2 27017.420 0.039 5 2 3 ~ 5 i 5 32017.100 -0.009 5 3 2 " 5 2 4 30825.470 -0.027 6 4 3 " 6 3 3 38840.460 -0.084 6 1 6 - 5 2 3 35147.900 -0.029 6 3 3 _ 6 2 6 33081.840 0.012 7 3 4 ~ 7 2 6 36831.050 0.027 8 4 5 - 8 3 6 34841.060 0.006 9 4 6 " 9 3 6 31487.850 -0.028 10 4 7 -10 3 7 27380.570 -0.018 13 8 g -13 4 9 36231.180 0.041 14 6 io-14 4 ,0 30781.710 0.061 15 7 g -14 8 6 38489.930 -0.073 16 8 8 -15 9 7 34566.220 0.010 IS 6 13-18 5 13 32904.330 -0.027 2212 11-2113 9 37330.000 0.076 153 392 TABLE 1 (continued) Transition Frequency Deviation" CDF237Cl 22 7 ig-22 e 16 33941.840 0.024 24j4 i i -23is 9 30131.920 -0.035 2514 ii-2415 9 38766.700 0.077 26 g i«-26 7 19 34063.040 -0.061 26 is 12-2516 io 35173.930 -0.037 2716 11-26 17 9 31609.750 -0.050 2817 12-27 is io 28068.140 0.008 29ie i i - 28 i9 9 24544.640 0.059 29 n i2_28i8 io 36646.120 -0.037 30 9 22— 30 g 22 33426.690 0.028 30i9 12-2920 10 21035.860 -0.015 •Observed frequencies minus the frequency calculated using the constants in Table 2. bMcLay and Mann, ref. 4. TABLE 2 Spectroscopic constants of chlorodifluoromethane CHF^Cl CHF237C1 CDF^Cl CDF237C1 Rotational constants (MHz) A 10234.7025(37)' 10233.8570(42) 9804.9203(45) 9803.9417(59) B 4861.2434(16) 4717.1378(20) 4749.2119(19) 4610.1091(26) C 3507.4501(13) 3431.8596(19) 3500.4025(20) 3424.3312(28) Centrifugal distortion constants (kHz) Dj 1.2831(87) 1.2412(94) 1.2124(95) 1.1434(117) DJK 6.229(31) 5.929(44) 5.580(46) 5.408(65) DK 3.514(16) 3.886(16) 2.565(18) 2.844(17) d, -0.4472(70) -0.3984(59) -0.3818(61) -0.4297(230) d2 -0.1327(69) -0.1361(61) -0.1227(59) -0.06(02) Chlorine nuclear quadrupole coupling constants (MHz) Xoc -65.119(18) -51.342(31) -65.503(63) -51.483(38) X»-X« 5.818(40) 4.499(49) 5.546(67) 4.869(43) 'Number in parentheses is one standard deviation in units of the last significant figures. sitions were included in the final analyses for CHF235C1 and CHF237C1, respec-tively; they are given in Table 1. Initially for the deuterated species the rotational constants were predicted using the previously reported structure [ 4 ], and the quadrupole constants were transferred from the normal species. This procedure predicted li,0<-00,0 within 2 MHz; several other low J transitions were similarly easily found, and were used in an initial analysis. The bootstrap procedure described above was then 154 393 applied, unitl 41 and 32 transitions of CDF^Cl and CDF237C1, respectively, had been measured; they are also in Table 1. Only c-type transitions were found for both species, in agreement with the previous report [4] that fia<0.1fi„ with fic~1.5 debye. In all cases, too, no high-order effects were found for the CI hyperfine structure, so the quadrupole splittings were fit to the two constants Xaa and (Xbb—Xcc) with the usual first order equation [9]. To obtain the rotational and distortion constants the hyperfine splittings were subtracted off, and the unsplit lines were then fit by least squares to the constants of Watson's S-reduction in its Ir representation [10]. Some of the transitions of ref. 4 were included. Good values for all rotational and quartic distortion constants were obtained, with the apparent exception of d2 for CDF237C1. All the derived constants are presented in Table 2. H A R M O N I C F O R C E F I E L D Since the centrifugal distortion constants provide new information about the harmonic force field, an attempt was made to refine it including them as new experimental data, along with the wavenumbers of Magill et al. [7]. The symmetry coordinates used are in Table 3; because CHF2C1 has C, symmetry they transform as 6A' + 3A" respectively, and there are 27 force constants. The structure used was the r„ structure obtained in the present work (see later). Some 56 pieces of data (37 wavenumbers and 19 distortion constants) span-ning 7 isotopic species were used in the fits. The wavenumbers were given T A B L E 3 Symmetry coordinates used in the harmonic force field refinement of CHF 2 C1 Internal coordinates' r, = r (CH) a , = M H C C 1 ) 6, = L (HCFj) r2 = r (CCl ) a 2 = ^ ( F , C F 2 ) Rc = r (CFi) # = L (ClCFi) Symmetry coordinates A' block S , = Ar , 5 2 = (AR, + A R 2 ) / 2 1 / 2 5 3 = A r 2 St = A a , S 5 = A a 2 S 6 = ( A & + A & ) / 2 I / 2 A " block S 7 = ( A f i , - A f l 2 ) / 2 1 / 2 S 8 = ( A 0 , - A 0 2 ) / 2 , / 2 SB= ( A £ - A & ) / 2 I / 2 •Values used were those of the substitution structure in Table 6. 