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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  transform interferometer and rotationally analyzed by combination  differences.  ( N H B H ) was 2  2  the 1550-1750 cm"  a new  search/match  Sub-bands  from  1  algorithm based  four  resonance between the v , 3  on ground  separate vibrational  was state  bands were  deduced to be a three-way  v + v , and 2 v 7  a Fourier  region of the spectrum  discovered in this region. The interaction scheme was anharmonic  recorded by  B  6  levels with the fourth  level, V f + c, » induced by a Coriolis mechanism with the members of the triad. 2  The first order anharmonic constants were approximated by a least squares fit of the triad intensities: W W  7  86 6  3  =  7 8  8.4±0.1 • cm" , W  =  1  36  6  15.8 + 0.4 cm"  1  with  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  allowed the vibrational  of the  3  $  - 3  2  electronic state to be  A^  system  determined: AG  =  986.351 cm" , 1  spacings of each AG  2 cm"  1  for the # 3  2  state and AG,  =  =. 1033.739cm"  1  for the A,  its expected position of 18025 cm" .  electronic state assignment  2  1  transition was  The  970  state. The  was  3  discovered  3  previously unassigned II, - A (0-0) sub-band 3  977.855  -'•2  cm"  1  below of this  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  T A B L E OF  CONTENTS  Abstract List of Figures  ii .  v  Acknowledgements  vi  INTRODUCTION  vii  Chapter 1. THEORY 1.1. Molecular Rotations 1.2. Molecular Vibrations 1.3. Selection Rules In The Infrared 1.4. Resonance Effects in the, Infrared 1.4.1. Anharmonic Resonance 1.4.2. Coriolis Interactions 1.5. Electronic Transitions: Heteronuclear Diatomics 1.5.1. Vibronic Transitions 1.5.2. Rovibronic Transitions  1 2 7 9 13 15 17 21 28 30  References  32  Chapter 2. EXPERIMENTAL 2.1. Aminoborane 2.2. Niobium Nitride 2.3. The Diode Array Detector 2.3.1. Introduction 2.3.2. Performance Characteristics 2.3.3. Operating Precautions 2.3.4. Software 2.3.4.1. Introduction 2.3.4.2. Detector Calibration 2.3.4.3. Graphics  34 34 34' 37 37 38 39 40 40 41 42  References  43  Chapter 3. AMINOBORANE 3.1. Background 3.2. Rotational Analysis 3.3. Vibrational Assignments: The 3.4. Least Squares Treatment 3.5. Discussion  44 44 46 59 64 75  System Model  References  76  Chapter 4. NIOBIUM NITRIDE 4.1. Background 4.2. Analysis 4.2.1. Rotational Analysis  78 78 81 83  iii  4.2.2. Determination of the Electronic States 4.3. Discussion 4.3.1. Results 4.3.2. Comment on Low-Lying States 4.3.3. Future Work  84 87 87 88 91  References  92  Appendix I : Aminoborane Line Assignments  94  Appendix II : Character Tables  149  Appendix III: Aminoborane  150  Residuals  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(a ), (b) case(a^)  ..27  a  Figure 1.4 Effect of case(a ) Coupling in NbN: Ft lines of * ( 1 ) - A , ( l ) band, P lines o f $ \ 0 ) - A, (0) band  28  Figure 2. LIF experimental apparatus  35  3  3  fl  2  3  3  2  Figure 3.1. Low-resolution Figure  3.2. Sub-band fundamental  transmittance  origins  spectrum of N H B H 2  of potential  interloper  (1510-1720cm" ) . 47 1  2  bands near  the v  48  Figure  3.3. Medium-resolution fundamental  Figure  3.4. High-resolution transmittance from all four vibrations present  transmittance  spectrum  of the A-type  2  2  51 T  +  of N H B H 2  cm"  1  Upper  6  55 2  3.7 Scaled  2v  2  Figure 3.6 Ground State Rotational Energy Levels of N H B H Figure  State  v„ 48  spectrum of N H B H ; sub-bands  Figure 3.5 Upper State Rotational Energies of the Levels - v T + V , and  3  57  2  Sub-band Origins of the 1609 and 1625  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 $ - A 3  Figure  4.4. Wavelength Resolved line of n , - A 3  3  2  2  3  1  system of NbN  Fluorescence  (0-0) Sub-Band  82  of Optically Pumped Q(13) 86  v  ACKNOWLEDGEMENTS  I would provided to me the  niobium  like to thank Dr. A.J. Merer  for the advice and guidance he  throughout this work. Thanks also to Dr. Y. Azuma for aid with  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  (NbN). The infrared of spectrum resolution spectrum  Fourier transform  of N H B H 2  2  ( N H B H ) and niobium 2  2  nitride  was recorded by means of a high  interferometer and the Doppler  limited  electronic  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  detector, used  chapter details the implementation  of a diode array  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 N H B H 2  NbN  and  2  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 N H B H 2  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 spectroscopic and  the basic theory  that was  necessary to carry out  analysis detailed in this thesis. Before discussing the rotational  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  the nuclei and  an electronic part. The  electrons cause their relative velocities to be so different that the  electrons follow the nuclei instantaneously. be  separated  into an  nuclear motions may  The  relative masses of  electronic (^ ) e  be analyzed  and  The  molecular wavefunction can  a nuclear  part (\/>) such that the n  independently of the electronic motions.  nuclear motions, rotation and vibration, cannot be completely  even though the energies  associated with these motions differ by  three orders of magnitude. The  then  vibration and  separated  approximately  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  significant, will cause perturbations  and  the interaction term, if  to the energy states predicted by  the pure  terms.  The  rotational and  vibrational Hamiltonians are considered  1  for polyatomic  THEORY / 2 molecules  since  an analysis  was  spectrum.  Strong  vibration-rotation  performed  on a  perturbations  interaction and various anharmonic resonances spectrum  region  resulting  were observed  of the from  a  NH BH 2  2  Coriolis  in the N H B H 2  2  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  H _ = r  r  J  2  21  + z  J  2  21  2  + _Y_ 21  x  (i.i)  y  where J , «J , Jy> are the angular momentum operators which represent the z  X  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 principal inertial moments are ordered as: I  a  <  a, b, and c, such  1^ <  I  c >  that  The molecule may  then be characterized by the rotational constants A, B, and C, which are related to  !  a ' b' X  J  c>  by:  I  a  a  x A  = I x B ° K  = I„xC c  =  h 8ir c 2  (1.2)  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 of the N H B H 2  There  2  chosen for the analysis  spectrum.  are  five  possible  types  of  rotors  depending  on  the  relative  magnitudes of I , Iw, I • 1. linear molecules  V  2. spherical tops  l  a  3. prolate symmetric tops  l  4. oblate symmmetric tops  X  5. asymmetric tops  l  The  Hamiltonian  (1.1) can  be  a  a  a  *b  =  b  = c  = 0,  -  l  <  J  b  l  =  = *b <  <  <  l  c  !  l  c  c-  conveniently represented in matrix  using the symmetric top rotational basis; in this basis the operators J have  the  sharp  eigenvalues  J(J+l)h  2  and  Kit  2  respectively  form  and J _ 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 J , 2  J , J , and J  the eigenvalue equations for  [5] and the commutation relations appropriate to molecule  fixed components [6]: [J ,Jy] = x  —ihJ  z  (plus the other two cyclic permutations),  equation (1.1) can be shown to have the non-vanishing matrix elements:  (1.3)  THEORY / 4 = i (B + C)J(J+1) + [ A -  <J,K|H |J,K> rr  <J,K±2|H |J,K> rr  B+C 2  ] K  (1.4)  2  = 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  symmetric tops (prolate in the I  molecules,  and oblate in the IH  spherical  tops and  representation), then  equation (1.5) vanishes leaving the Hamiltonian matrix diagonal. The rotational energy levels are calculated directly from (1.4): F(J,K) = BJ(J+1) + (A-B) K .  (1.6)  2  The linear  K  dependent term molecules  vanishes for spherical tops because A  because  a  linear  molecule  cannot  have  =  B, and  rotational  for  angular  momentum about its axis.  The  asymmetric rigid rotor energy  the Hamiltonian  matrix  for each  value of J greater than  separates at once into matrices for even <K±l|H|K>  matrix  elements,  levels are calculated by diagonalizing zero. The matrix  and odd J because there are no  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 , B^, B . The transformation has the effect of taking the sums a  c  and differences of the original symmetric top basis functions. Each of the four  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 J j ^ g j ^  notation [3]. K  and K  a  are the  c  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 Species  3  of Asymmetric Rotor Energy Levels  Submatrix  J even  J odd  E*  A(ee)  B (eo)  E"  B (eo) Cl  0  B (oe)  B (oo)  B (oo)  B (oe)  E  =  A(ee)  =  +  c  +  b  fa  c  a - the representations of A, B , Bj^, B in App. II. Q  A  are given in the D  2  character table  molecule is not a rigid rotor as it is distorted by centrifugal forces as  it rotates. Thus the instantaneous dependent on the molecule's angular for  c  centrifugal effects  Hamiltonian  moments of inertia of the molecule become momentum. The simplest method to account  in asymmetric  tops  is to use Watson's  A-reduced  [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  are given [9]  6  as:  B+C  —- ] K - A j J (J +1) - A J(J + 1)K -  < J,K|H |J,K > = i(B + C)J(J +1) + [A  2  r  2  2  2  J  K  Aj^K'+SjJ^J+l) **^ J (J+l) K +$ J(J-rl)K +$ K\ 3  2  2  2  K  <J,K±2|H |J,K>={i (B-C)-6 J(J+1)-£5 [(K±2) +K ]+0 2  r  J  2  K  i0 J(J+l)[(K±2) +K ] + i 0 2  2  JK  K  J (J+1) + 2  J  2  [(K±2)«+ K"]} X  {[J(J+ 1)-K(K± 1)][J(J+ 1)-(K± 1)(K±2)]}*,  in the I  (1.8)  4  R J  (1.9)  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 N H B H 2  2  spectra.  The rotational term values for a non-rigid diatomic molecule are given by:  THEORY / 7 F(J) = BJ(J + 1) - D J ( J + 1 ) 2  All centrifugal terms higher than D  2  +  HJ (J+1) 3  - ...higher terms.  3  (1.10)  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  has 12 vibrational degrees of freedom whereas NbN  NH BH 2  2  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  vibrations by introducing normal vibrations. A  separate fundamental  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  individual normal vibrations from each other.  The normal co-ordinates  are defined by the transformation:  the  THEORY / 8 q  = A Q\  where q represents the mass-weighted  (1.11)  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  A  = -  3  £ Q? + -  l\.  Q?  3  simplified form of the vibrational Hamiltonian, H , v  (1.12)  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 Q of normal vibrations. k  =  i 9  k  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:  k — d  E(v,,u ,...,w ,..) = I 2  k  kw  k  (v + k  ),  (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  In  infrared  RULES  IN THE  spectroscopy  INFRARED  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 :  <<^'|  where E(t) is the electric moment  field  of the molecule.  vibrational wavefunction,  A  E(t) -0 -|^,^;>,  (1.15)  of the source radiation product  wavefunction,  and U  |<//,^>, of the pure v  r  i / / and the pure rotational wavefunction, v  is the dipole  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:  THEORY / 10 <^,^|E <t)u z  where  (1.16)  \r;,4>;>,  2  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):  U  Z  = z*Zz u  +  u  x*Zx  +  u  y*Zy  (  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  wave functions, evaluation R  2  of the time-independent part of the transition moment  will reveal whether a transition is allowed:  R  R  z  = < ^ r l * Z z l*r>  <K\  u  z K>-  >  (L18  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 the  of the  normal  co-ordinates  may not be a constant; it is a function of  and so may  be represented  by  the Taylor  series  expansion:  3 u  z  u =(u_) +( 0  z  Substituting  z  , z )o Q k - < — 2 9Q 9Qj 1  3 2 u  +  9Q  k  k  ) Q-:Q +..-higher terms, 0  3  k  (1.19)  k  k  (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  =  < * r l *Zz \K>  KVo *vl*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  eigenfunctions and the direction cosines all can be classified under the D  2  top group  [5].  The  NH BH 2  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 aa <-> even.odd  J  J odd,even aa <->  J even,even  where the subscripts on J refer to the values of K_ AJ =  and  J odd.odd J J aa  K_  (1-21)  respectively  and  0,±1.  Evaluation of <i/>|  using the harmonic oscillator wave functions  v  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  completely  potential  energy  independent  expression.  by  definition  Normal but  real  vibrations are  assumed  vibrations cannot  be  to  be  separated  because they occur within an intimate molecular framework.  Electrical molecule's  anharmonicity  dipole moment on  refers  to  the  non-linear  nuclear displacements. By  dependence  of  the  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 very small nuclear displacements  be adequate for  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  because of the cross term linking two normal co-ordinates. The  (2^)  higher terms in  the expansion contribute to the higher overtone and combination vibrations.  1.4.  RESONANCE  The inadequacy  EFFECTS  infrared  IN  THE  INFRARED  spectra of polyatomics  are replete  with  examples of the  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  various  unperturbed its  mechanisms. When  rotational energy levels may  a  vibrational  level  is apparently  by  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 small  compared  levels must be diagonalized. If the off-diagonal elements are not to  the  energy  separation  of  the  interacting  levels  then  a  resonance condition exists.  Solving a 2X2 Consider  two  energy  interaction element  secular equation reveals the effect of a resonance condition. levels:  and  T  which  2  interact  via  W;  |tfi> T,- E  W  W  T -E  1*2  >  = 2  0  (1.22)  an  hermitian  THEORY / 14 The eigenvalues of this problem are:  E  =  iO^+Ta) ±  i(4|W| + 8 ) * 2  (1.23)  2  where 8 = ( T — T ) is the separation of the unperturbed levels. The 1  of the two i//, and  2  resulting states 2  where:  2  define  the  a*/^—bi// and \p~ = 2  2A+8  a =  4A  eigenstates (yp*,  which  \(/~) will be mixtures of the basis functions  \l> -  \p* =  The  and  eigenfunctions  \p~) degree  , b = 2  may of  2A-6 4A  b^+a^  (1.24)  A , and A=i(4|W| + 6 ) , 2  (1.25)  2  be represented by the eigenvectors (a,-b) and mixing  of  the  basis  functions  (\p ^,  (b,a)  v//).  The  2  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 6 = 0;  perturbation is most pronounced for a given W  the eigenfunctions will be  point. When the course of two  when  50:50 mixtures of the basis functions at this energy levels cross the sign of 8 changes and  the degree of basis function mixing and hence the character of each eigenstate is reversed avoided  compared to before the crossing. This phenomenon is often called crossing and  is shown in figure 1.1  an  : the dotted lines represent the  THEORY courses  of  resulting  the  unperturbed  eigenstates.  slopes of the upper  The  energy  reversal  levels of  and  character  and lower eigenstate  the is  solid  lines  revealed  energy levels  /  represent  by  the  15 the  change  in  (E ,E"). +  1.4.1. Anharmonic Resonance  A the  multitude  fundamental  combinations. nearly  This  phenomenon  C0 . 2  be  The  levels  because  the  first  same  energies,  was  first  overtone  the  same  stretch  v,  (1337  levels  seem  to  they  c m " ) . When 1  have  repelled  formulae  interact  the  1931 by F e r m i  frequency  other;  the  [13] in the  cm" ), 1  frequency  spectrum (0,2,0)  the  level  v  of  Figure  1.1  resonance.  spectrum of  which the  happens  to  symmetric  (0,2,0)  and  (1,0,0)  appears  at  1285.5  E o  and  should occur  2  .E  -6  from  overtones  anharmonic  fundamental  (667  fundamental  observed in the each  allow  v i a an  degenerate bending  as  polyatomic a p a r t  accidentally degenerate, that is i f they  may  fundamental  energy  possible i n a  energy  recognized i n  of the  a p p r o x i m a t e l y twice its nearly  the  If two vibrational levels are  have  at  of vibrational levels are  +6  Perturbation Effects in a T w o L e v e l S y s t e m .  THEORY / 16 cm"  1  while the (1,0,0) appears at 1388.3 cm" . In 1940 Darling and Dennison 1  [14] noticed a similar anharmonic resonance in the water vapour spectrum where two overtones, (2v  y  The potential  root  = 2v ),  of these  energy  were involved.  3  perturbations  function. Third  rank  is in the anharmonic resonances relate  terms  of  two or three  the  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  resonance. If the interaction element is W  through  an  anharmonic  and i/> denotes a simple harmonic  oscillator wavefunction, then the integral < \p |W|^ ^ > must be totally 2  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 the  comprises the higher order terms from the potential function  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 J | + w J z  + w J .  2  (1.26)  2  x  y  The matrix elements for an allowed interaction between two vibrational levels \fy ^ and \p  are then:  2  <* ;J,K|H |* J,K>=W +F Z K + F 2  2  f  i;  21  21  2 1  P [J(J+1)]  < // ;J,K±2|H |^ ;J,K>=F M [J(J+1)-K(K± 1)]* [J(J+1)-(K±1)(K±2)]* (1.27)' <  2  f  where F  2 1  1  Z=(w ) 2  2 1  21  , F ,P=i(w + w ) 2  x  y  2  ,, and F , M = i ( w - w ) ,. 2  x  y  2  1.4.2. Coriolis Interactions  The  Coriolis force, F , is a fictitious force used to explain the change in c  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  force it does cause  c  is an apparent  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 , hence a counter-clockwise swirl in c  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 , the two vibrations will be coupled via a Coriolis interaction. c  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 = - i k g [x (673y ) - y (3/3x )], 2  with  cyclic  permutations  a  of z_, x  a  a  a  and y_, which  (1.29)  are the mass-weighted  Cartesian displacement co-ordinates of nucleus a in the molecule. The complete  THEORY / 19 rotation-vibration Hamiltonian is then:  H=  ( J  - P ?_ > + ? 2I 2  Z  2  Z  ( J  x*- P 2L_ + ( Y. P Y_ + _ I 2I 2I 2 ) Z  J  X  ) 2  v  1  (p2 + x. *  v  X  y  The pure vibrational Hamiltonian, Hy is the pure rotational Hamiltonian,  k  Q?).  (1.30)  (1.13), is readily separable from (1.30) as (1.1), after some algebra; therefore (1.30)  can be expressed as:  H = H + H +H , V  where  H  may  c  problem. H  (1.31)  c  be treated as a perturbation to the pure  rotation-vibration  has the form:  c  H  =  - j V s - £ x £ i _  h The  r  last three terms in H  \ c  b d s .  \  +  j k ^ J k  2 I  z  2 I  x  +  2 I  J k /  .32)  (1  y  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  \ip ;\p > v  r  basis the first three terms in (1.32) yield vibration-rotation products of the type:  z The  z  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 j " Q k j ^ p  p  (1  - > 34  where £ j is the Coriolis zeta constant which is defined as: k  SSJ  =  k 3  where  and  constants  relate  IK — ) ( S  3Q  A  3Qj  k  are obtained two normal  )-(  —  )( —  3Qj  3Q  A  )],  (1-35)  k  by cyclic permutations of z,x,y. The zeta  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 can only differ from zero if the product  result is known as Jahn's rule [14]; of the symmetry species of  Recalling  and Q j contains the rotation R  e >  that the vibrational basis function is merely a product  harmonic oscillator functions of the normal co-ordinates, the matrix the vibrational angular normal  momenta will be non-vanishing  vibrations change  pronounced  perturbations  magnitude;  when  v£  by one quanta. Terms are those  <  which  and P j  >  elements of  only when each of the  which  connect  of the  result  energy or vice  in the most  levels  of similar  versa.  When two  fundamentals interact the matrix elements of the vibrational angular momentum are given as:  <i,o|p |o,i> e  = -ifeSgjO^,  (1.36)  THEORY / 21 where fl^j =  itCw^/cjj)^-  (toJ/CJ^)*], and CJ^ is the frequency  of the kth  normal vibration.  The (the  Coriolis interaction examined  vibrations  involved  matrix elements of J  transform  in this thesis  as the rotation  and equation  (1.36) will  is an x-axis interaction  about the x-axis). Thus the yield  the off-diagonal  matrix  elements for an x-axis interaction:  <*» + l;i»j|- — k  | f ; ^ j + l><J,K±l|J |J,K>= k  x  i$J j[J(J+l)-K(K±l)]*  L*  X  where  £ j k  together  (1.37)  has absorbed the rotational constant B  with  the vibration  dependent  terms  O^j  (in the I and  i> j» k  representation), 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  An  TRANSITIONS:  HETERONUCLEAR  DIATOMICS  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 states are labelled Z, II, A,  with A  =  |MjJ =  0,1,2...L. Electronic  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 n* 3  one  u  term of iodine [19]. There are two idealized limiting cases whereby  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  projection along The  coupling  of S  to the z-axis  dominates, S  has a  well-defined  the z-axis, Z, which has allowed values: S, S—1, S —2,... —S.  total angular momentum due to the electronic motion is fi where:  0 = |A + Z|.  (1.38)  THEORY / 23 Thus for every A corresponding  >  0 state there will be a multiplet  to the different possible  values  of 2S+1 components,  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. multiplet  are labelled by the post-subscript  The components of the  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 3  A  and will have the multiplet components: A , A , A . 