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High resolution spectroscopy of aminoborane and niobium nitride Lyne, Michael Peter 1987

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HIGH RESOLUTION SPECTROSCOPY OF AMINOBORANE AND NIOBIUM NITRIDE by MICHAEL PETER LYNE B.Sc. (Hon. Co-op) University of Waterloo, 1985 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Chemistry We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA 2 October 1987 © Michael Peter Lyne, 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at The University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Chemistry The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: 2 October 1987 ABSTRACT The infrared spectrum of aminoborane (NH 2BH 2) was recorded by a Fourier transform interferometer and the 1550-1750 cm" 1 region of the spectrum was rotationally analyzed by a new search/match algorithm based on ground state combination differences. Sub-bands from four separate vibrational bands were discovered in this region. The interaction scheme was deduced to be a three-way anharmonic resonance between the v 3 , v 7 + v B, and 2 v 6 levels with the fourth level, V f + c, 2» induced by a Coriolis mechanism with the members of the triad. The first order anharmonic constants were approximated by a least squares fit of the triad intensities: W 3 7 8 = 8.4±0.1 • cm" 1, W 3 6 6 = 15.8 + 0.4 cm"1 with W7 8 6 6 held fixed at zero. Perturbations from unseen interloper levels plus the fully correlated nature of the pure vibrational anharmonic interaction prevented a successful fit of the rotational structure of this system. Both the search/match and the intensity least squares algorithms were developed for this work. Four sub-bands in the red-orange region of the laser induced fluorescence spectrum of niobium nitride (NbN) were rotationally analyzed. Analysis of three sub-bands of the 3 $ 2 - 3 A ^  system allowed the vibrational spacings of each electronic state to be determined: AG = 986.351 cm"1, AG = 977.855 2 -'•2 cm"1 for the 3# 2 state and AG, =. 1033.739cm"1 for the 3A, state. The previously unassigned 3II, - 3 A 2 (0-0) sub-band was discovered 970 cm"1 below its expected position of 18025 cm"1. The electronic state assignment of this transition was confirmed by -wavelength resolved fluorescence measurements made with a diode array detector mounted on a spectrometer. A description of how the diode array detector was interfaced into the experiment is given. ii TABLE OF CONTENTS Abstract ii List of Figures . v Acknowledgements vi INTRODUCTION vii Chapter 1. THEORY 1 1.1. Molecular Rotations 2 1.2. Molecular Vibrations 7 1.3. Selection Rules In The Infrared 9 1.4. Resonance Effects in the, Infrared 13 1.4.1. Anharmonic Resonance 15 1.4.2. Coriolis Interactions 17 1.5. Electronic Transitions: Heteronuclear Diatomics 21 1.5.1. Vibronic Transitions 28 1.5.2. Rovibronic Transitions 30 References 32 Chapter 2. EXPERIMENTAL 34 2.1. Aminoborane 34 2.2. Niobium Nitride 34' 2.3. The Diode Array Detector 37 2.3.1. Introduction 37 2.3.2. Performance Characteristics 38 2.3.3. Operating Precautions 39 2.3.4. Software 40 2.3.4.1. Introduction 40 2.3.4.2. Detector Calibration 41 2.3.4.3. Graphics 42 References 43 Chapter 3. AMINOBORANE 44 3.1. Background 44 3.2. Rotational Analysis 46 3.3. Vibrational Assignments: The System Model 59 3.4. Least Squares Treatment 64 3.5. Discussion 75 References 76 Chapter 4. NIOBIUM NITRIDE 78 4.1. Background 78 4.2. Analysis 81 4.2.1. Rotational Analysis 83 iii 4.2.2. Determination of the Electronic States 84 4.3. Discussion 87 4.3.1. Results 87 4.3.2. Comment on Low-Lying States 88 4.3.3. Future Work 91 References 92 Appendix I : Aminoborane Line Assignments 94 Appendix II : Character Tables 149 Appendix III: Aminoborane Residuals 150 Appendix IV : NbN Line Assignments 158 iv List of Figures Figure 1.1 Perturbation Effects in a Two Level System 15 Figure 1.2 Hund's Case (a) Coupling 26 Figure 1.3 Hund's Coupling Cases: (a) case(aa), (b) case(a^) ..27 Figure 1.4 Effect of case(afl) Coupling in NbN: Ft lines of 3 * 2 ( 1 )- 3A,(l) band, P lines o f 3 $ 2 \ 0 ) - 3 A, (0) band 28 Figure 2. LIF experimental apparatus 35 Figure 3.1. Low-resolution transmittance spectrum of NH 2BH 2 (1510-1720cm" 1). 47 Figure 3.2. Sub-band origins of potential interloper bands near the v 3 fundamental 48 Figure 3.3. Medium-resolution transmittance spectrum of the A-type v „ fundamental 48 Figure 3.4. High-resolution transmittance spectrum of NH 2BH 2; sub-bands from all four vibrations present 51 Figure 3.5 Upper State Rotational Energies of the Levels - v T + VT, 2v6 and + of NH 2BH 2 55 Figure 3.6 Ground State Rotational Energy Levels of NH 2BH 2 57 Figure 3.7 Scaled Upper State Sub-band Origins of the 1609 and 1625 cm" 1 bands 60 Figure 3.8 Intensity Ratios for the 1609 and 1625 cm"1 bands 62 Figure 3.9 Matrix Representation of the Four Level Interaction 64 Figure 4.1. Molecular Orbitals of NbN. 79 Figure 4.2. Broad Band LIF spectrum of the 16950-17110 cm" 1 region of the NbN spectrum 81 Figure 4.3. Av = 0 sequence of the 3 $ 2 - 3 A 1 system of NbN 82 Figure 4.4. Wavelength Resolved Fluorescence of Optically Pumped Q(13) line of 3n,- 3A 2 (0-0) Sub-Band 86 v ACKNOWLEDGEMENTS I would like to thank Dr. A.J. Merer for the advice and guidance he provided to me throughout this work. Thanks also to Dr. Y. Azuma for aid with the niobium nitride work and to C. Chan for technical assistance with the aminoborane analysis. I have enjoyed working in the stimulating enviroment of the High Resolution Spectroscopy Group and I wish it much success in future endeavours. vi INTRODUCTION This thesis describes the measurement and rotational analyses of portions of the high resolution spectra of aminoborane (NH 2BH 2) and niobium nitride (NbN). The infrared of spectrum of NH 2BH 2 was recorded by means of a high resolution Fourier transform interferometer and the Doppler limited electronic spectrum of NbN was recorded by the laser induced fluorescence (LIF) technique. Both these molecules are being extensively studied by the High Resolution Group at the University of British Columbia; this work details the author's contribution to the group effort. The first chapter of this thesis presents the theory for infrared and electronic spectroscopy which is necessary knowledge for interpreting the spectra. The experimental details of both studies are covered separately in chapter 2. The bulk of the experimental chapter details the implementation of a diode array detector, used for wavelength resolved flourescence measurements, into the High Resolution Laboratory. The operating procedures and software is described with emphasis on the detector calibration. Background information on NH 2BH 2 and NbN is presented at the beginning of chapters 3 and 4 respectively and will not be given here. Two novel techniques were developed for the analysis of the NH 2BH 2 spectrum. The rotational structure was assigned with the aid of a search/match algorithm based on combination differences. This search/match algorithm proved to be an invaluable tool for assigning dense and perturbed spectra and is already vii being used by other members of the High Resolution Group. The first order anharmonic constants were approximated by a rotation-independent least squares fit on the line intensities of the members of the anharmonic triad. This least squares treatment of the intensities is valid when only one of the interacting levels can be assumed to donate all the oscillator strength to the system. viii CHAPTER 1. THEORY This section provides the basic theory that was necessary to carry out the spectroscopic analysis detailed in this thesis. Before discussing the rotational and vibrational Hamiltonians it is important to recall the Born-Oppenheimer approximation which effectively states that the total wavefunction of a molecule may be resolved into a nuclear and an electronic part. The relative masses of the nuclei and electrons cause their relative velocities to be so different that the electrons follow the nuclei instantaneously. The molecular wavefunction can then be separated into an electronic ( e^) and a nuclear part (\/>n) such that the nuclear motions may be analyzed independently of the electronic motions. The nuclear motions, rotation and vibration, cannot be completely separated even though the energies associated with these motions differ by approximately three orders of magnitude. The vibration and rotation are coupled in the kinetic energy portion of the nuclear Hamiltonian. It is possible, however, to divide the kinetic portion of the nuclear Hamiltonian into three discrete terms: Pure Rotational Kinetic Energy Pure Vibrational Kinetic Energy Vibration-Rotation Interaction Kinetic Energy. The pure motions can now be treated separately and the interaction term, if significant, will cause perturbations to the energy states predicted by the pure terms. The rotational and vibrational Hamiltonians are considered for polyatomic 1 THEORY / 2 molecules since an analysis was performed on a region of the NH 2BH 2 vibration-rotation spectrum. Strong perturbations resulting from a Coriolis interaction and various anharmonic resonances were observed in the NH 2BH 2 spectrum so the origins of these phenomena are examined. The limiting cases of the rotational and vibrational Hamiltonians for a diatomic molecule and elements of electronic spectroscopy pertinent to the analysis of NbN are also presented. 1.1. MOLECULAR ROTATIONS The Hamiltonian for a rigidly rotating molecule can be written [1,2] as: J 2 J 2 J 2 H _ = + + _Y_ (i.i) r r 21 21 21 z x y where J z , «JX, Jy> are the angular momentum operators which represent the molecule fixed components of the total rotational angular momentum J, and I , z I , I , are the principal moments of inertia in the molecule fixed axis system, y It is conventional to label the molecule fixed axes a, b, and c, such that principal inertial moments are ordered as: I a < 1^ < I c > The molecule may then be characterized by the rotational constants A, B, and C, which are related to !a' Xb' Jc>by: h I a x A = I K x B = I „ x C = (1.2) a ° c 8ir 2c where h is Planck's constant, c is the velocity of light and the inertial constants have units of cm" 1. There are six different ways to identify the a, b, c axes with the THEORY / 3 molecule fixed axis system; x, y, z. The I representation [3], where the z, x, y axes correspond to the a, b, c axes respectively, was chosen for the analysis of the NH 2BH 2 spectrum. There are five possible types of rotors depending on the relative magnitudes of I , Iw, I • 1. linear molecules V = 0, *b = 2. spherical tops la - lb = lc 3. prolate symmetric tops la < Jb = lc 4. oblate symmmetric tops Xa = *b < ! c 5. asymmetric tops la < < lc-The Hamiltonian (1.1) can be conveniently represented in matrix form using the symmetric top rotational basis; in this basis the operators J 2 and J_ have the sharp eigenvalues J(J+l)h 2 and Kit respectively and the eigenfunctions of these operators are labelled |J,K>, in Dirac's [4] notation. The space fixed component of J, that is M, has been omitted as no effective external fields are present in recording the spectra. From the eigenvalue equations for J 2 , J , J , and J [5] and the commutation relations appropriate to molecule fixed components [6]: [J x,Jy] = — i h J z (plus the other two cyclic permutations), (1.3) equation (1.1) can be shown to have the non-vanishing matrix elements: THEORY / 4 B+C <J,K|Hrr|J,K> = i (B + C)J(J+1) + [A- 2 ] K 2 (1.4) <J,K±2|Hrr|J,K> = i (B-C)[J(J+1) K(K±1)] |*X[J(J+1) -(K±1)(K±2)]*, (1.5) in the I representation. If B = C, which occurs for linear molecules, spherical tops and symmetric tops (prolate in the I and oblate in the IH representation), then equation (1.5) vanishes leaving the Hamiltonian matrix diagonal. The rotational energy levels are calculated directly from (1.4): The K dependent term vanishes for spherical tops because A = B, and for linear molecules because a linear molecule cannot have rotational angular momentum about its axis. The asymmetric rigid rotor energy levels are calculated by diagonalizing the Hamiltonian matrix for each value of J greater than zero. The matrix separates at once into matrices for even and odd J because there are no <K±l|H|K> matrix elements, and since both matrices for J are symmetric about both diagonals they can be factorized into a total of four submatrices by applying the Wang similarity transformation [7]. Each of the four submatrices have the properties of a different symmetry species of the D 2 group (see Appendix JT) and are labelled E +, E", O *, 0" corresponding to the symmetry species A, B a, B^, B c. The transformation has the effect of taking the sums and differences of the original symmetric top basis functions. Each of the four F(J,K) = BJ(J+1) + (A-B) K 2. (1.6) THEORY / 5 sub-blocks is then diagonalized to get the asymmetric rigid rotor energy levels. The resulting asymmetric rotor eigenfunctions are linear combinations of the symmetric rotor eigenfunctions. Since K is no longer a good quantum number for an asymmetric top, the energy levels are distinguished by the Jj^gj^ notation [3]. K a and K c are the values |K| would assume if the B constant was varied to the prolate or oblate symmetric top limit respectively. The symmetries of the rotational energy levels are determined by their respective quantum numbers [5] as is shown in table 1.1. Table 1.1 Symmetry Species3 of Asymmetric Rotor Energy Levels Submatrix J J even odd E* A(ee) B=(eo) E" B=(eo) A(ee) Cl 0 + Bc(oe) Bb(oo) E + Bfa(oo) Bc(oe) a - the representations of A, B Q, Bj^, B c are given in the D 2 character table in App. II. A molecule is not a rigid rotor as it is distorted by centrifugal forces as it rotates. Thus the instantaneous moments of inertia of the molecule become dependent on the molecule's angular momentum. The simplest method to account for centrifugal effects in asymmetric tops is to use Watson's A-reduced Hamiltonian [8]. Watson expands (1.1) in a Taylor series of the components of the total rotational angular momentum and transforms the Hamiltonian to a basis THEORY / 6 which contains determinable coefficients that account for centrifugal effects. Not surprisingly these coefficients can be related to terms in the potential energy function of the molecule [9]. The A-reduced Hamiltonian is convenient to use because it has the matrix elements of the type K = 0, ±2, and so retains the form of (1.1) except for the added higher order terms. When considering a very near symmetric top it is necessary to use Watson's S-reduced Hamiltonian [9]. The matrix elements of the A-reduced Hamiltonian,up to order J 6 are given [9] as: B+C < J,K|Hr |J,K > = i(B + C)J(J +1) + [A —- ] K 2 - A j J 2 (J +1) 2 - A J K J(J + 1)K 2 -A j ^ K ' + S j J ^ J + l ) 3 * * ^ J 2 ( J + l ) 2 K 2 + $ R J J ( J - r l ) K 4 + $ K K \ (1.8) <J,K±2|Hr|J,K>={i (B-C)-6 JJ(J+1)-£5 K[(K±2) 2+K 2]+0 J J 2(J+1) 2 + i0 J KJ(J+l)[(K±2) 2+K 2] + i 0 K [(K±2)«+ K"]} X {[J(J+ 1)-K(K± 1)][J(J+ 1)-(K± 1)(K±2)]}*, (1.9) in the I representation. The energy levels are calculated in the same manner as described for the rigid rotor. Equations of the form of (1.8) and (1.9) were used in the fitting of the NH 2BH 2 spectra. The rotational term values for a non-rigid diatomic molecule are given by: THEORY / 7 F(J) = BJ(J + 1) - DJ 2(J+1) 2 + HJ 3(J+1) 3 - ...higher terms. (1.10) All centrifugal terms higher than D were neglected in the fitting of the NbN spectra. 1.2. MOLECULAR VIBRATIONS It is easy to imagine the non-rigid bonds of a molecule as behaving like springs; in fact molecular vibration is a problem that can be analyzed almost completely by classical mechanics. Each free atom had three translational degrees of freedom before being bound into the molecule thus a molecule consisting of n atoms must have 3n degrees of freedom. Three of these degrees of freedom correspond to translation of the molecule, and three more degrees of freedom (or two if the molecule is linear) correspond to the free rotation of the molecule, leaving 3N-6 or (3N-5) vibrational degrees of freedom. In consequence NH 2BH 2 has 12 vibrational degrees of freedom whereas NbN has only 1 vibration. It is simplest to resolve the complicated motions of the nuclei, which arise from the superposition of all the internal motions, into separate fundamental vibrations by introducing normal vibrations. A normal vibration is one in which all nuclei move at the same frequency and in phase with each other [2]. The amplitudes of the motions of the different nuclei are what distinguish the individual normal vibrations from each other. The normal co-ordinates are defined by the transformation: q = A Q\ THEORY / 8 (1.11) where q represents the mass-weighted Cartesian displacement co-ordinates of the molecule and A is the matrix of the amplitudes of each nulceus in each normal vibration. By using an harmonic approximation the total vibrational energy (E v) is simply a sum of independent harmonic oscillators: E = - 3 £ Q? + - 3l\. Q? (1.12) A simplified form of the vibrational Hamiltonian, Hv, can now be written in terms of the normal co-ordinates; where P. = , is the momentum operator and k is a pointer for the set k i 9 Q k of normal vibrations. Recalling that the total vibrational wave function can be expressed as the product of the individual normal vibrational wavefunctions [2], and recalling also the familiar solution to the Schrb dinger equation for a harmonic oscillator [12], the vibrational energy levels of a polyatomic molecule in terms of the normal vibrations are given as: d k E(v,,u2,...,wk,..) = I kw k (vk+ — ), (1.14) THEORY / 9 where is the vibrational quantum number of the kth co-ordinate, which can have any positive integer value, d^ is the degeneracy, and (*>^ = *^k' It must be remembered that (1.14) is only valid for very small nuclear displacements. It clearly doesn't predict the true course of the vibrational energies for a molecular bond which has vibrational energies asymptotically approaching the bond's dissociation energy. 1.3. SELECTION RULES IN THE INFRARED In infrared spectroscopy transitions are driven by an oscillating electric field interacting with the dipole moment of a molecule. A transition is allowed between two states only when the following expression is non-zero : <<^'| E(t) -0 -|^ ,^ ;>, (1.15) where E(t) is the electric field of the source radiation and U is the dipole moment of the molecule. A product wavefunction, |<//v,^ r>, of the pure vibrational wavefunction, i / / v and the pure rotational wavefunction, can be used in first approximation to describe the energy states. Equation (1.15) may be simplified if the radiation beam is polarized along the space-fixed Z axis so that only one component of E(t) need be considered: <^,^|E z<t)u 2 \r;,4>;>, THEORY / 10 (1.16) where is the component of the molecular dipole moment defined with respect to the space-fixed axis Z which may be related to the molecule-fixed axis system (x,y,z) by direction cosines (5): UZ = u z * Z z + ux*Zx + u y * Z y ( L 1 7 ) For simplicity let us consider a transition resulting from an interaction of E^(t) with u z > Since E^(t) only operates on the time dependent portion of the wave functions, evaluation of the time-independent part of the transition moment R 2 will reveal whether a transition is allowed: R z = <^rl *Zz l*r> <K\ u z K>- (L18> R is separated here into the product of two integrals because v// is unchanged upon rotation and is independent of translation [10]. When a molecule vibrates u may not be a constant; it is a function of the normal co-ordinates and so may be represented by the Taylor series expansion: 3 u z 1 , 3 2 u z u =(u_)0+( )o Q k + - < — )0Q-:Qk+..-higher terms, (1.19) z z 9Q k k 2 9Q k9Qj 3 k Substituting (1.19) into (1.18) and neglecting powers of the series higher than THEORY / 11 one, the transition moment now has the form: R z = <*rl *Zz \K> K V o < * v l * C > + ( T ? ^<K\ % K> ] ( L 2 0 ) Examination of (1.20) reveals three key points: 1. a pure rotational transition about a molecular axis only occurs when a permanent dipole moment is present along that axis. 2. in order for a vibrational transition to occur the change of the dipole moment with respect to the normal co-ordinate must be non-zero. 3. any vibrational transition must also be accompanied by a rotational transition. A transition will be allowed between two rotational states if the direct product of the symmetry species representing the upper and lower states is of the same symmetry as the species representing the direction cosine relating any non-zero component of the molecule's dipole moment to the space fixed direction of the radiation beam. The symmetry species of the asymmetric top eigenfunctions and the direction cosines all can be classified under the D 2 group [5]. The NH 2BH 2 spectra discussed in this thesis are all driven by a vibration resulting in a dipole moment change along the a inertial axis and thus follow A-type rotational selection rules: THEORY / 12 J aa <-> J J aa <-> J J J aa (1-21) even.odd even,even odd,even odd.odd where the subscripts on J refer to the values of K_ and K_ respectively and AJ = 0,±1. Evaluation of <i/>v| using the harmonic oscillator wave functions yields the selection rule: Av^ = ±1, where v^ is the vibrational quantum number of the kth fundamental. Since the anharmonic terms from the potential function have been discarded in the derivation of the normal co-ordinates, anharmonicity must be reconsidered in order to explain the prescence of overtones and combination bands in infrared spectra. Anharmonicity is reintroduced via (1.19) in the form of mechanical and electrical anharmonicity. Mechanical anharmonicity, the more important of the two, results from the fact that higher order coupling terms between the normal co-ordinates occur in the full potential energy expression. Normal vibrations are assumed to be completely independent by definition but real vibrations cannot be separated because they occur within an intimate molecular framework. Electrical anharmonicity refers to the non-linear dependence of the molecule's dipole moment on nuclear displacements. By truncating (1.19) at the first order term the dipole derivative for the normal co-ordinate is assumed to be linearly dependent on the magnitude of the co-ordinate. This may be adequate for very small nuclear displacements but it clearly doesn't predict the behaviour of say, the bond in a heteronuclear diatomic whose dipole moment goes to zero at THEORY / 13 both very large and small nuclear separations. Inclusion of the second order term would allow for single combination bands (v^ + v^) and first overtones (2^) because of the cross term linking two normal co-ordinates. The higher terms in the expansion contribute to the higher overtone and combination vibrations. 1.4. RESONANCE EFFECTS IN THE INFRARED The infrared spectra of polyatomics are replete with examples of the inadequacy of the simple non-rigid rotor/harmonic oscillator Hamiltonian to predict the true energy levels of the system. Perturbations to the energy levels of the non-rigid model arise because the motions within the molecule are coupled by various mechanisms. When a vibrational level is apparently unperturbed its rotational energy levels may be obtained by diagonalizing the block matrix whose basis set spans that level alone. If two levels interact a matrix consisting of the two vibrational blocks on the diagonal and off-diagonal interaction matrix elements linking the two levels must be diagonalized. If the off-diagonal elements are not small compared to the energy separation of the interacting levels then a resonance condition exists. Solving a 2X2 secular equation reveals the effect of a resonance condition. Consider two energy levels: and T 2 which interact via an hermitian interaction element W; |tfi> 1*2 > T,- E W = 0 (1.22) W T 2 - E THEORY / 14 The eigenvalues of this problem are: E = iO^+Ta) ± i(4|W|2 + 8 2)* (1.23) where 8 = ( T 1 — T 2 ) is the separation of the unperturbed levels. The eigenfunctions of the two resulting states and \(/~) will be mixtures of the basis functions i//, and \l>2-\p* = a*/^—bi//2 and \p~ = b ^ + a ^ (1.24) 2A+8 2A-6 A where: a 2= , b 2= , and A=i(4|W|2 + 6 2) , (1.25) 4A 4A The eigenstates (yp*, \p~) may be represented by the eigenvectors (a,-b) and (b,a) which define the degree of mixing of the basis functions (\p ^, v//2). The properties of the eigenstate will resemble those of the major contributor to the eigenfunction; indicated by the largest element in the eigenstate's eigenvector. If there is no interaction (W = 0) then the roots of (1.22) are simply the unperturbed energy levels and the eigenfunctions are the pure basis functions. If a resonance condition exists the unperturbed levels are repelled from each other by an equal amount. The perturbation is most pronounced for a given W when 6 = 0; the eigenfunctions will be 50:50 mixtures of the basis functions at this point. When the course of two energy levels cross the sign of 8 changes and the degree of basis function mixing and hence the character of each eigenstate is reversed compared to before the crossing. This phenomenon is often called an avoided crossing and is shown in figure 1.1 : the dotted lines represent the T H E O R Y / 15 courses of the unperturbed energy levels and the solid lines represent the resulting eigenstates. The reversal of character is revealed by the change in slopes of the upper and lower eigenstate energy levels ( E + , E " ) . 1.4.1. Anharmonic Resonance A multitude of vibrational levels are possible in a polyatomic apart from the fundamental levels because the energy formulae allow overtones and combinations. If two vibrational levels are accidentally degenerate, that is i f they have nearly the same energies, they may interact v ia an anharmonic resonance. This phenomenon was first recognized in 1931 by F e r m i [13] in the spectrum of C 0 2 . The first overtone of the degenerate bending fundamental v2 should occur at approximately twice its fundamental frequency (667 c m " 1 ) , which happens to be nearly the same energy as the fundamental frequency of the symmetric stretch v, (1337 c m " 1 ) . When observed in the spectrum the (0,2,0) and (1,0,0) levels seem to have repelled each other; the (0,2,0) level appears at 1285.5 . E E -6 o +6 Figure 1.1 Perturbation Effects in a Two Leve l System. THEORY / 16 cm"1 while the (1,0,0) appears at 1388.3 cm"1. In 1940 Darling and Dennison [14] noticed a similar anharmonic resonance in the water vapour spectrum where two overtones, (2v y = 2v3), were involved. The root of these perturbations is in the anharmonic terms of the potential energy function. Third rank resonances relate two or three normal co-ordinates, fourth rank resonances relate two, three, or four normal co-ordinates and so on for higher terms; the Fermi resonance is third rank and the Darling-Dennison resonance is fourth rank. The resonances studied in this thesis were of the third and fourth rank. Not all near-degenerate vibrations interact through an anharmonic resonance. If the interaction element is W and i/> denotes a simple harmonic oscillator wavefunction, then the integral < \p 2 |W|^  ^  > must be totally symmetric for an interaction to occur. The potential energy function is totally symmetric in the molecular point group; it is invariant to rotations and translations of the molecule. Since W comprises the higher order terms from the potential function the essential rule for an anharmonic resonance is: the interacting levels must be of the same symmetry species. The first order terms of the third and fourth rank interaction parameters contribute constants to the interaction matrix which are directly related to the respective cubic and quartic terms in the potential function. Delving further into the expansion of the vibration-rotation Hamiltonian reveals rotation dependent anharmonic resonance terms [15]. The first and second order terms (H^ and H| THEORY / 17 respectively) of the anharmonic resonance operator are given as: H f = W H| = w z J | + w x J 2 + w yJ 2. (1.26) The matrix elements for an allowed interaction between two vibrational levels \fy ^ and \p2 are then: <* 2;J,K|H f|* i ;J,K>=W 2 1+F 2 1Z K 2 + F 2 1 P [J(J+1)] < <// 2;J,K±2|H f|^ 1;J,K>=F 2 1M [J(J+1)-K(K± 1)]* [J(J+1)-(K±1)(K±2)]* (1.27)' where F 2 1 Z = ( w 2 ) 2 1 , F 2 ,P=i(w x + w y) 2 ,, and F 2 , M=i(w x-w y) 2 ,. 