155 394 uncertainties of ±1%, with no account being taken for anharmonicity. The uncertainties of the distortion constants were assigned as ±5%. Although, except for d2, these are rather larger than those obtained from the analysis of the microwave spectra (Table 2), they were chosen to make the force field reproduce the vibrational wavenumbers. The data were given weights accord-ing to the reciprocals of the squares of the assigned uncertainties. Although there are many more experimental values than fitting parameters, many of the experimental values are effectively redundant, and not all the force constants could be obtained from the experimental data alone. We have T A B L E 4 Harmonic force constants of chlorodifluoromethane Ref. 7' Ab in i t io b F i t Species A' Fn 5.033 5.80 5.029(97) c Fa 0.169 0.253 0.217" F» 0.065 0.089 0.076" F14 - 0 . 0 7 4 - 0 . 0 6 4 - 0 . 0 5 5 " F » - 0 . 0 8 9 0.057 0.049" F 1 6 - 0 . 1 3 0 - 0 . 1 0 8 - 0 . 0 9 3 " F22 6.525 7.368 6.46(15) F23 0.733 0.861 0.739" - 0 . 3 5 0 - 0 . 4 8 1 - 0 . 4 1 3 d 0.397 0.438 0.376" F26 - 0 . 1 2 9 - 0 . 1 4 8 0.123 d F33 3.866 4.490 3.25(20) F 3 4 0.445 0.470 0.403" F* - 0 . 0 2 2 0.009 0.008" ^36 0.751 0.721 0.619" F„ 1.069 1.323 1.062(24) 0.401 0.364 0.312" F<e 0.784 0.865 0.742" F^ 2.174 2.297 2.174(45) F* 0.869 1.071 0.919" Fee 2.541 3.074 2.88(14) Species A" Fr, 5.347 5.816 6.39(26) Fn 0.656 0.624 0.510(61) F 7 9 0.641 0.558 1.62(26) •^88 0.779 0.965 0.789(17) F& 0.299 0.141 0.121" Fm 1.285 1.322 1.299(80) *The constants of ref. 7 were transformed with eqn. (2) to those used in the present work. b A b initio calculation of the present work. 'Numbers in parentheses are one standard deviation in units of the last significant figures. "These constants were fixed at the ab initio values scaled by (1.08)" 2 . 156 395 T A B L E 5 Observed and calculated wavenumbers and centrifugal distortion constants of chloro-difluoromethane " C H F ^ C I 1 2 C H F 2 3 7 C 1 " C D F j ^ C l " C D F 2 3 7 Cl Obs. Calc. Obs. Calc. Obs. Calc. Obs. Calc. Wavenumbers (cm'1) vy 3020.6 3032.8 • 3034 2260.5 2242.4 a 2243 v2 1313.2 1313.5 • 1313 1102.8 1100.6 a 1101 v3 1109.0 1101.8 1101 1012.7 1010.0 a 1010 vt 809.25 820.5 804.5 818.1 750.0 747.4 746.7 744.6 i's 596.3 598.1 595.4 597.4 592.1 593.7 591.1 593.0 v6 412.9 416.8 407.9 411.4 410.9 415.3 406.1 410.0 vn 1351.3 1353.4 • 1354 1161 1158.1 a 1157 v 8 1127.5 1126.8 1123 . 969 965.9 a 944 v9 365.0 365.8 • 364 365 362.7 a 361 Centrifugal distortion constants (kHz) Dj 1.270 1.260 1.260 1.200 1.210 1.198 1.140 1.084 DJK 6.24 6.05 6.06 5.81 5.58 5.26 5.41 5.10 DK 3.47 3.65 3.89 3.95 2.56 2.72 2.84 2.97 d, - 0 . 4 4 9 - 0 . 4 5 5 - 0 . 4 0 1 - 0 . 4 2 4 - 0 . 3 8 2 - 0 . 3 9 8 - 0 . 4 3 - 0 . 3 7 2 d2 - 0 . 1 3 2 - 0 . 1 8 4 - 0 . 1 4 0 - 0 . 1 7 4 - 0 . 1 2 3 - 0 . 1 5 0 - 0 . 0 6 " - 0 . 1 4 5 1 3 C H F 2 3 5 C 1 , 3 C H F 2 3 7 C1 1 3 C D F 2 M C 1 Obs. Calc. Obs. Calc. Obs. Calc. Wavenumbers (cm'1) vx 3010.6 3022.7 a 3024 a 2228 v2 1307.2 1306.9 a 1306 a 1072 v3 1083.5 1074.3 a 1075 1001.2 999.0 p< 788.9 797.7 785.5 795.2 a 735 v5 592.3 594.7 591.5 594.0 a 590 v6 412.8 416.6 407.8 411.1 a 415 vy 1346 1347.5 a 1348 a 1128 vt 1101 1104.8 • 1101 a 964 p9 363 362.8 a 361 a 360 "Not included in the least-squares fit. attempted to overcome the problem by doing an ab initio calculation of the force field, and then fixing some of the off-diagonal constants to their calcu-lated values in the fits to the experimental data. Although a similar ab initio calculation is reported in ref. 7, we have done a new evaluation using a different computer program, and a somewhat different basis set. Molecular orbital calculations were performed using the program Gaussian 157 396 82 [11]. A standard double-zeta basis was adopted [12], augmented with po-larization functions on all atoms (exponents were 0.6 for CI, 1.0 for F, 0.8 for C, and 1.0 for H). Force constants were calculated using SCF gradient proce-dures [ 13 ], adopting displacements of ± 0.02 A or 1 °, based on the experimen-tal reference geometry. The optimum geometry for CHF2C1 with this basis, at the SCF level is r(C-H): 1.075 A, r(C-F): 1.321 A, r(C-Cl): 1.759 A, L (HCCL): 109.5°, L (FCF): 108.1 % and L (FCC1): 109.8°, The C-H and C-F distances are slightly under-estimated, as is usually found for DZP SCF calculations [ 14 ], but the predicted C-Cl bond length is too large by 0.016 A; a larger basis on CI, with multiple polarization functions, would probably be needed for greater accuracy. Pre-dicted bond angles are correct to within about 1°, as again is expected for calculations at this level [ 14 ]. The SCF energy of CHF2C1 using our DZP basis is —696.85710 au. No attempt was made to account for anharmonicity in the vibrations. Least-squares refinements were made to the diagonal force constants along with various permutations of the off-diagonal constants shown by the Jacobian to be the most sensitive to the data. Because the ab initio calculation predicted wavenumbers about 8% higher than the measured values, the remaining con-stants were fixed at their calculated values, scaled down by (1.08) ~2. In the end the best fit was obtained with only F 7 8 and F 7 9 released. The results of both the ab initio calculation and the final fit are given in Table 4. A comparison of the observed wavenumbers and distortion constants with those calculated from the final force constants is given in Table 5. M O L E C U L A R S T R U C T U R E Because we now have additional isotopic information, attempts have been made to calculate a more definitive structure than was previously available T A B L E 6 Derived structural parameters of CHF 2 C1 r. r0 r, r ( C H ) (A) 1.098 1.100(86)" 1.098 r (CCl ) (A) 1.742 1.741(6)" 1.742 r (CF) (A) 1.346 b 1.354 « M H C C 1 ) ( ° ) H0 .8 b 110.7 Z.