3  3  1  3  2  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  electric  will  dipole  non-vanishing:  transition  be allowed  dipole transitions an electronic  if the transition  moment,  R , is g  THEORY / 24 (1.40)  where ^  g  is an  electronic eigenfunction and  is the electric dipole moment  vector n  resulting from the electrons only. The  may  &  Cartesian components to arrive at expressions  be separated into its three  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 heteronuclear  diatomic  group C (see App.  II). There is an  oov  about the z-axis and The  is cylindrically symmetric  thus an  according  thus belongs to the point  infinite number of reflection planes,  a , y  infinite number of representations in the group.  electronic eigenfunctions must also belong  labelled  and  is used. A  to the C  to their representation in the  o o v  group and  group. Inspection of the  character table reveals that the symmetry species are labelled by: Z , +  instead of the conventional labels: A  1 ;  A, 2  may  E,,  E , 2  be C  Z", II, A,  E ,... This situation 3  can be attributed to the electronic spectroscopists who  used emperical arguments  before  symmetry  the  group theory  rules were developed. The  species of the  electronic states discussed above are equivalent to the conventional labels of the C  e o v  table. The  components of n  &  axes, and transform as Z*  Equation  behave like translations along the  (z) and II (x,y).  (1.40) will be non-zero when the direct product of the symmetry  species of the upper state, lower state and the  totally  following  molecular  symmetric selection  species  rules  for  L*.  dipole moment components contains  Examination  electric  dipole  of the  C  transitions  a > v  in  table yields the  case  the (a)  THEORY / 25 approximation; 1.  AA=0,+ 1.  2.  +<-)->—  3.  AZ = 0.  The  third  rule  for Z—Z transitions.  exists  because  the dipole  moment operator  contains no spin  co-ordinates [11]. Combining rules one and three gives:  AS2 = 0,±1.  While  (1.41)  rules one and three lose their meaning for case (c) coupling situations,  (1.41) still holds.  The consists  total angular momentum  of more  than  that the photons encounter  the electronic  angular  in a diatomic  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 When analyzing an electronic spectrum  the possible coupling situations.  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  THEORY pertinent  to m y  analysis  of N b N . A complete  description of these cases  / 26  is given  b y H e r z b e r g [10].  The discussed  relationship between  above. I f the  individually  coupled  J, is obtained allowed (a)  present and The  cannot  be  + is  the  spin-orbit  the  a  R where good  S for  of nuclear  z-axis then  by coupling R  values  coupling  to  effect  and  L  to R  the  0,1,2,..  ; J  when  spin-orbit coupling is moderate  interaction  ignored  there  was  discussed  are  two  above.  possible  1.2).  an  orbital  L  angular  The q u a n t u m  can never  already  and  overall rotational  figure  aproximation  (a) coupling has  spin can be neglected  (see =  case  and  angular  are  S  momentum,  number  be less  been  than  J fi.  has Case  momentum  is  (A=100 c m " , B = l  cm" )  [20].  I f the  nuclear  spin  1  ways  of  effect  of the  coupling I in  1  the  case  (a)  model.  When orbital  and  the spin  magnetic moments  interaction is  Figure  of  sufficiently  1.2  the strong  H u n d ' s Case  nuclear I will  (a)  moment be  Coupling  with  the  directly coupled  electron to  the  THEORY z-axis and  the  projection of I on the  z-axis, I , will be well-defined where  I, I—1, I —2,...—I. T h i s is called case ( a )  coupling where  fl  of  in  I  the  momentum, highly  molecule-fixed  F, is  unlikely  = l/1000th uncouples  axis  I F  case system. as  noticable the  3  4>  2  at —  the  the- molecule  to  varies  since  by  system  coupling  coupling  (see  figure  energies  moments  of  The  This  type  nuclear  [21] so rotation  =  implies quantization  1.3a).  to fl + I .  R  I  total of  coupling  moments  of the  angular  are  is  only  molecule readily  I from the z-axis.  momentum called  obtained  of those for electron  When coupled  axis  a  / 27  3  more  stronglj'  is obtained  (a^) It  rotates,  by  than  been  shown  resulting  I is  coupling J  coupling where has  the  /3  to to  implies [21]  that  rotational  the I as  axis;  then  shown  in  quantization the  size  [ F ( F + 1)-I(I+ 1)-J(J+ 1)]/[J(J+1)]  so  low J  branches.  values  ^ 1 sub-bands  in  the  rotational  discussed i n this thesis  magnetic  the  of of  The  is  the  total  angular  figure  1.3b.  This  I  the  splitting  moment,  in  the  space-fixed  hyperfine effects  rotational  is  splitting  are  most  structure  displaj'ed clear examples  of  of case  THEORY (a^)  coupling (see  weaker  figure  <i> ( 1 ) - A, (1)  3  3  2  band saturated  the  1.4). The band  so  data the  in  figure  1.4 w a s lines  P(28)-P(33)  taken  of the  /  to analj'ze 3  $  28 the  ( 0 ) - A, (0) 3  2  detector.  1.5.1. Vibronic Transitions  The  selection  potential  curve  overtones  and  anharmonic transitions,  basis  of  II  1 1  16  IS  was  for  found  vibrational  to  combination  effects.  be  The  are  |  14  in  the  allowed  vibrational  within  no longer obey  to  a  the  Born-Oppenheimer  U |  13  |  12  - -^ -  I  I  io  11  II  I  9|  e  molecular  approximation  much  Av—±1  explained  approximation;  same  lesser  associated  vibronic transition is governed by the  be  the  harmonic  transitions  F r a n k - C o n d o n principle can the  transitions  Au= + 1  bands  vibronic transitions,  intensity of the  The  rule  where  degree  with  electronic  selection rule but  physical]}  because  the  by  7  recalling  electrons  move  •• 7 7  u  6|  •  so  •R -P  5_  3  fl  3  2  the  LTL_J  1.4 Effect of case(a ) Coupling i n N b N : R lines of $ band, P lines o f $ ( 0 ) - A, (0) band. 3  the  F r a n k - C o n d o n principle.  37  Figure  by  ( 1 ) - A, (1) 3  2  THEORY / 29 much faster  than  other  during  words  internuclear different  the nuclei, their motions may be treated the time  it takes  an electronic  independently. In  transition  to occur the  distance can be assumed to remain constant. As previously  electronic  states  are characterized  by different  molecular  stated, 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, Rg > is considered: V  Rv e  = <*evl " l*ev>'  where \J/  and u are. the vibronic  respectively.  The Born-Oppenheimer approximation  (  wavefunction and dipole allows <^  ev  L  4  2  )  moment operator 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, M + Mj^, so (1.42) becomes: e  R  The  e v  = <* l^e e  >  <K\  "N  K> <KK> +  first term will vanish for an electronic transition as <'/|</'g /  >  e  <  =  ^ e l *e  >  0 since the  electronic wavefunctions are chosen to be orthogonal. The integral <</'| Mg e  is defined in equation (1.40) as R  K\ Pq x  >  which for simplicity is assumed to be a  g  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)  (L43)  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  is a function hyperfine  transition. The rotational term value  of the total rotational angular momentum (J) of the molecule. If  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 Z 1  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 values  *  are similar  projection  0, which must be for case (a) coupling, the rotational term to those  of a symmetric  of the angular momentum  rotational constant A is necessarily the  top (equation  1.6) except the  on the z-axis can only be J2, and the zero. Neglecting centrifugal distortion terms,  rotational term values for a given vibronic  state  in a case (a) coupling  [J(J+1) - G ],  (1.45)  situation are:  F(J,0) = B  2  v  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, S j , associated with the transition. S j 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  the  emission  formulae  in the process is being selectively populated, the intensities of  transitions  for the line  depend strengths  solely  on the transition  of a  symmetric  line  strengths. The  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 = (J'-fi') ( J ' - l - n * / 4«T R  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  Organic  and R.L. Cook, Microwave Molecular Chemistry,  Spectra, in Technique of  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 & Mathews Ed.), Academic Press, Inc., 231-256(1972).  C.W.  C H A P T E R 2. E X P E R I M E N T A L  2.1.  AMINOBORANE  Aminoborane, N H B H , is a molecule 2  minutes  2  in the gas phase, which  makes  with a lifetime on the order of  Fourier  transform  spectroscopy the  method of choice for studying its gas phase infrared spectrum. Gaseous N H B H 2  was prepared by thermal decomposition of solid borane-ammonia, N H B H 3  Products), in a flow system exception; the N H B H 3  then  lowered  as described by Gerry  3  (Alpha  et al. [1] but with one  was heated to 67 - 68°C for the the first few hours  3  to 63 - 64 °C  while  the spectra  were  recorded. The heating  temperature was reduced from 70 °C [1] because it was found that the N H B H 3  underwent  uncontrolled  thermal  impurities in the N H B H 2  A record  BOMEM  2  decomposition  at — 71 °C.  The only detectable  spectrum were ammonia and water vapour.  2  model DA3.002 interferometric spectrophotometer  a high resolution  3  (0.004 cm" ) spectrum 1  was used to  of the 1500 - 1750 c m  - 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  Approximately  2 gm  using  the  laser-induced  of Niobium(V) chloride,  34  fluorescence NbCl  5  (Strem  technique  (LIF).  Chemicals), was  EXPERIMENTAL / 35 heated to about 80 °C in the flow system. The an Argon/Nitrogen flow (= mixture was  900  mTorr Ar, =  then subjected to a 2450 MHz  gaseous NbCl 50 mTorr N ) 2  NbN  amongst  discharge mixture  was  other  products  laser and  filter  photomultiplier. The  a  entrained in  and the resulting  to  form. The  to destroy the NbCl , 5  pinkish-blue tail  of the  pumped with a laser beam from a Coherent CR-599-21  tunable dye by  was  discharge just prior to being pumped  into the fluorescence cell. The effect of the discharge was allowing  5  the fluorescence measured laser  beam  through  was  a long pass optical  chopped  so  the  modulated  flourescence signal could be discerned from the background spectrum by using a lock-in amplifier. Portions of the beam interferometer  to  provide  a  relative  were also passed  calibration  fluorescence cell for absolute calibration. A  scale and  cm"  1  scans. The  a  through  1.5 an  PDP-11 microcomputer was  scan the laser and record the three signals (NbN, 1.4  through  GHz Iodine  used to  I , interferometer markers) for 2  digitized data were then reconverted to analog form  and  plotted by a three-pen chart recorder. The apparatus is shown in figure 2.  Individual neighboring  scans,  calibrated. The was  scans  were  allowing  taken a  so  series  that  there  of scans  amount of overlap was  was  to be  some  overlap  concatenated  and  with then  measured in interferometer markers and  usually an integral amount unless the laser couldn't be locked on like modes  between scans. The relative positions of the NbN fractional  marker  units by  plotting  computer graphics terminal and concatenated  spectrum  was  the  data  and I for an  2  lines were measured in individual  scan  on  the  overlapping a vertical cursor on the peaks. The then  calibrated  by  tThese values must be corrected by —0.0056cm" . 1  supplying  the  known t  I  2  EXPERIMENTAL  /  36  Tunable dye loser  Figure  wavenumbers  [2] and  Wavelength the  spectral  fluorescence Since  the  fitting  resolved  analysis. resulting diode  A  the  cm" /marker  array  was  performed  detector  selectively p u m p i n g  detector  is  a  new  apparatus,  data to a linear  1  fluorescence  diode  from  array  2. L I F experimental  was  used  on to  equation.  selected record  a k n o w n transition  addition  to  Dr.  lines the  to  dispersed  in the  Merer's  aid  lab  system. a  full  EXPERIMENTAL / 37 account of how  2.3.  THE  it was  interfaced to the experiment is given below.  DIODE ARRAY  DETECTOR  2.3.1. Introduction  This section describes a diode array detector that was existing  laser-induced  fluorescence  experiment  to  improve  interfaced to the  wavelength  resolved  fluorescence measurements.  Apart aquire  from interferometers there are two  spectral information:  monochromator  a  narrow  the  band  instruments  monochromator of diffracted  and  the  commonly used to spectrograph.  (or dispersed)  light  In  a  is projected  through an exit slit onto a single photomultiplier tube (or photodiode dectector). A spectrum is obtained by mechanically dispersed  spectrum  spectrograph,  the  is  swept  exit slit and  rotating the grating (or prism) so that the  across  the  exit  slit.  Traditionally,  single detector are replaced  plate in the focal plane and an entire spectrum is recorded  A diode array detector (DAD) electronic advantage  analog of  of the  the  DAD  the  plate used  photographic  simultaneously.  photographic  in spectrographs. plate  information is ready to analyze much more rapidly and available in digital form.  a  the  or optical multichannel array detector is the  photographic over  by  in  is  that  The the  main  spectral  intensity information is  EXPERIMENTAL / 38 An  EG&G  model 1421R-1024-G DAD  and detector on a SPEX model 1702  was  used to replace the exit slit  spectrometer. The DAD  was  a DIGITAL PDP-11 minicomputer via an EG&G model 1461  interfaced with  detector interface.  2.3.2. Performance Characteristics  The  1421  DAD  has  When the spectrometer was  1024  pixels with  converted  (im  dimensions 25  to a spectrograph  increased to give a dispersion of approximately  detector face. A  spectral window of about 600  may  at 600  1  2.5  mm.  the focal length of the o  exit mirrror was  cm"  x  9 A/mm  nm  on the  in first order  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 0.05  resolved fluorescence line measurements has cm"  1  been decreased  by converting the spectrometer to a DAD  time the detector is exposed signal strength. The associated with  to the  detector may  be  source cooled  may  reach a temperature of -40  °C. The  be  in  single  characteristics of the DAD  or  The the  to reduce the dark current noise  be  °C  is achieved  augmented by  real time response (0.02  double  to  varied depending on  detector is monitored with an oscilloscope while data curves may stored. digitally  1.00  equipped spectrograph.  photodiode detectors. Cooling down to 5  Peltier-effect thermoelectric cooler which may  from  precision.  More  by  a  liquid cooling to sec scans) of the be aquired  specific  and  performance  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 ft /hr 3  recommended that the DAD to the maximum  before turning the DAD  be purged even when its temperature  of 20 °C. The default temperature  °C  at temperatures  is  has been set  at start up is 5 °C so it  is imperative to begin purging before turning the DAD DAD  on. It  on. When operating the  less than 20 °C the temperature • should be brought to 20  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 reached  to 20 °C and then waits until the temperature is  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 subroutines assembler  controlling program plus the main language  DETECT  program  consists of a number  itself.  of macros and  The macros, written in Macro-11  [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 used to display data curves.  is also a separate program, GRAPH, which is  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" . The fractional channel 1  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 are  taken  as the system  it should be performed before any real data  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 QIKPIK  (remote graphics instruction set)[8]. A  is used  routine in DETECT  to check the quality of a spectrum  called  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 position. The wavelength  to get a fractional channel  of the peak maximum  calibration constants from the housekeeping  computed using the  record of the data file. As mentioned  above this method allows an accuracy of 0.05 c m defined spectral lines.  is then  number  - 1  in the measurement of well  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  1984.  43  Manual, Digital  Equip. Corp., U.S.A.,  C H A P T E R 3. AMINOBORANE  3.1.  BACKGROUND  Aminoborane, N H B H , 2  has been  2  the subject  spectroscopic studies. The B=N bond in N H B H 2  bond in ethylene making N H B H 2  molecular characteristics of N H B H 2  of ethylene. Spectroscopically  an inorganic  2  2  theoretical and  is isoelectronic with the C = C  analog of ethylene. Unveiling the  will provide an interesting contrast to those  2  NH BH  2  of both  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, N H B H 2  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°*  nt  group as:  T(vib) = 5A, + A  From the C 2  V  2  + 2B, + 4B . 2  (3.1)  character table (see Appendix n) it is seen that only the A  torsion is infrared inactive whilst the A,, B ^, and B 2  2  fundamentals give rise to  A, C, and B-type bands respectively.  Theoretical  predictions  of NH BH 's 2  2  fundamental frequencies have been  made [1] and the infrared spectrum of solid phase N H B H 2  44  2  has been measured  AMINOBORANE / 45 [2]. The only other gas phase spectroscopic analyses of N H B H 2  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 N H Symmetry  Vibration  v3  *U  2  B  8  v$ »6  A B,  *B *9  I'lO  ft  2  Assigned at UBC  cm"  Fundamental Motion  3451 2495 1625 1337.474 1223.567 1140 (821) 1004.684 612.198 3533.8 2564 1433 1130 742  NH symm. stretch BH symm. stretch NH symm. bend BN stretch 2  BH symm. bend Torsion BH out of plane wag NH out of plane wag NH asymm. stretch BH asymm. stretch 2  a  "7  2  BH  1  A,  2J>  11 2  1  "12  a - est. from perturbations to c  1 2  2  2  NH BH 2  2  asymm. bend (rock) asymm. bend (rock)  .  The infrared spectrum of N H B H 2  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  vibrational transitions listed in table 3.1 have been performed  of other  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" region of the N H B H 1  2  2  spectrum.  TABLE 3.2 Other Ro-Vibrational Analyses of N H Vibration  Reference  v2 v4 2v n 2v v v v  1 1 2  BH  2  Bands  Interactions  in progress [5] in progress [6] , in progress in progress [7] tl] [8] . in progress  Coriolis with V J + V J and/or v + v , 6  2  3  8  5  Coriolis effects at high K. Coriolis with v and v , y. Coriolis with v and . Coriolis with v a n d V\ . 7  0  7 e  v  9  "io v, !  5  t  6  Coriolis with v 5  2  and v . 7  a - T. Chandrakumar b - D.M. Steunenberg c - J.A. Barry  3.2. ROTATIONAL  Prior  ANALYSIS  to this analysis  it was not known how many  would be active in the 1500 - 1700 cm"  1  vibrational bands  region, although it was evident that  v  must be present and be the main source of intensity. Inspection of figure  3.1  does not reveal the obvious  3  simple structure one would expect for a lone  AMINOBORANE A-type  band;  about  instead  1625 c m "  Possible  A which  available at  plot of K  possibly interact equation  (2.4)  This  course  could  only  were  calculated  the  excited  values,  be  and  Figure  presence  table  might  be  the  only  by just  a at  in their  that  guide  stage,  s u m m i n g the  rotational for  rough  the  was  2  rotational  because and  the  pertinent  constants  will  levels  which  fundamental  K  made  near-degenerate  state  deduced  using  i n order  with  the  the  v  be  spectrum  v  e  and  to  v . 7  of N H B H 2  hence  see  the  vibrations  and  and  Figure  3.2.  frequency  overtone  frequencies.  equal  contained  3  predict  fundamental  6  fundamental  not  v  to  by setting J = 0 i n  constants;  combination  transitions;  3.1. Low-resolution transmittance  at  3.3.  'origins' were estimated  ground  centred  of two or m o r e ' v i b r a t i o n a l bands.  'origins' versus  it. The sub-band  estimated  especially  a s y m m e t r i c a l l y - w i n g e d envelope  time; see  levels  using  was  large  interloping vibrational bands were  sub-band  with  Coriolis-perturbed  the  energy  state  a  indicates the  for these  vibrational  of  sees  which  1  candidates  assignments  one  / 47  bands  Moreover  ground  state  which  were  Nonetheless  figure  (1510-1720cm" ) . 1  2  AMINOBORANE / 48  TABLE 3.3 Possible Interloper Levels in v 3 System Symmetry  Vibration  A A A, A, B, A, B  cm"  1  1747 1732 1642 1617 1563 1484 1433  2  " 8  2  +  " l 1  2v  6  V  + U  7  a  B  2*12  2  a - v assumed —821 cm" b - observed [5].  1  6  b  prior to this analysis,  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  level because the fundamental frequencies v  7  determined  symmetry species as v  6  could  in figure  an anharmonic  3  occur. The position of the 2 v 6  and u  7  had both been previously  e  and the combination frequency, in harmonic  to the centre of the envelope  V  was the v + v $ combination  approximation, fell close Vy + V j  3.1. Since  is of the same  resonance interaction between them can  overtone was uncertain since the position of the  only be estimated from  fundamental at 742 cm" . If 2v 1  6  perturbations caused  by v  in the v  6  was to appear in the 1550-1720 cm"  y  2  range  1  resonance with v . The  it would most likely be the result of an anharmonic  3  remaining possibilities in table 3.3 will interact with v  via Coriolis mechanisms  except for v,  resonance. The analysis  3  2  which would interact via an anharmonic  was begun assuming that at least two A-type vibrational bands (v were present and were centred about the 1610-1625 cm" region. 1  3  and v + v ) 7  B  A M I N O B O R A N E  01 3  3  4  5  6  7  *  /  49  9  K plotted as Figure  3.2.  