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Fourier transform microwave spectroscopy of lanthanum monohalides Rubinoff, Daryl Simon 2000

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F O U R I E R T R A N S F O R M M I C R O W A V E S P E C T R O S C O P Y O F L A N T H A N U M M O N O H A L I D E S By Daryl Simon Rubinoff B.Sc. Honors (Chemistry) University of Western Ontario A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE D E G R E E OF M A S T E R OF SCIENCE IN THE F A C U L T Y OF G R A D U A T E STUDIES DEPARTMENT OF CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 2000 © Daryl Simon Rubinoff, 2000 In presenting this thesis in partial fulfillment 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. Chemistry The University of British Columbia 2075 Westbrook Place Vancouver, Canada V6T 1Z1 Date: ABSTRACT The pure rotational spectra of the X 1 ! 4 " ground states of the lanthanum monohalides, 1 IQ t TO 11Q 1 "IQ LaF, LaCl, LaBr and Lal , have been measured using a pulsed-jet cavity Fourier transform microwave spectrometer in the range of 5-24 GHz. The molecules were prepared by ablating solid La with the second harmonic of a pulsed N d : Y A G laser and allowing the vapor to react with SF 6, C I 2 , Br 2 or CH 3 I precursor present as < 0.01% in an Ar carrier gas. Only the 7=1-0 rotational transition of LaF was measurable within the frequency range of the spectrometer, while multiple J transitions have been recorded for both L a 3 5 C l and L a 3 7 C l . The ground and first excited vibrational levels (v=0 and u=l) of LaF, L a 3 5 C l and L a 3 7 C l were recorded with an additional vibrational level, v=2, measured for LaF. Equilibrium geometries of LaF and LaCl have been evaluated and indicate a significant mass dependency indicating Born-Oppenheimer breakdown. The vibrational frequency, Q e, vibrational anharmonicity constant, C0eXe, and the dissociation energies have been estimated for both molecules and agree very well with the literature values. Several rotational transitions have been measured and are reported for La 7 9 Br and Lal in both the ground and first vibrational levels with only v=0 data collected for La 8 1 Br. For LaBr, this is the first reported observed spectrum and analysis thereof. Equilibrium geometries have been evaluated along with estimates of the vibrational frequency, o e , vibrational anharmonicity constant, C0e*e, and the bond dissociation energy, 2>e, for La 7 9 Br and Lal . ii Hyperfine structure due to lanthanum and halogen nuclei has been observed and used to determine nuclear quadrupole coupling constants and spin-rotation coupling constants for all nuclei with exception of fluorine which has no quadrupole moment. Using nuclear quadrupole coupling data, LaCl, LaBr and La l were all found to be highly ionic and generally follow trends predicted based on electronegativity differences of related species. Magnetic shielding parameters have been calculated from nuclear spin-rotation coupling constants and are reported herein. iii TABLE OF CONTENTS Abstract List of Figures List of Tables Abbreviations and Acronyms Acknowledgment 1 Introduction 2 Theory 2.1 Introduction 2.2 The Rigid Rotor Approximation 2.3 Vibrating Rotor 2.4 Equilibrium State & Bond Length Determination 2.5 The Born-Oppenheimer Approximation 2.6 Hyperfine Coupling 2.6.1 Wigner-Eckart Theorem 2.6.2 Nuclear Quadrupole Coupling 2.6.3 Nuclear Spin - Rotation Coupling 2.7 Interpretation of Nuclear Hyperfine Parameters 2.7.1 Nuclear Quadrupole Coupling Constants 2.7.2 Nuclear Spin-Rotation Coupling Constants 2.8 Theoretical Description of an F T M W Experiment 2.9 Supersonic Free Jet Expansion iv 3 Experimental Technique 32 3.1 Introduction 32 3.2 Microwave Cavity 32 3.3 Microwave Source 33 3.4 Electronic Circuitry 34 3.5 Data Acquisition 36 3.6 Laser Ablation System 37 4 Pure Rotational Spectroscopy of LaF and LaCI 46 4.1 Introduction 46 4.2 Experimental Details 47 4.3 Results 49 4.4 Analysis 51 5 Pure Rotational Spectroscopy of LaBr and L a l 67 5.1 Introduction 67 5.2 Experimental Details 67 5.3 Results 68 5.4 Analysis 70 6 Discussion and Conclusion 86 6.1 Breakdown of the Born-Oppenheimer Approximation 86 6.2 Halogen Nuclear Quadrupole Coupling Constants 88 6.3 Lanthanum Nuclear Quadrupole Coupling Constants 89 6.4 Nuclear Spin-Rotation Coupling Constants 91 6.5 Conclusions 92 v References Appendix A Appendix B L I S T O F F I G U R E S 3.1 Schematic diagram of microwave cavity showing location of mirrors, nozzle and antennae. 39 3.2 Control pulse sequence diagram for one experimental cycle. 40 3.3 Schematic diagram of the microwave circuitry. 41 3.4 Schematic diagram of the laser ablation system. 42 3.5 Diagram of laser ablation nozzle cap and motorized actuator. 43 3.6 Side view of stationary mirror showing the location of nozzle cap and motorized actuator. 44 3.7 Top view of the nozzle cap assembly and part of fixed aluminum mirror. 45 4.1 The 7=1-0, Fi=9/2-7/2 transitions of 1 3 9 L a 1 9 F (v=0). 54 4.2 The 7=3-2, Fi=7/2-5/2 transitions of 1 3 9 L a 3 5 C l O=0). 55 5.1 One of the 7=3-2 hyperfine components recorded for 1 3 9 L a 8 1 B r (v=0). 72 5.2 One of the 7=6-5 hyperfine components recorded for La I (v=l). 73 v i i L I S T O F T A B L E S 4.1 Measured frequencies of .7=1-0 transitions (in MHz) of LaF in v=0, v=\, and v=2 vibrational states. 56 4.2 Observed transition frequencies (in MHz) of 1 3 9 L a 3 5 C l in the v=0 and v=l vibrational states. 57 4.3 Observed transition frequencies (in MHz) of 1 3 9 L a 3 7 C l in the v=0 and v=\ vibrational states. 60 4.4 Molecular constants determined for LaF in MHz. 62 4.5 Molecular constants determined for LaCI in MHz. 63 4.6 Equilibrium molecular constants and vibrational parameters calculated for LaF. 64 4.7 Equilibrium molecular constants and vibrational parameters calculated for L a 3 5 C l . 65 4.8 Equilibrium molecular constants and vibrational parameters calculated for L a 3 7 C l . 66 5.1 Observed transition frequencies (in MHz) of 1 3 9 LaBr in the ground vibrational state. 74 5.2 Observed transition frequencies (in MHz) of 1 3 9 L a 7 9 B r in the first excited vibrational state. 79 5.3 Measured hyperfine components of 1 3 9 LaI in the r;=0 and v-l vibrational states. 80 5.4 Molecular constants calculated for LaBr in MHz. 82 5.5 Molecular constants calculated for Lal in MHz. 83 viii 5.6 Equilibrium molecular constants and vibrational parameters calculated for La 7 9 Br. 84 5.7 Equilibrium molecular constants and vibrational parameters calculated for Lal . 85 6.1 Comparison of equilibrium bond lengths in determining where the Born-Oppenheimer approximation is valid and/or fails. 94 6.2 Ground state halogen quadrupole coupling constants of lanthanum monohalides and related species. 95 6.3 Calculated ionic characters of lanthanum monohalides and related species. 96 6.4 Comparison of 1 3 9 L a and 4 5 Sc quadrupole coupling constants. 97 6.5 Nuclear and electronic contributions to the experimentally determined nuclear spin-rotation coupling constants of lanthanum monohalides. 98 6.6 Magnetic shielding of the nuclei in LaX. 99 6.7 Ground state and equilibrium bond lengths of lanthanum monohalides. 100 ix ABBREVIATIONS AND ACRONYMS B O A Born-Oppenheimer approximation BOB Born-Oppenheimer breakdown FID free induction decay FP Fabry-Perot F T M W Fourier transform microwave M W microwave N d : Y A G neodymium-doped yttrium aluminum garnet N M R nuclear magnetic resonance N Q C C nuclear quadrupole coupling constant RF radio frequency S/N signal-to-noise A C K N O W L E D G M E N T After spending the past six months writing this thesis, I am no closer today in knowing what I want to do with my life than before I started. What I can say though, with absolute certainty, is that I am grateful to my research supervisor, Dr. Mike Gerry, for providing me with the opportunity and wealth of experience working in his lab for the past two years. As both a friend and a scholar, I am indebted (maybe for life) to Dr. Corey Evans who not only taught me how to use the spectrometer, but also showed me how to get cheap drinks at The PIT. I would like to thank Dr. Nick Walker, Dr. Corey Evans and Chris Kingston for their time and help in proof reading this thesis. Linda Reynard, who I apparently taught too well how to operate the spectrometer, offered encouragement after having completed her 4 t h year thesis well in advance of my own. Many friends have helped me survive long enough to see this work through to its completion. Mostly I'd like to thank my friends Wai Hoong Kok and Emily Chung for making sure that I got out or at least got up in the mornings to face another day here in sun shiny Vancouver. Many thanks to my roommates; who over the past year made sure that there was never a dull moment. Always offering moral support from a far were my friends Iris Hollander, Ashley Chambers, and Raquel Heskin. Finally, I would like to thank my parents, sisters and bubbi for their support, encouragement, and understanding throughout the years. xi C H A P T E R 1 I N T R O D U C T I O N Microwave spectroscopy is generally regarded as a study of pure rotational transitions observed in gas phase molecules containing a permanent dipole moment. With the introduction of Fourier transform and free jet expansion techniques by Balle and Flygare [1, 2] in 1981, the resolution of such spectra is better than ever before. The observed resolution allows experimentalists to probe rotational fine and hyperfine structure to an accuracy and precision not previously available with other traditional spectroscopic techniques. While there is no clear division in recent literature of where the microwave region begins and ends, for practical purposes, Fourier transform microwave (FTMW) spectroscopy is generally carried out in the 1-80 GHz range. As of April 2000, some forty-eight research groups world wide presently use FTMW spectroscopy to probe a wide range of molecular constants, properties and structure. Of particular interest to theoreticians and physical chemists alike, nuclear quadrupole coupling constants (part of the molecular hyperfine structure) can be used to investigate the electric field gradients surrounding quadrupolar nuclei, and hence develop a better understanding of electron probability distributions. As a tool in understanding the role d orbitals play in bonding, there has been a considerable amount of interest in the spectroscopy of transition metal containing diatomic molecules. The simplest and most obvious starting point in developing an understanding of how d orbitals affect bonding is with the study of the first group of transition metals. 1 Chapter 1. Introduction 2 Specifically, because of their open d shell electronic configuration, (x\+\)s2x\dl, where a single electron occupies the valence d orbital. In this thesis, the pure rotational spectroscopy of four lanthanum monohalides, LaF, LaCI, LaBr and Lal , in their ground (X 'E + ) electronic state are presented for the first time. While there has been a considerable amount of spectroscopic interest placed on LaF [3-9], there has only been one previous publication each on the spectroscopy of LaCI [10] and L a l [11]. There has been no reported spectroscopic observation of LaBr. The present work has been carried out following the completion of the spectral assignment of yttrium monohalides [12-15] and scandium monohalides [16, 17] in the microwave region. Using the rotational constants determined in these studies, and from electronic work [7, 10, 11, 18], where microwave data was not available, the rotational constants of the lanthanum monohalides were predicted and measured. It is the purpose of chapters two and three in this thesis to present a general discussion of the theory of rotational spectroscopy and how this is applied in actual experiments to produce the observed spectra. Details of the rotational Hamiltonians will be developed, as they pertain to the molecules in this thesis. The various components of the pulsed jet Fourier transform microwave spectrometer and laser ablation system used to produce these molecules will be discussed. Chapter four begins with a brief review of the literature of lanthanum monofluoride and monochloride. A description and analysis of their respective measured spectra follows. The derived spectroscopic constants are presented and compared to the most precise literature values where appropriate. Vibrationally excited data allowed for the determination of several equilibrium constants and information about the molecular geometry. Isotopic Chapter 1. Introduction 3 substitution of lanthanum monochloride indicates that there is breakdown in the Born-Oppenheimer approximation. The F T M W spectra of lanthanum monobromide and monoiodide are discussed in Chapter five. The measured spectra, and analysis thereof, follows a synopsis of the Laser Induced Fluorescence spectroscopy results for the monoiodide. The fitted spectroscopic constants are presented and compared to literature constants where available. The equilibrium rotational constants are determined and used to evaluate the bond lengths, vibrational frequencies and other spectroscopic results. The focus of Chapter six is on the interpretation of the determined hyperfine constants. Townes-Dailey theory is used to evaluate the ionicities of the monohalides, and an attempt is made to rationalize the lanthanum quadrupole coupling constants. Nuclear spin-rotation coupling constants are used to estimate the magnetic shielding parameters for all nuclei. Lanthanum has only one known stable isotope, 1 3 9 L a (99.9098 %), and a second which has a sufficiently long lifetime as to allow for determination of its isotopic abundance, 1 3 8 L a (0.0902 %) [19]. Other isotopes with mass numbers between 120 and 152 are known but exhibit half-lives ranging from 150 nsec to 60 000 years [20]. Due to the reasonably weak signals observed for I 3 9 L a X species in the present work, only lanthanum-139 data has been collected. From this point on, wherever lanthanum is referred to in this thesis, it should be understood that the author is referring to 1 3 9 La . Due to the large quantity of figures and tables presented in this thesis, all such material has been moved to the end of their respective chapters to aid the reader. C H A P T E R 2 B A C K G R O U N D T H E O R Y 2.1 Introduction This chapter will discuss the relevant theory concerning the physical data collected during a Fourier transform microwave spectroscopy experiment as it pertains to this thesis. The principles of coherent molecular emission as well as the general theory of stabilizing gas phase samples will be covered. To simplify the discussion in this thesis, all theory being presented will assume diamagnetic behavior as all the molecules being observed are in their ' E + ground electronic states. In this state, there is no net electron orbital angular momentum (L=0) or electron spin angular momentum (S =0), so the rotational angular momentum, R, is simply equal to the total angular momentum, J . R + L = N (2.1) N + S = J (2.2) The Hamiltonian operator used to describe molecules such as the ones being discussed in this thesis, can be broken down into three major components, H = H r o t + H d i s t + H h y p e i f i n e (2.3) where H r o t , H d l s t , and H h y p e r f i n e represent the rotational, centrifugal distortion, and nuclear hyperfine Hamiltonians respectively. Each of these contributions and their significance will be discussed separately. 