1.4.2. Coriolis Interactions The Coriolis force, F c, is a fictitious force used to explain the change in the angular velocity of a body (in order to conserve angular momentum) as it changes its displacement from the rotation axis in a rotating frame of reference; it is expressed classically as: F c = 2 m vXu, (1.28) which is a cross product of the angular velocity, c3, and the velocity, v, of a body of mass m moving perpendicularity with respect to the rotation axis. When viewed from the rotating frame of reference the Coriolis force appears to be a THEORY / 18 tangential force opposing rotation of the body of mass m when v is directed away from the rotation axis and vice versa. Even though F c is an apparent force it does cause real effects in a rotating frame of reference such as a molecule or the earth. A familiar example is the water swirling as it drains out of the sink. The swirling action results because unequal Coriolis forces act on the water at different points about the drain. The water molecules closer to the pole of the earth have slightly less angular momentum than those closer to the equator thus they 'experience' a weaker F c, hence a counter-clockwise swirl in the northern hemisphere and a clockwise swirl in the southern hemisphere. If a nucleus in a rotating molecule vibrates in such a way that it is displaced with respect to a rotation axis it will experience a force F c orthogonal to the rotation and displacement vectors. If the same nucleus is involved in another vibration that has a displacement component in the same direction as F c, the two vibrations will be coupled via a Coriolis interaction. In the quantum mechanical treatment [16] the Coriolis effect is considered by subtracting components of the vibrational angular momentum from the respective components of the rotational angular momentum. A component of the vibrational angular momentum say p , is defined by: p 2 = - i k g [xa(673ya) - ya(3/3xa)], (1.29) with cyclic permutations of z_, x and y_, which are the mass-weighted Cartesian displacement co-ordinates of nucleus a in the molecule. The complete THEORY / 19 rotation-vibration Hamiltonian is then: ( JZ - P 2 > 2 ( J x - P X ) Z ( J v - P v ) 2 1 H= ? ?_ + * 2L_ + Y. Y_ + _ I (p2 + x. Q?). (1.30) 2I Z 2I X 2I y 2 k * The pure vibrational Hamiltonian, Hy (1.13), is readily separable from (1.30) as is the pure rotational Hamiltonian, (1.1), after some algebra; therefore (1.30) can be expressed as: H = H V + Hr+Hc, (1.31) where H c may be treated as a perturbation to the pure rotation-vibration problem. H c has the form: H = - j V s - £ x £ i _ b d s . + j k ^ J k + J k / (1.32) h \ \ 2 I z 2 Ix 2 I y The last three terms in H c may be neglected since they contain no rotational operators, while the vibrational angular momentum is usually small compared to the rotational angular momentum [16]. When H c is evaluated in the \ipv;\pr> basis the first three terms in (1.32) yield vibration-rotation products of the type: z z The matrix elements of the angular momentum operators in the symmetric top basis have already been referenced [5]. The matrix elements of the vibrational angular momentum operators are found by expressing them in terms of normal THEORY / 20 co-ordinates: p z = £ 5«kj [ Q k p j " Q k p j ^ (1-34> where £ kj is the Coriolis zeta constant which is defined as: S S J = I K — ) ( A ) - ( — )( — A )], (1-35) k 3 S 3Qk 3Qj 3Qj 3Qk where and are obtained by cyclic permutations of z,x,y. The zeta constants relate two normal co-ordinates through rotation about one of the molecule-fixed axes. The symmetry species of the two normal co-ordinates can be used to predict whether or not the $ will be zero (ie: no interaction). This result is known as Jahn's rule [14]; can only differ from zero if the product of the symmetry species of and Qj contains the rotation R e > Recalling that the vibrational basis function is merely a product of the harmonic oscillator functions of the normal co-ordinates, the matrix elements of the vibrational angular momenta will be non-vanishing only when each of the normal vibrations change by one quanta. Terms which result in the most pronounced perturbations are those which connect energy levels of similar magnitude; when v£ < and Pj > or vice versa. When two fundamentals interact the matrix elements of the vibrational angular momentum are given as: <i,o|pe|o,i> = - i f e S g j O ^ , (1.36) THEORY / 21 where fl^j = itCw^/cjj)^- (toJ/CJ^)*], and CJ^ is the frequency of the kth normal vibration. The Coriolis interaction examined in this thesis is an x-axis interaction (the vibrations involved transform as the rotation about the x-axis). Thus the matrix elements of J and equation (1.36) will yield the off-diagonal matrix elements for an x-axis interaction: <*» k + l;i»j|- — | f k ; ^ j + l><J,K±l|J x|J,K>= i$J j[J(J+l)-K(K±l)]* (1.37) X L* where £ kj has absorbed the rotational constant B (in the I representation), together with the vibration dependent terms O^j and i>kj» to become an effective interaction constant. If anharmonicity is considered higher order terms arise that introduce further rotational dependences on K ± 1 interactions and allow K+3,K± 5,...matrix elements to occur for an x-axis perturbation [18]. 1.5. ELECTRONIC TRANSITIONS: HETERONUCLEAR DIATOMICS An electronic transition involves an electron changing its state so that the initial and final electronic states of the molecule are different. Before examining which transitions are allowed the characteristics of electronic states will be discussed. When the overall rotation of the molecule and any nuclear spin of the nuclei are neglected the electronic state of the molecule may be characterized by THEORY / 22 the sum of the orbital angular momenta, L, and spin angular momenta, S, of the open shell electrons. In a diatomic the electrostatic field resulting from the nuclei is cylindrically symmetric about the internuclear axis (z-axis). The motion of the electrons is constrained by this field so that L strongly couples to and precesses about the field axis. While the magnitude of L cannot be measured, its projection on the z-axis, A, is defined with A = |MjJ = 0,1,2...L. Electronic states are labelled Z, II, A, corresponding to their A values of 0,1,2,3,... respectively. All states with A > 0 are doubly degenerate since A = ± M T j . For states with A>0 the orbital motion of the electrons induces a magnetic field along the z-axis. This magnetic field couples S to the z-axis and causes it to precess about the axis just as L does. There are cases, however, where S couples more strongty to L than the internuclear axis; for example the lowest 3n* u term of iodine [19]. There are two idealized limiting cases whereby one can envisage S coupling either solely to the z-axis or solely to L. These situations are called Hund's coupling cases (a) and (c) respectively; Hund's coupling cases will be discussed in more detail below. In reality, for states with A>0, these limiting cases are never attained but the situation may be close enough to one of them that it forms a basis for energy level calculations. When the magnetic coupling of S to the z-axis dominates, S has a well-defined projection along the z-axis, Z, which has allowed values: S, S—1, S —2,... —S. The total angular momentum due to the electronic motion is fi where: 0 = |A + Z|. (1.38) THEORY / 23 Thus for every A > 0 state there will be a multiplet of 2S+1 components, corresponding to the different possible values of the total electronic angular momentum. The interaction of S with the magnetic field produced by A, the so-called spin-orbit interaction, causes the components of the multiplet to be split, in first order, by an amount [10]: E' = AAI, (1.39) where A is the spin-orbit coupling constant. If A is positive the components of the multiplet will increase in energy with 0 and vice versa if A is negative; in either case the multiplet components will be evenly spaced. The multiplicity of an electronic state, 2S+1, is labelled as a pre-superscript. The components of the multiplet are labelled by the post-subscript A+Z, instead of fi since A + Z may have a negative value. Therefore a state • with S = 1 and A = 2 is designated as 3A and will have the multiplet components: 3A 1, 3A 2, 3A 3. If the spin-orbit coupling outweighs the spin-axis coupling, which occurs in diatomics containing at least one heavy nulceus, then 0 is the only well-defined quantity resulting from the motion of the electrons. The character of electronic states can be used to deduce which transitions will be allowed in our molecule where the rotation and nuclear angular momenta have been ignored. Just as for infrared electric dipole transitions an electronic electric dipole transition will be allowed if the transition moment, Rg, is non-vanishing: THEORY / 24 (1.40) where ^ g is an electronic eigenfunction and is the electric dipole moment resulting from the electrons only. The vector n& may be separated into its three Cartesian components to arrive at expressions similar to (1.18). The electronic eigenfunctions are those for the electronic state of the molecule. Evaluation of (1.40) is most straightforward if group theory is used. A heteronuclear diatomic is cylindrically symmetric and thus belongs to the point group Coov(see App. II). There is an infinite number of reflection planes, a y, about the z-axis and thus an infinite number of representations in the group. The electronic eigenfunctions must also belong to the C o o v group and may be labelled according to their representation in the group. Inspection of the C character table reveals that the symmetry species are labelled by: Z +, Z", II, A, instead of the conventional labels: A 1 ; A 2, E,, E 2, E3,... This situation can be attributed to the electronic spectroscopists who used emperical arguments before the group theory rules were developed. The symmetry species of the electronic states discussed above are equivalent to the conventional labels of the C e o v table. The components of n& behave like translations along the molecular axes, and transform as Z* (z) and II (x,y). Equation (1.40) will be non-zero when the direct product of the symmetry species of the upper state, lower state and dipole moment components contains the totally symmetric species L*. Examination of the C a > v table yields the following selection rules for electric dipole transitions in the case (a) THEORY / 25 approximation; 1. AA=0,+ 1. 2. +<-)->— for Z—Z transitions. 3. AZ = 0. The third rule exists because the dipole moment operator contains no spin co-ordinates [11]. Combining rules one and three gives: AS2 = 0,±1. (1.41) While rules one and three lose their meaning for case (c) coupling situations, (1.41) still holds. The total angular momentum that the photons encounter in a diatomic consists of more than the electronic angular momenta discussed above. The nuclear rotational angular momentum, R, associated with the molecule tumbling in space and possibly nuclear spin angular momentum, I, associated with the spin of one or more of the nuclei must also be considered. The total angular momentum associated with the molecule will be the resultant of all the momenta: L, S, R, I. It is impossible to know beforehand exactly how these momenta will couple but the set of limiting cases called Hund's coupling cases correspond to basis functions which can be used to approximate the possible coupling situations. When analyzing an electronic spectrum the coupling case is chosen such that the molecular Hamiltonian is most diagonal; the real deviations from the limiting case are called perturbations to the limiting case. It is not the intention of this thesis to catalogue all the Hund's coupling cases but to discuss' the coupling situation T H E O R Y / 26 pertinent to m y analysis of N b N . A complete description of these cases is given by Herzberg [10]. The relationship between L and S for case (a) coupling has already been discussed above. If the effect of nuclear spin can be neglected and L and S are individually coupled to the z-axis then the overall rotational angular momentum, J, is obtained by coupling R to (see figure 1.2). The quantum number J has allowed values + R where R = 0,1,2,.. ; J can never be less than fi. Case (a) coupling is a good aproximation when an orbital angular momentum is present and the spin-orbit coupling is moderate ( A = 1 0 0 c m " 1 , B = l c m " 1 ) [20]. The spin-orbit interaction was discussed above. If the effect of the nuclear spin cannot be ignored there are two possible ways of coupling I in the case (a) model. When the magnetic interaction of the nuclear moment with the electron orbital and spin moments is sufficiently strong I wi l l be directly coupled to the Figure 1.2 Hund 's Case (a) Coupling T H E O R Y / 27 z-axis and the projection of I on the z-axis, I , wi l l be well-defined where I = I, I—1, I —2,...—I. This is called case (a f l ) coupling where a implies quantization of I in the molecule-fixed axis system (see figure 1.3a). The total angular momentum, F, is obtained by coupling R to fl + I . This type of coupling is highly unlikely since the coupling energies of nuclear moments are only = l /1000 th of those for electron moments [21] so rotation of the molecule readily uncouples I from the z-axis. When the- molecule rotates, the resulting rotational magnetic moment, is coupled to I more stronglj ' than I is to the axis; then the total angular momentum F is obtained by coupling J to I as shown in figure 1.3b. This is called case (a^) coupling where /3 implies quantization of I in the space-fixed axis system. It has been shown [21] that the size of the hyperfine split t ing varies as [F (F+ 1)-I(I+ 1)-J(J+ 1)]/[J(J+1)] so the split t ing effects are most noticable at low J values in the rotational branches. The rotational structure of the 3 4> 2 — 3 ^ 1 sub-bands discussed in this thesis displaj'ed clear examples of case T H E O R Y / 28 (a^) coupling (see figure 1.4). The data in figure 1.4 was taken to analj'ze the weaker 3<i>2 ( 1 ) - 3 A, (1) band so the P(28)-P(33) lines of the 3 $ 2 ( 0 ) - 3 A, (0) band saturated the detector. 1.5.1. Vibronic Transitions The selection rule for vibrat ional transitions wi th in the same molecular potential curve was found to be Au= + 1 in the harmonic approximation where overtones and combination bands are allowed to a much lesser degree by anharmonic effects. The vibrational transitions associated with electronic transitions, vibronic transitions, no longer obey the Av—±1 selection rule but the intensity of the vibronic transition is governed by the Frank-Condon principle. The Frank-Condon principle can be explained physical]} 7 by recalling the basis of the Born-Oppenheimer approximation; because the electrons move so II U - - ^ - L T L _ J 1 1 | | | I I II I • 16 IS 14 13 12 11 io 9| e 7 • u • 7 6| 5_ 37 •R -P Figure 1.4 Effect of case(a f l) Coupling in N b N : R lines of 3 $ 2 ( 1 ) - 3 A, (1) band, P lines o f 3 $ 2 ( 0 ) - 3 A, (0) band. THEORY / 29 much faster than the nuclei, their motions may be treated independently. In other words during the time it takes an electronic transition to occur the internuclear distance can be assumed to remain constant. As previously stated, different electronic states are characterized by different molecular potential functions which may or may not have their minima at the same internuclear separation. The intensity of the transition will depend on the overlap of the upper and lower state vibrational wavefunctions. This concept is clearly displayed if the vibronic transition momemt, RgV> is considered: R ev = <*evl " l*ev>' ( L 4 2 ) where \J/ and u are. the vibronic wavefunction and dipole moment operator respectively. The Born-Oppenheimer approximation allows <^ev to be separated into the product wavefunction, '/'g^ 'y, and u into a sum of the dipole moments resulting from the electronic and nuclear charges, Me + Mj^ , so (1.42) becomes: R e v = < * e l ^ e > <K\ "N K> + <KK> < ^ e l *e K>- (L43) The first term will vanish for an electronic transition as <'//e|</'g> = 0 since the electronic wavefunctions are chosen to be orthogonal. The integral <</'e| Mg \xPq> is defined in equation (1.40) as R g which for simplicity is assumed to be a constant. Thus the intensity of a vibronic transition will be dependent on the square of the vibrational overlap integral which is called the FrankCondon factor; i 0 0 \<KK>\2- (1.44) THEORY / 30 The population of the initial vibronic state will also determine the relative strength of the transition. 1.5.2. Rovibronic Transitions Just as for infrared transitions, every vibronic transition will also have an associated rotational transition; a rovibronic transition. The rotational term value is a function of the total rotational angular momentum (J) of the molecule. If hyperfine splitting is significant the rotational energies are expressed as a function of the total rotational angular momentum including nuclear spin. The simplest case is that of a 1Z state where there is no angular momentum other than nuclear rotation. In this case the rotational energy terms are given by equation (1.10). The same selection rules on J hold as for infrared transitions giving rise to Q (AJ=0), P (AJ= —1), and R (AJ=1) branches. If A=0 in both states however, then AJ = 0 transitions are not allowed [10]. When A * 0, which must be for case (a) coupling, the rotational term values are similar to those of a symmetric top (equation 1.6) except the projection of the angular momentum on the z-axis can only be J2, and the rotational constant A is necessarily zero. Neglecting centrifugal distortion terms, the rotational term values for a given vibronic state in a case (a) coupling situation are: F(J,0) = B v [J(J+1) - G 2], (1.45) THEORY / 31 where B v is the rotational constant of vibronic state V. Since J2 remains constant within a multiplet, the doppler-limited rotational structure is analyzed as a function of J only (see equation 1.10). The relative intensities of rotational lines can be useful in the analysis of an electronic band. The relative intensity of an emission line within a rotational band will depend on the population of the initial state and the line strength, Sj, associated with the transition. Sj accounts for the rotational dependence of the transition moment. The wavelength resolved fluorescence technique involves selectively pumping a rovibronic transition and resolving the emission signal. Since the initial state in the process is being selectively populated, the intensities of the emission transitions depend solely on the transition line strengths. The formulae for the line strengths of a symmetric top are known as the Hbnl-London factors. The factors for R and P lines in a AJ2= —1 emission are given below; a complete list is given by Herzberg [10]. S R = (J'-fi') (J'-l-n* / 4«T S^ = (J*+l + n') (J'+ 2+0') / 4(J' + 1). (1.46) REFERENCES 1. C.H. Townes and A.L. Schawlow, Microwave Spectroscopy, McGraw-Hill, New York, 1955. 2. G.Herzberg, Molecular Spectra and Molecular Structure, Vol. II, D. Van Nostrand Co. Inc., Princeton, New Jersey, 1945. 3. G.W. King, R.M. Hainer and P.C. Cross, J. Chem. Phys., Vol. 11, 27(1943) 4. P.A.M. Dirac, The Principles of Quantum Mechanics, Ed. 4, Claredon Press, Oxford, 1958. 5. W. Gordy and R.L. Cook, Microwave Molecular Spectra, in Technique of Organic Chemistry, Vol LX, Part II, Interscience Publishers, New York, 1970. 6. J.H. Van Vleck, Rev. Mod. Phys., Vol. 23, 213(1951). 7. S.C. Wang, Phys. Rev., Vol. 34, 243(1929). 8. J.K.G. Watson, J. Chem. Phys., Vol. 46, 1935-1949(1967). 9. J.K.G. Watson, in Vibrational Spectra and Structure,(J.R. Durig, Ed.), Vol. 6, Elsevier Sci Pub. Co., New York, 1977. 10. G.Herzberg, Molecular Spectra and Molecular Structure, Vol. I, D. Van Nostrand Co. Inc., Princeton, New Jersey, 1945. 11. J.I. Steinfeld, Molecules and Radiation: An Introduction to Modern Molecular Spectroscopy, The MIT Press, Mass. 1978. 32 / 33 12. P.W. Atkins, Molecular Quantum Mechanics, Ed. 2, Oxford Univ. Press, New York, 1983. 13. E. Fermi, Z Physik, Vol. 71, 250(1931). 14. B.T. Darling and D.M. Dennison, Phys. Rev., Vol. 57, 128(1940). 15. M.R. Aliev and J.K.G. Watson, in Molecular Spectroscopy: Modern Research, Vol IH (K.N. Rao, Ed.), Academic Press, Inc., 2-63(1985). 16. I.M. Mills, Pure Appl. Chem., Vol. 11,325-344(1965). 17. H.A. Jahn, Proc. Royal Society (London), A138,469(1939). 18. J.W.C. Johns, K. Nakagawa and R.H. Schwendeman, J. Mol. Spec, Vol. 122, 462-476(1987). 19. J.M. Hollas,High Resolution Spectroscopy, Butterworths, London, 1982. 20. A.J. Merer, Chem. 519 course Notes, unpublished, Dept. of Chem., UBC, 1986. 21. T.M. Dunn, in Molecular Spectroscopy: Modern Research, (K.N. Rao & C.W. Mathews Ed.), Academic Press, Inc., 231-256(1972). CHAPTER 2. EXPERIMENTAL 2.1. AMINOBORANE Aminoborane, NH 2BH 2, is a molecule with a lifetime on the order of minutes in the gas phase, which makes Fourier transform spectroscopy the method of choice for studying its gas phase infrared spectrum. Gaseous NH 2BH 2 was prepared by thermal decomposition of solid borane-ammonia, NH 3BH 3 (Alpha Products), in a flow system as described by Gerry et al. [1] but with one exception; the NH 3BH 3 was heated to 67 - 68°C for the the first few hours then lowered to 63 - 64 °C while the spectra were recorded. The heating temperature was reduced from 70 °C [1] because it was found that the NH 3BH 3 underwent uncontrolled thermal decomposition at — 71 °C. The only detectable impurities in the NH 2BH 2 spectrum were ammonia and water vapour. A BOMEM model DA3.002 interferometric spectrophotometer was used to record a high resolution (0.004 cm"1) spectrum of the 1500 - 1750 cm - 1 region. The DA3.002 was equipped with a multiple reflection absorption cell with an effective path length of 9.75 m and a liquid nitrogen-cooled HgCdTe detector. 2.2. NIOBIUM NITRIDE Niobium nitride, NbN, was prepared in a flow system and a region of its spectrum recorded using the laser-induced fluorescence technique (LIF). Approximately 2 gm of Niobium(V) chloride, NbCl 5 (Strem Chemicals), was 34 EXPERIMENTAL / 35 heated to about 80 °C in the flow system. The gaseous NbCl 5 was entrained in an Argon/Nitrogen flow (= 900 mTorr Ar, = 50 mTorr N 2) and the resulting mixture was then subjected to a 2450 MHz discharge just prior to being pumped into the fluorescence cell. The effect of the discharge was to destroy the NbCl 5, allowing NbN amongst other products to form. The pinkish-blue tail of the discharge mixture was pumped with a laser beam from a Coherent CR-599-21 tunable dye laser and the fluorescence measured through a long pass optical filter by a photomultiplier. The laser beam was chopped so the modulated flourescence signal could be discerned from the background spectrum by using a lock-in amplifier. Portions of the beam were also passed through a 1.5 GHz interferometer to provide a relative calibration scale and through an Iodine fluorescence cell for absolute calibration. A PDP-11 microcomputer was used to scan the laser and record the three signals (NbN, I 2, interferometer markers) for 1.4 cm" 1 scans. The digitized data were then reconverted to analog form and plotted by a three-pen chart recorder. The apparatus is shown in figure 2. Individual scans were taken so that there was some overlap with neighboring scans, allowing a series of scans to be concatenated and then calibrated. The amount of overlap was measured in interferometer markers and was usually an integral amount unless the laser couldn't be locked on like modes between scans. The relative positions of the NbN and I 2 lines were measured in fractional marker units by plotting the data for an individual scan on the computer graphics terminal and overlapping a vertical cursor on the peaks. The concatenated spectrum was then calibrated by supplying the known t I 2 tThese values must be corrected by —0.0056cm" 1. E X P E R I M E N T A L / 36 Tunable dye loser Figure 2. L I F experimental apparatus, wavenumbers [2] and fitting the c m " 1 / m a r k e r data to a linear equation. Wavelength resolved fluorescence was performed on selected lines to aid the spectral analysis. A diode array detector was used to record the dispersed fluorescence resulting from selectively pumping a known transition in the system. Since the diode array detector is a new addition to Dr . Merer ' s lab a full EXPERIMENTAL / 37 account of how it was interfaced to the experiment is given below. 2.3. THE DIODE ARRAY DETECTOR 2.3.1. Introduction This section describes a diode array detector that was interfaced to the existing laser-induced fluorescence experiment to improve wavelength resolved fluorescence measurements. Apart from interferometers there are two instruments commonly used to aquire spectral information: the monochromator and the spectrograph. In a monochromator a narrow band of diffracted (or dispersed) light is projected through an exit slit onto a single photomultiplier tube (or photodiode dectector). A spectrum is obtained by mechanically rotating the grating (or prism) so that the dispersed spectrum is swept across the exit slit. Traditionally, in the spectrograph, the exit slit and single detector are replaced by a photographic plate in the focal plane and an entire spectrum is recorded simultaneously. A diode array detector (DAD) or optical multichannel array detector is the electronic analog of the photographic plate used in spectrographs. The main advantage of the DAD over the photographic plate is that the spectral information is ready to analyze much more rapidly and intensity information is available in digital form. EXPERIMENTAL / 38 An EG&G model 1421R-1024-G DAD was used to replace the exit slit and detector on a SPEX model 1702 spectrometer. The DAD was interfaced with a DIGITAL PDP-11 minicomputer via an EG&G model 1461 detector interface. 