Sub-band origins of potential  interloper bands near the  v  3  fundamental. The  usual  asymmetric  top  rotational  consists  structure  of  an  of a central O Q b r a n c h  A-type  band  feature  with  of  a  near-prolate  O R and  q  P  branch clusters i n the OR  and  be  seen  spanning  out  to  higher  and  rotational constants between  rotational  Op  branch  i n the  clusters  the  separated  fundamental  constants are  lower  larger  (figure  the  frequencies  respectively.  If the  combining levels is s m a l l , regularly by  a  3.3,  regularity  a  central  from of the  O Q ' p i k e ' appear  ref.[5]). branch  S  I f the  changes  structure  change spaced as in  can the  is modified;  AMINOBORANE  E/cnf  / 50  1  1380 i  Figure  for  1360  i  1  1  if  the  constant  in  (ie:  to lower frequency)  pushed  a  A  appreciably  Because  the by  the  fundamental Coriolis  first  transition  v  vibrations  3.34%,  approximation  ground  was  interactions.  and  state  value.  '  The  the  is  the  v +v 7  7  constant  a  of  the  both  rotational  complete  absence  3  structure of  2  the  the +v  v„  asymmetric  top  causes  v  resulting v +v  be  red-degraded  bending  motion  O R - and  and Op  v  3  other  both v  5.42% with  so that  the  branch  be  by to  than  a the  anharmonic  depression  to  hand  perturbed  less  These  its  decrease  B  value  apparent  eigenstates. 8  are  state be  decreases  .  2  and  1  associated an  7  of  should  mixing  of  will  symmetric  ground  e  1—  m a r g i n a l l y . O n the  constants  7  function v  NH  1300  A-type  combination band  8  A  of  and  of the  proportional to K  to decrease  effective  basis  in  a  amount  v  A  constants  in  by an  in  '————  K - r o t a t i o n a l structure  the  rotational  the  the  to  i' +j'  result  1  near-prolate  respectively, relative  between  cause  a  expected  The  resonance  constants  then  of  fundamental  3  state A constant  2.08%  1  1320  3.3. Medium-resolution transmittance spectrum fundamental.  example  upper  1310  of  depressed irregular  clusters  the A and  normally  AMINOBORANE associated was  w i t h A-type bands. E v e n i f the  well-behaved  the  structure  one  encounters  K  sub-band  Such by  the  to  be at  sheer  inconspicuous. high  for each  a density  density  resolution; of the  of lines results  pattern recognition almost  The Fourier  problem  resolving  blended  intrinsic  linewidths  Figure  of  self-deconvolution  1  1  four  lines  of lines Figure for  is a  technique  h—i—4-—i  7  spectrum  shows  the  only  the  and  would have  branch  3  of lines  structure  lines being blended  v  caused  typical density  vibrational levels has  of the  8  51  for  one  been  labelled.  and  analysis  impossible.  lines  [9].  3.4  interacting  in m a n y  structure of v + v  in the  clarity  blended  that  rotational  /  cannot  A  is  be  spectrum,  1  1  1  reduced  deconvoluting  w h i c h provides  a  instrumental^'  resolved  E(j>),  1  by  1  is  1  related  way  to  the  spectrum.  of computationally because its  of  their  corresponding  1—t—J—^—i——i—i—I  3.4. High-resolution transmittance spectrum of N H B H ; all four vibrations present. 2  2  sub-bands from  AMINOBORANE / 52 interferogram, I(x), by the Fourier  E(v) =  transformation:  J IW exp(i27r^x)dx = F{I(x)} (3.1)  I(x) = / E(p) exp(i27Tvx)dv  = F~ 1  {E(70},  where F{ } is the Fourier transform (FT), F~{ } is the inverse F T and the 1  integration  is from  —»  expressed as a convolution The  interferogram  to +». An  experimental  of a lineshape  spectrum,  E(v),  can be  function, G(v), and a spectrum, E'(v).  corresponding to E'(v) is just  F(x) = I(x)/F- {G(v)},  (3.2)  1  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  picking out branches, which are then spectroscopist  relies  on his/her  rotational branch patterns  rotational  assigned  experience  band  structure  involves  by combination differences: the  and intuition  and then uses combination  to recognize  differences to check the  assignment of the lines. Rotational combination differences (written ^ F " , A^'  typical  A F", 2  or A F') are the differences between the rotational energy levels of a 2  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 various  there  is considerable  overlap  bands, the process of pattern  of the rotational fine structure of  recognition  becomes more difficult and  assignment of the branches themselves a real challenge. For simple spectra, such as  1  Z - Z electronic transitions in a diatomic molecule, Loomis-Wood diagrams 1  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 out  curves or straight lines. This method is clearly impractical for sorting  the rotational structure  asymmetric  of a set of interacting vibrational bands  rotor because of the sheer number  of overlapping  of an  sub-bands that  must be dealt with in the spectrum.  It was decided that the most painless way to attack the 1550-1720 cm"  1  region of the N H B H 2  2  spectrum was to write a computer program that used  sets of A^F" and A F " combination differences to verify and assign any regular 2  branch  structure  combination  that  differences  could were  be picked used  out from  because  the spectrum. Ground  the ground  state  of N H B H 2  state 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. AyF"  3.  and  A F"  combination  2  differences  of selected  added to every line in the supplied branch and  sub-bands  are then  if both A i F " and  A F" 2  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 F " 2  combination differences is available. When the  Q branch structure is well-developed (K P, Q, and R merely  supplying the program  and  4) it was  found that portions of the  branches of a sub-band could be extracted from the data set by  thought to be. The AiF"  >  number of spurious matches made when checking for both sufficiently  small that the correct rotational  assignments  could be easily picked out from  the list of matches. When using  only  differences,  A F" 2  overwhelming A  A F"  with the spectral regions where the lines were  2  differences was  however,  the  number  of accidental  matches  becomes  because there are over 5000 lines in this region of the spectrum.  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 picked  out of the spectrum  sub-bands have K  structure of the most intense sub-bands could be without  too much  difficulty.  The most intense  =0, 2, and 4 (ie: low even values of K_, as expected  the Boltzmann factor and the nuclear spin statistics). N H B H 2  identical H  2  from  has two pairs of  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 K_  and antisymmetric for odd K_  a  2  rotation for even  [10] so that the expected intensity alternation  a  is Keven K ) : I(odd K ) = 5:3. a a. As spectrum  the analysis progressed with  the assigned  it was convenient to replot portions of the  lines  digitally  erased. This  technique  made the  process of pattern recognition for the unassigned lines much easier.  The  isotopic abundance ratio of  1 1  B:  1 0  B  is 4:1. When obvious  branch  structure could not be assigned using the B combination differences an attempt 11  was made using  1 0  B  combination  differences which had been determined  Barry in our laboratory [12]. Three sub-bands of v species, with K_ =0,1,2.  3  by J.  were assigned for the  1 0  B  AMINOBORANE  -i  1  50.00  1  1  1  150.00  1  1  1  250.00  n—i  350.00  1  45a 00  1  1  1  1  550.00  / 56  1  950. OC  750.00  J*CJ+1> Figure  3.5 U p p e r  State Rotational Energies v + v^ s  Sub-bands and in the  from  four  2  separate  of  next  section  3  2  + v , 2v 8  6  and  2  were  discovered  i n this  for each of the four vibrations  to the vibrational  but for now it w i l l  7  NH BH .  vibrations  the line assignments a n d intensities A p p e n d i x I. The logic leading  of the L e v e l s v ,v  be stated  that  analysis are given  assignments  will  be given in  the levels  v ,  v +v  3  7  B  and  AMINOBORANE / 57 2f  6  form an  anharmonic resonance triad and  interaction between v + v, 6  of the  four excited  and  2  that there is an  a member of the triad. The  vibrational states  were calculated  x-axis Coriolis  rotational energies  using the  state constants to predict the ground state rotational levels and  then adding the  appropriate transition frequencies to map  the  upper state energy levels as a function  of J(J+1) is given in figure 3.5;  energies have been scaled by subtracting 3.5  represents the  course of the  upper state  known ground  levels. A  0.7[J(J + 1)] cm" .  plot of the the  Each curve in figure  1  rotational levels within a  K  sub-band of a  a  vibrational eigenstate. This type of plot is very useful because it quickly shows the mutual effects that interacting levels have on one energies shown in figure 3.6  provide an  should behave in the absence of any  The 2v )  sub-band structure  could be  e  another. The  example of how  the rotational energies  perturbations.  of three of the  four vibrations v  assigned almost completely except for the  3  (J> ,  i> + c ,  K=3  and  3  K = 5 sub-bands, which are predicted to be nearly degenerate and strongly  with each other. The  vibrational band gives an 3.5  vibration labelled  indication of its strength; the  with it since v  3  v  clearly  level  obtaining  interaction  with  and  8  v  + v  7  &  to interact very  levels plotted  + 7  v  6  in figure 3.5  has  the  seem  in figure inconsistent  most levels associated  should give the strongest band in this region of the spectrum;  this point will be addressed in the next section. Only one interacting  7  number of rotational assignments made for each  are calculated from observed lines in the spectrum. It may  that the  ground state  (Vj + ^ i )  n a s  2  its the  intensity K=6  been identified so by  a  sub-band of  far; this has  rotation-dependent v  + 7  v; B  sub-band of the  the  two  K=7.  mechanism sub-bands bow  fourth It is  via  an  away  AMINOBORANE  /  58  J* (J+D Figure  from  each  As energy  3.6 Ground State Rotational E n e r g y  other (figure  can  levels  the  NH BH . 2  2  3.5).  be seen from figure of  L e v e l s of  four  3.5, there  interacting  is considerable  vibrations.  Localized  overlap  between  peturbations  the  (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 species (see C  character table, Appendix II) to interact. The  2 v  as the  B,  overall symmetry  species of the levels are given by the product of the symmetry species of the asymmetric vibration.  rotor For  eigenfunctions  instance  rotational level is a  in an  2  Overall  symmetry  the  (see  overall  table  1.1)  symmetry  A ^ vibration  species are important  be  totally  symmetric  species  VIBRATIONAL  The  localized  perturbations  interaction  observed origins  at  same  species, which  symmetry  1609,  interaction. This discovery PT + V 1663  B  and cm"  vibrational  1  1625  was  and  the  1663  indicates  cm" a  and  the ^  =  a  3  6  interactions because the interaction  to occur.  Localized  MODEL  three  vibrational  occur  1  three  bands  with  between levels of the  level  anharmonic  not unexpected since three  resonance  vibrations  (p , 3  2v ) were predicted to appear in this region of the spectrum. The 6  band was bands  assigned  was  not  so  as 2v  6  but the assignment of the two  straightforward.  Since  t>  3  is  vibration it should give the more intense band of the two. The 1609  ^j^ j^  of  3.5.  SYSTEM  between  the  of the levels and  for an  THE  symmetry  in a B ^ vibration.  in vibration-rotation  in order  ASSIGNMENTS:  of 2  perturbations are indicated by the squares in figure  3.3.  the  but will be b  group theory requires that the direct product operator  and  1625  cm"  1  bands  appear  to be  comparable  a  lower  fundamental  intensities of the  in figure  3.1.  This  AMINOBORANE indicates  that  since the v +v 8 7  origin  the  intensity  or  the in  unperturbed  If  of  is considered  examining course  figure v  3  ri—i  3.2. and  of  v  strong two  parentage  When  shown  of the  combination.  predicament  picture  unperturbed  3  7  levels m u s t be  8  fundamental levels  observed  has are  almost  been shared  intimately  eigenstates  degenerate  w i t h the  mixed,  becomes  weak  tracing  the  challenging;  this  below.  interaction  their The  rotational  scenario  p +y  1  v  v +v  vibrational  the  the  7  and  3  / 60  8  of  two  levels  i n figure  vibrations  vibrational by  3.2  separated  1  the has by  levels  it  sub-band the  helpful  origins,  rotational  a constant  is  was  levels of  amount  1  as  3.7  Scaled U p p e r  State Sub-band Origins of the bands.  1  r 1609  and  1625  the  (8cm" ),  K plotted as K*  Figure  to  cm"  1  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 v  3  is shown above v + v 7  in figure  B  3.2 the band observed at the higher frequency would be the more intense of the two. v  3  As explained in the previous section, however, the rotational constants of and v + v 7  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.  the intensity ratio of like rotational transitions from  2  each band  to vary  with J and K. Both of these phenomena were seen in the 1609 and 1625 cm"  1  NH BH 2  were  spectrum. The sub-band origins of the 1609 and 1625 cm"  1  2  extrapolated  subtracting and  from  a  [A-(B + C)/2]K  2  plot  similar  to figure  3.5 and then  scaled  C. The scaled observed sub-band origins were plotted as a function 1  Coriolis  interaction  extrapolation non-linear  bands by  where the ground state constants were used for A, B  (figure 3.7); the K=6 sub-band of the 1625 cm"  a  bands of the  and is not shown  since  of K  2  band is badly perturbed by a  the estimate  of its origin by  is unreliable. The sub-band origins of both eigenstates clearly show dependence on K . 2  Both  because the effective coefficients of K  curves  in figure  3.7 slope downward  are both less than that for the ground  2  state. The intensity ratios between like sub-bands of the 1609 and 1625 cm"  1  P and R transitions  for the K=0-4  bands are shown in figure  3.8. The  AMINOBORANE 1609  / 62  cm" band is the more intense of the two until midway through the K=2 1  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 v  3  K=4  sub-band which, as will be discussed later, was  found to be present. Since the v  band carries essentially all of the oscillator  3  strength, and the intensity of the eigenstates indicates how much v  3  in each, then v-j + v  B  the course  of the unperturbed  character is  rotational levels of the f  3  and  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 for  the interaction.  When  two interacting  basis  states  cross  matrix  the apparent  parentage of the resulting eigenstates will reverse at the crossing. For the sake of consistency the 1609 and 1625 cm"  bands were assigned according to their  1  parentage for zero rotation, as v  and v + v respectively. 7  3  As by  was noted above the lone sub-band of the fourth vibration is induced  a rotation-dependent  K=7  mechanism. Inspection  sub-band of the v + p , 2 6  with the K=6 sub-band of the v symmetry  e  to interact  with  of figure 3.5 reveals that the  vibration is predicted to be nearly degenerate vibration. The v  3  the V  3  6  + J>  12  K=7  level  K=6 level is allowed by 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  AMINOBORANE P branch  K  1  R branch 1 ^ . '° 1  R in ' rv • -  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.  / 63  AMINOBORANE / 64 between form  v , 3  in  energies terms. the  7  of the  3.9.  basis  when  LEAST  goodness  residuals hence  the  match  fitting  (observed  fit  contain  off diagonal  represented  the  in  blocks  contain  rotational  the  interaction  rotational constants of  calculate  the  interaction  parameters  shown  in  figure  is  matrix  observed  spectrum  matrix  unperturbed  work is to calculate the  is  a  technique  3.9  between  diagonalized  w i t h i n experimental  used  can  be  measured  by  m i n u s calculated values); the least  squares.  A  |f > 3  \vj  T  3  W  W  3  W  3  7 8  T  6  W  6  -^3612  Figure  is  in data  reduction  model such that its calculated values m a t c h  of the  name  blocks  the  to  the  model  the  uncertainty.  TREATMENT  squares  parameters of a The  the  This  2  while  and  SQUARES  Least  6  of this  vibrations  that  i> + v y .  diagonal  levels object  resulting eigenvalues  3.4.  and  6  The  four  The ultimate  such  2v  8  figure  four  them  v +v ,  3.9 M a t r i x  X  + v  3  7  7  spectroscopic  7  >  t  B  8  7  8  s  6  6  6  12  |2  v  W  3  6  7  8  T  6  6  X  6  Representation  6  fit  +  S  X  3  ^7  6  1  2  of the  T  6  observed  the  squares  sum  6  the  better  acceptable  V y i >  1  '  2  6 6 1 2  X 6  of  refine  the  is considered  \V  6  6  sum  lower the  >  6  W  the  to  ,  6  6  6  1  2  2  Four Level  Interaction.  the  values. of  the  the  fit  when  AMINOBORANE / 65 the residuals are comparable with the experimental uncertainty of the observed data. In  order  approximates  to  achieve  an  acceptable fit one  must  have  a  model that  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.  least  squares  techniques  will  A  full description of fitting spectroscopic data by  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  state values. The  first  Vj + v  guess constants for the  summing the differences of the known v  7  state values, and  more than  and  ve  then subtracting the sums from  5%  from  the ground  state were refined  B  constants from  by  the ground  the ground state values. The  centrifugal distortion constants should be the same as the ground state values, again v  s  +  K=7  v  except  \ 2  for  v +v, 7  8  band centre was  since there is no  change in electronic  approximated  1577  to be  cm"  1  state.  The  using its extrapolated  sub-band origin and the ground state rotational constants. The relative band  centres of the unperturbed estimated quantities  without are  levels involved in the anharmonic triad  considering the  completely  reasonably approximated,  anharmonic  correlated.  If  however, they may  the  interaction anharmonic  terms  cannot  because  constants  be  these  can  be held constant in the fit and  be a  AMINOBORANE  /  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:  S  ¥eig =  where S  T  T  (3.3)  "Pbasis,  is the 3 X 3 matrix of transposed eigenvectors. If the basis functions of  the three levels are denoted by |l>, | 2 > level denoted by | X > then  and | 3 >  the transition moments  and the ground corresponding  vibrational  to ground to  eigenstate transitions are given by:  R  R R  where  =  A  C  F A  = =  a, b, and  unperturbed  S,,<l|u|X> S S  1 2  1 3  c  vibrations,  <1|M|X>  <1|M|X>  represent  +  S  + +  2 1  <2|M|X>  S <2|/u|X> 22  S  2 3  <2|M|X>  the three  +  S  + +  3 1  S S  3 3  <3|M|X>,  3 2  <3|M|X>,  (3.4)  <3|/i|X>,  eigenstates.  If only  say |l>, has any oscillator strength then  ratios of like transitions from each of the three observed  one  of the  the intensity  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  / S „ ) . !  N  (3.5)  AMINOBORANE / 67 As  explained earlier  *>  3  should carry almost  system so it is not unreasonable intensity  contribution  compared  to that of v -  to assume, as a first approximation, that the  of the other 2  all the oscillator strength in the  Using  two vibrations  relationship  in the triad  is negligible  (3.5) then, the approximate first  order anharmonic values can be estimated.  Unfortunately  for a case  important  for sorting  unreliable  because  spectrum  like  the system  so many  this  where  intensity  out, the intensity  of the lines  information  is so  information is the most  are blended.  Deconvolution  of the  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 of  set of equations to be fitted may be represented by a block matrix  rotational and intensity data, where each block corresponds  basis state. The unknowns are the unperturbed values  and the first  observed  order  anharmonic  upper state rovibrational term  to a vibrational  upper state rovibrational  terms, the known  quantities  term  are  the  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  AMINOBORANE upper  state  averaged six  or  unknown  (P,Q,R)  three  unknown  observables  set  energy  T ,  block diagonal the  W  3  terms  Thus  the  blocks  w  eigenvector corrections  1 2  may  be  set  W  1  common  and  are  to  this  differentiation  fitting intensity  author by  In  supply  A . J . Merer.  this  associated  each  block,  with  however,  0  0  3  2 3  T,  may  be  refined  the  of p ^ ' s ,  of p a r t i a l case  the  than well  problem to  as the  energies  calculated  block  has  and  five  that  three for  a  matrix  is  separately:  J  ratios and  of  partial  intensities.  The  by:  (3.7)  5 N vector of the  derivatives  must  A subroutine least  of observables  observables  Hellman-Feynman  energies.  N  appropriate  N,  is the  general  be  iteratively diagonalizing the  observed  derivatives  the  may  (3.6)  and  are  68  The  so  £  b  eigenvalues  n D- i  N  by  it.  Since the  0  1  corresponding  as  )  2  Ei  rather  ratios  3  each  (S^/S^) )  0  3 N + 3 vector  unknowns.  2  and  3 N + 3 unknowns.  