4 Chapter 2. Background Theory 5 2.2 The R i g i d Rotor Approximat ion The primary features of a rotational spectrum can be explained, as a first approximation, by the rigid rotor model. Representing this non-vibrating rotor is the rotational Hamiltonian, where x, y and z are the principal inertial axes of the molecule. J ; (i=x,y,z) is the rotational angular momentum about each principal axis, and Bt are the molecular rotational constants which are related to the principal moments of inertia, of the molecule. B = —^—= 5053 79.07(43) M H z - a m u -A 2 / / , (2.5) 471/j For a linear molecule, the z-axis is chosen as the molecular bond axis, about which there is no rotational angular momentum: thus, ^J z ^ = 0 . The moments of inertia about the other two axes are equal (7x=/y and Iz=0), simplifying the rotational Hamiltonian to give where Bx = By = B, and the rotational energy levels can then be worked out for any given eigenfunction from: H r o t = / i x J 2 + / i y J 2 + / i z J 2 (2.4) H r o t = / i J 2 + J B J 2 (2.6) = BJ H[0tV = Bj(j + \)V (2.7) EI0t=Bj(j + l) (2.8) where J (=0,1,2....) represents the rotational quantum number. Chapter 2. Background Theory 6 For pure rotational transitions, the selection rule is AJ=±l, so that the transition (j + l)<—J has an energy gap of 25(7+1). This indicates a general series of rotational transitions, equally spaced, with separation 2B. 2.3 V ib ra t i ng Rotor While the rigid rotor model provides a good first approximation of the rotational energy levels, real molecules have flexible bonds that can stretch. As a molecule rotates, its bonds can lengthen as a result of centrifugal distortion; a second consequence of the molecules' flexibility is the rotational constants decreasing with vibration-rotation interaction. To account for these distortions, higher order terms of (j2)1, where n (nel > 1) is the order of the correction factor, are added to the rotational Hamiltonian H d i s l 0 r t =-/3(J 2 ) ! +//(J 2 ) 3 +.. . (2.9) to give the vibration-rotation Hamiltonian H v l b _ r o t = H r o t + H d j s t o r t (2.10) where the energy levels are expressed as E^mi=BvJ{J^)-DvJ2{J + tf (2.H) The energy term is truncated after the first distortion constant in Eq. (2.11), as no higher order terms were required to properly fit the data reported in this thesis. The rotational constants Bv and Dv indicate the vibrational dependence of the rotation and are given by Bv=Be-ae(v + i)+ye(v+2-J+- (2.12) ^=A+Pe(^ + i)+.. (2.13) Chapter 2. Background Theory 7 where Be and De are the equilibrium rotational and centrifugal distortion constants; a e , y e , and (3e are vibration-rotation interaction constants. 2.4 E q u i l i b r i u m State & Bond Length Determination The internuclear bond length of a diatomic molecule can be determined from the vibrationally dependent rotational constant, Bv. It can be expressed as B =—^—r = 505379.07(43) M H z - a m u - A 2 / ^ 2 (2.14) 4JTM;;2 where rv is the internuclear bond length and u. is the reduced mass u = m ' m ' (2.15) m, + m 2 with m, and m 2 representing the atomic masses. Determination of the rotational constants, Bv, for more than one vibrational level allows for the calculation of several equilibrium constants described in Eq. 's (2.12 & 2.13). More importantly, the equilibrium rotational constant, Be, and hence the equilibrium bond length can be determined. In bond length determination, electrons associated with their respective atoms are assumed to be concentrated at the nuclei. While this assumption holds well for electrons in a closed shell, valence electron distributions may be distorted considerably by bonding. In the most extreme case of a purely ionic species, there is complete charge transfer and it may be more appropriate to use ionic masses in determination of the reduced mass and hence re. This has been suggested as a method of estimating the magnitude of electronic effects in molecules [14]. The vibrational energy expression for a diatomic molecule is given in the form Chapter 2. Background Theory 8 G(v) = © e(v + i ) - © , x e ( i ; + i ) 2 +coe^e(^ + i ) 3 (2.16) where G(v) is the customary symbol for vibrational energy levels. The expression is truncated following the term involving C0e*e for a Morse oscillator/potential. Relationships developed by Kratzer [21] and Pekeris [22] are used to approximate the vibrational frequency and anharmonicity constants of such molecules from the equilibrium rotational constants discussed above. The Kratzer relationship, 4 / ? 3 applies to all realistic diatomic potentials, while the Pekeris relationship, coxB - B. V j (2.18) applies to a Morse potential. 2.5 The Born-Oppenheimer Approximation The Hamiltonian of a molecule may be expressed as the sum of kinetic and potential energies of all electrons and nuclei within. H = T e + T n + V e e + V n n + V e n (2.19) The kinetic terms f e and f n are dependent on the electron and nuclear masses respectively, and the potential terms V e e , and V e n represent the Coulombic electron repulsion, nuclear repulsion and electron-nuclear attraction, respectively. The Hamiltonian operates on the molecular wave function, Y ^ Q ) , which is a function of the electron coordinates, q, and the nuclear coordinates, Q, providing the total energy of the system, E. Chapter 2. Background Theory 9 m,(q,Q) = Ex¥(q,Q) (2.20) The Born-Oppenheimer approximation [23] assumes that electrons will adapt "instantaneously" to nuclear motion. This is the same as assuming that the nuclei are held fixed in position, or that the electrons are indifferent to the nuclear momenta. A consequence of this assumption is that the wave function describing such a system can be factored into two terms, one of which is an eigenfunction of the 'electronic Hamiltonian', H e = H e((9), which is parametrically dependent on the nuclear coordinates, \\i(q,Q); the second term, x(Q)> is an eigenfunction of the 'nuclear Hamiltonian', H n = f n . H = H e + H n (2.21) ¥fofi)=vfo-fi)(fe) (2-22) After substituting Equations (2.21) and (2.22) into (2.20), and integrating over the electronic coordinates, the Schrodinger equation for nuclear motion is obtained fcfe) + fB}x,fe) = £x„fe) (2-23) where UXO) = EXQ)+JMiq,Q)T^(q-,Q)dq (2.24) and nMr,Q) = E.(Q)faQ) (2.25) Ue(0) represents an effective potential energy function that governs the motion of the nuclei. The first term, Ee(Q), represents what the total energy would be if the nuclei, fixed in configuration Q, simply provided an electrostatic field for the electrons; the second term is comparatively very small and is generally neglected [24, 25]. In so doing, Ue(Q) is equivalent to Ee(Q) and is strictly independent of the nuclear masses. Therefore, as a direct Chapter 2. Background Theory 10 consequence of the Born-Oppenheimer approximation, the intramolecular potential and hence the equilibrium internuclear bond lengths should be isotopically invariant. 2.6 H y p e r f i n e C o u p l i n g Interactions involving nuclear spin angular momentum, I, produce what is referred to i as nuclear hyperfine structure. Commonly, in rotational spectroscopy, a nuclear spin, I , interacts with the rotational angular momentum, J , to produce the total angular momentum, F , of the system. J + I = F (2.26) If there are two nuclei present with I > Vi, then there are two possible coupling schemes to be considered as first approximations. In the simplest case where the coupling energy of one nucleus is large in comparison to the other the "series" coupling scheme is the best approach. Here, the nucleus with the larger coupling energy, I,, is first coupled to the rotational angular momentum to produce a resultant angular momentum, Fj. J + i ,=F, (2.27) The second nuclear spin, I 2 , is then coupled to the resultant to form the total angular momentum, F , Fj +12 = F (2.28) with the associated quantum numbers Fx = J + 7, ,J + IX-\,---,\J-l\ (2.29) F = Fl+I2,Fi+I2-l,-,\F1-I2\ (2.30) Chapter 2. Background Theory 11 On occasion, when the coupling energies of the two nuclei are comparable in both sign and magnitude, the "parallel" coupling scheme is more appropriate in characterizing the quantum numbers of the system. Here, the nuclei couple first with each other to generate a total nuclear spin angular momentum, I, which then couples to the rotational angular momentum, J , finally yielding the total angular momentum, F . i , + i 2 = i (2.3i) J + I = F (2.32) As above, the associated quantum numbers are given as follows: / = / , + / , , 7 1 + / 2 - l , - - - , | / 1 - / 2 | (2.33) F = J + I, J + I-\,---,\j-l\ - (2.34) Nuclear hyperfine interactions occur by way of magnetic and electrostatic means, with the observed structure falling into one of two categories. The Hamiltonian is hyperfine quadrupole spin-rotation where H q u a d r u p o l e refers to the nuclear electric quadrupole interaction and H s p i n _ r o t a t i o n refers to the magnetic nuclear spin-rotation interaction. Of course, there are other hyperfine interactions possible such as nuclear spin - nuclear spin and electron spin - nuclear spin interactions. These other interactions are simply not important in describing the molecules discussed in this thesis, and will not be covered here. In Cartesian tensor form, the quadrupolar and spin-rotation Hamiltonians are expressed as H q u a d n ] p o l e =2 |V , :Q, (2.36) Chapter 2. Background Theory 12 H s p i n . r o t 3 t l o n = S i i - C , - J (2.37) i=i with each being summed over all coupling nuclei. The Hamiltonians may also be expressed as the product of two second-rank and two first-rank spherical tensors respectively, H q u a d r u p o l e =£v(i)-Q(i) (2.38) i=l H s p m . r o t a t l o n = i m ( i ) . A ( i ) (2.39) i=l where V(i) , Q(i), rh(i) and are the electric field gradient (EFG), nuclear quadrupole, magnetic field and nuclear magnetic dipole tensors of the i t h nucleus respectively. Each of these tensor operators is also irreducible, meaning that they each transform like spherical harmonics, Y,m(0,<j)), under rotation. 2.6.1 Wigner -Eckar t Theorem The use of irreducible tensor operators can vastly simplify the computation of the matrix elements between states of definite angular momentum. This simplification arises because such matrix elements can be factored into geometrically dependent and physically dependent terms. If we consider the basis \TJM) where J and M represent the quantum numbers associated with J and J z , and x refers to all other observables, the matrix elements of the irreducible tensor operator, T^k) (q^k, k-\,...,-k), of rank k, can be determined by the Wigner-Eckart theorem [26, 27]. Chapter 2. Background Theory 13 (x\j'm'\T^\ym) = {-\y-' f k P 1 , , q m \ (2.40) The symbol in parentheses is a 3j symbol* which is related to Clebsch-Gordan coefficients and hence the geometry of the system. The term ^T ,y'| |7' ( i ) | x jj is the reduced matrix element of 7/ ( t ) and embodies the physical part of the problem. If two commuting tensor operators, T(k) and Uck), act on two separate subsystems such that Uik) commutes with subsystem 1, and T{k) commutes with subsystem 2, then the scalar product of these two tensors in the coupled basis, J = j , + j 2 , is given as J Ji h k h h) (2.41) where the symbol in braces is a 6j symbol* and ^x'1y1'|7'(*)|x17j^ and ^x272||f/ ( A : )j|x272^ represent the reduced matrix elements of T(k) and U(k). (xj[xJ2J'M'\T^ • U^\xJ,x2j2JM) = 2.6.2 Nuclear Quadrupole Coupl ing Of the various hyperfine interactions possible, the most important for closed shell molecules is nuclear quadrupole coupling. This interaction gives insight into the electronic structure and the nature of the chemical bond in question. A quadrupole moment in a nucleus arises from an asymmetrical distribution of protons and neutrons within itself. This nucleus, with a spin, I > V2, thus possesses a nuclear electric quadrupole moment, eQ, which can interact with the electric field surrounding the Chapter 2. Background Theory 14 nucleus. If the nucleus is elongated, the quadrupole moment is given a positive sign, and if flattened, the quadrupole moment has a negative sign. This asymmetrical charge distribution interacts with an electric field gradient (EFG) caused by a non-spherically symmetric charge distribution about the nucleus. For this reason, only a quadrupolar nucleus in an asymmetric E F G produces a measurable quadrupole coupling constant and hence its associated hyperfine structure. For the case of a single quadrupolar nucleus coupling to the rotational angular momentum, the matrix elements of the quadrupolar Hamiltonian are given by [28] \F I J') {T'J'IF\V(2)-Q™\TJIF) = (-\)J +I + F 2 J I (r'JJV&\\tj){l\\Q&\\l) (2.42) where the reduced matrix elements must be related to physically observable spectroscopic parameters. The quadrupole moment, Q, is defined as (l,M1=l\Q%\l,Ml=l) = \eQ. (2.43) Applying the Wigner-Eckart theorem then gives \eQ = {ll\0?\H) f I 2 1^ •I 0 I ('Hell') (2.44) which can be rewritten and solved for explicitly giving (121) i v-7 0 IY (2/ + l)(2/ + 2)(2/ + 3) (2.45) 8/(27-1) In this form, it is clear from the denominator, containing the term 8/(27-1), that nuclei with / < 1 can have no quadrupole moment (Q=0). Similarly, the E F G in the space fixed axis system, qrj, is defined as * See Appendix A Chapter 2. Background Theory 15 {T'J'MJ = J\V^\X,JMJ = J) = hqrj then applying the Wigner-Eckart theorem we have, (2.46) f v which can be rewritten as (x'J'lv xJ 7' 2 7 •J 0 J (J 2 7 v ' 7 0 -7 x'J'lv™ xJ (2.47) (2.48) Substituting Eq. 2.45 and 2.48 into 2.42, the general form of the quadrupole Hamiltonian for a single quadrupolar nucleus is obtained. F(.J 1 7'VY / 2 /V 1 (F I ./'I •eQqj'j (2-49) ( - i r y +  (  2 y y T 7 2 7 T \  < f > 4 J 0 -J, 0 7 y 2 J I (j'IF\Hquad\jIF) For a linear molecule, the nuclear quadrupole coupling constant in the space-fixed axis system, eQqrJ , can be transformed into the molecule fixed system, eOq, by [28] eQqJ,J={-lYJ{2J + l){2J'+\) (J 2 (J 2 J 0 -P 0 eQq (2.50) The presence of a second quadrupolar nucleus requires that we redefine our basis and hence the matrix elements describing the coupling behavior. For the more common "series" coupling scheme, the matrix elements for the first coupling nucleus are given in the same form as that of a single coupling nucleus, but with I\ replacing I in Eq. (2.49), (7'/, 7 (^1)17/, F,) f 7 2 y y r 2> -1 7 i f <J 0 j -h 2 7 VQqrA\) (2.51) Chapter 2. Background Theory 16 where we now represent the quadrupole Hamiltonian as the sum of two separate quadrupolar Hamiltonians, one for each nucleus, H q u a d r u p o l e = H Q (1) + H Q (2) . The nuclear quadrupole coupling constant may be transformed into the molecule fixed axis system as shown above. The matrix elements for the second quadrupolar Hamiltonian in the "series" coupling scheme is then given as follows. V l ) - 7 ( 2 ^ + 1 X 2 ^ + 1) (2.52) \eQqRJ(2) {X'J'IXF;I2F\%(2)\TJI1FXI2F)^ fJ 2 J'\'fl2 I2 2~\ J' Fx /, yFx J 2 F I2F, 2 Fx I2J J 0-J As discussed above, when the coupling energies of the two nuclei are comparable, as in the case of lanthanum monoiodide in this thesis, the "parallel" coupling scheme gives a better approximation to the energies. In this case we get the following matrix elements for the two quadrupolar nuclei: - V ( 2 / + lX2/'+l) (2.53) eQqj.Al) ( T J 7 / 2 / ' F | H Q ( 1 ) | T J / / 2 / F ) = fj.2 h 2 T U F r s X • •• > J 0 -J) 2 2 j i ( 1 W+/ ,+ / 2 + 27'+F (xJ ' / 1 / 2 / ' J F|H Q (2) |x7/ 1 / 2 /F> = V(2/ + lX2/'+l) (J 2 J'X h 2^ r 1 F r f X • •• > 0- Jl I h 2 2 j i (2.54) eQqj.j(2) where once again, the nuclear quadrupole coupling constants may be transformed into the molecule fixed axis system using Eq. (2.50). Chapter 2. Background Theory 17 The molecular nuclear quadrupole coupling constant, eQq, is made up of the nuclear quadrupole moment, eQ, as discussed above, and the E F G at the nucleus, q. Since the quadrupole moment is a constant for a given nucleus, knowledge of the E F G at that nucleus gives insight into the electronic structures and hence the bonding of the atoms present. In the case of a perfectly symmetric charge distribution surrounding the nucleus, there is zero E F G and no preferred nuclear orientation: hence the quadrupole coupling constant or energy is zero. 2.6.3 Nuclear Spin - Rotation Coupl ing The magnetic dipole moment of a nucleus (/ > Vz) can interact with the magnetic field generated by the rotation of the molecule containing it. This interaction is referred to as nuclear spin-rotation coupling and is usually a few orders of magnitude smaller in energy relative to the nuclear quadrupole coupling energy. The matrix elements for a single coupling nucleus are given by [28] \F I A (T JIF\A Spin-Rotation TJIF) = (-\y+1+Fh(J)h(I)\ 1 J I (2.55) where h(x) = -y/x(x +lX2x + l) and C j T , the nuclear spin rotation coupling constant in the J * rotational state, equals (2.56) Chapter 2. Background Theory 18 For a linear molecule with no resultant angular momentum about the molecular axis, Jz - 0, the coupling constants by symmetry are = C w = Q , which simplifies the definition of CSX so that J'T J(J+D \ / (2.57)  + l) where Q, the spin-rotation coupling constant of nucleus i, is equal to q=-gi i N h„ (2.58) with gj, u N and h^ representing the nuclear g-factor, the nuclear magneton, and the component of the magnetic field perpendicular to the molecular bond axis respectively. As with the quadrupole Hamiltonian, the spin-rotation Hamiltonian is further complicated by the coupling of more that one nucleus with a magnetic moment to the rotation of the molecule. As before, one has to consider both the "series" and "parallel" coupling schemes where we now represent the spin-rotation Hamiltonian as the sum of two separate spin-rotation Hamiltonians, H s p i n _ r o t a t i o n = H M ( l )+ H M (2) , one for each nucleus. The matrix elements of the spin-rotation Hamiltonian for the "series" coupling scheme are (T JIXFX | H m (1)|T JIXFx ) = {- l)h h(J)h(7, > = 0*0 )1 , -j (T / / , F 1 7 2 F | H m ( 2 ) | T JiAhF) - (- O'2 hOW2) FX IXJ 1 J I •C,.T (1) (2.59) x A /(2F 1 +l)(2F 1 '+l) F I2 K f J F;~ < >< > h . 