2.3.2. Performance Characteristics The 1421 DAD has 1024 pixels with dimensions 25 (im x 2.5 mm. When the spectrometer was converted to a spectrograph the focal length of the o exit mirrror was increased to give a dispersion of approximately 9 A/mm on the detector face. A spectral window of about 600 cm" 1 at 600 nm in first order may be viewed for a given grating setting. Calibration of the spectral window will be discussed later in the Software section but note that the uncertainty in the resolved fluorescence line measurements has been decreased from 1.00 to 0.05 cm" 1 by converting the spectrometer to a DAD equipped spectrograph. The time the detector is exposed to the source may be varied depending on the signal strength. The detector may be cooled to reduce the dark current noise associated with photodiode detectors. Cooling down to 5 °C is achieved by a Peltier-effect thermoelectric cooler which may be augmented by liquid cooling to reach a temperature of -40 °C. The real time response (0.02 sec scans) of the detector is monitored with an oscilloscope while data curves may be aquired and stored. digitally in single or double precision. More specific performance characteristics of the DAD are given in the Operating and Service Manual [3]. EXPERIMENTAL / 39 2.3.3. Operating Precautions There are two conditions which can seriously damage the DAD: 1) condensation on the detector face and, 2) light overload of individual pixels in the diode array. The detector should not be operated without continual flushing of N 2 (or another inert gas) or else catastrophic failure due to condensation may result. A flowmeter has been put on the N 2 line leading to the purging port of the DAD; the flow rate should be set to 5 ft3/hr before turning the DAD on. It is recommended that the DAD be purged even when its temperature has been set to the maximum of 20 °C. The default temperature at start up is 5 °C so it is imperative to begin purging before turning the DAD on. When operating the DAD at temperatures less than 20 °C the temperature • should be brought to 20 °C before shutting the DAD off then discontinuing purging. There is a session shutdown choice in the main menu of the control program which automatically sets the detector temperature to 20 °C and then waits until the temperature is reached before allowing the user to exit the program. The session shutdown choice should be used whenever turning the detector off. Light overload can cause spot damage to the individual elements of the diode array. Two instances where this is most likely to occur are: 1) calibrating the DAD with a tunable laser source and, 2) over-integrating a signal by setting the exposure time too high. A raw laser beam should never be shone into the spectrograph; use a scattered beam instead. A warning alarm (sounding much EXPERIMENTAL / 40 like a wristwatch alarm) will sound from the DAD if a light overload occurs. The entrance slit to the spectrograph should be blocked immediately if this alarm sounds. 2.3.4. Software 2.3.4.1. Introduction All the software discussed in this section was developed solely by the author. The DAD is controlled via the 1461 interface by a menu driven task (DETECT) from the PDP-11 minicomputer. The PDP communicates with the 1461 via a RS-232 serial line and recognizes the 1461 as physical device TT2 [4]. The controlling program DETECT consists of a number of macros and subroutines plus the main program itself. The macros, written in Macro-11 assembler language [5], handle the relaying of messages and the communication checking between the PDP and 1461. All the macros use common user-defined directives to check for and deal with communication problems. The communication software was written in assembler because it is much more efficient than higher level languages such as Fortran. The main program and subroutines, all written in Fortran-77 [6], perform functions such as: menu set up, data storage, spectral window calibration, etc. There is also a separate program, GRAPH, which is used to display data curves. EXPERIMENTAL / 41 2.3.4.2. Detector Calibration The DAD should be calibrated every time the grating position is changed as a new spectral window is being considered. Parabolic wavelength distribution across the linear array of pixels dictates that the detctor be calibrated to a quadratic equation. This is accomplished by tuning a laser to three points across the spectral window and recording the spectrum of the scattered laser beam for each point. The absolute frequency of the laser is given by a Burleigh model WA-20VIS wavemeter which is good to ± 0.01 cm"1. The fractional channel number of the laser line peak is determined by fitting five points about the peak to a quadratic equation and taking the first derivative. The three laser frequencies and corresponding peak fractional channel numbers are then also fitted to a quadratic equation to calibrate the current spectral window. This process may seem somewhat involved but can be carried out in less than five minutes using the DETECT program which guides the user through the calibration procedure. When calibration is necessary it should be performed before any real data are taken as the system was designed to automatically insert the current calibration constants into the housekeeping record of the real data files. If the user needs to change the calibration constants (for example; if real data was taken before calibration of the current window) in the housekeeping record of a file, the program FLXCAL should be used. When working in a region outside the range of the laser dye the window EXPERIMENTAL / 42 may still be calibrated using a Fe-Ne hollow cathode discharge lamp. An exposure is taken, then the fractional channel numbers of a few select lines are measured using the graphics routine. The absolute wavelengths of the lines [7] and the fractional channel numbers can be used to get the calibration constants using the program LSQMIN. This method allows calibration of the spectral window by a least squares treatment. 2.3.4.3. Graphics Graphics capabilities are a must to analyze the recorded spectra. The graphics routines were written for Digital's VT100 and VT200 graphics terminals using ReGIS (remote graphics instruction set)[8]. A routine in DETECT called QIKPIK is used to check the quality of a spectrum before storing it on the disk. QIKPIK scales the 1024 data points to the screen's 800 pixels and then plots every other point. QIKPIK was designed to instantly show the user what kind of spectrum has been recorded. GRAPH is a separate program that is used to analyze the spectra. Vertical and horizontal expansion, scrolling and, baseline adjusting are all available. Peak positions are found by placing a vertical cursor at the peak maximum. Five data points about the peak are fitted to a quadratic equation and the first derivative is taken to get a fractional channel number position. The wavelength of the peak maximum is then computed using the calibration constants from the housekeeping record of the data file. As mentioned above this method allows an accuracy of 0.05 cm - 1 in the measurement of well defined spectral lines. REFERENCES 1. M.C.L. Gerry, W. Lewis-Bevan, A.J. Merer, and N.P.C. Westwood, J. Mol. Spec, Vol. 110, 153-163(1985). 2. S. Gerstenkorn and P. Luc,Atlas du Spectre dAbsorption de la Molecule diode, CNRS Ed., Paris, France, 1978. 3. Operating and Service Manual, Models 1420 & 1421 Solid State Detectors, EG&G Princeton Applied Research, U.S.A., 1985. 4. RSX-11M Software Manual, Vol. 5, I/O Drivers Development and Reference, Digital Equip. Corp.,order # AA-2600E-TC, U.S.A., 1981. 5. RSX-11M Software Manual, Vol. 4A, PDP-11 Macro-11 Language Reference, Digital Equip. Corp., order # AA-L676A-TC, U.S.A., 1981. 6. PDP-11 Fortran-77, Digital Equip. Corp., order # AA-V193A-TK, U.S.A., 1981. 7. H.M. Crosswhite, J. Res. N.B.S. - App. Phys. and Chem., Vol. 79A, No. 1, Jan.-Feb. 1975. 8. VT240 series Programmer Reference Manual, Digital Equip. Corp., U.S.A., 1984. 43 CHAPTER 3. AMINOBORANE 3.1. BACKGROUND Aminoborane, NH 2BH 2, has been the subject of both theoretical and spectroscopic studies. The B=N bond in NH 2BH 2 is isoelectronic with the C = C bond in ethylene making NH 2BH 2 an inorganic analog of ethylene. Unveiling the molecular characteristics of NH 2BH 2 will provide an interesting contrast to those of ethylene. Spectroscopically NH 2BH 2 is of interest because eleven of its twelve normal vibrations are infrared active and so it provides many examples of the resonance effects discussed in chapter one. Because it is so light, NH 2BH 2 has very large rotational constants thus the resonance effects are magnified. Aminoborane is a planar molecule with 12 vibrational degrees of freedom which transform according to the irreducible representations of the P°* n t group as: T(vib) = 5A, + A 2 + 2B, + 4B2. (3.1) From the C2 V character table (see Appendix n) it is seen that only the A 2 torsion is infrared inactive whilst the A,, B ^, and B 2 fundamentals give rise to A, C, and B-type bands respectively. Theoretical predictions of NH 2BH 2's fundamental frequencies have been made [1] and the infrared spectrum of solid phase NH 2BH 2 has been measured 44 AMINOBORANE / 45 [2]. The only other gas phase spectroscopic analyses of NH 2BH 2 besides the work described below are microwave studies by Sugie et al. [3,4] which have confirmed the planar stucture and thus the C^ v symmetry of the molecule in its ground vibrational state. TABLE 3.1 Vibrational Bands of NH 2 1 1BH 2 Assigned at UBC Symmetry Vibration cm" 1 Fundamental Motion A, 3451 NH symm. stretch 2495 BH symm. stretch v 3 1625 NH 2 symm. bend *U 1337.474 BN stretch 2J>8 1223.567 v$ 1140 BH 2 symm. bend A 2 »6 (821)a Torsion B, " 7 1004.684 BH 2 out of plane wag * B 612.198 NH 2 out of plane wag B 2 * 9 3533.8 NH asymm. stretch I ' l O 2564 BH asymm. stretch 1433 ft 1 1130 NH 2 asymm. bend (rock) " 1 2 742 BH 2 asymm. bend (rock) a - est. from perturbations to c 1 2 . The infrared spectrum of NH 2BH 2 is being systematically analyzed by the high resolution spectroscopy group at the University of British Columbia. The vibrational assignments made prior to this analysis are given in Table 3.1. The assignments of the fundamentals were discussed by Gerry et al. [5] along with the rotational analysis of the v a fundamental. Rotational analyses of other vibrational transitions listed in table 3.1 have been performed and the prominent AMINOBORANE / 46 interactions discovered for each are listed in table 3.2. The objective behind the work described here was to assign and fit the rotational structure in the 1550-1750 cm" 1 region of the NH 2BH 2 spectrum. TABLE 3.2 Other Ro-Vibrational Analyses of N H 2 1 1 B H 2 Bands Vibration Reference Interactions v 2 in progress v 4 [5] Coriolis with V J + V J and/or v 6 + v , 2 2v n in progress3 2 v 8 [6] , Coriolis effects at high K. v 5 in progress Coriolis with v 7 and v , y. v7 in progress0 Coriolis with v5 and t. ve [7] Coriolis with v6 and V\2. v9 tl] "i o [8] . v , ! in progress Coriolis with v 5 and v 7 . a - T. Chandrakumar b - D.M. Steunenberg c - J.A. Barry 3.2. ROTATIONAL ANALYSIS Prior to this analysis it was not known how many vibrational bands would be active in the 1500 - 1700 cm" 1 region, although it was evident that v3 must be present and be the main source of intensity. Inspection of figure 3.1 does not reveal the obvious simple structure one would expect for a lone A M I N O B O R A N E / 47 A-type band; instead one sees a large asymmetrical ly-winged envelope centred at about 1625 c m " 1 which indicates the presence of two or more ' vibrat ional bands. Possible candidates for these interloping vibrational bands were deduced using the assignments available at the time; see table 3.3. A plot of K sub-band 'origins' versus K 2 was made in order to predict which vibrat ional energy levels might be near-degenerate wi th v 3 and hence possibly interact wi th it. The sub-band 'origins' were estimated by setting J = 0 in equation (2.4) and using the ground state rotational constants; see Figure 3.2. This of course was only a rough guide because the v 6 fundamental frequency could only be estimated at that stage, and the combination and overtone bands were calculated by just summing the pertinent fundamental frequencies. Moreover the excited state rotational constants wil l not be equal to the ground state values, especially for the levels which contained vibrations which were Coriolis-perturbed in their fundamental transitions; v e and v 7 . Nonetheless figure Figure 3.1. Low-resolution transmittance spectrum of N H 2 B H 2 (1510-1720cm" 1 ) . AMINOBORANE / 48 TABLE 3.3 Possible Interloper Levels in v 3 System Symmetry Vibration cm" 1A 2 1747 A 2 " 8 + " l 1 1732 A, 2v 6 1642a A, V 7 + UB 1617 B, 1563 A, 2 * 1 2 1484 B 2 1433b a - v6 assumed —821 cm" 1 prior to this analysis, b - observed [5]. 3.2 gave the author an idea of what might be in store during the analysis of this region. The prime candidate for interaction with v 3 was the v7 + v $ combination level because the fundamental frequencies v7 and ue had both been previously determined and the combination frequency, in harmonic approximation, fell close to the centre of the envelope in figure 3.1. Since V y + V j is of the same symmetry species as v3 an anharmonic resonance interaction between them can occur. The position of the 2 v 6 overtone was uncertain since the position of the V 6 could only be estimated from perturbations caused by v 6 in the v y 2 fundamental at 742 cm"1. If 2v6 was to appear in the 1550-1720 cm"1 range it would most likely be the result of an anharmonic resonance with v 3. The remaining possibilities in table 3.3 will interact with v 3 via Coriolis mechanisms except for v, 2 which would interact via an anharmonic resonance. The analysis was begun assuming that at least two A-type vibrational bands (v3 and v7 + vB) were present and were centred about the 1610-1625 cm" 1 region. A M I N O B O R A N E / 49 01 3 3 4 5 6 7 * 9 K plotted as Figure 3.2. Sub-band origins of potential interloper bands near the v3 fundamental. The usual rotational structure of an A-type band of a near-prolate asymmetric top consists of a central O Q branch feature with O R and q P branch clusters spanning out to higher and lower frequencies respectively. If the change in the rotational constants between the combining levels is small , regularly spaced O R and Op branch clusters separated by a a central O Q ' S p ike ' appear as can be seen in the fundamental (figure 3.3, from ref.[5]). If the changes in the rotational constants are larger the regulari ty of the branch structure is modified; A M I N O B O R A N E / 50 E/cnf1 1380 1360 1310 1320 1300 i i 1 1 1 1 ' '———— 1— Figure 3.3. Medium-resolution transmittance spectrum of the A-type v „ fundamental. for example i f the A constant of a near-prolate asymmetric top decreases appreciably in a transition then the K-rotat ional structure wi l l be red-degraded (ie: pushed to lower frequency) by an amount proportional to K 2 . Because the v3 fundamental is the N H 2 symmetric bending motion its upper state A constant was expected to decrease marginal ly . On the other hand the fundamental vibrations in the v 7 + v 8 combination band are both perturbed by Coriolis interactions. The effective A constants of v1 and vB decrease by 2.08% and 3.34%, respectively, relative to the ground state value so that to a first approximation the A constant of v7 + ve should be 5.42% less than the ground state value. The basis function mix ing associated with the anharmonic resonance between i' 7+j' a and v 3 causes an apparent depression of the rotational constants in both of the resulting eigenstates. These depressed A constants cause the rotational structure of v 7 + v 8 and v 3 to be irregular and result in a complete absence of the O R - and Op branch clusters normally A M I N O B O R A N E / 51 associated wi th A-type bands. Even i f the rotational structure of v 7 + v 8 and v 3 was well-behaved the sheer density of lines in the spectrum would have caused the structure to be inconspicuous. Figure 3.4 shows the typical density of lines one encounters at high resolution; for clarity only the branch structure for one K sub-band for each of the four interacting vibrational levels has been labelled. Such a density of lines results in many of the lines being blended and analysis by pattern recognition almost impossible. The problem of blended lines is reduced by deconvoluting the spectrum. Fourier self-deconvolution is a technique which provides a way of computationally resolving blended lines that cannot be ins t rumental^ ' resolved because of their intrinsic linewidths [9]. A spectrum, E(j>), is related to its corresponding 1 1 h—i—4-—i 1 1 1 1 1 1 1—t—J — ^ — i——i—i — I Figure 3.4. High-resolution transmittance spectrum of N H 2 B H 2 ; sub-bands from all four vibrations present. interferogram, I(x), by the Fourier transformation: AMINOBORANE / 52 E(v) = J IW exp(i27r^x)dx = F{I(x)} (3.1) I(x) = / E(p) exp(i27Tvx)dv = F~ 1 { E ( 7 0 } , where F{ } is the Fourier transform (FT), F~ 1{ } is the inverse FT and the integration is from — » to +». An experimental spectrum, E(v), can be expressed as a convolution of a lineshape function, G(v), and a spectrum, E'(v). The interferogram corresponding to E'(v) is just F(x) = I(x)/F- 1 {G(v)}, (3.2) so that the spectrum is obtained by taking the FT of I'(x). Since the Doppler effect is the dominant cause of line broadening in gas phase FTIR work, a Gaussian response factor is supplied for G(p). The usual procedure for analyzing rotational band structure involves picking out branches, which are then assigned by combination differences: the spectroscopist relies on his/her experience and intuition to recognize typical rotational branch patterns and then uses combination differences to check the assignment of the lines. Rotational combination differences (written ^ F " , A 2F", A^' or A2F') are the differences between the rotational energy levels of a vibronic state; the subscripts 1 and 2 refer to the difference in J between the two levels being considered and F" and F' refer to the lower and upper vibronic AMINOBORANE / 53 states, respectively. If the rotational energy levels of one of the vibronic states involved in a transition are known then assignment of the branch structure can be checked using the combination differences of the known vibronic state. When there is considerable overlap of the rotational fine structure of various bands, the process of pattern recognition becomes more difficult and assignment of the branches themselves a real challenge. For simple spectra, such as 1 Z - 1 Z electronic transitions in a diatomic molecule, Loomis-Wood diagrams can be very useful for sorting out overlapped rotational structure [11]. A series of lines assumed to be a branch is selected and the first and second differences for that branch are calculated and used to calculate the rest of the observed branch by extrapolation. A set of differences with neighboring lines is calculated for each line of the extrapolated branch and the results are plotted as a function of the arbitrary line numbering of the original branch. The differences corresponding to branches of the same band should reveal themselves as smoothly varying curves or straight lines. This method is clearly impractical for sorting out the rotational structure of a set of interacting vibrational bands of an asymmetric rotor because of the sheer number of overlapping sub-bands that must be dealt with in the spectrum. It was decided that the most painless way to attack the 1550-1720 cm" 1region of the NH 2BH 2 spectrum was to write a computer program that used sets of A^F" and A 2F" combination differences to verify and assign any regular branch structure that could be picked out from the spectrum. Ground state combination differences were used because the ground state of NH 2BH 2 is AMINOBORANE / 54 unperturbed and its rotational constants have been well determined [7]. The program is used as follows: 1. the user supplies a set of lines that are thought to belong to the same rotational sub-band. 2. depending on whether the supplied branch is believed to be a R, P or Q branch, the user selects regions of the spectrum to search for the accompanying branches of the sub-band. 3. AyF" and A 2F" combination differences of selected sub-bands are then added to every line in the supplied branch and if both AiF" and A 2F" matches are made the frequencies of the three lines involved in the match and their quantum numbers are stored. Since the Q branch structure for the lower K sub-bands is expected to be very a weak (non-existent for K a = 0 by the selection rules) the option to check P or R branch assignments by just A 2F" combination differences is available. When the Q branch structure is well-developed (K > 4) it was found that portions of the P, Q, and R branches of a sub-band could be extracted from the data set by merely supplying the program with the spectral regions where the lines were thought to be. The number of spurious matches made when checking for both AiF" and A 2F" differences was sufficiently small that the correct rotational assignments could be easily picked out from the list of matches. When using only A 2F" differences, however, the number of accidental matches becomes overwhelming because there are over 5000 lines in this region of the spectrum. A number of features were added to the program to cut down on the number of spurious matches : 1. an intensity threshold may be set; this proved very helpful in the early AMINOBORANE / 55 stages of the analysis when the strongest sub-bands were being assigned. 2. the user may direct the program to search only where the expected frequencies of the individual R or P lines are thought to be. 3. securely assigned lines may be suppressed temporarily from the data set. Portions of the branch structure of the most intense sub-bands could be picked out of the spectrum without too much difficulty. The most intense sub-bands have K =0, 2, and 4 (ie: low even values of K_, as expected from the Boltzmann factor and the nuclear spin statistics). NH 2BH 2 has two pairs of identical H atoms and therefore has sixteen proton spin wave functions; ten of these are symmetric and six are antisymmetric with respect to nuclear exchange. The rotational wavefunction is symmetric with respect to a C 2 rotation for even K_ and antisymmetric for odd K_ [10] so that the expected intensity alternation a a is Keven K ) : I(odd K ) = 5:3. a a. As the analysis progressed it was convenient to replot portions of the spectrum with the assigned lines digitally erased. This technique made the process of pattern recognition for the unassigned lines much easier. The isotopic abundance ratio of 1 1B: 1 0B is 4:1. When obvious branch structure could not be assigned using the 1 1B combination differences an attempt was made using 1 0 B combination differences which had been determined by J. Barry in our laboratory [12]. Three sub-bands of v3 were assigned for the 1 0 B species, with K_ =0,1,2. A M I N O B O R A N E / 56 - i 1 1 1 1 1 1 1 n — i 1 1 1 1 1 1 50.00 150.00 250.00 350.00 45a 00 550.00 950. OC 750.00 J*CJ+1> Figure 3.5 Upper State Rotational Energies of the Levels v 3,v 7 + v 8 , 2v 6 and vs + v^ 2 of N H 2 B H 2 . Sub-bands from four separate vibrations were discovered in this analysis and the line assignments and intensities for each of the four vibrations are given in Appendix I. The logic leading to the vibrational assignments w i l l be given in the next section but for now it w i l l be stated that the levels v 3 , v 7 + v B and AMINOBORANE / 57 2 f 6 form an anharmonic resonance triad and that there is an x-axis Coriolis interaction between v 6 + v, 2 and a member of the triad. The rotational energies of the four excited vibrational states were calculated using the known ground state constants to predict the ground state rotational levels and then adding the appropriate transition frequencies to map the upper state levels. A plot of the upper state energy levels as a function of J(J+1) is given in figure 3.5; the energies have been scaled by subtracting 0.7[J(J + 1)] cm"1. Each curve in figure 3.5 represents the course of the rotational levels within a K a sub-band of a vibrational eigenstate. This type of plot is very useful because it quickly shows the mutual effects that interacting levels have on one another. The ground state energies shown in figure 3.6 provide an example of how the rotational energies should behave in the absence of any perturbations. The sub-band structure of three of the four vibrations (J>3, i>7 + c 8, and 2ve) could be assigned almost completely except for the v3 K=3 and v7 + v& K = 5 sub-bands, which are predicted to be nearly degenerate and to interact very strongly with each other. The number of rotational assignments made for each vibrational band gives an indication of its strength; the levels plotted in figure 3.5 are calculated from observed lines in the spectrum. It may seem inconsistent that the vibration labelled v7 + v6 in figure 3.5 has the most levels associated with it since v3 should give the strongest band in this region of the spectrum; this point will be addressed in the next section. Only one sub-band of the fourth interacting level (Vj + ^ i 2) n a s been identified so far; this has K=7. It is clearly obtaining its intensity by a rotation-dependent mechanism via an interaction with the K=6 sub-band of v7 + vB; the two sub-bands bow away A M I N O B O R A N E / 58 J* (J+D Figure 3.6 Ground State Rotational Energy Levels of N H 2 B H 2 . from each other (figure 3.5). A s can be seen from figure 3.5, there is considerable overlap between the energy levels of the four interacting vibrations. Localized peturbations (avoided AMINOBORANE / 59 crossings) will occur when levels that are allowed by symmetry to interact become near-degenerate. For the three vibrations in the triad these perturbations occur between levels of the same rotational symmetry, while the x-axis Coriolis selection rule allows rotational levels whose direct product transforms as the B, species (see C 2 v character table, Appendix II) to interact. The overall symmetry species of the levels are given by the product of the symmetry species of the asymmetric rotor eigenfunctions (see table 1.1) and the symmetry of the vibration. For instance the overall symmetry species of the ^ j ^ a j ^ = ^ 3 6 rotational level is a 2 in an A ^  vibration but will be b 2 in a B ^  vibration. Overall symmetry species are important in vibration-rotation interactions because group theory requires that the direct product of the levels and the interaction operator be totally symmetric in order for an interaction to occur. Localized perturbations are indicated by the squares in figure 3.5. 3.3. VIBRATIONAL ASSIGNMENTS: THE SYSTEM MODEL The localized perturbations between the three vibrational bands with observed origins at 1609, 1625 and 1663 cm" 1 occur between levels of the same symmetry species, which indicates a three level anharmonic resonance interaction. This discovery was not unexpected since three vibrations (p 3, PT + VB and 2v 6) were predicted to appear in this region of the spectrum. The 1663 cm" 1 band was assigned as 2v 6 but the assignment of the two lower vibrational bands was not so straightforward. Since t>3 is a fundamental vibration it should give the more intense band of the two. The intensities of the 1609 and 1625 cm" 1 bands appear to be comparable in figure 3.1. This A M I N O B O R A N E / 60 indicates that the unperturbed v 3 and v 7 + v 8 levels must be almost degenerate since the intensity of the strong v 3 fundamental has been shared wi th the weak v 7 + v 8 combination. If two vibrational levels are intimately mixed, tracing the origin or parentage of the observed eigenstates becomes challenging; this predicament is considered below. When examining the interaction of two vibrational levels it is helpful to picture the course of their rotational levels by the sub-band origins, as was shown in figure 3.2. The scenario in figure 3.2 has the rotational levels of the unperturbed v 3 and p 7 + y 8 vibrations separated by a constant amount ( 8 c m " 1 ) , r i — i 1 1 1 r K plotted as K* Figure 3.7 Scaled Upper State Sub-band Origins of the 1609 and 1625 c m " 1 bands. AMINOBORANE / 61 so that when the anharmonic interaction is 'turned on' there will be a constant degree of basis function mixing throughout the rotational structure. The spectrum resulting from this scenario would have two vibrational bands apparently repelled from their unperturbed positions with one of the bands consistently more intense, by the same factor, than the other. Since v3 is shown above v7 + vB in figure 3.2 the band observed at the higher frequency would be the more intense of the two. As explained in the previous section, however, the rotational constants of v 3 and v 7 + v 8 are not expected to be the same so the degree of mixing between the two will vary with J and K. A variable degree of mixing will cause the following in the observed spectrum: 1. a non-linear dependence of the apparent sub-band origins on K 2. 