(C1CF)C) 110.5 0 111.0 Z . ( F C F ) ( t t ) 107.5 108.8(4)" 106.7 "Number in parentheses is one standard deviation in units of last significant figures. b Held fixed at the r, values. 158 397 [4]. Substitution (rg), ground state effective (r0) and ground state average (rx) parameters have all been obtained, as described below. The results are dis-played in Table 6. Since isotopic substitutions have been made at all atoms except F, an essen-tially full r, structure [15] has been obtained. The basis was 12CH19F235C1. Incorporating, in addition, the principal moments of inertia of 13CH19F236C1 from ref. 4, the coordinates of each atom (except F) along the a- and c-axes were calculated using Kraitchman's equations [16]. The coordinates of the F atoms were calculated using the first moment equations. As a check, the c-coordinates of F and Cl were also calculated by simultaneously solving the first moment and product of inertia equations. (This was done because the c-coor-dinate of Cl is very small and therefore uncertain [15].) The two calculations are in excellent agreement; the second gave in addition the sign of the Cl co-ordinate. The out-of-plane 6-coordinates of F were evaluated from the equation 4mFbF2 = Ia°+Ic°-Ib0-Ah (1) Ah, the inertial defect, was obtained from the harmonic parts of the a-con-stants calculated from the force field; the bF coordinates are thus only approx-imate rB coordinates and are better described as rz values [ 17 ]. An attempt was made to evaluate a ground state effective (r0) structure by fitting the rotational constants of all observed isotopic species to all six inde-pendent bond lengths and angles. Although there are some 15 rotational con-stants and only 6 unknowns, a definitive structure could not be obtained, partly because not all the constants are independent, but mostly because no isotopic substitution could be made at F, making several parameters very highly cor-related. The best that could be done was to float only three parameters, chosen to produce the least amount of correlation (r(C-H), r(C-Cl) and L (FCF)), with the remainder fixed at their substitution values. To obtain the ground state average (rz) parameters it was first necessary to correct the rotational constants using the harmonic parts of the a constants, obtained from the harmonic force field [17,18]. For the 1 3C species the data of ref. 4 were used. As with the r0 structure, attempts to fit the resulting con-stants to all the structural parameters produced very high correlations and uncertainties, chiefly because no isotopic substitution could be done at F. This approach was abandoned. The best that could be done was to repeat the r8 calculations with these moments of inertia to produce an approximate rz struc-ture. Clearly no account could be taken of the dependence of the average struc-ture on isotope, though since the variations are small they should make little difference. DISCUSSION AND CONCLUSIONS The present work represents the first report of the microwave spectrum of CDF2C1. As Table 2 shows, excellent values have been obtained for the rota-tional and quartic distortion constants for both 35C1 and 37C1 species. An ex-159 398 ception is the constant a\ for CDF237C1, which remained undefined after the least-squares fit, probably because of insufficient data. In addition, very sub-stantial improvement in the precision of the rotational constants of CHF2C1 has been obtained (as can be seen by comparing the values in Table 2 with those of refs. 4 and 5). We have also obtained the first measurements of the quartic distortion constants of the normal species. The constants have been obtained entirely from c-type transitions; we could find no a-type lines, con-sistent with the conclusions of both refs. 4 and 5. It is also clear from Table 2 that excellent values have been obtained for the CI quadrupole constants. For CHF2C1 the ratio ^*(35)/^ 6b(37) is 1.270, in excellent agreement with the ratio of the nuclear quadrupole moments (1.269); for CDF2C1 the ratio is 1.261, in poorer agreement, probably reflecting the lower precision of the constants. No evidence was found for high order quad-rupole coupling, in spite of the presence of some near degeneracies of the cor-rect symmetry. (For