1 FX J , (2.60) O , (2) Chapter 2. Background Theory 19 where \\=J+I\+F\, t2=7+/i+/2+2/7i+F+l, and ClT(i)=Ci represents the spin-rotation coupling constants of the i t h nucleus. Similarly, the matrix elements of the spin-rotation Hamiltonian for the "parallel" coupling scheme are given as (x JWF\UM(1)|T JIXI2I F) = (- l) r' h(J)h(/,) V(2/ + l)(2/'+l) (T JIJJ'F | H M (2)|T JIJJ F) = (- l ) r j h( J)h(/ 2 ) F J r 1 / J f/2 /, /'I I / / , (2.61) x v ' ( 2 / + l)(2/'+l) where r, =7 + 7, + / 2 + / + / '+F + l and r, = J + I} +I7+2I'+F + l [F J r) 7, / 2 / ' " (2.62) I i j \ K. J l / / , 1 ' ' z 2 . 7 Interpretation of Nuclear Hyperfine Parameters As mentioned previously, knowledge of the nuclear hyperfine parameters can be used to investigate the electronic structure and bonding within molecules. As an approximation, the character of a bond may be examined using a molecular orbital picture, which at the same time, gives insight to orbital hybridization. If we consider, as a model system, the singly bonded molecule, L a X (where X represents a halogen atom), the valence molecular orbitals can be represented by (2.63) ^ a = a w x + v r v ^ L a and (2.64) Chapter 2. Background Theory 20 where a 2 and (1-a2) are the fractional weights of the respective atomic orbitals in the bonding molecular orbital, Wa. Since Wa is normalized, it is possible to relate the difference of the fractional weights of the atomic orbitals to the polarization and hence the ionic character of the bond. electron density in the bond would transfer to a single atomic orbital, in this case the halogen. Conversely, for a purely covalent bond, /c=0, the fractional weights of the atomic orbitals in Wa would be equal, as they wi l l have an equal share of the electron density, a2=0.5. Consequently, the ionic character of the L a X bonds can be estimated by relating a 2 to an experimentally determinable quantity. 2.7.1 Nuclear Quadrupole Coupling Constants In the case of an isolated quadrupolar halogen atom, the coupling constant can be considered to be due to the unpaired valence electron occupying a p-orbital. These atomic constants have been previously determined and are tabulated in Ref. 28. In an effort to explain the bonding characteristics in halogen containing molecules, the Townes-Dailey model relates the molecular quadrupole coupling constant to that of an atomic halogen described above [29]. (2.65) = 2 a 2 - 1 For a purely ionic bond, / c =l , the fractional weighting of a 2 would be unity as all eQq(X)= n z -f J (2.66) Chapter 2. Background Theory 21 where n; refers to the number of electrons in the npx orbital, and the subscript, «10, on the atomic quadrupole coupling constant refers to the n, £, and m quantum numbers of the associated atom. The orbital populations can then be related to molecular orbital hybridization and the ionic character of the bond. Through the use of the Townes-Dailey model (Eq. (2.66)) it is possible to estimate the ionicity of a quadrupolar halogen-containing molecule. As a first assumption, following this approach, the npx and npy orbitals are considered full (nx=ny=2). The number of electrons in the npz orbital is dependent on the partition of W (=XPX) in the sigma bonding orbital, Wa . The fraction of the sigma bonded pair of electrons associated with the halogen equals 2a2 (nz=2a2), where a 2> Vi (i.e. halogens are far more electronegative than lanthanum). = (2a 2-2>^mo(x) (2.67) Using Eq. (2.65), a 2 = ^ (2.68) and combining this result with Eq. (2.67) gives e Q ^ \ (2.69) where the term ??q^l\ is negative with a magnitude less than one. Following this model, the molecular quadrupole coupling constant of the halogen must approach zero as the ionic character of the molecule increases. This is in accordance with the E F G surrounding the nucleus approaching perfect symmetry as would be expected for a full valence shell. Chapter 2. Background Theory 22 Interpreting the quadrupole coupling constants of lanthanum is not as straightforward because of the presence of valence shell ^/-orbitals. Here the Townes-Dailey model is supplemented by Brown et al. [30] to give ^ = ^ 5 . o [ n 5 P 2 - i ( n 5 P s + 0 1 + ^ 4 2 0 n 4 d 2 + T ( n 4d„ + n4dJ-(n4d + n 4 d 2 J L « V ' W J (2.70) = eQq5W[n5pa - i n 5 p 3 t ] + e ^ 4 2 o [ n 4 d a + T n 4 d , - n 4 d 8 ] where eQq5W and eOqm are the nuclear quadrupole coupling constants for the singly occupied atomic lanthanum 5p and 4d orbitals, and n„em are the orbital populations. Recently, this model has been proven to be suspect in reproducing experimentally determined results for transition metal compounds [16, 31], preventing further study of the molecular orbital hybridization picture at this time. 2.7.2 Nuclear Spin-Rotation Coupling Constants The relevance of the nuclear spin-rotation Hamiltonian is that it can provide information regarding the magnetic shielding constants of a molecule that may otherwise be too unstable to measure using conventional nuclear magnetic resonance (NMR) techniques. This is accomplished first by breaking up the spin-rotation coupling constant into two separate parts, with the first due to the nuclear arrangements, C " u c l , and the second due to the ground and excited state wavefunctions in the molecule, Cfec. C; = C " u c l + Cfec (2.71) Fortunately, the nuclear part can be solved for directly provided that we know the rotational constant of the molecule. We can therefore evaluate the electronic part by simple arithmetic. Chapter 2. Background Theory 23 Here, e is the magnitude of the electron charge; u N is the nuclear magneton; g ; is the nuclear g-factor of atom i ; Zj is the atomic number of the second nucleus, j ; B is the rotational constant; and R is the internuclear bond length} The nuclear and electronic spin-rotation coupling constants can be directly related to the paramagnetic, o p , and diamagnetic, o d , shielding constants respectively. The sum of the two shielding constants gives the average magnetic shielding constant, a a v g , which determines the chemical shift of a molecule in an N M R experiment. a a v g = o p + a d (2.73) The paramagnetic shielding constant of nucleus i may be determined directly from the electronic spin-rotation coupling constant o-O) = — Cfec (2.74) 6mcu Ng i7i where m is the electron mass. The diamagnetic shielding constant, on the other hand, can either be calculated directly from knowledge of the molecular-electronic wavefunction, or it can be accurately estimated, using the relationship developed by Flygare et al. [32, 33], o ^ o ^ f i - e e a t o m ) - ^ C ^ ' (2.75) 6mcu N g 1 / i Here a ^(free atom) represents the free atom diamagnetic shielding constant of nucleus i. Values for multiple nuclei have been calculated and tabulated elsewhere [34]. e, fi and J I n are given in cgs units Chapter 2. Background Theory 24 2.8 Theoretical Description of an FTMW Experiment At the most fundamental level of molecular spectroscopy is the ability of electromagnetic radiation to interact with the electric dipole moment of a sample generally in the gas phase. In an F T M W experiment, microwave radiation is used to create a measurable macroscopic polarization in a sample of interest. Following an excitation pulse, the molecules will emit radiation at their characteristic transition frequencies until Boltzmann equilibrium conditions have been reestablished. Since only a small fraction of the molecules irradiated will be polarized, it is impossible to represent an ensemble of particles by a simple wavefunction; rather, density matrix formalism allows one to represent the system as a statistical mixture of quantum mechanical states. Following the derivations of McGurk et al [35] and Dreizler [36, 37], i f we were to consider an ensemble of two-level particles, each with the identical wavefunction | Y ) = c,|<P1) + c 2|0 2> (2.76) where | 0 , ) and | 0 2 ) represent eigenfunctions of the time independent Hamiltonian, H 0 |O l ) = El|^ »1) (2.77) and i=l,2, the density operator for such a particle would be given such that pij=CiCj*. = (c1|01> + c2|a>2>Xc;(01| + c;(a>2|) (2.78) * * ~ C 1 C 1 C 1 C 2 * * _c2c, c 2 c 2 _ For an ensemble of N two level molecules, the density matrix elements can then be expressed as Chapter 2. Background Theory 25 A pulse of microwave radiation can then be considered as a time dependent perturbation to this ensemble, providing the total Hamiltonian describing the interaction of the dipole moment, u., with the applied electromagnetic radiation. H = H 0 + H p e r t u r b a l l o n (2.80) H p e r t u r b a l i o n =-2|iecos(o>t + 0) (2.81) where 2s, co and <p are the amplitude, angular frequency and phase respectively of the applied field and (i is the transition dipole moment operator. For the purpose of this discussion the matrix element of the dipole moment operator for an asymmetric top will be considered where u.i2 =u.2i and the diagonal elements are equal to zero (u.u=0, u.22=0). It has been shown elsewhere [38] for linear or symmetric top molecules that the inclusion of non-vanishing diagonal dipole moment matrix elements simply produces an additive "quasi-static" term to the polarization function. In the { , j 0 2 ) } basis, the matrix of the Hamiltonian is given as E, - 2 | J 1 2 e cos(cot + <p) -2u ] 2 e cos(cot + ip) E 2 where the time dependence of the system is given as follows: z T ^ = [H,p] (2.83) The resulting time dependent matrix elements are H (2.82) Chapter 2. Background Theory 26 Pn = '"x(p21 -p12)cos(o)t + 0) P22 =-' x(p 2 i -p12)cos(cot + 0) (2.84a-d) P12 = ' X (P 22 - P11 )cos(cot + 0) + /p 12co„ P21 = -«(p22 -p„)cos(cot + 0)~/p2 1(oo where x=2ui28/ti and ( O o ^ ^ - E O / h , the angular frequency of the rotational transition. The elements of the density matrix can then be transformed into the "rotating" coordinate system using P n = P n P 22 — P 22 to obtain p12=pV<^  Pu = y ( p 2 , - P , 2 ) P 2 2 = - y f 21-P12) P , 2 = y ( p 2 2 - P „ ) + i k - o ) ) p (p22 - P n J - i i k -G))P (2.85a-d) (2.86a-d) 12 P21 =" i x 2 where the "rotating wave approximation" has been applied [39], such that all oscillating terms in the above derivatives containing 2co have been neglected. Arbitrarily choosing the phase of the perturbing M W radiation pulse as zero, the induced macroscopic polarization is then expressed as Chapter 2. Background Theory 27 P(t) = N ( | l ) = KTrfp\i) = N u 1 2 ( p 2 1 + P l 2 ) ( 2 8 ? ) • =Nu 1 2 (p 2 1 e-^)+p 1 2 e 'W) = N u ] 2 (p21 +p 1 2)cos(tDt)-Nn 1 2/(p 2 I -p12)sin(cot) = N p 1 2 u(t)cos(oot)-Np12 v(t)sin((JL)t) where, u(t) = p 2 1 +p 1 2 and v(t) = /'(p21 - p 1 2 ) represent the real and imaginary parts of the polarization function. It is also useful to define the population difference between the two energy levels, A N = N(p n - p 2 2 ) = N w , for the following derivation where the derivatives of u, v and A N with respect to time are given as follows: it + vAco = 0 v-uAco + xw = 0 (2.88a-c) A N - N x v = 0 where Aa>=co0-co. In order to introduce relaxation phenomena, Eqs. (2.88a-c) are supplemented by appropriate terms, where it is assumed that u and v relax to zero with relaxation times T 2 and A N relaxes to A N 0 at thermal (Boltzmann) equilibrium with relaxation time T i . From this it follows ii + vAco + — = 0 T v-uAco + xw+—= 0 (2.89a-c) T2 . • , T A N - A N o _ A N - N x v + ^ = 0 Chapter 2. Background Theory 28 For the duration of the microwave pulse, it can be assumed that T t and T 2 are sufficiently large that no appreciable relaxation is occurring, (tp - 1 0 ) « T,, T 2 , and henceforth Eqs. (2.89a-c) can be approximated by Eqs. (2.88a-c) during this time. The microwave pulse frequency, co, is nearly in resonance with the rotational transition frequency, co0, such that Aco is very small, and the amplitude of the M W energy is then chosen to be x=2u.i2s/h » Aco. Then Eqs. (2.88a-c) are solved and approximated as u(t)=0 v(t)=-w 0sin(xt) (2.90a-c) AN(t)= AN0cos(xt) where the initial conditions, u(to)=0, v(to)=0 and AN(tQ)= A N 0 are satisfied. At time t=tp, the microwave pulse is turned off leaving «( t P ) = o v(tp) = -w osin(xt p) (2.91a-c) AN(t p) = AN 0cos(xt p) We now consider the system at some time, t>tp, after the microwave pulse has been turned off. After the M W pulse has ceased, the amplitude, 2s, of the perturbing radiation, and hence x=2u.i2s/h, is equal to zero. Hence, Eqs. (2.89a-c) are rewritten as ii + vAco + — = 0 T v-uAco + — = 0 (2.92a-c) .• T A N - A N . A AN + = 0 T, and can be solved for t>tp with the initial values of u, v and A N at time tp. Chapter 2. Background Theory 29 u(t) = -v(tp)sin^cot)e-t/T2 v(t)= v(tp)cos(Acot)e"t/T2 A N (t) = A N „ + [\N (tp) - A N „ ]e - t / T , (2.93a-c) Coming full circle, in the polarization function we can now substitute the values of u(t) and v(t) for t>tp which gives us P(t) = N|i1 2u(t)cos(cot)- N|j12v(t)sin(cot) The macroscopic polarization can then be maximized by choosing the appropriate pulse length such that sin(xtp)=sin(2u.i2Stp/h) is maximized, which is referred to as the "7t/2" condition or a 90° pulse. In other words tp=(2n+l)(7t/2)(lV2u.i2e), where n is any integer. From the above expression, it is clear that the macroscopic polarization will oscillate at co0 =(E 2 -E,)/7z. The polarization itself depends on the initial population difference, A N 0 , the strength of the transition dipole moment, u.i2, and the duration of the excitation pulse, tp. Therefore, for a fixed excitation amplitude, 2s, a shorter pulse length is needed for larger transition dipole moments and visa versa. •N|i]2v(tp)[sin(Aot)cos(ot)+cos(Aoot)sin((jOt)]e' Nn12v(tp)sin(coot)e-t (2.94) Chapter 2. Background Theory 3U 2.9 Supersonic Free Jet Expansion The use of a supersonic free jet allows for the gas phase preparation of internally cold and isolated molecules. With no intermolecular interactions to consider, and by vibrationally and rotationally cooling the sample, it is possible to produce and stabilize otherwise very reactive or transient species. The conditions necessary to generate such a free jet require the use of a gas reservoir maintained at relatively high pressure (typically 5-7 atm in this work). The high-pressure gas is allowed to expand through a small diameter nozzle into a region of lower background pressure maintained by a pumping system. It is important that the nozzle diameter be large with respect to the mean free path of the particles in the high-pressure region, to allow for multiple collisions in the expansion region. The collisions that take place in the expansion region translationally cool the gas mixture by reducing its degrees of freedom. In turn, the cold translational bath acts as a refrigerant for the vibrational and rotational degrees of freedom. In the absence of further collisions, the system remains in the same state that it had when prepared as no energy flow (in the internal degrees of freedom) is possible. The implied limit of performing a supersonic expansion is the adequate pumping capacity of the gas expanded through the nozzle. One method of circumventing this limit is to use a pulsed nozzle where the gas flow is limited to only a small fraction of time. In this circumstance, the pumping speed only needs to be fast enough to evacuate the chamber before the next pulse. The pump, therefore, restricts the repetition rate of the experiment. Supersonic free jet expansion has been demonstrated to produce rotational temperatures lower than 1 K [40] in some circumstances, and molecules once considered Chapter 2. Background Theory 31 impossible to make such as AuF have been stabilized enough to be characterized spectroscopically [41]. C H A P T E R 3 E X P E R I M E N T A L T E C H N I Q U E 3.1 Introduction A l l of the experiments described in this thesis were performed using a cavity pulsed jet Fourier transform microwave (FTMW) spectrometer. This system was modeled after the spectrometer developed by Balle and Flygare as a means of observing rotational transitions involved in weakly bound species [1, 2]. The heart of the spectrometer is a Fabry-Perot microwave cavity, which is formed from two spherical aluminum mirrors. The gas sample is introduced into the cavity as a supersonic expansion where it is excited by a pulse of microwave radiation. After the excitation pulse has dissipated, the molecular emission is recorded. This chapter will discuss the general technique and instrumentation associated with recording these molecular transitions. 