unknown parameters (p^)  5 N X ( 3 N + 3) m a t r i x  numerical  and  2  of  diagonal  E.  elements w i t h the  is  the  to  ) ,  ] 2  Each  W  comparing  A is the  W  up.  diagonalized  2 3  where  to  and  3  A =  the  (S, | / S  ratios  individual blocks m a y  parameters  unknowns  ,  2  w  W  1 3  to the  intensity  5 N knowns  2  unknown  of  1  are  symmetric  1  the  c  of N blocks there are  W  either  (E , E ^ , E ,  T ,  2  anharmonic  T, W  that  separate, equations  parameters (T,,  so  /  be  theorem was  with  D  respect  calculated  by  because  we  written  squares p r o g r a m  and  by  the  L S Q written  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 calculations the v  collected in groups of threes. From preliminary two X two v +v 7  B  v  and  - 2v  3  6  interaction  approximated to be 8 and 15 cm"  1  terms  (ie: W  and W )  378  -  3  were  36 6  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 v + v 7  B  and 2v ,  (W  6  78 6 6  ) , at  zero because fourth rank anharmonic constants should be at least an order of magnitude  smaller than  values of W  and W  378  36 6  the third  rank  constants  a set of deperturbed  [15]. Using  the preliminary  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" ) were omitted from the data set. Only 1  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 8.410.1cm"  and W  1  to be: W  3  78  =  = 15.8±0.4cm" . 1  3  66  y  The  £ 7 8 6  12  constant  was estimated  — 0.468 cm" . The position of the Vy Ve +  1  from  its lower  by a two X two  treatment  to be  K=6 sub-band origin was extrapolated  sub-band origins while the v + v^ 6  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  coupling  between  the v + v ^ 6  Coriolis  combination  2  constant  level  is a measure of the  and the v + v 7  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 tofitthe energies of the observed triad  to a three level model. The K = 6  sub-band of the f + f 7  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  phenomenon interacting  of the v^!2v  2  arises  Fermi  when there  diad of OF [16]. Jones revealed that this 2  is a varying  levels. In the symmetric  degree  prolate limit  of mixing  between two  the separation between like  rotational levels of the two interacting vibrational levels is:  6 = A P If W  + AB J(J+1) + (AA-AB)K . 2  0  is assumed to be much larger than  (3.8)  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) ],  (3.9)  2  which upon substitution of (3.8) yields: E  =  1  E  ±  (T,+T +T ), 2  (3.10)  3  where: T, T T  T  3  [l + i(A.* /2W) ] 2  0  f  = (Av /4W) [AB J ( J + 1 ) + (AA-AB)K ], 2  2  0  = (1/8W)[AB  3  = W  J (J+1)  2  2  + 2AB J(J+ 1)(AA-AB)K  2  2  +  (AA—AB) K']. 2  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 D j , and Dj^ which .may be related [ 1 7 ] to the corresponding terms in Watson's  DJJ^,  A-reduced Hamiltonian (equation 2.9).  In  the triad  near-degenerate  examined  degree  (v + v 7  B  and v ) are 3  and are predicted to have very different rotational constants so  that contributions from member  here, two of the levels  a term  similar to T  of the triad (2 v ) has 5 > 6  of mixing  should  be  W  should  be significant. The third  so that the effect of a varying  36 6  negligible  3  compared  to the pure  vibrational  contribution (T,). Since the centrifugal constants should remain constant within the state  same electronic state it would be appropriate to fix them at the ground values. This is reasonable  predicted  for the v 7 + v  8  involved in the combination  level  for the v  3  level but anomalous values are  due to Coriolis  effects  in the fundamentals  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 of 0.02  best fit achieved on the three level system had a standard deviation  cm" ,  ie: an  1  experiment.  As  achieved by  order of magnitude greater than  the resolution of the  will be shown later, even this unsatisfactory fit could only be  omitting a substantial number of energies from  the data set. An  unsatisfactory fit indicates that the  model is incapable of accounting for the  observed  asks: is the starting point for the model  energies. At this point one  wrong or is it the structure of the model which is inadequate?  The  intensity  information confirms the present assignment of the vibrational bands; the basis vibration  must  carry the  assumptions made to calculate without  them  problem  there is no  apart  from  a  logical choice. The  W  3 7 8  and  possible way  trial  information in the spectrum  majority of the intensity. The  and  error  W  3 6 6  were not  two  Thus  unreasonable  given  3  necessary  of tackling this completely approach.  v  the  and correlated available  the current interpretation of the triad is the most  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 Examination  made, each time reducing the data set.  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 the v  3  sub-band of  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: v  1.  band.  3  a.  K=0 -depressed after J = 7.  b.  K l-  c.  K=6 -effect of an avoided crossing at J = 8,9.  =  v +v  2.  7  -markedly depressed in comparison to 1^.  band.  B  a.  K=l  b.  K = l ^ -effect of an avoided crossing at J = 8.  c.  K=5 -slope indicative of an improper fit.  2v  3.  U  6  u  -markedly depressed after J =10.  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 + c 6  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 v  6  +  \2  and 4 sub-bands of  were found to be nearly degenerate with the K=0 sub-band of v and  v  3  the K = l sub-band of v + v 7  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 v +V\ 6  and v + v i {A ) 7  these  2  2  transitions  2  s o  that the 2t> (A ), v + v (B ), 12  1  6  B  2  v + v, ^ (A ), B  2  levels shown in figure 3.2 were then considered. Since none of has been  rotationally  analyzed  their  upper  state  rotational  AMINOBORANE / 74 energies  and hence  possible interactions  v  with  and Vy + v  3  e  can only be  estimated. The possible interactions are listed below: 1.  K=0 v  6  + v  or v 7 + v s  of  with  of 2 v 1 (anharmonic) or K — 7 of  K—6  2  8 (y-axis Coriolis).  2.  K=6 of p  3.  K=6 of 2v  4.  K = 5 of 2^6 with K = 0 of v + p! (z-axis Coriolis).  3  e  or f7 +  with K=9 of v +1> (y-axis Coriolis). 6  with K=4 of p + v , (z-axis Coriolis). 7  2  7  It  8  is almost  certain  that  2  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 anharmonic terms linking  centres v 3  of the three  and v + v 7  levels  and v  8  3  plus  the second  order  and 2 v , were allowed to 6  float. The data set gives the residuals shown in Appendix HI. The standard deviation of this best fit was ±0.02cm~ , which is still an order of magnitude 1  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  completely  of the  three  correlated with the anharmonic constants  members of the  triad  are  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 structure  far. One  had  factor may  to be  omitted  be  from  that because so  the  data  much of the rotational  set that there  information left to drive the fit to the real solution. The  was  not enough  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 anharmonic constants. The order constants  may  route remains, however, to attain the  surface of the model with respect to the three first  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  This  study  between molecular  has  revealed  an  impressively  complex  time.  series of interactions  motions at surprisingly low total energy; what was  be a straightforward four level interaction scheme turned out to be more  involved.  Assigning  the  rotational structure  by  the  new  thought to considerably 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 Structure of the 10  o  Spectrum  of Gaseous  Aminoborane;  Band, BSc. Thesis, University  Rotational  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,  Nostrand Co., Inc., Princeton, New Jersey, 1945.  76  D. Van  / 77 11.  G.  Herzberg,MoIecular  Nostrand 12. J.A.  Spectra  and  Co., Inc., Princeton, New  Barry,  Ph.D.  Molecular  Structure, Vol. I, D.  Van  Jersey, 1945.  Thesis, University of British  Columbia, Vancouver, in  press. 13. D.L.  Albritton, A.L. Schmeltekopf and  Modern  Research,  Vol.  II,  (K.N.  R.N.  Zare, in Molecular  Rao,  Ed.),  Academic  Spectroscopy: 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 6, Elsevier Sci. Pub. Co., New  Structure, (J.R. Durig, Ed.), Vol.  York, 1977.  C H A P T E R 4. NIOBIUM NITRIDE  4.1.  BACKGROUND  A brief discussion on the expected low lying electronic states of NbN given  followed by  a  summary  of the  optical  spectroscopy  performed  on  is 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  configurations of Nb  and  configuration N  of  NbN.  The  are KLM4s 4p 4d" 5s 2  6  ground  and  1  state  K2s 2p 2  3  electronic  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 of  symbols (a, ff, 6) refer to the magnitude (0,1,2)  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  d 2p orbitals z z than by combining the large, diffuse, spherical 5s with 2p . Using the buiding-up z a n  2  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 so the ground  state of NbN  will be  determined 78  by  it levels and  the configuration of the  NIOBIUM remaining  two  compared the  to  5sa  4d55sa. 4d55sa  electrons.  the  electron  repulsion  energy  A 5sa  would yield  configuration  2  configuration would yield  and  if Hund's  half-filled  electronic  so  the  3  state of a 4 d 6 5 s a  The and of  optical Rao in the  while none was splitting is the  3  spectrum  and  3  observed  3  i n the  to  F e r m i contact  Figure  3  3  -  3  A  interaction  is  a  nitride,  2  $  levels  both  electrons  in  is 5 s a  or  electronic  2  state while a  expected  molecular 3  A  1  to  be  regular  system  the  . The possible  [6]  ground  low  lying  4.1.  $ ~ A i 3  containing  ground  +  energy  4d6  state configuration  should be  niobium  3  Z  and  / 79  A electronic states. The 4dS orbital is  [1]. L a r g e hyperfine  1969  1  extended  i n table  of  by  structure  configuration  summarized  $„- A  is  5s a  ground a  3  A multiplet  the  gained  the  ' A and  multiplicity rule  electronic states are  lines  of  whether  than  R  separation  orbital will determine  less  Dunn  The  NITRIDE  2  NbN,  was  splitting was  sub-bands  of  sub-band.  The  of an  electron  first  examined  observed the  3  <I>- A 3  dominant  in the  4.1. M o l e c u l a r Orbitals of N b N .  3  in the (0-0) source  by  low  J  band of  the  A state w i t h  the  NIOBIUM NITRIDE / 80  TABLE 4.1 Expected Low-Lying Electronic States of NbN Electronic Configuration 5so SsaUdS  Electronic States  2  1  Z  1  z , Z ,  3  +  1  5soUdir* 5sa 4da 4dS 4d7T 4d6 1  1  1  2  1  4do 4d6 1  1  1  +  3  +  3  z Z', +  T  n, n , #, # 3  1  3  r  1  1  A,  3  A  r  r  a - subcript r refers to regular (opposed to inverted) multiplet structure. magnetic moment  of the Nb  partly from a Nb density  nucleus, that  is the A 3  state must be derived  5s electron in order to account for an appreciable  at the nucleus. The degree of splitting was discovered  proportional to J  2  coupling. The NbN  so it was deduced the A 3  spectrum  to be inversely  state was an example of case(a^)  was "revisited" by Dunn et al. in 1975 [2]  study the origins of the secondary hyperfme effects in the was revealed  electron  that there was a nonnegligible  3  3  to  A system. It  interaction of the Nb nuclear spin  with the electron orbital angular momentum in the $ state. 3  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 #- A system was reported 3  3  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" the  3  $- A  as a spin-orbit satellites of  1  system. Those results inconsistent with the work considered in this  3  thesis will be addressed in the discussion.  Most recently Femenias has performed (0-0) band of the 3  $  and  3  A system [5] which confirmed the regular nature of the  and A states. Rotational and spin orbit constants were reported for the $ 3  3  4.2.  3  A states.  ANALYSIS  A  complete assault  being performed effects in the the  3  a full rotational analysis of the  3  $- A 3  on the red-orange  region of the NbN  by the high resolution spectroscop}' group at UBC. The hyperfine  3  3  A system are being analyzed and rotational analyses of both  and I I - A bands are being performed. 3  The rotational analyses of  3  the <i> - A, (1-0), (1-1) and (2-1) sub-bands and the n , - A 3  spectrum is  3  3  2  3  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 3  II - A 3  1  (0-0) sub-band at 17057 cm" . 1  2  present in the P branch of the II, - A 3  3  2  3  II - A 3  1  2  A  strong atomic  Q head of the  line due to Nb is  (0-0) band. At higher resolution the  (0-0) sub-band did not exhibit the large hyperfine splitting associated  NIOBIUM n,- A  25  I  Figure  with  cm"  4.2. B r o a d  transitions  due  A-doubling  to  to  L I F spectrum of the 16950-17110 N b N spectrum.  involving  out  11 = 35 in  A^  or  where  the  2  the  3  II  1  3  $  lines  n - A  2  -  (0-0)  3  1  3  A ,  to have  2  (2-1)  lines  lines. The  n,- A  A The  Since  the  decreases ground  broad  band  sequence with  state  v,  bond  value. The  3  $  2  of the is  length  i n the  -  (1-1)  A  to  as  strong  located  at of  intensities;  corresponding  17131 c m "  T h i s rough  is  structure  relative the  only  probably  origin  The  as  at  were  broaden,  band  by considering the  times  region of the  lines  (0-0) R branch.  2  15800-16200  maximum  3  R  (2-1)  1  1  appears  1  appearance is  due  most like]}' N b O .  of the  intensity  and  3  side of its Q head.  spectrum,  cm"  begining  2  3  3  P  I> - A  (1-0) band  3  2  A v = 0 sequence  the  The  just  3 <  however  $ - A ,  3  scan  red-degraded  3  about  irregularities on either  to a n i m p u r i t y i n the  4.3.  are  were  the  two bands is readily separable 3  states.  3  The  1  the  A  3  state.  17075 c m " , right in the centre the  2  I  1  Band  followed  / 82  (o-0)  3  3  NITRIDE  1  3  at  cm" 4  >  _ 3 2  excited  band  A  the  region  1  system  1  (0-0) state  centre  is  shown  is at  figure  is clearly visible.  transition must  in  be  16097  and  similar cm"  1  quickly to  the  and  so  NIOBIUM  NITRIDE  / 83  (0-0)  as cm - i  (1-1)  Figure has  4 . 3 . Av = 0 sequence  its structure  located  at  overlapped  16145 c m " . 1  with  Once  of the  the P  again  3<  1> - A 2  3  branch  1  system of N b N  of the  the structure  from  3 <  t>  _ 3 2  A  1  each  band  assigning  and  (0-0) band w a s easily  discerned by considering the relative intensities of the lines.  4.2.1. Rotational Analysis  An rotational the  identical constants  Q, P ,  and R  procedure of the four branch  distortion, the frequency  J  so the difference  2(B' — B " ) ( J + 1 ) .  performed  sub-bands values  for  mentioned  is described  of a Q line (see equation  VQ(J)=VO  and  was  between  +  (B'-B")J  adjacent  T h e Q line separations  +  (with increase  above.  below.  fitting  the  T h e assignment  Neglecting  of  centrifugal  1.10) is given by:  (B'-B")J  values  J  (4.1)  2  and J + l ) Q lines  linearly w i t h  J  is  so a plot of Q  NIOBIUM NITRIDE / 84 line separations versus J yields a straight line with a J= —1 correct values of J are assigned to the Q  lines. The P and R line assignments  were made using A j F " combination  differences. Only  cm"  A^F"  1  was  used  to  calculate  the  intercept when the  values  a rough B"  but  this  value of 0.5  was  sufficient for  tentative assignments of the P or R lines.  The the form  rotational structure was fitted to the difference of two equations with 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) Bg\ A! F"  Dg,  and  the effective upper and  Dg). Any  values  determined  erroneous  mentioned  lower state rotational constants (B ', e  line assignments made by using the approximate  above  were  quickly  constants of each sub-band  discovered  and  are given in table  corrected.  4.2  The  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 $ - A , 3  3  2  had  (1-1) sub-band was  trivial since the (0-0) band  been studied and the Av = 0 sequence is obvious (Fig. 4.2). The  (2-1) bands  of the  3  $ - A 3  2  1  Av=l  sequence  vibrational spacings observed by Pazyuk et al.  were  assigned  by  noting the  [4], and comparing the hyperfine  structure of the two bands with the (0-0) transitions of the $ - A and 3  sub-bands. Pazyuk et al.  assigned the Q  heads at 17130.63 and  as the (1-0) and (2-1) bands of the 4 > - A 3  3  2  1  (1-0) and  A v = l sequence.  3  3  II- A 3  17072.37 cm"  1  NIOBIUM NITRIDE / 85  TABLE 4.2 Effective Rotational Constants of Select NbN States (cm" units) 1  Band  B  10 D' e  10 D" e  6  , a e  Assignment  6  16097.260(4)  0.49251(8)  0.452(40)  0.49748(8)  0.411(42)  17057.474(1)  0.49530(2)  0.498(15)  0.50173(2)  0.469(15)  17075.115(2)  0.48994(6)  0.555(37)  0.49767(6)  0.524(37)  17130.999(3)  0.49230(6)  0.494(31)  0.50014(6)  0.449(32)  - A,(1-D 3  3  n , - A (0-0) 3  2  - A,(2-1) 3  3  *  - A, (1-0) 3  2  Common State Constants Reported by Other Workers 16144.648(3)  0.49532(5)  0.495(7)  0.50015(5)  0.471(7)  3  16542.980(3)  0.49570(5)  0.488(7)  0.50160(5)  0.459(7)  3  17124°  .4950  0.5082  17064°  0.4953  0.5016  b  b  *  - A, (0-0) 3  2  <i> - A (0-0) 3  3  1  n(  2  3  n ? ) - z (c  1  A(0-0)  1  +  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 $ - A 3  very  similar  Doppler-limited  to the structure resolved  hyperfine  seen  (1-0) and (2-1) sub-bands was  3  2  1  in the 3> - A, 3  3  2  structure at J<5  (0-0) sub-bands; the  showed  identical  intensity  alternations.  The assignment of the II, - A 3  3  2  other  two sub-bands resulting  from  (0-0)  sub-band was not so easy. The  the triplet  transition had been assigned by Ranieri [3], n 3  3  II - A 3  0  (0-0) at 17905 cm" , but the middle 1  1  - 3 2  components A 3  in the I I - A 3  3  (0-0) at 18148 cm" and 1  3  n,- A 3  2  (0-0) sub-band was  NIOBIUM NITRIDE / 86 mysteriously  absent  from  its expected  negligible hyperfine effects in the I I  between  these  upper state, the missing  3  sub-band  position  1  should not exhibit strong hyperfine splitting  1  for the missing sub-band. The  3  AtF"  lower  band so it was A  2  state was  3  n  1  in the low  branches since the Fermi contact interaction is absent in the is no such splitting in, the 17057 cm"  two.  3  A  2  -  Assuming 3  J  A  2  (0-0)  rotational  state. There  considered as a suspect  confirmed by checking the  A F " combination differences against the differences calculated from  and  2  Femenias' analysis [5] of the  The  upper  3  II  1  measurements. Select Q of the resulting R Honl-London  3  4> - A  (0-0) system.  3  3  state was  2  confirmed by wavelength  lines were optically pumped and  resolved fluorescence the relative intensities  and P lines agreed with the intensity ratio predicted by the  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,- A 3  2  (0-0) sub-band is optically pumped. The predicted intensity ratio of the Q(13)  <  50 cm" '  1  P(14)  R(12) ,  Figure 4.4. Wavelength Resolved Fluorescence of Optical^ Pumped Q(13) line of n,- A (0-0) Sub-Band. 3  3  2  NIOBIUM NITRIDE / 87 P  to R  emission lines of a Afi =  -1  transition is S?/S?  =  1.69  while the  observed intensity ratio is 1.65.  4.3.  DISCUSSION  4.3.1. Results  The cm" ,  standard  deviation of all the  corresponding  1  to less than  10%  rotational fits was of a  less than  typical linewidth. The  0.002  rotational  constants obtained in this work show agreement within experimental uncertainty with three  those  of Femenias. The  to four  times  greater  uncertainty in the D than  that found  by  values  g  reported  Femenias. This  here is  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  the information in table 4.2. AG,  =  and  3  A ^ states can be calculated using  986.351cm"  and  1  AG  i  were obtained for the =  4.25  cm"  have AG  1  =  3  $  state which yields co  2  g  =  , = 1*  994.85 cm"  in agreement with Pazyuk's results. The  3  A,  977.855cm"  1  1  and  state was  u x g  e  found to  1033.739cm" . 1  0  Ranieri reported  analyzing two  bands at 5840 and  5860 A  which were  assigned as I1( II?) - Z*(0-0) and  ^-^(O-O) transitions respectively. Both of  these  for  1  3  assignments  agreement between  1  are  incorrect  Ranieri's B  values  reasons for the  stated  above.  17057 cm"  1  There band  is good with  the  NIOBIUM NITRIDE / 88 results reported cm"  band  1  here. It is puzzling that Ranieri did not consider  as  3  components of the  n, A _ 3  3  because  2  n A _ 3  she had analyzed  the other  transition and thus knew that the missing  the 17057 two spin 3  n - A 3  1  2  transition could be in the vicinity and she had analyzed the 4> - A transition 3  3  3  and  determined the. ground  cm" ;  state B  identical to the ground state B  1  Ranieri's rotational constants  value  e  g  of the A  2  state to be 0.5016  3  2  determined for the 17057 cm"  for the band at 17124 cm"  1  band.  do not agree well  1  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 4> and A states are regular in 3  3  nature, although there is anomalous splitting in each, in direct contradiction with Pazyuk's results. Pazyuk's assignment of the 17057 cm"  1  satellite band of the  3  3  band as a spin-orbit  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 A state could 3  be  accounted  account  for by a  for the line  1  I I state  broadening  nearly  degenerate  he observed  with  at high  3  A , which 2  could  J(—60) in the middle  component of triplet system, and also an interaction from below by the 'true' ground state; L * (5sa ). The line broadening effect mentioned above has been 1  2  shown to be a result of a case(a) to case(b) transition hv the X A state [7] so 3  the first of Femenias' hypotheses seems unlikely.  NIOBIUM NITRIDE / 89 It  is  instructive  to  molecules similar to NbN NbN's unseen low on  to try and  results  get  a  of  spectroscopic  feel for the  nitrides which is unfortunate. The  similar molecules to NbN  in that ZrO  ns  (where  2  n  is the  configurations opposed to 5s could  period  the  results published oxides  and  group IVa  TiO  are and  metals all  metal) in their ground electronic  situation in Nb.  1  on  relative positions of  is isoelectronic with NbN  of  studies  group IVa  have a similar number of open shell electrons. The  have  and  the  lying electronic states. There have been no  other group Va  HfO  compare  YF  also provide some insight into the  is also isoelectronic with  low-lying  NbN  electronic behaviour of  NbN.  