2. the intensity ratio of like rotational transitions from each band to vary with J and K. Both of these phenomena were seen in the 1609 and 1625 cm" 1 bands of the NH 2BH 2 spectrum. The sub-band origins of the 1609 and 1625 cm" 1 bands were extrapolated from a plot similar to figure 3.5 and then scaled by subtracting [A-(B + C)/2]K2 where the ground state constants were used for A, B and C. The scaled observed sub-band origins were plotted as a function of K 2 (figure 3.7); the K=6 sub-band of the 1625 cm" 1 band is badly perturbed by a Coriolis interaction and is not shown since the estimate of its origin by extrapolation is unreliable. The sub-band origins of both eigenstates clearly show a non-linear dependence on K 2. Both curves in figure 3.7 slope downward because the effective coefficients of K 2 are both less than that for the ground state. The intensity ratios between like P and R transitions for the K=0-4 sub-bands of the 1609 and 1625 cm" 1 bands are shown in figure 3.8. The AMINOBORANE / 62 1609 cm" 1 band is the more intense of the two until midway through the K=2 sub-band after which the intensity ratio reverses. The low J ratios of the K=4 sub-bands are greater than one but this inconsistency may be explained by a perturbation to the v3 K=4 sub-band which, as will be discussed later, was found to be present. Since the v 3 band carries essentially all of the oscillator strength, and the intensity of the eigenstates indicates how much v 3 character is in each, then the course of the unperturbed rotational levels of the f 3 and v-j + vB vibrations must cross (see figure 1.1). It is customary to give the parentage of an eigenstate according to which basis state donates the most character to it, or in other words, gives the largest coefficient in the eigenvector that results on diagonalizing the Hamiltonian matrix for the interaction. When two interacting basis states cross the apparent parentage of the resulting eigenstates will reverse at the crossing. For the sake of consistency the 1609 and 1625 cm" 1 bands were assigned according to their parentage for zero rotation, as v 3 and v 7 + v e respectively. As was noted above the lone sub-band of the fourth vibration is induced by a rotation-dependent mechanism. Inspection of figure 3.5 reveals that the K=7 sub-band of the v 6 + p , 2 vibration is predicted to be nearly degenerate with the K=6 sub-band of the v3 vibration. The v3 K=6 level is allowed by symmetry to interact with the V 6 + J> 1 2 K=7 level via an x-axis Coriolis mechanism which is rotation dependent (see equation 1.37). The information in the spectrum indicates a four level interaction scheme P branch K AMINOBORANE R branch / 63 1 R -i n - ' rv • 1 ^ . ' ° 1 S J a'1 ° i B \ 5l\ 4 s -I • upper asymmetry component, » lower asymmetry component. Figure 3.8 Intensity Ratios for the 1609 and 1625 cm" 1 bands. AMINOBORANE / 64 between v 3 , v 7 + v 8 , 2v 6 and i> 6 + v y 2 . This model is represented in matr ix form in figure 3.9. The diagonal blocks contain the unperturbed rotational energies of the four levels while the off diagonal blocks contain the interaction terms. The ultimate object of this work is to calculate the rotational constants of the four basis vibrations and to calculate the interaction parameters between them such that when the matr ix shown in figure 3.9 is diagonalized the resulting eigenvalues match the observed spectrum within experimental uncertainty. 3.4. LEAST SQUARES TREATMENT Leas t squares fitting is a technique used in data reduction to refine the parameters of a model such that its calculated values match the observed values. The goodness of the fit can be measured by the sum of the squares of the residuals (observed minus calculated values); the lower the sum the better the fit hence the name least squares. A spectroscopic fit is considered acceptable when |f 3> \vj + v t > |2 v 6 > \VS + V y i > T 3 W 3 7 B W 3 6 6 X 3 6 1 2 ' W 3 7 8 T 7 8 W 7 8 6 6 ^ 7 6 6 1 2 W 3 6 6 W 7 8 6 6 T 6 6 X 6 6 6 1 2 - ^ 3 6 1 2 X 7 s 6 1 2 X 6 6 6 1 2 T 6 , 2 Figure 3.9 M a t r i x Representation of the Four Leve l Interaction. AMINOBORANE / 65 the residuals are comparable with the experimental uncertainty of the observed data. In order to achieve an acceptable fit one must have a model that approximates the real situation. This means that the functional dependence of the model must mimic the real system and that approximate values of the constants of the model must be known. The first point is obvious, the second is necessary to avoid a false convergence. A full description of fitting spectroscopic data by least squares techniques will not be given here; the reader is referred to references [13,14] for a full description. In order to approximate the energy levels of the unperturbed vibrations, suitable guesses at their rotational constants and band centres must be made. A reasonable first guess at the rotational constants (A,B,C) would be the ground state values since none of the other upper states characterized to date [5,6,7] has effective rotational constants differing by more than 5% from the ground state values. The first guess constants for the Vj + vB state were refined by summing the differences of the known v 7 and v e constants from the ground state values, and then subtracting the sums from the ground state values. The centrifugal distortion constants should be the same as the ground state values, again except for v 7 + v 8, since there is no change in electronic state. The v s + v \ 2 band centre was approximated to be 1577 cm"1 using its extrapolated K=7 sub-band origin and the ground state rotational constants. The relative band centres of the unperturbed levels involved in the anharmonic triad cannot be estimated without considering the anharmonic interaction terms because these quantities are completely correlated. If the anharmonic constants can be reasonably approximated, however, they may be held constant in the fit and a A M I N O B O R A N E / 66 set of effective band centres can be calculated. The first order anharmonic terms may be approximated by using the intensity information in the spectrum. The intensity of a transition depends on the square of its transition moment. In a three level interaction the resulting eigenfunctions will be linear combinations of the interacting basis functions: ¥eig = S T "Pbasis, (3.3) where S T is the 3 X 3 matrix of transposed eigenvectors. If the basis functions of the three levels are denoted by |l>, |2> and |3> and the ground vibrational level denoted by | X > then the transition moments corresponding to ground to eigenstate transitions are given by: R A = S,,<l|u |X> + S 2 1 < 2 | M | X > + S 3 1 < 3 | M | X > , R F A = S 1 2 < 1 | M | X > + S 2 2 <2|/u |X> + S 3 2 < 3 | M | X > , (3.4) R C = S 1 3 < 1 | M | X > + S 2 3 < 2 | M | X > + S 3 3 < 3|/i | X > , where a, b, and c represent the three eigenstates. If only one of the unperturbed vibrations, say |l>, has any oscillator strength then the intensity ratios of like transitions from each of the three observed bands can be directly related to the ratios of the coefficients of the intensity-carrying vibration in each of the three eigenvectors: I(a)/I(b) = ( S ^ / S ^ ) 2 , I(a)/I(c) =. ( S N / S „ ) ! . (3.5) AMINOBORANE / 67 As explained earlier *>3 should carry almost all the oscillator strength in the system so it is not unreasonable to assume, as a first approximation, that the intensity contribution of the other two vibrations in the triad is negligible compared to that of v2- Using relationship (3.5) then, the approximate first order anharmonic values can be estimated. Unfortunately for a case like this where intensity information is so important for sorting the system out, the intensity information is the most unreliable because so many of the lines are blended. Deconvolution of the spectrum helps but cannot give the true spectrum. The scatter of the points in figure 3.8 gives an indication of the uncertainty in the intensity information. The general trend in the intensities is still of use however if the intensities and observed energies are fitted by a least squares approach. The resulting anharmonic constants will reflect the uncertainty in the intensities but at least they provide reasonable approximations with which to begin a full fit of the system. The set of equations to be fitted may be represented by a block matrix of rotational and intensity data, where each block corresponds to a vibrational basis state. The unknowns are the unperturbed upper state rovibrational term values and the first order anharmonic terms, the known quantities are the observed upper state rovibrational term values and the intensity ratios of the corresponding spectral lines. For various reasons it is only legitimate to compare intensities from identical rotational transitions so that the full matrix has non-zero blocks only on the diagonal. Three separate transitions may define the A M I N O B O R A N E / 68 upper state energy (P,Q,R) so that either the intensity ratios of each may be averaged or three separate, equations may be set up. Each diagonal block has six unknown parameters (E , E ^ , E c , ( S , | / S ] 2 ) 2 , and ( S ^ / S ^ ) 2 ) and five observables ( T , , T 2 , T 3 , W 1 2 , W 1 3 and W 2 3 ) associated wi th it. The three unknown anharmonic terms are common to each block, however, so that for a set of N blocks there are 5 N knowns and 3 N + 3 unknowns. Since the matr ix is block diagonal the symmetric individual blocks may diagonalized separately: T , W 1 2 W 1 3 w 1 2 W 2 3 W 1 3 w 2 3 T , E . 0 0 Ei 0 0 b £ J (3.6) Thus the unknown parameters may be refined by iteratively diagonalizing the N blocks of unknowns and comparing the eigenvalues and ratios of appropriate eigenvector elements wi th the corresponding observed energies and intensities. The corrections to the unknown parameters (p^) are calculated by: - n - i A = D N , (3.7) where A is the 3 N + 3 vector of p^ ' s , N is the 5 N vector of observables and D is the 5 N X ( 3 N + 3) matr ix of part ia l derivatives of the observables with respect to the unknowns. In this case the part ia l derivatives must be calculated by numerical differentiation rather than the Hel lman-Feynman theorem because we are fitting intensity ratios as well as energies. A subroutine was wri t ten by the author to supply this problem to the general least squares program L S Q writ ten by A . J . Mere r . AMINOBORANE / 69 Like the rotational lines, the intensity ratios and the upper state energies corresponding to the transitions from each of the three vibrational bands were collected in groups of threes. From preliminary two X two calculations the v3 -v 7 + v B and v 3 - 2 v 6 interaction terms (ie: W 3 7 8 and W 3 6 6) were approximated to be 8 and 15 cm" 1 respectively. It was found that only two of the three anharmonic constants could be determined uniquely. It was decided to fix the fourth rank anharmonic constant linking v7 + vB and 2v6, (W7 8 6 6), at zero because fourth rank anharmonic constants should be at least an order of magnitude smaller than the third rank constants [15]. Using the preliminary values of W 3 7 8 and W 3 6 6 a set of deperturbed energies was calculated for each of the levels in the triad. These approximate deperturbed energies were supplied as the diagonal elements of the N blocks to be diagonalized. To avoid spurious intensity values, lines which had neighboring lines with intensities greater than 10% of the line in question within a typical linewidth (0.01 cm" 1) were omitted from the data set. Only 19 out of a possible 75 sets of three lines met this criteria, which gives an indication of the density of the spectrum. The first order anharmonic constants were determined to be: W 3 7 8 = 8.410.1cm"1 and W 3 6 6 = 15.8±0.4cm" 1. y The £ 7 8 6 12 constant was estimated by a two X two treatment to be — 0.468 cm"1. The position of the Vy + Ve K=6 sub-band origin was extrapolated from its lower sub-band origins while the v6 + v^2 K=7 sub-band origin was extrapolated from its own J structure. The deperturbed J = 20 energy of each of the sub-bands was calculated using the ground state rotational constants. It AMINOBORANE / 70 should be stressed that this effective Coriolis constant is a measure of the coupling between the v 6 + v ^ 2 combination level and the v 7 + v B 'eigenstate' which is itself a mixture of the three levels of the anharmonic triad. Thus the observed Coriolis effect cannot be traced to the individual basis vibrations since only one example of the interaction was found in the spectrum. A four level algorithm written by W. Lewis-Bevant was used in attempts to fit these data. A first attempt was made to fit the energies of the observed triad to a three level model. The K = 6 sub-band of the f 7 + f 8 band was omitted from the data set from the start because of its Coriolis interaction with v 6 + v i 2 • The rotational constants A, B and C plus the band centres of each of the three triad members were allowed to float in the fit. The centrifugal distortion constants were not allowed to float in the fit because they are strongly dependent on the differences in the rotational constants of the interacting levels. This observation was first made by H. Jones et al. in their study of the v^!2v2 Fermi diad of OF2[16]. Jones revealed that this phenomenon arises when there is a varying degree of mixing between two interacting levels. In the symmetric prolate limit the separation between like rotational levels of the two interacting vibrational levels is: 6 = A P 0 + AB J(J+1) + (AA-AB)K2. (3.8) If W is assumed to be much larger than 6, equation (1.23) may be expanded to give: t present address: Dept. of Chemistry, University of Southern Illinois, Carbondale 111. AMINOBORANE / 71 E* = E ± W[l + i(8/2W)2], (3.9) which upon substitution of (3.8) yields: E 1 = E ± (T,+T 2+T 3), (3.10) where: T, = W [l + i(A .* 0 /2W) 2 ] f T 2 = (Av0/4W) [AB J(J+ 1 ) + (AA-AB)K 2], T 3 = (1/8W)[AB2 J 2 ( J + 1 ) 2 + 2AB J(J+ 1)(AA-AB)K 2 + (AA—AB)2K']. T 3 contributes directly to the rotational energies and so represents an additional term in the Hamiltonian introduced by a varying degree of mixing. T 3 has terms with the same rotational dependence as the quartic distortion constants Dj, DJJ^, and Dj^ which .may be related [ 1 7 ] to the corresponding terms in Watson's A-reduced Hamiltonian (equation 2.9). In the triad examined here, two of the levels (v7 + vB and v 3) are near-degenerate and are predicted to have very different rotational constants so that contributions from a term similar to T 3 should be significant. The third member of the triad (2 v 6) has 5 > W 3 6 6 so that the effect of a varying degree of mixing should be negligible compared to the pure vibrational contribution (T,). Since the centrifugal constants should remain constant within the same electronic state it would be appropriate to fix them at the ground state values. This is reasonable for the v 3 level but anomalous values are predicted for the v 7 + v 8 level due to Coriolis effects in the fundamentals involved in the combination band. The fit was restricted to values of J s l 5 to minimize the effect of the approximated centrifugal distortion constants. AMINOBORANE / 72 The best fit achieved on the three level system had a standard deviation of 0.02 cm"1, ie: an order of magnitude greater than the resolution of the experiment. As will be shown later, even this unsatisfactory fit could only be achieved by omitting a substantial number of energies from the data set. An unsatisfactory fit indicates that the model is incapable of accounting for the observed energies. At this point one asks: is the starting point for the model wrong or is it the structure of the model which is inadequate? The intensity information confirms the present assignment of the vibrational bands; the v 3 basis vibration must carry the majority of the intensity. The two necessary assumptions made to calculate W 3 7 8 and W 3 6 6 were not unreasonable and without them there is no possible way of tackling this completely correlated problem apart from a trial and error approach. Thus given the available information in the spectrum the current interpretation of the triad is the most logical choice. The structure of the model must be scrutinized; unseen vibrational levels might be perturbing the members of the triad. A series of least squares fits was made, each time reducing the data set. Examination of the residuals revealed systematic deviations for selected sub-bands in the spectrum. The residuals for the vibrations involved in the triad are shown in Appendix i n along with the uncertainties of the three selected fits. The reader will find that the trends in the residuals of particular sub-bands discussed below exemplify the irregular behaviour of the corresponding sub-bands shown in figure 3.5. The first fit revealed an obvious perturbation to the K=4 sub-band of the v3 vibration; it is being depressed by an interaction with an unseen level. This sub-band does not fit into the model and was removed from the data set. AMINOBORANE / 73 The residuals of the second fit showed several clear examples of data which were not explainable by the model: 1. v3 band. a. K=0 -depressed after J = 7. b. K = l - U -markedly depressed in comparison to 1^ . c. K=6 -effect of an avoided crossing at J = 8,9. 2. v7 + vB band. a. K = l u -markedly depressed after J =10. b. K = l ^ -effect of an avoided crossing at J = 8. c. K=5 -slope indicative of an improper fit. 3. 2v6 band. a. K=4 -sudden depression at J =13. b. K = 6 -structure pushed up with J. The roots of these effects must be other interloper levels (see figure 3.2) which have not yet been considered in the model. The first suspects would be the other unseen sub-bands of the v s + v ^ 2 band. The energy levels of the v 6 + c 1 2 band were predicted roughly, using the ground state rotational constants, and the results added to a figure similar to figure 3.5. The K=3 and 4 sub-bands of v6 + v\2 were found to be nearly degenerate with the K=0 sub-band of v 3 and the K = l sub-band of v 7 + v 6 ) respectively, which may explain the effects noted above since a AK = 3 interaction is allowed by symmetry between A, and B, vibrations. None of the other anomalies mentioned above may be accounted for by interactions with v6+V\2 s o that the 2t> 1 2(A 1), v6 + vB(B2), vB + v, ^ (A 2), and v7 + v i 2{A2) levels shown in figure 3.2 were then considered. Since none of these transitions has been rotationally analyzed their upper state rotational AMINOBORANE / 74 energies and hence possible interactions with v3 and Vy + ve can only be estimated. The possible interactions are listed below: 1. K=0 of or v 7 + v s with K—6 of 2 v 1 2 (anharmonic) or K — 7 of v 6 + v 8 (y-axis Coriolis). 2. K=6 of p 3 or f7 + with K=9 of v 6 +1> 8 (y-axis Coriolis). 3. K=6 of 2ve with K=4 of p 7 + v , 2(z-axis Coriolis). 4. K = 5 of 2^6 with K = 0 of v 7 + p! 2 (z-axis Coriolis). It is almost certain that some of the above interactions must be responsible for the anomalies found in the residuals. At present there is no way to cope with these interactions because the perturbing levels have not been seen in the spectrum. If, however, the perturbations extraneous to the four level model are removed, a fit of the remaining rotational structure is still feasible. A fit to the K<3 sub-bands of the three members of the triad, less the perturbed sub-bands in this group, was then performed. The rotational constants (A,B,C) and the band centres of the three levels plus the second order anharmonic terms linking v 3 and v 7 + v 8 and v 3 and 2 v 6, were allowed to float. The data set gives the residuals shown in Appendix HI. The standard deviation of this best fit was ±0.02cm~1, which is still an order of magnitude greater than the resolution of the experiment. Systematic trends in the high J values of the residuals increase with K (this is readily apparent in the residuals of fit B) indicating an improper fit to the model. AMINOBORANE / 75 3.5. DISCUSSION The pure vibrational energies of the three members of the triad are completely correlated with the anharmonic constants so that there is an infinite set of solutions to the pure vibrational problem. It is the rotational structure of the system then, that must guide the fit to the true solution. This has not been possible so far. One factor may be that because so much of the rotational structure had to be omitted from the data set that there was not enough information left to drive the fit to the real solution. The more likely reason is that the approximate anharmonic constants are still not close enough to the true values. The anharmonic constants reported here are the best that can be gleaned from the information in the spectrum. One route remains, however, to attain the anharmonic constants. The surface of the model with respect to the three first order constants may be mapped and the best combination of anharmonic terms would reveal itself as the best fit in the mapping procedure. This brute force method would require an unreasonably large amount of CPU time. This study has revealed an impressively complex series of interactions between molecular motions at surprisingly low total energy; what was thought to be a straightforward four level interaction scheme turned out to be considerably more involved. Assigning the rotational structure by the new search/match algorithm developed in this work proved to be an indispensible tool for tackling dense and perturbed spectra. Finally least squares fitting of the intensity information, while not ultimately successful, gave results that brought the analysis to within an order of magnitude of acceptability. REFERENCES 1. M.J.S. Dewar and M.L. McKee, J. Mol. Struct., Vol. 68, 105-118(1980). 2. C.T. Kwon and H.A. McGee, Inorg. Chem., Vol. 9, 2458-2461(1970). 3. M. Sugie, H. Takeo, and C. Matsumura, Chem. Phys. Lett., Vol. 64, 573-575(1975). 4. M. Sugie, H. Takeo, and C. Matsumura, J. Mol. Spec, Vol. 123, 286-292(1987). 5. M.C.L. Gerry, W. Lewis-Bevan, A.J. Merer, and N.P.C. Westwood, J. Mol. Spec, Vol. 110, 153-163(1985). 6. D. Anderson, Studies in High Resolution Spectroscopy, Phd. Thesis, University of British Columbia, Vancouver, 1986. 7. D. Steunenberg, The Infrared Spectrum of Gaseous Aminoborane; Rotational Structure of the _8^ Band, BSc. Thesis, University of British Columbia, Vancouver, 1986. 8. D. T. Cramb, The Infrared Spectrum of Gaseous Aminoborane; Rotational Structure of the 10o Band, BSc. Thesis, University of British Columbia, Vancouver, 1985. 9. W.E. Blass and G.W. Halsey,Deconvolution of Absorption Spectra , Academic Press, New York, 1981. 10. G. Herzberg.Molecular Spectra and Molecular Structure, Vol. n, D. Van Nostrand Co., Inc., Princeton, New Jersey, 1945. 76 / 77 11. G. Herzberg,MoIecular Spectra and Molecular Structure, Vol. I, D. Van Nostrand Co., Inc., Princeton, New Jersey, 1945. 12. J.A. Barry, Ph.D. Thesis, University of British Columbia, Vancouver, in press. 13. D.L. Albritton, A.L. Schmeltekopf and R.N. Zare, in Molecular Spectroscopy: Modern Research, Vol. II, (K.N. Rao, Ed.), Academic Press, Inc., 1-65(1976). 14. S. Castellano and A.A. Bothner-By, J. Chem. Phys., Vol. 41, 3863-3865(1964). 15. M.R. Aliev and J.K.G. Watson, in Molecular Spectroscopy: Modern Research, Vol. Ill, (K.N. Rao, Ed.), Academic Press, Inc., 2-63(1985). 16. G. Taubmann, H. Jones, H.D. Rudolph and M. Takami, J. Mol. Spect., Vol. 120, 90-100(1986). 17. J.K.G. Watson, in Vibrational Spectra and Structure, (J.R. Durig, Ed.), Vol. 6, Elsevier Sci. Pub. Co., New York, 1977. CHAPTER 4. NIOBIUM NITRIDE 4.1. BACKGROUND A brief discussion on the expected low lying electronic states of NbN is given followed by a summary of the optical spectroscopy performed on this molecule to date. A qualitative molecular orbital type model, where the molecular orbitals are constructed from allowed combinations of atomic orbitals, will be assumed for discussing the electronic configuration of NbN. The ground state electronic configurations of Nb and N are KLM4s 2 4p 6 4d" 5s1 and K2s 22p 3 respectively. Neglecting the filled sub-shells there are three atomic orbitals left with which to construct the molecular orbitals of NbN. Figure 4.1 shows the energy levels of the degenerate atomic sub-shells, the electrostatically split levels of each sub-shell and the molecular orbitals. The symbols (a, ff, 6) refer to the magnitude (0,1,2) of the projection of the angular momentum of the individual electrons on the space fixed Z-axis in the atoms and the internuclear axis in the molecule. Note that the 2po atomic orbital is shown to be combined with the 4do rather than the 5sa which is more energetically favourable. This is because there is greater overlap achieved by combining the localized lobes of the 4d 2 a n d 2p orbitals z z than by combining the large, diffuse, spherical 5s with 2p . Using the buiding-up z principle the eight valence electrons from the open atomic shells are loaded into the molecular orbitals. The first six electrons fill the lowest o and it levels and so the ground state of NbN will be determined by the configuration of the 78 N I O B I U M N I T R I D E / 79 remaining two electrons. The separation of the 5s a and 4d6 energy levels compared to the electron repulsion energy gained by containing both electrons in the 5sa orbital wi l l determine whether the ground state configuration is 5 s a 2 or 4d55sa . A 5 s a 2 configuration would yield a 1 Z + ground electronic state while a 4d55sa configuration would yield ' A and 3 A electronic states. The 4dS orbital is less than half-filled so the 3 A multiplet structure is expected to be regular [6] and i f Hund ' s multiplicity rule is extended to a molecular system the ground electronic state of a 4 d 6 5 s a configuration should be 3 A 1 . The possible low ly ing electronic states are summarized in table 4.1. The optical spectrum of niobium nitride, N b N , was first examined by Dunn and Rao in 1969 [1]. Large hyperfine splitting was observed in the low J R lines of the 3 $ „ - 3 A 3 and 3 $ 2 ~ 3 A i sub-bands of the 3<I>-3A (0-0) band while none was observed in the 3 $ 3 - 3 A 2 sub-band. The dominant source of the split t ing is the Fe rmi contact interaction of an electron in the 3 A state with the Figure 4.1. Molecular Orbitals of N b N . NIOBIUM NITRIDE / 80 TABLE 4.1 Expected Low-Lying Electronic States of NbN Electronic Configuration Electronic States3 5so 2 1 Z + SsaUdS 1 5soUdir* 5sa 14da 1 1 z + , 3 z + 4dS 2 1 Z + , 3 Z ' , T 4d7T14d61 1n, 3 n r , 1#, 3# r 4do 14d6 1 1A, 3 A r a - subcript r refers to regular (opposed to inverted) multiplet structure. magnetic moment of the Nb nucleus, that is the 3 A state must be derived partly from a Nb 5s electron in order to account for an appreciable electron density at the nucleus. The degree of splitting was discovered to be inversely proportional to J 2 so it was deduced the 3A state was an example of case(a^) coupling. The NbN spectrum was "revisited" by Dunn et al. in 1975 [2] to study the origins of the secondary hyperfme effects in the 3 3 A system. It was revealed that there was a nonnegligible interaction of the Nb nuclear spin with the electron orbital angular momentum in the 3 $ state. In her Ph.D. thesis, Ranieri reported a rotational analysis of eight bands in the visible optical emission spectrum of NbN [3]. Two of those bands, 17057 and 17131 cm"1, are also considered in this thesis. The electronic states involved in both of these transitions were incorrectly assigned. A vibrational analysis of the 3 #-3 A system was reported by Pazyuk et NIOBIUM NITRIDE / 81 al. [4] in 1986. The results in reference [4] are rife with errors, most notably the suggestions that the spin orbit splitting of both multiplets is inverted and assignment of the bands at 17057 and 17415 cm" 1 as a spin-orbit satellites of the 3 $ - 3 A system. Those results inconsistent with the work considered in this thesis will be addressed in the discussion. Most recently Femenias has performed a full rotational analysis of the (0-0) band of the 3 3 A system [5] which confirmed the regular nature of the 3 $ and 3 A states. Rotational and spin orbit constants were reported for the 3 $ and 3 A states. 