3.2 Microwave Cavity Within a stainless steel vacuum chamber of the F T M W spectrometer is a Fabry-Perot microwave cavity. The cavity is comprised of two spherical concave aluminum mirrors, 28 cm in diameter, with a radius of curvature of 38.4 cm. The mirrors are set approximately 30 cm apart such that one of the mirrors is fixed in position and the second movable mirror is used to tune the cavity into resonance at the desired microwave excitation frequency. The microwave power is coupled into the cavity through a tin coated copper "wire hook" antenna (of length ~ XIA) centered on the face of the tunable mirror. A second antenna centered on the fixed mirror is used to monitor the mode of the power being coupled into the cavity. 32 Chapter 3. Experimental Technique 33 Both mirrors are supported by three VA inch diameter aluminum rods, which are fastened to the walls of the vacuum chamber. The tuning mirror glides across the rods which run through teflon rings embedded in the wall of the mirror. The mirror is attached to a micrometer screw that is used to manually adjust the mirror's separation for each microwave excitation frequency. A pulsed nozzle is inset into the stationary mirror slightly off-center (-2-3 cm) to the antenna. In this orientation, the gas sample is injected parallel to the axis of the microwave cavity and microwave propagation. The line widths obtained from such a configuration are typically 7-10 kHz and appear as doublets because of the Doppler effect. A 6-inch diffusion pump, backed by a rotary pump, provides an operating cavity pressure of approximately lxlO" 6 Torr. The pumping capacity of the diffusion pump effectively limits the repetition rate of the experiment to 1 Hz. Altogether the cavity, designed to function between 4 and 26 GHz, has a bandwidth of 1 M H z while operating at 10 GHz. This bandwidth ultimately limits the search range of the spectrometer to 1 M H z intervals or less. A schematic diagram of the microwave cavity is depicted in Figure 3.1. 3.3 Mic rowave Source A Hewlett-Packard 8341A Synthesized Sweeper was used to synthesize microwave frequencies. The sweeper was referenced against a FS700 Loran C 10 M H z frequency standard. The microwave synthesizer has an internal standard that decays at a rate of lx l0" 9 per day. This is further improved by referencing itself to the Loran C signal, which has a short-term signal stability of 1 part in 101 0, and a long-term stability of 1 part in 10 1 2 with a frequency lock from one of the L O R A N signal broadcasting stations. A l l reported data was Chapter 3. Experimental Technique 34 recorded using the Loran C standard (with a signal lock) and was tested by recording the J=l-0 transition of OCS, a well-characterized molecule [42]. 3.4 Electronic Circuitry The timing of the FTMW experiment is controlled by a home built pulse sequence generator (PSG) and is based on the 10 MHz reference frequency. The PSG creates transistor-transistor logic (TTL) pulses which control the sample injection system, the laser trigger, the M W PIN diode switches, and the data acquisition trigger. A diagram detailing the pulse sequence for a single FTMW experiment is shown in Figure 3.2. A general schematic diagram of the rest of the circuit is given in Figure 3:3. The 10 M H z Loran C signal is initially doubled and then modulated to the desired microwave frequency in a double balanced mixer* against the synthesizers output of v M w + 20 MHz. The resulting microwave excitation frequency is then coupled into the cavity, via the circulator, through the antenna in the tuning mirror. The cavity is manually tuned into resonance at the excitation frequency, V M W , and monitored by the antenna in the fixed mirror via a gallium arsenide crystal detector (HP 8474C) and an oscilloscope (Hitachi V-212). In order to generate the microwave excitation pulse, two fast PIN diode switches (labeled MW-switch on the schematic) are closed for the desired pulse width (typically 0.2-0.5 pis in this study). Because these switches reflect M W power when they are open, isolators are used to minimize the influence of the reflections on the signal source. The microwave radiation, V M W , can then interact with the sample that has been injected into the cavity. After the pulse has been turned off, the molecules emit a coherent When operating from 18-26 GHz a single side band modulator is substituted for the double balanced mixer. Chapter 3. Experimental Technique 35 signal, V O = V M W + A V . This signal, which is slightly off-resonant from the excitation pulse, is then coupled out of the cavity via the circulator. A third "protective" PIN diode switch (leading from the circulator into the microwave amplifier) used to safeguard the microwave amplifier from damage during the excitation pulse, is then closed to allow the molecular emission through. The resulting emission is then amplified and mixed down to 2 0 M H z - Av. After amplifying the RF signal, it is once again mixed down to 5 M H z + Av and amplified. The signal is then passed through a 5 MHz bandpass filter (which eliminates aliasing), and is then monitored in the time domain by a transient recorder. The down-conversion from V M W + A V to 5 M H z + Av is carried out to facilitate the analog-to-digital (A/D) conversion which is much easier in the radio frequency range than in the microwave region. The actual F T M W experiment is performed in two sections, the first of which records the free induction decay (FID) of the microwave cavity alone, and the second, which records the combined FID of the cavity and the coherent molecular emission. The pulse sequences of the two sections are virtually identical (with exception to injecting the gas sample), and thus only the latter will be described. The pulse sequence begins by signaling the General Valve nozzle to initiate a gas pulse, which contains the precursor and backing gas mixture. As the gas mixture begins to flow over the target metal rod, the ablation laser is triggered to fire and the resulting plasma will have the opportunity to react as it supersonically expands into the FP microwave cavity. With the "protective" microwave switch being kept open, the MW-switches are closed and then opened again to generate the microwave excitation pulse. After an Chapter 3. Experimental Technique 36 adjustable period of time the "protective" microwave switch is closed and following a delay, the computer begins to record the FID. 3.5 Data Acquisition The FID of a microwave signal is recorded by an A/D conversion circuit board obtained from Dr. Strauss G M B H . The board, plugged into our personal computer, can be operated up to a maximum sampling rate of 25 MHz. In our instrument 4096 (4K) individual data points at a sampling interval of 50 ns are used to record the FID for a single experimental cycle. The data recorded from multiple experimental cycles was then transferred to the computer for signal averaging as a time domain signal and later Fourier transformed to give the power spectrum in the frequency domain. The molecular decay signal obtained by subtracting the FID of the background signal from the FID of the molecular-plus-background signal is stored by the computer, which adds together the results of successive experiments. The time domain signal is transformed into the frequency domain by a discrete Fourier transform where /(nAt) is the time domain signal collected at sampling intervals of At and consisting of n individual data points. The power spectrum is obtained by taking the square of the modulus of the resulting Fourier function at each frequency sampled. Peak positions are obtained by averaging the frequencies of Doppler components together from the power spectrum. For overlapping or closely spaced lines, distortions may occur in the power spectrum [43] and as a result, the line positions should be determined from the time domain spectrum directly. Due to the highly overlapped nature, specifically of N - l (3.1) n = 0 Chapter 3. Experimental Technique 37 LaCl lines, the DECAYFIT program [44] was unable to properly resolve a substantial quantity of the spectra obtained. Therefore, an alternative approach of "zero filling" the spectrum up to an 8K transform with 4K data points was used. The zero filling artificially enhances the spectrum, which was then fit to a computer model5 in order to verify peak positions. The standard deviation of the frequency of a well resolved line was estimated to be one-tenth the line width (ca. 1 kHz); for severely overlapped lines a standard deviation of one-quarter the line width was used. Overall, the lines measured in this work have an estimated accuracy believed to be better than ± 1 kHz. 3.6 Laser Abla t ion System The second harmonic of a Q-switched N d : Y A G laser (Continuum Surelite I-10) is used as the ablation source for the microwave experiments. The laser beam, guided by mirrors and a lens, is focused to a spot less than 1mm in diameter through a hole in the nozzle cap assembly. A schematic of the laser ablation system is given in Figure 3.4. A target metal rod passes through the stainless steel nozzle cap assembly at the focal point of the laser beam. The rod is continually rotated and translated through the nozzle cap by a motorized actuator (Oriel Motor Mike) in order to provide a fresh ablation surface for the laser with each successive experiment. This practice has been shown elsewhere [45] to provide the best possible signal strength in the associated microwave spectrum. A diagram of the nozzle cap, rod and motorized actuator is shown in Figure 3.5. Both the nozzle cap Modeling program was written by die author in Turbo Pascal. Please see the attached program code in Appendix B Chapter 3. Experimental Technique 38 and motorized actuator have been mounted in the back side of the stationary mirror by recessing into the aluminum surface (see Figure 3.6). Precursor molecules, present as no more than 0.01 % in an Ar carrier gas, are injected into the nozzle cap by a General Valve Series 9 pulsed nozzle towards the target metal rod. As the gas passes over the surface of the rod, the laser is timed to ablate the metal and initiate the reaction process; the optimal delay between the nozzle being fully opened and the laser pulse was determined to be -200-300 LIS. The ablated matter continues to react as it travels through the length of the nozzle cap assembly and is supersonically expanded into the microwave cavity. A brass extension disk with a 5 mm exit diameter is attached to the nozzle cap to bring the assembly to within 2.5 mm of the mirrors surface (see Figure 3.7). Chapter 3. Experimental Technique Figure 3.1: Schematic diagram of microwave cavity showing location of mirrors, nozzle and antennae. Chapter 3. Experimental Technique 40 valve trigger valve response mol. pulse width (300 L I S ) laser trigger M W pulse M W pulse width (0.2 - 0.8 us) mol. M W delay (550 L I S ) protective M W switch M W pulse width + adjustable width delay (3-5 (is) measurement trigger background signal sampling time x number of sample points (50 ns x 4096 data points) molecular + background signal Figure 3.2: Control pulse sequence diagram for one experimental cycle. Chapter 3. Experimental Technique 41 O s c i l l o s c o p e D e t e c t o r 1 0 M H z F r e q u e n c y S t a n d a r d H x 2 2 0 M H z D o u b l e b a l a n c e d m i x e r M W - s w i t c h C i r c u l a t o r 1 0 M H z M W - s w i t c h P r o t e c t i v e M W - s w i t c h M i c r o w a v e S y n t h e s i z e r J I P e r s o n a l C o m p u t e r i P o w e r d i v i d e r M W - a m p l i t i e r M W - m i x e r 2 0 M H z - Av 5 M H z b a n d p a s s O s c i l l o s c o p e R F - a m p l i f i e r R F - a m p l i f i e r 2 5 M H z b a n d p a s s 2 5 M H z 5 M H z + Av R F - m i x e r 2 0 M H z b a n d p a s s Figure 3.3: Schematic diagram of the microwave circuitry. A frequency doubler is placed between the microwave synthesizer and the power divider when VMW is between 18 and 26 GHz. Chapter 3. Experimental Technique 42 Nd:YAG Laser (532 nm) Lens Nozzle cap with rod Stationary Mirror Diffusion Pump Tuning Mirror Figure 3.4: Schematic diagram of the laser ablation system. The laser light is directed into the vacuum chamber and focused to a point on the metal rod inside of the nozzle cap. Chapter 3. Experimental Technique Figure 3.5: Diagram of laser ablation nozzle cap and motorized actuator. The metal rod coupled to the motorized actuator with a piece of flexible rubber tubing. Chapter 3. Experimental Technique 44 Lanthanum Rod General Valve nozzle attaches here Aluminum support for motor Motorized actuator Figure 3.6: Side view of stationary mirror showing the location of nozzle cap and motorized actuator. The long dashed vertical line shows the recesses made in back of the mirror necessary to mount the specified hardware. Chapter 3. Experimental Technique 45 Figure 3.7: Top view of the nozzle cap assembly and part of fixed aluminum mirror. The nozzle cap, left 2.5 mm from breaching the fixed mirror's surface, is mounted approximately 2.5 cm off center from the antenna. The unlabeled shaded part at the end of the gas channel is the nozzle cap extension; see Section 3.6 for details. The motorized actuator (not shown in diagram) is located below the plane of the paper. C H A P T E R 4 P U R E R O T A T I O N A L S P E C T R O S C O P Y O F LaF A N D LaCl 4.1 Introduction There has been a considerable amount of spectroscopic work carried out previously on lanthanum monofluoride (LaF). The first assigned measurements were reported on several rotationally analyzed visible absorption bands by Barrow et al. [3]. The results were later ascribed to several triplet - a3A transitions as well as to several singlet - X ! E + systems. Schall et al. [4] later confirmed that the ground state is X * E + and determined the energies of several excited electronic states including the low lying a 3Ai (1432 cm"1) state. Several other studies into the electronic states of LaF have since followed [5-9] providing a host of spectroscopic information. Multiconfiguration ligand field calculations, ab initio pseudopotential calculations, and relativistic ab initio SCF and correlated calculations have also been carried out [46-48] and give results which agree with the experimentally derived data. The spectroscopy of lanthanum monochloride (LaCl) is far less extensively studied. Previously, the only spectroscopic work performed on LaCl was the rotational analysis of an infrared band system performed by Xin and Klynning [10] based on its thermal emission spectrum. While the authors provided several equilibrium rotational constants on various electronic states, they were unable to choose between *E and 3 A as the ground state symmetry. Based on the work of Schall et al [4] and Langhoff et al. [49] they tentatively assigned *I as the ground electronic state. The a3A - X 1 ! separation once again is unknown 46 Chapter 4. Pure Rotational Spectroscopy of LaF and LaCl 47 but was predicted to be rather small based on the strong triplet transitions down to a 3A and from comparison to LaF [4]. This chapter describes the first reported pure rotational spectra of LaF and LaCl and their analyses. The high resolution and accuracy of the F T M W spectrometer has allowed for the first quantification of several hyperfine parameters including nuclear quadrupole coupling constants and nuclear spin-rotation coupling constants for all nuclei present. 