example the levels and 4^  are nearly degenerate, but no high order effects were seen in the transition 633-5^.) This is hardly sur-prising, however, because the C-Cl bond is only 14.4° from the a-axis in CHF235C1, so that | x*c I is very small (~ 26 MHz). An estimate of the principal values of the quadrupole tensor was neverthe-less made by assuming that the CC1 bond is the z-principal axis. The resulting values were %zz = —71.78 MHz andXxx = 36.31 MHz. Since Xzx~Xyy (=Xbb = 35.47 MHz), the bond is evidently essentially cylindrically symmetrical. With the reasonable assumptions that there is no re-back bonding from CI to C, and that the bonding orbital on CI has 15% s-character, application of the Townes-Dailey theory [19] suggests roughly 23% ionic character for the bond. The agreement between the observed wavenumbers and distortion con-stants and their corresponding values obtained from the force field (Table 5) would seem to confirm the validity of our force constants. They are compared with those of ref. 7 in Table 4; the latter had been transformed to the present symmetry coordinates with the following equation [20]: F! = PT 2 P (2) whereP = B 2B 1 t(B 1B 1 t)~ 1,F 1 andF2 are the matrices of force constants, and B x and B 2 are the corresponding B-matrices [21 ]. The agreement between the two sets of force constants is really quite good, with the only discrepancies of note in F 7 7 , F 7 9 and F 8 9 , all in the A" block. The cause of the discrepancies is unclear, especially since the trends of the ab initio constants and those of ref. 7 are similar; there are probably some linear dependences between the con-stants but we do not have enough data to distinguish them. Comparison of our "fit" force field and the ab initio field shows a similar discrepancy in these constants really only for F 7 9 , though there also seems to be some variation in F 3 3 . The differences between our ab initio field and that of ref. 7 (besides use of different programs, which should have little effect) are 160 399 that ours is better variationally, is more flexible, and has polarization functions on every atom. In ref. 7 there are d functions only in Cl; it was shown earlier for COFC1 [22] that this is probably not a good choice. In addition the struc-tural parameters used are slightly different. There is otherwise little to choose between the present force field and that of ref. 7. Both reproduce the wavenumbers reasonably well, entirely acceptably considering that anharmonicity has been ignored in both cases. The present force field, as it should, reproduces all the distortion constants about an order of magnitude better, except for d2 where the (obs—calc) values are compara-ble. The constant d2 has been difficult to reproduce in other cases as well [8]. For determination of rz structures both are reasonable, for the harmonic parts of the a-constants are very similar. The structures deserve comment. In general there is agreement between the r„ values and the structures reported earlier [4,5 ], though the angle L (HCC1) is 2-3° bigger. The r0 value is of limited utility because of the correlations mentioned above and because of the well-known difficulties of such structures [15]. The rz values are compatible in general with the rB values; because of the indeterminate nature of the rz structure, no attempt was made to obtain an approximate re structure. A C K N O W L E D G E M E N T S We thank W.F. Murphy for the samples of chlorodifluoromethane used in this work. We thank also D.B. McLay for helpful discussions. R E F E R E N C E S 1 Chem. Eng. News, 64 (Nov. 24,198C) 50. 2 A. Goldman, F.J. Murcray, R.D. Blatherwick, F.S. Bonomo, F .H . Murcray and D.G. Mur -cray, Geophys. Res. Lett., 8 (1981) 1012. 3 M .A .K . Khal i l and R.A. Rasmussen, Environ. Sci. Technol., 17 (1983) 157. 4 D.B. McLay and C R . Mann, Can. J . Phys., 40 (1962) 40. 5 E.L. Beeson,T.L. Weatherly and Q. Will iams, J . Chem. Phys., 37 (1962) 2926. 6 J .G. McLaughlin, M . Poliakoff and J J . Turner, J . Mo l . Struct., 82 (1982) 51. 7 J.V. Magil l , K . M . Gaugh and W.F. Murphy, Spectrochim. Acta, Part A, 42 (1986) 705. 8 D.T. Cramb, M.C.L . Gerry and W. Lewis-Bevan, J . Chem. Phys., 88 (1988) 3497. 9 C. Flanagan and L. Pierce, J . Chem. Phys, 38 (1963) 2963. 10 J . K . G . Watson, in J .R. Durig (Ed.), Vibrational Spectra and Structure, a Series of Advances, Elsevier, Amsterdam, 1976, vol. 6, pp. 1-89. 11 J .S. Binkley, M . J . Frisch, D.J. DeFrees, K. Raghavachari, R.A. Whiteside, H.B. Schlegel, E . M . Fluder and J -A. Pople, Chemistry Department, Carnegie-Mellon University, Pitts-burgh, 1983. 12 T . J . Dunning and P J . Hay, in H.F. Schaefer (Ed.), Methods of Electronic Structure Theory, Plenum Press, New York, 1977, Chap. 1. 