4.2. ANALYSIS A complete assault on the red-orange region of the NbN spectrum is being performed by the high resolution spectroscop}' group at UBC. The hyperfine effects in the 3 3 A system are being analyzed and rotational analyses of both the 3 $ - 3 A and 3 I I - 3 A bands are being performed. The rotational analyses of the 3<i>2-3A, (1-0), (1-1) and (2-1) sub-bands and the 3n,- 3A 2 (0-0) sub-band are discussed below. A broad band scan of the 16950-17110 cm' 1 region of the spectrum is shown in figure 4.2. The strongest feature is the red-degraded Q head of the 3 I I 1 - 3 A 2 (0-0) sub-band at 17057 cm"1. A strong atomic line due to Nb is present in the P branch of the 3II, - 3 A 2 (0-0) band. At higher resolution the 3 I I 1 - 3 A 2 (0-0) sub-band did not exhibit the large hyperfine splitting associated N I O B I U M N I T R I D E / 82 3 n , - 3 A 2 (o-0) 25 cm"1 I I Figure 4.2. Broad Band L I F spectrum of the 16950-17110 c m " 1 region of the N b N spectrum. wi th transitions involving 2A^ or 3 A 3 states. The P and R lines were only followed out to 11 = 35 where the lines were just begining to broaden, probably due to A-doubling in the 3II 1 state. The 3 < I > 2 - 3 A 1 (2-1) band origin is at 17075 c m " 1 , r ight in the centre the 3 n , - 3 A 2 (0-0) R branch. The structure of the two bands is readily separable however by considering the relative intensities; the 3 n 1 - 3 A 2 (0-0) lines are about 3 times as strong as the corresponding 3 $ 2 - 3 A , (2-1) lines. The 3 $ 2 - 3 A , (1-0) band located at 17131 c m " 1 appears to have irregularities on either side of its Q head. This rough appearance is due to an impur i ty in the spectrum, most like]}' N b O . A broad band scan of the 15800-16200 c m " 1 region is shown in figure 4.3. The red-degraded A v = 0 sequence of the 3 4 > 2 _ 3 A 1 system is clearly visible. Since the sequence intensity m a x i m u m is at the (0-0) transit ion and quickly decreases wi th v, the bond length in the excited state must be s imilar to the ground state value. The 3 $ 2 - 3 A 1 (1-1) band centre is at 16097 c m " 1 and so N I O B I U M N I T R I D E / 83 as cm - i (1-1) (0-0) Figure 4.3. Av = 0 sequence of the 3<1>2-3A1 system of N b N has its structure overlapped with the P branch of the 3 < t> 2 _ 3A 1 (0-0) band located at 16145 c m " 1 . Once again the structure from each band was easily discerned by considering the relative intensities of the lines. 4.2.1. Rotational Analysis A n identical procedure was performed for assigning and fitting the rotational constants of the four sub-bands mentioned above. The assignment of the Q, P , and R branch J values is described below. Neglecting centrifugal distortion, the frequency of a Q line (see equation 1.10) is given by: VQ(J)=VO + ( B ' - B " ) J + ( B ' - B " ) J 2 (4.1) and so the difference between adjacent (with values J and J + l ) Q lines is 2(B' — B")(J+1) . The Q line separations increase l inearly with J so a plot of Q NIOBIUM NITRIDE / 84 line separations versus J yields a straight line with a J= —1 intercept when the correct values of J are assigned to the Q lines. The P and R line assignments were made using AjF" combination differences. Only a rough B" value of 0.5 cm"1 was used to calculate the A^F" values but this was sufficient for tentative assignments of the P or R lines. The rotational structure was fitted to the difference of two equations with the form of equation 1.10, neglecting the third and higher order terms. For a given band five constants were determined: the difference between the two band centres (Av) and the effective upper and lower state rotational constants (Be', Bg\ Dg, Dg). Any erroneous line assignments made by using the approximate A! F" values mentioned above were quickly discovered and corrected. The determined constants of each sub-band are given in table 4.2 while the line assignments and residuals of the rotational fits are given in Appendix TV. 4.2.2. Determination of the Electronic States Identifying the 3 $ 2 - 3 A , (1-1) sub-band was trivial since the (0-0) band had been studied and the Av = 0 sequence is obvious (Fig. 4.2). The (1-0) and (2-1) bands of the 3 $ 2 - 3 A 1 Av=l sequence were assigned by noting the vibrational spacings observed by Pazyuk et al. [4], and comparing the hyperfine structure of the two bands with the (0-0) transitions of the 3 $ - 3 A and 3 I I - 3 A sub-bands. Pazyuk et al. assigned the Q heads at 17130.63 and 17072.37 cm" 1 as the (1-0) and (2-1) bands of the 34> 2- 3A 1 Av=l sequence. NIOBIUM NITRIDE / 85 TABLE 4.2 Effective Rotational Constants of Select NbN States (cm" 1 units) Band B e , a 10 6D' e 10 6 D" e Assignment 16097.260(4) 0.49251(8) 0.452(40) 0.49748(8) 0.411(42) -3A,(1-D 17057.474(1) 0.49530(2) 0.498(15) 0.50173(2) 0.469(15) 3 n , -3A2(0-0) 17075.115(2) 0.48994(6) 0.555(37) 0.49767(6) 0.524(37) -3A,(2-1) 17130.999(3) 0.49230(6) 0.494(31) 0.50014(6) 0.449(32) 3*2 - 3 A, (1-0) Common State Constants Reported by Other Workers 16144.648(3)b 0.49532(5) 0.495(7) 0.50015(5) 0.471(7) 3*2 - 3 A, (0-0) 16542.980(3)b 0.49570(5) 0.488(7) 0.50160(5) 0.459(7) 3<i>3 -3A2(0-0) 17124° .4950 0.5082 1 n ( 3 n ? ) - 1 z + (c 17064° 0.4953 0.5016 1 A(0-0) a - numbers in parentheses represents the uncertainty in the last digit, b - reference [5] c - reference [3], only Q head positions and B constants reported. The hyperfine structure in the 3 $ 2 - 3 A 1 (1-0) and (2-1) sub-bands was very similar to the structure seen in the 33>2-3A, (0-0) sub-bands; the Doppler-limited resolved hyperfine structure at J<5 showed identical intensity alternations. The assignment of the 3II, - 3 A 2 (0-0) sub-band was not so easy. The other two sub-bands resulting from the triplet components in the 3 I I - 3 A transition had been assigned by Ranieri [3], 3 n 2 - 3 A 3 (0-0) at 18148 cm"1 and 3 I I 0 - 3 A 1 (0-0) at 17905 cm"1, but the middle 3 n , - 3 A 2 (0-0) sub-band was NIOBIUM NITRIDE / 86 mysteriously absent from its expected position between these two. Assuming negligible hyperfine effects in the 3II 1 upper state, the missing 3 n 1 - 3 A 2 (0-0) sub-band should not exhibit strong hyperfine splitting in the low J rotational branches since the Fermi contact interaction is absent in the 3 A 2 state. There is no such splitting in, the 17057 cm" 1 band so it was considered as a suspect for the missing sub-band. The lower 3 A 2 state was confirmed by checking the A t F " and A 2 F " combination differences against the differences calculated from Femenias' analysis [5] of the 3 4 > 3 - 3 A 2 (0-0) system. The upper 3II 1 state was confirmed by wavelength resolved fluorescence measurements. Select Q lines were optically pumped and the relative intensities of the resulting R and P lines agreed with the intensity ratio predicted by the Honl-London formulae (equation 1.56) for a Afi = —1 transition. Figure 4.4 shows the wavelength resolved fluorescence observed when the Q(13) line of the 3 n , - 3 A 2 (0-0) sub-band is optically pumped. The predicted intensity ratio of the Q(13) 50 cm" ' < 1 R(12) , P(14) Figure 4.4. Wavelength Resolved Fluorescence of Optical^ Pumped Q(13) line of 3 n , - 3 A 2 (0-0) Sub-Band. P to R emission lines of a Afi observed intensity ratio is 1.65. 4.3. DISCUSSION 4.3.1. Results The standard deviation of all the rotational fits was less than 0.002 cm"1, corresponding to less than 10% of a typical linewidth. The rotational constants obtained in this work show agreement within experimental uncertainty with those of Femenias. The uncertainty in the D g values reported here is three to four times greater than that found by Femenias. This is because Femenias followed his branch structure out to much higher J (J = 70 compared to J=35 in this work) where centrifugal effects are more pronounced. Vibrational spacings in the 3 $ 2 and 3 A ^  states can be calculated using the information in table 4.2. AG, = 986.351cm"1 and AG , = 977.855cm"1 i 1* were obtained for the 3 $ 2 state which yields cog = 994.85 cm" 1 and u g x e = 4.25 cm" 1 in agreement with Pazyuk's results. The 3A, state was found to have AG = 1033.739cm"1. 0 Ranieri reported analyzing two bands at 5840 and 5860 A which were assigned as 1I1( 3II?) - 1Z*(0-0) and ^-^(O-O) transitions respectively. Both of these assignments are incorrect for reasons stated above. There is good agreement between Ranieri's B values for the 17057 cm" 1 band with the NIOBIUM NITRIDE / 87 = -1 transition is S?/S? = 1.69 while the NIOBIUM NITRIDE / 88 results reported here. It is puzzling that Ranieri did not consider the 17057 cm"1 band as 3 n, _ 3A 2 because she had analyzed the other two spin components of the 3 n _ 3A transition and thus knew that the missing 3 n 1 - 3 A 2 transition could be in the vicinity and she had analyzed the 3 4> 3 - 3 A 2 transition and determined the. ground state B e value of the 3 A 2 state to be 0.5016 cm"1; identical to the ground state B g determined for the 17057 cm"1 band. Ranieri's rotational constants for the band at 17124 cm" 1 do not agree well with the results found in this work. As mentioned previously, structure from an impurity is found in this region so it is possible that spurious lines were included in Ranieri's rotational fit. Femenias has shown [5] that both the 34> and 3 A states are regular in nature, although there is anomalous splitting in each, in direct contradiction with Pazyuk's results. Pazyuk's assignment of the 17057 cm" 1 band as a spin-orbit satellite band of the 3 3 A system has been shown above to be incorrect. 4.3.2. Comment on Low-Lying States Femenias suggests that the anomalous splitting in the X 3A state could be accounted for by a 1II state nearly degenerate with 3A 2, which could account for the line broadening he observed at high J(—60) in the middle component of triplet system, and also an interaction from below by the 'true' ground state; 1 L * (5sa2). The line broadening effect mentioned above has been shown to be a result of a case(a) to case(b) transition hv the X 3 A state [7] so the first of Femenias' hypotheses seems unlikely. NIOBIUM NITRIDE / 89 It is instructive to compare the results of spectroscopic studies on molecules similar to NbN to try and get a feel for the relative positions of NbN's unseen low lying electronic states. There have been no results published on other group Va nitrides which is unfortunate. The group IVa oxides are similar molecules to NbN in that ZrO is isoelectronic with NbN and TiO and HfO have a similar number of open shell electrons. The group IVa metals all have ns 2 (where n is the period of the metal) in their ground electronic configurations opposed to 5s1 situation in Nb. YF is also isoelectronic with NbN and could also provide some insight into the low-lying electronic behaviour of NbN. A summary of the emission spectra of ZrO is given by Pearse and Gaydon [8]. As expected there is a triplet and a singlet manifold. The lowest lying triplet state is 3 A r (5sa 14d6 1) and the ground state has been assigned by low temperature solid state spectroscopy [9] as 1Z + (5sa2). Further solid state work has shown the 1A (5sa 14d6 1) and 3 A r (5sa 14d5 1) states to be 5200 and 1650cm"1 above the X 1Z + state [10]. A gas phase study on ZrO [11] placed the 3 A r state 1700±250 cm"1 above the X 1Z* state supporting the matrix work. The electronic spectrum of HfO has been shown to be very similar to that of ZrO [12]. There has been a wealth of spectroscopic work done on TiO because of its importance in astrophysics. Again there are the expected triplet and singlet manifolds but in contrast to ZrO the ground state was found to be the 3 A r (4so 13d5 1) state [13]. 1A (4sa 13d6 1) is the lowest state in the singlet NIOBIUM NITRIDE / 90 manifold and was found to be roughly 3500 cm" 1 above the X 3 A r state in a solid state study [14]. A comparable spacing of 2800 cm" 1 was found between the 1II and 3I1 (4sa 13dir 1) states [14]. In contrast to NbN, many more singlet than triplet transitions have been observed for YF [15]. The ground state has been assigned as 1 Z * (5sa2) [15]. Anomalous triplet component splitting in the 3 A (4sa 13d6 1) state was uncovered during the analysis of the 3 $ - 3 A system by Shenyavskaya et al[16]. Shenyavskaya speculated that the so far unseen 1 A (4sa 13d6 1) was the cause of the perturbation. The above information allows us to make some empirical guesses at the the arrangement, of the low-lying electronic states of NbN. Both ZrO and TiO have similar separations between their 11I-3II and 1 A - 3 A isoconfigurational states so it reasonable to suppose a similar situation in NbN. In a group IVa metal oxide the more ionic in character the metal-oxygen bond is the greater the isoconfigurational splitting will be since the two state determining electrons will become more localized on the metal. One expects the NbN bond to be much less ionic than the ZrO bond so the isoconfigurational splitting to be likewise smaller. The 1 A (4sa 13d6 1) state should be considered as a candidate for causing the anomalous multiplet splitting in 3 A (4so 13d6 1) state as should the 1 n (4sa 13d7T 1) state be likewise considered as the root of the perturbation causing the massive shift of the 3 II 1 (4sa 13d7T 1) component. Following the trend in the fifth period, a 1 Z * (5sa2) ground state does not seem unreasonable and is accommodated neatly into the above model. Of course this is all speculation NIOBIUM NITRIDE / 91 based on empirical knowledge and points out the need for future work 4.3.3. Future Work There remain several unanswered questions about NbN: 1. what is the true ground state? 2. where is the singlet manifold with respect to the triplet manifold? 3. what is causing the anomalous multiplet splitting in the 3 A state? 4. what is causing the large shift of the 3II 1 multiplet component from its expected position? The first question could be addressed by a low temperature solid state study on NbN. In order for the second question to be answered a number of singlet transitions must be analyzed to profile the manifold and some case (a) forbidden transitions must be observed to get the relative positions of the singlet and triplet states. An effort has been made in our lab to observe some forbidden transition by wavelength resolved fluorescence but unfortunately no conclusive results have been obtained yet. Again a solid state study may prove useful as otherwise forbidden transitons can become 'allowed' by matrix-induced effects [9,10,14]. The shift of the 3II 1 multiplet component from its expected position of = 18025cm" 1 is probably the result of an interaction with a nearly degenerate electronic state. The mapping of the singlet manifold energies and the relative positions of these energy states might well reveal the presence of an interacting state at = 18990cm" \ displaced an equal and opposite amount from its expected position which would be near-degenerate with 3 0 -t. REFERENCES 1. T.M. Dunn and K.M. Rao, Nature, Vol. 222, 266-267(1969). 2. J.L. Femenias, C. Athenour, and T.M. Dunn, J. Chem. Phys., Vol. 63, 2861-2867(1975). 3. Ranieri, N.L., Optical Emission and Laser Excitation Spectra of Niobium Nitride, Ph.D. Thesis, University of Michigan, Chair. T.M. Dunn, Order No. 7916799, Diss, Abs., Int. B, Vol. 40,(2) 772(1979). 4. E.A. Pazyuk, E.N. Moskvitina, Yu.Ya. Kuzyakov, Spect. Lett., Vol. 19, 627-638(1986). 5. J.L. Femenias, in press. 6. J.M. Hollas, High Resolution Spectroscopy, Butterworths, London, 1982. 7. J.A. Barry, Ph.D. Thesis, University of British Columbia, Vancouver, in press. 8. R.W.B. Pearse and A.G. Gaydon, The Identification of Molecular Spectra, Ed. 3, John Wiley and Sons, New York, 1963. 9. W. Weltner Jr. and D. McLeod Jr., J. Phys. Chem., Vol. 69, 3488-3500(1965). 10. L.J. Lauchlan, J.M. Brom Jr. and H.P. Broida, J. Chem. Phys., Vol. 65, 2672-2678(1976). 11. I.V. Veits, L.V. Gurvich, A.I. Kobylianski, A.D. Smirnov and A.A. Suslov, J. Quant. Spect. Radiat. Trans., Vol. 14, 221(1974). 92 / 93 12. A. Gatterer, J. Junkes, E.W. Salpeter and B. Rosen, Molecular Spectra of Metallic Oxides, Vatican Press, Vatican City, 1957. 13. J.G. Phillips, Astrophys. J., Vol. 115, 567-568(1952). 14. J.M. Brom Jr. and H.P. Broida, J. Chem. Phys., Vol. 63, 3718-3726(1975) 15. R.F. Barrow, M.W. Bastin, D.L.G. Moore and C.J. Pott, Nature, Vol. 215, 1072-1073(1967). 16. E.A. Shenyavskaya and L.V. Gurvich, J. Mol. Spect., Vol. 68, 41-47(1977). APPENDIX I : AMINOBORANE LINE ASSIGNMENTS J' K- K' J" K" K" Freq.(cm" 1) Intensity3 1 0 1 0 0 0 1610.93403 0.0818 2 0 2 1 0 1 1612.62720 0.1365 3 0 3 2 0 2 1614.31567 0.2191 4 0 4 3 0 3 1615.99218 0.3497 5 0 5 4 0 4 1617.64557 0.6579 6 0 6 5 0 5 1619.26356 0.5175 7 0 7 6 0 6 1620.84345 0.9063 8 0 8 7 0 7 1622.38691 0.5336 9 0 9 8 0 8 1623.91155 0.4205 10 0 10 9 0 9 1625.42914 0.5687 11 0 11 10 0 10 1626.94948 0.8304 12 0 12 11 0 11 1628.47762 0.5863 13 0 13 12 0 12 1630.01943 0.5031 14 0 14 13 0 13 1631.57812 0.5530 15 0 15 14 0 14 1633.15609 0.5004 16 0 16 15 0 15 1634.75632 0.5550 17 0 17 16 0 16 1636.38071 0.3518 18 0 18 17 0 17 1638.03591 0.3861 19 0 19 18 0 18 1639.72959 0.3646 20 0 20 19 0 .19 1641.47087 . 0.2586 21 0 21 20 0 20 1643.27020 0.5009 22 0 22 21 0 21 1645.15273 0.2329 23 0 23 22 0 22 1647.12780 0.1589 24 0 24 23 0 23 1649.21416 0.1102 25 0 25 24 0 24 1651.41592 0.0985 2 1 1 1 1 0 1612.69489 0.0631 2 1 2 1 1 1 1612.37025 0.0631 3 1 2 2 1 1 1614.48309 0.1103 3 1 3 2 1 2 1613.98840 0.1260 4 1 3 3 1 2 1616.27767 0.1399 4 1 4 3 1 3 1615.60089 0.0429 5 1 4 4 1 3 1618.06977 0.2351 5 1 5 4 1 4 1617.23304 0.2244 6 1 5 5 1 4 1619.79028 0.5252 6 1 6 5 1 5 1618.85492 0.5952 7 1 6 6 1 5 1621.63347 0.2493 94 / 95 J ' K ' K ' j " K " K ; a c Freq.(cm" 1) Intensity3 7 1 7 6 1 6 1620.47325 0.2429 8 1 7 7 1 6 1623.39372 0.2438 8 1 8 7 1 7 1622.08828 0.6796 9 1 8 8 1 7 1625.13074 0.3051 9 1 9 8 1 8 1623.70172 0.3343 10 1 9 9 1 8 1626.84134 0.2324 10 1 10 9 1 9 1625.31197 0.3380 11 1 10 10 1 9 1628.51922 0.3746 11 1 11 10 1 10 1626.91982 0.4356 12 1 11 11 1 10 1630.15975 0.2451 12 1 12 11 1 11 1628.52629 0.4085 13 1 12 12 1 11 1631.76196 0.2857 13 1 13 12 1 12 1630.13597 0.3838 14 1 13 13 1 12 1633.32366 0.2499 14 1 14 13 1 13 1631.74846 0.4532 15 1 14 14 1 13 1634.84810 0.2094 15 1 15 14 1 14 1633.36761 0.4086 16 1 15 15 1 14 1636.33978 0.3741 16 1 16 15 1 15 1634.99977 0.2886 17 1 16 16 1 15 1637.80810 0.2183 17 1 17 16 1 16 1636.64913 0.2478 18 1 17 17 1 16 1639.26455 0.1252 18 1 18 17 1 17 1638.32297 0.2800 19 1 18 18 1 17 1640.71830 0.1669 19 1 19 18 1 18 1640.03187 0.1768 20 1 19 19 1 18 1642.18329 0.0958 20 1 20 19 1 19 1641.78666 0.1618 21 1 20 20 1 19 1643.67044 0.0904 21 1 21 20 1 20 1643.60474 0.2509 22 1 21 21 1 20 1645.16313 0.0753 22 1 22 21 1 21 1645.50678 0.1076 23 1 22 22 1 21 1646.74678 0.0631 23 1 23 22 1 22 1647.51932 0.0822 24 1 23 23 1 22 1648.35443 0.0488 3 2 1 2 2 0 1613.95270 0.1129 3 2 2 2 2 1 1613.93372 0.1032 4 2 2 3 2 1 1615.70306 0.2321 4 2 3 3 2 2 1615.65795 0.4488 5 2 3 4 2 2 1617.47266 0.3107 5 2 4 4 2 3 1617.38810 0.3372 6 2 4 5 2 3 1619.25035 0.3556 6 2 5 5 2 4 1619.11887 0.4494 7 2 5 6 2 4 1620.98313 0.3019 7 2 6 6 2 5 1620.84345 0.9063 8 2 6 7 2 5 1623.10135 0.3113 / 96 J' K ' K' J" K" K" a c Freq.(cm" 1) Intensity3 8 2 7 7 2 6 1622.57130 0.4496 9 2 7 8 2 6 1624.87091 0.2984 9 2 8 8 2 7 1624.28737 0.5810 10 2 8 9 2 7 1626.68268 0.3723 10 2 9 9 2 8 1625.99392 0.4636 11 2 9 10 2 8 1628.49001 0.4248 11 2 10 10 2 9 1627.68943 0.4280 12 2 10 11 2 9 1630.27732 0.6433 12 2 11 11 2 10 1629.37183 0.4569 13 2 11 12 2 10 1632.03341 0.3799 13 2 12 12 2 11 1631.04173 0.4723 14 2 12 13 2 11 1633.75427 0.3360 14 2 13 13 2 12 1632.69743 0.4039 15 2 13 14 2 12 1635.43557 0.3004 15 2 14 14 2 13 1634.34006 0.3132 16 2 14 15 2 13 1637.07430 0.2350 16 2 15 15 2 14 1635.96710 0.5458 17 2 15 16 2 14 1638.67128 0.2321 17 2 16 16 2 15 1637.57248 0.1714 18 2 16 17 2 15 1640.22473 0.1615 18 2 17 17 2 16 .1639.09725 0.1490 19 2 17 18 2 16 1641.73573 0.1589 19 2 18 18 2 17 1641.01262 0.1167 20 2 18 19 2 17 1643.20566 0.3870 21 2 19 20 2 18 1644.63584 0.1167 21 2 20 20 2 19 1644.33937 0.0974 22 2 20 21 2 19 1646.02986 0.1184 23 2 21 22 2 20 1647.53093 0.0746 4 3 2 3 3 1 1615.16065 0.1474 5 3 2 4 3 1 1616.98418 0.1918 5 3 3 4 3 2 1616.98418 0.1918 6 3 4 5 3 3 1618.80409 0.1449 7 3 4 6 3 3 1620.63445 0.1285 7 3 5 6 3 4 1620.62302 0.1201 8 3 5 7 3 4 1622.45686 0.1606 8 3 6 7 3 5 1622.43569 0.1181 9 3 6 8 3 5 1624.27312 0.1114 9 3 7 8 3 6 1624.23731 0.1748 10 3 J 9 3 6 1626.08091 0.1667 10 3 8 9 3 7 1626.02429 0.1445 11 3 8 10 3 7 1627.87690 0.1750 11 3 9 10 3 8 1627.79317 0.1863 12 3 9 11 3 8 1629.65934 0.1718 12 3 10 11 3 9 1629.54185 0.1741 13 3 10 12 3 9 1631.41683 0.1740 / 97 J' K a K c J" K a K c Freq.(cm" 1) Intensity3 13 3 11 12 3 10 1631.26961 0.2053 14 3 11 13 3 10 1633.17285 0.1444 14 3 12 13 3 11 1632.97470 0.1829 15 3 12 14 3 11 1634.93424 0.1097 15 3 13 14 3 12 1634.65650 0.1074 16 3 13 15 3 12 1636.59992 0.1213 16 3 14 15 3 13 1636.31475 0.1665 17 3 14 16 3 13 1638.27363 0.0923 17 3 15 16 3 14 1637.95080 0.1480 18 3 15 17 3 14 1639.91517 0.0785 18 3 16 17 3 15 1639.56451 0.1723 19 3 16 18 3 15 1641.52134 0.0645 19 3 17 18 3 16 1641.15815 0.0791 20 3 17 19 3 16 1643.09020 0.0381 20 3 18 19 3 17 1642.73121 0.0856 21 3 18 20 3 17 1644.62208 0.0922 21 3 19 20 3 18 1644.28402 0.0470 22 3 19 21 3 18 1646.10936 0.0790 22 3 20 21 3 19 1645.78259 0.3468 23 3 20 22 3 19 1647.55773 0.0825 23 3 21 22 3 20 1647.20276 0.0663 5 4 2 1 4 4 1 1615.67840 0.1358 6 4 3 » 5 4 2 1617.11019 0.2248 7 4 4 6 4 3 1618.53250 0.3170 8 4 5 7 4 4 1619.95037 0.3358 9 4 5 8 4 4 1621.37158 0.1987 9 4 6 8 4 5 1621.36101 0.4085 10 4 6 9 4 5 1622.79258 0.2182 10 4 7 9 4 6 1622.77529 0.2463 11 4 7 10 4 6 1624.21923 0.2397 11 4 8 10 4 7 1624.18747 0.2326 12 4 8 11 4 7 1625.64985 0.1938 12 4 9 11 4 8 1625.60070 0.2436 13 4 9 12 •4 8 1627.08548 0.1814 13 4 10 12 4 9 1627.01190 0.2527 14 4 11 13 4 10 1628.42043 0.4419 15 4 11 14 4 10 1629.96920 0.1788 15 4 12 14 4 11 1629.82356 0.1844 16 4 13 15 4 12 1631.22006 0.1314 17 4 13 16 4 12 1632.86730 0.1371 17 4 14 16 4 13 1632.60584 0.1420 18 4 14 17 4 13 1634.30999 0.1347 18 4 15 17 4 14 1633.97683 0.1750 19 4 15 18 4 14 1635.74916 0.0883 19 4 16 18 4 15 1635.32962 0.0858 / 98 J' K' K' J" K" K" a C Freq.(cm" ') Intensity3 20 4 16 19 4 15 1637.17682 0.0848 20 4 17 19 4 16 1636.65976 0.0850 21 4 17 20 4 16 1638.57932 0.1454 21 4 18 20 4 17 1637.96118 0.0551 22 4 18 21 4 17 1639.72959 0.3646 22 4 19 21 4 18 1639.11345 0.1490 7 6 2 6 6 1 1616.45057 0.0471 8 6 3 7 6 2 1617.98526 0.1441 9 6 4 8 6 3 1619.92845 0.1014 10 6 5 9 6 4 1621.43635 0.1848 11 6 6 10 6 5 1623.00919 0.5724 12 6 7 11 6 6 1624.59179 0.2077 13 6 8 12 6 7 1626.17257 0.2547 14 6 9 13 6 8 1627.75006 0.2522 15 6 10 14 6 9 1629.32224 0.3041 16 6 11 15 6 10 1630.89339 0.1387 18 6 13 17 6 12 1634.06736 0.1139 1 0 1 2 0 2 1605.89854 0.1436 2 0 2 3 0 3 1604.25054 0.4399 3 0 3 4 0 4 1602.62152 0.3582 4 0 .4 5 0 5 1601.01203 0.3597 5 0 5 6 0 6 1599,41904 0.3797 6 0 6 7 0 7 1597.83570 0.6568 7 0 7 8 0 8 1596.25702 0.6055 8 0 8 9 0 9 1594.69000 0.5368 9 0 9 10 0 10 1593.13906 0.6021 10 0 10 11 0 11 1591.60698 0.7244 11 0 11 12 0 12 1590.09745 0.6147 12 0 12 13 0 13 1588.60530 0.5728 13 0 13 14 0 14 1587.13066 0.5326 14 0 14 15 0 15 1585.67153 0.6921 15 0 15 16 0 16 1584.22882 0.5255 16 0 16 17 0 17 1582.80529 0.4776 17 0 17 18 0 18 1581.40360 0.5075 18 0 18 19 0 19 1580.02851 0.3648 19 0 19 20 0 20 1578.68972 0.3115 20 0 20 21 0 21 1577.39648 0.2681 21 0 21 22 0 22 1576.16402 0.3288 22 0 22 23 0 23 1575.00795 0.2151 23 0 23 24 0 24 1573.94674 0.0931 24 0 24 25 0 25 1572.99694 0.0696 25 0 25 26 0 26 1572.16471 0.0686 2 1 1 3 1 2 1603.91333 0.1424 2 1 2 3 1 3 1604.35612 0.1295 3 1 2 4 1 3 1602.19892 0.1831 / 99 J' K' K' J" K" K" cl C Freq.(cm" 1) Intensity3 3 1 3 4 1 4 1602.77845 0.1863 4 1 3 5 1 4 1600.49753 0.2143 4 1 4 5 1 5 1601.20540 0.0832 5 1 4 6 1 5 1598.80864 0.2855 5 1 5 6 1 6 1599.65398 0.2702 6 1 5 7 1 6 1597.06246 0.3100 6 1 6 7 1 7 1598.10649 0.4201 7 1 6 8 1 7 1595.46058 0.5526 7 1 7 8 1 8 1596.56932 0.3291 8 1 7 9 1 8 1593.79723 0.2765 8 1 8 9 1 9 1595.04068 0.3365 9 1 8 10 1 9 1592.14243 0.2579 9 1 9 10 1 10 1593.52137 0.3727 10 1 9 11 1 10 1590.49536 0.4070 10 1 10 11 1 11 1592.01125 0.4248 11 1 10 12 1 11 1588.85629 0.3076 11 1 11 12 1 12 1590.51059 0.3975 12 1 11 13 1 12 1587.22678 0.3139 12 1 12 13 1 13 1589.01963 0.2835 13 1 12 14 1 13 1585.60730 0.2845 13 1 13 14 1 14 1587.54033 0.3855 14 1 13 15 1 14 1583.99872 0.2394 14 1 14 15 1 15 1586.07291 0.3203 15 1 14 16 1 15 1582.40314 0.2460 15 1 15 16 1 16 1584.62035 0.3447 16 1 15 17 1 16 1580.82138 0.1989 16 1 16 17 1 17 1583.18653 0.3533 17 1 16 18 1 17 1579.25323 0.1946 17 1 17 18 1 18 . 1581.77414 0.3125 18 1 17 19 1 18 1577.69970 0.1564 18 1 18 19 1 19 1580.39329 0.1902 19 1 18 20 1 19 1576.16402 0.3288 19 1 19 20 1 20 1579.04931 0.1368 20 1 19 21 1 20 1574.64804 0.1443 20 1 20 21 1 21 1577.75504 0.1250 21 1 20 22 1 21 1573.15769 0.0893 21 1 21 22 1 22 1576.52676 0.1095 22 1 21 23 1 22 1571.67062 0.0678 22 1 22 23 1 23 1575.38481 0.0738 23 1 22 24 1 23 1570.26887 0.0790 23 1 23 24 1 24 1574.35452 0.0577 24 1 23 25 1 24 1568.88383 0.0552 3 2 1 4 2 2 1602.13244 0.4098 3 2 2 4 2 3 1602.17815 0.2282 4 2 2 5 2 3 1600.45982 0.3065 / 100 J' K' K' J" K" K" Freq.