4.2 Experimental Details Gas phase lanthanum monofluoride and lanthanum monochloride were prepared by reacting the ablated matter of a lanthanum rod (Alfa AESAR, 99.9%) with a 0.01% gas mixture of sulfur hexafluoride (instrument grade) or chlorine gas (high purity > 99.5%) respectively in 5-7 atmospheres of argon carrier gas. The gas mixtures were prepared by successive dilution of the precursor gas with ultra high purity argon. As with other group III metals, lanthanum exhibits a strong preference for a +3 oxidation state. Not surprisingly, in previous microwave investigations in this lab of yttrium monohalides [12-15] and scandium monohalides [16, 17], a very low concentration of the halogen precursor, SF6/CI2, was used to promote the formation of the monohalides over that of the di- and trihalides. The observed transitions of LaF were considerably weaker than those observed for its yttrium (7=y) counterpart. However, the drop in intensity can be accounted for by the spin of lanthanum, I=\, which will subdivide each line of the spectrum with the added nuclear quadrupole coupling not possible with yttrium. Scandium (/=y) monofluoride signals were, surprisingly, reported to be substantially weaker than LaF signals. Typical ScF measurements reportedly required 50-90 minutes of Chapter 4. Pure Rotational Spectroscopy of LaF and LaCI 48 signal averaging time while LaF only required 3-5 minutes of signal averaging to achieve good signal to noise* in the ground vibrational state. There may have been several factors that can account for this observation, one possibility being the rod diameter. Both scandium and lanthanum rods were originally purchased with a diameter exceeding 6 mm; the lanthanum fluoride spectrum exhibited an improvement in S/N when the metal rod was lathed down to a 5.0 mm diameter. The spectrometer itself may have had a hand in the S/N improvement observed for the lanthanum monofluoride over that of the scandium monofluoride. While the spectrometer is designed to operate from 4-26 GHz, its optimal operating range is between 8-18 GHz; the scandium monofluoride lines were measured in the 23 GHz range while the lanthanum monofluoride spectra were recorded in the 14 GHz region. LaCI spectra were considerably weaker than that observed for LaF. This can be accounted for again with the added nuclear quadrupole splitting introduced by the chlorine nucleus. Further complicating things, the quadrupole coupling constant of chlorine was found to be quite small thus causing a high degree of overlap in the hyperfine components observed. Even with the strong resolving power inherent to the jet pulsed F T M W technique, a considerable amount of signal averaging was required to resolve the hyperfine components. Generally 35-70 minutes of signal averaging time was required to resolve most hyperfine components in the ground vibrational state. 4.3 Results The transition frequencies of LaF iv-0) were predicted using the accurate values of Bo and D0 available from an earlier electronic study [7]. The first transition lines of LaF were * Spectrometer operates at a repetition rate of 1 Hz Chapter 4. Pure Rotational Spectroscopy of LaF and LaCI 49 found within 10 M H z of the prediction, and consisted of two overlapping Doppler pairs, chiefly split by the spin-rotation coupling of the fluorine nucleus (see Figure 4.1). The S/N of the ground and first two excited vibrational state lines were strong enough such that they were easily recorded with a maximum of 2000 averaging cycles or just over 30 minutes of measurement time. Using the equilibrium rotational constants published by Xin and Klynning [10], the ground vibrational state transition frequencies for L a 3 5 C l were predicted. The rotational transition frequencies of L a 3 7 C l were then predicted by mass scaling the rotational constant of L a 3 5 C l . Transitions of each isotopomer were found within a few M H z of their predicted frequencies. Unlike LaF, where only the 7=1-0 transition was within the measurable range of our spectrometer, transitions between the lowest four rotational levels, 7=1-0, 7=2-1, 7=3-2, and 7=4-3, o f L a 3 5 C l and the 7=2-1 and 7=3-2 transitions of L a 3 7 C l were observed. The vibrationally excited transitions were considerably weaker than those observed in the ground state, requiring as many as 16000 averaging cycles to achieve sufficient S/N. Painstakingly, many of the rotational transitions observed in the ground state were again recorded in the v=\ state for both isotopomers. The four strongest hyperfine components of the 7=3-2, F i = j - | transition lines in L a 3 5 C l (t;=0) are shown in Figure 4.2. The overlapping of the Doppler components seen here was very typical throughout the rotational transitions recorded for LaCI. The "series" coupling scheme was used to assign the transition lines recorded for both molecules: L + M (4.1a) I X + F , = F (4.1b) Chapter 4. Pure Rotational Spectroscopy of LaF and LaCI 50 The nuclear spin of 1 3 9 L a (99.91%) is \ with that of 3 5C1 (75.77%), 3 7C1 (24.23%) and 1 9 F (100%) being f , \ and \ respectively. Al l the measured lines and their assignments are listed in Tables 4.1, 4.2 and 4.3 for LaF, L a 3 5 C l and L a 3 7 C l respectively. The Hamiltonian as described in Chapter 2 is given as FI — H v i b _ r o t + H q u a d r U p 0 | e + H s p | n _ r o t 3 t i o n (4.2) where H v l b _ r o t = 5 0 J 2 - / ) 0 J 4 (4.3) H =I(v(2)6(2) + V ( 2 )6 ( 2 )) C4 4) O H s p , n _ r o t a t i o n = C L a i L a - J + C x i x - J (4.5) The transitions of both molecules were fit using Pickett's exact fitting program, SPFIT [50]. The centrifugal distortion constant (Dv) of LaF was fixed in the fit to the value calculated from reference 9 because only the J=l-0 transition was available for measure in the frequency range of the spectrometer. Tables 4.4 and 4.5 contain a comparison of the resulting spectroscopic constants with the most precisely determined values from electronic spectroscopy. There is clearly a significant improvement in the determination of Bv for both LaF and L a 3 5 C l , which reflects the accuracy and precision of the F T M W measurements. In the case of LaF, the most recent and precise literature result, given by Bernard et al. [9], do not agree within four standard deviations. It has been noted elsewhere [15, 16] that this research group may have either a calibration error or a systematic error in the use of a global fitting program that continues to provide inaccurate rotational constants in their recent publications. This conclusion has been drawn primarily on the basis that it is very difficult to conceive Chapter 4. Pure Rotational Spectroscopy of LaF and LaCl 51 how the results presented here could be inaccurate to the degree of the discrepancy. The measurement accuracy, of the narrow line widths observed, is based on an absolute frequency standard accurate to 1 part in 101 2. With Xin and Klynning [10] suggesting that they recorded "J-value regions up to 200", it is not surprising that they determined £>0 for L a 3 5 C l with greater precision, whereas only the four lowest J transitions were measured in the present work. The ground state effective bond lengths, ro, have been calculated from Bo using Eq. (2.14). The resulting bond lengths are 2.0258894(9) A, 2.5003977(11) A and 2.5003415(11) A for LaF, L a 3 5 C l and L a 3 7 C l respectively with the given uncertainties reflecting the accuracy of the atomic masses and fundamental constants used in the calculation. As a result of the supersonic expansion used to create these molecules (see Section 2.9), it can be inferred that the observed spectra were due to rotational transitions in the ground electronic state. With this in mind, the observed hyperfine pattern measured for LaCl confirms the tentative assignment made by Xin and Klynning of a X ! E + ground electronic state. 4.4 Analysis The equilibrium rotational constants, Be, were evaluated for both molecules using Bv=B.-afr + l)+y.(v + lf (4-6) where Bv is the rotational constant for the vih vibrational state, and a e and y e are the vibration-rotation interaction constants. The equilibrium structure of the two molecules was investigated using four different methods. With only two vibrational states having been characterized for LaCl, Method 1 entailed setting ye (normally very small) to zero and then Chapter 4. Pure Rotational Spectroscopy of LaF and LaCl 52 evaluating Be and a e . With three vibrational states characterized for LaF, Be, a e and y e were determined directly as Method 2. As was found elsewhere [51, 52], y e was determined to be three orders of magnitude smaller than oce for LaF. Using this result, Method 2 for LaCl estimated y e at ae/1000 and then re-evaluated Be and oce. The resulting equilibrium constants and bond lengths, r e, are tabulated in Tables 4.6, 4.7 and 4.8 for LaF, L a 3 5 C l and L a 3 7 C l respectively. Given the high degree of ionic character (see section 6.2) reported for LaCl and data to be presented later in this thesis for LaBr and Lal (/c>96.5 %), the equilibrium bond lengths were also recalculated using ionic masses. This corresponds to Methods 3 and 4 where the rotational and vibration-rotation interaction constants are determined identically as in Methods 1 and 2 respectively. The results are given alongside Methods 1 and 2 in Tables 4.6, 4.7 and 4.8 together with the most precisely determined spectroscopic data for comparison. The harmonic vibrational frequency, coe, and the vibrational anharmonicity constant, coe^e, of LaF and LaCl have been estimated using the relationships developed by Kratzer [21] and Pekeris [22] f /y m \ (2.18) co.x, - B. f \ 2 ^4 + 1 v 6 # j where De is the equilibrium centrifugal distortion constant, which was approximated as the ground state value, Do, for LaCl. Similarly, the bond dissociation energy, 2>e, assuming a Morse potential, is approximated by Chapter 4. Pure Rotational Spectroscopy of LaF and LaCl 53 4oje. (4.7) The calculated values of coe, C0e*e and 2>e are given in Tables 4.6, 4.7 and 4.8 with reference values for LaF, L a 3 5 C l and L a 3 7 C l respectively. The differences between the calculated values and those derived directly from experiment are better than 2% for ©e and C0e* e m both LaF and L a 3 5 C l ; clearly this is a remarkable result considering that the Kratzer and Pekeris relations are strictly approximations to the vibrational parameters. With no experimental results available for comparison the bond dissociation energy, 2>e was calculated in the same manner described above from the literature values of coe and a>^ce. Chapter 4. Pure Rotational Spectroscopy of LaF and LaCI 54 F = 5 - 4 F = 4 - 4 F = 4 - 3 14742.698 Frequency / M H z 14743.198 Figure 4.1: The 7=1-0, Fi=9/2-7/2 transitions of 1 3 9 L a 1 9 F (v=0). This spectrum was obtained with 250 averaging cycles. The microwave excitation frequency was 14742.928 M H z operating at a pulse width of 0.4u.s. 4K data points were recorded at 50 ns sampling intervals; 8K transform is shown here. Chapter 4. Pure Rotational Spectroscopy of LaF and LaCI 55 F = 5 - 4 17351.360 Frequency / M H z 17351.860 Figure 4.2: The 7=3-2, Fi=7/2-5/2 transitions of " X a ^ C l (v=0). This spectrum was obtained with 3500 averaging cycles. The microwave excitation frequency was 17351.600 MHz operating at a pulse width of 0.4u.s. 4K data points were recorded at 50 ns sampling intervals; 8K transform is shown here. Chapter 4. Pare Rotational Spectroscopy of LaF and LaCl 56 Table 4.1: Measured frequencies of J= 1 -0 transitions (in MHz) of 1 3 9LaF in v=0, v=1, and v=2 vibrational states. -K F' - F" v = 0 0-Ca v= 1 o-ca v = 2 o-ca 7 2 _ 2 2 3-4 14715.1488 4.5 14642.0053 4.5 14568.7977 4.5 2 2 7 2 3-3 14715.1488 4.5 14642.0053 4.5 14568.7977 4.5 2 2 _ 2 2 4-4 14715.1488 -4.5 14642.0053 -4.5 14568.7977 -4.5 2 2 _ 2 2 4-3 14715.1488 -4.5 14642.0053 -4.5 14568.7977 -4.5 9 2 7 2 4-4 14742.9268 -0.9 14669.5579 -0.8 14596.1270 -0.7 _ 2 7 2 4-3 14742.9268 -0.9 14669.5579 -0.8 14596.1270 -0.7 9 2 2 2 5-4 14742.9680 0.9 14669.5987 0.8 14596.1677 0.7 5 2 7 2 3-4 14751.0899 1.1 14677.6513 1.0 14604.1526 0.9 5. 2 7 2 3-3 14751.0899 1.1 14677.6513 1.0 14604.1526 0.9 5 2 _ 2 2 2-3 14751.1181 -1.1 14677.6796 -1.0 14604.1811 -0.9 'Observed - calculated residuals (kHz) Chapter 4. Pure Rotational Spectroscopy of LaF and LaCI Table 4.2: Observed transition frequencies (in MHz) of 1 3 9 La 3 5 Cl in the v=0 and v=l vibrational states. J - j" F;-F; F -F" v = 0 0-C a v= 1 0-C a 1-0 2 2 5-5 5768.1231 0.1 1 - 1 2 2 3-3 5768.2301 0.6 7 _ 2 2 2 4-4 5768.3026 -0.5 1 - 1 2 2 5-4 5793.7378 -0.7 5771.8751 0.0 1 - 1 2 2 4-3 5793.7715 0.9 5771.9146 0.5 1 - 1 2 2 6-5 5793.8677 -0.9 5772.0337 -0.1 1 - 1 2 2 3-2 5793.8994 1.7 1 - 1 2 2 3-4 5801.2628 -0.9 1 - 1 2 2 4-5 5801.3167 -0.3 2-1 1 - 1 2 2 5-4 11549.1935 -0.7 11505.6967 -0.4 1 — 1 2 2 3-2 11549.2740 -0.1 7 5 2 2 4-3 11549.3439 -0.1 11505.8822 0.0 9 £ 2 2 3-3 11554.6363 0.2 9 9 2 2 6-6 11554.6805 1.2 1 - 1 2 2 4-4 11554.7606 -0.3 9 _ 1 2 2 5-5 11554.7927 0.2 5 _5 2 2 4-4 11563.3210 -0.5 11519.7451 0.1 1 - 1 2 2 3-3 11563.5065 0.3 11519.9722 -0.7 11 9 2 2 6-5 11577.0961 -1.1 11533.4559 -0.5 Jl _ £ 2 2 5-4 11577.1042 0.6 11 9 2 2 7-6 11577.1464 -0.3 11533.5174 1.0 n_ _ £ 2 2 4-3 11577.1464 1.0 11533.5174 -0.3 £ _ 2 2 2 5-4 11580.2293 1-5. 11536.5449 -0.6 2 _ 1 2 2 2-2 11580.2293 -0.2 3 5 2 2 3-4 11580.2559 0.7 2 _ 1 2 2 2-3 11580.2559 -4.1 2 _ 2 2 2 4-3 11580.3018 -0.2 11536.6390 0.9 3 5 2 2 1-2 11536.6390 -0.7 3 5 2 2 0-1 11536.6390 -1.0 9 _ 2 2 2 6-5 11580.4247 -0.2 11536.7872 -0.2 "Observed - calculated residuals (kHz) Chapter 4. Pure Rotational Spectroscopy of LaF and LaCI 58 Table 4.2 (continued). f-j" F / - F , " F ' -F" v = 0 o - e v= 1 0-C a 9 7 2 2 3-2 11580.4856 0.8 11536.8628 0.7 1 2 2 2 4-4 11582.3062 1.6 11538.6301 0.9 2 _ 2 2 2 3-3 11582.3411 2.1 1 - 1 2 2 5-5 11582.3882 0.0 11538.7328 0.4 1 - 1 2 2 2-2 11582.4115 0.3 5 7 2 2 2-3 11596.4664 0.2 11552.7183 0.0 1 _ 1 2 2 3-4 11596.4664 -0.3 11552.7183 -1.5 1 - 1 2 2 1-2 11596.5155 0.1 11552.7806 0.0 1 - 1 2 2 4-5 11596.5155 0.0 11552.7806 0.3 0 11 11 2 2 4-4 17342.2528 -1.7 T _ ~2 7-7 17342.2786 1.3 J l _ J l 2 2 5-5 17342.3300 -1.5 J l _ J l 2 2 6-6 17342.3604 2.0 5 3 2 2 4-3 17345.6849 -0.9 1 _ 2 2 2 3-2 17345.8382 -0.4 7 5 2 2 4-3 17351.5586 0.5 17286.1701 0.7 2_1 2 2 3-2 17351.6039 -0.1 2 _ 2 2 2 5-4 17351.6373 0.2 17286.2651 -0.2 2 _ 2 2 2 2-1 17351.6713 0.0 3 3 2 2 3-3 17356.6998 0.1 17291.2834 -0.2 2_2 2 2 1-2 17356.7463 0.3 2 _ 2 2 2 3-2 17356.7463 -1.4 2 _ 2 2 2 2-1 17356.8158 0.6 2 _ 2 2 2 2-3 17356.8285 2.5 3 3 2 2 2-2 17356.8732 -0.7 2 _ 2 2 2 5-4 17359.1021 0.6 17293.6679 1.8 £ _ 2 2 2 4-3 17359.1345 -0.5 17293.7057 -0.4 2 _ 2 2 2 6-5 17359.2121 0.5 17293.7998 0.8 _9 _2 2 2 3-2 17359.2480 -1.5 17293.8489 -0.8 2 _2 2 2 4-4 17361.1753 3.2 17295.7434 2.2 'Observed - calculated residuals (kHz) Chapter 4. Pure Rotational Spectroscopy of LaF and LaCl 59 Table 4.2 (continued). J'-J" F,' -K F ' - F " v = 0 0-Ca v= 1 o-c a 2 _9_ 2 6-6 17361.1753 0.4 17295.7434 -0.4 £ 2 _ 9. 2 3-3 17361.1753 -0.7 17295.7502 2.1 9_ 2 _ 9. 2 5-5 17361.1753 -3.1 17295.7502 0.3 5 2 5 2 3-3 17362.5898 -2.5 2 _ 1 2 4-4 17362.6200 0.5 J l 2 ~~ T 6-5 17362.9003 -0.7 J l 2 _ J l 2 7-6 17362.9016 -4.2 J l 2 _ J l 2 5-4 17362.9207 0.1 13 2 11 2 8-7 17362.9323 1.1 1 2 3 2 2-2 17299.2054 -5.3 j _ 2 1 2 1-2 17364.6615 0.9 17299.2213 -0.4 _n 2 _ 9. 2 6-5 17364.6615 -1.7 17299.2054 -1.6 J l 2 _ 9_ 2 5-4 17364.6761 1.9 17299.2213 1.7 J l 2 _ 9_ 2 7-6 17364.7440 -0.6 17299.3042 -0.1 J l 2 _ 9_ 2 4-3 17364.7629 -0.8 4-3 f _ i l 2 7-6 23149.3250 2.2 J5_ 2 _ J l 2 8-7 23149.3250 -3.8 J l 2 13 2 6-5 23149.3250 -7.5 15 2 13 2 9-8 23149.3464 2.2 J3. 2 _ J l 2 7-6 23150.4418 -0.5 J l 2 _ T 6-5 23150.4523 2.5 J l 2 _ J l 2 5-4 23150.4903 0.6 J l 2 _ J l 2 8-7 23150.4903 -1.9 'Observed - calculated residuals (in kHz) Chapter 4. Pure Rotational Spectroscopy of LaF and LaCI Table 4.3: Observed transition frequencies (in MHz) of 1 3 9 La 3 7 Cl in the v=0 and v=l vibrational states. J'-J" F[-FX" F' -F" v = 0 0-C a v= 1 0-C a 2-1 2 2 5-4 11050.1690 0.4 7 _ 5_ 2 2. 3-2 11050.2322 -0.3 1 - 1 2 2 4-3 11050.2882 0.1 1 - 1 2 2 3-3 11055.6225 1.1 9 _ JL 2 2 6-6 11055.6548 0.3 £ _ 9. 2 2 4-4 11055.7193 0.5 £ _ 1 2 2 5-5 11055.7436 -1.1 5 5 2 2 4-4 11064.3009 0.1 5 5 2 2 3-3 11064.4468 0.1 11 _ £ 2 2 6-5 11078.0666 -0.7 11037.2296 5.5 11-1 2 2 5-4 11078.0721 0.1 11037.2296 -1.1 11-1 2 2 4-3 11078.1045 -1.1 11037.2697 -1.0 11-1 2 2 7-6 11078.1045 -1.3 11037.2697 0.0 3 5 2 2 2-2 11040.3415 0.9 2 _ 1 2 2 1-1 11040.3415 -1.4 9 7 2 2 5-4 11081.2190 -1.4 11040.3415 -4.2 2_2 2 2 3-4 11081.2276 0.7 11040.3685 3.2 1 - 1 2 2 2-3 11081.2276 -2.4 11040.3685 -0.4 1 - 1 2 2 1-2 11081.2536 2.1 1 - 1 2 2 0-1 11081.2536 1.8 3 _5 2 2 3-3 11040.4123 -3.4 1 - 1 2 2 4-3 11081.2808 1.9 11040.4123 -3.8 i - i 2 2 6-5 11081.3733 -1.3 11040.5291 -0.6 9 7 2 2 3-2 11081.4243 0.1 11040.5893 0.5 2 _ 2 2 2 4-4 11083.2856 1.4 11042.4095 0.8 2_2 2 2 5-5 11083.3493 0.0 11042.4864 -0.2 5 7 2 2 2-3 11097.4420 -0.4 1 _ 2 2 2 3-4 11097.4420 -1.0 5 7 2 2 1-2 11097.4819 0.7 1_1 2 2 4-5 11097.4819 0.4 "Observed - calculated residuals (in kHz) Chapter 4. Pure Rotational Spectroscopy of LaF and LaCl 61 Table 4.3 (continued). J'-J" F[-F{ F ' - F " v = 0 0-C a v= 1 o-c a 3-2 2 2 4-4 16593.7184 -2.0 11 _U 2 2 7-7 16593.7406 2.7 i l _ J l 2 2 5-5 16593.7792 -2.4 i i _ JLL 2 2 6-6 16593.8016 -0.1 1 _ 1 2 2 4-3 16603.0227 0.2 1 _ 5. 2 2 5-4 16603.0849 1.2 2 _ 2 2 2 3-3 16608.1645 1.4 £ _ 2. 