161 400 13 P. Pulay, inHJ\ Schaefer (Ed), Applications of Electronic Structure Theory, Plenum Press, New York, 1977, Chap. 5. 14 JA. Pople, in HT. Schaefer (Ed), Applications of Electronic Structure Theory, Plenum Press, New York, 1977, Chap. 1. 15 CC. Costain, J. Chem. Phys., 29 (1958) 864. 16 J. Kraitchman, Am. J. Phys., 21 (1953) 17. 17 D.R. Herechbachand V.W. Laurie, J. Chem. Phys.,37 (1962) 1668,1687; 38 (1964) 3142. 18 T. Oka, J. Phys. Soc. Jpn., 15 (1960 ) 2274. 19 W. Gordy and R.L. Cook, Microwave Molecular Spectra, 3rd edn., Wiley, New York, 1984. 20 J.L. Duncan, PA. Laurie, GD. Nivellini, F. Tullini, A.M. Ferguson, J. Harper and K.H. Jorge, J. Mol., Spectrosc., 121 (1987 ) 294. 21 E.B. Wilson, Jr., J.C. Decius and P.C. Crow, Molecular Vibrations, McGraw-Hill, New York, 1955. 22 WD. Anderson, M.C.L. Gerry and C J . Marsden, J. Mol. Spectrosc., 114 (1985 ) 70. 162 Appendix B A Reprint (with permission) of a Report of the Microwave Spectru Propargyl Bromide. 163 J O U R N A L O F M O L E C U L A R SPECTROSCOPY 127, 549-555 (1988) Effects of Nuclear Quadrupole Coupling and Centrifugal Distortion in the Microwave Spectrum of Propargyl Bromide, BrH2CCCH The microwave spectrum of propargyl bromide was among the first observed to have perturbed Br quad-rupole hyperfine structure (7). An anomaly in the pattern of 12,.,, * - 12o,,2 was used to evaluate the off-diagonal coupling constant by second-order perturbation theory. Though the analysis gave reasonable values for both the rotational and the quadrupole constants, their accuracies were not so high as are usually obtainable by microwave spectroscopy. This was partly because not all the data were used in the analysis. It is clear from Ref. (7) that many other transitions are to some degree perturbed; one, 7 l i 6 — 101, is particularly so. Their inclusion in the analysis would probably have greatly decreased the uncertainties of the constants. We have recently measured the perturbed microwave spectra of several halogen-containing substances (2-4). In each case the measured transitions were included in a global least-squares fit, from which accurate rotational, centrifugal distortion, and nuclear quadrupole coupling constants were obtained. This was done using a specially written computer program. In some cases accurate values were even obtained for constants which were otherwise unmeasurable (3, 4). Because of the deficiencies mentioned above, propargyl bromide was also a good candidate for application of the method. Because the data for the program are measured transition frequencies, and these generally were not reported in Ref. (7), we have remeasured the relevant parts of the spectrum and have extended the mea-surements to higher J and Ka. Particular attention has been paid to transitions involving the levels 12,,n, 112.9, and 7,«. For the "Br species, for example, the first two, when unsplit, are only 975.3 MHz apart and interact strongly through the Br quadrupole matrix elements; the unsplit level 7,6 is only 239.5 MHz from 52,«, with which it interacts by the same mechanism. Similar considerations appl) for the "Br species. Transitions were observed between 20 and 54 GHz using a 100-kHz Stark-modulated spectrometer, in the latter part of the work it was interfaced to a Digital Micro PDP-11 computer for control of the source and for data acquisition and storage (4). The measured transitions of the ''Br and "Br isotopic species are given in Table I. Analyses with our program were carried out using both the A- and S-reductions of Watson's Hamiltonian (5) in its V repre-sentation. For a given species the goodness of the fit was essentially the same for both reductions. We report the results from the S-reduction in Table II, in comparison with the results of Ref. (7). We have clearly been able to improve the accuracies of the rotational and quadrupole constants, as well as to determine the quartic distortion constants for the first time. Table II also contains the diagonal elements of the Br quadrupole coupling tensors, as well as the angles 6 (between the r-principal quadrupole axis and the a-inertial axis) and V (between the C-Br bond and the d-axis). Clearly the z-axis and C-Br bond are essentially coincident. The ratio ij = (X„ - X„)/Xu is a measure of the deviation from cylindrical symmetry of the C-Br bond. Our values are internally more consistent than those of Kikuchi et al. (7) and imply that the bond is even more symmetrical than they suggest. If we assume that the bond has thus essentially zero T-character, then simple application of the Townes-Dailey theory (6) gives 0.22 as its ionic character. 549 0022-2852/88 $3.00 Copyright C 1988 by Academic Pres. Inc. AU rights of reproduction in toy form reserved. 