A  summary  Gaydon [8]. As  of the  (5sa 4d6 ) and  3  low  spectra  of ZrO  expected there is a triplet and  lying triplet state is A by  emission  1  r  5200 and  shown the  1650cm"  1  [11] placed  the  3  A  the ground state has  1  A  (5sa 4d6 ) and 1  above the X Z 1  state  r  1  1  3  1700±250 cm"  1  Z  (5sa ).  +  2  1  gas  electronic spectrum of HfO  similar to that of ZrO  [12].  been assigned Further solid  has  1  (4so 3d5 ) 1  1  in contrast to ZrO state  [13].  1  A  been shown to be  work done on  the ground state was  (4sa 3d6 ) 1  1  is the  ZrO  state supporting  TiO  lowest  found to be state  in  very  because of  its importance in astrophysics. Again there are the expected triplet and manifolds but  and  lowest  phase study on 1  been a wealth of spectroscopic  Pearse  (5sa 4d5 ) states to be  r  above the X Z *  the matrix work. The  There has  A  1  state [10]. A  +  by  a singlet manifold. The  temperature solid state spectroscopy [9] as  state work has  is given  the  singlet  the  3  A  r  singlet  NIOBIUM NITRIDE / 90 manifold  and  was  found to be roughly 3500 cm"  solid state study [14]. A the  1  II  and  comparable spacing  3  of 2800 cm"  1  was  r  state in a  found between  I1 (4sa 3dir ) states [14].  3  1  1  In contrast to NbN, observed for YF  many more singlet than triplet transitions have been  [15]. The  ground state has  Anomalous triplet component splitting in the during  above the X A  1  the  analysis  of  Shenyavskaya speculated  the  3  $- A  been assigned 3  1  Z*  (5sa ) [15].  A (4sa 3d6 ) state was 1  system  3  as  that the so far unseen  1  1  by  Shenyavskaya  A  (4sa 3d6 ) was 1  1  2  uncovered et  al[16].  the cause  of the perturbation.  The  above information  the arrangement, of the have  similar  allows us to make some empirical guesses at the  low-lying electronic states of NbN.  separations  between  their  1  1I- II  and  3  1  A-  Both ZrO 3  A  states so it reasonable to suppose a similar situation in NbN.  and  TiO  isoconfigurational 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  become more localized on the metal. One ionic than the ZrO The  1  A  anomalous  multiplet 1  splitting  accommodated  1  Z*  neatly  in  3  A  bond to be much less  3  II  1  (5sa ) ground 2  into the  1  state  as  should  as the root of the perturbation  (4sa 3d7T ) 1  1  as a candidate for causing  (4so 3d6 )  likewise considered  the massive shift of the fifth period, a  expects the NbN  considered  1  (4sa 3d7T ) state be 1  state determining electrons will  bond so the isoconfigurational splitting to be likewise smaller.  (4sa 3d6 ) state should be 1  two  1  the  the 1  n  causing  component. Following the trend in the  state does not  above model. Of  seem  unreasonable and  is  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  4.  what is causing the large shift of the I I  3  A state?  multiplet component from its  3  1  expected position? The first question could be addressed by a low temperature NbN.  In order for the second  question to be  answered  solid state study on a number of singlet  transitions must be analyzed to profile the manifold and some case (a) forbidden transitions must be triplet states. An transition  by  observed  effort has  wavelength  to get the relative  positions of the singlet  been made in our lab to observe some forbidden  resolved fluorescence but  unfortunately no conclusive  results have been obtained yet. Again a solid state study may otherwise  forbidden  [9,10,14]. The = 18025cm"  1  transitons can  shift of the I I  and  3  1  become  'allowed' by  prove useful as  matrix-induced  effects  multiplet component from its expected position of  is probably the result of an interaction with a nearly degenerate  electronic state. The  mapping of the singlet manifold energies and  positions of these energy  the relative  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, 15. R.F. Barrow, M.W.  3718-3726(1975)  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  J' K-  K'  10 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 20 0 20 21 0 21 22 0 22 23 0 23 24 0 24 25 0 25 2 11 2 12 3 12 3 13 4 13 4 14 5 14 5 15 6 15 6 16 7 16  LINE ASSIGNMENTS  J" K" K"  Freq.(cm" )  0 0 0 10 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 .19 20 0 20 21 0 21 22 0 22 23 0 23 24 0 24 110 111 2 11 2 12 3 12 3 13 4 13 4 14 5 14 5 15 6 15  1610.93403 1612.62720 1614.31567 1615.99218 1617.64557 1619.26356 1620.84345 1622.38691 1623.91155 1625.42914 1626.94948 1628.47762 1630.01943 1631.57812 1633.15609 1634.75632 1636.38071 1638.03591 1639.72959 1641.47087 . 1643.27020 1645.15273 1647.12780 1649.21416 1651.41592 1612.69489 1612.37025 1614.48309 1613.98840 1616.27767 1615.60089 1618.06977 1617.23304 1619.79028 1618.85492 1621.63347  1  94  Intensity  3  0.0818 0.1365 0.2191 0.3497 0.6579 0.5175 0.9063 0.5336 0.4205 0.5687 0.8304 0.5863 0.5031 0.5530 0.5004 0.5550 0.3518 0.3861 0.3646 0.2586 0.5009 0.2329 0.1589 0.1102 0.0985 0.0631 0.0631 0.1103 0.1260 0.1399 0.0429 0.2351 0.2244 0.5252 0.5952 0.2493  / 95 J' K '  K '  7 17 8 17 8 18 9 1 8 9 1 9 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 15 1 15 16 1 15 16 1 16 17 1 16 17 1 17 18 1 17 18 1 18 19 1 18 19 1 19 20 1 19 20 1 20 21 1 20 21 1 21 22 1 21 22 1 22 23 1 22 23 1 23 24 1 23 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6  j"  K "  K ;  a  c  6 16 7 16 7 17 8 17 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 15 1 15 16 1 15 16 1 16 17 1 16 17 1 17 18 1 17 18 1 18 19 1 18 19 1 19 20 1 19 20 1 20 21 1 20 21 1 21 22 1 21 22 1 22 23 1 22 2 2 0 2 2 1 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5  Freq.(cm" ) 1  1620.47325 1623.39372 1622.08828 1625.13074 1623.70172 1626.84134 1625.31197 1628.51922 1626.91982 1630.15975 1628.52629 1631.76196 1630.13597 1633.32366 1631.74846 1634.84810 1633.36761 1636.33978 1634.99977 1637.80810 1636.64913 1639.26455 1638.32297 1640.71830 1640.03187 1642.18329 1641.78666 1643.67044 1643.60474 1645.16313 1645.50678 1646.74678 1647.51932 1648.35443 1613.95270 1613.93372 1615.70306 1615.65795 1617.47266 1617.38810 1619.25035 1619.11887 1620.98313 1620.84345 1623.10135  Intensity  3  0.2429 0.2438 0.6796 0.3051 0.3343 0.2324 0.3380 0.3746 0.4356 0.2451 0.4085 0.2857 0.3838 0.2499 0.4532 0.2094 0.4086 0.3741 0.2886 0.2183 0.2478 0.1252 0.2800 0.1669 0.1768 0.0958 0.1618 0.0904 0.2509 0.0753 0.1076 0.0631 0.0822 0.0488 0.1129 0.1032 0.2321 0.4488 0.3107 0.3372 0.3556 0.4494 0.3019 0.9063 0.3113  / 96 J' K '  K'  8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 19 2 18 20 2 18 21 2 19 21 2 20 22 2 20 23 2 21 4 3 2 5 3 2 5 3 3 6 3 4 7 3 4 7 3 5 8 3 5 8 3 6 9 3 6 9 3 7 10 3 J 10 3 8 11 3 8 11 3 9 12 3 9 12 3 10 13 3 10  J" K" a  K" c  7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 20 2 18 20 2 19 21 2 19 22 2 20 3 3 1 4 3 1 4 3 2 5 3 3 6 3 3 6 3 4 7 3 4 7 3 5 8 3 5 8 3 6 9 3 6 9 3 7 10 3 7 10 3 8 11 3 8 11 3 9 12 3 9  Freq.(cm" ) 1  1622.57130 1624.87091 1624.28737 1626.68268 1625.99392 1628.49001 1627.68943 1630.27732 1629.37183 1632.03341 1631.04173 1633.75427 1632.69743 1635.43557 1634.34006 1637.07430 1635.96710 1638.67128 1637.57248 1640.22473 .1639.09725 1641.73573 1641.01262 1643.20566 1644.63584 1644.33937 1646.02986 1647.53093 1615.16065 1616.98418 1616.98418 1618.80409 1620.63445 1620.62302 1622.45686 1622.43569 1624.27312 1624.23731 1626.08091 1626.02429 1627.87690 1627.79317 1629.65934 1629.54185 1631.41683  Intensity  3  0.4496 0.2984 0.5810 0.3723 0.4636 0.4248 0.4280 0.6433 0.4569 0.3799 0.4723 0.3360 0.4039 0.3004 0.3132 0.2350 0.5458 0.2321 0.1714 0.1615 0.1490 0.1589 0.1167 0.3870 0.1167 0.0974 0.1184 0.0746 0.1474 0.1918 0.1918 0.1449 0.1285 0.1201 0.1606 0.1181 0.1114 0.1748 0.1667 0.1445 0.1750 0.1863 0.1718 0.1741 0.1740  / 97 J' K  a  K  c  13 3 11 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 19 3 16 19 3 17 20 3 17 20 3 18 21 3 18 21 3 19 22 3 19 22 3 20 23 3 20 23 3 21 5 4 21 6 4 3 7 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 11 15 4 11 15 4 12 16 4 13 17 4 13 17 4 14 18 4 14 18 4 15 19 4 15 19 4 16 »  J" K  a  K  c  12 3 10 13 3 10 13 3 11 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 19 3 16 19 3 17 20 3 17 20 3 18 21 3 18 21 3 19 22 3 19 22 3 20 4 4 1 5 4 2 6 4 3 7 4 4 8 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 •4 8 12 4 9 13 4 10 14 4 10 14 4 11 15 4 12 16 4 12 16 4 13 17 4 13 17 4 14 18 4 14 18 4 15  Freq.(cm" ) 1  1631.26961 1633.17285 1632.97470 1634.93424 1634.65650 1636.59992 1636.31475 1638.27363 1637.95080 1639.91517 1639.56451 1641.52134 1641.15815 1643.09020 1642.73121 1644.62208 1644.28402 1646.10936 1645.78259 1647.55773 1647.20276 1615.67840 1617.11019 1618.53250 1619.95037 1621.37158 1621.36101 1622.79258 1622.77529 1624.21923 1624.18747 1625.64985 1625.60070 1627.08548 1627.01190 1628.42043 1629.96920 1629.82356 1631.22006 1632.86730 1632.60584 1634.30999 1633.97683 1635.74916 1635.32962  Intensity  3  0.2053 0.1444 0.1829 0.1097 0.1074 0.1213 0.1665 0.0923 0.1480 0.0785 0.1723 0.0645 0.0791 0.0381 0.0856 0.0922 0.0470 0.0790 0.3468 0.0825 0.0663 0.1358 0.2248 0.3170 0.3358 0.1987 0.4085 0.2182 0.2463 0.2397 0.2326 0.1938 0.2436 0.1814 0.2527 0.4419 0.1788 0.1844 0.1314 0.1371 0.1420 0.1347 0.1750 0.0883 0.0858  / 98 J' K ' K'  20 4 16 20 4 17 21 4 17 21 4 18 22 4 18 22 4 19 7 6 2 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 18 6 13 10 1 2 0 2 3 0 3 4 0 .4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 20 0 20 21 0 21 22 0 22 23 0 23 24 0 24 25 0 25 2 11 2 12 3 12  J" K" a  K"  19 4 15 19 4 16 20 4 16 20 4 17 21 4 17 21 4 18 6 6 1 7 6 2 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 17 6 12 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 20 0 20 21 0 21 22 0 22 23 0 23 24 0 24 25 0 25 26 0 26 3 12 3 13 4 13  Freq.(cm" ')  Intensity  3  C  1637.17682 1636.65976 1638.57932 1637.96118 1639.72959 1639.11345 1616.45057 1617.98526 1619.92845 1621.43635 1623.00919 1624.59179 1626.17257 1627.75006 1629.32224 1630.89339 1634.06736 1605.89854 1604.25054 1602.62152 1601.01203 1599,41904 1597.83570 1596.25702 1594.69000 1593.13906 1591.60698 1590.09745 1588.60530 1587.13066 1585.67153 1584.22882 1582.80529 1581.40360 1580.02851 1578.68972 1577.39648 1576.16402 1575.00795 1573.94674 1572.99694 1572.16471 1603.91333 1604.35612 1602.19892  0.0848 0.0850 0.1454 0.0551 0.3646 0.1490 0.0471 0.1441 0.1014 0.1848 0.5724 0.2077 0.2547 0.2522 0.3041 0.1387 0.1139 0.1436 0.4399 0.3582 0.3597 0.3797 0.6568 0.6055 0.5368 0.6021 0.7244 0.6147 0.5728 0.5326 0.6921 0.5255 0.4776 0.5075 0.3648 0.3115 0.2681 0.3288 0.2151 0.0931 0.0696 0.0686 0.1424 0.1295 0.1831  / 99 J' K'  K'  3 1 3 4 13 4 14 5 14 5 15 6 15 6 16 7 16 7 17 8 17 8 1 8 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 15 1 15 16 1 15 16 1 16 17 1 16 17 1 17 18 1 17 18 1 18 19 1 18 19 1 19 20 1 19 20 1 20 21 1 20 21 1 21 22 1 21 22 1 22 23 1 22 23 1 23 24 1 23 3 2 1 3 2 2 4 2 2  J" K"  K"  cl  C  4 14 5 14 5 15 6 15 6 16 7 16 7 17 8 17 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 15 1 15 16 1 15 16 1 16 17 1 16 17 1 17 18 1 17 18 1 18 19 1 18 19 1 19 20 1 19 20 1 20 21 1 20 21 1 21 22 1 21 22 1 22 23 1 22 23 1 23 24 1 23 24 1 24 25 1 24 4 2 2 4 2 3 5 2 3  Freq.(cm" ) 1  1602.77845 1600.49753 1601.20540 1598.80864 1599.65398 1597.06246 1598.10649 1595.46058 1596.56932 1593.79723 1595.04068 1592.14243 1593.52137 1590.49536 1592.01125 1588.85629 1590.51059 1587.22678 1589.01963 1585.60730 1587.54033 1583.99872 1586.07291 1582.40314 1584.62035 1580.82138 1583.18653 1579.25323 . 1581.77414 1577.69970 1580.39329 1576.16402 1579.04931 1574.64804 1577.75504 1573.15769 1576.52676 1571.67062 1575.38481 1570.26887 1574.35452 1568.88383 1602.13244 1602.17815 1600.45982  Intensity  3  0.1863 0.2143 0.0832 0.2855 0.2702 0.3100 0.4201 0.5526 0.3291 0.2765 0.3365 0.2579 0.3727 0.4070 0.4248 0.3076 0.3975 0.3139 0.2835 0.2845 0.3855 0.2394 0.3203 0.2460 0.3447 0.1989 0.3533 0.1946 0.3125 0.1564 0.1902 0.3288 0.1368 0.1443 0.1250 0.0893 0.1095 0.0678 0.0738 0.0790 0.0577 0.0552 0.4098 0.2282 0.3065  / 100 J' K'  K'  4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 19 2 18 20 2 18 22 2 20 5 3 3 6 3 4 7 3 4 7 3 5 8 3 5 8 3 6 9 3 6 9 3 7 10. 3 7 10 3 8 11 3 8 11 3 9  J" K"  K"  5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 19 2 18 20 2 18 20 2 19 21 2 19 23 2 21 6 3 4 7 3 5 8 3 5 8 3 6 9 3 6 9 3 7 10 3 7 10 3 8 11 3 8 11 3 9 12 3 9 12 3 10  Freq.(cm" ) 1  1600.55427 1598.77418 1598.94198 1597.06246 1597.33975 1595.27158 1595.74617 1593.83533 1594.15979 1592.02911 1592.57954 1590.25482 1591.00410 1588.47723 1589.43305 1586.69137 1587.86642 1584.89760 1586.30428 1583.09563 1584.74653 1581.28981' 1583.19331 1579.48193 1581.64475 1577.67595 1580.08833 1575.87453 1578.47089 1574.08527 1577.25904 1572.30969 1568.81606 1598.46930 1596.91135 1595.32858 1595.35033 1593.73906 1593.78114 1592.12514 1592.19828 1590.48070 1590.60132 1588.79450 1588.98812  Intensity  3  0.3041 0.3512 0.3915 0.3100 0.3914 0.3750 0.4254 0.3540 0.5143 0.4925 0.4932 0.4907 0.4121 0.4850 0.3550 0.4909 0.4638 0.5076 0.5012 0.3422 0.3732 0.4054 0.2923 0.2987 0.3411 0.3956 0.3156 0.1890 0.2312 0.1976 0.1260 0.1618 0.1007 0.4167 0.1341 0.1478 0.1731 0.1954 0.2314 0.1295 0.1626 0.2846 0.1878 0.4484 0.1851  / 101 J' K'  K'  12 3 9 12 3 10 13 3 10 13 3 11 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 1 0 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 20 0 20 21 0 21 22 0 22 23 0 23 24 0 24 25 0 25 2 11 2 12 3 12 3 13 4 13 4 14  J" K"  K"  a  C  13 3 10 13 3 11 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 T8 3 16 19 3 16 19 3 17 0 0 0 10 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 20 0 20 21 0 21 22 0 22 23 0 23 24 0 24 1 1 0 111 2 11 2 1 2 3 12 3 13  Freq.(cm* ) 1  1587.06931 1587.36035 1585.29241 1585.71615 1583.46354 1584.05663 1581.61964 1582.38861 1579.65531 1580.70812 1577.68444 1579.02193 1575.67842 1577.32947 1610.93403 1612.62720 1614.31567 1615.99218 1617.64557 1619.26356 1620.84345 1622.38691 1623.91155 1625.42914 1626.94948 1628.47762 1630.01943 1631.57812 1633.15609 1634.75632 1636.38071 1638.03591 1639.72959 1641.47087 1643.27020 1645.15273 1647.12780 1649.21416 1651.41592 1612.69489 1612.37025 1614.48309 1613.98840 1616.27767 1615.60089  Intensity  3  0.1514 0.1734 0.1468 0.1926 0.3088 0.1998 0.0652 0.1398 0.0911 0.1332 0.0787 0.1054 0.0721 0.1407 0.0818 0.1365 0.2191 0.3497 0.6579 0.5175 0.9063 0.5336 0.4205 0.5687 0.8304 0.5863 0.5031 0.5530 0.5004 0.5550 0.3518 0.3861 0.3646 0.2586 0.5009 0.2329 0.1589 0.1102 0.0985 0.0631 0.0631 0.1103 0.1260 0.1399 0.0429  / 102 J' K'  K'  5 14 5 15 6 15 6 16 7 16 7 17 8 17 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 15 1 15 16 1 15 16 1 16 17 1 16 17 1 17 18 1 17 18 1 18 19 1 18 19 1 19 20 1 19 20 1 20 21 1 20 21 1 21 22 1 21 22 1 22 23 1 22 23 1 23 24 1 23 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4  J" K"  K"  a  C  4 1 3 4 14 5 14 5 15 6 15 6 16 7 16 7 17 8 17 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 15 1 15 16 1 15 16 1 16 17 1 16 17 1 17 18 1 17 18 1 18 19 1 18 19 1 19 20 1 19 20 1 20 21 1 20 21 1 21 22 1 21 22 1 22 23 1 22 2 2 0 2 2 1 3 2 1 3 2 2 4 2 2 4 2 3  Freq.(cm" ) 1  1618.06977 1617.23304 1619.79028 1618.85492 1621.63347 1620.47325 1623.39372 1622.08828 1625.13074 1623.70172 1626.84134 1625.31197 1628.51922 1626.91982 1630.15975 1628.52629 1631.76196 1630.13597 1633.32366 1631.74846 1634.848.10 1633.36761 1636.33978 1634.99977 1637.80810 1636.64913 1639.26455 1638.32297 1640.71830 1640.03187 1642.18329 1641.78666 1643.67044 1643.60474 1645.16313 1645.50678 1646.74678 1647.51932 1648.35443 1613.95270 1613.93372 1615.70306 1615.65795 1617.47266 1617.38810  Intensity  3  0.2351 0.2244 0.5252 0.5952 0.2493 0.2429 0.2438 0.6796 0.3051 0.3343 0.2324 0.3380 0.3746 0.4356 0.2451 0.4085 0.2857 0.3838 0.2499 0.4532 0.2094 0.4086 0.3741 0.2886 0.2183 0.2478 0.1252 0.2800 0.1669 0.1768 0.0958 0.1618 0.0904 0.2509 0.0753 0.1076 0.0631 0.0822 0.0483 0.1129 0.1032 0.2321 0.4488 0.3107 0.3372  / 103  j'  K •  K :  a  c  6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 19 2 18 20 2 18 21 2 19 21 2 20 22 2 20 23 2 21 4 3 2 5 3 2 5 3 3 6 3 4 7 3 4 7 3 5 8 3 5 8 3 6 9 3 6 9 3 7 10 3 7 10 3 8  J"  K " CL  K " C  5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 112 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 20 2 18 20 2 19 21 2 19 22 2 20 3 3 1 4 3 1 4 3 2 5 3 3 6 3 3 6 3 4 7 3 4 7 3 5 8 3 5 8 3 6 9 3 6 9 3 7  Freq.(cm~  1619.25035 1619.11887 1620.98313 1620.84345 1623.10135 1622.57130 1624.87091 1624.28737 1626.68268 1625.99392 1628.49001 1627.68943 1630.27732 1629.37183 1632.03341 1631.04173 1633.75427 1632.69743 1635.43557 1634.34006 1637.07430 1635.96710 1638.67128 1637.57248 1640.22473 1639.09725 1641.73573 1641.01262 1643.20566 1644.63584 1644.33937 1646.02986 1647.53093 1615.16065 1616.98418 1616.98418 1618.80409 1620.63445 1620.62302 1622.45686 1622.43569 1624.27312 1624.23731 1626.08091 1626.02429  Intensity  3  0.3556 0.4494 0.3019 0.9063 0.3113 0.4496 0.2984 0.5810 0.3723 0.4636 0.4248 0.4280 0.6433 0.4569 0.3799 0.4723 0.3360 0.4039 0.3004 0.3132 0.2350 0.5458 0.2321 0.1714 0.1615 0.1490 0.1589 0.1167 0.3870 ~ 0.1167 0.0974 0.1184 0.0746 0.1474 0.1918 0.1918 0.1449 0.1285 0.1201 0.1606 0.1181 0.1114 0.1748 0.1667 0.1445  / 104 J'  K '  K'  11 3 8 11 3 9 12 3 9 < • 12 3 10 13 3 10 13 3 11 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 19 3 16 19 3 17 20 3 17 20 3 18 21 3 18 21 3 19 22 3 19 22 3 20 23 3 20 23 3 21 5 4 2 6 4 3 7 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 11 15 4 11 15 4 12 16 4 13 17 4 13  j"  K " cl  K ; C  10 3 7 10 3 8 11 3 8 11 3 9 12 3 9 12 3 10 13 3 10 13 3 11 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 19 3 16 19 3 17 20 3 17 20 3 18 21 3 18 21 3 19 22 3 19 22 3 20 4 4 1 5 4 2 6 4 3 7 4 4 8 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 10 14 4 10 14 4 11 • 15 4 12 16 4 12  Freq.(cm" ) 1  1627.87690 1627.79317 1629.65934 1629.54185 1631.41683 1631.26961 1633.17285 1632.97470 1634.93424 1634.65650 1636.59992 1636.31475 1638.27363 1637.95080 1639.91517 1639.56451 1641.52134 1641.15815 1643.09020 1642.73121 1644.62208 1644.28402 1646.10936 1645.78259 1647.55773 1647.20276 1615.67840 1617.11019 1618.53250 1619.95037 1621.37158 1621.36101 1622.79258 1622.77529 1624.21923 1624.18747 1625.64985 1625.60070 1627.08548 1627.01190 1628.42043 1629.96920 1629.82356 1631.22006 1632.86730  Intensity  3  0.1750 0.1863 0.1718 0.1741 0.1740 0.2053 0.1444 0.1829 0.1097 0.1074 0.1213 0.1665 0.0923 0.1480 0.0785 0.1723 0.0645 0.0791 0.0381 0.0856 0.0922 0.0470 0.0790 0.3468 0.0825 0.0663 0.1358 0.2248 0.3170 0.3358 0.1987 0.4085 0.2182 0.2463 0.2397 0.2326 0.1938 0.2436 0.1814 0.2527 0.4419 0.1788 0.1844 0.1314 0.1371  / 105 J' K • K'  J" K"  17 4 14 18 4 14 18 4 15 19 4 15 19 4 16 20 4 16 20 4 17 21 4 17 21 4 18 22 4 18 22 4 19 7 6 2 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 18 6 13 1 0 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 20 0 20 21 0 21 22 0 22 23 0 23  16 4 13 17 4 13 17 4 14 18 4 14 18 4 15 19 4 15 19 4 16 20 4 16 20 4 17 21 4 17 21 4 18 6 6 1 7 6 2 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 . 17 6 12 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 20 0 20 21 0 21 22 0 22 23 0 23 24 0 24  K"  Freq.(cm" ')  1632.60584 1634.30999 1633.97683 1635.74916 1635.32962 1637.17682 1636.65976 1638.57932 1637.96118 1639.72959 1639.11345 1616.45057 1617.98526 1619.92845 1621.43635 1623.00919 1624.59179 1626.17257 1627.75006 1629.32224 1630.89339 1634.06736 1605.89854 1604.25054 1602.62152 1601.01203 1599.41904 1597.83570 1596.25702 1594.69000 1593.13906 1591.60698 1590.09745 1588.60530 1587.13066 1585.67153 1584.22882 1582.80529 1581.40360 1580.02851 1578.68972 1577.39648 1576.16402 1575.00795 1573.94674  Intensity  3  0.1420 0.1347 0.1750 0.0883 0.0858 0.0848 0.0850 0.1454 0.0551 0.3646 0.1490 0.0471 0.1441 0.1014 0.1848 0.5724 0.2077 0.2547 0.2522 0.3041 0.1387 0.1139 0.1436 0.4399 0.3582 0.3597 0.3797 0.6568 0.6055 0.5368 0.6021 0.7244 0.6147 0.5728 0.5326 0.6921 0.5255 0.4776 0.5075 0.3648 0.3115 0.2681 0.3288 0.2151 0.0931  / 106 J' K'  24 25 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23  K '  0 24 0 25 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 1 9 1 10 1 10 1 11 1 11 1 12 1 12 1 13 1 13 1 14 1 14 1 15 1 15 1 16 1 16 1 17 1 17 1 18 1 18 1 19 1 19 1 20 1 20 1 21 1 21 1 22 1 22  j"  25 26 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24  K "  K ;  a  c  0 25 0 26 12 13 13 14 14 15 15 16 16 17 17 18 18 19 1 9 1 10 1 10 1 11 1 11 1 12 1 12 1 13 1 13 1 14 1 14 1 15 1 15 1 16 1 16 1 17 1 17 1 18 1 18 1 19 1 19 1 20 1 20 1 21 1 21 1 22 1 22 1 23 1 23  Freq.(cm" ) 1  1572.99694 1572.16471 1603.91333 1604.35612 1602.19892 1602.77845 1600.49753 1601.20540 1598.80864 1599.65398 1597.06246 1598.10649 1595.46058 1596.56932 1593.79723 1595.04068 1592.14243 1593.52137 1590.49536 1592.01125 1588.85629 1590.51059 1587.22678 1589.01963 1585.60730 1587.54033 1583.99872 1586.07291 1582.40314 1584.62035 1580.82138 1583.18653 1579.25323 1581.77414 1577.69970 1580.39329 1576.16402 1579.04931 1574.64804 1577.75504 1573.15769 1576.52676 1571.67062 1575.38481 1570.26887  Intensity  3  0.0696 0.0686 0.1424 0.1295 0.1831 0.1863 0.2143 0.0832 0.2855 0.2702 0.3100 0.4201 0.5526 0.3291 0.2765 0.3365 0.2579 0.3727 0.4070 0.4248 0.3076 0.3975 0.3139 0.2835 0.2845 0.3855 0.2394 0.3203 0.2460 0.3447 0.1989 0.3533 0.1946 0.3125 0.1564 0.1902 0.3288 0.1368 0.1443 0.1250 0.0893 0.1095 0.0678 0.0738 0.0790  / 107 j'  K :  K ;  a  c  23 1 23 24 1 23 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 19 2 18 20 2 18 22 2 20 5 3 3 6 3 4 7 3 4 7 3 5 8 3 5 8 3 6 9 3 6  J"  K " a.  K " C  24 1 24 25 1 24 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 .2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 19 2 18 20 2 18 20 2 19 21 2 19 23 2 21 6 3 4 7 3 5 8 3 5 8 3 6 9 3 6 9 3 7 10 3 7  Freq.