2 2 5-4 16610.5675 -2.4 £ _ 1 2 2 4-3 16610.5983 0.5 9. _ 1 2 2 6-5 16610.6557 -1.2 £ _ £ 2 2 4-4 16612.6312 1.4 £ _ JL 2 2 6-6 16612.6312 -1.0 £ _ £ 2 2 3-3 16612.6312 -0.5 £ _ £ 2 2 5-5 16612.6312 -2.6 i l _ i i 2 2 6-5 16614.3550 -2.2 16553.1079 -0.5 i l _ i i 2 2 7-6 16614.3550 -5.5 16553.1079 -4.2 i l _ i i 2 2 5-4 16614.3773 4.4 i l _ i i 2 2 8-7 16614.3841 4.1 16553.1358 0.6 1 _ 1 2 2 2-3 16616.0591 -1.7 1 _ 1 2 2 1-1 16616.0591 -2.0 i i _ £ 2 2 6-5 16616.1226 -1.6 ii_£ 2 2 5-4 16616.1379 3.2 i i _ £ 2 2 7-6 16616.1876 -1.6 11 9 2 2 4-3 16616.2046 0.0 'Observed - calculated residuals (kHz) Chapter 4. Pure Rotational Spectroscopy of LaF and LaCI 62 t j 3 5 NO 00 >n T f ' ON tN o • * ON ON «n T f tN II T f tN O •n tN <r, T f ' ON tN r-T f ON O N in T f ON >n f i o in ON O O N > T f NO f l f l o f i 00 o NO T f T f T f tN f l NO f l f l 00 o NO T f T f © 00 T f •n o r~ tN in fN T f 60 •3 -8 c o o 3 o T f T f D D J 3 > o II S ' f l in X NO f l tN © tN r~ NO 00 f-' NO f l f i • ^ f tN —i S f l T f s f i •n f i 2 2 NJ o w i r~ oo tN ON ca a o ON o a e P ID 3 to es > > J ^ 41 1 S S Chapter 4. Pare Rotational Spectroscopy of LaF and LaCl oo <r, oo' >n r-C N oo O O V O OS OS Os Os OS 0 0 - 9 ca - J oo © 0 0 0 0 V 0 r-C N V O in H^ m 0 0 o in 0 0 es © C N V O C N m oo OV T l -1> C s >o Tl r-r-C N 0 0 0 0 C N C N 0 0 r<"> Os O cs —1 m o o V O vp C N 0 0 0 0 C N oo 0 0 Os O V O o o V O V O C N WI 0 0 0 0 0 0 o m V O o V O , 0 0 vq c*i o> 0 0 C N V O m O 03 o V O Os • * V O <r> r o ' O s 0 0 C N 5" 5" r o W0 C N C N ' ' O 1 r o O a s C N O <—i •* o V O C N o <n Os 1> t5 03 O H o 3 0 v> v> O) O l cu Chapter 4. Pure Rotational Spectroscopy of LaF and LaCI 64 Table 4.6: Equilibrium molecular constants and vibrational parameters calculated for LaF. Parameter Present Work Literature Valueb M2° M4C Bc 1 MHz 7386.18335(55) 7386.231(10) a e / M H z 36.62453(90) 36.62510(36) y e /kHz -15.52(29) -13.185(42) rjk 2.0233760(9) 2.0233507(9) 2.0233694(16)d we 1 cm"1 574.948(25) 575.20538(11) ft)eXe / cm"1 2.11302(14) 2.133415(33) 4.84909(53) 4.807033(74)e "One Standard deviation in parentheses, in units of least significant digit. bReference 9. °M2 and M4 represent metiiods 2 and 4 of calculating the rotational constants as described in the text. Calculated from Be of reference 9 using atomic masses. "Calculated from constants in reference 9. Chapter 4. Pure Rotational Spectroscopy of LaF and LaCl 65 Table 4.7: Equilibrium molecular constants and vibrational parameters calculated for La CI. Parameter Present Work Lit. Valueb M l c M2C M3° M4° BJMRT. 2899.01743(12) 2899.02561(12) 2899.01743(12) 2899.02561(12) 2899.14(6) at / MHz 10.90494(14) 10.926745(70) 10.90494(14) 10.926745(70) 10.9121(9) r . / A 2.4980452(11) 2.4980417(11) 2.4980306(11) 2.4980270(11) 2.49799(3/ oje 1 cm"' 341.43(62)tle 341.603(1) a»eXe / cm"1 0.9986(25)e 0.9797(5) 3.618(16)e 3.692(2)g aOne Standard deviation in parentheses, in units of least significant digit. ^Reference 10. °M1, M2, M3 and M4 represent methods 1, 2, 3 and 4 of detennining the rotational constants for LaCl. dcue is determined using D0 in place of De. eRotational constants from M l used to evaluate these constants. Calculated from BE of in reference 10 using atomic masses. Calculated from constants in reference 10. Chapter 4. Pure Rotational Spectroscopy of LaF and LaCl 66 Table 4.8: Equilibrium molecular constants and vibrational parameters calculated for La CI. Parameter Present Work M l b M2 b M3 b M4 b 7J e/MHz 2773.90946(59) 2773.91711(59) 2773.90946(59) 2773.91711(59) a e / M H z 10.2072(11) 10.22761(11) 10.2072(11) 10.22761(11) rjk 2.4980403(11) 2.4980369(11) 2.4980267(11) 2.4980233(11) a>e / cm"1 334.7(14)°'d ft)^ / Cm"1 0.9583(53)d 3.623(36)d "One Standard deviation in parentheses, in units of least significant digit. b M l , M2, M3 and M4 represent methods 1, 2, 3 and 4 of determining the rotational constants for LaCl. c<ye is determined using D0 in place of De. dRotational constants from M l used to evaluate these constants. CHAPTER 5 PURE ROTATIONAL SPECTROSCOPY OF LaBr AND Lal 5.1 Introduction The pure rotational spectra of lanthanum monobromide (LaBr) and lanthanum monoiodide (Lal) observed using FTMW spectroscopy form the subject of this chapter. There has only been one previous spectroscopic study published for either of the two molecules. Laser induced fluorescence (LIF) data recorded on lanthanum monoiodide by Effantin et al. [11] provided preliminary rovibrational data on four low-lying electronic states; the lower two being X ! I + and a3A (1064.33 cm"1). Effantin et al. reported molecular constants, B,„ av, Dm and coj:v for the ground electronic state of Lal ( X 1 ^ ) with the index, v, referring to the lowest vibrational level observed. With the microwave data reported herein, it is evident that the lowest level recorded by Effantin et al. was in fact the ground vibrational state. There is no previous report of a spectrum of any kind for LaBr. In the present work spectra have been recorded for La l and both isotopomers of LaBr 79 in the ground vibrational state, with vibrationally excited data recorded only for the La Br isotopomer and Lal . From these transitions, rotational and centrifugal distortion constants have been determined along with equilibrium bond lengths, re, and vibrational frequency data for both molecules. Nuclear hyperfine constants were determined for all nuclei involved and will be discussed along with the LaF and LaCl constants in Chapter 6. 5.2 Exper imental Details Gas phase lanthanum monobromide was prepared by reacting the ablated matter of a lanthanum rod (Alfa AESAR, 99.9%) with a 0.006 % gas mixture of bromine (Fisher 67 Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 68 Scientific, 99.9%) in 5-7 atmospheres of argon carrier gas. The gas mixture was prepared by successive dilution of the precursor with ultra high purity argon gas. Lanthanum monoiodide was prepared in the same manner using a 0.01 % gas mixture of iodomethane (BDH, 99% min) in 5-7 atmospheres of argon carrier gas. As was found for LaF and LaCI a very low precursor gas concentration was used to achieve the best signals for LaBr and Lal . Typically 3000-6000 averaging cycles were required to achieve good signal-to-noise for LaBr ground state lines and 4000-7000 averaging cycles for Lal ground state lines. Vibrationally excited data for La 7 9 Br and Lal required 15000-20000 averaging cycles (4 - 5.5 hours) to achieve a sufficient S/N ratio to merit a measurement. 5.3 Results The transition frequencies of La 7 9 Br and La 8 1 Br ( X 1 ! ^ were predicted by mass scaling and comparing ratios of the accurate rotational constants from yttrium, scandium and lanthanum monohalides from present and previous microwave studies [12-17] and, where these were not available, from electronic studies [11, 18]. After optimizing experimental conditions, LaBr lines were readily found within 15 MHz of their predicted frequencies. The assignment was verified by predicting and measuring other rotational transitions in both isotopomers. The signal strength of the ground state lines was comparable to that seen for L a 3 5 C l (v=0) rotational transitions. However, in stark contrast to L a 3 5 C l , the S/N level observed for the vibrationally excited state, v=l, was extremely poor to the point where vibrationally Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 69 excited data was only collected for the La 7 9 Br isotopomer. The strongest transition of the J=3-2 hyperfine component of La 8 1 Br (i;=0) is depicted in Figure 5.1. The transition frequencies of Lal (X ! E + ) were predicted using the literature values of Bv and Dv reported by Effantin et al. [11]. Transition lines were found within a few M H z of the predicted frequency and after a brief search the observed lines were assigned to the ground vibrational state. With the added nuclear quadrupole splitting caused by the high spin iodine nucleus (7=-|), L a l spectra were even weaker than LaBr spectra, at least in the ground state. Figure 5.2 depicts one of the vibrational excited hyperfine components recorded for Lal . Even following 15,000 averaging cycles (~4.5 hours) the S/N level was still poor. The coupling scheme used to assign the transitions for LaBr was once again the I L a + J = F, (5.1a) I B r + F , = F (5.1b) "series" coupling scheme. The nuclear spin of 1 3 9 L a is y and | for both 7 9 B r (50.69 %) and 8 1 B r (49.31 %) nuclei. A l l of the measured ground state lines and their assignments are listed in Table 5.1. The vibrationally excited transitions recorded for L a 7 9 B r are given in Table 5.2. Alternatively, for Lal , since the quadrupole coupling energies of lanthanum and iodine (7=4) are comparable, the "parallel" coupling scheme is more appropriate for I L a + i , = i (5.2 a) I + J = F (5.2 b) characterizing the quantum numbers of the system. Once more, all of the measured lines and their assignments are listed in Table 5.3. Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 70 The Hamiltonian for this system is once again given as H ~ F I v j b _ r o t + Hquadrupole -^ "^ spin —rotation (4-2) where H v l b _ r o t = / i 0 J 2 - Z y 4 (4.3) H =I(v (2)6 (2) + V(2)6(2)) (4 4) O H s p i n _ r o l a t l o n = C L a i L a - J + C x I x - J (4.5) The transitions of Lal and both isotopomers of LaBr were each fit using Pickett's exact fitting program, SPFIT [50], The resulting constants, and a comparison thereof for Lal to those of reference 11, are listed in Tables 5.4 and 5.5 for LaBr and La l respectively. Certainly there is some room for improvement in determining the vibrationally excited state constants for La 7 9 Br. Unfortunately, due to the extremely poor S/N very few lines were characterized. At the same time though the rotational constant, B\, was sufficiently determined to allow for accurate structural determination. There is clearly a great improvement in the determination of the rotational constants, Bv, for La l over the previous electronic result [11], which again indicates both the accuracy and the precision of F T M W measurements. The ground state effective bond lengths, ro, determined from B0 values are 2.6539588(11), 2.6539417(11) and 2.8806018(12) A for La 7 9 Br, La 8 1 Br and Lal respectively. 5.4 Analysis The equilibrium rotational constants, Be, of La 7 9 Br and La l were evaluated using Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 71 where the rotational constants Bv, ac and y e have been defined previously (section 2.3). The equilibrium structure was evaluated using the four methods described in Chapter 4 for LaCl. As a recap, y e was taken as zero and only Be and oce were evaluated for Method 1. Method 2 involves keeping y e fixed at a exlO" 3 and re-evaluating Be and a e . Methods 3 and 4 parallel Methods 1 and 2 respectively but instead use ionic reduced masses instead of atomic reduced masses to evaluate the equilibrium bond length. The resulting constants and bond lengths are listed in Tables 5.6 and 5.7. The harmonic vibration frequency, coe, and the vibrational anharmonicity constant, C0e*e, of L a 7 9 B r and La l were estimated using the relations developed by Kratzer [21] and Pekeris [22], respectively. The equilibrium centrifugal distortion constant, De, is approximated as the ground state value, Do, for La 7 9 Br as De was not sufficiently determined. The dissociation energy, 2>e, is again approximated by the relation \ = (4.7) These expressions have been found to provide reasonable estimates of the vibrational frequency and dissociation energy for both LaF and LaCl. The results for L a 7 9 B r and L a l are given in Tables 5.6 and 5.7 with reference values for comparison where available. It is interesting to note that while the calculated vibrational frequency of La l appears to be in good agreement with the literature value, the calculated vibrational anharmonicity constant, CDeXe, differs from the literature result by more than 11%. Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 72 6.5,8-5.5,7 6.5,6-5.5,5 6.5,7-5.5,6 6.5,5 - 5.5,4 F 1 ' , F ' - F 1 " , F " 2.5,3-2.5,3 5.5,6-3.5,5 8421.040 Frequency / M H z 8421.490 Figure 5.1: One of the 7=3-2 hyperfine components recorded for 1 3 9La 8 1F3r (v-0) This spectrum was obtained with 4000 averaging cycles. The microwave excitation frequency was 8421.240 MHz operating at a pulse width of 0.4 (is. 4K data points were recorded at 50 ns sampling intervals; 8K transform is shown here. Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 73 5,9-5,8 6,12-6,11 r,F'-r,F" 5,10-5,9 10994.325 Frequency / MHz 10994.925 Figure 5.2: One of the J=6-5 hyperfine components recorded for La I (v=l). This spectrum was obtained with 15000 averaging cycles. The microwave excitation frequency was 10994.625 MHz operating at a pulse width of 0.2 u.s. 4K data points were recorded at 50 ns sampling intervals; 8K transform is shown here. Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal Table 5.1: Observed transition frequencies (in MHz) of , 3 9LaBr in the ground vibrational state. F' -F" 1 3 9 La 7 9 Br o-c a 1 3 9 La 8 1 Br 0-C a 2 2 1-1 8536.7875 0.0 7 5 2 2 5-4 8545.3368 0.4 7 5 2 2 3-2 8545.4746 -0.8 < 3 . - . J . 2 2 3-3 8550.6668 0.7 8415.9812 1.3 9 7 2 2 3-2 8550.7451 0.3 8416.4578 0.2 9 _ 1 2 2 6-5 8550.9506 -0.2 8416.6621 -0.1 9. _ 1 2 2 4-3 8416.7136 -0.1 £ _ 1 2 2 5-4 8552.9021 -0.5 8418.2712 -0.8 £ _ 1 2 2 4-4 8553.7499 0.4 8419.2807 -0.6 £ _ £ 2 2 6-6 8553.9246 0.9 8419.4188 0.8 £ _ £ 2 2 6-5 8554.1896 -1.6 8419.6116 -2.6 £ _ £ 2 2 4-3 8554.2808 -1.1 8419.7158 -1.0 £ _ £ 2 2 5-5 8554.4615 -0.7 8419.8230 0.1 9 9_ 2 2 3-3 8554.7885 -0.7 8420.0735 -0.1 l i _ 1 2 2 4-3 8555.0875 0.9 8420.5535 1.3 A _ 1 2 2 4-4 8555.5011 0.5 8420.9247 1.1 13 H . 2 2 5-4 8555.6490 0.5 8421.0964 -1.0 i i _ i i 2 2 8-7 8555.7105 -0.6 8421.1443 -0.8 1 _ 1 2 2 3-3 8421.2215 0.4 11 7 2 2 6-5 8421.2805 -0.1 i l _ 1 L 2 2 6-5 8555.9849 -1.3 8421.3775 -1.2 i l _ i i 2 2 7-6 8555.9996 0.4 8421.3877 0.8 i i _ £ 2 2 7-6 8557.1117 -0.4 8422.5914 -0.4 1 _ 2 2 2 2-3 8557.7288 1.1 8423.0950 1.8 2 _ 1 2 2 2-2 8557.9555 0.4 8423.4765 -0.4 11 9 2 2 5-4 8558.0808 0.5 8423.3804 0.0 2 _ 2 2 2 3-3 8558.1726 -0.3 8423.6688 -0.6 i i _ £ 2 2 4-3 8558.4779 1.5 8423.5553 0.0 2 _ 2 2 2 5-5 8558.5431 0.2 8423.9142 0.9 2 _ 2 2 2 4-4 8558.9277 0.3 8424.2821 -0.5 'Observed - calculated residuals (kHz) Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 75 Table 5.1 (continued). F;-F; F'-F" , 3 9La7 9f3r O - C , 3 9 La 8 1 Br 0-C a 11 _ 1 2 2 6-5 8559.1745 -1.5 8424.2312 -1.4 11 - i l 2 2 7-7 11388.0463 0.9 13 13 2 2 6-6 11388.1941 -0.5 i l _ i l 2 2 8-8 11388.6380 -0.1 JZ. _ 5. 2 2 2-1 11398.6122 -0.8 5 3 2 2 4-3 11398.8487 -0.3 11219.4145 0.0 7 5 2 2 5-4 11399.8316 0.1 11220.4057 -0.8 5 3 2 2 3-2 11399.9212 -1.5 11220.3334 1.2 1 _ 1 2 2 3-2 11400.1888 1.3 11220.7026 -0.2 7 5 2 2 3-2 11400.5178 0.4 11220.9587 -0.8 7 5 2 2 4-3 11400.9377 -0.4 11221.3682 -0.5 11 11 2 2 6-6 11401.3247 1.0 9 2 2 2 3-2 11401.5916 -1.0 11222.3380 0.7 2 _ 1 2 2 6-5 11402.0288 -0.3 11222.7163 -0.6 i l _ i i 2 2 5-5 11402.1257 0.7 11 J l 2 2 7-7 11402.3929 0.5 11222.9719 1.1 9 7 2 2 5-4 11403.1092 0.4 11223.6341 -0.1 9 7 2 2 4-3 11403.3453 0.5 11223.7682 0.3 2 ._ i l 2 2 6-6 11404.6363 -0.2 13 7 2 2 5-4 11404.7216 1.7 11-1 2 2 6-5 11404.8785 0.2 11225.4654 2.7 11-1 2 2 4-3 11404.8927 1.5 11225.5832 0.0 11 9 2 2 4-4 11225.9405 0.6 11-1 2 2 7-6 11405.5800 -0.9 11226.1440 -0.6 i l _ 1 2 2 6-5 11406.0373 -0.3 11226.5909 -0.4 11 _ £ 2 2 5-4 11406.4561 0.3 11226.8697 -0.5 i l _ i l 2 2 6-5 11406.6321 -1.6 11227.1940 -1.9 15 13 2 2 9-8 11406.6459 0.5 11227.2065 0.6 i l _ i l 2 2 8-7 11406.7983 -0.4 11227.3350 0.5 15 13 2 2 7-6 11406.8390 0.1 11227.3653 -0.8 "Observed - calculated residuals (kHz) Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 76 Table 5.1 (continued). j'-j" Fj-Fx" F -F" 1 3 9 La 7 9 Br 0-C a 1 3 9 La 8 1 Br o-c a 13 11 2 2 5-4 11407.4146 0.1 11228.0097 -0.6 i l _ i i 2 2 8-7 11407.5614 -0.4 11228.1462 -0.5 13 11 2 2 7-6 11408.0187 0.1 11228.5428 0.2 13 11 2 2 6-5 11408.7330 -0.1 11229.0391 0.1 9 9. 2 2 3-3 11408.8022 -0.7 11229.3560 -0.6 £ _ 9. 2 2 5-5 11409.1334 -0.2 11229.6456 0.8 1 _ 1 2 2 4-4 11409.1859 1.2 11229.7684 1.0 9. _ 2. 