164 550 NOTES TABLE I Measured Rotational Transitions (in MHz) of Propargyl Bromide Transit ion normaliBed' Observed Residuals* F' - P" Weight Frequency Without Y With x > f c "BrH.CCCH Transit ions 29037.649 -0.156 -0.029 29035.710 -0.953 0.041 29034.800 -0.533 0.08B 29033.900 -0.287 -0.306 29712.599 -10.313 -0.007 29721.944 -0.028 -0.025 29715.580 -5.592 -0.012 29720.483 0.224 -0.026 28458.783 0.054 0.027 28460.468 0.041 0.038 28461.757 -0.212 -0.006 26463.417 -0.270 0.007 33972.609 11.368 -0.002 33960.432 -0.027 0.008 33965.791 5.B5B 0.005 33959.377 0.209 0.074 33361.276 0.0 -0.056 33360.326 0.077 -0.002 33358.464 -0.058 -0.037 33357.712 0.178 0.001 49537.315 -0.016 -0.012 49536.543 -0.055 -0.016 49535.395 -0.089 "0.027 49534.761 0.007 -0.003 50879.345 -0.030 -0.063 50875.237 -4.513 0.007 50875.880 -4.332 0.026 50880.464 -0.128 -0.068 48731.448 0.025 0.053 4B730.666 -0.038 0.031 48730.270 -0.008 0.030 48729.627 0.065 0.055 49844.380 3.275 0.015 49840.486 0.001 0.002 49842.575 2.929 -0.244 49839.090 0.048 -0.027 39300.360 -0.178 0.001 39301.920 0.595 0.0 7 . , 6 0 1 13/2 - 11/2 1.000 11/2 - 9/2 1 .000 15/2 - 13/2 0.0 17/2 - 15/2 0.0 7 , . 6 t • 13/2 - 11/2 1.000 15/2 - 13/2 1.000 11/2 - 9/2 1.000 17/2 - 15/2 1 .000 7 , , 6 i c 17/2 - 15/2 1.000 15/2 - 13/2 1 .000 11/2 - 9/2 1.000 13/2 - 11/2 1.000 8 , , 7 i c 15/2 - 13/2 1 .000 17/2 - 15/2 1.000 13/2 - 11/2 1.000 19/2 17/2 1.000 8 , . 7 > • 15/2 - 13/2 1 .000 17/2 - 15/2 1.000 13/2 - 11/2 1 .000 19/2 - 17/2 1.000 12 o 1 3 - 11 0 I 1 23/2 - 21/2 1.000 25/2 - 23/2 1.000 21/2 - 19/2 1.000 27/2 25/2 1.000 12 , 1 1 - 11 1 1 0 27/2 25/2 1.000 21/2 - 19/2 1.000 25/2 - 23/2 1.000 23/2 - 21/2 1.000 12 , 1 > - 11 1 1 1 23/2 21/2 1.000 21/2 - 19/2 1.000 25/2 - 23/2 1.000 27/2 - 25/2 1.000 12 , 1 1 - 11 1 1 0 23/2 - 21/2 1.000 25/2 - 23/2 1.000 21/2 - 19/2 0.0 27/2 - 25/2 1.000 «2 , 1 O - 13 1 1 1 21/2 - 23/2 1.000 27/2 - 29/2 1.000 ' Measurements were weighted according to 1/c', where o is the uncertainty in the measurements. Unit weight corresponded to an uncertainty of 0.05 KHz. ' Observed frequency minus the frequency calculated using the constants in Table II. 165 NOTES TABLE I—Continued Transition Normalised Observed Residuals f - F* Weight Frequency Without % . With x 6 i • 9/2 15/2 11/2 13/2 -6 9/2 15/2 11/2 13/2 e 1 .000 1.000 0.0 1 .000 20920.372 20911.689 20877.757 20867.480 -2.406 -0.686 -1.479 -1.490 0.039 -0.016 0.150 -0.009 7 , , 1 1/2 17/2 13/2 15/2 -7 11/2 17/2 13/2 15/2 0 'l.OOO 1.000 1.000 1.000 21600.243 21598.033 21552.548 21554.733 -7.043 -0.415 -11.796 -0.876 -0.013 0.024 0.012 -0.013 8 , , 13/2 19/2 15/2 17/2 - 8 13/2 19/2 15/2 17/2 0 *1.000 1 .000 1.000 1.000 22408.191 22400.888 22365.637 22357.789 -0.787 -0.321 -0.405 -0.569 0.009 -0.001 -0.016 0.090 9 , . 15/2 21/2 17/2 19/2 -9 15/2 21/2 17/2 19/2 0 *1.000 1 .000 1 .000 1.000 23333.892 23327.422 23290.939 23283.818 -0.794 -0.261 -0.428 -0.618 -0.005 -0.012 -0.038 -0.016 10 , 17/2 23/2 19/2 21/2 i - 10 17/2 23/2 19/2 21/2 0 1 0 1 .000 1 .000 1.000 1.000 24390.940 24385.2B6 24347.479 24340.889 -0.910 -0.189 -0.382 -0.672 -0.043 0.014 -0.033 -0.008 12 , 21/2 27/2 23/2 25/2 i » - 12 21/2 27/2 23/2 25/2 0 1  0.0 0.0 1.000 1.000 26927.000 26927.000 26886.555 2687.6. 121 -5.864 -0.210 -0.398 -5.303 -0.171 -0.063 -0.026 0.002 13 , 23/2 29/2 25/2 27/2 i > - 13 23/2 29/2 25/2 27/2 0 11 1.000 1.000 1 .000 1.000 28434.038 26427.326 28365.607 28381.647 1.291 -0.118 -0.181 1.096 0.039 0.012 0.036 -0.009 l« . 25/2 31/2 27/2 29/2 11 - 14 25/2 31/2 27/2 29/2 0 1 a 1.000 1.000 1.000 1.000 30096.520 30090.920 30047.770 30043.410 0.437 -0.101 -0.180 0.450 -0.029 0.014 0.031 -0.011 11 » 23/2 21/2 25/2 19/2 • - 11 23/2 21/2 25/2 19/2 1 1 0 1.000 1.000 1.000 1.000 51865.981 51868.297 51852.635 51845.426 0.692 5.399 5.337 0.504 -0.046 0.005 -0.035 0.033 12 , 25/2 23/2 27/2 21/2 1 0 - 12 25/2 23/2 27/2 21/2 1  1 1.000 1.000 1.000 1.000 51187.861 51180.673 51165.051 51170.239 5.048 -0.097 -1.007 6.213 0.081 -0.067 0.025 -0.017 15 , 33/2 27/2 1 s - 15 33/2 27/2 1 1 « 1.000 1.000 49276.155 49274.650 -0.109 -0.499 0.023 0.065 16 , 35/2 29/2 i « - 16 35/2 29/2 1 1 • 1.000 1.000 48749.510 4B74B.253 -0.154 -0.561 -0.064 -0.066 166 552 NOTES TABLE I—Continued Transit ion normalised Observed Residuals F' - F" Weight Frequency Without x > b With x b 17 , i , - 17 , , , • 35/2 - 35/2 0 . 0 4 B 3 0 7 . 0 1 B - 0 . 5 9 4 - -0.133 3 3 / 2 - 3 3 / 2 0 . 0 4 B 3 0 7 . 0 1 B - 0 . 0 0 8 0 . 0 2 7 3 7 / 2 - 37/2 1 . 0 0 0 4 8 3 0 0 . 5 4 4 - 0 . 0 2 6 0 . 0 3 8 31 /2 - 31/2 1 . 0 0 0 4 8 2 9 9 . 5 1 4 - 0 . 4 6 6 0 . 0 1 4 *'BrH,CCCH Transit ions 2 4 2 4 3 . 2 3 8 - 0 . 0 6 3 0 . 0 0 7 2 4 2 4 1 . 1 3 7 - 0 . 0 3 2 0 . 0 1 8 2 4 2 3 9 . 7 1 0 0 . 0 3 1 0 . 0 2 4 2 4 2 3 7 . 6 1 9 0 . 0 4 8 0 . 0 2 1 2 8 8 4 5 . 2 3 2 - 0 . 1 3 7 - 0 . 0 4 5 2 B B 4 3 . 6 B 7 - 0 . 7 4 1 - 0 . 0 2 3 2 8 8 4 2 . 6 2 1 - 0 . 4 6 6 - 0 . 0 1 4 2 8 8 4 2 . 3 6 2 0 . 0 1 9 0 . 0 0 6 2 9 5 1 9 . 4 1 4 - 2 . 3 7 6 0 . 