(cm" ) 1  1574.35452 1568.88383 1602.13244 1602.17815 1600.45982 1600.55427 1598.77418 1598.94198 1597.06246 1597.33975 1595.27158 1595.74617 1593.83533 1594.15979 1592.02911 1592.57954 1590.25482 1591.00410 1588.47723 1589.43305 . 1586.69137 1587.86642 1584.89760 1586.30428 1583.09563 1584.74653 1581.28981 1583.19331 1579.48193 1581.64475 1577.67595 1580.08833 1575.87453 1578.47089 1574.08527 1577.25904 1572.30969 1568.81606 1598.46930 1596.91135 1595.32858 1595.35033 1593.73906 1593.78114 1592.12514  Intensity  3  0.0577 0.0552 0.4098 0.2282 0.3065 0.3041 0.3512 0.3915 0.3100 0.3914 0.3750 0.4254 0.3540 0.5143 0.4925 0.4932 0.4907 0.4121 0.4850 0.3550 0.4909 0.4638 0.5076 0.5012 0.3422 0.3732 0.4054 0.2923 0.2987 0.3411 0.3956 0.3156 0.1890 0.2312 0.1976 0.1260 0.1618 0.1007 0.4167 0.1341 0.1478 0.1731 0.1954 0.2314 0.1295  / 108 J' K'  K'  9 3 7 10 3 7 10 3 8 11 3 8 11 3 9 12 3 9 12 3 10 13 3 10 1.3 3 11 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 1 0 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 ,18 19 0 19 20 0 20 21 0 21 22 0 22 23 0 23 24 0 24 25 0 25 2 1 1  J" K  Freq.(cm" ) 1  a  K  c  10 3 8 11 3 8 11 3 9 12 3 9 12 3 10 13 3 10 13 3 11 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 19 3 16 19 3 17 0 0 0 1 0 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 20 0 20 21 0 21 22 0 22 23 0 23 24 0 24 1 1 0  1592.19828 1590.48070 1590.60132 1588.79450 1588.98812 1587.06931 1587.36035 1585.29241 1585.71615 1583.46354 1584.05663 1581.61964 1582.38861 1579.65531 1580.70812 1577.68444 1579.02193 1575.67842 1577.32947 1610.93403 1612.62720 1614.31567 1615.99218 1617.64557 1619.26356 1620.84345 1622.38691 1623.91155 1625.42914 1626.94948 1628.47762 1630.01943 1631.57812 1633.15609 1634.75632 1636.38071 1638.03591 1639.72959 1641.47087 1643.27020 1645.15273 1647.12780 1649.21416 1651.41592 1612.69489  Intensity  3  0.1626 0.2846 0.1878 0.4484 0.1851 0.1514 0.1734 0.1468 0.1926 0.3088 0.1998 0.0652 0.1398 0.0911 0.1332 0.0787 0.1054 0.0721 0.1407 0.0818 0.1365 0.1823 0.3497 0.6579 0.5175 0.9063 0.5336 0.4205 0.0411 0.8304 0.5863 0.5031 0.5530 0.5004 0.5550 0.3518 0.3861 0.3646 0.2586 0.5009 0.2329 0.1589 0.1102 0.0985 0.0631  / J'  K '  K '  j"  K "  K ;  Freq.(cm" ) }  109  Intensity  3  2  1 2  I  I  I  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  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  8  1  8  1623.70172  0.3343  1  8  1626.84134  0.0392  1625.31197  0.3380  7  9  1  1  10  1  9  9  10  1  10  9  1 9  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  1613.95270  0.1129  3  2  1  2  2  0  / 110 j  1  K *  K :  a  c  3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 19 2 18 20 2 18 21 2 19 21 2 20 22 2 20 23 2 21 4 3 2 5 3 2 5 3 3 6 3 4 7 3 4 7 3 5 8 3 5  j"  K " CL  K : C  2 2 1 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 20 2 18 20 2 19 21 2 19 22 2 20 3 3 1 4 3 1 4 3 2 5 3 3 6 3 3 6 3 4 7 3 4  Freq.(cm~ ) 1  1613.93372 1615.70306 1615.65795 1617.47266 - 1617.38810 1619.25035 1619.11887 1620.98313 1620.84345 1623.10135 1622.57130 1624.87091 1624.28737 1626.68268 1625.99392 1628.49001 1627.68943 1630.27732 1629.37183 1632.03341 1631.04173 1633.75427 1632.69743 1635.43557 1634.34006 1637.07430 1635.96710 1638.67128 1637.57248 1640.22473 1639.09725 1641.73573 1641.01262 1643.20566 1644.63584 1644.33937 1646.02986 1647.53093 1615.16065 1616.98418 1616.98418 1618.80409 1620.63445 1620.62302 1622.45686  Intensity  3  0.1032 0.2321 0.4488 0.3107 0.3372 0.3556 0.4494 0.3019 0.9063 0.3113 0.4496 0.1711 0.5810 0.3723 0.4636 0.4248 0.4280 0.6433 0.4569 0.3799 0.4723 0.3360 0.4039 0.3004 0.3132 0.2350 0.5458 0.2321 0.1714 0.1615 0.1490 0.1589 0.1167 0.3870 0.1167 0.0974 0.1184 0.0746 0.1474 0.1918 0.1918 0.1449 0.1285 0.1201 0.1606  / 111 J' K'  K'  8 3 6 9 3 6 9 3 7 10 3 7 10 3 8 11 3 8 11 3 9 12 3 9 12 3 10 13 3 10 13 3 11 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 19 3 16 19 3 17 20 3 17 20 3 18 21 3 18 21 3 19 22 3 19 22 3 20 23 3 20 23 3 21 5 4 2 6 4 3 7 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10  J" K"  K"  a  C  7 3 5 8 3 5 8 3 6 9 3 6 9 3 7 10 3 7 10 3 8 11 3 8 11 3 9 12 3 9 12 3 10 13 3 10 13 3 11 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 • 17 3 15 18 3 15 18 3 16 19 3 16 19 3 17 20 3 17 20 3 18 21 3 18 21 3 19 22 3 19 22 3 20 4 4 1 5 4 2 6 4 3 7 4 4 8 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9  Freq.(cm" ) 1  1622.43569 1624.27312 1624.23731 1626.08091 1626.02429 1627.87690 1627.79317 1629.65934 1629.54185 1631.41683 1631.26961 1633.17285 1632.97470 1634.93424 1634.65650 1636.59992 1636.31475 1638.27363 1637.95080 1639.91517 1639.56451 1641.52134 1641.15815 1643.09020 1642.73121 1644.62208 1644.28402 1646.10936 1645.78259 1647.55773 1647.20276 1615.67840 1617.11019 1618.53250 1619.95037 1621.37158 1621.36101 1622.79258 1622.77529 1624.21923 1624.18747 1625.64985 1625.60070 1627.08548 1627.01190  Intensity  9  0.1181 0.1114 0.1748 0.1667 0.1445 0.1750 0.1863 0.1718 0.1741 0.1740 0.2053 0.1444 0.1829 0.1097 0.1074 0.1213 0.1665 0.0923 0.1480 0.0785 0.1723 0.0645 0.1772 0.0381 0.0847 0.0922 0.0470 0.0790 0.3468 0.0825 0.0663 0.1358 0.2248 0.3170 0.3358 0.1987 0.4085 0.2182 0.2463 0.0373 0.0386 0.1938 0.2436 0.1814 0.2527  / 112 j  1  K '  K :  a  c  14 4 11 15 4 11 15 4 12 16 4 13 17 4 13 17 4 14 18 4 14 18 4 15 19 4 15 19 4 16 20 4 16 20 4 17 21 4 17 21 4 18 22 4 18 22 4 19 7 6 2 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 18 6 13 10 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 , 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 .17 0 17 18 0 18  j"  K "  K ;  a  c  13 4 10 14 4 10 14 4 11 15 4 12 16 4 12 16 4 13 17 4 13 17 4 14 18 4 14 18 4 15 19 4 15 19 4 16 20 4 16 20 4 17 21 4 17 21 4 18 6 6 1 7 6 2 8 6 3 • 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 17 6 12 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19  Freq.(cm" ) 1  1628.42043 1629.96920 1629.82356 1631.22006 1632.86730 1632.60584 1634.30999 1633.97683 1635.74916 1635.32962 1637.17682 1636.65976 1638.57932 1637.96118 1639.72959 1639.11345 1616.45057 1617.98526 1619.92845 1621.43635 1623.00919 1624.59179 1626.17257 1627.75006 1629.32224 1630.89339 1634.06736 1605.89854 1604.25054 1602.62152 1601.01203 1599.41904 1597.83570 1596.25702 1594.69000 1593.13906 1591.60698 1590.09745 1588.60530 1587.13066 1585.67153 1584.22882 1582.80529 1581.40360 1580.02851  Intensity  3  0.4419 0.0522 0.1844 0.1314 0.1371 0.1420 0.1347 0.1750 0.0883 0.0858 0.0848 0.0850 0.1454 0.0551 0.3646 0.1490 0.0471 0.1441 0.1014 0.1848 0.5724 0.2077 0.2547 0.2522 0.3041 0.1387 0.1139 0.1436 0.4399 0.3582 0.3597 0.3797 0.6568 0.6055 0.5368 0.6021 0.7244 0.6147 0.5728 0.5326 0.6921 0.5255 0.4776 0.0393 0.3648  / 113 j'  K '  K :  a  19 0 19 20 0 20 21 0 21 22 0 22 23 0 23 24 0 24 25 0 25 2 1 1 2 12 3 12 3 13 4 1 3 4 14 5 14 5 15 6 15 6 16 7 16 7 17 8 17 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 15 1 15 16 1 15 16 1 16 17 1 16 17 1 17 18 1 17 18 1 18 19 1 18 19 1 19 20 1 19 20 1 20  c  J"  K "  a  K "  20 0 20 21 0 21 22 0 22 23 0 23 24 0 24 25 0 25 26 0 26 3 12 3 13 4 13 4 14 5 1 4 5 1 5 6 1 5 6 1 6 7 16 7 17 8 17 8 18 9 18 9 1 9 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 15 1 15 16 1 15 16 1 16 17 1 16 17 1 17 18 1 17 18 1 18 19 1 18 19 1 19 20 1 19 20 1 20 21 1 20 21 1 21  c  Freq.(cm"  1578.68972 1577.39648 1576.16402 1575.00795 1573.94674 1572.99694 1572.16471 1603.91333 1604.35612 1602.19892 1602.77845 1600.49753 1601.20540 1598.80864 1599.65398 1597.06246 1598.10649 1595.46058 1596.56932 1593.79723 1595.04068 1592.14243 1593.52137 1590.49536 1592.01125 1588.85629 1590.51059 1587.22678 1589.01963 1585.60730 1587.54033 1583.99872 1586.07291 1582.40314 1584.62035 1580.82138 1583.18653 1579.25323 1581.77414 1577.69970 1580.39329 1576.16402 1579.04931 1574.64804 1577.75504  Intensity  3  0.3115 0.2681 0.3288 0.2151 0.0931 0.0696 0.0686 0.1424 0.1295 0.1831 0.1863 0.2143 0.0832 0.2855 0.2702 0.3100 0.4201 0.5526 0.3291 0.2765 0.3365 0.2579 0.3727 0.4070 0.4248 0.3076 0.3975 0.3139 0.0536 0.2845 0.3855 0.2394 0.3203 0.2460 0.3447 0.1989 0.3533 0.1946 0.3125 0.1564 0.1902 0.3288 0.1368 0.1443 0.1250  / 114 J' K' K' a c  J" K"  K"  a  C  21 1 20 21 1 21 22 1 21 22 1 22 23 1 22 23 1 23 24 1 23 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 19 2 18 20 2 18 22 2 20 5 3 3 6 3 4  22 1 21 22 1 22 23 1 22 23 1 23 24 1 23 24 1 24 25 1 24 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 911 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 19 2 18 20 2 18 20 2 19 21 2 19 23 2 21 6 3 4 7 3 5  Freq.(cm" ^)  1573.15769 1576.52676 1571.67062 1575.38481 1570.26887 1574.35452 1568.88383 1602.13244 1602.17815 1600.45982 1600.55427 1598.77418 1598.94198 1597.06246 1597.33975 1595.27158 1595.74617 1593.83533 1594.15979 1592.02911 1592.57954 1590.25482 ' 1591.00410 1588.47723 1589.43305 1586.69137 1587.86642 1584.89760 1586.30428 1583.09563 1584.74653 1581.28981 1583.19331 1579.48193 1581.64475 1577.67595 1580.08833 1575.87453 1578.47089 1574.08527 1577.25904 1572.30969 1568.81606 1598.46930 1596.91135  Intensity  3  0.0893 0.1095 0.0678 0.0738 0.0790 0.0577 0.0552 0.4098 0.2282 0.3065 0.3041 0.3512 0.3915 0.3100 0.3914 0.3750 0.4254 0.3540 0.5143 0.4925 0.4932 0.4907 0.4121 0.4850 0.3550 0.4909 0.4638 0.5076 0.5012 0.3422 0.3732 0.4054 0.2923 0.2987 0.3411 0.3956 0.3156 0.1890 0.2312 0.1976 0.1260 0.1618 0.1007 0.4167 0.1341  / 115 J" K. a  7 3 4 7 3 5 8 3 5 8 3 6 9 3 6 9 3 7 10 3 7 10 3 8 11 3 8 11 3 9 12 3 9 12 3 10 13 3 10 13 3 11 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 19 3 16 19 3 17 20 3 17 20 3 18 21 3 18 21 3 19 22 3 19 22 3 20 23 3 20 23 3 21 5 4 2 6 4 3 7 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 "4 8 12 4 9  c  8 3 5 8 3 6 9 3 6 9 3 7 10 3 7 10 3 8 11 3 8 11 3 9 12 3 9 12 3 10 13 3 10 13 3 11 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 19 3 16 19 3 17 20 3 17 20 3 18 21 3 18 21 3 19 22 3 19 22 3 20 23 3 20 23 3 21 24 3 21 24 3 22 6 4 3 7 4 4 8 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 . 12 4 8 12 4 9 13 4 10  Freq.(cm" ) 1  1595.32858 1595.35033 1593.73906 1593.78114 1592.12514 1592.19828 1590.48070 1590.60132 1588.79450 1588.98812 1587.06931 1587.36035 1585.29241 1585.71615 1583.46354 1584.05663 1581.61964 1582.38861 1579.65531 1580.70812 1577.68444 1579.02193 1575.67842 1577.32947 1573.64651 1575.63395 1571.59892 1573.93879 1569.54229 1572.24300 1567.48479 1570.51794 1565.43085 1568.72566 1597.17769 1595.23802 1593.28580 1591.32422 1589.35430 1589.35430 1587.38059 1587.38059 1585.41798 1585.40098 1583.41735  Intensity  3  0.1478 0.1731 0.1954 0.2314 0.1295 0.1626 0.2846 0.1878 0.4484 0.2835 0.1514 0.1734 0.1468 0.1926 0.3088 0.1998 0.0652 0.1398 0.0911 0.1332 0.0787 0.1054 0.0721 0.1407 0.0924 0.0687 0.0676 0.0769 0.0640 0.0740 0.0410 0.0387 0.0709 0.0633 0.2995 0.4751 0.6909 0.5804 0.3329 0.3329 0.2530 0.2530 0.2190 0.2279 0.3103  / 116 J' K-  K'  13 4 9 13 4 10 14 4 11 15 4 11 15 4 12 16 4 13 17 4 13 17 4 14 18 4 14 18 4 15 19 4 15 19 4 16 20 4 16 20 4 17 21 4 17 21 4 18 22 4 18 22 4 19 6 6 1 7 6 2. 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 18 6 13 2 11 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 8 2 6 8 2 7 11 2 10 12 2 11 13 2 12  J" K" K" o C  14 4 10 14 4 11 15 4 12 16 4 12 16 4 13 17 4 14 18 4 14 18 4 15 19 4 15 19 4 16 20 4 16 20 4 17 21 4 17 21 4 18 22 4 18 22 4 19 23 4 19 23 4 20 7 6 2 8 6 3 . 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 17 6 12 19 6 14 2 12 3 2 2 3 2 1 4 2 3 4 2 2 5 2 4 5 2 3 6 2 5 6 2 4 7 2 6 8 2 7 8 2 6 11 2 9 12 2 10 13 2 11  Freq.(cm" ')  1581.45925 1581.42629 1579.43174 1577.46562 1577.42876 1575.41730 1573.40740 1573.40740 1571.34005 1571.35887 1569.23766 1569.30885 1567.09012 1567.24209 1564.88727 1565.15551 1562.40008 1562.93048 1592.99688 1591.23536 1589.40391 1587.97875 1586.11503 1584.31778 1582.52512 1580.72925 1578.92695 1577.11733 1575.30177 1571.69486 1609.64100 1608.91711 1608.87140 1609.01053 1608.87140 1609.15428 1608.83664 1609.35599 1608.73842 1609.58451 1610.29375 1608.25888 1606.51098 1605.60508 1604.53456  Intensity  3  0.0482 0.2059 0.2167 0.1743 0.2304 0.2061 0.2024 0.2024 0.1332 0.1704 0.1380 0.1374 0.0845 0.0898 0.0625 0.0939 0.0557 0.0687 0.1029 0.1614 0.1916 0.1139 0.3122 0.2611 0.2303 0.2768 0.2351 0.2238 0.1948 0.0678 0.1326 0.1837 0.2977 0.1339 0.2977 0.0852 0.1010 0.0673 0.0919 0.0665 0.1241 0.0710 0.3133 0.0957 0.6075  / 117 J' K  J " K£  a  K£  15 2 14 5 3 3 6 3 4 7 3 4 7 3 5 8 3 5 10 3 7 12 3 10 18 3 15 5 4 2 6 4 3 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 13 4 9 14 4 11 15 4 11 15 4 12 6 6 1 7 6 2 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10  15 2 13 5 3 2 6 3 3 7 3 5 7 3 4 8 3 6 10 3 8 12 3 9 18 3 16 5 4 1 6 4 2 9 4 6 9 4 5 10 4 7 10 4 6 11 4 8 11 4 7 13 4 10 14 4 10 15 4 12 15 4 11 6 6 0 7 6 1 8 6 2 9 6 3 10 6 4 11 6 5 12 6 6 13 6 7 14 6 8 15 6 9  J' K  J" K  1 2 3 4 5 6  0 0 0 0 0 0  a  1 2 3 4 5 6  0 1 2 3 4 5  0 0 0 0 0 0  a  0 1 2 3 4 5  K£  Freq.(cm- ) 1  1601.91270 1608.56857 1608.69411 1608.85090 1608.81388 1608.99450 1609.29696 1608.87140 1607.90003 1607.27057 1607.01735 1606.21453 1606.20326 1605.94355 1605.92019 1605.67757 1605.63428 1605.16144 1604.71748 1604.68443 1604.37703 1604.76191 , 1604.68443 1604.53456 1604.79558 1604.61908 1604.50785 1604.40227 1604.29590 1604.18373 1604.06633  Freq.(cm- ) 1  1627.18457 1628.86923 1630.55015 1632.22163 1633.88399 1635.54044  Intensity  3  0.0559 0.1261 0.0717 0.4143 0.1010 0.0909 0.0408 0.2977 0.0510 0.6200 0.4781 0.0881 0.1118 0.1605 0.0745 0.0690 0.0811 0.0641 0.0379 0.4899 0.0398 0.5343 0.4899 0.6075 0.1222 0.1917 0.3482 0.1394 0.1161 0.0839 0.0641  Intensity  3  0.1025 0.0749 0.1105 0.1446 0.1895 0.2415  / 118 J' K-  K'  7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 20 0 20 2 11 3 12 4 13 5 14 5 15 6 15 6 16 7 16 7 17 8 17 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 15 1 15 16 1 15 16 1 16 17 1 16 17 1 17 18 1 17 18 1 18  J" K'  a  K£  6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 110 2 1 1 3 12 4 13 4 14 5 14 5 15 6 15 6 16 7 16 7 17 8 1 7 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 15 1 15 16 1 15 16 1 16 17 1 16 17 1 17  Freq.(cm" ) 1  1637.23962 1638.54617 1640.18752 1641.76849 1643.33147 1644.89132 1646.45594 1648.02376 1649.62972 1651.26294 1652.97230 1654.68432 1656.48095 1658.64722 1628.87348 1630.65378 1632.42607 1634.19849 1633.82473 1635.96710 1635.26312 1637.72517 1636.62893 1639.46825 1638.10092 1641.18588 1639.83063 1642.85717 1641.42429 1644.44173 1643.01358 1645.92970 1644.59943 1647.43850 1646.18238 1648.95518 1647.76501 1650.40667 1649.34814 1651.66855 1650.92310 1652.81318 1.652.52005 1653.94146 1654.11305  Intensity  3  0.1962 0.1740 0.3316 0.4464 0.3860 0.2782 0.2831 0.0434 0.2777 0.3132 0.3366 0.0839 0.1282 0.1399 0.0749 0.0634 0.0780 0.1088 0.0572 0.5458 0.0470 0.1701 0.1521 0.1829 0.1200 0.1772 0.1483 0.1745 0.1702 0.1644 0.1676 0.0571 0.1848 0.1827 0.2357 0.1903 0.1674 0.0707 0.2208 0.0618 0.3272 0.0726 0.1457 0.0806 0.1657  / 119 J' K'  K'  19 1 18 19 1 19 20 1 19 20 1 20 21 1 20 21 1 21 22 1 22 23 1 23 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19- 2 18 20 2 18 20 2 19 21 2 19 21 2 20 22 2 20  J"  18 1 17 18 1 18 19 1 18 19 1 19 20 1 19 20 1 20 21 1 21 22 1 22 2 2 1 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 . 18 2 17 19 2 17 19 2 18 20 2 18 20 2 19 21 2 19  Freq.(cm~ ) 1  1655.17488 1655.71234 1656.27507 1657.31952 1657.35760 1658.93670 1660.55739 1662.21139 1629.99295 1631.74845 1631.69906 1633.50988 1633.40920 1635.29504 1635.11876 1637.10698 1636.82969 1638.94201 1638.53877 1640.79611 1640.24421 1642.66061 1641.94443 1644.52671 1643.63799 1646.38727 1645.32335 1648.23197 1646.99991 1650.05338 1648.66652 1651.84514 1650.32276 1653.58928 1651.96887 1655.26850 1653.60565 1656.80048 1655.23461 1656.85648 1660.69357 1658.47355 1662.08215 1660.08923 1663.50219  Intensity  3  0.0528 0.1905 0.0926 0.1073 0.0673 0.0976 0.1128 0.1232 0.0522 0.4532 0.1212 0.2545 0.3109 0.1937 0.2002 0.2322 0.2661 0.2785 0.3530 0.2912 0.2395 0.3804 0.3494 0.3095 0.2870 0.6129 0.3288 0.4635 0.2935 0.3544 0.4080 0.7106 0.2910 0.3763 0.3698 0.3081 0.3769 0.2445 0.2891 0.2406 0.1975 0.2549 0.1937 0.2108 0.1966  / 120 J' K'  K '  22 2 21 23 2 21 23 2 22 24 2 22 24 2 23 25 2 23 25 2 24 26 2 24 26 2 25 27 2 25 27 2 26 8 3 6 9 3 6 9 3 7 10 3 7 10 3 8 11 3 8 11 3 9 12 3 9 12 3 10 13 3 10 13 3 11 14 3 11 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 19 3 16 19 3 17 20 3 17 20 3 18 21 3 18 21 3 19 22 3 19 22 3 20 23 3 20 23 3 21 24 3 22 25 3 23 26 3 24 5 4 2  j"  K "  K ;  a  C  21 2 20 22 2 20 22 2 21 23 2 21 23 2 22 24 2 22 24 2 23 25 2 23 25 2 24 26 2 24 26 2 25 7 3 5 8 3 5 8 3 6 9 3 6 9 3 7 10 3 7 10 3 8 11 3 8 11 3 9 12 3 9 12 3 10 13 3 10 14 3 11 14 3 12 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 19 3 16 19 3 17 20 3 17 20 3 18 21 3 18 21 3 19 22 3 19 22 3 20 23 3 21 24 3 22 25 3 23 4 4 1  Freq.(cm" ) 1  1661.70545 1664.89749 1663.32549 1666.26858 1664.95166 1667.62772 1666.59036 1668.99195 1668.24423 1670.38344 1669.91885 1638.03591 1639.94278 1639.88202 1641.76849 1641.66299 1643.61336 1643.43503 1645.47463 1645.16311 1647.35450 1646.82878 1649.24992 1651.15927 1650.97601 1653.07685 1652.64803 1654.99755 1654.36690 1656.91078 1656.09352 1658.80654 1657.81428 1660.65548 1659.52611 1662.58097 1661.22620 1664.32023 1662.91535 1666.01094 1664.59103 . 1666.25610 1667.91079 1669.55117 1631.97166  Intensity  9  0.1852 0.1713 0.1794 0.1386 0.1630 0.1196 0.1331 0.2657 0.1360 0.0964 0.0931 0.3861 0.2250 0.1479 0.4464 0.1298 0.2036 0.1773 0.1864 0.0753 0.2194 0.1607 0.1660 0.2314 0.1597 0.1771 0.1676 0.2008 0.1591 0.2037 0.1783 0.1493 0.1624 0.1873 0.1516 0.2795 0.1126 0.1114 0.2884 0.0958 0.0980 0.0890 0.0865 0.0556 0.1162  / 121 J*  K '  a  K ;  6 4 3 7 4 4 8 4 5 9 4 6 10 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 15 4 12 16 4 12 16 4 13 17 4 13 17 4 14 18 4 14 18 4 15 19 4 15 19 4 16 20 4 16 20 4 17 21 4 17 21 4 18 22 4 18 22 4 19 23 4 19 23 4 20 24 4 20 24 4 21 25 4 21 25 4 22 26 4 22 26 4 23 27 4 23 28 4 24 7 5 3 8 5 4 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9  c  J"  K "  K ;  5 4 2 6 4 3 7 4 4 8 4 5 9 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 15 4 12 16 4 12 16 4 13 17 4 13 17 4 14 18 4 14 18 4 15 19 4 15 19 4 16 20 4 16 20 4 17 21 4 17 21 4 18 22 4 18 22 4 19 23 4 19 23 4 20 24 4 20 24 4 21 25 4 21 25 4 22 26 4 22 27 4 23 6 5 2 7 5 3 8 5 4 9 5 5 10 5 6 11 5 7 12 5 8  Freq.(cm" ')  1633.81133 1635.67218 1637.55213 1639.44788 1641.35443 1643.27020 1644.84702 1645.18730 1646.84090 1647.10393 1648.78507 1649.01400 1650.71282 1650.91479 1652.63208 1652.80315 1654.54605 1654.67536 1656.45738 1656.53388 1657.62011 1658.37562 1660.27382 1660.20022 1662.18008 1662.00986 1664.08527 1663.80224 1665.98861 1665.57826 1667.88611 1667.33907 1669.77693 1669.08290 1671.65276 1670.96410 1673.50698 1675.33114 1635.27081 1637.41909 1639.54681 1641.65367 1643.73862 1645.80183 1647.84103  Intensity  3  0.2469 0.1923 0.2328 0.2571 0.3165 0.5009 0.2485 0.4692 0.2856 0.3324 0.2796 0.3018 0.2323 0.3272 0.2954 0.3115 0.3928 0.3257 0.2577 0.3132 0.0957 0.1642 0.2190 0.2097 0.1765 0.1752 0.1736 0.1945 0.1352 0.1622 0.1553 0.8084 0.1212 0.1181 0.0860 0.0966 0.0830 0.0571 0.1976 0.1879 0.2209 0.2585 0.3235 0.3468 0.2533  / 122 j*  K '  K :  a  c  14 5 10 15 5 11 16 5 12 17 5 13 18 5 13 18 5 14 19 5 14 19 5 15 20 5 15 20 5 16 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 17 6 12 18 6 13 19 6 14 20 6 15 11 7 5 12 7 6 13 7 7 14 7 8 15 7 9 16 7 10 17 7 11 18 7 12 19 7 13 20 7 14 21 7 15 22 7 16 23 7 17 24 7 18 9 8 2 10 8 2 11 8 4 12 8 4 13 8 6 14 8 6 15 8 8 16 8 8  J"  K "  K "  d  C  13 5 9 14 5 10 15 5 11 16 5 12 17 5 12 17 5 13 18 5 13 18 5 14 19 5 14 19 5 15 7 6 2 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 17 6 12 18 6 1.3 19 6 14 10 7 4 11 7 5 12 7 6 13 7 7 14 7 8 15 7 9 16 7 10 17 7 11 18 7 12 19 7 13 20 7 14 21 7 15 22 7 16 23 7 17 8 8 1 9 8 1 10 8 3 11 8 3 12 8 5 13 8 5 14 8 7 15 8 7  Freq.(cm" ) 1  1649.85671 1651.84514 1653.81643 1655.75905 1657.68657 1657.67814 1659.58717 1659.57416 1661.46579 1661.45034 1634.04377 1635.38353 1636.78187 1638.22769 1639.70618 1641.21369 1642.74810 1644.30434 1645.88146 1647.48085 1649.09760 1650.74154 1652.41213 1640.04489 1641.56413 1643.14551 1644.75898 1646.38727 1648.03085 1649.67885 1651.33589 1653.04166 1654.69520 1656.35057 1658.03962 1659.74118 1661.43144 1634.93424 1636.37099 1637.78162 1639.13201 1640.40623 1641.59046 1642.67037 1643.63185  Intensity  3  0.2815 0.7106 0.2053 0.1550 0.0736 0.1141 0.1315 0.0939 0.1019 0.1032 0.2684 0.1586 0.2331 0.2336 0.1978 0.1629 0.1833 0.2045 0.3949 , 0.1521 0.0906 0.0673 0.0525 0.1009 0.1478 0.1550 0.1463 0.6129 0.4621 0.1461 0.1159 0.0837 0.0454 0.1014 0.0790 0.0500 0.0478 0.1097 0.1205 0.1886 0.1778 0.1354 0.1272 0.0976 0.1290  / 123 J' K'  K'  17 8 10 18 8 10 19 8 12 14 10 4 15 10 6 16 10 6 17 10 8 18 10 8 10 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 20 0 20 2 11 3 12 4 13 5 1 4 5 15 6 15 6 16 7 16 7 17 8 17 8 18 9 1 8 9 19 10 1 9 10 1 10 11 1 10 11 1 11  J" K" a  K" c  16 8 9 17 8 9 18 8 11 13 10 3 14 10 5 15 10 5 16 10 7 17 10 7 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 20 0 20 21 0 21 3 1 2 4 1 3 5 1 4 6 1 5 6 1 6 7 1 6 7 17 8 17 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12  Freq.(cm" ')  1644.47023 1645.18730 1645.79131 1641.70188 1643.19229 1644.66190 1646.10936 1647.61938 1622.14855 1620.49296 1618.85492 1617.24260 1615.65795 1614.11310 1612.65525 1610.84944 1609.41498 1607.94740 1606.48046 1605.01927 1603.56624 1602.11575 1600.70334 1599.31303 1597.99508 1596.67672 1595.43689 1594.57311 1620.09971 1618.36838 1616.64771 1614.93629 1616.24716 1613.23837 1614.51503 1611.55142 1612.72529 1609.87215 1611.05220 1608.19743 1609.64961 1606.51098 1608.12329 1604.77925 1606.60393  Intensity  3  0.1070 0.4692 0.3468 0.1123 0.1211 0.0823 0.0790 0.0776 0.0968 0.1314 0.5952 0.1887 0.4488 0.1936 0.3364 0.3150 0.5128 0.4507 0.6247 0.2803 0.3099 0.0537 0.2933 0.6124 0.2596 0.0281 0.1862 0.0743 0.0577 0.0527 0.1187 0.1472 0.0429 0.2525 0.0488 0.1902 0.1685 0.1744 0.1531 0.1789 0.1326 0.3133 0.1933 0.2868 0.1618  / 124 J' K -  K'  12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 15 1 15 16 1 15 16 1 16 17 1 16 17 1 17 18 1 17 18 1 18 19 1 18 19 1 19 20 1 19 20 1 20 21 1 20 21 1 21 22 1 22 23 1 23 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7. 