(cm" 1) Intensity3 4 2 3 5 2 4 1600.55427 0.3041 5 2 3 6 2 4 1598.77418 0.3512 5 2 4 6 2 5 1598.94198 0.3915 6 2 4 7 2 5 1597.06246 0.3100 6 2 5 7 2 6 1597.33975 0.3914 7 2 5 8 2 6 1595.27158 0.3750 7 2 6 8 2 7 1595.74617 0.4254 8 2 6 9 2 7 1593.83533 0.3540 8 2 7 9 2 8 1594.15979 0.5143 9 2 7 10 2 8 1592.02911 0.4925 9 2 8 10 2 9 1592.57954 0.4932 10 2 8 11 2 9 1590.25482 0.4907 10 2 9 11 2 10 1591.00410 0.4121 11 2 9 12 2 10 1588.47723 0.4850 11 2 10 12 2 11 1589.43305 0.3550 12 2 10 13 2 11 1586.69137 0.4909 12 2 11 13 2 12 1587.86642 0.4638 13 2 11 14 2 12 1584.89760 0.5076 13 2 12 14 2 13 1586.30428 0.5012 14 2 12 15 2 13 1583.09563 0.3422 14 2 13 15 2 14 1584.74653 0.3732 15 2 13 16 2 14 1581.28981' 0.4054 15 2 14 16 2 15 1583.19331 0.2923 16 2 14 17 2 15 1579.48193 0.2987 16 2 15 17 2 16 1581.64475 0.3411 17 2 15 18 2 16 1577.67595 0.3956 17 2 16 18 2 17 1580.08833 0.3156 18 2 16 19 2 17 1575.87453 0.1890 18 2 17 19 2 18 1578.47089 0.2312 19 2 17 20 2 18 1574.08527 0.1976 19 2 18 20 2 19 1577.25904 0.1260 20 2 18 21 2 19 1572.30969 0.1618 22 2 20 23 2 21 1568.81606 0.1007 5 3 3 6 3 4 1598.46930 0.4167 6 3 4 7 3 5 1596.91135 0.1341 7 3 4 8 3 5 1595.32858 0.1478 7 3 5 8 3 6 1595.35033 0.1731 8 3 5 9 3 6 1593.73906 0.1954 8 3 6 9 3 7 1593.78114 0.2314 9 3 6 10 3 7 1592.12514 0.1295 9 3 7 10 3 8 1592.19828 0.1626 10. 3 7 11 3 8 1590.48070 0.2846 10 3 8 11 3 9 1590.60132 0.1878 11 3 8 12 3 9 1588.79450 0.4484 11 3 9 12 3 10 1588.98812 0.1851 / 101 J' K' K' J" K" K" a C Freq.(cm* 1) Intensity3 12 3 9 13 3 10 1587.06931 0.1514 12 3 10 13 3 11 1587.36035 0.1734 13 3 10 14 3 11 1585.29241 0.1468 13 3 11 14 3 12 1585.71615 0.1926 14 3 11 15 3 12 1583.46354 0.3088 14 3 12 15 3 13 1584.05663 0.1998 15 3 12 16 3 13 1581.61964 0.0652 15 3 13 16 3 14 1582.38861 0.1398 16 3 13 17 3 14 1579.65531 0.0911 16 3 14 17 3 15 1580.70812 0.1332 17 3 14 18 3 15 1577.68444 0.0787 17 3 15 T8 3 16 1579.02193 0.1054 18 3 15 19 3 16 1575.67842 0.0721 18 3 16 19 3 17 1577.32947 0.1407 1 0 1 0 0 0 1610.93403 0.0818 2 0 2 1 0 1 1612.62720 0.1365 3 0 3 2 0 2 1614.31567 0.2191 4 0 4 3 0 3 1615.99218 0.3497 5 0 5 4 0 4 1617.64557 0.6579 6 0 6 5 0 5 1619.26356 0.5175 7 0 7 6 0 6 1620.84345 0.9063 8 0 8 7 0 7 1622.38691 0.5336 9 0 9 8 0 8 1623.91155 0.4205 10 0 10 9 0 9 1625.42914 0.5687 11 0 11 10 0 10 1626.94948 0.8304 12 0 12 11 0 11 1628.47762 0.5863 13 0 13 12 0 12 1630.01943 0.5031 14 0 14 13 0 13 1631.57812 0.5530 15 0 15 14 0 14 1633.15609 0.5004 16 0 16 15 0 15 1634.75632 0.5550 17 0 17 16 0 16 1636.38071 0.3518 18 0 18 17 0 17 1638.03591 0.3861 19 0 19 18 0 18 1639.72959 0.3646 20 0 20 19 0 19 1641.47087 0.2586 21 0 21 20 0 20 1643.27020 0.5009 22 0 22 21 0 21 1645.15273 0.2329 23 0 23 22 0 22 1647.12780 0.1589 24 0 24 23 0 23 1649.21416 0.1102 25 0 25 24 0 24 1651.41592 0.0985 2 1 1 1 1 0 1612.69489 0.0631 2 1 2 1 1 1 1612.37025 0.0631 3 1 2 2 1 1 1614.48309 0.1103 3 1 3 2 1 2 1613.98840 0.1260 4 1 3 3 1 2 1616.27767 0.1399 4 1 4 3 1 3 1615.60089 0.0429 / 102 J' K' K' J" K" K" a C Freq.(cm" 1) Intensity3 5 1 4 4 1 3 1618.06977 0.2351 5 1 5 4 1 4 1617.23304 0.2244 6 1 5 5 1 4 1619.79028 0.5252 6 1 6 5 1 5 1618.85492 0.5952 7 1 6 6 1 5 1621.63347 0.2493 7 1 7 6 1 6 1620.47325 0.2429 8 1 7 7 1 6 1623.39372 0.2438 8 1 8 7 1 7 1622.08828 0.6796 9 1 8 8 1 7 1625.13074 0.3051 9 1 9 8 1 8 1623.70172 0.3343 10 1 9 9 1 8 1626.84134 0.2324 10 1 10 9 1 9 1625.31197 0.3380 11 1 10 10 1 9 1628.51922 0.3746 11 1 11 10 1 10 1626.91982 0.4356 12 1 11 11 1 10 1630.15975 0.2451 12 1 12 11 1 11 1628.52629 0.4085 13 1 12 12 1 11 1631.76196 0.2857 13 1 13 12 1 12 1630.13597 0.3838 14 1 13 13 1 12 1633.32366 0.2499 14 1 14 13 1 13 1631.74846 0.4532 15 1 14 14 1 13 1634.848.10 0.2094 15 1 15 14 1 14 1633.36761 0.4086 16 1 15 15 1 14 1636.33978 0.3741 16 1 16 15 1 15 1634.99977 0.2886 17 1 16 16 1 15 1637.80810 0.2183 17 1 17 16 1 16 1636.64913 0.2478 18 1 17 17 1 16 1639.26455 0.1252 18 1 18 17 1 17 1638.32297 0.2800 19 1 18 18 1 17 1640.71830 0.1669 19 1 19 18 1 18 1640.03187 0.1768 20 1 19 19 1 18 1642.18329 0.0958 20 1 20 19 1 19 1641.78666 0.1618 21 1 20 20 1 19 1643.67044 0.0904 21 1 21 20 1 20 1643.60474 0.2509 22 1 21 21 1 20 1645.16313 0.0753 22 1 22 21 1 21 1645.50678 0.1076 23 1 22 22 1 21 1646.74678 0.0631 23 1 23 22 1 22 1647.51932 0.0822 24 1 23 23 1 22 1648.35443 0.0483 3 2 1 2 2 0 1613.95270 0.1129 3 2 2 2 2 1 1613.93372 0.1032 4 2 2 3 2 1 1615.70306 0.2321 4 2 3 3 2 2 1615.65795 0.4488 5 2 3 4 2 2 1617.47266 0.3107 5 2 4 4 2 3 1617.38810 0.3372 / 103 j ' K • K : a c J" K " K " CL C Freq.(cm~ Intensity3 6 2 4 5 2 3 1619.25035 0.3556 6 2 5 5 2 4 1619.11887 0.4494 7 2 5 6 2 4 1620.98313 0.3019 7 2 6 6 2 5 1620.84345 0.9063 8 2 6 7 2 5 1623.10135 0.3113 8 2 7 7 2 6 1622.57130 0.4496 9 2 7 8 2 6 1624.87091 0.2984 9 2 8 8 2 7 1624.28737 0.5810 10 2 8 9 2 7 1626.68268 0.3723 10 2 9 9 2 8 1625.99392 0.4636 11 2 9 10 2 8 1628.49001 0.4248 11 2 10 10 2 9 1627.68943 0.4280 12 2 10 112 9 1630.27732 0.6433 12 2 11 11 2 10 1629.37183 0.4569 13 2 11 12 2 10 1632.03341 0.3799 13 2 12 12 2 11 1631.04173 0.4723 14 2 12 13 2 11 1633.75427 0.3360 14 2 13 13 2 12 1632.69743 0.4039 15 2 13 14 2 12 1635.43557 0.3004 15 2 14 14 2 13 1634.34006 0.3132 16 2 14 15 2 13 1637.07430 0.2350 16 2 15 15 2 14 1635.96710 0.5458 17 2 15 16 2 14 1638.67128 0.2321 17 2 16 16 2 15 1637.57248 0.1714 18 2 16 17 2 15 1640.22473 0.1615 18 2 17 17 2 16 1639.09725 0.1490 19 2 17 18 2 16 1641.73573 0.1589 19 2 18 18 2 17 1641.01262 0.1167 20 2 18 19 2 17 1643.20566 0.3870 21 2 19 20 2 18 1644.63584 ~ 0.1167 21 2 20 20 2 19 1644.33937 0.0974 22 2 20 21 2 19 1646.02986 0.1184 23 2 21 22 2 20 1647.53093 0.0746 4 3 2 3 3 1 1615.16065 0.1474 5 3 2 4 3 1 1616.98418 0.1918 5 3 3 4 3 2 1616.98418 0.1918 6 3 4 5 3 3 1618.80409 0.1449 7 3 4 6 3 3 1620.63445 0.1285 7 3 5 6 3 4 1620.62302 0.1201 8 3 5 7 3 4 1622.45686 0.1606 8 3 6 7 3 5 1622.43569 0.1181 9 3 6 8 3 5 1624.27312 0.1114 9 3 7 8 3 6 1624.23731 0.1748 10 3 7 9 3 6 1626.08091 0.1667 10 3 8 9 3 7 1626.02429 0.1445 / 104 J' K ' K' j " K " K ; cl C Freq.(cm" 1) Intensity3 11 3 8 10 3 7 1627.87690 0.1750 11 3 9 10 3 8 1627.79317 0.1863 12 3 9 < • 11 3 8 1629.65934 0.1718 12 3 10 11 3 9 1629.54185 0.1741 13 3 10 12 3 9 1631.41683 0.1740 13 3 11 12 3 10 1631.26961 0.2053 14 3 11 13 3 10 1633.17285 0.1444 14 3 12 13 3 11 1632.97470 0.1829 15 3 12 14 3 11 1634.93424 0.1097 15 3 13 14 3 12 1634.65650 0.1074 16 3 13 15 3 12 1636.59992 0.1213 16 3 14 15 3 13 1636.31475 0.1665 17 3 14 16 3 13 1638.27363 0.0923 17 3 15 16 3 14 1637.95080 0.1480 18 3 15 17 3 14 1639.91517 0.0785 18 3 16 17 3 15 1639.56451 0.1723 19 3 16 18 3 15 1641.52134 0.0645 19 3 17 18 3 16 1641.15815 0.0791 20 3 17 19 3 16 1643.09020 0.0381 20 3 18 19 3 17 1642.73121 0.0856 21 3 18 20 3 17 1644.62208 0.0922 21 3 19 20 3 18 1644.28402 0.0470 22 3 19 21 3 18 1646.10936 0.0790 22 3 20 21 3 19 1645.78259 0.3468 23 3 20 22 3 19 1647.55773 0.0825 23 3 21 22 3 20 1647.20276 0.0663 5 4 2 4 4 1 1615.67840 0.1358 6 4 3 5 4 2 1617.11019 0.2248 7 4 4 6 4 3 1618.53250 0.3170 8 4 5 7 4 4 1619.95037 0.3358 9 4 5 8 4 4 1621.37158 0.1987 9 4 6 8 4 5 1621.36101 0.4085 10 4 6 9 4 5 1622.79258 0.2182 10 4 7 9 4 6 1622.77529 0.2463 11 4 7 10 4 6 1624.21923 0.2397 11 4 8 10 4 7 1624.18747 0.2326 12 4 8 11 4 7 1625.64985 0.1938 12 4 9 11 4 8 1625.60070 0.2436 13 4 9 12 4 8 1627.08548 0.1814 13 4 10 12 4 9 1627.01190 0.2527 14 4 11 13 4 10 1628.42043 0.4419 15 4 11 14 4 10 1629.96920 0.1788 15 4 12 14 4 11 1629.82356 0.1844 16 4 13 • 15 4 12 1631.22006 0.1314 17 4 13 16 4 12 1632.86730 0.1371 / 105 J' K • K' J" K" K" Freq.(cm" ') Intensity3 17 4 14 16 4 13 1632.60584 0.1420 18 4 14 17 4 13 1634.30999 0.1347 18 4 15 17 4 14 1633.97683 0.1750 19 4 15 18 4 14 1635.74916 0.0883 19 4 16 18 4 15 1635.32962 0.0858 20 4 16 19 4 15 1637.17682 0.0848 20 4 17 19 4 16 1636.65976 0.0850 21 4 17 20 4 16 1638.57932 0.1454 21 4 18 20 4 17 1637.96118 0.0551 22 4 18 21 4 17 1639.72959 0.3646 22 4 19 21 4 18 1639.11345 0.1490 7 6 2 6 6 1 1616.45057 0.0471 8 6 3 7 6 2 1617.98526 0.1441 9 6 4 8 6 3 1619.92845 0.1014 10 6 5 9 6 4 1621.43635 0.1848 11 6 6 10 6 5 1623.00919 0.5724 12 6 7 11 6 6 1624.59179 0.2077 13 6 8 12 6 7 1626.17257 0.2547 14 6 9 13 6 8 1627.75006 0.2522 15 6 10 14 6 9 1629.32224 0.3041 16 6 11 15 6 10 . 1630.89339 0.1387 18 6 13 17 6 12 1634.06736 0.1139 1 0 1 2 0 2 1605.89854 0.1436 2 0 2 3 0 3 1604.25054 0.4399 3 0 3 4 0 4 1602.62152 0.3582 4 0 4 5 0 5 1601.01203 0.3597 5 0 5 6 0 6 1599.41904 0.3797 6 0 6 7 0 7 1597.83570 0.6568 7 0 7 8 0 8 1596.25702 0.6055 8 0 8 9 0 9 1594.69000 0.5368 9 0 9 10 0 10 1593.13906 0.6021 10 0 10 11 0 11 1591.60698 0.7244 11 0 11 12 0 12 1590.09745 0.6147 12 0 12 13 0 13 1588.60530 0.5728 13 0 13 14 0 14 1587.13066 0.5326 14 0 14 15 0 15 1585.67153 0.6921 15 0 15 16 0 16 1584.22882 0.5255 16 0 16 17 0 17 1582.80529 0.4776 17 0 17 18 0 18 1581.40360 0.5075 18 0 18 19 0 19 1580.02851 0.3648 19 0 19 20 0 20 1578.68972 0.3115 20 0 20 21 0 21 1577.39648 0.2681 21 0 21 22 0 22 1576.16402 0.3288 22 0 22 23 0 23 1575.00795 0.2151 23 0 23 24 0 24 1573.94674 0.0931 / 106 J' K' K ' j" K " K ; a c Freq.(cm" 1) Intensity3 24 0 24 25 0 25 1572.99694 0.0696 25 0 25 26 0 26 1572.16471 0.0686 2 1 1 3 1 2 1603.91333 0.1424 2 1 2 3 1 3 1604.35612 0.1295 3 1 2 4 1 3 1602.19892 0.1831 3 1 3 4 1 4 1602.77845 0.1863 4 1 3 5 1 4 1600.49753 0.2143 4 1 4 5 1 5 1601.20540 0.0832 5 1 4 6 1 5 1598.80864 0.2855 5 1 5 6 1 6 1599.65398 0.2702 6 1 5 7 1 6 1597.06246 0.3100 6 1 6 7 1 7 1598.10649 0.4201 7 1 6 8 1 7 1595.46058 0.5526 7 1 7 8 1 8 1596.56932 0.3291 8 1 7 9 1 8 1593.79723 0.2765 8 1 8 9 1 9 1595.04068 0.3365 9 1 8 10 1 9 1592.14243 0.2579 9 1 9 10 1 10 1593.52137 0.3727 10 1 9 11 1 10 1590.49536 0.4070 10 1 10 11 1 11 1592.01125 0.4248 11 1 10 12 1 11 1588.85629 0.3076 11 1 11 12 1 12 1590.51059 0.3975 12 1 11 13 1 12 1587.22678 0.3139 12 1 12 13 1 13 1589.01963 0.2835 13 1 12 14 1 13 1585.60730 0.2845 13 1 13 14 1 14 1587.54033 0.3855 14 1 13 15 1 14 1583.99872 0.2394 14 1 14 15 1 15 1586.07291 0.3203 15 1 14 16 1 15 1582.40314 0.2460 15 1 15 16 1 16 1584.62035 0.3447 16 1 15 17 1 16 1580.82138 0.1989 16 1 16 17 1 17 1583.18653 0.3533 17 1 16 18 1 17 1579.25323 0.1946 17 1 17 18 1 18 1581.77414 0.3125 18 1 17 19 1 18 1577.69970 0.1564 18 1 18 19 1 19 1580.39329 0.1902 19 1 18 20 1 19 1576.16402 0.3288 19 1 19 20 1 20 1579.04931 0.1368 20 1 19 21 1 20 1574.64804 0.1443 20 1 20 21 1 21 1577.75504 0.1250 21 1 20 22 1 21 1573.15769 0.0893 21 1 21 22 1 22 1576.52676 0.1095 22 1 21 23 1 22 1571.67062 0.0678 22 1 22 23 1 23 1575.38481 0.0738 23 1 22 24 1 23 1570.26887 0.0790 / 107 j' K : K ; a c J" K " K " a. C Freq.(cm" 1) Intensity3 23 1 23 24 1 24 1574.35452 0.0577 24 1 23 25 1 24 1568.88383 0.0552 3 2 1 4 2 2 1602.13244 0.4098 3 2 2 4 2 3 1602.17815 0.2282 4 2 2 5 2 3 1600.45982 0.3065 4 2 3 5 2 4 1600.55427 0.3041 5 2 3 6 2 4 1598.77418 0.3512 5 2 4 6 2 5 1598.94198 0.3915 6 2 4 7 2 5 1597.06246 0.3100 6 2 5 7 2 6 1597.33975 0.3914 7 2 5 8 2 6 1595.27158 0.3750 7 2 6 8 2 7 1595.74617 0.4254 8 2 6 9 2 7 1593.83533 0.3540 8 2 7 9 2 8 1594.15979 0.5143 9 2 7 10 2 8 1592.02911 0.4925 9 2 8 10 2 9 1592.57954 0.4932 10 2 8 11 2 9 1590.25482 0.4907 10 2 9 11 2 10 1591.00410 0.4121 11 2 9 12 2 10 1588.47723 0.4850 11 2 10 12 2 11 1589.43305 . 0.3550 12 2 10 13 .2 11 1586.69137 0.4909 12 2 11 13 2 12 1587.86642 0.4638 13 2 11 14 2 12 1584.89760 0.5076 13 2 12 14 2 13 1586.30428 0.5012 14 2 12 15 2 13 1583.09563 0.3422 14 2 13 15 2 14 1584.74653 0.3732 15 2 13 16 2 14 1581.28981 0.4054 15 2 14 16 2 15 1583.19331 0.2923 16 2 14 17 2 15 1579.48193 0.2987 16 2 15 17 2 16 1581.64475 0.3411 17 2 15 18 2 16 1577.67595 0.3956 17 2 16 18 2 17 1580.08833 0.3156 18 2 16 19 2 17 1575.87453 0.1890 18 2 17 19 2 18 1578.47089 0.2312 19 2 17 20 2 18 1574.08527 0.1976 19 2 18 20 2 19 1577.25904 0.1260 20 2 18 21 2 19 1572.30969 0.1618 22 2 20 23 2 21 1568.81606 0.1007 5 3 3 6 3 4 1598.46930 0.4167 6 3 4 7 3 5 1596.91135 0.1341 7 3 4 8 3 5 1595.32858 0.1478 7 3 5 8 3 6 1595.35033 0.1731 8 3 5 9 3 6 1593.73906 0.1954 8 3 6 9 3 7 1593.78114 0.2314 9 3 6 10 3 7 1592.12514 0.1295 / 108 J' K' K' J" K a K c Freq.(cm" 1) Intensity3 9 3 7 10 3 8 1592.19828 0.1626 10 3 7 11 3 8 1590.48070 0.2846 10 3 8 11 3 9 1590.60132 0.1878 11 3 8 12 3 9 1588.79450 0.4484 11 3 9 12 3 10 1588.98812 0.1851 12 3 9 13 3 10 1587.06931 0.1514 12 3 10 13 3 11 1587.36035 0.1734 13 3 10 14 3 11 1585.29241 0.1468 1.3 3 11 14 3 12 1585.71615 0.1926 14 3 11 15 3 12 1583.46354 0.3088 14 3 12 15 3 13 1584.05663 0.1998 15 3 12 16 3 13 1581.61964 0.0652 15 3 13 16 3 14 1582.38861 0.1398 16 3 13 17 3 14 1579.65531 0.0911 16 3 14 17 3 15 1580.70812 0.1332 17 3 14 18 3 15 1577.68444 0.0787 17 3 15 18 3 16 1579.02193 0.1054 18 3 15 19 3 16 1575.67842 0.0721 18 3 16 19 3 17 1577.32947 0.1407 1 0 1 0 0 0 1610.93403 0.0818 2 0 2 1 0 1 1612.62720 0.1365 3 0 3 2 0 2 1614.31567 0.1823 4 0 4 3 0 3 1615.99218 0.3497 5 0 5 4 0 4 1617.64557 0.6579 6 0 6 5 0 5 1619.26356 0.5175 7 0 7 6 0 6 1620.84345 0.9063 8 0 8 7 0 7 1622.38691 0.5336 9 0 9 8 0 8 1623.91155 0.4205 10 0 10 9 0 9 1625.42914 0.0411 11 0 11 10 0 10 1626.94948 0.8304 12 0 12 11 0 11 1628.47762 0.5863 13 0 13 12 0 12 1630.01943 0.5031 14 0 14 13 0 13 1631.57812 0.5530 15 0 15 14 0 14 1633.15609 0.5004 16 0 16 15 0 15 1634.75632 0.5550 17 0 17 16 0 16 1636.38071 0.3518 18 0 ,18 17 0 17 1638.03591 0.3861 19 0 19 18 0 18 1639.72959 0.3646 20 0 20 19 0 19 1641.47087 0.2586 21 0 21 20 0 20 1643.27020 0.5009 22 0 22 21 0 21 1645.15273 0.2329 23 0 23 22 0 22 1647.12780 0.1589 24 0 24 23 0 23 1649.21416 0.1102 25 0 25 24 0 24 1651.41592 0.0985 2 1 1 1 1 0 1612.69489 0.0631 / 1 0 9 J ' K ' K ' j " K " K ; Freq.(cm" }) Intensity3 2 1 2 I I I 1 6 1 2 . 3 7 0 2 5 0 . 0 6 3 1 3 1 2 2 1 1 1 6 1 4 . 4 8 3 0 9 0 . 1 1 0 3 3 1 3 2 1 2 1 6 1 3 . 9 8 8 4 0 0 . 1 2 6 0 4 1 3 3 1 2 1 6 1 6 . 2 7 7 6 7 0 . 1 3 9 9 4 1 4 3 1 3 1 6 1 5 . 6 0 0 8 9 0 . 0 4 2 9 5 1 4 4 1 3 1 6 1 8 . 0 6 9 7 7 0 . 2 3 5 1 5 1 5 4 1 4 1 6 1 7 . 2 3 3 0 4 0 . 2 2 4 4 6 1 5 5 1 4 1 6 1 9 . 7 9 0 2 8 0 . 5 2 5 2 6 1 6 5 1 5 1 6 1 8 . 8 5 4 9 2 0 . 5 9 5 2 7 1 6 6 1 5 1 6 2 1 . 6 3 3 4 7 0 . 2 4 9 3 7 1 7 6 1 6 1 6 2 0 . 4 7 3 2 5 0 . 2 4 2 9 8 1 7 7 1 6 1 6 2 3 . 3 9 3 7 2 0 . 2 4 3 8 8 1 8 7 1 7 1 6 2 2 . 0 8 8 2 8 0 . 6 7 9 6 9 1 8 8 1 7 1 6 2 5 . 1 3 0 7 4 0 . 3 0 5 1 9 1 9 8 1 8 1 6 2 3 . 7 0 1 7 2 0 . 3 3 4 3 1 0 1 9 9 1 8 1 6 2 6 . 8 4 1 3 4 0 . 0 3 9 2 1 0 1 1 0 9 1 9 1 6 2 5 . 3 1 1 9 7 0 . 3 3 8 0 1 1 1 1 0 1 0 1 9 1 6 2 8 . 5 1 9 2 2 0 . 3 7 4 6 1 1 1 1 1 1 0 1 1 0 1 6 2 6 . 9 1 9 8 2 0 . 4 3 5 6 1 2 1 1 1 1 1 1 1 0 1 6 3 0 . 1 5 9 7 5 0 . 2 4 5 1 1 2 1 1 2 1 1 1 1 1 1 6 2 8 . 5 2 6 2 9 0 . 4 0 8 5 1 3 1 1 2 1 2 1 1 1 1 6 3 1 . 7 6 1 9 6 0 . 2 8 5 7 1 3 1 1 3 1 2 1 1 2 1 6 3 0 . 1 3 5 9 7 0 . 3 8 3 8 1 4 1 1 3 1 3 1 1 2 1 6 3 3 . 3 2 3 6 6 0 . 2 4 9 9 1 4 1 1 4 1 3 1 1 3 1 6 3 1 . 7 4 8 4 6 0 . 4 5 3 2 1 5 1 1 4 1 4 1 1 3 1 6 3 4 . 8 4 8 1 0 0 . 2 0 9 4 1 5 1 1 5 1 4 1 1 4 1 6 3 3 . 3 6 7 6 1 0 . 4 0 8 6 1 6 1 1 5 1 5 1 1 4 1 6 3 6 . 3 3 9 7 8 0 . 3 7 4 1 1 6 1 1 6 1 5 1 1 5 1 6 3 4 . 9 9 9 7 7 0 . 2 8 8 6 1 7 1 1 6 1 6 1 1 5 1 6 3 7 . 8 0 8 1 0 0 . 2 1 8 3 1 7 1 1 7 1 6 1 1 6 1 6 3 6 . 6 4 9 1 3 0 . 2 4 7 8 1 8 1 1 7 1 7 1 1 6 1 6 3 9 . 2 6 4 5 5 0 . 1 2 5 2 1 8 1 1 8 1 7 1 1 7 1 6 3 8 . 3 2 2 9 7 0 . 2 8 0 0 1 9 1 1 8 1 8 1 1 7 1 6 4 0 . 7 1 8 3 0 0 . 1 6 6 9 1 9 1 1 9 1 8 1 1 8 1 6 4 0 . 0 3 1 8 7 0 . 1 7 6 8 2 0 1 1 9 1 9 1 1 8 1 6 4 2 . 1 8 3 2 9 0 . 0 9 5 8 2 0 1 2 0 1 9 1 1 9 1 6 4 1 . 7 8 6 6 6 0 . 1 6 1 8 2 1 1 2 0 2 0 1 1 9 1 6 4 3 . 6 7 0 4 4 0 . 0 9 0 4 2 1 1 2 1 2 0 1 2 0 1 6 4 3 . 6 0 4 7 4 0 . 2 5 0 9 2 2 1 2 1 2 1 1 2 0 1 6 4 5 . 1 6 3 1 3 0 . 0 7 5 3 2 2 1 2 2 2 1 1 2 1 1 6 4 5 . 5 0 6 7 8 0 . 1 0 7 6 2 3 1 2 2 2 2 1 2 1 1 6 4 6 . 7 4 6 7 8 0 . 0 6 3 1 2 3 1 2 3 2 2 1 2 2 1 6 4 7 . 5 1 9 3 2 0 . 0 8 2 2 2 4 1 2 3 2 3 1 2 2 1 6 4 8 . 3 5 4 4 3 0 . 0 4 8 8 3 2 1 2 2 0 1 6 1 3 . 9 5 2 7 0 0 . 1 1 2 9 / 110 j 1 K * K : a c j " K " K : CL C Freq.(cm~ 1) Intensity3 3 2 2 2 2 1 1613.93372 0.1032 4 2 2 3 2 1 1615.70306 0.2321 4 2 3 3 2 2 1615.65795 0.4488 5 2 3 4 2 2 1617.47266 0.3107 5 2 4 4 2 3 - 1617.38810 0.3372 6 2 4 5 2 3 1619.25035 0.3556 6 2 5 5 2 4 1619.11887 0.4494 7 2 5 6 2 4 1620.98313 0.3019 7 2 6 6 2 5 1620.84345 0.9063 8 2 6 7 2 5 1623.10135 0.3113 8 2 7 7 2 6 1622.57130 0.4496 9 2 7 8 2 6 1624.87091 0.1711 9 2 8 8 2 7 1624.28737 0.5810 10 2 8 9 2 7 1626.68268 0.3723 10 2 9 9 2 8 1625.99392 0.4636 11 2 9 10 2 8 1628.49001 0.4248 11 2 10 10 2 9 1627.68943 0.4280 12 2 10 11 2 9 1630.27732 0.6433 12 2 11 11 2 10 1629.37183 0.4569 13 2 11 12 2 10 1632.03341 0.3799 13 2 12 12 2 11 1631.04173 0.4723 14 2 12 13 2 11 1633.75427 0.3360 14 2 13 13 2 12 1632.69743 0.4039 15 2 13 14 2 12 1635.43557 0.3004 15 2 14 14 2 13 1634.34006 0.3132 16 2 14 15 2 13 1637.07430 0.2350 16 2 15 15 2 14 1635.96710 0.5458 17 2 15 16 2 14 1638.67128 0.2321 17 2 16 16 2 15 1637.57248 0.1714 18 2 16 17 2 15 1640.22473 0.1615 18 2 17 17 2 16 1639.09725 0.1490 19 2 17 18 2 16 1641.73573 0.1589 19 2 18 18 2 17 1641.01262 0.1167 20 2 18 19 2 17 1643.20566 0.3870 21 2 19 20 2 18 1644.63584 0.1167 21 2 20 20 2 19 1644.33937 0.0974 22 2 20 21 2 19 1646.02986 0.1184 23 2 21 22 2 20 1647.53093 0.0746 4 3 2 3 3 1 1615.16065 0.1474 5 3 2 4 3 1 1616.98418 0.1918 5 3 3 4 3 2 1616.98418 0.1918 6 3 4 5 3 3 1618.80409 0.1449 7 3 4 6 3 3 1620.63445 0.1285 7 3 5 6 3 4 1620.62302 0.1201 8 3 5 7 3 4 1622.45686 0.1606 / 111 J' K' K' J" K" K" a C Freq.(cm" 1) Intensity9 8 3 6 7 3 5 1622.43569 0.1181 9 3 6 8 3 5 1624.27312 0.1114 9 3 7 8 3 6 1624.23731 0.1748 10 3 7 9 3 6 1626.08091 0.1667 10 3 8 9 3 7 1626.02429 0.1445 11 3 8 10 3 7 1627.87690 0.1750 11 3 9 10 3 8 1627.79317 0.1863 12 3 9 11 3 8 1629.65934 0.1718 12 3 10 11 3 9 1629.54185 0.1741 13 3 10 12 3 9 1631.41683 0.1740 13 3 11 12 3 10 1631.26961 0.2053 14 3 11 13 3 10 1633.17285 0.1444 14 3 12 13 3 11 1632.97470 0.1829 15 3 12 14 3 11 1634.93424 0.1097 15 3 13 14 3 12 1634.65650 0.1074 16 3 13 15 3 12 1636.59992 0.1213 16 3 14 15 3 13 1636.31475 0.1665 17 3 14 16 3 13 1638.27363 0.0923 17 3 15 16 3 14 1637.95080 0.1480 18 3 15 17 3 14 1639.91517 0.0785 18 3 16 • 17 3 15 1639.56451 0.1723 19 3 16 18 3 15 1641.52134 0.0645 19 3 17 18 3 16 1641.15815 0.1772 20 3 17 19 3 16 1643.09020 0.0381 20 3 18 19 3 17 1642.73121 0.0847 21 3 18 20 3 17 1644.62208 0.0922 21 3 19 20 3 18 1644.28402 0.0470 22 3 19 21 3 18 1646.10936 0.0790 22 3 20 21 3 19 1645.78259 0.3468 23 3 20 22 3 19 1647.55773 0.0825 23 3 21 22 3 20 1647.20276 0.0663 5 4 2 4 4 1 1615.67840 0.1358 6 4 3 5 4 2 1617.11019 0.2248 7 4 4 6 4 3 1618.53250 0.3170 8 4 5 7 4 4 1619.95037 0.3358 9 4 5 8 4 4 1621.37158 0.1987 9 4 6 8 4 5 1621.36101 0.4085 10 4 6 9 4 5 1622.79258 0.2182 10 4 7 9 4 6 1622.77529 0.2463 11 4 7 10 4 6 1624.21923 0.0373 11 4 8 10 4 7 1624.18747 0.0386 12 4 8 11 4 7 1625.64985 0.1938 12 4 9 11 4 8 1625.60070 0.2436 13 4 9 12 4 8 1627.08548 0.1814 13 4 10 12 4 9 1627.01190 0.2527 / 112 j 1 K ' K : a c j " K " K ; a c Freq.(cm" 1) Intensity3 14 4 11 13 4 10 1628.42043 0.4419 15 4 11 14 4 10 1629.96920 0.0522 15 4 12 14 4 11 1629.82356 0.1844 16 4 13 15 4 12 1631.22006 0.1314 17 4 13 16 4 12 1632.86730 0.1371 17 4 14 16 4 13 1632.60584 0.1420 18 4 14 17 4 13 1634.30999 0.1347 18 4 15 17 4 14 1633.97683 0.1750 19 4 15 18 4 14 1635.74916 0.0883 19 4 16 18 4 15 1635.32962 0.0858 20 4 16 19 4 15 1637.17682 0.0848 20 4 17 19 4 16 1636.65976 0.0850 21 4 17 20 4 16 1638.57932 0.1454 21 4 18 20 4 17 1637.96118 0.0551 22 4 18 21 4 17 1639.72959 0.3646 22 4 19 21 4 18 1639.11345 0.1490 7 6 2 6 6 1 1616.45057 0.0471 8 6 3 7 6 2 1617.98526 0.1441 9 6 4 8 6 3 1619.92845 0.1014 10 6 5 • 9 6 4 1621.43635 0.1848 11 6 6 10 6 5 1623.00919 0.5724 12 6 7 11 6 6 1624.59179 0.2077 13 6 8 12 6 7 1626.17257 0.2547 14 6 9 13 6 8 1627.75006 0.2522 15 6 10 14 6 9 1629.32224 0.3041 16 6 11 15 6 10 1630.89339 0.1387 18 6 13 17 6 12 1634.06736 0.1139 1 0 1 2 0 2 1605.89854 0.1436 2 0 2 3 0 3 1604.25054 0.4399 3 0 3 4 0 4 1602.62152 0.3582 4 0 4 5 0 5 1601.01203 0.3597 5 0 5 6 0 6 1599.41904 0.3797 6 0 6 7 0 7 1597.83570 0.6568 7 0 7 8 0 8 1596.25702 0.6055 8 0 8 9 0 9 1594.69000 0.5368 9 0 9 10 0 10 1593.13906 0.6021 10 0 10 , 11 0 11 1591.60698 0.7244 11 0 11 12 0 12 1590.09745 0.6147 12 0 12 13 0 13 1588.60530 0.5728 13 0 13 14 0 14 1587.13066 0.5326 14 0 14 15 0 15 1585.67153 0.6921 15 0 15 16 0 16 1584.22882 0.5255 16 0 16 17 0 17 1582.80529 0.4776 .17 0 17 18 0 18 1581.40360 0.0393 18 0 18 19 0 19 1580.02851 0.3648 / 113 j ' K ' K : a c J" K " K " a c Freq.(cm" Intensity3 19 0 19 20 0 20 1578.68972 0.3115 20 0 20 21 0 21 1577.39648 0.2681 21 0 21 22 0 22 1576.16402 0.3288 22 0 22 23 0 23 1575.00795 0.2151 23 0 23 24 0 24 1573.94674 0.0931 24 0 24 25 0 25 1572.99694 0.0696 25 0 25 26 0 26 1572.16471 0.0686 2 1 1 3 1 2 1603.91333 0.1424 2 1 2 3 1 3 1604.35612 0.1295 3 1 2 4 1 3 1602.19892 0.1831 3 1 3 4 1 4 1602.77845 0.1863 4 1 3 5 1 4 1600.49753 0.2143 4 1 4 5 1 5 1601.20540 0.0832 5 1 4 6 1 5 1598.80864 0.2855 5 1 5 6 1 6 1599.65398 0.2702 6 1 5 7 1 6 1597.06246 0.3100 6 1 6 7 1 7 1598.10649 0.4201 7 1 6 8 1 7 1595.46058 0.5526 7 1 7 8 1 8 1596.56932 0.3291 8 1 7 9 1 8 1593.79723 0.2765 8 1 8 9 1 9 1595.04068 0.3365 9 1 8 10 1 9 1592.14243 0.2579 9 1 9 10 1 10 1593.52137 0.3727 10 1 9 11 1 10 1590.49536 0.4070 10 1 10 11 1 11 1592.01125 0.4248 11 1 10 12 1 11 1588.85629 0.3076 11 1 11 12 1 12 1590.51059 0.3975 12 1 11 13 1 12 1587.22678 0.3139 12 1 12 13 1 13 1589.01963 0.0536 13 1 12 14 1 13 1585.60730 0.2845 13 1 13 14 1 14 1587.54033 0.3855 14 1 13 15 1 14 1583.99872 0.2394 14 1 14 15 1 15 1586.07291 0.3203 15 1 14 16 1 15 1582.40314 0.2460 15 1 15 16 1 16 1584.62035 0.3447 16 1 15 17 1 16 1580.82138 0.1989 16 1 16 17 1 17 1583.18653 0.3533 17 1 16 18 1 17 1579.25323 0.1946 17 1 17 18 1 18 1581.77414 0.3125 18 1 17 19 1 18 1577.69970 0.1564 18 1 18 19 1 19 1580.39329 0.1902 19 1 18 20 1 19 1576.16402 0.3288 19 1 19 20 1 20 1579.04931 0.1368 20 1 19 21 1 20 1574.64804 0.1443 20 1 20 21 1 21 1577.75504 0.1250 / 114 J' K' K' a c J" K" K" a C Freq.(cm" ^) Intensity3 21 1 20 22 1 21 1573.15769 0.0893 21 1 21 22 1 22 1576.52676 0.1095 22 1 21 23 1 22 1571.67062 0.0678 22 1 22 23 1 23 1575.38481 0.0738 23 1 22 24 1 23 1570.26887 0.0790 23 1 23 24 1 24 1574.35452 0.0577 24 1 23 25 1 24 1568.88383 0.0552 3 2 1 4 2 2 1602.13244 0.4098 3 2 2 4 2 3 1602.17815 0.2282 4 2 2 5 2 3 1600.45982 0.3065 4 2 3 5 2 4 1600.55427 0.3041 5 2 3 6 2 4 1598.77418 0.3512 5 2 4 6 2 5 1598.94198 0.3915 6 2 4 7 2 5 1597.06246 0.3100 6 2 5 7 2 6 1597.33975 0.3914 7 2 5 8 2 6 1595.27158 0.3750 7 2 6 8 2 7 1595.74617 0.4254 8 2 6 9 2 7 1593.83533 0.3540 8 2 7 9 2 8 1594.15979 0.5143 9 2 7 10 2 8 1592.02911 0.4925 9 2 8 10 2 9- 1592.57954 0.4932 10 2 8 11 2 9 1590.25482 ' 0.4907 10 2 9 11 2 10 1591.00410 0.4121 11 2 9 12 2 10 1588.47723 0.4850 11 2 10 12 2 11 1589.43305 0.3550 12 2 10 13 2 11 1586.69137 0.4909 12 2 11 13 2 12 1587.86642 0.4638 13 2 11 14 2 12 1584.89760 0.5076 13 2 12 14 2 13 1586.30428 0.5012 14 2 12 15 2 13 1583.09563 0.3422 14 2 13 15 2 14 1584.74653 0.3732 15 2 13 16 2 14 1581.28981 0.4054 15 2 14 16 2 15 1583.19331 0.2923 16 2 14 17 2 15 1579.48193 0.2987 16 2 15 17 2 16 1581.64475 0.3411 17 2 15 18 2 16 1577.67595 0.3956 17 2 16 18 2 17 1580.08833 0.3156 18 2 16 19 2 17 1575.87453 0.1890 18 2 17 19 2 18 1578.47089 0.2312 19 2 17 20 2 18 1574.08527 0.1976 19 2 18 20 2 19 1577.25904 0.1260 20 2 18 21 2 19 1572.30969 0.1618 22 2 20 23 2 21 1568.81606 0.1007 5 3 3 6 3 4 1598.46930 0.4167 6 3 4 7 3 5 1596.91135 0.1341 / 115 J" K. a c Freq.(cm" 1) Intensity3 7 3 4 8 3 5 1595.32858 0.1478 7 3 5 8 3 6 1595.35033 0.1731 8 3 5 9 3 6 1593.73906 0.1954 8 3 6 9 3 7 1593.78114 0.2314 9 3 6 10 3 7 1592.12514 0.1295 9 3 7 10 3 8 1592.19828 0.1626 10 3 7 11 3 8 1590.48070 0.2846 10 3 8 11 3 9 1590.60132 0.1878 11 3 8 12 3 9 1588.79450 0.4484 11 3 9 12 3 10 1588.98812 0.2835 12 3 9 13 3 10 1587.06931 0.1514 12 3 10 13 3 11 1587.36035 0.1734 13 3 10 14 3 11 1585.29241 0.1468 13 3 11 14 3 12 1585.71615 0.1926 14 3 11 15 3 12 1583.46354 0.3088 14 3 12 15 3 13 1584.05663 0.1998 15 3 12 16 3 13 1581.61964 0.0652 15 3 13 16 3 14 1582.38861 0.1398 16 3 13 17 3 14 1579.65531 0.0911 16 3 14 17 3 15 1580.70812 0.1332 17 3 14 18 3 15 1577.68444 0.0787 17 3 15 18 3 16 1579.02193 0.1054 18 3 15 19 3 16 1575.67842 0.0721 18 3 16 19 3 17 1577.32947 0.1407 19 3 16 20 3 17 1573.64651 0.0924 19 3 17 20 3 18 1575.63395 0.0687 20 3 17 21 3 18 1571.59892 0.0676 20 3 18 21 3 19 1573.93879 0.0769 21 3 18 22 3 19 1569.54229 0.0640 21 3 19 22 3 20 1572.24300 0.0740 22 3 19 23 3 20 1567.48479 0.0410 22 3 20 23 3 21 1570.51794 0.0387 23 3 20 24 3 21 1565.43085 0.0709 23 3 21 24 3 22 1568.72566 0.0633 5 4 2 6 4 3 1597.17769 0.2995 6 4 3 7 4 4 1595.23802 0.4751 7 4 4 8 4 5 1593.28580 0.6909 8 4 5 9 4 6 1591.32422 0.5804 9 4 5 10 4 6 1589.35430 0.3329 9 4 6 10 4 7 1589.35430 0.3329 10 4 6 11 4 7 1587.38059 - 0.2530 10 4 7 11 4 8 . 1587.38059 0.2530 11 4 7 12 4 8 1585.41798 0.2190 11 "4 8 12 4 9 1585.40098 0.2279 12 4 9 13 4 10 1583.41735 0.3103 / 116 J' K- K' J" K" K" o C Freq.(cm" ') Intensity3 13 4 9 14 4 10 1581.45925 0.0482 13 4 10 14 4 11 1581.42629 0.2059 14 4 11 15 4 12 1579.43174 0.2167 15 4 11 16 4 12 1577.46562 0.1743 15 4 12 16 4 13 1577.42876 0.2304 16 4 13 17 4 14 1575.41730 0.2061 17 4 13 18 4 14 1573.40740 0.2024 17 4 14 18 4 15 1573.40740 0.2024 18 4 14 19 4 15 1571.34005 0.1332 18 4 15 19 4 16 1571.35887 0.1704 19 4 15 20 4 16 1569.23766 0.1380 19 4 16 20 4 17 1569.30885 0.1374 20 4 16 21 4 17 1567.09012 0.0845 20 4 17 21 4 18 1567.24209 0.0898 21 4 17 22 4 18 1564.88727 0.0625 21 4 18 22 4 19 1565.15551 0.0939 22 4 18 23 4 19 1562.40008 0.0557 22 4 19 23 4 20 1562.93048 0.0687 6 6 1 7 6 2 1592.99688 0.1029 7 6 2 . 8 6 3 1591.23536 0.1614 8 6 3 . 9 6 4 1589.40391 0.1916 9 6 4 10 6 5 1587.97875 0.1139 10 6 5 11 6 6 1586.11503 0.3122 11 6 6 12 6 7 1584.31778 0.2611 12 6 7 13 6 8 1582.52512 0.2303 13 6 8 14 6 9 1580.72925 0.2768 14 6 9 15 6 10 1578.92695 0.2351 15 6 10 16 6 11 1577.11733 0.2238 16 6 11 17 6 12 1575.30177 0.1948 18 6 13 19 6 14 1571.69486 0.0678 2 1 1 2 1 2 1609.64100 0.1326 3 2 1 3 2 2 1608.91711 0.1837 3 2 2 3 2 1 1608.87140 0.2977 4 2 2 4 2 3 1609.01053 0.1339 4 2 3 4 2 2 1608.87140 0.2977 5 2 3 5 2 4 1609.15428 0.0852 5 2 4 5 2 3 1608.83664 0.1010 6 2 4 6 2 5 1609.35599 0.0673 6 2 5 6 2 4 1608.73842 0.0919 7 2 5 7 2 6 1609.58451 0.0665 8 2 6 8 2 7 1610.29375 0.1241 8 2 7 8 2 6 1608.25888 0.0710 11 2 10 11 2 9 1606.51098 0.3133 12 2 11 12 2 10 1605.60508 0.0957 13 2 12 13 2 11 1604.53456 0.6075 / 117 J' K a J" K£ K£ Freq.(cm-1) Intensity3 15 2 14 15 2 13 1601.91270 0.0559 5 3 3 5 3 2 1608.56857 0.1261 6 3 4 6 3 3 1608.69411 0.0717 7 3 4 7 3 5 1608.85090 0.4143 7 3 5 7 3 4 1608.81388 0.1010 8 3 5 8 3 6 1608.99450 0.0909 10 3 7 10 3 8 1609.29696 0.0408 12 3 10 12 3 9 1608.87140 0.2977 18 3 15 18 3 16 1607.90003 0.0510 5 4 2 5 4 1 1607.27057 0.6200 6 4 3 6 4 2 1607.01735 0.4781 9 4 5 9 4 6 1606.21453 0.0881 9 4 6 9 4 5 1606.20326 0.1118 10 4 6 10 4 7 1605.94355 0.1605 10 4 7 10 4 6 1605.92019 0.0745 11 4 7 11 4 8 1605.67757 0.0690 11 4 8 11 4 7 1605.63428 0.0811 13 4 9 13 4 10 1605.16144 0.0641 14 4 11 14 4 10 1604.71748 0.0379 15 4 11 15 4 12 1604.68443 0.4899 15 4 12 15 4 11 1604.37703 0.0398 6 6 1 6 6 0 1604.76191 0.5343 7 6 2 7 6 1 , 1604.68443 0.4899 8 6 3 8 6 2 1604.53456 0.6075 9 6 4 9 6 3 1604.79558 0.1222 10 6 5 10 6 4 1604.61908 0.1917 11 6 6 11 6 5 1604.50785 0.3482 12 6 7 12 6 6 1604.40227 0.1394 13 6 8 13 6 7 1604.29590 0.1161 14 6 9 14 6 8 1604.18373 0.0839 15 6 10 15 6 9 1604.06633 0.0641 J' K a J" K a K£ Freq.(cm-1) Intensity3 1 0 1 0 0 0 1627.18457 0.1025 2 0 2 1 0 1 1628.86923 0.0749 3 0 3 2 0 2 1630.55015 0.1105 4 0 4 3 0 3 1632.22163 0.1446 5 0 5 4 0 4 1633.88399 0.1895 6 0 6 5 0 5 1635.54044 0.2415 / 118 J' K- K' J" K'a K£ Freq.