0 7 1 2 9 5 2 0 . 9 9 0 0 . 0 0 2 ' 0 . 0 0 3 2 9 5 1 8 . 5 6 4 - 1 . 7 7 0 - 0 . 0 0 9 2 9 5 1 9 . 7 4 2 0 . 1 9 0 0 . 0 1 1 2 8 2 7 7 . 2 1 1 - 0 . 1 6 6 0 . 0 1 3 2 B 2 7 5 . 8 3 9 - 0 . 1 0 1 0 . 0 3 4 2 8 2 7 4 . 6 5 4 0 . 0 0 8 0 . 0 0 5 2 8 2 7 3 . 2 5 1 0 . 0 2 6 0 . 0 0 8 3 2 9 4 0 . 2 6 0 - 0 . 0 2 6 0 . 0 0 7 3 2 9 3 8 . 9 0 7 - 0 . 3 2 9 - 0 . 0 5 B 3 2 9 3 8 . 5 6 7 - 0 . 1 9 7 - 0 . 0 2 6 32937.681 -0.010 - 0 . 0 2 1 3 3 7 3 4 . 7 9 9 3 . 1 6 6 - 0 . 0 3 4 3 3 7 3 0 . 9 0 2 - 0 . 0 6 5 - 0 . 0 4 2 3 3 7 3 2 . 4 5 4 1.913 - 0 . 0 4 5 3 3 7 2 9 . 9 7 8 0 . 0 9 0 - 0 . 0 0 6 4 1 2 7 5 . 8 6 8 - 0 . 0 0 8 0 . 0 0 6 4 1 2 7 5 . 2 5 5 0 . 0 3 1 0 . 0 2 6 4 1 2 7 3 . 9 6 8 - 0 . 0 4 1 - 0 . 0 0 8 4 1 2 7 3 . 4 2 3 0 . 0 4 8 0 . 0 1 5 4 5 6 6 6 . 9 7 0 2 . 0 8 3 0 . 0 0 7 4 5 6 6 4 . 7 0 3 - 0 . 1 3 0 - 0 . 0 2 5 4 5 6 6 4 . 3 0 6 0 . 0 9 7 0 . 0 5 1 4 5 6 6 6 . 1 9 7 2 . 0 3 1 - 0 . 0 1 5 6 , , - 5 , I 11/2 - 9 / 2 1 . 000 9 / 2 - 7 / 2 1 . 0 0 0 1 3 / 2 - 11/2 1 . 000 15/2 - 1 3 / 2 1 . 0 0 0 7 o » - 6 o < 1 3 / 2 - 1 1 / 2 1 . 0 0 0 1 1 / 2 - 9 / 2 1 . 000 15/2 - 1 3 / 2 1 . 0 0 0 1 7 / 2 - 1 5 / 2 1 . 0 0 0 7 , « - 6 , 1 1 3 / 2 - 1 1 / 2 1 . 0 0 0 1 5 / 2 - 1 3 / 2 1 . 0 0 0 1 1 / 2 - 9 / 2 1 . 000 1 7 / 2 - 1 5 / 2 1 . 0 0 0 7 , , - 6 , < 1 3 / 2 - 1 1 / 2 1 . 0 0 0 1 1/2 - 9 / 2 1 . 0 0 0 1 5 / 2 - 1 3 / 2 1.000 1 7 / 2 - 1 5 / 2 1.000 8 c . - 7 o 7 1 5 / 2 - 1 3 / 2 1 . 0 0 0 1 3 / 2 - 1 1 / 2 1 . 0 0 0 1 7 / 2 - 1 5 / 2 1 . 0 0 0 19/2 - 1 7 / 2 1 . 0 0 0 B , , - 7 , • 15/2 - 1 3 / 2 1 . 0 0 0 1 7 / 2 - 1 5 / 2 1 . 0 0 0 1 3 / 2 - 1 1 / 2 1 . 0 0 0 19/2 - 1 7 / 2 1 . 0 0 0 10 , , - 9 , • 1 9 / 2 - 1 7 / 2 1.000 2 1 / 2 - 1 9 / 2 1 . 0 0 0 1 7 / 2 - 1 5 / 2 1 . 0 0 0 2 3 / 2 - 2 1 / 2 1 . 0 0 0 '1 . • 10 , • 2 1 / 2 - 19/2 1 .000 1 9 / 2 - 1 7 / 2 1 .000 2 3 / 2 - 2 1 / 2 1 .000 2 5 / 2 - 2 3 / 2 1 .000 11 2 t> - 10 , f 2 1 / 2 - 19/2 1 .000 4 5 3 9 4 . 1 8 4 - 0 . 0 3 7 0 . 0 3 4 2 3 / 2 - 2 1 / 2 1 .000 4 5 3 9 3 . 6 8 9 0 . 0 5 3 0 . 0 5 2 19/2 - 1 7 / 2 1 .000 4 5 3 9 2 . 6 6 9 - 0 . 0 7 2 0 . 0 1 6 2 5 / 2 - 2 3 / 2 1 .000 4 5 3 9 2 . 2 8 3 0 . 1 1 3 0 . 0 7 6 12 > i o - 11 J * 2 1 / 2 - 1 9 / 2 1 . 000 4 9 8 6 0 . 9 4 2 1 .141 - 0 . 0 1 5 2 3 / 2 - 2 1 / 2 1 . 000 4 9 8 5 6 . 8 0 3 - 2 . 6 9 4 - 0 . 0 5 2 2 7 / 2 - 2 5 / 2 1 . 0 0 0 4 9 6 5 5 . 7 1 4 - 3 . 4 8 6 0 . 0 1 1 2 5 / 2 - 2 3 / 2 1 . 000 4 9 8 5 8 . 7 2 4 - 0 . 1 6 4 - 0 . 0 9 3 167 TABLE I—Continued Transit ion Normalised Observed Residuals F' P" Height Frequency Without xth 14 , i i - 15 i 1 • 31/2 - 33/2 1.000 33463.156 -0.715 -0.012 25/2 - 87/2 1.000 33464.453 -0.047 0.023 14 , 11 - 15 > i a 25/2 - 27/2 1.000 30499.662 -0.089 -0.030 31/2 - 33/2 1.000 30501.169 0.294 0.025 27/2 - 29/2 1.000 30505.931 0.213 -0.002 29/2 31/2 0.0 30506.574 -0.108 -0.131 7 , . 11/2 7 11/2 0 'l.OOO 21556.910 -2.738 0.041 17/2 - 17/2 1.000 21552.017 -0.2B9 0.022 13/2 - 13/2 1.000 21520.430 -3.484 0.017 15/2 15/2 1.000 21516.042 -0.602 0.008 9 , . 15/2 _ 9 15/2 0 *1.000 23263.859 -0.515 0.031 21/2 - 21/2 1.000 23258.376 -0.188 -0.012 17/2 - 17/2 1.000 23228.103 -0.251 0.021 19/2 - 19/2 1.000 23222.147 -0.447 -0.028 '0 , • - 10 0 1 0 17/2 17/2 1 .000 24306.616 -0.612 -0.017 23/2 - 23/2 1.000 24301.780 -0.159 -0.016 19/2 - 19/2 1.000 24270.478 -0.185 0.058 21/2 - 21/2 1.000 24264.988 -0.439 0.016 12 , - 12 0 i a 21/2 - 21/2 1 .000 26809.830 -3.025 -0.031 27/2 - 27/2 1.000 26808.020 -0.195 -0.092 23/2 - 23/2 1.000 26774.470 -0.295 -0.055 25/2 - 25/2 1.000 26767.440 -2.730 -0.065 13 , 1 3 - 13 0 \ 1 23/2 - 23/2 1 .000 28292.550 1.017 0.040 29/2 - 29/2 1 .000 26287.030 -0.106 -0.015 25/2 - 25/2 1.000 28252.360 -0.170 -0.020 27/2 - 27/2 1.000 28249.070 0.891 0.032 14 , 1 1 - 14 0 1 • 25/2 - 25/2 1.000 29931.470 0.402 0.058 31/2 - 31/2 1 .000 29926.800 -0.072 0.009 27/2 - 27/2 1 .000 29B90.940 -0.157 -0.010 29/2 29/2 1.000 29887.340 0.390 0.051 20 , 1 1 - 20 0 1 0 41/2 41/2 1 .000 43404.964 0.105 0.022 39/2 - 39/2 1 .000 43406.786 -0.109 -0.004 43/2 - 43/2 1.000 43448.792 -0.085 -0.034 37/2 37/2 1.000 43453.138 0.052 0.010 15 1 1 1 - 15 1 1 « 31/2 - 31/2 1 .000 49310.442 -0.421 -0.028 29/2 - 29/2 1.000 49309.857 -0.062 -0.005 33/2 - 33/2 1 .000 49301.087 -0.107 -0.011 27/2 - 27/2 1.000 49299.834 -0.417 -0.019 16 , 1 1 - 16 1 1 1 29/2 29/2 1.000 48770.430 -0.317 0.029 35/2 - 35/2 1.000 48771.449 -0.022 0.043 33/2 - 33/2 1.000 48779.018 -0.363 -0.025 31/2 - 31/2 1.000 46778.686 0.029 0.065 17 , 1 1 - 17 1 31/2 31/2 1.000 48316.038 -0.346 -0.013 37/2 - 37/2 1.000 48316.844 -0.054 -0.008 33/2 - 33/2 0.0 48322.513 0.072 0.096 35/2 - 35/2 0.0 48322.513 -0.441 -0.120 IB , 1 ( - IB 1 1 » 37/2 - 37/2 0.0 47955.925 -0.373 -0.039 35/2 - 35/2 0.0 47955.925 -0.029 -0.010 39/2 - 39/2 1.000 47952.069 -0.095 -0.060 33/2 33/2 1.000 47951.475 -0.345 0.007 553 168 TABLE I—Continued Transit ion Normalised Observed Residuals