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13  J" K  a  13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 15 1 15 16 1 15 16 1 16 17 1 16 17 1 17 18 1 17 18 1 18 19 1 18 19 1 19 20 1 19 20 1 20 21 1 20 21 1 21 22 1 21 22 1 22 23 1 23 24 1 24 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14  Freq.(cm" ) 1  c  /  1602.99679 1605.09226 1601.28275 1603.58681 1599.62973 1602.09008 1597.96297 1600.60002 1596.14954 1599.11837 1594.25678 1597.64528 1592.37906 1596.18275 1590.62179 1594.72960 1588.74423 1593.28580 1586.84336 1591.85490 1590.44280 1589.04878 1618.23738 1616.50512 1616.59378 1614.81101 1614.96187 1613.10741 1613.34027 1611.39500 1611.72917 1609.67573 1610.12791 1607.95387 1608.53655 1606.23212 1606.95453 1604.51440 1605.38192 1602.80149 1603.81729 1601.09548 1602.26358 1599.39509 1600.71589  Intensity  3  0.1747 0.1643 0.0723 0.2297 0.0878 0.1471 0.2108 0.2187 0.1071 0.1396 0.1071 0.2379 0.1042 0.1966 0.0833 0.1437 0.1332 0.6909 0.0553 0.3514 0.0882 0.1424 0.0937 0.1377 0.1458 0.1979 0.1779 0.2450 0.2513 0.3042 0.2525 0.3294 0.3410 0.2759 0.3144 0.4456 0.3325 0.4167 0.3275 0.4148 0.5455 0.3094 0.4287 0.4461 0.4613  / 125 J' K"  J" K" a  15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 18 20 2 18 20 2 19 21 2 19 21 2 20 22 2 20 22 2 21 23 2 21 23 2 22 24 2 22 24 2 23 25 2 23 25 2 24 26 2 24 26 2 25 27 2 25 27 2 26 8 3 6 9 3 6 9 3 7 10 3 7 10 3 8 11 3 8 11 3 9 12 3 9 12 3 10 13 3 10 13 3 11 14 3 11 15 3 12 15 3 13 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16  16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 19 2 18 20 2 19 21 2 19' 21 2 20 22 2 20 22 2 21 23 2 21 23 2 22 24 2 22 24 2 23 25 2 23 25 2 24 26 2 24 26 2 25 27 2 25 27 2 26 28 2 26 28 2 27 9 :3 '7 10 3 7 10 3 8 11 3 8 11 3 9 12 3 9 12 3 10 13 3 10 13 3 11 14 3 11 14 3 12 15 3 12 16 3 13 16 3 14 17 3 14 17 3 15 18 3 15 18 3 16 19 3 16 19 3 17  K; c  Freq.(cm" ) 1  1597.69750 1599.17650 1595.99551 1597.64528 1594.27190 1596.12266 1592.45034 1594.60758 1593.10227 1589.79817 1591.60698 1587.99901 1590.12329 1586.28783 1588.65240 1584.60718 1587.19503 1582.94891 1585.75466 1581.31697 1584.33294 1579.72087 1582.93411 1578.16629 1581.56332 1609.38227 1607.79581 1607.84353 1606.16904 1606.24035 1604.53456 1604.62990 1602.88487 1602.98144 1601.22126 1601.27506 1599.54145 1597.84529 1598.70788 1596.13370 1597.04032 1594.40869 1595.43689 1592.67444 1593.85700  Intensity  3  0.4179 0.3509 0.3664 0.2379 0.2944 0.3244 0.2668 0.2815 0.2421 0.2743 0.7244 0.2409 0.1831 0.2430 0.2381 0.1615 0.1696 0.1580 0.1609 0.1120 0.1045 0.1276 0.0975 0.0754 0.0611 0.0764 0.1721 0.2058 0.1369 0.0985 0.6075 0.1927 0.1829 0.3325 0.1833 0.1949 0.2126 0.1698 0.1661 0.1965 0.1412 0.1868 0.1862 0.1628 0.1327  / 126  19 3 16 19 3 17 20 3 17 20 3 18 21 3 18 21 3 19 22 3 19 22 3 20 23 3 20 23 3 21 24 3 22 25 3 23 26 3 24 5 4 2l 6 4 3i 7 4 4 8 4 5 9 4 e 10 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 15 4 12 16 4 12 16 4 13 17 4 13 17 4 14 18 4 14 18 4 15 19 4 15 19 4 16 20 4 16 20 4 17 21 4 17 21 4 18 22 4 18 22 4 19 23 4 19 23 4 20 24 4 20  J"  Freq.(cm" )  20 3 17 20 3 18 21 3 18 21 3 19 22 3 19 22 3 20 23 3 20 23 3 21 24 3 21 24 3 22 25 3 23 26 3 24 27 3 25 6 •4 ;3 7 •4 4 8 •4 ,5 9 4 6< 10 4 7 11 4 8 12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 15 4 12 16 4 12 16 4 13 17 4 13 17 4 14 18 4 14 18 4 15 19 4 15 19 4 16 20 4 16 20 4 17 21 4 17 21 4 18 22 4 18 22 4 19 23 4 19 23 4 20 24 4 20 24 4 21 25 4 21  1590.93295 1592.29043 1589.17465 1590.73341 1587.50319 1589.18654 1585.69512 1587.64522 1583.88408 1586.11502 1584.59414 1583.08177 1581.57552 1613.47037 1611.93953 1610.42655 1608.92712 1607.43952 1605.95965 1604.48244 1602.64013 1603.00456 1601.21354 1601.51955 1599.72808 1600.02575 1598.20922 1598.52006 1596.66327 1596.99673 1595.09042 1595.46058 1593.48820 1593.91614 1591.59977 1592.35465 1590.18782 1590.78280 1588.48797 1589.20440 1586.75621 1587.61867 1584.99243 1586.03010 1583.20988  1  Intensity  9  0.4322 0.1291 0.2325 0.1259 0.1101 0.1201 0.0939 0.1400 0.1079 0.3122 0.0928 0.0542 0.0822 0.2535 0.4633 0.4138 0.2407 0.2649 0.4108 0.3012 0.5696 0.2645 0.7746 0.2966 0.3301 0.4837 0.3091 0.4937 0.3670 0.3984 0.2483 0.5526 0.2663 0.4453 0.0566 0.2490 0.2173 0.2204 0.1580 0.2855 0.1488 0.1670 0.2076 0.1337 0.1468  / 127 J" K.II \r fl a c K  24 4 21 25 4 21 25 4 22 26 4 22 26 4 23 27 4 23 28 4 24 7 5 3| 8 5 4 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9 14 5 10 15 5 11 16 5 12 17 5 13 18 5 13 18 5 14 . 19 5 14 19 5 15 20 5 15 20 5 16 8 6 St 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 17 6 12 18 6 13 19 6 14 11 7 5 12 7 6 13 7 7 14 7 8 15 7 9 16 7 10 17 7 11 18 7 12 19 7 13  25 4 22 26 4 22 26 4 23 27 4 23 27 4 24 28 4 24 29 4 25 8 5 4 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9 14 5 10 15 5 11 16 5 12 17 5 13 18 5 14 19 5 14 19 5 15 20 5 15 20 5 16 21 5 16 21 5 17 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 17 6 12 18 6 13 19 6 14 20 6 15 12 7 6 13 7 7 14 7 8 15 7 9 16 7 10 17 7 11 18 7 12 19 7 13 20 7 14  Freq.(cm~ ) 1  1584.44176 1581.41066 1582.85274 1579.59629 1581.42106 1577.77920 1574.13562 1610.04428 1608.82099 1607.57315 1606.30487 1605.01054 1603.68932 1602.33990 1600.96379 1599.55789 1598.12241 1596.65541 1595.15979 1595.17443 • 1593.62949 1593.65774 1592.07118 1592.11630 1605.46178 1603.43331 1601.46229 1599.53429 1597.63972 1595.77065 1593.92511 1592.09858 1590.29025 1588.49970 1584.97370 1583.24500 1601.37706 1599.52812 1597.74012 1595.98122 1594.23661 1592.50177 1590.77308 1589.04878 1587.37296  Intensity  3  0.1309 0.0393 0.0902 0.1223 0.1081 0.0863 0.0491 0.1676 0.2118 0.3436 0.2849 0.3609 0.5433 0.4071 0.2655 0.2752 0.1606 0.1549 0.1039 0.1184 0.1060 0.0899 0.1171 0.1347 0.2006 0.2570 0.2692 0.2454 0.3877 0.1964 0.2217 0.2639 0.2076 0.1722 0.0687 0.0785 0.1413 0.1780 0.1279 0.1723 0.1828 0.1650 0.1824 0.1424 0.2016  / 128 J' K'  K'  20 7 14 21 7 15 22 7 16 23 7 17 24 7 18 8 8 1 9 8 2 10 8 2 11 8 4 12 8 4 13 8 6 14 8 6 15 8 8 16 8 8 17 8 10 18 8 10 19 8 12 14 10 4 15 10 6 16 10 6 17 10 8 18 10 8 5 4 2 6 4 3 7 4 4 8 4 5 9 4 6 7 5 3 10 5 6 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 15 6 10 16 6 11 11 7 5 12 7 6 13 7 7 14 7 8 15 7 9 16 7 10 17 7 11 19 7 13  J " K" a  K" c  21 7 15 22 7 16 23 7 17 24 7 18 25 7 19 9 8 2 10 8 3 11 8 3 12 8 5 13 8 5 14 8 7 15 8 7 16 8 9 17 8 9 18 8 11 19 8 11 20 8 13 15 10 5 16 10 7 17 10 7 18 10 9 19 10 9 5 4 1 6 4 2 7 4 3 8 4 4 9 4 5 7 5 2 10 5 5 8 6 2 9 6 3 10 6 4 11 6 5 12 6 6 13 6 7 15 6 9 16 6 10 11 7 4 12 7 5 13 7 6 14 7 7 15 7 8 16 7 9 17 7 10 19 7 12  Freq.(cm" ) 1  1585.65004 1583.91066 1582.21126 1580.51742 1578.81083 1604.85221 1602.98144 1601.08658 1599.13345 1597.11910 1595.02743 1592.84530 1590.55695 1588.14959 1585.61855 1582.96289 1580.19525 1593.00527 1591.13542 1589.24487 1587.33107 1585.47883 1623.56197 1623.71828 1623.89400 1624.08438 1624.28737 1623.50055 1624.82401 1620.59505 1620.25025 1619.96566 1619.72393 1619.51631 1619.33793 1619.04703 1618.93242 1621.55291 1621.38785 1621.28591 1621.21284 . 1621.15643 1621.11084 1621.07110 1621.05224  Intensity  3  0.1063 0.1059 0.0615 0.0668 0.0684 0.0802 0.3325 0.1364 0.2687 0.1979 0.1915 0.1869 0.1121 0.1223 0.2338 0.0920 0.0764 0.1138 0.1117 0.0761 0.1908 0.0790 0.5828 0.4515 0.2164 0.1609 0.5810 0.2406 0.1494 0.4500 0.3359 0.2225 0.1878 0.1359 0.0775 0.0628 0.0651 0.1731 0.1078 0.1099 0.0860 0.0605 0.0645 0.0569 0.0569  / 129 J'  K '  K '  J"  K "  K "  8 8 1 9 8 2 10 8 3 11 8 4 12 8 5 13 8 6 14 8 7 15 8 8 16 8 9 17 8 10 14 10 5 15 10 6 16 10 7 17 10 8 18 10 9  8 8 0 9 8 1 10 8 2 11 8 3 12 8 4 13 8 5 14 8 6 15 8 7 16 8 8 17 8 9 14 10 4 15 10 5 16 10 6 17 10 7 18 10 8  j'  J"  K :  K •  a  c  2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 21 0 21 22 0 22 23 0 23 4 14 5 1 4  K "  a  1  1619.97108 1619.79028 1619.56911 1619.29866 1618.96650 1618.55838 1618.06037 1617.45561 1616.73280 1615.88777 1618.19206 1618.00355 1617.79403 1617.56020 1617.38810  K "  3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 22 0 22 23 0 23 24 0 24 5 15 6 15  Freq.(cm" )  c  Freq.(cm~ ) 1  1658.98736 1657.46355 1655.98582 1654.54605 1653.13260 1651.73490 1650.34417 1648.95518 1647.56474 1646.17001 1644.77699 1643.39095 1642.01180 1640.64651 1639.30047 1637.99383 1636.80118 1632.30685 1631.07387 1629.84594 1655.99515 1654.25892  Intensity  3  0.3765 0.5252 0.5064 0.3222 0.2448 0.1996 0.2158 0.0951 0.0822 0.0656 0.3010 0.1570 0.0973 0.0826 0.3372  Intensity  3  0.0544 0.0796 0.0774 0.3928 0.0994 0.1035 0.1174 0.1903 0.1203 0.0953 0.1283 0.1419 0.1064 0.1539 0.1053 0.0935 0.0736 0.0509 0.0542 0.1303 0.0774 0.0775  / 130  j'  K :  K ;  a 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 21 0 21 22 0 22 23 0 23 4 14 5 14 5 15 6 15 6 16 7 16 7 1 7 8 17 8 1 8 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 15 1 14 15 1 15 16 1 15 16 1 16 17 1 17  c  j"  K "  K ;  3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 22 0 22 23 0 23 24 0 24 5 1 5 6 1 5 6 1 6 7 16 7 17 8 17 8 18 9 1 8 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 16 1 15 16 1 16 17 1 16 17 1 17 18 1 18  Freq.(cm" ) 1  1658.98736 1657.46355 1655.98582 1654.54605 1653.13260 1651.73490 1650.34417 1648.95518 1647.56474 1646.17001 1644.77699 1643.39095 1642.01180 1640.64651 1639.30047 1637.99383 1636.80118 1632.30685 1631.07387 1629.84594 1655.99515 1654.25892 1654.52239 1652.92875 1653.07006 1651.63503 1651.64647 1650.41517 1650.23640 1649.22351 1648.84431 1648.07467 1647.46958 1646.94995 1646.11706 1645.83682 1644.80335 1644.72831 1643.58800 1643.62585 1642.46868 1640.32235 1641.31896 1639.08961 1637.81717  Intensity  3  0.0544 0.0796 0.0774 0.3928 0.0994 0.1035 0.1174 0.1903 0.1203 0.0953 0.1283 0.1419 0.1064 0.1539 0.1053 0.0935 0.0736 0.0509 0.0542 0.1303 0.0774 0.0775 0.1680 0.0589 0.0424 0.1071 0.0483 0.0361 0.1275 0.0446 0.0780 0.0675 0.0936 0.0736 0.0444 0.0663 0.1579 0.0702 0.0575 0.0729 0.0520 0.0621 0.1300 0.0755 0.2183  / 131 j'  K :  K :  a  c  18 1 18 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 19 2 18 20 2 19 21 2 20 5 4 2 6 4 3 7 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8  j"  K "  K :  a  c  19 1 19 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 12 14 2 12 14 2 13 15 2 13. 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 20 2 19 21 2 20 22 2 21 6 4 3 7 4 4 8 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9  Freq.(cm" ) 1  1636.53366 1656.89941 1656.92776 1655.40255 1655.44663 1653.96273 1654.01116 1652.58605 1652.61929 1651.27782 1651.26807 1650.04069 1649.95567 1648.86259 1648.68056 1647.69628 1647.43850 1647.45371 1646.22788 1645.04875 1645.28968 1643.89923 1644.43281 1642.77915 1643.62585 1641.68882 1642.84590 1640.62737 1642.07713 1639.59598 1641.30318 1637.61888 1636.68313 1635.78233 1652.48841 1651.13625 1649.83919 1648.59432 1647.40552 1647.40552 1646.26083 1646.26875 1645.18013 1645.18013 1644.15560  Intensity  3  0.0530 0.0507 0.0527 0.0485 0.0751 0.0806 0.0921 0.0825 0.0863 0.1110 0.0739 0.1116 0.0977 0.1011 0.1676 0.0982 0.1827 0.0609 0.1980 0.1159 0.0720 0.0795 0.1123 0.0680 0.0729 0.0738 0.0631 0.0707 0.0490 0.1855 0.1003 0.1676 0.0886 0.0483 0.0886 0.1040 0.1513 0.1460 0.2738 0.2738 0.0455 0.1196 0.5307 0.5307 0.2225  / 132 j'  K '  K :  a  12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 8 5 4 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9 14 5 10 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 16 6 11 17 6 12 18 6 13 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 21 0 21 22 0 22 23 0 23 4 14 5 14  c  J"  K "  K "  13 4 10 14 4 10 14 4 11 15 4 11 15 4 12 16 4 12 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9 14 5 10 15 5 11 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 17 6 12 18 6 13 19 6 14 1 0 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 20 0 20 21 0 21 22 0 22 3 13 4 13  Freq.(cm" ) 1  1644.14008 1643.17356 1643.14551 1642.23247 1642.17625 1641.30318 1647.54195 1646.37953 1645.30990 1644.27757 1643.29653 1642.36605 1641.48874 1646.22788 1645.16313 1644.15560 1643.21350 1642.32109 1641.48246 1640.69044 1639.24249 1638.56416 1637.94599 1667.36341 1669.15888 1670.96410 1672.77080 1674.55916 1676.31852 1678.04128 1679.72755 1681.38428 1683.02138 1684.65042 1686.28057 1687.91877 1689.57298 1691.25045 1692.97133 1694.80964 1699.41606 1701.21898 1703.02630 1670.39238 1673.52025  Intensity  3  0.0553 0.0818 0.1550 0.0567 0.0728 0.1003 0.0676 0.0355 0.0701 0.0789 0.0562 0.0756 0.2370 0.1980 0.0753 0.2225 0.1778 0.1313 0.1522 0.0737 0.0602 0.0556 0.0600 0.0532 0.0498 0.0966 0.0941 0.0998 0.0900 0.1116 0.1131 0.1256 0.1189 0.1210 0.1023 0.1160 0.0932 0.1144 0.0882 0.0697 0.0642 0.0532 0.0553 0.0553 0.0830  / 133 J' K'  K'  5 15 6 15 6 1 6 7 16 7 17 8 1 7 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 15 1 14 15 1 15 16 1 15 16 1 16 17 1 17 18 1 18 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 21 0 21 22 0 22 23 0 23 4 14  J" K"  K"  cL  C  4 14 5 14 5 15 6 15 6 16 7 16 7 17 8 17 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 14 1 13 14 1 14 15 1 14 15 1 15 16 1 16 17 1 17 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 22 0 22 23 0 23 24 0 24 5 15  Freq.(cm" ) 1  1672.10112 1675.65761 1673.82129 1677.80844 1675.55037 1680.01687 1677.28505 1682.21105 1679.02497 1684.42068 1680.77095 1686.61229 1682.52701 1688.77024 1684.30939 1690.88244 1686.18418 1692.94679 1694.91273 1689.06892 1696.83919 1690.90308 1692.68972 1694.46401 1658.98736 1657.46355 1655.98582 1654.54605 1653.13260 1651.73490 1650.34417 1648.95518 1647.56474 1646.17001 1644.77699 1643.39095 1642.01180 1640.64651 1639.30047 1637.99383 1636.80118 1632.30685 1631.07387 1629.84594 1655.99515  Intensity  3  0.0666 0.0377 0.0467 0.0447 0.0485 0.0685 0.0660 0.0522 0.0589 0.0503 0.0615 0.0552 0.0710 0.0533 0.0579 0.0400 0.0454 0.0101 0.0397 0.0502 0.0244 0.0491 0.0516 0.0507 0.0544 0.0796 0.0774 0.3928 0.0994 0.1035 0.1174 0.1903 0.1203 0.0953 0.1283 0.1419 0.1064 0.1539 0.1053 0.0935 0.0736 0.0509 0.0542 0.1303 0.0774  / 134 j'  K '  a  K :  c  5 14 5 15 6 15 6 16 7 16 7 17 8 17 8 18 9 1 8 9 1 9 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 15 1 14 15 1 15 16 1 15 " 16 1 16 17 1 17 18 1 18 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 11 13 2 11  J"  K "  K "  a  C  6 15 6 16 7 16 7 17 8 17 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 16 1 15 16 1 16 17 1 16 17 1 17 18 1 18 19 1 19 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 12 14 2 12  Freq.(cm" ) 1  1654.25892 1654.52239 1652.92875 1653.07006 1651.63503 1651.64647 1650.41517 1650.23640 1649.22351 1648.84431 1648.07467 1647.46958 1646.94995 1646.11706 1645.83682 1644.80335 1644.72831 1643.58800 1643.62585 1642.46868 1640.32235 1641.31896 1639.08961 1637.81717 1636.53366 1656.89941 1656.92776 1655.40255 1655.44663 1653.96273 1654.01116 1652.58605 1652.61929 1651.27782 1651.26807 1650.04069 1649.95567 1648.86259 1648.68056 1647.69628 1647.43850 1647.45371 1646.22788 1645.04875 1645.28968  Intensity  3  0.0775 0.1680 0.0589 0.0424 0.1071 0.0483 0.0361 0.1275 0.0446 0.0780 0.0675 0.0936 0.0736 0.0444 0.0663 0.1579 0.0702 0.0575 0.0729 0.0520 0.0621 0.1300 0.0755 0.2183 0.0530 0.0507 0.0527 0.0485 0.0751 0.0806 0.0921 0.0825 0.0863 0.1110 0.0739 0.1116 0.0977 0.1011 0.1676 0.0982 0.1827 0.0609 0.1980 0.1159 0.0720  / 135 j ' K' a  K' c  13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 19 2 18 20 2 19 21 2 20 5 4 2 6 4 3 7 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 8 5 4 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9 14 5 10 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 16 6 11  J" K" a  K"  14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 20 2 19 21 2 20 22 2 21 6 4 3 7 4 4 8 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 15 4 12 16 4 12 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9 14 5 10 15 5 11 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 17 6 12  Freq.(cm" ) 1  Intensity  3  C  1643.89923 1644.43281 1642.77915 1643.62585 1641.68882 1642.84590 1640.62737 1642.07713 1639.59598 1641.30318 1637.61888 1636.68313 1635.78233 1652.48841 1651.13625 1649.83919 1648.59432 1647.40552 1647.40552 1646.26083 1646.26875 . 1645.18013 1645.18013 1644.15560 1644.14008 1643.17356 1643.14551 1642.23247 1642.17625 1641.30318 1647.54195 1646.37953 1645.30990 1644.27757 1643.29653 1642.36605 1641.48874 1646.22788 1645.16313 1644.15560 1643.21350 1642.32109 1641.48246 1640.69044 1639.24249  0.0795 0.1123 0.0680 0.0729 0.0738 0.0631 0.0707 0.0490 0.1855 0.1003 0.1676 0.0886 0.0483 0.0886 0.1040 0.1513 0.1460 0.2738 0.2738 0.0455 0.1196 0.5307 0.5307 0.2225 0.0553 0.0818 0.1550 0.0567 0.0728 0.1003 0.0676 0.0355 0.0701 0.0789 0.0562 0.0756 0.2370 0.1980 0.0753 0.2225 0.1778 0.1313 0.1522 0.0737 0.0602  / 136 j'  K •  K :  a  c  17 6 12 18 6 13 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 21 0 21 22 0 22 23 0 23 4 14 5 1 4 5 1 5 6 15 6 1 6 7 16 7 17 8 1 7 8 1 8 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 .12 1 12 13 1 12 13 1 13 14 1 13 15 1 14 15 1 15 16 1 15  J"  K "  a  K "  18 6 13 19 6 14 10 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 20 0 20 21 0 21 22 0 22 3 13 4 13 4 14 5 14 5 1 5 6 15 6 1 6 7 16 7 17 8 1 7 8 1 8 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 14 1 13 14 1 14 15 1 14  c  Freq.(cm" ) 1  1638.56416 1637.94599 1667.36341 1669.15888 1670.96410 1672.77080 1674.55916 1676.31852 1678.04128 1679.72755 1681.38428 1683.02138 1684.65042 1686.28057 1687.91877 1689.57298 1691.25045 1692.97133 1694.80964 1699.41606 1701.21898 1703.02630 1670.39238 1673.52025 1672.10112 1675.65761 1673.82129 1677.80844 1675.55037 1680.01687 1677.28505 1682.21105 1679.02497 1684.42068 1680.77095 1686.61229 1682.52701 1688.77024 1684.30939 1690.88244 1686.18418 1692.94679 1694.91273 1689.06892 1696.83919  Intensity  3  0.0556 0.0600 0.0532 0.0498 0.0966 0.0941 0.0998 0.0900 0.1116 0.1131 0.1256 0.1189 0.1210 0.1023 0.1160 0.0932 0.1144 0.0882 0.0697 0.0642 0.0532 0.0553 0.0553 0.0830 0.0666 0.0377 0.0467 0.0447 0.0485 0.0685 0.0660 0.0522 0.0589 0.0503 0.0615 0.0552 0.0710 0.0533 0.0579 0.0400 0.0454 0.0101 0.0397 0.0502 0.0244  / 137 J' K'  K'  16 1 16 17 1 17 18 1 18 3 2 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 21 0 21 22 0 22 23 0 23 4 14 5 14 5 1 5 6 1 5 6 16 7 16 7 17 8 17 8 18 9 1 8 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 15 1 14  J " K£ K £  Freq.(cm" )  15 1 15 16 1 16 17 1 17 2 2 0 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 22 0 22 23 0 23 24 0 24 5 1 5 6 1 5 6 1 6 7 16 7 1 7 8 17 8 1 8 9 18 9 1 9 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 16 1 15  1690.90308 1692.68972 1694.46401 1668.71889 1658.98736 1657.46355 1655.98582 1654.54605 1653.13260 1651.73490 1650.34417 1648.95518 1647.56474 1646.17001 1644.77699 1643.39095 1642.01180 1640.64651 1639.30047 1637.99383 1636.80118 1632.30685 1631.07387 1629.84594 1655.99515 1654.25892 1654.52239 1652.92875 1653.07006 1651.63503 1651.64647 1650.41517 1650.23640 1649.22351 1648.84431 1648.07467 1647.46958 1646.94995 1646.11706 1645.83682 1644.80335 1644.72831 1643.58800 1643.62585 1642.46868  1  Intensity  3  0.0491 0.0516 0.0507 0.0560 0.0544 0.0796 0.0774 0.3928 0.0994 0.1035 0.1174 0.1903 0.1203 0.0953 0.1283 0.1419 0.1064 0.1539 0.1053 0.0935 0.0736 0.0509 0.0542 0.1303 0.0774 0.0775 0.1680 0.0589 0.0424 0.1071 0.0483 0.0361 0.1275 0.0446 0.0780 0.0675 0.0936 0.0736 0.0444 0.0663 0.1579 0:0702 0.0575 0.0729 0.0520  / 138 J' K  a  K'  15 1 15 16 1 15 16 1 16 17 1 17 18 1 18 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 ' 11 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 19 2 18 20 2 19 21 2 20 5 4 2 6 4 3 7 4 4 8 4 5 9 4 5 9 4 6 10 4 6  J " K"  K"  16 1 16 17 1 16 17 1 17 18 1 18 19 1 19 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2. 17 20 2 19 21 2 20 22 2 21 6 4 3 7 4 4 8 4 5 9 4 6 10 4 6 10 4 7 11 4 7  Freq.(cm" ) 1  1640.32235 1641.31896 1639.08961 1637.81717 1636.53366 1656.89941 1656.92776 1655.40255 1655.44663 1653.96273 1654.01116 1652.58605 1652.61929 1651.27782 1651.26807 1650.04069 1649.95567 1648.86259 1648.68056 1647.69628 1647.43850 . 1647.45371 1646.22788 1645.04875 1645.28968 1643.89923 1644.43281 1642.77915 1643.62585 1641.68882 1642.84590 1640.62737 1642.07713 1639.59598 1641.30318 1637.61888 1636.68313 1635.78233 1652.48841 1651.13625 1649.83919 1648.59432 1647.40552 1647.40552 1646.26083  Intensity  3  0.0621 0.1300 0.0755 0.2183 0.0530 0.0507 0.0527 0.0485 0.0751 0.0806 0.0921 0.0825 0.0863 0.1110 0.0739 0.1116 0.0977 0.1011 0.1676 0.0982 0.1827 0.0609 0.1980 0.1159 0.0720 0.0795 0.1123 0.0680 0.0729 0.0738 0.0623 0.0707 0.0490 0.1855 0.1003 0.1676 0.0886 0.0483 0.0886 0.1040 0.1513 0.1460 0.2738 0.2738 0.0455  / 139 J'  K '  K •  10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 8 5 4 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9 14 5 10 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 16 6 11 17 6 12 18 6 13 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 21 0 21  J"  K "  a  K ;  c  11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 15 4 12 16 4 12 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9 14 5 10 15 5 11 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 . 14 6 9 15 6 10 17 6 12 18 6 13 19 6 14 10 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 20 0 20  Freq.