(cm" 1) Intensity3 7 0 7 6 0 6 1637.23962 0.1962 8 0 8 7 0 7 1638.54617 0.1740 9 0 9 8 0 8 1640.18752 0.3316 10 0 10 9 0 9 1641.76849 0.4464 11 0 11 10 0 10 1643.33147 0.3860 12 0 12 11 0 11 1644.89132 0.2782 13 0 13 12 0 12 1646.45594 0.2831 14 0 14 13 0 13 1648.02376 0.0434 15 0 15 14 0 14 1649.62972 0.2777 16 0 16 15 0 15 1651.26294 0.3132 17 0 17 16 0 16 1652.97230 0.3366 18 0 18 17 0 17 1654.68432 0.0839 19 0 19 18 0 18 1656.48095 0.1282 20 0 20 19 0 19 1658.64722 0.1399 2 1 1 1 1 0 1628.87348 0.0749 3 1 2 2 1 1 1630.65378 0.0634 4 1 3 3 1 2 1632.42607 0.0780 5 1 4 4 1 3 1634.19849 0.1088 5 1 5 4 1 4 1633.82473 0.0572 6 1 5 5 1 4 1635.96710 0.5458 6 1 6 5 1 5 1635.26312 0.0470 7 1 6 6 1 5 1637.72517 0.1701 7 1 7 6 1 6 1636.62893 0.1521 8 1 7 7 1 6 1639.46825 0.1829 8 1 8 7 1 7 1638.10092 0.1200 9 1 8 8 1 7 1641.18588 0.1772 9 1 9 8 1 8 1639.83063 0.1483 10 1 9 9 1 8 1642.85717 0.1745 10 1 10 9 1 9 1641.42429 0.1702 11 1 10 10 1 9 1644.44173 0.1644 11 1 11 10 1 10 1643.01358 0.1676 12 1 11 11 1 10 1645.92970 0.0571 12 1 12 11 1 11 1644.59943 0.1848 13 1 12 12 1 11 1647.43850 0.1827 13 1 13 12 1 12 1646.18238 0.2357 14 1 13 13 1 12 1648.95518 0.1903 14 1 14 13 1 13 1647.76501 0.1674 15 1 14 14 1 13 1650.40667 0.0707 15 1 15 14 1 14 1649.34814 0.2208 16 1 15 15 1 14 1651.66855 0.0618 16 1 16 15 1 15 1650.92310 0.3272 17 1 16 16 1 15 1652.81318 0.0726 17 1 17 16 1 16 1.652.52005 0.1457 18 1 17 17 1 16 1653.94146 0.0806 18 1 18 17 1 17 1654.11305 0.1657 / 119 J' K' K' J" Freq.(cm~ 1) Intensity3 19 1 18 18 1 17 1655.17488 0.0528 19 1 19 18 1 18 1655.71234 0.1905 20 1 19 19 1 18 1656.27507 0.0926 20 1 20 19 1 19 1657.31952 0.1073 21 1 20 20 1 19 1657.35760 0.0673 21 1 21 20 1 20 1658.93670 0.0976 22 1 22 21 1 21 1660.55739 0.1128 23 1 23 22 1 22 1662.21139 0.1232 3 2 2 2 2 1 1629.99295 0.0522 4 2 2 3 2 1 1631.74845 0.4532 4 2 3 3 2 2 1631.69906 0.1212 5 2 3 4 2 2 1633.50988 0.2545 5 2 4 4 2 3 1633.40920 0.3109 6 2 4 5 2 3 1635.29504 0.1937 6 2 5 5 2 4 1635.11876 0.2002 7 2 5 6 2 4 1637.10698 0.2322 7 2 6 6 2 5 1636.82969 0.2661 8 2 6 7 2 5 1638.94201 0.2785 8 2 7 7 2 6 1638.53877 0.3530 9 2 7 8 2 6 1640.79611 0.2912 9 2 8 8 2 7 1640.24421 0.2395 10 2 8 9 2 7 1642.66061 0.3804 10 2 9 9 2 8 1641.94443 0.3494 11 2 9 10 2 8 1644.52671 0.3095 11 2 10 10 2 9 1643.63799 0.2870 12 2 10 11 2 9 1646.38727 0.6129 12 2 11 11 2 10 1645.32335 0.3288 13 2 11 12 2 10 1648.23197 0.4635 13 2 12 12 2 11 1646.99991 0.2935 14 2 12 13 2 11 1650.05338 0.3544 14 2 13 13 2 12 1648.66652 0.4080 15 2 13 14 2 12 1651.84514 0.7106 15 2 14 14 2 13 1650.32276 0.2910 16 2 14 15 2 13 1653.58928 0.3763 16 2 15 15 2 14 1651.96887 0.3698 17 2 15 16 2 14 1655.26850 0.3081 17 2 16 16 2 15 1653.60565 0.3769 18 2 16 17 2 15 1656.80048 0.2445 18 2 17 17 2 16 1655.23461 0.2891 19- 2 18 . 18 2 17 1656.85648 0.2406 20 2 18 19 2 17 1660.69357 0.1975 20 2 19 19 2 18 1658.47355 0.2549 21 2 19 20 2 18 1662.08215 0.1937 21 2 20 20 2 19 1660.08923 0.2108 22 2 20 21 2 19 1663.50219 0.1966 / 120 J' K' K ' j " K " K ; a C Freq.(cm" 1) Intensity9 22 2 21 21 2 20 1661.70545 0.1852 23 2 21 22 2 20 1664.89749 0.1713 23 2 22 22 2 21 1663.32549 0.1794 24 2 22 23 2 21 1666.26858 0.1386 24 2 23 23 2 22 1664.95166 0.1630 25 2 23 24 2 22 1667.62772 0.1196 25 2 24 24 2 23 1666.59036 0.1331 26 2 24 25 2 23 1668.99195 0.2657 26 2 25 25 2 24 1668.24423 0.1360 27 2 25 26 2 24 1670.38344 0.0964 27 2 26 26 2 25 1669.91885 0.0931 8 3 6 7 3 5 1638.03591 0.3861 9 3 6 8 3 5 1639.94278 0.2250 9 3 7 8 3 6 1639.88202 0.1479 10 3 7 9 3 6 1641.76849 0.4464 10 3 8 9 3 7 1641.66299 0.1298 11 3 8 10 3 7 1643.61336 0.2036 11 3 9 10 3 8 1643.43503 0.1773 12 3 9 11 3 8 1645.47463 0.1864 12 3 10 11 3 9 1645.16311 0.0753 13 3 10 12 3 9 1647.35450 0.2194 13 3 11 12 3 10 1646.82878 0.1607 14 3 11 13 3 10 1649.24992 0.1660 15 3 12 14 3 11 1651.15927 0.2314 15 3 13 14 3 12 1650.97601 0.1597 16 3 13 15 3 12 1653.07685 0.1771 16 3 14 15 3 13 1652.64803 0.1676 17 3 14 16 3 13 1654.99755 0.2008 17 3 15 16 3 14 1654.36690 0.1591 18 3 15 17 3 14 1656.91078 0.2037 18 3 16 17 3 15 1656.09352 0.1783 19 3 16 18 3 15 1658.80654 0.1493 19 3 17 18 3 16 1657.81428 0.1624 20 3 17 19 3 16 1660.65548 0.1873 20 3 18 19 3 17 1659.52611 0.1516 21 3 18 20 3 17 1662.58097 0.2795 21 3 19 20 3 18 1661.22620 0.1126 22 3 19 21 3 18 1664.32023 0.1114 22 3 20 21 3 19 1662.91535 0.2884 23 3 20 22 3 19 1666.01094 0.0958 23 3 21 22 3 20 1664.59103 0.0980 24 3 22 23 3 21 . 1666.25610 0.0890 25 3 23 24 3 22 1667.91079 0.0865 26 3 24 25 3 23 1669.55117 0.0556 5 4 2 4 4 1 1631.97166 0.1162 / 121 J * K ' K ; a c J " K " K ; Freq.(cm" ') Intensity3 6 4 3 5 4 2 1633.81133 0.2469 7 4 4 6 4 3 1635.67218 0.1923 8 4 5 7 4 4 1637.55213 0.2328 9 4 6 8 4 5 1639.44788 0.2571 10 4 7 9 4 6 1641.35443 0.3165 11 4 8 10 4 7 1643.27020 0.5009 12 4 8 11 4 7 1644.84702 0.2485 12 4 9 11 4 8 1645.18730 0.4692 13 4 9 12 4 8 1646.84090 0.2856 13 4 10 12 4 9 1647.10393 0.3324 14 4 10 13 4 9 1648.78507 0.2796 14 4 11 13 4 10 1649.01400 0.3018 15 4 11 14 4 10 1650.71282 0.2323 15 4 12 14 4 11 1650.91479 0.3272 16 4 12 15 4 11 1652.63208 0.2954 16 4 13 15 4 12 1652.80315 0.3115 17 4 13 16 4 12 1654.54605 0.3928 17 4 14 16 4 13 1654.67536 0.3257 18 4 14 17 4 13 1656.45738 0.2577 18 4 15 17 4 14 1656.53388 0.3132 19 4 15 18 4 14 1657.62011 0.0957 19 4 16 18 4 15 1658.37562 0.1642 20 4 16 19 4 15 1660.27382 0.2190 20 4 17 19 4 16 1660.20022 0.2097 21 4 17 20 4 16 1662.18008 0.1765 21 4 18 20 4 17 1662.00986 0.1752 22 4 18 21 4 17 1664.08527 0.1736 22 4 19 21 4 18 1663.80224 0.1945 23 4 19 22 4 18 1665.98861 0.1352 23 4 20 22 4 19 1665.57826 0.1622 24 4 20 23 4 19 1667.88611 0.1553 24 4 21 23 4 20 1667.33907 0.8084 25 4 21 24 4 20 1669.77693 0.1212 25 4 22 24 4 21 1669.08290 0.1181 26 4 22 25 4 21 1671.65276 0.0860 26 4 23 25 4 22 1670.96410 0.0966 27 4 23 26 4 22 1673.50698 0.0830 28 4 24 27 4 23 1675.33114 0.0571 7 5 3 6 5 2 1635.27081 0.1976 8 5 4 7 5 3 1637.41909 0.1879 9 5 5 8 5 4 1639.54681 0.2209 10 5 6 9 5 5 1641.65367 0.2585 11 5 7 10 5 6 1643.73862 0.3235 12 5 8 11 5 7 1645.80183 0.3468 13 5 9 12 5 8 1647.84103 0.2533 / 122 j* K ' K : a c J" K " K " d C Freq.(cm" 1) Intensity3 14 5 10 13 5 9 1649.85671 0.2815 15 5 11 14 5 10 1651.84514 0.7106 16 5 12 15 5 11 1653.81643 0.2053 17 5 13 16 5 12 1655.75905 0.1550 18 5 13 17 5 12 1657.68657 0.0736 18 5 14 17 5 13 1657.67814 0.1141 19 5 14 18 5 13 1659.58717 0.1315 19 5 15 18 5 14 1659.57416 0.0939 20 5 15 19 5 14 1661.46579 0.1019 20 5 16 19 5 15 1661.45034 0.1032 8 6 3 7 6 2 1634.04377 0.2684 9 6 4 8 6 3 1635.38353 0.1586 10 6 5 9 6 4 1636.78187 0.2331 11 6 6 10 6 5 1638.22769 0.2336 12 6 7 11 6 6 1639.70618 0.1978 13 6 8 12 6 7 1641.21369 0.1629 14 6 9 13 6 8 1642.74810 0.1833 15 6 10 14 6 9 1644.30434 0.2045 16 6 11 15 6 10 1645.88146 0.3949 17 6 12 16 6 11 1647.48085 , 0.1521 18 6 13 17 6 12 1649.09760 0.0906 19 6 14 18 6 1.3 1650.74154 0.0673 20 6 15 19 6 14 1652.41213 0.0525 11 7 5 10 7 4 1640.04489 0.1009 12 7 6 11 7 5 1641.56413 0.1478 13 7 7 12 7 6 1643.14551 0.1550 14 7 8 13 7 7 1644.75898 0.1463 15 7 9 14 7 8 1646.38727 0.6129 16 7 10 15 7 9 1648.03085 0.4621 17 7 11 16 7 10 1649.67885 0.1461 18 7 12 17 7 11 1651.33589 0.1159 19 7 13 18 7 12 1653.04166 0.0837 20 7 14 19 7 13 1654.69520 0.0454 21 7 15 20 7 14 1656.35057 0.1014 22 7 16 21 7 15 1658.03962 0.0790 23 7 17 22 7 16 1659.74118 0.0500 24 7 18 23 7 17 1661.43144 0.0478 9 8 2 8 8 1 1634.93424 0.1097 10 8 2 9 8 1 1636.37099 0.1205 11 8 4 10 8 3 1637.78162 0.1886 12 8 4 11 8 3 1639.13201 0.1778 13 8 6 12 8 5 1640.40623 0.1354 14 8 6 13 8 5 1641.59046 0.1272 15 8 8 14 8 7 1642.67037 0.0976 16 8 8 15 8 7 1643.63185 0.1290 / 123 J' K' K' J" K" K" a c Freq.(cm" ') Intensity3 17 8 10 16 8 9 1644.47023 0.1070 18 8 10 17 8 9 1645.18730 0.4692 19 8 12 18 8 11 1645.79131 0.3468 14 10 4 13 10 3 1641.70188 0.1123 15 10 6 14 10 5 1643.19229 0.1211 16 10 6 15 10 5 1644.66190 0.0823 17 10 8 16 10 7 1646.10936 0.0790 18 10 8 17 10 7 1647.61938 0.0776 1 0 1 2 0 2 1622.14855 0.0968 2 0 2 3 0 3 1620.49296 0.1314 3 0 3 4 0 4 1618.85492 0.5952 4 0 4 5 0 5 1617.24260 0.1887 5 0 5 6 0 6 1615.65795 0.4488 6 0 6 7 0 7 1614.11310 0.1936 7 0 7 8 0 8 1612.65525 0.3364 8 0 8 9 0 9 1610.84944 0.3150 9 0 9 10 0 10 1609.41498 0.5128 10 0 10 11 0 11 1607.94740 0.4507 11 0 11 12 0 12 1606.48046 0.6247 12 0 12 13 0 13 1605.01927 0.2803 13 0 13 14 0 14 1603.56624 0.3099 14 0 14 15 0 15 1602.11575 0.0537 15 0 15 16 0 16 1600.70334 0.2933 16 0 16 17 0 17 1599.31303 0.6124 17 0 17 18 0 18 1597.99508 0.2596 18 0 18 19 0 19 1596.67672 0.0281 19 0 19 20 0 20 1595.43689 0.1862 20 0 20 21 0 21 1594.57311 0.0743 2 1 1 3 1 2 1620.09971 0.0577 3 1 2 4 1 3 1618.36838 0.0527 4 1 3 5 1 4 1616.64771 0.1187 5 1 4 6 1 5 1614.93629 0.1472 5 1 5 6 1 6 1616.24716 0.0429 6 1 5 7 1 6 1613.23837 0.2525 6 1 6 7 1 7 1614.51503 0.0488 7 1 6 8 1 7 1611.55142 0.1902 7 1 7 8 1 8 1612.72529 0.1685 8 1 7 9 1 8 1609.87215 0.1744 8 1 8 9 1 9 1611.05220 0.1531 9 1 8 10 1 9 1608.19743 0.1789 9 1 9 10 1 10 1609.64961 0.1326 10 1 9 11 1 10 1606.51098 0.3133 10 1 10 11 1 11 1608.12329 0.1933 11 1 10 12 1 11 1604.77925 0.2868 11 1 11 12 1 12 1606.60393 0.1618 / 124 J ' K - K' J " K a c Freq.(cm" 1) Intensity3 12 1 11 13 1 12 1602.99679 0.1747 12 1 12 13 1 13 1605.09226 0.1643 13 1 12 14 1 13 1601.28275 0.0723 13 1 13 14 1 14 1603.58681 0.2297 14 1 13 15 1 14 1599.62973 0.0878 14 1 14 15 1 15 1602.09008 0.1471 15 1 14 16 1 15 1597.96297 0.2108 15 1 15 16 1 16 1600.60002 0.2187 16 1 15 17 1 16 1596.14954 0.1071 16 1 16 17 1 17 1599.11837 0.1396 17 1 16 18 1 17 1594.25678 0.1071 17 1 17 18 1 18 1597.64528 0.2379 18 1 17 19 1 18 1592.37906 0.1042 18 1 18 19 1 19 1596.18275 0.1966 19 1 18 20 1 19 1590.62179 0.0833 19 1 19 20 1 20 1594.72960 0.1437 20 1 19 21 1 20 1588.74423 0.1332 20 1 20 21 1 21 1593.28580 0.6909 21 1 20 22 1 21 1586.84336 0.0553 21 1 21 22 1 22 1591.85490 0.3514 22 1 22 23 1 23 1590.44280 0.0882 23 1 23 24 1 24 1589.04878 0.1424 3 2 2 4 2 3 1618.23738 0.0937 4 2 2 5 2 3 1616.50512 0.1377 4 2 3 5 2 4 1616.59378 0.1458 5 2 3 6 2 4 1614.81101 0.1979 5 2 4 6 2 5 1614.96187 0.1779 6 2 4 7 2 5 1613.10741 0.2450 6 2 5 7 2 6 1613.34027 0.2513 7 2 5 8 2 6 1611.39500 0.3042 7. 2 6 8 2 7 1611.72917 0.2525 8 2 6 9 2 7 1609.67573 0.3294 8 2 7 9 2 8 1610.12791 0.3410 9 2 7 10 2 8 1607.95387 0.2759 9 2 8 10 2 9 1608.53655 0.3144 10 2 8 11 2 9 / 1606.23212 0.4456 10 2 9 11 2 10 1606.95453 0.3325 11 2 9 12 2 10 1604.51440 0.4167 11 2 10 12 2 11 1605.38192 0.3275 12 2 10 13 2 11 1602.80149 0.4148 12 2 11 13 2 12 1603.81729 0.5455 13 2 11 14 2 12 1601.09548 0.3094 13 2 12 14 2 13 1602.26358 0.4287 14 2 12 15 2 13 1599.39509 0.4461 14 2 13 15 2 14 1600.71589 0.4613 / 125 J' K" J" K" K; a c Freq.(cm" 1) Intensity3 15 2 13 16 2 14 1597.69750 0.4179 15 2 14 16 2 15 1599.17650 0.3509 16 2 14 17 2 15 1595.99551 0.3664 16 2 15 17 2 16 1597.64528 0.2379 17 2 15 18 2 16 1594.27190 0.2944 17 2 16 18 2 17 1596.12266 0.3244 18 2 16 19 2 17 1592.45034 0.2668 18 2 17 19 2 18 1594.60758 0.2815 19 2 18 20 2 19 1593.10227 0.2421 20 2 18 21 2 19' 1589.79817 0.2743 20 2 19 21 2 20 1591.60698 0.7244 21 2 19 22 2 20 1587.99901 0.2409 21 2 20 22 2 21 1590.12329 0.1831 22 2 20 23 2 21 1586.28783 0.2430 22 2 21 23 2 22 1588.65240 0.2381 23 2 21 24 2 22 1584.60718 0.1615 23 2 22 24 2 23 1587.19503 0.1696 24 2 22 25 2 23 1582.94891 0.1580 24 2 23 25 2 24 1585.75466 0.1609 25 2 23 26 2 24 1581.31697 0.1120 25 2 24 26 2 25 1584.33294 0.1045 26 2 24 27 2 25 1579.72087 0.1276 26 2 25 27 2 26 1582.93411 0.0975 27 2 25 28 2 26 1578.16629 0.0754 27 2 26 28 2 27 1581.56332 0.0611 8 3 6 9 : 3 ' 7 1609.38227 0.0764 9 3 6 10 3 7 1607.79581 0.1721 9 3 7 10 3 8 1607.84353 0.2058 10 3 7 11 3 8 1606.16904 0.1369 10 3 8 11 3 9 1606.24035 0.0985 11 3 8 12 3 9 1604.53456 0.6075 11 3 9 12 3 10 1604.62990 0.1927 12 3 9 13 3 10 1602.88487 0.1829 12 3 10 13 3 11 1602.98144 0.3325 13 3 10 14 3 11 1601.22126 0.1833 13 3 11 14 3 12 1601.27506 0.1949 14 3 11 15 3 12 1599.54145 0.2126 15 3 12 16 3 13 1597.84529 0.1698 15 3 13 16 3 14 1598.70788 0.1661 16 3 13 17 3 14 1596.13370 0.1965 16 3 14 17 3 15 1597.04032 0.1412 17 3 14 18 3 15 1594.40869 0.1868 17 3 15 18 3 16 1595.43689 0.1862 18 3 15 19 3 16 1592.67444 0.1628 18 3 16 19 3 17 1593.85700 0.1327 / 126 J" Freq.(cm" 1) Intensity9 19 3 16 20 3 17 1590.93295 0.4322 19 3 17 20 3 18 1592.29043 0.1291 20 3 17 21 3 18 1589.17465 0.2325 20 3 18 21 3 19 1590.73341 0.1259 21 3 18 22 3 19 1587.50319 0.1101 21 3 19 22 3 20 1589.18654 0.1201 22 3 19 23 3 20 1585.69512 0.0939 22 3 20 23 3 21 1587.64522 0.1400 23 3 20 24 3 21 1583.88408 0.1079 23 3 21 24 3 22 1586.11502 0.3122 24 3 22 25 3 23 1584.59414 0.0928 25 3 23 26 3 24 1583.08177 0.0542 26 3 24 27 3 25 1581.57552 0.0822 5 4 2 l 6 • 4 ; 3 1613.47037 0.2535 6 4 3 i 7 • 4 4 1611.93953 0.4633 7 4 4 8 • 4 , 5 1610.42655 0.4138 8 4 5 9 4 < 6 1608.92712 0.2407 9 4 e 10 4 7 1607.43952 0.2649 10 4 7 11 4 8 1605.95965 0.4108 11 4 8 12 4 9 1604.48244 0.3012 12 4 8 13 4 9 1602.64013 0.5696 12 4 9 13 4 10 1603.00456 0.2645 13 4 9 14 4 10 1601.21354 0.7746 13 4 10 14 4 11 1601.51955 0.2966 14 4 10 15 4 11 1599.72808 0.3301 14 4 11 15 4 12 1600.02575 0.4837 15 4 11 16 4 12 1598.20922 0.3091 15 4 12 16 4 13 1598.52006 0.4937 16 4 12 17 4 13 1596.66327 0.3670 16 4 13 17 4 14 1596.99673 0.3984 17 4 13 18 4 14 1595.09042 0.2483 17 4 14 18 4 15 1595.46058 0.5526 18 4 14 19 4 15 1593.48820 0.2663 18 4 15 19 4 16 1593.91614 0.4453 19 4 15 20 4 16 1591.59977 0.0566 19 4 16 20 4 17 1592.35465 0.2490 20 4 16 21 4 17 1590.18782 0.2173 20 4 17 21 4 18 1590.78280 0.2204 21 4 17 22 4 18 1588.48797 0.1580 21 4 18 22 4 19 1589.20440 0.2855 22 4 18 23 4 19 1586.75621 0.1488 22 4 19 23 4 20 1587.61867 0.1670 23 4 19 24 4 20 1584.99243 0.2076 23 4 20 24 4 21 1586.03010 0.1337 24 4 20 25 4 21 1583.20988 0.1468 / 127 J" K. II \r fl a K c Freq.(cm~ 1) Intensity3 24 4 21 25 4 22 1584.44176 0.1309 25 4 21 26 4 22 1581.41066 0.0393 25 4 22 26 4 23 1582.85274 0.0902 26 4 22 27 4 23 1579.59629 0.1223 26 4 23 27 4 24 1581.42106 0.1081 27 4 23 28 4 24 1577.77920 0.0863 28 4 24 29 4 25 1574.13562 0.0491 7 5 3 | 8 5 4 1610.04428 0.1676 8 5 4 9 5 5 1608.82099 0.2118 9 5 5 10 5 6 1607.57315 0.3436 10 5 6 11 5 7 1606.30487 0.2849 11 5 7 12 5 8 1605.01054 0.3609 12 5 8 13 5 9 1603.68932 0.5433 13 5 9 14 5 10 1602.33990 0.4071 14 5 10 15 5 11 1600.96379 0.2655 15 5 11 16 5 12 1599.55789 0.2752 16 5 12 17 5 13 1598.12241 0.1606 17 5 13 18 5 14 1596.65541 0.1549 18 5 13 19 5 14 1595.15979 0.1039 18 5 14 . 19 5 15 1595.17443 0.1184 19 5 14 20 5 15 • 1593.62949 0.1060 19 5 15 20 5 16 1593.65774 0.0899 20 5 15 21 5 16 1592.07118 0.1171 20 5 16 21 5 17 1592.11630 0.1347 8 6 S t 9 6 4 1605.46178 0.2006 9 6 4 10 6 5 1603.43331 0.2570 10 6 5 11 6 6 1601.46229 0.2692 11 6 6 12 6 7 1599.53429 0.2454 12 6 7 13 6 8 1597.63972 0.3877 13 6 8 14 6 9 1595.77065 0.1964 14 6 9 15 6 10 1593.92511 0.2217 15 6 10 16 6 11 1592.09858 0.2639 16 6 11 17 6 12 1590.29025 0.2076 17 6 12 18 6 13 1588.49970 0.1722 18 6 13 19 6 14 1584.97370 0.0687 19 6 14 20 6 15 1583.24500 0.0785 11 7 5 12 7 6 1601.37706 0.1413 12 7 6 13 7 7 1599.52812 0.1780 13 7 7 14 7 8 1597.74012 0.1279 14 7 8 15 7 9 1595.98122 0.1723 15 7 9 16 7 10 1594.23661 0.1828 16 7 10 17 7 11 1592.50177 0.1650 17 7 11 18 7 12 1590.77308 0.1824 18 7 12 19 7 13 1589.04878 0.1424 19 7 13 20 7 14 1587.37296 0.2016 / 128 J' K' K' J" K" K" a c Freq.(cm" 1) Intensity3 20 7 14 21 7 15 1585.65004 0.1063 21 7 15 22 7 16 1583.91066 0.1059 22 7 16 23 7 17 1582.21126 0.0615 23 7 17 24 7 18 1580.51742 0.0668 24 7 18 25 7 19 1578.81083 0.0684 8 8 1 9 8 2 1604.85221 0.0802 9 8 2 10 8 3 1602.98144 0.3325 10 8 2 11 8 3 1601.08658 0.1364 11 8 4 12 8 5 1599.13345 0.2687 12 8 4 13 8 5 1597.11910 0.1979 13 8 6 14 8 7 1595.02743 0.1915 14 8 6 15 8 7 1592.84530 0.1869 15 8 8 16 8 9 1590.55695 0.1121 16 8 8 17 8 9 1588.14959 0.1223 17 8 10 18 8 11 1585.61855 0.2338 18 8 10 19 8 11 1582.96289 0.0920 19 8 12 20 8 13 1580.19525 0.0764 14 10 4 15 10 5 1593.00527 0.1138 15 10 6 16 10 7 1591.13542 0.1117 16 10 6 17 10 7 1589.24487 0.0761 17 10 8 18 10 9 1587.33107 0.1908 18 10 8 19 10 9 1585.47883 0.0790 5 4 2 5 4 1 1623.56197 0.5828 6 4 3 6 4 2 1623.71828 0.4515 7 4 4 7 4 3 1623.89400 0.2164 8 4 5 8 4 4 1624.08438 0.1609 9 4 6 9 4 5 1624.28737 0.5810 7 5 3 7 5 2 1623.50055 0.2406 10 5 6 10 5 5 1624.82401 0.1494 8 6 3 8 6 2 1620.59505 0.4500 9 6 4 9 6 3 1620.25025 0.3359 10 6 5 10 6 4 1619.96566 0.2225 11 6 6 11 6 5 1619.72393 0.1878 12 6 7 12 6 6 1619.51631 0.1359 13 6 8 13 6 7 1619.33793 0.0775 15 6 10 15 6 9 1619.04703 0.0628 16 6 11 16 6 10 1618.93242 0.0651 11 7 5 11 7 4 1621.55291 0.1731 12 7 6 12 7 5 1621.38785 0.1078 13 7 7 13 7 6 1621.28591 0.1099 14 7 8 14 7 7 1621.21284 0.0860 15 7 9 15 7 8 . 1621.15643 0.0605 16 7 10 16 7 9 1621.11084 0.0645 17 7 11 17 7 10 1621.07110 0.0569 19 7 13 19 7 12 1621.05224 0.0569 / 129 J' K ' K ' J" K " K " Freq.(cm" 1) Intensity3 8 8 1 8 8 0 1619.97108 0.3765 9 8 2 9 8 1 1619.79028 0.5252 10 8 3 10 8 2 1619.56911 0.5064 11 8 4 11 8 3 1619.29866 0.3222 12 8 5 12 8 4 1618.96650 0.2448 13 8 6 13 8 5 1618.55838 0.1996 14 8 7 14 8 6 1618.06037 0.2158 15 8 8 15 8 7 1617.45561 0.0951 16 8 9 16 8 8 1616.73280 0.0822 17 8 10 17 8 9 1615.88777 0.0656 14 10 5 14 10 4 1618.19206 0.3010 15 10 6 15 10 5 1618.00355 0.1570 16 10 7 16 10 6 1617.79403 0.0973 17 10 8 17 10 7 1617.56020 0.0826 18 10 9 18 10 8 1617.38810 0.3372 j' K : K • a c J" K " K " a c Freq.(cm~ 1) Intensity3 2 0 2 3 0 3 1658.98736 0.0544 3 0 3 4 0 4 1657.46355 0.0796 4 0 4 5 0 5 1655.98582 0.0774 5 0 5 6 0 6 1654.54605 0.3928 6 0 6 7 0 7 1653.13260 0.0994 7 0 7 8 0 8 1651.73490 0.1035 8 0 8 9 0 9 1650.34417 0.1174 9 0 9 10 0 10 1648.95518 0.1903 10 0 10 11 0 11 1647.56474 0.1203 11 0 11 12 0 12 1646.17001 0.0953 12 0 12 13 0 13 1644.77699 0.1283 13 0 13 14 0 14 1643.39095 0.1419 14 0 14 15 0 15 1642.01180 0.1064 15 0 15 16 0 16 1640.64651 0.1539 16 0 16 17 0 17 1639.30047 0.1053 17 0 17 18 0 18 1637.99383 0.0935 18 0 18 19 0 19 1636.80118 0.0736 21 0 21 22 0 22 1632.30685 0.0509 22 0 22 23 0 23 1631.07387 0.0542 23 0 23 24 0 24 1629.84594 0.1303 4 1 4 5 1 5 1655.99515 0.0774 5 1 4 6 1 5 1654.25892 0.0775 / 130 j ' K : K ; a c j" K " K ; Freq.(cm" 1) Intensity3 2 0 2 3 0 3 1658.98736 0.0544 3 0 3 4 0 4 1657.46355 0.0796 4 0 4 5 0 5 1655.98582 0.0774 5 0 5 6 0 6 1654.54605 0.3928 6 0 6 7 0 7 1653.13260 0.0994 7 0 7 8 0 8 1651.73490 0.1035 8 0 8 9 0 9 1650.34417 0.1174 9 0 9 10 0 10 1648.95518 0.1903 10 0 10 11 0 11 1647.56474 0.1203 11 0 11 12 0 12 1646.17001 0.0953 12 0 12 13 0 13 1644.77699 0.1283 13 0 13 14 0 14 1643.39095 0.1419 14 0 14 15 0 15 1642.01180 0.1064 15 0 15 16 0 16 1640.64651 0.1539 16 0 16 17 0 17 1639.30047 0.1053 17 0 17 18 0 18 1637.99383 0.0935 18 0 18 19 0 19 1636.80118 0.0736 21 0 21 22 0 22 1632.30685 0.0509 22 0 22 23 0 23 1631.07387 0.0542 23 0 23 24 0 24 1629.84594 0.1303 4 1 4 5 1 5 1655.99515 0.0774 5 1 4 6 1 5 1654.25892 0.0775 5 1 5 6 1 6 1654.52239 0.1680 6 1 5 7 1 6 1652.92875 0.0589 6 1 6 7 1 7 1653.07006 0.0424 7 1 6 8 1 7 1651.63503 0.1071 7 1 7 8 1 8 1651.64647 0.0483 8 1 7 9 1 8 1650.41517 0.0361 8 1 8 9 1 9 1650.23640 0.1275 9 1 8 10 1 9 1649.22351 0.0446 9 1 9 10 1 10 1648.84431 0.0780 10 1 9 11 1 10 1648.07467 0.0675 10 1 10 11 1 11 1647.46958 0.0936 11 1 10 12 1 11 1646.94995 0.0736 11 1 11 12 1 12 1646.11706 0.0444 12 1 11 13 1 12 1645.83682 0.0663 12 1 12 13 1 13 1644.80335 0.1579 13 1 12 14 1 13 1644.72831 0.0702 13 1 13 14 1 14 1643.58800 0.0575 14 1 13 15 1 14 1643.62585 0.0729 15 1 14 16 1 15 1642.46868 0.0520 15 1 15 16 1 16 1640.32235 0.0621 16 1 15 17 1 16 1641.31896 0.1300 16 1 16 17 1 17 1639.08961 0.0755 17 1 17 18 1 18 1637.81717 0.2183 / 131 j' K : K : a c j " K " K : a c Freq.(cm" 1) Intensity3 18 1 18 19 1 19 1636.53366 0.0530 3 2 1 4 2 2 1656.89941 0.0507 3 2 2 4 2 3 1656.92776 0.0527 4 2 2 5 2 3 1655.40255 0.0485 4 2 3 5 2 4 1655.44663 0.0751 5 2 3 6 2 4 1653.96273 0.0806 5 2 4 6 2 5 1654.01116 0.0921 6 2 4 7 2 5 1652.58605 0.0825 6 2 5 7 2 6 1652.61929 0.0863 7 2 5 8 2 6 1651.27782 0.1110 7 2 6 8 2 7 1651.26807 0.0739 8 2 6 9 2 7 1650.04069 0.1116 8 2 7 9 2 8 1649.95567 0.0977 9 2 7 10 2 8 1648.86259 0.1011 9 2 8 10 2 9 1648.68056 0.1676 10 2 8 11 2 9 1647.69628 0.0982 10 2 9 11 2 10 1647.43850 0.1827 11 2 9 12 2 10 1647.45371 0.0609 11 2 10 12 2 11 1646.22788 0.1980 12 2 11 13 2 12 1645.04875 0.1159 13 2 11 14 2 12 1645.28968 0.0720 13 2 12 14 2 13 1643.89923 0.0795 14 2 12 15 2 13. 1644.43281 0.1123 14 2 13 15 2 14 1642.77915 0.0680 15 2 13 16 2 14 1643.62585 0.0729 15 2 14 16 2 15 1641.68882 0.0738 16 2 14 17 2 15 1642.84590 0.0631 16 2 15 17 2 16 1640.62737 0.0707 17 2 15 18 2 16 1642.07713 0.0490 17 2 16 18 2 17 1639.59598 0.1855 18 2 16 19 2 17 1641.30318 0.1003 19 2 18 20 2 19 1637.61888 0.1676 20 2 19 21 2 20 1636.68313 0.0886 21 2 20 22 2 21 1635.78233 0.0483 5 4 2 6 4 3 1652.48841 0.0886 6 4 3 7 4 4 1651.13625 0.1040 7 4 4 8 4 5 1649.83919 0.1513 8 4 5 9 4 6 1648.59432 0.1460 9 4 5 10 4 6 1647.40552 0.2738 9 4 6 10 4 7 1647.40552 0.2738 10 4 6 11 4 7 1646.26083 0.0455 10 4 7 11 4 8 1646.26875 0.1196 11 4 7 12 4 8 1645.18013 0.5307 11 4 8 12 4 9 1645.18013 0.5307 12 4 8 13 4 9 1644.15560 0.2225 / 132 j' K ' K : a c J" K " K " Freq.(cm" 1) Intensity3 12 4 9 13 4 10 1644.14008 0.0553 13 4 9 14 4 10 1643.17356 0.0818 13 4 10 14 4 11 1643.14551 0.1550 14 4 10 15 4 11 1642.23247 0.0567 14 4 11 15 4 12 1642.17625 0.0728 15 4 11 16 4 12 1641.30318 0.1003 8 5 4 9 5 5 1647.54195 0.0676 9 5 5 10 5 6 1646.37953 0.0355 10 5 6 11 5 7 1645.30990 0.0701 11 5 7 12 5 8 1644.27757 0.0789 12 5 8 13 5 9 1643.29653 0.0562 13 5 9 14 5 10 1642.36605 0.0756 14 5 10 15 5 11 1641.48874 0.2370 8 6 3 9 6 4 1646.22788 0.1980 9 6 4 10 6 5 1645.16313 0.0753 10 6 5 11 6 6 1644.15560 0.2225 11 6 6 12 6 7 1643.21350 0.1778 12 6 7 13 6 8 1642.32109 0.1313 13 6 8 14 6 9 1641.48246 0.1522 14 6 9 15 6 10 1640.69044 0.0737 16 6 11 17 6 12 1639.24249 0.0602 17 6 12 18 6 13 1638.56416 0.0556 18 6 13 19 6 14 1637.94599 0.0600 2 0 2 1 0 1 1667.36341 0.0532 3 0 3 2 0 2 1669.15888 0.0498 4 0 4 3 0 3 1670.96410 0.0966 5 0 5 4 0 4 1672.77080 0.0941 6 0 6 5 0 5 1674.55916 0.0998 7 0 7 6 0 6 1676.31852 0.0900 8 0 8 7 0 7 1678.04128 0.1116 9 0 9 8 0 8 1679.72755 0.1131 10 0 10 9 0 9 1681.38428 0.1256 11 0 11 10 0 10 1683.02138 0.1189 12 0 12 11 0 11 1684.65042 0.1210 13 0 13 12 0 12 1686.28057 0.1023 14 0 14 13 0 13 1687.91877 0.1160 15 0 15 14 0 14 1689.57298 0.0932 16 0 16 15 0 15 1691.25045 0.1144 17 0 17 16 0 16 1692.97133 0.0882 18 0 18 17 0 17 1694.80964 0.0697 21 0 21 20 0 20 1699.41606 0.0642 22 0 22 21 0 21 1701.21898 0.0532 23 0 23 22 0 22 1703.02630 0.0553 4 1 4 3 1 3 1670.39238 0.0553 5 1 4 4 1 3 1673.52025 0.0830 / 133 J' K' K' J" K" K" cL C Freq.(cm" 1) Intensity3 5 1 5 4 1 4 1672.10112 0.0666 6 1 5 5 1 4 1675.65761 0.0377 6 1 6 5 1 5 1673.82129 0.0467 7 1 6 6 1 5 1677.80844 0.0447 7 1 7 6 1 6 1675.55037 0.0485 8 1 7 7 1 6 1680.01687 0.0685 8 1 8 7 1 7 1677.28505 0.0660 9 1 8 8 1 7 1682.21105 0.0522 9 1 9 8 1 8 1679.02497 0.0589 10 1 9 9 1 8 1684.42068 0.0503 10 1 10 9 1 9 1680.77095 0.0615 11 1 10 10 1 9 1686.61229 0.0552 11 1 11 10 1 10 1682.52701 0.0710 12 1 11 11 1 10 1688.77024 0.0533 12 1 12 11 1 11 1684.30939 0.0579 13 1 12 12 1 11 1690.88244 0.0400 13 1 13 12 1 12 1686.18418 0.0454 14 1 13 13 1 12 1692.94679 0.0101 15 1 14 14 1 13 1694.91273 0.0397 15 1 15 14 1 14 1689.06892 0.0502 16 1 15 15 1 14 1696.83919 0.0244 16 1 16 15 1 15 1690.90308 0.0491 17 1 17 16 1 16 1692.68972 0.0516 18 1 18 17 1 17 1694.46401 0.0507 2 0 2 3 0 3 1658.98736 0.0544 3 0 3 4 0 4 1657.46355 0.0796 4 0 4 5 0 5 1655.98582 0.0774 5 0 5 6 0 6 1654.54605 0.3928 6 0 6 7 0 7 1653.13260 0.0994 7 0 7 8 0 8 1651.73490 0.1035 8 0 8 9 0 9 1650.34417 0.1174 9 0 9 10 0 10 1648.95518 0.1903 10 0 10 11 0 11 1647.56474 0.1203 11 0 11 12 0 12 1646.17001 0.0953 12 0 12 13 0 13 1644.77699 0.1283 13 0 13 14 0 14 1643.39095 0.1419 14 0 14 15 0 15 1642.01180 0.1064 15 0 15 16 0 16 1640.64651 0.1539 16 0 16 17 0 17 1639.30047 0.1053 17 0 17 18 0 18 1637.99383 0.0935 18 0 18 19 0 19 1636.80118 0.0736 21 0 21 22 0 22 1632.30685 0.0509 22 0 22 23 0 23 1631.07387 0.0542 23 0 23 24 0 24 1629.84594 0.1303 4 1 4 5 1 5 1655.99515 0.0774 / 134 j ' K ' K : a c J" K " K " a C Freq.(cm" 1) Intensity3 5 1 4 6 1 5 1654.25892 0.0775 5 1 5 6 1 6 1654.52239 0.1680 6 1 5 7 1 6 1652.92875 0.0589 6 1 6 7 1 7 1653.07006 0.0424 7 1 6 8 1 7 1651.63503 0.1071 7 1 7 8 1 8 1651.64647 0.0483 8 1 7 9 1 8 1650.41517 0.0361 8 1 8 9 1 9 1650.23640 0.1275 9 1 8 10 1 9 1649.22351 0.0446 9 1 9 10 1 10 1648.84431 0.0780 10 1 9 11 1 10 1648.07467 0.0675 10 1 10 11 1 11 1647.46958 0.0936 11 1 10 12 1 11 1646.94995 0.0736 11 1 11 12 1 12 1646.11706 0.0444 12 1 11 13 1 12 1645.83682 0.0663 12 1 12 13 1 13 1644.80335 0.1579 13 1 12 14 1 13 1644.72831 0.0702 13 1 13 14 1 14 1643.58800 0.0575 14 1 13 15 1 14 1643.62585 0.0729 15 1 14 16 1 15 1642.46868 0.0520 15 1 15 16 1 16 1640.32235 0.0621 16 1 15 " 17 1 16 1641.31896 0.1300 16 1 16 17 1 17 1639.08961 0.0755 17 1 17 18 1 18 1637.81717 0.2183 18 1 18 19 1 19 1636.53366 0.0530 3 2 1 4 2 2 1656.89941 0.0507 3 2 2 4 2 3 1656.92776 0.0527 4 2 2 5 2 3 1655.40255 0.0485 4 2 3 5 2 4 1655.44663 0.0751 5 2 3 6 2 4 1653.96273 0.0806 5 2 4 6 2 5 1654.01116 0.0921 6 2 4 7 2 5 1652.58605 0.0825 6 2 5 7 2 6 1652.61929 0.0863 7 2 5 8 2 6 1651.27782 0.1110 7 2 6 8 2 7 1651.26807 0.0739 8 2 6 9 2 7 1650.04069 0.1116 8 2 7 9 2 8 1649.95567 0.0977 9 2 7 10 2 8 1648.86259 0.1011 9 2 8 - 10 2 9 1648.68056 0.1676 10 2 8 11 2 9 1647.69628 0.0982 10 2 9 11 2 10 1647.43850 0.1827 11 2 9 12 2 10 1647.45371 0.0609 11 2 10 12 2 11 1646.22788 0.1980 12 2 11 13 2 12 1645.04875 0.1159 13 2 11 14 2 12 1645.28968 0.0720 / 135 j ' K' K' a c J" K" K" a C Freq.(cm" 1) Intensity3 13 2 12 14 2 13 1643.89923 0.0795 14 2 12 15 2 13 1644.43281 0.1123 14 2 13 15 2 14 1642.77915 0.0680 15 2 13 16 2 14 1643.62585 0.0729 15 2 14 16 2 15 1641.68882 0.0738 16 2 14 17 2 15 1642.84590 0.0631 16 2 15 17 2 16 1640.62737 0.0707 17 2 15 18 2 16 1642.07713 0.0490 17 2 16 18 2 17 1639.59598 0.1855 18 2 16 19 2 17 1641.30318 0.1003 19 2 18 20 2 19 1637.61888 0.1676 20 2 19 21 2 20 1636.68313 0.0886 21 2 20 22 2 21 1635.78233 0.0483 5 4 2 6 4 3 1652.48841 0.0886 6 4 3 7 4 4 1651.13625 0.1040 7 4 4 8 4 5 1649.83919 0.1513 8 4 5 9 4 6 1648.59432 0.1460 9 4 5 10 4 6 1647.40552 0.2738 9 4 6 10 4 7 1647.40552 0.2738 10 4 6 11 4 7 1646.26083 0.0455 10 4 7 11 4 8 1646.26875 0.1196 11 4 7 12 4 8 . 1645.18013 0.5307 11 4 8 12 4 9 1645.18013 0.5307 12 4 8 13 4 9 1644.15560 0.2225 12 4 9 13 4 10 1644.14008 0.0553 13 4 9 14 4 10 1643.17356 0.0818 13 4 10 14 4 11 1643.14551 0.1550 14 4 10 15 4 11 1642.23247 0.0567 14 4 11 15 4 12 1642.17625 0.0728 15 4 11 16 4 12 1641.30318 0.1003 8 5 4 9 5 5 1647.54195 0.0676 9 5 5 10 5 6 1646.37953 0.0355 10 5 6 11 5 7 1645.30990 0.0701 11 5 7 12 5 8 1644.27757 0.0789 12 5 8 13 5 9 1643.29653 0.0562 13 5 9 14 5 10 1642.36605 0.0756 14 5 10 15 5 11 1641.48874 0.2370 8 6 3 9 6 4 1646.22788 0.1980 9 6 4 10 6 5 1645.16313 0.0753 10 6 5 11 6 6 1644.15560 0.2225 11 6 6 12 6 7 1643.21350 0.1778 12 6 7 13 6 8 1642.32109 0.1313 13 6 8 14 6 9 1641.48246 0.1522 14 6 9 15 6 10 1640.69044 0.0737 16 6 11 17 6 12 1639.24249 0.0602 / 136 j ' K • K : a c J" K " K " a c Freq.(cm" 1) Intensity3 17 6 12 18 6 13 1638.56416 0.0556 18 6 13 19 6 14 1637.94599 0.0600 2 0 2 1 0 1 1667.36341 0.0532 3 0 3 2 0 2 1669.15888 0.0498 4 0 4 3 0 3 1670.96410 0.0966 5 0 5 4 0 4 1672.77080 0.0941 6 0 6 5 0 5 1674.55916 0.0998 7 0 7 6 0 6 1676.31852 0.0900 8 0 8 7 0 7 1678.04128 0.1116 9 0 9 8 0 8 1679.72755 0.1131 10 0 10 9 0 9 1681.38428 0.1256 11 0 11 10 0 10 1683.02138 0.1189 12 0 12 11 0 11 1684.65042 0.1210 13 0 13 12 0 12 1686.28057 0.1023 14 0 14 13 0 13 1687.91877 0.1160 15 0 15 14 0 14 1689.57298 0.0932 16 0 16 15 0 15 1691.25045 0.1144 17 0 17 16 0 16 1692.97133 0.0882 18 0 18 17 0 17 1694.80964 0.0697 21 0 21 20 0 20 1699.41606 0.0642 22 0 22 21 0 21 1701.21898 0.0532 23 0 23 22 0 22 1703.02630 0.0553 4 1 4 3 1 3 1670.39238 0.0553 5 1 4 4 1 3 1673.52025 0.0830 5 1 5 4 1 4 1672.10112 0.0666 6 1 5 5 1 4 1675.65761 0.0377 6 1 6 5 1 5 1673.82129 0.0467 7 1 6 6 1 5 1677.80844 0.0447 7 1 7 6 1 6 1675.55037 0.0485 8 1 7 7 1 6 1680.01687 0.0685 8 1 8 7 1 7 1677.28505 0.0660 9 1 8 8 1 7 1682.21105 0.0522 9 1 9 8 1 8 1679.02497 0.0589 10 1 9 9 1 8 1684.42068 0.0503 10 1 10 9 1 9 1680.77095 0.0615 11 1 10 10 1 9 1686.61229 0.0552 11 1 11 10 1 10 1682.52701 0.0710 12 1 11 11 1 10 1688.77024 0.0533 .12 1 12 11 1 11 1684.30939 0.0579 13 1 12 12 1 11 1690.88244 0.0400 13 1 13 12 1 12 1686.18418 0.0454 14 1 13 13 1 12 1692.94679 0.0101 15 1 14 14 1 13 1694.91273 0.0397 15 1 15 14 1 14 1689.06892 0.0502 16 1 15 15 1 14 1696.83919 0.0244 / 137 J' K' K' J" K£ K£ Freq.