F" ~ F" Weight Frequency Without x . With x . ab 19 , 1 7 - 19 i i • 41/2 - 41/2 1.000 47691.291 -0.009 0.018 35/2 - 35/2 1.000 47690.717 -0.412 0.009 IB , 1 T - 17 1 1 1 33/2 - 31/2 1.000 31691.794 0.322 0.051 39/2 - 37/2 1.000 31890.348 1.200 0.004 35/2 - 33/2 1.000 31668.944 1.428 0.001 37/2 - 35/2 1.000 31865.579 0.290 -0.010 20 , 1 f - 19 t I t 37/2 - 35/2 1.000 43131.195 0.269 -0.023 43/2 - 41/2 1.000 43127.869 0.259 -0.020 39/2 - 37/2 1.000 43106.990 0.294 0.011 41/2 - 39/2 1.000 43105.871 0.309 0.005 TABLE II Spectroscopic Constants of Propargyl Bromide "BrBjCCCH •'SrHjCCCH Parameter This work lef-(I) This work Ref-O) Rotational con»t«nt«/KHz A„ 21010.306(12)" 21010.0(30) 20986.383(15) 20986.5(30) Bo 2169.3287(10) 2169.31(20) 2154.41049(64) 2154.37(20) Co 1989.0591(11) 1989.09(20) 1976.29845(73) 1976.34(20) Centrifugal distortion constants/kHz D J 0.9045(41) - 0.9022(23) -D JK -35.20(16) - -34.955(50) -Dlt 583.3(21) - 581.62(70) -"I -0.1627(10) - -0.15847(25) -"! -0.0046(11) - -0.00413(18) -Bromine nuclear quadrupole coupling constanta/MRz "a. 320.82(90) 316 269.45(95) 259 *bb " Xcc 281.241(94) 264 234.075(78) 233 H.bl 415.95(32) 403 346.52(65) 336 \z 599.99(42) 587 500.97(67) 484 \* -298.95(42) -286 -249.21(69) -238 -301.04(45) -301 -251.77(48) -246 eb 33*52'(2') 33*48' 33*45'(3') 33*59' e-b 34'2" 34*21 33*58' 33*58' nb 0.003 0.026 0.005 0.017 *Nuabers ID parentheses are standard deviations In units of the last algnlfleant figures. ^Following Bef. O), 0 la the angle between the quadrupole {.-axis and the a-lnertlal axis, 9' la the angle between the C-Br bond and the a-axls, and 554 169 NOTES 555 A C K N O W L E D G M E N T S This work was supported by the Natural Sciences and Engineering Research Council of Canada. Use of the C R A Y 1-S and X-MP computers of the Atmospheric Environment Service of Canada is gratefully acknowledged. REFERENCES 1. Y . K I X U C H I , E. H I R O T A , A N D Y. M O R I N O , / Chem. Phys. 31 , 1139-1140 (1959); Bull. Chem. Soc. Japan 34, 348-353 (1961). 2. M . C. L. G E R R Y , W. L E W I S - B E V A N , A N D N. P. C. W E S T W O O D , / Chem. Phys. 79,4655-4663 (1983). 3. H . M . JEMSON, VV. L E W I S - B E V A N , N. P. C. W E S T W O O D , A N D M . C. L . G E R R Y , / Mol. Spectrosc. 118, 481-499 (1986); 119, 22-37 (1986). 4. D . T. C R A M B , W. L E W I S - B E V A N , A N D M . C. L . G E R R Y , J. Chem Phys., to be published. 5. J. K. G. W A T S O N , in "Vibrational Spectra and Structure: A Series of Advances" (J. R. Durig, Ed.), Vol. 6, pp. 1-89, Elsevier, New York, 1977. 6. W. G O R D Y A N D R. L. C O O K , "Microwave Molecular Spectra," 3rd ed., in "Techniques of Chemistry" (A. Weissberger, Ed), Vol. 18, pp. 725-802, Wiley, New York, 1984. P . K . J . D U F F Y CHRISTINE H W A N G D A V I D T . C R A M B W. L E W I S - B E V A N * M . C. L. G E R R Y Department of Chemistry University of British Columbia 2036 Main Mall Vancouver. British Columbia Canada V6T1Y6 Received August 7. 1987 * Present address: Department of Chemistry and Biochemistry', Southern Illinois University at Carbondale. Carbondale. IL 62901. 170 Appendix C A Listing of Unassigned Ion Lines in the 18400 cm' 1 Region. £7 171 Table C l : Observed transitions in the 18400 cm 1 region 18310.106 18317.006 18320.676 18332.409 18334.606 18339.311 18343.347 18367.226 18375.072 18399.636 18403.903 18421.219 18425.670 18434.828 18438.715 18442.123 18443.759 18448.024 18451.985 18455.134 18458.202 18461.939 18463.851 18470.328 18475.307 18480.920 18483.780 18488.749 18491.244 18503.111 18507.153 18312.157 18318.636 18321.207 18333.006 18334.802 18341.622 18343.738 18367.357 18383.463 18402.137 18405.000 18421.740 18425.966 18435.073 18439.181 18442.298 18444.354 18449.652 18452.084 18455.364 18458.686 18462.130 18466.010 18470.580 18475.465 18481.778 18485.379 18488.877 18491.377 18503.456 18313.010 18318.786 18327.893 18333.208 18334.959 18341.997 18363.009 18374.355 18386.399 18402.217 18407.172 18421.923 18432.173 18435.624 18440.871 18443.297 18444.416 18449.775 18452.747 18455.540 18460.030 18462.261 18466.901 18471.510 18476.569 18482.010 18487.401 18488.963 18492.599 18504.095 18315.534 18319.547 18328.872 18333.689 18338.442 18342.521 18363.849 18374.481 18386.651 18402.517 18410.508 18422.142 18432.322 18435.839 18441.010 18443.380 18444.890 18450.818 18452.896 18456.601 18461.550 18462.396 18467.717 18471.835 18479.678 18483.043 18487.554 18489.689 18493.619 18504.212 18315.613 18319.618 18332.211 18333.729 18338.565 18342.647 18364.519 18374.719 18399.322 18402.879 18417.461 18425.467 18433.546 18438.473 18441.716 18443.541 18447.386 18450.884 18453.122 18457.839 18461.767 18462.565 18468.059 18472.649 18480.163 18483.266 18488.669 18490.882 18493.996 18506.188 172 

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