(cm" ')  1646.26875 1645.18013 1645.18013 1644.15560 1644.14008 1643.17356 1643.14551 1642.23247 1642.17625 1641.30318 1647.54195 1646.37953 1645.30990 1644.27757 1643.29653 1642.36605 1641.48874 1646.22788 1645.16313 1644.15560 1643.21350 1642.32109 1641.48246 1640.69044 1639.24249 1638.56416 1637.94599 1667.36341 1669.15888 1670.96410 1672.77080 1674.55916 1676.31852 1678.04128 1679.72755 1681.38428 1683.02138 1684.65042 1686.28057 1687.91877 1689.57298 1691.25045 1692.97133 1694.80964 1699.41606  Intensity  3  0.1196 0.5307 0.5307 0.2225 0.0553 0.0818 0.1550 0.0567 0.0728 0.1003 0.0676 0.0355 0.0701 0.0789 0.0562 0.0756 0.2370 0.1980 0.0753 0.2225 0.1778 0.1313 0.1522 0.0737 0.0602 0.0556 0.0600 0.0532 0.0498 0.0966 0.0941 0.0998 0.0900 0.1116 0.1131 0.1256 0.1189 0.1210 0.1023 0.1160 0.0932 0.1144 0.0882 0.0697 0.0642  / 140 J' K•  K-  22 0 22 23 0 23 4 14 5 14 5 15 6 15 6 16 7 16 7 17 8 17 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 15 1 14 15 1 15 16 1 15 16 1 16 17 1 17 18 1 18 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9  J" K"  K"  21 0 21 22 0 22 3 13 4 1 3 4 14 5 14 5 15 6 15 6 16 7 16 7 17 8 17 8 18 9 18 9 19 10 1 9 10 .1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 14 1 13 14 1 14 15 1 14 15 1 15 16 1 16 17 1 17 2 2 0 2 2 1 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8  Freq.(cm" ) 1  1701.21898 1703.02630 1670.39238 1673.52025 1672.10112 1675.65761 1673.82129 1677.80844 1675.55037 1680.01687 1677.28505 1682.21105 1679.02497 1684.42068 1680.77095 1686.61229 1682.52701 1688.77024 1684.30939 1690.88244 1686.18418 • 1692i94679 1694.91273 1689.06892 1696.83919 1690.90308 1692.68972 1694.46401 1668.71889 1668.68415 1670.64593 1670.55190 1672.66155 1672.45688 1674.77432 1674.39847 1676.98987 1676.36922 1679.30537 1678.36776 1681.70441 1680.38783 1684.12408 1682.42742 1687.46504  Intensity  3  0.0532 0.0553 0.0553 0.0830 0.0666 0.0377 0.0467 0.0447 0.0485 0.0685 0.0660 0.0522 0.0589 0.0503 0.0615 0.0552 0.0710 0.0533 0.0579 0.0400 0.0454 0.0101 0.0397 0.0502 0.0244 0.0491 0.0516 0.0507 0.0560 0.0560 0.0468 0.0599 0.0513 0.0764 0.0727 0.0897 0.0758 0.0779 0.0731 0.1381 0.0727 0.0985 0.0662 0.0934 0.0376  / 141 J' K-  K'  11 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 18 20 2 19 21 2 20 5 4 2 6 4 3 7 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 8 5 4 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9 14 5 10 8 6 3 9 6 4 10 6 5 11 6 6  J" K"  K"  10 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 17 19 2 18 20 2 19 4 4 1 5 4 2 6 4 3 7 4 4 8 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 7 5 3 8 5 4 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9 7 6 2 8 6 3 9 6 410 6 5  Freq.(cm" ) 1  1684.48340 1686.55312 1692.42524 1688.63636 1695.09143 1690.73076 1697.77091 1692.83583 1700.43752 1694.95165 1703.07189 1697.07646 1705.65519 1699.21784 1701.37266 1703.54691 1705.74657 1670.99017 1673.00958 1675.08627 1677.22175 1679.41647 1679.41192 1681.66298 1681.66298 1683.98032 1683.96714 1686.36403 1686.32380 1688.79979 1688.72579 1691.29035 1691.16409 1693.80685 1676.13892 1678.35090 1680.65932 1683.00596 1685.40938 1687.86801 1690.37875 1674.81039 . 1677.11318 1679.47811 1681.90448  Intensity  3  0.0857 0.0980 0.0686 0.0821 0.0588 0.0675 0.0514 0.0679 0.0378 0.0643 0.0369 0.0449 0.0344 0.0422 0.0410 0.0333 0.0269 0.0528 0.0742 0.1432 0.1127 0.0925 0.0925 0.0844 0.0844 0.1007 0.0462 0.0581 0.0588 0.0574 0.0543 0.0591 0.0624 0.0315 0.0488 0.1381 0.0545 0.0506 0.0550 0.0462 0.0337 0.0546 0.1124 0.0818 0.0563  / 142 J' K-  K'  12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 17 6 12 18 6 13 8 5 3 10 5 5 11 5 6 13 5 8 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 21 0 21 22 0 22 23 0 23 4 14 5 14 5 15 6 15 6 16 7 16 7 17 8 17 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10  J" K"  Freq.(cm~ )  11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 17 6 12 8 5 4 10 5 6 11 5 7 13 5 9 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 19 0 19 22 0 22 23 0 23 24 0 24 5 1 5 6 15 6 16 7 1 6 7 17 8 17 8 18 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11  1684.38695 1686.92479 1689.51273 1692.15083 1694.83377 1697.54734 1700.32073 1662.68413 1663.82957 1664.48661 1665.96220 1658.98736 1657.46355 1655.98582 1654.54605 1653.13260 1651.73490 1650.34417 1648.95518 1647.56474 1646.17001 1644.77699 1643.39095 1642.01180 1640.64651 1639.30047 1637.99383 1636.80118 1632.30685 1631.07387 1629.84594 1655.99515 1654.25892 1654.52239 1652.92875 1653.07006 1651.63503 1651.64647 1650.41517 1650.23640 1649.22351 1648.84431 1648.07467 1647.46958 1646.94995  1  Intensity  3  0.0772 0.0714 0.0511 0.0528 0.0514 0.0569 0.0322 0.0567 0.0634 0.0419 0.1352 0.0544 0.0796 0.0774 0.3928 0.0994 0.1035 0.1174 0.1903 0.1203 0.0953 0.1283 0.1419 0.1064 0.1539 0.1053 0.0935 0.0736 0.0509 0.0542 0.1303 0.0774 0.0775 0.1680 0.0589 0.0424 0.1071 0.0483 . 0.0361 0.1275 0.0446 0.0780 0.0675 0.0936 0.0736  / 143 J'  K-  K'  11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 15 1 14 15 1 15 16 1 15 16 1 16 17 1 17 18 1 18 3 2.1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 19 2 18 20 2 19 21 2 20  J" K"  K"  12 1 12 13 1 12 13 1 13 14 1 13 14 1 14 15 1 14 16 1 15 16 1 16 17 1 16 17 1 17 18 1 18 19 1 19 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 10 12 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 17 20 2 19 21 2 20 22 2 21  Freq.(cm" ) 1  1646.11706 1645.83682 1644.80335 1644.72831 1643.58800 1643.62585 1642.46868 1640.32235 1641.31896 1639.08961 1637.81717 1636.53366 1656.89941 1656.92776 1655.40255 1655.44663 1653.96273 1654.01116 1652.58605 1652.61929 1651.27782 1651.26807 1650.04069 1649.95567 1648.86259 1648.68056 1647.69628 1647.43850 1647.45371 1646.22788 1645.04875 1645.28968 1643.89923 1644.43281 1642.77915 1643.62585 1641.68882 1642.84590 1640.62737 1642.07713 1639.59598 1641.30318 1637.61888 1636.68313 1635.78233  Intensity  3  0.0444 0.0663 0.1579 0.0702 0.0575 0.0729 0.0520 0.0621 0.0297 0.0755 0.2183 0.0530 0.0507 0.0527 0.0485 0.0751 0.0806 0.0921 0.0825 0.0863 0.1110 0.0739 0.1116 0.0977 0.1011 0.1676 0.0982 0.0936 0.0936 0.1980 0.1159 0.0720 0.0795 0.1123 0.0683 0.0729 0.0738 0.0623 0.0707 0.0490 0.1855 0.0297 0.1676 0.0886 0.0483  / 144 J' K' K' a c  J" K"  5 4 2 6 4 3 7 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 8 5 4 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9 14 5 10 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 16 6 11 17 6 12 18 6 13 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11 12 0 12  6 4 3 7 4 4 8 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 15 4 12 16 4 12 9 5 5 10 5 6 11 5 7 12 5 8 13 5 9 14 5 10 15 5 11 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 17 6 12 18 6 13 19 6 14 10 1 2 0 2 3 0 3 4 0 4 5 0 5 6 0 6 7 0 7 8 0 8 9 0 9 10 0 10 11 0 11  K"  a.  C  Freq.(cm" ) 1  1652.48841 1651.13625 1649.83919 1648.59432 1647.40552 1647.40552 1646.26083 1646.26875 1645.18013 1645.18013 1644.15560 1644.14008 1643.17356 1643.14551 1642.23247 1642.17625 1641.30318 1647.54195 1646.37953 1645.30990 1644.27757 1643.29653 1642.36605 1641.48874 1646.22788 1645.16313 1644.15560 1643.21350 1642.32109 1641.48246 1640.69044 1639.24249 1638.56416 1637.94599 1667.36341 1669.15888 1670.96410 1672.77080 1674.55916 1676.31852 1678.04128 1679.72755 1681.38428 1683.02138 1684.65042  Intensity  3  0.0886 0.1040 0.1513 0.1460 0.1827 0.1827 0.0455 0.1196 0.5307 0.5307 0.2225 0.0553 0.1211 0.0818 0.0567 0.0728 0.0297 0.0676 0.0355 0.0701 . 0.0789 0.0562 0.0756 0.2370 0.1980 0.0753 0.2225 0.1778 0.1313 0.1522 0.0737 0.0602 0.0556 0.0600 0.0532 0.0498 0.0966 0.0941 0.0998 0.0900 0.1116 0.1131 0.1256 0.1189 0.1210  / 145  13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 18 0 18 21 0 21 22 0 22 23 0 23 4 14 5 14 5 15 6 15 6 1 6 7 16 7 1 7 8 17 8 1 8 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 13 1 13 14 1 13 15 1 14 15 1 15 16 1 15 16 1 16 17 1 17 18 1 18 3 2 1 3 2 2 4 2 2 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5 7 2 5 7 2 6  J" K"  K"  ci  C  12 0 12 13 0 13 14 0 14 15 0 15 16 0 16 17 0 17 20 0 20 21 0 21 22 0 22 3 13 4 13 4 14 5 14 5 15 6 1 5 6 1 6 7 1 6 7 17 8 1 7 8 1 8 9 18 9 19 10 1 9 10 1 10 11 1 10 11 1 11 12 1 11 12 1 12 13 1 12 14 1 13 14 1 14 15 1 14 15 1 15 16 1 16 17 1 17 2 2 0 2 2 1 3 2 1 3 2 2 4 2 2" 4 2 3 5 2 3 5 2 4 6 2 4 6 2 5  Freq.(cm" ')  1686.28057 1687.91877 1689.57298 1691.25045 1692.97133 1694.80964 1699.41606 1701.21898 1703.02630 1670.39238 1673.52025 1672.10112 1675.65761 1673.82129 1677.80844 1675.55037 1680.01687 1677.28505 1682.21105 1679.02497 1684.42068 1680.77095 1686.61229 1682.52701 1688.77024 1684.30939 1690.88244 1686.18418 1692.94679 1694.91273 1689.06892 1696.83919 1690.90308 1692.68972 1694.46401 1668.71889 1668.68415 1670.64593 1670.55190 1672.66155 1672.45688 1674.77432 1674.39847 1676.98987 1676.36922  Intensity  3  0.1023 0.1160 0.0932 0.1144 0.0882 0.0697 0.0642 0.0532 0.0553 0.0553 0.0830 0.0666 0.0377 0.0467 0.0447 0.0485 0.0685 0.0660 0.0522 0.0589 0.0503 0.0615 0.0552 0.0710 0.0533 0.0579 0.0400 0.0454 0.0101 0.0397 0.0502 0.0244 0.0491 0.0516 0.0507 0.0560 0.0560 0.0468 0.0599 0.0513 0.0764 0.0727 0.0897 0.0758 0.0779  / 146 J' K'  K-  8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 9 11 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 16 18 2 17 19 2 18 20 2 19 21 2 20 5 4 2 6 4 3 7 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 14 4 11 15 4 11 8 5 4 9 5 5 10 5 6 11 5 7  J" K" K" a c  7 2 5 7 2 6 8 2 6 8 2 7 9 2 7 9 2 8 10 2 8 10 2 9 11 2 10 12 2 10 12 2 11 13 2 11 13 2 12 14 2 12 14 2 13 15 2 13 15 2 14 16 2 14 16 2 15 17 2 15 17 2 16 18 2 17 19 2 18 20 2 19 4 4 1 5 4 2 6 4 3 7 4 4 8 4 4 8 4 5 9 4 5 9 4 6 10 4 6 10 4 7 11 4 7 11 4 8 12 4 8 12 4 9 13 4 9 13 4 10 14 4 10 7 5 3 8 5 4 9 5 5 10 5 6  . Freq.(cm" ) 1  1679.30537 1678.36776 1681.70441 1680.38783 1684.12408 1682.42742 1687.46504 1684.48340 1686.55312 1692.42524 1688.63636 1695.09143 1690.73076 1697.77091 1692.83583 1700.43752 1694.95165 1703.07189 1697.07646 1705.65519 1699.21784 1701.37266 1703.54691 1705.74657 1670.99017 1673.00958 1675.08627 1677.22175 1679.41647 1679.41192 1681.66298 1681.66298 1683.98032 1683.96714 1686.36403 1686.32380 1688.79979 1688.72579 1691.29035 1691.16409 1693.80685 1676.13892 1678.35090 1680.65932 1683.00596  Intensity  3  0.0731 0.1381 0.0727 0.0985 0.0662 0.0934 0.0376 0.0857 0.0980 0.0686 0.0821 0.0588 0.0675 0.0514 0.0679 0.0378 0.0643 0.0369 0.0449 0.0344 0.0422 0.0410 0.0333 0.0269 0.0528 0.0742 0.1432 0.1127 0.0925 0.0925 0.0844 0.0844 0.1007 0.0462 0.0581 0.0588 0.0574 0.0543 0.0591 0.0624 0.0315 0.0488 0.1381 0.0545 0.0506  / 147 J' K' a  K' c  J" K"  K"  cL  C  Freq.(cm~ ) 1  12 5 8 13 5 9 14 5 10 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 17 6 12 18 6 13 8 5 3 10 5 5 11 5 6 13 5 8 14 5 9 8 6 2 9 6 3 10 6 4 11 6 5 12 6 6 13 6 7 14 6 8  11 5 7 12 5 8 13 5 9 7 6 2 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9 15 6 10 16 6 11 17 6 12 8 5 4 10 5 6 11 5 7 13 5 9 14 5 10 8 6 3 9 6 4 10 6 5 11 6 6 12 6 7 13 6 8 14 6 9  1685.40938 1687.86801 1690.37875 1674.81039 1677.11318 1679.47811 1681.90448 1684.38695 1686.92479 1689.51273. 1692.15083 1694.83377 1697.54734 1700.32073 1662.68413 1663.82957 1664.48661 1665.96220 1666.78146 1661.36222 1661.98035 1662.66072 1663.40154 1664.19712 1665.04665 1665.94783  J' K'  J" K"  Freq.(cm" )  K'  8 7 3 9 7 4 10 7 5 11 7 6 12 7 7 13 7 8 14 7 9 15 7 10 16 7 11 17 7 12 18 7 13  K"  9 7 4 10 7 5 11 7 6 12 7 7 13 7 8 14 7 9 15 7 10 16 7 11 17 7 12 18 7 13 19 7 14  1  1612.33456 1611.26619 1610.13483 1608.94026 1607.70100 1606.40955 1605.07285 1603.68932 1602.27092 1600.81112 1599.30575  Intensity  3  0.0550 0.0462 0.0337 0.0546 0.1124 0.0818 0.0563 0.0772 0.0714 0.0511 0.0528 0.0514 0.0569 0.0322 0.0567 0.0634 0.0419 0.1352 0.0471 0.1503 0.1034 0.0751 0.0704 0.0470 0.0408 0.1352  Intensity  3  0.1020 0.0921 0.0807 0.3889 0.1981 0.1685 0.1861 0.5433 0.2073 0.1926 0.0684  / 148 j'  K :  a  J"  K :  . c  19 7 14 20 7 15 21 7 16 22 7 16 22 7 17 8 7 3 9 7 4 10 7 5 11 7 6 12 7 7 13 7 8 14 7 9 15 7 10 16 7 11 17 7 12 18 7 13 19 7 14 20 7 15 21 7 16 22 7 16 22 7 17  K "  a  K "  20 7 15 21 7 16 22 7 17 23 7 17 23 7 18 7 7 2 8 7 3 9 7 4 10 7 5 11 7 6 12 7 7 13 7 8 14 7 9 15 7 10 16 7 11 17 7 12 18 7 13 19 7 14 20 7 15 21 7 15 21 7 16  c  Freq.(cm" ) 1  1597.78516 1596.22179 1594.62940 1593.00905 1593.00527 1640.91671 1643.21619 1645.45427 1647.63555 1649.76731 1651.85230 1653.89509 1655.89756 1657.86261 1659.79116 1661.67543 1663.55355 1665.39161 1667.20447 1668.99611 1668.98430  Intensity  3  0.1843 0.1323 0.1476 0.1138 0.1138 0.0683 0.1778 0.1246 0.1680 0.2983 0.2202 0.2906 0.2062 0.2520 0.2342 0.2806 0.2017 0.2027 0.1803 0.2657 0.0338  a - line frequencies and intensities from deconvoluted spectra, FWHM of response factor = 0.008 cm" . 1  APPENDIX II : C H A R A C T E R  E  d  1  1  1 1  1 -  *  £, = n £ = 0 3  x ,y\z  1 - 1  R, x, R,  xy  1  y, R,  -  1  - 1 - 1  E  C {z)  1  1  C (y)  2  1  1  -  1  -  -  £  2C^  1 1  1 1  2 2 2  2 cos O  1  1  z, R  -  1  >\ Ry xz x, R yz  1  •  149  z  y\z  2  x  00 o„ 1 -1  cos 30 •  x\ xy  -  1  2 cos 2<t> • 2  2  1 -  2  xz  1  1 1  2  C (x)  2  1  1  *-  z  1  1 - 1 1  a'Xyz)  o-,.(xr)  1  TABLES  0 0 0  x  2 (x, y)AR,.  R,)  +  1  (xz, (x  2  y ,: 2  2  yz) — y, 2  xy)  APPENDIX III: AMINOBORANE RESIDUALS The K value for each plot is given in the top left corner. © = upper asymmetry component, * = lower asymmetry component. Fit A : Standard Deviation = 1.2 cm" Q  1  • «  CD "I  Be *1  1  8 ;  fcOO  100  11.00  HOD  LOO  \0D  IDS  *0D  HOD  13.X  "1 4  *1  • • i t• oBi  1  4--  •  100  LCD  7.00  1,00  HOD  1&.0D  .  S  •—T ~ l 1 HOD HOD  1 6  • ••  a  •  l*tt  HOD  150  -f LOB  l  i i 100  i  1  1  1  1  1  1— —r ILOO  i rHOD 1S.00  / y  7 + y<  1 ft  •  as* *1  oi]  " I .  0 8  *1 8I  *1  11.00  It. 00  J10D *•*  *•<*>  '-CD  fcOD  11.00  HOD  HDD  I LOO  IS. 00  1 1  J1  §.1  1  i 8 I  -i  n.oo  ix. a  *0D  3.00  LOD  fl,OD  ft in -  100  7.0D J  100  HOD  IV OP  lfcOD  IB. 00  151  /  152  • • •  *1 —i  10.D  1  r — i IB  1  ISO  1  1  1  1—-i 10O  7.00  1  1  11.00  1  1100  J  T—-i  110.0  Si •  i  : in -t  8"]  " 1 11  1 LCD  100  7. DO  LCD  ILOO  IX 00  liflC  "1 6  il-aD 110.0  1  1-00  r~—i IIS  1  1  1,00  i i O T.D  1  1  t.00  1  1  1U0O  r —i U.  1  00  1  IV3  / 153 Fit B : Standard Deviation =  0.11 cm"  1  i o  1 3  cn -i  SV  11 8 '  *1  iOD  11  T.00  1.00  110.0  11.00  IS.  00  dl  !  8.]  I  1  .1  • ••  Yft in  7*1  LCD  &00  B.0D  T.OC  1.00  1.00  LOO  T.OD  too  ii. on  i*oo  ii. rr  11.00  110.0  130.0  4 1-s I  i  8;  11  —\ r  t  i T" •  l>0D  1.00  T.00  kVOO  HDD  J  19.00  S.0D  J  *1 ft  4--  ?1 8 t  l  f t  1  i  T  1  r-  •.•>  -T  1  ii.«  ?  r-  /  1 0  1  3  Si  .1  =1  5s;  \  a.  »! ItVOD  JS.QP  -t—i—.I.OD  - 4  Si  -1 a i i *i  J  8'  *1  <1  .1 * dl  1 "  1  8  * •  (  8  •  •  *1  1  / 155 2{v ) s  1  0  9 d  • ••• •  4--  IOC  T.OD  -t  100  J  1.00  400  IOD  t.00  4 CO  T.S  400  11.00  142  5  * * • • l/>  i  *1 •I  8 : *1  8 !  *1 100  S.1  ILOO  1 1 0 .1  14 00  1400  /  Fit C : Standard Deviation = 0.02 cm"  1  156  / 157 2(Pc)  7. X  J  100  fi  5  h  • • *  e  ILOC  1S.OD  14.00  APPENDIX IV : NBN LINE  3  ASSIGNMENTS  * ( D - A,(0) 3  2  Line  Freq.(cm" )  Weight  Q(36) Q(35) Q(34) Q(33) Q(32) Q(31) Q(31) Q(30) Q(29) Q(29) Q(28) Q(27) Q(26) Q(25) Q(25) Q(24) Q(23) Q(22) Q(21) Q(20) Q(19) Q(19) Q(18) R(12) R(13) R(14) R(15) R(16) R(17) R(18) R(19) R(20) R(21) R(21) R(22) R(23) R(24) R(24) R(25) R(26) R(27)  17120.8853 17121.4367 17121.9740 17122.4897 17122.9972 17123.4821 17123.4830 17123.9553 17124.4118 17124.4114 17124.8530 17125.2793 17125.6896 17126.0852 17126.0848 17126.4651 17126.8285 17127.1754 17127.5094 17127.8268 17128.1309 17128.1300 17128.4166 17142.6227 17143.4108 17144.1864 17144.9422 17145.6798 17146.4050 17147.1205 17147.8133 17148.4973 17149.1597 17149.1585 17149.8049 17150.4403 17151.0582 17151.0563 17151.6585 17152.2459 17152.8148  1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  1  158  Obs-Calc.  a  -0.0010 -0.0004 0.0019 -0.0017 0.0022 -0.0009 0.0000 0.0000 -0.0003 -0.0007 -0.0004 0.0002 0.0002 0.0010 0.0006 0.0014 0.0008 -0.0009 -0.0003 -0.0009 0.0005 -0.0004 -0.0012 -0.0007 -0.0003 0.0029 0.0017 -0.0023 -0.0034 0.0014 -0.0011 0.0031 0.0012 0.0000 -0.0023 0.0001 0.0005 -0.0014 -0.0009 0.0005 -0.0009  / 159 Line  Freq.(cm" )  Weight  R(28) R(29) R(30) R(31) R(32) R(33) R(34) R(35) R(36) R(37) R(38)  17153.3734 17153.9096 17154.4339 17154.9379 17155.4280 17155.9021 17156.3602 17156.8015 17157.2312 17157.6423 17158.0381  1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  1  3  a  0.0033 0.0009 0.0025 -0.0002 -0.0009 -0.0016 -0.0021 -0.0034 -0.0001 0.0009 0.0028  * , ( D - A,(1) 3  Line  Freq.(cm" )  Weight  Q(14) Q(15) Q(16) Q(17) Q(18) Q(19) Q(20) Q(21) Q(22) Q(23) Q(24) Q(25) Q(26) Q(27) Q(28) Q(29) Q(30) Q(31) Q(32) Q(33) Q(34) Q(35) Q(36) Q(37) R(14) R(15)  16096.2120 16096.0644 16095.9063 16095.7409 16095.5575 16095.3669 16095.1666 16094.9602 16094.7416 16094.5018 16094.2619 16094.0132 16093.7537 16093.4776 16093.1980 16092.9078 16092.5997 16092.2886 16091.9682 16091.6320 16091.2894 16090.9391 16090.5704 16090.1952 16110.9827 16111.8161  1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  1  Obs-Calc.  Obs-Calc.  a  -0.0031 -0.0011 0.0005 0.0048 0.0012 0.0005 0.0003 0.0041 0.0058 -0.0034 -0.0026 -0.0003 0.0014 -0.0032 -0.0010 0.0010 -0.0046 -0.0027 0.0002 -0.0022 -0.0005 0.0040 0.0007 0.0015 -0.0016 -0.0023  / 160 Line  Freq.(cm" )  Weight  R(16) R(16) R(17) R(19) R(20) R(21) R(21) R(22) R(23) R(24) R(25) R(26) R(27) R(28) R(29) R(29) R(30) R(31) R(32) R(32) R(33) R(3'4) R(36) R(38)  16112.6412 16112.6421 16113.4552 16115.0529 16115.8360 16116.6075 16116.6075 16117.3686 16118.1204 16118.8613 16119.5944 16120.3134 16121.0226 16121.7214 16122.4087 16122.4095 16123.0866 16123.7538 16124.4086 16124.4086 16125.0529 16125.6876 16126.9224 16128.1158  1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  1  3  Obs-Calc.  a  -0.0011 -0.0002 -0.0007 0.0006 0.0010 0.0001 0.0001 -0.0007 -0.0004 -0.0005 0.0021 0.0011 0.0009 0.0009 0.0001 0.0009 0.0005 0.0010 -0.0001 -0.0001 -0.0010 -0.0005 -0.0015 0.0001  * ( 2 ) - A,(1). 2  J  Line  Freq.(cm" ')  Weight  P(33) P(32) P(32) P(31) P(30) P(29) P(27) P(27) P(26) P(25) P(24) P(23) P(22)  17034.1472 17035.6359 17035.6352 17037.1080 17038.5653 17040.0066 17042.8407 17042.8425 17044.2355 17045.6148 17046.9814 17048.3309 17049.6616  1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  Obs-Calc.  a  -0.0010 0.0002 -0.0005 0.0003 0.0011 0.0012 -0.0009 0.0009 -0.0011 -0.0014 0.0009 0.0016 -0.0013  / 161 Line  Freq.(cm~ ')  Weight  P(21) P(21) Q(39) Q(38) Q(38) Q(36) Q(35) Q(34) Q(33) Q(32) Q(31) Q(32) Q(31) Q(30) Q(30) Q(29) Q(28) Q(27) Q(26) Q(25) Q(24) Q(23) Q(23) Q(22) Q(21) Q(20) Q(19) Q(18) Q(17) Q(16) Q(15) Q(14) Q(13) Q(12)  17050.9811 17050.9808 17062.9846 17063.5892 17063.5923 17064.7675 17065.3262 17065.8737 17066.4040 17066.9181 17067.4161 17066.9201 17067.4174 17067.9008 17067.9014 17068.3685 17068.8188 17069.2548 17069.6737 17070.0778 17070.4663 17070.8401 17070.8397 17071.1957 17071.5370 17071.8654 17072.1740 17072.4676 17072.7477 17073.0096 17073.2602 17073.4897 17073.7063 17073.9097  1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  Obs-Calc.  a  0.0000 -0.0003 0.0023 -0.0033 -0.0002 0.0024 -0.0012 -0.0001 -0.0003 -0.0008 -0.0015 0.0012 -0.0002 0.0003 0.0009 0.0009 -0.0001 0.0003 -0.0006 -0.0005 -0.0004 0.0007 0.0003 -0.0008 -0.0008 0.0018 0.0003 -0.0007 0.0005 -0.0010 0.0018 -0.0010 -0.0011 0.0010  (0)- A,(0) 3  Line  Freq.(cm~ )  Weight  P(30) P(29) P(28)  17021.8098 17023.1867 17024.5439  1.00 1.00 1.00  1  Obs-Calc.  a  0.0014 0.0042 0.0001  / 162 Line  Freq.(cm" ')  Weight  P(27) P(27) P(26) P(25) P(25) P(24) P(23) P(22) P(21) P(20) P(20) P(19) P(18) P(17) P(17) P(16) P(15) P(14) P(13) P(12) P(12) P(ll) P(10) Q(39) Q(38) P( 9) Q(38) P( 9) Q(37) Q(36) Q(36) Q(35) Q(34) Q(33) Q(32) Q(31) Q(31) Q(30) Q(29) Q(30) Q(29) Q(28) Q(27) Q(26) Q(25)  17025.8907 17025.8918 17027.2265 17028.5501 17028.5513 17029.8608 17031.1570 17032.4422 17033.7136 17034.9747 17034.9732 17036.2184 17037.4528 17038.6750 17038.6761 17039.8836 17041.0782 17042.2604 17043.4309 17044.5879 17044.5874 17045.7291 17046.8642 17047.3780 17047.8836 17047.9809 17047.8847 17047.9826 17048.3848 17048.8620 17048.8655 17049.3322 17049.7851 17050.2278 17050.6560 17051.0709 17051.0710 17051.4738 17051.8602 17051.4733 17051.8624 17052.2373 17052.6001 17052.9488 17053.2858  1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  Obs-Calc.  a  -0.0016 -0.0005 -0.0015 -0.0008 0.0004 -0.0002 -0.0014 -0.0008 -0.0012 0.0008 -0.0007 -0.0018 -0.0009 0.0005 0.0016 0.0011 0.0004 0.0001 0.0008 0.0008 0.0003 -0.0022 0.0014 -0.0009 -0.0034 -0.0006 -0.0023 0.0011 0.0031 -0.0011 0.0024 0.0010 -0.0008 0.0003 0.0003 0.0001 0.0002 0.0011 -0.0012 0.0006 0.0010 0.0004 0.0008 0.0002 0.0010  / 163 Line  Freq.(cm" )  Weight  Q(24) Q(23) Q(22) Q(21) Q(21) Q(20) Q(19) Q(18) Q(17) Q(17) Q(16) Q(15) Q(14) Q(13) Q(12) Q(12) Q(ii) QUO) Q( 9) Q( 8) R( 7) R( 8) R( 9) R(10) R(10) R(ll) R(12) R(13) R(14) R(14) R(15) R(15) R(16) R(17) R(18) R(19) R(19) R(20) R(21) R(22) R(22) R(23) R(23) R(24) R(25)  17053.6061 17053.9175 17054.2141 17054.4983 17054.4990 17054.7701 17055.0281 17055.2718 17055.5047 17055.5054 17055.7236 17055.9298 17056.1228 17056.3037 17056.4708 17056.4709 17056.6264 17056.7678 17056.8944 17057.0108 17065.0371 17065.9247 17066.7982 17067.6597 17067.6604 17068.5086 17069.3438 17070.1670 17070.9757 17070.9760 17071.7714 17071.7733 17072.5549 17073.3252 17074.0814 17074.8244 17074.8250 17075.5553 17076.2725 17076.9764 17076.9738 17077.6657 17077.6656 17078.3411 17079.0014  1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  1  Obs-Calc.  a  -0.0018 -0.0005 -0.0009 -0.0006 0.0001 0.0002 0.0002 -0.0011 -0.0002 0.0005 -0.0004 -0.0003 -0.0004 0.0002 0.0000 0.0001 0.0011 0.0010 -0.0010 -0.0004 -0.0007 -0.0004 -0.0012 -0.0010 -0.0003 -0.0004 -0.0004 0.0006 0.0002 0.0005 -0.0001 0.0018 0.0005 0.0011 0.0008 0.0004 0.0010 0.0012 0.0016 0.0019 -0.0007 0.0009 0.0008 -0.0007 -0.0040  / 164 Line  Freq.(cm" )  Weight  R(26) R(26) R(27) R(28) R(29) R(30) R(31) R(31) R(33) R(33) R(34) R(35) R(36)  17079.6529 17079.6555 17080.2919 17080.9136 17081.5240 17082.1205 17082.7048 17082.7035 17083.8296 17083.8325 17084.3761 17084.8995 17085.4138  1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  1  a - calculation described in section 4.2.1.  Obs-Calc.  a  -0.0027 -0.0001 -0.0005 -0.0021 -0.0016 -0.0015 0.0000 -0.0013 0.0000 0.0029 0.0045 -0.0004 -0.0006  

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