(cm" 1) Intensity3 16 1 16 15 1 15 1690.90308 0.0491 17 1 17 16 1 16 1692.68972 0.0516 18 1 18 17 1 17 1694.46401 0.0507 3 2 1 2 2 0 1668.71889 0.0560 2 0 2 3 0 3 1658.98736 0.0544 3 0 3 4 0 4 1657.46355 0.0796 4 0 4 5 0 5 1655.98582 0.0774 5 0 5 6 0 6 1654.54605 0.3928 6 0 6 7 0 7 1653.13260 0.0994 7 0 7 8 0 8 1651.73490 0.1035 8 0 8 9 0 9 1650.34417 0.1174 9 0 9 10 0 10 1648.95518 0.1903 10 0 10 11 0 11 1647.56474 0.1203 11 0 11 12 0 12 1646.17001 0.0953 12 0 12 13 0 13 1644.77699 0.1283 13 0 13 14 0 14 1643.39095 0.1419 14 0 14 15 0 15 1642.01180 0.1064 15 0 15 16 0 16 1640.64651 0.1539 16 0 16 17 0 17 1639.30047 0.1053 17 0 17 18 0 18 1637.99383 0.0935 18 0 18 19 0 19 1636.80118 0.0736 21 0 21 22 0 22 1632.30685 0.0509 22 0 22 23 0 23 1631.07387 0.0542 23 0 23 24 0 24 1629.84594 0.1303 4 1 4 5 1 5 1655.99515 0.0774 5 1 4 6 1 5 1654.25892 0.0775 5 1 5 6 1 6 1654.52239 0.1680 6 1 5 7 1 6 1652.92875 0.0589 6 1 6 7 1 7 1653.07006 0.0424 7 1 6 8 1 7 1651.63503 0.1071 7 1 7 8 1 8 1651.64647 0.0483 8 1 7 9 1 8 1650.41517 0.0361 8 1 8 9 1 9 1650.23640 0.1275 9 1 8 10 1 9 1649.22351 0.0446 9 1 9 10 1 10 1648.84431 0.0780 10 1 9 11 1 10 1648.07467 0.0675 10 1 10 11 1 11 1647.46958 0.0936 11 1 10 12 1 11 1646.94995 0.0736 11 1 11 12 1 12 1646.11706 0.0444 12 1 11 13 1 12 1645.83682 0.0663 12 1 12 13 1 13 1644.80335 0.1579 13 1 12 14 1 13 1644.72831 0:0702 13 1 13 14 1 14 1643.58800 0.0575 14 1 13 15 1 14 1643.62585 0.0729 15 1 14 16 1 15 1642.46868 0.0520 / 138 J' K a K' J" K" K" Freq.(cm" 1) Intensity3 15 1 15 16 1 16 1640.32235 0.0621 16 1 15 17 1 16 1641.31896 0.1300 16 1 16 17 1 17 1639.08961 0.0755 17 1 17 18 1 18 1637.81717 0.2183 18 1 18 19 1 19 1636.53366 0.0530 3 2 1 4 2 2 1656.89941 0.0507 3 2 2 4 2 3 1656.92776 0.0527 4 2 2 5 2 3 1655.40255 0.0485 4 2 3 5 2 4 1655.44663 0.0751 5 2 3 6 2 4 1653.96273 0.0806 5 2 4 6 2 5 1654.01116 0.0921 6 2 4 7 2 5 1652.58605 0.0825 6 2 5 7 2 6 1652.61929 0.0863 7 2 5 8 2 6 1651.27782 0.1110 7 2 6 8 2 7 1651.26807 0.0739 8 2 6 9 2 7 1650.04069 0.1116 8 2 7 9 2 8 1649.95567 0.0977 9 2 7 10 2 8 1648.86259 0.1011 9 2 8 10 2 9 1648.68056 0.1676 10 2 8 11 2 9 1647.69628 0.0982 10 2 9 11 2 10 1647.43850 0.1827 11 2 9 ' 12 2 10 . 1647.45371 0.0609 11 2 10 12 2 11 1646.22788 0.1980 12 2 11 13 2 12 1645.04875 0.1159 13 2 11 14 2 12 1645.28968 0.0720 13 2 12 14 2 13 1643.89923 0.0795 14 2 12 15 2 13 1644.43281 0.1123 14 2 13 15 2 14 1642.77915 0.0680 15 2 13 16 2 14 1643.62585 0.0729 15 2 14 16 2 15 1641.68882 0.0738 16 2 14 17 2 15 1642.84590 0.0623 16 2 15 17 2 16 1640.62737 0.0707 17 2 15 18 2 16 1642.07713 0.0490 17 2 16 18 2 17 1639.59598 0.1855 18 2 16 19 2. 17 1641.30318 0.1003 19 2 18 20 2 19 1637.61888 0.1676 20 2 19 21 2 20 1636.68313 0.0886 21 2 20 22 2 21 1635.78233 0.0483 5 4 2 6 4 3 1652.48841 0.0886 6 4 3 7 4 4 1651.13625 0.1040 7 4 4 8 4 5 1649.83919 0.1513 8 4 5 9 4 6 1648.59432 0.1460 9 4 5 10 4 6 1647.40552 0.2738 9 4 6 10 4 7 1647.40552 0.2738 10 4 6 11 4 7 1646.26083 0.0455 / 139 J ' K ' K • J " K " K ; a c Freq.(cm" ') Intensity3 10 4 7 11 4 8 1646.26875 0.1196 11 4 7 12 4 8 1645.18013 0.5307 11 4 8 12 4 9 1645.18013 0.5307 12 4 8 13 4 9 1644.15560 0.2225 12 4 9 13 4 10 1644.14008 0.0553 13 4 9 14 4 10 1643.17356 0.0818 13 4 10 14 4 11 1643.14551 0.1550 14 4 10 15 4 11 1642.23247 0.0567 14 4 11 15 4 12 1642.17625 0.0728 15 4 11 16 4 12 1641.30318 0.1003 8 5 4 9 5 5 1647.54195 0.0676 9 5 5 10 5 6 1646.37953 0.0355 10 5 6 11 5 7 1645.30990 0.0701 11 5 7 12 5 8 1644.27757 0.0789 12 5 8 13 5 9 1643.29653 0.0562 13 5 9 14 5 10 1642.36605 0.0756 14 5 10 15 5 11 1641.48874 0.2370 8 6 3 9 6 4 1646.22788 0.1980 9 6 4 10 6 5 1645.16313 0.0753 10 6 5 11 6 6 1644.15560 0.2225 11 6 6 12 6 7 1643.21350 0.1778 12 6 7 13 6 8 . 1642.32109 0.1313 13 6 8 14 6 9 1641.48246 0.1522 14 6 9 15 6 10 1640.69044 0.0737 16 6 11 17 6 12 1639.24249 0.0602 17 6 12 18 6 13 1638.56416 0.0556 18 6 13 19 6 14 1637.94599 0.0600 2 0 2 1 0 1 1667.36341 0.0532 3 0 3 2 0 2 1669.15888 0.0498 4 0 4 3 0 3 1670.96410 0.0966 5 0 5 4 0 4 1672.77080 0.0941 6 0 6 5 0 5 1674.55916 0.0998 7 0 7 6 0 6 1676.31852 0.0900 8 0 8 7 0 7 1678.04128 0.1116 9 0 9 8 0 8 1679.72755 0.1131 10 0 10 9 0 9 1681.38428 0.1256 11 0 11 10 0 10 1683.02138 0.1189 12 0 12 11 0 11 1684.65042 0.1210 13 0 13 12 0 12 1686.28057 0.1023 14 0 14 13 0 13 1687.91877 0.1160 15 0 15 14 0 14 1689.57298 0.0932 16 0 16 15 0 15 1691.25045 0.1144 17 0 17 16 0 16 1692.97133 0.0882 18 0 18 17 0 17 1694.80964 0.0697 21 0 21 20 0 20 1699.41606 0.0642 / 140 J' K• K- J" K" K" Freq.(cm" 1) Intensity3 22 0 22 21 0 21 1701.21898 0.0532 23 0 23 22 0 22 1703.02630 0.0553 4 1 4 3 1 3 1670.39238 0.0553 5 1 4 4 1 3 1673.52025 0.0830 5 1 5 4 1 4 1672.10112 0.0666 6 1 5 5 1 4 1675.65761 0.0377 6 1 6 5 1 5 1673.82129 0.0467 7 1 6 6 1 5 1677.80844 0.0447 7 1 7 6 1 6 1675.55037 0.0485 8 1 7 7 1 6 1680.01687 0.0685 8 1 8 7 1 7 1677.28505 0.0660 9 1 8 8 1 7 1682.21105 0.0522 9 1 9 8 1 8 1679.02497 0.0589 10 1 9 9 1 8 1684.42068 0.0503 10 1 10 9 1 9 1680.77095 0.0615 11 1 10 10 1 9 1686.61229 0.0552 11 1 11 10 .1 10 1682.52701 0.0710 12 1 11 11 1 10 1688.77024 0.0533 12 1 12 11 1 11 1684.30939 0.0579 13 1 12 12 1 11 1690.88244 0.0400 13 1 13 12 1 12 1686.18418 • 0.0454 14 1 13 13 1 12 1692i94679 0.0101 15 1 14 14 1 13 1694.91273 0.0397 15 1 15 14 1 14 1689.06892 0.0502 16 1 15 15 1 14 1696.83919 0.0244 16 1 16 15 1 15 1690.90308 0.0491 17 1 17 16 1 16 1692.68972 0.0516 18 1 18 17 1 17 1694.46401 0.0507 3 2 1 2 2 0 1668.71889 0.0560 3 2 2 2 2 1 1668.68415 0.0560 4 2 2 3 2 1 1670.64593 0.0468 4 2 3 3 2 2 1670.55190 0.0599 5 2 3 4 2 2 1672.66155 0.0513 5 2 4 4 2 3 1672.45688 0.0764 6 2 4 5 2 3 1674.77432 0.0727 6 2 5 5 2 4 1674.39847 0.0897 7 2 5 6 2 4 1676.98987 0.0758 7 2 6 6 2 5 1676.36922 0.0779 8 2 6 7 2 5 1679.30537 0.0731 8 2 7 7 2 6 1678.36776 0.1381 9 2 7 8 2 6 1681.70441 0.0727 9 2 8 8 2 7 1680.38783 0.0985 10 2 8 9 2 7 1684.12408 0.0662 10 2 9 9 2 8 1682.42742 0.0934 11 2 9 10 2 8 1687.46504 0.0376 / 141 J' K- K' J" K" K" Freq.(cm" 1) Intensity3 11 2 10 10 2 9 1684.48340 0.0857 12 2 11 11 2 10 1686.55312 0.0980 13 2 11 12 2 10 1692.42524 0.0686 13 2 12 12 2 11 1688.63636 0.0821 14 2 12 13 2 11 1695.09143 0.0588 14 2 13 13 2 12 1690.73076 0.0675 15 2 13 14 2 12 1697.77091 0.0514 15 2 14 14 2 13 1692.83583 0.0679 16 2 14 15 2 13 1700.43752 0.0378 16 2 15 15 2 14 1694.95165 0.0643 17 2 15 16 2 14 1703.07189 0.0369 17 2 16 16 2 15 1697.07646 0.0449 18 2 16 17 2 15 1705.65519 0.0344 18 2 17 17 2 16 1699.21784 0.0422 19 2 18 18 2 17 1701.37266 0.0410 20 2 19 19 2 18 1703.54691 0.0333 21 2 20 20 2 19 1705.74657 0.0269 5 4 2 4 4 1 1670.99017 0.0528 6 4 3 5 4 2 1673.00958 0.0742 7 4 4 6 4 3 1675.08627 0.1432 8 4 5 7 4 4 1677.22175 0.1127 9 4 5 8 4 4 1679.41647 0.0925 9 4 6 8 4 5 1679.41192 0.0925 10 4 6 9 4 5 1681.66298 0.0844 10 4 7 9 4 6 1681.66298 0.0844 11 4 7 10 4 6 1683.98032 0.1007 11 4 8 10 4 7 1683.96714 0.0462 12 4 8 11 4 7 1686.36403 0.0581 12 4 9 11 4 8 1686.32380 0.0588 13 4 9 12 4 8 1688.79979 0.0574 13 4 10 12 4 9 1688.72579 0.0543 14 4 10 13 4 9 1691.29035 0.0591 14 4 11 13 4 10 1691.16409 0.0624 15 4 11 14 4 10 1693.80685 0.0315 8 5 4 7 5 3 1676.13892 0.0488 9 5 5 8 5 4 1678.35090 0.1381 10 5 6 9 5 5 1680.65932 0.0545 11 5 7 10 5 6 1683.00596 0.0506 12 5 8 11 5 7 1685.40938 0.0550 13 5 9 12 5 8 1687.86801 0.0462 14 5 10 13 5 9 1690.37875 0.0337 8 6 3 7 6 2 1674.81039 . 0.0546 9 6 4 8 6 3 1677.11318 0.1124 10 6 5 9 6 4- 1679.47811 0.0818 11 6 6 10 6 5 1681.90448 0.0563 / 142 J' K- K' J" K" Freq.(cm~ 1) Intensity3 12 6 7 11 6 6 1684.38695 0.0772 13 6 8 12 6 7 1686.92479 0.0714 14 6 9 13 6 8 1689.51273 0.0511 15 6 10 14 6 9 1692.15083 0.0528 16 6 11 15 6 10 1694.83377 0.0514 17 6 12 16 6 11 1697.54734 0.0569 18 6 13 17 6 12 1700.32073 0.0322 8 5 3 8 5 4 1662.68413 0.0567 10 5 5 10 5 6 1663.82957 0.0634 11 5 6 11 5 7 1664.48661 0.0419 13 5 8 13 5 9 1665.96220 0.1352 2 0 2 3 0 3 1658.98736 0.0544 3 0 3 4 0 4 1657.46355 0.0796 4 0 4 5 0 5 1655.98582 0.0774 5 0 5 6 0 6 1654.54605 0.3928 6 0 6 7 0 7 1653.13260 0.0994 7 0 7 8 0 8 1651.73490 0.1035 8 0 8 9 0 9 1650.34417 0.1174 9 0 9 10 0 10 1648.95518 0.1903 10 0 10 11 0 11 1647.56474 0.1203 11 0 11 12 0 12 1646.17001 0.0953 12 0 12 13 0 13 1644.77699 0.1283 13 0 13 14 0 14 1643.39095 0.1419 14 0 14 15 0 15 1642.01180 0.1064 15 0 15 16 0 16 1640.64651 0.1539 16 0 16 17 0 17 1639.30047 0.1053 17 0 17 18 0 18 1637.99383 0.0935 18 0 18 19 0 19 1636.80118 0.0736 21 0 21 22 0 22 1632.30685 0.0509 22 0 22 23 0 23 1631.07387 0.0542 23 0 23 24 0 24 1629.84594 0.1303 4 1 4 5 1 5 1655.99515 0.0774 5 1 4 6 1 5 1654.25892 0.0775 5 1 5 6 1 6 1654.52239 0.1680 6 1 5 7 1 6 1652.92875 0.0589 6 1 6 7 1 7 1653.07006 0.0424 7 1 6 8 1 7 1651.63503 0.1071 7 1 7 8 1 8 1651.64647 0.0483 8 1 7 9 1 8 1650.41517 . 0.0361 8 1 8 9 1 9 1650.23640 0.1275 9 1 8 10 1 9 1649.22351 0.0446 9 1 9 10 1 10 1648.84431 0.0780 10 1 9 11 1 10 1648.07467 0.0675 10 1 10 11 1 11 1647.46958 0.0936 11 1 10 12 1 11 1646.94995 0.0736 / 143 J' K- K' J" K" K" Freq.(cm" 1) Intensity3 11 1 11 12 1 12 1646.11706 0.0444 12 1 11 13 1 12 1645.83682 0.0663 12 1 12 13 1 13 1644.80335 0.1579 13 1 12 14 1 13 1644.72831 0.0702 13 1 13 14 1 14 1643.58800 0.0575 14 1 13 15 1 14 1643.62585 0.0729 15 1 14 16 1 15 1642.46868 0.0520 15 1 15 16 1 16 1640.32235 0.0621 16 1 15 17 1 16 1641.31896 0.0297 16 1 16 17 1 17 1639.08961 0.0755 17 1 17 18 1 18 1637.81717 0.2183 18 1 18 19 1 19 1636.53366 0.0530 3 2.1 4 2 2 1656.89941 0.0507 3 2 2 4 2 3 1656.92776 0.0527 4 2 2 5 2 3 1655.40255 0.0485 4 2 3 5 2 4 1655.44663 0.0751 5 2 3 6 2 4 1653.96273 0.0806 5 2 4 6 2 5 1654.01116 0.0921 6 2 4 7 2 5 1652.58605 0.0825 6 2 5 7 2 6 1652.61929 0.0863 7 2 5 8 2 6 1651.27782 0.1110 7 2 6 8 2 7 1651.26807 0.0739 8 2 6 9 2 7 1650.04069 0.1116 8 2 7 9 2 8 1649.95567 0.0977 9 2 7 10 2 8 1648.86259 0.1011 9 2 8 10 2 9 1648.68056 0.1676 10 2 8 11 2 9 1647.69628 0.0982 10 2 9 11 2 10 1647.43850 0.0936 11 2 9 12 2 10 1647.45371 0.0936 11 2 10 12 2 11 1646.22788 0.1980 12 2 11 13 2 12 1645.04875 0.1159 13 2 11 14 2 12 1645.28968 0.0720 13 2 12 14 2 13 1643.89923 0.0795 14 2 12 15 2 13 1644.43281 0.1123 14 2 13 15 2 14 1642.77915 0.0683 15 2 13 16 2 14 1643.62585 0.0729 15 2 14 16 2 15 1641.68882 0.0738 16 2 14 17 2 15 1642.84590 0.0623 16 2 15 17 2 16 1640.62737 0.0707 17 2 15 18 2 16 1642.07713 0.0490 17 2 16 18 2 17 1639.59598 0.1855 18 2 16 19 2 17 1641.30318 0.0297 19 2 18 20 2 19 1637.61888 0.1676 20 2 19 21 2 20 1636.68313 0.0886 21 2 20 22 2 21 1635.78233 0.0483 / 144 J' K' K' a c J" K" K" a. C Freq.(cm" 1) Intensity3 5 4 2 6 4 3 1652.48841 0.0886 6 4 3 7 4 4 1651.13625 0.1040 7 4 4 8 4 5 1649.83919 0.1513 8 4 5 9 4 6 1648.59432 0.1460 9 4 5 10 4 6 1647.40552 0.1827 9 4 6 10 4 7 1647.40552 0.1827 10 4 6 11 4 7 1646.26083 0.0455 10 4 7 11 4 8 1646.26875 0.1196 11 4 7 12 4 8 1645.18013 0.5307 11 4 8 12 4 9 1645.18013 0.5307 12 4 8 13 4 9 1644.15560 0.2225 12 4 9 13 4 10 1644.14008 0.0553 13 4 9 14 4 10 1643.17356 0.1211 13 4 10 14 4 11 1643.14551 0.0818 14 4 10 15 4 11 1642.23247 0.0567 14 4 11 15 4 12 1642.17625 0.0728 15 4 11 16 4 12 1641.30318 0.0297 8 5 4 9 5 5 1647.54195 0.0676 9 5 5 10 5 6 1646.37953 0.0355 10 5 6 11 5 7 1645.30990 0.0701 11 5 7 12 5 8 1644.27757 . 0.0789 12 5 8 13 5 9 1643.29653 0.0562 13 5 9 14 5 10 1642.36605 0.0756 14 5 10 15 5 11 1641.48874 0.2370 8 6 3 9 6 4 1646.22788 0.1980 9 6 4 10 6 5 1645.16313 0.0753 10 6 5 11 6 6 1644.15560 0.2225 11 6 6 12 6 7 1643.21350 0.1778 12 6 7 13 6 8 1642.32109 0.1313 13 6 8 14 6 9 1641.48246 0.1522 14 6 9 15 6 10 1640.69044 0.0737 16 6 11 17 6 12 1639.24249 0.0602 17 6 12 18 6 13 1638.56416 0.0556 18 6 13 19 6 14 1637.94599 0.0600 2 0 2 1 0 1 1667.36341 0.0532 3 0 3 2 0 2 1669.15888 0.0498 4 0 4 3 0 3 1670.96410 0.0966 5 0 5 4 0 4 1672.77080 0.0941 6 0 6 5 0 5 1674.55916 0.0998 7 0 7 6 0 6 1676.31852 0.0900 8 0 8 7 0 7 1678.04128 0.1116 9 0 9 8 0 8 1679.72755 0.1131 10 0 10 9 0 9 1681.38428 0.1256 11 0 11 10 0 10 1683.02138 0.1189 12 0 12 11 0 11 1684.65042 0.1210 / 145 J" K" K" ci C Freq.(cm" ') Intensity3 13 0 13 12 0 12 1686.28057 0.1023 14 0 14 13 0 13 1687.91877 0.1160 15 0 15 14 0 14 1689.57298 0.0932 16 0 16 15 0 15 1691.25045 0.1144 17 0 17 16 0 16 1692.97133 0.0882 18 0 18 17 0 17 1694.80964 0.0697 21 0 21 20 0 20 1699.41606 0.0642 22 0 22 21 0 21 1701.21898 0.0532 23 0 23 22 0 22 1703.02630 0.0553 4 1 4 3 1 3 1670.39238 0.0553 5 1 4 4 1 3 1673.52025 0.0830 5 1 5 4 1 4 1672.10112 0.0666 6 1 5 5 1 4 1675.65761 0.0377 6 1 6 5 1 5 1673.82129 0.0467 7 1 6 6 1 5 1677.80844 0.0447 7 1 7 6 1 6 1675.55037 0.0485 8 1 7 7 1 6 1680.01687 0.0685 8 1 8 7 1 7 1677.28505 0.0660 9 1 8 8 1 7 1682.21105 0.0522 9 1 9 8 1 8 1679.02497 0.0589 10 1 9 9 1 8 1684.42068 0.0503 10 1 10 9 1 9 1680.77095 0.0615 11 1 10 10 1 9 1686.61229 0.0552 11 1 11 10 1 10 1682.52701 0.0710 12 1 11 11 1 10 1688.77024 0.0533 12 1 12 11 1 11 1684.30939 0.0579 13 1 12 12 1 11 1690.88244 0.0400 13 1 13 12 1 12 1686.18418 0.0454 14 1 13 13 1 12 1692.94679 0.0101 15 1 14 14 1 13 1694.91273 0.0397 15 1 15 14 1 14 1689.06892 0.0502 16 1 15 15 1 14 1696.83919 0.0244 16 1 16 15 1 15 1690.90308 0.0491 17 1 17 16 1 16 1692.68972 0.0516 18 1 18 17 1 17 1694.46401 0.0507 3 2 1 2 2 0 1668.71889 0.0560 3 2 2 2 2 1 1668.68415 0.0560 4 2 2 3 2 1 1670.64593 0.0468 4 2 3 3 2 2 1670.55190 0.0599 5 2 3 4 2 2" 1672.66155 0.0513 5 2 4 4 2 3 1672.45688 0.0764 6 2 4 5 2 3 1674.77432 0.0727 6 2 5 5 2 4 1674.39847 0.0897 7 2 5 6 2 4 1676.98987 0.0758 7 2 6 6 2 5 1676.36922 0.0779 / 146 J' K' K- J" K" K" a c . Freq.(cm" 1) Intensity3 8 2 6 7 2 5 1679.30537 0.0731 8 2 7 7 2 6 1678.36776 0.1381 9 2 7 8 2 6 1681.70441 0.0727 9 2 8 8 2 7 1680.38783 0.0985 10 2 8 9 2 7 1684.12408 0.0662 10 2 9 9 2 8 1682.42742 0.0934 11 2 9 10 2 8 1687.46504 0.0376 11 2 10 10 2 9 1684.48340 0.0857 12 2 11 11 2 10 1686.55312 0.0980 13 2 11 12 2 10 1692.42524 0.0686 13 2 12 12 2 11 1688.63636 0.0821 14 2 12 13 2 11 1695.09143 0.0588 14 2 13 13 2 12 1690.73076 0.0675 15 2 13 14 2 12 1697.77091 0.0514 15 2 14 14 2 13 1692.83583 0.0679 16 2 14 15 2 13 1700.43752 0.0378 16 2 15 15 2 14 1694.95165 0.0643 17 2 15 16 2 14 1703.07189 0.0369 17 2 16 16 2 15 1697.07646 0.0449 18 2 16 17 2 15 1705.65519 0.0344 18 2 17 17 2 16 1699.21784 0.0422 19 2 18 18 2 17 1701.37266 0.0410 20 2 19 19 2 18 1703.54691 0.0333 21 2 20 20 2 19 1705.74657 0.0269 5 4 2 4 4 1 1670.99017 0.0528 6 4 3 5 4 2 1673.00958 0.0742 7 4 4 6 4 3 1675.08627 0.1432 8 4 5 7 4 4 1677.22175 0.1127 9 4 5 8 4 4 1679.41647 0.0925 9 4 6 8 4 5 1679.41192 0.0925 10 4 6 9 4 5 1681.66298 0.0844 10 4 7 9 4 6 1681.66298 0.0844 11 4 7 10 4 6 1683.98032 0.1007 11 4 8 10 4 7 1683.96714 0.0462 12 4 8 11 4 7 1686.36403 0.0581 12 4 9 11 4 8 1686.32380 0.0588 13 4 9 12 4 8 1688.79979 0.0574 13 4 10 12 4 9 1688.72579 0.0543 14 4 10 13 4 9 1691.29035 0.0591 14 4 11 13 4 10 1691.16409 0.0624 15 4 11 14 4 10 1693.80685 0.0315 8 5 4 7 5 3 1676.13892 0.0488 9 5 5 8 5 4 1678.35090 0.1381 10 5 6 9 5 5 1680.65932 0.0545 11 5 7 10 5 6 1683.00596 0.0506 / 147 J' K' K' a c J" K" K" cL C Freq.(cm~ 1) Intensity3 12 5 8 11 5 7 1685.40938 0.0550 13 5 9 12 5 8 1687.86801 0.0462 14 5 10 13 5 9 1690.37875 0.0337 8 6 3 7 6 2 1674.81039 0.0546 9 6 4 8 6 3 1677.11318 0.1124 10 6 5 9 6 4 1679.47811 0.0818 11 6 6 10 6 5 1681.90448 0.0563 12 6 7 11 6 6 1684.38695 0.0772 13 6 8 12 6 7 1686.92479 0.0714 14 6 9 13 6 8 1689.51273. 0.0511 15 6 10 14 6 9 1692.15083 0.0528 16 6 11 15 6 10 1694.83377 0.0514 17 6 12 16 6 11 1697.54734 0.0569 18 6 13 17 6 12 1700.32073 0.0322 8 5 3 8 5 4 1662.68413 0.0567 10 5 5 10 5 6 1663.82957 0.0634 11 5 6 11 5 7 1664.48661 0.0419 13 5 8 13 5 9 1665.96220 0.1352 14 5 9 14 5 10 1666.78146 0.0471 8 6 2 8 6 3 1661.36222 0.1503 9 6 3 9 6 4 1661.98035 0.1034 10 6 4 10 6 5 1662.66072 0.0751 11 6 5 11 6 6 1663.40154 0.0704 12 6 6 12 6 7 1664.19712 0.0470 13 6 7 13 6 8 1665.04665 0.0408 14 6 8 14 6 9 1665.94783 0.1352 J' K' K' J" K" K" Freq.(cm" 1) Intensity3 8 7 3 9 7 4 1612.33456 0.1020 9 7 4 10 7 5 1611.26619 0.0921 10 7 5 11 7 6 1610.13483 0.0807 11 7 6 12 7 7 1608.94026 0.3889 12 7 7 13 7 8 1607.70100 0.1981 13 7 8 14 7 9 1606.40955 0.1685 14 7 9 15 7 10 1605.07285 0.1861 15 7 10 16 7 11 1603.68932 0.5433 16 7 11 17 7 12 1602.27092 0.2073 17 7 12 18 7 13 1600.81112 0.1926 18 7 13 19 7 14 1599.30575 0.0684 / 148 j ' K : K : a . c J" K " K " a c Freq.(cm" 1) Intensity3 19 7 14 20 7 15 1597.78516 0.1843 20 7 15 21 7 16 1596.22179 0.1323 21 7 16 22 7 17 1594.62940 0.1476 22 7 16 23 7 17 1593.00905 0.1138 22 7 17 23 7 18 1593.00527 0.1138 8 7 3 7 7 2 1640.91671 0.0683 9 7 4 8 7 3 1643.21619 0.1778 10 7 5 9 7 4 1645.45427 0.1246 11 7 6 10 7 5 1647.63555 0.1680 12 7 7 11 7 6 1649.76731 0.2983 13 7 8 12 7 7 1651.85230 0.2202 14 7 9 13 7 8 1653.89509 0.2906 15 7 10 14 7 9 1655.89756 0.2062 16 7 11 15 7 10 1657.86261 0.2520 17 7 12 16 7 11 1659.79116 0.2342 18 7 13 17 7 12 1661.67543 0.2806 19 7 14 18 7 13 1663.55355 0.2017 20 7 15 19 7 14 1665.39161 0.2027 21 7 16 20 7 15 1667.20447 0.1803 22 7 16 21 7 15 1668.99611 0.2657 22 7 17 21 7 16 1668.98430 0.0338 a - line frequencies and intensities from deconvoluted spectra, FWHM of response factor = 0.008 cm" 1. APPENDIX II : CHARACTER TABLES E d o-,.(xr) a'Xyz) 1 1 1 1 z x2,y\z2 1 1 - 1 - 1 R, xy 1 - 1 1 - 1 x, R, xz 1 - 1 - 1 1 y, R, E C2{z) C2(y) C2(x) 1 1 1 1 x\ y\z2 1 1 - 1 - 1 z, Rz xy 1 - 1 1 - 1 >\ Ry xz 1 - 1 - 1 1 x, Rx yz £ 2C^ • 00 o„ 1 1 1 2 x1 + y 2 , : 2 1 1 - 1 *- £, =n 2 2 cos O 0 (x, y)AR,. R,) (xz, yz) 2 2 cos 2<t> • 0 (x2 — y2, xy) * £ 3 = 0 2 2 cos 30 • 0 149 APPENDIX III: AMINOBORANE RESIDUALS The K Q value for each plot is given in the top left corner. © = upper asymmetry component, * = lower asymmetry component. Fit A : Standard Deviation = 1.2 cm" 1 Be *1 • « fcOO 100 11.00 HOD CD "I 1 8 ; LOO \0D HOD 13.X "1 4 *1 • • i t • 1 4--100 LCD 7.00 1,00 HOD 1&.0D o B i IDS *0D • . S •—T ~ l 1 HOD HOD 1 6 • • • a • l * t t HOD - f l i i i 1 1 1 1 1 1— —r i r -LOB 100 ILOO HOD 1S.00 150 / 151 ft oi] • a s * y 7 + y< 11.00 It. 00 J10D 1 1 1 *1 0 8 *1 8 I *1 " I . *•* *•<*> '-CD fcOD 11.00 HOD HDD J1 §.1 i 8 I -i n.oo ix. a 1 *0D 3.00 I LOO IS. 00 ft in -100 7.0D 100 J HOD IV OP LOD fl,OD lfcOD IB. 00 / 152 — i 1 r — i 1 1 1 1 1—-i 1 1 1 T — - i 1.0D I B ISO 7.00 10O 11.00 1100 11.00 J • i : *1 • • • Si in -t 8"] "1 11 1 LCD 100 7. DO LCD ILOO IX 00 liflC "1 6 il-aD 11.00 1 r~—i 1 1 i i 1 1 1 1 r —i 1 1 1-00 I I S 1,00 T.OD t.00 1U0O U. 00 IV3 / 153 Fit B : Standard Deviation = 0.11 cm" 1 i o cn -i SV 11 1 3 8 ' *1 iOD T.00 1.00 11.00 11.00 IS. 0  1 1 d l I 1 Yft in 4 1-s I i 8; 11 • • • 7*1 ! 8.] .1 LCD &00 B.0D T.OC too i i . on i*oo i i . rr —\ r t i T" • 1.00 l>0D S.0D T.00 kVOO J HDD 19.00 ft ?1 J *1 4-- 1.00 1.00 LOO T.OD 11.00 11.00 13.00 8 t l f t 1 i T 1 r- -T 1 ? r -•.•> ii.« / 1 1 0 .1 5s; »! ItVOD JS.QP 1 3 Si =1 \ a. - t — i — . -I.OD - 4 Si J <1 -1 a i i *i 8 ' *1 d l 1 " 1 * • ( 8 • • .1 * 8 *1 / 155 2{vs) 1 0 4--IOC T.OD 100 9 d -t • • • • • 1.00 400 IOD T.S 400 11.00 142 J 5 8 : *1 * * • • 100 ILOO 11.01 l/> i *1 •I 8 ! *1 t.00 4 CO 14 00 1400 S.1 Fit C : Standard Deviation = 0.02 cm" 1 / 156 / 157 2(Pc) 7. X 100 ILOC 1S.OD 14.00 J fi 5 h • • * e APPENDIX IV : NBN LINE ASSIGNMENTS 3 * 2 ( D - 3A,(0) Line Freq.(cm" 1) Weight Obs-Calc.a Q(36) 17120.8853 1.00 -0.0010 Q(35) 17121.4367 1.00 -0.0004 Q(34) 17121.9740 1.00 0.0019 Q(33) 17122.4897 1.00 -0.0017 Q(32) 17122.9972 1.00 0.0022 Q(31) 17123.4821 1.00 -0.0009 Q(31) 17123.4830 1.00 0.0000 Q(30) 17123.9553 1.00 0.0000 Q(29) 17124.4118 1.00 -0.0003 Q(29) 17124.4114 1.00 -0.0007 Q(28) 17124.8530 1.00 -0.0004 Q(27) 17125.2793 1.00 0.0002 Q(26) 17125.6896 1.00 0.0002 Q(25) 17126.0852 1.00 0.0010 Q(25) 17126.0848 1.00 0.0006 Q(24) 17126.4651 1.00 0.0014 Q(23) 17126.8285 1.00 0.0008 Q(22) 17127.1754 1.00 -0.0009 Q(21) 17127.5094 1.00 -0.0003 Q(20) 17127.8268 1.00 -0.0009 Q(19) 17128.1309 1.00 0.0005 Q(19) 17128.1300 1.00 -0.0004 Q(18) 17128.4166 1.00 -0.0012 R(12) 17142.6227 1.00 -0.0007 R(13) 17143.4108 1.00 -0.0003 R(14) 17144.1864 1.00 0.0029 R(15) 17144.9422 1.00 0.0017 R(16) 17145.6798 1.00 -0.0023 R(17) 17146.4050 1.00 -0.0034 R(18) 17147.1205 1.00 0.0014 R(19) 17147.8133 1.00 -0.0011 R(20) 17148.4973 1.00 0.0031 R(21) 17149.1597 1.00 0.0012 R(21) 17149.1585 1.00 0.0000 R(22) 17149.8049 1.00 -0.0023 R(23) 17150.4403 1.00 0.0001 R(24) 17151.0582 1.00 0.0005 R(24) 17151.0563 1.00 -0.0014 R(25) 17151.6585 1.00 -0.0009 R(26) 17152.2459 1.00 0.0005 R(27) 17152.8148 1.00 -0.0009 158 / 159 Line Freq.(cm" 1) Weight Obs-Calc.a R(28) 17153.3734 1.00 0.0033 R(29) 17153.9096 1.00 0.0009 R(30) 17154.4339 1.00 0.0025 R(31) 17154.9379 1.00 -0.0002 R(32) 17155.4280 1.00 -0.0009 R(33) 17155.9021 1.00 -0.0016 R(34) 17156.3602 1.00 -0.0021 R(35) 17156.8015 1.00 -0.0034 R(36) 17157.2312 1.00 -0.0001 R(37) 17157.6423 1.00 0.0009 R(38) 17158.0381 1.00 0.0028 3 * , ( D - 3A,(1) Line Freq.(cm" 1) Weight Obs-Calc.a Q(14) 16096.2120 1.00 -0.0031 Q(15) 16096.0644 1.00 -0.0011 Q(16) 16095.9063 1.00 0.0005 Q(17) 16095.7409 1.00 0.0048 Q(18) 16095.5575 1.00 0.0012 Q(19) 16095.3669 1.00 0.0005 Q(20) 16095.1666 1.00 0.0003 Q(21) 16094.9602 1.00 0.0041 Q(22) 16094.7416 1.00 0.0058 Q(23) 16094.5018 1.00 -0.0034 Q(24) 16094.2619 1.00 -0.0026 Q(25) 16094.0132 1.00 -0.0003 Q(26) 16093.7537 1.00 0.0014 Q(27) 16093.4776 1.00 -0.0032 Q(28) 16093.1980 1.00 -0.0010 Q(29) 16092.9078 1.00 0.0010 Q(30) 16092.5997 1.00 -0.0046 Q(31) 16092.2886 1.00 -0.0027 Q(32) 16091.9682 1.00 0.0002 Q(33) 16091.6320 1.00 -0.0022 Q(34) 16091.2894 1.00 -0.0005 Q(35) 16090.9391 1.00 0.0040 Q(36) 16090.5704 1.00 0.0007 Q(37) 16090.1952 1.00 0.0015 R(14) 16110.9827 1.00 -0.0016 R(15) 16111.8161 1.00 -0.0023 / 160 Line Freq.(cm" 1) Weight Obs-Calc.a R(16) 16112.6412 1.00 -0.0011 R(16) 16112.6421 1.00 -0.0002 R(17) 16113.4552 1.00 -0.0007 R(19) 16115.0529 1.00 0.0006 R(20) 16115.8360 1.00 0.0010 R(21) 16116.6075 1.00 0.0001 R(21) 16116.6075 1.00 0.0001 R(22) 16117.3686 1.00 -0.0007 R(23) 16118.1204 1.00 -0.0004 R(24) 16118.8613 1.00 -0.0005 R(25) 16119.5944 1.00 0.0021 R(26) 16120.3134 1.00 0.0011 R(27) 16121.0226 1.00 0.0009 R(28) 16121.7214 1.00 0.0009 R(29) 16122.4087 1.00 0.0001 R(29) 16122.4095 1.00 0.0009 R(30) 16123.0866 1.00 0.0005 R(31) 16123.7538 1.00 0.0010 R(32) 16124.4086 1.00 -0.0001 R(32) 16124.4086 1.00 -0.0001 R(33) 16125.0529 1.00 -0.0010 R(3'4) 16125.6876 1.00 -0.0005 R(36) 16126.9224 1.00 -0.0015 R(38) 16128.1158 1.00 0.0001 3 * 2 ( 2 ) - JA,(1). Line Freq.(cm" ') Weight Obs-Calc.a P(33) 17034.1472 1.00 -0.0010 P(32) 17035.6359 1.00 0.0002 P(32) 17035.6352 1.00 -0.0005 P(31) 17037.1080 1.00 0.0003 P(30) 17038.5653 1.00 0.0011 P(29) 17040.0066 1.00 0.0012 P(27) 17042.8407 1.00 -0.0009 P(27) 17042.8425 1.00 0.0009 P(26) 17044.2355 1.00 -0.0011 P(25) 17045.6148 1.00 -0.0014 P(24) 17046.9814 1.00 0.0009 P(23) 17048.3309 1.00 0.0016 P(22) 17049.6616 1.00 -0.0013 / 161 Line Freq.(cm~ ') Weight Obs-Calc.a P(21) 17050.9811 1.00 0.0000 P(21) 17050.9808 1.00 -0.0003 Q(39) 17062.9846 1.00 0.0023 Q(38) 17063.5892 1.00 -0.0033 Q(38) 17063.5923 1.00 -0.0002 Q(36) 17064.7675 1.00 0.0024 Q(35) 17065.3262 1.00 -0.0012 Q(34) 17065.8737 1.00 -0.0001 Q(33) 17066.4040 1.00 -0.0003 Q(32) 17066.9181 1.00 -0.0008 Q(31) 17067.4161 1.00 -0.0015 Q(32) 17066.9201 1.00 0.0012 Q(31) 17067.4174 1.00 -0.0002 Q(30) 17067.9008 1.00 0.0003 Q(30) 17067.9014 1.00 0.0009 Q(29) 17068.3685 1.00 0.0009 Q(28) 17068.8188 1.00 -0.0001 Q(27) 17069.2548 1.00 0.0003 Q(26) 17069.6737 1.00 -0.0006 Q(25) 17070.0778 1.00 -0.0005 Q(24) 17070.4663 1.00 -0.0004 Q(23) 17070.8401 1.00 0.0007 Q(23) 17070.8397 1.00 0.0003 Q(22) 17071.1957 1.00 -0.0008 Q(21) 17071.5370 1.00 -0.0008 Q(20) 17071.8654 1.00 0.0018 Q(19) 17072.1740 1.00 0.0003 Q(18) 17072.4676 1.00 -0.0007 Q(17) 17072.7477 1.00 0.0005 Q(16) 17073.0096 1.00 -0.0010 Q(15) 17073.2602 1.00 0.0018 Q(14) 17073.4897 1.00 -0.0010 Q(13) 17073.7063 1.00 -0.0011 Q(12) 17073.9097 1.00 0.0010 (0)- 3A,(0) Line Freq.(cm~ 1) Weight Obs-Calc.a P(30) 17021.8098 1.00 0.0014 P(29) 17023.1867 1.00 0.0042 P(28) 17024.5439 1.00 0.0001 Line Freq.(cm" ') Weight / 162 Obs-Calc.a P(27) 17025.8907 P(27) 17025.8918 P(26) 17027.2265 P(25) 17028.5501 P(25) 17028.5513 P(24) 17029.8608 P(23) 17031.1570 P(22) 17032.4422 P(21) 17033.7136 P(20) 17034.9747 P(20) 17034.9732 P(19) 17036.2184 P(18) 17037.4528 P(17) 17038.6750 P(17) 17038.6761 P(16) 17039.8836 P(15) 17041.0782 P(14) 17042.2604 P(13) 17043.4309 P(12) 17044.5879 P(12) 17044.5874 P(ll) 17045.7291 P(10) 17046.8642 Q(39) 17047.3780 Q(38) 17047.8836 P( 9) 17047.9809 Q(38) 17047.8847 P( 9) 17047.9826 Q(37) 17048.3848 Q(36) 17048.8620 Q(36) 17048.8655 Q(35) 17049.3322 Q(34) 17049.7851 Q(33) 17050.2278 Q(32) 17050.6560 Q(31) 17051.0709 Q(31) 17051.0710 Q(30) 17051.4738 Q(29) 17051.8602 Q(30) 17051.4733 Q(29) 17051.8624 Q(28) 17052.2373 Q(27) 17052.6001 Q(26) 17052.9488 Q(25) 17053.2858 1.00 -0.0016 1.00 -0.0005 1.00 -0.0015 1.00 -0.0008 1.00 0.0004 1.00 -0.0002 1.00 -0.0014 1.00 -0.0008 1.00 -0.0012 1.00 0.0008 1.00 -0.0007 1.00 -0.0018 1.00 -0.0009 1.00 0.0005 1.00 0.0016 1.00 0.0011 1.00 0.0004 1.00 0.0001 1.00 0.0008 1.00 0.0008 1.00 0.0003 1.00 -0.0022 1.00 0.0014 1.00 -0.0009 1.00 -0.0034 1.00 -0.0006 1.00 -0.0023 1.00 0.0011 1.00 0.0031 1.00 -0.0011 1.00 0.0024 1.00 0.0010 1.00 -0.0008 1.00 0.0003 1.00 0.0003 1.00 0.0001 1.00 0.0002 1.00 0.0011 1.00 -0.0012 1.00 0.0006 1.00 0.0010 1.00 0.0004 1.00 0.0008 1.00 0.0002 1.00 0.0010 / 163 Line Freq.(cm" 1) Weight Obs-Calc.a Q(24) 17053.6061 1.00 -0.0018 Q(23) 17053.9175 1.00 -0.0005 Q(22) 17054.2141 1.00 -0.0009 Q(21) 17054.4983 1.00 -0.0006 Q(21) 17054.4990 1.00 0.0001 Q(20) 17054.7701 1.00 0.0002 Q(19) 17055.0281 1.00 0.0002 Q(18) 17055.2718 1.00 -0.0011 Q(17) 17055.5047 1.00 -0.0002 Q(17) 17055.5054 1.00 0.0005 Q(16) 17055.7236 1.00 -0.0004 Q(15) 17055.9298 1.00 -0.0003 Q(14) 17056.1228 1.00 -0.0004 Q(13) 17056.3037 1.00 0.0002 Q(12) 17056.4708 1.00 0.0000 Q(12) 17056.4709 1.00 0.0001 Q(ii) 17056.6264 1.00 0.0011 QUO) 17056.7678 1.00 0.0010 Q( 9) 17056.8944 1.00 -0.0010 Q( 8) 17057.0108 1.00 -0.0004 R( 7) 17065.0371 1.00 -0.0007 R( 8) 17065.9247 1.00 -0.0004 R( 9) 17066.7982 1.00 -0.0012 R(10) 17067.6597 1.00 -0.0010 R(10) 17067.6604 1.00 -0.0003 R(ll) 17068.5086 1.00 -0.0004 R(12) 17069.3438 1.00 -0.0004 R(13) 17070.1670 1.00 0.0006 R(14) 17070.9757 1.00 0.0002 R(14) 17070.9760 1.00 0.0005 R(15) 17071.7714 1.00 -0.0001 R(15) 17071.7733 1.00 0.0018 R(16) 17072.5549 1.00 0.0005 R(17) 17073.3252 1.00 0.0011 R(18) 17074.0814 1.00 0.0008 R(19) 17074.8244 1.00 0.0004 R(19) 17074.8250 1.00 0.0010 R(20) 17075.5553 1.00 0.0012 R(21) 17076.2725 1.00 0.0016 R(22) 17076.9764 1.00 0.0019 R(22) 17076.9738 1.00 -0.0007 R(23) 17077.6657 1.00 0.0009 R(23) 17077.6656 1.00 0.0008 R(24) 17078.3411 1.00 -0.0007 R(25) 17079.0014 1.00 -0.0040 / 164 Line Freq.(cm" 1) Weight Obs-Calc.a R(26) 17079.6529 1.00 -0.0027 R(26) 17079.6555 1.00 -0.0001 R(27) 17080.2919 1.00 -0.0005 R(28) 17080.9136 1.00 -0.0021 R(29) 17081.5240 1.00 -0.0016 R(30) 17082.1205 1.00 -0.0015 R(31) 17082.7048 1.00 0.0000 R(31) 17082.7035 1.00 -0.0013 R(33) 17083.8296 1.00 0.0000 R(33) 17083.8325 1.00 0.0029 R(34) 17084.3761 1.00 0.0045 R(35) 17084.8995 1.00 -0.0004 R(36) 17085.4138 1.00 -0.0006 a - calculation described in section 4.2.1. 

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