2 2 6-6 11409.6216 0.3 11229.9684 0.4 1 - 1 2 2 2-2 11409.8724 -1.3 11230.5343 -1.2 2 _ 2 2 2 5-5 11409.9968 1.1 11230.6563 0.7 1 _ 1 2 2 3-3 11409.9968 -1.6 11230.4681 1.3 2 _ 1 2 2 3-3 11410.6570 0.2 11231.1791 -1.1 2_2 2 2 4-4 11410.7475 0.6 11231.2819 -0.3 5-4 - 7 - - 1 J -+ 2 2 5-4 14253.1896 0.0 14028.9204 -0.6 1 - 1 2 2 4-3 14253.5576 0.3 14029.2969 0.4 1 - 1 2 2 3-2 14029.3366 -1.0 7 5 2 2 3-2 14253.9228 0.1 14029.5233 0.3 2 _ 2 2 2 6-5 14254.0264 -0.2 14029.7346 -0.5 7 5 2 2 4-3 14254.2565 -1.1 14029.8374 -0.8 2_2 2 2 4-3 14254.6936 0.2 14030.3009 0.1 2 _ 2 2 2 5-4 14254.8420 -0.2 14030.4513 1.0 1 - 1 2 2 3-2 14030.4513 -3.9 i l _ 2 2 2 4-3 14255.2779 0.8 i i _ 2 2 2 5-4 14256.2567 1.1 14031.8822 1.3 i i _ 2 2 2 6-5 14256.3098 -1.3 14031.9334 -2.3 i l _ 2 2 2 7-6 14256.4413 0.5 i l i i 2 2 5-4 14257.1094 -0.8 14032.8376 0.7 11 11 2 2 7-6 14257.1818 0.8 i l _ i l 2 2 7-6 14032.9652 -0.6 i l _ i l 2 2 8-7 14257.3678 -0.6 14033.0721 -0.8 "Observed - calculated residuals (kHz) Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 11 Table 5.1 (continued). J'-J" F[-F{ F ' -F" 1 3 9 La 7 9 Br O - C 1 3 9 La 8 1 Br O - C i l _ Jl 2 2 10-9 14257.7813 -0.2 14033.4732 -0.6 17 _ J5_ 2 2 7-6 14257.7813 -0.8 14033.4732 0.4 J l _ 15 2 2 9-8 14257.8720 0.5 14033.5488 0.0 17 J l 2 2 8-7 14257.9157 -1.0 14033.5836 -0.6 13 11 2 2 6-5 14257.9794 0.7 15 13 2 2 6-5 14258.1297 0.2 14033.9014 1.0 J5 _ J l 2 2 9-8 14258.4267 -0.8 14034.1339 -0.4 11 _ Jl 2 2 7-6 14258.5911 0.6 14034.2936 1.0 15 J l 2 2 8-7 14258.7223 0.0 14034.3875 0.0 9. _ 9_ 2 2 3-3 14037.5360 0.2 £ _ £ 2 2 5-5 14038.0981 -0.2 1 _ 1 2 2 5-5 14038.2821 0.3 z ' « 7 5 6-5 — — 5-4 17106.1385 -0.2 Ji _ £ 2 2 4-3 17106.4649 0.6 £ _ 1 2 2 4-3 17106.5771 0.6 Ji _ £ 2 2 7-6 17106.6389 -0.2 16837.4802 -1.0 9 1 2 2 5-4 17106.7295 1.1 16837.4802 0.6 Ji _ £ 2 2 5-4 17107.1054 -1.1 11 9 2 2 6-5 17107.1874 -0.2 5 3 2 2 4-3 17107.1874 -0.6 13 J l 2 2 7-6 17108.1272 2.4 16838.9273 0.1 J l _ J l 2 2 6-5 17108.1272 -1.8 16838.9273 1.3 J l _ J l 2 2 8-7 17108.2603 -1.0 Jl _ Jl 2 2 8-7 17108.6072 -0.3 Jl _ Jl 2 2 8-7 16839.1269 -0.7 Jl _ Ji 2 2 8-7 16839.3685 0.8 Jl _ Jl 2 2 6-5 17108.7379 -0.7 16839.5634 0.2 Jl _ Jl 2 2 9-8 17108.8325 0.6 16839.6689 -0.1 19 J l 2 2 11-10 17108.9956 1.3 16839.8218 0.6 J£ _ JI 2' 2 8-7 17108.9956 -2.3 16839.8218 0.0 'Observed - calculated residuals (kHz) Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal Table 5.1 (continued). 78 / 7 ; _ / 7 " F _ F " 1 3 9 La 7 9 Br 0-C a , 3 9 La 8 1 Br O-C !2._!7_ 2 2 10-9 17109.0505 0.0 16839.8653 -2.2 JA _ J3_ 2 2 7-6 17109.2365 0.7 16839.9859 -0.6 i l _ i l 2 2 7-6 17109.3486 0.0 16840.2085 0.1 i l _ i l 2 . 2 10-9 17109.4740 0.4 16840.3100 0.0 17 15 2 2 9-8 16840.4701 -1.6 i l _ i l 2 2 8-7 16840.4862 1.9 "Observed - calculated residuals (kHz) Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal Table 5.2: Observed transition frequencies (in MHz) of 1 3 9 La 7 9 Br in the first excited vibrational state. J'-J" tf - t f ' F -F" v=l 0-C a 4-3 2 13 2 6-5 11374.3271 -1.7 15 2 J l 2 9-8 11374.3473 1.9 15 2 _ i i 2 8-7 11374.5129 0.9 15 2 _ 13 2 7-6 11374.5550 -1.3 i i 2 _ J l 2 5-4 11375.0933 1.4 13 2 J l 2 8-7 11375.2423 -1.4 i i 2 _ J l 2 7-6 11375.7350 0.3 6-5 i i 2 _ J l 2 9-8 17060.3879 0.1 12. 2 17 2 11-10 17060.5581 1.0 12. 2 _ i l 2 8-7 17060.5581 -1.1 'Observed - calculated residuals (kHz) Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal Table 5.3: Measured hyperfine components of 1 3 5 Lal in the v =0 and v=\ vibrational states. J'-J" I'-l" F' - F" v = 0 O-C v= 1 O - C 5-4 2-2 6-5 9183.5376 0.2 4-4 8-7 9183.6752 0.5 3-3 7-6 9183.6897 1.8 6-6 8-7 9183.7794 -1.8 3-3 8-7 9183.7909 -0.1 4-4 9-8 9183.9860 -0.4 1-1 6-5 9184.2832 1.1 5-5 10-9 9184.3596 -0.3 5-5 8-7 9184.7514 0.4 9162.4757 0.4 6-6 11-10 9184.8869 0.6 9162.6315 0.8 5-5 9-8 9185.0032 0.2 9162.7719 -1.2 6-6 9-8 9185.7728 -0.3 6-6 10-9 9186.4420 -0.5 6-5 6-6 7-6 11018.5340 1.3 5-5 6-5 11018.7216 -1.1 5-5 5-4 11018.8344 0.6 4-4 6-5 11019.4258 -0.5 5-5 7-6 11019.4598 -1.1 3-3 7-6 11019.5984 0.4 3-3 5-4 11019.6492 0.4 3-3 6-5 11019.7810 0.7 4-4 4-3 11019.8008 -1.3 4-4 8-7 11019.9296 -0.4 6-6 8-7 11019.9474 0.4 2-2 5-4 10993.6222 3.5 2-2 4-3 10993.6222 -2.7 3-3 8-7 11020.4588 0.3 4-4 9-8 10993.8108 -1.4 1-1 5-4 11020.5429 0.7 2-2 8-7 11020.5429 -0.3 aObserved - calculated residuals (kHz) Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal Table 5.3 (continued). 81 J - j" / ' - / " F' - F" v = 0 0-C a v= 1 O - C 3-3 9-8 11020.5646 -1.3 10993.8108 0.0 4-4 10-9 11020.7096 -0.6 10993.9530 0.0 1-1 7-6 11020.8538 0.7 10994.1090 0.1 5-5 11-10 11020.9511 -0.3 10994.2245 0.1 6-6 9-8 11021.0361 -1.3 2-2 6-5 11021.1580 1.0 5-5 9-8 11021.2965 0.9 10994.5646 -0.6 6-6 12-11 11021.3386 -0.2 10994.6218 -0.2 5-5 10-9 11021.4070 0.4 10994.7140 1.0 6-6 10-9 11022.1967 0.2 10995.4939 -0.8 6-6 11-10 11022.4779 0.1 10995.7838 0.6 7-6 2-2 7-6 12857.8590 -0.3 5-5 10-9 12857.8590 -1.4 6-6 11-10 12858.6257 0.3 6-6 12-11 12858.7441 -0.4 8-7 5-5 11-10 14694.4470 1.9 2-2 8-7 14694.4470 -0.6 "Observed - calculated residuals (kHz) Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 82 Table 5.4: Molecular constants calculated for LaBr in MHz. Parameter La 7 9Br (v=0) La79Br(w=l) La 8 1 Br (w=0) B„ 1425.726965(30) 1421.69045(58) 1403.294661(33) Dv x 103 0.23223(60) 0.2280(58) 0.22560(68) CLa x 103 8.694(35) 9.55(72) 8.552(36) CBr x 103 6.957(57) 7.59(23) 7.405(64) eQqv(La) -125.3037(28) -124.94(11) -125.2999(46) eQqv(Br) 13.6242(21) 14.969(42) 11.3750(22) 'One Standard deviation in parentheses, in units of least significant digit. Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 83 Table 5.5: Molecular constants calculated for Lal in MHz.8 Parameter v=0 Lit. Valueb v=\ Lit. Valueb Bv 918.384255(66) 918.47(12) 916.15771(24) 916.21(12) Dv x 103 0.10076(78) 0.1031(9) 0.1095(32) C L a x 103 9.53(13) 8.30(31) Cix 103 5.79(11) 5.63(30) eQq (La) -117.546(28) -117.43(11) eQq (I) -81.197(23) -84.889(78) "One Standard deviation in parentheses, in units of least significant digit. bReference 11. Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 84 Table 5.6: Equilibrium molecular constants and vibrational parameters calculated for La 7 9Br. Parameter M l b M2b M3 b M4 b 73e/MHz 1427.74522(29) 1427.74825(29) 1427.74522(29) 1427.74825(29) a e / M H z 4.03651(58) 4.044587(30) 4.03651(58) 4.044587(30) rjk 2.6520823(12) 2.6520795(12) 2.6520783(12) 2.6520755(12) cve 1 cm"1 236.17(3 l) c , d ojeXe 1 cm"1 0.5302(10)d 2>e/eV 3.261(10)d "One Standard deviation in parentheses, in units of least significant digit. b M l , M2, M3 and M4 represent methods 1, 2, 3 and 4 of determining the rotational constants. c<we is determined using fixed value of D 0 . dRotational constants from M l are used to evaluate these constants. Chapter 5. Pure Rotational Spectroscopy of LaBr and Lal 85 Table 5.7: Equilibrium molecular constants and vibrational parameters calculated for Lal. Parameter Present Work Literature Value"3 M l c M2° M3C M4C 5 e / M H z 919.49753(15) 919.49920(15) 919.49753(15) 919.49920(15) 919.60(12) a e / MHz 2.22654(24) 2.230995(66) 2.22654(24) 2.230995(66) 2.257(3) rjk 2.8788575(13) 2.8788548(13) 2.8788569(13) 2.8788543(13) 2.87870(19)d coe / cm"1 189.5(19)e 184.43(2)f C0<Jte / Cm"' 0.3742(54)" 0.334(l)f 2.973(74)e "One Standard deviation in parentheses, in units of least significant digit. bReference 11. CM1, M2, M3 and M4 represent methods 1, 2, 3 and 4 of determining the rotational constants for Lal. Calculated from 5 e of reference 11 using atomic masses. eRotational constants from M l are used to evaluate these constants. fGrouhd state effective vibrational frequencies. C H A P T E R 6 DISCUSSION & C O N C L U S I O N 6.1 Breakdown of the Born-Oppenheimer Approximation Under the assumption that the Born-Oppenheimer approximation (BOA) is valid, the Schrodinger equation for nuclear motion is strictly dependent on nuclear masses (Section Generally, the nuclear masses are approximated by atomic masses, which actually provide better agreement with experimental results. This is essentially the case because inner shell electrons are generally spherically distributed about their respective nuclei and therefore add to the apparent nuclear mass. It is only the valence electrons in non-spherically symmetric orbitals that do not move as though their masses were centered at the nuclei. For this reason, the variation in the bond lengths calculated between atomic and ionic masses (as in Methods 1 and 3 and Methods 2 and 4), has been referred to as a general indicator of where breakdown in the Born-Oppenheimer approximation might be expected to occur [25, 53]. For LaF and LaCI, the variation between Methods 1 and 3 or Methods 2 and 4 is on the order of ~10"5 A; well beyond the error limits of the given standard deviations, indicating that the B O A may not hold well here. In a recent study performed by Beaton and Gerry [55] on zirconium monosulfide and zirconium monoxide, a low lying 3 A electronic state (-500 cm"1) perturbed the ground state electronic wave functions to the extent of producing measurable Born-Oppenheimer breakdown (BOB). With reported low lying 3 A electronic states for LaF (1432 cm"1) and La l 2.5). (6.1) 86 Chapter 6. Discussion & Conclusion 87 (1064.33 cm"1) [7, 11], it would be reasonable, as suggested by Xin and Klynning [10], that the observed a 3A state of LaCI also be relatively low in energy. If the a3A - X ! Z + energy gap is in fact small enough, there exists the possibility of observing and quantifying BOB. Fundamentally, it is agreed that the potential energy function and hence the equilibrium bond length, of a molecule remains unchanged upon isotopic substitution so long as the B O A holds [25, 54]. Therefore, a more rigorous (and clearly defined) test of BOB is in comparison of equilibrium bond lengths upon isotopic substitution. Isotopic substitution in L a 3 5 C l and L a 3 7 C l shows that the two equilibrium bond lengths (calculated identically) differ by four and a half times the calculated uncertainty; clearly indicating the breakdown of the Born-Oppenheimer approximation. To illustrate this point further^ in similar molecules where no evidence of B O B was found, such as Y B r [14] and ScBr [17], overlap of the equilibrium bond lengths between different isotopomers was within one standard deviation of the error limits. This result should be compared to the situation for ZrO and ZrS, where BOB has been quantified, and for which bond lengths differed by 27.7 and 7.7 times the calculated uncertainties, respectively [55]. Additional isotopic data is clearly needed to properly document (and quantify) this case of BOB, specifically of the lanthanum nucleus. Furthermore, there is presently no molecular fitting program available that can calculate Born-Oppenheimer correction factors while taking into account quadrupole coupling effects. The equilibrium bond lengths of La 7 9 Br calculated using atomic and ionic reduced masses shows cause for concern with the bond length variation just exceeding three standard deviations. This is however a modest deviation as compared to scandium bromide (see Table Chapter 6. Discussion & Conclusion 88 6.1) where isotopic data was collected and no evidence of BOB was otherwise observed. Without vibrationally excited data available for La 8 1 Br (due to poor S/N) the possibility of BOB can not be confirmed nor entirely discounted especially when considering the results of LaCl. For Lal , the equilibrium bond lengths calculated using atomic and ionic reduced masses showed variation within its' uncertainties ~10"6 A, indicating no observable Born-Oppenheimer breakdown. 6.2 Halogen Nuclear Quadrupole Coupling Constants The ionic characters of LaCl, LaBr and La l can be calculated from their respective halogen nuclear quadrupole coupling constants (NQCC). If the ^/-orbital contributions from the halogens are ignored, the ionic character can be related to the coupling constants by: h=l + eOq(x)/eQqn]0(x) (2.57) where eQq„\o(X) is the quadrupole coupling constant (in MFIz) for a singly occupied npz orbital of the atomic halogen; e(2^3io(35Cl)=109.74, eg^4io(7 9Br)=-769.76 and e^5io(1 2 7I)=2292.71 [28]. The ionic characters of the three molecules have been determined to be 99.1%, 98.2% and 96.5% for LaCl, LaBr and Lal respectively. Comparatively NaCl, which is generally regarded as fully ionic, is similarly determined to have 94.9 % ionic character [56]. Unfortunately this treatment will not work for LaF as 1 9 F has no quadrupole moment. Nevertheless, strictly based on electronegativity arguments, it would be reasonable to infer that LaF should be even more ionic than LaCl. The high ionic character evaluated here validates methods 3 and 4 of determining the equilibrium bond lengths from ionic reduced masses. Table 6.1 numerically summarizes the argument that follows. Chapter 6. Discussion & Conclusion 89 With the culmination of this group's research efforts into the group III metal monohalides, cumulative indexes of their halogen NQCC and calculated ionicities, along with those of several alkali and alkaline earth metal monohalides, are presented in Tables 6.2 and 6.3. A l l the molecules exhibited in these tables show an extremely high degree of ionic character and generally follow the expected periodic trend of ionicity based on electronegativity differences. The ionicities of alkali and alkaline earth metal monohalides clearly follow this trend, however there is a slight kink noticed within the group III metal monohalides where the ionicities of yttrium and lanthanum are almost identical, Sc < Y ~ La. Given this result, it is important to remember that the Townes-Dailey model is used as an approximation of halogen quadrupole coupling constants and also produces the erroneous result of greater than 100 % ionic character observed in Table 6.3. 6.3 Lanthanum Nuclear Quadrupole Coupling Constants Based on lanthanum's ground state electronic configuration, [Xe]6s25d1, and recent ab initio results [48], it is expected that both d- and /-orbitals should both play a role in lanthanum chemistry. As discussed in section 2.7.1 Brown's method [30] attempts to consider the effects of ^-orbital contributions to the quadrupole coupling constant but it is not equipped to handle /-orbitals. The quadrupole coupling constants of lanthanum in the four observed monohalides are listed in Table 6.4 along with that of LaO for comparison. Clearly, there is a significant change in the coupling constants of lanthanum between the monoxide and that of the monohalides. This implies that there is a change in electronic structure near the lanthanum Chapter 6. Discussion & Conclusion 90 nucleus; hardly a surprising result considering that lanthanum is in a different oxidation state in the monoxide. What is, however, surprising about this result comes in comparison to another group in analogue. Scandium monoxide's quadrupole coupling constant is very close to that of the scandium monohalides (see Table 6.4). In the case of scandium, these values were investigated using Brown's equation [30] (Eq. (2.63)) where values of eQq^v) and eQq^ were estimated with ab initio results from Sc + ion [57, 58], The orbital populations were obtained assuming the valence MO's to be the same in ScO and ScF. However, when the orbital populations were solved for directly using a preliminary ab initio calculation, the results strongly contradicted the above assumption, but at the same time produced a plausible qualitative rationale of the halogen coupling constants. The ab initio populations did not even come close to reproducing the experimentally observed results or trends; however, they were also used to determine field gradients which reproduced the quadrupole coupling constants quite well. What was drawn from these results was that simple use of Brown's equation for transition metals must be viewed with extreme caution. With this result, coupled with the lack of /-orbital consideration, there seems little point in pursuing in any detailed way, application of Brown's equation for the lanthanum monohalides. A better approach may be in pursuing ab initio calculations to determine the coupling constants directly. Unfortunately such calculations were beyond the scope of this thesis, not least because it has not been determined how to incorporate the lanthanum basis set of Laerdahl et al. [48] into Gaussian 98 format. An alternative approach has been taken recently where very accurate ab initio field gradients were calculated for both 9 1 ZrO/ 9 1 ZrS [59] and 4 5 S c X [60]. These field gradients, in Chapter 6. Discussion & Conclusion 91 conjunction with the eQq values from FTMW spectroscopy, were then used to improve the accuracy of the quadrupole moments of 9 I Z r and 4 5 Sc. A similar project would seen to be in order for La. 6.4 Nuclear Spin-Rotation Coupling Constants Using the expressions developed in Section 2.7.2, the spin-rotation coupling constants, Cj, of a diatomic molecule are expressed as the sum of nuclear and electronic terms [61, 62]. The nuclear part, C™ 0 1 , is calculated directly once the rotational constant, B, has been evaluated. The electronic part, C ; e l e c , is then determined by a simple difference C =C n u c l +C e l e c (2.64) C n u c i = _ 2 e u N g 1 / j Z j L ( 2 6 5 ) tic R with the constants e, fi and u N in cgs units; all constants having been defined in 2.7.2. Using this result, the average magnetic shielding of each nucleus, o^ g , is determined from the sum of the paramagnetic, op'', and diamagnetic parts, o§. o f = - - — — — - C , e l e c (2.67) p 6mcu N g i / i o j ^ o ^ f r e e a t o m ) C ^ ' (2.68) 6mcu N g 1 5 The electronic and nuclear parts of the spin-rotation coupling constant are listed in Table 6.5 along with the experimentally determined coupling constants for all nuclei. Using previously determined values of o^(freeatom) [34] the diamagnetic shielding term is determined. These Chapter 6. Discussion & Conclusion 92 results are listed in Table 6.6 along with the paramagnetic and average shielding constants for each nucleus. 6.5 Conclusions The pure rotational spectra of four lanthanum monohalides, LaF, LaCl, LaBr and La l have been measured for the first time. Rotational transitions have been measured for all isotopomers in their ground and vibrationally excited states, with the exception of La 8 1 Br, for which only ground state data was recorded. Rotational constants and centrifugal distortion constants have been presented along with the nuclear quadrupole coupling and nuclear spin-rotation coupling constants for all of the molecules in each state observed. The ground electronic state of all molecules studied was confirmed to have XlI,+ symmetry based on the intensity of the transition lines and the observed hyperfine patterns. The halogen nuclear quadrupole coupling constants were used to evaluate the ionic characters of the LaX bonds. Using spin-rotation coupling constants, average magnetic shielding constants have been determined for all isotopomers. The rotational constants determined for LaF indicate a discrepancy in the recently determined literature values. For reasons discussed in Chapter 4, the rotational constants from this work are believed to be more accurate and quite observably more precise. Such was the case for the other lanthanum monohalides and, consequently, there is a vast improvement in the accuracy and precision of the equilibrium bond lengths for all molecules. With no previous LaBr data for comparison, the ground state and equilibrium bond lengths of all L a X species observed are listed in Table 6.7 for comparison with each other and literature values where available. Chapter 6. Discussion & Conclusion 93 The equilibrium structures were determined using both atomic and ionic masses. Variation between these two methods of investigating the equilibrium geometry for LaF, LaCl and LaBr lead to the discovery of Born-Oppenheimer breakdown in LaCl. Equilibrium rotational constants were further used to calculate the vibrational frequencies and estimate the bond dissociation energies of all molecules. This work brings to a conclusion the rotational analysis and study of group III metal monohalides in this research group. A better model of rationalizing nuclear quadrupole coupling constants is clearly required to make better use of such data reported herein. New sample entry systems are currently being explored in an effort to improve the S/N of the F T M W spectrometer. If there is any substantial improvement, the equilibrium structure of La 8 1 Br should be examined to confirm whether the Born-Oppenheimer approximation does in fact hold for LaBr. Chapter 6. Discussion & Conclusion Table 6.1: Comparison of equilibrium bond lengths in determining where the Born-Oppenheimer approximation is valid and/or fails." Molecule r e "/A r.' /A ( r , V , V o ( r J (#-.V.p) / a(re)b 9 0 Y 7 9 B r 2.534 613(1)° 2.534 612(1)° 1.0 9 V ! B r 2.534 612(1)° 2.534 611(1)° 1.0 4 0Sc 7 9Br 2.380 846 5(10)d 2.380 843 5(10)d 3.0 4 0Sc 8 ,Br 2.380 845 l(10)d 2.380 842 3(10)d 2.8 1 3 9 La 7 9 Br 2.652 082 3(12) 2.652 078 3(12) 3.3 1 3 9 La 3 5 Cl 2.498 045 2(11) 2.498 030 6(11) 13.3 1 3 9 La 3 7 Cl 2.498 040 3(11) 2.498 026 7(11) 12.4 1 3 9 La 1 9 F 2.023 376 0(9) 2.023 350 7(9) 28.1 9 0 Zr 3 2 S 2.156 676 49(92)e 2.156 652 65(92/ 25.9 ^Zr^S 2.156 669 40(92)e 2.156 647 73(92)f 23.6 9 0 Z r , 6 Q 1.711 952 42(73)e 1.711 904 15(73)f 66.1 9 0 Z r 1 8 Q 1.711 932 18(73)e 1.711 890 45(73)f 57.2 4.5 "One Standard deviation in parentheses, in units of least significant digit. bIndexes a and |3 refer to the two different isotopomers. °Reference 14. dReference 17. "Reference 55. Calculated from Reference 55 assuming two electron transfer. Chapter 6. Discussion & Conclusion Table 6.2: Ground state halogen quadrupole coupling constants of lanthanum monohalides and related species. Metals are listed in order of decreasing Pauling electronegativity. eQq01 MHz M35C1 M37C1 M7 9 Br M 8 1 Br MI 4 5Sc -3.7861(35)a -2.9824(36)a 39.0857(24)b 32.6438(19/ 2 4 Mg -11.622(21)° 110.3133(36)d 92.1532(35/ -0.8216(43)e -0.621(20)e 12.9352(16/ 10.8017(16/ -82.982(19)g 1 3 9 L a -0.9501(24) -0.7496(28) 13.6242(21) 11.3750(22) -81.197(23) 4 0 Ca -1.002(4)h -0.810(4)h 20.015(7/ 16.714(6/ -131.84(4/, 8 8Sr 3.96(84/ 7.15(46/ 5.54(4iy -54.42(47/ 2 3Na -5.6468(60/ -4.4470(13/ 58.06890(3/ 48.50868(1/ -262.1407(10/ 1 3 7 Ba -33.62(12/ 3 9 K 0.0559(4/ 0.0449(3/ 10.2383(7/ 8.5513(10/ -86.79(10/ 8 5Rb 0.774(9/ 3.50(29/ 2.86(27/ -59.89(30)' 1 3 3Cs 1.76517(6/ 1.39230(6/ -6.47(16/ -15.33(15/ a Ref. 16. b Ref. 17.c Ref. 63. d Ref. 64.e Ref. 13.f Ref. 14. 8 Ref. 15. h Ref. 65.1 Ref. 66. J Ref. 67.k Ref. 68.1 Ref. 69. Chapter 6. Discussion & Conclusion Table 6.3: Calculated ionic characters of lanthanum monohalides and related species.3 Metals are once again listed in order of decreasing Pauling electronegativity. l c / % M35C1 M37C1 M 7 9 Br M 8 1 Br MI 4 5Sc 96.5 96.6 94.9 94.9 2 4 Mg 89.4 85.7 85.7 99.3 99.3 98.3 98.3 96.4 1 3 9 L a 99.1 99.1 98.2 98.2 96.5 4 0 Ca 99.1 99.1 97.4 97.4 94.2 8 8Sr 103.6 99.1 99.1 97.6 2 3Na 94.9 94.9 92.5 92.5 88.6 1 3 7 Ba 98.5 3 9 K 100.1 100.1 98.7 98.7 96.2 8 5Rb 100.7 99.5 99.6 97.4 , 3 3 Cs 101.6 101.6 100.8 99.3 Ionic character is determined using Eq. 2.69 with the halogen quadrupole coupling constants from Table 6.2. Chapter 6. Discussion & Conclusion 97 Table 6.4: Comparison of 1 3 9 La and 4 5Sc quadrupole coupling constants. MX eQq0C5Sc) 1 MHz e(9c7o(139La)/MHz M 1 6 0 72.240(5)b -84.28273(51)° M' 9 F 74.0861(51)d -143.9287(50) M3 5C1 68.2067(29)d -132.6047(16) M3 7C1 68.2062(29)d -132.6127(17) M 7 9 Br 65.2558(32)e -125.3037(28) M 8 1 Br 65.2597(38)e -125.2999(46) M 1 2 9 I -117.546(28) "One standard deviation in parentheses, in units of least significant digit. Reference 70. Evaluated using Pickett's exact fitting program, SPFIT [50], using measured transition frequencies in reference 71. dReference 16. Reference 17. Chapter 6. Discussion & Conclusion 98 60 _g ~Cu 3 O cj a o 3 8 a 'S. cs O g c j fi CS e S •c <L> D . X! c j CJ •3 I o cj = 3 ts -s fi S3 u i n vd to 1 X C3 © ' — CN in i - H ro VO 00 CN CN •n ro CN >n oo CN Os ON T t in CN . V r- T t >n VO, m o »—1 VO r-' oo' vd jo a\ vo' T t ' CN 00 o o VO VO 00 Os T t ^ H Ov o •n T t •n o in T t VO r~ ©' i o 1 © ' 1 9 o CN in" vq ro m' r-ro CN in r-CN in m Ov >n ro T t ' CN OV i-l ——< - 00 T t CO in >n CO ro O in © <n as CN 1-1 T t OS VO 00 T t >n o T t VO 00 00 VO ro CN >n in C3 CS I—I —l CN T t 00 ro 9 OS ro T t as T t CN CN CN CN o 00 of © 00 ro >n as 00 o ro r> CN T t T t o T t o r- T t 00 CN as o as as in VO as T t CN CN CN o ro <N CN CN CN CN ©' 1 ©' i o 1 © o' 1 9 CO in o o m m ~ CS 60 •3 o I CA CD ( A <L> •5 c 2i c3 " c " . If 5 H x) vj I d fi 111 O X Chapter 6. Discussion & Conclusion 6 , a. cu C N O N N O O N C N 0 0 O O N 0 0 C O O N O N O o C N 2 , CU Cu in ro C O C O 0 0 <n in C N C N 0 0 ro C O ro N O H H - H C O ro <n Q. a. r~ C N 0 0 5" T ^ 0 0 N O T t , H H l - H N O © >n O N >n r-N O in C N ro C N o C O ro N O T—1 C N C N ro cu O N T t O N T t N O o 0 0 r-O N O in ro ro •n C N C N * - H I - H N O C N O N CO a. a, O N O N O N O N 0 0 o C N C N 0 0 0 0 C O C N N O N O N O N O N O N O Cu Cu ro N O O N o l-H l-H l -H C N N — ' 0 0 in o 0 0 m ro C N T t H H H H O in in 0 0 0 0 ro ro T t T t o T t N O <J O 03 PQ M —1 ca cs cc ee Chapter 6. Discussion & Conclusion 100 Table 6.7: Ground state and equilibrium bond lengths of lanthanum monohalides.1 LaX ro Ik rjk Present Literature Present Literature LaF 2.025 889 4(9) 2.025 882 8(16)° 2.023 376 0(9) 2.023 344 2(16)c La 3 5 Cl 2.500 397 7(11) 2.500 34(3)d 2.498 045 2(11) 2.497 99(3)d La 3 7 Cl 2.500 341 5(11) 2.498 040 3(11) La 7 9Br 2.653 958 8(11) 2.652 082 3(12) La 8 1 Br 2.653 941 7(11) Lal 2.880 601 8(12) 2.880 47(19)e 2.878 857 5(13) 2.878 70(19)e aOne standard deviation in parentheses, in units of least significant digit. bEquilibrium bond lengdis from Method 1 (Method 2 for LaF). Calculated from constants in reference 9 using atomic masses. Calculated from constants in reference 10 using atomic masses. Calculated from constants in reference 11 using atomic masses. R E F E R E N C E S T. J. Balle, E. J. Campbell, M . R. Keenan, and W. H. Flygare, J. Chem. Phys. 71, 2723 (1979). T. J. Balle and W. H. Flygare, Rev. Scient. Instrum. 52, 33 (1981). R. F. Barrow, M . W. 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Appendix A The Wigner 3-j symbol can be evaluated directly by solving Ji h h V m i m 2 m 3 7 = (-l) i'- j--A01 j 2 j 3 W ^ Jl J2 J 3 v m, m 2 m 3 y (A- l ) where A(a b c) = (a + b - c)(a - b + c)(- a + b + c) (a + b + c +1) (A-2) and f Jl J2 J3 ^ w v m , m 2 m 3 y = [Oi + m i)0i -mi)0 2 + m 2)0 2 -m 2)G 3 + m3>G3 - m 3 r f x T h 2 ( A " 3 ) z z ! ( J i + j 2 - J3 - z)0i - m i - Z ) ( J 2 + m 2 - z) x ( j 3 - j 2 + m , - z ) ( j 3 - j , - m 2 - z ) The summation is over all positive integers of z such that no factorial expression in Eq. [A-3] is negative. The Wigner 6-j symbol is determined similarly by evaluating Ji J 2 J3 I J 4 Js JeJ = A(j, j 2 j 3 )A( j 1 j 5 j 6 ) A ( j 4 j 2 j 6 ) A ( j 4 j 5 j 3 V Ji J 2 J3 LJ4 JS J 6 (A-4) where A(a b c) is defined as above, and Ji J 2 J 3 L J 4 J 5 J 6 =z- (-l)z(z + l ) (A-5) ' ( Z - Jl - J2 - J 3 ) ( Z - Jl - 'h ~ J e X 2 " J4 - h ~ J 6 ) ( Z - J4 " J5 " J 3 ) X x ( j l + J 2 + J 4 + J 5 - Z ) ( J 2 + J 3 + J 5 + J 6 - Z ) ( J 3 + J 1 + J 6 + J 4 - Z ) Once again, the summation is over all positive integers of z such that no factorial expression in Eq. [A-5] is negative. 105 Appendix B Program Model_Line_Shapes; Uses Crt, Graph; Type SpecPtr = ASpectra; . Spectra = record Int : Real; Link : SpecPtr; end; Var GraphDriver, GraphMode, DELTAnu, NuOO, Doppler Spectrum, Last, Next Factor nuO, i n t e n s i t y Loglnt F i r s t p a r t L i n e L i s t , data Filename i,k,n,width x, y max, min Scale-Backing_Gas V ErrorCode :integer; :real; :SpecPtr; :Integer; :array [1..200] of r e a l ; :array [1..200] of r e a l ; :string[31]; :text; :string; :integer; :integer; : r e a l ; : r e a l ; :string[2]; :real; {backing gas velocity} Const C = 299792458; {speed of l i g h t i n m/s} Ar = 561.52; {speed of gas and ablated matter i n m/s} Ne = 744.79; {speed of gas and ablated matter i n m/s} Procedure Read_Plot_Data; Begin Assign(Data,'Info.dat') ; Reset(Data); ReadLn(Data,FileName); ReadLn(Data,Min); ReadLn(Data,Max); ReadLn(Data,DELTAnu); ReadLn(Data,Width) ; ReadLn(Data,Backing_Gas); If Backing_Gas='Ar' then V:=Ar Else V:=Ne; If Width > 5000 then Begin Factor:=5; Width:=Round(Width/Factor) ; End Else Factor:=1; 106 Appendix B 107 Close(Data); End; Procedure Save_HPGL_File; Var O u t f i l e HScale YN PlotName VScale Text; Integer; Char; String; Real; Begin Repeat yn:='y'; OutTextXY(8,50, 1 F i l e name to write to : ' ) ; { W r i t e ( ' F i l e name to write to : ' ) ; } ReadLn(PlotName); Assign(Outfile,PlotName); {$1-} Rese t ( O u t f i l e ) ; {$1+) If IOResult = 0 then Begin OutTextXY(8,60, 1 F i l e already e x i s t s ! Do you want to overwrite? (y/n) ' ) ; Readln(yn); End; U n t i l UpCase(yn) = 'Y' ; Rewrite(Outfile); {send i n t i a l codes to f i l e } WriteLn(Outfile, 'IN;'); WriteLn(Outfile,'IPO 0 8636 11176;'); WriteLn(Outfile,'SC-4249 4249 -5498 5498;'); WriteLn(Outfile) ; WriteLn(Outfile, 'SP1;'); {put t i t l e on p l o t - so you don't forget which f i l e i t is} WriteLn(Outfile, 'PU',-Length(FileName)*50, ' 5000;'); WriteLn(Outfile, 1L04LB ',FileName,Chr(3) , ' ; ' ) ; {put f i l e data on plot} WriteLn(Outfile,'PU 250 1000;'); WriteLn(Outfile,'LB ',' Half_width_at_half_peak_height_=', DELTAnu*1000:0:2,'_kHz',Chr(3),';'); WriteLn(Outfile,'PU 250 800;'); WriteLn(Outfile,'LB ',' Doppler_splitting=', (Nu00*V*2000/(C-V)):0:2,' kHz',Chr(3),';'); {calculate dispersion} HScale:=Round(7000/(2*width+l)) ; VScale:=9000/(Max-Min); {start i n lower l e f t corner} X:=-3500; Y:=-4500; {start w r i t i n g points to f i l e } Next:=Spectrum; WriteLn(Outfile,'PU',x,' ',(round(Next A.Int*VScale)-4500),';'); For i := -Width+1 to Width do Begin Next:=Next A.Link; Appendix B x:=x+HScale; y:=round(Next A.Int*VScale)-4500; WriteLn(Outfile,'PD',x,' ',y,';'); End; {enter axes and labels) WriteLn(Outfile,'PU',x-720, 1 -5000;'); WriteLn(Outfile, 'LB', (NuOO+Width*Factor/1000) :0:3, '_MHz',chr(3), ' ; ' ) WriteLn(Outfile,'PU',x,' -4750;'); WriteLn(Outfile, 1PD',x,' -4625;'); WriteLn(Outfile,'PD-3500 -4625;'); WriteLn(Outfile,'PD-3500 -4750;'); WriteLn(Outfile,'PU-4270 -5000;'); WriteLn(Outfile, 'LB', (Nu00-Width*Factor/1000) :0:3, '_MHz',chr(3), ' ; ' ) {put i n s t i c k spectrum) { HScale:=round((x+3500)/(2*width+l)); for k:=l to 2*i do begin WriteLn(Outfile,'PU ',(round(HScale*((nuO[k]-nuOO)*1000+width) 3500)) , 1 -4500;'); WriteLn(Outfile,'PD ',(round(HScale*(1000*(nuO[k]-nuOO)+width) 3500)) ,' ',(round(intensity[k]*90-4500)),';'); end; } C l o s e ( O u t f i l e ) ; End; Procedure Show_Graph_Info; Var Nu :Real; Number :String; Begin OutTextXY(8, 5,'Data F i l e : '+FileName); Str(DELTAnu*1000:0:2,Number); OutTextXY(8,2 0,'Line Width: '+Number+' kHz'); Str(Round(nu00*V*2000 / (C - V)),Number); OutTextXY(420,5,'Doppler S p l i t t i n g : '+Number+' kHz'); Line(0,455,640,455); Line(64,455,64,460); Line(576,455,576,460); Line(320,455,320,460); S e t T e x t J u s t i f y ( l , 2 ) ; Nu:=Nu00-(width*factor*0.9/1000) ; Str(Nu:0:2,Number); 0utTextXY(64, 4 65,Number) ; Nu:=Nu00+(width*factor*0.9/1000) ; Str(Nu:0:2,Number); 0utTextXY(576,465,Number); Str(Nu00:0:2,Number) ; OutTextXY(320, 465,Number) ; End; Appendix B Procedure Draw_Spectrum; Var Number :String; Begin SetViewPort(0, 4 0, 639, 449,ClipOn) ; ClearViewPort; MoveTo(l, trunc(408 - 348* (Spectrum A.Int-min)/(max-min))); Last:=Spectrum; For n:=-width+l to width do Begin LineTo(trunc(640.0*(n+width)/(2.0*width)), trunc(408.0 - 400.0*Scale*(Last A.Int-Min)/(Max-Min))); Last:=Last A.Link; End; {put i n s t i c k spectrum) for k:=l to 2*i do Begin MoveTo(trunc(64 0.0*(1000.0*(nuO[k]-nuOO)+width)/(2.0*width)),408); LineTo(trunc(64 0.0*(1000.0*(nuO[k]-nuOO)+width)/(2.0*width)), 408-trunc(Scale*intensity[k]*4.0)); End; SetViewPort(0, 0, 639, 47 9,ClipOn) ; SetTextJustify(0,2); Str(Round(Scale*100),Number); S e t F i l l S t y l e ( S o l i d F i l l , Black); Bar(475,20,530,26); OutTextXY(420,20,'Scale: '+Number+' % ' ) ; End; Procedure Calculate_Spectrum; Procedure NewVar(Var DataPt : SpecPtr); Begin New(DataPt); DataPt A.Int:=0; DataPt A.Link:=NIL; End; Begin {calculate doppler components for lines} nuOO := (nuO[1]+nu0[i])/2; For k:=l to i do Begin Doppler := nu0[k]*V / (C - V); nu0[i+k] := nu0[k] + Doppler; nu0[k] := nu0[k] - Doppler; intensity[i+k] := i n t e n s i t y [ k ] ; End; NewVar(Spectrum); NewVar(Last); Spectrum:=Last; {calculate lineshape - one point per kilohertz} for k:=-width to width do Appendix B Begin {expression for lorentizan l i n e shape - see kroto p 86) For n:=l to 2*i do Begin Last A.Int:= L a s t A . I n t + Sqr(intensity[n] * DELTAnu (Sqr(nu00 - nuO[n] + k*Factor/1000) + Sqr(DELTAnu))); End; NewVar(Next); Last A.Link:=Next; Last:=Next; End; Last:=Spectrum; Max := L a s t A . I n t ; Min := Max; Repeat I f L a s t A . I n t > Max then Max := L a s t A . I n t Else I f L a s t A . I n t < Min then Min := L a s t A . I n t ; Last:=Last A.link; U n t i l Last A.link=NIL; End; Label 1; Var CHI, CH2 :Char; BEGIN Read_Plot_Data; DELTAnu := DELTAnu/1000.0; As s i g n ( L i n e L i s t , FileName); Re s e t ( L i n e L i s t ) ; {read i n t r a n s i t i o n data from FileName.cat) i : = l ; While not EOF(LineList) do Begin ReadLn(LineList, LogInt[i], I n t e n s i t y [ i ] , f i r s t p a r t , nuO[ I f (Nu0[i] > min) and (Nu0[i] < max) then I n c ( i ) ; End; Dec(i) ; C l o s e ( L i n e L i s t ) ; Calculate_Spectrum; GraphDriver := Detect; InitGraph(GraphDriver, GraphMode, ' ' ) ; ErrorCode := GraphResult; Scale := 1; Show_Graph_Info; Draw_Spectrum; 1: Repeat Appendix B 111 CHI:=Readkey; If CHI = #0 then Begin CH2:=readkey; If Ch2 = #72 then Scale := Scale + 0.2 Else I f (Ch2 = #80) and (Scale > 0) then Scale := Scale - 0.2 Else Goto 1; Draw_Spectrum; End Else I f Upcase(CHl) = 'S1 then Save_HPGL_File; U n t i l CH1=#13; CloseGraph; END. 

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